From b094d6c4bf572654a031ecc4afe675154c886dc5 Mon Sep 17 00:00:00 2001 From: Jing Yu Date: Thu, 22 Jul 2010 14:03:48 -0700 Subject: commit gcc-4.4.3 which is used to build gcc-4.4.3 Android toolchain in master. The source is based on fsf gcc-4.4.3 and contains local patches which are recorded in gcc-4.4.3/README.google. Change-Id: Id8c6d6927df274ae9749196a1cc24dbd9abc9887 --- gcc-4.4.3/libgcc/ChangeLog | 649 + gcc-4.4.3/libgcc/Makefile.in | 971 + gcc-4.4.3/libgcc/config.host | 608 + gcc-4.4.3/libgcc/config/alpha/t-crtfm | 6 + gcc-4.4.3/libgcc/config/avr/t-avr | 19 + gcc-4.4.3/libgcc/config/i386/32/sfp-machine.h | 209 + gcc-4.4.3/libgcc/config/i386/32/t-fprules-softfp | 8 + gcc-4.4.3/libgcc/config/i386/32/tf-signs.c | 62 + gcc-4.4.3/libgcc/config/i386/64/_divtc3.c | 14 + gcc-4.4.3/libgcc/config/i386/64/_multc3.c | 14 + gcc-4.4.3/libgcc/config/i386/64/_powitf2.c | 14 + gcc-4.4.3/libgcc/config/i386/64/eqtf2.c | 13 + gcc-4.4.3/libgcc/config/i386/64/getf2.c | 13 + gcc-4.4.3/libgcc/config/i386/64/letf2.c | 13 + gcc-4.4.3/libgcc/config/i386/64/sfp-machine.h | 143 + gcc-4.4.3/libgcc/config/i386/64/t-softfp-compat | 15 + gcc-4.4.3/libgcc/config/i386/t-crtfm | 5 + gcc-4.4.3/libgcc/config/i386/t-crtpc | 8 + gcc-4.4.3/libgcc/config/i386/t-cygming | 11 + gcc-4.4.3/libgcc/config/i386/t-darwin | 1 + gcc-4.4.3/libgcc/config/i386/t-darwin64 | 1 + gcc-4.4.3/libgcc/config/i386/t-nwld | 31 + gcc-4.4.3/libgcc/config/i386/t-sol2 | 34 + gcc-4.4.3/libgcc/config/ia64/__divxf3.asm | 11 + gcc-4.4.3/libgcc/config/ia64/_fixtfdi.asm | 11 + gcc-4.4.3/libgcc/config/ia64/_fixunstfdi.asm | 11 + gcc-4.4.3/libgcc/config/ia64/_floatditf.asm | 11 + gcc-4.4.3/libgcc/config/ia64/t-fprules-softfp | 2 + gcc-4.4.3/libgcc/config/ia64/t-ia64 | 18 + gcc-4.4.3/libgcc/config/ia64/t-softfp-compat | 7 + gcc-4.4.3/libgcc/config/ia64/tf-signs.c | 60 + gcc-4.4.3/libgcc/config/libbid/ChangeLog | 383 + gcc-4.4.3/libgcc/config/libbid/_addsub_dd.c | 46 + gcc-4.4.3/libgcc/config/libbid/_addsub_sd.c | 54 + gcc-4.4.3/libgcc/config/libbid/_addsub_td.c | 46 + gcc-4.4.3/libgcc/config/libbid/_dd_to_df.c | 36 + gcc-4.4.3/libgcc/config/libbid/_dd_to_di.c | 39 + gcc-4.4.3/libgcc/config/libbid/_dd_to_sd.c | 36 + gcc-4.4.3/libgcc/config/libbid/_dd_to_sf.c | 36 + gcc-4.4.3/libgcc/config/libbid/_dd_to_si.c | 39 + gcc-4.4.3/libgcc/config/libbid/_dd_to_td.c | 36 + gcc-4.4.3/libgcc/config/libbid/_dd_to_tf.c | 38 + gcc-4.4.3/libgcc/config/libbid/_dd_to_udi.c | 39 + gcc-4.4.3/libgcc/config/libbid/_dd_to_usi.c | 39 + gcc-4.4.3/libgcc/config/libbid/_dd_to_xf.c | 36 + gcc-4.4.3/libgcc/config/libbid/_df_to_dd.c | 33 + gcc-4.4.3/libgcc/config/libbid/_df_to_sd.c | 34 + gcc-4.4.3/libgcc/config/libbid/_df_to_td.c | 33 + gcc-4.4.3/libgcc/config/libbid/_di_to_dd.c | 35 + gcc-4.4.3/libgcc/config/libbid/_di_to_sd.c | 36 + gcc-4.4.3/libgcc/config/libbid/_di_to_td.c | 35 + gcc-4.4.3/libgcc/config/libbid/_div_dd.c | 36 + gcc-4.4.3/libgcc/config/libbid/_div_sd.c | 40 + gcc-4.4.3/libgcc/config/libbid/_div_td.c | 36 + gcc-4.4.3/libgcc/config/libbid/_eq_dd.c | 41 + gcc-4.4.3/libgcc/config/libbid/_eq_sd.c | 44 + gcc-4.4.3/libgcc/config/libbid/_eq_td.c | 41 + gcc-4.4.3/libgcc/config/libbid/_ge_dd.c | 39 + gcc-4.4.3/libgcc/config/libbid/_ge_sd.c | 42 + gcc-4.4.3/libgcc/config/libbid/_ge_td.c | 39 + gcc-4.4.3/libgcc/config/libbid/_gt_dd.c | 37 + gcc-4.4.3/libgcc/config/libbid/_gt_sd.c | 40 + gcc-4.4.3/libgcc/config/libbid/_gt_td.c | 37 + gcc-4.4.3/libgcc/config/libbid/_isinfd128.c | 37 + gcc-4.4.3/libgcc/config/libbid/_isinfd32.c | 39 + gcc-4.4.3/libgcc/config/libbid/_isinfd64.c | 37 + gcc-4.4.3/libgcc/config/libbid/_le_dd.c | 41 + gcc-4.4.3/libgcc/config/libbid/_le_sd.c | 44 + gcc-4.4.3/libgcc/config/libbid/_le_td.c | 41 + gcc-4.4.3/libgcc/config/libbid/_lt_dd.c | 37 + gcc-4.4.3/libgcc/config/libbid/_lt_sd.c | 40 + gcc-4.4.3/libgcc/config/libbid/_lt_td.c | 37 + gcc-4.4.3/libgcc/config/libbid/_mul_dd.c | 36 + gcc-4.4.3/libgcc/config/libbid/_mul_sd.c | 40 + gcc-4.4.3/libgcc/config/libbid/_mul_td.c | 36 + gcc-4.4.3/libgcc/config/libbid/_ne_dd.c | 37 + gcc-4.4.3/libgcc/config/libbid/_ne_sd.c | 40 + gcc-4.4.3/libgcc/config/libbid/_ne_td.c | 37 + gcc-4.4.3/libgcc/config/libbid/_sd_to_dd.c | 36 + gcc-4.4.3/libgcc/config/libbid/_sd_to_df.c | 36 + gcc-4.4.3/libgcc/config/libbid/_sd_to_di.c | 41 + gcc-4.4.3/libgcc/config/libbid/_sd_to_sf.c | 36 + gcc-4.4.3/libgcc/config/libbid/_sd_to_si.c | 41 + gcc-4.4.3/libgcc/config/libbid/_sd_to_td.c | 36 + gcc-4.4.3/libgcc/config/libbid/_sd_to_tf.c | 38 + gcc-4.4.3/libgcc/config/libbid/_sd_to_udi.c | 41 + gcc-4.4.3/libgcc/config/libbid/_sd_to_usi.c | 41 + gcc-4.4.3/libgcc/config/libbid/_sd_to_xf.c | 36 + gcc-4.4.3/libgcc/config/libbid/_sf_to_dd.c | 33 + gcc-4.4.3/libgcc/config/libbid/_sf_to_sd.c | 33 + gcc-4.4.3/libgcc/config/libbid/_sf_to_td.c | 33 + gcc-4.4.3/libgcc/config/libbid/_si_to_dd.c | 34 + gcc-4.4.3/libgcc/config/libbid/_si_to_sd.c | 36 + gcc-4.4.3/libgcc/config/libbid/_si_to_td.c | 34 + gcc-4.4.3/libgcc/config/libbid/_td_to_dd.c | 36 + gcc-4.4.3/libgcc/config/libbid/_td_to_df.c | 36 + gcc-4.4.3/libgcc/config/libbid/_td_to_di.c | 39 + gcc-4.4.3/libgcc/config/libbid/_td_to_sd.c | 36 + gcc-4.4.3/libgcc/config/libbid/_td_to_sf.c | 36 + gcc-4.4.3/libgcc/config/libbid/_td_to_si.c | 38 + gcc-4.4.3/libgcc/config/libbid/_td_to_tf.c | 38 + gcc-4.4.3/libgcc/config/libbid/_td_to_udi.c | 41 + gcc-4.4.3/libgcc/config/libbid/_td_to_usi.c | 40 + gcc-4.4.3/libgcc/config/libbid/_td_to_xf.c | 36 + gcc-4.4.3/libgcc/config/libbid/_tf_to_dd.c | 38 + gcc-4.4.3/libgcc/config/libbid/_tf_to_sd.c | 38 + gcc-4.4.3/libgcc/config/libbid/_tf_to_td.c | 38 + gcc-4.4.3/libgcc/config/libbid/_udi_to_dd.c | 35 + gcc-4.4.3/libgcc/config/libbid/_udi_to_sd.c | 36 + gcc-4.4.3/libgcc/config/libbid/_udi_to_td.c | 35 + gcc-4.4.3/libgcc/config/libbid/_unord_dd.c | 37 + gcc-4.4.3/libgcc/config/libbid/_unord_sd.c | 41 + gcc-4.4.3/libgcc/config/libbid/_unord_td.c | 37 + gcc-4.4.3/libgcc/config/libbid/_usi_to_dd.c | 35 + gcc-4.4.3/libgcc/config/libbid/_usi_to_sd.c | 36 + gcc-4.4.3/libgcc/config/libbid/_usi_to_td.c | 35 + gcc-4.4.3/libgcc/config/libbid/_xf_to_dd.c | 33 + gcc-4.4.3/libgcc/config/libbid/_xf_to_sd.c | 33 + gcc-4.4.3/libgcc/config/libbid/_xf_to_td.c | 33 + gcc-4.4.3/libgcc/config/libbid/bid128.c | 4333 + gcc-4.4.3/libgcc/config/libbid/bid128_2_str.h | 33 + .../libgcc/config/libbid/bid128_2_str_macros.h | 149 + .../libgcc/config/libbid/bid128_2_str_tables.c | 642 + gcc-4.4.3/libgcc/config/libbid/bid128_add.c | 2941 + gcc-4.4.3/libgcc/config/libbid/bid128_compare.c | 4346 + gcc-4.4.3/libgcc/config/libbid/bid128_div.c | 1851 + gcc-4.4.3/libgcc/config/libbid/bid128_fma.c | 4460 + gcc-4.4.3/libgcc/config/libbid/bid128_logb.c | 58 + gcc-4.4.3/libgcc/config/libbid/bid128_minmax.c | 1095 + gcc-4.4.3/libgcc/config/libbid/bid128_mul.c | 423 + gcc-4.4.3/libgcc/config/libbid/bid128_next.c | 643 + gcc-4.4.3/libgcc/config/libbid/bid128_noncomp.c | 1200 + gcc-4.4.3/libgcc/config/libbid/bid128_quantize.c | 274 + gcc-4.4.3/libgcc/config/libbid/bid128_rem.c | 217 + .../libgcc/config/libbid/bid128_round_integral.c | 1951 + gcc-4.4.3/libgcc/config/libbid/bid128_scalb.c | 96 + gcc-4.4.3/libgcc/config/libbid/bid128_sqrt.c | 564 + gcc-4.4.3/libgcc/config/libbid/bid128_string.c | 672 + gcc-4.4.3/libgcc/config/libbid/bid128_to_int16.c | 67 + gcc-4.4.3/libgcc/config/libbid/bid128_to_int32.c | 3659 + gcc-4.4.3/libgcc/config/libbid/bid128_to_int64.c | 2994 + gcc-4.4.3/libgcc/config/libbid/bid128_to_int8.c | 67 + gcc-4.4.3/libgcc/config/libbid/bid128_to_uint16.c | 68 + gcc-4.4.3/libgcc/config/libbid/bid128_to_uint32.c | 3588 + gcc-4.4.3/libgcc/config/libbid/bid128_to_uint64.c | 3401 + gcc-4.4.3/libgcc/config/libbid/bid128_to_uint8.c | 67 + gcc-4.4.3/libgcc/config/libbid/bid32_to_bid128.c | 264 + gcc-4.4.3/libgcc/config/libbid/bid32_to_bid64.c | 216 + gcc-4.4.3/libgcc/config/libbid/bid64_add.c | 595 + gcc-4.4.3/libgcc/config/libbid/bid64_compare.c | 3172 + gcc-4.4.3/libgcc/config/libbid/bid64_div.c | 1795 + gcc-4.4.3/libgcc/config/libbid/bid64_fma.c | 506 + gcc-4.4.3/libgcc/config/libbid/bid64_logb.c | 68 + gcc-4.4.3/libgcc/config/libbid/bid64_minmax.c | 854 + gcc-4.4.3/libgcc/config/libbid/bid64_mul.c | 374 + gcc-4.4.3/libgcc/config/libbid/bid64_next.c | 481 + gcc-4.4.3/libgcc/config/libbid/bid64_noncomp.c | 954 + gcc-4.4.3/libgcc/config/libbid/bid64_quantize.c | 236 + gcc-4.4.3/libgcc/config/libbid/bid64_rem.c | 228 + .../libgcc/config/libbid/bid64_round_integral.c | 1221 + gcc-4.4.3/libgcc/config/libbid/bid64_scalb.c | 105 + gcc-4.4.3/libgcc/config/libbid/bid64_sqrt.c | 552 + gcc-4.4.3/libgcc/config/libbid/bid64_string.c | 511 + gcc-4.4.3/libgcc/config/libbid/bid64_to_bid128.c | 262 + gcc-4.4.3/libgcc/config/libbid/bid64_to_int16.c | 67 + gcc-4.4.3/libgcc/config/libbid/bid64_to_int32.c | 2587 + gcc-4.4.3/libgcc/config/libbid/bid64_to_int64.c | 2329 + gcc-4.4.3/libgcc/config/libbid/bid64_to_int8.c | 69 + gcc-4.4.3/libgcc/config/libbid/bid64_to_uint16.c | 67 + gcc-4.4.3/libgcc/config/libbid/bid64_to_uint32.c | 2270 + gcc-4.4.3/libgcc/config/libbid/bid64_to_uint64.c | 2273 + gcc-4.4.3/libgcc/config/libbid/bid64_to_uint8.c | 67 + gcc-4.4.3/libgcc/config/libbid/bid_b2d.h | 3055 + gcc-4.4.3/libgcc/config/libbid/bid_binarydecimal.c | 147479 ++++++++++++++++++ gcc-4.4.3/libgcc/config/libbid/bid_conf.h | 1171 + gcc-4.4.3/libgcc/config/libbid/bid_convert_data.c | 2108 + gcc-4.4.3/libgcc/config/libbid/bid_decimal_data.c | 1293 + .../libgcc/config/libbid/bid_decimal_globals.c | 100 + gcc-4.4.3/libgcc/config/libbid/bid_div_macros.h | 540 + gcc-4.4.3/libgcc/config/libbid/bid_dpd.c | 782 + .../libgcc/config/libbid/bid_flag_operations.c | 345 + gcc-4.4.3/libgcc/config/libbid/bid_from_int.c | 349 + gcc-4.4.3/libgcc/config/libbid/bid_functions.h | 3279 + .../libgcc/config/libbid/bid_gcc_intrinsics.h | 295 + gcc-4.4.3/libgcc/config/libbid/bid_inline_add.h | 1253 + gcc-4.4.3/libgcc/config/libbid/bid_internal.h | 2607 + gcc-4.4.3/libgcc/config/libbid/bid_round.c | 1049 + gcc-4.4.3/libgcc/config/libbid/bid_sqrt_macros.h | 331 + gcc-4.4.3/libgcc/config/rs6000/t-darwin | 1 + gcc-4.4.3/libgcc/config/rs6000/t-ldbl128 | 3 + gcc-4.4.3/libgcc/config/rs6000/t-ppccomm | 103 + gcc-4.4.3/libgcc/config/sh/t-linux | 37 + gcc-4.4.3/libgcc/config/sparc/t-crtfm | 2 + gcc-4.4.3/libgcc/config/t-slibgcc-darwin | 122 + gcc-4.4.3/libgcc/config/t-softfp | 14 + gcc-4.4.3/libgcc/config/t-tls | 2 + gcc-4.4.3/libgcc/configure | 4665 + gcc-4.4.3/libgcc/configure.ac | 260 + gcc-4.4.3/libgcc/empty.mk | 2 + gcc-4.4.3/libgcc/fixed-obj.mk | 31 + gcc-4.4.3/libgcc/gen-fixed.sh | 105 + gcc-4.4.3/libgcc/gstdint.h | 6 + gcc-4.4.3/libgcc/shared-object.mk | 34 + gcc-4.4.3/libgcc/siditi-object.mk | 22 + gcc-4.4.3/libgcc/static-object.mk | 25 + 205 files changed, 240106 insertions(+) create mode 100644 gcc-4.4.3/libgcc/ChangeLog create mode 100644 gcc-4.4.3/libgcc/Makefile.in create mode 100644 gcc-4.4.3/libgcc/config.host create mode 100644 gcc-4.4.3/libgcc/config/alpha/t-crtfm create mode 100644 gcc-4.4.3/libgcc/config/avr/t-avr create mode 100644 gcc-4.4.3/libgcc/config/i386/32/sfp-machine.h create mode 100644 gcc-4.4.3/libgcc/config/i386/32/t-fprules-softfp create mode 100644 gcc-4.4.3/libgcc/config/i386/32/tf-signs.c create 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create mode 100644 gcc-4.4.3/libgcc/config/libbid/_mul_sd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_mul_td.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_ne_dd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_ne_sd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_ne_td.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_sd_to_dd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_sd_to_df.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_sd_to_di.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_sd_to_sf.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_sd_to_si.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_sd_to_td.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_sd_to_tf.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_sd_to_udi.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_sd_to_usi.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_sd_to_xf.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_sf_to_dd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_sf_to_sd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_sf_to_td.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_si_to_dd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_si_to_sd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_si_to_td.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_td_to_dd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_td_to_df.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_td_to_di.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_td_to_sd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_td_to_sf.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_td_to_si.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_td_to_tf.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_td_to_udi.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_td_to_usi.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_td_to_xf.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_tf_to_dd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_tf_to_sd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_tf_to_td.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_udi_to_dd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_udi_to_sd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_udi_to_td.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_unord_dd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_unord_sd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_unord_td.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_usi_to_dd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_usi_to_sd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_usi_to_td.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_xf_to_dd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_xf_to_sd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/_xf_to_td.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_2_str.h create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_2_str_macros.h create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_2_str_tables.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_add.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_compare.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_div.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_fma.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_logb.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_minmax.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_mul.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_next.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_noncomp.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_quantize.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_rem.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_round_integral.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_scalb.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_sqrt.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_string.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_to_int16.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_to_int32.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_to_int64.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_to_int8.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_to_uint16.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_to_uint32.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_to_uint64.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid128_to_uint8.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid32_to_bid128.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid32_to_bid64.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_add.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_compare.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_div.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_fma.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_logb.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_minmax.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_mul.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_next.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_noncomp.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_quantize.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_rem.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_round_integral.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_scalb.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_sqrt.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_string.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_to_bid128.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_to_int16.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_to_int32.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_to_int64.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_to_int8.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_to_uint16.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_to_uint32.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_to_uint64.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid64_to_uint8.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_b2d.h create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_binarydecimal.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_conf.h create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_convert_data.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_decimal_data.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_decimal_globals.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_div_macros.h create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_dpd.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_flag_operations.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_from_int.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_functions.h create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_gcc_intrinsics.h create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_inline_add.h create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_internal.h create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_round.c create mode 100644 gcc-4.4.3/libgcc/config/libbid/bid_sqrt_macros.h create mode 100644 gcc-4.4.3/libgcc/config/rs6000/t-darwin create mode 100644 gcc-4.4.3/libgcc/config/rs6000/t-ldbl128 create mode 100644 gcc-4.4.3/libgcc/config/rs6000/t-ppccomm create mode 100644 gcc-4.4.3/libgcc/config/sh/t-linux create mode 100644 gcc-4.4.3/libgcc/config/sparc/t-crtfm create mode 100644 gcc-4.4.3/libgcc/config/t-slibgcc-darwin create mode 100644 gcc-4.4.3/libgcc/config/t-softfp create mode 100644 gcc-4.4.3/libgcc/config/t-tls create mode 100644 gcc-4.4.3/libgcc/configure create mode 100644 gcc-4.4.3/libgcc/configure.ac create mode 100644 gcc-4.4.3/libgcc/empty.mk create mode 100644 gcc-4.4.3/libgcc/fixed-obj.mk create mode 100644 gcc-4.4.3/libgcc/gen-fixed.sh create mode 100644 gcc-4.4.3/libgcc/gstdint.h create mode 100644 gcc-4.4.3/libgcc/shared-object.mk create mode 100644 gcc-4.4.3/libgcc/siditi-object.mk create mode 100644 gcc-4.4.3/libgcc/static-object.mk (limited to 'gcc-4.4.3/libgcc') diff --git a/gcc-4.4.3/libgcc/ChangeLog b/gcc-4.4.3/libgcc/ChangeLog new file mode 100644 index 000000000..81c337489 --- /dev/null +++ b/gcc-4.4.3/libgcc/ChangeLog @@ -0,0 +1,649 @@ +2010-01-21 Release Manager + + * GCC 4.4.3 released. + +2009-10-15 Release Manager + + * GCC 4.4.2 released. + +2009-07-22 Release Manager + + * GCC 4.4.1 released. + +2009-04-21 Release Manager + + * GCC 4.4.0 released. + +2009-04-17 Aurelien Jarno + + * config.host: Add i386/${host_address}/t-fprules-softfp to + tmake_file for i[34567]86-*-kfreebsd*-gnu, x86_64-*-kfreebsd*-gnu*. + +2009-04-09 Nick Clifton + + * config/ia64/tf-signs.c: Change copyright header to refer to + version 3 of the GNU General Public License with version 3.1 + of the GCC Runtime Library Exception and to point readers at + the COPYING3 and COPYING3.RUNTIME files and the FSF's license + web page. + * config/i386/32/tf-signs.c: Likewise. + * config/libbid/_addsub_dd.c: Likewise. + * config/libbid/_addsub_sd.c: Likewise. + * config/libbid/_addsub_td.c: Likewise. + * config/libbid/_dd_to_df.c: Likewise. + * config/libbid/_dd_to_di.c: Likewise. + * config/libbid/_dd_to_sd.c: Likewise. + * config/libbid/_dd_to_sf.c: Likewise. + * config/libbid/_dd_to_si.c: Likewise. + * config/libbid/_dd_to_td.c: Likewise. + * config/libbid/_dd_to_tf.c: Likewise. + * config/libbid/_dd_to_udi.c: Likewise. + * config/libbid/_dd_to_usi.c: Likewise. + * config/libbid/_dd_to_xf.c: Likewise. + * config/libbid/_df_to_dd.c: Likewise. + * config/libbid/_df_to_sd.c: Likewise. + * config/libbid/_df_to_td.c: Likewise. + * config/libbid/_di_to_dd.c: Likewise. + * config/libbid/_di_to_sd.c: Likewise. + * config/libbid/_di_to_td.c: Likewise. + * config/libbid/_div_dd.c: Likewise. + * config/libbid/_div_sd.c: Likewise. + * config/libbid/_div_td.c: Likewise. + * config/libbid/_eq_dd.c: Likewise. + * config/libbid/_eq_sd.c: Likewise. + * config/libbid/_eq_td.c: Likewise. + * config/libbid/_ge_dd.c: Likewise. + * config/libbid/_ge_sd.c: Likewise. + * config/libbid/_ge_td.c: Likewise. + * config/libbid/_gt_dd.c: Likewise. + * config/libbid/_gt_sd.c: Likewise. + * config/libbid/_gt_td.c: Likewise. + * config/libbid/_isinfd128.c: Likewise. + * config/libbid/_isinfd32.c: Likewise. + * config/libbid/_isinfd64.c: Likewise. + * config/libbid/_le_dd.c: Likewise. + * config/libbid/_le_sd.c: Likewise. + * config/libbid/_le_td.c: Likewise. + * config/libbid/_lt_dd.c: Likewise. + * config/libbid/_lt_sd.c: Likewise. + * config/libbid/_lt_td.c: Likewise. + * config/libbid/_mul_dd.c: Likewise. + * config/libbid/_mul_sd.c: Likewise. + * config/libbid/_mul_td.c: Likewise. + * config/libbid/_ne_dd.c: Likewise. + * config/libbid/_ne_sd.c: Likewise. + * config/libbid/_ne_td.c: Likewise. + * config/libbid/_sd_to_dd.c: Likewise. + * config/libbid/_sd_to_df.c: Likewise. + * config/libbid/_sd_to_di.c: Likewise. + * config/libbid/_sd_to_sf.c: Likewise. + * config/libbid/_sd_to_si.c: Likewise. + * config/libbid/_sd_to_td.c: Likewise. + * config/libbid/_sd_to_tf.c: Likewise. + * config/libbid/_sd_to_udi.c: Likewise. + * config/libbid/_sd_to_usi.c: Likewise. + * config/libbid/_sd_to_xf.c: Likewise. + * config/libbid/_sf_to_dd.c: Likewise. + * config/libbid/_sf_to_sd.c: Likewise. + * config/libbid/_sf_to_td.c: Likewise. + * config/libbid/_si_to_dd.c: Likewise. + * config/libbid/_si_to_sd.c: Likewise. + * config/libbid/_si_to_td.c: Likewise. + * config/libbid/_td_to_dd.c: Likewise. + * config/libbid/_td_to_df.c: Likewise. + * config/libbid/_td_to_di.c: Likewise. + * config/libbid/_td_to_sd.c: Likewise. + * config/libbid/_td_to_sf.c: Likewise. + * config/libbid/_td_to_si.c: Likewise. + * config/libbid/_td_to_tf.c: Likewise. + * config/libbid/_td_to_udi.c: Likewise. + * config/libbid/_td_to_usi.c: Likewise. + * config/libbid/_td_to_xf.c: Likewise. + * config/libbid/_tf_to_dd.c: Likewise. + * config/libbid/_tf_to_sd.c: Likewise. + * config/libbid/_tf_to_td.c: Likewise. + * config/libbid/_udi_to_dd.c: Likewise. + * config/libbid/_udi_to_sd.c: Likewise. + * config/libbid/_udi_to_td.c: Likewise. + * config/libbid/_unord_dd.c: Likewise. + * config/libbid/_unord_sd.c: Likewise. + * config/libbid/_unord_td.c: Likewise. + * config/libbid/_usi_to_dd.c: Likewise. + * config/libbid/_usi_to_sd.c: Likewise. + * config/libbid/_usi_to_td.c: Likewise. + * config/libbid/_xf_to_dd.c: Likewise. + * config/libbid/_xf_to_sd.c: Likewise. + * config/libbid/_xf_to_td.c: Likewise. + * config/libbid/bid128.c: Likewise. + * config/libbid/bid128_2_str.h: Likewise. + * config/libbid/bid128_2_str_macros.h: Likewise. + * config/libbid/bid128_2_str_tables.c: Likewise. + * config/libbid/bid128_add.c: Likewise. + * config/libbid/bid128_compare.c: Likewise. + * config/libbid/bid128_div.c: Likewise. + * config/libbid/bid128_fma.c: Likewise. + * config/libbid/bid128_logb.c: Likewise. + * config/libbid/bid128_minmax.c: Likewise. + * config/libbid/bid128_mul.c: Likewise. + * config/libbid/bid128_next.c: Likewise. + * config/libbid/bid128_noncomp.c: Likewise. + * config/libbid/bid128_quantize.c: Likewise. + * config/libbid/bid128_rem.c: Likewise. + * config/libbid/bid128_round_integral.c: Likewise. + * config/libbid/bid128_scalb.c: Likewise. + * config/libbid/bid128_sqrt.c: Likewise. + * config/libbid/bid128_string.c: Likewise. + * config/libbid/bid128_to_int16.c: Likewise. + * config/libbid/bid128_to_int32.c: Likewise. + * config/libbid/bid128_to_int64.c: Likewise. + * config/libbid/bid128_to_int8.c: Likewise. + * config/libbid/bid128_to_uint16.c: Likewise. + * config/libbid/bid128_to_uint32.c: Likewise. + * config/libbid/bid128_to_uint64.c: Likewise. + * config/libbid/bid128_to_uint8.c: Likewise. + * config/libbid/bid32_to_bid128.c: Likewise. + * config/libbid/bid32_to_bid64.c: Likewise. + * config/libbid/bid64_add.c: Likewise. + * config/libbid/bid64_compare.c: Likewise. + * config/libbid/bid64_div.c: Likewise. + * config/libbid/bid64_fma.c: Likewise. + * config/libbid/bid64_logb.c: Likewise. + * config/libbid/bid64_minmax.c: Likewise. + * config/libbid/bid64_mul.c: Likewise. + * config/libbid/bid64_next.c: Likewise. + * config/libbid/bid64_noncomp.c: Likewise. + * config/libbid/bid64_quantize.c: Likewise. + * config/libbid/bid64_rem.c: Likewise. + * config/libbid/bid64_round_integral.c: Likewise. + * config/libbid/bid64_scalb.c: Likewise. + * config/libbid/bid64_sqrt.c: Likewise. + * config/libbid/bid64_string.c: Likewise. + * config/libbid/bid64_to_bid128.c: Likewise. + * config/libbid/bid64_to_int16.c: Likewise. + * config/libbid/bid64_to_int32.c: Likewise. + * config/libbid/bid64_to_int64.c: Likewise. + * config/libbid/bid64_to_int8.c: Likewise. + * config/libbid/bid64_to_uint16.c: Likewise. + * config/libbid/bid64_to_uint32.c: Likewise. + * config/libbid/bid64_to_uint64.c: Likewise. + * config/libbid/bid64_to_uint8.c: Likewise. + * config/libbid/bid_b2d.h: Likewise. + * config/libbid/bid_binarydecimal.c: Likewise. + * config/libbid/bid_conf.h: Likewise. + * config/libbid/bid_convert_data.c: Likewise. + * config/libbid/bid_decimal_data.c: Likewise. + * config/libbid/bid_decimal_globals.c: Likewise. + * config/libbid/bid_div_macros.h: Likewise. + * config/libbid/bid_dpd.c: Likewise. + * config/libbid/bid_flag_operations.c: Likewise. + * config/libbid/bid_from_int.c: Likewise. + * config/libbid/bid_functions.h: Likewise. + * config/libbid/bid_gcc_intrinsics.h: Likewise. + * config/libbid/bid_inline_add.h: Likewise. + * config/libbid/bid_internal.h: Likewise. + * config/libbid/bid_round.c: Likewise. + * config/libbid/bid_sqrt_macros.h: Likewise. + +2009-04-09 Jakub Jelinek + + * Makefile.in: Change copyright header to refer to version + 3 of the GNU General Public License and to point readers at the + COPYING3 file and the FSF's license web page. + * config.host: Likewise. + +2009-02-12 Uros Bizjak + + * config.host (ia64*-*-linux*): Add t-softfp to tmake_file. + * config/ia64/tf-signs.c (__copysigntf3, __fabstf2): Prototype. + +2009-02-12 H.J. Lu + + * config.host (ia64*-*-linux*): Add ia64/t-fprules-softfp and + ia64/t-softfp-compat to tmake_file. + + * Makefile.in (gen-hide-list): Ignore .*_compat and .*@.*. + + * config/ia64/__divxf3.asm: New. + * config/ia64/_fixtfdi.asm: Likewise. + * config/ia64/_fixunstfdi.asm: Likewise. + * config/ia64/_floatditf.asm: Likewise. + * config/ia64/t-fprules-softfp: Likewise. + * config/ia64/t-softfp-compat: Likewise. + * config/ia64/tf-signs.c: Likewise. + +2009-01-18 Ben Elliston + + * config/i386/32/tf-signs.c (__copysigntf3, __fabstf2): Prototype. + +2009-01-16 Ben Elliston + + * config.host (i[34567]86-*-linux*, x86_64-*-linux*): Add t-softfp + to tmake_file. + +2009-01-13 Ben Elliston + + * config/t-softfp: New file. + * config.host (powerpc64-*-linux*, powerpc64-*-gnu*): Add t-softfp. + (powerpc-*-linux*spe*, powerpc-*-linux*): Likewise. + +2009-01-05 Joel Sherrill + + * config.host: Add m32r*-*-rtems*. + +2008-12-01 Joel Sherrill + + * config.host: Add m32c*-*-rtems*. + +2008-11-20 Rainer Orth + + PR bootstrap/33100 + * configure.ac (i?86-*-solaris2.1[0-9]*): Only include + i386/t-crtstuff if linker supports ZERO terminator unwind entries. + * configure: Regenerate. + * config.host (i[34567]86-*-solaris2*): Move i386/t-sol2 in + tmake_file here from gcc/config.gcc. + Move extra_parts here from gcc/config.gcc. + * config/i386/t-sol2: Move here from gcc/config/i386. + Use gcc_srcdir instead of srcdir. + +2008-11-18 Adam Nemet + + * config.host (mipsisa64r2-*-elf* | mipsisa64r2el-*-elf*): New + case. + +2008-11-09 Thomas Schwinge + + * config.host : Also enable for GNU/kFreeBSD and GNU/kNetBSD. + +2008-10-08 Thomas Schwinge + + * config.host: Fold `*-*-gnu*' cases into the Linux ones. + +2008-09-03 Hari Sandanagobalane + + Add picoChip port. + * config.host: Add picochip-*-*. + +2008-08-06 Bob Wilson + + * config.host: Match more processor names for Xtensa. + +2008-07-08 H.J. Lu + + * config/i386/64/t-softfp-compat: Update comments. + +2008-07-07 H.J. Lu + + * config/i386/64/_divtc3-compat.c: Moved to ... + * config/i386/64/_divtc3.c: Here. + + * config/i386/64/_multc3-compat.c: Moved to ... + * config/i386/64/_multc3.c: Here. + + * config/i386/64/_powitf2-compat.c: Moved to ... + * config/i386/64/_powitf2.c: Here. + + * config/i386/64/t-softfp-compat (libgcc2-tf-compats): Add + .c suffix instead of -compat.c. + +2008-07-05 Uros Bizjak + + * config/i386/32/sfp-machine.h (_FP_MUL_MEAT_S): Remove. + (_FP_MUL_MEAT_D): Ditto. + (_FP_DIV_MEAT_S): Ditto. + (_FP_DIV_MEAT_D): Ditto. + +2008-07-03 Richard Sandiford + + * Makefile.in: Add support for __sync_* libgcc functions. + +2008-07-03 H.J. Lu + + * shared-object.mk ($(base)_s$(objext)): Remove -DSHARED. + +2008-07-02 H.J. Lu + + PR boostrap/36702 + * config.host: Only include 32bit t-fprules-softfp for Darwin/x86 + and Linux/x86. Include 64bit t-softfp-compat for Linux/x86. + + * config/i386/64/t-fprules-softfp: Moved to ... + * config/i386/64/t-softfp-compat: This. New. + +2008-07-02 Uros Bizjak + + * config/i386/32/sfp-machine.h (FP_HANDLE_EXCEPTIONS) [FP_EX_INVALID]: + Initialize f with 0.0. + +2008-07-02 H.J. Lu + + PR target/36669 + * shared-object.mk ($(base)_s$(objext)): Add -DSHARED. + + * config/i386/64/_divtc3-compat.c: New. + * config/i386/64/_multc3-compat.c: Likewise. + * config/i386/64/_powitf2-compat.c: Likewise. + * config/i386/64/eqtf2.c: Likewise. + * config/i386/64/getf2.c: Likewise. + * config/i386/64/letf2.c: Likewise. + * config/i386/64/t-fprules-softfp: Likewise. + +2008-07-02 H.J. Lu + + * config.host: Add i386/${host_address}/t-fprules-softfp to + tmake_file for i[34567]86-*-darwin*, x86_64-*-darwin*, + i[34567]86-*-linux*, x86_64-*-linux*. + + * configure.ac: Set host_address to 64 or 32 for x86. + * configure: Regenerated. + + * Makefile.in (config.status): Also depend on + $(srcdir)/config.host. + + * config/i386/32/t-fprules-softfp: New. + * config/i386/32/tf-signs.c: Likewise. + + * config/i386/64/sfp-machine.h: New. Moved from gcc. + +2008-07-02 H.J. Lu + Uros Bizjak + + * config/i386/32/sfp-machine.h: New. + +2008-06-26 Nathan Froyd + + * config/rs6000/t-ppccomm: Remove rules that conflict with + auto-generated rules. + +2008-06-17 Ralf Wildenhues + + * configure.ac: sinclude override.m4. + * configure: Regenerate. + +2008-06-11 Bernhard Fischer + + * configure: Regenerate. + +2008-06-10 Joseph Myers + + * Makefile.in (DECNUMINC): Remove + -I$(MULTIBUILDTOP)../../libdecnumber. + * gstdint.h: New. + +2008-06-07 Joseph Myers + + * config.host (strongarm*-*-*, ep9312*-*-*, xscale-*-*, + parisc*-*-*, m680[012]0-*-*, *-*-linux*libc1*, *-*-linux*aout*, + alpha*-*-unicosmk*, strongarm*-*-freebsd*, ep9312-*-elf, + arm*-*-kaos*, cris-*-aout, parisc*64*-*-linux*, parisc*-*-linux*, + hppa1.1-*-pro*, hppa1.1-*-osf*, hppa1.1-*-bsd*, + i[34567]86-sequent-ptx4*, i[34567]86-sequent-sysv4*, + i[34567]86-*-beoself*, i[34567]86-*-beos*, i[34567]86-*-sco3.2v5*, + i[34567]86-*-sysv5*, i[34567]86-*-sysv4*, i[34567]86-*-uwin*, + i[34567]86-*-kaos*, m68020-*-elf*, m68010-*-netbsdelf*, + mips-wrs-windiss, mt-*-elf, powerpc-*-beos*, powerpc-*-chorusos*, + powerpc-wrs-windiss*, powerpcle-*-sysv*, powerpc-*-kaos*, + powerpcle-*-kaos*, sh*-*-kaos*, sparc-*-sysv4*, strongarm-*-elf*, + strongarm-*-pe, strongarm-*-kaos*, vax-*-bsd*, vax-*-sysv*, + vax-*-ultrix*, xscale-*-elf, xscale-*-coff): Remove. + +2008-05-25 Arthur Loiret + + * config.host (sh2[lbe]*-*-linux*): Allow target. + +2008-04-30 Nathan Froyd + + * config/rs6000/t-ppccomm: Add build rules for new files. + (LIB2ADD_ST): New variable. + +2008-04-07 Andy Hutchinson + + PR target/34210 + PR target/35508 + * config.host (avr-*-*): Add avr cpu_type and avr tmake_file. + * config/t-avr: New file. Build 16bit libgcc functions. + +2008-03-02 Jakub Jelinek + + PR target/35401 + * config/t-slibgcc-darwin: Make install-leaf dependent on + install-darwin-libgcc-stubs instead of install. + +2008-01-25 Joseph Myers + + * config.host (tic4x-*-*, c4x-*-rtems*, tic4x-*-rtems*, c4x-*, + tic4x-*, h8300-*-rtemscoff*, ns32k-*-netbsdelf*, ns32k-*-netbsd*, + sh-*-rtemscoff*): Remove cases. + +2007-12-27 Richard Sandiford + + * Makefile.in (all): Use install-leaf rather than install. + (install): Split most of the rule into... + (install-leaf): ...this new one. + +2007-12-19 Etsushi Kato + Paolo Bonzini + + PR target/30572 + * Makefile.in: Use @shlib_slibdir@ substitution to get + correct install name on darwin. + * config/t-slibgcc-darwin: Use @shlib_slibdir@ for -install_name. + +2007-12-15 Hans-Peter Nilsson + + * config.host (crisv32-*-elf, crisv32-*-none): New, same as + cris-*-elf and cris-*-none. + (crisv32-*-linux*): Similar, as cris-*-linux*. + +2007-11-20 Rask Ingemann Lambertsen + + * config.host (ia64*-*-elf*): Build ia64 specific libgcc parts. + +2007-10-27 H.J. Lu + + PR regression/33926 + * configure.ac: Replace have_cc_tls with gcc_cv_have_cc_tls. + * configure: Regenerated. + +2007-09-27 H.J. Lu + + * Makefile.in (dfp-filenames): Replace decimal_globals, + decimal_data, binarydecimal and convert_data with + bid_decimal_globals, bid_decimal_data, bid_binarydecimal + and bid_convert_data, respectively. + +2007-09-17 Chao-ying Fu + Nigel Stephens + + * fixed-obj.mk: New file to support fine-grain fixed-point functions. + * Makefile.in (fixed_point): Define. + Check if fixed_point is yes to build support functions. + * configure.ac: Check for fixed_point support. + * configure: Regenerated. + * gen-fixed.sh: New file to generate lists of fixed-point labels, + funcs, modes, from, to. + +2007-09-11 Janis Johnson + + * Makefile.in (dfp-filenames): Remove decUtility, add + decDouble, decPacked, decQuad, decSingle. + +2007-08-27 Hans Kester + + * config.host : Add x86_64-elf target. + +2007-07-06 H.J. Lu + + * configure.ac (set_have_cc_tls): Add a missing =. + * configure: Regenerated. + +2007-07-06 H.J. Lu + + * config.host (tmake_file): Add t-tls for i[34567]86-*-linux* + and x86_64-*-linux*. + + * config/t-tls: New file. + + * Makefile.in (INTERNAL_CFLAGS): Add @set_have_cc_tls@. + + * configure.ac: Include ../config/enable.m4 and + ../config/tls.m4. Use GCC_CHECK_CC_TLS to check if assembler + supports TLS and substitute set_have_cc_tls. + * configure: Regenerated. + +2007-07-04 H.J. Lu + + * Makefile.in: Use libbid for DFP when BID is enabled. + +2007-06-14 Danny Smith + + * config.host(*-cygwin* |*-mingw* ): Add crtbegin.o, crtend.o to + extra_parts. Add config/i386/t-cygming to tmake_file. + * config/i386/t-cygming: New file with rules for crtbegin.o, crtend.o. + +2007-05-29 Zuxy Meng + Danny Smith + + PR target/29498 + * config.host (i[34567]86-*-cygwin* | i[34567]86-*-mingw*) Add + crtfastmath.o to extra_parts. Add i386/t-crtfm to tmake_file. + * config/i386/t-crtfm: Compile crtfastmath.o with + -minline-all-stringops. + +2007-05-10 Richard Sandiford + + * config.host (sparc-wrs-vxworks): New target. + +2007-04-14 Kazu Hirata + + * config.host: Recognize fido. + +2007-04-04 Janis Johnson + + * configure: Check host, not target, for decimal float support. + +2007-04-03 Uros Bizjak + + * config/i386/t-crtpc: New file. + * config.host (i[34567]86-*-linux*): Add i386/t-crtpc to tm-file. + (x86_64-*-linux*): Ditto. + +2007-02-30 Kai Tietz + + * config.host (x86_64-*-mingw*): New target. + +2007-03-23 Michael Meissner + H.J. Lu + + * Makefile.in (enable_decimal_float): New. + (DECNUMINC): Add + -I$(srcdir)/../libdecnumber/$(enable_decimal_float). + (dec-objects): Move decimal32, decimal64 and decimal128 to ... + (decbits-filenames): This. + (decbits-objects): New. + (libgcc-objects): Add $(decbits-objects). + + * configure.ac: Support * --enable-decimal-float={no,yes,bid,dpd}. + Substitute enable_decimal_float. + * configure: Regenerated. + +2007-03-19 Hans-Peter Nilsson + + * config.host (cris-*-elf | cris-*-none): Set extra_parts. + +2007-03-12 Brooks Moses + + * Makefile.in (install-info): New dummy target. + +2007-03-05 Bernd Schmidt + + * config.host (bfin*-linux-uclibc*): Set extra_parts. + +2007-03-01 Brooks Moses + + * Makefile.in: Add install-html and install-pdf dummy + targets. + +2007-02-05 Roger Sayle + Daniel Jacobowitz + + * Makefile.in : Make libgcc_s.so depend on libunwind.so. + (libgcc_s.so): Append -B./ to CFLAGS for $(SHLIB_LINK). + (libunwind.so): Likewise for $(SHLIBUNWIND_LINK). + +2007-01-29 Janis Johnson + + * Makefile.in (dec-filenames): Add decExcept. + +2007-01-28 Daniel Jacobowitz + + PR bootstrap/30469 + * Makefile.in (CFLAGS): Forcibly remove -fprofile-generate and + -fprofile-use. + +2007-01-25 Daniel Jacobowitz + + * configure.ac: Add --enable-version-specific-runtime-libs. + Correct $slibdir default. + * configure: Regenerated. + +2007-01-23 Joseph Myers + + * config/rs6000/t-ldbl128: Always use -mlong-double-128. + +2007-01-21 Andrew Pinski + + PR target/30519 + * config.host (alpha*-*-linux*): Set extra_parts. + +2007-01-09 Kaz Kojima + + * config/sh/t-linux: New. + * config.host (sh*-*-linux*): Set tmake_file. + +2007-01-05 Daniel Jacobowitz + + * Makefile.in (install): Handle multilibs. + +2007-01-04 Brooks Moses + + * Makefile.in: Added .PHONY entry for documentation targets. + +2007-01-04 Brooks Moses + + * Makefile.in: Add empty info, html, dvi, pdf targets. + +2007-01-04 Mike Stump + + * Makefile.in (MAKEINFO): Remove. + (PERL): Likewise. + +2007-01-04 Paolo Bonzini + + * configure.ac: Add GCC_TOPLEV_SUBDIRS. + * configure: Regenerate. + * Makefile.in (host_subdir): Substitute it. + (gcc_objdir): Use it. + +2007-01-04 Daniel Jacobowitz + + * config.host (ia64*-*-linux*): Set tmake_file. + +2007-01-04 Daniel Jacobowitz + + * Makefile.in (version): Define. + +2007-01-03 Daniel Jacobowitz + Paolo Bonzini + + * Makefile.in, config/i386/t-darwin, config/i386/t-darwin64, + config/i386/t-nwld, config/rs6000/t-darwin, config/rs6000/t-ldbl128, + config/i386/t-crtfm, config/alpha/t-crtfm, config/ia64/t-ia64, + config/sparc/t-crtfm, config/t-slibgcc-darwin, + config/rs6000/t-ppccomm, config.host, configure.ac, empty.mk, + shared-object.mk, siditi-object.mk, static-object.mk: New files. + * configure: Generated. diff --git a/gcc-4.4.3/libgcc/Makefile.in b/gcc-4.4.3/libgcc/Makefile.in new file mode 100644 index 000000000..a7b3d829d --- /dev/null +++ b/gcc-4.4.3/libgcc/Makefile.in @@ -0,0 +1,971 @@ +# Makefile.in + +# Copyright (C) 2005, 2006, 2009 Free Software Foundation +# +# This file is part of GCC. +# +# GCC is free software; you can redistribute it and/or modify it under the +# terms of the GNU Library General Public License as published by the Free +# Software Foundation; either version 3 of the License, or (at your option) +# any later version. +# +# GCC is distributed in the hope that it will be useful, but WITHOUT ANY +# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +# FOR A PARTICULAR PURPOSE. See the GNU General Public License for +# more details. +# +# You should have received a copy of the GNU General Public License along +# with GCC; see the file COPYING3. If not see +# . +# + +libgcc_topdir = @libgcc_topdir@ +host_subdir = @host_subdir@ + +gcc_srcdir = $(libgcc_topdir)/gcc +gcc_objdir = $(MULTIBUILDTOP)../../$(host_subdir)/gcc + +srcdir = @srcdir@ + +prefix = @prefix@ + +exec_prefix = @exec_prefix@ +libdir = @libdir@ +shlib_slibdir = @slibdir@ + +SHELL = @SHELL@ + +enable_shared = @enable_shared@ +decimal_float = @decimal_float@ +enable_decimal_float = @enable_decimal_float@ +fixed_point = @fixed_point@ + +host_noncanonical = @host_noncanonical@ + +# List of extra object files that should be compiled for this target machine. +# The rules for compiling them should be in the t-* file for the machine. +EXTRA_PARTS = @extra_parts@ + +# Multilib support variables. +MULTISRCTOP = +MULTIBUILDTOP = +MULTIDIRS = +MULTISUBDIR = +MULTIDO = true +MULTICLEAN = true + +INSTALL = @INSTALL@ +INSTALL_PROGRAM = @INSTALL_PROGRAM@ +INSTALL_DATA = @INSTALL_DATA@ +mkinstalldirs = $(SHELL) $(libgcc_topdir)/mkinstalldirs + +objext = .o + +AR = @AR@ +AR_FLAGS = rc + +CC = @CC@ +CFLAGS = @CFLAGS@ +RANLIB = @RANLIB@ +LN_S = @LN_S@ + +PWD_COMMAND = $${PWDCMD-pwd} + +# Flags to pass to a recursive make. +FLAGS_TO_PASS = \ + "AR=$(AR)" \ + "AR_FLAGS=$(AR_FLAGS)" \ + "CC=$(CC)" \ + "CFLAGS=$(CFLAGS)" \ + "DESTDIR=$(DESTDIR)" \ + "EXTRA_OFILES=$(EXTRA_OFILES)" \ + "HDEFINES=$(HDEFINES)" \ + "INSTALL=$(INSTALL)" \ + "INSTALL_DATA=$(INSTALL_DATA)" \ + "INSTALL_PROGRAM=$(INSTALL_PROGRAM)" \ + "LDFLAGS=$(LDFLAGS)" \ + "LOADLIBES=$(LOADLIBES)" \ + "RANLIB=$(RANLIB)" \ + "SHELL=$(SHELL)" \ + "prefix=$(prefix)" \ + "exec_prefix=$(exec_prefix)" \ + "libdir=$(libdir)" \ + "libsubdir=$(libsubdir)" \ + "tooldir=$(tooldir)" + +# Dependencies for "all" are set later in the file. +all: all-multi + # Now that we have built all the objects, we need to copy + # them back to the GCC directory. Too many things (other + # in-tree libraries, and DejaGNU) know about the layout + # of the build tree, for now. + $(MAKE) install-leaf DESTDIR=$(gcc_objdir) \ + slibdir= libsubdir= MULTIOSDIR=$(MULTIDIR) + +.PHONY: all-multi +all-multi: + # If this is the top-level multilib, build all the other + # multilibs. + @: $(MAKE) ; exec $(MULTIDO) $(FLAGS_TO_PASS) multi-do DO=all + +.PHONY: check installcheck +check: +installcheck: + +.PHONY: all clean + +clean: + -rm -f config.h stamp-h stmp-ldirs libgcc.map + -rm -f *$(objext) + -rm -f *.dep + -rm -f *.a + -rm -f libunwind$(SHLIB_EXT) + -rm -f libgcc_s* + @$(MULTICLEAN) multi-clean DO=clean +distclean: clean + @$(MULTICLEAN) multi-clean DO=distclean + -rm -f *~ Makefile config.cache config.status multilib.out + -rm -f config.log +maintainer-clean realclean: distclean + +Makefile: $(srcdir)/Makefile.in config.status + CONFIG_FILES=Makefile CONFIG_HEADERS= $(SHELL) ./config.status + +# Depending on Makefile makes sure that config.status has been re-run +# if needed. This prevents problems with parallel builds. +config.h: stamp-h ; @true +stamp-h: $(srcdir)/config.in config.status Makefile + CONFIG_FILES= CONFIG_HEADERS=config.h:$(srcdir)/config.in $(SHELL) ./config.status + +config.status: $(srcdir)/configure $(srcdir)/config.host + $(SHELL) ./config.status --recheck + +include $(gcc_objdir)/libgcc.mvars + +# Flags to pass to recursive makes. + +AR_FOR_TARGET = $(AR) +AR_FLAGS_FOR_TARGET = +AR_CREATE_FOR_TARGET = $(AR_FOR_TARGET) $(AR_FLAGS_FOR_TARGET) rc +AR_EXTRACT_FOR_TARGET = $(AR_FOR_TARGET) $(AR_FLAGS_FOR_TARGET) x +AWK = @AWK@ +GCC_FOR_TARGET = $(CC) +LIPO = @LIPO@ +LIPO_FOR_TARGET = $(LIPO) +MACHMODE_H = machmode.h mode-classes.def insn-modes.h +NM = @NM@ +NM_FOR_TARGET = $(NM) +RANLIB_FOR_TARGET = $(RANLIB) +STRIP = @STRIP@ +STRIP_FOR_TARGET = $(STRIP) + +# Directory in which the compiler finds libraries etc. +libsubdir = $(libdir)/gcc/$(host_noncanonical)/$(version) +# Used to install the shared libgcc. +slibdir = @slibdir@ + +export AR_FOR_TARGET +export AR_CREATE_FOR_TARGET +export AR_FLAGS_FOR_TARGET +export AR_EXTRACT_FOR_TARGET +export AWK +export DESTDIR +export GCC_FOR_TARGET +export INCLUDES +export INSTALL_DATA +export LIB1ASMSRC +export LIBGCC2_CFLAGS +export LIPO_FOR_TARGET +export MACHMODE_H +export NM_FOR_TARGET +export STRIP_FOR_TARGET +export RANLIB_FOR_TARGET +export libsubdir +export slibdir + +version := $(shell $(CC) -dumpversion) + +ifeq ($(decimal_float),yes) +ifeq ($(enable_decimal_float),bid) +DECNUMINC = -I$(srcdir)/config/libbid -DENABLE_DECIMAL_BID_FORMAT +else +DECNUMINC = -I$(srcdir)/../libdecnumber/$(enable_decimal_float) \ + -I$(srcdir)/../libdecnumber +endif +else +DECNUMINC = +endif + +# Specify the directories to be searched for header files. +# Both . and srcdir are used, in that order, +# so that *config.h will be found in the compilation +# subdirectory rather than in the source directory. +# -I$(@D) and -I$(srcdir)/$(@D) cause the subdirectory of the file +# currently being compiled, in both source trees, to be examined as well. +INCLUDES = -I. -I$(@D) -I$(gcc_objdir) \ + -I$(srcdir) -I$(srcdir)/$(@D) -I$(srcdir)/../gcc \ + -I$(srcdir)/../include $(DECNUMINC) + +# Forcibly remove any profiling-related flags. There is no point +# in supporting profiled bootstrap in this library. +override CFLAGS := $(filter-out -fprofile-generate -fprofile-use,$(CFLAGS)) + +# CFLAGS first is not perfect; normally setting CFLAGS should override any +# options in LIBGCC2_CFLAGS. But LIBGCC2_CFLAGS may contain -g0, and CFLAGS +# will usually contain -g, so for the moment CFLAGS goes first. We must +# include CFLAGS - that's where multilib options live. +INTERNAL_CFLAGS = $(CFLAGS) $(LIBGCC2_CFLAGS) $(HOST_LIBGCC2_CFLAGS) \ + $(INCLUDES) @set_have_cc_tls@ + +MULTIDIR := $(shell $(CC) $(CFLAGS) -print-multi-directory) +MULTIOSDIR := $(shell $(CC) $(CFLAGS) -print-multi-os-directory) + +MULTIOSSUBDIR := $(shell if test $(MULTIOSDIR) != .; then echo /$(MULTIOSDIR); fi) +inst_libdir = $(libsubdir)$(MULTISUBDIR) +inst_slibdir = $(slibdir)$(MULTIOSSUBDIR) + +gcc_compile_bare = $(CC) $(INTERNAL_CFLAGS) +compile_deps = -MT $@ -MD -MP -MF $(basename $@).dep +gcc_compile = $(gcc_compile_bare) -o $@ $(compile_deps) +gcc_s_compile = $(gcc_compile) -DSHARED + +objects = $(filter %$(objext),$^) + +# Collect any host-specific information from Makefile fragments. +tmake_file = @tmake_file@ +include $(srcdir)/empty.mk $(tmake_file) + +# Only handle shared libraries if both: +# - the user requested them +# - we know how to build them +ifeq ($(SHLIB_LINK),) + enable_shared := no +endif + +ifeq ($(enable_shared),yes) + iterator = $(srcdir)/empty.mk $(patsubst %,$(srcdir)/shared-object.mk,$(iter-items)) + + install-shared = install-shared + + ifneq ($(LIBUNWIND),) + install-libunwind = install-libunwind + endif + +# For -fvisibility=hidden. We need both a -fvisibility=hidden on +# the command line, and a #define to prevent libgcc2.h etc from +# overriding that with #pragmas. +vis_hide = @vis_hide@ + +ifneq (,$(vis_hide)) + +# If we have -fvisibility=hidden, then we need to generate hide +# lists for object files implemented in assembly. +ASM_HIDDEN_OP = @asm_hidden_op@ + +define gen-hide-list +$(NM) -pg $< | \ + $(AWK) 'NF == 3 && $$2 !~ /^[UN]$$/ && $$3 !~ /.*_compat/ \ + && $$3 !~ /.*@.*/ \ + { print "\t$(ASM_HIDDEN_OP)", $$3 }' > $@T +mv -f $@T $@ +endef +else +gen-hide-list = echo > $@ +endif + +else +# Not enable_shared. +iterator = $(srcdir)/empty.mk $(patsubst %,$(srcdir)/static-object.mk,$(iter-items)) +vis_hide = +gen-hide-list = echo > \$@ +endif + +ifneq ($(EXTRA_PARTS),) + extra-parts = libgcc-extra-parts + INSTALL_PARTS = $(EXTRA_PARTS) +else +ifneq ($(GCC_EXTRA_PARTS),) + extra-parts = gcc-extra-parts + INSTALL_PARTS = $(GCC_EXTRA_PARTS) +endif +endif + +# Library members defined in libgcc2.c. +lib2funcs = _muldi3 _negdi2 _lshrdi3 _ashldi3 _ashrdi3 _cmpdi2 _ucmpdi2 \ + _clear_cache _enable_execute_stack _trampoline __main _absvsi2 \ + _absvdi2 _addvsi3 _addvdi3 _subvsi3 _subvdi3 _mulvsi3 _mulvdi3 \ + _negvsi2 _negvdi2 _ctors _ffssi2 _ffsdi2 _clz _clzsi2 _clzdi2 \ + _ctzsi2 _ctzdi2 _popcount_tab _popcountsi2 _popcountdi2 \ + _paritysi2 _paritydi2 _powisf2 _powidf2 _powixf2 _powitf2 \ + _mulsc3 _muldc3 _mulxc3 _multc3 _divsc3 _divdc3 _divxc3 \ + _divtc3 _bswapsi2 _bswapdi2 + +# The floating-point conversion routines that involve a single-word integer. +# XX stands for the integer mode. +swfloatfuncs = $(patsubst %,_fixuns%XX,sf df xf) + +# Likewise double-word routines. +dwfloatfuncs = $(patsubst %,_fix%XX,sf df xf tf) \ + $(patsubst %,_fixuns%XX,sf df xf tf) \ + $(patsubst %,_floatXX%,sf df xf tf) \ + $(patsubst %,_floatunXX%,sf df xf tf) + +ifeq ($(LIB2_SIDITI_CONV_FUNCS),) + lib2funcs += $(subst XX,si,$(swfloatfuncs)) + lib2funcs += $(subst XX,di,$(dwfloatfuncs)) +endif + +# These might cause a divide overflow trap and so are compiled with +# unwinder info. +LIB2_DIVMOD_FUNCS = _divdi3 _moddi3 _udivdi3 _umoddi3 _udiv_w_sdiv _udivmoddi4 + +# Remove any objects from lib2funcs and LIB2_DIVMOD_FUNCS that are +# defined as optimized assembly code in LIB1ASMFUNCS or as C code +# in LIB2FUNCS_EXCLUDE. +lib2funcs := $(filter-out $(LIB2FUNCS_EXCLUDE) $(LIB1ASMFUNCS),$(lib2funcs)) +LIB2_DIVMOD_FUNCS := $(filter-out $(LIB2FUNCS_EXCLUDE) $(LIB1ASMFUNCS), \ + $(LIB2_DIVMOD_FUNCS)) + +# Build "libgcc1" (assembly) components. +ifeq ($(enable_shared),yes) + +lib1asmfuncs-o = $(patsubst %,%$(objext),$(LIB1ASMFUNCS)) +$(lib1asmfuncs-o): %$(objext): $(gcc_srcdir)/config/$(LIB1ASMSRC) %.vis + $(gcc_compile) -DL$* -xassembler-with-cpp \ + -c $(gcc_srcdir)/config/$(LIB1ASMSRC) -include $*.vis +$(patsubst %,%.vis,$(LIB1ASMFUNCS)): %.vis: %_s$(objext) + $(gen-hide-list) +libgcc-objects += $(lib1asmfuncs-o) + +lib1asmfuncs-s-o = $(patsubst %,%_s$(objext),$(LIB1ASMFUNCS)) +$(lib1asmfuncs-s-o): %_s$(objext): $(gcc_srcdir)/config/$(LIB1ASMSRC) + $(gcc_s_compile) -DL$* -xassembler-with-cpp \ + -c $(gcc_srcdir)/config/$(LIB1ASMSRC) +libgcc-s-objects += $(lib1asmfuncs-s-o) + +else + +lib1asmfuncs-o = $(patsubst %,%$(objext),$(LIB1ASMFUNCS)) +$(lib1asmfuncs-o): %$(objext): $(gcc_srcdir)/config/$(LIB1ASMSRC) + $(gcc_compile) -DL$* -xassembler-with-cpp \ + -c $(gcc_srcdir)/config/$(LIB1ASMSRC) +libgcc-objects += $(lib1asmfuncs-o) + +endif + +# Build lib2funcs. For the static library also include LIB2FUNCS_ST. +lib2funcs-o = $(patsubst %,%$(objext),$(lib2funcs) $(LIB2FUNCS_ST)) +$(lib2funcs-o): %$(objext): $(gcc_srcdir)/libgcc2.c + $(gcc_compile) -DL$* -c $(gcc_srcdir)/libgcc2.c \ + $(vis_hide) +libgcc-objects += $(lib2funcs-o) + +ifeq ($(enable_shared),yes) +lib2funcs-s-o = $(patsubst %,%_s$(objext),$(lib2funcs)) +$(lib2funcs-s-o): %_s$(objext): $(gcc_srcdir)/libgcc2.c + $(gcc_s_compile) -DL$* -c $(gcc_srcdir)/libgcc2.c +libgcc-s-objects += $(lib2funcs-s-o) +endif + +ifneq ($(LIB2_SIDITI_CONV_FUNCS),) +# Build libgcc2.c for each conversion function, with a specific +# L definition and LIBGCC2_UNITS_PER_WORD setting. The DImode +# functions are built with a wordsize of 4; the TImode functions are +# built with the same labels, but a wordsize of 8. + +sifuncs = $(subst XX,si,$(swfloatfuncs)) +difuncs = $(subst XX,di,$(dwfloatfuncs)) +tifuncs = $(subst XX,ti,$(dwfloatfuncs)) + +iter-items := $(sifuncs) $(difuncs) $(tifuncs) +iter-labels := $(sifuncs) $(difuncs) $(difuncs) +iter-sizes := $(patsubst %,4,$(sifuncs) $(difuncs)) $(patsubst %,8,$(tifuncs)) + +include $(srcdir)/empty.mk $(patsubst %,$(srcdir)/siditi-object.mk,$(iter-items)) + +libgcc-objects += $(patsubst %,%$(objext),$(sifuncs) $(difuncs) $(tifuncs)) +ifeq ($(enable_shared),yes) +libgcc-s-objects += $(patsubst %,%_s$(objext),$(sifuncs) $(difuncs) $(tifuncs)) +endif +endif + +# Build LIB2_DIVMOD_FUNCS. +lib2-divmod-o = $(patsubst %,%$(objext),$(LIB2_DIVMOD_FUNCS)) +$(lib2-divmod-o): %$(objext): $(gcc_srcdir)/libgcc2.c + $(gcc_compile) -DL$* -c $(gcc_srcdir)/libgcc2.c \ + -fexceptions -fnon-call-exceptions $(vis_hide) +libgcc-objects += $(lib2-divmod-o) + +ifeq ($(enable_shared),yes) +lib2-divmod-s-o = $(patsubst %,%_s$(objext),$(LIB2_DIVMOD_FUNCS)) +$(lib2-divmod-s-o): %_s$(objext): $(gcc_srcdir)/libgcc2.c + $(gcc_s_compile) -DL$* -c $(gcc_srcdir)/libgcc2.c \ + -fexceptions -fnon-call-exceptions +libgcc-s-objects += $(lib2-divmod-s-o) +endif + +# $(FPBIT) et al. are pathnames relative to the GCC build +# directory; the supporting files are made by the GCC +# Makefile. +# FIXME: Soon we will be able to move this logic into this directory. + +ifneq ($(fpbit-in-libgcc),yes) +FPBIT:=$(if $(FPBIT),$(gcc_objdir)/$(FPBIT),) +DPBIT:=$(if $(DPBIT),$(gcc_objdir)/$(DPBIT),) +TPBIT:=$(if $(TPBIT),$(gcc_objdir)/$(TPBIT),) +endif + +ifeq ($(TPBIT),) +# _sf_to_tf and _df_to_tf require tp-bit.c being compiled in. +FPBIT_FUNCS := $(filter-out _sf_to_tf,$(FPBIT_FUNCS)) +DPBIT_FUNCS := $(filter-out _df_to_tf,$(DPBIT_FUNCS)) +endif + +# Build FPBIT. +ifneq ($(FPBIT),) +fpbit-o = $(patsubst %,%$(objext),$(FPBIT_FUNCS)) +$(fpbit-o): %$(objext): $(FPBIT) + $(gcc_compile) -DFINE_GRAINED_LIBRARIES -DL$* -c $(FPBIT) $(vis_hide) +libgcc-objects += $(fpbit-o) + +ifeq ($(enable_shared),yes) +fpbit-s-o = $(patsubst %,%_s$(objext),$(FPBIT_FUNCS)) +$(fpbit-s-o): %_s$(objext): $(FPBIT) + $(gcc_s_compile) -DFINE_GRAINED_LIBRARIES -DL$* -c $(FPBIT) +libgcc-s-objects += $(fpbit-s-o) +endif +endif + +# Build DPBIT. +ifneq ($(DPBIT),) +dpbit-o = $(patsubst %,%$(objext),$(DPBIT_FUNCS)) +$(dpbit-o): %$(objext): $(DPBIT) + $(gcc_compile) -DFINE_GRAINED_LIBRARIES -DL$* -c $(DPBIT) $(vis_hide) +libgcc-objects += $(dpbit-o) + +ifeq ($(enable_shared),yes) +dpbit-s-o = $(patsubst %,%_s$(objext),$(DPBIT_FUNCS)) +$(dpbit-s-o): %_s$(objext): $(DPBIT) + $(gcc_s_compile) -DFINE_GRAINED_LIBRARIES -DL$* -c $(DPBIT) +libgcc-s-objects += $(dpbit-s-o) +endif +endif + +# Build TPBIT. +ifneq ($(TPBIT),) +tpbit-o = $(patsubst %,%$(objext),$(TPBIT_FUNCS)) +$(tpbit-o): %$(objext): $(TPBIT) + $(gcc_compile) -DFINE_GRAINED_LIBRARIES -DL$* -c $(TPBIT) $(vis_hide) +libgcc-objects += $(tpbit-o) + +ifeq ($(enable_shared),yes) +tpbit-s-o = $(patsubst %,%_s$(objext),$(TPBIT_FUNCS)) +$(tpbit-s-o): %_s$(objext): $(TPBIT) + $(gcc_s_compile) -DFINE_GRAINED_LIBRARIES -DL$* -c $(TPBIT) +libgcc-s-objects += $(tpbit-s-o) +endif +endif + +# Build decimal floating point support. +ifeq ($(decimal_float),yes) + +# If $DFP_ENABLE is set, then we want all data type sizes. +ifneq ($(DFP_ENABLE),) +D32PBIT = 1 +D64PBIT = 1 +D128PBIT = 1 +endif + +dfp-filenames = +ifneq ($(D32PBIT)$(D64PBIT)$(D128PBIT),) +ifeq ($(enable_decimal_float),bid) +dfp-filenames += bid_decimal_globals bid_decimal_data \ + bid_binarydecimal bid_convert_data \ + _isinfd32 _isinfd64 _isinfd128 bid64_noncomp \ + bid128_noncomp bid128_fma bid_round bid_from_int \ + bid64_add bid128_add bid64_div bid128_div \ + bid64_mul bid128_mul bid64_compare bid128_compare \ + bid128 bid32_to_bid64 bid32_to_bid128 bid64_to_bid128 \ + bid64_to_int32 bid64_to_int64 \ + bid64_to_uint32 bid64_to_uint64 \ + bid128_to_int32 bid128_to_int64 \ + bid128_to_uint32 bid128_to_uint64 +else +dfp-filenames += decContext decNumber decExcept decRound decLibrary decDouble decPacked decQuad decSingle +endif +endif + +dfp-objects = $(patsubst %,%$(objext),$(dfp-filenames)) +ifeq ($(enable_decimal_float),bid) +$(dfp-objects): %$(objext): $(srcdir)/config/libbid/%.c +else +$(dfp-objects): %$(objext): $(srcdir)/../libdecnumber/%.c +endif + $(gcc_compile) -c $< +libgcc-objects += $(dfp-objects) + +decbits-filenames = +ifneq ($(enable_decimal_float),bid) +ifneq ($(D32PBIT),) +decbits-filenames += decimal32 +endif + +ifneq ($(D64PBIT),) +decbits-filenames += decimal64 +endif + +ifneq ($(D128PBIT),) +decbits-filenames += decimal128 +endif +endif + +decbits-objects = $(patsubst %,%$(objext),$(decbits-filenames)) +ifeq ($(enable_decimal_float),bid) +$(decbits-objects): %$(objext): $(srcdir)/config/libbid/%.c +else +$(decbits-objects): %$(objext): $(srcdir)/../libdecnumber/$(enable_decimal_float)/%.c +endif + $(gcc_compile) -c $< +libgcc-objects += $(decbits-objects) + +# Next build individual support functions. +ifeq ($(enable_decimal_float),bid) +ifneq ($(D32PBIT),) +D32PBIT_FUNCS:=$(filter-out _plus_sd _minus_sd _conv_sd, $(D32PBIT_FUNCS)) +endif + +ifneq ($(D64PBIT),) +D64PBIT_FUNCS:=$(filter-out _plus_dd _minus_dd _conv_dd, $(D64PBIT_FUNCS)) +endif + +ifneq ($(D128PBIT),) +D128PBIT_FUNCS:=$(filter-out _plus_td _minus_td _conv_td, $(D128PBIT_FUNCS)) +endif +endif + +ifneq ($(D32PBIT),) +d32pbit-o = $(patsubst %,%$(objext),$(D32PBIT_FUNCS)) +ifeq ($(enable_decimal_float),bid) +$(d32pbit-o): %$(objext): $(srcdir)/config/libbid/%.c +else +$(d32pbit-o): %$(objext): $(gcc_srcdir)/config/dfp-bit.c +endif + $(gcc_compile) -DFINE_GRAINED_LIBRARIES -DL$* -DWIDTH=32 -c $< +libgcc-objects += $(d32pbit-o) +endif + +ifneq ($(D64PBIT),) +d64pbit-o = $(patsubst %,%$(objext),$(D64PBIT_FUNCS)) +ifeq ($(enable_decimal_float),bid) +$(d64pbit-o): %$(objext): $(srcdir)/config/libbid/%.c +else +$(d64pbit-o): %$(objext): $(gcc_srcdir)/config/dfp-bit.c +endif + $(gcc_compile) -DFINE_GRAINED_LIBRARIES -DL$* -DWIDTH=64 -c $< +libgcc-objects += $(d64pbit-o) +endif + +ifneq ($(D128PBIT),) +d128pbit-o = $(patsubst %,%$(objext),$(D128PBIT_FUNCS)) +ifeq ($(enable_decimal_float),bid) +$(d128pbit-o): %$(objext): $(srcdir)/config/libbid/%.c +else +$(d128pbit-o): %$(objext): $(gcc_srcdir)/config/dfp-bit.c +endif + $(gcc_compile) -DFINE_GRAINED_LIBRARIES -DL$* -DWIDTH=128 -c $< +libgcc-objects += $(d128pbit-o) +endif + +endif + +ifeq ($(LIBGCC_SYNC),yes) +libgcc-sync-size-funcs := $(foreach op, add sub or and xor nand, \ + sync_fetch_and_$(op) \ + sync_$(op)_and_fetch) \ + sync_bool_compare_and_swap \ + sync_val_compare_and_swap \ + sync_lock_test_and_set + +libgcc-sync-size-funcs := $(foreach prefix, $(libgcc-sync-size-funcs), \ + $(foreach suffix, 1 2 4 8 16, \ + $(prefix)_$(suffix))) + +libgcc-sync-size-funcs-o = $(patsubst %,%$(objext),$(libgcc-sync-size-funcs)) +$(libgcc-sync-size-funcs-o): %$(objext): $(gcc_srcdir)/config/sync.c + $(gcc_compile) $(LIBGCC_SYNC_CFLAGS) \ + -DFN=`echo "$*" | sed 's/_[^_]*$$//'` \ + -DSIZE=`echo "$*" | sed 's/.*_//'` \ + -c $(gcc_srcdir)/config/sync.c $(vis_hide) +libgcc-objects += $(libgcc-sync-size-funcs-o) + +libgcc-sync-funcs := sync_synchronize + +libgcc-sync-funcs-o = $(patsubst %,%$(objext),$(libgcc-sync-funcs)) +$(libgcc-sync-funcs-o): %$(objext): $(gcc_srcdir)/config/sync.c + $(gcc_compile) $(LIBGCC_SYNC_CFLAGS) \ + -DL$* \ + -c $(gcc_srcdir)/config/sync.c $(vis_hide) +libgcc-objects += $(libgcc-sync-funcs-o) + +ifeq ($(enable_shared),yes) +libgcc-sync-size-funcs-s-o = $(patsubst %,%_s$(objext), \ + $(libgcc-sync-size-funcs)) +$(libgcc-sync-size-funcs-s-o): %_s$(objext): $(gcc_srcdir)/config/sync.c + $(gcc_s_compile) $(LIBGCC_SYNC_CFLAGS) \ + -DFN=`echo "$*" | sed 's/_[^_]*$$//'` \ + -DSIZE=`echo "$*" | sed 's/.*_//'` \ + -c $(gcc_srcdir)/config/sync.c +libgcc-s-objects += $(libgcc-sync-size-funcs-s-o) + +libgcc-sync-funcs-s-o = $(patsubst %,%_s$(objext),$(libgcc-sync-funcs)) +$(libgcc-sync-funcs-s-o): %_s$(objext): $(gcc_srcdir)/config/sync.c + $(gcc_s_compile) $(LIBGCC_SYNC_CFLAGS) \ + -DL$* \ + -c $(gcc_srcdir)/config/sync.c +libgcc-s-objects += $(libgcc-sync-funcs-s-o) +endif +endif + +# Build fixed-point support. +ifeq ($(fixed_point),yes) + +# Generate permutations of function name and mode +fixed-labels := $(shell $(SHELL) $(srcdir)/gen-fixed.sh arith labels) +fixed-funcs := $(shell $(SHELL) $(srcdir)/gen-fixed.sh arith funcs) +fixed-modes := $(shell $(SHELL) $(srcdir)/gen-fixed.sh arith modes) + +# Generate the rules for each arithmetic function +iter-items := $(fixed-funcs) +iter-labels := $(fixed-labels) +iter-from := $(fixed-modes) +iter-to := $(fixed-modes) +include $(srcdir)/empty.mk $(patsubst %,$(srcdir)/fixed-obj.mk,$(iter-items)) + +# Add arithmetic functions to list of objects to be built +libgcc-objects += $(patsubst %,%$(objext),$(fixed-funcs)) +ifeq ($(enable_shared),yes) +libgcc-s-objects += $(patsubst %,%_s$(objext),$(fixed-funcs)) +endif + +# Convert from or to fractional +fixed-conv-funcs := $(shell $(SHELL) $(srcdir)/gen-fixed.sh conv funcs) +fixed-conv-labels := $(shell $(SHELL) $(srcdir)/gen-fixed.sh conv labels) +fixed-conv-from := $(shell $(SHELL) $(srcdir)/gen-fixed.sh conv from) +fixed-conv-to := $(shell $(SHELL) $(srcdir)/gen-fixed.sh conv to) + +# Generate the make rules for each conversion function +iter-items := $(fixed-conv-funcs) +iter-labels := $(fixed-conv-labels) +iter-from := $(fixed-conv-from) +iter-to := $(fixed-conv-to) +include $(srcdir)/empty.mk $(patsubst %,$(srcdir)/fixed-obj.mk,$(iter-items)) + +# Add conversion functions to list of objects to be built +libgcc-objects += $(patsubst %,%$(objext),$(fixed-conv-funcs)) +ifeq ($(enable_shared),yes) +libgcc-s-objects += $(patsubst %,%_s$(objext),$(fixed-conv-funcs)) +endif + +endif + +# Build LIB2ADD and LIB2ADD_ST. +ifneq ($(filter-out %.c %.S %.asm,$(LIB2ADD) $(LIB2ADD_ST)),) +$(error Unsupported files in LIB2ADD or LIB2ADD_ST.) +endif + +libgcc-objects += $(addsuffix $(objext),$(basename $(notdir $(LIB2ADD)))) +libgcc-objects += $(addsuffix $(objext),$(basename $(notdir $(LIB2ADD_ST)))) + +c_flags := +iter-items := $(LIB2ADD) $(LIB2ADD_ST) +include $(iterator) + +ifeq ($(enable_shared),yes) +libgcc-s-objects += $(addsuffix _s$(objext),$(basename $(notdir $(LIB2ADD)))) +endif + +# Build LIB2ADDEH, LIB2ADDEHSTATIC, and LIB2ADDEHSHARED. If we don't have +# libgcc_eh.a, only LIB2ADDEH matters. If we do, only LIB2ADDEHSTATIC and +# LIB2ADDEHSHARED matter. (Usually all three are identical.) + +c_flags := -fexceptions + +ifeq ($(enable_shared),yes) + +libgcc-eh-objects += $(addsuffix $(objext),$(basename $(notdir $(LIB2ADDEHSTATIC)))) +libgcc-s-objects += $(addsuffix _s$(objext),$(basename $(notdir $(LIB2ADDEHSHARED)))) + +iter-items := $(sort $(LIB2ADDEHSTATIC) $(LIB2ADDEHSHARED)) +include $(iterator) + +else +# Not shared. LIB2ADDEH are added to libgcc.a. + +libgcc-objects += $(addsuffix $(objext),$(basename $(notdir $(LIB2ADDEH)))) + +iter-items := $(LIB2ADDEH) +include $(iterator) + +endif + +# Build LIBUNWIND. + +c_flags := -fexceptions + +libunwind-objects += $(addsuffix $(objext),$(basename $(notdir $(LIBUNWIND)))) + +ifeq ($(enable_shared),yes) +libunwind-s-objects += $(addsuffix _s$(objext),$(basename $(notdir $(LIBUNWIND)))) +endif + +iter-items := $(LIBUNWIND) +include $(iterator) + +# Build libgcov components. +libgcov-objects = $(patsubst %,%$(objext),$(LIBGCOV)) +$(libgcov-objects): %$(objext): $(gcc_srcdir)/libgcov.c + $(gcc_compile) -DL$* -c $(gcc_srcdir)/libgcov.c + +dyn-ipa.o: %$(objext): $(gcc_srcdir)/libgcov.c + $(gcc_compile) -c $(gcc_srcdir)/dyn-ipa.c + + +# Static libraries. +libgcc.a: $(libgcc-objects) +libgcov.a: $(libgcov-objects) dyn-ipa$(objext) +libunwind.a: $(libunwind-objects) +libgcc_eh.a: $(libgcc-eh-objects) + +libgcc.a libgcov.a libunwind.a libgcc_eh.a: + -rm -f $@ + + objects="$(objects)"; \ + if test -z "$$objects"; then \ + echo 'int __libgcc_eh_dummy;' > eh_dummy.c; \ + $(gcc_compile_bare) $(vis_hide) -c eh_dummy.c \ + -o eh_dummy$(objext); \ + objects=eh_dummy$(objext); \ + fi; \ + $(AR_CREATE_FOR_TARGET) $@ $$objects + + $(RANLIB) $@ + +all: libgcc.a libgcov.a + +ifneq ($(LIBUNWIND),) +all: libunwind.a +libgcc_s$(SHLIB_EXT): libunwind$(SHLIB_EXT) +endif + +ifeq ($(enable_shared),yes) +all: libgcc_eh.a libgcc_s$(SHLIB_EXT) +ifneq ($(LIBUNWIND),) +all: libunwind$(SHLIB_EXT) +endif +endif + +ifeq ($(enable_shared),yes) + +# Map-file generation. +ifneq ($(SHLIB_MKMAP),) +libgcc.map: $(SHLIB_MKMAP) $(SHLIB_MAPFILES) $(libgcc-s-objects) + { $(NM) $(SHLIB_NM_FLAGS) $(libgcc-s-objects); echo %%; \ + cat $(SHLIB_MAPFILES) \ + | sed -e '/^[ ]*#/d' \ + -e 's/^%\(if\|else\|elif\|endif\|define\)/#\1/' \ + | $(gcc_compile_bare) -E -xassembler-with-cpp -; \ + } | $(AWK) -f $(SHLIB_MKMAP) $(SHLIB_MKMAP_OPTS) > tmp-$@ + mv tmp-$@ $@ +libgcc_s$(SHLIB_EXT): libgcc.map +mapfile = libgcc.map +endif + +libgcc_s$(SHLIB_EXT): $(libgcc-s-objects) $(extra-parts) + # @multilib_flags@ is still needed because this may use + # $(GCC_FOR_TARGET) and $(LIBGCC2_CFLAGS) directly. + # @multilib_dir@ is not really necessary, but sometimes it has + # more uses than just a directory name. + $(mkinstalldirs) $(MULTIDIR) + $(subst @multilib_flags@,$(CFLAGS) -B./,$(subst \ + @multilib_dir@,$(MULTIDIR),$(subst \ + @shlib_objs@,$(objects),$(subst \ + @shlib_base_name@,libgcc_s,$(subst \ + @shlib_map_file@,$(mapfile),$(subst \ + @shlib_slibdir_qual@,$(MULTIOSSUBDIR),$(subst \ + @shlib_slibdir@,$(shlib_slibdir),$(SHLIB_LINK)))))))) + +libunwind$(SHLIB_EXT): $(libunwind-s-objects) $(extra-parts) + # @multilib_flags@ is still needed because this may use + # $(GCC_FOR_TARGET) and $(LIBGCC2_CFLAGS) directly. + # @multilib_dir@ is not really necessary, but sometimes it has + # more uses than just a directory name. + $(mkinstalldirs) $(MULTIDIR) + $(subst @multilib_flags@,$(CFLAGS) -B./,$(subst \ + @multilib_dir@,$(MULTIDIR),$(subst \ + @shlib_objs@,$(objects),$(subst \ + @shlib_base_name@,libunwind,$(subst \ + @shlib_slibdir_qual@,$(MULTIOSSUBDIR),$(SHLIBUNWIND_LINK)))))) + +endif + +# Build the standard GCC startfiles and endfiles. +ALL_CRT_CFLAGS = $(CFLAGS) $(CRTSTUFF_CFLAGS) $(INCLUDES) +crt_compile = $(CC) $(ALL_CRT_CFLAGS) -o $@ $(compile_deps) + +ifeq ($(CUSTOM_CRTSTUFF),) +crtbegin$(objext): $(gcc_srcdir)/crtstuff.c + $(crt_compile) $(CRTSTUFF_T_CFLAGS) \ + -c $(gcc_srcdir)/crtstuff.c -DCRT_BEGIN + +crtend$(objext): $(gcc_srcdir)/crtstuff.c + $(crt_compile) $(CRTSTUFF_T_CFLAGS) \ + -c $(gcc_srcdir)/crtstuff.c -DCRT_END + +# These are versions of crtbegin and crtend for shared libraries. +crtbeginS$(objext): $(gcc_srcdir)/crtstuff.c + $(crt_compile) $(CRTSTUFF_T_CFLAGS_S) \ + -c $(gcc_srcdir)/crtstuff.c -DCRT_BEGIN -DCRTSTUFFS_O + +crtendS$(objext): $(gcc_srcdir)/crtstuff.c + $(crt_compile) $(CRTSTUFF_T_CFLAGS_S) \ + -c $(gcc_srcdir)/crtstuff.c -DCRT_END -DCRTSTUFFS_O + +# This is a version of crtbegin for -static links. +crtbeginT.o: $(gcc_srcdir)/crtstuff.c + $(crt_compile) $(CRTSTUFF_T_CFLAGS) \ + -c $(gcc_srcdir)/crtstuff.c -DCRT_BEGIN -DCRTSTUFFT_O +endif + +# Build extra startfiles in the libgcc directory. +.PHONY: libgcc-extra-parts +libgcc-extra-parts: $(EXTRA_PARTS) +ifneq ($(GCC_EXTRA_PARTS),) +ifneq ($(sort $(EXTRA_PARTS)),$(GCC_EXTRA_PARTS)) + # If the gcc directory specifies which extra parts to + # build for this target, and the libgcc configuration also + # specifies, make sure they match. This can be removed + # when the gcc directory no longer holds libgcc configuration; + # it is useful when migrating a target. + @echo "Configuration mismatch!" + @echo "Extra parts from gcc directory: $(GCC_EXTRA_PARTS)" + @echo "Extra parts from libgcc: $(EXTRA_PARTS)" + exit 1 +endif +endif + + # Early copyback; see "all" above for the rationale. The + # early copy is necessary so that the gcc -B options find + # the right startup files when linking shared libgcc. + $(mkinstalldirs) $(gcc_objdir)$(MULTISUBDIR) + parts="$(EXTRA_PARTS)"; \ + for file in $$parts; do \ + rm -f $(gcc_objdir)$(MULTISUBDIR)/$$file; \ + $(INSTALL_DATA) $$file $(gcc_objdir)$(MULTISUBDIR)/; \ + done + +# Build extra startfiles in the gcc directory, for unconverted +# targets. +.PHONY: gcc-extra-parts +gcc-extra-parts: + # Recursively invoke make in the GCC directory to build any + # startfiles (for now). We must do this just once, passing + # it all the GCC_EXTRA_PARTS as simultaneous goal targets, + # so that rules which cannot execute simultaneously are properly + # serialized. We indirect through T_TARGET in case any multilib + # directories contain an equals sign, to prevent make from + # interpreting any of the goals as variable assignments. + + # We must use cd && make rather than make -C, or else the stage + # number will be embedded in debug information. + + T=`$(PWD_COMMAND)`/ \ + && cd $(gcc_objdir) \ + && $(MAKE) GCC_FOR_TARGET="$(CC)" \ + MULTILIB_CFLAGS="$(CFLAGS)" \ + T=$$T \ + T_TARGET="$(patsubst %,$${T}%,$(GCC_EXTRA_PARTS))" \ + T_TARGET + + # Early copyback; see "all" above for the rationale. The + # early copy is necessary so that the gcc -B options find + # the right startup files when linking shared libgcc. + $(mkinstalldirs) $(gcc_objdir)$(MULTISUBDIR) + parts="$(GCC_EXTRA_PARTS)"; \ + for file in $$parts; do \ + rm -f $(gcc_objdir)$(MULTISUBDIR)/$$file; \ + $(INSTALL_DATA) $$file $(gcc_objdir)$(MULTISUBDIR)/; \ + done + +all: $(extra-parts) + +# Documentation targets (empty). +.PHONY: info html dvi pdf install-info install-html install-pdf + +info: +install-info: +html: +install-html: +dvi: +pdf: +install-pdf: + +# Install rules. These do not depend on "all", so that they can be invoked +# recursively from it. +install-libunwind: + $(mkinstalldirs) $(DESTDIR)$(inst_slibdir) + + # NOTE: Maybe this should go into $(inst_libdir), but this + # is where the old mklibgcc.in put it. + $(INSTALL_DATA) libunwind.a $(DESTDIR)$(inst_slibdir)/ + chmod 644 $(DESTDIR)$(inst_slibdir)/libunwind.a + $(RANLIB) $(DESTDIR)$(inst_slibdir)/libunwind.a + + $(subst @multilib_dir@,$(MULTIDIR),$(subst \ + @shlib_base_name@,libunwind,$(subst \ + @shlib_slibdir_qual@,$(MULTIOSSUBDIR),$(SHLIBUNWIND_INSTALL)))) + +install-shared: + $(mkinstalldirs) $(DESTDIR)$(inst_libdir) + + $(INSTALL_DATA) libgcc_eh.a $(DESTDIR)$(inst_libdir)/ + chmod 644 $(DESTDIR)$(inst_libdir)/libgcc_eh.a + $(RANLIB) $(DESTDIR)$(inst_libdir)/libgcc_eh.a + + $(subst @multilib_dir@,$(MULTIDIR),$(subst \ + @shlib_base_name@,libgcc_s,$(subst \ + @shlib_slibdir_qual@,$(MULTIOSSUBDIR),$(SHLIB_INSTALL)))) + +install-leaf: $(install-shared) $(install-libunwind) + $(mkinstalldirs) $(DESTDIR)$(inst_libdir) + + $(INSTALL_DATA) libgcc.a $(DESTDIR)$(inst_libdir)/ + chmod 644 $(DESTDIR)$(inst_libdir)/libgcc.a + $(RANLIB) $(DESTDIR)$(inst_libdir)/libgcc.a + $(INSTALL_DATA) libgcov.a $(DESTDIR)$(inst_libdir)/ + chmod 644 $(DESTDIR)$(inst_libdir)/libgcov.a + $(RANLIB) $(DESTDIR)$(inst_libdir)/libgcov.a + + parts="$(INSTALL_PARTS)"; \ + for file in $$parts; do \ + rm -f $(DESTDIR)$(inst_libdir)/$$file; \ + $(INSTALL_DATA) $$file $(DESTDIR)$(inst_libdir)/; \ + done + +install: install-leaf + @$(MULTIDO) $(FLAGS_TO_PASS) multi-do DO=install + +.PHONY: install install-shared install-libunwind + +# Don't export variables to the environment, in order to not confuse +# configure. +.NOEXPORT: + +include $(srcdir)/empty.mk $(wildcard *.dep) + +# TODO QUEUE: +# Garbage collect in gcc/: +# $(LIBGCC) settings in t-* are now unused +# +# Remove use of $(gcc_srcdir). Source files referenced using $(gcc_srcdir) +# should move into the libgcc directory. + diff --git a/gcc-4.4.3/libgcc/config.host b/gcc-4.4.3/libgcc/config.host new file mode 100644 index 000000000..55af65160 --- /dev/null +++ b/gcc-4.4.3/libgcc/config.host @@ -0,0 +1,608 @@ +# libgcc host-specific configuration file. +# Copyright 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, +# 2008, 2009 Free Software Foundation, Inc. + +#This file is part of GCC. + +#GCC is free software; you can redistribute it and/or modify it under +#the terms of the GNU General Public License as published by the Free +#Software Foundation; either version 3, or (at your option) any later +#version. + +#GCC is distributed in the hope that it will be useful, but WITHOUT +#ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or +#FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +#for more details. + +#You should have received a copy of the GNU General Public License +#along with GCC; see the file COPYING3. If not see +#. + +# This is the libgcc host-specific configuration file +# where a configuration type is mapped to different system-specific +# definitions and files. This is invoked by the autoconf-generated +# configure script. Putting it in a separate shell file lets us skip +# running autoconf when modifying host-specific information. + +# This file bears an obvious resemblance to gcc/config.gcc. The cases +# should be kept similar, to ease moving library-specific settings +# from config.gcc to this file. That is also why tmake_file is +# left as tmake_file, rather than hmake_file, even though this library +# switches on ${host}. + +# This file switches on the shell variable ${host}, and also uses the +# following shell variables: +# +# with_* Various variables as set by configure. + +# This file sets the following shell variables for use by the +# autoconf-generated configure script: +# +# asm_hidden_op The assembler pseudo-op to use for hide +# lists for object files implemented in +# assembly (with -fvisibility=hidden for C). +# The default is ".hidden". +# cpu_type The name of the cpu, if different from the first +# chunk of the canonical host name. +# extra_parts List of extra object files that should be compiled +# for this target machine. This may be overridden +# by setting EXTRA_PARTS in a tmake_file fragment. +# If either is set, EXTRA_PARTS and +# EXTRA_MULTILIB_PARTS inherited from the GCC +# subdirectory will be ignored. +# tmake_file A list of machine-description-specific +# makefile-fragments, if different from +# "$cpu_type/t-$cpu_type". + +asm_hidden_op=.hidden +extra_parts= +tmake_file= + +# Set default cpu_type so it can be updated in each machine entry. +cpu_type=`echo ${host} | sed 's/-.*$//'` +case ${host} in +m32c*-*-*) + cpu_type=m32c + ;; +alpha*-*-*) + cpu_type=alpha + ;; +am33_2.0-*-linux*) + cpu_type=mn10300 + ;; +arm*-*-*) + cpu_type=arm + ;; +avr-*-*) + cpu_type=avr + ;; +bfin*-*) + cpu_type=bfin + ;; +fido-*-*) + cpu_type=m68k + ;; +frv*) cpu_type=frv + ;; +i[34567]86-*-*) + cpu_type=i386 + ;; +x86_64-*-*) + cpu_type=i386 + ;; +ia64-*-*) + ;; +hppa*-*-*) + cpu_type=pa + ;; +m32r*-*-*) + cpu_type=m32r + ;; +m68k-*-*) + ;; +mips*-*-*) + cpu_type=mips + ;; +powerpc*-*-*) + cpu_type=rs6000 + ;; +rs6000*-*-*) + ;; +score*-*-*) + cpu_type=score + ;; +sparc64*-*-*) + cpu_type=sparc + ;; +sparc*-*-*) + cpu_type=sparc + ;; +spu*-*-*) + cpu_type=spu + ;; +s390*-*-*) + cpu_type=s390 + ;; +# Note the 'l'; we need to be able to match e.g. "shle" or "shl". +sh[123456789lbe]*-*-*) + cpu_type=sh + ;; +esac + +# Common parts for widely ported systems. +case ${host} in +*-*-darwin*) + asm_hidden_op=.private_extern + tmake_file="t-darwin ${cpu_type}/t-darwin t-slibgcc-darwin" + ;; +*-*-freebsd[12] | *-*-freebsd[12].* | *-*-freebsd*aout*) + # This is the place-holder for the generic a.out configuration + # of FreeBSD. No actual configuration resides here since + # there was only ever a bare-bones ix86 configuration for + # a.out and it exists solely in the machine-specific section. + # This place-holder must exist to avoid dropping into + # the generic ELF configuration of FreeBSD (i.e. it must be + # ordered before that section). + ;; +*-*-freebsd*) + # This is the generic ELF configuration of FreeBSD. Later + # machine-specific sections may refine and add to this + # configuration. + ;; +*-*-linux* | frv-*-*linux* | *-*-kfreebsd*-gnu | *-*-knetbsd*-gnu | *-*-gnu*) + extra_parts="crtbegin.o crtbeginS.o crtbeginT.o crtend.o crtendS.o" + ;; +*-*-netbsd*) + ;; +*-*-openbsd*) + ;; +*-*-rtems*) + ;; +*-*-vxworks*) + ;; +*-*-elf) + ;; +esac + +case ${host} in +# Support site-specific machine types. +*local*) + rest=`echo ${host} | sed -e "s/$cpu_type-//"` + if test -f $srcdir/config/${cpu_type}/t-$rest + then tmake_file=${cpu_type}/t-$rest + fi + ;; +alpha*-*-linux* | alpha*-*-gnu*) + tmake_file="${tmake_file} alpha/t-crtfm" + extra_parts="$extra_parts crtfastmath.o" + ;; +alpha*-*-freebsd*) + ;; +alpha*-*-netbsd*) + ;; +alpha*-*-openbsd*) + ;; +alpha*-dec-osf[45]*) + ;; +alpha64-dec-*vms*) + ;; +alpha*-dec-*vms*) + ;; +arc-*-elf*) + ;; +arm-*-coff* | armel-*-coff*) + ;; +arm-semi-aof | armel-semi-aof) + ;; +arm-wrs-vxworks) + ;; +arm*-*-freebsd*) + ;; +arm*-*-netbsdelf*) + ;; +arm*-*-netbsd*) + ;; +arm*-*-linux*) # ARM GNU/Linux with ELF + ;; +arm*-*-uclinux*) # ARM ucLinux + ;; +arm*-*-ecos-elf) + ;; +arm*-*-eabi* | arm*-*-symbianelf* ) + ;; +arm*-*-rtems*) + ;; +arm*-*-elf) + ;; +arm*-wince-pe*) + ;; +arm-*-pe*) + ;; +avr-*-rtems*) + ;; +avr-*-*) + # Make HImode functions for AVR + tmake_file=${cpu_type}/t-avr + ;; +bfin*-elf*) + ;; +bfin*-uclinux*) + ;; +bfin*-linux-uclibc*) + # No need to build crtbeginT.o on uClibc systems. Should probably + # be moved to the OS specific section above. + extra_parts="crtbegin.o crtbeginS.o crtend.o crtendS.o" + ;; +bfin*-*) + ;; +crisv32-*-elf | crisv32-*-none | cris-*-elf | cris-*-none) + extra_parts="crtbegin.o crtend.o" + ;; +cris-*-linux* | crisv32-*-linux*) + ;; +crx-*-elf) + ;; +fido-*-elf) + ;; +fr30-*-elf) + ;; +frv-*-elf) + ;; +frv-*-*linux*) + ;; +h8300-*-rtems*) + ;; +h8300-*-elf*) + ;; +h8300-*-*) + ;; +hppa*64*-*-linux*) + ;; +hppa*-*-linux*) + ;; +hppa[12]*-*-hpux10*) + ;; +hppa*64*-*-hpux11*) + ;; +hppa[12]*-*-hpux11*) + ;; +i[34567]86-*-darwin*) + ;; +x86_64-*-darwin*) + tmake_file="t-darwin ${cpu_type}/t-darwin64 t-slibgcc-darwin" + ;; +i[34567]86-*-elf*) + ;; +x86_64-*-elf*) + ;; +i[34567]86-*-aout*) + ;; +i[34567]86-*-freebsd*) + ;; +x86_64-*-freebsd*) + ;; +i[34567]86-*-netbsdelf*) + ;; +i[34567]86-*-netbsd*) + ;; +x86_64-*-netbsd*) + ;; +i[34567]86-*-openbsd2.*|i[34567]86-*openbsd3.[0123]) + ;; +i[34567]86-*-openbsd*) + ;; +i[34567]86-*-coff*) + ;; +i[34567]86-*-linux* | i[34567]86-*-kfreebsd*-gnu | i[34567]86-*-knetbsd*-gnu | i[34567]86-*-gnu*) + extra_parts="$extra_parts crtprec32.o crtprec64.o crtprec80.o crtfastmath.o" + tmake_file="${tmake_file} i386/t-crtpc i386/t-crtfm" + ;; +x86_64-*-linux* | x86_64-*-kfreebsd*-gnu | x86_64-*-knetbsd*-gnu) + extra_parts="$extra_parts crtprec32.o crtprec64.o crtprec80.o crtfastmath.o" + tmake_file="${tmake_file} i386/t-crtpc i386/t-crtfm" + ;; +i[34567]86-pc-msdosdjgpp*) + ;; +i[34567]86-*-lynxos*) + ;; +i[3456x]86-*-netware*) + case /${with_ld} in + */nwld) + tmake_file="${tmake_file} i386/t-nwld" + ;; + esac + ;; +i[34567]86-*-nto-qnx*) + ;; +i[34567]86-*-rtems*) + ;; +i[34567]86-*-solaris2*) + tmake_file="${tmake_file} i386/t-sol2" + case ${host} in + *-*-solaris2.1[0-9]*) + # Solaris 2.10 provides crt1.o, crti.o, crtn.o, and gcrt1.o as + # part of the base system. + extra_parts="gmon.o crtbegin.o crtend.o" + ;; + *) + extra_parts="crt1.o crti.o crtn.o gcrt1.o gmon.o crtbegin.o crtend.o" + ;; + esac + ;; +i[4567]86-wrs-vxworks|i[4567]86-wrs-vxworksae) + ;; +i[34567]86-*-pe) + ;; +i[34567]86-*-cygwin* | i[34567]86-*-mingw*) + extra_parts="crtbegin.o crtend.o crtfastmath.o" + tmake_file="i386/t-cygming i386/t-crtfm" + ;; +x86_64-*-mingw*) + ;; +i[34567]86-*-interix3*) + ;; +ia64*-*-elf*) + extra_parts="crtbegin.o crtend.o crtbeginS.o crtendS.o crtfastmath.o" + tmake_file="ia64/t-ia64" + ;; +ia64*-*-freebsd*) + ;; +ia64*-*-linux*) + extra_parts="crtbegin.o crtend.o crtbeginS.o crtendS.o crtfastmath.o" + tmake_file="ia64/t-ia64 t-softfp ia64/t-fprules-softfp ia64/t-softfp-compat" + ;; +ia64*-*-hpux*) + ;; +iq2000*-*-elf*) + ;; +m32r-*-elf*|m32r-*-rtems*) + ;; +m32rle-*-elf*) + ;; +m32r-*-linux*) + ;; +m32rle-*-linux*) + ;; +m68hc11-*-*|m6811-*-*) + ;; +m68hc12-*-*|m6812-*-*) + ;; +m68k-*-aout*) + ;; +m68k-*-coff*) + ;; +m68k-*-elf*) + ;; +m68k*-*-netbsdelf*) + ;; +m68k*-*-openbsd*) + ;; +m68k-*-uclinux*) # Motorola m68k/ColdFire running uClinux with uClibc + ;; +m68k-*-linux*) # Motorola m68k's running GNU/Linux + # with ELF format using glibc 2 + # aka the GNU/Linux C library 6. + ;; +m68k-*-rtems*) + ;; +mcore-*-elf) + ;; +mcore-*-pe*) + ;; +mips-sgi-irix[56]*) + ;; +mips*-*-netbsd*) # NetBSD/mips, either endian. + ;; +mips64*-*-linux*) + ;; +mips*-*-linux*) # Linux MIPS, either endian. + ;; +mips*-*-openbsd*) + ;; +mipsisa32-*-elf* | mipsisa32el-*-elf*) + ;; +mipsisa32r2-*-elf* | mipsisa32r2el-*-elf*) + ;; +mipsisa64-*-elf* | mipsisa64el-*-elf*) + ;; +mipsisa64r2-*-elf* | mipsisa64r2el-*-elf*) + ;; +mipsisa64sr71k-*-elf*) + ;; +mipsisa64sb1-*-elf* | mipsisa64sb1el-*-elf*) + ;; +mips-*-elf* | mipsel-*-elf*) + ;; +mips64-*-elf* | mips64el-*-elf*) + ;; +mips64vr-*-elf* | mips64vrel-*-elf*) + ;; +mips64orion-*-elf* | mips64orionel-*-elf*) + ;; +mips*-*-rtems*) + ;; +mips-wrs-vxworks) + ;; +mipstx39-*-elf* | mipstx39el-*-elf*) + ;; +mmix-knuth-mmixware) + ;; +mn10300-*-*) + ;; +pdp11-*-bsd) + ;; +pdp11-*-*) + ;; +picochip-*-*) + ;; +powerpc64-*-linux*) + tmake_file="${tmake_file} rs6000/t-ppccomm rs6000/t-ldbl128 t-softfp" + ;; +powerpc64-*-gnu*) + tmake_file="${tmake_file} rs6000/t-ldbl128 t-softfp" + ;; +powerpc-*-darwin*) + ;; +powerpc64-*-darwin*) + ;; +powerpc*-*-freebsd*) + ;; +powerpc-*-netbsd*) + ;; +powerpc-*-eabispe*) + ;; +powerpc-*-eabisimaltivec*) + ;; +powerpc-*-eabisim*) + ;; +powerpc-*-elf*) + ;; +powerpc-*-eabialtivec*) + ;; +powerpc-*-eabi*) + ;; +powerpc-*-rtems*) + ;; +powerpc-*-linux*altivec*) + tmake_file="${tmake_file} rs6000/t-ppccomm rs6000/t-ldbl128" + ;; +powerpc-*-linux*spe*) + tmake_file="${tmake_file} rs6000/t-ppccomm rs6000/t-ldbl128 t-softfp" + ;; +powerpc-*-linux*) + tmake_file="${tmake_file} rs6000/t-ppccomm rs6000/t-ldbl128 t-softfp" + ;; +powerpc-*-gnu-gnualtivec*) + tmake_file="${tmake_file} rs6000/t-ldbl128" + ;; +powerpc-*-gnu*) + tmake_file="${tmake_file} rs6000/t-ldbl128" + ;; +powerpc-wrs-vxworks|powerpc-wrs-vxworksae) + ;; +powerpc-*-lynxos*) + ;; +powerpcle-*-elf*) + ;; +powerpcle-*-eabisim*) + ;; +powerpcle-*-eabi*) + ;; +rs6000-ibm-aix4.[12]* | powerpc-ibm-aix4.[12]*) + ;; +rs6000-ibm-aix4.[3456789]* | powerpc-ibm-aix4.[3456789]*) + ;; +rs6000-ibm-aix5.1.* | powerpc-ibm-aix5.1.*) + ;; +rs6000-ibm-aix[56789].* | powerpc-ibm-aix[56789].*) + ;; +s390-*-linux*) + ;; +s390x-*-linux*) + ;; +s390x-ibm-tpf*) + ;; +score-*-elf) + ;; +sh-*-elf* | sh[12346l]*-*-elf* | \ +sh-*-symbianelf* | sh[12346l]*-*-symbianelf* | \ + sh-*-linux* | sh[2346lbe]*-*-linux* | \ + sh-*-netbsdelf* | shl*-*-netbsdelf* | sh5-*-netbsd* | sh5l*-*-netbsd* | \ + sh64-*-netbsd* | sh64l*-*-netbsd*) + case ${host} in + sh*-*-linux*) + tmake_file="${tmake_file} sh/t-linux" + ;; + esac + ;; +sh-*-rtems*) + ;; +sh-wrs-vxworks) + ;; +sh-*-*) + ;; +sparc-*-netbsdelf*) + ;; +sparc64-*-openbsd*) + ;; +sparc-*-elf*) + ;; +sparc-*-linux*) # SPARC's running GNU/Linux, libc6 + extra_parts="$extra_parts crtfastmath.o" + tmake_file="${tmake_file} sparc/t-crtfm" + ;; +sparc-*-rtems*) + ;; +sparc64-*-solaris2* | sparcv9-*-solaris2*) + ;; +sparc-*-solaris2*) + ;; +sparc64-*-elf*) + ;; +sparc-wrs-vxworks) + ;; +sparc64-*-freebsd*|ultrasparc-*-freebsd*) + ;; +sparc64-*-linux*) # 64-bit SPARC's running GNU/Linux + extra_parts="$extra_parts crtfastmath.o" + tmake_file="${tmake_file} sparc/t-crtfm" + ;; +sparc64-*-netbsd*) + ;; +spu-*-elf*) + ;; +v850e1-*-*) + ;; +v850e-*-*) + ;; +v850-*-*) + ;; +vax-*-netbsdelf*) + ;; +vax-*-netbsd*) + ;; +vax-*-openbsd*) + ;; +xstormy16-*-elf) + ;; +xtensa*-*-elf*) + ;; +xtensa*-*-linux*) + ;; +am33_2.0-*-linux*) + extra_parts="crtbegin.o crtend.o crtbeginS.o crtendS.o" + ;; +m32c-*-elf*|m32c-*-rtems*) + ;; +*) + echo "*** Configuration ${host} not supported" 1>&2 + exit 1 + ;; +esac + +case ${host} in +i[34567]86-*-linux* | x86_64-*-linux* | \ + i[34567]86-*-kfreebsd*-gnu | i[34567]86-*-knetbsd*-gnu | \ + i[34567]86-*-gnu*) + tmake_file="${tmake_file} t-tls" + ;; +esac + +case ${host} in +i[34567]86-*-darwin* | x86_64-*-darwin* | \ + i[34567]86-*-kfreebsd*-gnu | x86_64-*-kfreebsd*-gnu | \ + i[34567]86-*-linux* | x86_64-*-linux*) + if test "${host_address}" = 32; then + tmake_file="${tmake_file} t-softfp i386/${host_address}/t-fprules-softfp" + fi + ;; +esac + +case ${host} in +i[34567]86-*-linux* | x86_64-*-linux*) + # Provide backward binary compatibility for 64bit Linux/x86. + if test "${host_address}" = 64; then + tmake_file="${tmake_file} i386/${host_address}/t-softfp-compat" + fi + ;; +esac diff --git a/gcc-4.4.3/libgcc/config/alpha/t-crtfm b/gcc-4.4.3/libgcc/config/alpha/t-crtfm new file mode 100644 index 000000000..48c21d88f --- /dev/null +++ b/gcc-4.4.3/libgcc/config/alpha/t-crtfm @@ -0,0 +1,6 @@ +# FIXME drow/20061228 - I have preserved this -frandom-seed option +# while migrating this rule from the GCC directory, but I do not +# know why it is necessary if no other crt file uses it. +crtfastmath.o: $(gcc_srcdir)/config/alpha/crtfastmath.c + $(gcc_compile) -frandom-seed=gcc-crtfastmath -c \ + $(gcc_srcdir)/config/alpha/crtfastmath.c diff --git a/gcc-4.4.3/libgcc/config/avr/t-avr b/gcc-4.4.3/libgcc/config/avr/t-avr new file mode 100644 index 000000000..ee5707241 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/avr/t-avr @@ -0,0 +1,19 @@ +# Extra 16-bit integer functions. +intfuncs16 = _absvXX2 _addvXX3 _subvXX3 _mulvXX3 _negvXX2 _ffsXX2 _clzXX2 \ + _ctzXX2 _popcountXX2 _parityXX2 +hiintfuncs16 = $(subst XX,hi,$(intfuncs16)) +siintfuncs16 = $(subst XX,si,$(intfuncs16)) + +iter-items := $(hiintfuncs16) +iter-labels := $(siintfuncs16) +iter-sizes := $(patsubst %,2,$(siintfuncs16)) $(patsubst %,2,$(hiintfuncs16)) + + +include $(srcdir)/empty.mk $(patsubst %,$(srcdir)/siditi-object.mk,$(iter-items)) +libgcc-objects += $(patsubst %,%$(objext),$(hiintfuncs16)) + +ifeq ($(enable_shared),yes) +libgcc-s-objects += $(patsubst %,%_s$(objext),$(hiintfuncs16)) +endif + + diff --git a/gcc-4.4.3/libgcc/config/i386/32/sfp-machine.h b/gcc-4.4.3/libgcc/config/i386/32/sfp-machine.h new file mode 100644 index 000000000..746ae7c12 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/32/sfp-machine.h @@ -0,0 +1,209 @@ +#define _FP_W_TYPE_SIZE 32 +#define _FP_W_TYPE unsigned int +#define _FP_WS_TYPE signed int +#define _FP_I_TYPE int + +/* The type of the result of a floating point comparison. This must + match `__libgcc_cmp_return__' in GCC for the target. */ +typedef int __gcc_CMPtype __attribute__ ((mode (__libgcc_cmp_return__))); +#define CMPtype __gcc_CMPtype + +#define __FP_FRAC_ADD_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0) \ + __asm__ ("add{l} {%11,%3|%3,%11}\n\t" \ + "adc{l} {%9,%2|%2,%9}\n\t" \ + "adc{l} {%7,%1|%1,%7}\n\t" \ + "adc{l} {%5,%0|%0,%5}" \ + : "=r" ((USItype) (r3)), \ + "=&r" ((USItype) (r2)), \ + "=&r" ((USItype) (r1)), \ + "=&r" ((USItype) (r0)) \ + : "%0" ((USItype) (x3)), \ + "g" ((USItype) (y3)), \ + "%1" ((USItype) (x2)), \ + "g" ((USItype) (y2)), \ + "%2" ((USItype) (x1)), \ + "g" ((USItype) (y1)), \ + "%3" ((USItype) (x0)), \ + "g" ((USItype) (y0))) +#define __FP_FRAC_ADD_3(r2,r1,r0,x2,x1,x0,y2,y1,y0) \ + __asm__ ("add{l} {%8,%2|%2,%8}\n\t" \ + "adc{l} {%6,%1|%1,%6}\n\t" \ + "adc{l} {%4,%0|%0,%4}" \ + : "=r" ((USItype) (r2)), \ + "=&r" ((USItype) (r1)), \ + "=&r" ((USItype) (r0)) \ + : "%0" ((USItype) (x2)), \ + "g" ((USItype) (y2)), \ + "%1" ((USItype) (x1)), \ + "g" ((USItype) (y1)), \ + "%2" ((USItype) (x0)), \ + "g" ((USItype) (y0))) + +/* FIXME: Change last operand constraint + from "im" to "g" when reload works properly. */ +#define __FP_FRAC_SUB_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0) \ + __asm__ ("sub{l} {%11,%3|%3,%11}\n\t" \ + "sbb{l} {%9,%2|%2,%9}\n\t" \ + "sbb{l} {%7,%1|%1,%7}\n\t" \ + "sbb{l} {%5,%0|%0,%5}" \ + : "=r" ((USItype) (r3)), \ + "=&r" ((USItype) (r2)), \ + "=&r" ((USItype) (r1)), \ + "=&r" ((USItype) (r0)) \ + : "0" ((USItype) (x3)), \ + "g" ((USItype) (y3)), \ + "1" ((USItype) (x2)), \ + "g" ((USItype) (y2)), \ + "2" ((USItype) (x1)), \ + "g" ((USItype) (y1)), \ + "3" ((USItype) (x0)), \ + "im" ((USItype) (y0))) +#define __FP_FRAC_SUB_3(r2,r1,r0,x2,x1,x0,y2,y1,y0) \ + __asm__ ("sub{l} {%8,%2|%2,%8}\n\t" \ + "sbb{l} {%6,%1|%1,%6}\n\t" \ + "sbb{l} {%4,%0|%0,%4}" \ + : "=r" ((USItype) (r2)), \ + "=&r" ((USItype) (r1)), \ + "=&r" ((USItype) (r0)) \ + : "0" ((USItype) (x2)), \ + "g" ((USItype) (y2)), \ + "1" ((USItype) (x1)), \ + "g" ((USItype) (y1)), \ + "2" ((USItype) (x0)), \ + "g" ((USItype) (y0))) + + +#define _FP_MUL_MEAT_Q(R,X,Y) \ + _FP_MUL_MEAT_4_wide(_FP_WFRACBITS_Q,R,X,Y,umul_ppmm) + +#define _FP_DIV_MEAT_Q(R,X,Y) _FP_DIV_MEAT_4_udiv(Q,R,X,Y) + +#define _FP_NANFRAC_S _FP_QNANBIT_S +#define _FP_NANFRAC_D _FP_QNANBIT_D, 0 +/* Even if XFmode is 12byte, we have to pad it to + 16byte since soft-fp emulation is done in 16byte. */ +#define _FP_NANFRAC_E _FP_QNANBIT_E, 0, 0, 0 +#define _FP_NANFRAC_Q _FP_QNANBIT_Q, 0, 0, 0 +#define _FP_NANSIGN_S 1 +#define _FP_NANSIGN_D 1 +#define _FP_NANSIGN_E 1 +#define _FP_NANSIGN_Q 1 + +#define _FP_KEEPNANFRACP 1 + +/* Here is something Intel misdesigned: the specs don't define + the case where we have two NaNs with same mantissas, but + different sign. Different operations pick up different NaNs. */ +#define _FP_CHOOSENAN(fs, wc, R, X, Y, OP) \ + do { \ + if (_FP_FRAC_GT_##wc(X, Y) \ + || (_FP_FRAC_EQ_##wc(X,Y) && (OP == '+' || OP == '*'))) \ + { \ + R##_s = X##_s; \ + _FP_FRAC_COPY_##wc(R,X); \ + } \ + else \ + { \ + R##_s = Y##_s; \ + _FP_FRAC_COPY_##wc(R,Y); \ + } \ + R##_c = FP_CLS_NAN; \ + } while (0) + +#define FP_EX_INVALID 0x01 +#define FP_EX_DENORM 0x02 +#define FP_EX_DIVZERO 0x04 +#define FP_EX_OVERFLOW 0x08 +#define FP_EX_UNDERFLOW 0x10 +#define FP_EX_INEXACT 0x20 + +struct fenv +{ + unsigned short int __control_word; + unsigned short int __unused1; + unsigned short int __status_word; + unsigned short int __unused2; + unsigned short int __tags; + unsigned short int __unused3; + unsigned int __eip; + unsigned short int __cs_selector; + unsigned int __opcode:11; + unsigned int __unused4:5; + unsigned int __data_offset; + unsigned short int __data_selector; + unsigned short int __unused5; +}; + +#define FP_HANDLE_EXCEPTIONS \ + do { \ + if (_fex & FP_EX_INVALID) \ + { \ + float f = 0.0; \ + __asm__ __volatile__ ("fdiv %0" : "+t" (f)); \ + __asm__ __volatile__ ("fwait"); \ + } \ + if (_fex & FP_EX_DIVZERO) \ + { \ + float f = 1.0, g = 0.0; \ + __asm__ __volatile__ ("fdivp" : "=t" (f) \ + : "0" (f), "u" (g) \ + : "st(1)"); \ + __asm__ __volatile__ ("fwait"); \ + } \ + if (_fex & FP_EX_OVERFLOW) \ + { \ + struct fenv temp; \ + __asm__ __volatile__ ("fnstenv %0" : "=m" (temp)); \ + temp.__status_word |= FP_EX_OVERFLOW; \ + __asm__ __volatile__ ("fldenv %0" : : "m" (temp)); \ + __asm__ __volatile__ ("fwait"); \ + } \ + if (_fex & FP_EX_UNDERFLOW) \ + { \ + struct fenv temp; \ + __asm__ __volatile__ ("fnstenv %0" : "=m" (temp)); \ + temp.__status_word |= FP_EX_UNDERFLOW; \ + __asm__ __volatile__ ("fldenv %0" : : "m" (temp)); \ + __asm__ __volatile__ ("fwait"); \ + } \ + if (_fex & FP_EX_INEXACT) \ + { \ + struct fenv temp; \ + __asm__ __volatile__ ("fnstenv %0" : "=m" (temp)); \ + temp.__status_word |= FP_EX_INEXACT; \ + __asm__ __volatile__ ("fldenv %0" : : "m" (temp)); \ + __asm__ __volatile__ ("fwait"); \ + } \ + } while (0) + +#define FP_RND_NEAREST 0 +#define FP_RND_ZERO 0xc00 +#define FP_RND_PINF 0x800 +#define FP_RND_MINF 0x400 + +#define _FP_DECL_EX \ + unsigned short _fcw __attribute__ ((unused)) = FP_RND_NEAREST + +#define FP_INIT_ROUNDMODE \ + do { \ + __asm__ ("fnstcw %0" : "=m" (_fcw)); \ + } while (0) + +#define FP_ROUNDMODE (_fcw & 0xc00) + +#define __LITTLE_ENDIAN 1234 +#define __BIG_ENDIAN 4321 + +#define __BYTE_ORDER __LITTLE_ENDIAN + +/* Define ALIASNAME as a strong alias for NAME. */ +#if defined __MACH__ +/* Mach-O doesn't support aliasing. If these functions ever return + anything but CMPtype we need to revisit this... */ +#define strong_alias(name, aliasname) \ + CMPtype aliasname (TFtype a, TFtype b) { return name(a, b); } +#else +# define strong_alias(name, aliasname) _strong_alias(name, aliasname) +# define _strong_alias(name, aliasname) \ + extern __typeof (name) aliasname __attribute__ ((alias (#name))); +#endif diff --git a/gcc-4.4.3/libgcc/config/i386/32/t-fprules-softfp b/gcc-4.4.3/libgcc/config/i386/32/t-fprules-softfp new file mode 100644 index 000000000..8e7f3233b --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/32/t-fprules-softfp @@ -0,0 +1,8 @@ +# Filter out TImode functions +tifunctions = fixtfti.c fixunstfti.c floattitf.c floatuntitf.c +tifunctions := $(addprefix $(gcc_srcdir)/config/soft-fp/, $(tifunctions)) + +LIB2ADD := $(filter-out $(tifunctions), $(LIB2ADD)) + +# Provide fallbacks for __builtin_copysignq and __builtin_fabsq. +LIB2ADD += $(srcdir)/config/i386/32/tf-signs.c diff --git a/gcc-4.4.3/libgcc/config/i386/32/tf-signs.c b/gcc-4.4.3/libgcc/config/i386/32/tf-signs.c new file mode 100644 index 000000000..2bc1a855c --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/32/tf-signs.c @@ -0,0 +1,62 @@ +/* Copyright (C) 2008, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +union _FP_UNION_Q +{ + __float128 flt; + struct + { + unsigned long frac0 : 32; + unsigned long frac1 : 32; + unsigned long frac2 : 32; + unsigned long frac3 : 16; + unsigned exp : 15; + unsigned sign : 1; + } bits __attribute__((packed)); +}; + +__float128 __copysigntf3 (__float128, __float128); +__float128 __fabstf2 (__float128); + +__float128 +__copysigntf3 (__float128 a, __float128 b) +{ + union _FP_UNION_Q A, B; + + A.flt = a; + B.flt = b; + A.bits.sign = B.bits.sign; + + return A.flt; +} + +__float128 +__fabstf2 (__float128 a) +{ + union _FP_UNION_Q A; + + A.flt = a; + A.bits.sign = 0; + + return A.flt; +} diff --git a/gcc-4.4.3/libgcc/config/i386/64/_divtc3.c b/gcc-4.4.3/libgcc/config/i386/64/_divtc3.c new file mode 100644 index 000000000..57ee350b7 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/64/_divtc3.c @@ -0,0 +1,14 @@ +#ifdef SHARED +#define __divtc3 __divtc3_shared +#endif + +#define L_divtc3 +#include "libgcc2.c" + +#ifdef SHARED +#undef __divtc3 +extern __typeof__ (__divtc3_shared) __divtc3_compat __attribute__((alias ("__divtc3_shared"))); + +asm (".symver __divtc3_compat,__divtc3@GCC_4.0.0"); +asm (".symver __divtc3_shared,__divtc3@@GCC_4.3.0"); +#endif diff --git a/gcc-4.4.3/libgcc/config/i386/64/_multc3.c b/gcc-4.4.3/libgcc/config/i386/64/_multc3.c new file mode 100644 index 000000000..49141a938 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/64/_multc3.c @@ -0,0 +1,14 @@ +#ifdef SHARED +#define __multc3 __multc3_shared +#endif + +#define L_multc3 +#include "libgcc2.c" + +#ifdef SHARED +#undef __multc3 +extern __typeof__ (__multc3_shared) __multc3_compat __attribute__((alias ("__multc3_shared"))); + +asm (".symver __multc3_compat,__multc3@GCC_4.0.0"); +asm (".symver __multc3_shared,__multc3@@GCC_4.3.0"); +#endif diff --git a/gcc-4.4.3/libgcc/config/i386/64/_powitf2.c b/gcc-4.4.3/libgcc/config/i386/64/_powitf2.c new file mode 100644 index 000000000..3bc3c904d --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/64/_powitf2.c @@ -0,0 +1,14 @@ +#ifdef SHARED +#define __powitf2 __powitf2_shared +#endif + +#define L_powitf2 +#include "libgcc2.c" + +#ifdef SHARED +#undef __powitf2 +extern __typeof__ (__powitf2_shared) __powitf2_compat __attribute__((alias ("__powitf2_shared"))); + +asm (".symver __powitf2_compat,__powitf2@GCC_4.0.0"); +asm (".symver __powitf2_shared,__powitf2@@GCC_4.3.0"); +#endif diff --git a/gcc-4.4.3/libgcc/config/i386/64/eqtf2.c b/gcc-4.4.3/libgcc/config/i386/64/eqtf2.c new file mode 100644 index 000000000..d9baba689 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/64/eqtf2.c @@ -0,0 +1,13 @@ +#ifdef SHARED +#define __netf2 __netf2_shared +#endif + +#include "config/soft-fp/eqtf2.c" + +#ifdef SHARED +#undef __netf2 +strong_alias (__netf2_shared, __netf2_compat); + +asm (".symver __netf2_compat,__netf2@GCC_3.0"); +asm (".symver __netf2_shared,__netf2@@GCC_4.3.0"); +#endif diff --git a/gcc-4.4.3/libgcc/config/i386/64/getf2.c b/gcc-4.4.3/libgcc/config/i386/64/getf2.c new file mode 100644 index 000000000..30885cc0c --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/64/getf2.c @@ -0,0 +1,13 @@ +#ifdef SHARED +#define __gttf2 __gttf2_shared +#endif + +#include "config/soft-fp/getf2.c" + +#ifdef SHARED +#undef __gttf2 +strong_alias (__gttf2_shared, __gttf2_compat); + +asm (".symver __gttf2_compat,__gttf2@GCC_3.0"); +asm (".symver __gttf2_shared,__gttf2@@GCC_4.3.0"); +#endif diff --git a/gcc-4.4.3/libgcc/config/i386/64/letf2.c b/gcc-4.4.3/libgcc/config/i386/64/letf2.c new file mode 100644 index 000000000..231f981c8 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/64/letf2.c @@ -0,0 +1,13 @@ +#ifdef SHARED +#define __lttf2 __lttf2_shared +#endif + +#include "config/soft-fp/letf2.c" + +#ifdef SHARED +#undef __lttf2 +strong_alias (__lttf2_shared, __lttf2_compat); + +asm (".symver __lttf2_compat,__lttf2@GCC_3.0"); +asm (".symver __lttf2_shared,__lttf2@@GCC_4.3.0"); +#endif diff --git a/gcc-4.4.3/libgcc/config/i386/64/sfp-machine.h b/gcc-4.4.3/libgcc/config/i386/64/sfp-machine.h new file mode 100644 index 000000000..190e3cb0e --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/64/sfp-machine.h @@ -0,0 +1,143 @@ +#define _FP_W_TYPE_SIZE 64 +#define _FP_W_TYPE unsigned long +#define _FP_WS_TYPE signed long +#define _FP_I_TYPE long + +typedef int TItype __attribute__ ((mode (TI))); +typedef unsigned int UTItype __attribute__ ((mode (TI))); + +#define TI_BITS (__CHAR_BIT__ * (int)sizeof(TItype)) + +/* The type of the result of a floating point comparison. This must + match `__libgcc_cmp_return__' in GCC for the target. */ +typedef int __gcc_CMPtype __attribute__ ((mode (__libgcc_cmp_return__))); +#define CMPtype __gcc_CMPtype + +#define _FP_MUL_MEAT_Q(R,X,Y) \ + _FP_MUL_MEAT_2_wide(_FP_WFRACBITS_Q,R,X,Y,umul_ppmm) + +#define _FP_DIV_MEAT_Q(R,X,Y) _FP_DIV_MEAT_2_udiv(Q,R,X,Y) + +#define _FP_NANFRAC_S _FP_QNANBIT_S +#define _FP_NANFRAC_D _FP_QNANBIT_D +#define _FP_NANFRAC_E _FP_QNANBIT_E, 0 +#define _FP_NANFRAC_Q _FP_QNANBIT_Q, 0 +#define _FP_NANSIGN_S 1 +#define _FP_NANSIGN_D 1 +#define _FP_NANSIGN_E 1 +#define _FP_NANSIGN_Q 1 + +#define _FP_KEEPNANFRACP 1 + +/* Here is something Intel misdesigned: the specs don't define + the case where we have two NaNs with same mantissas, but + different sign. Different operations pick up different NaNs. */ +#define _FP_CHOOSENAN(fs, wc, R, X, Y, OP) \ + do { \ + if (_FP_FRAC_GT_##wc(X, Y) \ + || (_FP_FRAC_EQ_##wc(X,Y) && (OP == '+' || OP == '*'))) \ + { \ + R##_s = X##_s; \ + _FP_FRAC_COPY_##wc(R,X); \ + } \ + else \ + { \ + R##_s = Y##_s; \ + _FP_FRAC_COPY_##wc(R,Y); \ + } \ + R##_c = FP_CLS_NAN; \ + } while (0) + +#define FP_EX_INVALID 0x01 +#define FP_EX_DENORM 0x02 +#define FP_EX_DIVZERO 0x04 +#define FP_EX_OVERFLOW 0x08 +#define FP_EX_UNDERFLOW 0x10 +#define FP_EX_INEXACT 0x20 + +struct fenv +{ + unsigned short int __control_word; + unsigned short int __unused1; + unsigned short int __status_word; + unsigned short int __unused2; + unsigned short int __tags; + unsigned short int __unused3; + unsigned int __eip; + unsigned short int __cs_selector; + unsigned int __opcode:11; + unsigned int __unused4:5; + unsigned int __data_offset; + unsigned short int __data_selector; + unsigned short int __unused5; +}; + +#define FP_HANDLE_EXCEPTIONS \ + do { \ + if (_fex & FP_EX_INVALID) \ + { \ + float f = 0.0; \ + __asm__ __volatile__ ("divss %0, %0 " : : "x" (f)); \ + } \ + if (_fex & FP_EX_DIVZERO) \ + { \ + float f = 1.0, g = 0.0; \ + __asm__ __volatile__ ("divss %1, %0" : : "x" (f), "x" (g)); \ + } \ + if (_fex & FP_EX_OVERFLOW) \ + { \ + struct fenv temp; \ + __asm__ __volatile__ ("fnstenv %0" : "=m" (temp)); \ + temp.__status_word |= FP_EX_OVERFLOW; \ + __asm__ __volatile__ ("fldenv %0" : : "m" (temp)); \ + __asm__ __volatile__ ("fwait"); \ + } \ + if (_fex & FP_EX_UNDERFLOW) \ + { \ + struct fenv temp; \ + __asm__ __volatile__ ("fnstenv %0" : "=m" (temp)); \ + temp.__status_word |= FP_EX_UNDERFLOW; \ + __asm__ __volatile__ ("fldenv %0" : : "m" (temp)); \ + __asm__ __volatile__ ("fwait"); \ + } \ + if (_fex & FP_EX_INEXACT) \ + { \ + struct fenv temp; \ + __asm__ __volatile__ ("fnstenv %0" : "=m" (temp)); \ + temp.__status_word |= FP_EX_INEXACT; \ + __asm__ __volatile__ ("fldenv %0" : : "m" (temp)); \ + __asm__ __volatile__ ("fwait"); \ + } \ + } while (0) + +#define FP_RND_NEAREST 0 +#define FP_RND_ZERO 0xc00 +#define FP_RND_PINF 0x800 +#define FP_RND_MINF 0x400 + +#define _FP_DECL_EX \ + unsigned short _fcw __attribute__ ((unused)) = FP_RND_NEAREST + +#define FP_INIT_ROUNDMODE \ + do { \ + __asm__ ("fnstcw %0" : "=m" (_fcw)); \ + } while (0) + +#define FP_ROUNDMODE (_fcw & 0xc00) + +#define __LITTLE_ENDIAN 1234 +#define __BIG_ENDIAN 4321 + +#define __BYTE_ORDER __LITTLE_ENDIAN + +/* Define ALIASNAME as a strong alias for NAME. */ +#if defined __MACH__ +/* Mach-O doesn't support aliasing. If these functions ever return + anything but CMPtype we need to revisit this... */ +#define strong_alias(name, aliasname) \ + CMPtype aliasname (TFtype a, TFtype b) { return name(a, b); } +#else +# define strong_alias(name, aliasname) _strong_alias(name, aliasname) +# define _strong_alias(name, aliasname) \ + extern __typeof (name) aliasname __attribute__ ((alias (#name))); +#endif diff --git a/gcc-4.4.3/libgcc/config/i386/64/t-softfp-compat b/gcc-4.4.3/libgcc/config/i386/64/t-softfp-compat new file mode 100644 index 000000000..afaa526ae --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/64/t-softfp-compat @@ -0,0 +1,15 @@ +# When TFmode was first added to x86-64 in gcc 4.3.0, some TFmode +# support functions got improper versions by accident. Here we +# correct the version and provide backward binary compatibility. + +# Filter out the following TFmode functions. +tf-compats = getf2.c letf2.c eqtf2.c +tf-functions := $(addprefix $(gcc_srcdir)/config/soft-fp/, $(tf-compats)) +LIB2ADD := $(filter-out $(tf-functions), $(LIB2ADD)) +LIB2ADD += $(addprefix $(srcdir)/config/i386/64/, $(tf-compats)) + +# Replace _divtc3, _multc3 and _powitf2. +libgcc2-tf-functions = _divtc3 _multc3 _powitf2 +LIB2FUNCS_EXCLUDE += $(libgcc2-tf-functions) +libgcc2-tf-compats = $(addsuffix .c, $(libgcc2-tf-functions)) +LIB2ADD += $(addprefix $(srcdir)/config/i386/64/, $(libgcc2-tf-compats)) diff --git a/gcc-4.4.3/libgcc/config/i386/t-crtfm b/gcc-4.4.3/libgcc/config/i386/t-crtfm new file mode 100644 index 000000000..6e89296b2 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/t-crtfm @@ -0,0 +1,5 @@ +# This is an endfile, Use -minline-all-stringops to ensure +# that __builtin_memset doesn't refer to the lib function memset(). +crtfastmath.o: $(gcc_srcdir)/config/i386/crtfastmath.c + $(gcc_compile) -msse -minline-all-stringops -c \ + $(gcc_srcdir)/config/i386/crtfastmath.c diff --git a/gcc-4.4.3/libgcc/config/i386/t-crtpc b/gcc-4.4.3/libgcc/config/i386/t-crtpc new file mode 100644 index 000000000..c231ce195 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/t-crtpc @@ -0,0 +1,8 @@ +crtprec32.o: $(gcc_srcdir)/config/i386/crtprec.c + $(gcc_compile) -D__PREC=32 -c $< + +crtprec64.o: $(gcc_srcdir)/config/i386/crtprec.c + $(gcc_compile) -D__PREC=64 -c $< + +crtprec80.o: $(gcc_srcdir)/config/i386/crtprec.c + $(gcc_compile) -D__PREC=80 -c $< diff --git a/gcc-4.4.3/libgcc/config/i386/t-cygming b/gcc-4.4.3/libgcc/config/i386/t-cygming new file mode 100644 index 000000000..048cadbd5 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/t-cygming @@ -0,0 +1,11 @@ +CUSTOM_CRTSTUFF = yes + +crtbegin.o: $(gcc_srcdir)/config/i386/cygming-crtbegin.c + $(crt_compile) -fno-omit-frame-pointer -c \ + $(gcc_srcdir)/config/i386/cygming-crtbegin.c + +# We intentionally use a implementation-reserved init priority of 0, +# so allow the warning. +crtend.o: $(gcc_srcdir)/config/i386/cygming-crtend.c + $(crt_compile) -fno-omit-frame-pointer -Wno-error -c \ + $(gcc_srcdir)/config/i386/cygming-crtend.c diff --git a/gcc-4.4.3/libgcc/config/i386/t-darwin b/gcc-4.4.3/libgcc/config/i386/t-darwin new file mode 100644 index 000000000..4578f74c3 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/t-darwin @@ -0,0 +1 @@ +SHLIB_VERPFX = $(gcc_srcdir)/config/i386/darwin-libgcc diff --git a/gcc-4.4.3/libgcc/config/i386/t-darwin64 b/gcc-4.4.3/libgcc/config/i386/t-darwin64 new file mode 100644 index 000000000..4578f74c3 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/t-darwin64 @@ -0,0 +1 @@ +SHLIB_VERPFX = $(gcc_srcdir)/config/i386/darwin-libgcc diff --git a/gcc-4.4.3/libgcc/config/i386/t-nwld b/gcc-4.4.3/libgcc/config/i386/t-nwld new file mode 100644 index 000000000..408587273 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/t-nwld @@ -0,0 +1,31 @@ +# Build a shared libgcc library for NetWare. + +SHLIB_EXT = .nlm +SHLIB_NAME = @shlib_base_name@.nlm +SHLIB_SLIBDIR_QUAL = @shlib_slibdir_qual@ +SHLIB_DEF = $(gcc_srcdir)/config/i386/netware-libgcc.def +SHLIB_MAP = $(gcc_srcdir)/config/i386/netware-libgcc.exp +SHLIB_SRC = $(gcc_srcdir)/config/i386/netware-libgcc.c + +SHLIB_LINK = set -e; \ + cat $(SHLIB_DEF) >@shlib_base_name@.def; \ + echo "name $(SHLIB_NAME)" >>@shlib_base_name@.def; \ + echo "version $(version)" | sed "s!\.!,!g" >>@shlib_base_name@.def; \ + touch build; \ + echo "build $$(expr $$(>@shlib_base_name@.def; \ + echo "export @$(SHLIB_MAP)" >>@shlib_base_name@.def; \ + if mpkxdc -n -p @shlib_base_name@.xdc; \ + then echo "xdcdata @shlib_base_name@.xdc" >>@shlib_base_name@.def; \ + else echo "WARNING: $(SHLIB_NAME) built without XDC data will not work well." 1>&2; \ + fi; \ + $(CC) $(LIBGCC2_CFLAGS) -o $(SHLIB_NAME) \ + $(SHLIB_SRC) -posix -static-libgcc -lnetware \ + -Wl,--Map,--map-info,full,--strip-all,--def-file,@shlib_base_name@.def; \ + rm -f @shlib_base_name@.imp; $(LN_S) $(SHLIB_MAP) @shlib_base_name@.imp; \ + rm -f libgcc.imp; $(LN_S) @shlib_base_name@.imp libgcc.imp; \ + expr $$(build + +SHLIB_INSTALL = \ + $(SHELL) $(srcdir)/mkinstalldirs $(slibdir)$(SHLIB_SLIBDIR_QUAL); \ + $(INSTALL_DATA) $(SHLIB_NAME) $(slibdir)$(SHLIB_SLIBDIR_QUAL)/$(SHLIB_NAME); \ + $(INSTALL_DATA) @shlib_base_name@.imp $(DESTDIR)$(libsubdir)/ diff --git a/gcc-4.4.3/libgcc/config/i386/t-sol2 b/gcc-4.4.3/libgcc/config/i386/t-sol2 new file mode 100644 index 000000000..24b7c7c10 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/i386/t-sol2 @@ -0,0 +1,34 @@ +# gmon build rule: +$(T)gmon.o: $(gcc_srcdir)/config/i386/gmon-sol2.c $(GCC_PASSES) $(CONFIG_H) + $(GCC_FOR_TARGET) $(GCC_CFLAGS) $(INCLUDES) $(MULTILIB_CFLAGS) \ + -c $(gcc_srcdir)/config/i386/gmon-sol2.c -o $(T)gmon.o + +# Assemble startup files. +# Apparently Sun believes that assembler files don't need comments, because no +# single ASCII character is valid (tried them all). So we manually strip out +# the comments with sed. This bug may only be in the Early Access releases. +$(T)gcrt1.o: $(gcc_srcdir)/config/i386/sol2-gc1.asm $(GCC_PASSES) + sed -e '/^!/d' <$(gcc_srcdir)/config/i386/sol2-gc1.asm >gcrt1.s + $(GCC_FOR_TARGET) $(MULTILIB_CFLAGS) -c -o $(T)gcrt1.o gcrt1.s +$(T)crt1.o: $(gcc_srcdir)/config/i386/sol2-c1.asm $(GCC_PASSES) + sed -e '/^!/d' <$(gcc_srcdir)/config/i386/sol2-c1.asm >crt1.s + $(GCC_FOR_TARGET) $(MULTILIB_CFLAGS) -c -o $(T)crt1.o crt1.s +$(T)crti.o: $(gcc_srcdir)/config/i386/sol2-ci.asm $(GCC_PASSES) + sed -e '/^!/d' <$(gcc_srcdir)/config/i386/sol2-ci.asm >crti.s + $(GCC_FOR_TARGET) $(MULTILIB_CFLAGS) -c -o $(T)crti.o crti.s +$(T)crtn.o: $(gcc_srcdir)/config/i386/sol2-cn.asm $(GCC_PASSES) + sed -e '/^!/d' <$(gcc_srcdir)/config/i386/sol2-cn.asm >crtn.s + $(GCC_FOR_TARGET) $(MULTILIB_CFLAGS) -c -o $(T)crtn.o crtn.s + +# We need to use -fPIC when we are using gcc to compile the routines in +# crtstuff.c. This is only really needed when we are going to use gcc/g++ +# to produce a shared library, but since we don't know ahead of time when +# we will be doing that, we just always use -fPIC when compiling the +# routines in crtstuff.c. +# +# We must also enable optimization to avoid having any code appear after +# the call & alignment statement, but before we switch back to the +# .text section. + +CRTSTUFF_T_CFLAGS = -fPIC -O2 +TARGET_LIBGCC2_CFLAGS = -fPIC diff --git a/gcc-4.4.3/libgcc/config/ia64/__divxf3.asm b/gcc-4.4.3/libgcc/config/ia64/__divxf3.asm new file mode 100644 index 000000000..f741bdaf9 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/ia64/__divxf3.asm @@ -0,0 +1,11 @@ +#ifdef SHARED +#define __divtf3 __divtf3_compat +#endif + +#define L__divxf3 +#include "config/ia64/lib1funcs.asm" + +#ifdef SHARED +#undef __divtf3 +.symver __divtf3_compat, __divtf3@GCC_3.0 +#endif diff --git a/gcc-4.4.3/libgcc/config/ia64/_fixtfdi.asm b/gcc-4.4.3/libgcc/config/ia64/_fixtfdi.asm new file mode 100644 index 000000000..4d13c808c --- /dev/null +++ b/gcc-4.4.3/libgcc/config/ia64/_fixtfdi.asm @@ -0,0 +1,11 @@ +#ifdef SHARED +#define __fixtfti __fixtfti_compat +#endif + +#define L_fixtfdi +#include "config/ia64/lib1funcs.asm" + +#ifdef SHARED +#undef __fixtfti +.symver __fixtfti_compat, __fixtfti@GCC_3.0 +#endif diff --git a/gcc-4.4.3/libgcc/config/ia64/_fixunstfdi.asm b/gcc-4.4.3/libgcc/config/ia64/_fixunstfdi.asm new file mode 100644 index 000000000..b722d9e90 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/ia64/_fixunstfdi.asm @@ -0,0 +1,11 @@ +#ifdef SHARED +#define __fixunstfti __fixunstfti_compat +#endif + +#define L_fixunstfdi +#include "config/ia64/lib1funcs.asm" + +#ifdef SHARED +#undef __fixunstfti +.symver __fixunstfti_compat, __fixunstfti@GCC_3.0 +#endif diff --git a/gcc-4.4.3/libgcc/config/ia64/_floatditf.asm b/gcc-4.4.3/libgcc/config/ia64/_floatditf.asm new file mode 100644 index 000000000..21d770281 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/ia64/_floatditf.asm @@ -0,0 +1,11 @@ +#ifdef SHARED +#define __floattitf __floattitf_compat +#endif + +#define L_floatditf +#include "config/ia64/lib1funcs.asm" + +#ifdef SHARED +#undef __floattitf +.symver __floattitf_compat, __floattitf@GCC_3.0 +#endif diff --git a/gcc-4.4.3/libgcc/config/ia64/t-fprules-softfp b/gcc-4.4.3/libgcc/config/ia64/t-fprules-softfp new file mode 100644 index 000000000..90acc376e --- /dev/null +++ b/gcc-4.4.3/libgcc/config/ia64/t-fprules-softfp @@ -0,0 +1,2 @@ +# Provide fallbacks for __builtin_copysignq and __builtin_fabsq. +LIB2ADD += $(srcdir)/config/ia64/tf-signs.c diff --git a/gcc-4.4.3/libgcc/config/ia64/t-ia64 b/gcc-4.4.3/libgcc/config/ia64/t-ia64 new file mode 100644 index 000000000..d9c7566cf --- /dev/null +++ b/gcc-4.4.3/libgcc/config/ia64/t-ia64 @@ -0,0 +1,18 @@ +CUSTOM_CRTSTUFF = yes + +# Assemble startup files. +crtbegin.o: $(gcc_srcdir)/config/ia64/crtbegin.asm + $(CC) $(compile_deps) -I. -I$(gcc_objdir) -c -x assembler-with-cpp \ + -o $@ $(gcc_srcdir)/config/ia64/crtbegin.asm +crtend.o: $(gcc_srcdir)/config/ia64/crtend.asm + $(CC) $(compile_deps) -I. -I$(gcc_objdir) -c -x assembler-with-cpp \ + -o $@ $(gcc_srcdir)/config/ia64/crtend.asm +crtbeginS.o: $(gcc_srcdir)/config/ia64/crtbegin.asm + $(CC) $(compile_deps) -I. -I$(gcc_objdir) -c -x assembler-with-cpp \ + -o $@ -DSHARED $(gcc_srcdir)/config/ia64/crtbegin.asm +crtendS.o: $(gcc_srcdir)/config/ia64/crtend.asm + $(CC) $(compile_deps) -I. -I$(gcc_objdir) -c -x assembler-with-cpp \ + -o $@ -DSHARED $(gcc_srcdir)/config/ia64/crtend.asm + +crtfastmath.o: $(gcc_srcdir)/config/ia64/crtfastmath.c + $(gcc_compile) -c $(gcc_srcdir)/config/ia64/crtfastmath.c diff --git a/gcc-4.4.3/libgcc/config/ia64/t-softfp-compat b/gcc-4.4.3/libgcc/config/ia64/t-softfp-compat new file mode 100644 index 000000000..d3dad68c4 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/ia64/t-softfp-compat @@ -0,0 +1,7 @@ +# Filter out the following TImode functions and provide backward binary +# compatibility. +# Replace __dvxf3 _fixtfdi _fixunstfdi _floatditf +libgcc1-tf-functions = __divxf3 _fixtfdi _fixunstfdi _floatditf +LIB1ASMFUNCS := $(filter-out $(libgcc1-tf-functions), $(LIB1ASMFUNCS)) +libgcc1-tf-compats = $(addsuffix .asm, $(libgcc1-tf-functions)) +LIB2ADD += $(addprefix $(srcdir)/config/ia64/, $(libgcc1-tf-compats)) diff --git a/gcc-4.4.3/libgcc/config/ia64/tf-signs.c b/gcc-4.4.3/libgcc/config/ia64/tf-signs.c new file mode 100644 index 000000000..bbcae503e --- /dev/null +++ b/gcc-4.4.3/libgcc/config/ia64/tf-signs.c @@ -0,0 +1,60 @@ +/* Copyright (C) 2008, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +union _FP_UNION_Q +{ + __float128 flt; + struct + { + unsigned long frac1 : 64; + unsigned long frac0 : 48; + unsigned exp : 15; + unsigned sign : 1; + } bits __attribute__((packed)); +}; + +__float128 __copysigntf3 (__float128, __float128); +__float128 __fabstf2 (__float128); + +__float128 +__copysigntf3 (__float128 a, __float128 b) +{ + union _FP_UNION_Q A, B; + + A.flt = a; + B.flt = b; + A.bits.sign = B.bits.sign; + + return A.flt; +} + +__float128 +__fabstf2 (__float128 a) +{ + union _FP_UNION_Q A; + + A.flt = a; + A.bits.sign = 0; + + return A.flt; +} diff --git a/gcc-4.4.3/libgcc/config/libbid/ChangeLog b/gcc-4.4.3/libgcc/config/libbid/ChangeLog new file mode 100644 index 000000000..7ae07b4e1 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/ChangeLog @@ -0,0 +1,383 @@ +2010-01-21 Release Manager + + * GCC 4.4.3 released. + +2009-10-15 Release Manager + + * GCC 4.4.2 released. + +2009-07-22 Release Manager + + * GCC 4.4.1 released. + +2009-04-21 Release Manager + + * GCC 4.4.0 released. + +2007-09-27 H.J. Lu + + * bid128_fromstring.c: Removed. + + * bid_dpd.c: New from libbid 2007-09-26. + * bid128_to_int16.c: Likewise. + * bid128_to_int8.c: Likewise. + * bid128_to_uint8.c: Likewise. + * bid128_to_uint16.c: Likewise. + * bid64_to_int16.c: Likewise. + * bid64_to_int8.c: Likewise. + * bid64_to_uint16.c: Likewise. + * bid64_to_uint8.c: Likewise. + + * bid128_2_str.h: Updated from libbid 2007-09-26. + * bid128_2_str_macros.h: Likewise. + * bid128_2_str_tables.c: Likewise. + * bid128_add.c: Likewise. + * bid128.c: Likewise. + * bid128_compare.c: Likewise. + * bid128_div.c: Likewise. + * bid128_fma.c: Likewise. + * bid128_logb.c: Likewise. + * bid128_minmax.c: Likewise. + * bid128_mul.c: Likewise. + * bid128_next.c: Likewise. + * bid128_noncomp.c: Likewise. + * bid128_quantize.c: Likewise. + * bid128_rem.c: Likewise. + * bid128_round_integral.c: Likewise. + * bid128_scalb.c: Likewise. + * bid128_sqrt.c: Likewise. + * bid128_string.c: Likewise. + * bid128_to_int32.c: Likewise. + * bid128_to_int64.c: Likewise. + * bid128_to_uint32.c: Likewise. + * bid128_to_uint64.c: Likewise. + * bid32_to_bid128.c: Likewise. + * bid32_to_bid64.c: Likewise. + * bid64_add.c: Likewise. + * bid64_compare.c: Likewise. + * bid64_div.c: Likewise. + * bid64_fma.c: Likewise. + * bid64_logb.c: Likewise. + * bid64_minmax.c: Likewise. + * bid64_mul.c: Likewise. + * bid64_next.c: Likewise. + * bid64_noncomp.c: Likewise. + * bid64_quantize.c: Likewise. + * bid64_rem.c: Likewise. + * bid64_round_integral.c: Likewise. + * bid64_scalb.c: Likewise. + * bid64_sqrt.c: Likewise. + * bid64_string.c: Likewise. + * bid64_to_bid128.c: Likewise. + * bid64_to_int32.c: Likewise. + * bid64_to_int64.c: Likewise. + * bid64_to_uint32.c: Likewise. + * bid64_to_uint64.c: Likewise. + * bid_b2d.h: Likewise. + * bid_binarydecimal.c: Likewise. + * bid_conf.h: Likewise. + * bid_convert_data.c: Likewise. + * bid_decimal_data.c: Likewise. + * bid_decimal_globals.c: Likewise. + * bid_div_macros.h: Likewise. + * bid_flag_operations.c: Likewise. + * bid_from_int.c: Likewise. + * bid_functions.h: Likewise. + * bid_gcc_intrinsics.h: Likewise. + * bid_inline_add.h: Likewise. + * bid_internal.h: Likewise. + * bid_round.c: Likewise. + * bid_sqrt_macros.h: Likewise. + * _addsub_dd.c: Likewise. + * _addsub_sd.c: Likewise. + * _addsub_td.c: Likewise. + * _dd_to_df.c: Likewise. + * _dd_to_di.c: Likewise. + * _dd_to_sd.c: Likewise. + * _dd_to_sf.c: Likewise. + * _dd_to_si.c: Likewise. + * _dd_to_td.c: Likewise. + * _dd_to_tf.c: Likewise. + * _dd_to_udi.c: Likewise. + * _dd_to_usi.c: Likewise. + * _dd_to_xf.c: Likewise. + * _df_to_dd.c: Likewise. + * _df_to_sd.c: Likewise. + * _df_to_td.c: Likewise. + * _di_to_dd.c: Likewise. + * _di_to_sd.c: Likewise. + * _di_to_td.c: Likewise. + * _div_dd.c: Likewise. + * _div_sd.c: Likewise. + * _div_td.c: Likewise. + * _eq_dd.c: Likewise. + * _eq_sd.c: Likewise. + * _eq_td.c: Likewise. + * _ge_dd.c: Likewise. + * _ge_sd.c: Likewise. + * _ge_td.c: Likewise. + * _gt_dd.c: Likewise. + * _gt_sd.c: Likewise. + * _gt_td.c: Likewise. + * _isinfd128.c: Likewise. + * _isinfd32.c: Likewise. + * _isinfd64.c: Likewise. + * _le_dd.c: Likewise. + * _le_sd.c: Likewise. + * _le_td.c: Likewise. + * _lt_dd.c: Likewise. + * _lt_sd.c: Likewise. + * _lt_td.c: Likewise. + * _mul_dd.c: Likewise. + * _mul_sd.c: Likewise. + * _mul_td.c: Likewise. + * _ne_dd.c: Likewise. + * _ne_sd.c: Likewise. + * _ne_td.c: Likewise. + * _sd_to_dd.c: Likewise. + * _sd_to_df.c: Likewise. + * _sd_to_di.c: Likewise. + * _sd_to_sf.c: Likewise. + * _sd_to_si.c: Likewise. + * _sd_to_td.c: Likewise. + * _sd_to_tf.c: Likewise. + * _sd_to_udi.c: Likewise. + * _sd_to_usi.c: Likewise. + * _sd_to_xf.c: Likewise. + * _sf_to_dd.c: Likewise. + * _sf_to_sd.c: Likewise. + * _sf_to_td.c: Likewise. + * _si_to_dd.c: Likewise. + * _si_to_sd.c: Likewise. + * _si_to_td.c: Likewise. + * _td_to_dd.c: Likewise. + * _td_to_df.c: Likewise. + * _td_to_di.c: Likewise. + * _td_to_sd.c: Likewise. + * _td_to_sf.c: Likewise. + * _td_to_si.c: Likewise. + * _td_to_tf.c: Likewise. + * _td_to_udi.c: Likewise. + * _td_to_usi.c: Likewise. + * _td_to_xf.c: Likewise. + * _tf_to_dd.c: Likewise. + * _tf_to_sd.c: Likewise. + * _tf_to_td.c: Likewise. + * _udi_to_dd.c: Likewise. + * _udi_to_sd.c: Likewise. + * _udi_to_td.c: Likewise. + * _unord_dd.c: Likewise. + * _unord_sd.c: Likewise. + * _unord_td.c: Likewise. + * _usi_to_dd.c: Likewise. + * _usi_to_sd.c: Likewise. + * _usi_to_td.c: Likewise. + * _xf_to_dd.c: Likewise. + * _xf_to_sd.c: Likewise. + * _xf_to_td.c: Likewise. + +2007-09-27 H.J. Lu + + * b2d.h: Renamed to ... + * bid_b2d.h: This. + + * bid128_to_string.c: Renamed to ... + * bid128_string.c: This. + + * bid_intrinsics.h: Renamed to ... + * bid_gcc_intrinsics.h: This. + + * bid_string.c: Renamed to ... + * bid64_string.c: This. + + * binarydecimal.c: Renamed to ... + * bid_decimal_globals.c: This. + + * convert_data.c: Renamed to ... + * bid_convert_data.c: This. + + * decimal_data.c: Renamed to ... + * bid_decimal_data.c: This. + + * decimal_globals.c: Renamed to ... + * bid_decimal_globals.c: This. + + * div_macros.h: Renamed to ... + * bid_div_macros.h: This. + + * inline_bid_add.h: Renamed to ... + * bid_inline_add.h: This. + + * sqrt_macros.h: Renamed to ... + * bid_sqrt_macros.h: This. + +2007-07-06 H.J. Lu + + Updated from Intel BID library: + * bid_conf.h (BID_THREAD): Defined only if both HAVE_CC_TLS + and USE_TLS are defined. + +2007-07-05 H.J. Lu + + Updated from Intel BID library: + * bid_conf.h (BID_THREAD): Defined. + (__bid_IDEC_glbround): Add BID_THREAD in declaration. + (__bid_IDEC_glbflags): Likewise. + + * decimal_globals.c (__bid_IDEC_glbround): Add BID_THREAD in + declaration. + (__bid_IDEC_glbflags): Likewise. + +2007-07-04 Marius Cornea + H.J. Lu + + * _addsub_dd.c: New file from Intel BID library. + * _addsub_sd.c: Likewise. + * _addsub_td.c: Likewise. + * _dd_to_df.c: Likewise. + * _dd_to_di.c: Likewise. + * _dd_to_sd.c: Likewise. + * _dd_to_sf.c: Likewise. + * _dd_to_si.c: Likewise. + * _dd_to_td.c: Likewise. + * _dd_to_tf.c: Likewise. + * _dd_to_udi.c: Likewise. + * _dd_to_usi.c: Likewise. + * _dd_to_xf.c: Likewise. + * _df_to_dd.c: Likewise. + * _df_to_sd.c: Likewise. + * _df_to_td.c: Likewise. + * _di_to_dd.c: Likewise. + * _di_to_sd.c: Likewise. + * _di_to_td.c: Likewise. + * _div_dd.c: Likewise. + * _div_sd.c: Likewise. + * _div_td.c: Likewise. + * _eq_dd.c: Likewise. + * _eq_sd.c: Likewise. + * _eq_td.c: Likewise. + * _ge_dd.c: Likewise. + * _ge_sd.c: Likewise. + * _ge_td.c: Likewise. + * _gt_dd.c: Likewise. + * _gt_sd.c: Likewise. + * _gt_td.c: Likewise. + * _isinfd128.c: Likewise. + * _isinfd32.c: Likewise. + * _isinfd64.c: Likewise. + * _le_dd.c: Likewise. + * _le_sd.c: Likewise. + * _le_td.c: Likewise. + * _lt_dd.c: Likewise. + * _lt_sd.c: Likewise. + * _lt_td.c: Likewise. + * _mul_dd.c: Likewise. + * _mul_sd.c: Likewise. + * _mul_td.c: Likewise. + * _ne_dd.c: Likewise. + * _ne_sd.c: Likewise. + * _ne_td.c: Likewise. + * _sd_to_dd.c: Likewise. + * _sd_to_df.c: Likewise. + * _sd_to_di.c: Likewise. + * _sd_to_sf.c: Likewise. + * _sd_to_si.c: Likewise. + * _sd_to_td.c: Likewise. + * _sd_to_tf.c: Likewise. + * _sd_to_udi.c: Likewise. + * _sd_to_usi.c: Likewise. + * _sd_to_xf.c: Likewise. + * _sf_to_dd.c: Likewise. + * _sf_to_sd.c: Likewise. + * _sf_to_td.c: Likewise. + * _si_to_dd.c: Likewise. + * _si_to_sd.c: Likewise. + * _si_to_td.c: Likewise. + * _td_to_dd.c: Likewise. + * _td_to_df.c: Likewise. + * _td_to_di.c: Likewise. + * _td_to_sd.c: Likewise. + * _td_to_sf.c: Likewise. + * _td_to_si.c: Likewise. + * _td_to_tf.c: Likewise. + * _td_to_udi.c: Likewise. + * _td_to_usi.c: Likewise. + * _td_to_xf.c: Likewise. + * _tf_to_dd.c: Likewise. + * _tf_to_sd.c: Likewise. + * _tf_to_td.c: Likewise. + * _udi_to_dd.c: Likewise. + * _udi_to_sd.c: Likewise. + * _udi_to_td.c: Likewise. + * _unord_dd.c: Likewise. + * _unord_sd.c: Likewise. + * _unord_td.c: Likewise. + * _usi_to_dd.c: Likewise. + * _usi_to_sd.c: Likewise. + * _usi_to_td.c: Likewise. + * _xf_to_dd.c: Likewise. + * _xf_to_sd.c: Likewise. + * _xf_to_td.c: Likewise. + +2007-07-04 Marius Cornea + + * b2d.h: New file from Intel BID library. + * bid128_2_str.h: Likewise. + * bid128_2_str_macros.h: Likewise. + * bid128_2_str_tables.c: Likewise. + * bid128_add.c: Likewise. + * bid128.c: Likewise. + * bid128_compare.c: Likewise. + * bid128_div.c: Likewise. + * bid128_fma.c: Likewise. + * bid128_fromstring.c: Likewise. + * bid128_logb.c: Likewise. + * bid128_minmax.c: Likewise. + * bid128_mul.c: Likewise. + * bid128_next.c: Likewise. + * bid128_noncomp.c: Likewise. + * bid128_quantize.c: Likewise. + * bid128_rem.c: Likewise. + * bid128_round_integral.c: Likewise. + * bid128_scalb.c: Likewise. + * bid128_sqrt.c: Likewise. + * bid128_to_int32.c: Likewise. + * bid128_to_int64.c: Likewise. + * bid128_to_string.c: Likewise. + * bid128_to_uint32.c: Likewise. + * bid128_to_uint64.c: Likewise. + * bid32_to_bid128.c: Likewise. + * bid32_to_bid64.c: Likewise. + * bid64_add.c: Likewise. + * bid64_compare.c: Likewise. + * bid64_div.c: Likewise. + * bid64_fma.c: Likewise. + * bid64_logb.c: Likewise. + * bid64_minmax.c: Likewise. + * bid64_mul.c: Likewise. + * bid64_next.c: Likewise. + * bid64_noncomp.c: Likewise. + * bid64_quantize.c: Likewise. + * bid64_rem.c: Likewise. + * bid64_round_integral.c: Likewise. + * bid64_scalb.c: Likewise. + * bid64_sqrt.c: Likewise. + * bid64_to_bid128.c: Likewise. + * bid64_to_int32.c: Likewise. + * bid64_to_int64.c: Likewise. + * bid64_to_uint32.c: Likewise. + * bid64_to_uint64.c: Likewise. + * bid_conf.h: Likewise. + * bid_flag_operations.c: Likewise. + * bid_from_int.c: Likewise. + * bid_functions.h: Likewise. + * bid_internal.h: Likewise. + * bid_round.c: Likewise. + * bid_string.c: Likewise. + * binarydecimal.c: Likewise. + * convert_data.c: Likewise. + * decimal_data.c: Likewise. + * decimal_globals.c: Likewise. + * div_macros.h: Likewise. + * inline_bid_add.h: Likewise. + * sqrt_macros.h: Likewise. diff --git a/gcc-4.4.3/libgcc/config/libbid/_addsub_dd.c b/gcc-4.4.3/libgcc/config/libbid/_addsub_dd.c new file mode 100644 index 000000000..ef5f778d4 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_addsub_dd.c @@ -0,0 +1,46 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal64 +__bid_adddd3 (_Decimal64 x, _Decimal64 y) { + union decimal64 ux, uy, res; + + ux.d = x; + uy.d = y; + res.i = __bid64_add (ux.i, uy.i); + return (res.d); +} + +_Decimal64 +__bid_subdd3 (_Decimal64 x, _Decimal64 y) { + union decimal64 ux, uy, res; + + ux.d = x; + uy.d = y; + res.i = __bid64_sub (ux.i, uy.i); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_addsub_sd.c b/gcc-4.4.3/libgcc/config/libbid/_addsub_sd.c new file mode 100644 index 000000000..5224e57fa --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_addsub_sd.c @@ -0,0 +1,54 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal32 +__bid_addsd3 (_Decimal32 x, _Decimal32 y) { + UINT64 x64, y64, res64; + union decimal32 ux, uy, res; + + ux.d = x; + uy.d = y; + x64 = __bid32_to_bid64 (ux.i); + y64 = __bid32_to_bid64 (uy.i); + res64 = __bid64_add (x64, y64); + res.i = __bid64_to_bid32 (res64); + return (res.d); +} + +_Decimal32 +__bid_subsd3 (_Decimal32 x, _Decimal32 y) { + UINT64 x64, y64, res64; + union decimal32 ux, uy, res; + + ux.d = x; + uy.d = y; + x64 = __bid32_to_bid64 (ux.i); + y64 = __bid32_to_bid64 (uy.i); + res64 = __bid64_sub (x64, y64); + res.i = __bid64_to_bid32 (res64); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_addsub_td.c b/gcc-4.4.3/libgcc/config/libbid/_addsub_td.c new file mode 100644 index 000000000..f37aeafcc --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_addsub_td.c @@ -0,0 +1,46 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal128 +__bid_addtd3 (_Decimal128 x, _Decimal128 y) { + union decimal128 ux, uy, res; + + ux.d = x; + uy.d = y; + res.i = __bid128_add (ux.i, uy.i); + return (res.d); +} + +_Decimal128 +__bid_subtd3 (_Decimal128 x, _Decimal128 y) { + union decimal128 ux, uy, res; + + ux.d = x; + uy.d = y; + res.i = __bid128_sub (ux.i, uy.i); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_dd_to_df.c b/gcc-4.4.3/libgcc/config/libbid/_dd_to_df.c new file mode 100644 index 000000000..af08295a0 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_dd_to_df.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +DFtype +__bid_truncdddf (_Decimal64 x) { + DFtype res; + union decimal64 ux; + + ux.d = x; + res = __bid64_to_binary64 (ux.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_dd_to_di.c b/gcc-4.4.3/libgcc/config/libbid/_dd_to_di.c new file mode 100644 index 000000000..a89c19923 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_dd_to_di.c @@ -0,0 +1,39 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +DItype +__bid_fixdddi (_Decimal64 x) { + DItype res = 0xbaddbaddbaddbaddull; + union decimal64 ux; + + ux.d = x; + res = __bid64_to_int64_xint (ux.i); + + return (res); +} + + diff --git a/gcc-4.4.3/libgcc/config/libbid/_dd_to_sd.c b/gcc-4.4.3/libgcc/config/libbid/_dd_to_sd.c new file mode 100644 index 000000000..e81cccd33 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_dd_to_sd.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal32 +__bid_truncddsd2 (_Decimal64 x) { + union decimal32 res; + union decimal64 ux; + + ux.d = x; + res.i = __bid64_to_bid32 (ux.i); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_dd_to_sf.c b/gcc-4.4.3/libgcc/config/libbid/_dd_to_sf.c new file mode 100644 index 000000000..5fd560b27 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_dd_to_sf.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +SFtype +__bid_truncddsf (_Decimal64 x) { + SFtype res; + union decimal64 ux; + + ux.d = x; + res = __bid64_to_binary32 (ux.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_dd_to_si.c b/gcc-4.4.3/libgcc/config/libbid/_dd_to_si.c new file mode 100644 index 000000000..5780739c8 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_dd_to_si.c @@ -0,0 +1,39 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +SItype +__bid_fixddsi (_Decimal64 x) { + SItype res = 0xbaddbadd; + union decimal64 ux; + + ux.d = x; + res = __bid64_to_int32_xint (ux.i); + + return (res); +} + + diff --git a/gcc-4.4.3/libgcc/config/libbid/_dd_to_td.c b/gcc-4.4.3/libgcc/config/libbid/_dd_to_td.c new file mode 100644 index 000000000..cb13ee67a --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_dd_to_td.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal128 +__bid_extendddtd2 (_Decimal64 x) { + union decimal128 res; + union decimal64 ux; + + ux.d = x; + res.i = __bid64_to_bid128 (ux.i); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_dd_to_tf.c b/gcc-4.4.3/libgcc/config/libbid/_dd_to_tf.c new file mode 100644 index 000000000..fa6be8774 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_dd_to_tf.c @@ -0,0 +1,38 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +#if LIBGCC2_HAS_TF_MODE || BID_HAS_TF_MODE +TFtype +__bid_extendddtf (_Decimal64 x) { + union float128 res; + union decimal64 ux; + + ux.d = x; + res.i = __bid64_to_binary128 (ux.i); + return (res.f); +} +#endif diff --git a/gcc-4.4.3/libgcc/config/libbid/_dd_to_udi.c b/gcc-4.4.3/libgcc/config/libbid/_dd_to_udi.c new file mode 100644 index 000000000..b39909d0a --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_dd_to_udi.c @@ -0,0 +1,39 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +UDItype +__bid_fixunsdddi (_Decimal64 x) { + UDItype res = 0xbaddbaddbaddbaddull; + union decimal64 ux; + + ux.d = x; + res = __bid64_to_uint64_xint (ux.i); + + if (res == 0x8000000000000000ull) res = 0; // for NaNs too + return (res); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_dd_to_usi.c b/gcc-4.4.3/libgcc/config/libbid/_dd_to_usi.c new file mode 100644 index 000000000..e0fd8bb9d --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_dd_to_usi.c @@ -0,0 +1,39 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +USItype +__bid_fixunsddsi (_Decimal64 x) { + USItype res = 0xbaddbadd; + union decimal64 ux; + + ux.d = x; + res = __bid64_to_uint32_xint (ux.i); + + if (res == 0x80000000) res = 0; // for NaNs too + return (res); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_dd_to_xf.c b/gcc-4.4.3/libgcc/config/libbid/_dd_to_xf.c new file mode 100644 index 000000000..fb0dce67d --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_dd_to_xf.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +XFtype +__bid_extendddxf (_Decimal64 x) { + XFtype res; + union decimal64 ux; + + ux.d = x; + res = __bid64_to_binary80 (ux.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_df_to_dd.c b/gcc-4.4.3/libgcc/config/libbid/_df_to_dd.c new file mode 100644 index 000000000..4e7ccdd43 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_df_to_dd.c @@ -0,0 +1,33 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal64 +__bid_extenddfdd (DFtype x) { + union decimal64 res; + res.i = __binary64_to_bid64 (x); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_df_to_sd.c b/gcc-4.4.3/libgcc/config/libbid/_df_to_sd.c new file mode 100644 index 000000000..8be9859c7 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_df_to_sd.c @@ -0,0 +1,34 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal32 +__bid_truncdfsd (DFtype x) { + union decimal32 res; + + res.i = __binary64_to_bid32 (x); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_df_to_td.c b/gcc-4.4.3/libgcc/config/libbid/_df_to_td.c new file mode 100644 index 000000000..896646afd --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_df_to_td.c @@ -0,0 +1,33 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal128 +__bid_extenddftd (DFtype x) { + union decimal128 res; + res.i = __binary64_to_bid128 (x); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_di_to_dd.c b/gcc-4.4.3/libgcc/config/libbid/_di_to_dd.c new file mode 100644 index 000000000..4f4f1617c --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_di_to_dd.c @@ -0,0 +1,35 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal64 +__bid_floatdidd (DItype x) { + union decimal64 res; + + res.i = __bid64_from_int64 (x); + return (res.d); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_di_to_sd.c b/gcc-4.4.3/libgcc/config/libbid/_di_to_sd.c new file mode 100644 index 000000000..603392441 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_di_to_sd.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal32 +__bid_floatdisd (DItype x) { + union decimal32 res; + UINT64 res64; + + res64 = __bid64_from_int64 (x); + res.i = __bid64_to_bid32 (res64); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_di_to_td.c b/gcc-4.4.3/libgcc/config/libbid/_di_to_td.c new file mode 100644 index 000000000..0cadeb4d9 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_di_to_td.c @@ -0,0 +1,35 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal128 +__bid_floatditd (DItype x) { + union decimal128 res; + + res.i = __bid128_from_int64 (x); + return (res.d); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_div_dd.c b/gcc-4.4.3/libgcc/config/libbid/_div_dd.c new file mode 100644 index 000000000..324087455 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_div_dd.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal64 +__bid_divdd3 (_Decimal64 x, _Decimal64 y) { + union decimal64 ux, uy, res; + + ux.d = x; + uy.d = y; + res.i = __bid64_div (ux.i, uy.i); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_div_sd.c b/gcc-4.4.3/libgcc/config/libbid/_div_sd.c new file mode 100644 index 000000000..2a37a9b82 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_div_sd.c @@ -0,0 +1,40 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal32 +__bid_divsd3 (_Decimal32 x, _Decimal32 y) { + UINT64 x64, y64, res64; + union decimal32 ux, uy, res; + + ux.d = x; + uy.d = y; + x64 = __bid32_to_bid64 (ux.i); + y64 = __bid32_to_bid64 (uy.i); + res64 = __bid64_div (x64, y64); + res.i = __bid64_to_bid32 (res64); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_div_td.c b/gcc-4.4.3/libgcc/config/libbid/_div_td.c new file mode 100644 index 000000000..165e2009f --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_div_td.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal128 +__bid_divtd3 (_Decimal128 x, _Decimal128 y) { + union decimal128 ux, uy, res; + + ux.d = x; + uy.d = y; + res.i = __bid128_div (ux.i, uy.i); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_eq_dd.c b/gcc-4.4.3/libgcc/config/libbid/_eq_dd.c new file mode 100644 index 000000000..8d189f4a3 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_eq_dd.c @@ -0,0 +1,41 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_eqdd2 (_Decimal64 x, _Decimal64 y) { + CMPtype res; + union decimal64 ux, uy; + + ux.d = x; + uy.d = y; + res = __bid64_quiet_equal (ux.i, uy.i); + if (res == 0) + res = 1; + else + res = 0; + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_eq_sd.c b/gcc-4.4.3/libgcc/config/libbid/_eq_sd.c new file mode 100644 index 000000000..d94ac8376 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_eq_sd.c @@ -0,0 +1,44 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_eqsd2 (_Decimal32 x, _Decimal32 y) { + CMPtype res; + UINT64 x64, y64; + union decimal32 ux, uy; + + ux.d = x; + uy.d = y; + x64 = __bid32_to_bid64 (ux.i); + y64 = __bid32_to_bid64 (uy.i); + res = __bid64_quiet_equal (x64, y64); + if (res == 0) + res = 1; + else + res = 0; + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_eq_td.c b/gcc-4.4.3/libgcc/config/libbid/_eq_td.c new file mode 100644 index 000000000..d48a0ceeb --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_eq_td.c @@ -0,0 +1,41 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_eqtd2 (_Decimal128 x, _Decimal128 y) { + CMPtype res; + union decimal128 ux, uy; + + ux.d = x; + uy.d = y; + res = __bid128_quiet_equal (ux.i, uy.i); + if (res == 0) + res = 1; + else + res = 0; + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_ge_dd.c b/gcc-4.4.3/libgcc/config/libbid/_ge_dd.c new file mode 100644 index 000000000..461c0e522 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_ge_dd.c @@ -0,0 +1,39 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_gedd2 (_Decimal64 x, _Decimal64 y) { + CMPtype res; + union decimal64 ux, uy; + + ux.d = x; + uy.d = y; + res = __bid64_quiet_greater_equal (ux.i, uy.i); + if (res == 0) res = -1; + + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_ge_sd.c b/gcc-4.4.3/libgcc/config/libbid/_ge_sd.c new file mode 100644 index 000000000..4781ddc35 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_ge_sd.c @@ -0,0 +1,42 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_gesd2 (_Decimal32 x, _Decimal32 y) { + CMPtype res; + UINT64 x64, y64; + union decimal32 ux, uy; + + ux.d = x; + uy.d = y; + x64 = __bid32_to_bid64 (ux.i); + y64 = __bid32_to_bid64 (uy.i); + res = __bid64_quiet_greater_equal (x64, y64); + if (res == 0) res = -1; + + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_ge_td.c b/gcc-4.4.3/libgcc/config/libbid/_ge_td.c new file mode 100644 index 000000000..9f16619d7 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_ge_td.c @@ -0,0 +1,39 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_getd2 (_Decimal128 x, _Decimal128 y) { + CMPtype res; + union decimal128 ux, uy; + + ux.d = x; + uy.d = y; + res = __bid128_quiet_greater_equal (ux.i, uy.i); + if (res == 0) res = -1; + + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_gt_dd.c b/gcc-4.4.3/libgcc/config/libbid/_gt_dd.c new file mode 100644 index 000000000..078faad8d --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_gt_dd.c @@ -0,0 +1,37 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_gtdd2 (_Decimal64 x, _Decimal64 y) { + CMPtype res; + union decimal64 ux, uy; + + ux.d = x; + uy.d = y; + res = __bid64_quiet_greater (ux.i, uy.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_gt_sd.c b/gcc-4.4.3/libgcc/config/libbid/_gt_sd.c new file mode 100644 index 000000000..03f6a9396 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_gt_sd.c @@ -0,0 +1,40 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_gtsd2 (_Decimal32 x, _Decimal32 y) { + CMPtype res; + UINT64 x64, y64; + union decimal32 ux, uy; + + ux.d = x; + uy.d = y; + x64 = __bid32_to_bid64 (ux.i); + y64 = __bid32_to_bid64 (uy.i); + res = __bid64_quiet_greater (x64, y64); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_gt_td.c b/gcc-4.4.3/libgcc/config/libbid/_gt_td.c new file mode 100644 index 000000000..528886e2e --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_gt_td.c @@ -0,0 +1,37 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_gttd2 (_Decimal128 x, _Decimal128 y) { + CMPtype res; + union decimal128 ux, uy; + + ux.d = x; + uy.d = y; + res = __bid128_quiet_greater (ux.i, uy.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_isinfd128.c b/gcc-4.4.3/libgcc/config/libbid/_isinfd128.c new file mode 100644 index 000000000..10448dcbb --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_isinfd128.c @@ -0,0 +1,37 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +int +isinfd128 (_Decimal128 x) { + int res; + union decimal128 ux; + + ux.d = x; + res = __bid128_isInf (ux.i); + return (res); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_isinfd32.c b/gcc-4.4.3/libgcc/config/libbid/_isinfd32.c new file mode 100644 index 000000000..bed78aefe --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_isinfd32.c @@ -0,0 +1,39 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +int +isinfd32 (_Decimal32 x) { + int res; + UINT64 x64; + union decimal32 ux; + + ux.d = x; + x64 = __bid32_to_bid64 (ux.i); + res = __bid64_isInf (x64); + return (res); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_isinfd64.c b/gcc-4.4.3/libgcc/config/libbid/_isinfd64.c new file mode 100644 index 000000000..7de1d1932 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_isinfd64.c @@ -0,0 +1,37 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +int +isinfd64 (_Decimal64 x) { + int res; + union decimal64 ux; + + ux.d = x; + res = __bid64_isInf (ux.i); + return (res); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_le_dd.c b/gcc-4.4.3/libgcc/config/libbid/_le_dd.c new file mode 100644 index 000000000..32f0d96cd --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_le_dd.c @@ -0,0 +1,41 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_ledd2 (_Decimal64 x, _Decimal64 y) { + CMPtype res; + union decimal64 ux, uy; + + ux.d = x; + uy.d = y; + res = __bid64_quiet_less_equal (ux.i, uy.i); + if (res != 0) + res = -1; + else + res = 1; + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_le_sd.c b/gcc-4.4.3/libgcc/config/libbid/_le_sd.c new file mode 100644 index 000000000..565632ba0 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_le_sd.c @@ -0,0 +1,44 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_lesd2 (_Decimal32 x, _Decimal32 y) { + CMPtype res; + UINT64 x64, y64; + union decimal32 ux, uy; + + ux.d = x; + uy.d = y; + x64 = __bid32_to_bid64 (ux.i); + y64 = __bid32_to_bid64 (uy.i); + res = __bid64_quiet_less_equal (x64, y64); + if (res != 0) + res = -1; + else + res = 1; + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_le_td.c b/gcc-4.4.3/libgcc/config/libbid/_le_td.c new file mode 100644 index 000000000..1fefc8e80 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_le_td.c @@ -0,0 +1,41 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_letd2 (_Decimal128 x, _Decimal128 y) { + CMPtype res; + union decimal128 ux, uy; + + ux.d = x; + uy.d = y; + res = __bid128_quiet_less_equal (ux.i, uy.i); + if (res != 0) + res = -1; + else + res = 1; + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_lt_dd.c b/gcc-4.4.3/libgcc/config/libbid/_lt_dd.c new file mode 100644 index 000000000..868890d72 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_lt_dd.c @@ -0,0 +1,37 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_ltdd2 (_Decimal64 x, _Decimal64 y) { + CMPtype res; + union decimal64 ux, uy; + + ux.d = x; + uy.d = y; + res = -__bid64_quiet_less (ux.i, uy.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_lt_sd.c b/gcc-4.4.3/libgcc/config/libbid/_lt_sd.c new file mode 100644 index 000000000..5810f6a01 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_lt_sd.c @@ -0,0 +1,40 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_ltsd2 (_Decimal32 x, _Decimal32 y) { + CMPtype res; + UINT64 x64, y64; + union decimal32 ux, uy; + + ux.d = x; + uy.d = y; + x64 = __bid32_to_bid64 (ux.i); + y64 = __bid32_to_bid64 (uy.i); + res = -__bid64_quiet_less (x64, y64); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_lt_td.c b/gcc-4.4.3/libgcc/config/libbid/_lt_td.c new file mode 100644 index 000000000..1a31b32a9 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_lt_td.c @@ -0,0 +1,37 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_lttd2 (_Decimal128 x, _Decimal128 y) { + CMPtype res; + union decimal128 ux, uy; + + ux.d = x; + uy.d = y; + res = -__bid128_quiet_less (ux.i, uy.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_mul_dd.c b/gcc-4.4.3/libgcc/config/libbid/_mul_dd.c new file mode 100644 index 000000000..d0082f701 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_mul_dd.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal64 +__bid_muldd3 (_Decimal64 x, _Decimal64 y) { + union decimal64 ux, uy, res; + + ux.d = x; + uy.d = y; + res.i = __bid64_mul (ux.i, uy.i); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_mul_sd.c b/gcc-4.4.3/libgcc/config/libbid/_mul_sd.c new file mode 100644 index 000000000..73b11e952 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_mul_sd.c @@ -0,0 +1,40 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal32 +__bid_mulsd3 (_Decimal32 x, _Decimal32 y) { + UINT64 x64, y64, res64; + union decimal32 ux, uy, res; + + ux.d = x; + uy.d = y; + x64 = __bid32_to_bid64 (ux.i); + y64 = __bid32_to_bid64 (uy.i); + res64 = __bid64_mul (x64, y64); + res.i = __bid64_to_bid32 (res64); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_mul_td.c b/gcc-4.4.3/libgcc/config/libbid/_mul_td.c new file mode 100644 index 000000000..0c2983c2a --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_mul_td.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal128 +__bid_multd3 (_Decimal128 x, _Decimal128 y) { + union decimal128 ux, uy, res; + + ux.d = x; + uy.d = y; + res.i = __bid128_mul (ux.i, uy.i); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_ne_dd.c b/gcc-4.4.3/libgcc/config/libbid/_ne_dd.c new file mode 100644 index 000000000..3b62f0d78 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_ne_dd.c @@ -0,0 +1,37 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_nedd2 (_Decimal64 x, _Decimal64 y) { + CMPtype res; + union decimal64 ux, uy; + + ux.d = x; + uy.d = y; + res = __bid64_quiet_not_equal (ux.i, uy.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_ne_sd.c b/gcc-4.4.3/libgcc/config/libbid/_ne_sd.c new file mode 100644 index 000000000..1b311ba68 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_ne_sd.c @@ -0,0 +1,40 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_nesd2 (_Decimal32 x, _Decimal32 y) { + CMPtype res; + UINT64 x64, y64; + union decimal32 ux, uy; + + ux.d = x; + uy.d = y; + x64 = __bid32_to_bid64 (ux.i); + y64 = __bid32_to_bid64 (uy.i); + res = __bid64_quiet_not_equal (x64, y64); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_ne_td.c b/gcc-4.4.3/libgcc/config/libbid/_ne_td.c new file mode 100644 index 000000000..9f2c5dab3 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_ne_td.c @@ -0,0 +1,37 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_netd2 (_Decimal128 x, _Decimal128 y) { + CMPtype res; + union decimal128 ux, uy; + + ux.d = x; + uy.d = y; + res = __bid128_quiet_not_equal (ux.i, uy.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_sd_to_dd.c b/gcc-4.4.3/libgcc/config/libbid/_sd_to_dd.c new file mode 100644 index 000000000..0d03b484a --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_sd_to_dd.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal64 +__bid_extendsddd2 (_Decimal32 x) { + union decimal64 res; + union decimal32 ux; + + ux.d = x; + res.i = __bid32_to_bid64 (ux.i); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_sd_to_df.c b/gcc-4.4.3/libgcc/config/libbid/_sd_to_df.c new file mode 100644 index 000000000..8e864f5aa --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_sd_to_df.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +DFtype +__bid_extendsddf (_Decimal32 x) { + DFtype res; + union decimal32 ux; + + ux.d = x; + res = __bid32_to_binary64 (ux.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_sd_to_di.c b/gcc-4.4.3/libgcc/config/libbid/_sd_to_di.c new file mode 100644 index 000000000..7e83b4c7e --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_sd_to_di.c @@ -0,0 +1,41 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +DItype +__bid_fixsddi (_Decimal32 x) { + DItype res = 0xbaddbaddbaddbaddull; + UINT64 x64; + union decimal32 ux; + + ux.d = x; + x64 = __bid32_to_bid64 (ux.i); + res = __bid64_to_int64_xint (x64); + + return (res); +} + + diff --git a/gcc-4.4.3/libgcc/config/libbid/_sd_to_sf.c b/gcc-4.4.3/libgcc/config/libbid/_sd_to_sf.c new file mode 100644 index 000000000..645bec29d --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_sd_to_sf.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +SFtype +__bid_truncsdsf (_Decimal32 x) { + SFtype res; + union decimal32 ux; + + ux.d = x; + res = __bid32_to_binary32 (ux.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_sd_to_si.c b/gcc-4.4.3/libgcc/config/libbid/_sd_to_si.c new file mode 100644 index 000000000..55d7402ca --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_sd_to_si.c @@ -0,0 +1,41 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +SItype +__bid_fixsdsi (_Decimal32 x) { + SItype res = 0xbaddbadd; + UINT64 x64; + union decimal32 ux; + + ux.d = x; + x64 = __bid32_to_bid64 (ux.i); + res = __bid64_to_int32_xint (x64); + + return (res); +} + + diff --git a/gcc-4.4.3/libgcc/config/libbid/_sd_to_td.c b/gcc-4.4.3/libgcc/config/libbid/_sd_to_td.c new file mode 100644 index 000000000..e2c955d24 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_sd_to_td.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal128 +__bid_extendsdtd2 (_Decimal32 x) { + union decimal128 res; + union decimal32 ux; + + ux.d = x; + res.i = __bid32_to_bid128 (ux.i); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_sd_to_tf.c b/gcc-4.4.3/libgcc/config/libbid/_sd_to_tf.c new file mode 100644 index 000000000..2b1109afe --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_sd_to_tf.c @@ -0,0 +1,38 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +#if LIBGCC2_HAS_TF_MODE || BID_HAS_TF_MODE +TFtype +__bid_extendsdtf (_Decimal32 x) { + union float128 res; + union decimal32 ux; + + ux.d = x; + res.i = __bid32_to_binary128 (ux.i); + return (res.f); +} +#endif diff --git a/gcc-4.4.3/libgcc/config/libbid/_sd_to_udi.c b/gcc-4.4.3/libgcc/config/libbid/_sd_to_udi.c new file mode 100644 index 000000000..0c3840082 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_sd_to_udi.c @@ -0,0 +1,41 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +UDItype +__bid_fixunssddi (_Decimal32 x) { + UDItype res = 0xbaddbaddbaddbaddull; + UINT64 x64; + union decimal32 ux; + + ux.d = x; + x64 = __bid32_to_bid64 (ux.i); + res = __bid64_to_uint64_xint (x64); + + if (res == 0x8000000000000000ull) res = 0; // for NaNs too + return (res); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_sd_to_usi.c b/gcc-4.4.3/libgcc/config/libbid/_sd_to_usi.c new file mode 100644 index 000000000..742cae857 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_sd_to_usi.c @@ -0,0 +1,41 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +USItype +__bid_fixunssdsi (_Decimal32 x) { + USItype res = 0xbaddbadd; + UINT64 x64; + union decimal32 ux; + + ux.d = x; + x64 = __bid32_to_bid64 (ux.i); + res = __bid64_to_uint32_xint (x64); + + if (res == 0x80000000) res = 0; // for NaNs too + return (res); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_sd_to_xf.c b/gcc-4.4.3/libgcc/config/libbid/_sd_to_xf.c new file mode 100644 index 000000000..23c06d2a0 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_sd_to_xf.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +XFtype +__bid_extendsdxf (_Decimal32 x) { + XFtype res; + union decimal32 ux; + + ux.d = x; + res = __bid32_to_binary80 (ux.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_sf_to_dd.c b/gcc-4.4.3/libgcc/config/libbid/_sf_to_dd.c new file mode 100644 index 000000000..15fc298c2 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_sf_to_dd.c @@ -0,0 +1,33 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal64 +__bid_extendsfdd (SFtype x) { + union decimal64 res; + res.i = __binary32_to_bid64 (x); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_sf_to_sd.c b/gcc-4.4.3/libgcc/config/libbid/_sf_to_sd.c new file mode 100644 index 000000000..465ced0ea --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_sf_to_sd.c @@ -0,0 +1,33 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal32 +__bid_extendsfsd (SFtype x) { + union decimal32 res; + res.i = __binary32_to_bid32 (x); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_sf_to_td.c b/gcc-4.4.3/libgcc/config/libbid/_sf_to_td.c new file mode 100644 index 000000000..a1fe5b9c4 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_sf_to_td.c @@ -0,0 +1,33 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal128 +__bid_extendsftd (SFtype x) { + union decimal128 res; + res.i = __binary32_to_bid128 (x); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_si_to_dd.c b/gcc-4.4.3/libgcc/config/libbid/_si_to_dd.c new file mode 100644 index 000000000..0487ec8d5 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_si_to_dd.c @@ -0,0 +1,34 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal64 +__bid_floatsidd (SItype x) { + union decimal64 res; + + res.i = __bid64_from_int32 (x); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_si_to_sd.c b/gcc-4.4.3/libgcc/config/libbid/_si_to_sd.c new file mode 100644 index 000000000..6f1b97135 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_si_to_sd.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal32 +__bid_floatsisd (SItype x) { + union decimal32 res; + UINT64 res64; + + res64 = __bid64_from_int32 (x); + res.i = __bid64_to_bid32 (res64); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_si_to_td.c b/gcc-4.4.3/libgcc/config/libbid/_si_to_td.c new file mode 100644 index 000000000..f78b73ee7 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_si_to_td.c @@ -0,0 +1,34 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal128 +__bid_floatsitd (SItype x) { + union decimal128 res; + + res.i = __bid128_from_int32 (x); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_td_to_dd.c b/gcc-4.4.3/libgcc/config/libbid/_td_to_dd.c new file mode 100644 index 000000000..5535b8427 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_td_to_dd.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal64 +__bid_trunctddd2 (_Decimal128 x) { + union decimal128 ux; + union decimal64 res; + + ux.d = x; + res.i = __bid128_to_bid64 (ux.i); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_td_to_df.c b/gcc-4.4.3/libgcc/config/libbid/_td_to_df.c new file mode 100644 index 000000000..1b9c646a5 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_td_to_df.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +DFtype +__bid_trunctddf (_Decimal128 x) { + DFtype res; + union decimal128 ux; + + ux.d = x; + res = __bid128_to_binary64 (ux.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_td_to_di.c b/gcc-4.4.3/libgcc/config/libbid/_td_to_di.c new file mode 100644 index 000000000..2c54cf026 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_td_to_di.c @@ -0,0 +1,39 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +DItype +__bid_fixtddi (_Decimal128 x) { + DItype res = 0xbaddbaddbaddbaddull; + union decimal128 ux; + + ux.d = x; + res = __bid128_to_int64_xint (ux.i); + + return (res); +} + + diff --git a/gcc-4.4.3/libgcc/config/libbid/_td_to_sd.c b/gcc-4.4.3/libgcc/config/libbid/_td_to_sd.c new file mode 100644 index 000000000..30cf94232 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_td_to_sd.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal32 +__bid_trunctdsd2 (_Decimal128 x) { + union decimal128 ux; + union decimal32 res; + + ux.d = x; + res.i = __bid128_to_bid32 (ux.i); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_td_to_sf.c b/gcc-4.4.3/libgcc/config/libbid/_td_to_sf.c new file mode 100644 index 000000000..d0cf871fb --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_td_to_sf.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +SFtype +__bid_trunctdsf (_Decimal128 x) { + SFtype res; + union decimal128 ux; + + ux.d = x; + res = __bid128_to_binary32 (ux.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_td_to_si.c b/gcc-4.4.3/libgcc/config/libbid/_td_to_si.c new file mode 100644 index 000000000..8d0c70c3f --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_td_to_si.c @@ -0,0 +1,38 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +SItype +__bid_fixtdsi (_Decimal128 x) { + union decimal128 ux; + SItype res = 0xbaddbadd; + + ux.d = x; + res = __bid128_to_int32_xint (ux.i); + + return (res); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_td_to_tf.c b/gcc-4.4.3/libgcc/config/libbid/_td_to_tf.c new file mode 100644 index 000000000..ff66312df --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_td_to_tf.c @@ -0,0 +1,38 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +#if LIBGCC2_HAS_TF_MODE || BID_HAS_TF_MODE +TFtype +__bid_trunctdtf (_Decimal128 x) { + union float128 res; + union decimal128 ux; + + ux.d = x; + res.i = __bid128_to_binary128 (ux.i); + return (res.f); +} +#endif diff --git a/gcc-4.4.3/libgcc/config/libbid/_td_to_udi.c b/gcc-4.4.3/libgcc/config/libbid/_td_to_udi.c new file mode 100644 index 000000000..305f1a81f --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_td_to_udi.c @@ -0,0 +1,41 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +UDItype +__bid_fixunstddi (_Decimal128 x) { + UDItype res = 0xbaddbaddbaddbaddull; + union decimal128 ux; + + ux.d = x; + + res = __bid128_to_uint64_xint (ux.i); + + if (res == 0x8000000000000000ull) res = 0; // for NaNs too + return (res); +} + + diff --git a/gcc-4.4.3/libgcc/config/libbid/_td_to_usi.c b/gcc-4.4.3/libgcc/config/libbid/_td_to_usi.c new file mode 100644 index 000000000..9c69c6510 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_td_to_usi.c @@ -0,0 +1,40 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +USItype +__bid_fixunstdsi (_Decimal128 x) { + USItype res = 0xbaddbadd; + union decimal128 ux; + + ux.d = x; + res = __bid128_to_uint32_xint (ux.i); + + if (res == 0x80000000) res = 0; // for NaNs too + return (res); +} + + diff --git a/gcc-4.4.3/libgcc/config/libbid/_td_to_xf.c b/gcc-4.4.3/libgcc/config/libbid/_td_to_xf.c new file mode 100644 index 000000000..c57987396 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_td_to_xf.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +XFtype +__bid_trunctdxf (_Decimal128 x) { + XFtype res; + union decimal128 ux; + + ux.d = x; + res = __bid128_to_binary80 (ux.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_tf_to_dd.c b/gcc-4.4.3/libgcc/config/libbid/_tf_to_dd.c new file mode 100644 index 000000000..70686013a --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_tf_to_dd.c @@ -0,0 +1,38 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +#if LIBGCC2_HAS_TF_MODE || BID_HAS_TF_MODE +_Decimal64 +__bid_trunctfdd (TFtype x) { + union decimal64 res; + union float128 ux; + + ux.f = x; + res.i = __binary128_to_bid64 (ux.i); + return (res.d); +} +#endif diff --git a/gcc-4.4.3/libgcc/config/libbid/_tf_to_sd.c b/gcc-4.4.3/libgcc/config/libbid/_tf_to_sd.c new file mode 100644 index 000000000..c5462f6a5 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_tf_to_sd.c @@ -0,0 +1,38 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +#if LIBGCC2_HAS_TF_MODE || BID_HAS_TF_MODE +_Decimal32 +__bid_trunctfsd (TFtype x) { + union decimal32 res; + union float128 ux; + + ux.f = x; + res.i = __binary128_to_bid32 (ux.i); + return (res.d); +} +#endif diff --git a/gcc-4.4.3/libgcc/config/libbid/_tf_to_td.c b/gcc-4.4.3/libgcc/config/libbid/_tf_to_td.c new file mode 100644 index 000000000..df503ac54 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_tf_to_td.c @@ -0,0 +1,38 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +#if LIBGCC2_HAS_TF_MODE || BID_HAS_TF_MODE +_Decimal128 +__bid_extendtftd (TFtype x) { + union decimal128 res; + union float128 ux; + + ux.f = x; + res.i = __binary128_to_bid128 (ux.i); + return (res.d); +} +#endif diff --git a/gcc-4.4.3/libgcc/config/libbid/_udi_to_dd.c b/gcc-4.4.3/libgcc/config/libbid/_udi_to_dd.c new file mode 100644 index 000000000..166d13619 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_udi_to_dd.c @@ -0,0 +1,35 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal64 +__bid_floatunsdidd (UDItype x) { + union decimal64 res; + + res.i = __bid64_from_uint64 (x); + return (res.d); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_udi_to_sd.c b/gcc-4.4.3/libgcc/config/libbid/_udi_to_sd.c new file mode 100644 index 000000000..56873cf7d --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_udi_to_sd.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal32 +__bid_floatunsdisd (UDItype x) { + union decimal32 res; + UINT64 res64; + + res64 = __bid64_from_uint64 (x); + res.i = __bid64_to_bid32 (res64); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_udi_to_td.c b/gcc-4.4.3/libgcc/config/libbid/_udi_to_td.c new file mode 100644 index 000000000..dac5d8f10 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_udi_to_td.c @@ -0,0 +1,35 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal128 +__bid_floatunsditd (UDItype x) { + union decimal128 res; + + res.i = __bid128_from_uint64 (x); + return (res.d); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_unord_dd.c b/gcc-4.4.3/libgcc/config/libbid/_unord_dd.c new file mode 100644 index 000000000..8828edebc --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_unord_dd.c @@ -0,0 +1,37 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_unorddd2 (_Decimal64 x, _Decimal64 y) { + CMPtype res; + union decimal64 ux, uy; + + ux.d = x; + uy.d = y; + res = __bid64_quiet_unordered (ux.i, uy.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_unord_sd.c b/gcc-4.4.3/libgcc/config/libbid/_unord_sd.c new file mode 100644 index 000000000..c5595447d --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_unord_sd.c @@ -0,0 +1,41 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_unordsd2 (_Decimal32 x, _Decimal32 y) { + CMPtype res; + UINT64 x64, y64; + union decimal32 ux, uy; + + ux.d = x; + uy.d = y; + x64 = __bid32_to_bid64 (ux.i); + y64 = __bid32_to_bid64 (uy.i); + res = __bid64_quiet_unordered (x64, y64); + return (res); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_unord_td.c b/gcc-4.4.3/libgcc/config/libbid/_unord_td.c new file mode 100644 index 000000000..f45dceb8a --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_unord_td.c @@ -0,0 +1,37 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +CMPtype +__bid_unordtd2 (_Decimal128 x, _Decimal128 y) { + CMPtype res; + union decimal128 ux, uy; + + ux.d = x; + uy.d = y; + res = __bid128_quiet_unordered (ux.i, uy.i); + return (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_usi_to_dd.c b/gcc-4.4.3/libgcc/config/libbid/_usi_to_dd.c new file mode 100644 index 000000000..71796effd --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_usi_to_dd.c @@ -0,0 +1,35 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal64 +__bid_floatunssidd (USItype x) { + union decimal64 res; + + res.i = __bid64_from_uint32 (x); + return (res.d); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_usi_to_sd.c b/gcc-4.4.3/libgcc/config/libbid/_usi_to_sd.c new file mode 100644 index 000000000..42c0ac4e3 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_usi_to_sd.c @@ -0,0 +1,36 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal32 +__bid_floatunssisd (USItype x) { + union decimal32 res; + UINT64 res64; + + res64 = __bid64_from_uint32 (x); + res.i = __bid64_to_bid32 (res64); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_usi_to_td.c b/gcc-4.4.3/libgcc/config/libbid/_usi_to_td.c new file mode 100644 index 000000000..afc9087ad --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_usi_to_td.c @@ -0,0 +1,35 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal128 +__bid_floatunssitd (USItype x) { + union decimal128 res; + + res.i = __bid128_from_uint32 (x); + return (res.d); +} + diff --git a/gcc-4.4.3/libgcc/config/libbid/_xf_to_dd.c b/gcc-4.4.3/libgcc/config/libbid/_xf_to_dd.c new file mode 100644 index 000000000..f8ae78e98 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_xf_to_dd.c @@ -0,0 +1,33 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal64 +__bid_truncxfdd (XFtype x) { + union decimal64 res; + res.i = __binary80_to_bid64 (x); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_xf_to_sd.c b/gcc-4.4.3/libgcc/config/libbid/_xf_to_sd.c new file mode 100644 index 000000000..d5924fa1c --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_xf_to_sd.c @@ -0,0 +1,33 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal32 +__bid_truncxfsd (XFtype x) { + union decimal32 res; + res.i = __binary80_to_bid32 (x); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/_xf_to_td.c b/gcc-4.4.3/libgcc/config/libbid/_xf_to_td.c new file mode 100644 index 000000000..7d2f27842 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/_xf_to_td.c @@ -0,0 +1,33 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_conf.h" +#include "bid_functions.h" +#include "bid_gcc_intrinsics.h" + +_Decimal128 +__bid_extendxftd (XFtype x) { + union decimal128 res; + res.i = __binary80_to_bid128 (x); + return (res.d); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128.c b/gcc-4.4.3/libgcc/config/libbid/bid128.c new file mode 100644 index 000000000..617340962 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128.c @@ -0,0 +1,4333 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +// the first entry of nr_digits[i - 1] (where 1 <= i <= 113), indicates +// the number of decimal digits needed to represent a binary number with i bits; +// however, if a binary number of i bits may require either k or k + 1 decimal +// digits, then the first entry of nr_digits[i - 1] is 0; in this case if the +// number is less than the value represented by the second and third entries +// concatenated, then the number of decimal digits k is the fourth entry, else +// the number of decimal digits is the fourth entry plus 1 +DEC_DIGITS nr_digits[] = { // only the first entry is used if it is not 0 + {1, 0x0000000000000000ULL, 0x000000000000000aULL, 1} + , // 1-bit n < 10^1 + {1, 0x0000000000000000ULL, 0x000000000000000aULL, 1} + , // 2-bit n < 10^1 + {1, 0x0000000000000000ULL, 0x000000000000000aULL, 1} + , // 3-bit n < 10^1 + {0, 0x0000000000000000ULL, 0x000000000000000aULL, 1} + , // 4-bit n ? 10^1 + {2, 0x0000000000000000ULL, 0x0000000000000064ULL, 2} + , // 5-bit n < 10^2 + {2, 0x0000000000000000ULL, 0x0000000000000064ULL, 2} + , // 6-bit n < 10^2 + {0, 0x0000000000000000ULL, 0x0000000000000064ULL, 2} + , // 7-bit n ? 10^2 + {3, 0x0000000000000000ULL, 0x00000000000003e8ULL, 3} + , // 8-bit n < 10^3 + {3, 0x0000000000000000ULL, 0x00000000000003e8ULL, 3} + , // 9-bit n < 10^3 + {0, 0x0000000000000000ULL, 0x00000000000003e8ULL, 3} + , // 10-bit n ? 10^3 + {4, 0x0000000000000000ULL, 0x0000000000002710ULL, 4} + , // 11-bit n < 10^4 + {4, 0x0000000000000000ULL, 0x0000000000002710ULL, 4} + , // 12-bit n < 10^4 + {4, 0x0000000000000000ULL, 0x0000000000002710ULL, 4} + , // 13-bit n < 10^4 + {0, 0x0000000000000000ULL, 0x0000000000002710ULL, 4} + , // 14-bit n ? 10^4 + {5, 0x0000000000000000ULL, 0x00000000000186a0ULL, 5} + , // 15-bit n < 10^5 + {5, 0x0000000000000000ULL, 0x00000000000186a0ULL, 5} + , // 16-bit n < 10^5 + {0, 0x0000000000000000ULL, 0x00000000000186a0ULL, 5} + , // 17-bit n ? 10^5 + {6, 0x0000000000000000ULL, 0x00000000000f4240ULL, 6} + , // 18-bit n < 10^6 + {6, 0x0000000000000000ULL, 0x00000000000f4240ULL, 6} + , // 19-bit n < 10^6 + {0, 0x0000000000000000ULL, 0x00000000000f4240ULL, 6} + , // 20-bit n ? 10^6 + {7, 0x0000000000000000ULL, 0x0000000000989680ULL, 7} + , // 21-bit n < 10^7 + {7, 0x0000000000000000ULL, 0x0000000000989680ULL, 7} + , // 22-bit n < 10^7 + {7, 0x0000000000000000ULL, 0x0000000000989680ULL, 7} + , // 23-bit n < 10^7 + {0, 0x0000000000000000ULL, 0x0000000000989680ULL, 7} + , // 24-bit n ? 10^7 + {8, 0x0000000000000000ULL, 0x0000000005f5e100ULL, 8} + , // 25-bit n < 10^8 + {8, 0x0000000000000000ULL, 0x0000000005f5e100ULL, 8} + , // 26-bit n < 10^8 + {0, 0x0000000000000000ULL, 0x0000000005f5e100ULL, 8} + , // 27-bit n ? 10^8 + {9, 0x0000000000000000ULL, 0x000000003b9aca00ULL, 9} + , // 28-bit n < 10^9 + {9, 0x0000000000000000ULL, 0x000000003b9aca00ULL, 9} + , // 29-bit n < 10^9 + {0, 0x0000000000000000ULL, 0x000000003b9aca00ULL, 9} + , // 30-bit n ? 10^9 + {10, 0x0000000000000000ULL, 0x00000002540be400ULL, 10} + , // 31-bit n < 10^10 + {10, 0x0000000000000000ULL, 0x00000002540be400ULL, 10} + , // 32-bit n < 10^10 + {10, 0x0000000000000000ULL, 0x00000002540be400ULL, 10} + , // 33-bit n < 10^10 + {0, 0x0000000000000000ULL, 0x00000002540be400ULL, 10} + , // 34-bit n ? 10^10 + {11, 0x0000000000000000ULL, 0x000000174876e800ULL, 11} + , // 35-bit n < 10^11 + {11, 0x0000000000000000ULL, 0x000000174876e800ULL, 11} + , // 36-bit n < 10^11 + {0, 0x0000000000000000ULL, 0x000000174876e800ULL, 11} + , // 37-bit n ? 10^11 + {12, 0x0000000000000000ULL, 0x000000e8d4a51000ULL, 12} + , // 38-bit n < 10^12 + {12, 0x0000000000000000ULL, 0x000000e8d4a51000ULL, 12} + , // 39-bit n < 10^12 + {0, 0x0000000000000000ULL, 0x000000e8d4a51000ULL, 12} + , // 40-bit n ? 10^12 + {13, 0x0000000000000000ULL, 0x000009184e72a000ULL, 13} + , // 41-bit n < 10^13 + {13, 0x0000000000000000ULL, 0x000009184e72a000ULL, 13} + , // 42-bit n < 10^13 + {13, 0x0000000000000000ULL, 0x000009184e72a000ULL, 13} + , // 43-bit n < 10^13 + {0, 0x0000000000000000ULL, 0x000009184e72a000ULL, 13} + , // 44-bit n ? 10^13 + {14, 0x0000000000000000ULL, 0x00005af3107a4000ULL, 14} + , // 45-bit n < 10^14 + {14, 0x0000000000000000ULL, 0x00005af3107a4000ULL, 14} + , // 46-bit n < 10^14 + {0, 0x0000000000000000ULL, 0x00005af3107a4000ULL, 14} + , // 47-bit n ? 10^14 + {15, 0x0000000000000000ULL, 0x00038d7ea4c68000ULL, 15} + , // 48-bit n < 10^15 + {15, 0x0000000000000000ULL, 0x00038d7ea4c68000ULL, 15} + , // 49-bit n < 10^15 + {0, 0x0000000000000000ULL, 0x00038d7ea4c68000ULL, 15} + , // 50-bit n ? 10^15 + {16, 0x0000000000000000ULL, 0x002386f26fc10000ULL, 16} + , // 51-bit n < 10^16 + {16, 0x0000000000000000ULL, 0x002386f26fc10000ULL, 16} + , // 52-bit n < 10^16 + {16, 0x0000000000000000ULL, 0x002386f26fc10000ULL, 16} + , // 53-bit n < 10^16 + {0, 0x0000000000000000ULL, 0x002386f26fc10000ULL, 16} + , // 54-bit n ? 10^16 + {17, 0x0000000000000000ULL, 0x016345785d8a0000ULL, 17} + , // 55-bit n < 10^17 + {17, 0x0000000000000000ULL, 0x016345785d8a0000ULL, 17} + , // 56-bit n < 10^17 + {0, 0x0000000000000000ULL, 0x016345785d8a0000ULL, 17} + , // 57-bit n ? 10^17 + {18, 0x0000000000000000ULL, 0x0de0b6b3a7640000ULL, 18} + , // 58-bit n < 10^18 + {18, 0x0000000000000000ULL, 0x0de0b6b3a7640000ULL, 18} + , // 59-bit n < 10^18 + {0, 0x0000000000000000ULL, 0x0de0b6b3a7640000ULL, 18} + , // 60-bit n ? 10^18 + {19, 0x0000000000000000ULL, 0x8ac7230489e80000ULL, 19} + , // 61-bit n < 10^19 + {19, 0x0000000000000000ULL, 0x8ac7230489e80000ULL, 19} + , // 62-bit n < 10^19 + {19, 0x0000000000000000ULL, 0x8ac7230489e80000ULL, 19} + , // 63-bit n < 10^19 + {0, 0x0000000000000000ULL, 0x8ac7230489e80000ULL, 19} + , // 64-bit n ? 10^19 + {20, 0x0000000000000005ULL, 0x6bc75e2d63100000ULL, 20} + , // 65-bit n < 10^20 + {20, 0x0000000000000005ULL, 0x6bc75e2d63100000ULL, 20} + , // 66-bit n < 10^20 + {0, 0x0000000000000005ULL, 0x6bc75e2d63100000ULL, 20} + , // 67-bit n ? 10^20 + {21, 0x0000000000000036ULL, 0x35c9adc5dea00000ULL, 21} + , // 68-bit n < 10^21 + {21, 0x0000000000000036ULL, 0x35c9adc5dea00000ULL, 21} + , // 69-bit n < 10^21 + {0, 0x0000000000000036ULL, 0x35c9adc5dea00000ULL, 21} + , // 70-bit n ? 10^21 + {22, 0x000000000000021eULL, 0x19e0c9bab2400000ULL, 22} + , // 71-bit n < 10^22 + {22, 0x000000000000021eULL, 0x19e0c9bab2400000ULL, 22} + , // 72-bit n < 10^22 + {22, 0x000000000000021eULL, 0x19e0c9bab2400000ULL, 22} + , // 73-bit n < 10^22 + {0, 0x000000000000021eULL, 0x19e0c9bab2400000ULL, 22} + , // 74-bit n ? 10^22 + {23, 0x000000000000152dULL, 0x02c7e14af6800000ULL, 23} + , // 75-bit n < 10^23 + {23, 0x000000000000152dULL, 0x02c7e14af6800000ULL, 23} + , // 76-bit n < 10^23 + {0, 0x000000000000152dULL, 0x02c7e14af6800000ULL, 23} + , // 77-bit n ? 10^23 + {24, 0x000000000000d3c2ULL, 0x1bcecceda1000000ULL, 24} + , // 78-bit n < 10^24 + {24, 0x000000000000d3c2ULL, 0x1bcecceda1000000ULL, 24} + , // 79-bit n < 10^24 + {0, 0x000000000000d3c2ULL, 0x1bcecceda1000000ULL, 24} + , // 80-bit n ? 10^24 + {25, 0x0000000000084595ULL, 0x161401484a000000ULL, 25} + , // 81-bit n < 10^25 + {25, 0x0000000000084595ULL, 0x161401484a000000ULL, 25} + , // 82-bit n < 10^25 + {25, 0x0000000000084595ULL, 0x161401484a000000ULL, 25} + , // 83-bit n < 10^25 + {0, 0x0000000000084595ULL, 0x161401484a000000ULL, 25} + , // 84-bit n ? 10^25 + {26, 0x000000000052b7d2ULL, 0xdcc80cd2e4000000ULL, 26} + , // 85-bit n < 10^26 + {26, 0x000000000052b7d2ULL, 0xdcc80cd2e4000000ULL, 26} + , // 86-bit n < 10^26 + {0, 0x000000000052b7d2ULL, 0xdcc80cd2e4000000ULL, 26} + , // 87-bit n ? 10^26 + {27, 0x00000000033b2e3cULL, 0x9fd0803ce8000000ULL, 27} + , // 88-bit n < 10^27 + {27, 0x00000000033b2e3cULL, 0x9fd0803ce8000000ULL, 27} + , // 89-bit n < 10^27 + {0, 0x00000000033b2e3cULL, 0x9fd0803ce8000000ULL, 27} + , // 90-bit n ? 10^27 + {28, 0x00000000204fce5eULL, 0x3e25026110000000ULL, 28} + , // 91-bit n < 10^28 + {28, 0x00000000204fce5eULL, 0x3e25026110000000ULL, 28} + , // 92-bit n < 10^28 + {28, 0x00000000204fce5eULL, 0x3e25026110000000ULL, 28} + , // 93-bit n < 10^28 + {0, 0x00000000204fce5eULL, 0x3e25026110000000ULL, 28} + , // 94-bit n ? 10^28 + {29, 0x00000001431e0faeULL, 0x6d7217caa0000000ULL, 29} + , // 95-bit n < 10^29 + {29, 0x00000001431e0faeULL, 0x6d7217caa0000000ULL, 29} + , // 96-bit n < 10^29 + {0, 0x00000001431e0faeULL, 0x6d7217caa0000000ULL, 29} + , // 97-bit n ? 10^29 + {30, 0x0000000c9f2c9cd0ULL, 0x4674edea40000000ULL, 30} + , // 98-bit n < 10^30 + {30, 0x0000000c9f2c9cd0ULL, 0x4674edea40000000ULL, 30} + , // 99-bit n < 10^30 + {0, 0x0000000c9f2c9cd0ULL, 0x4674edea40000000ULL, 30} + , // 100-bit n ? 10^30 + {31, 0x0000007e37be2022ULL, 0xc0914b2680000000ULL, 31} + , // 101-bit n < 10^31 + {31, 0x0000007e37be2022ULL, 0xc0914b2680000000ULL, 31} + , // 102-bit n < 10^31 + {0, 0x0000007e37be2022ULL, 0xc0914b2680000000ULL, 31} + , // 103-bit n ? 10^31 + {32, 0x000004ee2d6d415bULL, 0x85acef8100000000ULL, 32} + , // 104-bit n < 10^32 + {32, 0x000004ee2d6d415bULL, 0x85acef8100000000ULL, 32} + , // 105-bit n < 10^32 + {32, 0x000004ee2d6d415bULL, 0x85acef8100000000ULL, 32} + , // 106-bit n < 10^32 + {0, 0x000004ee2d6d415bULL, 0x85acef8100000000ULL, 32} + , // 107-bit n ? 10^32 + {33, 0x0000314dc6448d93ULL, 0x38c15b0a00000000ULL, 33} + , // 108-bit n < 10^33 + {33, 0x0000314dc6448d93ULL, 0x38c15b0a00000000ULL, 33} + , // 109-bit n < 10^33 + {0, 0x0000314dc6448d93ULL, 0x38c15b0a00000000ULL, 33} + , // 100-bit n ? 10^33 + {34, 0x0001ed09bead87c0ULL, 0x378d8e6400000000ULL, 34} + , // 111-bit n < 10^34 + {34, 0x0001ed09bead87c0ULL, 0x378d8e6400000000ULL, 34} + , // 112-bit n < 10^34 + {0, 0x0001ed09bead87c0ULL, 0x378d8e6400000000ULL, 34} // 113-bit n ? 10^34 +//{ 35, 0x0013426172c74d82ULL, 0x2b878fe800000000ULL, 35 } // 114-bit n < 10^35 +}; + +// midpoint64[i - 1] = 1/2 * 10^i = 5 * 10^(i-1), 1 <= i <= 19 +UINT64 midpoint64[] = { + 0x0000000000000005ULL, // 1/2 * 10^1 = 5 * 10^0 + 0x0000000000000032ULL, // 1/2 * 10^2 = 5 * 10^1 + 0x00000000000001f4ULL, // 1/2 * 10^3 = 5 * 10^2 + 0x0000000000001388ULL, // 1/2 * 10^4 = 5 * 10^3 + 0x000000000000c350ULL, // 1/2 * 10^5 = 5 * 10^4 + 0x000000000007a120ULL, // 1/2 * 10^6 = 5 * 10^5 + 0x00000000004c4b40ULL, // 1/2 * 10^7 = 5 * 10^6 + 0x0000000002faf080ULL, // 1/2 * 10^8 = 5 * 10^7 + 0x000000001dcd6500ULL, // 1/2 * 10^9 = 5 * 10^8 + 0x000000012a05f200ULL, // 1/2 * 10^10 = 5 * 10^9 + 0x0000000ba43b7400ULL, // 1/2 * 10^11 = 5 * 10^10 + 0x000000746a528800ULL, // 1/2 * 10^12 = 5 * 10^11 + 0x0000048c27395000ULL, // 1/2 * 10^13 = 5 * 10^12 + 0x00002d79883d2000ULL, // 1/2 * 10^14 = 5 * 10^13 + 0x0001c6bf52634000ULL, // 1/2 * 10^15 = 5 * 10^14 + 0x0011c37937e08000ULL, // 1/2 * 10^16 = 5 * 10^15 + 0x00b1a2bc2ec50000ULL, // 1/2 * 10^17 = 5 * 10^16 + 0x06f05b59d3b20000ULL, // 1/2 * 10^18 = 5 * 10^17 + 0x4563918244f40000ULL // 1/2 * 10^19 = 5 * 10^18 +}; + +// midpoint128[i - 20] = 1/2 * 10^i = 5 * 10^(i-1), 20 <= i <= 38 +UINT128 midpoint128[] = { // the 64-bit word order is L, H + {{0xb5e3af16b1880000ULL, 0x0000000000000002ULL} + } + , // 1/2 * 10^20 = 5 * 10^19 + {{0x1ae4d6e2ef500000ULL, 0x000000000000001bULL} + } + , // 1/2 * 10^21 = 5 * 10^20 + {{0x0cf064dd59200000ULL, 0x000000000000010fULL} + } + , // 1/2 * 10^22 = 5 * 10^21 + {{0x8163f0a57b400000ULL, 0x0000000000000a96ULL} + } + , // 1/2 * 10^23 = 5 * 10^22 + {{0x0de76676d0800000ULL, 0x00000000000069e1ULL} + } + , // 1/2 * 10^24 = 5 * 10^23 + {{0x8b0a00a425000000ULL, 0x00000000000422caULL} + } + , // 1/2 * 10^25 = 5 * 10^24 + {{0x6e64066972000000ULL, 0x0000000000295be9ULL} + } + , // 1/2 * 10^26 = 5 * 10^25 + {{0x4fe8401e74000000ULL, 0x00000000019d971eULL} + } + , // 1/2 * 10^27 = 5 * 10^26 + {{0x1f12813088000000ULL, 0x000000001027e72fULL} + } + , // 1/2 * 10^28 = 5 * 10^27 + {{0x36b90be550000000ULL, 0x00000000a18f07d7ULL} + } + , // 1/2 * 10^29 = 5 * 10^28 + {{0x233a76f520000000ULL, 0x000000064f964e68ULL} + } + , // 1/2 * 10^30 = 5 * 10^29 + {{0x6048a59340000000ULL, 0x0000003f1bdf1011ULL} + } + , // 1/2 * 10^31 = 5 * 10^30 + {{0xc2d677c080000000ULL, 0x0000027716b6a0adULL} + } + , // 1/2 * 10^32 = 5 * 10^31 + {{0x9c60ad8500000000ULL, 0x000018a6e32246c9ULL} + } + , // 1/2 * 10^33 = 5 * 10^32 + {{0x1bc6c73200000000ULL, 0x0000f684df56c3e0ULL} + } + , // 1/2 * 10^34 = 5 * 10^33 + {{0x15c3c7f400000000ULL, 0x0009a130b963a6c1ULL} + } + , // 1/2 * 10^35 = 5 * 10^34 + {{0xd9a5cf8800000000ULL, 0x00604be73de4838aULL} + } + , // 1/2 * 10^36 = 5 * 10^35 + {{0x807a1b5000000000ULL, 0x03c2f7086aed236cULL} + } + , // 1/2 * 10^37 = 5 * 10^36 + {{0x04c5112000000000ULL, 0x259da6542d43623dULL} + } // 1/2 * 10^38 = 5 * 10^37 +}; + +// midpoint192[i - 39] = 1/2 * 10^i = 5 * 10^(i-1), 39 <= i <= 58 +UINT192 midpoint192[] = { // the 64-bit word order is L, M, H + {{0x2fb2ab4000000000ULL, 0x78287f49c4a1d662ULL, 0x0000000000000001ULL} + } + , + // 1/2 * 10^39 = 5 * 10^38 + {{0xdcfab08000000000ULL, 0xb194f8e1ae525fd5ULL, 0x000000000000000eULL} + } + , + // 1/2 * 10^40 = 5 * 10^39 + {{0xa1cae50000000000ULL, 0xefd1b8d0cf37be5aULL, 0x0000000000000092ULL} + } + , + // 1/2 * 10^41 = 5 * 10^40 + {{0x51ecf20000000000ULL, 0x5e313828182d6f8aULL, 0x00000000000005bdULL} + } + , + // 1/2 * 10^42 = 5 * 10^41 + {{0x3341740000000000ULL, 0xadec3190f1c65b67ULL, 0x0000000000003965ULL} + } + , + // 1/2 * 10^43 = 5 * 10^42 + {{0x008e880000000000ULL, 0xcb39efa971bf9208ULL, 0x0000000000023df8ULL} + } + , + // 1/2 * 10^44 = 5 * 10^43 + {{0x0591500000000000ULL, 0xf0435c9e717bb450ULL, 0x0000000000166bb7ULL} + } + , + // 1/2 * 10^45 = 5 * 10^44 + {{0x37ad200000000000ULL, 0x62a19e306ed50b20ULL, 0x0000000000e0352fULL} + } + , + // 1/2 * 10^46 = 5 * 10^45 + {{0x2cc3400000000000ULL, 0xda502de454526f42ULL, 0x0000000008c213d9ULL} + } + , + // 1/2 * 10^47 = 5 * 10^46 + {{0xbfa0800000000000ULL, 0x8721caeb4b385895ULL, 0x000000005794c682ULL} + } + , + // 1/2 * 10^48 = 5 * 10^47 + {{0x7c45000000000000ULL, 0x4751ed30f03375d9ULL, 0x000000036bcfc119ULL} + } + , + // 1/2 * 10^49 = 5 * 10^48 + {{0xdab2000000000000ULL, 0xc93343e962029a7eULL, 0x00000022361d8afcULL} + } + , + // 1/2 * 10^50 = 5 * 10^49 + {{0x8af4000000000000ULL, 0xdc00a71dd41a08f4ULL, 0x000001561d276ddfULL} + } + , + // 1/2 * 10^51 = 5 * 10^50 + {{0x6d88000000000000ULL, 0x9806872a4904598dULL, 0x00000d5d238a4abeULL} + } + , + // 1/2 * 10^52 = 5 * 10^51 + {{0x4750000000000000ULL, 0xf04147a6da2b7f86ULL, 0x000085a36366eb71ULL} + } + , + // 1/2 * 10^53 = 5 * 10^52 + {{0xc920000000000000ULL, 0x628ccc8485b2fb3eULL, 0x00053861e2053273ULL} + } + , + // 1/2 * 10^54 = 5 * 10^53 + {{0xdb40000000000000ULL, 0xd97ffd2d38fdd073ULL, 0x003433d2d433f881ULL} + } + , + // 1/2 * 10^55 = 5 * 10^54 + {{0x9080000000000000ULL, 0x7effe3c439ea2486ULL, 0x020a063c4a07b512ULL} + } + , + // 1/2 * 10^56 = 5 * 10^55 + {{0xa500000000000000ULL, 0xf5fee5aa43256d41ULL, 0x14643e5ae44d12b8ULL} + } + , + // 1/2 * 10^57 = 5 * 10^56 + {{0x7200000000000000ULL, 0x9bf4f8a69f764490ULL, 0xcbea6f8ceb02bb39ULL} + } + // 1/2 * 10^58 = 5 * 10^57 +}; + +// midpoint256[i - 59] = 1/2 * 10^i = 5 * 10^(i-1), 59 <= i <= 68 +UINT256 midpoint256[] = { // the 64-bit word order is LL, LH, HL, HH + {{0x7400000000000000ULL, 0x1791b6823a9eada4ULL, + 0xf7285b812e1b5040ULL, 0x0000000000000007ULL} + } + , // 1/2 * 10^59 = 5 * 10^58 + {{0x8800000000000000ULL, 0xebb121164a32c86cULL, + 0xa793930bcd112280ULL, 0x000000000000004fULL} + } + , // 1/2 * 10^60 = 5 * 10^59 + {{0x5000000000000000ULL, 0x34eb4adee5fbd43dULL, + 0x8bc3be7602ab5909ULL, 0x000000000000031cULL} + } + , // 1/2 * 10^61 = 5 * 10^60 + {{0x2000000000000000ULL, 0x1130ecb4fbd64a65ULL, + 0x75a5709c1ab17a5cULL, 0x0000000000001f1dULL} + } + , // 1/2 * 10^62 = 5 * 10^61 + {{0x4000000000000000ULL, 0xabe93f11d65ee7f3ULL, + 0x987666190aeec798ULL, 0x0000000000013726ULL} + } + , // 1/2 * 10^63 = 5 * 10^62 + {{0x8000000000000000ULL, 0xb71c76b25fb50f80ULL, + 0xf49ffcfa6d53cbf6ULL, 0x00000000000c2781ULL} + } + , // 1/2 * 10^64 = 5 * 10^63 + {{0x0000000000000000ULL, 0x271ca2f7bd129b05ULL, + 0x8e3fe1c84545f7a3ULL, 0x0000000000798b13ULL} + } + , // 1/2 * 10^65 = 5 * 10^64 + {{0x0000000000000000ULL, 0x871e5dad62ba0e32ULL, + 0x8e7ed1d2b4bbac5fULL, 0x0000000004bf6ec3ULL} + } + , // 1/2 * 10^66 = 5 * 10^65 + {{0x0000000000000000ULL, 0x472fa8c5db448df4ULL, + 0x90f4323b0f54bbbbULL, 0x000000002f7a53a3ULL} + } + , // 1/2 * 10^67 = 5 * 10^66 + {{0x0000000000000000ULL, 0xc7dc97ba90ad8b88ULL, + 0xa989f64e994f5550ULL, 0x00000001dac74463ULL} + } + , // 1/2 * 10^68 = 5 * 10^67 + {{0x0000000000000000ULL, 0xce9ded49a6c77350ULL, + 0x9f639f11fd195527ULL, 0x000000128bc8abe4ULL} + } + , // 1/2 * 10^69 = 5 * 10^68 + {{0x0000000000000000ULL, 0x122b44e083ca8120ULL, + 0x39e436b3e2fd538eULL, 0x000000b975d6b6eeULL} + } + , // 1/2 * 10^70 = 5 * 10^69 + {{0x0000000000000000ULL, 0xb5b0b0c525e90b40ULL, + 0x42ea2306dde5438cULL, 0x0000073e9a63254eULL} + } + , // 1/2 * 10^71 = 5 * 10^70 + {{0x0000000000000000ULL, 0x18e6e7b37b1a7080ULL, + 0x9d255e44aaf4a37fULL, 0x0000487207df750eULL} + } + , // 1/2 * 10^72 = 5 * 10^71 + {{0x0000000000000000ULL, 0xf9050d02cf086500ULL, + 0x2375aeaead8e62f6ULL, 0x0002d4744eba9292ULL} + } + , // 1/2 * 10^73 = 5 * 10^72 + {{0x0000000000000000ULL, 0xba32821c1653f200ULL, + 0x6298d2d2c78fdda5ULL, 0x001c4c8b1349b9b5ULL} + } + , // 1/2 * 10^74 = 5 * 10^73 + {{0x0000000000000000ULL, 0x45f91518df477400ULL, + 0xd9f83c3bcb9ea879ULL, 0x011afd6ec0e14115ULL} + } + , // 1/2 * 10^75 = 5 * 10^74 + {{0x0000000000000000ULL, 0xbbbad2f8b8ca8800ULL, + 0x83b25a55f43294bcULL, 0x0b0de65388cc8adaULL} + } + , // 1/2 * 10^76 = 5 * 10^75 + {{0x0000000000000000ULL, 0x554c3db737e95000ULL, + 0x24f7875b89f9cf5fULL, 0x6e8aff4357fd6c89ULL} + } // 1/2 * 10^77 = 5 * 10^76 +}; + +// ten2k64[i] = 10^i, 0 <= i <= 19 +UINT64 ten2k64[] = { + 0x0000000000000001ULL, // 10^0 + 0x000000000000000aULL, // 10^1 + 0x0000000000000064ULL, // 10^2 + 0x00000000000003e8ULL, // 10^3 + 0x0000000000002710ULL, // 10^4 + 0x00000000000186a0ULL, // 10^5 + 0x00000000000f4240ULL, // 10^6 + 0x0000000000989680ULL, // 10^7 + 0x0000000005f5e100ULL, // 10^8 + 0x000000003b9aca00ULL, // 10^9 + 0x00000002540be400ULL, // 10^10 + 0x000000174876e800ULL, // 10^11 + 0x000000e8d4a51000ULL, // 10^12 + 0x000009184e72a000ULL, // 10^13 + 0x00005af3107a4000ULL, // 10^14 + 0x00038d7ea4c68000ULL, // 10^15 + 0x002386f26fc10000ULL, // 10^16 + 0x016345785d8a0000ULL, // 10^17 + 0x0de0b6b3a7640000ULL, // 10^18 + 0x8ac7230489e80000ULL // 10^19 (20 digits) +}; + + +// ten2k128[i - 20] = 10^i, 20 <= i <= 38 +UINT128 ten2k128[] = { // the 64-bit word order is L, H + {{0x6bc75e2d63100000ULL, 0x0000000000000005ULL} + } + , // 10^20 + {{0x35c9adc5dea00000ULL, 0x0000000000000036ULL} + } + , // 10^21 + {{0x19e0c9bab2400000ULL, 0x000000000000021eULL} + } + , // 10^22 + {{0x02c7e14af6800000ULL, 0x000000000000152dULL} + } + , // 10^23 + {{0x1bcecceda1000000ULL, 0x000000000000d3c2ULL} + } + , // 10^24 + {{0x161401484a000000ULL, 0x0000000000084595ULL} + } + , // 10^25 + {{0xdcc80cd2e4000000ULL, 0x000000000052b7d2ULL} + } + , // 10^26 + {{0x9fd0803ce8000000ULL, 0x00000000033b2e3cULL} + } + , // 10^27 + {{0x3e25026110000000ULL, 0x00000000204fce5eULL} + } + , // 10^28 + {{0x6d7217caa0000000ULL, 0x00000001431e0faeULL} + } + , // 10^29 + {{0x4674edea40000000ULL, 0x0000000c9f2c9cd0ULL} + } + , // 10^30 + {{0xc0914b2680000000ULL, 0x0000007e37be2022ULL} + } + , // 10^31 + {{0x85acef8100000000ULL, 0x000004ee2d6d415bULL} + } + , // 10^32 + {{0x38c15b0a00000000ULL, 0x0000314dc6448d93ULL} + } + , // 10^33 + {{0x378d8e6400000000ULL, 0x0001ed09bead87c0ULL} + } + , // 10^34 + {{0x2b878fe800000000ULL, 0x0013426172c74d82ULL} + } + , // 10^35 + {{0xb34b9f1000000000ULL, 0x00c097ce7bc90715ULL} + } + , // 10^36 + {{0x00f436a000000000ULL, 0x0785ee10d5da46d9ULL} + } + , // 10^37 + {{0x098a224000000000ULL, 0x4b3b4ca85a86c47aULL} + } // 10^38 (39 digits) +}; + +// might split into ten2k192[] and ten2k256[] + +// ten2k256[i - 39] = 10^i, 39 <= i <= 68 +UINT256 ten2k256[] = { // the 64-bit word order is LL, LH, HL, HH + {{0x5f65568000000000ULL, 0xf050fe938943acc4ULL, + 0x0000000000000002ULL, 0x0000000000000000ULL} + } + , // 10^39 + {{0xb9f5610000000000ULL, 0x6329f1c35ca4bfabULL, + 0x000000000000001dULL, 0x0000000000000000ULL} + } + , // 10^40 + {{0x4395ca0000000000ULL, 0xdfa371a19e6f7cb5ULL, + 0x0000000000000125ULL, 0x0000000000000000ULL} + } + , // 10^41 + {{0xa3d9e40000000000ULL, 0xbc627050305adf14ULL, + 0x0000000000000b7aULL, 0x0000000000000000ULL} + } + , // 10^42 + {{0x6682e80000000000ULL, 0x5bd86321e38cb6ceULL, + 0x00000000000072cbULL, 0x0000000000000000ULL} + } + , // 10^43 + {{0x011d100000000000ULL, 0x9673df52e37f2410ULL, + 0x0000000000047bf1ULL, 0x0000000000000000ULL} + } + , // 10^44 + {{0x0b22a00000000000ULL, 0xe086b93ce2f768a0ULL, + 0x00000000002cd76fULL, 0x0000000000000000ULL} + } + , // 10^45 + {{0x6f5a400000000000ULL, 0xc5433c60ddaa1640ULL, + 0x0000000001c06a5eULL, 0x0000000000000000ULL} + } + , // 10^46 + {{0x5986800000000000ULL, 0xb4a05bc8a8a4de84ULL, + 0x00000000118427b3ULL, 0x0000000000000000ULL} + } + , // 10^47 + {{0x7f41000000000000ULL, 0x0e4395d69670b12bULL, + 0x00000000af298d05ULL, 0x0000000000000000ULL} + } + , // 10^48 + {{0xf88a000000000000ULL, 0x8ea3da61e066ebb2ULL, + 0x00000006d79f8232ULL, 0x0000000000000000ULL} + } + , // 10^49 + {{0xb564000000000000ULL, 0x926687d2c40534fdULL, + 0x000000446c3b15f9ULL, 0x0000000000000000ULL} + } + , // 10^50 + {{0x15e8000000000000ULL, 0xb8014e3ba83411e9ULL, + 0x000002ac3a4edbbfULL, 0x0000000000000000ULL} + } + , // 10^51 + {{0xdb10000000000000ULL, 0x300d0e549208b31aULL, + 0x00001aba4714957dULL, 0x0000000000000000ULL} + } + , // 10^52 + {{0x8ea0000000000000ULL, 0xe0828f4db456ff0cULL, + 0x00010b46c6cdd6e3ULL, 0x0000000000000000ULL} + } + , // 10^53 + {{0x9240000000000000ULL, 0xc51999090b65f67dULL, + 0x000a70c3c40a64e6ULL, 0x0000000000000000ULL} + } + , // 10^54 + {{0xb680000000000000ULL, 0xb2fffa5a71fba0e7ULL, + 0x006867a5a867f103ULL, 0x0000000000000000ULL} + } + , // 10^55 + {{0x2100000000000000ULL, 0xfdffc78873d4490dULL, + 0x04140c78940f6a24ULL, 0x0000000000000000ULL} + } + , // 10^56 + {{0x4a00000000000000ULL, 0xebfdcb54864ada83ULL, + 0x28c87cb5c89a2571ULL, 0x0000000000000000ULL} + } + , // 10^57 (58 digits) + {{0xe400000000000000ULL, 0x37e9f14d3eec8920ULL, + 0x97d4df19d6057673ULL, 0x0000000000000001ULL} + } + , // 10^58 + {{0xe800000000000000ULL, 0x2f236d04753d5b48ULL, + 0xee50b7025c36a080ULL, 0x000000000000000fULL} + } + , // 10^59 + {{0x1000000000000000ULL, 0xd762422c946590d9ULL, + 0x4f2726179a224501ULL, 0x000000000000009fULL} + } + , // 10^60 + {{0xa000000000000000ULL, 0x69d695bdcbf7a87aULL, + 0x17877cec0556b212ULL, 0x0000000000000639ULL} + } + , // 10^61 + {{0x4000000000000000ULL, 0x2261d969f7ac94caULL, + 0xeb4ae1383562f4b8ULL, 0x0000000000003e3aULL} + } + , // 10^62 + {{0x8000000000000000ULL, 0x57d27e23acbdcfe6ULL, + 0x30eccc3215dd8f31ULL, 0x0000000000026e4dULL} + } + , // 10^63 + {{0x0000000000000000ULL, 0x6e38ed64bf6a1f01ULL, + 0xe93ff9f4daa797edULL, 0x0000000000184f03ULL} + } + , // 10^64 + {{0x0000000000000000ULL, 0x4e3945ef7a25360aULL, + 0x1c7fc3908a8bef46ULL, 0x0000000000f31627ULL} + } + , // 10^65 + {{0x0000000000000000ULL, 0x0e3cbb5ac5741c64ULL, + 0x1cfda3a5697758bfULL, 0x00000000097edd87ULL} + } + , // 10^66 + {{0x0000000000000000ULL, 0x8e5f518bb6891be8ULL, + 0x21e864761ea97776ULL, 0x000000005ef4a747ULL} + } + , // 10^67 + {{0x0000000000000000ULL, 0x8fb92f75215b1710ULL, + 0x5313ec9d329eaaa1ULL, 0x00000003b58e88c7ULL} + } + , // 10^68 + {{0x0000000000000000ULL, 0x9d3bda934d8ee6a0ULL, + 0x3ec73e23fa32aa4fULL, 0x00000025179157c9ULL} + } + , // 10^69 + {{0x0000000000000000ULL, 0x245689c107950240ULL, + 0x73c86d67c5faa71cULL, 0x00000172ebad6ddcULL} + } + , // 10^70 + {{0x0000000000000000ULL, 0x6b61618a4bd21680ULL, + 0x85d4460dbbca8719ULL, 0x00000e7d34c64a9cULL} + } + , // 10^71 + {{0x0000000000000000ULL, 0x31cdcf66f634e100ULL, + 0x3a4abc8955e946feULL, 0x000090e40fbeea1dULL} + } + , // 10^72 + {{0x0000000000000000ULL, 0xf20a1a059e10ca00ULL, + 0x46eb5d5d5b1cc5edULL, 0x0005a8e89d752524ULL} + } + , // 10^73 + {{0x0000000000000000ULL, 0x746504382ca7e400ULL, + 0xc531a5a58f1fbb4bULL, 0x003899162693736aULL} + } + , // 10^74 + {{0x0000000000000000ULL, 0x8bf22a31be8ee800ULL, + 0xb3f07877973d50f2ULL, 0x0235fadd81c2822bULL} + } + , // 10^75 + {{0x0000000000000000ULL, 0x7775a5f171951000ULL, + 0x0764b4abe8652979ULL, 0x161bcca7119915b5ULL} + } + , // 10^76 + {{0x0000000000000000ULL, 0xaa987b6e6fd2a000ULL, + 0x49ef0eb713f39ebeULL, 0xdd15fe86affad912ULL} + } // 10^77 +}; + +// ten2mk128[k - 1] = 10^(-k) * 2^exp (k), where 1 <= k <= 34 and +// exp (k) = shiftright128[k - 1] + 128 +UINT128 ten2mk128[] = { + {{0x999999999999999aULL, 0x1999999999999999ULL} + } + , // 10^(-1) * 2^128 + {{0x28f5c28f5c28f5c3ULL, 0x028f5c28f5c28f5cULL} + } + , // 10^(-2) * 2^128 + {{0x9db22d0e56041894ULL, 0x004189374bc6a7efULL} + } + , // 10^(-3) * 2^128 + {{0x4af4f0d844d013aaULL, 0x00346dc5d6388659ULL} + } + , // 10^(-4) * 2^131 + {{0x08c3f3e0370cdc88ULL, 0x0029f16b11c6d1e1ULL} + } + , // 10^(-5) * 2^134 + {{0x6d698fe69270b06dULL, 0x00218def416bdb1aULL} + } + , // 10^(-6) * 2^137 + {{0xaf0f4ca41d811a47ULL, 0x0035afe535795e90ULL} + } + , // 10^(-7) * 2^141 + {{0xbf3f70834acdaea0ULL, 0x002af31dc4611873ULL} + } + , // 10^(-8) * 2^144 + {{0x65cc5a02a23e254dULL, 0x00225c17d04dad29ULL} + } + , // 10^(-9) * 2^147 + {{0x6fad5cd10396a214ULL, 0x0036f9bfb3af7b75ULL} + } + , // 10^(-10) * 2^151 + {{0xbfbde3da69454e76ULL, 0x002bfaffc2f2c92aULL} + } + , // 10^(-11) * 2^154 + {{0x32fe4fe1edd10b92ULL, 0x00232f33025bd422ULL} + } + , // 10^(-12) * 2^157 + {{0x84ca19697c81ac1cULL, 0x00384b84d092ed03ULL} + } + , // 10^(-13) * 2^161 + {{0x03d4e1213067bce4ULL, 0x002d09370d425736ULL} + } + , // 10^(-14) * 2^164 + {{0x3643e74dc052fd83ULL, 0x0024075f3dceac2bULL} + } + , // 10^(-15) * 2^167 + {{0x56d30baf9a1e626bULL, 0x0039a5652fb11378ULL} + } + , // 10^(-16) * 2^171 + {{0x12426fbfae7eb522ULL, 0x002e1dea8c8da92dULL} + } + , // 10^(-17) * 2^174 + {{0x41cebfcc8b9890e8ULL, 0x0024e4bba3a48757ULL} + } + , // 10^(-18) * 2^177 + {{0x694acc7a78f41b0dULL, 0x003b07929f6da558ULL} + } + , // 10^(-19) * 2^181 + {{0xbaa23d2ec729af3eULL, 0x002f394219248446ULL} + } + , // 10^(-20) * 2^184 + {{0xfbb4fdbf05baf298ULL, 0x0025c768141d369eULL} + } + , // 10^(-21) * 2^187 + {{0x2c54c931a2c4b759ULL, 0x003c7240202ebdcbULL} + } + , // 10^(-22) * 2^191 + {{0x89dd6dc14f03c5e1ULL, 0x00305b66802564a2ULL} + } + , // 10^(-23) * 2^194 + {{0xd4b1249aa59c9e4eULL, 0x0026af8533511d4eULL} + } + , // 10^(-24) * 2^197 + {{0x544ea0f76f60fd49ULL, 0x003de5a1ebb4fbb1ULL} + } + , // 10^(-25) * 2^201 + {{0x76a54d92bf80caa1ULL, 0x00318481895d9627ULL} + } + , // 10^(-26) * 2^204 + {{0x921dd7a89933d54eULL, 0x00279d346de4781fULL} + } + , // 10^(-27) * 2^207 + {{0x8362f2a75b862215ULL, 0x003f61ed7ca0c032ULL} + } + , // 10^(-28) * 2^211 + {{0xcf825bb91604e811ULL, 0x0032b4bdfd4d668eULL} + } + , // 10^(-29) * 2^214 + {{0x0c684960de6a5341ULL, 0x00289097fdd7853fULL} + } + , // 10^(-30) * 2^217 + {{0x3d203ab3e521dc34ULL, 0x002073accb12d0ffULL} + } + , // 10^(-31) * 2^220 + {{0x2e99f7863b696053ULL, 0x0033ec47ab514e65ULL} + } + , // 10^(-32) * 2^224 + {{0x587b2c6b62bab376ULL, 0x002989d2ef743eb7ULL} + } + , // 10^(-33) * 2^227 + {{0xad2f56bc4efbc2c5ULL, 0x00213b0f25f69892ULL} + } + , // 10^(-34) * 2^230 +}; + + +// shiftright128[] contains the right shift count to obtain C2* from the top +// 128 bits of the 128x128-bit product C2 * Kx +int shiftright128[] = { + 0, // 128 - 128 + 0, // 128 - 128 + 0, // 128 - 128 + + 3, // 131 - 128 + 6, // 134 - 128 + 9, // 137 - 128 + 13, // 141 - 128 + 16, // 144 - 128 + 19, // 147 - 128 + 23, // 151 - 128 + 26, // 154 - 128 + 29, // 157 - 128 + 33, // 161 - 128 + 36, // 164 - 128 + 39, // 167 - 128 + 43, // 171 - 128 + 46, // 174 - 128 + 49, // 177 - 128 + 53, // 181 - 128 + 56, // 184 - 128 + 59, // 187 - 128 + 63, // 191 - 128 + + 66, // 194 - 128 + 69, // 197 - 128 + 73, // 201 - 128 + 76, // 204 - 128 + 79, // 207 - 128 + 83, // 211 - 128 + 86, // 214 - 128 + 89, // 217 - 128 + 92, // 220 - 128 + 96, // 224 - 128 + 99, // 227 - 128 + 102 // 230 - 128 +}; + + +// maskhigh128[] contains the mask to apply to the top 128 bits of the +// 128x128-bit product in order to obtain the high bits of f2* +// the 64-bit word order is L, H +UINT64 maskhigh128[] = { + 0x0000000000000000ULL, // 0 = 128 - 128 bits + 0x0000000000000000ULL, // 0 = 128 - 128 bits + 0x0000000000000000ULL, // 0 = 128 - 128 bits + 0x0000000000000007ULL, // 3 = 131 - 128 bits + 0x000000000000003fULL, // 6 = 134 - 128 bits + 0x00000000000001ffULL, // 9 = 137 - 128 bits + 0x0000000000001fffULL, // 13 = 141 - 128 bits + 0x000000000000ffffULL, // 16 = 144 - 128 bits + 0x000000000007ffffULL, // 19 = 147 - 128 bits + 0x00000000007fffffULL, // 23 = 151 - 128 bits + 0x0000000003ffffffULL, // 26 = 154 - 128 bits + 0x000000001fffffffULL, // 29 = 157 - 128 bits + 0x00000001ffffffffULL, // 33 = 161 - 128 bits + 0x0000000fffffffffULL, // 36 = 164 - 128 bits + 0x0000007fffffffffULL, // 39 = 167 - 128 bits + 0x000007ffffffffffULL, // 43 = 171 - 128 bits + 0x00003fffffffffffULL, // 46 = 174 - 128 bits + 0x0001ffffffffffffULL, // 49 = 177 - 128 bits + 0x001fffffffffffffULL, // 53 = 181 - 128 bits + 0x00ffffffffffffffULL, // 56 = 184 - 128 bits + 0x07ffffffffffffffULL, // 59 = 187 - 128 bits + 0x7fffffffffffffffULL, // 63 = 191 - 128 bits + 0x0000000000000003ULL, // 2 = 194 - 192 bits + 0x000000000000001fULL, // 5 = 197 - 192 bits + 0x00000000000001ffULL, // 9 = 201 - 192 bits + 0x0000000000000fffULL, // 12 = 204 - 192 bits + 0x0000000000007fffULL, // 15 = 207 - 192 bits + 0x000000000007ffffULL, // 21 = 211 - 192 bits + 0x00000000003fffffULL, // 22 = 214 - 192 bits + 0x0000000001ffffffULL, // 25 = 217 - 192 bits + 0x000000000fffffffULL, // 28 = 220 - 192 bits + 0x00000000ffffffffULL, // 32 = 224 - 192 bits + 0x00000007ffffffffULL, // 35 = 227 - 192 bits + 0x0000003fffffffffULL // 38 = 230 - 192 bits +}; + + +// onehalf128[] contains the high bits of 1/2 positioned correctly for +// comparison with the high bits of f2* +// the 64-bit word order is L, H +UINT64 onehalf128[] = { + 0x0000000000000000ULL, // 0 bits + 0x0000000000000000ULL, // 0 bits + 0x0000000000000000ULL, // 0 bits + 0x0000000000000004ULL, // 3 bits + 0x0000000000000020ULL, // 6 bits + 0x0000000000000100ULL, // 9 bits + 0x0000000000001000ULL, // 13 bits + 0x0000000000008000ULL, // 16 bits + 0x0000000000040000ULL, // 19 bits + 0x0000000000400000ULL, // 23 bits + 0x0000000002000000ULL, // 26 bits + 0x0000000010000000ULL, // 29 bits + 0x0000000100000000ULL, // 33 bits + 0x0000000800000000ULL, // 36 bits + 0x0000004000000000ULL, // 39 bits + 0x0000040000000000ULL, // 43 bits + 0x0000200000000000ULL, // 46 bits + 0x0001000000000000ULL, // 49 bits + 0x0010000000000000ULL, // 53 bits + 0x0080000000000000ULL, // 56 bits + 0x0400000000000000ULL, // 59 bits + 0x4000000000000000ULL, // 63 bits + 0x0000000000000002ULL, // 66 bits + 0x0000000000000010ULL, // 69 bits + 0x0000000000000100ULL, // 73 bits + 0x0000000000000800ULL, // 76 bits + 0x0000000000004000ULL, // 79 bits + 0x0000000000040000ULL, // 83 bits + 0x0000000000200000ULL, // 86 bits + 0x0000000001000000ULL, // 89 bits + 0x0000000008000000ULL, // 92 bits + 0x0000000080000000ULL, // 96 bits + 0x0000000400000000ULL, // 99 bits + 0x0000002000000000ULL // 102 bits +}; + +UINT64 ten2mk64[] = { + 0x199999999999999aULL, // 10^(-1) * 2^ 64 + 0x028f5c28f5c28f5dULL, // 10^(-2) * 2^ 64 + 0x004189374bc6a7f0ULL, // 10^(-3) * 2^ 64 + 0x00346dc5d638865aULL, // 10^(-4) * 2^ 67 + 0x0029f16b11c6d1e2ULL, // 10^(-5) * 2^ 70 + 0x00218def416bdb1bULL, // 10^(-6) * 2^ 73 + 0x0035afe535795e91ULL, // 10^(-7) * 2^ 77 + 0x002af31dc4611874ULL, // 10^(-8) * 2^ 80 + 0x00225c17d04dad2aULL, // 10^(-9) * 2^ 83 + 0x0036f9bfb3af7b76ULL, // 10^(-10) * 2^ 87 + 0x002bfaffc2f2c92bULL, // 10^(-11) * 2^ 90 + 0x00232f33025bd423ULL, // 10^(-12) * 2^ 93 + 0x00384b84d092ed04ULL, // 10^(-13) * 2^ 97 + 0x002d09370d425737ULL, // 10^(-14) * 2^100 + 0x0024075f3dceac2cULL, // 10^(-15) * 2^103 + 0x0039a5652fb11379ULL, // 10^(-16) * 2^107 +}; + +// ten2mk128trunc[] contains T*, the top Ex >= 128 bits of 10^(-k), +// for 1 <= k <= 34 +// the 64-bit word order is L, H +UINT128 ten2mk128trunc[] = { + {{0x9999999999999999ULL, 0x1999999999999999ULL}}, // 10^(-1) * 2^128 + {{0x28f5c28f5c28f5c2ULL, 0x028f5c28f5c28f5cULL}}, // 10^(-2) * 2^128 + {{0x9db22d0e56041893ULL, 0x004189374bc6a7efULL}}, // 10^(-3) * 2^128 + {{0x4af4f0d844d013a9ULL, 0x00346dc5d6388659ULL}}, // 10^(-4) * 2^131 + {{0x08c3f3e0370cdc87ULL, 0x0029f16b11c6d1e1ULL}}, // 10^(-5) * 2^134 + {{0x6d698fe69270b06cULL, 0x00218def416bdb1aULL}}, // 10^(-6) * 2^137 + {{0xaf0f4ca41d811a46ULL, 0x0035afe535795e90ULL}}, // 10^(-7) * 2^141 + {{0xbf3f70834acdae9fULL, 0x002af31dc4611873ULL}}, // 10^(-8) * 2^144 + {{0x65cc5a02a23e254cULL, 0x00225c17d04dad29ULL}}, // 10^(-9) * 2^147 + {{0x6fad5cd10396a213ULL, 0x0036f9bfb3af7b75ULL}}, // 10^(-10) * 2^151 + {{0xbfbde3da69454e75ULL, 0x002bfaffc2f2c92aULL}}, // 10^(-11) * 2^154 + {{0x32fe4fe1edd10b91ULL, 0x00232f33025bd422ULL}}, // 10^(-12) * 2^157 + {{0x84ca19697c81ac1bULL, 0x00384b84d092ed03ULL}}, // 10^(-13) * 2^161 + {{0x03d4e1213067bce3ULL, 0x002d09370d425736ULL}}, // 10^(-14) * 2^164 + {{0x3643e74dc052fd82ULL, 0x0024075f3dceac2bULL}}, // 10^(-15) * 2^167 + {{0x56d30baf9a1e626aULL, 0x0039a5652fb11378ULL}}, // 10^(-16) * 2^171 + {{0x12426fbfae7eb521ULL, 0x002e1dea8c8da92dULL}}, // 10^(-17) * 2^174 + {{0x41cebfcc8b9890e7ULL, 0x0024e4bba3a48757ULL}}, // 10^(-18) * 2^177 + {{0x694acc7a78f41b0cULL, 0x003b07929f6da558ULL}}, // 10^(-19) * 2^181 + {{0xbaa23d2ec729af3dULL, 0x002f394219248446ULL}}, // 10^(-20) * 2^184 + {{0xfbb4fdbf05baf297ULL, 0x0025c768141d369eULL}}, // 10^(-21) * 2^187 + {{0x2c54c931a2c4b758ULL, 0x003c7240202ebdcbULL}}, // 10^(-22) * 2^191 + {{0x89dd6dc14f03c5e0ULL, 0x00305b66802564a2ULL}}, // 10^(-23) * 2^194 + {{0xd4b1249aa59c9e4dULL, 0x0026af8533511d4eULL}}, // 10^(-24) * 2^197 + {{0x544ea0f76f60fd48ULL, 0x003de5a1ebb4fbb1ULL}}, // 10^(-25) * 2^201 + {{0x76a54d92bf80caa0ULL, 0x00318481895d9627ULL}}, // 10^(-26) * 2^204 + {{0x921dd7a89933d54dULL, 0x00279d346de4781fULL}}, // 10^(-27) * 2^207 + {{0x8362f2a75b862214ULL, 0x003f61ed7ca0c032ULL}}, // 10^(-28) * 2^211 + {{0xcf825bb91604e810ULL, 0x0032b4bdfd4d668eULL}}, // 10^(-29) * 2^214 + {{0x0c684960de6a5340ULL, 0x00289097fdd7853fULL}}, // 10^(-30) * 2^217 + {{0x3d203ab3e521dc33ULL, 0x002073accb12d0ffULL}}, // 10^(-31) * 2^220 + {{0x2e99f7863b696052ULL, 0x0033ec47ab514e65ULL}}, // 10^(-32) * 2^224 + {{0x587b2c6b62bab375ULL, 0x002989d2ef743eb7ULL}}, // 10^(-33) * 2^227 + {{0xad2f56bc4efbc2c4ULL, 0x00213b0f25f69892ULL}}, // 10^(-34) * 2^230 +}; + +// ten2mk128M[k - 1] = 10^(-k) * 2^exp (k), where 1 <= k <= 4 and +// exp (k) = shiftright128[k - 1] + 128 +// the 64-bit word order is L, H +UINT128 ten2mk128M[] = { + {{0xcccccccccccccccdULL, 0xccccccccccccccccULL}}, // 10^(-1) * 2^131 + {{0x3d70a3d70a3d70a4ULL, 0xa3d70a3d70a3d70aULL}}, // 10^(-2) * 2^134 + {{0x645a1cac083126eaULL, 0x83126e978d4fdf3bULL}}, // 10^(-3) * 2^137 + {{0xd3c36113404ea4a9ULL, 0xd1b71758e219652bULL}} // 10^(-4) * 2^141 +}; + +// ten2mk128truncM[] contains T*, the top Ex >= 128 bits of 10^(-k), +// for 1 <= k <= 4; the top bits which are 0 are not represented +// the 64-bit word order is L, H +UINT128 ten2mk128truncM[] = { + {{0xccccccccccccccccULL, 0xccccccccccccccccULL}}, // 10^(-1) * 2^131 + {{0x3d70a3d70a3d70a3ULL, 0xa3d70a3d70a3d70aULL}}, // 10^(-2) * 2^134 + {{0x645a1cac083126e9ULL, 0x83126e978d4fdf3bULL}}, // 10^(-3) * 2^137 + {{0xd3c36113404ea4a8ULL, 0xd1b71758e219652bULL}} // 10^(-4) * 2^141 +}; + +// shiftright128M[] contains the right shift count to obtain C2* from the top +// 128 bits of the 128x128-bit product C2 * Kx +int shiftright128M[] = { + 3, // 131 - 128 + 6, // 134 - 128 + 9, // 137 - 128 + 13 // 141 - 128 +}; + +// maskhigh128M[] contains the mask to apply to the top 128 bits of the +// 128x128-bit product in order to obtain the high bits of f* +// the high 64 bits of the mask are 0, so only the low 64 bits are represented +UINT64 maskhigh128M[] = { + 0x0000000000000007ULL, // 3 = 131 - 128 bits + 0x000000000000003fULL, // 6 = 134 - 128 bits + 0x00000000000001ffULL, // 9 = 137 - 128 bits + 0x0000000000001fffULL // 13 = 141 - 128 bits +}; + +// onehalf128M[] contains 1/2 positioned correctly for +// comparison with the high bits of f* +// the high 64 bits are 0, so only the low 64 bits are represented +UINT64 onehalf128M[] = { + 0x0000000000000004ULL, // 3 bits + 0x0000000000000020ULL, // 6 bits + 0x0000000000000100ULL, // 9 bits + 0x0000000000001000ULL // 13 bits +}; + +// ten2mk192M[k - 1] = 10^(-k-4) * 2^exp (k), where 1 <= k <= 19 and +// exp (k) = shiftright128[k - 1] + 128 +// the 64-bit word order is L, M, H +UINT192 ten2mk192M[] = { + {{0xcddd6e04c0592104ULL, 0x0fcf80dc33721d53ULL, + 0xa7c5ac471b478423ULL}}, + // 10^(-5) * 2^208 + {{0xd7e45803cd141a6aULL, 0xa63f9a49c2c1b10fULL, + 0x8637bd05af6c69b5ULL}}, + // 10^(-6) * 2^211 + {{0x8ca08cd2e1b9c3dcULL, 0x3d32907604691b4cULL, + 0xd6bf94d5e57a42bcULL}}, + // 10^(-7) * 2^215 + {{0x3d4d3d758161697dULL, 0xfdc20d2b36ba7c3dULL, + 0xabcc77118461cefcULL}}, + // 10^(-8) * 2^218 + {{0xfdd7645e011abacaULL, 0x31680a88f8953030ULL, + 0x89705f4136b4a597ULL}}, + // 10^(-9) * 2^221 + {{0x2fbf06fcce912addULL, 0xb573440e5a884d1bULL, + 0xdbe6fecebdedd5beULL}}, + // 10^(-10) * 2^225 + {{0xf2ff38ca3eda88b1ULL, 0xf78f69a51539d748ULL, + 0xafebff0bcb24aafeULL}}, + // 10^(-11) * 2^228 + {{0xf598fa3b657ba08eULL, 0xf93f87b7442e45d3ULL, + 0x8cbccc096f5088cbULL}}, + // 10^(-12) * 2^231 + {{0x88f4c3923bf900e3ULL, 0x2865a5f206b06fb9ULL, + 0xe12e13424bb40e13ULL}}, + // 10^(-13) * 2^235 + {{0x6d909c74fcc733e9ULL, 0x538484c19ef38c94ULL, + 0xb424dc35095cd80fULL}}, + // 10^(-14) * 2^238 + {{0x57a6e390ca38f654ULL, 0x0f9d37014bf60a10ULL, + 0x901d7cf73ab0acd9ULL}}, + // 10^(-15) * 2^241 + {{0xbf716c1add27f086ULL, 0x4c2ebe687989a9b3ULL, + 0xe69594bec44de15bULL}}, + // 10^(-16) * 2^245 + {{0xff8df0157db98d38ULL, 0x09befeb9fad487c2ULL, + 0xb877aa3236a4b449ULL}}, + // 10^(-17) * 2^248 + {{0x32d7f344649470faULL, 0x3aff322e62439fcfULL, + 0x9392ee8e921d5d07ULL}}, + // 10^(-18) * 2^251 + {{0x1e2652070753e7f5ULL, 0x2b31e9e3d06c32e5ULL, + 0xec1e4a7db69561a5ULL}}, + // 10^(-19) * 2^255 + {{0x181ea8059f76532bULL, 0x88f4bb1ca6bcf584ULL, + 0xbce5086492111aeaULL}}, + // 10^(-20) * 2^258 + {{0x467eecd14c5ea8efULL, 0xd3f6fc16ebca5e03ULL, + 0x971da05074da7beeULL}}, + // 10^(-21) * 2^261 + {{0x70cb148213caa7e5ULL, 0x5324c68b12dd6338ULL, + 0xf1c90080baf72cb1ULL}}, + // 10^(-22) * 2^265 + {{0x8d6f439b43088651ULL, 0x75b7053c0f178293ULL, 0xc16d9a0095928a27ULL}} + // 10^(-23) * 2^268 +}; + +// ten2mk192truncM[] contains T*, the top Ex >= 192 bits of 10^(-k), +// for 5 <= k <= 23; the top bits which are 0 are not represented +// the 64-bit word order is L, M, H +UINT192 ten2mk192truncM[] = { + {{0xcddd6e04c0592103ULL, 0x0fcf80dc33721d53ULL, + 0xa7c5ac471b478423ULL}}, + // 10^(-5) * 2^208 + {{0xd7e45803cd141a69ULL, 0xa63f9a49c2c1b10fULL, + 0x8637bd05af6c69b5ULL}}, + // 10^(-6) * 2^211 + {{0x8ca08cd2e1b9c3dbULL, 0x3d32907604691b4cULL, + 0xd6bf94d5e57a42bcULL}}, + // 10^(-7) * 2^215 + {{0x3d4d3d758161697cULL, 0xfdc20d2b36ba7c3dULL, + 0xabcc77118461cefcULL}}, + // 10^(-8) * 2^218 + {{0xfdd7645e011abac9ULL, 0x31680a88f8953030ULL, + 0x89705f4136b4a597ULL}}, + // 10^(-9) * 2^221 + {{0x2fbf06fcce912adcULL, 0xb573440e5a884d1bULL, + 0xdbe6fecebdedd5beULL}}, + // 10^(-10) * 2^225 + {{0xf2ff38ca3eda88b0ULL, 0xf78f69a51539d748ULL, + 0xafebff0bcb24aafeULL}}, + // 10^(-11) * 2^228 + {{0xf598fa3b657ba08dULL, 0xf93f87b7442e45d3ULL, + 0x8cbccc096f5088cbULL}}, + // 10^(-12) * 2^231 + {{0x88f4c3923bf900e2ULL, 0x2865a5f206b06fb9ULL, + 0xe12e13424bb40e13ULL}}, + // 10^(-13) * 2^235 + {{0x6d909c74fcc733e8ULL, 0x538484c19ef38c94ULL, + 0xb424dc35095cd80fULL}}, + // 10^(-14) * 2^238 + {{0x57a6e390ca38f653ULL, 0x0f9d37014bf60a10ULL, + 0x901d7cf73ab0acd9ULL}}, + // 10^(-15) * 2^241 + {{0xbf716c1add27f085ULL, 0x4c2ebe687989a9b3ULL, + 0xe69594bec44de15bULL}}, + // 10^(-16) * 2^245 + {{0xff8df0157db98d37ULL, 0x09befeb9fad487c2ULL, + 0xb877aa3236a4b449ULL}}, + // 10^(-17) * 2^248 + {{0x32d7f344649470f9ULL, 0x3aff322e62439fcfULL, + 0x9392ee8e921d5d07ULL}}, + // 10^(-18) * 2^251 + {{0x1e2652070753e7f4ULL, 0x2b31e9e3d06c32e5ULL, + 0xec1e4a7db69561a5ULL}}, + // 10^(-19) * 2^255 + {{0x181ea8059f76532aULL, 0x88f4bb1ca6bcf584ULL, + 0xbce5086492111aeaULL}}, + // 10^(-20) * 2^258 + {{0x467eecd14c5ea8eeULL, 0xd3f6fc16ebca5e03ULL, + 0x971da05074da7beeULL}}, + // 10^(-21) * 2^261 + {{0x70cb148213caa7e4ULL, 0x5324c68b12dd6338ULL, + 0xf1c90080baf72cb1ULL}}, + // 10^(-22) * 2^265 + {{0x8d6f439b43088650ULL, 0x75b7053c0f178293ULL, 0xc16d9a0095928a27ULL}} + // 10^(-23) * 2^268 +}; + +// shiftright192M[] contains the right shift count to obtain C2* from the top +// 192 bits of the 192x192-bit product C2 * Kx if 0 <= ind <= 14 where ind is +// the index in the table, or from the top 128 bits if 15 <= ind <= 18 +int shiftright192M[] = { + 16, // 208 - 192 + 19, // 211 - 192 + 23, // 215 - 192 + 26, // 218 - 192 + 29, // 221 - 192 + 33, // 225 - 192 + 36, // 228 - 192 + 39, // 231 - 192 + 43, // 235 - 192 + 46, // 238 - 192 + 49, // 241 - 192 + 53, // 245 - 192 + 56, // 248 - 192 + 59, // 251 - 192 + 63, // 255 - 192 + 2, // 258 - 256 + 5, // 261 - 256 + 9, // 265 - 256 + 12 // 268 - 256 +}; + +// maskhigh192M[] contains the mask to apply to the top 192 bits of the +// 192x192-bit product in order to obtain the high bits of f* +// if 0 <= ind <= 14 where ind is the index in the table, then the high 128 bits +// of the 384-bit mask are 0; if 15 <= ind <= 18 then the high 64 bits are 0 +UINT64 maskhigh192M[] = { + 0x000000000000ffffULL, // 16 = 208 - 192 bits + 0x000000000007ffffULL, // 19 = 211 - 192 bits + 0x00000000007fffffULL, // 23 = 215 - 192 bits + 0x0000000003ffffffULL, // 26 = 218 - 192 bits + 0x000000001fffffffULL, // 29 = 221 - 192 bits + 0x00000001ffffffffULL, // 33 = 225 - 192 bits + 0x0000000fffffffffULL, // 36 = 228 - 192 bits + 0x0000007fffffffffULL, // 39 = 231 - 192 bits + 0x000007ffffffffffULL, // 43 = 235 - 192 bits + 0x00003fffffffffffULL, // 46 = 238 - 192 bits + 0x0001ffffffffffffULL, // 49 = 241 - 192 bits + 0x001fffffffffffffULL, // 53 = 245 - 192 bits + 0x00ffffffffffffffULL, // 56 = 248 - 192 bits + 0x07ffffffffffffffULL, // 59 = 251 - 192 bits + 0x7fffffffffffffffULL, // 63 = 255 - 192 bits + 0x0000000000000003ULL, // 2 = 258 - 256 bits + 0x000000000000001fULL, // 5 = 261 - 256 bits + 0x00000000000001ffULL, // 9 = 265 - 256 bits + 0x0000000000000fffULL // 12 = 268 - 256 bits +}; + +// onehalf192M[] contains 1/2 positioned correctly for +// comparison with the high bits of f* +// if 0 <= ind <= 14 where ind is the index in the table, then the high 128 bits +// of the 384-bit mask are 0; if 15 <= ind <= 18 then the high 648 bits are 0 +UINT64 onehalf192M[] = { + 0x0000000000008000ULL, // 16 = 208 - 192 bits + 0x0000000000040000ULL, // 19 = 211 - 192 bits + 0x0000000000400000ULL, // 23 = 215 - 192 bits + 0x0000000002000000ULL, // 26 = 218 - 192 bits + 0x0000000010000000ULL, // 29 = 221 - 192 bits + 0x0000000100000000ULL, // 33 = 225 - 192 bits + 0x0000000800000000ULL, // 36 = 228 - 192 bits + 0x0000004000000000ULL, // 39 = 231 - 192 bits + 0x0000040000000000ULL, // 43 = 235 - 192 bits + 0x0000200000000000ULL, // 46 = 238 - 192 bits + 0x0001000000000000ULL, // 49 = 241 - 192 bits + 0x0010000000000000ULL, // 53 = 245 - 192 bits + 0x0080000000000000ULL, // 56 = 248 - 192 bits + 0x0400000000000000ULL, // 59 = 251 - 192 bits + 0x4000000000000000ULL, // 63 = 255 - 192 bits + 0x0000000000000002ULL, // 2 = 258 - 256 bits + 0x0000000000000010ULL, // 5 = 261 - 256 bits + 0x0000000000000100ULL, // 9 = 265 - 256 bits + 0x0000000000000800ULL // 12 = 268 - 256 bits +}; + +// ten2mk256M[k - 1] = 10^(-k-23) * 2^exp (k), where 1 <= k <= 11 and +// exp (k) = shiftright128[k - 1] + 128 +UINT256 ten2mk256M[] = { // the 64-bit word order is LL, LH, HL, HH + {{0xf23472530ce6e3edULL, 0xd78c3615cf3a050cULL, + 0xc4926a9672793542ULL, 0x9abe14cd44753b52ULL}}, // 10^(-24) * 2^335 + {{0xe9ed83b814a49fe1ULL, 0x8c1389bc7ec33b47ULL, + 0x3a83ddbd83f52204ULL, 0xf79687aed3eec551ULL}}, // 10^(-25) * 2^339 + {{0x87f1362cdd507fe7ULL, 0x3cdc6e306568fc39ULL, + 0x95364afe032a819dULL, 0xc612062576589ddaULL}}, // 10^(-26) * 2^342 + {{0x9ff42b5717739986ULL, 0xca49f1c05120c9c7ULL, + 0x775ea264cf55347dULL, 0x9e74d1b791e07e48ULL}}, // 10^(-27) * 2^345 + {{0xccb9def1bf1f5c09ULL, 0x76dcb60081ce0fa5ULL, + 0x8bca9d6e188853fcULL, 0xfd87b5f28300ca0dULL}}, // 10^(-28) * 2^349 + {{0xa3c7e58e327f7cd4ULL, 0x5f16f80067d80c84ULL, + 0x096ee45813a04330ULL, 0xcad2f7f5359a3b3eULL}}, // 10^(-29) * 2^352 + {{0xb6398471c1ff9710ULL, 0x18df2ccd1fe00a03ULL, + 0xa1258379a94d028dULL, 0xa2425ff75e14fc31ULL}}, // 10^(-30) * 2^355 + {{0xf82e038e34cc78daULL, 0x4718f0a419800802ULL, + 0x80eacf948770ced7ULL, 0x81ceb32c4b43fcf4ULL}}, // 10^(-31) * 2^358 + {{0x59e338e387ad8e29ULL, 0x0b5b1aa028ccd99eULL, + 0x67de18eda5814af2ULL, 0xcfb11ead453994baULL}}, // 10^(-32) * 2^362 + {{0x47e8fa4f9fbe0b54ULL, 0x6f7c154ced70ae18ULL, + 0xecb1ad8aeacdd58eULL, 0xa6274bbdd0fadd61ULL}}, // 10^(-33) * 2^365 + {{0xd320c83fb2fe6f76ULL, 0xbf967770bdf3be79ULL, + 0xbd5af13bef0b113eULL, 0x84ec3c97da624ab4ULL}} // 10^(-34) * 2^368 +}; + +// ten2mk256truncM[] contains T*, the top Ex >= 256 bits of 10^(-k), +// for 24 <= k <= 34; the top bits which are 0 are not represented +UINT256 ten2mk256truncM[] = { // the 64-bit word order is LL, LH, HL, HH + {{0xf23472530ce6e3ecULL, 0xd78c3615cf3a050cULL, + 0xc4926a9672793542ULL, 0x9abe14cd44753b52ULL}}, // 10^(-24) * 2^335 + {{0xe9ed83b814a49fe0ULL, 0x8c1389bc7ec33b47ULL, + 0x3a83ddbd83f52204ULL, 0xf79687aed3eec551ULL}}, // 10^(-25) * 2^339 + {{0x87f1362cdd507fe6ULL, 0x3cdc6e306568fc39ULL, + 0x95364afe032a819dULL, 0xc612062576589ddaULL}}, // 10^(-26) * 2^342 + {{0x775ea264cf55347cULL, 0x9ff42b5717739986ULL, + 0xca49f1c05120c9c7ULL, 0x9e74d1b791e07e48ULL}}, // 10^(-27) * 2^345 + {{0xccb9def1bf1f5c08ULL, 0x76dcb60081ce0fa5ULL, + 0x8bca9d6e188853fcULL, 0xfd87b5f28300ca0dULL}}, // 10^(-28) * 2^349 + {{0xa3c7e58e327f7cd3ULL, 0x5f16f80067d80c84ULL, + 0x096ee45813a04330ULL, 0xcad2f7f5359a3b3eULL}}, // 10^(-29) * 2^352 + {{0xb6398471c1ff970fULL, 0x18df2ccd1fe00a03ULL, + 0xa1258379a94d028dULL, 0xa2425ff75e14fc31ULL}}, // 10^(-30) * 2^355 + {{0xf82e038e34cc78d9ULL, 0x4718f0a419800802ULL, + 0x80eacf948770ced7ULL, 0x81ceb32c4b43fcf4ULL}}, // 10^(-31) * 2^358 + {{0x59e338e387ad8e28ULL, 0x0b5b1aa028ccd99eULL, + 0x67de18eda5814af2ULL, 0xcfb11ead453994baULL}}, // 10^(-32) * 2^362 + {{0x47e8fa4f9fbe0b53ULL, 0x6f7c154ced70ae18ULL, + 0xecb1ad8aeacdd58eULL, 0xa6274bbdd0fadd61ULL}}, // 10^(-33) * 2^365 + {{0xd320c83fb2fe6f75ULL, 0xbf967770bdf3be79ULL, + 0xbd5af13bef0b113eULL, 0x84ec3c97da624ab4ULL}} // 10^(-34) * 2^368 +}; + +// shiftright256M[] contains the right shift count to obtain C2* from the top +// 192 bits of the 256x256-bit product C2 * Kx +int shiftright256M[] = { + 15, // 335 - 320 + 19, // 339 - 320 + 22, // 342 - 320 + 25, // 345 - 320 + 29, // 349 - 320 + 32, // 352 - 320 // careful of 32-bit machines! + 35, // 355 - 320 + 38, // 358 - 320 + 42, // 362 - 320 + 45, // 365 - 320 + 48 // 368 - 320 +}; + +// maskhigh256M[] contains the mask to apply to the top 192 bits of the +// 256x256-bit product in order to obtain the high bits of f* +UINT64 maskhigh256M[] = { + 0x0000000000007fffULL, // 15 = 335 - 320 bits + 0x000000000007ffffULL, // 19 = 339 - 320 bits + 0x00000000003fffffULL, // 22 = 342 - 320 bits + 0x0000000001ffffffULL, // 25 = 345 - 320 bits + 0x000000001fffffffULL, // 29 = 349 - 320 bits + 0x00000000ffffffffULL, // 32 = 352 - 320 bits + 0x00000007ffffffffULL, // 35 = 355 - 320 bits + 0x0000003fffffffffULL, // 38 = 358 - 320 bits + 0x000003ffffffffffULL, // 42 = 362 - 320 bits + 0x00001fffffffffffULL, // 45 = 365 - 320 bits + 0x0000ffffffffffffULL // 48 = 368 - 320 bits +}; + +// onehalf256M[] contains 1/2 positioned correctly for comparison with the +// high bits of f*; the high 128 bits of the 512-bit mask are 0 +UINT64 onehalf256M[] = { + 0x0000000000004000ULL, // 15 = 335 - 320 bits + 0x0000000000040000ULL, // 19 = 339 - 320 bits + 0x0000000000200000ULL, // 22 = 342 - 320 bits + 0x0000000001000000ULL, // 25 = 345 - 320 bits + 0x0000000010000000ULL, // 29 = 349 - 320 bits + 0x0000000080000000ULL, // 32 = 352 - 320 bits + 0x0000000400000000ULL, // 35 = 355 - 320 bits + 0x0000002000000000ULL, // 38 = 358 - 320 bits + 0x0000020000000000ULL, // 42 = 362 - 320 bits + 0x0000100000000000ULL, // 45 = 365 - 320 bits + 0x0000800000000000ULL // 48 = 368 - 320 bits +}; + + +// char_table2[] is used to convert n to string, where 10 <= n <= 99 +unsigned char char_table2[180] = { + '1', '0', + '1', '1', + '1', '2', + '1', '3', + '1', '4', + '1', '5', + '1', '6', + '1', '7', + '1', '8', + '1', '9', + '2', '0', + '2', '1', + '2', '2', + '2', '3', + '2', '4', + '2', '5', + '2', '6', + '2', '7', + '2', '8', + '2', '9', + '3', '0', + '3', '1', + '3', '2', + '3', '3', + '3', '4', + '3', '5', + '3', '6', + '3', '7', + '3', '8', + '3', '9', + '4', '0', + '4', '1', + '4', '2', + '4', '3', + '4', '4', + '4', '5', + '4', '6', + '4', '7', + '4', '8', + '4', '9', + '5', '0', + '5', '1', + '5', '2', + '5', '3', + '5', '4', + '5', '5', + '5', '6', + '5', '7', + '5', '8', + '5', '9', + '6', '0', + '6', '1', + '6', '2', + '6', '3', + '6', '4', + '6', '5', + '6', '6', + '6', '7', + '6', '8', + '6', '9', + '7', '0', + '7', '1', + '7', '2', + '7', '3', + '7', '4', + '7', '5', + '7', '6', + '7', '7', + '7', '8', + '7', '9', + '8', '0', + '8', '1', + '8', '2', + '8', '3', + '8', '4', + '8', '5', + '8', '6', + '8', '7', + '8', '8', + '8', '9', + '9', '0', + '9', '1', + '9', '2', + '9', '3', + '9', '4', + '9', '5', + '9', '6', + '9', '7', + '9', '8', + '9', '9' +}; + + +// char_table3[] is used to convert n to string, where 000 <= n <= 999 +unsigned char char_table3[3000] = { + '0', '0', '0', + '0', '0', '1', + '0', '0', '2', + '0', '0', '3', + '0', '0', '4', + '0', '0', '5', + '0', '0', '6', + '0', '0', '7', + '0', '0', '8', + '0', '0', '9', + '0', '1', '0', + '0', '1', '1', + '0', '1', '2', + '0', '1', '3', + '0', '1', '4', + '0', '1', '5', + '0', '1', '6', + '0', '1', '7', + '0', '1', '8', + '0', '1', '9', + '0', '2', '0', + '0', '2', '1', + '0', '2', '2', + '0', '2', '3', + '0', '2', '4', + '0', '2', '5', + '0', '2', '6', + '0', '2', '7', + '0', '2', '8', + '0', '2', '9', + '0', '3', '0', + '0', '3', '1', + '0', '3', '2', + '0', '3', '3', + '0', '3', '4', + '0', '3', '5', + '0', '3', '6', + '0', '3', '7', + '0', '3', '8', + '0', '3', '9', + '0', '4', '0', + '0', '4', '1', + '0', '4', '2', + '0', '4', '3', + '0', '4', '4', + '0', '4', '5', + '0', '4', '6', + '0', '4', '7', + '0', '4', '8', + '0', '4', '9', + '0', '5', '0', + '0', '5', '1', + '0', '5', '2', + '0', '5', '3', + '0', '5', '4', + '0', '5', '5', + '0', '5', '6', + '0', '5', '7', + '0', '5', '8', + '0', '5', '9', + '0', '6', '0', + '0', '6', '1', + '0', '6', '2', + '0', '6', '3', + '0', '6', '4', + '0', '6', '5', + '0', '6', '6', + '0', '6', '7', + '0', '6', '8', + '0', '6', '9', + '0', '7', '0', + '0', '7', '1', + '0', '7', '2', + '0', '7', '3', + '0', '7', '4', + '0', '7', '5', + '0', '7', '6', + '0', '7', '7', + '0', '7', '8', + '0', '7', '9', + '0', '8', '0', + '0', '8', '1', + '0', '8', '2', + '0', '8', '3', + '0', '8', '4', + '0', '8', '5', + '0', '8', '6', + '0', '8', '7', + '0', '8', '8', + '0', '8', '9', + '0', '9', '0', + '0', '9', '1', + '0', '9', '2', + '0', '9', '3', + '0', '9', '4', + '0', '9', '5', + '0', '9', '6', + '0', '9', '7', + '0', '9', '8', + '0', '9', '9', + '1', '0', '0', + '1', '0', '1', + '1', '0', '2', + '1', '0', '3', + '1', '0', '4', + '1', '0', '5', + '1', '0', '6', + '1', '0', '7', + '1', '0', '8', + '1', '0', '9', + '1', '1', '0', + '1', '1', '1', + '1', '1', '2', + '1', '1', '3', + '1', '1', '4', + '1', '1', '5', + '1', '1', '6', + '1', '1', '7', + '1', '1', '8', + '1', '1', '9', + '1', '2', '0', + '1', '2', '1', + '1', '2', '2', + '1', '2', '3', + '1', '2', '4', + '1', '2', '5', + '1', '2', '6', + '1', '2', '7', + '1', '2', '8', + '1', '2', '9', + '1', '3', '0', + '1', '3', '1', + '1', '3', '2', + '1', '3', '3', + '1', '3', '4', + '1', '3', '5', + '1', '3', '6', + '1', '3', '7', + '1', '3', '8', + '1', '3', '9', + '1', '4', '0', + '1', '4', '1', + '1', '4', '2', + '1', '4', '3', + '1', '4', '4', + '1', '4', '5', + '1', '4', '6', + '1', '4', '7', + '1', '4', '8', + '1', '4', '9', + '1', '5', '0', + '1', '5', '1', + '1', '5', '2', + '1', '5', '3', + '1', '5', '4', + '1', '5', '5', + '1', '5', '6', + '1', '5', '7', + '1', '5', '8', + '1', '5', '9', + '1', '6', '0', + '1', '6', '1', + '1', '6', '2', + '1', '6', '3', + '1', '6', '4', + '1', '6', '5', + '1', '6', '6', + '1', '6', '7', + '1', '6', '8', + '1', '6', '9', + '1', '7', '0', + '1', '7', '1', + '1', '7', '2', + '1', '7', '3', + '1', '7', '4', + '1', '7', '5', + '1', '7', '6', + '1', '7', '7', + '1', '7', '8', + '1', '7', '9', + '1', '8', '0', + '1', '8', '1', + '1', '8', '2', + '1', '8', '3', + '1', '8', '4', + '1', '8', '5', + '1', '8', '6', + '1', '8', '7', + '1', '8', '8', + '1', '8', '9', + '1', '9', '0', + '1', '9', '1', + '1', '9', '2', + '1', '9', '3', + '1', '9', '4', + '1', '9', '5', + '1', '9', '6', + '1', '9', '7', + '1', '9', '8', + '1', '9', '9', + '2', '0', '0', + '2', '0', '1', + '2', '0', '2', + '2', '0', '3', + '2', '0', '4', + '2', '0', '5', + '2', '0', '6', + '2', '0', '7', + '2', '0', '8', + '2', '0', '9', + '2', '1', '0', + '2', '1', '1', + '2', '1', '2', + '2', '1', '3', + '2', '1', '4', + '2', '1', '5', + '2', '1', '6', + '2', '1', '7', + '2', '1', '8', + '2', '1', '9', + '2', '2', '0', + '2', '2', '1', + '2', '2', '2', + '2', '2', '3', + '2', '2', '4', + '2', '2', '5', + '2', '2', '6', + '2', '2', '7', + '2', '2', '8', + '2', '2', '9', + '2', '3', '0', + '2', '3', '1', + '2', '3', '2', + '2', '3', '3', + '2', '3', '4', + '2', '3', '5', + '2', '3', '6', + '2', '3', '7', + '2', '3', '8', + '2', '3', '9', + '2', '4', '0', + '2', '4', '1', + '2', '4', '2', + '2', '4', '3', + '2', '4', '4', + '2', '4', '5', + '2', '4', '6', + '2', '4', '7', + '2', '4', '8', + '2', '4', '9', + '2', '5', '0', + '2', '5', '1', + '2', '5', '2', + '2', '5', '3', + '2', '5', '4', + '2', '5', '5', + '2', '5', '6', + '2', '5', '7', + '2', '5', '8', + '2', '5', '9', + '2', '6', '0', + '2', '6', '1', + '2', '6', '2', + '2', '6', '3', + '2', '6', '4', + '2', '6', '5', + '2', '6', '6', + '2', '6', '7', + '2', '6', '8', + '2', '6', '9', + '2', '7', '0', + '2', '7', '1', + '2', '7', '2', + '2', '7', '3', + '2', '7', '4', + '2', '7', '5', + '2', '7', '6', + '2', '7', '7', + '2', '7', '8', + '2', '7', '9', + '2', '8', '0', + '2', '8', '1', + '2', '8', '2', + '2', '8', '3', + '2', '8', '4', + '2', '8', '5', + '2', '8', '6', + '2', '8', '7', + '2', '8', '8', + '2', '8', '9', + '2', '9', '0', + '2', '9', '1', + '2', '9', '2', + '2', '9', '3', + '2', '9', '4', + '2', '9', '5', + '2', '9', '6', + '2', '9', '7', + '2', '9', '8', + '2', '9', '9', + '3', '0', '0', + '3', '0', '1', + '3', '0', '2', + '3', '0', '3', + '3', '0', '4', + '3', '0', '5', + '3', '0', '6', + '3', '0', '7', + '3', '0', '8', + '3', '0', '9', + '3', '1', '0', + '3', '1', '1', + '3', '1', '2', + '3', '1', '3', + '3', '1', '4', + '3', '1', '5', + '3', '1', '6', + '3', '1', '7', + '3', '1', '8', + '3', '1', '9', + '3', '2', '0', + '3', '2', '1', + '3', '2', '2', + '3', '2', '3', + '3', '2', '4', + '3', '2', '5', + '3', '2', '6', + '3', '2', '7', + '3', '2', '8', + '3', '2', '9', + '3', '3', '0', + '3', '3', '1', + '3', '3', '2', + '3', '3', '3', + '3', '3', '4', + '3', '3', '5', + '3', '3', '6', + '3', '3', '7', + '3', '3', '8', + '3', '3', '9', + '3', '4', '0', + '3', '4', '1', + '3', '4', '2', + '3', '4', '3', + '3', '4', '4', + '3', '4', '5', + 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'9', '2', + '9', '9', '3', + '9', '9', '4', + '9', '9', '5', + '9', '9', '6', + '9', '9', '7', + '9', '9', '8', + '9', '9', '9' +}; + +// ten2m3k64[], shift_ten2m3k64[] used for conversion from BID128 to string +UINT64 ten2m3k64[] = { + 0x4189374bc6a7ef9eull, // 4189374bc6a7ef9e * 2^-72 = (10^-3)RP,63 + 0x10c6f7a0b5ed8d37ull, // 10c6f7a0b5ed8d37 * 2^-80 = (10^-6)RP,61 + 0x44b82fa09b5a52ccull, // 44b82fa09b5a52cc * 2^-92 = (10^-9)RP,63 + 0x119799812dea111aull, // 119799812dea111a * 2^-100 = (10^-12)RP,61 + 0x480ebe7b9d58566dull // 480ebe7b9d58566d * 2^-112 = (10^-15)RP,63 +}; + +unsigned int shift_ten2m3k64[] = { + 8, // 72 - 64 + 16, // 80 - 64 + 28, // 92 - 64 + 36, // 100 - 64 + 48 // 112 - 64 +}; + +UINT128 ten2m3k128[] = { + {{0xb22d0e5604189375ull, 0x4189374bc6a7ef9dull}}, + // 4189374bc6a7ef9d b22d0e5604189375 * 2^-136 = (10^-3)RP,127 + {{0xb4c7f34938583622ull, 0x10c6f7a0b5ed8d36ull}}, + // 10c6f7a0b5ed8d36 b4c7f34938583622 * 2^-144 = (10^-6)RP,125 + {{0x98b405447c4a9819ull, 0x44b82fa09b5a52cbull}}, + // 44b82fa09b5a52cb 98b405447c4a9819 * 2^-156 = (10^-9)RP,127 + {{0x7f27f0f6e885c8bbull, 0x119799812dea1119ull}}, + // 119799812dea1119 7f27f0f6e885c8bb * 2^-164 = (10^-12)RP,125 + {{0x87ce9b80a5fb0509ull, 0x480ebe7b9d58566cull}}, + // 480ebe7b9d58566c 87ce9b80a5fb0509 * 2^-176 = (10^-15)RP,127 + {{0xe75fe645cc4873faull, 0x12725dd1d243aba0ull}}, + // 12725dd1d243aba0 e75fe645cc4873fa * 2^-184 = (10^-18)RP,125 + {{0x69fb7e0b75e52f02ull, 0x4b8ed0283a6d3df7ull}}, + // 4b8ed0283a6d3df7 69fb7e0b75e52f02 * 2^-196 = (10^-21)RP,127 + {{0x58924d52ce4f26a9ull, 0x1357c299a88ea76aull}}, + // 1357c299a88ea76a 58924d52ce4f26a9 * 2^-204 = (10^-24)RP,125 + {{0x3baf513267aa9a3full, 0x4f3a68dbc8f03f24ull}}, + // 4f3a68dbc8f03f24 3baf513267aa9a3f * 2^-216 = (10^-27)RP,127 + {{0x3424b06f3529a052ull, 0x14484bfeebc29f86ull}}, + // 14484bfeebc29f86 3424b06f3529a052 * 2^-224 = (10^-30)RP,125 + {{0xf658d6c57566eac8ull, 0x5313a5dee87d6eb0ull}} + // 5313a5dee87d6eb0 f658d6c57566eac8 * 2^-236 = (10^-33)RP,127 +}; + +unsigned int shift_ten2m3k128[] = { + 8, // 136 - 128 + 16, // 144 - 128 + 28, // 156 - 128 + 36, // 164 - 128 + 48, // 176 - 128 + 56, // 184 - 128 + 4, // 196 - 192 + 12, // 204 - 192 + 24, // 216 - 192 + 32, // 224 - 192 + 44 // 236 - 192 +}; + + +/*************************************************************************** + *************** TABLES FOR GENERAL ROUNDING FUNCTIONS ********************* + ***************************************************************************/ +// Note: not all entries in these tables will be used with IEEE 754R decimal +// floating-point arithmetic +// a) In round128_2_18() numbers with 2 <= q <= 18 will be rounded only +// for 1 <= x <= 3: +// x = 1 or x = 2 when q = 17 +// x = 2 or x = 3 when q = 18 +// b) In round128_19_38() numbers with 19 <= q <= 38 will be rounded only +// for 1 <= x <= 23: +// x = 3 or x = 4 when q = 19 +// x = 4 or x = 5 when q = 20 +// ... +// x = 18 or x = 19 when q = 34 +// x = 1 or x = 2 or x = 19 or x = 20 when q = 35 +// x = 2 or x = 3 or x = 20 or x = 21 when q = 36 +// x = 3 or x = 4 or x = 21 or x = 22 when q = 37 +// x = 4 or x = 5 or x = 22 or x = 23 when q = 38 +// c) ... +// However, for generality and possible uses outside the frame of IEEE 754R +// this implementation includes table values for all x in [1, q - 1] + +// Note: 64-bit tables generated with ten2mx64.ma; output in ten2mx64.out + +// Kx from 10^(-x) ~= Kx * 2^(-Ex); Kx rounded up to 64 bits, 1 <= x <= 17 +UINT64 Kx64[] = { + 0xcccccccccccccccdULL, // 10^-1 ~= cccccccccccccccd * 2^-67 + 0xa3d70a3d70a3d70bULL, // 10^-2 ~= a3d70a3d70a3d70b * 2^-70 + 0x83126e978d4fdf3cULL, // 10^-3 ~= 83126e978d4fdf3c * 2^-73 + 0xd1b71758e219652cULL, // 10^-4 ~= d1b71758e219652c * 2^-77 + 0xa7c5ac471b478424ULL, // 10^-5 ~= a7c5ac471b478424 * 2^-80 + 0x8637bd05af6c69b6ULL, // 10^-6 ~= 8637bd05af6c69b6 * 2^-83 + 0xd6bf94d5e57a42bdULL, // 10^-7 ~= d6bf94d5e57a42bd * 2^-87 + 0xabcc77118461cefdULL, // 10^-8 ~= abcc77118461cefd * 2^-90 + 0x89705f4136b4a598ULL, // 10^-9 ~= 89705f4136b4a598 * 2^-93 + 0xdbe6fecebdedd5bfULL, // 10^-10 ~= dbe6fecebdedd5bf * 2^-97 + 0xafebff0bcb24aaffULL, // 10^-11 ~= afebff0bcb24aaff * 2^-100 + 0x8cbccc096f5088ccULL, // 10^-12 ~= 8cbccc096f5088cc * 2^-103 + 0xe12e13424bb40e14ULL, // 10^-13 ~= e12e13424bb40e14 * 2^-107 + 0xb424dc35095cd810ULL, // 10^-14 ~= b424dc35095cd810 * 2^-110 + 0x901d7cf73ab0acdaULL, // 10^-15 ~= 901d7cf73ab0acda * 2^-113 + 0xe69594bec44de15cULL, // 10^-16 ~= e69594bec44de15c * 2^-117 + 0xb877aa3236a4b44aULL // 10^-17 ~= b877aa3236a4b44a * 2^-120 +}; + +// Ex-64 from 10^(-x) ~= Kx * 2^(-Ex); Kx rounded up to 64 bits, 1 <= x <= 17 +unsigned int Ex64m64[] = { + 3, // 67 - 64, Ex = 67 + 6, // 70 - 64, Ex = 70 + 9, // 73 - 64, Ex = 73 + 13, // 77 - 64, Ex = 77 + 16, // 80 - 64, Ex = 80 + 19, // 83 - 64, Ex = 83 + 23, // 87 - 64, Ex = 87 + 26, // 90 - 64, Ex = 90 + 29, // 93 - 64, Ex = 93 + 33, // 97 - 64, Ex = 97 + 36, // 100 - 64, Ex = 100 + 39, // 103 - 64, Ex = 103 + 43, // 107 - 64, Ex = 107 + 46, // 110 - 64, Ex = 110 + 49, // 113 - 64, Ex = 113 + 53, // 117 - 64, Ex = 117 + 56 // 120 - 64, Ex = 120 +}; + +// Values of 1/2 in the right position to be compared with the fraction from +// C * kx, 1 <= x <= 17; the fraction consists of the low Ex bits in C * kx +// (these values are aligned with the high 64 bits of the fraction) +UINT64 half64[] = { + 0x0000000000000004ULL, // half / 2^64 = 4 + 0x0000000000000020ULL, // half / 2^64 = 20 + 0x0000000000000100ULL, // half / 2^64 = 100 + 0x0000000000001000ULL, // half / 2^64 = 1000 + 0x0000000000008000ULL, // half / 2^64 = 8000 + 0x0000000000040000ULL, // half / 2^64 = 40000 + 0x0000000000400000ULL, // half / 2^64 = 400000 + 0x0000000002000000ULL, // half / 2^64 = 2000000 + 0x0000000010000000ULL, // half / 2^64 = 10000000 + 0x0000000100000000ULL, // half / 2^64 = 100000000 + 0x0000000800000000ULL, // half / 2^64 = 800000000 + 0x0000004000000000ULL, // half / 2^64 = 4000000000 + 0x0000040000000000ULL, // half / 2^64 = 40000000000 + 0x0000200000000000ULL, // half / 2^64 = 200000000000 + 0x0001000000000000ULL, // half / 2^64 = 1000000000000 + 0x0010000000000000ULL, // half / 2^64 = 10000000000000 + 0x0080000000000000ULL // half / 2^64 = 80000000000000 +}; + +// Values of mask in the right position to obtain the high Ex - 64 bits +// of the fraction from C * kx, 1 <= x <= 17; the fraction consists of +// the low Ex bits in C * kx +UINT64 mask64[] = { + 0x0000000000000007ULL, // mask / 2^64 + 0x000000000000003fULL, // mask / 2^64 + 0x00000000000001ffULL, // mask / 2^64 + 0x0000000000001fffULL, // mask / 2^64 + 0x000000000000ffffULL, // mask / 2^64 + 0x000000000007ffffULL, // mask / 2^64 + 0x00000000007fffffULL, // mask / 2^64 + 0x0000000003ffffffULL, // mask / 2^64 + 0x000000001fffffffULL, // mask / 2^64 + 0x00000001ffffffffULL, // mask / 2^64 + 0x0000000fffffffffULL, // mask / 2^64 + 0x0000007fffffffffULL, // mask / 2^64 + 0x000007ffffffffffULL, // mask / 2^64 + 0x00003fffffffffffULL, // mask / 2^64 + 0x0001ffffffffffffULL, // mask / 2^64 + 0x001fffffffffffffULL, // mask / 2^64 + 0x00ffffffffffffffULL // mask / 2^64 +}; + +// Values of 10^(-x) trancated to Ex bits beyond the binary point, and +// in the right position to be compared with the fraction from C * kx, +// 1 <= x <= 17; the fraction consists of the low Ex bits in C * kx +// (these values are aligned with the low 64 bits of the fraction) +UINT64 ten2mxtrunc64[] = { + 0xccccccccccccccccULL, // (ten2mx >> 64) = cccccccccccccccc + 0xa3d70a3d70a3d70aULL, // (ten2mx >> 64) = a3d70a3d70a3d70a + 0x83126e978d4fdf3bULL, // (ten2mx >> 64) = 83126e978d4fdf3b + 0xd1b71758e219652bULL, // (ten2mx >> 64) = d1b71758e219652b + 0xa7c5ac471b478423ULL, // (ten2mx >> 64) = a7c5ac471b478423 + 0x8637bd05af6c69b5ULL, // (ten2mx >> 64) = 8637bd05af6c69b5 + 0xd6bf94d5e57a42bcULL, // (ten2mx >> 64) = d6bf94d5e57a42bc + 0xabcc77118461cefcULL, // (ten2mx >> 64) = abcc77118461cefc + 0x89705f4136b4a597ULL, // (ten2mx >> 64) = 89705f4136b4a597 + 0xdbe6fecebdedd5beULL, // (ten2mx >> 64) = dbe6fecebdedd5be + 0xafebff0bcb24aafeULL, // (ten2mx >> 64) = afebff0bcb24aafe + 0x8cbccc096f5088cbULL, // (ten2mx >> 64) = 8cbccc096f5088cb + 0xe12e13424bb40e13ULL, // (ten2mx >> 64) = e12e13424bb40e13 + 0xb424dc35095cd80fULL, // (ten2mx >> 64) = b424dc35095cd80f + 0x901d7cf73ab0acd9ULL, // (ten2mx >> 64) = 901d7cf73ab0acd9 + 0xe69594bec44de15bULL, // (ten2mx >> 64) = e69594bec44de15b + 0xb877aa3236a4b449ULL // (ten2mx >> 64) = b877aa3236a4b449 +}; + +// Note: 128-bit tables generated with ten2mx128.ma; output in ten2mx128.out +// The order of the 64-bit components is L, H + +// Kx from 10^(-x) ~= Kx * 2^(-Ex); Kx rounded up to 128 bits, 1 <= x <= 37 +UINT128 Kx128[] = { + {{0xcccccccccccccccdULL, 0xccccccccccccccccULL}}, + // 10^-1 ~= cccccccccccccccccccccccccccccccd * 2^-131 + {{0x3d70a3d70a3d70a4ULL, 0xa3d70a3d70a3d70aULL}}, + // 10^-2 ~= a3d70a3d70a3d70a3d70a3d70a3d70a4 * 2^-134 + {{0x645a1cac083126eaULL, 0x83126e978d4fdf3bULL}}, + // 10^-3 ~= 83126e978d4fdf3b645a1cac083126ea * 2^-137 + {{0xd3c36113404ea4a9ULL, 0xd1b71758e219652bULL}}, + // 10^-4 ~= d1b71758e219652bd3c36113404ea4a9 * 2^-141 + {{0x0fcf80dc33721d54ULL, 0xa7c5ac471b478423ULL}}, + // 10^-5 ~= a7c5ac471b4784230fcf80dc33721d54 * 2^-144 + {{0xa63f9a49c2c1b110ULL, 0x8637bd05af6c69b5ULL}}, + // 10^-6 ~= 8637bd05af6c69b5a63f9a49c2c1b110 * 2^-147 + {{0x3d32907604691b4dULL, 0xd6bf94d5e57a42bcULL}}, + // 10^-7 ~= d6bf94d5e57a42bc3d32907604691b4d * 2^-151 + {{0xfdc20d2b36ba7c3eULL, 0xabcc77118461cefcULL}}, + // 10^-8 ~= abcc77118461cefcfdc20d2b36ba7c3e * 2^-154 + {{0x31680a88f8953031ULL, 0x89705f4136b4a597ULL}}, + // 10^-9 ~= 89705f4136b4a59731680a88f8953031 * 2^-157 + {{0xb573440e5a884d1cULL, 0xdbe6fecebdedd5beULL}}, + // 10^-10 ~= dbe6fecebdedd5beb573440e5a884d1c * 2^-161 + {{0xf78f69a51539d749ULL, 0xafebff0bcb24aafeULL}}, + // 10^-11 ~= afebff0bcb24aafef78f69a51539d749 * 2^-164 + {{0xf93f87b7442e45d4ULL, 0x8cbccc096f5088cbULL}}, + // 10^-12 ~= 8cbccc096f5088cbf93f87b7442e45d4 * 2^-167 + {{0x2865a5f206b06fbaULL, 0xe12e13424bb40e13ULL}}, + // 10^-13 ~= e12e13424bb40e132865a5f206b06fba * 2^-171 + {{0x538484c19ef38c95ULL, 0xb424dc35095cd80fULL}}, + // 10^-14 ~= b424dc35095cd80f538484c19ef38c95 * 2^-174 + {{0x0f9d37014bf60a11ULL, 0x901d7cf73ab0acd9ULL}}, + // 10^-15 ~= 901d7cf73ab0acd90f9d37014bf60a11 * 2^-177 + {{0x4c2ebe687989a9b4ULL, 0xe69594bec44de15bULL}}, + // 10^-16 ~= e69594bec44de15b4c2ebe687989a9b4 * 2^-181 + {{0x09befeb9fad487c3ULL, 0xb877aa3236a4b449ULL}}, + // 10^-17 ~= b877aa3236a4b44909befeb9fad487c3 * 2^-184 + {{0x3aff322e62439fd0ULL, 0x9392ee8e921d5d07ULL}}, + // 10^-18 ~= 9392ee8e921d5d073aff322e62439fd0 * 2^-187 + {{0x2b31e9e3d06c32e6ULL, 0xec1e4a7db69561a5ULL}}, + // 10^-19 ~= ec1e4a7db69561a52b31e9e3d06c32e6 * 2^-191 + {{0x88f4bb1ca6bcf585ULL, 0xbce5086492111aeaULL}}, + // 10^-20 ~= bce5086492111aea88f4bb1ca6bcf585 * 2^-194 + {{0xd3f6fc16ebca5e04ULL, 0x971da05074da7beeULL}}, + // 10^-21 ~= 971da05074da7beed3f6fc16ebca5e04 * 2^-197 + {{0x5324c68b12dd6339ULL, 0xf1c90080baf72cb1ULL}}, + // 10^-22 ~= f1c90080baf72cb15324c68b12dd6339 * 2^-201 + {{0x75b7053c0f178294ULL, 0xc16d9a0095928a27ULL}}, + // 10^-23 ~= c16d9a0095928a2775b7053c0f178294 * 2^-204 + {{0xc4926a9672793543ULL, 0x9abe14cd44753b52ULL}}, + // 10^-24 ~= 9abe14cd44753b52c4926a9672793543 * 2^-207 + {{0x3a83ddbd83f52205ULL, 0xf79687aed3eec551ULL}}, + // 10^-25 ~= f79687aed3eec5513a83ddbd83f52205 * 2^-211 + {{0x95364afe032a819eULL, 0xc612062576589ddaULL}}, + // 10^-26 ~= c612062576589dda95364afe032a819e * 2^-214 + {{0x775ea264cf55347eULL, 0x9e74d1b791e07e48ULL}}, + // 10^-27 ~= 9e74d1b791e07e48775ea264cf55347e * 2^-217 + {{0x8bca9d6e188853fdULL, 0xfd87b5f28300ca0dULL}}, + // 10^-28 ~= fd87b5f28300ca0d8bca9d6e188853fd * 2^-221 + {{0x096ee45813a04331ULL, 0xcad2f7f5359a3b3eULL}}, + // 10^-29 ~= cad2f7f5359a3b3e096ee45813a04331 * 2^-224 + {{0xa1258379a94d028eULL, 0xa2425ff75e14fc31ULL}}, + // 10^-30 ~= a2425ff75e14fc31a1258379a94d028e * 2^-227 + {{0x80eacf948770ced8ULL, 0x81ceb32c4b43fcf4ULL}}, + // 10^-31 ~= 81ceb32c4b43fcf480eacf948770ced8 * 2^-230 + {{0x67de18eda5814af3ULL, 0xcfb11ead453994baULL}}, + // 10^-32 ~= cfb11ead453994ba67de18eda5814af3 * 2^-234 + {{0xecb1ad8aeacdd58fULL, 0xa6274bbdd0fadd61ULL}}, + // 10^-33 ~= a6274bbdd0fadd61ecb1ad8aeacdd58f * 2^-237 + {{0xbd5af13bef0b113fULL, 0x84ec3c97da624ab4ULL}}, + // 10^-34 ~= 84ec3c97da624ab4bd5af13bef0b113f * 2^-240 + {{0x955e4ec64b44e865ULL, 0xd4ad2dbfc3d07787ULL}}, + // 10^-35 ~= d4ad2dbfc3d07787955e4ec64b44e865 * 2^-244 + {{0xdde50bd1d5d0b9eaULL, 0xaa242499697392d2ULL}}, + // 10^-36 ~= aa242499697392d2dde50bd1d5d0b9ea * 2^-247 + {{0x7e50d64177da2e55ULL, 0x881cea14545c7575ULL}} + // 10^-37 ~= 881cea14545c75757e50d64177da2e55 * 2^-250 +}; + +// Ex-128 from 10^(-x) ~= Kx*2^(-Ex); Kx rounded up to 128 bits, 1 <= x <= 37 +unsigned int Ex128m128[] = { + 3, // 131 - 128, Ex = 131 + 6, // 134 - 128, Ex = 134 + 9, // 137 - 128, Ex = 137 + 13, // 141 - 128, Ex = 141 + 16, // 144 - 128, Ex = 144 + 19, // 147 - 128, Ex = 147 + 23, // 151 - 128, Ex = 151 + 26, // 154 - 128, Ex = 154 + 29, // 157 - 128, Ex = 157 + 33, // 161 - 128, Ex = 161 + 36, // 164 - 128, Ex = 164 + 39, // 167 - 128, Ex = 167 + 43, // 171 - 128, Ex = 171 + 46, // 174 - 128, Ex = 174 + 49, // 177 - 128, Ex = 177 + 53, // 181 - 128, Ex = 181 + 56, // 184 - 128, Ex = 184 + 59, // 187 - 128, Ex = 187 + 63, // 191 - 128, Ex = 191 + 2, // 194 - 192, Ex = 194 + 5, // 197 - 192, Ex = 197 + 9, // 201 - 192, Ex = 201 + 12, // 204 - 192, Ex = 204 + 15, // 207 - 192, Ex = 207 + 19, // 211 - 192, Ex = 211 + 22, // 214 - 192, Ex = 214 + 25, // 217 - 192, Ex = 217 + 29, // 221 - 192, Ex = 221 + 32, // 224 - 192, Ex = 224 + 35, // 227 - 192, Ex = 227 + 38, // 230 - 192, Ex = 230 + 42, // 234 - 192, Ex = 234 + 45, // 237 - 192, Ex = 237 + 48, // 240 - 192, Ex = 240 + 52, // 244 - 192, Ex = 244 + 55, // 247 - 192, Ex = 247 + 58 // 250 - 192, Ex = 250 +}; + +// Values of 1/2 in the right position to be compared with the fraction from +// C * kx, 1 <= x <= 37; the fraction consists of the low Ex bits in C * kx +// (these values are aligned with the high 128 bits of the fraction) +UINT64 half128[] = { + 0x0000000000000004ULL, // half / 2^128 = 4 + 0x0000000000000020ULL, // half / 2^128 = 20 + 0x0000000000000100ULL, // half / 2^128 = 100 + 0x0000000000001000ULL, // half / 2^128 = 1000 + 0x0000000000008000ULL, // half / 2^128 = 8000 + 0x0000000000040000ULL, // half / 2^128 = 40000 + 0x0000000000400000ULL, // half / 2^128 = 400000 + 0x0000000002000000ULL, // half / 2^128 = 2000000 + 0x0000000010000000ULL, // half / 2^128 = 10000000 + 0x0000000100000000ULL, // half / 2^128 = 100000000 + 0x0000000800000000ULL, // half / 2^128 = 800000000 + 0x0000004000000000ULL, // half / 2^128 = 4000000000 + 0x0000040000000000ULL, // half / 2^128 = 40000000000 + 0x0000200000000000ULL, // half / 2^128 = 200000000000 + 0x0001000000000000ULL, // half / 2^128 = 1000000000000 + 0x0010000000000000ULL, // half / 2^128 = 10000000000000 + 0x0080000000000000ULL, // half / 2^128 = 80000000000000 + 0x0400000000000000ULL, // half / 2^128 = 400000000000000 + 0x4000000000000000ULL, // half / 2^128 = 4000000000000000 + 0x0000000000000002ULL, // half / 2^192 = 2 + 0x0000000000000010ULL, // half / 2^192 = 10 + 0x0000000000000100ULL, // half / 2^192 = 100 + 0x0000000000000800ULL, // half / 2^192 = 800 + 0x0000000000004000ULL, // half / 2^192 = 4000 + 0x0000000000040000ULL, // half / 2^192 = 40000 + 0x0000000000200000ULL, // half / 2^192 = 200000 + 0x0000000001000000ULL, // half / 2^192 = 1000000 + 0x0000000010000000ULL, // half / 2^192 = 10000000 + 0x0000000080000000ULL, // half / 2^192 = 80000000 + 0x0000000400000000ULL, // half / 2^192 = 400000000 + 0x0000002000000000ULL, // half / 2^192 = 2000000000 + 0x0000020000000000ULL, // half / 2^192 = 20000000000 + 0x0000100000000000ULL, // half / 2^192 = 100000000000 + 0x0000800000000000ULL, // half / 2^192 = 800000000000 + 0x0008000000000000ULL, // half / 2^192 = 8000000000000 + 0x0040000000000000ULL, // half / 2^192 = 40000000000000 + 0x0200000000000000ULL // half / 2^192 = 200000000000000 +}; + +// Values of mask in the right position to obtain the high Ex - 128 or Ex - 192 +// bits of the fraction from C * kx, 1 <= x <= 37; the fraction consists of +// the low Ex bits in C * kx +UINT64 mask128[] = { + 0x0000000000000007ULL, // mask / 2^128 + 0x000000000000003fULL, // mask / 2^128 + 0x00000000000001ffULL, // mask / 2^128 + 0x0000000000001fffULL, // mask / 2^128 + 0x000000000000ffffULL, // mask / 2^128 + 0x000000000007ffffULL, // mask / 2^128 + 0x00000000007fffffULL, // mask / 2^128 + 0x0000000003ffffffULL, // mask / 2^128 + 0x000000001fffffffULL, // mask / 2^128 + 0x00000001ffffffffULL, // mask / 2^128 + 0x0000000fffffffffULL, // mask / 2^128 + 0x0000007fffffffffULL, // mask / 2^128 + 0x000007ffffffffffULL, // mask / 2^128 + 0x00003fffffffffffULL, // mask / 2^128 + 0x0001ffffffffffffULL, // mask / 2^128 + 0x001fffffffffffffULL, // mask / 2^128 + 0x00ffffffffffffffULL, // mask / 2^128 + 0x07ffffffffffffffULL, // mask / 2^128 + 0x7fffffffffffffffULL, // mask / 2^128 + 0x0000000000000003ULL, // mask / 2^192 + 0x000000000000001fULL, // mask / 2^192 + 0x00000000000001ffULL, // mask / 2^192 + 0x0000000000000fffULL, // mask / 2^192 + 0x0000000000007fffULL, // mask / 2^192 + 0x000000000007ffffULL, // mask / 2^192 + 0x00000000003fffffULL, // mask / 2^192 + 0x0000000001ffffffULL, // mask / 2^192 + 0x000000001fffffffULL, // mask / 2^192 + 0x00000000ffffffffULL, // mask / 2^192 + 0x00000007ffffffffULL, // mask / 2^192 + 0x0000003fffffffffULL, // mask / 2^192 + 0x000003ffffffffffULL, // mask / 2^192 + 0x00001fffffffffffULL, // mask / 2^192 + 0x0000ffffffffffffULL, // mask / 2^192 + 0x000fffffffffffffULL, // mask / 2^192 + 0x007fffffffffffffULL, // mask / 2^192 + 0x03ffffffffffffffULL // mask / 2^192 +}; + +// Values of 10^(-x) trancated to Ex bits beyond the binary point, and +// in the right position to be compared with the fraction from C * kx, +// 1 <= x <= 37; the fraction consists of the low Ex bits in C * kx +// (these values are aligned with the low 128 bits of the fraction) +UINT128 ten2mxtrunc128[] = { + {{0xccccccccccccccccULL, 0xccccccccccccccccULL}}, + // (ten2mx >> 128) = cccccccccccccccccccccccccccccccc + {{0x3d70a3d70a3d70a3ULL, 0xa3d70a3d70a3d70aULL}}, + // (ten2mx >> 128) = a3d70a3d70a3d70a3d70a3d70a3d70a3 + {{0x645a1cac083126e9ULL, 0x83126e978d4fdf3bULL}}, + // (ten2mx >> 128) = 83126e978d4fdf3b645a1cac083126e9 + {{0xd3c36113404ea4a8ULL, 0xd1b71758e219652bULL}}, + // (ten2mx >> 128) = d1b71758e219652bd3c36113404ea4a8 + {{0x0fcf80dc33721d53ULL, 0xa7c5ac471b478423ULL}}, + // (ten2mx >> 128) = a7c5ac471b4784230fcf80dc33721d53 + {{0xa63f9a49c2c1b10fULL, 0x8637bd05af6c69b5ULL}}, + // (ten2mx >> 128) = 8637bd05af6c69b5a63f9a49c2c1b10f + {{0x3d32907604691b4cULL, 0xd6bf94d5e57a42bcULL}}, + // (ten2mx >> 128) = d6bf94d5e57a42bc3d32907604691b4c + {{0xfdc20d2b36ba7c3dULL, 0xabcc77118461cefcULL}}, + // (ten2mx >> 128) = abcc77118461cefcfdc20d2b36ba7c3d + {{0x31680a88f8953030ULL, 0x89705f4136b4a597ULL}}, + // (ten2mx >> 128) = 89705f4136b4a59731680a88f8953030 + {{0xb573440e5a884d1bULL, 0xdbe6fecebdedd5beULL}}, + // (ten2mx >> 128) = dbe6fecebdedd5beb573440e5a884d1b + {{0xf78f69a51539d748ULL, 0xafebff0bcb24aafeULL}}, + // (ten2mx >> 128) = afebff0bcb24aafef78f69a51539d748 + {{0xf93f87b7442e45d3ULL, 0x8cbccc096f5088cbULL}}, + // (ten2mx >> 128) = 8cbccc096f5088cbf93f87b7442e45d3 + {{0x2865a5f206b06fb9ULL, 0xe12e13424bb40e13ULL}}, + // (ten2mx >> 128) = e12e13424bb40e132865a5f206b06fb9 + {{0x538484c19ef38c94ULL, 0xb424dc35095cd80fULL}}, + // (ten2mx >> 128) = b424dc35095cd80f538484c19ef38c94 + {{0x0f9d37014bf60a10ULL, 0x901d7cf73ab0acd9ULL}}, + // (ten2mx >> 128) = 901d7cf73ab0acd90f9d37014bf60a10 + {{0x4c2ebe687989a9b3ULL, 0xe69594bec44de15bULL}}, + // (ten2mx >> 128) = e69594bec44de15b4c2ebe687989a9b3 + {{0x09befeb9fad487c2ULL, 0xb877aa3236a4b449ULL}}, + // (ten2mx >> 128) = b877aa3236a4b44909befeb9fad487c2 + {{0x3aff322e62439fcfULL, 0x9392ee8e921d5d07ULL}}, + // (ten2mx >> 128) = 9392ee8e921d5d073aff322e62439fcf + {{0x2b31e9e3d06c32e5ULL, 0xec1e4a7db69561a5ULL}}, + // (ten2mx >> 128) = ec1e4a7db69561a52b31e9e3d06c32e5 + {{0x88f4bb1ca6bcf584ULL, 0xbce5086492111aeaULL}}, + // (ten2mx >> 128) = bce5086492111aea88f4bb1ca6bcf584 + {{0xd3f6fc16ebca5e03ULL, 0x971da05074da7beeULL}}, + // (ten2mx >> 128) = 971da05074da7beed3f6fc16ebca5e03 + {{0x5324c68b12dd6338ULL, 0xf1c90080baf72cb1ULL}}, + // (ten2mx >> 128) = f1c90080baf72cb15324c68b12dd6338 + {{0x75b7053c0f178293ULL, 0xc16d9a0095928a27ULL}}, + // (ten2mx >> 128) = c16d9a0095928a2775b7053c0f178293 + {{0xc4926a9672793542ULL, 0x9abe14cd44753b52ULL}}, + // (ten2mx >> 128) = 9abe14cd44753b52c4926a9672793542 + {{0x3a83ddbd83f52204ULL, 0xf79687aed3eec551ULL}}, + // (ten2mx >> 128) = f79687aed3eec5513a83ddbd83f52204 + {{0x95364afe032a819dULL, 0xc612062576589ddaULL}}, + // (ten2mx >> 128) = c612062576589dda95364afe032a819d + {{0x775ea264cf55347dULL, 0x9e74d1b791e07e48ULL}}, + // (ten2mx >> 128) = 9e74d1b791e07e48775ea264cf55347d + {{0x8bca9d6e188853fcULL, 0xfd87b5f28300ca0dULL}}, + // (ten2mx >> 128) = fd87b5f28300ca0d8bca9d6e188853fc + {{0x096ee45813a04330ULL, 0xcad2f7f5359a3b3eULL}}, + // (ten2mx >> 128) = cad2f7f5359a3b3e096ee45813a04330 + {{0xa1258379a94d028dULL, 0xa2425ff75e14fc31ULL}}, + // (ten2mx >> 128) = a2425ff75e14fc31a1258379a94d028d + {{0x80eacf948770ced7ULL, 0x81ceb32c4b43fcf4ULL}}, + // (ten2mx >> 128) = 81ceb32c4b43fcf480eacf948770ced7 + {{0x67de18eda5814af2ULL, 0xcfb11ead453994baULL}}, + // (ten2mx >> 128) = cfb11ead453994ba67de18eda5814af2 + {{0xecb1ad8aeacdd58eULL, 0xa6274bbdd0fadd61ULL}}, + // (ten2mx >> 128) = a6274bbdd0fadd61ecb1ad8aeacdd58e + {{0xbd5af13bef0b113eULL, 0x84ec3c97da624ab4ULL}}, + // (ten2mx >> 128) = 84ec3c97da624ab4bd5af13bef0b113e + {{0x955e4ec64b44e864ULL, 0xd4ad2dbfc3d07787ULL}}, + // (ten2mx >> 128) = d4ad2dbfc3d07787955e4ec64b44e864 + {{0xdde50bd1d5d0b9e9ULL, 0xaa242499697392d2ULL}}, + // (ten2mx >> 128) = aa242499697392d2dde50bd1d5d0b9e9 + {{0x7e50d64177da2e54ULL, 0x881cea14545c7575ULL}} + // (ten2mx >> 128) = 881cea14545c75757e50d64177da2e54 +}; + +UINT192 Kx192[] = { + {{0xcccccccccccccccdULL, 0xccccccccccccccccULL, + 0xccccccccccccccccULL}}, + // 10^-1 ~= cccccccccccccccccccccccccccccccccccccccccccccccd * 2^-195 + {{0xd70a3d70a3d70a3eULL, 0x3d70a3d70a3d70a3ULL, + 0xa3d70a3d70a3d70aULL}}, + // 10^-2 ~= a3d70a3d70a3d70a3d70a3d70a3d70a3d70a3d70a3d70a3e * 2^-198 + {{0x78d4fdf3b645a1cbULL, 0x645a1cac083126e9ULL, + 0x83126e978d4fdf3bULL}}, + // 10^-3 ~= 83126e978d4fdf3b645a1cac083126e978d4fdf3b645a1cb * 2^-201 + {{0xc154c985f06f6945ULL, 0xd3c36113404ea4a8ULL, + 0xd1b71758e219652bULL}}, + // 10^-4 ~= d1b71758e219652bd3c36113404ea4a8c154c985f06f6945 * 2^-205 + {{0xcddd6e04c0592104ULL, 0x0fcf80dc33721d53ULL, + 0xa7c5ac471b478423ULL}}, + // 10^-5 ~= a7c5ac471b4784230fcf80dc33721d53cddd6e04c0592104 * 2^-208 + {{0xd7e45803cd141a6aULL, 0xa63f9a49c2c1b10fULL, + 0x8637bd05af6c69b5ULL}}, + // 10^-6 ~= 8637bd05af6c69b5a63f9a49c2c1b10fd7e45803cd141a6a * 2^-211 + {{0x8ca08cd2e1b9c3dcULL, 0x3d32907604691b4cULL, + 0xd6bf94d5e57a42bcULL}}, + // 10^-7 ~= d6bf94d5e57a42bc3d32907604691b4c8ca08cd2e1b9c3dc * 2^-215 + {{0x3d4d3d758161697dULL, 0xfdc20d2b36ba7c3dULL, + 0xabcc77118461cefcULL}}, + // 10^-8 ~= abcc77118461cefcfdc20d2b36ba7c3d3d4d3d758161697d * 2^-218 + {{0xfdd7645e011abacaULL, 0x31680a88f8953030ULL, + 0x89705f4136b4a597ULL}}, + // 10^-9 ~= 89705f4136b4a59731680a88f8953030fdd7645e011abaca * 2^-221 + {{0x2fbf06fcce912addULL, 0xb573440e5a884d1bULL, + 0xdbe6fecebdedd5beULL}}, + // 10^-10 ~= dbe6fecebdedd5beb573440e5a884d1b2fbf06fcce912add * 2^-225 + {{0xf2ff38ca3eda88b1ULL, 0xf78f69a51539d748ULL, + 0xafebff0bcb24aafeULL}}, + // 10^-11 ~= afebff0bcb24aafef78f69a51539d748f2ff38ca3eda88b1 * 2^-228 + {{0xf598fa3b657ba08eULL, 0xf93f87b7442e45d3ULL, + 0x8cbccc096f5088cbULL}}, + // 10^-12 ~= 8cbccc096f5088cbf93f87b7442e45d3f598fa3b657ba08e * 2^-231 + {{0x88f4c3923bf900e3ULL, 0x2865a5f206b06fb9ULL, + 0xe12e13424bb40e13ULL}}, + // 10^-13 ~= e12e13424bb40e132865a5f206b06fb988f4c3923bf900e3 * 2^-235 + {{0x6d909c74fcc733e9ULL, 0x538484c19ef38c94ULL, + 0xb424dc35095cd80fULL}}, + // 10^-14 ~= b424dc35095cd80f538484c19ef38c946d909c74fcc733e9 * 2^-238 + {{0x57a6e390ca38f654ULL, 0x0f9d37014bf60a10ULL, + 0x901d7cf73ab0acd9ULL}}, + // 10^-15 ~= 901d7cf73ab0acd90f9d37014bf60a1057a6e390ca38f654 * 2^-241 + {{0xbf716c1add27f086ULL, 0x4c2ebe687989a9b3ULL, + 0xe69594bec44de15bULL}}, + // 10^-16 ~= e69594bec44de15b4c2ebe687989a9b3bf716c1add27f086 * 2^-245 + {{0xff8df0157db98d38ULL, 0x09befeb9fad487c2ULL, + 0xb877aa3236a4b449ULL}}, + // 10^-17 ~= b877aa3236a4b44909befeb9fad487c2ff8df0157db98d38 * 2^-248 + {{0x32d7f344649470faULL, 0x3aff322e62439fcfULL, + 0x9392ee8e921d5d07ULL}}, + // 10^-18 ~= 9392ee8e921d5d073aff322e62439fcf32d7f344649470fa * 2^-251 + {{0x1e2652070753e7f5ULL, 0x2b31e9e3d06c32e5ULL, + 0xec1e4a7db69561a5ULL}}, + // 10^-19 ~= ec1e4a7db69561a52b31e9e3d06c32e51e2652070753e7f5 * 2^-255 + {{0x181ea8059f76532bULL, 0x88f4bb1ca6bcf584ULL, + 0xbce5086492111aeaULL}}, + // 10^-20 ~= bce5086492111aea88f4bb1ca6bcf584181ea8059f76532b * 2^-258 + {{0x467eecd14c5ea8efULL, 0xd3f6fc16ebca5e03ULL, + 0x971da05074da7beeULL}}, + // 10^-21 ~= 971da05074da7beed3f6fc16ebca5e03467eecd14c5ea8ef * 2^-261 + {{0x70cb148213caa7e5ULL, 0x5324c68b12dd6338ULL, + 0xf1c90080baf72cb1ULL}}, + // 10^-22 ~= f1c90080baf72cb15324c68b12dd633870cb148213caa7e5 * 2^-265 + {{0x8d6f439b43088651ULL, 0x75b7053c0f178293ULL, + 0xc16d9a0095928a27ULL}}, + // 10^-23 ~= c16d9a0095928a2775b7053c0f1782938d6f439b43088651 * 2^-268 + {{0xd78c3615cf3a050dULL, 0xc4926a9672793542ULL, + 0x9abe14cd44753b52ULL}}, + // 10^-24 ~= 9abe14cd44753b52c4926a9672793542d78c3615cf3a050d * 2^-271 + {{0x8c1389bc7ec33b48ULL, 0x3a83ddbd83f52204ULL, + 0xf79687aed3eec551ULL}}, + // 10^-25 ~= f79687aed3eec5513a83ddbd83f522048c1389bc7ec33b48 * 2^-275 + {{0x3cdc6e306568fc3aULL, 0x95364afe032a819dULL, + 0xc612062576589ddaULL}}, + // 10^-26 ~= c612062576589dda95364afe032a819d3cdc6e306568fc3a * 2^-278 + {{0xca49f1c05120c9c8ULL, 0x775ea264cf55347dULL, + 0x9e74d1b791e07e48ULL}}, + // 10^-27 ~= 9e74d1b791e07e48775ea264cf55347dca49f1c05120c9c8 * 2^-281 + {{0x76dcb60081ce0fa6ULL, 0x8bca9d6e188853fcULL, + 0xfd87b5f28300ca0dULL}}, + // 10^-28 ~= fd87b5f28300ca0d8bca9d6e188853fc76dcb60081ce0fa6 * 2^-285 + {{0x5f16f80067d80c85ULL, 0x096ee45813a04330ULL, + 0xcad2f7f5359a3b3eULL}}, + // 10^-29 ~= cad2f7f5359a3b3e096ee45813a043305f16f80067d80c85 * 2^-288 + {{0x18df2ccd1fe00a04ULL, 0xa1258379a94d028dULL, + 0xa2425ff75e14fc31ULL}}, + // 10^-30 ~= a2425ff75e14fc31a1258379a94d028d18df2ccd1fe00a04 * 2^-291 + {{0x4718f0a419800803ULL, 0x80eacf948770ced7ULL, + 0x81ceb32c4b43fcf4ULL}}, + // 10^-31 ~= 81ceb32c4b43fcf480eacf948770ced74718f0a419800803 * 2^-294 + {{0x0b5b1aa028ccd99fULL, 0x67de18eda5814af2ULL, + 0xcfb11ead453994baULL}}, + // 10^-32 ~= cfb11ead453994ba67de18eda5814af20b5b1aa028ccd99f * 2^-298 + {{0x6f7c154ced70ae19ULL, 0xecb1ad8aeacdd58eULL, + 0xa6274bbdd0fadd61ULL}}, + // 10^-33 ~= a6274bbdd0fadd61ecb1ad8aeacdd58e6f7c154ced70ae19 * 2^-301 + {{0xbf967770bdf3be7aULL, 0xbd5af13bef0b113eULL, + 0x84ec3c97da624ab4ULL}}, + // 10^-34 ~= 84ec3c97da624ab4bd5af13bef0b113ebf967770bdf3be7a * 2^-304 + {{0x65bd8be79652ca5dULL, 0x955e4ec64b44e864ULL, + 0xd4ad2dbfc3d07787ULL}}, + // 10^-35 ~= d4ad2dbfc3d07787955e4ec64b44e86465bd8be79652ca5d * 2^-308 + {{0xeafe098611dbd517ULL, 0xdde50bd1d5d0b9e9ULL, + 0xaa242499697392d2ULL}}, + // 10^-36 ~= aa242499697392d2dde50bd1d5d0b9e9eafe098611dbd517 * 2^-311 + {{0xbbfe6e04db164413ULL, 0x7e50d64177da2e54ULL, + 0x881cea14545c7575ULL}}, + // 10^-37 ~= 881cea14545c75757e50d64177da2e54bbfe6e04db164413 * 2^-314 + {{0x2cca49a15e8a0684ULL, 0x96e7bd358c904a21ULL, + 0xd9c7dced53c72255ULL}}, + // 10^-38 ~= d9c7dced53c7225596e7bd358c904a212cca49a15e8a0684 * 2^-318 + {{0x8a3b6e1ab2080537ULL, 0xabec975e0a0d081aULL, + 0xae397d8aa96c1b77ULL}}, + // 10^-39 ~= ae397d8aa96c1b77abec975e0a0d081a8a3b6e1ab2080537 * 2^-321 + {{0x3b62be7bc1a0042cULL, 0x2323ac4b3b3da015ULL, + 0x8b61313bbabce2c6ULL}}, + // 10^-40 ~= 8b61313bbabce2c62323ac4b3b3da0153b62be7bc1a0042c * 2^-324 + {{0x5f0463f935ccd379ULL, 0x6b6c46dec52f6688ULL, + 0xdf01e85f912e37a3ULL}}, + // 10^-41 ~= df01e85f912e37a36b6c46dec52f66885f0463f935ccd379 * 2^-328 + {{0x7f36b660f7d70f94ULL, 0x55f038b237591ed3ULL, + 0xb267ed1940f1c61cULL}}, + // 10^-42 ~= b267ed1940f1c61c55f038b237591ed37f36b660f7d70f94 * 2^-331 + {{0xcc2bc51a5fdf3faaULL, 0x77f3608e92adb242ULL, + 0x8eb98a7a9a5b04e3ULL}}, + // 10^-43 ~= 8eb98a7a9a5b04e377f3608e92adb242cc2bc51a5fdf3faa * 2^-334 + {{0xe046082a32fecc42ULL, 0x8cb89a7db77c506aULL, + 0xe45c10c42a2b3b05ULL}}, + // 10^-44 ~= e45c10c42a2b3b058cb89a7db77c506ae046082a32fecc42 * 2^-338 + {{0x4d04d354f598a368ULL, 0x3d607b97c5fd0d22ULL, + 0xb6b00d69bb55c8d1ULL}}, + // 10^-45 ~= b6b00d69bb55c8d13d607b97c5fd0d224d04d354f598a368 * 2^-341 + {{0x3d9d75dd9146e920ULL, 0xcab3961304ca70e8ULL, + 0x9226712162ab070dULL}}, + // 10^-46 ~= 9226712162ab070dcab3961304ca70e83d9d75dd9146e920 * 2^-344 + {{0xc8fbefc8e8717500ULL, 0xaab8f01e6e10b4a6ULL, + 0xe9d71b689dde71afULL}}, + // 10^-47 ~= e9d71b689dde71afaab8f01e6e10b4a6c8fbefc8e8717500 * 2^-348 + {{0x3a63263a538df734ULL, 0x5560c018580d5d52ULL, + 0xbb127c53b17ec159ULL}}, + // 10^-48 ~= bb127c53b17ec1595560c018580d5d523a63263a538df734 * 2^-351 + {{0x2eb5b82ea93e5f5dULL, 0xdde7001379a44aa8ULL, + 0x95a8637627989aadULL}}, + // 10^-49 ~= 95a8637627989aaddde7001379a44aa82eb5b82ea93e5f5d * 2^-354 + {{0x4abc59e441fd6561ULL, 0x963e66858f6d4440ULL, + 0xef73d256a5c0f77cULL}}, + // 10^-50 ~= ef73d256a5c0f77c963e66858f6d44404abc59e441fd6561 * 2^-358 + {{0x6efd14b69b311de7ULL, 0xde98520472bdd033ULL, + 0xbf8fdb78849a5f96ULL}}, + // 10^-51 ~= bf8fdb78849a5f96de98520472bdd0336efd14b69b311de7 * 2^-361 + {{0x259743c548f417ecULL, 0xe546a8038efe4029ULL, + 0x993fe2c6d07b7fabULL}}, + // 10^-52 ~= 993fe2c6d07b7fabe546a8038efe4029259743c548f417ec * 2^-364 + {{0x3c25393ba7ecf313ULL, 0xd53dd99f4b3066a8ULL, + 0xf53304714d9265dfULL}}, + // 10^-53 ~= f53304714d9265dfd53dd99f4b3066a83c25393ba7ecf313 * 2^-368 + {{0x96842dc95323f5a9ULL, 0xaa97e14c3c26b886ULL, + 0xc428d05aa4751e4cULL}}, + // 10^-54 ~= c428d05aa4751e4caa97e14c3c26b88696842dc95323f5a9 * 2^-371 + {{0xab9cf16ddc1cc487ULL, 0x55464dd69685606bULL, + 0x9ced737bb6c4183dULL}}, + // 10^-55 ~= 9ced737bb6c4183d55464dd69685606bab9cf16ddc1cc487 * 2^-374 + {{0xac2e4f162cfad40bULL, 0xeed6e2f0f0d56712ULL, 0xfb158592be068d2eULL}} + // 10^-56 ~= fb158592be068d2eeed6e2f0f0d56712ac2e4f162cfad40b * 2^-378 +}; + +unsigned int Ex192m192[] = { + 3, // 195 - 192, Ex = 195 + 6, // 198 - 192, Ex = 198 + 9, // 201 - 192, Ex = 201 + 13, // 205 - 192, Ex = 205 + 16, // 208 - 192, Ex = 208 + 19, // 211 - 192, Ex = 211 + 23, // 215 - 192, Ex = 215 + 26, // 218 - 192, Ex = 218 + 29, // 221 - 192, Ex = 221 + 33, // 225 - 192, Ex = 225 + 36, // 228 - 192, Ex = 228 + 39, // 231 - 192, Ex = 231 + 43, // 235 - 192, Ex = 235 + 46, // 238 - 192, Ex = 238 + 49, // 241 - 192, Ex = 241 + 53, // 245 - 192, Ex = 245 + 56, // 248 - 192, Ex = 248 + 59, // 251 - 192, Ex = 251 + 63, // 255 - 192, Ex = 255 + 2, // 258 - 256, Ex = 258 + 5, // 261 - 256, Ex = 261 + 9, // 265 - 256, Ex = 265 + 12, // 268 - 256, Ex = 268 + 15, // 271 - 256, Ex = 271 + 19, // 275 - 256, Ex = 275 + 22, // 278 - 256, Ex = 278 + 25, // 281 - 256, Ex = 281 + 29, // 285 - 256, Ex = 285 + 32, // 288 - 256, Ex = 288 + 35, // 291 - 256, Ex = 291 + 38, // 294 - 256, Ex = 294 + 42, // 298 - 256, Ex = 298 + 45, // 301 - 256, Ex = 301 + 48, // 304 - 256, Ex = 304 + 52, // 308 - 256, Ex = 308 + 55, // 311 - 256, Ex = 311 + 58, // 314 - 256, Ex = 314 + 62, // 318 - 256, Ex = 318 + 1, // 321 - 320, Ex = 321 + 4, // 324 - 320, Ex = 324 + 8, // 328 - 320, Ex = 328 + 11, // 331 - 320, Ex = 331 + 14, // 334 - 320, Ex = 334 + 18, // 338 - 320, Ex = 338 + 21, // 341 - 320, Ex = 341 + 24, // 344 - 320, Ex = 344 + 28, // 348 - 320, Ex = 348 + 31, // 351 - 320, Ex = 351 + 34, // 354 - 320, Ex = 354 + 38, // 358 - 320, Ex = 358 + 41, // 361 - 320, Ex = 361 + 44, // 364 - 320, Ex = 364 + 48, // 368 - 320, Ex = 368 + 51, // 371 - 320, Ex = 371 + 54, // 374 - 320, Ex = 374 + 58 // 378 - 320, Ex = 378 +}; + +UINT64 half192[] = { + 0x0000000000000004ULL, // half / 2^192 = 4 + 0x0000000000000020ULL, // half / 2^192 = 20 + 0x0000000000000100ULL, // half / 2^192 = 100 + 0x0000000000001000ULL, // half / 2^192 = 1000 + 0x0000000000008000ULL, // half / 2^192 = 8000 + 0x0000000000040000ULL, // half / 2^192 = 40000 + 0x0000000000400000ULL, // half / 2^192 = 400000 + 0x0000000002000000ULL, // half / 2^192 = 2000000 + 0x0000000010000000ULL, // half / 2^192 = 10000000 + 0x0000000100000000ULL, // half / 2^192 = 100000000 + 0x0000000800000000ULL, // half / 2^192 = 800000000 + 0x0000004000000000ULL, // half / 2^192 = 4000000000 + 0x0000040000000000ULL, // half / 2^192 = 40000000000 + 0x0000200000000000ULL, // half / 2^192 = 200000000000 + 0x0001000000000000ULL, // half / 2^192 = 1000000000000 + 0x0010000000000000ULL, // half / 2^192 = 10000000000000 + 0x0080000000000000ULL, // half / 2^192 = 80000000000000 + 0x0400000000000000ULL, // half / 2^192 = 400000000000000 + 0x4000000000000000ULL, // half / 2^192 = 4000000000000000 + 0x0000000000000002ULL, // half / 2^256 = 2 + 0x0000000000000010ULL, // half / 2^256 = 10 + 0x0000000000000100ULL, // half / 2^256 = 100 + 0x0000000000000800ULL, // half / 2^256 = 800 + 0x0000000000004000ULL, // half / 2^256 = 4000 + 0x0000000000040000ULL, // half / 2^256 = 40000 + 0x0000000000200000ULL, // half / 2^256 = 200000 + 0x0000000001000000ULL, // half / 2^256 = 1000000 + 0x0000000010000000ULL, // half / 2^256 = 10000000 + 0x0000000080000000ULL, // half / 2^256 = 80000000 + 0x0000000400000000ULL, // half / 2^256 = 400000000 + 0x0000002000000000ULL, // half / 2^256 = 2000000000 + 0x0000020000000000ULL, // half / 2^256 = 20000000000 + 0x0000100000000000ULL, // half / 2^256 = 100000000000 + 0x0000800000000000ULL, // half / 2^256 = 800000000000 + 0x0008000000000000ULL, // half / 2^256 = 8000000000000 + 0x0040000000000000ULL, // half / 2^256 = 40000000000000 + 0x0200000000000000ULL, // half / 2^256 = 200000000000000 + 0x2000000000000000ULL, // half / 2^256 = 2000000000000000 + 0x0000000000000001ULL, // half / 2^320 = 1 + 0x0000000000000008ULL, // half / 2^320 = 8 + 0x0000000000000080ULL, // half / 2^320 = 80 + 0x0000000000000400ULL, // half / 2^320 = 400 + 0x0000000000002000ULL, // half / 2^320 = 2000 + 0x0000000000020000ULL, // half / 2^320 = 20000 + 0x0000000000100000ULL, // half / 2^320 = 100000 + 0x0000000000800000ULL, // half / 2^320 = 800000 + 0x0000000008000000ULL, // half / 2^320 = 8000000 + 0x0000000040000000ULL, // half / 2^320 = 40000000 + 0x0000000200000000ULL, // half / 2^320 = 200000000 + 0x0000002000000000ULL, // half / 2^320 = 2000000000 + 0x0000010000000000ULL, // half / 2^320 = 10000000000 + 0x0000080000000000ULL, // half / 2^320 = 80000000000 + 0x0000800000000000ULL, // half / 2^320 = 800000000000 + 0x0004000000000000ULL, // half / 2^320 = 4000000000000 + 0x0020000000000000ULL, // half / 2^320 = 20000000000000 + 0x0200000000000000ULL // half / 2^320 = 200000000000000 +}; + +UINT64 mask192[] = { + 0x0000000000000007ULL, // mask / 2^192 + 0x000000000000003fULL, // mask / 2^192 + 0x00000000000001ffULL, // mask / 2^192 + 0x0000000000001fffULL, // mask / 2^192 + 0x000000000000ffffULL, // mask / 2^192 + 0x000000000007ffffULL, // mask / 2^192 + 0x00000000007fffffULL, // mask / 2^192 + 0x0000000003ffffffULL, // mask / 2^192 + 0x000000001fffffffULL, // mask / 2^192 + 0x00000001ffffffffULL, // mask / 2^192 + 0x0000000fffffffffULL, // mask / 2^192 + 0x0000007fffffffffULL, // mask / 2^192 + 0x000007ffffffffffULL, // mask / 2^192 + 0x00003fffffffffffULL, // mask / 2^192 + 0x0001ffffffffffffULL, // mask / 2^192 + 0x001fffffffffffffULL, // mask / 2^192 + 0x00ffffffffffffffULL, // mask / 2^192 + 0x07ffffffffffffffULL, // mask / 2^192 + 0x7fffffffffffffffULL, // mask / 2^192 + 0x0000000000000003ULL, // mask / 2^256 + 0x000000000000001fULL, // mask / 2^256 + 0x00000000000001ffULL, // mask / 2^256 + 0x0000000000000fffULL, // mask / 2^256 + 0x0000000000007fffULL, // mask / 2^256 + 0x000000000007ffffULL, // mask / 2^256 + 0x00000000003fffffULL, // mask / 2^256 + 0x0000000001ffffffULL, // mask / 2^256 + 0x000000001fffffffULL, // mask / 2^256 + 0x00000000ffffffffULL, // mask / 2^256 + 0x00000007ffffffffULL, // mask / 2^256 + 0x0000003fffffffffULL, // mask / 2^256 + 0x000003ffffffffffULL, // mask / 2^256 + 0x00001fffffffffffULL, // mask / 2^256 + 0x0000ffffffffffffULL, // mask / 2^256 + 0x000fffffffffffffULL, // mask / 2^256 + 0x007fffffffffffffULL, // mask / 2^256 + 0x03ffffffffffffffULL, // mask / 2^256 + 0x3fffffffffffffffULL, // mask / 2^256 + 0x0000000000000001ULL, // mask / 2^320 + 0x000000000000000fULL, // mask / 2^320 + 0x00000000000000ffULL, // mask / 2^320 + 0x00000000000007ffULL, // mask / 2^320 + 0x0000000000003fffULL, // mask / 2^320 + 0x000000000003ffffULL, // mask / 2^320 + 0x00000000001fffffULL, // mask / 2^320 + 0x0000000000ffffffULL, // mask / 2^320 + 0x000000000fffffffULL, // mask / 2^320 + 0x000000007fffffffULL, // mask / 2^320 + 0x00000003ffffffffULL, // mask / 2^320 + 0x0000003fffffffffULL, // mask / 2^320 + 0x000001ffffffffffULL, // mask / 2^320 + 0x00000fffffffffffULL, // mask / 2^320 + 0x0000ffffffffffffULL, // mask / 2^320 + 0x0007ffffffffffffULL, // mask / 2^320 + 0x003fffffffffffffULL, // mask / 2^320 + 0x03ffffffffffffffULL // mask / 2^320 +}; + +UINT192 ten2mxtrunc192[] = { + {{0xccccccccccccccccULL, 0xccccccccccccccccULL, + 0xccccccccccccccccULL}}, + // (ten2mx >> 192) = cccccccccccccccccccccccccccccccccccccccccccccccc + {{0xd70a3d70a3d70a3dULL, 0x3d70a3d70a3d70a3ULL, + 0xa3d70a3d70a3d70aULL}}, + // (ten2mx >> 192) = a3d70a3d70a3d70a3d70a3d70a3d70a3d70a3d70a3d70a3d + {{0x78d4fdf3b645a1caULL, 0x645a1cac083126e9ULL, + 0x83126e978d4fdf3bULL}}, + // (ten2mx >> 192) = 83126e978d4fdf3b645a1cac083126e978d4fdf3b645a1ca + {{0xc154c985f06f6944ULL, 0xd3c36113404ea4a8ULL, + 0xd1b71758e219652bULL}}, + // (ten2mx >> 192) = d1b71758e219652bd3c36113404ea4a8c154c985f06f6944 + {{0xcddd6e04c0592103ULL, 0x0fcf80dc33721d53ULL, + 0xa7c5ac471b478423ULL}}, + // (ten2mx >> 192) = a7c5ac471b4784230fcf80dc33721d53cddd6e04c0592103 + {{0xd7e45803cd141a69ULL, 0xa63f9a49c2c1b10fULL, + 0x8637bd05af6c69b5ULL}}, + // (ten2mx >> 192) = 8637bd05af6c69b5a63f9a49c2c1b10fd7e45803cd141a69 + {{0x8ca08cd2e1b9c3dbULL, 0x3d32907604691b4cULL, + 0xd6bf94d5e57a42bcULL}}, + // (ten2mx >> 192) = d6bf94d5e57a42bc3d32907604691b4c8ca08cd2e1b9c3db + {{0x3d4d3d758161697cULL, 0xfdc20d2b36ba7c3dULL, + 0xabcc77118461cefcULL}}, + // (ten2mx >> 192) = abcc77118461cefcfdc20d2b36ba7c3d3d4d3d758161697c + {{0xfdd7645e011abac9ULL, 0x31680a88f8953030ULL, + 0x89705f4136b4a597ULL}}, + // (ten2mx >> 192) = 89705f4136b4a59731680a88f8953030fdd7645e011abac9 + {{0x2fbf06fcce912adcULL, 0xb573440e5a884d1bULL, + 0xdbe6fecebdedd5beULL}}, + // (ten2mx >> 192) = dbe6fecebdedd5beb573440e5a884d1b2fbf06fcce912adc + {{0xf2ff38ca3eda88b0ULL, 0xf78f69a51539d748ULL, + 0xafebff0bcb24aafeULL}}, + // (ten2mx >> 192) = afebff0bcb24aafef78f69a51539d748f2ff38ca3eda88b0 + {{0xf598fa3b657ba08dULL, 0xf93f87b7442e45d3ULL, + 0x8cbccc096f5088cbULL}}, + // (ten2mx >> 192) = 8cbccc096f5088cbf93f87b7442e45d3f598fa3b657ba08d + {{0x88f4c3923bf900e2ULL, 0x2865a5f206b06fb9ULL, + 0xe12e13424bb40e13ULL}}, + // (ten2mx >> 192) = e12e13424bb40e132865a5f206b06fb988f4c3923bf900e2 + {{0x6d909c74fcc733e8ULL, 0x538484c19ef38c94ULL, + 0xb424dc35095cd80fULL}}, + // (ten2mx >> 192) = b424dc35095cd80f538484c19ef38c946d909c74fcc733e8 + {{0x57a6e390ca38f653ULL, 0x0f9d37014bf60a10ULL, + 0x901d7cf73ab0acd9ULL}}, + // (ten2mx >> 192) = 901d7cf73ab0acd90f9d37014bf60a1057a6e390ca38f653 + {{0xbf716c1add27f085ULL, 0x4c2ebe687989a9b3ULL, + 0xe69594bec44de15bULL}}, + // (ten2mx >> 192) = e69594bec44de15b4c2ebe687989a9b3bf716c1add27f085 + {{0xff8df0157db98d37ULL, 0x09befeb9fad487c2ULL, + 0xb877aa3236a4b449ULL}}, + // (ten2mx >> 192) = b877aa3236a4b44909befeb9fad487c2ff8df0157db98d37 + {{0x32d7f344649470f9ULL, 0x3aff322e62439fcfULL, + 0x9392ee8e921d5d07ULL}}, + // (ten2mx >> 192) = 9392ee8e921d5d073aff322e62439fcf32d7f344649470f9 + {{0x1e2652070753e7f4ULL, 0x2b31e9e3d06c32e5ULL, + 0xec1e4a7db69561a5ULL}}, + // (ten2mx >> 192) = ec1e4a7db69561a52b31e9e3d06c32e51e2652070753e7f4 + {{0x181ea8059f76532aULL, 0x88f4bb1ca6bcf584ULL, + 0xbce5086492111aeaULL}}, + // (ten2mx >> 192) = bce5086492111aea88f4bb1ca6bcf584181ea8059f76532a + {{0x467eecd14c5ea8eeULL, 0xd3f6fc16ebca5e03ULL, + 0x971da05074da7beeULL}}, + // (ten2mx >> 192) = 971da05074da7beed3f6fc16ebca5e03467eecd14c5ea8ee + {{0x70cb148213caa7e4ULL, 0x5324c68b12dd6338ULL, + 0xf1c90080baf72cb1ULL}}, + // (ten2mx >> 192) = f1c90080baf72cb15324c68b12dd633870cb148213caa7e4 + {{0x8d6f439b43088650ULL, 0x75b7053c0f178293ULL, + 0xc16d9a0095928a27ULL}}, + // (ten2mx >> 192) = c16d9a0095928a2775b7053c0f1782938d6f439b43088650 + {{0xd78c3615cf3a050cULL, 0xc4926a9672793542ULL, + 0x9abe14cd44753b52ULL}}, + // (ten2mx >> 192) = 9abe14cd44753b52c4926a9672793542d78c3615cf3a050c + {{0x8c1389bc7ec33b47ULL, 0x3a83ddbd83f52204ULL, + 0xf79687aed3eec551ULL}}, + // (ten2mx >> 192) = f79687aed3eec5513a83ddbd83f522048c1389bc7ec33b47 + {{0x3cdc6e306568fc39ULL, 0x95364afe032a819dULL, + 0xc612062576589ddaULL}}, + // (ten2mx >> 192) = c612062576589dda95364afe032a819d3cdc6e306568fc39 + {{0xca49f1c05120c9c7ULL, 0x775ea264cf55347dULL, + 0x9e74d1b791e07e48ULL}}, + // (ten2mx >> 192) = 9e74d1b791e07e48775ea264cf55347dca49f1c05120c9c7 + {{0x76dcb60081ce0fa5ULL, 0x8bca9d6e188853fcULL, + 0xfd87b5f28300ca0dULL}}, + // (ten2mx >> 192) = fd87b5f28300ca0d8bca9d6e188853fc76dcb60081ce0fa5 + {{0x5f16f80067d80c84ULL, 0x096ee45813a04330ULL, + 0xcad2f7f5359a3b3eULL}}, + // (ten2mx >> 192) = cad2f7f5359a3b3e096ee45813a043305f16f80067d80c84 + {{0x18df2ccd1fe00a03ULL, 0xa1258379a94d028dULL, + 0xa2425ff75e14fc31ULL}}, + // (ten2mx >> 192) = a2425ff75e14fc31a1258379a94d028d18df2ccd1fe00a03 + {{0x4718f0a419800802ULL, 0x80eacf948770ced7ULL, + 0x81ceb32c4b43fcf4ULL}}, + // (ten2mx >> 192) = 81ceb32c4b43fcf480eacf948770ced74718f0a419800802 + {{0x0b5b1aa028ccd99eULL, 0x67de18eda5814af2ULL, + 0xcfb11ead453994baULL}}, + // (ten2mx >> 192) = cfb11ead453994ba67de18eda5814af20b5b1aa028ccd99e + {{0x6f7c154ced70ae18ULL, 0xecb1ad8aeacdd58eULL, + 0xa6274bbdd0fadd61ULL}}, + // (ten2mx >> 192) = a6274bbdd0fadd61ecb1ad8aeacdd58e6f7c154ced70ae18 + {{0xbf967770bdf3be79ULL, 0xbd5af13bef0b113eULL, + 0x84ec3c97da624ab4ULL}}, + // (ten2mx >> 192) = 84ec3c97da624ab4bd5af13bef0b113ebf967770bdf3be79 + {{0x65bd8be79652ca5cULL, 0x955e4ec64b44e864ULL, + 0xd4ad2dbfc3d07787ULL}}, + // (ten2mx >> 192) = d4ad2dbfc3d07787955e4ec64b44e86465bd8be79652ca5c + {{0xeafe098611dbd516ULL, 0xdde50bd1d5d0b9e9ULL, + 0xaa242499697392d2ULL}}, + // (ten2mx >> 192) = aa242499697392d2dde50bd1d5d0b9e9eafe098611dbd516 + {{0xbbfe6e04db164412ULL, 0x7e50d64177da2e54ULL, + 0x881cea14545c7575ULL}}, + // (ten2mx >> 192) = 881cea14545c75757e50d64177da2e54bbfe6e04db164412 + {{0x2cca49a15e8a0683ULL, 0x96e7bd358c904a21ULL, + 0xd9c7dced53c72255ULL}}, + // (ten2mx >> 192) = d9c7dced53c7225596e7bd358c904a212cca49a15e8a0683 + {{0x8a3b6e1ab2080536ULL, 0xabec975e0a0d081aULL, + 0xae397d8aa96c1b77ULL}}, + // (ten2mx >> 192) = ae397d8aa96c1b77abec975e0a0d081a8a3b6e1ab2080536 + {{0x3b62be7bc1a0042bULL, 0x2323ac4b3b3da015ULL, + 0x8b61313bbabce2c6ULL}}, + // (ten2mx >> 192) = 8b61313bbabce2c62323ac4b3b3da0153b62be7bc1a0042b + {{0x5f0463f935ccd378ULL, 0x6b6c46dec52f6688ULL, + 0xdf01e85f912e37a3ULL}}, + // (ten2mx >> 192) = df01e85f912e37a36b6c46dec52f66885f0463f935ccd378 + {{0x7f36b660f7d70f93ULL, 0x55f038b237591ed3ULL, + 0xb267ed1940f1c61cULL}}, + // (ten2mx >> 192) = b267ed1940f1c61c55f038b237591ed37f36b660f7d70f93 + {{0xcc2bc51a5fdf3fa9ULL, 0x77f3608e92adb242ULL, + 0x8eb98a7a9a5b04e3ULL}}, + // (ten2mx >> 192) = 8eb98a7a9a5b04e377f3608e92adb242cc2bc51a5fdf3fa9 + {{0xe046082a32fecc41ULL, 0x8cb89a7db77c506aULL, + 0xe45c10c42a2b3b05ULL}}, + // (ten2mx >> 192) = e45c10c42a2b3b058cb89a7db77c506ae046082a32fecc41 + {{0x4d04d354f598a367ULL, 0x3d607b97c5fd0d22ULL, + 0xb6b00d69bb55c8d1ULL}}, + // (ten2mx >> 192) = b6b00d69bb55c8d13d607b97c5fd0d224d04d354f598a367 + {{0x3d9d75dd9146e91fULL, 0xcab3961304ca70e8ULL, + 0x9226712162ab070dULL}}, + // (ten2mx >> 192) = 9226712162ab070dcab3961304ca70e83d9d75dd9146e91f + {{0xc8fbefc8e87174ffULL, 0xaab8f01e6e10b4a6ULL, + 0xe9d71b689dde71afULL}}, + // (ten2mx >> 192) = e9d71b689dde71afaab8f01e6e10b4a6c8fbefc8e87174ff + {{0x3a63263a538df733ULL, 0x5560c018580d5d52ULL, + 0xbb127c53b17ec159ULL}}, + // (ten2mx >> 192) = bb127c53b17ec1595560c018580d5d523a63263a538df733 + {{0x2eb5b82ea93e5f5cULL, 0xdde7001379a44aa8ULL, + 0x95a8637627989aadULL}}, + // (ten2mx >> 192) = 95a8637627989aaddde7001379a44aa82eb5b82ea93e5f5c + {{0x4abc59e441fd6560ULL, 0x963e66858f6d4440ULL, + 0xef73d256a5c0f77cULL}}, + // (ten2mx >> 192) = ef73d256a5c0f77c963e66858f6d44404abc59e441fd6560 + {{0x6efd14b69b311de6ULL, 0xde98520472bdd033ULL, + 0xbf8fdb78849a5f96ULL}}, + // (ten2mx >> 192) = bf8fdb78849a5f96de98520472bdd0336efd14b69b311de6 + {{0x259743c548f417ebULL, 0xe546a8038efe4029ULL, + 0x993fe2c6d07b7fabULL}}, + // (ten2mx >> 192) = 993fe2c6d07b7fabe546a8038efe4029259743c548f417eb + {{0x3c25393ba7ecf312ULL, 0xd53dd99f4b3066a8ULL, + 0xf53304714d9265dfULL}}, + // (ten2mx >> 192) = f53304714d9265dfd53dd99f4b3066a83c25393ba7ecf312 + {{0x96842dc95323f5a8ULL, 0xaa97e14c3c26b886ULL, + 0xc428d05aa4751e4cULL}}, + // (ten2mx >> 192) = c428d05aa4751e4caa97e14c3c26b88696842dc95323f5a8 + {{0xab9cf16ddc1cc486ULL, 0x55464dd69685606bULL, + 0x9ced737bb6c4183dULL}}, + // (ten2mx >> 192) = 9ced737bb6c4183d55464dd69685606bab9cf16ddc1cc486 + {{0xac2e4f162cfad40aULL, 0xeed6e2f0f0d56712ULL, 0xfb158592be068d2eULL}} + // (ten2mx >> 192) = fb158592be068d2eeed6e2f0f0d56712ac2e4f162cfad40a +}; + +UINT256 Kx256[] = { + {{0xcccccccccccccccdULL, 0xccccccccccccccccULL, + 0xccccccccccccccccULL, 0xccccccccccccccccULL}}, + // 10^-1 ~= cccccccccccccccc cccccccccccccccc + // cccccccccccccccccccccccccccccccd * 2^-259 + {{0x70a3d70a3d70a3d8ULL, 0xd70a3d70a3d70a3dULL, + 0x3d70a3d70a3d70a3ULL, 0xa3d70a3d70a3d70aULL}}, + // 10^-2 ~= a3d70a3d70a3d70a 3d70a3d70a3d70a3 + // d70a3d70a3d70a3d70a3d70a3d70a3d8 * 2^-262 + {{0xc083126e978d4fe0ULL, 0x78d4fdf3b645a1caULL, + 0x645a1cac083126e9ULL, 0x83126e978d4fdf3bULL}}, + // 10^-3 ~= 83126e978d4fdf3b 645a1cac083126e9 + // 78d4fdf3b645a1cac083126e978d4fe0 * 2^-265 + {{0x67381d7dbf487fccULL, 0xc154c985f06f6944ULL, + 0xd3c36113404ea4a8ULL, 0xd1b71758e219652bULL}}, + // 10^-4 ~= d1b71758e219652b d3c36113404ea4a8 + // c154c985f06f694467381d7dbf487fcc * 2^-269 + {{0x85c67dfe32a0663dULL, 0xcddd6e04c0592103ULL, + 0x0fcf80dc33721d53ULL, 0xa7c5ac471b478423ULL}}, + // 10^-5 ~= a7c5ac471b478423 fcf80dc33721d53 + // cddd6e04c059210385c67dfe32a0663d * 2^-272 + {{0x37d1fe64f54d1e97ULL, 0xd7e45803cd141a69ULL, + 0xa63f9a49c2c1b10fULL, 0x8637bd05af6c69b5ULL}}, + // 10^-6 ~= 8637bd05af6c69b5 a63f9a49c2c1b10f + // d7e45803cd141a6937d1fe64f54d1e97 * 2^-275 + {{0x8c8330a1887b6425ULL, 0x8ca08cd2e1b9c3dbULL, + 0x3d32907604691b4cULL, 0xd6bf94d5e57a42bcULL}}, + // 10^-7 ~= d6bf94d5e57a42bc 3d32907604691b4c + // 8ca08cd2e1b9c3db8c8330a1887b6425 * 2^-279 + {{0x7068f3b46d2f8351ULL, 0x3d4d3d758161697cULL, + 0xfdc20d2b36ba7c3dULL, 0xabcc77118461cefcULL}}, + // 10^-8 ~= abcc77118461cefc fdc20d2b36ba7c3d + // 3d4d3d758161697c7068f3b46d2f8351 * 2^-282 + {{0xf387295d242602a7ULL, 0xfdd7645e011abac9ULL, + 0x31680a88f8953030ULL, 0x89705f4136b4a597ULL}}, + // 10^-9 ~= 89705f4136b4a597 31680a88f8953030 + // fdd7645e011abac9f387295d242602a7 * 2^-285 + {{0xb8d8422ea03cd10bULL, 0x2fbf06fcce912adcULL, + 0xb573440e5a884d1bULL, 0xdbe6fecebdedd5beULL}}, + // 10^-10 ~= dbe6fecebdedd5be b573440e5a884d1b + // 2fbf06fcce912adcb8d8422ea03cd10b * 2^-289 + {{0x93e034f219ca40d6ULL, 0xf2ff38ca3eda88b0ULL, + 0xf78f69a51539d748ULL, 0xafebff0bcb24aafeULL}}, + // 10^-11 ~= afebff0bcb24aafe f78f69a51539d748 + // f2ff38ca3eda88b093e034f219ca40d6 * 2^-292 + {{0x4319c3f4e16e9a45ULL, 0xf598fa3b657ba08dULL, + 0xf93f87b7442e45d3ULL, 0x8cbccc096f5088cbULL}}, + // 10^-12 ~= 8cbccc096f5088cb f93f87b7442e45d3 + // f598fa3b657ba08d4319c3f4e16e9a45 * 2^-295 + {{0x04f606549be42a07ULL, 0x88f4c3923bf900e2ULL, + 0x2865a5f206b06fb9ULL, 0xe12e13424bb40e13ULL}}, + // 10^-13 ~= e12e13424bb40e13 2865a5f206b06fb9 + // 88f4c3923bf900e204f606549be42a07 * 2^-299 + {{0x03f805107cb68806ULL, 0x6d909c74fcc733e8ULL, + 0x538484c19ef38c94ULL, 0xb424dc35095cd80fULL}}, + // 10^-14 ~= b424dc35095cd80f 538484c19ef38c94 + // 6d909c74fcc733e803f805107cb68806 * 2^-302 + {{0x3660040d3092066bULL, 0x57a6e390ca38f653ULL, + 0x0f9d37014bf60a10ULL, 0x901d7cf73ab0acd9ULL}}, + // 10^-15 ~= 901d7cf73ab0acd9 f9d37014bf60a10 + // 57a6e390ca38f6533660040d3092066b * 2^-305 + {{0x23ccd3484db670abULL, 0xbf716c1add27f085ULL, + 0x4c2ebe687989a9b3ULL, 0xe69594bec44de15bULL}}, + // 10^-16 ~= e69594bec44de15b 4c2ebe687989a9b3 + // bf716c1add27f08523ccd3484db670ab * 2^-309 + {{0x4fd70f6d0af85a23ULL, 0xff8df0157db98d37ULL, + 0x09befeb9fad487c2ULL, 0xb877aa3236a4b449ULL}}, + // 10^-17 ~= b877aa3236a4b449 9befeb9fad487c2 + // ff8df0157db98d374fd70f6d0af85a23 * 2^-312 + {{0x0cac0c573bf9e1b6ULL, 0x32d7f344649470f9ULL, + 0x3aff322e62439fcfULL, 0x9392ee8e921d5d07ULL}}, + // 10^-18 ~= 9392ee8e921d5d07 3aff322e62439fcf + // 32d7f344649470f90cac0c573bf9e1b6 * 2^-315 + {{0xe11346f1f98fcf89ULL, 0x1e2652070753e7f4ULL, + 0x2b31e9e3d06c32e5ULL, 0xec1e4a7db69561a5ULL}}, + // 10^-19 ~= ec1e4a7db69561a5 2b31e9e3d06c32e5 + // 1e2652070753e7f4e11346f1f98fcf89 * 2^-319 + {{0x4da9058e613fd93aULL, 0x181ea8059f76532aULL, + 0x88f4bb1ca6bcf584ULL, 0xbce5086492111aeaULL}}, + // 10^-20 ~= bce5086492111aea 88f4bb1ca6bcf584 + // 181ea8059f76532a4da9058e613fd93a * 2^-322 + {{0xa48737a51a997a95ULL, 0x467eecd14c5ea8eeULL, + 0xd3f6fc16ebca5e03ULL, 0x971da05074da7beeULL}}, + // 10^-21 ~= 971da05074da7bee d3f6fc16ebca5e03 + // 467eecd14c5ea8eea48737a51a997a95 * 2^-325 + {{0x3a71f2a1c428c421ULL, 0x70cb148213caa7e4ULL, + 0x5324c68b12dd6338ULL, 0xf1c90080baf72cb1ULL}}, + // 10^-22 ~= f1c90080baf72cb1 5324c68b12dd6338 + // 70cb148213caa7e43a71f2a1c428c421 * 2^-329 + {{0x2ec18ee7d0209ce8ULL, 0x8d6f439b43088650ULL, + 0x75b7053c0f178293ULL, 0xc16d9a0095928a27ULL}}, + // 10^-23 ~= c16d9a0095928a27 75b7053c0f178293 + // 8d6f439b430886502ec18ee7d0209ce8 * 2^-332 + {{0xf23472530ce6e3edULL, 0xd78c3615cf3a050cULL, + 0xc4926a9672793542ULL, 0x9abe14cd44753b52ULL}}, + // 10^-24 ~= 9abe14cd44753b52 c4926a9672793542 + // d78c3615cf3a050cf23472530ce6e3ed * 2^-335 + {{0xe9ed83b814a49fe1ULL, 0x8c1389bc7ec33b47ULL, + 0x3a83ddbd83f52204ULL, 0xf79687aed3eec551ULL}}, + // 10^-25 ~= f79687aed3eec551 3a83ddbd83f52204 + // 8c1389bc7ec33b47e9ed83b814a49fe1 * 2^-339 + {{0x87f1362cdd507fe7ULL, 0x3cdc6e306568fc39ULL, + 0x95364afe032a819dULL, 0xc612062576589ddaULL}}, + // 10^-26 ~= c612062576589dda 95364afe032a819d + // 3cdc6e306568fc3987f1362cdd507fe7 * 2^-342 + {{0x9ff42b5717739986ULL, 0xca49f1c05120c9c7ULL, + 0x775ea264cf55347dULL, 0x9e74d1b791e07e48ULL}}, + // 10^-27 ~= 9e74d1b791e07e48 775ea264cf55347d + // ca49f1c05120c9c79ff42b5717739986 * 2^-345 + {{0xccb9def1bf1f5c09ULL, 0x76dcb60081ce0fa5ULL, + 0x8bca9d6e188853fcULL, 0xfd87b5f28300ca0dULL}}, + // 10^-28 ~= fd87b5f28300ca0d 8bca9d6e188853fc + // 76dcb60081ce0fa5ccb9def1bf1f5c09 * 2^-349 + {{0xa3c7e58e327f7cd4ULL, 0x5f16f80067d80c84ULL, + 0x096ee45813a04330ULL, 0xcad2f7f5359a3b3eULL}}, + // 10^-29 ~= cad2f7f5359a3b3e 96ee45813a04330 + // 5f16f80067d80c84a3c7e58e327f7cd4 * 2^-352 + {{0xb6398471c1ff9710ULL, 0x18df2ccd1fe00a03ULL, + 0xa1258379a94d028dULL, 0xa2425ff75e14fc31ULL}}, + // 10^-30 ~= a2425ff75e14fc31 a1258379a94d028d + // 18df2ccd1fe00a03b6398471c1ff9710 * 2^-355 + {{0xf82e038e34cc78daULL, 0x4718f0a419800802ULL, + 0x80eacf948770ced7ULL, 0x81ceb32c4b43fcf4ULL}}, + // 10^-31 ~= 81ceb32c4b43fcf4 80eacf948770ced7 + // 4718f0a419800802f82e038e34cc78da * 2^-358 + {{0x59e338e387ad8e29ULL, 0x0b5b1aa028ccd99eULL, + 0x67de18eda5814af2ULL, 0xcfb11ead453994baULL}}, + // 10^-32 ~= cfb11ead453994ba 67de18eda5814af2 + // b5b1aa028ccd99e59e338e387ad8e29 * 2^-362 + {{0x47e8fa4f9fbe0b54ULL, 0x6f7c154ced70ae18ULL, + 0xecb1ad8aeacdd58eULL, 0xa6274bbdd0fadd61ULL}}, + // 10^-33 ~= a6274bbdd0fadd61 ecb1ad8aeacdd58e + // 6f7c154ced70ae1847e8fa4f9fbe0b54 * 2^-365 + {{0xd320c83fb2fe6f76ULL, 0xbf967770bdf3be79ULL, + 0xbd5af13bef0b113eULL, 0x84ec3c97da624ab4ULL}}, + // 10^-34 ~= 84ec3c97da624ab4 bd5af13bef0b113e + // bf967770bdf3be79d320c83fb2fe6f76 * 2^-368 + {{0x85014065eb30b257ULL, 0x65bd8be79652ca5cULL, + 0x955e4ec64b44e864ULL, 0xd4ad2dbfc3d07787ULL}}, + // 10^-35 ~= d4ad2dbfc3d07787 955e4ec64b44e864 + // 65bd8be79652ca5c85014065eb30b257 * 2^-372 + {{0xd0cdcd1e55c08eacULL, 0xeafe098611dbd516ULL, + 0xdde50bd1d5d0b9e9ULL, 0xaa242499697392d2ULL}}, + // 10^-36 ~= aa242499697392d2 dde50bd1d5d0b9e9 + // eafe098611dbd516d0cdcd1e55c08eac * 2^-375 + {{0x40a4a418449a0bbdULL, 0xbbfe6e04db164412ULL, + 0x7e50d64177da2e54ULL, 0x881cea14545c7575ULL}}, + // 10^-37 ~= 881cea14545c7575 7e50d64177da2e54 + // bbfe6e04db16441240a4a418449a0bbd * 2^-378 + {{0x9aa1068d3a9012c8ULL, 0x2cca49a15e8a0683ULL, + 0x96e7bd358c904a21ULL, 0xd9c7dced53c72255ULL}}, + // 10^-38 ~= d9c7dced53c72255 96e7bd358c904a21 + // 2cca49a15e8a06839aa1068d3a9012c8 * 2^-382 + {{0x154d9ed7620cdbd3ULL, 0x8a3b6e1ab2080536ULL, + 0xabec975e0a0d081aULL, 0xae397d8aa96c1b77ULL}}, + // 10^-39 ~= ae397d8aa96c1b77 abec975e0a0d081a + // 8a3b6e1ab2080536154d9ed7620cdbd3 * 2^-385 + {{0x443e18ac4e70afdcULL, 0x3b62be7bc1a0042bULL, + 0x2323ac4b3b3da015ULL, 0x8b61313bbabce2c6ULL}}, + // 10^-40 ~= 8b61313bbabce2c6 2323ac4b3b3da015 + // 3b62be7bc1a0042b443e18ac4e70afdc * 2^-388 + {{0x6d30277a171ab2f9ULL, 0x5f0463f935ccd378ULL, + 0x6b6c46dec52f6688ULL, 0xdf01e85f912e37a3ULL}}, + // 10^-41 ~= df01e85f912e37a3 6b6c46dec52f6688 + // 5f0463f935ccd3786d30277a171ab2f9 * 2^-392 + {{0x8a8cec61ac155bfbULL, 0x7f36b660f7d70f93ULL, + 0x55f038b237591ed3ULL, 0xb267ed1940f1c61cULL}}, + // 10^-42 ~= b267ed1940f1c61c 55f038b237591ed3 + // 7f36b660f7d70f938a8cec61ac155bfb * 2^-395 + {{0x3ba3f04e23444996ULL, 0xcc2bc51a5fdf3fa9ULL, + 0x77f3608e92adb242ULL, 0x8eb98a7a9a5b04e3ULL}}, + // 10^-43 ~= 8eb98a7a9a5b04e3 77f3608e92adb242 + // cc2bc51a5fdf3fa93ba3f04e23444996 * 2^-398 + {{0xf9064d49d206dc22ULL, 0xe046082a32fecc41ULL, + 0x8cb89a7db77c506aULL, 0xe45c10c42a2b3b05ULL}}, + // 10^-44 ~= e45c10c42a2b3b05 8cb89a7db77c506a + // e046082a32fecc41f9064d49d206dc22 * 2^-402 + {{0xfa6b7107db38b01bULL, 0x4d04d354f598a367ULL, + 0x3d607b97c5fd0d22ULL, 0xb6b00d69bb55c8d1ULL}}, + // 10^-45 ~= b6b00d69bb55c8d1 3d607b97c5fd0d22 + // 4d04d354f598a367fa6b7107db38b01b * 2^-405 + {{0xfb8927397c2d59b0ULL, 0x3d9d75dd9146e91fULL, + 0xcab3961304ca70e8ULL, 0x9226712162ab070dULL}}, + // 10^-46 ~= 9226712162ab070d cab3961304ca70e8 + // 3d9d75dd9146e91ffb8927397c2d59b0 * 2^-408 + {{0xf8db71f5937bc2b2ULL, 0xc8fbefc8e87174ffULL, + 0xaab8f01e6e10b4a6ULL, 0xe9d71b689dde71afULL}}, + // 10^-47 ~= e9d71b689dde71af aab8f01e6e10b4a6 + // c8fbefc8e87174fff8db71f5937bc2b2 * 2^-412 + {{0x2d7c5b2adc630228ULL, 0x3a63263a538df733ULL, + 0x5560c018580d5d52ULL, 0xbb127c53b17ec159ULL}}, + // 10^-48 ~= bb127c53b17ec159 5560c018580d5d52 + // 3a63263a538df7332d7c5b2adc630228 * 2^-415 + {{0x24637c2249e8ce87ULL, 0x2eb5b82ea93e5f5cULL, + 0xdde7001379a44aa8ULL, 0x95a8637627989aadULL}}, + // 10^-49 ~= 95a8637627989aad dde7001379a44aa8 + // 2eb5b82ea93e5f5c24637c2249e8ce87 * 2^-418 + {{0x3a38c69d430e173eULL, 0x4abc59e441fd6560ULL, + 0x963e66858f6d4440ULL, 0xef73d256a5c0f77cULL}}, + // 10^-50 ~= ef73d256a5c0f77c 963e66858f6d4440 + // 4abc59e441fd65603a38c69d430e173e * 2^-422 + {{0x94fa387dcf3e78feULL, 0x6efd14b69b311de6ULL, + 0xde98520472bdd033ULL, 0xbf8fdb78849a5f96ULL}}, + // 10^-51 ~= bf8fdb78849a5f96 de98520472bdd033 + // 6efd14b69b311de694fa387dcf3e78fe * 2^-425 + {{0xaa61c6cb0c31fa65ULL, 0x259743c548f417ebULL, + 0xe546a8038efe4029ULL, 0x993fe2c6d07b7fabULL}}, + // 10^-52 ~= 993fe2c6d07b7fab e546a8038efe4029 + // 259743c548f417ebaa61c6cb0c31fa65 * 2^-428 + {{0xaa360ade79e990a2ULL, 0x3c25393ba7ecf312ULL, + 0xd53dd99f4b3066a8ULL, 0xf53304714d9265dfULL}}, + // 10^-53 ~= f53304714d9265df d53dd99f4b3066a8 + // 3c25393ba7ecf312aa360ade79e990a2 * 2^-432 + {{0x882b3be52e5473b5ULL, 0x96842dc95323f5a8ULL, + 0xaa97e14c3c26b886ULL, 0xc428d05aa4751e4cULL}}, + // 10^-54 ~= c428d05aa4751e4c aa97e14c3c26b886 + // 96842dc95323f5a8882b3be52e5473b5 * 2^-435 + {{0xd355c98425105c91ULL, 0xab9cf16ddc1cc486ULL, + 0x55464dd69685606bULL, 0x9ced737bb6c4183dULL}}, + // 10^-55 ~= 9ced737bb6c4183d 55464dd69685606b + // ab9cf16ddc1cc486d355c98425105c91 * 2^-438 + {{0xebbc75a03b4d60e7ULL, 0xac2e4f162cfad40aULL, + 0xeed6e2f0f0d56712ULL, 0xfb158592be068d2eULL}}, + // 10^-56 ~= fb158592be068d2e eed6e2f0f0d56712 + // ac2e4f162cfad40aebbc75a03b4d60e7 * 2^-442 + {{0x8963914cfc3de71fULL, 0x568b727823fbdcd5ULL, + 0xf245825a5a445275ULL, 0xc8de047564d20a8bULL}}, + // 10^-57 ~= c8de047564d20a8b f245825a5a445275 + // 568b727823fbdcd58963914cfc3de71f * 2^-445 + {{0xd44fa770c9cb1f4cULL, 0x453c5b934ffcb0aaULL, + 0x5b6aceaeae9d0ec4ULL, 0xa0b19d2ab70e6ed6ULL}}, + // 10^-58 ~= a0b19d2ab70e6ed6 5b6aceaeae9d0ec4 + // 453c5b934ffcb0aad44fa770c9cb1f4c * 2^-448 + {{0xdd0c85f3d4a27f70ULL, 0x37637c75d996f3bbULL, + 0xe2bbd88bbee40bd0ULL, 0x808e17555f3ebf11ULL}}, + // 10^-59 ~= 808e17555f3ebf11 e2bbd88bbee40bd0 + // 37637c75d996f3bbdd0c85f3d4a27f70 * 2^-451 + {{0x61ada31fba9d98b3ULL, 0x256bfa5628f185f9ULL, + 0x3792f412cb06794dULL, 0xcdb02555653131b6ULL}}, + // 10^-60 ~= cdb02555653131b6 3792f412cb06794d + // 256bfa5628f185f961ada31fba9d98b3 * 2^-455 + {{0xe7be1c196217ad5cULL, 0x51232eab53f46b2dULL, + 0x5fa8c3423c052dd7ULL, 0xa48ceaaab75a8e2bULL}}, + // 10^-61 ~= a48ceaaab75a8e2b 5fa8c3423c052dd7 + // 51232eab53f46b2de7be1c196217ad5c * 2^-458 + {{0x52fe7ce11b46244aULL, 0x40e8f222a99055beULL, + 0x1953cf68300424acULL, 0x83a3eeeef9153e89ULL}}, + // 10^-62 ~= 83a3eeeef9153e89 1953cf68300424ac + // 40e8f222a99055be52fe7ce11b46244a * 2^-461 + {{0x51972e34f8703a10ULL, 0x34a7e9d10f4d55fdULL, + 0x8eec7f0d19a03aadULL, 0xd29fe4b18e88640eULL}}, + // 10^-63 ~= d29fe4b18e88640e 8eec7f0d19a03aad + // 34a7e9d10f4d55fd51972e34f8703a10 * 2^-465 + {{0x0e128b5d938cfb40ULL, 0x2a1fee40d90aab31ULL, + 0x3f2398d747b36224ULL, 0xa87fea27a539e9a5ULL}}, + // 10^-64 ~= a87fea27a539e9a5 3f2398d747b36224 + // 2a1fee40d90aab310e128b5d938cfb40 * 2^-468 + {{0x3e753c4adc70c900ULL, 0xbb4cbe9a473bbc27ULL, + 0x98e947129fc2b4e9ULL, 0x86ccbb52ea94baeaULL}}, + // 10^-65 ~= 86ccbb52ea94baea 98e947129fc2b4e9 + // bb4cbe9a473bbc273e753c4adc70c900 * 2^-471 + {{0x30bb93aafa4e0e66ULL, 0x9214642a0b92c6a5ULL, + 0x5b0ed81dcc6abb0fULL, 0xd7adf884aa879177ULL}}, + // 10^-66 ~= d7adf884aa879177 5b0ed81dcc6abb0f + // 9214642a0b92c6a530bb93aafa4e0e66 * 2^-475 + {{0xc0960fbbfb71a51fULL, 0xa8105021a2dbd21dULL, + 0xe272467e3d222f3fULL, 0xac8b2d36eed2dac5ULL}}, + // 10^-67 ~= ac8b2d36eed2dac5 e272467e3d222f3f + // a8105021a2dbd21dc0960fbbfb71a51f * 2^-478 + {{0x66de72fcc927b74cULL, 0xb9a6a6814f1641b1ULL, + 0x1b8e9ecb641b58ffULL, 0x8a08f0f8bf0f156bULL}}, + // 10^-68 ~= 8a08f0f8bf0f156b 1b8e9ecb641b58ff + // b9a6a6814f1641b166de72fcc927b74c * 2^-481 + {{0xd7ca5194750c5879ULL, 0xf5d770cee4f0691bULL, + 0xf8e431456cf88e65ULL, 0xdcdb1b2798182244ULL}}, + // 10^-69 ~= dcdb1b2798182244 f8e431456cf88e65 + // f5d770cee4f0691bd7ca5194750c5879 * 2^-485 + {{0xdfd50e105da379faULL, 0x9179270bea59edafULL, + 0x2d835a9df0c6d851ULL, 0xb0af48ec79ace837ULL}}, + // 10^-70 ~= b0af48ec79ace837 2d835a9df0c6d851 + // 9179270bea59edafdfd50e105da379fa * 2^-488 + {{0x19773e737e1c6195ULL, 0x0dfa85a321e18af3ULL, + 0x579c487e5a38ad0eULL, 0x8d590723948a535fULL}}, + // 10^-71 ~= 8d590723948a535f 579c487e5a38ad0e + // dfa85a321e18af319773e737e1c6195 * 2^-491 + {{0xf58b971f302d68efULL, 0x165da29e9c9c1184ULL, + 0x25c6da63c38de1b0ULL, 0xe2280b6c20dd5232ULL}}, + // 10^-72 ~= e2280b6c20dd5232 25c6da63c38de1b0 + // 165da29e9c9c1184f58b971f302d68ef * 2^-495 + {{0xc46fac18f3578725ULL, 0x4517b54bb07cdad0ULL, + 0x1e38aeb6360b1af3ULL, 0xb4ecd5f01a4aa828ULL}}, + // 10^-73 ~= b4ecd5f01a4aa828 1e38aeb6360b1af3 + // 4517b54bb07cdad0c46fac18f3578725 * 2^-498 + {{0x36bfbce0c2ac6c1eULL, 0x9dac910959fd7bdaULL, + 0xb1c6f22b5e6f48c2ULL, 0x90bd77f3483bb9b9ULL}}, + // 10^-74 ~= 90bd77f3483bb9b9 b1c6f22b5e6f48c2 + // 9dac910959fd7bda36bfbce0c2ac6c1e * 2^-501 + {{0x2465fb01377a4696ULL, 0x2f7a81a88ffbf95dULL, + 0xb60b1d1230b20e04ULL, 0xe7958cb87392c2c2ULL}} + // 10^-75 ~= e7958cb87392c2c2 b60b1d1230b20e04 + // 2f7a81a88ffbf95d2465fb01377a4696 * 2^-505 +}; + +unsigned int Ex256m256[] = { + 3, // 259 - 256, Ex = 259 + 6, // 262 - 256, Ex = 262 + 9, // 265 - 256, Ex = 265 + 13, // 269 - 256, Ex = 269 + 16, // 272 - 256, Ex = 272 + 19, // 275 - 256, Ex = 275 + 23, // 279 - 256, Ex = 279 + 26, // 282 - 256, Ex = 282 + 29, // 285 - 256, Ex = 285 + 33, // 289 - 256, Ex = 289 + 36, // 292 - 256, Ex = 292 + 39, // 295 - 256, Ex = 295 + 43, // 299 - 256, Ex = 299 + 46, // 302 - 256, Ex = 302 + 49, // 305 - 256, Ex = 305 + 53, // 309 - 256, Ex = 309 + 56, // 312 - 256, Ex = 312 + 59, // 315 - 256, Ex = 315 + 63, // 319 - 256, Ex = 319 + 2, // 322 - 320, Ex = 322 + 5, // 325 - 320, Ex = 325 + 9, // 329 - 320, Ex = 329 + 12, // 332 - 320, Ex = 332 + 15, // 335 - 320, Ex = 335 + 19, // 339 - 320, Ex = 339 + 22, // 342 - 320, Ex = 342 + 25, // 345 - 320, Ex = 345 + 29, // 349 - 320, Ex = 349 + 32, // 352 - 320, Ex = 352 + 35, // 355 - 320, Ex = 355 + 38, // 358 - 320, Ex = 358 + 42, // 362 - 320, Ex = 362 + 45, // 365 - 320, Ex = 365 + 48, // 368 - 320, Ex = 368 + 52, // 372 - 320, Ex = 372 + 55, // 375 - 320, Ex = 375 + 58, // 378 - 320, Ex = 378 + 62, // 382 - 320, Ex = 382 + 1, // 385 - 384, Ex = 385 + 4, // 388 - 384, Ex = 388 + 8, // 392 - 384, Ex = 392 + 11, // 395 - 384, Ex = 395 + 14, // 398 - 384, Ex = 398 + 18, // 402 - 384, Ex = 402 + 21, // 405 - 384, Ex = 405 + 24, // 408 - 384, Ex = 408 + 28, // 412 - 384, Ex = 412 + 31, // 415 - 384, Ex = 415 + 34, // 418 - 384, Ex = 418 + 38, // 422 - 384, Ex = 422 + 41, // 425 - 384, Ex = 425 + 44, // 428 - 384, Ex = 428 + 48, // 432 - 384, Ex = 432 + 51, // 435 - 384, Ex = 435 + 54, // 438 - 384, Ex = 438 + 58, // 442 - 384, Ex = 442 + 61, // 445 - 384, Ex = 445 + 0, // 448 - 448, Ex = 448 + 3, // 451 - 448, Ex = 451 + 7, // 455 - 448, Ex = 455 + 10, // 458 - 448, Ex = 458 + 13, // 461 - 448, Ex = 461 + 17, // 465 - 448, Ex = 465 + 20, // 468 - 448, Ex = 468 + 23, // 471 - 448, Ex = 471 + 27, // 475 - 448, Ex = 475 + 30, // 478 - 448, Ex = 478 + 33, // 481 - 448, Ex = 481 + 37, // 485 - 448, Ex = 485 + 40, // 488 - 448, Ex = 488 + 43, // 491 - 448, Ex = 491 + 47, // 495 - 448, Ex = 495 + 50, // 498 - 448, Ex = 498 + 53, // 501 - 448, Ex = 501 + 57 // 505 - 448, Ex = 505 +}; + +UINT64 half256[] = { + 0x0000000000000004ULL, // half / 2^256 = 4 + 0x0000000000000020ULL, // half / 2^256 = 20 + 0x0000000000000100ULL, // half / 2^256 = 100 + 0x0000000000001000ULL, // half / 2^256 = 1000 + 0x0000000000008000ULL, // half / 2^256 = 8000 + 0x0000000000040000ULL, // half / 2^256 = 40000 + 0x0000000000400000ULL, // half / 2^256 = 400000 + 0x0000000002000000ULL, // half / 2^256 = 2000000 + 0x0000000010000000ULL, // half / 2^256 = 10000000 + 0x0000000100000000ULL, // half / 2^256 = 100000000 + 0x0000000800000000ULL, // half / 2^256 = 800000000 + 0x0000004000000000ULL, // half / 2^256 = 4000000000 + 0x0000040000000000ULL, // half / 2^256 = 40000000000 + 0x0000200000000000ULL, // half / 2^256 = 200000000000 + 0x0001000000000000ULL, // half / 2^256 = 1000000000000 + 0x0010000000000000ULL, // half / 2^256 = 10000000000000 + 0x0080000000000000ULL, // half / 2^256 = 80000000000000 + 0x0400000000000000ULL, // half / 2^256 = 400000000000000 + 0x4000000000000000ULL, // half / 2^256 = 4000000000000000 + 0x0000000000000002ULL, // half / 2^320 = 2 + 0x0000000000000010ULL, // half / 2^320 = 10 + 0x0000000000000100ULL, // half / 2^320 = 100 + 0x0000000000000800ULL, // half / 2^320 = 800 + 0x0000000000004000ULL, // half / 2^320 = 4000 + 0x0000000000040000ULL, // half / 2^320 = 40000 + 0x0000000000200000ULL, // half / 2^320 = 200000 + 0x0000000001000000ULL, // half / 2^320 = 1000000 + 0x0000000010000000ULL, // half / 2^320 = 10000000 + 0x0000000080000000ULL, // half / 2^320 = 80000000 + 0x0000000400000000ULL, // half / 2^320 = 400000000 + 0x0000002000000000ULL, // half / 2^320 = 2000000000 + 0x0000020000000000ULL, // half / 2^320 = 20000000000 + 0x0000100000000000ULL, // half / 2^320 = 100000000000 + 0x0000800000000000ULL, // half / 2^320 = 800000000000 + 0x0008000000000000ULL, // half / 2^320 = 8000000000000 + 0x0040000000000000ULL, // half / 2^320 = 40000000000000 + 0x0200000000000000ULL, // half / 2^320 = 200000000000000 + 0x2000000000000000ULL, // half / 2^320 = 2000000000000000 + 0x0000000000000001ULL, // half / 2^384 = 1 + 0x0000000000000008ULL, // half / 2^384 = 8 + 0x0000000000000080ULL, // half / 2^384 = 80 + 0x0000000000000400ULL, // half / 2^384 = 400 + 0x0000000000002000ULL, // half / 2^384 = 2000 + 0x0000000000020000ULL, // half / 2^384 = 20000 + 0x0000000000100000ULL, // half / 2^384 = 100000 + 0x0000000000800000ULL, // half / 2^384 = 800000 + 0x0000000008000000ULL, // half / 2^384 = 8000000 + 0x0000000040000000ULL, // half / 2^384 = 40000000 + 0x0000000200000000ULL, // half / 2^384 = 200000000 + 0x0000002000000000ULL, // half / 2^384 = 2000000000 + 0x0000010000000000ULL, // half / 2^384 = 10000000000 + 0x0000080000000000ULL, // half / 2^384 = 80000000000 + 0x0000800000000000ULL, // half / 2^384 = 800000000000 + 0x0004000000000000ULL, // half / 2^384 = 4000000000000 + 0x0020000000000000ULL, // half / 2^384 = 20000000000000 + 0x0200000000000000ULL, // half / 2^384 = 200000000000000 + 0x1000000000000000ULL, // half / 2^384 = 1000000000000000 + 0x8000000000000000ULL, // half / 2^384 = 8000000000000000 + 0x0000000000000004ULL, // half / 2^448 = 4 + 0x0000000000000040ULL, // half / 2^448 = 40 + 0x0000000000000200ULL, // half / 2^448 = 200 + 0x0000000000001000ULL, // half / 2^448 = 1000 + 0x0000000000010000ULL, // half / 2^448 = 10000 + 0x0000000000080000ULL, // half / 2^448 = 80000 + 0x0000000000400000ULL, // half / 2^448 = 400000 + 0x0000000004000000ULL, // half / 2^448 = 4000000 + 0x0000000020000000ULL, // half / 2^448 = 20000000 + 0x0000000100000000ULL, // half / 2^448 = 100000000 + 0x0000001000000000ULL, // half / 2^448 = 1000000000 + 0x0000008000000000ULL, // half / 2^448 = 8000000000 + 0x0000040000000000ULL, // half / 2^448 = 40000000000 + 0x0000400000000000ULL, // half / 2^448 = 400000000000 + 0x0002000000000000ULL, // half / 2^448 = 2000000000000 + 0x0010000000000000ULL, // half / 2^448 = 10000000000000 + 0x0100000000000000ULL // half / 2^448 = 100000000000000 +}; + +UINT64 mask256[] = { + 0x0000000000000007ULL, // mask / 2^256 + 0x000000000000003fULL, // mask / 2^256 + 0x00000000000001ffULL, // mask / 2^256 + 0x0000000000001fffULL, // mask / 2^256 + 0x000000000000ffffULL, // mask / 2^256 + 0x000000000007ffffULL, // mask / 2^256 + 0x00000000007fffffULL, // mask / 2^256 + 0x0000000003ffffffULL, // mask / 2^256 + 0x000000001fffffffULL, // mask / 2^256 + 0x00000001ffffffffULL, // mask / 2^256 + 0x0000000fffffffffULL, // mask / 2^256 + 0x0000007fffffffffULL, // mask / 2^256 + 0x000007ffffffffffULL, // mask / 2^256 + 0x00003fffffffffffULL, // mask / 2^256 + 0x0001ffffffffffffULL, // mask / 2^256 + 0x001fffffffffffffULL, // mask / 2^256 + 0x00ffffffffffffffULL, // mask / 2^256 + 0x07ffffffffffffffULL, // mask / 2^256 + 0x7fffffffffffffffULL, // mask / 2^256 + 0x0000000000000003ULL, // mask / 2^320 + 0x000000000000001fULL, // mask / 2^320 + 0x00000000000001ffULL, // mask / 2^320 + 0x0000000000000fffULL, // mask / 2^320 + 0x0000000000007fffULL, // mask / 2^320 + 0x000000000007ffffULL, // mask / 2^320 + 0x00000000003fffffULL, // mask / 2^320 + 0x0000000001ffffffULL, // mask / 2^320 + 0x000000001fffffffULL, // mask / 2^320 + 0x00000000ffffffffULL, // mask / 2^320 + 0x00000007ffffffffULL, // mask / 2^320 + 0x0000003fffffffffULL, // mask / 2^320 + 0x000003ffffffffffULL, // mask / 2^320 + 0x00001fffffffffffULL, // mask / 2^320 + 0x0000ffffffffffffULL, // mask / 2^320 + 0x000fffffffffffffULL, // mask / 2^320 + 0x007fffffffffffffULL, // mask / 2^320 + 0x03ffffffffffffffULL, // mask / 2^320 + 0x3fffffffffffffffULL, // mask / 2^320 + 0x0000000000000001ULL, // mask / 2^384 + 0x000000000000000fULL, // mask / 2^384 + 0x00000000000000ffULL, // mask / 2^384 + 0x00000000000007ffULL, // mask / 2^384 + 0x0000000000003fffULL, // mask / 2^384 + 0x000000000003ffffULL, // mask / 2^384 + 0x00000000001fffffULL, // mask / 2^384 + 0x0000000000ffffffULL, // mask / 2^384 + 0x000000000fffffffULL, // mask / 2^384 + 0x000000007fffffffULL, // mask / 2^384 + 0x00000003ffffffffULL, // mask / 2^384 + 0x0000003fffffffffULL, // mask / 2^384 + 0x000001ffffffffffULL, // mask / 2^384 + 0x00000fffffffffffULL, // mask / 2^384 + 0x0000ffffffffffffULL, // mask / 2^384 + 0x0007ffffffffffffULL, // mask / 2^384 + 0x003fffffffffffffULL, // mask / 2^384 + 0x03ffffffffffffffULL, // mask / 2^384 + 0x1fffffffffffffffULL, // mask / 2^384 + 0xffffffffffffffffULL, // mask / 2^384 + 0x0000000000000007ULL, // mask / 2^448 + 0x000000000000007fULL, // mask / 2^448 + 0x00000000000003ffULL, // mask / 2^448 + 0x0000000000001fffULL, // mask / 2^448 + 0x000000000001ffffULL, // mask / 2^448 + 0x00000000000fffffULL, // mask / 2^448 + 0x00000000007fffffULL, // mask / 2^448 + 0x0000000007ffffffULL, // mask / 2^448 + 0x000000003fffffffULL, // mask / 2^448 + 0x00000001ffffffffULL, // mask / 2^448 + 0x0000001fffffffffULL, // mask / 2^448 + 0x000000ffffffffffULL, // mask / 2^448 + 0x000007ffffffffffULL, // mask / 2^448 + 0x00007fffffffffffULL, // mask / 2^448 + 0x0003ffffffffffffULL, // mask / 2^448 + 0x001fffffffffffffULL, // mask / 2^448 + 0x01ffffffffffffffULL // mask / 2^448 +}; + +UINT256 ten2mxtrunc256[] = { + {{0xccccccccccccccccULL, 0xccccccccccccccccULL, + 0xccccccccccccccccULL, 0xccccccccccccccccULL}}, + // (ten2mx >> 256) = cccccccccccccccc cccccccccccccccc + // cccccccccccccccccccccccccccccccc + {{0x70a3d70a3d70a3d7ULL, 0xd70a3d70a3d70a3dULL, + 0x3d70a3d70a3d70a3ULL, 0xa3d70a3d70a3d70aULL}}, + // (ten2mx >> 256) = a3d70a3d70a3d70a 3d70a3d70a3d70a3 + // d70a3d70a3d70a3d70a3d70a3d70a3d7 + {{0xc083126e978d4fdfULL, 0x78d4fdf3b645a1caULL, + 0x645a1cac083126e9ULL, 0x83126e978d4fdf3bULL}}, + // (ten2mx >> 256) = 83126e978d4fdf3b 645a1cac083126e9 + // 78d4fdf3b645a1cac083126e978d4fdf + {{0x67381d7dbf487fcbULL, 0xc154c985f06f6944ULL, + 0xd3c36113404ea4a8ULL, 0xd1b71758e219652bULL}}, + // (ten2mx >> 256) = d1b71758e219652b d3c36113404ea4a8 + // c154c985f06f694467381d7dbf487fcb + {{0x85c67dfe32a0663cULL, 0xcddd6e04c0592103ULL, + 0x0fcf80dc33721d53ULL, 0xa7c5ac471b478423ULL}}, + // (ten2mx >> 256) = a7c5ac471b478423 fcf80dc33721d53 + // cddd6e04c059210385c67dfe32a0663c + {{0x37d1fe64f54d1e96ULL, 0xd7e45803cd141a69ULL, + 0xa63f9a49c2c1b10fULL, 0x8637bd05af6c69b5ULL}}, + // (ten2mx >> 256) = 8637bd05af6c69b5 a63f9a49c2c1b10f + // d7e45803cd141a6937d1fe64f54d1e96 + {{0x8c8330a1887b6424ULL, 0x8ca08cd2e1b9c3dbULL, + 0x3d32907604691b4cULL, 0xd6bf94d5e57a42bcULL}}, + // (ten2mx >> 256) = d6bf94d5e57a42bc 3d32907604691b4c + // 8ca08cd2e1b9c3db8c8330a1887b6424 + {{0x7068f3b46d2f8350ULL, 0x3d4d3d758161697cULL, + 0xfdc20d2b36ba7c3dULL, 0xabcc77118461cefcULL}}, + // (ten2mx >> 256) = abcc77118461cefc fdc20d2b36ba7c3d + // 3d4d3d758161697c7068f3b46d2f8350 + {{0xf387295d242602a6ULL, 0xfdd7645e011abac9ULL, + 0x31680a88f8953030ULL, 0x89705f4136b4a597ULL}}, + // (ten2mx >> 256) = 89705f4136b4a597 31680a88f8953030 + // fdd7645e011abac9f387295d242602a6 + {{0xb8d8422ea03cd10aULL, 0x2fbf06fcce912adcULL, + 0xb573440e5a884d1bULL, 0xdbe6fecebdedd5beULL}}, + // (ten2mx >> 256) = dbe6fecebdedd5be b573440e5a884d1b + // 2fbf06fcce912adcb8d8422ea03cd10a + {{0x93e034f219ca40d5ULL, 0xf2ff38ca3eda88b0ULL, + 0xf78f69a51539d748ULL, 0xafebff0bcb24aafeULL}}, + // (ten2mx >> 256) = afebff0bcb24aafe f78f69a51539d748 + // f2ff38ca3eda88b093e034f219ca40d5 + {{0x4319c3f4e16e9a44ULL, 0xf598fa3b657ba08dULL, + 0xf93f87b7442e45d3ULL, 0x8cbccc096f5088cbULL}}, + // (ten2mx >> 256) = 8cbccc096f5088cb f93f87b7442e45d3 + // f598fa3b657ba08d4319c3f4e16e9a44 + {{0x04f606549be42a06ULL, 0x88f4c3923bf900e2ULL, + 0x2865a5f206b06fb9ULL, 0xe12e13424bb40e13ULL}}, + // (ten2mx >> 256) = e12e13424bb40e13 2865a5f206b06fb9 + // 88f4c3923bf900e204f606549be42a06 + {{0x03f805107cb68805ULL, 0x6d909c74fcc733e8ULL, + 0x538484c19ef38c94ULL, 0xb424dc35095cd80fULL}}, + // (ten2mx >> 256) = b424dc35095cd80f 538484c19ef38c94 + // 6d909c74fcc733e803f805107cb68805 + {{0x3660040d3092066aULL, 0x57a6e390ca38f653ULL, + 0x0f9d37014bf60a10ULL, 0x901d7cf73ab0acd9ULL}}, + // (ten2mx >> 256) = 901d7cf73ab0acd9 f9d37014bf60a10 + // 57a6e390ca38f6533660040d3092066a + {{0x23ccd3484db670aaULL, 0xbf716c1add27f085ULL, + 0x4c2ebe687989a9b3ULL, 0xe69594bec44de15bULL}}, + // (ten2mx >> 256) = e69594bec44de15b 4c2ebe687989a9b3 + // bf716c1add27f08523ccd3484db670aa + {{0x4fd70f6d0af85a22ULL, 0xff8df0157db98d37ULL, + 0x09befeb9fad487c2ULL, 0xb877aa3236a4b449ULL}}, + // (ten2mx >> 256) = b877aa3236a4b449 9befeb9fad487c2 + // ff8df0157db98d374fd70f6d0af85a22 + {{0x0cac0c573bf9e1b5ULL, 0x32d7f344649470f9ULL, + 0x3aff322e62439fcfULL, 0x9392ee8e921d5d07ULL}}, + // (ten2mx >> 256) = 9392ee8e921d5d07 3aff322e62439fcf + // 32d7f344649470f90cac0c573bf9e1b5 + {{0xe11346f1f98fcf88ULL, 0x1e2652070753e7f4ULL, + 0x2b31e9e3d06c32e5ULL, 0xec1e4a7db69561a5ULL}}, + // (ten2mx >> 256) = ec1e4a7db69561a5 2b31e9e3d06c32e5 + // 1e2652070753e7f4e11346f1f98fcf88 + {{0x4da9058e613fd939ULL, 0x181ea8059f76532aULL, + 0x88f4bb1ca6bcf584ULL, 0xbce5086492111aeaULL}}, + // (ten2mx >> 256) = bce5086492111aea 88f4bb1ca6bcf584 + // 181ea8059f76532a4da9058e613fd939 + {{0xa48737a51a997a94ULL, 0x467eecd14c5ea8eeULL, + 0xd3f6fc16ebca5e03ULL, 0x971da05074da7beeULL}}, + // (ten2mx >> 256) = 971da05074da7bee d3f6fc16ebca5e03 + // 467eecd14c5ea8eea48737a51a997a94 + {{0x3a71f2a1c428c420ULL, 0x70cb148213caa7e4ULL, + 0x5324c68b12dd6338ULL, 0xf1c90080baf72cb1ULL}}, + // (ten2mx >> 256) = f1c90080baf72cb1 5324c68b12dd6338 + // 70cb148213caa7e43a71f2a1c428c420 + {{0x2ec18ee7d0209ce7ULL, 0x8d6f439b43088650ULL, + 0x75b7053c0f178293ULL, 0xc16d9a0095928a27ULL}}, + // (ten2mx >> 256) = c16d9a0095928a27 75b7053c0f178293 + // 8d6f439b430886502ec18ee7d0209ce7 + {{0xf23472530ce6e3ecULL, 0xd78c3615cf3a050cULL, + 0xc4926a9672793542ULL, 0x9abe14cd44753b52ULL}}, + // (ten2mx >> 256) = 9abe14cd44753b52 c4926a9672793542 + // d78c3615cf3a050cf23472530ce6e3ec + {{0xe9ed83b814a49fe0ULL, 0x8c1389bc7ec33b47ULL, + 0x3a83ddbd83f52204ULL, 0xf79687aed3eec551ULL}}, + // (ten2mx >> 256) = f79687aed3eec551 3a83ddbd83f52204 + // 8c1389bc7ec33b47e9ed83b814a49fe0 + {{0x87f1362cdd507fe6ULL, 0x3cdc6e306568fc39ULL, + 0x95364afe032a819dULL, 0xc612062576589ddaULL}}, + // (ten2mx >> 256) = c612062576589dda 95364afe032a819d + // 3cdc6e306568fc3987f1362cdd507fe6 + {{0x9ff42b5717739985ULL, 0xca49f1c05120c9c7ULL, + 0x775ea264cf55347dULL, 0x9e74d1b791e07e48ULL}}, + // (ten2mx >> 256) = 9e74d1b791e07e48 775ea264cf55347d + // ca49f1c05120c9c79ff42b5717739985 + {{0xccb9def1bf1f5c08ULL, 0x76dcb60081ce0fa5ULL, + 0x8bca9d6e188853fcULL, 0xfd87b5f28300ca0dULL}}, + // (ten2mx >> 256) = fd87b5f28300ca0d 8bca9d6e188853fc + // 76dcb60081ce0fa5ccb9def1bf1f5c08 + {{0xa3c7e58e327f7cd3ULL, 0x5f16f80067d80c84ULL, + 0x096ee45813a04330ULL, 0xcad2f7f5359a3b3eULL}}, + // (ten2mx >> 256) = cad2f7f5359a3b3e 96ee45813a04330 + // 5f16f80067d80c84a3c7e58e327f7cd3 + {{0xb6398471c1ff970fULL, 0x18df2ccd1fe00a03ULL, + 0xa1258379a94d028dULL, 0xa2425ff75e14fc31ULL}}, + // (ten2mx >> 256) = a2425ff75e14fc31 a1258379a94d028d + // 18df2ccd1fe00a03b6398471c1ff970f + {{0xf82e038e34cc78d9ULL, 0x4718f0a419800802ULL, + 0x80eacf948770ced7ULL, 0x81ceb32c4b43fcf4ULL}}, + // (ten2mx >> 256) = 81ceb32c4b43fcf4 80eacf948770ced7 + // 4718f0a419800802f82e038e34cc78d9 + {{0x59e338e387ad8e28ULL, 0x0b5b1aa028ccd99eULL, + 0x67de18eda5814af2ULL, 0xcfb11ead453994baULL}}, + // (ten2mx >> 256) = cfb11ead453994ba 67de18eda5814af2 + // b5b1aa028ccd99e59e338e387ad8e28 + {{0x47e8fa4f9fbe0b53ULL, 0x6f7c154ced70ae18ULL, + 0xecb1ad8aeacdd58eULL, 0xa6274bbdd0fadd61ULL}}, + // (ten2mx >> 256) = a6274bbdd0fadd61 ecb1ad8aeacdd58e + // 6f7c154ced70ae1847e8fa4f9fbe0b53 + {{0xd320c83fb2fe6f75ULL, 0xbf967770bdf3be79ULL, + 0xbd5af13bef0b113eULL, 0x84ec3c97da624ab4ULL}}, + // (ten2mx >> 256) = 84ec3c97da624ab4 bd5af13bef0b113e + // bf967770bdf3be79d320c83fb2fe6f75 + {{0x85014065eb30b256ULL, 0x65bd8be79652ca5cULL, + 0x955e4ec64b44e864ULL, 0xd4ad2dbfc3d07787ULL}}, + // (ten2mx >> 256) = d4ad2dbfc3d07787 955e4ec64b44e864 + // 65bd8be79652ca5c85014065eb30b256 + {{0xd0cdcd1e55c08eabULL, 0xeafe098611dbd516ULL, + 0xdde50bd1d5d0b9e9ULL, 0xaa242499697392d2ULL}}, + // (ten2mx >> 256) = aa242499697392d2 dde50bd1d5d0b9e9 + // eafe098611dbd516d0cdcd1e55c08eab + {{0x40a4a418449a0bbcULL, 0xbbfe6e04db164412ULL, + 0x7e50d64177da2e54ULL, 0x881cea14545c7575ULL}}, + // (ten2mx >> 256) = 881cea14545c7575 7e50d64177da2e54 + // bbfe6e04db16441240a4a418449a0bbc + {{0x9aa1068d3a9012c7ULL, 0x2cca49a15e8a0683ULL, + 0x96e7bd358c904a21ULL, 0xd9c7dced53c72255ULL}}, + // (ten2mx >> 256) = d9c7dced53c72255 96e7bd358c904a21 + // 2cca49a15e8a06839aa1068d3a9012c7 + {{0x154d9ed7620cdbd2ULL, 0x8a3b6e1ab2080536ULL, + 0xabec975e0a0d081aULL, 0xae397d8aa96c1b77ULL}}, + // (ten2mx >> 256) = ae397d8aa96c1b77 abec975e0a0d081a + // 8a3b6e1ab2080536154d9ed7620cdbd2 + {{0x443e18ac4e70afdbULL, 0x3b62be7bc1a0042bULL, + 0x2323ac4b3b3da015ULL, 0x8b61313bbabce2c6ULL}}, + // (ten2mx >> 256) = 8b61313bbabce2c6 2323ac4b3b3da015 + // 3b62be7bc1a0042b443e18ac4e70afdb + {{0x6d30277a171ab2f8ULL, 0x5f0463f935ccd378ULL, + 0x6b6c46dec52f6688ULL, 0xdf01e85f912e37a3ULL}}, + // (ten2mx >> 256) = df01e85f912e37a3 6b6c46dec52f6688 + // 5f0463f935ccd3786d30277a171ab2f8 + {{0x8a8cec61ac155bfaULL, 0x7f36b660f7d70f93ULL, + 0x55f038b237591ed3ULL, 0xb267ed1940f1c61cULL}}, + // (ten2mx >> 256) = b267ed1940f1c61c 55f038b237591ed3 + // 7f36b660f7d70f938a8cec61ac155bfa + {{0x3ba3f04e23444995ULL, 0xcc2bc51a5fdf3fa9ULL, + 0x77f3608e92adb242ULL, 0x8eb98a7a9a5b04e3ULL}}, + // (ten2mx >> 256) = 8eb98a7a9a5b04e3 77f3608e92adb242 + // cc2bc51a5fdf3fa93ba3f04e23444995 + {{0xf9064d49d206dc21ULL, 0xe046082a32fecc41ULL, + 0x8cb89a7db77c506aULL, 0xe45c10c42a2b3b05ULL}}, + // (ten2mx >> 256) = e45c10c42a2b3b05 8cb89a7db77c506a + // e046082a32fecc41f9064d49d206dc21 + {{0xfa6b7107db38b01aULL, 0x4d04d354f598a367ULL, + 0x3d607b97c5fd0d22ULL, 0xb6b00d69bb55c8d1ULL}}, + // (ten2mx >> 256) = b6b00d69bb55c8d1 3d607b97c5fd0d22 + // 4d04d354f598a367fa6b7107db38b01a + {{0xfb8927397c2d59afULL, 0x3d9d75dd9146e91fULL, + 0xcab3961304ca70e8ULL, 0x9226712162ab070dULL}}, + // (ten2mx >> 256) = 9226712162ab070d cab3961304ca70e8 + // 3d9d75dd9146e91ffb8927397c2d59af + {{0xf8db71f5937bc2b1ULL, 0xc8fbefc8e87174ffULL, + 0xaab8f01e6e10b4a6ULL, 0xe9d71b689dde71afULL}}, + // (ten2mx >> 256) = e9d71b689dde71af aab8f01e6e10b4a6 + // c8fbefc8e87174fff8db71f5937bc2b1 + {{0x2d7c5b2adc630227ULL, 0x3a63263a538df733ULL, + 0x5560c018580d5d52ULL, 0xbb127c53b17ec159ULL}}, + // (ten2mx >> 256) = bb127c53b17ec159 5560c018580d5d52 + // 3a63263a538df7332d7c5b2adc630227 + {{0x24637c2249e8ce86ULL, 0x2eb5b82ea93e5f5cULL, + 0xdde7001379a44aa8ULL, 0x95a8637627989aadULL}}, + // (ten2mx >> 256) = 95a8637627989aad dde7001379a44aa8 + // 2eb5b82ea93e5f5c24637c2249e8ce86 + {{0x3a38c69d430e173dULL, 0x4abc59e441fd6560ULL, + 0x963e66858f6d4440ULL, 0xef73d256a5c0f77cULL}}, + // (ten2mx >> 256) = ef73d256a5c0f77c 963e66858f6d4440 + // 4abc59e441fd65603a38c69d430e173d + {{0x94fa387dcf3e78fdULL, 0x6efd14b69b311de6ULL, + 0xde98520472bdd033ULL, 0xbf8fdb78849a5f96ULL}}, + // (ten2mx >> 256) = bf8fdb78849a5f96 de98520472bdd033 + // 6efd14b69b311de694fa387dcf3e78fd + {{0xaa61c6cb0c31fa64ULL, 0x259743c548f417ebULL, + 0xe546a8038efe4029ULL, 0x993fe2c6d07b7fabULL}}, + // (ten2mx >> 256) = 993fe2c6d07b7fab e546a8038efe4029 + // 259743c548f417ebaa61c6cb0c31fa64 + {{0xaa360ade79e990a1ULL, 0x3c25393ba7ecf312ULL, + 0xd53dd99f4b3066a8ULL, 0xf53304714d9265dfULL}}, + // (ten2mx >> 256) = f53304714d9265df d53dd99f4b3066a8 + // 3c25393ba7ecf312aa360ade79e990a1 + {{0x882b3be52e5473b4ULL, 0x96842dc95323f5a8ULL, + 0xaa97e14c3c26b886ULL, 0xc428d05aa4751e4cULL}}, + // (ten2mx >> 256) = c428d05aa4751e4c aa97e14c3c26b886 + // 96842dc95323f5a8882b3be52e5473b4 + {{0xd355c98425105c90ULL, 0xab9cf16ddc1cc486ULL, + 0x55464dd69685606bULL, 0x9ced737bb6c4183dULL}}, + // (ten2mx >> 256) = 9ced737bb6c4183d 55464dd69685606b + // ab9cf16ddc1cc486d355c98425105c90 + {{0xebbc75a03b4d60e6ULL, 0xac2e4f162cfad40aULL, + 0xeed6e2f0f0d56712ULL, 0xfb158592be068d2eULL}}, + // (ten2mx >> 256) = fb158592be068d2e eed6e2f0f0d56712 + // ac2e4f162cfad40aebbc75a03b4d60e6 + {{0x8963914cfc3de71eULL, 0x568b727823fbdcd5ULL, + 0xf245825a5a445275ULL, 0xc8de047564d20a8bULL}}, + // (ten2mx >> 256) = c8de047564d20a8b f245825a5a445275 + // 568b727823fbdcd58963914cfc3de71e + {{0xd44fa770c9cb1f4bULL, 0x453c5b934ffcb0aaULL, + 0x5b6aceaeae9d0ec4ULL, 0xa0b19d2ab70e6ed6ULL}}, + // (ten2mx >> 256) = a0b19d2ab70e6ed6 5b6aceaeae9d0ec4 + // 453c5b934ffcb0aad44fa770c9cb1f4b + {{0xdd0c85f3d4a27f6fULL, 0x37637c75d996f3bbULL, + 0xe2bbd88bbee40bd0ULL, 0x808e17555f3ebf11ULL}}, + // (ten2mx >> 256) = 808e17555f3ebf11 e2bbd88bbee40bd0 + // 37637c75d996f3bbdd0c85f3d4a27f6f + {{0x61ada31fba9d98b2ULL, 0x256bfa5628f185f9ULL, + 0x3792f412cb06794dULL, 0xcdb02555653131b6ULL}}, + // (ten2mx >> 256) = cdb02555653131b6 3792f412cb06794d + // 256bfa5628f185f961ada31fba9d98b2 + {{0xe7be1c196217ad5bULL, 0x51232eab53f46b2dULL, + 0x5fa8c3423c052dd7ULL, 0xa48ceaaab75a8e2bULL}}, + // (ten2mx >> 256) = a48ceaaab75a8e2b 5fa8c3423c052dd7 + // 51232eab53f46b2de7be1c196217ad5b + {{0x52fe7ce11b462449ULL, 0x40e8f222a99055beULL, + 0x1953cf68300424acULL, 0x83a3eeeef9153e89ULL}}, + // (ten2mx >> 256) = 83a3eeeef9153e89 1953cf68300424ac + // 40e8f222a99055be52fe7ce11b462449 + {{0x51972e34f8703a0fULL, 0x34a7e9d10f4d55fdULL, + 0x8eec7f0d19a03aadULL, 0xd29fe4b18e88640eULL}}, + // (ten2mx >> 256) = d29fe4b18e88640e 8eec7f0d19a03aad + // 34a7e9d10f4d55fd51972e34f8703a0f + {{0x0e128b5d938cfb3fULL, 0x2a1fee40d90aab31ULL, + 0x3f2398d747b36224ULL, 0xa87fea27a539e9a5ULL}}, + // (ten2mx >> 256) = a87fea27a539e9a5 3f2398d747b36224 + // 2a1fee40d90aab310e128b5d938cfb3f + {{0x3e753c4adc70c8ffULL, 0xbb4cbe9a473bbc27ULL, + 0x98e947129fc2b4e9ULL, 0x86ccbb52ea94baeaULL}}, + // (ten2mx >> 256) = 86ccbb52ea94baea 98e947129fc2b4e9 + // bb4cbe9a473bbc273e753c4adc70c8ff + {{0x30bb93aafa4e0e65ULL, 0x9214642a0b92c6a5ULL, + 0x5b0ed81dcc6abb0fULL, 0xd7adf884aa879177ULL}}, + // (ten2mx >> 256) = d7adf884aa879177 5b0ed81dcc6abb0f + // 9214642a0b92c6a530bb93aafa4e0e65 + {{0xc0960fbbfb71a51eULL, 0xa8105021a2dbd21dULL, + 0xe272467e3d222f3fULL, 0xac8b2d36eed2dac5ULL}}, + // (ten2mx >> 256) = ac8b2d36eed2dac5 e272467e3d222f3f + // a8105021a2dbd21dc0960fbbfb71a51e + {{0x66de72fcc927b74bULL, 0xb9a6a6814f1641b1ULL, + 0x1b8e9ecb641b58ffULL, 0x8a08f0f8bf0f156bULL}}, + // (ten2mx >> 256) = 8a08f0f8bf0f156b 1b8e9ecb641b58ff + // b9a6a6814f1641b166de72fcc927b74b + {{0xd7ca5194750c5878ULL, 0xf5d770cee4f0691bULL, + 0xf8e431456cf88e65ULL, 0xdcdb1b2798182244ULL}}, + // (ten2mx >> 256) = dcdb1b2798182244 f8e431456cf88e65 + // f5d770cee4f0691bd7ca5194750c5878 + {{0xdfd50e105da379f9ULL, 0x9179270bea59edafULL, + 0x2d835a9df0c6d851ULL, 0xb0af48ec79ace837ULL}}, + // (ten2mx >> 256) = b0af48ec79ace837 2d835a9df0c6d851 + // 9179270bea59edafdfd50e105da379f9 + {{0x19773e737e1c6194ULL, 0x0dfa85a321e18af3ULL, + 0x579c487e5a38ad0eULL, 0x8d590723948a535fULL}}, + // (ten2mx >> 256) = 8d590723948a535f 579c487e5a38ad0e + // dfa85a321e18af319773e737e1c6194 + {{0xf58b971f302d68eeULL, 0x165da29e9c9c1184ULL, + 0x25c6da63c38de1b0ULL, 0xe2280b6c20dd5232ULL}}, + // (ten2mx >> 256) = e2280b6c20dd5232 25c6da63c38de1b0 + // 165da29e9c9c1184f58b971f302d68ee + {{0xc46fac18f3578724ULL, 0x4517b54bb07cdad0ULL, + 0x1e38aeb6360b1af3ULL, 0xb4ecd5f01a4aa828ULL}}, + // (ten2mx >> 256) = b4ecd5f01a4aa828 1e38aeb6360b1af3 + // 4517b54bb07cdad0c46fac18f3578724 + {{0x36bfbce0c2ac6c1dULL, 0x9dac910959fd7bdaULL, + 0xb1c6f22b5e6f48c2ULL, 0x90bd77f3483bb9b9ULL}}, + // (ten2mx >> 256) = 90bd77f3483bb9b9 b1c6f22b5e6f48c2 + // 9dac910959fd7bda36bfbce0c2ac6c1d + {{0x2465fb01377a4695ULL, 0x2f7a81a88ffbf95dULL, + 0xb60b1d1230b20e04ULL, 0xe7958cb87392c2c2ULL}} + // (ten2mx >> 256) = e7958cb87392c2c2 b60b1d1230b20e04 + // 2f7a81a88ffbf95d2465fb01377a4695 +}; diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_2_str.h b/gcc-4.4.3/libgcc/config/libbid/bid128_2_str.h new file mode 100644 index 000000000..7f7287ec6 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_2_str.h @@ -0,0 +1,33 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +extern UINT64 Twoto60_m_10to18; +extern UINT64 Twoto60; +extern UINT64 Inv_Tento9; +extern UINT32 Twoto30_m_10to9; +extern UINT32 Tento9; +extern UINT32 Tento6; +extern UINT32 Tento3; + +extern char midi_tbl[1000][3]; +extern UINT64 mod10_18_tbl[9][128]; diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_2_str_macros.h b/gcc-4.4.3/libgcc/config/libbid/bid128_2_str_macros.h new file mode 100644 index 000000000..965501d10 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_2_str_macros.h @@ -0,0 +1,149 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#define __L0_Normalize_10to18( X_hi, X_lo ) \ +{ \ +UINT64 L0_tmp; \ +L0_tmp = (X_lo) + Twoto60_m_10to18; \ +if (L0_tmp & Twoto60) \ + {(X_hi)=(X_hi)+1;(X_lo)=((L0_tmp<<4)>>4);} \ +} + + +#define __L0_Normalize_10to9( X_hi, X_lo ) \ +{ \ +UINT32 L0_tmp; \ +L0_tmp = (X_lo) + Twoto30_m_10to9; \ +if (L0_tmp & 0x40000000) \ + {(X_hi)=(X_hi)+1;(X_lo)=((L0_tmp<<2)>>2);} \ +} + + +#define __L0_Split_MiDi_2( X, ptr ) \ +{ \ +UINT32 L0_head, L0_tail, L0_tmp; \ + L0_head = (X) >> 10; \ + L0_tail = ((X)&(0x03FF))+(L0_head<<5)-(L0_head<<3); \ + L0_tmp = (L0_tail)>>10; L0_head += L0_tmp; \ + L0_tail = (L0_tail&(0x03FF))+(L0_tmp<<5)-(L0_tmp<<3); \ + if (L0_tail > 999){L0_tail -= 1000; L0_head += 1;} \ + *((ptr)++) = L0_head; *((ptr)++) = L0_tail; \ +} + + +#define __L0_Split_MiDi_3( X, ptr ) \ +{ \ +UINT32 L0_X, L0_head, L0_mid, L0_tail, L0_tmp; \ + L0_X = (UINT32)((X)); \ + L0_head = ((L0_X>>17)*34359)>>18; \ + L0_X -= L0_head*1000000; \ + if (L0_X >= 1000000){L0_X -= 1000000;L0_head+=1;} \ + L0_mid = L0_X >> 10; \ + L0_tail = (L0_X & (0x03FF))+(L0_mid<<5)-(L0_mid<<3); \ + L0_tmp = (L0_tail)>>10; L0_mid += L0_tmp; \ + L0_tail = (L0_tail&(0x3FF))+(L0_tmp<<5)-(L0_tmp<<3); \ + if (L0_tail>999){L0_tail-=1000;L0_mid+=1;} \ + *((ptr)++)=L0_head;*((ptr)++)=L0_mid; \ + *((ptr)++)=L0_tail; \ +} + +#define __L1_Split_MiDi_6( X, ptr ) \ +{ \ +UINT32 L1_X_hi, L1_X_lo; \ +UINT64 L1_Xhi_64, L1_Xlo_64; \ +L1_Xhi_64 = ( ((X)>>28)*Inv_Tento9 ) >> 33; \ +L1_Xlo_64 = (X) - L1_Xhi_64*(UINT64)Tento9; \ +if (L1_Xlo_64 >= (UINT64)Tento9) \ + {L1_Xlo_64-=(UINT64)Tento9;L1_Xhi_64+=1;} \ +L1_X_hi=(UINT32)L1_Xhi_64; L1_X_lo=(UINT32)L1_Xlo_64; \ +__L0_Split_MiDi_3(L1_X_hi,(ptr)); \ +__L0_Split_MiDi_3(L1_X_lo,(ptr)); \ +} + +#define __L1_Split_MiDi_6_Lead( X, ptr ) \ +{ \ +UINT32 L1_X_hi, L1_X_lo; \ +UINT64 L1_Xhi_64, L1_Xlo_64; \ +if ((X)>=(UINT64)Tento9){ \ + L1_Xhi_64 = ( ((X)>>28)*Inv_Tento9 ) >> 33; \ + L1_Xlo_64 = (X) - L1_Xhi_64*(UINT64)Tento9; \ + if (L1_Xlo_64 >= (UINT64)Tento9) \ + {L1_Xlo_64-=(UINT64)Tento9;L1_Xhi_64+=1;} \ + L1_X_hi=(UINT32)L1_Xhi_64; \ + L1_X_lo=(UINT32)L1_Xlo_64; \ + if (L1_X_hi>=Tento6){ \ + __L0_Split_MiDi_3(L1_X_hi,(ptr)); \ + __L0_Split_MiDi_3(L1_X_lo,(ptr)); \ + } \ + else if (L1_X_hi>=Tento3){ \ + __L0_Split_MiDi_2(L1_X_hi,(ptr)); \ + __L0_Split_MiDi_3(L1_X_lo,(ptr)); \ + } \ + else { \ + *((ptr)++) = L1_X_hi; \ + __L0_Split_MiDi_3(L1_X_lo,(ptr)); \ + } \ +} \ +else { \ + L1_X_lo = (UINT32)(X); \ + if (L1_X_lo>=Tento6){ \ + __L0_Split_MiDi_3(L1_X_lo,(ptr)); \ + } \ + else if (L1_X_lo>=Tento3){ \ + __L0_Split_MiDi_2(L1_X_lo,(ptr)); \ + } \ + else { \ + *((ptr)++) = L1_X_lo; \ + } \ +} \ +} + + +#define __L0_MiDi2Str( X, c_ptr ) \ +{ \ +char *L0_src; \ + L0_src = midi_tbl[(X)]; \ + *((c_ptr)++) = *(L0_src++); \ + *((c_ptr)++) = *(L0_src++); \ + *((c_ptr)++) = *(L0_src); \ +} + +#define __L0_MiDi2Str_Lead( X, c_ptr ) \ +{ \ +char *L0_src; \ + L0_src = midi_tbl[(X)]; \ + if ((X)>=100){ \ + *((c_ptr)++) = *(L0_src++); \ + *((c_ptr)++) = *(L0_src++); \ + *((c_ptr)++) = *(L0_src); \ + } \ + else if ((X)>=10){ \ + L0_src++; \ + *((c_ptr)++) = *(L0_src++); \ + *((c_ptr)++) = *(L0_src); \ + } \ + else { \ + L0_src++;L0_src++; \ + *((c_ptr)++) = *(L0_src); \ +} \ +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_2_str_tables.c b/gcc-4.4.3/libgcc/config/libbid/bid128_2_str_tables.c new file mode 100644 index 000000000..f1517ed56 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_2_str_tables.c @@ -0,0 +1,642 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +UINT64 Twoto60_m_10to18 = 152921504606846976LL; +UINT64 Twoto60 = 0x1000000000000000LL; +UINT64 Inv_Tento9 = 2305843009LL; /* floor(2^61/10^9) */ +UINT32 Twoto30_m_10to9 = 73741824; +UINT32 Tento9 = 1000000000; +UINT32 Tento6 = 1000000; +UINT32 Tento3 = 1000; + +const char midi_tbl[1000][3] = { + "000", "001", "002", "003", "004", "005", "006", "007", "008", "009", + "010", "011", "012", "013", "014", "015", "016", "017", "018", "019", + "020", "021", "022", "023", "024", "025", "026", "027", "028", "029", + "030", "031", "032", "033", "034", "035", "036", "037", "038", "039", + "040", "041", "042", "043", "044", "045", "046", "047", "048", "049", + "050", "051", "052", "053", "054", "055", "056", "057", "058", "059", + "060", "061", "062", "063", "064", "065", "066", "067", "068", "069", + "070", "071", "072", "073", "074", "075", "076", "077", "078", "079", + "080", "081", "082", "083", "084", "085", "086", "087", "088", "089", + "090", "091", "092", "093", "094", "095", "096", "097", "098", "099", + "100", "101", "102", "103", "104", "105", "106", "107", "108", "109", + "110", "111", "112", "113", "114", "115", "116", "117", "118", "119", + "120", "121", "122", "123", "124", "125", "126", "127", "128", "129", + "130", "131", "132", "133", "134", "135", "136", "137", "138", "139", + "140", "141", "142", "143", "144", "145", "146", "147", "148", "149", + "150", "151", "152", "153", "154", "155", "156", "157", "158", "159", + "160", "161", "162", "163", "164", "165", "166", "167", "168", "169", + "170", "171", "172", "173", "174", "175", "176", "177", "178", "179", + "180", "181", "182", "183", "184", "185", "186", "187", "188", "189", + "190", "191", "192", "193", "194", "195", "196", "197", "198", "199", + "200", "201", "202", "203", "204", "205", "206", "207", "208", "209", + "210", "211", "212", "213", "214", "215", "216", "217", "218", "219", + "220", "221", "222", "223", "224", "225", "226", "227", "228", "229", + "230", "231", "232", "233", "234", "235", "236", "237", "238", "239", + "240", "241", "242", "243", "244", "245", "246", "247", "248", "249", + "250", "251", "252", "253", "254", "255", "256", "257", "258", "259", + "260", "261", "262", "263", "264", "265", "266", "267", "268", "269", + "270", "271", "272", "273", "274", "275", "276", "277", "278", "279", + "280", "281", "282", "283", "284", "285", "286", "287", "288", "289", + "290", "291", "292", "293", "294", "295", "296", "297", "298", "299", + "300", "301", "302", "303", "304", "305", "306", "307", "308", "309", + "310", "311", "312", "313", "314", "315", "316", "317", "318", "319", + "320", "321", "322", "323", "324", "325", "326", "327", "328", "329", + "330", "331", "332", "333", "334", "335", "336", "337", "338", "339", + "340", "341", "342", "343", "344", "345", "346", "347", "348", "349", + "350", "351", "352", "353", "354", "355", "356", "357", "358", "359", + "360", "361", "362", "363", "364", "365", "366", "367", "368", "369", + "370", "371", "372", "373", "374", "375", "376", "377", "378", "379", + "380", "381", "382", "383", "384", "385", "386", "387", "388", "389", + "390", "391", "392", "393", "394", "395", "396", "397", "398", "399", + "400", "401", "402", "403", "404", "405", "406", "407", "408", "409", + "410", "411", "412", "413", "414", "415", "416", "417", "418", "419", + "420", "421", "422", "423", "424", "425", "426", "427", "428", "429", + "430", "431", "432", "433", "434", "435", "436", "437", "438", "439", + "440", "441", "442", "443", "444", "445", "446", "447", "448", "449", + "450", "451", "452", "453", "454", "455", "456", "457", "458", "459", + "460", "461", "462", "463", "464", "465", "466", "467", "468", "469", + "470", "471", "472", "473", "474", "475", "476", "477", "478", "479", + "480", "481", "482", "483", "484", "485", "486", "487", "488", "489", + "490", "491", "492", "493", "494", "495", "496", "497", "498", "499", + "500", "501", "502", "503", "504", "505", "506", "507", "508", "509", + "510", "511", "512", "513", "514", "515", "516", "517", "518", "519", + "520", "521", "522", "523", "524", "525", "526", "527", "528", "529", + "530", "531", "532", "533", "534", "535", "536", "537", "538", "539", + "540", "541", "542", "543", "544", "545", "546", "547", "548", "549", + "550", "551", "552", "553", "554", "555", "556", "557", "558", "559", + "560", "561", "562", "563", "564", "565", "566", "567", "568", "569", + "570", "571", "572", "573", "574", "575", "576", "577", "578", "579", + "580", "581", "582", "583", "584", "585", "586", "587", "588", "589", + "590", "591", "592", "593", "594", "595", "596", "597", "598", "599", + "600", "601", "602", "603", "604", "605", "606", "607", "608", "609", + "610", "611", "612", "613", "614", "615", "616", "617", "618", "619", + "620", "621", "622", "623", "624", "625", "626", "627", "628", "629", + "630", "631", "632", "633", "634", "635", "636", "637", "638", "639", + "640", "641", "642", "643", "644", "645", "646", "647", "648", "649", + "650", "651", "652", "653", "654", "655", "656", "657", "658", "659", + "660", "661", "662", "663", "664", "665", "666", "667", "668", "669", + "670", "671", "672", "673", "674", "675", "676", "677", "678", "679", + "680", "681", "682", "683", "684", "685", "686", "687", "688", "689", + "690", "691", "692", "693", "694", "695", "696", "697", "698", "699", + "700", "701", "702", "703", "704", "705", "706", "707", "708", "709", + "710", "711", "712", "713", "714", "715", "716", "717", "718", "719", + "720", "721", "722", "723", "724", "725", "726", "727", "728", "729", + "730", "731", "732", "733", "734", "735", "736", "737", "738", "739", + "740", "741", "742", "743", "744", "745", "746", "747", "748", "749", + "750", "751", "752", "753", "754", "755", "756", "757", "758", "759", + "760", "761", "762", "763", "764", "765", "766", "767", "768", "769", + "770", "771", "772", "773", "774", "775", "776", "777", "778", "779", + "780", "781", "782", "783", "784", "785", "786", "787", "788", "789", + "790", "791", "792", "793", "794", "795", "796", "797", "798", "799", + "800", "801", "802", "803", "804", "805", "806", "807", "808", "809", + "810", "811", "812", "813", "814", "815", "816", "817", "818", "819", + "820", "821", "822", "823", "824", "825", "826", "827", "828", "829", + "830", "831", "832", "833", "834", "835", "836", "837", "838", "839", + "840", "841", "842", "843", "844", "845", "846", "847", "848", "849", + "850", "851", "852", "853", "854", "855", "856", "857", "858", "859", + "860", "861", "862", "863", "864", "865", "866", "867", "868", "869", + "870", "871", "872", "873", "874", "875", "876", "877", "878", "879", + "880", "881", "882", "883", "884", "885", "886", "887", "888", "889", + "890", "891", "892", "893", "894", "895", "896", "897", "898", "899", + "900", "901", "902", "903", "904", "905", "906", "907", "908", "909", + "910", "911", "912", "913", "914", "915", "916", "917", "918", "919", + "920", "921", "922", "923", "924", "925", "926", "927", "928", "929", + "930", "931", "932", "933", "934", "935", "936", "937", "938", "939", + "940", "941", "942", "943", "944", "945", "946", "947", "948", "949", + "950", "951", "952", "953", "954", "955", "956", "957", "958", "959", + "960", "961", "962", "963", "964", "965", "966", "967", "968", "969", + "970", "971", "972", "973", "974", "975", "976", "977", "978", "979", + "980", "981", "982", "983", "984", "985", "986", "987", "988", "989", + "990", "991", "992", "993", "994", "995", "996", "997", "998", "999" +}; + +const UINT64 mod10_18_tbl[9][128] = { + // 2^59 = 576460752303423488, A and B breakdown, where data = A*10^18 + B + + { + 0LL, 0LL, 0LL, 576460752303423488LL, + // 0*2^59, 1*2^59 + 1LL, 152921504606846976LL, 1LL, 729382256910270464LL, + // 2*2^59, 3*2^59 + 2LL, 305843009213693952LL, 2LL, 882303761517117440LL, + // 4*2^59, 5*2^59 + 3LL, 458764513820540928LL, 4LL, 35225266123964416LL, + // 6*2^59, 7*2^59 + 4LL, 611686018427387904LL, 5LL, 188146770730811392LL, + // 8*2^59, 9*2^59 + 5LL, 764607523034234880LL, 6LL, 341068275337658368LL, + // 10*2^59, 11*2^59 + 6LL, 917529027641081856LL, 7LL, 493989779944505344LL, + // 12*2^59, 13*2^59 + 8LL, 70450532247928832LL, 8LL, 646911284551352320LL, + // 14*2^59, 15*2^59 + 9LL, 223372036854775808LL, 9LL, 799832789158199296LL, + // 16*2^59, 17*2^59 + 10LL, 376293541461622784LL, 10LL, 952754293765046272LL, + // 18*2^59, 19*2^59 + 11LL, 529215046068469760LL, 12LL, 105675798371893248LL, + // 20*2^59, 21*2^59 + 12LL, 682136550675316736LL, 13LL, 258597302978740224LL, + // 22*2^59, 23*2^59 + 13LL, 835058055282163712LL, 14LL, 411518807585587200LL, + // 24*2^59, 25*2^59 + 14LL, 987979559889010688LL, 15LL, 564440312192434176LL, + // 26*2^59, 27*2^59 + 16LL, 140901064495857664LL, 16LL, 717361816799281152LL, + // 28*2^59, 29*2^59 + 17LL, 293822569102704640LL, 17LL, 870283321406128128LL, + // 30*2^59, 31*2^59 + 18LL, 446744073709551616LL, 19LL, 23204826012975104LL, + // 32*2^59, 33*2^59 + 19LL, 599665578316398592LL, 20LL, 176126330619822080LL, + // 34*2^59, 35*2^59 + 20LL, 752587082923245568LL, 21LL, 329047835226669056LL, + // 36*2^59, 37*2^59 + 21LL, 905508587530092544LL, 22LL, 481969339833516032LL, + // 38*2^59, 39*2^59 + 23LL, 58430092136939520LL, 23LL, 634890844440363008LL, + // 40*2^59, 41*2^59 + 24LL, 211351596743786496LL, 24LL, 787812349047209984LL, + // 42*2^59, 43*2^59 + 25LL, 364273101350633472LL, 25LL, 940733853654056960LL, + // 44*2^59, 45*2^59 + 26LL, 517194605957480448LL, 27LL, 93655358260903936LL, + // 46*2^59, 47*2^59 + 27LL, 670116110564327424LL, 28LL, 246576862867750912LL, + // 48*2^59, 49*2^59 + 28LL, 823037615171174400LL, 29LL, 399498367474597888LL, + // 50*2^59, 51*2^59 + 29LL, 975959119778021376LL, 30LL, 552419872081444864LL, + // 52*2^59, 53*2^59 + 31LL, 128880624384868352LL, 31LL, 705341376688291840LL, + // 54*2^59, 55*2^59 + 32LL, 281802128991715328LL, 32LL, 858262881295138816LL, + // 56*2^59, 57*2^59 + 33LL, 434723633598562304LL, 34LL, 11184385901985792LL, + // 58*2^59, 59*2^59 + 34LL, 587645138205409280LL, 35LL, 164105890508832768LL, + // 60*2^59, 61*2^59 + 35LL, 740566642812256256LL, 36LL, 317027395115679744LL, + // 62*2^59, 63*2^59 + }, + + { + // 2^65 = 36*10^18 + 893488147419103232 + 0LL, 0LL, 36LL, 893488147419103232LL, + // 0*2^65, 1*2^65 + 73LL, 786976294838206464LL, 110LL, 680464442257309696LL, + // 2*2^65, 3*2^65 + 147LL, 573952589676412928LL, 184LL, 467440737095516160LL, + // 4*2^65, 5*2^65 + 221LL, 360928884514619392LL, 258LL, 254417031933722624LL, + // 6*2^65, 7*2^65 + 295LL, 147905179352825856LL, 332LL, 41393326771929088LL, + // 8*2^65, 9*2^65 + 368LL, 934881474191032320LL, 405LL, 828369621610135552LL, + // 0*2^65, 1*2^65 + 442LL, 721857769029238784LL, 479LL, 615345916448342016LL, + // 2*2^65, 3*2^65 + 516LL, 508834063867445248LL, 553LL, 402322211286548480LL, + // 4*2^65, 5*2^65 + 590LL, 295810358705651712LL, 627LL, 189298506124754944LL, + // 6*2^65, 7*2^65 + 664LL, 82786653543858176LL, 700LL, 976274800962961408LL, + // 8*2^65, 9*2^65 + 737LL, 869762948382064640LL, 774LL, 763251095801167872LL, + // 0*2^65, 1*2^65 + 811LL, 656739243220271104LL, 848LL, 550227390639374336LL, + // 2*2^65, 3*2^65 + 885LL, 443715538058477568LL, 922LL, 337203685477580800LL, + // 4*2^65, 5*2^65 + 959LL, 230691832896684032LL, 996LL, 124179980315787264LL, + // 6*2^65, 7*2^65 + 1033LL, 17668127734890496LL, 1069LL, 911156275153993728LL, + // 8*2^65, 9*2^65 + 1106LL, 804644422573096960LL, 1143LL, 698132569992200192LL, + // 0*2^65, 1*2^65 + 1180LL, 591620717411303424LL, 1217LL, 485108864830406656LL, + // 2*2^65, 3*2^65 + 1254LL, 378597012249509888LL, 1291LL, 272085159668613120LL, + // 4*2^65, 5*2^65 + 1328LL, 165573307087716352LL, 1365LL, 59061454506819584LL, + // 6*2^65, 7*2^65 + 1401LL, 952549601925922816LL, 1438LL, 846037749345026048LL, + // 8*2^65, 9*2^65 + 1475LL, 739525896764129280LL, 1512LL, 633014044183232512LL, + // 0*2^65, 1*2^65 + 1549LL, 526502191602335744LL, 1586LL, 419990339021438976LL, + // 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b/gcc-4.4.3/libgcc/config/libbid/bid128_add.c new file mode 100644 index 000000000..dacc7a1f6 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_add.c @@ -0,0 +1,2941 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64dq_add (UINT64 * pres, UINT64 * px, UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64dq_add (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res = 0xbaddbaddbaddbaddull; + UINT128 x1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64qq_add (&res, &x1, py + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid64qq_add (x1, y + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64qd_add (UINT64 * pres, UINT128 * px, UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64qd_add (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res = 0xbaddbaddbaddbaddull; + UINT128 y1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64qq_add (&res, px, &y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid64qq_add (x, y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64qq_add (UINT64 * pres, UINT128 * px, UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px, y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64qq_add (UINT128 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 one = { {0x0000000000000001ull, 0x3040000000000000ull} + }; + UINT64 res = 0xbaddbaddbaddbaddull; + + BID_SWAP128 (one); +#if DECIMAL_CALL_BY_REFERENCE + bid64qqq_fma (&res, &one, &x, &y + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + res = bid64qqq_fma (one, x, y + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128dd_add (UINT128 * pres, UINT64 * px, UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px, y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128dd_add (UINT64 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} + }; + UINT128 x1, y1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_add (&res, &x1, &y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_add (x1, y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128dq_add (UINT128 * pres, UINT64 * px, UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128dq_add (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} + }; + UINT128 x1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_add (&res, &x1, py + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_add (x1, y + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128qd_add (UINT128 * pres, UINT128 * px, UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128qd_add (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} + }; + UINT128 y1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_add (&res, px, &y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_add (x, y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +// bid128_add stands for bid128qq_add + + +/***************************************************************************** + * BID64/BID128 sub + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64dq_sub (UINT64 * pres, UINT64 * px, UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64dq_sub (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res = 0xbaddbaddbaddbaddull; + UINT128 x1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64qq_sub (&res, &x1, py + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid64qq_sub (x1, y + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64qd_sub (UINT64 * pres, UINT128 * px, UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64qd_sub (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res = 0xbaddbaddbaddbaddull; + UINT128 y1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64qq_sub (&res, px, &y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid64qq_sub (x, y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64qq_sub (UINT64 * pres, UINT128 * px, UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px, y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64qq_sub (UINT128 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 one = { {0x0000000000000001ull, 0x3040000000000000ull} + }; + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 y_sign; + + BID_SWAP128 (one); + if ((y.w[HIGH_128W] & MASK_NAN) != MASK_NAN) { // y is not NAN + // change its sign + y_sign = y.w[HIGH_128W] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + if (y_sign) + y.w[HIGH_128W] = y.w[HIGH_128W] & 0x7fffffffffffffffull; + else + y.w[HIGH_128W] = y.w[HIGH_128W] | 0x8000000000000000ull; + } +#if DECIMAL_CALL_BY_REFERENCE + bid64qqq_fma (&res, &one, &x, &y + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + res = bid64qqq_fma (one, x, y + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128dd_sub (UINT128 * pres, UINT64 * px, UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px, y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128dd_sub (UINT64 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} + }; + UINT128 x1, y1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_sub (&res, &x1, &y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_sub (x1, y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128dq_sub (UINT128 * pres, UINT64 * px, UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128dq_sub (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} + }; + UINT128 x1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_sub (&res, &x1, py + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_sub (x1, y + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128qd_sub (UINT128 * pres, UINT128 * px, UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128qd_sub (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} + }; + UINT128 y1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_sub (&res, px, &y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_sub (x, y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_add (UINT128 * pres, UINT128 * px, UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px, y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128_add (UINT128 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} + }; + UINT64 x_sign, y_sign, tmp_sign; + UINT64 x_exp, y_exp, tmp_exp; // e1 = x_exp, e2 = y_exp + UINT64 C1_hi, C2_hi, tmp_signif_hi; + UINT64 C1_lo, C2_lo, tmp_signif_lo; + // Note: C1.w[1], C1.w[0] represent C1_hi, C1_lo (all UINT64) + // Note: C2.w[1], C2.w[0] represent C2_hi, C2_lo (all UINT64) + UINT64 tmp64, tmp64A, tmp64B; + BID_UI64DOUBLE tmp1, tmp2; + int x_nr_bits, y_nr_bits; + int q1, q2, delta, scale, x1, ind, shift, tmp_inexact = 0; + UINT64 halfulp64; + UINT128 halfulp128; + UINT128 C1, C2; + UINT128 ten2m1; + UINT128 highf2star; // top 128 bits in f2*; low 128 bits in R256[1], R256[0] + UINT256 P256, Q256, R256; + int is_inexact = 0, is_midpoint_lt_even = 0, is_midpoint_gt_even = 0; + int is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; + int second_pass = 0; + + BID_SWAP128 (x); + BID_SWAP128 (y); + x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + y_sign = y.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + + // check for NaN or Infinity + if (((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) + || ((y.w[1] & MASK_SPECIAL) == MASK_SPECIAL)) { + // x is special or y is special + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + // check first for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) + && (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res.w[1] = x.w[1] & 0xfc003fffffffffffull; + // clear out also G[6]-G[16] + res.w[0] = x.w[0]; + } else { // x is QNaN + // return x + res.w[1] = x.w[1] & 0xfc003fffffffffffull; + // clear out G[6]-G[16] + res.w[0] = x.w[0]; + // if y = SNaN signal invalid exception + if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + } + } + BID_SWAP128 (res); + BID_RETURN (res); + } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN + // check first for non-canonical NaN payload + if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) + && (y.w[0] > 0x38c15b09ffffffffull))) { + y.w[1] = y.w[1] & 0xffffc00000000000ull; + y.w[0] = 0x0ull; + } + if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (y) + res.w[1] = y.w[1] & 0xfc003fffffffffffull; + // clear out also G[6]-G[16] + res.w[0] = y.w[0]; + } else { // y is QNaN + // return y + res.w[1] = y.w[1] & 0xfc003fffffffffffull; + // clear out G[6]-G[16] + res.w[0] = y.w[0]; + } + BID_SWAP128 (res); + BID_RETURN (res); + } else { // neither x not y is NaN; at least one is infinity + if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x is infinity + if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y is infinity + // if same sign, return either of them + if ((x.w[1] & MASK_SIGN) == (y.w[1] & MASK_SIGN)) { + res.w[1] = x_sign | MASK_INF; + res.w[0] = 0x0ull; + } else { // x and y are infinities of opposite signs + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return QNaN Indefinite + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0x0000000000000000ull; + } + } else { // y is 0 or finite + // return x + res.w[1] = x_sign | MASK_INF; + res.w[0] = 0x0ull; + } + } else { // x is not NaN or infinity, so y must be infinity + res.w[1] = y_sign | MASK_INF; + res.w[0] = 0x0ull; + } + BID_SWAP128 (res); + BID_RETURN (res); + } + } + // unpack the arguments + + // unpack x + C1_hi = x.w[1] & MASK_COEFF; + C1_lo = x.w[0]; + // test for non-canonical values: + // - values whose encoding begins with x00, x01, or x10 and whose + // coefficient is larger than 10^34 -1, or + // - values whose encoding begins with x1100, x1101, x1110 (if NaNs + // and infinitis were eliminated already this test is reduced to + // checking for x10x) + + // x is not infinity; check for non-canonical values - treated as zero + if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { + // G0_G1=11; non-canonical + x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C1_hi = 0; // significand high + C1_lo = 0; // significand low + } else { // G0_G1 != 11 + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C1_hi > 0x0001ed09bead87c0ull || + (C1_hi == 0x0001ed09bead87c0ull + && C1_lo > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + C1_hi = 0; + C1_lo = 0; + } else { // canonical + ; + } + } + + // unpack y + C2_hi = y.w[1] & MASK_COEFF; + C2_lo = y.w[0]; + // y is not infinity; check for non-canonical values - treated as zero + if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { + // G0_G1=11; non-canonical + y_exp = (y.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C2_hi = 0; // significand high + C2_lo = 0; // significand low + } else { // G0_G1 != 11 + y_exp = y.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C2_hi > 0x0001ed09bead87c0ull || + (C2_hi == 0x0001ed09bead87c0ull + && C2_lo > 0x378d8e63ffffffffull)) { + // y is non-canonical if coefficient is larger than 10^34 -1 + C2_hi = 0; + C2_lo = 0; + } else { // canonical + ; + } + } + + if ((C1_hi == 0x0ull) && (C1_lo == 0x0ull)) { + // x is 0 and y is not special + // if y is 0 return 0 with the smaller exponent + if ((C2_hi == 0x0ull) && (C2_lo == 0x0ull)) { + if (x_exp < y_exp) + res.w[1] = x_exp; + else + res.w[1] = y_exp; + if (x_sign && y_sign) + res.w[1] = res.w[1] | x_sign; // both negative + else if (rnd_mode == ROUNDING_DOWN && x_sign != y_sign) + res.w[1] = res.w[1] | 0x8000000000000000ull; // -0 + // else; // res = +0 + res.w[0] = 0; + } else { + // for 0 + y return y, with the preferred exponent + if (y_exp <= x_exp) { + res.w[1] = y.w[1]; + res.w[0] = y.w[0]; + } else { // if y_exp > x_exp + // return (C2 * 10^scale) * 10^(y_exp - scale) + // where scale = min (P34-q2, y_exp-x_exp) + // determine q2 = nr. of decimal digits in y + // determine first the nr. of bits in y (y_nr_bits) + + if (C2_hi == 0) { // y_bits is the nr. of bits in C2_lo + if (C2_lo >= 0x0020000000000000ull) { // y >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid + // rounding errors + if (C2_lo >= 0x0000000100000000ull) { // y >= 2^32 + tmp2.d = (double) (C2_lo >> 32); // exact conversion + y_nr_bits = + 32 + + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // y < 2^32 + tmp2.d = (double) (C2_lo); // exact conversion + y_nr_bits = + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if y < 2^53 + tmp2.d = (double) C2_lo; // exact conversion + y_nr_bits = + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C2_hi != 0 => nr. bits = 64 + nr_bits (C2_hi) + tmp2.d = (double) C2_hi; // exact conversion + y_nr_bits = + 64 + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q2 = nr_digits[y_nr_bits].digits; + if (q2 == 0) { + q2 = nr_digits[y_nr_bits].digits1; + if (C2_hi > nr_digits[y_nr_bits].threshold_hi || + (C2_hi == nr_digits[y_nr_bits].threshold_hi && + C2_lo >= nr_digits[y_nr_bits].threshold_lo)) + q2++; + } + // return (C2 * 10^scale) * 10^(y_exp - scale) + // where scale = min (P34-q2, y_exp-x_exp) + scale = P34 - q2; + ind = (y_exp - x_exp) >> 49; + if (ind < scale) + scale = ind; + if (scale == 0) { + res.w[1] = y.w[1]; + res.w[0] = y.w[0]; + } else if (q2 <= 19) { // y fits in 64 bits + if (scale <= 19) { // 10^scale fits in 64 bits + // 64 x 64 C2_lo * ten2k64[scale] + __mul_64x64_to_128MACH (res, C2_lo, ten2k64[scale]); + } else { // 10^scale fits in 128 bits + // 64 x 128 C2_lo * ten2k128[scale - 20] + __mul_128x64_to_128 (res, C2_lo, ten2k128[scale - 20]); + } + } else { // y fits in 128 bits, but 10^scale must fit in 64 bits + // 64 x 128 ten2k64[scale] * C2 + C2.w[1] = C2_hi; + C2.w[0] = C2_lo; + __mul_128x64_to_128 (res, ten2k64[scale], C2); + } + // subtract scale from the exponent + y_exp = y_exp - ((UINT64) scale << 49); + res.w[1] = res.w[1] | y_sign | y_exp; + } + } + BID_SWAP128 (res); + BID_RETURN (res); + } else if ((C2_hi == 0x0ull) && (C2_lo == 0x0ull)) { + // y is 0 and x is not special, and not zero + // for x + 0 return x, with the preferred exponent + if (x_exp <= y_exp) { + res.w[1] = x.w[1]; + res.w[0] = x.w[0]; + } else { // if x_exp > y_exp + // return (C1 * 10^scale) * 10^(x_exp - scale) + // where scale = min (P34-q1, x_exp-y_exp) + // determine q1 = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1_hi == 0) { // x_bits is the nr. of bits in C1_lo + if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid + // rounding errors + if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1_lo >> 32); // exact conversion + x_nr_bits = + 32 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - + 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1_lo); // exact conversion + x_nr_bits = + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1_lo; // exact conversion + x_nr_bits = + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi) + tmp1.d = (double) C1_hi; // exact conversion + x_nr_bits = + 64 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q1 = nr_digits[x_nr_bits].digits; + if (q1 == 0) { + q1 = nr_digits[x_nr_bits].digits1; + if (C1_hi > nr_digits[x_nr_bits].threshold_hi || + (C1_hi == nr_digits[x_nr_bits].threshold_hi && + C1_lo >= nr_digits[x_nr_bits].threshold_lo)) + q1++; + } + // return (C1 * 10^scale) * 10^(x_exp - scale) + // where scale = min (P34-q1, x_exp-y_exp) + scale = P34 - q1; + ind = (x_exp - y_exp) >> 49; + if (ind < scale) + scale = ind; + if (scale == 0) { + res.w[1] = x.w[1]; + res.w[0] = x.w[0]; + } else if (q1 <= 19) { // x fits in 64 bits + if (scale <= 19) { // 10^scale fits in 64 bits + // 64 x 64 C1_lo * ten2k64[scale] + __mul_64x64_to_128MACH (res, C1_lo, ten2k64[scale]); + } else { // 10^scale fits in 128 bits + // 64 x 128 C1_lo * ten2k128[scale - 20] + __mul_128x64_to_128 (res, C1_lo, ten2k128[scale - 20]); + } + } else { // x fits in 128 bits, but 10^scale must fit in 64 bits + // 64 x 128 ten2k64[scale] * C1 + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + __mul_128x64_to_128 (res, ten2k64[scale], C1); + } + // subtract scale from the exponent + x_exp = x_exp - ((UINT64) scale << 49); + res.w[1] = res.w[1] | x_sign | x_exp; + } + BID_SWAP128 (res); + BID_RETURN (res); + } else { // x and y are not canonical, not special, and are not zero + // note that the result may still be zero, and then it has to have the + // preferred exponent + if (x_exp < y_exp) { // if exp_x < exp_y then swap x and y + tmp_sign = x_sign; + tmp_exp = x_exp; + tmp_signif_hi = C1_hi; + tmp_signif_lo = C1_lo; + x_sign = y_sign; + x_exp = y_exp; + C1_hi = C2_hi; + C1_lo = C2_lo; + y_sign = tmp_sign; + y_exp = tmp_exp; + C2_hi = tmp_signif_hi; + C2_lo = tmp_signif_lo; + } + // q1 = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1_hi == 0) { // x_bits is the nr. of bits in C1_lo + if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53 + //split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1_lo >> 32); // exact conversion + x_nr_bits = + 32 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1_lo); // exact conversion + x_nr_bits = + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1_lo; // exact conversion + x_nr_bits = + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi) + tmp1.d = (double) C1_hi; // exact conversion + x_nr_bits = + 64 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + + q1 = nr_digits[x_nr_bits].digits; + if (q1 == 0) { + q1 = nr_digits[x_nr_bits].digits1; + if (C1_hi > nr_digits[x_nr_bits].threshold_hi || + (C1_hi == nr_digits[x_nr_bits].threshold_hi && + C1_lo >= nr_digits[x_nr_bits].threshold_lo)) + q1++; + } + // q2 = nr. of decimal digits in y + // determine first the nr. of bits in y (y_nr_bits) + if (C2_hi == 0) { // y_bits is the nr. of bits in C2_lo + if (C2_lo >= 0x0020000000000000ull) { // y >= 2^53 + //split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C2_lo >= 0x0000000100000000ull) { // y >= 2^32 + tmp2.d = (double) (C2_lo >> 32); // exact conversion + y_nr_bits = + 32 + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // y < 2^32 + tmp2.d = (double) (C2_lo); // exact conversion + y_nr_bits = + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if y < 2^53 + tmp2.d = (double) C2_lo; // exact conversion + y_nr_bits = + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C2_hi != 0 => nr. bits = 64 + nr_bits (C2_hi) + tmp2.d = (double) C2_hi; // exact conversion + y_nr_bits = + 64 + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + + q2 = nr_digits[y_nr_bits].digits; + if (q2 == 0) { + q2 = nr_digits[y_nr_bits].digits1; + if (C2_hi > nr_digits[y_nr_bits].threshold_hi || + (C2_hi == nr_digits[y_nr_bits].threshold_hi && + C2_lo >= nr_digits[y_nr_bits].threshold_lo)) + q2++; + } + + delta = q1 + (int) (x_exp >> 49) - q2 - (int) (y_exp >> 49); + + if (delta >= P34) { + // round the result directly because 0 < C2 < ulp (C1 * 10^(x_exp-e2)) + // n = C1 * 10^e1 or n = C1 +/- 10^(q1-P34)) * 10^e1 + // the result is inexact; the preferred exponent is the least possible + + if (delta >= P34 + 1) { + // for RN the result is the operand with the larger magnitude, + // possibly scaled up by 10^(P34-q1) + // an overflow cannot occur in this case (rounding to nearest) + if (q1 < P34) { // scale C1 up by 10^(P34-q1) + // Note: because delta >= P34+1 it is certain that + // x_exp - ((UINT64)scale << 49) will stay above e_min + scale = P34 - q1; + if (q1 <= 19) { // C1 fits in 64 bits + // 1 <= q1 <= 19 => 15 <= scale <= 33 + if (scale <= 19) { // 10^scale fits in 64 bits + __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); + } else { // if 20 <= scale <= 33 + // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where + // (C1 * 10^(scale-19)) fits in 64 bits + C1_lo = C1_lo * ten2k64[scale - 19]; + __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); + } + } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits + // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + // C1 = ten2k64[P34 - q1] * C1 + __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); + } + x_exp = x_exp - ((UINT64) scale << 49); + C1_hi = C1.w[1]; + C1_lo = C1.w[0]; + } + // some special cases arise: if delta = P34 + 1 and C1 = 10^(P34-1) + // (after scaling) and x_sign != y_sign and C2 > 5*10^(q2-1) => + // subtract 1 ulp + // Note: do this only for rounding to nearest; for other rounding + // modes the correction will be applied next + if ((rnd_mode == ROUNDING_TO_NEAREST + || rnd_mode == ROUNDING_TIES_AWAY) && delta == (P34 + 1) + && C1_hi == 0x0000314dc6448d93ull + && C1_lo == 0x38c15b0a00000000ull && x_sign != y_sign + && ((q2 <= 19 && C2_lo > midpoint64[q2 - 1]) || (q2 >= 20 + && (C2_hi > + midpoint128 + [q2 - + 20]. + w[1] + || + (C2_hi + == + midpoint128 + [q2 - + 20]. + w[1] + && + C2_lo + > + midpoint128 + [q2 - + 20]. + w + [0]))))) + { + // C1 = 10^34 - 1 and decrement x_exp by 1 (no underflow possible) + C1_hi = 0x0001ed09bead87c0ull; + C1_lo = 0x378d8e63ffffffffull; + x_exp = x_exp - EXP_P1; + } + if (rnd_mode != ROUNDING_TO_NEAREST) { + if ((rnd_mode == ROUNDING_DOWN && x_sign && y_sign) || + (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) { + // add 1 ulp and then check for overflow + C1_lo = C1_lo + 1; + if (C1_lo == 0) { // rounding overflow in the low 64 bits + C1_hi = C1_hi + 1; + } + if (C1_hi == 0x0001ed09bead87c0ull + && C1_lo == 0x378d8e6400000000ull) { + // C1 = 10^34 => rounding overflow + C1_hi = 0x0000314dc6448d93ull; + C1_lo = 0x38c15b0a00000000ull; // 10^33 + x_exp = x_exp + EXP_P1; + if (x_exp == EXP_MAX_P1) { // overflow + C1_hi = 0x7800000000000000ull; // +inf + C1_lo = 0x0ull; + x_exp = 0; // x_sign is preserved + // set overflow flag (the inexact flag was set too) + *pfpsf |= OVERFLOW_EXCEPTION; + } + } + } else if ((rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) || + (rnd_mode == ROUNDING_UP && x_sign && !y_sign) || + (rnd_mode == ROUNDING_TO_ZERO + && x_sign != y_sign)) { + // subtract 1 ulp from C1 + // Note: because delta >= P34 + 1 the result cannot be zero + C1_lo = C1_lo - 1; + if (C1_lo == 0xffffffffffffffffull) + C1_hi = C1_hi - 1; + // if the coefficient is 10^33 - 1 then make it 10^34 - 1 and + // decrease the exponent by 1 (because delta >= P34 + 1 the + // exponent will not become less than e_min) + // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff + // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff + if (C1_hi == 0x0000314dc6448d93ull + && C1_lo == 0x38c15b09ffffffffull) { + // make C1 = 10^34 - 1 + C1_hi = 0x0001ed09bead87c0ull; + C1_lo = 0x378d8e63ffffffffull; + x_exp = x_exp - EXP_P1; + } + } else { + ; // the result is already correct + } + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // assemble the result + res.w[1] = x_sign | x_exp | C1_hi; + res.w[0] = C1_lo; + } else { // delta = P34 + // in most cases, the smaller operand may be < or = or > 1/2 ulp of the + // larger operand + // however, the case C1 = 10^(q1-1) and x_sign != y_sign is special due + // to accuracy loss after subtraction, and will be treated separately + if (x_sign == y_sign || (q1 <= 20 + && (C1_hi != 0 + || C1_lo != ten2k64[q1 - 1])) + || (q1 >= 21 && (C1_hi != ten2k128[q1 - 21].w[1] + || C1_lo != ten2k128[q1 - 21].w[0]))) { + // if x_sign == y_sign or C1 != 10^(q1-1) + // compare C2 with 1/2 ulp = 5 * 10^(q2-1), the latter read from table + // Note: cases q1<=19 and q1>=20 can be coalesced at some latency cost + if (q2 <= 19) { // C2 and 5*10^(q2-1) both fit in 64 bits + halfulp64 = midpoint64[q2 - 1]; // 5 * 10^(q2-1) + if (C2_lo < halfulp64) { // n2 < 1/2 ulp (n1) + // for RN the result is the operand with the larger magnitude, + // possibly scaled up by 10^(P34-q1) + // an overflow cannot occur in this case (rounding to nearest) + if (q1 < P34) { // scale C1 up by 10^(P34-q1) + // Note: because delta = P34 it is certain that + // x_exp - ((UINT64)scale << 49) will stay above e_min + scale = P34 - q1; + if (q1 <= 19) { // C1 fits in 64 bits + // 1 <= q1 <= 19 => 15 <= scale <= 33 + if (scale <= 19) { // 10^scale fits in 64 bits + __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); + } else { // if 20 <= scale <= 33 + // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where + // (C1 * 10^(scale-19)) fits in 64 bits + C1_lo = C1_lo * ten2k64[scale - 19]; + __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); + } + } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits + // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + // C1 = ten2k64[P34 - q1] * C1 + __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); + } + x_exp = x_exp - ((UINT64) scale << 49); + C1_hi = C1.w[1]; + C1_lo = C1.w[0]; + } + if (rnd_mode != ROUNDING_TO_NEAREST) { + if ((rnd_mode == ROUNDING_DOWN && x_sign && y_sign) || + (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) { + // add 1 ulp and then check for overflow + C1_lo = C1_lo + 1; + if (C1_lo == 0) { // rounding overflow in the low 64 bits + C1_hi = C1_hi + 1; + } + if (C1_hi == 0x0001ed09bead87c0ull + && C1_lo == 0x378d8e6400000000ull) { + // C1 = 10^34 => rounding overflow + C1_hi = 0x0000314dc6448d93ull; + C1_lo = 0x38c15b0a00000000ull; // 10^33 + x_exp = x_exp + EXP_P1; + if (x_exp == EXP_MAX_P1) { // overflow + C1_hi = 0x7800000000000000ull; // +inf + C1_lo = 0x0ull; + x_exp = 0; // x_sign is preserved + // set overflow flag (the inexact flag was set too) + *pfpsf |= OVERFLOW_EXCEPTION; + } + } + } else + if ((rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) + || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) + || (rnd_mode == ROUNDING_TO_ZERO + && x_sign != y_sign)) { + // subtract 1 ulp from C1 + // Note: because delta >= P34 + 1 the result cannot be zero + C1_lo = C1_lo - 1; + if (C1_lo == 0xffffffffffffffffull) + C1_hi = C1_hi - 1; + // if the coefficient is 10^33-1 then make it 10^34-1 and + // decrease the exponent by 1 (because delta >= P34 + 1 the + // exponent will not become less than e_min) + // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff + // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff + if (C1_hi == 0x0000314dc6448d93ull + && C1_lo == 0x38c15b09ffffffffull) { + // make C1 = 10^34 - 1 + C1_hi = 0x0001ed09bead87c0ull; + C1_lo = 0x378d8e63ffffffffull; + x_exp = x_exp - EXP_P1; + } + } else { + ; // the result is already correct + } + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // assemble the result + res.w[1] = x_sign | x_exp | C1_hi; + res.w[0] = C1_lo; + } else if ((C2_lo == halfulp64) + && (q1 < P34 || ((C1_lo & 0x1) == 0))) { + // n2 = 1/2 ulp (n1) and C1 is even + // the result is the operand with the larger magnitude, + // possibly scaled up by 10^(P34-q1) + // an overflow cannot occur in this case (rounding to nearest) + if (q1 < P34) { // scale C1 up by 10^(P34-q1) + // Note: because delta = P34 it is certain that + // x_exp - ((UINT64)scale << 49) will stay above e_min + scale = P34 - q1; + if (q1 <= 19) { // C1 fits in 64 bits + // 1 <= q1 <= 19 => 15 <= scale <= 33 + if (scale <= 19) { // 10^scale fits in 64 bits + __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); + } else { // if 20 <= scale <= 33 + // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where + // (C1 * 10^(scale-19)) fits in 64 bits + C1_lo = C1_lo * ten2k64[scale - 19]; + __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); + } + } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits + // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + // C1 = ten2k64[P34 - q1] * C1 + __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); + } + x_exp = x_exp - ((UINT64) scale << 49); + C1_hi = C1.w[1]; + C1_lo = C1.w[0]; + } + if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign == y_sign + && (C1_lo & 0x01)) || (rnd_mode == ROUNDING_TIES_AWAY + && x_sign == y_sign) + || (rnd_mode == ROUNDING_UP && !x_sign && !y_sign) + || (rnd_mode == ROUNDING_DOWN && x_sign && y_sign)) { + // add 1 ulp and then check for overflow + C1_lo = C1_lo + 1; + if (C1_lo == 0) { // rounding overflow in the low 64 bits + C1_hi = C1_hi + 1; + } + if (C1_hi == 0x0001ed09bead87c0ull + && C1_lo == 0x378d8e6400000000ull) { + // C1 = 10^34 => rounding overflow + C1_hi = 0x0000314dc6448d93ull; + C1_lo = 0x38c15b0a00000000ull; // 10^33 + x_exp = x_exp + EXP_P1; + if (x_exp == EXP_MAX_P1) { // overflow + C1_hi = 0x7800000000000000ull; // +inf + C1_lo = 0x0ull; + x_exp = 0; // x_sign is preserved + // set overflow flag (the inexact flag was set too) + *pfpsf |= OVERFLOW_EXCEPTION; + } + } + } else + if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign != y_sign + && (C1_lo & 0x01)) || (rnd_mode == ROUNDING_DOWN + && !x_sign && y_sign) + || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) + || (rnd_mode == ROUNDING_TO_ZERO + && x_sign != y_sign)) { + // subtract 1 ulp from C1 + // Note: because delta >= P34 + 1 the result cannot be zero + C1_lo = C1_lo - 1; + if (C1_lo == 0xffffffffffffffffull) + C1_hi = C1_hi - 1; + // if the coefficient is 10^33 - 1 then make it 10^34 - 1 + // and decrease the exponent by 1 (because delta >= P34 + 1 + // the exponent will not become less than e_min) + // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff + // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff + if (C1_hi == 0x0000314dc6448d93ull + && C1_lo == 0x38c15b09ffffffffull) { + // make C1 = 10^34 - 1 + C1_hi = 0x0001ed09bead87c0ull; + C1_lo = 0x378d8e63ffffffffull; + x_exp = x_exp - EXP_P1; + } + } else { + ; // the result is already correct + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // assemble the result + res.w[1] = x_sign | x_exp | C1_hi; + res.w[0] = C1_lo; + } else { // if C2_lo > halfulp64 || + // (C2_lo == halfulp64 && q1 == P34 && ((C1_lo & 0x1) == 1)), i.e. + // 1/2 ulp(n1) < n2 < 1 ulp(n1) or n2 = 1/2 ulp(n1) and C1 odd + // res = x+1 ulp if n1*n2 > 0 and res = x-1 ulp if n1*n2 < 0 + if (q1 < P34) { // then 1 ulp = 10^(e1+q1-P34) < 10^e1 + // Note: if (q1 == P34) then 1 ulp = 10^(e1+q1-P34) = 10^e1 + // because q1 < P34 we must first replace C1 by + // C1 * 10^(P34-q1), and must decrease the exponent by + // (P34-q1) (it will still be at least e_min) + scale = P34 - q1; + if (q1 <= 19) { // C1 fits in 64 bits + // 1 <= q1 <= 19 => 15 <= scale <= 33 + if (scale <= 19) { // 10^scale fits in 64 bits + __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); + } else { // if 20 <= scale <= 33 + // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where + // (C1 * 10^(scale-19)) fits in 64 bits + C1_lo = C1_lo * ten2k64[scale - 19]; + __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); + } + } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits + // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + // C1 = ten2k64[P34 - q1] * C1 + __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); + } + x_exp = x_exp - ((UINT64) scale << 49); + C1_hi = C1.w[1]; + C1_lo = C1.w[0]; + // check for rounding overflow + if (C1_hi == 0x0001ed09bead87c0ull + && C1_lo == 0x378d8e6400000000ull) { + // C1 = 10^34 => rounding overflow + C1_hi = 0x0000314dc6448d93ull; + C1_lo = 0x38c15b0a00000000ull; // 10^33 + x_exp = x_exp + EXP_P1; + } + } + if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign != y_sign) + || (rnd_mode == ROUNDING_TIES_AWAY && x_sign != y_sign + && C2_lo != halfulp64) + || (rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) + || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) + || (rnd_mode == ROUNDING_TO_ZERO + && x_sign != y_sign)) { + // the result is x - 1 + // for RN n1 * n2 < 0; underflow not possible + C1_lo = C1_lo - 1; + if (C1_lo == 0xffffffffffffffffull) + C1_hi--; + // check if we crossed into the lower decade + if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 + C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 + C1_lo = 0x378d8e63ffffffffull; + x_exp = x_exp - EXP_P1; // no underflow, because n1 >> n2 + } + } else + if ((rnd_mode == ROUNDING_TO_NEAREST + && x_sign == y_sign) + || (rnd_mode == ROUNDING_TIES_AWAY + && x_sign == y_sign) + || (rnd_mode == ROUNDING_DOWN && x_sign && y_sign) + || (rnd_mode == ROUNDING_UP && !x_sign + && !y_sign)) { + // the result is x + 1 + // for RN x_sign = y_sign, i.e. n1*n2 > 0 + C1_lo = C1_lo + 1; + if (C1_lo == 0) { // rounding overflow in the low 64 bits + C1_hi = C1_hi + 1; + } + if (C1_hi == 0x0001ed09bead87c0ull + && C1_lo == 0x378d8e6400000000ull) { + // C1 = 10^34 => rounding overflow + C1_hi = 0x0000314dc6448d93ull; + C1_lo = 0x38c15b0a00000000ull; // 10^33 + x_exp = x_exp + EXP_P1; + if (x_exp == EXP_MAX_P1) { // overflow + C1_hi = 0x7800000000000000ull; // +inf + C1_lo = 0x0ull; + x_exp = 0; // x_sign is preserved + // set the overflow flag + *pfpsf |= OVERFLOW_EXCEPTION; + } + } + } else { + ; // the result is x + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // assemble the result + res.w[1] = x_sign | x_exp | C1_hi; + res.w[0] = C1_lo; + } + } else { // if q2 >= 20 then 5*10^(q2-1) and C2 (the latter in + // most cases) fit only in more than 64 bits + halfulp128 = midpoint128[q2 - 20]; // 5 * 10^(q2-1) + if ((C2_hi < halfulp128.w[1]) + || (C2_hi == halfulp128.w[1] + && C2_lo < halfulp128.w[0])) { + // n2 < 1/2 ulp (n1) + // the result is the operand with the larger magnitude, + // possibly scaled up by 10^(P34-q1) + // an overflow cannot occur in this case (rounding to nearest) + if (q1 < P34) { // scale C1 up by 10^(P34-q1) + // Note: because delta = P34 it is certain that + // x_exp - ((UINT64)scale << 49) will stay above e_min + scale = P34 - q1; + if (q1 <= 19) { // C1 fits in 64 bits + // 1 <= q1 <= 19 => 15 <= scale <= 33 + if (scale <= 19) { // 10^scale fits in 64 bits + __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); + } else { // if 20 <= scale <= 33 + // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where + // (C1 * 10^(scale-19)) fits in 64 bits + C1_lo = C1_lo * ten2k64[scale - 19]; + __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); + } + } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits + // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + // C1 = ten2k64[P34 - q1] * C1 + __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); + } + C1_hi = C1.w[1]; + C1_lo = C1.w[0]; + x_exp = x_exp - ((UINT64) scale << 49); + } + if (rnd_mode != ROUNDING_TO_NEAREST) { + if ((rnd_mode == ROUNDING_DOWN && x_sign && y_sign) || + (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) { + // add 1 ulp and then check for overflow + C1_lo = C1_lo + 1; + if (C1_lo == 0) { // rounding overflow in the low 64 bits + C1_hi = C1_hi + 1; + } + if (C1_hi == 0x0001ed09bead87c0ull + && C1_lo == 0x378d8e6400000000ull) { + // C1 = 10^34 => rounding overflow + C1_hi = 0x0000314dc6448d93ull; + C1_lo = 0x38c15b0a00000000ull; // 10^33 + x_exp = x_exp + EXP_P1; + if (x_exp == EXP_MAX_P1) { // overflow + C1_hi = 0x7800000000000000ull; // +inf + C1_lo = 0x0ull; + x_exp = 0; // x_sign is preserved + // set overflow flag (the inexact flag was set too) + *pfpsf |= OVERFLOW_EXCEPTION; + } + } + } else + if ((rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) + || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) + || (rnd_mode == ROUNDING_TO_ZERO + && x_sign != y_sign)) { + // subtract 1 ulp from C1 + // Note: because delta >= P34 + 1 the result cannot be zero + C1_lo = C1_lo - 1; + if (C1_lo == 0xffffffffffffffffull) + C1_hi = C1_hi - 1; + // if the coefficient is 10^33-1 then make it 10^34-1 and + // decrease the exponent by 1 (because delta >= P34 + 1 the + // exponent will not become less than e_min) + // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff + // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff + if (C1_hi == 0x0000314dc6448d93ull + && C1_lo == 0x38c15b09ffffffffull) { + // make C1 = 10^34 - 1 + C1_hi = 0x0001ed09bead87c0ull; + C1_lo = 0x378d8e63ffffffffull; + x_exp = x_exp - EXP_P1; + } + } else { + ; // the result is already correct + } + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // assemble the result + res.w[1] = x_sign | x_exp | C1_hi; + res.w[0] = C1_lo; + } else if ((C2_hi == halfulp128.w[1] + && C2_lo == halfulp128.w[0]) + && (q1 < P34 || ((C1_lo & 0x1) == 0))) { + // midpoint & lsb in C1 is 0 + // n2 = 1/2 ulp (n1) and C1 is even + // the result is the operand with the larger magnitude, + // possibly scaled up by 10^(P34-q1) + // an overflow cannot occur in this case (rounding to nearest) + if (q1 < P34) { // scale C1 up by 10^(P34-q1) + // Note: because delta = P34 it is certain that + // x_exp - ((UINT64)scale << 49) will stay above e_min + scale = P34 - q1; + if (q1 <= 19) { // C1 fits in 64 bits + // 1 <= q1 <= 19 => 15 <= scale <= 33 + if (scale <= 19) { // 10^scale fits in 64 bits + __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); + } else { // if 20 <= scale <= 33 + // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where + // (C1 * 10^(scale-19)) fits in 64 bits + C1_lo = C1_lo * ten2k64[scale - 19]; + __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); + } + } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits + // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + // C1 = ten2k64[P34 - q1] * C1 + __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); + } + x_exp = x_exp - ((UINT64) scale << 49); + C1_hi = C1.w[1]; + C1_lo = C1.w[0]; + } + if (rnd_mode != ROUNDING_TO_NEAREST) { + if ((rnd_mode == ROUNDING_TIES_AWAY && x_sign == y_sign) + || (rnd_mode == ROUNDING_UP && !y_sign)) { + // add 1 ulp and then check for overflow + C1_lo = C1_lo + 1; + if (C1_lo == 0) { // rounding overflow in the low 64 bits + C1_hi = C1_hi + 1; + } + if (C1_hi == 0x0001ed09bead87c0ull + && C1_lo == 0x378d8e6400000000ull) { + // C1 = 10^34 => rounding overflow + C1_hi = 0x0000314dc6448d93ull; + C1_lo = 0x38c15b0a00000000ull; // 10^33 + x_exp = x_exp + EXP_P1; + if (x_exp == EXP_MAX_P1) { // overflow + C1_hi = 0x7800000000000000ull; // +inf + C1_lo = 0x0ull; + x_exp = 0; // x_sign is preserved + // set overflow flag (the inexact flag was set too) + *pfpsf |= OVERFLOW_EXCEPTION; + } + } + } else if ((rnd_mode == ROUNDING_DOWN && y_sign) + || (rnd_mode == ROUNDING_TO_ZERO + && x_sign != y_sign)) { + // subtract 1 ulp from C1 + // Note: because delta >= P34 + 1 the result cannot be zero + C1_lo = C1_lo - 1; + if (C1_lo == 0xffffffffffffffffull) + C1_hi = C1_hi - 1; + // if the coefficient is 10^33 - 1 then make it 10^34 - 1 + // and decrease the exponent by 1 (because delta >= P34 + 1 + // the exponent will not become less than e_min) + // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff + // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff + if (C1_hi == 0x0000314dc6448d93ull + && C1_lo == 0x38c15b09ffffffffull) { + // make C1 = 10^34 - 1 + C1_hi = 0x0001ed09bead87c0ull; + C1_lo = 0x378d8e63ffffffffull; + x_exp = x_exp - EXP_P1; + } + } else { + ; // the result is already correct + } + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // assemble the result + res.w[1] = x_sign | x_exp | C1_hi; + res.w[0] = C1_lo; + } else { // if C2 > halfulp128 || + // (C2 == halfulp128 && q1 == P34 && ((C1 & 0x1) == 1)), i.e. + // 1/2 ulp(n1) < n2 < 1 ulp(n1) or n2 = 1/2 ulp(n1) and C1 odd + // res = x+1 ulp if n1*n2 > 0 and res = x-1 ulp if n1*n2 < 0 + if (q1 < P34) { // then 1 ulp = 10^(e1+q1-P34) < 10^e1 + // Note: if (q1 == P34) then 1 ulp = 10^(e1+q1-P34) = 10^e1 + // because q1 < P34 we must first replace C1 by C1*10^(P34-q1), + // and must decrease the exponent by (P34-q1) (it will still be + // at least e_min) + scale = P34 - q1; + if (q1 <= 19) { // C1 fits in 64 bits + // 1 <= q1 <= 19 => 15 <= scale <= 33 + if (scale <= 19) { // 10^scale fits in 64 bits + __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); + } else { // if 20 <= scale <= 33 + // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where + // (C1 * 10^(scale-19)) fits in 64 bits + C1_lo = C1_lo * ten2k64[scale - 19]; + __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); + } + } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits + // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + // C1 = ten2k64[P34 - q1] * C1 + __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); + } + C1_hi = C1.w[1]; + C1_lo = C1.w[0]; + x_exp = x_exp - ((UINT64) scale << 49); + } + if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign != y_sign) + || (rnd_mode == ROUNDING_TIES_AWAY && x_sign != y_sign + && (C2_hi != halfulp128.w[1] + || C2_lo != halfulp128.w[0])) + || (rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) + || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) + || (rnd_mode == ROUNDING_TO_ZERO + && x_sign != y_sign)) { + // the result is x - 1 + // for RN n1 * n2 < 0; underflow not possible + C1_lo = C1_lo - 1; + if (C1_lo == 0xffffffffffffffffull) + C1_hi--; + // check if we crossed into the lower decade + if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 + C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 + C1_lo = 0x378d8e63ffffffffull; + x_exp = x_exp - EXP_P1; // no underflow, because n1 >> n2 + } + } else + if ((rnd_mode == ROUNDING_TO_NEAREST + && x_sign == y_sign) + || (rnd_mode == ROUNDING_TIES_AWAY + && x_sign == y_sign) + || (rnd_mode == ROUNDING_DOWN && x_sign && y_sign) + || (rnd_mode == ROUNDING_UP && !x_sign + && !y_sign)) { + // the result is x + 1 + // for RN x_sign = y_sign, i.e. n1*n2 > 0 + C1_lo = C1_lo + 1; + if (C1_lo == 0) { // rounding overflow in the low 64 bits + C1_hi = C1_hi + 1; + } + if (C1_hi == 0x0001ed09bead87c0ull + && C1_lo == 0x378d8e6400000000ull) { + // C1 = 10^34 => rounding overflow + C1_hi = 0x0000314dc6448d93ull; + C1_lo = 0x38c15b0a00000000ull; // 10^33 + x_exp = x_exp + EXP_P1; + if (x_exp == EXP_MAX_P1) { // overflow + C1_hi = 0x7800000000000000ull; // +inf + C1_lo = 0x0ull; + x_exp = 0; // x_sign is preserved + // set the overflow flag + *pfpsf |= OVERFLOW_EXCEPTION; + } + } + } else { + ; // the result is x + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // assemble the result + res.w[1] = x_sign | x_exp | C1_hi; + res.w[0] = C1_lo; + } + } // end q1 >= 20 + // end case where C1 != 10^(q1-1) + } else { // C1 = 10^(q1-1) and x_sign != y_sign + // instead of C' = (C1 * 10^(e1-e2) + C2)rnd,P34 + // calculate C' = C1 * 10^(e1-e2-x1) + (C2 * 10^(-x1))rnd,P34 + // where x1 = q2 - 1, 0 <= x1 <= P34 - 1 + // Because C1 = 10^(q1-1) and x_sign != y_sign, C' will have P34 + // digits and n = C' * 10^(e2+x1) + // If the result has P34+1 digits, redo the steps above with x1+1 + // If the result has P34-1 digits or less, redo the steps above with + // x1-1 but only if initially x1 >= 1 + // NOTE: these two steps can be improved, e.g we could guess if + // P34+1 or P34-1 digits will be obtained by adding/subtracting + // just the top 64 bits of the two operands + // The result cannot be zero, and it cannot overflow + x1 = q2 - 1; // 0 <= x1 <= P34-1 + // Calculate C1 * 10^(e1-e2-x1) where 1 <= e1-e2-x1 <= P34 + // scale = (int)(e1 >> 49) - (int)(e2 >> 49) - x1; 0 <= scale <= P34-1 + scale = P34 - q1 + 1; // scale=e1-e2-x1 = P34+1-q1; 1<=scale<=P34 + // either C1 or 10^(e1-e2-x1) may not fit is 64 bits, + // but their product fits with certainty in 128 bits + if (scale >= 20) { //10^(e1-e2-x1) doesn't fit in 64 bits, but C1 does + __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); + } else { // if (scale >= 1 + // if 1 <= scale <= 19 then 10^(e1-e2-x1) fits in 64 bits + if (q1 <= 19) { // C1 fits in 64 bits + __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); + } else { // q1 >= 20 + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + __mul_128x64_to_128 (C1, ten2k64[scale], C1); + } + } + tmp64 = C1.w[0]; // C1.w[1], C1.w[0] contains C1 * 10^(e1-e2-x1) + + // now round C2 to q2-x1 = 1 decimal digit + // C2' = C2 + 1/2 * 10^x1 = C2 + 5 * 10^(x1-1) + ind = x1 - 1; // -1 <= ind <= P34 - 2 + if (ind >= 0) { // if (x1 >= 1) + C2.w[0] = C2_lo; + C2.w[1] = C2_hi; + if (ind <= 18) { + C2.w[0] = C2.w[0] + midpoint64[ind]; + if (C2.w[0] < C2_lo) + C2.w[1]++; + } else { // 19 <= ind <= 32 + C2.w[0] = C2.w[0] + midpoint128[ind - 19].w[0]; + C2.w[1] = C2.w[1] + midpoint128[ind - 19].w[1]; + if (C2.w[0] < C2_lo) + C2.w[1]++; + } + // the approximation of 10^(-x1) was rounded up to 118 bits + __mul_128x128_to_256 (R256, C2, ten2mk128[ind]); // R256 = C2*, f2* + // calculate C2* and f2* + // C2* is actually floor(C2*) in this case + // C2* and f2* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // the top Ex bits of 10^(-x1) are T* = ten2mk128trunc[ind], e.g. + // if x1=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f2* < 10^(-x1)) then + // if floor(C1+C2*) is even then C2* = floor(C2*) - logical right + // shift; C2* has p decimal digits, correct by Prop. 1) + // else if floor(C1+C2*) is odd C2* = floor(C2*)-1 (logical right + // shift; C2* has p decimal digits, correct by Pr. 1) + // else + // C2* = floor(C2*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C2* * 10^(e2+x1) + + if (ind <= 2) { + highf2star.w[1] = 0x0; + highf2star.w[0] = 0x0; // low f2* ok + } else if (ind <= 21) { + highf2star.w[1] = 0x0; + highf2star.w[0] = R256.w[2] & maskhigh128[ind]; // low f2* ok + } else { + highf2star.w[1] = R256.w[3] & maskhigh128[ind]; + highf2star.w[0] = R256.w[2]; // low f2* is ok + } + // shift right C2* by Ex-128 = shiftright128[ind] + if (ind >= 3) { + shift = shiftright128[ind]; + if (shift < 64) { // 3 <= shift <= 63 + R256.w[2] = + (R256.w[2] >> shift) | (R256.w[3] << (64 - shift)); + R256.w[3] = (R256.w[3] >> shift); + } else { // 66 <= shift <= 102 + R256.w[2] = (R256.w[3] >> (shift - 64)); + R256.w[3] = 0x0ULL; + } + } + // redundant + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + // determine inexactness of the rounding of C2* + // (cannot be followed by a second rounding) + // if (0 < f2* - 1/2 < 10^(-x1)) then + // the result is exact + // else (if f2* - 1/2 > T* then) + // the result of is inexact + if (ind <= 2) { + if (R256.w[1] > 0x8000000000000000ull || + (R256.w[1] == 0x8000000000000000ull + && R256.w[0] > 0x0ull)) { + // f2* > 1/2 and the result may be exact + tmp64A = R256.w[1] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64A > ten2mk128trunc[ind].w[1] + || (tmp64A == ten2mk128trunc[ind].w[1] + && R256.w[0] >= ten2mk128trunc[ind].w[0]))) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // this rounding is applied to C2 only! + // x_sign != y_sign + is_inexact_gt_midpoint = 1; + } // else the result is exact + // rounding down, unless a midpoint in [ODD, EVEN] + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // this rounding is applied to C2 only! + // x_sign != y_sign + is_inexact_lt_midpoint = 1; + } + } else if (ind <= 21) { // if 3 <= ind <= 21 + if (highf2star.w[1] > 0x0 || (highf2star.w[1] == 0x0 + && highf2star.w[0] > + onehalf128[ind]) + || (highf2star.w[1] == 0x0 + && highf2star.w[0] == onehalf128[ind] + && (R256.w[1] || R256.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64A = highf2star.w[0] - onehalf128[ind]; + tmp64B = highf2star.w[1]; + if (tmp64A > highf2star.w[0]) + tmp64B--; + if (tmp64B || tmp64A + || R256.w[1] > ten2mk128trunc[ind].w[1] + || (R256.w[1] == ten2mk128trunc[ind].w[1] + && R256.w[0] > ten2mk128trunc[ind].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // this rounding is applied to C2 only! + // x_sign != y_sign + is_inexact_gt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // this rounding is applied to C2 only! + // x_sign != y_sign + is_inexact_lt_midpoint = 1; + } + } else { // if 22 <= ind <= 33 + if (highf2star.w[1] > onehalf128[ind] + || (highf2star.w[1] == onehalf128[ind] + && (highf2star.w[0] || R256.w[1] + || R256.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + // tmp64A = highf2star.w[0]; + tmp64B = highf2star.w[1] - onehalf128[ind]; + if (tmp64B || highf2star.w[0] + || R256.w[1] > ten2mk128trunc[ind].w[1] + || (R256.w[1] == ten2mk128trunc[ind].w[1] + && R256.w[0] > ten2mk128trunc[ind].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // this rounding is applied to C2 only! + // x_sign != y_sign + is_inexact_gt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // this rounding is applied to C2 only! + // x_sign != y_sign + is_inexact_lt_midpoint = 1; + } + } + // check for midpoints after determining inexactness + if ((R256.w[1] || R256.w[0]) && (highf2star.w[1] == 0) + && (highf2star.w[0] == 0) + && (R256.w[1] < ten2mk128trunc[ind].w[1] + || (R256.w[1] == ten2mk128trunc[ind].w[1] + && R256.w[0] <= ten2mk128trunc[ind].w[0]))) { + // the result is a midpoint + if ((tmp64 + R256.w[2]) & 0x01) { // MP in [EVEN, ODD] + // if floor(C2*) is odd C = floor(C2*) - 1; the result may be 0 + R256.w[2]--; + if (R256.w[2] == 0xffffffffffffffffull) + R256.w[3]--; + // this rounding is applied to C2 only! + // x_sign != y_sign + is_midpoint_lt_even = 1; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } else { + // else MP in [ODD, EVEN] + // this rounding is applied to C2 only! + // x_sign != y_sign + is_midpoint_gt_even = 1; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } + } + } else { // if (ind == -1) only when x1 = 0 + R256.w[2] = C2_lo; + R256.w[3] = C2_hi; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } + // and now subtract C1 * 10^(e1-e2-x1) - (C2 * 10^(-x1))rnd,P34 + // because x_sign != y_sign this last operation is exact + C1.w[0] = C1.w[0] - R256.w[2]; + C1.w[1] = C1.w[1] - R256.w[3]; + if (C1.w[0] > tmp64) + C1.w[1]--; // borrow + if (C1.w[1] >= 0x8000000000000000ull) { // negative coefficient! + C1.w[0] = ~C1.w[0]; + C1.w[0]++; + C1.w[1] = ~C1.w[1]; + if (C1.w[0] == 0x0) + C1.w[1]++; + tmp_sign = y_sign; // the result will have the sign of y + } else { + tmp_sign = x_sign; + } + // the difference has exactly P34 digits + x_sign = tmp_sign; + if (x1 >= 1) + y_exp = y_exp + ((UINT64) x1 << 49); + C1_hi = C1.w[1]; + C1_lo = C1.w[0]; + // general correction from RN to RA, RM, RP, RZ; result uses y_exp + if (rnd_mode != ROUNDING_TO_NEAREST) { + if ((!x_sign + && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) + || + ((rnd_mode == ROUNDING_TIES_AWAY + || rnd_mode == ROUNDING_UP) + && is_midpoint_gt_even))) || (x_sign + && + ((rnd_mode == + ROUNDING_DOWN + && + is_inexact_lt_midpoint) + || + ((rnd_mode == + ROUNDING_TIES_AWAY + || rnd_mode == + ROUNDING_DOWN) + && + is_midpoint_gt_even)))) + { + // C1 = C1 + 1 + C1_lo = C1_lo + 1; + if (C1_lo == 0) { // rounding overflow in the low 64 bits + C1_hi = C1_hi + 1; + } + if (C1_hi == 0x0001ed09bead87c0ull + && C1_lo == 0x378d8e6400000000ull) { + // C1 = 10^34 => rounding overflow + C1_hi = 0x0000314dc6448d93ull; + C1_lo = 0x38c15b0a00000000ull; // 10^33 + y_exp = y_exp + EXP_P1; + } + } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) + && + ((x_sign + && (rnd_mode == ROUNDING_UP + || rnd_mode == ROUNDING_TO_ZERO)) + || (!x_sign + && (rnd_mode == ROUNDING_DOWN + || rnd_mode == ROUNDING_TO_ZERO)))) { + // C1 = C1 - 1 + C1_lo = C1_lo - 1; + if (C1_lo == 0xffffffffffffffffull) + C1_hi--; + // check if we crossed into the lower decade + if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 + C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 + C1_lo = 0x378d8e63ffffffffull; + y_exp = y_exp - EXP_P1; + // no underflow, because delta + q2 >= P34 + 1 + } + } else { + ; // exact, the result is already correct + } + } + // assemble the result + res.w[1] = x_sign | y_exp | C1_hi; + res.w[0] = C1_lo; + } + } // end delta = P34 + } else { // if (|delta| <= P34 - 1) + if (delta >= 0) { // if (0 <= delta <= P34 - 1) + if (delta <= P34 - 1 - q2) { + // calculate C' directly; the result is exact + // in this case 1<=q1<=P34-1, 1<=q2<=P34-1 and 0 <= e1-e2 <= P34-2 + // The coefficient of the result is C1 * 10^(e1-e2) + C2 and the + // exponent is e2; either C1 or 10^(e1-e2) may not fit is 64 bits, + // but their product fits with certainty in 128 bits (actually in 113) + scale = delta - q1 + q2; // scale = (int)(e1 >> 49) - (int)(e2 >> 49) + + if (scale >= 20) { // 10^(e1-e2) does not fit in 64 bits, but C1 does + __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); + C1_hi = C1.w[1]; + C1_lo = C1.w[0]; + } else if (scale >= 1) { + // if 1 <= scale <= 19 then 10^(e1-e2) fits in 64 bits + if (q1 <= 19) { // C1 fits in 64 bits + __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); + } else { // q1 >= 20 + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + __mul_128x64_to_128 (C1, ten2k64[scale], C1); + } + C1_hi = C1.w[1]; + C1_lo = C1.w[0]; + } else { // if (scale == 0) C1 is unchanged + C1.w[0] = C1_lo; // C1.w[1] = C1_hi; + } + // now add C2 + if (x_sign == y_sign) { + // the result cannot overflow + C1_lo = C1_lo + C2_lo; + C1_hi = C1_hi + C2_hi; + if (C1_lo < C1.w[0]) + C1_hi++; + } else { // if x_sign != y_sign + C1_lo = C1_lo - C2_lo; + C1_hi = C1_hi - C2_hi; + if (C1_lo > C1.w[0]) + C1_hi--; + // the result can be zero, but it cannot overflow + if (C1_lo == 0 && C1_hi == 0) { + // assemble the result + if (x_exp < y_exp) + res.w[1] = x_exp; + else + res.w[1] = y_exp; + res.w[0] = 0; + if (rnd_mode == ROUNDING_DOWN) { + res.w[1] |= 0x8000000000000000ull; + } + BID_SWAP128 (res); + BID_RETURN (res); + } + if (C1_hi >= 0x8000000000000000ull) { // negative coefficient! + C1_lo = ~C1_lo; + C1_lo++; + C1_hi = ~C1_hi; + if (C1_lo == 0x0) + C1_hi++; + x_sign = y_sign; // the result will have the sign of y + } + } + // assemble the result + res.w[1] = x_sign | y_exp | C1_hi; + res.w[0] = C1_lo; + } else if (delta == P34 - q2) { + // calculate C' directly; the result may be inexact if it requires + // P34+1 decimal digits; in this case the 'cutoff' point for addition + // is at the position of the lsb of C2, so 0 <= e1-e2 <= P34-1 + // The coefficient of the result is C1 * 10^(e1-e2) + C2 and the + // exponent is e2; either C1 or 10^(e1-e2) may not fit is 64 bits, + // but their product fits with certainty in 128 bits (actually in 113) + scale = delta - q1 + q2; // scale = (int)(e1 >> 49) - (int)(e2 >> 49) + if (scale >= 20) { // 10^(e1-e2) does not fit in 64 bits, but C1 does + __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); + } else if (scale >= 1) { + // if 1 <= scale <= 19 then 10^(e1-e2) fits in 64 bits + if (q1 <= 19) { // C1 fits in 64 bits + __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); + } else { // q1 >= 20 + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + __mul_128x64_to_128 (C1, ten2k64[scale], C1); + } + } else { // if (scale == 0) C1 is unchanged + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; // only the low part is necessary + } + C1_hi = C1.w[1]; + C1_lo = C1.w[0]; + // now add C2 + if (x_sign == y_sign) { + // the result can overflow! + C1_lo = C1_lo + C2_lo; + C1_hi = C1_hi + C2_hi; + if (C1_lo < C1.w[0]) + C1_hi++; + // test for overflow, possible only when C1 >= 10^34 + if (C1_hi > 0x0001ed09bead87c0ull || (C1_hi == 0x0001ed09bead87c0ull && C1_lo >= 0x378d8e6400000000ull)) { // C1 >= 10^34 + // in this case q = P34 + 1 and x = q - P34 = 1, so multiply + // C'' = C'+ 5 = C1 + 5 by k1 ~ 10^(-1) calculated for P34 + 1 + // decimal digits + // Calculate C'' = C' + 1/2 * 10^x + if (C1_lo >= 0xfffffffffffffffbull) { // low half add has carry + C1_lo = C1_lo + 5; + C1_hi = C1_hi + 1; + } else { + C1_lo = C1_lo + 5; + } + // the approximation of 10^(-1) was rounded up to 118 bits + // 10^(-1) =~ 33333333333333333333333333333400 * 2^-129 + // 10^(-1) =~ 19999999999999999999999999999a00 * 2^-128 + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; // C'' + ten2m1.w[1] = 0x1999999999999999ull; + ten2m1.w[0] = 0x9999999999999a00ull; + __mul_128x128_to_256 (P256, C1, ten2m1); // P256 = C*, f* + // C* is actually floor(C*) in this case + // the top Ex = 128 bits of 10^(-1) are + // T* = 0x00199999999999999999999999999999 + // if (0 < f* < 10^(-x)) then + // if floor(C*) is even then C = floor(C*) - logical right + // shift; C has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C = floor(C*) - 1 (logical right + // shift; C has p decimal digits, correct by Pr. 1) + // else + // C = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C * 10^(e2+x) + if ((P256.w[1] || P256.w[0]) + && (P256.w[1] < 0x1999999999999999ull + || (P256.w[1] == 0x1999999999999999ull + && P256.w[0] <= 0x9999999999999999ull))) { + // the result is a midpoint + if (P256.w[2] & 0x01) { + is_midpoint_gt_even = 1; + // if floor(C*) is odd C = floor(C*) - 1; the result is not 0 + P256.w[2]--; + if (P256.w[2] == 0xffffffffffffffffull) + P256.w[3]--; + } else { + is_midpoint_lt_even = 1; + } + } + // n = Cstar * 10^(e2+1) + y_exp = y_exp + EXP_P1; + // C* != 10^P because C* has P34 digits + // check for overflow + if (y_exp == EXP_MAX_P1 + && (rnd_mode == ROUNDING_TO_NEAREST + || rnd_mode == ROUNDING_TIES_AWAY)) { + // overflow for RN + res.w[1] = x_sign | 0x7800000000000000ull; // +/-inf + res.w[0] = 0x0ull; + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // set the overflow flag + *pfpsf |= OVERFLOW_EXCEPTION; + BID_SWAP128 (res); + BID_RETURN (res); + } + // if (0 < f* - 1/2 < 10^(-x)) then + // the result of the addition is exact + // else + // the result of the addition is inexact + if (P256.w[1] > 0x8000000000000000ull || (P256.w[1] == 0x8000000000000000ull && P256.w[0] > 0x0ull)) { // the result may be exact + tmp64 = P256.w[1] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > 0x1999999999999999ull + || (tmp64 == 0x1999999999999999ull + && P256.w[0] >= 0x9999999999999999ull))) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact = 1; + } // else the result is exact + } else { // the result is inexact + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact = 1; + } + C1_hi = P256.w[3]; + C1_lo = P256.w[2]; + if (!is_midpoint_gt_even && !is_midpoint_lt_even) { + is_inexact_lt_midpoint = is_inexact + && (P256.w[1] & 0x8000000000000000ull); + is_inexact_gt_midpoint = is_inexact + && !(P256.w[1] & 0x8000000000000000ull); + } + // general correction from RN to RA, RM, RP, RZ; + // result uses y_exp + if (rnd_mode != ROUNDING_TO_NEAREST) { + if ((!x_sign + && + ((rnd_mode == ROUNDING_UP + && is_inexact_lt_midpoint) + || + ((rnd_mode == ROUNDING_TIES_AWAY + || rnd_mode == ROUNDING_UP) + && is_midpoint_gt_even))) || (x_sign + && + ((rnd_mode == + ROUNDING_DOWN + && + is_inexact_lt_midpoint) + || + ((rnd_mode == + ROUNDING_TIES_AWAY + || rnd_mode == + ROUNDING_DOWN) + && + is_midpoint_gt_even)))) + { + // C1 = C1 + 1 + C1_lo = C1_lo + 1; + if (C1_lo == 0) { // rounding overflow in the low 64 bits + C1_hi = C1_hi + 1; + } + if (C1_hi == 0x0001ed09bead87c0ull + && C1_lo == 0x378d8e6400000000ull) { + // C1 = 10^34 => rounding overflow + C1_hi = 0x0000314dc6448d93ull; + C1_lo = 0x38c15b0a00000000ull; // 10^33 + y_exp = y_exp + EXP_P1; + } + } else + if ((is_midpoint_lt_even || is_inexact_gt_midpoint) + && + ((x_sign + && (rnd_mode == ROUNDING_UP + || rnd_mode == ROUNDING_TO_ZERO)) + || (!x_sign + && (rnd_mode == ROUNDING_DOWN + || rnd_mode == ROUNDING_TO_ZERO)))) { + // C1 = C1 - 1 + C1_lo = C1_lo - 1; + if (C1_lo == 0xffffffffffffffffull) + C1_hi--; + // check if we crossed into the lower decade + if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 + C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 + C1_lo = 0x378d8e63ffffffffull; + y_exp = y_exp - EXP_P1; + // no underflow, because delta + q2 >= P34 + 1 + } + } else { + ; // exact, the result is already correct + } + // in all cases check for overflow (RN and RA solved already) + if (y_exp == EXP_MAX_P1) { // overflow + if ((rnd_mode == ROUNDING_DOWN && x_sign) || // RM and res < 0 + (rnd_mode == ROUNDING_UP && !x_sign)) { // RP and res > 0 + C1_hi = 0x7800000000000000ull; // +inf + C1_lo = 0x0ull; + } else { // RM and res > 0, RP and res < 0, or RZ + C1_hi = 0x5fffed09bead87c0ull; + C1_lo = 0x378d8e63ffffffffull; + } + y_exp = 0; // x_sign is preserved + // set the inexact flag (in case the exact addition was exact) + *pfpsf |= INEXACT_EXCEPTION; + // set the overflow flag + *pfpsf |= OVERFLOW_EXCEPTION; + } + } + } // else if (C1 < 10^34) then C1 is the coeff.; the result is exact + } else { // if x_sign != y_sign the result is exact + C1_lo = C1_lo - C2_lo; + C1_hi = C1_hi - C2_hi; + if (C1_lo > C1.w[0]) + C1_hi--; + // the result can be zero, but it cannot overflow + if (C1_lo == 0 && C1_hi == 0) { + // assemble the result + if (x_exp < y_exp) + res.w[1] = x_exp; + else + res.w[1] = y_exp; + res.w[0] = 0; + if (rnd_mode == ROUNDING_DOWN) { + res.w[1] |= 0x8000000000000000ull; + } + BID_SWAP128 (res); + BID_RETURN (res); + } + if (C1_hi >= 0x8000000000000000ull) { // negative coefficient! + C1_lo = ~C1_lo; + C1_lo++; + C1_hi = ~C1_hi; + if (C1_lo == 0x0) + C1_hi++; + x_sign = y_sign; // the result will have the sign of y + } + } + // assemble the result + res.w[1] = x_sign | y_exp | C1_hi; + res.w[0] = C1_lo; + } else { // if (delta >= P34 + 1 - q2) + // instead of C' = (C1 * 10^(e1-e2) + C2)rnd,P34 + // calculate C' = C1 * 10^(e1-e2-x1) + (C2 * 10^(-x1))rnd,P34 + // where x1 = q1 + e1 - e2 - P34, 1 <= x1 <= P34 - 1 + // In most cases C' will have P34 digits, and n = C' * 10^(e2+x1) + // If the result has P34+1 digits, redo the steps above with x1+1 + // If the result has P34-1 digits or less, redo the steps above with + // x1-1 but only if initially x1 >= 1 + // NOTE: these two steps can be improved, e.g we could guess if + // P34+1 or P34-1 digits will be obtained by adding/subtracting just + // the top 64 bits of the two operands + // The result cannot be zero, but it can overflow + x1 = delta + q2 - P34; // 1 <= x1 <= P34-1 + roundC2: + // Calculate C1 * 10^(e1-e2-x1) where 0 <= e1-e2-x1 <= P34 - 1 + // scale = (int)(e1 >> 49) - (int)(e2 >> 49) - x1; 0 <= scale <= P34-1 + scale = delta - q1 + q2 - x1; // scale = e1 - e2 - x1 = P34 - q1 + // either C1 or 10^(e1-e2-x1) may not fit is 64 bits, + // but their product fits with certainty in 128 bits (actually in 113) + if (scale >= 20) { //10^(e1-e2-x1) doesn't fit in 64 bits, but C1 does + __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); + } else if (scale >= 1) { + // if 1 <= scale <= 19 then 10^(e1-e2-x1) fits in 64 bits + if (q1 <= 19) { // C1 fits in 64 bits + __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); + } else { // q1 >= 20 + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + __mul_128x64_to_128 (C1, ten2k64[scale], C1); + } + } else { // if (scale == 0) C1 is unchanged + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + } + tmp64 = C1.w[0]; // C1.w[1], C1.w[0] contains C1 * 10^(e1-e2-x1) + + // now round C2 to q2-x1 decimal digits, where 1<=x1<=q2-1<=P34-1 + // (but if we got here a second time after x1 = x1 - 1, then + // x1 >= 0; note that for x1 = 0 C2 is unchanged) + // C2' = C2 + 1/2 * 10^x1 = C2 + 5 * 10^(x1-1) + ind = x1 - 1; // 0 <= ind <= q2-2<=P34-2=32; but note that if x1 = 0 + // during a second pass, then ind = -1 + if (ind >= 0) { // if (x1 >= 1) + C2.w[0] = C2_lo; + C2.w[1] = C2_hi; + if (ind <= 18) { + C2.w[0] = C2.w[0] + midpoint64[ind]; + if (C2.w[0] < C2_lo) + C2.w[1]++; + } else { // 19 <= ind <= 32 + C2.w[0] = C2.w[0] + midpoint128[ind - 19].w[0]; + C2.w[1] = C2.w[1] + midpoint128[ind - 19].w[1]; + if (C2.w[0] < C2_lo) + C2.w[1]++; + } + // the approximation of 10^(-x1) was rounded up to 118 bits + __mul_128x128_to_256 (R256, C2, ten2mk128[ind]); // R256 = C2*, f2* + // calculate C2* and f2* + // C2* is actually floor(C2*) in this case + // C2* and f2* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // the top Ex bits of 10^(-x1) are T* = ten2mk128trunc[ind], e.g. + // if x1=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f2* < 10^(-x1)) then + // if floor(C1+C2*) is even then C2* = floor(C2*) - logical right + // shift; C2* has p decimal digits, correct by Prop. 1) + // else if floor(C1+C2*) is odd C2* = floor(C2*)-1 (logical right + // shift; C2* has p decimal digits, correct by Pr. 1) + // else + // C2* = floor(C2*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C2* * 10^(e2+x1) + + if (ind <= 2) { + highf2star.w[1] = 0x0; + highf2star.w[0] = 0x0; // low f2* ok + } else if (ind <= 21) { + highf2star.w[1] = 0x0; + highf2star.w[0] = R256.w[2] & maskhigh128[ind]; // low f2* ok + } else { + highf2star.w[1] = R256.w[3] & maskhigh128[ind]; + highf2star.w[0] = R256.w[2]; // low f2* is ok + } + // shift right C2* by Ex-128 = shiftright128[ind] + if (ind >= 3) { + shift = shiftright128[ind]; + if (shift < 64) { // 3 <= shift <= 63 + R256.w[2] = + (R256.w[2] >> shift) | (R256.w[3] << (64 - shift)); + R256.w[3] = (R256.w[3] >> shift); + } else { // 66 <= shift <= 102 + R256.w[2] = (R256.w[3] >> (shift - 64)); + R256.w[3] = 0x0ULL; + } + } + if (second_pass) { + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } + // determine inexactness of the rounding of C2* (this may be + // followed by a second rounding only if we get P34+1 + // decimal digits) + // if (0 < f2* - 1/2 < 10^(-x1)) then + // the result is exact + // else (if f2* - 1/2 > T* then) + // the result of is inexact + if (ind <= 2) { + if (R256.w[1] > 0x8000000000000000ull || + (R256.w[1] == 0x8000000000000000ull + && R256.w[0] > 0x0ull)) { + // f2* > 1/2 and the result may be exact + tmp64A = R256.w[1] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64A > ten2mk128trunc[ind].w[1] + || (tmp64A == ten2mk128trunc[ind].w[1] + && R256.w[0] >= ten2mk128trunc[ind].w[0]))) { + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; // may be set again during a second pass + // this rounding is applied to C2 only! + if (x_sign == y_sign) + is_inexact_lt_midpoint = 1; + else // if (x_sign != y_sign) + is_inexact_gt_midpoint = 1; + } // else the result is exact + // rounding down, unless a midpoint in [ODD, EVEN] + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; // just in case we will round a second time + // rounding up, unless a midpoint in [EVEN, ODD] + // this rounding is applied to C2 only! + if (x_sign == y_sign) + is_inexact_gt_midpoint = 1; + else // if (x_sign != y_sign) + is_inexact_lt_midpoint = 1; + } + } else if (ind <= 21) { // if 3 <= ind <= 21 + if (highf2star.w[1] > 0x0 || (highf2star.w[1] == 0x0 + && highf2star.w[0] > + onehalf128[ind]) + || (highf2star.w[1] == 0x0 + && highf2star.w[0] == onehalf128[ind] + && (R256.w[1] || R256.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64A = highf2star.w[0] - onehalf128[ind]; + tmp64B = highf2star.w[1]; + if (tmp64A > highf2star.w[0]) + tmp64B--; + if (tmp64B || tmp64A + || R256.w[1] > ten2mk128trunc[ind].w[1] + || (R256.w[1] == ten2mk128trunc[ind].w[1] + && R256.w[0] > ten2mk128trunc[ind].w[0])) { + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; // may be set again during a second pass + // this rounding is applied to C2 only! + if (x_sign == y_sign) + is_inexact_lt_midpoint = 1; + else // if (x_sign != y_sign) + is_inexact_gt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; // may be set again during a second pass + // rounding up, unless a midpoint in [EVEN, ODD] + // this rounding is applied to C2 only! + if (x_sign == y_sign) + is_inexact_gt_midpoint = 1; + else // if (x_sign != y_sign) + is_inexact_lt_midpoint = 1; + } + } else { // if 22 <= ind <= 33 + if (highf2star.w[1] > onehalf128[ind] + || (highf2star.w[1] == onehalf128[ind] + && (highf2star.w[0] || R256.w[1] + || R256.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + // tmp64A = highf2star.w[0]; + tmp64B = highf2star.w[1] - onehalf128[ind]; + if (tmp64B || highf2star.w[0] + || R256.w[1] > ten2mk128trunc[ind].w[1] + || (R256.w[1] == ten2mk128trunc[ind].w[1] + && R256.w[0] > ten2mk128trunc[ind].w[0])) { + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; // may be set again during a second pass + // this rounding is applied to C2 only! + if (x_sign == y_sign) + is_inexact_lt_midpoint = 1; + else // if (x_sign != y_sign) + is_inexact_gt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; // may be set again during a second pass + // rounding up, unless a midpoint in [EVEN, ODD] + // this rounding is applied to C2 only! + if (x_sign == y_sign) + is_inexact_gt_midpoint = 1; + else // if (x_sign != y_sign) + is_inexact_lt_midpoint = 1; + } + } + // check for midpoints + if ((R256.w[1] || R256.w[0]) && (highf2star.w[1] == 0) + && (highf2star.w[0] == 0) + && (R256.w[1] < ten2mk128trunc[ind].w[1] + || (R256.w[1] == ten2mk128trunc[ind].w[1] + && R256.w[0] <= ten2mk128trunc[ind].w[0]))) { + // the result is a midpoint + if ((tmp64 + R256.w[2]) & 0x01) { // MP in [EVEN, ODD] + // if floor(C2*) is odd C = floor(C2*) - 1; the result may be 0 + R256.w[2]--; + if (R256.w[2] == 0xffffffffffffffffull) + R256.w[3]--; + // this rounding is applied to C2 only! + if (x_sign == y_sign) + is_midpoint_gt_even = 1; + else // if (x_sign != y_sign) + is_midpoint_lt_even = 1; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } else { + // else MP in [ODD, EVEN] + // this rounding is applied to C2 only! + if (x_sign == y_sign) + is_midpoint_lt_even = 1; + else // if (x_sign != y_sign) + is_midpoint_gt_even = 1; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } + } + // end if (ind >= 0) + } else { // if (ind == -1); only during a 2nd pass, and when x1 = 0 + R256.w[2] = C2_lo; + R256.w[3] = C2_hi; + tmp_inexact = 0; + // to correct a possible setting to 1 from 1st pass + if (second_pass) { + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } + } + // and now add/subtract C1 * 10^(e1-e2-x1) +/- (C2 * 10^(-x1))rnd,P34 + if (x_sign == y_sign) { // addition; could overflow + // no second pass is possible this way (only for x_sign != y_sign) + C1.w[0] = C1.w[0] + R256.w[2]; + C1.w[1] = C1.w[1] + R256.w[3]; + if (C1.w[0] < tmp64) + C1.w[1]++; // carry + // if the sum has P34+1 digits, i.e. C1>=10^34 redo the calculation + // with x1=x1+1 + if (C1.w[1] > 0x0001ed09bead87c0ull || (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] >= 0x378d8e6400000000ull)) { // C1 >= 10^34 + // chop off one more digit from the sum, but make sure there is + // no double-rounding error (see table - double rounding logic) + // now round C1 from P34+1 to P34 decimal digits + // C1' = C1 + 1/2 * 10 = C1 + 5 + if (C1.w[0] >= 0xfffffffffffffffbull) { // low half add has carry + C1.w[0] = C1.w[0] + 5; + C1.w[1] = C1.w[1] + 1; + } else { + C1.w[0] = C1.w[0] + 5; + } + // the approximation of 10^(-1) was rounded up to 118 bits + __mul_128x128_to_256 (Q256, C1, ten2mk128[0]); // Q256 = C1*, f1* + // C1* is actually floor(C1*) in this case + // the top 128 bits of 10^(-1) are + // T* = ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f1* < 10^(-1)) then + // if floor(C1*) is even then C1* = floor(C1*) - logical right + // shift; C1* has p decimal digits, correct by Prop. 1) + // else if floor(C1*) is odd C1* = floor(C1*) - 1 (logical right + // shift; C1* has p decimal digits, correct by Pr. 1) + // else + // C1* = floor(C1*) (logical right shift; C has p decimal digits + // correct by Property 1) + // n = C1* * 10^(e2+x1+1) + if ((Q256.w[1] || Q256.w[0]) + && (Q256.w[1] < ten2mk128trunc[0].w[1] + || (Q256.w[1] == ten2mk128trunc[0].w[1] + && Q256.w[0] <= ten2mk128trunc[0].w[0]))) { + // the result is a midpoint + if (is_inexact_lt_midpoint) { // for the 1st rounding + is_inexact_gt_midpoint = 1; + is_inexact_lt_midpoint = 0; + is_midpoint_gt_even = 0; + is_midpoint_lt_even = 0; + } else if (is_inexact_gt_midpoint) { // for the 1st rounding + Q256.w[2]--; + if (Q256.w[2] == 0xffffffffffffffffull) + Q256.w[3]--; + is_inexact_gt_midpoint = 0; + is_inexact_lt_midpoint = 1; + is_midpoint_gt_even = 0; + is_midpoint_lt_even = 0; + } else if (is_midpoint_gt_even) { // for the 1st rounding + // Note: cannot have is_midpoint_lt_even + is_inexact_gt_midpoint = 0; + is_inexact_lt_midpoint = 1; + is_midpoint_gt_even = 0; + is_midpoint_lt_even = 0; + } else { // the first rounding must have been exact + if (Q256.w[2] & 0x01) { // MP in [EVEN, ODD] + // the truncated result is correct + Q256.w[2]--; + if (Q256.w[2] == 0xffffffffffffffffull) + Q256.w[3]--; + is_inexact_gt_midpoint = 0; + is_inexact_lt_midpoint = 0; + is_midpoint_gt_even = 1; + is_midpoint_lt_even = 0; + } else { // MP in [ODD, EVEN] + is_inexact_gt_midpoint = 0; + is_inexact_lt_midpoint = 0; + is_midpoint_gt_even = 0; + is_midpoint_lt_even = 1; + } + } + tmp_inexact = 1; // in all cases + } else { // the result is not a midpoint + // determine inexactness of the rounding of C1 (the sum C1+C2*) + // if (0 < f1* - 1/2 < 10^(-1)) then + // the result is exact + // else (if f1* - 1/2 > T* then) + // the result of is inexact + // ind = 0 + if (Q256.w[1] > 0x8000000000000000ull + || (Q256.w[1] == 0x8000000000000000ull + && Q256.w[0] > 0x0ull)) { + // f1* > 1/2 and the result may be exact + Q256.w[1] = Q256.w[1] - 0x8000000000000000ull; // f1* - 1/2 + if ((Q256.w[1] > ten2mk128trunc[0].w[1] + || (Q256.w[1] == ten2mk128trunc[0].w[1] + && Q256.w[0] > ten2mk128trunc[0].w[0]))) { + is_inexact_gt_midpoint = 0; + is_inexact_lt_midpoint = 1; + is_midpoint_gt_even = 0; + is_midpoint_lt_even = 0; + // set the inexact flag + tmp_inexact = 1; + // *pfpsf |= INEXACT_EXCEPTION; + } else { // else the result is exact for the 2nd rounding + if (tmp_inexact) { // if the previous rounding was inexact + if (is_midpoint_lt_even) { + is_inexact_gt_midpoint = 1; + is_midpoint_lt_even = 0; + } else if (is_midpoint_gt_even) { + is_inexact_lt_midpoint = 1; + is_midpoint_gt_even = 0; + } else { + ; // no change + } + } + } + // rounding down, unless a midpoint in [ODD, EVEN] + } else { // the result is inexact; f1* <= 1/2 + is_inexact_gt_midpoint = 1; + is_inexact_lt_midpoint = 0; + is_midpoint_gt_even = 0; + is_midpoint_lt_even = 0; + // set the inexact flag + tmp_inexact = 1; + // *pfpsf |= INEXACT_EXCEPTION; + } + } // end 'the result is not a midpoint' + // n = C1 * 10^(e2+x1) + C1.w[1] = Q256.w[3]; + C1.w[0] = Q256.w[2]; + y_exp = y_exp + ((UINT64) (x1 + 1) << 49); + } else { // C1 < 10^34 + // C1.w[1] and C1.w[0] already set + // n = C1 * 10^(e2+x1) + y_exp = y_exp + ((UINT64) x1 << 49); + } + // check for overflow + if (y_exp == EXP_MAX_P1 + && (rnd_mode == ROUNDING_TO_NEAREST + || rnd_mode == ROUNDING_TIES_AWAY)) { + res.w[1] = 0x7800000000000000ull | x_sign; // +/-inf + res.w[0] = 0x0ull; + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // set the overflow flag + *pfpsf |= OVERFLOW_EXCEPTION; + BID_SWAP128 (res); + BID_RETURN (res); + } // else no overflow + } else { // if x_sign != y_sign the result of this subtract. is exact + C1.w[0] = C1.w[0] - R256.w[2]; + C1.w[1] = C1.w[1] - R256.w[3]; + if (C1.w[0] > tmp64) + C1.w[1]--; // borrow + if (C1.w[1] >= 0x8000000000000000ull) { // negative coefficient! + C1.w[0] = ~C1.w[0]; + C1.w[0]++; + C1.w[1] = ~C1.w[1]; + if (C1.w[0] == 0x0) + C1.w[1]++; + tmp_sign = y_sign; + // the result will have the sign of y if last rnd + } else { + tmp_sign = x_sign; + } + // if the difference has P34-1 digits or less, i.e. C1 < 10^33 then + // redo the calculation with x1=x1-1; + // redo the calculation also if C1 = 10^33 and + // (is_inexact_gt_midpoint or is_midpoint_lt_even); + // (the last part should have really been + // (is_inexact_lt_midpoint or is_midpoint_gt_even) from + // the rounding of C2, but the position flags have been reversed) + // 10^33 = 0x0000314dc6448d93 0x38c15b0a00000000 + if ((C1.w[1] < 0x0000314dc6448d93ull || (C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] < 0x38c15b0a00000000ull)) || (C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] == 0x38c15b0a00000000ull && (is_inexact_gt_midpoint || is_midpoint_lt_even))) { // C1=10^33 + x1 = x1 - 1; // x1 >= 0 + if (x1 >= 0) { + // clear position flags and tmp_inexact + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + tmp_inexact = 0; + second_pass = 1; + goto roundC2; // else result has less than P34 digits + } + } + // if the coefficient of the result is 10^34 it means that this + // must be the second pass, and we are done + if (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] == 0x378d8e6400000000ull) { // if C1 = 10^34 + C1.w[1] = 0x0000314dc6448d93ull; // C1 = 10^33 + C1.w[0] = 0x38c15b0a00000000ull; + y_exp = y_exp + ((UINT64) 1 << 49); + } + x_sign = tmp_sign; + if (x1 >= 1) + y_exp = y_exp + ((UINT64) x1 << 49); + // x1 = -1 is possible at the end of a second pass when the + // first pass started with x1 = 1 + } + C1_hi = C1.w[1]; + C1_lo = C1.w[0]; + // general correction from RN to RA, RM, RP, RZ; result uses y_exp + if (rnd_mode != ROUNDING_TO_NEAREST) { + if ((!x_sign + && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) + || + ((rnd_mode == ROUNDING_TIES_AWAY + || rnd_mode == ROUNDING_UP) + && is_midpoint_gt_even))) || (x_sign + && + ((rnd_mode == + ROUNDING_DOWN + && + is_inexact_lt_midpoint) + || + ((rnd_mode == + ROUNDING_TIES_AWAY + || rnd_mode == + ROUNDING_DOWN) + && + is_midpoint_gt_even)))) + { + // C1 = C1 + 1 + C1_lo = C1_lo + 1; + if (C1_lo == 0) { // rounding overflow in the low 64 bits + C1_hi = C1_hi + 1; + } + if (C1_hi == 0x0001ed09bead87c0ull + && C1_lo == 0x378d8e6400000000ull) { + // C1 = 10^34 => rounding overflow + C1_hi = 0x0000314dc6448d93ull; + C1_lo = 0x38c15b0a00000000ull; // 10^33 + y_exp = y_exp + EXP_P1; + } + } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) + && + ((x_sign + && (rnd_mode == ROUNDING_UP + || rnd_mode == ROUNDING_TO_ZERO)) + || (!x_sign + && (rnd_mode == ROUNDING_DOWN + || rnd_mode == ROUNDING_TO_ZERO)))) { + // C1 = C1 - 1 + C1_lo = C1_lo - 1; + if (C1_lo == 0xffffffffffffffffull) + C1_hi--; + // check if we crossed into the lower decade + if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 + C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 + C1_lo = 0x378d8e63ffffffffull; + y_exp = y_exp - EXP_P1; + // no underflow, because delta + q2 >= P34 + 1 + } + } else { + ; // exact, the result is already correct + } + // in all cases check for overflow (RN and RA solved already) + if (y_exp == EXP_MAX_P1) { // overflow + if ((rnd_mode == ROUNDING_DOWN && x_sign) || // RM and res < 0 + (rnd_mode == ROUNDING_UP && !x_sign)) { // RP and res > 0 + C1_hi = 0x7800000000000000ull; // +inf + C1_lo = 0x0ull; + } else { // RM and res > 0, RP and res < 0, or RZ + C1_hi = 0x5fffed09bead87c0ull; + C1_lo = 0x378d8e63ffffffffull; + } + y_exp = 0; // x_sign is preserved + // set the inexact flag (in case the exact addition was exact) + *pfpsf |= INEXACT_EXCEPTION; + // set the overflow flag + *pfpsf |= OVERFLOW_EXCEPTION; + } + } + // assemble the result + res.w[1] = x_sign | y_exp | C1_hi; + res.w[0] = C1_lo; + if (tmp_inexact) + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if (-P34 + 1 <= delta <= -1) <=> 1 <= -delta <= P34 - 1 + // NOTE: the following, up to "} else { // if x_sign != y_sign + // the result is exact" is identical to "else if (delta == P34 - q2) {" + // from above; also, the code is not symmetric: a+b and b+a may take + // different paths (need to unify eventually!) + // calculate C' = C2 + C1 * 10^(e1-e2) directly; the result may be + // inexact if it requires P34 + 1 decimal digits; in either case the + // 'cutoff' point for addition is at the position of the lsb of C2 + // The coefficient of the result is C1 * 10^(e1-e2) + C2 and the + // exponent is e2; either C1 or 10^(e1-e2) may not fit is 64 bits, + // but their product fits with certainty in 128 bits (actually in 113) + // Note that 0 <= e1 - e2 <= P34 - 2 + // -P34 + 1 <= delta <= -1 <=> -P34 + 1 <= delta <= -1 <=> + // -P34 + 1 <= q1 + e1 - q2 - e2 <= -1 <=> + // q2 - q1 - P34 + 1 <= e1 - e2 <= q2 - q1 - 1 <=> + // 1 - P34 - P34 + 1 <= e1-e2 <= P34 - 1 - 1 => 0 <= e1-e2 <= P34 - 2 + scale = delta - q1 + q2; // scale = (int)(e1 >> 49) - (int)(e2 >> 49) + if (scale >= 20) { // 10^(e1-e2) does not fit in 64 bits, but C1 does + __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); + } else if (scale >= 1) { + // if 1 <= scale <= 19 then 10^(e1-e2) fits in 64 bits + if (q1 <= 19) { // C1 fits in 64 bits + __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); + } else { // q1 >= 20 + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; + __mul_128x64_to_128 (C1, ten2k64[scale], C1); + } + } else { // if (scale == 0) C1 is unchanged + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; // only the low part is necessary + } + C1_hi = C1.w[1]; + C1_lo = C1.w[0]; + // now add C2 + if (x_sign == y_sign) { + // the result can overflow! + C1_lo = C1_lo + C2_lo; + C1_hi = C1_hi + C2_hi; + if (C1_lo < C1.w[0]) + C1_hi++; + // test for overflow, possible only when C1 >= 10^34 + if (C1_hi > 0x0001ed09bead87c0ull || (C1_hi == 0x0001ed09bead87c0ull && C1_lo >= 0x378d8e6400000000ull)) { // C1 >= 10^34 + // in this case q = P34 + 1 and x = q - P34 = 1, so multiply + // C'' = C'+ 5 = C1 + 5 by k1 ~ 10^(-1) calculated for P34 + 1 + // decimal digits + // Calculate C'' = C' + 1/2 * 10^x + if (C1_lo >= 0xfffffffffffffffbull) { // low half add has carry + C1_lo = C1_lo + 5; + C1_hi = C1_hi + 1; + } else { + C1_lo = C1_lo + 5; + } + // the approximation of 10^(-1) was rounded up to 118 bits + // 10^(-1) =~ 33333333333333333333333333333400 * 2^-129 + // 10^(-1) =~ 19999999999999999999999999999a00 * 2^-128 + C1.w[1] = C1_hi; + C1.w[0] = C1_lo; // C'' + ten2m1.w[1] = 0x1999999999999999ull; + ten2m1.w[0] = 0x9999999999999a00ull; + __mul_128x128_to_256 (P256, C1, ten2m1); // P256 = C*, f* + // C* is actually floor(C*) in this case + // the top Ex = 128 bits of 10^(-1) are + // T* = 0x00199999999999999999999999999999 + // if (0 < f* < 10^(-x)) then + // if floor(C*) is even then C = floor(C*) - logical right + // shift; C has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C = floor(C*) - 1 (logical right + // shift; C has p decimal digits, correct by Pr. 1) + // else + // C = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C * 10^(e2+x) + if ((P256.w[1] || P256.w[0]) + && (P256.w[1] < 0x1999999999999999ull + || (P256.w[1] == 0x1999999999999999ull + && P256.w[0] <= 0x9999999999999999ull))) { + // the result is a midpoint + if (P256.w[2] & 0x01) { + is_midpoint_gt_even = 1; + // if floor(C*) is odd C = floor(C*) - 1; the result is not 0 + P256.w[2]--; + if (P256.w[2] == 0xffffffffffffffffull) + P256.w[3]--; + } else { + is_midpoint_lt_even = 1; + } + } + // n = Cstar * 10^(e2+1) + y_exp = y_exp + EXP_P1; + // C* != 10^P34 because C* has P34 digits + // check for overflow + if (y_exp == EXP_MAX_P1 + && (rnd_mode == ROUNDING_TO_NEAREST + || rnd_mode == ROUNDING_TIES_AWAY)) { + // overflow for RN + res.w[1] = x_sign | 0x7800000000000000ull; // +/-inf + res.w[0] = 0x0ull; + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // set the overflow flag + *pfpsf |= OVERFLOW_EXCEPTION; + BID_SWAP128 (res); + BID_RETURN (res); + } + // if (0 < f* - 1/2 < 10^(-x)) then + // the result of the addition is exact + // else + // the result of the addition is inexact + if (P256.w[1] > 0x8000000000000000ull || (P256.w[1] == 0x8000000000000000ull && P256.w[0] > 0x0ull)) { // the result may be exact + tmp64 = P256.w[1] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > 0x1999999999999999ull + || (tmp64 == 0x1999999999999999ull + && P256.w[0] >= 0x9999999999999999ull))) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact = 1; + } // else the result is exact + } else { // the result is inexact + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact = 1; + } + C1_hi = P256.w[3]; + C1_lo = P256.w[2]; + if (!is_midpoint_gt_even && !is_midpoint_lt_even) { + is_inexact_lt_midpoint = is_inexact + && (P256.w[1] & 0x8000000000000000ull); + is_inexact_gt_midpoint = is_inexact + && !(P256.w[1] & 0x8000000000000000ull); + } + // general correction from RN to RA, RM, RP, RZ; result uses y_exp + if (rnd_mode != ROUNDING_TO_NEAREST) { + if ((!x_sign + && ((rnd_mode == ROUNDING_UP + && is_inexact_lt_midpoint) + || ((rnd_mode == ROUNDING_TIES_AWAY + || rnd_mode == ROUNDING_UP) + && is_midpoint_gt_even))) || (x_sign + && + ((rnd_mode == + ROUNDING_DOWN + && + is_inexact_lt_midpoint) + || + ((rnd_mode == + ROUNDING_TIES_AWAY + || rnd_mode + == + ROUNDING_DOWN) + && + is_midpoint_gt_even)))) + { + // C1 = C1 + 1 + C1_lo = C1_lo + 1; + if (C1_lo == 0) { // rounding overflow in the low 64 bits + C1_hi = C1_hi + 1; + } + if (C1_hi == 0x0001ed09bead87c0ull + && C1_lo == 0x378d8e6400000000ull) { + // C1 = 10^34 => rounding overflow + C1_hi = 0x0000314dc6448d93ull; + C1_lo = 0x38c15b0a00000000ull; // 10^33 + y_exp = y_exp + EXP_P1; + } + } else + if ((is_midpoint_lt_even || is_inexact_gt_midpoint) && + ((x_sign && (rnd_mode == ROUNDING_UP || + rnd_mode == ROUNDING_TO_ZERO)) || + (!x_sign && (rnd_mode == ROUNDING_DOWN || + rnd_mode == ROUNDING_TO_ZERO)))) { + // C1 = C1 - 1 + C1_lo = C1_lo - 1; + if (C1_lo == 0xffffffffffffffffull) + C1_hi--; + // check if we crossed into the lower decade + if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 + C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 + C1_lo = 0x378d8e63ffffffffull; + y_exp = y_exp - EXP_P1; + // no underflow, because delta + q2 >= P34 + 1 + } + } else { + ; // exact, the result is already correct + } + // in all cases check for overflow (RN and RA solved already) + if (y_exp == EXP_MAX_P1) { // overflow + if ((rnd_mode == ROUNDING_DOWN && x_sign) || // RM and res < 0 + (rnd_mode == ROUNDING_UP && !x_sign)) { // RP and res > 0 + C1_hi = 0x7800000000000000ull; // +inf + C1_lo = 0x0ull; + } else { // RM and res > 0, RP and res < 0, or RZ + C1_hi = 0x5fffed09bead87c0ull; + C1_lo = 0x378d8e63ffffffffull; + } + y_exp = 0; // x_sign is preserved + // set the inexact flag (in case the exact addition was exact) + *pfpsf |= INEXACT_EXCEPTION; + // set the overflow flag + *pfpsf |= OVERFLOW_EXCEPTION; + } + } + } // else if (C1 < 10^34) then C1 is the coeff.; the result is exact + // assemble the result + res.w[1] = x_sign | y_exp | C1_hi; + res.w[0] = C1_lo; + } else { // if x_sign != y_sign the result is exact + C1_lo = C2_lo - C1_lo; + C1_hi = C2_hi - C1_hi; + if (C1_lo > C2_lo) + C1_hi--; + if (C1_hi >= 0x8000000000000000ull) { // negative coefficient! + C1_lo = ~C1_lo; + C1_lo++; + C1_hi = ~C1_hi; + if (C1_lo == 0x0) + C1_hi++; + x_sign = y_sign; // the result will have the sign of y + } + // the result can be zero, but it cannot overflow + if (C1_lo == 0 && C1_hi == 0) { + // assemble the result + if (x_exp < y_exp) + res.w[1] = x_exp; + else + res.w[1] = y_exp; + res.w[0] = 0; + if (rnd_mode == ROUNDING_DOWN) { + res.w[1] |= 0x8000000000000000ull; + } + BID_SWAP128 (res); + BID_RETURN (res); + } + // assemble the result + res.w[1] = y_sign | y_exp | C1_hi; + res.w[0] = C1_lo; + } + } + } + BID_SWAP128 (res); + BID_RETURN (res) + } +} + + + +// bid128_sub stands for bid128qq_sub + +/***************************************************************************** + * BID128 sub + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_sub (UINT128 * pres, UINT128 * px, UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px, y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128_sub (UINT128 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 res; + UINT64 y_sign; + + if ((y.w[HIGH_128W] & MASK_NAN) != MASK_NAN) { // y is not NAN + // change its sign + y_sign = y.w[HIGH_128W] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + if (y_sign) + y.w[HIGH_128W] = y.w[HIGH_128W] & 0x7fffffffffffffffull; + else + y.w[HIGH_128W] = y.w[HIGH_128W] | 0x8000000000000000ull; + } +#if DECIMAL_CALL_BY_REFERENCE + bid128_add (&res, &x, &y + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + res = bid128_add (x, y + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_compare.c b/gcc-4.4.3/libgcc/config/libbid/bid128_compare.c new file mode 100644 index 000000000..18ed94284 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_compare.c @@ -0,0 +1,4346 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_equal, x, y) + + int res; + int exp_x, exp_y, exp_t; + UINT128 sig_x, sig_y, sig_t; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +if ((x.w[1] & MASK_SNAN) == MASK_SNAN + || (y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; +} +{ + res = 0; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equivalent. +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 1; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + if ((y.w[1] & MASK_INF) == MASK_INF) { + res = (((x.w[1] ^ y.w[1]) & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } else { + res = 0; + BID_RETURN (res); + } +} +if ((y.w[1] & MASK_INF) == MASK_INF) { + res = 0; + BID_RETURN (res); +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + +if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); +} else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) { + res = 0; + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ => not equal : return 0 +if ((x.w[1] ^ y.w[1]) & MASK_SIGN) { + res = 0; + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) +if (exp_x > exp_y) { // to simplify the loop below, + SWAP (exp_x, exp_y, exp_t); // put the larger exp in y, + SWAP (sig_x.w[1], sig_y.w[1], sig_t.w[1]); // and the smaller exp in x + SWAP (sig_x.w[0], sig_y.w[0], sig_t.w[0]); // and the smaller exp in x +} + + +if (exp_y - exp_x > 33) { + res = 0; + BID_RETURN (res); +} // difference cannot be greater than 10^33 + +if (exp_y - exp_x > 19) { + // recalculate y's significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, + ten2k128[exp_y - exp_x - 20]); + { + res = ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) + && (sig_n_prime256.w[1] == sig_x.w[1]) + && (sig_n_prime256.w[0] == sig_x.w[0])); + BID_RETURN (res); + } + +} + //else{ + // recalculate y's significand upwards +__mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y); +{ + res = ((sig_n_prime192.w[2] == 0) + && (sig_n_prime192.w[1] == sig_x.w[1]) + && (sig_n_prime192.w[0] == sig_x.w[0])); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_greater, x, + y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, rather than + // equal : return 0 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +if ((x.w[1] & MASK_SNAN) == MASK_SNAN + || (y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; +} +{ + res = 0; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 0; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return 0 + if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { + res = 0; + BID_RETURN (res); + } + // x is pos infinity, it is greater, unless y is positive infinity => + // return y!=pos_infinity + else { + res = (((y.w[1] & MASK_INF) != MASK_INF) + || ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison + // of the significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if ((sig_x.w[1] > sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) + && exp_x >= exp_y) { + { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } +} +if ((sig_x.w[1] < sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) + && exp_x <= exp_y) { + { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = (((sig_n_prime192.w[2] > 0) || + (sig_n_prime192.w[1] > sig_y.w[1]) || + (sig_n_prime192.w[1] == sig_y.w[1] && + sig_n_prime192.w[0] > sig_y.w[0])) ^ + ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 || + (sig_n_prime256.w[1] > sig_x.w[1] || + (sig_n_prime256.w[1] == sig_x.w[1] && + sig_n_prime256.w[0] > sig_x.w[0]))) ^ + ((x.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); +} // if equal, return 0 +{ + res = (sig_n_prime192.w[2] != 0 + || (sig_n_prime192.w[1] > sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, + bid128_quiet_greater_equal, x, + y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 1 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +if ((x.w[1] & MASK_SNAN) == MASK_SNAN + || (y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; +} +{ + res = 0; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 1; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } + if ((x.w[1] & MASK_SIGN) == MASK_SIGN) + // x is -inf, so it is less than y unless y is -inf + { + res = (((y.w[1] & MASK_INF) == MASK_INF) + && (y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } else + // x is pos_inf, no way for it to be less than y + { + res = 1; + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison of the + // significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0] + && exp_x > exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} +if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0] + && exp_x < exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 1 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 1 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 1 + { + res = ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 + && (sig_n_prime256.w[1] < sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] < + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); +} // if equal, return 1 +{ + res = (sig_n_prime192.w[2] == 0 + && (sig_n_prime192.w[1] < sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] < + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, + bid128_quiet_greater_unordered, + x, y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than + // equal : return 1 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +if ((x.w[1] & MASK_SNAN) == MASK_SNAN + || (y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; +} +{ + res = 1; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 0; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return 0 + if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { + res = 0; + BID_RETURN (res); + } + // x is pos infinity, it is greater, unless y is positive infinity => + // return y!=pos_infinity + else { + res = (((y.w[1] & MASK_INF) != MASK_INF) + || ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison of the + // significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0] + && exp_x > exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} +if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0] + && exp_x < exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 + && (sig_n_prime256.w[1] < sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] < + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); +} // if equal, return 0 +{ + res = (sig_n_prime192.w[2] == 0 + && (sig_n_prime192.w[1] < sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] < + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_less, x, y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +if ((x.w[1] & MASK_SNAN) == MASK_SNAN + || (y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; +} +{ + res = 0; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal. +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 0; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } + if ((x.w[1] & MASK_SIGN) == MASK_SIGN) + // x is -inf, so it is less than y unless y is -inf + { + res = (((y.w[1] & MASK_INF) != MASK_INF) + || (y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } else + // x is pos_inf, no way for it to be less than y + { + res = 0; + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison of the + // significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if ((sig_x.w[1] > sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) + && exp_x >= exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +if ((sig_x.w[1] < sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) + && exp_x <= exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 1 + { + res = ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 + || (sig_n_prime256.w[1] > sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] > + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); +} // if equal, return 0 +{ + res = (sig_n_prime192.w[2] != 0 + || (sig_n_prime192.w[1] > sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_less_equal, + x, y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +if ((x.w[1] & MASK_SNAN) == MASK_SNAN + || (y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; +} +{ + res = 0; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 1; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return 1 + if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { + res = 1; + BID_RETURN (res); + } + // x is pos infinity, it is greater, unless y is positive infinity => + // return y!=pos_infinity + else { + res = (((y.w[1] & MASK_INF) == MASK_INF) + && ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison of the + // significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) || (sig_x.w[1] == sig_y.w[1] && + sig_x.w[0] >= + sig_y.w[0])) ^ ((x. + w[1] & + MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if ((sig_x.w[1] > sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) + && exp_x >= exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +if ((sig_x.w[1] < sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) + && exp_x <= exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 0 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 0 + { + res = + ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 + || (sig_n_prime256.w[1] > sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] > + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); +} // if equal, return 0 +{ + res = (sig_n_prime192.w[2] != 0 + || (sig_n_prime192.w[1] > sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, + bid128_quiet_less_unordered, + x, y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +if ((x.w[1] & MASK_SNAN) == MASK_SNAN + || (y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; +} +{ + res = 1; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal. +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 0; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } + if ((x.w[1] & MASK_SIGN) == MASK_SIGN) + // x is -inf, so it is less than y unless y is -inf + { + res = (((y.w[1] & MASK_INF) != MASK_INF) + || (y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } else + // x is pos_inf, no way for it to be less than y + { + res = 0; + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison + // of the significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if ((sig_x.w[1] > sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) + && exp_x >= exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +if ((sig_x.w[1] < sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) + && exp_x <= exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 1 + { + res = + ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 + || (sig_n_prime256.w[1] > sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] > + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); +} // if equal, return 0 +{ + res = (sig_n_prime192.w[2] != 0 + || (sig_n_prime192.w[1] > sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_equal, + x, y) + + int res; + int exp_x, exp_y, exp_t; + UINT128 sig_x, sig_y, sig_t; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +if ((x.w[1] & MASK_SNAN) == MASK_SNAN + || (y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; +} +{ + res = 1; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equivalent. +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 0; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + if ((y.w[1] & MASK_INF) == MASK_INF) { + res = (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } else { + res = 1; + BID_RETURN (res); + } +} +if ((y.w[1] & MASK_INF) == MASK_INF) { + res = 1; + BID_RETURN (res); +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + +if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); +} else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) { + res = 1; + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ => not equal : return 0 +if ((x.w[1] ^ y.w[1]) & MASK_SIGN) { + res = 1; + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) +if (exp_x > exp_y) { // to simplify the loop below, + SWAP (exp_x, exp_y, exp_t); // put the larger exp in y, + SWAP (sig_x.w[1], sig_y.w[1], sig_t.w[1]); // and the smaller exp in x + SWAP (sig_x.w[0], sig_y.w[0], sig_t.w[0]); // and the smaller exp in x +} + + +if (exp_y - exp_x > 33) { + res = 1; + BID_RETURN (res); +} // difference cannot be greater than 10^33 + +if (exp_y - exp_x > 19) { + // recalculate y's significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, + ten2k128[exp_y - exp_x - 20]); + { + res = ((sig_n_prime256.w[3] != 0) || (sig_n_prime256.w[2] != 0) + || (sig_n_prime256.w[1] != sig_x.w[1]) + || (sig_n_prime256.w[0] != sig_x.w[0])); + BID_RETURN (res); + } + +} + //else{ + // recalculate y's significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y); +{ + res = ((sig_n_prime192.w[2] != 0) + || (sig_n_prime192.w[1] != sig_x.w[1]) + || (sig_n_prime192.w[0] != sig_x.w[0])); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_greater, + x, y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +if ((x.w[1] & MASK_SNAN) == MASK_SNAN + || (y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; +} +{ + res = 1; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 1; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return 1 + if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { + res = 1; + BID_RETURN (res); + } + // x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity + else { + res = (((y.w[1] & MASK_INF) == MASK_INF) + && ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison + // of the significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if ((sig_x.w[1] > sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) + && exp_x >= exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +if ((sig_x.w[1] < sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) + && exp_x <= exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 0 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 0 + { + res = + ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 + || (sig_n_prime256.w[1] > sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] > + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); +} // if equal, return 0 +{ + res = (sig_n_prime192.w[2] != 0 + || (sig_n_prime192.w[1] > sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_less, x, + y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 1 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +if ((x.w[1] & MASK_SNAN) == MASK_SNAN + || (y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; +} +{ + res = 1; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 1; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } + if ((x.w[1] & MASK_SIGN) == MASK_SIGN) + // x is -inf, so it is less than y unless y is -inf + { + res = (((y.w[1] & MASK_INF) == MASK_INF) + && (y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } else + // x is pos_inf, no way for it to be less than y + { + res = 1; + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + + // if exponents are the same, then we have a simple comparison + // of the significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0] + && exp_x > exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} +if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0] + && exp_x < exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 1 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 1 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 1 + { + res = + ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 + && (sig_n_prime256.w[1] < sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] < + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); +} // if equal, return 1 +{ + res = (sig_n_prime192.w[2] == 0 + && (sig_n_prime192.w[1] < sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] < + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_ordered, x, + y) + + int res; + + // NaN (CASE1) + // if either number is NAN, the comparison is ordered : return 1 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +if ((x.w[1] & MASK_SNAN) == MASK_SNAN + || (y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; +} +{ + res = 0; + BID_RETURN (res); +} +} +{ + res = 1; + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_unordered, + x, y) + + int res; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered : return 1 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +if ((x.w[1] & MASK_SNAN) == MASK_SNAN + || (y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; +} +{ + res = 1; + BID_RETURN (res); +} +} +{ + res = 0; + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_signaling_greater, + x, y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +*pfpsf |= INVALID_EXCEPTION; +{ + res = 0; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 0; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return 0 + if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { + res = 0; + BID_RETURN (res); + } + // x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity + else { + res = (((y.w[1] & MASK_INF) != MASK_INF) + || ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison + // of the significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if ((sig_x.w[1] > sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) + && exp_x >= exp_y) { + { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } +} +if ((sig_x.w[1] < sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) + && exp_x <= exp_y) { + { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = + ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 + || (sig_n_prime256.w[1] > sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] > + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); +} // if equal, return 0 +{ + res = (sig_n_prime192.w[2] != 0 + || (sig_n_prime192.w[1] > sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, + bid128_signaling_greater_equal, + x, y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 1 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +*pfpsf |= INVALID_EXCEPTION; +{ + res = 0; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 1; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } + if ((x.w[1] & MASK_SIGN) == MASK_SIGN) + // x is -inf, so it is less than y unless y is -inf + { + res = (((y.w[1] & MASK_INF) == MASK_INF) + && (y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } else + // x is pos_inf, no way for it to be less than y + { + res = 1; + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison + // of the significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0] + && exp_x > exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} +if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0] + && exp_x < exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 1 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 1 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 1 + { + res = + ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 + && (sig_n_prime256.w[1] < sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] < + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); +} // if equal, return 1 +{ + res = (sig_n_prime192.w[2] == 0 + && (sig_n_prime192.w[1] < sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] < + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, + bid128_signaling_greater_unordered, + x, y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 1 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +*pfpsf |= INVALID_EXCEPTION; +{ + res = 1; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 0; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return 0 + if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { + res = 0; + BID_RETURN (res); + } + // x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity + else { + res = (((y.w[1] & MASK_INF) != MASK_INF) + || ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison + // of the significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0] + && exp_x > exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} +if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0] + && exp_x < exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = + ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 + && (sig_n_prime256.w[1] < sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] < + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); +} // if equal, return 0 +{ + res = (sig_n_prime192.w[2] == 0 + && (sig_n_prime192.w[1] < sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] < + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_signaling_less, x, + y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +*pfpsf |= INVALID_EXCEPTION; +{ + res = 0; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal. +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 0; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } + if ((x.w[1] & MASK_SIGN) == MASK_SIGN) + // x is -inf, so it is less than y unless y is -inf + { + res = (((y.w[1] & MASK_INF) != MASK_INF) + || (y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } else + // x is pos_inf, no way for it to be less than y + { + res = 0; + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison + // of the significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if ((sig_x.w[1] > sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) + && exp_x >= exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +if ((sig_x.w[1] < sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) + && exp_x <= exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, |x| < |y|, return 1 if positive +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 1 + { + res = + ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 + || (sig_n_prime256.w[1] > sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] > + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); +} // if equal, return 0 +{ + res = (sig_n_prime192.w[2] != 0 + || (sig_n_prime192.w[1] > sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, + bid128_signaling_less_equal, + x, y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +*pfpsf |= INVALID_EXCEPTION; +{ + res = 0; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 1; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return 1 + if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { + res = 1; + BID_RETURN (res); + } + // x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity + else { + res = (((y.w[1] & MASK_INF) == MASK_INF) + && ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison + // of the significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if ((sig_x.w[1] > sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) + && exp_x >= exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +if ((sig_x.w[1] < sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) + && exp_x <= exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 0 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 0 + { + res = + ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 + || (sig_n_prime256.w[1] > sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] > + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); +} // if equal, return 0 +{ + res = (sig_n_prime192.w[2] != 0 + || (sig_n_prime192.w[1] > sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, + bid128_signaling_less_unordered, + x, y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +*pfpsf |= INVALID_EXCEPTION; +{ + res = 1; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal. +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 0; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } + if ((x.w[1] & MASK_SIGN) == MASK_SIGN) + // x is -inf, so it is less than y unless y is -inf + { + res = (((y.w[1] & MASK_INF) != MASK_INF) + || (y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } else + // x is pos_inf, no way for it to be less than y + { + res = 0; + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison + // of the significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if ((sig_x.w[1] > sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) + && exp_x >= exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +if ((sig_x.w[1] < sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) + && exp_x <= exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 0 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); + } // if equal, return 1 + { + res = + ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 + || (sig_n_prime256.w[1] > sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] > + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 0; + BID_RETURN (res); +} // if equal, return 0 +{ + res = (sig_n_prime192.w[2] != 0 + || (sig_n_prime192.w[1] > sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, + bid128_signaling_not_greater, + x, y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +*pfpsf |= INVALID_EXCEPTION; +{ + res = 1; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 1; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return 1 + if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) { + res = 1; + BID_RETURN (res); + } + // x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity + else { + res = (((y.w[1] & MASK_INF) == MASK_INF) + && ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison + // of the significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if ((sig_x.w[1] > sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) + && exp_x >= exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +if ((sig_x.w[1] < sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) + && exp_x <= exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 0 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 0 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 0 + { + res = + ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 + || (sig_n_prime256.w[1] > sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] > + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger + // (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); +} // if equal, return 0 +{ + res = (sig_n_prime192.w[2] != 0 + || (sig_n_prime192.w[1] > sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, + bid128_signaling_not_less, x, + y) + + int res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 1 +if (((x.w[1] & MASK_NAN) == MASK_NAN) + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { +*pfpsf |= INVALID_EXCEPTION; +{ + res = 1; + BID_RETURN (res); +} +} + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). +if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = 1; + BID_RETURN (res); +} + // INFINITY (CASE3) +if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } + if ((x.w[1] & MASK_SIGN) == MASK_SIGN) + // x is -inf, so it is less than y unless y is -inf + { + res = (((y.w[1] & MASK_INF) == MASK_INF) + && (y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } else + // x is pos_inf, no way for it to be less than y + { + res = 1; + BID_RETURN (res); + } +} else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } +} + // CONVERT X +sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; +sig_x.w[0] = x.w[0]; +exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF X IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_x = 1; +else + non_canon_x = 0; + + // CONVERT Y +exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; +sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; +sig_y.w[0] = y.w[0]; + + // CHECK IF Y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. +if ((sig_y.w[1] > 0x0001ed09bead87c0ull) + || ((sig_y.w[1] == 0x0001ed09bead87c0ull) + && (sig_y.w[0] > 0x378d8e63ffffffffull)) + || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) + non_canon_y = 1; +else + non_canon_y = 0; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore + // ignore the exponent field + // (Any non-canonical # is considered 0) +if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; +} +if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; +} + // if both numbers are zero, neither is greater => return NOTGREATERTHAN +if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); +} + // is x is zero, it is greater if Y is negative +else if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // is y is zero, X is greater if it is positive +else if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative +if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + // REDUNDANT REPRESENTATIONS (CASE6) + + // if exponents are the same, then we have a simple comparison + // of the significands +if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); +} + // if both components are either bigger or smaller, + // it is clear what needs to be done +if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0] + && exp_x > exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); +} +if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0] + && exp_x < exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand +if (diff > 0) { // to simplify the loop below, + + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } // difference cannot be greater than 10^33 + + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 1 + { + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } + //else { //128 by 64 bit multiply -> 192 bits + __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x); + + // if postitive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 1 + { + res = (((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + +diff = exp_y - exp_x; + + // if exp_x is 33 less than exp_y, no need for compensation +if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); + } // if equal, return 1 + { + res = + ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 + && (sig_n_prime256.w[1] < sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] < + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } +} + //else { //128 by 64 bit multiply -> 192 bits + // adjust the y significand upwards +__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y); + + // if postitive, return whichever significand is larger (converse if negative) +if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = 1; + BID_RETURN (res); +} // if equal, return 1 +{ + res = (sig_n_prime192.w[2] == 0 + && (sig_n_prime192.w[1] < sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] < + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_div.c b/gcc-4.4.3/libgcc/config/libbid/bid128_div.c new file mode 100644 index 000000000..d052c378b --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_div.c @@ -0,0 +1,1851 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#define BID_128RES +#include "bid_div_macros.h" +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +#include + +#define FE_ALL_FLAGS FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT +#endif + +extern UINT32 convert_table[5][128][2]; +extern SINT8 factors[][2]; +extern UINT8 packed_10000_zeros[]; + +BID128_FUNCTION_ARG2 (bid128_div, x, y) + + UINT256 CA4, CA4r, P256; + UINT128 CX, CY, T128, CQ, CR, CA, TP128, Qh, Ql, res; + UINT64 sign_x, sign_y, T, carry64, D, Q_high, Q_low, QX, PD, + valid_y; + int_float fx, fy, f64; + UINT32 QX32, tdigit[3], digit, digit_h, digit_low; + int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, + digits_q, amount; + int nzeros, i, j, k, d5; + unsigned rmode; +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + fexcept_t binaryflags = 0; +#endif + +valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y); + + // unpack arguments, check for NaN or Infinity +if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { + // test if x is NaN +if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN + (y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = (CX.w[1]) & QUIET_MASK64; + res.w[0] = CX.w[0]; + BID_RETURN (res); +} + // x is Infinity? +if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { + // check if y is Inf. + if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull)) + // return NaN + { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } + // y is NaN? + if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) + // return NaN + { + // return +/-Inf + res.w[1] = ((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) | + 0x7800000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } +} + // x is 0 +if ((y.w[1] & 0x7800000000000000ull) < 0x7800000000000000ull) { + if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // x=y=0, return NaN + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } + // return 0 + res.w[1] = (x.w[1] ^ y.w[1]) & 0x8000000000000000ull; + exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128; + if (exponent_x > DECIMAL_MAX_EXPON_128) + exponent_x = DECIMAL_MAX_EXPON_128; + else if (exponent_x < 0) + exponent_x = 0; + res.w[1] |= (((UINT64) exponent_x) << 49); + res.w[0] = 0; + BID_RETURN (res); +} +} +if (!valid_y) { + // y is Inf. or NaN + + // test if y is NaN + if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = CY.w[1] & QUIET_MASK64; + res.w[0] = CY.w[0]; + BID_RETURN (res); + } + // y is Infinity? + if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { + // return +/-0 + res.w[1] = sign_x ^ sign_y; + res.w[0] = 0; + BID_RETURN (res); + } + // y is 0, return +/-Inf +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); +#endif + res.w[1] = + ((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; + res.w[0] = 0; + BID_RETURN (res); +} +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128; + +if (__unsigned_compare_gt_128 (CY, CX)) { + // CX < CY + + // 2^64 + f64.i = 0x5f800000; + + // fx ~ CX, fy ~ CY + fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; + fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; + // expon_cy - expon_cx + bin_index = (fy.i - fx.i) >> 23; + + if (CX.w[1]) { + T = power10_index_binexp_128[bin_index].w[0]; + __mul_64x128_short (CA, T, CX); + } else { + T128 = power10_index_binexp_128[bin_index]; + __mul_64x128_short (CA, CX.w[0], T128); + } + + ed2 = 33; + if (__unsigned_compare_gt_128 (CY, CA)) + ed2++; + + T128 = power10_table_128[ed2]; + __mul_128x128_to_256 (CA4, CA, T128); + + ed2 += estimate_decimal_digits[bin_index]; + CQ.w[0] = CQ.w[1] = 0; + diff_expon = diff_expon - ed2; + +} else { + // get CQ = CX/CY + __div_128_by_128 (&CQ, &CR, CX, CY); + + if (!CR.w[1] && !CR.w[0]) { + get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, + pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + // get number of decimal digits in CQ + // 2^64 + f64.i = 0x5f800000; + fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; + // binary expon. of CQ + bin_expon = (fx.i - 0x3f800000) >> 23; + + digits_q = estimate_decimal_digits[bin_expon]; + TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; + TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; + if (__unsigned_compare_ge_128 (CQ, TP128)) + digits_q++; + + ed2 = 34 - digits_q; + T128.w[0] = power10_table_128[ed2].w[0]; + T128.w[1] = power10_table_128[ed2].w[1]; + __mul_128x128_to_256 (CA4, CR, T128); + diff_expon = diff_expon - ed2; + __mul_128x128_low (CQ, CQ, T128); + +} + +__div_256_by_128 (&CQ, &CA4, CY); + +#ifdef SET_STATUS_FLAGS +if (CA4.w[0] || CA4.w[1]) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); +} +#ifndef LEAVE_TRAILING_ZEROS +else +#endif +#else +#ifndef LEAVE_TRAILING_ZEROS +if (!CA4.w[0] && !CA4.w[1]) +#endif +#endif +#ifndef LEAVE_TRAILING_ZEROS + // check whether result is exact +{ + // check whether CX, CY are short + if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { + i = (int) CY.w[0] - 1; + j = (int) CX.w[0] - 1; + // difference in powers of 2 factors for Y and X + nzeros = ed2 - factors[i][0] + factors[j][0]; + // difference in powers of 5 factors + d5 = ed2 - factors[i][1] + factors[j][1]; + if (d5 < nzeros) + nzeros = d5; + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128_long (CQ, Qh, amount); + + diff_expon += nzeros; + } else { + // decompose Q as Qh*10^17 + Ql + //T128 = reciprocals10_128[17]; + T128.w[0] = 0x44909befeb9fad49ull; + T128.w[1] = 0x000b877aa3236a4bull; + __mul_128x128_to_256 (P256, CQ, T128); + //amount = recip_scale[17]; + Q_high = (P256.w[2] >> 44) | (P256.w[3] << (64 - 44)); + Q_low = CQ.w[0] - Q_high * 100000000000000000ull; + + if (!Q_low) { + diff_expon += 17; + + tdigit[0] = Q_high & 0x3ffffff; + tdigit[1] = 0; + QX = Q_high >> 26; + QX32 = QX; + nzeros = 0; + + for (j = 0; QX32; j++, QX32 >>= 7) { + k = (QX32 & 127); + tdigit[0] += convert_table[j][k][0]; + tdigit[1] += convert_table[j][k][1]; + if (tdigit[0] >= 100000000) { + tdigit[0] -= 100000000; + tdigit[1]++; + } + } + + if (tdigit[1] >= 100000000) { + tdigit[1] -= 100000000; + if (tdigit[1] >= 100000000) + tdigit[1] -= 100000000; + } + + digit = tdigit[0]; + if (!digit && !tdigit[1]) + nzeros += 16; + else { + if (!digit) { + nzeros += 8; + digit = tdigit[1]; + } + // decompose digit + PD = (UINT64) digit *0x068DB8BBull; + digit_h = (UINT32) (PD >> 40); + digit_low = digit - digit_h * 10000; + + if (!digit_low) + nzeros += 4; + else + digit_h = digit_low; + + if (!(digit_h & 1)) + nzeros += + 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> + (digit_h & 7)); + } + + if (nzeros) { + __mul_64x64_to_128 (CQ, Q_high, reciprocals10_64[nzeros]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-64 + amount = short_recip_scale[nzeros]; + CQ.w[0] = CQ.w[1] >> amount; + } else + CQ.w[0] = Q_high; + CQ.w[1] = 0; + + diff_expon += nzeros; + } else { + tdigit[0] = Q_low & 0x3ffffff; + tdigit[1] = 0; + QX = Q_low >> 26; + QX32 = QX; + nzeros = 0; + + for (j = 0; QX32; j++, QX32 >>= 7) { + k = (QX32 & 127); + tdigit[0] += convert_table[j][k][0]; + tdigit[1] += convert_table[j][k][1]; + if (tdigit[0] >= 100000000) { + tdigit[0] -= 100000000; + tdigit[1]++; + } + } + + if (tdigit[1] >= 100000000) { + tdigit[1] -= 100000000; + if (tdigit[1] >= 100000000) + tdigit[1] -= 100000000; + } + + digit = tdigit[0]; + if (!digit && !tdigit[1]) + nzeros += 16; + else { + if (!digit) { + nzeros += 8; + digit = tdigit[1]; + } + // decompose digit + PD = (UINT64) digit *0x068DB8BBull; + digit_h = (UINT32) (PD >> 40); + digit_low = digit - digit_h * 10000; + + if (!digit_low) + nzeros += 4; + else + digit_h = digit_low; + + if (!(digit_h & 1)) + nzeros += + 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> + (digit_h & 7)); + } + + if (nzeros) { + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + + //now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128 (CQ, Qh, amount); + } + diff_expon += nzeros; + + } + } + get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); +} +#endif + +if (diff_expon >= 0) { +#ifdef IEEE_ROUND_NEAREST + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; +#else +#ifdef IEEE_ROUND_NEAREST_TIES_AWAY + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; +#else + rmode = rnd_mode; + if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + switch (rmode) { + case ROUNDING_TO_NEAREST: // round to nearest code + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_TIES_AWAY: + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + break; + default: // rounding up + CQ.w[0]++; + if (!CQ.w[0]) + CQ.w[1]++; + break; + } +#endif +#endif + +} else { +#ifdef SET_STATUS_FLAGS + if (CA4.w[0] || CA4.w[1]) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#endif + + handle_UF_128_rem (&res, sign_x ^ sign_y, diff_expon, CQ, + CA4.w[1] | CA4.w[0], &rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + +} + +get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +BID_RETURN (res); +} + + +//#define LEAVE_TRAILING_ZEROS + +TYPE0_FUNCTION_ARGTYPE1_ARGTYPE2 (UINT128, bid128dd_div, UINT64, x, + UINT64, y) + + UINT256 CA4, CA4r, P256; + UINT128 CX, CY, T128, CQ, CR, CA, TP128, Qh, Ql, res; + UINT64 sign_x, sign_y, T, carry64, D, Q_high, Q_low, QX, PD, + valid_y; + int_float fx, fy, f64; + UINT32 QX32, tdigit[3], digit, digit_h, digit_low; + int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, + digits_q, amount; + int nzeros, i, j, k, d5; + unsigned rmode; +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + fexcept_t binaryflags = 0; +#endif + +valid_y = unpack_BID64 (&sign_y, &exponent_y, &CY.w[0], y); + + // unpack arguments, check for NaN or Infinity +CX.w[1] = 0; +if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], (x))) { +#ifdef SET_STATUS_FLAGS +if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + + // test if x is NaN +if ((x & NAN_MASK64) == NAN_MASK64) { +#ifdef SET_STATUS_FLAGS + if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[0] = (CX.w[0] & 0x0003ffffffffffffull); + __mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]); + res.w[1] |= ((CX.w[0]) & 0xfc00000000000000ull); + BID_RETURN (res); +} + // x is Infinity? +if (((x) & 0x7800000000000000ull) == 0x7800000000000000ull) { + // check if y is Inf. + if ((((y) & 0x7c00000000000000ull) == 0x7800000000000000ull)) + // return NaN + { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } + if ((((y) & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { + // otherwise return +/-Inf + res.w[1] = + (((x) ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } +} + // x is 0 +if ((((y) & 0x7800000000000000ull) != 0x7800000000000000ull)) { + if(!CY.w[0]) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // x=y=0, return NaN + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); +} + // return 0 +res.w[1] = ((x) ^ (y)) & 0x8000000000000000ull; +if (((y) & 0x6000000000000000ull) == 0x6000000000000000ull) + exponent_y = ((UINT32) ((y) >> 51)) & 0x3ff; +else + exponent_y = ((UINT32) ((y) >> 53)) & 0x3ff; +exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128; +if (exponent_x > DECIMAL_MAX_EXPON_128) + exponent_x = DECIMAL_MAX_EXPON_128; +else if (exponent_x < 0) + exponent_x = 0; +res.w[1] |= (((UINT64) exponent_x) << 49); +res.w[0] = 0; +BID_RETURN (res); +} +} + +CY.w[1] = 0; +if (!valid_y) { + // y is Inf. or NaN + + // test if y is NaN + if ((y & NAN_MASK64) == NAN_MASK64) { +#ifdef SET_STATUS_FLAGS + if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[0] = (CY.w[0] & 0x0003ffffffffffffull); + __mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]); + res.w[1] |= ((CY.w[0]) & 0xfc00000000000000ull); + BID_RETURN (res); + } + // y is Infinity? + if (((y) & 0x7800000000000000ull) == 0x7800000000000000ull) { + // return +/-0 + res.w[1] = sign_x ^ sign_y; + res.w[0] = 0; + BID_RETURN (res); + } + // y is 0, return +/-Inf + res.w[1] = + (((x) ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull; + res.w[0] = 0; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); +#endif + BID_RETURN (res); +} +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128; + +if (__unsigned_compare_gt_128 (CY, CX)) { + // CX < CY + + // 2^64 + f64.i = 0x5f800000; + + // fx ~ CX, fy ~ CY + fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; + fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; + // expon_cy - expon_cx + bin_index = (fy.i - fx.i) >> 23; + + if (CX.w[1]) { + T = power10_index_binexp_128[bin_index].w[0]; + __mul_64x128_short (CA, T, CX); + } else { + T128 = power10_index_binexp_128[bin_index]; + __mul_64x128_short (CA, CX.w[0], T128); + } + + ed2 = 33; + if (__unsigned_compare_gt_128 (CY, CA)) + ed2++; + + T128 = power10_table_128[ed2]; + __mul_128x128_to_256 (CA4, CA, T128); + + ed2 += estimate_decimal_digits[bin_index]; + CQ.w[0] = CQ.w[1] = 0; + diff_expon = diff_expon - ed2; + +} else { + // get CQ = CX/CY + __div_128_by_128 (&CQ, &CR, CX, CY); + + if (!CR.w[1] && !CR.w[0]) { + get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, + pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + // get number of decimal digits in CQ + // 2^64 + f64.i = 0x5f800000; + fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; + // binary expon. of CQ + bin_expon = (fx.i - 0x3f800000) >> 23; + + digits_q = estimate_decimal_digits[bin_expon]; + TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; + TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; + if (__unsigned_compare_ge_128 (CQ, TP128)) + digits_q++; + + ed2 = 34 - digits_q; + T128.w[0] = power10_table_128[ed2].w[0]; + T128.w[1] = power10_table_128[ed2].w[1]; + __mul_128x128_to_256 (CA4, CR, T128); + diff_expon = diff_expon - ed2; + __mul_128x128_low (CQ, CQ, T128); + +} + +__div_256_by_128 (&CQ, &CA4, CY); + + +#ifdef SET_STATUS_FLAGS + if (CA4.w[0] || CA4.w[1]) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#ifndef LEAVE_TRAILING_ZEROS + else +#endif +#else +#ifndef LEAVE_TRAILING_ZEROS + if (!CA4.w[0] && !CA4.w[1]) +#endif +#endif +#ifndef LEAVE_TRAILING_ZEROS + // check whether result is exact + { + // check whether CX, CY are short + if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { + i = (int) CY.w[0] - 1; + j = (int) CX.w[0] - 1; + // difference in powers of 2 factors for Y and X + nzeros = ed2 - factors[i][0] + factors[j][0]; + // difference in powers of 5 factors + d5 = ed2 - factors[i][1] + factors[j][1]; + if (d5 < nzeros) + nzeros = d5; + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + //__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2]; + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128_long (CQ, Qh, amount); + + diff_expon += nzeros; + } else { + // decompose Q as Qh*10^17 + Ql + //T128 = reciprocals10_128[17]; + T128.w[0] = 0x44909befeb9fad49ull; + T128.w[1] = 0x000b877aa3236a4bull; + __mul_128x128_to_256 (P256, CQ, T128); + //amount = recip_scale[17]; + Q_high = (P256.w[2] >> 44) | (P256.w[3] << (64 - 44)); + Q_low = CQ.w[0] - Q_high * 100000000000000000ull; + + if (!Q_low) { + diff_expon += 17; + + tdigit[0] = Q_high & 0x3ffffff; + tdigit[1] = 0; + QX = Q_high >> 26; + QX32 = QX; + nzeros = 0; + + for (j = 0; QX32; j++, QX32 >>= 7) { + k = (QX32 & 127); + tdigit[0] += convert_table[j][k][0]; + tdigit[1] += convert_table[j][k][1]; + if (tdigit[0] >= 100000000) { + tdigit[0] -= 100000000; + tdigit[1]++; + } + } + + + if (tdigit[1] >= 100000000) { + tdigit[1] -= 100000000; + if (tdigit[1] >= 100000000) + tdigit[1] -= 100000000; + } + + digit = tdigit[0]; + if (!digit && !tdigit[1]) + nzeros += 16; + else { + if (!digit) { + nzeros += 8; + digit = tdigit[1]; + } + // decompose digit + PD = (UINT64) digit *0x068DB8BBull; + digit_h = (UINT32) (PD >> 40); + digit_low = digit - digit_h * 10000; + + if (!digit_low) + nzeros += 4; + else + digit_h = digit_low; + + if (!(digit_h & 1)) + nzeros += + 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> + (digit_h & 7)); + } + + if (nzeros) { + __mul_64x64_to_128 (CQ, Q_high, reciprocals10_64[nzeros]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-64 + amount = short_recip_scale[nzeros]; + CQ.w[0] = CQ.w[1] >> amount; + } else + CQ.w[0] = Q_high; + CQ.w[1] = 0; + + diff_expon += nzeros; + } else { + tdigit[0] = Q_low & 0x3ffffff; + tdigit[1] = 0; + QX = Q_low >> 26; + QX32 = QX; + nzeros = 0; + + for (j = 0; QX32; j++, QX32 >>= 7) { + k = (QX32 & 127); + tdigit[0] += convert_table[j][k][0]; + tdigit[1] += convert_table[j][k][1]; + if (tdigit[0] >= 100000000) { + tdigit[0] -= 100000000; + tdigit[1]++; + } + } + + if (tdigit[1] >= 100000000) { + tdigit[1] -= 100000000; + if (tdigit[1] >= 100000000) + tdigit[1] -= 100000000; + } + + digit = tdigit[0]; + if (!digit && !tdigit[1]) + nzeros += 16; + else { + if (!digit) { + nzeros += 8; + digit = tdigit[1]; + } + // decompose digit + PD = (UINT64) digit *0x068DB8BBull; + digit_h = (UINT32) (PD >> 40); + digit_low = digit - digit_h * 10000; + + if (!digit_low) + nzeros += 4; + else + digit_h = digit_low; + + if (!(digit_h & 1)) + nzeros += + 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> + (digit_h & 7)); + } + + if (nzeros) { + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128 (CQ, Qh, amount); + } + diff_expon += nzeros; + + } + } + get_BID128(&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode,pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } +#endif + +if (diff_expon >= 0) { +#ifdef IEEE_ROUND_NEAREST + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; +#else +#ifdef IEEE_ROUND_NEAREST_TIES_AWAY + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; +#else + rmode = rnd_mode; + if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + switch (rmode) { + case ROUNDING_TO_NEAREST: // round to nearest code + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_TIES_AWAY: + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + break; + default: // rounding up + CQ.w[0]++; + if (!CQ.w[0]) + CQ.w[1]++; + break; + } +#endif +#endif + +} else { +#ifdef SET_STATUS_FLAGS + if (CA4.w[0] || CA4.w[1]) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#endif + handle_UF_128_rem (&res, sign_x ^ sign_y, diff_expon, CQ, + CA4.w[1] | CA4.w[0], &rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + +} + +get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +BID_RETURN (res); +} + + +BID128_FUNCTION_ARGTYPE1_ARG128 (bid128dq_div, UINT64, x, y) + UINT256 CA4, CA4r, P256; + UINT128 CX, CY, T128, CQ, CR, CA, TP128, Qh, Ql, res; + UINT64 sign_x, sign_y, T, carry64, D, Q_high, Q_low, QX, valid_y, + PD; + int_float fx, fy, f64; + UINT32 QX32, tdigit[3], digit, digit_h, digit_low; + int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, + digits_q, amount; + int nzeros, i, j, k, d5; + unsigned rmode; +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + fexcept_t binaryflags = 0; +#endif + +valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y); + + // unpack arguments, check for NaN or Infinity +CX.w[1] = 0; +if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], x)) { +#ifdef SET_STATUS_FLAGS +if ((y.w[1] & SNAN_MASK64) == SNAN_MASK64) // y is sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + + // test if x is NaN +if ((x & NAN_MASK64) == NAN_MASK64) { +#ifdef SET_STATUS_FLAGS + if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[0] = (CX.w[0] & 0x0003ffffffffffffull); + __mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]); + res.w[1] |= ((CX.w[0]) & 0xfc00000000000000ull); + BID_RETURN (res); +} + // x is Infinity? +if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) { + // check if y is Inf. + if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull)) + // return NaN + { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } + if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { + // otherwise return +/-Inf + res.w[1] = + ((x ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } +} + // x is 0 +if ((y.w[1] & INFINITY_MASK64) != INFINITY_MASK64) { + if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // x=y=0, return NaN + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } + // return 0 + res.w[1] = (x ^ y.w[1]) & 0x8000000000000000ull; + exponent_x = exponent_x - exponent_y + (DECIMAL_EXPONENT_BIAS_128<<1) - DECIMAL_EXPONENT_BIAS; + if (exponent_x > DECIMAL_MAX_EXPON_128) + exponent_x = DECIMAL_MAX_EXPON_128; + else if (exponent_x < 0) + exponent_x = 0; + res.w[1] |= (((UINT64) exponent_x) << 49); + res.w[0] = 0; + BID_RETURN (res); +} +} +exponent_x += (DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS); + +if (!valid_y) { + // y is Inf. or NaN + + // test if y is NaN + if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = CY.w[1] & QUIET_MASK64; + res.w[0] = CY.w[0]; + BID_RETURN (res); + } + // y is Infinity? + if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { + // return +/-0 + res.w[1] = sign_x ^ sign_y; + res.w[0] = 0; + BID_RETURN (res); + } + // y is 0, return +/-Inf + res.w[1] = + ((x ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; + res.w[0] = 0; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); +#endif + BID_RETURN (res); +} +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128; + +if (__unsigned_compare_gt_128 (CY, CX)) { + // CX < CY + + // 2^64 + f64.i = 0x5f800000; + + // fx ~ CX, fy ~ CY + fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; + fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; + // expon_cy - expon_cx + bin_index = (fy.i - fx.i) >> 23; + + if (CX.w[1]) { + T = power10_index_binexp_128[bin_index].w[0]; + __mul_64x128_short (CA, T, CX); + } else { + T128 = power10_index_binexp_128[bin_index]; + __mul_64x128_short (CA, CX.w[0], T128); + } + + ed2 = 33; + if (__unsigned_compare_gt_128 (CY, CA)) + ed2++; + + T128 = power10_table_128[ed2]; + __mul_128x128_to_256 (CA4, CA, T128); + + ed2 += estimate_decimal_digits[bin_index]; + CQ.w[0] = CQ.w[1] = 0; + diff_expon = diff_expon - ed2; + +} else { + // get CQ = CX/CY + __div_128_by_128 (&CQ, &CR, CX, CY); + + if (!CR.w[1] && !CR.w[0]) { + get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, + pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + // get number of decimal digits in CQ + // 2^64 + f64.i = 0x5f800000; + fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; + // binary expon. of CQ + bin_expon = (fx.i - 0x3f800000) >> 23; + + digits_q = estimate_decimal_digits[bin_expon]; + TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; + TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; + if (__unsigned_compare_ge_128 (CQ, TP128)) + digits_q++; + + ed2 = 34 - digits_q; + T128.w[0] = power10_table_128[ed2].w[0]; + T128.w[1] = power10_table_128[ed2].w[1]; + __mul_128x128_to_256 (CA4, CR, T128); + diff_expon = diff_expon - ed2; + __mul_128x128_low (CQ, CQ, T128); + +} + +__div_256_by_128 (&CQ, &CA4, CY); + +#ifdef SET_STATUS_FLAGS + if (CA4.w[0] || CA4.w[1]) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#ifndef LEAVE_TRAILING_ZEROS + else +#endif +#else +#ifndef LEAVE_TRAILING_ZEROS + if (!CA4.w[0] && !CA4.w[1]) +#endif +#endif +#ifndef LEAVE_TRAILING_ZEROS + // check whether result is exact + { + //printf("ed2=%d,nz=%d,a=%d,CQ="LX16","LX16", RH="LX16", RL="LX16"\n",ed2,nzeros,amount,CQ.w[1],CQ.w[0],reciprocals10_128[nzeros].w[1],reciprocals10_128[nzeros].w[0]);fflush(stdout); + // check whether CX, CY are short + if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { + i = (int) CY.w[0] - 1; + j = (int) CX.w[0] - 1; + // difference in powers of 2 factors for Y and X + nzeros = ed2 - factors[i][0] + factors[j][0]; + // difference in powers of 5 factors + d5 = ed2 - factors[i][1] + factors[j][1]; + if (d5 < nzeros) + nzeros = d5; + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + //__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2]; + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128_long (CQ, Qh, amount); + + diff_expon += nzeros; + } else { + // decompose Q as Qh*10^17 + Ql + //T128 = reciprocals10_128[17]; + T128.w[0] = 0x44909befeb9fad49ull; + T128.w[1] = 0x000b877aa3236a4bull; + __mul_128x128_to_256 (P256, CQ, T128); + //amount = recip_scale[17]; + Q_high = (P256.w[2] >> 44) | (P256.w[3] << (64 - 44)); + Q_low = CQ.w[0] - Q_high * 100000000000000000ull; + + if (!Q_low) { + diff_expon += 17; + + tdigit[0] = Q_high & 0x3ffffff; + tdigit[1] = 0; + QX = Q_high >> 26; + QX32 = QX; + nzeros = 0; + + for (j = 0; QX32; j++, QX32 >>= 7) { + k = (QX32 & 127); + tdigit[0] += convert_table[j][k][0]; + tdigit[1] += convert_table[j][k][1]; + if (tdigit[0] >= 100000000) { + tdigit[0] -= 100000000; + tdigit[1]++; + } + } + + + if (tdigit[1] >= 100000000) { + tdigit[1] -= 100000000; + if (tdigit[1] >= 100000000) + tdigit[1] -= 100000000; + } + + digit = tdigit[0]; + if (!digit && !tdigit[1]) + nzeros += 16; + else { + if (!digit) { + nzeros += 8; + digit = tdigit[1]; + } + // decompose digit + PD = (UINT64) digit *0x068DB8BBull; + digit_h = (UINT32) (PD >> 40); + //printf("i=%d, nz=%d, digit=%d (%d, %016I64x %016I64x)\n",i,nzeros,digit_h,digit,PD,digit_h);fflush(stdout); + digit_low = digit - digit_h * 10000; + + if (!digit_low) + nzeros += 4; + else + digit_h = digit_low; + + if (!(digit_h & 1)) + nzeros += + 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> + (digit_h & 7)); + } + + if (nzeros) { + __mul_64x64_to_128 (CQ, Q_high, reciprocals10_64[nzeros]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-64 + amount = short_recip_scale[nzeros]; + CQ.w[0] = CQ.w[1] >> amount; + } else + CQ.w[0] = Q_high; + CQ.w[1] = 0; + + diff_expon += nzeros; + } else { + tdigit[0] = Q_low & 0x3ffffff; + tdigit[1] = 0; + QX = Q_low >> 26; + QX32 = QX; + nzeros = 0; + + for (j = 0; QX32; j++, QX32 >>= 7) { + k = (QX32 & 127); + tdigit[0] += convert_table[j][k][0]; + tdigit[1] += convert_table[j][k][1]; + if (tdigit[0] >= 100000000) { + tdigit[0] -= 100000000; + tdigit[1]++; + } + } + + if (tdigit[1] >= 100000000) { + tdigit[1] -= 100000000; + if (tdigit[1] >= 100000000) + tdigit[1] -= 100000000; + } + + digit = tdigit[0]; + if (!digit && !tdigit[1]) + nzeros += 16; + else { + if (!digit) { + nzeros += 8; + digit = tdigit[1]; + } + // decompose digit + PD = (UINT64) digit *0x068DB8BBull; + digit_h = (UINT32) (PD >> 40); + //printf("i=%d, nz=%d, digit=%d (%d, %016I64x %016I64x)\n",i,nzeros,digit_h,digit,PD,digit_h);fflush(stdout); + digit_low = digit - digit_h * 10000; + + if (!digit_low) + nzeros += 4; + else + digit_h = digit_low; + + if (!(digit_h & 1)) + nzeros += + 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> + (digit_h & 7)); + } + + if (nzeros) { + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128 (CQ, Qh, amount); + } + diff_expon += nzeros; + + } + } + get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, + pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } +#endif + +if (diff_expon >= 0) { +#ifdef IEEE_ROUND_NEAREST + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; +#else +#ifdef IEEE_ROUND_NEAREST_TIES_AWAY + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; +#else + rmode = rnd_mode; + if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + switch (rmode) { + case ROUNDING_TO_NEAREST: // round to nearest code + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_TIES_AWAY: + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + break; + default: // rounding up + CQ.w[0]++; + if (!CQ.w[0]) + CQ.w[1]++; + break; + } +#endif +#endif + +} else { +#ifdef SET_STATUS_FLAGS + if (CA4.w[0] || CA4.w[1]) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#endif + handle_UF_128_rem (&res, sign_x ^ sign_y, diff_expon, CQ, + CA4.w[1] | CA4.w[0], &rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); +} + +get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +BID_RETURN (res); + +} + + +BID128_FUNCTION_ARG128_ARGTYPE2 (bid128qd_div, x, UINT64, y) + UINT256 CA4, CA4r, P256; + UINT128 CX, CY, T128, CQ, CR, CA, TP128, Qh, Ql, res; + UINT64 sign_x, sign_y, T, carry64, D, Q_high, Q_low, QX, PD, + valid_y; + int_float fx, fy, f64; + UINT32 QX32, tdigit[3], digit, digit_h, digit_low; + int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, + digits_q, amount; + int nzeros, i, j, k, d5, rmode; +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + fexcept_t binaryflags = 0; +#endif + + +valid_y = unpack_BID64 (&sign_y, &exponent_y, &CY.w[0], y); + // unpack arguments, check for NaN or Infinity +if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { + // test if x is NaN +if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN + (y & 0x7e00000000000000ull) == 0x7e00000000000000ull) + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = (CX.w[1]) & QUIET_MASK64; + res.w[0] = CX.w[0]; + BID_RETURN (res); +} + // x is Infinity? +if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { + // check if y is Inf. + if (((y & 0x7c00000000000000ull) == 0x7800000000000000ull)) + // return NaN + { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } + // y is NaN? + if (((y & 0x7c00000000000000ull) != 0x7c00000000000000ull)) + // return NaN + { + // return +/-Inf + res.w[1] = ((x.w[1] ^ y) & 0x8000000000000000ull) | + 0x7800000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } +} + // x is 0 +if ((y & 0x7800000000000000ull) < 0x7800000000000000ull) { + if (!CY.w[0]) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // x=y=0, return NaN + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } + // return 0 + res.w[1] = (x.w[1] ^ y) & 0x8000000000000000ull; + exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; + if (exponent_x > DECIMAL_MAX_EXPON_128) + exponent_x = DECIMAL_MAX_EXPON_128; + else if (exponent_x < 0) + exponent_x = 0; + res.w[1] |= (((UINT64) exponent_x) << 49); + res.w[0] = 0; + BID_RETURN (res); +} +} +CY.w[1] = 0; +if (!valid_y) { + // y is Inf. or NaN + + // test if y is NaN + if ((y & NAN_MASK64) == NAN_MASK64) { +#ifdef SET_STATUS_FLAGS + if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[0] = (CY.w[0] & 0x0003ffffffffffffull); + __mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]); + res.w[1] |= ((CY.w[0]) & 0xfc00000000000000ull); + BID_RETURN (res); + } + // y is Infinity? + if ((y & INFINITY_MASK64) == INFINITY_MASK64) { + // return +/-0 + res.w[1] = ((x.w[1] ^ y) & 0x8000000000000000ull); + res.w[0] = 0; + BID_RETURN (res); + } + // y is 0 +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); +#endif + res.w[1] = (sign_x ^ sign_y) | INFINITY_MASK64; + res.w[0] = 0; + BID_RETURN (res); +} +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; + +if (__unsigned_compare_gt_128 (CY, CX)) { + // CX < CY + + // 2^64 + f64.i = 0x5f800000; + + // fx ~ CX, fy ~ CY + fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; + fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; + // expon_cy - expon_cx + bin_index = (fy.i - fx.i) >> 23; + + if (CX.w[1]) { + T = power10_index_binexp_128[bin_index].w[0]; + __mul_64x128_short (CA, T, CX); + } else { + T128 = power10_index_binexp_128[bin_index]; + __mul_64x128_short (CA, CX.w[0], T128); + } + + ed2 = 33; + if (__unsigned_compare_gt_128 (CY, CA)) + ed2++; + + T128 = power10_table_128[ed2]; + __mul_128x128_to_256 (CA4, CA, T128); + + ed2 += estimate_decimal_digits[bin_index]; + CQ.w[0] = CQ.w[1] = 0; + diff_expon = diff_expon - ed2; + +} else { + // get CQ = CX/CY + __div_128_by_128 (&CQ, &CR, CX, CY); + + if (!CR.w[1] && !CR.w[0]) { + get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, + pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + // get number of decimal digits in CQ + // 2^64 + f64.i = 0x5f800000; + fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; + // binary expon. of CQ + bin_expon = (fx.i - 0x3f800000) >> 23; + + digits_q = estimate_decimal_digits[bin_expon]; + TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; + TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; + if (__unsigned_compare_ge_128 (CQ, TP128)) + digits_q++; + + ed2 = 34 - digits_q; + T128.w[0] = power10_table_128[ed2].w[0]; + T128.w[1] = power10_table_128[ed2].w[1]; + __mul_128x128_to_256 (CA4, CR, T128); + diff_expon = diff_expon - ed2; + __mul_128x128_low (CQ, CQ, T128); + +} + +__div_256_by_128 (&CQ, &CA4, CY); + + +#ifdef SET_STATUS_FLAGS + if (CA4.w[0] || CA4.w[1]) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#ifndef LEAVE_TRAILING_ZEROS + else +#endif +#else +#ifndef LEAVE_TRAILING_ZEROS + if (!CA4.w[0] && !CA4.w[1]) +#endif +#endif +#ifndef LEAVE_TRAILING_ZEROS + // check whether result is exact + { + // check whether CX, CY are short + if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { + i = (int) CY.w[0] - 1; + j = (int) CX.w[0] - 1; + // difference in powers of 2 factors for Y and X + nzeros = ed2 - factors[i][0] + factors[j][0]; + // difference in powers of 5 factors + d5 = ed2 - factors[i][1] + factors[j][1]; + if (d5 < nzeros) + nzeros = d5; + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + //__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2]; + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128_long (CQ, Qh, amount); + + diff_expon += nzeros; + } else { + // decompose Q as Qh*10^17 + Ql + //T128 = reciprocals10_128[17]; + T128.w[0] = 0x44909befeb9fad49ull; + T128.w[1] = 0x000b877aa3236a4bull; + __mul_128x128_to_256 (P256, CQ, T128); + //amount = recip_scale[17]; + Q_high = (P256.w[2] >> 44) | (P256.w[3] << (64 - 44)); + Q_low = CQ.w[0] - Q_high * 100000000000000000ull; + + if (!Q_low) { + diff_expon += 17; + + tdigit[0] = Q_high & 0x3ffffff; + tdigit[1] = 0; + QX = Q_high >> 26; + QX32 = QX; + nzeros = 0; + + for (j = 0; QX32; j++, QX32 >>= 7) { + k = (QX32 & 127); + tdigit[0] += convert_table[j][k][0]; + tdigit[1] += convert_table[j][k][1]; + if (tdigit[0] >= 100000000) { + tdigit[0] -= 100000000; + tdigit[1]++; + } + } + + + if (tdigit[1] >= 100000000) { + tdigit[1] -= 100000000; + if (tdigit[1] >= 100000000) + tdigit[1] -= 100000000; + } + + digit = tdigit[0]; + if (!digit && !tdigit[1]) + nzeros += 16; + else { + if (!digit) { + nzeros += 8; + digit = tdigit[1]; + } + // decompose digit + PD = (UINT64) digit *0x068DB8BBull; + digit_h = (UINT32) (PD >> 40); + digit_low = digit - digit_h * 10000; + + if (!digit_low) + nzeros += 4; + else + digit_h = digit_low; + + if (!(digit_h & 1)) + nzeros += + 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> + (digit_h & 7)); + } + + if (nzeros) { + __mul_64x64_to_128 (CQ, Q_high, reciprocals10_64[nzeros]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-64 + amount = short_recip_scale[nzeros]; + CQ.w[0] = CQ.w[1] >> amount; + } else + CQ.w[0] = Q_high; + CQ.w[1] = 0; + + diff_expon += nzeros; + } else { + tdigit[0] = Q_low & 0x3ffffff; + tdigit[1] = 0; + QX = Q_low >> 26; + QX32 = QX; + nzeros = 0; + + for (j = 0; QX32; j++, QX32 >>= 7) { + k = (QX32 & 127); + tdigit[0] += convert_table[j][k][0]; + tdigit[1] += convert_table[j][k][1]; + if (tdigit[0] >= 100000000) { + tdigit[0] -= 100000000; + tdigit[1]++; + } + } + + if (tdigit[1] >= 100000000) { + tdigit[1] -= 100000000; + if (tdigit[1] >= 100000000) + tdigit[1] -= 100000000; + } + + digit = tdigit[0]; + if (!digit && !tdigit[1]) + nzeros += 16; + else { + if (!digit) { + nzeros += 8; + digit = tdigit[1]; + } + // decompose digit + PD = (UINT64) digit *0x068DB8BBull; + digit_h = (UINT32) (PD >> 40); + digit_low = digit - digit_h * 10000; + + if (!digit_low) + nzeros += 4; + else + digit_h = digit_low; + + if (!(digit_h & 1)) + nzeros += + 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> + (digit_h & 7)); + } + + if (nzeros) { + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128 (CQ, Qh, amount); + } + diff_expon += nzeros; + + } + } + get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode,pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } +#endif + +if (diff_expon >= 0) { +#ifdef IEEE_ROUND_NEAREST + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; +#else +#ifdef IEEE_ROUND_NEAREST_TIES_AWAY + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; +#else + rmode = rnd_mode; + if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + switch (rmode) { + case ROUNDING_TO_NEAREST: // round to nearest code + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_TIES_AWAY: + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + break; + default: // rounding up + CQ.w[0]++; + if (!CQ.w[0]) + CQ.w[1]++; + break; + } +#endif +#endif + +} else { +#ifdef SET_STATUS_FLAGS + if (CA4.w[0] || CA4.w[1]) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#endif + handle_UF_128_rem (&res, sign_x ^ sign_y, diff_expon, CQ, + CA4.w[1] | CA4.w[0], &rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + +} + +get_BID128 (&res, sign_x ^ sign_y, diff_expon, CQ, &rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +BID_RETURN (res); + +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_fma.c b/gcc-4.4.3/libgcc/config/libbid/bid128_fma.c new file mode 100644 index 000000000..016f71cc3 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_fma.c @@ -0,0 +1,4460 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +/***************************************************************************** + * + * BID128 fma x * y + z + * + ****************************************************************************/ + +#include "bid_internal.h" + +static void +rounding_correction (unsigned int rnd_mode, + unsigned int is_inexact_lt_midpoint, + unsigned int is_inexact_gt_midpoint, + unsigned int is_midpoint_lt_even, + unsigned int is_midpoint_gt_even, + int unbexp, + UINT128 * ptrres, _IDEC_flags * ptrfpsf) { + // unbiased true exponent unbexp may be larger than emax + + UINT128 res = *ptrres; // expected to have the correct sign and coefficient + // (the exponent field is ignored, as unbexp is used instead) + UINT64 sign, exp; + UINT64 C_hi, C_lo; + + // general correction from RN to RA, RM, RP, RZ + // Note: if the result is negative, then is_inexact_lt_midpoint, + // is_inexact_gt_midpoint, is_midpoint_lt_even, and is_midpoint_gt_even + // have to be considered as if determined for the absolute value of the + // result (so they seem to be reversed) + + if (is_inexact_lt_midpoint || is_inexact_gt_midpoint || + is_midpoint_lt_even || is_midpoint_gt_even) { + *ptrfpsf |= INEXACT_EXCEPTION; + } + // apply correction to result calculated with unbounded exponent + sign = res.w[1] & MASK_SIGN; + exp = (UINT64) (unbexp + 6176) << 49; // valid only if expmin<=unbexp<=expmax + C_hi = res.w[1] & MASK_COEFF; + C_lo = res.w[0]; + if ((!sign && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) || + ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_UP) && + is_midpoint_gt_even))) || + (sign && ((rnd_mode == ROUNDING_DOWN && is_inexact_lt_midpoint) || + ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_DOWN) && + is_midpoint_gt_even)))) { + // C = C + 1 + C_lo = C_lo + 1; + if (C_lo == 0) + C_hi = C_hi + 1; + if (C_hi == 0x0001ed09bead87c0ull && C_lo == 0x378d8e6400000000ull) { + // C = 10^34 => rounding overflow + C_hi = 0x0000314dc6448d93ull; + C_lo = 0x38c15b0a00000000ull; // 10^33 + // exp = exp + EXP_P1; + unbexp = unbexp + 1; + exp = (UINT64) (unbexp + 6176) << 49; + } + } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) && + ((sign && (rnd_mode == ROUNDING_UP || rnd_mode == ROUNDING_TO_ZERO)) || + (!sign && (rnd_mode == ROUNDING_DOWN || rnd_mode == ROUNDING_TO_ZERO)))) { + // C = C - 1 + C_lo = C_lo - 1; + if (C_lo == 0xffffffffffffffffull) + C_hi--; + // check if we crossed into the lower decade + if (C_hi == 0x0000314dc6448d93ull && C_lo == 0x38c15b09ffffffffull) { + // C = 10^33 - 1 + if (exp > 0) { + C_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 + C_lo = 0x378d8e63ffffffffull; + // exp = exp - EXP_P1; + unbexp = unbexp - 1; + exp = (UINT64) (unbexp + 6176) << 49; + } else { // if exp = 0 + if (is_midpoint_lt_even || is_midpoint_lt_even || + is_inexact_gt_midpoint || is_inexact_gt_midpoint) // tiny & inexact + *ptrfpsf |= UNDERFLOW_EXCEPTION; + } + } + } else { + ; // the result is already correct + } + if (unbexp > expmax) { // 6111 + *ptrfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION); + exp = 0; + if (!sign) { // result is positive + if (rnd_mode == ROUNDING_UP || rnd_mode == ROUNDING_TIES_AWAY) { // +inf + C_hi = 0x7800000000000000ull; + C_lo = 0x0000000000000000ull; + } else { // res = +MAXFP = (10^34-1) * 10^emax + C_hi = 0x5fffed09bead87c0ull; + C_lo = 0x378d8e63ffffffffull; + } + } else { // result is negative + if (rnd_mode == ROUNDING_DOWN || rnd_mode == ROUNDING_TIES_AWAY) { // -inf + C_hi = 0xf800000000000000ull; + C_lo = 0x0000000000000000ull; + } else { // res = -MAXFP = -(10^34-1) * 10^emax + C_hi = 0xdfffed09bead87c0ull; + C_lo = 0x378d8e63ffffffffull; + } + } + } + // assemble the result + res.w[1] = sign | exp | C_hi; + res.w[0] = C_lo; + *ptrres = res; +} + +static void +add256 (UINT256 x, UINT256 y, UINT256 * pz) { + // *z = x + yl assume the sum fits in 256 bits + UINT256 z; + z.w[0] = x.w[0] + y.w[0]; + if (z.w[0] < x.w[0]) { + x.w[1]++; + if (x.w[1] == 0x0000000000000000ull) { + x.w[2]++; + if (x.w[2] == 0x0000000000000000ull) { + x.w[3]++; + } + } + } + z.w[1] = x.w[1] + y.w[1]; + if (z.w[1] < x.w[1]) { + x.w[2]++; + if (x.w[2] == 0x0000000000000000ull) { + x.w[3]++; + } + } + z.w[2] = x.w[2] + y.w[2]; + if (z.w[2] < x.w[2]) { + x.w[3]++; + } + z.w[3] = x.w[3] + y.w[3]; // it was assumed that no carry is possible + *pz = z; +} + +static void +sub256 (UINT256 x, UINT256 y, UINT256 * pz) { + // *z = x - y; assume x >= y + UINT256 z; + z.w[0] = x.w[0] - y.w[0]; + if (z.w[0] > x.w[0]) { + x.w[1]--; + if (x.w[1] == 0xffffffffffffffffull) { + x.w[2]--; + if (x.w[2] == 0xffffffffffffffffull) { + x.w[3]--; + } + } + } + z.w[1] = x.w[1] - y.w[1]; + if (z.w[1] > x.w[1]) { + x.w[2]--; + if (x.w[2] == 0xffffffffffffffffull) { + x.w[3]--; + } + } + z.w[2] = x.w[2] - y.w[2]; + if (z.w[2] > x.w[2]) { + x.w[3]--; + } + z.w[3] = x.w[3] - y.w[3]; // no borrow possible, because x >= y + *pz = z; +} + + +static int +nr_digits256 (UINT256 R256) { + int ind; + // determine the number of decimal digits in R256 + if (R256.w[3] == 0x0 && R256.w[2] == 0x0 && R256.w[1] == 0x0) { + // between 1 and 19 digits + for (ind = 1; ind <= 19; ind++) { + if (R256.w[0] < ten2k64[ind]) { + break; + } + } + // ind digits + } else if (R256.w[3] == 0x0 && R256.w[2] == 0x0 && + (R256.w[1] < ten2k128[0].w[1] || + (R256.w[1] == ten2k128[0].w[1] + && R256.w[0] < ten2k128[0].w[0]))) { + // 20 digits + ind = 20; + } else if (R256.w[3] == 0x0 && R256.w[2] == 0x0) { + // between 21 and 38 digits + for (ind = 1; ind <= 18; ind++) { + if (R256.w[1] < ten2k128[ind].w[1] || + (R256.w[1] == ten2k128[ind].w[1] && + R256.w[0] < ten2k128[ind].w[0])) { + break; + } + } + // ind + 20 digits + ind = ind + 20; + } else if (R256.w[3] == 0x0 && + (R256.w[2] < ten2k256[0].w[2] || + (R256.w[2] == ten2k256[0].w[2] && + R256.w[1] < ten2k256[0].w[1]) || + (R256.w[2] == ten2k256[0].w[2] && + R256.w[1] == ten2k256[0].w[1] && + R256.w[0] < ten2k256[0].w[0]))) { + // 39 digits + ind = 39; + } else { + // between 40 and 68 digits + for (ind = 1; ind <= 29; ind++) { + if (R256.w[3] < ten2k256[ind].w[3] || + (R256.w[3] == ten2k256[ind].w[3] && + R256.w[2] < ten2k256[ind].w[2]) || + (R256.w[3] == ten2k256[ind].w[3] && + R256.w[2] == ten2k256[ind].w[2] && + R256.w[1] < ten2k256[ind].w[1]) || + (R256.w[3] == ten2k256[ind].w[3] && + R256.w[2] == ten2k256[ind].w[2] && + R256.w[1] == ten2k256[ind].w[1] && + R256.w[0] < ten2k256[ind].w[0])) { + break; + } + } + // ind + 39 digits + ind = ind + 39; + } + return (ind); +} + +// add/subtract C4 and C3 * 10^scale; this may follow a previous rounding, so +// use the rounding information from ptr_is_* to avoid a double rounding error +static void +add_and_round (int q3, + int q4, + int e4, + int delta, + int p34, + UINT64 z_sign, + UINT64 p_sign, + UINT128 C3, + UINT256 C4, + int rnd_mode, + int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint, + _IDEC_flags * ptrfpsf, UINT128 * ptrres) { + + int scale; + int x0; + int ind; + UINT64 R64; + UINT128 P128, R128; + UINT192 P192, R192; + UINT256 R256; + int is_midpoint_lt_even = 0; + int is_midpoint_gt_even = 0; + int is_inexact_lt_midpoint = 0; + int is_inexact_gt_midpoint = 0; + int is_midpoint_lt_even0 = 0; + int is_midpoint_gt_even0 = 0; + int is_inexact_lt_midpoint0 = 0; + int is_inexact_gt_midpoint0 = 0; + int incr_exp = 0; + int is_tiny = 0; + int lt_half_ulp = 0; + int eq_half_ulp = 0; + // int gt_half_ulp = 0; + UINT128 res = *ptrres; + + // scale C3 up by 10^(q4-delta-q3), 0 <= q4-delta-q3 <= 2*P34-2 = 66 + scale = q4 - delta - q3; // 0 <= scale <= 66 (or 0 <= scale <= 68 if this + // comes from Cases (2), (3), (4), (5), (6), with 0 <= |delta| <= 1 + + // calculate C3 * 10^scale in R256 (it has at most 67 decimal digits for + // Cases (15),(16),(17) and at most 69 for Cases (2),(3),(4),(5),(6)) + if (scale == 0) { + R256.w[3] = 0x0ull; + R256.w[2] = 0x0ull; + R256.w[1] = C3.w[1]; + R256.w[0] = C3.w[0]; + } else if (scale <= 19) { // 10^scale fits in 64 bits + P128.w[1] = 0; + P128.w[0] = ten2k64[scale]; + __mul_128x128_to_256 (R256, P128, C3); + } else if (scale <= 38) { // 10^scale fits in 128 bits + __mul_128x128_to_256 (R256, ten2k128[scale - 20], C3); + } else if (scale <= 57) { // 39 <= scale <= 57 + // 10^scale fits in 192 bits but C3 * 10^scale fits in 223 or 230 bits + // (10^67 has 223 bits; 10^69 has 230 bits); + // must split the computation: + // 10^scale * C3 = 10*38 * 10^(scale-38) * C3 where 10^38 takes 127 + // bits and so 10^(scale-38) * C3 fits in 128 bits with certainty + // Note that 1 <= scale - 38 <= 19 => 10^(scale-38) fits in 64 bits + __mul_64x128_to_128 (R128, ten2k64[scale - 38], C3); + // now multiply R128 by 10^38 + __mul_128x128_to_256 (R256, R128, ten2k128[18]); + } else { // 58 <= scale <= 66 + // 10^scale takes between 193 and 220 bits, + // and C3 * 10^scale fits in 223 bits (10^67/10^69 has 223/230 bits) + // must split the computation: + // 10^scale * C3 = 10*38 * 10^(scale-38) * C3 where 10^38 takes 127 + // bits and so 10^(scale-38) * C3 fits in 128 bits with certainty + // Note that 20 <= scale - 38 <= 30 => 10^(scale-38) fits in 128 bits + // Calculate first 10^(scale-38) * C3, which fits in 128 bits; because + // 10^(scale-38) takes more than 64 bits, C3 will take less than 64 + __mul_64x128_to_128 (R128, C3.w[0], ten2k128[scale - 58]); + // now calculate 10*38 * 10^(scale-38) * C3 + __mul_128x128_to_256 (R256, R128, ten2k128[18]); + } + // C3 * 10^scale is now in R256 + + // for Cases (15), (16), (17) C4 > C3 * 10^scale because C4 has at least + // one extra digit; for Cases (2), (3), (4), (5), or (6) any order is + // possible + // add/subtract C4 and C3 * 10^scale; the exponent is e4 + if (p_sign == z_sign) { // R256 = C4 + R256 + // calculate R256 = C4 + C3 * 10^scale = C4 + R256 which is exact, + // but may require rounding + add256 (C4, R256, &R256); + } else { // if (p_sign != z_sign) { // R256 = C4 - R256 + // calculate R256 = C4 - C3 * 10^scale = C4 - R256 or + // R256 = C3 * 10^scale - C4 = R256 - C4 which is exact, + // but may require rounding + + // compare first R256 = C3 * 10^scale and C4 + if (R256.w[3] > C4.w[3] || (R256.w[3] == C4.w[3] && R256.w[2] > C4.w[2]) || + (R256.w[3] == C4.w[3] && R256.w[2] == C4.w[2] && R256.w[1] > C4.w[1]) || + (R256.w[3] == C4.w[3] && R256.w[2] == C4.w[2] && R256.w[1] == C4.w[1] && + R256.w[0] >= C4.w[0])) { // C3 * 10^scale >= C4 + // calculate R256 = C3 * 10^scale - C4 = R256 - C4, which is exact, + // but may require rounding + sub256 (R256, C4, &R256); + // flip p_sign too, because the result has the sign of z + p_sign = z_sign; + } else { // if C4 > C3 * 10^scale + // calculate R256 = C4 - C3 * 10^scale = C4 - R256, which is exact, + // but may require rounding + sub256 (C4, R256, &R256); + } + // if the result is pure zero, the sign depends on the rounding mode + // (x*y and z had opposite signs) + if (R256.w[3] == 0x0ull && R256.w[2] == 0x0ull && + R256.w[1] == 0x0ull && R256.w[0] == 0x0ull) { + if (rnd_mode != ROUNDING_DOWN) + p_sign = 0x0000000000000000ull; + else + p_sign = 0x8000000000000000ull; + // the exponent is max (e4, expmin) + if (e4 < -6176) + e4 = expmin; + // assemble result + res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49); + res.w[0] = 0x0; + *ptrres = res; + return; + } + } + + // determine the number of decimal digits in R256 + ind = nr_digits256 (R256); + + // the exact result is (-1)^p_sign * R256 * 10^e4 where q (R256) = ind; + // round to the destination precision, with unbounded exponent + + if (ind <= p34) { + // result rounded to the destination precision with unbounded exponent + // is exact + if (ind + e4 < p34 + expmin) { + is_tiny = 1; // applies to all rounding modes + } + res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | R256.w[1]; + res.w[0] = R256.w[0]; + // Note: res is correct only if expmin <= e4 <= expmax + } else { // if (ind > p34) + // if more than P digits, round to nearest to P digits + // round R256 to p34 digits + x0 = ind - p34; // 1 <= x0 <= 34 as 35 <= ind <= 68 + if (ind <= 38) { + P128.w[1] = R256.w[1]; + P128.w[0] = R256.w[0]; + round128_19_38 (ind, x0, P128, &R128, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint); + } else if (ind <= 57) { + P192.w[2] = R256.w[2]; + P192.w[1] = R256.w[1]; + P192.w[0] = R256.w[0]; + round192_39_57 (ind, x0, P192, &R192, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint); + R128.w[1] = R192.w[1]; + R128.w[0] = R192.w[0]; + } else { // if (ind <= 68) + round256_58_76 (ind, x0, R256, &R256, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint); + R128.w[1] = R256.w[1]; + R128.w[0] = R256.w[0]; + } + // the rounded result has p34 = 34 digits + e4 = e4 + x0 + incr_exp; + if (rnd_mode == ROUNDING_TO_NEAREST) { + if (e4 < expmin) { + is_tiny = 1; // for other rounding modes apply correction + } + } else { + // for RM, RP, RZ, RA apply correction in order to determine tininess + // but do not save the result; apply the correction to + // (-1)^p_sign * significand * 10^0 + P128.w[1] = p_sign | 0x3040000000000000ull | R128.w[1]; + P128.w[0] = R128.w[0]; + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, is_midpoint_lt_even, + is_midpoint_gt_even, 0, &P128, ptrfpsf); + scale = ((P128.w[1] & MASK_EXP) >> 49) - 6176; // -1, 0, or +1 + // the number of digits in the significand is p34 = 34 + if (e4 + scale < expmin) { + is_tiny = 1; + } + } + ind = p34; // the number of decimal digits in the signifcand of res + res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | R128.w[1]; // RN + res.w[0] = R128.w[0]; + // Note: res is correct only if expmin <= e4 <= expmax + // set the inexact flag after rounding with bounded exponent, if any + } + // at this point we have the result rounded with unbounded exponent in + // res and we know its tininess: + // res = (-1)^p_sign * significand * 10^e4, + // where q (significand) = ind <= p34 + // Note: res is correct only if expmin <= e4 <= expmax + + // check for overflow if RN + if (rnd_mode == ROUNDING_TO_NEAREST && (ind + e4) > (p34 + expmax)) { + res.w[1] = p_sign | 0x7800000000000000ull; + res.w[0] = 0x0000000000000000ull; + *ptrres = res; + *ptrfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION); + return; // BID_RETURN (res) + } // else not overflow or not RN, so continue + + // if (e4 >= expmin) we have the result rounded with bounded exponent + if (e4 < expmin) { + x0 = expmin - e4; // x0 >= 1; the number of digits to chop off of res + // where the result rounded [at most] once is + // (-1)^p_sign * significand_res * 10^e4 + + // avoid double rounding error + is_inexact_lt_midpoint0 = is_inexact_lt_midpoint; + is_inexact_gt_midpoint0 = is_inexact_gt_midpoint; + is_midpoint_lt_even0 = is_midpoint_lt_even; + is_midpoint_gt_even0 = is_midpoint_gt_even; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + + if (x0 > ind) { + // nothing is left of res when moving the decimal point left x0 digits + is_inexact_lt_midpoint = 1; + res.w[1] = p_sign | 0x0000000000000000ull; + res.w[0] = 0x0000000000000000ull; + e4 = expmin; + } else if (x0 == ind) { // 1 <= x0 = ind <= p34 = 34 + // this is <, =, or > 1/2 ulp + // compare the ind-digit value in the significand of res with + // 1/2 ulp = 5*10^(ind-1), i.e. determine whether it is + // less than, equal to, or greater than 1/2 ulp (significand of res) + R128.w[1] = res.w[1] & MASK_COEFF; + R128.w[0] = res.w[0]; + if (ind <= 19) { + if (R128.w[0] < midpoint64[ind - 1]) { // < 1/2 ulp + lt_half_ulp = 1; + is_inexact_lt_midpoint = 1; + } else if (R128.w[0] == midpoint64[ind - 1]) { // = 1/2 ulp + eq_half_ulp = 1; + is_midpoint_gt_even = 1; + } else { // > 1/2 ulp + // gt_half_ulp = 1; + is_inexact_gt_midpoint = 1; + } + } else { // if (ind <= 38) { + if (R128.w[1] < midpoint128[ind - 20].w[1] || + (R128.w[1] == midpoint128[ind - 20].w[1] && + R128.w[0] < midpoint128[ind - 20].w[0])) { // < 1/2 ulp + lt_half_ulp = 1; + is_inexact_lt_midpoint = 1; + } else if (R128.w[1] == midpoint128[ind - 20].w[1] && + R128.w[0] == midpoint128[ind - 20].w[0]) { // = 1/2 ulp + eq_half_ulp = 1; + is_midpoint_gt_even = 1; + } else { // > 1/2 ulp + // gt_half_ulp = 1; + is_inexact_gt_midpoint = 1; + } + } + if (lt_half_ulp || eq_half_ulp) { + // res = +0.0 * 10^expmin + res.w[1] = 0x0000000000000000ull; + res.w[0] = 0x0000000000000000ull; + } else { // if (gt_half_ulp) + // res = +1 * 10^expmin + res.w[1] = 0x0000000000000000ull; + res.w[0] = 0x0000000000000001ull; + } + res.w[1] = p_sign | res.w[1]; + e4 = expmin; + } else { // if (1 <= x0 <= ind - 1 <= 33) + // round the ind-digit result to ind - x0 digits + + if (ind <= 18) { // 2 <= ind <= 18 + round64_2_18 (ind, x0, res.w[0], &R64, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint); + res.w[1] = 0x0; + res.w[0] = R64; + } else if (ind <= 38) { + P128.w[1] = res.w[1] & MASK_COEFF; + P128.w[0] = res.w[0]; + round128_19_38 (ind, x0, P128, &res, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + } + e4 = e4 + x0; // expmin + // we want the exponent to be expmin, so if incr_exp = 1 then + // multiply the rounded result by 10 - it will still fit in 113 bits + if (incr_exp) { + // 64 x 128 -> 128 + P128.w[1] = res.w[1] & MASK_COEFF; + P128.w[0] = res.w[0]; + __mul_64x128_to_128 (res, ten2k64[1], P128); + } + res.w[1] = + p_sign | ((UINT64) (e4 + 6176) << 49) | (res.w[1] & MASK_COEFF); + // avoid a double rounding error + if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && + is_midpoint_lt_even) { // double rounding error upward + // res = res - 1 + res.w[0]--; + if (res.w[0] == 0xffffffffffffffffull) + res.w[1]--; + // Note: a double rounding error upward is not possible; for this + // the result after the first rounding would have to be 99...95 + // (35 digits in all), possibly followed by a number of zeros; this + // is not possible in Cases (2)-(6) or (15)-(17) which may get here + is_midpoint_lt_even = 0; + is_inexact_lt_midpoint = 1; + } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && + is_midpoint_gt_even) { // double rounding error downward + // res = res + 1 + res.w[0]++; + if (res.w[0] == 0) + res.w[1]++; + is_midpoint_gt_even = 0; + is_inexact_gt_midpoint = 1; + } else if (!is_midpoint_lt_even && !is_midpoint_gt_even && + !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) { + // if this second rounding was exact the result may still be + // inexact because of the first rounding + if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) { + is_inexact_gt_midpoint = 1; + } + if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) { + is_inexact_lt_midpoint = 1; + } + } else if (is_midpoint_gt_even && + (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) { + // pulled up to a midpoint + is_inexact_lt_midpoint = 1; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else if (is_midpoint_lt_even && + (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) { + // pulled down to a midpoint + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 1; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else { + ; + } + } + } + // res contains the correct result + // apply correction if not rounding to nearest + if (rnd_mode != ROUNDING_TO_NEAREST) { + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, is_inexact_gt_midpoint, + is_midpoint_lt_even, is_midpoint_gt_even, + e4, &res, ptrfpsf); + } + if (is_midpoint_lt_even || is_midpoint_gt_even || + is_inexact_lt_midpoint || is_inexact_gt_midpoint) { + // set the inexact flag + *ptrfpsf |= INEXACT_EXCEPTION; + if (is_tiny) + *ptrfpsf |= UNDERFLOW_EXCEPTION; + } + + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + *ptrres = res; + return; +} + + +#if DECIMAL_CALL_BY_REFERENCE +static void +bid128_ext_fma (int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint, UINT128 * pres, + UINT128 * px, UINT128 * py, + UINT128 * + pz _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px, y = *py, z = *pz; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +static UINT128 +bid128_ext_fma (int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint, UINT128 x, UINT128 y, + UINT128 z _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; + UINT64 x_sign, y_sign, z_sign, p_sign, tmp_sign; + UINT64 x_exp = 0, y_exp = 0, z_exp = 0, p_exp; + int true_p_exp; + UINT128 C1, C2, C3; + UINT256 C4; + int q1 = 0, q2 = 0, q3 = 0, q4; + int e1, e2, e3, e4; + int scale, ind, delta, x0; + int p34 = P34; // used to modify the limit on the number of digits + BID_UI64DOUBLE tmp; + int x_nr_bits, y_nr_bits, z_nr_bits; + unsigned int save_fpsf; + int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0; + int is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; + int is_midpoint_lt_even0 = 0, is_midpoint_gt_even0 = 0; + int is_inexact_lt_midpoint0 = 0, is_inexact_gt_midpoint0 = 0; + int incr_exp = 0; + int lsb; + int lt_half_ulp = 0; + int eq_half_ulp = 0; + int gt_half_ulp = 0; + int is_tiny = 0; + UINT64 R64, tmp64; + UINT128 P128, R128; + UINT192 P192, R192; + UINT256 R256; + + // the following are based on the table of special cases for fma; the NaN + // behavior is similar to that of the IA-64 Architecture fma + + // identify cases where at least one operand is NaN + + BID_SWAP128 (x); + BID_SWAP128 (y); + BID_SWAP128 (z); + if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN + // if x = {0, f, inf, NaN}, y = NaN, z = {0, f, inf, NaN} then res = Q (y) + // check first for non-canonical NaN payload + if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (y.w[0] > 0x38c15b09ffffffffull))) { + y.w[1] = y.w[1] & 0xffffc00000000000ull; + y.w[0] = 0x0ull; + } + if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (y) + res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] + res.w[0] = y.w[0]; + } else { // y is QNaN + // return y + res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] + res.w[0] = y.w[0]; + // if z = SNaN or x = SNaN signal invalid exception + if ((z.w[1] & MASK_SNAN) == MASK_SNAN || + (x.w[1] & MASK_SNAN) == MASK_SNAN) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + } + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } else if ((z.w[1] & MASK_NAN) == MASK_NAN) { // z is NAN + // if x = {0, f, inf, NaN}, y = {0, f, inf}, z = NaN then res = Q (z) + // check first for non-canonical NaN payload + if (((z.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((z.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (z.w[0] > 0x38c15b09ffffffffull))) { + z.w[1] = z.w[1] & 0xffffc00000000000ull; + z.w[0] = 0x0ull; + } + if ((z.w[1] & MASK_SNAN) == MASK_SNAN) { // z is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (z) + res.w[1] = z.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] + res.w[0] = z.w[0]; + } else { // z is QNaN + // return z + res.w[1] = z.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] + res.w[0] = z.w[0]; + // if x = SNaN signal invalid exception + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + } + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } else if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + // if x = NaN, y = {0, f, inf}, z = {0, f, inf} then res = Q (x) + // check first for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] + res.w[0] = x.w[0]; + } else { // x is QNaN + // return x + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] + res.w[0] = x.w[0]; + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } + // x, y, z are 0, f, or inf but not NaN => unpack the arguments and check + // for non-canonical values + + x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + if ((x.w[1] & MASK_ANY_INF) != MASK_INF) { // x != inf + // if x is not infinity check for non-canonical values - treated as zero + if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + // non-canonical + x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C1.w[1] = 0; // significand high + C1.w[0] = 0; // significand low + } else { // G0_G1 != 11 + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C1.w[1] > 0x0001ed09bead87c0ull || + (C1.w[1] == 0x0001ed09bead87c0ull && + C1.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + C1.w[1] = 0; + C1.w[0] = 0; + } else { // canonical + ; + } + } + } + y_sign = y.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + C2.w[1] = y.w[1] & MASK_COEFF; + C2.w[0] = y.w[0]; + if ((y.w[1] & MASK_ANY_INF) != MASK_INF) { // y != inf + // if y is not infinity check for non-canonical values - treated as zero + if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + // non-canonical + y_exp = (y.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C2.w[1] = 0; // significand high + C2.w[0] = 0; // significand low + } else { // G0_G1 != 11 + y_exp = y.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C2.w[1] > 0x0001ed09bead87c0ull || + (C2.w[1] == 0x0001ed09bead87c0ull && + C2.w[0] > 0x378d8e63ffffffffull)) { + // y is non-canonical if coefficient is larger than 10^34 -1 + C2.w[1] = 0; + C2.w[0] = 0; + } else { // canonical + ; + } + } + } + z_sign = z.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + C3.w[1] = z.w[1] & MASK_COEFF; + C3.w[0] = z.w[0]; + if ((z.w[1] & MASK_ANY_INF) != MASK_INF) { // z != inf + // if z is not infinity check for non-canonical values - treated as zero + if ((z.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + // non-canonical + z_exp = (z.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C3.w[1] = 0; // significand high + C3.w[0] = 0; // significand low + } else { // G0_G1 != 11 + z_exp = z.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C3.w[1] > 0x0001ed09bead87c0ull || + (C3.w[1] == 0x0001ed09bead87c0ull && + C3.w[0] > 0x378d8e63ffffffffull)) { + // z is non-canonical if coefficient is larger than 10^34 -1 + C3.w[1] = 0; + C3.w[0] = 0; + } else { // canonical + ; + } + } + } + + p_sign = x_sign ^ y_sign; // sign of the product + + // identify cases where at least one operand is infinity + + if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf + if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf + if ((z.w[1] & MASK_ANY_INF) == MASK_INF) { // z = inf + if (p_sign == z_sign) { + res.w[1] = z_sign | MASK_INF; + res.w[0] = 0x0; + } else { + // return QNaN Indefinite + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0x0000000000000000ull; + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + } + } else { // z = 0 or z = f + res.w[1] = p_sign | MASK_INF; + res.w[0] = 0x0; + } + } else if (C2.w[1] != 0 || C2.w[0] != 0) { // y = f + if ((z.w[1] & MASK_ANY_INF) == MASK_INF) { // z = inf + if (p_sign == z_sign) { + res.w[1] = z_sign | MASK_INF; + res.w[0] = 0x0; + } else { + // return QNaN Indefinite + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0x0000000000000000ull; + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + } + } else { // z = 0 or z = f + res.w[1] = p_sign | MASK_INF; + res.w[0] = 0x0; + } + } else { // y = 0 + // return QNaN Indefinite + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0x0000000000000000ull; + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf + if ((z.w[1] & MASK_ANY_INF) == MASK_INF) { // z = inf + // x = f, necessarily + if ((p_sign != z_sign) + || (C1.w[1] == 0x0ull && C1.w[0] == 0x0ull)) { + // return QNaN Indefinite + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0x0000000000000000ull; + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + } else { + res.w[1] = z_sign | MASK_INF; + res.w[0] = 0x0; + } + } else if (C1.w[1] == 0x0 && C1.w[0] == 0x0) { // x = 0 + // z = 0, f, inf + // return QNaN Indefinite + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0x0000000000000000ull; + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + } else { + // x = f and z = 0, f, necessarily + res.w[1] = p_sign | MASK_INF; + res.w[0] = 0x0; + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } else if ((z.w[1] & MASK_ANY_INF) == MASK_INF) { // z = inf + // x = 0, f and y = 0, f, necessarily + res.w[1] = z_sign | MASK_INF; + res.w[0] = 0x0; + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } + + true_p_exp = (x_exp >> 49) - 6176 + (y_exp >> 49) - 6176; + if (true_p_exp < -6176) + p_exp = 0; // cannot be less than EXP_MIN + else + p_exp = (UINT64) (true_p_exp + 6176) << 49; + + if (((C1.w[1] == 0x0 && C1.w[0] == 0x0) || (C2.w[1] == 0x0 && C2.w[0] == 0x0)) && C3.w[1] == 0x0 && C3.w[0] == 0x0) { // (x = 0 or y = 0) and z = 0 + // the result is 0 + if (p_exp < z_exp) + res.w[1] = p_exp; // preferred exponent + else + res.w[1] = z_exp; // preferred exponent + if (p_sign == z_sign) { + res.w[1] |= z_sign; + res.w[0] = 0x0; + } else { // x * y and z have opposite signs + if (rnd_mode == ROUNDING_DOWN) { + // res = -0.0 + res.w[1] |= MASK_SIGN; + res.w[0] = 0x0; + } else { + // res = +0.0 + // res.w[1] |= 0x0; + res.w[0] = 0x0; + } + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } + // from this point on, we may need to know the number of decimal digits + // in the significands of x, y, z when x, y, z != 0 + + if (C1.w[1] != 0 || C1.w[0] != 0) { // x = f (non-zero finite) + // q1 = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q1 = nr_digits[x_nr_bits - 1].digits; + if (q1 == 0) { + q1 = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi || + (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi && + C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q1++; + } + } + + if (C2.w[1] != 0 || C2.w[0] != 0) { // y = f (non-zero finite) + if (C2.w[1] == 0) { + if (C2.w[0] >= 0x0020000000000000ull) { // y >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C2.w[0] >= 0x0000000100000000ull) { // y >= 2^32 + tmp.d = (double) (C2.w[0] >> 32); // exact conversion + y_nr_bits = + 32 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // y < 2^32 + tmp.d = (double) C2.w[0]; // exact conversion + y_nr_bits = + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if y < 2^53 + tmp.d = (double) C2.w[0]; // exact conversion + y_nr_bits = + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C2.w[1] != 0 => nr. bits = 64 + nr_bits (C2.w[1]) + tmp.d = (double) C2.w[1]; // exact conversion + y_nr_bits = + 64 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + + q2 = nr_digits[y_nr_bits].digits; + if (q2 == 0) { + q2 = nr_digits[y_nr_bits].digits1; + if (C2.w[1] > nr_digits[y_nr_bits].threshold_hi || + (C2.w[1] == nr_digits[y_nr_bits].threshold_hi && + C2.w[0] >= nr_digits[y_nr_bits].threshold_lo)) + q2++; + } + } + + if (C3.w[1] != 0 || C3.w[0] != 0) { // z = f (non-zero finite) + if (C3.w[1] == 0) { + if (C3.w[0] >= 0x0020000000000000ull) { // z >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C3.w[0] >= 0x0000000100000000ull) { // z >= 2^32 + tmp.d = (double) (C3.w[0] >> 32); // exact conversion + z_nr_bits = + 32 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // z < 2^32 + tmp.d = (double) C3.w[0]; // exact conversion + z_nr_bits = + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if z < 2^53 + tmp.d = (double) C3.w[0]; // exact conversion + z_nr_bits = + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C3.w[1] != 0 => nr. bits = 64 + nr_bits (C3.w[1]) + tmp.d = (double) C3.w[1]; // exact conversion + z_nr_bits = + 64 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + + q3 = nr_digits[z_nr_bits].digits; + if (q3 == 0) { + q3 = nr_digits[z_nr_bits].digits1; + if (C3.w[1] > nr_digits[z_nr_bits].threshold_hi || + (C3.w[1] == nr_digits[z_nr_bits].threshold_hi && + C3.w[0] >= nr_digits[z_nr_bits].threshold_lo)) + q3++; + } + } + + if ((C1.w[1] == 0x0 && C1.w[0] == 0x0) || + (C2.w[1] == 0x0 && C2.w[0] == 0x0)) { + // x = 0 or y = 0 + // z = f, necessarily; for 0 + z return z, with the preferred exponent + // the result is z, but need to get the preferred exponent + if (z_exp <= p_exp) { // the preferred exponent is z_exp + res.w[1] = z_sign | (z_exp & MASK_EXP) | C3.w[1]; + res.w[0] = C3.w[0]; + } else { // if (p_exp < z_exp) the preferred exponent is p_exp + // return (C3 * 10^scale) * 10^(z_exp - scale) + // where scale = min (p34-q3, (z_exp-p_exp) >> 49) + scale = p34 - q3; + ind = (z_exp - p_exp) >> 49; + if (ind < scale) + scale = ind; + if (scale == 0) { + res.w[1] = z.w[1]; // & MASK_COEFF, which is redundant + res.w[0] = z.w[0]; + } else if (q3 <= 19) { // z fits in 64 bits + if (scale <= 19) { // 10^scale fits in 64 bits + // 64 x 64 C3.w[0] * ten2k64[scale] + __mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]); + } else { // 10^scale fits in 128 bits + // 64 x 128 C3.w[0] * ten2k128[scale - 20] + __mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]); + } + } else { // z fits in 128 bits, but 10^scale must fit in 64 bits + // 64 x 128 ten2k64[scale] * C3 + __mul_128x64_to_128 (res, ten2k64[scale], C3); + } + // subtract scale from the exponent + z_exp = z_exp - ((UINT64) scale << 49); + res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1]; + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } else { + ; // continue with x = f, y = f, z = 0 or x = f, y = f, z = f + } + + e1 = (x_exp >> 49) - 6176; // unbiased exponent of x + e2 = (y_exp >> 49) - 6176; // unbiased exponent of y + e3 = (z_exp >> 49) - 6176; // unbiased exponent of z + e4 = e1 + e2; // unbiased exponent of the exact x * y + + // calculate C1 * C2 and its number of decimal digits, q4 + + // the exact product has either q1 + q2 - 1 or q1 + q2 decimal digits + // where 2 <= q1 + q2 <= 68 + // calculate C4 = C1 * C2 and determine q + C4.w[3] = C4.w[2] = C4.w[1] = C4.w[0] = 0; + if (q1 + q2 <= 19) { // if 2 <= q1 + q2 <= 19, C4 = C1 * C2 fits in 64 bits + C4.w[0] = C1.w[0] * C2.w[0]; + // if C4 < 10^(q1+q2-1) then q4 = q1 + q2 - 1 else q4 = q1 + q2 + if (C4.w[0] < ten2k64[q1 + q2 - 1]) + q4 = q1 + q2 - 1; // q4 in [1, 18] + else + q4 = q1 + q2; // q4 in [2, 19] + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 64; + } else if (q1 + q2 == 20) { // C4 = C1 * C2 fits in 64 or 128 bits + // q1 <= 19 and q2 <= 19 so both C1 and C2 fit in 64 bits + __mul_64x64_to_128MACH (C4, C1.w[0], C2.w[0]); + // if C4 < 10^(q1+q2-1) = 10^19 then q4 = q1+q2-1 = 19 else q4 = q1+q2 = 20 + if (C4.w[1] == 0 && C4.w[0] < ten2k64[19]) { // 19 = q1+q2-1 + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 64; + q4 = 19; // 19 = q1 + q2 - 1 + } else { + // if (C4.w[1] == 0) + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 64; + // else + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 128; + q4 = 20; // 20 = q1 + q2 + } + } else if (q1 + q2 <= 38) { // 21 <= q1 + q2 <= 38 + // C4 = C1 * C2 fits in 64 or 128 bits + // (64 bits possibly, but only when q1 + q2 = 21 and C4 has 20 digits) + // at least one of C1, C2 has at most 19 decimal digits & fits in 64 bits + if (q1 <= 19) { + __mul_128x64_to_128 (C4, C1.w[0], C2); + } else { // q2 <= 19 + __mul_128x64_to_128 (C4, C2.w[0], C1); + } + // if C4 < 10^(q1+q2-1) then q4 = q1 + q2 - 1 else q4 = q1 + q2 + if (C4.w[1] < ten2k128[q1 + q2 - 21].w[1] || + (C4.w[1] == ten2k128[q1 + q2 - 21].w[1] && + C4.w[0] < ten2k128[q1 + q2 - 21].w[0])) { + // if (C4.w[1] == 0) // q4 = 20, necessarily + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 64; + // else + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 128; + q4 = q1 + q2 - 1; // q4 in [20, 37] + } else { + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 128; + q4 = q1 + q2; // q4 in [21, 38] + } + } else if (q1 + q2 == 39) { // C4 = C1 * C2 fits in 128 or 192 bits + // both C1 and C2 fit in 128 bits (actually in 113 bits) + // may replace this by 128x128_to192 + __mul_128x128_to_256 (C4, C1, C2); // C4.w[3] is 0 + // if C4 < 10^(q1+q2-1) = 10^38 then q4 = q1+q2-1 = 38 else q4 = q1+q2 = 39 + if (C4.w[2] == 0 && (C4.w[1] < ten2k128[18].w[1] || + (C4.w[1] == ten2k128[18].w[1] + && C4.w[0] < ten2k128[18].w[0]))) { + // 18 = 38 - 20 = q1+q2-1 - 20 + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 128; + q4 = 38; // 38 = q1 + q2 - 1 + } else { + // if (C4.w[2] == 0) + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 128; + // else + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 192; + q4 = 39; // 39 = q1 + q2 + } + } else if (q1 + q2 <= 57) { // 40 <= q1 + q2 <= 57 + // C4 = C1 * C2 fits in 128 or 192 bits + // (128 bits possibly, but only when q1 + q2 = 40 and C4 has 39 digits) + // both C1 and C2 fit in 128 bits (actually in 113 bits); at most one + // may fit in 64 bits + if (C1.w[1] == 0) { // C1 fits in 64 bits + // __mul_64x128_full (REShi64, RESlo128, A64, B128) + __mul_64x128_full (C4.w[2], C4, C1.w[0], C2); + } else if (C2.w[1] == 0) { // C2 fits in 64 bits + // __mul_64x128_full (REShi64, RESlo128, A64, B128) + __mul_64x128_full (C4.w[2], C4, C2.w[0], C1); + } else { // both C1 and C2 require 128 bits + // may use __mul_128x128_to_192 (C4.w[2], C4.w[0], C2.w[0], C1); + __mul_128x128_to_256 (C4, C1, C2); // C4.w[3] = 0 + } + // if C4 < 10^(q1+q2-1) then q4 = q1 + q2 - 1 else q4 = q1 + q2 + if (C4.w[2] < ten2k256[q1 + q2 - 40].w[2] || + (C4.w[2] == ten2k256[q1 + q2 - 40].w[2] && + (C4.w[1] < ten2k256[q1 + q2 - 40].w[1] || + (C4.w[1] == ten2k256[q1 + q2 - 40].w[1] && + C4.w[0] < ten2k256[q1 + q2 - 40].w[0])))) { + // if (C4.w[2] == 0) // q4 = 39, necessarily + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 128; + // else + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 192; + q4 = q1 + q2 - 1; // q4 in [39, 56] + } else { + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 192; + q4 = q1 + q2; // q4 in [40, 57] + } + } else if (q1 + q2 == 58) { // C4 = C1 * C2 fits in 192 or 256 bits + // both C1 and C2 fit in 128 bits (actually in 113 bits); at most one + // may fit in 64 bits + if (C1.w[1] == 0) { // C1 * C2 will fit in 192 bits + __mul_64x128_full (C4.w[2], C4, C1.w[0], C2); // may use 64x128_to_192 + } else if (C2.w[1] == 0) { // C1 * C2 will fit in 192 bits + __mul_64x128_full (C4.w[2], C4, C2.w[0], C1); // may use 64x128_to_192 + } else { // C1 * C2 will fit in 192 bits or in 256 bits + __mul_128x128_to_256 (C4, C1, C2); + } + // if C4 < 10^(q1+q2-1) = 10^57 then q4 = q1+q2-1 = 57 else q4 = q1+q2 = 58 + if (C4.w[3] == 0 && (C4.w[2] < ten2k256[18].w[2] || + (C4.w[2] == ten2k256[18].w[2] + && (C4.w[1] < ten2k256[18].w[1] + || (C4.w[1] == ten2k256[18].w[1] + && C4.w[0] < ten2k256[18].w[0]))))) { + // 18 = 57 - 39 = q1+q2-1 - 39 + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 192; + q4 = 57; // 57 = q1 + q2 - 1 + } else { + // if (C4.w[3] == 0) + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 192; + // else + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 256; + q4 = 58; // 58 = q1 + q2 + } + } else { // if 59 <= q1 + q2 <= 68 + // C4 = C1 * C2 fits in 192 or 256 bits + // (192 bits possibly, but only when q1 + q2 = 59 and C4 has 58 digits) + // both C1 and C2 fit in 128 bits (actually in 113 bits); none fits in + // 64 bits + // may use __mul_128x128_to_192 (C4.w[2], C4.w[0], C2.w[0], C1); + __mul_128x128_to_256 (C4, C1, C2); // C4.w[3] = 0 + // if C4 < 10^(q1+q2-1) then q4 = q1 + q2 - 1 else q4 = q1 + q2 + if (C4.w[3] < ten2k256[q1 + q2 - 40].w[3] || + (C4.w[3] == ten2k256[q1 + q2 - 40].w[3] && + (C4.w[2] < ten2k256[q1 + q2 - 40].w[2] || + (C4.w[2] == ten2k256[q1 + q2 - 40].w[2] && + (C4.w[1] < ten2k256[q1 + q2 - 40].w[1] || + (C4.w[1] == ten2k256[q1 + q2 - 40].w[1] && + C4.w[0] < ten2k256[q1 + q2 - 40].w[0])))))) { + // if (C4.w[3] == 0) // q4 = 58, necessarily + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 192; + // else + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 256; + q4 = q1 + q2 - 1; // q4 in [58, 67] + } else { + // length of C1 * C2 rounded up to a multiple of 64 bits is len = 256; + q4 = q1 + q2; // q4 in [59, 68] + } + } + + if (C3.w[1] == 0x0 && C3.w[0] == 0x0) { // x = f, y = f, z = 0 + save_fpsf = *pfpsf; // sticky bits - caller value must be preserved + *pfpsf = 0; + + if (q4 > p34) { + + // truncate C4 to p34 digits into res + // x = q4-p34, 1 <= x <= 34 because 35 <= q4 <= 68 + x0 = q4 - p34; + if (q4 <= 38) { + P128.w[1] = C4.w[1]; + P128.w[0] = C4.w[0]; + round128_19_38 (q4, x0, P128, &res, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + } else if (q4 <= 57) { // 35 <= q4 <= 57 + P192.w[2] = C4.w[2]; + P192.w[1] = C4.w[1]; + P192.w[0] = C4.w[0]; + round192_39_57 (q4, x0, P192, &R192, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + res.w[0] = R192.w[0]; + res.w[1] = R192.w[1]; + } else { // if (q4 <= 68) + round256_58_76 (q4, x0, C4, &R256, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + res.w[0] = R256.w[0]; + res.w[1] = R256.w[1]; + } + e4 = e4 + x0; + if (incr_exp) { + e4 = e4 + 1; + } + q4 = p34; + // res is now the coefficient of the result rounded to the destination + // precision, with unbounded exponent; the exponent is e4; q4=digits(res) + } else { // if (q4 <= p34) + // C4 * 10^e4 is the result rounded to the destination precision, with + // unbounded exponent (which is exact) + + if ((q4 + e4 <= p34 + expmax) && (e4 > expmax)) { + // e4 is too large, but can be brought within range by scaling up C4 + scale = e4 - expmax; // 1 <= scale < P-q4 <= P-1 => 1 <= scale <= P-2 + // res = (C4 * 10^scale) * 10^expmax + if (q4 <= 19) { // C4 fits in 64 bits + if (scale <= 19) { // 10^scale fits in 64 bits + // 64 x 64 C4.w[0] * ten2k64[scale] + __mul_64x64_to_128MACH (res, C4.w[0], ten2k64[scale]); + } else { // 10^scale fits in 128 bits + // 64 x 128 C4.w[0] * ten2k128[scale - 20] + __mul_128x64_to_128 (res, C4.w[0], ten2k128[scale - 20]); + } + } else { // C4 fits in 128 bits, but 10^scale must fit in 64 bits + // 64 x 128 ten2k64[scale] * CC43 + __mul_128x64_to_128 (res, ten2k64[scale], C4); + } + e4 = e4 - scale; // expmax + q4 = q4 + scale; + } else { + res.w[1] = C4.w[1]; + res.w[0] = C4.w[0]; + } + // res is the coefficient of the result rounded to the destination + // precision, with unbounded exponent (it has q4 digits); the exponent + // is e4 (exact result) + } + + // check for overflow + if (q4 + e4 > p34 + expmax) { + if (rnd_mode == ROUNDING_TO_NEAREST) { + res.w[1] = p_sign | 0x7800000000000000ull; // +/-inf + res.w[0] = 0x0000000000000000ull; + *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION); + } else { + res.w[1] = p_sign | res.w[1]; + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, is_midpoint_gt_even, + e4, &res, pfpsf); + } + *pfpsf |= save_fpsf; + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } + // check for underflow + if (q4 + e4 < expmin + P34) { + is_tiny = 1; // the result is tiny + if (e4 < expmin) { + // if e4 < expmin, we must truncate more of res + x0 = expmin - e4; // x0 >= 1 + is_inexact_lt_midpoint0 = is_inexact_lt_midpoint; + is_inexact_gt_midpoint0 = is_inexact_gt_midpoint; + is_midpoint_lt_even0 = is_midpoint_lt_even; + is_midpoint_gt_even0 = is_midpoint_gt_even; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + // the number of decimal digits in res is q4 + if (x0 < q4) { // 1 <= x0 <= q4-1 => round res to q4 - x0 digits + if (q4 <= 18) { // 2 <= q4 <= 18, 1 <= x0 <= 17 + round64_2_18 (q4, x0, res.w[0], &R64, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + if (incr_exp) { + // R64 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 1, 1 <= q4 - x0 <= 17 + R64 = ten2k64[q4 - x0]; + } + // res.w[1] = 0; (from above) + res.w[0] = R64; + } else { // if (q4 <= 34) + // 19 <= q4 <= 38 + P128.w[1] = res.w[1]; + P128.w[0] = res.w[0]; + round128_19_38 (q4, x0, P128, &res, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + if (incr_exp) { + // increase coefficient by a factor of 10; this will be <= 10^33 + // R128 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 1, 1 <= q4 - x0 <= 37 + if (q4 - x0 <= 19) { // 1 <= q4 - x0 <= 19 + // res.w[1] = 0; + res.w[0] = ten2k64[q4 - x0]; + } else { // 20 <= q4 - x0 <= 37 + res.w[0] = ten2k128[q4 - x0 - 20].w[0]; + res.w[1] = ten2k128[q4 - x0 - 20].w[1]; + } + } + } + e4 = e4 + x0; // expmin + } else if (x0 == q4) { + // the second rounding is for 0.d(0)d(1)...d(q4-1) * 10^emin + // determine relationship with 1/2 ulp + if (q4 <= 19) { + if (res.w[0] < midpoint64[q4 - 1]) { // < 1/2 ulp + lt_half_ulp = 1; + is_inexact_lt_midpoint = 1; + } else if (res.w[0] == midpoint64[q4 - 1]) { // = 1/2 ulp + eq_half_ulp = 1; + is_midpoint_gt_even = 1; + } else { // > 1/2 ulp + // gt_half_ulp = 1; + is_inexact_gt_midpoint = 1; + } + } else { // if (q4 <= 34) + if (res.w[1] < midpoint128[q4 - 20].w[1] || + (res.w[1] == midpoint128[q4 - 20].w[1] && + res.w[0] < midpoint128[q4 - 20].w[0])) { // < 1/2 ulp + lt_half_ulp = 1; + is_inexact_lt_midpoint = 1; + } else if (res.w[1] == midpoint128[q4 - 20].w[1] && + res.w[0] == midpoint128[q4 - 20].w[0]) { // = 1/2 ulp + eq_half_ulp = 1; + is_midpoint_gt_even = 1; + } else { // > 1/2 ulp + // gt_half_ulp = 1; + is_inexact_gt_midpoint = 1; + } + } + if (lt_half_ulp || eq_half_ulp) { + // res = +0.0 * 10^expmin + res.w[1] = 0x0000000000000000ull; + res.w[0] = 0x0000000000000000ull; + } else { // if (gt_half_ulp) + // res = +1 * 10^expmin + res.w[1] = 0x0000000000000000ull; + res.w[0] = 0x0000000000000001ull; + } + e4 = expmin; + } else { // if (x0 > q4) + // the second rounding is for 0.0...d(0)d(1)...d(q4-1) * 10^emin + res.w[1] = 0; + res.w[0] = 0; + e4 = expmin; + is_inexact_lt_midpoint = 1; + } + // avoid a double rounding error + if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && + is_midpoint_lt_even) { // double rounding error upward + // res = res - 1 + res.w[0]--; + if (res.w[0] == 0xffffffffffffffffull) + res.w[1]--; + // Note: a double rounding error upward is not possible; for this + // the result after the first rounding would have to be 99...95 + // (35 digits in all), possibly followed by a number of zeros; this + // not possible for f * f + 0 + is_midpoint_lt_even = 0; + is_inexact_lt_midpoint = 1; + } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && + is_midpoint_gt_even) { // double rounding error downward + // res = res + 1 + res.w[0]++; + if (res.w[0] == 0) + res.w[1]++; + is_midpoint_gt_even = 0; + is_inexact_gt_midpoint = 1; + } else if (!is_midpoint_lt_even && !is_midpoint_gt_even && + !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) { + // if this second rounding was exact the result may still be + // inexact because of the first rounding + if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) { + is_inexact_gt_midpoint = 1; + } + if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) { + is_inexact_lt_midpoint = 1; + } + } else if (is_midpoint_gt_even && + (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) { + // pulled up to a midpoint + is_inexact_lt_midpoint = 1; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else if (is_midpoint_lt_even && + (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) { + // pulled down to a midpoint + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 1; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else { + ; + } + } else { // if e4 >= emin then q4 < P and the result is tiny and exact + if (e3 < e4) { + // if (e3 < e4) the preferred exponent is e3 + // return (C4 * 10^scale) * 10^(e4 - scale) + // where scale = min (p34-q4, (e4 - e3)) + scale = p34 - q4; + ind = e4 - e3; + if (ind < scale) + scale = ind; + if (scale == 0) { + ; // res and e4 are unchanged + } else if (q4 <= 19) { // C4 fits in 64 bits + if (scale <= 19) { // 10^scale fits in 64 bits + // 64 x 64 res.w[0] * ten2k64[scale] + __mul_64x64_to_128MACH (res, res.w[0], ten2k64[scale]); + } else { // 10^scale fits in 128 bits + // 64 x 128 res.w[0] * ten2k128[scale - 20] + __mul_128x64_to_128 (res, res.w[0], ten2k128[scale - 20]); + } + } else { // res fits in 128 bits, but 10^scale must fit in 64 bits + // 64 x 128 ten2k64[scale] * C3 + __mul_128x64_to_128 (res, ten2k64[scale], res); + } + // subtract scale from the exponent + e4 = e4 - scale; + } + } + + // check for inexact result + if (is_inexact_lt_midpoint || is_inexact_gt_midpoint || + is_midpoint_lt_even || is_midpoint_gt_even) { + // set the inexact flag and the underflow flag + *pfpsf |= INEXACT_EXCEPTION; + *pfpsf |= UNDERFLOW_EXCEPTION; + } + res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | res.w[1]; + if (rnd_mode != ROUNDING_TO_NEAREST) { + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, is_midpoint_gt_even, + e4, &res, pfpsf); + } + *pfpsf |= save_fpsf; + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } + // no overflow, and no underflow for rounding to nearest + res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | res.w[1]; + + if (rnd_mode != ROUNDING_TO_NEAREST) { + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, is_midpoint_gt_even, + e4, &res, pfpsf); + // if e4 = expmin && significand < 10^33 => result is tiny (for RD, RZ) + if (e4 == expmin) { + if ((res.w[1] & MASK_COEFF) < 0x0000314dc6448d93ull || + ((res.w[1] & MASK_COEFF) == 0x0000314dc6448d93ull && + res.w[0] < 0x38c15b0a00000000ull)) { + is_tiny = 1; + } + } + } + + if (is_inexact_lt_midpoint || is_inexact_gt_midpoint || + is_midpoint_lt_even || is_midpoint_gt_even) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + if (is_tiny) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + + if ((*pfpsf & INEXACT_EXCEPTION) == 0) { // x * y is exact + // need to ensure that the result has the preferred exponent + p_exp = res.w[1] & MASK_EXP; + if (z_exp < p_exp) { // the preferred exponent is z_exp + // signficand of res in C3 + C3.w[1] = res.w[1] & MASK_COEFF; + C3.w[0] = res.w[0]; + // the number of decimal digits of x * y is q4 <= 34 + // Note: the coefficient fits in 128 bits + + // return (C3 * 10^scale) * 10^(p_exp - scale) + // where scale = min (p34-q4, (p_exp-z_exp) >> 49) + scale = p34 - q4; + ind = (p_exp - z_exp) >> 49; + if (ind < scale) + scale = ind; + // subtract scale from the exponent + p_exp = p_exp - ((UINT64) scale << 49); + if (scale == 0) { + ; // leave res unchanged + } else if (q4 <= 19) { // x * y fits in 64 bits + if (scale <= 19) { // 10^scale fits in 64 bits + // 64 x 64 C3.w[0] * ten2k64[scale] + __mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]); + } else { // 10^scale fits in 128 bits + // 64 x 128 C3.w[0] * ten2k128[scale - 20] + __mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]); + } + res.w[1] = p_sign | (p_exp & MASK_EXP) | res.w[1]; + } else { // x * y fits in 128 bits, but 10^scale must fit in 64 bits + // 64 x 128 ten2k64[scale] * C3 + __mul_128x64_to_128 (res, ten2k64[scale], C3); + res.w[1] = p_sign | (p_exp & MASK_EXP) | res.w[1]; + } + } // else leave the result as it is, because p_exp <= z_exp + } + *pfpsf |= save_fpsf; + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } // else we have f * f + f + + // continue with x = f, y = f, z = f + + delta = q3 + e3 - q4 - e4; +delta_ge_zero: + if (delta >= 0) { + + if (p34 <= delta - 1 || // Case (1') + (p34 == delta && e3 + 6176 < p34 - q3)) { // Case (1''A) + // check for overflow, which can occur only in Case (1') + if ((q3 + e3) > (p34 + expmax) && p34 <= delta - 1) { + // e3 > expmax implies p34 <= delta-1 and e3 > expmax is a necessary + // condition for (q3 + e3) > (p34 + expmax) + if (rnd_mode == ROUNDING_TO_NEAREST) { + res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf + res.w[0] = 0x0000000000000000ull; + *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION); + } else { + if (p_sign == z_sign) { + is_inexact_lt_midpoint = 1; + } else { + is_inexact_gt_midpoint = 1; + } + // q3 <= p34; if (q3 < p34) scale C3 up by 10^(p34-q3) + scale = p34 - q3; + if (scale == 0) { + res.w[1] = z_sign | C3.w[1]; + res.w[0] = C3.w[0]; + } else { + if (q3 <= 19) { // C3 fits in 64 bits + if (scale <= 19) { // 10^scale fits in 64 bits + // 64 x 64 C3.w[0] * ten2k64[scale] + __mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]); + } else { // 10^scale fits in 128 bits + // 64 x 128 C3.w[0] * ten2k128[scale - 20] + __mul_128x64_to_128 (res, C3.w[0], + ten2k128[scale - 20]); + } + } else { // C3 fits in 128 bits, but 10^scale must fit in 64 bits + // 64 x 128 ten2k64[scale] * C3 + __mul_128x64_to_128 (res, ten2k64[scale], C3); + } + // the coefficient in res has q3 + scale = p34 digits + } + e3 = e3 - scale; + res.w[1] = z_sign | res.w[1]; + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, is_midpoint_gt_even, + e3, &res, pfpsf); + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } + // res = z + if (q3 < p34) { // the preferred exponent is z_exp - (p34 - q3) + // return (C3 * 10^scale) * 10^(z_exp - scale) + // where scale = min (p34-q3, z_exp-EMIN) + scale = p34 - q3; + ind = e3 + 6176; + if (ind < scale) + scale = ind; + if (scale == 0) { + res.w[1] = C3.w[1]; + res.w[0] = C3.w[0]; + } else if (q3 <= 19) { // z fits in 64 bits + if (scale <= 19) { // 10^scale fits in 64 bits + // 64 x 64 C3.w[0] * ten2k64[scale] + __mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]); + } else { // 10^scale fits in 128 bits + // 64 x 128 C3.w[0] * ten2k128[scale - 20] + __mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]); + } + } else { // z fits in 128 bits, but 10^scale must fit in 64 bits + // 64 x 128 ten2k64[scale] * C3 + __mul_128x64_to_128 (res, ten2k64[scale], C3); + } + // the coefficient in res has q3 + scale digits + // subtract scale from the exponent + z_exp = z_exp - ((UINT64) scale << 49); + e3 = e3 - scale; + res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1]; + if (scale + q3 < p34) + *pfpsf |= UNDERFLOW_EXCEPTION; + } else { + scale = 0; + res.w[1] = z_sign | ((UINT64) (e3 + 6176) << 49) | C3.w[1]; + res.w[0] = C3.w[0]; + } + + // use the following to avoid double rounding errors when operating on + // mixed formats in rounding to nearest, and for correcting the result + // if not rounding to nearest + if ((p_sign != z_sign) && (delta == (q3 + scale + 1))) { + // there is a gap of exactly one digit between the scaled C3 and C4 + // C3 * 10^ scale = 10^(q3+scale-1) <=> C3 = 10^(q3-1) is special case + if ((q3 <= 19 && C3.w[0] != ten2k64[q3 - 1]) || + (q3 == 20 && (C3.w[1] != 0 || C3.w[0] != ten2k64[19])) || + (q3 >= 21 && (C3.w[1] != ten2k128[q3 - 21].w[1] || + C3.w[0] != ten2k128[q3 - 21].w[0]))) { + // C3 * 10^ scale != 10^(q3-1) + // if ((res.w[1] & MASK_COEFF) != 0x0000314dc6448d93ull || + // res.w[0] != 0x38c15b0a00000000ull) { // C3 * 10^scale != 10^33 + is_inexact_gt_midpoint = 1; // if (z_sign), set as if for abs. value + } else { // if C3 * 10^scale = 10^(q3+scale-1) + // ok from above e3 = (z_exp >> 49) - 6176; + // the result is always inexact + if (q4 == 1) { + R64 = C4.w[0]; + } else { + // if q4 > 1 then truncate C4 from q4 digits to 1 digit; + // x = q4-1, 1 <= x <= 67 and check if this operation is exact + if (q4 <= 18) { // 2 <= q4 <= 18 + round64_2_18 (q4, q4 - 1, C4.w[0], &R64, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + } else if (q4 <= 38) { + P128.w[1] = C4.w[1]; + P128.w[0] = C4.w[0]; + round128_19_38 (q4, q4 - 1, P128, &R128, &incr_exp, + &is_midpoint_lt_even, + &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + R64 = R128.w[0]; // one decimal digit + } else if (q4 <= 57) { + P192.w[2] = C4.w[2]; + P192.w[1] = C4.w[1]; + P192.w[0] = C4.w[0]; + round192_39_57 (q4, q4 - 1, P192, &R192, &incr_exp, + &is_midpoint_lt_even, + &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + R64 = R192.w[0]; // one decimal digit + } else { // if (q4 <= 68) + round256_58_76 (q4, q4 - 1, C4, &R256, &incr_exp, + &is_midpoint_lt_even, + &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + R64 = R256.w[0]; // one decimal digit + } + if (incr_exp) { + R64 = 10; + } + } + if (q4 == 1 && C4.w[0] == 5) { + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 1; + is_midpoint_gt_even = 0; + } else if ((e3 == expmin) || + R64 < 5 || (R64 == 5 && is_inexact_gt_midpoint)) { + // result does not change + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 1; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else { + is_inexact_lt_midpoint = 1; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + // result decremented is 10^(q3+scale) - 1 + if ((q3 + scale) <= 19) { + res.w[1] = 0; + res.w[0] = ten2k64[q3 + scale]; + } else { // if ((q3 + scale + 1) <= 35) + res.w[1] = ten2k128[q3 + scale - 20].w[1]; + res.w[0] = ten2k128[q3 + scale - 20].w[0]; + } + res.w[0] = res.w[0] - 1; // borrow never occurs + z_exp = z_exp - EXP_P1; + e3 = e3 - 1; + res.w[1] = z_sign | ((UINT64) (e3 + 6176) << 49) | res.w[1]; + } + if (e3 == expmin) { + if (R64 < 5 || (R64 == 5 && !is_inexact_lt_midpoint)) { + ; // result not tiny (in round-to-nearest mode) + } else { + *pfpsf |= UNDERFLOW_EXCEPTION; + } + } + } // end 10^(q3+scale-1) + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { + if (p_sign == z_sign) { + // if (z_sign), set as if for absolute value + is_inexact_lt_midpoint = 1; + } else { // if (p_sign != z_sign) + // if (z_sign), set as if for absolute value + is_inexact_gt_midpoint = 1; + } + *pfpsf |= INEXACT_EXCEPTION; + } + // the result is always inexact => set the inexact flag + // Determine tininess: + // if (exp > expmin) + // the result is not tiny + // else // if exp = emin + // if (q3 + scale < p34) + // the result is tiny + // else // if (q3 + scale = p34) + // if (C3 * 10^scale > 10^33) + // the result is not tiny + // else // if C3 * 10^scale = 10^33 + // if (xy * z > 0) + // the result is not tiny + // else // if (xy * z < 0) + // if (z > 0) + // if rnd_mode != RP + // the result is tiny + // else // if RP + // the result is not tiny + // else // if (z < 0) + // if rnd_mode != RM + // the result is tiny + // else // if RM + // the result is not tiny + // endif + // endif + // endif + // endif + // endif + // endif + if ((e3 == expmin && (q3 + scale) < p34) || + (e3 == expmin && (q3 + scale) == p34 && + (res.w[1] & MASK_COEFF) == 0x0000314dc6448d93ull && // 10^33_high + res.w[0] == 0x38c15b0a00000000ull && // 10^33_low + z_sign != p_sign && ((!z_sign && rnd_mode != ROUNDING_UP) || + (z_sign && rnd_mode != ROUNDING_DOWN)))) { + *pfpsf |= UNDERFLOW_EXCEPTION; + } + if (rnd_mode != ROUNDING_TO_NEAREST) { + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, is_midpoint_gt_even, + e3, &res, pfpsf); + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + + } else if (p34 == delta) { // Case (1''B) + + // because Case (1''A) was treated above, e3 + 6176 >= p34 - q3 + // and C3 can be scaled up to p34 digits if needed + + // scale C3 to p34 digits if needed + scale = p34 - q3; // 0 <= scale <= p34 - 1 + if (scale == 0) { + res.w[1] = C3.w[1]; + res.w[0] = C3.w[0]; + } else if (q3 <= 19) { // z fits in 64 bits + if (scale <= 19) { // 10^scale fits in 64 bits + // 64 x 64 C3.w[0] * ten2k64[scale] + __mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]); + } else { // 10^scale fits in 128 bits + // 64 x 128 C3.w[0] * ten2k128[scale - 20] + __mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]); + } + } else { // z fits in 128 bits, but 10^scale must fit in 64 bits + // 64 x 128 ten2k64[scale] * C3 + __mul_128x64_to_128 (res, ten2k64[scale], C3); + } + // subtract scale from the exponent + z_exp = z_exp - ((UINT64) scale << 49); + e3 = e3 - scale; + // now z_sign, z_exp, and res correspond to a z scaled to p34 = 34 digits + + // determine whether x * y is less than, equal to, or greater than + // 1/2 ulp (z) + if (q4 <= 19) { + if (C4.w[0] < midpoint64[q4 - 1]) { // < 1/2 ulp + lt_half_ulp = 1; + } else if (C4.w[0] == midpoint64[q4 - 1]) { // = 1/2 ulp + eq_half_ulp = 1; + } else { // > 1/2 ulp + gt_half_ulp = 1; + } + } else if (q4 <= 38) { + if (C4.w[2] == 0 && (C4.w[1] < midpoint128[q4 - 20].w[1] || + (C4.w[1] == midpoint128[q4 - 20].w[1] && + C4.w[0] < midpoint128[q4 - 20].w[0]))) { // < 1/2 ulp + lt_half_ulp = 1; + } else if (C4.w[2] == 0 && C4.w[1] == midpoint128[q4 - 20].w[1] && + C4.w[0] == midpoint128[q4 - 20].w[0]) { // = 1/2 ulp + eq_half_ulp = 1; + } else { // > 1/2 ulp + gt_half_ulp = 1; + } + } else if (q4 <= 58) { + if (C4.w[3] == 0 && (C4.w[2] < midpoint192[q4 - 39].w[2] || + (C4.w[2] == midpoint192[q4 - 39].w[2] && + C4.w[1] < midpoint192[q4 - 39].w[1]) || + (C4.w[2] == midpoint192[q4 - 39].w[2] && + C4.w[1] == midpoint192[q4 - 39].w[1] && + C4.w[0] < midpoint192[q4 - 39].w[0]))) { // < 1/2 ulp + lt_half_ulp = 1; + } else if (C4.w[3] == 0 && C4.w[2] == midpoint192[q4 - 39].w[2] && + C4.w[1] == midpoint192[q4 - 39].w[1] && + C4.w[0] == midpoint192[q4 - 39].w[0]) { // = 1/2 ulp + eq_half_ulp = 1; + } else { // > 1/2 ulp + gt_half_ulp = 1; + } + } else { + if (C4.w[3] < midpoint256[q4 - 59].w[3] || + (C4.w[3] == midpoint256[q4 - 59].w[3] && + C4.w[2] < midpoint256[q4 - 59].w[2]) || + (C4.w[3] == midpoint256[q4 - 59].w[3] && + C4.w[2] == midpoint256[q4 - 59].w[2] && + C4.w[1] < midpoint256[q4 - 59].w[1]) || + (C4.w[3] == midpoint256[q4 - 59].w[3] && + C4.w[2] == midpoint256[q4 - 59].w[2] && + C4.w[1] == midpoint256[q4 - 59].w[1] && + C4.w[0] < midpoint256[q4 - 59].w[0])) { // < 1/2 ulp + lt_half_ulp = 1; + } else if (C4.w[3] == midpoint256[q4 - 59].w[3] && + C4.w[2] == midpoint256[q4 - 59].w[2] && + C4.w[1] == midpoint256[q4 - 59].w[1] && + C4.w[0] == midpoint256[q4 - 59].w[0]) { // = 1/2 ulp + eq_half_ulp = 1; + } else { // > 1/2 ulp + gt_half_ulp = 1; + } + } + + if (p_sign == z_sign) { + if (lt_half_ulp) { + res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1]; + // use the following to avoid double rounding errors when operating on + // mixed formats in rounding to nearest + is_inexact_lt_midpoint = 1; // if (z_sign), as if for absolute value + } else if ((eq_half_ulp && (res.w[0] & 0x01)) || gt_half_ulp) { + // add 1 ulp to the significand + res.w[0]++; + if (res.w[0] == 0x0ull) + res.w[1]++; + // check for rounding overflow, when coeff == 10^34 + if ((res.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull && + res.w[0] == 0x378d8e6400000000ull) { // coefficient = 10^34 + e3 = e3 + 1; + // coeff = 10^33 + z_exp = ((UINT64) (e3 + 6176) << 49) & MASK_EXP; + res.w[1] = 0x0000314dc6448d93ull; + res.w[0] = 0x38c15b0a00000000ull; + } + // end add 1 ulp + res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1]; + if (eq_half_ulp) { + is_midpoint_lt_even = 1; // if (z_sign), as if for absolute value + } else { + is_inexact_gt_midpoint = 1; // if (z_sign), as if for absolute value + } + } else { // if (eq_half_ulp && !(res.w[0] & 0x01)) + // leave unchanged + res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1]; + is_midpoint_gt_even = 1; // if (z_sign), as if for absolute value + } + // the result is always inexact, and never tiny + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // check for overflow + if (e3 > expmax && rnd_mode == ROUNDING_TO_NEAREST) { + res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf + res.w[0] = 0x0000000000000000ull; + *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION); + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } + if (rnd_mode != ROUNDING_TO_NEAREST) { + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, is_midpoint_gt_even, + e3, &res, pfpsf); + z_exp = res.w[1] & MASK_EXP; + } + } else { // if (p_sign != z_sign) + // consider two cases, because C3 * 10^scale = 10^33 is a special case + if (res.w[1] != 0x0000314dc6448d93ull || + res.w[0] != 0x38c15b0a00000000ull) { // C3 * 10^scale != 10^33 + if (lt_half_ulp) { + res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1]; + // use the following to avoid double rounding errors when operating + // on mixed formats in rounding to nearest + is_inexact_gt_midpoint = 1; // if (z_sign), as if for absolute value + } else if ((eq_half_ulp && (res.w[0] & 0x01)) || gt_half_ulp) { + // subtract 1 ulp from the significand + res.w[0]--; + if (res.w[0] == 0xffffffffffffffffull) + res.w[1]--; + res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1]; + if (eq_half_ulp) { + is_midpoint_gt_even = 1; // if (z_sign), as if for absolute value + } else { + is_inexact_lt_midpoint = 1; //if(z_sign), as if for absolute value + } + } else { // if (eq_half_ulp && !(res.w[0] & 0x01)) + // leave unchanged + res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1]; + is_midpoint_lt_even = 1; // if (z_sign), as if for absolute value + } + // the result is always inexact, and never tiny + // check for overflow for RN + if (e3 > expmax) { + if (rnd_mode == ROUNDING_TO_NEAREST) { + res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf + res.w[0] = 0x0000000000000000ull; + *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION); + } else { + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, + is_midpoint_gt_even, e3, &res, + pfpsf); + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + if (rnd_mode != ROUNDING_TO_NEAREST) { + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, + is_midpoint_gt_even, e3, &res, pfpsf); + } + z_exp = res.w[1] & MASK_EXP; + } else { // if C3 * 10^scale = 10^33 + e3 = (z_exp >> 49) - 6176; + if (e3 > expmin) { + // the result is exact if exp > expmin and C4 = d*10^(q4-1), + // where d = 1, 2, 3, ..., 9; it could be tiny too, but exact + if (q4 == 1) { + // if q4 = 1 the result is exact + // result coefficient = 10^34 - C4 + res.w[1] = 0x0001ed09bead87c0ull; + res.w[0] = 0x378d8e6400000000ull - C4.w[0]; + z_exp = z_exp - EXP_P1; + e3 = e3 - 1; + res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1]; + } else { + // if q4 > 1 then truncate C4 from q4 digits to 1 digit; + // x = q4-1, 1 <= x <= 67 and check if this operation is exact + if (q4 <= 18) { // 2 <= q4 <= 18 + round64_2_18 (q4, q4 - 1, C4.w[0], &R64, &incr_exp, + &is_midpoint_lt_even, + &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + } else if (q4 <= 38) { + P128.w[1] = C4.w[1]; + P128.w[0] = C4.w[0]; + round128_19_38 (q4, q4 - 1, P128, &R128, &incr_exp, + &is_midpoint_lt_even, + &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + R64 = R128.w[0]; // one decimal digit + } else if (q4 <= 57) { + P192.w[2] = C4.w[2]; + P192.w[1] = C4.w[1]; + P192.w[0] = C4.w[0]; + round192_39_57 (q4, q4 - 1, P192, &R192, &incr_exp, + &is_midpoint_lt_even, + &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + R64 = R192.w[0]; // one decimal digit + } else { // if (q4 <= 68) + round256_58_76 (q4, q4 - 1, C4, &R256, &incr_exp, + &is_midpoint_lt_even, + &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + R64 = R256.w[0]; // one decimal digit + } + if (!is_midpoint_lt_even && !is_midpoint_gt_even && + !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) { + // the result is exact: 10^34 - R64 + // incr_exp = 0 with certainty + z_exp = z_exp - EXP_P1; + e3 = e3 - 1; + res.w[1] = + z_sign | (z_exp & MASK_EXP) | 0x0001ed09bead87c0ull; + res.w[0] = 0x378d8e6400000000ull - R64; + } else { + // We want R64 to be the top digit of C4, but we actually + // obtained (C4 * 10^(-q4+1))RN; a correction may be needed, + // because the top digit is (C4 * 10^(-q4+1))RZ + // however, if incr_exp = 1 then R64 = 10 with certainty + if (incr_exp) { + R64 = 10; + } + // the result is inexact as C4 has more than 1 significant digit + // and C3 * 10^scale = 10^33 + // example of case that is treated here: + // 100...0 * 10^e3 - 0.41 * 10^e3 = + // 0999...9.59 * 10^e3 -> rounds to 99...96*10^(e3-1) + // note that (e3 > expmin} + // in order to round, subtract R64 from 10^34 and then compare + // C4 - R64 * 10^(q4-1) with 1/2 ulp + // calculate 10^34 - R64 + res.w[1] = 0x0001ed09bead87c0ull; + res.w[0] = 0x378d8e6400000000ull - R64; + z_exp = z_exp - EXP_P1; // will be OR-ed with sign & significand + // calculate C4 - R64 * 10^(q4-1); this is a rare case and + // R64 is small, 1 <= R64 <= 9 + e3 = e3 - 1; + if (is_inexact_lt_midpoint) { + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 1; + } else if (is_inexact_gt_midpoint) { + is_inexact_gt_midpoint = 0; + is_inexact_lt_midpoint = 1; + } else if (is_midpoint_lt_even) { + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 1; + } else if (is_midpoint_gt_even) { + is_midpoint_gt_even = 0; + is_midpoint_lt_even = 1; + } else { + ; + } + // the result is always inexact, and never tiny + // check for overflow for RN + if (e3 > expmax) { + if (rnd_mode == ROUNDING_TO_NEAREST) { + res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf + res.w[0] = 0x0000000000000000ull; + *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION); + } else { + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, + is_midpoint_gt_even, e3, &res, + pfpsf); + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + res.w[1] = + z_sign | ((UINT64) (e3 + 6176) << 49) | res.w[1]; + if (rnd_mode != ROUNDING_TO_NEAREST) { + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, + is_midpoint_gt_even, e3, &res, + pfpsf); + } + z_exp = res.w[1] & MASK_EXP; + } // end result is inexact + } // end q4 > 1 + } else { // if (e3 = emin) + // if e3 = expmin the result is also tiny (the condition for + // tininess is C4 > 050...0 [q4 digits] which is met because + // the msd of C4 is not zero) + // the result is tiny and inexact in all rounding modes; + // it is either 100...0 or 0999...9 (use lt_half_ulp, eq_half_ulp, + // gt_half_ulp to calculate) + // if (lt_half_ulp || eq_half_ulp) res = 10^33 stays unchanged + + // p_sign != z_sign so swap gt_half_ulp and lt_half_ulp + if (gt_half_ulp) { // res = 10^33 - 1 + res.w[1] = 0x0000314dc6448d93ull; + res.w[0] = 0x38c15b09ffffffffull; + } else { + res.w[1] = 0x0000314dc6448d93ull; + res.w[0] = 0x38c15b0a00000000ull; + } + res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1]; + *pfpsf |= UNDERFLOW_EXCEPTION; // inexact is set later + + if (eq_half_ulp) { + is_midpoint_lt_even = 1; // if (z_sign), as if for absolute value + } else if (lt_half_ulp) { + is_inexact_gt_midpoint = 1; //if(z_sign), as if for absolute value + } else { // if (gt_half_ulp) + is_inexact_lt_midpoint = 1; //if(z_sign), as if for absolute value + } + + if (rnd_mode != ROUNDING_TO_NEAREST) { + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, + is_midpoint_gt_even, e3, &res, + pfpsf); + z_exp = res.w[1] & MASK_EXP; + } + } // end e3 = emin + // set the inexact flag (if the result was not exact) + if (is_inexact_lt_midpoint || is_inexact_gt_midpoint || + is_midpoint_lt_even || is_midpoint_gt_even) + *pfpsf |= INEXACT_EXCEPTION; + } // end 10^33 + } // end if (p_sign != z_sign) + res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1]; + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + + } else if (((q3 <= delta && delta < p34 && p34 < delta + q4) || // Case (2) + (q3 <= delta && delta + q4 <= p34) || // Case (3) + (delta < q3 && p34 < delta + q4) || // Case (4) + (delta < q3 && q3 <= delta + q4 && delta + q4 <= p34) || // Case (5) + (delta + q4 < q3)) && // Case (6) + !(delta <= 1 && p_sign != z_sign)) { // Case (2), (3), (4), (5) or (6) + + // the result has the sign of z + + if ((q3 <= delta && delta < p34 && p34 < delta + q4) || // Case (2) + (delta < q3 && p34 < delta + q4)) { // Case (4) + // round first the sum x * y + z with unbounded exponent + // scale C3 up by scale = p34 - q3, 1 <= scale <= p34-1, + // 1 <= scale <= 33 + // calculate res = C3 * 10^scale + scale = p34 - q3; + x0 = delta + q4 - p34; + } else if (delta + q4 < q3) { // Case (6) + // make Case (6) look like Case (3) or Case (5) with scale = 0 + // by scaling up C4 by 10^(q3 - delta - q4) + scale = q3 - delta - q4; // 1 <= scale <= 33 + if (q4 <= 19) { // 1 <= scale <= 19; C4 fits in 64 bits + if (scale <= 19) { // 10^scale fits in 64 bits + // 64 x 64 C4.w[0] * ten2k64[scale] + __mul_64x64_to_128MACH (P128, C4.w[0], ten2k64[scale]); + } else { // 10^scale fits in 128 bits + // 64 x 128 C4.w[0] * ten2k128[scale - 20] + __mul_128x64_to_128 (P128, C4.w[0], ten2k128[scale - 20]); + } + } else { // C4 fits in 128 bits, but 10^scale must fit in 64 bits + // 64 x 128 ten2k64[scale] * C4 + __mul_128x64_to_128 (P128, ten2k64[scale], C4); + } + C4.w[0] = P128.w[0]; + C4.w[1] = P128.w[1]; + // e4 does not need adjustment, as it is not used from this point on + scale = 0; + x0 = 0; + // now Case (6) looks like Case (3) or Case (5) with scale = 0 + } else { // if Case (3) or Case (5) + // Note: Case (3) is similar to Case (2), but scale differs and the + // result is exact, unless it is tiny (so x0 = 0 when calculating the + // result with unbounded exponent) + + // calculate first the sum x * y + z with unbounded exponent (exact) + // scale C3 up by scale = delta + q4 - q3, 1 <= scale <= p34-1, + // 1 <= scale <= 33 + // calculate res = C3 * 10^scale + scale = delta + q4 - q3; + x0 = 0; + // Note: the comments which follow refer [mainly] to Case (2)] + } + + case2_repeat: + if (scale == 0) { // this could happen e.g. if we return to case2_repeat + // or in Case (4) + res.w[1] = C3.w[1]; + res.w[0] = C3.w[0]; + } else if (q3 <= 19) { // 1 <= scale <= 19; z fits in 64 bits + if (scale <= 19) { // 10^scale fits in 64 bits + // 64 x 64 C3.w[0] * ten2k64[scale] + __mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]); + } else { // 10^scale fits in 128 bits + // 64 x 128 C3.w[0] * ten2k128[scale - 20] + __mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]); + } + } else { // z fits in 128 bits, but 10^scale must fit in 64 bits + // 64 x 128 ten2k64[scale] * C3 + __mul_128x64_to_128 (res, ten2k64[scale], C3); + } + // e3 is already calculated + e3 = e3 - scale; + // now res = C3 * 10^scale and e3 = e3 - scale + // Note: C3 * 10^scale could be 10^34 if we returned to case2_repeat + // because the result was too small + + // round C4 to nearest to q4 - x0 digits, where x0 = delta + q4 - p34, + // 1 <= x0 <= min (q4 - 1, 2 * p34 - 1) <=> 1 <= x0 <= min (q4 - 1, 67) + // Also: 1 <= q4 - x0 <= p34 -1 => 1 <= q4 - x0 <= 33 (so the result of + // the rounding fits in 128 bits!) + // x0 = delta + q4 - p34 (calculated before reaching case2_repeat) + // because q3 + q4 - x0 <= P => x0 >= q3 + q4 - p34 + if (x0 == 0) { // this could happen only if we return to case2_repeat, or + // for Case (3) or Case (6) + R128.w[1] = C4.w[1]; + R128.w[0] = C4.w[0]; + } else if (q4 <= 18) { + // 2 <= q4 <= 18, max(1, q3+q4-p34) <= x0 <= q4 - 1, 1 <= x0 <= 17 + round64_2_18 (q4, x0, C4.w[0], &R64, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint); + if (incr_exp) { + // R64 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 1, 1 <= q4 - x0 <= 17 + R64 = ten2k64[q4 - x0]; + } + R128.w[1] = 0; + R128.w[0] = R64; + } else if (q4 <= 38) { + // 19 <= q4 <= 38, max(1, q3+q4-p34) <= x0 <= q4 - 1, 1 <= x0 <= 37 + P128.w[1] = C4.w[1]; + P128.w[0] = C4.w[0]; + round128_19_38 (q4, x0, P128, &R128, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + if (incr_exp) { + // R128 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 1, 1 <= q4 - x0 <= 37 + if (q4 - x0 <= 19) { // 1 <= q4 - x0 <= 19 + R128.w[0] = ten2k64[q4 - x0]; + // R128.w[1] stays 0 + } else { // 20 <= q4 - x0 <= 37 + R128.w[0] = ten2k128[q4 - x0 - 20].w[0]; + R128.w[1] = ten2k128[q4 - x0 - 20].w[1]; + } + } + } else if (q4 <= 57) { + // 38 <= q4 <= 57, max(1, q3+q4-p34) <= x0 <= q4 - 1, 5 <= x0 <= 56 + P192.w[2] = C4.w[2]; + P192.w[1] = C4.w[1]; + P192.w[0] = C4.w[0]; + round192_39_57 (q4, x0, P192, &R192, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + // R192.w[2] is always 0 + if (incr_exp) { + // R192 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 5, 1 <= q4 - x0 <= 52 + if (q4 - x0 <= 19) { // 1 <= q4 - x0 <= 19 + R192.w[0] = ten2k64[q4 - x0]; + // R192.w[1] stays 0 + // R192.w[2] stays 0 + } else { // 20 <= q4 - x0 <= 33 + R192.w[0] = ten2k128[q4 - x0 - 20].w[0]; + R192.w[1] = ten2k128[q4 - x0 - 20].w[1]; + // R192.w[2] stays 0 + } + } + R128.w[1] = R192.w[1]; + R128.w[0] = R192.w[0]; + } else { + // 58 <= q4 <= 68, max(1, q3+q4-p34) <= x0 <= q4 - 1, 25 <= x0 <= 67 + round256_58_76 (q4, x0, C4, &R256, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + // R256.w[3] and R256.w[2] are always 0 + if (incr_exp) { + // R256 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 25, 1 <= q4 - x0 <= 43 + if (q4 - x0 <= 19) { // 1 <= q4 - x0 <= 19 + R256.w[0] = ten2k64[q4 - x0]; + // R256.w[1] stays 0 + // R256.w[2] stays 0 + // R256.w[3] stays 0 + } else { // 20 <= q4 - x0 <= 33 + R256.w[0] = ten2k128[q4 - x0 - 20].w[0]; + R256.w[1] = ten2k128[q4 - x0 - 20].w[1]; + // R256.w[2] stays 0 + // R256.w[3] stays 0 + } + } + R128.w[1] = R256.w[1]; + R128.w[0] = R256.w[0]; + } + // now add C3 * 10^scale in res and the signed top (q4-x0) digits of C4, + // rounded to nearest, which were copied into R128 + if (z_sign == p_sign) { + lsb = res.w[0] & 0x01; // lsb of C3 * 10^scale + // the sum can result in [up to] p34 or p34 + 1 digits + res.w[0] = res.w[0] + R128.w[0]; + res.w[1] = res.w[1] + R128.w[1]; + if (res.w[0] < R128.w[0]) + res.w[1]++; // carry + // if res > 10^34 - 1 need to increase x0 and decrease scale by 1 + if (res.w[1] > 0x0001ed09bead87c0ull || + (res.w[1] == 0x0001ed09bead87c0ull && + res.w[0] > 0x378d8e63ffffffffull)) { + // avoid double rounding error + is_inexact_lt_midpoint0 = is_inexact_lt_midpoint; + is_inexact_gt_midpoint0 = is_inexact_gt_midpoint; + is_midpoint_lt_even0 = is_midpoint_lt_even; + is_midpoint_gt_even0 = is_midpoint_gt_even; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + P128.w[1] = res.w[1]; + P128.w[0] = res.w[0]; + round128_19_38 (35, 1, P128, &res, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + // incr_exp is 0 with certainty in this case + // avoid a double rounding error + if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && + is_midpoint_lt_even) { // double rounding error upward + // res = res - 1 + res.w[0]--; + if (res.w[0] == 0xffffffffffffffffull) + res.w[1]--; + // Note: a double rounding error upward is not possible; for this + // the result after the first rounding would have to be 99...95 + // (35 digits in all), possibly followed by a number of zeros; this + // not possible in Cases (2)-(6) or (15)-(17) which may get here + is_midpoint_lt_even = 0; + is_inexact_lt_midpoint = 1; + } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && + is_midpoint_gt_even) { // double rounding error downward + // res = res + 1 + res.w[0]++; + if (res.w[0] == 0) + res.w[1]++; + is_midpoint_gt_even = 0; + is_inexact_gt_midpoint = 1; + } else if (!is_midpoint_lt_even && !is_midpoint_gt_even && + !is_inexact_lt_midpoint + && !is_inexact_gt_midpoint) { + // if this second rounding was exact the result may still be + // inexact because of the first rounding + if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) { + is_inexact_gt_midpoint = 1; + } + if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) { + is_inexact_lt_midpoint = 1; + } + } else if (is_midpoint_gt_even && + (is_inexact_gt_midpoint0 + || is_midpoint_lt_even0)) { + // pulled up to a midpoint + is_inexact_lt_midpoint = 1; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else if (is_midpoint_lt_even && + (is_inexact_lt_midpoint0 + || is_midpoint_gt_even0)) { + // pulled down to a midpoint + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 1; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else { + ; + } + // adjust exponent + e3 = e3 + 1; + if (!is_midpoint_lt_even && !is_midpoint_gt_even && + !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) { + if (is_midpoint_lt_even0 || is_midpoint_gt_even0 || + is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0) { + is_inexact_lt_midpoint = 1; + } + } + } else { + // this is the result rounded with unbounded exponent, unless a + // correction is needed + res.w[1] = res.w[1] & MASK_COEFF; + if (lsb == 1) { + if (is_midpoint_gt_even) { + // res = res + 1 + is_midpoint_gt_even = 0; + is_midpoint_lt_even = 1; + res.w[0]++; + if (res.w[0] == 0x0) + res.w[1]++; + // check for rounding overflow + if (res.w[1] == 0x0001ed09bead87c0ull && + res.w[0] == 0x378d8e6400000000ull) { + // res = 10^34 => rounding overflow + res.w[1] = 0x0000314dc6448d93ull; + res.w[0] = 0x38c15b0a00000000ull; // 10^33 + e3++; + } + } else if (is_midpoint_lt_even) { + // res = res - 1 + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 1; + res.w[0]--; + if (res.w[0] == 0xffffffffffffffffull) + res.w[1]--; + // if the result is pure zero, the sign depends on the rounding + // mode (x*y and z had opposite signs) + if (res.w[1] == 0x0ull && res.w[0] == 0x0ull) { + if (rnd_mode != ROUNDING_DOWN) + z_sign = 0x0000000000000000ull; + else + z_sign = 0x8000000000000000ull; + // the exponent is max (e3, expmin) + res.w[1] = 0x0; + res.w[0] = 0x0; + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } + } else { + ; + } + } + } + } else { // if (z_sign != p_sign) + lsb = res.w[0] & 0x01; // lsb of C3 * 10^scale; R128 contains rounded C4 + // used to swap rounding indicators if p_sign != z_sign + // the sum can result in [up to] p34 or p34 - 1 digits + tmp64 = res.w[0]; + res.w[0] = res.w[0] - R128.w[0]; + res.w[1] = res.w[1] - R128.w[1]; + if (res.w[0] > tmp64) + res.w[1]--; // borrow + // if res < 10^33 and exp > expmin need to decrease x0 and + // increase scale by 1 + if (e3 > expmin && ((res.w[1] < 0x0000314dc6448d93ull || + (res.w[1] == 0x0000314dc6448d93ull && + res.w[0] < 0x38c15b0a00000000ull)) || + (is_inexact_lt_midpoint + && res.w[1] == 0x0000314dc6448d93ull + && res.w[0] == 0x38c15b0a00000000ull)) + && x0 >= 1) { + x0 = x0 - 1; + // first restore e3, otherwise it will be too small + e3 = e3 + scale; + scale = scale + 1; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + incr_exp = 0; + goto case2_repeat; + } + // else this is the result rounded with unbounded exponent; + // because the result has opposite sign to that of C4 which was + // rounded, need to change the rounding indicators + if (is_inexact_lt_midpoint) { + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 1; + } else if (is_inexact_gt_midpoint) { + is_inexact_gt_midpoint = 0; + is_inexact_lt_midpoint = 1; + } else if (lsb == 0) { + if (is_midpoint_lt_even) { + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 1; + } else if (is_midpoint_gt_even) { + is_midpoint_gt_even = 0; + is_midpoint_lt_even = 1; + } else { + ; + } + } else if (lsb == 1) { + if (is_midpoint_lt_even) { + // res = res + 1 + res.w[0]++; + if (res.w[0] == 0x0) + res.w[1]++; + // check for rounding overflow + if (res.w[1] == 0x0001ed09bead87c0ull && + res.w[0] == 0x378d8e6400000000ull) { + // res = 10^34 => rounding overflow + res.w[1] = 0x0000314dc6448d93ull; + res.w[0] = 0x38c15b0a00000000ull; // 10^33 + e3++; + } + } else if (is_midpoint_gt_even) { + // res = res - 1 + res.w[0]--; + if (res.w[0] == 0xffffffffffffffffull) + res.w[1]--; + // if the result is pure zero, the sign depends on the rounding + // mode (x*y and z had opposite signs) + if (res.w[1] == 0x0ull && res.w[0] == 0x0ull) { + if (rnd_mode != ROUNDING_DOWN) + z_sign = 0x0000000000000000ull; + else + z_sign = 0x8000000000000000ull; + // the exponent is max (e3, expmin) + res.w[1] = 0x0; + res.w[0] = 0x0; + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } + } else { + ; + } + } else { + ; + } + } + // check for underflow + if (e3 == expmin) { // and if significand < 10^33 => result is tiny + if ((res.w[1] & MASK_COEFF) < 0x0000314dc6448d93ull || + ((res.w[1] & MASK_COEFF) == 0x0000314dc6448d93ull && + res.w[0] < 0x38c15b0a00000000ull)) { + is_tiny = 1; + } + } else if (e3 < expmin) { + // the result is tiny, so we must truncate more of res + is_tiny = 1; + x0 = expmin - e3; + is_inexact_lt_midpoint0 = is_inexact_lt_midpoint; + is_inexact_gt_midpoint0 = is_inexact_gt_midpoint; + is_midpoint_lt_even0 = is_midpoint_lt_even; + is_midpoint_gt_even0 = is_midpoint_gt_even; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + // determine the number of decimal digits in res + if (res.w[1] == 0x0) { + // between 1 and 19 digits + for (ind = 1; ind <= 19; ind++) { + if (res.w[0] < ten2k64[ind]) { + break; + } + } + // ind digits + } else if (res.w[1] < ten2k128[0].w[1] || + (res.w[1] == ten2k128[0].w[1] + && res.w[0] < ten2k128[0].w[0])) { + // 20 digits + ind = 20; + } else { // between 21 and 38 digits + for (ind = 1; ind <= 18; ind++) { + if (res.w[1] < ten2k128[ind].w[1] || + (res.w[1] == ten2k128[ind].w[1] && + res.w[0] < ten2k128[ind].w[0])) { + break; + } + } + // ind + 20 digits + ind = ind + 20; + } + + // at this point ind >= x0; because delta >= 2 on this path, the case + // ind = x0 can occur only in Case (2) or case (3), when C3 has one + // digit (q3 = 1) equal to 1 (C3 = 1), e3 is expmin (e3 = expmin), + // the signs of x * y and z are opposite, and through cancellation + // the most significant decimal digit in res has the weight + // 10^(emin-1); however, it is clear that in this case the most + // significant digit is 9, so the result before rounding is + // 0.9... * 10^emin + // Otherwise, ind > x0 because there are non-zero decimal digits in the + // result with weight of at least 10^emin, and correction for underflow + // can be carried out using the round*_*_2_* () routines + if (x0 == ind) { // the result before rounding is 0.9... * 10^emin + res.w[1] = 0x0; + res.w[0] = 0x1; + is_inexact_gt_midpoint = 1; + } else if (ind <= 18) { // check that 2 <= ind + // 2 <= ind <= 18, 1 <= x0 <= 17 + round64_2_18 (ind, x0, res.w[0], &R64, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + if (incr_exp) { + // R64 = 10^(ind-x0), 1 <= ind - x0 <= ind - 1, 1 <= ind - x0 <= 17 + R64 = ten2k64[ind - x0]; + } + res.w[1] = 0; + res.w[0] = R64; + } else if (ind <= 38) { + // 19 <= ind <= 38 + P128.w[1] = res.w[1]; + P128.w[0] = res.w[0]; + round128_19_38 (ind, x0, P128, &res, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + if (incr_exp) { + // R128 = 10^(ind-x0), 1 <= ind - x0 <= ind - 1, 1 <= ind - x0 <= 37 + if (ind - x0 <= 19) { // 1 <= ind - x0 <= 19 + res.w[0] = ten2k64[ind - x0]; + // res.w[1] stays 0 + } else { // 20 <= ind - x0 <= 37 + res.w[0] = ten2k128[ind - x0 - 20].w[0]; + res.w[1] = ten2k128[ind - x0 - 20].w[1]; + } + } + } + // avoid a double rounding error + if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && + is_midpoint_lt_even) { // double rounding error upward + // res = res - 1 + res.w[0]--; + if (res.w[0] == 0xffffffffffffffffull) + res.w[1]--; + // Note: a double rounding error upward is not possible; for this + // the result after the first rounding would have to be 99...95 + // (35 digits in all), possibly followed by a number of zeros; this + // not possible in Cases (2)-(6) which may get here + is_midpoint_lt_even = 0; + is_inexact_lt_midpoint = 1; + } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && + is_midpoint_gt_even) { // double rounding error downward + // res = res + 1 + res.w[0]++; + if (res.w[0] == 0) + res.w[1]++; + is_midpoint_gt_even = 0; + is_inexact_gt_midpoint = 1; + } else if (!is_midpoint_lt_even && !is_midpoint_gt_even && + !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) { + // if this second rounding was exact the result may still be + // inexact because of the first rounding + if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) { + is_inexact_gt_midpoint = 1; + } + if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) { + is_inexact_lt_midpoint = 1; + } + } else if (is_midpoint_gt_even && + (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) { + // pulled up to a midpoint + is_inexact_lt_midpoint = 1; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else if (is_midpoint_lt_even && + (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) { + // pulled down to a midpoint + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 1; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else { + ; + } + // adjust exponent + e3 = e3 + x0; + if (!is_midpoint_lt_even && !is_midpoint_gt_even && + !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) { + if (is_midpoint_lt_even0 || is_midpoint_gt_even0 || + is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0) { + is_inexact_lt_midpoint = 1; + } + } + } else { + ; // not underflow + } + // check for inexact result + if (is_inexact_lt_midpoint || is_inexact_gt_midpoint || + is_midpoint_lt_even || is_midpoint_gt_even) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + if (is_tiny) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + // now check for significand = 10^34 (may have resulted from going + // back to case2_repeat) + if (res.w[1] == 0x0001ed09bead87c0ull && + res.w[0] == 0x378d8e6400000000ull) { // if res = 10^34 + res.w[1] = 0x0000314dc6448d93ull; // res = 10^33 + res.w[0] = 0x38c15b0a00000000ull; + e3 = e3 + 1; + } + res.w[1] = z_sign | ((UINT64) (e3 + 6176) << 49) | res.w[1]; + // check for overflow + if (rnd_mode == ROUNDING_TO_NEAREST && e3 > expmax) { + res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf + res.w[0] = 0x0000000000000000ull; + *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION); + } + if (rnd_mode != ROUNDING_TO_NEAREST) { + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, is_midpoint_gt_even, + e3, &res, pfpsf); + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + + } else { + + // we get here only if delta <= 1 in Cases (2), (3), (4), (5), or (6) and + // the signs of x*y and z are opposite; in these cases massive + // cancellation can occur, so it is better to scale either C3 or C4 and + // to perform the subtraction before rounding; rounding is performed + // next, depending on the number of decimal digits in the result and on + // the exponent value + // Note: overlow is not possible in this case + // this is similar to Cases (15), (16), and (17) + + if (delta + q4 < q3) { // from Case (6) + // Case (6) with 0<= delta <= 1 is similar to Cases (15), (16), and + // (17) if we swap (C3, C4), (q3, q4), (e3, e4), (z_sign, p_sign) + // and call add_and_round; delta stays positive + // C4.w[3] = 0 and C4.w[2] = 0, so swap just the low part of C4 with C3 + P128.w[1] = C3.w[1]; + P128.w[0] = C3.w[0]; + C3.w[1] = C4.w[1]; + C3.w[0] = C4.w[0]; + C4.w[1] = P128.w[1]; + C4.w[0] = P128.w[0]; + ind = q3; + q3 = q4; + q4 = ind; + ind = e3; + e3 = e4; + e4 = ind; + tmp_sign = z_sign; + z_sign = p_sign; + p_sign = tmp_sign; + } else { // from Cases (2), (3), (4), (5) + // In Cases (2), (3), (4), (5) with 0 <= delta <= 1 C3 has to be + // scaled up by q4 + delta - q3; this is the same as in Cases (15), + // (16), and (17) if we just change the sign of delta + delta = -delta; + } + add_and_round (q3, q4, e4, delta, p34, z_sign, p_sign, C3, C4, + rnd_mode, &is_midpoint_lt_even, + &is_midpoint_gt_even, &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint, pfpsf, &res); + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + + } + + } else { // if delta < 0 + + delta = -delta; + + if (p34 < q4 && q4 <= delta) { // Case (7) + + // truncate C4 to p34 digits into res + // x = q4-p34, 1 <= x <= 34 because 35 <= q4 <= 68 + x0 = q4 - p34; + if (q4 <= 38) { + P128.w[1] = C4.w[1]; + P128.w[0] = C4.w[0]; + round128_19_38 (q4, x0, P128, &res, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + } else if (q4 <= 57) { // 35 <= q4 <= 57 + P192.w[2] = C4.w[2]; + P192.w[1] = C4.w[1]; + P192.w[0] = C4.w[0]; + round192_39_57 (q4, x0, P192, &R192, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + res.w[0] = R192.w[0]; + res.w[1] = R192.w[1]; + } else { // if (q4 <= 68) + round256_58_76 (q4, x0, C4, &R256, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + res.w[0] = R256.w[0]; + res.w[1] = R256.w[1]; + } + e4 = e4 + x0; + if (incr_exp) { + e4 = e4 + 1; + } + if (!is_midpoint_lt_even && !is_midpoint_gt_even && + !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) { + // if C4 rounded to p34 digits is exact then the result is inexact, + // in a way that depends on the signs of x * y and z + if (p_sign == z_sign) { + is_inexact_lt_midpoint = 1; + } else { // if (p_sign != z_sign) + if (res.w[1] != 0x0000314dc6448d93ull || + res.w[0] != 0x38c15b0a00000000ull) { // res != 10^33 + is_inexact_gt_midpoint = 1; + } else { // res = 10^33 and exact is a special case + // if C3 < 1/2 ulp then res = 10^33 and is_inexact_gt_midpoint = 1 + // if C3 = 1/2 ulp then res = 10^33 and is_midpoint_lt_even = 1 + // if C3 > 1/2 ulp then res = 10^34-1 and is_inexact_lt_midpoint = 1 + // Note: ulp is really ulp/10 (after borrow which propagates to msd) + if (delta > p34 + 1) { // C3 < 1/2 + // res = 10^33, unchanged + is_inexact_gt_midpoint = 1; + } else { // if (delta == p34 + 1) + if (q3 <= 19) { + if (C3.w[0] < midpoint64[q3 - 1]) { // C3 < 1/2 ulp + // res = 10^33, unchanged + is_inexact_gt_midpoint = 1; + } else if (C3.w[0] == midpoint64[q3 - 1]) { // C3 = 1/2 ulp + // res = 10^33, unchanged + is_midpoint_lt_even = 1; + } else { // if (C3.w[0] > midpoint64[q3-1]), C3 > 1/2 ulp + res.w[1] = 0x0001ed09bead87c0ull; // 10^34 - 1 + res.w[0] = 0x378d8e63ffffffffull; + e4 = e4 - 1; + is_inexact_lt_midpoint = 1; + } + } else { // if (20 <= q3 <=34) + if (C3.w[1] < midpoint128[q3 - 20].w[1] || + (C3.w[1] == midpoint128[q3 - 20].w[1] && + C3.w[0] < midpoint128[q3 - 20].w[0])) { // C3 < 1/2 ulp + // res = 10^33, unchanged + is_inexact_gt_midpoint = 1; + } else if (C3.w[1] == midpoint128[q3 - 20].w[1] && + C3.w[0] == midpoint128[q3 - 20].w[0]) { // C3 = 1/2 ulp + // res = 10^33, unchanged + is_midpoint_lt_even = 1; + } else { // if (C3 > midpoint128[q3-20]), C3 > 1/2 ulp + res.w[1] = 0x0001ed09bead87c0ull; // 10^34 - 1 + res.w[0] = 0x378d8e63ffffffffull; + e4 = e4 - 1; + is_inexact_lt_midpoint = 1; + } + } + } + } + } + } else if (is_midpoint_lt_even) { + if (z_sign != p_sign) { + // needs correction: res = res - 1 + res.w[0] = res.w[0] - 1; + if (res.w[0] == 0xffffffffffffffffull) + res.w[1]--; + // if it is (10^33-1)*10^e4 then the corect result is + // (10^34-1)*10(e4-1) + if (res.w[1] == 0x0000314dc6448d93ull && + res.w[0] == 0x38c15b09ffffffffull) { + res.w[1] = 0x0001ed09bead87c0ull; // 10^34 - 1 + res.w[0] = 0x378d8e63ffffffffull; + e4 = e4 - 1; + } + is_midpoint_lt_even = 0; + is_inexact_lt_midpoint = 1; + } else { // if (z_sign == p_sign) + is_midpoint_lt_even = 0; + is_inexact_gt_midpoint = 1; + } + } else if (is_midpoint_gt_even) { + if (z_sign == p_sign) { + // needs correction: res = res + 1 (cannot cross in the next binade) + res.w[0] = res.w[0] + 1; + if (res.w[0] == 0x0000000000000000ull) + res.w[1]++; + is_midpoint_gt_even = 0; + is_inexact_gt_midpoint = 1; + } else { // if (z_sign != p_sign) + is_midpoint_gt_even = 0; + is_inexact_lt_midpoint = 1; + } + } else { + ; // the rounded result is already correct + } + // check for overflow + if (rnd_mode == ROUNDING_TO_NEAREST && e4 > expmax) { + res.w[1] = p_sign | 0x7800000000000000ull; + res.w[0] = 0x0000000000000000ull; + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + } else { // no overflow or not RN + p_exp = ((UINT64) (e4 + 6176) << 49); + res.w[1] = p_sign | (p_exp & MASK_EXP) | res.w[1]; + } + if (rnd_mode != ROUNDING_TO_NEAREST) { + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, is_midpoint_gt_even, + e4, &res, pfpsf); + } + if (is_inexact_lt_midpoint || is_inexact_gt_midpoint || + is_midpoint_lt_even || is_midpoint_gt_even) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + + } else if ((q4 <= p34 && p34 <= delta) || // Case (8) + (q4 <= delta && delta < p34 && p34 < delta + q3) || // Case (9) + (q4 <= delta && delta + q3 <= p34) || // Case (10) + (delta < q4 && q4 <= p34 && p34 < delta + q3) || // Case (13) + (delta < q4 && q4 <= delta + q3 && delta + q3 <= p34) || // Case (14) + (delta + q3 < q4 && q4 <= p34)) { // Case (18) + + // Case (8) is similar to Case (1), with C3 and C4 swapped + // Case (9) is similar to Case (2), with C3 and C4 swapped + // Case (10) is similar to Case (3), with C3 and C4 swapped + // Case (13) is similar to Case (4), with C3 and C4 swapped + // Case (14) is similar to Case (5), with C3 and C4 swapped + // Case (18) is similar to Case (6), with C3 and C4 swapped + + // swap (C3, C4), (q3, q4), (e3, 34), (z_sign, p_sign), (z_exp, p_exp) + // and go back to delta_ge_zero + // C4.w[3] = 0 and C4.w[2] = 0, so swap just the low part of C4 with C3 + P128.w[1] = C3.w[1]; + P128.w[0] = C3.w[0]; + C3.w[1] = C4.w[1]; + C3.w[0] = C4.w[0]; + C4.w[1] = P128.w[1]; + C4.w[0] = P128.w[0]; + ind = q3; + q3 = q4; + q4 = ind; + ind = e3; + e3 = e4; + e4 = ind; + tmp_sign = z_sign; + z_sign = p_sign; + p_sign = tmp_sign; + tmp.ui64 = z_exp; + z_exp = p_exp; + p_exp = tmp.ui64; + goto delta_ge_zero; + + } else if ((p34 <= delta && delta < q4 && q4 < delta + q3) || // Case (11) + (delta < p34 && p34 < q4 && q4 < delta + q3)) { // Case (12) + + // round C3 to nearest to q3 - x0 digits, where x0 = e4 - e3, + // 1 <= x0 <= q3 - 1 <= p34 - 1 + x0 = e4 - e3; // or x0 = delta + q3 - q4 + if (q3 <= 18) { // 2 <= q3 <= 18 + round64_2_18 (q3, x0, C3.w[0], &R64, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint); + // C3.w[1] = 0; + C3.w[0] = R64; + } else if (q3 <= 38) { + round128_19_38 (q3, x0, C3, &R128, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + C3.w[1] = R128.w[1]; + C3.w[0] = R128.w[0]; + } + // the rounded result has q3 - x0 digits + // we want the exponent to be e4, so if incr_exp = 1 then + // multiply the rounded result by 10 - it will still fit in 113 bits + if (incr_exp) { + // 64 x 128 -> 128 + P128.w[1] = C3.w[1]; + P128.w[0] = C3.w[0]; + __mul_64x128_to_128 (C3, ten2k64[1], P128); + } + e3 = e3 + x0; // this is e4 + // now add/subtract the 256-bit C4 and the new (and shorter) 128-bit C3; + // the result will have the sign of x * y; the exponent is e4 + R256.w[3] = 0; + R256.w[2] = 0; + R256.w[1] = C3.w[1]; + R256.w[0] = C3.w[0]; + if (p_sign == z_sign) { // R256 = C4 + R256 + add256 (C4, R256, &R256); + } else { // if (p_sign != z_sign) { // R256 = C4 - R256 + sub256 (C4, R256, &R256); // the result cannot be pure zero + // because the result has opposite sign to that of R256 which was + // rounded, need to change the rounding indicators + lsb = C4.w[0] & 0x01; + if (is_inexact_lt_midpoint) { + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 1; + } else if (is_inexact_gt_midpoint) { + is_inexact_gt_midpoint = 0; + is_inexact_lt_midpoint = 1; + } else if (lsb == 0) { + if (is_midpoint_lt_even) { + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 1; + } else if (is_midpoint_gt_even) { + is_midpoint_gt_even = 0; + is_midpoint_lt_even = 1; + } else { + ; + } + } else if (lsb == 1) { + if (is_midpoint_lt_even) { + // res = res + 1 + R256.w[0]++; + if (R256.w[0] == 0x0) { + R256.w[1]++; + if (R256.w[1] == 0x0) { + R256.w[2]++; + if (R256.w[2] == 0x0) { + R256.w[3]++; + } + } + } + // no check for rounding overflow - R256 was a difference + } else if (is_midpoint_gt_even) { + // res = res - 1 + R256.w[0]--; + if (R256.w[0] == 0xffffffffffffffffull) { + R256.w[1]--; + if (R256.w[1] == 0xffffffffffffffffull) { + R256.w[2]--; + if (R256.w[2] == 0xffffffffffffffffull) { + R256.w[3]--; + } + } + } + } else { + ; + } + } else { + ; + } + } + // determine the number of decimal digits in R256 + ind = nr_digits256 (R256); // ind >= p34 + // if R256 is sum, then ind > p34; if R256 is a difference, then + // ind >= p34; this means that we can calculate the result rounded to + // the destination precision, with unbounded exponent, starting from R256 + // and using the indicators from the rounding of C3 to avoid a double + // rounding error + + if (ind < p34) { + ; + } else if (ind == p34) { + // the result rounded to the destination precision with + // unbounded exponent + // is (-1)^p_sign * R256 * 10^e4 + res.w[1] = R256.w[1]; + res.w[0] = R256.w[0]; + } else { // if (ind > p34) + // if more than P digits, round to nearest to P digits + // round R256 to p34 digits + x0 = ind - p34; // 1 <= x0 <= 34 as 35 <= ind <= 68 + // save C3 rounding indicators to help avoid double rounding error + is_inexact_lt_midpoint0 = is_inexact_lt_midpoint; + is_inexact_gt_midpoint0 = is_inexact_gt_midpoint; + is_midpoint_lt_even0 = is_midpoint_lt_even; + is_midpoint_gt_even0 = is_midpoint_gt_even; + // initialize rounding indicators + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + // round to p34 digits; the result fits in 113 bits + if (ind <= 38) { + P128.w[1] = R256.w[1]; + P128.w[0] = R256.w[0]; + round128_19_38 (ind, x0, P128, &R128, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + } else if (ind <= 57) { + P192.w[2] = R256.w[2]; + P192.w[1] = R256.w[1]; + P192.w[0] = R256.w[0]; + round192_39_57 (ind, x0, P192, &R192, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + R128.w[1] = R192.w[1]; + R128.w[0] = R192.w[0]; + } else { // if (ind <= 68) + round256_58_76 (ind, x0, R256, &R256, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + R128.w[1] = R256.w[1]; + R128.w[0] = R256.w[0]; + } + // the rounded result has p34 = 34 digits + e4 = e4 + x0 + incr_exp; + + res.w[1] = R128.w[1]; + res.w[0] = R128.w[0]; + + // avoid a double rounding error + if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && + is_midpoint_lt_even) { // double rounding error upward + // res = res - 1 + res.w[0]--; + if (res.w[0] == 0xffffffffffffffffull) + res.w[1]--; + is_midpoint_lt_even = 0; + is_inexact_lt_midpoint = 1; + // Note: a double rounding error upward is not possible; for this + // the result after the first rounding would have to be 99...95 + // (35 digits in all), possibly followed by a number of zeros; this + // not possible in Cases (2)-(6) or (15)-(17) which may get here + // if this is 10^33 - 1 make it 10^34 - 1 and decrement exponent + if (res.w[1] == 0x0000314dc6448d93ull && + res.w[0] == 0x38c15b09ffffffffull) { // 10^33 - 1 + res.w[1] = 0x0001ed09bead87c0ull; // 10^34 - 1 + res.w[0] = 0x378d8e63ffffffffull; + e4--; + } + } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && + is_midpoint_gt_even) { // double rounding error downward + // res = res + 1 + res.w[0]++; + if (res.w[0] == 0) + res.w[1]++; + is_midpoint_gt_even = 0; + is_inexact_gt_midpoint = 1; + } else if (!is_midpoint_lt_even && !is_midpoint_gt_even && + !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) { + // if this second rounding was exact the result may still be + // inexact because of the first rounding + if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) { + is_inexact_gt_midpoint = 1; + } + if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) { + is_inexact_lt_midpoint = 1; + } + } else if (is_midpoint_gt_even && + (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) { + // pulled up to a midpoint + is_inexact_lt_midpoint = 1; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else if (is_midpoint_lt_even && + (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) { + // pulled down to a midpoint + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 1; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else { + ; + } + } + + // determine tininess + if (rnd_mode == ROUNDING_TO_NEAREST) { + if (e4 < expmin) { + is_tiny = 1; // for other rounding modes apply correction + } + } else { + // for RM, RP, RZ, RA apply correction in order to determine tininess + // but do not save the result; apply the correction to + // (-1)^p_sign * res * 10^0 + P128.w[1] = p_sign | 0x3040000000000000ull | res.w[1]; + P128.w[0] = res.w[0]; + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, is_midpoint_gt_even, + 0, &P128, pfpsf); + scale = ((P128.w[1] & MASK_EXP) >> 49) - 6176; // -1, 0, or +1 + // the number of digits in the significand is p34 = 34 + if (e4 + scale < expmin) { + is_tiny = 1; + } + } + + // the result rounded to the destination precision with unbounded exponent + // is (-1)^p_sign * res * 10^e4 + res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | res.w[1]; // RN + // res.w[0] unchanged; + // Note: res is correct only if expmin <= e4 <= expmax + ind = p34; // the number of decimal digits in the signifcand of res + + // at this point we have the result rounded with unbounded exponent in + // res and we know its tininess: + // res = (-1)^p_sign * significand * 10^e4, + // where q (significand) = ind = p34 + // Note: res is correct only if expmin <= e4 <= expmax + + // check for overflow if RN + if (rnd_mode == ROUNDING_TO_NEAREST + && (ind + e4) > (p34 + expmax)) { + res.w[1] = p_sign | 0x7800000000000000ull; + res.w[0] = 0x0000000000000000ull; + *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION); + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + } // else not overflow or not RN, so continue + + // from this point on this is similar to the last part of the computation + // for Cases (15), (16), (17) + + // if (e4 >= expmin) we have the result rounded with bounded exponent + if (e4 < expmin) { + x0 = expmin - e4; // x0 >= 1; the number of digits to chop off of res + // where the result rounded [at most] once is + // (-1)^p_sign * significand_res * 10^e4 + + // avoid double rounding error + is_inexact_lt_midpoint0 = is_inexact_lt_midpoint; + is_inexact_gt_midpoint0 = is_inexact_gt_midpoint; + is_midpoint_lt_even0 = is_midpoint_lt_even; + is_midpoint_gt_even0 = is_midpoint_gt_even; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + + if (x0 > ind) { + // nothing is left of res when moving the decimal point left x0 digits + is_inexact_lt_midpoint = 1; + res.w[1] = p_sign | 0x0000000000000000ull; + res.w[0] = 0x0000000000000000ull; + e4 = expmin; + } else if (x0 == ind) { // 1 <= x0 = ind <= p34 = 34 + // this is <, =, or > 1/2 ulp + // compare the ind-digit value in the significand of res with + // 1/2 ulp = 5*10^(ind-1), i.e. determine whether it is + // less than, equal to, or greater than 1/2 ulp (significand of res) + R128.w[1] = res.w[1] & MASK_COEFF; + R128.w[0] = res.w[0]; + if (ind <= 19) { + if (R128.w[0] < midpoint64[ind - 1]) { // < 1/2 ulp + lt_half_ulp = 1; + is_inexact_lt_midpoint = 1; + } else if (R128.w[0] == midpoint64[ind - 1]) { // = 1/2 ulp + eq_half_ulp = 1; + is_midpoint_gt_even = 1; + } else { // > 1/2 ulp + gt_half_ulp = 1; + is_inexact_gt_midpoint = 1; + } + } else { // if (ind <= 38) + if (R128.w[1] < midpoint128[ind - 20].w[1] || + (R128.w[1] == midpoint128[ind - 20].w[1] && + R128.w[0] < midpoint128[ind - 20].w[0])) { // < 1/2 ulp + lt_half_ulp = 1; + is_inexact_lt_midpoint = 1; + } else if (R128.w[1] == midpoint128[ind - 20].w[1] && + R128.w[0] == midpoint128[ind - 20].w[0]) { // = 1/2 ulp + eq_half_ulp = 1; + is_midpoint_gt_even = 1; + } else { // > 1/2 ulp + gt_half_ulp = 1; + is_inexact_gt_midpoint = 1; + } + } + if (lt_half_ulp || eq_half_ulp) { + // res = +0.0 * 10^expmin + res.w[1] = 0x0000000000000000ull; + res.w[0] = 0x0000000000000000ull; + } else { // if (gt_half_ulp) + // res = +1 * 10^expmin + res.w[1] = 0x0000000000000000ull; + res.w[0] = 0x0000000000000001ull; + } + res.w[1] = p_sign | res.w[1]; + e4 = expmin; + } else { // if (1 <= x0 <= ind - 1 <= 33) + // round the ind-digit result to ind - x0 digits + + if (ind <= 18) { // 2 <= ind <= 18 + round64_2_18 (ind, x0, res.w[0], &R64, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + res.w[1] = 0x0; + res.w[0] = R64; + } else if (ind <= 38) { + P128.w[1] = res.w[1] & MASK_COEFF; + P128.w[0] = res.w[0]; + round128_19_38 (ind, x0, P128, &res, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint); + } + e4 = e4 + x0; // expmin + // we want the exponent to be expmin, so if incr_exp = 1 then + // multiply the rounded result by 10 - it will still fit in 113 bits + if (incr_exp) { + // 64 x 128 -> 128 + P128.w[1] = res.w[1] & MASK_COEFF; + P128.w[0] = res.w[0]; + __mul_64x128_to_128 (res, ten2k64[1], P128); + } + res.w[1] = + p_sign | ((UINT64) (e4 + 6176) << 49) | (res. + w[1] & MASK_COEFF); + // avoid a double rounding error + if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && + is_midpoint_lt_even) { // double rounding error upward + // res = res - 1 + res.w[0]--; + if (res.w[0] == 0xffffffffffffffffull) + res.w[1]--; + // Note: a double rounding error upward is not possible; for this + // the result after the first rounding would have to be 99...95 + // (35 digits in all), possibly followed by a number of zeros; this + // not possible in this underflow case + is_midpoint_lt_even = 0; + is_inexact_lt_midpoint = 1; + } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && + is_midpoint_gt_even) { // double rounding error downward + // res = res + 1 + res.w[0]++; + if (res.w[0] == 0) + res.w[1]++; + is_midpoint_gt_even = 0; + is_inexact_gt_midpoint = 1; + } else if (!is_midpoint_lt_even && !is_midpoint_gt_even && + !is_inexact_lt_midpoint + && !is_inexact_gt_midpoint) { + // if this second rounding was exact the result may still be + // inexact because of the first rounding + if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) { + is_inexact_gt_midpoint = 1; + } + if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) { + is_inexact_lt_midpoint = 1; + } + } else if (is_midpoint_gt_even && + (is_inexact_gt_midpoint0 + || is_midpoint_lt_even0)) { + // pulled up to a midpoint + is_inexact_lt_midpoint = 1; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else if (is_midpoint_lt_even && + (is_inexact_lt_midpoint0 + || is_midpoint_gt_even0)) { + // pulled down to a midpoint + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 1; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else { + ; + } + } + } + // res contains the correct result + // apply correction if not rounding to nearest + if (rnd_mode != ROUNDING_TO_NEAREST) { + rounding_correction (rnd_mode, + is_inexact_lt_midpoint, + is_inexact_gt_midpoint, + is_midpoint_lt_even, is_midpoint_gt_even, + e4, &res, pfpsf); + } + if (is_midpoint_lt_even || is_midpoint_gt_even || + is_inexact_lt_midpoint || is_inexact_gt_midpoint) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + if (is_tiny) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + + } else if ((p34 <= delta && delta + q3 <= q4) || // Case (15) + (delta < p34 && p34 < delta + q3 && delta + q3 <= q4) || //Case (16) + (delta + q3 <= p34 && p34 < q4)) { // Case (17) + + // calculate first the result rounded to the destination precision, with + // unbounded exponent + + add_and_round (q3, q4, e4, delta, p34, z_sign, p_sign, C3, C4, + rnd_mode, &is_midpoint_lt_even, + &is_midpoint_gt_even, &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint, pfpsf, &res); + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + + } else { + ; + } + + } // end if delta < 0 + + *ptr_is_midpoint_lt_even = is_midpoint_lt_even; + *ptr_is_midpoint_gt_even = is_midpoint_gt_even; + *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint; + *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint; + BID_SWAP128 (res); + BID_RETURN (res) + +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_fma (UINT128 * pres, UINT128 * px, UINT128 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px, y = *py, z = *pz; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128_fma (UINT128 x, UINT128 y, UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int is_midpoint_lt_even, is_midpoint_gt_even, + is_inexact_lt_midpoint, is_inexact_gt_midpoint; + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; + +#if DECIMAL_CALL_BY_REFERENCE + bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint, + &res, &x, &y, &z + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint, x, y, + z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128ddd_fma (UINT128 * pres, UINT64 * px, UINT64 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px, y = *py, z = *pz; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128ddd_fma (UINT64 x, UINT64 y, UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0, + is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; + UINT128 x1, y1, z1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint, + &res, &x1, &y1, &z1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint, x1, y1, + z1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128ddq_fma (UINT128 * pres, UINT64 * px, UINT64 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px, y = *py; + UINT128 z = *pz; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128ddq_fma (UINT64 x, UINT64 y, UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0, + is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; + UINT128 x1, y1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint, + &res, &x1, &y1, &z + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint, x1, y1, + z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128dqd_fma (UINT128 * pres, UINT64 * px, UINT128 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px, z = *pz; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128dqd_fma (UINT64 x, UINT128 y, UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0, + is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; + UINT128 x1, z1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint, + &res, &x1, py, &z1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint, x1, y, + z1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128dqq_fma (UINT128 * pres, UINT64 * px, UINT128 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128dqq_fma (UINT64 x, UINT128 y, UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0, + is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; + UINT128 x1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint, + &res, &x1, py, pz + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint, x1, y, + z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128qdd_fma (UINT128 * pres, UINT128 * px, UINT64 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 y = *py, z = *pz; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128qdd_fma (UINT128 x, UINT64 y, UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0, + is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; + UINT128 y1, z1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint, + &res, px, &y1, &z1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint, x, y1, + z1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128qdq_fma (UINT128 * pres, UINT128 * px, UINT64 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128qdq_fma (UINT128 x, UINT64 y, UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0, + is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; + UINT128 y1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint, + &res, px, &y1, pz + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint, x, y1, + z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128qqd_fma (UINT128 * pres, UINT128 * px, UINT128 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 z = *pz; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128qqd_fma (UINT128 x, UINT128 y, UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0, + is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; + UINT128 z1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint, + &res, px, py, &z1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, + &is_inexact_gt_midpoint, x, y, + z1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + +// Note: bid128qqq_fma is represented by bid128_fma + +// Note: bid64ddd_fma is represented by bid64_fma + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64ddq_fma (UINT64 * pres, UINT64 * px, UINT64 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px, y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64ddq_fma (UINT64 x, UINT64 y, UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res1 = 0xbaddbaddbaddbaddull; + UINT128 x1, y1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64qqq_fma (&res1, &x1, &y1, pz + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res1 = bid64qqq_fma (x1, y1, z + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res1); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64dqd_fma (UINT64 * pres, UINT64 * px, UINT128 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px, z = *pz; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64dqd_fma (UINT64 x, UINT128 y, UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res1 = 0xbaddbaddbaddbaddull; + UINT128 x1, z1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64qqq_fma (&res1, &x1, py, &z1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res1 = bid64qqq_fma (x1, y, z1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res1); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64dqq_fma (UINT64 * pres, UINT64 * px, UINT128 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64dqq_fma (UINT64 x, UINT128 y, UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res1 = 0xbaddbaddbaddbaddull; + UINT128 x1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64qqq_fma (&res1, &x1, py, pz + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res1 = bid64qqq_fma (x1, y, z + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res1); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64qdd_fma (UINT64 * pres, UINT128 * px, UINT64 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 y = *py, z = *pz; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64qdd_fma (UINT128 x, UINT64 y, UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res1 = 0xbaddbaddbaddbaddull; + UINT128 y1, z1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64qqq_fma (&res1, px, &y1, &z1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res1 = bid64qqq_fma (x, y1, z1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res1); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64qdq_fma (UINT64 * pres, UINT128 * px, UINT64 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64qdq_fma (UINT128 x, UINT64 y, UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res1 = 0xbaddbaddbaddbaddull; + UINT128 y1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64qqq_fma (&res1, px, &y1, pz + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res1 = bid64qqq_fma (x, y1, z + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res1); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64qqd_fma (UINT64 * pres, UINT128 * px, UINT128 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 z = *pz; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64qqd_fma (UINT128 x, UINT128 y, UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res1 = 0xbaddbaddbaddbaddull; + UINT128 z1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64qqq_fma (&res1, px, py, &z1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res1 = bid64qqq_fma (x, y, z1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res1); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64qqq_fma (UINT64 * pres, UINT128 * px, UINT128 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px, y = *py, z = *pz; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64qqq_fma (UINT128 x, UINT128 y, UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int is_midpoint_lt_even0 = 0, is_midpoint_gt_even0 = 0, + is_inexact_lt_midpoint0 = 0, is_inexact_gt_midpoint0 = 0; + int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0, + is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; + int incr_exp; + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; + UINT128 res128 = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; + UINT64 res1 = 0xbaddbaddbaddbaddull; + unsigned int save_fpsf; // needed because of the call to bid128_ext_fma + UINT64 sign; + UINT64 exp; + int unbexp; + UINT128 C; + BID_UI64DOUBLE tmp; + int nr_bits; + int q, x0; + int scale; + int lt_half_ulp = 0, eq_half_ulp = 0; + + // Note: for rounding modes other than RN or RA, the result can be obtained + // by rounding first to BID128 and then to BID64 + + save_fpsf = *pfpsf; // sticky bits - caller value must be preserved + *pfpsf = 0; + +#if DECIMAL_CALL_BY_REFERENCE + bid128_ext_fma (&is_midpoint_lt_even0, &is_midpoint_gt_even0, + &is_inexact_lt_midpoint0, &is_inexact_gt_midpoint0, + &res, &x, &y, &z + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + res = bid128_ext_fma (&is_midpoint_lt_even0, &is_midpoint_gt_even0, + &is_inexact_lt_midpoint0, + &is_inexact_gt_midpoint0, x, y, + z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + + if ((rnd_mode == ROUNDING_DOWN) || (rnd_mode == ROUNDING_UP) || + (rnd_mode == ROUNDING_TO_ZERO) || // no double rounding error is possible + ((res.w[HIGH_128W] & MASK_NAN) == MASK_NAN) || //res=QNaN (cannot be SNaN) + ((res.w[HIGH_128W] & MASK_ANY_INF) == MASK_INF)) { // result is infinity +#if DECIMAL_CALL_BY_REFERENCE + bid128_to_bid64 (&res1, &res _RND_MODE_ARG _EXC_FLAGS_ARG); +#else + res1 = bid128_to_bid64 (res _RND_MODE_ARG _EXC_FLAGS_ARG); +#endif + // determine the unbiased exponent of the result + unbexp = ((res1 >> 53) & 0x3ff) - 398; + + // if subnormal, res1 must have exp = -398 + // if tiny and inexact set underflow and inexact status flags + if (!((res1 & MASK_NAN) == MASK_NAN) && // res1 not NaN + (unbexp == -398) + && ((res1 & MASK_BINARY_SIG1) < 1000000000000000ull) + && (is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0 + || is_midpoint_lt_even0 || is_midpoint_gt_even0)) { + // set the inexact flag and the underflow flag + *pfpsf |= (INEXACT_EXCEPTION | UNDERFLOW_EXCEPTION); + } else if (is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0 || + is_midpoint_lt_even0 || is_midpoint_gt_even0) { + // set the inexact flag and the underflow flag + *pfpsf |= INEXACT_EXCEPTION; + } + + *pfpsf |= save_fpsf; + BID_RETURN (res1); + } // else continue, and use rounding to nearest to round to 16 digits + + // at this point the result is rounded to nearest (even or away) to 34 digits + // (or less if exact), and it is zero or finite non-zero canonical [sub]normal + sign = res.w[HIGH_128W] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + exp = res.w[HIGH_128W] & MASK_EXP; // biased and shifted left 49 bits + unbexp = (exp >> 49) - 6176; + C.w[1] = res.w[HIGH_128W] & MASK_COEFF; + C.w[0] = res.w[LOW_128W]; + + if ((C.w[1] == 0x0 && C.w[0] == 0x0) || // result is zero + (unbexp <= (-398 - 35)) || (unbexp >= (369 + 16))) { + // clear under/overflow +#if DECIMAL_CALL_BY_REFERENCE + bid128_to_bid64 (&res1, &res _RND_MODE_ARG _EXC_FLAGS_ARG); +#else + res1 = bid128_to_bid64 (res _RND_MODE_ARG _EXC_FLAGS_ARG); +#endif + *pfpsf |= save_fpsf; + BID_RETURN (res1); + } // else continue + + // -398 - 34 <= unbexp <= 369 + 15 + if (rnd_mode == ROUNDING_TIES_AWAY) { + // apply correction, if needed, to make the result rounded to nearest-even + if (is_midpoint_gt_even) { + // res = res - 1 + res1--; // res1 is now even + } // else the result is already correctly rounded to nearest-even + } + // at this point the result is finite, non-zero canonical normal or subnormal, + // and in most cases overflow or underflow will not occur + + // determine the number of digits q in the result + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C.w[1] == 0) { + if (C.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp.d = (double) (C.w[0] >> 32); // exact conversion + nr_bits = + 33 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp.d = (double) (C.w[0]); // exact conversion + nr_bits = + 1 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp.d = (double) C.w[0]; // exact conversion + nr_bits = + 1 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C.w[1] != 0 => nr. bits = 64 + nr_bits (C.w[1]) + tmp.d = (double) C.w[1]; // exact conversion + nr_bits = + 65 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[nr_bits - 1].digits1; + if (C.w[1] > nr_digits[nr_bits - 1].threshold_hi || + (C.w[1] == nr_digits[nr_bits - 1].threshold_hi && + C.w[0] >= nr_digits[nr_bits - 1].threshold_lo)) + q++; + } + // if q > 16, round to nearest even to 16 digits (but for underflow it may + // have to be truncated even more) + if (q > 16) { + x0 = q - 16; + if (q <= 18) { + round64_2_18 (q, x0, C.w[0], &res1, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint); + } else { // 19 <= q <= 34 + round128_19_38 (q, x0, C, &res128, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint); + res1 = res128.w[0]; // the result fits in 64 bits + } + unbexp = unbexp + x0; + if (incr_exp) + unbexp++; + q = 16; // need to set in case denormalization is necessary + } else { + // the result does not require a second rounding (and it must have + // been exact in the first rounding, since q <= 16) + res1 = C.w[0]; + } + + // avoid a double rounding error + if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && + is_midpoint_lt_even) { // double rounding error upward + // res = res - 1 + res1--; // res1 becomes odd + is_midpoint_lt_even = 0; + is_inexact_lt_midpoint = 1; + if (res1 == 0x00038d7ea4c67fffull) { // 10^15 - 1 + res1 = 0x002386f26fc0ffffull; // 10^16 - 1 + unbexp--; + } + } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && + is_midpoint_gt_even) { // double rounding error downward + // res = res + 1 + res1++; // res1 becomes odd (so it cannot be 10^16) + is_midpoint_gt_even = 0; + is_inexact_gt_midpoint = 1; + } else if (!is_midpoint_lt_even && !is_midpoint_gt_even && + !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) { + // if this second rounding was exact the result may still be + // inexact because of the first rounding + if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) { + is_inexact_gt_midpoint = 1; + } + if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) { + is_inexact_lt_midpoint = 1; + } + } else if (is_midpoint_gt_even && + (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) { + // pulled up to a midpoint + is_inexact_lt_midpoint = 1; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else if (is_midpoint_lt_even && + (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) { + // pulled down to a midpoint + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 1; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else { + ; + } + // this is the result rounded correctly to nearest even, with unbounded exp. + + // check for overflow + if (q + unbexp > P16 + expmax16) { + res1 = sign | 0x7800000000000000ull; + *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION); + *pfpsf |= save_fpsf; + BID_RETURN (res1) + } else if (unbexp > expmax16) { // q + unbexp <= P16 + expmax16 + // not overflow; the result must be exact, and we can multiply res1 by + // 10^(unbexp - expmax16) and the product will fit in 16 decimal digits + scale = unbexp - expmax16; + res1 = res1 * ten2k64[scale]; // res1 * 10^scale + unbexp = expmax16; // unbexp - scale + } else { + ; // continue + } + + // check for underflow + if (q + unbexp < P16 + expmin16) { + if (unbexp < expmin16) { + // we must truncate more of res + x0 = expmin16 - unbexp; // x0 >= 1 + is_inexact_lt_midpoint0 = is_inexact_lt_midpoint; + is_inexact_gt_midpoint0 = is_inexact_gt_midpoint; + is_midpoint_lt_even0 = is_midpoint_lt_even; + is_midpoint_gt_even0 = is_midpoint_gt_even; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + // the number of decimal digits in res1 is q + if (x0 < q) { // 1 <= x0 <= q-1 => round res to q - x0 digits + // 2 <= q <= 16, 1 <= x0 <= 15 + round64_2_18 (q, x0, res1, &res1, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint); + if (incr_exp) { + // res1 = 10^(q-x0), 1 <= q - x0 <= q - 1, 1 <= q - x0 <= 15 + res1 = ten2k64[q - x0]; + } + unbexp = unbexp + x0; // expmin16 + } else if (x0 == q) { + // the second rounding is for 0.d(0)d(1)...d(q-1) * 10^emin + // determine relationship with 1/2 ulp + // q <= 16 + if (res1 < midpoint64[q - 1]) { // < 1/2 ulp + lt_half_ulp = 1; + is_inexact_lt_midpoint = 1; + } else if (res1 == midpoint64[q - 1]) { // = 1/2 ulp + eq_half_ulp = 1; + is_midpoint_gt_even = 1; + } else { // > 1/2 ulp + // gt_half_ulp = 1; + is_inexact_gt_midpoint = 1; + } + if (lt_half_ulp || eq_half_ulp) { + // res = +0.0 * 10^expmin16 + res1 = 0x0000000000000000ull; + } else { // if (gt_half_ulp) + // res = +1 * 10^expmin16 + res1 = 0x0000000000000001ull; + } + unbexp = expmin16; + } else { // if (x0 > q) + // the second rounding is for 0.0...d(0)d(1)...d(q-1) * 10^emin + res1 = 0x0000000000000000ull; + unbexp = expmin16; + is_inexact_lt_midpoint = 1; + } + // avoid a double rounding error + if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && + is_midpoint_lt_even) { // double rounding error upward + // res = res - 1 + res1--; // res1 becomes odd + is_midpoint_lt_even = 0; + is_inexact_lt_midpoint = 1; + } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && + is_midpoint_gt_even) { // double rounding error downward + // res = res + 1 + res1++; // res1 becomes odd + is_midpoint_gt_even = 0; + is_inexact_gt_midpoint = 1; + } else if (!is_midpoint_lt_even && !is_midpoint_gt_even && + !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) { + // if this rounding was exact the result may still be + // inexact because of the previous roundings + if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) { + is_inexact_gt_midpoint = 1; + } + if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) { + is_inexact_lt_midpoint = 1; + } + } else if (is_midpoint_gt_even && + (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) { + // pulled up to a midpoint + is_inexact_lt_midpoint = 1; + is_inexact_gt_midpoint = 0; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else if (is_midpoint_lt_even && + (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) { + // pulled down to a midpoint + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 1; + is_midpoint_lt_even = 0; + is_midpoint_gt_even = 0; + } else { + ; + } + } + // else if unbexp >= emin then q < P (because q + unbexp < P16 + expmin16) + // and the result is tiny and exact + + // check for inexact result + if (is_inexact_lt_midpoint || is_inexact_gt_midpoint || + is_midpoint_lt_even || is_midpoint_gt_even || + is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0 || + is_midpoint_lt_even0 || is_midpoint_gt_even0) { + // set the inexact flag and the underflow flag + *pfpsf |= (INEXACT_EXCEPTION | UNDERFLOW_EXCEPTION); + } + } else if (is_inexact_lt_midpoint || is_inexact_gt_midpoint || + is_midpoint_lt_even || is_midpoint_gt_even) { + *pfpsf |= INEXACT_EXCEPTION; + } + // this is the result rounded correctly to nearest, with bounded exponent + + if (rnd_mode == ROUNDING_TIES_AWAY && is_midpoint_gt_even) { // correction + // res = res + 1 + res1++; // res1 is now odd + } // else the result is already correct + + // assemble the result + if (res1 < 0x0020000000000000ull) { // res < 2^53 + res1 = sign | ((UINT64) (unbexp + 398) << 53) | res1; + } else { // res1 >= 2^53 + res1 = sign | MASK_STEERING_BITS | + ((UINT64) (unbexp + 398) << 51) | (res1 & MASK_BINARY_SIG2); + } + *pfpsf |= save_fpsf; + BID_RETURN (res1); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_logb.c b/gcc-4.4.3/libgcc/config/libbid/bid128_logb.c new file mode 100644 index 000000000..f462cf6a6 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_logb.c @@ -0,0 +1,58 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#define BID_128RES +#include "bid_internal.h" + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(int, bid128_logb, x) + + UINT128 CX; + UINT64 sign_x; + SINT64 D; + int_float f64, fx; + int exponent_x, bin_expon_cx, digits; + + if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN_VAL (0x80000000); + } + // find number of digits in coefficient + // 2^64 + f64.i = 0x5f800000; + // fx ~ CX + fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; + bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f; + digits = estimate_decimal_digits[bin_expon_cx]; + // scale = 38-estimate_decimal_digits[bin_expon_cx]; + D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1]; + if (D > 0 || (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0])) { + digits++; + } + + exponent_x = exponent_x - DECIMAL_EXPONENT_BIAS_128 - 1 + digits; + + BID_RETURN_VAL (exponent_x); + +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_minmax.c b/gcc-4.4.3/libgcc/config/libbid/bid128_minmax.c new file mode 100644 index 000000000..2bb049b13 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_minmax.c @@ -0,0 +1,1095 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#define BID_128RES +#include "bid_internal.h" + +/***************************************************************************** + * BID128 minimum number + *****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_minnum (UINT128 * pres, UINT128 * px, + UINT128 * py _EXC_FLAGS_PARAM) { + UINT128 x = *px; + UINT128 y = *py; +#else +UINT128 +bid128_minnum (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) { +#endif + + UINT128 res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0; + + BID_SWAP128 (x); + BID_SWAP128 (y); + + // check for non-canonical x + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16] + // check for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + } else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf + x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF); + x.w[0] = 0x0ull; + } else { // x is not special + // check for non-canonical values - treated as zero + if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11 + // non-canonical + x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP); + x.w[0] = 0x0ull; + } else { // G0_G1 != 11 + if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull || + ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull + && x.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP); + x.w[0] = 0x0ull; + } else { // canonical + ; + } + } + } + // check for non-canonical y + if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN + y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16] + // check for non-canonical NaN payload + if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (y.w[0] > 0x38c15b09ffffffffull))) { + y.w[1] = y.w[1] & 0xffffc00000000000ull; + y.w[0] = 0x0ull; + } + } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf + y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF); + y.w[0] = 0x0ull; + } else { // y is not special + // check for non-canonical values - treated as zero + if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11 + // non-canonical + y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP); + y.w[0] = 0x0ull; + } else { // G0_G1 != 11 + if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull || + ((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull + && y.w[0] > 0x378d8e63ffffffffull)) { + // y is non-canonical if coefficient is larger than 10^34 -1 + y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP); + y.w[0] = 0x0ull; + } else { // canonical + ; + } + } + } + + // NaN (CASE1) + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN + // if x is SNAN, then return quiet (x) + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x + res = x; + } else { // x is QNaN + if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN + if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN + *pfpsf |= INVALID_EXCEPTION; // set invalid flag + } + res = x; + } else { + res = y; + } + } + BID_RETURN (res); + } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not + if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y + res = y; + } else { + // will return x (which is not NaN) + res = x; + } + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). + if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = x; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return 0 + res = (((x.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y; + BID_RETURN (res); + } else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } + // CONVERT X + sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; + sig_x.w[0] = x.w[0]; + exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CONVERT Y + exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; + sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; + sig_y.w[0] = y.w[0]; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => ignore the exponent + // field + // (Any non-canonical # is considered 0) + if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) { + x_is_zero = 1; + } + if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) { + y_is_zero = 1; + } + + if (x_is_zero && y_is_zero) { + // if both numbers are zero, neither is greater => return either number + res = x; + BID_RETURN (res); + } else if (x_is_zero) { + // is x is zero, it is greater if Y is negative + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } else if (y_is_zero) { + // is y is zero, X is greater if it is positive + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x; + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative + if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison of + // the significands + if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)) ? y : x; + BID_RETURN (res); + } + // if both components are either bigger or smaller, it is clear what + // needs to be done + if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0] + && exp_x > exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x; + BID_RETURN (res); + } + if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0] + && exp_x < exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } + + diff = exp_x - exp_y; + + // if |exp_x - exp_y| < 33, it comes down to the compensated significand + if (diff > 0) { // to simplify the loop below, + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + // difference cannot be greater than 10^33 + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x; + BID_RETURN (res); + } + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + // if postitive, return whichever significand is larger + // (converse if negative) + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == + MASK_SIGN)) ? y : x; + BID_RETURN (res); + } + __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x); + // if postitive, return whichever significand is larger + // (converse if negative) + res = + (((sig_n_prime192.w[2] > 0) || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)) ? y : x; + BID_RETURN (res); + } + diff = exp_y - exp_x; + // if exp_x is 33 less than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + // if postitive, return whichever significand is larger + // (converse if negative) + res = + ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 + || (sig_n_prime256.w[1] > sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] > + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)) ? x : y; + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y); + // if postitive, return whichever significand is larger (converse if negative) + res = + ((sig_n_prime192.w[2] != 0 + || (sig_n_prime192.w[1] > sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > sig_x.w[0]))) + ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y; + BID_RETURN (res); +} + +/***************************************************************************** + * BID128 minimum magnitude function - returns greater of two numbers + *****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_minnum_mag (UINT128 * pres, UINT128 * px, + UINT128 * py _EXC_FLAGS_PARAM) { + UINT128 x = *px; + UINT128 y = *py; +#else +UINT128 +bid128_minnum_mag (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) { +#endif + + UINT128 res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + + BID_SWAP128 (x); + BID_SWAP128 (y); + + // check for non-canonical x + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16] + // check for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + } else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf + x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF); + x.w[0] = 0x0ull; + } else { // x is not special + // check for non-canonical values - treated as zero + if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11 + // non-canonical + x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP); + x.w[0] = 0x0ull; + } else { // G0_G1 != 11 + if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull || + ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull + && x.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP); + x.w[0] = 0x0ull; + } else { // canonical + ; + } + } + } + // check for non-canonical y + if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN + y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16] + // check for non-canonical NaN payload + if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (y.w[0] > 0x38c15b09ffffffffull))) { + y.w[1] = y.w[1] & 0xffffc00000000000ull; + y.w[0] = 0x0ull; + } + } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf + y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF); + y.w[0] = 0x0ull; + } else { // y is not special + // check for non-canonical values - treated as zero + if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11 + // non-canonical + y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP); + y.w[0] = 0x0ull; + } else { // G0_G1 != 11 + if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull || + ((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull + && y.w[0] > 0x378d8e63ffffffffull)) { + // y is non-canonical if coefficient is larger than 10^34 -1 + y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP); + y.w[0] = 0x0ull; + } else { // canonical + ; + } + } + } + + // NaN (CASE1) + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN + // if x is SNAN, then return quiet (x) + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x + res = x; + } else { // x is QNaN + if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN + if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN + *pfpsf |= INVALID_EXCEPTION; // set invalid flag + } + res = x; + } else { + res = y; + } + } + BID_RETURN (res); + } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not + if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y + res = y; + } else { + // will return x (which is not NaN) + res = x; + } + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). + if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = y; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x infinity, it has maximum magnitude. + // Check if magnitudes are equal. If x is negative, return it. + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN + && (y.w[1] & MASK_INF) == MASK_INF) ? x : y; + BID_RETURN (res); + } else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is infinity, then x is less in magnitude + res = x; + BID_RETURN (res); + } + // CONVERT X + sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; + sig_x.w[0] = x.w[0]; + exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CONVERT Y + exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; + sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; + sig_y.w[0] = y.w[0]; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) { + res = x; + BID_RETURN (res); + } + if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) { + res = y; + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // check if exponents are the same and significands are the same + if (exp_y == exp_x && sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] == sig_y.w[0]) { + if (x.w[1] & 0x8000000000000000ull) { // x is negative + res = x; + BID_RETURN (res); + } else { + res = y; + BID_RETURN (res); + } + } else if (((sig_x.w[1] > sig_y.w[1] || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] > sig_y.w[0])) + && exp_x == exp_y) + || ((sig_x.w[1] > sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) + && exp_x > exp_y)) { + // if both components are either bigger or smaller, it is clear what + // needs to be done; also if the magnitudes are equal + res = y; + BID_RETURN (res); + } else if (((sig_y.w[1] > sig_x.w[1] || (sig_y.w[1] == sig_x.w[1] + && sig_y.w[0] > sig_x.w[0])) + && exp_y == exp_x) + || ((sig_y.w[1] > sig_x.w[1] + || (sig_y.w[1] == sig_x.w[1] + && sig_y.w[0] >= sig_x.w[0])) + && exp_y > exp_x)) { + res = x; + BID_RETURN (res); + } else { + ; // continue + } + diff = exp_x - exp_y; + // if |exp_x - exp_y| < 33, it comes down to the compensated significand + if (diff > 0) { // to simplify the loop below, + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = y; // difference cannot be greater than 10^33 + BID_RETURN (res); + } + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + // if positive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x; // if equal + BID_RETURN (res); + } + res = (((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > sig_y.w[0])) ? y : x; + BID_RETURN (res); + } + __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x); + // if positive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + // if = in magnitude, return +, (if possible) + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } + res = ((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > sig_y.w[0])) ? y : x; + BID_RETURN (res); + } + diff = exp_y - exp_x; + // if exp_x is 33 less than exp_y, no need for compensation + if (diff > 33) { + res = x; + BID_RETURN (res); + } + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + // if positive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + // if = in magnitude, return +, (if possible) + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } + res = (sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 + && (sig_n_prime256.w[1] < sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] < sig_x.w[0]))) ? y : x; + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y); + // if positive, return whichever significand is larger (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + // if = in magnitude, return +, if possible) + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } + res = (sig_n_prime192.w[2] == 0 + && (sig_n_prime192.w[1] < sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] < sig_x.w[0]))) ? y : x; + BID_RETURN (res); +} + +/***************************************************************************** + * BID128 maximum function - returns greater of two numbers + *****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_maxnum (UINT128 * pres, UINT128 * px, + UINT128 * py _EXC_FLAGS_PARAM) { + UINT128 x = *px; + UINT128 y = *py; +#else +UINT128 +bid128_maxnum (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) { +#endif + + UINT128 res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0; + + BID_SWAP128 (x); + BID_SWAP128 (y); + + // check for non-canonical x + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16] + // check for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + } else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf + x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF); + x.w[0] = 0x0ull; + } else { // x is not special + // check for non-canonical values - treated as zero + if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11 + // non-canonical + x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP); + x.w[0] = 0x0ull; + } else { // G0_G1 != 11 + if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull || + ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull + && x.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP); + x.w[0] = 0x0ull; + } else { // canonical + ; + } + } + } + // check for non-canonical y + if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN + y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16] + // check for non-canonical NaN payload + if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (y.w[0] > 0x38c15b09ffffffffull))) { + y.w[1] = y.w[1] & 0xffffc00000000000ull; + y.w[0] = 0x0ull; + } + } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf + y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF); + y.w[0] = 0x0ull; + } else { // y is not special + // check for non-canonical values - treated as zero + if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11 + // non-canonical + y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP); + y.w[0] = 0x0ull; + } else { // G0_G1 != 11 + if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull || + ((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull + && y.w[0] > 0x378d8e63ffffffffull)) { + // y is non-canonical if coefficient is larger than 10^34 -1 + y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP); + y.w[0] = 0x0ull; + } else { // canonical + ; + } + } + } + + // NaN (CASE1) + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN + // if x is SNAN, then return quiet (x) + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x + res = x; + } else { // x is QNaN + if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN + if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN + *pfpsf |= INVALID_EXCEPTION; // set invalid flag + } + res = x; + } else { + res = y; + } + } + BID_RETURN (res); + } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not + if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y + res = y; + } else { + // will return x (which is not NaN) + res = x; + } + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). + if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = x; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x.w[1] & MASK_INF) == MASK_INF) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } + // CONVERT X + sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; + sig_x.w[0] = x.w[0]; + exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CONVERT Y + exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; + sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; + sig_y.w[0] = y.w[0]; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) { + x_is_zero = 1; + } + if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) { + y_is_zero = 1; + } + + if (x_is_zero && y_is_zero) { + // if both numbers are zero, neither is greater => return either number + res = x; + BID_RETURN (res); + } else if (x_is_zero) { + // is x is zero, it is greater if Y is negative + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } else if (y_is_zero) { + // is y is zero, X is greater if it is positive + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y; + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative + if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if exponents are the same, then we have a simple comparison of + // the significands + if (exp_y == exp_x) { + res = (((sig_x.w[1] > sig_y.w[1]) || (sig_x.w[1] == sig_y.w[1] && + sig_x.w[0] >= sig_y.w[0])) ^ + ((x.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y; + BID_RETURN (res); + } + // if both components are either bigger or smaller, it is clear what + // needs to be done + if ((sig_x.w[1] > sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) + && exp_x >= exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y; + BID_RETURN (res); + } + if ((sig_x.w[1] < sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) + && exp_x <= exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } + diff = exp_x - exp_y; + // if |exp_x - exp_y| < 33, it comes down to the compensated significand + if (diff > 0) { // to simplify the loop below, + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + // difference cannot be greater than 10^33 + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y; + BID_RETURN (res); + } + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + // if postitive, return whichever significand is larger + // (converse if negative) + res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == + MASK_SIGN)) ? x : y; + BID_RETURN (res); + } + __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x); + // if postitive, return whichever significand is larger + // (converse if negative) + res = + (((sig_n_prime192.w[2] > 0) || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > + sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y; + BID_RETURN (res); + } + diff = exp_y - exp_x; + // if exp_x is 33 less than exp_y, no need for compensation + if (diff > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + // if postitive, return whichever significand is larger + // (converse if negative) + res = + ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 + || (sig_n_prime256.w[1] > sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] > + sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) != + MASK_SIGN)) ? x : y; + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y); + // if postitive, return whichever significand is larger (converse if negative) + res = + ((sig_n_prime192.w[2] != 0 + || (sig_n_prime192.w[1] > sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > + sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) != + MASK_SIGN)) ? x : y; + BID_RETURN (res); +} + +/***************************************************************************** + * BID128 maximum magnitude function - returns greater of two numbers + *****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_maxnum_mag (UINT128 * pres, UINT128 * px, + UINT128 * py _EXC_FLAGS_PARAM) { + UINT128 x = *px; + UINT128 y = *py; +#else +UINT128 +bid128_maxnum_mag (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) { +#endif + + UINT128 res; + int exp_x, exp_y; + int diff; + UINT128 sig_x, sig_y; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + + BID_SWAP128 (x); + BID_SWAP128 (y); + + // check for non-canonical x + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16] + // check for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + } else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf + x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF); + x.w[0] = 0x0ull; + } else { // x is not special + // check for non-canonical values - treated as zero + if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11 + // non-canonical + x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP); + x.w[0] = 0x0ull; + } else { // G0_G1 != 11 + if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull || + ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull + && x.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP); + x.w[0] = 0x0ull; + } else { // canonical + ; + } + } + } + // check for non-canonical y + if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN + y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16] + // check for non-canonical NaN payload + if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (y.w[0] > 0x38c15b09ffffffffull))) { + y.w[1] = y.w[1] & 0xffffc00000000000ull; + y.w[0] = 0x0ull; + } + } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf + y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF); + y.w[0] = 0x0ull; + } else { // y is not special + // check for non-canonical values - treated as zero + if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11 + // non-canonical + y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP); + y.w[0] = 0x0ull; + } else { // G0_G1 != 11 + if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull || + ((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull && + y.w[0] > 0x378d8e63ffffffffull)) { + // y is non-canonical if coefficient is larger than 10^34 -1 + y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP); + y.w[0] = 0x0ull; + } else { // canonical + ; + } + } + } + + // NaN (CASE1) + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN + // if x is SNAN, then return quiet (x) + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x + res = x; + } else { // x is QNaN + if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN + if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN + *pfpsf |= INVALID_EXCEPTION; // set invalid flag + } + res = x; + } else { + res = y; + } + } + BID_RETURN (res); + } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not + if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y + res = y; + } else { + // will return x (which is not NaN) + res = x; + } + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). + if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) { + res = y; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x infinity, it has maximum magnitude + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN + && (y.w[1] & MASK_INF) == MASK_INF) ? y : x; + BID_RETURN (res); + } else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + res = y; + BID_RETURN (res); + } + // CONVERT X + sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; + sig_x.w[0] = x.w[0]; + exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CONVERT Y + exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; + sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; + sig_y.w[0] = y.w[0]; + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) { + res = y; + BID_RETURN (res); + } + if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) { + res = x; + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + if (exp_y == exp_x && sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] == sig_y.w[0]) { + // check if exponents are the same and significands are the same + if (x.w[1] & 0x8000000000000000ull) { // x is negative + res = y; + BID_RETURN (res); + } else { + res = x; + BID_RETURN (res); + } + } else if (((sig_x.w[1] > sig_y.w[1] || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] > sig_y.w[0])) + && exp_x == exp_y) + || ((sig_x.w[1] > sig_y.w[1] + || (sig_x.w[1] == sig_y.w[1] + && sig_x.w[0] >= sig_y.w[0])) + && exp_x > exp_y)) { + // if both components are either bigger or smaller, it is clear what + // needs to be done; also if the magnitudes are equal + res = x; + BID_RETURN (res); + } else if (((sig_y.w[1] > sig_x.w[1] || (sig_y.w[1] == sig_x.w[1] + && sig_y.w[0] > sig_x.w[0])) + && exp_y == exp_x) + || ((sig_y.w[1] > sig_x.w[1] + || (sig_y.w[1] == sig_x.w[1] + && sig_y.w[0] >= sig_x.w[0])) + && exp_y > exp_x)) { + res = y; + BID_RETURN (res); + } else { + ; // continue + } + diff = exp_x - exp_y; + // if |exp_x - exp_y| < 33, it comes down to the compensated significand + if (diff > 0) { // to simplify the loop below, + // if exp_x is 33 greater than exp_y, no need for compensation + if (diff > 33) { + res = x; // difference cannot be greater than 10^33 + BID_RETURN (res); + } + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]); + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_y.w[1] + && (sig_n_prime256.w[0] == sig_y.w[0])) { + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y; // if equal + BID_RETURN (res); + } + res = (((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0) + || (sig_n_prime256.w[1] > sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] > sig_y.w[0])) ? x : y; + BID_RETURN (res); + } + __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x); + // if postitive, return whichever significand is larger (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + // if equal, return positive magnitude + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } + res = ((sig_n_prime192.w[2] > 0) + || (sig_n_prime192.w[1] > sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] > sig_y.w[0])) ? x : y; + BID_RETURN (res); + } + diff = exp_y - exp_x; + // if exp_x is 33 less than exp_y, no need for compensation + if (diff > 33) { + res = y; + BID_RETURN (res); + } + if (diff > 19) { //128 by 128 bit multiply -> 256 bits + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]); + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0) + && sig_n_prime256.w[1] == sig_x.w[1] + && (sig_n_prime256.w[0] == sig_x.w[0])) { + // if equal, return positive (if possible) + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } + res = (sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0 + && (sig_n_prime256.w[1] < sig_x.w[1] + || (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] < sig_x.w[0]))) ? x : y; + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y); + // if postitive, return whichever significand is larger (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1] + && (sig_n_prime192.w[0] == sig_x.w[0])) { + // if equal, return positive (if possible) + res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } + res = (sig_n_prime192.w[2] == 0 + && (sig_n_prime192.w[1] < sig_x.w[1] + || (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] < sig_x.w[0]))) ? x : y; + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_mul.c b/gcc-4.4.3/libgcc/config/libbid/bid128_mul.c new file mode 100644 index 000000000..88391e84f --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_mul.c @@ -0,0 +1,423 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64dq_mul (UINT64 * pres, UINT64 * px, UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64dq_mul (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res = 0xbaddbaddbaddbaddull; + UINT128 x1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64qq_mul (&res, &x1, py + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid64qq_mul (x1, y + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64qd_mul (UINT64 * pres, UINT128 * px, UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64qd_mul (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res = 0xbaddbaddbaddbaddull; + UINT128 y1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64qq_mul (&res, px, &y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid64qq_mul (x, y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64qq_mul (UINT64 * pres, UINT128 * px, UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px, y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64qq_mul (UINT128 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 z = { {0x0000000000000000ull, 0x5ffe000000000000ull} + }; + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 x_sign, y_sign, p_sign; + UINT64 x_exp, y_exp, p_exp; + int true_p_exp; + UINT128 C1, C2; + + BID_SWAP128 (z); + // skip cases where at least one operand is NaN or infinity + if (!(((x.w[HIGH_128W] & MASK_NAN) == MASK_NAN) || + ((y.w[HIGH_128W] & MASK_NAN) == MASK_NAN) || + ((x.w[HIGH_128W] & MASK_ANY_INF) == MASK_INF) || + ((y.w[HIGH_128W] & MASK_ANY_INF) == MASK_INF))) { + // x, y are 0 or f but not inf or NaN => unpack the arguments and check + // for non-canonical values + + x_sign = x.w[HIGH_128W] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + C1.w[1] = x.w[HIGH_128W] & MASK_COEFF; + C1.w[0] = x.w[LOW_128W]; + // check for non-canonical values - treated as zero + if ((x.w[HIGH_128W] & 0x6000000000000000ull) == + 0x6000000000000000ull) { + // G0_G1=11 => non-canonical + x_exp = (x.w[HIGH_128W] << 2) & MASK_EXP; // biased and shifted left 49 bits + C1.w[1] = 0; // significand high + C1.w[0] = 0; // significand low + } else { // G0_G1 != 11 + x_exp = x.w[HIGH_128W] & MASK_EXP; // biased and shifted left 49 bits + if (C1.w[1] > 0x0001ed09bead87c0ull || + (C1.w[1] == 0x0001ed09bead87c0ull && + C1.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + C1.w[1] = 0; + C1.w[0] = 0; + } else { // canonical + ; + } + } + y_sign = y.w[HIGH_128W] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + C2.w[1] = y.w[HIGH_128W] & MASK_COEFF; + C2.w[0] = y.w[LOW_128W]; + // check for non-canonical values - treated as zero + if ((y.w[HIGH_128W] & 0x6000000000000000ull) == + 0x6000000000000000ull) { + // G0_G1=11 => non-canonical + y_exp = (y.w[HIGH_128W] << 2) & MASK_EXP; // biased and shifted left 49 bits + C2.w[1] = 0; // significand high + C2.w[0] = 0; // significand low + } else { // G0_G1 != 11 + y_exp = y.w[HIGH_128W] & MASK_EXP; // biased and shifted left 49 bits + if (C2.w[1] > 0x0001ed09bead87c0ull || + (C2.w[1] == 0x0001ed09bead87c0ull && + C2.w[0] > 0x378d8e63ffffffffull)) { + // y is non-canonical if coefficient is larger than 10^34 -1 + C2.w[1] = 0; + C2.w[0] = 0; + } else { // canonical + ; + } + } + p_sign = x_sign ^ y_sign; // sign of the product + + true_p_exp = (x_exp >> 49) - 6176 + (y_exp >> 49) - 6176; + // true_p_exp, p_exp are used only for 0 * 0, 0 * f, or f * 0 + if (true_p_exp < -398) + p_exp = 0; // cannot be less than EXP_MIN + else if (true_p_exp > 369) + p_exp = (UINT64) (369 + 398) << 53; // cannot be more than EXP_MAX + else + p_exp = (UINT64) (true_p_exp + 398) << 53; + + if ((C1.w[1] == 0x0 && C1.w[0] == 0x0) || + (C2.w[1] == 0x0 && C2.w[0] == 0x0)) { + // x = 0 or y = 0 + // the result is 0 + res = p_sign | p_exp; // preferred exponent in [EXP_MIN, EXP_MAX] + BID_RETURN (res) + } // else continue + } + // swap x and y - ensure that a NaN in x has 'higher precedence' than one in y +#if DECIMAL_CALL_BY_REFERENCE + bid64qqq_fma (&res, &y, &x, &z + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + res = bid64qqq_fma (y, x, z + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128dd_mul (UINT128 * pres, UINT64 * px, UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px, y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128dd_mul (UINT64 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} + }; + UINT128 x1, y1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_mul (&res, &x1, &y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_mul (x1, y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128dq_mul (UINT128 * pres, UINT64 * px, UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128dq_mul (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} + }; + UINT128 x1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_mul (&res, &x1, py + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_mul (x1, y + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128qd_mul (UINT128 * pres, UINT128 * px, UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT128 +bid128qd_mul (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} + }; + UINT128 y1; + +#if DECIMAL_CALL_BY_REFERENCE + bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid128_mul (&res, px, &y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res = bid128_mul (x, y1 + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} + + +// bid128_mul stands for bid128qq_mul +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_mul (UINT128 * pres, UINT128 * px, + UINT128 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px, y = *py; + +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; + +#endif +#else +UINT128 +bid128_mul (UINT128 x, + UINT128 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + +#endif + UINT128 z = { {0x0000000000000000ull, 0x5ffe000000000000ull} + }; + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} + }; + UINT64 x_sign, y_sign, p_sign; + UINT64 x_exp, y_exp, p_exp; + int true_p_exp; + UINT128 C1, C2; + + BID_SWAP128 (x); + BID_SWAP128 (y); + // skip cases where at least one operand is NaN or infinity + if (!(((x.w[1] & MASK_NAN) == MASK_NAN) || + ((y.w[1] & MASK_NAN) == MASK_NAN) || + ((x.w[1] & MASK_ANY_INF) == MASK_INF) || + ((y.w[1] & MASK_ANY_INF) == MASK_INF))) { + // x, y are 0 or f but not inf or NaN => unpack the arguments and check + // for non-canonical values + + x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + // check for non-canonical values - treated as zero + if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { + // G0_G1=11 => non-canonical + x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C1.w[1] = 0; // significand high + C1.w[0] = 0; // significand low + } else { // G0_G1 != 11 + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C1.w[1] > 0x0001ed09bead87c0ull || + (C1.w[1] == 0x0001ed09bead87c0ull && + C1.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + C1.w[1] = 0; + C1.w[0] = 0; + } else { // canonical + ; + } + } + y_sign = y.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + C2.w[1] = y.w[1] & MASK_COEFF; + C2.w[0] = y.w[0]; + // check for non-canonical values - treated as zero + if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { + // G0_G1=11 => non-canonical + y_exp = (y.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C2.w[1] = 0; // significand high + C2.w[0] = 0; // significand low + } else { // G0_G1 != 11 + y_exp = y.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C2.w[1] > 0x0001ed09bead87c0ull || + (C2.w[1] == 0x0001ed09bead87c0ull && + C2.w[0] > 0x378d8e63ffffffffull)) { + // y is non-canonical if coefficient is larger than 10^34 -1 + C2.w[1] = 0; + C2.w[0] = 0; + } else { // canonical + ; + } + } + p_sign = x_sign ^ y_sign; // sign of the product + + true_p_exp = (x_exp >> 49) - 6176 + (y_exp >> 49) - 6176; + // true_p_exp, p_exp are used only for 0 * 0, 0 * f, or f * 0 + if (true_p_exp < -6176) + p_exp = 0; // cannot be less than EXP_MIN + else if (true_p_exp > 6111) + p_exp = (UINT64) (6111 + 6176) << 49; // cannot be more than EXP_MAX + else + p_exp = (UINT64) (true_p_exp + 6176) << 49; + + if ((C1.w[1] == 0x0 && C1.w[0] == 0x0) || + (C2.w[1] == 0x0 && C2.w[0] == 0x0)) { + // x = 0 or y = 0 + // the result is 0 + res.w[1] = p_sign | p_exp; // preferred exponent in [EXP_MIN, EXP_MAX] + res.w[0] = 0x0; + BID_SWAP128 (res); + BID_RETURN (res) + } // else continue + } + + BID_SWAP128 (x); + BID_SWAP128 (y); + BID_SWAP128 (z); + // swap x and y - ensure that a NaN in x has 'higher precedence' than one in y +#if DECIMAL_CALL_BY_REFERENCE + bid128_fma (&res, &y, &x, &z + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + res = bid128_fma (y, x, z + _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_next.c b/gcc-4.4.3/libgcc/config/libbid/bid128_next.c new file mode 100644 index 000000000..11688c1c1 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_next.c @@ -0,0 +1,643 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#define BID_128RES +#include "bid_internal.h" + +/***************************************************************************** + * BID128 nextup + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_nextup (UINT128 * pres, + UINT128 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +UINT128 +bid128_nextup (UINT128 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q1, ind; + UINT128 C1; // C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (UINT64) + + BID_SWAP128 (x); + // unpack the argument + x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + + // check for NaN or Infinity + if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + // if x = NaN, then res = Q (x) + // check first for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) + && (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] + res.w[0] = x.w[0]; + } else { // x is QNaN + // return x + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] + res.w[0] = x.w[0]; + } + } else { // x is not NaN, so it must be infinity + if (!x_sign) { // x is +inf + res.w[1] = 0x7800000000000000ull; // +inf + res.w[0] = 0x0000000000000000ull; + } else { // x is -inf + res.w[1] = 0xdfffed09bead87c0ull; // -MAXFP = -999...99 * 10^emax + res.w[0] = 0x378d8e63ffffffffull; + } + } + BID_RETURN (res); + } + // check for non-canonical values (treated as zero) + if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + // non-canonical + x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C1.w[1] = 0; // significand high + C1.w[0] = 0; // significand low + } else { // G0_G1 != 11 + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C1.w[1] > 0x0001ed09bead87c0ull || + (C1.w[1] == 0x0001ed09bead87c0ull + && C1.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + C1.w[1] = 0; + C1.w[0] = 0; + } else { // canonical + ; + } + } + + if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is +/-0 + res.w[1] = 0x0000000000000000ull; // +1 * 10^emin + res.w[0] = 0x0000000000000001ull; + } else { // x is not special and is not zero + if (x.w[1] == 0x5fffed09bead87c0ull + && x.w[0] == 0x378d8e63ffffffffull) { + // x = +MAXFP = 999...99 * 10^emax + res.w[1] = 0x7800000000000000ull; // +inf + res.w[0] = 0x0000000000000000ull; + } else if (x.w[1] == 0x8000000000000000ull + && x.w[0] == 0x0000000000000001ull) { + // x = -MINFP = 1...99 * 10^emin + res.w[1] = 0x8000000000000000ull; // -0 + res.w[0] = 0x0000000000000000ull; + } else { // -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp + // can add/subtract 1 ulp to the significand + + // Note: we could check here if x >= 10^34 to speed up the case q1 = 34 + // q1 = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rnd errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - + 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - + 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q1 = nr_digits[x_nr_bits - 1].digits; + if (q1 == 0) { + q1 = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q1++; + } + // if q1 < P34 then pad the significand with zeros + if (q1 < P34) { + exp = (x_exp >> 49) - 6176; + if (exp + 6176 > P34 - q1) { + ind = P34 - q1; // 1 <= ind <= P34 - 1 + // pad with P34 - q1 zeros, until exponent = emin + // C1 = C1 * 10^ind + if (q1 <= 19) { // 64-bit C1 + if (ind <= 19) { // 64-bit 10^ind and 64-bit C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]); + } else { // 128-bit 10^ind and 64-bit C1 + __mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]); + } + } else { // C1 is (most likely) 128-bit + if (ind <= 14) { // 64-bit 10^ind and 128-bit C1 (most likely) + __mul_128x64_to_128 (C1, ten2k64[ind], C1); + } else if (ind <= 19) { // 64-bit 10^ind and 64-bit C1 (q1 <= 19) + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]); + } else { // 128-bit 10^ind and 64-bit C1 (C1 must be 64-bit) + __mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]); + } + } + x_exp = x_exp - ((UINT64) ind << 49); + } else { // pad with zeros until the exponent reaches emin + ind = exp + 6176; + // C1 = C1 * 10^ind + if (ind <= 19) { // 1 <= P34 - q1 <= 19 <=> 15 <= q1 <= 33 + if (q1 <= 19) { // 64-bit C1, 64-bit 10^ind + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]); + } else { // 20 <= q1 <= 33 => 128-bit C1, 64-bit 10^ind + __mul_128x64_to_128 (C1, ten2k64[ind], C1); + } + } else { // if 20 <= P34 - q1 <= 33 <=> 1 <= q1 <= 14 => + // 64-bit C1, 128-bit 10^ind + __mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]); + } + x_exp = EXP_MIN; + } + } + if (!x_sign) { // x > 0 + // add 1 ulp (add 1 to the significand) + C1.w[0]++; + if (C1.w[0] == 0) + C1.w[1]++; + if (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] == 0x378d8e6400000000ull) { // if C1 = 10^34 + C1.w[1] = 0x0000314dc6448d93ull; // C1 = 10^33 + C1.w[0] = 0x38c15b0a00000000ull; + x_exp = x_exp + EXP_P1; + } + } else { // x < 0 + // subtract 1 ulp (subtract 1 from the significand) + C1.w[0]--; + if (C1.w[0] == 0xffffffffffffffffull) + C1.w[1]--; + if (x_exp != 0 && C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] == 0x38c15b09ffffffffull) { // if C1 = 10^33 - 1 + C1.w[1] = 0x0001ed09bead87c0ull; // C1 = 10^34 - 1 + C1.w[0] = 0x378d8e63ffffffffull; + x_exp = x_exp - EXP_P1; + } + } + // assemble the result + res.w[1] = x_sign | x_exp | C1.w[1]; + res.w[0] = C1.w[0]; + } // end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp + } // end x is not special and is not zero + BID_RETURN (res); +} + +/***************************************************************************** + * BID128 nextdown + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_nextdown (UINT128 * pres, + UINT128 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +UINT128 +bid128_nextdown (UINT128 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q1, ind; + UINT128 C1; // C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (UINT64) + + BID_SWAP128 (x); + // unpack the argument + x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + + // check for NaN or Infinity + if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + // if x = NaN, then res = Q (x) + // check first for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) + && (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] + res.w[0] = x.w[0]; + } else { // x is QNaN + // return x + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] + res.w[0] = x.w[0]; + } + } else { // x is not NaN, so it must be infinity + if (!x_sign) { // x is +inf + res.w[1] = 0x5fffed09bead87c0ull; // +MAXFP = +999...99 * 10^emax + res.w[0] = 0x378d8e63ffffffffull; + } else { // x is -inf + res.w[1] = 0xf800000000000000ull; // -inf + res.w[0] = 0x0000000000000000ull; + } + } + BID_RETURN (res); + } + // check for non-canonical values (treated as zero) + if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + // non-canonical + x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C1.w[1] = 0; // significand high + C1.w[0] = 0; // significand low + } else { // G0_G1 != 11 + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C1.w[1] > 0x0001ed09bead87c0ull || + (C1.w[1] == 0x0001ed09bead87c0ull + && C1.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + C1.w[1] = 0; + C1.w[0] = 0; + } else { // canonical + ; + } + } + + if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is +/-0 + res.w[1] = 0x8000000000000000ull; // -1 * 10^emin + res.w[0] = 0x0000000000000001ull; + } else { // x is not special and is not zero + if (x.w[1] == 0xdfffed09bead87c0ull + && x.w[0] == 0x378d8e63ffffffffull) { + // x = -MAXFP = -999...99 * 10^emax + res.w[1] = 0xf800000000000000ull; // -inf + res.w[0] = 0x0000000000000000ull; + } else if (x.w[1] == 0x0ull && x.w[0] == 0x0000000000000001ull) { // +MINFP + res.w[1] = 0x0000000000000000ull; // +0 + res.w[0] = 0x0000000000000000ull; + } else { // -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp + // can add/subtract 1 ulp to the significand + + // Note: we could check here if x >= 10^34 to speed up the case q1 = 34 + // q1 = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rnd errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - + 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - + 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q1 = nr_digits[x_nr_bits - 1].digits; + if (q1 == 0) { + q1 = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q1++; + } + // if q1 < P then pad the significand with zeros + if (q1 < P34) { + exp = (x_exp >> 49) - 6176; + if (exp + 6176 > P34 - q1) { + ind = P34 - q1; // 1 <= ind <= P34 - 1 + // pad with P34 - q1 zeros, until exponent = emin + // C1 = C1 * 10^ind + if (q1 <= 19) { // 64-bit C1 + if (ind <= 19) { // 64-bit 10^ind and 64-bit C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]); + } else { // 128-bit 10^ind and 64-bit C1 + __mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]); + } + } else { // C1 is (most likely) 128-bit + if (ind <= 14) { // 64-bit 10^ind and 128-bit C1 (most likely) + __mul_128x64_to_128 (C1, ten2k64[ind], C1); + } else if (ind <= 19) { // 64-bit 10^ind and 64-bit C1 (q1 <= 19) + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]); + } else { // 128-bit 10^ind and 64-bit C1 (C1 must be 64-bit) + __mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]); + } + } + x_exp = x_exp - ((UINT64) ind << 49); + } else { // pad with zeros until the exponent reaches emin + ind = exp + 6176; + // C1 = C1 * 10^ind + if (ind <= 19) { // 1 <= P34 - q1 <= 19 <=> 15 <= q1 <= 33 + if (q1 <= 19) { // 64-bit C1, 64-bit 10^ind + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]); + } else { // 20 <= q1 <= 33 => 128-bit C1, 64-bit 10^ind + __mul_128x64_to_128 (C1, ten2k64[ind], C1); + } + } else { // if 20 <= P34 - q1 <= 33 <=> 1 <= q1 <= 14 => + // 64-bit C1, 128-bit 10^ind + __mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]); + } + x_exp = EXP_MIN; + } + } + if (x_sign) { // x < 0 + // add 1 ulp (add 1 to the significand) + C1.w[0]++; + if (C1.w[0] == 0) + C1.w[1]++; + if (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] == 0x378d8e6400000000ull) { // if C1 = 10^34 + C1.w[1] = 0x0000314dc6448d93ull; // C1 = 10^33 + C1.w[0] = 0x38c15b0a00000000ull; + x_exp = x_exp + EXP_P1; + } + } else { // x > 0 + // subtract 1 ulp (subtract 1 from the significand) + C1.w[0]--; + if (C1.w[0] == 0xffffffffffffffffull) + C1.w[1]--; + if (x_exp != 0 && C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] == 0x38c15b09ffffffffull) { // if C1 = 10^33 - 1 + C1.w[1] = 0x0001ed09bead87c0ull; // C1 = 10^34 - 1 + C1.w[0] = 0x378d8e63ffffffffull; + x_exp = x_exp - EXP_P1; + } + } + // assemble the result + res.w[1] = x_sign | x_exp | C1.w[1]; + res.w[0] = C1.w[0]; + } // end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp + } // end x is not special and is not zero + BID_RETURN (res); +} + +/***************************************************************************** + * BID128 nextafter + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_nextafter (UINT128 * pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ + UINT128 x = *px; + UINT128 y = *py; + UINT128 xnswp = *px; + UINT128 ynswp = *py; +#else +UINT128 +bid128_nextafter (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 xnswp = x; + UINT128 ynswp = y; +#endif + + UINT128 res; + UINT128 tmp1, tmp2, tmp3; + FPSC tmp_fpsf = 0; // dummy fpsf for calls to comparison functions + int res1, res2; + UINT64 x_exp; + + + BID_SWAP128 (x); + BID_SWAP128 (y); + // check for NaNs + if (((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) + || ((y.w[1] & MASK_SPECIAL) == MASK_SPECIAL)) { + // x is special or y is special + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + // if x = NaN, then res = Q (x) + // check first for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) + && (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] + res.w[0] = x.w[0]; + } else { // x is QNaN + // return x + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] + res.w[0] = x.w[0]; + if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + } + } + BID_RETURN (res) + } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN + // if x = NaN, then res = Q (x) + // check first for non-canonical NaN payload + if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) + && (y.w[0] > 0x38c15b09ffffffffull))) { + y.w[1] = y.w[1] & 0xffffc00000000000ull; + y.w[0] = 0x0ull; + } + if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] + res.w[0] = y.w[0]; + } else { // x is QNaN + // return x + res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] + res.w[0] = y.w[0]; + } + BID_RETURN (res) + } else { // at least one is infinity + if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf + x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF); + x.w[0] = 0x0ull; + } + if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf + y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF); + y.w[0] = 0x0ull; + } + } + } + // neither x nor y is NaN + + // if not infinity, check for non-canonical values x (treated as zero) + if ((x.w[1] & MASK_ANY_INF) != MASK_INF) { // x != inf + if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + // non-canonical + x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + x.w[1] = (x.w[1] & MASK_SIGN) | x_exp; + x.w[0] = 0x0ull; + } else { // G0_G1 != 11 + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits + if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull || + ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull + && x.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + x.w[1] = (x.w[1] & MASK_SIGN) | x_exp; + x.w[0] = 0x0ull; + } else { // canonical + ; + } + } + } + // no need to check for non-canonical y + + // neither x nor y is NaN + tmp_fpsf = *pfpsf; // save fpsf +#if DECIMAL_CALL_BY_REFERENCE + bid128_quiet_equal (&res1, &xnswp, + &ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); + bid128_quiet_greater (&res2, &xnswp, + &ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + res1 = + bid128_quiet_equal (xnswp, + ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); + res2 = + bid128_quiet_greater (xnswp, + ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + *pfpsf = tmp_fpsf; // restore fpsf + + if (res1) { // x = y + // return x with the sign of y + res.w[1] = + (x.w[1] & 0x7fffffffffffffffull) | (y. + w[1] & 0x8000000000000000ull); + res.w[0] = x.w[0]; + } else if (res2) { // x > y +#if DECIMAL_CALL_BY_REFERENCE + bid128_nextdown (&res, + &xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + res = + bid128_nextdown (xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_SWAP128 (res); + } else { // x < y +#if DECIMAL_CALL_BY_REFERENCE + bid128_nextup (&res, + &xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); +#else + res = + bid128_nextup (xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); +#endif + BID_SWAP128 (res); + } + // if the operand x is finite but the result is infinite, signal + // overflow and inexact + if (((x.w[1] & MASK_SPECIAL) != MASK_SPECIAL) + && ((res.w[1] & MASK_SPECIAL) == MASK_SPECIAL)) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // set the overflow flag + *pfpsf |= OVERFLOW_EXCEPTION; + } + // if the result is in (-10^emin, 10^emin), and is different from the + // operand x, signal underflow and inexact + tmp1.w[HIGH_128W] = 0x0000314dc6448d93ull; + tmp1.w[LOW_128W] = 0x38c15b0a00000000ull; // +100...0[34] * 10^emin + tmp2.w[HIGH_128W] = res.w[1] & 0x7fffffffffffffffull; + tmp2.w[LOW_128W] = res.w[0]; + tmp3.w[HIGH_128W] = res.w[1]; + tmp3.w[LOW_128W] = res.w[0]; + tmp_fpsf = *pfpsf; // save fpsf +#if DECIMAL_CALL_BY_REFERENCE + bid128_quiet_greater (&res1, &tmp1, + &tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); + bid128_quiet_not_equal (&res2, &xnswp, + &tmp3 _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + res1 = + bid128_quiet_greater (tmp1, + tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); + res2 = + bid128_quiet_not_equal (xnswp, + tmp3 _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + *pfpsf = tmp_fpsf; // restore fpsf + if (res1 && res2) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // set the underflow flag + *pfpsf |= UNDERFLOW_EXCEPTION; + } + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_noncomp.c b/gcc-4.4.3/libgcc/config/libbid/bid128_noncomp.c new file mode 100644 index 000000000..5fce7ea6f --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_noncomp.c @@ -0,0 +1,1200 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * + * BID128 non-computational functions: + * - bid128_isSigned + * - bid128_isNormal + * - bid128_isSubnormal + * - bid128_isFinite + * - bid128_isZero + * - bid128_isInf + * - bid128_isSignaling + * - bid128_isCanonical + * - bid128_isNaN + * - bid128_copy + * - bid128_negate + * - bid128_abs + * - bid128_copySign + * - bid128_class + * - bid128_totalOrder + * - bid128_totalOrderMag + * - bid128_sameQuantum + * - bid128_radix + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_isSigned (int *pres, + UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +int +bid128_isSigned (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + + res = ((x.w[HIGH_128W] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +// return 1 iff x is not zero, nor NaN nor subnormal nor infinity +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_isNormal (int *pres, + UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +int +bid128_isNormal (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + UINT64 x_exp, C1_hi, C1_lo; + BID_UI64DOUBLE tmp1; + int exp, q, x_nr_bits; + + BID_SWAP128 (x); + // test for special values - infinity or NaN + if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special + res = 0; + BID_RETURN (res); + } + // unpack x + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions + C1_hi = x.w[1] & MASK_COEFF; + C1_lo = x.w[0]; + // test for zero + if (C1_hi == 0 && C1_lo == 0) { + res = 0; + BID_RETURN (res); + } + // test for non-canonical values of the argument x + if ((((C1_hi > 0x0001ed09bead87c0ull) + || ((C1_hi == 0x0001ed09bead87c0ull) + && (C1_lo > 0x378d8e63ffffffffull))) + && ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0; + BID_RETURN (res); + } + // x is subnormal or normal + // determine the number of digits q in the significand + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1_hi == 0) { + if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1_lo >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1_lo); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1_lo; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi) + tmp1.d = (double) C1_hi; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1_hi > nr_digits[x_nr_bits - 1].threshold_hi || + (C1_hi == nr_digits[x_nr_bits - 1].threshold_hi && + C1_lo >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (int) (x_exp >> 49) - 6176; + // test for subnormal values of x + if (exp + q <= -6143) { + res = 0; + BID_RETURN (res); + } else { + res = 1; + BID_RETURN (res); + } +} + +// return 1 iff x is not zero, nor NaN nor normal nor infinity +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_isSubnormal (int *pres, + UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +int +bid128_isSubnormal (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + UINT64 x_exp, C1_hi, C1_lo; + BID_UI64DOUBLE tmp1; + int exp, q, x_nr_bits; + + BID_SWAP128 (x); + // test for special values - infinity or NaN + if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special + res = 0; + BID_RETURN (res); + } + // unpack x + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions + C1_hi = x.w[1] & MASK_COEFF; + C1_lo = x.w[0]; + // test for zero + if (C1_hi == 0 && C1_lo == 0) { + res = 0; + BID_RETURN (res); + } + // test for non-canonical values of the argument x + if ((((C1_hi > 0x0001ed09bead87c0ull) + || ((C1_hi == 0x0001ed09bead87c0ull) + && (C1_lo > 0x378d8e63ffffffffull))) + && ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0; + BID_RETURN (res); + } + // x is subnormal or normal + // determine the number of digits q in the significand + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1_hi == 0) { + if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1_lo >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1_lo); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1_lo; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi) + tmp1.d = (double) C1_hi; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1_hi > nr_digits[x_nr_bits - 1].threshold_hi || + (C1_hi == nr_digits[x_nr_bits - 1].threshold_hi && + C1_lo >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (int) (x_exp >> 49) - 6176; + // test for subnormal values of x + if (exp + q <= -6143) { + res = 1; + } else { + res = 0; + } + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_isFinite (int *pres, + UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +int +bid128_isFinite (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + res = ((x.w[HIGH_128W] & MASK_INF) != MASK_INF); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_isZero (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +int +bid128_isZero (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + UINT128 sig_x; + + BID_SWAP128 (x); + if ((x.w[1] & MASK_INF) == MASK_INF) { + res = 0; + BID_RETURN (res); + } + sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; + sig_x.w[0] = x.w[0]; + if ((sig_x.w[1] > 0x0001ed09bead87c0ull) || // significand is non-canonical + ((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull)) || // significand is non-canonical + ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull && (x.w[1] & MASK_INF) != MASK_INF) || // significand is non-canonical + (sig_x.w[1] == 0 && sig_x.w[0] == 0)) { // significand is 0 + res = 1; + BID_RETURN (res); + } + res = 0; + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_isInf (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +int +bid128_isInf (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + res = ((x.w[HIGH_128W] & MASK_INF) == MASK_INF) + && ((x.w[HIGH_128W] & MASK_NAN) != MASK_NAN); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_isSignaling (int *pres, + UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +int +bid128_isSignaling (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + + res = ((x.w[HIGH_128W] & MASK_SNAN) == MASK_SNAN); + BID_RETURN (res); +} + +// return 1 iff x is a canonical number ,infinity, or NaN. +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_isCanonical (int *pres, + UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +int +bid128_isCanonical (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + UINT128 sig_x; + + BID_SWAP128 (x); + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // NaN + if (x.w[1] & 0x01ffc00000000000ull) { + res = 0; + BID_RETURN (res); + } + sig_x.w[1] = x.w[1] & 0x00003fffffffffffull; // 46 bits + sig_x.w[0] = x.w[0]; // 64 bits + // payload must be < 10^33 = 0x0000314dc6448d93_38c15b0a00000000 + if (sig_x.w[1] < 0x0000314dc6448d93ull + || (sig_x.w[1] == 0x0000314dc6448d93ull + && sig_x.w[0] < 0x38c15b0a00000000ull)) { + res = 1; + } else { + res = 0; + } + BID_RETURN (res); + } else if ((x.w[1] & MASK_INF) == MASK_INF) { // infinity + if ((x.w[1] & 0x03ffffffffffffffull) || x.w[0]) { + res = 0; + } else { + res = 1; + } + BID_RETURN (res); + } + // not NaN or infinity; extract significand to ensure it is canonical + sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; + sig_x.w[0] = x.w[0]; + // a canonical number has a coefficient < 10^34 + // (0x0001ed09_bead87c0_378d8e64_00000000) + if ((sig_x.w[1] > 0x0001ed09bead87c0ull) || // significand is non-canonical + ((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull)) || // significand is non-canonical + ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0; + } else { + res = 1; + } + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_isNaN (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +int +bid128_isNaN (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + + res = ((x.w[HIGH_128W] & MASK_NAN) == MASK_NAN); + BID_RETURN (res); +} + +// copies a floating-point operand x to destination y, with no change +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_copy (UINT128 * pres, + UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +UINT128 +bid128_copy (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 res; + + res = x; + BID_RETURN (res); +} + +// copies a floating-point operand x to destination y, reversing the sign +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_negate (UINT128 * pres, + UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +UINT128 +bid128_negate (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 res; + + x.w[HIGH_128W] ^= MASK_SIGN; + res = x; + BID_RETURN (res); +} + +// copies a floating-point operand x to destination y, changing the sign to positive +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_abs (UINT128 * pres, + UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +UINT128 +bid128_abs (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 res; + + x.w[HIGH_128W] &= ~MASK_SIGN; + res = x; + BID_RETURN (res); +} + +// copies operand x to destination in the same format as x, but with the sign of y +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_copySign (UINT128 * pres, UINT128 * px, + UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; + UINT128 y = *py; +#else +UINT128 +bid128_copySign (UINT128 x, UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 res; + + x.w[HIGH_128W] = + (x.w[HIGH_128W] & ~MASK_SIGN) | (y.w[HIGH_128W] & MASK_SIGN); + res = x; + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_class (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +int +bid128_class (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + UINT256 sig_x_prime256; + UINT192 sig_x_prime192; + UINT128 sig_x; + int exp_x; + + BID_SWAP128 (x); + if ((x.w[1] & MASK_NAN) == MASK_NAN) { + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { + res = signalingNaN; + } else { + res = quietNaN; + } + BID_RETURN (res); + } + if ((x.w[1] & MASK_INF) == MASK_INF) { + if ((x.w[1] & MASK_SIGN) == MASK_SIGN) { + res = negativeInfinity; + } else { + res = positiveInfinity; + } + BID_RETURN (res); + } + // decode number into exponent and significand + sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; + sig_x.w[0] = x.w[0]; + // check for zero or non-canonical + if ((sig_x.w[1] > 0x0001ed09bead87c0ull) + || ((sig_x.w[1] == 0x0001ed09bead87c0ull) + && (sig_x.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) + || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + if ((x.w[1] & MASK_SIGN) == MASK_SIGN) { + res = negativeZero; + } else { + res = positiveZero; + } + BID_RETURN (res); + } + exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + // if exponent is less than -6176, the number may be subnormal + // (less than the smallest normal value) + // the smallest normal value is 1 x 10^-6143 = 10^33 x 10^-6176 + // if (exp_x - 6176 < -6143) + if (exp_x < 33) { // sig_x * 10^exp_x + if (exp_x > 19) { + __mul_128x128_to_256 (sig_x_prime256, sig_x, + ten2k128[exp_x - 20]); + // 10^33 = 0x0000314dc6448d93_38c15b0a00000000 + if ((sig_x_prime256.w[3] == 0) && (sig_x_prime256.w[2] == 0) + && ((sig_x_prime256.w[1] < 0x0000314dc6448d93ull) + || ((sig_x_prime256.w[1] == 0x0000314dc6448d93ull) + && (sig_x_prime256.w[0] < 0x38c15b0a00000000ull)))) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? negativeSubnormal : + positiveSubnormal; + BID_RETURN (res); + } + } else { + __mul_64x128_to_192 (sig_x_prime192, ten2k64[exp_x], sig_x); + // 10^33 = 0x0000314dc6448d93_38c15b0a00000000 + if ((sig_x_prime192.w[2] == 0) + && ((sig_x_prime192.w[1] < 0x0000314dc6448d93ull) + || ((sig_x_prime192.w[1] == 0x0000314dc6448d93ull) + && (sig_x_prime192.w[0] < 0x38c15b0a00000000ull)))) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? negativeSubnormal : + positiveSubnormal; + BID_RETURN (res); + } + } + } + // otherwise, normal number, determine the sign + res = + ((x.w[1] & MASK_SIGN) == + MASK_SIGN) ? negativeNormal : positiveNormal; + BID_RETURN (res); +} + +// true if the exponents of x and y are the same, false otherwise. +// The special cases of sameQuantum(NaN, NaN) and sameQuantum(Inf, Inf) are true +// If exactly one operand is infinite or exactly one operand is NaN, then false +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_sameQuantum (int *pres, UINT128 * px, + UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; + UINT128 y = *py; +#else +int +bid128_sameQuantum (UINT128 x, + UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + UINT64 x_exp, y_exp; + + BID_SWAP128 (x); + BID_SWAP128 (y); + // if both operands are NaN, return true + if ((x.w[1] & MASK_NAN) == MASK_NAN + || ((y.w[1] & MASK_NAN) == MASK_NAN)) { + res = ((x.w[1] & MASK_NAN) == MASK_NAN + && (y.w[1] & MASK_NAN) == MASK_NAN); + BID_RETURN (res); + } + // if both operands are INF, return true + if ((x.w[1] & MASK_INF) == MASK_INF + || (y.w[1] & MASK_INF) == MASK_INF) { + res = ((x.w[1] & MASK_INF) == MASK_INF) + && ((y.w[1] & MASK_INF) == MASK_INF); + BID_RETURN (res); + } + // decode exponents for both numbers, and return true if they match + if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + } else { // G0_G1 != 11 + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits + } + if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + y_exp = (y.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + } else { // G0_G1 != 11 + y_exp = y.w[1] & MASK_EXP; // biased and shifted left 49 bits + } + res = (x_exp == y_exp); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_totalOrder (int *pres, UINT128 * px, + UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; + UINT128 y = *py; +#else +int +bid128_totalOrder (UINT128 x, + UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT128 sig_x, sig_y, pyld_y, pyld_x; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0; + + BID_SWAP128 (x); + BID_SWAP128 (y); + // NaN (CASE 1) + // if x and y are unordered numerically because either operand is NaN + // (1) totalOrder(-NaN, number) is true + // (2) totalOrder(number, +NaN) is true + // (3) if x and y are both NaN: + // i) negative sign bit < positive sign bit + // ii) signaling < quiet for +NaN, reverse for -NaN + // iii) lesser payload < greater payload for +NaN (reverse for -NaN) + // iv) else if bitwise identical (in canonical form), return 1 + if ((x.w[1] & MASK_NAN) == MASK_NAN) { + // if x is -NaN + if ((x.w[1] & MASK_SIGN) == MASK_SIGN) { + // return true, unless y is -NaN also + if ((y.w[1] & MASK_NAN) != MASK_NAN + || (y.w[1] & MASK_SIGN) != MASK_SIGN) { + res = 1; // y is a number, return 1 + BID_RETURN (res); + } else { // if y and x are both -NaN + pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull; + pyld_x.w[0] = x.w[0]; + pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull; + pyld_y.w[0] = y.w[0]; + if ((pyld_x.w[1] > 0x0000314dc6448d93ull) + || ((pyld_x.w[1] == 0x0000314dc6448d93ull) + && (pyld_x.w[0] > 0x38c15b09ffffffffull))) { + pyld_x.w[1] = 0; + pyld_x.w[0] = 0; + } + if ((pyld_y.w[1] > 0x0000314dc6448d93ull) + || ((pyld_y.w[1] == 0x0000314dc6448d93ull) + && (pyld_y.w[0] > 0x38c15b09ffffffffull))) { + pyld_y.w[1] = 0; + pyld_y.w[0] = 0; + } + // if x and y are both -SNaN or both -QNaN, we have to compare payloads + // this statement evaluates to true if both are SNaN or QNaN + if (! + (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^ + ((x.w[1] & MASK_SNAN) == MASK_SNAN))) { + // it comes down to the payload. we want to return true if x has a + // larger payload, or if the payloads are equal (canonical forms + // are bitwise identical) + if ((pyld_x.w[1] > pyld_y.w[1]) || + ((pyld_x.w[1] == pyld_y.w[1]) + && (pyld_x.w[0] >= pyld_y.w[0]))) + res = 1; + else + res = 0; + BID_RETURN (res); + } else { + // either x = -SNaN and y = -QNaN or x = -QNaN and y = -SNaN + res = ((y.w[1] & MASK_SNAN) == MASK_SNAN); + // totalOrder (-QNaN, -SNaN) == 1 + BID_RETURN (res); + } + } + } else { // x is +NaN + // return false, unless y is +NaN also + if ((y.w[1] & MASK_NAN) != MASK_NAN + || (y.w[1] & MASK_SIGN) == MASK_SIGN) { + res = 0; // y is a number, return 1 + BID_RETURN (res); + } else { + // x and y are both +NaN; + pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull; + pyld_x.w[0] = x.w[0]; + pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull; + pyld_y.w[0] = y.w[0]; + if ((pyld_x.w[1] > 0x0000314dc6448d93ull) + || ((pyld_x.w[1] == 0x0000314dc6448d93ull) + && (pyld_x.w[0] > 0x38c15b09ffffffffull))) { + pyld_x.w[1] = 0; + pyld_x.w[0] = 0; + } + if ((pyld_y.w[1] > 0x0000314dc6448d93ull) + || ((pyld_y.w[1] == 0x0000314dc6448d93ull) + && (pyld_y.w[0] > 0x38c15b09ffffffffull))) { + pyld_y.w[1] = 0; + pyld_y.w[0] = 0; + } + // if x and y are both +SNaN or both +QNaN, we have to compare payloads + // this statement evaluates to true if both are SNaN or QNaN + if (! + (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^ + ((x.w[1] & MASK_SNAN) == MASK_SNAN))) { + // it comes down to the payload. we want to return true if x has a + // smaller payload, or if the payloads are equal (canonical forms + // are bitwise identical) + if ((pyld_x.w[1] < pyld_y.w[1]) || + ((pyld_x.w[1] == pyld_y.w[1]) + && (pyld_x.w[0] <= pyld_y.w[0]))) + res = 1; + else + res = 0; + BID_RETURN (res); + } else { + // either x = SNaN and y = QNaN or x = QNaN and y = SNaN + res = ((x.w[1] & MASK_SNAN) == MASK_SNAN); + // totalOrder (-QNaN, -SNaN) == 1 + BID_RETURN (res); + } + } + } + } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { + // x is certainly not NAN in this case. + // return true if y is positive + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // SIMPLE (CASE 2) + // if all the bits are the same, the numbers are equal. + if ((x.w[1] == y.w[1]) && (x.w[0] == y.w[0])) { + res = 1; + BID_RETURN (res); + } + // OPPOSITE SIGNS (CASE 3) + // if signs are opposite, return 1 if x is negative + // (if x < y, totalOrder is true) + if (((x.w[1] & MASK_SIGN) == MASK_SIGN) ^ ((y.w[1] & MASK_SIGN) == + MASK_SIGN)) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // INFINITY (CASE 4) + if ((x.w[1] & MASK_INF) == MASK_INF) { + // if x == neg_inf, return (y == neg_inf); + if ((x.w[1] & MASK_SIGN) == MASK_SIGN) { + res = 1; + BID_RETURN (res); + } else { + // x is positive infinity, only return1 if y is positive infinity as well + res = ((y.w[1] & MASK_INF) == MASK_INF); + BID_RETURN (res); + // && (y & MASK_SIGN) != MASK_SIGN); (we know y has same sign as x) + } + } else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so: + // if y is +inf, xy + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // CONVERT x + sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; + sig_x.w[0] = x.w[0]; + exp_x = (x.w[1] >> 49) & 0x000000000003fffull; + + // CHECK IF x IS CANONICAL + // 9999999999999999999999999999999999 (decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. + if ((((sig_x.w[1] > 0x0001ed09bead87c0ull) || + ((sig_x.w[1] == 0x0001ed09bead87c0ull) && + (sig_x.w[0] > 0x378d8e63ffffffffull))) && + ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) || + ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) || + ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; + // check for the case where the exponent is shifted right by 2 bits! + if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { + exp_x = (x.w[1] >> 47) & 0x000000000003fffull; + } + } + // CONVERT y + exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; + sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; + sig_y.w[0] = y.w[0]; + + // CHECK IF y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. + if ((((sig_y.w[1] > 0x0001ed09bead87c0ull) || + ((sig_y.w[1] == 0x0001ed09bead87c0ull) && + (sig_y.w[0] > 0x378d8e63ffffffffull))) && + ((y.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) || + ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) || + ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; + // check for the case where the exponent is shifted right by 2 bits! + if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { + exp_y = (y.w[1] >> 47) & 0x000000000003fffull; + } + } + // ZERO (CASE 5) + // if x and y represent the same entities, and both are negative + // return true iff exp_x <= exp_y + if (x_is_zero && y_is_zero) { + // we know that signs must be the same because we would have caught it + // in case3 if signs were different + // totalOrder(x,y) iff exp_x >= exp_y for negative numbers + // totalOrder(x,y) iff exp_x <= exp_y for positive numbers + if (exp_x == exp_y) { + res = 1; + BID_RETURN (res); + } + res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + // if x is zero and y isn't, clearly x has the smaller payload + if (x_is_zero) { + res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if y is zero, and x isn't, clearly y has the smaller payload + if (y_is_zero) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE 6) + // if both components are either bigger or smaller + if (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) + && exp_x >= exp_y) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + if (((sig_x.w[1] < sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) + && exp_x <= exp_y) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 33, it comes down to the compensated significand + if (exp_x > exp_y) { + // if exp_x is 33 greater than exp_y, it is definitely larger, + // so no need for compensation + if (exp_x - exp_y > 33) { + res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + // difference cannot be greater than 10^33 + } + // otherwise adjust the x significand upwards + if (exp_x - exp_y > 19) { + __mul_128x128_to_256 (sig_n_prime256, sig_x, + ten2k128[exp_x - exp_y - 20]); + // the compensated significands are equal (ie "x and y represent the same + // entities") return 1 if (negative && expx > expy) || + // (positive && expx < expy) + if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) + && (sig_n_prime256.w[1] == sig_y.w[1]) + && (sig_n_prime256.w[0] == sig_y.w[0])) { + // the case exp_x == exp_y cannot occur, because all bits must be + // the same - would have been caught if (x == y) + res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + // if positive, return 1 if adjusted x is smaller than y + res = (((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) + && ((sig_n_prime256.w[1] < sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] < + sig_y.w[0]))) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_x - exp_y], sig_x); + // if positive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + res = (((sig_n_prime192.w[2] == 0) + && ((sig_n_prime192.w[1] < sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] < + sig_y.w[0]))) ^ ((x.w[1] & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + // if exp_x is 33 less than exp_y, it is definitely smaller, + // no need for compensation + if (exp_y - exp_x > 33) { + res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + if (exp_y - exp_x > 19) { + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, + ten2k128[exp_y - exp_x - 20]); + // if x and y represent the same entities and both are negative + // return true iff exp_x <= exp_y + if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) + && (sig_n_prime256.w[1] == sig_x.w[1]) + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = (exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // values are not equal, for positive numbers return 1 if x is less than y + // and 0 otherwise + res = (((sig_n_prime256.w[3] != 0) || + // if upper128 bits of compensated y are non-zero, y is bigger + (sig_n_prime256.w[2] != 0) || + // if upper128 bits of compensated y are non-zero, y is bigger + (sig_n_prime256.w[1] > sig_x.w[1]) || + // if compensated y is bigger, y is bigger + (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] > + sig_x.w[0])) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y); + if ((sig_n_prime192.w[2] == 0) && (sig_n_prime192.w[1] == sig_x.w[1]) + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = (exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + res = (((sig_n_prime192.w[2] != 0) || + // if upper128 bits of compensated y are non-zero, y is bigger + (sig_n_prime192.w[1] > sig_x.w[1]) || + // if compensated y is bigger, y is bigger + (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > + sig_x.w[0])) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_totalOrderMag (int *pres, UINT128 * px, + UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; + UINT128 y = *py; +#else +int +bid128_totalOrderMag (UINT128 x, + UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT128 sig_x, sig_y, pyld_y, pyld_x; + UINT192 sig_n_prime192; + UINT256 sig_n_prime256; + char x_is_zero = 0, y_is_zero = 0; + + BID_SWAP128 (x); + BID_SWAP128 (y); + x.w[1] = x.w[1] & 0x7fffffffffffffffull; + y.w[1] = y.w[1] & 0x7fffffffffffffffull; + + // NaN (CASE 1) + // if x and y are unordered numerically because either operand is NaN + // (1) totalOrder(number, +NaN) is true + // (2) if x and y are both NaN: + // i) signaling < quiet for +NaN + // ii) lesser payload < greater payload for +NaN + // iii) else if bitwise identical (in canonical form), return 1 + if ((x.w[1] & MASK_NAN) == MASK_NAN) { + // x is +NaN + // return false, unless y is +NaN also + if ((y.w[1] & MASK_NAN) != MASK_NAN) { + res = 0; // y is a number, return 0 + BID_RETURN (res); + } else { + // x and y are both +NaN; + pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull; + pyld_x.w[0] = x.w[0]; + pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull; + pyld_y.w[0] = y.w[0]; + if ((pyld_x.w[1] > 0x0000314dc6448d93ull) + || ((pyld_x.w[1] == 0x0000314dc6448d93ull) + && (pyld_x.w[0] > 0x38c15b09ffffffffull))) { + pyld_x.w[1] = 0; + pyld_x.w[0] = 0; + } + if ((pyld_y.w[1] > 0x0000314dc6448d93ull) + || ((pyld_y.w[1] == 0x0000314dc6448d93ull) + && (pyld_y.w[0] > 0x38c15b09ffffffffull))) { + pyld_y.w[1] = 0; + pyld_y.w[0] = 0; + } + // if x and y are both +SNaN or both +QNaN, we have to compare payloads + // this statement evaluates to true if both are SNaN or QNaN + if (! + (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^ + ((x.w[1] & MASK_SNAN) == MASK_SNAN))) { + // it comes down to the payload. we want to return true if x has a + // smaller payload, or if the payloads are equal (canonical forms + // are bitwise identical) + if ((pyld_x.w[1] < pyld_y.w[1]) || + ((pyld_x.w[1] == pyld_y.w[1]) + && (pyld_x.w[0] <= pyld_y.w[0]))) { + res = 1; + } else { + res = 0; + } + BID_RETURN (res); + } else { + // either x = SNaN and y = QNaN or x = QNaN and y = SNaN + res = ((x.w[1] & MASK_SNAN) == MASK_SNAN); + // totalOrder (-QNaN, -SNaN) == 1 + BID_RETURN (res); + } + } + } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { + // x is certainly not NAN in this case. + // return true because y is positive + res = 1; + BID_RETURN (res); + } + // SIMPLE (CASE 2) + // if all the bits are the same, the numbers are equal. + if ((x.w[1] == y.w[1]) && (x.w[0] == y.w[0])) { + res = 1; + BID_RETURN (res); + } + // INFINITY (CASE 3) + if ((x.w[1] & MASK_INF) == MASK_INF) { + // x is positive infinity, only return 1 if y is positive infinity as well + res = ((y.w[1] & MASK_INF) == MASK_INF); + BID_RETURN (res); + // (we know y has same sign as x) + } else if ((y.w[1] & MASK_INF) == MASK_INF) { + // x is finite, so: + // since y is +inf, x> 49) & 0x000000000003fffull; + + // CHECK IF x IS CANONICAL + // 9999999999999999999999999999999999 (decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. + if ((((sig_x.w[1] > 0x0001ed09bead87c0ull) || + ((sig_x.w[1] == 0x0001ed09bead87c0ull) && + (sig_x.w[0] > 0x378d8e63ffffffffull))) && + ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) || + ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) || + ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { + x_is_zero = 1; + // check for the case where the exponent is shifted right by 2 bits! + if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { + exp_x = (x.w[1] >> 47) & 0x000000000003fffull; + } + } + // CONVERT y + exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; + sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; + sig_y.w[0] = y.w[0]; + + // CHECK IF y IS CANONICAL + // 9999999999999999999999999999999999(decimal) = + // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) + // [0, 10^34) is the 754r supported canonical range. + // If the value exceeds that, it is interpreted as 0. + if ((((sig_y.w[1] > 0x0001ed09bead87c0ull) || + ((sig_y.w[1] == 0x0001ed09bead87c0ull) && + (sig_y.w[0] > 0x378d8e63ffffffffull))) && + ((y.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) || + ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) || + ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { + y_is_zero = 1; + // check for the case where the exponent is shifted right by 2 bits! + if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { + exp_y = (y.w[1] >> 47) & 0x000000000003fffull; + } + } + // ZERO (CASE 4) + if (x_is_zero && y_is_zero) { + // we know that signs must be the same because we would have caught it + // in case3 if signs were different + // totalOrder(x,y) iff exp_x <= exp_y for positive numbers + if (exp_x == exp_y) { + res = 1; + BID_RETURN (res); + } + res = (exp_x <= exp_y); + BID_RETURN (res); + } + // if x is zero and y isn't, clearly x has the smaller payload + if (x_is_zero) { + res = 1; + BID_RETURN (res); + } + // if y is zero, and x isn't, clearly y has the smaller payload + if (y_is_zero) { + res = 0; + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE 5) + // if both components are either bigger or smaller + if (((sig_x.w[1] > sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) + && exp_x >= exp_y) { + res = 0; + BID_RETURN (res); + } + if (((sig_x.w[1] < sig_y.w[1]) + || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) + && exp_x <= exp_y) { + res = 1; + BID_RETURN (res); + } + // if |exp_x - exp_y| < 33, it comes down to the compensated significand + if (exp_x > exp_y) { + // if exp_x is 33 greater than exp_y, it is definitely larger, + // so no need for compensation + if (exp_x - exp_y > 33) { + res = 0; // difference cannot be greater than 10^33 + BID_RETURN (res); + } + // otherwise adjust the x significand upwards + if (exp_x - exp_y > 19) { + __mul_128x128_to_256 (sig_n_prime256, sig_x, + ten2k128[exp_x - exp_y - 20]); + // the compensated significands are equal (ie "x and y represent the same + // entities") return 1 if (negative && expx > expy) || + // (positive && expx < expy) + if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) + && (sig_n_prime256.w[1] == sig_y.w[1]) + && (sig_n_prime256.w[0] == sig_y.w[0])) { + // the case (exp_x == exp_y) cannot occur, because all bits must be + // the same - would have been caught if (x == y) + res = (exp_x <= exp_y); + BID_RETURN (res); + } + // since positive, return 1 if adjusted x is smaller than y + res = ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) + && ((sig_n_prime256.w[1] < sig_y.w[1]) + || (sig_n_prime256.w[1] == sig_y.w[1] + && sig_n_prime256.w[0] < sig_y.w[0]))); + BID_RETURN (res); + } + __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_x - exp_y], sig_x); + // if positive, return whichever significand is larger + // (converse if negative) + if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] + && (sig_n_prime192.w[0] == sig_y.w[0])) { + res = (exp_x <= exp_y); + BID_RETURN (res); + } + res = ((sig_n_prime192.w[2] == 0) + && ((sig_n_prime192.w[1] < sig_y.w[1]) + || (sig_n_prime192.w[1] == sig_y.w[1] + && sig_n_prime192.w[0] < sig_y.w[0]))); + BID_RETURN (res); + } + // if exp_x is 33 less than exp_y, it is definitely smaller, + // no need for compensation + if (exp_y - exp_x > 33) { + res = 1; + BID_RETURN (res); + } + if (exp_y - exp_x > 19) { + // adjust the y significand upwards + __mul_128x128_to_256 (sig_n_prime256, sig_y, + ten2k128[exp_y - exp_x - 20]); + if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) + && (sig_n_prime256.w[1] == sig_x.w[1]) + && (sig_n_prime256.w[0] == sig_x.w[0])) { + res = (exp_x <= exp_y); + BID_RETURN (res); + } + // values are not equal, for positive numbers return 1 if x is less than y + // and 0 otherwise + res = ((sig_n_prime256.w[3] != 0) || + // if upper128 bits of compensated y are non-zero, y is bigger + (sig_n_prime256.w[2] != 0) || + // if upper128 bits of compensated y are non-zero, y is bigger + (sig_n_prime256.w[1] > sig_x.w[1]) || + // if compensated y is bigger, y is bigger + (sig_n_prime256.w[1] == sig_x.w[1] + && sig_n_prime256.w[0] > sig_x.w[0])); + BID_RETURN (res); + } + __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y); + if ((sig_n_prime192.w[2] == 0) && (sig_n_prime192.w[1] == sig_x.w[1]) + && (sig_n_prime192.w[0] == sig_x.w[0])) { + res = (exp_x <= exp_y); + BID_RETURN (res); + } + res = ((sig_n_prime192.w[2] != 0) || + // if upper128 bits of compensated y are non-zero, y is bigger + (sig_n_prime192.w[1] > sig_x.w[1]) || + // if compensated y is bigger, y is bigger + (sig_n_prime192.w[1] == sig_x.w[1] + && sig_n_prime192.w[0] > sig_x.w[0])); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_radix (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +int +bid128_radix (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + if (x.w[LOW_128W]) // dummy test + res = 10; + else + res = 10; + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_quantize.c b/gcc-4.4.3/libgcc/config/libbid/bid128_quantize.c new file mode 100644 index 000000000..3fa48d118 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_quantize.c @@ -0,0 +1,274 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#define BID_128RES +#include "bid_internal.h" + +BID128_FUNCTION_ARG2 (bid128_quantize, x, y) + + UINT256 CT; + UINT128 CX, CY, T, CX2, CR, Stemp, res, REM_H, C2N; + UINT64 sign_x, sign_y, remainder_h, carry, CY64, valid_x; + int_float tempx; + int exponent_x, exponent_y, digits_x, extra_digits, amount; + int expon_diff, total_digits, bin_expon_cx, rmode, status; + +valid_x = unpack_BID128_value (&sign_x, &exponent_x, &CX, x); + + // unpack arguments, check for NaN or Infinity +if (!unpack_BID128_value (&sign_y, &exponent_y, &CY, y)) { + // y is Inf. or NaN +#ifdef SET_STATUS_FLAGS +if ((x.w[1] & SNAN_MASK64) == SNAN_MASK64) // y is sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + + // test if y is NaN +if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) { + // set status flags + __set_status_flags (pfpsf, INVALID_EXCEPTION); + } +#endif + if ((x.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull) { + res.w[1] = CY.w[1] & QUIET_MASK64; + res.w[0] = CY.w[0]; + } else { + res.w[1] = CX.w[1] & QUIET_MASK64; + res.w[0] = CX.w[0]; + } + BID_RETURN (res); +} + // y is Infinity? +if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { + // check if x is not Inf. + if (((x.w[1] & 0x7c00000000000000ull) < 0x7800000000000000ull)) { + // return NaN +#ifdef SET_STATUS_FLAGS + // set status flags + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } else + if (((x.w[1] & 0x7c00000000000000ull) <= 0x7800000000000000ull)) { + res.w[1] = CX.w[1] & QUIET_MASK64; + res.w[0] = CX.w[0]; + BID_RETURN (res); + } +} + +} + +if (!valid_x) { + // test if x is NaN or Inf + if ((x.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull) { +#ifdef SET_STATUS_FLAGS + // set status flags + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } else if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { + if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) { +#ifdef SET_STATUS_FLAGS + // set status flags + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + } + res.w[1] = CX.w[1] & QUIET_MASK64; + res.w[0] = CX.w[0]; + BID_RETURN (res); + } + if (!CX.w[1] && !CX.w[0]) { + get_BID128_very_fast (&res, sign_x, exponent_y, CX); + BID_RETURN (res); + } +} + // get number of decimal digits in coefficient_x +if (CX.w[1]) { + tempx.d = (float) CX.w[1]; + bin_expon_cx = ((tempx.i >> 23) & 0xff) - 0x7f + 64; +} else { + tempx.d = (float) CX.w[0]; + bin_expon_cx = ((tempx.i >> 23) & 0xff) - 0x7f; +} + +digits_x = estimate_decimal_digits[bin_expon_cx]; +if (CX.w[1] > power10_table_128[digits_x].w[1] + || (CX.w[1] == power10_table_128[digits_x].w[1] + && CX.w[0] >= power10_table_128[digits_x].w[0])) + digits_x++; + +expon_diff = exponent_x - exponent_y; +total_digits = digits_x + expon_diff; + +if ((UINT32) total_digits <= 34) { + if (expon_diff >= 0) { + T = power10_table_128[expon_diff]; + __mul_128x128_low (CX2, T, CX); + get_BID128_very_fast (&res, sign_x, exponent_y, CX2); + BID_RETURN (res); + } +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = rnd_mode; + if (sign_x && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#else + rmode = 0; +#endif +#else + rmode = 0; +#endif + // must round off -expon_diff digits + extra_digits = -expon_diff; + __add_128_128 (CX, CX, round_const_table_128[rmode][extra_digits]); + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_to_256 (CT, CX, reciprocals10_128[extra_digits]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 + amount = recip_scale[extra_digits]; + CX2.w[0] = CT.w[2]; + CX2.w[1] = CT.w[3]; + if (amount >= 64) { + CR.w[1] = 0; + CR.w[0] = CX2.w[1] >> (amount - 64); + } else { + __shr_128 (CR, CX2, amount); + } + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rnd_mode == 0) +#endif + if (CR.w[0] & 1) { + // check whether fractional part of initial_P/10^extra_digits is + // exactly .5 this is the same as fractional part of + // (initial_P + 0.5*10^extra_digits)/10^extra_digits is exactly zero + + // get remainder + if (amount >= 64) { + remainder_h = CX2.w[0] | (CX2.w[1] << (128 - amount)); + } else + remainder_h = CX2.w[0] << (64 - amount); + + // test whether fractional part is 0 + if (!remainder_h + && (CT.w[1] < reciprocals10_128[extra_digits].w[1] + || (CT.w[1] == reciprocals10_128[extra_digits].w[1] + && CT.w[0] < reciprocals10_128[extra_digits].w[0]))) { + CR.w[0]--; + } + } +#endif + +#ifdef SET_STATUS_FLAGS + status = INEXACT_EXCEPTION; + + // get remainder + if (amount >= 64) { + REM_H.w[1] = (CX2.w[1] << (128 - amount)); + REM_H.w[0] = CX2.w[0]; + } else { + REM_H.w[1] = CX2.w[0] << (64 - amount); + REM_H.w[0] = 0; + } + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if (REM_H.w[1] == 0x8000000000000000ull && !REM_H.w[0] + && (CT.w[1] < reciprocals10_128[extra_digits].w[1] + || (CT.w[1] == reciprocals10_128[extra_digits].w[1] + && CT.w[0] < reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if (!(REM_H.w[1] | REM_H.w[0]) + && (CT.w[1] < reciprocals10_128[extra_digits].w[1] + || (CT.w[1] == reciprocals10_128[extra_digits].w[1] + && CT.w[0] < reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (Stemp.w[0], CY64, CT.w[0], + reciprocals10_128[extra_digits].w[0]); + __add_carry_in_out (Stemp.w[1], carry, CT.w[1], + reciprocals10_128[extra_digits].w[1], CY64); + if (amount < 64) { + C2N.w[1] = 0; + C2N.w[0] = ((UINT64) 1) << amount; + REM_H.w[0] = REM_H.w[1] >> (64 - amount); + REM_H.w[1] = 0; + } else { + C2N.w[1] = ((UINT64) 1) << (amount - 64); + C2N.w[0] = 0; + REM_H.w[1] >>= (128 - amount); + } + REM_H.w[0] += carry; + if (REM_H.w[0] < carry) + REM_H.w[1]++; + if (__unsigned_compare_ge_128 (REM_H, C2N)) + status = EXACT_STATUS; + } + + __set_status_flags (pfpsf, status); + +#endif + get_BID128_very_fast (&res, sign_x, exponent_y, CR); + BID_RETURN (res); +} +if (total_digits < 0) { + CR.w[1] = CR.w[0] = 0; +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = rnd_mode; + if (sign_x && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + if (rmode == ROUNDING_UP) + CR.w[0] = 1; +#endif +#endif +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INEXACT_EXCEPTION); +#endif + get_BID128_very_fast (&res, sign_x, exponent_y, CR); + BID_RETURN (res); +} + // else more than 34 digits in coefficient +#ifdef SET_STATUS_FLAGS +__set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif +res.w[1] = 0x7c00000000000000ull; +res.w[0] = 0; +BID_RETURN (res); + +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_rem.c b/gcc-4.4.3/libgcc/config/libbid/bid128_rem.c new file mode 100644 index 000000000..dd460df84 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_rem.c @@ -0,0 +1,217 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#define BID_128RES +#include "bid_div_macros.h" + + +BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (UINT128, bid128_rem, x, y) + + UINT256 P256; + UINT128 CX, CY, CX2, CQ, CR, T, CXS, P128, res; + UINT64 sign_x, sign_y, valid_y; + SINT64 D; + int_float f64, fx; + int exponent_x, exponent_y, diff_expon, bin_expon_cx, scale, + scale0; + + // unpack arguments, check for NaN or Infinity + +valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y); + +if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { +#ifdef SET_STATUS_FLAGS +if ((y.w[1] & SNAN_MASK64) == SNAN_MASK64) // y is sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // test if x is NaN +if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((x.w[1] & SNAN_MASK64) == SNAN_MASK64) // y is sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = CX.w[1] & QUIET_MASK64; + res.w[0] = CX.w[0]; + BID_RETURN (res); +} + // x is Infinity? +if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { + // check if y is Inf. + if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) + // return NaN + { +#ifdef SET_STATUS_FLAGS + // set status flags + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } + +} + // x is 0 +if ((!CY.w[1]) && (!CY.w[0])) { +#ifdef SET_STATUS_FLAGS + // set status flags + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // x=y=0, return NaN + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); +} +if (valid_y || ((y.w[1] & NAN_MASK64) == INFINITY_MASK64)) { + // return 0 + if ((exponent_x > exponent_y) + && ((y.w[1] & NAN_MASK64) != INFINITY_MASK64)) + exponent_x = exponent_y; + + res.w[1] = sign_x | (((UINT64) exponent_x) << 49); + res.w[0] = 0; + BID_RETURN (res); +} +} +if (!valid_y) { + // y is Inf. or NaN + + // test if y is NaN + if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((y.w[1] & SNAN_MASK64) == SNAN_MASK64) // y is sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = CY.w[1] & QUIET_MASK64; + res.w[0] = CY.w[0]; + BID_RETURN (res); + } + // y is Infinity? + if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { + // return x + res.w[1] = x.w[1]; + res.w[0] = x.w[0]; + BID_RETURN (res); + } + // y is 0 +#ifdef SET_STATUS_FLAGS + // set status flags + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); +} + +diff_expon = exponent_x - exponent_y; + +if (diff_expon <= 0) { + diff_expon = -diff_expon; + + if (diff_expon > 34) { + // |x|<|y| in this case + res = x; + BID_RETURN (res); + } + // set exponent of y to exponent_x, scale coefficient_y + T = power10_table_128[diff_expon]; + __mul_128x128_to_256 (P256, CY, T); + + if (P256.w[2] || P256.w[3]) { + // |x|<|y| in this case + res = x; + BID_RETURN (res); + } + + CX2.w[1] = (CX.w[1] << 1) | (CX.w[0] >> 63); + CX2.w[0] = CX.w[0] << 1; + if (__unsigned_compare_ge_128 (P256, CX2)) { + // |x|<|y| in this case + res = x; + BID_RETURN (res); + } + + P128.w[0] = P256.w[0]; + P128.w[1] = P256.w[1]; + __div_128_by_128 (&CQ, &CR, CX, P128); + + CX2.w[1] = (CR.w[1] << 1) | (CR.w[0] >> 63); + CX2.w[0] = CR.w[0] << 1; + if ((__unsigned_compare_gt_128 (CX2, P256)) + || (CX2.w[1] == P256.w[1] && CX2.w[0] == P256.w[0] + && (CQ.w[0] & 1))) { + __sub_128_128 (CR, P256, CR); + sign_x ^= 0x8000000000000000ull; + } + + get_BID128_very_fast (&res, sign_x, exponent_x, CR); + BID_RETURN (res); +} + // 2^64 +f64.i = 0x5f800000; + +scale0 = 38; +if (!CY.w[1]) + scale0 = 34; + +while (diff_expon > 0) { + // get number of digits in CX and scale=38-digits + // fx ~ CX + fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; + bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f; + scale = scale0 - estimate_decimal_digits[bin_expon_cx]; + // scale = 38-estimate_decimal_digits[bin_expon_cx]; + D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1]; + if (D > 0 + || (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0])) + scale--; + + if (diff_expon >= scale) + diff_expon -= scale; + else { + scale = diff_expon; + diff_expon = 0; + } + + T = power10_table_128[scale]; + __mul_128x128_low (CXS, CX, T); + + __div_128_by_128 (&CQ, &CX, CXS, CY); + + // check for remainder == 0 + if (!CX.w[1] && !CX.w[0]) { + get_BID128_very_fast (&res, sign_x, exponent_y, CX); + BID_RETURN (res); + } +} + +CX2.w[1] = (CX.w[1] << 1) | (CX.w[0] >> 63); +CX2.w[0] = CX.w[0] << 1; +if ((__unsigned_compare_gt_128 (CX2, CY)) + || (CX2.w[1] == CY.w[1] && CX2.w[0] == CY.w[0] && (CQ.w[0] & 1))) { + __sub_128_128 (CX, CY, CX); + sign_x ^= 0x8000000000000000ull; +} + +get_BID128_very_fast (&res, sign_x, exponent_y, CX); +BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_round_integral.c b/gcc-4.4.3/libgcc/config/libbid/bid128_round_integral.c new file mode 100644 index 000000000..6efcd4743 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_round_integral.c @@ -0,0 +1,1951 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#define BID_128RES + +#include "bid_internal.h" + +/***************************************************************************** + * BID128_round_integral_exact + ****************************************************************************/ + +BID128_FUNCTION_ARG1 (bid128_round_integral_exact, x) + + UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} + }; +UINT64 x_sign; +UINT64 x_exp; +int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) +UINT64 tmp64; +BID_UI64DOUBLE tmp1; +unsigned int x_nr_bits; +int q, ind, shift; +UINT128 C1; +UINT256 fstar; +UINT256 P256; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + // if x = NaN, then res = Q (x) + // check first for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] + res.w[0] = x.w[0]; + } else { // x is QNaN + // return x + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] + res.w[0] = x.w[0]; + } + BID_RETURN (res) + } else { // x is not a NaN, so it must be infinity + if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf + // return +inf + res.w[1] = 0x7800000000000000ull; + res.w[0] = 0x0000000000000000ull; + } else { // x is -inf + // return -inf + res.w[1] = 0xf800000000000000ull; + res.w[0] = 0x0000000000000000ull; + } + BID_RETURN (res); + } +} + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for non-canonical values (treated as zero) +if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + // non-canonical + x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C1.w[1] = 0; // significand high + C1.w[0] = 0; // significand low +} else { // G0_G1 != 11 + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C1.w[1] > 0x0001ed09bead87c0ull || + (C1.w[1] == 0x0001ed09bead87c0ull + && C1.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + C1.w[1] = 0; + C1.w[0] = 0; + } else { // canonical + ; + } +} + + // test for input equal to zero +if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + // return 0 preserving the sign bit and the preferred exponent + // of MAX(Q(x), 0) + if (x_exp <= (0x1820ull << 49)) { + res.w[1] = (x.w[1] & 0x8000000000000000ull) | 0x3040000000000000ull; + } else { + res.w[1] = x_sign | x_exp; + } + res.w[0] = 0x0000000000000000ull; + BID_RETURN (res); +} + // x is not special and is not zero + +switch (rnd_mode) { +case ROUNDING_TO_NEAREST: +case ROUNDING_TIES_AWAY: + // if (exp <= -(p+1)) return 0.0 + if (x_exp <= 0x2ffa000000000000ull) { // 0x2ffa000000000000ull == -35 + res.w[1] = x_sign | 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; +case ROUNDING_DOWN: + // if (exp <= -p) return -1.0 or +0.0 + if (x_exp <= 0x2ffc000000000000ull) { // 0x2ffa000000000000ull == -34 + if (x_sign) { + // if negative, return negative 1, because we know coefficient + // is non-zero (would have been caught above) + res.w[1] = 0xb040000000000000ull; + res.w[0] = 0x0000000000000001ull; + } else { + // if positive, return positive 0, because we know coefficient is + // non-zero (would have been caught above) + res.w[1] = 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + } + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; +case ROUNDING_UP: + // if (exp <= -p) return -0.0 or +1.0 + if (x_exp <= 0x2ffc000000000000ull) { // 0x2ffc000000000000ull == -34 + if (x_sign) { + // if negative, return negative 0, because we know the coefficient + // is non-zero (would have been caught above) + res.w[1] = 0xb040000000000000ull; + res.w[0] = 0x0000000000000000ull; + } else { + // if positive, return positive 1, because we know coefficient is + // non-zero (would have been caught above) + res.w[1] = 0x3040000000000000ull; + res.w[0] = 0x0000000000000001ull; + } + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; +case ROUNDING_TO_ZERO: + // if (exp <= -p) return -0.0 or +0.0 + if (x_exp <= 0x2ffc000000000000ull) { // 0x2ffc000000000000ull == -34 + res.w[1] = x_sign | 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; +} + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x +if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } +} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); +} + +q = nr_digits[x_nr_bits - 1].digits; +if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi || + (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi && + C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; +} +exp = (x_exp >> 49) - 6176; +if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res.w[1] = x.w[1]; + res.w[0] = x.w[0]; + BID_RETURN (res); +} + // exp < 0 +switch (rnd_mode) { +case ROUNDING_TO_NEAREST: + if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^x where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 34 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + // determine the value of res and fstar + + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + // Note: we are going to use ten2mk128[] instead of ten2mk128trunc[] + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + // redundant shift = shiftright128[ind - 1]; // shift = 0 + res.w[1] = P256.w[3]; + res.w[0] = P256.w[2]; + // redundant fstar.w[3] = 0; + // redundant fstar.w[2] = 0; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* < 10^(-x) <=> midpoint + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + // if 0 < fstar < 10^(-x), subtract 1 if odd (for rounding to even) + if ((res.w[0] & 0x0000000000000001ull) && // is result odd? + ((fstar.w[1] < (ten2mk128[ind - 1].w[1])) + || ((fstar.w[1] == ten2mk128[ind - 1].w[1]) + && (fstar.w[0] < ten2mk128[ind - 1].w[0])))) { + // subract 1 to make even + if (res.w[0]-- == 0) { + res.w[1]--; + } + } + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128[ind - 1].w[1] || + (tmp64 == ten2mk128[ind - 1].w[1] && + fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res.w[1] = (P256.w[3] >> shift); + res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift); + // redundant fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* < 10^(-x) <=> midpoint + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if ((res.w[0] & 0x0000000000000001ull) && // is result odd? + fstar.w[2] == 0 && (fstar.w[1] < ten2mk128[ind - 1].w[1] || + (fstar.w[1] == ten2mk128[ind - 1].w[1] && + fstar.w[0] < ten2mk128[ind - 1].w[0]))) { + // subract 1 to make even + if (res.w[0]-- == 0) { + res.w[1]--; + } + } + if (fstar.w[2] > onehalf128[ind - 1] || + (fstar.w[2] == onehalf128[ind - 1] + && (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[1] > ten2mk128[ind - 1].w[1] || + (fstar.w[1] == ten2mk128[ind - 1].w[1] && + fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // 22 <= ind - 1 <= 33 + shift = shiftright128[ind - 1] - 64; // 2 <= shift <= 38 + res.w[1] = 0; + res.w[0] = P256.w[3] >> shift; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* < 10^(-x) <=> midpoint + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if ((res.w[0] & 0x0000000000000001ull) && // is result odd? + fstar.w[3] == 0 && fstar.w[2] == 0 && + (fstar.w[1] < ten2mk128[ind - 1].w[1] || + (fstar.w[1] == ten2mk128[ind - 1].w[1] && + fstar.w[0] < ten2mk128[ind - 1].w[0]))) { + // subract 1 to make even + if (res.w[0]-- == 0) { + res.w[1]--; + } + } + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1] + || (fstar.w[1] == ten2mk128[ind - 1].w[1] + && fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + res.w[1] = x_sign | 0x3040000000000000ull | res.w[1]; + BID_RETURN (res); + } else { // if ((q + exp) < 0) <=> q < -exp + // the result is +0 or -0 + res.w[1] = x_sign | 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; +case ROUNDING_TIES_AWAY: + if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^x where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 34 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // determine also the inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + // Note: we are going to use ten2mk128[] instead of ten2mk128trunc[] + // shift right C* by Ex-128 = shiftright128[ind] + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + // redundant shift = shiftright128[ind - 1]; // shift = 0 + res.w[1] = P256.w[3]; + res.w[0] = P256.w[2]; + // redundant fstar.w[3] = 0; + // redundant fstar.w[2] = 0; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > ten2mk128[ind - 1].w[1] || + (tmp64 == ten2mk128[ind - 1].w[1] && + fstar.w[0] >= ten2mk128[ind - 1].w[0]))) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res.w[1] = (P256.w[3] >> shift); + res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift); + // redundant fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + if (fstar.w[2] > onehalf128[ind - 1] || + (fstar.w[2] == onehalf128[ind - 1] + && (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[1] > ten2mk128[ind - 1].w[1] || + (fstar.w[1] == ten2mk128[ind - 1].w[1] && + fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // 22 <= ind - 1 <= 33 + shift = shiftright128[ind - 1] - 64; // 2 <= shift <= 38 + res.w[1] = 0; + res.w[0] = P256.w[3] >> shift; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1] + || (fstar.w[1] == ten2mk128[ind - 1].w[1] + && fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + // if the result was a midpoint, it was already rounded away from zero + res.w[1] |= x_sign | 0x3040000000000000ull; + BID_RETURN (res); + } else { // if ((q + exp) < 0) <=> q < -exp + // the result is +0 or -0 + res.w[1] = x_sign | 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; +case ROUNDING_DOWN: + if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x' + // (number of digits to be chopped off) + // chop off ind digits from the lower part of C1 + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + // FOR ROUND_TO_ZERO, WE DON'T NEED TO ADD 1/2 ULP + // FOR ROUND_TO_POSITIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF POSITIVE + // FOR ROUND_TO_NEGATIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF NEGATIVE + // tmp64 = C1.w[0]; + // if (ind <= 19) { + // C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + // } else { + // C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + // C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + // } + // if (C1.w[0] < tmp64) C1.w[1]++; + // if carry-out from C1.w[0], increment C1.w[1] + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 34 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res.w[1] = P256.w[3]; + res.w[0] = P256.w[2]; + // redundant fstar.w[3] = 0; + // redundant fstar.w[2] = 0; + // redundant fstar.w[1] = P256.w[1]; + // redundant fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if ((P256.w[1] > ten2mk128[ind - 1].w[1]) + || (P256.w[1] == ten2mk128[ind - 1].w[1] + && (P256.w[0] >= ten2mk128[ind - 1].w[0]))) { + *pfpsf |= INEXACT_EXCEPTION; + // if positive, the truncated value is already the correct result + if (x_sign) { // if negative + if (++res.w[0] == 0) { + res.w[1]++; + } + } + } + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + res.w[1] = (P256.w[3] >> shift); + res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift); + // redundant fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if (fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1] || + (fstar.w[1] == ten2mk128[ind - 1].w[1] && + fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + *pfpsf |= INEXACT_EXCEPTION; + // if positive, the truncated value is already the correct result + if (x_sign) { // if negative + if (++res.w[0] == 0) { + res.w[1]++; + } + } + } + } else { // 22 <= ind - 1 <= 33 + shift = shiftright128[ind - 1] - 64; // 2 <= shift <= 38 + res.w[1] = 0; + res.w[0] = P256.w[3] >> shift; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128[ind - 1].w[1] + || (fstar.w[1] == ten2mk128[ind - 1].w[1] + && fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + *pfpsf |= INEXACT_EXCEPTION; + // if positive, the truncated value is already the correct result + if (x_sign) { // if negative + if (++res.w[0] == 0) { + res.w[1]++; + } + } + } + } + res.w[1] = x_sign | 0x3040000000000000ull | res.w[1]; + BID_RETURN (res); + } else { // if exp < 0 and q + exp <= 0 + if (x_sign) { // negative rounds down to -1.0 + res.w[1] = 0xb040000000000000ull; + res.w[0] = 0x0000000000000001ull; + } else { // positive rpunds down to +0.0 + res.w[1] = 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + } + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; +case ROUNDING_UP: + if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x' + // (number of digits to be chopped off) + // chop off ind digits from the lower part of C1 + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + // FOR ROUND_TO_ZERO, WE DON'T NEED TO ADD 1/2 ULP + // FOR ROUND_TO_POSITIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF POSITIVE + // FOR ROUND_TO_NEGATIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF NEGATIVE + // tmp64 = C1.w[0]; + // if (ind <= 19) { + // C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + // } else { + // C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + // C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + // } + // if (C1.w[0] < tmp64) C1.w[1]++; + // if carry-out from C1.w[0], increment C1.w[1] + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 34 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res.w[1] = P256.w[3]; + res.w[0] = P256.w[2]; + // redundant fstar.w[3] = 0; + // redundant fstar.w[2] = 0; + // redundant fstar.w[1] = P256.w[1]; + // redundant fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if ((P256.w[1] > ten2mk128[ind - 1].w[1]) + || (P256.w[1] == ten2mk128[ind - 1].w[1] + && (P256.w[0] >= ten2mk128[ind - 1].w[0]))) { + *pfpsf |= INEXACT_EXCEPTION; + // if negative, the truncated value is already the correct result + if (!x_sign) { // if positive + if (++res.w[0] == 0) { + res.w[1]++; + } + } + } + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res.w[1] = (P256.w[3] >> shift); + res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift); + // redundant fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if (fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1] || + (fstar.w[1] == ten2mk128[ind - 1].w[1] && + fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + *pfpsf |= INEXACT_EXCEPTION; + // if negative, the truncated value is already the correct result + if (!x_sign) { // if positive + if (++res.w[0] == 0) { + res.w[1]++; + } + } + } + } else { // 22 <= ind - 1 <= 33 + shift = shiftright128[ind - 1] - 64; // 2 <= shift <= 38 + res.w[1] = 0; + res.w[0] = P256.w[3] >> shift; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128[ind - 1].w[1] + || (fstar.w[1] == ten2mk128[ind - 1].w[1] + && fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + *pfpsf |= INEXACT_EXCEPTION; + // if negative, the truncated value is already the correct result + if (!x_sign) { // if positive + if (++res.w[0] == 0) { + res.w[1]++; + } + } + } + } + res.w[1] = x_sign | 0x3040000000000000ull | res.w[1]; + BID_RETURN (res); + } else { // if exp < 0 and q + exp <= 0 + if (x_sign) { // negative rounds up to -0.0 + res.w[1] = 0xb040000000000000ull; + res.w[0] = 0x0000000000000000ull; + } else { // positive rpunds up to +1.0 + res.w[1] = 0x3040000000000000ull; + res.w[0] = 0x0000000000000001ull; + } + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; +case ROUNDING_TO_ZERO: + if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x' + // (number of digits to be chopped off) + // chop off ind digits from the lower part of C1 + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + // FOR ROUND_TO_ZERO, WE DON'T NEED TO ADD 1/2 ULP + // FOR ROUND_TO_POSITIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF POSITIVE + // FOR ROUND_TO_NEGATIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF NEGATIVE + //tmp64 = C1.w[0]; + // if (ind <= 19) { + // C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + // } else { + // C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + // C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + // } + // if (C1.w[0] < tmp64) C1.w[1]++; + // if carry-out from C1.w[0], increment C1.w[1] + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 34 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res.w[1] = P256.w[3]; + res.w[0] = P256.w[2]; + // redundant fstar.w[3] = 0; + // redundant fstar.w[2] = 0; + // redundant fstar.w[1] = P256.w[1]; + // redundant fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if ((P256.w[1] > ten2mk128[ind - 1].w[1]) + || (P256.w[1] == ten2mk128[ind - 1].w[1] + && (P256.w[0] >= ten2mk128[ind - 1].w[0]))) { + *pfpsf |= INEXACT_EXCEPTION; + } + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res.w[1] = (P256.w[3] >> shift); + res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift); + // redundant fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if (fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1] || + (fstar.w[1] == ten2mk128[ind - 1].w[1] && + fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // 22 <= ind - 1 <= 33 + shift = shiftright128[ind - 1] - 64; // 2 <= shift <= 38 + res.w[1] = 0; + res.w[0] = P256.w[3] >> shift; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128[ind - 1].w[1] + || (fstar.w[1] == ten2mk128[ind - 1].w[1] + && fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + *pfpsf |= INEXACT_EXCEPTION; + } + } + res.w[1] = x_sign | 0x3040000000000000ull | res.w[1]; + BID_RETURN (res); + } else { // if exp < 0 and q + exp <= 0 the result is +0 or -0 + res.w[1] = x_sign | 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_round_integral_nearest_even + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND (bid128_round_integral_nearest_even, x) + + UINT128 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1; + // UINT128 res is C* at first - represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + // if x = NaN, then res = Q (x) + // check first for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] + res.w[0] = x.w[0]; + } else { // x is QNaN + // return x + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] + res.w[0] = x.w[0]; + } + BID_RETURN (res) +} else { // x is not a NaN, so it must be infinity + if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf + // return +inf + res.w[1] = 0x7800000000000000ull; + res.w[0] = 0x0000000000000000ull; + } else { // x is -inf + // return -inf + res.w[1] = 0xf800000000000000ull; + res.w[0] = 0x0000000000000000ull; + } + BID_RETURN (res); +} +} + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for non-canonical values (treated as zero) +if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + // non-canonical + x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C1.w[1] = 0; // significand high + C1.w[0] = 0; // significand low +} else { // G0_G1 != 11 + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C1.w[1] > 0x0001ed09bead87c0ull || + (C1.w[1] == 0x0001ed09bead87c0ull + && C1.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + C1.w[1] = 0; + C1.w[0] = 0; + } else { // canonical + ; + } +} + + // test for input equal to zero +if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + // return 0 preserving the sign bit and the preferred exponent + // of MAX(Q(x), 0) + if (x_exp <= (0x1820ull << 49)) { + res.w[1] = (x.w[1] & 0x8000000000000000ull) | 0x3040000000000000ull; + } else { + res.w[1] = x_sign | x_exp; + } + res.w[0] = 0x0000000000000000ull; + BID_RETURN (res); +} + // x is not special and is not zero + + // if (exp <= -(p+1)) return 0 +if (x_exp <= 0x2ffa000000000000ull) { // 0x2ffa000000000000ull == -35 + res.w[1] = x_sign | 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + BID_RETURN (res); +} + // q = nr. of decimal digits in x + // determine first the nr. of bits in x +if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } +} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); +} + +q = nr_digits[x_nr_bits - 1].digits; +if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi && + C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; +} +exp = (x_exp >> 49) - 6176; +if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res.w[1] = x.w[1]; + res.w[0] = x.w[0]; + BID_RETURN (res); +} else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^x where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 34 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + // determine the value of res and fstar + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + // redundant shift = shiftright128[ind - 1]; // shift = 0 + res.w[1] = P256.w[3]; + res.w[0] = P256.w[2]; + // redundant fstar.w[3] = 0; + // redundant fstar.w[2] = 0; + // redundant fstar.w[1] = P256.w[1]; + // redundant fstar.w[0] = P256.w[0]; + // fraction f* < 10^(-x) <=> midpoint + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + // if 0 < fstar < 10^(-x), subtract 1 if odd (for rounding to even) + if ((res.w[0] & 0x0000000000000001ull) && // is result odd? + ((P256.w[1] < (ten2mk128[ind - 1].w[1])) + || ((P256.w[1] == ten2mk128[ind - 1].w[1]) + && (P256.w[0] < ten2mk128[ind - 1].w[0])))) { + // subract 1 to make even + if (res.w[0]-- == 0) { + res.w[1]--; + } + } + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res.w[1] = (P256.w[3] >> shift); + res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift); + // redundant fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* < 10^(-x) <=> midpoint + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if ((res.w[0] & 0x0000000000000001ull) && // is result odd? + fstar.w[2] == 0 && (fstar.w[1] < ten2mk128[ind - 1].w[1] || + (fstar.w[1] == ten2mk128[ind - 1].w[1] && + fstar.w[0] < ten2mk128[ind - 1].w[0]))) { + // subract 1 to make even + if (res.w[0]-- == 0) { + res.w[1]--; + } + } + } else { // 22 <= ind - 1 <= 33 + shift = shiftright128[ind - 1] - 64; // 2 <= shift <= 38 + res.w[1] = 0; + res.w[0] = P256.w[3] >> shift; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* < 10^(-x) <=> midpoint + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if ((res.w[0] & 0x0000000000000001ull) && // is result odd? + fstar.w[3] == 0 && fstar.w[2] == 0 + && (fstar.w[1] < ten2mk128[ind - 1].w[1] + || (fstar.w[1] == ten2mk128[ind - 1].w[1] + && fstar.w[0] < ten2mk128[ind - 1].w[0]))) { + // subract 1 to make even + if (res.w[0]-- == 0) { + res.w[1]--; + } + } + } + res.w[1] = x_sign | 0x3040000000000000ull | res.w[1]; + BID_RETURN (res); +} else { // if ((q + exp) < 0) <=> q < -exp + // the result is +0 or -0 + res.w[1] = x_sign | 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + BID_RETURN (res); +} +} + +/***************************************************************************** + * BID128_round_integral_negative + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND (bid128_round_integral_negative, x) + + UINT128 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo + // (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1; + // UINT128 res is C* at first - represents up to 34 decimal digits ~ + // 113 bits + UINT256 fstar; + UINT256 P256; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + // if x = NaN, then res = Q (x) + // check first for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] + res.w[0] = x.w[0]; + } else { // x is QNaN + // return x + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] + res.w[0] = x.w[0]; + } + BID_RETURN (res) +} else { // x is not a NaN, so it must be infinity + if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf + // return +inf + res.w[1] = 0x7800000000000000ull; + res.w[0] = 0x0000000000000000ull; + } else { // x is -inf + // return -inf + res.w[1] = 0xf800000000000000ull; + res.w[0] = 0x0000000000000000ull; + } + BID_RETURN (res); +} +} + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for non-canonical values (treated as zero) +if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + // non-canonical + x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C1.w[1] = 0; // significand high + C1.w[0] = 0; // significand low +} else { // G0_G1 != 11 + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C1.w[1] > 0x0001ed09bead87c0ull || + (C1.w[1] == 0x0001ed09bead87c0ull + && C1.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + C1.w[1] = 0; + C1.w[0] = 0; + } else { // canonical + ; + } +} + + // test for input equal to zero +if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + // return 0 preserving the sign bit and the preferred exponent + // of MAX(Q(x), 0) + if (x_exp <= (0x1820ull << 49)) { + res.w[1] = (x.w[1] & 0x8000000000000000ull) | 0x3040000000000000ull; + } else { + res.w[1] = x_sign | x_exp; + } + res.w[0] = 0x0000000000000000ull; + BID_RETURN (res); +} + // x is not special and is not zero + + // if (exp <= -p) return -1.0 or +0.0 +if (x_exp <= 0x2ffc000000000000ull) { // 0x2ffc000000000000ull == -34 + if (x_sign) { + // if negative, return negative 1, because we know the coefficient + // is non-zero (would have been caught above) + res.w[1] = 0xb040000000000000ull; + res.w[0] = 0x0000000000000001ull; + } else { + // if positive, return positive 0, because we know coefficient is + // non-zero (would have been caught above) + res.w[1] = 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + } + BID_RETURN (res); +} + // q = nr. of decimal digits in x + // determine first the nr. of bits in x +if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } +} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); +} + +q = nr_digits[x_nr_bits - 1].digits; +if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi || + (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi && + C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; +} +exp = (x_exp >> 49) - 6176; +if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res.w[1] = x.w[1]; + res.w[0] = x.w[0]; + BID_RETURN (res); +} else if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x' + // (number of digits to be chopped off) + // chop off ind digits from the lower part of C1 + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + // FOR ROUND_TO_ZERO, WE DON'T NEED TO ADD 1/2 ULP + // FOR ROUND_TO_POSITIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF POSITIVE + // FOR ROUND_TO_NEGATIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF NEGATIVE + //tmp64 = C1.w[0]; + // if (ind <= 19) { + // C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + // } else { + // C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + // C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + // } + // if (C1.w[0] < tmp64) C1.w[1]++; + // if carry-out from C1.w[0], increment C1.w[1] + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 34 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res.w[1] = P256.w[3]; + res.w[0] = P256.w[2]; + // if positive, the truncated value is already the correct result + if (x_sign) { // if negative + // redundant fstar.w[3] = 0; + // redundant fstar.w[2] = 0; + // redundant fstar.w[1] = P256.w[1]; + // redundant fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if ((P256.w[1] > ten2mk128[ind - 1].w[1]) + || (P256.w[1] == ten2mk128[ind - 1].w[1] + && (P256.w[0] >= ten2mk128[ind - 1].w[0]))) { + if (++res.w[0] == 0) { + res.w[1]++; + } + } + } + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + res.w[1] = (P256.w[3] >> shift); + res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift); + // if positive, the truncated value is already the correct result + if (x_sign) { // if negative + // redundant fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if (fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1] || + (fstar.w[1] == ten2mk128[ind - 1].w[1] && + fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + if (++res.w[0] == 0) { + res.w[1]++; + } + } + } + } else { // 22 <= ind - 1 <= 33 + shift = shiftright128[ind - 1] - 64; // 2 <= shift <= 38 + res.w[1] = 0; + res.w[0] = P256.w[3] >> shift; + // if positive, the truncated value is already the correct result + if (x_sign) { // if negative + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128[ind - 1].w[1] + || (fstar.w[1] == ten2mk128[ind - 1].w[1] + && fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + if (++res.w[0] == 0) { + res.w[1]++; + } + } + } + } + res.w[1] = x_sign | 0x3040000000000000ull | res.w[1]; + BID_RETURN (res); +} else { // if exp < 0 and q + exp <= 0 + if (x_sign) { // negative rounds down to -1.0 + res.w[1] = 0xb040000000000000ull; + res.w[0] = 0x0000000000000001ull; + } else { // positive rpunds down to +0.0 + res.w[1] = 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + } + BID_RETURN (res); +} +} + +/***************************************************************************** + * BID128_round_integral_positive + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND (bid128_round_integral_positive, x) + + UINT128 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo + // (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1; + // UINT128 res is C* at first - represents up to 34 decimal digits ~ + // 113 bits + UINT256 fstar; + UINT256 P256; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + // if x = NaN, then res = Q (x) + // check first for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] + res.w[0] = x.w[0]; + } else { // x is QNaN + // return x + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] + res.w[0] = x.w[0]; + } + BID_RETURN (res) +} else { // x is not a NaN, so it must be infinity + if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf + // return +inf + res.w[1] = 0x7800000000000000ull; + res.w[0] = 0x0000000000000000ull; + } else { // x is -inf + // return -inf + res.w[1] = 0xf800000000000000ull; + res.w[0] = 0x0000000000000000ull; + } + BID_RETURN (res); +} +} + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for non-canonical values (treated as zero) +if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + // non-canonical + x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C1.w[1] = 0; // significand high + C1.w[0] = 0; // significand low +} else { // G0_G1 != 11 + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C1.w[1] > 0x0001ed09bead87c0ull || + (C1.w[1] == 0x0001ed09bead87c0ull + && C1.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + C1.w[1] = 0; + C1.w[0] = 0; + } else { // canonical + ; + } +} + + // test for input equal to zero +if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + // return 0 preserving the sign bit and the preferred exponent + // of MAX(Q(x), 0) + if (x_exp <= (0x1820ull << 49)) { + res.w[1] = (x.w[1] & 0x8000000000000000ull) | 0x3040000000000000ull; + } else { + res.w[1] = x_sign | x_exp; + } + res.w[0] = 0x0000000000000000ull; + BID_RETURN (res); +} + // x is not special and is not zero + + // if (exp <= -p) return -0.0 or +1.0 +if (x_exp <= 0x2ffc000000000000ull) { // 0x2ffc000000000000ull == -34 + if (x_sign) { + // if negative, return negative 0, because we know the coefficient + // is non-zero (would have been caught above) + res.w[1] = 0xb040000000000000ull; + res.w[0] = 0x0000000000000000ull; + } else { + // if positive, return positive 1, because we know coefficient is + // non-zero (would have been caught above) + res.w[1] = 0x3040000000000000ull; + res.w[0] = 0x0000000000000001ull; + } + BID_RETURN (res); +} + // q = nr. of decimal digits in x + // determine first the nr. of bits in x +if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } +} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); +} + +q = nr_digits[x_nr_bits - 1].digits; +if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi || + (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi && + C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; +} +exp = (x_exp >> 49) - 6176; +if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res.w[1] = x.w[1]; + res.w[0] = x.w[0]; + BID_RETURN (res); +} else if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x' + // (number of digits to be chopped off) + // chop off ind digits from the lower part of C1 + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + // FOR ROUND_TO_ZERO, WE DON'T NEED TO ADD 1/2 ULP + // FOR ROUND_TO_POSITIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF POSITIVE + // FOR ROUND_TO_NEGATIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF NEGATIVE + // tmp64 = C1.w[0]; + // if (ind <= 19) { + // C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + // } else { + // C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + // C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + // } + // if (C1.w[0] < tmp64) C1.w[1]++; + // if carry-out from C1.w[0], increment C1.w[1] + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 34 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res.w[1] = P256.w[3]; + res.w[0] = P256.w[2]; + // if negative, the truncated value is already the correct result + if (!x_sign) { // if positive + // redundant fstar.w[3] = 0; + // redundant fstar.w[2] = 0; + // redundant fstar.w[1] = P256.w[1]; + // redundant fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if ((P256.w[1] > ten2mk128[ind - 1].w[1]) + || (P256.w[1] == ten2mk128[ind - 1].w[1] + && (P256.w[0] >= ten2mk128[ind - 1].w[0]))) { + if (++res.w[0] == 0) { + res.w[1]++; + } + } + } + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res.w[1] = (P256.w[3] >> shift); + res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift); + // if negative, the truncated value is already the correct result + if (!x_sign) { // if positive + // redundant fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if (fstar.w[2] || fstar.w[1] > ten2mk128[ind - 1].w[1] || + (fstar.w[1] == ten2mk128[ind - 1].w[1] && + fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + if (++res.w[0] == 0) { + res.w[1]++; + } + } + } + } else { // 22 <= ind - 1 <= 33 + shift = shiftright128[ind - 1] - 64; // 2 <= shift <= 38 + res.w[1] = 0; + res.w[0] = P256.w[3] >> shift; + // if negative, the truncated value is already the correct result + if (!x_sign) { // if positive + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + // fraction f* > 10^(-x) <=> inexact + // f* is in the right position to be compared with + // 10^(-x) from ten2mk128[] + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128[ind - 1].w[1] + || (fstar.w[1] == ten2mk128[ind - 1].w[1] + && fstar.w[0] >= ten2mk128[ind - 1].w[0])) { + if (++res.w[0] == 0) { + res.w[1]++; + } + } + } + } + res.w[1] = x_sign | 0x3040000000000000ull | res.w[1]; + BID_RETURN (res); +} else { // if exp < 0 and q + exp <= 0 + if (x_sign) { // negative rounds up to -0.0 + res.w[1] = 0xb040000000000000ull; + res.w[0] = 0x0000000000000000ull; + } else { // positive rpunds up to +1.0 + res.w[1] = 0x3040000000000000ull; + res.w[0] = 0x0000000000000001ull; + } + BID_RETURN (res); +} +} + +/***************************************************************************** + * BID128_round_integral_zero + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND (bid128_round_integral_zero, x) + + UINT128 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo + // (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1; + // UINT128 res is C* at first - represents up to 34 decimal digits ~ + // 113 bits + UINT256 P256; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + // if x = NaN, then res = Q (x) + // check first for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] + res.w[0] = x.w[0]; + } else { // x is QNaN + // return x + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] + res.w[0] = x.w[0]; + } + BID_RETURN (res) +} else { // x is not a NaN, so it must be infinity + if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf + // return +inf + res.w[1] = 0x7800000000000000ull; + res.w[0] = 0x0000000000000000ull; + } else { // x is -inf + // return -inf + res.w[1] = 0xf800000000000000ull; + res.w[0] = 0x0000000000000000ull; + } + BID_RETURN (res); +} +} + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for non-canonical values (treated as zero) +if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + // non-canonical + x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C1.w[1] = 0; // significand high + C1.w[0] = 0; // significand low +} else { // G0_G1 != 11 + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C1.w[1] > 0x0001ed09bead87c0ull || + (C1.w[1] == 0x0001ed09bead87c0ull + && C1.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + C1.w[1] = 0; + C1.w[0] = 0; + } else { // canonical + ; + } +} + + // test for input equal to zero +if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + // return 0 preserving the sign bit and the preferred exponent + // of MAX(Q(x), 0) + if (x_exp <= (0x1820ull << 49)) { + res.w[1] = (x.w[1] & 0x8000000000000000ull) | 0x3040000000000000ull; + } else { + res.w[1] = x_sign | x_exp; + } + res.w[0] = 0x0000000000000000ull; + BID_RETURN (res); +} + // x is not special and is not zero + + // if (exp <= -p) return -0.0 or +0.0 +if (x_exp <= 0x2ffc000000000000ull) { // 0x2ffc000000000000ull == -34 + res.w[1] = x_sign | 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + BID_RETURN (res); +} + // q = nr. of decimal digits in x + // determine first the nr. of bits in x +if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } +} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); +} + +q = nr_digits[x_nr_bits - 1].digits; +if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi || + (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi && + C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; +} +exp = (x_exp >> 49) - 6176; +if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res.w[1] = x.w[1]; + res.w[0] = x.w[0]; + BID_RETURN (res); +} else if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x' + // (number of digits to be chopped off) + // chop off ind digits from the lower part of C1 + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + // FOR ROUND_TO_ZERO, WE DON'T NEED TO ADD 1/2 ULP + // FOR ROUND_TO_POSITIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF POSITIVE + // FOR ROUND_TO_NEGATIVE_INFINITY, WE TRUNCATE, THEN ADD 1 IF NEGATIVE + //tmp64 = C1.w[0]; + // if (ind <= 19) { + // C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + // } else { + // C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + // C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + // } + // if (C1.w[0] < tmp64) C1.w[1]++; + // if carry-out from C1.w[0], increment C1.w[1] + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 34 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res.w[1] = P256.w[3]; + res.w[0] = P256.w[2]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res.w[1] = (P256.w[3] >> shift); + res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift); + } else { // 22 <= ind - 1 <= 33 + shift = shiftright128[ind - 1] - 64; // 2 <= shift <= 38 + res.w[1] = 0; + res.w[0] = P256.w[3] >> shift; + } + res.w[1] = x_sign | 0x3040000000000000ull | res.w[1]; + BID_RETURN (res); +} else { // if exp < 0 and q + exp <= 0 the result is +0 or -0 + res.w[1] = x_sign | 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + BID_RETURN (res); +} +} + +/***************************************************************************** + * BID128_round_integral_nearest_away + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND (bid128_round_integral_nearest_away, x) + + UINT128 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo + // (all are UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1; + // UINT128 res is C* at first - represents up to 34 decimal digits ~ + // 113 bits + // UINT256 fstar; + UINT256 P256; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + // if x = NaN, then res = Q (x) + // check first for non-canonical NaN payload + if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || + (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && + (x.w[0] > 0x38c15b09ffffffffull))) { + x.w[1] = x.w[1] & 0xffffc00000000000ull; + x.w[0] = 0x0ull; + } + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] + res.w[0] = x.w[0]; + } else { // x is QNaN + // return x + res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] + res.w[0] = x.w[0]; + } + BID_RETURN (res) +} else { // x is not a NaN, so it must be infinity + if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf + // return +inf + res.w[1] = 0x7800000000000000ull; + res.w[0] = 0x0000000000000000ull; + } else { // x is -inf + // return -inf + res.w[1] = 0xf800000000000000ull; + res.w[0] = 0x0000000000000000ull; + } + BID_RETURN (res); +} +} + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for non-canonical values (treated as zero) +if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 + // non-canonical + x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits + C1.w[1] = 0; // significand high + C1.w[0] = 0; // significand low +} else { // G0_G1 != 11 + x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits + if (C1.w[1] > 0x0001ed09bead87c0ull || + (C1.w[1] == 0x0001ed09bead87c0ull + && C1.w[0] > 0x378d8e63ffffffffull)) { + // x is non-canonical if coefficient is larger than 10^34 -1 + C1.w[1] = 0; + C1.w[0] = 0; + } else { // canonical + ; + } +} + + // test for input equal to zero +if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + // return 0 preserving the sign bit and the preferred exponent + // of MAX(Q(x), 0) + if (x_exp <= (0x1820ull << 49)) { + res.w[1] = (x.w[1] & 0x8000000000000000ull) | 0x3040000000000000ull; + } else { + res.w[1] = x_sign | x_exp; + } + res.w[0] = 0x0000000000000000ull; + BID_RETURN (res); +} + // x is not special and is not zero + + // if (exp <= -(p+1)) return 0.0 +if (x_exp <= 0x2ffa000000000000ull) { // 0x2ffa000000000000ull == -35 + res.w[1] = x_sign | 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + BID_RETURN (res); +} + // q = nr. of decimal digits in x + // determine first the nr. of bits in x +if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } +} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); +} + +q = nr_digits[x_nr_bits - 1].digits; +if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi || + (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi && + C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; +} +exp = (x_exp >> 49) - 6176; +if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res.w[1] = x.w[1]; + res.w[0] = x.w[0]; + BID_RETURN (res); +} else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 34; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^x where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 34 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res.w[1] = P256.w[3]; + res.w[0] = P256.w[2]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res.w[0] = (P256.w[3] << (64 - shift)) | (P256.w[2] >> shift); + res.w[1] = (P256.w[3] >> shift); + } else { // 22 <= ind - 1 <= 33 + shift = shiftright128[ind - 1]; // 2 <= shift <= 38 + res.w[1] = 0; + res.w[0] = (P256.w[3] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result was a midpoint, it was already rounded away from zero + res.w[1] |= x_sign | 0x3040000000000000ull; + BID_RETURN (res); +} else { // if ((q + exp) < 0) <=> q < -exp + // the result is +0 or -0 + res.w[1] = x_sign | 0x3040000000000000ull; + res.w[0] = 0x0000000000000000ull; + BID_RETURN (res); +} +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_scalb.c b/gcc-4.4.3/libgcc/config/libbid/bid128_scalb.c new file mode 100644 index 000000000..589713476 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_scalb.c @@ -0,0 +1,96 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#define BID_128RES +#include "bid_internal.h" + +#define DECIMAL_EXPONENT_BIAS_128 6176 +#define MAX_DECIMAL_EXPONENT_128 12287 + + + +BID128_FUNCTION_ARG128_ARGTYPE2 (bid128_scalb, x, int, n) + + UINT128 CX, CX2, CX8, res; + SINT64 exp64; + UINT64 sign_x; + int exponent_x, rmode; + + // unpack arguments, check for NaN or Infinity +if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { + // x is Inf. or NaN or 0 +#ifdef SET_STATUS_FLAGS +if ((x.w[1] & SNAN_MASK64) == SNAN_MASK64) // y is sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif +res.w[1] = CX.w[1] & QUIET_MASK64; +res.w[0] = CX.w[0]; +if (!CX.w[1]) { + exp64 = (SINT64) exponent_x + (SINT64) n; + if(exp64<0) exp64=0; + if(exp64>MAX_DECIMAL_EXPONENT_128) exp64=MAX_DECIMAL_EXPONENT_128; + exponent_x = exp64; + get_BID128_very_fast (&res, sign_x, exponent_x, CX); +} +BID_RETURN (res); +} + +exp64 = (SINT64) exponent_x + (SINT64) n; +exponent_x = exp64; + +if ((UINT32) exponent_x <= MAX_DECIMAL_EXPONENT_128) { + get_BID128_very_fast (&res, sign_x, exponent_x, CX); + BID_RETURN (res); +} + // check for overflow +if (exp64 > MAX_DECIMAL_EXPONENT_128) { + if (CX.w[1] < 0x314dc6448d93ull) { + // try to normalize coefficient + do { + CX8.w[1] = (CX.w[1] << 3) | (CX.w[0] >> 61); + CX8.w[0] = CX.w[0] << 3; + CX2.w[1] = (CX.w[1] << 1) | (CX.w[0] >> 63); + CX2.w[0] = CX.w[0] << 1; + __add_128_128 (CX, CX2, CX8); + + exponent_x--; + exp64--; + } + while (CX.w[1] < 0x314dc6448d93ull + && exp64 > MAX_DECIMAL_EXPONENT_128); + + } + if (exp64 <= MAX_DECIMAL_EXPONENT_128) { + get_BID128_very_fast (&res, sign_x, exponent_x, CX); + BID_RETURN (res); + } else + exponent_x = 0x7fffffff; // overflow +} + // exponent < 0 + // the BID pack routine will round the coefficient +rmode = rnd_mode; +get_BID128 (&res, sign_x, exponent_x, CX, (unsigned int *) &rmode, + pfpsf); +BID_RETURN (res); + +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_sqrt.c b/gcc-4.4.3/libgcc/config/libbid/bid128_sqrt.c new file mode 100644 index 000000000..298f67f25 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_sqrt.c @@ -0,0 +1,564 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#define BID_128RES +#include "bid_internal.h" +#include "bid_sqrt_macros.h" +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +#include + +#define FE_ALL_FLAGS FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT +#endif + +BID128_FUNCTION_ARG1 (bid128_sqrt, x) + + UINT256 M256, C256, C4, C8; + UINT128 CX, CX1, CX2, A10, S2, T128, TP128, CS, CSM, res; + UINT64 sign_x, Carry; + SINT64 D; + int_float fx, f64; + int exponent_x, bin_expon_cx; + int digits, scale, exponent_q; +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + fexcept_t binaryflags = 0; +#endif + + // unpack arguments, check for NaN or Infinity +if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { +res.w[1] = CX.w[1]; +res.w[0] = CX.w[0]; + // NaN ? +if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[1] = CX.w[1] & QUIET_MASK64; + BID_RETURN (res); +} + // x is Infinity? +if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { + res.w[1] = CX.w[1]; + if (sign_x) { + // -Inf, return NaN + res.w[1] = 0x7c00000000000000ull; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + } + BID_RETURN (res); +} + // x is 0 otherwise + +res.w[1] = + sign_x | + ((((UINT64) (exponent_x + DECIMAL_EXPONENT_BIAS_128)) >> 1) << 49); +res.w[0] = 0; +BID_RETURN (res); +} +if (sign_x) { + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (res); +} +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + // 2^64 +f64.i = 0x5f800000; + + // fx ~ CX +fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; +bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f; +digits = estimate_decimal_digits[bin_expon_cx]; + +A10 = CX; +if (exponent_x & 1) { + A10.w[1] = (CX.w[1] << 3) | (CX.w[0] >> 61); + A10.w[0] = CX.w[0] << 3; + CX2.w[1] = (CX.w[1] << 1) | (CX.w[0] >> 63); + CX2.w[0] = CX.w[0] << 1; + __add_128_128 (A10, A10, CX2); +} + +CS.w[0] = short_sqrt128 (A10); +CS.w[1] = 0; + // check for exact result +if (CS.w[0] * CS.w[0] == A10.w[0]) { + __mul_64x64_to_128_fast (S2, CS.w[0], CS.w[0]); + if (S2.w[1] == A10.w[1]) // && S2.w[0]==A10.w[0]) + { + get_BID128_very_fast (&res, 0, + (exponent_x + + DECIMAL_EXPONENT_BIAS_128) >> 1, CS); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } +} + // get number of digits in CX +D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1]; +if (D > 0 + || (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0])) + digits++; + + // if exponent is odd, scale coefficient by 10 +scale = 67 - digits; +exponent_q = exponent_x - scale; +scale += (exponent_q & 1); // exp. bias is even + +if (scale > 38) { + T128 = power10_table_128[scale - 37]; + __mul_128x128_low (CX1, CX, T128); + + TP128 = power10_table_128[37]; + __mul_128x128_to_256 (C256, CX1, TP128); +} else { + T128 = power10_table_128[scale]; + __mul_128x128_to_256 (C256, CX, T128); +} + + + // 4*C256 +C4.w[3] = (C256.w[3] << 2) | (C256.w[2] >> 62); +C4.w[2] = (C256.w[2] << 2) | (C256.w[1] >> 62); +C4.w[1] = (C256.w[1] << 2) | (C256.w[0] >> 62); +C4.w[0] = C256.w[0] << 2; + +long_sqrt128 (&CS, C256); + +#ifndef IEEE_ROUND_NEAREST +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +if (!((rnd_mode) & 3)) { +#endif +#endif + // compare to midpoints + CSM.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63); + CSM.w[0] = (CS.w[0] + CS.w[0]) | 1; + // CSM^2 + //__mul_128x128_to_256(M256, CSM, CSM); + __sqr128_to_256 (M256, CSM); + + if (C4.w[3] > M256.w[3] + || (C4.w[3] == M256.w[3] + && (C4.w[2] > M256.w[2] + || (C4.w[2] == M256.w[2] + && (C4.w[1] > M256.w[1] + || (C4.w[1] == M256.w[1] + && C4.w[0] > M256.w[0])))))) { + // round up + CS.w[0]++; + if (!CS.w[0]) + CS.w[1]++; + } else { + C8.w[1] = (CS.w[1] << 3) | (CS.w[0] >> 61); + C8.w[0] = CS.w[0] << 3; + // M256 - 8*CSM + __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]); + __sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry); + __sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry); + M256.w[3] = M256.w[3] - Carry; + + // if CSM' > C256, round up + if (M256.w[3] > C4.w[3] + || (M256.w[3] == C4.w[3] + && (M256.w[2] > C4.w[2] + || (M256.w[2] == C4.w[2] + && (M256.w[1] > C4.w[1] + || (M256.w[1] == C4.w[1] + && M256.w[0] > C4.w[0])))))) { + // round down + if (!CS.w[0]) + CS.w[1]--; + CS.w[0]--; + } + } +#ifndef IEEE_ROUND_NEAREST +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +} else { + __sqr128_to_256 (M256, CS); + C8.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63); + C8.w[0] = CS.w[0] << 1; + if (M256.w[3] > C256.w[3] + || (M256.w[3] == C256.w[3] + && (M256.w[2] > C256.w[2] + || (M256.w[2] == C256.w[2] + && (M256.w[1] > C256.w[1] + || (M256.w[1] == C256.w[1] + && M256.w[0] > C256.w[0])))))) { + __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]); + __sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry); + __sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry); + M256.w[3] = M256.w[3] - Carry; + M256.w[0]++; + if (!M256.w[0]) { + M256.w[1]++; + if (!M256.w[1]) { + M256.w[2]++; + if (!M256.w[2]) + M256.w[3]++; + } + } + + if (!CS.w[0]) + CS.w[1]--; + CS.w[0]--; + + if (M256.w[3] > C256.w[3] + || (M256.w[3] == C256.w[3] + && (M256.w[2] > C256.w[2] + || (M256.w[2] == C256.w[2] + && (M256.w[1] > C256.w[1] + || (M256.w[1] == C256.w[1] + && M256.w[0] > C256.w[0])))))) { + + if (!CS.w[0]) + CS.w[1]--; + CS.w[0]--; + } + } + + else { + __add_carry_out (M256.w[0], Carry, M256.w[0], C8.w[0]); + __add_carry_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry); + __add_carry_in_out (M256.w[2], Carry, M256.w[2], 0, Carry); + M256.w[3] = M256.w[3] + Carry; + M256.w[0]++; + if (!M256.w[0]) { + M256.w[1]++; + if (!M256.w[1]) { + M256.w[2]++; + if (!M256.w[2]) + M256.w[3]++; + } + } + if (M256.w[3] < C256.w[3] + || (M256.w[3] == C256.w[3] + && (M256.w[2] < C256.w[2] + || (M256.w[2] == C256.w[2] + && (M256.w[1] < C256.w[1] + || (M256.w[1] == C256.w[1] + && M256.w[0] <= C256.w[0])))))) { + + CS.w[0]++; + if (!CS.w[0]) + CS.w[1]++; + } + } + // RU? + if ((rnd_mode) == ROUNDING_UP) { + CS.w[0]++; + if (!CS.w[0]) + CS.w[1]++; + } + +} +#endif +#endif + +#ifdef SET_STATUS_FLAGS +__set_status_flags (pfpsf, INEXACT_EXCEPTION); +#endif +get_BID128_fast (&res, 0, + (exponent_q + DECIMAL_EXPONENT_BIAS_128) >> 1, CS); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +BID_RETURN (res); +} + + + +BID128_FUNCTION_ARGTYPE1 (bid128d_sqrt, UINT64, x) + + UINT256 M256, C256, C4, C8; + UINT128 CX, CX1, CX2, A10, S2, T128, TP128, CS, CSM, res; + UINT64 sign_x, Carry; + SINT64 D; + int_float fx, f64; + int exponent_x, bin_expon_cx; + int digits, scale, exponent_q; +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + fexcept_t binaryflags = 0; +#endif + + // unpack arguments, check for NaN or Infinity + // unpack arguments, check for NaN or Infinity +CX.w[1] = 0; +if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], x)) { +res.w[1] = CX.w[0]; +res.w[0] = 0; + // NaN ? +if ((x & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[0] = (CX.w[0] & 0x0003ffffffffffffull); + __mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]); + res.w[1] |= ((CX.w[0]) & 0xfc00000000000000ull); + BID_RETURN (res); +} + // x is Infinity? +if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) { + if (sign_x) { + // -Inf, return NaN + res.w[1] = 0x7c00000000000000ull; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + } + BID_RETURN (res); +} + // x is 0 otherwise + +exponent_x = + exponent_x - DECIMAL_EXPONENT_BIAS + DECIMAL_EXPONENT_BIAS_128; +res.w[1] = + sign_x | ((((UINT64) (exponent_x + DECIMAL_EXPONENT_BIAS_128)) >> 1) + << 49); +res.w[0] = 0; +BID_RETURN (res); +} +if (sign_x) { + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (res); +} +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +exponent_x = + exponent_x - DECIMAL_EXPONENT_BIAS + DECIMAL_EXPONENT_BIAS_128; + + // 2^64 +f64.i = 0x5f800000; + + // fx ~ CX +fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; +bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f; +digits = estimate_decimal_digits[bin_expon_cx]; + +A10 = CX; +if (exponent_x & 1) { + A10.w[1] = (CX.w[1] << 3) | (CX.w[0] >> 61); + A10.w[0] = CX.w[0] << 3; + CX2.w[1] = (CX.w[1] << 1) | (CX.w[0] >> 63); + CX2.w[0] = CX.w[0] << 1; + __add_128_128 (A10, A10, CX2); +} + +CS.w[0] = short_sqrt128 (A10); +CS.w[1] = 0; + // check for exact result +if (CS.w[0] * CS.w[0] == A10.w[0]) { + __mul_64x64_to_128_fast (S2, CS.w[0], CS.w[0]); + if (S2.w[1] == A10.w[1]) { + get_BID128_very_fast (&res, 0, + (exponent_x + DECIMAL_EXPONENT_BIAS_128) >> 1, + CS); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } +} + // get number of digits in CX +D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1]; +if (D > 0 + || (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0])) + digits++; + + // if exponent is odd, scale coefficient by 10 +scale = 67 - digits; +exponent_q = exponent_x - scale; +scale += (exponent_q & 1); // exp. bias is even + +if (scale > 38) { + T128 = power10_table_128[scale - 37]; + __mul_128x128_low (CX1, CX, T128); + + TP128 = power10_table_128[37]; + __mul_128x128_to_256 (C256, CX1, TP128); +} else { + T128 = power10_table_128[scale]; + __mul_128x128_to_256 (C256, CX, T128); +} + + + // 4*C256 +C4.w[3] = (C256.w[3] << 2) | (C256.w[2] >> 62); +C4.w[2] = (C256.w[2] << 2) | (C256.w[1] >> 62); +C4.w[1] = (C256.w[1] << 2) | (C256.w[0] >> 62); +C4.w[0] = C256.w[0] << 2; + +long_sqrt128 (&CS, C256); + +#ifndef IEEE_ROUND_NEAREST +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +if (!((rnd_mode) & 3)) { +#endif +#endif + // compare to midpoints + CSM.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63); + CSM.w[0] = (CS.w[0] + CS.w[0]) | 1; + // CSM^2 + //__mul_128x128_to_256(M256, CSM, CSM); + __sqr128_to_256 (M256, CSM); + + if (C4.w[3] > M256.w[3] + || (C4.w[3] == M256.w[3] + && (C4.w[2] > M256.w[2] + || (C4.w[2] == M256.w[2] + && (C4.w[1] > M256.w[1] + || (C4.w[1] == M256.w[1] + && C4.w[0] > M256.w[0])))))) { + // round up + CS.w[0]++; + if (!CS.w[0]) + CS.w[1]++; + } else { + C8.w[1] = (CS.w[1] << 3) | (CS.w[0] >> 61); + C8.w[0] = CS.w[0] << 3; + // M256 - 8*CSM + __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]); + __sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry); + __sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry); + M256.w[3] = M256.w[3] - Carry; + + // if CSM' > C256, round up + if (M256.w[3] > C4.w[3] + || (M256.w[3] == C4.w[3] + && (M256.w[2] > C4.w[2] + || (M256.w[2] == C4.w[2] + && (M256.w[1] > C4.w[1] + || (M256.w[1] == C4.w[1] + && M256.w[0] > C4.w[0])))))) { + // round down + if (!CS.w[0]) + CS.w[1]--; + CS.w[0]--; + } + } +#ifndef IEEE_ROUND_NEAREST +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +} else { + __sqr128_to_256 (M256, CS); + C8.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63); + C8.w[0] = CS.w[0] << 1; + if (M256.w[3] > C256.w[3] + || (M256.w[3] == C256.w[3] + && (M256.w[2] > C256.w[2] + || (M256.w[2] == C256.w[2] + && (M256.w[1] > C256.w[1] + || (M256.w[1] == C256.w[1] + && M256.w[0] > C256.w[0])))))) { + __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]); + __sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry); + __sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry); + M256.w[3] = M256.w[3] - Carry; + M256.w[0]++; + if (!M256.w[0]) { + M256.w[1]++; + if (!M256.w[1]) { + M256.w[2]++; + if (!M256.w[2]) + M256.w[3]++; + } + } + + if (!CS.w[0]) + CS.w[1]--; + CS.w[0]--; + + if (M256.w[3] > C256.w[3] + || (M256.w[3] == C256.w[3] + && (M256.w[2] > C256.w[2] + || (M256.w[2] == C256.w[2] + && (M256.w[1] > C256.w[1] + || (M256.w[1] == C256.w[1] + && M256.w[0] > C256.w[0])))))) { + + if (!CS.w[0]) + CS.w[1]--; + CS.w[0]--; + } + } + + else { + __add_carry_out (M256.w[0], Carry, M256.w[0], C8.w[0]); + __add_carry_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry); + __add_carry_in_out (M256.w[2], Carry, M256.w[2], 0, Carry); + M256.w[3] = M256.w[3] + Carry; + M256.w[0]++; + if (!M256.w[0]) { + M256.w[1]++; + if (!M256.w[1]) { + M256.w[2]++; + if (!M256.w[2]) + M256.w[3]++; + } + } + if (M256.w[3] < C256.w[3] + || (M256.w[3] == C256.w[3] + && (M256.w[2] < C256.w[2] + || (M256.w[2] == C256.w[2] + && (M256.w[1] < C256.w[1] + || (M256.w[1] == C256.w[1] + && M256.w[0] <= C256.w[0])))))) { + + CS.w[0]++; + if (!CS.w[0]) + CS.w[1]++; + } + } + // RU? + if ((rnd_mode) == ROUNDING_UP) { + CS.w[0]++; + if (!CS.w[0]) + CS.w[1]++; + } + +} +#endif +#endif + +#ifdef SET_STATUS_FLAGS +__set_status_flags (pfpsf, INEXACT_EXCEPTION); +#endif +get_BID128_fast (&res, 0, (exponent_q + DECIMAL_EXPONENT_BIAS_128) >> 1, + CS); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +BID_RETURN (res); + + +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_string.c b/gcc-4.4.3/libgcc/config/libbid/bid128_string.c new file mode 100644 index 000000000..b7aacd1fc --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_string.c @@ -0,0 +1,672 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +/***************************************************************************** + * BID128_to_string + ****************************************************************************/ + +#define BID_128RES +#include +#include "bid_internal.h" +#include "bid128_2_str.h" +#include "bid128_2_str_macros.h" + +extern int bid128_coeff_2_string (UINT64 X_hi, UINT64 X_lo, + char *char_ptr); + +#if DECIMAL_CALL_BY_REFERENCE + +void +bid128_to_string (char *str, + UINT128 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x; +#else + +void +bid128_to_string (char *str, UINT128 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + int ind; + UINT128 C1; + unsigned int k = 0; // pointer in the string + unsigned int d0, d123; + UINT64 HI_18Dig, LO_18Dig, Tmp; + UINT32 MiDi[12], *ptr; + char *c_ptr_start, *c_ptr; + int midi_ind, k_lcv, len; + +#if DECIMAL_CALL_BY_REFERENCE + x = *px; +#endif + + BID_SWAP128(x); + // check for NaN or Infinity + if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special + if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + str[0] = ((SINT64)x.w[1]<0)? '-':'+'; + str[1] = 'S'; + str[2] = 'N'; + str[3] = 'a'; + str[4] = 'N'; + str[5] = '\0'; + } else { // x is QNaN + str[0] = ((SINT64)x.w[1]<0)? '-':'+'; + str[1] = 'Q'; + str[2] = 'N'; + str[3] = 'a'; + str[4] = 'N'; + str[5] = '\0'; + } + } else { // x is not a NaN, so it must be infinity + if ((x.w[1] & MASK_SIGN) == 0x0ull) { // x is +inf + str[0] = '+'; + str[1] = 'I'; + str[2] = 'n'; + str[3] = 'f'; + str[4] = '\0'; + } else { // x is -inf + str[0] = '-'; + str[1] = 'I'; + str[2] = 'n'; + str[3] = 'f'; + str[4] = '\0'; + } + } + return; + } else if (((x.w[1] & MASK_COEFF) == 0x0ull) && (x.w[0] == 0x0ull)) { + // x is 0 + len = 0; + + //determine if +/- + if (x.w[1] & MASK_SIGN) + str[len++] = '-'; + else + str[len++] = '+'; + str[len++] = '0'; + str[len++] = 'E'; + + // extract the exponent and print + exp = (int) (((x.w[1] & MASK_EXP) >> 49) - 6176); + if(exp > (((0x5ffe)>>1) - (6176))) { + exp = (int) ((((x.w[1]<<2) & MASK_EXP) >> 49) - 6176); + } + if (exp >= 0) { + str[len++] = '+'; + len += sprintf (str + len, "%u", exp);// should not use sprintf (should + // use sophisticated algorithm, since we know range of exp is limited) + str[len++] = '\0'; + } else { + len += sprintf (str + len, "%d", exp);// should not use sprintf (should + // use sophisticated algorithm, since we know range of exp is limited) + str[len++] = '\0'; + } + return; + } else { // x is not special and is not zero + // unpack x + x_sign = x.w[1] & MASK_SIGN;// 0 for positive, MASK_SIGN for negative + x_exp = x.w[1] & MASK_EXP;// biased and shifted left 49 bit positions + if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) + x_exp = (x.w[1]<<2) & MASK_EXP;// biased and shifted left 49 bit positions + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + exp = (x_exp >> 49) - 6176; + + // determine sign's representation as a char + if (x_sign) + str[k++] = '-';// negative number + else + str[k++] = '+';// positive number + + // determine coefficient's representation as a decimal string + + // if zero or non-canonical, set coefficient to '0' + if ((C1.w[1] > 0x0001ed09bead87c0ull) || + (C1.w[1] == 0x0001ed09bead87c0ull && + (C1.w[0] > 0x378d8e63ffffffffull)) || + ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) || + ((C1.w[1] == 0) && (C1.w[0] == 0))) { + str[k++] = '0'; + } else { + /* **************************************************** + This takes a bid coefficient in C1.w[1],C1.w[0] + and put the converted character sequence at location + starting at &(str[k]). The function returns the number + of MiDi returned. Note that the character sequence + does not have leading zeros EXCEPT when the input is of + zero value. It will then output 1 character '0' + The algorithm essentailly tries first to get a sequence of + Millenial Digits "MiDi" and then uses table lookup to get the + character strings of these MiDis. + **************************************************** */ + /* Algorithm first decompose possibly 34 digits in hi and lo + 18 digits. (The high can have at most 16 digits). It then + uses macro that handle 18 digit portions. + The first step is to get hi and lo such that + 2^(64) C1.w[1] + C1.w[0] = hi * 10^18 + lo, 0 <= lo < 10^18. + We use a table lookup method to obtain the hi and lo 18 digits. + [C1.w[1],C1.w[0]] = c_8 2^(107) + c_7 2^(101) + ... + c_0 2^(59) + d + where 0 <= d < 2^59 and each c_j has 6 bits. Because d fits in + 18 digits, we set hi = 0, and lo = d to begin with. + We then retrieve from a table, for j = 0, 1, ..., 8 + that gives us A and B where c_j 2^(59+6j) = A * 10^18 + B. + hi += A ; lo += B; After each accumulation into lo, we normalize + immediately. So at the end, we have the decomposition as we need. */ + + Tmp = C1.w[0] >> 59; + LO_18Dig = (C1.w[0] << 5) >> 5; + Tmp += (C1.w[1] << 5); + HI_18Dig = 0; + k_lcv = 0; + // Tmp = {C1.w[1]{49:0}, C1.w[0]{63:59}} + // Lo_18Dig = {C1.w[0]{58:0}} + + while (Tmp) { + midi_ind = (int) (Tmp & 0x000000000000003FLL); + midi_ind <<= 1; + Tmp >>= 6; + HI_18Dig += mod10_18_tbl[k_lcv][midi_ind++]; + LO_18Dig += mod10_18_tbl[k_lcv++][midi_ind]; + __L0_Normalize_10to18 (HI_18Dig, LO_18Dig); + } + ptr = MiDi; + if (HI_18Dig == 0LL) { + __L1_Split_MiDi_6_Lead (LO_18Dig, ptr); + } else { + __L1_Split_MiDi_6_Lead (HI_18Dig, ptr); + __L1_Split_MiDi_6 (LO_18Dig, ptr); + } + len = ptr - MiDi; + c_ptr_start = &(str[k]); + c_ptr = c_ptr_start; + + /* now convert the MiDi into character strings */ + __L0_MiDi2Str_Lead (MiDi[0], c_ptr); + for (k_lcv = 1; k_lcv < len; k_lcv++) { + __L0_MiDi2Str (MiDi[k_lcv], c_ptr); + } + k = k + (c_ptr - c_ptr_start); + } + + // print E and sign of exponent + str[k++] = 'E'; + if (exp < 0) { + exp = -exp; + str[k++] = '-'; + } else { + str[k++] = '+'; + } + + // determine exponent's representation as a decimal string + // d0 = exp / 1000; + // Use Property 1 + d0 = (exp * 0x418a) >> 24;// 0x418a * 2^-24 = (10^(-3))RP,15 + d123 = exp - 1000 * d0; + + if (d0) { // 1000 <= exp <= 6144 => 4 digits to return + str[k++] = d0 + 0x30;// ASCII for decimal digit d0 + ind = 3 * d123; + str[k++] = char_table3[ind]; + str[k++] = char_table3[ind + 1]; + str[k++] = char_table3[ind + 2]; + } else { // 0 <= exp <= 999 => d0 = 0 + if (d123 < 10) { // 0 <= exp <= 9 => 1 digit to return + str[k++] = d123 + 0x30;// ASCII + } else if (d123 < 100) { // 10 <= exp <= 99 => 2 digits to return + ind = 2 * (d123 - 10); + str[k++] = char_table2[ind]; + str[k++] = char_table2[ind + 1]; + } else { // 100 <= exp <= 999 => 3 digits to return + ind = 3 * d123; + str[k++] = char_table3[ind]; + str[k++] = char_table3[ind + 1]; + str[k++] = char_table3[ind + 2]; + } + } + str[k] = '\0'; + + } + return; + +} + + +#define MAX_FORMAT_DIGITS_128 34 +#define MAX_STRING_DIGITS_128 100 +#define MAX_SEARCH MAX_STRING_DIGITS_128-MAX_FORMAT_DIGITS_128-1 + + +#if DECIMAL_CALL_BY_REFERENCE + +void +bid128_from_string (UINT128 * pres, + char *ps _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#else + +UINT128 +bid128_from_string (char *ps _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 CX, res; + UINT64 sign_x, coeff_high, coeff_low, coeff2, coeff_l2, carry = 0x0ull, + scale_high, right_radix_leading_zeros; + int ndigits_before, ndigits_after, ndigits_total, dec_expon, sgn_exp, + i, d2, rdx_pt_enc; + char c, buffer[MAX_STRING_DIGITS_128]; + int save_rnd_mode; + int save_fpsf; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + + save_rnd_mode = rnd_mode; // dummy + save_fpsf = *pfpsf; // dummy + + right_radix_leading_zeros = rdx_pt_enc = 0; + + // if null string, return NaN + if (!ps) { + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } + // eliminate leading white space + while ((*ps == ' ') || (*ps == '\t')) + ps++; + + // c gets first character + c = *ps; + + + // if c is null or not equal to a (radix point, negative sign, + // positive sign, or number) it might be SNaN, sNaN, Infinity + if (!c + || (c != '.' && c != '-' && c != '+' + && ((unsigned) (c - '0') > 9))) { + res.w[0] = 0; + // Infinity? + if ((tolower_macro (ps[0]) == 'i' && tolower_macro (ps[1]) == 'n' + && tolower_macro (ps[2]) == 'f') + && (!ps[3] + || (tolower_macro (ps[3]) == 'i' + && tolower_macro (ps[4]) == 'n' + && tolower_macro (ps[5]) == 'i' + && tolower_macro (ps[6]) == 't' + && tolower_macro (ps[7]) == 'y' && !ps[8]) + )) { + res.w[1] = 0x7800000000000000ull; + BID_RETURN (res); + } + // return sNaN + if (tolower_macro (ps[0]) == 's' && tolower_macro (ps[1]) == 'n' && + tolower_macro (ps[2]) == 'a' && tolower_macro (ps[3]) == 'n') { + // case insensitive check for snan + res.w[1] = 0x7e00000000000000ull; + BID_RETURN (res); + } else { + // return qNaN + res.w[1] = 0x7c00000000000000ull; + BID_RETURN (res); + } + } + // if +Inf, -Inf, +Infinity, or -Infinity (case insensitive check for inf) + if ((tolower_macro (ps[1]) == 'i' && tolower_macro (ps[2]) == 'n' && + tolower_macro (ps[3]) == 'f') && (!ps[4] || + (tolower_macro (ps[4]) == 'i' && tolower_macro (ps[5]) == 'n' && + tolower_macro (ps[6]) == 'i' && tolower_macro (ps[7]) == 't' && + tolower_macro (ps[8]) == 'y' && !ps[9]))) { // ci check for infinity + res.w[0] = 0; + + if (c == '+') + res.w[1] = 0x7800000000000000ull; + else if (c == '-') + res.w[1] = 0xf800000000000000ull; + else + res.w[1] = 0x7c00000000000000ull; + + BID_RETURN (res); + } + // if +sNaN, +SNaN, -sNaN, or -SNaN + if (tolower_macro (ps[1]) == 's' && tolower_macro (ps[2]) == 'n' + && tolower_macro (ps[3]) == 'a' && tolower_macro (ps[4]) == 'n') { + res.w[0] = 0; + if (c == '-') + res.w[1] = 0xfe00000000000000ull; + else + res.w[1] = 0x7e00000000000000ull; + BID_RETURN (res); + } + // set up sign_x to be OR'ed with the upper word later + if (c == '-') + sign_x = 0x8000000000000000ull; + else + sign_x = 0; + + // go to next character if leading sign + if (c == '-' || c == '+') + ps++; + + c = *ps; + + // if c isn't a decimal point or a decimal digit, return NaN + if (c != '.' && ((unsigned) (c - '0') > 9)) { + res.w[1] = 0x7c00000000000000ull | sign_x; + res.w[0] = 0; + BID_RETURN (res); + } + // detect zero (and eliminate/ignore leading zeros) + if (*(ps) == '0') { + + // if all numbers are zeros (with possibly 1 radix point, the number is zero + // should catch cases such as: 000.0 + while (*ps == '0') { + + ps++; + + // for numbers such as 0.0000000000000000000000000000000000001001, + // we want to count the leading zeros + if (rdx_pt_enc) { + right_radix_leading_zeros++; + } + // if this character is a radix point, make sure we haven't already + // encountered one + if (*(ps) == '.') { + if (rdx_pt_enc == 0) { + rdx_pt_enc = 1; + // if this is the first radix point, and the next character is NULL, + // we have a zero + if (!*(ps + 1)) { + res.w[1] = + (0x3040000000000000ull - + (right_radix_leading_zeros << 49)) | sign_x; + res.w[0] = 0; + BID_RETURN (res); + } + ps = ps + 1; + } else { + // if 2 radix points, return NaN + res.w[1] = 0x7c00000000000000ull | sign_x; + res.w[0] = 0; + BID_RETURN (res); + } + } else if (!*(ps)) { + //res.w[1] = 0x3040000000000000ull | sign_x; + res.w[1] = + (0x3040000000000000ull - + (right_radix_leading_zeros << 49)) | sign_x; + res.w[0] = 0; + BID_RETURN (res); + } + } + } + + c = *ps; + + // initialize local variables + ndigits_before = ndigits_after = ndigits_total = 0; + sgn_exp = 0; + // pstart_coefficient = ps; + + if (!rdx_pt_enc) { + // investigate string (before radix point) + while ((unsigned) (c - '0') <= 9 + && ndigits_before < MAX_STRING_DIGITS_128) { + buffer[ndigits_before] = c; + ps++; + c = *ps; + ndigits_before++; + } + + ndigits_total = ndigits_before; + if (c == '.') { + ps++; + if ((c = *ps)) { + + // investigate string (after radix point) + while ((unsigned) (c - '0') <= 9 + && ndigits_total < MAX_STRING_DIGITS_128) { + buffer[ndigits_total] = c; + ps++; + c = *ps; + ndigits_total++; + } + ndigits_after = ndigits_total - ndigits_before; + } + } + } else { + // we encountered a radix point while detecting zeros + //if (c = *ps){ + + c = *ps; + ndigits_total = 0; + // investigate string (after radix point) + while ((unsigned) (c - '0') <= 9 + && ndigits_total < MAX_STRING_DIGITS_128) { + buffer[ndigits_total] = c; + ps++; + c = *ps; + ndigits_total++; + } + ndigits_after = ndigits_total - ndigits_before; + } + + // get exponent + dec_expon = 0; + if (ndigits_total < MAX_STRING_DIGITS_128) { + if (c) { + if (c != 'e' && c != 'E') { + // return NaN + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } + ps++; + c = *ps; + + if (((unsigned) (c - '0') > 9) + && ((c != '+' && c != '-') || (unsigned) (ps[1] - '0') > 9)) { + // return NaN + res.w[1] = 0x7c00000000000000ull; + res.w[0] = 0; + BID_RETURN (res); + } + + if (c == '-') { + sgn_exp = -1; + ps++; + c = *ps; + } else if (c == '+') { + ps++; + c = *ps; + } + + dec_expon = c - '0'; + i = 1; + ps++; + c = *ps - '0'; + while (((unsigned) c) <= 9 && i < 7) { + d2 = dec_expon + dec_expon; + dec_expon = (d2 << 2) + d2 + c; + ps++; + c = *ps - '0'; + i++; + } + } + + dec_expon = (dec_expon + sgn_exp) ^ sgn_exp; + } + + + if (ndigits_total <= MAX_FORMAT_DIGITS_128) { + dec_expon += + DECIMAL_EXPONENT_BIAS_128 - ndigits_after - + right_radix_leading_zeros; + if (dec_expon < 0) { + res.w[1] = 0 | sign_x; + res.w[0] = 0; + } + if (ndigits_total == 0) { + CX.w[0] = 0; + CX.w[1] = 0; + } else if (ndigits_total <= 19) { + coeff_high = buffer[0] - '0'; + for (i = 1; i < ndigits_total; i++) { + coeff2 = coeff_high + coeff_high; + coeff_high = (coeff2 << 2) + coeff2 + buffer[i] - '0'; + } + CX.w[0] = coeff_high; + CX.w[1] = 0; + } else { + coeff_high = buffer[0] - '0'; + for (i = 1; i < ndigits_total - 17; i++) { + coeff2 = coeff_high + coeff_high; + coeff_high = (coeff2 << 2) + coeff2 + buffer[i] - '0'; + } + coeff_low = buffer[i] - '0'; + i++; + for (; i < ndigits_total; i++) { + coeff_l2 = coeff_low + coeff_low; + coeff_low = (coeff_l2 << 2) + coeff_l2 + buffer[i] - '0'; + } + // now form the coefficient as coeff_high*10^19+coeff_low+carry + scale_high = 100000000000000000ull; + __mul_64x64_to_128_fast (CX, coeff_high, scale_high); + + CX.w[0] += coeff_low; + if (CX.w[0] < coeff_low) + CX.w[1]++; + } + get_BID128 (&res, sign_x, dec_expon, CX,&rnd_mode,pfpsf); + BID_RETURN (res); + } else { + // simply round using the digits that were read + + dec_expon += + ndigits_before + DECIMAL_EXPONENT_BIAS_128 - + MAX_FORMAT_DIGITS_128 - right_radix_leading_zeros; + + if (dec_expon < 0) { + res.w[1] = 0 | sign_x; + res.w[0] = 0; + } + + coeff_high = buffer[0] - '0'; + for (i = 1; i < MAX_FORMAT_DIGITS_128 - 17; i++) { + coeff2 = coeff_high + coeff_high; + coeff_high = (coeff2 << 2) + coeff2 + buffer[i] - '0'; + } + coeff_low = buffer[i] - '0'; + i++; + for (; i < MAX_FORMAT_DIGITS_128; i++) { + coeff_l2 = coeff_low + coeff_low; + coeff_low = (coeff_l2 << 2) + coeff_l2 + buffer[i] - '0'; + } + switch(rnd_mode) { + case ROUNDING_TO_NEAREST: + carry = ((unsigned) ('4' - buffer[i])) >> 31; + if ((buffer[i] == '5' && !(coeff_low & 1)) || dec_expon < 0) { + if (dec_expon >= 0) { + carry = 0; + i++; + } + for (; i < ndigits_total; i++) { + if (buffer[i] > '0') { + carry = 1; + break; + } + } + } + break; + + case ROUNDING_DOWN: + if(sign_x) + for (; i < ndigits_total; i++) { + if (buffer[i] > '0') { + carry = 1; + break; + } + } + break; + case ROUNDING_UP: + if(!sign_x) + for (; i < ndigits_total; i++) { + if (buffer[i] > '0') { + carry = 1; + break; + } + } + break; + case ROUNDING_TO_ZERO: + carry=0; + break; + case ROUNDING_TIES_AWAY: + carry = ((unsigned) ('4' - buffer[i])) >> 31; + if (dec_expon < 0) { + for (; i < ndigits_total; i++) { + if (buffer[i] > '0') { + carry = 1; + break; + } + } + } + break; + + + } + // now form the coefficient as coeff_high*10^17+coeff_low+carry + scale_high = 100000000000000000ull; + if (dec_expon < 0) { + if (dec_expon > -MAX_FORMAT_DIGITS_128) { + scale_high = 1000000000000000000ull; + coeff_low = (coeff_low << 3) + (coeff_low << 1); + dec_expon--; + } + if (dec_expon == -MAX_FORMAT_DIGITS_128 + && coeff_high > 50000000000000000ull) + carry = 0; + } + + __mul_64x64_to_128_fast (CX, coeff_high, scale_high); + + coeff_low += carry; + CX.w[0] += coeff_low; + if (CX.w[0] < coeff_low) + CX.w[1]++; + + + get_BID128(&res, sign_x, dec_expon, CX, &rnd_mode, pfpsf); + BID_RETURN (res); + } +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_to_int16.c b/gcc-4.4.3/libgcc/config/libbid/bid128_to_int16.c new file mode 100644 index 000000000..832adb137 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_to_int16.c @@ -0,0 +1,67 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +#define SIZE_MASK 0xffff8000 +#define INVALID_RESULT 0x8000 + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid128_to_int16_rnint, UINT128, x, + bid128_to_int32_rnint, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid128_to_int16_xrnint, UINT128, + x, bid128_to_int32_xrnint, int, + SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid128_to_int16_rninta, UINT128, + x, bid128_to_int32_rninta, int, + SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid128_to_int16_xrninta, UINT128, + x, bid128_to_int32_xrninta, int, + SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid128_to_int16_int, UINT128, x, + bid128_to_int32_int, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid128_to_int16_xint, UINT128, x, + bid128_to_int32_xint, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid128_to_int16_floor, UINT128, x, + bid128_to_int32_floor, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid128_to_int16_ceil, UINT128, x, + bid128_to_int32_ceil, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid128_to_int16_xfloor, UINT128, + x, bid128_to_int32_xfloor, int, + SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid128_to_int16_xceil, UINT128, x, + bid128_to_int32_xceil, int, SIZE_MASK, + INVALID_RESULT) diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_to_int32.c b/gcc-4.4.3/libgcc/config/libbid/bid128_to_int32.c new file mode 100644 index 000000000..2d60c4710 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_to_int32.c @@ -0,0 +1,3659 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID128_to_int32_rnint + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_rnint, x) + + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n < -2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x500000005ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005 <=> + // C > 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31+1/2 up) + tmp64 = 0x500000005ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x4fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb <=> + // C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31-1/2 up) + tmp64 = 0x4fffffffbull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffff; // return -1 + } else { // n > 0 + res = 0x00000001; // return +1 + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] <= midpoint128[ind - 19].w[0]))) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffff; // return -1 + } else { // n > 0 + res = 0x00000001; // return +1 + } + } + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // -2^31-1/2 <= x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded + // to nearest to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + } // else MP in [ODD, EVEN] + } + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int32_xrnint + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xrnint, + x) + + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n < -2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x500000005ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005 <=> + // C > 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31+1/2 up) + tmp64 = 0x500000005ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x4fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb <=> + // C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31-1/2 up) + tmp64 = 0x4fffffffbull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffff; // return -1 + } else { // n > 0 + res = 0x00000001; // return +1 + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] <= midpoint128[ind - 19].w[0]))) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffff; // return -1 + } else { // n > 0 + res = 0x00000001; // return +1 + } + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // -2^31-1/2 <= x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded + // to nearest to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + } // else MP in [ODD, EVEN] + } + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int32_floor + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_floor, x) + + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + int is_inexact_lt_midpoint = 0; + int is_inexact_gt_midpoint = 0; + int is_midpoint_lt_even = 0; + int is_midpoint_gt_even = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n < -2^31 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x500000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000 <=> + // C > 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31 up) + tmp64 = 0x500000000ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x500000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000 <=> + // C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31 up) + tmp64 = 0x500000000ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 <= n < 2^31 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { + // n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) + // return 0 + if (x_sign) + res = 0xffffffff; + else + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // -2^31 <= x <= -1 or 1 <= x < 2^31 so x can be rounded + // toward negative infinity to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + is_midpoint_gt_even = 1; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + is_midpoint_lt_even = 1; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } + } + // general correction for RM + if (x_sign && (is_midpoint_gt_even || is_inexact_lt_midpoint)) { + Cstar.w[0] = Cstar.w[0] + 1; + } else if (!x_sign + && (is_midpoint_lt_even || is_inexact_gt_midpoint)) { + Cstar.w[0] = Cstar.w[0] - 1; + } else { + ; // the result is already correct + } + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + + +/***************************************************************************** + * BID128_to_int32_xfloor + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xfloor, + x) + + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + int is_inexact_lt_midpoint = 0; + int is_inexact_gt_midpoint = 0; + int is_midpoint_lt_even = 0; + int is_midpoint_gt_even = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n < -2^31 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x500000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000 <=> + // C > 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31 up) + tmp64 = 0x500000000ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x500000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000 <=> + // C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31 up) + tmp64 = 0x500000000ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 <= n < 2^31 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { + // n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + if (x_sign) + res = 0xffffffff; + else + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // -2^31 <= x <= -1 or 1 <= x < 2^31 so x can be rounded + // toward negative infinity to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + is_midpoint_gt_even = 1; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + is_midpoint_lt_even = 1; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } + } + // general correction for RM + if (x_sign && (is_midpoint_gt_even || is_inexact_lt_midpoint)) { + Cstar.w[0] = Cstar.w[0] + 1; + } else if (!x_sign + && (is_midpoint_lt_even || is_inexact_gt_midpoint)) { + Cstar.w[0] = Cstar.w[0] - 1; + } else { + ; // the result is already correct + } + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int32_ceil + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_ceil, x) + + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + int is_inexact_lt_midpoint = 0; + int is_inexact_gt_midpoint = 0; + int is_midpoint_lt_even = 0; + int is_midpoint_gt_even = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -2^31-1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x50000000aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a <=> + // C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31+1 up) + tmp64 = 0x50000000aull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n > 2^31 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 - 1 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x4fffffff6ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6 <=> + // C > 0x4fffffff6 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31 up) + tmp64 = 0x4fffffff6ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31-1 < n <= 2^31-1 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { + // n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) + // return 0 + if (x_sign) + res = 0x00000000; + else + res = 0x00000001; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // -2^31-1 < x <= -1 or 1 <= x <= 2^31-1 so x can be rounded + // toward positive infinity to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + is_midpoint_gt_even = 1; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + is_midpoint_lt_even = 1; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } + } + // general correction for RM + if (x_sign && (is_midpoint_lt_even || is_inexact_gt_midpoint)) { + Cstar.w[0] = Cstar.w[0] - 1; + } else if (!x_sign + && (is_midpoint_gt_even || is_inexact_lt_midpoint)) { + Cstar.w[0] = Cstar.w[0] + 1; + } else { + ; // the result is already correct + } + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int32_xceil + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xceil, x) + + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + int is_inexact_lt_midpoint = 0; + int is_inexact_gt_midpoint = 0; + int is_midpoint_lt_even = 0; + int is_midpoint_gt_even = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -2^31-1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x50000000aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a <=> + // C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31+1 up) + tmp64 = 0x50000000aull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n > 2^31 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 - 1 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x4fffffff6ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6 <=> + // C > 0x4fffffff6 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31 up) + tmp64 = 0x4fffffff6ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31-1 < n <= 2^31-1 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { + // n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + if (x_sign) + res = 0x00000000; + else + res = 0x00000001; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // -2^31-1 < x <= -1 or 1 <= x <= 2^31-1 so x can be rounded + // toward positive infinity to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + is_midpoint_gt_even = 1; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + is_midpoint_lt_even = 1; + is_inexact_lt_midpoint = 0; + is_inexact_gt_midpoint = 0; + } + } + // general correction for RM + if (x_sign && (is_midpoint_lt_even || is_inexact_gt_midpoint)) { + Cstar.w[0] = Cstar.w[0] - 1; + } else if (!x_sign + && (is_midpoint_gt_even || is_inexact_lt_midpoint)) { + Cstar.w[0] = Cstar.w[0] + 1; + } else { + ; // the result is already correct + } + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int32_int + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_int, x) + + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + int is_inexact_gt_midpoint = 0; + int is_midpoint_lt_even = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -2^31 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x50000000aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a <=> + // C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31+1 up) + tmp64 = 0x50000000aull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x500000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000 <=> + // C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31-1/2 up) + tmp64 = 0x500000000ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1 < n < 2^31 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { + // n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded + // toward zero to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0]))) { + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) && + (fstar.w[1] || fstar.w[0]) && + (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] || + (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] && + fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + is_midpoint_lt_even = 1; + is_inexact_gt_midpoint = 0; + } + } + // general correction for RZ + if (is_midpoint_lt_even || is_inexact_gt_midpoint) { + Cstar.w[0] = Cstar.w[0] - 1; + } else { + ; // exact, the result is already correct + } + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int32_xint + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xint, x) + + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + int is_inexact_gt_midpoint = 0; + int is_midpoint_lt_even = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -2^31 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x50000000aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a <=> + // C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31+1 up) + tmp64 = 0x50000000aull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x500000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000 <=> + // C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31-1/2 up) + tmp64 = 0x500000000ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1 < n < 2^31 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { + // n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded + // toward zero to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && (fstar.w[2] || + fstar.w[1] + || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + is_midpoint_lt_even = 1; + is_inexact_gt_midpoint = 0; + } + } + // general correction for RZ + if (is_midpoint_lt_even || is_inexact_gt_midpoint) { + Cstar.w[0] = Cstar.w[0] - 1; + } else { + ; // exact, the result is already correct + } + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int32_rninta + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_rninta, + x) + + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x500000005ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005 <=> + // C >= 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31+1/2 up) + tmp64 = 0x500000005ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x4fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb <=> + // C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31-1/2 up) + tmp64 = 0x4fffffffbull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffff; // return -1 + } else { // n > 0 + res = 0x00000001; // return +1 + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] < midpoint128[ind - 19].w[0]))) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffff; // return -1 + } else { // n > 0 + res = 0x00000001; // return +1 + } + } + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // -2^31-1/2 < x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded + // to nearest-away to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result was a midpoint, it was already rounded away from zero + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + // no need to check for midpoints - already rounded away from zero! + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int32_xrninta + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xrninta, + x) + + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x500000005ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005 <=> + // C >= 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31+1/2 up) + tmp64 = 0x500000005ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x4fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb <=> + // C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^31-1/2 up) + tmp64 = 0x4fffffffbull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffff; // return -1 + } else { // n > 0 + res = 0x00000001; // return +1 + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] < midpoint128[ind - 19].w[0]))) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffff; // return -1 + } else { // n > 0 + res = 0x00000001; // return +1 + } + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // -2^31-1/2 < x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded + // to nearest-away to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result was a midpoint, it was already rounded away from zero + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0]))) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] || + fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + // no need to check for midpoints - already rounded away from zero! + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_to_int64.c b/gcc-4.4.3/libgcc/config/libbid/bid128_to_int64.c new file mode 100644 index 000000000..09935f5a4 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_to_int64.c @@ -0,0 +1,2994 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID128_to_int64_rnint + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (SINT64, bid128_to_int64_rnint, + x) + + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) || + (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n < -2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64+1), 1<=q<=34 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000005, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0000000000000005ull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=34 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=34 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffffbull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } + } + // n is not too large to be converted to int64: -2^63-1/2 <= n < 2^63-1/2 + // Note: some of the cases tested for above fall through to this point + // Restore C1 which may have been modified above + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] <= midpoint128[ind - 19].w[0]))) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + } + } else { // if (1 <= q + exp <= 19, 1 <= q <= 34, -33 <= exp <= 18) + // -2^63-1/2 <= x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) && + (fstar.w[1] || fstar.w[0]) && + (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] || + (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] && + fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + } // else MP in [ODD, EVEN] + } + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 19 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp>0) => 1 <= exp <= 18, 1 <= q < 18, 2 <= q + exp <= 19 + // res = +/-C * 10^exp (exact) where this fits in 64-bit integer + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int64_xrnint + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (SINT64, + bid128_to_int64_xrnint, x) + + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n < -2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64+1), 1<=q<=34 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000005, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0000000000000005ull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=34 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=34 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffffbull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } + } + // n is not too large to be converted to int64: -2^63-1/2 <= n < 2^63-1/2 + // Note: some of the cases tested for above fall through to this point + // Restore C1 which may have been modified above + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] <= midpoint128[ind - 19].w[0]))) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 19, 1 <= q <= 34, -33 <= exp <= 18) + // -2^63-1/2 <= x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) && + (fstar.w[1] || fstar.w[0]) && + (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] || + (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] && + fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + } // else MP in [ODD, EVEN] + } + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 19 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp>0) => 1 <= exp <= 18, 1 <= q < 18, 2 <= q + exp <= 19 + // res = +/-C * 10^exp (exact) where this fits in 64-bit integer + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int64_floor + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (SINT64, bid128_to_int64_floor, + x) + + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n < -2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 10*2^63, 1<=q<=34 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000000, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=34 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } + } + // n is not too large to be converted to int64: -2^63-1 < n < 2^63 + // Note: some of the cases tested for above fall through to this point + // Restore C1 which may have been modified above + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // return -1 or 0 + if (x_sign) + res = 0xffffffffffffffffull; + else + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 34, -33 <= exp <= 18) + // -2^63 <= x <= -1 or 1 <= x < 2^63 so x can be rounded + // toward zero to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result is negative and inexact, need to add 1 to it + + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1] || + (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] && + fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + } // else the result is exact + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + } // else the result is exact + } else { // if 22 <= ind <= 33 + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + } // else the result is exact + } + + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 19 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp>0) => 1 <= exp <= 18, 1 <= q < 18, 2 <= q + exp <= 19 + // res = +/-C * 10^exp (exact) where this fits in 64-bit integer + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int64_xfloor + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (SINT64, + bid128_to_int64_xfloor, x) + + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n < -2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 10*2^63, 1<=q<=34 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000000, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=34 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } + } + // n is not too large to be converted to int64: -2^63-1 < n < 2^63 + // Note: some of the cases tested for above fall through to this point + // Restore C1 which may have been modified above + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return -1 or 0 + if (x_sign) + res = 0xffffffffffffffffull; + else + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 34, -33 <= exp <= 18) + // -2^63 <= x <= -1 or 1 <= x < 2^63 so x can be rounded + // toward zero to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result is negative and inexact, need to add 1 to it + + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1] || + (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] && + fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 22 <= ind <= 33 + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 19 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp>0) => 1 <= exp <= 18, 1 <= q < 18, 2 <= q + exp <= 19 + // res = +/-C * 10^exp (exact) where this fits in 64-bit integer + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int64_ceil + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (SINT64, bid128_to_int64_ceil, + x) + + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64+2), 1<=q<=34 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x5000000000000000a, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x000000000000000aull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n > 2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 - 1 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 10*(2^63-1), 1<=q<=34 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 0x4fffffffffffffff6, 1<=q<=34 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffff6ull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } + } + // n is not too large to be converted to int64: -2^63-1 < n <= 2^63 - 1 + // Note: some of the cases tested for above fall through to this point + // Restore C1 which may have been modified above + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // return 0 or 1 + if (x_sign) + res = 0x0000000000000000ull; + else + res = 0x0000000000000001ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 34, -33 <= exp <= 18) + // -2^63-1 < x <= -1 or 1 <= x <= 2^63 - 1 so x can be rounded + // up to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result is positive and inexact, need to add 1 to it + + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (!x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + } // else the result is exact + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (!x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + } // else the result is exact + } else { // if 22 <= ind <= 33 + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (!x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + } // else the result is exact + } + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 19 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp>0) => 1 <= exp <= 18, 1 <= q < 18, 2 <= q + exp <= 19 + // res = +/-C * 10^exp (exact) where this fits in 64-bit integer + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int64_xceil + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (SINT64, bid128_to_int64_xceil, + x) + + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64+2), 1<=q<=34 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x5000000000000000a, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x000000000000000aull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n > 2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 - 1 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 10*(2^63-1), 1<=q<=34 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 0x4fffffffffffffff6, 1<=q<=34 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffff6ull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } + } + // n is not too large to be converted to int64: -2^63-1 < n <= 2^63 - 1 + // Note: some of the cases tested for above fall through to this point + // Restore C1 which may have been modified above + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 or 1 + if (x_sign) + res = 0x0000000000000000ull; + else + res = 0x0000000000000001ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 34, -33 <= exp <= 18) + // -2^63-1 < x <= -1 or 1 <= x <= 2^63 - 1 so x can be rounded + // up to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result is positive and inexact, need to add 1 to it + + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (!x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (!x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 22 <= ind <= 33 + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (!x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 19 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp>0) => 1 <= exp <= 18, 1 <= q < 18, 2 <= q + exp <= 19 + // res = +/-C * 10^exp (exact) where this fits in 64-bit integer + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int64_int + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (SINT64, bid128_to_int64_int, + x) + + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=34 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x000000000000000aull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=34 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } + } + // n is not too large to be converted to int64: -2^63-1 < n < 2^63 + // Note: some of the cases tested for above fall through to this point + // Restore C1 which may have been modified above + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 34, -33 <= exp <= 18) + // -2^63-1 < x <= -1 or 1 <= x < 2^63 so x can be rounded + // toward zero to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 19 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp>0) => 1 <= exp <= 18, 1 <= q < 18, 2 <= q + exp <= 19 + // res = +/-C * 10^exp (exact) where this fits in 64-bit integer + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_xint64_xint + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (SINT64, bid128_to_int64_xint, + x) + + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=34 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x000000000000000aull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=34 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } + } + // n is not too large to be converted to int64: -2^63-1 < n < 2^63 + // Note: some of the cases tested for above fall through to this point + // Restore C1 which may have been modified above + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 34, -33 <= exp <= 18) + // -2^63-1 < x <= -1 or 1 <= x < 2^63 so x can be rounded + // toward zero to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 19 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp>0) => 1 <= exp <= 18, 1 <= q < 18, 2 <= q + exp <= 19 + // res = +/-C * 10^exp (exact) where this fits in 64-bit integer + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int64_rninta + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (SINT64, + bid128_to_int64_rninta, x) + + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+1), 1<=q<=34 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000005, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0000000000000005ull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=34 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=34 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffffbull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } + } + // n is not too large to be converted to int64: -2^63-1/2 <= n < 2^63-1/2 + // Note: some of the cases tested for above fall through to this point + // Restore C1 which may have been modified above + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] < midpoint128[ind - 19].w[0]))) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + } + } else { // if (1 <= q + exp <= 19, 1 <= q <= 34, -33 <= exp <= 18) + // -2^63-1/2 <= x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + + // if the result was a midpoint it was rounded away from zero + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 19 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp>0) => 1 <= exp <= 18, 1 <= q < 18, 2 <= q + exp <= 19 + // res = +/-C * 10^exp (exact) where this fits in 64-bit integer + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_int64_xrninta + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (SINT64, + bid128_to_int64_xrninta, x) + + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+1), 1<=q<=34 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000005, 1<=q<=34 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0000000000000005ull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=34 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=34 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffffbull; + if (q <= 19) { // 1 <= q <= 19 => 1 <= 20-q <= 19 => + // 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[20 - q]); + } else if (q == 20) { + ; // C1 * 10^0 = C1 + } else { // if 21 <= q <= 34 + __mul_128x64_to_128 (C, ten2k64[q - 20], C); // max 47-bit x 67-bit + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } + } + // n is not too large to be converted to int64: -2^63-1/2 <= n < 2^63-1/2 + // Note: some of the cases tested for above fall through to this point + // Restore C1 which may have been modified above + C1.w[1] = x.w[1] & MASK_COEFF; + C1.w[0] = x.w[0]; + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] < midpoint128[ind - 19].w[0]))) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 19, 1 <= q <= 34, -33 <= exp <= 18) + // -2^63-1/2 <= x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + // if the result was a midpoint it was rounded away from zero + if (x_sign) + res = -Cstar.w[0]; + else + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 19 + // res = +/-C (exact) + if (x_sign) + res = -C1.w[0]; + else + res = C1.w[0]; + } else { // if (exp>0) => 1 <= exp <= 18, 1 <= q < 18, 2 <= q + exp <= 19 + // res = +/-C * 10^exp (exact) where this fits in 64-bit integer + if (x_sign) + res = -C1.w[0] * ten2k64[exp]; + else + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_to_int8.c b/gcc-4.4.3/libgcc/config/libbid/bid128_to_int8.c new file mode 100644 index 000000000..ebbc49b21 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_to_int8.c @@ -0,0 +1,67 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +#define SIZE_MASK 0xffffff80 +#define INVALID_RESULT 0x80 + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid128_to_int8_rnint, UINT128, x, + bid128_to_int32_rnint, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid128_to_int8_xrnint, UINT128, x, + bid128_to_int32_xrnint, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid128_to_int8_rninta, UINT128, x, + bid128_to_int32_rninta, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid128_to_int8_xrninta, UINT128, x, + bid128_to_int32_xrninta, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid128_to_int8_int, UINT128, x, + bid128_to_int32_int, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid128_to_int8_xint, UINT128, x, + bid128_to_int32_xint, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid128_to_int8_floor, UINT128, x, + bid128_to_int32_floor, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid128_to_int8_ceil, UINT128, x, + bid128_to_int32_ceil, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid128_to_int8_xfloor, UINT128, x, + bid128_to_int32_xfloor, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid128_to_int8_xceil, UINT128, x, + bid128_to_int32_xceil, int, SIZE_MASK, + INVALID_RESULT) diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_to_uint16.c b/gcc-4.4.3/libgcc/config/libbid/bid128_to_uint16.c new file mode 100644 index 000000000..2dd9d5d5b --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_to_uint16.c @@ -0,0 +1,68 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +#define SIZE_MASK 0xffff0000 +#define INVALID_RESULT 0x8000 + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid128_to_uint16_rnint, + UINT128, x, bid128_to_uint32_rnint, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid128_to_uint16_xrnint, + UINT128, x, bid128_to_uint32_xrnint, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid128_to_uint16_rninta, + UINT128, x, bid128_to_uint32_rninta, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, + bid128_to_uint16_xrninta, UINT128, x, + bid128_to_uint32_xrninta, unsigned int, + SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid128_to_uint16_int, + UINT128, x, bid128_to_uint32_int, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid128_to_uint16_xint, + UINT128, x, bid128_to_uint32_xint, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid128_to_uint16_floor, + UINT128, x, bid128_to_uint32_floor, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid128_to_uint16_ceil, + UINT128, x, bid128_to_uint32_ceil, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid128_to_uint16_xfloor, + UINT128, x, bid128_to_uint32_xfloor, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid128_to_uint16_xceil, + UINT128, x, bid128_to_uint32_xceil, + unsigned int, SIZE_MASK, INVALID_RESULT) diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_to_uint32.c b/gcc-4.4.3/libgcc/config/libbid/bid128_to_uint32.c new file mode 100644 index 000000000..3d8f44c87 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_to_uint32.c @@ -0,0 +1,3588 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID128_to_uint32_rnint + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, + bid128_to_uint32_rnint, x) + + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in an unsigned 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n < -1/2 then n cannot be converted to uint32 with RN + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x05, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x05ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 > 0x05 <=> + // C > 0x05 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 1/2 up) + tmp64 = 0x05ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^32 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x9fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb <=> + // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^32-1/2 up) + tmp64 = 0x9fffffffbull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -1/2 <= n < 2^32 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { + res = 0x00000000; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x80000000; + *pfpsf |= INVALID_EXCEPTION; + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] <= midpoint128[ind - 19].w[0]))) { + res = 0x00000000; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x80000000; + *pfpsf |= INVALID_EXCEPTION; + } + } + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // 1 <= x < 2^32-1/2 so x can be rounded + // to nearest to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + } // else MP in [ODD, EVEN] + } + res = Cstar.w[0]; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = C (exact) + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = C * 10^exp (exact) + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint32_xrnint + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, + bid128_to_uint32_xrnint, x) + + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + unsigned int tmp_inexact = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in an unsigned 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n < -1/2 then n cannot be converted to uint32 with RN + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x05, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x05ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 > 0x05 <=> + // C > 0x05 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 1/2 up) + tmp64 = 0x05ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^32 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x9fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb <=> + // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^32-1/2 up) + tmp64 = 0x9fffffffbull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -1/2 <= n < 2^32 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { + res = 0x00000000; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x80000000; + *pfpsf |= INVALID_EXCEPTION; + BID_RETURN (res); + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] <= midpoint128[ind - 19].w[0]))) { + res = 0x00000000; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x80000000; + *pfpsf |= INVALID_EXCEPTION; + BID_RETURN (res); + } + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // 1 <= x < 2^32-1/2 so x can be rounded + // to nearest to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + } // else MP in [ODD, EVEN] + } + res = Cstar.w[0]; // the result is positive + if (tmp_inexact) + *pfpsf |= INEXACT_EXCEPTION; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = C (exact) + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = C * 10^exp (exact) + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint32_floor + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, + bid128_to_uint32_floor, x) + + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + int is_inexact_gt_midpoint = 0; + int is_midpoint_lt_even = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + // x < 0 is invalid + if (x_sign) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // x > 0 from this point on + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + // n > 0 and q + exp = 10 + // if n >= 2^32 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0xa00000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000 <=> + // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^32 up) + tmp64 = 0xa00000000ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + // n is not too large to be converted to int32: 0 <= n < 2^31 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { + // n = +0.0...c(0)c(1)...c(q-1) or n = +0.c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // 1 <= x < 2^32 so x can be rounded down to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + is_midpoint_lt_even = 1; + is_inexact_gt_midpoint = 0; + } + } + // general correction for RM + if (is_midpoint_lt_even || is_inexact_gt_midpoint) { + Cstar.w[0] = Cstar.w[0] - 1; + } else { + ; // the result is already correct + } + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint32_xfloor + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, + bid128_to_uint32_xfloor, x) + + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + int is_inexact_gt_midpoint = 0; + int is_midpoint_lt_even = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + // x < 0 is invalid + if (x_sign) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // x > 0 from this point on + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + // n > 0 and q + exp = 10 + // if n >= 2^32 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0xa00000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000 <=> + // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^32 up) + tmp64 = 0xa00000000ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + // n is not too large to be converted to int32: 0 <= n < 2^31 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { + // n = +0.0...c(0)c(1)...c(q-1) or n = +0.c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // 1 <= x < 2^32 so x can be rounded down to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + is_midpoint_lt_even = 1; + is_inexact_gt_midpoint = 0; + } + } + // general correction for RM + if (is_midpoint_lt_even || is_inexact_gt_midpoint) { + Cstar.w[0] = Cstar.w[0] - 1; + } else { + ; // the result is already correct + } + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint32_ceil + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, + bid128_to_uint32_ceil, x) + + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + int is_inexact_lt_midpoint = 0; + int is_midpoint_gt_even = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x0aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a <=> + // C >= 0x0a * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 1 up) + tmp64 = 0x0aull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n > 2^32 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x9fffffff6ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6 <=> + // C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^32 up) + tmp64 = 0x9fffffff6ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^32-1 < n <= 2^32-1 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { + // n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) + // return 0 + if (x_sign) + res = 0x00000000; + else + res = 0x00000001; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // -2^32-1 < x <= -1 or 1 <= x <= 2^32-1 so x can be rounded + // toward positive infinity to a 32-bit signed integer + if (x_sign) { // x <= -1 is invalid + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // x > 0 from this point on + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + ; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + ; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + is_midpoint_gt_even = 1; + is_inexact_lt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + is_inexact_lt_midpoint = 0; + } + } + // general correction for RM + if (is_midpoint_gt_even || is_inexact_lt_midpoint) { + Cstar.w[0] = Cstar.w[0] + 1; + } else { + ; // the result is already correct + } + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint32_xceil + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, + bid128_to_uint32_xceil, x) + + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + int is_inexact_lt_midpoint = 0; + int is_midpoint_gt_even = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x0aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a <=> + // C >= 0x0a * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 1 up) + tmp64 = 0x0aull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n > 2^32 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x9fffffff6ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6 <=> + // C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^32 up) + tmp64 = 0x9fffffff6ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^32-1 < n <= 2^32-1 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { + // n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + if (x_sign) + res = 0x00000000; + else + res = 0x00000001; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // -2^32-1 < x <= -1 or 1 <= x <= 2^32-1 so x can be rounded + // toward positive infinity to a 32-bit signed integer + if (x_sign) { // x <= -1 is invalid + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // x > 0 from this point on + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + is_midpoint_gt_even = 1; + is_inexact_lt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + is_inexact_lt_midpoint = 0; + } + } + // general correction for RM + if (is_midpoint_gt_even || is_inexact_lt_midpoint) { + Cstar.w[0] = Cstar.w[0] + 1; + } else { + ; // the result is already correct + } + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint32_int + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, + bid128_to_uint32_int, x) + + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + int is_inexact_gt_midpoint = 0; + int is_midpoint_lt_even = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x0aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit uint fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a <=> + // C >= 0x0a * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 1 up) + tmp64 = 0x0aull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^32 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0xa00000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit uint fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000 <=> + // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^32 up) + tmp64 = 0xa00000000ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to uint32: -2^32 < n < 2^32 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { + // n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // x = d(0)...d(k).d(k+1)..., k >= 0, d(0) != 0 + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // x > 0 from this point on + // 1 <= x < 2^32 so x can be rounded to zero to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + is_inexact_gt_midpoint = 1; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + is_midpoint_lt_even = 1; + is_inexact_gt_midpoint = 0; + } + } + // general correction for RZ + if (is_midpoint_lt_even || is_inexact_gt_midpoint) { + Cstar.w[0] = Cstar.w[0] - 1; + } else { + ; // exact, the result is already correct + } + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint32_xint + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, + bid128_to_uint32_xint, x) + + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + int is_inexact_gt_midpoint = 0; + int is_midpoint_lt_even = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x0aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit uint fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a <=> + // C >= 0x0a * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 1 up) + tmp64 = 0x0aull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^32 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0xa00000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit uint fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000 <=> + // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^32 up) + tmp64 = 0xa00000000ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to uint32: -2^32 < n < 2^32 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { + // n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + // x = d(0)...d(k).d(k+1)..., k >= 0, d(0) != 0 + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // x > 0 from this point on + // 1 <= x < 2^32 so x can be rounded to zero to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + is_inexact_gt_midpoint = 1; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + is_midpoint_lt_even = 1; + is_inexact_gt_midpoint = 0; + } + } + // general correction for RZ + if (is_midpoint_lt_even || is_inexact_gt_midpoint) { + Cstar.w[0] = Cstar.w[0] - 1; + } else { + ; // exact, the result is already correct + } + res = Cstar.w[0]; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint32_rninta + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, + bid128_to_uint32_rninta, x) + + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x05, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x05ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x05 <=> + // C >= 0x05 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 1/2 up) + tmp64 = 0x05ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^32 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x9fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb <=> + // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^32-1/2 up) + tmp64 = 0x9fffffffbull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -1/2 < n < 2^32 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { + res = 0x00000000; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x80000000; + *pfpsf |= INVALID_EXCEPTION; + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] < midpoint128[ind - 19].w[0]))) { + res = 0x00000000; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x80000000; + *pfpsf |= INVALID_EXCEPTION; + } + } + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // 1 <= x < 2^31-1/2 so x can be rounded + // to nearest-away to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result was a midpoint, it was already rounded away from zero + res = Cstar.w[0]; // always positive + // no need to check for midpoints - already rounded away from zero! + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint32_xrninta + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, + bid128_to_uint32_xrninta, x) + + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + unsigned int tmp_inexact = 0; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x00000000; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x05, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x05ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x05 <=> + // C >= 0x05 * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 1/2 up) + tmp64 = 0x05ull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^32 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 + // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=34 + if (q <= 11) { + tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x9fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 + // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb <=> + // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 + // (scale 2^32-1/2 up) + tmp64 = 0x9fffffffbull; + if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits + __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); + } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits + __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); + } + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -1/2 < n < 2^32 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { + res = 0x00000000; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x80000000; + *pfpsf |= INVALID_EXCEPTION; + BID_RETURN (res); + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] < midpoint128[ind - 19].w[0]))) { + res = 0x00000000; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x80000000; + *pfpsf |= INVALID_EXCEPTION; + BID_RETURN (res); + } + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // 1 <= x < 2^31-1/2 so x can be rounded + // to nearest-away to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result was a midpoint, it was already rounded away from zero + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + // *pfpsf |= INEXACT_EXCEPTION; + tmp_inexact = 1; + } + } + // no need to check for midpoints - already rounded away from zero! + res = Cstar.w[0]; // the result is positive + if (tmp_inexact) + *pfpsf |= INEXACT_EXCEPTION; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1.w[0]; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_to_uint64.c b/gcc-4.4.3/libgcc/config/libbid/bid128_to_uint64.c new file mode 100644 index 000000000..77921d3fa --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_to_uint64.c @@ -0,0 +1,3401 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID128_to_uint64_rnint + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, + bid128_to_uint64_rnint, x) + + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 + // if n < -1/2 then n cannot be converted to uint64 with RN + // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^21 > 0x05, 1<=q<=34 + // <=> C * 10^(21-q) > 0x05, 1<=q<=34 + if (q == 21) { + // C > 5 + if (C1.w[1] != 0 || C1.w[0] > 0x05ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to 64-bit unsigned int fall through + // to '1 <= q + exp <= 20' + } else { + // if 1 <= q <= 20 + // C * 10^(21-q) > 5 is true because C >= 1 and 10^(21-q) >= 10 + // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C > 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + } else { // if n > 0 and q + exp = 20 + // if n >= 2^64 - 1/2 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) + // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34 + if (q == 1) { + // C * 10^20 >= 0x9fffffffffffffffb + __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C + if (C.w[1] > 0x09 || (C.w[1] == 0x09 + && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q <= 19) { + // C * 10^(21-q) >= 0x9fffffffffffffffb + __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); + if (C.w[1] > 0x09 || (C.w[1] == 0x09 + && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 20) { + // C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff + C.w[0] = C1.w[0] + C1.w[0]; + C.w[1] = C1.w[1] + C1.w[1]; + if (C.w[0] < C1.w[0]) + C.w[1]++; + if (C.w[1] > 0x01 || (C.w[1] == 0x01 + && C.w[0] >= 0xffffffffffffffffull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 21) { + // C >= 0x9fffffffffffffffb + if (C1.w[1] > 0x09 || (C1.w[1] == 0x09 + && C1.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits + C.w[1] = 0x09; + C.w[0] = 0xfffffffffffffffbull; + __mul_128x64_to_128 (C, ten2k64[q - 21], C); + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { + res = 0x0000000000000000ull; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x8000000000000000ull; + *pfpsf |= INVALID_EXCEPTION; + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] <= midpoint128[ind - 19].w[0]))) { + res = 0x0000000000000000ull; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x8000000000000000ull; + *pfpsf |= INVALID_EXCEPTION; + } + } + } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x < 2^64-1/2 so x can be rounded + // to nearest to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + } // else MP in [ODD, EVEN] + } + res = Cstar.w[0]; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 + // res = C (exact) + res = C1.w[0]; + } else { + // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 + // res = C * 10^exp (exact) - must fit in 64 bits + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint64_xrnint + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, + bid128_to_uint64_xrnint, x) + + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 + // if n < -1/2 then n cannot be converted to uint64 with RN + // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^21 > 0x05, 1<=q<=34 + // <=> C * 10^(21-q) > 0x05, 1<=q<=34 + if (q == 21) { + // C > 5 + if (C1.w[1] != 0 || C1.w[0] > 0x05ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to 64-bit unsigned int fall through + // to '1 <= q + exp <= 20' + } else { + // if 1 <= q <= 20 + // C * 10^(21-q) > 5 is true because C >= 1 and 10^(21-q) >= 10 + // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C > 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + } else { // if n > 0 and q + exp = 20 + // if n >= 2^64 - 1/2 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) + // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34 + if (q == 1) { + // C * 10^20 >= 0x9fffffffffffffffb + __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C + if (C.w[1] > 0x09 || (C.w[1] == 0x09 + && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q <= 19) { + // C * 10^(21-q) >= 0x9fffffffffffffffb + __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); + if (C.w[1] > 0x09 || (C.w[1] == 0x09 + && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 20) { + // C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff + C.w[0] = C1.w[0] + C1.w[0]; + C.w[1] = C1.w[1] + C1.w[1]; + if (C.w[0] < C1.w[0]) + C.w[1]++; + if (C.w[1] > 0x01 || (C.w[1] == 0x01 + && C.w[0] >= 0xffffffffffffffffull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 21) { + // C >= 0x9fffffffffffffffb + if (C1.w[1] > 0x09 || (C1.w[1] == 0x09 + && C1.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits + C.w[1] = 0x09; + C.w[0] = 0xfffffffffffffffbull; + __mul_128x64_to_128 (C, ten2k64[q - 21], C); + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { + res = 0x0000000000000000ull; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x8000000000000000ull; + *pfpsf |= INVALID_EXCEPTION; + BID_RETURN (res); + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] <= midpoint128[ind - 19].w[0]))) { + res = 0x0000000000000000ull; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x8000000000000000ull; + *pfpsf |= INVALID_EXCEPTION; + BID_RETURN (res); + } + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x < 2^64-1/2 so x can be rounded + // to nearest to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[3] == 0) && (fstar.w[2] == 0) + && (fstar.w[1] || fstar.w[0]) + && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { + // the result is a midpoint; round to nearest + if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar.w[0]--; // Cstar.w[0] is now even + } // else MP in [ODD, EVEN] + } + res = Cstar.w[0]; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 + // res = C (exact) + res = C1.w[0]; + } else { + // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 + // res = C * 10^exp (exact) - must fit in 64 bits + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint64_floor + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, + bid128_to_uint64_floor, x) + + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // if n < 0 then n cannot be converted to uint64 with RM + if (x_sign) { // if n < 0 and q + exp = 20 + // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 0 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + // if n > 0 and q + exp = 20 + // if n >= 2^64 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65 + // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34 + if (q == 1) { + // C * 10^20 >= 0xa0000000000000000 + __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q <= 19) { + // C * 10^(21-q) >= 0xa0000000000000000 + __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 20) { + // C >= 0x10000000000000000 + if (C1.w[1] >= 0x01) { + // actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 21) { + // C >= 0xa0000000000000000 + if (C1.w[1] >= 0x0a) { + // actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits + C.w[1] = 0x0a; + C.w[0] = 0x0000000000000000ull; + __mul_128x64_to_128 (C, ten2k64[q - 21], C); + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + // n is not too large to be converted to int64 if 0 <= n < 2^64 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) + // 1 <= x < 2^64 so x can be rounded + // down to a 64-bit unsigned signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + res = Cstar.w[0]; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 + // res = C (exact) + res = C1.w[0]; + } else { + // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 + // res = C * 10^exp (exact) - must fit in 64 bits + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint64_xfloor + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, + bid128_to_uint64_xfloor, x) + + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // if n < 0 then n cannot be converted to uint64 with RM + if (x_sign) { // if n < 0 and q + exp = 20 + // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 0 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + // if n > 0 and q + exp = 20 + // if n >= 2^64 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65 + // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34 + if (q == 1) { + // C * 10^20 >= 0xa0000000000000000 + __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q <= 19) { + // C * 10^(21-q) >= 0xa0000000000000000 + __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 20) { + // C >= 0x10000000000000000 + if (C1.w[1] >= 0x01) { + // actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 21) { + // C >= 0xa0000000000000000 + if (C1.w[1] >= 0x0a) { + // actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits + C.w[1] = 0x0a; + C.w[0] = 0x0000000000000000ull; + __mul_128x64_to_128 (C, ten2k64[q - 21], C); + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + // n is not too large to be converted to int64 if 0 <= n < 2^64 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) + // 1 <= x < 2^64 so x can be rounded + // down to a 64-bit unsigned signed integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1] || + (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] && + fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 22 <= ind <= 33 + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + res = Cstar.w[0]; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 + // res = C (exact) + res = C1.w[0]; + } else { + // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 + // res = C * 10^exp (exact) - must fit in 64 bits + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint64_ceil + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, bid128_to_uint64_ceil, + x) + + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 + // if n <= -1 then n cannot be converted to uint64 with RZ + // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1 + // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34 + // <=> C * 10^(21-q) >= 0x0a, 1<=q<=34 + if (q == 21) { + // C >= a + if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to 64-bit unsigned int fall through + // to '1 <= q + exp <= 20' + } else { + // if 1 <= q <= 20 + // C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10 + // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + } else { // if n > 0 and q + exp = 20 + // if n > 2^64 - 1 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 > 10 * (2^64 - 1) + // <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=34 + if (q == 1) { + // C * 10^20 > 0x9fffffffffffffff6 + __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C + if (C.w[1] > 0x09 || (C.w[1] == 0x09 + && C.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q <= 19) { + // C * 10^(21-q) > 0x9fffffffffffffff6 + __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); + if (C.w[1] > 0x09 || (C.w[1] == 0x09 + && C.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 20) { + // C > 0xffffffffffffffff + if (C1.w[1]) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 21) { + // C > 0x9fffffffffffffff6 + if (C1.w[1] > 0x09 || (C1.w[1] == 0x09 + && C1.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C > 10^(q-21) * 0x9fffffffffffffff6 max 44 bits x 68 bits + C.w[1] = 0x09; + C.w[0] = 0xfffffffffffffff6ull; + __mul_128x64_to_128 (C, ten2k64[q - 21], C); + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1 < n <= 2^64 - 1 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // return 0 or 1 + if (x_sign) + res = 0x0000000000000000ull; + else + res = 0x0000000000000001ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded + // to zero to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x <= 2^64 - 1 so x can be rounded + // to zero to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result is positive and inexact, need to add 1 to it + + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (!x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + } // else the result is exact + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (!x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + } // else the result is exact + } else { // if 22 <= ind <= 33 + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (!x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + } // else the result is exact + } + + res = Cstar.w[0]; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 + // res = C (exact) + res = C1.w[0]; + } else { + // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 + // res = C * 10^exp (exact) - must fit in 64 bits + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint64_xceil + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, + bid128_to_uint64_xceil, x) + + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 + // if n <= -1 then n cannot be converted to uint64 with RZ + // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1 + // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34 + // <=> C * 10^(21-q) >= 0x0a, 1<=q<=34 + if (q == 21) { + // C >= a + if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to 64-bit unsigned int fall through + // to '1 <= q + exp <= 20' + } else { + // if 1 <= q <= 20 + // C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10 + // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + } else { // if n > 0 and q + exp = 20 + // if n > 2^64 - 1 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 > 10 * (2^64 - 1) + // <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=34 + if (q == 1) { + // C * 10^20 > 0x9fffffffffffffff6 + __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C + if (C.w[1] > 0x09 || (C.w[1] == 0x09 + && C.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q <= 19) { + // C * 10^(21-q) > 0x9fffffffffffffff6 + __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); + if (C.w[1] > 0x09 || (C.w[1] == 0x09 + && C.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 20) { + // C > 0xffffffffffffffff + if (C1.w[1]) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 21) { + // C > 0x9fffffffffffffff6 + if (C1.w[1] > 0x09 || (C1.w[1] == 0x09 + && C1.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C > 10^(q-21) * 0x9fffffffffffffff6 max 44 bits x 68 bits + C.w[1] = 0x09; + C.w[0] = 0xfffffffffffffff6ull; + __mul_128x64_to_128 (C, ten2k64[q - 21], C); + if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1 < n <= 2^64 - 1 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 or 1 + if (x_sign) + res = 0x0000000000000000ull; + else + res = 0x0000000000000001ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded + // to zero to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x <= 2^64 - 1 so x can be rounded + // to zero to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // if the result is positive and inexact, need to add 1 to it + + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (!x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (!x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 22 <= ind <= 33 + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + if (!x_sign) { // positive and inexact + Cstar.w[0]++; + if (Cstar.w[0] == 0x0) + Cstar.w[1]++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + res = Cstar.w[0]; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 + // res = C (exact) + res = C1.w[0]; + } else { + // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 + // res = C * 10^exp (exact) - must fit in 64 bits + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint64_int + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, bid128_to_uint64_int, + x) + + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 + // if n <= -1 then n cannot be converted to uint64 with RZ + // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1 + // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34 + // <=> C * 10^(21-q) >= 0x0a, 1<=q<=34 + if (q == 21) { + // C >= a + if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to 64-bit unsigned int fall through + // to '1 <= q + exp <= 20' + } else { + // if 1 <= q <= 20 + // C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10 + // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + } else { // if n > 0 and q + exp = 20 + // if n >= 2^64 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65 + // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34 + if (q == 1) { + // C * 10^20 >= 0xa0000000000000000 + __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q <= 19) { + // C * 10^(21-q) >= 0xa0000000000000000 + __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 20) { + // C >= 0x10000000000000000 + if (C1.w[1] >= 0x01) { + // actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 21) { + // C >= 0xa0000000000000000 + if (C1.w[1] >= 0x0a) { + // actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits + C.w[1] = 0x0a; + C.w[0] = 0x0000000000000000ull; + __mul_128x64_to_128 (C, ten2k64[q - 21], C); + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1 < n < 2^64 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded + // to zero to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x < 2^64 so x can be rounded + // to zero to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + res = Cstar.w[0]; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 + // res = C (exact) + res = C1.w[0]; + } else { + // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 + // res = C * 10^exp (exact) - must fit in 64 bits + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint64_xint + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, bid128_to_uint64_xint, + x) + + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 + // if n <= -1 then n cannot be converted to uint64 with RZ + // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1 + // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34 + // <=> C * 10^(21-q) >= 0x0a, 1<=q<=34 + if (q == 21) { + // C >= a + if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to 64-bit unsigned int fall through + // to '1 <= q + exp <= 20' + } else { + // if 1 <= q <= 20 + // C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10 + // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + } else { // if n > 0 and q + exp = 20 + // if n >= 2^64 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65 + // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34 + if (q == 1) { + // C * 10^20 >= 0xa0000000000000000 + __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q <= 19) { + // C * 10^(21-q) >= 0xa0000000000000000 + __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 20) { + // C >= 0x10000000000000000 + if (C1.w[1] >= 0x01) { + // actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 21) { + // C >= 0xa0000000000000000 + if (C1.w[1] >= 0x0a) { + // actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits + C.w[1] = 0x0a; + C.w[0] = 0x0000000000000000ull; + __mul_128x64_to_128 (C, ten2k64[q - 21], C); + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1 < n < 2^64 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded + // to zero to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x < 2^64 so x can be rounded + // to zero to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 22 <= ind <= 33 + if (fstar.w[3] || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + res = Cstar.w[0]; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 + // res = C (exact) + res = C1.w[0]; + } else { + // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 + // res = C * 10^exp (exact) - must fit in 64 bits + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint64_rninta + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, + bid128_to_uint64_rninta, x) + + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 + // if n <= -1/2 then n cannot be converted to uint64 with RN + // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x05, 1<=q<=34 + // <=> C * 10^(21-q) >= 0x05, 1<=q<=34 + if (q == 21) { + // C >= 5 + if (C1.w[1] != 0 || C1.w[0] >= 0x05ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to 64-bit unsigned int fall through + // to '1 <= q + exp <= 20' + } else { + // if 1 <= q <= 20 + // C * 10^(21-q) >= 5 is true because C >= 1 and 10^(21-q) >= 10 + // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + } else { // if n > 0 and q + exp = 20 + // if n >= 2^64 - 1/2 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) + // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34 + if (q == 1) { + // C * 10^20 >= 0x9fffffffffffffffb + __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C + if (C.w[1] > 0x09 || (C.w[1] == 0x09 + && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q <= 19) { + // C * 10^(21-q) >= 0x9fffffffffffffffb + __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); + if (C.w[1] > 0x09 || (C.w[1] == 0x09 + && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 20) { + // C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff + C.w[0] = C1.w[0] + C1.w[0]; + C.w[1] = C1.w[1] + C1.w[1]; + if (C.w[0] < C1.w[0]) + C.w[1]++; + if (C.w[1] > 0x01 || (C.w[1] == 0x01 + && C.w[0] >= 0xffffffffffffffffull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 21) { + // C >= 0x9fffffffffffffffb + if (C1.w[1] > 0x09 || (C1.w[1] == 0x09 + && C1.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits + C.w[1] = 0x09; + C.w[0] = 0xfffffffffffffffbull; + __mul_128x64_to_128 (C, ten2k64[q - 21], C); + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1/2 < n < 2^64 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { + res = 0x0000000000000000ull; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] < midpoint128[ind - 19].w[0]))) { + res = 0x0000000000000000ull; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + } + } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x < 2^64-1/2 so x can be rounded + // to nearest to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + + // if the result was a midpoint it was rounded away from zero + res = Cstar.w[0]; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 + // res = C (exact) + res = C1.w[0]; + } else { + // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 + // res = C * 10^exp (exact) - must fit in 64 bits + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} + +/***************************************************************************** + * BID128_to_uint64_xrninta + ****************************************************************************/ + +BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, + bid128_to_uint64_xrninta, x) + + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + UINT64 tmp64, tmp64A; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT128 C1, C; + UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits + UINT256 fstar; + UINT256 P256; + + // unpack x +x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative +x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions +C1.w[1] = x.w[1] & MASK_COEFF; +C1.w[0] = x.w[0]; + + // check for NaN or Infinity +if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { + // x is special +if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is QNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} else { // x is not a NaN, so it must be infinity + if (!x_sign) { // x is +inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } else { // x is -inf + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + } + BID_RETURN (res); +} +} + // check for non-canonical values (after the check for special values) +if ((C1.w[1] > 0x0001ed09bead87c0ull) + || (C1.w[1] == 0x0001ed09bead87c0ull + && (C1.w[0] > 0x378d8e63ffffffffull)) + || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { + res = 0x0000000000000000ull; + BID_RETURN (res); +} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); +} else { // x is not special and is not zero + + // q = nr. of decimal digits in x + // determine first the nr. of bits in x + if (C1.w[1] == 0) { + if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1.w[0] >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) (C1.w[0]); // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1.w[0]; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) + tmp1.d = (double) C1.w[1]; // exact conversion + x_nr_bits = + 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi + || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi + && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) + q++; + } + exp = (x_exp >> 49) - 6176; + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 + // if n <= -1/2 then n cannot be converted to uint64 with RN + // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x05, 1<=q<=34 + // <=> C * 10^(21-q) >= 0x05, 1<=q<=34 + if (q == 21) { + // C >= 5 + if (C1.w[1] != 0 || C1.w[0] >= 0x05ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to 64-bit unsigned int fall through + // to '1 <= q + exp <= 20' + } else { + // if 1 <= q <= 20 + // C * 10^(21-q) >= 5 is true because C >= 1 and 10^(21-q) >= 10 + // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + } else { // if n > 0 and q + exp = 20 + // if n >= 2^64 - 1/2 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) + // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34 + if (q == 1) { + // C * 10^20 >= 0x9fffffffffffffffb + __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C + if (C.w[1] > 0x09 || (C.w[1] == 0x09 + && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q <= 19) { + // C * 10^(21-q) >= 0x9fffffffffffffffb + __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); + if (C.w[1] > 0x09 || (C.w[1] == 0x09 + && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 20) { + // C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff + C.w[0] = C1.w[0] + C1.w[0]; + C.w[1] = C1.w[1] + C1.w[1]; + if (C.w[0] < C1.w[0]) + C.w[1]++; + if (C.w[1] > 0x01 || (C.w[1] == 0x01 + && C.w[0] >= 0xffffffffffffffffull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else if (q == 21) { + // C >= 0x9fffffffffffffffb + if (C1.w[1] > 0x09 || (C1.w[1] == 0x09 + && C1.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 + // C >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits + C.w[1] = 0x09; + C.w[0] = 0xfffffffffffffffbull; + __mul_128x64_to_128 (C, ten2k64[q - 21], C); + if (C1.w[1] > C.w[1] + || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1/2 < n < 2^64 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; + if (ind <= 18) { // 0 <= ind <= 18 + if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { + res = 0x0000000000000000ull; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x8000000000000000ull; + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + } else { // 19 <= ind <= 33 + if ((C1.w[1] < midpoint128[ind - 19].w[1]) + || ((C1.w[1] == midpoint128[ind - 19].w[1]) + && (C1.w[0] < midpoint128[ind - 19].w[0]))) { + res = 0x0000000000000000ull; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x00000001; // return +1 + } else { + res = 0x8000000000000000ull; + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x < 2^64-1/2 so x can be rounded + // to nearest to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits + tmp64 = C1.w[0]; + if (ind <= 19) { + C1.w[0] = C1.w[0] + midpoint64[ind - 1]; + } else { + C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; + C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; + } + if (C1.w[0] < tmp64) + C1.w[1]++; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 33 + // kx = 10^(-x) = ten2mk128[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 118 bits + __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[1] = P256.w[3]; + Cstar.w[0] = P256.w[2]; + fstar.w[3] = 0; + fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } else { // 22 <= ind - 1 <= 33 + Cstar.w[1] = 0; + Cstar.w[0] = P256.w[3]; + fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; + fstar.w[2] = P256.w[2]; + fstar.w[1] = P256.w[1]; + fstar.w[0] = P256.w[0]; + } + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. + // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-128 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 102 + if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 + Cstar.w[0] = + (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); + // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); + } else { // 22 <= ind - 1 <= 33 + Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[1] > 0x8000000000000000ull || + (fstar.w[1] == 0x8000000000000000ull + && fstar.w[0] > 0x0ull)) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 + if (tmp64 > ten2mk128trunc[ind - 1].w[1] + || (tmp64 == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 + if (fstar.w[3] > 0x0 || + (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || + (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && + (fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[2] - onehalf128[ind - 1]; + tmp64A = fstar.w[3]; + if (tmp64 > fstar.w[2]) + tmp64A--; + if (tmp64A || tmp64 + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 22 <= ind <= 33 + if (fstar.w[3] > onehalf128[ind - 1] || + (fstar.w[3] == onehalf128[ind - 1] && + (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[3] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[2] + || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] + || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] + && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + // if the result was a midpoint it was rounded away from zero + res = Cstar.w[0]; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 + // res = C (exact) + res = C1.w[0]; + } else { + // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 + // res = C * 10^exp (exact) - must fit in 64 bits + res = C1.w[0] * ten2k64[exp]; + } + } +} + +BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid128_to_uint8.c b/gcc-4.4.3/libgcc/config/libbid/bid128_to_uint8.c new file mode 100644 index 000000000..fe9e31ea5 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid128_to_uint8.c @@ -0,0 +1,67 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +#define SIZE_MASK 0xffffff00 +#define INVALID_RESULT 0x80 + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid128_to_uint8_rnint, + UINT128, x, bid128_to_uint32_rnint, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid128_to_uint8_xrnint, + UINT128, x, bid128_to_uint32_xrnint, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid128_to_uint8_rninta, + UINT128, x, bid128_to_uint32_rninta, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid128_to_uint8_xrninta, + UINT128, x, bid128_to_uint32_xrninta, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid128_to_uint8_int, + UINT128, x, bid128_to_uint32_int, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid128_to_uint8_xint, + UINT128, x, bid128_to_uint32_xint, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid128_to_uint8_floor, + UINT128, x, bid128_to_uint32_floor, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid128_to_uint8_ceil, + UINT128, x, bid128_to_uint32_ceil, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid128_to_uint8_xfloor, + UINT128, x, bid128_to_uint32_xfloor, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid128_to_uint8_xceil, + UINT128, x, bid128_to_uint32_xceil, + unsigned int, SIZE_MASK, INVALID_RESULT) diff --git a/gcc-4.4.3/libgcc/config/libbid/bid32_to_bid128.c b/gcc-4.4.3/libgcc/config/libbid/bid32_to_bid128.c new file mode 100644 index 000000000..a023fbc43 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid32_to_bid128.c @@ -0,0 +1,264 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#define BID_128RES +#include "bid_internal.h" + +/* + * Takes a BID32 as input and converts it to a BID128 and returns it. + */ +TYPE0_FUNCTION_ARGTYPE1_NORND (UINT128, bid32_to_bid128, UINT32, x) + + UINT128 new_coeff, res; + UINT32 sign_x; + int exponent_x; + UINT32 coefficient_x; + +if (!unpack_BID32 (&sign_x, &exponent_x, &coefficient_x, x)) { +if (((x) & 0x78000000) == 0x78000000) { +#ifdef SET_STATUS_FLAGS + if (((x) & 0x7e000000) == 0x7e000000) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[0] = (coefficient_x & 0x000fffff); + __mul_64x128_low (res, res.w[0], power10_table_128[27]); + res.w[1] |= + ((((UINT64) coefficient_x) << 32) & 0xfc00000000000000ull); + + BID_RETURN (res); +} +} + +new_coeff.w[0] = coefficient_x; +new_coeff.w[1] = 0; +get_BID128_very_fast (&res, ((UINT64) sign_x) << 32, + exponent_x + DECIMAL_EXPONENT_BIAS_128 - + DECIMAL_EXPONENT_BIAS_32, new_coeff); +BID_RETURN (res); +} // convert_bid32_to_bid128 + + +/* + * Takes a BID128 as input and converts it to a BID32 and returns it. + */ +#if DECIMAL_CALL_BY_REFERENCE + +void +bid128_to_bid32 (UINT32 * pres, + UINT128 * + px _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px; +#else + +UINT32 +bid128_to_bid32 (UINT128 x _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 CX, T128, TP128, Qh, Ql, Qh1, Stemp, Tmp, Tmp1, CX1; + UINT64 sign_x, carry, cy; + SINT64 D; + UINT32 res; + int_float f64, fx; + int exponent_x, extra_digits, amount, bin_expon_cx, uf_check = 0; + unsigned rmode, status; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + + BID_SWAP128 (x); + // unpack arguments, check for NaN or Infinity or 0 + if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { + if (((x.w[1]) & 0x7800000000000000ull) == 0x7800000000000000ull) { + Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull); + Tmp.w[0] = CX.w[0]; + TP128 = reciprocals10_128[27]; + __mul_128x128_full (Qh, Ql, Tmp, TP128); + amount = recip_scale[27] - 64; + res = ((CX.w[1] >> 32) & 0xfc000000) | (Qh.w[1] >> amount); +#ifdef SET_STATUS_FLAGS + if ((x.w[1] & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN_VAL (res); + } + // x is 0 + exponent_x = + exponent_x - DECIMAL_EXPONENT_BIAS_128 + DECIMAL_EXPONENT_BIAS_32; + if (exponent_x < 0) + exponent_x = 0; + if (exponent_x > DECIMAL_MAX_EXPON_32) + exponent_x = DECIMAL_MAX_EXPON_32; + res = (sign_x >> 32) | (exponent_x << 23); + BID_RETURN_VAL (res); + + } + + if (CX.w[1] || (CX.w[0] >= 10000000)) { + // find number of digits in coefficient + // 2^64 + f64.i = 0x5f800000; + // fx ~ CX + fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; + bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f; + extra_digits = estimate_decimal_digits[bin_expon_cx] - 7; + // scale = 38-estimate_decimal_digits[bin_expon_cx]; + D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1]; + if (D > 0 + || (!D + && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0])) + extra_digits++; + + exponent_x += extra_digits; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = rnd_mode; + if (sign_x && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#else + rmode = 0; +#endif +#else + rmode = 0; +#endif + if (exponent_x < + DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS_32) { + uf_check = 1; + if (-extra_digits + exponent_x - DECIMAL_EXPONENT_BIAS_128 + + DECIMAL_EXPONENT_BIAS_32 + 35 >= 0) { + if (exponent_x == + DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS_32 - 1) { + T128 = round_const_table_128[rmode][extra_digits]; + __add_carry_out (CX1.w[0], carry, T128.w[0], CX.w[0]); + CX1.w[1] = CX.w[1] + T128.w[1] + carry; + if (__unsigned_compare_ge_128 + (CX1, power10_table_128[extra_digits + 7])) + uf_check = 0; + } + extra_digits = + extra_digits + DECIMAL_EXPONENT_BIAS_128 - + DECIMAL_EXPONENT_BIAS_32 - exponent_x; + exponent_x = + DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS_32; + } else + rmode = ROUNDING_TO_ZERO; + } + + T128 = round_const_table_128[rmode][extra_digits]; + __add_carry_out (CX.w[0], carry, T128.w[0], CX.w[0]); + CX.w[1] = CX.w[1] + T128.w[1] + carry; + + TP128 = reciprocals10_128[extra_digits]; + __mul_128x128_full (Qh, Ql, CX, TP128); + amount = recip_scale[extra_digits]; + + if (amount >= 64) { + CX.w[0] = Qh.w[1] >> (amount - 64); + CX.w[1] = 0; + } else { + __shr_128 (CX, Qh, amount); + } + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (!(rnd_mode)) +#endif + if (CX.w[0] & 1) { + // check whether fractional part of initial_P/10^ed1 is exactly .5 + + // get remainder + __shl_128_long (Qh1, Qh, (128 - amount)); + + if (!Qh1.w[1] && !Qh1.w[0] + && (Ql.w[1] < reciprocals10_128[extra_digits].w[1] + || (Ql.w[1] == reciprocals10_128[extra_digits].w[1] + && Ql.w[0] < reciprocals10_128[extra_digits].w[0]))) { + CX.w[0]--; + } + } +#endif + + + { + status = INEXACT_EXCEPTION; + // get remainder + __shl_128_long (Qh1, Qh, (128 - amount)); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if (Qh1.w[1] == 0x8000000000000000ull && (!Qh1.w[0]) + && (Ql.w[1] < reciprocals10_128[extra_digits].w[1] + || (Ql.w[1] == reciprocals10_128[extra_digits].w[1] + && Ql.w[0] < reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if ((!Qh1.w[1]) && (!Qh1.w[0]) + && (Ql.w[1] < reciprocals10_128[extra_digits].w[1] + || (Ql.w[1] == reciprocals10_128[extra_digits].w[1] + && Ql.w[0] < reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (Stemp.w[0], cy, Ql.w[0], + reciprocals10_128[extra_digits].w[0]); + __add_carry_in_out (Stemp.w[1], carry, Ql.w[1], + reciprocals10_128[extra_digits].w[1], cy); + __shr_128_long (Qh, Qh1, (128 - amount)); + Tmp.w[0] = 1; + Tmp.w[1] = 0; + __shl_128_long (Tmp1, Tmp, amount); + Qh.w[0] += carry; + if (Qh.w[0] < carry) + Qh.w[1]++; + if (__unsigned_compare_ge_128 (Qh, Tmp1)) + status = EXACT_STATUS; + } + + if (status != EXACT_STATUS) { + if (uf_check) { + status |= UNDERFLOW_EXCEPTION; + } +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, status); +#endif + } + } + + } + + res = + get_BID32 ((UINT32) (sign_x >> 32), + exponent_x - DECIMAL_EXPONENT_BIAS_128 + + DECIMAL_EXPONENT_BIAS_32, CX.w[0], rnd_mode, pfpsf); + BID_RETURN_VAL (res); + +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid32_to_bid64.c b/gcc-4.4.3/libgcc/config/libbid/bid32_to_bid64.c new file mode 100644 index 000000000..c52596b34 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid32_to_bid64.c @@ -0,0 +1,216 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/* + * Takes a BID32 as input and converts it to a BID64 and returns it. + */ +TYPE0_FUNCTION_ARGTYPE1_NORND (UINT64, bid32_to_bid64, UINT32, x) + + UINT64 res; + UINT32 sign_x; + int exponent_x; + UINT32 coefficient_x; + +if (!unpack_BID32 (&sign_x, &exponent_x, &coefficient_x, x)) { + // Inf, NaN, 0 +if (((x) & 0x78000000) == 0x78000000) { + if (((x) & 0x7e000000) == 0x7e000000) { // sNaN +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + } + res = (coefficient_x & 0x000fffff); + res *= 1000000000; + res |= ((((UINT64) coefficient_x) << 32) & 0xfc00000000000000ull); + + BID_RETURN (res); +} +} + +res = +very_fast_get_BID64_small_mantissa (((UINT64) sign_x) << 32, + exponent_x + + DECIMAL_EXPONENT_BIAS - + DECIMAL_EXPONENT_BIAS_32, + (UINT64) coefficient_x); +BID_RETURN (res); +} // convert_bid32_to_bid64 + + +/* + * Takes a BID64 as input and converts it to a BID32 and returns it. + */ +#if DECIMAL_CALL_BY_REFERENCE + +void +bid64_to_bid32 (UINT32 * pres, + UINT64 * + px _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x; +#else + +UINT32 +bid64_to_bid32 (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 Q; + UINT64 sign_x, coefficient_x, remainder_h, carry, Stemp; + UINT32 res; + int_float tempx; + int exponent_x, bin_expon_cx, extra_digits, rmode = 0, amount; + unsigned status = 0; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif + x = *px; +#endif + + // unpack arguments, check for NaN or Infinity, 0 + if (!unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x)) { + if (((x) & 0x7800000000000000ull) == 0x7800000000000000ull) { + res = (coefficient_x & 0x0003ffffffffffffull); + res /= 1000000000ull; + res |= ((coefficient_x >> 32) & 0xfc000000); +#ifdef SET_STATUS_FLAGS + if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (res); + } + exponent_x = + exponent_x - DECIMAL_EXPONENT_BIAS + DECIMAL_EXPONENT_BIAS_32; + if (exponent_x < 0) + exponent_x = 0; + if (exponent_x > DECIMAL_MAX_EXPON_32) + exponent_x = DECIMAL_MAX_EXPON_32; + res = (sign_x >> 32) | (exponent_x << 23); + BID_RETURN (res); + } + + exponent_x = + exponent_x - DECIMAL_EXPONENT_BIAS + DECIMAL_EXPONENT_BIAS_32; + + // check number of digits + if (coefficient_x >= 10000000) { + tempx.d = (float) coefficient_x; + bin_expon_cx = ((tempx.i >> 23) & 0xff) - 0x7f; + extra_digits = estimate_decimal_digits[bin_expon_cx] - 7; + // add test for range + if (coefficient_x >= power10_index_binexp[bin_expon_cx]) + extra_digits++; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = rnd_mode; + if (sign_x && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#else + rmode = 0; +#endif +#else + rmode = 0; +#endif + + exponent_x += extra_digits; + if ((exponent_x < 0) && (exponent_x + MAX_FORMAT_DIGITS_32 >= 0)) { + status = UNDERFLOW_EXCEPTION; + if (exponent_x == -1) + if (coefficient_x + round_const_table[rmode][extra_digits] >= + power10_table_128[extra_digits + 7].w[0]) + status = 0; + extra_digits -= exponent_x; + exponent_x = 0; + } + coefficient_x += round_const_table[rmode][extra_digits]; + __mul_64x64_to_128 (Q, coefficient_x, + reciprocals10_64[extra_digits]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = short_recip_scale[extra_digits]; + + coefficient_x = Q.w[1] >> amount; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == 0) //ROUNDING_TO_NEAREST +#endif + if (coefficient_x & 1) { + // check whether fractional part of initial_P/10^extra_digits + // is exactly .5 + + // get remainder + remainder_h = Q.w[1] << (64 - amount); + + if (!remainder_h && (Q.w[0] < reciprocals10_64[extra_digits])) + coefficient_x--; + } +#endif + +#ifdef SET_STATUS_FLAGS + + { + status |= INEXACT_EXCEPTION; + // get remainder + remainder_h = Q.w[1] << (64 - amount); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if (remainder_h == 0x8000000000000000ull + && (Q.w[0] < reciprocals10_64[extra_digits])) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if (!remainder_h && (Q.w[0] < reciprocals10_64[extra_digits])) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (Stemp, carry, Q.w[0], + reciprocals10_64[extra_digits]); + if ((remainder_h >> (64 - amount)) + carry >= + (((UINT64) 1) << amount)) + status = EXACT_STATUS; + } + + if (status != EXACT_STATUS) + __set_status_flags (pfpsf, status); + } + +#endif + + } + + res = + get_BID32 ((UINT32) (sign_x >> 32), + exponent_x, coefficient_x, rnd_mode, pfpsf); + BID_RETURN (res); + +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_add.c b/gcc-4.4.3/libgcc/config/libbid/bid64_add.c new file mode 100644 index 000000000..00dea4a51 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_add.c @@ -0,0 +1,595 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +/***************************************************************************** + * BID64 add + ***************************************************************************** + * + * Algorithm description: + * + * if(exponent_a < exponent_b) + * switch a, b + * diff_expon = exponent_a - exponent_b + * if(diff_expon > 16) + * return normalize(a) + * if(coefficient_a*10^diff_expon guaranteed below 2^62) + * S = sign_a*coefficient_a*10^diff_expon + sign_b*coefficient_b + * if(|S|<10^16) + * return get_BID64(sign(S),exponent_b,|S|) + * else + * determine number of extra digits in S (1, 2, or 3) + * return rounded result + * else // large exponent difference + * if(number_digits(coefficient_a*10^diff_expon) +/- 10^16) + * guaranteed the same as + * number_digits(coefficient_a*10^diff_expon) ) + * S = normalize(coefficient_a + (sign_a^sign_b)*10^(16-diff_expon)) + * corr = 10^16 + (sign_a^sign_b)*coefficient_b + * corr*10^exponent_b is rounded so it aligns with S*10^exponent_S + * return get_BID64(sign_a,exponent(S),S+rounded(corr)) + * else + * add sign_a*coefficient_a*10^diff_expon, sign_b*coefficient_b + * in 128-bit integer arithmetic, then round to 16 decimal digits + * + * + ****************************************************************************/ + +#include "bid_internal.h" + +#if DECIMAL_CALL_BY_REFERENCE +void bid64_add (UINT64 * pres, UINT64 * px, + UINT64 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); +#else +UINT64 bid64_add (UINT64 x, + UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); +#endif + +#if DECIMAL_CALL_BY_REFERENCE + +void +bid64_sub (UINT64 * pres, UINT64 * px, + UINT64 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 y = *py; +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif + // check if y is not NaN + if (((y & NAN_MASK64) != NAN_MASK64)) + y ^= 0x8000000000000000ull; + bid64_add (pres, px, + &y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +} +#else + +UINT64 +bid64_sub (UINT64 x, + UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + // check if y is not NaN + if (((y & NAN_MASK64) != NAN_MASK64)) + y ^= 0x8000000000000000ull; + + return bid64_add (x, + y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +} +#endif + + + +#if DECIMAL_CALL_BY_REFERENCE + +void +bid64_add (UINT64 * pres, UINT64 * px, + UINT64 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x, y; +#else + +UINT64 +bid64_add (UINT64 x, + UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT128 CA, CT, CT_new; + UINT64 sign_x, sign_y, coefficient_x, coefficient_y, C64_new; + UINT64 valid_x, valid_y; + UINT64 res; + UINT64 sign_a, sign_b, coefficient_a, coefficient_b, sign_s, sign_ab, + rem_a; + UINT64 saved_ca, saved_cb, C0_64, C64, remainder_h, T1, carry, tmp; + int_double tempx; + int exponent_x, exponent_y, exponent_a, exponent_b, diff_dec_expon; + int bin_expon_ca, extra_digits, amount, scale_k, scale_ca; + unsigned rmode, status; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif + x = *px; + y = *py; +#endif + + valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x); + valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y); + + // unpack arguments, check for NaN or Infinity + if (!valid_x) { + // x is Inf. or NaN + + // test if x is NaN + if ((x & NAN_MASK64) == NAN_MASK64) { +#ifdef SET_STATUS_FLAGS + if (((x & SNAN_MASK64) == SNAN_MASK64) // sNaN + || ((y & SNAN_MASK64) == SNAN_MASK64)) + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res = coefficient_x & QUIET_MASK64; + BID_RETURN (res); + } + // x is Infinity? + if ((x & INFINITY_MASK64) == INFINITY_MASK64) { + // check if y is Inf + if (((y & NAN_MASK64) == INFINITY_MASK64)) { + if (sign_x == (y & 0x8000000000000000ull)) { + res = coefficient_x; + BID_RETURN (res); + } + // return NaN + { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res = NAN_MASK64; + BID_RETURN (res); + } + } + // check if y is NaN + if (((y & NAN_MASK64) == NAN_MASK64)) { + res = coefficient_y & QUIET_MASK64; +#ifdef SET_STATUS_FLAGS + if (((y & SNAN_MASK64) == SNAN_MASK64)) + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (res); + } + // otherwise return +/-Inf + { + res = coefficient_x; + BID_RETURN (res); + } + } + // x is 0 + { + if (((y & INFINITY_MASK64) != INFINITY_MASK64) && coefficient_y) { + if (exponent_y <= exponent_x) { + res = y; + BID_RETURN (res); + } + } + } + + } + if (!valid_y) { + // y is Inf. or NaN? + if (((y & INFINITY_MASK64) == INFINITY_MASK64)) { +#ifdef SET_STATUS_FLAGS + if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res = coefficient_y & QUIET_MASK64; + BID_RETURN (res); + } + // y is 0 + if (!coefficient_x) { // x==0 + if (exponent_x <= exponent_y) + res = ((UINT64) exponent_x) << 53; + else + res = ((UINT64) exponent_y) << 53; + if (sign_x == sign_y) + res |= sign_x; +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rnd_mode == ROUNDING_DOWN && sign_x != sign_y) + res |= 0x8000000000000000ull; +#endif +#endif + BID_RETURN (res); + } else if (exponent_y >= exponent_x) { + res = x; + BID_RETURN (res); + } + } + // sort arguments by exponent + if (exponent_x < exponent_y) { + sign_a = sign_y; + exponent_a = exponent_y; + coefficient_a = coefficient_y; + sign_b = sign_x; + exponent_b = exponent_x; + coefficient_b = coefficient_x; + } else { + sign_a = sign_x; + exponent_a = exponent_x; + coefficient_a = coefficient_x; + sign_b = sign_y; + exponent_b = exponent_y; + coefficient_b = coefficient_y; + } + + // exponent difference + diff_dec_expon = exponent_a - exponent_b; + + /* get binary coefficients of x and y */ + + //--- get number of bits in the coefficients of x and y --- + + // version 2 (original) + tempx.d = (double) coefficient_a; + bin_expon_ca = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff; + + if (diff_dec_expon > MAX_FORMAT_DIGITS) { + // normalize a to a 16-digit coefficient + + scale_ca = estimate_decimal_digits[bin_expon_ca]; + if (coefficient_a >= power10_table_128[scale_ca].w[0]) + scale_ca++; + + scale_k = 16 - scale_ca; + + coefficient_a *= power10_table_128[scale_k].w[0]; + + diff_dec_expon -= scale_k; + exponent_a -= scale_k; + + /* get binary coefficients of x and y */ + + //--- get number of bits in the coefficients of x and y --- + tempx.d = (double) coefficient_a; + bin_expon_ca = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff; + + if (diff_dec_expon > MAX_FORMAT_DIGITS) { +#ifdef SET_STATUS_FLAGS + if (coefficient_b) { + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#endif + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (((rnd_mode) & 3) && coefficient_b) // not ROUNDING_TO_NEAREST + { + switch (rnd_mode) { + case ROUNDING_DOWN: + if (sign_b) { + coefficient_a -= ((((SINT64) sign_a) >> 63) | 1); + if (coefficient_a < 1000000000000000ull) { + exponent_a--; + coefficient_a = 9999999999999999ull; + } else if (coefficient_a >= 10000000000000000ull) { + exponent_a++; + coefficient_a = 1000000000000000ull; + } + } + break; + case ROUNDING_UP: + if (!sign_b) { + coefficient_a += ((((SINT64) sign_a) >> 63) | 1); + if (coefficient_a < 1000000000000000ull) { + exponent_a--; + coefficient_a = 9999999999999999ull; + } else if (coefficient_a >= 10000000000000000ull) { + exponent_a++; + coefficient_a = 1000000000000000ull; + } + } + break; + default: // RZ + if (sign_a != sign_b) { + coefficient_a--; + if (coefficient_a < 1000000000000000ull) { + exponent_a--; + coefficient_a = 9999999999999999ull; + } + } + break; + } + } else +#endif +#endif + // check special case here + if ((coefficient_a == 1000000000000000ull) + && (diff_dec_expon == MAX_FORMAT_DIGITS + 1) + && (sign_a ^ sign_b) + && (coefficient_b > 5000000000000000ull)) { + coefficient_a = 9999999999999999ull; + exponent_a--; + } + + res = + fast_get_BID64_check_OF (sign_a, exponent_a, coefficient_a, + rnd_mode, pfpsf); + BID_RETURN (res); + } + } + // test whether coefficient_a*10^(exponent_a-exponent_b) may exceed 2^62 + if (bin_expon_ca + estimate_bin_expon[diff_dec_expon] < 60) { + // coefficient_a*10^(exponent_a-exponent_b)<2^63 + + // multiply by 10^(exponent_a-exponent_b) + coefficient_a *= power10_table_128[diff_dec_expon].w[0]; + + // sign mask + sign_b = ((SINT64) sign_b) >> 63; + // apply sign to coeff. of b + coefficient_b = (coefficient_b + sign_b) ^ sign_b; + + // apply sign to coefficient a + sign_a = ((SINT64) sign_a) >> 63; + coefficient_a = (coefficient_a + sign_a) ^ sign_a; + + coefficient_a += coefficient_b; + // get sign + sign_s = ((SINT64) coefficient_a) >> 63; + coefficient_a = (coefficient_a + sign_s) ^ sign_s; + sign_s &= 0x8000000000000000ull; + + // coefficient_a < 10^16 ? + if (coefficient_a < power10_table_128[MAX_FORMAT_DIGITS].w[0]) { +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rnd_mode == ROUNDING_DOWN && (!coefficient_a) + && sign_a != sign_b) + sign_s = 0x8000000000000000ull; +#endif +#endif + res = very_fast_get_BID64 (sign_s, exponent_b, coefficient_a); + BID_RETURN (res); + } + // otherwise rounding is necessary + + // already know coefficient_a<10^19 + // coefficient_a < 10^17 ? + if (coefficient_a < power10_table_128[17].w[0]) + extra_digits = 1; + else if (coefficient_a < power10_table_128[18].w[0]) + extra_digits = 2; + else + extra_digits = 3; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = rnd_mode; + if (sign_s && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#else + rmode = 0; +#endif +#else + rmode = 0; +#endif + coefficient_a += round_const_table[rmode][extra_digits]; + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_64x64_to_128 (CT, coefficient_a, + reciprocals10_64[extra_digits]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 + amount = short_recip_scale[extra_digits]; + C64 = CT.w[1] >> amount; + + } else { + // coefficient_a*10^(exponent_a-exponent_b) is large + sign_s = sign_a; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = rnd_mode; + if (sign_s && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#else + rmode = 0; +#endif +#else + rmode = 0; +#endif + + // check whether we can take faster path + scale_ca = estimate_decimal_digits[bin_expon_ca]; + + sign_ab = sign_a ^ sign_b; + sign_ab = ((SINT64) sign_ab) >> 63; + + // T1 = 10^(16-diff_dec_expon) + T1 = power10_table_128[16 - diff_dec_expon].w[0]; + + // get number of digits in coefficient_a + if (coefficient_a >= power10_table_128[scale_ca].w[0]) { + scale_ca++; + } + + scale_k = 16 - scale_ca; + + // addition + saved_ca = coefficient_a - T1; + coefficient_a = + (SINT64) saved_ca *(SINT64) power10_table_128[scale_k].w[0]; + extra_digits = diff_dec_expon - scale_k; + + // apply sign + saved_cb = (coefficient_b + sign_ab) ^ sign_ab; + // add 10^16 and rounding constant + coefficient_b = + saved_cb + 10000000000000000ull + + round_const_table[rmode][extra_digits]; + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_64x64_to_128 (CT, coefficient_b, + reciprocals10_64[extra_digits]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 + amount = short_recip_scale[extra_digits]; + C0_64 = CT.w[1] >> amount; + + // result coefficient + C64 = C0_64 + coefficient_a; + // filter out difficult (corner) cases + // this test ensures the number of digits in coefficient_a does not change + // after adding (the appropriately scaled and rounded) coefficient_b + if ((UINT64) (C64 - 1000000000000000ull - 1) > + 9000000000000000ull - 2) { + if (C64 >= 10000000000000000ull) { + // result has more than 16 digits + if (!scale_k) { + // must divide coeff_a by 10 + saved_ca = saved_ca + T1; + __mul_64x64_to_128 (CA, saved_ca, 0x3333333333333334ull); + //reciprocals10_64[1]); + coefficient_a = CA.w[1] >> 1; + rem_a = + saved_ca - (coefficient_a << 3) - (coefficient_a << 1); + coefficient_a = coefficient_a - T1; + + saved_cb += rem_a * power10_table_128[diff_dec_expon].w[0]; + } else + coefficient_a = + (SINT64) (saved_ca - T1 - + (T1 << 3)) * (SINT64) power10_table_128[scale_k - + 1].w[0]; + + extra_digits++; + coefficient_b = + saved_cb + 100000000000000000ull + + round_const_table[rmode][extra_digits]; + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_64x64_to_128 (CT, coefficient_b, + reciprocals10_64[extra_digits]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 + amount = short_recip_scale[extra_digits]; + C0_64 = CT.w[1] >> amount; + + // result coefficient + C64 = C0_64 + coefficient_a; + } else if (C64 <= 1000000000000000ull) { + // less than 16 digits in result + coefficient_a = + (SINT64) saved_ca *(SINT64) power10_table_128[scale_k + + 1].w[0]; + //extra_digits --; + exponent_b--; + coefficient_b = + (saved_cb << 3) + (saved_cb << 1) + 100000000000000000ull + + round_const_table[rmode][extra_digits]; + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_64x64_to_128 (CT_new, coefficient_b, + reciprocals10_64[extra_digits]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 + amount = short_recip_scale[extra_digits]; + C0_64 = CT_new.w[1] >> amount; + + // result coefficient + C64_new = C0_64 + coefficient_a; + if (C64_new < 10000000000000000ull) { + C64 = C64_new; +#ifdef SET_STATUS_FLAGS + CT = CT_new; +#endif + } else + exponent_b++; + } + + } + + } + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == 0) //ROUNDING_TO_NEAREST +#endif + if (C64 & 1) { + // check whether fractional part of initial_P/10^extra_digits is + // exactly .5 + // this is the same as fractional part of + // (initial_P + 0.5*10^extra_digits)/10^extra_digits is exactly zero + + // get remainder + remainder_h = CT.w[1] << (64 - amount); + + // test whether fractional part is 0 + if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits])) { + C64--; + } + } +#endif + +#ifdef SET_STATUS_FLAGS + status = INEXACT_EXCEPTION; + + // get remainder + remainder_h = CT.w[1] << (64 - amount); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if ((remainder_h == 0x8000000000000000ull) + && (CT.w[0] < reciprocals10_64[extra_digits])) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits])) + status = EXACT_STATUS; + //if(!C64 && rmode==ROUNDING_DOWN) sign_s=sign_y; + break; + default: + // round up + __add_carry_out (tmp, carry, CT.w[0], + reciprocals10_64[extra_digits]); + if ((remainder_h >> (64 - amount)) + carry >= + (((UINT64) 1) << amount)) + status = EXACT_STATUS; + break; + } + __set_status_flags (pfpsf, status); + +#endif + + res = + fast_get_BID64_check_OF (sign_s, exponent_b + extra_digits, C64, + rnd_mode, pfpsf); + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_compare.c b/gcc-4.4.3/libgcc/config/libbid/bid64_compare.c new file mode 100644 index 000000000..a1118df9f --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_compare.c @@ -0,0 +1,3172 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +static const UINT64 mult_factor[16] = { + 1ull, 10ull, 100ull, 1000ull, + 10000ull, 100000ull, 1000000ull, 10000000ull, + 100000000ull, 1000000000ull, 10000000000ull, 100000000000ull, + 1000000000000ull, 10000000000000ull, + 100000000000000ull, 1000000000000000ull +}; + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_quiet_equal (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_quiet_equal (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y, exp_t; + UINT64 sig_x, sig_y, sig_t; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y, lcv; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN + } + res = 0; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equivalent. + if (x == y) { + res = 1; + BID_RETURN (res); + } + // INFINITY (CASE3) + if (((x & MASK_INF) == MASK_INF) && ((y & MASK_INF) == MASK_INF)) { + res = (((x ^ y) & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // ONE INFINITY (CASE3') + if (((x & MASK_INF) == MASK_INF) || ((y & MASK_INF) == MASK_INF)) { + res = 0; + BID_RETURN (res); + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); + } else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) { + res = 0; + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ => not equal : return 0 + if ((x ^ y) & MASK_SIGN) { + res = 0; + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + if (exp_x > exp_y) { // to simplify the loop below, + SWAP (exp_x, exp_y, exp_t); // put the larger exp in y, + SWAP (sig_x, sig_y, sig_t); // and the smaller exp in x + } + if (exp_y - exp_x > 15) { + res = 0; // difference cannot be greater than 10^15 + BID_RETURN (res); + } + for (lcv = 0; lcv < (exp_y - exp_x); lcv++) { + // recalculate y's significand upwards + sig_y = sig_y * 10; + if (sig_y > 9999999999999999ull) { + res = 0; + BID_RETURN (res); + } + } + res = (sig_y == sig_x); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_quiet_greater (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_quiet_greater (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, rather than equal : + // return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN + } + res = 0; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). + if (x == y) { + res = 0; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return 0 + if (((x & MASK_SIGN) == MASK_SIGN)) { + res = 0; + BID_RETURN (res); + } else { + // x is pos infinity, it is greater, unless y is positive + // infinity => return y!=pos_infinity + res = (((y & MASK_INF) != MASK_INF) + || ((y & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + // ZERO (CASE4) + // some properties: + //(+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + //(ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore ignore the + // exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + // if both numbers are zero, neither is greater => return NOTGREATERTHAN + if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); + } else if (x_is_zero) { + // is x is zero, it is greater if Y is negative + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } else if (y_is_zero) { + // is y is zero, X is greater if it is positive + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller, + // it is clear what needs to be done + if (sig_x > sig_y && exp_x > exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x < exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { // difference cannot be greater than 10^15 + if (x & MASK_SIGN) // if both are negative + res = 0; + else // if both are positive + res = 1; + BID_RETURN (res); + } + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + if (x & MASK_SIGN) // if both are negative + res = 1; + else // if both are positive + res = 0; + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + // if postitive, return whichever significand is larger (converse if neg.) + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 0; + BID_RETURN (res); + } + res = (((sig_n_prime.w[1] > 0) + || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 0; + BID_RETURN (res); + } + res = (((sig_n_prime.w[1] == 0) + && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_quiet_greater_equal (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_quiet_greater_equal (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered : return 1 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN + } + res = 0; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal. + if (x == y) { + res = 1; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } + if ((x & MASK_SIGN) == MASK_SIGN) { + // x is -inf, so it is less than y unless y is -inf + res = (((y & MASK_INF) == MASK_INF) + && (y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } else { // x is pos_inf, no way for it to be less than y + res = 1; + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so: + // if y is +inf, xy + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + if (x_is_zero && y_is_zero) { + // if both numbers are zero, they are equal + res = 1; + BID_RETURN (res); + } else if (x_is_zero) { + // if x is zero, it is lessthan if Y is positive + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } else if (y_is_zero) { + // if y is zero, X is less if it is negative + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is less than if y is positive + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + // difference cannot be greater than 10^15 + BID_RETURN (res); + } + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + // return 1 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 1; + BID_RETURN (res); + } + // if postitive, return whichever significand abs is smaller + // (converse if negative) + res = (((sig_n_prime.w[1] == 0) + && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 1; + BID_RETURN (res); + } + // if positive, return whichever significand abs is smaller + // (converse if negative) + res = (((sig_n_prime.w[1] > 0) + || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_quiet_greater_unordered (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_quiet_greater_unordered (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, rather than equal : + // return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN + } + res = 1; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). + if (x == y) { + res = 0; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return 0 + if (((x & MASK_SIGN) == MASK_SIGN)) { + res = 0; + BID_RETURN (res); + } else { + // x is pos infinity, it is greater, unless y is positive infinity => + // return y!=pos_infinity + res = (((y & MASK_INF) != MASK_INF) + || ((y & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + // if both numbers are zero, neither is greater => return NOTGREATERTHAN + if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); + } else if (x_is_zero) { + // is x is zero, it is greater if Y is negative + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } else if (y_is_zero) { + // is y is zero, X is greater if it is positive + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + // difference cannot be greater than 10^15 + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 0; + BID_RETURN (res); + } + res = (((sig_n_prime.w[1] > 0) + || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + // if postitive, return whichever significand is larger (converse if negative) + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 0; + BID_RETURN (res); + } + res = (((sig_n_prime.w[1] == 0) + && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_quiet_less (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_quiet_less (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered : return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN + } + res = 0; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal. + if (x == y) { + res = 0; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) } + if ((x & MASK_SIGN) == MASK_SIGN) { + // x is -inf, so it is less than y unless y is -inf + res = (((y & MASK_INF) != MASK_INF) + || (y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } else { + // x is pos_inf, no way for it to be less than y + res = 0; + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so: + // if y is +inf, xy + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + if (x_is_zero && y_is_zero) { + // if both numbers are zero, they are equal + res = 0; + BID_RETURN (res); + } else if (x_is_zero) { + // if x is zero, it is lessthan if Y is positive + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } else if (y_is_zero) { + // if y is zero, X is less if it is negative + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is less than if y is positive + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller, + // it is clear what needs to be done + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + // difference cannot be greater than 10^15 + BID_RETURN (res); + } + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 0; + BID_RETURN (res); + } + // if postitive, return whichever significand abs is smaller + // (converse if negative) + res = (((sig_n_prime.w[1] == 0) + && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 0; + BID_RETURN (res); + } + // if positive, return whichever significand abs is smaller + // (converse if negative) + res = (((sig_n_prime.w[1] > 0) + || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_quiet_less_equal (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_quiet_less_equal (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, rather than equal : + // return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN + } + res = 0; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (LESSEQUAL). + if (x == y) { + res = 1; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + if (((x & MASK_SIGN) == MASK_SIGN)) { + // if x is neg infinity, it must be lessthan or equal to y return 1 + res = 1; + BID_RETURN (res); + } else { + // x is pos infinity, it is greater, unless y is positive infinity => + // return y==pos_infinity + res = !(((y & MASK_INF) != MASK_INF) + || ((y & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 1 + // if y is negative infinity, then x is greater, return 0 + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + if (x_is_zero && y_is_zero) { + // if both numbers are zero, they are equal -> return 1 + res = 1; + BID_RETURN (res); + } else if (x_is_zero) { + // if x is zero, it is lessthan if Y is positive + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } else if (y_is_zero) { + // if y is zero, X is less if it is negative + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is less than if y is positive + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + // difference cannot be greater than 10^15 + BID_RETURN (res); + } + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + // return 1 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 1; + BID_RETURN (res); + } + // if postitive, return whichever significand abs is smaller + // (converse if negative) + res = (((sig_n_prime.w[1] == 0) + && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + // return 1 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 1; + BID_RETURN (res); + } + // if positive, return whichever significand abs is smaller + // (converse if negative) + res = (((sig_n_prime.w[1] > 0) + || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_quiet_less_unordered (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_quiet_less_unordered (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered : return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN + } + res = 1; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal. + if (x == y) { + res = 0; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) } + if ((x & MASK_SIGN) == MASK_SIGN) { + // x is -inf, so it is less than y unless y is -inf + res = (((y & MASK_INF) != MASK_INF) + || (y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } else { + // x is pos_inf, no way for it to be less than y + res = 0; + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so: + // if y is +inf, xy + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + if (x_is_zero && y_is_zero) { + // if both numbers are zero, they are equal + res = 0; + BID_RETURN (res); + } else if (x_is_zero) { + // if x is zero, it is lessthan if Y is positive + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } else if (y_is_zero) { + // if y is zero, X is less if it is negative + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is less than if y is positive + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + // difference cannot be greater than 10^15 + BID_RETURN (res); + } + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 0; + BID_RETURN (res); + } + // if postitive, return whichever significand abs is smaller + // (converse if negative) + res = (((sig_n_prime.w[1] == 0) + && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 0; + BID_RETURN (res); + } + // if positive, return whichever significand abs is smaller + // (converse if negative) + res = (((sig_n_prime.w[1] > 0) + || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_quiet_not_equal (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_quiet_not_equal (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y, exp_t; + UINT64 sig_x, sig_y, sig_t; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y, lcv; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 1 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN + } + res = 1; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equivalent. + if (x == y) { + res = 0; + BID_RETURN (res); + } + // INFINITY (CASE3) + if (((x & MASK_INF) == MASK_INF) && ((y & MASK_INF) == MASK_INF)) { + res = (((x ^ y) & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // ONE INFINITY (CASE3') + if (((x & MASK_INF) == MASK_INF) || ((y & MASK_INF) == MASK_INF)) { + res = 1; + BID_RETURN (res); + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + + if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); + } else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) { + res = 1; + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ => not equal : return 1 + if ((x ^ y) & MASK_SIGN) { + res = 1; + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + if (exp_x > exp_y) { // to simplify the loop below, + SWAP (exp_x, exp_y, exp_t); // put the larger exp in y, + SWAP (sig_x, sig_y, sig_t); // and the smaller exp in x + } + + if (exp_y - exp_x > 15) { + res = 1; + BID_RETURN (res); + } + // difference cannot be greater than 10^16 + + for (lcv = 0; lcv < (exp_y - exp_x); lcv++) { + + // recalculate y's significand upwards + sig_y = sig_y * 10; + if (sig_y > 9999999999999999ull) { + res = 1; + BID_RETURN (res); + } + } + + { + res = sig_y != sig_x; + BID_RETURN (res); + } + +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_quiet_not_greater (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_quiet_not_greater (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN + } + res = 1; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (LESSEQUAL). + if (x == y) { + res = 1; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x is neg infinity, it must be lessthan or equal to y return 1 + if (((x & MASK_SIGN) == MASK_SIGN)) { + res = 1; + BID_RETURN (res); + } + // x is pos infinity, it is greater, unless y is positive + // infinity => return y==pos_infinity + else { + res = !(((y & MASK_INF) != MASK_INF) + || ((y & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 1 + // if y is negative infinity, then x is greater, return 0 + { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither + // number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + // if both numbers are zero, they are equal -> return 1 + if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); + } + // if x is zero, it is lessthan if Y is positive + else if (x_is_zero) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if y is zero, X is less if it is negative + else if (y_is_zero) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is less than if y is positive + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // difference cannot be greater than 10^15 + + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + + // return 1 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 1; + BID_RETURN (res); + } + // if postitive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] == 0) + && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // return 1 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 1; + BID_RETURN (res); + } + // if positive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] > 0) + || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_quiet_not_less (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_quiet_not_less (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered : return 1 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN + } + res = 1; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal. + if (x == y) { + res = 1; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } + if ((x & MASK_SIGN) == MASK_SIGN) + // x is -inf, so it is less than y unless y is -inf + { + res = (((y & MASK_INF) == MASK_INF) + && (y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } else + // x is pos_inf, no way for it to be less than y + { + res = 1; + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so: + // if y is +inf, xy + { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither + // number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + // if both numbers are zero, they are equal + if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); + } + // if x is zero, it is lessthan if Y is positive + else if (x_is_zero) { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if y is zero, X is less if it is negative + else if (y_is_zero) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is less than if y is positive + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // difference cannot be greater than 10^15 + + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 1; + BID_RETURN (res); + } + // if postitive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] == 0) + && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); + } + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 1; + BID_RETURN (res); + } + // if positive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] > 0) + || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); + } +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_quiet_ordered (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_quiet_ordered (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + + // NaN (CASE1) + // if either number is NAN, the comparison is ordered, rather than equal : return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN + } + res = 0; + BID_RETURN (res); + } else { + res = 1; + BID_RETURN (res); + } +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_quiet_unordered (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_quiet_unordered (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN + } + res = 1; + BID_RETURN (res); + } else { + res = 0; + BID_RETURN (res); + } +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_signaling_greater (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_signaling_greater (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN + res = 0; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). + if (x == y) { + res = 0; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return 0 + if (((x & MASK_SIGN) == MASK_SIGN)) { + res = 0; + BID_RETURN (res); + } + // x is pos infinity, it is greater, + // unless y is positive infinity => return y!=pos_infinity + else { + res = (((y & MASK_INF) != MASK_INF) + || ((y & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + // if both numbers are zero, neither is greater => return NOTGREATERTHAN + if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); + } + // is x is zero, it is greater if Y is negative + else if (x_is_zero) { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // is y is zero, X is greater if it is positive + else if (y_is_zero) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // difference cannot be greater than 10^15 + + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 0; + BID_RETURN (res); + } + + { + res = (((sig_n_prime.w[1] > 0) + || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 0; + BID_RETURN (res); + } + { + res = (((sig_n_prime.w[1] == 0) + && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_signaling_greater_equal (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_signaling_greater_equal (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered : return 1 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN + res = 0; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal. + if (x == y) { + res = 1; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } + if ((x & MASK_SIGN) == MASK_SIGN) + // x is -inf, so it is less than y unless y is -inf + { + res = (((y & MASK_INF) == MASK_INF) + && (y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } else + // x is pos_inf, no way for it to be less than y + { + res = 1; + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so: + // if y is +inf, xy + { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + // if both numbers are zero, they are equal + if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); + } + // if x is zero, it is lessthan if Y is positive + else if (x_is_zero) { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if y is zero, X is less if it is negative + else if (y_is_zero) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is less than if y is positive + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // difference cannot be greater than 10^15 + + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + + // return 1 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 1; + BID_RETURN (res); + } + // if postitive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] == 0) + && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); + } + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 1; + BID_RETURN (res); + } + // if positive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] > 0) + || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); + } +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_signaling_greater_unordered (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_signaling_greater_unordered (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN + res = 1; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). + if (x == y) { + res = 0; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return 0 + if (((x & MASK_SIGN) == MASK_SIGN)) { + res = 0; + BID_RETURN (res); + } + // x is pos infinity, it is greater, + // unless y is positive infinity => return y!=pos_infinity + else { + res = (((y & MASK_INF) != MASK_INF) + || ((y & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 0 + // if y is negative infinity, then x is greater, return 1 + { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + // if both numbers are zero, neither is greater => return NOTGREATERTHAN + if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); + } + // is x is zero, it is greater if Y is negative + else if (x_is_zero) { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // is y is zero, X is greater if it is positive + else if (y_is_zero) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // difference cannot be greater than 10^15 + + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 0; + BID_RETURN (res); + } + + { + res = (((sig_n_prime.w[1] > 0) + || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 0; + BID_RETURN (res); + } + { + res = (((sig_n_prime.w[1] == 0) + && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_signaling_less (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_signaling_less (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered : return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN + res = 0; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal. + if (x == y) { + res = 0; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) } + if ((x & MASK_SIGN) == MASK_SIGN) + // x is -inf, so it is less than y unless y is -inf + { + res = (((y & MASK_INF) != MASK_INF) + || (y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } else + // x is pos_inf, no way for it to be less than y + { + res = 0; + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so: + // if y is +inf, xy + { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + // if both numbers are zero, they are equal + if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); + } + // if x is zero, it is lessthan if Y is positive + else if (x_is_zero) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if y is zero, X is less if it is negative + else if (y_is_zero) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is less than if y is positive + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // difference cannot be greater than 10^15 + + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 0; + BID_RETURN (res); + } + // if postitive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] == 0) + && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 0; + BID_RETURN (res); + } + // if positive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] > 0) + || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_signaling_less_equal (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_signaling_less_equal (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN + res = 0; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (LESSEQUAL). + if (x == y) { + res = 1; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x is neg infinity, it must be lessthan or equal to y return 1 + if (((x & MASK_SIGN) == MASK_SIGN)) { + res = 1; + BID_RETURN (res); + } + // x is pos infinity, it is greater, + // unless y is positive infinity => return y==pos_infinity + else { + res = !(((y & MASK_INF) != MASK_INF) + || ((y & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 1 + // if y is negative infinity, then x is greater, return 0 + { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + // if both numbers are zero, they are equal -> return 1 + if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); + } + // if x is zero, it is lessthan if Y is positive + else if (x_is_zero) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if y is zero, X is less if it is negative + else if (y_is_zero) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is less than if y is positive + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // difference cannot be greater than 10^15 + + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + + // return 1 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 1; + BID_RETURN (res); + } + // if postitive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] == 0) + && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // return 1 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 1; + BID_RETURN (res); + } + // if positive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] > 0) + || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_signaling_less_unordered (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_signaling_less_unordered (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered : return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN + res = 1; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal. + if (x == y) { + res = 0; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) } + if ((x & MASK_SIGN) == MASK_SIGN) + // x is -inf, so it is less than y unless y is -inf + { + res = (((y & MASK_INF) != MASK_INF) + || (y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } else + // x is pos_inf, no way for it to be less than y + { + res = 0; + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so: + // if y is +inf, xy + { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + // if both numbers are zero, they are equal + if (x_is_zero && y_is_zero) { + res = 0; + BID_RETURN (res); + } + // if x is zero, it is lessthan if Y is positive + else if (x_is_zero) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if y is zero, X is less if it is negative + else if (y_is_zero) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is less than if y is positive + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // difference cannot be greater than 10^15 + + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 0; + BID_RETURN (res); + } + // if postitive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] == 0) + && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 0; + BID_RETURN (res); + } + // if positive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] > 0) + || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_signaling_not_greater (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_signaling_not_greater (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered, + // rather than equal : return 0 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN + res = 1; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (LESSEQUAL). + if (x == y) { + res = 1; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x is neg infinity, it must be lessthan or equal to y return 1 + if (((x & MASK_SIGN) == MASK_SIGN)) { + res = 1; + BID_RETURN (res); + } + // x is pos infinity, it is greater, + // unless y is positive infinity => return y==pos_infinity + else { + res = !(((y & MASK_INF) != MASK_INF) + || ((y & MASK_SIGN) == MASK_SIGN)); + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return 1 + // if y is negative infinity, then x is greater, return 0 + { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + // if both numbers are zero, they are equal -> return 1 + if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); + } + // if x is zero, it is lessthan if Y is positive + else if (x_is_zero) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if y is zero, X is less if it is negative + else if (y_is_zero) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is less than if y is positive + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // difference cannot be greater than 10^15 + + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + + // return 1 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 1; + BID_RETURN (res); + } + // if postitive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] == 0) + && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // return 1 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 1; + BID_RETURN (res); + } + // if positive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] > 0) + || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)); + BID_RETURN (res); + } +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_signaling_not_less (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_signaling_not_less (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; + + // NaN (CASE1) + // if either number is NAN, the comparison is unordered : return 1 + if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { + *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN + res = 1; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal. + if (x == y) { + res = 1; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } + if ((x & MASK_SIGN) == MASK_SIGN) + // x is -inf, so it is less than y unless y is -inf + { + res = (((y & MASK_INF) == MASK_INF) + && (y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } else + // x is pos_inf, no way for it to be less than y + { + res = 1; + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so: + // if y is +inf, xy + { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull) { + non_canon_x = 1; + } else { + non_canon_x = 0; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + non_canon_x = 0; + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull) { + non_canon_y = 1; + } else { + non_canon_y = 0; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + non_canon_y = 0; + } + + // ZERO (CASE4) + // some properties: + // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // therefore ignore the exponent field + // (Any non-canonical # is considered 0) + if (non_canon_x || sig_x == 0) { + x_is_zero = 1; + } + if (non_canon_y || sig_y == 0) { + y_is_zero = 1; + } + // if both numbers are zero, they are equal + if (x_is_zero && y_is_zero) { + res = 1; + BID_RETURN (res); + } + // if x is zero, it is lessthan if Y is positive + else if (x_is_zero) { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if y is zero, X is less if it is negative + else if (y_is_zero) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is less than if y is positive + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // difference cannot be greater than 10^15 + + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = 1; + BID_RETURN (res); + } + // if postitive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] == 0) + && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); + } + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // return 0 if values are equal + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = 1; + BID_RETURN (res); + } + // if positive, return whichever significand abs is smaller + // (converse if negative) + { + res = (((sig_n_prime.w[1] > 0) + || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) != + MASK_SIGN)); + BID_RETURN (res); + } +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_div.c b/gcc-4.4.3/libgcc/config/libbid/bid64_div.c new file mode 100644 index 000000000..089bc7129 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_div.c @@ -0,0 +1,1795 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +/***************************************************************************** + * BID64 divide + ***************************************************************************** + * + * Algorithm description: + * + * if(coefficient_x=B, 1 otherwise + * Q = 0 + * else + * get Q=(int)(coefficient_x/coefficient_y) + * (based on double precision divide) + * check for exact divide case + * Let R = coefficient_x - Q*coefficient_y + * Let m=16-number_digits(Q) + * CA=R*10^m, Q=Q*10^m + * B = coefficient_y + * endif + * if (CA<2^64) + * Q += CA/B (64-bit unsigned divide) + * else + * get final Q using double precision divide, followed by 3 integer + * iterations + * if exact result, eliminate trailing zeros + * check for underflow + * round coefficient to nearest + * + ****************************************************************************/ + +#include "bid_internal.h" +#include "bid_div_macros.h" +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +#include + +#define FE_ALL_FLAGS FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT +#endif + +extern UINT32 convert_table[5][128][2]; +extern SINT8 factors[][2]; +extern UINT8 packed_10000_zeros[]; + + +#if DECIMAL_CALL_BY_REFERENCE + +void +bid64_div (UINT64 * pres, UINT64 * px, + UINT64 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x, y; +#else + +UINT64 +bid64_div (UINT64 x, + UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 CA, CT; + UINT64 sign_x, sign_y, coefficient_x, coefficient_y, A, B, QX, PD; + UINT64 A2, Q, Q2, B2, B4, B5, R, T, DU, res; + UINT64 valid_x, valid_y; + SINT64 D; + int_double t_scale, tempq, temp_b; + int_float tempx, tempy; + double da, db, dq, da_h, da_l; + int exponent_x, exponent_y, bin_expon_cx; + int diff_expon, ed1, ed2, bin_index; + int rmode, amount; + int nzeros, i, j, k, d5; + UINT32 QX32, tdigit[3], digit, digit_h, digit_low; +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + fexcept_t binaryflags = 0; +#endif + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif + x = *px; + y = *py; +#endif + + valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x); + valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y); + + // unpack arguments, check for NaN or Infinity + if (!valid_x) { + // x is Inf. or NaN +#ifdef SET_STATUS_FLAGS + if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + + // test if x is NaN + if ((x & NAN_MASK64) == NAN_MASK64) { +#ifdef SET_STATUS_FLAGS + if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (coefficient_x & QUIET_MASK64); + } + // x is Infinity? + if ((x & INFINITY_MASK64) == INFINITY_MASK64) { + // check if y is Inf or NaN + if ((y & INFINITY_MASK64) == INFINITY_MASK64) { + // y==Inf, return NaN + if ((y & NAN_MASK64) == INFINITY_MASK64) { // Inf/Inf +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (NAN_MASK64); + } + } else { + // otherwise return +/-Inf + BID_RETURN (((x ^ y) & 0x8000000000000000ull) | + INFINITY_MASK64); + } + } + // x==0 + if (((y & INFINITY_MASK64) != INFINITY_MASK64) + && !(coefficient_y)) { + // y==0 , return NaN +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (NAN_MASK64); + } + if (((y & INFINITY_MASK64) != INFINITY_MASK64)) { + if ((y & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64) + exponent_y = ((UINT32) (y >> 51)) & 0x3ff; + else + exponent_y = ((UINT32) (y >> 53)) & 0x3ff; + sign_y = y & 0x8000000000000000ull; + + exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; + if (exponent_x > DECIMAL_MAX_EXPON_64) + exponent_x = DECIMAL_MAX_EXPON_64; + else if (exponent_x < 0) + exponent_x = 0; + BID_RETURN ((sign_x ^ sign_y) | (((UINT64) exponent_x) << 53)); + } + + } + if (!valid_y) { + // y is Inf. or NaN + + // test if y is NaN + if ((y & NAN_MASK64) == NAN_MASK64) { +#ifdef SET_STATUS_FLAGS + if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (coefficient_y & QUIET_MASK64); + } + // y is Infinity? + if ((y & INFINITY_MASK64) == INFINITY_MASK64) { + // return +/-0 + BID_RETURN (((x ^ y) & 0x8000000000000000ull)); + } + // y is 0 +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); +#endif + BID_RETURN ((sign_x ^ sign_y) | INFINITY_MASK64); + } +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; + + if (coefficient_x < coefficient_y) { + // get number of decimal digits for c_x, c_y + + //--- get number of bits in the coefficients of x and y --- + tempx.d = (float) coefficient_x; + tempy.d = (float) coefficient_y; + bin_index = (tempy.i - tempx.i) >> 23; + + A = coefficient_x * power10_index_binexp[bin_index]; + B = coefficient_y; + + temp_b.d = (double) B; + + // compare A, B + DU = (A - B) >> 63; + ed1 = 15 + (int) DU; + ed2 = estimate_decimal_digits[bin_index] + ed1; + T = power10_table_128[ed1].w[0]; + __mul_64x64_to_128 (CA, A, T); + + Q = 0; + diff_expon = diff_expon - ed2; + + // adjust double precision db, to ensure that later A/B - (int)(da/db) > -1 + if (coefficient_y < 0x0020000000000000ull) { + temp_b.i += 1; + db = temp_b.d; + } else + db = (double) (B + 2 + (B & 1)); + + } else { + // get c_x/c_y + + // set last bit before conversion to DP + A2 = coefficient_x | 1; + da = (double) A2; + + db = (double) coefficient_y; + + tempq.d = da / db; + Q = (UINT64) tempq.d; + + R = coefficient_x - coefficient_y * Q; + + // will use to get number of dec. digits of Q + bin_expon_cx = (tempq.i >> 52) - 0x3ff; + + // R<0 ? + D = ((SINT64) R) >> 63; + Q += D; + R += (coefficient_y & D); + + // exact result ? + if (((SINT64) R) <= 0) { + // can have R==-1 for coeff_y==1 + res = + get_BID64 (sign_x ^ sign_y, diff_expon, (Q + R), rnd_mode, + pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + // get decimal digits of Q + DU = power10_index_binexp[bin_expon_cx] - Q - 1; + DU >>= 63; + + ed2 = 16 - estimate_decimal_digits[bin_expon_cx] - (int) DU; + + T = power10_table_128[ed2].w[0]; + __mul_64x64_to_128 (CA, R, T); + B = coefficient_y; + + Q *= power10_table_128[ed2].w[0]; + diff_expon -= ed2; + + } + + if (!CA.w[1]) { + Q2 = CA.w[0] / B; + B2 = B + B; + B4 = B2 + B2; + R = CA.w[0] - Q2 * B; + Q += Q2; + } else { + + // 2^64 + t_scale.i = 0x43f0000000000000ull; + // convert CA to DP + da_h = CA.w[1]; + da_l = CA.w[0]; + da = da_h * t_scale.d + da_l; + + // quotient + dq = da / db; + Q2 = (UINT64) dq; + + // get w[0] remainder + R = CA.w[0] - Q2 * B; + + // R<0 ? + D = ((SINT64) R) >> 63; + Q2 += D; + R += (B & D); + + // now R<6*B + + // quick divide + + // 4*B + B2 = B + B; + B4 = B2 + B2; + + R = R - B4; + // R<0 ? + D = ((SINT64) R) >> 63; + // restore R if negative + R += (B4 & D); + Q2 += ((~D) & 4); + + R = R - B2; + // R<0 ? + D = ((SINT64) R) >> 63; + // restore R if negative + R += (B2 & D); + Q2 += ((~D) & 2); + + R = R - B; + // R<0 ? + D = ((SINT64) R) >> 63; + // restore R if negative + R += (B & D); + Q2 += ((~D) & 1); + + Q += Q2; + } + +#ifdef SET_STATUS_FLAGS + if (R) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#ifndef LEAVE_TRAILING_ZEROS + else +#endif +#else +#ifndef LEAVE_TRAILING_ZEROS + if (!R) +#endif +#endif +#ifndef LEAVE_TRAILING_ZEROS + { + // eliminate trailing zeros + + // check whether CX, CY are short + if ((coefficient_x <= 1024) && (coefficient_y <= 1024)) { + i = (int) coefficient_y - 1; + j = (int) coefficient_x - 1; + // difference in powers of 2 factors for Y and X + nzeros = ed2 - factors[i][0] + factors[j][0]; + // difference in powers of 5 factors + d5 = ed2 - factors[i][1] + factors[j][1]; + if (d5 < nzeros) + nzeros = d5; + + __mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 + amount = short_recip_scale[nzeros]; + Q = CT.w[1] >> amount; + + diff_expon += nzeros; + } else { + tdigit[0] = Q & 0x3ffffff; + tdigit[1] = 0; + QX = Q >> 26; + QX32 = QX; + nzeros = 0; + + for (j = 0; QX32; j++, QX32 >>= 7) { + k = (QX32 & 127); + tdigit[0] += convert_table[j][k][0]; + tdigit[1] += convert_table[j][k][1]; + if (tdigit[0] >= 100000000) { + tdigit[0] -= 100000000; + tdigit[1]++; + } + } + + digit = tdigit[0]; + if (!digit && !tdigit[1]) + nzeros += 16; + else { + if (!digit) { + nzeros += 8; + digit = tdigit[1]; + } + // decompose digit + PD = (UINT64) digit *0x068DB8BBull; + digit_h = (UINT32) (PD >> 40); + digit_low = digit - digit_h * 10000; + + if (!digit_low) + nzeros += 4; + else + digit_h = digit_low; + + if (!(digit_h & 1)) + nzeros += + 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> + (digit_h & 7)); + } + + if (nzeros) { + __mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 + amount = short_recip_scale[nzeros]; + Q = CT.w[1] >> amount; + } + diff_expon += nzeros; + + } + if (diff_expon >= 0) { + res = + fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q, + rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + } +#endif + + if (diff_expon >= 0) { +#ifdef IEEE_ROUND_NEAREST + // round to nearest code + // R*10 + R += R; + R = (R << 2) + R; + B5 = B4 + B; + + // compare 10*R to 5*B + R = B5 - R; + // correction for (R==0 && (Q&1)) + R -= (Q & 1); + // R<0 ? + D = ((UINT64) R) >> 63; + Q += D; +#else +#ifdef IEEE_ROUND_NEAREST_TIES_AWAY + // round to nearest code + // R*10 + R += R; + R = (R << 2) + R; + B5 = B4 + B; + + // compare 10*R to 5*B + R = B5 - R; + // correction for (R==0 && (Q&1)) + R -= (Q & 1); + // R<0 ? + D = ((UINT64) R) >> 63; + Q += D; +#else + rmode = rnd_mode; + if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + switch (rmode) { + case 0: // round to nearest code + case ROUNDING_TIES_AWAY: + // R*10 + R += R; + R = (R << 2) + R; + B5 = B4 + B; + // compare 10*R to 5*B + R = B5 - R; + // correction for (R==0 && (Q&1)) + R -= ((Q | (rmode >> 2)) & 1); + // R<0 ? + D = ((UINT64) R) >> 63; + Q += D; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + break; + default: // rounding up + Q++; + break; + } +#endif +#endif + + res = + fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q, rnd_mode, + pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } else { + // UF occurs + +#ifdef SET_STATUS_FLAGS + if ((diff_expon + 16 < 0)) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#endif + rmode = rnd_mode; + res = + get_BID64_UF (sign_x ^ sign_y, diff_expon, Q, R, rmode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + + } +} + + + +TYPE0_FUNCTION_ARGTYPE1_ARG128 (UINT64, bid64dq_div, UINT64, x, y) + UINT256 CA4 = + { {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256; +UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp; +UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res; +int_float fx, fy, f64; +UINT32 QX32, tdigit[3], digit, digit_h, digit_low; +int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, + digits_q, amount; +int nzeros, i, j, k, d5, done = 0; +unsigned rmode; +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +fexcept_t binaryflags = 0; +#endif + +valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y); + + // unpack arguments, check for NaN or Infinity +CX.w[1] = 0; +if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], (x))) { +#ifdef SET_STATUS_FLAGS + if (((y.w[1] & SNAN_MASK64) == SNAN_MASK64) || // y is sNaN + ((x & SNAN_MASK64) == SNAN_MASK64)) + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // test if x is NaN + if (((x) & 0x7c00000000000000ull) == 0x7c00000000000000ull) { + res = CX.w[0]; + BID_RETURN (res & QUIET_MASK64); + } + // x is Infinity? + if (((x) & 0x7800000000000000ull) == 0x7800000000000000ull) { + // check if y is Inf. + if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull)) + // return NaN + { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res = 0x7c00000000000000ull; + BID_RETURN (res); + } + if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { + // otherwise return +/-Inf + res = + (((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; + BID_RETURN (res); + } + } + // x is 0 + if ((y.w[1] & INFINITY_MASK64) != INFINITY_MASK64) { + if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // x=y=0, return NaN + res = 0x7c00000000000000ull; + BID_RETURN (res); + } + // return 0 + res = ((x) ^ y.w[1]) & 0x8000000000000000ull; + exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128; + if (exponent_x > DECIMAL_MAX_EXPON_64) + exponent_x = DECIMAL_MAX_EXPON_64; + else if (exponent_x < 0) + exponent_x = 0; + res |= (((UINT64) exponent_x) << 53); + BID_RETURN (res); + } +} +exponent_x += (DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS); +if (!valid_y) { + // y is Inf. or NaN + + // test if y is NaN + if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull); + Tmp.w[0] = CY.w[0]; + TP128 = reciprocals10_128[18]; + __mul_128x128_full (Qh, Ql, Tmp, TP128); + amount = recip_scale[18]; + __shr_128 (Tmp, Qh, amount); + res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; + BID_RETURN (res); + } + // y is Infinity? + if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { + // return +/-0 + res = sign_x ^ sign_y; + BID_RETURN (res); + } + // y is 0, return +/-Inf + res = + (((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); +#endif + BID_RETURN (res); +} +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; + +if (__unsigned_compare_gt_128 (CY, CX)) { + // CX < CY + + // 2^64 + f64.i = 0x5f800000; + + // fx ~ CX, fy ~ CY + fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; + fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; + // expon_cy - expon_cx + bin_index = (fy.i - fx.i) >> 23; + + if (CX.w[1]) { + T = power10_index_binexp_128[bin_index].w[0]; + __mul_64x128_short (CA, T, CX); + } else { + T128 = power10_index_binexp_128[bin_index]; + __mul_64x128_short (CA, CX.w[0], T128); + } + + ed2 = 15; + if (__unsigned_compare_gt_128 (CY, CA)) + ed2++; + + T128 = power10_table_128[ed2]; + __mul_128x128_to_256 (CA4, CA, T128); + + ed2 += estimate_decimal_digits[bin_index]; + CQ.w[0] = CQ.w[1] = 0; + diff_expon = diff_expon - ed2; + +} else { + // get CQ = CX/CY + __div_128_by_128 (&CQ, &CR, CX, CY); + + // get number of decimal digits in CQ + // 2^64 + f64.i = 0x5f800000; + fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; + // binary expon. of CQ + bin_expon = (fx.i - 0x3f800000) >> 23; + + digits_q = estimate_decimal_digits[bin_expon]; + TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; + TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; + if (__unsigned_compare_ge_128 (CQ, TP128)) + digits_q++; + + if (digits_q <= 16) { + if (!CR.w[1] && !CR.w[0]) { + res = get_BID64 (sign_x ^ sign_y, diff_expon, + CQ.w[0], rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + + ed2 = 16 - digits_q; + T128.w[0] = power10_table_128[ed2].w[0]; + __mul_64x128_to_192 (CA4, (T128.w[0]), CR); + diff_expon = diff_expon - ed2; + CQ.w[0] *= T128.w[0]; + } else { + ed2 = digits_q - 16; + diff_expon += ed2; + T128 = reciprocals10_128[ed2]; + __mul_128x128_to_256 (P256, CQ, T128); + amount = recip_scale[ed2]; + CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount)); + CQ.w[1] = 0; + + __mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0])); + + __mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]); + QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0]; + + CA4.w[1] = CX.w[1] - QB256.w[1]; + CA4.w[0] = CX.w[0] - QB256.w[0]; + if (CX.w[0] < QB256.w[0]) + CA4.w[1]--; + if (CR.w[0] || CR.w[1]) + CA4.w[0] |= 1; + done = 1; + + } + +} +if (!done) { + __div_256_by_128 (&CQ, &CA4, CY); +} + + + +#ifdef SET_STATUS_FLAGS + if (CA4.w[0] || CA4.w[1]) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#ifndef LEAVE_TRAILING_ZEROS + else +#endif +#else +#ifndef LEAVE_TRAILING_ZEROS + if (!CA4.w[0] && !CA4.w[1]) +#endif +#endif +#ifndef LEAVE_TRAILING_ZEROS + // check whether result is exact + { + // check whether CX, CY are short + if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { + i = (int) CY.w[0] - 1; + j = (int) CX.w[0] - 1; + // difference in powers of 2 factors for Y and X + nzeros = ed2 - factors[i][0] + factors[j][0]; + // difference in powers of 5 factors + d5 = ed2 - factors[i][1] + factors[j][1]; + if (d5 < nzeros) + nzeros = d5; + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128_long (CQ, Qh, amount); + + diff_expon += nzeros; + } else { + // decompose Q as Qh*10^17 + Ql + Q_low = CQ.w[0]; + + { + tdigit[0] = Q_low & 0x3ffffff; + tdigit[1] = 0; + QX = Q_low >> 26; + QX32 = QX; + nzeros = 0; + + for (j = 0; QX32; j++, QX32 >>= 7) { + k = (QX32 & 127); + tdigit[0] += convert_table[j][k][0]; + tdigit[1] += convert_table[j][k][1]; + if (tdigit[0] >= 100000000) { + tdigit[0] -= 100000000; + tdigit[1]++; + } + } + + if (tdigit[1] >= 100000000) { + tdigit[1] -= 100000000; + if (tdigit[1] >= 100000000) + tdigit[1] -= 100000000; + } + + digit = tdigit[0]; + if (!digit && !tdigit[1]) + nzeros += 16; + else { + if (!digit) { + nzeros += 8; + digit = tdigit[1]; + } + // decompose digit + PD = (UINT64) digit *0x068DB8BBull; + digit_h = (UINT32) (PD >> 40); + digit_low = digit - digit_h * 10000; + + if (!digit_low) + nzeros += 4; + else + digit_h = digit_low; + + if (!(digit_h & 1)) + nzeros += + 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> + (digit_h & 7)); + } + + if (nzeros) { + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128 (CQ, Qh, amount); + } + diff_expon += nzeros; + + } + } + if(diff_expon>=0){ + res = + fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], + rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + } +#endif + + if (diff_expon >= 0) { +#ifdef IEEE_ROUND_NEAREST + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + + CQ.w[0] += carry64; +#else +#ifdef IEEE_ROUND_NEAREST_TIES_AWAY + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; +#else + rmode = rnd_mode; + if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + switch (rmode) { + case ROUNDING_TO_NEAREST: // round to nearest code + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_TIES_AWAY: + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + break; + default: // rounding up + CQ.w[0]++; + if (!CQ.w[0]) + CQ.w[1]++; + break; + } +#endif +#endif + + res = + fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, + pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } else { + // UF occurs + +#ifdef SET_STATUS_FLAGS + if ((diff_expon + 16 < 0)) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#endif + rmode = rnd_mode; + res = + get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + + } + +} + + +//#define LEAVE_TRAILING_ZEROS + +TYPE0_FUNCTION_ARG128_ARGTYPE2 (UINT64, bid64qd_div, x, UINT64, y) + + UINT256 CA4 = + { {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256; +UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp; +UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, PD, res, valid_y; +int_float fx, fy, f64; +UINT32 QX32, tdigit[3], digit, digit_h, digit_low; +int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, + digits_q, amount; +int nzeros, i, j, k, d5, done = 0; +unsigned rmode; +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +fexcept_t binaryflags = 0; +#endif + +valid_y = unpack_BID64 (&sign_y, &exponent_y, &CY.w[0], (y)); + + // unpack arguments, check for NaN or Infinity +if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { + // test if x is NaN + if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN + (y & 0x7e00000000000000ull) == 0x7e00000000000000ull) + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull); + Tmp.w[0] = CX.w[0]; + TP128 = reciprocals10_128[18]; + __mul_128x128_full (Qh, Ql, Tmp, TP128); + amount = recip_scale[18]; + __shr_128 (Tmp, Qh, amount); + res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; + BID_RETURN (res); + } + // x is Infinity? + if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { + // check if y is Inf. + if (((y & 0x7c00000000000000ull) == 0x7800000000000000ull)) + // return NaN + { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res = 0x7c00000000000000ull; + BID_RETURN (res); + } + if (((y & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { + // otherwise return +/-Inf + res = + ((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull; + BID_RETURN (res); + } + } + // x is 0 + if (((y & INFINITY_MASK64) != INFINITY_MASK64) && + !(CY.w[0])) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // x=y=0, return NaN + res = 0x7c00000000000000ull; + BID_RETURN (res); + } + // return 0 + if (((y & 0x7800000000000000ull) != 0x7800000000000000ull)) { + if (!CY.w[0]) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res = 0x7c00000000000000ull; + BID_RETURN (res); + } + exponent_x = + exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 + + (DECIMAL_EXPONENT_BIAS << 1); + if (exponent_x > DECIMAL_MAX_EXPON_64) + exponent_x = DECIMAL_MAX_EXPON_64; + else if (exponent_x < 0) + exponent_x = 0; + res = (sign_x ^ sign_y) | (((UINT64) exponent_x) << 53); + BID_RETURN (res); + } +} +CY.w[1] = 0; +if (!valid_y) { + // y is Inf. or NaN + + // test if y is NaN + if ((y & NAN_MASK64) == NAN_MASK64) { +#ifdef SET_STATUS_FLAGS + if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (CY.w[0] & QUIET_MASK64); + } + // y is Infinity? + if (((y) & 0x7800000000000000ull) == 0x7800000000000000ull) { + // return +/-0 + res = sign_x ^ sign_y; + BID_RETURN (res); + } + // y is 0, return +/-Inf + res = + ((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); +#endif + BID_RETURN (res); +} +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +diff_expon = + exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 + + (DECIMAL_EXPONENT_BIAS << 1); + +if (__unsigned_compare_gt_128 (CY, CX)) { + // CX < CY + + // 2^64 + f64.i = 0x5f800000; + + // fx ~ CX, fy ~ CY + fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; + fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; + // expon_cy - expon_cx + bin_index = (fy.i - fx.i) >> 23; + + if (CX.w[1]) { + T = power10_index_binexp_128[bin_index].w[0]; + __mul_64x128_short (CA, T, CX); + } else { + T128 = power10_index_binexp_128[bin_index]; + __mul_64x128_short (CA, CX.w[0], T128); + } + + ed2 = 15; + if (__unsigned_compare_gt_128 (CY, CA)) + ed2++; + + T128 = power10_table_128[ed2]; + __mul_128x128_to_256 (CA4, CA, T128); + + ed2 += estimate_decimal_digits[bin_index]; + CQ.w[0] = CQ.w[1] = 0; + diff_expon = diff_expon - ed2; + +} else { + // get CQ = CX/CY + __div_128_by_128 (&CQ, &CR, CX, CY); + + // get number of decimal digits in CQ + // 2^64 + f64.i = 0x5f800000; + fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; + // binary expon. of CQ + bin_expon = (fx.i - 0x3f800000) >> 23; + + digits_q = estimate_decimal_digits[bin_expon]; + TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; + TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; + if (__unsigned_compare_ge_128 (CQ, TP128)) + digits_q++; + + if (digits_q <= 16) { + if (!CR.w[1] && !CR.w[0]) { + res = get_BID64 (sign_x ^ sign_y, diff_expon, + CQ.w[0], rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + + ed2 = 16 - digits_q; + T128.w[0] = power10_table_128[ed2].w[0]; + __mul_64x128_to_192 (CA4, (T128.w[0]), CR); + diff_expon = diff_expon - ed2; + CQ.w[0] *= T128.w[0]; + } else { + ed2 = digits_q - 16; + diff_expon += ed2; + T128 = reciprocals10_128[ed2]; + __mul_128x128_to_256 (P256, CQ, T128); + amount = recip_scale[ed2]; + CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount)); + CQ.w[1] = 0; + + __mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0])); + + __mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]); + QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0]; + + CA4.w[1] = CX.w[1] - QB256.w[1]; + CA4.w[0] = CX.w[0] - QB256.w[0]; + if (CX.w[0] < QB256.w[0]) + CA4.w[1]--; + if (CR.w[0] || CR.w[1]) + CA4.w[0] |= 1; + done = 1; + if(CA4.w[1]|CA4.w[0]) { + __mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY); + } + + } + +} + +if (!done) { + __div_256_by_128 (&CQ, &CA4, CY); +} + +#ifdef SET_STATUS_FLAGS + if (CA4.w[0] || CA4.w[1]) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#ifndef LEAVE_TRAILING_ZEROS + else +#endif +#else +#ifndef LEAVE_TRAILING_ZEROS + if (!CA4.w[0] && !CA4.w[1]) +#endif +#endif +#ifndef LEAVE_TRAILING_ZEROS + // check whether result is exact + { + if(!done) { + // check whether CX, CY are short + if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { + i = (int) CY.w[0] - 1; + j = (int) CX.w[0] - 1; + // difference in powers of 2 factors for Y and X + nzeros = ed2 - factors[i][0] + factors[j][0]; + // difference in powers of 5 factors + d5 = ed2 - factors[i][1] + factors[j][1]; + if (d5 < nzeros) + nzeros = d5; + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + //__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2]; + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128_long (CQ, Qh, amount); + + diff_expon += nzeros; + } else { + // decompose Q as Qh*10^17 + Ql + //T128 = reciprocals10_128[17]; + Q_low = CQ.w[0]; + + { + tdigit[0] = Q_low & 0x3ffffff; + tdigit[1] = 0; + QX = Q_low >> 26; + QX32 = QX; + nzeros = 0; + + for (j = 0; QX32; j++, QX32 >>= 7) { + k = (QX32 & 127); + tdigit[0] += convert_table[j][k][0]; + tdigit[1] += convert_table[j][k][1]; + if (tdigit[0] >= 100000000) { + tdigit[0] -= 100000000; + tdigit[1]++; + } + } + + if (tdigit[1] >= 100000000) { + tdigit[1] -= 100000000; + if (tdigit[1] >= 100000000) + tdigit[1] -= 100000000; + } + + digit = tdigit[0]; + if (!digit && !tdigit[1]) + nzeros += 16; + else { + if (!digit) { + nzeros += 8; + digit = tdigit[1]; + } + // decompose digit + PD = (UINT64) digit *0x068DB8BBull; + digit_h = (UINT32) (PD >> 40); + digit_low = digit - digit_h * 10000; + + if (!digit_low) + nzeros += 4; + else + digit_h = digit_low; + + if (!(digit_h & 1)) + nzeros += + 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> + (digit_h & 7)); + } + + if (nzeros) { + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128 (CQ, Qh, amount); + } + diff_expon += nzeros; + + } + } + } + if(diff_expon>=0){ + res = + fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], + rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + } +#endif + + if (diff_expon >= 0) { +#ifdef IEEE_ROUND_NEAREST + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + + CQ.w[0] += carry64; + //if(CQ.w[0]> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; +#else + rmode = rnd_mode; + if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + switch (rmode) { + case ROUNDING_TO_NEAREST: // round to nearest code + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_TIES_AWAY: + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + break; + default: // rounding up + CQ.w[0]++; + if (!CQ.w[0]) + CQ.w[1]++; + break; + } +#endif +#endif + + + res = + fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, + pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } else { + // UF occurs + +#ifdef SET_STATUS_FLAGS + if ((diff_expon + 16 < 0)) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#endif + rmode = rnd_mode; + res = + get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + + } + +} + +//#define LEAVE_TRAILING_ZEROS + +extern UINT32 convert_table[5][128][2]; +extern SINT8 factors[][2]; +extern UINT8 packed_10000_zeros[]; + + +//UINT64* bid64_div128x128(UINT64 res, UINT128 *px, UINT128 *py, unsigned rnd_mode, unsigned *pfpsf) + +TYPE0_FUNCTION_ARG128_ARG128 (UINT64, bid64qq_div, x, y) + UINT256 CA4 = + { {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256; +UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp; +UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res; +int_float fx, fy, f64; +UINT32 QX32, tdigit[3], digit, digit_h, digit_low; +int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, + digits_q, amount; +int nzeros, i, j, k, d5, done = 0; +unsigned rmode; +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +fexcept_t binaryflags = 0; +#endif + +valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y); + + // unpack arguments, check for NaN or Infinity +if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { + // test if x is NaN + if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN + (y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull); + Tmp.w[0] = CX.w[0]; + TP128 = reciprocals10_128[18]; + __mul_128x128_full (Qh, Ql, Tmp, TP128); + amount = recip_scale[18]; + __shr_128 (Tmp, Qh, amount); + res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; + BID_RETURN (res); + } + // x is Infinity? + if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { + // check if y is Inf. + if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull)) + // return NaN + { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res = 0x7c00000000000000ull; + BID_RETURN (res); + } + if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { + // otherwise return +/-Inf + res = + ((x.w[1] ^ y. + w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; + BID_RETURN (res); + } + } + // x is 0 + if (((y.w[1] & 0x7800000000000000ull) != 0x7800000000000000ull)) { + if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // x=y=0, return NaN + res = 0x7c00000000000000ull; + BID_RETURN (res); + } + // return 0 + res = (x.w[1] ^ y.w[1]) & 0x8000000000000000ull; + exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; + if (exponent_x > DECIMAL_MAX_EXPON_64) + exponent_x = DECIMAL_MAX_EXPON_64; + else if (exponent_x < 0) + exponent_x = 0; + res |= (((UINT64) exponent_x) << 53); + BID_RETURN (res); + } +} +if (!valid_y) { + // y is Inf. or NaN + + // test if y is NaN + if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull); + Tmp.w[0] = CY.w[0]; + TP128 = reciprocals10_128[18]; + __mul_128x128_full (Qh, Ql, Tmp, TP128); + amount = recip_scale[18]; + __shr_128 (Tmp, Qh, amount); + res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; + BID_RETURN (res); + } + // y is Infinity? + if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { + // return +/-0 + res = sign_x ^ sign_y; + BID_RETURN (res); + } + // y is 0, return +/-Inf + res = + ((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); +#endif + BID_RETURN (res); +} +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif +diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; + +if (__unsigned_compare_gt_128 (CY, CX)) { + // CX < CY + + // 2^64 + f64.i = 0x5f800000; + + // fx ~ CX, fy ~ CY + fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; + fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; + // expon_cy - expon_cx + bin_index = (fy.i - fx.i) >> 23; + + if (CX.w[1]) { + T = power10_index_binexp_128[bin_index].w[0]; + __mul_64x128_short (CA, T, CX); + } else { + T128 = power10_index_binexp_128[bin_index]; + __mul_64x128_short (CA, CX.w[0], T128); + } + + ed2 = 15; + if (__unsigned_compare_gt_128 (CY, CA)) + ed2++; + + T128 = power10_table_128[ed2]; + __mul_128x128_to_256 (CA4, CA, T128); + + ed2 += estimate_decimal_digits[bin_index]; + CQ.w[0] = CQ.w[1] = 0; + diff_expon = diff_expon - ed2; + +} else { + // get CQ = CX/CY + __div_128_by_128 (&CQ, &CR, CX, CY); + + // get number of decimal digits in CQ + // 2^64 + f64.i = 0x5f800000; + fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; + // binary expon. of CQ + bin_expon = (fx.i - 0x3f800000) >> 23; + + digits_q = estimate_decimal_digits[bin_expon]; + TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; + TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; + if (__unsigned_compare_ge_128 (CQ, TP128)) + digits_q++; + + if (digits_q <= 16) { + if (!CR.w[1] && !CR.w[0]) { + res = get_BID64 (sign_x ^ sign_y, diff_expon, + CQ.w[0], rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + + ed2 = 16 - digits_q; + T128.w[0] = power10_table_128[ed2].w[0]; + __mul_64x128_to_192 (CA4, (T128.w[0]), CR); + diff_expon = diff_expon - ed2; + CQ.w[0] *= T128.w[0]; + } else { + ed2 = digits_q - 16; + diff_expon += ed2; + T128 = reciprocals10_128[ed2]; + __mul_128x128_to_256 (P256, CQ, T128); + amount = recip_scale[ed2]; + CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount)); + CQ.w[1] = 0; + + __mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0])); + + __mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]); + QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0]; + + CA4.w[1] = CX.w[1] - QB256.w[1]; + CA4.w[0] = CX.w[0] - QB256.w[0]; + if (CX.w[0] < QB256.w[0]) + CA4.w[1]--; + if (CR.w[0] || CR.w[1]) + CA4.w[0] |= 1; + done = 1; + if(CA4.w[1]|CA4.w[0]) { + __mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY); + } + } + +} + +if (!done) { + __div_256_by_128 (&CQ, &CA4, CY); +} + + + +#ifdef SET_STATUS_FLAGS + if (CA4.w[0] || CA4.w[1]) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#ifndef LEAVE_TRAILING_ZEROS + else +#endif +#else +#ifndef LEAVE_TRAILING_ZEROS + if (!CA4.w[0] && !CA4.w[1]) +#endif +#endif +#ifndef LEAVE_TRAILING_ZEROS + // check whether result is exact + { + if(!done) { + // check whether CX, CY are short + if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { + i = (int) CY.w[0] - 1; + j = (int) CX.w[0] - 1; + // difference in powers of 2 factors for Y and X + nzeros = ed2 - factors[i][0] + factors[j][0]; + // difference in powers of 5 factors + d5 = ed2 - factors[i][1] + factors[j][1]; + if (d5 < nzeros) + nzeros = d5; + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + //__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2]; + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128_long (CQ, Qh, amount); + + diff_expon += nzeros; + } else { + // decompose Q as Qh*10^17 + Ql + //T128 = reciprocals10_128[17]; + Q_low = CQ.w[0]; + + { + tdigit[0] = Q_low & 0x3ffffff; + tdigit[1] = 0; + QX = Q_low >> 26; + QX32 = QX; + nzeros = 0; + + for (j = 0; QX32; j++, QX32 >>= 7) { + k = (QX32 & 127); + tdigit[0] += convert_table[j][k][0]; + tdigit[1] += convert_table[j][k][1]; + if (tdigit[0] >= 100000000) { + tdigit[0] -= 100000000; + tdigit[1]++; + } + } + + if (tdigit[1] >= 100000000) { + tdigit[1] -= 100000000; + if (tdigit[1] >= 100000000) + tdigit[1] -= 100000000; + } + + digit = tdigit[0]; + if (!digit && !tdigit[1]) + nzeros += 16; + else { + if (!digit) { + nzeros += 8; + digit = tdigit[1]; + } + // decompose digit + PD = (UINT64) digit *0x068DB8BBull; + digit_h = (UINT32) (PD >> 40); + digit_low = digit - digit_h * 10000; + + if (!digit_low) + nzeros += 4; + else + digit_h = digit_low; + + if (!(digit_h & 1)) + nzeros += + 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> + (digit_h & 7)); + } + + if (nzeros) { + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[nzeros]; + __shr_128 (CQ, Qh, amount); + } + diff_expon += nzeros; + + } + } + } + if(diff_expon>=0){ + res = + fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], + rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + } +#endif + + if(diff_expon>=0) { + +#ifdef IEEE_ROUND_NEAREST + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + + CQ.w[0] += carry64; + //if(CQ.w[0]> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; +#else + rmode = rnd_mode; + if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + switch (rmode) { + case ROUNDING_TO_NEAREST: // round to nearest code + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_TIES_AWAY: + // rounding + // 2*CA4 - CY + CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); + CA4r.w[0] = CA4.w[0] + CA4.w[0]; + __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); + CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; + D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; + carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; + CQ.w[0] += carry64; + if (CQ.w[0] < carry64) + CQ.w[1]++; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + break; + default: // rounding up + CQ.w[0]++; + if (!CQ.w[0]) + CQ.w[1]++; + break; + } +#endif +#endif + + + res = + fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, + pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } else { + // UF occurs + +#ifdef SET_STATUS_FLAGS + if ((diff_expon + 16 < 0)) { + // set status flags + __set_status_flags (pfpsf, INEXACT_EXCEPTION); + } +#endif + rmode = rnd_mode; + res = + get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + + } + +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_fma.c b/gcc-4.4.3/libgcc/config/libbid/bid64_fma.c new file mode 100644 index 000000000..b1ac88bb1 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_fma.c @@ -0,0 +1,506 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +/***************************************************************************** + * BID64 fma + ***************************************************************************** + * + * Algorithm description: + * + * if multiplication is guranteed exact (short coefficients) + * call the unpacked arg. equivalent of bid64_add(x*y, z) + * else + * get full coefficient_x*coefficient_y product + * call subroutine to perform addition of 64-bit argument + * to 128-bit product + * + ****************************************************************************/ + +#include "bid_inline_add.h" + +#if DECIMAL_CALL_BY_REFERENCE +extern void bid64_mul (UINT64 * pres, UINT64 * px, + UINT64 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); +#else + +extern UINT64 bid64_mul (UINT64 x, + UINT64 y _RND_MODE_PARAM + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); +#endif + +#if DECIMAL_CALL_BY_REFERENCE + +void +bid64_fma (UINT64 * pres, UINT64 * px, UINT64 * py, + UINT64 * + pz _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x, y, z; +#else + +UINT64 +bid64_fma (UINT64 x, UINT64 y, + UINT64 z _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 P, PU, CT, CZ; + UINT64 sign_x, sign_y, coefficient_x, coefficient_y, sign_z, + coefficient_z; + UINT64 C64, remainder_y, res; + UINT64 CYh, CY0L, T, valid_x, valid_y, valid_z; + int_double tempx, tempy; + int extra_digits, exponent_x, exponent_y, bin_expon_cx, bin_expon_cy, + bin_expon_product, rmode; + int digits_p, bp, final_exponent, exponent_z, digits_z, ez, ey, + scale_z, uf_status; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif + x = *px; + y = *py; + z = *pz; +#endif + + valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x); + valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y); + valid_z = unpack_BID64 (&sign_z, &exponent_z, &coefficient_z, z); + + // unpack arguments, check for NaN, Infinity, or 0 + if (!valid_x || !valid_y || !valid_z) { + + if ((y & MASK_NAN) == MASK_NAN) { // y is NAN + // if x = {0, f, inf, NaN}, y = NaN, z = {0, f, inf, NaN} then res = Q (y) + // check first for non-canonical NaN payload + y = y & 0xfe03ffffffffffffull; // clear G6-G12 + if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { + y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + } + if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (y) + res = y & 0xfdffffffffffffffull; + } else { // y is QNaN + // return y + res = y; + // if z = SNaN or x = SNaN signal invalid exception + if ((z & MASK_SNAN) == MASK_SNAN + || (x & MASK_SNAN) == MASK_SNAN) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + } + } + BID_RETURN (res) + } else if ((z & MASK_NAN) == MASK_NAN) { // z is NAN + // if x = {0, f, inf, NaN}, y = {0, f, inf}, z = NaN then res = Q (z) + // check first for non-canonical NaN payload + z = z & 0xfe03ffffffffffffull; // clear G6-G12 + if ((z & 0x0003ffffffffffffull) > 999999999999999ull) { + z = z & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + } + if ((z & MASK_SNAN) == MASK_SNAN) { // z is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (z) + res = z & 0xfdffffffffffffffull; + } else { // z is QNaN + // return z + res = z; + // if x = SNaN signal invalid exception + if ((x & MASK_SNAN) == MASK_SNAN) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + } + } + BID_RETURN (res) + } else if ((x & MASK_NAN) == MASK_NAN) { // x is NAN + // if x = NaN, y = {0, f, inf}, z = {0, f, inf} then res = Q (x) + // check first for non-canonical NaN payload + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + } + if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res = x & 0xfdffffffffffffffull; + } else { // x is QNaN + // return x + res = x; // clear out G[6]-G[16] + } + BID_RETURN (res) + } + + if (!valid_x) { + // x is Inf. or 0 + + // x is Infinity? + if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) { + // check if y is 0 + if (!coefficient_y) { + // y==0, return NaN +#ifdef SET_STATUS_FLAGS + if ((z & 0x7e00000000000000ull) != 0x7c00000000000000ull) + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (0x7c00000000000000ull); + } + // test if z is Inf of oposite sign + if (((z & 0x7c00000000000000ull) == 0x7800000000000000ull) + && (((x ^ y) ^ z) & 0x8000000000000000ull)) { + // return NaN +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (0x7c00000000000000ull); + } + // otherwise return +/-Inf + BID_RETURN (((x ^ y) & 0x8000000000000000ull) | + 0x7800000000000000ull); + } + // x is 0 + if (((y & 0x7800000000000000ull) != 0x7800000000000000ull) + && ((z & 0x7800000000000000ull) != 0x7800000000000000ull)) { + + if (coefficient_z) { + exponent_y = exponent_x - DECIMAL_EXPONENT_BIAS + exponent_y; + + sign_z = z & 0x8000000000000000ull; + + if (exponent_y >= exponent_z) + BID_RETURN (z); + res = + add_zero64 (exponent_y, sign_z, exponent_z, coefficient_z, + &rnd_mode, pfpsf); + BID_RETURN (res); + } + } + } + if (!valid_y) { + // y is Inf. or 0 + + // y is Infinity? + if ((y & 0x7800000000000000ull) == 0x7800000000000000ull) { + // check if x is 0 + if (!coefficient_x) { + // y==0, return NaN +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (0x7c00000000000000ull); + } + // test if z is Inf of oposite sign + if (((z & 0x7c00000000000000ull) == 0x7800000000000000ull) + && (((x ^ y) ^ z) & 0x8000000000000000ull)) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // return NaN + BID_RETURN (0x7c00000000000000ull); + } + // otherwise return +/-Inf + BID_RETURN (((x ^ y) & 0x8000000000000000ull) | + 0x7800000000000000ull); + } + // y is 0 + if (((z & 0x7800000000000000ull) != 0x7800000000000000ull)) { + + if (coefficient_z) { + exponent_y += exponent_x - DECIMAL_EXPONENT_BIAS; + + sign_z = z & 0x8000000000000000ull; + + if (exponent_y >= exponent_z) + BID_RETURN (z); + res = + add_zero64 (exponent_y, sign_z, exponent_z, coefficient_z, + &rnd_mode, pfpsf); + BID_RETURN (res); + } + } + } + + if (!valid_z) { + // y is Inf. or 0 + + // test if y is NaN/Inf + if ((z & 0x7800000000000000ull) == 0x7800000000000000ull) { + BID_RETURN (coefficient_z & QUIET_MASK64); + } + // z is 0, return x*y + if ((!coefficient_x) || (!coefficient_y)) { + //0+/-0 + exponent_x += exponent_y - DECIMAL_EXPONENT_BIAS; + if (exponent_x > DECIMAL_MAX_EXPON_64) + exponent_x = DECIMAL_MAX_EXPON_64; + else if (exponent_x < 0) + exponent_x = 0; + if (exponent_x <= exponent_z) + res = ((UINT64) exponent_x) << 53; + else + res = ((UINT64) exponent_z) << 53; + if ((sign_x ^ sign_y) == sign_z) + res |= sign_z; +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + else if (rnd_mode == ROUNDING_DOWN) + res |= 0x8000000000000000ull; +#endif +#endif + BID_RETURN (res); + } + } + } + + /* get binary coefficients of x and y */ + + //--- get number of bits in the coefficients of x and y --- + // version 2 (original) + tempx.d = (double) coefficient_x; + bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52); + + tempy.d = (double) coefficient_y; + bin_expon_cy = ((tempy.i & MASK_BINARY_EXPONENT) >> 52); + + // magnitude estimate for coefficient_x*coefficient_y is + // 2^(unbiased_bin_expon_cx + unbiased_bin_expon_cx) + bin_expon_product = bin_expon_cx + bin_expon_cy; + + // check if coefficient_x*coefficient_y<2^(10*k+3) + // equivalent to unbiased_bin_expon_cx + unbiased_bin_expon_cx < 10*k+1 + if (bin_expon_product < UPPER_EXPON_LIMIT + 2 * BINARY_EXPONENT_BIAS) { + // easy multiply + C64 = coefficient_x * coefficient_y; + final_exponent = exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS; + if ((final_exponent > 0) || (!coefficient_z)) { + res = + get_add64 (sign_x ^ sign_y, + final_exponent, C64, sign_z, exponent_z, coefficient_z, rnd_mode, pfpsf); + BID_RETURN (res); + } else { + P.w[0] = C64; + P.w[1] = 0; + extra_digits = 0; + } + } else { + if (!coefficient_z) { +#if DECIMAL_CALL_BY_REFERENCE + bid64_mul (&res, px, + py _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + res = + bid64_mul (x, + y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + BID_RETURN (res); + } + // get 128-bit product: coefficient_x*coefficient_y + __mul_64x64_to_128 (P, coefficient_x, coefficient_y); + + // tighten binary range of P: leading bit is 2^bp + // unbiased_bin_expon_product <= bp <= unbiased_bin_expon_product+1 + bin_expon_product -= 2 * BINARY_EXPONENT_BIAS; + __tight_bin_range_128 (bp, P, bin_expon_product); + + // get number of decimal digits in the product + digits_p = estimate_decimal_digits[bp]; + if (!(__unsigned_compare_gt_128 (power10_table_128[digits_p], P))) + digits_p++; // if power10_table_128[digits_p] <= P + + // determine number of decimal digits to be rounded out + extra_digits = digits_p - MAX_FORMAT_DIGITS; + final_exponent = + exponent_x + exponent_y + extra_digits - DECIMAL_EXPONENT_BIAS; + } + + if (((unsigned) final_exponent) >= 3 * 256) { + if (final_exponent < 0) { + //--- get number of bits in the coefficients of z --- + tempx.d = (double) coefficient_z; + bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff; + // get number of decimal digits in the coeff_x + digits_z = estimate_decimal_digits[bin_expon_cx]; + if (coefficient_z >= power10_table_128[digits_z].w[0]) + digits_z++; + // underflow + if ((final_exponent + 16 < 0) + || (exponent_z + digits_z > 33 + final_exponent)) { + res = + BID_normalize (sign_z, exponent_z, coefficient_z, + sign_x ^ sign_y, 1, rnd_mode, pfpsf); + BID_RETURN (res); + } + + ez = exponent_z + digits_z - 16; + if (ez < 0) + ez = 0; + scale_z = exponent_z - ez; + coefficient_z *= power10_table_128[scale_z].w[0]; + ey = final_exponent - extra_digits; + extra_digits = ez - ey; + if (extra_digits > 33) { + res = + BID_normalize (sign_z, exponent_z, coefficient_z, + sign_x ^ sign_y, 1, rnd_mode, pfpsf); + BID_RETURN (res); + } + //else // extra_digits<=32 + + if (extra_digits > 17) { + CYh = __truncate (P, 16); + // get remainder + T = power10_table_128[16].w[0]; + __mul_64x64_to_64 (CY0L, CYh, T); + remainder_y = P.w[0] - CY0L; + + extra_digits -= 16; + P.w[0] = CYh; + P.w[1] = 0; + } else + remainder_y = 0; + + // align coeff_x, CYh + __mul_64x64_to_128 (CZ, coefficient_z, + power10_table_128[extra_digits].w[0]); + + if (sign_z == (sign_y ^ sign_x)) { + __add_128_128 (CT, CZ, P); + if (__unsigned_compare_ge_128 + (CT, power10_table_128[16 + extra_digits])) { + extra_digits++; + ez++; + } + } else { + if (remainder_y && (__unsigned_compare_ge_128 (CZ, P))) { + P.w[0]++; + if (!P.w[0]) + P.w[1]++; + } + __sub_128_128 (CT, CZ, P); + if (((SINT64) CT.w[1]) < 0) { + sign_z = sign_y ^ sign_x; + CT.w[0] = 0 - CT.w[0]; + CT.w[1] = 0 - CT.w[1]; + if (CT.w[0]) + CT.w[1]--; + } else if(!(CT.w[1]|CT.w[0])) + sign_z = (rnd_mode!=ROUNDING_DOWN)? 0: 0x8000000000000000ull; + if (ez + && + (__unsigned_compare_gt_128 + (power10_table_128[15 + extra_digits], CT))) { + extra_digits--; + ez--; + } + } + +#ifdef SET_STATUS_FLAGS + uf_status = 0; + if ((!ez) + && + __unsigned_compare_gt_128 (power10_table_128 + [extra_digits + 15], CT)) { + rmode = rnd_mode; + if (sign_z && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + //__add_128_64(PU, CT, round_const_table[rmode][extra_digits]); + PU = power10_table_128[extra_digits + 15]; + PU.w[0]--; + if (__unsigned_compare_gt_128 (PU, CT) + || (rmode == ROUNDING_DOWN) + || (rmode == ROUNDING_TO_ZERO)) + uf_status = UNDERFLOW_EXCEPTION; + else if (extra_digits < 2) { + if ((rmode == ROUNDING_UP)) { + if (!extra_digits) + uf_status = UNDERFLOW_EXCEPTION; + else { + if (remainder_y && (sign_z != (sign_y ^ sign_x))) + remainder_y = power10_table_128[16].w[0] - remainder_y; + + if (power10_table_128[15].w[0] > remainder_y) + uf_status = UNDERFLOW_EXCEPTION; + } + } else // RN or RN_away + { + if (remainder_y && (sign_z != (sign_y ^ sign_x))) + remainder_y = power10_table_128[16].w[0] - remainder_y; + + if (!extra_digits) { + remainder_y += round_const_table[rmode][15]; + if (remainder_y < power10_table_128[16].w[0]) + uf_status = UNDERFLOW_EXCEPTION; + } else { + if (remainder_y < round_const_table[rmode][16]) + uf_status = UNDERFLOW_EXCEPTION; + } + } + //__set_status_flags (pfpsf, uf_status); + } + } +#endif + res = + __bid_full_round64_remainder (sign_z, ez - extra_digits, CT, + extra_digits, remainder_y, + rnd_mode, pfpsf, uf_status); + BID_RETURN (res); + + } else { + if ((sign_z == (sign_x ^ sign_y)) + || (final_exponent > 3 * 256 + 15)) { + res = + fast_get_BID64_check_OF (sign_x ^ sign_y, final_exponent, + 1000000000000000ull, rnd_mode, + pfpsf); + BID_RETURN (res); + } + } + } + + + if (extra_digits > 0) { + res = + get_add128 (sign_z, exponent_z, coefficient_z, sign_x ^ sign_y, + final_exponent, P, extra_digits, rnd_mode, pfpsf); + BID_RETURN (res); + } + // go to convert_format and exit + else { + C64 = __low_64 (P); + + res = + get_add64 (sign_x ^ sign_y, + exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS, C64, + sign_z, exponent_z, coefficient_z, + rnd_mode, pfpsf); + BID_RETURN (res); + } +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_logb.c b/gcc-4.4.3/libgcc/config/libbid/bid64_logb.c new file mode 100644 index 000000000..eeb3fac2a --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_logb.c @@ -0,0 +1,68 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +#define MAX_FORMAT_DIGITS 16 +#define DECIMAL_EXPONENT_BIAS 398 + +#if DECIMAL_CALL_BY_REFERENCE + +void +bid64_logb (int * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x; +#else + +int +bid64_logb (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT64 sign_x, coefficient_x; + int_double dx; + int exponent_x, bin_expon_cx, digits; + +#if DECIMAL_CALL_BY_REFERENCE + x = *px; +#endif + // unpack arguments, check for NaN or Infinity + if (!unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x)) { + // x is Inf. or NaN +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (0x80000000); + } + // find number of digits in coefficient + if (coefficient_x >= 1000000000000000ull) { + digits = 16; + } else { + dx.d = (double)coefficient_x; // exact conversion; + bin_expon_cx = (int)(dx.i >> 52) - 1023; + digits = estimate_decimal_digits[bin_expon_cx]; + if (coefficient_x >= power10_table_128[digits].w[0]) + digits++; + } + exponent_x = exponent_x - DECIMAL_EXPONENT_BIAS + digits - 1; + + BID_RETURN (exponent_x); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_minmax.c b/gcc-4.4.3/libgcc/config/libbid/bid64_minmax.c new file mode 100644 index 000000000..d678f94a1 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_minmax.c @@ -0,0 +1,854 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID64 minimum function - returns greater of two numbers + *****************************************************************************/ + +static const UINT64 mult_factor[16] = { + 1ull, 10ull, 100ull, 1000ull, + 10000ull, 100000ull, 1000000ull, 10000000ull, + 100000000ull, 1000000000ull, 10000000000ull, 100000000000ull, + 1000000000000ull, 10000000000000ull, + 100000000000000ull, 1000000000000000ull +}; + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_minnum (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +UINT64 +bid64_minnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) { +#endif + + UINT64 res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0; + + // check for non-canonical x + if ((x & MASK_NAN) == MASK_NAN) { // x is NaN + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + } + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + x = x & (MASK_SIGN | MASK_INF); + } else { // x is not special + // check for non-canonical values - treated as zero + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11, then the exponent is G[0:w+1] + if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > + 9999999999999999ull) { + // non-canonical + x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); + } // else canonical + } // else canonical + } + + // check for non-canonical y + if ((y & MASK_NAN) == MASK_NAN) { // y is NaN + y = y & 0xfe03ffffffffffffull; // clear G6-G12 + if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { + y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + } + } else if ((y & MASK_INF) == MASK_INF) { // check for Infinity + y = y & (MASK_SIGN | MASK_INF); + } else { // y is not special + // check for non-canonical values - treated as zero + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11, then the exponent is G[0:w+1] + if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > + 9999999999999999ull) { + // non-canonical + y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2); + } // else canonical + } // else canonical + } + + // NaN (CASE1) + if ((x & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN + // if x is SNAN, then return quiet (x) + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + x = x & 0xfdffffffffffffffull; // quietize x + res = x; + } else { // x is QNaN + if ((y & MASK_NAN) == MASK_NAN) { // y is NAN + if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN + *pfpsf |= INVALID_EXCEPTION; // set invalid flag + } + res = x; + } else { + res = y; + } + } + BID_RETURN (res); + } else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not + if ((y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + y = y & 0xfdffffffffffffffull; // quietize y + res = y; + } else { + // will return x (which is not NaN) + res = x; + } + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal, return either number + if (x == y) { + res = x; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return x + if (((x & MASK_SIGN) == MASK_SIGN)) { + res = x; + BID_RETURN (res); + } + // x is pos infinity, return y + else { + res = y; + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return y + // if y is negative infinity, then x is greater, return x + res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + } + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore + // ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // ignore the exponent field + // (Any non-canonical # is considered 0) + if (sig_x == 0) { + x_is_zero = 1; + } + if (sig_y == 0) { + y_is_zero = 1; + } + + if (x_is_zero && y_is_zero) { + // if both numbers are zero, neither is greater => return either + res = y; + BID_RETURN (res); + } else if (x_is_zero) { + // is x is zero, it is greater if Y is negative + res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } else if (y_is_zero) { + // is y is zero, X is greater if it is positive + res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x;; + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + + // if both components are either bigger or smaller, + // it is clear what needs to be done + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x; + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x; // difference cannot be >10^15 + BID_RETURN (res); + } + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = y; + BID_RETURN (res); + } + + res = (((sig_n_prime.w[1] > 0) + || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)) ? y : x; + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // if postitive, return whichever significand is larger (converse if negative) + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = y; + BID_RETURN (res); + } + res = (((sig_n_prime.w[1] == 0) + && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)) ? y : x; + BID_RETURN (res); +} + +/***************************************************************************** + * BID64 minimum magnitude function - returns greater of two numbers + *****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_minnum_mag (UINT64 * pres, UINT64 * px, + UINT64 * py _EXC_FLAGS_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +UINT64 +bid64_minnum_mag (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) { +#endif + + UINT64 res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + + // check for non-canonical x + if ((x & MASK_NAN) == MASK_NAN) { // x is NaN + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + } + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + x = x & (MASK_SIGN | MASK_INF); + } else { // x is not special + // check for non-canonical values - treated as zero + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11, then the exponent is G[0:w+1] + if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > + 9999999999999999ull) { + // non-canonical + x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); + } // else canonical + } // else canonical + } + + // check for non-canonical y + if ((y & MASK_NAN) == MASK_NAN) { // y is NaN + y = y & 0xfe03ffffffffffffull; // clear G6-G12 + if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { + y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + } + } else if ((y & MASK_INF) == MASK_INF) { // check for Infinity + y = y & (MASK_SIGN | MASK_INF); + } else { // y is not special + // check for non-canonical values - treated as zero + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11, then the exponent is G[0:w+1] + if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > + 9999999999999999ull) { + // non-canonical + y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2); + } // else canonical + } // else canonical + } + + // NaN (CASE1) + if ((x & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN + // if x is SNAN, then return quiet (x) + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + x = x & 0xfdffffffffffffffull; // quietize x + res = x; + } else { // x is QNaN + if ((y & MASK_NAN) == MASK_NAN) { // y is NAN + if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN + *pfpsf |= INVALID_EXCEPTION; // set invalid flag + } + res = x; + } else { + res = y; + } + } + BID_RETURN (res); + } else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not + if ((y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + y = y & 0xfdffffffffffffffull; // quietize y + res = y; + } else { + // will return x (which is not NaN) + res = x; + } + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal, return either number + if (x == y) { + res = x; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // x is infinity, its magnitude is greater than or equal to y + // return x only if y is infinity and x is negative + res = ((x & MASK_SIGN) == MASK_SIGN + && (y & MASK_INF) == MASK_INF) ? x : y; + BID_RETURN (res); + } else if ((y & MASK_INF) == MASK_INF) { + // y is infinity, then it must be greater in magnitude, return x + res = x; + BID_RETURN (res); + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + } + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore + // ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // ignore the exponent field + // (Any non-canonical # is considered 0) + if (sig_x == 0) { + res = x; // x_is_zero, its magnitude must be smaller than y + BID_RETURN (res); + } + if (sig_y == 0) { + res = y; // y_is_zero, its magnitude must be smaller than x + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller, + // it is clear what needs to be done + if (sig_x > sig_y && exp_x >= exp_y) { + res = y; + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = x; + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = y; // difference cannot be greater than 10^15 + BID_RETURN (res); + } + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = x; + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + // now, sig_n_prime has: sig_x * 10^(exp_x-exp_y), this is + // the compensated signif. + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + // two numbers are equal, return minNum(x,y) + res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x; + BID_RETURN (res); + } + // now, if compensated_x (sig_n_prime) is greater than y, return y, + // otherwise return x + res = ((sig_n_prime.w[1] != 0) || sig_n_prime.w[0] > sig_y) ? y : x; + BID_RETURN (res); + } + // exp_y must be greater than exp_x, thus adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x; + // two numbers are equal, return either + BID_RETURN (res); + } + + res = ((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ? y : x; + BID_RETURN (res); +} + +/***************************************************************************** + * BID64 maximum function - returns greater of two numbers + *****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_maxnum (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +UINT64 +bid64_maxnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) { +#endif + + UINT64 res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0; + + // check for non-canonical x + if ((x & MASK_NAN) == MASK_NAN) { // x is NaN + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + } + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + x = x & (MASK_SIGN | MASK_INF); + } else { // x is not special + // check for non-canonical values - treated as zero + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11, then the exponent is G[0:w+1] + if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > + 9999999999999999ull) { + // non-canonical + x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); + } // else canonical + } // else canonical + } + + // check for non-canonical y + if ((y & MASK_NAN) == MASK_NAN) { // y is NaN + y = y & 0xfe03ffffffffffffull; // clear G6-G12 + if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { + y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + } + } else if ((y & MASK_INF) == MASK_INF) { // check for Infinity + y = y & (MASK_SIGN | MASK_INF); + } else { // y is not special + // check for non-canonical values - treated as zero + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11, then the exponent is G[0:w+1] + if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > + 9999999999999999ull) { + // non-canonical + y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2); + } // else canonical + } // else canonical + } + + // NaN (CASE1) + if ((x & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN + // if x is SNAN, then return quiet (x) + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + x = x & 0xfdffffffffffffffull; // quietize x + res = x; + } else { // x is QNaN + if ((y & MASK_NAN) == MASK_NAN) { // y is NAN + if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN + *pfpsf |= INVALID_EXCEPTION; // set invalid flag + } + res = x; + } else { + res = y; + } + } + BID_RETURN (res); + } else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not + if ((y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + y = y & 0xfdffffffffffffffull; // quietize y + res = y; + } else { + // will return x (which is not NaN) + res = x; + } + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal (not Greater). + if (x == y) { + res = x; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // if x is neg infinity, there is no way it is greater than y, return y + // x is pos infinity, it is greater, unless y is positive infinity => + // return y!=pos_infinity + if (((x & MASK_SIGN) == MASK_SIGN)) { + res = y; + BID_RETURN (res); + } else { + res = (((y & MASK_INF) != MASK_INF) + || ((y & MASK_SIGN) == MASK_SIGN)) ? x : y; + BID_RETURN (res); + } + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so if y is positive infinity, then x is less, return y + // if y is negative infinity, then x is greater, return x + res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + } + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore + // ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // ignore the exponent field + // (Any non-canonical # is considered 0) + if (sig_x == 0) { + x_is_zero = 1; + } + if (sig_y == 0) { + y_is_zero = 1; + } + + if (x_is_zero && y_is_zero) { + // if both numbers are zero, neither is greater => return NOTGREATERTHAN + res = y; + BID_RETURN (res); + } else if (x_is_zero) { + // is x is zero, it is greater if Y is negative + res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } else if (y_is_zero) { + // is y is zero, X is greater if it is positive + res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y;; + BID_RETURN (res); + } + // OPPOSITE SIGN (CASE5) + // now, if the sign bits differ, x is greater if y is negative + if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { + res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + + // if both components are either bigger or smaller, + // it is clear what needs to be done + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y; + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y; + // difference cannot be > 10^15 + BID_RETURN (res); + } + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + // if postitive, return whichever significand is larger + // (converse if negative) + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + res = y; + BID_RETURN (res); + } + res = (((sig_n_prime.w[1] > 0) + || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN)) ? x : y; + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // if postitive, return whichever significand is larger (converse if negative) + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = y; + BID_RETURN (res); + } + res = (((sig_n_prime.w[1] == 0) + && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN)) ? x : y; + BID_RETURN (res); +} + +/***************************************************************************** + * BID64 maximum magnitude function - returns greater of two numbers + *****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_maxnum_mag (UINT64 * pres, UINT64 * px, + UINT64 * py _EXC_FLAGS_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +UINT64 +bid64_maxnum_mag (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) { +#endif + + UINT64 res; + int exp_x, exp_y; + UINT64 sig_x, sig_y; + UINT128 sig_n_prime; + + // check for non-canonical x + if ((x & MASK_NAN) == MASK_NAN) { // x is NaN + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + } + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + x = x & (MASK_SIGN | MASK_INF); + } else { // x is not special + // check for non-canonical values - treated as zero + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11, then the exponent is G[0:w+1] + if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > + 9999999999999999ull) { + // non-canonical + x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); + } // else canonical + } // else canonical + } + + // check for non-canonical y + if ((y & MASK_NAN) == MASK_NAN) { // y is NaN + y = y & 0xfe03ffffffffffffull; // clear G6-G12 + if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { + y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + } + } else if ((y & MASK_INF) == MASK_INF) { // check for Infinity + y = y & (MASK_SIGN | MASK_INF); + } else { // y is not special + // check for non-canonical values - treated as zero + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11, then the exponent is G[0:w+1] + if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > + 9999999999999999ull) { + // non-canonical + y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2); + } // else canonical + } // else canonical + } + + // NaN (CASE1) + if ((x & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN + // if x is SNAN, then return quiet (x) + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + x = x & 0xfdffffffffffffffull; // quietize x + res = x; + } else { // x is QNaN + if ((y & MASK_NAN) == MASK_NAN) { // y is NAN + if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN + *pfpsf |= INVALID_EXCEPTION; // set invalid flag + } + res = x; + } else { + res = y; + } + } + BID_RETURN (res); + } else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not + if ((y & MASK_SNAN) == MASK_SNAN) { + *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN + y = y & 0xfdffffffffffffffull; // quietize y + res = y; + } else { + // will return x (which is not NaN) + res = x; + } + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal, return either number + if (x == y) { + res = x; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // x is infinity, its magnitude is greater than or equal to y + // return y as long as x isn't negative infinity + res = ((x & MASK_SIGN) == MASK_SIGN + && (y & MASK_INF) == MASK_INF) ? y : x; + BID_RETURN (res); + } else if ((y & MASK_INF) == MASK_INF) { + // y is infinity, then it must be greater in magnitude + res = y; + BID_RETURN (res); + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + } + + // ZERO (CASE4) + // some properties: + // (+ZERO == -ZERO) => therefore + // ignore the sign, and neither number is greater + // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => + // ignore the exponent field + // (Any non-canonical # is considered 0) + if (sig_x == 0) { + res = y; // x_is_zero, its magnitude must be smaller than y + BID_RETURN (res); + } + if (sig_y == 0) { + res = x; // y_is_zero, its magnitude must be smaller than x + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller, + // it is clear what needs to be done + if (sig_x > sig_y && exp_x >= exp_y) { + res = x; + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = y; + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, no need for compensation + if (exp_x - exp_y > 15) { + res = x; // difference cannot be greater than 10^15 + BID_RETURN (res); + } + // if exp_x is 15 less than exp_y, no need for compensation + if (exp_y - exp_x > 15) { + res = y; + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down to the compensated significand + if (exp_x > exp_y) { // to simplify the loop below, + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + // now, sig_n_prime has: sig_x * 10^(exp_x-exp_y), + // this is the compensated signif. + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + // two numbers are equal, return maxNum(x,y) + res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y; + BID_RETURN (res); + } + // now, if compensated_x (sig_n_prime) is greater than y return y, + // otherwise return x + res = ((sig_n_prime.w[1] != 0) || sig_n_prime.w[0] > sig_y) ? x : y; + BID_RETURN (res); + } + // exp_y must be greater than exp_x, thus adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y; + // two numbers are equal, return either + BID_RETURN (res); + } + + res = ((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ? x : y; + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_mul.c b/gcc-4.4.3/libgcc/config/libbid/bid64_mul.c new file mode 100644 index 000000000..163c65410 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_mul.c @@ -0,0 +1,374 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +/***************************************************************************** + * BID64 multiply + ***************************************************************************** + * + * Algorithm description: + * + * if(number_digits(coefficient_x)+number_digits(coefficient_y) guaranteed + * below 16) + * return get_BID64(sign_x^sign_y, exponent_x + exponent_y - dec_bias, + * coefficient_x*coefficient_y) + * else + * get long product: coefficient_x*coefficient_y + * determine number of digits to round off (extra_digits) + * rounding is performed as a 128x128-bit multiplication by + * 2^M[extra_digits]/10^extra_digits, followed by a shift + * M[extra_digits] is sufficiently large for required accuracy + * + ****************************************************************************/ + +#include "bid_internal.h" + +#if DECIMAL_CALL_BY_REFERENCE + +void +bid64_mul (UINT64 * pres, UINT64 * px, + UINT64 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x, y; +#else + +UINT64 +bid64_mul (UINT64 x, + UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 P, PU, C128, Q_high, Q_low, Stemp; + UINT64 sign_x, sign_y, coefficient_x, coefficient_y; + UINT64 C64, remainder_h, carry, CY, res; + UINT64 valid_x, valid_y; + int_double tempx, tempy; + int extra_digits, exponent_x, exponent_y, bin_expon_cx, bin_expon_cy, + bin_expon_product; + int rmode, digits_p, bp, amount, amount2, final_exponent, round_up; + unsigned status, uf_status; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif + x = *px; + y = *py; +#endif + + valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x); + valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y); + + // unpack arguments, check for NaN or Infinity + if (!valid_x) { + +#ifdef SET_STATUS_FLAGS + if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // x is Inf. or NaN + + // test if x is NaN + if ((x & NAN_MASK64) == NAN_MASK64) { +#ifdef SET_STATUS_FLAGS + if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (coefficient_x & QUIET_MASK64); + } + // x is Infinity? + if ((x & INFINITY_MASK64) == INFINITY_MASK64) { + // check if y is 0 + if (((y & INFINITY_MASK64) != INFINITY_MASK64) + && !coefficient_y) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // y==0 , return NaN + BID_RETURN (NAN_MASK64); + } + // check if y is NaN + if ((y & NAN_MASK64) == NAN_MASK64) + // y==NaN , return NaN + BID_RETURN (coefficient_y & QUIET_MASK64); + // otherwise return +/-Inf + BID_RETURN (((x ^ y) & 0x8000000000000000ull) | INFINITY_MASK64); + } + // x is 0 + if (((y & INFINITY_MASK64) != INFINITY_MASK64)) { + if ((y & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64) + exponent_y = ((UINT32) (y >> 51)) & 0x3ff; + else + exponent_y = ((UINT32) (y >> 53)) & 0x3ff; + sign_y = y & 0x8000000000000000ull; + + exponent_x += exponent_y - DECIMAL_EXPONENT_BIAS; + if (exponent_x > DECIMAL_MAX_EXPON_64) + exponent_x = DECIMAL_MAX_EXPON_64; + else if (exponent_x < 0) + exponent_x = 0; + BID_RETURN ((sign_x ^ sign_y) | (((UINT64) exponent_x) << 53)); + } + } + if (!valid_y) { + // y is Inf. or NaN + + // test if y is NaN + if ((y & NAN_MASK64) == NAN_MASK64) { +#ifdef SET_STATUS_FLAGS + if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (coefficient_y & QUIET_MASK64); + } + // y is Infinity? + if ((y & INFINITY_MASK64) == INFINITY_MASK64) { + // check if x is 0 + if (!coefficient_x) { + __set_status_flags (pfpsf, INVALID_EXCEPTION); + // x==0, return NaN + BID_RETURN (NAN_MASK64); + } + // otherwise return +/-Inf + BID_RETURN (((x ^ y) & 0x8000000000000000ull) | INFINITY_MASK64); + } + // y is 0 + exponent_x += exponent_y - DECIMAL_EXPONENT_BIAS; + if (exponent_x > DECIMAL_MAX_EXPON_64) + exponent_x = DECIMAL_MAX_EXPON_64; + else if (exponent_x < 0) + exponent_x = 0; + BID_RETURN ((sign_x ^ sign_y) | (((UINT64) exponent_x) << 53)); + } + //--- get number of bits in the coefficients of x and y --- + // version 2 (original) + tempx.d = (double) coefficient_x; + bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52); + tempy.d = (double) coefficient_y; + bin_expon_cy = ((tempy.i & MASK_BINARY_EXPONENT) >> 52); + + // magnitude estimate for coefficient_x*coefficient_y is + // 2^(unbiased_bin_expon_cx + unbiased_bin_expon_cx) + bin_expon_product = bin_expon_cx + bin_expon_cy; + + // check if coefficient_x*coefficient_y<2^(10*k+3) + // equivalent to unbiased_bin_expon_cx + unbiased_bin_expon_cx < 10*k+1 + if (bin_expon_product < UPPER_EXPON_LIMIT + 2 * BINARY_EXPONENT_BIAS) { + // easy multiply + C64 = coefficient_x * coefficient_y; + + res = + get_BID64_small_mantissa (sign_x ^ sign_y, + exponent_x + exponent_y - + DECIMAL_EXPONENT_BIAS, C64, rnd_mode, + pfpsf); + BID_RETURN (res); + } else { + uf_status = 0; + // get 128-bit product: coefficient_x*coefficient_y + __mul_64x64_to_128 (P, coefficient_x, coefficient_y); + + // tighten binary range of P: leading bit is 2^bp + // unbiased_bin_expon_product <= bp <= unbiased_bin_expon_product+1 + bin_expon_product -= 2 * BINARY_EXPONENT_BIAS; + + __tight_bin_range_128 (bp, P, bin_expon_product); + + // get number of decimal digits in the product + digits_p = estimate_decimal_digits[bp]; + if (!(__unsigned_compare_gt_128 (power10_table_128[digits_p], P))) + digits_p++; // if power10_table_128[digits_p] <= P + + // determine number of decimal digits to be rounded out + extra_digits = digits_p - MAX_FORMAT_DIGITS; + final_exponent = + exponent_x + exponent_y + extra_digits - DECIMAL_EXPONENT_BIAS; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = rnd_mode; + if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#else + rmode = 0; +#endif +#else + rmode = 0; +#endif + + round_up = 0; + if (((unsigned) final_exponent) >= 3 * 256) { + if (final_exponent < 0) { + // underflow + if (final_exponent + 16 < 0) { + res = sign_x ^ sign_y; + __set_status_flags (pfpsf, + UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); + if (rmode == ROUNDING_UP) + res |= 1; + BID_RETURN (res); + } + + uf_status = UNDERFLOW_EXCEPTION; + if (final_exponent == -1) { + __add_128_64 (PU, P, round_const_table[rmode][extra_digits]); + if (__unsigned_compare_ge_128 + (PU, power10_table_128[extra_digits + 16])) + uf_status = 0; + } + extra_digits -= final_exponent; + final_exponent = 0; + + if (extra_digits > 17) { + __mul_128x128_full (Q_high, Q_low, P, reciprocals10_128[16]); + + amount = recip_scale[16]; + __shr_128 (P, Q_high, amount); + + // get sticky bits + amount2 = 64 - amount; + remainder_h = 0; + remainder_h--; + remainder_h >>= amount2; + remainder_h = remainder_h & Q_high.w[0]; + + extra_digits -= 16; + if (remainder_h || (Q_low.w[1] > reciprocals10_128[16].w[1] + || (Q_low.w[1] == + reciprocals10_128[16].w[1] + && Q_low.w[0] >= + reciprocals10_128[16].w[0]))) { + round_up = 1; + __set_status_flags (pfpsf, + UNDERFLOW_EXCEPTION | + INEXACT_EXCEPTION); + P.w[0] = (P.w[0] << 3) + (P.w[0] << 1); + P.w[0] |= 1; + extra_digits++; + } + } + } else { + res = + fast_get_BID64_check_OF (sign_x ^ sign_y, final_exponent, + 1000000000000000ull, rnd_mode, + pfpsf); + BID_RETURN (res); + } + } + + + if (extra_digits > 0) { + // will divide by 10^(digits_p - 16) + + // add a constant to P, depending on rounding mode + // 0.5*10^(digits_p - 16) for round-to-nearest + __add_128_64 (P, P, round_const_table[rmode][extra_digits]); + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Q_high, Q_low, P, + reciprocals10_128[extra_digits]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[extra_digits]; + __shr_128 (C128, Q_high, amount); + + C64 = __low_64 (C128); + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == 0) //ROUNDING_TO_NEAREST +#endif + if ((C64 & 1) && !round_up) { + // check whether fractional part of initial_P/10^extra_digits + // is exactly .5 + // this is the same as fractional part of + // (initial_P + 0.5*10^extra_digits)/10^extra_digits is exactly zero + + // get remainder + remainder_h = Q_high.w[0] << (64 - amount); + + // test whether fractional part is 0 + if (!remainder_h + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) { + C64--; + } + } +#endif + +#ifdef SET_STATUS_FLAGS + status = INEXACT_EXCEPTION | uf_status; + + // get remainder + remainder_h = Q_high.w[0] << (64 - amount); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if (remainder_h == 0x8000000000000000ull + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if (!remainder_h + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (Stemp.w[0], CY, Q_low.w[0], + reciprocals10_128[extra_digits].w[0]); + __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], + reciprocals10_128[extra_digits].w[1], CY); + if ((remainder_h >> (64 - amount)) + carry >= + (((UINT64) 1) << amount)) + status = EXACT_STATUS; + } + + __set_status_flags (pfpsf, status); +#endif + + // convert to BID and return + res = + fast_get_BID64_check_OF (sign_x ^ sign_y, final_exponent, C64, + rmode, pfpsf); + BID_RETURN (res); + } + // go to convert_format and exit + C64 = __low_64 (P); + res = + get_BID64 (sign_x ^ sign_y, + exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS, C64, + rmode, pfpsf); + BID_RETURN (res); + } +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_next.c b/gcc-4.4.3/libgcc/config/libbid/bid64_next.c new file mode 100644 index 000000000..00f1c79e7 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_next.c @@ -0,0 +1,481 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID64 nextup + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_nextup (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_nextup (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q1, ind; + UINT64 C1; // C1 represents x_signif (UINT64) + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + if (!(x & 0x8000000000000000ull)) { // x is +inf + res = 0x7800000000000000ull; + } else { // x is -inf + res = 0xf7fb86f26fc0ffffull; // -MAXFP = -999...99 * 10^emax + } + BID_RETURN (res); + } + // unpack the argument + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000001ull; // MINFP = 1 * 10^emin + } else { // x is not special and is not zero + if (x == 0x77fb86f26fc0ffffull) { + // x = +MAXFP = 999...99 * 10^emax + res = 0x7800000000000000ull; // +inf + } else if (x == 0x8000000000000001ull) { + // x = -MINFP = 1...99 * 10^emin + res = 0x8000000000000000ull; // -0 + } else { // -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp + // can add/subtract 1 ulp to the significand + + // Note: we could check here if x >= 10^16 to speed up the case q1 =16 + // q1 = nr. of decimal digits in x (1 <= q1 <= 54) + // determine first the nr. of bits in x + if (C1 >= MASK_BINARY_OR2) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q1 = nr_digits[x_nr_bits - 1].digits; + if (q1 == 0) { + q1 = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q1++; + } + // if q1 < P16 then pad the significand with zeros + if (q1 < P16) { + if (x_exp > (UINT64) (P16 - q1)) { + ind = P16 - q1; // 1 <= ind <= P16 - 1 + // pad with P16 - q1 zeros, until exponent = emin + // C1 = C1 * 10^ind + C1 = C1 * ten2k64[ind]; + x_exp = x_exp - ind; + } else { // pad with zeros until the exponent reaches emin + ind = x_exp; + C1 = C1 * ten2k64[ind]; + x_exp = EXP_MIN; + } + } + if (!x_sign) { // x > 0 + // add 1 ulp (add 1 to the significand) + C1++; + if (C1 == 0x002386f26fc10000ull) { // if C1 = 10^16 + C1 = 0x00038d7ea4c68000ull; // C1 = 10^15 + x_exp++; + } + // Ok, because MAXFP = 999...99 * 10^emax was caught already + } else { // x < 0 + // subtract 1 ulp (subtract 1 from the significand) + C1--; + if (C1 == 0x00038d7ea4c67fffull && x_exp != 0) { // if C1 = 10^15 - 1 + C1 = 0x002386f26fc0ffffull; // C1 = 10^16 - 1 + x_exp--; + } + } + // assemble the result + // if significand has 54 bits + if (C1 & MASK_BINARY_OR2) { + res = + x_sign | (x_exp << 51) | MASK_STEERING_BITS | (C1 & + MASK_BINARY_SIG2); + } else { // significand fits in 53 bits + res = x_sign | (x_exp << 53) | C1; + } + } // end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp + } // end x is not special and is not zero + BID_RETURN (res); +} + +/***************************************************************************** + * BID64 nextdown + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_nextdown (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_nextdown (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q1, ind; + UINT64 C1; // C1 represents x_signif (UINT64) + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + if (x & 0x8000000000000000ull) { // x is -inf + res = 0xf800000000000000ull; + } else { // x is +inf + res = 0x77fb86f26fc0ffffull; // +MAXFP = +999...99 * 10^emax + } + BID_RETURN (res); + } + // unpack the argument + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x8000000000000001ull; // -MINFP = -1 * 10^emin + } else { // x is not special and is not zero + if (x == 0xf7fb86f26fc0ffffull) { + // x = -MAXFP = -999...99 * 10^emax + res = 0xf800000000000000ull; // -inf + } else if (x == 0x0000000000000001ull) { + // x = +MINFP = 1...99 * 10^emin + res = 0x0000000000000000ull; // -0 + } else { // -MAXFP + 1ulp <= x <= -MINFP OR MINFP + 1 ulp <= x <= MAXFP + // can add/subtract 1 ulp to the significand + + // Note: we could check here if x >= 10^16 to speed up the case q1 =16 + // q1 = nr. of decimal digits in x (1 <= q1 <= 16) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid + // rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q1 = nr_digits[x_nr_bits - 1].digits; + if (q1 == 0) { + q1 = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q1++; + } + // if q1 < P16 then pad the significand with zeros + if (q1 < P16) { + if (x_exp > (UINT64) (P16 - q1)) { + ind = P16 - q1; // 1 <= ind <= P16 - 1 + // pad with P16 - q1 zeros, until exponent = emin + // C1 = C1 * 10^ind + C1 = C1 * ten2k64[ind]; + x_exp = x_exp - ind; + } else { // pad with zeros until the exponent reaches emin + ind = x_exp; + C1 = C1 * ten2k64[ind]; + x_exp = EXP_MIN; + } + } + if (x_sign) { // x < 0 + // add 1 ulp (add 1 to the significand) + C1++; + if (C1 == 0x002386f26fc10000ull) { // if C1 = 10^16 + C1 = 0x00038d7ea4c68000ull; // C1 = 10^15 + x_exp++; + // Ok, because -MAXFP = -999...99 * 10^emax was caught already + } + } else { // x > 0 + // subtract 1 ulp (subtract 1 from the significand) + C1--; + if (C1 == 0x00038d7ea4c67fffull && x_exp != 0) { // if C1 = 10^15 - 1 + C1 = 0x002386f26fc0ffffull; // C1 = 10^16 - 1 + x_exp--; + } + } + // assemble the result + // if significand has 54 bits + if (C1 & MASK_BINARY_OR2) { + res = + x_sign | (x_exp << 51) | MASK_STEERING_BITS | (C1 & + MASK_BINARY_SIG2); + } else { // significand fits in 53 bits + res = x_sign | (x_exp << 53) | C1; + } + } // end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp + } // end x is not special and is not zero + BID_RETURN (res); +} + +/***************************************************************************** + * BID64 nextafter + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_nextafter (UINT64 * pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +UINT64 +bid64_nextafter (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 res; + UINT64 tmp1, tmp2; + FPSC tmp_fpsf = 0; // dummy fpsf for calls to comparison functions + int res1, res2; + + // check for NaNs or infinities + if (((x & MASK_SPECIAL) == MASK_SPECIAL) || + ((y & MASK_SPECIAL) == MASK_SPECIAL)) { + // x is NaN or infinity or y is NaN or infinity + + if ((x & MASK_NAN) == MASK_NAN) { // x is NAN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (x) + res = x & 0xfdffffffffffffffull; + } else { // x is QNaN + if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + } + // return x + res = x; + } + BID_RETURN (res); + } else if ((y & MASK_NAN) == MASK_NAN) { // y is NAN + if ((y & 0x0003ffffffffffffull) > 999999999999999ull) + y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + y = y & 0xfe03ffffffffffffull; // clear G6-G12 + if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (y) + res = y & 0xfdffffffffffffffull; + } else { // y is QNaN + // return y + res = y; + } + BID_RETURN (res); + } else { // at least one is infinity + if ((x & MASK_ANY_INF) == MASK_INF) { // x = inf + x = x & (MASK_SIGN | MASK_INF); + } + if ((y & MASK_ANY_INF) == MASK_INF) { // y = inf + y = y & (MASK_SIGN | MASK_INF); + } + } + } + // neither x nor y is NaN + + // if not infinity, check for non-canonical values x (treated as zero) + if ((x & MASK_ANY_INF) != MASK_INF) { // x != inf + // unpack x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11 (condition will be 0), then + // the exponent is G[0:w+1] + if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > + 9999999999999999ull) { + // non-canonical + x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); + } + } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) x is unch. + ; // canonical + } + } + // no need to check for non-canonical y + + // neither x nor y is NaN + tmp_fpsf = *pfpsf; // save fpsf +#if DECIMAL_CALL_BY_REFERENCE + bid64_quiet_equal (&res1, px, + py _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + bid64_quiet_greater (&res2, px, + py _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); +#else + res1 = + bid64_quiet_equal (x, + y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); + res2 = + bid64_quiet_greater (x, + y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); +#endif + *pfpsf = tmp_fpsf; // restore fpsf + if (res1) { // x = y + // return x with the sign of y + res = (y & 0x8000000000000000ull) | (x & 0x7fffffffffffffffull); + } else if (res2) { // x > y +#if DECIMAL_CALL_BY_REFERENCE + bid64_nextdown (&res, + px _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); +#else + res = + bid64_nextdown (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); +#endif + } else { // x < y +#if DECIMAL_CALL_BY_REFERENCE + bid64_nextup (&res, px _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); +#else + res = bid64_nextup (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); +#endif + } + // if the operand x is finite but the result is infinite, signal + // overflow and inexact + if (((x & MASK_INF) != MASK_INF) && ((res & MASK_INF) == MASK_INF)) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // set the overflow flag + *pfpsf |= OVERFLOW_EXCEPTION; + } + // if the result is in (-10^emin, 10^emin), and is different from the + // operand x, signal underflow and inexact + tmp1 = 0x00038d7ea4c68000ull; // +100...0[16] * 10^emin + tmp2 = res & 0x7fffffffffffffffull; + tmp_fpsf = *pfpsf; // save fpsf +#if DECIMAL_CALL_BY_REFERENCE + bid64_quiet_greater (&res1, &tmp1, + &tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); + bid64_quiet_not_equal (&res2, &x, + &res _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#else + res1 = + bid64_quiet_greater (tmp1, + tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); + res2 = + bid64_quiet_not_equal (x, + res _EXC_FLAGS_ARG _EXC_MASKS_ARG + _EXC_INFO_ARG); +#endif + *pfpsf = tmp_fpsf; // restore fpsf + if (res1 && res2) { + // if (bid64_quiet_greater (tmp1, tmp2, &tmp_fpsf) && + // bid64_quiet_not_equal (x, res, &tmp_fpsf)) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // set the underflow flag + *pfpsf |= UNDERFLOW_EXCEPTION; + } + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_noncomp.c b/gcc-4.4.3/libgcc/config/libbid/bid64_noncomp.c new file mode 100644 index 000000000..5e10a52b1 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_noncomp.c @@ -0,0 +1,954 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +static const UINT64 mult_factor[16] = { + 1ull, 10ull, 100ull, 1000ull, + 10000ull, 100000ull, 1000000ull, 10000000ull, + 100000000ull, 1000000000ull, 10000000000ull, 100000000000ull, + 1000000000000ull, 10000000000000ull, + 100000000000000ull, 1000000000000000ull +}; + +/***************************************************************************** + * BID64 non-computational functions: + * - bid64_isSigned + * - bid64_isNormal + * - bid64_isSubnormal + * - bid64_isFinite + * - bid64_isZero + * - bid64_isInf + * - bid64_isSignaling + * - bid64_isCanonical + * - bid64_isNaN + * - bid64_copy + * - bid64_negate + * - bid64_abs + * - bid64_copySign + * - bid64_class + * - bid64_sameQuantum + * - bid64_totalOrder + * - bid64_totalOrderMag + * - bid64_radix + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_isSigned (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_isSigned (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); +} + +// return 1 iff x is not zero, nor NaN nor subnormal nor infinity +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_isNormal (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_isNormal (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + UINT128 sig_x_prime; + UINT64 sig_x; + unsigned int exp_x; + + if ((x & MASK_INF) == MASK_INF) { // x is either INF or NaN + res = 0; + } else { + // decode number into exponent and significand + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + // check for zero or non-canonical + if (sig_x > 9999999999999999ull || sig_x == 0) { + res = 0; // zero or non-canonical + BID_RETURN (res); + } + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + } else { + sig_x = (x & MASK_BINARY_SIG1); + if (sig_x == 0) { + res = 0; // zero + BID_RETURN (res); + } + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + } + // if exponent is less than -383, the number may be subnormal + // if (exp_x - 398 = -383) the number may be subnormal + if (exp_x < 15) { + __mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]); + if (sig_x_prime.w[1] == 0 + && sig_x_prime.w[0] < 1000000000000000ull) { + res = 0; // subnormal + } else { + res = 1; // normal + } + } else { + res = 1; // normal + } + } + BID_RETURN (res); +} + +// return 1 iff x is not zero, nor NaN nor normal nor infinity +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_isSubnormal (int *pres, + UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_isSubnormal (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + UINT128 sig_x_prime; + UINT64 sig_x; + unsigned int exp_x; + + if ((x & MASK_INF) == MASK_INF) { // x is either INF or NaN + res = 0; + } else { + // decode number into exponent and significand + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + // check for zero or non-canonical + if (sig_x > 9999999999999999ull || sig_x == 0) { + res = 0; // zero or non-canonical + BID_RETURN (res); + } + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + } else { + sig_x = (x & MASK_BINARY_SIG1); + if (sig_x == 0) { + res = 0; // zero + BID_RETURN (res); + } + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + } + // if exponent is less than -383, the number may be subnormal + // if (exp_x - 398 = -383) the number may be subnormal + if (exp_x < 15) { + __mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]); + if (sig_x_prime.w[1] == 0 + && sig_x_prime.w[0] < 1000000000000000ull) { + res = 1; // subnormal + } else { + res = 0; // normal + } + } else { + res = 0; // normal + } + } + BID_RETURN (res); +} + +//iff x is zero, subnormal or normal (not infinity or NaN) +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_isFinite (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_isFinite (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + + res = ((x & MASK_INF) != MASK_INF); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_isZero (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_isZero (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + + // if infinity or nan, return 0 + if ((x & MASK_INF) == MASK_INF) { + res = 0; + } else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] + // => sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + // if(sig_x > 9999999999999999ull) {return 1;} + res = + (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > + 9999999999999999ull); + } else { + res = ((x & MASK_BINARY_SIG1) == 0); + } + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_isInf (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_isInf (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + + res = ((x & MASK_INF) == MASK_INF) && ((x & MASK_NAN) != MASK_NAN); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_isSignaling (int *pres, + UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_isSignaling (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + + res = ((x & MASK_SNAN) == MASK_SNAN); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_isCanonical (int *pres, + UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_isCanonical (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + + if ((x & MASK_NAN) == MASK_NAN) { // NaN + if (x & 0x01fc000000000000ull) { + res = 0; + } else if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { // payload + res = 0; + } else { + res = 1; + } + } else if ((x & MASK_INF) == MASK_INF) { + if (x & 0x03ffffffffffffffull) { + res = 0; + } else { + res = 1; + } + } else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // 54-bit coeff. + res = + (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) <= + 9999999999999999ull); + } else { // 53-bit coeff. + res = 1; + } + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_isNaN (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_isNaN (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + + res = ((x & MASK_NAN) == MASK_NAN); + BID_RETURN (res); +} + +// copies a floating-point operand x to destination y, with no change +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_copy (UINT64 * pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_copy (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT64 res; + + res = x; + BID_RETURN (res); +} + +// copies a floating-point operand x to destination y, reversing the sign +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_negate (UINT64 * pres, + UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_negate (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT64 res; + + res = x ^ MASK_SIGN; + BID_RETURN (res); +} + +// copies a floating-point operand x to destination y, changing the sign to positive +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_abs (UINT64 * pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_abs (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT64 res; + + res = x & ~MASK_SIGN; + BID_RETURN (res); +} + +// copies operand x to destination in the same format as x, but +// with the sign of y +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_copySign (UINT64 * pres, UINT64 * px, + UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +UINT64 +bid64_copySign (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT64 res; + + res = (x & ~MASK_SIGN) | (y & MASK_SIGN); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_class (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_class (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + UINT128 sig_x_prime; + UINT64 sig_x; + int exp_x; + + if ((x & MASK_NAN) == MASK_NAN) { + // is the NaN signaling? + if ((x & MASK_SNAN) == MASK_SNAN) { + res = signalingNaN; + BID_RETURN (res); + } + // if NaN and not signaling, must be quietNaN + res = quietNaN; + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { + // is the Infinity negative? + if ((x & MASK_SIGN) == MASK_SIGN) { + res = negativeInfinity; + } else { + // otherwise, must be positive infinity + res = positiveInfinity; + } + BID_RETURN (res); + } else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // decode number into exponent and significand + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + // check for zero or non-canonical + if (sig_x > 9999999999999999ull || sig_x == 0) { + if ((x & MASK_SIGN) == MASK_SIGN) { + res = negativeZero; + } else { + res = positiveZero; + } + BID_RETURN (res); + } + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + } else { + sig_x = (x & MASK_BINARY_SIG1); + if (sig_x == 0) { + res = + ((x & MASK_SIGN) == MASK_SIGN) ? negativeZero : positiveZero; + BID_RETURN (res); + } + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + } + // if exponent is less than -383, number may be subnormal + // if (exp_x - 398 < -383) + if (exp_x < 15) { // sig_x *10^exp_x + __mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]); + if (sig_x_prime.w[1] == 0 + && (sig_x_prime.w[0] < 1000000000000000ull)) { + res = + ((x & MASK_SIGN) == + MASK_SIGN) ? negativeSubnormal : positiveSubnormal; + BID_RETURN (res); + } + } + // otherwise, normal number, determine the sign + res = + ((x & MASK_SIGN) == MASK_SIGN) ? negativeNormal : positiveNormal; + BID_RETURN (res); +} + +// true if the exponents of x and y are the same, false otherwise. +// The special cases of sameQuantum (NaN, NaN) and sameQuantum (Inf, Inf) are +// true. +// If exactly one operand is infinite or exactly one operand is NaN, then false +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_sameQuantum (int *pres, UINT64 * px, + UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_sameQuantum (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + unsigned int exp_x, exp_y; + + // if both operands are NaN, return true; if just one is NaN, return false + if ((x & MASK_NAN) == MASK_NAN || ((y & MASK_NAN) == MASK_NAN)) { + res = ((x & MASK_NAN) == MASK_NAN && (y & MASK_NAN) == MASK_NAN); + BID_RETURN (res); + } + // if both operands are INF, return true; if just one is INF, return false + if ((x & MASK_INF) == MASK_INF || (y & MASK_INF) == MASK_INF) { + res = ((x & MASK_INF) == MASK_INF && (y & MASK_INF) == MASK_INF); + BID_RETURN (res); + } + // decode exponents for both numbers, and return true if they match + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + } + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + } + res = (exp_x == exp_y); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_totalOrder (int *pres, UINT64 * px, + UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_totalOrder (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y, pyld_y, pyld_x; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0; + + // NaN (CASE1) + // if x and y are unordered numerically because either operand is NaN + // (1) totalOrder(-NaN, number) is true + // (2) totalOrder(number, +NaN) is true + // (3) if x and y are both NaN: + // i) negative sign bit < positive sign bit + // ii) signaling < quiet for +NaN, reverse for -NaN + // iii) lesser payload < greater payload for +NaN (reverse for -NaN) + // iv) else if bitwise identical (in canonical form), return 1 + if ((x & MASK_NAN) == MASK_NAN) { + // if x is -NaN + if ((x & MASK_SIGN) == MASK_SIGN) { + // return true, unless y is -NaN also + if ((y & MASK_NAN) != MASK_NAN || (y & MASK_SIGN) != MASK_SIGN) { + res = 1; // y is a number, return 1 + BID_RETURN (res); + } else { // if y and x are both -NaN + // if x and y are both -sNaN or both -qNaN, we have to compare payloads + // this xnor statement evaluates to true if both are sNaN or qNaN + if (! + (((y & MASK_SNAN) == MASK_SNAN) ^ ((x & MASK_SNAN) == + MASK_SNAN))) { + // it comes down to the payload. we want to return true if x has a + // larger payload, or if the payloads are equal (canonical forms + // are bitwise identical) + pyld_y = y & 0x0003ffffffffffffull; + pyld_x = x & 0x0003ffffffffffffull; + if (pyld_y > 999999999999999ull || pyld_y == 0) { + // if y is zero, x must be less than or numerically equal + // y's payload is 0 + res = 1; + BID_RETURN (res); + } + // if x is zero and y isn't, x has the smaller payload + // definitely (since we know y isn't 0 at this point) + if (pyld_x > 999999999999999ull || pyld_x == 0) { + // x's payload is 0 + res = 0; + BID_RETURN (res); + } + res = (pyld_x >= pyld_y); + BID_RETURN (res); + } else { + // either x = -sNaN and y = -qNaN or x = -qNaN and y = -sNaN + res = (y & MASK_SNAN) == MASK_SNAN; // totalOrder(-qNaN, -sNaN) == 1 + BID_RETURN (res); + } + } + } else { // x is +NaN + // return false, unless y is +NaN also + if ((y & MASK_NAN) != MASK_NAN || (y & MASK_SIGN) == MASK_SIGN) { + res = 0; // y is a number, return 1 + BID_RETURN (res); + } else { + // x and y are both +NaN; + // must investigate payload if both quiet or both signaling + // this xnor statement will be true if both x and y are +qNaN or +sNaN + if (! + (((y & MASK_SNAN) == MASK_SNAN) ^ ((x & MASK_SNAN) == + MASK_SNAN))) { + // it comes down to the payload. we want to return true if x has a + // smaller payload, or if the payloads are equal (canonical forms + // are bitwise identical) + pyld_y = y & 0x0003ffffffffffffull; + pyld_x = x & 0x0003ffffffffffffull; + // if x is zero and y isn't, x has the smaller + // payload definitely (since we know y isn't 0 at this point) + if (pyld_x > 999999999999999ull || pyld_x == 0) { + res = 1; + BID_RETURN (res); + } + if (pyld_y > 999999999999999ull || pyld_y == 0) { + // if y is zero, x must be less than or numerically equal + res = 0; + BID_RETURN (res); + } + res = (pyld_x <= pyld_y); + BID_RETURN (res); + } else { + // return true if y is +qNaN and x is +sNaN + // (we know they're different bc of xor if_stmt above) + res = ((x & MASK_SNAN) == MASK_SNAN); + BID_RETURN (res); + } + } + } + } else if ((y & MASK_NAN) == MASK_NAN) { + // x is certainly not NAN in this case. + // return true if y is positive + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits are the same, these numbers are equal. + if (x == y) { + res = 1; + BID_RETURN (res); + } + // OPPOSITE SIGNS (CASE 3) + // if signs are opposite, return 1 if x is negative + // (if xy + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull || sig_x == 0) { + x_is_zero = 1; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + if (sig_x == 0) { + x_is_zero = 1; + } + } + + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull || sig_y == 0) { + y_is_zero = 1; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + if (sig_y == 0) { + y_is_zero = 1; + } + } + + // ZERO (CASE 5) + // if x and y represent the same entities, and + // both are negative , return true iff exp_x <= exp_y + if (x_is_zero && y_is_zero) { + if (!((x & MASK_SIGN) == MASK_SIGN) ^ + ((y & MASK_SIGN) == MASK_SIGN)) { + // if signs are the same: + // totalOrder(x,y) iff exp_x >= exp_y for negative numbers + // totalOrder(x,y) iff exp_x <= exp_y for positive numbers + if (exp_x == exp_y) { + res = 1; + BID_RETURN (res); + } + res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } else { + // signs are different. + // totalOrder(-0, +0) is true + // totalOrder(+0, -0) is false + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + } + // if x is zero and y isn't, clearly x has the smaller payload. + if (x_is_zero) { + res = ((y & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if y is zero, and x isn't, clearly y has the smaller payload. + if (y_is_zero) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller, + // it is clear what needs to be done + if (sig_x > sig_y && exp_x >= exp_y) { + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, it is + // definitely larger, so no need for compensation + if (exp_x - exp_y > 15) { + // difference cannot be greater than 10^15 + res = ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if exp_x is 15 less than exp_y, it is + // definitely smaller, no need for compensation + if (exp_y - exp_x > 15) { + res = ((x & MASK_SIGN) != MASK_SIGN); + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down + // to the compensated significand + if (exp_x > exp_y) { + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + // if x and y represent the same entities, + // and both are negative, return true iff exp_x <= exp_y + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + // case cannot occure, because all bits must + // be the same - would have been caught if (x==y) + res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // if positive, return 1 if adjusted x is smaller than y + res = ((sig_n_prime.w[1] == 0) + && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == + MASK_SIGN); + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // if x and y represent the same entities, + // and both are negative, return true iff exp_x <= exp_y + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + // Cannot occur, because all bits must be the same. + // Case would have been caught if (x==y) + res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN); + BID_RETURN (res); + } + // values are not equal, for positive numbers return 1 + // if x is less than y. 0 otherwise + res = ((sig_n_prime.w[1] > 0) + || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == + MASK_SIGN); + BID_RETURN (res); +} + +// totalOrderMag is TotalOrder(abs(x), abs(y)) +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_totalOrderMag (int *pres, UINT64 * px, + UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; + UINT64 y = *py; +#else +int +bid64_totalOrderMag (UINT64 x, + UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + int exp_x, exp_y; + UINT64 sig_x, sig_y, pyld_y, pyld_x; + UINT128 sig_n_prime; + char x_is_zero = 0, y_is_zero = 0; + + // NaN (CASE 1) + // if x and y are unordered numerically because either operand is NaN + // (1) totalOrder(number, +NaN) is true + // (2) if x and y are both NaN: + // i) signaling < quiet for +NaN + // ii) lesser payload < greater payload for +NaN + // iii) else if bitwise identical (in canonical form), return 1 + if ((x & MASK_NAN) == MASK_NAN) { + // x is +NaN + + // return false, unless y is +NaN also + if ((y & MASK_NAN) != MASK_NAN) { + res = 0; // y is a number, return 1 + BID_RETURN (res); + + } else { + + // x and y are both +NaN; + // must investigate payload if both quiet or both signaling + // this xnor statement will be true if both x and y are +qNaN or +sNaN + if (! + (((y & MASK_SNAN) == MASK_SNAN) ^ ((x & MASK_SNAN) == + MASK_SNAN))) { + // it comes down to the payload. we want to return true if x has a + // smaller payload, or if the payloads are equal (canonical forms + // are bitwise identical) + pyld_y = y & 0x0003ffffffffffffull; + pyld_x = x & 0x0003ffffffffffffull; + // if x is zero and y isn't, x has the smaller + // payload definitely (since we know y isn't 0 at this point) + if (pyld_x > 999999999999999ull || pyld_x == 0) { + res = 1; + BID_RETURN (res); + } + + if (pyld_y > 999999999999999ull || pyld_y == 0) { + // if y is zero, x must be less than or numerically equal + res = 0; + BID_RETURN (res); + } + res = (pyld_x <= pyld_y); + BID_RETURN (res); + + } else { + // return true if y is +qNaN and x is +sNaN + // (we know they're different bc of xor if_stmt above) + res = ((x & MASK_SNAN) == MASK_SNAN); + BID_RETURN (res); + } + } + + } else if ((y & MASK_NAN) == MASK_NAN) { + // x is certainly not NAN in this case. + // return true if y is positive + res = 1; + BID_RETURN (res); + } + // SIMPLE (CASE2) + // if all the bits (except sign bit) are the same, + // these numbers are equal. + if ((x & ~MASK_SIGN) == (y & ~MASK_SIGN)) { + res = 1; + BID_RETURN (res); + } + // INFINITY (CASE3) + if ((x & MASK_INF) == MASK_INF) { + // x is positive infinity, only return1 + // if y is positive infinity as well + res = ((y & MASK_INF) == MASK_INF); + BID_RETURN (res); + } else if ((y & MASK_INF) == MASK_INF) { + // x is finite, so: + // if y is +inf, x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; + sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_x > 9999999999999999ull || sig_x == 0) { + x_is_zero = 1; + } + } else { + exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; + sig_x = (x & MASK_BINARY_SIG1); + if (sig_x == 0) { + x_is_zero = 1; + } + } + + // if steering bits are 11 (condition will be 0), + // then exponent is G[0:w+1] => + if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; + sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (sig_y > 9999999999999999ull || sig_y == 0) { + y_is_zero = 1; + } + } else { + exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; + sig_y = (y & MASK_BINARY_SIG1); + if (sig_y == 0) { + y_is_zero = 1; + } + } + + // ZERO (CASE 5) + // if x and y represent the same entities, + // and both are negative , return true iff exp_x <= exp_y + if (x_is_zero && y_is_zero) { + // totalOrder(x,y) iff exp_x <= exp_y for positive numbers + res = (exp_x <= exp_y); + BID_RETURN (res); + } + // if x is zero and y isn't, clearly x has the smaller payload. + if (x_is_zero) { + res = 1; + BID_RETURN (res); + } + // if y is zero, and x isn't, clearly y has the smaller payload. + if (y_is_zero) { + res = 0; + BID_RETURN (res); + } + // REDUNDANT REPRESENTATIONS (CASE6) + // if both components are either bigger or smaller + if (sig_x > sig_y && exp_x >= exp_y) { + res = 0; + BID_RETURN (res); + } + if (sig_x < sig_y && exp_x <= exp_y) { + res = 1; + BID_RETURN (res); + } + // if exp_x is 15 greater than exp_y, it is definitely + // larger, so no need for compensation + if (exp_x - exp_y > 15) { + res = 0; // difference cannot be greater than 10^15 + BID_RETURN (res); + } + // if exp_x is 15 less than exp_y, it is definitely + // smaller, no need for compensation + if (exp_y - exp_x > 15) { + res = 1; + BID_RETURN (res); + } + // if |exp_x - exp_y| < 15, it comes down + // to the compensated significand + if (exp_x > exp_y) { + + // otherwise adjust the x significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_x, + mult_factor[exp_x - exp_y]); + + // if x and y represent the same entities, + // and both are negative, return true iff exp_x <= exp_y + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { + // case cannot occur, because all bits + // must be the same - would have been caught if (x==y) + res = (exp_x <= exp_y); + BID_RETURN (res); + } + // if positive, return 1 if adjusted x is smaller than y + res = ((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y); + BID_RETURN (res); + } + // adjust the y significand upwards + __mul_64x64_to_128MACH (sig_n_prime, sig_y, + mult_factor[exp_y - exp_x]); + + // if x and y represent the same entities, + // and both are negative, return true iff exp_x <= exp_y + if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { + res = (exp_x <= exp_y); + BID_RETURN (res); + } + // values are not equal, for positive numbers + // return 1 if x is less than y. 0 otherwise + res = ((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])); + BID_RETURN (res); + +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_radix (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_radix (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + int res; + if (x) // dummy test + res = 10; + else + res = 10; + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_quantize.c b/gcc-4.4.3/libgcc/config/libbid/bid64_quantize.c new file mode 100644 index 000000000..d5c28cc76 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_quantize.c @@ -0,0 +1,236 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +#define MAX_FORMAT_DIGITS 16 +#define DECIMAL_EXPONENT_BIAS 398 +#define MAX_DECIMAL_EXPONENT 767 + +#if DECIMAL_CALL_BY_REFERENCE + +void +bid64_quantize (UINT64 * pres, UINT64 * px, + UINT64 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x, y; +#else + +UINT64 +bid64_quantize (UINT64 x, + UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 CT; + UINT64 sign_x, sign_y, coefficient_x, coefficient_y, remainder_h, C64, + valid_x; + UINT64 tmp, carry, res; + int_float tempx; + int exponent_x, exponent_y, digits_x, extra_digits, amount, amount2; + int expon_diff, total_digits, bin_expon_cx; + unsigned rmode, status; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif + x = *px; + y = *py; +#endif + + valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x); + // unpack arguments, check for NaN or Infinity + if (!unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y)) { + // Inf. or NaN or 0 +#ifdef SET_STATUS_FLAGS + if ((x & SNAN_MASK64) == SNAN_MASK64) // y is sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + + // x=Inf, y=Inf? + if (((coefficient_x << 1) == 0xf000000000000000ull) + && ((coefficient_y << 1) == 0xf000000000000000ull)) { + res = coefficient_x; + BID_RETURN (res); + } + // Inf or NaN? + if ((y & 0x7800000000000000ull) == 0x7800000000000000ull) { +#ifdef SET_STATUS_FLAGS + if (((y & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN + || (((y & 0x7c00000000000000ull) == 0x7800000000000000ull) && //Inf + ((x & 0x7c00000000000000ull) < 0x7800000000000000ull))) + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + if ((y & NAN_MASK64) != NAN_MASK64) + coefficient_y = 0; + if ((x & NAN_MASK64) != NAN_MASK64) { + res = 0x7c00000000000000ull | (coefficient_y & QUIET_MASK64); + if (((y & NAN_MASK64) != NAN_MASK64) && ((x & NAN_MASK64) == 0x7800000000000000ull)) + res = x; + BID_RETURN (res); + } + } + } + // unpack arguments, check for NaN or Infinity + if (!valid_x) { + // x is Inf. or NaN or 0 + + // Inf or NaN? + if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) { +#ifdef SET_STATUS_FLAGS + if (((x & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN + || ((x & 0x7c00000000000000ull) == 0x7800000000000000ull)) //Inf + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + if ((x & NAN_MASK64) != NAN_MASK64) + coefficient_x = 0; + res = 0x7c00000000000000ull | (coefficient_x & QUIET_MASK64); + BID_RETURN (res); + } + + res = very_fast_get_BID64_small_mantissa (sign_x, exponent_y, 0); + BID_RETURN (res); + } + // get number of decimal digits in coefficient_x + tempx.d = (float) coefficient_x; + bin_expon_cx = ((tempx.i >> 23) & 0xff) - 0x7f; + digits_x = estimate_decimal_digits[bin_expon_cx]; + if (coefficient_x >= power10_table_128[digits_x].w[0]) + digits_x++; + + expon_diff = exponent_x - exponent_y; + total_digits = digits_x + expon_diff; + + // check range of scaled coefficient + if ((UINT32) (total_digits + 1) <= 17) { + if (expon_diff >= 0) { + coefficient_x *= power10_table_128[expon_diff].w[0]; + res = very_fast_get_BID64 (sign_x, exponent_y, coefficient_x); + BID_RETURN (res); + } + // must round off -expon_diff digits + extra_digits = -expon_diff; +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = rnd_mode; + if (sign_x && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#else + rmode = 0; +#endif +#else + rmode = 0; +#endif + coefficient_x += round_const_table[rmode][extra_digits]; + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_64x64_to_128 (CT, coefficient_x, + reciprocals10_64[extra_digits]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 + amount = short_recip_scale[extra_digits]; + C64 = CT.w[1] >> amount; +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rnd_mode == 0) +#endif + if (C64 & 1) { + // check whether fractional part of initial_P/10^extra_digits + // is exactly .5 + // this is the same as fractional part of + // (initial_P + 0.5*10^extra_digits)/10^extra_digits is exactly zero + + // get remainder + amount2 = 64 - amount; + remainder_h = 0; + remainder_h--; + remainder_h >>= amount2; + remainder_h = remainder_h & CT.w[1]; + + // test whether fractional part is 0 + if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits])) { + C64--; + } + } +#endif + +#ifdef SET_STATUS_FLAGS + status = INEXACT_EXCEPTION; + // get remainder + remainder_h = CT.w[1] << (64 - amount); + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if ((remainder_h == 0x8000000000000000ull) + && (CT.w[0] < reciprocals10_64[extra_digits])) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits])) + status = EXACT_STATUS; + //if(!C64 && rmode==ROUNDING_DOWN) sign_s=sign_y; + break; + default: + // round up + __add_carry_out (tmp, carry, CT.w[0], + reciprocals10_64[extra_digits]); + if ((remainder_h >> (64 - amount)) + carry >= + (((UINT64) 1) << amount)) + status = EXACT_STATUS; + break; + } + __set_status_flags (pfpsf, status); +#endif + + res = very_fast_get_BID64_small_mantissa (sign_x, exponent_y, C64); + BID_RETURN (res); + } + + if (total_digits < 0) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INEXACT_EXCEPTION); +#endif + C64 = 0; +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = rnd_mode; + if (sign_x && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + if (rmode == ROUNDING_UP) + C64 = 1; +#endif +#endif + res = very_fast_get_BID64_small_mantissa (sign_x, exponent_y, C64); + BID_RETURN (res); + } + // else more than 16 digits in coefficient +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res = 0x7c00000000000000ull; + BID_RETURN (res); + +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_rem.c b/gcc-4.4.3/libgcc/config/libbid/bid64_rem.c new file mode 100644 index 000000000..f3baaf778 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_rem.c @@ -0,0 +1,228 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +/***************************************************************************** + * BID64 remainder + ***************************************************************************** + * + * Algorithm description: + * + * if(exponent_x < exponent_y) + * scale coefficient_y so exponents are aligned + * perform coefficient divide (64-bit integer divide), unless + * coefficient_y is longer than 64 bits (clearly larger + * than coefficient_x) + * else // exponent_x > exponent_y + * use a loop to scale coefficient_x to 18_digits, divide by + * coefficient_y (64-bit integer divide), calculate remainder + * as new_coefficient_x and repeat until final remainder is obtained + * (when new_exponent_x < exponent_y) + * + ****************************************************************************/ + +#include "bid_internal.h" + +#define MAX_FORMAT_DIGITS 16 +#define DECIMAL_EXPONENT_BIAS 398 +#define MASK_BINARY_EXPONENT 0x7ff0000000000000ull +#define BINARY_EXPONENT_BIAS 0x3ff +#define UPPER_EXPON_LIMIT 51 + +#if DECIMAL_CALL_BY_REFERENCE + +void +bid64_rem (UINT64 * pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x, y; +#else + +UINT64 +bid64_rem (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 CY; + UINT64 sign_x, sign_y, coefficient_x, coefficient_y, res; + UINT64 Q, R, R2, T, valid_y, valid_x; + int_float tempx; + int exponent_x, exponent_y, bin_expon, e_scale; + int digits_x, diff_expon; + +#if DECIMAL_CALL_BY_REFERENCE + x = *px; + y = *py; +#endif + + valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y); + valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x); + + // unpack arguments, check for NaN or Infinity + if (!valid_x) { + // x is Inf. or NaN or 0 +#ifdef SET_STATUS_FLAGS + if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + + // test if x is NaN + if ((x & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if (((x & SNAN_MASK64) == SNAN_MASK64)) + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res = coefficient_x & QUIET_MASK64;; + BID_RETURN (res); + } + // x is Infinity? + if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) { + if (((y & NAN_MASK64) != NAN_MASK64)) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + // return NaN + res = 0x7c00000000000000ull; + BID_RETURN (res); + } + } + // x is 0 + // return x if y != 0 + if (((y & 0x7800000000000000ull) < 0x7800000000000000ull) && + coefficient_y) { + if ((y & 0x6000000000000000ull) == 0x6000000000000000ull) + exponent_y = (y >> 51) & 0x3ff; + else + exponent_y = (y >> 53) & 0x3ff; + + if (exponent_y < exponent_x) + exponent_x = exponent_y; + + x = exponent_x; + x <<= 53; + + res = x | sign_x; + BID_RETURN (res); + } + + } + if (!valid_y) { + // y is Inf. or NaN + + // test if y is NaN + if ((y & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if (((y & SNAN_MASK64) == SNAN_MASK64)) + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res = coefficient_y & QUIET_MASK64;; + BID_RETURN (res); + } + // y is Infinity? + if ((y & 0x7800000000000000ull) == 0x7800000000000000ull) { + res = very_fast_get_BID64 (sign_x, exponent_x, coefficient_x); + BID_RETURN (res); + } + // y is 0, return NaN + { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res = 0x7c00000000000000ull; + BID_RETURN (res); + } + } + + + diff_expon = exponent_x - exponent_y; + if (diff_expon <= 0) { + diff_expon = -diff_expon; + + if (diff_expon > 16) { + // |x|<|y| in this case + res = x; + BID_RETURN (res); + } + // set exponent of y to exponent_x, scale coefficient_y + T = power10_table_128[diff_expon].w[0]; + __mul_64x64_to_128 (CY, coefficient_y, T); + + if (CY.w[1] || CY.w[0] > (coefficient_x << 1)) { + res = x; + BID_RETURN (res); + } + + Q = coefficient_x / CY.w[0]; + R = coefficient_x - Q * CY.w[0]; + + R2 = R + R; + if (R2 > CY.w[0] || (R2 == CY.w[0] && (Q & 1))) { + R = CY.w[0] - R; + sign_x ^= 0x8000000000000000ull; + } + + res = very_fast_get_BID64 (sign_x, exponent_x, R); + BID_RETURN (res); + } + + + while (diff_expon > 0) { + // get number of digits in coeff_x + tempx.d = (float) coefficient_x; + bin_expon = ((tempx.i >> 23) & 0xff) - 0x7f; + digits_x = estimate_decimal_digits[bin_expon]; + // will not use this test, dividend will have 18 or 19 digits + //if(coefficient_x >= power10_table_128[digits_x].w[0]) + // digits_x++; + + e_scale = 18 - digits_x; + if (diff_expon >= e_scale) { + diff_expon -= e_scale; + } else { + e_scale = diff_expon; + diff_expon = 0; + } + + // scale dividend to 18 or 19 digits + coefficient_x *= power10_table_128[e_scale].w[0]; + + // quotient + Q = coefficient_x / coefficient_y; + // remainder + coefficient_x -= Q * coefficient_y; + + // check for remainder == 0 + if (!coefficient_x) { + res = very_fast_get_BID64_small_mantissa (sign_x, exponent_y, 0); + BID_RETURN (res); + } + } + + R2 = coefficient_x + coefficient_x; + if (R2 > coefficient_y || (R2 == coefficient_y && (Q & 1))) { + coefficient_x = coefficient_y - coefficient_x; + sign_x ^= 0x8000000000000000ull; + } + + res = very_fast_get_BID64 (sign_x, exponent_y, coefficient_x); + BID_RETURN (res); + +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_round_integral.c b/gcc-4.4.3/libgcc/config/libbid/bid64_round_integral.c new file mode 100644 index 000000000..e89f47bb7 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_round_integral.c @@ -0,0 +1,1221 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID64_round_integral_exact + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_round_integral_exact (UINT64 * pres, + UINT64 * + px _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 x_sign; + int exp; // unbiased exponent + // Note: C1 represents the significand (UINT64) + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q, ind, shift; + UINT64 C1; + // UINT64 res is C* at first - represents up to 16 decimal digits <= 54 bits + UINT128 fstar = { {0x0ull, 0x0ull} }; + UINT128 P128; + + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + res = x_sign | 0x7800000000000000ull; + BID_RETURN (res); + } + // unpack x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11 (condition will be 0), then + // the exponent is G[0:w+1] + exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + C1 = 0; + } + } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) + exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; + C1 = (x & MASK_BINARY_SIG1); + } + + // if x is 0 or non-canonical return 0 preserving the sign bit and + // the preferred exponent of MAX(Q(x), 0) + if (C1 == 0) { + if (exp < 0) + exp = 0; + res = x_sign | (((UINT64) exp + 398) << 53); + BID_RETURN (res); + } + // x is a finite non-zero number (not 0, non-canonical, or special) + + switch (rnd_mode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // return 0 if (exp <= -(p+1)) + if (exp <= -17) { + res = x_sign | 0x31c0000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_DOWN: + // return 0 if (exp <= -p) + if (exp <= -16) { + if (x_sign) { + res = 0xb1c0000000000001ull; + } else { + res = 0x31c0000000000000ull; + } + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_UP: + // return 0 if (exp <= -p) + if (exp <= -16) { + if (x_sign) { + res = 0xb1c0000000000000ull; + } else { + res = 0x31c0000000000001ull; + } + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_TO_ZERO: + // return 0 if (exp <= -p) + if (exp <= -16) { + res = x_sign | 0x31c0000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + } // end switch () + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + q = 16; + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + } + + if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res = x; + BID_RETURN (res); + } + + switch (rnd_mode) { + case ROUNDING_TO_NEAREST: + if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (0 < f* < 10^(-x)) then the result is a midpoint + // since round_to_even, subtract 1 if current result is odd + if ((res & 0x0000000000000001ull) && (fstar.w[1] == 0) + && (fstar.w[0] < ten2mk64[ind - 1])) { + res--; + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > 0x8000000000000000ull) { + // f* > 1/2 and the result may be exact + // fstar.w[0] - 0x8000000000000000ull is f* - 1/2 + if ((fstar.w[0] - 0x8000000000000000ull) > ten2mk64[ind - 1]) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 3 <= ind - 1 <= 21 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + if (fstar.w[1] > onehalf128[ind - 1] + || fstar.w[0] > ten2mk64[ind - 1]) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp < 0 + // the result is +0 or -0 + res = x_sign | 0x31c0000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_TIES_AWAY: + if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // if (0 < f* < 10^(-x)) then the result is a midpoint + // C* = floor(C*) - logical right shift; C* has p decimal digits, + // correct by Prop. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // midpoints are already rounded correctly + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > 0x8000000000000000ull) { + // f* > 1/2 and the result may be exact + // fstar.w[0] - 0x8000000000000000ull is f* - 1/2 + if ((fstar.w[0] - 0x8000000000000000ull) > ten2mk64[ind - 1]) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 3 <= ind - 1 <= 21 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + if (fstar.w[1] > onehalf128[ind - 1] + || fstar.w[0] > ten2mk64[ind - 1]) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp < 0 + // the result is +0 or -0 + res = x_sign | 0x31c0000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_DOWN: + if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // if (0 < f* < 10^(-x)) then the result is exact + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (f* > 10^(-x)) then the result is inexact + if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) { + if (x_sign) { + // if negative and not exact, increment magnitude + res++; + } + *pfpsf |= INEXACT_EXCEPTION; + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp <= 0 + // the result is +0 or -1 + if (x_sign) { + res = 0xb1c0000000000001ull; + } else { + res = 0x31c0000000000000ull; + } + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_UP: + if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // if (0 < f* < 10^(-x)) then the result is exact + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (f* > 10^(-x)) then the result is inexact + if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) { + if (!x_sign) { + // if positive and not exact, increment magnitude + res++; + } + *pfpsf |= INEXACT_EXCEPTION; + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp <= 0 + // the result is -0 or +1 + if (x_sign) { + res = 0xb1c0000000000000ull; + } else { + res = 0x31c0000000000001ull; + } + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_TO_ZERO: + if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // if (0 < f* < 10^(-x)) then the result is exact + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (f* > 10^(-x)) then the result is inexact + if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) { + *pfpsf |= INEXACT_EXCEPTION; + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp < 0 + // the result is +0 or -0 + res = x_sign | 0x31c0000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + } // end switch () + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_round_integral_nearest_even + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_round_integral_nearest_even (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_round_integral_nearest_even (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 x_sign; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 fstar; + UINT128 P128; + + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + res = x_sign | 0x7800000000000000ull; + BID_RETURN (res); + } + // unpack x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11 (condition will be 0), then + // the exponent is G[0:w+1] + exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + C1 = 0; + } + } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) + exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; + C1 = (x & MASK_BINARY_SIG1); + } + + // if x is 0 or non-canonical + if (C1 == 0) { + if (exp < 0) + exp = 0; + res = x_sign | (((UINT64) exp + 398) << 53); + BID_RETURN (res); + } + // x is a finite non-zero number (not 0, non-canonical, or special) + + // return 0 if (exp <= -(p+1)) + if (exp <= -17) { + res = x_sign | 0x31c0000000000000ull; + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + q = 16; + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + } + + if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res = x; + BID_RETURN (res); + } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (0 < f* < 10^(-x)) then the result is a midpoint + // since round_to_even, subtract 1 if current result is odd + if ((res & 0x0000000000000001ull) && (fstar.w[1] == 0) + && (fstar.w[0] < ten2mk64[ind - 1])) { + res--; + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp < 0 + // the result is +0 or -0 + res = x_sign | 0x31c0000000000000ull; + BID_RETURN (res); + } +} + +/***************************************************************************** + * BID64_round_integral_negative + *****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_round_integral_negative (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_round_integral_negative (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 x_sign; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q, ind, shift; + UINT64 C1; + // UINT64 res is C* at first - represents up to 34 decimal digits ~ 113 bits + UINT128 fstar; + UINT128 P128; + + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + res = x_sign | 0x7800000000000000ull; + BID_RETURN (res); + } + // unpack x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11 (condition will be 0), then + // the exponent is G[0:w+1] + exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + C1 = 0; + } + } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) + exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; + C1 = (x & MASK_BINARY_SIG1); + } + + // if x is 0 or non-canonical + if (C1 == 0) { + if (exp < 0) + exp = 0; + res = x_sign | (((UINT64) exp + 398) << 53); + BID_RETURN (res); + } + // x is a finite non-zero number (not 0, non-canonical, or special) + + // return 0 if (exp <= -p) + if (exp <= -16) { + if (x_sign) { + res = 0xb1c0000000000001ull; + } else { + res = 0x31c0000000000000ull; + } + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + q = 16; + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + } + + if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res = x; + BID_RETURN (res); + } else if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // if (0 < f* < 10^(-x)) then the result is exact + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (f* > 10^(-x)) then the result is inexact + if (x_sign + && ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1]))) { + // if negative and not exact, increment magnitude + res++; + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp <= 0 + // the result is +0 or -1 + if (x_sign) { + res = 0xb1c0000000000001ull; + } else { + res = 0x31c0000000000000ull; + } + BID_RETURN (res); + } +} + +/***************************************************************************** + * BID64_round_integral_positive + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_round_integral_positive (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_round_integral_positive (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 x_sign; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q, ind, shift; + UINT64 C1; + // UINT64 res is C* at first - represents up to 34 decimal digits ~ 113 bits + UINT128 fstar; + UINT128 P128; + + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + res = x_sign | 0x7800000000000000ull; + BID_RETURN (res); + } + // unpack x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11 (condition will be 0), then + // the exponent is G[0:w+1] + exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + C1 = 0; + } + } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) + exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; + C1 = (x & MASK_BINARY_SIG1); + } + + // if x is 0 or non-canonical + if (C1 == 0) { + if (exp < 0) + exp = 0; + res = x_sign | (((UINT64) exp + 398) << 53); + BID_RETURN (res); + } + // x is a finite non-zero number (not 0, non-canonical, or special) + + // return 0 if (exp <= -p) + if (exp <= -16) { + if (x_sign) { + res = 0xb1c0000000000000ull; + } else { + res = 0x31c0000000000001ull; + } + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + q = 16; + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + } + + if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res = x; + BID_RETURN (res); + } else if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // if (0 < f* < 10^(-x)) then the result is exact + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (f* > 10^(-x)) then the result is inexact + if (!x_sign + && ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1]))) { + // if positive and not exact, increment magnitude + res++; + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp <= 0 + // the result is -0 or +1 + if (x_sign) { + res = 0xb1c0000000000000ull; + } else { + res = 0x31c0000000000001ull; + } + BID_RETURN (res); + } +} + +/***************************************************************************** + * BID64_round_integral_zero + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_round_integral_zero (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_round_integral_zero (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 x_sign; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q, ind, shift; + UINT64 C1; + // UINT64 res is C* at first - represents up to 34 decimal digits ~ 113 bits + UINT128 P128; + + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + res = x_sign | 0x7800000000000000ull; + BID_RETURN (res); + } + // unpack x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11 (condition will be 0), then + // the exponent is G[0:w+1] + exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + C1 = 0; + } + } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) + exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; + C1 = (x & MASK_BINARY_SIG1); + } + + // if x is 0 or non-canonical + if (C1 == 0) { + if (exp < 0) + exp = 0; + res = x_sign | (((UINT64) exp + 398) << 53); + BID_RETURN (res); + } + // x is a finite non-zero number (not 0, non-canonical, or special) + + // return 0 if (exp <= -p) + if (exp <= -16) { + res = x_sign | 0x31c0000000000000ull; + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + q = 16; + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + } + + if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res = x; + BID_RETURN (res); + } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // if (0 < f* < 10^(-x)) then the result is exact + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + // redundant fstar.w[1] = 0; + // redundant fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + // redundant fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + // redundant fstar.w[0] = P128.w[0]; + } + // if (f* > 10^(-x)) then the result is inexact + // if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind-1])){ + // // redundant + // } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp < 0 + // the result is +0 or -0 + res = x_sign | 0x31c0000000000000ull; + BID_RETURN (res); + } +} + +/***************************************************************************** + * BID64_round_integral_nearest_away + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_round_integral_nearest_away (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_round_integral_nearest_away (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 x_sign; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 P128; + + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + res = x_sign | 0x7800000000000000ull; + BID_RETURN (res); + } + // unpack x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11 (condition will be 0), then + // the exponent is G[0:w+1] + exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + C1 = 0; + } + } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) + exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; + C1 = (x & MASK_BINARY_SIG1); + } + + // if x is 0 or non-canonical + if (C1 == 0) { + if (exp < 0) + exp = 0; + res = x_sign | (((UINT64) exp + 398) << 53); + BID_RETURN (res); + } + // x is a finite non-zero number (not 0, non-canonical, or special) + + // return 0 if (exp <= -(p+1)) + if (exp <= -17) { + res = x_sign | 0x31c0000000000000ull; + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + q = 16; + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + } + + if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res = x; + BID_RETURN (res); + } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // if (0 < f* < 10^(-x)) then the result is a midpoint + // C* = floor(C*) - logical right shift; C* has p decimal digits, + // correct by Prop. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + } + // midpoints are already rounded correctly + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp < 0 + // the result is +0 or -0 + res = x_sign | 0x31c0000000000000ull; + BID_RETURN (res); + } +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_scalb.c b/gcc-4.4.3/libgcc/config/libbid/bid64_scalb.c new file mode 100644 index 000000000..a565d6598 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_scalb.c @@ -0,0 +1,105 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +#define MAX_FORMAT_DIGITS 16 +#define DECIMAL_EXPONENT_BIAS 398 +#define MAX_DECIMAL_EXPONENT 767 + +#if DECIMAL_CALL_BY_REFERENCE + +void +bid64_scalb (UINT64 * pres, UINT64 * px, + int *pn _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x; + int n; +#else + +UINT64 +bid64_scalb (UINT64 x, + int n _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 sign_x, coefficient_x, res; + SINT64 exp64; + int exponent_x, rmode; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif + x = *px; + n = *pn; +#endif + + // unpack arguments, check for NaN or Infinity + if (!unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x)) { + // x is Inf. or NaN or 0 +#ifdef SET_STATUS_FLAGS + if ((x & SNAN_MASK64) == SNAN_MASK64) // y is sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + if (coefficient_x) + res = coefficient_x & QUIET_MASK64; + else { + exp64 = (SINT64) exponent_x + (SINT64) n; + if(exp64<0) exp64=0; + if(exp64>MAX_DECIMAL_EXPONENT) exp64=MAX_DECIMAL_EXPONENT; + exponent_x = exp64; + res = very_fast_get_BID64 (sign_x, exponent_x, coefficient_x); // 0 + } + BID_RETURN (res); + } + + exp64 = (SINT64) exponent_x + (SINT64) n; + exponent_x = exp64; + + if ((UINT32) exponent_x <= MAX_DECIMAL_EXPONENT) { + res = very_fast_get_BID64 (sign_x, exponent_x, coefficient_x); + BID_RETURN (res); + } + // check for overflow + if (exp64 > MAX_DECIMAL_EXPONENT) { + // try to normalize coefficient + while ((coefficient_x < 1000000000000000ull) + && (exp64 > MAX_DECIMAL_EXPONENT)) { + // coefficient_x < 10^15, scale by 10 + coefficient_x = (coefficient_x << 1) + (coefficient_x << 3); + exponent_x--; + exp64--; + } + if (exp64 <= MAX_DECIMAL_EXPONENT) { + res = very_fast_get_BID64 (sign_x, exponent_x, coefficient_x); + BID_RETURN (res); + } else + exponent_x = 0x7fffffff; // overflow + } + // exponent < 0 + // the BID pack routine will round the coefficient + rmode = rnd_mode; + res = get_BID64 (sign_x, exponent_x, coefficient_x, rmode, pfpsf); + BID_RETURN (res); + +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_sqrt.c b/gcc-4.4.3/libgcc/config/libbid/bid64_sqrt.c new file mode 100644 index 000000000..310ab9459 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_sqrt.c @@ -0,0 +1,552 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +/***************************************************************************** + * BID64 square root + ***************************************************************************** + * + * Algorithm description: + * + * if(exponent_x is odd) + * scale coefficient_x by 10, adjust exponent + * - get lower estimate for number of digits in coefficient_x + * - scale coefficient x to between 31 and 33 decimal digits + * - in parallel, check for exact case and return if true + * - get high part of result coefficient using double precision sqrt + * - compute remainder and refine coefficient in one iteration (which + * modifies it by at most 1) + * - result exponent is easy to compute from the adjusted arg. exponent + * + ****************************************************************************/ + +#include "bid_internal.h" +#include "bid_sqrt_macros.h" +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +#include + +#define FE_ALL_FLAGS FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT +#endif + +extern double sqrt (double); + +#if DECIMAL_CALL_BY_REFERENCE + +void +bid64_sqrt (UINT64 * pres, + UINT64 * + px _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x; +#else + +UINT64 +bid64_sqrt (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 CA, CT; + UINT64 sign_x, coefficient_x; + UINT64 Q, Q2, A10, C4, R, R2, QE, res; + SINT64 D; + int_double t_scale; + int_float tempx; + double da, dq, da_h, da_l, dqe; + int exponent_x, exponent_q, bin_expon_cx; + int digits_x; + int scale; +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + fexcept_t binaryflags = 0; +#endif + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif + x = *px; +#endif + + // unpack arguments, check for NaN or Infinity + if (!unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x)) { + // x is Inf. or NaN or 0 + if ((x & INFINITY_MASK64) == INFINITY_MASK64) { + res = coefficient_x; + if ((coefficient_x & SSNAN_MASK64) == SINFINITY_MASK64) // -Infinity + { + res = NAN_MASK64; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + } +#ifdef SET_STATUS_FLAGS + if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (res & QUIET_MASK64); + } + // x is 0 + exponent_x = (exponent_x + DECIMAL_EXPONENT_BIAS) >> 1; + res = sign_x | (((UINT64) exponent_x) << 53); + BID_RETURN (res); + } + // x<0? + if (sign_x && coefficient_x) { + res = NAN_MASK64; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (res); + } +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + //--- get number of bits in the coefficient of x --- + tempx.d = (float) coefficient_x; + bin_expon_cx = ((tempx.i >> 23) & 0xff) - 0x7f; + digits_x = estimate_decimal_digits[bin_expon_cx]; + // add test for range + if (coefficient_x >= power10_index_binexp[bin_expon_cx]) + digits_x++; + + A10 = coefficient_x; + if (exponent_x & 1) { + A10 = (A10 << 2) + A10; + A10 += A10; + } + + dqe = sqrt ((double) A10); + QE = (UINT32) dqe; + if (QE * QE == A10) { + res = + very_fast_get_BID64 (0, (exponent_x + DECIMAL_EXPONENT_BIAS) >> 1, + QE); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + // if exponent is odd, scale coefficient by 10 + scale = 31 - digits_x; + exponent_q = exponent_x - scale; + scale += (exponent_q & 1); // exp. bias is even + + CT = power10_table_128[scale]; + __mul_64x128_short (CA, coefficient_x, CT); + + // 2^64 + t_scale.i = 0x43f0000000000000ull; + // convert CA to DP + da_h = CA.w[1]; + da_l = CA.w[0]; + da = da_h * t_scale.d + da_l; + + dq = sqrt (da); + + Q = (UINT64) dq; + + // get sign(sqrt(CA)-Q) + R = CA.w[0] - Q * Q; + R = ((SINT64) R) >> 63; + D = R + R + 1; + + exponent_q = (exponent_q + DECIMAL_EXPONENT_BIAS) >> 1; + +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INEXACT_EXCEPTION); +#endif + +#ifndef IEEE_ROUND_NEAREST +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY + if (!((rnd_mode) & 3)) { +#endif +#endif + + // midpoint to check + Q2 = Q + Q + D; + C4 = CA.w[0] << 2; + + // get sign(-sqrt(CA)+Midpoint) + R2 = Q2 * Q2 - C4; + R2 = ((SINT64) R2) >> 63; + + // adjust Q if R!=R2 + Q += (D & (R ^ R2)); +#ifndef IEEE_ROUND_NEAREST +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY + } else { + C4 = CA.w[0]; + Q += D; + if ((SINT64) (Q * Q - C4) > 0) + Q--; + if (rnd_mode == ROUNDING_UP) + Q++; + } +#endif +#endif + + res = fast_get_BID64 (0, exponent_q, Q); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); +} + + +TYPE0_FUNCTION_ARG1 (UINT64, bid64q_sqrt, x) + + UINT256 M256, C4, C8; + UINT128 CX, CX2, A10, S2, T128, CS, CSM, CS2, C256, CS1, + mul_factor2_long = { {0x0ull, 0x0ull} }, QH, Tmp, TP128, Qh, Ql; +UINT64 sign_x, Carry, B10, res, mul_factor, mul_factor2 = 0x0ull, CS0; +SINT64 D; +int_float fx, f64; +int exponent_x, bin_expon_cx, done = 0; +int digits, scale, exponent_q = 0, exact = 1, amount, extra_digits; +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +fexcept_t binaryflags = 0; +#endif + + // unpack arguments, check for NaN or Infinity +if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { + res = CX.w[1]; + // NaN ? + if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { +#ifdef SET_STATUS_FLAGS + if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull); + Tmp.w[0] = CX.w[0]; + TP128 = reciprocals10_128[18]; + __mul_128x128_full (Qh, Ql, Tmp, TP128); + amount = recip_scale[18]; + __shr_128 (Tmp, Qh, amount); + res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; + BID_RETURN (res); + } + // x is Infinity? + if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { + if (sign_x) { + // -Inf, return NaN + res = 0x7c00000000000000ull; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + } + BID_RETURN (res); + } + // x is 0 otherwise + + exponent_x = + ((exponent_x - DECIMAL_EXPONENT_BIAS_128) >> 1) + + DECIMAL_EXPONENT_BIAS; + if (exponent_x < 0) + exponent_x = 0; + if (exponent_x > DECIMAL_MAX_EXPON_64) + exponent_x = DECIMAL_MAX_EXPON_64; + //res= sign_x | (((UINT64)exponent_x)<<53); + res = get_BID64 (sign_x, exponent_x, 0, rnd_mode, pfpsf); + BID_RETURN (res); +} +if (sign_x) { + res = 0x7c00000000000000ull; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN (res); +} +#ifdef UNCHANGED_BINARY_STATUS_FLAGS +(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + + // 2^64 +f64.i = 0x5f800000; + + // fx ~ CX +fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; +bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f; +digits = estimate_decimal_digits[bin_expon_cx]; + +A10 = CX; +if (exponent_x & 1) { + A10.w[1] = (CX.w[1] << 3) | (CX.w[0] >> 61); + A10.w[0] = CX.w[0] << 3; + CX2.w[1] = (CX.w[1] << 1) | (CX.w[0] >> 63); + CX2.w[0] = CX.w[0] << 1; + __add_128_128 (A10, A10, CX2); +} + +C256.w[1] = A10.w[1]; +C256.w[0] = A10.w[0]; +CS.w[0] = short_sqrt128 (A10); +CS.w[1] = 0; +mul_factor = 0; + // check for exact result +if (CS.w[0] < 10000000000000000ull) { + if (CS.w[0] * CS.w[0] == A10.w[0]) { + __sqr64_fast (S2, CS.w[0]); + if (S2.w[1] == A10.w[1]) // && S2.w[0]==A10.w[0]) + { + res = + get_BID64 (0, + ((exponent_x - DECIMAL_EXPONENT_BIAS_128) >> 1) + + DECIMAL_EXPONENT_BIAS, CS.w[0], rnd_mode, pfpsf); +#ifdef UNCHANGED_BINARY_STATUS_FLAGS + (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); +#endif + BID_RETURN (res); + } + } + if (CS.w[0] >= 1000000000000000ull) { + done = 1; + exponent_q = exponent_x; + C256.w[1] = A10.w[1]; + C256.w[0] = A10.w[0]; + } +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INEXACT_EXCEPTION); +#endif + exact = 0; +} else { + B10 = 0x3333333333333334ull; + __mul_64x64_to_128_full (CS2, CS.w[0], B10); + CS0 = CS2.w[1] >> 1; + if (CS.w[0] != ((CS0 << 3) + (CS0 << 1))) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INEXACT_EXCEPTION); +#endif + exact = 0; + } + done = 1; + CS.w[0] = CS0; + exponent_q = exponent_x + 2; + mul_factor = 10; + mul_factor2 = 100; + if (CS.w[0] >= 10000000000000000ull) { + __mul_64x64_to_128_full (CS2, CS.w[0], B10); + CS0 = CS2.w[1] >> 1; + if (CS.w[0] != ((CS0 << 3) + (CS0 << 1))) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INEXACT_EXCEPTION); +#endif + exact = 0; + } + exponent_q += 2; + CS.w[0] = CS0; + mul_factor = 100; + mul_factor2 = 10000; + } + if (exact) { + CS0 = CS.w[0] * mul_factor; + __sqr64_fast (CS1, CS0) + if ((CS1.w[0] != A10.w[0]) || (CS1.w[1] != A10.w[1])) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, INEXACT_EXCEPTION); +#endif + exact = 0; + } + } +} + +if (!done) { + // get number of digits in CX + D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1]; + if (D > 0 + || (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0])) + digits++; + + // if exponent is odd, scale coefficient by 10 + scale = 31 - digits; + exponent_q = exponent_x - scale; + scale += (exponent_q & 1); // exp. bias is even + + T128 = power10_table_128[scale]; + __mul_128x128_low (C256, CX, T128); + + + CS.w[0] = short_sqrt128 (C256); +} + //printf("CS=%016I64x\n",CS.w[0]); + +exponent_q = + ((exponent_q - DECIMAL_EXPONENT_BIAS_128) >> 1) + + DECIMAL_EXPONENT_BIAS; +if ((exponent_q < 0) && (exponent_q + MAX_FORMAT_DIGITS >= 0)) { + extra_digits = -exponent_q; + exponent_q = 0; + + // get coeff*(2^M[extra_digits])/10^extra_digits + __mul_64x64_to_128 (QH, CS.w[0], reciprocals10_64[extra_digits]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = short_recip_scale[extra_digits]; + + CS0 = QH.w[1] >> amount; + +#ifdef SET_STATUS_FLAGS + if (exact) { + if (CS.w[0] != CS0 * power10_table_128[extra_digits].w[0]) + exact = 0; + } + if (!exact) + __set_status_flags (pfpsf, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); +#endif + + CS.w[0] = CS0; + if (!mul_factor) + mul_factor = 1; + mul_factor *= power10_table_128[extra_digits].w[0]; + __mul_64x64_to_128 (mul_factor2_long, mul_factor, mul_factor); + if (mul_factor2_long.w[1]) + mul_factor2 = 0; + else + mul_factor2 = mul_factor2_long.w[1]; +} + // 4*C256 +C4.w[1] = (C256.w[1] << 2) | (C256.w[0] >> 62); +C4.w[0] = C256.w[0] << 2; + +#ifndef IEEE_ROUND_NEAREST +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +if (!((rnd_mode) & 3)) { +#endif +#endif + // compare to midpoints + CSM.w[0] = (CS.w[0] + CS.w[0]) | 1; + //printf("C256=%016I64x %016I64x, CSM=%016I64x %016I64x %016I64x\n",C4.w[1],C4.w[0],CSM.w[1],CSM.w[0], CS.w[0]); + if (mul_factor) + CSM.w[0] *= mul_factor; + // CSM^2 + __mul_64x64_to_128 (M256, CSM.w[0], CSM.w[0]); + //__mul_128x128_to_256(M256, CSM, CSM); + + if (C4.w[1] > M256.w[1] || + (C4.w[1] == M256.w[1] && C4.w[0] > M256.w[0])) { + // round up + CS.w[0]++; + } else { + C8.w[0] = CS.w[0] << 3; + C8.w[1] = 0; + if (mul_factor) { + if (mul_factor2) { + __mul_64x64_to_128 (C8, C8.w[0], mul_factor2); + } else { + __mul_64x128_low (C8, C8.w[0], mul_factor2_long); + } + } + // M256 - 8*CSM + __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]); + M256.w[1] = M256.w[1] - C8.w[1] - Carry; + + // if CSM' > C256, round up + if (M256.w[1] > C4.w[1] || + (M256.w[1] == C4.w[1] && M256.w[0] > C4.w[0])) { + // round down + if (CS.w[0]) + CS.w[0]--; + } + } +#ifndef IEEE_ROUND_NEAREST +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +} else { + CS.w[0]++; + CSM.w[0] = CS.w[0]; + C8.w[0] = CSM.w[0] << 1; + if (mul_factor) + CSM.w[0] *= mul_factor; + __mul_64x64_to_128 (M256, CSM.w[0], CSM.w[0]); + C8.w[1] = 0; + if (mul_factor) { + if (mul_factor2) { + __mul_64x64_to_128 (C8, C8.w[0], mul_factor2); + } else { + __mul_64x128_low (C8, C8.w[0], mul_factor2_long); + } + } + //printf("C256=%016I64x %016I64x, CSM=%016I64x %016I64x %016I64x\n",C256.w[1],C256.w[0],M256.w[1],M256.w[0], CS.w[0]); + + if (M256.w[1] > C256.w[1] || + (M256.w[1] == C256.w[1] && M256.w[0] > C256.w[0])) { + __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]); + M256.w[1] = M256.w[1] - Carry - C8.w[1]; + M256.w[0]++; + if (!M256.w[0]) { + M256.w[1]++; + + } + + if ((M256.w[1] > C256.w[1] || + (M256.w[1] == C256.w[1] && M256.w[0] > C256.w[0])) + && (CS.w[0] > 1)) { + + CS.w[0]--; + + if (CS.w[0] > 1) { + __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]); + M256.w[1] = M256.w[1] - Carry - C8.w[1]; + M256.w[0]++; + if (!M256.w[0]) { + M256.w[1]++; + } + + if (M256.w[1] > C256.w[1] || + (M256.w[1] == C256.w[1] && M256.w[0] > C256.w[0])) + CS.w[0]--; + } + } + } + + else { + /*__add_carry_out(M256.w[0], Carry, M256.w[0], C8.w[0]); + M256.w[1] = M256.w[1] + Carry + C8.w[1]; + M256.w[0]++; + if(!M256.w[0]) + { + M256.w[1]++; + } + CS.w[0]++; + if(M256.w[1]. */ + +#include +#include "bid_internal.h" +#include "bid128_2_str.h" +#include "bid128_2_str_macros.h" + +#define MAX_FORMAT_DIGITS 16 +#define DECIMAL_EXPONENT_BIAS 398 +#define MAX_DECIMAL_EXPONENT 767 + +#if DECIMAL_CALL_BY_REFERENCE + +void +bid64_to_string (char *ps, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x; +#else + +void +bid64_to_string (char *ps, UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif +// the destination string (pointed to by ps) must be pre-allocated + UINT64 sign_x, coefficient_x, D, ER10; + int istart, exponent_x, j, digits_x, bin_expon_cx; + int_float tempx; + UINT32 MiDi[12], *ptr; + UINT64 HI_18Dig, LO_18Dig, Tmp; + char *c_ptr_start, *c_ptr; + int midi_ind, k_lcv, len; + unsigned int save_fpsf; + +#if DECIMAL_CALL_BY_REFERENCE + x = *px; +#endif + + save_fpsf = *pfpsf; // place holder only + // unpack arguments, check for NaN or Infinity + if (!unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x)) { + // x is Inf. or NaN or 0 + + // Inf or NaN? + if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) { + if ((x & 0x7c00000000000000ull) == 0x7c00000000000000ull) { + ps[0] = (sign_x) ? '-' : '+'; + ps[1] = ((x & MASK_SNAN) == MASK_SNAN)? 'S':'Q'; + ps[2] = 'N'; + ps[3] = 'a'; + ps[4] = 'N'; + ps[5] = 0; + return; + } + // x is Inf + ps[0] = (sign_x) ? '-' : '+'; + ps[1] = 'I'; + ps[2] = 'n'; + ps[3] = 'f'; + ps[4] = 0; + return; + } + // 0 + istart = 0; + if (sign_x) { + ps[istart++] = '-'; + } + + ps[istart++] = '0'; + ps[istart++] = 'E'; + + exponent_x -= 398; + if (exponent_x < 0) { + ps[istart++] = '-'; + exponent_x = -exponent_x; + } else + ps[istart++] = '+'; + + if (exponent_x) { + // get decimal digits in coefficient_x + tempx.d = (float) exponent_x; + bin_expon_cx = ((tempx.i >> 23) & 0xff) - 0x7f; + digits_x = estimate_decimal_digits[bin_expon_cx]; + if ((UINT64)exponent_x >= power10_table_128[digits_x].w[0]) + digits_x++; + + j = istart + digits_x - 1; + istart = j + 1; + + // 2^32/10 + ER10 = 0x1999999a; + + while (exponent_x > 9) { + D = (UINT64) exponent_x *ER10; + D >>= 32; + exponent_x = exponent_x - (D << 1) - (D << 3); + + ps[j--] = '0' + (char) exponent_x; + exponent_x = D; + } + ps[j] = '0' + (char) exponent_x; + } else { + ps[istart++] = '0'; + } + + ps[istart] = 0; + + return; + } + // convert expon, coeff to ASCII + exponent_x -= DECIMAL_EXPONENT_BIAS; + + ER10 = 0x1999999a; + + istart = 0; + if (sign_x) { + ps[0] = '-'; + istart = 1; + } + // if zero or non-canonical, set coefficient to '0' + if ((coefficient_x > 9999999999999999ull) || // non-canonical + ((coefficient_x == 0)) // significand is zero + ) { + ps[istart++] = '0'; + } else { + /* **************************************************** + This takes a bid coefficient in C1.w[1],C1.w[0] + and put the converted character sequence at location + starting at &(str[k]). The function returns the number + of MiDi returned. Note that the character sequence + does not have leading zeros EXCEPT when the input is of + zero value. It will then output 1 character '0' + The algorithm essentailly tries first to get a sequence of + Millenial Digits "MiDi" and then uses table lookup to get the + character strings of these MiDis. + **************************************************** */ + /* Algorithm first decompose possibly 34 digits in hi and lo + 18 digits. (The high can have at most 16 digits). It then + uses macro that handle 18 digit portions. + The first step is to get hi and lo such that + 2^(64) C1.w[1] + C1.w[0] = hi * 10^18 + lo, 0 <= lo < 10^18. + We use a table lookup method to obtain the hi and lo 18 digits. + [C1.w[1],C1.w[0]] = c_8 2^(107) + c_7 2^(101) + ... + c_0 2^(59) + d + where 0 <= d < 2^59 and each c_j has 6 bits. Because d fits in + 18 digits, we set hi = 0, and lo = d to begin with. + We then retrieve from a table, for j = 0, 1, ..., 8 + that gives us A and B where c_j 2^(59+6j) = A * 10^18 + B. + hi += A ; lo += B; After each accumulation into lo, we normalize + immediately. So at the end, we have the decomposition as we need. */ + + Tmp = coefficient_x >> 59; + LO_18Dig = (coefficient_x << 5) >> 5; + HI_18Dig = 0; + k_lcv = 0; + + while (Tmp) { + midi_ind = (int) (Tmp & 0x000000000000003FLL); + midi_ind <<= 1; + Tmp >>= 6; + HI_18Dig += mod10_18_tbl[k_lcv][midi_ind++]; + LO_18Dig += mod10_18_tbl[k_lcv++][midi_ind]; + __L0_Normalize_10to18 (HI_18Dig, LO_18Dig); + } + + ptr = MiDi; + __L1_Split_MiDi_6_Lead (LO_18Dig, ptr); + len = ptr - MiDi; + c_ptr_start = &(ps[istart]); + c_ptr = c_ptr_start; + + /* now convert the MiDi into character strings */ + __L0_MiDi2Str_Lead (MiDi[0], c_ptr); + for (k_lcv = 1; k_lcv < len; k_lcv++) { + __L0_MiDi2Str (MiDi[k_lcv], c_ptr); + } + istart = istart + (c_ptr - c_ptr_start); + } + + ps[istart++] = 'E'; + + if (exponent_x < 0) { + ps[istart++] = '-'; + exponent_x = -exponent_x; + } else + ps[istart++] = '+'; + + if (exponent_x) { + // get decimal digits in coefficient_x + tempx.d = (float) exponent_x; + bin_expon_cx = ((tempx.i >> 23) & 0xff) - 0x7f; + digits_x = estimate_decimal_digits[bin_expon_cx]; + if ((UINT64)exponent_x >= power10_table_128[digits_x].w[0]) + digits_x++; + + j = istart + digits_x - 1; + istart = j + 1; + + // 2^32/10 + ER10 = 0x1999999a; + + while (exponent_x > 9) { + D = (UINT64) exponent_x *ER10; + D >>= 32; + exponent_x = exponent_x - (D << 1) - (D << 3); + + ps[j--] = '0' + (char) exponent_x; + exponent_x = D; + } + ps[j] = '0' + (char) exponent_x; + } else { + ps[istart++] = '0'; + } + + ps[istart] = 0; + + return; + +} + + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_from_string (UINT64 * pres, char *ps + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#else +UINT64 +bid64_from_string (char *ps + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT64 sign_x, coefficient_x = 0, rounded = 0, res; + int expon_x = 0, sgn_expon, ndigits, add_expon = 0, midpoint = + 0, rounded_up = 0; + int dec_expon_scale = 0, right_radix_leading_zeros = 0, rdx_pt_enc = + 0; + unsigned fpsc; + char c; + unsigned int save_fpsf; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + + save_fpsf = *pfpsf; // place holder only + // eliminate leading whitespace + while (((*ps == ' ') || (*ps == '\t')) && (*ps)) + ps++; + + // get first non-whitespace character + c = *ps; + + // detect special cases (INF or NaN) + if (!c || (c != '.' && c != '-' && c != '+' && (c < '0' || c > '9'))) { + // Infinity? + if ((tolower_macro (ps[0]) == 'i' && tolower_macro (ps[1]) == 'n' && + tolower_macro (ps[2]) == 'f') && (!ps[3] || + (tolower_macro (ps[3]) == 'i' && + tolower_macro (ps[4]) == 'n' && tolower_macro (ps[5]) == 'i' && + tolower_macro (ps[6]) == 't' && tolower_macro (ps[7]) == 'y' && + !ps[8]))) { + res = 0x7800000000000000ull; + BID_RETURN (res); + } + // return sNaN + if (tolower_macro (ps[0]) == 's' && tolower_macro (ps[1]) == 'n' && + tolower_macro (ps[2]) == 'a' && tolower_macro (ps[3]) == 'n') { + // case insensitive check for snan + res = 0x7e00000000000000ull; + BID_RETURN (res); + } else { + // return qNaN + res = 0x7c00000000000000ull; + BID_RETURN (res); + } + } + // detect +INF or -INF + if ((tolower_macro (ps[1]) == 'i' && tolower_macro (ps[2]) == 'n' && + tolower_macro (ps[3]) == 'f') && (!ps[4] || + (tolower_macro (ps[4]) == 'i' && tolower_macro (ps[5]) == 'n' && + tolower_macro (ps[6]) == 'i' && tolower_macro (ps[7]) == 't' && + tolower_macro (ps[8]) == 'y' && !ps[9]))) { + if (c == '+') + res = 0x7800000000000000ull; + else if (c == '-') + res = 0xf800000000000000ull; + else + res = 0x7c00000000000000ull; + BID_RETURN (res); + } + // if +sNaN, +SNaN, -sNaN, or -SNaN + if (tolower_macro (ps[1]) == 's' && tolower_macro (ps[2]) == 'n' + && tolower_macro (ps[3]) == 'a' && tolower_macro (ps[4]) == 'n') { + if (c == '-') + res = 0xfe00000000000000ull; + else + res = 0x7e00000000000000ull; + BID_RETURN (res); + } + // determine sign + if (c == '-') + sign_x = 0x8000000000000000ull; + else + sign_x = 0; + + // get next character if leading +/- sign + if (c == '-' || c == '+') { + ps++; + c = *ps; + } + // if c isn't a decimal point or a decimal digit, return NaN + if (c != '.' && (c < '0' || c > '9')) { + // return NaN + res = 0x7c00000000000000ull | sign_x; + BID_RETURN (res); + } + + rdx_pt_enc = 0; + + // detect zero (and eliminate/ignore leading zeros) + if (*(ps) == '0' || *(ps) == '.') { + + if (*(ps) == '.') { + rdx_pt_enc = 1; + ps++; + } + // if all numbers are zeros (with possibly 1 radix point, the number is zero + // should catch cases such as: 000.0 + while (*ps == '0') { + ps++; + // for numbers such as 0.0000000000000000000000000000000000001001, + // we want to count the leading zeros + if (rdx_pt_enc) { + right_radix_leading_zeros++; + } + // if this character is a radix point, make sure we haven't already + // encountered one + if (*(ps) == '.') { + if (rdx_pt_enc == 0) { + rdx_pt_enc = 1; + // if this is the first radix point, and the next character is NULL, + // we have a zero + if (!*(ps + 1)) { + res = + ((UINT64) (398 - right_radix_leading_zeros) << 53) | + sign_x; + BID_RETURN (res); + } + ps = ps + 1; + } else { + // if 2 radix points, return NaN + res = 0x7c00000000000000ull | sign_x; + BID_RETURN (res); + } + } else if (!*(ps)) { + //pres->w[1] = 0x3040000000000000ull | sign_x; + res = + ((UINT64) (398 - right_radix_leading_zeros) << 53) | sign_x; + BID_RETURN (res); + } + } + } + + c = *ps; + + ndigits = 0; + while ((c >= '0' && c <= '9') || c == '.') { + if (c == '.') { + if (rdx_pt_enc) { + // return NaN + res = 0x7c00000000000000ull | sign_x; + BID_RETURN (res); + } + rdx_pt_enc = 1; + ps++; + c = *ps; + continue; + } + dec_expon_scale += rdx_pt_enc; + + ndigits++; + if (ndigits <= 16) { + coefficient_x = (coefficient_x << 1) + (coefficient_x << 3); + coefficient_x += (UINT64) (c - '0'); + } else if (ndigits == 17) { + // coefficient rounding + switch(rnd_mode){ + case ROUNDING_TO_NEAREST: + midpoint = (c == '5' && !(coefficient_x & 1)) ? 1 : 0; + // if coefficient is even and c is 5, prepare to round up if + // subsequent digit is nonzero + // if str[MAXDIG+1] > 5, we MUST round up + // if str[MAXDIG+1] == 5 and coefficient is ODD, ROUND UP! + if (c > '5' || (c == '5' && (coefficient_x & 1))) { + coefficient_x++; + rounded_up = 1; + break; + + case ROUNDING_DOWN: + if(sign_x) { coefficient_x++; rounded_up=1; } + break; + case ROUNDING_UP: + if(!sign_x) { coefficient_x++; rounded_up=1; } + break; + case ROUNDING_TIES_AWAY: + if(c>='5') { coefficient_x++; rounded_up=1; } + break; + } + if (coefficient_x == 10000000000000000ull) { + coefficient_x = 1000000000000000ull; + add_expon = 1; + } + } + if (c > '0') + rounded = 1; + add_expon += 1; + } else { // ndigits > 17 + add_expon++; + if (midpoint && c > '0') { + coefficient_x++; + midpoint = 0; + rounded_up = 1; + } + if (c > '0') + rounded = 1; + } + ps++; + c = *ps; + } + + add_expon -= (dec_expon_scale + right_radix_leading_zeros); + + if (!c) { + res = + fast_get_BID64_check_OF (sign_x, + add_expon + DECIMAL_EXPONENT_BIAS, + coefficient_x, 0, &fpsc); + BID_RETURN (res); + } + + if (c != 'E' && c != 'e') { + // return NaN + res = 0x7c00000000000000ull | sign_x; + BID_RETURN (res); + } + ps++; + c = *ps; + sgn_expon = (c == '-') ? 1 : 0; + if (c == '-' || c == '+') { + ps++; + c = *ps; + } + if (!c || c < '0' || c > '9') { + // return NaN + res = 0x7c00000000000000ull | sign_x; + BID_RETURN (res); + } + + while (c >= '0' && c <= '9') { + expon_x = (expon_x << 1) + (expon_x << 3); + expon_x += (int) (c - '0'); + + ps++; + c = *ps; + } + + if (c) { + // return NaN + res = 0x7c00000000000000ull | sign_x; + BID_RETURN (res); + } + + if (sgn_expon) + expon_x = -expon_x; + + expon_x += add_expon + DECIMAL_EXPONENT_BIAS; + + if (expon_x < 0) { + if (rounded_up) + coefficient_x--; + rnd_mode = 0; + res = + get_BID64_UF (sign_x, expon_x, coefficient_x, rounded, rnd_mode, + &fpsc); + BID_RETURN (res); + } + res = get_BID64 (sign_x, expon_x, coefficient_x, rnd_mode, &fpsc); + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_to_bid128.c b/gcc-4.4.3/libgcc/config/libbid/bid64_to_bid128.c new file mode 100644 index 000000000..5809a086b --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_to_bid128.c @@ -0,0 +1,262 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#define BID_128RES +#include "bid_internal.h" + +/* + * Takes a BID64 as input and converts it to a BID128 and returns it. + */ +TYPE0_FUNCTION_ARGTYPE1_NORND (UINT128, bid64_to_bid128, UINT64, x) + + UINT128 new_coeff, res; + UINT64 sign_x; + int exponent_x; + UINT64 coefficient_x; + +if (!unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x)) { +if (((x) << 1) >= 0xf000000000000000ull) { +#ifdef SET_STATUS_FLAGS + if (((x) & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + res.w[0] = (coefficient_x & 0x0003ffffffffffffull); + __mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]); + res.w[1] |= ((coefficient_x) & 0xfc00000000000000ull); + BID_RETURN (res); +} +} + +new_coeff.w[0] = coefficient_x; +new_coeff.w[1] = 0; +get_BID128_very_fast (&res, sign_x, + exponent_x + DECIMAL_EXPONENT_BIAS_128 - + DECIMAL_EXPONENT_BIAS, new_coeff); +BID_RETURN (res); +} // convert_bid64_to_bid128 + + + +/* + * Takes a BID128 as input and converts it to a BID64 and returns it. + */ +#if DECIMAL_CALL_BY_REFERENCE + +void +bid128_to_bid64 (UINT64 * pres, + UINT128 * + px _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px; +#else + +UINT64 +bid128_to_bid64 (UINT128 x _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 CX, T128, TP128, Qh, Ql, Qh1, Stemp, Tmp, Tmp1, CX1; + UINT64 sign_x, carry, cy, res; + SINT64 D; + int_float f64, fx; + int exponent_x, extra_digits, amount, bin_expon_cx; + unsigned rmode, status, uf_check = 0; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + + BID_SWAP128 (x); + // unpack arguments, check for NaN or Infinity or 0 + if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { + if ((x.w[1] << 1) >= 0xf000000000000000ull) { + Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull); + Tmp.w[0] = CX.w[0]; + TP128 = reciprocals10_128[18]; + __mul_128x128_full (Qh, Ql, Tmp, TP128); + amount = recip_scale[18]; + __shr_128 (Tmp, Qh, amount); + res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; +#ifdef SET_STATUS_FLAGS + if ((x.w[1] & SNAN_MASK64) == SNAN_MASK64) // sNaN + __set_status_flags (pfpsf, INVALID_EXCEPTION); +#endif + BID_RETURN_VAL (res); + } + exponent_x = + exponent_x - DECIMAL_EXPONENT_BIAS_128 + DECIMAL_EXPONENT_BIAS; + if (exponent_x < 0) { + res = sign_x; + BID_RETURN_VAL (res); + } + if (exponent_x > DECIMAL_MAX_EXPON_64) + exponent_x = DECIMAL_MAX_EXPON_64; + res = sign_x | (((UINT64) exponent_x) << 53); + BID_RETURN_VAL (res); + } + + if (CX.w[1] || (CX.w[0] >= 10000000000000000ull)) { + // find number of digits in coefficient + // 2^64 + f64.i = 0x5f800000; + // fx ~ CX + fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; + bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f; + extra_digits = estimate_decimal_digits[bin_expon_cx] - 16; + // scale = 38-estimate_decimal_digits[bin_expon_cx]; + D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1]; + if (D > 0 + || (!D + && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0])) + extra_digits++; + + exponent_x += extra_digits; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = rnd_mode; + if (sign_x && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#else + rmode = 0; +#endif +#else + rmode = 0; +#endif + if (exponent_x < DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS) { + uf_check = 1; + if (-extra_digits + exponent_x - DECIMAL_EXPONENT_BIAS_128 + + DECIMAL_EXPONENT_BIAS + 35 >= 0) { + if (exponent_x == + DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS - 1) { + T128 = round_const_table_128[rmode][extra_digits]; + __add_carry_out (CX1.w[0], carry, T128.w[0], CX.w[0]); + CX1.w[1] = CX.w[1] + T128.w[1] + carry; + if (__unsigned_compare_ge_128 + (CX1, power10_table_128[extra_digits + 16])) + uf_check = 0; + } + extra_digits = + extra_digits + DECIMAL_EXPONENT_BIAS_128 - + DECIMAL_EXPONENT_BIAS - exponent_x; + exponent_x = DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS; + //uf_check = 2; + } else + rmode = ROUNDING_TO_ZERO; + } + + T128 = round_const_table_128[rmode][extra_digits]; + __add_carry_out (CX.w[0], carry, T128.w[0], CX.w[0]); + CX.w[1] = CX.w[1] + T128.w[1] + carry; + + TP128 = reciprocals10_128[extra_digits]; + __mul_128x128_full (Qh, Ql, CX, TP128); + amount = recip_scale[extra_digits]; + + if (amount >= 64) { + CX.w[0] = Qh.w[1] >> (amount - 64); + CX.w[1] = 0; + } else { + __shr_128 (CX, Qh, amount); + } + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (!(rmode)) +#endif + if (CX.w[0] & 1) { + // check whether fractional part of initial_P/10^ed1 is exactly .5 + + // get remainder + __shl_128_long (Qh1, Qh, (128 - amount)); + + if (!Qh1.w[1] && !Qh1.w[0] + && (Ql.w[1] < reciprocals10_128[extra_digits].w[1] + || (Ql.w[1] == reciprocals10_128[extra_digits].w[1] + && Ql.w[0] < reciprocals10_128[extra_digits].w[0]))) { + CX.w[0]--; + } + } +#endif + + { + status = INEXACT_EXCEPTION; + // get remainder + __shl_128_long (Qh1, Qh, (128 - amount)); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if (Qh1.w[1] == 0x8000000000000000ull && (!Qh1.w[0]) + && (Ql.w[1] < reciprocals10_128[extra_digits].w[1] + || (Ql.w[1] == reciprocals10_128[extra_digits].w[1] + && Ql.w[0] < reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if ((!Qh1.w[1]) && (!Qh1.w[0]) + && (Ql.w[1] < reciprocals10_128[extra_digits].w[1] + || (Ql.w[1] == reciprocals10_128[extra_digits].w[1] + && Ql.w[0] < reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (Stemp.w[0], cy, Ql.w[0], + reciprocals10_128[extra_digits].w[0]); + __add_carry_in_out (Stemp.w[1], carry, Ql.w[1], + reciprocals10_128[extra_digits].w[1], cy); + __shr_128_long (Qh, Qh1, (128 - amount)); + Tmp.w[0] = 1; + Tmp.w[1] = 0; + __shl_128_long (Tmp1, Tmp, amount); + Qh.w[0] += carry; + if (Qh.w[0] < carry) + Qh.w[1]++; + if (__unsigned_compare_ge_128 (Qh, Tmp1)) + status = EXACT_STATUS; + } + + if (status != EXACT_STATUS) { + if (uf_check) + status |= UNDERFLOW_EXCEPTION; +#ifdef SET_STATUS_FLAGS + __set_status_flags (pfpsf, status); +#endif + } + + + } + + } + + res = + get_BID64 (sign_x, + exponent_x - DECIMAL_EXPONENT_BIAS_128 + + DECIMAL_EXPONENT_BIAS, CX.w[0], rnd_mode, pfpsf); + BID_RETURN_VAL (res); + +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_to_int16.c b/gcc-4.4.3/libgcc/config/libbid/bid64_to_int16.c new file mode 100644 index 000000000..5a682dbe5 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_to_int16.c @@ -0,0 +1,67 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +#define SIZE_MASK 0xffff8000 +#define INVALID_RESULT 0x8000 + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid64_to_int16_rnint, UINT64, x, + bid64_to_int32_rnint, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid64_to_int16_xrnint, UINT64, x, + bid64_to_int32_xrnint, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid64_to_int16_rninta, UINT64, x, + bid64_to_int32_rninta, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid64_to_int16_xrninta, UINT64, x, + bid64_to_int32_xrninta, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid64_to_int16_int, UINT64, x, + bid64_to_int32_int, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid64_to_int16_xint, UINT64, x, + bid64_to_int32_xint, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid64_to_int16_floor, UINT64, x, + bid64_to_int32_floor, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid64_to_int16_ceil, UINT64, x, + bid64_to_int32_ceil, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid64_to_int16_xfloor, UINT64, x, + bid64_to_int32_xfloor, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (short, bid64_to_int16_xceil, UINT64, x, + bid64_to_int32_xceil, int, SIZE_MASK, + INVALID_RESULT) diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_to_int32.c b/gcc-4.4.3/libgcc/config/libbid/bid64_to_int32.c new file mode 100644 index 000000000..8fd41f8cf --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_to_int32.c @@ -0,0 +1,2587 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID64_to_int32_rnint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int32_rnint (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_to_int32_rnint (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n < -2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005, 1<=q<=16 + // <=> C * 10^(11-q) > 0x500000005, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x500000005ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) > 0x500000005 <=> + // C > 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31+1/2 up) + // Note: 0x500000005*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x500000005ull * ten2k64[q - 11]; + if (C1 > tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x4fffffffb, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x4fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x4fffffffb <=> + // C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31-1/2 up) + // Note: 0x4fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x4fffffffbull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1/2 <= n < 2^31 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; + if (C1 <= midpoint64[ind]) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffff; // return -1 + } else { // n > 0 + res = 0x00000001; // return +1 + } + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^31-1/2 <= x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded + // to nearest to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[1] == 0) && fstar.w[0] + && (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // the result is a midpoint; round to nearest + if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar--; // Cstar is now even + } // else MP in [ODD, EVEN] + } + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int32_xrnint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int32_xrnint (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_to_int32_xrnint (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n < -2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005, 1<=q<=16 + // <=> C * 10^(11-q) > 0x500000005, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x500000005ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) > 0x500000005 <=> + // C > 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31+1/2 up) + // Note: 0x500000005*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x500000005ull * ten2k64[q - 11]; + if (C1 > tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x4fffffffb, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x4fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x4fffffffb <=> + // C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31-1/2 up) + // Note: 0x4fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x4fffffffbull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; + if (C1 <= midpoint64[ind]) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffff; // return -1 + } else { // n > 0 + res = 0x00000001; // return +1 + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^31-1/2 <= x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded + // to nearest to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > 0x8000000000000000ull) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[1] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[1] == 0) && fstar.w[0] + && (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // the result is a midpoint; round to nearest + if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar--; // Cstar is now even + } // else MP in [ODD, EVEN] + } + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int32_floor + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int32_floor (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_to_int32_floor (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n < -2^31 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x500000000, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000000 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x500000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) > 0x500000000 <=> + // C > 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31+1 up) + // Note: 0x500000000*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x500000000ull * ten2k64[q - 11]; + if (C1 > tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x500000000, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000000 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x500000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x500000000 <=> + // C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31-1 up) + // Note: 0x500000000*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x500000000ull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 <= n < 2^31 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // return -1 or 0 + if (x_sign) + res = 0xffffffff; + else + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded + // to nearest to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (x_sign) { // negative and inexact + Cstar++; + } + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (x_sign) { // negative and inexact + Cstar++; + } + } // else the result is exact + } + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int32_xfloor + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int32_xfloor (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_to_int32_xfloor (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n < -2^31 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x500000000, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000000 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x500000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) > 0x500000000 <=> + // C > 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31+1 up) + // Note: 0x500000000*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x500000000ull * ten2k64[q - 11]; + if (C1 > tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x500000000, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000000 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x500000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x500000000 <=> + // C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31-1 up) + // Note: 0x500000000*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x500000000ull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 <= n < 2^31 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return -1 or 0 + if (x_sign) + res = 0xffffffff; + else + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded + // to nearest to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (x_sign) { // negative and inexact + Cstar++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (x_sign) { // negative and inexact + Cstar++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int32_ceil + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int32_ceil (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_to_int32_ceil (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -2^31 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x50000000a, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x50000000a, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x50000000a has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x50000000aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x50000000a <=> + // C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31+1 up) + // Note: 0x50000000a*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x50000000aull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n > 2^31 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 - 1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6, 1<=q<=16 + // <=> C * 10^(11-q) > 0x4fffffff6, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x4fffffff6 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x4fffffff6ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) > 0x4fffffff6 <=> + // C > 0x4fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31-1 up) + // Note: 0x4fffffff6*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x4fffffff6ull * ten2k64[q - 11]; + if (C1 > tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1 < n <= 2^31 - 1 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // return 0 or 1 + if (x_sign) + res = 0x00000000; + else + res = 0x00000001; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^31-1 < x <= -1 or 1 <= x <= 2^31-1 so x can be rounded + // to nearest to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (!x_sign) { // positive and inexact + Cstar++; + } + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (!x_sign) { // positive and inexact + Cstar++; + } + } // else the result is exact + } + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int32_xceil + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int32_xceil (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_to_int32_xceil (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -2^31 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x50000000a, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x50000000a, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x50000000a has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x50000000aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x50000000a <=> + // C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31+1 up) + // Note: 0x50000000a*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x50000000aull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n > 2^31 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 - 1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6, 1<=q<=16 + // <=> C * 10^(11-q) > 0x4fffffff6, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x4fffffff6 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x4fffffff6ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) > 0x4fffffff6 <=> + // C > 0x4fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31-1 up) + // Note: 0x4fffffff6*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x4fffffff6ull * ten2k64[q - 11]; + if (C1 > tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1 < n <= 2^31 - 1 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 or 1 + if (x_sign) + res = 0x00000000; + else + res = 0x00000001; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^31-1 < x <= -1 or 1 <= x <= 2^31-1 so x can be rounded + // to nearest to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (!x_sign) { // positive and inexact + Cstar++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (!x_sign) { // positive and inexact + Cstar++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int32_int + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int32_int (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_to_int32_int (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -2^31 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x50000000a, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x50000000a, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x50000000a has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x50000000aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x50000000a <=> + // C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31+1 up) + // Note: 0x50000000a*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x50000000aull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x500000000, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000000 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x500000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x500000000 <=> + // C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31-1 up) + // Note: 0x500000000*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x500000000ull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1 < n < 2^31 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded + // to nearest to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int32_xint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int32_xint (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_to_int32_xint (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -2^31 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x50000000a, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x50000000a, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x50000000a has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x50000000aull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x50000000a <=> + // C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31+1 up) + // Note: 0x50000000a*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x50000000aull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x500000000, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000000 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x500000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x500000000 <=> + // C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31-1 up) + // Note: 0x500000000*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x500000000ull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1 < n < 2^31 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded + // to nearest to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int32_rninta + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int32_rninta (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_to_int32_rninta (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x500000005, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x500000005ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x500000005 <=> + // C >= 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31+1/2 up) + // Note: 0x500000005*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x500000005ull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x4fffffffb, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x4fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x4fffffffb <=> + // C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31-1/2 up) + // Note: 0x4fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x4fffffffbull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; + if (C1 < midpoint64[ind]) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffff; // return -1 + } else { // n > 0 + res = 0x00000001; // return +1 + } + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^31-1/2 <= x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded + // to nearest away to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*)-1 (logical right shift; C* has p decimal digits, + // correct by Pr. 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + + // if the result was a midpoint it was rounded away from zero + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int32_xrninta + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int32_xrninta (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +int +bid64_to_int32_xrninta (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in a signed 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 + // if n <= -2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x500000005, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x500000005ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x500000005 <=> + // C >= 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31+1/2 up) + // Note: 0x500000005*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x500000005ull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } else { // if n > 0 and q + exp = 10 + // if n >= 2^31 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x4fffffffb, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x4fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x4fffffffb <=> + // C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^31-1/2 up) + // Note: 0x4fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x4fffffffbull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; + if (C1 < midpoint64[ind]) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffff; // return -1 + } else { // n > 0 + res = 0x00000001; // return +1 + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^31-1/2 <= x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded + // to nearest away to a 32-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*)-1 (logical right shift; C* has p decimal digits, + // correct by Pr. 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > 0x8000000000000000ull) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[1] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + // if the result was a midpoint it was rounded away from zero + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_to_int64.c b/gcc-4.4.3/libgcc/config/libbid/bid64_to_int64.c new file mode 100644 index 000000000..e56bcbac5 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_to_int64.c @@ -0,0 +1,2329 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID64_to_int64_rnint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_rnint (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_rnint (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n < -2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64+1), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000005, 1<=q<=16 + // <=> C * 10^(20-q) > 0x50000000000000005, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x50000000000000005, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] > 0x05ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x4fffffffffffffffb, 1<=q<=16 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffffbull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] > 0x04ull || + (C.w[1] == 0x04ull && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1/2 <= n < 2^63-1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; // 0 <= ind <= 15 + if (C1 <= midpoint64[ind]) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1/2 <= x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[1] == 0) && fstar.w[0] && + (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // the result is a midpoint; round to nearest + if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar--; // Cstar is now even + } // else MP in [ODD, EVEN] + } + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_xrnint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_xrnint (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_xrnint (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n < -2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64+1), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000005, 1<=q<=16 + // <=> C * 10^(20-q) > 0x50000000000000005, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x50000000000000005, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] > 0x05ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x4fffffffffffffffb, 1<=q<=16 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffffbull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] > 0x04ull || + (C.w[1] == 0x04ull && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1/2 <= n < 2^63-1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; // 0 <= ind <= 15 + if (C1 <= midpoint64[ind]) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1/2 <= x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > 0x8000000000000000ull) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[1] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[1] == 0) && fstar.w[0] && + (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // the result is a midpoint; round to nearest + if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar--; // Cstar is now even + } // else MP in [ODD, EVEN] + } + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_floor + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_floor (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_floor (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n < -2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000000, 1<=q<=16 + // <=> C * 10^(20-q) > 0x50000000000000000, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] != 0)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x50000000000000000, 1<=q<=16 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] >= 0x05ull) { + // actually C.w[1] == 0x05ull && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63 <= n < 2^63 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return -1 or 0 + if (x_sign) + res = 0xffffffffffffffffull; + else + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63 <= x <= -1 or 1 <= x < 2^63 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (x_sign) { // negative and inexact + Cstar++; + } + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (x_sign) { // negative and inexact + Cstar++; + } + } // else the result is exact + } + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_xfloor + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_xfloor (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_xfloor (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n < -2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000000, 1<=q<=16 + // <=> C * 10^(20-q) > 0x50000000000000000, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] != 0)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x50000000000000000, 1<=q<=16 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] >= 0x05ull) { + // actually C.w[1] == 0x05ull && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63 <= n < 2^63 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return -1 or 0 + if (x_sign) + res = 0xffffffffffffffffull; + else + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63 <= x <= -1 or 1 <= x < 2^63 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (x_sign) { // negative and inexact + Cstar++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (x_sign) { // negative and inexact + Cstar++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_ceil + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_ceil (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_ceil (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=16 + // <=> C * 10^(20-q) >= 0x5000000000000000a, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x0aull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n > 2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 - 1 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64-2), 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 0x4fffffffffffffff6, 1<=q<=16 + // <=> if C * 10^(20-q) > 0x4fffffffffffffff6, 1<=q<=16 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffff6ull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] > 0x04ull || + (C.w[1] == 0x04ull && C.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1 < n < 2^63 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 or 1 + if (x_sign) + res = 0x00000000; + else + res = 0x00000001; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1 < x <= -1 or 1 <= x <= 2^63 - 1 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (!x_sign) { // positive and inexact + Cstar++; + } + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (!x_sign) { // positive and inexact + Cstar++; + } + } // else the result is exact + } + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_xceil + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_xceil (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_xceil (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=16 + // <=> C * 10^(20-q) >= 0x5000000000000000a, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x0aull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n > 2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 - 1 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64-2), 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 0x4fffffffffffffff6, 1<=q<=16 + // <=> if C * 10^(20-q) > 0x4fffffffffffffff6, 1<=q<=16 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffff6ull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] > 0x04ull || + (C.w[1] == 0x04ull && C.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1 < n < 2^63 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 or 1 + if (x_sign) + res = 0x00000000; + else + res = 0x00000001; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1 < x <= -1 or 1 <= x <= 2^63 - 1 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (!x_sign) { // positive and inexact + Cstar++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + if (!x_sign) { // positive and inexact + Cstar++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_int + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_int (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_int (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=16 + // <=> C * 10^(20-q) >= 0x5000000000000000a, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x0aull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x50000000000000000, 1<=q<=16 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] >= 0x05ull) { + // actually C.w[1] == 0x05ull && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1 < n < 2^63 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1 < x <= -1 or 1 <= x < 2^63 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_xint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_xint (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_xint (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=16 + // <=> C * 10^(20-q) >= 0x5000000000000000a, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x0aull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x50000000000000000, 1<=q<=16 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] >= 0x05ull) { + // actually C.w[1] == 0x05ull && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1 < n < 2^63 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1 < x <= -1 or 1 <= x < 2^63 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_rninta + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_rninta (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_rninta (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+1), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000005, 1<=q<=16 + // <=> C * 10^(20-q) >= 0x50000000000000005, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x50000000000000005, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x05ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x4fffffffffffffffb, 1<=q<=16 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffffbull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] > 0x04ull || + (C.w[1] == 0x04ull && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1/2 < n < 2^63-1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; // 0 <= ind <= 15 + if (C1 < midpoint64[ind]) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1/2 < x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + + // if the result was a midpoint it was rounded away from zero + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_xrninta + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_xrninta (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_xrninta (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+1), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000005, 1<=q<=16 + // <=> C * 10^(20-q) >= 0x50000000000000005, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x50000000000000005, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x05ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x4fffffffffffffffb, 1<=q<=16 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffffbull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] > 0x04ull || + (C.w[1] == 0x04ull && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1/2 < n < 2^63-1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; // 0 <= ind <= 15 + if (C1 < midpoint64[ind]) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1/2 < x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > 0x8000000000000000ull) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[1] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + // if the result was a midpoint it was rounded away from zero + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_to_int8.c b/gcc-4.4.3/libgcc/config/libbid/bid64_to_int8.c new file mode 100644 index 000000000..5b8e4f59a --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_to_int8.c @@ -0,0 +1,69 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +#define SIZE_MASK 0xffffff80 +#define INVALID_RESULT 0x80 + + + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid64_to_int8_rnint, UINT64, x, + bid64_to_int32_rnint, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid64_to_int8_xrnint, UINT64, x, + bid64_to_int32_xrnint, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid64_to_int8_rninta, UINT64, x, + bid64_to_int32_rninta, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid64_to_int8_xrninta, UINT64, x, + bid64_to_int32_xrninta, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid64_to_int8_int, UINT64, x, + bid64_to_int32_int, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid64_to_int8_xint, UINT64, x, + bid64_to_int32_xint, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid64_to_int8_floor, UINT64, x, + bid64_to_int32_floor, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid64_to_int8_ceil, UINT64, x, + bid64_to_int32_ceil, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid64_to_int8_xfloor, UINT64, x, + bid64_to_int32_xfloor, int, SIZE_MASK, + INVALID_RESULT) + +BID_TO_SMALL_INT_CVT_FUNCTION (char, bid64_to_int8_xceil, UINT64, x, + bid64_to_int32_xceil, int, SIZE_MASK, + INVALID_RESULT) diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_to_uint16.c b/gcc-4.4.3/libgcc/config/libbid/bid64_to_uint16.c new file mode 100644 index 000000000..39af7762e --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_to_uint16.c @@ -0,0 +1,67 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +#define SIZE_MASK 0xffff0000 +#define INVALID_RESULT 0x8000 + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid64_to_uint16_rnint, + UINT64, x, bid64_to_uint32_rnint, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid64_to_uint16_xrnint, + UINT64, x, bid64_to_uint32_xrnint, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid64_to_uint16_rninta, + UINT64, x, bid64_to_uint32_rninta, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid64_to_uint16_xrninta, + UINT64, x, bid64_to_uint32_xrninta, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid64_to_uint16_int, + UINT64, x, bid64_to_uint32_int, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid64_to_uint16_xint, + UINT64, x, bid64_to_uint32_xint, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid64_to_uint16_floor, + UINT64, x, bid64_to_uint32_floor, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid64_to_uint16_ceil, + UINT64, x, bid64_to_uint32_ceil, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid64_to_uint16_xfloor, + UINT64, x, bid64_to_uint32_xfloor, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned short, bid64_to_uint16_xceil, + UINT64, x, bid64_to_uint32_xceil, + unsigned int, SIZE_MASK, INVALID_RESULT) diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_to_uint32.c b/gcc-4.4.3/libgcc/config/libbid/bid64_to_uint32.c new file mode 100644 index 000000000..94bda1e48 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_to_uint32.c @@ -0,0 +1,2270 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID64_to_uint32_rnint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint32_rnint (unsigned int *pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +unsigned int +bid64_to_uint32_rnint (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in an unsigned 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 10 + // if n >= 2^32 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x9fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit unsigned int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x9fffffffb <=> + // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^32-1/2 up) + // Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x9fffffffbull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32 if -1/2 <= n < 2^32 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; + if (C1 <= midpoint64[ind]) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else { // n > 0 + res = 0x00000001; // return +1 + } + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be + // rounded to nearest to a 32-bit unsigned integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // 1 <= x < 2^32-1/2 so x can be rounded + // to nearest to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[1] == 0) && fstar.w[0] && + (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // the result is a midpoint; round to nearest + if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar--; // Cstar is now even + } // else MP in [ODD, EVEN] + } + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint32_xrnint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint32_xrnint (unsigned int *pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +unsigned int +bid64_to_uint32_xrnint (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in an unsigned 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 10 + // if n >= 2^32 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x9fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit unsigned int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x9fffffffb <=> + // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^32-1/2 up) + // Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x9fffffffbull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32 if -1/2 <= n < 2^32 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; + if (C1 <= midpoint64[ind]) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else { // n > 0 + res = 0x00000001; // return +1 + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be + // rounded to nearest to a 32-bit unsigned integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // 1 <= x < 2^32-1/2 so x can be rounded + // to nearest to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > 0x8000000000000000ull) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[1] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[1] == 0) && fstar.w[0] && + (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // the result is a midpoint; round to nearest + if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar--; // Cstar is now even + } // else MP in [ODD, EVEN] + } + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint32_floor + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint32_floor (unsigned int *pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +unsigned int +bid64_to_uint32_floor (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + if (x_sign) { // if n < 0 the conversion is invalid + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in an unsigned 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + // n > 0 and q + exp = 10 + // if n >= 2^32 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 + // <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0xa00000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit unsigned int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0xa00000000 <=> + // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^32-1/2 up) + // Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0xa00000000ull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + // n is not too large to be converted to int32 if -1 < n < 2^32 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // 1 <= x < 2^32 so x can be rounded + // to nearest to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint32_xfloor + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint32_xfloor (unsigned int *pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +unsigned int +bid64_to_uint32_xfloor (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + if (x_sign) { // if n < 0 the conversion is invalid + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in an unsigned 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + // if n > 0 and q + exp = 10 + // if n >= 2^32 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 + // <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0xa00000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit unsigned int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0xa00000000 <=> + // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^32-1/2 up) + // Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0xa00000000ull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + // n is not too large to be converted to int32 if -1 < n < 2^32 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // 1 <= x < 2^32 so x can be rounded + // to nearest to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint32_ceil + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint32_ceil (unsigned int *pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +unsigned int +bid64_to_uint32_ceil (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in an unsigned 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 10 + // if n > 2^32 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=16 + // <=> C * 10^(11-q) > 0x9fffffff6, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffff6 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x9fffffff6ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit unsigned int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) > 0x9fffffff6 <=> + // C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^32-1 up) + // Note: 0x9fffffff6*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x9fffffff6ull * ten2k64[q - 11]; + if (C1 > tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32 if -1 < n < 2^32 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // return 0 or 1 + if (x_sign) + res = 0x00000000; + else + res = 0x00000001; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // x <= -1 or 1 <= x <= 2^32 - 1 so if positive, x can be + // rounded to nearest to a 32-bit unsigned integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // 1 <= x <= 2^32 - 1 so x can be rounded + // to nearest to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + Cstar++; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + Cstar++; + } // else the result is exact + } + + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint32_xceil + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint32_xceil (unsigned int *pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +unsigned int +bid64_to_uint32_xceil (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in an unsigned 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 10 + // if n > 2^32 - 1 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=16 + // <=> C * 10^(11-q) > 0x9fffffff6, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffff6 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 > 0x9fffffff6ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit unsigned int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) > 0x9fffffff6 <=> + // C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^32-1 up) + // Note: 0x9fffffff6*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x9fffffff6ull * ten2k64[q - 11]; + if (C1 > tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32 if -1 < n < 2^32 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 or 1 + if (x_sign) + res = 0x00000000; + else + res = 0x00000001; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // x <= -1 or 1 <= x < 2^32 so if positive, x can be + // rounded to nearest to a 32-bit unsigned integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // 1 <= x < 2^32 so x can be rounded + // to nearest to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + Cstar++; + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + Cstar++; + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint32_int + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint32_int (unsigned int *pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ + UINT64 x = *px; +#else +unsigned int +bid64_to_uint32_int (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ +#endif + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in an unsigned 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 10 + // if n >= 2^32 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 + // <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0xa00000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit unsigned int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0xa00000000 <=> + // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^32-1/2 up) + // Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0xa00000000ull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32 if -1 < n < 2^32 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // x <= -1 or 1 <= x < 2^32 so if positive, x can be + // rounded to nearest to a 32-bit unsigned integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // 1 <= x < 2^32 so x can be rounded + // to nearest to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint32_xint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint32_xint (unsigned int *pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +unsigned int +bid64_to_uint32_xint (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in an unsigned 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 10 + // if n >= 2^32 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 + // <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0xa00000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit unsigned int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0xa00000000 <=> + // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^32-1/2 up) + // Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0xa00000000ull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32 if -1 < n < 2^32 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // x <= -1 or 1 <= x < 2^32 so if positive, x can be + // rounded to nearest to a 32-bit unsigned integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // 1 <= x < 2^32 so x can be rounded + // to nearest to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint32_rninta + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint32_rninta (unsigned int *pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +unsigned int +bid64_to_uint32_rninta (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in an unsigned 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 10 + // if n >= 2^32 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x9fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit unsigned int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x9fffffffb <=> + // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^32-1/2 up) + // Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x9fffffffbull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32 if -1/2 < n < 2^32 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; + if (C1 < midpoint64[ind]) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else { // n > 0 + res = 0x00000001; // return +1 + } + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be + // rounded to nearest to a 32-bit unsigned integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // 1 <= x < 2^32-1/2 so x can be rounded + // to nearest to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + + // if the result was a midpoint it was rounded away from zero + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint32_xrninta + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint32_xrninta (unsigned int *pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +unsigned int +bid64_to_uint32_xrninta (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + unsigned int res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x00000000; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... + // so x rounded to an integer may or may not fit in an unsigned 32-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 10' + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 10 + // if n >= 2^32 - 1/2 then n is too large + // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 + // <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 + if (q <= 11) { + // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int + // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) + if (tmp64 >= 0x9fffffffbull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit unsigned int fall through + // to '1 <= q + exp <= 10' + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + // C * 10^(11-q) >= 0x9fffffffb <=> + // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 + // (scale 2^32-1/2 up) + // Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 + tmp64 = 0x9fffffffbull * ten2k64[q - 11]; + if (C1 >= tmp64) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // else cases that can be rounded to a 32-bit int fall through + // to '1 <= q + exp <= 10' + } + } + } + // n is not too large to be converted to int32 if -1/2 < n < 2^32 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x00000000; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; + if (C1 < midpoint64[ind]) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } else { // n > 0 + res = 0x00000001; // return +1 + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + // -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be + // rounded to nearest to a 32-bit unsigned integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x80000000; + BID_RETURN (res); + } + // 1 <= x < 2^32-1/2 so x can be rounded + // to nearest to a 32-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > 0x8000000000000000ull) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[1] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + // if the result was a midpoint it was rounded away from zero + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_to_uint64.c b/gcc-4.4.3/libgcc/config/libbid/bid64_to_uint64.c new file mode 100644 index 000000000..1bb673453 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_to_uint64.c @@ -0,0 +1,2273 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID64_to_uint64_rnint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint64_rnint (UINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_to_uint64_rnint (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1/2 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 20 + // if n >= 2^64 - 1/2 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) + // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=16 + if (q == 1) { + // C * 10^20 >= 0x9fffffffffffffffb + __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C + if (C.w[1] > 0x09 || + (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 + // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb + // has 21 digits + __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); + if (C.w[1] > 0x09 || + (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; // 0 <= ind <= 15 + if (C1 <= midpoint64[ind]) { + res = 0x0000000000000000ull; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x0000000000000001ull; // return +1 + } else { // if n < 0 + res = 0x8000000000000000ull; + *pfpsf |= INVALID_EXCEPTION; + BID_RETURN (res); + } + } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x < 2^64-1/2 so x can be rounded + // to nearest to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[1] == 0) && fstar.w[0] && + (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // the result is a midpoint; round to nearest + if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar--; // Cstar is now even + } // else MP in [ODD, EVEN] + } + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint64_xrnint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint64_xrnint (UINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_to_uint64_xrnint (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1/2 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 20 + // if n >= 2^64 - 1/2 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) + // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=16 + if (q == 1) { + // C * 10^20 >= 0x9fffffffffffffffb + __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C + if (C.w[1] > 0x09 || + (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 + // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb + // has 21 digits + __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); + if (C.w[1] > 0x09 || + (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; // 0 <= ind <= 15 + if (C1 <= midpoint64[ind]) { + res = 0x0000000000000000ull; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x0000000000000001ull; // return +1 + } else { // if n < 0 + res = 0x8000000000000000ull; + *pfpsf |= INVALID_EXCEPTION; + BID_RETURN (res); + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x < 2^64-1/2 so x can be rounded + // to nearest to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > 0x8000000000000000ull) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[1] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + // if the result was a midpoint it was rounded away from zero, so + // it will need a correction + // check for midpoints + if ((fstar.w[1] == 0) && fstar.w[0] && + (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // the result is a midpoint; round to nearest + if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 + Cstar--; // Cstar is now even + } // else MP in [ODD, EVEN] + } + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint64_floor + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint64_floor (UINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_to_uint64_floor (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + if (x_sign) { // if n < 0 the conversion is invalid + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + // n > 0 and q + exp = 20 + // if n >= 2^64 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65) + // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=16 + if (q == 1) { + // C * 10^20 >= 0xa0000000000000000 + __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 + // Note: C * 10^(21-q) has 20 or 21 digits; 0xa0000000000000000 + // has 21 digits + __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + // n is not too large to be converted to int64 if -1 < n < 2^64 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) + // 1 <= x < 2^64 so x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint64_xfloor + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint64_xfloor (UINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_to_uint64_xfloor (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + if (x_sign) { // if n < 0 the conversion is invalid + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + // n > 0 and q + exp = 20 + // if n >= 2^64 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65) + // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=16 + if (q == 1) { + // C * 10^20 >= 0xa0000000000000000 + __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 + // Note: C * 10^(21-q) has 20 or 21 digits; 0xa0000000000000000 + // has 21 digits + __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + // n is not too large to be converted to int64 if -1 < n < 2^64 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) + // 1 <= x < 2^64 so x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint64_ceil + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint64_ceil (UINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_to_uint64_ceil (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 20 + // if n > 2^64 - 1 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65 - 2) + // <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=16 + if (q == 1) { + // C * 10^20 > 0x9fffffffffffffff6 + __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C + if (C.w[1] > 0x09 || + (C.w[1] == 0x09 && C.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 + // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffff6 + // has 21 digits + __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); + if (C.w[1] > 0x09 || + (C.w[1] == 0x09 && C.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1 < n < 2^64 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // return 0 or 1 + if (x_sign) + res = 0x0000000000000000ull; + else + res = 0x0000000000000001ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) + // x <= -1 or 1 <= x <= 2^64 - 1 so if positive x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x <= 2^64 - 1 so x can be rounded + // to nearest to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + Cstar++; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + Cstar++; + } // else the result is exact + } + + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint64_xceil + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint64_xceil (UINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_to_uint64_xceil (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 20 + // if n > 2^64 - 1 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65 - 2) + // <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=16 + if (q == 1) { + // C * 10^20 > 0x9fffffffffffffff6 + __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C + if (C.w[1] > 0x09 || + (C.w[1] == 0x09 && C.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 + // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffff6 + // has 21 digits + __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); + if (C.w[1] > 0x09 || + (C.w[1] == 0x09 && C.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1 < n < 2^64 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 or 1 + if (x_sign) + res = 0x0000000000000000ull; + else + res = 0x0000000000000001ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) + // x <= -1 or 1 <= x <= 2^64 - 1 so if positive x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x <= 2^64 - 1 so x can be rounded + // to nearest to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + Cstar++; + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + Cstar++; + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint64_int + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint64_int (UINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ + UINT64 x = *px; +#else +UINT64 +bid64_to_uint64_int (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ +#endif + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 20 + // if n >= 2^64 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65) + // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=16 + if (q == 1) { + // C * 10^20 >= 0xa0000000000000000 + __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 + // Note: C * 10^(21-q) has 20 or 21 digits; 0xa0000000000000000 + // has 21 digits + __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1 < n < 2^64 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x < 2^64 so x can be rounded + // to nearest to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint64_xint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint64_xint (UINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_to_uint64_xint (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 20 + // if n >= 2^64 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65) + // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=16 + if (q == 1) { + // C * 10^20 >= 0xa0000000000000000 + __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 + // Note: C * 10^(21-q) has 20 or 21 digits; 0xa0000000000000000 + // has 21 digits + __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); + if (C.w[1] >= 0x0a) { + // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1 < n < 2^64 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x < 2^64 so x can be rounded + // to nearest to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* < 10^(-x)) then + // the result is exact + // else // if (f* > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint64_rninta + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint64_rninta (UINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_to_uint64_rninta (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1/2 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 20 + // if n >= 2^64 - 1/2 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) + // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=16 + if (q == 1) { + // C * 10^20 >= 0x9fffffffffffffffb + __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C + if (C.w[1] > 0x09 || + (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 + // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb + // has 21 digits + __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); + if (C.w[1] > 0x09 || + (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; // 0 <= ind <= 15 + if (C1 < midpoint64[ind]) { + res = 0x0000000000000000ull; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x0000000000000001ull; // return +1 + } else { // if n < 0 + res = 0x8000000000000000ull; + *pfpsf |= INVALID_EXCEPTION; + BID_RETURN (res); + } + } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x < 2^64-1/2 so x can be rounded + // to nearest to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + + // if the result was a midpoint it was rounded away from zero + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_uint64_xrninta + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_uint64_xrninta (UINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_to_uint64_xrninta (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in an unsigned 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 20' + if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1/2 + // => set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else { // if n > 0 and q + exp = 20 + // if n >= 2^64 - 1/2 then n is too large + // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 + // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) + // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=16 + if (q == 1) { + // C * 10^20 >= 0x9fffffffffffffffb + __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C + if (C.w[1] > 0x09 || + (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 + // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb + // has 21 digits + __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); + if (C.w[1] > 0x09 || + (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 20' + } + } + } + // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) + // res = 0 + // else if x > 0 + // res = +1 + // else // if x < 0 + // invalid exc + ind = q - 1; // 0 <= ind <= 15 + if (C1 < midpoint64[ind]) { + res = 0x0000000000000000ull; // return 0 + } else if (!x_sign) { // n > 0 + res = 0x0000000000000001ull; // return +1 + } else { // if n < 0 + res = 0x8000000000000000ull; + *pfpsf |= INVALID_EXCEPTION; + BID_RETURN (res); + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) + // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded + // to nearest to a 64-bit unsigned signed integer + if (x_sign) { // x <= -1 + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // 1 <= x < 2^64-1/2 so x can be rounded + // to nearest to a 64-bit unsigned integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > 0x8000000000000000ull) { + // f* > 1/2 and the result may be exact + tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + tmp64 = fstar.w[1] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + + // if the result was a midpoint it was rounded away from zero + res = Cstar; // the result is positive + } else if (exp == 0) { + // 1 <= q <= 10 + // res = +C (exact) + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + // res = +C * 10^exp (exact) + res = C1 * ten2k64[exp]; // the result is positive + } + } + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid64_to_uint8.c b/gcc-4.4.3/libgcc/config/libbid/bid64_to_uint8.c new file mode 100644 index 000000000..ef68bbce6 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid64_to_uint8.c @@ -0,0 +1,67 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +#define SIZE_MASK 0xffffff00 +#define INVALID_RESULT 0x80 + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid64_to_uint8_rnint, + UINT64, x, bid64_to_uint32_rnint, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid64_to_uint8_xrnint, + UINT64, x, bid64_to_uint32_xrnint, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid64_to_uint8_rninta, + UINT64, x, bid64_to_uint32_rninta, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid64_to_uint8_xrninta, + UINT64, x, bid64_to_uint32_xrninta, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid64_to_uint8_int, + UINT64, x, bid64_to_uint32_int, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid64_to_uint8_xint, + UINT64, x, bid64_to_uint32_xint, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid64_to_uint8_floor, + UINT64, x, bid64_to_uint32_floor, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid64_to_uint8_ceil, + UINT64, x, bid64_to_uint32_ceil, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid64_to_uint8_xfloor, + UINT64, x, bid64_to_uint32_xfloor, + unsigned int, SIZE_MASK, INVALID_RESULT) + +BID_TO_SMALL_UINT_CVT_FUNCTION (unsigned char, bid64_to_uint8_xceil, + UINT64, x, bid64_to_uint32_xceil, + unsigned int, SIZE_MASK, INVALID_RESULT) diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_b2d.h b/gcc-4.4.3/libgcc/config/libbid/bid_b2d.h new file mode 100644 index 000000000..0b9b35552 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_b2d.h @@ -0,0 +1,3055 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +const UINT64 d2b[] = + { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 80, 81, 800, 801, 880, 881, + 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 90, 91, 810, 811, 890, 891, + 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 82, 83, 820, 821, 808, 809, + 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 92, 93, 830, 831, 818, 819, + 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 84, 85, 840, 841, 88, 89, + 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 94, 95, 850, 851, 98, 99, + 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 86, 87, 860, 861, 888, 889, + 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 96, 97, 870, 871, 898, 899, + 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 180, 181, 900, 901, + 980, 981, + 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 190, 191, 910, 911, + 990, 991, + 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 182, 183, 920, 921, + 908, 909, + 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 192, 193, 930, 931, + 918, 919, + 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 184, 185, 940, 941, + 188, 189, + 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 194, 195, 950, 951, + 198, 199, + 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 186, 187, 960, 961, + 988, 989, + 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 196, 197, 970, 971, + 998, 999, + 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 280, 281, 802, 803, + 882, 883, + 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 290, 291, 812, 813, + 892, 893, + 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 282, 283, 822, 823, + 828, 829, + 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 292, 293, 832, 833, + 838, 839, + 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 284, 285, 842, 843, + 288, 289, + 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 294, 295, 852, 853, + 298, 299, + 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 286, 287, 862, 863, + 888, 889, + 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 296, 297, 872, 873, + 898, 899, + 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 380, 381, 902, 903, + 982, 983, + 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 390, 391, 912, 913, + 992, 993, + 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 382, 383, 922, 923, + 928, 929, + 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 392, 393, 932, 933, + 938, 939, + 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 384, 385, 942, 943, + 388, 389, + 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 394, 395, 952, 953, + 398, 399, + 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 386, 387, 962, 963, + 988, 989, + 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 396, 397, 972, 973, + 998, 999, + 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 480, 481, 804, 805, + 884, 885, + 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 490, 491, 814, 815, + 894, 895, + 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 482, 483, 824, 825, + 848, 849, + 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 492, 493, 834, 835, + 858, 859, + 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 484, 485, 844, 845, + 488, 489, + 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 494, 495, 854, 855, + 498, 499, + 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 486, 487, 864, 865, + 888, 889, + 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 496, 497, 874, 875, + 898, 899, + 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 580, 581, 904, 905, + 984, 985, + 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 590, 591, 914, 915, + 994, 995, + 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 582, 583, 924, 925, + 948, 949, + 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 592, 593, 934, 935, + 958, 959, + 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 584, 585, 944, 945, + 588, 589, + 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 594, 595, 954, 955, + 598, 599, + 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 586, 587, 964, 965, + 988, 989, + 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 596, 597, 974, 975, + 998, 999, + 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 680, 681, 806, 807, + 886, 887, + 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 690, 691, 816, 817, + 896, 897, + 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 682, 683, 826, 827, + 868, 869, + 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 692, 693, 836, 837, + 878, 879, + 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 684, 685, 846, 847, + 688, 689, + 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 694, 695, 856, 857, + 698, 699, + 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 686, 687, 866, 867, + 888, 889, + 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 696, 697, 876, 877, + 898, 899, + 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 780, 781, 906, 907, + 986, 987, + 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 790, 791, 916, 917, + 996, 997, + 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 782, 783, 926, 927, + 968, 969, + 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 792, 793, 936, 937, + 978, 979, + 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 784, 785, 946, 947, + 788, 789, + 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 794, 795, 956, 957, + 798, 799, + 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 786, 787, 966, 967, + 988, 989, + 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 796, 797, 976, 977, + 998, 999 +}; + +const UINT64 d2b2[] = + { 0000ull, 1000ull, 2000ull, 3000ull, 4000ull, 5000ull, 6000ull, + 7000ull, 8000ull, 9000ull, 80000ull, 81000ull, 800000ull, 801000ull, + 880000ull, + 881000ull, + 10000ull, 11000ull, 12000ull, 13000ull, 14000ull, 15000ull, 16000ull, + 17000ull, 18000ull, 19000ull, 90000ull, 91000ull, 810000ull, + 811000ull, 890000ull, 891000ull, + 20000ull, 21000ull, 22000ull, 23000ull, 24000ull, 25000ull, 26000ull, + 27000ull, 28000ull, 29000ull, 82000ull, 83000ull, 820000ull, + 821000ull, 808000ull, 809000ull, + 30000ull, 31000ull, 32000ull, 33000ull, 34000ull, 35000ull, 36000ull, + 37000ull, 38000ull, 39000ull, 92000ull, 93000ull, 830000ull, + 831000ull, 818000ull, 819000ull, + 40000ull, 41000ull, 42000ull, 43000ull, 44000ull, 45000ull, 46000ull, + 47000ull, 48000ull, 49000ull, 84000ull, 85000ull, 840000ull, + 841000ull, 88000ull, 89000ull, + 50000ull, 51000ull, 52000ull, 53000ull, 54000ull, 55000ull, 56000ull, + 57000ull, 58000ull, 59000ull, 94000ull, 95000ull, 850000ull, + 851000ull, 98000ull, 99000ull, + 60000ull, 61000ull, 62000ull, 63000ull, 64000ull, 65000ull, 66000ull, + 67000ull, 68000ull, 69000ull, 86000ull, 87000ull, 860000ull, + 861000ull, 888000ull, 889000ull, + 70000ull, 71000ull, 72000ull, 73000ull, 74000ull, 75000ull, 76000ull, + 77000ull, 78000ull, 79000ull, 96000ull, 97000ull, 870000ull, + 871000ull, 898000ull, 899000ull, + 100000ull, 101000ull, 102000ull, 103000ull, 104000ull, 105000ull, + 106000ull, 107000ull, 108000ull, 109000ull, 180000ull, 181000ull, + 900000ull, 901000ull, 980000ull, 981000ull, + 110000ull, 111000ull, 112000ull, 113000ull, 114000ull, 115000ull, + 116000ull, 117000ull, 118000ull, 119000ull, 190000ull, 191000ull, + 910000ull, 911000ull, 990000ull, 991000ull, + 120000ull, 121000ull, 122000ull, 123000ull, 124000ull, 125000ull, + 126000ull, 127000ull, 128000ull, 129000ull, 182000ull, 183000ull, + 920000ull, 921000ull, 908000ull, 909000ull, + 130000ull, 131000ull, 132000ull, 133000ull, 134000ull, 135000ull, + 136000ull, 137000ull, 138000ull, 139000ull, 192000ull, 193000ull, + 930000ull, 931000ull, 918000ull, 919000ull, + 140000ull, 141000ull, 142000ull, 143000ull, 144000ull, 145000ull, + 146000ull, 147000ull, 148000ull, 149000ull, 184000ull, 185000ull, + 940000ull, 941000ull, 188000ull, 189000ull, + 150000ull, 151000ull, 152000ull, 153000ull, 154000ull, 155000ull, + 156000ull, 157000ull, 158000ull, 159000ull, 194000ull, 195000ull, + 950000ull, 951000ull, 198000ull, 199000ull, + 160000ull, 161000ull, 162000ull, 163000ull, 164000ull, 165000ull, + 166000ull, 167000ull, 168000ull, 169000ull, 186000ull, 187000ull, + 960000ull, 961000ull, 988000ull, 989000ull, + 170000ull, 171000ull, 172000ull, 173000ull, 174000ull, 175000ull, + 176000ull, 177000ull, 178000ull, 179000ull, 196000ull, 197000ull, + 970000ull, 971000ull, 998000ull, 999000ull, + 200000ull, 201000ull, 202000ull, 203000ull, 204000ull, 205000ull, + 206000ull, 207000ull, 208000ull, 209000ull, 280000ull, 281000ull, + 802000ull, 803000ull, 882000ull, 883000ull, + 210000ull, 211000ull, 212000ull, 213000ull, 214000ull, 215000ull, + 216000ull, 217000ull, 218000ull, 219000ull, 290000ull, 291000ull, + 812000ull, 813000ull, 892000ull, 893000ull, + 220000ull, 221000ull, 222000ull, 223000ull, 224000ull, 225000ull, + 226000ull, 227000ull, 228000ull, 229000ull, 282000ull, 283000ull, + 822000ull, 823000ull, 828000ull, 829000ull, + 230000ull, 231000ull, 232000ull, 233000ull, 234000ull, 235000ull, + 236000ull, 237000ull, 238000ull, 239000ull, 292000ull, 293000ull, + 832000ull, 833000ull, 838000ull, 839000ull, + 240000ull, 241000ull, 242000ull, 243000ull, 244000ull, 245000ull, + 246000ull, 247000ull, 248000ull, 249000ull, 284000ull, 285000ull, + 842000ull, 843000ull, 288000ull, 289000ull, + 250000ull, 251000ull, 252000ull, 253000ull, 254000ull, 255000ull, + 256000ull, 257000ull, 258000ull, 259000ull, 294000ull, 295000ull, + 852000ull, 853000ull, 298000ull, 299000ull, + 260000ull, 261000ull, 262000ull, 263000ull, 264000ull, 265000ull, + 266000ull, 267000ull, 268000ull, 269000ull, 286000ull, 287000ull, + 862000ull, 863000ull, 888000ull, 889000ull, + 270000ull, 271000ull, 272000ull, 273000ull, 274000ull, 275000ull, + 276000ull, 277000ull, 278000ull, 279000ull, 296000ull, 297000ull, + 872000ull, 873000ull, 898000ull, 899000ull, + 300000ull, 301000ull, 302000ull, 303000ull, 304000ull, 305000ull, + 306000ull, 307000ull, 308000ull, 309000ull, 380000ull, 381000ull, + 902000ull, 903000ull, 982000ull, 983000ull, + 310000ull, 311000ull, 312000ull, 313000ull, 314000ull, 315000ull, + 316000ull, 317000ull, 318000ull, 319000ull, 390000ull, 391000ull, + 912000ull, 913000ull, 992000ull, 993000ull, + 320000ull, 321000ull, 322000ull, 323000ull, 324000ull, 325000ull, + 326000ull, 327000ull, 328000ull, 329000ull, 382000ull, 383000ull, + 922000ull, 923000ull, 928000ull, 929000ull, + 330000ull, 331000ull, 332000ull, 333000ull, 334000ull, 335000ull, + 336000ull, 337000ull, 338000ull, 339000ull, 392000ull, 393000ull, + 932000ull, 933000ull, 938000ull, 939000ull, + 340000ull, 341000ull, 342000ull, 343000ull, 344000ull, 345000ull, + 346000ull, 347000ull, 348000ull, 349000ull, 384000ull, 385000ull, + 942000ull, 943000ull, 388000ull, 389000ull, + 350000ull, 351000ull, 352000ull, 353000ull, 354000ull, 355000ull, + 356000ull, 357000ull, 358000ull, 359000ull, 394000ull, 395000ull, + 952000ull, 953000ull, 398000ull, 399000ull, + 360000ull, 361000ull, 362000ull, 363000ull, 364000ull, 365000ull, + 366000ull, 367000ull, 368000ull, 369000ull, 386000ull, 387000ull, + 962000ull, 963000ull, 988000ull, 989000ull, + 370000ull, 371000ull, 372000ull, 373000ull, 374000ull, 375000ull, + 376000ull, 377000ull, 378000ull, 379000ull, 396000ull, 397000ull, + 972000ull, 973000ull, 998000ull, 999000ull, + 400000ull, 401000ull, 402000ull, 403000ull, 404000ull, 405000ull, + 406000ull, 407000ull, 408000ull, 409000ull, 480000ull, 481000ull, + 804000ull, 805000ull, 884000ull, 885000ull, + 410000ull, 411000ull, 412000ull, 413000ull, 414000ull, 415000ull, + 416000ull, 417000ull, 418000ull, 419000ull, 490000ull, 491000ull, + 814000ull, 815000ull, 894000ull, 895000ull, + 420000ull, 421000ull, 422000ull, 423000ull, 424000ull, 425000ull, + 426000ull, 427000ull, 428000ull, 429000ull, 482000ull, 483000ull, + 824000ull, 825000ull, 848000ull, 849000ull, + 430000ull, 431000ull, 432000ull, 433000ull, 434000ull, 435000ull, + 436000ull, 437000ull, 438000ull, 439000ull, 492000ull, 493000ull, + 834000ull, 835000ull, 858000ull, 859000ull, + 440000ull, 441000ull, 442000ull, 443000ull, 444000ull, 445000ull, + 446000ull, 447000ull, 448000ull, 449000ull, 484000ull, 485000ull, + 844000ull, 845000ull, 488000ull, 489000ull, + 450000ull, 451000ull, 452000ull, 453000ull, 454000ull, 455000ull, + 456000ull, 457000ull, 458000ull, 459000ull, 494000ull, 495000ull, + 854000ull, 855000ull, 498000ull, 499000ull, + 460000ull, 461000ull, 462000ull, 463000ull, 464000ull, 465000ull, + 466000ull, 467000ull, 468000ull, 469000ull, 486000ull, 487000ull, + 864000ull, 865000ull, 888000ull, 889000ull, + 470000ull, 471000ull, 472000ull, 473000ull, 474000ull, 475000ull, + 476000ull, 477000ull, 478000ull, 479000ull, 496000ull, 497000ull, + 874000ull, 875000ull, 898000ull, 899000ull, + 500000ull, 501000ull, 502000ull, 503000ull, 504000ull, 505000ull, + 506000ull, 507000ull, 508000ull, 509000ull, 580000ull, 581000ull, + 904000ull, 905000ull, 984000ull, 985000ull, + 510000ull, 511000ull, 512000ull, 513000ull, 514000ull, 515000ull, + 516000ull, 517000ull, 518000ull, 519000ull, 590000ull, 591000ull, + 914000ull, 915000ull, 994000ull, 995000ull, + 520000ull, 521000ull, 522000ull, 523000ull, 524000ull, 525000ull, + 526000ull, 527000ull, 528000ull, 529000ull, 582000ull, 583000ull, + 924000ull, 925000ull, 948000ull, 949000ull, + 530000ull, 531000ull, 532000ull, 533000ull, 534000ull, 535000ull, + 536000ull, 537000ull, 538000ull, 539000ull, 592000ull, 593000ull, + 934000ull, 935000ull, 958000ull, 959000ull, + 540000ull, 541000ull, 542000ull, 543000ull, 544000ull, 545000ull, + 546000ull, 547000ull, 548000ull, 549000ull, 584000ull, 585000ull, + 944000ull, 945000ull, 588000ull, 589000ull, + 550000ull, 551000ull, 552000ull, 553000ull, 554000ull, 555000ull, + 556000ull, 557000ull, 558000ull, 559000ull, 594000ull, 595000ull, + 954000ull, 955000ull, 598000ull, 599000ull, + 560000ull, 561000ull, 562000ull, 563000ull, 564000ull, 565000ull, + 566000ull, 567000ull, 568000ull, 569000ull, 586000ull, 587000ull, + 964000ull, 965000ull, 988000ull, 989000ull, + 570000ull, 571000ull, 572000ull, 573000ull, 574000ull, 575000ull, + 576000ull, 577000ull, 578000ull, 579000ull, 596000ull, 597000ull, + 974000ull, 975000ull, 998000ull, 999000ull, + 600000ull, 601000ull, 602000ull, 603000ull, 604000ull, 605000ull, + 606000ull, 607000ull, 608000ull, 609000ull, 680000ull, 681000ull, + 806000ull, 807000ull, 886000ull, 887000ull, + 610000ull, 611000ull, 612000ull, 613000ull, 614000ull, 615000ull, + 616000ull, 617000ull, 618000ull, 619000ull, 690000ull, 691000ull, + 816000ull, 817000ull, 896000ull, 897000ull, + 620000ull, 621000ull, 622000ull, 623000ull, 624000ull, 625000ull, + 626000ull, 627000ull, 628000ull, 629000ull, 682000ull, 683000ull, + 826000ull, 827000ull, 868000ull, 869000ull, + 630000ull, 631000ull, 632000ull, 633000ull, 634000ull, 635000ull, + 636000ull, 637000ull, 638000ull, 639000ull, 692000ull, 693000ull, + 836000ull, 837000ull, 878000ull, 879000ull, + 640000ull, 641000ull, 642000ull, 643000ull, 644000ull, 645000ull, + 646000ull, 647000ull, 648000ull, 649000ull, 684000ull, 685000ull, + 846000ull, 847000ull, 688000ull, 689000ull, + 650000ull, 651000ull, 652000ull, 653000ull, 654000ull, 655000ull, + 656000ull, 657000ull, 658000ull, 659000ull, 694000ull, 695000ull, + 856000ull, 857000ull, 698000ull, 699000ull, + 660000ull, 661000ull, 662000ull, 663000ull, 664000ull, 665000ull, + 666000ull, 667000ull, 668000ull, 669000ull, 686000ull, 687000ull, + 866000ull, 867000ull, 888000ull, 889000ull, + 670000ull, 671000ull, 672000ull, 673000ull, 674000ull, 675000ull, + 676000ull, 677000ull, 678000ull, 679000ull, 696000ull, 697000ull, + 876000ull, 877000ull, 898000ull, 899000ull, + 700000ull, 701000ull, 702000ull, 703000ull, 704000ull, 705000ull, + 706000ull, 707000ull, 708000ull, 709000ull, 780000ull, 781000ull, + 906000ull, 907000ull, 986000ull, 987000ull, + 710000ull, 711000ull, 712000ull, 713000ull, 714000ull, 715000ull, + 716000ull, 717000ull, 718000ull, 719000ull, 790000ull, 791000ull, + 916000ull, 917000ull, 996000ull, 997000ull, + 720000ull, 721000ull, 722000ull, 723000ull, 724000ull, 725000ull, + 726000ull, 727000ull, 728000ull, 729000ull, 782000ull, 783000ull, + 926000ull, 927000ull, 968000ull, 969000ull, + 730000ull, 731000ull, 732000ull, 733000ull, 734000ull, 735000ull, + 736000ull, 737000ull, 738000ull, 739000ull, 792000ull, 793000ull, + 936000ull, 937000ull, 978000ull, 979000ull, + 740000ull, 741000ull, 742000ull, 743000ull, 744000ull, 745000ull, + 746000ull, 747000ull, 748000ull, 749000ull, 784000ull, 785000ull, + 946000ull, 947000ull, 788000ull, 789000ull, + 750000ull, 751000ull, 752000ull, 753000ull, 754000ull, 755000ull, + 756000ull, 757000ull, 758000ull, 759000ull, 794000ull, 795000ull, + 956000ull, 957000ull, 798000ull, 799000ull, + 760000ull, 761000ull, 762000ull, 763000ull, 764000ull, 765000ull, + 766000ull, 767000ull, 768000ull, 769000ull, 786000ull, 787000ull, + 966000ull, 967000ull, 988000ull, 989000ull, + 770000ull, 771000ull, 772000ull, 773000ull, 774000ull, 775000ull, + 776000ull, 777000ull, 778000ull, 779000ull, 796000ull, 797000ull, + 976000ull, 977000ull, 998000ull, 999000ull +}; + +const UINT64 d2b3[] = + { 0000000ull, 1000000ull, 2000000ull, 3000000ull, 4000000ull, + 5000000ull, 6000000ull, 7000000ull, 8000000ull, 9000000ull, + 80000000ull, + 81000000ull, 800000000ull, 801000000ull, 880000000ull, 881000000ull, + 10000000ull, 11000000ull, 12000000ull, 13000000ull, 14000000ull, + 15000000ull, 16000000ull, 17000000ull, 18000000ull, 19000000ull, + 90000000ull, 91000000ull, 810000000ull, 811000000ull, 890000000ull, + 891000000ull, + 20000000ull, 21000000ull, 22000000ull, 23000000ull, 24000000ull, + 25000000ull, 26000000ull, 27000000ull, 28000000ull, 29000000ull, + 82000000ull, 83000000ull, 820000000ull, 821000000ull, 808000000ull, + 809000000ull, + 30000000ull, 31000000ull, 32000000ull, 33000000ull, 34000000ull, + 35000000ull, 36000000ull, 37000000ull, 38000000ull, 39000000ull, + 92000000ull, 93000000ull, 830000000ull, 831000000ull, 818000000ull, + 819000000ull, + 40000000ull, 41000000ull, 42000000ull, 43000000ull, 44000000ull, + 45000000ull, 46000000ull, 47000000ull, 48000000ull, 49000000ull, + 84000000ull, 85000000ull, 840000000ull, 841000000ull, 88000000ull, + 89000000ull, + 50000000ull, 51000000ull, 52000000ull, 53000000ull, 54000000ull, + 55000000ull, 56000000ull, 57000000ull, 58000000ull, 59000000ull, + 94000000ull, 95000000ull, 850000000ull, 851000000ull, 98000000ull, + 99000000ull, + 60000000ull, 61000000ull, 62000000ull, 63000000ull, 64000000ull, + 65000000ull, 66000000ull, 67000000ull, 68000000ull, 69000000ull, + 86000000ull, 87000000ull, 860000000ull, 861000000ull, 888000000ull, + 889000000ull, + 70000000ull, 71000000ull, 72000000ull, 73000000ull, 74000000ull, + 75000000ull, 76000000ull, 77000000ull, 78000000ull, 79000000ull, + 96000000ull, 97000000ull, 870000000ull, 871000000ull, 898000000ull, + 899000000ull, + 100000000ull, 101000000ull, 102000000ull, 103000000ull, 104000000ull, + 105000000ull, 106000000ull, 107000000ull, 108000000ull, + 109000000ull, 180000000ull, 181000000ull, 900000000ull, + 901000000ull, 980000000ull, 981000000ull, + 110000000ull, 111000000ull, 112000000ull, 113000000ull, 114000000ull, + 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963000000ull, 988000000ull, 989000000ull, + 370000000ull, 371000000ull, 372000000ull, 373000000ull, 374000000ull, + 375000000ull, 376000000ull, 377000000ull, 378000000ull, + 379000000ull, 396000000ull, 397000000ull, 972000000ull, + 973000000ull, 998000000ull, 999000000ull, + 400000000ull, 401000000ull, 402000000ull, 403000000ull, 404000000ull, + 405000000ull, 406000000ull, 407000000ull, 408000000ull, + 409000000ull, 480000000ull, 481000000ull, 804000000ull, + 805000000ull, 884000000ull, 885000000ull, + 410000000ull, 411000000ull, 412000000ull, 413000000ull, 414000000ull, + 415000000ull, 416000000ull, 417000000ull, 418000000ull, + 419000000ull, 490000000ull, 491000000ull, 814000000ull, + 815000000ull, 894000000ull, 895000000ull, + 420000000ull, 421000000ull, 422000000ull, 423000000ull, 424000000ull, + 425000000ull, 426000000ull, 427000000ull, 428000000ull, + 429000000ull, 482000000ull, 483000000ull, 824000000ull, + 825000000ull, 848000000ull, 849000000ull, + 430000000ull, 431000000ull, 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477000000ull, 478000000ull, + 479000000ull, 496000000ull, 497000000ull, 874000000ull, + 875000000ull, 898000000ull, 899000000ull, + 500000000ull, 501000000ull, 502000000ull, 503000000ull, 504000000ull, + 505000000ull, 506000000ull, 507000000ull, 508000000ull, + 509000000ull, 580000000ull, 581000000ull, 904000000ull, + 905000000ull, 984000000ull, 985000000ull, + 510000000ull, 511000000ull, 512000000ull, 513000000ull, 514000000ull, + 515000000ull, 516000000ull, 517000000ull, 518000000ull, + 519000000ull, 590000000ull, 591000000ull, 914000000ull, + 915000000ull, 994000000ull, 995000000ull, + 520000000ull, 521000000ull, 522000000ull, 523000000ull, 524000000ull, + 525000000ull, 526000000ull, 527000000ull, 528000000ull, + 529000000ull, 582000000ull, 583000000ull, 924000000ull, + 925000000ull, 948000000ull, 949000000ull, + 530000000ull, 531000000ull, 532000000ull, 533000000ull, 534000000ull, + 535000000ull, 536000000ull, 537000000ull, 538000000ull, + 539000000ull, 592000000ull, 593000000ull, 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600000000ull, 601000000ull, 602000000ull, 603000000ull, 604000000ull, + 605000000ull, 606000000ull, 607000000ull, 608000000ull, + 609000000ull, 680000000ull, 681000000ull, 806000000ull, + 807000000ull, 886000000ull, 887000000ull, + 610000000ull, 611000000ull, 612000000ull, 613000000ull, 614000000ull, + 615000000ull, 616000000ull, 617000000ull, 618000000ull, + 619000000ull, 690000000ull, 691000000ull, 816000000ull, + 817000000ull, 896000000ull, 897000000ull, + 620000000ull, 621000000ull, 622000000ull, 623000000ull, 624000000ull, + 625000000ull, 626000000ull, 627000000ull, 628000000ull, + 629000000ull, 682000000ull, 683000000ull, 826000000ull, + 827000000ull, 868000000ull, 869000000ull, + 630000000ull, 631000000ull, 632000000ull, 633000000ull, 634000000ull, + 635000000ull, 636000000ull, 637000000ull, 638000000ull, + 639000000ull, 692000000ull, 693000000ull, 836000000ull, + 837000000ull, 878000000ull, 879000000ull, + 640000000ull, 641000000ull, 642000000ull, 643000000ull, 644000000ull, + 645000000ull, 646000000ull, 647000000ull, 648000000ull, + 649000000ull, 684000000ull, 685000000ull, 846000000ull, + 847000000ull, 688000000ull, 689000000ull, + 650000000ull, 651000000ull, 652000000ull, 653000000ull, 654000000ull, + 655000000ull, 656000000ull, 657000000ull, 658000000ull, + 659000000ull, 694000000ull, 695000000ull, 856000000ull, + 857000000ull, 698000000ull, 699000000ull, + 660000000ull, 661000000ull, 662000000ull, 663000000ull, 664000000ull, + 665000000ull, 666000000ull, 667000000ull, 668000000ull, + 669000000ull, 686000000ull, 687000000ull, 866000000ull, + 867000000ull, 888000000ull, 889000000ull, + 670000000ull, 671000000ull, 672000000ull, 673000000ull, 674000000ull, + 675000000ull, 676000000ull, 677000000ull, 678000000ull, + 679000000ull, 696000000ull, 697000000ull, 876000000ull, + 877000000ull, 898000000ull, 899000000ull, + 700000000ull, 701000000ull, 702000000ull, 703000000ull, 704000000ull, + 705000000ull, 706000000ull, 707000000ull, 708000000ull, + 709000000ull, 780000000ull, 781000000ull, 906000000ull, + 907000000ull, 986000000ull, 987000000ull, + 710000000ull, 711000000ull, 712000000ull, 713000000ull, 714000000ull, + 715000000ull, 716000000ull, 717000000ull, 718000000ull, + 719000000ull, 790000000ull, 791000000ull, 916000000ull, + 917000000ull, 996000000ull, 997000000ull, + 720000000ull, 721000000ull, 722000000ull, 723000000ull, 724000000ull, + 725000000ull, 726000000ull, 727000000ull, 728000000ull, + 729000000ull, 782000000ull, 783000000ull, 926000000ull, + 927000000ull, 968000000ull, 969000000ull, + 730000000ull, 731000000ull, 732000000ull, 733000000ull, 734000000ull, + 735000000ull, 736000000ull, 737000000ull, 738000000ull, + 739000000ull, 792000000ull, 793000000ull, 936000000ull, + 937000000ull, 978000000ull, 979000000ull, + 740000000ull, 741000000ull, 742000000ull, 743000000ull, 744000000ull, + 745000000ull, 746000000ull, 747000000ull, 748000000ull, + 749000000ull, 784000000ull, 785000000ull, 946000000ull, + 947000000ull, 788000000ull, 789000000ull, + 750000000ull, 751000000ull, 752000000ull, 753000000ull, 754000000ull, + 755000000ull, 756000000ull, 757000000ull, 758000000ull, + 759000000ull, 794000000ull, 795000000ull, 956000000ull, + 957000000ull, 798000000ull, 799000000ull, + 760000000ull, 761000000ull, 762000000ull, 763000000ull, 764000000ull, + 765000000ull, 766000000ull, 767000000ull, 768000000ull, + 769000000ull, 786000000ull, 787000000ull, 966000000ull, + 967000000ull, 988000000ull, 989000000ull, + 770000000ull, 771000000ull, 772000000ull, 773000000ull, 774000000ull, + 775000000ull, 776000000ull, 777000000ull, 778000000ull, + 779000000ull, 796000000ull, 797000000ull, 976000000ull, + 977000000ull, 998000000ull, 999000000ull +}; + +const UINT64 d2b4[] = + { 0000000000ull, 1000000000ull, 2000000000ull, 3000000000ull, + 4000000000ull, 5000000000ull, 6000000000ull, 7000000000ull, + 8000000000ull, + 9000000000ull, 80000000000ull, 81000000000ull, 800000000000ull, + 801000000000ull, + 880000000000ull, 881000000000ull, + 10000000000ull, 11000000000ull, 12000000000ull, 13000000000ull, + 14000000000ull, 15000000000ull, 16000000000ull, 17000000000ull, + 18000000000ull, 19000000000ull, 90000000000ull, 91000000000ull, + 810000000000ull, 811000000000ull, 890000000000ull, 891000000000ull, + 20000000000ull, 21000000000ull, 22000000000ull, 23000000000ull, + 24000000000ull, 25000000000ull, 26000000000ull, 27000000000ull, + 28000000000ull, 29000000000ull, 82000000000ull, 83000000000ull, + 820000000000ull, 821000000000ull, 808000000000ull, 809000000000ull, + 30000000000ull, 31000000000ull, 32000000000ull, 33000000000ull, + 34000000000ull, 35000000000ull, 36000000000ull, 37000000000ull, + 38000000000ull, 39000000000ull, 92000000000ull, 93000000000ull, + 830000000000ull, 831000000000ull, 818000000000ull, 819000000000ull, + 40000000000ull, 41000000000ull, 42000000000ull, 43000000000ull, + 44000000000ull, 45000000000ull, 46000000000ull, 47000000000ull, + 48000000000ull, 49000000000ull, 84000000000ull, 85000000000ull, + 840000000000ull, 841000000000ull, 88000000000ull, 89000000000ull, + 50000000000ull, 51000000000ull, 52000000000ull, 53000000000ull, + 54000000000ull, 55000000000ull, 56000000000ull, 57000000000ull, + 58000000000ull, 59000000000ull, 94000000000ull, 95000000000ull, + 850000000000ull, 851000000000ull, 98000000000ull, 99000000000ull, + 60000000000ull, 61000000000ull, 62000000000ull, 63000000000ull, + 64000000000ull, 65000000000ull, 66000000000ull, 67000000000ull, + 68000000000ull, 69000000000ull, 86000000000ull, 87000000000ull, + 860000000000ull, 861000000000ull, 888000000000ull, 889000000000ull, + 70000000000ull, 71000000000ull, 72000000000ull, 73000000000ull, + 74000000000ull, 75000000000ull, 76000000000ull, 77000000000ull, + 78000000000ull, 79000000000ull, 96000000000ull, 97000000000ull, + 870000000000ull, 871000000000ull, 898000000000ull, 899000000000ull, + 100000000000ull, 101000000000ull, 102000000000ull, 103000000000ull, + 104000000000ull, 105000000000ull, 106000000000ull, 107000000000ull, + 108000000000ull, 109000000000ull, 180000000000ull, 181000000000ull, + 900000000000ull, 901000000000ull, 980000000000ull, 981000000000ull, + 110000000000ull, 111000000000ull, 112000000000ull, 113000000000ull, + 114000000000ull, 115000000000ull, 116000000000ull, 117000000000ull, + 118000000000ull, 119000000000ull, 190000000000ull, 191000000000ull, + 910000000000ull, 911000000000ull, 990000000000ull, 991000000000ull, + 120000000000ull, 121000000000ull, 122000000000ull, 123000000000ull, + 124000000000ull, 125000000000ull, 126000000000ull, 127000000000ull, + 128000000000ull, 129000000000ull, 182000000000ull, 183000000000ull, + 920000000000ull, 921000000000ull, 908000000000ull, 909000000000ull, + 130000000000ull, 131000000000ull, 132000000000ull, 133000000000ull, + 134000000000ull, 135000000000ull, 136000000000ull, 137000000000ull, + 138000000000ull, 139000000000ull, 192000000000ull, 193000000000ull, + 930000000000ull, 931000000000ull, 918000000000ull, 919000000000ull, + 140000000000ull, 141000000000ull, 142000000000ull, 143000000000ull, + 144000000000ull, 145000000000ull, 146000000000ull, 147000000000ull, + 148000000000ull, 149000000000ull, 184000000000ull, 185000000000ull, + 940000000000ull, 941000000000ull, 188000000000ull, 189000000000ull, + 150000000000ull, 151000000000ull, 152000000000ull, 153000000000ull, + 154000000000ull, 155000000000ull, 156000000000ull, 157000000000ull, + 158000000000ull, 159000000000ull, 194000000000ull, 195000000000ull, + 950000000000ull, 951000000000ull, 198000000000ull, 199000000000ull, + 160000000000ull, 161000000000ull, 162000000000ull, 163000000000ull, + 164000000000ull, 165000000000ull, 166000000000ull, 167000000000ull, + 168000000000ull, 169000000000ull, 186000000000ull, 187000000000ull, + 960000000000ull, 961000000000ull, 988000000000ull, 989000000000ull, + 170000000000ull, 171000000000ull, 172000000000ull, 173000000000ull, + 174000000000ull, 175000000000ull, 176000000000ull, 177000000000ull, + 178000000000ull, 179000000000ull, 196000000000ull, 197000000000ull, + 970000000000ull, 971000000000ull, 998000000000ull, 999000000000ull, + 200000000000ull, 201000000000ull, 202000000000ull, 203000000000ull, + 204000000000ull, 205000000000ull, 206000000000ull, 207000000000ull, + 208000000000ull, 209000000000ull, 280000000000ull, 281000000000ull, + 802000000000ull, 803000000000ull, 882000000000ull, 883000000000ull, + 210000000000ull, 211000000000ull, 212000000000ull, 213000000000ull, + 214000000000ull, 215000000000ull, 216000000000ull, 217000000000ull, + 218000000000ull, 219000000000ull, 290000000000ull, 291000000000ull, + 812000000000ull, 813000000000ull, 892000000000ull, 893000000000ull, + 220000000000ull, 221000000000ull, 222000000000ull, 223000000000ull, + 224000000000ull, 225000000000ull, 226000000000ull, 227000000000ull, + 228000000000ull, 229000000000ull, 282000000000ull, 283000000000ull, + 822000000000ull, 823000000000ull, 828000000000ull, 829000000000ull, + 230000000000ull, 231000000000ull, 232000000000ull, 233000000000ull, + 234000000000ull, 235000000000ull, 236000000000ull, 237000000000ull, + 238000000000ull, 239000000000ull, 292000000000ull, 293000000000ull, + 832000000000ull, 833000000000ull, 838000000000ull, 839000000000ull, + 240000000000ull, 241000000000ull, 242000000000ull, 243000000000ull, + 244000000000ull, 245000000000ull, 246000000000ull, 247000000000ull, + 248000000000ull, 249000000000ull, 284000000000ull, 285000000000ull, + 842000000000ull, 843000000000ull, 288000000000ull, 289000000000ull, + 250000000000ull, 251000000000ull, 252000000000ull, 253000000000ull, + 254000000000ull, 255000000000ull, 256000000000ull, 257000000000ull, + 258000000000ull, 259000000000ull, 294000000000ull, 295000000000ull, + 852000000000ull, 853000000000ull, 298000000000ull, 299000000000ull, + 260000000000ull, 261000000000ull, 262000000000ull, 263000000000ull, + 264000000000ull, 265000000000ull, 266000000000ull, 267000000000ull, + 268000000000ull, 269000000000ull, 286000000000ull, 287000000000ull, + 862000000000ull, 863000000000ull, 888000000000ull, 889000000000ull, + 270000000000ull, 271000000000ull, 272000000000ull, 273000000000ull, + 274000000000ull, 275000000000ull, 276000000000ull, 277000000000ull, + 278000000000ull, 279000000000ull, 296000000000ull, 297000000000ull, + 872000000000ull, 873000000000ull, 898000000000ull, 899000000000ull, + 300000000000ull, 301000000000ull, 302000000000ull, 303000000000ull, + 304000000000ull, 305000000000ull, 306000000000ull, 307000000000ull, + 308000000000ull, 309000000000ull, 380000000000ull, 381000000000ull, + 902000000000ull, 903000000000ull, 982000000000ull, 983000000000ull, + 310000000000ull, 311000000000ull, 312000000000ull, 313000000000ull, + 314000000000ull, 315000000000ull, 316000000000ull, 317000000000ull, + 318000000000ull, 319000000000ull, 390000000000ull, 391000000000ull, + 912000000000ull, 913000000000ull, 992000000000ull, 993000000000ull, + 320000000000ull, 321000000000ull, 322000000000ull, 323000000000ull, + 324000000000ull, 325000000000ull, 326000000000ull, 327000000000ull, + 328000000000ull, 329000000000ull, 382000000000ull, 383000000000ull, + 922000000000ull, 923000000000ull, 928000000000ull, 929000000000ull, + 330000000000ull, 331000000000ull, 332000000000ull, 333000000000ull, + 334000000000ull, 335000000000ull, 336000000000ull, 337000000000ull, + 338000000000ull, 339000000000ull, 392000000000ull, 393000000000ull, + 932000000000ull, 933000000000ull, 938000000000ull, 939000000000ull, + 340000000000ull, 341000000000ull, 342000000000ull, 343000000000ull, + 344000000000ull, 345000000000ull, 346000000000ull, 347000000000ull, + 348000000000ull, 349000000000ull, 384000000000ull, 385000000000ull, + 942000000000ull, 943000000000ull, 388000000000ull, 389000000000ull, + 350000000000ull, 351000000000ull, 352000000000ull, 353000000000ull, + 354000000000ull, 355000000000ull, 356000000000ull, 357000000000ull, + 358000000000ull, 359000000000ull, 394000000000ull, 395000000000ull, + 952000000000ull, 953000000000ull, 398000000000ull, 399000000000ull, + 360000000000ull, 361000000000ull, 362000000000ull, 363000000000ull, + 364000000000ull, 365000000000ull, 366000000000ull, 367000000000ull, + 368000000000ull, 369000000000ull, 386000000000ull, 387000000000ull, + 962000000000ull, 963000000000ull, 988000000000ull, 989000000000ull, + 370000000000ull, 371000000000ull, 372000000000ull, 373000000000ull, + 374000000000ull, 375000000000ull, 376000000000ull, 377000000000ull, + 378000000000ull, 379000000000ull, 396000000000ull, 397000000000ull, + 972000000000ull, 973000000000ull, 998000000000ull, 999000000000ull, + 400000000000ull, 401000000000ull, 402000000000ull, 403000000000ull, + 404000000000ull, 405000000000ull, 406000000000ull, 407000000000ull, + 408000000000ull, 409000000000ull, 480000000000ull, 481000000000ull, + 804000000000ull, 805000000000ull, 884000000000ull, 885000000000ull, + 410000000000ull, 411000000000ull, 412000000000ull, 413000000000ull, + 414000000000ull, 415000000000ull, 416000000000ull, 417000000000ull, + 418000000000ull, 419000000000ull, 490000000000ull, 491000000000ull, + 814000000000ull, 815000000000ull, 894000000000ull, 895000000000ull, + 420000000000ull, 421000000000ull, 422000000000ull, 423000000000ull, + 424000000000ull, 425000000000ull, 426000000000ull, 427000000000ull, + 428000000000ull, 429000000000ull, 482000000000ull, 483000000000ull, + 824000000000ull, 825000000000ull, 848000000000ull, 849000000000ull, + 430000000000ull, 431000000000ull, 432000000000ull, 433000000000ull, + 434000000000ull, 435000000000ull, 436000000000ull, 437000000000ull, + 438000000000ull, 439000000000ull, 492000000000ull, 493000000000ull, + 834000000000ull, 835000000000ull, 858000000000ull, 859000000000ull, + 440000000000ull, 441000000000ull, 442000000000ull, 443000000000ull, + 444000000000ull, 445000000000ull, 446000000000ull, 447000000000ull, + 448000000000ull, 449000000000ull, 484000000000ull, 485000000000ull, + 844000000000ull, 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686000000000ull, 687000000000ull, + 866000000000ull, 867000000000ull, 888000000000ull, 889000000000ull, + 670000000000ull, 671000000000ull, 672000000000ull, 673000000000ull, + 674000000000ull, 675000000000ull, 676000000000ull, 677000000000ull, + 678000000000ull, 679000000000ull, 696000000000ull, 697000000000ull, + 876000000000ull, 877000000000ull, 898000000000ull, 899000000000ull, + 700000000000ull, 701000000000ull, 702000000000ull, 703000000000ull, + 704000000000ull, 705000000000ull, 706000000000ull, 707000000000ull, + 708000000000ull, 709000000000ull, 780000000000ull, 781000000000ull, + 906000000000ull, 907000000000ull, 986000000000ull, 987000000000ull, + 710000000000ull, 711000000000ull, 712000000000ull, 713000000000ull, + 714000000000ull, 715000000000ull, 716000000000ull, 717000000000ull, + 718000000000ull, 719000000000ull, 790000000000ull, 791000000000ull, + 916000000000ull, 917000000000ull, 996000000000ull, 997000000000ull, + 720000000000ull, 721000000000ull, 722000000000ull, 723000000000ull, + 724000000000ull, 725000000000ull, 726000000000ull, 727000000000ull, + 728000000000ull, 729000000000ull, 782000000000ull, 783000000000ull, + 926000000000ull, 927000000000ull, 968000000000ull, 969000000000ull, + 730000000000ull, 731000000000ull, 732000000000ull, 733000000000ull, + 734000000000ull, 735000000000ull, 736000000000ull, 737000000000ull, + 738000000000ull, 739000000000ull, 792000000000ull, 793000000000ull, + 936000000000ull, 937000000000ull, 978000000000ull, 979000000000ull, + 740000000000ull, 741000000000ull, 742000000000ull, 743000000000ull, + 744000000000ull, 745000000000ull, 746000000000ull, 747000000000ull, + 748000000000ull, 749000000000ull, 784000000000ull, 785000000000ull, + 946000000000ull, 947000000000ull, 788000000000ull, 789000000000ull, + 750000000000ull, 751000000000ull, 752000000000ull, 753000000000ull, + 754000000000ull, 755000000000ull, 756000000000ull, 757000000000ull, + 758000000000ull, 759000000000ull, 794000000000ull, 795000000000ull, + 956000000000ull, 957000000000ull, 798000000000ull, 799000000000ull, + 760000000000ull, 761000000000ull, 762000000000ull, 763000000000ull, + 764000000000ull, 765000000000ull, 766000000000ull, 767000000000ull, + 768000000000ull, 769000000000ull, 786000000000ull, 787000000000ull, + 966000000000ull, 967000000000ull, 988000000000ull, 989000000000ull, + 770000000000ull, 771000000000ull, 772000000000ull, 773000000000ull, + 774000000000ull, 775000000000ull, 776000000000ull, 777000000000ull, + 778000000000ull, 779000000000ull, 796000000000ull, 797000000000ull, + 976000000000ull, 977000000000ull, 998000000000ull, 999000000000ull +}; + +const UINT64 d2b5[] = { 0000000000000ull, 1000000000000ull, 2000000000000ull, + 3000000000000ull, 4000000000000ull, 5000000000000ull, + 6000000000000ull, + 7000000000000ull, 8000000000000ull, 9000000000000ull, + 80000000000000ull, + 81000000000000ull, 800000000000000ull, 801000000000000ull, + 880000000000000ull, + 881000000000000ull, + 10000000000000ull, 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265000000000000ull, + 266000000000000ull, 267000000000000ull, 268000000000000ull, + 269000000000000ull, 286000000000000ull, 287000000000000ull, + 862000000000000ull, 863000000000000ull, 888000000000000ull, + 889000000000000ull, + 270000000000000ull, 271000000000000ull, 272000000000000ull, + 273000000000000ull, 274000000000000ull, 275000000000000ull, + 276000000000000ull, 277000000000000ull, 278000000000000ull, + 279000000000000ull, 296000000000000ull, 297000000000000ull, + 872000000000000ull, 873000000000000ull, 898000000000000ull, + 899000000000000ull, + 300000000000000ull, 301000000000000ull, 302000000000000ull, + 303000000000000ull, 304000000000000ull, 305000000000000ull, + 306000000000000ull, 307000000000000ull, 308000000000000ull, + 309000000000000ull, 380000000000000ull, 381000000000000ull, + 902000000000000ull, 903000000000000ull, 982000000000000ull, + 983000000000000ull, + 310000000000000ull, 311000000000000ull, 312000000000000ull, + 313000000000000ull, 314000000000000ull, 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345000000000000ull, + 346000000000000ull, 347000000000000ull, 348000000000000ull, + 349000000000000ull, 384000000000000ull, 385000000000000ull, + 942000000000000ull, 943000000000000ull, 388000000000000ull, + 389000000000000ull, + 350000000000000ull, 351000000000000ull, 352000000000000ull, + 353000000000000ull, 354000000000000ull, 355000000000000ull, + 356000000000000ull, 357000000000000ull, 358000000000000ull, + 359000000000000ull, 394000000000000ull, 395000000000000ull, + 952000000000000ull, 953000000000000ull, 398000000000000ull, + 399000000000000ull, + 360000000000000ull, 361000000000000ull, 362000000000000ull, + 363000000000000ull, 364000000000000ull, 365000000000000ull, + 366000000000000ull, 367000000000000ull, 368000000000000ull, + 369000000000000ull, 386000000000000ull, 387000000000000ull, + 962000000000000ull, 963000000000000ull, 988000000000000ull, + 989000000000000ull, + 370000000000000ull, 371000000000000ull, 372000000000000ull, + 373000000000000ull, 374000000000000ull, 375000000000000ull, + 376000000000000ull, 377000000000000ull, 378000000000000ull, + 379000000000000ull, 396000000000000ull, 397000000000000ull, + 972000000000000ull, 973000000000000ull, 998000000000000ull, + 999000000000000ull, + 400000000000000ull, 401000000000000ull, 402000000000000ull, + 403000000000000ull, 404000000000000ull, 405000000000000ull, + 406000000000000ull, 407000000000000ull, 408000000000000ull, + 409000000000000ull, 480000000000000ull, 481000000000000ull, + 804000000000000ull, 805000000000000ull, 884000000000000ull, + 885000000000000ull, + 410000000000000ull, 411000000000000ull, 412000000000000ull, + 413000000000000ull, 414000000000000ull, 415000000000000ull, + 416000000000000ull, 417000000000000ull, 418000000000000ull, + 419000000000000ull, 490000000000000ull, 491000000000000ull, + 814000000000000ull, 815000000000000ull, 894000000000000ull, + 895000000000000ull, + 420000000000000ull, 421000000000000ull, 422000000000000ull, + 423000000000000ull, 424000000000000ull, 425000000000000ull, + 426000000000000ull, 427000000000000ull, 428000000000000ull, + 429000000000000ull, 482000000000000ull, 483000000000000ull, + 824000000000000ull, 825000000000000ull, 848000000000000ull, + 849000000000000ull, + 430000000000000ull, 431000000000000ull, 432000000000000ull, + 433000000000000ull, 434000000000000ull, 435000000000000ull, + 436000000000000ull, 437000000000000ull, 438000000000000ull, + 439000000000000ull, 492000000000000ull, 493000000000000ull, + 834000000000000ull, 835000000000000ull, 858000000000000ull, + 859000000000000ull, + 440000000000000ull, 441000000000000ull, 442000000000000ull, + 443000000000000ull, 444000000000000ull, 445000000000000ull, + 446000000000000ull, 447000000000000ull, 448000000000000ull, + 449000000000000ull, 484000000000000ull, 485000000000000ull, + 844000000000000ull, 845000000000000ull, 488000000000000ull, + 489000000000000ull, + 450000000000000ull, 451000000000000ull, 452000000000000ull, + 453000000000000ull, 454000000000000ull, 455000000000000ull, + 456000000000000ull, 457000000000000ull, 458000000000000ull, + 459000000000000ull, 494000000000000ull, 495000000000000ull, + 854000000000000ull, 855000000000000ull, 498000000000000ull, + 499000000000000ull, + 460000000000000ull, 461000000000000ull, 462000000000000ull, + 463000000000000ull, 464000000000000ull, 465000000000000ull, + 466000000000000ull, 467000000000000ull, 468000000000000ull, + 469000000000000ull, 486000000000000ull, 487000000000000ull, + 864000000000000ull, 865000000000000ull, 888000000000000ull, + 889000000000000ull, + 470000000000000ull, 471000000000000ull, 472000000000000ull, + 473000000000000ull, 474000000000000ull, 475000000000000ull, + 476000000000000ull, 477000000000000ull, 478000000000000ull, + 479000000000000ull, 496000000000000ull, 497000000000000ull, + 874000000000000ull, 875000000000000ull, 898000000000000ull, + 899000000000000ull, + 500000000000000ull, 501000000000000ull, 502000000000000ull, + 503000000000000ull, 504000000000000ull, 505000000000000ull, + 506000000000000ull, 507000000000000ull, 508000000000000ull, + 509000000000000ull, 580000000000000ull, 581000000000000ull, + 904000000000000ull, 905000000000000ull, 984000000000000ull, + 985000000000000ull, + 510000000000000ull, 511000000000000ull, 512000000000000ull, + 513000000000000ull, 514000000000000ull, 515000000000000ull, + 516000000000000ull, 517000000000000ull, 518000000000000ull, + 519000000000000ull, 590000000000000ull, 591000000000000ull, + 914000000000000ull, 915000000000000ull, 994000000000000ull, + 995000000000000ull, + 520000000000000ull, 521000000000000ull, 522000000000000ull, + 523000000000000ull, 524000000000000ull, 525000000000000ull, + 526000000000000ull, 527000000000000ull, 528000000000000ull, + 529000000000000ull, 582000000000000ull, 583000000000000ull, + 924000000000000ull, 925000000000000ull, 948000000000000ull, + 949000000000000ull, + 530000000000000ull, 531000000000000ull, 532000000000000ull, + 533000000000000ull, 534000000000000ull, 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565000000000000ull, + 566000000000000ull, 567000000000000ull, 568000000000000ull, + 569000000000000ull, 586000000000000ull, 587000000000000ull, + 964000000000000ull, 965000000000000ull, 988000000000000ull, + 989000000000000ull, + 570000000000000ull, 571000000000000ull, 572000000000000ull, + 573000000000000ull, 574000000000000ull, 575000000000000ull, + 576000000000000ull, 577000000000000ull, 578000000000000ull, + 579000000000000ull, 596000000000000ull, 597000000000000ull, + 974000000000000ull, 975000000000000ull, 998000000000000ull, + 999000000000000ull, + 600000000000000ull, 601000000000000ull, 602000000000000ull, + 603000000000000ull, 604000000000000ull, 605000000000000ull, + 606000000000000ull, 607000000000000ull, 608000000000000ull, + 609000000000000ull, 680000000000000ull, 681000000000000ull, + 806000000000000ull, 807000000000000ull, 886000000000000ull, + 887000000000000ull, + 610000000000000ull, 611000000000000ull, 612000000000000ull, + 613000000000000ull, 614000000000000ull, 615000000000000ull, + 616000000000000ull, 617000000000000ull, 618000000000000ull, + 619000000000000ull, 690000000000000ull, 691000000000000ull, + 816000000000000ull, 817000000000000ull, 896000000000000ull, + 897000000000000ull, + 620000000000000ull, 621000000000000ull, 622000000000000ull, + 623000000000000ull, 624000000000000ull, 625000000000000ull, + 626000000000000ull, 627000000000000ull, 628000000000000ull, + 629000000000000ull, 682000000000000ull, 683000000000000ull, + 826000000000000ull, 827000000000000ull, 868000000000000ull, + 869000000000000ull, + 630000000000000ull, 631000000000000ull, 632000000000000ull, + 633000000000000ull, 634000000000000ull, 635000000000000ull, + 636000000000000ull, 637000000000000ull, 638000000000000ull, + 639000000000000ull, 692000000000000ull, 693000000000000ull, + 836000000000000ull, 837000000000000ull, 878000000000000ull, + 879000000000000ull, + 640000000000000ull, 641000000000000ull, 642000000000000ull, + 643000000000000ull, 644000000000000ull, 645000000000000ull, + 646000000000000ull, 647000000000000ull, 648000000000000ull, + 649000000000000ull, 684000000000000ull, 685000000000000ull, + 846000000000000ull, 847000000000000ull, 688000000000000ull, + 689000000000000ull, + 650000000000000ull, 651000000000000ull, 652000000000000ull, + 653000000000000ull, 654000000000000ull, 655000000000000ull, + 656000000000000ull, 657000000000000ull, 658000000000000ull, + 659000000000000ull, 694000000000000ull, 695000000000000ull, + 856000000000000ull, 857000000000000ull, 698000000000000ull, + 699000000000000ull, + 660000000000000ull, 661000000000000ull, 662000000000000ull, + 663000000000000ull, 664000000000000ull, 665000000000000ull, + 666000000000000ull, 667000000000000ull, 668000000000000ull, + 669000000000000ull, 686000000000000ull, 687000000000000ull, + 866000000000000ull, 867000000000000ull, 888000000000000ull, + 889000000000000ull, + 670000000000000ull, 671000000000000ull, 672000000000000ull, + 673000000000000ull, 674000000000000ull, 675000000000000ull, + 676000000000000ull, 677000000000000ull, 678000000000000ull, + 679000000000000ull, 696000000000000ull, 697000000000000ull, + 876000000000000ull, 877000000000000ull, 898000000000000ull, + 899000000000000ull, + 700000000000000ull, 701000000000000ull, 702000000000000ull, + 703000000000000ull, 704000000000000ull, 705000000000000ull, + 706000000000000ull, 707000000000000ull, 708000000000000ull, + 709000000000000ull, 780000000000000ull, 781000000000000ull, + 906000000000000ull, 907000000000000ull, 986000000000000ull, + 987000000000000ull, + 710000000000000ull, 711000000000000ull, 712000000000000ull, + 713000000000000ull, 714000000000000ull, 715000000000000ull, + 716000000000000ull, 717000000000000ull, 718000000000000ull, + 719000000000000ull, 790000000000000ull, 791000000000000ull, + 916000000000000ull, 917000000000000ull, 996000000000000ull, + 997000000000000ull, + 720000000000000ull, 721000000000000ull, 722000000000000ull, + 723000000000000ull, 724000000000000ull, 725000000000000ull, + 726000000000000ull, 727000000000000ull, 728000000000000ull, + 729000000000000ull, 782000000000000ull, 783000000000000ull, + 926000000000000ull, 927000000000000ull, 968000000000000ull, + 969000000000000ull, + 730000000000000ull, 731000000000000ull, 732000000000000ull, + 733000000000000ull, 734000000000000ull, 735000000000000ull, + 736000000000000ull, 737000000000000ull, 738000000000000ull, + 739000000000000ull, 792000000000000ull, 793000000000000ull, + 936000000000000ull, 937000000000000ull, 978000000000000ull, + 979000000000000ull, + 740000000000000ull, 741000000000000ull, 742000000000000ull, + 743000000000000ull, 744000000000000ull, 745000000000000ull, + 746000000000000ull, 747000000000000ull, 748000000000000ull, + 749000000000000ull, 784000000000000ull, 785000000000000ull, + 946000000000000ull, 947000000000000ull, 788000000000000ull, + 789000000000000ull, + 750000000000000ull, 751000000000000ull, 752000000000000ull, + 753000000000000ull, 754000000000000ull, 755000000000000ull, + 756000000000000ull, 757000000000000ull, 758000000000000ull, + 759000000000000ull, 794000000000000ull, 795000000000000ull, + 956000000000000ull, 957000000000000ull, 798000000000000ull, + 799000000000000ull, + 760000000000000ull, 761000000000000ull, 762000000000000ull, + 763000000000000ull, 764000000000000ull, 765000000000000ull, + 766000000000000ull, 767000000000000ull, 768000000000000ull, + 769000000000000ull, 786000000000000ull, 787000000000000ull, + 966000000000000ull, 967000000000000ull, 988000000000000ull, + 989000000000000ull, + 770000000000000ull, 771000000000000ull, 772000000000000ull, + 773000000000000ull, 774000000000000ull, 775000000000000ull, + 776000000000000ull, 777000000000000ull, 778000000000000ull, + 779000000000000ull, 796000000000000ull, 797000000000000ull, + 976000000000000ull, 977000000000000ull, 998000000000000ull, + 999000000000000ull +}; + +const UINT64 d2b6[] = + { 0000000000000000ull, 1000000000000000ull, 2000000000000000ull, + 3000000000000000ull, 4000000000000000ull, 5000000000000000ull, + 6000000000000000ull, 7000000000000000ull, 8000000000000000ull, + 9000000000000000ull, 80000000000000000ull, 81000000000000000ull, + 800000000000000000ull, 801000000000000000ull, 880000000000000000ull, + 881000000000000000ull, + 10000000000000000ull, 11000000000000000ull, 12000000000000000ull, + 13000000000000000ull, 14000000000000000ull, 15000000000000000ull, + 16000000000000000ull, 17000000000000000ull, 18000000000000000ull, + 19000000000000000ull, 90000000000000000ull, 91000000000000000ull, + 810000000000000000ull, 811000000000000000ull, 890000000000000000ull, + 891000000000000000ull, + 20000000000000000ull, 21000000000000000ull, 22000000000000000ull, + 23000000000000000ull, 24000000000000000ull, 25000000000000000ull, + 26000000000000000ull, 27000000000000000ull, 28000000000000000ull, + 29000000000000000ull, 82000000000000000ull, 83000000000000000ull, + 820000000000000000ull, 821000000000000000ull, 808000000000000000ull, + 809000000000000000ull, + 30000000000000000ull, 31000000000000000ull, 32000000000000000ull, + 33000000000000000ull, 34000000000000000ull, 35000000000000000ull, + 36000000000000000ull, 37000000000000000ull, 38000000000000000ull, + 39000000000000000ull, 92000000000000000ull, 93000000000000000ull, + 830000000000000000ull, 831000000000000000ull, 818000000000000000ull, + 819000000000000000ull, + 40000000000000000ull, 41000000000000000ull, 42000000000000000ull, + 43000000000000000ull, 44000000000000000ull, 45000000000000000ull, + 46000000000000000ull, 47000000000000000ull, 48000000000000000ull, + 49000000000000000ull, 84000000000000000ull, 85000000000000000ull, + 840000000000000000ull, 841000000000000000ull, 88000000000000000ull, + 89000000000000000ull, + 50000000000000000ull, 51000000000000000ull, 52000000000000000ull, + 53000000000000000ull, 54000000000000000ull, 55000000000000000ull, + 56000000000000000ull, 57000000000000000ull, 58000000000000000ull, + 59000000000000000ull, 94000000000000000ull, 95000000000000000ull, + 850000000000000000ull, 851000000000000000ull, 98000000000000000ull, + 99000000000000000ull, + 60000000000000000ull, 61000000000000000ull, 62000000000000000ull, + 63000000000000000ull, 64000000000000000ull, 65000000000000000ull, + 66000000000000000ull, 67000000000000000ull, 68000000000000000ull, + 69000000000000000ull, 86000000000000000ull, 87000000000000000ull, + 860000000000000000ull, 861000000000000000ull, 888000000000000000ull, + 889000000000000000ull, + 70000000000000000ull, 71000000000000000ull, 72000000000000000ull, + 73000000000000000ull, 74000000000000000ull, 75000000000000000ull, + 76000000000000000ull, 77000000000000000ull, 78000000000000000ull, + 79000000000000000ull, 96000000000000000ull, 97000000000000000ull, + 870000000000000000ull, 871000000000000000ull, 898000000000000000ull, + 899000000000000000ull, + 100000000000000000ull, 101000000000000000ull, 102000000000000000ull, + 103000000000000000ull, 104000000000000000ull, 105000000000000000ull, + 106000000000000000ull, 107000000000000000ull, 108000000000000000ull, + 109000000000000000ull, 180000000000000000ull, 181000000000000000ull, + 900000000000000000ull, 901000000000000000ull, 980000000000000000ull, + 981000000000000000ull, + 110000000000000000ull, 111000000000000000ull, 112000000000000000ull, + 113000000000000000ull, 114000000000000000ull, 115000000000000000ull, + 116000000000000000ull, 117000000000000000ull, 118000000000000000ull, + 119000000000000000ull, 190000000000000000ull, 191000000000000000ull, + 910000000000000000ull, 911000000000000000ull, 990000000000000000ull, + 991000000000000000ull, + 120000000000000000ull, 121000000000000000ull, 122000000000000000ull, + 123000000000000000ull, 124000000000000000ull, 125000000000000000ull, + 126000000000000000ull, 127000000000000000ull, 128000000000000000ull, + 129000000000000000ull, 182000000000000000ull, 183000000000000000ull, + 920000000000000000ull, 921000000000000000ull, 908000000000000000ull, + 909000000000000000ull, + 130000000000000000ull, 131000000000000000ull, 132000000000000000ull, + 133000000000000000ull, 134000000000000000ull, 135000000000000000ull, + 136000000000000000ull, 137000000000000000ull, 138000000000000000ull, + 139000000000000000ull, 192000000000000000ull, 193000000000000000ull, + 930000000000000000ull, 931000000000000000ull, 918000000000000000ull, + 919000000000000000ull, + 140000000000000000ull, 141000000000000000ull, 142000000000000000ull, + 143000000000000000ull, 144000000000000000ull, 145000000000000000ull, + 146000000000000000ull, 147000000000000000ull, 148000000000000000ull, + 149000000000000000ull, 184000000000000000ull, 185000000000000000ull, + 940000000000000000ull, 941000000000000000ull, 188000000000000000ull, + 189000000000000000ull, + 150000000000000000ull, 151000000000000000ull, 152000000000000000ull, + 153000000000000000ull, 154000000000000000ull, 155000000000000000ull, + 156000000000000000ull, 157000000000000000ull, 158000000000000000ull, + 159000000000000000ull, 194000000000000000ull, 195000000000000000ull, + 950000000000000000ull, 951000000000000000ull, 198000000000000000ull, + 199000000000000000ull, + 160000000000000000ull, 161000000000000000ull, 162000000000000000ull, + 163000000000000000ull, 164000000000000000ull, 165000000000000000ull, + 166000000000000000ull, 167000000000000000ull, 168000000000000000ull, + 169000000000000000ull, 186000000000000000ull, 187000000000000000ull, + 960000000000000000ull, 961000000000000000ull, 988000000000000000ull, + 989000000000000000ull, + 170000000000000000ull, 171000000000000000ull, 172000000000000000ull, + 173000000000000000ull, 174000000000000000ull, 175000000000000000ull, + 176000000000000000ull, 177000000000000000ull, 178000000000000000ull, + 179000000000000000ull, 196000000000000000ull, 197000000000000000ull, + 970000000000000000ull, 971000000000000000ull, 998000000000000000ull, + 999000000000000000ull, + 200000000000000000ull, 201000000000000000ull, 202000000000000000ull, + 203000000000000000ull, 204000000000000000ull, 205000000000000000ull, + 206000000000000000ull, 207000000000000000ull, 208000000000000000ull, + 209000000000000000ull, 280000000000000000ull, 281000000000000000ull, + 802000000000000000ull, 803000000000000000ull, 882000000000000000ull, + 883000000000000000ull, + 210000000000000000ull, 211000000000000000ull, 212000000000000000ull, + 213000000000000000ull, 214000000000000000ull, 215000000000000000ull, + 216000000000000000ull, 217000000000000000ull, 218000000000000000ull, + 219000000000000000ull, 290000000000000000ull, 291000000000000000ull, + 812000000000000000ull, 813000000000000000ull, 892000000000000000ull, + 893000000000000000ull, + 220000000000000000ull, 221000000000000000ull, 222000000000000000ull, + 223000000000000000ull, 224000000000000000ull, 225000000000000000ull, + 226000000000000000ull, 227000000000000000ull, 228000000000000000ull, + 229000000000000000ull, 282000000000000000ull, 283000000000000000ull, + 822000000000000000ull, 823000000000000000ull, 828000000000000000ull, + 829000000000000000ull, + 230000000000000000ull, 231000000000000000ull, 232000000000000000ull, + 233000000000000000ull, 234000000000000000ull, 235000000000000000ull, + 236000000000000000ull, 237000000000000000ull, 238000000000000000ull, + 239000000000000000ull, 292000000000000000ull, 293000000000000000ull, + 832000000000000000ull, 833000000000000000ull, 838000000000000000ull, + 839000000000000000ull, + 240000000000000000ull, 241000000000000000ull, 242000000000000000ull, + 243000000000000000ull, 244000000000000000ull, 245000000000000000ull, + 246000000000000000ull, 247000000000000000ull, 248000000000000000ull, + 249000000000000000ull, 284000000000000000ull, 285000000000000000ull, + 842000000000000000ull, 843000000000000000ull, 288000000000000000ull, + 289000000000000000ull, + 250000000000000000ull, 251000000000000000ull, 252000000000000000ull, + 253000000000000000ull, 254000000000000000ull, 255000000000000000ull, + 256000000000000000ull, 257000000000000000ull, 258000000000000000ull, + 259000000000000000ull, 294000000000000000ull, 295000000000000000ull, + 852000000000000000ull, 853000000000000000ull, 298000000000000000ull, + 299000000000000000ull, + 260000000000000000ull, 261000000000000000ull, 262000000000000000ull, + 263000000000000000ull, 264000000000000000ull, 265000000000000000ull, + 266000000000000000ull, 267000000000000000ull, 268000000000000000ull, + 269000000000000000ull, 286000000000000000ull, 287000000000000000ull, + 862000000000000000ull, 863000000000000000ull, 888000000000000000ull, + 889000000000000000ull, + 270000000000000000ull, 271000000000000000ull, 272000000000000000ull, + 273000000000000000ull, 274000000000000000ull, 275000000000000000ull, + 276000000000000000ull, 277000000000000000ull, 278000000000000000ull, + 279000000000000000ull, 296000000000000000ull, 297000000000000000ull, + 872000000000000000ull, 873000000000000000ull, 898000000000000000ull, + 899000000000000000ull, + 300000000000000000ull, 301000000000000000ull, 302000000000000000ull, + 303000000000000000ull, 304000000000000000ull, 305000000000000000ull, + 306000000000000000ull, 307000000000000000ull, 308000000000000000ull, + 309000000000000000ull, 380000000000000000ull, 381000000000000000ull, + 902000000000000000ull, 903000000000000000ull, 982000000000000000ull, + 983000000000000000ull, + 310000000000000000ull, 311000000000000000ull, 312000000000000000ull, + 313000000000000000ull, 314000000000000000ull, 315000000000000000ull, + 316000000000000000ull, 317000000000000000ull, 318000000000000000ull, + 319000000000000000ull, 390000000000000000ull, 391000000000000000ull, + 912000000000000000ull, 913000000000000000ull, 992000000000000000ull, + 993000000000000000ull, + 320000000000000000ull, 321000000000000000ull, 322000000000000000ull, + 323000000000000000ull, 324000000000000000ull, 325000000000000000ull, + 326000000000000000ull, 327000000000000000ull, 328000000000000000ull, + 329000000000000000ull, 382000000000000000ull, 383000000000000000ull, + 922000000000000000ull, 923000000000000000ull, 928000000000000000ull, + 929000000000000000ull, + 330000000000000000ull, 331000000000000000ull, 332000000000000000ull, + 333000000000000000ull, 334000000000000000ull, 335000000000000000ull, + 336000000000000000ull, 337000000000000000ull, 338000000000000000ull, + 339000000000000000ull, 392000000000000000ull, 393000000000000000ull, + 932000000000000000ull, 933000000000000000ull, 938000000000000000ull, + 939000000000000000ull, + 340000000000000000ull, 341000000000000000ull, 342000000000000000ull, + 343000000000000000ull, 344000000000000000ull, 345000000000000000ull, + 346000000000000000ull, 347000000000000000ull, 348000000000000000ull, + 349000000000000000ull, 384000000000000000ull, 385000000000000000ull, + 942000000000000000ull, 943000000000000000ull, 388000000000000000ull, + 389000000000000000ull, + 350000000000000000ull, 351000000000000000ull, 352000000000000000ull, + 353000000000000000ull, 354000000000000000ull, 355000000000000000ull, + 356000000000000000ull, 357000000000000000ull, 358000000000000000ull, + 359000000000000000ull, 394000000000000000ull, 395000000000000000ull, + 952000000000000000ull, 953000000000000000ull, 398000000000000000ull, + 399000000000000000ull, + 360000000000000000ull, 361000000000000000ull, 362000000000000000ull, + 363000000000000000ull, 364000000000000000ull, 365000000000000000ull, + 366000000000000000ull, 367000000000000000ull, 368000000000000000ull, + 369000000000000000ull, 386000000000000000ull, 387000000000000000ull, + 962000000000000000ull, 963000000000000000ull, 988000000000000000ull, + 989000000000000000ull, + 370000000000000000ull, 371000000000000000ull, 372000000000000000ull, + 373000000000000000ull, 374000000000000000ull, 375000000000000000ull, + 376000000000000000ull, 377000000000000000ull, 378000000000000000ull, + 379000000000000000ull, 396000000000000000ull, 397000000000000000ull, + 972000000000000000ull, 973000000000000000ull, 998000000000000000ull, + 999000000000000000ull, + 400000000000000000ull, 401000000000000000ull, 402000000000000000ull, + 403000000000000000ull, 404000000000000000ull, 405000000000000000ull, + 406000000000000000ull, 407000000000000000ull, 408000000000000000ull, + 409000000000000000ull, 480000000000000000ull, 481000000000000000ull, + 804000000000000000ull, 805000000000000000ull, 884000000000000000ull, + 885000000000000000ull, + 410000000000000000ull, 411000000000000000ull, 412000000000000000ull, + 413000000000000000ull, 414000000000000000ull, 415000000000000000ull, + 416000000000000000ull, 417000000000000000ull, 418000000000000000ull, + 419000000000000000ull, 490000000000000000ull, 491000000000000000ull, + 814000000000000000ull, 815000000000000000ull, 894000000000000000ull, + 895000000000000000ull, + 420000000000000000ull, 421000000000000000ull, 422000000000000000ull, + 423000000000000000ull, 424000000000000000ull, 425000000000000000ull, + 426000000000000000ull, 427000000000000000ull, 428000000000000000ull, + 429000000000000000ull, 482000000000000000ull, 483000000000000000ull, + 824000000000000000ull, 825000000000000000ull, 848000000000000000ull, + 849000000000000000ull, + 430000000000000000ull, 431000000000000000ull, 432000000000000000ull, + 433000000000000000ull, 434000000000000000ull, 435000000000000000ull, + 436000000000000000ull, 437000000000000000ull, 438000000000000000ull, + 439000000000000000ull, 492000000000000000ull, 493000000000000000ull, + 834000000000000000ull, 835000000000000000ull, 858000000000000000ull, + 859000000000000000ull, + 440000000000000000ull, 441000000000000000ull, 442000000000000000ull, + 443000000000000000ull, 444000000000000000ull, 445000000000000000ull, + 446000000000000000ull, 447000000000000000ull, 448000000000000000ull, + 449000000000000000ull, 484000000000000000ull, 485000000000000000ull, + 844000000000000000ull, 845000000000000000ull, 488000000000000000ull, + 489000000000000000ull, + 450000000000000000ull, 451000000000000000ull, 452000000000000000ull, + 453000000000000000ull, 454000000000000000ull, 455000000000000000ull, + 456000000000000000ull, 457000000000000000ull, 458000000000000000ull, + 459000000000000000ull, 494000000000000000ull, 495000000000000000ull, + 854000000000000000ull, 855000000000000000ull, 498000000000000000ull, + 499000000000000000ull, + 460000000000000000ull, 461000000000000000ull, 462000000000000000ull, + 463000000000000000ull, 464000000000000000ull, 465000000000000000ull, + 466000000000000000ull, 467000000000000000ull, 468000000000000000ull, + 469000000000000000ull, 486000000000000000ull, 487000000000000000ull, + 864000000000000000ull, 865000000000000000ull, 888000000000000000ull, + 889000000000000000ull, + 470000000000000000ull, 471000000000000000ull, 472000000000000000ull, + 473000000000000000ull, 474000000000000000ull, 475000000000000000ull, + 476000000000000000ull, 477000000000000000ull, 478000000000000000ull, + 479000000000000000ull, 496000000000000000ull, 497000000000000000ull, + 874000000000000000ull, 875000000000000000ull, 898000000000000000ull, + 899000000000000000ull, + 500000000000000000ull, 501000000000000000ull, 502000000000000000ull, + 503000000000000000ull, 504000000000000000ull, 505000000000000000ull, + 506000000000000000ull, 507000000000000000ull, 508000000000000000ull, + 509000000000000000ull, 580000000000000000ull, 581000000000000000ull, + 904000000000000000ull, 905000000000000000ull, 984000000000000000ull, + 985000000000000000ull, + 510000000000000000ull, 511000000000000000ull, 512000000000000000ull, + 513000000000000000ull, 514000000000000000ull, 515000000000000000ull, + 516000000000000000ull, 517000000000000000ull, 518000000000000000ull, + 519000000000000000ull, 590000000000000000ull, 591000000000000000ull, + 914000000000000000ull, 915000000000000000ull, 994000000000000000ull, + 995000000000000000ull, + 520000000000000000ull, 521000000000000000ull, 522000000000000000ull, + 523000000000000000ull, 524000000000000000ull, 525000000000000000ull, + 526000000000000000ull, 527000000000000000ull, 528000000000000000ull, + 529000000000000000ull, 582000000000000000ull, 583000000000000000ull, + 924000000000000000ull, 925000000000000000ull, 948000000000000000ull, + 949000000000000000ull, + 530000000000000000ull, 531000000000000000ull, 532000000000000000ull, + 533000000000000000ull, 534000000000000000ull, 535000000000000000ull, + 536000000000000000ull, 537000000000000000ull, 538000000000000000ull, + 539000000000000000ull, 592000000000000000ull, 593000000000000000ull, + 934000000000000000ull, 935000000000000000ull, 958000000000000000ull, + 959000000000000000ull, + 540000000000000000ull, 541000000000000000ull, 542000000000000000ull, + 543000000000000000ull, 544000000000000000ull, 545000000000000000ull, + 546000000000000000ull, 547000000000000000ull, 548000000000000000ull, + 549000000000000000ull, 584000000000000000ull, 585000000000000000ull, + 944000000000000000ull, 945000000000000000ull, 588000000000000000ull, + 589000000000000000ull, + 550000000000000000ull, 551000000000000000ull, 552000000000000000ull, + 553000000000000000ull, 554000000000000000ull, 555000000000000000ull, + 556000000000000000ull, 557000000000000000ull, 558000000000000000ull, + 559000000000000000ull, 594000000000000000ull, 595000000000000000ull, + 954000000000000000ull, 955000000000000000ull, 598000000000000000ull, + 599000000000000000ull, + 560000000000000000ull, 561000000000000000ull, 562000000000000000ull, + 563000000000000000ull, 564000000000000000ull, 565000000000000000ull, + 566000000000000000ull, 567000000000000000ull, 568000000000000000ull, + 569000000000000000ull, 586000000000000000ull, 587000000000000000ull, + 964000000000000000ull, 965000000000000000ull, 988000000000000000ull, + 989000000000000000ull, + 570000000000000000ull, 571000000000000000ull, 572000000000000000ull, + 573000000000000000ull, 574000000000000000ull, 575000000000000000ull, + 576000000000000000ull, 577000000000000000ull, 578000000000000000ull, + 579000000000000000ull, 596000000000000000ull, 597000000000000000ull, + 974000000000000000ull, 975000000000000000ull, 998000000000000000ull, + 999000000000000000ull, + 600000000000000000ull, 601000000000000000ull, 602000000000000000ull, + 603000000000000000ull, 604000000000000000ull, 605000000000000000ull, + 606000000000000000ull, 607000000000000000ull, 608000000000000000ull, + 609000000000000000ull, 680000000000000000ull, 681000000000000000ull, + 806000000000000000ull, 807000000000000000ull, 886000000000000000ull, + 887000000000000000ull, + 610000000000000000ull, 611000000000000000ull, 612000000000000000ull, + 613000000000000000ull, 614000000000000000ull, 615000000000000000ull, + 616000000000000000ull, 617000000000000000ull, 618000000000000000ull, + 619000000000000000ull, 690000000000000000ull, 691000000000000000ull, + 816000000000000000ull, 817000000000000000ull, 896000000000000000ull, + 897000000000000000ull, + 620000000000000000ull, 621000000000000000ull, 622000000000000000ull, + 623000000000000000ull, 624000000000000000ull, 625000000000000000ull, + 626000000000000000ull, 627000000000000000ull, 628000000000000000ull, + 629000000000000000ull, 682000000000000000ull, 683000000000000000ull, + 826000000000000000ull, 827000000000000000ull, 868000000000000000ull, + 869000000000000000ull, + 630000000000000000ull, 631000000000000000ull, 632000000000000000ull, + 633000000000000000ull, 634000000000000000ull, 635000000000000000ull, + 636000000000000000ull, 637000000000000000ull, 638000000000000000ull, + 639000000000000000ull, 692000000000000000ull, 693000000000000000ull, + 836000000000000000ull, 837000000000000000ull, 878000000000000000ull, + 879000000000000000ull, + 640000000000000000ull, 641000000000000000ull, 642000000000000000ull, + 643000000000000000ull, 644000000000000000ull, 645000000000000000ull, + 646000000000000000ull, 647000000000000000ull, 648000000000000000ull, + 649000000000000000ull, 684000000000000000ull, 685000000000000000ull, + 846000000000000000ull, 847000000000000000ull, 688000000000000000ull, + 689000000000000000ull, + 650000000000000000ull, 651000000000000000ull, 652000000000000000ull, + 653000000000000000ull, 654000000000000000ull, 655000000000000000ull, + 656000000000000000ull, 657000000000000000ull, 658000000000000000ull, + 659000000000000000ull, 694000000000000000ull, 695000000000000000ull, + 856000000000000000ull, 857000000000000000ull, 698000000000000000ull, + 699000000000000000ull, + 660000000000000000ull, 661000000000000000ull, 662000000000000000ull, + 663000000000000000ull, 664000000000000000ull, 665000000000000000ull, + 666000000000000000ull, 667000000000000000ull, 668000000000000000ull, + 669000000000000000ull, 686000000000000000ull, 687000000000000000ull, + 866000000000000000ull, 867000000000000000ull, 888000000000000000ull, + 889000000000000000ull, + 670000000000000000ull, 671000000000000000ull, 672000000000000000ull, + 673000000000000000ull, 674000000000000000ull, 675000000000000000ull, + 676000000000000000ull, 677000000000000000ull, 678000000000000000ull, + 679000000000000000ull, 696000000000000000ull, 697000000000000000ull, + 876000000000000000ull, 877000000000000000ull, 898000000000000000ull, + 899000000000000000ull, + 700000000000000000ull, 701000000000000000ull, 702000000000000000ull, + 703000000000000000ull, 704000000000000000ull, 705000000000000000ull, + 706000000000000000ull, 707000000000000000ull, 708000000000000000ull, + 709000000000000000ull, 780000000000000000ull, 781000000000000000ull, + 906000000000000000ull, 907000000000000000ull, 986000000000000000ull, + 987000000000000000ull, + 710000000000000000ull, 711000000000000000ull, 712000000000000000ull, + 713000000000000000ull, 714000000000000000ull, 715000000000000000ull, + 716000000000000000ull, 717000000000000000ull, 718000000000000000ull, + 719000000000000000ull, 790000000000000000ull, 791000000000000000ull, + 916000000000000000ull, 917000000000000000ull, 996000000000000000ull, + 997000000000000000ull, + 720000000000000000ull, 721000000000000000ull, 722000000000000000ull, + 723000000000000000ull, 724000000000000000ull, 725000000000000000ull, + 726000000000000000ull, 727000000000000000ull, 728000000000000000ull, + 729000000000000000ull, 782000000000000000ull, 783000000000000000ull, + 926000000000000000ull, 927000000000000000ull, 968000000000000000ull, + 969000000000000000ull, + 730000000000000000ull, 731000000000000000ull, 732000000000000000ull, + 733000000000000000ull, 734000000000000000ull, 735000000000000000ull, + 736000000000000000ull, 737000000000000000ull, 738000000000000000ull, + 739000000000000000ull, 792000000000000000ull, 793000000000000000ull, + 936000000000000000ull, 937000000000000000ull, 978000000000000000ull, + 979000000000000000ull, + 740000000000000000ull, 741000000000000000ull, 742000000000000000ull, + 743000000000000000ull, 744000000000000000ull, 745000000000000000ull, + 746000000000000000ull, 747000000000000000ull, 748000000000000000ull, + 749000000000000000ull, 784000000000000000ull, 785000000000000000ull, + 946000000000000000ull, 947000000000000000ull, 788000000000000000ull, + 789000000000000000ull, + 750000000000000000ull, 751000000000000000ull, 752000000000000000ull, + 753000000000000000ull, 754000000000000000ull, 755000000000000000ull, + 756000000000000000ull, 757000000000000000ull, 758000000000000000ull, + 759000000000000000ull, 794000000000000000ull, 795000000000000000ull, + 956000000000000000ull, 957000000000000000ull, 798000000000000000ull, + 799000000000000000ull, + 760000000000000000ull, 761000000000000000ull, 762000000000000000ull, + 763000000000000000ull, 764000000000000000ull, 765000000000000000ull, + 766000000000000000ull, 767000000000000000ull, 768000000000000000ull, + 769000000000000000ull, 786000000000000000ull, 787000000000000000ull, + 966000000000000000ull, 967000000000000000ull, 988000000000000000ull, + 989000000000000000ull, + 770000000000000000ull, 771000000000000000ull, 772000000000000000ull, + 773000000000000000ull, 774000000000000000ull, 775000000000000000ull, + 776000000000000000ull, 777000000000000000ull, 778000000000000000ull, + 779000000000000000ull, 796000000000000000ull, 797000000000000000ull, + 976000000000000000ull, 977000000000000000ull, 998000000000000000ull, + 999000000000000000ull +}; + +const UINT64 b2d[] = + { 0x000ull, 0x001ull, 0x002ull, 0x003ull, 0x004ull, 0x005ull, + 0x006ull, 0x007ull, 0x008ull, 0x009ull, + 0x010ull, 0x011ull, 0x012ull, 0x013ull, 0x014ull, 0x015ull, 0x016ull, + 0x017ull, 0x018ull, 0x019ull, + 0x020ull, 0x021ull, 0x022ull, 0x023ull, 0x024ull, 0x025ull, 0x026ull, + 0x027ull, 0x028ull, 0x029ull, + 0x030ull, 0x031ull, 0x032ull, 0x033ull, 0x034ull, 0x035ull, 0x036ull, + 0x037ull, 0x038ull, 0x039ull, + 0x040ull, 0x041ull, 0x042ull, 0x043ull, 0x044ull, 0x045ull, 0x046ull, + 0x047ull, 0x048ull, 0x049ull, + 0x050ull, 0x051ull, 0x052ull, 0x053ull, 0x054ull, 0x055ull, 0x056ull, + 0x057ull, 0x058ull, 0x059ull, + 0x060ull, 0x061ull, 0x062ull, 0x063ull, 0x064ull, 0x065ull, 0x066ull, + 0x067ull, 0x068ull, 0x069ull, + 0x070ull, 0x071ull, 0x072ull, 0x073ull, 0x074ull, 0x075ull, 0x076ull, + 0x077ull, 0x078ull, 0x079ull, + 0x00aull, 0x00bull, 0x02aull, 0x02bull, 0x04aull, 0x04bull, 0x06aull, + 0x06bull, 0x04eull, 0x04full, + 0x01aull, 0x01bull, 0x03aull, 0x03bull, 0x05aull, 0x05bull, 0x07aull, + 0x07bull, 0x05eull, 0x05full, + 0x080ull, 0x081ull, 0x082ull, 0x083ull, 0x084ull, 0x085ull, 0x086ull, + 0x087ull, 0x088ull, 0x089ull, + 0x090ull, 0x091ull, 0x092ull, 0x093ull, 0x094ull, 0x095ull, 0x096ull, + 0x097ull, 0x098ull, 0x099ull, + 0x0a0ull, 0x0a1ull, 0x0a2ull, 0x0a3ull, 0x0a4ull, 0x0a5ull, 0x0a6ull, + 0x0a7ull, 0x0a8ull, 0x0a9ull, + 0x0b0ull, 0x0b1ull, 0x0b2ull, 0x0b3ull, 0x0b4ull, 0x0b5ull, 0x0b6ull, + 0x0b7ull, 0x0b8ull, 0x0b9ull, + 0x0c0ull, 0x0c1ull, 0x0c2ull, 0x0c3ull, 0x0c4ull, 0x0c5ull, 0x0c6ull, + 0x0c7ull, 0x0c8ull, 0x0c9ull, + 0x0d0ull, 0x0d1ull, 0x0d2ull, 0x0d3ull, 0x0d4ull, 0x0d5ull, 0x0d6ull, + 0x0d7ull, 0x0d8ull, 0x0d9ull, + 0x0e0ull, 0x0e1ull, 0x0e2ull, 0x0e3ull, 0x0e4ull, 0x0e5ull, 0x0e6ull, + 0x0e7ull, 0x0e8ull, 0x0e9ull, + 0x0f0ull, 0x0f1ull, 0x0f2ull, 0x0f3ull, 0x0f4ull, 0x0f5ull, 0x0f6ull, + 0x0f7ull, 0x0f8ull, 0x0f9ull, + 0x08aull, 0x08bull, 0x0aaull, 0x0abull, 0x0caull, 0x0cbull, 0x0eaull, + 0x0ebull, 0x0ceull, 0x0cfull, + 0x09aull, 0x09bull, 0x0baull, 0x0bbull, 0x0daull, 0x0dbull, 0x0faull, + 0x0fbull, 0x0deull, 0x0dfull, + 0x100ull, 0x101ull, 0x102ull, 0x103ull, 0x104ull, 0x105ull, 0x106ull, + 0x107ull, 0x108ull, 0x109ull, + 0x110ull, 0x111ull, 0x112ull, 0x113ull, 0x114ull, 0x115ull, 0x116ull, + 0x117ull, 0x118ull, 0x119ull, + 0x120ull, 0x121ull, 0x122ull, 0x123ull, 0x124ull, 0x125ull, 0x126ull, + 0x127ull, 0x128ull, 0x129ull, + 0x130ull, 0x131ull, 0x132ull, 0x133ull, 0x134ull, 0x135ull, 0x136ull, + 0x137ull, 0x138ull, 0x139ull, + 0x140ull, 0x141ull, 0x142ull, 0x143ull, 0x144ull, 0x145ull, 0x146ull, + 0x147ull, 0x148ull, 0x149ull, + 0x150ull, 0x151ull, 0x152ull, 0x153ull, 0x154ull, 0x155ull, 0x156ull, + 0x157ull, 0x158ull, 0x159ull, + 0x160ull, 0x161ull, 0x162ull, 0x163ull, 0x164ull, 0x165ull, 0x166ull, + 0x167ull, 0x168ull, 0x169ull, + 0x170ull, 0x171ull, 0x172ull, 0x173ull, 0x174ull, 0x175ull, 0x176ull, + 0x177ull, 0x178ull, 0x179ull, + 0x10aull, 0x10bull, 0x12aull, 0x12bull, 0x14aull, 0x14bull, 0x16aull, + 0x16bull, 0x14eull, 0x14full, + 0x11aull, 0x11bull, 0x13aull, 0x13bull, 0x15aull, 0x15bull, 0x17aull, + 0x17bull, 0x15eull, 0x15full, + 0x180ull, 0x181ull, 0x182ull, 0x183ull, 0x184ull, 0x185ull, 0x186ull, + 0x187ull, 0x188ull, 0x189ull, + 0x190ull, 0x191ull, 0x192ull, 0x193ull, 0x194ull, 0x195ull, 0x196ull, + 0x197ull, 0x198ull, 0x199ull, + 0x1a0ull, 0x1a1ull, 0x1a2ull, 0x1a3ull, 0x1a4ull, 0x1a5ull, 0x1a6ull, + 0x1a7ull, 0x1a8ull, 0x1a9ull, + 0x1b0ull, 0x1b1ull, 0x1b2ull, 0x1b3ull, 0x1b4ull, 0x1b5ull, 0x1b6ull, + 0x1b7ull, 0x1b8ull, 0x1b9ull, + 0x1c0ull, 0x1c1ull, 0x1c2ull, 0x1c3ull, 0x1c4ull, 0x1c5ull, 0x1c6ull, + 0x1c7ull, 0x1c8ull, 0x1c9ull, + 0x1d0ull, 0x1d1ull, 0x1d2ull, 0x1d3ull, 0x1d4ull, 0x1d5ull, 0x1d6ull, + 0x1d7ull, 0x1d8ull, 0x1d9ull, + 0x1e0ull, 0x1e1ull, 0x1e2ull, 0x1e3ull, 0x1e4ull, 0x1e5ull, 0x1e6ull, + 0x1e7ull, 0x1e8ull, 0x1e9ull, + 0x1f0ull, 0x1f1ull, 0x1f2ull, 0x1f3ull, 0x1f4ull, 0x1f5ull, 0x1f6ull, + 0x1f7ull, 0x1f8ull, 0x1f9ull, + 0x18aull, 0x18bull, 0x1aaull, 0x1abull, 0x1caull, 0x1cbull, 0x1eaull, + 0x1ebull, 0x1ceull, 0x1cfull, + 0x19aull, 0x19bull, 0x1baull, 0x1bbull, 0x1daull, 0x1dbull, 0x1faull, + 0x1fbull, 0x1deull, 0x1dfull, + 0x200ull, 0x201ull, 0x202ull, 0x203ull, 0x204ull, 0x205ull, 0x206ull, + 0x207ull, 0x208ull, 0x209ull, + 0x210ull, 0x211ull, 0x212ull, 0x213ull, 0x214ull, 0x215ull, 0x216ull, + 0x217ull, 0x218ull, 0x219ull, + 0x220ull, 0x221ull, 0x222ull, 0x223ull, 0x224ull, 0x225ull, 0x226ull, + 0x227ull, 0x228ull, 0x229ull, + 0x230ull, 0x231ull, 0x232ull, 0x233ull, 0x234ull, 0x235ull, 0x236ull, + 0x237ull, 0x238ull, 0x239ull, + 0x240ull, 0x241ull, 0x242ull, 0x243ull, 0x244ull, 0x245ull, 0x246ull, + 0x247ull, 0x248ull, 0x249ull, + 0x250ull, 0x251ull, 0x252ull, 0x253ull, 0x254ull, 0x255ull, 0x256ull, + 0x257ull, 0x258ull, 0x259ull, + 0x260ull, 0x261ull, 0x262ull, 0x263ull, 0x264ull, 0x265ull, 0x266ull, + 0x267ull, 0x268ull, 0x269ull, + 0x270ull, 0x271ull, 0x272ull, 0x273ull, 0x274ull, 0x275ull, 0x276ull, + 0x277ull, 0x278ull, 0x279ull, + 0x20aull, 0x20bull, 0x22aull, 0x22bull, 0x24aull, 0x24bull, 0x26aull, + 0x26bull, 0x24eull, 0x24full, + 0x21aull, 0x21bull, 0x23aull, 0x23bull, 0x25aull, 0x25bull, 0x27aull, + 0x27bull, 0x25eull, 0x25full, + 0x280ull, 0x281ull, 0x282ull, 0x283ull, 0x284ull, 0x285ull, 0x286ull, + 0x287ull, 0x288ull, 0x289ull, + 0x290ull, 0x291ull, 0x292ull, 0x293ull, 0x294ull, 0x295ull, 0x296ull, + 0x297ull, 0x298ull, 0x299ull, + 0x2a0ull, 0x2a1ull, 0x2a2ull, 0x2a3ull, 0x2a4ull, 0x2a5ull, 0x2a6ull, + 0x2a7ull, 0x2a8ull, 0x2a9ull, + 0x2b0ull, 0x2b1ull, 0x2b2ull, 0x2b3ull, 0x2b4ull, 0x2b5ull, 0x2b6ull, + 0x2b7ull, 0x2b8ull, 0x2b9ull, + 0x2c0ull, 0x2c1ull, 0x2c2ull, 0x2c3ull, 0x2c4ull, 0x2c5ull, 0x2c6ull, + 0x2c7ull, 0x2c8ull, 0x2c9ull, + 0x2d0ull, 0x2d1ull, 0x2d2ull, 0x2d3ull, 0x2d4ull, 0x2d5ull, 0x2d6ull, + 0x2d7ull, 0x2d8ull, 0x2d9ull, + 0x2e0ull, 0x2e1ull, 0x2e2ull, 0x2e3ull, 0x2e4ull, 0x2e5ull, 0x2e6ull, + 0x2e7ull, 0x2e8ull, 0x2e9ull, + 0x2f0ull, 0x2f1ull, 0x2f2ull, 0x2f3ull, 0x2f4ull, 0x2f5ull, 0x2f6ull, + 0x2f7ull, 0x2f8ull, 0x2f9ull, + 0x28aull, 0x28bull, 0x2aaull, 0x2abull, 0x2caull, 0x2cbull, 0x2eaull, + 0x2ebull, 0x2ceull, 0x2cfull, + 0x29aull, 0x29bull, 0x2baull, 0x2bbull, 0x2daull, 0x2dbull, 0x2faull, + 0x2fbull, 0x2deull, 0x2dfull, + 0x300ull, 0x301ull, 0x302ull, 0x303ull, 0x304ull, 0x305ull, 0x306ull, + 0x307ull, 0x308ull, 0x309ull, + 0x310ull, 0x311ull, 0x312ull, 0x313ull, 0x314ull, 0x315ull, 0x316ull, + 0x317ull, 0x318ull, 0x319ull, + 0x320ull, 0x321ull, 0x322ull, 0x323ull, 0x324ull, 0x325ull, 0x326ull, + 0x327ull, 0x328ull, 0x329ull, + 0x330ull, 0x331ull, 0x332ull, 0x333ull, 0x334ull, 0x335ull, 0x336ull, + 0x337ull, 0x338ull, 0x339ull, + 0x340ull, 0x341ull, 0x342ull, 0x343ull, 0x344ull, 0x345ull, 0x346ull, + 0x347ull, 0x348ull, 0x349ull, + 0x350ull, 0x351ull, 0x352ull, 0x353ull, 0x354ull, 0x355ull, 0x356ull, + 0x357ull, 0x358ull, 0x359ull, + 0x360ull, 0x361ull, 0x362ull, 0x363ull, 0x364ull, 0x365ull, 0x366ull, + 0x367ull, 0x368ull, 0x369ull, + 0x370ull, 0x371ull, 0x372ull, 0x373ull, 0x374ull, 0x375ull, 0x376ull, + 0x377ull, 0x378ull, 0x379ull, + 0x30aull, 0x30bull, 0x32aull, 0x32bull, 0x34aull, 0x34bull, 0x36aull, + 0x36bull, 0x34eull, 0x34full, + 0x31aull, 0x31bull, 0x33aull, 0x33bull, 0x35aull, 0x35bull, 0x37aull, + 0x37bull, 0x35eull, 0x35full, + 0x380ull, 0x381ull, 0x382ull, 0x383ull, 0x384ull, 0x385ull, 0x386ull, + 0x387ull, 0x388ull, 0x389ull, + 0x390ull, 0x391ull, 0x392ull, 0x393ull, 0x394ull, 0x395ull, 0x396ull, + 0x397ull, 0x398ull, 0x399ull, + 0x3a0ull, 0x3a1ull, 0x3a2ull, 0x3a3ull, 0x3a4ull, 0x3a5ull, 0x3a6ull, + 0x3a7ull, 0x3a8ull, 0x3a9ull, + 0x3b0ull, 0x3b1ull, 0x3b2ull, 0x3b3ull, 0x3b4ull, 0x3b5ull, 0x3b6ull, + 0x3b7ull, 0x3b8ull, 0x3b9ull, + 0x3c0ull, 0x3c1ull, 0x3c2ull, 0x3c3ull, 0x3c4ull, 0x3c5ull, 0x3c6ull, + 0x3c7ull, 0x3c8ull, 0x3c9ull, + 0x3d0ull, 0x3d1ull, 0x3d2ull, 0x3d3ull, 0x3d4ull, 0x3d5ull, 0x3d6ull, + 0x3d7ull, 0x3d8ull, 0x3d9ull, + 0x3e0ull, 0x3e1ull, 0x3e2ull, 0x3e3ull, 0x3e4ull, 0x3e5ull, 0x3e6ull, + 0x3e7ull, 0x3e8ull, 0x3e9ull, + 0x3f0ull, 0x3f1ull, 0x3f2ull, 0x3f3ull, 0x3f4ull, 0x3f5ull, 0x3f6ull, + 0x3f7ull, 0x3f8ull, 0x3f9ull, + 0x38aull, 0x38bull, 0x3aaull, 0x3abull, 0x3caull, 0x3cbull, 0x3eaull, + 0x3ebull, 0x3ceull, 0x3cfull, + 0x39aull, 0x39bull, 0x3baull, 0x3bbull, 0x3daull, 0x3dbull, 0x3faull, + 0x3fbull, 0x3deull, 0x3dfull, + 0x00cull, 0x00dull, 0x10cull, 0x10dull, 0x20cull, 0x20dull, 0x30cull, + 0x30dull, 0x02eull, 0x02full, + 0x01cull, 0x01dull, 0x11cull, 0x11dull, 0x21cull, 0x21dull, 0x31cull, + 0x31dull, 0x03eull, 0x03full, + 0x02cull, 0x02dull, 0x12cull, 0x12dull, 0x22cull, 0x22dull, 0x32cull, + 0x32dull, 0x12eull, 0x12full, + 0x03cull, 0x03dull, 0x13cull, 0x13dull, 0x23cull, 0x23dull, 0x33cull, + 0x33dull, 0x13eull, 0x13full, + 0x04cull, 0x04dull, 0x14cull, 0x14dull, 0x24cull, 0x24dull, 0x34cull, + 0x34dull, 0x22eull, 0x22full, + 0x05cull, 0x05dull, 0x15cull, 0x15dull, 0x25cull, 0x25dull, 0x35cull, + 0x35dull, 0x23eull, 0x23full, + 0x06cull, 0x06dull, 0x16cull, 0x16dull, 0x26cull, 0x26dull, 0x36cull, + 0x36dull, 0x32eull, 0x32full, + 0x07cull, 0x07dull, 0x17cull, 0x17dull, 0x27cull, 0x27dull, 0x37cull, + 0x37dull, 0x33eull, 0x33full, + 0x00eull, 0x00full, 0x10eull, 0x10full, 0x20eull, 0x20full, 0x30eull, + 0x30full, 0x06eull, 0x06full, + 0x01eull, 0x01full, 0x11eull, 0x11full, 0x21eull, 0x21full, 0x31eull, + 0x31full, 0x07eull, 0x07full, + 0x08cull, 0x08dull, 0x18cull, 0x18dull, 0x28cull, 0x28dull, 0x38cull, + 0x38dull, 0x0aeull, 0x0afull, + 0x09cull, 0x09dull, 0x19cull, 0x19dull, 0x29cull, 0x29dull, 0x39cull, + 0x39dull, 0x0beull, 0x0bfull, + 0x0acull, 0x0adull, 0x1acull, 0x1adull, 0x2acull, 0x2adull, 0x3acull, + 0x3adull, 0x1aeull, 0x1afull, + 0x0bcull, 0x0bdull, 0x1bcull, 0x1bdull, 0x2bcull, 0x2bdull, 0x3bcull, + 0x3bdull, 0x1beull, 0x1bfull, + 0x0ccull, 0x0cdull, 0x1ccull, 0x1cdull, 0x2ccull, 0x2cdull, 0x3ccull, + 0x3cdull, 0x2aeull, 0x2afull, + 0x0dcull, 0x0ddull, 0x1dcull, 0x1ddull, 0x2dcull, 0x2ddull, 0x3dcull, + 0x3ddull, 0x2beull, 0x2bfull, + 0x0ecull, 0x0edull, 0x1ecull, 0x1edull, 0x2ecull, 0x2edull, 0x3ecull, + 0x3edull, 0x3aeull, 0x3afull, + 0x0fcull, 0x0fdull, 0x1fcull, 0x1fdull, 0x2fcull, 0x2fdull, 0x3fcull, + 0x3fdull, 0x3beull, 0x3bfull, + 0x08eull, 0x08full, 0x18eull, 0x18full, 0x28eull, 0x28full, 0x38eull, + 0x38full, 0x0eeull, 0x0efull, + 0x09eull, 0x09full, 0x19eull, 0x19full, 0x29eull, 0x29full, 0x39eull, + 0x39full, 0x0feull, 0x0ffull +}; + +const UINT64 b2d2[] = + { 0x000ull << 10, 0x001ull << 10, 0x002ull << 10, 0x003ull << 10, + 0x004ull << 10, 0x005ull << 10, 0x006ull << 10, 0x007ull << 10, + 0x008ull << 10, + 0x009ull << 10, + 0x010ull << 10, 0x011ull << 10, 0x012ull << 10, 0x013ull << 10, + 0x014ull << 10, 0x015ull << 10, 0x016ull << 10, 0x017ull << 10, + 0x018ull << 10, 0x019ull << 10, + 0x020ull << 10, 0x021ull << 10, 0x022ull << 10, 0x023ull << 10, + 0x024ull << 10, 0x025ull << 10, 0x026ull << 10, 0x027ull << 10, + 0x028ull << 10, 0x029ull << 10, + 0x030ull << 10, 0x031ull << 10, 0x032ull << 10, 0x033ull << 10, + 0x034ull << 10, 0x035ull << 10, 0x036ull << 10, 0x037ull << 10, + 0x038ull << 10, 0x039ull << 10, + 0x040ull << 10, 0x041ull << 10, 0x042ull << 10, 0x043ull << 10, + 0x044ull << 10, 0x045ull << 10, 0x046ull << 10, 0x047ull << 10, + 0x048ull << 10, 0x049ull << 10, + 0x050ull << 10, 0x051ull << 10, 0x052ull << 10, 0x053ull << 10, + 0x054ull << 10, 0x055ull << 10, 0x056ull << 10, 0x057ull << 10, + 0x058ull << 10, 0x059ull << 10, + 0x060ull << 10, 0x061ull << 10, 0x062ull << 10, 0x063ull << 10, + 0x064ull << 10, 0x065ull << 10, 0x066ull << 10, 0x067ull << 10, + 0x068ull << 10, 0x069ull << 10, + 0x070ull << 10, 0x071ull << 10, 0x072ull << 10, 0x073ull << 10, + 0x074ull << 10, 0x075ull << 10, 0x076ull << 10, 0x077ull << 10, + 0x078ull << 10, 0x079ull << 10, + 0x00aull << 10, 0x00bull << 10, 0x02aull << 10, 0x02bull << 10, + 0x04aull << 10, 0x04bull << 10, 0x06aull << 10, 0x06bull << 10, + 0x04eull << 10, 0x04full << 10, + 0x01aull << 10, 0x01bull << 10, 0x03aull << 10, 0x03bull << 10, + 0x05aull << 10, 0x05bull << 10, 0x07aull << 10, 0x07bull << 10, + 0x05eull << 10, 0x05full << 10, + 0x080ull << 10, 0x081ull << 10, 0x082ull << 10, 0x083ull << 10, + 0x084ull << 10, 0x085ull << 10, 0x086ull << 10, 0x087ull << 10, + 0x088ull << 10, 0x089ull << 10, + 0x090ull << 10, 0x091ull << 10, 0x092ull << 10, 0x093ull << 10, + 0x094ull << 10, 0x095ull << 10, 0x096ull << 10, 0x097ull << 10, + 0x098ull << 10, 0x099ull << 10, + 0x0a0ull << 10, 0x0a1ull << 10, 0x0a2ull << 10, 0x0a3ull << 10, + 0x0a4ull << 10, 0x0a5ull << 10, 0x0a6ull << 10, 0x0a7ull << 10, + 0x0a8ull << 10, 0x0a9ull << 10, + 0x0b0ull << 10, 0x0b1ull << 10, 0x0b2ull << 10, 0x0b3ull << 10, + 0x0b4ull << 10, 0x0b5ull << 10, 0x0b6ull << 10, 0x0b7ull << 10, + 0x0b8ull << 10, 0x0b9ull << 10, + 0x0c0ull << 10, 0x0c1ull << 10, 0x0c2ull << 10, 0x0c3ull << 10, + 0x0c4ull << 10, 0x0c5ull << 10, 0x0c6ull << 10, 0x0c7ull << 10, + 0x0c8ull << 10, 0x0c9ull << 10, + 0x0d0ull << 10, 0x0d1ull << 10, 0x0d2ull << 10, 0x0d3ull << 10, + 0x0d4ull << 10, 0x0d5ull << 10, 0x0d6ull << 10, 0x0d7ull << 10, + 0x0d8ull << 10, 0x0d9ull << 10, + 0x0e0ull << 10, 0x0e1ull << 10, 0x0e2ull << 10, 0x0e3ull << 10, + 0x0e4ull << 10, 0x0e5ull << 10, 0x0e6ull << 10, 0x0e7ull << 10, + 0x0e8ull << 10, 0x0e9ull << 10, + 0x0f0ull << 10, 0x0f1ull << 10, 0x0f2ull << 10, 0x0f3ull << 10, + 0x0f4ull << 10, 0x0f5ull << 10, 0x0f6ull << 10, 0x0f7ull << 10, + 0x0f8ull << 10, 0x0f9ull << 10, + 0x08aull << 10, 0x08bull << 10, 0x0aaull << 10, 0x0abull << 10, + 0x0caull << 10, 0x0cbull << 10, 0x0eaull << 10, 0x0ebull << 10, + 0x0ceull << 10, 0x0cfull << 10, + 0x09aull << 10, 0x09bull << 10, 0x0baull << 10, 0x0bbull << 10, + 0x0daull << 10, 0x0dbull << 10, 0x0faull << 10, 0x0fbull << 10, + 0x0deull << 10, 0x0dfull << 10, + 0x100ull << 10, 0x101ull << 10, 0x102ull << 10, 0x103ull << 10, + 0x104ull << 10, 0x105ull << 10, 0x106ull << 10, 0x107ull << 10, + 0x108ull << 10, 0x109ull << 10, + 0x110ull << 10, 0x111ull << 10, 0x112ull << 10, 0x113ull << 10, + 0x114ull << 10, 0x115ull << 10, 0x116ull << 10, 0x117ull << 10, + 0x118ull << 10, 0x119ull << 10, + 0x120ull << 10, 0x121ull << 10, 0x122ull << 10, 0x123ull << 10, + 0x124ull << 10, 0x125ull << 10, 0x126ull << 10, 0x127ull << 10, + 0x128ull << 10, 0x129ull << 10, + 0x130ull << 10, 0x131ull << 10, 0x132ull << 10, 0x133ull << 10, + 0x134ull << 10, 0x135ull << 10, 0x136ull << 10, 0x137ull << 10, + 0x138ull << 10, 0x139ull << 10, + 0x140ull << 10, 0x141ull << 10, 0x142ull << 10, 0x143ull << 10, + 0x144ull << 10, 0x145ull << 10, 0x146ull << 10, 0x147ull << 10, + 0x148ull << 10, 0x149ull << 10, + 0x150ull << 10, 0x151ull << 10, 0x152ull << 10, 0x153ull << 10, + 0x154ull << 10, 0x155ull << 10, 0x156ull << 10, 0x157ull << 10, + 0x158ull << 10, 0x159ull << 10, + 0x160ull << 10, 0x161ull << 10, 0x162ull << 10, 0x163ull << 10, + 0x164ull << 10, 0x165ull << 10, 0x166ull << 10, 0x167ull << 10, + 0x168ull << 10, 0x169ull << 10, + 0x170ull << 10, 0x171ull << 10, 0x172ull << 10, 0x173ull << 10, + 0x174ull << 10, 0x175ull << 10, 0x176ull << 10, 0x177ull << 10, + 0x178ull << 10, 0x179ull << 10, + 0x10aull << 10, 0x10bull << 10, 0x12aull << 10, 0x12bull << 10, + 0x14aull << 10, 0x14bull << 10, 0x16aull << 10, 0x16bull << 10, + 0x14eull << 10, 0x14full << 10, + 0x11aull << 10, 0x11bull << 10, 0x13aull << 10, 0x13bull << 10, + 0x15aull << 10, 0x15bull << 10, 0x17aull << 10, 0x17bull << 10, + 0x15eull << 10, 0x15full << 10, + 0x180ull << 10, 0x181ull << 10, 0x182ull << 10, 0x183ull << 10, + 0x184ull << 10, 0x185ull << 10, 0x186ull << 10, 0x187ull << 10, + 0x188ull << 10, 0x189ull << 10, + 0x190ull << 10, 0x191ull << 10, 0x192ull << 10, 0x193ull << 10, + 0x194ull << 10, 0x195ull << 10, 0x196ull << 10, 0x197ull << 10, + 0x198ull << 10, 0x199ull << 10, + 0x1a0ull << 10, 0x1a1ull << 10, 0x1a2ull << 10, 0x1a3ull << 10, + 0x1a4ull << 10, 0x1a5ull << 10, 0x1a6ull << 10, 0x1a7ull << 10, + 0x1a8ull << 10, 0x1a9ull << 10, + 0x1b0ull << 10, 0x1b1ull << 10, 0x1b2ull << 10, 0x1b3ull << 10, + 0x1b4ull << 10, 0x1b5ull << 10, 0x1b6ull << 10, 0x1b7ull << 10, + 0x1b8ull << 10, 0x1b9ull << 10, + 0x1c0ull << 10, 0x1c1ull << 10, 0x1c2ull << 10, 0x1c3ull << 10, + 0x1c4ull << 10, 0x1c5ull << 10, 0x1c6ull << 10, 0x1c7ull << 10, + 0x1c8ull << 10, 0x1c9ull << 10, + 0x1d0ull << 10, 0x1d1ull << 10, 0x1d2ull << 10, 0x1d3ull << 10, + 0x1d4ull << 10, 0x1d5ull << 10, 0x1d6ull << 10, 0x1d7ull << 10, + 0x1d8ull << 10, 0x1d9ull << 10, + 0x1e0ull << 10, 0x1e1ull << 10, 0x1e2ull << 10, 0x1e3ull << 10, + 0x1e4ull << 10, 0x1e5ull << 10, 0x1e6ull << 10, 0x1e7ull << 10, + 0x1e8ull << 10, 0x1e9ull << 10, + 0x1f0ull << 10, 0x1f1ull << 10, 0x1f2ull << 10, 0x1f3ull << 10, + 0x1f4ull << 10, 0x1f5ull << 10, 0x1f6ull << 10, 0x1f7ull << 10, + 0x1f8ull << 10, 0x1f9ull << 10, + 0x18aull << 10, 0x18bull << 10, 0x1aaull << 10, 0x1abull << 10, + 0x1caull << 10, 0x1cbull << 10, 0x1eaull << 10, 0x1ebull << 10, + 0x1ceull << 10, 0x1cfull << 10, + 0x19aull << 10, 0x19bull << 10, 0x1baull << 10, 0x1bbull << 10, + 0x1daull << 10, 0x1dbull << 10, 0x1faull << 10, 0x1fbull << 10, + 0x1deull << 10, 0x1dfull << 10, + 0x200ull << 10, 0x201ull << 10, 0x202ull << 10, 0x203ull << 10, + 0x204ull << 10, 0x205ull << 10, 0x206ull << 10, 0x207ull << 10, + 0x208ull << 10, 0x209ull << 10, + 0x210ull << 10, 0x211ull << 10, 0x212ull << 10, 0x213ull << 10, + 0x214ull << 10, 0x215ull << 10, 0x216ull << 10, 0x217ull << 10, + 0x218ull << 10, 0x219ull << 10, + 0x220ull << 10, 0x221ull << 10, 0x222ull << 10, 0x223ull << 10, + 0x224ull << 10, 0x225ull << 10, 0x226ull << 10, 0x227ull << 10, + 0x228ull << 10, 0x229ull << 10, + 0x230ull << 10, 0x231ull << 10, 0x232ull << 10, 0x233ull << 10, + 0x234ull << 10, 0x235ull << 10, 0x236ull << 10, 0x237ull << 10, + 0x238ull << 10, 0x239ull << 10, + 0x240ull << 10, 0x241ull << 10, 0x242ull << 10, 0x243ull << 10, + 0x244ull << 10, 0x245ull << 10, 0x246ull << 10, 0x247ull << 10, + 0x248ull << 10, 0x249ull << 10, + 0x250ull << 10, 0x251ull << 10, 0x252ull << 10, 0x253ull << 10, + 0x254ull << 10, 0x255ull << 10, 0x256ull << 10, 0x257ull << 10, + 0x258ull << 10, 0x259ull << 10, + 0x260ull << 10, 0x261ull << 10, 0x262ull << 10, 0x263ull << 10, + 0x264ull << 10, 0x265ull << 10, 0x266ull << 10, 0x267ull << 10, + 0x268ull << 10, 0x269ull << 10, + 0x270ull << 10, 0x271ull << 10, 0x272ull << 10, 0x273ull << 10, + 0x274ull << 10, 0x275ull << 10, 0x276ull << 10, 0x277ull << 10, + 0x278ull << 10, 0x279ull << 10, + 0x20aull << 10, 0x20bull << 10, 0x22aull << 10, 0x22bull << 10, + 0x24aull << 10, 0x24bull << 10, 0x26aull << 10, 0x26bull << 10, + 0x24eull << 10, 0x24full << 10, + 0x21aull << 10, 0x21bull << 10, 0x23aull << 10, 0x23bull << 10, + 0x25aull << 10, 0x25bull << 10, 0x27aull << 10, 0x27bull << 10, + 0x25eull << 10, 0x25full << 10, + 0x280ull << 10, 0x281ull << 10, 0x282ull << 10, 0x283ull << 10, + 0x284ull << 10, 0x285ull << 10, 0x286ull << 10, 0x287ull << 10, + 0x288ull << 10, 0x289ull << 10, + 0x290ull << 10, 0x291ull << 10, 0x292ull << 10, 0x293ull << 10, + 0x294ull << 10, 0x295ull << 10, 0x296ull << 10, 0x297ull << 10, + 0x298ull << 10, 0x299ull << 10, + 0x2a0ull << 10, 0x2a1ull << 10, 0x2a2ull << 10, 0x2a3ull << 10, + 0x2a4ull << 10, 0x2a5ull << 10, 0x2a6ull << 10, 0x2a7ull << 10, + 0x2a8ull << 10, 0x2a9ull << 10, + 0x2b0ull << 10, 0x2b1ull << 10, 0x2b2ull << 10, 0x2b3ull << 10, + 0x2b4ull << 10, 0x2b5ull << 10, 0x2b6ull << 10, 0x2b7ull << 10, + 0x2b8ull << 10, 0x2b9ull << 10, + 0x2c0ull << 10, 0x2c1ull << 10, 0x2c2ull << 10, 0x2c3ull << 10, + 0x2c4ull << 10, 0x2c5ull << 10, 0x2c6ull << 10, 0x2c7ull << 10, + 0x2c8ull << 10, 0x2c9ull << 10, + 0x2d0ull << 10, 0x2d1ull << 10, 0x2d2ull << 10, 0x2d3ull << 10, + 0x2d4ull << 10, 0x2d5ull << 10, 0x2d6ull << 10, 0x2d7ull << 10, + 0x2d8ull << 10, 0x2d9ull << 10, + 0x2e0ull << 10, 0x2e1ull << 10, 0x2e2ull << 10, 0x2e3ull << 10, + 0x2e4ull << 10, 0x2e5ull << 10, 0x2e6ull << 10, 0x2e7ull << 10, + 0x2e8ull << 10, 0x2e9ull << 10, + 0x2f0ull << 10, 0x2f1ull << 10, 0x2f2ull << 10, 0x2f3ull << 10, + 0x2f4ull << 10, 0x2f5ull << 10, 0x2f6ull << 10, 0x2f7ull << 10, + 0x2f8ull << 10, 0x2f9ull << 10, + 0x28aull << 10, 0x28bull << 10, 0x2aaull << 10, 0x2abull << 10, + 0x2caull << 10, 0x2cbull << 10, 0x2eaull << 10, 0x2ebull << 10, + 0x2ceull << 10, 0x2cfull << 10, + 0x29aull << 10, 0x29bull << 10, 0x2baull << 10, 0x2bbull << 10, + 0x2daull << 10, 0x2dbull << 10, 0x2faull << 10, 0x2fbull << 10, + 0x2deull << 10, 0x2dfull << 10, + 0x300ull << 10, 0x301ull << 10, 0x302ull << 10, 0x303ull << 10, + 0x304ull << 10, 0x305ull << 10, 0x306ull << 10, 0x307ull << 10, + 0x308ull << 10, 0x309ull << 10, + 0x310ull << 10, 0x311ull << 10, 0x312ull << 10, 0x313ull << 10, + 0x314ull << 10, 0x315ull << 10, 0x316ull << 10, 0x317ull << 10, + 0x318ull << 10, 0x319ull << 10, + 0x320ull << 10, 0x321ull << 10, 0x322ull << 10, 0x323ull << 10, + 0x324ull << 10, 0x325ull << 10, 0x326ull << 10, 0x327ull << 10, + 0x328ull << 10, 0x329ull << 10, + 0x330ull << 10, 0x331ull << 10, 0x332ull << 10, 0x333ull << 10, + 0x334ull << 10, 0x335ull << 10, 0x336ull << 10, 0x337ull << 10, + 0x338ull << 10, 0x339ull << 10, + 0x340ull << 10, 0x341ull << 10, 0x342ull << 10, 0x343ull << 10, + 0x344ull << 10, 0x345ull << 10, 0x346ull << 10, 0x347ull << 10, + 0x348ull << 10, 0x349ull << 10, + 0x350ull << 10, 0x351ull << 10, 0x352ull << 10, 0x353ull << 10, + 0x354ull << 10, 0x355ull << 10, 0x356ull << 10, 0x357ull << 10, + 0x358ull << 10, 0x359ull << 10, + 0x360ull << 10, 0x361ull << 10, 0x362ull << 10, 0x363ull << 10, + 0x364ull << 10, 0x365ull << 10, 0x366ull << 10, 0x367ull << 10, + 0x368ull << 10, 0x369ull << 10, + 0x370ull << 10, 0x371ull << 10, 0x372ull << 10, 0x373ull << 10, + 0x374ull << 10, 0x375ull << 10, 0x376ull << 10, 0x377ull << 10, + 0x378ull << 10, 0x379ull << 10, + 0x30aull << 10, 0x30bull << 10, 0x32aull << 10, 0x32bull << 10, + 0x34aull << 10, 0x34bull << 10, 0x36aull << 10, 0x36bull << 10, + 0x34eull << 10, 0x34full << 10, + 0x31aull << 10, 0x31bull << 10, 0x33aull << 10, 0x33bull << 10, + 0x35aull << 10, 0x35bull << 10, 0x37aull << 10, 0x37bull << 10, + 0x35eull << 10, 0x35full << 10, + 0x380ull << 10, 0x381ull << 10, 0x382ull << 10, 0x383ull << 10, + 0x384ull << 10, 0x385ull << 10, 0x386ull << 10, 0x387ull << 10, + 0x388ull << 10, 0x389ull << 10, + 0x390ull << 10, 0x391ull << 10, 0x392ull << 10, 0x393ull << 10, + 0x394ull << 10, 0x395ull << 10, 0x396ull << 10, 0x397ull << 10, + 0x398ull << 10, 0x399ull << 10, + 0x3a0ull << 10, 0x3a1ull << 10, 0x3a2ull << 10, 0x3a3ull << 10, + 0x3a4ull << 10, 0x3a5ull << 10, 0x3a6ull << 10, 0x3a7ull << 10, + 0x3a8ull << 10, 0x3a9ull << 10, + 0x3b0ull << 10, 0x3b1ull << 10, 0x3b2ull << 10, 0x3b3ull << 10, + 0x3b4ull << 10, 0x3b5ull << 10, 0x3b6ull << 10, 0x3b7ull << 10, + 0x3b8ull << 10, 0x3b9ull << 10, + 0x3c0ull << 10, 0x3c1ull << 10, 0x3c2ull << 10, 0x3c3ull << 10, + 0x3c4ull << 10, 0x3c5ull << 10, 0x3c6ull << 10, 0x3c7ull << 10, + 0x3c8ull << 10, 0x3c9ull << 10, + 0x3d0ull << 10, 0x3d1ull << 10, 0x3d2ull << 10, 0x3d3ull << 10, + 0x3d4ull << 10, 0x3d5ull << 10, 0x3d6ull << 10, 0x3d7ull << 10, + 0x3d8ull << 10, 0x3d9ull << 10, + 0x3e0ull << 10, 0x3e1ull << 10, 0x3e2ull << 10, 0x3e3ull << 10, + 0x3e4ull << 10, 0x3e5ull << 10, 0x3e6ull << 10, 0x3e7ull << 10, + 0x3e8ull << 10, 0x3e9ull << 10, + 0x3f0ull << 10, 0x3f1ull << 10, 0x3f2ull << 10, 0x3f3ull << 10, + 0x3f4ull << 10, 0x3f5ull << 10, 0x3f6ull << 10, 0x3f7ull << 10, + 0x3f8ull << 10, 0x3f9ull << 10, + 0x38aull << 10, 0x38bull << 10, 0x3aaull << 10, 0x3abull << 10, + 0x3caull << 10, 0x3cbull << 10, 0x3eaull << 10, 0x3ebull << 10, + 0x3ceull << 10, 0x3cfull << 10, + 0x39aull << 10, 0x39bull << 10, 0x3baull << 10, 0x3bbull << 10, + 0x3daull << 10, 0x3dbull << 10, 0x3faull << 10, 0x3fbull << 10, + 0x3deull << 10, 0x3dfull << 10, + 0x00cull << 10, 0x00dull << 10, 0x10cull << 10, 0x10dull << 10, + 0x20cull << 10, 0x20dull << 10, 0x30cull << 10, 0x30dull << 10, + 0x02eull << 10, 0x02full << 10, + 0x01cull << 10, 0x01dull << 10, 0x11cull << 10, 0x11dull << 10, + 0x21cull << 10, 0x21dull << 10, 0x31cull << 10, 0x31dull << 10, + 0x03eull << 10, 0x03full << 10, + 0x02cull << 10, 0x02dull << 10, 0x12cull << 10, 0x12dull << 10, + 0x22cull << 10, 0x22dull << 10, 0x32cull << 10, 0x32dull << 10, + 0x12eull << 10, 0x12full << 10, + 0x03cull << 10, 0x03dull << 10, 0x13cull << 10, 0x13dull << 10, + 0x23cull << 10, 0x23dull << 10, 0x33cull << 10, 0x33dull << 10, + 0x13eull << 10, 0x13full << 10, + 0x04cull << 10, 0x04dull << 10, 0x14cull << 10, 0x14dull << 10, + 0x24cull << 10, 0x24dull << 10, 0x34cull << 10, 0x34dull << 10, + 0x22eull << 10, 0x22full << 10, + 0x05cull << 10, 0x05dull << 10, 0x15cull << 10, 0x15dull << 10, + 0x25cull << 10, 0x25dull << 10, 0x35cull << 10, 0x35dull << 10, + 0x23eull << 10, 0x23full << 10, + 0x06cull << 10, 0x06dull << 10, 0x16cull << 10, 0x16dull << 10, + 0x26cull << 10, 0x26dull << 10, 0x36cull << 10, 0x36dull << 10, + 0x32eull << 10, 0x32full << 10, + 0x07cull << 10, 0x07dull << 10, 0x17cull << 10, 0x17dull << 10, + 0x27cull << 10, 0x27dull << 10, 0x37cull << 10, 0x37dull << 10, + 0x33eull << 10, 0x33full << 10, + 0x00eull << 10, 0x00full << 10, 0x10eull << 10, 0x10full << 10, + 0x20eull << 10, 0x20full << 10, 0x30eull << 10, 0x30full << 10, + 0x06eull << 10, 0x06full << 10, + 0x01eull << 10, 0x01full << 10, 0x11eull << 10, 0x11full << 10, + 0x21eull << 10, 0x21full << 10, 0x31eull << 10, 0x31full << 10, + 0x07eull << 10, 0x07full << 10, + 0x08cull << 10, 0x08dull << 10, 0x18cull << 10, 0x18dull << 10, + 0x28cull << 10, 0x28dull << 10, 0x38cull << 10, 0x38dull << 10, + 0x0aeull << 10, 0x0afull << 10, + 0x09cull << 10, 0x09dull << 10, 0x19cull << 10, 0x19dull << 10, + 0x29cull << 10, 0x29dull << 10, 0x39cull << 10, 0x39dull << 10, + 0x0beull << 10, 0x0bfull << 10, + 0x0acull << 10, 0x0adull << 10, 0x1acull << 10, 0x1adull << 10, + 0x2acull << 10, 0x2adull << 10, 0x3acull << 10, 0x3adull << 10, + 0x1aeull << 10, 0x1afull << 10, + 0x0bcull << 10, 0x0bdull << 10, 0x1bcull << 10, 0x1bdull << 10, + 0x2bcull << 10, 0x2bdull << 10, 0x3bcull << 10, 0x3bdull << 10, + 0x1beull << 10, 0x1bfull << 10, + 0x0ccull << 10, 0x0cdull << 10, 0x1ccull << 10, 0x1cdull << 10, + 0x2ccull << 10, 0x2cdull << 10, 0x3ccull << 10, 0x3cdull << 10, + 0x2aeull << 10, 0x2afull << 10, + 0x0dcull << 10, 0x0ddull << 10, 0x1dcull << 10, 0x1ddull << 10, + 0x2dcull << 10, 0x2ddull << 10, 0x3dcull << 10, 0x3ddull << 10, + 0x2beull << 10, 0x2bfull << 10, + 0x0ecull << 10, 0x0edull << 10, 0x1ecull << 10, 0x1edull << 10, + 0x2ecull << 10, 0x2edull << 10, 0x3ecull << 10, 0x3edull << 10, + 0x3aeull << 10, 0x3afull << 10, + 0x0fcull << 10, 0x0fdull << 10, 0x1fcull << 10, 0x1fdull << 10, + 0x2fcull << 10, 0x2fdull << 10, 0x3fcull << 10, 0x3fdull << 10, + 0x3beull << 10, 0x3bfull << 10, + 0x08eull << 10, 0x08full << 10, 0x18eull << 10, 0x18full << 10, + 0x28eull << 10, 0x28full << 10, 0x38eull << 10, 0x38full << 10, + 0x0eeull << 10, 0x0efull << 10, + 0x09eull << 10, 0x09full << 10, 0x19eull << 10, 0x19full << 10, + 0x29eull << 10, 0x29full << 10, 0x39eull << 10, 0x39full << 10, + 0x0feull << 10, 0x0ffull << 10 +}; + +const UINT64 b2d3[] = + { 0x000ull << 20, 0x001ull << 20, 0x002ull << 20, 0x003ull << 20, + 0x004ull << 20, 0x005ull << 20, 0x006ull << 20, 0x007ull << 20, + 0x008ull << 20, + 0x009ull << 20, + 0x010ull << 20, 0x011ull << 20, 0x012ull << 20, 0x013ull << 20, + 0x014ull << 20, 0x015ull << 20, 0x016ull << 20, 0x017ull << 20, + 0x018ull << 20, 0x019ull << 20, + 0x020ull << 20, 0x021ull << 20, 0x022ull << 20, 0x023ull << 20, + 0x024ull << 20, 0x025ull << 20, 0x026ull << 20, 0x027ull << 20, + 0x028ull << 20, 0x029ull << 20, + 0x030ull << 20, 0x031ull << 20, 0x032ull << 20, 0x033ull << 20, + 0x034ull << 20, 0x035ull << 20, 0x036ull << 20, 0x037ull << 20, + 0x038ull << 20, 0x039ull << 20, + 0x040ull << 20, 0x041ull << 20, 0x042ull << 20, 0x043ull << 20, + 0x044ull << 20, 0x045ull << 20, 0x046ull << 20, 0x047ull << 20, + 0x048ull << 20, 0x049ull << 20, + 0x050ull << 20, 0x051ull << 20, 0x052ull << 20, 0x053ull << 20, + 0x054ull << 20, 0x055ull << 20, 0x056ull << 20, 0x057ull << 20, + 0x058ull << 20, 0x059ull << 20, + 0x060ull << 20, 0x061ull << 20, 0x062ull << 20, 0x063ull << 20, + 0x064ull << 20, 0x065ull << 20, 0x066ull << 20, 0x067ull << 20, + 0x068ull << 20, 0x069ull << 20, + 0x070ull << 20, 0x071ull << 20, 0x072ull << 20, 0x073ull << 20, + 0x074ull << 20, 0x075ull << 20, 0x076ull << 20, 0x077ull << 20, + 0x078ull << 20, 0x079ull << 20, + 0x00aull << 20, 0x00bull << 20, 0x02aull << 20, 0x02bull << 20, + 0x04aull << 20, 0x04bull << 20, 0x06aull << 20, 0x06bull << 20, + 0x04eull << 20, 0x04full << 20, + 0x01aull << 20, 0x01bull << 20, 0x03aull << 20, 0x03bull << 20, + 0x05aull << 20, 0x05bull << 20, 0x07aull << 20, 0x07bull << 20, + 0x05eull << 20, 0x05full << 20, + 0x080ull << 20, 0x081ull << 20, 0x082ull << 20, 0x083ull << 20, + 0x084ull << 20, 0x085ull << 20, 0x086ull << 20, 0x087ull << 20, + 0x088ull << 20, 0x089ull << 20, + 0x090ull << 20, 0x091ull << 20, 0x092ull << 20, 0x093ull << 20, + 0x094ull << 20, 0x095ull << 20, 0x096ull << 20, 0x097ull << 20, + 0x098ull << 20, 0x099ull << 20, + 0x0a0ull << 20, 0x0a1ull << 20, 0x0a2ull << 20, 0x0a3ull << 20, + 0x0a4ull << 20, 0x0a5ull << 20, 0x0a6ull << 20, 0x0a7ull << 20, + 0x0a8ull << 20, 0x0a9ull << 20, + 0x0b0ull << 20, 0x0b1ull << 20, 0x0b2ull << 20, 0x0b3ull << 20, + 0x0b4ull << 20, 0x0b5ull << 20, 0x0b6ull << 20, 0x0b7ull << 20, + 0x0b8ull << 20, 0x0b9ull << 20, + 0x0c0ull << 20, 0x0c1ull << 20, 0x0c2ull << 20, 0x0c3ull << 20, + 0x0c4ull << 20, 0x0c5ull << 20, 0x0c6ull << 20, 0x0c7ull << 20, + 0x0c8ull << 20, 0x0c9ull << 20, + 0x0d0ull << 20, 0x0d1ull << 20, 0x0d2ull << 20, 0x0d3ull << 20, + 0x0d4ull << 20, 0x0d5ull << 20, 0x0d6ull << 20, 0x0d7ull << 20, + 0x0d8ull << 20, 0x0d9ull << 20, + 0x0e0ull << 20, 0x0e1ull << 20, 0x0e2ull << 20, 0x0e3ull << 20, + 0x0e4ull << 20, 0x0e5ull << 20, 0x0e6ull << 20, 0x0e7ull << 20, + 0x0e8ull << 20, 0x0e9ull << 20, + 0x0f0ull << 20, 0x0f1ull << 20, 0x0f2ull << 20, 0x0f3ull << 20, + 0x0f4ull << 20, 0x0f5ull << 20, 0x0f6ull << 20, 0x0f7ull << 20, + 0x0f8ull << 20, 0x0f9ull << 20, + 0x08aull << 20, 0x08bull << 20, 0x0aaull << 20, 0x0abull << 20, + 0x0caull << 20, 0x0cbull << 20, 0x0eaull << 20, 0x0ebull << 20, + 0x0ceull << 20, 0x0cfull << 20, + 0x09aull << 20, 0x09bull << 20, 0x0baull << 20, 0x0bbull << 20, + 0x0daull << 20, 0x0dbull << 20, 0x0faull << 20, 0x0fbull << 20, + 0x0deull << 20, 0x0dfull << 20, + 0x100ull << 20, 0x101ull << 20, 0x102ull << 20, 0x103ull << 20, + 0x104ull << 20, 0x105ull << 20, 0x106ull << 20, 0x107ull << 20, + 0x108ull << 20, 0x109ull << 20, + 0x110ull << 20, 0x111ull << 20, 0x112ull << 20, 0x113ull << 20, + 0x114ull << 20, 0x115ull << 20, 0x116ull << 20, 0x117ull << 20, + 0x118ull << 20, 0x119ull << 20, + 0x120ull << 20, 0x121ull << 20, 0x122ull << 20, 0x123ull << 20, + 0x124ull << 20, 0x125ull << 20, 0x126ull << 20, 0x127ull << 20, + 0x128ull << 20, 0x129ull << 20, + 0x130ull << 20, 0x131ull << 20, 0x132ull << 20, 0x133ull << 20, + 0x134ull << 20, 0x135ull << 20, 0x136ull << 20, 0x137ull << 20, + 0x138ull << 20, 0x139ull << 20, + 0x140ull << 20, 0x141ull << 20, 0x142ull << 20, 0x143ull << 20, + 0x144ull << 20, 0x145ull << 20, 0x146ull << 20, 0x147ull << 20, + 0x148ull << 20, 0x149ull << 20, + 0x150ull << 20, 0x151ull << 20, 0x152ull << 20, 0x153ull << 20, + 0x154ull << 20, 0x155ull << 20, 0x156ull << 20, 0x157ull << 20, + 0x158ull << 20, 0x159ull << 20, + 0x160ull << 20, 0x161ull << 20, 0x162ull << 20, 0x163ull << 20, + 0x164ull << 20, 0x165ull << 20, 0x166ull << 20, 0x167ull << 20, + 0x168ull << 20, 0x169ull << 20, + 0x170ull << 20, 0x171ull << 20, 0x172ull << 20, 0x173ull << 20, + 0x174ull << 20, 0x175ull << 20, 0x176ull << 20, 0x177ull << 20, + 0x178ull << 20, 0x179ull << 20, + 0x10aull << 20, 0x10bull << 20, 0x12aull << 20, 0x12bull << 20, + 0x14aull << 20, 0x14bull << 20, 0x16aull << 20, 0x16bull << 20, + 0x14eull << 20, 0x14full << 20, + 0x11aull << 20, 0x11bull << 20, 0x13aull << 20, 0x13bull << 20, + 0x15aull << 20, 0x15bull << 20, 0x17aull << 20, 0x17bull << 20, + 0x15eull << 20, 0x15full << 20, + 0x180ull << 20, 0x181ull << 20, 0x182ull << 20, 0x183ull << 20, + 0x184ull << 20, 0x185ull << 20, 0x186ull << 20, 0x187ull << 20, + 0x188ull << 20, 0x189ull << 20, + 0x190ull << 20, 0x191ull << 20, 0x192ull << 20, 0x193ull << 20, + 0x194ull << 20, 0x195ull << 20, 0x196ull << 20, 0x197ull << 20, + 0x198ull << 20, 0x199ull << 20, + 0x1a0ull << 20, 0x1a1ull << 20, 0x1a2ull << 20, 0x1a3ull << 20, + 0x1a4ull << 20, 0x1a5ull << 20, 0x1a6ull << 20, 0x1a7ull << 20, + 0x1a8ull << 20, 0x1a9ull << 20, + 0x1b0ull << 20, 0x1b1ull << 20, 0x1b2ull << 20, 0x1b3ull << 20, + 0x1b4ull << 20, 0x1b5ull << 20, 0x1b6ull << 20, 0x1b7ull << 20, + 0x1b8ull << 20, 0x1b9ull << 20, + 0x1c0ull << 20, 0x1c1ull << 20, 0x1c2ull << 20, 0x1c3ull << 20, + 0x1c4ull << 20, 0x1c5ull << 20, 0x1c6ull << 20, 0x1c7ull << 20, + 0x1c8ull << 20, 0x1c9ull << 20, + 0x1d0ull << 20, 0x1d1ull << 20, 0x1d2ull << 20, 0x1d3ull << 20, + 0x1d4ull << 20, 0x1d5ull << 20, 0x1d6ull << 20, 0x1d7ull << 20, + 0x1d8ull << 20, 0x1d9ull << 20, + 0x1e0ull << 20, 0x1e1ull << 20, 0x1e2ull << 20, 0x1e3ull << 20, + 0x1e4ull << 20, 0x1e5ull << 20, 0x1e6ull << 20, 0x1e7ull << 20, + 0x1e8ull << 20, 0x1e9ull << 20, + 0x1f0ull << 20, 0x1f1ull << 20, 0x1f2ull << 20, 0x1f3ull << 20, + 0x1f4ull << 20, 0x1f5ull << 20, 0x1f6ull << 20, 0x1f7ull << 20, + 0x1f8ull << 20, 0x1f9ull << 20, + 0x18aull << 20, 0x18bull << 20, 0x1aaull << 20, 0x1abull << 20, + 0x1caull << 20, 0x1cbull << 20, 0x1eaull << 20, 0x1ebull << 20, + 0x1ceull << 20, 0x1cfull << 20, + 0x19aull << 20, 0x19bull << 20, 0x1baull << 20, 0x1bbull << 20, + 0x1daull << 20, 0x1dbull << 20, 0x1faull << 20, 0x1fbull << 20, + 0x1deull << 20, 0x1dfull << 20, + 0x200ull << 20, 0x201ull << 20, 0x202ull << 20, 0x203ull << 20, + 0x204ull << 20, 0x205ull << 20, 0x206ull << 20, 0x207ull << 20, + 0x208ull << 20, 0x209ull << 20, + 0x210ull << 20, 0x211ull << 20, 0x212ull << 20, 0x213ull << 20, + 0x214ull << 20, 0x215ull << 20, 0x216ull << 20, 0x217ull << 20, + 0x218ull << 20, 0x219ull << 20, + 0x220ull << 20, 0x221ull << 20, 0x222ull << 20, 0x223ull << 20, + 0x224ull << 20, 0x225ull << 20, 0x226ull << 20, 0x227ull << 20, + 0x228ull << 20, 0x229ull << 20, + 0x230ull << 20, 0x231ull << 20, 0x232ull << 20, 0x233ull << 20, + 0x234ull << 20, 0x235ull << 20, 0x236ull << 20, 0x237ull << 20, + 0x238ull << 20, 0x239ull << 20, + 0x240ull << 20, 0x241ull << 20, 0x242ull << 20, 0x243ull << 20, + 0x244ull << 20, 0x245ull << 20, 0x246ull << 20, 0x247ull << 20, + 0x248ull << 20, 0x249ull << 20, + 0x250ull << 20, 0x251ull << 20, 0x252ull << 20, 0x253ull << 20, + 0x254ull << 20, 0x255ull << 20, 0x256ull << 20, 0x257ull << 20, + 0x258ull << 20, 0x259ull << 20, + 0x260ull << 20, 0x261ull << 20, 0x262ull << 20, 0x263ull << 20, + 0x264ull << 20, 0x265ull << 20, 0x266ull << 20, 0x267ull << 20, + 0x268ull << 20, 0x269ull << 20, + 0x270ull << 20, 0x271ull << 20, 0x272ull << 20, 0x273ull << 20, + 0x274ull << 20, 0x275ull << 20, 0x276ull << 20, 0x277ull << 20, + 0x278ull << 20, 0x279ull << 20, + 0x20aull << 20, 0x20bull << 20, 0x22aull << 20, 0x22bull << 20, + 0x24aull << 20, 0x24bull << 20, 0x26aull << 20, 0x26bull << 20, + 0x24eull << 20, 0x24full << 20, + 0x21aull << 20, 0x21bull << 20, 0x23aull << 20, 0x23bull << 20, + 0x25aull << 20, 0x25bull << 20, 0x27aull << 20, 0x27bull << 20, + 0x25eull << 20, 0x25full << 20, + 0x280ull << 20, 0x281ull << 20, 0x282ull << 20, 0x283ull << 20, + 0x284ull << 20, 0x285ull << 20, 0x286ull << 20, 0x287ull << 20, + 0x288ull << 20, 0x289ull << 20, + 0x290ull << 20, 0x291ull << 20, 0x292ull << 20, 0x293ull << 20, + 0x294ull << 20, 0x295ull << 20, 0x296ull << 20, 0x297ull << 20, + 0x298ull << 20, 0x299ull << 20, + 0x2a0ull << 20, 0x2a1ull << 20, 0x2a2ull << 20, 0x2a3ull << 20, + 0x2a4ull << 20, 0x2a5ull << 20, 0x2a6ull << 20, 0x2a7ull << 20, + 0x2a8ull << 20, 0x2a9ull << 20, + 0x2b0ull << 20, 0x2b1ull << 20, 0x2b2ull << 20, 0x2b3ull << 20, + 0x2b4ull << 20, 0x2b5ull << 20, 0x2b6ull << 20, 0x2b7ull << 20, + 0x2b8ull << 20, 0x2b9ull << 20, + 0x2c0ull << 20, 0x2c1ull << 20, 0x2c2ull << 20, 0x2c3ull << 20, + 0x2c4ull << 20, 0x2c5ull << 20, 0x2c6ull << 20, 0x2c7ull << 20, + 0x2c8ull << 20, 0x2c9ull << 20, + 0x2d0ull << 20, 0x2d1ull << 20, 0x2d2ull << 20, 0x2d3ull << 20, + 0x2d4ull << 20, 0x2d5ull << 20, 0x2d6ull << 20, 0x2d7ull << 20, + 0x2d8ull << 20, 0x2d9ull << 20, + 0x2e0ull << 20, 0x2e1ull << 20, 0x2e2ull << 20, 0x2e3ull << 20, + 0x2e4ull << 20, 0x2e5ull << 20, 0x2e6ull << 20, 0x2e7ull << 20, + 0x2e8ull << 20, 0x2e9ull << 20, + 0x2f0ull << 20, 0x2f1ull << 20, 0x2f2ull << 20, 0x2f3ull << 20, + 0x2f4ull << 20, 0x2f5ull << 20, 0x2f6ull << 20, 0x2f7ull << 20, + 0x2f8ull << 20, 0x2f9ull << 20, + 0x28aull << 20, 0x28bull << 20, 0x2aaull << 20, 0x2abull << 20, + 0x2caull << 20, 0x2cbull << 20, 0x2eaull << 20, 0x2ebull << 20, + 0x2ceull << 20, 0x2cfull << 20, + 0x29aull << 20, 0x29bull << 20, 0x2baull << 20, 0x2bbull << 20, + 0x2daull << 20, 0x2dbull << 20, 0x2faull << 20, 0x2fbull << 20, + 0x2deull << 20, 0x2dfull << 20, + 0x300ull << 20, 0x301ull << 20, 0x302ull << 20, 0x303ull << 20, + 0x304ull << 20, 0x305ull << 20, 0x306ull << 20, 0x307ull << 20, + 0x308ull << 20, 0x309ull << 20, + 0x310ull << 20, 0x311ull << 20, 0x312ull << 20, 0x313ull << 20, + 0x314ull << 20, 0x315ull << 20, 0x316ull << 20, 0x317ull << 20, + 0x318ull << 20, 0x319ull << 20, + 0x320ull << 20, 0x321ull << 20, 0x322ull << 20, 0x323ull << 20, + 0x324ull << 20, 0x325ull << 20, 0x326ull << 20, 0x327ull << 20, + 0x328ull << 20, 0x329ull << 20, + 0x330ull << 20, 0x331ull << 20, 0x332ull << 20, 0x333ull << 20, + 0x334ull << 20, 0x335ull << 20, 0x336ull << 20, 0x337ull << 20, + 0x338ull << 20, 0x339ull << 20, + 0x340ull << 20, 0x341ull << 20, 0x342ull << 20, 0x343ull << 20, + 0x344ull << 20, 0x345ull << 20, 0x346ull << 20, 0x347ull << 20, + 0x348ull << 20, 0x349ull << 20, + 0x350ull << 20, 0x351ull << 20, 0x352ull << 20, 0x353ull << 20, + 0x354ull << 20, 0x355ull << 20, 0x356ull << 20, 0x357ull << 20, + 0x358ull << 20, 0x359ull << 20, + 0x360ull << 20, 0x361ull << 20, 0x362ull << 20, 0x363ull << 20, + 0x364ull << 20, 0x365ull << 20, 0x366ull << 20, 0x367ull << 20, + 0x368ull << 20, 0x369ull << 20, + 0x370ull << 20, 0x371ull << 20, 0x372ull << 20, 0x373ull << 20, + 0x374ull << 20, 0x375ull << 20, 0x376ull << 20, 0x377ull << 20, + 0x378ull << 20, 0x379ull << 20, + 0x30aull << 20, 0x30bull << 20, 0x32aull << 20, 0x32bull << 20, + 0x34aull << 20, 0x34bull << 20, 0x36aull << 20, 0x36bull << 20, + 0x34eull << 20, 0x34full << 20, + 0x31aull << 20, 0x31bull << 20, 0x33aull << 20, 0x33bull << 20, + 0x35aull << 20, 0x35bull << 20, 0x37aull << 20, 0x37bull << 20, + 0x35eull << 20, 0x35full << 20, + 0x380ull << 20, 0x381ull << 20, 0x382ull << 20, 0x383ull << 20, + 0x384ull << 20, 0x385ull << 20, 0x386ull << 20, 0x387ull << 20, + 0x388ull << 20, 0x389ull << 20, + 0x390ull << 20, 0x391ull << 20, 0x392ull << 20, 0x393ull << 20, + 0x394ull << 20, 0x395ull << 20, 0x396ull << 20, 0x397ull << 20, + 0x398ull << 20, 0x399ull << 20, + 0x3a0ull << 20, 0x3a1ull << 20, 0x3a2ull << 20, 0x3a3ull << 20, + 0x3a4ull << 20, 0x3a5ull << 20, 0x3a6ull << 20, 0x3a7ull << 20, + 0x3a8ull << 20, 0x3a9ull << 20, + 0x3b0ull << 20, 0x3b1ull << 20, 0x3b2ull << 20, 0x3b3ull << 20, + 0x3b4ull << 20, 0x3b5ull << 20, 0x3b6ull << 20, 0x3b7ull << 20, + 0x3b8ull << 20, 0x3b9ull << 20, + 0x3c0ull << 20, 0x3c1ull << 20, 0x3c2ull << 20, 0x3c3ull << 20, + 0x3c4ull << 20, 0x3c5ull << 20, 0x3c6ull << 20, 0x3c7ull << 20, + 0x3c8ull << 20, 0x3c9ull << 20, + 0x3d0ull << 20, 0x3d1ull << 20, 0x3d2ull << 20, 0x3d3ull << 20, + 0x3d4ull << 20, 0x3d5ull << 20, 0x3d6ull << 20, 0x3d7ull << 20, + 0x3d8ull << 20, 0x3d9ull << 20, + 0x3e0ull << 20, 0x3e1ull << 20, 0x3e2ull << 20, 0x3e3ull << 20, + 0x3e4ull << 20, 0x3e5ull << 20, 0x3e6ull << 20, 0x3e7ull << 20, + 0x3e8ull << 20, 0x3e9ull << 20, + 0x3f0ull << 20, 0x3f1ull << 20, 0x3f2ull << 20, 0x3f3ull << 20, + 0x3f4ull << 20, 0x3f5ull << 20, 0x3f6ull << 20, 0x3f7ull << 20, + 0x3f8ull << 20, 0x3f9ull << 20, + 0x38aull << 20, 0x38bull << 20, 0x3aaull << 20, 0x3abull << 20, + 0x3caull << 20, 0x3cbull << 20, 0x3eaull << 20, 0x3ebull << 20, + 0x3ceull << 20, 0x3cfull << 20, + 0x39aull << 20, 0x39bull << 20, 0x3baull << 20, 0x3bbull << 20, + 0x3daull << 20, 0x3dbull << 20, 0x3faull << 20, 0x3fbull << 20, + 0x3deull << 20, 0x3dfull << 20, + 0x00cull << 20, 0x00dull << 20, 0x10cull << 20, 0x10dull << 20, + 0x20cull << 20, 0x20dull << 20, 0x30cull << 20, 0x30dull << 20, + 0x02eull << 20, 0x02full << 20, + 0x01cull << 20, 0x01dull << 20, 0x11cull << 20, 0x11dull << 20, + 0x21cull << 20, 0x21dull << 20, 0x31cull << 20, 0x31dull << 20, + 0x03eull << 20, 0x03full << 20, + 0x02cull << 20, 0x02dull << 20, 0x12cull << 20, 0x12dull << 20, + 0x22cull << 20, 0x22dull << 20, 0x32cull << 20, 0x32dull << 20, + 0x12eull << 20, 0x12full << 20, + 0x03cull << 20, 0x03dull << 20, 0x13cull << 20, 0x13dull << 20, + 0x23cull << 20, 0x23dull << 20, 0x33cull << 20, 0x33dull << 20, + 0x13eull << 20, 0x13full << 20, + 0x04cull << 20, 0x04dull << 20, 0x14cull << 20, 0x14dull << 20, + 0x24cull << 20, 0x24dull << 20, 0x34cull << 20, 0x34dull << 20, + 0x22eull << 20, 0x22full << 20, + 0x05cull << 20, 0x05dull << 20, 0x15cull << 20, 0x15dull << 20, + 0x25cull << 20, 0x25dull << 20, 0x35cull << 20, 0x35dull << 20, + 0x23eull << 20, 0x23full << 20, + 0x06cull << 20, 0x06dull << 20, 0x16cull << 20, 0x16dull << 20, + 0x26cull << 20, 0x26dull << 20, 0x36cull << 20, 0x36dull << 20, + 0x32eull << 20, 0x32full << 20, + 0x07cull << 20, 0x07dull << 20, 0x17cull << 20, 0x17dull << 20, + 0x27cull << 20, 0x27dull << 20, 0x37cull << 20, 0x37dull << 20, + 0x33eull << 20, 0x33full << 20, + 0x00eull << 20, 0x00full << 20, 0x10eull << 20, 0x10full << 20, + 0x20eull << 20, 0x20full << 20, 0x30eull << 20, 0x30full << 20, + 0x06eull << 20, 0x06full << 20, + 0x01eull << 20, 0x01full << 20, 0x11eull << 20, 0x11full << 20, + 0x21eull << 20, 0x21full << 20, 0x31eull << 20, 0x31full << 20, + 0x07eull << 20, 0x07full << 20, + 0x08cull << 20, 0x08dull << 20, 0x18cull << 20, 0x18dull << 20, + 0x28cull << 20, 0x28dull << 20, 0x38cull << 20, 0x38dull << 20, + 0x0aeull << 20, 0x0afull << 20, + 0x09cull << 20, 0x09dull << 20, 0x19cull << 20, 0x19dull << 20, + 0x29cull << 20, 0x29dull << 20, 0x39cull << 20, 0x39dull << 20, + 0x0beull << 20, 0x0bfull << 20, + 0x0acull << 20, 0x0adull << 20, 0x1acull << 20, 0x1adull << 20, + 0x2acull << 20, 0x2adull << 20, 0x3acull << 20, 0x3adull << 20, + 0x1aeull << 20, 0x1afull << 20, + 0x0bcull << 20, 0x0bdull << 20, 0x1bcull << 20, 0x1bdull << 20, + 0x2bcull << 20, 0x2bdull << 20, 0x3bcull << 20, 0x3bdull << 20, + 0x1beull << 20, 0x1bfull << 20, + 0x0ccull << 20, 0x0cdull << 20, 0x1ccull << 20, 0x1cdull << 20, + 0x2ccull << 20, 0x2cdull << 20, 0x3ccull << 20, 0x3cdull << 20, + 0x2aeull << 20, 0x2afull << 20, + 0x0dcull << 20, 0x0ddull << 20, 0x1dcull << 20, 0x1ddull << 20, + 0x2dcull << 20, 0x2ddull << 20, 0x3dcull << 20, 0x3ddull << 20, + 0x2beull << 20, 0x2bfull << 20, + 0x0ecull << 20, 0x0edull << 20, 0x1ecull << 20, 0x1edull << 20, + 0x2ecull << 20, 0x2edull << 20, 0x3ecull << 20, 0x3edull << 20, + 0x3aeull << 20, 0x3afull << 20, + 0x0fcull << 20, 0x0fdull << 20, 0x1fcull << 20, 0x1fdull << 20, + 0x2fcull << 20, 0x2fdull << 20, 0x3fcull << 20, 0x3fdull << 20, + 0x3beull << 20, 0x3bfull << 20, + 0x08eull << 20, 0x08full << 20, 0x18eull << 20, 0x18full << 20, + 0x28eull << 20, 0x28full << 20, 0x38eull << 20, 0x38full << 20, + 0x0eeull << 20, 0x0efull << 20, + 0x09eull << 20, 0x09full << 20, 0x19eull << 20, 0x19full << 20, + 0x29eull << 20, 0x29full << 20, 0x39eull << 20, 0x39full << 20, + 0x0feull << 20, 0x0ffull << 20 +}; + +const UINT64 b2d4[] = + { 0x000ull << 30, 0x001ull << 30, 0x002ull << 30, 0x003ull << 30, + 0x004ull << 30, 0x005ull << 30, 0x006ull << 30, 0x007ull << 30, + 0x008ull << 30, + 0x009ull << 30, + 0x010ull << 30, 0x011ull << 30, 0x012ull << 30, 0x013ull << 30, + 0x014ull << 30, 0x015ull << 30, 0x016ull << 30, 0x017ull << 30, + 0x018ull << 30, 0x019ull << 30, + 0x020ull << 30, 0x021ull << 30, 0x022ull << 30, 0x023ull << 30, + 0x024ull << 30, 0x025ull << 30, 0x026ull << 30, 0x027ull << 30, + 0x028ull << 30, 0x029ull << 30, + 0x030ull << 30, 0x031ull << 30, 0x032ull << 30, 0x033ull << 30, + 0x034ull << 30, 0x035ull << 30, 0x036ull << 30, 0x037ull << 30, + 0x038ull << 30, 0x039ull << 30, + 0x040ull << 30, 0x041ull << 30, 0x042ull << 30, 0x043ull << 30, + 0x044ull << 30, 0x045ull << 30, 0x046ull << 30, 0x047ull << 30, + 0x048ull << 30, 0x049ull << 30, + 0x050ull << 30, 0x051ull << 30, 0x052ull << 30, 0x053ull << 30, + 0x054ull << 30, 0x055ull << 30, 0x056ull << 30, 0x057ull << 30, + 0x058ull << 30, 0x059ull << 30, + 0x060ull << 30, 0x061ull << 30, 0x062ull << 30, 0x063ull << 30, + 0x064ull << 30, 0x065ull << 30, 0x066ull << 30, 0x067ull << 30, + 0x068ull << 30, 0x069ull << 30, + 0x070ull << 30, 0x071ull << 30, 0x072ull << 30, 0x073ull << 30, + 0x074ull << 30, 0x075ull << 30, 0x076ull << 30, 0x077ull << 30, + 0x078ull << 30, 0x079ull << 30, + 0x00aull << 30, 0x00bull << 30, 0x02aull << 30, 0x02bull << 30, + 0x04aull << 30, 0x04bull << 30, 0x06aull << 30, 0x06bull << 30, + 0x04eull << 30, 0x04full << 30, + 0x01aull << 30, 0x01bull << 30, 0x03aull << 30, 0x03bull << 30, + 0x05aull << 30, 0x05bull << 30, 0x07aull << 30, 0x07bull << 30, + 0x05eull << 30, 0x05full << 30, + 0x080ull << 30, 0x081ull << 30, 0x082ull << 30, 0x083ull << 30, + 0x084ull << 30, 0x085ull << 30, 0x086ull << 30, 0x087ull << 30, + 0x088ull << 30, 0x089ull << 30, + 0x090ull << 30, 0x091ull << 30, 0x092ull << 30, 0x093ull << 30, + 0x094ull << 30, 0x095ull << 30, 0x096ull << 30, 0x097ull << 30, + 0x098ull << 30, 0x099ull << 30, + 0x0a0ull << 30, 0x0a1ull << 30, 0x0a2ull << 30, 0x0a3ull << 30, + 0x0a4ull << 30, 0x0a5ull << 30, 0x0a6ull << 30, 0x0a7ull << 30, + 0x0a8ull << 30, 0x0a9ull << 30, + 0x0b0ull << 30, 0x0b1ull << 30, 0x0b2ull << 30, 0x0b3ull << 30, + 0x0b4ull << 30, 0x0b5ull << 30, 0x0b6ull << 30, 0x0b7ull << 30, + 0x0b8ull << 30, 0x0b9ull << 30, + 0x0c0ull << 30, 0x0c1ull << 30, 0x0c2ull << 30, 0x0c3ull << 30, + 0x0c4ull << 30, 0x0c5ull << 30, 0x0c6ull << 30, 0x0c7ull << 30, + 0x0c8ull << 30, 0x0c9ull << 30, + 0x0d0ull << 30, 0x0d1ull << 30, 0x0d2ull << 30, 0x0d3ull << 30, + 0x0d4ull << 30, 0x0d5ull << 30, 0x0d6ull << 30, 0x0d7ull << 30, + 0x0d8ull << 30, 0x0d9ull << 30, + 0x0e0ull << 30, 0x0e1ull << 30, 0x0e2ull << 30, 0x0e3ull << 30, + 0x0e4ull << 30, 0x0e5ull << 30, 0x0e6ull << 30, 0x0e7ull << 30, + 0x0e8ull << 30, 0x0e9ull << 30, + 0x0f0ull << 30, 0x0f1ull << 30, 0x0f2ull << 30, 0x0f3ull << 30, + 0x0f4ull << 30, 0x0f5ull << 30, 0x0f6ull << 30, 0x0f7ull << 30, + 0x0f8ull << 30, 0x0f9ull << 30, + 0x08aull << 30, 0x08bull << 30, 0x0aaull << 30, 0x0abull << 30, + 0x0caull << 30, 0x0cbull << 30, 0x0eaull << 30, 0x0ebull << 30, + 0x0ceull << 30, 0x0cfull << 30, + 0x09aull << 30, 0x09bull << 30, 0x0baull << 30, 0x0bbull << 30, + 0x0daull << 30, 0x0dbull << 30, 0x0faull << 30, 0x0fbull << 30, + 0x0deull << 30, 0x0dfull << 30, + 0x100ull << 30, 0x101ull << 30, 0x102ull << 30, 0x103ull << 30, + 0x104ull << 30, 0x105ull << 30, 0x106ull << 30, 0x107ull << 30, + 0x108ull << 30, 0x109ull << 30, + 0x110ull << 30, 0x111ull << 30, 0x112ull << 30, 0x113ull << 30, + 0x114ull << 30, 0x115ull << 30, 0x116ull << 30, 0x117ull << 30, + 0x118ull << 30, 0x119ull << 30, + 0x120ull << 30, 0x121ull << 30, 0x122ull << 30, 0x123ull << 30, + 0x124ull << 30, 0x125ull << 30, 0x126ull << 30, 0x127ull << 30, + 0x128ull << 30, 0x129ull << 30, + 0x130ull << 30, 0x131ull << 30, 0x132ull << 30, 0x133ull << 30, + 0x134ull << 30, 0x135ull << 30, 0x136ull << 30, 0x137ull << 30, + 0x138ull << 30, 0x139ull << 30, + 0x140ull << 30, 0x141ull << 30, 0x142ull << 30, 0x143ull << 30, + 0x144ull << 30, 0x145ull << 30, 0x146ull << 30, 0x147ull << 30, + 0x148ull << 30, 0x149ull << 30, + 0x150ull << 30, 0x151ull << 30, 0x152ull << 30, 0x153ull << 30, + 0x154ull << 30, 0x155ull << 30, 0x156ull << 30, 0x157ull << 30, + 0x158ull << 30, 0x159ull << 30, + 0x160ull << 30, 0x161ull << 30, 0x162ull << 30, 0x163ull << 30, + 0x164ull << 30, 0x165ull << 30, 0x166ull << 30, 0x167ull << 30, + 0x168ull << 30, 0x169ull << 30, + 0x170ull << 30, 0x171ull << 30, 0x172ull << 30, 0x173ull << 30, + 0x174ull << 30, 0x175ull << 30, 0x176ull << 30, 0x177ull << 30, + 0x178ull << 30, 0x179ull << 30, + 0x10aull << 30, 0x10bull << 30, 0x12aull << 30, 0x12bull << 30, + 0x14aull << 30, 0x14bull << 30, 0x16aull << 30, 0x16bull << 30, + 0x14eull << 30, 0x14full << 30, + 0x11aull << 30, 0x11bull << 30, 0x13aull << 30, 0x13bull << 30, + 0x15aull << 30, 0x15bull << 30, 0x17aull << 30, 0x17bull << 30, + 0x15eull << 30, 0x15full << 30, + 0x180ull << 30, 0x181ull << 30, 0x182ull << 30, 0x183ull << 30, + 0x184ull << 30, 0x185ull << 30, 0x186ull << 30, 0x187ull << 30, + 0x188ull << 30, 0x189ull << 30, + 0x190ull << 30, 0x191ull << 30, 0x192ull << 30, 0x193ull << 30, + 0x194ull << 30, 0x195ull << 30, 0x196ull << 30, 0x197ull << 30, + 0x198ull << 30, 0x199ull << 30, + 0x1a0ull << 30, 0x1a1ull << 30, 0x1a2ull << 30, 0x1a3ull << 30, + 0x1a4ull << 30, 0x1a5ull << 30, 0x1a6ull << 30, 0x1a7ull << 30, + 0x1a8ull << 30, 0x1a9ull << 30, + 0x1b0ull << 30, 0x1b1ull << 30, 0x1b2ull << 30, 0x1b3ull << 30, + 0x1b4ull << 30, 0x1b5ull << 30, 0x1b6ull << 30, 0x1b7ull << 30, + 0x1b8ull << 30, 0x1b9ull << 30, + 0x1c0ull << 30, 0x1c1ull << 30, 0x1c2ull << 30, 0x1c3ull << 30, + 0x1c4ull << 30, 0x1c5ull << 30, 0x1c6ull << 30, 0x1c7ull << 30, + 0x1c8ull << 30, 0x1c9ull << 30, + 0x1d0ull << 30, 0x1d1ull << 30, 0x1d2ull << 30, 0x1d3ull << 30, + 0x1d4ull << 30, 0x1d5ull << 30, 0x1d6ull << 30, 0x1d7ull << 30, + 0x1d8ull << 30, 0x1d9ull << 30, + 0x1e0ull << 30, 0x1e1ull << 30, 0x1e2ull << 30, 0x1e3ull << 30, + 0x1e4ull << 30, 0x1e5ull << 30, 0x1e6ull << 30, 0x1e7ull << 30, + 0x1e8ull << 30, 0x1e9ull << 30, + 0x1f0ull << 30, 0x1f1ull << 30, 0x1f2ull << 30, 0x1f3ull << 30, + 0x1f4ull << 30, 0x1f5ull << 30, 0x1f6ull << 30, 0x1f7ull << 30, + 0x1f8ull << 30, 0x1f9ull << 30, + 0x18aull << 30, 0x18bull << 30, 0x1aaull << 30, 0x1abull << 30, + 0x1caull << 30, 0x1cbull << 30, 0x1eaull << 30, 0x1ebull << 30, + 0x1ceull << 30, 0x1cfull << 30, + 0x19aull << 30, 0x19bull << 30, 0x1baull << 30, 0x1bbull << 30, + 0x1daull << 30, 0x1dbull << 30, 0x1faull << 30, 0x1fbull << 30, + 0x1deull << 30, 0x1dfull << 30, + 0x200ull << 30, 0x201ull << 30, 0x202ull << 30, 0x203ull << 30, + 0x204ull << 30, 0x205ull << 30, 0x206ull << 30, 0x207ull << 30, + 0x208ull << 30, 0x209ull << 30, + 0x210ull << 30, 0x211ull << 30, 0x212ull << 30, 0x213ull << 30, + 0x214ull << 30, 0x215ull << 30, 0x216ull << 30, 0x217ull << 30, + 0x218ull << 30, 0x219ull << 30, + 0x220ull << 30, 0x221ull << 30, 0x222ull << 30, 0x223ull << 30, + 0x224ull << 30, 0x225ull << 30, 0x226ull << 30, 0x227ull << 30, + 0x228ull << 30, 0x229ull << 30, + 0x230ull << 30, 0x231ull << 30, 0x232ull << 30, 0x233ull << 30, + 0x234ull << 30, 0x235ull << 30, 0x236ull << 30, 0x237ull << 30, + 0x238ull << 30, 0x239ull << 30, + 0x240ull << 30, 0x241ull << 30, 0x242ull << 30, 0x243ull << 30, + 0x244ull << 30, 0x245ull << 30, 0x246ull << 30, 0x247ull << 30, + 0x248ull << 30, 0x249ull << 30, + 0x250ull << 30, 0x251ull << 30, 0x252ull << 30, 0x253ull << 30, + 0x254ull << 30, 0x255ull << 30, 0x256ull << 30, 0x257ull << 30, + 0x258ull << 30, 0x259ull << 30, + 0x260ull << 30, 0x261ull << 30, 0x262ull << 30, 0x263ull << 30, + 0x264ull << 30, 0x265ull << 30, 0x266ull << 30, 0x267ull << 30, + 0x268ull << 30, 0x269ull << 30, + 0x270ull << 30, 0x271ull << 30, 0x272ull << 30, 0x273ull << 30, + 0x274ull << 30, 0x275ull << 30, 0x276ull << 30, 0x277ull << 30, + 0x278ull << 30, 0x279ull << 30, + 0x20aull << 30, 0x20bull << 30, 0x22aull << 30, 0x22bull << 30, + 0x24aull << 30, 0x24bull << 30, 0x26aull << 30, 0x26bull << 30, + 0x24eull << 30, 0x24full << 30, + 0x21aull << 30, 0x21bull << 30, 0x23aull << 30, 0x23bull << 30, + 0x25aull << 30, 0x25bull << 30, 0x27aull << 30, 0x27bull << 30, + 0x25eull << 30, 0x25full << 30, + 0x280ull << 30, 0x281ull << 30, 0x282ull << 30, 0x283ull << 30, + 0x284ull << 30, 0x285ull << 30, 0x286ull << 30, 0x287ull << 30, + 0x288ull << 30, 0x289ull << 30, + 0x290ull << 30, 0x291ull << 30, 0x292ull << 30, 0x293ull << 30, + 0x294ull << 30, 0x295ull << 30, 0x296ull << 30, 0x297ull << 30, + 0x298ull << 30, 0x299ull << 30, + 0x2a0ull << 30, 0x2a1ull << 30, 0x2a2ull << 30, 0x2a3ull << 30, + 0x2a4ull << 30, 0x2a5ull << 30, 0x2a6ull << 30, 0x2a7ull << 30, + 0x2a8ull << 30, 0x2a9ull << 30, + 0x2b0ull << 30, 0x2b1ull << 30, 0x2b2ull << 30, 0x2b3ull << 30, + 0x2b4ull << 30, 0x2b5ull << 30, 0x2b6ull << 30, 0x2b7ull << 30, + 0x2b8ull << 30, 0x2b9ull << 30, + 0x2c0ull << 30, 0x2c1ull << 30, 0x2c2ull << 30, 0x2c3ull << 30, + 0x2c4ull << 30, 0x2c5ull << 30, 0x2c6ull << 30, 0x2c7ull << 30, + 0x2c8ull << 30, 0x2c9ull << 30, + 0x2d0ull << 30, 0x2d1ull << 30, 0x2d2ull << 30, 0x2d3ull << 30, + 0x2d4ull << 30, 0x2d5ull << 30, 0x2d6ull << 30, 0x2d7ull << 30, + 0x2d8ull << 30, 0x2d9ull << 30, + 0x2e0ull << 30, 0x2e1ull << 30, 0x2e2ull << 30, 0x2e3ull << 30, + 0x2e4ull << 30, 0x2e5ull << 30, 0x2e6ull << 30, 0x2e7ull << 30, + 0x2e8ull << 30, 0x2e9ull << 30, + 0x2f0ull << 30, 0x2f1ull << 30, 0x2f2ull << 30, 0x2f3ull << 30, + 0x2f4ull << 30, 0x2f5ull << 30, 0x2f6ull << 30, 0x2f7ull << 30, + 0x2f8ull << 30, 0x2f9ull << 30, + 0x28aull << 30, 0x28bull << 30, 0x2aaull << 30, 0x2abull << 30, + 0x2caull << 30, 0x2cbull << 30, 0x2eaull << 30, 0x2ebull << 30, + 0x2ceull << 30, 0x2cfull << 30, + 0x29aull << 30, 0x29bull << 30, 0x2baull << 30, 0x2bbull << 30, + 0x2daull << 30, 0x2dbull << 30, 0x2faull << 30, 0x2fbull << 30, + 0x2deull << 30, 0x2dfull << 30, + 0x300ull << 30, 0x301ull << 30, 0x302ull << 30, 0x303ull << 30, + 0x304ull << 30, 0x305ull << 30, 0x306ull << 30, 0x307ull << 30, + 0x308ull << 30, 0x309ull << 30, + 0x310ull << 30, 0x311ull << 30, 0x312ull << 30, 0x313ull << 30, + 0x314ull << 30, 0x315ull << 30, 0x316ull << 30, 0x317ull << 30, + 0x318ull << 30, 0x319ull << 30, + 0x320ull << 30, 0x321ull << 30, 0x322ull << 30, 0x323ull << 30, + 0x324ull << 30, 0x325ull << 30, 0x326ull << 30, 0x327ull << 30, + 0x328ull << 30, 0x329ull << 30, + 0x330ull << 30, 0x331ull << 30, 0x332ull << 30, 0x333ull << 30, + 0x334ull << 30, 0x335ull << 30, 0x336ull << 30, 0x337ull << 30, + 0x338ull << 30, 0x339ull << 30, + 0x340ull << 30, 0x341ull << 30, 0x342ull << 30, 0x343ull << 30, + 0x344ull << 30, 0x345ull << 30, 0x346ull << 30, 0x347ull << 30, + 0x348ull << 30, 0x349ull << 30, + 0x350ull << 30, 0x351ull << 30, 0x352ull << 30, 0x353ull << 30, + 0x354ull << 30, 0x355ull << 30, 0x356ull << 30, 0x357ull << 30, + 0x358ull << 30, 0x359ull << 30, + 0x360ull << 30, 0x361ull << 30, 0x362ull << 30, 0x363ull << 30, + 0x364ull << 30, 0x365ull << 30, 0x366ull << 30, 0x367ull << 30, + 0x368ull << 30, 0x369ull << 30, + 0x370ull << 30, 0x371ull << 30, 0x372ull << 30, 0x373ull << 30, + 0x374ull << 30, 0x375ull << 30, 0x376ull << 30, 0x377ull << 30, + 0x378ull << 30, 0x379ull << 30, + 0x30aull << 30, 0x30bull << 30, 0x32aull << 30, 0x32bull << 30, + 0x34aull << 30, 0x34bull << 30, 0x36aull << 30, 0x36bull << 30, + 0x34eull << 30, 0x34full << 30, + 0x31aull << 30, 0x31bull << 30, 0x33aull << 30, 0x33bull << 30, + 0x35aull << 30, 0x35bull << 30, 0x37aull << 30, 0x37bull << 30, + 0x35eull << 30, 0x35full << 30, + 0x380ull << 30, 0x381ull << 30, 0x382ull << 30, 0x383ull << 30, + 0x384ull << 30, 0x385ull << 30, 0x386ull << 30, 0x387ull << 30, + 0x388ull << 30, 0x389ull << 30, + 0x390ull << 30, 0x391ull << 30, 0x392ull << 30, 0x393ull << 30, + 0x394ull << 30, 0x395ull << 30, 0x396ull << 30, 0x397ull << 30, + 0x398ull << 30, 0x399ull << 30, + 0x3a0ull << 30, 0x3a1ull << 30, 0x3a2ull << 30, 0x3a3ull << 30, + 0x3a4ull << 30, 0x3a5ull << 30, 0x3a6ull << 30, 0x3a7ull << 30, + 0x3a8ull << 30, 0x3a9ull << 30, + 0x3b0ull << 30, 0x3b1ull << 30, 0x3b2ull << 30, 0x3b3ull << 30, + 0x3b4ull << 30, 0x3b5ull << 30, 0x3b6ull << 30, 0x3b7ull << 30, + 0x3b8ull << 30, 0x3b9ull << 30, + 0x3c0ull << 30, 0x3c1ull << 30, 0x3c2ull << 30, 0x3c3ull << 30, + 0x3c4ull << 30, 0x3c5ull << 30, 0x3c6ull << 30, 0x3c7ull << 30, + 0x3c8ull << 30, 0x3c9ull << 30, + 0x3d0ull << 30, 0x3d1ull << 30, 0x3d2ull << 30, 0x3d3ull << 30, + 0x3d4ull << 30, 0x3d5ull << 30, 0x3d6ull << 30, 0x3d7ull << 30, + 0x3d8ull << 30, 0x3d9ull << 30, + 0x3e0ull << 30, 0x3e1ull << 30, 0x3e2ull << 30, 0x3e3ull << 30, + 0x3e4ull << 30, 0x3e5ull << 30, 0x3e6ull << 30, 0x3e7ull << 30, + 0x3e8ull << 30, 0x3e9ull << 30, + 0x3f0ull << 30, 0x3f1ull << 30, 0x3f2ull << 30, 0x3f3ull << 30, + 0x3f4ull << 30, 0x3f5ull << 30, 0x3f6ull << 30, 0x3f7ull << 30, + 0x3f8ull << 30, 0x3f9ull << 30, + 0x38aull << 30, 0x38bull << 30, 0x3aaull << 30, 0x3abull << 30, + 0x3caull << 30, 0x3cbull << 30, 0x3eaull << 30, 0x3ebull << 30, + 0x3ceull << 30, 0x3cfull << 30, + 0x39aull << 30, 0x39bull << 30, 0x3baull << 30, 0x3bbull << 30, + 0x3daull << 30, 0x3dbull << 30, 0x3faull << 30, 0x3fbull << 30, + 0x3deull << 30, 0x3dfull << 30, + 0x00cull << 30, 0x00dull << 30, 0x10cull << 30, 0x10dull << 30, + 0x20cull << 30, 0x20dull << 30, 0x30cull << 30, 0x30dull << 30, + 0x02eull << 30, 0x02full << 30, + 0x01cull << 30, 0x01dull << 30, 0x11cull << 30, 0x11dull << 30, + 0x21cull << 30, 0x21dull << 30, 0x31cull << 30, 0x31dull << 30, + 0x03eull << 30, 0x03full << 30, + 0x02cull << 30, 0x02dull << 30, 0x12cull << 30, 0x12dull << 30, + 0x22cull << 30, 0x22dull << 30, 0x32cull << 30, 0x32dull << 30, + 0x12eull << 30, 0x12full << 30, + 0x03cull << 30, 0x03dull << 30, 0x13cull << 30, 0x13dull << 30, + 0x23cull << 30, 0x23dull << 30, 0x33cull << 30, 0x33dull << 30, + 0x13eull << 30, 0x13full << 30, + 0x04cull << 30, 0x04dull << 30, 0x14cull << 30, 0x14dull << 30, + 0x24cull << 30, 0x24dull << 30, 0x34cull << 30, 0x34dull << 30, + 0x22eull << 30, 0x22full << 30, + 0x05cull << 30, 0x05dull << 30, 0x15cull << 30, 0x15dull << 30, + 0x25cull << 30, 0x25dull << 30, 0x35cull << 30, 0x35dull << 30, + 0x23eull << 30, 0x23full << 30, + 0x06cull << 30, 0x06dull << 30, 0x16cull << 30, 0x16dull << 30, + 0x26cull << 30, 0x26dull << 30, 0x36cull << 30, 0x36dull << 30, + 0x32eull << 30, 0x32full << 30, + 0x07cull << 30, 0x07dull << 30, 0x17cull << 30, 0x17dull << 30, + 0x27cull << 30, 0x27dull << 30, 0x37cull << 30, 0x37dull << 30, + 0x33eull << 30, 0x33full << 30, + 0x00eull << 30, 0x00full << 30, 0x10eull << 30, 0x10full << 30, + 0x20eull << 30, 0x20full << 30, 0x30eull << 30, 0x30full << 30, + 0x06eull << 30, 0x06full << 30, + 0x01eull << 30, 0x01full << 30, 0x11eull << 30, 0x11full << 30, + 0x21eull << 30, 0x21full << 30, 0x31eull << 30, 0x31full << 30, + 0x07eull << 30, 0x07full << 30, + 0x08cull << 30, 0x08dull << 30, 0x18cull << 30, 0x18dull << 30, + 0x28cull << 30, 0x28dull << 30, 0x38cull << 30, 0x38dull << 30, + 0x0aeull << 30, 0x0afull << 30, + 0x09cull << 30, 0x09dull << 30, 0x19cull << 30, 0x19dull << 30, + 0x29cull << 30, 0x29dull << 30, 0x39cull << 30, 0x39dull << 30, + 0x0beull << 30, 0x0bfull << 30, + 0x0acull << 30, 0x0adull << 30, 0x1acull << 30, 0x1adull << 30, + 0x2acull << 30, 0x2adull << 30, 0x3acull << 30, 0x3adull << 30, + 0x1aeull << 30, 0x1afull << 30, + 0x0bcull << 30, 0x0bdull << 30, 0x1bcull << 30, 0x1bdull << 30, + 0x2bcull << 30, 0x2bdull << 30, 0x3bcull << 30, 0x3bdull << 30, + 0x1beull << 30, 0x1bfull << 30, + 0x0ccull << 30, 0x0cdull << 30, 0x1ccull << 30, 0x1cdull << 30, + 0x2ccull << 30, 0x2cdull << 30, 0x3ccull << 30, 0x3cdull << 30, + 0x2aeull << 30, 0x2afull << 30, + 0x0dcull << 30, 0x0ddull << 30, 0x1dcull << 30, 0x1ddull << 30, + 0x2dcull << 30, 0x2ddull << 30, 0x3dcull << 30, 0x3ddull << 30, + 0x2beull << 30, 0x2bfull << 30, + 0x0ecull << 30, 0x0edull << 30, 0x1ecull << 30, 0x1edull << 30, + 0x2ecull << 30, 0x2edull << 30, 0x3ecull << 30, 0x3edull << 30, + 0x3aeull << 30, 0x3afull << 30, + 0x0fcull << 30, 0x0fdull << 30, 0x1fcull << 30, 0x1fdull << 30, + 0x2fcull << 30, 0x2fdull << 30, 0x3fcull << 30, 0x3fdull << 30, + 0x3beull << 30, 0x3bfull << 30, + 0x08eull << 30, 0x08full << 30, 0x18eull << 30, 0x18full << 30, + 0x28eull << 30, 0x28full << 30, 0x38eull << 30, 0x38full << 30, + 0x0eeull << 30, 0x0efull << 30, + 0x09eull << 30, 0x09full << 30, 0x19eull << 30, 0x19full << 30, + 0x29eull << 30, 0x29full << 30, 0x39eull << 30, 0x39full << 30, + 0x0feull << 30, 0x0ffull << 30 +}; + +const UINT64 b2d5[] = + { 0x000ull << 40, 0x001ull << 40, 0x002ull << 40, 0x003ull << 40, + 0x004ull << 40, 0x005ull << 40, 0x006ull << 40, 0x007ull << 40, + 0x008ull << 40, + 0x009ull << 40, + 0x010ull << 40, 0x011ull << 40, 0x012ull << 40, 0x013ull << 40, + 0x014ull << 40, 0x015ull << 40, 0x016ull << 40, 0x017ull << 40, + 0x018ull << 40, 0x019ull << 40, + 0x020ull << 40, 0x021ull << 40, 0x022ull << 40, 0x023ull << 40, + 0x024ull << 40, 0x025ull << 40, 0x026ull << 40, 0x027ull << 40, + 0x028ull << 40, 0x029ull << 40, + 0x030ull << 40, 0x031ull << 40, 0x032ull << 40, 0x033ull << 40, + 0x034ull << 40, 0x035ull << 40, 0x036ull << 40, 0x037ull << 40, + 0x038ull << 40, 0x039ull << 40, + 0x040ull << 40, 0x041ull << 40, 0x042ull << 40, 0x043ull << 40, + 0x044ull << 40, 0x045ull << 40, 0x046ull << 40, 0x047ull << 40, + 0x048ull << 40, 0x049ull << 40, + 0x050ull << 40, 0x051ull << 40, 0x052ull << 40, 0x053ull << 40, + 0x054ull << 40, 0x055ull << 40, 0x056ull << 40, 0x057ull << 40, + 0x058ull << 40, 0x059ull << 40, + 0x060ull << 40, 0x061ull << 40, 0x062ull << 40, 0x063ull << 40, + 0x064ull << 40, 0x065ull << 40, 0x066ull << 40, 0x067ull << 40, + 0x068ull << 40, 0x069ull << 40, + 0x070ull << 40, 0x071ull << 40, 0x072ull << 40, 0x073ull << 40, + 0x074ull << 40, 0x075ull << 40, 0x076ull << 40, 0x077ull << 40, + 0x078ull << 40, 0x079ull << 40, + 0x00aull << 40, 0x00bull << 40, 0x02aull << 40, 0x02bull << 40, + 0x04aull << 40, 0x04bull << 40, 0x06aull << 40, 0x06bull << 40, + 0x04eull << 40, 0x04full << 40, + 0x01aull << 40, 0x01bull << 40, 0x03aull << 40, 0x03bull << 40, + 0x05aull << 40, 0x05bull << 40, 0x07aull << 40, 0x07bull << 40, + 0x05eull << 40, 0x05full << 40, + 0x080ull << 40, 0x081ull << 40, 0x082ull << 40, 0x083ull << 40, + 0x084ull << 40, 0x085ull << 40, 0x086ull << 40, 0x087ull << 40, + 0x088ull << 40, 0x089ull << 40, + 0x090ull << 40, 0x091ull << 40, 0x092ull << 40, 0x093ull << 40, + 0x094ull << 40, 0x095ull << 40, 0x096ull << 40, 0x097ull << 40, + 0x098ull << 40, 0x099ull << 40, + 0x0a0ull << 40, 0x0a1ull << 40, 0x0a2ull << 40, 0x0a3ull << 40, + 0x0a4ull << 40, 0x0a5ull << 40, 0x0a6ull << 40, 0x0a7ull << 40, + 0x0a8ull << 40, 0x0a9ull << 40, + 0x0b0ull << 40, 0x0b1ull << 40, 0x0b2ull << 40, 0x0b3ull << 40, + 0x0b4ull << 40, 0x0b5ull << 40, 0x0b6ull << 40, 0x0b7ull << 40, + 0x0b8ull << 40, 0x0b9ull << 40, + 0x0c0ull << 40, 0x0c1ull << 40, 0x0c2ull << 40, 0x0c3ull << 40, + 0x0c4ull << 40, 0x0c5ull << 40, 0x0c6ull << 40, 0x0c7ull << 40, + 0x0c8ull << 40, 0x0c9ull << 40, + 0x0d0ull << 40, 0x0d1ull << 40, 0x0d2ull << 40, 0x0d3ull << 40, + 0x0d4ull << 40, 0x0d5ull << 40, 0x0d6ull << 40, 0x0d7ull << 40, + 0x0d8ull << 40, 0x0d9ull << 40, + 0x0e0ull << 40, 0x0e1ull << 40, 0x0e2ull << 40, 0x0e3ull << 40, + 0x0e4ull << 40, 0x0e5ull << 40, 0x0e6ull << 40, 0x0e7ull << 40, + 0x0e8ull << 40, 0x0e9ull << 40, + 0x0f0ull << 40, 0x0f1ull << 40, 0x0f2ull << 40, 0x0f3ull << 40, + 0x0f4ull << 40, 0x0f5ull << 40, 0x0f6ull << 40, 0x0f7ull << 40, + 0x0f8ull << 40, 0x0f9ull << 40, + 0x08aull << 40, 0x08bull << 40, 0x0aaull << 40, 0x0abull << 40, + 0x0caull << 40, 0x0cbull << 40, 0x0eaull << 40, 0x0ebull << 40, + 0x0ceull << 40, 0x0cfull << 40, + 0x09aull << 40, 0x09bull << 40, 0x0baull << 40, 0x0bbull << 40, + 0x0daull << 40, 0x0dbull << 40, 0x0faull << 40, 0x0fbull << 40, + 0x0deull << 40, 0x0dfull << 40, + 0x100ull << 40, 0x101ull << 40, 0x102ull << 40, 0x103ull << 40, + 0x104ull << 40, 0x105ull << 40, 0x106ull << 40, 0x107ull << 40, + 0x108ull << 40, 0x109ull << 40, + 0x110ull << 40, 0x111ull << 40, 0x112ull << 40, 0x113ull << 40, + 0x114ull << 40, 0x115ull << 40, 0x116ull << 40, 0x117ull << 40, + 0x118ull << 40, 0x119ull << 40, + 0x120ull << 40, 0x121ull << 40, 0x122ull << 40, 0x123ull << 40, + 0x124ull << 40, 0x125ull << 40, 0x126ull << 40, 0x127ull << 40, + 0x128ull << 40, 0x129ull << 40, + 0x130ull << 40, 0x131ull << 40, 0x132ull << 40, 0x133ull << 40, + 0x134ull << 40, 0x135ull << 40, 0x136ull << 40, 0x137ull << 40, + 0x138ull << 40, 0x139ull << 40, + 0x140ull << 40, 0x141ull << 40, 0x142ull << 40, 0x143ull << 40, + 0x144ull << 40, 0x145ull << 40, 0x146ull << 40, 0x147ull << 40, + 0x148ull << 40, 0x149ull << 40, + 0x150ull << 40, 0x151ull << 40, 0x152ull << 40, 0x153ull << 40, + 0x154ull << 40, 0x155ull << 40, 0x156ull << 40, 0x157ull << 40, + 0x158ull << 40, 0x159ull << 40, + 0x160ull << 40, 0x161ull << 40, 0x162ull << 40, 0x163ull << 40, + 0x164ull << 40, 0x165ull << 40, 0x166ull << 40, 0x167ull << 40, + 0x168ull << 40, 0x169ull << 40, + 0x170ull << 40, 0x171ull << 40, 0x172ull << 40, 0x173ull << 40, + 0x174ull << 40, 0x175ull << 40, 0x176ull << 40, 0x177ull << 40, + 0x178ull << 40, 0x179ull << 40, + 0x10aull << 40, 0x10bull << 40, 0x12aull << 40, 0x12bull << 40, + 0x14aull << 40, 0x14bull << 40, 0x16aull << 40, 0x16bull << 40, + 0x14eull << 40, 0x14full << 40, + 0x11aull << 40, 0x11bull << 40, 0x13aull << 40, 0x13bull << 40, + 0x15aull << 40, 0x15bull << 40, 0x17aull << 40, 0x17bull << 40, + 0x15eull << 40, 0x15full << 40, + 0x180ull << 40, 0x181ull << 40, 0x182ull << 40, 0x183ull << 40, + 0x184ull << 40, 0x185ull << 40, 0x186ull << 40, 0x187ull << 40, + 0x188ull << 40, 0x189ull << 40, + 0x190ull << 40, 0x191ull << 40, 0x192ull << 40, 0x193ull << 40, + 0x194ull << 40, 0x195ull << 40, 0x196ull << 40, 0x197ull << 40, + 0x198ull << 40, 0x199ull << 40, + 0x1a0ull << 40, 0x1a1ull << 40, 0x1a2ull << 40, 0x1a3ull << 40, + 0x1a4ull << 40, 0x1a5ull << 40, 0x1a6ull << 40, 0x1a7ull << 40, + 0x1a8ull << 40, 0x1a9ull << 40, + 0x1b0ull << 40, 0x1b1ull << 40, 0x1b2ull << 40, 0x1b3ull << 40, + 0x1b4ull << 40, 0x1b5ull << 40, 0x1b6ull << 40, 0x1b7ull << 40, + 0x1b8ull << 40, 0x1b9ull << 40, + 0x1c0ull << 40, 0x1c1ull << 40, 0x1c2ull << 40, 0x1c3ull << 40, + 0x1c4ull << 40, 0x1c5ull << 40, 0x1c6ull << 40, 0x1c7ull << 40, + 0x1c8ull << 40, 0x1c9ull << 40, + 0x1d0ull << 40, 0x1d1ull << 40, 0x1d2ull << 40, 0x1d3ull << 40, + 0x1d4ull << 40, 0x1d5ull << 40, 0x1d6ull << 40, 0x1d7ull << 40, + 0x1d8ull << 40, 0x1d9ull << 40, + 0x1e0ull << 40, 0x1e1ull << 40, 0x1e2ull << 40, 0x1e3ull << 40, + 0x1e4ull << 40, 0x1e5ull << 40, 0x1e6ull << 40, 0x1e7ull << 40, + 0x1e8ull << 40, 0x1e9ull << 40, + 0x1f0ull << 40, 0x1f1ull << 40, 0x1f2ull << 40, 0x1f3ull << 40, + 0x1f4ull << 40, 0x1f5ull << 40, 0x1f6ull << 40, 0x1f7ull << 40, + 0x1f8ull << 40, 0x1f9ull << 40, + 0x18aull << 40, 0x18bull << 40, 0x1aaull << 40, 0x1abull << 40, + 0x1caull << 40, 0x1cbull << 40, 0x1eaull << 40, 0x1ebull << 40, + 0x1ceull << 40, 0x1cfull << 40, + 0x19aull << 40, 0x19bull << 40, 0x1baull << 40, 0x1bbull << 40, + 0x1daull << 40, 0x1dbull << 40, 0x1faull << 40, 0x1fbull << 40, + 0x1deull << 40, 0x1dfull << 40, + 0x200ull << 40, 0x201ull << 40, 0x202ull << 40, 0x203ull << 40, + 0x204ull << 40, 0x205ull << 40, 0x206ull << 40, 0x207ull << 40, + 0x208ull << 40, 0x209ull << 40, + 0x210ull << 40, 0x211ull << 40, 0x212ull << 40, 0x213ull << 40, + 0x214ull << 40, 0x215ull << 40, 0x216ull << 40, 0x217ull << 40, + 0x218ull << 40, 0x219ull << 40, + 0x220ull << 40, 0x221ull << 40, 0x222ull << 40, 0x223ull << 40, + 0x224ull << 40, 0x225ull << 40, 0x226ull << 40, 0x227ull << 40, + 0x228ull << 40, 0x229ull << 40, + 0x230ull << 40, 0x231ull << 40, 0x232ull << 40, 0x233ull << 40, + 0x234ull << 40, 0x235ull << 40, 0x236ull << 40, 0x237ull << 40, + 0x238ull << 40, 0x239ull << 40, + 0x240ull << 40, 0x241ull << 40, 0x242ull << 40, 0x243ull << 40, + 0x244ull << 40, 0x245ull << 40, 0x246ull << 40, 0x247ull << 40, + 0x248ull << 40, 0x249ull << 40, + 0x250ull << 40, 0x251ull << 40, 0x252ull << 40, 0x253ull << 40, + 0x254ull << 40, 0x255ull << 40, 0x256ull << 40, 0x257ull << 40, + 0x258ull << 40, 0x259ull << 40, + 0x260ull << 40, 0x261ull << 40, 0x262ull << 40, 0x263ull << 40, + 0x264ull << 40, 0x265ull << 40, 0x266ull << 40, 0x267ull << 40, + 0x268ull << 40, 0x269ull << 40, + 0x270ull << 40, 0x271ull << 40, 0x272ull << 40, 0x273ull << 40, + 0x274ull << 40, 0x275ull << 40, 0x276ull << 40, 0x277ull << 40, + 0x278ull << 40, 0x279ull << 40, + 0x20aull << 40, 0x20bull << 40, 0x22aull << 40, 0x22bull << 40, + 0x24aull << 40, 0x24bull << 40, 0x26aull << 40, 0x26bull << 40, + 0x24eull << 40, 0x24full << 40, + 0x21aull << 40, 0x21bull << 40, 0x23aull << 40, 0x23bull << 40, + 0x25aull << 40, 0x25bull << 40, 0x27aull << 40, 0x27bull << 40, + 0x25eull << 40, 0x25full << 40, + 0x280ull << 40, 0x281ull << 40, 0x282ull << 40, 0x283ull << 40, + 0x284ull << 40, 0x285ull << 40, 0x286ull << 40, 0x287ull << 40, + 0x288ull << 40, 0x289ull << 40, + 0x290ull << 40, 0x291ull << 40, 0x292ull << 40, 0x293ull << 40, + 0x294ull << 40, 0x295ull << 40, 0x296ull << 40, 0x297ull << 40, + 0x298ull << 40, 0x299ull << 40, + 0x2a0ull << 40, 0x2a1ull << 40, 0x2a2ull << 40, 0x2a3ull << 40, + 0x2a4ull << 40, 0x2a5ull << 40, 0x2a6ull << 40, 0x2a7ull << 40, + 0x2a8ull << 40, 0x2a9ull << 40, + 0x2b0ull << 40, 0x2b1ull << 40, 0x2b2ull << 40, 0x2b3ull << 40, + 0x2b4ull << 40, 0x2b5ull << 40, 0x2b6ull << 40, 0x2b7ull << 40, + 0x2b8ull << 40, 0x2b9ull << 40, + 0x2c0ull << 40, 0x2c1ull << 40, 0x2c2ull << 40, 0x2c3ull << 40, + 0x2c4ull << 40, 0x2c5ull << 40, 0x2c6ull << 40, 0x2c7ull << 40, + 0x2c8ull << 40, 0x2c9ull << 40, + 0x2d0ull << 40, 0x2d1ull << 40, 0x2d2ull << 40, 0x2d3ull << 40, + 0x2d4ull << 40, 0x2d5ull << 40, 0x2d6ull << 40, 0x2d7ull << 40, + 0x2d8ull << 40, 0x2d9ull << 40, + 0x2e0ull << 40, 0x2e1ull << 40, 0x2e2ull << 40, 0x2e3ull << 40, + 0x2e4ull << 40, 0x2e5ull << 40, 0x2e6ull << 40, 0x2e7ull << 40, + 0x2e8ull << 40, 0x2e9ull << 40, + 0x2f0ull << 40, 0x2f1ull << 40, 0x2f2ull << 40, 0x2f3ull << 40, + 0x2f4ull << 40, 0x2f5ull << 40, 0x2f6ull << 40, 0x2f7ull << 40, + 0x2f8ull << 40, 0x2f9ull << 40, + 0x28aull << 40, 0x28bull << 40, 0x2aaull << 40, 0x2abull << 40, + 0x2caull << 40, 0x2cbull << 40, 0x2eaull << 40, 0x2ebull << 40, + 0x2ceull << 40, 0x2cfull << 40, + 0x29aull << 40, 0x29bull << 40, 0x2baull << 40, 0x2bbull << 40, + 0x2daull << 40, 0x2dbull << 40, 0x2faull << 40, 0x2fbull << 40, + 0x2deull << 40, 0x2dfull << 40, + 0x300ull << 40, 0x301ull << 40, 0x302ull << 40, 0x303ull << 40, + 0x304ull << 40, 0x305ull << 40, 0x306ull << 40, 0x307ull << 40, + 0x308ull << 40, 0x309ull << 40, + 0x310ull << 40, 0x311ull << 40, 0x312ull << 40, 0x313ull << 40, + 0x314ull << 40, 0x315ull << 40, 0x316ull << 40, 0x317ull << 40, + 0x318ull << 40, 0x319ull << 40, + 0x320ull << 40, 0x321ull << 40, 0x322ull << 40, 0x323ull << 40, + 0x324ull << 40, 0x325ull << 40, 0x326ull << 40, 0x327ull << 40, + 0x328ull << 40, 0x329ull << 40, + 0x330ull << 40, 0x331ull << 40, 0x332ull << 40, 0x333ull << 40, + 0x334ull << 40, 0x335ull << 40, 0x336ull << 40, 0x337ull << 40, + 0x338ull << 40, 0x339ull << 40, + 0x340ull << 40, 0x341ull << 40, 0x342ull << 40, 0x343ull << 40, + 0x344ull << 40, 0x345ull << 40, 0x346ull << 40, 0x347ull << 40, + 0x348ull << 40, 0x349ull << 40, + 0x350ull << 40, 0x351ull << 40, 0x352ull << 40, 0x353ull << 40, + 0x354ull << 40, 0x355ull << 40, 0x356ull << 40, 0x357ull << 40, + 0x358ull << 40, 0x359ull << 40, + 0x360ull << 40, 0x361ull << 40, 0x362ull << 40, 0x363ull << 40, + 0x364ull << 40, 0x365ull << 40, 0x366ull << 40, 0x367ull << 40, + 0x368ull << 40, 0x369ull << 40, + 0x370ull << 40, 0x371ull << 40, 0x372ull << 40, 0x373ull << 40, + 0x374ull << 40, 0x375ull << 40, 0x376ull << 40, 0x377ull << 40, + 0x378ull << 40, 0x379ull << 40, + 0x30aull << 40, 0x30bull << 40, 0x32aull << 40, 0x32bull << 40, + 0x34aull << 40, 0x34bull << 40, 0x36aull << 40, 0x36bull << 40, + 0x34eull << 40, 0x34full << 40, + 0x31aull << 40, 0x31bull << 40, 0x33aull << 40, 0x33bull << 40, + 0x35aull << 40, 0x35bull << 40, 0x37aull << 40, 0x37bull << 40, + 0x35eull << 40, 0x35full << 40, + 0x380ull << 40, 0x381ull << 40, 0x382ull << 40, 0x383ull << 40, + 0x384ull << 40, 0x385ull << 40, 0x386ull << 40, 0x387ull << 40, + 0x388ull << 40, 0x389ull << 40, + 0x390ull << 40, 0x391ull << 40, 0x392ull << 40, 0x393ull << 40, + 0x394ull << 40, 0x395ull << 40, 0x396ull << 40, 0x397ull << 40, + 0x398ull << 40, 0x399ull << 40, + 0x3a0ull << 40, 0x3a1ull << 40, 0x3a2ull << 40, 0x3a3ull << 40, + 0x3a4ull << 40, 0x3a5ull << 40, 0x3a6ull << 40, 0x3a7ull << 40, + 0x3a8ull << 40, 0x3a9ull << 40, + 0x3b0ull << 40, 0x3b1ull << 40, 0x3b2ull << 40, 0x3b3ull << 40, + 0x3b4ull << 40, 0x3b5ull << 40, 0x3b6ull << 40, 0x3b7ull << 40, + 0x3b8ull << 40, 0x3b9ull << 40, + 0x3c0ull << 40, 0x3c1ull << 40, 0x3c2ull << 40, 0x3c3ull << 40, + 0x3c4ull << 40, 0x3c5ull << 40, 0x3c6ull << 40, 0x3c7ull << 40, + 0x3c8ull << 40, 0x3c9ull << 40, + 0x3d0ull << 40, 0x3d1ull << 40, 0x3d2ull << 40, 0x3d3ull << 40, + 0x3d4ull << 40, 0x3d5ull << 40, 0x3d6ull << 40, 0x3d7ull << 40, + 0x3d8ull << 40, 0x3d9ull << 40, + 0x3e0ull << 40, 0x3e1ull << 40, 0x3e2ull << 40, 0x3e3ull << 40, + 0x3e4ull << 40, 0x3e5ull << 40, 0x3e6ull << 40, 0x3e7ull << 40, + 0x3e8ull << 40, 0x3e9ull << 40, + 0x3f0ull << 40, 0x3f1ull << 40, 0x3f2ull << 40, 0x3f3ull << 40, + 0x3f4ull << 40, 0x3f5ull << 40, 0x3f6ull << 40, 0x3f7ull << 40, + 0x3f8ull << 40, 0x3f9ull << 40, + 0x38aull << 40, 0x38bull << 40, 0x3aaull << 40, 0x3abull << 40, + 0x3caull << 40, 0x3cbull << 40, 0x3eaull << 40, 0x3ebull << 40, + 0x3ceull << 40, 0x3cfull << 40, + 0x39aull << 40, 0x39bull << 40, 0x3baull << 40, 0x3bbull << 40, + 0x3daull << 40, 0x3dbull << 40, 0x3faull << 40, 0x3fbull << 40, + 0x3deull << 40, 0x3dfull << 40, + 0x00cull << 40, 0x00dull << 40, 0x10cull << 40, 0x10dull << 40, + 0x20cull << 40, 0x20dull << 40, 0x30cull << 40, 0x30dull << 40, + 0x02eull << 40, 0x02full << 40, + 0x01cull << 40, 0x01dull << 40, 0x11cull << 40, 0x11dull << 40, + 0x21cull << 40, 0x21dull << 40, 0x31cull << 40, 0x31dull << 40, + 0x03eull << 40, 0x03full << 40, + 0x02cull << 40, 0x02dull << 40, 0x12cull << 40, 0x12dull << 40, + 0x22cull << 40, 0x22dull << 40, 0x32cull << 40, 0x32dull << 40, + 0x12eull << 40, 0x12full << 40, + 0x03cull << 40, 0x03dull << 40, 0x13cull << 40, 0x13dull << 40, + 0x23cull << 40, 0x23dull << 40, 0x33cull << 40, 0x33dull << 40, + 0x13eull << 40, 0x13full << 40, + 0x04cull << 40, 0x04dull << 40, 0x14cull << 40, 0x14dull << 40, + 0x24cull << 40, 0x24dull << 40, 0x34cull << 40, 0x34dull << 40, + 0x22eull << 40, 0x22full << 40, + 0x05cull << 40, 0x05dull << 40, 0x15cull << 40, 0x15dull << 40, + 0x25cull << 40, 0x25dull << 40, 0x35cull << 40, 0x35dull << 40, + 0x23eull << 40, 0x23full << 40, + 0x06cull << 40, 0x06dull << 40, 0x16cull << 40, 0x16dull << 40, + 0x26cull << 40, 0x26dull << 40, 0x36cull << 40, 0x36dull << 40, + 0x32eull << 40, 0x32full << 40, + 0x07cull << 40, 0x07dull << 40, 0x17cull << 40, 0x17dull << 40, + 0x27cull << 40, 0x27dull << 40, 0x37cull << 40, 0x37dull << 40, + 0x33eull << 40, 0x33full << 40, + 0x00eull << 40, 0x00full << 40, 0x10eull << 40, 0x10full << 40, + 0x20eull << 40, 0x20full << 40, 0x30eull << 40, 0x30full << 40, + 0x06eull << 40, 0x06full << 40, + 0x01eull << 40, 0x01full << 40, 0x11eull << 40, 0x11full << 40, + 0x21eull << 40, 0x21full << 40, 0x31eull << 40, 0x31full << 40, + 0x07eull << 40, 0x07full << 40, + 0x08cull << 40, 0x08dull << 40, 0x18cull << 40, 0x18dull << 40, + 0x28cull << 40, 0x28dull << 40, 0x38cull << 40, 0x38dull << 40, + 0x0aeull << 40, 0x0afull << 40, + 0x09cull << 40, 0x09dull << 40, 0x19cull << 40, 0x19dull << 40, + 0x29cull << 40, 0x29dull << 40, 0x39cull << 40, 0x39dull << 40, + 0x0beull << 40, 0x0bfull << 40, + 0x0acull << 40, 0x0adull << 40, 0x1acull << 40, 0x1adull << 40, + 0x2acull << 40, 0x2adull << 40, 0x3acull << 40, 0x3adull << 40, + 0x1aeull << 40, 0x1afull << 40, + 0x0bcull << 40, 0x0bdull << 40, 0x1bcull << 40, 0x1bdull << 40, + 0x2bcull << 40, 0x2bdull << 40, 0x3bcull << 40, 0x3bdull << 40, + 0x1beull << 40, 0x1bfull << 40, + 0x0ccull << 40, 0x0cdull << 40, 0x1ccull << 40, 0x1cdull << 40, + 0x2ccull << 40, 0x2cdull << 40, 0x3ccull << 40, 0x3cdull << 40, + 0x2aeull << 40, 0x2afull << 40, + 0x0dcull << 40, 0x0ddull << 40, 0x1dcull << 40, 0x1ddull << 40, + 0x2dcull << 40, 0x2ddull << 40, 0x3dcull << 40, 0x3ddull << 40, + 0x2beull << 40, 0x2bfull << 40, + 0x0ecull << 40, 0x0edull << 40, 0x1ecull << 40, 0x1edull << 40, + 0x2ecull << 40, 0x2edull << 40, 0x3ecull << 40, 0x3edull << 40, + 0x3aeull << 40, 0x3afull << 40, + 0x0fcull << 40, 0x0fdull << 40, 0x1fcull << 40, 0x1fdull << 40, + 0x2fcull << 40, 0x2fdull << 40, 0x3fcull << 40, 0x3fdull << 40, + 0x3beull << 40, 0x3bfull << 40, + 0x08eull << 40, 0x08full << 40, 0x18eull << 40, 0x18full << 40, + 0x28eull << 40, 0x28full << 40, 0x38eull << 40, 0x38full << 40, + 0x0eeull << 40, 0x0efull << 40, + 0x09eull << 40, 0x09full << 40, 0x19eull << 40, 0x19full << 40, + 0x29eull << 40, 0x29full << 40, 0x39eull << 40, 0x39full << 40, + 0x0feull << 40, 0x0ffull << 40 +}; diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_binarydecimal.c b/gcc-4.4.3/libgcc/config/libbid/bid_binarydecimal.c new file mode 100644 index 000000000..d7d39a551 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_binarydecimal.c @@ -0,0 +1,147479 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +// Counting leading zeros in an unsigned 32-bit word +// The "_nz" version will return the wrong answer (31) for zero inputs + +#define CLZ32_MASK16 0xFFFF0000ul +#define CLZ32_MASK8 0xFF00FF00ul +#define CLZ32_MASK4 0xF0F0F0F0ul +#define CLZ32_MASK2 0xCCCCCCCCul +#define CLZ32_MASK1 0xAAAAAAAAul + +#define clz32_nz(n) \ + (((((n) & CLZ32_MASK16) <= ((n) & ~CLZ32_MASK16)) ? 16 : 0) + \ + ((((n) & CLZ32_MASK8) <= ((n) & ~CLZ32_MASK8)) ? 8 : 0) + \ + ((((n) & CLZ32_MASK4) <= ((n) & ~CLZ32_MASK4)) ? 4 : 0) + \ + ((((n) & CLZ32_MASK2) <= ((n) & ~CLZ32_MASK2)) ? 2 : 0) + \ + ((((n) & CLZ32_MASK1) <= ((n) & ~CLZ32_MASK1)) ? 1 : 0)) + +#define clz32(n) (((n)==0) ? 32 : clz32_nz(n)) + +// Counting trailing zeros in an unsigned 32-bit word +// The ctz32_1bit version is for a single bit + +#define ctz32_1bit(n) \ + ((((n) & ~CLZ32_MASK16) ? 0 : 16) + \ + (((n) & ~CLZ32_MASK8) ? 0 : 8) + \ + (((n) & ~CLZ32_MASK4) ? 0 : 4) + \ + (((n) & ~CLZ32_MASK2) ? 0 : 2) + \ + (((n) & ~CLZ32_MASK1) ? 0 : 1)) + +#define ctz32(n) (((n) == 0) ? 32 : ctz32_1bit((n) & -(n))) + +// Counting leading zeros in an unsigned 64-bit word +// The "_nz" version will return the wrong answer (63) for zero inputs + +#define CLZ64_MASK32 0xFFFFFFFF00000000ull +#define CLZ64_MASK16 0xFFFF0000FFFF0000ull +#define CLZ64_MASK8 0xFF00FF00FF00FF00ull +#define CLZ64_MASK4 0xF0F0F0F0F0F0F0F0ull +#define CLZ64_MASK2 0xCCCCCCCCCCCCCCCCull +#define CLZ64_MASK1 0xAAAAAAAAAAAAAAAAull + +#define clz64_nz(n) \ + (((((n) & CLZ64_MASK32) <= ((n) & ~CLZ64_MASK32)) ? 32 : 0) + \ + ((((n) & CLZ64_MASK16) <= ((n) & ~CLZ64_MASK16)) ? 16 : 0) + \ + ((((n) & CLZ64_MASK8) <= ((n) & ~CLZ64_MASK8)) ? 8 : 0) + \ + ((((n) & CLZ64_MASK4) <= ((n) & ~CLZ64_MASK4)) ? 4 : 0) + \ + ((((n) & CLZ64_MASK2) <= ((n) & ~CLZ64_MASK2)) ? 2 : 0) + \ + ((((n) & CLZ64_MASK1) <= ((n) & ~CLZ64_MASK1)) ? 1 : 0)) \ + +#define clz64(n) (((n)==0) ? 64 : clz64_nz(n)) + +// Counting trailing zeros in an unsigned 64-bit word +// The ctz64_1bit version is for a single bit + +#define ctz64_1bit(n) \ + ((((n) & ~CLZ64_MASK32) ? 0 : 32) + \ + (((n) & ~CLZ64_MASK16) ? 0 : 16) + \ + (((n) & ~CLZ64_MASK8) ? 0 : 8) + \ + (((n) & ~CLZ64_MASK4) ? 0 : 4) + \ + (((n) & ~CLZ64_MASK2) ? 0 : 2) + \ + (((n) & ~CLZ64_MASK1) ? 0 : 1)) + +#define ctz64(n) (((n) == 0) ? 64 : ctz64_1bit((n) & -(n))) + +// Counting leading zeros in an unsigned 2-part 128-bit word + +#define clz128(n_hi,n_lo) (((n_hi) == 0) ? 64 + clz64(n_lo) : clz64_nz(n_hi)) + +// Counting trailing zeros in a 2-part 128-bit word + +#define ctz128(hi,lo) (((lo) == 0) ? 64 + ctz64(hi) : ctz64(lo)) + +// Shift 2-part 2^64 * hi + lo left by "c" bits +// The "short" form requires a shift 0 < c < 64 and will be faster +// Note that shifts of 64 can't be relied on as ANSI + +#define sll128_short(hi,lo,c) \ + ((hi) = ((hi) << (c)) + ((lo)>>(64-(c))), \ + (lo) = (lo) << (c) \ + ) + +#define sll128(hi,lo,c) \ + (((c) == 0) ? hi = hi, lo = lo : \ + (((c) >= 64) ? hi = lo << ((c) - 64), lo = 0 : sll128_short(hi,lo,c))) + +// Shift 2-part 2^64 * hi + lo right by "c" bits +// The "short" form requires a shift 0 < c < 64 and will be faster +// Note that shifts of 64 can't be relied on as ANSI + +#define srl128_short(hi,lo,c) \ + ((lo) = ((hi) << (64 - (c))) + ((lo) >> (c)), \ + (hi) = (hi) >> (c) \ + ) + +#define srl128(hi,lo,c) \ + (((c) == 0) ? hi = hi, lo = lo : \ + (((c) >= 64) ? lo = hi >> ((c) - 64), hi = 0 : srl128_short(hi,lo,c))) + +// Shift 4-part 2^196 * x3 + 2^128 * x2 + 2^64 * x1 + x0 +// right by "c" bits (must have c < 64) + +#define srl256(x3,x2,x1,x0,c) \ + ((x0) = ((x1) << (64 - (c))) + ((x0) >> (c)), \ + (x1) = ((x2) << (64 - (c))) + ((x1) >> (c)), \ + (x2) = ((x3) << (64 - (c))) + ((x2) >> (c)), \ + (x3) = (x3) >> (c) \ + ) + +// Compare "<" two 2-part unsigned integers + +#define lt128(x_hi,x_lo,y_hi,y_lo) \ + (((x_hi) < (y_hi)) || (((x_hi) == (y_hi)) && ((x_lo) < (y_lo)))) + +// Likewise "<=" + +#define le128(x_hi,x_lo,y_hi,y_lo) \ + (((x_hi) < (y_hi)) || (((x_hi) == (y_hi)) && ((x_lo) <= (y_lo)))) + +// 128x256->384 bit multiplication (missing from existing macros) +// I derived this by propagating (A).w[2] = 0 in __mul_192x256_to_448 + +#define __mul_128x256_to_384(P, A, B) \ +{ \ +UINT512 P0,P1; \ +UINT64 CY; \ + __mul_64x256_to_320(P0, (A).w[0], B); \ + __mul_64x256_to_320(P1, (A).w[1], B); \ + (P).w[0] = P0.w[0]; \ + __add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]); \ + __add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \ + __add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \ + __add_carry_in_out((P).w[4],CY,P1.w[3],P0.w[4],CY); \ + (P).w[5] = P1.w[4] + CY; \ +} + +// Multiply a 64-bit number by 10, getting "carry" and "sum" + +#define __mul_10x64(sum,carryout,input,carryin) \ +{ unsigned long long s3 = (input) + ((input) >> 2); \ + (carryout) = ((s3 < (unsigned long long)(input))<<3) + (s3>>61); \ + s3 = (s3<<3) + ((input&3)<<1); \ + (sum) = s3 + (carryin); \ + if ((unsigned long long)(sum) < s3) ++(carryout); \ +} + +// Multiply a 256-bit number by 10, assuming no overflow + +#define __mul_10x256_to_256(p3,p2,p1,p0,a3,a2,a1,a0) \ +{ unsigned long long c0,c1,c2,c3; \ + __mul_10x64(p0,c0,a0,0ull); \ + __mul_10x64(p1,c1,a1,c0); \ + __mul_10x64(p2,c2,a2,c1); \ + __mul_10x64(p3,c3,a3,c2); \ +} + +// Set up indices for low and high parts, depending on the endian-ness. +// Note that this only affects 128-bit input and output operands, not any +// of the internal workings, where w[0] is always the low-order part. + +#if BID_BIG_ENDIAN +typedef union { + struct { + unsigned short hi; + unsigned short lo1; + unsigned short lo2; + unsigned short lo3; + unsigned short lo4; + unsigned short pad; + unsigned pad128; + } i; + BINARY80 f; +} +BID_BINARY80LDOUBLE; +#else +typedef union { + struct { + unsigned short lo4; + unsigned short lo3; + unsigned short lo2; + unsigned short lo1; + unsigned short hi; + unsigned short pad; + unsigned pad128; + } i; + BINARY80 f; +} +BID_BINARY80LDOUBLE; +#endif + +// Pack and return binary floating-point numbers from raw fields + +#if !DECIMAL_CALL_BY_REFERENCE +#define return_binary32(s,e,c) \ + { union {UINT32 i; float f; } x_out; \ + x_out.i = (((UINT32)(s)) << 31) + \ + (((UINT32)(e)) << 23) + \ + (c); \ + return x_out.f; \ +} +#else +#define return_binary32(s,e,c) \ + { union {UINT32 i; float f; } x_out; \ + x_out.i = (((UINT32)(s)) << 31) + \ + (((UINT32)(e)) << 23) + \ + (c); \ + *pres = x_out.f; \ + return; \ +} +#endif + +#if !DECIMAL_CALL_BY_REFERENCE +#define return_binary64(s,e,c) \ + { union {UINT64 i; double f; } x_out; \ + x_out.i = (((UINT64)(s)) << 63) + \ + (((UINT64)(e)) << 52) + \ + (c); \ + return x_out.f; \ + } +#else +#define return_binary64(s,e,c) \ + { union {UINT64 i; double f; } x_out; \ + x_out.i = (((UINT64)(s)) << 63) + \ + (((UINT64)(e)) << 52) + \ + (c); \ + *pres = x_out.f; \ + return; \ + } +#endif + +#if !DECIMAL_CALL_BY_REFERENCE +#define return_binary80(s,e,c) \ + { BID_BINARY80LDOUBLE x_out; \ + x_out.i.pad128 = 0; \ + x_out.i.pad = 0; \ + x_out.i.lo4 = (c)&0xffff; \ + x_out.i.lo3 = ((c)&0xffff0000) >> 16; \ + x_out.i.lo2 = ((c)&0xffff00000000ull) >> 32; \ + x_out.i.lo1 = ((c)&0xffff000000000000ull) >> 48; \ + x_out.i.hi = (((UINT64)(s)) << 15) + \ + (e); \ + return x_out.f; \ + } +#else +#define return_binary80(s,e,c) \ + { BID_BINARY80LDOUBLE x_out; \ + x_out.i.pad128 = 0; \ + x_out.i.pad = 0; \ + x_out.i.lo4 = (c)&0xffff; \ + x_out.i.lo3 = ((c)&0xffff0000) >> 16; \ + x_out.i.lo2 = ((c)&0xffff00000000ull) >> 32; \ + x_out.i.lo1 = ((c)&0xffff000000000000ull) >> 48; \ + x_out.i.hi = ((s) << 15) + \ + (e); \ + *pres = x_out.f; \ + return; \ + } +#endif + +#if !DECIMAL_CALL_BY_REFERENCE +#define return_binary128(s,e,c_hi,c_lo) \ + { union {UINT128 i; BINARY128 f; } x_out; \ + x_out.i.w[LOW_128W] = (c_lo); \ + x_out.i.w[HIGH_128W] = (((UINT64)(s)) << 63) + \ + (((UINT64)(e)) << 48) + \ + (c_hi); \ + return x_out.f; \ + } +#else +#define return_binary128(s,e,c_hi,c_lo) \ + { union {UINT128 i; BINARY128 f; } x_out; \ + x_out.i.w[LOW_128W] = (c_lo); \ + x_out.i.w[HIGH_128W] = (((UINT64)(s)) << 63) + \ + (((UINT64)(e)) << 48) + \ + (c_hi); \ + *pres = x_out.f; \ + return; \ + } +#endif + +// Special cases of returning zero, infinity, NaN as binary FP +// Take parameters for the sign, and for NaN the significand + +#define return_binary32_zero(s) return_binary32(s,0,0) +#define return_binary32_inf(s) return_binary32(s,255,0) +#define return_binary32_nan(s,c_hi,c_lo) \ + return_binary32(s,255,(c_hi>>42)+(1ul<<22)) + +#define return_binary64_zero(s) return_binary64(s,0,0) +#define return_binary64_inf(s) return_binary64(s,2047,0) +#define return_binary64_nan(s,c_hi,c_lo) \ + return_binary64(s,2047,(c_hi>>13)+(1ull<<51)) + +#define return_binary80_zero(s) return_binary80(s,0,0) +#define return_binary80_inf(s) return_binary80(s,32767,(1ull<<63)) +#define return_binary80_nan(s,c_hi,c_lo) \ + return_binary80(s,32767,(c_hi>>2)+(3ull<<62)) + +#define return_binary128_zero(s) return_binary128(s,0,0,0) +#define return_binary128_inf(s) return_binary128(s,32767,0,0) +#define return_binary128_nan(s,c_hi,c_lo) \ + return_binary128(s,32767,(c_hi>>17)+(1ull<<47),((c_lo>>17)+(c_hi<<47))) + +// Return finite values of maximal magnitude in the various formats + +#define return_binary32_max(s) return_binary32(s,254,((1ul<<23)-1ul)) +#define return_binary64_max(s) return_binary64(s,2046,((1ull<<52)-1ull)) +#define return_binary80_max(s) return_binary80(s,32766,0xFFFFFFFFFFFFFFFFull) +#define return_binary128_max(s) \ + return_binary128(s,32766,((1ull<<48)-1ull),0xFFFFFFFFFFFFFFFFull) + +#define return_bid32_max(s) return_bid32(s,191,9999999ul) +#define return_bid64_max(s) return_bid64(s,767,9999999999999999ull) +#define return_bid128_max(s) \ + return_bid128(s,12287,542101086242752ull,4003012203950112767ull) + +// Handle overflow by either infinity or maximal value as appropriate + +#define return_binary32_ovf(s) \ +{ if ((rnd_mode==ROUNDING_TO_ZERO) || \ + (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN))) \ + return_binary32_max(s) \ + else return_binary32_inf(s) \ +} + +#define return_binary64_ovf(s) \ +{ if ((rnd_mode==ROUNDING_TO_ZERO) || \ + (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN))) \ + return_binary64_max(s) \ + else return_binary64_inf(s) \ +} + +#define return_binary80_ovf(s) \ +{ if ((rnd_mode==ROUNDING_TO_ZERO) || \ + (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN))) \ + return_binary80_max(s) \ + else return_binary80_inf(s) \ +} + +#define return_binary128_ovf(s) \ +{ if ((rnd_mode==ROUNDING_TO_ZERO) || \ + (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN))) \ + return_binary128_max(s) \ + else return_binary128_inf(s) \ +} + +#define return_bid32_ovf(s) \ +{ if ((rnd_mode==ROUNDING_TO_ZERO) || \ + (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN))) \ + return_bid32_max(s) \ + else return_bid32_inf(s) \ +} + +#define return_bid64_ovf(s) \ +{ if ((rnd_mode==ROUNDING_TO_ZERO) || \ + (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN))) \ + return_bid64_max(s) \ + else return_bid64_inf(s) \ +} + +#define return_bid128_ovf(s) \ +{ if ((rnd_mode==ROUNDING_TO_ZERO) || \ + (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN))) \ + return_bid128_max(s) \ + else return_bid128_inf(s) \ +} + +// Unpack binary floating-point number x into +// +// int s (sign in the LSB) +// int e (true "integer" exponent) +// c (normalized coefficient with explicit 1 bit) +// t (trailing zero count, valid in normalized case only) +// [c_hi,c_lo in the case of quad] +// +// Call the given zero, infinity or nan macros if appropriate + +#define unpack_binary32(x,s,e,c,t,zero,inf,nan) \ +{ union { UINT32 i; float f; } x_in; \ + x_in.f = x; \ + c = x_in.i; \ + e = (c >> 23) & ((1ull<<8)-1); \ + s = c >> 31; \ + c = c & ((1ull<<23)-1); \ + if (e == 0) \ + { int l; \ + if (c == 0) zero; \ + l = clz32(c) - (32 - 24); \ + c = c << l; \ + e = -(l + 149); \ + t = 0; \ + *pfpsf |= DENORMAL_EXCEPTION; \ + } \ + else if (e == ((1ull<<8)-1)) \ + { if (c == 0) inf; \ + if ((c&(1ul<<22))==0) *pfpsf |= INVALID_EXCEPTION; \ + nan(s,(((unsigned long long) c)) << 42,0ull) \ + } \ + else \ + { c += 1ull<<23; \ + t = ctz32(c); \ + e -= 150; \ + } \ +} + +#define unpack_binary64(x,s,e,c,t,zero,inf,nan) \ +{ union { UINT64 i; double f; } x_in; \ + x_in.f = x; \ + c = x_in.i; \ + e = (c >> 52) & ((1ull<<11)-1); \ + s = c >> 63; \ + c = c & ((1ull<<52)-1); \ + if (e == 0) \ + { int l; \ + if (c == 0) zero; \ + l = clz64(c) - (64 - 53); \ + c = c << l; \ + e = -(l + 1074); \ + t = 0; \ + *pfpsf |= DENORMAL_EXCEPTION; \ + } \ + else if (e == ((1ull<<11)-1)) \ + { if (c == 0) inf; \ + if ((c&(1ull<<51))==0) *pfpsf |= INVALID_EXCEPTION; \ + nan(s,(((unsigned long long) c) << 13),0ull) \ + } \ + else \ + { c += 1ull<<52; \ + t = ctz64(c); \ + e -= 1075; \ + } \ +} + +#define unpack_binary80(x,s,e,c,t,zero,inf,nan) \ +{ BID_BINARY80LDOUBLE x_in; \ + x_in.f = x; \ + c = x_in.i.lo4 + ((UINT64)x_in.i.lo3 << 16) + \ + ((UINT64)x_in.i.lo2 << 32) + ((UINT64)x_in.i.lo1 << 48); \ + e = x_in.i.hi; \ + s = e >> 15; \ + e = (e & ((1<<15)-1)); \ + if (e == 0) \ + { int l; \ + if (c == 0) zero; \ + l = clz64(c); \ + c = c << l; \ + e -= (l + 16445); \ + t = 0; \ + *pfpsf |= DENORMAL_EXCEPTION; \ + } \ + else if (e == ((1ull<<15)-1)) \ + { if ((c & ((1ull<<63)-1)) == 0) inf; \ + if ((c&(1ull<<62))==0) *pfpsf |= INVALID_EXCEPTION; \ + nan(s,(((unsigned long long) c) << 2),0ull) \ + } \ + else \ + { t = ctz64(c); \ + e -= 16446; \ + } \ +} + +#define unpack_binary128(x,s,e,c_hi,c_lo,t,zero,inf,nan) \ +{ union { UINT128 i; BINARY128 f; } x_in; \ + x_in.f = x; \ + c_lo = x_in.i.w[LOW_128W]; \ + c_hi = x_in.i.w[HIGH_128W]; \ + e = (c_hi >> 48) & ((1ull<<15)-1); \ + s = c_hi >> 63; \ + c_hi = c_hi & ((1ull<<48)-1); \ + if (e == 0) \ + { int l; \ + if ((c_hi == 0) && (c_lo == 0)) zero; \ + l = clz128(c_hi,c_lo) - (128 - 113); \ + sll128(c_hi,c_lo,l); \ + e = -(l + 16494); \ + t = 0; \ + *pfpsf |= DENORMAL_EXCEPTION; \ + } \ + else if (e == ((1ull<<15)-1)) \ + { if ((c_hi == 0) && (c_lo == 0)) inf; \ + if ((c_hi&(1ull<<47))==0) *pfpsf |= INVALID_EXCEPTION; \ + nan(s,((((unsigned long long) c_hi) << 17) + \ + (((unsigned long long) c_lo) >> 47)), \ + (((unsigned long long) c_lo) << 17)) \ + } \ + else \ + { c_hi += 1ull<<48; \ + t = ctz128(c_hi,c_lo); \ + e -= 16495; \ + } \ +} + +// Pack and return decimal number from raw fields + +#if !DECIMAL_CALL_BY_REFERENCE +#define return_bid32(s,e,c) \ + { if ((UINT32) (c) < (1ul<<23)) \ + return (((UINT32) (s) << 31) + ((UINT32) (e) << 23) + (UINT32) (c)); \ + else \ + return (((UINT32) (s) << 31) + ((0x3ull<<29) - (1ull<<23)) + \ + ((UINT32) (e) << 21) + (UINT32) (c)); \ + } +#else +#define return_bid32(s,e,c) \ + { if ((UINT32) (c) < (1ul<<23)) \ + *pres = (((UINT32) (s) << 31) + ((UINT32) (e) << 23) + (UINT32) (c)); \ + else \ + *pres = (((UINT32) (s) << 31) + ((0x3ull<<29) - (1ull<<23)) + \ + ((UINT32) (e) << 21) + (UINT32) (c)); \ + return; \ + } +#endif + +#if !DECIMAL_CALL_BY_REFERENCE +#define return_bid64(s,e,c) \ + { if ((c) < (1ull<<53)) \ + return (((UINT64) (s) << 63) + ((UINT64) (e) << 53) + (c)); \ + else \ + return (((UINT64) (s) << 63) + ((0x3ull<<61) - (1ull<<53)) + \ + ((UINT64) (e) << 51) + (c)); \ + } +#else +#define return_bid64(s,e,c) \ + { if ((c) < (1ull<<53)) \ + *pres = (((UINT64) (s) << 63) + ((UINT64) (e) << 53) + (c)); \ + else \ + *pres = (((UINT64) (s) << 63) + ((0x3ull<<61) - (1ull<<53)) + \ + ((UINT64) (e) << 51) + (c)); \ + return; \ + } +#endif + +#if !DECIMAL_CALL_BY_REFERENCE +#define return_bid128(s,e,c_hi,c_lo) \ + { UINT128 x_out; \ + x_out.w[LOW_128W] = c_lo; \ + x_out.w[HIGH_128W] = ((UINT64) (s) << 63) + ((UINT64) (e) << 49) + \ + (c_hi); \ + return x_out; \ + } +#else +#define return_bid128(s,e,c_hi,c_lo) \ + { UINT128 x_out; \ + x_out.w[LOW_128W] = c_lo; \ + x_out.w[HIGH_128W] = ((UINT64) (s) << 63) + ((UINT64) (e) << 49) + (c_hi); \ + *pres = x_out; \ + return; \ + } +#endif + +// Special cases of returning zero, infinity, NaN as decimal FP +// Take parameters for the sign, and for NaN the significand + +#define return_bid32_zero(s) return_bid32(s,101,0) +#define return_bid32_inf(s) return_bid32(s,(0xF<<4),0) +#define return_bid32_nan(s,c_hi,c_lo) \ + return_bid32(s,(0x1F<<3),(((c_hi>>44) > 999999ul) ? 0 : (c_hi>>44))); + +#define return_bid64_zero(s) return_bid64(s,398,0) +#define return_bid64_inf(s) return_bid64(s,(0xF<<6),0) +#define return_bid64_nan(s,c_hi,c_lo) \ + return_bid64(s,(0x1F<<5), \ + (((c_hi>>14) > 999999999999999ull) ? 0 : (c_hi>>14))); + +#define return_bid128_zero(s) return_bid128(s,6176,0,0) +#define return_bid128_inf(s) return_bid128(s,(0xF<<10),0,0) +#define return_bid128_nan(s,c_hi,c_lo) \ + { if (lt128(54210108624275ull,4089650035136921599ull, \ + (c_hi>>18),((c_lo>>18)+(c_hi<<46)))) \ + return_bid128(s,(0x1F<<9),0ull,0ull) \ + else return_bid128(s,(0x1F<<9),(c_hi>>18),((c_lo>>18)+(c_hi<<46))) \ + } + +// Unpack decimal floating-point number x into sign,exponent,coefficient +// In special cases, call the macros provided +// Coefficient is normalized in the binary sense with postcorrection k, +// so that x = 10^e * c / 2^k and the range of c is: +// +// 2^23 <= c < 2^24 (decimal32) +// 2^53 <= c < 2^54 (decimal64) +// 2^112 <= c < 2^113 (decimal128) + +#define unpack_bid32(x,s,e,k,c,zero,inf,nan) \ +{ s = x >> 31; \ + if ((x & (3ull<<29)) == (3ull<<29)) \ + { if ((x & (0xFull<<27)) == (0xFull<<27)) \ + { if ((x & (0x1Full<<26)) != (0x1Full<<26)) inf; \ + if ((x & (1ul<<25))!=0) *pfpsf |= INVALID_EXCEPTION; \ + nan(s,((((x) & 0xFFFFul) > 999999ul) ? 0 : \ + (((unsigned long long) x) << 44)),0ull); \ + } \ + e = ((x >> 21) & ((1ull<<8)-1)) - 101; \ + c = (1ull<<23) + (x & ((1ull<<21)-1)); \ + if ((unsigned long)(c) > 9999999ul) c = 0; \ + k = 0; \ + } \ + else \ + { e = ((x >> 23) & ((1ull<<8)-1)) - 101; \ + c = x & ((1ull<<23)-1); \ + if (c == 0) zero; \ + k = clz32(c) - 8; \ + c = c << k; \ + } \ +} + +#define unpack_bid64(x,s,e,k,c,zero,inf,nan) \ +{ s = x >> 63; \ + if ((x & (3ull<<61)) == (3ull<<61)) \ + { if ((x & (0xFull<<59)) == (0xFull<<59)) \ + { if ((x & (0x1Full<<58)) != (0x1Full<<58)) inf; \ + if ((x & (1ull<<57))!=0) *pfpsf |= INVALID_EXCEPTION; \ + nan(s,((((x) & 0x3FFFFFFFFFFFFull) > 999999999999999ull) ? 0 : \ + (((unsigned long long) x) << 14)),0ull); \ + } \ + e = ((x >> 51) & ((1ull<<10)-1)) - 398; \ + c = (1ull<<53) + (x & ((1ull<<51)-1)); \ + if ((unsigned long long)(c) > 9999999999999999ull) c = 0; \ + k = 0; \ + } \ + else \ + { e = ((x >> 53) & ((1ull<<10)-1)) - 398; \ + c = x & ((1ull<<53)-1); \ + if (c == 0) zero; \ + k = clz64(c) - 10; \ + c = c << k; \ + } \ +} + +#define unpack_bid128(x,s,e,k,c,zero,inf,nan) \ +{ s = x.w[HIGH_128W] >> 63; \ + if ((x.w[HIGH_128W] & (3ull<<61)) == (3ull<<61)) \ + { if ((x.w[HIGH_128W] & (0xFull<<59)) == (0xFull<<59)) \ + { if ((x.w[HIGH_128W] & (0x1Full<<58)) != (0x1Full<<58)) inf; \ + if ((x.w[HIGH_128W] & (1ull<<57))!=0) \ + *pfpsf |= INVALID_EXCEPTION; \ + if (lt128(54210108624275ull,4089650035136921599ull, \ + (x.w[HIGH_128W] & 0x3FFFFFFFFFFFull),x.w[LOW_128W])) \ + nan(s,0ull,0ull); \ + nan(s,((((unsigned long long) x.w[HIGH_128W]) << 18) + \ + (((unsigned long long) x.w[LOW_128W]) >> 46)), \ + (((unsigned long long) x.w[LOW_128W]) << 18)); \ + } \ + zero; \ + } \ + else \ + { e = ((x.w[HIGH_128W] >> 49) & ((1ull<<14)-1)) - 6176; \ + c.w[1] = x.w[HIGH_128W] & ((1ull<<49)-1); \ + c.w[0] = x.w[LOW_128W]; \ + if (lt128(542101086242752ull,4003012203950112767ull, \ + c.w[1],c.w[0])) \ + { c.w[1] = 0ull; c.w[0] = 0ull; } \ + if ((c.w[1] == 0) && (c.w[0] == 0)) zero; \ + k = clz128(c.w[1],c.w[0]) - 15; \ + sll128(c.w[1],c.w[0],k); \ + } \ +} + +// Rounding boundaries table, indexed by +// 4 * rounding_mode + 2 * sign + lsb of truncation +// We round up if the round/sticky data is strictly > this boundary +// +// NB: This depends on the particular values of the rounding mode +// numbers, which are supposed to be defined as here: +// +// #define ROUNDING_TO_NEAREST 0x00000 +// #define ROUNDING_DOWN 0x00001 +// #define ROUNDING_UP 0x00002 +// #define ROUNDING_TO_ZERO 0x00003 +// #define ROUNDING_TIES_AWAY 0x00004 +// +// Some of the shortcuts below in "underflow after rounding" also use +// the concrete values. +// +// So we add a directive here to double-check that this is the case + +#if ((ROUNDING_TO_NEAREST!=0) || (ROUNDING_DOWN!=1) || \ + (ROUNDING_UP!=2) || (ROUNDING_TO_ZERO!=3) || \ + (ROUNDING_TIES_AWAY!=4)) +#error "Rounding mode numbers don't match tables for binary/decimal conversion" +#endif + +static const UINT128 roundbound_128[] = { {{0ull, (1ull << 63)}}, // ROUNDING_TO_NEAREST | positive | even +{{~0ull, (1ull << 63) - 1}}, // ROUNDING_TO_NEAREST | positive | odd +{{0ull, (1ull << 63)}}, // ROUNDING_TO_NEAREST | negative | even +{{~0ull, (1ull << 63) - 1}}, // ROUNDING_TO_NEAREST | negative | odd + +{{~0ull, ~0ull}}, // ROUNDING_DOWN | positive | even +{{~0ull, ~0ull}}, // ROUNDING_DOWN | positive | odd +{{0ull, 0ull}}, // ROUNDING_DOWN | negative | even +{{0ull, 0ull}}, // ROUNDING_DOWN | negative | odd + +{{0ull, 0ull}}, // ROUNDING_UP | positive | even +{{0ull, 0ull}}, // ROUNDING_UP | positive | odd +{{~0ull, ~0ull}}, // ROUNDING_UP | negative | even +{{~0ull, ~0ull}}, // ROUNDING_UP | negative | odd + +{{~0ull, ~0ull}}, // ROUNDING_TO_ZERO | positive | even +{{~0ull, ~0ull}}, // ROUNDING_TO_ZERO | positive | odd +{{~0ull, ~0ull}}, // ROUNDING_TO_ZERO | negative | even +{{~0ull, ~0ull}}, // ROUNDING_TO_ZERO | negative | odd + +{{~0ull, (1ull << 63) - 1}}, // ROUNDING_TIES_AWAY | positive | even +{{~0ull, (1ull << 63) - 1}}, // ROUNDING_TIES_AWAY | positive | odd +{{~0ull, (1ull << 63) - 1}}, // ROUNDING_TIES_AWAY | negative | even +{{~0ull, (1ull << 63) - 1}} // ROUNDING_TIES_AWAY | negative | odd +}; + +// Table of powers of 5 + +static const UINT128 power_five[] = { {{1ull, 0ull}}, +{{5ull, 0ull}}, +{{25ull, 0ull}}, +{{125ull, 0ull}}, +{{625ull, 0ull}}, +{{3125ull, 0ull}}, +{{15625ull, 0ull}}, +{{78125ull, 0ull}}, +{{390625ull, 0ull}}, +{{1953125ull, 0ull}}, +{{9765625ull, 0ull}}, +{{48828125ull, 0ull}}, +{{244140625ull, 0ull}}, +{{1220703125ull, 0ull}}, +{{6103515625ull, 0ull}}, +{{30517578125ull, 0ull}}, +{{152587890625ull, 0ull}}, +{{762939453125ull, 0ull}}, +{{3814697265625ull, 0ull}}, +{{19073486328125ull, 0ull}}, +{{95367431640625ull, 0ull}}, +{{476837158203125ull, 0ull}}, +{{2384185791015625ull, 0ull}}, +{{11920928955078125ull, 0ull}}, +{{59604644775390625ull, 0ull}}, +{{298023223876953125ull, 0ull}}, +{{1490116119384765625ull, 0ull}}, +{{7450580596923828125ull, 0ull}}, +{{359414837200037393ull, 2ull}}, +{{1797074186000186965ull, 10ull}}, +{{8985370930000934825ull, 50ull}}, +{{8033366502585570893ull, 252ull}}, +{{3273344365508751233ull, 1262ull}}, +{{16366721827543756165ull, 6310ull}}, +{{8046632842880574361ull, 31554ull}}, +{{3339676066983768573ull, 157772ull}}, +{{16698380334918842865ull, 788860ull}}, +{{9704925379756007861ull, 3944304ull}}, +{{11631138751360936073ull, 19721522ull}}, +{{2815461535676025517ull, 98607613ull}}, +{{14077307678380127585ull, 493038065ull}}, +{{15046306170771983077ull, 2465190328ull}}, +{{1444554559021708921ull, 12325951644ull}}, +{{7222772795108544605ull, 61629758220ull}}, +{{17667119901833171409ull, 308148791101ull}}, +{{14548623214327650581ull, 1540743955509ull}}, +{{17402883850509598057ull, 7703719777548ull}}, +{{13227442957709783821ull, 38518598887744ull}}, +{{10796982567420264257ull, 192592994438723ull}} +}; + + +// Tables of values for the various conversions: +// +// exponents: table of output exponents +// breakpoints: test values to decide between two possible exponents +// multipliers1/multipliers2: corresponding reciprocal multipliers +// coefflimits: used in exactness checks +// + +static const UINT128 breakpoints_binary32[] = + { {{17291492046443221751ull, 474778387287989ull}}, +{{17522542451896487724ull, 379822709830391ull}}, +{{10328685146775279856ull, 303858167864313ull}}, +{{12836547420098537447ull, 486173068582901ull}}, +{{6579889121336919634ull, 388938454866321ull}}, +{{1574562482327625384ull, 311150763893057ull}}, +{{6208648786466110938ull, 497841222228891ull}}, +{{1277570214430978427ull, 398272977783113ull}}, +{{8400753801028603388ull, 318618382226490ull}}, +{{13441206081645765421ull, 509789411562384ull}}, +{{14442313680058522660ull, 407831529249907ull}}, +{{4175153314562997481ull, 326265223399926ull}}, +{{17748291747526526940ull, 522024357439881ull}}, +{{10509284583279311229ull, 417619485951905ull}}, +{{8407427666623448983ull, 334095588761524ull}}, +{{2383837822371787403ull, 534552942018439ull}}, +{{5596419072639340246ull, 427642353614751ull}}, +{{787786443369561873ull, 342113882891801ull}}, +{{12328504753617029967ull, 547382212626881ull}}, +{{6173454988151713650ull, 437905770101505ull}}, +{{4938763990521370920ull, 350324616081204ull}}, +{{15280720014318014119ull, 560519385729926ull}}, +{{8535227196712500972ull, 448415508583941ull}}, +{{3138832942628090454ull, 358732406867153ull}}, +{{9889763983586293010ull, 286985925493722ull}}, +{{1066227114770427523ull, 459177480789956ull}}, +{{15610376950783983311ull, 367341984631964ull}}, +{{16177650375369096972ull, 293873587705571ull}}, +{{58798897397182893ull, 470197740328915ull}}, +{{47039117917746314ull, 376158192263132ull}}, +{{11105677738559928021ull, 300926553810505ull}}, +{{17769084381695884834ull, 481482486096808ull}}, +{{3147221061130976897ull, 385185988877447ull}}, +{{13585823293130512487ull, 308148791101957ull}}, +{{6979922010041178687ull, 493038065763132ull}}, +{{16651984052258673919ull, 394430452610505ull}}, +{{13321587241806939135ull, 315544362088404ull}}, +{{10246493142665371647ull, 504870979341447ull}}, +{{818496884648476671ull, 403896783473158ull}}, +{{8033495137202601983ull, 323117426778526ull}}, +{{5474894590040342527ull, 516987882845642ull}}, +{{15447962116258004991ull, 413590306276513ull}}, +{{1290323248780673023ull, 330872245021211ull}}, +{{13132563642274807807ull, 529395592033937ull}}, +{{3127353284336025599ull, 423516473627150ull}}, +{{2501882627468820479ull, 338813178901720ull}}, +{{4003012203950112767ull, 542101086242752ull}}, +{{14270456207385821183ull, 433680868994201ull}}, +{{7727016151166746623ull, 346944695195361ull}}, +{{4984528212382973951ull, 555111512312578ull}}, +{{11366320199390199807ull, 444089209850062ull}}, +{{1714358530028339199ull, 355271367880050ull}}, +{{1371486824022671359ull, 284217094304040ull}}, +{{2194378918436274175ull, 454747350886464ull}}, +{{5444851949490929663ull, 363797880709171ull}}, +{{666532744850833407ull, 291038304567337ull}}, +{{4755801206503243775ull, 465661287307739ull}}, +{{7493989779944505343ull, 372529029846191ull}}, +{{2305843009213693951ull, 298023223876953ull}}, +{{18446744073709551615ull, 476837158203124ull}}, +{{18446744073709551615ull, 381469726562499ull}}, +{{18446744073709551615ull, 305175781249999ull}}, +{{18446744073709551615ull, 488281249999999ull}}, +{{18446744073709551615ull, 390624999999999ull}}, +{{18446744073709551615ull, 312499999999999ull}}, +{{18446744073709551615ull, 499999999999999ull}}, +{{18446744073709551615ull, 399999999999999ull}}, +{{18446744073709551615ull, 319999999999999ull}}, +{{18446744073709551615ull, 511999999999999ull}}, +{{18446744073709551615ull, 409599999999999ull}}, +{{18446744073709551615ull, 327679999999999ull}}, +{{18446744073709551615ull, 524287999999999ull}}, +{{18446744073709551615ull, 419430399999999ull}}, +{{18446744073709551615ull, 335544319999999ull}}, +{{18446744073709551615ull, 536870911999999ull}}, +{{18446744073709551615ull, 429496729599999ull}}, +{{18446744073709551615ull, 343597383679999ull}}, +{{18446744073709551615ull, 549755813887999ull}}, +{{18446744073709551615ull, 439804651110399ull}}, +{{18446744073709551615ull, 351843720888319ull}}, +{{18446744073709551615ull, 281474976710655ull}}, +{{11068046444225730969ull, 450359962737049ull}}, +{{12543785970122495098ull, 360287970189639ull}}, +{{13724377590839906402ull, 288230376151711ull}}, +{{14580306515860029597ull, 461168601842738ull}}, +{{596198768462292708ull, 368934881474191ull}}, +{{15234354273737475459ull, 295147905179352ull}}, +{{9617571579012319442ull, 472236648286964ull}}, +{{11383406077951765876ull, 377789318629571ull}}, +{{5417376047619502378ull, 302231454903657ull}}, +{{12357150490933114128ull, 483570327845851ull}}, +{{6196371578004580979ull, 386856262276681ull}}, +{{1267748447661754460ull, 309485009821345ull}}, +{{2028397516258807136ull, 495176015714152ull}}, +{{12690764457232776679ull, 396140812571321ull}}, +{{6463262751044311020ull, 316912650057057ull}}, +{{14030569216412807955ull, 507060240091291ull}}, +{{7535106558388336041ull, 405648192073033ull}}, +{{13406782876194489479ull, 324518553658426ull}}, +{{14072154972427362520ull, 519229685853482ull}}, +{{3879026348458069369ull, 415383748682786ull}}, +{{17860616337734096788ull, 332306998946228ull}}, +{{6440893251923092922ull, 531691198313966ull}}, +{{1463365786796564015ull, 425352958651173ull}}, +{{8549390258921071858ull, 340282366920938ull}}, +{{9989675599531804650ull, 544451787073501ull}}, +{{4302391664883533397ull, 435561429658801ull}}, +{{18199308590874468010ull, 348449143727040ull}}, +{{10672149671689597200ull, 557518629963265ull}}, +{{8537719737351677760ull, 446014903970612ull}}, +{{17898222234107073178ull, 356811923176489ull}}, +{{18007926602027568865ull, 285449538541191ull}}, +{{2987240860050737922ull, 456719261665907ull}}, +{{13457839132266321307ull, 365375409332725ull}}, +{{10766271305813057046ull, 292300327466180ull}}, +{{17226034089300891273ull, 467680523945888ull}}, +{{2712780827214982049ull, 374144419156711ull}}, +{{16927619920739626932ull, 299315535325368ull}}, +{{4948098984731941152ull, 478904856520590ull}}, +{{3958479187785552922ull, 383123885216472ull}} +}; + +static const int exponents_binary32[] = { -27, + -24, + -21, + -17, + -14, + -11, + -7, + -4, + -1, + 3, + 6, + 9, + 13, + 16, + 19, + 23, + 26, + 29, + 33, + 36, + 39, + 43, + 46, + 49, + 52, + 56, + 59, + 62, + 66, + 69, + 72, + 76, + 79, + 82, + 86, + 89, + 92, + 96, + 99, + 102, + 106, + 109, + 112, + 116, + 119, + 122, + 126, + 129, + 132, + 136, + 139, + 142, + 145, + 149, + 152, + 155, + 159, + 162, + 165, + 169, + 172, + 175, + 179, + 182, + 185, + 189, + 192, + 195, + 199, + 202, + 205, + 209, + 212, + 215, + 219, + 222, + 225, + 229, + 232, + 235, + 238, + 242, + 245, + 248, + 252, + 255, + 258, + 262, + 265, + 268, + 272, + 275, + 278, + 282, + 285, + 288, + 292, + 295, + 298, + 302, + 305, + 308, + 312, + 315, + 318, + 322, + 325, + 328, + 332, + 335, + 338, + 341, + 345, + 348, + 351, + 355, + 358, + 361, + 365, + 368, +}; + +static const UINT256 multipliers1_binary32[] = + { {{6013890151484785128ull, 7481633477359093489ull, + 655737588518723529ull, 651851512427ull}}, +{{12129048707783369314ull, 13963727865126254765ull, + 14654730040930568123ull, 814814390533ull}}, +{{1326252829447047930ull, 12842973812980430553ull, + 4483354495881046442ull, 1018517988167ull}}, +{{12358123064472874716ull, 12638544651540156999ull, + 9719625587566735882ull, 636573742604ull}}, +{{10835967812163705491ull, 6574808777570420441ull, + 12149531984458419853ull, 795717178255ull}}, +{{18156645783632019768ull, 12830196990390413455ull, + 10575228962145636912ull, 994646472819ull}}, +{{18265432642411094211ull, 8018873118994008409ull, + 4303675092127329118ull, 621654045512ull}}, +{{8996732747731704052ull, 800219361887734704ull, 5379593865159161398ull, + 777067556890ull}}, +{{11245915934664630065ull, 10223646239214444188ull, + 15947864368303727555ull, 971334446112ull}}, +{{16252069496020169599ull, 4083935890295333665ull, + 9967415230189829722ull, 607084028820ull}}, +{{6480028814743048286ull, 14328291899723942890ull, + 12459269037737287152ull, 758855036025ull}}, +{{17323408055283586166ull, 17910364874654928612ull, + 1739028241889445228ull, 948568795032ull}}, +{{1603757997697465546ull, 1970606009804554575ull, + 1086892651180903268ull, 592855496895ull}}, +{{15839755552403995644ull, 2463257512255693218ull, + 15193673869258292797ull, 741069371118ull}}, +{{10576322403650218747ull, 7690757908747004427ull, + 9768720299718090188ull, 926336713898ull}}, +{{4304358493067692765ull, 14030095729821653575ull, + 10717136205751194271ull, 578960446186ull}}, +{{768762097907228052ull, 12925933643849679065ull, + 4173048220334217031ull, 723700557733ull}}, +{{5572638640811422969ull, 11545731036384710927ull, + 9827996293845159193ull, 904625697166ull}}, +{{10400428178148221212ull, 298552870099362473ull, + 1530811665225836592ull, 565391060729ull}}, +{{17612221241112664419ull, 373191087624203091ull, + 6525200599959683644ull, 706738825911ull}}, +{{17403590532963442619ull, 466488859530253864ull, + 3544814731522216651ull, 883423532389ull}}, +{{10877244083102151637ull, 16432456601702266329ull, + 4521352216415079358ull, 552139707743ull}}, +{{18208241122305077450ull, 11317198715273057103ull, + 1040004252091461294ull, 690174634679ull}}, +{{18148615384453958909ull, 4923126357236545571ull, + 15135063370396490330ull, 862718293348ull}}, +{{18074083212140060732ull, 15377279983400457772ull, + 472085139286061296ull, 1078397866686ull}}, +{{2072929970732762150ull, 9610799989625286108ull, + 14130111267335952022ull, 673998666678ull}}, +{{2591162463415952687ull, 2790127950176831827ull, + 8439267047315164220ull, 842498333348ull}}, +{{17074011134552104570ull, 3487659937721039783ull, + 10549083809143955275ull, 1053122916685ull}}, +{{17588785986736147213ull, 18320688525571507528ull, + 8899020389928665998ull, 658201822928ull}}, +{{3539238409710632400ull, 13677488620109608603ull, + 11123775487410832498ull, 822752278660ull}}, +{{18259106067420454212ull, 7873488738282234945ull, + 13904719359263540623ull, 1028440348325ull}}, +{{4494412264496702026ull, 11838459489067478697ull, + 10996292608753406841ull, 642775217703ull}}, +{{10229701349048265437ull, 963016306052184659ull, + 9133679742514370648ull, 803469022129ull}}, +{{8175440667882943892ull, 1203770382565230824ull, + 16028785696570351214ull, 1004336277661ull}}, +{{5109650417426839933ull, 14587414544385432977ull, + 12323834069570163460ull, 627710173538ull}}, +{{10998749040210937820ull, 18234268180481791221ull, + 6181420550107928517ull, 784637716923ull}}, +{{18360122318691060179ull, 8957777170320075314ull, + 3115089669207522743ull, 980797146154ull}}, +{{16086762467609300516ull, 12516139759091128927ull, + 6558617061682089618ull, 612998216346ull}}, +{{15496767066084237741ull, 6421802662009135351ull, + 17421643363957387831ull, 766247770432ull}}, +{{14759272814177909272ull, 3415567309084031285ull, + 3330310131237183173ull, 957809713041ull}}, +{{11530388518074887247ull, 4440572577391213505ull, + 13610658878091709243ull, 598631070650ull}}, +{{577927592311445347ull, 939029703311628978ull, 7789951560759860746ull, + 748288838313ull}}, +{{9945781527244082491ull, 10397159165994312030ull, + 14349125469377213836ull, 935361047891ull}}, +{{1604427436100163653ull, 15721596515601220827ull, + 6662360409147064695ull, 584600654932ull}}, +{{15840592350407368278ull, 15040309626074138129ull, + 8327950511433830869ull, 730750818665ull}}, +{{5965682382727046636ull, 4965328977310508950ull, + 15021624157719676491ull, 913438523331ull}}, +{{17563609544486567859ull, 797487601605374141ull, + 7082672089361103855ull, 570899077082ull}}, +{{8119453875326046112ull, 14831917557288881389ull, + 18076712148556155626ull, 713623846352ull}}, +{{14761003362584945544ull, 9316524909756325928ull, + 4149146111985642917ull, 892029807941ull}}, +{{9225627101615590965ull, 8128671077811397657ull, + 4899059329204720775ull, 557518629963ull}}, +{{16143719895446876610ull, 5549152828836859167ull, + 1512138143078513065ull, 696898287454ull}}, +{{15567963850881207859ull, 11548127054473461863ull, + 11113544715702917139ull, 871122859317ull}}, +{{14848268795174121920ull, 9823472799664439425ull, 56872839346482712ull, + 1088903574147ull}}, +{{2362638969342744344ull, 6139670499790274641ull, + 16176446589087409359ull, 680564733841ull}}, +{{7564984730105818334ull, 3062902106310455397ull, + 6385500181077097987ull, 850705917302ull}}, +{{14067916931059660821ull, 17663685688170232958ull, + 17205247263201148291ull, 1063382396627ull}}, +{{4180762063484900109ull, 8733960545892701647ull, + 8447436530287023730ull, 664613997892ull}}, +{{614266560928737233ull, 1694078645511101251ull, + 10559295662858779663ull, 830767497365ull}}, +{{14602891256443085253ull, 15952656362171040275ull, + 17810805597000862482ull, 1038459371706ull}}, +{{6820964026063234331ull, 14582096244784288076ull, + 15743439516552926955ull, 649037107316ull}}, +{{8526205032579042914ull, 13615934287552972191ull, + 1232555321981607078ull, 811296384146ull}}, +{{6046070272296415738ull, 7796545822586439431ull, + 10764066189331784656ull, 1014120480182ull}}, +{{10696322947826341692ull, 4872841139116524644ull, + 2115855349904977506ull, 633825300114ull}}, +{{13370403684782927115ull, 15314423460750431613ull, + 11868191224235997690ull, 792281625142ull}}, +{{2877946550696495182ull, 9919657289083263709ull, + 5611866993440221305ull, 990352031428ull}}, +{{4104559603399003441ull, 17729000851745509578ull, + 12730788907754914123ull, 618970019642ull}}, +{{14354071541103530109ull, 17549565046254499068ull, + 6690114097838866846ull, 773712524553ull}}, +{{17942589426379412636ull, 12713584270963348027ull, + 12974328640725971462ull, 967140655691ull}}, +{{8908275382273438946ull, 3334304150924704613ull, + 5803112391240038212ull, 604462909807ull}}, +{{15747030246269186586ull, 4167880188655880766ull, + 2642204470622659861ull, 755578637259ull}}, +{{10460415770981707425ull, 9821536254247238862ull, + 17137813643560488538ull, 944473296573ull}}, +{{1926073838436179237ull, 10750146177331912193ull, + 13016976536438999288ull, 590295810358ull}}, +{{7019278316472611950ull, 13437682721664890241ull, + 7047848633693973302ull, 737869762948ull}}, +{{13385783914018152841ull, 7573731365226336993ull, + 8809810792117466628ull, 922337203685ull}}, +{{1448585918620263670ull, 13956954140121236429ull, + 7811974754287110594ull, 576460752303ull}}, +{{6422418416702717491ull, 8222820638296769728ull, + 5153282424431500339ull, 720575940379ull}}, +{{8028023020878396864ull, 5666839779443574256ull, + 1829917012111987520ull, 900719925474ull}}, +{{5017514388048998040ull, 3541774862152233910ull, + 5755384150997380104ull, 562949953421ull}}, +{{15495265021916023358ull, 4427218577690292387ull, + 11805916207174113034ull, 703687441776ull}}, +{{14757395258967641293ull, 14757395258967641292ull, + 14757395258967641292ull, 879609302220ull}}, +{{0ull, 0ull, 0ull, 1099511627776ull}}, +{{0ull, 0ull, 0ull, 687194767360ull}}, +{{0ull, 0ull, 0ull, 858993459200ull}}, +{{0ull, 0ull, 0ull, 1073741824000ull}}, +{{0ull, 0ull, 0ull, 671088640000ull}}, +{{0ull, 0ull, 0ull, 838860800000ull}}, +{{0ull, 0ull, 0ull, 1048576000000ull}}, +{{0ull, 0ull, 0ull, 655360000000ull}}, +{{0ull, 0ull, 0ull, 819200000000ull}}, +{{0ull, 0ull, 0ull, 1024000000000ull}}, +{{0ull, 0ull, 0ull, 640000000000ull}}, +{{0ull, 0ull, 0ull, 800000000000ull}}, +{{0ull, 0ull, 0ull, 1000000000000ull}}, +{{0ull, 0ull, 0ull, 625000000000ull}}, +{{0ull, 0ull, 0ull, 781250000000ull}}, +{{0ull, 0ull, 0ull, 976562500000ull}}, +{{0ull, 0ull, 0ull, 610351562500ull}}, +{{0ull, 0ull, 0ull, 762939453125ull}}, +{{0ull, 0ull, 4611686018427387904ull, 953674316406ull}}, +{{0ull, 0ull, 16717361816799281152ull, 596046447753ull}}, +{{0ull, 0ull, 7061644215716937728ull, 745058059692ull}}, +{{0ull, 0ull, 8827055269646172160ull, 931322574615ull}}, +{{0ull, 0ull, 12434438571169939456ull, 582076609134ull}}, +{{0ull, 0ull, 6319676177107648512ull, 727595761418ull}}, +{{0ull, 0ull, 17122967258239336448ull, 909494701772ull}}, +{{0ull, 0ull, 1478482499544809472ull, 568434188608ull}}, +{{0ull, 0ull, 1848103124431011840ull, 710542735760ull}}, +{{0ull, 0ull, 2310128905538764800ull, 888178419700ull}}, +{{0ull, 0ull, 10667202602816503808ull, 555111512312ull}}, +{{0ull, 0ull, 13334003253520629760ull, 693889390390ull}}, +{{0ull, 0ull, 7444132030046011392ull, 867361737988ull}}, +{{0ull, 0ull, 9305165037557514240ull, 1084202172485ull}}, +{{0ull, 0ull, 8121571157687140352ull, 677626357803ull}}, +{{0ull, 0ull, 5540277928681537536ull, 847032947254ull}}, +{{0ull, 0ull, 16148719447706697728ull, 1058791184067ull}}, +{{0ull, 0ull, 7787106645602992128ull, 661744490042ull}}, +{{0ull, 0ull, 510511270148964352ull, 827180612553ull}}, +{{0ull, 0ull, 5249825106113593344ull, 1033975765691ull}}, +{{0ull, 0ull, 975297682107301888ull, 646234853557ull}}, +{{0ull, 0ull, 5830808121061515264ull, 807793566946ull}} +}; + +static const UINT256 multipliers2_binary32[] = + { {{12230317112597168372ull, 12964188775534322552ull, + 9551240831114137572ull, 325925756213ull}}, +{{15287896390746460465ull, 16205235969417903190ull, + 16550737057320059869ull, 407407195266ull}}, +{{9886498451578299773ull, 6421486906490215276ull, + 11465049284795299029ull, 509258994083ull}}, +{{15402433569091213166ull, 6319272325770078499ull, + 4859812793783367941ull, 318286871302ull}}, +{{14641355942936628554ull, 12510776425639986028ull, + 15298138029083985734ull, 397858589127ull}}, +{{18301694928670785692ull, 6415098495195206727ull, + 14510986517927594264ull, 497323236409ull}}, +{{18356088358060322914ull, 4009436559497004204ull, + 2151837546063664559ull, 310827022756ull}}, +{{4498366373865852026ull, 400109680943867352ull, 2689796932579580699ull, + 388533778445ull}}, +{{5622957967332315033ull, 14335195156461997902ull, + 7973932184151863777ull, 485667223056ull}}, +{{17349406784864860608ull, 2041967945147666832ull, + 4983707615094914861ull, 303542014410ull}}, +{{3240014407371524143ull, 7164145949861971445ull, + 15453006555723419384ull, 379427518012ull}}, +{{8661704027641793083ull, 8955182437327464306ull, 869514120944722614ull, + 474284397516ull}}, +{{10025251035703508581ull, 985303004902277287ull, + 9766818362445227442ull, 296427748447ull}}, +{{7919877776201997822ull, 10455000792982622417ull, + 7596836934629146398ull, 370534685559ull}}, +{{14511533238679885182ull, 3845378954373502213ull, + 4884360149859045094ull, 463168356949ull}}, +{{11375551283388622191ull, 16238419901765602595ull, + 5358568102875597135ull, 289480223093ull}}, +{{9607753085808389834ull, 15686338858779615340ull, + 11309896147021884323ull, 361850278866ull}}, +{{12009691357260487293ull, 14996237555047131271ull, + 4913998146922579596ull, 452312848583ull}}, +{{14423586125928886414ull, 149276435049681236ull, + 9988777869467694104ull, 282695530364ull}}, +{{18029482657411108018ull, 186595543812101545ull, + 12485972336834617630ull, 353369412955ull}}, +{{8701795266481721310ull, 9456616466619902740ull, + 10995779402615884133ull, 441711766194ull}}, +{{14661994078405851627ull, 8216228300851133164ull, + 11484048145062315487ull, 276069853871ull}}, +{{18327492598007314533ull, 5658599357636528551ull, + 9743374162900506455ull, 345087317339ull}}, +{{18297679729081755263ull, 2461563178618272785ull, + 7567531685198245165ull, 431359146674ull}}, +{{9037041606070030366ull, 7688639991700228886ull, 236042569643030648ull, + 539198933343ull}}, +{{1036464985366381075ull, 4805399994812643054ull, + 7065055633667976011ull, 336999333339ull}}, +{{10518953268562752152ull, 1395063975088415913ull, + 4219633523657582110ull, 421249166674ull}}, +{{17760377604130828093ull, 10967202005715295699ull, + 14497913941426753445ull, 526561458342ull}}, +{{8794392993368073607ull, 9160344262785753764ull, + 4449510194964332999ull, 329100911464ull}}, +{{10992991241710092008ull, 6838744310054804301ull, + 5561887743705416249ull, 411376139330ull}}, +{{18352925070565002914ull, 13160116405995893280ull, + 16175731716486546119ull, 514220174162ull}}, +{{11470578169103126821ull, 15142601781388515156ull, + 14721518341231479228ull, 321387608851ull}}, +{{14338222711378908527ull, 481508153026092329ull, + 13790211908111961132ull, 401734511064ull}}, +{{4087720333941471946ull, 601885191282615412ull, + 17237764885139951415ull, 502168138830ull}}, +{{11778197245568195775ull, 7293707272192716488ull, + 6161917034785081730ull, 313855086769ull}}, +{{14722746556960244718ull, 18340506127095671418ull, + 12314082311908740066ull, 392318858461ull}}, +{{9180061159345530090ull, 13702260622014813465ull, + 1557544834603761371ull, 490398573077ull}}, +{{17266753270659426066ull, 6258069879545564463ull, + 3279308530841044809ull, 306499108173ull}}, +{{16971755569896894679ull, 12434273367859343483ull, + 8710821681978693915ull, 383123885216ull}}, +{{16603008443943730444ull, 10931155691396791450ull, + 10888527102473367394ull, 478904856520ull}}, +{{14988566295892219432ull, 11443658325550382560ull, + 6805329439045854621ull, 299315535325ull}}, +{{288963796155722674ull, 469514851655814489ull, 13118347817234706181ull, + 374144419156ull}}, +{{4972890763622041246ull, 5198579582997156015ull, + 16397934771543382726ull, 467680523945ull}}, +{{10025585754904857635ull, 17084170294655386221ull, + 3331180204573532347ull, 292300327466ull}}, +{{17143668212058459947ull, 16743526849891844872ull, + 13387347292571691242ull, 365375409332ull}}, +{{2982841191363523318ull, 11706036525510030283ull, + 16734184115714614053ull, 456719261665ull}}, +{{18005176809098059738ull, 9622115837657462878ull, + 3541336044680551927ull, 285449538541ull}}, +{{13283098974517798864ull, 7415958778644440694ull, + 9038356074278077813ull, 356811923176ull}}, +{{7380501681292472772ull, 13881634491732938772ull, + 11297945092847597266ull, 446014903970ull}}, +{{13836185587662571291ull, 13287707575760474636ull, + 11672901701457136195ull, 278759314981ull}}, +{{17295231984578214113ull, 11997948451273205391ull, + 756069071539256532ull, 348449143727ull}}, +{{17007353962295379738ull, 14997435564091506739ull, + 14780144394706234377ull, 435561429658ull}}, +{{16647506434441836768ull, 4911736399832219712ull, + 9251808456528017164ull, 544451787073ull}}, +{{10404691521526147980ull, 12293207286749913128ull, + 17311595331398480487ull, 340282366920ull}}, +{{13005864401907684975ull, 10754823090010003506ull, + 3192750090538548993ull, 425352958651ull}}, +{{7033958465529830411ull, 18055214880939892287ull, + 17825995668455349953ull, 531691198313ull}}, +{{11313753068597225863ull, 4366980272946350823ull, + 4223718265143511865ull, 332306998946ull}}, +{{9530505317319144425ull, 10070411359610326433ull, + 14503019868284165639ull, 415383748682ull}}, +{{16524817665076318435ull, 7976328181085520137ull, + 8905402798500431241ull, 519229685853ull}}, +{{3410482013031617166ull, 16514420159246919846ull, + 7871719758276463477ull, 324518553658ull}}, +{{13486474553144297265ull, 6807967143776486095ull, + 616277660990803539ull, 405648192073ull}}, +{{12246407173002983677ull, 3898272911293219715ull, + 5382033094665892328ull, 507060240091ull}}, +{{5348161473913170846ull, 2436420569558262322ull, + 1057927674952488753ull, 316912650057ull}}, +{{15908573879246239366ull, 7657211730375215806ull, + 5934095612117998845ull, 396140812571ull}}, +{{10662345312203023399ull, 14183200681396407662ull, + 2805933496720110652ull, 495176015714ull}}, +{{2052279801699501721ull, 18087872462727530597ull, + 6365394453877457061ull, 309485009821ull}}, +{{7177035770551765055ull, 8774782523127249534ull, + 12568429085774209231ull, 386856262276ull}}, +{{18194666750044482126ull, 6356792135481674013ull, + 15710536357217761539ull, 483570327845ull}}, +{{13677509727991495281ull, 1667152075462352306ull, + 12124928232474794914ull, 302231454903ull}}, +{{7873515123134593293ull, 11307312131182716191ull, + 10544474272166105738ull, 377789318629ull}}, +{{5230207885490853713ull, 4910768127123619431ull, + 17792278858635020077ull, 472236648286ull}}, +{{10186408956072865427ull, 5375073088665956096ull, + 6508488268219499644ull, 295147905179ull}}, +{{12733011195091081783ull, 6718841360832445120ull, + 3523924316846986651ull, 368934881474ull}}, +{{15916263993863852229ull, 3786865682613168496ull, + 13628277432913509122ull, 461168601842ull}}, +{{9947664996164907643ull, 6978477070060618214ull, + 13129359413998331105ull, 288230376151ull}}, +{{3211209208351358746ull, 13334782356003160672ull, + 11800013249070525977ull, 360287970189ull}}, +{{4014011510439198432ull, 2833419889721787128ull, 914958506055993760ull, + 450359962737ull}}, +{{2508757194024499020ull, 1770887431076116955ull, + 12101064112353465860ull, 281474976710ull}}, +{{16971004547812787487ull, 2213609288845146193ull, + 5902958103587056517ull, 351843720888ull}}, +{{7378697629483820647ull, 7378697629483820646ull, + 7378697629483820646ull, 439804651110ull}}, +{{0ull, 0ull, 0ull, 549755813888ull}}, +{{0ull, 0ull, 0ull, 343597383680ull}}, +{{0ull, 0ull, 0ull, 429496729600ull}}, +{{0ull, 0ull, 0ull, 536870912000ull}}, +{{0ull, 0ull, 0ull, 335544320000ull}}, +{{0ull, 0ull, 0ull, 419430400000ull}}, +{{0ull, 0ull, 0ull, 524288000000ull}}, +{{0ull, 0ull, 0ull, 327680000000ull}}, +{{0ull, 0ull, 0ull, 409600000000ull}}, +{{0ull, 0ull, 0ull, 512000000000ull}}, +{{0ull, 0ull, 0ull, 320000000000ull}}, +{{0ull, 0ull, 0ull, 400000000000ull}}, +{{0ull, 0ull, 0ull, 500000000000ull}}, +{{0ull, 0ull, 0ull, 312500000000ull}}, +{{0ull, 0ull, 0ull, 390625000000ull}}, +{{0ull, 0ull, 0ull, 488281250000ull}}, +{{0ull, 0ull, 0ull, 305175781250ull}}, +{{0ull, 0ull, 9223372036854775808ull, 381469726562ull}}, +{{0ull, 0ull, 2305843009213693952ull, 476837158203ull}}, +{{0ull, 0ull, 17582052945254416384ull, 298023223876ull}}, +{{0ull, 0ull, 3530822107858468864ull, 372529029846ull}}, +{{0ull, 0ull, 13636899671677861888ull, 465661287307ull}}, +{{0ull, 0ull, 6217219285584969728ull, 291038304567ull}}, +{{0ull, 0ull, 3159838088553824256ull, 363797880709ull}}, +{{0ull, 0ull, 8561483629119668224ull, 454747350886ull}}, +{{0ull, 0ull, 739241249772404736ull, 284217094304ull}}, +{{0ull, 0ull, 924051562215505920ull, 355271367880ull}}, +{{0ull, 0ull, 1155064452769382400ull, 444089209850ull}}, +{{0ull, 0ull, 5333601301408251904ull, 277555756156ull}}, +{{0ull, 0ull, 6667001626760314880ull, 346944695195ull}}, +{{0ull, 0ull, 3722066015023005696ull, 433680868994ull}}, +{{0ull, 0ull, 13875954555633532928ull, 542101086242ull}}, +{{0ull, 0ull, 13284157615698345984ull, 338813178901ull}}, +{{0ull, 0ull, 2770138964340768768ull, 423516473627ull}}, +{{0ull, 0ull, 17297731760708124672ull, 529395592033ull}}, +{{0ull, 0ull, 3893553322801496064ull, 330872245021ull}}, +{{0ull, 0ull, 9478627671929257984ull, 413590306276ull}}, +{{0ull, 0ull, 11848284589911572480ull, 516987882845ull}}, +{{0ull, 0ull, 9711020877908426752ull, 323117426778ull}}, +{{0ull, 0ull, 2915404060530757632ull, 403896783473ull}} +}; + +// ********************************************************************** + +static const UINT128 breakpoints_binary64[] = + { {{5261314576080512960ull, 21426681862861333ull}}, +{{4728754506986910400ull, 34282690980578133ull}}, +{{11161701235073348928ull, 27426152784462506ull}}, +{{5240012173316768832ull, 21940922227570005ull}}, +{{8384019477306830144ull, 35105475564112008ull}}, +{{14085913211329284736ull, 28084380451289606ull}}, +{{7579381754321517504ull, 22467504361031685ull}}, +{{12127010806914427968ull, 35948006977650696ull}}, +{{6012259830789632064ull, 28758405582120557ull}}, +{{15877854308857436608ull, 23006724465696445ull}}, +{{12702283447085949312ull, 18405379572557156ull}}, +{{12944955885853698240ull, 29448607316091450ull}}, +{{10355964708682958592ull, 23558885852873160ull}}, +{{8284771766946366848ull, 18847108682298528ull}}, +{{9566286012372276672ull, 30155373891677645ull}}, +{{7653028809897821312ull, 24124299113342116ull}}, +{{2433074233176346752ull, 19299439290673693ull}}, +{{203569958340244480ull, 30879102865077909ull}}, +{{3852204781414105920ull, 24703282292062327ull}}, +{{14149810269357015680ull, 19762625833649861ull}}, +{{15260998801487404480ull, 31620201333839778ull}}, +{{1140752596964192576ull, 25296161067071823ull}}, +{{8291299707055174720ull, 20236928853657458ull}}, +{{9576730716546369216ull, 32379086165851933ull}}, +{{15040082202720916032ull, 25903268932681546ull}}, +{{8342716947434822464ull, 20722615146145237ull}}, +{{17037695930637626304ull, 33156184233832379ull}}, +{{17319505559252011392ull, 26524947387065903ull}}, +{{2787558003175878144ull, 21219957909652723ull}}, +{{770743990339494720ull, 33951932655444357ull}}, +{{11684641636497326720ull, 27161546124355485ull}}, +{{9347713309197861376ull, 21729236899484388ull}}, +{{11266992479974667904ull, 34766779039175021ull}}, +{{5324245169237824000ull, 27813423231340017ull}}, +{{15327442579615990144ull, 22250738585072013ull}}, +{{2387815238934122304ull, 35601181736115222ull}}, +{{12978298635373028800ull, 28480945388892177ull}}, +{{3003941278814602368ull, 22784756311113742ull}}, +{{13471199467277412864ull, 18227805048890993ull}}, +{{17864570332901950336ull, 29164488078225589ull}}, +{{17981005081063470592ull, 23331590462580471ull}}, +{{10695455250108866112ull, 18665272370064377ull}}, +{{2355333141206544512ull, 29864435792103004ull}}, +{{5573615327707145920ull, 23891548633682403ull}}, +{{11837589891649537408ull, 19113238906945922ull}}, +{{4182748567671618560ull, 30581182251113476ull}}, +{{18103594113104936128ull, 24464945800890780ull}}, +{{14482875290483948864ull, 19571956640712624ull}}, +{{12104554020548587264ull, 31315130625140199ull}}, +{{13372992031180780160ull, 25052104500112159ull}}, +{{14387742439686534400ull, 20041683600089727ull}}, +{{8262992644530813824ull, 32066693760143564ull}}, +{{10299742930366561344ull, 25653355008114851ull}}, +{{4550445529551338752ull, 20522684006491881ull}}, +{{18348759291507873024ull, 32836294410387009ull}}, +{{18368356247948208704ull, 26269035528309607ull}}, +{{7315987368874746304ull, 21015228422647686ull}}, +{{4326882160715773504ull, 33624365476236298ull}}, +{{10840203358056439424ull, 26899492380989038ull}}, +{{16050860315928972160ull, 21519593904791230ull}}, +{{7234632431776803904ull, 34431350247665969ull}}, +{{9477054760163353472ull, 27545080198132775ull}}, +{{7581643808130682752ull, 22036064158506220ull}}, +{{12130630093009092416ull, 35257702653609952ull}}, +{{2325806444923453248ull, 28206162122887962ull}}, 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+{{11187941737021610816ull, 20837545102749544ull}}, +{{6832660335008846336ull, 33340072164399271ull}}, +{{1776779453265166784ull, 26672057731519417ull}}, +{{12489470006837864384ull, 21337646185215533ull}}, +{{16293803196198672704ull, 34140233896344853ull}}, +{{1966996112733207168ull, 27312187117075883ull}}, +{{8952294519670386368ull, 21849749693660706ull}}, +{{6944973601988797568ull, 34959599509857130ull}}, +{{5555978881591038080ull, 27967679607885704ull}}, +{{8134131920014740736ull, 22374143686308563ull}}, +{{9325262257281674880ull, 35798629898093701ull}}, +{{3770860991083429568ull, 28638903918474961ull}}, +{{17774084051834384960ull, 22911123134779968ull}}, +{{3151220797241777024ull, 18328898507823975ull}}, +{{5041953275586843200ull, 29326237612518360ull}}, +{{4033562620469474560ull, 23460990090014688ull}}, +{{10605547725859400320ull, 18768792072011750ull}}, +{{16968876361375040512ull, 30030067315218800ull}}, +{{13575101089100032384ull, 24024053852175040ull}}, +{{10860080871280025920ull, 19219243081740032ull}}, +{{2618734135080400192ull, 30750788930784052ull}}, +{{13163033752290051072ull, 24600631144627241ull}}, +{{6841078187090130560ull, 19680504915701793ull}}, +{{7256376284602298560ull, 31488807865122869ull}}, +{{9494449842423749184ull, 25191046292098295ull}}, +{{7595559873938999360ull, 20152837033678636ull}}, +{{4774198168818578304ull, 32244539253885818ull}}, +{{11198056164538683264ull, 25795631403108654ull}}, +{{12647793746372856960ull, 20636505122486923ull}}, +{{16547121179454660800ull, 33018408195979077ull}}, +{{5858999314079907968ull, 26414726556783262ull}}, +{{15755245895489657344ull, 21131781245426609ull}}, +{{14140346988557720832ull, 33810849992682575ull}}, +{{11312277590846176640ull, 27048679994146060ull}}, +{{9049822072676941312ull, 21638943995316848ull}}, +{{10790366501541195776ull, 34622310392506957ull}}, +{{1253595571749136000ull, 27697848314005566ull}}, +{{15760271716366950080ull, 22158278651204452ull}}, +{{10459039487219478848ull, 35453245841927124ull}}, +{{12056580404517493376ull, 28362596673541699ull}}, +{{13334613138355905024ull, 22690077338833359ull}}, +{{14357039325426634368ull, 18152061871066687ull}}, +{{8213867661714973696ull, 29043298993706700ull}}, +{{6571094129371978944ull, 23234639194965360ull}}, +{{5256875303497583168ull, 18587711355972288ull}}, +{{4721651670854222720ull, 29740338169555661ull}}, +{{87972521941467840ull, 23792270535644529ull}}, +{{3759726832295084608ull, 19033816428515623ull}}, +{{2326214116930225024ull, 30454106285624997ull}}, +{{12929017737769910976ull, 24363285028499997ull}}, +{{2964516560732108160ull, 19490628022799998ull}}, +{{1053877682429462720ull, 31185004836479997ull}}, +{{11911148590169301120ull, 24948003869183997ull}}, +{{2150221242651620288ull, 19958403095347198ull}}, +{{18197749247210233728ull, 31933444952555516ull}}, +{{10868850583026276672ull, 25546755962044413ull}}, +{{16073778095904841984ull, 20437404769635530ull}}, +{{7271300879738195520ull, 32699847631416849ull}}, +{{9506389518532466752ull, 26159878105133479ull}}, +{{11294460429567883712ull, 20927902484106783ull}}, +{{14381787872566703680ull, 33484643974570853ull}}, +{{437383853827631936ull, 26787715179656683ull}}, +{{7728604712545926208ull, 21430172143725346ull}}, +{{4987069910589661312ull, 34288275429960554ull}}, +{{7679004743213639360ull, 27430620343968443ull}}, +{{13521901424054732096ull, 21944496275174754ull}}, +{{10566995834261840448ull, 35111194040279607ull}}, +{{1074899037925651712ull, 28088955232223686ull}}, +{{15617314489308162624ull, 22471164185778948ull}}, +{{2851610294441598336ull, 35953862697246318ull}}, +{{9659985865037099264ull, 28763090157797054ull}}, +{{11417337506771589760ull, 23010472126237643ull}}, +{{16512567634901092416ull, 18408377700990114ull}}, +{{15352061771616016960ull, 29453404321584183ull}}, +{{1213602973067082560ull, 23562723457267347ull}}, +{{12038928822679397056ull, 18850178765813877ull}}, +{{4504890857319393984ull, 30160286025302204ull}}, +{{7293261500597425472ull, 24128228820241763ull}}, +{{13213306829961761024ull, 19302583056193410ull}}, +{{2694546854229266048ull, 30884132889909457ull}}, +{{13223683927609143808ull, 24707306311927565ull}}, +{{10578947142087315072ull, 19765845049542052ull}}, +{{2168920168372062784ull, 31625352079267284ull}}, +{{5424484949439560576ull, 25300281663413827ull}}, +{{15407634403777379392ull, 20240225330731061ull}}, +{{17273517416559986432ull, 32384360529169698ull}}, +{{2750767489022258176ull, 25907488423335759ull}} +}; + +static const int exponents_binary64[] = { -55, + -51, + -48, + -45, + -41, + -38, + -35, + -31, + -28, + -25, + -22, + -18, + -15, + -12, + -8, + -5, + -2, + 2, + 5, + 8, + 12, + 15, + 18, + 22, + 25, + 28, + 32, + 35, + 38, + 42, + 45, + 48, + 52, + 55, + 58, + 62, + 65, + 68, + 71, + 75, + 78, + 81, + 85, + 88, + 91, + 95, + 98, + 101, + 105, + 108, + 111, + 115, + 118, + 121, + 125, + 128, + 131, + 135, + 138, + 141, + 145, + 148, + 151, + 155, + 158, + 161, + 164, + 168, + 171, + 174, + 178, + 181, + 184, + 188, + 191, + 194, + 198, + 201, + 204, + 208, + 211, + 214, + 218, + 221, + 224, + 228, + 231, + 234, + 238, + 241, + 244, + 248, + 251, + 254, + 258, + 261, + 264, + 267, + 271, + 274, + 277, + 281, + 284, + 287, + 291, + 294, + 297, + 301, + 304, + 307, + 311, + 314, + 317, + 321, + 324, + 327, + 331, + 334, + 337, + 341, + 344, + 347, + 351, + 354, + 357, + 360, + 364, + 367, + 370, + 374, + 377, + 380, + 384, + 387, + 390, + 394, + 397, + 400, + 404, + 407, + 410, + 414, + 417, + 420, + 424, + 427, + 430, + 434, + 437, + 440, + 444, + 447, + 450, + 454, + 457, + 460, + 463, + 467, + 470, + 473, + 477, + 480, + 483, + 487, + 490, + 493, + 497, + 500, + 503, + 507, + 510, + 513, + 517, + 520, + 523, + 527, + 530, + 533, + 537, + 540, + 543, + 547, + 550, + 553, + 556, + 560, + 563, + 566, + 570, + 573, + 576, + 580, + 583, + 586, + 590, + 593, + 596, + 600, + 603, + 606, + 610, + 613, + 616, + 620, + 623, + 626, + 630, + 633, + 636, + 640, + 643, + 646, + 649, + 653, + 656, + 659, + 663, + 666, + 669, + 673, + 676, + 679, + 683, + 686, + 689, + 693, + 696, + 699, + 703, + 706, + 709, + 713, + 716, + 719, + 723, + 726, + 729, + 733, + 736, + 739, + 743, + 746, + 749, + 752, + 756, + 759, + 762, + 766, + 769, + 772, + 776, + 779, + 782, + 786, + 789, + 792, + 796, + 799, + 802, + 806, + 809, + 812, + 816, + 819, + 822, + 826, + 829, + 832, + 836, + 839, + 842, + 845, + 849, + 852, + 855, + 859, + 862, + 865, + 869, + 872, + 875, + 879, + 882, + 885, + 889, + 892, + 895, + 899, + 902, + 905, + 909, + 912, + 915, + 919, + 922, + 925, + 929, + 932, + 935, + 939, + 942, + 945, + 948, + 952, + 955, + 958, + 962, + 965, + 968, + 972, + 975, + 978, + 982, + 985, + 988, + 992, + 995, + 998, + 1002, + 1005, + 1008, + 1012, + 1015, + 1018, + 1022, + 1025, + 1028, + 1032, + 1035, + 1038, + 1041, + 1045, + 1048, + 1051, + 1055, + 1058, + 1061, + 1065, + 1068, + 1071, + 1075, + 1078, + 1081, + 1085, + 1088, + 1091, + 1095, + 1098, + 1101, + 1105, + 1108, + 1111, + 1115, + 1118, + 1121, + 1125, + 1128, + 1131, + 1134, + 1138, + 1141, + 1144, + 1148, + 1151, + 1154, + 1158, + 1161, + 1164, + 1168, + 1171, + 1174, + 1178, + 1181, + 1184, + 1188, + 1191, + 1194, + 1198, + 1201, + 1204, + 1208, + 1211, + 1214, + 1218, + 1221, + 1224, + 1228, + 1231, + 1234, + 1237, + 1241, + 1244, + 1247, + 1251, + 1254, + 1257, + 1261, + 1264, + 1267, + 1271, + 1274, + 1277, + 1281, + 1284, + 1287, + 1291, + 1294, + 1297, + 1301, + 1304, + 1307, + 1311, + 1314, + 1317, + 1321, + 1324, + 1327, + 1330, + 1334, + 1337, + 1340, + 1344, + 1347, + 1350, + 1354, + 1357, + 1360, + 1364, + 1367, + 1370, + 1374, + 1377, + 1380, + 1384, + 1387, + 1390, + 1394, + 1397, + 1400, + 1404, + 1407, + 1410, + 1414, + 1417, + 1420, + 1424, + 1427, + 1430, + 1433, + 1437, + 1440, + 1443, + 1447, + 1450, + 1453, + 1457, + 1460, + 1463, + 1467, + 1470, + 1473, + 1477, + 1480, + 1483, + 1487, + 1490, + 1493, + 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1912, + 1915, + 1918, + 1922, + 1925, + 1928, + 1932, + 1935, + 1938, + 1942, + 1945, + 1948, + 1952, + 1955, + 1958, + 1962, + 1965, + 1968, + 1972, + 1975, + 1978, + 1982, + 1985, + 1988, + 1992, + 1995, + 1998, + 2002, + 2005, + 2008, + 2011, + 2015, + 2018, + 2021, + 2025, + 2028, + 2031, + 2035, + 2038, + 2041, + 2045, + 2048, + 2051, + 2055, + 2058, + 2061, + 2065, + 2068, + 2071, + 2075, + 2078, + 2081, + 2085, + 2088, + 2091, + 2095, + 2098, + 2101, + 2105, + 2108, + 2111, + 2114, + 2118, + 2121, + 2124, + 2128, + 2131, + 2134, + 2138, + 2141, + 2144, + 2148, + 2151, + 2154, + 2158, + 2161, +}; + +static const UINT256 multipliers1_binary64[] = + { {{1837554224478941466ull, 10276842184138466546ull, + 11651621577776737258ull, 7754513766366540701ull}}, +{{5760157408726726321ull, 11034712383513929495ull, + 9588106495324154738ull, 4846571103979087938ull}}, +{{2588510742481019997ull, 4570018442537636061ull, + 2761761082300417615ull, 6058213879973859923ull}}, +{{7847324446528662900ull, 1100837034744657172ull, + 17287259408157685731ull, 7572767349967324903ull}}, +{{14127949815935190120ull, 16828924211211268396ull, + 17722066157739635437ull, 4732979593729578064ull}}, +{{17659937269918987650ull, 7201097208731921783ull, + 3705838623464992681ull, 5916224492161972581ull}}, +{{17463235568971346659ull, 13613057529342290133ull, + 9243984297758628755ull, 7395280615202465726ull}}, +{{13220365239820785614ull, 6202317946625237381ull, + 1165804167671755068ull, 4622050384501541079ull}}, +{{2690398494493818305ull, 7752897433281546727ull, + 15292313264871857547ull, 5777562980626926348ull}}, +{{17198056173399436594ull, 5079435773174545504ull, + 668647507380270318ull, 7221953725783657936ull}}, +{{3050826143039744126ull, 15572666753322957689ull, + 835809384225337897ull, 9027442157229572420ull}}, +{{13435981385468309839ull, 2815387693185766699ull, + 9745752901995611994ull, 5642151348268482762ull}}, +{{12183290713407999394ull, 12742606653336984182ull, + 2958819090639739184ull, 7052689185335603453ull}}, +{{6005741354905223435ull, 15928258316671230228ull, + 8310209881727061884ull, 8815861481669504316ull}}, +{{12976960383670540455ull, 731789411064743084ull, + 14417253212934189486ull, 5509913426043440197ull}}, +{{16221200479588175569ull, 10138108800685704663ull, + 4186508460885573145ull, 6887391782554300247ull}}, +{{15664814581057831557ull, 17284322019284518733ull, + 621449557679578527ull, 8609239728192875309ull}}, +{{12096352122374838675ull, 17720230289693906064ull, + 2694248982763430531ull, 5380774830120547068ull}}, +{{15120440152968548344ull, 17538601843689994676ull, + 3367811228454288164ull, 6725968537650683835ull}}, +{{453806117501133814ull, 3476508230902941730ull, + 18044822090850023918ull, 8407460672063354793ull}}, +{{4895314841865596538ull, 16007875699596502293ull, + 4360484779140183092ull, 5254662920039596746ull}}, +{{10730829570759383576ull, 1563100550786076250ull, + 14673978010780004674ull, 6568328650049495932ull}}, +{{4190164926594453662ull, 11177247725337371121ull, + 18342472513475005842ull, 8210410812561869915ull}}, +{{14148068125190003299ull, 11597465846763244854ull, + 9158202311708184699ull, 5131506757851168697ull}}, +{{8461713119632728315ull, 9885146290026668164ull, + 16059438908062618778ull, 6414383447313960871ull}}, +{{10577141399540910394ull, 3133060825678559397ull, + 15462612616650885569ull, 8017979309142451089ull}}, +{{8916556383926762949ull, 13487378062117569383ull, + 2746603857765721624ull, 5011237068214031931ull}}, +{{6534009461481065782ull, 16859222577646961729ull, + 17268312877489315742ull, 6264046335267539913ull}}, +{{12779197845278720131ull, 11850656185203926353ull, + 7750333041579480966ull, 7830057919084424892ull}}, +{{1069469625658118226ull, 2794974097325066067ull, + 14067330187841951412ull, 4893786199427765557ull}}, +{{15171895087354811494ull, 3493717621656332583ull, + 3749104679520275553ull, 6117232749284706947ull}}, +{{14353182840766126464ull, 8978833045497803633ull, 74694830972956537ull, + 7646540936605883684ull}}, +{{2053210247837747184ull, 17140985699504597031ull, + 9270056306212873643ull, 4779088085378677302ull}}, +{{16401570865079347692ull, 16814546105953358384ull, + 2364198345911316246ull, 5973860106723346628ull}}, +{{2055219507639632999ull, 11794810595586922173ull, + 2955247932389145308ull, 7467325133404183285ull}}, +{{3590355201488464576ull, 16595128659096602166ull, + 4152872966956909769ull, 4667078208377614553ull}}, +{{13711316038715356528ull, 6908852768588588995ull, + 9802777227123525116ull, 5833847760472018191ull}}, +{{12527459029966807756ull, 8636065960735736244ull, + 7641785515477018491ull, 7292309700590022739ull}}, +{{15659323787458509695ull, 6183396432492282401ull, + 4940545875918885210ull, 9115387125737528424ull}}, +{{2869548339520486704ull, 8476308788735064405ull, + 3087841172449303256ull, 5697116953585955265ull}}, +{{8198621442827996284ull, 10595385985918830506ull, + 8471487483989016974ull, 7121396191982444081ull}}, +{{1024904766680219546ull, 4020860445543762325ull, + 15201045373413659122ull, 8901745239978055101ull}}, +{{2946408488388831169ull, 7124723796892239357ull, + 11806496367597230903ull, 5563590774986284438ull}}, +{{8294696628913426865ull, 4294218727687911292ull, + 5534748422641762821ull, 6954488468732855548ull}}, +{{10368370786141783581ull, 9979459428037277019ull, + 6918435528302203526ull, 8693110585916069435ull}}, +{{4174388732124920786ull, 1625476124095910233ull, + 2018179195975183252ull, 5433194116197543397ull}}, +{{9829671933583538887ull, 2031845155119887791ull, + 7134410013396366969ull, 6791492645246929246ull}}, +{{7675403898552035704ull, 7151492462327247643ull, + 18141384553600234519ull, 8489365806558661557ull}}, +{{2491284427381328363ull, 11387211816595611633ull, + 13644208355213840526ull, 5305853629099163473ull}}, +{{7725791552654048358ull, 5010642733889738733ull, + 3220202388735136946ull, 6632317036373954342ull}}, +{{14268925459244948351ull, 15486675454216949224ull, + 13248625022773696990ull, 8290396295467442927ull}}, +{{8918078412028092720ull, 5067486140458205361ull, + 15197919666874642475ull, 5181497684667151829ull}}, +{{15759284033462503804ull, 1722671657145368797ull, + 5162341528311139382ull, 6476872105833939787ull}}, +{{5864046986545966042ull, 11376711608286486805ull, + 1841240891961536323ull, 8096090132292424734ull}}, +{{5970872375804922729ull, 4804601745965360301ull, + 14985833612758123914ull, 5060056332682765458ull}}, +{{12075276488183541315ull, 15229124219311476184ull, + 9508919979092879084ull, 6325070415853456823ull}}, +{{15094095610229426643ull, 589661200429793614ull, + 7274463955438710952ull, 7906338019816821029ull}}, +{{4822123737966003748ull, 368538250268621009ull, 6852382981362888297ull, + 4941461262385513143ull}}, +{{10639340690884892589ull, 5072358831263164165ull, + 3953792708276222467ull, 6176826577981891429ull}}, +{{17910861882033503640ull, 1728762520651567302ull, + 9553926903772665988ull, 7721033222477364286ull}}, +{{6582602657843551871ull, 10303848612262005372ull, + 1359518296430528338ull, 4825645764048352679ull}}, +{{8228253322304439839ull, 3656438728472730907ull, + 15534455925820324135ull, 6032057205060440848ull}}, +{{5673630634453161895ull, 18405606465873077346ull, + 971325833565853552ull, 7540071506325551061ull}}, +{{8157705164960614088ull, 11503504041170673341ull, + 2912921655192352422ull, 4712544691453469413ull}}, +{{14808817474628155514ull, 5156008014608565868ull, + 8252838087417828432ull, 5890680864316836766ull}}, +{{64277769575642777ull, 6445010018260707336ull, 1092675572417509732ull, + 7363351080396045958ull}}, +{{80347211969553471ull, 8056262522825884170ull, 10589216502376662973ull, + 9204188850495057447ull}}, +{{4661903025908358824ull, 7341007085979871558ull, + 13535789341626496214ull, 5752618031559410904ull}}, +{{15050750819240224337ull, 18399630894329615255ull, + 16919736677033120267ull, 7190772539449263630ull}}, +{{14201752505622892517ull, 18387852599484631165ull, + 11926298809436624526ull, 8988465674311579538ull}}, +{{11181938325228001776ull, 6880721856250506574ull, + 12065622774325278233ull, 5617791046444737211ull}}, +{{4754050869680226411ull, 13212588338740521122ull, + 10470342449479209887ull, 7022238808055921514ull}}, +{{15165935623955058822ull, 11904049404998263498ull, + 3864556024994236551ull, 8777798510069901893ull}}, +{{14090395783399299668ull, 14357559905764996542ull, + 4721190524835091796ull, 5486124068793688683ull}}, +{{8389622692394348777ull, 17946949882206245678ull, + 1289802137616476841ull, 6857655085992110854ull}}, +{{1263656328638160163ull, 8598629297475643386ull, + 10835624708875371860ull, 8572068857490138567ull}}, +{{5401471223826238006ull, 14597515347777052924ull, + 13689794470688189268ull, 5357543035931336604ull}}, +{{6751839029782797507ull, 18246894184721316155ull, + 17112243088360236585ull, 6696928794914170755ull}}, +{{3828112768801108980ull, 8973559675619481482ull, + 16778617842022907828ull, 8371160993642713444ull}}, +{{7004256498928081017ull, 14831846834116951734ull, + 1263264114409541584ull, 5231975621026695903ull}}, +{{17978692660514877079ull, 93064468936638051ull, + 15414138198294090693ull, 6539969526283369878ull}}, +{{17861679807216208444ull, 4728016604598185468ull, + 10044300711012837558ull, 8174961907854212348ull}}, +{{1940177842655354470ull, 16790068433156029630ull, + 15501059981237799281ull, 5109351192408882717ull}}, +{{11648594340173968895ull, 7152527486162873325ull, + 5541266921265085390ull, 6386688990511103397ull}}, +{{725684869935297407ull, 18164031394558367465ull, + 11538269670008744641ull, 7983361238138879246ull}}, +{{11982768089778030640ull, 4434990593957897809ull, + 2599732525328077497ull, 4989600773836799529ull}}, +{{1143402056940374587ull, 10155424260874760166ull, + 7861351675087484775ull, 6237000967295999411ull}}, +{{10652624608030244042ull, 8082594307666062303ull, + 5215003575431968065ull, 7796251209119999264ull}}, +{{13575419407659984382ull, 16580836488359758699ull, + 3259377234644980040ull, 4872657005699999540ull}}, +{{12357588241147592574ull, 2279301536740146758ull, + 4074221543306225051ull, 6090821257124999425ull}}, +{{6223613264579714909ull, 16684184976207347160ull, + 9704462947560169217ull, 7613526571406249281ull}}, +{{3889758290362321819ull, 3510086582488510119ull, + 17594504388293575521ull, 4758454107128905800ull}}, +{{250511844525514369ull, 8999294246538025553ull, 3546386411657417785ull, + 5948067633911132251ull}}, +{{4924825824084280865ull, 15860803826599919845ull, + 18268041069853935943ull, 7435084542388915313ull}}, +{{5383859149266369493ull, 16830531419266031759ull, + 4499996641017628108ull, 4646927838993072071ull}}, +{{2118137918155573962ull, 2591420200372988083ull, + 1013309782844647232ull, 5808659798741340089ull}}, +{{16482730452976631164ull, 3239275250466235103ull, + 5878323246983196944ull, 7260824748426675111ull}}, +{{15991727047793401051ull, 4049094063082793879ull, + 2736218040301608276ull, 9076030935533343889ull}}, +{{16912358432511957513ull, 11754055826281521982ull, + 13239351321256974932ull, 5672519334708339930ull}}, +{{11917076003785171083ull, 14692569782851902478ull, + 7325817114716442857ull, 7090649168385424913ull}}, +{{5672972967876688046ull, 4530654173282714386ull, + 13768957411822941476ull, 8863311460481781141ull}}, +{{8157294123350317933ull, 12055030895156472299ull, + 10911441391603032374ull, 5539569662801113213ull}}, +{{5584931635760509512ull, 5845416582090814566ull, + 18250987757931178372ull, 6924462078501391516ull}}, +{{16204536581555412698ull, 7306770727613518207ull, + 4366990623704421349ull, 8655577598126739396ull}}, +{{17045364391113214793ull, 6872574713972142831ull, + 11952741176670039151ull, 5409735998829212122ull}}, +{{16695019470464130587ull, 3979032374037790635ull, + 5717554433982773131ull, 6762169998536515153ull}}, +{{16257088319652775329ull, 362104449119850390ull, + 11758629060905854318ull, 8452712498170643941ull}}, +{{5548994181355596677ull, 14061373335982070206ull, + 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+{{7803105218212952879ull, 18044654874084636016ull, + 7777860448100626703ull, 5776622002767454643ull}}, +{{9753881522766191098ull, 17944132574178407116ull, + 5110639541698395475ull, 7220777503459318304ull}}, +{{12192351903457738873ull, 17818479699295620991ull, + 6388299427122994344ull, 9025971879324147880ull}}, +{{14537748967302168652ull, 11136549812059763119ull, + 3992687141951871465ull, 5641232424577592425ull}}, +{{13560500190700322911ull, 85629209792540187ull, 9602544945867227236ull, + 7051540530721990531ull}}, +{{12338939219948015734ull, 107036512240675234ull, + 7391495163906646141ull, 8814425663402488164ull}}, +{{12323523030894897738ull, 2372740829364115973ull, + 13843056514296429646ull, 5509016039626555102ull}}, +{{1569345733336458460ull, 12189298073559920775ull, + 8080448606015761249ull, 6886270049533193878ull}}, +{{15796740221952736787ull, 1401564536667737256ull, + 877188720664925754ull, 8607837561916492348ull}}, +{{9872962638720460492ull, 5487663853844723689ull, + 9771614987270354404ull, 5379898476197807717ull}}, +{{16952889316827963519ull, 6859579817305904611ull, + 16826204752515330909ull, 6724873095247259646ull}}, +{{16579425627607566495ull, 13186160790059768668ull, + 11809383903789387828ull, 8406091369059074558ull}}, +{{1138768980399953251ull, 17464722530642131226ull, + 2769178921440979488ull, 5253807105661921599ull}}, +{{10646833262354717372ull, 3384159089593112416ull, + 17296531707083388073ull, 6567258882077401998ull}}, +{{13308541577943396715ull, 8841884880418778424ull, + 12397292596999459283ull, 8209073602596752498ull}}, +{{8317838486214622947ull, 3220335041048042563ull, + 12359993891552049956ull, 5130671001622970311ull}}, +{{5785612089340890780ull, 4025418801310053204ull, + 10838306346012674541ull, 6413338752028712889ull}} +}; + +static const UINT256 multipliers2_binary64[] = + { {{918777112239470733ull, 5138421092069233273ull, + 15049182825743144437ull, 3877256883183270350ull}}, +{{12103450741218138969ull, 5517356191756964747ull, + 4794053247662077369ull, 2423285551989543969ull}}, +{{10517627408095285807ull, 11508381258123593838ull, + 10604252578004984615ull, 3029106939986929961ull}}, +{{3923662223264331450ull, 9773790554227104394ull, + 17867001740933618673ull, 3786383674983662451ull}}, +{{7063974907967595060ull, 17637834142460410006ull, + 8861033078869817718ull, 2366489796864789032ull}}, +{{18053340671814269633ull, 12823920641220736699ull, + 11076291348587272148ull, 2958112246080986290ull}}, +{{17954989821340449138ull, 16029900801525920874ull, + 4621992148879314377ull, 3697640307601232863ull}}, +{{15833554656765168615ull, 3101158973312618690ull, + 9806274120690653342ull, 2311025192250770539ull}}, +{{10568571284101684961ull, 13099820753495549171ull, + 7646156632435928773ull, 2888781490313463174ull}}, +{{8599028086699718297ull, 2539717886587272752ull, 334323753690135159ull, + 3610976862891828968ull}}, +{{10748785108374647871ull, 17009705413516254652ull, + 417904692112668948ull, 4513721078614786210ull}}, +{{15941362729588930728ull, 1407693846592883349ull, + 4872876450997805997ull, 2821075674134241381ull}}, +{{6091645356703999697ull, 6371303326668492091ull, + 10702781582174645400ull, 3526344592667801726ull}}, +{{3002870677452611718ull, 7964129158335615114ull, + 4155104940863530942ull, 4407930740834752158ull}}, +{{6488480191835270228ull, 365894705532371542ull, + 16431998643321870551ull, 2754956713021720098ull}}, +{{17333972276648863593ull, 14292426437197628139ull, + 11316626267297562380ull, 3443695891277150123ull}}, +{{17055779327383691587ull, 17865533046497035174ull, + 9534096815694565071ull, 4304619864096437654ull}}, +{{6048176061187419338ull, 18083487181701728840ull, + 1347124491381715265ull, 2690387415060273534ull}}, +{{7560220076484274172ull, 8769300921844997338ull, + 10907277651081919890ull, 3362984268825341917ull}}, +{{226903058750566907ull, 1738254115451470865ull, + 18245783082279787767ull, 4203730336031677396ull}}, +{{11671029457787574077ull, 8003937849798251146ull, + 2180242389570091546ull, 2627331460019798373ull}}, +{{5365414785379691788ull, 781550275393038125ull, 7336989005390002337ull, + 3284164325024747966ull}}, +{{11318454500152002639ull, 5588623862668685560ull, + 18394608293592278729ull, 4105205406280934957ull}}, +{{7074034062595001650ull, 15022104960236398235ull, + 13802473192708868157ull, 2565753378925584348ull}}, +{{4230856559816364158ull, 4942573145013334082ull, + 17253091490886085197ull, 3207191723656980435ull}}, +{{14511942736625231005ull, 10789902449694055506ull, + 16954678345180218592ull, 4008989654571225544ull}}, +{{13681650228818157283ull, 6743689031058784691ull, + 10596673965737636620ull, 2505618534107015965ull}}, +{{12490376767595308699ull, 8429611288823480864ull, + 17857528475599433679ull, 3132023167633769956ull}}, +{{15612970959494135874ull, 5925328092601963176ull, + 3875166520789740483ull, 3915028959542212446ull}}, +{{9758106849683834921ull, 1397487048662533033ull, + 16257037130775751514ull, 2446893099713882778ull}}, +{{16809319580532181555ull, 10970230847682942099ull, + 11097924376614913584ull, 3058616374642353473ull}}, +{{16399963457237839040ull, 13712788559603677624ull, + 37347415486478268ull, 3823270468302941842ull}}, +{{10249977160773649400ull, 17793864886607074323ull, + 4635028153106436821ull, 2389544042689338651ull}}, +{{8200785432539673846ull, 8407273052976679192ull, + 1182099172955658123ull, 2986930053361673314ull}}, +{{10250981790674592308ull, 5897405297793461086ull, + 10700996003049348462ull, 3733662566702091642ull}}, +{{1795177600744232288ull, 17520936366403076891ull, + 11299808520333230692ull, 2333539104188807276ull}}, +{{16079030056212454072ull, 3454426384294294497ull, + 14124760650416538366ull, 2916923880236009095ull}}, +{{6263729514983403878ull, 13541405017222643930ull, + 13044264794593285053ull, 3646154850295011369ull}}, +{{17053033930584030656ull, 3091698216246141200ull, + 2470272937959442605ull, 4557693562868764212ull}}, +{{10658146206615019160ull, 4238154394367532202ull, + 10767292623079427436ull, 2848558476792977632ull}}, +{{4099310721413998142ull, 5297692992959415253ull, + 13459115778849284295ull, 3560698095991222040ull}}, +{{9735824420194885581ull, 2010430222771881162ull, + 16823894723561605369ull, 4450872619989027550ull}}, +{{10696576281049191393ull, 12785733935300895486ull, + 5903248183798615451ull, 2781795387493142219ull}}, +{{4147348314456713433ull, 11370481400698731454ull, + 2767374211320881410ull, 3477244234366427774ull}}, +{{14407557429925667599ull, 4989729714018638509ull, + 12682589801005877571ull, 4346555292958034717ull}}, +{{11310566402917236201ull, 812738062047955116ull, + 10232461634842367434ull, 2716597058098771698ull}}, +{{14138208003646545252ull, 10239294614414719703ull, + 3567205006698183484ull, 3395746322623464623ull}}, +{{13061073986130793660ull, 12799118268018399629ull, + 18294064313654893067ull, 4244682903279330778ull}}, +{{10469014250545439990ull, 5693605908297805816ull, + 16045476214461696071ull, 2652926814549581736ull}}, +{{13086267813181799987ull, 2505321366944869366ull, + 1610101194367568473ull, 3316158518186977171ull}}, +{{7134462729622474176ull, 7743337727108474612ull, + 15847684548241624303ull, 4145198147733721463ull}}, +{{13682411242868822168ull, 11757115107083878488ull, + 16822331870292097045ull, 2590748842333575914ull}}, +{{17103014053586027710ull, 861335828572684398ull, + 11804542801010345499ull, 3238436052916969893ull}}, +{{12155395530127758829ull, 14911727840998019210ull, + 920620445980768161ull, 4048045066146212367ull}}, +{{12208808224757237173ull, 2402300872982680150ull, + 7492916806379061957ull, 2530028166341382729ull}}, +{{6037638244091770658ull, 7614562109655738092ull, + 13977832026401215350ull, 3162535207926728411ull}}, +{{7547047805114713322ull, 294830600214896807ull, + 12860604014574131284ull, 3953169009908410514ull}}, +{{11634433905837777682ull, 9407641161989086312ull, + 12649563527536219956ull, 2470730631192756571ull}}, +{{14543042382297222103ull, 11759551452486357890ull, + 11200268390992887041ull, 3088413288990945714ull}}, +{{8955430941016751820ull, 864381260325783651ull, 4776963451886332994ull, + 3860516611238682143ull}}, +{{3291301328921775936ull, 5151924306131002686ull, + 9903131185070039977ull, 2412822882024176339ull}}, +{{13337498698006995728ull, 11051591401091141261ull, + 7767227962910162067ull, 3016028602530220424ull}}, +{{2836815317226580948ull, 9202803232936538673ull, + 9709034953637702584ull, 3770035753162775530ull}}, +{{13302224619335082852ull, 5751752020585336670ull, + 10679832864450952019ull, 2356272345726734706ull}}, +{{7404408737314077757ull, 2578004007304282934ull, + 4126419043708914216ull, 2945340432158418383ull}}, +{{32138884787821389ull, 3222505009130353668ull, 546337786208754866ull, + 3681675540198022979ull}}, +{{40173605984776736ull, 13251503298267717893ull, + 14517980288043107294ull, 4602094425247528723ull}}, +{{2330951512954179412ull, 3670503542989935779ull, + 6767894670813248107ull, 2876309015779705452ull}}, +{{16748747446474887977ull, 18423187484019583435ull, + 8459868338516560133ull, 3595386269724631815ull}}, +{{16324248289666222067ull, 9193926299742315582ull, + 5963149404718312263ull, 4494232837155789769ull}}, +{{5590969162614000888ull, 12663732964980029095ull, + 15256183424017414924ull, 2808895523222368605ull}}, +{{2377025434840113206ull, 15829666206225036369ull, + 5235171224739604943ull, 3511119404027960757ull}}, +{{7582967811977529411ull, 15175396739353907557ull, + 11155650049351894083ull, 4388899255034950946ull}}, +{{7045197891699649834ull, 7178779952882498271ull, + 11583967299272321706ull, 2743062034396844341ull}}, +{{4194811346197174389ull, 18196846977957898647ull, + 644901068808238420ull, 3428827542996055427ull}}, +{{631828164319080082ull, 4299314648737821693ull, + 14641184391292461738ull, 4286034428745069283ull}}, +{{2700735611913119003ull, 7298757673888526462ull, + 6844897235344094634ull, 2678771517965668302ull}}, +{{12599291551746174562ull, 18346819129215433885ull, + 17779493581034894100ull, 3348464397457085377ull}}, +{{1914056384400554490ull, 4486779837809740741ull, + 8389308921011453914ull, 4185580496821356722ull}}, +{{3502128249464040509ull, 7415923417058475867ull, + 9855004094059546600ull, 2615987810513347951ull}}, +{{18212718367112214348ull, 9269904271323094833ull, + 7707069099147045346ull, 3269984763141684939ull}}, +{{8930839903608104222ull, 2364008302299092734ull, + 5022150355506418779ull, 4087480953927106174ull}}, +{{970088921327677235ull, 17618406253432790623ull, + 16973902027473675448ull, 2554675596204441358ull}}, +{{15047669206941760256ull, 3576263743081436662ull, + 11994005497487318503ull, 3193344495255551698ull}}, +{{9586214471822424512ull, 18305387734133959540ull, + 5769134835004372320ull, 3991680619069439623ull}}, +{{15214756081743791128ull, 11440867333833724712ull, + 10523238299518814556ull, 2494800386918399764ull}}, +{{571701028470187294ull, 14301084167292155891ull, + 13154047874398518195ull, 3118500483647999705ull}}, +{{14549684340869897829ull, 13264669190687806959ull, + 2607501787715984032ull, 3898125604559999632ull}}, +{{16011081740684767999ull, 8290418244179879349ull, + 1629688617322490020ull, 2436328502849999770ull}}, +{{6178794120573796287ull, 10363022805224849187ull, + 11260482808507888333ull, 3045410628562499712ull}}, +{{3111806632289857455ull, 17565464524958449388ull, + 14075603510634860416ull, 3806763285703124640ull}}, +{{11168251182035936718ull, 10978415328099030867ull, + 8797252194146787760ull, 2379227053564452900ull}}, +{{9348627959117532993ull, 13723019160123788584ull, + 10996565242683484700ull, 2974033816955566125ull}}, +{{11685784948896916241ull, 17153773950154735730ull, + 18357392571781743779ull, 3717542271194457656ull}}, +{{11915301611487960555ull, 8415265709633015879ull, + 11473370357363589862ull, 2323463919496536035ull}}, +{{10282440995932562789ull, 1295710100186494041ull, + 9730026928277099424ull, 2904329899370670044ull}}, +{{17464737263343091390ull, 1619637625233117551ull, + 12162533660346374280ull, 3630412374213337555ull}}, +{{17219235560751476334ull, 2024547031541396939ull, + 10591481057005579946ull, 4538015467766671944ull}}, +{{8456179216255978757ull, 5877027913140760991ull, + 6619675660628487466ull, 2836259667354169965ull}}, +{{5958538001892585542ull, 16569656928280727047ull, + 12886280594212997236ull, 3545324584192712456ull}}, +{{2836486483938344023ull, 2265327086641357193ull, + 16107850742766246546ull, 4431655730240890570ull}}, +{{13302019098529934775ull, 6027515447578236149ull, + 14679092732656291995ull, 2769784831400556606ull}}, +{{2792465817880254756ull, 2922708291045407283ull, + 9125493878965589186ull, 3462231039250695758ull}}, +{{17325640327632482157ull, 12876757400661534911ull, + 2183495311852210674ull, 4327788799063369698ull}}, +{{17746054232411383205ull, 12659659393840847223ull, + 5976370588335019575ull, 2704867999414606061ull}}, +{{17570881772086841102ull, 11212888223873671125ull, + 12082149253846162373ull, 3381084999268257576ull}}, +{{8128544159826387665ull, 181052224559925195ull, + 15102686567307702967ull, 4226356249085321970ull}}, +{{2774497090677798339ull, 7030686667991035103ull, + 14050865122994702258ull, 2641472655678326231ull}}, +{{17303179418629411635ull, 18011730371843569686ull, + 12951895385315989918ull, 3301840819597907789ull}}, +{{12405602236431988736ull, 13291290927949686300ull, + 2354811176362823686ull, 4127301024497384737ull}}, +{{16976873434624768768ull, 3695370811541166033ull, + 13000972031295234564ull, 2579563140310865460ull}}, +{{7386033737998797248ull, 4619213514426457542ull, + 16251215039119043205ull, 3224453925388581825ull}}, +{{9170135643720752ull, 10385702911460459832ull, 6478960743616640294ull, + 4030567406735727282ull}}, +{{5731334777325470ull, 1879378301235399491ull, 8661036483187788088ull, + 2519104629209829551ull}}, +{{13842222223753820550ull, 2349222876544249363ull, + 6214609585557347206ull, 3148880786512286939ull}}, +{{12691091761264887783ull, 12159900632535087512ull, + 3156575963519296103ull, 3936100983140358674ull}}, +{{7931932350790554864ull, 14517466922975511551ull, + 6584545995626947968ull, 2460063114462724171ull}}, +{{5303229420060805676ull, 18146833653719389439ull, + 3618996476106297056ull, 3075078893078405214ull}}, +{{2017350756648619191ull, 4236797993439685183ull, + 13747117631987647129ull, 3843848616348006517ull}}, +{{8178373250546468851ull, 14177213791968272999ull, + 10897791529205973407ull, 2402405385217504073ull}}, +{{5611280544755698159ull, 13109831221532953345ull, + 18233925429934854663ull, 3003006731521880091ull}}, +{{11625786699372010603ull, 11775603008488803777ull, + 18180720768991180425ull, 3753758414402350114ull}}, +{{348587659466424771ull, 442222852664420505ull, 15974636499046875670ull, + 2346099009001468821ull}}, +{{5047420592760418868ull, 9776150602685301439ull, + 6133237568526430875ull, 2932623761251836027ull}}, +{{1697589722523135681ull, 7608502234929238895ull, + 3054860942230650690ull, 3665779701564795034ull}}, 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3443135024766596939ull}}, +{{7898370110976368394ull, 700782268333868628ull, 438594360332462877ull, + 4303918780958246174ull}}, +{{14159853356215006054ull, 2743831926922361844ull, + 14109179530489953010ull, 2689949238098903858ull}}, +{{17699816695268757568ull, 12653161945507728113ull, + 8413102376257665454ull, 3362436547623629823ull}}, +{{8289712813803783248ull, 6593080395029884334ull, + 5904691951894693914ull, 4203045684529537279ull}}, +{{569384490199976626ull, 8732361265321065613ull, + 10607961497575265552ull, 2626903552830960799ull}}, +{{5323416631177358686ull, 10915451581651332016ull, + 8648265853541694036ull, 3283629441038700999ull}}, +{{6654270788971698358ull, 13644314477064165020ull, + 6198646298499729641ull, 4104536801298376249ull}}, +{{13382291279962087282ull, 1610167520524021281ull, + 15403368982630800786ull, 2565335500811485155ull}}, +{{2892806044670445390ull, 11236081437509802410ull, + 14642525209861113078ull, 3206669376014356444ull}} +}; + +// ********************************************************************** + +#if __ENABLE_BINARY80__ + +static const UINT128 breakpoints_binary80[] = + { {{6337302757928054309ull, 494016656451265ull}}, +{{5069842206342443447ull, 395213325161012ull}}, +{{15123920209299685727ull, 316170660128809ull}}, +{{13130225890653766194ull, 505873056206095ull}}, +{{10504180712523012955ull, 404698444964876ull}}, +{{4713995755276500041ull, 323758755971901ull}}, +{{163695578958579419ull, 518014009555042ull}}, +{{11199002907392594505ull, 414411207644033ull}}, +{{16337899955397896250ull, 331528966115226ull}}, +{{315198225443261738ull, 530446345784363ull}}, +{{7630856209838430037ull, 424357076627490ull}}, +{{6104684967870744030ull, 339485661301992ull}}, +{{13456844763335100771ull, 543177058083187ull}}, +{{3386778181184259970ull, 434541646466550ull}}, +{{2709422544947407976ull, 347633317173240ull}}, +{{4335076071915852762ull, 556213307477184ull}}, +{{7157409672274592533ull, 444970645981747ull}}, +{{16793974182045404996ull, 355976516785397ull}}, +{{6056481716152503350ull, 284781213428318ull}}, +{{6001021931102095037ull, 455649941485309ull}}, +{{8490166359623586353ull, 364519953188247ull}}, +{{17860179531924600052ull, 291615962550597ull}}, +{{13818891992111718790ull, 466585540080956ull}}, +{{7365764778947464709ull, 373268432064765ull}}, +{{5892611823157971767ull, 298614745651812ull}}, +{{13117527731794665151ull, 477783593042899ull}}, +{{14183371000177642444ull, 382226874434319ull}}, +{{15036045614884024278ull, 305781499547455ull}}, +{{5610928910104887229ull, 489250399275929ull}}, +{{8178091942825820106ull, 391400319420743ull}}, +{{13921171183744476731ull, 313120255536594ull}}, +{{11205827449765431801ull, 500992408858551ull}}, +{{5275313145070435117ull, 400793927086841ull}}, +{{530901701314437771ull, 320635141669473ull}}, +{{15606837981070741726ull, 513016226671156ull}}, +{{8796121570114683058ull, 410412981336925ull}}, +{{7036897256091746446ull, 328330385069540ull}}, +{{11259035609746794314ull, 525328616111264ull}}, +{{12696577302539345774ull, 420262892889011ull}}, +{{6467913027289566296ull, 336210314311209ull}}, +{{17727358473147126720ull, 537936502897934ull}}, +{{17871235593259611699ull, 430349202318347ull}}, +{{6918290845123868713ull, 344279361854678ull}}, +{{7379916537456279618ull, 550846978967485ull}}, +{{5903933229965023694ull, 440677583173988ull}}, +{{12101844213455839602ull, 352542066539190ull}}, +{{9681475370764671681ull, 282033653231352ull}}, +{{732965334255833398ull, 451253845170164ull}}, +{{4275721082146577041ull, 361003076136131ull}}, +{{18177972124684902926ull, 288802460908904ull}}, +{{18016708955270113712ull, 462083937454247ull}}, +{{7034669534732270323ull, 369667149963398ull}}, +{{13006433257269636905ull, 295733719970718ull}}, +{{17120944396889508724ull, 473173951953149ull}}, +{{17386104332253517303ull, 378539161562519ull}}, +{{17598232280544724165ull, 302831329250015ull}}, +{{9710427575162007049ull, 484530126800025ull}}, +{{7768342060129605639ull, 387624101440020ull}}, +{{6214673648103684511ull, 310099281152016ull}}, +{{2564780207482074571ull, 496158849843226ull}}, +{{16809219424953300950ull, 396927079874580ull}}, +{{13447375539962640760ull, 317541663899664ull}}, +{{10447754419714494246ull, 508066662239463ull}}, +{{15736901165255416043ull, 406453329791570ull}}, +{{12589520932204332835ull, 325162663833256ull}}, +{{12764535862043111889ull, 520260262133210ull}}, +{{10211628689634489511ull, 416208209706568ull}}, +{{15548000581191412255ull, 332966567765254ull}}, +{{13808754485680528639ull, 532746508424407ull}}, +{{3668305959060602265ull, 426197206739526ull}}, +{{17692040026216123105ull, 340957765391620ull}}, +{{9860519968236245352ull, 545532424626593ull}}, +{{15267113604072816928ull, 436425939701274ull}}, +{{15903039698000163865ull, 349140751761019ull}}, +{{14376817072574531215ull, 558625202817631ull}}, +{{7812104843317714649ull, 446900162254105ull}}, +{{6249683874654171719ull, 357520129803284ull}}, +{{8689095914465247698ull, 286016103842627ull}}, +{{17591902277886306641ull, 457625766148203ull}}, +{{3005475378083314343ull, 366100612918563ull}}, +{{9783077931950472121ull, 292880490334850ull}}, +{{15652924691120755393ull, 468608784535760ull}}, +{{12522339752896604314ull, 374887027628608ull}}, +{{17396569431801104098ull, 299909622102886ull}}, +{{2009069387688394294ull, 479855395364619ull}}, +{{5296604324892625759ull, 383884316291695ull}}, +{{4237283459914100607ull, 307107453033356ull}}, +{{17847699980088291941ull, 491371924853369ull}}, +{{17967508798812543876ull, 393097539882695ull}}, +{{14374007039050035101ull, 314478031906156ull}}, +{{15619713632996235515ull, 503164851049850ull}}, +{{12495770906396988412ull, 402531880839880ull}}, +{{9996616725117590729ull, 322025504671904ull}}, +{{4926540315962414197ull, 515240807475047ull}}, +{{15009278696995662327ull, 412192645980037ull}}, +{{4628725328112709215ull, 329754116784030ull}}, +{{7405960524980334745ull, 527606586854448ull}}, +{{13303466049468088442ull, 422085269483558ull}}, +{{18021470469058291400ull, 337668215586846ull}}, +{{3008911047299893978ull, 540269144938955ull}}, +{{2407128837839915182ull, 432215315951164ull}}, +{{5615051885013842469ull, 345772252760931ull}}, +{{1605385386538327304ull, 553235604417490ull}}, +{{1284308309230661843ull, 442588483533992ull}}, +{{12095493091610260444ull, 354070786827193ull}}, +{{17055092102772029002ull, 283256629461754ull}}, +{{16220100920209515433ull, 453210607138807ull}}, +{{5597383106683791700ull, 362568485711046ull}}, +{{788557670605123037ull, 290054788568837ull}}, +{{4951041087710107183ull, 464087661710139ull}}, +{{7650181684909996069ull, 371270129368111ull}}, +{{2430796533186086532ull, 297016103494489ull}}, +{{11267972082581559098ull, 475225765591182ull}}, +{{1635680036581426632ull, 380180612472946ull}}, +{{16065939288232782598ull, 304144489978356ull}}, +{{18326805231688631511ull, 486631183965370ull}}, +{{14661444185350905209ull, 389304947172296ull}}, +{{8039806533538813844ull, 311443957737837ull}}, +{{16553039268404012473ull, 498310332380539ull}}, +{{16931780229465120302ull, 398648265904431ull}}, +{{9856075368830185918ull, 318918612723545ull}}, +{{15769720590128297469ull, 510269780357672ull}}, +{{5237078842618817329ull, 408215824286138ull}}, +{{11568360703578874509ull, 326572659428910ull}}, +{{62633052016647599ull, 522516255086257ull}}, +{{11118152885839049049ull, 418013004069005ull}}, +{{8894522308671239239ull, 334410403255204ull}}, +{{3163189249648251813ull, 535056645208327ull}}, +{{13598597843944332420ull, 428045316166661ull}}, +{{7189529460413555613ull, 342436252933329ull}}, +{{435200692435958011ull, 547898004693327ull}}, +{{11416206998174497378ull, 438318403754661ull}}, +{{5443616783797687579ull, 350654723003729ull}}, +{{16088484483560120774ull, 561047556805966ull}}, +{{9181438772106186296ull, 448838045444773ull}}, +{{14723848647168769683ull, 359070436355818ull}}, +{{711032473509284777ull, 287256349084655ull}}, +{{1137651957614855643ull, 459610158535448ull}}, +{{8288819195575705161ull, 367688126828358ull}}, +{{14009752985944384775ull, 294150501462686ull}}, +{{15036907148027194994ull, 470640802340298ull}}, +{{961479274196025025ull, 376512641872239ull}}, +{{4458532234098730343ull, 301210113497791ull}}, +{{18201698018783699519ull, 481936181596465ull}}, +{{14561358415026959615ull, 385548945277172ull}}, +{{4270389102537747046ull, 308439156221738ull}}, +{{3143273749318484950ull, 493502649954781ull}}, +{{17272014258422429253ull, 394802119963824ull}}, +{{17506960221479853725ull, 315841695971059ull}}, +{{16943089910142034991ull, 505346713553695ull}}, +{{13554471928113627993ull, 404277370842956ull}}, +{{7154228727748992071ull, 323421896674365ull}}, +{{11446765964398387314ull, 517475034678984ull}}, +{{12846761586260620174ull, 413980027743187ull}}, +{{2898711639524675493ull, 331184022194550ull}}, +{{4637938623239480789ull, 529894435511280ull}}, +{{3710350898591584631ull, 423915548409024ull}}, +{{6657629533615178028ull, 339132438727219ull}}, +{{18030904883268105491ull, 542611901963550ull}}, +{{14424723906614484393ull, 434089521570840ull}}, +{{11539779125291587514ull, 347271617256672ull}}, +{{3706251341498898730ull, 555634587610676ull}}, +{{17722396332166760277ull, 444507670088540ull}}, +{{14177917065733408221ull, 355606136070832ull}}, +{{3963636023102905931ull, 284484908856666ull}}, +{{17409864081190380459ull, 455175854170665ull}}, +{{13927891264952304367ull, 364140683336532ull}}, +{{3763615382478022847ull, 291312546669226ull}}, +{{17089831056190567525ull, 466100074670761ull}}, +{{9982516030210543697ull, 372880059736609ull}}, +{{11675361638910345281ull, 298304047789287ull}}, +{{3923183363288911157ull, 477286476462860ull}}, +{{3138546690631128925ull, 381829181170288ull}}, +{{9889534981988723786ull, 305463344936230ull}}, +{{15823255971181958059ull, 488741351897968ull}}, +{{1590558332719835477ull, 390993081518375ull}}, +{{1272446666175868382ull, 312794465214700ull}}, +{{2035914665881389411ull, 500471144343520ull}}, +{{1628731732705111529ull, 400376915474816ull}}, +{{16060380645131730516ull, 320301532379852ull}}, +{{10939213773243127533ull, 512482451807764ull}}, +{{12440719833336412349ull, 409985961446211ull}}, +{{6263227051927219556ull, 327988769156969ull}}, +{{17399860912567371936ull, 524782030651150ull}}, +{{13919888730053897549ull, 419825624520920ull}}, +{{11135910984043118039ull, 335860499616736ull}}, +{{10438759944985168216ull, 537376799386778ull}}, +{{15729705585471955219ull, 429901439509422ull}}, +{{5205066838893743529ull, 343921151607538ull}}, +{{4638758127488079324ull, 550273842572061ull}}, +{{21657687248553136ull, 440219074057649ull}}, +{{3706674964540752832ull, 352175259246119ull}}, +{{6654688786374512588ull, 281740207396895ull}}, +{{10647502058199220142ull, 450784331835032ull}}, +{{1139304017075555467ull, 360627465468026ull}}, +{{15668838472628085666ull, 288501972374420ull}}, +{{6623397482495385450ull, 461603155799073ull}}, +{{12677415615480129006ull, 369282524639258ull}}, +{{17520630121867923851ull, 295426019711406ull}}, +{{2207566491795305900ull, 472681631538251ull}}, +{{16523448452403886013ull, 378145305230600ull}}, +{{13218758761923108810ull, 302516244184480ull}}, +{{2703269945367422481ull, 484025990695169ull}}, +{{5851964771035848308ull, 387220792556135ull}}, +{{4681571816828678646ull, 309776634044908ull}}, +{{3801166092183975511ull, 495642614471853ull}}, +{{10419630503231001055ull, 396514091577482ull}}, +{{957006773100980197ull, 317211273261986ull}}, +{{12599257281187299286ull, 507538037219177ull}}, +{{2700708195466018782ull, 406030429775342ull}}, +{{13228613000598545995ull, 324824343820273ull}}, +{{17476431986215763269ull, 519718950112437ull}}, +{{6602447959488789969ull, 415775160089950ull}}, +{{5281958367591031975ull, 332620128071960ull}}, +{{8451133388145651160ull, 532192204915136ull}}, +{{3071557895774610605ull, 425753763932109ull}}, +{{6146595131361598807ull, 340603011145687ull}}, +{{13523901024920468415ull, 544964817833099ull}}, +{{14508469634678285055ull, 435971854266479ull}}, +{{15296124522484538367ull, 348777483413183ull}}, +{{2337706347523799448ull, 558043973461094ull}}, +{{5559513892760949882ull, 446435178768875ull}}, +{{4447611114208759905ull, 357148143015100ull}}, +{{3558088891367007924ull, 285718514412080ull}}, +{{5692942226187212679ull, 457149623059328ull}}, +{{11933051410433590789ull, 365719698447462ull}}, +{{2167743498863051985ull, 292575758757970ull}}, +{{3468389598180883176ull, 468121214012752ull}}, +{{13842758122770437511ull, 374496971210201ull}}, +{{7384857683474439685ull, 299597576968161ull}}, +{{4437074664075282850ull, 479356123149058ull}}, +{{10928357360744046927ull, 383484898519246ull}}, +{{5053337073853327218ull, 306787918815397ull}}, +{{11774688132907233872ull, 490860670104635ull}}, +{{9419750506325787098ull, 392688536083708ull}}, +{{14914498034544450324ull, 314150828866966ull}}, +{{16484499225787299873ull, 502641326187146ull}}, +{{9498250565887929575ull, 402113060949717ull}}, +{{219902823226523014ull, 321690448759774ull}}, +{{7730542146646257468ull, 514704718015638ull}}, +{{13563131346800826621ull, 411763774412510ull}}, +{{10850505077440661297ull, 329411019530008ull}}, +{{13671459309163147752ull, 527057631248013ull}}, +{{18315865076814338848ull, 421646104998410ull}}, +{{14652692061451471078ull, 337316883998728ull}}, +{{1308214409870891786ull, 539707014397966ull}}, +{{15803966786864354722ull, 431765611518372ull}}, +{{5264475800007663131ull, 345412489214698ull}}, +{{4733812465270350686ull, 552659982743517ull}}, +{{14855096416442011519ull, 442127986194813ull}}, +{{816030688927878245ull, 353702388955851ull}}, +{{15410219810109943889ull, 282961911164680ull}}, +{{6209607622466358606ull, 452739057863489ull}}, +{{8657034912714997208ull, 362191246290791ull}}, +{{3236279115430087443ull, 289752997032633ull}}, +{{1488697769946229586ull, 463604795252213ull}}, +{{8569655845440804315ull, 370883836201770ull}}, +{{6855724676352643452ull, 296707068961416ull}}, +{{3590461852680408877ull, 474731310338266ull}}, +{{17629764741111968395ull, 379785048270612ull}}, +{{6725114163405754069ull, 303828038616490ull}}, +{{10760182661449206511ull, 486124861786384ull}}, +{{12297494943901275532ull, 388899889429107ull}}, +{{2459298325637199779ull, 311119911543286ull}}, +{{15002923765245250616ull, 497791858469257ull}}, +{{4623641382712379847ull, 398233486775406ull}}, +{{9564291427993554ull, 318586789420325ull}}, +{{15302866284789687ull, 509738863072520ull}}, +{{12242293027831749ull, 407791090458016ull}}, +{{14767189093389906692ull, 326232872366412ull}}, +{{8870107290456209415ull, 521972595786260ull}}, +{{7096085832364967532ull, 417578076629008ull}}, +{{13055566295375794672ull, 334062461303206ull}}, +{{13510208443117450829ull, 534499938085130ull}}, +{{10808166754493960663ull, 427599950468104ull}}, +{{12335882218337078853ull, 342079960374483ull}}, +{{16048062734597415842ull, 547327936599173ull}}, 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+{{10930175315611246358ull, 282429400335717ull}}, +{{2730885246010352881ull, 451887040537148ull}}, +{{9563405826292102951ull, 361509632429718ull}}, +{{15029422290517503007ull, 289207705943774ull}}, +{{12979029220602273842ull, 462732329510039ull}}, +{{14072572191223729397ull, 370185863608031ull}}, +{{7568708938237073194ull, 296148690886425ull}}, +{{12109934301179317111ull, 473837905418280ull}}, +{{9687947440943453688ull, 379070324334624ull}}, +{{11439706767496673274ull, 303256259467699ull}}, +{{7235484383768946269ull, 485210015148319ull}}, +{{9477736321757067338ull, 388168012118655ull}}, +{{7582189057405653870ull, 310534409694924ull}}, +{{1063456047623315223ull, 496855055511879ull}}, +{{4540113652840562502ull, 397484044409503ull}}, +{{11010788551756270648ull, 317987235527602ull}}, +{{2859866423842391744ull, 508779576844164ull}}, +{{5977241953815823718ull, 407023661475331ull}}, +{{1092444748310748651ull, 325618929180265ull}}, +{{1747911597297197842ull, 520990286688424ull}}, +{{5087678092579668597ull, 416792229350739ull}}, +{{7759491288805645201ull, 333433783480591ull}}, +{{5036488432605211675ull, 533494053568946ull}}, +{{339841931342259017ull, 426795242855157ull}}, +{{11339919989299538183ull, 341436194284125ull}}, +{{18143871982879261093ull, 546297910854600ull}}, +{{14515097586303408874ull, 437038328683680ull}}, +{{11612078069042727099ull, 349630662946944ull}}, +{{7511278466242632389ull, 559409060715111ull}}, +{{2319673958252195588ull, 447527248572089ull}}, +{{5545087981343666794ull, 358021798857671ull}}, +{{746721570333023112ull, 286417439086137ull}}, +{{4884103327274747302ull, 458267902537819ull}}, +{{7596631476561708165ull, 366614322030255ull}}, +{{6077305181249366532ull, 293291457624204ull}}, +{{17102385919482807098ull, 469266332198726ull}}, +{{9992559920844335355ull, 375413065758981ull}}, +{{4304699121933557960ull, 300330452607185ull}}, +{{6887518595093692737ull, 480528724171496ull}}, +{{1820666061333043866ull, 384422979337197ull}}, +{{12524579293292166063ull, 307538383469757ull}}, +{{5281931610299824408ull, 492061413551612ull}}, +{{15293591732465590496ull, 393649130841289ull}}, +{{15924222200714382720ull, 314919304673031ull}}, +{{18100057891659191705ull, 503870887476850ull}}, +{{14480046313327353364ull, 403096709981480ull}}, +{{11584037050661882691ull, 322477367985184ull}}, +{{7466412836833281337ull, 515963788776295ull}}, +{{5973130269466625069ull, 412771031021036ull}}, +{{1089155400831389732ull, 330216824816829ull}}, +{{9121346270814044218ull, 528346919706926ull}}, +{{3607728201909325051ull, 422677535765541ull}}, +{{17643577820495101334ull, 338142028612432ull}}, +{{13472329253824520841ull, 541027245779892ull}}, +{{3399165773575796026ull, 432821796623914ull}}, +{{6408681433602547144ull, 346257437299131ull}}, +{{2875192664280254785ull, 554011899678610ull}}, +{{2300154131424203828ull, 443209519742888ull}}, +{{9218820934623183708ull, 354567615794310ull}}, +{{7375056747698546967ull, 283654092635448ull}}, +{{8110741981575764824ull, 453846548216717ull}}, +{{17556640029486342828ull, 363077238573373ull}}, +{{2977265579363343293ull, 290461790858699ull}}, +{{12142322556465169916ull, 464738865373918ull}}, +{{17092555674655956579ull, 371791092299134ull}}, +{{17363393354466675586ull, 297432873839307ull}}, +{{13024034108179039645ull, 475892598142892ull}}, +{{3040529657059411070ull, 380714078514314ull}}, +{{6121772540389439179ull, 304571262811451ull}}, +{{2416138435139282040ull, 487314020498322ull}}, +{{13000957192337156602ull, 389851216398657ull}}, +{{3022068124385904635ull, 311880973118926ull}}, +{{15903355443243178386ull, 499009556990281ull}}, +{{9033335539852632385ull, 399207645592225ull}}, +{{7226668431882105908ull, 319366116473780ull}}, +{{11562669491011369453ull, 510985786358048ull}}, +{{16628833222292916209ull, 408788629086438ull}}, +{{2235020133608601997ull, 327030903269151ull}}, +{{14644078657999494166ull, 523249445230641ull}}, +{{8025914111657685009ull, 418599556184513ull}}, +{{13799428918809968654ull, 334879644947610ull}}, +{{3632342196386398230ull, 535807431916177ull}} +}; + +static const int exponents_binary80[] = { -65, + -62, + -59, + -55, + -52, + -49, + -45, + -42, + -39, + -35, + -32, + -29, + -25, + -22, + -19, + -15, + -12, + -9, + -6, + -2, + 1, + 4, + 8, + 11, + 14, + 18, + 21, + 24, + 28, + 31, + 34, + 38, + 41, + 44, + 48, + 51, + 54, + 58, + 61, + 64, + 68, + 71, + 74, + 78, + 81, + 84, + 87, + 91, + 94, + 97, + 101, + 104, + 107, + 111, + 114, + 117, + 121, + 124, + 127, + 131, + 134, + 137, + 141, + 144, + 147, + 151, + 154, + 157, + 161, + 164, + 167, + 171, + 174, + 177, + 181, + 184, + 187, + 190, + 194, + 197, + 200, + 204, + 207, + 210, + 214, + 217, + 220, + 224, + 227, + 230, + 234, + 237, + 240, + 244, + 247, + 250, + 254, + 257, + 260, + 264, + 267, + 270, + 274, + 277, + 280, + 283, + 287, + 290, + 293, + 297, + 300, + 303, + 307, + 310, + 313, + 317, + 320, + 323, + 327, + 330, + 333, + 337, + 340, + 343, + 347, + 350, + 353, + 357, + 360, + 363, + 367, + 370, + 373, + 377, + 380, + 383, + 386, + 390, + 393, + 396, + 400, + 403, + 406, + 410, + 413, + 416, + 420, + 423, + 426, + 430, + 433, + 436, + 440, + 443, + 446, + 450, + 453, + 456, + 460, + 463, + 466, + 470, + 473, + 476, + 479, + 483, + 486, + 489, + 493, + 496, + 499, + 503, + 506, + 509, + 513, + 516, + 519, + 523, + 526, + 529, + 533, + 536, + 539, + 543, + 546, + 549, + 553, + 556, + 559, + 563, + 566, + 569, + 572, + 576, + 579, + 582, + 586, + 589, + 592, + 596, + 599, + 602, + 606, + 609, + 612, + 616, + 619, + 622, + 626, + 629, + 632, + 636, + 639, + 642, + 646, + 649, + 652, + 656, + 659, + 662, + 666, + 669, + 672, + 675, + 679, + 682, + 685, + 689, + 692, + 695, + 699, + 702, + 705, + 709, + 712, + 715, + 719, + 722, + 725, + 729, + 732, + 735, + 739, + 742, + 745, + 749, + 752, + 755, + 759, + 762, + 765, + 768, + 772, + 775, + 778, + 782, + 785, + 788, + 792, + 795, + 798, + 802, + 805, + 808, + 812, + 815, + 818, + 822, + 825, + 828, + 832, + 835, + 838, + 842, + 845, + 848, + 852, + 855, + 858, + 862, + 865, + 868, + 871, + 875, + 878, + 881, + 885, + 888, + 891, + 895, + 898, + 901, + 905, + 908, + 911, + 915, + 918, + 921, + 925, + 928, + 931, + 935, + 938, + 941, + 945, + 948, + 951, + 955, + 958, + 961, + 964, + 968, + 971, + 974, + 978, + 981, + 984, + 988, + 991, + 994, + 998, + 1001, + 1004, + 1008, + 1011, + 1014, + 1018, + 1021, + 1024, + 1028, + 1031, + 1034, + 1038, + 1041, + 1044, + 1048, + 1051, + 1054, + 1058, + 1061, + 1064, + 1067, + 1071, + 1074, + 1077, + 1081, + 1084, + 1087, + 1091, + 1094, + 1097, + 1101, + 1104, + 1107, + 1111, + 1114, + 1117, + 1121, + 1124, + 1127, + 1131, + 1134, + 1137, + 1141, + 1144, + 1147, + 1151, + 1154, + 1157, + 1160, + 1164, + 1167, + 1170, + 1174, + 1177, + 1180, + 1184, + 1187, + 1190, + 1194, + 1197, + 1200, + 1204, + 1207, + 1210, + 1214, + 1217, + 1220, + 1224, + 1227, + 1230, + 1234, + 1237, + 1240, + 1244, + 1247, + 1250, + 1253, + 1257, + 1260, + 1263, + 1267, + 1270, + 1273, + 1277, + 1280, + 1283, + 1287, + 1290, + 1293, + 1297, + 1300, + 1303, + 1307, + 1310, + 1313, + 1317, + 1320, + 1323, + 1327, + 1330, + 1333, + 1337, + 1340, + 1343, + 1347, + 1350, + 1353, + 1356, + 1360, + 1363, + 1366, + 1370, + 1373, + 1376, + 1380, + 1383, + 1386, + 1390, + 1393, + 1396, + 1400, + 1403, + 1406, + 1410, + 1413, + 1416, + 1420, + 1423, + 1426, + 1430, + 1433, + 1436, + 1440, + 1443, + 1446, + 1449, + 1453, + 1456, + 1459, + 1463, + 1466, + 1469, + 1473, + 1476, + 1479, + 1483, + 1486, + 1489, + 1493, + 1496, + 1499, + 1503, + 1506, + 1509, + 1513, + 1516, + 1519, + 1523, + 1526, + 1529, + 1533, + 1536, + 1539, + 1543, + 1546, + 1549, + 1552, + 1556, + 1559, + 1562, + 1566, + 1569, + 1572, + 1576, + 1579, + 1582, + 1586, + 1589, + 1592, + 1596, + 1599, + 1602, + 1606, + 1609, + 1612, + 1616, + 1619, + 1622, + 1626, + 1629, + 1632, + 1636, + 1639, + 1642, + 1645, + 1649, + 1652, + 1655, + 1659, + 1662, + 1665, + 1669, + 1672, + 1675, + 1679, + 1682, + 1685, + 1689, + 1692, + 1695, + 1699, + 1702, + 1705, + 1709, + 1712, + 1715, + 1719, + 1722, + 1725, + 1729, + 1732, + 1735, + 1738, + 1742, + 1745, + 1748, + 1752, + 1755, + 1758, + 1762, + 1765, + 1768, + 1772, + 1775, + 1778, + 1782, + 1785, + 1788, + 1792, + 1795, + 1798, + 1802, + 1805, + 1808, + 1812, + 1815, + 1818, + 1822, + 1825, + 1828, + 1832, + 1835, + 1838, + 1841, + 1845, + 1848, + 1851, + 1855, + 1858, + 1861, + 1865, + 1868, + 1871, + 1875, + 1878, + 1881, + 1885, + 1888, + 1891, + 1895, + 1898, + 1901, + 1905, + 1908, + 1911, + 1915, + 1918, + 1921, + 1925, + 1928, + 1931, + 1934, + 1938, + 1941, + 1944, + 1948, + 1951, + 1954, + 1958, + 1961, + 1964, + 1968, + 1971, + 1974, + 1978, + 1981, + 1984, + 1988, + 1991, + 1994, + 1998, + 2001, + 2004, + 2008, + 2011, + 2014, + 2018, + 2021, + 2024, + 2028, + 2031, + 2034, + 2037, + 2041, + 2044, + 2047, + 2051, + 2054, + 2057, + 2061, + 2064, + 2067, + 2071, + 2074, + 2077, + 2081, + 2084, + 2087, + 2091, + 2094, + 2097, + 2101, + 2104, + 2107, + 2111, + 2114, + 2117, + 2121, + 2124, + 2127, + 2130, + 2134, + 2137, + 2140, + 2144, + 2147, + 2150, + 2154, + 2157, + 2160, + 2164, + 2167, + 2170, + 2174, + 2177, + 2180, + 2184, + 2187, + 2190, + 2194, + 2197, + 2200, + 2204, + 2207, + 2210, + 2214, + 2217, + 2220, + 2223, + 2227, + 2230, + 2233, + 2237, + 2240, + 2243, + 2247, + 2250, + 2253, + 2257, + 2260, + 2263, + 2267, + 2270, + 2273, + 2277, + 2280, + 2283, + 2287, + 2290, + 2293, + 2297, + 2300, + 2303, + 2307, + 2310, + 2313, + 2317, + 2320, + 2323, + 2326, + 2330, + 2333, + 2336, + 2340, + 2343, + 2346, + 2350, + 2353, + 2356, + 2360, + 2363, + 2366, + 2370, + 2373, + 2376, + 2380, + 2383, + 2386, + 2390, + 2393, + 2396, + 2400, + 2403, + 2406, + 2410, + 2413, + 2416, + 2419, + 2423, + 2426, + 2429, + 2433, + 2436, + 2439, + 2443, + 2446, + 2449, + 2453, + 2456, + 2459, + 2463, + 2466, + 2469, + 2473, + 2476, + 2479, + 2483, + 2486, + 2489, + 2493, + 2496, + 2499, + 2503, + 2506, + 2509, + 2513, + 2516, + 2519, + 2522, + 2526, + 2529, + 2532, + 2536, + 2539, + 2542, + 2546, + 2549, + 2552, + 2556, + 2559, + 2562, + 2566, + 2569, + 2572, + 2576, + 2579, + 2582, + 2586, + 2589, + 2592, + 2596, + 2599, + 2602, + 2606, + 2609, + 2612, + 2615, + 2619, + 2622, + 2625, + 2629, + 2632, + 2635, + 2639, + 2642, + 2645, + 2649, + 2652, + 2655, + 2659, + 2662, + 2665, + 2669, + 2672, + 2675, + 2679, + 2682, + 2685, + 2689, + 2692, + 2695, + 2699, + 2702, + 2705, + 2708, + 2712, + 2715, + 2718, + 2722, + 2725, + 2728, + 2732, + 2735, + 2738, + 2742, + 2745, + 2748, + 2752, + 2755, + 2758, + 2762, + 2765, + 2768, + 2772, + 2775, + 2778, + 2782, + 2785, + 2788, + 2792, + 2795, + 2798, + 2802, + 2805, + 2808, + 2811, + 2815, + 2818, + 2821, + 2825, + 2828, + 2831, + 2835, + 2838, + 2841, + 2845, + 2848, + 2851, + 2855, + 2858, + 2861, + 2865, + 2868, + 2871, + 2875, + 2878, + 2881, + 2885, + 2888, + 2891, + 2895, + 2898, + 2901, + 2904, + 2908, + 2911, + 2914, + 2918, + 2921, + 2924, + 2928, + 2931, + 2934, + 2938, + 2941, + 2944, + 2948, + 2951, + 2954, + 2958, + 2961, + 2964, + 2968, + 2971, + 2974, + 2978, + 2981, + 2984, + 2988, + 2991, + 2994, + 2998, + 3001, + 3004, + 3007, + 3011, + 3014, + 3017, + 3021, + 3024, + 3027, + 3031, + 3034, + 3037, + 3041, + 3044, + 3047, + 3051, + 3054, + 3057, + 3061, + 3064, + 3067, + 3071, + 3074, + 3077, + 3081, + 3084, + 3087, + 3091, + 3094, + 3097, + 3100, + 3104, + 3107, + 3110, + 3114, + 3117, + 3120, + 3124, + 3127, + 3130, + 3134, + 3137, + 3140, + 3144, + 3147, + 3150, + 3154, + 3157, + 3160, + 3164, + 3167, + 3170, + 3174, + 3177, + 3180, + 3184, + 3187, + 3190, + 3193, + 3197, + 3200, + 3203, + 3207, + 3210, + 3213, + 3217, + 3220, + 3223, + 3227, + 3230, + 3233, + 3237, + 3240, + 3243, + 3247, + 3250, + 3253, + 3257, + 3260, + 3263, + 3267, + 3270, + 3273, + 3277, + 3280, + 3283, + 3287, + 3290, + 3293, + 3296, + 3300, + 3303, + 3306, + 3310, + 3313, + 3316, + 3320, + 3323, + 3326, + 3330, + 3333, + 3336, + 3340, + 3343, + 3346, + 3350, + 3353, + 3356, + 3360, + 3363, + 3366, + 3370, + 3373, + 3376, + 3380, + 3383, + 3386, + 3389, + 3393, + 3396, + 3399, + 3403, + 3406, + 3409, + 3413, + 3416, + 3419, + 3423, + 3426, + 3429, + 3433, + 3436, + 3439, + 3443, + 3446, + 3449, + 3453, + 3456, + 3459, + 3463, + 3466, + 3469, + 3473, + 3476, + 3479, + 3483, + 3486, + 3489, + 3492, + 3496, + 3499, + 3502, + 3506, + 3509, + 3512, + 3516, + 3519, + 3522, + 3526, + 3529, + 3532, + 3536, + 3539, + 3542, + 3546, + 3549, + 3552, + 3556, + 3559, + 3562, + 3566, + 3569, + 3572, + 3576, + 3579, + 3582, + 3585, + 3589, + 3592, + 3595, + 3599, + 3602, + 3605, + 3609, + 3612, + 3615, + 3619, + 3622, + 3625, + 3629, + 3632, + 3635, + 3639, + 3642, + 3645, + 3649, + 3652, + 3655, + 3659, + 3662, + 3665, + 3669, + 3672, + 3675, + 3679, + 3682, + 3685, + 3688, + 3692, + 3695, + 3698, + 3702, + 3705, + 3708, + 3712, + 3715, + 3718, + 3722, + 3725, + 3728, + 3732, + 3735, + 3738, + 3742, + 3745, + 3748, + 3752, + 3755, + 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32848, + 32852, + 32855, + 32858, + 32862, + 32865, + 32868, + 32872, + 32875, + 32878, + 32882, +}; + +static const UINT256 multipliers1_binary80[] = + { {{12415850090107640902ull, 14557465677128539270ull, + 4938398379086257084ull, 5255184001115807319ull}}, +{{6296440575779775320ull, 18196832096410674088ull, + 1561311955430433451ull, 6568980001394759149ull}}, +{{7870550719724719149ull, 18134354102085954706ull, + 6563325962715429718ull, 8211225001743448936ull}}, +{{9530780218255337373ull, 6722285295376333787ull, + 4102078726697143574ull, 5132015626089655585ull}}, +{{7301789254391783812ull, 17626228656075193042ull, + 9739284426798817371ull, 6415019532612069481ull}}, +{{18350608604844505572ull, 17421099801666603398ull, + 16785791551925909618ull, 8018774415765086851ull}}, +{{6857444359600428079ull, 15499873394469015028ull, + 8185276710739999559ull, 5011734009853179282ull}}, +{{8571805449500535098ull, 14763155724658880881ull, + 1008223851570223641ull, 6264667512316474103ull}}, 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+{{8549702918292575412ull, 14043676391062638287ull, + 12336374434731266227ull, 5202602621332106919ull}}, +{{6075442629438331361ull, 12942909470400909955ull, + 10808782024986694880ull, 6503253276665133649ull}}, +{{2982617268370526297ull, 16178636838001137444ull, + 18122663549660756504ull, 8129066595831417061ull}}, +{{11087507829586354744ull, 10111648023750710902ull, + 13632507727751666767ull, 5080666622394635663ull}}, +{{4636012750128167622ull, 8027874011261000724ull, + 12428948641262195555ull, 6350833277993294579ull}}, +{{5795015937660209527ull, 5423156495648863001ull, + 10924499783150356540ull, 7938541597491618224ull}}, +{{15151100007106100715ull, 12612844846635315183ull, + 6827812364468972837ull, 4961588498432261390ull}}, +{{14327188990455237989ull, 1930998003011980267ull, + 17758137492440991855ull, 6201985623040326737ull}}, +{{13297300219641659582ull, 16248805559047139046ull, + 8362613810269076106ull, 7752482028800408422ull}}, +{{3699126618848649335ull, 14767189492831849808ull, + 614947612990784662ull, 4845301268000255264ull}} +}; + +static const UINT256 multipliers2_binary80[] = + { {{6207925045053820451ull, 7278732838564269635ull, + 11692571226397904350ull, 2627592000557903659ull}}, +{{3148220287889887660ull, 18321788085060112852ull, + 10004028014569992533ull, 3284490000697379574ull}}, +{{3935275359862359575ull, 9067177051042977353ull, + 3281662981357714859ull, 4105612500871724468ull}}, +{{13988762145982444495ull, 3361142647688166893ull, + 11274411400203347595ull, 2566007813044827792ull}}, +{{3650894627195891906ull, 18036486364892372329ull, + 14093014250254184493ull, 3207509766306034740ull}}, +{{9175304302422252786ull, 8710549900833301699ull, + 17616267812817730617ull, 4009387207882543425ull}}, +{{3428722179800214040ull, 16973308734089283322ull, + 4092638355369999779ull, 2505867004926589641ull}}, +{{13509274761605043357ull, 16604949899184216248ull, + 9727483962639887628ull, 3132333756158237051ull}}, +{{16886593452006304197ull, 2309443300270718694ull, + 7547668934872471632ull, 3915417195197796314ull}}, +{{5942434889076552219ull, 1443402062669199184ull, + 9328979102722682674ull, 2447135746998622696ull}}, +{{7428043611345690274ull, 11027624615191274788ull, + 11661223878403353342ull, 3058919683748278370ull}}, +{{9285054514182112842ull, 4561158732134317677ull, + 5353157811149415870ull, 3823649604685347963ull}}, +{{8109002080577514479ull, 16685782262866112260ull, + 1039880622754690966ull, 2389781002928342477ull}}, +{{10136252600721893098ull, 11633855791727864517ull, + 5911536796870751612ull, 2987226253660428096ull}}, +{{17282001769329754276ull, 14542319739659830646ull, + 7389420996088439515ull, 3734032817075535120ull}}, +{{6189565087403708519ull, 6783106828073700202ull, + 4618388122555274697ull, 2333770510672209450ull}}, +{{16960328396109411457ull, 13090569553519513156ull, + 14996357190048869179ull, 2917213138340261812ull}}, +{{2753666421427212705ull, 11751525923472003542ull, + 298702413851534858ull, 3646516422925327266ull}}, +{{12665455063638791689ull, 5466035367485228619ull, + 9596750054169194381ull, 4558145528656659082ull}}, +{{5610066405560550854ull, 5722115113891961839ull, + 10609654802283134392ull, 2848840955410411926ull}}, +{{2400896988523300663ull, 7152643892364952299ull, + 4038696465999142182ull, 3561051194263014908ull}}, +{{16836179290936289540ull, 18164176902310966181ull, + 5048370582498927727ull, 4451313992828768635ull}}, +{{12828455066048874915ull, 18270139591585435719ull, + 849388604848135877ull, 2782071245517980397ull}}, +{{11423882814133705740ull, 9002616434199630937ull, + 5673421774487557751ull, 3477589056897475496ull}}, +{{444795462384968462ull, 6641584524322150768ull, 7091777218109447189ull, + 4346986321121844370ull}}, +{{277997163990605289ull, 6456833336915038182ull, 9044046779745792397ull, + 2716866450701152731ull}}, +{{9570868491843032419ull, 12682727689571185631ull, + 6693372456254852592ull, 3396083063376440914ull}}, +{{7351899596376402620ull, 15853409611963982039ull, + 17590087607173341548ull, 4245103829220551142ull}}, +{{11512466275376333494ull, 685008970622712966ull, + 6382118736055950564ull, 2653189893262844464ull}}, +{{5167210807365641059ull, 856261213278391208ull, 7977648420069938205ull, + 3316487366578555580ull}}, +{{6459013509207051324ull, 5682012535025376914ull, + 9972060525087422756ull, 4145609208223194475ull}}, +{{8648569461681794981ull, 12774629871245636379ull, + 3926694818965945270ull, 2591005755139496547ull}}, +{{6199025808674855823ull, 6744915302202269666ull, 296682505280043684ull, + 3238757193924370684ull}}, +{{16972154297698345586ull, 8431144127752837082ull, + 370853131600054605ull, 4048446492405463355ull}}, +{{15219282454488853896ull, 7575308089059217128ull, + 16372684271745891792ull, 2530279057753414596ull}}, +{{577358994401515753ull, 9469135111324021411ull, 2019111265972813124ull, + 3162848822191768246ull}}, +{{14556756798284058404ull, 11836418889155026763ull, + 11747261119320792213ull, 3953561027739710307ull}}, +{{6792129989713842550ull, 9703604814935585679ull, + 5036195190361801181ull, 2470975642337318942ull}}, +{{3878476468714915284ull, 16741192037096870003ull, + 15518616024807027284ull, 3088719552921648677ull}}, +{{236409567466256201ull, 2479745972661535888ull, 5563211975726620394ull, + 3860899441152060847ull}}, +{{147755979666410126ull, 6161527251340847834ull, + 10394536512470219602ull, 2413062150720038029ull}}, +{{9408067011437788465ull, 16925281101030835600ull, + 17604856659015162406ull, 3016327688400047536ull}}, +{{11760083764297235581ull, 11933229339433768692ull, + 3559326750059401392ull, 3770409610500059421ull}}, +{{16573424389540548046ull, 7458268337146105432ull, + 4530422228000819822ull, 2356506006562537138ull}}, +{{2270036413216133442ull, 99463384577855983ull, 14886399821855800586ull, + 2945632508203171422ull}}, +{{16672603571802330514ull, 9347701267577095786ull, + 9384627740464974924ull, 3682040635253964278ull}}, +{{11617382427898137335ull, 11684626584471369733ull, + 2507412638726442847ull, 4602550794067455348ull}}, +{{9566707026650029786ull, 14220420642935687939ull, + 10790504936058802587ull, 2876594246292159592ull}}, +{{7346697764885149329ull, 13163839785242222020ull, + 13488131170073503234ull, 3595742807865199490ull}}, +{{9183372206106436661ull, 7231427694698001717ull, + 7636791925737103235ull, 4494678509831499363ull}}, +{{8045450638030216865ull, 2213799299972557121ull, + 2467151944371995570ull, 2809174068644687102ull}}, +{{14668499315965158985ull, 11990621161820472209ull, + 12307311967319770270ull, 3511467585805858877ull}}, +{{4500566089674285020ull, 5764904415420814454ull, + 1549081903867549126ull, 4389334482257323597ull}}, +{{16647911861328591849ull, 17438123314920172745ull, + 3274019199130912155ull, 2743334051410827248ull}}, +{{6974831771378576100ull, 17185968125222828028ull, + 4092523998913640194ull, 3429167564263534060ull}}, +{{8718539714223220124ull, 12259088119673759227ull, + 5115654998642050243ull, 4286459455329417575ull}}, +{{3143244312175818626ull, 5356087065582405565ull, + 10114813401792363258ull, 2679037159580885984ull}}, +{{8540741408647161186ull, 15918480868832782764ull, + 12643516752240454072ull, 3348796449476107480ull}}, +{{10675926760808951483ull, 1451357012331426839ull, + 15804395940300567591ull, 4185995561845134350ull}}, +{{13589983253146676533ull, 7824627160348223630ull, + 5266061444260466840ull, 2616247226153208969ull}}, +{{7764107029578569858ull, 9780783950435279538ull, + 11194262823752971454ull, 3270309032691511211ull}}, +{{481761750118436514ull, 3002607901189323615ull, 9381142511263826414ull, + 4087886290864389014ull}}, +{{7218630121465104678ull, 15711687993525490971ull, + 1251528051112503604ull, 2554928931790243134ull}}, +{{4411601633403992943ull, 1192865918197312098ull, + 10787782100745405314ull, 3193661164737803917ull}}, +{{14737874078609766987ull, 10714454434601415930ull, + 18096413644359144546ull, 3992076455922254896ull}}, +{{13822857317558492271ull, 11308220040053272860ull, + 11310258527724465341ull, 2495047784951409310ull}}, +{{17278571646948115338ull, 300216994784427363ull, + 4914451122800805869ull, 3118809731189261638ull}}, +{{16986528540257756269ull, 4986957261907922108ull, + 15366435940355783144ull, 3898512163986577047ull}}, +{{1393208300806321860ull, 3116848288692451318ull, + 16521551490363446321ull, 2436570102491610654ull}}, +{{10964882412862678133ull, 8507746379292952051ull, + 11428567326099532093ull, 3045712628114513318ull}}, +{{9094416997650959762ull, 15246368992543577968ull, + 5062337120769639308ull, 3807140785143141648ull}}, +{{5684010623531849852ull, 305608583484960422ull, 3163960700481024568ull, + 2379462990714463530ull}}, +{{16328385316269588122ull, 382010729356200527ull, + 13178322912456056518ull, 2974328738393079412ull}}, +{{15798795626909597249ull, 9700885448550026467ull, + 16472903640570070647ull, 3717910922991349265ull}}, +{{7568404257604804329ull, 12980582432984848398ull, + 3378035747715212298ull, 2323694326869593291ull}}, +{{237133285151229603ull, 7002356004376284690ull, + 18057602739926179085ull, 2904617908586991613ull}}, +{{9519788643293812811ull, 13364631023897743766ull, + 8736945369625560144ull, 3630772385733739517ull}}, +{{2676363767262490206ull, 16705788779872179708ull, + 15532867730459338084ull, 4538465482167174396ull}}, +{{10896099391393832187ull, 1217745950565336509ull, + 484670294682310495ull, 2836540926354483998ull}}, +{{18231810257669678138ull, 15357240493488834348ull, + 9829209905207663926ull, 3545676157943104997ull}}, +{{4343018748377546056ull, 9973178580006267128ull, + 16898198399936967812ull, 4432095197428881246ull}}, +{{2714386717735966285ull, 15456608649358692763ull, + 5949687981533216978ull, 2770059498393050779ull}}, +{{17228041452452121568ull, 10097388774843590145ull, + 2825423958489133319ull, 3462574372991313474ull}}, +{{7699993760282988248ull, 8010049950127099778ull, + 12755151984966192457ull, 4328217966239141842ull}}, +{{9424182118604255559ull, 16535496264897907121ull, + 12583656009031258189ull, 2705136228899463651ull}}, +{{16391913666682707353ull, 6834312275840220189ull, + 11117883992861684833ull, 3381420286124329564ull}}, +{{6654834028071220479ull, 13154576363227663141ull, + 13897354991077106041ull, 4226775357655411955ull}}, +{{6465114276758206752ull, 1304081199376207607ull, + 6380003860209497324ull, 2641734598534632472ull}}, +{{3469706827520370535ull, 1630101499220259509ull, + 7975004825261871655ull, 3302168248168290590ull}}, +{{8948819552827851073ull, 15872684929307488098ull, + 745383994722563760ull, 4127710310210363238ull}}, +{{10204698238944794825ull, 9920428080817180061ull, + 14300923051983766062ull, 2579818943881477023ull}}, +{{17367558817108381435ull, 3177163064166699268ull, + 13264467796552319674ull, 3224773679851846279ull}}, +{{3262704447675925178ull, 13194825867063149894ull, + 11968898727263011688ull, 4030967099814807849ull}}, +{{15874248335079616948ull, 8246766166914468683ull, + 563032676898300449ull, 2519354437384254906ull}}, +{{15231124400422133281ull, 14920143727070473758ull, + 9927162882977651369ull, 3149193046730318632ull}}, +{{9815533463672890793ull, 4815121603555928486ull, + 12408953603722064212ull, 3936491308412898290ull}}, +{{1523022396368168842ull, 12232823039077231112ull, + 12367282020753678036ull, 2460307067758061431ull}}, +{{1903777995460211052ull, 15291028798846538890ull, + 10847416507514709641ull, 3075383834697576789ull}}, +{{11603094531180039623ull, 5278727943276009900ull, + 18170956652820774956ull, 3844229793371970986ull}}, +{{16475306118842300573ull, 12522577001402281995ull, + 15968533926440372251ull, 2402643620857481866ull}}, +{{15982446630125487812ull, 11041535233325464590ull, + 10737295371195689506ull, 3003304526071852333ull}}, +{{10754686250802083957ull, 4578547004802054930ull, + 18033305232421999787ull, 3754130657589815416ull}}, +{{11333364925178690377ull, 555748868787590379ull, + 11270815770263749867ull, 2346331660993634635ull}}, +{{9555020138045975067ull, 14529744141266651686ull, + 9476833694402299429ull, 2932914576242043294ull}}, +{{2720403135702693026ull, 4327122121301150896ull, + 2622670081148098479ull, 3666143220302554118ull}}, +{{3400503919628366282ull, 797216633199050716ull, + 12501709638289898907ull, 4582679025378192647ull}}, +{{11348686986622504735ull, 16639161460245264361ull, + 14731097551572268672ull, 2864174390861370404ull}}, +{{350800677995967206ull, 2352207751597028836ull, + 18413871939465335841ull, 3580217988576713005ull}}, +{{438500847494959008ull, 7551945707923673949ull, 9182281869049506089ull, + 4475272485720891257ull}}, +{{2579906038898043332ull, 16249181113520765978ull, + 17268141214224411065ull, 2797045303575557035ull}}, +{{12448254585477329973ull, 6476418336618793760ull, + 16973490499353125928ull, 3496306629469446294ull}}, +{{15560318231846662466ull, 8095522920773492200ull, + 11993491087336631602ull, 4370383286836807868ull}}, +{{9725198894904164041ull, 9671387843910820529ull, + 16719303966440170559ull, 2731489554273004917ull}}, +{{16768184637057592956ull, 7477548786461137757ull, + 7064071902768049487ull, 3414361942841256147ull}}, +{{7125172741039827482ull, 4735249964649034293ull, + 4218403860032673955ull, 4267952428551570184ull}}, +{{6759075972363586129ull, 653688218691952481ull, 2636502412520421222ull, + 2667470267844731365ull}}, +{{13060530983881870565ull, 10040482310219716409ull, + 7907314034077914431ull, 3334337834805914206ull}}, +{{2490605674570174494ull, 7938916869347257608ull, 660770505742617231ull, + 4167922293507392758ull}}, +{{1556628546606359059ull, 11879352070983117861ull, + 14248039621371299481ull, 2604951433442120473ull}}, +{{6557471701685336727ull, 1014132033446733614ull, + 3974991471431960640ull, 3256189291802650592ull}}, +{{17420211663961446717ull, 1267665041808417017ull, + 4968739339289950800ull, 4070236614753313240ull}}, +{{3970103262334822342ull, 792290651130260636ull, 3105462087056219250ull, + 2543897884220820775ull}}, +{{4962629077918527928ull, 10213735350767601603ull, + 17716885664102437774ull, 3179872355276025968ull}}, +{{1591600328970772006ull, 3543797151604726196ull, + 3699363006418495602ull, 3974840444095032461ull}}, +{{10218122242461508312ull, 6826559238180341776ull, + 4617944888225253703ull, 2484275277559395288ull}}, +{{12772652803076885390ull, 3921513029298039316ull, + 5772431110281567129ull, 3105344096949244110ull}}, +{{15965816003846106737ull, 9513577305049937049ull, + 16438910924706734719ull, 3881680121186555137ull}}, +{{3061105974762734855ull, 12863514843297292512ull, + 3356790300300627343ull, 2426050075741596961ull}}, +{{3826382468453418568ull, 11467707535694227736ull, + 8807673893803172083ull, 3032562594676996201ull}}, +{{4782978085566773210ull, 9722948401190396766ull, + 15621278385681353008ull, 3790703243346245251ull}}, +{{16824419358761396969ull, 6076842750743997978ull, + 7457455981837151678ull, 2369189527091403282ull}}, +{{11807152161596970403ull, 16819425475284773281ull, + 98447940441663789ull, 2961486908864254103ull}}, 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+{{17844653936760480384ull, 7879444388312919738ull, + 4149217004770514598ull, 4425884835339920696ull}}, +{{15764594728902688144ull, 312966724268186932ull, + 2593260627981571624ull, 2766178022087450435ull}}, +{{1258999337418808564ull, 391208405335233666ull, + 17076633840259128242ull, 3457722527609313043ull}}, +{{10797121208628286513ull, 9712382543523817890ull, + 16734106281896522398ull, 4322153159511641304ull}}, +{{11359886773820066975ull, 1458553071274998277ull, + 10458816426185326499ull, 2701345724694775815ull}}, +{{364800411992920006ull, 15658249394375911559ull, + 8461834514304270219ull, 3376682155868469769ull}}, +{{14291058570273313720ull, 14961125724542501544ull, + 15188979161307725678ull, 4220852694835587211ull}}, +{{8931911606420821075ull, 4739017559411675561ull, + 7187268966603634597ull, 2638032934272242007ull}}, +{{15776575526453414248ull, 10535457967691982355ull, + 4372400189827155342ull, 3297541167840302509ull}}, +{{15109033389639379905ull, 3945950422760202136ull, + 10077186255711332082ull, 4121926459800378136ull}}, +{{9443145868524612441ull, 7077905032652514239ull, + 6298241409819582551ull, 2576204037375236335ull}}, +{{7192246317228377647ull, 4235695272388254895ull, + 3261115743847090285ull, 3220255046719045419ull}}, +{{4378621878108084155ull, 9906305108912706523ull, + 17911452735091026568ull, 4025318808398806773ull}}, +{{430795664603858645ull, 6191440693070441577ull, + 13500500968645585557ull, 2515824255249254233ull}}, +{{5150180599182211210ull, 12350986884765439875ull, + 3040568155524818234ull, 3144780319061567792ull}}, +{{1826039730550376108ull, 6215361569102024036ull, + 3800710194406022793ull, 3930975398826959740ull}}, +{{10364646868448760876ull, 15413816026757234782ull, + 11598815908358540053ull, 2456859624266849837ull}}, +{{3732436548706175287ull, 5432211978164379766ull, 663461830166011355ull, + 3071074530333562297ull}}, +{{13888917722737494916ull, 2178578954278086803ull, + 5441013306134902098ull, 3838843162916952871ull}}, +{{6374730567497240371ull, 5973297864851192156ull, + 10318162343975395667ull, 2399276976823095544ull}}, +{{7968413209371550464ull, 2854936312636602291ull, + 12897702929969244584ull, 2999096221028869430ull}}, +{{5348830493287050175ull, 3568670390795752864ull, + 6898756625606779922ull, 3748870276286086788ull}}, +{{3343019058304406360ull, 6842105012674733444ull, + 13535094927859013259ull, 2343043922678804242ull}}, +{{4178773822880507950ull, 3940945247416028901ull, + 7695496622968990766ull, 2928804903348505303ull}}, +{{9835153297028022841ull, 14149553596124811934ull, + 5007684760283850553ull, 3661006129185631629ull}}, +{{3070569584430252743ull, 3851883939873851206ull, + 10871291968782201096ull, 4576257661482039536ull}}, +{{15754164045551071677ull, 2407427462421157003ull, + 6794557480488875685ull, 2860161038426274710ull}}, +{{15081019038511451692ull, 7620970346453834158ull, + 17716568887465870414ull, 3575201298032843387ull}}, +{{9627901761284538806ull, 302840896212516890ull, + 17534025090904950114ull, 4469001622541054234ull}}, +{{10629124619230224658ull, 4800961578560210960ull, + 15570451700242981725ull, 2793126014088158896ull}}, +{{13286405774037780823ull, 10612887991627651604ull, + 1016320551594175540ull, 3491407517610198621ull}}, +{{16608007217547226028ull, 13266109989534564505ull, + 5882086707920107329ull, 4364259397012748276ull}}, +{{3462475483325934412ull, 1373789715818020960ull, + 12899676229304842889ull, 2727662123132967672ull}}, +{{4328094354157418015ull, 6328923163199914104ull, + 16124595286631053611ull, 3409577653916209590ull}}, +{{5410117942696772518ull, 3299467935572504726ull, + 10932372071434041206ull, 4261972067395261988ull}}, +{{17216381769467646536ull, 15897225515014979165ull, + 16056104581501051561ull, 2663732542122038742ull}}, +{{7685419156552394458ull, 6036473838486560245ull, + 10846758690021538644ull, 3329665677652548428ull}}, +{{14218459964117880976ull, 7545592298108200306ull, + 13558448362526923305ull, 4162082097065685535ull}}, +{{13498223496001063514ull, 16245210232386094951ull, + 15391559254220408921ull, 2601301310666053459ull}}, +{{12261093351573941489ull, 6471454735200454977ull, + 14627763049348123248ull, 3251626638332566824ull}}, +{{1491308634185263149ull, 8089318419000568722ull, + 18284703811685154060ull, 4064533297915708530ull}}, +{{5543753914793177372ull, 14279196048730131259ull, + 16039625900730609191ull, 2540333311197317831ull}}, +{{2318006375064083811ull, 13237309042485276170ull, + 15437846357485873585ull, 3175416638996647289ull}}, +{{12120880005684880572ull, 2711578247824431500ull, + 5462249891575178270ull, 3969270798745809112ull}}, +{{16798922040407826166ull, 15529794460172433399ull, + 3413906182234486418ull, 2480794249216130695ull}}, +{{16386966532082394803ull, 10188871038360765941ull, + 18102440783075271735ull, 3100992811520163368ull}}, +{{6648650109820829791ull, 8124402779523569523ull, + 4181306905134538053ull, 3876241014400204211ull}}, +{{1849563309424324668ull, 7383594746415924904ull, 307473806495392331ull, + 2422650634000127632ull}} +}; + +#endif // matches #if __ENABLE_BINARY80__ + +// ********************************************************************** + +static const UINT128 breakpoints_binary128[] = + { {{2195700805160846264ull, 1755099732929698ull}}, +{{9135258273612497656ull, 1404079786343758ull}}, +{{10927064423038085928ull, 2246527658150013ull}}, +{{16120349167914289388ull, 1797222126520010ull}}, +{{12896279334331431512ull, 1437777701216008ull}}, +{{17695721096948965856ull, 1150222160972806ull}}, +{{2487712051924973104ull, 1840355457556491ull}}, +{{16747564900507619776ull, 1472284366045192ull}}, +{{6019354290922275176ull, 1177827492836154ull}}, +{{17009664494959460928ull, 1884523988537846ull}}, +{{9918382781225658420ull, 1507619190830277ull}}, +{{556008595496706088ull, 1206095352664222ull}}, +{{4578962567536640064ull, 1929752564262755ull}}, +{{3663170054029312052ull, 1543802051410204ull}}, +{{6619884857965359964ull, 1235041641128163ull}}, +{{6902466958002665620ull, 1976066625805061ull}}, +{{1832624751660222172ull, 1580853300644049ull}}, +{{5155448616070088060ull, 1264682640515239ull}}, +{{15627415415195961544ull, 2023492224824382ull}}, +{{5123234702672948588ull, 1618793779859506ull}}, +{{409238947396448548ull, 1295035023887605ull}}, +{{654782315834317676ull, 2072056038220168ull}}, +{{7902523482151274788ull, 1657644830576134ull}}, +{{10011367600462930152ull, 1326115864460907ull}}, +{{1260792901773046952ull, 2121785383137452ull}}, +{{12076680765644168532ull, 1697428306509961ull}}, +{{5971995797773424504ull, 1357942645207969ull}}, +{{16933890905921299852ull, 2172708232332750ull}}, +{{13547112724737039880ull, 1738166585866200ull}}, +{{10837690179789631904ull, 1390533268692960ull}}, +{{17340304287663411048ull, 2224853229908736ull}}, +{{10182894615388818516ull, 1779882583926989ull}}, +{{11835664507052965136ull, 1423906067141591ull}}, +{{5779182790900461784ull, 1139124853713273ull}}, +{{5557343650698828532ull, 1822599765941237ull}}, +{{15513921364784793796ull, 1458079812752989ull}}, +{{16100485906569745360ull, 1166463850202391ull}}, +{{18382079821027771928ull, 1866342160323826ull}}, +{{11016315042080307220ull, 1493073728259061ull}}, +{{5123703218922335452ull, 1194458982607249ull}}, +{{15576622779759557372ull, 1911134372171598ull}}, +{{1393251779581914928ull, 1528907497737279ull}}, +{{4803950238407442264ull, 1223125998189823ull}}, +{{3996971566709997300ull, 1957001597103717ull}}, +{{14265623697593728808ull, 1565601277682973ull}}, +{{344452513849252076ull, 1252481022146379ull}}, +{{7929821651642623972ull, 2003969635434206ull}}, +{{2654508506572188852ull, 1603175708347365ull}}, +{{2123606805257751084ull, 1282540566677892ull}}, +{{7087119703154312056ull, 2052064906684627ull}}, +{{16737742206749180616ull, 1641651925347701ull}}, +{{9700844950657434168ull, 1313321540278161ull}}, +{{8142654291568074024ull, 2101314464445058ull}}, +{{13892821062738279864ull, 1681051571556046ull}}, +{{7424908035448713568ull, 1344841257244837ull}}, +{{15569201671459852032ull, 2151746011591739ull}}, +{{16144710151909791948ull, 1721396809273391ull}}, +{{9226419306785923236ull, 1377117447418713ull}}, +{{11072922076115566856ull, 2203387915869941ull}}, +{{5168988846150543160ull, 1762710332695953ull}}, +{{11513888706404255176ull, 1410168266156762ull}}, +{{1832413335639583492ull, 1128134612925410ull}}, +{{2931861337023333592ull, 1805015380680656ull}}, +{{17102884328586308164ull, 1444012304544524ull}}, +{{17371656277610956856ull, 1155209843635619ull}}, +{{16726603599951800000ull, 1848335749816991ull}}, +{{9691934065219529676ull, 1478668599853593ull}}, +{{15132244881659444388ull, 1182934879882874ull}}, +{{13143545366429380048ull, 1892695807812599ull}}, +{{14204185107885414364ull, 1514156646250079ull}}, +{{15052696901050241812ull, 1211325317000063ull}}, +{{1948222153228924964ull, 1938120507200102ull}}, +{{12626624166808870940ull, 1550496405760081ull}}, +{{6411950518705186428ull, 1240397124608065ull}}, +{{10259120829928298284ull, 1984635399372904ull}}, +{{11896645478684548952ull, 1587708319498323ull}}, +{{16896014012431459808ull, 1270166655598658ull}}, +{{4897529531438873752ull, 2032266648957854ull}}, +{{7607372439893009324ull, 1625813319166283ull}}, +{{13464595581398228108ull, 1300650655333026ull}}, +{{14164655300753344324ull, 2081041048532842ull}}, +{{3953026611118854812ull, 1664832838826274ull}}, +{{6851770103636994172ull, 1331866271061019ull}}, +{{18341529795303011324ull, 2130986033697630ull}}, +{{14673223836242409060ull, 1704788826958104ull}}, +{{15427927883735837572ull, 1363831061566483ull}}, +{{2548591725525878176ull, 2182129698506374ull}}, +{{5728222195162612864ull, 1745703758805099ull}}, +{{8271926570872000612ull, 1396563007044079ull}}, +{{2167036069169470012ull, 2234500811270527ull}}, +{{12801675299561306980ull, 1787600649016421ull}}, +{{6551991424907135260ull, 1430080519213137ull}}, +{{16309639584151439176ull, 1144064415370509ull}}, +{{15027376890416571716ull, 1830503064592815ull}}, +{{12021901512333257372ull, 1464402451674252ull}}, +{{2238823580382785252ull, 1171521961339402ull}}, +{{7271466543354366724ull, 1874435138143043ull}}, +{{13195870864167314024ull, 1499548110514434ull}}, +{{14246045506075761544ull, 1199638488411547ull}}, +{{8036277550753577176ull, 1919421581458476ull}}, +{{2739673225860951420ull, 1535537265166781ull}}, +{{16949133839656402428ull, 1228429812133424ull}}, +{{16050567699224512916ull, 1965487699413479ull}}, +{{16529802974121520656ull, 1572390159530783ull}}, +{{2155795935071485556ull, 1257912127624627ull}}, +{{7138622310856287212ull, 2012659404199403ull}}, +{{13089595478168850416ull, 1610127523359522ull}}, +{{3092978753051259684ull, 1288102018687618ull}}, +{{1259417190140105172ull, 2060963229900189ull}}, +{{4696882566853994460ull, 1648770583920151ull}}, +{{68157238741285244ull, 1319016467136121ull}}, +{{11177098026211787364ull, 2110426347417793ull}}, +{{16320376050453250536ull, 1688341077934234ull}}, +{{16745649655104510752ull, 1350672862347387ull}}, +{{12035644189199575912ull, 2161076579755820ull}}, +{{9628515351359660728ull, 1728861263804656ull}}, +{{4013463466345818260ull, 1383089011043725ull}}, +{{6421541546153309216ull, 2212942417669960ull}}, +{{5137233236922647372ull, 1770353934135968ull}}, +{{11488484219021938544ull, 1416283147308774ull}}, +{{12880136189959461160ull, 1133026517847019ull}}, +{{9540171459709406884ull, 1812842428555231ull}}, +{{3942788353025615184ull, 1450273942844185ull}}, +{{3154230682420492148ull, 1160219154275348ull}}, +{{1357420277130877116ull, 1856350646840557ull}}, +{{12153982665930432660ull, 1485080517472445ull}}, +{{9723186132744346128ull, 1188064413977956ull}}, +{{8178400182907133160ull, 1900903062364730ull}}, +{{6542720146325706528ull, 1520722449891784ull}}, +{{8923524931802475544ull, 1216577959913427ull}}, +{{17966988705625871196ull, 1946524735861483ull}}, +{{3305544520274965988ull, 1557219788689187ull}}, +{{13712482060445703760ull, 1245775830951349ull}}, +{{10871924852487395044ull, 1993241329522159ull}}, +{{12386888696731826360ull, 1594593063617727ull}}, +{{2530813327901640440ull, 1275674450894182ull}}, +{{7738650139384535028ull, 2041079121430691ull}}, +{{2501571296765717700ull, 1632863297144553ull}}, +{{9379954666896394804ull, 1306290637715642ull}}, +{{250532208066590396ull, 2090065020345028ull}}, +{{7579123395937092964ull, 1672052016276022ull}}, +{{17131345160975405340ull, 1337641613020817ull}}, +{{12652756998593007252ull, 2140226580833308ull}}, +{{17500903228358226448ull, 1712181264666646ull}}, +{{10311373767944670836ull, 1369745011733317ull}}, +{{1740802769743832044ull, 2191592018773308ull}}, +{{8771339845278886280ull, 1753273615018646ull}}, +{{3327723061481198700ull, 1402618892014917ull}}, +{{9013705713111828248ull, 2244190227223867ull}}, +{{18279011014715193568ull, 1795352181779093ull}}, +{{3555162367546423884ull, 1436281745423275ull}}, +{{2844129894037139108ull, 1149025396338620ull}}, +{{4550607830459422572ull, 1838440634141792ull}}, +{{14708532708593269028ull, 1470752507313433ull}}, +{{698779722648884252ull, 1176602005850747ull}}, +{{4807396370980125128ull, 1882563209361195ull}}, +{{3845917096784100100ull, 1506050567488956ull}}, +{{17834128936394921372ull, 1204840453991164ull}}, +{{17466559854006143228ull, 1927744726385863ull}}, +{{2905201438979183612ull, 1542195781108691ull}}, +{{17081556410150988184ull, 1233756624886952ull}}, +{{12573094997273939800ull, 1974010599819124ull}}, +{{13747824812561062164ull, 1579208479855299ull}}, +{{14687608664790760052ull, 1263366783884239ull}}, +{{12432127419439485116ull, 2021386854214783ull}}, +{{17324399565035408740ull, 1617109483371826ull}}, +{{10170170837286416668ull, 1293687586697461ull}}, +{{8893575710174446024ull, 2069900138715938ull}}, +{{14493558197623377464ull, 1655920110972750ull}}, +{{11594846558098701972ull, 1324736088778200ull}}, +{{105010419248371540ull, 2119577742045121ull}}, +{{14841403594366338524ull, 1695662193636096ull}}, +{{8183774060751160496ull, 1356529754908877ull}}, +{{16783387311943767116ull, 2170447607854203ull}}, +{{2358663405329282724ull, 1736358086283363ull}}, +{{9265628353747246824ull, 1389086469026690ull}}, +{{14825005365995594920ull, 2222538350442704ull}}, +{{15549353107538386260ull, 1778030680354163ull}}, +{{1371436041804978036ull, 1422424544283331ull}}, +{{15854544092411623724ull, 1137939635426664ull}}, +{{14299224103632866988ull, 1820703416682663ull}}, +{{371332838680562620ull, 1456562733346131ull}}, +{{15054461529912091388ull, 1165250186676904ull}}, +{{13019092003633615252ull, 1864400298683047ull}}, +{{3036575973423071556ull, 1491520238946438ull}}, +{{9807958408222277892ull, 1193216191157150ull}}, +{{15692733453155644628ull, 1909145905851440ull}}, +{{12554186762524515700ull, 1527316724681152ull}}, +{{2664651780535791912ull, 1221853379744922ull}}, +{{7952791663599177388ull, 1954965407591875ull}}, +{{6362233330879341908ull, 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2206479690122793ull}}, +{{17585049519869022796ull, 1765183752098234ull}}, +{{17757388430637128560ull, 1412147001678587ull}}, +{{6827213115025882200ull, 1129717601342870ull}}, +{{10923540984041411524ull, 1807548162148592ull}}, +{{1360135157749308572ull, 1446038529718874ull}}, +{{4777456940941357180ull, 1156830823775099ull}}, +{{15022628734989992136ull, 1850929318040158ull}}, +{{950056543766262740ull, 1480743454432127ull}}, +{{11828091679238741160ull, 1184594763545701ull}}, +{{11546249057298165212ull, 1895351621673122ull}}, +{{1858301616354711520ull, 1516281297338498ull}}, +{{8865338922567589864ull, 1213025037870798ull}}, +{{10495193461366233460ull, 1940840060593277ull}}, +{{1017457139609166120ull, 1552672048474622ull}}, +{{11882012155913063864ull, 1242137638779697ull}}, +{{4253824190493260892ull, 1987420222047516ull}}, +{{18160454611362250008ull, 1589936177638012ull}}, +{{7149666059605979360ull, 1271948942110410ull}}, +{{11439465695369566976ull, 2035118307376656ull}}, +{{5462223741553743256ull, 1628094645901325ull}}, +{{4369778993242994604ull, 1302475716721060ull}}, +{{6991646389188791368ull, 2083961146753696ull}}, +{{1903968296609122772ull, 1667168917402957ull}}, +{{12591221081513029188ull, 1333735133922365ull}}, +{{1699209656711295084ull, 2133976214275785ull}}, +{{1359367725369036068ull, 1707180971420628ull}}, +{{8466191809779049500ull, 1365744777136502ull}}, +{{17235255710388389524ull, 2185191643418403ull}}, +{{2720158124084980648ull, 1748153314734723ull}}, +{{9554824128751805164ull, 1398522651787778ull}}, +{{11598369791260977940ull, 2237636242860445ull}}, +{{9278695833008782352ull, 1790108994288356ull}}, +{{3733607851665115560ull, 1432087195430685ull}}, +{{2986886281332092448ull, 1145669756344548ull}}, +{{1089669235389437592ull, 1833071610151277ull}}, +{{11939781832537281044ull, 1466457288121021ull}}, +{{5862476651287914512ull, 1173165830496817ull}}, +{{13069311456802573544ull, 1877065328794907ull}}, +{{3076751535958238188ull, 1501652263035926ull}}, +{{17218796487734231840ull, 1201321810428740ull}}, +{{9103330306665219332ull, 1922114896685985ull}}, +{{7282664245332175464ull, 1537691917348788ull}}, +{{13204829025749561020ull, 1230153533879030ull}}, +{{2680982367489746016ull, 1968245654206449ull}}, +{{5834134708733707136ull, 1574596523365159ull}}, +{{8356656581728876032ull, 1259677218692127ull}}, +{{17059999345508111972ull, 2015483549907403ull}}, +{{2579953032180758608ull, 1612386839925923ull}}, +{{9442660055228427532ull, 1289909471940738ull}}, +{{11418907273623573732ull, 2063855155105181ull}}, +{{5445777004156948660ull, 1651084124084145ull}}, +{{4356621603325558928ull, 1320867299267316ull}}, +{{18038641009546625256ull, 2113387678827705ull}}, +{{14430912807637300204ull, 1690710143062164ull}}, +{{15234079060851750488ull, 1352568114449731ull}}, +{{16995828867878980132ull, 2164108983119570ull}}, +{{13596663094303184104ull, 1731287186495656ull}}, +{{7187981660700636960ull, 1385029749196525ull}}, +{{11500770657121019140ull, 2216047598714440ull}}, +{{9200616525696815312ull, 1772838078971552ull}}, +{{18428539664783183216ull, 1418270463177241ull}}, +{{11053482917084636252ull, 1134616370541793ull}}, +{{13996223852593507680ull, 1815386192866869ull}}, +{{14886327896816716464ull, 1452308954293495ull}}, +{{11909062317453373172ull, 1161847163434796ull}}, +{{11675802078441576432ull, 1858955461495674ull}}, +{{13029990477495171468ull, 1487164369196539ull}}, +{{14113341196738047496ull, 1189731495357231ull}}, +{{15202648285297055348ull, 1903570392571570ull}}, +{{12162118628237644280ull, 1522856314057256ull}}, +{{6040346087848205100ull, 1218285051245805ull}}, +{{9664553740557128160ull, 1949256081993288ull}}, +{{15110340621929523176ull, 1559404865594630ull}}, +{{12088272497543618540ull, 1247523892475704ull}}, +{{8273189551844058696ull, 1996038227961127ull}}, +{{17686598085700977924ull, 1596830582368901ull}}, +{{10459929653818872016ull, 1277464465895121ull}}, +{{9357189816626374580ull, 2043943145432194ull}}, +{{11175100668043009988ull, 1635154516345755ull}}, +{{8940080534434407988ull, 1308123613076604ull}}, +{{3236082410869321816ull, 2092997780922567ull}}, +{{13656912372921188420ull, 1674398224738053ull}}, +{{18304227527820771384ull, 1339518579790442ull}}, +{{14529368785545592920ull, 2143229727664708ull}} +}; + +static const int exponents_binary128[] = { -115, + -112, + -108, + -105, + -102, + -99, + -95, + -92, + -89, + -85, + -82, + -79, + -75, + -72, + -69, + -65, + -62, + -59, + -55, + -52, + -49, + -45, + -42, + -39, + -35, + -32, + -29, + -25, + -22, + -19, + -15, + -12, + -9, + -6, + -2, + 1, + 4, + 8, + 11, + 14, + 18, + 21, + 24, + 28, + 31, + 34, + 38, + 41, + 44, + 48, + 51, + 54, + 58, + 61, + 64, + 68, + 71, + 74, + 78, + 81, + 84, + 87, + 91, + 94, + 97, + 101, + 104, + 107, + 111, + 114, + 117, + 121, + 124, + 127, + 131, + 134, + 137, + 141, + 144, + 147, + 151, + 154, + 157, + 161, + 164, + 167, + 171, + 174, + 177, + 181, + 184, + 187, + 190, + 194, + 197, + 200, + 204, + 207, + 210, + 214, + 217, + 220, + 224, + 227, + 230, + 234, + 237, + 240, + 244, + 247, + 250, + 254, + 257, + 260, + 264, + 267, + 270, + 274, + 277, + 280, + 283, + 287, + 290, + 293, + 297, + 300, + 303, + 307, + 310, + 313, + 317, + 320, + 323, + 327, + 330, + 333, + 337, + 340, + 343, + 347, + 350, + 353, + 357, + 360, + 363, + 367, + 370, + 373, + 377, + 380, + 383, + 386, + 390, + 393, + 396, + 400, + 403, + 406, + 410, + 413, + 416, + 420, + 423, + 426, + 430, + 433, + 436, + 440, + 443, + 446, + 450, + 453, + 456, + 460, + 463, + 466, + 470, + 473, + 476, + 479, + 483, + 486, + 489, + 493, + 496, + 499, + 503, + 506, + 509, + 513, + 516, + 519, + 523, + 526, + 529, + 533, + 536, + 539, + 543, + 546, + 549, + 553, + 556, + 559, + 563, + 566, + 569, + 572, + 576, + 579, + 582, + 586, + 589, + 592, + 596, + 599, + 602, + 606, + 609, + 612, + 616, + 619, + 622, + 626, + 629, + 632, + 636, + 639, + 642, + 646, + 649, + 652, + 656, + 659, + 662, + 666, + 669, + 672, + 675, + 679, + 682, + 685, + 689, + 692, + 695, + 699, + 702, + 705, + 709, + 712, + 715, + 719, + 722, + 725, + 729, + 732, + 735, + 739, + 742, + 745, + 749, + 752, + 755, + 759, + 762, + 765, + 768, + 772, + 775, + 778, + 782, + 785, + 788, + 792, + 795, + 798, + 802, + 805, + 808, + 812, + 815, + 818, + 822, + 825, + 828, + 832, + 835, + 838, + 842, + 845, + 848, + 852, + 855, + 858, + 862, + 865, + 868, + 871, + 875, + 878, + 881, + 885, + 888, + 891, + 895, + 898, + 901, + 905, + 908, + 911, + 915, + 918, + 921, + 925, + 928, + 931, + 935, + 938, + 941, + 945, + 948, + 951, + 955, + 958, + 961, + 964, + 968, + 971, + 974, + 978, + 981, + 984, + 988, + 991, + 994, + 998, + 1001, + 1004, + 1008, + 1011, + 1014, + 1018, + 1021, + 1024, + 1028, + 1031, + 1034, + 1038, + 1041, + 1044, + 1048, + 1051, + 1054, + 1058, + 1061, + 1064, + 1067, + 1071, + 1074, + 1077, + 1081, + 1084, + 1087, + 1091, + 1094, + 1097, + 1101, + 1104, + 1107, + 1111, + 1114, + 1117, + 1121, + 1124, + 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1958, + 1961, + 1964, + 1968, + 1971, + 1974, + 1978, + 1981, + 1984, + 1988, + 1991, + 1994, + 1998, + 2001, + 2004, + 2008, + 2011, + 2014, + 2018, + 2021, + 2024, + 2028, + 2031, + 2034, + 2037, + 2041, + 2044, + 2047, + 2051, + 2054, + 2057, + 2061, + 2064, + 2067, + 2071, + 2074, + 2077, + 2081, + 2084, + 2087, + 2091, + 2094, + 2097, + 2101, + 2104, + 2107, + 2111, + 2114, + 2117, + 2121, + 2124, + 2127, + 2130, + 2134, + 2137, + 2140, + 2144, + 2147, + 2150, + 2154, + 2157, + 2160, + 2164, + 2167, + 2170, + 2174, + 2177, + 2180, + 2184, + 2187, + 2190, + 2194, + 2197, + 2200, + 2204, + 2207, + 2210, + 2214, + 2217, + 2220, + 2223, + 2227, + 2230, + 2233, + 2237, + 2240, + 2243, + 2247, + 2250, + 2253, + 2257, + 2260, + 2263, + 2267, + 2270, + 2273, + 2277, + 2280, + 2283, + 2287, + 2290, + 2293, + 2297, + 2300, + 2303, + 2307, + 2310, + 2313, + 2317, + 2320, + 2323, + 2326, + 2330, + 2333, + 2336, + 2340, + 2343, + 2346, + 2350, + 2353, + 2356, + 2360, + 2363, + 2366, + 2370, + 2373, + 2376, + 2380, + 2383, + 2386, + 2390, + 2393, + 2396, + 2400, + 2403, + 2406, + 2410, + 2413, + 2416, + 2419, + 2423, + 2426, + 2429, + 2433, + 2436, + 2439, + 2443, + 2446, + 2449, + 2453, + 2456, + 2459, + 2463, + 2466, + 2469, + 2473, + 2476, + 2479, + 2483, + 2486, + 2489, + 2493, + 2496, + 2499, + 2503, + 2506, + 2509, + 2513, + 2516, + 2519, + 2522, + 2526, + 2529, + 2532, + 2536, + 2539, + 2542, + 2546, + 2549, + 2552, + 2556, + 2559, + 2562, + 2566, + 2569, + 2572, + 2576, + 2579, + 2582, + 2586, + 2589, + 2592, + 2596, + 2599, + 2602, + 2606, + 2609, + 2612, + 2615, + 2619, + 2622, + 2625, + 2629, + 2632, + 2635, + 2639, + 2642, + 2645, + 2649, + 2652, + 2655, + 2659, + 2662, + 2665, + 2669, + 2672, + 2675, + 2679, + 2682, + 2685, + 2689, + 2692, + 2695, + 2699, + 2702, + 2705, + 2708, + 2712, + 2715, + 2718, + 2722, + 2725, + 2728, + 2732, + 2735, + 2738, + 2742, + 2745, + 2748, + 2752, + 2755, + 2758, + 2762, + 2765, + 2768, + 2772, + 2775, + 2778, + 2782, + 2785, + 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multipliers2_binary128[] = + { {{7710430832988809084ull, 13621041698348090301ull, + 15069458432386386555ull, 2958405588648567759ull}}, +{{14249724559663399259ull, 12414616104507724972ull, + 14225137022055595290ull, 3698006985810709699ull}}, +{{18129449886644400345ull, 12370821083744716011ull, + 6584867629571053104ull, 2311254366131693562ull}}, +{{18050126339878112527ull, 15463526354680895014ull, + 17454456573818592188ull, 2889067957664616952ull}}, +{{13339285887992864851ull, 882663869641567152ull, + 3371326643563688620ull, 3611334947080771191ull}}, +{{16674107359991081063ull, 1103329837051958940ull, + 18049216359736774487ull, 4514168683850963988ull}}, +{{1197945063139649857ull, 7607110175798556194ull, + 2057388187980708246ull, 2821355427406852493ull}}, +{{10720803365779338129ull, 285515682893419434ull, + 7183421253403273212ull, 3526694284258565616ull}}, +{{4177632170369396853ull, 356894603616774293ull, 8979276566754091515ull, + 4408367855323207020ull}}, +{{4916863115694566985ull, 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18421717263241434555ull, + 13325226743472638266ull, 4596101585354480616ull}}, +{{3564172081345348886ull, 16125259307953284501ull, + 8328266714670398916ull, 2872563490846550385ull}}, +{{9066901120109074011ull, 1709830061232054010ull, + 15022019411765386550ull, 3590704363558187981ull}}, +{{2110254363281566706ull, 11360659613394843321ull, + 4942466209424569475ull, 4488380454447734977ull}}, +{{12848124023119448951ull, 4794569249158083123ull, + 14618256426958825682ull, 2805237784029834360ull}}, +{{11448469010471923285ull, 15216583598302379712ull, + 18272820533698532102ull, 3506547230037292950ull}}, +{{14310586263089904106ull, 9797357461023198832ull, + 13617653630268389320ull, 4383184037546616188ull}}, +{{8944116414431190067ull, 6123348413139499270ull, + 17734405555772519133ull, 2739490023466635117ull}}, +{{1956773481184211775ull, 12265871534851761992ull, + 8332948889433485204ull, 3424362529333293897ull}}, +{{2445966851480264719ull, 15332339418564702490ull, + 15027872130219244409ull, 4280453161666617371ull}}, +{{6140415300602553353ull, 2665183108961857200ull, + 7086577072173333804ull, 2675283226041635857ull}}, +{{7675519125753191692ull, 3331478886202321500ull, + 13469907358644055159ull, 3344104032552044821ull}}, +{{9594398907191489614ull, 17999406663035065587ull, + 3002326143022905236ull, 4180130040690056027ull}}, +{{3690656307780987057ull, 2026257127542140184ull, + 18017354903885173437ull, 2612581275431285016ull}}, +{{4613320384726233821ull, 7144507427855063134ull, + 4074949556146915180ull, 3265726594289106271ull}}, +{{14990022517762568085ull, 8930634284818828917ull, + 482000926756256071ull, 4082158242861382839ull}}, +{{11674607082815299005ull, 12499175455652849929ull, + 7218779606863741900ull, 2551348901788364274ull}}, +{{758200798236960044ull, 15623969319566062412ull, + 18246846545434453183ull, 3189186127235455342ull}}, +{{947750997796200055ull, 14918275631030190111ull, + 13585186144938290671ull, 3986482659044319178ull}}, +{{7509873401263706891ull, 16241451297034950675ull, + 13102427359013819573ull, 2491551661902699486ull}}, +{{4775655733152245709ull, 6466756066011524632ull, + 7154662161912498659ull, 3114439577378374358ull}}, +{{5969569666440307136ull, 3471759064087017886ull, + 18166699739245399132ull, 3893049471722967947ull}}, +{{17566039096807355672ull, 11393221451909161986ull, + 9048344327814680505ull, 2433155919826854967ull}}, +{{12734176834154418782ull, 406468759604288771ull, + 6698744391340962728ull, 3041444899783568709ull}}, +{{11306035024265635574ull, 508085949505360964ull, + 12985116507603591314ull, 3801806124729460886ull}}, +{{16289643927020798042ull, 4929239736868238506ull, + 3504011798824856667ull, 2376128827955913054ull}}, +{{11138682871921221744ull, 1549863652657910229ull, + 13603386785385846642ull, 2970161034944891317ull}}, +{{88295534619363468ull, 11160701602677163595ull, 3169175426450144590ull, + 3712701293681114147ull}}, +{{16196085773632959832ull, 2363752483245839342ull, + 18121635706027198033ull, 2320438308550696341ull}}, +{{11021735180186423982ull, 7566376622484687082ull, + 8816986577251833829ull, 2900547885688370427ull}}, +{{4553796938378254169ull, 14069656796533246757ull, + 6409547203137404382ull, 3625684857110463034ull}}, +{{10303932191400205615ull, 8363698958811782638ull, + 17235306040776531286ull, 4532106071388078792ull}}, +{{1828271601197740605ull, 615625830829976245ull, + 10772066275485332054ull, 2832566294617549245ull}}, +{{6897025519924563661ull, 9992904325392246114ull, + 18076768862784052971ull, 3540707868271936556ull}}, +{{17844653936760480384ull, 7879444388312919738ull, + 4149217004770514598ull, 4425884835339920696ull}}, +{{15764594728902688144ull, 312966724268186932ull, + 2593260627981571624ull, 2766178022087450435ull}}, +{{1258999337418808564ull, 391208405335233666ull, + 17076633840259128242ull, 3457722527609313043ull}}, +{{10797121208628286513ull, 9712382543523817890ull, + 16734106281896522398ull, 4322153159511641304ull}}, +{{11359886773820066975ull, 1458553071274998277ull, + 10458816426185326499ull, 2701345724694775815ull}}, +{{364800411992920006ull, 15658249394375911559ull, + 8461834514304270219ull, 3376682155868469769ull}}, +{{14291058570273313720ull, 14961125724542501544ull, + 15188979161307725678ull, 4220852694835587211ull}}, +{{8931911606420821075ull, 4739017559411675561ull, + 7187268966603634597ull, 2638032934272242007ull}}, +{{15776575526453414248ull, 10535457967691982355ull, + 4372400189827155342ull, 3297541167840302509ull}}, +{{15109033389639379905ull, 3945950422760202136ull, + 10077186255711332082ull, 4121926459800378136ull}}, +{{9443145868524612441ull, 7077905032652514239ull, + 6298241409819582551ull, 2576204037375236335ull}}, +{{7192246317228377647ull, 4235695272388254895ull, + 3261115743847090285ull, 3220255046719045419ull}}, +{{4378621878108084155ull, 9906305108912706523ull, + 17911452735091026568ull, 4025318808398806773ull}}, +{{430795664603858645ull, 6191440693070441577ull, + 13500500968645585557ull, 2515824255249254233ull}}, +{{5150180599182211210ull, 12350986884765439875ull, + 3040568155524818234ull, 3144780319061567792ull}}, +{{1826039730550376108ull, 6215361569102024036ull, + 3800710194406022793ull, 3930975398826959740ull}}, +{{10364646868448760876ull, 15413816026757234782ull, + 11598815908358540053ull, 2456859624266849837ull}}, +{{3732436548706175287ull, 5432211978164379766ull, 663461830166011355ull, + 3071074530333562297ull}}, +{{13888917722737494916ull, 2178578954278086803ull, + 5441013306134902098ull, 3838843162916952871ull}}, +{{6374730567497240371ull, 5973297864851192156ull, + 10318162343975395667ull, 2399276976823095544ull}}, +{{7968413209371550464ull, 2854936312636602291ull, + 12897702929969244584ull, 2999096221028869430ull}}, +{{5348830493287050175ull, 3568670390795752864ull, + 6898756625606779922ull, 3748870276286086788ull}}, +{{3343019058304406360ull, 6842105012674733444ull, + 13535094927859013259ull, 2343043922678804242ull}}, +{{4178773822880507950ull, 3940945247416028901ull, + 7695496622968990766ull, 2928804903348505303ull}}, +{{9835153297028022841ull, 14149553596124811934ull, + 5007684760283850553ull, 3661006129185631629ull}}, +{{3070569584430252743ull, 3851883939873851206ull, + 10871291968782201096ull, 4576257661482039536ull}}, +{{15754164045551071677ull, 2407427462421157003ull, + 6794557480488875685ull, 2860161038426274710ull}}, +{{15081019038511451692ull, 7620970346453834158ull, + 17716568887465870414ull, 3575201298032843387ull}}, +{{9627901761284538806ull, 302840896212516890ull, + 17534025090904950114ull, 4469001622541054234ull}}, +{{10629124619230224658ull, 4800961578560210960ull, + 15570451700242981725ull, 2793126014088158896ull}}, +{{13286405774037780823ull, 10612887991627651604ull, + 1016320551594175540ull, 3491407517610198621ull}}, +{{16608007217547226028ull, 13266109989534564505ull, + 5882086707920107329ull, 4364259397012748276ull}}, +{{3462475483325934412ull, 1373789715818020960ull, + 12899676229304842889ull, 2727662123132967672ull}}, +{{4328094354157418015ull, 6328923163199914104ull, + 16124595286631053611ull, 3409577653916209590ull}}, +{{5410117942696772518ull, 3299467935572504726ull, + 10932372071434041206ull, 4261972067395261988ull}}, +{{17216381769467646536ull, 15897225515014979165ull, + 16056104581501051561ull, 2663732542122038742ull}}, +{{7685419156552394458ull, 6036473838486560245ull, + 10846758690021538644ull, 3329665677652548428ull}}, +{{14218459964117880976ull, 7545592298108200306ull, + 13558448362526923305ull, 4162082097065685535ull}}, +{{13498223496001063514ull, 16245210232386094951ull, + 15391559254220408921ull, 2601301310666053459ull}}, +{{12261093351573941489ull, 6471454735200454977ull, + 14627763049348123248ull, 3251626638332566824ull}}, +{{1491308634185263149ull, 8089318419000568722ull, + 18284703811685154060ull, 4064533297915708530ull}}, +{{5543753914793177372ull, 14279196048730131259ull, + 16039625900730609191ull, 2540333311197317831ull}}, +{{2318006375064083811ull, 13237309042485276170ull, + 15437846357485873585ull, 3175416638996647289ull}}, +{{12120880005684880572ull, 2711578247824431500ull, + 5462249891575178270ull, 3969270798745809112ull}}, +{{16798922040407826166ull, 15529794460172433399ull, + 3413906182234486418ull, 2480794249216130695ull}}, +{{16386966532082394803ull, 10188871038360765941ull, + 18102440783075271735ull, 3100992811520163368ull}}, +{{6648650109820829791ull, 8124402779523569523ull, + 4181306905134538053ull, 3876241014400204211ull}}, +{{1849563309424324668ull, 7383594746415924904ull, 307473806495392331ull, + 2422650634000127632ull}} +}; + +// ********************************************************************** + +static const UINT128 breakpoints_bid32[] = { {{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{11908810229357645280ull, 469708516554766ull}}, +{{5954405114678822640ull, 234854258277383ull}}, +{{12200574594194187128ull, 117427129138691ull}}, +{{15323659333951869372ull, 58713564569345ull}}, +{{2831320374921140396ull, 293567822846729ull}}, +{{10639032224315346006ull, 146783911423364ull}}, +{{5319516112157673003ull, 73391955711682ull}}, +{{8150836487078813399ull, 366959778558411ull}}, +{{13298790280394182507ull, 183479889279205ull}}, +{{15872767177051867061ull, 91739944639602ull}}, +{{5576859590421128845ull, 458699723198014ull}}, +{{2788429795210564422ull, 229349861599007ull}}, +{{10617586934460058019ull, 114674930799503ull}}, +{{14532165504084804817ull, 57337465399751ull}}, +{{17320595299295369240ull, 286687326998758ull}}, +{{8660297649647684620ull, 143343663499379ull}}, +{{13553520861678618118ull, 71671831749689ull}}, +{{12427372087264435742ull, 358359158748448ull}}, +{{6213686043632217871ull, 179179579374224ull}}, +{{3106843021816108935ull, 89589789687112ull}}, +{{15534215109080544677ull, 447948948435560ull}}, +{{7767107554540272338ull, 223974474217780ull}}, +{{3883553777270136169ull, 111987237108890ull}}, +{{971024812641129231ull, 559936185544451ull}}, +{{9708884443175340423ull, 279968092772225ull}}, +{{14077814258442446019ull, 139984046386112ull}}, +{{7038907129221223009ull, 69992023193056ull}}, +{{16747791572396563433ull, 349960115965281ull}}, +{{17597267823053057524ull, 174980057982640ull}}, +{{8798633911526528762ull, 87490028991320ull}}, +{{7099681410213540580ull, 437450144956602ull}}, +{{3549840705106770290ull, 218725072478301ull}}, +{{10998292389408160953ull, 109362536239150ull}}, +{{18097973799621701533ull, 546812681195752ull}}, +{{9048986899810850766ull, 273406340597876ull}}, +{{4524493449905425383ull, 136703170298938ull}}, +{{2262246724952712691ull, 68351585149469ull}}, +{{11311233624763563458ull, 341757925747345ull}}, +{{14878988849236557537ull, 170878962873672ull}}, +{{7439494424618278768ull, 85439481436836ull}}, +{{303983975672290610ull, 427197407184182ull}}, +{{151991987836145305ull, 213598703592091ull}}, +{{9299368030772848460ull, 106799351796045ull}}, +{{9603352006445139071ull, 533996758980227ull}}, +{{14025048040077345343ull, 266998379490113ull}}, +{{16235896056893448479ull, 133499189745056ull}}, +{{8117948028446724239ull, 66749594872528ull}}, +{{3696251994814517967ull, 333747974362642ull}}, +{{1848125997407258983ull, 166873987181321ull}}, +{{10147435035558405299ull, 83436993590660ull}}, +{{13843687030372923267ull, 417184967953302ull}}, +{{6921843515186461633ull, 208592483976651ull}}, +{{12684293794448006624ull, 104296241988325ull}}, +{{8081236751111378276ull, 521481209941628ull}}, +{{4040618375555689138ull, 260740604970814ull}}, +{{2020309187777844569ull, 130370302485407ull}}, +{{10233526630743698092ull, 65185151242703ull}}, +{{14274145006299387230ull, 325925756213517ull}}, +{{16360444540004469423ull, 162962878106758ull}}, +{{8180222270002234711ull, 81481439053379ull}}, +{{4007623202592070326ull, 407407195266897ull}}, +{{11227183638150810971ull, 203703597633448ull}}, +{{5613591819075405485ull, 101851798816724ull}}, +{{9621215021667475812ull, 509258994083621ull}}, +{{14033979547688513714ull, 254629497041810ull}}, +{{7016989773844256857ull, 127314748520905ull}}, +{{12731866923776904236ull, 63657374260452ull}}, +{{8319102397755866334ull, 318286871302263ull}}, +{{13382923235732708975ull, 159143435651131ull}}, +{{15914833654721130295ull, 79571717825565ull}}, +{{5787191978767445014ull, 397858589127829ull}}, +{{12116968026238498315ull, 198929294563914ull}}, +{{6058484013119249157ull, 99464647281957ull}}, +{{11845675991886694171ull, 497323236409786ull}}, +{{5922837995943347085ull, 248661618204893ull}}, +{{12184791034826449350ull, 124330809102446ull}}, +{{6092395517413224675ull, 62165404551223ull}}, +{{12015233513356571761ull, 310827022756116ull}}, +{{6007616756678285880ull, 155413511378058ull}}, +{{3003808378339142940ull, 77706755689029ull}}, +{{15019041891695714701ull, 388533778445145ull}}, +{{16732892982702633158ull, 194266889222572ull}}, +{{8366446491351316579ull, 97133444611286ull}}, +{{4938744309337479665ull, 485667223056432ull}}, +{{2469372154668739832ull, 242833611528216ull}}, +{{1234686077334369916ull, 121416805764108ull}}, +{{617343038667184958ull, 60708402882054ull}}, +{{3086715193335924790ull, 303542014410270ull}}, +{{1543357596667962395ull, 151771007205135ull}}, +{{9995050835188757005ull, 75885503602567ull}}, +{{13081766028524681796ull, 379427518012837ull}}, +{{15764255051117116706ull, 189713759006418ull}}, +{{7882127525558558353ull, 94856879503209ull}}, +{{2517149480373688533ull, 474284397516047ull}}, +{{10481946777041620074ull, 237142198758023ull}}, +{{14464345425375585845ull, 118571099379011ull}}, +{{16455544749542568730ull, 59285549689505ull}}, +{{8490747452874637189ull, 296427748447529ull}}, +{{13468745763292094402ull, 148213874223764ull}}, +{{6734372881646047201ull, 74106937111882ull}}, +{{15225120334520684390ull, 370534685559411ull}}, +{{16835932204115118003ull, 185267342779705ull}}, +{{17641338138912334809ull, 92633671389852ull}}, +{{14419714399723467584ull, 463168356949264ull}}, +{{7209857199861733792ull, 231584178474632ull}}, +{{3604928599930866896ull, 115792089237316ull}}, +{{1802464299965433448ull, 57896044618658ull}}, +{{9012321499827167240ull, 289480223093290ull}}, +{{4506160749913583620ull, 144740111546645ull}}, +{{11476452411811567618ull, 72370055773322ull}}, +{{2042029837929183242ull, 361850278866613ull}}, +{{10244386955819367429ull, 180925139433306ull}}, +{{5122193477909683714ull, 90462569716653ull}}, +{{7164223315838866956ull, 452312848583266ull}}, +{{3582111657919433478ull, 226156424291633ull}}, +{{11014427865814492547ull, 113078212145816ull}}, +{{5507213932907246273ull, 56539106072908ull}}, 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109476442525376ull}}, +{{12328504753617029967ull, 547382212626881ull}}, +{{15387624413663290791ull, 273691106313440ull}}, +{{7693812206831645395ull, 136845553156720ull}}, +{{3846906103415822697ull, 68422776578360ull}}, +{{787786443369561873ull, 342113882891801ull}}, +{{9617265258539556744ull, 171056941445900ull}}, +{{4808632629269778372ull, 85528470722950ull}}, +{{5596419072639340246ull, 427642353614751ull}}, +{{12021581573174445931ull, 213821176807375ull}}, +{{15234162823441998773ull, 106910588403687ull}}, +{{2383837822371787403ull, 534552942018439ull}}, +{{10415290948040669509ull, 267276471009219ull}}, +{{14431017510875110562ull, 133638235504609ull}}, +{{16438880792292331089ull, 66819117752304ull}}, +{{8407427666623448983ull, 334095588761524ull}}, +{{4203713833311724491ull, 167047794380762ull}}, +{{2101856916655862245ull, 83523897190381ull}}, +{{10509284583279311229ull, 417619485951905ull}}, +{{14478014328494431422ull, 208809742975952ull}}, +{{7239007164247215711ull, 104404871487976ull}}, +{{17748291747526526940ull, 522024357439881ull}}, +{{18097517910618039278ull, 261012178719940ull}}, +{{9048758955309019639ull, 130506089359970ull}}, +{{4524379477654509819ull, 65253044679985ull}}, +{{4175153314562997481ull, 326265223399926ull}}, +{{2087576657281498740ull, 163132611699963ull}}, +{{10267160365495525178ull, 81566305849981ull}}, +{{14442313680058522660ull, 407831529249907ull}}, +{{16444528876884037138ull, 203915764624953ull}}, +{{17445636475296794377ull, 101957882312476ull}}, +{{13441206081645765421ull, 509789411562384ull}}, +{{6720603040822882710ull, 254894705781192ull}}, +{{3360301520411441355ull, 127447352890596ull}}, +{{1680150760205720677ull, 63723676445298ull}}, +{{8400753801028603388ull, 318618382226490ull}}, +{{4200376900514301694ull, 159309191113245ull}}, +{{11323560487111926655ull, 79654595556622ull}}, +{{1277570214430978427ull, 398272977783113ull}}, +{{9862157144070265021ull, 199136488891556ull}}, +{{4931078572035132510ull, 99568244445778ull}}, +{{6208648786466110938ull, 497841222228891ull}}, +{{12327696430087831277ull, 248920611114445ull}}, +{{15387220251898691446ull, 124460305557222ull}}, +{{7693610125949345723ull, 62230152778611ull}}, +{{1574562482327625384ull, 311150763893057ull}}, +{{10010653278018588500ull, 155575381946528ull}}, +{{5005326639009294250ull, 77787690973264ull}}, +{{6579889121336919634ull, 388938454866321ull}}, +{{12513316597523235625ull, 194469227433160ull}}, +{{6256658298761617812ull, 97234613716580ull}}, +{{12836547420098537447ull, 486173068582901ull}}, +{{15641645746904044531ull, 243086534291450ull}}, +{{7820822873452022265ull, 121543267145725ull}}, +{{13133783473580786940ull, 60771633572862ull}}, +{{10328685146775279856ull, 303858167864313ull}}, +{{14387714610242415736ull, 151929083932156ull}}, +{{7193857305121207868ull, 75964541966078ull}}, +{{17522542451896487724ull, 379822709830391ull}}, +{{17984643262803019670ull, 189911354915195ull}}, +{{18215693668256285643ull, 94955677457597ull}}, +{{17291492046443221751ull, 474778387287989ull}}, +{{17869118060076386683ull, 237389193643994ull}}, +{{8934559030038193341ull, 118694596821997ull}}, +{{13690651551873872478ull, 59347298410998ull}}, +{{13113025538240707546ull, 296736492054993ull}}, +{{15779884805975129581ull, 148368246027496ull}}, +{{7889942402987564790ull, 74184123013748ull}}, +{{2556223867518720721ull, 370920615068742ull}}, +{{1278111933759360360ull, 185460307534371ull}}, +{{9862428003734455988ull, 92730153767185ull}}, +{{12418651871253176710ull, 463650768835927ull}}, +{{15432697972481364163ull, 231825384417963ull}}, +{{16939721023095457889ull, 115912692208981ull}}, +{{17693232548402504752ull, 57956346104490ull}}, +{{14679186447174317299ull, 289781730522454ull}}, +{{7339593223587158649ull, 144890865261227ull}}, +{{12893168648648355132ull, 72445432630613ull}}, +{{9125611022113120816ull, 362227163153068ull}}, +{{4562805511056560408ull, 181113581576534ull}}, +{{2281402755528280204ull, 90556790788267ull}}, +{{11407013777641401020ull, 452783953941335ull}}, +{{14926878925675476318ull, 226391976970667ull}}, +{{16686811499692513967ull, 113195988485333ull}}, +{{17566777786701032791ull, 56597994242666ull}}, +{{14046912638666957494ull, 282989971213334ull}}, +{{7023456319333478747ull, 141494985606667ull}}, +{{12735100196521515181ull, 70747492803333ull}}, +{{8335268761478921059ull, 353737464016668ull}}, +{{4167634380739460529ull, 176868732008334ull}}, +{{2083817190369730264ull, 88434366004167ull}}, +{{10419085951848651324ull, 442171830020835ull}}, +{{14432915012779101470ull, 221085915010417ull}}, +{{16439829543244326543ull, 110542957505208ull}}, +{{8412171421383426251ull, 552714787526044ull}}, +{{4206085710691713125ull, 276357393763022ull}}, +{{2103042855345856562ull, 138178696881511ull}}, +{{10274893464527704089ull, 69089348440755ull}}, +{{14480979175219417215ull, 345446742203777ull}}, +{{16463861624464484415ull, 172723371101888ull}}, +{{8231930812232242207ull, 86361685550944ull}}, +{{4266165913742107807ull, 431808427754722ull}}, +{{2133082956871053903ull, 215904213877361ull}}, +{{10289913515290302759ull, 107952106938680ull}}, +{{14556079429032410566ull, 539760534693402ull}}, +{{7278039714516205283ull, 269880267346701ull}}, +{{12862391894112878449ull, 134940133673350ull}}, +{{6431195947056439224ull, 67470066836675ull}}, +{{13709235661572644508ull, 337350334183376ull}}, +{{6854617830786322254ull, 168675167091688ull}}, +{{3427308915393161127ull, 84337583545844ull}}, +{{17136544576965805635ull, 421687917729220ull}}, +{{8568272288482902817ull, 210843958864610ull}}, +{{4284136144241451408ull, 105421979432305ull}}, +{{2973936647497705428ull, 527109897161526ull}}, +{{1486968323748852714ull, 263554948580763ull}}, +{{9966856198729202165ull, 131777474290381ull}}, +{{14206800136219376890ull, 65888737145190ull}}, +{{15693768459968229604ull, 329443685725953ull}}, +{{17070256266838890610ull, 164721842862976ull}} +}; + +static const int exponents_bid32[] = { -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + 0, + 0, + 0, + 0, + 1, + 1, + 1, + 2, + 2, + 2, + 3, + 3, + 3, + 3, + 4, + 4, + 4, + 5, + 5, + 5, + 6, + 6, + 6, + 7, + 7, + 7, + 7, + 8, + 8, + 8, + 9, + 9, + 9, + 10, + 10, + 10, + 10, + 11, + 11, + 11, + 12, + 12, + 12, + 13, + 13, + 13, + 13, + 14, + 14, + 14, + 15, + 15, + 15, + 16, + 16, + 16, + 16, + 17, + 17, + 17, + 18, + 18, + 18, + 19, + 19, + 19, + 19, + 20, + 20, + 20, + 21, + 21, + 21, + 22, + 22, + 22, + 22, + 23, + 23, + 23, + 24, + 24, + 24, + 25, + 25, + 25, + 25, + 26, + 26, + 26, + 27, + 27, + 27, + 28, + 28, + 28, + 28, + 29, + 29, + 29, + 30, + 30, + 30, + 31, + 31, + 31, + 31, + 32, + 32, + 32, + 33, + 33, + 33, + 34, + 34, + 34, + 34, + 35, + 35, + 35, + 36, + 36, + 36, + 37, + 37, + 37, + 38, + 38, + 38, + 38, + 39, + 39, + 39, + 40, + 40, + 40, + 41, + 41, + 41, + 41, + 42, + 42, + 42, + 43, + 43, + 43, + 44, + 44, + 44, + 44, + 45, + 45, + 45, + 46, + 46, + 46, + 47, + 47, + 47, + 47, + 48, + 48, + 48, + 49, + 49, + 49, + 50, + 50, + 50, + 50, + 51, + 51, + 51, + 52, + 52, + 52, + 53, + 53, + 53, + 53, + 54, + 54, + 54, + 55, + 55, + 55, + 56, + 56, + 56, + 56, + 57, + 57, + 57, + 58, + 58, + 58, + 59, + 59, + 59, + 59, + 60, + 60, + 60, + 61, + 61, + 61, + 62, + 62, + 62, + 62, + 63, + 63, + 63, + 64, + 64, + 64, + 65, + 65, + 65, + 66, + 66, + 66, + 66, + 67, + 67, + 67, + 68, + 68, + 68, + 69, + 69, + 69, + 69, + 70, + 70, + 70, + 71, + 71, + 71, + 72, + 72, + 72, + 72, + 73, + 73, + 73, + 74, + 74, + 74, + 75, + 75, + 75, + 75, + 76, + 76, + 76, + 77, + 77, + 77, + 78, + 78, + 78, + 78, + 79, + 79, + 79, + 80, + 80, + 80, + 81, + 81, + 81, + 81, + 82, + 82, + 82, + 83, + 83, + 83, + 84, + 84, + 84, + 84, + 85, + 85, + 85, + 86, + 86, + 86, + 87, + 87, + 87, + 87, + 88, + 88, + 88, + 89, + 89, + 89, + 90, + 90, + 90, + 90, + 91, + 91, + 91, + 92, + 92, + 92, + 93, + 93, + 93, + 93, + 94, + 94, + 94, + 95, + 95, + 95, + 96, + 96, + 96, + 97, + 97, + 97, + 97, + 98, + 98, + 98, + 99, + 99, + 99, + 100, + 100, + 100, + 100, + 101, + 101, + 101, + 102, + 102, + 102, + 103, + 103, + 103, + 103, + 104, + 104, + 104, + 105, + 105, + 105, + 106, + 106, + 106, + 106, + 107, + 107, + 107, + 108, + 108, + 108, + 109, + 109, + 109, + 109, + 110, + 110, + 110, + 111, + 111, + 111, + 112, + 112, + 112, + 112, + 113, + 113, + 113, + 114, + 114, + 114, + 115, + 115, + 115, + 115, + 116, + 116, + 116, + 117, + 117, + 117, + 118, + 118, + 118, + 118, + 119, + 119, + 119, + 120, + 120, + 120, + 121, + 121, + 121, + 121, + 122, + 122, + 122, + 123, + 123, + 123, + 124, + 124, + 124, + 125, + 125, + 125, + 125, + 126, + 126, + 126, + 127, + 127, + 127, + 128, + 128, + 128, + 128, + 129, + 129, + 129, + 130, + 130, + 130, + 131, + 131, + 131, + 131, + 132, + 132, + 132, + 133, + 133, + 133, + 134, + 134, + 134, + 134, + 135, + 135, + 135, + 136, + 136, + 136, + 137, + 137, + 137, + 137, + 138, + 138, + 138, + 139, + 139, + 139, + 140, + 140, + 140, + 140, + 141, + 141, + 141, + 142, + 142, + 142, + 143, + 143, + 143, + 143, + 144, + 144, + 144, + 145, + 145, + 145, + 146, + 146, + 146, + 146, + 147, + 147, + 147, + 148, + 148, + 148, + 149, + 149, + 149, + 149, + 150, + 150, + 150, + 151, + 151, + 151, + 152, + 152, + 152, + 153, + 153, + 153, + 153, + 154, + 154, + 154, + 155, + 155, + 155, + 156, + 156, + 156, + 156, + 157, + 157, + 157, + 158, + 158, + 158, + 159, + 159, + 159, + 159, + 160, + 160, + 160, + 161, + 161, + 161, + 162, + 162, + 162, + 162, + 163, + 163, + 163, + 164, + 164, + 164, + 165, + 165, + 165, + 165, + 166, + 166, + 166, + 167, + 167, + 167, + 168, + 168, + 168, + 168, + 169, + 169, + 169, + 170, + 170, + 170, + 171, + 171, + 171, + 171, + 172, + 172, + 172, + 173, + 173, + 173, + 174, + 174, + 174, + 174, + 175, + 175, + 175, + 176, + 176, + 176, + 177, + 177, + 177, + 177, + 178, + 178, + 178, + 179, + 179, + 179, + 180, + 180, + 180, + 180, + 181, + 181, + 181, + 182, + 182, + 182, + 183, + 183, + 183, + 184, + 184, + 184, + 184, + 185, + 185, + 185, + 186, + 186, + 186, + 187, + 187, + 187, + 187, + 188, + 188, + 188, + 189, + 189, + 189, + 190, + 190, + 190, + 190, + 191, + 191, +}; + +static const UINT256 multipliers1_bid32[] = { {{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{8022453891189237964ull, 4305922861044245892ull, + 15091728617112590342ull, 392727477223ull}}, +{{16044907782378475927ull, 8611845722088491784ull, + 11736713160515629068ull, 785454954447ull}}, +{{13643071491047400238ull, 17223691444176983569ull, + 5026682247321706520ull, 1570909908895ull}}, +{{8839398908385248859ull, 16000638814644415523ull, + 10053364494643413041ull, 3141819817790ull}}, +{{16525275040644691065ull, 6889476577670793427ull, + 2010672898928682608ull, 628363963558ull}}, +{{14603806007579830513ull, 13778953155341586855ull, + 4021345797857365216ull, 1256727927116ull}}, +{{10760867941450109410ull, 9111162236973622095ull, + 8042691595714730433ull, 2513455854232ull}}, +{{2152173588290021882ull, 1822232447394724419ull, + 8987235948626766733ull, 502691170846ull}}, +{{4304347176580043764ull, 3644464894789448838ull, + 17974471897253533466ull, 1005382341692ull}}, +{{8608694353160087528ull, 7288929789578897676ull, + 17502199720797515316ull, 2010764683385ull}}, +{{9100436500115838152ull, 5147134772657689858ull, + 3500439944159503063ull, 402152936677ull}}, +{{18200873000231676304ull, 10294269545315379716ull, + 7000879888319006126ull, 804305873354ull}}, +{{17955001926753800992ull, 2141795016921207817ull, + 14001759776638012253ull, 1608611746708ull}}, +{{17463259779798050368ull, 4283590033842415635ull, + 9556775479566472890ull, 3217223493417ull}}, +{{10871349585443430720ull, 8235415636252303773ull, + 9290052725397115224ull, 643444698683ull}}, +{{3295955097177309824ull, 16470831272504607547ull, + 133361377084678832ull, 1286889397367ull}}, +{{6591910194354619648ull, 14494918471299663478ull, + 266722754169357665ull, 2573778794734ull}}, +{{8697079668354744576ull, 17656378953227573988ull, + 14810739809801512825ull, 514755758946ull}}, +{{17394159336709489152ull, 16866013832745596360ull, + 11174735545893474035ull, 1029511517893ull}}, +{{16341574599709426688ull, 15285283591781641105ull, + 3902727018077396455ull, 2059023035787ull}}, +{{10647012549425705984ull, 10435754347840148867ull, + 8159243033099299937ull, 411804607157ull}}, +{{2847281025141860352ull, 2424764621970746119ull, + 16318486066198599875ull, 823609214314ull}}, +{{5694562050283720704ull, 4849529243941492238ull, + 14190228058687648134ull, 1647218428629ull}}, +{{4828261224798654464ull, 12037952293014029417ull, + 17595440870705170919ull, 329443685725ull}}, +{{9656522449597308928ull, 5629160512318507218ull, + 16744137667700790223ull, 658887371451ull}}, +{{866300825485066240ull, 11258321024637014437ull, + 15041531261692028830ull, 1317774742903ull}}, +{{1732601650970132480ull, 4069897975564477258ull, + 11636318449674506045ull, 2635549485807ull}}, +{{346520330194026496ull, 8192677224596716098ull, 9705961319418721855ull, + 527109897161ull}}, +{{693040660388052992ull, 16385354449193432196ull, 965178565127892094ull, + 1054219794323ull}}, +{{1386081320776105984ull, 14323964824677312776ull, + 1930357130255784189ull, 2108439588646ull}}, +{{3966565078897131520ull, 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+{{12539004110472395632ull, 13660690458741524766ull, + 1985014202847840298ull, 2546294970418ull}}, +{{9886498451578299773ull, 6421486906490215276ull, + 11465049284795299029ull, 509258994083ull}}, +{{1326252829447047930ull, 12842973812980430553ull, + 4483354495881046442ull, 1018517988167ull}}, +{{2652505658894095859ull, 7239203552251309490ull, + 8966708991762092885ull, 2037035976334ull}}, +{{15287896390746460465ull, 16205235969417903190ull, + 16550737057320059869ull, 407407195266ull}}, +{{12129048707783369314ull, 13963727865126254765ull, + 14654730040930568123ull, 814814390533ull}}, +{{5811353341857187011ull, 9480711656542957915ull, + 10862716008151584631ull, 1629628781067ull}}, +{{11622706683714374021ull, 514679239376364214ull, + 3278687942593617647ull, 3259257562135ull}}, +{{6013890151484785128ull, 7481633477359093489ull, 655737588518723529ull, + 651851512427ull}}, +{{12027780302969570255ull, 14963266954718186978ull, + 1311475177037447058ull, 1303703024854ull}}, +{{5608816532229588893ull, 11479789835726822341ull, + 2622950354074894117ull, 2607406049708ull}}, +{{4811112121187828102ull, 2295957967145364468ull, + 11592636515040709793ull, 521481209941ull}}, +{{9622224242375656204ull, 4591915934290728936ull, + 4738528956371867970ull, 1042962419883ull}}, +{{797704411041760792ull, 9183831868581457873ull, 9477057912743735940ull, + 2085924839766ull}}, +{{14916936141175993452ull, 5526115188458201897ull, + 5584760397290657511ull, 417184967953ull}}, +{{11387128208642435287ull, 11052230376916403795ull, + 11169520794581315022ull, 834369935906ull}}, +{{4327512343575318957ull, 3657716680123255975ull, + 3892297515453078429ull, 1668739871813ull}}, +{{8244200098198884438ull, 8110240965508471841ull, + 11846505947316346655ull, 333747974362ull}}, +{{16488400196397768876ull, 16220481931016943682ull, + 5246267820923141694ull, 667495948725ull}}, +{{14530056319085986135ull, 13994219788324335749ull, + 10492535641846283389ull, 1334991897450ull}}, +{{10613368564462420654ull, 9541695502939119883ull, + 2538327209983015163ull, 2669983794901ull}}, +{{9501371342376304778ull, 16665734359555465269ull, + 4197014256738513355ull, 533996758980ull}}, +{{555998611043057939ull, 14884724645401378923ull, + 8394028513477026711ull, 1067993517960ull}}, +{{1111997222086115877ull, 11322705217093206230ull, + 16788057026954053423ull, 2135987035920ull}}, +{{11290445888642954145ull, 13332587487644372215ull, + 3357611405390810684ull, 427197407184ull}}, +{{4134147703576356674ull, 8218430901579192815ull, + 6715222810781621369ull, 854394814368ull}}, +{{8268295407152713348ull, 16436861803158385630ull, + 13430445621563242738ull, 1708789628736ull}}, +{{16411054340398183963ull, 18044767619599318418ull, + 6375437939054558870ull, 341757925747ull}}, +{{14375364607086816309ull, 17642791165489085221ull, + 12750875878109117741ull, 683515851494ull}}, +{{10303985140464081001ull, 16838838257268618827ull, + 7055007682508683867ull, 1367031702989ull}}, +{{2161226207218610386ull, 15230932440827686039ull, + 14110015365017367735ull, 2734063405978ull}}, +{{7810942870927542724ull, 14114232932391268177ull, + 13890049517229204516ull, 546812681195ull}}, +{{15621885741855085448ull, 9781721791072984738ull, + 9333354960748857417ull, 1093625362391ull}}, +{{12797027410000619279ull, 1116699508436417861ull, + 219965847788163219ull, 2187250724783ull}}, +{{13627451926225854826ull, 7602037531171104218ull, + 11112039613783363613ull, 437450144956ull}}, +{{8808159778742158035ull, 15204075062342208437ull, + 3777335153857175610ull, 874900289913ull}}, +{{17616319557484316070ull, 11961406050974865258ull, + 7554670307714351221ull, 1749800579826ull}}, +{{3523263911496863214ull, 9770978839678793698ull, + 5200282876284780567ull, 349960115965ull}}, +{{7046527822993726428ull, 1095213605648035780ull, + 10400565752569561135ull, 699920231930ull}}, +{{14093055645987452856ull, 2190427211296071560ull, + 2354387431429570654ull, 1399840463861ull}}, +{{9739367218265354095ull, 4380854422592143121ull, + 4708774862859141308ull, 2799680927722ull}}, +{{5637222258394981143ull, 876170884518428624ull, 8320452602055648908ull, + 559936185544ull}}, +{{11274444516789962285ull, 1752341769036857248ull, + 16640905204111297816ull, 1119872371088ull}} +}; + +static const UINT256 multipliers2_bid32[] = + { {{7156996302188685206ull, 14694123111064470433ull, + 3521238664523520994ull, 11704ull}}, +{{14313992604377370412ull, 10941502148419389250ull, + 7042477329047041989ull, 23408ull}}, +{{10181241135045189207ull, 3436260223129226885ull, + 14084954658094083979ull, 46816ull}}, +{{1915738196380826798ull, 6872520446258453771ull, + 9723165242478616342ull, 93633ull}}, +{{3831476392761653595ull, 13745040892516907542ull, + 999586411247681068ull, 187267ull}}, +{{7662952785523307189ull, 9043337711324263468ull, + 1999172822495362137ull, 374534ull}}, +{{15325905571046614378ull, 18086675422648526936ull, + 3998345644990724274ull, 749068ull}}, +{{12205067068383677139ull, 17726606771587502257ull, + 7996691289981448549ull, 1498136ull}}, +{{5963390063057802661ull, 17006469469465452899ull, + 15993382579962897099ull, 2996272ull}}, +{{11926780126115605321ull, 15566194865221354182ull, + 13540021086216242583ull, 5992545ull}}, +{{5406816178521659026ull, 12685645656733156749ull, + 8633298098722933551ull, 11985091ull}}, +{{10813632357043318052ull, 6924547239756761882ull, + 17266596197445867103ull, 23970182ull}}, +{{3180520640377084488ull, 13849094479513523765ull, + 16086448321182182590ull, 47940365ull}}, +{{6361041280754168975ull, 9251444885317495914ull, + 13726152568654813565ull, 95880731ull}}, +{{12722082561508337950ull, 56145696925440212ull, 9005561063600075515ull, + 191761463ull}}, +{{6997421049307124283ull, 112291393850880425ull, + 18011122127200151030ull, 383522926ull}}, +{{13994842098614248565ull, 224582787701760850ull, + 17575500180690750444ull, 767045853ull}}, +{{9542940123518945513ull, 449165575403521701ull, + 16704256287671949272ull, 1534091707ull}}, +{{639136173328339410ull, 898331150807043403ull, 14961768501634346928ull, + 3068183415ull}}, +{{1278272346656678820ull, 1796662301614086806ull, + 11476792929559142240ull, 6136366831ull}}, +{{2556544693313357639ull, 3593324603228173612ull, + 4506841785408732864ull, 12272733663ull}}, +{{5113089386626715277ull, 7186649206456347224ull, + 9013683570817465728ull, 24545467326ull}}, +{{10226178773253430554ull, 14373298412912694448ull, + 18027367141634931456ull, 49090934652ull}}, +{{2005613472797309491ull, 10299852752115837281ull, + 17607990209560311297ull, 98181869305ull}}, +{{4011226945594618982ull, 2152961430522122946ull, + 16769236345411070979ull, 196363738611ull}}, +{{4491594203860834120ull, 430592286104424589ull, 7043196083824124519ull, + 39272747722ull}}, +{{8983188407721668240ull, 861184572208849178ull, + 14086392167648249038ull, 78545495444ull}}, +{{17966376815443336479ull, 1722369144417698356ull, + 9726040261586946460ull, 157090990889ull}}, +{{17486009557177121341ull, 3444738288835396713ull, + 1005336449464341304ull, 314181981779ull}}, +{{7186550726177334592ull, 11756994101992810312ull, + 14958462548860509553ull, 62836396355ull}}, +{{14373101452354669183ull, 5067244130276069008ull, + 11470181024011467491ull, 125672792711ull}}, +{{10299458830999786749ull, 10134488260552138017ull, + 4493617974313383366ull, 251345585423ull}}, +{{5749240580941867673ull, 16784292911078068896ull, + 11966770039088407642ull, 50269117084ull}}, +{{11498481161883735346ull, 15121841748446586176ull, + 5486796004467263669ull, 100538234169ull}}, +{{4550218250057919076ull, 11796939423183620737ull, + 10973592008934527339ull, 201076468338ull}}, +{{15667438908979225108ull, 9738085514120544793ull, + 13262764846012636437ull, 40215293667ull}}, +{{12888133744248898600ull, 1029426954531537971ull, + 8078785618315721259ull, 80430587335ull}}, +{{7329523414788245584ull, 2058853909063075943ull, + 16157571236631442518ull, 160861174670ull}}, +{{14659046829576491168ull, 4117707818126151886ull, + 13868398399553333420ull, 321722349341ull}}, +{{10310506995399118880ull, 4512890378367140700ull, + 6463028494652577007ull, 64344469868ull}}, +{{2174269917088686144ull, 9025780756734281401ull, + 12926056989305154014ull, 128688939736ull}}, +{{4348539834177372288ull, 18051561513468562802ull, + 7405369904900756412ull, 257377879473ull}}, +{{8248405596319295104ull, 3610312302693712560ull, + 12549120425205882252ull, 51475575894ull}}, +{{16496811192638590208ull, 7220624605387425120ull, + 6651496776702212888ull, 102951151789ull}}, +{{14546878311567628800ull, 14441249210774850241ull, + 13302993553404425776ull, 205902303578ull}}, +{{2909375662313525760ull, 17645645101122611341ull, + 13728645154906616124ull, 41180460715ull}}, +{{5818751324627051520ull, 16844546128535671066ull, + 9010546236103680633ull, 82360921431ull}}, +{{11637502649254103040ull, 15242348183361790516ull, + 18021092472207361267ull, 164721842862ull}}, +{{2327500529850820608ull, 17805864895639999396ull, + 10982916123925292899ull, 32944368572ull}}, +{{4655001059701641216ull, 17164985717570447176ull, + 3519088174141034183ull, 65888737145ull}}, +{{9310002119403282432ull, 15883227361431342736ull, + 7038176348282068367ull, 131777474290ull}}, +{{173260165097013248ull, 13319710649153133857ull, + 14076352696564136735ull, 263554948580ull}}, +{{7413349662503223296ull, 2663942129830626771ull, + 2815270539312827347ull, 52710989716ull}}, +{{14826699325006446592ull, 5327884259661253542ull, + 5630541078625654694ull, 105421979432ull}}, +{{11206654576303341568ull, 10655768519322507085ull, + 11261082157251309388ull, 210843958864ull}}, +{{9620028544744488960ull, 9509851333348322063ull, + 17009611690417903170ull, 42168791772ull}}, +{{793313015779426304ull, 572958592987092511ull, 15572479307126254725ull, + 84337583545ull}}, +{{1586626031558852608ull, 1145917185974185022ull, + 12698214540542957834ull, 168675167091ull}}, +{{7696022835795591168ull, 229183437194837004ull, 6228991722850501890ull, + 33735033418ull}}, +{{15392045671591182336ull, 458366874389674008ull, + 12457983445701003780ull, 67470066836ull}}, +{{12337347269472813056ull, 916733748779348017ull, + 6469222817692455944ull, 134940133673ull}}, +{{6227950465236074496ull, 1833467497558696035ull, + 12938445635384911888ull, 269880267346ull}}, +{{16002985352014856192ull, 15124088758479380499ull, + 6277037941818892700ull, 53976053469ull}}, +{{13559226630320160768ull, 11801433443249209383ull, + 12554075883637785401ull, 107952106938ull}}, +{{8671709186930769920ull, 5156122812788867151ull, + 6661407693566019187ull, 215904213877ull}}, +{{1734341837386153984ull, 15788619821525414723ull, + 8710979168197024483ull, 43180842775ull}}, +{{3468683674772307968ull, 13130495569341277830ull, + 17421958336394048967ull, 86361685550ull}}, +{{6937367349544615936ull, 7814247064973004044ull, + 16397172599078546319ull, 172723371101ull}}, +{{16144868728876564480ull, 1562849412994600808ull, + 6968783334557619587ull, 34544674220ull}}, +{{13842993384043577344ull, 3125698825989201617ull, + 13937566669115239174ull, 69089348440ull}}, +{{9239242694377603072ull, 6251397651978403235ull, + 9428389264520926732ull, 138178696881ull}}, +{{31741315045654528ull, 12502795303956806471ull, 410034455332301848ull, + 276357393763ull}}, +{{7385045892492951552ull, 6189907875533271617ull, + 11150053335292191339ull, 55271478752ull}}, +{{14770091784985903104ull, 12379815751066543234ull, + 3853362596874831062ull, 110542957505ull}}, +{{11093439496262254592ull, 6312887428423534853ull, + 7706725193749662125ull, 221085915010ull}}, +{{13286734343478181888ull, 1262577485684706970ull, + 1541345038749932425ull, 44217183002ull}}, +{{8126724613246812160ull, 2525154971369413941ull, + 3082690077499864850ull, 88434366004ull}}, +{{16253449226493624320ull, 5050309942738827882ull, + 6165380154999729700ull, 176868732008ull}}, +{{3250689845298724864ull, 12078108432773496546ull, + 12301122475225676909ull, 35373746401ull}}, +{{6501379690597449728ull, 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11320747285832603495ull, 72445432630ull}}, +{{17299322326264840192ull, 8889095178479228297ull, + 4194750497955655375ull, 144890865261ull}}, +{{16151900578820128768ull, 17778190356958456595ull, + 8389500995911310750ull, 289781730522ull}}, +{{10609077745247846400ull, 10934335700875511965ull, + 9056597828666082796ull, 57956346104ull}}, +{{2771411416786141184ull, 3421927328041472315ull, + 18113195657332165593ull, 115912692208ull}}, +{{5542822833572282368ull, 6843854656082944630ull, + 17779647240954779570ull, 231825384417ull}}, +{{8487262196198277120ull, 8747468560700409572ull, + 10934627077674776560ull, 46365076883ull}}, +{{16974524392396554240ull, 17494937121400819144ull, + 3422510081640001504ull, 92730153767ull}}, +{{15502304711083556864ull, 16543130169092086673ull, + 6845020163280003009ull, 185460307534ull}}, +{{6789809756958621696ull, 14376672478044148304ull, + 16126399291623641894ull, 37092061506ull}}, +{{13579619513917243392ull, 10306600882378744992ull, + 13806054509537732173ull, 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+{{9824761052003254321ull, 2592837755106864510ull, + 12978294610448558484ull, 65185151242ull}}, +{{1202778030296957026ull, 5185675510213729021ull, + 7509845147187565352ull, 130370302485ull}}, +{{2405556060593914051ull, 10371351020427458042ull, + 15019690294375130704ull, 260740604970ull}}, +{{4170460026860693134ull, 16831665463053132901ull, + 3003938058875026140ull, 52148120994ull}}, +{{8340920053721386267ull, 15216586852396714186ull, + 6007876117750052281ull, 104296241988ull}}, +{{16681840107442772534ull, 11986429631083876756ull, + 12015752235500104563ull, 208592483976ull}}, +{{3336368021488554507ull, 17154681185184416644ull, + 6092499261841931235ull, 41718496795ull}}, +{{6672736042977109014ull, 15862618296659281672ull, + 12184998523683862471ull, 83436993590ull}}, +{{13345472085954218027ull, 13278492519609011728ull, + 5923252973658173327ull, 166873987181ull}}, +{{6358443231932753929ull, 13723744948147533315ull, + 4873999409473544988ull, 33374797436ull}}, +{{12716886463865507858ull, 9000745822585515014ull, + 9747998818947089977ull, 66749594872ull}}, +{{6987028854021464099ull, 18001491645171030029ull, + 1049253564184628338ull, 133499189745ull}}, +{{13974057708042928197ull, 17556239216632508442ull, + 2098507128369256677ull, 266998379490ull}}, +{{17552206800576226933ull, 10889945472810322334ull, + 419701425673851335ull, 53399675898ull}}, +{{16657669527442902249ull, 3333146871911093053ull, + 839402851347702671ull, 106799351796ull}}, +{{14868594981176252881ull, 6666293743822186107ull, + 1678805702695405342ull, 213598703592ull}}, +{{6663067810977160900ull, 16090654007732078514ull, + 7714458770022901714ull, 42719740718ull}}, +{{13326135621954321799ull, 13734563941754605412ull, + 15428917540045803429ull, 85439481436ull}}, +{{8205527170199091982ull, 9022383809799659209ull, + 12411091006382055243ull, 170878962873ull}}, +{{1641105434039818397ull, 5493825576701842165ull, + 13550264645502142018ull, 34175792574ull}}, +{{3282210868079636793ull, 10987651153403684330ull, + 8653785217294732420ull, 68351585149ull}}, +{{6564421736159273585ull, 3528558233097817044ull, + 17307570434589464841ull, 136703170298ull}}, +{{13128843472318547170ull, 7057116466195634088ull, + 16168396795469378066ull, 273406340597ull}}, +{{6315117509205619758ull, 12479469737464857787ull, + 10612376988577696259ull, 54681268119ull}}, +{{12630235018411239515ull, 6512195401220163958ull, + 2778009903445840903ull, 109362536239ull}}, +{{6813725963112927413ull, 13024390802440327917ull, + 5556019806891681806ull, 218725072478ull}}, +{{5052094007364495806ull, 17362273419455706876ull, + 12179250405604067330ull, 43745014495ull}}, +{{10104188014728991612ull, 16277802765201862136ull, + 5911756737498583045ull, 87490028991ull}}, +{{1761631955748431607ull, 14108861456694172657ull, + 11823513474997166091ull, 174980057982ull}}, +{{352326391149686322ull, 13889818735564565501ull, + 9743400324483253864ull, 34996011596ull}}, +{{704652782299372643ull, 9332893397419579386ull, 1040056575256956113ull, + 69992023193ull}}, +{{1409305564598745286ull, 219042721129607156ull, 2080113150513912227ull, + 139984046386ull}}, +{{2818611129197490572ull, 438085442259214312ull, 4160226301027824454ull, + 279968092772ull}}, +{{11631768670065229084ull, 3776965903193753185ull, + 8210742889689385537ull, 55993618554ull}}, +{{4816793266420906552ull, 7553931806387506371ull, + 16421485779378771074ull, 111987237108ull}} +}; + +static const UINT128 coefflimits_bid32[] = { {{10000000ull, 0ull}}, +{{2000000ull, 0ull}}, +{{400000ull, 0ull}}, +{{80000ull, 0ull}}, +{{16000ull, 0ull}}, +{{3200ull, 0ull}}, +{{640ull, 0ull}}, +{{128ull, 0ull}}, +{{25ull, 0ull}}, +{{5ull, 0ull}}, +{{1ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}} +}; + +// ********************************************************************** + +static const UINT128 breakpoints_bid64[] = { {{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{632147898099709952ull, 73239311802481213ull}}, +{{9539445985904630784ull, 36619655901240606ull}}, +{{4769722992952315392ull, 18309827950620303ull}}, +{{5401870891052025344ull, 91549139753101516ull}}, +{{2700935445526012672ull, 45774569876550758ull}}, +{{1350467722763006208ull, 22887284938275379ull}}, +{{6752338613815031552ull, 114436424691376895ull}}, +{{12599541343762291456ull, 57218212345688447ull}}, +{{15523142708735921408ull, 28609106172844223ull}}, +{{3828737248841401600ull, 143045530864221119ull}}, +{{11137740661275476480ull, 71522765432110559ull}}, +{{14792242367492514048ull, 35761382716055279ull}}, +{{16619493220601032704ull, 17880691358027639ull}}, +{{9310489808166957824ull, 89403456790138199ull}}, +{{13878616940938254592ull, 44701728395069099ull}}, +{{16162680507323902976ull, 22350864197534549ull}}, +{{7026426241781309440ull, 111754320987672749ull}}, +{{12736585157745430528ull, 55877160493836374ull}}, +{{6368292578872715264ull, 27938580246918187ull}}, +{{13394718820654024704ull, 139692901234590936ull}}, +{{6697359410327012352ull, 69846450617295468ull}}, +{{3348679705163506176ull, 34923225308647734ull}}, +{{1674339852581753088ull, 17461612654323867ull}}, +{{8371699262908765440ull, 87308063271619335ull}}, +{{13409221668309158400ull, 43654031635809667ull}}, +{{15927982871009355008ull, 21827015817904833ull}}, +{{5852938060208568832ull, 109135079089524169ull}}, +{{12149841066959060224ull, 54567539544762084ull}}, +{{6074920533479529984ull, 27283769772381042ull}}, +{{11927858593688099072ull, 136418848861905211ull}}, +{{15187301333698825216ull, 68209424430952605ull}}, +{{16817022703704188416ull, 34104712215476302ull}}, +{{8408511351852094208ull, 17052356107738151ull}}, +{{5149068611841367808ull, 85261780538690757ull}}, +{{11797906342775459584ull, 42630890269345378ull}}, +{{5898953171387729664ull, 21315445134672689ull}}, +{{11048021783229097728ull, 106577225673363446ull}}, +{{5524010891614548736ull, 53288612836681723ull}}, +{{11985377482662050048ull, 26644306418340861ull}}, +{{4586655192181596416ull, 133221532091704308ull}}, +{{2293327596090798080ull, 66610766045852154ull}}, +{{1146663798045399040ull, 33305383022926077ull}}, +{{9796703935877475328ull, 16652691511463038ull}}, +{{12090031531968273664ull, 83263457557315192ull}}, +{{6045015765984136704ull, 41631728778657596ull}}, +{{3022507882992068352ull, 20815864389328798ull}}, +{{15112539414960342016ull, 104079321946643990ull}}, +{{7556269707480171008ull, 52039660973321995ull}}, +{{13001506890594861312ull, 26019830486660997ull}}, +{{9667302231845651712ull, 130099152433304988ull}}, +{{4833651115922825728ull, 65049576216652494ull}}, +{{2416825557961412864ull, 32524788108326247ull}}, +{{10431784815835482112ull, 16262394054163123ull}}, +{{15265435931758308096ull, 81311970270815617ull}}, +{{16856090002733929728ull, 40655985135407808ull}}, +{{8428045001366964736ull, 20327992567703904ull}}, +{{5246736859415721472ull, 101639962838519522ull}}, +{{2623368429707860736ull, 50819981419259761ull}}, +{{10535056251708706048ull, 25409990709629880ull}}, +{{15781793111124427520ull, 127049953548149402ull}}, +{{7890896555562213632ull, 63524976774074701ull}}, +{{13168820314635882496ull, 31762488387037350ull}}, +{{6584410157317941248ull, 15881244193518675ull}}, +{{14475306712880155136ull, 79406220967593376ull}}, +{{7237653356440077568ull, 39703110483796688ull}}, +{{3618826678220038656ull, 19851555241898344ull}}, +{{18094133391100194048ull, 99257776209491720ull}}, +{{9047066695550096896ull, 49628888104745860ull}}, +{{4523533347775048448ull, 24814444052372930ull}}, +{{4170922665165690880ull, 124072220261864651ull}}, +{{11308833369437621248ull, 62036110130932325ull}}, +{{14877788721573586432ull, 31018055065466162ull}}, +{{7438894360786793216ull, 15509027532733081ull}}, +{{300983656514862848ull, 77545137663665407ull}}, +{{9373863865112207104ull, 38772568831832703ull}}, +{{13910303969410879232ull, 19386284415916351ull}}, +{{14211287625925742080ull, 96931422079581758ull}}, +{{7105643812962871040ull, 48465711039790879ull}}, +{{12776193943336211200ull, 24232855519895439ull}}, +{{8540737495552401920ull, 121164277599477198ull}}, +{{4270368747776200960ull, 60582138799738599ull}}, +{{11358556410742876160ull, 30291069399869299ull}}, +{{14902650242226213888ull, 15145534699934649ull}}, +{{726274916292863232ull, 75727673499673249ull}}, +{{9586509495001207296ull, 37863836749836624ull}}, +{{4793254747500603648ull, 18931918374918312ull}}, +{{5519529663793467136ull, 94659591874591561ull}}, +{{11983136868751509248ull, 47329795937295780ull}}, +{{5991568434375754496ull, 23664897968647890ull}}, +{{11511098098169221632ull, 118324489843239451ull}}, +{{14978921085939386624ull, 59162244921619725ull}}, +{{16712832579824468992ull, 29581122460809862ull}}, +{{8356416289912234496ull, 14790561230404931ull}}, +{{4888593302142069504ull, 73952806152024657ull}}, +{{11667668687925810432ull, 36976403076012328ull}}, +{{5833834343962905088ull, 18488201538006164ull}}, +{{10722427646104974848ull, 92441007690030821ull}}, +{{14584585859907263232ull, 46220503845015410ull}}, +{{7292292929953631488ull, 23110251922507705ull}}, +{{18014720576058606592ull, 115551259612538526ull}}, +{{9007360288029303296ull, 57775629806269263ull}}, +{{13727052180869427456ull, 28887814903134631ull}}, +{{16086898127289489408ull, 14443907451567315ull}}, +{{6647514341609241088ull, 72219537257836579ull}}, +{{12547129207659396352ull, 36109768628918289ull}}, +{{15496936640684473856ull, 18054884314459144ull}}, +{{3697706908584163584ull, 90274421572295724ull}}, +{{1848853454292081664ull, 45137210786147862ull}}, +{{924426727146040832ull, 22568605393073931ull}}, +{{4622133635730204416ull, 112843026965369655ull}}, +{{11534438854719877888ull, 56421513482684827ull}}, +{{14990591464214714624ull, 28210756741342413ull}}, +{{1165981026235367680ull, 141053783706712069ull}}, +{{9806362549972459520ull, 70526891853356034ull}}, +{{4903181274986229760ull, 35263445926678017ull}}, +{{11674962674347890688ull, 17631722963339008ull}}, +{{3034581150610798848ull, 88158614816695043ull}}, +{{10740662612160175104ull, 44079307408347521ull}}, +{{14593703342934863360ull, 22039653704173760ull}}, +{{17628284493545662208ull, 110198268520868803ull}}, +{{18037514283627606784ull, 55099134260434401ull}}, +{{18242129178668579072ull, 27549567130217200ull}}, +{{17423669598504689920ull, 137747835651086004ull}}, +{{8711834799252344832ull, 68873917825543002ull}}, +{{4355917399626172416ull, 34436958912771501ull}}, +{{11401330736667862016ull, 17218479456385750ull}}, +{{1666421462210655232ull, 86092397281928753ull}}, +{{10056582767960103424ull, 43046198640964376ull}}, +{{5028291383980051712ull, 21523099320482188ull}}, +{{6694712846190706944ull, 107615496602410941ull}}, +{{12570728459950129152ull, 53807748301205470ull}}, +{{6285364229975064576ull, 26903874150602735ull}}, +{{12980077076165771776ull, 134519370753013676ull}}, +{{6490038538082885888ull, 67259685376506838ull}}, +{{3245019269041442816ull, 33629842688253419ull}}, +{{10845881671375497216ull, 16814921344126709ull}}, +{{17335920209458383104ull, 84074606720633547ull}}, +{{17891332141583967232ull, 42037303360316773ull}}, +{{18169038107646759424ull, 21018651680158386ull}}, +{{17058214243395590912ull, 105093258400791934ull}}, +{{8529107121697795328ull, 52546629200395967ull}}, +{{13487925597703673344ull, 26273314600197983ull}}, +{{12099395767389712896ull, 131366573000989918ull}}, +{{6049697883694856448ull, 65683286500494959ull}}, +{{12248220978702203904ull, 32841643250247479ull}}, +{{15347482526205877760ull, 16420821625123739ull}}, +{{2950436336191182592ull, 82104108125618699ull}}, +{{10698590204950366976ull, 41052054062809349ull}}, +{{14572667139329959168ull, 20526027031404674ull}}, +{{17523103475521142016ull, 102630135157023373ull}}, +{{17984923774615346688ull, 51315067578511686ull}}, +{{8992461887307673344ull, 25657533789255843ull}}, +{{8068821289119264000ull, 128287668946279217ull}}, +{{13257782681414407680ull, 64143834473139608ull}}, +{{6628891340707203840ull, 32071917236569804ull}}, +{{3314445670353601792ull, 16035958618284902ull}}, +{{16572228351768009728ull, 80179793091424510ull}}, +{{8286114175884004864ull, 40089896545712255ull}}, +{{13366429124796778240ull, 20044948272856127ull}}, +{{11491913402855236352ull, 100224741364280638ull}}, +{{5745956701427618048ull, 50112370682140319ull}}, +{{12096350387568584704ull, 25056185341070159ull}}, +{{5141519716714269696ull, 125280926705350798ull}}, +{{2570759858357134848ull, 62640463352675399ull}}, +{{10508751966033343232ull, 31320231676337699ull}}, +{{14477748019871447296ull, 15660115838168849ull}}, +{{17048507878228582144ull, 78300579190844248ull}}, +{{8524253939114290944ull, 39150289595422124ull}}, +{{4262126969557145344ull, 19575144797711062ull}}, +{{2863890774076176128ull, 97875723988555311ull}}, +{{10655317423892863744ull, 48937861994277655ull}}, +{{14551030748801207552ull, 24468930997138827ull}}, +{{17414921522877383936ull, 122344654985694138ull}}, +{{8707460761438691840ull, 61172327492847069ull}}, +{{13577102417574121728ull, 30586163746423534ull}}, +{{6788551208787060736ull, 15293081873211767ull}}, +{{15496011970225752832ull, 76465409366058836ull}}, +{{7748005985112876288ull, 38232704683029418ull}}, +{{3874002992556438016ull, 19116352341514709ull}}, +{{923270889072639488ull, 95581761707573546ull}}, +{{461635444536319744ull, 47790880853786773ull}}, +{{9454189759122935552ull, 23895440426893386ull}}, +{{10377460648195575040ull, 119477202134466932ull}}, 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+{{3304665369756940032ull, 60898292596395246ull}}, +{{1652332684878469888ull, 30449146298197623ull}}, +{{10049538379294010624ull, 15224573149098811ull}}, +{{13354203749050950912ull, 76122865745494057ull}}, +{{15900473911380251136ull, 38061432872747028ull}}, +{{7950236955690125568ull, 19030716436373514ull}}, +{{2857696631031525120ull, 95153582181867572ull}}, +{{1428848315515762432ull, 47576791090933786ull}}, +{{714424157757881088ull, 23788395545466893ull}}, +{{3572120788789406464ull, 118941977727334465ull}}, +{{11009432431249478912ull, 59470988863667232ull}}, +{{5504716215624739328ull, 29735494431833616ull}}, +{{2752358107812369664ull, 14867747215916808ull}}, +{{13761790539061848832ull, 74338736079584040ull}}, +{{6880895269530924288ull, 37169368039792020ull}}, +{{3440447634765462016ull, 18584684019896010ull}}, +{{17202238173827310848ull, 92923420099480050ull}}, +{{8601119086913655296ull, 46461710049740025ull}}, +{{13523931580311603456ull, 23230855024870012ull}}, +{{12279425680429362944ull, 116154275124350063ull}}, +{{15363084877069457152ull, 58077137562175031ull}}, +{{16904914475389504256ull, 29038568781087515ull}}, +{{17675829274549527808ull, 14519284390543757ull}}, +{{14592170077909433600ull, 72596421952718789ull}}, +{{16519457075809492480ull, 36298210976359394ull}}, +{{8259728537904746240ull, 18149105488179697ull}}, +{{4405154542104628224ull, 90745527440898487ull}}, +{{11425949307907089920ull, 45372763720449243ull}}, +{{14936346690808320768ull, 22686381860224621ull}}, +{{894757159203397632ull, 113431909301123109ull}}, +{{9670750616456474624ull, 56715954650561554ull}}, +{{4835375308228237312ull, 28357977325280777ull}}, +{{5730132467431634944ull, 141789886626403886ull}}, +{{2865066233715817472ull, 70894943313201943ull}}, +{{10655905153712684544ull, 35447471656600971ull}}, +{{14551324613711118080ull, 17723735828300485ull}}, +{{17416390847426935552ull, 88618679141502428ull}}, +{{8708195423713467648ull, 44309339570751214ull}}, +{{4354097711856733696ull, 22154669785375607ull}}, +{{3323744485574117632ull, 110773348926878036ull}}, +{{1661872242787058688ull, 55386674463439018ull}}, +{{830936121393529344ull, 27693337231719509ull}}, +{{4154680606967647232ull, 138466686158597545ull}}, +{{11300712340338599424ull, 69233343079298772ull}} +}; + +static const int exponents_bid64[] = { -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + 0, + 0, + 0, + 1, + 1, + 1, + 2, + 2, + 2, + 3, + 3, + 3, + 3, + 4, + 4, + 4, + 5, + 5, + 5, + 6, + 6, + 6, + 6, + 7, + 7, + 7, + 8, + 8, + 8, + 9, + 9, + 9, + 9, + 10, + 10, + 10, + 11, + 11, + 11, + 12, + 12, + 12, + 12, + 13, + 13, + 13, + 14, + 14, + 14, + 15, + 15, + 15, + 15, + 16, + 16, + 16, + 17, + 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287, + 287, + 288, + 288, + 288, + 288, + 289, + 289, + 289, + 290, + 290, + 290, + 291, + 291, + 291, + 291, + 292, + 292, + 292, + 293, + 293, + 293, + 294, + 294, + 294, + 295, + 295, + 295, + 295, + 296, + 296, + 296, + 297, + 297, + 297, + 298, + 298, + 298, + 298, + 299, + 299, + 299, + 300, + 300, + 300, + 301, + 301, + 301, + 301, + 302, + 302, + 302, + 303, + 303, + 303, + 304, + 304, + 304, + 304, + 305, + 305, + 305, + 306, + 306, + 306, + 307, + 307, + 307, + 307, + 308, + 308, + 308, + 309, + 309, + 309, + 310, + 310, + 310, + 310, + 311, + 311, + 311, + 312, + 312, + 312, + 313, + 313, + 313, + 313, + 314, + 314, + 314, + 315, + 315, + 315, + 316, + 316, + 316, + 316, + 317, + 317, + 317, + 318, + 318, + 318, + 319, + 319, + 319, + 319, + 320, + 320, + 320, + 321, + 321, + 321, + 322, + 322, + 322, + 322, + 323, + 323, + 323, + 324, + 324, + 324, + 325, + 325, + 325, + 326, + 326, + 326, + 326, + 327, + 327, + 327, + 328, + 328, + 328, + 329, + 329, + 329, + 329, + 330, + 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674, + 675, + 675, + 675, + 676, + 676, + 676, + 677, + 677, + 677, + 677, + 678, + 678, + 678, + 679, + 679, + 679, + 680, + 680, + 680, + 680, + 681, + 681, + 681, + 682, + 682, + 682, + 683, + 683, + 683, + 683, + 684, + 684, + 684, + 685, + 685, + 685, + 686, + 686, + 686, + 686, + 687, + 687, + 687, + 688, + 688, + 688, + 689, + 689, + 689, + 689, + 690, + 690, + 690, + 691, + 691, + 691, + 692, + 692, + 692, + 692, + 693, + 693, + 693, + 694, + 694, + 694, + 695, + 695, + 695, + 695, + 696, + 696, + 696, + 697, + 697, + 697, + 698, + 698, + 698, + 698, + 699, + 699, + 699, + 700, + 700, + 700, + 701, + 701, + 701, + 701, + 702, + 702, + 702, + 703, + 703, + 703, + 704, + 704, + 704, + 705, + 705, + 705, + 705, + 706, + 706, + 706, + 707, + 707, + 707, + 708, + 708, + 708, + 708, + 709, + 709, + 709, + 710, + 710, + 710, + 711, + 711, + 711, + 711, + 712, + 712, + 712, + 713, + 713, + 713, + 714, + 714, + 714, + 714, + 715, + 715, + 715, + 716, + 716, + 716, + 717, + 717, + 717, + 717, + 718, + 718, + 718, + 719, + 719, + 719, + 720, + 720, + 720, + 720, + 721, + 721, + 721, + 722, + 722, + 722, + 723, + 723, + 723, + 723, + 724, + 724, + 724, + 725, + 725, + 725, + 726, + 726, + 726, + 726, + 727, + 727, + 727, + 728, + 728, + 728, + 729, + 729, + 729, + 729, + 730, + 730, + 730, + 731, + 731, + 731, + 732, + 732, + 732, + 733, + 733, + 733, + 733, + 734, + 734, + 734, + 735, + 735, + 735, + 736, + 736, + 736, + 736, + 737, + 737, + 737, + 738, + 738, + 738, + 739, + 739, + 739, + 739, + 740, + 740, + 740, + 741, + 741, + 741, + 742, + 742, + 742, + 742, + 743, + 743, + 743, + 744, + 744, + 744, + 745, + 745, + 745, + 745, + 746, + 746, + 746, + 747, + 747, + 747, + 748, + 748, + 748, + 748, + 749, + 749, + 749, + 750, + 750, + 750, + 751, + 751, + 751, + 751, + 752, + 752, + 752, + 753, + 753, + 753, + 754, + 754, + 754, + 754, + 755, + 755, + 755, + 756, + 756, + 756, + 757, + 757, + 757, + 757, + 758, + 758, + 758, + 759, + 759, + 759, + 760, + 760, + 760, + 760, + 761, + 761, + 761, + 762, + 762, + 762, + 763, + 763, + 763, + 764, + 764, + 764, + 764, + 765, + 765, + 765, + 766, + 766, + 766, + 767, + 767, +}; + +static const UINT256 multipliers1_bid64[] = { {{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{0ull, 0ull, 0ull, 0ull}}, +{{11950291386221365447ull, 9908758460416160234ull, + 6069031768864303422ull, 2518694348665986494ull}}, +{{5453838698733179278ull, 1370772847122768853ull, + 12138063537728606845ull, 5037388697331972988ull}}, +{{10907677397466358555ull, 2741545694245537706ull, + 5829383001747662074ull, 10074777394663945977ull}}, +{{9560233108977092358ull, 4237657953591017864ull, + 8544574229833353061ull, 2014955478932789195ull}}, +{{673722144244633099ull, 8475315907182035729ull, + 17089148459666706122ull, 4029910957865578390ull}}, +{{1347444288489266198ull, 16950631814364071458ull, + 15731552845623860628ull, 8059821915731156781ull}}, +{{7648186487181673886ull, 18147521621840455584ull, + 6835659383866682448ull, 1611964383146231356ull}}, +{{15296372974363347772ull, 17848299169971359552ull, + 13671318767733364897ull, 3223928766292462712ull}}, +{{12146001875017143928ull, 17249854266233167489ull, + 8895893461757178179ull, 6447857532584925425ull}}, +{{13497246819229159756ull, 18207366112214274790ull, + 1779178692351435635ull, 1289571506516985085ull}}, +{{8547749564748767895ull, 17967988150718997965ull, + 3558357384702871271ull, 2579143013033970170ull}}, +{{17095499129497535789ull, 17489232227728444314ull, + 7116714769405742543ull, 5158286026067940340ull}}, +{{15744254185285519961ull, 16531720381747337013ull, + 14233429538811485087ull, 10316572052135880680ull}}, +{{3148850837057103993ull, 10685041705833288049ull, + 2846685907762297017ull, 2063314410427176136ull}}, +{{6297701674114207985ull, 2923339337957024482ull, + 5693371815524594035ull, 4126628820854352272ull}}, +{{12595403348228415969ull, 5846678675914048964ull, + 11386743631049188070ull, 8253257641708704544ull}}, +{{13587127113871414164ull, 15926730994150451085ull, + 17034743985177478906ull, 1650651528341740908ull}}, +{{8727510154033276711ull, 13406717914591350555ull, + 15622743896645406197ull, 3301303056683481817ull}}, +{{17455020308066553422ull, 8366691755473149494ull, + 12798743719581260779ull, 6602606113366963635ull}}, +{{14559050505839041654ull, 16430733610062271191ull, + 2559748743916252155ull, 1320521222673392727ull}}, +{{10671356937968531692ull, 14414723146414990767ull, + 5119497487832504311ull, 2641042445346785454ull}}, +{{2895969802227511768ull, 10382702219120429919ull, + 10238994975665008623ull, 5282084890693570908ull}}, +{{5791939604455023535ull, 2318660364531308222ull, + 2031245877620465631ull, 10564169781387141817ull}}, +{{1158387920891004707ull, 11531778517131992614ull, + 7784946805007913772ull, 2112833956277428363ull}}, +{{2316775841782009414ull, 4616812960554433612ull, + 15569893610015827545ull, 4225667912554856726ull}}, +{{4633551683564018828ull, 9233625921108867224ull, + 12693043146322103474ull, 8451335825109713453ull}}, +{{4616059151454714089ull, 9225422813705594091ull, + 13606655073490151664ull, 1690267165021942690ull}}, +{{9232118302909428178ull, 4101553701636566ull, 8766566073270751713ull, + 3380534330043885381ull}}, +{{17492532109304740ull, 8203107403273133ull, 17533132146541503426ull, + 6761068660087770762ull}}, +{{3692847321163771272ull, 11069687065706385596ull, + 10885324058792121331ull, 1352213732017554152ull}}, +{{7385694642327542543ull, 3692630057703219576ull, + 3323904043874691047ull, 2704427464035108305ull}}, +{{14771389284655085085ull, 7385260115406439152ull, + 6647808087749382094ull, 5408854928070216610ull}}, +{{11096034495600618553ull, 14770520230812878305ull, + 13295616175498764188ull, 10817709856140433220ull}}, +{{13287253343345854681ull, 14022150490388306630ull, + 2659123235099752837ull, 2163541971228086644ull}}, +{{8127762612982157745ull, 9597556907067061645ull, + 5318246470199505675ull, 4327083942456173288ull}}, +{{16255525225964315489ull, 748369740424571674ull, + 10636492940399011351ull, 8654167884912346576ull}}, +{{6940453859934773421ull, 7528371577568734981ull, + 5816647402821712593ull, 1730833576982469315ull}}, +{{13880907719869546842ull, 15056743155137469962ull, + 11633294805643425186ull, 3461667153964938630ull}}, +{{9315071366029542068ull, 11666742236565388309ull, + 4819845537577298757ull, 6923334307929877261ull}}, +{{9241711902689729060ull, 13401394891538808631ull, + 4653317922257370074ull, 1384666861585975452ull}}, +{{36679731669906504ull, 8356045709368065647ull, 9306635844514740149ull, + 2769333723171950904ull}}, +{{73359463339813008ull, 16712091418736131294ull, 166527615319928682ull, + 5538667446343901809ull}}, +{{146718926679626015ull, 14977438763762710972ull, 333055230639857365ull, + 11077334892687803618ull}}, +{{29343785335925203ull, 14063534196978273164ull, + 11134657490353702442ull, 2215466978537560723ull}}, +{{58687570671850406ull, 9680324320246994712ull, 3822570906997853269ull, + 4430933957075121447ull}}, +{{117375141343700812ull, 913904566784437808ull, 7645141813995706539ull, + 8861867914150242894ull}}, +{{3712823843010650486ull, 11250827357582618531ull, + 16286423621766782600ull, 1772373582830048578ull}}, +{{7425647686021300972ull, 4054910641455685446ull, + 14126103169824013585ull, 3544747165660097157ull}}, +{{14851295372042601943ull, 8109821282911370892ull, + 9805462265938475554ull, 7089494331320194315ull}}, +{{6659607889150430712ull, 16379359515549915471ull, + 1961092453187695110ull, 1417898866264038863ull}}, +{{13319215778300861424ull, 14311974957390279326ull, + 3922184906375390221ull, 2835797732528077726ull}}, +{{8191687482892171231ull, 10177205841071007037ull, + 7844369812750780443ull, 5671595465056155452ull}}, +{{16383374965784342462ull, 1907667608432462458ull, + 15688739625501560887ull, 11343190930112310904ull}}, +{{18034070252124509786ull, 4070882336428402814ull, + 17895143184067953470ull, 2268638186022462180ull}}, +{{17621396430539467955ull, 8141764672856805629ull, + 17343542294426355324ull, 4537276372044924361ull}}, +{{16796048787369384293ull, 16283529345713611259ull, + 16240340515143159032ull, 9074552744089848723ull}}, +{{18116605016441518152ull, 3256705869142722251ull, + 14316114547254362776ull, 1814910548817969744ull}}, +{{17786465959173484687ull, 6513411738285444503ull, + 10185485020799173936ull, 3629821097635939489ull}}, +{{17126187844637417758ull, 13026823476570889007ull, + 1924225967888796256ull, 7259642195271878979ull}}, +{{10803935198411304198ull, 2605364695314177801ull, + 15142240452545400544ull, 1451928439054375795ull}}, +{{3161126323113056780ull, 5210729390628355603ull, + 11837736831381249472ull, 2903856878108751591ull}}, +{{6322252646226113560ull, 10421458781256711206ull, + 5228729589052947328ull, 5807713756217503183ull}}, +{{12644505292452227119ull, 2396173488803870796ull, + 10457459178105894657ull, 11615427512435006366ull}}, +{{17286296317458086717ull, 11547281141986505128ull, + 5780840650363089254ull, 2323085502487001273ull}}, +{{16125848561206621817ull, 4647818210263458641ull, + 11561681300726178509ull, 4646171004974002546ull}}, +{{13804953048703692018ull, 9295636420526917283ull, + 4676618527742805402ull, 9292342009948005093ull}}, +{{13829037053966469374ull, 1859127284105383456ull, + 12003370149774292050ull, 1858468401989601018ull}}, +{{9211330034223387131ull, 3718254568210766913ull, + 5559996225839032484ull, 3716936803979202037ull}}, +{{18422660068446774261ull, 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10092499094580511240ull, + 9122891541139893883ull, 2101865168015838698ull}}, +{{226903058750566907ull, 1738254115451470865ull, + 18245783082279787767ull, 4203730336031677396ull}}, +{{453806117501133814ull, 3476508230902941730ull, + 18044822090850023918ull, 8407460672063354793ull}}, +{{3780110038242137086ull, 4384650460922498669ull, + 14677010862395735753ull, 1681492134412670958ull}}, +{{7560220076484274172ull, 8769300921844997338ull, + 10907277651081919890ull, 3362984268825341917ull}}, +{{15120440152968548344ull, 17538601843689994676ull, + 3367811228454288164ull, 6725968537650683835ull}}, +{{3024088030593709669ull, 18265115627705640228ull, + 673562245690857632ull, 1345193707530136767ull}}, +{{6048176061187419338ull, 18083487181701728840ull, + 1347124491381715265ull, 2690387415060273534ull}}, +{{12096352122374838675ull, 17720230289693906064ull, + 2694248982763430531ull, 5380774830120547068ull}}, +{{5745960171040125734ull, 16993716505678260513ull, + 5388497965526861063ull, 10761549660241094136ull}}, +{{8527889663691845794ull, 18156138560103293395ull, + 4767048407847282535ull, 2152309932048218827ull}}, +{{17055779327383691587ull, 17865533046497035174ull, + 9534096815694565071ull, 4304619864096437654ull}}, +{{15664814581057831557ull, 17284322019284518733ull, + 621449557679578527ull, 8609239728192875309ull}}, +{{17890358175179207605ull, 7146213218598814069ull, + 14881685170503556998ull, 1721847945638575061ull}}, +{{17333972276648863593ull, 14292426437197628139ull, + 11316626267297562380ull, 3443695891277150123ull}}, +{{16221200479588175569ull, 10138108800685704663ull, + 4186508460885573145ull, 6887391782554300247ull}}, +{{3244240095917635114ull, 9406319389620961579ull, + 8215999321660935275ull, 1377478356510860049ull}}, +{{6488480191835270228ull, 365894705532371542ull, + 16431998643321870551ull, 2754956713021720098ull}}, +{{12976960383670540455ull, 731789411064743084ull, + 14417253212934189486ull, 5509913426043440197ull}}, +{{7507176693631529294ull, 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11508381258123593838ull, + 10604252578004984615ull, 3029106939986929961ull}}, +{{2588510742481019997ull, 4570018442537636061ull, + 2761761082300417615ull, 6058213879973859923ull}}, +{{5177021484962039993ull, 9140036885075272122ull, + 5523522164600835230ull, 12116427759947719846ull}}, +{{12103450741218138969ull, 5517356191756964747ull, + 4794053247662077369ull, 2423285551989543969ull}}, +{{5760157408726726321ull, 11034712383513929495ull, + 9588106495324154738ull, 4846571103979087938ull}}, +{{11520314817453452641ull, 3622680693318307374ull, + 729468916938757861ull, 9693142207958175877ull}}, +{{9682760592974511175ull, 11792582582889392444ull, + 7524591412871572218ull, 1938628441591635175ull}}, +{{918777112239470733ull, 5138421092069233273ull, + 15049182825743144437ull, 3877256883183270350ull}}, +{{1837554224478941466ull, 10276842184138466546ull, + 11651621577776737258ull, 7754513766366540701ull}}, +{{367510844895788294ull, 16812763695795334602ull, + 6019673130297257774ull, 1550902753273308140ull}}, +{{735021689791576587ull, 15178783317881117588ull, + 12039346260594515549ull, 3101805506546616280ull}}, +{{1470043379583153173ull, 11910822562052683560ull, + 5631948447479479483ull, 6203611013093232561ull}}, +{{2940086759166306346ull, 5374901050395815504ull, + 11263896894958958967ull, 12407222026186465122ull}}, +{{11656063796058992239ull, 15832375469046804393ull, + 9631477008475612439ull, 2481444405237293024ull}}, +{{4865383518408432862ull, 13218006864384057171ull, + 816209943241673263ull, 4962888810474586049ull}}, +{{9730767036816865723ull, 7989269655058562726ull, + 1632419886483346527ull, 9925777620949172098ull}}, +{{5635502222105283468ull, 1597853931011712545ull, + 11394530421522400275ull, 1985155524189834419ull}}, +{{11271004444210566936ull, 3195707862023425090ull, + 4342316769335248934ull, 3970311048379668839ull}}, +{{4095264814711582255ull, 6391415724046850181ull, + 8684633538670497868ull, 7940622096759337678ull}}, +{{8197750592426137098ull, 4967631959551280359ull, + 12804973151959830543ull, 1588124419351867535ull}}, +{{16395501184852274195ull, 9935263919102560718ull, + 7163202230210109470ull, 3176248838703735071ull}}, +{{14344258295994996774ull, 1423783764495569821ull, + 14326404460420218941ull, 6352497677407470142ull}}, +{{10241772518280441931ull, 2847567528991139643ull, + 10206064847130886266ull, 12704995354814940285ull}}, +{{16805749762623729679ull, 4258862320540138251ull, + 2041212969426177253ull, 2540999070962988057ull}}, +{{15164755451537907742ull, 8517724641080276503ull, + 4082425938852354506ull, 5081998141925976114ull}}, +{{11882766829366263868ull, 17035449282160553007ull, + 8164851877704709012ull, 10163996283851952228ull}}, +{{9755250995357073420ull, 3407089856432110601ull, + 12701016819766672772ull, 2032799256770390445ull}}, +{{1063757917004595224ull, 6814179712864221203ull, + 6955289565823793928ull, 4065598513540780891ull}}, +{{2127515834009190448ull, 13628359425728442406ull, + 13910579131647587856ull, 8131197027081561782ull}}, +{{15182898425769479383ull, 13793718329371419450ull, + 10160813455813338217ull, 1626239405416312356ull}}, +{{11919052777829407149ull, 9140692585033287285ull, + 1874882837917124819ull, 3252478810832624713ull}}, +{{5391361481949262682ull, 18281385170066574571ull, + 3749765675834249638ull, 6504957621665249426ull}}, +{{1078272296389852537ull, 18413672292980956207ull, + 4439301949908760250ull, 1300991524333049885ull}}, +{{2156544592779705073ull, 18380600512252360798ull, + 8878603899817520501ull, 2601983048666099770ull}}, +{{4313089185559410146ull, 18314456950795169980ull, + 17757207799635041003ull, 5203966097332199540ull}}, +{{8626178371118820291ull, 18182169827880788344ull, + 17067671525560530391ull, 10407932194664399081ull}}, +{{5414584488965674382ull, 11015131595059978315ull, + 7102883119854016401ull, 2081586438932879816ull}}, +{{10829168977931348763ull, 3583519116410405014ull, + 14205766239708032803ull, 4163172877865759632ull}}, +{{3211593882153145910ull, 7167038232820810029ull, + 9964788405706513990ull, 8326345755731519265ull}}, +{{15399714035398270475ull, 1433407646564162005ull, + 1992957681141302798ull, 1665269151146303853ull}}, +{{12352683997086989334ull, 2866815293128324011ull, + 3985915362282605596ull, 3330538302292607706ull}}, +{{6258623920464427051ull, 5733630586256648023ull, + 7971830724565211192ull, 6661076604585215412ull}}, +{{8630422413576706057ull, 15904121376218970897ull, + 8973063774396862884ull, 1332215320917043082ull}}, +{{17260844827153412114ull, 13361498678728390178ull, + 17946127548793725769ull, 2664430641834086164ull}} +}; + +static const UINT256 multipliers2_bid64[] = + { {{9438227768328448678ull, 4145630637659340425ull, + 17596454752367787604ull, 34ull}}, +{{429711462947345740ull, 8291261275318680851ull, + 16746165431026023592ull, 69ull}}, +{{859422925894691480ull, 16582522550637361702ull, + 15045586788342495568ull, 139ull}}, +{{1718845851789382959ull, 14718301027565171788ull, + 11644429502975439521ull, 279ull}}, +{{3437691703578765918ull, 10989857981420791960ull, + 4842114932241327427ull, 559ull}}, +{{6875383407157531835ull, 3532971889132032304ull, + 9684229864482654855ull, 1118ull}}, +{{13750766814315063670ull, 7065943778264064608ull, + 921715655255758094ull, 2237ull}}, +{{9054789554920575724ull, 14131887556528129217ull, + 1843431310511516188ull, 4474ull}}, +{{18109579109841151448ull, 9817031039346706818ull, + 3686862621023032377ull, 8948ull}}, +{{17772414145972751280ull, 1187318004983862021ull, + 7373725242046064755ull, 17896ull}}, +{{17098084218235950944ull, 2374636009967724043ull, + 14747450484092129510ull, 35792ull}}, +{{15749424362762350272ull, 4749272019935448087ull, + 11048156894474707404ull, 71585ull}}, +{{13052104651815148928ull, 9498544039870896175ull, + 3649569715239863192ull, 143171ull}}, +{{7657465229920746239ull, 550344006032240735ull, 7299139430479726385ull, + 286342ull}}, +{{15314930459841492478ull, 1100688012064481470ull, + 14598278860959452770ull, 572684ull}}, +{{12183116845973433340ull, 2201376024128962941ull, + 10749813648209353924ull, 1145369ull}}, +{{5919489618237315063ull, 4402752048257925883ull, + 3052883222709156232ull, 2290739ull}}, +{{11838979236474630126ull, 8805504096515851766ull, + 6105766445418312464ull, 4581478ull}}, +{{5231214399239708635ull, 17611008193031703533ull, + 12211532890836624928ull, 9162956ull}}, +{{10462428798479417270ull, 16775272312353855450ull, + 5976321707963698241ull, 18325913ull}}, +{{2478113523249282924ull, 15103800550998159285ull, + 11952643415927396483ull, 36651826ull}}, +{{4956227046498565847ull, 11760857028286766954ull, + 5458542758145241351ull, 73303653ull}}, +{{9912454092997131693ull, 5074969982863982292ull, + 10917085516290482703ull, 146607306ull}}, +{{1378164112284711770ull, 10149939965727964585ull, + 3387426958871413790ull, 293214613ull}}, +{{2756328224569423540ull, 1853135857746377554ull, + 6774853917742827581ull, 586429226ull}}, +{{5512656449138847079ull, 3706271715492755108ull, + 13549707835485655162ull, 1172858452ull}}, +{{11025312898277694158ull, 7412543430985510216ull, + 8652671597261758708ull, 2345716905ull}}, +{{3603881722845836699ull, 14825086861971020433ull, + 17305343194523517416ull, 4691433810ull}}, +{{7207763445691673397ull, 11203429650232489250ull, + 16163942315337483217ull, 9382867621ull}}, +{{14415526891383346794ull, 3960115226755426884ull, + 13881140556965414819ull, 18765735243ull}}, +{{10384309709057141972ull, 7920230453510853769ull, + 9315537040221278022ull, 37531470487ull}}, +{{2321875344404732328ull, 15840460907021707539ull, + 184330006733004428ull, 75062940975ull}}, +{{4643750688809464655ull, 13234177740333863462ull, + 368660013466008857ull, 150125881950ull}}, +{{9287501377618929309ull, 8021611406958175308ull, 737320026932017715ull, + 300251763900ull}}, +{{128258681528307001ull, 16043222813916350617ull, + 1474640053864035430ull, 600503527800ull}}, +{{256517363056614002ull, 13639701554123149618ull, + 2949280107728070861ull, 1201007055600ull}}, +{{513034726113228003ull, 8832659034536747620ull, 5898560215456141723ull, + 2402014111200ull}}, +{{1026069452226456005ull, 17665318069073495240ull, + 11797120430912283446ull, 4804028222400ull}}, +{{2052138904452912009ull, 16883892064437438864ull, + 5147496788115015277ull, 9608056444801ull}}, +{{4104277808905824018ull, 15321040055165326112ull, + 10294993576230030555ull, 19216112889602ull}}, +{{8208555617811648035ull, 12195336036621100608ull, + 2143243078750509495ull, 38432225779205ull}}, +{{16417111235623296070ull, 5943927999532649600ull, + 4286486157501018991ull, 76864451558410ull}}, +{{14387478397537040523ull, 11887855999065299201ull, + 8572972315002037982ull, 153728903116820ull}}, +{{10328212721364529429ull, 5328967924421046787ull, + 17145944630004075965ull, 307457806233640ull}}, +{{2209681369019507241ull, 10657935848842093575ull, + 15845145186298600314ull, 614915612467281ull}}, +{{4419362738039014482ull, 2869127623974635534ull, + 13243546298887649013ull, 1229831224934563ull}}, 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130099152433304988ull}}, +{{7594352088761791154ull, 3682734458596191241ull, 887860389981752050ull, + 260198304866609977ull}}, +{{15188704177523582308ull, 7365468917192382482ull, + 1775720779963504100ull, 520396609733219954ull}}, +{{11930664281337612999ull, 14730937834384764965ull, + 3551441559927008200ull, 1040793219466439908ull}}, +{{13454179300493253570ull, 14014234011102683962ull, + 11778334756211132609ull, 208158643893287981ull}}, +{{8461614527276955523ull, 9581723948495816309ull, + 5109925438712713603ull, 416317287786575963ull}}, +{{16923229054553911046ull, 716703823282081002ull, + 10219850877425427207ull, 832634575573151926ull}}, +{{3384645810910782210ull, 11211387208882147170ull, + 5733318990226995764ull, 166526915114630385ull}}, +{{6769291621821564419ull, 3976030344054742724ull, + 11466637980453991529ull, 333053830229260770ull}}, +{{13538583243643128837ull, 7952060688109485448ull, + 4486531887198431442ull, 666107660458521541ull}}, +{{6397065463470536091ull, 12658458581847628059ull, + 4586655192181596611ull, 133221532091704308ull}}, +{{12794130926941072181ull, 6870173089985704502ull, + 9173310384363193223ull, 266443064183408616ull}} +}; + +static const UINT128 coefflimits_bid64[] = { {{10000000000000000ull, 0ull}}, +{{2000000000000000ull, 0ull}}, +{{400000000000000ull, 0ull}}, +{{80000000000000ull, 0ull}}, +{{16000000000000ull, 0ull}}, +{{3200000000000ull, 0ull}}, +{{640000000000ull, 0ull}}, +{{128000000000ull, 0ull}}, +{{25600000000ull, 0ull}}, +{{5120000000ull, 0ull}}, +{{1024000000ull, 0ull}}, +{{204800000ull, 0ull}}, +{{40960000ull, 0ull}}, +{{8192000ull, 0ull}}, +{{1638400ull, 0ull}}, +{{327680ull, 0ull}}, +{{65536ull, 0ull}}, +{{13107ull, 0ull}}, +{{2621ull, 0ull}}, +{{524ull, 0ull}}, +{{104ull, 0ull}}, +{{20ull, 0ull}}, +{{4ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}}, +{{0ull, 0ull}} +}; + +// ********************************************************************** + +static const UINT128 coefflimits_bid128[] = + { {{4003012203950112768ull, 542101086242752ull}}, +{{8179300070273843200ull, 108420217248550ull}}, +{{1635860014054768640ull, 21684043449710ull}}, +{{327172002810953728ull, 4336808689942ull}}, +{{7444132030046011392ull, 867361737988ull}}, +{{12556872850234933248ull, 173472347597ull}}, +{{9890072199530807296ull, 34694469519ull}}, +{{16735409698873802752ull, 6938893903ull}}, +{{14415128384000491520ull, 1387778780ull}}, +{{2883025676800098304ull, 277555756ull}}, +{{4265953950101929984ull, 55511151ull}}, +{{4542539604762296320ull, 11102230ull}}, +{{908507920952459264ull, 2220446ull}}, +{{3871050398932402176ull, 444089ull}}, +{{15531605338754121728ull, 88817ull}}, +{{10485018697234644992ull, 17763ull}}, +{{13165050183672659968ull, 3552ull}}, +{{10011707666218352640ull, 710ull}}, +{{2002341533243670528ull, 142ull}}, +{{7779165936132554752ull, 28ull}}, +{{12623879631452241920ull, 5ull}}, +{{2524775926290448384ull, 1ull}}, +{{4194304000000000000ull, 0ull}}, +{{838860800000000000ull, 0ull}}, +{{167772160000000000ull, 0ull}}, +{{33554432000000000ull, 0ull}}, +{{6710886400000000ull, 0ull}}, +{{1342177280000000ull, 0ull}}, +{{268435456000000ull, 0ull}}, +{{53687091200000ull, 0ull}}, +{{10737418240000ull, 0ull}}, +{{2147483648000ull, 0ull}}, +{{429496729600ull, 0ull}}, +{{85899345920ull, 0ull}}, +{{17179869184ull, 0ull}}, +{{3435973836ull, 0ull}}, +{{687194767ull, 0ull}}, +{{137438953ull, 0ull}}, +{{27487790ull, 0ull}}, +{{5497558ull, 0ull}}, +{{1099511ull, 0ull}}, +{{219902ull, 0ull}}, +{{43980ull, 0ull}}, +{{8796ull, 0ull}}, +{{1759ull, 0ull}}, +{{351ull, 0ull}}, +{{70ull, 0ull}}, +{{14ull, 0ull}}, +{{2ull, 0ull}} +}; + +// These are the different, bipartite, tables for conversion to bid128 +// Using the same approach, the tables become extremely large +// And things are more amenable here since there's never overflow/underflow + +static const UINT256 outertable_sig[] = + { {{16710528681477587410ull, 1427578414467097172ull, + 17470362193306814444ull, 17633471421292828081ull}}, +{{15880413049339289368ull, 3169162604521042544ull, + 12421848348224877000ull, 10175591536883283100ull}}, +{{728324709502741634ull, 5487234822932806241ull, + 14277366029702694882ull, 11743877385420605756ull}}, +{{5270439690693945016ull, 5335305964155802506ull, + 4731239033579481048ull, 13553871098685738146ull}}, +{{15770926697301461842ull, 17478494563481727979ull, + 12172666691698088779ull, 15642825255298684824ull}}, +{{6706015564063194464ull, 9524484409513358023ull, + 3584925281718916951ull, 18053733887991431306ull}}, +{{11970480524618434228ull, 11405570099769256704ull, + 15462553542164535233ull, 10418108684938663938ull}}, +{{6786207772287397676ull, 2319456072422691258ull, + 3306628541457879036ull, 12023771840725819358ull}}, +{{11981052113010165492ull, 3504057943690712651ull, + 1876153621163772099ull, 13876903538819465956ull}}, +{{9393164661428669080ull, 12786250932199773041ull, + 1469280998340568779ull, 16015644206874417279ull}}, +{{16924685242153318850ull, 18017830257179898541ull, + 8443357802200517361ull, 9242006282008467740ull}}, +{{10964968671057563176ull, 5039440430669711539ull, + 5426243050445487622ull, 10666405798403203685ull}}, +{{10955754838860298353ull, 7697974614691938479ull, + 5802604364043796934ull, 12310337083160321132ull}}, +{{2020816881108765590ull, 11827301330378587775ull, + 11428107909474365520ull, 14207634883319258514ull}}, +{{17088069107880998350ull, 4283872614129133981ull, + 3596834484036483711ull, 16397348635874181367ull}}, +{{17878879927905357932ull, 16765016545576715295ull, + 16689816215723394984ull, 9462273083962776199ull}}, +{{13121733289080687293ull, 18283685101712419716ull, + 16276586284347626380ull, 10920620632484725600ull}}, +{{17814811358648632259ull, 13245640156276305425ull, + 16363965810173909683ull, 12603732099085151178ull}}, +{{4756697993914874888ull, 11508234184157253656ull, + 5137266535116401279ull, 14546248621894116172ull}}, +{{5318236458935323174ull, 6543830884414701181ull, + 6453355338781772809ull, 16788150311867950084ull}}, +{{6485710970464102310ull, 9658720758000782538ull, + 1405691438411884535ull, 9687789553853107178ull}}, +{{16668567668910748869ull, 7353216905500064137ull, + 16398637311140236340ull, 11180894225541718927ull}}, +{{10250898639443956700ull, 17209112682100433509ull, + 10404161081088486903ull, 12904119664018836844ull}}, +{{8190593687966138954ull, 9395575747272723417ull, + 5270639644724875979ull, 14892932617404296676ull}}, +{{16096765186944088526ull, 5812137315202163815ull, + 13827109944906121794ull, 17188266051577202911ull}}, +{{13125058493821651226ull, 13878096157524874998ull, + 7819283672493662452ull, 9918680808189048078ull}}, +{{10784977039313888136ull, 7095114120404217728ull, + 5980679097159643429ull, 11447370977331402726ull}}, +{{18074025829186132275ull, 1141984379626550674ull, + 7557580538320593620ull, 13211666432945230258ull}}, +{{884127375074722974ull, 5630658839879210216ull, 8888788495242174599ull, + 15247879210087606793ull}}, +{{14794677677148287412ull, 15991859528909753139ull, + 2255166953101703543ull, 17597917839164816062ull}}, +{{11781503818372409883ull, 16487377189598053250ull, + 1614766483381505408ull, 10155074945409931597ull}}, +{{13901203812957478350ull, 17671725616207330354ull, + 9774501520532043416ull, 11720198729122693309ull}}, +{{2841277750318224700ull, 62614824260888948ull, 7875289095414864909ull, + 13526543032773672749ull}}, +{{4177215723684349918ull, 5549883551398310595ull, + 6548711429670794128ull, 15611285324269742443ull}}, +{{10113135653152274419ull, 1238174514434849746ull, + 15010187426055142985ull, 18017332949391848572ull}}, +{{15332868447221136909ull, 16659234357027498643ull, + 8156814090647504084ull, 10397103116953834012ull}}, +{{15245187402216469644ull, 12129929088655149192ull, + 9861651730211963150ull, 11999528845718521943ull}}, +{{11169863271521019024ull, 11690833164181629132ull, + 18055231442152805128ull, 13848924157002783033ull}}, +{{5681139181384005971ull, 16315598095635316730ull, + 12429006944274865118ull, 15983352577617880224ull}}, +{{0ull, 0ull, 0ull, 9223372036854775808ull}}, +{{847738094735128551ull, 159020156881263929ull, 14298703881791668535ull, + 10644899600020376799ull}}, +{{12571812103339493257ull, 9592188640606484874ull, + 15977522551232326327ull, 12285516299433008781ull}}, +{{11255846670375652269ull, 16219642565822741785ull, + 1164180458167399492ull, 14178988662640388631ull}}, +{{4768530159026621925ull, 11269558331910606010ull, + 14728279675391465720ull, 16364287392998134214ull}}, +{{10435171899994305314ull, 3358688235984080491ull, + 10873005112892106269ull, 9443194724678278428ull}}, +{{9001934648837042518ull, 12742858465034581069ull, + 7821978264675184102ull, 10898601872067700364ull}}, +{{17621267265258286727ull, 4697230115438671198ull, + 9730745556445007669ull, 12578319756070083561ull}}, +{{15489206033570711069ull, 5939008219696634639ull, + 7281543418588385486ull, 14516919669433371671ull}}, +{{5582382164278045428ull, 1021128504191590019ull, + 15859662269683349667ull, 16754301112998936544ull}}, +{{13306060077138970688ull, 17077419079040409017ull, + 602300193611639289ull, 9668256495766433483ull}}, +{{16144900726383728979ull, 6332437060439625781ull, + 3394061071468721991ull, 11158350687084940805ull}}, +{{841527738022137013ull, 8576187517129556015ull, 4780478900157118356ull, + 12878101662951253988ull}}, +{{6209518431268106959ull, 6563228687006195825ull, + 8680557599339190037ull, 14862904661462481806ull}}, +{{13777918056850427098ull, 13980713634323581067ull, + 3260730320187665275ull, 17153610117183879308ull}}, +{{14026398967643035423ull, 16044002814696042637ull, + 13563648246219923183ull, 9898682214361989196ull}}, +{{8580849201736980837ull, 7652064075251385167ull, + 12055336643618066002ull, 11424290153682525668ull}}, +{{7703450277136593061ull, 30939122015382097ull, 1733744904199768989ull, + 13185028339041359606ull}}, +{{16645858086931268484ull, 268706294728574543ull, + 4562366333509913804ull, 15217135591158481007ull}}, +{{1535817262145462730ull, 16249574698204674087ull, + 1726174694286833848ull, 17562435942139069664ull}}, +{{1327779613951528273ull, 12607890553358950732ull, + 6773080245737622022ull, 10134599720625107110ull}}, +{{10146669700226523625ull, 6816618733538609533ull, + 17338427607494047961ull, 11696567815043613180ull}}, +{{1218646606393179524ull, 8053984438814192242ull, + 5512554737593155320ull, 13499270067222312908ull}}, +{{8529816360522570005ull, 2898610325645650649ull, + 12799329154556421864ull, 15579808985797328396ull}}, +{{8976626101186384018ull, 17306366585957786234ull, + 18289272351796647404ull, 17981005404381600394ull}}, +{{13259258789938866699ull, 3853966764738768487ull, + 3962898110873089456ull, 10376139901559067117ull}}, +{{899097863387258947ull, 18205835716688941338ull, + 5828614502416977816ull, 11975334730781032005ull}}, +{{6805696657844643720ull, 11269663690239600300ull, + 15713752492130876427ull, 13821001188766021149ull}}, +{{1390669429605106863ull, 9874674503958832077ull, + 10784451562526769943ull, 15951126056533488631ull}}, +{{5704986635434998471ull, 13359511205918707297ull, + 13484363347568202582ull, 18409550726197325520ull}}, +{{8031416311578790746ull, 15203770801091158414ull, + 10108131133879485063ull, 10623436763626360685ull}}, +{{14540970352057967818ull, 10823414366732926995ull, + 16152175176069010361ull, 12260745560745135745ull}}, +{{15950896424073439808ull, 7311065895593189991ull, + 14504991862333000338ull, 14150400200058902426ull}}, +{{5978819348613013533ull, 5596367464999577452ull, + 9804643584580705193ull, 16331292810031855499ull}}, +{{8586457898440847299ull, 6018330550275346810ull, + 7956755163056284140ull, 9424154832238877876ull}}, +{{1114429888821394320ull, 1760611426277998851ull, + 9839409379426382903ull, 10876627507095459665ull}}, +{{7554605751361075608ull, 6504275622057553570ull, + 9148491728899045148ull, 12552958650829068784ull}}, +{{9208049516541304162ull, 15518058123431536615ull, + 17563500997894963674ull, 14487649851631658771ull}}, +{{1484107481346855224ull, 16657394431011607502ull, + 12009304572091620947ull, 16720520162760224108ull}}, +{{14325586681310127114ull, 11250726580617083666ull, + 2403442209646777766ull, 9648762821313776241ull}}, +{{14963893077912294692ull, 3450059817568720983ull, + 15313875826588494017ull, 11135852602159508258ull}} +}; + +static const UINT256 innertable_sig[] = + { {{1014026100135492416ull, 3035406636157676337ull, + 4549648098962661924ull, 12141680576410806693ull}}, +{{5879218643596753424ull, 3794258295197095421ull, + 10298746142130715309ull, 15177100720513508366ull}}, +{{5980354661461664842ull, 4677254443711878590ull, + 1825030320404309164ull, 9485687950320942729ull}}, +{{16698815363681856860ull, 5846568054639848237ull, + 6892973918932774359ull, 11857109937901178411ull}}, +{{7038461149320157363ull, 2696524049872422393ull, + 4004531380238580045ull, 14821387422376473014ull}}, +{{15928253264393568112ull, 3991170540383957947ull, + 16337890167931276240ull, 9263367138985295633ull}}, +{{15298630562064572236ull, 4988963175479947434ull, + 6587304654631931588ull, 11579208923731619542ull}}, +{{9899916165725939487ull, 6236203969349934293ull, + 17457502855144690293ull, 14474011154664524427ull}}, +{{16986581225584812263ull, 12406940980114805770ull, + 17210192550503474962ull, 18092513943330655534ull}}, +{{15228299284417895569ull, 12366024130999141510ull, + 6144684325637283947ull, 11307821214581659709ull}}, +{{9812002068667593653ull, 10845844145321538984ull, + 12292541425473992838ull, 14134776518227074636ull}}, +{{12265002585834492066ull, 4333933144797147922ull, + 15365676781842491048ull, 17668470647783843295ull}}, +{{12277312634573945445ull, 2708708215498217451ull, + 16521077016292638761ull, 11042794154864902059ull}}, +{{10734954774790043902ull, 7997571287800159718ull, + 16039660251938410547ull, 13803492693581127574ull}}, +{{4195321431632779070ull, 5385278091322811744ull, + 10826203278068237376ull, 17254365866976409468ull}}, +{{2622075894770486919ull, 3365798807076757340ull, + 15989749085647424168ull, 10783978666860255917ull}}, +{{3277594868463108648ull, 4207248508845946675ull, + 6152128301777116498ull, 13479973333575319897ull}}, +{{17932051640861049522ull, 14482432672912209151ull, + 12301846395648783526ull, 16849966666969149871ull}}, +{{18125061303179237808ull, 4439834402142742815ull, + 14606183024921571560ull, 10531229166855718669ull}}, +{{18044640610546659355ull, 5549793002678428519ull, + 4422670725869800738ull, 13164036458569648337ull}}, +{{17944114744755936290ull, 16160613290202811457ull, + 10140024425764638826ull, 16455045573212060421ull}}, +{{4297542687831378326ull, 14712069324804145065ull, + 8643358275316593218ull, 10284403483257537763ull}}, +{{9983614378216610811ull, 9166714619150405523ull, + 6192511825718353619ull, 12855504354071922204ull}}, +{{7867831954343375609ull, 6846707255510619000ull, + 7740639782147942024ull, 16069380442589902755ull}}, +{{4917394971464609756ull, 4279192034694136875ull, + 2532056854628769813ull, 10043362776618689222ull}}, +{{1535057695903374291ull, 9960676061795058998ull, + 12388443105140738074ull, 12554203470773361527ull}}, +{{11142194156733993672ull, 3227473040389047939ull, + 10873867862998534689ull, 15692754338466701909ull}}, +{{4658028338745052093ull, 13546385696311624722ull, + 9102010423587778132ull, 9807971461541688693ull}}, +{{15045907460286090924ull, 16932982120389530902ull, + 15989199047912110569ull, 12259964326927110866ull}}, +{{9584012288502837847ull, 7331169595204749916ull, + 10763126773035362404ull, 15324955408658888583ull}}, +{{15213379717169049462ull, 13805353033857744505ull, + 13644483260788183358ull, 9578097130411805364ull}}, +{{5181666591179148116ull, 8033319255467404824ull, + 17055604075985229198ull, 11972621413014756705ull}}, +{{6477083238973935145ull, 818277032479480222ull, 7484447039699372786ull, + 14965776766268445882ull}}, +{{17883235079640873178ull, 5123109163727063042ull, + 9289465418239495895ull, 9353610478917778676ull}}, +{{13130671812696315664ull, 1792200436231440899ull, + 11611831772799369869ull, 11692013098647223345ull}}, +{{11801653747443006676ull, 6851936563716689028ull, + 679731660717048624ull, 14615016373309029182ull}}, +{{14752067184303758345ull, 8564920704645861285ull, + 10073036612751086588ull, 18268770466636286477ull}}, +{{11525884999403542918ull, 14576447477258439111ull, + 8601490892183123069ull, 11417981541647679048ull}}, +{{9795670230827040743ull, 4385501291290885177ull, + 10751863615228903837ull, 14272476927059598810ull}}, +{{16856273806961188833ull, 10093562632540994375ull, + 4216457482181353988ull, 17840596158824498513ull}}, +{{17452700156991824877ull, 15531848682192897292ull, + 14164500972431816002ull, 11150372599265311570ull}}, +{{3369131122530229480ull, 10191438815886345808ull, + 8482254178684994195ull, 13937965749081639463ull}}, +{{4211413903162786849ull, 8127612501430544356ull, + 5991131704928854840ull, 17422457186352049329ull}}, +{{11855505726331517589ull, 5079757813394090222ull, + 15273672361649004035ull, 10889035741470030830ull}}, +{{5596010121059621178ull, 1738011248315224874ull, + 9868718415206479236ull, 13611294676837538538ull}}, +{{16218384688179302281ull, 2172514060394031092ull, + 3112525982153323237ull, 17014118346046923173ull}}, +{{913118393257288118ull, 3663664296959963385ull, 4251171748059520975ull, + 10633823966279326983ull}}, +{{5753084009998998051ull, 18414638426482117943ull, + 702278666647013314ull, 13292279957849158729ull}}, +{{2579668994071359659ull, 13794925996247871621ull, + 5489534351736154547ull, 16615349947311448411ull}}, +{{3918136130508293739ull, 6315985738441225811ull, + 1125115960621402640ull, 10384593717069655257ull}}, +{{285984144707979270ull, 7894982173051532264ull, 6018080969204141204ull, + 12980742146337069071ull}}, +{{357480180884974087ull, 9868727716314415330ull, 2910915193077788601ull, + 16225927682921336339ull}}, +{{4835111131480496709ull, 17697169868764979341ull, + 17960223060169475539ull, 10141204801825835211ull}}, +{{10655574932778008790ull, 17509776317528836272ull, + 17838592806784456520ull, 12676506002282294014ull}}, +{{13319468665972510987ull, 3440476323201493724ull, + 13074868971625794843ull, 15845632502852867518ull}}, +{{17548039953087595175ull, 18291198766496791241ull, + 3560107088838733872ull, 9903520314283042199ull}}, +{{8099991886077330257ull, 4417254384411437436ull, + 18285191916330581053ull, 12379400392853802748ull}}, +{{10124989857596662821ull, 10133253998941684699ull, + 4409745821703674700ull, 15474250491067253436ull}}, +{{4022275651784220311ull, 15556655786193328745ull, + 11979463175419572495ull, 9671406556917033397ull}}, +{{9639530583157663293ull, 14834133714314273027ull, + 1139270913992301907ull, 12089258196146291747ull}}, +{{7437727210519691212ull, 13930981124465453380ull, + 15259146697772541096ull, 15111572745182864683ull}}, +{{13871951543429582816ull, 8706863202790908362ull, + 7231123676894144233ull, 9444732965739290427ull}}, +{{8116567392432202712ull, 15495265021916023357ull, + 4427218577690292387ull, 11805916207174113034ull}}, +{{14757395258967641293ull, 14757395258967641292ull, + 14757395258967641292ull, 14757395258967641292ull}}, +{{0ull, 0ull, 0ull, 9223372036854775808ull}}, +{{0ull, 0ull, 0ull, 11529215046068469760ull}}, +{{0ull, 0ull, 0ull, 14411518807585587200ull}}, +{{0ull, 0ull, 0ull, 18014398509481984000ull}}, +{{0ull, 0ull, 0ull, 11258999068426240000ull}}, +{{0ull, 0ull, 0ull, 14073748835532800000ull}}, +{{0ull, 0ull, 0ull, 17592186044416000000ull}}, +{{0ull, 0ull, 0ull, 10995116277760000000ull}}, +{{0ull, 0ull, 0ull, 13743895347200000000ull}}, +{{0ull, 0ull, 0ull, 17179869184000000000ull}}, +{{0ull, 0ull, 0ull, 10737418240000000000ull}}, +{{0ull, 0ull, 0ull, 13421772800000000000ull}}, +{{0ull, 0ull, 0ull, 16777216000000000000ull}}, +{{0ull, 0ull, 0ull, 10485760000000000000ull}}, +{{0ull, 0ull, 0ull, 13107200000000000000ull}}, +{{0ull, 0ull, 0ull, 16384000000000000000ull}}, +{{0ull, 0ull, 0ull, 10240000000000000000ull}}, +{{0ull, 0ull, 0ull, 12800000000000000000ull}}, +{{0ull, 0ull, 0ull, 16000000000000000000ull}}, +{{0ull, 0ull, 0ull, 10000000000000000000ull}}, +{{0ull, 0ull, 0ull, 12500000000000000000ull}}, +{{0ull, 0ull, 0ull, 15625000000000000000ull}}, +{{0ull, 0ull, 0ull, 9765625000000000000ull}}, +{{0ull, 0ull, 0ull, 12207031250000000000ull}}, +{{0ull, 0ull, 0ull, 15258789062500000000ull}}, +{{0ull, 0ull, 0ull, 9536743164062500000ull}}, +{{0ull, 0ull, 0ull, 11920928955078125000ull}}, +{{0ull, 0ull, 0ull, 14901161193847656250ull}}, +{{0ull, 0ull, 4611686018427387904ull, 9313225746154785156ull}}, +{{0ull, 0ull, 5764607523034234880ull, 11641532182693481445ull}}, +{{0ull, 0ull, 11817445422220181504ull, 14551915228366851806ull}}, +{{0ull, 0ull, 5548434740920451072ull, 18189894035458564758ull}}, +{{0ull, 0ull, 17302829768357445632ull, 11368683772161602973ull}}, +{{0ull, 0ull, 7793479155164643328ull, 14210854715202003717ull}}, +{{0ull, 0ull, 14353534962383192064ull, 17763568394002504646ull}}, +{{0ull, 0ull, 4359273333062107136ull, 11102230246251565404ull}}, +{{0ull, 0ull, 5449091666327633920ull, 13877787807814456755ull}}, +{{0ull, 0ull, 2199678564482154496ull, 17347234759768070944ull}}, +{{0ull, 0ull, 1374799102801346560ull, 10842021724855044340ull}}, +{{0ull, 0ull, 1718498878501683200ull, 13552527156068805425ull}}, +{{0ull, 0ull, 6759809616554491904ull, 16940658945086006781ull}}, +{{0ull, 0ull, 6530724019560251392ull, 10587911840678754238ull}}, +{{0ull, 0ull, 17386777061305090048ull, 13234889800848442797ull}}, +{{0ull, 0ull, 7898413271349198848ull, 16543612251060553497ull}}, +{{0ull, 0ull, 16465723340661719040ull, 10339757656912845935ull}}, +{{0ull, 0ull, 15970468157399760896ull, 12924697071141057419ull}}, +{{0ull, 0ull, 15351399178322313216ull, 16155871338926321774ull}}, +{{0ull, 0ull, 4982938468024057856ull, 10097419586828951109ull}}, +{{0ull, 0ull, 10840359103457460224ull, 12621774483536188886ull}}, +{{0ull, 0ull, 4327076842467049472ull, 15777218104420236108ull}}, +{{0ull, 0ull, 11927795063396681728ull, 9860761315262647567ull}}, +{{0ull, 0ull, 10298057810818464256ull, 12325951644078309459ull}}, +{{0ull, 0ull, 8260886245095692416ull, 15407439555097886824ull}}, +{{0ull, 0ull, 5163053903184807760ull, 9629649721936179265ull}}, +{{0ull, 0ull, 11065503397408397604ull, 12037062152420224081ull}}, +{{0ull, 0ull, 18443565265187884909ull, 15046327690525280101ull}}, +{{0ull, 2305843009213693952ull, 13833071299956122020ull, + 9403954806578300063ull}}, +{{0ull, 2882303761517117440ull, 12679653106517764621ull, + 11754943508222875079ull}}, +{{0ull, 8214565720323784704ull, 11237880364719817872ull, + 14693679385278593849ull}}, +{{0ull, 10268207150404730880ull, 212292400617608628ull, + 18367099231598242312ull}}, +{{0ull, 15641001505857732608ull, 132682750386005392ull, + 11479437019748901445ull}}, +{{0ull, 1104507808612614144ull, 4777539456409894645ull, + 14349296274686126806ull}}, +{{0ull, 5992320779193155584ull, 15195296357367144114ull, + 17936620343357658507ull}}, +{{0ull, 8356886505423110144ull, 7191217214140771119ull, + 11210387714598536567ull}} +}; + +static const int outertable_exp[] = { -16839, + -16413, + -15988, + -15563, + -15138, + -14713, + -14287, + -13862, + -13437, + -13012, + -12586, + -12161, + -11736, + -11311, + -10886, + -10460, + -10035, + -9610, + -9185, + -8760, + -8334, + -7909, + -7484, + -7059, + -6634, + -6208, + -5783, + -5358, + -4933, + -4508, + -4082, + -3657, + -3232, + -2807, + -2382, + -1956, + -1531, + -1106, + -681, + -255, + 170, + 595, + 1020, + 1445, + 1871, + 2296, + 2721, + 3146, + 3571, + 3997, + 4422, + 4847, + 5272, + 5697, + 6123, + 6548, + 6973, + 7398, + 7823, + 8249, + 8674, + 9099, + 9524, + 9949, + 10375, + 10800, + 11225, + 11650, + 12075, + 12501, + 12926, + 13351, + 13776, + 14202, + 14627, + 15052, + 15477, + 15902, + 16328, + 16753, +}; + +static const int innertable_exp[] = { -468, + -465, + -461, + -458, + -455, + -451, + -448, + -445, + -442, + -438, + -435, + -432, + -428, + -425, + -422, + -418, + -415, + -412, + -408, + -405, + -402, + -398, + -395, + -392, + -388, + -385, + -382, + -378, + -375, + -372, + -368, + -365, + -362, + -358, + -355, + -352, + -349, + -345, + -342, + -339, + -335, + -332, + -329, + -325, + -322, + -319, + -315, + -312, + -309, + -305, + -302, + -299, + -295, + -292, + -289, + -285, + -282, + -279, + -275, + -272, + -269, + -265, + -262, + -259, + -255, + -252, + -249, + -246, + -242, + -239, + -236, + -232, + -229, + -226, + -222, + -219, + -216, + -212, + -209, + -206, + -202, + -199, + -196, + -192, + -189, + -186, + -182, + -179, + -176, + -172, + -169, + -166, + -162, + -159, + -156, + -153, + -149, + -146, + -143, + -139, + -136, + -133, + -129, + -126, + -123, + -119, + -116, + -113, + -109, + -106, + -103, + -99, + -96, + -93, + -89, + -86, + -83, + -79, + -76, + -73, + -69, + -66, + -63, + -60, + -56, + -53, + -50, + -46, +}; + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +bid32_to_binary32 (float *pres, UINT32 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT32 x = *px; +#else +float +bid32_to_binary32 (UINT32 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 c_prov; + UINT128 c; + UINT128 m_min; + int s, e, k, e_out; + UINT256 r; + UINT384 z; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + + unpack_bid32 (x, s, e, k, (c.w[1]), return_binary32_zero (s), + return_binary32_inf (s), return_binary32_nan); + +// Correct to 2^112 <= c < 2^113 with corresponding exponent adding 113-24=89 +// Thus a shift of 25 given that we've already upacked in c.w[1] + + c.w[1] = c.w[1] << 25; + c.w[0] = 0; + k = k + 89; + +// Check for "trivial" overflow, when 10^e * 1 > 2^{sci_emax+1}, just to +// keep tables smaller (it would be intercepted later otherwise). +// +// (Note that we may have normalized the coefficient, but we have a +// corresponding exponent postcorrection to account for; this can +// afford to be conservative anyway.) +// +// We actually check if e >= ceil((sci_emax + 1) * log_10(2)) +// which in this case is e >= ceil(128 * log_10(2)) = 39 + + if (e >= 39) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary32_ovf (s); + } +// Also check for "trivial" underflow, when 10^e * 2^113 <= 2^emin * 1/4, +// so test e <= floor((emin - 115) * log_10(2)) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -80) + e = -80; + +// Look up the breakpoint and approximate exponent + + m_min = (breakpoints_binary32 + 80)[e]; + e_out = (exponents_binary32 + 80)[e] - k; + +// Choose provisional exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_binary32 + 80)[e]; + } else { + r = (multipliers2_binary32 + 80)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) +// Check for exponent underflow and compensate by shifting the product +// Cut off the process at precision+2, since we can't really shift further + if (e_out < 1) { + int d; + d = 1 - e_out; + if (d > 26) + d = 26; + e_out = 1; + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], d); + } + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill into the next binade, correct +// Flag underflow where it may be needed even for |result| = SNN + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == (1ull << 24)) { + c_prov = 1ull << 23; + e_out = e_out + 1; + } else if ((c_prov == (1ull << 23)) && (e_out == 1)) { + if ((((rnd_mode & 3) == 0) && (z.w[4] < (3ull << 62))) || + ((rnd_mode + (s & 1) == 2) && (z.w[4] < (1ull << 63)))) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + } +// Check for overflow + + if (e_out >= 255) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary32_ovf (s); + } +// Modify exponent for a tiny result, otherwise lop the implicit bit + + if (c_prov < (1ull << 23)) + e_out = 0; + else + c_prov = c_prov & ((1ull << 23) - 1); + +// Set the inexact and underflow flag as appropriate + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (e_out == 0) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result as a binary floating-point number + + return_binary32 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_binary32 (float *pres, UINT64 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +float +bid64_to_binary32 (UINT64 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 c_prov; + UINT128 c; + UINT128 m_min; + int s, e, k, e_out; + UINT256 r; + UINT384 z; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + + unpack_bid64 (x, s, e, k, (c.w[0]), return_binary32_zero (s), + return_binary32_inf (s), return_binary32_nan); + c.w[1] = 0; + +// Correct to 2^112 <= c < 2^113 with corresponding exponent adding 113-54=59 + + sll128_short (c.w[1], c.w[0], 59); + k = k + 59; + +// Check for "trivial" overflow, when 10^e * 1 > 2^{sci_emax+1}, just to +// keep tables smaller (it would be intercepted later otherwise). +// +// (Note that we may have normalized the coefficient, but we have a +// corresponding exponent postcorrection to account for; this can +// afford to be conservative anyway.) +// +// We actually check if e >= ceil((sci_emax + 1) * log_10(2)) +// which in this case is e >= ceil(128 * log_10(2)) = 39 + + if (e >= 39) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary32_ovf (s); + } +// Also check for "trivial" underflow, when 10^e * 2^113 <= 2^emin * 1/4, +// so test e <= floor((emin - 115) * log_10(2)) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -80) + e = -80; + +// Look up the breakpoint and approximate exponent + + m_min = (breakpoints_binary32 + 80)[e]; + e_out = (exponents_binary32 + 80)[e] - k; + +// Choose provisional exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_binary32 + 80)[e]; + } else { + r = (multipliers2_binary32 + 80)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) +// Check for exponent underflow and compensate by shifting the product +// Cut off the process at precision+2, since we can't really shift further + if (e_out < 1) { + int d; + d = 1 - e_out; + if (d > 26) + d = 26; + e_out = 1; + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], d); + } + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill into the next binade, correct +// Flag underflow where it may be needed even for |result| = SNN + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == (1ull << 24)) { + c_prov = 1ull << 23; + e_out = e_out + 1; + } else if ((c_prov == (1ull << 23)) && (e_out == 1)) { + if ((((rnd_mode & 3) == 0) && (z.w[4] < (3ull << 62))) || + ((rnd_mode + (s & 1) == 2) && (z.w[4] < (1ull << 63)))) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + } +// Check for overflow + + if (e_out >= 255) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary32_ovf (s); + } +// Modify exponent for a tiny result, otherwise lop the implicit bit + + if (c_prov < (1ull << 23)) + e_out = 0; + else + c_prov = c_prov & ((1ull << 23) - 1); + +// Set the inexact and underflow flag as appropriate + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (e_out == 0) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result as a binary floating-point number + + return_binary32 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_to_binary32 (float *pres, UINT128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +float +bid128_to_binary32 (UINT128 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 c_prov; + UINT128 c; + UINT128 m_min; + int s, e, k, e_out; + UINT256 r; + UINT384 z; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + + unpack_bid128 (x, s, e, k, c, return_binary32_zero (s), + return_binary32_inf (s), return_binary32_nan); + +// Check for "trivial" overflow, when 10^e * 1 > 2^{sci_emax+1}, just to +// keep tables smaller (it would be intercepted later otherwise). +// +// (Note that we may have normalized the coefficient, but we have a +// corresponding exponent postcorrection to account for; this can +// afford to be conservative anyway.) +// +// We actually check if e >= ceil((sci_emax + 1) * log_10(2)) +// which in this case is e >= ceil(128 * log_10(2)) = 39 + + if (e >= 39) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary32_ovf (s); + } +// Also check for "trivial" underflow, when 10^e * 2^113 <= 2^emin * 1/4, +// so test e <= floor((emin - 115) * log_10(2)) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -80) + e = -80; + +// Look up the breakpoint and approximate exponent + + m_min = (breakpoints_binary32 + 80)[e]; + e_out = (exponents_binary32 + 80)[e] - k; + +// Choose provisional exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_binary32 + 80)[e]; + } else { + r = (multipliers2_binary32 + 80)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) +// Check for exponent underflow and compensate by shifting the product +// Cut off the process at precision+2, since we can't really shift further + if (e_out < 1) { + int d; + d = 1 - e_out; + if (d > 26) + d = 26; + e_out = 1; + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], d); + } + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill into the next binade, correct +// Flag underflow where it may be needed even for |result| = SNN + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == (1ull << 24)) { + c_prov = 1ull << 23; + e_out = e_out + 1; + } else if ((c_prov == (1ull << 23)) && (e_out == 1)) { + if ((((rnd_mode & 3) == 0) && (z.w[4] < (3ull << 62))) || + ((rnd_mode + (s & 1) == 2) && (z.w[4] < (1ull << 63)))) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + } +// Check for overflow + + if (e_out >= 255) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary32_ovf (s); + } +// Modify exponent for a tiny result, otherwise lop the implicit bit + + if (c_prov < (1ull << 23)) + e_out = 0; + else + c_prov = c_prov & ((1ull << 23) - 1); + +// Set the inexact and underflow flag as appropriate + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (e_out == 0) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result as a binary floating-point number + + return_binary32 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +bid32_to_binary64 (double *pres, UINT32 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT32 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#else +double +bid32_to_binary64 (UINT32 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 c_prov; + UINT128 c; + UINT128 m_min; + int s, e, k, e_out; + UINT256 r; + UINT384 z; + + unpack_bid32 (x, s, e, k, (c.w[1]), return_binary64_zero (s), + return_binary64_inf (s), return_binary64_nan); + +// Correct to 2^112 <= c < 2^113 with corresponding exponent adding 113-24=89 +// In fact shift a further 6 places ready for reciprocal multiplication +// Thus (113-24)+6=95, a shift of 31 given that we've already upacked in c.w[1] + + c.w[1] = c.w[1] << 31; + c.w[0] = 0; + k = k + 89; + +// Check for "trivial" overflow, when 10^e * 1 > 2^{sci_emax+1}, just to +// keep tables smaller (it would be intercepted later otherwise). +// +// (Note that we may have normalized the coefficient, but we have a +// corresponding exponent postcorrection to account for; this can +// afford to be conservative anyway.) +// +// We actually check if e >= ceil((sci_emax + 1) * log_10(2)) +// which in this case is e >= ceil(1024 * log_10(2)) = ceil(308.25) = 309 + + if (e >= 309) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary64_ovf (s); + } +// Also check for "trivial" underflow, when 10^e * 2^113 <= 2^emin * 1/4, +// so test e <= floor((emin - 115) * log_10(2)) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -358) + e = -358; + +// Look up the breakpoint and approximate exponent + + m_min = (breakpoints_binary64 + 358)[e]; + e_out = (exponents_binary64 + 358)[e] - k; + +// Choose provisional exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_binary64 + 358)[e]; + } else { + r = (multipliers2_binary64 + 358)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) +// Check for exponent underflow and compensate by shifting the product +// Cut off the process at precision+2, since we can't really shift further + if (e_out < 1) { + int d; + d = 1 - e_out; + if (d > 55) + d = 55; + e_out = 1; + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], d); + } + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill into the next binade, correct + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == (1ull << 53)) { + c_prov = 1ull << 52; + e_out = e_out + 1; + } + } +// Check for overflow + + if (e_out >= 2047) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary64_ovf (s); + } +// Modify exponent for a tiny result, otherwise lop the implicit bit + + if (c_prov < (1ull << 52)) + e_out = 0; + else + c_prov = c_prov & ((1ull << 52) - 1); + +// Set the inexact and underflow flag as appropriate + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (e_out == 0) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result as a binary floating-point number + + return_binary64 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_binary64 (double *pres, UINT64 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#else +double +bid64_to_binary64 (UINT64 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 c_prov; + UINT128 c; + UINT128 m_min; + int s, e, k, e_out; + UINT256 r; + UINT384 z; + + unpack_bid64 (x, s, e, k, (c.w[1]), return_binary64_zero (s), + return_binary64_inf (s), return_binary64_nan); + +// Correct to 2^112 <= c < 2^113 with corresponding exponent adding 113-54=59 +// In fact shift a further 6 places ready for reciprocal multiplication +// Thus (113-54)+6=65, a shift of 1 given that we've already upacked in c.w[1] + + c.w[1] = c.w[1] << 1; + c.w[0] = 0; + k = k + 59; + +// Check for "trivial" overflow, when 10^e * 1 > 2^{sci_emax+1}, just to +// keep tables smaller (it would be intercepted later otherwise). +// +// (Note that we may have normalized the coefficient, but we have a +// corresponding exponent postcorrection to account for; this can +// afford to be conservative anyway.) +// +// We actually check if e >= ceil((sci_emax + 1) * log_10(2)) +// which in this case is 2 >= ceil(1024 * log_10(2)) = ceil(308.25) = 309 + + if (e >= 309) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary64_ovf (s); + } +// Also check for "trivial" underflow, when 10^e * 2^113 <= 2^emin * 1/4, +// so test e <= floor((emin - 115) * log_10(2)) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -358) + e = -358; + +// Look up the breakpoint and approximate exponent + + m_min = (breakpoints_binary64 + 358)[e]; + e_out = (exponents_binary64 + 358)[e] - k; + +// Choose provisional exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_binary64 + 358)[e]; + } else { + r = (multipliers2_binary64 + 358)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) +// Check for exponent underflow and compensate by shifting the product +// Cut off the process at precision+2, since we can't really shift further + if (e_out < 1) { + int d; + d = 1 - e_out; + if (d > 55) + d = 55; + e_out = 1; + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], d); + } + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill into the next binade, correct +// Flag underflow where it may be needed even for |result| = SNN + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == (1ull << 53)) { + c_prov = 1ull << 52; + e_out = e_out + 1; + } else if ((c_prov == (1ull << 52)) && (e_out == 1)) + { + if ((((rnd_mode & 3) == 0) && (z.w[4] < (3ull << 62))) || + ((rnd_mode + (s & 1) == 2) && (z.w[4] < (1ull << 63)))) + + *pfpsf |= UNDERFLOW_EXCEPTION; + } + } +// Check for overflow + + if (e_out >= 2047) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary64_ovf (s); + } +// Modify exponent for a tiny result, otherwise lop the implicit bit + + if (c_prov < (1ull << 52)) + e_out = 0; + else + c_prov = c_prov & ((1ull << 52) - 1); + +// Set the inexact and underflow flag as appropriate + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (e_out == 0) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result as a binary floating-point number + + return_binary64 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_to_binary64 (double *pres, UINT128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#else +double +bid128_to_binary64 (UINT128 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 c_prov; + UINT128 c; + UINT128 m_min; + int s, e, k, e_out; + UINT256 r; + UINT384 z; + + unpack_bid128 (x, s, e, k, c, return_binary64_zero (s), + return_binary64_inf (s), return_binary64_nan); + +// Shift 6 more places left ready for reciprocal multiplication + + sll128_short (c.w[1], c.w[0], 6); + +// Check for "trivial" overflow, when 10^e * 1 > 2^{sci_emax+1}, just to +// keep tables smaller (it would be intercepted later otherwise). +// +// (Note that we may have normalized the coefficient, but we have a +// corresponding exponent postcorrection to account for; this can +// afford to be conservative anyway.) +// +// We actually check if e >= ceil((sci_emax + 1) * log_10(2)) +// which in this case is 2 >= ceil(1024 * log_10(2)) = ceil(308.25) = 309 + + if (e >= 309) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary64_ovf (s); + } +// Also check for "trivial" underflow, when 10^e * 2^113 <= 2^emin * 1/4, +// so test e <= floor((emin - 115) * log_10(2)) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -358) + e = -358; + +// Look up the breakpoint and approximate exponent + + m_min = (breakpoints_binary64 + 358)[e]; + e_out = (exponents_binary64 + 358)[e] - k; + +// Choose provisional exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_binary64 + 358)[e]; + } else { + r = (multipliers2_binary64 + 358)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) +// Check for exponent underflow and compensate by shifting the product +// Cut off the process at precision+2, since we can't really shift further + if (e_out < 1) { + int d; + d = 1 - e_out; + if (d > 55) + d = 55; + e_out = 1; + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], d); + } + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill into the next binade, correct +// Flag underflow where it may be needed even for |result| = SNN + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == (1ull << 53)) { + c_prov = 1ull << 52; + e_out = e_out + 1; + } else if ((c_prov == (1ull << 52)) && (e_out == 1)) { + if ((((rnd_mode & 3) == 0) && (z.w[4] < (3ull << 62))) || + ((rnd_mode + (s & 1) == 2) && (z.w[4] < (1ull << 63)))) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + } +// Check for overflow + + if (e_out >= 2047) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary64_ovf (s); + } +// Modify exponent for a tiny result, otherwise lop the implicit bit + + if (c_prov < (1ull << 52)) + e_out = 0; + else + c_prov = c_prov & ((1ull << 52) - 1); + +// Set the inexact and underflow flag as appropriate + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (e_out == 0) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result as a binary floating-point number + + return_binary64 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if __ENABLE_BINARY80__ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid32_to_binary80 (BINARY80 * pres, UINT32 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT32 x = *px; +#else +BINARY80 +bid32_to_binary80 (UINT32 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT64 c_prov; + UINT128 c; + UINT128 m_min; + int s, e, k, e_out; + UINT256 r; + UINT384 z; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + + unpack_bid32 (x, s, e, k, (c.w[1]), return_binary80_zero (s), + return_binary80_inf (s), return_binary80_nan); + +// Correct to 2^112 <= c < 2^113 with corresponding exponent adding 113-24=89 +// Given that we've unpacked in the high part (<<64), that's just <<25 + + c.w[1] = c.w[1] << 25; + c.w[0] = 0; + k = k + 89; + +// Check for "trivial" overflow, when 10^e * 1 > 2^{sci_emax+1}, just to +// keep tables smaller (it would be intercepted later otherwise). +// +// (Note that we may have normalized the coefficient, but we have a +// corresponding exponent postcorrection to account for; this can +// afford to be conservative anyway.) +// +// We actually check if e >= ceil((sci_emax + 1) * log_10(2)) +// which in this case is 2 >= ceil(16384 * log_10(2)) = ceil(4932.07544) = 4933 + + if (e >= 4933) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary80_ovf (s); + } +// Also check for "trivial" underflow, when 10^e * 2^113 <= 2^emin * 1/4, +// so test e <= floor((emin - 115) * log_10(2)) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -4985) + e = -4985; + +// Look up the breakpoint and approximate exponent + + m_min = (breakpoints_binary80 + 4985)[e]; + e_out = (exponents_binary80 + 4985)[e] - k; + +// Choose provisional exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_binary80 + 4985)[e]; + } else { + r = (multipliers2_binary80 + 4985)[e]; + e_out = e_out + 1; + } + + +// Do the reciprocal multiplication; make an effective shift of 303 bits +// by shifting 47 places right and taking the result from word 4 + + __mul_128x256_to_384 (z, c, r) + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], 47); + +// Check for exponent underflow and compensate by shifting the product +// Cut off the process at precision+2, since we can't really shift further + + if (e_out < 1) { + int d; + d = 1 - e_out; + if (d > 66) + d = 66; + if (d >= 64) { + d -= 64; + z.w[1] = z.w[2], z.w[2] = z.w[3], z.w[3] = z.w[4], z.w[4] = 0; + } + e_out = 1; + srl256 (z.w[4], z.w[3], z.w[2], z.w[1], d); + } + c_prov = z.w[4]; + +// Round using round-sticky words +// If we spill into the next binade, correct + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[3], z.w[2])) { + c_prov = c_prov + 1; + if (c_prov == 0) { + c_prov = 1ull << 63; + e_out = e_out + 1; + } + } +// Check for overflow + + if (e_out >= 32767) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary80_ovf (s); + } +// Modify exponent for a tiny result + + if (c_prov < (1ull << 63)) + e_out = 0; + +// Set the inexact and underflow flag as appropriate + + if ((z.w[3] != 0) || (z.w[2] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (e_out == 0) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result as a binary floating-point number + + return_binary80 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_binary80 (BINARY80 * pres, UINT64 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +BINARY80 +bid64_to_binary80 (UINT64 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 c_prov; + UINT128 c; + UINT128 m_min; + int s, e, k, e_out; + UINT256 r; + UINT384 z; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + + unpack_bid64 (x, s, e, k, (c.w[0]), return_binary80_zero (s), + return_binary80_inf (s), return_binary80_nan); + c.w[1] = 0; + +// Correct to 2^112 <= c < 2^113 with corresponding exponent adding 113-54=59 + + sll128_short (c.w[1], c.w[0], 59); + k = k + 59; + +// Check for "trivial" overflow, when 10^e * 1 > 2^{sci_emax+1}, just to +// keep tables smaller (it would be intercepted later otherwise). +// +// (Note that we may have normalized the coefficient, but we have a +// corresponding exponent postcorrection to account for; this can +// afford to be conservative anyway.) +// +// We actually check if e >= ceil((sci_emax + 1) * log_10(2)) +// which in this case is 2 >= ceil(16384 * log_10(2)) = ceil(4932.07544) = 4933 + + if (e >= 4933) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary80_ovf (s); + } +// Also check for "trivial" underflow, when 10^e * 2^113 <= 2^emin * 1/4, +// so test e <= floor((emin - 115) * log_10(2)) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -4985) + e = -4985; + +// Look up the breakpoint and approximate exponent + + m_min = (breakpoints_binary80 + 4985)[e]; + e_out = (exponents_binary80 + 4985)[e] - k; + +// Choose provisional exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_binary80 + 4985)[e]; + } else { + r = (multipliers2_binary80 + 4985)[e]; + e_out = e_out + 1; + } + + +// Do the reciprocal multiplication; make an effective shift of 303 bits +// by shifting 47 places right and taking the result from word 4 + + __mul_128x256_to_384 (z, c, r) + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], 47); + +// Check for exponent underflow and compensate by shifting the product +// Cut off the process at precision+2, since we can't really shift further + + if (e_out < 1) { + int d; + d = 1 - e_out; + if (d > 66) + d = 66; + if (d >= 64) { + d -= 64; + z.w[1] = z.w[2], z.w[2] = z.w[3], z.w[3] = z.w[4], z.w[4] = 0; + } + e_out = 1; + srl256 (z.w[4], z.w[3], z.w[2], z.w[1], d); + } + c_prov = z.w[4]; + +// Round using round-sticky words +// If we spill into the next binade, correct + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[3], z.w[2])) { + c_prov = c_prov + 1; + if (c_prov == 0) { + c_prov = 1ull << 63; + e_out = e_out + 1; + } + } +// Check for overflow + + if (e_out >= 32767) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary80_ovf (s); + } +// Modify exponent for a tiny result + + if (c_prov < (1ull << 63)) + e_out = 0; + +// Set the inexact and underflow flag as appropriate + + if ((z.w[3] != 0) || (z.w[2] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (e_out == 0) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result as a binary floating-point number + + return_binary80 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_to_binary80 (BINARY80 * pres, UINT128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +BINARY80 +bid128_to_binary80 (UINT128 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 c_prov; + UINT128 c; + UINT128 m_min; + int s, e, k, e_out; + UINT256 r; + UINT384 z; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + + unpack_bid128 (x, s, e, k, c, return_binary80_zero (s), + return_binary80_inf (s), return_binary80_nan); + +// Check for "trivial" overflow, when 10^e * 1 > 2^{sci_emax+1}, just to +// keep tables smaller (it would be intercepted later otherwise). +// +// (Note that we may have normalized the coefficient, but we have a +// corresponding exponent postcorrection to account for; this can +// afford to be conservative anyway.) +// +// We actually check if e >= ceil((sci_emax + 1) * log_10(2)) +// which in this case is 2 >= ceil(16384 * log_10(2)) = ceil(4932.07544) = 4933 + + if (e >= 4933) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary80_ovf (s); + } +// Also check for "trivial" underflow, when 10^e * 2^113 <= 2^emin * 1/4, +// so test e <= floor((emin - 115) * log_10(2)) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -4985) + e = -4985; + +// Look up the breakpoint and approximate exponent + + m_min = (breakpoints_binary80 + 4985)[e]; + e_out = (exponents_binary80 + 4985)[e] - k; + +// Choose provisional exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_binary80 + 4985)[e]; + } else { + r = (multipliers2_binary80 + 4985)[e]; + e_out = e_out + 1; + } + + +// Do the reciprocal multiplication; make an effective shift of 303 bits +// by shifting 47 places right and taking the result from word 4 + + __mul_128x256_to_384 (z, c, r) + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], 47); + +// Check for exponent underflow and compensate by shifting the product +// Cut off the process at precision+2, since we can't really shift further + + if (e_out < 1) { + int d; + d = 1 - e_out; + if (d > 66) + d = 66; + if (d >= 64) { + d -= 64; + z.w[1] = z.w[2], z.w[2] = z.w[3], z.w[3] = z.w[4], z.w[4] = 0; + } + e_out = 1; + srl256 (z.w[4], z.w[3], z.w[2], z.w[1], d); + } + c_prov = z.w[4]; + +// Round using round-sticky words +// If we spill into the next binade, correct +// Flag underflow where it may be needed even for |result| = SNN + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[3], z.w[2])) { + c_prov = c_prov + 1; + if (c_prov == 0) { + c_prov = 1ull << 63; + e_out = e_out + 1; + } else if ((c_prov == (1ull << 63)) && (e_out == 1)) { + if ((((rnd_mode & 3) == 0) && (z.w[3] < (3ull << 62))) || + ((rnd_mode + (s & 1) == 2) && (z.w[3] < (1ull << 63)))) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + } +// Check for overflow + + if (e_out >= 32767) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary80_ovf (s); + } +// Modify exponent for a tiny result + + if (c_prov < (1ull << 63)) + e_out = 0; + +// Set the inexact and underflow flag as appropriate + + if ((z.w[3] != 0) || (z.w[2] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (e_out == 0) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result as a binary floating-point number + + return_binary80 (s, e_out, c_prov); +} + +#endif // matches #if __ENABLE_BINARY80__ + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +bid32_to_binary128 (BINARY128 * pres, UINT32 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT32 x = *px; +#else +BINARY128 +bid32_to_binary128 (UINT32 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 c_prov_hi, c_prov_lo; + UINT128 c; + UINT128 m_min; + int s, e, k, e_out; + UINT256 r; + UINT384 z; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + + unpack_bid32 (x, s, e, k, (c.w[1]), return_binary128_zero (s), + return_binary128_inf (s), return_binary128_nan); + +// Correct to 2^112 <= c < 2^113 with corresponding exponent adding 113-24=89 +// But also make an additional shift of 2 places to get a whole-word lop: +// (c * r) >> 254 = ((c << 2) * r) >> 256. Given that we unpack in the high +// end, our shift is (89+2)-64 = 27 + + c.w[0] = 0; + c.w[1] = c.w[1] << 27; + k = k + 89; + +// Check for "trivial" overflow, when 10^e * 1 > 2^{sci_emax+1}, just to +// keep tables smaller (it would be intercepted later otherwise). +// +// (Note that we may have normalized the coefficient, but we have a +// corresponding exponent postcorrection to account for; this can +// afford to be conservative anyway.) +// +// We actually check if e >= ceil((sci_emax + 1) * log_10(2)) +// which in this case is 2 >= ceil(16384 * log_10(2)) = ceil(4932.07544) = 4933 + + if (e >= 4933) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary128_ovf (s); + } +// Also check for "trivial" underflow, when 10^e * 2^113 <= 2^emin * 1/4, +// so test e <= floor((emin - 114) * log_10(2)) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -5000) + e = -5000; + +// Look up the breakpoint and approximate exponent + + m_min = (breakpoints_binary128 + 5000)[e]; + e_out = (exponents_binary128 + 5000)[e] - k; + +// Choose provisional exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_binary128 + 5000)[e]; + } else { + r = (multipliers2_binary128 + 5000)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication; make an effective shift of 254 bits +// (given that we already shifted left 2 places) by lopping from word 4 + + __mul_128x256_to_384 (z, c, r) +// Check for exponent underflow and compensate by shifting the product +// Cut off the process at precision+2, since we can't really shift further + if (e_out < 1) { + int d; + d = 1 - e_out; + if (d > 115) + d = 115; + if (d >= 64) { + d -= 64; + z.w[2] = z.w[3], z.w[3] = z.w[4], z.w[4] = z.w[5], z.w[5] = 0; + } + e_out = 1; + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], d); + } + c_prov_hi = z.w[5]; + c_prov_lo = z.w[4]; + +// Round using round-sticky words +// If we spill into the next binade, correct + + if (lt128 + (roundbound_128 + [(rnd_mode << 2) + ((s & 1) << 1) + (c_prov_lo & 1)].w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov_lo & 1)].w[0], z.w[3], z.w[2])) { + c_prov_lo = c_prov_lo + 1; + if (c_prov_lo == 0) { + c_prov_hi = c_prov_hi + 1; + if (c_prov_hi == 1ull << 49) { + c_prov_hi = 1ull << 48; + e_out = e_out + 1; + } + } + } +// Check for overflow + + if (e_out >= 32767) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary128_ovf (s); + } +// Modify exponent for a tiny result; otherwise lop off the implicit bit + + if (c_prov_hi < (1ull << 48)) + e_out = 0; + else + c_prov_hi = c_prov_hi & ((1ull << 48) - 1); + +// Set the inexact and underflow flag as appropriate + + if ((z.w[3] != 0) || (z.w[2] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (e_out == 0) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result as a binary floating-point number + + return_binary128 (s, e_out, c_prov_hi, c_prov_lo); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_binary128 (BINARY128 * pres, UINT64 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +BINARY128 +bid64_to_binary128 (UINT64 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 c_prov_hi, c_prov_lo; + UINT128 c; + UINT128 m_min; + int s, e, k, e_out; + UINT256 r; + UINT384 z; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + + unpack_bid64 (x, s, e, k, (c.w[0]), return_binary128_zero (s), + return_binary128_inf (s), return_binary128_nan); + c.w[1] = 0; + +// Correct to 2^112 <= c < 2^113 with corresponding exponent adding 113-54=59 +// But also make an additional shift of 2 places to get a whole-word lop: +// (c * r) >> 254 = ((c << 2) * r) >> 256 + + sll128_short (c.w[1], c.w[0], 61); + k = k + 59; + +// Check for "trivial" overflow, when 10^e * 1 > 2^{sci_emax+1}, just to +// keep tables smaller (it would be intercepted later otherwise). +// +// (Note that we may have normalized the coefficient, but we have a +// corresponding exponent postcorrection to account for; this can +// afford to be conservative anyway.) +// +// We actually check if e >= ceil((sci_emax + 1) * log_10(2)) +// which in this case is 2 >= ceil(16384 * log_10(2)) = ceil(4932.07544) = 4933 + + if (e >= 4933) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary128_ovf (s); + } +// Also check for "trivial" underflow, when 10^e * 2^113 <= 2^emin * 1/4, +// so test e <= floor((emin - 114) * log_10(2)) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -5000) + e = -5000; + +// Look up the breakpoint and approximate exponent + + m_min = (breakpoints_binary128 + 5000)[e]; + e_out = (exponents_binary128 + 5000)[e] - k; + +// Choose provisional exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_binary128 + 5000)[e]; + } else { + r = (multipliers2_binary128 + 5000)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication; make an effective shift of 254 bits +// (given that we already shifted left 2 places) by lopping from word 4 + + __mul_128x256_to_384 (z, c, r) +// Check for exponent underflow and compensate by shifting the product +// Cut off the process at precision+2, since we can't really shift further + if (e_out < 1) { + int d; + d = 1 - e_out; + if (d > 115) + d = 115; + if (d >= 64) { + d -= 64; + z.w[2] = z.w[3], z.w[3] = z.w[4], z.w[4] = z.w[5], z.w[5] = 0; + } + e_out = 1; + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], d); + } + c_prov_hi = z.w[5]; + c_prov_lo = z.w[4]; + +// Round using round-sticky words +// If we spill into the next binade, correct + + if (lt128 + (roundbound_128 + [(rnd_mode << 2) + ((s & 1) << 1) + (c_prov_lo & 1)].w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov_lo & 1)].w[0], z.w[3], z.w[2])) { + c_prov_lo = c_prov_lo + 1; + if (c_prov_lo == 0) { + c_prov_hi = c_prov_hi + 1; + if (c_prov_hi == 1ull << 49) { + c_prov_hi = 1ull << 48; + e_out = e_out + 1; + } + } + } +// Check for overflow + + if (e_out >= 32767) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary128_ovf (s); + } +// Modify exponent for a tiny result; otherwise lop off the implicit bit + + if (c_prov_hi < (1ull << 48)) + e_out = 0; + else + c_prov_hi = c_prov_hi & ((1ull << 48) - 1); + +// Set the inexact and underflow flag as appropriate + + if ((z.w[3] != 0) || (z.w[2] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (e_out == 0) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result as a binary floating-point number + + return_binary128 (s, e_out, c_prov_hi, c_prov_lo); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_to_binary128 (BINARY128 * pres, UINT128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT128 x = *px; +#else +BINARY128 +bid128_to_binary128 (UINT128 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 c_prov_hi, c_prov_lo; + UINT128 c; + UINT128 m_min; + int s, e, k, e_out; + UINT256 r; + UINT384 z; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + +// Unpack the input and shift two further places for reciprocal multiplication + + unpack_bid128 (x, s, e, k, c, return_binary128_zero (s), + return_binary128_inf (s), return_binary128_nan); + sll128_short (c.w[1], c.w[0], 2); + +// Check for "trivial" overflow, when 10^e * 1 > 2^{sci_emax+1}, just to +// keep tables smaller (it would be intercepted later otherwise). +// +// (Note that we may have normalized the coefficient, but we have a +// corresponding exponent postcorrection to account for; this can +// afford to be conservative anyway.) +// +// We actually check if e >= ceil((sci_emax + 1) * log_10(2)) +// which in this case is 2 >= ceil(16384 * log_10(2)) = ceil(4932.07544) = 4933 + + if (e >= 4933) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary128_ovf (s); + } +// Also check for "trivial" underflow, when 10^e * 2^113 <= 2^emin * 1/4, +// so test e <= floor((emin - 114) * log_10(2)) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -5000) + e = -5000; + +// Look up the breakpoint and approximate exponent + + m_min = (breakpoints_binary128 + 5000)[e]; + e_out = (exponents_binary128 + 5000)[e] - k; + +// Choose provisional exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_binary128 + 5000)[e]; + } else { + r = (multipliers2_binary128 + 5000)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication; make an effective shift of 254 bits +// (given that we already shifted left 2 places) by lopping from word 4 + + __mul_128x256_to_384 (z, c, r) +// Check for exponent underflow and compensate by shifting the product +// Cut off the process at precision+2, since we can't really shift further + if (e_out < 1) { + int d; + d = 1 - e_out; + if (d > 115) + d = 115; + if (d >= 64) { + d -= 64; + z.w[2] = z.w[3], z.w[3] = z.w[4], z.w[4] = z.w[5], z.w[5] = 0; + } + e_out = 1; + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], d); + } + c_prov_hi = z.w[5]; + c_prov_lo = z.w[4]; + +// Round using round-sticky words +// If we spill into the next binade, correct +// Flag underflow where it may be needed even for |result| = SNN + + if (lt128 + (roundbound_128 + [(rnd_mode << 2) + ((s & 1) << 1) + (c_prov_lo & 1)].w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov_lo & 1)].w[0], z.w[3], z.w[2])) { + c_prov_lo = c_prov_lo + 1; + if (c_prov_lo == 0) { + c_prov_hi = c_prov_hi + 1; + if (c_prov_hi == 1ull << 49) { + c_prov_hi = 1ull << 48; + e_out = e_out + 1; + } else if ((c_prov_hi == (1ull << 48)) && (e_out == 1)) { + if ((((rnd_mode & 3) == 0) && (z.w[3] < (3ull << 62))) || + ((rnd_mode + (s & 1) == 2) && (z.w[3] < (1ull << 63)))) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + } + } +// Check for overflow + + if (e_out >= 32767) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_binary128_ovf (s); + } +// Modify exponent for a tiny result; otherwise lop off the implicit bit + + if (c_prov_hi < (1ull << 48)) + e_out = 0; + else + c_prov_hi = c_prov_hi & ((1ull << 48) - 1); + +// Set the inexact and underflow flag as appropriate + + if ((z.w[3] != 0) || (z.w[2] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (e_out == 0) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result as a binary floating-point number + + return_binary128 (s, e_out, c_prov_hi, c_prov_lo); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +binary32_to_bid32 (UINT32 * pres, float *px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + float x = *px; +#else +UINT32 +binary32_to_bid32 (float x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT128 c; + UINT64 c_prov; + UINT128 m_min; + UINT256 r; + UINT384 z; + + int e, s, t, e_out; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + +// Unpack the input + + unpack_binary32 (x, s, e, c.w[1], t, return_bid32_zero (s), + return_bid32_inf (s), return_bid32_nan); + +// Treat like a quad input for uniformity, so (2^{113-24} * c * r) >> 320, +// where 320 is the truncation value for the reciprocal multiples, exactly +// five 64-bit words. So we shift 113-24=89 places. Since we unpacked in +// the high end, shift a further 89-64=25 places +// +// Remember to compensate for the fact that exponents are integer for quad + + c.w[0] = 0; + c.w[1] = c.w[1] << 25; + t += (113 - 24); + e -= (113 - 24); + +// Check for "trivial" overflow, when 2^e * 2^112 > 10^emax * 10^d. +// We actually check if e >= ceil((emax + d) * log_2(10) - 112) +// This could be intercepted later, but it's convenient to keep tables smaller + + if (e >= 211) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid32_ovf (s); + } +// Now filter out all the exact cases where we need to specially force +// the exponent to 0. We can let through inexact cases and those where the +// main path will do the right thing anyway, e.g. integers outside coeff range. +// +// First check that e <= 0, because if e > 0, the input must be >= 2^113, +// which is too large for the coefficient of any target decimal format. +// We write a = -(e + t) +// +// (1) If e + t >= 0 <=> a <= 0 the input is an integer; treat it specially +// iff it fits in the coefficient range. Shift c' = c >> -e, and +// compare with the coefficient range; if it's in range then c' is +// our coefficient, exponent is 0. Otherwise we pass through. +// +// (2) If a > 0 then we have a non-integer input. The special case would +// arise as c' / 2^a where c' = c >> t, i.e. 10^-a * (5^a c'). Now +// if a > 48 we can immediately forget this, since 5^49 > 10^34. +// Otherwise we determine whether we're in range by a table based on +// a, and if so get the multiplier also from a table based on a. + + if (e <= 0) { + UINT128 cint; + int a = -(e + t); + cint.w[1] = c.w[1], cint.w[0] = c.w[0]; + if (a <= 0) { + srl128 (cint.w[1], cint.w[0], -e); + if ((cint.w[1] == 0) && (cint.w[0] < 10000000ull)) + return_bid32 (s, 101, cint.w[0]); + } else if (a <= 48) { + UINT128 pow5 = coefflimits_bid32[a]; + srl128 (cint.w[1], cint.w[0], t); + if (le128 (cint.w[1], cint.w[0], pow5.w[1], pow5.w[0])) { + UINT128 cc; + cc.w[1] = cint.w[1]; + cc.w[0] = cint.w[0]; + pow5 = power_five[a]; + __mul_128x128_low (cc, cc, pow5); + return_bid32 (s, 101 - a, cc.w[0]); + } + } + } +// Check for "trivial" underflow, when 2^e * 2^113 <= 10^emin * 1/4, +// so test e <= floor(emin * log_2(10) - 115) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -450) + e = -450; + +// Now look up our exponent e, and the breakpoint between e and e+1 + + m_min = (breakpoints_bid32 + 450)[e]; + e_out = (exponents_bid32 + 450)[e]; + +// Choose exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_bid32 + 450)[e]; + } else { + r = (multipliers2_bid32 + 450)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill over into the next decade, correct + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == 10000000ull) { + c_prov = 1000000ull; + e_out = e_out + 1; + } + } +// Check for overflow + + if (e_out > 90 + 101) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid32_ovf (s); + } +// Set the inexact flag as appropriate and check underflow +// It's no doubt superfluous to check inexactness, but anyway... + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (c_prov < 1000000ull) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result + + return_bid32 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +binary64_to_bid32 (UINT32 * pres, double *px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + double x = *px; +#else +UINT32 +binary64_to_bid32 (double x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + UINT128 c; + UINT64 c_prov; + UINT128 m_min; + UINT256 r; + UINT384 z; + + int e, s, t, e_out; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + +// Unpack the input + + unpack_binary64 (x, s, e, c.w[0], t, return_bid32_zero (s), + return_bid32_inf (s), return_bid32_nan); + +// Treat like a quad input for uniformity, so (2^{113-53} * c * r) >> 320, +// where 320 is the truncation value for the reciprocal multiples, exactly +// five 64-bit words. So we shift 113-53=60 places +// +// Remember to compensate for the fact that exponents are integer for quad + + c.w[1] = 0; + sll128_short (c.w[1], c.w[0], 60); + t += (113 - 53); + e -= (113 - 53); + +// Check for "trivial" overflow, when 2^e * 2^112 > 10^emax * 10^d. +// We actually check if e >= ceil((emax + d) * log_2(10) - 112) +// This could be intercepted later, but it's convenient to keep tables smaller + + if (e >= 211) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid32_ovf (s); + } +// Now filter out all the exact cases where we need to specially force +// the exponent to 0. We can let through inexact cases and those where the +// main path will do the right thing anyway, e.g. integers outside coeff range. +// +// First check that e <= 0, because if e > 0, the input must be >= 2^113, +// which is too large for the coefficient of any target decimal format. +// We write a = -(e + t) +// +// (1) If e + t >= 0 <=> a <= 0 the input is an integer; treat it specially +// iff it fits in the coefficient range. Shift c' = c >> -e, and +// compare with the coefficient range; if it's in range then c' is +// our coefficient, exponent is 0. Otherwise we pass through. +// +// (2) If a > 0 then we have a non-integer input. The special case would +// arise as c' / 2^a where c' = c >> t, i.e. 10^-a * (5^a c'). Now +// if a > 48 we can immediately forget this, since 5^49 > 10^34. +// Otherwise we determine whether we're in range by a table based on +// a, and if so get the multiplier also from a table based on a. + + if (e <= 0) { + UINT128 cint; + int a = -(e + t); + cint.w[1] = c.w[1], cint.w[0] = c.w[0]; + if (a <= 0) { + srl128 (cint.w[1], cint.w[0], -e); + if ((cint.w[1] == 0) && (cint.w[0] < 10000000ull)) + return_bid32 (s, 101, cint.w[0]); + } else if (a <= 48) { + UINT128 pow5 = coefflimits_bid32[a]; + srl128 (cint.w[1], cint.w[0], t); + if (le128 (cint.w[1], cint.w[0], pow5.w[1], pow5.w[0])) { + UINT128 cc; + cc.w[1] = cint.w[1]; + cc.w[0] = cint.w[0]; + pow5 = power_five[a]; + __mul_128x128_low (cc, cc, pow5); + return_bid32 (s, 101 - a, cc.w[0]); + } + } + } +// Check for "trivial" underflow, when 2^e * 2^113 <= 10^emin * 1/4, +// so test e <= floor(emin * log_2(10) - 115) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -450) + e = -450; + +// Now look up our exponent e, and the breakpoint between e and e+1 + + m_min = (breakpoints_bid32 + 450)[e]; + e_out = (exponents_bid32 + 450)[e]; + +// Choose exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_bid32 + 450)[e]; + } else { + r = (multipliers2_bid32 + 450)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill over into the next decade, correct +// Flag underflow where it may be needed even for |result| = SNN + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == 10000000ull) { + c_prov = 1000000ull; + e_out = e_out + 1; + } else if ((c_prov == 1000000ull) && (e_out == 0)) { + if ((((rnd_mode & 3) == 0) && (z.w[4] <= 17524406870024074035ull)) + || ((rnd_mode + (s & 1) == 2) + && (z.w[4] <= 16602069666338596454ull))) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + } +// Check for overflow + + if (e_out > 90 + 101) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid32_ovf (s); + } +// Set the inexact flag as appropriate and check underflow +// It's no doubt superfluous to check inexactness, but anyway... + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (c_prov < 1000000ull) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result + + return_bid32 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if __ENABLE_BINARY80__ + +#if DECIMAL_CALL_BY_REFERENCE +void +binary80_to_bid32 (UINT32 * pres, BINARY80 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + BINARY80 x = *px; +#else +UINT32 +binary80_to_bid32 (BINARY80 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 c; + UINT64 c_prov; + UINT128 m_min; + UINT256 r; + UINT384 z; + + int e, s, t, e_out; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + +// Unpack the input + + unpack_binary80 (x, s, e, c.w[0], t, return_bid32_zero (s), + return_bid32_inf (s), return_bid32_nan); + +// Treat like a quad input for uniformity, so (2^{113-64} * c * r) >> 320, +// where 320 is the truncation value for the reciprocal multiples, exactly +// five 64-bit words. So we shift 113-64=49 places +// +// Remember to compensate for the fact that exponents are integer for quad + + c.w[1] = 0; + sll128_short (c.w[1], c.w[0], 49); + t += (113 - 64); + e -= (113 - 64); + +// Check for "trivial" overflow, when 2^e * 2^112 > 10^emax * 10^d. +// We actually check if e >= ceil((emax + d) * log_2(10) - 112) +// This could be intercepted later, but it's convenient to keep tables smaller + + if (e >= 211) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid32_ovf (s); + } +// Now filter out all the exact cases where we need to specially force +// the exponent to 0. We can let through inexact cases and those where the +// main path will do the right thing anyway, e.g. integers outside coeff range. +// +// First check that e <= 0, because if e > 0, the input must be >= 2^113, +// which is too large for the coefficient of any target decimal format. +// We write a = -(e + t) +// +// (1) If e + t >= 0 <=> a <= 0 the input is an integer; treat it specially +// iff it fits in the coefficient range. Shift c' = c >> -e, and +// compare with the coefficient range; if it's in range then c' is +// our coefficient, exponent is 0. Otherwise we pass through. +// +// (2) If a > 0 then we have a non-integer input. The special case would +// arise as c' / 2^a where c' = c >> t, i.e. 10^-a * (5^a c'). Now +// if a > 48 we can immediately forget this, since 5^49 > 10^34. +// Otherwise we determine whether we're in range by a table based on +// a, and if so get the multiplier also from a table based on a. + + if (e <= 0) { + UINT128 cint; + int a = -(e + t); + cint.w[1] = c.w[1], cint.w[0] = c.w[0]; + if (a <= 0) { + srl128 (cint.w[1], cint.w[0], -e); + if ((cint.w[1] == 0) && (cint.w[0] < 10000000ull)) + return_bid32 (s, 101, cint.w[0]); + } else if (a <= 48) { + UINT128 pow5 = coefflimits_bid32[a]; + srl128 (cint.w[1], cint.w[0], t); + if (le128 (cint.w[1], cint.w[0], pow5.w[1], pow5.w[0])) { + UINT128 cc; + cc.w[1] = cint.w[1]; + cc.w[0] = cint.w[0]; + pow5 = power_five[a]; + __mul_128x128_low (cc, cc, pow5); + return_bid32 (s, 101 - a, cc.w[0]); + } + } + } +// Check for "trivial" underflow, when 2^e * 2^113 <= 10^emin * 1/4, +// so test e <= floor(emin * log_2(10) - 115) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -450) + e = -450; + +// Now look up our exponent e, and the breakpoint between e and e+1 + + m_min = (breakpoints_bid32 + 450)[e]; + e_out = (exponents_bid32 + 450)[e]; + +// Choose exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_bid32 + 450)[e]; + } else { + r = (multipliers2_bid32 + 450)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill over into the next decade, correct +// Flag underflow where it may be needed even for |result| = SNN + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == 10000000ull) { + c_prov = 1000000ull; + e_out = e_out + 1; + } else if ((c_prov == 1000000ull) && (e_out == 0)) { + if ((((rnd_mode & 3) == 0) && (z.w[4] <= 17524406870024074035ull)) + || ((rnd_mode + (s & 1) == 2) + && (z.w[4] <= 16602069666338596454ull))) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + } +// Check for overflow + + if (e_out > 90 + 101) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid32_ovf (s); + } +// Set the inexact flag as appropriate and check underflow +// It's no doubt superfluous to check inexactness, but anyway... + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (c_prov < 1000000ull) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result + + return_bid32 (s, e_out, c_prov); +} + +#endif // matches #if __ENABLE_BINARY80__ + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +binary128_to_bid32 (UINT32 * pres, BINARY128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + BINARY128 x = *px; +#else +UINT32 +binary128_to_bid32 (BINARY128 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 c; + UINT64 c_prov; + UINT128 m_min; + UINT256 r; + UINT384 z; + + int e, s, t, e_out; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + +// Unpack the input + + unpack_binary128 (x, s, e, c.w[1], c.w[0], t, return_bid32_zero (s), + return_bid32_inf (s), return_bid32_nan); + +// Check for "trivial" overflow, when 2^e * 2^112 > 10^emax * 10^d. +// We actually check if e >= ceil((emax + d) * log_2(10) - 112) +// This could be intercepted later, but it's convenient to keep tables smaller + + if (e >= 211) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid32_ovf (s); + } +// Now filter out all the exact cases where we need to specially force +// the exponent to 0. We can let through inexact cases and those where the +// main path will do the right thing anyway, e.g. integers outside coeff range. +// +// First check that e <= 0, because if e > 0, the input must be >= 2^113, +// which is too large for the coefficient of any target decimal format. +// We write a = -(e + t) +// +// (1) If e + t >= 0 <=> a <= 0 the input is an integer; treat it specially +// iff it fits in the coefficient range. Shift c' = c >> -e, and +// compare with the coefficient range; if it's in range then c' is +// our coefficient, exponent is 0. Otherwise we pass through. +// +// (2) If a > 0 then we have a non-integer input. The special case would +// arise as c' / 2^a where c' = c >> t, i.e. 10^-a * (5^a c'). Now +// if a > 48 we can immediately forget this, since 5^49 > 10^34. +// Otherwise we determine whether we're in range by a table based on +// a, and if so get the multiplier also from a table based on a. + + if (e <= 0) { + UINT128 cint; + int a = -(e + t); + cint.w[1] = c.w[1], cint.w[0] = c.w[0]; + if (a <= 0) { + srl128 (cint.w[1], cint.w[0], -e); + if ((cint.w[1] == 0) && (cint.w[0] < 10000000ull)) + return_bid32 (s, 101, cint.w[0]); + } else if (a <= 48) { + UINT128 pow5 = coefflimits_bid32[a]; + srl128 (cint.w[1], cint.w[0], t); + if (le128 (cint.w[1], cint.w[0], pow5.w[1], pow5.w[0])) { + UINT128 cc; + cc.w[1] = cint.w[1]; + cc.w[0] = cint.w[0]; + pow5 = power_five[a]; + __mul_128x128_low (cc, cc, pow5); + return_bid32 (s, 101 - a, cc.w[0]); + } + } + } +// Check for "trivial" underflow, when 2^e * 2^113 <= 10^emin * 1/4, +// so test e <= floor(emin * log_2(10) - 115) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -450) + e = -450; + +// Now look up our exponent e, and the breakpoint between e and e+1 + + m_min = (breakpoints_bid32 + 450)[e]; + e_out = (exponents_bid32 + 450)[e]; + +// Choose exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_bid32 + 450)[e]; + } else { + r = (multipliers2_bid32 + 450)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill over into the next decade, correct +// Flag underflow where it may be needed even for |result| = SNN +// This needs to be done in extra precision because of the precision disparity +// and the fact that the breakpoint isn't an exact binary number. + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == 10000000ull) { + c_prov = 1000000ull; + e_out = e_out + 1; + } else if ((c_prov == 1000000ull) && (e_out == 0)) { + if ((((rnd_mode & 3) == 0) && + le128 (z.w[4], z.w[3], + 17524406870024074035ull, 3689348814741910323ull)) || + ((rnd_mode + (s & 1) == 2) && + le128 (z.w[4], z.w[3], + 16602069666338596454ull, 7378697629483820646ull))) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + } +// Check for overflow + + if (e_out > 90 + 101) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid32_ovf (s); + } +// Set the inexact flag as appropriate and check underflow +// It's no doubt superfluous to check inexactness, but anyway... + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (c_prov < 1000000ull) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result + + return_bid32 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +binary32_to_bid64 (UINT64 * pres, float *px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + float x = *px; +#else +UINT64 +binary32_to_bid64 (float x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 c; + UINT64 c_prov; + UINT128 m_min; + UINT256 r; + UINT384 z; + + int e, s, t, e_out; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + +// Unpack the input + + unpack_binary32 (x, s, e, c.w[1], t, return_bid64_zero (s), + return_bid64_inf (s), return_bid64_nan); + +// Treat like a quad input for uniformity, so (2^{113-24} * c * r) >> 312 +// (312 is the shift value for these tables) which can be written as +// (2^97 c * r) >> 320, lopping off exactly 320 bits = 5 words. Thus we put +// input coefficient as the high part of c (<<64) shifted by 33 bits (<<97) +// +// Remember to compensate for the fact that exponents are integer for quad + + c.w[1] = c.w[1] << 33; + c.w[0] = 0; + t += (113 - 24); + e -= (113 - 24); + +// Check for "trivial" overflow, when 2^e * 2^112 > 10^emax * 10^d. +// We actually check if e >= ceil((emax + d) * log_2(10) - 112) +// This could be intercepted later, but it's convenient to keep tables smaller + + if (e >= 1168) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid64_ovf (s); + } +// Now filter out all the exact cases where we need to specially force +// the exponent to 0. We can let through inexact cases and those where the +// main path will do the right thing anyway, e.g. integers outside coeff range. +// +// First check that e <= 0, because if e > 0, the input must be >= 2^113, +// which is too large for the coefficient of any target decimal format. +// We write a = -(e + t) +// +// (1) If e + t >= 0 <=> a <= 0 the input is an integer; treat it specially +// iff it fits in the coefficient range. Shift c' = c >> -e, and +// compare with the coefficient range; if it's in range then c' is +// our coefficient, exponent is 0. Otherwise we pass through. +// +// (2) If a > 0 then we have a non-integer input. The special case would +// arise as c' / 2^a where c' = c >> t, i.e. 10^-a * (5^a c'). Now +// if a > 48 we can immediately forget this, since 5^49 > 10^34. +// Otherwise we determine whether we're in range by a table based on +// a, and if so get the multiplier also from a table based on a. +// +// Note that when we shift, we need to take into account the fact that +// c is already 8 places to the left in preparation for the reciprocal +// multiplication; thus we add 8 to all the shift counts + + if (e <= 0) { + UINT128 cint; + int a = -(e + t); + cint.w[1] = c.w[1], cint.w[0] = c.w[0]; + if (a <= 0) { + srl128 (cint.w[1], cint.w[0], 8 - e); + if ((cint.w[1] == 0) && (cint.w[0] < 10000000000000000ull)) + return_bid64 (s, 398, cint.w[0]); + } else if (a <= 48) { + UINT128 pow5 = coefflimits_bid64[a]; + srl128 (cint.w[1], cint.w[0], 8 + t); + if (le128 (cint.w[1], cint.w[0], pow5.w[1], pow5.w[0])) { + UINT128 cc; + cc.w[1] = cint.w[1]; + cc.w[0] = cint.w[0]; + pow5 = power_five[a]; + __mul_128x128_low (cc, cc, pow5); + return_bid64 (s, 398 - a, cc.w[0]); + } + } + } +// Check for "trivial" underflow, when 2^e * 2^113 <= 10^emin * 1/4, +// so test e <= floor(emin * log_2(10) - 115) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -1437) + e = -1437; + +// Now look up our exponent e, and the breakpoint between e and e+1 + + m_min = (breakpoints_bid64 + 1437)[e]; + e_out = (exponents_bid64 + 1437)[e]; + +// Choose exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_bid64 + 1437)[e]; + } else { + r = (multipliers2_bid64 + 1437)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill over into the next decade, correct + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == 10000000000000000ull) { + c_prov = 1000000000000000ull; + e_out = e_out + 1; + } + } +// Check for overflow + + if (e_out > 369 + 398) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid64_ovf (s); + } +// Set the inexact flag as appropriate and check underflow +// It's no doubt superfluous to check inexactness, but anyway... + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (c_prov < 1000000000000000ull) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result + + return_bid64 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +binary64_to_bid64 (UINT64 * pres, double *px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + double x = *px; +#else +UINT64 +binary64_to_bid64 (double x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 c; + UINT64 c_prov; + UINT128 m_min; + UINT256 r; + UINT384 z; + + int e, s, t, e_out; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + +// Unpack the input + + unpack_binary64 (x, s, e, c.w[1], t, return_bid64_zero (s), + return_bid64_inf (s), return_bid64_nan); + +// Treat like a quad input for uniformity, so (2^{113-53} * c * r) >> 312 +// (312 is the shift value for these tables) which can be written as +// (2^68 c * r) >> 320, lopping off exactly 320 bits = 5 words. Thus we put +// input coefficient as the high part of c (<<64) shifted by 4 bits (<<68) +// +// Remember to compensate for the fact that exponents are integer for quad + + c.w[1] = c.w[1] << 4; + c.w[0] = 0; + t += (113 - 53); + e -= (113 - 53); + +// Check for "trivial" overflow, when 2^e * 2^112 > 10^emax * 10^d. +// We actually check if e >= ceil((emax + d) * log_2(10) - 112) +// This could be intercepted later, but it's convenient to keep tables smaller + + if (e >= 1168) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid64_ovf (s); + } +// Now filter out all the exact cases where we need to specially force +// the exponent to 0. We can let through inexact cases and those where the +// main path will do the right thing anyway, e.g. integers outside coeff range. +// +// First check that e <= 0, because if e > 0, the input must be >= 2^113, +// which is too large for the coefficient of any target decimal format. +// We write a = -(e + t) +// +// (1) If e + t >= 0 <=> a <= 0 the input is an integer; treat it specially +// iff it fits in the coefficient range. Shift c' = c >> -e, and +// compare with the coefficient range; if it's in range then c' is +// our coefficient, exponent is 0. Otherwise we pass through. +// +// (2) If a > 0 then we have a non-integer input. The special case would +// arise as c' / 2^a where c' = c >> t, i.e. 10^-a * (5^a c'). Now +// if a > 48 we can immediately forget this, since 5^49 > 10^34. +// Otherwise we determine whether we're in range by a table based on +// a, and if so get the multiplier also from a table based on a. +// +// Note that when we shift, we need to take into account the fact that +// c is already 8 places to the left in preparation for the reciprocal +// multiplication; thus we add 8 to all the shift counts + + if (e <= 0) { + UINT128 cint; + int a = -(e + t); + cint.w[1] = c.w[1], cint.w[0] = c.w[0]; + if (a <= 0) { + srl128 (cint.w[1], cint.w[0], 8 - e); + if ((cint.w[1] == 0) && (cint.w[0] < 10000000000000000ull)) + return_bid64 (s, 398, cint.w[0]); + } else if (a <= 48) { + UINT128 pow5 = coefflimits_bid64[a]; + srl128 (cint.w[1], cint.w[0], 8 + t); + if (le128 (cint.w[1], cint.w[0], pow5.w[1], pow5.w[0])) { + UINT128 cc; + cc.w[1] = cint.w[1]; + cc.w[0] = cint.w[0]; + pow5 = power_five[a]; + __mul_128x128_low (cc, cc, pow5); + return_bid64 (s, 398 - a, cc.w[0]); + } + } + } +// Check for "trivial" underflow, when 2^e * 2^113 <= 10^emin * 1/4, +// so test e <= floor(emin * log_2(10) - 115) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -1437) + e = -1437; + +// Now look up our exponent e, and the breakpoint between e and e+1 + + m_min = (breakpoints_bid64 + 1437)[e]; + e_out = (exponents_bid64 + 1437)[e]; + +// Choose exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_bid64 + 1437)[e]; + } else { + r = (multipliers2_bid64 + 1437)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill over into the next decade, correct + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == 10000000000000000ull) { + c_prov = 1000000000000000ull; + e_out = e_out + 1; + } + } +// Check for overflow + + if (e_out > 369 + 398) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid64_ovf (s); + } +// Set the inexact flag as appropriate and check underflow +// It's no doubt superfluous to check inexactness, but anyway... + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (c_prov < 1000000000000000ull) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result + + return_bid64 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if __ENABLE_BINARY80__ + +#if DECIMAL_CALL_BY_REFERENCE +void +binary80_to_bid64 (UINT64 * pres, BINARY80 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + BINARY80 x = *px; +#else +UINT64 +binary80_to_bid64 (BINARY80 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 c; + UINT64 c_prov; + UINT128 m_min; + UINT256 r; + UINT384 z; + + int e, s, t, e_out; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + +// Unpack the input + + unpack_binary80 (x, s, e, c.w[1], t, return_bid64_zero (s), + return_bid64_inf (s), return_bid64_nan); + +// Treat like a quad input for uniformity, so (2^{113-64} * c * r) >> 312 +// (312 is the shift value for these tables) which can be written as +// (2^57 c * r) >> 320, lopping off exactly 320 bits = 5 words. Thus we put the +// input in the high part then shift right 7 places + + c.w[0] = 0; + srl128_short (c.w[1], c.w[0], 7); + t += (113 - 64); + e -= (113 - 64); + +// Check for "trivial" overflow, when 2^e * 2^112 > 10^emax * 10^d. +// We actually check if e >= ceil((emax + d) * log_2(10) - 112) +// This could be intercepted later, but it's convenient to keep tables smaller + + if (e >= 1168) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid64_ovf (s); + } +// Now filter out all the exact cases where we need to specially force +// the exponent to 0. We can let through inexact cases and those where the +// main path will do the right thing anyway, e.g. integers outside coeff range. +// +// First check that e <= 0, because if e > 0, the input must be >= 2^113, +// which is too large for the coefficient of any target decimal format. +// We write a = -(e + t) +// +// (1) If e + t >= 0 <=> a <= 0 the input is an integer; treat it specially +// iff it fits in the coefficient range. Shift c' = c >> -e, and +// compare with the coefficient range; if it's in range then c' is +// our coefficient, exponent is 0. Otherwise we pass through. +// +// (2) If a > 0 then we have a non-integer input. The special case would +// arise as c' / 2^a where c' = c >> t, i.e. 10^-a * (5^a c'). Now +// if a > 48 we can immediately forget this, since 5^49 > 10^34. +// Otherwise we determine whether we're in range by a table based on +// a, and if so get the multiplier also from a table based on a. +// +// Note that when we shift, we need to take into account the fact that +// c is already 8 places to the left in preparation for the reciprocal +// multiplication; thus we add 8 to all the shift counts + + if (e <= 0) { + UINT128 cint; + int a = -(e + t); + cint.w[1] = c.w[1], cint.w[0] = c.w[0]; + if (a <= 0) { + srl128 (cint.w[1], cint.w[0], 8 - e); + if ((cint.w[1] == 0) && (cint.w[0] < 10000000000000000ull)) + return_bid64 (s, 398, cint.w[0]); + } else if (a <= 48) { + UINT128 pow5 = coefflimits_bid64[a]; + srl128 (cint.w[1], cint.w[0], 8 + t); + if (le128 (cint.w[1], cint.w[0], pow5.w[1], pow5.w[0])) { + UINT128 cc; + cc.w[1] = cint.w[1]; + cc.w[0] = cint.w[0]; + pow5 = power_five[a]; + __mul_128x128_low (cc, cc, pow5); + return_bid64 (s, 398 - a, cc.w[0]); + } + } + } +// Check for "trivial" underflow, when 2^e * 2^113 <= 10^emin * 1/4, +// so test e <= floor(emin * log_2(10) - 115) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -1437) + e = -1437; + +// Now look up our exponent e, and the breakpoint between e and e+1 + + m_min = (breakpoints_bid64 + 1437)[e]; + e_out = (exponents_bid64 + 1437)[e]; + +// Choose exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_bid64 + 1437)[e]; + } else { + r = (multipliers2_bid64 + 1437)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill over into the next decade, correct +// Flag underflow where it may be needed even for |result| = SNN + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == 10000000000000000ull) { + c_prov = 1000000000000000ull; + e_out = e_out + 1; + } else if ((c_prov == 1000000000000000ull) && (e_out == 0)) { + if ((((rnd_mode & 3) == 0) && (z.w[4] <= 17524406870024074035ull)) + || ((rnd_mode + (s & 1) == 2) + && (z.w[4] <= 16602069666338596454ull))) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + } +// Check for overflow + + if (e_out > 369 + 398) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid64_ovf (s); + } +// Set the inexact flag as appropriate and check underflow +// It's no doubt superfluous to check inexactness, but anyway... + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (c_prov < 1000000000000000ull) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result + + return_bid64 (s, e_out, c_prov); +} + +#endif // matches #if __ENABLE_BINARY80__ + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +binary128_to_bid64 (UINT64 * pres, BINARY128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + BINARY128 x = *px; +#else +UINT64 +binary128_to_bid64 (BINARY128 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 c; + UINT64 c_prov; + UINT128 m_min; + UINT256 r; + UINT384 z; + + int e, s, t, e_out; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + +// Unpack the input + + unpack_binary128 (x, s, e, c.w[1], c.w[0], t, return_bid64_zero (s), + return_bid64_inf (s), return_bid64_nan); + +// Shift left 8 spaces so (c * r) >> 312 = ((c<<8) * r) >> 320 and we +// can lop off exactly 5 words + + sll128_short (c.w[1], c.w[0], 8); + +// Check for "trivial" overflow, when 2^e * 2^112 > 10^emax * 10^d. +// We actually check if e >= ceil((emax + d) * log_2(10) - 112) +// This could be intercepted later, but it's convenient to keep tables smaller + + if (e >= 1168) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid64_ovf (s); + } +// Now filter out all the exact cases where we need to specially force +// the exponent to 0. We can let through inexact cases and those where the +// main path will do the right thing anyway, e.g. integers outside coeff range. +// +// First check that e <= 0, because if e > 0, the input must be >= 2^113, +// which is too large for the coefficient of any target decimal format. +// We write a = -(e + t) +// +// (1) If e + t >= 0 <=> a <= 0 the input is an integer; treat it specially +// iff it fits in the coefficient range. Shift c' = c >> -e, and +// compare with the coefficient range; if it's in range then c' is +// our coefficient, exponent is 0. Otherwise we pass through. +// +// (2) If a > 0 then we have a non-integer input. The special case would +// arise as c' / 2^a where c' = c >> t, i.e. 10^-a * (5^a c'). Now +// if a > 48 we can immediately forget this, since 5^49 > 10^34. +// Otherwise we determine whether we're in range by a table based on +// a, and if so get the multiplier also from a table based on a. +// +// Note that when we shift, we need to take into account the fact that +// c is already 8 places to the left in preparation for the reciprocal +// multiplication; thus we add 8 to all the shift counts + + if (e <= 0) { + UINT128 cint; + int a = -(e + t); + cint.w[1] = c.w[1], cint.w[0] = c.w[0]; + if (a <= 0) { + srl128 (cint.w[1], cint.w[0], 8 - e); + if ((cint.w[1] == 0) && (cint.w[0] < 10000000000000000ull)) + return_bid64 (s, 398, cint.w[0]); + } else if (a <= 48) { + UINT128 pow5 = coefflimits_bid64[a]; + srl128 (cint.w[1], cint.w[0], 8 + t); + if (le128 (cint.w[1], cint.w[0], pow5.w[1], pow5.w[0])) { + UINT128 cc; + cc.w[1] = cint.w[1]; + cc.w[0] = cint.w[0]; + pow5 = power_five[a]; + __mul_128x128_low (cc, cc, pow5); + return_bid64 (s, 398 - a, cc.w[0]); + } + } + } +// Check for "trivial" underflow, when 2^e * 2^113 <= 10^emin * 1/4, +// so test e <= floor(emin * log_2(10) - 115) +// In this case just fix ourselves at that value for uniformity. +// +// This is important not only to keep the tables small but to maintain the +// testing of the round/sticky words as a correct rounding method + + if (e <= -1437) + e = -1437; + +// Now look up our exponent e, and the breakpoint between e and e+1 + + m_min = (breakpoints_bid64 + 1437)[e]; + e_out = (exponents_bid64 + 1437)[e]; + +// Choose exponent and reciprocal multiplier based on breakpoint + + if (le128 (c.w[1], c.w[0], m_min.w[1], m_min.w[0])) { + r = (multipliers1_bid64 + 1437)[e]; + } else { + r = (multipliers2_bid64 + 1437)[e]; + e_out = e_out + 1; + } + +// Do the reciprocal multiplication + + __mul_128x256_to_384 (z, c, r) + c_prov = z.w[5]; + +// Round using round-sticky words +// If we spill over into the next decade, correct +// Flag underflow where it may be needed even for |result| = SNN + + if (lt128 + (roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + (c_prov & 1)]. + w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov & 1)].w[0], z.w[4], z.w[3])) { + c_prov = c_prov + 1; + if (c_prov == 10000000000000000ull) { + c_prov = 1000000000000000ull; + e_out = e_out + 1; + } else if ((c_prov == 1000000000000000ull) && (e_out == 0)) { + if ((((rnd_mode & 3) == 0) && (z.w[4] <= 17524406870024074035ull)) + || ((rnd_mode + (s & 1) == 2) + && (z.w[4] <= 16602069666338596454ull))) + *pfpsf |= UNDERFLOW_EXCEPTION; + } + } +// Check for overflow + + if (e_out > 369 + 398) { + *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + return_bid64_ovf (s); + } +// Set the inexact flag as appropriate and check underflow +// It's no doubt superfluous to check inexactness, but anyway... + + if ((z.w[4] != 0) || (z.w[3] != 0)) { + *pfpsf |= INEXACT_EXCEPTION; + if (c_prov < 1000000000000000ull) + *pfpsf |= UNDERFLOW_EXCEPTION; + } +// Package up the result + + return_bid64 (s, e_out, c_prov); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +binary32_to_bid128 (UINT128 * pres, float *px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + float x = *px; +#else +UINT128 +binary32_to_bid128 (float x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 c; + UINT64 c_prov_hi, c_prov_lo; + UINT256 r; + UINT384 z; + + int e, s, t, e_out, e_plus, e_hi, e_lo, f; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + +// Unpack the input + + unpack_binary32 (x, s, e, c.w[1], t, return_bid128_zero (s), + return_bid128_inf (s), return_bid128_nan); + +// Shift up to the top: like a pure quad coefficient with a shift of 15. +// In our case, this is 2^{113-24+15} times the core, so unpack at the +// high end shifted by 40. + + c.w[0] = 0; + c.w[1] = c.w[1] << 40; + + t += (113 - 24); + e -= (113 - 24); + +// (We never need to check for overflow: this format is the biggest of all!) + +// Now filter out all the exact cases where we need to specially force +// the exponent to 0. We can let through inexact cases and those where the +// main path will do the right thing anyway, e.g. integers outside coeff range. +// +// First check that e <= 0, because if e > 0, the input must be >= 2^113, +// which is too large for the coefficient of any target decimal format. +// We write a = -(e + t) +// +// (1) If e + t >= 0 <=> a <= 0 the input is an integer; treat it specially +// iff it fits in the coefficient range. Shift c' = c >> -e, and +// compare with the coefficient range; if it's in range then c' is +// our coefficient, exponent is 0. Otherwise we pass through. +// +// (2) If a > 0 then we have a non-integer input. The special case would +// arise as c' / 2^a where c' = c >> t, i.e. 10^-a * (5^a c'). Now +// if a > 48 we can immediately forget this, since 5^49 > 10^34. +// Otherwise we determine whether we're in range by a table based on +// a, and if so get the multiplier also from a table based on a. +// +// Note that when we shift, we need to take into account the fact that +// c is already 15 places to the left in preparation for the reciprocal +// multiplication; thus we add 15 to all the shift counts + + if (e <= 0) { + UINT128 cint; + int a = -(e + t); + cint.w[1] = c.w[1], cint.w[0] = c.w[0]; + if (a <= 0) { + srl128 (cint.w[1], cint.w[0], 15 - e); + if (lt128 (cint.w[1], cint.w[0], + 542101086242752ull, 4003012203950112768ull)) + return_bid128 (s, 6176, cint.w[1], cint.w[0]); + } else if (a <= 48) { + UINT128 pow5 = coefflimits_bid128[a]; + srl128 (cint.w[1], cint.w[0], 15 + t); + if (le128 (cint.w[1], cint.w[0], pow5.w[1], pow5.w[0])) { + UINT128 cc; + cc.w[1] = cint.w[1]; + cc.w[0] = cint.w[0]; + pow5 = power_five[a]; + __mul_128x128_low (cc, cc, pow5); + return_bid128 (s, 6176 - a, cc.w[1], cc.w[0]); + } + } + } +// Input exponent can stretch between the maximal and minimal +// exponents (remembering we force normalization): -16607 <= e <= 16271 + +// Compute the estimated decimal exponent e_out; the provisional exponent +// will be either "e_out" or "e_out-1" depending on later significand check +// NB: this is the *biased* exponent + + e_plus = e + 42152; + e_out = (((19728 * e_plus) + ((19779 * e_plus) >> 16)) >> 16) - 6512; + +// Set up pointers into the bipartite table + + e_hi = 11232 - e_out; + e_lo = e_hi & 127; + e_hi = e_hi >> 7; + +// Look up the inner entry first + + r = innertable_sig[e_lo], f = innertable_exp[e_lo]; + +// If we need the other entry, multiply significands and add exponents + + if (e_hi != 39) { + UINT256 s = outertable_sig[e_hi]; + UINT512 t; + f = f + 256 + outertable_exp[e_hi]; + __mul_256x256_to_512 (t, r, s); + r.w[0] = t.w[4] + 1, r.w[1] = t.w[5], + r.w[2] = t.w[6], r.w[3] = t.w[7]; + } + + __mul_128x256_to_384 (z, c, r); + +// Make adjustive shift, ignoring the lower 128 bits + + e = -(241 + e + f); + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], e); + +// Now test against 10^33 and so decide on adjustment +// I feel there ought to be a smarter way of doing the multiplication + + if (lt128 (z.w[5], z.w[4], 54210108624275ull, 4089650035136921600ull)) { + __mul_10x256_to_256 (z.w[5], z.w[4], z.w[3], z.w[2], z.w[5], z.w[4], + z.w[3], z.w[2]); + e_out = e_out - 1; + } +// Set up provisional results + + c_prov_hi = z.w[5]; + c_prov_lo = z.w[4]; + +// Round using round-sticky words +// If we spill over into the next decade, correct + + if (lt128 + (roundbound_128 + [(rnd_mode << 2) + ((s & 1) << 1) + (c_prov_lo & 1)].w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov_lo & 1)].w[0], z.w[3], z.w[2])) { + c_prov_lo = c_prov_lo + 1; + if (c_prov_lo == 0) + c_prov_hi = c_prov_hi + 1; + else if ((c_prov_lo == 4003012203950112768ull) && + (c_prov_hi == 542101086242752ull)) { + c_prov_hi = 54210108624275ull; + c_prov_lo = 4089650035136921600ull; + e_out = e_out + 1; + } + } +// Don't need to check overflow or underflow; however set inexact flag + + if ((z.w[3] != 0) || (z.w[2] != 0)) + *pfpsf |= INEXACT_EXCEPTION; + +// Package up the result + + return_bid128 (s, e_out, c_prov_hi, c_prov_lo); +} + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +binary64_to_bid128 (UINT128 * pres, double *px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + double x = *px; +#else +UINT128 +binary64_to_bid128 (double x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 c; + UINT64 c_prov_hi, c_prov_lo; + UINT256 r; + UINT384 z; + + int e, s, t, e_out, e_plus, e_hi, e_lo, f; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + +// Unpack the input + + unpack_binary64 (x, s, e, c.w[1], t, return_bid128_zero (s), + return_bid128_inf (s), return_bid128_nan); + +// Shift up to the top: like a pure quad coefficient with a shift of 15. +// In our case, this is 2^{113-53+15} times the core, so unpack at the +// high end shifted by 11. + + c.w[0] = 0; + c.w[1] = c.w[1] << 11; + + t += (113 - 53); + e -= (113 - 53); + +// (We never need to check for overflow: this format is the biggest of all!) + +// Now filter out all the exact cases where we need to specially force +// the exponent to 0. We can let through inexact cases and those where the +// main path will do the right thing anyway, e.g. integers outside coeff range. +// +// First check that e <= 0, because if e > 0, the input must be >= 2^113, +// which is too large for the coefficient of any target decimal format. +// We write a = -(e + t) +// +// (1) If e + t >= 0 <=> a <= 0 the input is an integer; treat it specially +// iff it fits in the coefficient range. Shift c' = c >> -e, and +// compare with the coefficient range; if it's in range then c' is +// our coefficient, exponent is 0. Otherwise we pass through. +// +// (2) If a > 0 then we have a non-integer input. The special case would +// arise as c' / 2^a where c' = c >> t, i.e. 10^-a * (5^a c'). Now +// if a > 48 we can immediately forget this, since 5^49 > 10^34. +// Otherwise we determine whether we're in range by a table based on +// a, and if so get the multiplier also from a table based on a. +// +// Note that when we shift, we need to take into account the fact that +// c is already 15 places to the left in preparation for the reciprocal +// multiplication; thus we add 15 to all the shift counts + + if (e <= 0) { + UINT128 cint; + int a = -(e + t); + cint.w[1] = c.w[1], cint.w[0] = c.w[0]; + if (a <= 0) { + srl128 (cint.w[1], cint.w[0], 15 - e); + if (lt128 (cint.w[1], cint.w[0], + 542101086242752ull, 4003012203950112768ull)) + return_bid128 (s, 6176, cint.w[1], cint.w[0]); + } else if (a <= 48) { + UINT128 pow5 = coefflimits_bid128[a]; + srl128 (cint.w[1], cint.w[0], 15 + t); + if (le128 (cint.w[1], cint.w[0], pow5.w[1], pow5.w[0])) { + UINT128 cc; + cc.w[1] = cint.w[1]; + cc.w[0] = cint.w[0]; + pow5 = power_five[a]; + __mul_128x128_low (cc, cc, pow5); + return_bid128 (s, 6176 - a, cc.w[1], cc.w[0]); + } + } + } +// Input exponent can stretch between the maximal and minimal +// exponents (remembering we force normalization): -16607 <= e <= 16271 + +// Compute the estimated decimal exponent e_out; the provisional exponent +// will be either "e_out" or "e_out-1" depending on later significand check +// NB: this is the *biased* exponent + + e_plus = e + 42152; + e_out = (((19728 * e_plus) + ((19779 * e_plus) >> 16)) >> 16) - 6512; + +// Set up pointers into the bipartite table + + e_hi = 11232 - e_out; + e_lo = e_hi & 127; + e_hi = e_hi >> 7; + +// Look up the inner entry first + + r = innertable_sig[e_lo], f = innertable_exp[e_lo]; + +// If we need the other entry, multiply significands and add exponents + + if (e_hi != 39) { + UINT256 s = outertable_sig[e_hi]; + UINT512 t; + f = f + 256 + outertable_exp[e_hi]; + __mul_256x256_to_512 (t, r, s); + r.w[0] = t.w[4] + 1, r.w[1] = t.w[5], + r.w[2] = t.w[6], r.w[3] = t.w[7]; + } + + __mul_128x256_to_384 (z, c, r); + +// Make adjustive shift, ignoring the lower 128 bits + + e = -(241 + e + f); + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], e); + +// Now test against 10^33 and so decide on adjustment +// I feel there ought to be a smarter way of doing the multiplication + + if (lt128 (z.w[5], z.w[4], 54210108624275ull, 4089650035136921600ull)) { + __mul_10x256_to_256 (z.w[5], z.w[4], z.w[3], z.w[2], z.w[5], z.w[4], + z.w[3], z.w[2]); + e_out = e_out - 1; + } +// Set up provisional results + + c_prov_hi = z.w[5]; + c_prov_lo = z.w[4]; + +// Round using round-sticky words +// If we spill over into the next decade, correct + + if (lt128 + (roundbound_128 + [(rnd_mode << 2) + ((s & 1) << 1) + (c_prov_lo & 1)].w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov_lo & 1)].w[0], z.w[3], z.w[2])) { + c_prov_lo = c_prov_lo + 1; + if (c_prov_lo == 0) + c_prov_hi = c_prov_hi + 1; + else if ((c_prov_lo == 4003012203950112768ull) && + (c_prov_hi == 542101086242752ull)) { + c_prov_hi = 54210108624275ull; + c_prov_lo = 4089650035136921600ull; + e_out = e_out + 1; + } + } +// Don't need to check overflow or underflow; however set inexact flag + + if ((z.w[3] != 0) || (z.w[2] != 0)) + *pfpsf |= INEXACT_EXCEPTION; + +// Package up the result + + return_bid128 (s, e_out, c_prov_hi, c_prov_lo); +} + +// ********************************************************************** + +#if __ENABLE_BINARY80__ + +#if DECIMAL_CALL_BY_REFERENCE +void +binary80_to_bid128 (UINT128 * pres, BINARY80 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + BINARY80 x = *px; +#else +UINT128 +binary80_to_bid128 (BINARY80 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 c; + UINT64 c_prov_hi, c_prov_lo; + UINT256 r; + UINT384 z; + + int e, s, t, e_out, e_plus, e_hi, e_lo, f; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + +// Unpack the input + + unpack_binary80 (x, s, e, c.w[1], t, return_bid128_zero (s), + return_bid128_inf (s), return_bid128_nan); + +// Treat like a pure quad coefficient with a shift of 15. We get this +// just by unpacking at the high end + + c.w[0] = 0; + + t += (113 - 64); + e -= (113 - 64); + +// (We never need to check for overflow: this format is the biggest of all!) + +// Now filter out all the exact cases where we need to specially force +// the exponent to 0. We can let through inexact cases and those where the +// main path will do the right thing anyway, e.g. integers outside coeff range. +// +// First check that e <= 0, because if e > 0, the input must be >= 2^113, +// which is too large for the coefficient of any target decimal format. +// We write a = -(e + t) +// +// (1) If e + t >= 0 <=> a <= 0 the input is an integer; treat it specially +// iff it fits in the coefficient range. Shift c' = c >> -e, and +// compare with the coefficient range; if it's in range then c' is +// our coefficient, exponent is 0. Otherwise we pass through. +// +// (2) If a > 0 then we have a non-integer input. The special case would +// arise as c' / 2^a where c' = c >> t, i.e. 10^-a * (5^a c'). Now +// if a > 48 we can immediately forget this, since 5^49 > 10^34. +// Otherwise we determine whether we're in range by a table based on +// a, and if so get the multiplier also from a table based on a. +// +// Note that when we shift, we need to take into account the fact that +// c is already 15 places to the left in preparation for the reciprocal +// multiplication; thus we add 15 to all the shift counts + + if (e <= 0) { + UINT128 cint; + int a = -(e + t); + cint.w[1] = c.w[1], cint.w[0] = c.w[0]; + if (a <= 0) { + srl128 (cint.w[1], cint.w[0], 15 - e); + if (lt128 (cint.w[1], cint.w[0], + 542101086242752ull, 4003012203950112768ull)) + return_bid128 (s, 6176, cint.w[1], cint.w[0]); + } else if (a <= 48) { + UINT128 pow5 = coefflimits_bid128[a]; + srl128 (cint.w[1], cint.w[0], 15 + t); + if (le128 (cint.w[1], cint.w[0], pow5.w[1], pow5.w[0])) { + UINT128 cc; + cc.w[1] = cint.w[1]; + cc.w[0] = cint.w[0]; + pow5 = power_five[a]; + __mul_128x128_low (cc, cc, pow5); + return_bid128 (s, 6176 - a, cc.w[1], cc.w[0]); + } + } + } +// Input exponent can stretch between the maximal and minimal +// exponents (remembering we force normalization): -16607 <= e <= 16271 + +// Compute the estimated decimal exponent e_out; the provisional exponent +// will be either "e_out" or "e_out-1" depending on later significand check +// NB: this is the *biased* exponent + + e_plus = e + 42152; + e_out = (((19728 * e_plus) + ((19779 * e_plus) >> 16)) >> 16) - 6512; + +// Set up pointers into the bipartite table + + e_hi = 11232 - e_out; + e_lo = e_hi & 127; + e_hi = e_hi >> 7; + +// Look up the inner entry first + + r = innertable_sig[e_lo], f = innertable_exp[e_lo]; + +// If we need the other entry, multiply significands and add exponents + + if (e_hi != 39) { + UINT256 s = outertable_sig[e_hi]; + UINT512 t; + f = f + 256 + outertable_exp[e_hi]; + __mul_256x256_to_512 (t, r, s); + r.w[0] = t.w[4] + 1, r.w[1] = t.w[5], + r.w[2] = t.w[6], r.w[3] = t.w[7]; + } + + __mul_128x256_to_384 (z, c, r); + +// Make adjustive shift, ignoring the lower 128 bits + + e = -(241 + e + f); + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], e); + +// Now test against 10^33 and so decide on adjustment +// I feel there ought to be a smarter way of doing the multiplication + + if (lt128 (z.w[5], z.w[4], 54210108624275ull, 4089650035136921600ull)) { + __mul_10x256_to_256 (z.w[5], z.w[4], z.w[3], z.w[2], z.w[5], z.w[4], + z.w[3], z.w[2]); + e_out = e_out - 1; + } +// Set up provisional results + + c_prov_hi = z.w[5]; + c_prov_lo = z.w[4]; + +// Round using round-sticky words +// If we spill over into the next decade, correct + + if (lt128 + (roundbound_128 + [(rnd_mode << 2) + ((s & 1) << 1) + (c_prov_lo & 1)].w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov_lo & 1)].w[0], z.w[3], z.w[2])) { + c_prov_lo = c_prov_lo + 1; + if (c_prov_lo == 0) + c_prov_hi = c_prov_hi + 1; + else if ((c_prov_lo == 4003012203950112768ull) && + (c_prov_hi == 542101086242752ull)) { + c_prov_hi = 54210108624275ull; + c_prov_lo = 4089650035136921600ull; + e_out = e_out + 1; + } + } +// Don't need to check overflow or underflow; however set inexact flag + + if ((z.w[3] != 0) || (z.w[2] != 0)) + *pfpsf |= INEXACT_EXCEPTION; + +// Package up the result + + return_bid128 (s, e_out, c_prov_hi, c_prov_lo); +} + +#endif // matches #if __ENABLE_BINARY80__ + +// ********************************************************************** + +#if DECIMAL_CALL_BY_REFERENCE +void +binary128_to_bid128 (UINT128 * pres, BINARY128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + BINARY128 x = *px; +#else +UINT128 +binary128_to_bid128 (BINARY128 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT128 c; + UINT64 c_prov_hi, c_prov_lo; + UINT256 r; + UINT384 z; + + int e, s, t, e_out, e_plus, e_hi, e_lo, f; + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round rnd_mode = *prnd_mode; +#endif +#endif + +// Unpack the input + + unpack_binary128 (x, s, e, c.w[1], c.w[0], t, return_bid128_zero (s), + return_bid128_inf (s), return_bid128_nan); + +// Shift up 15 places to move to the top + + sll128_short (c.w[1], c.w[0], 15); + +// (We never need to check for overflow: this format is the biggest of all!) + +// Now filter out all the exact cases where we need to specially force +// the exponent to 0. We can let through inexact cases and those where the +// main path will do the right thing anyway, e.g. integers outside coeff range. +// +// First check that e <= 0, because if e > 0, the input must be >= 2^113, +// which is too large for the coefficient of any target decimal format. +// We write a = -(e + t) +// +// (1) If e + t >= 0 <=> a <= 0 the input is an integer; treat it specially +// iff it fits in the coefficient range. Shift c' = c >> -e, and +// compare with the coefficient range; if it's in range then c' is +// our coefficient, exponent is 0. Otherwise we pass through. +// +// (2) If a > 0 then we have a non-integer input. The special case would +// arise as c' / 2^a where c' = c >> t, i.e. 10^-a * (5^a c'). Now +// if a > 48 we can immediately forget this, since 5^49 > 10^34. +// Otherwise we determine whether we're in range by a table based on +// a, and if so get the multiplier also from a table based on a. +// +// Note that when we shift, we need to take into account the fact that +// c is already 15 places to the left in preparation for the reciprocal +// multiplication; thus we add 15 to all the shift counts + + if (e <= 0) { + UINT128 cint; + int a = -(e + t); + cint.w[1] = c.w[1], cint.w[0] = c.w[0]; + if (a <= 0) { + srl128 (cint.w[1], cint.w[0], 15 - e); + if (lt128 (cint.w[1], cint.w[0], + 542101086242752ull, 4003012203950112768ull)) + return_bid128 (s, 6176, cint.w[1], cint.w[0]); + } else if (a <= 48) { + UINT128 pow5 = coefflimits_bid128[a]; + srl128 (cint.w[1], cint.w[0], 15 + t); + if (le128 (cint.w[1], cint.w[0], pow5.w[1], pow5.w[0])) { + UINT128 cc; + cc.w[1] = cint.w[1]; + cc.w[0] = cint.w[0]; + pow5 = power_five[a]; + __mul_128x128_low (cc, cc, pow5); + return_bid128 (s, 6176 - a, cc.w[1], cc.w[0]); + } + } + } +// Input exponent can stretch between the maximal and minimal +// exponents (remembering we force normalization): -16607 <= e <= 16271 + +// Compute the estimated decimal exponent e_out; the provisional exponent +// will be either "e_out" or "e_out-1" depending on later significand check +// NB: this is the *biased* exponent + + e_plus = e + 42152; + e_out = (((19728 * e_plus) + ((19779 * e_plus) >> 16)) >> 16) - 6512; + +// Set up pointers into the bipartite table + + e_hi = 11232 - e_out; + e_lo = e_hi & 127; + e_hi = e_hi >> 7; + +// Look up the inner entry first + + r = innertable_sig[e_lo], f = innertable_exp[e_lo]; + +// If we need the other entry, multiply significands and add exponents + + if (e_hi != 39) { + UINT256 s = outertable_sig[e_hi]; + UINT512 t; + f = f + 256 + outertable_exp[e_hi]; + __mul_256x256_to_512 (t, r, s); + // *** NB I should run an exhaustive check this +1 doesn't overflow + r.w[0] = t.w[4] + 1, r.w[1] = t.w[5], + r.w[2] = t.w[6], r.w[3] = t.w[7]; + } + + __mul_128x256_to_384 (z, c, r); + +// Make adjustive shift, ignoring the lower 128 bits + + e = -(241 + e + f); + srl256 (z.w[5], z.w[4], z.w[3], z.w[2], e); + +// Now test against 10^33 and so decide on adjustment +// I feel there ought to be a smarter way of doing the multiplication + + if (lt128 (z.w[5], z.w[4], 54210108624275ull, 4089650035136921600ull)) { + __mul_10x256_to_256 (z.w[5], z.w[4], z.w[3], z.w[2], z.w[5], z.w[4], + z.w[3], z.w[2]); + e_out = e_out - 1; + } +// Set up provisional results + + c_prov_hi = z.w[5]; + c_prov_lo = z.w[4]; + +// Round using round-sticky words +// If we spill over into the next decade, correct + + if (lt128 + (roundbound_128 + [(rnd_mode << 2) + ((s & 1) << 1) + (c_prov_lo & 1)].w[1], + roundbound_128[(rnd_mode << 2) + ((s & 1) << 1) + + (c_prov_lo & 1)].w[0], z.w[3], z.w[2])) { + c_prov_lo = c_prov_lo + 1; + if (c_prov_lo == 0) + c_prov_hi = c_prov_hi + 1; + else if ((c_prov_lo == 4003012203950112768ull) && + (c_prov_hi == 542101086242752ull)) { + c_prov_hi = 54210108624275ull; + c_prov_lo = 4089650035136921600ull; + e_out = e_out + 1; + } + } +// Don't need to check overflow or underflow; however set inexact flag + + if ((z.w[3] != 0) || (z.w[2] != 0)) + *pfpsf |= INEXACT_EXCEPTION; + +// Package up the result + + return_bid128 (s, e_out, c_prov_hi, c_prov_lo); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_conf.h b/gcc-4.4.3/libgcc/config/libbid/bid_conf.h new file mode 100644 index 000000000..d22980d9d --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_conf.h @@ -0,0 +1,1171 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#ifndef _BID_CONF_H +#define _BID_CONF_H + +// Name Changes + +#define _IDEC_glbflags __bid_IDEC_glbflags +#define _IDEC_glbround __bid_IDEC_glbround +#define _IDEC_glbexcepthandling __bid_IDEC_glbexcepthandling +#define _IDEC_glbexceptionmasks __bid_IDEC_glbexceptionmasks +#define bid64_add __bid64_add +#define bid64_sub __bid64_sub +#define bid64_mul __bid64_mul +#define bid64_div __bid64_div +#define bid64dq_div __bid64dq_div +#define bid64qd_div __bid64qd_div +#define bid64qq_div __bid64qq_div +#define bid64q_sqrt __bid64q_sqrt +#define bid64_sqrt __bid64_sqrt +#define bid64_rem __bid64_rem +#define bid64_fma __bid64_fma +#define bid64_scalb __bid64_scalb +#define round128_19_38 __bid_round128_19_38 +#define round192_39_57 __bid_round192_39_57 +#define round256_58_76 __bid_round256_58_76 +#define round64_2_18 __bid_round64_2_18 +#define bid64_nextafter __bid64_nextafter +#define bid64_nextdown __bid64_nextdown +#define bid64_nextup __bid64_nextup +#define b2d __bid_b2d +#define b2d2 __bid_b2d2 +#define b2d3 __bid_b2d3 +#define b2d4 __bid_b2d4 +#define b2d5 __bid_b2d5 +#define bid128_canonize __bid128_canonize +#define bid32_canonize __bid32_canonize +#define bid64_canonize __bid64_canonize +#define bid_to_bid128 __bid_to_bid128 +#define bid_to_bid32 __bid_to_bid32 +#define bid_to_bid64 __bid_to_bid64 +#define bid_to_dpd128 __bid_to_dpd128 +#define bid_to_dpd32 __bid_to_dpd32 +#define bid_to_dpd64 __bid_to_dpd64 +#define d2b __bid_d2b +#define d2b2 __bid_d2b2 +#define d2b3 __bid_d2b3 +#define d2b4 __bid_d2b4 +#define d2b5 __bid_d2b5 +#define d2b6 __bid_d2b6 +#define dpd_to_bid128 __bid_dpd_to_bid128 +#define dpd_to_bid32 __bid_dpd_to_bid32 +#define dpd_to_bid64 __bid_dpd_to_bid64 +#define bid128_nextafter __bid128_nextafter +#define bid128_nextdown __bid128_nextdown +#define bid128_nextup __bid128_nextup +#define bid64_logb __bid64_logb +#define bid64_quantize __bid64_quantize +#define estimate_bin_expon __bid_estimate_bin_expon +#define estimate_decimal_digits __bid_estimate_decimal_digits +#define power10_index_binexp __bid_power10_index_binexp +#define power10_index_binexp_128 __bid_power10_index_binexp_128 +#define power10_table_128 __bid_power10_table_128 +#define reciprocals10_128 __bid_reciprocals10_128 +#define reciprocals10_64 __bid_reciprocals10_64 +#define recip_scale __bid_recip_scale +#define round_const_table __bid_round_const_table +#define round_const_table_128 __bid_round_const_table_128 +#define short_recip_scale __bid_short_recip_scale +#define bid64_from_string __bid64_from_string +#define bid64_to_string __bid64_to_string +#define Inv_Tento9 __bid_Inv_Tento9 +#define midi_tbl __bid_midi_tbl +#define Tento3 __bid_Tento3 +#define Tento6 __bid_Tento6 +#define Tento9 __bid_Tento9 +#define Twoto30_m_10to9 __bid_Twoto30_m_10to9 +#define Twoto60 __bid_Twoto60 +#define Twoto60_m_10to18 __bid_Twoto60_m_10to18 +#define convert_table __bid_convert_table +#define factors __bid_factors +#define packed_10000_zeros __bid_packed_10000_zeros +#define char_table2 __bid_char_table2 +#define char_table3 __bid_char_table3 +#define Ex128m128 __bid_Ex128m128 +#define Ex192m192 __bid_Ex192m192 +#define Ex256m256 __bid_Ex256m256 +#define Ex64m64 __bid_Ex64m64 +#define half128 __bid_half128 +#define half192 __bid_half192 +#define half256 __bid_half256 +#define half64 __bid_half64 +#define Kx128 __bid_Kx128 +#define Kx192 __bid_Kx192 +#define Kx256 __bid_Kx256 +#define Kx64 __bid_Kx64 +#define mask128 __bid_mask128 +#define mask192 __bid_mask192 +#define mask256 __bid_mask256 +#define mask64 __bid_mask64 +#define maskhigh128 __bid_maskhigh128 +#define maskhigh128M __bid_maskhigh128M +#define maskhigh192M __bid_maskhigh192M +#define maskhigh256M __bid_maskhigh256M +#define midpoint128 __bid_midpoint128 +#define midpoint192 __bid_midpoint192 +#define midpoint256 __bid_midpoint256 +#define midpoint64 __bid_midpoint64 +#define nr_digits __bid_nr_digits +#define onehalf128 __bid_onehalf128 +#define onehalf128M __bid_onehalf128M +#define onehalf192M __bid_onehalf192M +#define onehalf256M __bid_onehalf256M +#define shiftright128 __bid_shiftright128 +#define shiftright128M __bid_shiftright128M +#define shiftright192M __bid_shiftright192M +#define shiftright256M __bid_shiftright256M +#define shift_ten2m3k128 __bid_shift_ten2m3k128 +#define shift_ten2m3k64 __bid_shift_ten2m3k64 +#define ten2k128 __bid_ten2k128 +#define ten2k256 __bid_ten2k256 +#define ten2k64 __bid_ten2k64 +#define ten2m3k128 __bid_ten2m3k128 +#define ten2m3k64 __bid_ten2m3k64 +#define ten2mk128 __bid_ten2mk128 +#define ten2mk128M __bid_ten2mk128M +#define ten2mk128trunc __bid_ten2mk128trunc +#define ten2mk128truncM __bid_ten2mk128truncM +#define ten2mk192M __bid_ten2mk192M +#define ten2mk192truncM __bid_ten2mk192truncM +#define ten2mk256M __bid_ten2mk256M +#define ten2mk256truncM __bid_ten2mk256truncM +#define ten2mk64 __bid_ten2mk64 +#define ten2mxtrunc128 __bid_ten2mxtrunc128 +#define ten2mxtrunc192 __bid_ten2mxtrunc192 +#define ten2mxtrunc256 __bid_ten2mxtrunc256 +#define ten2mxtrunc64 __bid_ten2mxtrunc64 +#define bid128_add __bid128_add +#define bid128dd_add __bid128dd_add +#define bid128dd_sub __bid128dd_sub +#define bid128dq_add __bid128dq_add +#define bid128dq_sub __bid128dq_sub +#define bid128qd_add __bid128qd_add +#define bid128qd_sub __bid128qd_sub +#define bid128_sub __bid128_sub +#define bid64dq_add __bid64dq_add +#define bid64dq_sub __bid64dq_sub +#define bid64qd_add __bid64qd_add +#define bid64qd_sub __bid64qd_sub +#define bid64qq_add __bid64qq_add +#define bid64qq_sub __bid64qq_sub +#define bid128dd_mul __bid128dd_mul +#define bid128dq_mul __bid128dq_mul +#define bid128_mul __bid128_mul +#define bid128qd_mul __bid128qd_mul +#define bid64dq_mul __bid64dq_mul +#define bid64qd_mul __bid64qd_mul +#define bid64qq_mul __bid64qq_mul +#define bid128dd_div __bid128dd_div +#define bid128_div __bid128_div +#define bid128dq_div __bid128dq_div +#define bid128qd_div __bid128qd_div +#define bid128d_sqrt __bid128d_sqrt +#define bid128_sqrt __bid128_sqrt +#define bid128ddd_fma __bid128ddd_fma +#define bid128ddq_fma __bid128ddq_fma +#define bid128dqd_fma __bid128dqd_fma +#define bid128dqq_fma __bid128dqq_fma +#define bid128_fma __bid128_fma +#define bid128qdd_fma __bid128qdd_fma +#define bid128qdq_fma __bid128qdq_fma +#define bid128qqd_fma __bid128qqd_fma +#define bid64ddq_fma __bid64ddq_fma +#define bid64dqd_fma __bid64dqd_fma +#define bid64dqq_fma __bid64dqq_fma +#define bid64qdd_fma __bid64qdd_fma +#define bid64qdq_fma __bid64qdq_fma +#define bid64qqd_fma __bid64qqd_fma +#define bid64qqq_fma __bid64qqq_fma +#define bid128_round_integral_exact __bid128_round_integral_exact +#define bid128_round_integral_nearest_away __bid128_round_integral_nearest_away +#define bid128_round_integral_nearest_even __bid128_round_integral_nearest_even +#define bid128_round_integral_negative __bid128_round_integral_negative +#define bid128_round_integral_positive __bid128_round_integral_positive +#define bid128_round_integral_zero __bid128_round_integral_zero +#define bid64_round_integral_exact __bid64_round_integral_exact +#define bid64_round_integral_nearest_away __bid64_round_integral_nearest_away +#define bid64_round_integral_nearest_even __bid64_round_integral_nearest_even +#define bid64_round_integral_negative __bid64_round_integral_negative +#define bid64_round_integral_positive __bid64_round_integral_positive +#define bid64_round_integral_zero __bid64_round_integral_zero +#define bid128_quantize __bid128_quantize +#define bid128_scalb __bid128_scalb +#define bid64_maxnum __bid64_maxnum +#define bid64_maxnum_mag __bid64_maxnum_mag +#define bid64_minnum __bid64_minnum +#define bid64_minnum_mag __bid64_minnum_mag +#define bid128_maxnum __bid128_maxnum +#define bid128_maxnum_mag __bid128_maxnum_mag +#define bid128_minnum __bid128_minnum +#define bid128_minnum_mag __bid128_minnum_mag +#define bid128_rem __bid128_rem +#define bid128_logb __bid128_logb +#define getDecimalRoundingDirection __bid_getDecimalRoundingDirection +#define is754 __bid_is754 +#define is754R __bid_is754R +#define signalException __bid_signalException +#define lowerFlags __bid_lowerFlags +#define restoreFlags __bid_restoreFlags +#define saveFlags __bid_saveFlags +#define setDecimalRoundingDirection __bid_setDecimalRoundingDirection +#define testFlags __bid_testFlags +#define testSavedFlags __bid_testSavedFlags +#define bid32_to_bid64 __bid32_to_bid64 +#define bid64_to_bid32 __bid64_to_bid32 +#define bid128_to_string __bid128_to_string +#define mod10_18_tbl __bid_mod10_18_tbl +#define bid128_to_bid32 __bid128_to_bid32 +#define bid32_to_bid128 __bid32_to_bid128 +#define bid128_to_bid64 __bid128_to_bid64 +#define bid64_to_bid128 __bid64_to_bid128 +#define bid128_from_string __bid128_from_string +#define bid128_from_int32 __bid128_from_int32 +#define bid128_from_int64 __bid128_from_int64 +#define bid128_from_uint32 __bid128_from_uint32 +#define bid128_from_uint64 __bid128_from_uint64 +#define bid64_from_int32 __bid64_from_int32 +#define bid64_from_int64 __bid64_from_int64 +#define bid64_from_uint32 __bid64_from_uint32 +#define bid64_from_uint64 __bid64_from_uint64 +#define bid64_abs __bid64_abs +#define bid64_class __bid64_class +#define bid64_copy __bid64_copy +#define bid64_copySign __bid64_copySign +#define bid64_isCanonical __bid64_isCanonical +#define bid64_isFinite __bid64_isFinite +#define bid64_isInf __bid64_isInf +#define bid64_isNaN __bid64_isNaN +#define bid64_isNormal __bid64_isNormal +#define bid64_isSignaling __bid64_isSignaling +#define bid64_isSigned __bid64_isSigned +#define bid64_isSubnormal __bid64_isSubnormal +#define bid64_isZero __bid64_isZero +#define bid64_negate __bid64_negate +#define bid64_radix __bid64_radix +#define bid64_sameQuantum __bid64_sameQuantum +#define bid64_totalOrder __bid64_totalOrder +#define bid64_totalOrderMag __bid64_totalOrderMag +#define bid128_abs __bid128_abs +#define bid128_class __bid128_class +#define bid128_copy __bid128_copy +#define bid128_copySign __bid128_copySign +#define bid128_isCanonical __bid128_isCanonical +#define bid128_isFinite __bid128_isFinite +#define bid128_isInf __bid128_isInf +#define bid128_isNaN __bid128_isNaN +#define bid128_isNormal __bid128_isNormal +#define bid128_isSignaling __bid128_isSignaling +#define bid128_isSigned __bid128_isSigned +#define bid128_isSubnormal __bid128_isSubnormal +#define bid128_isZero __bid128_isZero +#define bid128_negate __bid128_negate +#define bid128_radix __bid128_radix +#define bid128_sameQuantum __bid128_sameQuantum +#define bid128_totalOrder __bid128_totalOrder +#define bid128_totalOrderMag __bid128_totalOrderMag +#define bid64_quiet_equal __bid64_quiet_equal +#define bid64_quiet_greater __bid64_quiet_greater +#define bid64_quiet_greater_equal __bid64_quiet_greater_equal +#define bid64_quiet_greater_unordered __bid64_quiet_greater_unordered +#define bid64_quiet_less __bid64_quiet_less +#define bid64_quiet_less_equal __bid64_quiet_less_equal +#define bid64_quiet_less_unordered __bid64_quiet_less_unordered +#define bid64_quiet_not_equal __bid64_quiet_not_equal +#define bid64_quiet_not_greater __bid64_quiet_not_greater +#define bid64_quiet_not_less __bid64_quiet_not_less +#define bid64_quiet_ordered __bid64_quiet_ordered +#define bid64_quiet_unordered __bid64_quiet_unordered +#define bid64_signaling_greater __bid64_signaling_greater +#define bid64_signaling_greater_equal __bid64_signaling_greater_equal +#define bid64_signaling_greater_unordered __bid64_signaling_greater_unordered +#define bid64_signaling_less __bid64_signaling_less +#define bid64_signaling_less_equal __bid64_signaling_less_equal +#define bid64_signaling_less_unordered __bid64_signaling_less_unordered +#define bid64_signaling_not_greater __bid64_signaling_not_greater +#define bid64_signaling_not_less __bid64_signaling_not_less +#define bid128_quiet_equal __bid128_quiet_equal +#define bid128_quiet_greater __bid128_quiet_greater +#define bid128_quiet_greater_equal __bid128_quiet_greater_equal +#define bid128_quiet_greater_unordered __bid128_quiet_greater_unordered +#define bid128_quiet_less __bid128_quiet_less +#define bid128_quiet_less_equal __bid128_quiet_less_equal +#define bid128_quiet_less_unordered __bid128_quiet_less_unordered +#define bid128_quiet_not_equal __bid128_quiet_not_equal +#define bid128_quiet_not_greater __bid128_quiet_not_greater +#define bid128_quiet_not_less __bid128_quiet_not_less +#define bid128_quiet_ordered __bid128_quiet_ordered +#define bid128_quiet_unordered __bid128_quiet_unordered +#define bid128_signaling_greater __bid128_signaling_greater +#define bid128_signaling_greater_equal __bid128_signaling_greater_equal +#define bid128_signaling_greater_unordered __bid128_signaling_greater_unordered +#define bid128_signaling_less __bid128_signaling_less +#define bid128_signaling_less_equal __bid128_signaling_less_equal +#define bid128_signaling_less_unordered __bid128_signaling_less_unordered +#define bid128_signaling_not_greater __bid128_signaling_not_greater +#define bid128_signaling_not_less __bid128_signaling_not_less +#define bid64_to_int32_ceil __bid64_to_int32_ceil +#define bid64_to_int32_floor __bid64_to_int32_floor +#define bid64_to_int32_int __bid64_to_int32_int +#define bid64_to_int32_rnint __bid64_to_int32_rnint +#define bid64_to_int32_rninta __bid64_to_int32_rninta +#define bid64_to_int32_xceil __bid64_to_int32_xceil +#define bid64_to_int32_xfloor __bid64_to_int32_xfloor +#define bid64_to_int32_xint __bid64_to_int32_xint +#define bid64_to_int32_xrnint __bid64_to_int32_xrnint +#define bid64_to_int32_xrninta __bid64_to_int32_xrninta +#define bid64_to_uint32_ceil __bid64_to_uint32_ceil +#define bid64_to_uint32_floor __bid64_to_uint32_floor +#define bid64_to_uint32_int __bid64_to_uint32_int +#define bid64_to_uint32_rnint __bid64_to_uint32_rnint +#define bid64_to_uint32_rninta __bid64_to_uint32_rninta +#define bid64_to_uint32_xceil __bid64_to_uint32_xceil +#define bid64_to_uint32_xfloor __bid64_to_uint32_xfloor +#define bid64_to_uint32_xint __bid64_to_uint32_xint +#define bid64_to_uint32_xrnint __bid64_to_uint32_xrnint +#define bid64_to_uint32_xrninta __bid64_to_uint32_xrninta +#define bid64_to_int64_ceil __bid64_to_int64_ceil +#define bid64_to_int64_floor __bid64_to_int64_floor +#define bid64_to_int64_int __bid64_to_int64_int +#define bid64_to_int64_rnint __bid64_to_int64_rnint +#define bid64_to_int64_rninta __bid64_to_int64_rninta +#define bid64_to_int64_xceil __bid64_to_int64_xceil +#define bid64_to_int64_xfloor __bid64_to_int64_xfloor +#define bid64_to_int64_xint __bid64_to_int64_xint +#define bid64_to_int64_xrnint __bid64_to_int64_xrnint +#define bid64_to_int64_xrninta __bid64_to_int64_xrninta +#define bid64_to_uint64_ceil __bid64_to_uint64_ceil +#define bid64_to_uint64_floor __bid64_to_uint64_floor +#define bid64_to_uint64_int __bid64_to_uint64_int +#define bid64_to_uint64_rnint __bid64_to_uint64_rnint +#define bid64_to_uint64_rninta __bid64_to_uint64_rninta +#define bid64_to_uint64_xceil __bid64_to_uint64_xceil +#define bid64_to_uint64_xfloor __bid64_to_uint64_xfloor +#define bid64_to_uint64_xint __bid64_to_uint64_xint +#define bid64_to_uint64_xrnint __bid64_to_uint64_xrnint +#define bid64_to_uint64_xrninta __bid64_to_uint64_xrninta +#define bid128_to_int32_ceil __bid128_to_int32_ceil +#define bid128_to_int32_floor __bid128_to_int32_floor +#define bid128_to_int32_int __bid128_to_int32_int +#define bid128_to_int32_rnint __bid128_to_int32_rnint +#define bid128_to_int32_rninta __bid128_to_int32_rninta +#define bid128_to_int32_xceil __bid128_to_int32_xceil +#define bid128_to_int32_xfloor __bid128_to_int32_xfloor +#define bid128_to_int32_xint __bid128_to_int32_xint +#define bid128_to_int32_xrnint __bid128_to_int32_xrnint +#define bid128_to_int32_xrninta __bid128_to_int32_xrninta +#define bid128_to_uint32_ceil __bid128_to_uint32_ceil +#define bid128_to_uint32_floor __bid128_to_uint32_floor +#define bid128_to_uint32_int __bid128_to_uint32_int +#define bid128_to_uint32_rnint __bid128_to_uint32_rnint +#define bid128_to_uint32_rninta __bid128_to_uint32_rninta +#define bid128_to_uint32_xceil __bid128_to_uint32_xceil +#define bid128_to_uint32_xfloor __bid128_to_uint32_xfloor +#define bid128_to_uint32_xint __bid128_to_uint32_xint +#define bid128_to_uint32_xrnint __bid128_to_uint32_xrnint +#define bid128_to_uint32_xrninta __bid128_to_uint32_xrninta +#define bid128_to_int64_ceil __bid128_to_int64_ceil +#define bid128_to_int64_floor __bid128_to_int64_floor +#define bid128_to_int64_int __bid128_to_int64_int +#define bid128_to_int64_rnint __bid128_to_int64_rnint +#define bid128_to_int64_rninta __bid128_to_int64_rninta +#define bid128_to_int64_xceil __bid128_to_int64_xceil +#define bid128_to_int64_xfloor __bid128_to_int64_xfloor +#define bid128_to_int64_xint __bid128_to_int64_xint +#define bid128_to_int64_xrnint __bid128_to_int64_xrnint +#define bid128_to_int64_xrninta __bid128_to_int64_xrninta +#define bid128_to_uint64_ceil __bid128_to_uint64_ceil +#define bid128_to_uint64_floor __bid128_to_uint64_floor +#define bid128_to_uint64_int __bid128_to_uint64_int +#define bid128_to_uint64_rnint __bid128_to_uint64_rnint +#define bid128_to_uint64_rninta __bid128_to_uint64_rninta +#define bid128_to_uint64_xceil __bid128_to_uint64_xceil +#define bid128_to_uint64_xfloor __bid128_to_uint64_xfloor +#define bid128_to_uint64_xint __bid128_to_uint64_xint +#define bid128_to_uint64_xrnint __bid128_to_uint64_xrnint +#define bid128_to_uint64_xrninta __bid128_to_uint64_xrninta +#define bid128_to_binary128 __bid128_to_binary128 +#define bid128_to_binary32 __bid128_to_binary32 +#define bid128_to_binary64 __bid128_to_binary64 +#define bid128_to_binary80 __bid128_to_binary80 +#define bid32_to_binary128 __bid32_to_binary128 +#define bid32_to_binary32 __bid32_to_binary32 +#define bid32_to_binary64 __bid32_to_binary64 +#define bid32_to_binary80 __bid32_to_binary80 +#define bid64_to_binary128 __bid64_to_binary128 +#define bid64_to_binary32 __bid64_to_binary32 +#define bid64_to_binary64 __bid64_to_binary64 +#define bid64_to_binary80 __bid64_to_binary80 +#define binary128_to_bid128 __binary128_to_bid128 +#define binary128_to_bid32 __binary128_to_bid32 +#define binary128_to_bid64 __binary128_to_bid64 +#define binary32_to_bid128 __binary32_to_bid128 +#define binary32_to_bid32 __binary32_to_bid32 +#define binary32_to_bid64 __binary32_to_bid64 +#define binary64_to_bid128 __binary64_to_bid128 +#define binary64_to_bid32 __binary64_to_bid32 +#define binary64_to_bid64 __binary64_to_bid64 +#define binary80_to_bid128 __binary80_to_bid128 +#define binary80_to_bid32 __binary80_to_bid32 +#define binary80_to_bid64 __binary80_to_bid64 +#define bid64_to_uint16_ceil __bid64_to_uint16_ceil +#define bid64_to_uint16_floor __bid64_to_uint16_floor +#define bid64_to_uint16_int __bid64_to_uint16_int +#define bid64_to_uint16_rnint __bid64_to_uint16_rnint +#define bid64_to_uint16_rninta __bid64_to_uint16_rninta +#define bid64_to_uint16_xceil __bid64_to_uint16_xceil +#define bid64_to_uint16_xfloor __bid64_to_uint16_xfloor +#define bid64_to_uint16_xint __bid64_to_uint16_xint +#define bid64_to_uint16_xrnint __bid64_to_uint16_xrnint +#define bid64_to_uint16_xrninta __bid64_to_uint16_xrninta +#define bid64_to_int16_ceil __bid64_to_int16_ceil +#define bid64_to_int16_floor __bid64_to_int16_floor +#define bid64_to_int16_int __bid64_to_int16_int +#define bid64_to_int16_rnint __bid64_to_int16_rnint +#define bid64_to_int16_rninta __bid64_to_int16_rninta +#define bid64_to_int16_xceil __bid64_to_int16_xceil +#define bid64_to_int16_xfloor __bid64_to_int16_xfloor +#define bid64_to_int16_xint __bid64_to_int16_xint +#define bid64_to_int16_xrnint __bid64_to_int16_xrnint +#define bid64_to_int16_xrninta __bid64_to_int16_xrninta +#define bid128_to_uint16_ceil __bid128_to_uint16_ceil +#define bid128_to_uint16_floor __bid128_to_uint16_floor +#define bid128_to_uint16_int __bid128_to_uint16_int +#define bid128_to_uint16_rnint __bid128_to_uint16_rnint +#define bid128_to_uint16_rninta __bid128_to_uint16_rninta +#define bid128_to_uint16_xceil __bid128_to_uint16_xceil +#define bid128_to_uint16_xfloor __bid128_to_uint16_xfloor +#define bid128_to_uint16_xint __bid128_to_uint16_xint +#define bid128_to_uint16_xrnint __bid128_to_uint16_xrnint +#define bid128_to_uint16_xrninta __bid128_to_uint16_xrninta +#define bid128_to_int16_ceil __bid128_to_int16_ceil +#define bid128_to_int16_floor __bid128_to_int16_floor +#define bid128_to_int16_int __bid128_to_int16_int +#define bid128_to_int16_rnint __bid128_to_int16_rnint +#define bid128_to_int16_rninta __bid128_to_int16_rninta +#define bid128_to_int16_xceil __bid128_to_int16_xceil +#define bid128_to_int16_xfloor __bid128_to_int16_xfloor +#define bid128_to_int16_xint __bid128_to_int16_xint +#define bid128_to_int16_xrnint __bid128_to_int16_xrnint +#define bid128_to_int16_xrninta __bid128_to_int16_xrninta +#define bid64_to_uint8_ceil __bid64_to_uint8_ceil +#define bid64_to_uint8_floor __bid64_to_uint8_floor +#define bid64_to_uint8_int __bid64_to_uint8_int +#define bid64_to_uint8_rnint __bid64_to_uint8_rnint +#define bid64_to_uint8_rninta __bid64_to_uint8_rninta +#define bid64_to_uint8_xceil __bid64_to_uint8_xceil +#define bid64_to_uint8_xfloor __bid64_to_uint8_xfloor +#define bid64_to_uint8_xint __bid64_to_uint8_xint +#define bid64_to_uint8_xrnint __bid64_to_uint8_xrnint +#define bid64_to_uint8_xrninta __bid64_to_uint8_xrninta +#define bid64_to_int8_ceil __bid64_to_int8_ceil +#define bid64_to_int8_floor __bid64_to_int8_floor +#define bid64_to_int8_int __bid64_to_int8_int +#define bid64_to_int8_rnint __bid64_to_int8_rnint +#define bid64_to_int8_rninta __bid64_to_int8_rninta +#define bid64_to_int8_xceil __bid64_to_int8_xceil +#define bid64_to_int8_xfloor __bid64_to_int8_xfloor +#define bid64_to_int8_xint __bid64_to_int8_xint +#define bid64_to_int8_xrnint __bid64_to_int8_xrnint +#define bid64_to_int8_xrninta __bid64_to_int8_xrninta +#define bid128_to_uint8_ceil __bid128_to_uint8_ceil +#define bid128_to_uint8_floor __bid128_to_uint8_floor +#define bid128_to_uint8_int __bid128_to_uint8_int +#define bid128_to_uint8_rnint __bid128_to_uint8_rnint +#define bid128_to_uint8_rninta __bid128_to_uint8_rninta +#define bid128_to_uint8_xceil __bid128_to_uint8_xceil +#define bid128_to_uint8_xfloor __bid128_to_uint8_xfloor +#define bid128_to_uint8_xint __bid128_to_uint8_xint +#define bid128_to_uint8_xrnint __bid128_to_uint8_xrnint +#define bid128_to_uint8_xrninta __bid128_to_uint8_xrninta +#define bid128_to_int8_ceil __bid128_to_int8_ceil +#define bid128_to_int8_floor __bid128_to_int8_floor +#define bid128_to_int8_int __bid128_to_int8_int +#define bid128_to_int8_rnint __bid128_to_int8_rnint +#define bid128_to_int8_rninta __bid128_to_int8_rninta +#define bid128_to_int8_xceil __bid128_to_int8_xceil +#define bid128_to_int8_xfloor __bid128_to_int8_xfloor +#define bid128_to_int8_xint __bid128_to_int8_xint +#define bid128_to_int8_xrnint __bid128_to_int8_xrnint +#define bid128_to_int8_xrninta __bid128_to_int8_xrninta + +#ifdef IN_LIBGCC2 +#if !defined ENABLE_DECIMAL_BID_FORMAT || !ENABLE_DECIMAL_BID_FORMAT +#error BID not enabled in libbid +#endif + +#ifndef BID_BIG_ENDIAN +#define BID_BIG_ENDIAN LIBGCC2_FLOAT_WORDS_BIG_ENDIAN +#endif + +#ifndef BID_THREAD +#if defined (HAVE_CC_TLS) && defined (USE_TLS) +#define BID_THREAD __thread +#endif +#endif + +#define _intptr_t_defined +#define DECIMAL_CALL_BY_REFERENCE 0 +#define DECIMAL_GLOBAL_ROUNDING 1 +#define DECIMAL_GLOBAL_ROUNDING_ACCESS_FUNCTIONS 1 +#define DECIMAL_GLOBAL_EXCEPTION_FLAGS 1 +#define DECIMAL_GLOBAL_EXCEPTION_FLAGS_ACCESS_FUNCTIONS 1 +#define BID_HAS_GCC_DECIMAL_INTRINSICS 1 +#endif /* IN_LIBGCC2 */ + +// Configuration Options + +#define SET_STATUS_FLAGS + +#ifndef BID_THREAD +#define BID_THREAD +#endif + +#ifndef BID_HAS_GCC_DECIMAL_INTRINSICS +#define BID_HAS_GCC_DECIMAL_INTRINSICS 0 +#endif + +#if !defined(WINDOWS) || defined(__INTEL_COMPILER) +// #define UNCHANGED_BINARY_STATUS_FLAGS +#endif +// #define HPUX_OS + +// If DECIMAL_CALL_BY_REFERENCE is defined then numerical arguments and results +// are passed by reference otherwise they are passed by value (except that +// a pointer is always passed to the status flags) + +#ifndef DECIMAL_CALL_BY_REFERENCE +#define DECIMAL_CALL_BY_REFERENCE 0 +#endif + +// If DECIMAL_GLOBAL_ROUNDING is defined then the rounding mode is a global +// variable _IDEC_glbround, otherwise it is passed as a parameter when needed + +#ifndef DECIMAL_GLOBAL_ROUNDING +#define DECIMAL_GLOBAL_ROUNDING 0 +#endif + +#ifndef DECIMAL_GLOBAL_ROUNDING_ACCESS_FUNCTIONS +#define DECIMAL_GLOBAL_ROUNDING_ACCESS_FUNCTIONS 0 +#endif + +// If DECIMAL_GLOBAL_EXCEPTION_FLAGS is defined then the exception status flags +// are represented by a global variable _IDEC_glbflags, otherwise they are +// passed as a parameter when needed + +#ifndef DECIMAL_GLOBAL_EXCEPTION_FLAGS +#define DECIMAL_GLOBAL_EXCEPTION_FLAGS 0 +#endif + +#ifndef DECIMAL_GLOBAL_EXCEPTION_FLAGS_ACCESS_FUNCTIONS +#define DECIMAL_GLOBAL_EXCEPTION_FLAGS_ACCESS_FUNCTIONS 0 +#endif + +// If DECIMAL_ALTERNATE_EXCEPTION_HANDLING is defined then the exception masks +// are examined and exception handling information is provided to the caller +// if alternate exception handling is necessary + +#ifndef DECIMAL_ALTERNATE_EXCEPTION_HANDLING +#define DECIMAL_ALTERNATE_EXCEPTION_HANDLING 0 +#endif + +typedef unsigned int _IDEC_round; +typedef unsigned int _IDEC_flags; // could be a struct with diagnostic info + +#if DECIMAL_ALTERNATE_EXCEPTION_HANDLING + // If DECIMAL_GLOBAL_EXCEPTION_MASKS is defined then the exception mask bits + // are represented by a global variable _IDEC_exceptionmasks, otherwise they + // are passed as a parameter when needed; DECIMAL_GLOBAL_EXCEPTION_MASKS is + // ignored + // if DECIMAL_ALTERNATE_EXCEPTION_HANDLING is not defined + // ************************************************************************** +#define DECIMAL_GLOBAL_EXCEPTION_MASKS 0 + // ************************************************************************** + + // If DECIMAL_GLOBAL_EXCEPTION_INFO is defined then the alternate exception + // handling information is represented by a global data structure + // _IDEC_glbexcepthandling, otherwise it is passed by reference as a + // parameter when needed; DECIMAL_GLOBAL_EXCEPTION_INFO is ignored + // if DECIMAL_ALTERNATE_EXCEPTION_HANDLING is not defined + // ************************************************************************** +#define DECIMAL_GLOBAL_EXCEPTION_INFO 0 + // ************************************************************************** +#endif + +// Notes: 1) rnd_mode from _RND_MODE_ARG is used by the caller of a function +// from this library, and can be any name +// 2) rnd_mode and prnd_mode from _RND_MODE_PARAM are fixed names +// and *must* be used in the library functions +// 3) _IDEC_glbround is the fixed name for the global variable holding +// the rounding mode + +#if !DECIMAL_GLOBAL_ROUNDING +#if DECIMAL_CALL_BY_REFERENCE +#define _RND_MODE_ARG , &rnd_mode +#define _RND_MODE_PARAM , _IDEC_round *prnd_mode +#define _RND_MODE_ARG_ALONE &rnd_mode +#define _RND_MODE_PARAM_ALONE _IDEC_round *prnd_mode +#else +#define _RND_MODE_ARG , rnd_mode +#define _RND_MODE_PARAM , _IDEC_round rnd_mode +#define _RND_MODE_ARG_ALONE rnd_mode +#define _RND_MODE_PARAM_ALONE _IDEC_round rnd_mode +#endif +#else +#define _RND_MODE_ARG +#define _RND_MODE_PARAM +#define _RND_MODE_ARG_ALONE +#define _RND_MODE_PARAM_ALONE +#define rnd_mode _IDEC_glbround +#endif + +// Notes: 1) pfpsf from _EXC_FLAGS_ARG is used by the caller of a function +// from this library, and can be any name +// 2) pfpsf from _EXC_FLAGS_PARAM is a fixed name and *must* be used +// in the library functions +// 3) _IDEC_glbflags is the fixed name for the global variable holding +// the floating-point status flags +#if !DECIMAL_GLOBAL_EXCEPTION_FLAGS +#define _EXC_FLAGS_ARG , pfpsf +#define _EXC_FLAGS_PARAM , _IDEC_flags *pfpsf +#else +#define _EXC_FLAGS_ARG +#define _EXC_FLAGS_PARAM +#define pfpsf &_IDEC_glbflags +#endif + +#if DECIMAL_GLOBAL_ROUNDING +extern BID_THREAD _IDEC_round _IDEC_glbround; +#endif + +#if DECIMAL_GLOBAL_EXCEPTION_FLAGS +extern BID_THREAD _IDEC_flags _IDEC_glbflags; +#endif + +#if DECIMAL_ALTERNATE_EXCEPTION_HANDLING +#if DECIMAL_GLOBAL_EXCEPTION_MASKS +extern BID_THREAD _IDEC_exceptionmasks _IDEC_glbexceptionmasks; +#endif +#if DECIMAL_GLOBAL_EXCEPTION_INFO +extern BID_THREAD _IDEC_excepthandling _IDEC_glbexcepthandling; +#endif +#endif + +#if DECIMAL_ALTERNATE_EXCEPTION_HANDLING + + // Notes: 1) exc_mask from _EXC_MASKS_ARG is used by the caller of a function + // from this library, and can be any name + // 2) exc_mask and pexc_mask from _EXC_MASKS_PARAM are fixed names + // and *must* be used in the library functions + // 3) _IDEC_glbexceptionmasks is the fixed name for the global + // variable holding the floating-point exception masks +#if !DECIMAL_GLOBAL_EXCEPTION_MASKS +#if DECIMAL_CALL_BY_REFERENCE +#define _EXC_MASKS_ARG , &exc_mask +#define _EXC_MASKS_PARAM , _IDEC_exceptionmasks *pexc_mask +#else +#define _EXC_MASKS_ARG , exc_mask +#define _EXC_MASKS_PARAM , _IDEC_exceptionmasks exc_mask +#endif +#else +#define _EXC_MASKS_ARG +#define _EXC_MASKS_PARAM +#define exc_mask _IDEC_glbexceptionmasks +#endif + + // Notes: 1) pexc_info from _EXC_INFO_ARG is used by the caller of a function + // from this library, and can be any name + // 2) pexc_info from _EXC_INFO_PARAM is a fixed name and *must* be + // used in the library functions + // 3) _IDEC_glbexcepthandling is the fixed name for the global + // variable holding the floating-point exception information +#if !DECIMAL_GLOBAL_EXCEPTION_INFO +#define _EXC_INFO_ARG , pexc_info +#define _EXC_INFO_PARAM , _IDEC_excepthandling *pexc_info +#else +#define _EXC_INFO_ARG +#define _EXC_INFO_PARAM +#define pexc_info &_IDEC_glbexcepthandling +#endif +#else +#define _EXC_MASKS_ARG +#define _EXC_MASKS_PARAM +#define _EXC_INFO_ARG +#define _EXC_INFO_PARAM +#endif + + +#ifndef BID_BIG_ENDIAN +#define BID_BIG_ENDIAN 0 +#endif + +#if BID_BIG_ENDIAN +#define BID_SWAP128(x) { \ + UINT64 sw; \ + sw = (x).w[1]; \ + (x).w[1] = (x).w[0]; \ + (x).w[0] = sw; \ + } +#else +#define BID_SWAP128(x) +#endif + +#if DECIMAL_CALL_BY_REFERENCE +#define BID_RETURN_VAL(x) { *pres = (x); return; } +#if BID_BIG_ENDIAN && defined BID_128RES +#define BID_RETURN(x) { BID_SWAP128(x); *pres = (x); return; } +#else +#define BID_RETURN(x) { *pres = (x); return; } +#endif +#else +#define BID_RETURN_VAL(x) return(x); +#if BID_BIG_ENDIAN && defined BID_128RES +#define BID_RETURN(x) { BID_SWAP128(x); return(x); } +#else +#define BID_RETURN(x) return(x); +#endif +#endif + +#if DECIMAL_CALL_BY_REFERENCE +#define BIDECIMAL_CALL1(_FUNC, _RES, _OP1) \ + _FUNC(&(_RES), &(_OP1) _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL1_NORND(_FUNC, _RES, _OP1) \ + _FUNC(&(_RES), &(_OP1) _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL2(_FUNC, _RES, _OP1, _OP2) \ + _FUNC(&(_RES), &(_OP1), &(_OP2) _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL2_NORND(_FUNC, _RES, _OP1, _OP2) \ + _FUNC(&(_RES), &(_OP1), &(_OP2) _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL1_NORND_RESREF(_FUNC, _RES, _OP1) \ + _FUNC((_RES), &(_OP1) _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL1_RESARG(_FUNC, _RES, _OP1) \ + _FUNC(&(_RES), (_OP1) _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL1_RESREF(_FUNC, _RES, _OP1) \ + _FUNC((_RES), &(_OP1) _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL1_NORND_NOSTAT(_FUNC, _RES, _OP1) \ + _FUNC(&(_RES), &(_OP1) _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL2_NORND_NOSTAT(_FUNC, _RES, _OP1, _OP2) \ + _FUNC(&(_RES), &(_OP1), &(_OP2) _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL3(_FUNC, _RES, _OP1, _OP2, _OP3) \ + _FUNC(&(_RES), &(_OP1), &(_OP2), &(_OP3) _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL1_NORND_NOMASK_NOINFO(_FUNC, _RES, _OP1) \ + _FUNC(&(_RES), &(_OP1) _EXC_FLAGS_ARG ) +#define BIDECIMAL_CALL1_NORND_NOFLAGS_NOMASK_NOINFO(_FUNC, _RES, _OP1) \ + _FUNC(&(_RES), &(_OP1) ) +#define BIDECIMAL_CALL2_NORND_NOFLAGS_NOMASK_NOINFO(_FUNC, _RES, _OP1, _OP2) \ + _FUNC(&(_RES), &(_OP1), &(_OP2) ) +#define BIDECIMAL_CALL1_NORND_NOMASK_NOINFO_RESVOID(_FUNC, _OP1) \ + _FUNC(&(_OP1) _EXC_FLAGS_ARG ) +#define BIDECIMAL_CALL2_NORND_NOMASK_NOINFO_RESVOID(_FUNC, _OP1, _OP2) \ + _FUNC(&(_OP1), &(_OP2) _EXC_FLAGS_ARG ) +#define BIDECIMAL_CALLV_NOFLAGS_NOMASK_NOINFO(_FUNC, _RES) \ + _FUNC(&(_RES) _RND_MODE_ARG) +#define BIDECIMAL_CALL1_NOFLAGS_NOMASK_NOINFO(_FUNC, _RES, _OP1) \ + _FUNC(&(_OP1) _RND_MODE_ARG) +#else +#define BIDECIMAL_CALL1(_FUNC, _RES, _OP1) \ + _RES = _FUNC((_OP1) _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL1_NORND(_FUNC, _RES, _OP1) \ + _RES = _FUNC((_OP1) _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL2(_FUNC, _RES, _OP1, _OP2) \ + _RES = _FUNC((_OP1), (_OP2) _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL2_NORND(_FUNC, _RES, _OP1, _OP2) \ + _RES = _FUNC((_OP1), (_OP2) _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL1_NORND_RESREF(_FUNC, _RES, _OP1) \ + _FUNC((_RES), _OP1 _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL1_RESARG(_FUNC, _RES, _OP1) \ + _RES = _FUNC((_OP1) _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL1_RESREF(_FUNC, _RES, _OP1) \ + _FUNC((_RES), _OP1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL1_NORND_NOSTAT(_FUNC, _RES, _OP1) \ + _RES = _FUNC((_OP1) _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL2_NORND_NOSTAT(_FUNC, _RES, _OP1, _OP2) \ + _RES = _FUNC((_OP1), (_OP2) _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL3(_FUNC, _RES, _OP1, _OP2, _OP3) \ + _RES = _FUNC((_OP1), (_OP2), (_OP3) _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG) +#define BIDECIMAL_CALL1_NORND_NOMASK_NOINFO(_FUNC, _RES, _OP1) \ + _RES = _FUNC((_OP1) _EXC_FLAGS_ARG) +#define BIDECIMAL_CALL1_NORND_NOFLAGS_NOMASK_NOINFO(_FUNC, _RES, _OP1) \ + _RES = _FUNC((_OP1) ) +#define BIDECIMAL_CALL2_NORND_NOFLAGS_NOMASK_NOINFO(_FUNC, _RES, _OP1, _OP2) \ + _RES = _FUNC((_OP1), (_OP2) ) +#define BIDECIMAL_CALL1_NORND_NOMASK_NOINFO_RESVOID(_FUNC, _OP1) \ + _FUNC((_OP1) _EXC_FLAGS_ARG) +#define BIDECIMAL_CALL2_NORND_NOMASK_NOINFO_RESVOID(_FUNC, _OP1, _OP2) \ + _FUNC((_OP1), (_OP2) _EXC_FLAGS_ARG) +#define BIDECIMAL_CALLV_NOFLAGS_NOMASK_NOINFO(_FUNC, _RES) \ + _RES = _FUNC(_RND_MODE_ARG_ALONE) +#if !DECIMAL_GLOBAL_ROUNDING +#define BIDECIMAL_CALL1_NOFLAGS_NOMASK_NOINFO(_FUNC, _RES, _OP1) \ + _RES = _FUNC((_OP1) _RND_MODE_ARG) +#else +#define BIDECIMAL_CALL1_NOFLAGS_NOMASK_NOINFO(_FUNC, _RES, _OP1) \ + _FUNC((_OP1) _RND_MODE_ARG) +#endif +#endif + +#if BID_BIG_ENDIAN +#define HIGH_128W 0 +#define LOW_128W 1 +#else +#define HIGH_128W 1 +#define LOW_128W 0 +#endif + +#if BID_BIG_ENDIAN +#define COPY_ARG_REF(arg_name) \ + UINT128 arg_name={ pbid_##arg_name->w[1], pbid_##arg_name->w[0]}; +#define COPY_ARG_VAL(arg_name) \ + UINT128 arg_name={ bid_##arg_name.w[1], bid_##arg_name.w[0]}; +#else +#define COPY_ARG_REF(arg_name) \ + UINT128 arg_name=*pbid_##arg_name; +#define COPY_ARG_VAL(arg_name) \ + UINT128 arg_name= bid_##arg_name; +#endif + +#define COPY_ARG_TYPE_REF(type, arg_name) \ + type arg_name=*pbid_##arg_name; +#define COPY_ARG_TYPE_VAL(type, arg_name) \ + type arg_name= bid_##arg_name; + +#if !DECIMAL_GLOBAL_ROUNDING +#define SET_RND_MODE() \ + _IDEC_round rnd_mode = *prnd_mode; +#else +#define SET_RND_MODE() +#endif + +#define PROLOG_REF(arg_name) \ + COPY_ARG_REF(arg_name) + +#define PROLOG_VAL(arg_name) \ + COPY_ARG_VAL(arg_name) + +#define PROLOG_TYPE_REF(type, arg_name) \ + COPY_ARG_TYPE_REF(type, arg_name) + +#define PROLOG_TYPE_VAL(type, arg_name) \ + COPY_ARG_TYPE_VAL(type, arg_name) + +#define OTHER_PROLOG_REF() +#define OTHER_PROLOG_VAL() + +#if DECIMAL_CALL_BY_REFERENCE +#define BID128_FUNCTION_ARG1(fn_name, arg_name)\ + void fn_name (UINT128 * pres, \ + UINT128 * \ + pbid_##arg_name _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_REF(arg_name) \ + SET_RND_MODE() \ + OTHER_PROLOG_REF() + +#define BID128_FUNCTION_ARG1_NORND(fn_name, arg_name)\ + void fn_name (UINT128 * pres, \ + UINT128 * \ + pbid_##arg_name _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_REF(arg_name) \ + OTHER_PROLOG_REF() + +#define BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(restype, fn_name, arg_name)\ + void fn_name (restype * pres, \ + UINT128 * \ + pbid_##arg_name _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_REF(arg_name) \ + OTHER_PROLOG_REF() + +#define BID128_FUNCTION_ARG2(fn_name, arg_name1, arg_name2)\ + void fn_name (UINT128 * pres, \ + UINT128 *pbid_##arg_name1, UINT128 *pbid_##arg_name2 \ + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_REF(arg_name1) \ + PROLOG_REF(arg_name2) \ + SET_RND_MODE() \ + OTHER_PROLOG_REF() + +#define BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE(restype, fn_name, arg_name1, arg_name2)\ + void fn_name (restype * pres, \ + UINT128 *pbid_##arg_name1, UINT128 *pbid_##arg_name2 \ + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_REF(arg_name1) \ + PROLOG_REF(arg_name2) \ + OTHER_PROLOG_REF() + +#define BID128_FUNCTION_ARG128_ARGTYPE2(fn_name, arg_name1, type2, arg_name2)\ + void fn_name (UINT128 * pres, \ + UINT128 *pbid_##arg_name1, type2 *pbid_##arg_name2 \ + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_REF(arg_name1) \ + PROLOG_TYPE_REF(type2, arg_name2) \ + SET_RND_MODE() \ + OTHER_PROLOG_REF() + +#define TYPE0_FUNCTION_ARGTYPE1_ARGTYPE2(type0, fn_name, type1, arg_name1, type2, arg_name2)\ + void fn_name (type0 *pres, \ + type1 *pbid_##arg_name1, type2 *pbid_##arg_name2 \ + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_TYPE_REF(type1, arg_name1) \ + PROLOG_TYPE_REF(type2, arg_name2) \ + SET_RND_MODE() \ + OTHER_PROLOG_REF() + +#define BID128_FUNCTION_ARGTYPE1_ARG128(fn_name, type1, arg_name1, arg_name2)\ + void fn_name (UINT128 * pres, \ + type1 *pbid_##arg_name1, UINT128 *pbid_##arg_name2 \ + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_TYPE_REF(type1, arg_name1) \ + PROLOG_REF(arg_name2) \ + SET_RND_MODE() \ + OTHER_PROLOG_REF() + +#define TYPE0_FUNCTION_ARG128_ARGTYPE2(type0, fn_name, arg_name1, type2, arg_name2)\ + void fn_name (type0 *pres, \ + UINT128 *pbid_##arg_name1, type2 *pbid_##arg_name2 \ + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_REF(arg_name1) \ + PROLOG_TYPE_REF(type2, arg_name2) \ + SET_RND_MODE() \ + OTHER_PROLOG_REF() + +#define TYPE0_FUNCTION_ARGTYPE1_ARG128(type0, fn_name, type1, arg_name1, arg_name2)\ + void fn_name (type0 *pres, \ + type1 *pbid_##arg_name1, UINT128 *pbid_##arg_name2 \ + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_TYPE_REF(type1, arg_name1) \ + PROLOG_REF(arg_name2) \ + SET_RND_MODE() \ + OTHER_PROLOG_REF() + +#define TYPE0_FUNCTION_ARG128_ARG128(type0, fn_name, arg_name1, arg_name2)\ + void fn_name (type0 * pres, \ + UINT128 *pbid_##arg_name1, UINT128 *pbid_##arg_name2 \ + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_REF(arg_name1) \ + PROLOG_REF(arg_name2) \ + SET_RND_MODE() \ + OTHER_PROLOG_REF() + +#define TYPE0_FUNCTION_ARG1(type0, fn_name, arg_name)\ + void fn_name (type0 * pres, \ + UINT128 * \ + pbid_##arg_name _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_REF(arg_name) \ + SET_RND_MODE() \ + OTHER_PROLOG_REF() + +#define BID128_FUNCTION_ARGTYPE1(fn_name, type1, arg_name)\ + void fn_name (UINT128 * pres, \ + type1 * \ + pbid_##arg_name _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_TYPE_REF(type1, arg_name) \ + SET_RND_MODE() \ + OTHER_PROLOG_REF() + +#define TYPE0_FUNCTION_ARGTYPE1(type0, fn_name, type1, arg_name)\ + void fn_name (type0 * pres, \ + type1 * \ + pbid_##arg_name _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_TYPE_REF(type1, arg_name) \ + SET_RND_MODE() \ + OTHER_PROLOG_REF() + +#define TYPE0_FUNCTION_ARGTYPE1_NORND(type0, fn_name, type1, arg_name)\ + void fn_name (type0 * pres, \ + type1 * \ + pbid_##arg_name _EXC_FLAGS_PARAM _EXC_MASKS_PARAM \ + _EXC_INFO_PARAM) {\ + PROLOG_TYPE_REF(type1, arg_name) \ + OTHER_PROLOG_REF() + +////////////////////////////////////////// +///////////////////////////////////////// +//////////////////////////////////////// + +#else + +////////////////////////////////////////// +///////////////////////////////////////// +//////////////////////////////////////// + +#define BID128_FUNCTION_ARG1(fn_name, arg_name)\ + UINT128 \ + fn_name (UINT128 bid_##arg_name _RND_MODE_PARAM _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_VAL(arg_name) \ + OTHER_PROLOG_VAL() + +#define BID128_FUNCTION_ARG1_NORND(fn_name, arg_name)\ + UINT128 \ + fn_name (UINT128 bid_##arg_name _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_VAL(arg_name) \ + OTHER_PROLOG_VAL() + +#define BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(restype, fn_name, arg_name)\ + restype \ + fn_name (UINT128 bid_##arg_name _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_VAL(arg_name) \ + OTHER_PROLOG_VAL() + +#define BID128_FUNCTION_ARG2(fn_name, arg_name1, arg_name2)\ + UINT128 \ + fn_name (UINT128 bid_##arg_name1, \ + UINT128 bid_##arg_name2 _RND_MODE_PARAM _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_VAL(arg_name1) \ + PROLOG_VAL(arg_name2) \ + OTHER_PROLOG_VAL() + +#define BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE(restype, fn_name, arg_name1, arg_name2)\ + restype \ + fn_name (UINT128 bid_##arg_name1, \ + UINT128 bid_##arg_name2 _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_VAL(arg_name1) \ + PROLOG_VAL(arg_name2) \ + OTHER_PROLOG_VAL() + +#define BID128_FUNCTION_ARG128_ARGTYPE2(fn_name, arg_name1, type2, arg_name2)\ + UINT128 \ + fn_name (UINT128 bid_##arg_name1, \ + type2 bid_##arg_name2 _RND_MODE_PARAM _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_VAL(arg_name1) \ + PROLOG_TYPE_VAL(type2, arg_name2) \ + OTHER_PROLOG_VAL() + +#define TYPE0_FUNCTION_ARGTYPE1_ARGTYPE2(type0, fn_name, type1, arg_name1, type2, arg_name2)\ + type0 \ + fn_name (type1 bid_##arg_name1, \ + type2 bid_##arg_name2 _RND_MODE_PARAM _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_TYPE_VAL(type1, arg_name1) \ + PROLOG_TYPE_VAL(type2, arg_name2) \ + OTHER_PROLOG_VAL() + +#define BID128_FUNCTION_ARGTYPE1_ARG128(fn_name, type1, arg_name1, arg_name2)\ + UINT128 \ + fn_name (type1 bid_##arg_name1, \ + UINT128 bid_##arg_name2 _RND_MODE_PARAM _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_TYPE_VAL(type1, arg_name1) \ + PROLOG_VAL(arg_name2) \ + OTHER_PROLOG_VAL() + +#define TYPE0_FUNCTION_ARG128_ARGTYPE2(type0, fn_name, arg_name1, type2, arg_name2)\ + type0 \ + fn_name (UINT128 bid_##arg_name1, \ + type2 bid_##arg_name2 _RND_MODE_PARAM _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_VAL(arg_name1) \ + PROLOG_TYPE_VAL(type2, arg_name2) \ + OTHER_PROLOG_VAL() + +#define TYPE0_FUNCTION_ARGTYPE1_ARG128(type0, fn_name, type1, arg_name1, arg_name2)\ + type0 \ + fn_name (type1 bid_##arg_name1, \ + UINT128 bid_##arg_name2 _RND_MODE_PARAM _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_TYPE_VAL(type1, arg_name1) \ + PROLOG_VAL(arg_name2) \ + OTHER_PROLOG_VAL() + +#define TYPE0_FUNCTION_ARG128_ARG128(type0, fn_name, arg_name1, arg_name2)\ + type0 \ + fn_name (UINT128 bid_##arg_name1, \ + UINT128 bid_##arg_name2 _RND_MODE_PARAM _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_VAL(arg_name1) \ + PROLOG_VAL(arg_name2) \ + OTHER_PROLOG_VAL() + +#define TYPE0_FUNCTION_ARG1(type0, fn_name, arg_name)\ + type0 \ + fn_name (UINT128 bid_##arg_name _RND_MODE_PARAM _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_VAL(arg_name) \ + OTHER_PROLOG_VAL() + +#define BID128_FUNCTION_ARGTYPE1(fn_name, type1, arg_name)\ + UINT128 \ + fn_name (type1 bid_##arg_name _RND_MODE_PARAM _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_TYPE_VAL(type1, arg_name) \ + OTHER_PROLOG_VAL() + +#define TYPE0_FUNCTION_ARGTYPE1(type0, fn_name, type1, arg_name)\ + type0 \ + fn_name (type1 bid_##arg_name _RND_MODE_PARAM _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_TYPE_VAL(type1, arg_name) \ + OTHER_PROLOG_VAL() + +#define TYPE0_FUNCTION_ARGTYPE1_NORND(type0, fn_name, type1, arg_name)\ + type0 \ + fn_name (type1 bid_##arg_name _EXC_FLAGS_PARAM \ + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { \ + PROLOG_TYPE_VAL(type1, arg_name) \ + OTHER_PROLOG_VAL() + +#endif + + + +#define BID_TO_SMALL_UINT_CVT_FUNCTION(type0, fn_name, type1, arg_name, cvt_fn_name, type2, size_mask, invalid_res)\ + TYPE0_FUNCTION_ARGTYPE1_NORND(type0, fn_name, type1, arg_name)\ + type2 res; \ + _IDEC_flags saved_fpsc=*pfpsf; \ + BIDECIMAL_CALL1_NORND(cvt_fn_name, res, arg_name); \ + if(res & size_mask) { \ + *pfpsf = saved_fpsc | INVALID_EXCEPTION; \ + res = invalid_res; } \ + BID_RETURN_VAL((type0)res); \ + } + +#define BID_TO_SMALL_INT_CVT_FUNCTION(type0, fn_name, type1, arg_name, cvt_fn_name, type2, size_mask, invalid_res)\ + TYPE0_FUNCTION_ARGTYPE1_NORND(type0, fn_name, type1, arg_name)\ + type2 res, sgn_mask; \ + _IDEC_flags saved_fpsc=*pfpsf; \ + BIDECIMAL_CALL1_NORND(cvt_fn_name, res, arg_name); \ + sgn_mask = res & size_mask; \ + if(sgn_mask && (sgn_mask != (type2)size_mask)) { \ + *pfpsf = saved_fpsc | INVALID_EXCEPTION; \ + res = invalid_res; } \ + BID_RETURN_VAL((type0)res); \ + } +#endif diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_convert_data.c b/gcc-4.4.3/libgcc/config/libbid/bid_convert_data.c new file mode 100644 index 000000000..fca394cb9 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_convert_data.c @@ -0,0 +1,2108 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +// convert_table[j][k][i] = digit i (base 10^8) of k*2^(26+7*j) +const UINT32 convert_table[5][128][2] = { + {{0, 0} + , {67108864, 0} + , {34217728, 1} + , {1326592, 2} + , {68435456, 2} + , + {35544320, 3} + , {2653184, 4} + , {69762048, 4} + , {36870912, 5} + , {3979776, 6} + , + {71088640, 6} + , {38197504, 7} + , {5306368, 8} + , {72415232, 8} + , {39524096, 9} + , + {6632960, 10} + , {73741824, 10} + , {40850688, 11} + , {7959552, 12} + , {75068416, 12} + , + {42177280, 13} + , {9286144, 14} + , {76395008, 14} + , {43503872, 15} + , {10612736, 16} + , + {77721600, 16} + , {44830464, 17} + , {11939328, 18} + , {79048192, 18} + , {46157056, 19} + , + {13265920, 20} + , {80374784, 20} + , {47483648, 21} + , {14592512, 22} + , {81701376, 22} + , + {48810240, 23} + , {15919104, 24} + , {83027968, 24} + , {50136832, 25} + , {17245696, 26} + , + {84354560, 26} + , {51463424, 27} + , {18572288, 28} + , {85681152, 28} + , {52790016, 29} + , + {19898880, 30} + , {87007744, 30} + , {54116608, 31} + , {21225472, 32} + , {88334336, 32} + , + {55443200, 33} + , {22552064, 34} + , {89660928, 34} + , {56769792, 35} + , {23878656, 36} + , + {90987520, 36} + , {58096384, 37} + , {25205248, 38} + , {92314112, 38} + , {59422976, 39} + , + {26531840, 40} + , {93640704, 40} + , {60749568, 41} + , {27858432, 42} + , {94967296, 42} + , + {62076160, 43} + , {29185024, 44} + , {96293888, 44} + , {63402752, 45} + , {30511616, 46} + , + {97620480, 46} + , {64729344, 47} + , {31838208, 48} + , {98947072, 48} + , {66055936, 49} + , + {33164800, 50} + , {273664, 51} + , {67382528, 51} + , {34491392, 52} + , {1600256, 53} + , + {68709120, 53} + , {35817984, 54} + , {2926848, 55} + , {70035712, 55} + , {37144576, 56} + , + {4253440, 57} + , {71362304, 57} + , {38471168, 58} + , {5580032, 59} + , {72688896, 59} + , + {39797760, 60} + , {6906624, 61} + , {74015488, 61} + , {41124352, 62} + , {8233216, 63} + , + {75342080, 63} + , {42450944, 64} + , {9559808, 65} + , {76668672, 65} + , {43777536, 66} + , + {10886400, 67} + , {77995264, 67} + , {45104128, 68} + , {12212992, 69} + , {79321856, 69} + , + {46430720, 70} + , {13539584, 71} + , {80648448, 71} + , {47757312, 72} + , {14866176, 73} + , + {81975040, 73} + , {49083904, 74} + , {16192768, 75} + , {83301632, 75} + , {50410496, 76} + , + {17519360, 77} + , {84628224, 77} + , {51737088, 78} + , {18845952, 79} + , {85954816, 79} + , + {53063680, 80} + , {20172544, 81} + , {87281408, 81} + , {54390272, 82} + , {21499136, 83} + , + {88608000, 83} + , {55716864, 84} + , {22825728, 85} + , + } + , + + {{0, 0} + , {89934592, 85} + , {79869184, 171} + , {69803776, 257} + , {59738368, 343} + , + {49672960, 429} + , {39607552, 515} + , {29542144, 601} + , {19476736, 687} + , {9411328, 773} + , + {99345920, 858} + , {89280512, 944} + , {79215104, 1030} + , {69149696, 1116} + , {59084288, 1202} + , + {49018880, 1288} + , {38953472, 1374} + , {28888064, 1460} + , {18822656, 1546} + , {8757248, 1632} + , + {98691840, 1717} + , {88626432, 1803} + , {78561024, 1889} + , {68495616, 1975} + , {58430208, 2061} + , + {48364800, 2147} + , {38299392, 2233} + , {28233984, 2319} + , {18168576, 2405} + , {8103168, 2491} + , + {98037760, 2576} + , {87972352, 2662} + , {77906944, 2748} + , {67841536, 2834} + , {57776128, 2920} + , + {47710720, 3006} + , {37645312, 3092} + , {27579904, 3178} + , {17514496, 3264} + , {7449088, 3350} + , + {97383680, 3435} + , {87318272, 3521} + , {77252864, 3607} + , {67187456, 3693} + , {57122048, 3779} + , + {47056640, 3865} + , {36991232, 3951} + , {26925824, 4037} + , {16860416, 4123} + , {6795008, 4209} + , + {96729600, 4294} + , {86664192, 4380} + , {76598784, 4466} + , {66533376, 4552} + , {56467968, 4638} + , + {46402560, 4724} + , {36337152, 4810} + , {26271744, 4896} + , {16206336, 4982} + , {6140928, 5068} + , + {96075520, 5153} + , {86010112, 5239} + , {75944704, 5325} + , {65879296, 5411} + , {55813888, 5497} + , + {45748480, 5583} + , {35683072, 5669} + , {25617664, 5755} + , {15552256, 5841} + , {5486848, 5927} + , + {95421440, 6012} + , {85356032, 6098} + , {75290624, 6184} + , {65225216, 6270} + , {55159808, 6356} + , + {45094400, 6442} + , {35028992, 6528} + , {24963584, 6614} + , {14898176, 6700} + , {4832768, 6786} + , + {94767360, 6871} + , {84701952, 6957} + , {74636544, 7043} + , {64571136, 7129} + , {54505728, 7215} + , + {44440320, 7301} + , {34374912, 7387} + , {24309504, 7473} + , {14244096, 7559} + , {4178688, 7645} + , + {94113280, 7730} + , {84047872, 7816} + , {73982464, 7902} + , {63917056, 7988} + , {53851648, 8074} + , + {43786240, 8160} + , {33720832, 8246} + , {23655424, 8332} + , {13590016, 8418} + , {3524608, 8504} + , + {93459200, 8589} + , {83393792, 8675} + , {73328384, 8761} + , {63262976, 8847} + , {53197568, 8933} + , + {43132160, 9019} + , {33066752, 9105} + , {23001344, 9191} + , {12935936, 9277} + , {2870528, 9363} + , + {92805120, 9448} + , {82739712, 9534} + , {72674304, 9620} + , {62608896, 9706} + , {52543488, 9792} + , + {42478080, 9878} + , {32412672, 9964} + , {22347264, 10050} + , {12281856, 10136} + , {2216448, 10222} + , + {92151040, 10307} + , {82085632, 10393} + , {72020224, 10479} + , {61954816, 10565} + , {51889408, 10651} + , + {41824000, 10737} + , {31758592, 10823} + , {21693184, 10909} + , + } + , + + {{0, 0} + , {11627776, 10995} + , {23255552, 21990} + , {34883328, 32985} + , {46511104, 43980} + , + {58138880, 54975} + , {69766656, 65970} + , {81394432, 76965} + , {93022208, 87960} + , {4649984, 98956} + , + {16277760, 109951} + , {27905536, 120946} + , {39533312, 131941} + , {51161088, 142936} + , {62788864, 153931} + , + {74416640, 164926} + , {86044416, 175921} + , {97672192, 186916} + , {9299968, 197912} + , {20927744, 208907} + , + {32555520, 219902} + , {44183296, 230897} + , {55811072, 241892} + , {67438848, 252887} + , {79066624, 263882} + , + {90694400, 274877} + , {2322176, 285873} + , {13949952, 296868} + , {25577728, 307863} + , {37205504, 318858} + , + {48833280, 329853} + , {60461056, 340848} + , {72088832, 351843} + , {83716608, 362838} + , {95344384, 373833} + , + {6972160, 384829} + , {18599936, 395824} + , {30227712, 406819} + , {41855488, 417814} + , {53483264, 428809} + , + {65111040, 439804} + , {76738816, 450799} + , {88366592, 461794} + , {99994368, 472789} + , {11622144, 483785} + , + {23249920, 494780} + , {34877696, 505775} + , {46505472, 516770} + , {58133248, 527765} + , {69761024, 538760} + , + {81388800, 549755} + , {93016576, 560750} + , {4644352, 571746} + , {16272128, 582741} + , {27899904, 593736} + , + {39527680, 604731} + , {51155456, 615726} + , {62783232, 626721} + , {74411008, 637716} + , {86038784, 648711} + , + {97666560, 659706} + , {9294336, 670702} + , {20922112, 681697} + , {32549888, 692692} + , {44177664, 703687} + , + {55805440, 714682} + , {67433216, 725677} + , {79060992, 736672} + , {90688768, 747667} + , {2316544, 758663} + , + {13944320, 769658} + , {25572096, 780653} + , {37199872, 791648} + , {48827648, 802643} + , {60455424, 813638} + , + {72083200, 824633} + , {83710976, 835628} + , {95338752, 846623} + , {6966528, 857619} + , {18594304, 868614} + , + {30222080, 879609} + , {41849856, 890604} + , {53477632, 901599} + , {65105408, 912594} + , {76733184, 923589} + , + {88360960, 934584} + , {99988736, 945579} + , {11616512, 956575} + , {23244288, 967570} + , {34872064, 978565} + , + {46499840, 989560} + , {58127616, 1000555} + , {69755392, 1011550} + , {81383168, 1022545} + , {93010944, 1033540} + , + {4638720, 1044536} + , {16266496, 1055531} + , {27894272, 1066526} + , {39522048, 1077521} + , {51149824, 1088516} + , + {62777600, 1099511} + , {74405376, 1110506} + , {86033152, 1121501} + , {97660928, 1132496} + , {9288704, 1143492} + , + {20916480, 1154487} + , {32544256, 1165482} + , {44172032, 1176477} + , {55799808, 1187472} + , {67427584, 1198467} + , + {79055360, 1209462} + , {90683136, 1220457} + , {2310912, 1231453} + , {13938688, 1242448} + , {25566464, 1253443} + , + {37194240, 1264438} + , {48822016, 1275433} + , {60449792, 1286428} + , {72077568, 1297423} + , {83705344, 1308418} + , + {95333120, 1319413} + , {6960896, 1330409} + , {18588672, 1341404} + , {30216448, 1352399} + , {41844224, 1363394} + , + {53472000, 1374389} + , {65099776, 1385384} + , {76727552, 1396379} + , + } + , + + {{0, 0} + , {88355328, 1407374} + , {76710656, 2814749} + , {65065984, 4222124} + , {53421312, 5629499} + , + {41776640, 7036874} + , {30131968, 8444249} + , {18487296, 9851624} + , {6842624, 11258999} + , {95197952, 12666373} + , + {83553280, 14073748} + , {71908608, 15481123} + , {60263936, 16888498} + , {48619264, 18295873} + , {36974592, 19703248} + , + {25329920, 21110623} + , {13685248, 22517998} + , {2040576, 23925373} + , {90395904, 25332747} + , {78751232, 26740122} + , + {67106560, 28147497} + , {55461888, 29554872} + , {43817216, 30962247} + , {32172544, 32369622} + , {20527872, 33776997} + , + {8883200, 35184372} + , {97238528, 36591746} + , {85593856, 37999121} + , {73949184, 39406496} + , {62304512, 40813871} + , + {50659840, 42221246} + , {39015168, 43628621} + , {27370496, 45035996} + , {15725824, 46443371} + , {4081152, 47850746} + , + {92436480, 49258120} + , {80791808, 50665495} + , {69147136, 52072870} + , {57502464, 53480245} + , {45857792, 54887620} + , + {34213120, 56294995} + , {22568448, 57702370} + , {10923776, 59109745} + , {99279104, 60517119} + , {87634432, 61924494} + , + {75989760, 63331869} + , {64345088, 64739244} + , {52700416, 66146619} + , {41055744, 67553994} + , {29411072, 68961369} + , + {17766400, 70368744} + , {6121728, 71776119} + , {94477056, 73183493} + , {82832384, 74590868} + , {71187712, 75998243} + , + {59543040, 77405618} + , {47898368, 78812993} + , {36253696, 80220368} + , {24609024, 81627743} + , {12964352, 83035118} + , + {1319680, 84442493} + , {89675008, 85849867} + , {78030336, 87257242} + , {66385664, 88664617} + , {54740992, 90071992} + , + {43096320, 91479367} + , {31451648, 92886742} + , {19806976, 94294117} + , {8162304, 95701492} + , {96517632, 97108866} + , + {84872960, 98516241} + , {73228288, 99923616} + , {61583616, 1330991} + , {49938944, 2738366} + , {38294272, 4145741} + , + {26649600, 5553116} + , {15004928, 6960491} + , {3360256, 8367866} + , {91715584, 9775240} + , {80070912, 11182615} + , + {68426240, 12589990} + , {56781568, 13997365} + , {45136896, 15404740} + , {33492224, 16812115} + , {21847552, 18219490} + , + {10202880, 19626865} + , {98558208, 21034239} + , {86913536, 22441614} + , {75268864, 23848989} + , {63624192, 25256364} + , + {51979520, 26663739} + , {40334848, 28071114} + , {28690176, 29478489} + , {17045504, 30885864} + , {5400832, 32293239} + , + {93756160, 33700613} + , {82111488, 35107988} + , {70466816, 36515363} + , {58822144, 37922738} + , {47177472, 39330113} + , + {35532800, 40737488} + , {23888128, 42144863} + , {12243456, 43552238} + , {598784, 44959613} + , {88954112, 46366987} + , + {77309440, 47774362} + , {65664768, 49181737} + , {54020096, 50589112} + , {42375424, 51996487} + , {30730752, 53403862} + , + {19086080, 54811237} + , {7441408, 56218612} + , {95796736, 57625986} + , {84152064, 59033361} + , {72507392, 60440736} + , + {60862720, 61848111} + , {49218048, 63255486} + , {37573376, 64662861} + , {25928704, 66070236} + , {14284032, 67477611} + , + {2639360, 68884986} + , {90994688, 70292360} + , {79350016, 71699735} + , {67705344, 73107110} + , {56060672, 74514485} + , + {44416000, 75921860} + , {32771328, 77329235} + , {21126656, 78736610} + , + } + , + + {{0, 0} + , {9481984, 80143985} + , {18963968, 60287970} + , {28445952, 40431955} + , {37927936, 20575940} + , + {47409920, 719925} + , {56891904, 80863910} + , {66373888, 61007895} + , {75855872, 41151880} + , {85337856, 21295865} + , + {94819840, 1439850} + , {4301824, 81583836} + , {13783808, 61727821} + , {23265792, 41871806} + , {32747776, 22015791} + , + {42229760, 2159776} + , {51711744, 82303761} + , {61193728, 62447746} + , {70675712, 42591731} + , {80157696, 22735716} + , + {89639680, 2879701} + , {99121664, 83023686} + , {8603648, 63167672} + , {18085632, 43311657} + , {27567616, 23455642} + , + {37049600, 3599627} + , {46531584, 83743612} + , {56013568, 63887597} + , {65495552, 44031582} + , {74977536, 24175567} + , + {84459520, 4319552} + , {93941504, 84463537} + , {3423488, 64607523} + , {12905472, 44751508} + , {22387456, 24895493} + , + {31869440, 5039478} + , {41351424, 85183463} + , {50833408, 65327448} + , {60315392, 45471433} + , {69797376, 25615418} + , + {79279360, 5759403} + , {88761344, 85903388} + , {98243328, 66047373} + , {7725312, 46191359} + , {17207296, 26335344} + , + {26689280, 6479329} + , {36171264, 86623314} + , {45653248, 66767299} + , {55135232, 46911284} + , {64617216, 27055269} + , + {74099200, 7199254} + , {83581184, 87343239} + , {93063168, 67487224} + , {2545152, 47631210} + , {12027136, 27775195} + , + {21509120, 7919180} + , {30991104, 88063165} + , {40473088, 68207150} + , {49955072, 48351135} + , {59437056, 28495120} + , + {68919040, 8639105} + , {78401024, 88783090} + , {87883008, 68927075} + , {97364992, 49071060} + , {6846976, 29215046} + , + {16328960, 9359031} + , {25810944, 89503016} + , {35292928, 69647001} + , {44774912, 49790986} + , {54256896, 29934971} + , + {63738880, 10078956} + , {73220864, 90222941} + , {82702848, 70366926} + , {92184832, 50510911} + , {1666816, 30654897} + , + {11148800, 10798882} + , {20630784, 90942867} + , {30112768, 71086852} + , {39594752, 51230837} + , {49076736, 31374822} + , + {58558720, 11518807} + , {68040704, 91662792} + , {77522688, 71806777} + , {87004672, 51950762} + , {96486656, 32094747} + , + {5968640, 12238733} + , {15450624, 92382718} + , {24932608, 72526703} + , {34414592, 52670688} + , {43896576, 32814673} + , + {53378560, 12958658} + , {62860544, 93102643} + , {72342528, 73246628} + , {81824512, 53390613} + , {91306496, 33534598} + , + {788480, 13678584} + , {10270464, 93822569} + , {19752448, 73966554} + , {29234432, 54110539} + , {38716416, 34254524} + , + {48198400, 14398509} + , {57680384, 94542494} + , {67162368, 74686479} + , {76644352, 54830464} + , {86126336, 34974449} + , + {95608320, 15118434} + , {5090304, 95262420} + , {14572288, 75406405} + , {24054272, 55550390} + , {33536256, 35694375} + , + {43018240, 15838360} + , {52500224, 95982345} + , {61982208, 76126330} + , {71464192, 56270315} + , {80946176, 36414300} + , + {90428160, 16558285} + , {99910144, 96702270} + , {9392128, 76846256} + , {18874112, 56990241} + , {28356096, 37134226} + , + {37838080, 17278211} + , {47320064, 97422196} + , {56802048, 77566181} + , {66284032, 57710166} + , {75766016, 37854151} + , + {85248000, 17998136} + , {94729984, 98142121} + , {4211968, 78286107} + , + } + , +}; + +// for j>=min_j[i+1], there is k s.t. convert_table[i][j][k]>0 +// int min_j[] = { 0, 0, 0, 3 }; + +// for even k, ((packed_10000_zeros[k>>3])>>(k&7))&3)=greatest(i) s.t. 10^i divides k +const UINT8 packed_10000_zeros[] = { + + 0x3, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, + 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, + 0x1, 0x4, 0x10, + 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, + 0x4, 0x20, 0x40, + 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, + 0x10, 0x40, 0x0, + 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, + 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, + 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, + 0x3, 0x4, 0x10, + 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, + 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, + 0x40, 0x0, 0x2, + 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, + 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, + 0x1, 0x4, 0x10, + 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, + 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, + 0x20, 0x40, 0x0, + 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x3, 0x4, 0x10, + 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, + 0x1, 0x4, 0x20, + 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, + 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, + 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, + 0x40, 0x0, 0x1, + 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, + 0x0, 0x2, 0x4, + 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, + 0x1, 0x4, 0x10, + 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x3, 0x4, 0x10, 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, + 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, + 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, + 0x1, 0x4, 0x10, + 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, + 0x4, 0x20, 0x40, + 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, + 0x10, 0x40, 0x0, + 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, + 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, 0x0, 0x3, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, + 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, + 0x2, 0x4, 0x10, + 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, + 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, + 0x40, 0x0, 0x2, + 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, + 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, + 0x1, 0x4, 0x10, + 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, + 0x0, 0x3, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, + 0x20, 0x40, 0x0, + 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, + 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, + 0x1, 0x4, 0x20, + 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, + 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, + 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, + 0x40, 0x0, 0x1, + 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, + 0x0, 0x3, 0x4, + 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, + 0x1, 0x4, 0x10, + 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, + 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, + 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, + 0x1, 0x4, 0x10, + 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, + 0x4, 0x20, 0x40, + 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x3, 0x4, + 0x10, 0x40, 0x0, + 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, + 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, + 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, + 0x2, 0x4, 0x10, + 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, + 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, + 0x40, 0x0, 0x2, + 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, + 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x3, 0x4, 0x10, 0x40, 0x0, + 0x1, 0x4, 0x10, + 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, + 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, + 0x20, 0x40, 0x0, + 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, + 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, + 0x1, 0x4, 0x20, + 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, + 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, + 0x1, 0x4, 0x10, 0x40, 0x0, 0x3, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, + 0x40, 0x0, 0x1, + 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, + 0x0, 0x2, 0x4, + 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, + 0x1, 0x4, 0x10, + 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, + 0x2, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, + 0x40, 0x0, 0x1, + 0x4, 0x10, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, 0x2, 0x4, 0x10, 0x40, + 0x0, 0x1, 0x4, + 0x10, 0x40, 0x0, 0x1, 0x4, 0x20, 0x40, 0x0, 0x1, 0x4, 0x10, 0x40, 0x0, + 0x1, 0x4, 0x10, + 0x40, 0x0, +}; + + +const SINT8 factors[1024][2] = { + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {4, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 2} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {5, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {3, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {4, 0} + , {0, 0} + , {1, 2} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {6, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 2} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {4, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {5, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 2} + , + {0, 0} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {4, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {3, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 3} + , {1, 0} + , {0, 0} + , {7, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {4, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 2} + , + {0, 0} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {5, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 2} + , {4, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {6, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {3, 2} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {4, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {5, 0} + , {0, 2} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {4, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 0} + , {1, 3} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {8, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {4, 0} + , {0, 0} + , {1, 0} + , {0, 2} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {3, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {5, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 2} + , + {0, 0} + , {1, 0} + , {0, 0} + , {4, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {6, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 2} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {4, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 2} + , + {0, 0} + , {5, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {3, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {4, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 3} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {7, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {4, 2} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {5, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 2} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {4, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {3, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {6, 0} + , {0, 0} + , {1, 2} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {4, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 2} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {5, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {4, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 3} + , + {0, 0} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {9, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {3, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 2} + , {1, 0} + , {0, 0} + , {4, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {5, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 2} + , + {0, 0} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {4, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 2} + , {6, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {4, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {3, 2} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {5, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {4, 0} + , {0, 4} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {7, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 0} + , {1, 2} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {4, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {5, 0} + , {0, 0} + , {1, 0} + , {0, 2} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {3, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {4, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 2} + , + {0, 0} + , {1, 0} + , {0, 0} + , {6, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {4, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 2} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {5, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 3} + , + {0, 0} + , {4, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {3, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {8, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 2} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {4, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {5, 2} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {4, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 2} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {6, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {3, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {4, 0} + , {0, 0} + , {1, 2} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {5, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 3} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {4, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {7, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 2} + , + {0, 0} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {4, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {3, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 2} + , {1, 0} + , {0, 0} + , {5, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {4, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 2} + , + {0, 0} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {6, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 2} + , {4, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {3, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {5, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {3, 3} + , + {0, 0} + , {1, 0} + , {0, 0} + , {2, 0} + , {0, 1} + , {1, 0} + , {0, 0} + , {4, 0} + , {0, 0} + , {1, 1} + , + {0, 0} + , {2, 0} + , {0, 0} + , {1, 0} + , {0, 1} + , {3, 0} + , {0, 0} + , {1, 0} + , {0, 0} + , {2, 1} + , + {0, 0} + , {1, 0} + , {0, 0} + , {10, 0} + , +}; diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_decimal_data.c b/gcc-4.4.3/libgcc/config/libbid/bid_decimal_data.c new file mode 100644 index 000000000..81284f826 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_decimal_data.c @@ -0,0 +1,1293 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +UINT64 round_const_table[][19] = { + { // RN + 0ull, // 0 extra digits + 5ull, // 1 extra digits + 50ull, // 2 extra digits + 500ull, // 3 extra digits + 5000ull, // 4 extra digits + 50000ull, // 5 extra digits + 500000ull, // 6 extra digits + 5000000ull, // 7 extra digits + 50000000ull, // 8 extra digits + 500000000ull, // 9 extra digits + 5000000000ull, // 10 extra digits + 50000000000ull, // 11 extra digits + 500000000000ull, // 12 extra digits + 5000000000000ull, // 13 extra digits + 50000000000000ull, // 14 extra digits + 500000000000000ull, // 15 extra digits + 5000000000000000ull, // 16 extra digits + 50000000000000000ull, // 17 extra digits + 500000000000000000ull // 18 extra digits + } + , + { // RD + 0ull, // 0 extra digits + 0ull, // 1 extra digits + 0ull, // 2 extra digits + 00ull, // 3 extra digits + 000ull, // 4 extra digits + 0000ull, // 5 extra digits + 00000ull, // 6 extra digits + 000000ull, // 7 extra digits + 0000000ull, // 8 extra digits + 00000000ull, // 9 extra digits + 000000000ull, // 10 extra digits + 0000000000ull, // 11 extra digits + 00000000000ull, // 12 extra digits + 000000000000ull, // 13 extra digits + 0000000000000ull, // 14 extra digits + 00000000000000ull, // 15 extra digits + 000000000000000ull, // 16 extra digits + 0000000000000000ull, // 17 extra digits + 00000000000000000ull // 18 extra digits + } + , + { // round to Inf + 0ull, // 0 extra digits + 9ull, // 1 extra digits + 99ull, // 2 extra digits + 999ull, // 3 extra digits + 9999ull, // 4 extra digits + 99999ull, // 5 extra digits + 999999ull, // 6 extra digits + 9999999ull, // 7 extra digits + 99999999ull, // 8 extra digits + 999999999ull, // 9 extra digits + 9999999999ull, // 10 extra digits + 99999999999ull, // 11 extra digits + 999999999999ull, // 12 extra digits + 9999999999999ull, // 13 extra digits + 99999999999999ull, // 14 extra digits + 999999999999999ull, // 15 extra digits + 9999999999999999ull, // 16 extra digits + 99999999999999999ull, // 17 extra digits + 999999999999999999ull // 18 extra digits + } + , + { // RZ + 0ull, // 0 extra digits + 0ull, // 1 extra digits + 0ull, // 2 extra digits + 00ull, // 3 extra digits + 000ull, // 4 extra digits + 0000ull, // 5 extra digits + 00000ull, // 6 extra digits + 000000ull, // 7 extra digits + 0000000ull, // 8 extra digits + 00000000ull, // 9 extra digits + 000000000ull, // 10 extra digits + 0000000000ull, // 11 extra digits + 00000000000ull, // 12 extra digits + 000000000000ull, // 13 extra digits + 0000000000000ull, // 14 extra digits + 00000000000000ull, // 15 extra digits + 000000000000000ull, // 16 extra digits + 0000000000000000ull, // 17 extra digits + 00000000000000000ull // 18 extra digits + } + , + { // round ties away from 0 + 0ull, // 0 extra digits + 5ull, // 1 extra digits + 50ull, // 2 extra digits + 500ull, // 3 extra digits + 5000ull, // 4 extra digits + 50000ull, // 5 extra digits + 500000ull, // 6 extra digits + 5000000ull, // 7 extra digits + 50000000ull, // 8 extra digits + 500000000ull, // 9 extra digits + 5000000000ull, // 10 extra digits + 50000000000ull, // 11 extra digits + 500000000000ull, // 12 extra digits + 5000000000000ull, // 13 extra digits + 50000000000000ull, // 14 extra digits + 500000000000000ull, // 15 extra digits + 5000000000000000ull, // 16 extra digits + 50000000000000000ull, // 17 extra digits + 500000000000000000ull // 18 extra digits + } + , +}; + +UINT128 round_const_table_128[][36] = { + { //RN + {{0ull, 0ull} + } + , // 0 extra digits + {{5ull, 0ull} + } + , // 1 extra digits + {{50ull, 0ull} + } + , // 2 extra digits + {{500ull, 0ull} + } + , // 3 extra digits + {{5000ull, 0ull} + } + , // 4 extra digits + {{50000ull, 0ull} + } + , // 5 extra digits + {{500000ull, 0ull} + } + , // 6 extra digits + {{5000000ull, 0ull} + } + , // 7 extra digits + {{50000000ull, 0ull} + } + , // 8 extra digits + {{500000000ull, 0ull} + } + , // 9 extra digits + {{5000000000ull, 0ull} + } + , // 10 extra digits + {{50000000000ull, 0ull} + } + , // 11 extra digits + {{500000000000ull, 0ull} + } + , // 12 extra digits + {{5000000000000ull, 0ull} + } + , // 13 extra digits + {{50000000000000ull, 0ull} + } + , // 14 extra digits + {{500000000000000ull, 0ull} + } + , // 15 extra digits + {{5000000000000000ull, 0ull} + } + , // 16 extra digits + {{50000000000000000ull, 0ull} + } + , // 17 extra digits + {{500000000000000000ull, 0ull} + } + , // 18 extra digits + {{5000000000000000000ull, 0ull} + } + , // 19 extra digits + {{0xb5e3af16b1880000ull, 2ull} + } + , //20 + {{0x1ae4d6e2ef500000ull, 27ull} + } + , //21 + {{0xcf064dd59200000ull, 271ull} + } + , //22 + {{0x8163f0a57b400000ull, 2710ull} + } + , //23 + {{0xde76676d0800000ull, 27105ull} + } + , //24 + {{0x8b0a00a425000000ull, 0x422caull} + } + , //25 + {{0x6e64066972000000ull, 0x295be9ull} + } + , //26 + {{0x4fe8401e74000000ull, 0x19d971eull} + } + , //27 + {{0x1f12813088000000ull, 0x1027e72full} + } + , //28 + {{0x36b90be550000000ull, 0xa18f07d7ull} + } + , //29 + {{0x233a76f520000000ull, 0x64f964e68ull} + } + , //30 + {{0x6048a59340000000ull, 0x3f1bdf1011ull} + } + , //31 + {{0xc2d677c080000000ull, 0x27716b6a0adull} + } + , //32 + {{0x9c60ad8500000000ull, 0x18a6e32246c9ull} + } + , //33 + {{0x1bc6c73200000000ull, 0xf684df56c3e0ull} + } + , //34 + {{0x15c3c7f400000000ull, 0x9a130b963a6c1ull} + } + , //35 + } + , + { //RD + {{0ull, 0ull} + } + , // 0 extra digits + {{0ull, 0ull} + } + , // 1 extra digits + {{0ull, 0ull} + } + , // 2 extra digits + {{00ull, 0ull} + } + , // 3 extra digits + {{000ull, 0ull} + } + , // 4 extra digits + {{0000ull, 0ull} + } + , // 5 extra digits + {{00000ull, 0ull} + } + , // 6 extra digits + {{000000ull, 0ull} + } + , // 7 extra digits + {{0000000ull, 0ull} + } + , // 8 extra digits + {{00000000ull, 0ull} + } + , // 9 extra digits + {{000000000ull, 0ull} + } + , // 10 extra digits + {{0000000000ull, 0ull} + } + , // 11 extra digits + {{00000000000ull, 0ull} + } + , // 12 extra digits + {{000000000000ull, 0ull} + } + , // 13 extra digits + {{0000000000000ull, 0ull} + } + , // 14 extra digits + {{00000000000000ull, 0ull} + } + , // 15 extra digits + {{000000000000000ull, 0ull} + } + , // 16 extra digits + {{0000000000000000ull, 0ull} + } + , // 17 extra digits + {{00000000000000000ull, 0ull} + } + , // 18 extra digits + {{000000000000000000ull, 0ull} + } + , // 19 extra digits + {{0ull, 0ull} + } + , //20 + {{0ull, 0ull} + } + , //21 + {{0ull, 0ull} + } + , //22 + {{0ull, 0ull} + } + , //23 + {{0ull, 0ull} + } + , //24 + {{0ull, 0ull} + } + , //25 + {{0ull, 0ull} + } + , //26 + {{0ull, 0ull} + } + , //27 + {{0ull, 0ull} + } + , //28 + {{0ull, 0ull} + } + , //29 + {{0ull, 0ull} + } + , //30 + {{0ull, 0ull} + } + , //31 + {{0ull, 0ull} + } + , //32 + {{0ull, 0ull} + } + , //33 + {{0ull, 0ull} + } + , //34 + {{0ull, 0ull} + } + , //35 + } + , + { //RU + {{0ull, 0ull} + } + , // 0 extra digits + {{9ull, 0ull} + } + , // 1 extra digits + {{99ull, 0ull} + } + , // 2 extra digits + {{999ull, 0ull} + } + , // 3 extra digits + {{9999ull, 0ull} + } + , // 4 extra digits + {{99999ull, 0ull} + } + , // 5 extra digits + {{999999ull, 0ull} + } + , // 6 extra digits + {{9999999ull, 0ull} + } + , // 7 extra digits + {{99999999ull, 0ull} + } + , // 8 extra digits + {{999999999ull, 0ull} + } + , // 9 extra digits + {{9999999999ull, 0ull} + } + , // 10 extra digits + {{99999999999ull, 0ull} + } + , // 11 extra digits + {{999999999999ull, 0ull} + } + , // 12 extra digits + {{9999999999999ull, 0ull} + } + , // 13 extra digits + {{99999999999999ull, 0ull} + } + , // 14 extra digits + {{999999999999999ull, 0ull} + } + , // 15 extra digits + {{9999999999999999ull, 0ull} + } + , // 16 extra digits + {{99999999999999999ull, 0ull} + } + , // 17 extra digits + {{999999999999999999ull, 0ull} + } + , // 18 extra digits + {{9999999999999999999ull, 0ull} + } + , // 19 extra digits + {{0x6BC75E2D630FFFFFull, 0x5ull} + } + , //20 + {{0x35C9ADC5DE9FFFFFull, 0x36ull} + } + , //21 + {{0x19E0C9BAB23FFFFFull, 0x21eull} + } + , //22 + {{0x2C7E14AF67FFFFFull, 0x152dull} + } + , //23 + {{0x1BCECCEDA0FFFFFFull, 0xd3c2ull} + } + , //24 + {{0x1614014849FFFFFFull, 0x84595ull} + } + , //25 + {{0xDCC80CD2E3FFFFFFull, 0x52b7d2ull} + } + , //26 + {{0x9FD0803CE7FFFFFFull, 0x33B2E3Cull} + } + , //27 + {{0x3E2502610FFFFFFFull, 0x204FCE5Eull} + } + , //28 + {{0x6D7217CA9FFFFFFFull, 0x1431E0FAEull} + } + , //29 + {{0x4674EDEA3FFFFFFFull, 0xC9F2C9CD0ull} + } + , //30 + {{0xC0914B267FFFFFFFull, 0x7E37BE2022ull} + } + , //31 + {{0x85ACEF80FFFFFFFFull, 0x4EE2D6D415Bull} + } + , //32 + {{0x38c15b09ffffffffull, 0x314dc6448d93ull} + } + , //33 + {{0x378d8e63ffffffffull, 0x1ed09bead87c0ull} + } + , //34 + {{0x2b878fe7ffffffffull, 0x13426172c74d82ull} + } + , //35 + } + , + { //RZ + {{0ull, 0ull} + } + , // 0 extra digits + {{0ull, 0ull} + } + , // 1 extra digits + {{0ull, 0ull} + } + , // 2 extra digits + {{00ull, 0ull} + } + , // 3 extra digits + {{000ull, 0ull} + } + , // 4 extra digits + {{0000ull, 0ull} + } + , // 5 extra digits + {{00000ull, 0ull} + } + , // 6 extra digits + {{000000ull, 0ull} + } + , // 7 extra digits + {{0000000ull, 0ull} + } + , // 8 extra digits + {{00000000ull, 0ull} + } + , // 9 extra digits + {{000000000ull, 0ull} + } + , // 10 extra digits + {{0000000000ull, 0ull} + } + , // 11 extra digits + {{00000000000ull, 0ull} + } + , // 12 extra digits + {{000000000000ull, 0ull} + } + , // 13 extra digits + {{0000000000000ull, 0ull} + } + , // 14 extra digits + {{00000000000000ull, 0ull} + } + , // 15 extra digits + {{000000000000000ull, 0ull} + } + , // 16 extra digits + {{0000000000000000ull, 0ull} + } + , // 17 extra digits + {{00000000000000000ull, 0ull} + } + , // 18 extra digits + {{000000000000000000ull, 0ull} + } + , // 19 extra digits + {{0ull, 0ull} + } + , //20 + {{0ull, 0ull} + } + , //21 + {{0ull, 0ull} + } + , //22 + {{0ull, 0ull} + } + , //23 + {{0ull, 0ull} + } + , //24 + {{0ull, 0ull} + } + , //25 + {{0ull, 0ull} + } + , //26 + {{0ull, 0ull} + } + , //27 + {{0ull, 0ull} + } + , //28 + {{0ull, 0ull} + } + , //29 + {{0ull, 0ull} + } + , //30 + {{0ull, 0ull} + } + , //31 + {{0ull, 0ull} + } + , //32 + {{0ull, 0ull} + } + , //33 + {{0ull, 0ull} + } + , //34 + {{0ull, 0ull} + } + , //35 + } + , + { //RN, ties away + {{0ull, 0ull} + } + , // 0 extra digits + {{5ull, 0ull} + } + , // 1 extra digits + {{50ull, 0ull} + } + , // 2 extra digits + {{500ull, 0ull} + } + , // 3 extra digits + {{5000ull, 0ull} + } + , // 4 extra digits + {{50000ull, 0ull} + } + , // 5 extra digits + {{500000ull, 0ull} + } + , // 6 extra digits + {{5000000ull, 0ull} + } + , // 7 extra digits + {{50000000ull, 0ull} + } + , // 8 extra digits + {{500000000ull, 0ull} + } + , // 9 extra digits + {{5000000000ull, 0ull} + } + , // 10 extra digits + {{50000000000ull, 0ull} + } + , // 11 extra digits + {{500000000000ull, 0ull} + } + , // 12 extra digits + {{5000000000000ull, 0ull} + } + , // 13 extra digits + {{50000000000000ull, 0ull} + } + , // 14 extra digits + {{500000000000000ull, 0ull} + } + , // 15 extra digits + {{5000000000000000ull, 0ull} + } + , // 16 extra digits + {{50000000000000000ull, 0ull} + } + , // 17 extra digits + {{500000000000000000ull, 0ull} + } + , // 18 extra digits + {{5000000000000000000ull, 0ull} + } + , // 19 extra digits + {{0xb5e3af16b1880000ull, 2ull} + } + , //20 + {{0x1ae4d6e2ef500000ull, 27ull} + } + , //21 + {{0xcf064dd59200000ull, 271ull} + } + , //22 + {{0x8163f0a57b400000ull, 2710ull} + } + , //23 + {{0xde76676d0800000ull, 27105ull} + } + , //24 + {{0x8b0a00a425000000ull, 0x422caull} + } + , //25 + {{0x6e64066972000000ull, 0x295be9ull} + } + , //26 + {{0x4fe8401e74000000ull, 0x19d971eull} + } + , //27 + {{0x1f12813088000000ull, 0x1027e72full} + } + , //28 + {{0x36b90be550000000ull, 0xa18f07d7ull} + } + , //29 + {{0x233a76f520000000ull, 0x64f964e68ull} + } + , //30 + {{0x6048a59340000000ull, 0x3f1bdf1011ull} + } + , //31 + {{0xc2d677c080000000ull, 0x27716b6a0adull} + } + , //32 + {{0x9c60ad8500000000ull, 0x18a6e32246c9ull} + } + , //33 + {{0x1bc6c73200000000ull, 0xf684df56c3e0ull} + } + , //34 + {{0x15c3c7f400000000ull, 0x9a130b963a6c1ull} + } + , //35 + } +}; + + +UINT128 reciprocals10_128[] = { + {{0ull, 0ull} + } + , // 0 extra digits + {{0x3333333333333334ull, 0x3333333333333333ull} + } + , // 1 extra digit + {{0x51eb851eb851eb86ull, 0x051eb851eb851eb8ull} + } + , // 2 extra digits + {{0x3b645a1cac083127ull, 0x0083126e978d4fdfull} + } + , // 3 extra digits + {{0x4af4f0d844d013aaULL, 0x00346dc5d6388659ULL} + } + , // 10^(-4) * 2^131 + {{0x08c3f3e0370cdc88ULL, 0x0029f16b11c6d1e1ULL} + } + , // 10^(-5) * 2^134 + {{0x6d698fe69270b06dULL, 0x00218def416bdb1aULL} + } + , // 10^(-6) * 2^137 + {{0xaf0f4ca41d811a47ULL, 0x0035afe535795e90ULL} + } + , // 10^(-7) * 2^141 + {{0xbf3f70834acdaea0ULL, 0x002af31dc4611873ULL} + } + , // 10^(-8) * 2^144 + {{0x65cc5a02a23e254dULL, 0x00225c17d04dad29ULL} + } + , // 10^(-9) * 2^147 + {{0x6fad5cd10396a214ULL, 0x0036f9bfb3af7b75ULL} + } + , // 10^(-10) * 2^151 + {{0xbfbde3da69454e76ULL, 0x002bfaffc2f2c92aULL} + } + , // 10^(-11) * 2^154 + {{0x32fe4fe1edd10b92ULL, 0x00232f33025bd422ULL} + } + , // 10^(-12) * 2^157 + {{0x84ca19697c81ac1cULL, 0x00384b84d092ed03ULL} + } + , // 10^(-13) * 2^161 + {{0x03d4e1213067bce4ULL, 0x002d09370d425736ULL} + } + , // 10^(-14) * 2^164 + {{0x3643e74dc052fd83ULL, 0x0024075f3dceac2bULL} + } + , // 10^(-15) * 2^167 + {{0x56d30baf9a1e626bULL, 0x0039a5652fb11378ULL} + } + , // 10^(-16) * 2^171 + {{0x12426fbfae7eb522ULL, 0x002e1dea8c8da92dULL} + } + , // 10^(-17) * 2^174 + {{0x41cebfcc8b9890e8ULL, 0x0024e4bba3a48757ULL} + } + , // 10^(-18) * 2^177 + {{0x694acc7a78f41b0dULL, 0x003b07929f6da558ULL} + } + , // 10^(-19) * 2^181 + {{0xbaa23d2ec729af3eULL, 0x002f394219248446ULL} + } + , // 10^(-20) * 2^184 + {{0xfbb4fdbf05baf298ULL, 0x0025c768141d369eULL} + } + , // 10^(-21) * 2^187 + {{0x2c54c931a2c4b759ULL, 0x003c7240202ebdcbULL} + } + , // 10^(-22) * 2^191 + {{0x89dd6dc14f03c5e1ULL, 0x00305b66802564a2ULL} + } + , // 10^(-23) * 2^194 + {{0xd4b1249aa59c9e4eULL, 0x0026af8533511d4eULL} + } + , // 10^(-24) * 2^197 + {{0x544ea0f76f60fd49ULL, 0x003de5a1ebb4fbb1ULL} + } + , // 10^(-25) * 2^201 + {{0x76a54d92bf80caa1ULL, 0x00318481895d9627ULL} + } + , // 10^(-26) * 2^204 + {{0x921dd7a89933d54eULL, 0x00279d346de4781fULL} + } + , // 10^(-27) * 2^207 + {{0x8362f2a75b862215ULL, 0x003f61ed7ca0c032ULL} + } + , // 10^(-28) * 2^211 + {{0xcf825bb91604e811ULL, 0x0032b4bdfd4d668eULL} + } + , // 10^(-29) * 2^214 + {{0x0c684960de6a5341ULL, 0x00289097fdd7853fULL} + } + , // 10^(-30) * 2^217 + {{0x3d203ab3e521dc34ULL, 0x002073accb12d0ffULL} + } + , // 10^(-31) * 2^220 + {{0x2e99f7863b696053ULL, 0x0033ec47ab514e65ULL} + } + , // 10^(-32) * 2^224 + {{0x587b2c6b62bab376ULL, 0x002989d2ef743eb7ULL} + } + , // 10^(-33) * 2^227 + {{0xad2f56bc4efbc2c5ULL, 0x00213b0f25f69892ULL} + } + , // 10^(-34) * 2^230 + {{0x0f2abc9d8c9689d1ull, 0x01a95a5b7f87a0efull} + } + , // 35 extra digits +}; + + +int recip_scale[] = { + 129 - 128, // 1 + 129 - 128, // 1/10 + 129 - 128, // 1/10^2 + 129 - 128, // 1/10^3 + 3, // 131 - 128 + 6, // 134 - 128 + 9, // 137 - 128 + 13, // 141 - 128 + 16, // 144 - 128 + 19, // 147 - 128 + 23, // 151 - 128 + 26, // 154 - 128 + 29, // 157 - 128 + 33, // 161 - 128 + 36, // 164 - 128 + 39, // 167 - 128 + 43, // 171 - 128 + 46, // 174 - 128 + 49, // 177 - 128 + 53, // 181 - 128 + 56, // 184 - 128 + 59, // 187 - 128 + 63, // 191 - 128 + + 66, // 194 - 128 + 69, // 197 - 128 + 73, // 201 - 128 + 76, // 204 - 128 + 79, // 207 - 128 + 83, // 211 - 128 + 86, // 214 - 128 + 89, // 217 - 128 + 92, // 220 - 128 + 96, // 224 - 128 + 99, // 227 - 128 + 102, // 230 - 128 + 109, // 237 - 128, 1/10^35 +}; + + +// tables used in computation +int estimate_decimal_digits[129] = { + 1, //2^0 =1 < 10^0 + 1, //2^1 =2 < 10^1 + 1, //2^2 =4 < 10^1 + 1, //2^3 =8 < 10^1 + 2, //2^4 =16 < 10^2 + 2, //2^5 =32 < 10^2 + 2, //2^6 =64 < 10^2 + 3, //2^7 =128 < 10^3 + 3, //2^8 =256 < 10^3 + 3, //2^9 =512 < 10^3 + 4, //2^10=1024 < 10^4 + 4, //2^11=2048 < 10^4 + 4, //2^12=4096 < 10^4 + 4, //2^13=8192 < 10^4 + 5, //2^14=16384 < 10^5 + 5, //2^15=32768 < 10^5 + + 5, //2^16=65536 < 10^5 + 6, //2^17=131072 < 10^6 + 6, //2^18=262144 < 10^6 + 6, //2^19=524288 < 10^6 + 7, //2^20=1048576 < 10^7 + 7, //2^21=2097152 < 10^7 + 7, //2^22=4194304 < 10^7 + 7, //2^23=8388608 < 10^7 + 8, //2^24=16777216 < 10^8 + 8, //2^25=33554432 < 10^8 + 8, //2^26=67108864 < 10^8 + 9, //2^27=134217728 < 10^9 + 9, //2^28=268435456 < 10^9 + 9, //2^29=536870912 < 10^9 + 10, //2^30=1073741824< 10^10 + 10, //2^31=2147483648< 10^10 + + 10, //2^32=4294967296 < 10^10 + 10, //2^33=8589934592 < 10^10 + 11, //2^34=17179869184 < 10^11 + 11, //2^35=34359738368 < 10^11 + 11, //2^36=68719476736 < 10^11 + 12, //2^37=137438953472 < 10^12 + 12, //2^38=274877906944 < 10^12 + 12, //2^39=549755813888 < 10^12 + 13, //2^40=1099511627776 < 10^13 + 13, //2^41=2199023255552 < 10^13 + 13, //2^42=4398046511104 < 10^13 + 13, //2^43=8796093022208 < 10^13 + 14, //2^44=17592186044416 < 10^14 + 14, //2^45=35184372088832 < 10^14 + 14, //2^46=70368744177664 < 10^14 + 15, //2^47=140737488355328< 10^15 + + 15, //2^48=281474976710656 < 10^15 + 15, //2^49=562949953421312 < 10^15 + 16, //2^50=1125899906842624 < 10^16 + 16, //2^51=2251799813685248 < 10^16 + 16, //2^52=4503599627370496 < 10^16 + 16, //2^53=9007199254740992 < 10^16 + 17, //2^54=18014398509481984 < 10^17 + 17, //2^55=36028797018963968 < 10^17 + 17, //2^56=72057594037927936 < 10^17 + 18, //2^57=144115188075855872 < 10^18 + 18, //2^58=288230376151711744 < 10^18 + 18, //2^59=576460752303423488 < 10^18 + 19, //2^60=1152921504606846976< 10^19 + 19, //2^61=2305843009213693952< 10^19 + 19, //2^62=4611686018427387904< 10^19 + 19, //2^63=9223372036854775808< 10^19 + + 20, //2^64=18446744073709551616 + 20, //2^65=36893488147419103232 + 20, //2^66=73786976294838206464 + 21, //2^67=147573952589676412928 + 21, //2^68=295147905179352825856 + 21, //2^69=590295810358705651712 + 22, //2^70=1180591620717411303424 + 22, //2^71=2361183241434822606848 + 22, //2^72=4722366482869645213696 + 22, //2^73=9444732965739290427392 + 23, //2^74=18889465931478580854784 + 23, //2^75=37778931862957161709568 + 23, //2^76=75557863725914323419136 + 24, //2^77=151115727451828646838272 + 24, //2^78=302231454903657293676544 + 24, //2^79=604462909807314587353088 + + 25, //2^80=1208925819614629174706176 + 25, //2^81=2417851639229258349412352 + 25, //2^82=4835703278458516698824704 + 25, //2^83=9671406556917033397649408 + 26, //2^84=19342813113834066795298816 + 26, //2^85=38685626227668133590597632 + 26, //2^86=77371252455336267181195264 + 27, //2^87=154742504910672534362390528 + 27, //2^88=309485009821345068724781056 + 27, //2^89=618970019642690137449562112 + 28, //2^90=1237940039285380274899124224 + 28, //2^91=2475880078570760549798248448 + 28, //2^92=4951760157141521099596496896 + 28, //2^93=9903520314283042199192993792 + 29, //2^94=19807040628566084398385987584 + 29, //2^95=39614081257132168796771975168 + 29, //2^96=79228162514264337593543950336 + + 30, //2^97=158456325028528675187087900672 + 30, //2^98=316912650057057350374175801344 + 30, //2^99=633825300114114700748351602688 + 31, //2^100=1267650600228229401496703205376 + 31, //2^101=2535301200456458802993406410752 + 31, //2^102=5070602400912917605986812821504 + 32, //2^103=10141204801825835211973625643008 + 32, //2^104=20282409603651670423947251286016 + 32, //2^105=40564819207303340847894502572032 + 32, //2^106=81129638414606681695789005144064 + 33, //2^107=162259276829213363391578010288128 + 33, // 2^108 + 33, // 2^109 + 34, // 2^110 + 34, // 2^111 + 34, // 2^112 + 35, // 2^113 + 35, // 2^114 + 35, // 2^115 + 35, // 2^116 + 36, // 2^117 + 36, // 2^118 + 36, // 2^119 + 37, // 2^120 + 37, // 2^121 + 37, // 2^122 + 38, // 2^123 + 38, // 2^124 + 38, // 2^125 + 38, // 2^126 + 39, // 2^127 + 39 // 2^128 +}; + + +UINT128 power10_table_128[] = { + {{0x0000000000000001ull, 0x0000000000000000ull}}, // 10^0 + {{0x000000000000000aull, 0x0000000000000000ull}}, // 10^1 + {{0x0000000000000064ull, 0x0000000000000000ull}}, // 10^2 + {{0x00000000000003e8ull, 0x0000000000000000ull}}, // 10^3 + {{0x0000000000002710ull, 0x0000000000000000ull}}, // 10^4 + {{0x00000000000186a0ull, 0x0000000000000000ull}}, // 10^5 + {{0x00000000000f4240ull, 0x0000000000000000ull}}, // 10^6 + {{0x0000000000989680ull, 0x0000000000000000ull}}, // 10^7 + {{0x0000000005f5e100ull, 0x0000000000000000ull}}, // 10^8 + {{0x000000003b9aca00ull, 0x0000000000000000ull}}, // 10^9 + {{0x00000002540be400ull, 0x0000000000000000ull}}, // 10^10 + {{0x000000174876e800ull, 0x0000000000000000ull}}, // 10^11 + {{0x000000e8d4a51000ull, 0x0000000000000000ull}}, // 10^12 + {{0x000009184e72a000ull, 0x0000000000000000ull}}, // 10^13 + {{0x00005af3107a4000ull, 0x0000000000000000ull}}, // 10^14 + {{0x00038d7ea4c68000ull, 0x0000000000000000ull}}, // 10^15 + {{0x002386f26fc10000ull, 0x0000000000000000ull}}, // 10^16 + {{0x016345785d8a0000ull, 0x0000000000000000ull}}, // 10^17 + {{0x0de0b6b3a7640000ull, 0x0000000000000000ull}}, // 10^18 + {{0x8ac7230489e80000ull, 0x0000000000000000ull}}, // 10^19 + {{0x6bc75e2d63100000ull, 0x0000000000000005ull}}, // 10^20 + {{0x35c9adc5dea00000ull, 0x0000000000000036ull}}, // 10^21 + {{0x19e0c9bab2400000ull, 0x000000000000021eull}}, // 10^22 + {{0x02c7e14af6800000ull, 0x000000000000152dull}}, // 10^23 + {{0x1bcecceda1000000ull, 0x000000000000d3c2ull}}, // 10^24 + {{0x161401484a000000ull, 0x0000000000084595ull}}, // 10^25 + {{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}}, // 10^26 + {{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}}, // 10^27 + {{0x3e25026110000000ull, 0x00000000204fce5eull}}, // 10^28 + {{0x6d7217caa0000000ull, 0x00000001431e0faeull}}, // 10^29 + {{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}}, // 10^30 + {{0xc0914b2680000000ull, 0x0000007e37be2022ull}}, // 10^31 + {{0x85acef8100000000ull, 0x000004ee2d6d415bull}}, // 10^32 + {{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}}, // 10^33 + {{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}}, // 10^34 + {{0x2b878fe800000000ull, 0x0013426172c74d82ull}}, // 10^35 + {{0xb34b9f1000000000ull, 0x00c097ce7bc90715ull}}, // 10^36 + {{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}}, // 10^37 + {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}}, // 10^38 +}; + + +int estimate_bin_expon[] = { + 0, // 10^0 + 3, // 10^1 + 6, // 10^2 + 9, // 10^3 + 13, // 10^4 + 16, // 10^5 + 19, // 10^6 + 23, // 10^7 + 26, // 10^8 + 29, // 10^9 + 33, // 10^10 + 36, // 10^11 + 39, // 10^12 + 43, // 10^13 + 46, // 10^14 + 49, // 10^15 + 53 // 10^16 +}; + + +UINT64 power10_index_binexp[] = { + 0x000000000000000aull, + 0x000000000000000aull, + 0x000000000000000aull, + 0x000000000000000aull, + 0x0000000000000064ull, + 0x0000000000000064ull, + 0x0000000000000064ull, + 0x00000000000003e8ull, + 0x00000000000003e8ull, + 0x00000000000003e8ull, + 0x0000000000002710ull, + 0x0000000000002710ull, + 0x0000000000002710ull, + 0x0000000000002710ull, + 0x00000000000186a0ull, + 0x00000000000186a0ull, + 0x00000000000186a0ull, + 0x00000000000f4240ull, + 0x00000000000f4240ull, + 0x00000000000f4240ull, + 0x0000000000989680ull, + 0x0000000000989680ull, + 0x0000000000989680ull, + 0x0000000000989680ull, + 0x0000000005f5e100ull, + 0x0000000005f5e100ull, + 0x0000000005f5e100ull, + 0x000000003b9aca00ull, + 0x000000003b9aca00ull, + 0x000000003b9aca00ull, + 0x00000002540be400ull, + 0x00000002540be400ull, + 0x00000002540be400ull, + 0x00000002540be400ull, + 0x000000174876e800ull, + 0x000000174876e800ull, + 0x000000174876e800ull, + 0x000000e8d4a51000ull, + 0x000000e8d4a51000ull, + 0x000000e8d4a51000ull, + 0x000009184e72a000ull, + 0x000009184e72a000ull, + 0x000009184e72a000ull, + 0x000009184e72a000ull, + 0x00005af3107a4000ull, + 0x00005af3107a4000ull, + 0x00005af3107a4000ull, + 0x00038d7ea4c68000ull, + 0x00038d7ea4c68000ull, + 0x00038d7ea4c68000ull, + 0x002386f26fc10000ull, + 0x002386f26fc10000ull, + 0x002386f26fc10000ull, + 0x002386f26fc10000ull, + 0x016345785d8a0000ull, + 0x016345785d8a0000ull, + 0x016345785d8a0000ull, + 0x0de0b6b3a7640000ull, + 0x0de0b6b3a7640000ull, + 0x0de0b6b3a7640000ull, + 0x8ac7230489e80000ull, + 0x8ac7230489e80000ull, + 0x8ac7230489e80000ull, + 0x8ac7230489e80000ull +}; + + +int short_recip_scale[] = { + 1, + 65 - 64, + 69 - 64, + 71 - 64, + 75 - 64, + 78 - 64, + 81 - 64, + 85 - 64, + 88 - 64, + 91 - 64, + 95 - 64, + 98 - 64, + 101 - 64, + 105 - 64, + 108 - 64, + 111 - 64, + 115 - 64, //114 - 64 + 118 - 64 +}; + + +UINT64 reciprocals10_64[] = { + 1ull, // dummy value for 0 extra digits + 0x3333333333333334ull, // 1 extra digit + 0x51eb851eb851eb86ull, + 0x20c49ba5e353f7cfull, + 0x346dc5d63886594bull, + 0x29f16b11c6d1e109ull, + 0x218def416bdb1a6eull, + 0x35afe535795e90b0ull, + 0x2af31dc4611873c0ull, + 0x225c17d04dad2966ull, + 0x36f9bfb3af7b7570ull, + 0x2bfaffc2f2c92ac0ull, + 0x232f33025bd42233ull, + 0x384b84d092ed0385ull, + 0x2d09370d42573604ull, + 0x24075f3dceac2b37ull, + 0x39a5652fb1137857ull, + 0x2e1dea8c8da92d13ull +}; + + + +UINT128 power10_index_binexp_128[] = { + {{0x000000000000000aull, 0x0000000000000000ull}}, + {{0x000000000000000aull, 0x0000000000000000ull}}, + {{0x000000000000000aull, 0x0000000000000000ull}}, + {{0x000000000000000aull, 0x0000000000000000ull}}, + {{0x0000000000000064ull, 0x0000000000000000ull}}, + {{0x0000000000000064ull, 0x0000000000000000ull}}, + {{0x0000000000000064ull, 0x0000000000000000ull}}, + {{0x00000000000003e8ull, 0x0000000000000000ull}}, + {{0x00000000000003e8ull, 0x0000000000000000ull}}, + {{0x00000000000003e8ull, 0x0000000000000000ull}}, + {{0x0000000000002710ull, 0x0000000000000000ull}}, + {{0x0000000000002710ull, 0x0000000000000000ull}}, + {{0x0000000000002710ull, 0x0000000000000000ull}}, + {{0x0000000000002710ull, 0x0000000000000000ull}}, + {{0x00000000000186a0ull, 0x0000000000000000ull}}, + {{0x00000000000186a0ull, 0x0000000000000000ull}}, + {{0x00000000000186a0ull, 0x0000000000000000ull}}, + {{0x00000000000f4240ull, 0x0000000000000000ull}}, + {{0x00000000000f4240ull, 0x0000000000000000ull}}, + {{0x00000000000f4240ull, 0x0000000000000000ull}}, + {{0x0000000000989680ull, 0x0000000000000000ull}}, + {{0x0000000000989680ull, 0x0000000000000000ull}}, + {{0x0000000000989680ull, 0x0000000000000000ull}}, + {{0x0000000000989680ull, 0x0000000000000000ull}}, + {{0x0000000005f5e100ull, 0x0000000000000000ull}}, + {{0x0000000005f5e100ull, 0x0000000000000000ull}}, + {{0x0000000005f5e100ull, 0x0000000000000000ull}}, + {{0x000000003b9aca00ull, 0x0000000000000000ull}}, + {{0x000000003b9aca00ull, 0x0000000000000000ull}}, + {{0x000000003b9aca00ull, 0x0000000000000000ull}}, + {{0x00000002540be400ull, 0x0000000000000000ull}}, + {{0x00000002540be400ull, 0x0000000000000000ull}}, + {{0x00000002540be400ull, 0x0000000000000000ull}}, + {{0x00000002540be400ull, 0x0000000000000000ull}}, + {{0x000000174876e800ull, 0x0000000000000000ull}}, + {{0x000000174876e800ull, 0x0000000000000000ull}}, + {{0x000000174876e800ull, 0x0000000000000000ull}}, + {{0x000000e8d4a51000ull, 0x0000000000000000ull}}, + {{0x000000e8d4a51000ull, 0x0000000000000000ull}}, + {{0x000000e8d4a51000ull, 0x0000000000000000ull}}, + {{0x000009184e72a000ull, 0x0000000000000000ull}}, + {{0x000009184e72a000ull, 0x0000000000000000ull}}, + {{0x000009184e72a000ull, 0x0000000000000000ull}}, + {{0x000009184e72a000ull, 0x0000000000000000ull}}, + {{0x00005af3107a4000ull, 0x0000000000000000ull}}, + {{0x00005af3107a4000ull, 0x0000000000000000ull}}, + {{0x00005af3107a4000ull, 0x0000000000000000ull}}, + {{0x00038d7ea4c68000ull, 0x0000000000000000ull}}, + {{0x00038d7ea4c68000ull, 0x0000000000000000ull}}, + {{0x00038d7ea4c68000ull, 0x0000000000000000ull}}, + {{0x002386f26fc10000ull, 0x0000000000000000ull}}, + {{0x002386f26fc10000ull, 0x0000000000000000ull}}, + {{0x002386f26fc10000ull, 0x0000000000000000ull}}, + {{0x002386f26fc10000ull, 0x0000000000000000ull}}, + {{0x016345785d8a0000ull, 0x0000000000000000ull}}, + {{0x016345785d8a0000ull, 0x0000000000000000ull}}, + {{0x016345785d8a0000ull, 0x0000000000000000ull}}, + {{0x0de0b6b3a7640000ull, 0x0000000000000000ull}}, + {{0x0de0b6b3a7640000ull, 0x0000000000000000ull}}, + {{0x0de0b6b3a7640000ull, 0x0000000000000000ull}}, + {{0x8ac7230489e80000ull, 0x0000000000000000ull}}, + {{0x8ac7230489e80000ull, 0x0000000000000000ull}}, + {{0x8ac7230489e80000ull, 0x0000000000000000ull}}, + {{0x8ac7230489e80000ull, 0x0000000000000000ull}}, + {{0x6bc75e2d63100000ull, 0x0000000000000005ull}}, // 10^20 + {{0x6bc75e2d63100000ull, 0x0000000000000005ull}}, // 10^20 + {{0x6bc75e2d63100000ull, 0x0000000000000005ull}}, // 10^20 + {{0x35c9adc5dea00000ull, 0x0000000000000036ull}}, // 10^21 + {{0x35c9adc5dea00000ull, 0x0000000000000036ull}}, // 10^21 + {{0x35c9adc5dea00000ull, 0x0000000000000036ull}}, // 10^21 + {{0x19e0c9bab2400000ull, 0x000000000000021eull}}, // 10^22 + {{0x19e0c9bab2400000ull, 0x000000000000021eull}}, // 10^22 + {{0x19e0c9bab2400000ull, 0x000000000000021eull}}, // 10^22 + {{0x19e0c9bab2400000ull, 0x000000000000021eull}}, // 10^22 + {{0x02c7e14af6800000ull, 0x000000000000152dull}}, // 10^23 + {{0x02c7e14af6800000ull, 0x000000000000152dull}}, // 10^23 + {{0x02c7e14af6800000ull, 0x000000000000152dull}}, // 10^23 + {{0x1bcecceda1000000ull, 0x000000000000d3c2ull}}, // 10^24 + {{0x1bcecceda1000000ull, 0x000000000000d3c2ull}}, // 10^24 + {{0x1bcecceda1000000ull, 0x000000000000d3c2ull}}, // 10^24 + {{0x161401484a000000ull, 0x0000000000084595ull}}, // 10^25 + {{0x161401484a000000ull, 0x0000000000084595ull}}, // 10^25 + {{0x161401484a000000ull, 0x0000000000084595ull}}, // 10^25 + {{0x161401484a000000ull, 0x0000000000084595ull}}, // 10^25 + {{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}}, // 10^26 + {{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}}, // 10^26 + {{0xdcc80cd2e4000000ull, 0x000000000052b7d2ull}}, // 10^26 + {{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}}, // 10^27 + {{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}}, // 10^27 + {{0x9fd0803ce8000000ull, 0x00000000033b2e3cull}}, // 10^27 + {{0x3e25026110000000ull, 0x00000000204fce5eull}}, // 10^28 + {{0x3e25026110000000ull, 0x00000000204fce5eull}}, // 10^28 + {{0x3e25026110000000ull, 0x00000000204fce5eull}}, // 10^28 + {{0x3e25026110000000ull, 0x00000000204fce5eull}}, // 10^28 + {{0x6d7217caa0000000ull, 0x00000001431e0faeull}}, // 10^29 + {{0x6d7217caa0000000ull, 0x00000001431e0faeull}}, // 10^29 + {{0x6d7217caa0000000ull, 0x00000001431e0faeull}}, // 10^29 + {{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}}, // 10^30 + {{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}}, // 10^30 + {{0x4674edea40000000ull, 0x0000000c9f2c9cd0ull}}, // 10^30 + {{0xc0914b2680000000ull, 0x0000007e37be2022ull}}, // 10^31 + {{0xc0914b2680000000ull, 0x0000007e37be2022ull}}, // 10^31 + {{0xc0914b2680000000ull, 0x0000007e37be2022ull}}, // 10^31 + {{0x85acef8100000000ull, 0x000004ee2d6d415bull}}, // 10^32 + {{0x85acef8100000000ull, 0x000004ee2d6d415bull}}, // 10^32 + {{0x85acef8100000000ull, 0x000004ee2d6d415bull}}, // 10^32 + {{0x85acef8100000000ull, 0x000004ee2d6d415bull}}, // 10^32 + {{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}}, // 10^33 + {{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}}, // 10^33 + {{0x38c15b0a00000000ull, 0x0000314dc6448d93ull}}, // 10^33, entry 112 + {{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}}, // 10^34 + {{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}}, // 10^34 + {{0x378d8e6400000000ull, 0x0001ed09bead87c0ull}}, // 10^34 + {{0x2b878fe800000000ull, 0x0013426172c74d82ull}}, // 10^35 + {{0x2b878fe800000000ull, 0x0013426172c74d82ull}}, // 10^35 + {{0x2b878fe800000000ull, 0x0013426172c74d82ull}}, // 10^35 + {{0x2b878fe800000000ull, 0x0013426172c74d82ull}}, // 10^35 + {{0xb34b9f1000000000ull, 0x00c097ce7bc90715ull}}, // 10^36 + {{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}}, // 10^37 + {{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}}, // 10^37 + {{0x00f436a000000000ull, 0x0785ee10d5da46d9ull}}, // 10^37 + {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}}, // 10^38 + {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}}, // 10^38 + {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}}, // 10^38 + {{0x098a224000000000ull, 0x4b3b4ca85a86c47aull}}, // 10^38 +}; diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_decimal_globals.c b/gcc-4.4.3/libgcc/config/libbid/bid_decimal_globals.c new file mode 100644 index 000000000..5e10d28ce --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_decimal_globals.c @@ -0,0 +1,100 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" +#include "bid_gcc_intrinsics.h" + +#if DECIMAL_GLOBAL_ROUNDING +BID_THREAD _IDEC_round _IDEC_glbround = ROUNDING_TO_NEAREST; + +#if DECIMAL_GLOBAL_ROUNDING_ACCESS_FUNCTIONS +void +__dfp_set_round (int mode) { + _IDEC_glbround = mode; +} + +int +__dfp_get_round (void) { + return _IDEC_glbround; +} +#endif +#endif + +#if DECIMAL_GLOBAL_EXCEPTION_FLAGS +BID_THREAD _IDEC_flags _IDEC_glbflags = EXACT_STATUS; + +#if DECIMAL_GLOBAL_EXCEPTION_FLAGS_ACCESS_FUNCTIONS +#include + +void +__dfp_clear_except (void) { + _IDEC_glbflags &= ~FLAG_MASK; +} + +int +__dfp_test_except (int mask) { + int flags = 0; + + if ((_IDEC_glbflags & INEXACT_EXCEPTION) != 0) + flags |= mask & FE_INEXACT; + if ((_IDEC_glbflags & UNDERFLOW_EXCEPTION) != 0) + flags |= mask & FE_UNDERFLOW; + if ((_IDEC_glbflags & OVERFLOW_EXCEPTION) != 0) + flags |= mask & FE_OVERFLOW; + if ((_IDEC_glbflags & ZERO_DIVIDE_EXCEPTION) != 0) + flags |= mask & FE_DIVBYZERO; + if ((_IDEC_glbflags & INVALID_EXCEPTION) != 0) + flags |= mask & FE_INVALID; + + return flags; +} + +void +__dfp_raise_except (int mask) { + _IDEC_flags flags = 0; + + if ((mask & FE_INEXACT) != 0) + flags |= INEXACT_EXCEPTION; + if ((mask & FE_UNDERFLOW) != 0) + flags |= UNDERFLOW_EXCEPTION; + if ((mask & FE_OVERFLOW) != 0) + flags |= OVERFLOW_EXCEPTION; + if ((mask & FE_DIVBYZERO) != 0) + flags |= ZERO_DIVIDE_EXCEPTION; + if ((mask & FE_INVALID) != 0) + flags |= INVALID_EXCEPTION; + + _IDEC_glbflags |= flags; +} +#endif +#endif + +#if DECIMAL_ALTERNATE_EXCEPTION_HANDLING +#if DECIMAL_GLOBAL_EXCEPTION_MASKS +BID_THREAD _IDEC_exceptionmasks _IDEC_glbexceptionmasks = + _IDEC_allexcmasksset; +#endif +#if DECIMAL_GLOBAL_EXCEPTION_INFO +BID_THREAD _IDEC_excepthandling _IDEC_glbexcepthandling; +#endif +#endif diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_div_macros.h b/gcc-4.4.3/libgcc/config/libbid/bid_div_macros.h new file mode 100644 index 000000000..c972dc7c8 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_div_macros.h @@ -0,0 +1,540 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#ifndef _DIV_MACROS_H_ +#define _DIV_MACROS_H_ + +#include "bid_internal.h" + +#define FENCE __fence +//#define FENCE + +//#define DOUBLE_EXTENDED_ON + +#if DOUBLE_EXTENDED_ON + + +__BID_INLINE__ void +__div_128_by_128 (UINT128 * pCQ, UINT128 * pCR, UINT128 CX, UINT128 CY) { + UINT128 CB, CB2, CB4, CB8, CQB, CA; + int_double d64, dm64, ds; + int_float t64; + double dx, dq, dqh; + BINARY80 lq, lx, ly; + UINT64 Rh, R, B2, B4, Ph, Ql, Ql2, carry, Qh; + + if (!CY.w[1]) { + pCR->w[1] = 0; + + if (!CX.w[1]) { + pCQ->w[0] = CX.w[0] / CY.w[0]; + pCQ->w[1] = 0; + pCR->w[1] = 0; + pCR->w[0] = CX.w[0] - pCQ->w[0] * CY.w[0]; + } else { + + // This path works for CX<2^116 only + + // 2^64 + d64.i = 0x43f0000000000000; + // 2^64 + dm64.i = 0x3bf0000000000000; + // 1.5*2^(-52) + ds.i = 0x3cb8000000000000; + dx = (BINARY80) CX.w[1] * d64.d + (BINARY80) CX.w[0]; + dq = dx / (BINARY80) CY.w[0]; + dq -= dq * (ds.d); + dqh = dq * dm64.d; + Qh = (UINT64) dqh; + Ql = (UINT64) (dq - ((double) Qh) * d64.d); + + Rh = CX.w[0] - Ql * CY.w[0]; + Ql2 = Rh / CY.w[0]; + pCR->w[0] = Rh - Ql2 * CY.w[0]; + __add_carry_out ((pCQ->w[0]), carry, Ql, Ql2); + pCQ->w[1] = Qh + carry; + + } + return; + } + // now CY.w[1] > 0 + + // 2^64 + t64.i = 0x5f800000; + lx = (BINARY80) CX.w[1] * (BINARY80) t64.d + (BINARY80) CX.w[0]; + ly = (BINARY80) CY.w[1] * (BINARY80) t64.d + (BINARY80) CY.w[0]; + lq = lx / ly; + pCQ->w[0] = (UINT64) lq; + + pCQ->w[1] = 0; + + if (!pCQ->w[0]) { + /*if(__unsigned_compare_ge_128(CX,CY)) + { + pCQ->w[0] = 1; + __sub_128_128((*pCR), CX, CY); + } + else */ + { + pCR->w[1] = CX.w[1]; + pCR->w[0] = CX.w[0]; + } + return; + } + + if (CY.w[1] >= 16 || pCQ->w[0] <= 0x1000000000000000ull) { + pCQ->w[0] = (UINT64) lq - 1; + __mul_64x128_full (Ph, CQB, (pCQ->w[0]), CY); + __sub_128_128 (CA, CX, CQB); + if (__unsigned_compare_ge_128 (CA, CY)) { + __sub_128_128 (CA, CA, CY); + pCQ->w[0]++; + if (__unsigned_compare_ge_128 (CA, CY)) { + __sub_128_128 (CA, CA, CY); + pCQ->w[0]++; + } + } + pCR->w[1] = CA.w[1]; + pCR->w[0] = CA.w[0]; + } else { + pCQ->w[0] = (UINT64) lq - 6; + + __mul_64x128_full (Ph, CQB, (pCQ->w[0]), CY); + __sub_128_128 (CA, CX, CQB); + + CB8.w[1] = (CY.w[1] << 3) | (CY.w[0] >> 61); + CB8.w[0] = CY.w[0] << 3; + CB4.w[1] = (CY.w[1] << 2) | (CY.w[0] >> 62); + CB4.w[0] = CY.w[0] << 2; + CB2.w[1] = (CY.w[1] << 1) | (CY.w[0] >> 63); + CB2.w[0] = CY.w[0] << 1; + + if (__unsigned_compare_ge_128 (CA, CB8)) { + pCQ->w[0] += 8; + __sub_128_128 (CA, CA, CB8); + } + if (__unsigned_compare_ge_128 (CA, CB4)) { + pCQ->w[0] += 4; + __sub_128_128 (CA, CA, CB4); + } + if (__unsigned_compare_ge_128 (CA, CB2)) { + pCQ->w[0] += 2; + __sub_128_128 (CA, CA, CB2); + } + if (__unsigned_compare_ge_128 (CA, CY)) { + pCQ->w[0] += 1; + __sub_128_128 (CA, CA, CY); + } + + pCR->w[1] = CA.w[1]; + pCR->w[0] = CA.w[0]; + } +} + + + + + + +__BID_INLINE__ void +__div_256_by_128 (UINT128 * pCQ, UINT256 * pCA4, UINT128 CY) { + UINT256 CQ2Y; + UINT128 CQ2, CQ3Y; + UINT64 Q3, carry64; + int_double d64; + BINARY80 lx, ly, lq, l64, l128; + + // 2^64 + d64.i = 0x43f0000000000000ull; + l64 = (BINARY80) d64.d; + // 2^128 + l128 = l64 * l64; + + lx = + ((BINARY80) (*pCA4).w[3] * l64 + + (BINARY80) (*pCA4).w[2]) * l128 + + (BINARY80) (*pCA4).w[1] * l64 + (BINARY80) (*pCA4).w[0]; + ly = (BINARY80) CY.w[1] * l128 + (BINARY80) CY.w[0] * l64; + + lq = lx / ly; + CQ2.w[1] = (UINT64) lq; + lq = (lq - CQ2.w[1]) * l64; + CQ2.w[0] = (UINT64) lq; + + // CQ2*CY + __mul_128x128_to_256 (CQ2Y, CY, CQ2); + + // CQ2Y <= (*pCA4) ? + if (CQ2Y.w[3] < (*pCA4).w[3] + || (CQ2Y.w[3] == (*pCA4).w[3] + && (CQ2Y.w[2] < (*pCA4).w[2] + || (CQ2Y.w[2] == (*pCA4).w[2] + && (CQ2Y.w[1] < (*pCA4).w[1] + || (CQ2Y.w[1] == (*pCA4).w[1] + && (CQ2Y.w[0] <= (*pCA4).w[0]))))))) { + + // (*pCA4) -CQ2Y, guaranteed below 5*2^49*CY < 5*2^(49+128) + __sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CQ2Y.w[0]); + __sub_borrow_in_out ((*pCA4).w[1], carry64, (*pCA4).w[1], CQ2Y.w[1], + carry64); + (*pCA4).w[2] = (*pCA4).w[2] - CQ2Y.w[2] - carry64; + + lx = ((BINARY80) (*pCA4).w[2] * l128 + + ((BINARY80) (*pCA4).w[1] * l64 + + (BINARY80) (*pCA4).w[0])) * l64; + lq = lx / ly; + Q3 = (UINT64) lq; + + if (Q3) { + Q3--; + __mul_64x128_short (CQ3Y, Q3, CY); + __sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CQ3Y.w[0]); + (*pCA4).w[1] = (*pCA4).w[1] - CQ3Y.w[1] - carry64; + + if ((*pCA4).w[1] > CY.w[1] + || ((*pCA4).w[1] == CY.w[1] && (*pCA4).w[0] >= CY.w[0])) { + Q3++; + __sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CY.w[0]); + (*pCA4).w[1] = (*pCA4).w[1] - CY.w[1] - carry64; + if ((*pCA4).w[1] > CY.w[1] + || ((*pCA4).w[1] == CY.w[1] && (*pCA4).w[0] >= CY.w[0])) { + Q3++; + __sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0], + CY.w[0]); + (*pCA4).w[1] = (*pCA4).w[1] - CY.w[1] - carry64; + } + } + // add Q3 to Q2 + __add_carry_out (CQ2.w[0], carry64, Q3, CQ2.w[0]); + CQ2.w[1] += carry64; + } + } else { + // CQ2Y - (*pCA4), guaranteed below 5*2^(49+128) + __sub_borrow_out ((*pCA4).w[0], carry64, CQ2Y.w[0], (*pCA4).w[0]); + __sub_borrow_in_out ((*pCA4).w[1], carry64, CQ2Y.w[1], (*pCA4).w[1], + carry64); + (*pCA4).w[2] = CQ2Y.w[2] - (*pCA4).w[2] - carry64; + + lx = + ((BINARY80) (*pCA4).w[2] * l128 + + (BINARY80) (*pCA4).w[1] * l64 + (BINARY80) (*pCA4).w[0]) * l64; + lq = lx / ly; + Q3 = 1 + (UINT64) lq; + + __mul_64x128_short (CQ3Y, Q3, CY); + __sub_borrow_out ((*pCA4).w[0], carry64, CQ3Y.w[0], (*pCA4).w[0]); + (*pCA4).w[1] = CQ3Y.w[1] - (*pCA4).w[1] - carry64; + + if ((SINT64) (*pCA4).w[1] > (SINT64) CY.w[1] + || ((*pCA4).w[1] == CY.w[1] && (*pCA4).w[0] >= CY.w[0])) { + Q3--; + __sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CY.w[0]); + (*pCA4).w[1] = (*pCA4).w[1] - CY.w[1] - carry64; + } else if ((SINT64) (*pCA4).w[1] < 0) { + Q3++; + __add_carry_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CY.w[0]); + (*pCA4).w[1] = (*pCA4).w[1] + CY.w[1] + carry64; + } + // subtract Q3 from Q2 + __sub_borrow_out (CQ2.w[0], carry64, CQ2.w[0], Q3); + CQ2.w[1] -= carry64; + } + + // (*pCQ) + CQ2 + carry + __add_carry_out ((*pCQ).w[0], carry64, CQ2.w[0], (*pCQ).w[0]); + (*pCQ).w[1] = (*pCQ).w[1] + CQ2.w[1] + carry64; + + +} +#else + +__BID_INLINE__ void +__div_128_by_128 (UINT128 * pCQ, UINT128 * pCR, UINT128 CX0, UINT128 CY) { + UINT128 CY36, CY51, CQ, A2, CX, CQT; + UINT64 Q; + int_double t64, d49, d60; + double lx, ly, lq; + + if (!CX0.w[1] && !CY.w[1]) { + pCQ->w[0] = CX0.w[0] / CY.w[0]; + pCQ->w[1] = 0; + pCR->w[1] = pCR->w[0] = 0; + pCR->w[0] = CX0.w[0] - pCQ->w[0] * CY.w[0]; + return; + } + + CX.w[1] = CX0.w[1]; + CX.w[0] = CX0.w[0]; + + // 2^64 + t64.i = 0x43f0000000000000ull; + lx = (double) CX.w[1] * t64.d + (double) CX.w[0]; + ly = (double) CY.w[1] * t64.d + (double) CY.w[0]; + lq = lx / ly; + + CY36.w[1] = CY.w[0] >> (64 - 36); + CY36.w[0] = CY.w[0] << 36; + + CQ.w[1] = CQ.w[0] = 0; + + // Q >= 2^100 ? + if (!CY.w[1] && !CY36.w[1] && (CX.w[1] >= CY36.w[0])) { + // then Q >= 2^100 + + // 2^(-60)*CX/CY + d60.i = 0x3c30000000000000ull; + lq *= d60.d; + Q = (UINT64) lq - 4ull; + + // Q*CY + __mul_64x64_to_128 (A2, Q, CY.w[0]); + + // A2 <<= 60 + A2.w[1] = (A2.w[1] << 60) | (A2.w[0] >> (64 - 60)); + A2.w[0] <<= 60; + + __sub_128_128 (CX, CX, A2); + + lx = (double) CX.w[1] * t64.d + (double) CX.w[0]; + lq = lx / ly; + + CQ.w[1] = Q >> (64 - 60); + CQ.w[0] = Q << 60; + } + + + CY51.w[1] = (CY.w[1] << 51) | (CY.w[0] >> (64 - 51)); + CY51.w[0] = CY.w[0] << 51; + + if (CY.w[1] < (UINT64) (1 << (64 - 51)) + && (__unsigned_compare_gt_128 (CX, CY51))) { + // Q > 2^51 + + // 2^(-49)*CX/CY + d49.i = 0x3ce0000000000000ull; + lq *= d49.d; + + Q = (UINT64) lq - 1ull; + + // Q*CY + __mul_64x64_to_128 (A2, Q, CY.w[0]); + A2.w[1] += Q * CY.w[1]; + + // A2 <<= 49 + A2.w[1] = (A2.w[1] << 49) | (A2.w[0] >> (64 - 49)); + A2.w[0] <<= 49; + + __sub_128_128 (CX, CX, A2); + + CQT.w[1] = Q >> (64 - 49); + CQT.w[0] = Q << 49; + __add_128_128 (CQ, CQ, CQT); + + lx = (double) CX.w[1] * t64.d + (double) CX.w[0]; + lq = lx / ly; + } + + Q = (UINT64) lq; + + __mul_64x64_to_128 (A2, Q, CY.w[0]); + A2.w[1] += Q * CY.w[1]; + + __sub_128_128 (CX, CX, A2); + if ((SINT64) CX.w[1] < 0) { + Q--; + CX.w[0] += CY.w[0]; + if (CX.w[0] < CY.w[0]) + CX.w[1]++; + CX.w[1] += CY.w[1]; + if ((SINT64) CX.w[1] < 0) { + Q--; + CX.w[0] += CY.w[0]; + if (CX.w[0] < CY.w[0]) + CX.w[1]++; + CX.w[1] += CY.w[1]; + } + } else if (__unsigned_compare_ge_128 (CX, CY)) { + Q++; + __sub_128_128 (CX, CX, CY); + } + + __add_128_64 (CQ, CQ, Q); + + + pCQ->w[1] = CQ.w[1]; + pCQ->w[0] = CQ.w[0]; + pCR->w[1] = CX.w[1]; + pCR->w[0] = CX.w[0]; + return; +} + + +__BID_INLINE__ void +__div_256_by_128 (UINT128 * pCQ, UINT256 * pCA4, UINT128 CY) { + UINT256 CA4, CA2, CY51, CY36; + UINT128 CQ, A2, A2h, CQT; + UINT64 Q, carry64; + int_double t64, d49, d60; + double lx, ly, lq, d128, d192; + + // the quotient is assumed to be at most 113 bits, + // as needed by BID128 divide routines + + // initial dividend + CA4.w[3] = (*pCA4).w[3]; + CA4.w[2] = (*pCA4).w[2]; + CA4.w[1] = (*pCA4).w[1]; + CA4.w[0] = (*pCA4).w[0]; + CQ.w[1] = (*pCQ).w[1]; + CQ.w[0] = (*pCQ).w[0]; + + // 2^64 + t64.i = 0x43f0000000000000ull; + d128 = t64.d * t64.d; + d192 = d128 * t64.d; + lx = (double) CA4.w[3] * d192 + ((double) CA4.w[2] * d128 + + ((double) CA4.w[1] * t64.d + + (double) CA4.w[0])); + ly = (double) CY.w[1] * t64.d + (double) CY.w[0]; + lq = lx / ly; + + CY36.w[2] = CY.w[1] >> (64 - 36); + CY36.w[1] = (CY.w[1] << 36) | (CY.w[0] >> (64 - 36)); + CY36.w[0] = CY.w[0] << 36; + + CQ.w[1] = (*pCQ).w[1]; + CQ.w[0] = (*pCQ).w[0]; + + // Q >= 2^100 ? + if (CA4.w[3] > CY36.w[2] + || (CA4.w[3] == CY36.w[2] + && (CA4.w[2] > CY36.w[1] + || (CA4.w[2] == CY36.w[1] && CA4.w[1] >= CY36.w[0])))) { + // 2^(-60)*CA4/CY + d60.i = 0x3c30000000000000ull; + lq *= d60.d; + Q = (UINT64) lq - 4ull; + + // Q*CY + __mul_64x128_to_192 (CA2, Q, CY); + + // CA2 <<= 60 + // CA2.w[3] = CA2.w[2] >> (64-60); + CA2.w[2] = (CA2.w[2] << 60) | (CA2.w[1] >> (64 - 60)); + CA2.w[1] = (CA2.w[1] << 60) | (CA2.w[0] >> (64 - 60)); + CA2.w[0] <<= 60; + + // CA4 -= CA2 + __sub_borrow_out (CA4.w[0], carry64, CA4.w[0], CA2.w[0]); + __sub_borrow_in_out (CA4.w[1], carry64, CA4.w[1], CA2.w[1], + carry64); + CA4.w[2] = CA4.w[2] - CA2.w[2] - carry64; + + lx = ((double) CA4.w[2] * d128 + + ((double) CA4.w[1] * t64.d + (double) CA4.w[0])); + lq = lx / ly; + + CQT.w[1] = Q >> (64 - 60); + CQT.w[0] = Q << 60; + __add_128_128 (CQ, CQ, CQT); + } + + CY51.w[2] = CY.w[1] >> (64 - 51); + CY51.w[1] = (CY.w[1] << 51) | (CY.w[0] >> (64 - 51)); + CY51.w[0] = CY.w[0] << 51; + + if (CA4.w[2] > CY51.w[2] || ((CA4.w[2] == CY51.w[2]) + && + (__unsigned_compare_gt_128 (CA4, CY51)))) + { + // Q > 2^51 + + // 2^(-49)*CA4/CY + d49.i = 0x3ce0000000000000ull; + lq *= d49.d; + + Q = (UINT64) lq - 1ull; + + // Q*CY + __mul_64x64_to_128 (A2, Q, CY.w[0]); + __mul_64x64_to_128 (A2h, Q, CY.w[1]); + A2.w[1] += A2h.w[0]; + if (A2.w[1] < A2h.w[0]) + A2h.w[1]++; + + // A2 <<= 49 + CA2.w[2] = (A2h.w[1] << 49) | (A2.w[1] >> (64 - 49)); + CA2.w[1] = (A2.w[1] << 49) | (A2.w[0] >> (64 - 49)); + CA2.w[0] = A2.w[0] << 49; + + __sub_borrow_out (CA4.w[0], carry64, CA4.w[0], CA2.w[0]); + __sub_borrow_in_out (CA4.w[1], carry64, CA4.w[1], CA2.w[1], + carry64); + CA4.w[2] = CA4.w[2] - CA2.w[2] - carry64; + + CQT.w[1] = Q >> (64 - 49); + CQT.w[0] = Q << 49; + __add_128_128 (CQ, CQ, CQT); + + lx = ((double) CA4.w[2] * d128 + + ((double) CA4.w[1] * t64.d + (double) CA4.w[0])); + lq = lx / ly; + } + + Q = (UINT64) lq; + __mul_64x64_to_128 (A2, Q, CY.w[0]); + A2.w[1] += Q * CY.w[1]; + + __sub_128_128 (CA4, CA4, A2); + if ((SINT64) CA4.w[1] < 0) { + Q--; + CA4.w[0] += CY.w[0]; + if (CA4.w[0] < CY.w[0]) + CA4.w[1]++; + CA4.w[1] += CY.w[1]; + if ((SINT64) CA4.w[1] < 0) { + Q--; + CA4.w[0] += CY.w[0]; + if (CA4.w[0] < CY.w[0]) + CA4.w[1]++; + CA4.w[1] += CY.w[1]; + } + } else if (__unsigned_compare_ge_128 (CA4, CY)) { + Q++; + __sub_128_128 (CA4, CA4, CY); + } + + __add_128_64 (CQ, CQ, Q); + + pCQ->w[1] = CQ.w[1]; + pCQ->w[0] = CQ.w[0]; + pCA4->w[1] = CA4.w[1]; + pCA4->w[0] = CA4.w[0]; + return; + + + +} + +#endif +#endif diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_dpd.c b/gcc-4.4.3/libgcc/config/libbid/bid_dpd.c new file mode 100644 index 000000000..46648f23f --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_dpd.c @@ -0,0 +1,782 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#define DECNUMDIGITS 34 // work with up to 34 digits + +#include "bid_internal.h" +#include "bid_b2d.h" + +UINT32 +bid_to_bid32 (UINT32 ba) { + UINT32 res; + UINT32 sign, comb, exp; + UINT32 trailing; + UINT32 bcoeff; + + sign = (ba & 0x80000000ul); + comb = (ba & 0x7ff00000ul) >> 20; + trailing = (ba & 0x000ffffful); + + if ((comb & 0x780) == 0x780) { + ba &= 0xfff0000ul; + return ba; + } else { + if ((comb & 0x600) == 0x600) { // G0..G1 = 11 -> exp is G2..G11 + exp = (comb >> 1) & 0xff; + bcoeff = ((8 + (comb & 1)) << 20) | trailing; + } else { + exp = (comb >> 3) & 0xff; + bcoeff = ((comb & 7) << 20) | trailing; + } + if (bcoeff >= 10000000) + bcoeff = 0; + res = very_fast_get_BID32 (sign, exp, bcoeff); + } + return res; +} + +UINT64 +bid_to_bid64 (UINT64 ba) { + UINT64 res; + UINT64 sign, comb, exp; + UINT64 trailing; + UINT64 bcoeff; + + sign = (ba & 0x8000000000000000ull); + comb = (ba & 0x7ffc000000000000ull) >> 50; + trailing = (ba & 0x0003ffffffffffffull); + + if ((comb & 0x1e00) == 0x1e00) { + ba &= 0xfff000000000000ULL; + return ba; + } else { + if ((comb & 0x1800) == 0x1800) { // G0..G1 = 11 -> exp is G2..G11 + exp = (comb >> 1) & 0x3ff; + bcoeff = ((8 + (comb & 1)) << 50) | trailing; + } else { + exp = (comb >> 3) & 0x3ff; + bcoeff = ((comb & 7) << 50) | trailing; + } + if (bcoeff >= 10000000000000000ull) + bcoeff = 0ull; + res = very_fast_get_BID64 (sign, exp, bcoeff); + } + return res; +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid_to_dpd32 (UINT32 * pres, UINT32 * pba) { + UINT32 ba = *pba; +#else +UINT32 +bid_to_dpd32 (UINT32 ba) { +#endif + UINT32 res; + + UINT32 sign, comb, exp, trailing; + UINT32 b0, b1, b2; + UINT32 bcoeff, dcoeff; + UINT32 nanb = 0; + + sign = (ba & 0x80000000); + comb = (ba & 0x7ff00000) >> 20; + trailing = (ba & 0xfffff); + + // Detect infinity, and return canonical infinity + if ((comb & 0x7c0) == 0x780) { + res = sign | 0x78000000; + BID_RETURN (res); + // Detect NaN, and canonicalize trailing + } else if ((comb & 0x7c0) == 0x7c0) { + if (trailing > 999999) + trailing = 0; + nanb = ba & 0xfe000000; + exp = 0; + bcoeff = trailing; + } else { // Normal number + if ((comb & 0x600) == 0x600) { // G0..G1 = 11 -> exp is G2..G11 + exp = (comb >> 1) & 0xff; + bcoeff = ((8 + (comb & 1)) << 20) | trailing; + } else { + exp = (comb >> 3) & 0xff; + bcoeff = ((comb & 7) << 20) | trailing; + } + // Zero the coefficient if non-canonical (>= 10^7) + if (bcoeff >= 10000000) + bcoeff = 0; + } + + b0 = bcoeff / 1000000; + b1 = (bcoeff / 1000) % 1000; + b2 = bcoeff % 1000; + dcoeff = (b2d[b1] << 10) | b2d[b2]; + + if (b0 >= 8) // is b0 8 or 9? + res = + sign | + ((0x600 | ((exp >> 6) << 7) | ((b0 & 1) << 6) | (exp & 0x3f)) << + 20) | dcoeff; + else // else b0 is 0..7 + res = + sign | ((((exp >> 6) << 9) | (b0 << 6) | (exp & 0x3f)) << 20) | + dcoeff; + + res |= nanb; + + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid_to_dpd64 (UINT64 * pres, UINT64 * pba) { + UINT64 ba = *pba; +#else +UINT64 +bid_to_dpd64 (UINT64 ba) { +#endif + UINT64 res; + + UINT64 sign, comb, exp; + UINT64 trailing; + UINT32 b0, b1, b2, b3, b4, b5; + UINT64 bcoeff; + UINT64 dcoeff; + UINT32 yhi, ylo; + UINT64 nanb = 0; + +//printf("arg bid "FMT_LLX16" \n", ba); + sign = (ba & 0x8000000000000000ull); + comb = (ba & 0x7ffc000000000000ull) >> 50; + trailing = (ba & 0x0003ffffffffffffull); + + // Detect infinity, and return canonical infinity + if ((comb & 0x1f00) == 0x1e00) { + res = sign | 0x7800000000000000ull; + BID_RETURN (res); + // Detect NaN, and canonicalize trailing + } else if ((comb & 0x1e00) == 0x1e00) { + if (trailing > 999999999999999ull) + trailing = 0; + nanb = ba & 0xfe00000000000000ull; + exp = 0; + bcoeff = trailing; + } else { // Normal number + if ((comb & 0x1800) == 0x1800) { // G0..G1 = 11 -> exp is G2..G11 + exp = (comb >> 1) & 0x3ff; + bcoeff = ((8 + (comb & 1)) << 50) | trailing; + } else { + exp = (comb >> 3) & 0x3ff; + bcoeff = ((comb & 7) << 50) | trailing; + } + + // Zero the coefficient if it is non-canonical (>= 10^16) + if (bcoeff >= 10000000000000000ull) + bcoeff = 0; + } + +// Floor(2^61 / 10^9) +#define D61 (2305843009ull) + +// Multipy the binary coefficient by ceil(2^64 / 1000), and take the upper +// 64-bits in order to compute a division by 1000. + +#if 1 + yhi = + ((UINT64) D61 * + (UINT64) (UINT32) (bcoeff >> (UINT64) 27)) >> (UINT64) 34; + ylo = bcoeff - 1000000000ull * yhi; + if (ylo >= 1000000000) { + ylo = ylo - 1000000000; + yhi = yhi + 1; + } +#else + yhi = bcoeff / 1000000000ull; + ylo = bcoeff % 1000000000ull; +#endif + + // yhi = ABBBCCC ylo = DDDEEEFFF + b5 = ylo % 1000; // b5 = FFF + b3 = ylo / 1000000; // b3 = DDD + b4 = (ylo / 1000) - (1000 * b3); // b4 = EEE + b2 = yhi % 1000; // b2 = CCC + b0 = yhi / 1000000; // b0 = A + b1 = (yhi / 1000) - (1000 * b0); // b1 = BBB + + dcoeff = b2d[b5] | b2d2[b4] | b2d3[b3] | b2d4[b2] | b2d5[b1]; + + if (b0 >= 8) // is b0 8 or 9? + res = + sign | + ((0x1800 | ((exp >> 8) << 9) | ((b0 & 1) << 8) | (exp & 0xff)) << + 50) | dcoeff; + else // else b0 is 0..7 + res = + sign | ((((exp >> 8) << 11) | (b0 << 8) | (exp & 0xff)) << 50) | + dcoeff; + + res |= nanb; + + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +dpd_to_bid32 (UINT32 * pres, UINT32 * pda) { + UINT32 da = *pda; +#else +UINT32 +dpd_to_bid32 (UINT32 da) { +#endif + UINT32 in = *(UINT32 *) & da; + UINT32 res; + + UINT32 sign, comb, exp; + UINT32 trailing; + UINT32 d0 = 0, d1, d2; + UINT64 bcoeff; + UINT32 nanb = 0; + + sign = (in & 0x80000000); + comb = (in & 0x7ff00000) >> 20; + trailing = (in & 0x000fffff); + + if ((comb & 0x7e0) == 0x780) { // G0..G4 = 1111 -> Inf + res = in & 0xf8000000; + BID_RETURN (res); + } else if ((comb & 0x7c0) == 0x7c0) { // G0..G5 = 11111 -> NaN + nanb = in & 0xfe000000; + exp = 0; + } else { // Normal number + if ((comb & 0x600) == 0x600) { // G0..G1 = 11 -> d0 = 8 + G4 + d0 = ((comb >> 6) & 1) | 8; + exp = ((comb & 0x180) >> 1) | (comb & 0x3f); + } else { + d0 = (comb >> 6) & 0x7; + exp = ((comb & 0x600) >> 3) | (comb & 0x3f); + } + } + d1 = d2b2[(trailing >> 10) & 0x3ff]; + d2 = d2b[(trailing) & 0x3ff]; + + bcoeff = d2 + d1 + (1000000 * d0); + if (bcoeff < 0x800000) { + res = (exp << 23) | bcoeff | sign; + } else { + res = (exp << 21) | sign | 0x60000000 | (bcoeff & 0x1fffff); + } + + res |= nanb; + + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +dpd_to_bid64 (UINT64 * pres, UINT64 * pda) { + UINT64 da = *pda; +#else +UINT64 +dpd_to_bid64 (UINT64 da) { +#endif + UINT64 in = *(UINT64 *) & da; + UINT64 res; + + UINT64 sign, comb, exp; + UINT64 trailing; + // UINT64 d0, d1, d2, d3, d4, d5; + + UINT64 d1, d2; + UINT32 d0, d3, d4, d5; + UINT64 bcoeff; + UINT64 nanb = 0; + +//printf("arg dpd "FMT_LLX16" \n", in); + sign = (in & 0x8000000000000000ull); + comb = (in & 0x7ffc000000000000ull) >> 50; + trailing = (in & 0x0003ffffffffffffull); + + if ((comb & 0x1f00) == 0x1e00) { // G0..G4 = 1111 -> Inf + res = in & 0xf800000000000000ull; + BID_RETURN (res); + } else if ((comb & 0x1f00) == 0x1f00) { // G0..G5 = 11111 -> NaN + nanb = in & 0xfe00000000000000ull; + exp = 0; + d0 = 0; + } else { // Normal number + if ((comb & 0x1800) == 0x1800) { // G0..G1 = 11 -> d0 = 8 + G4 + d0 = ((comb >> 8) & 1) | 8; + // d0 = (comb & 0x0100 ? 9 : 8); + exp = (comb & 0x600) >> 1; + // exp = (comb & 0x0400 ? 1 : 0) * 0x200 + (comb & 0x0200 ? 1 : 0) * 0x100; // exp leading bits are G2..G3 + } else { + d0 = (comb >> 8) & 0x7; + exp = (comb & 0x1800) >> 3; + // exp = (comb & 0x1000 ? 1 : 0) * 0x200 + (comb & 0x0800 ? 1 : 0) * 0x100; // exp loading bits are G0..G1 + } + } + d1 = d2b5[(trailing >> 40) & 0x3ff]; + d2 = d2b4[(trailing >> 30) & 0x3ff]; + d3 = d2b3[(trailing >> 20) & 0x3ff]; + d4 = d2b2[(trailing >> 10) & 0x3ff]; + d5 = d2b[(trailing) & 0x3ff]; + + bcoeff = (d5 + d4 + d3) + d2 + d1 + (1000000000000000ull * d0); + exp += (comb & 0xff); + res = very_fast_get_BID64 (sign, exp, bcoeff); + + res |= nanb; + + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid_to_dpd128 (UINT128 * pres, UINT128 * pba) { + UINT128 ba = *pba; +#else +UINT128 +bid_to_dpd128 (UINT128 ba) { +#endif + UINT128 res; + + UINT128 sign; + UINT32 comb, exp; + UINT128 trailing; + UINT128 d0, d1, d2, d3, d4, d5, d6, d7, d8, d9, d10, d11; + UINT128 bcoeff; + UINT128 dcoeff; + UINT64 nanb = 0; + + sign.w[1] = (ba.w[HIGH_128W] & 0x8000000000000000ull); + sign.w[0] = 0; + comb = (ba.w[HIGH_128W] & 0x7fffc00000000000ull) >> 46; + trailing.w[1] = (ba.w[HIGH_128W] & 0x00003fffffffffffull); + trailing.w[0] = ba.w[LOW_128W]; + exp = 0; + + if ((comb & 0x1f000) == 0x1e000) { // G0..G4 = 1111 -> Inf + res.w[HIGH_128W] = ba.w[HIGH_128W] & 0xf800000000000000ull; + res.w[LOW_128W] = 0; + BID_RETURN (res); + // Detect NaN, and canonicalize trailing + } else if ((comb & 0x1f000) == 0x1f000) { + if ((trailing.w[1] > 0x0000314dc6448d93ULL) || // significand is non-canonical + ((trailing.w[1] == 0x0000314dc6448d93ULL) + && (trailing.w[0] >= 0x38c15b0a00000000ULL)) + // significand is non-canonical + ) { + trailing.w[1] = trailing.w[0] = 0ull; + } + bcoeff.w[1] = trailing.w[1]; + bcoeff.w[0] = trailing.w[0]; + nanb = ba.w[HIGH_128W] & 0xfe00000000000000ull; + exp = 0; + } else { // Normal number + if ((comb & 0x18000) == 0x18000) { // G0..G1 = 11 -> exp is G2..G11 + exp = (comb >> 1) & 0x3fff; + bcoeff.w[1] = + ((UINT64) (8 + (comb & 1)) << (UINT64) 46) | trailing.w[1]; + bcoeff.w[0] = trailing.w[0]; + } else { + exp = (comb >> 3) & 0x3fff; + bcoeff.w[1] = + ((UINT64) (comb & 7) << (UINT64) 46) | trailing.w[1]; + bcoeff.w[0] = trailing.w[0]; + } + // Zero the coefficient if non-canonical (>= 10^34) + if (bcoeff.w[1] > 0x1ed09bead87c0ull || + (bcoeff.w[1] == 0x1ed09bead87c0ull + && bcoeff.w[0] >= 0x378D8E6400000000ull)) { + bcoeff.w[0] = bcoeff.w[1] = 0; + } + } + // Constant 2^128 / 1000 + 1 + { + UINT128 t; + UINT64 t2; + UINT128 d1000; + UINT128 b11, b10, b9, b8, b7, b6, b5, b4, b3, b2, b1; + d1000.w[1] = 0x4189374BC6A7EFull; + d1000.w[0] = 0x9DB22D0E56041894ull; + __mul_128x128_high (b11, bcoeff, d1000); + __mul_128x128_high (b10, b11, d1000); + __mul_128x128_high (b9, b10, d1000); + __mul_128x128_high (b8, b9, d1000); + __mul_128x128_high (b7, b8, d1000); + __mul_128x128_high (b6, b7, d1000); + __mul_128x128_high (b5, b6, d1000); + __mul_128x128_high (b4, b5, d1000); + __mul_128x128_high (b3, b4, d1000); + __mul_128x128_high (b2, b3, d1000); + __mul_128x128_high (b1, b2, d1000); + + + __mul_64x128_full (t2, t, 1000ull, b11); + __sub_128_128 (d11, bcoeff, t); + __mul_64x128_full (t2, t, 1000ull, b10); + __sub_128_128 (d10, b11, t); + __mul_64x128_full (t2, t, 1000ull, b9); + __sub_128_128 (d9, b10, t); + __mul_64x128_full (t2, t, 1000ull, b8); + __sub_128_128 (d8, b9, t); + __mul_64x128_full (t2, t, 1000ull, b7); + __sub_128_128 (d7, b8, t); + __mul_64x128_full (t2, t, 1000ull, b6); + __sub_128_128 (d6, b7, t); + __mul_64x128_full (t2, t, 1000ull, b5); + __sub_128_128 (d5, b6, t); + __mul_64x128_full (t2, t, 1000ull, b4); + __sub_128_128 (d4, b5, t); + __mul_64x128_full (t2, t, 1000ull, b3); + __sub_128_128 (d3, b4, t); + __mul_64x128_full (t2, t, 1000ull, b2); + __sub_128_128 (d2, b3, t); + __mul_64x128_full (t2, t, 1000ull, b1); + __sub_128_128 (d1, b2, t); + d0 = b1; + + } + + dcoeff.w[0] = b2d[d11.w[0]] | (b2d[d10.w[0]] << 10) | + (b2d[d9.w[0]] << 20) | (b2d[d8.w[0]] << 30) | (b2d[d7.w[0]] << 40) | + (b2d[d6.w[0]] << 50) | (b2d[d5.w[0]] << 60); + dcoeff.w[1] = + (b2d[d5.w[0]] >> 4) | (b2d[d4.w[0]] << 6) | (b2d[d3.w[0]] << 16) | + (b2d[d2.w[0]] << 26) | (b2d[d1.w[0]] << 36); + + res.w[0] = dcoeff.w[0]; + if (d0.w[0] >= 8) { + res.w[1] = + sign. + w[1] | + ((0x18000 | ((exp >> 12) << 13) | ((d0.w[0] & 1) << 12) | + (exp & 0xfff)) << 46) | dcoeff.w[1]; + } else { + res.w[1] = + sign. + w[1] | ((((exp >> 12) << 15) | (d0.w[0] << 12) | (exp & 0xfff)) + << 46) | dcoeff.w[1]; + } + + res.w[1] |= nanb; + + BID_SWAP128 (res); + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +dpd_to_bid128 (UINT128 * pres, UINT128 * pda) { + UINT128 da = *pda; +#else +UINT128 +dpd_to_bid128 (UINT128 da) { +#endif + UINT128 in = *(UINT128 *) & da; + UINT128 res; + + UINT128 sign; + UINT64 exp, comb; + UINT128 trailing; + UINT64 d0, d1, d2, d3, d4, d5, d6, d7, d8, d9, d10, d11; + UINT128 bcoeff; + UINT64 tl, th; + UINT64 nanb = 0; + + sign.w[1] = (in.w[HIGH_128W] & 0x8000000000000000ull); + sign.w[0] = 0; + comb = (in.w[HIGH_128W] & 0x7fffc00000000000ull) >> 46; + trailing.w[1] = (in.w[HIGH_128W] & 0x00003fffffffffffull); + trailing.w[0] = in.w[LOW_128W]; + exp = 0; + + if ((comb & 0x1f000) == 0x1e000) { // G0..G4 = 1111 -> Inf + res.w[HIGH_128W] = in.w[HIGH_128W] & 0xf800000000000000ull; + res.w[LOW_128W] = 0ull; + BID_RETURN (res); + } else if ((comb & 0x1f000) == 0x1f000) { // G0..G4 = 11111 -> NaN + nanb = in.w[HIGH_128W] & 0xfe00000000000000ull; + exp = 0; + d0 = 0; + } else { // Normal number + if ((comb & 0x18000) == 0x18000) { // G0..G1 = 11 -> d0 = 8 + G4 + d0 = 8 + (comb & 0x01000 ? 1 : 0); + exp = + (comb & 0x04000 ? 1 : 0) * 0x2000 + + (comb & 0x02000 ? 1 : 0) * 0x1000; + // exp leading bits are G2..G3 + } else { + d0 = + 4 * (comb & 0x04000 ? 1 : 0) + 2 * (comb & 0x2000 ? 1 : 0) + + (comb & 0x1000 ? 1 : 0); + exp = + (comb & 0x10000 ? 1 : 0) * 0x2000 + + (comb & 0x08000 ? 1 : 0) * 0x1000; + // exp loading bits are G0..G1 + } + } + + d11 = d2b[(trailing.w[0]) & 0x3ff]; + d10 = d2b[(trailing.w[0] >> 10) & 0x3ff]; + d9 = d2b[(trailing.w[0] >> 20) & 0x3ff]; + d8 = d2b[(trailing.w[0] >> 30) & 0x3ff]; + d7 = d2b[(trailing.w[0] >> 40) & 0x3ff]; + d6 = d2b[(trailing.w[0] >> 50) & 0x3ff]; + d5 = d2b[(trailing.w[0] >> 60) | ((trailing.w[1] & 0x3f) << 4)]; + d4 = d2b[(trailing.w[1] >> 6) & 0x3ff]; + d3 = d2b[(trailing.w[1] >> 16) & 0x3ff]; + d2 = d2b[(trailing.w[1] >> 26) & 0x3ff]; + d1 = d2b[(trailing.w[1] >> 36) & 0x3ff]; + + tl = + d11 + (d10 * 1000ull) + (d9 * 1000000ull) + (d8 * 1000000000ull) + + (d7 * 1000000000000ull) + (d6 * 1000000000000000ull); + th = + d5 + (d4 * 1000ull) + (d3 * 1000000ull) + (d2 * 1000000000ull) + + (d1 * 1000000000000ull) + (d0 * 1000000000000000ull); + __mul_64x64_to_128 (bcoeff, th, 1000000000000000000ull); + __add_128_64 (bcoeff, bcoeff, tl); + + if (!nanb) + exp += (comb & 0xfff); + + res.w[0] = bcoeff.w[0]; + res.w[1] = (exp << 49) | sign.w[1] | bcoeff.w[1]; + + res.w[1] |= nanb; + + BID_SWAP128 (res); + BID_RETURN (res); +} + +UINT128 +bid_to_bid128 (UINT128 bq) { + UINT128 res; + UINT64 sign, comb, exp; + UINT64 trailing; + UINT64 bcoeff; + + UINT128 rq; + UINT128 qcoeff; + UINT64 ba, bb; + + ba = *((UINT64 *) & bq + HIGH_128W); + bb = *((UINT64 *) & bq + LOW_128W); + + sign = (ba & 0x8000000000000000ull); + comb = (ba & 0x7fffc00000000000ull) >> 46; + trailing = (ba & 0x00003fffffffffffull); + + if ((comb & 0x18000) == 0x18000) { // G0..G1 = 11 -> exp is G2..G11 + exp = (comb >> 1) & 0x3fff; + bcoeff = ((8 + (comb & 1)) << 46) | trailing; + } else { + exp = (comb >> 3) & 0x3fff; + bcoeff = ((comb & 7) << 46) | trailing; + } + + if ((comb & 0x1f000) == 0x1f000) { //NaN + ba &= 0xfe003fffffffffffULL; // make exponent 0 + bcoeff &= 0x00003fffffffffffull; // NaN payloat is only T. + if ((bcoeff > 0x0000314dc6448d93ULL) || // significand is non-canonical + ((bcoeff == 0x0000314dc6448d93ULL) + && (bb >= 0x38c15b0a00000000ULL)) + // significand is non-canonical + ) { + bcoeff = 0ull; + ba &= ~0x00003fffffffffffull; + bb = 0ull; + } + *((UINT64 *) & rq + HIGH_128W) = ba; + *((UINT64 *) & rq + LOW_128W) = bb; + return rq; + } else if ((comb & 0x1e000) == 0x1e000) { //Inf + ba &= 0xf800000000000000ULL; // make exponent and significand 0 + bb = 0; + *((UINT64 *) & rq + HIGH_128W) = ba; + *((UINT64 *) & rq + LOW_128W) = bb; + return rq; + } + + if ((bcoeff > 0x0001ed09bead87c0ull) + || ((bcoeff == 0x0001ed09bead87c0ull) + && (bb > 0x378d8e63ffffffffull))) { + // significand is non-canonical + bcoeff = 0ull; + bb = 0ull; + } + + *((UINT64 *) & qcoeff + 1) = bcoeff; + *((UINT64 *) & qcoeff + 0) = bb; + + get_BID128_fast (&res, sign, exp, qcoeff); + + BID_SWAP128 (res); + return res; +} + +UINT32 +bid32_canonize (UINT32 ba) { + FPSC bidrnd; + unsigned int rnd = 0; + + UINT32 res; + UINT32 sign, comb, exp; + UINT32 trailing; + UINT32 bcoeff; + + sign = (ba & 0x80000000); + comb = (ba & 0x7ff00000) >> 20; + trailing = (ba & 0x000fffff); + + if ((comb & 0x600) == 0x600) { // G0..G1 = 11 -> exp is G2..G11 + exp = (comb >> 1) & 0xff; + bcoeff = ((8 + (comb & 1)) << 20) | trailing; + } else { + exp = (comb >> 3) & 0xff; + bcoeff = ((comb & 7) << 20) | trailing; + } + + if ((comb & 0x7c0) == 0x7c0) { //NaN + ba &= 0xfe0fffff; // make exponent 0 + bcoeff &= 0x000fffff; // NaN payloat is only T. + if (bcoeff >= 1000000) + ba &= 0xfff00000; //treat non-canonical significand + return ba; + } else if ((comb & 0x780) == 0x780) { //Inf + ba &= 0xf8000000; // make exponent and significand 0 + return ba; + } + + if (bcoeff >= 10000000) + bcoeff = 0; + rnd = bidrnd = ROUNDING_TO_NEAREST; + res = get_BID32 (sign, exp, bcoeff, rnd, &bidrnd); + return res; +} + +UINT64 +bid64_canonize (UINT64 ba) { + UINT64 res; + UINT64 sign, comb, exp; + UINT64 trailing; + UINT64 bcoeff; + + sign = (ba & 0x8000000000000000ull); + comb = (ba & 0x7ffc000000000000ull) >> 50; + trailing = (ba & 0x0003ffffffffffffull); + + + if ((comb & 0x1800) == 0x1800) { // G0..G1 = 11 -> exp is G2..G11 + exp = (comb >> 1) & 0x3ff; + bcoeff = ((8 + (comb & 1)) << 50) | trailing; + } else { + exp = (comb >> 3) & 0x3ff; + bcoeff = ((comb & 7) << 50) | trailing; + } + + if ((comb & 0x1f00) == 0x1f00) { //NaN + ba &= 0xfe03ffffffffffffULL; // make exponent 0 + bcoeff &= 0x0003ffffffffffffull; // NaN payloat is only T. + if (bcoeff >= 1000000000000000ull) + ba &= 0xfe00000000000000ull; // treat non canonical significand and zero G6-G12 + return ba; + } else if ((comb & 0x1e00) == 0x1e00) { //Inf + ba &= 0xf800000000000000ULL; // make exponent and significand 0 + return ba; + } + + if (bcoeff >= 10000000000000000ull) { + bcoeff = 0ull; + } + res = very_fast_get_BID64 (sign, exp, bcoeff); + return res; +} + +UINT128 +bid128_canonize (UINT128 bq) { + UINT128 res; + UINT64 sign, comb, exp; + UINT64 trailing; + UINT64 bcoeff; + + UINT128 rq; + UINT128 qcoeff; + UINT64 ba, bb; + + ba = *((UINT64 *) & bq + HIGH_128W); + bb = *((UINT64 *) & bq + LOW_128W); + + sign = (ba & 0x8000000000000000ull); + comb = (ba & 0x7fffc00000000000ull) >> 46; + trailing = (ba & 0x00003fffffffffffull); + + if ((comb & 0x18000) == 0x18000) { // G0..G1 = 11 -> exp is G2..G11 + exp = (comb >> 1) & 0x3fff; + bcoeff = ((8 + (comb & 1)) << 46) | trailing; + } else { + exp = (comb >> 3) & 0x3fff; + bcoeff = ((comb & 7) << 46) | trailing; + } + + if ((comb & 0x1f000) == 0x1f000) { //NaN + ba &= 0xfe003fffffffffffULL; // make exponent 0 + bcoeff &= 0x00003fffffffffffull; // NaN payload is only T. + + if ((bcoeff > 0x0000314dc6448d93ULL) || // significand is non-canonical + ((bcoeff == 0x0000314dc6448d93ULL) + && (bb >= 0x38c15b0a00000000ULL)) + // significand is non-canonical + ) { + bcoeff = 0ull; + ba &= ~0x00003fffffffffffull; + bb = 0ull; + } + *((UINT64 *) & rq + HIGH_128W) = ba; + *((UINT64 *) & rq + LOW_128W) = bb; + return rq; + } else if ((comb & 0x1e000) == 0x1e000) { //Inf + ba &= 0xf800000000000000ULL; // make exponent and significand 0 + bb = 0; + *((UINT64 *) & rq + HIGH_128W) = ba; + *((UINT64 *) & rq + LOW_128W) = bb; + return rq; + } + + if ((bcoeff > 0x0001ed09bead87c0ull) || // significand is non-canonical + ((bcoeff == 0x0001ed09bead87c0ull) + && (bb > 0x378d8e63ffffffffull)) + // significand is non-canonical + ) { + bcoeff = 0ull; + bb = 0ull; + } + + *((UINT64 *) & qcoeff + 1) = bcoeff; + *((UINT64 *) & qcoeff + 0) = bb; + + get_BID128_fast (&res, sign, exp, qcoeff); + BID_SWAP128 (res); + return res; +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_flag_operations.c b/gcc-4.4.3/libgcc/config/libbid/bid_flag_operations.c new file mode 100644 index 000000000..23d8a5678 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_flag_operations.c @@ -0,0 +1,345 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +/***************************************************************************** + * Non-computational Operations on Flags: + ****************************************************************************/ + +#include "bid_internal.h" + +// Note the following definitions from bid_conf.h: if the status flags are +// global, they have a fixed name recognized by the library functions: +// _IDEC_glbflags; pfpsf, defined as &_IDEC_glbflags, can be used instead; no +// argument is passed for the status flags to the library functions; if the +// status flags are local then they are passed as an arument, always by +// reference, to the library functions +// +// #if !DECIMAL_GLOBAL_EXCEPTION_FLAGS +// #define _EXC_FLAGS_PARAM , _IDEC_flags *pfpsf +// #else +// extern _IDEC_flags _IDEC_glbflags; +// #define _EXC_FLAGS_PARAM +// #define pfpsf &_IDEC_glbflags +// #endif + +#if DECIMAL_CALL_BY_REFERENCE +void +signalException (_IDEC_flags * pflagsmask _EXC_FLAGS_PARAM) { + // *pflagsmask is the logical OR of the flags to be set, e.g. + // *pflagsmask =INVALID_EXCEPTION | ZERO_DIVIDE_EXCEPTION | OVERFLOW_EXCEPTION + // UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION to set all five IEEE 754R + // exception flags + *pfpsf = *pfpsf | (*pflagsmask & BID_IEEE_FLAGS); +} +#else +void +signalException (_IDEC_flags flagsmask _EXC_FLAGS_PARAM) { + // flagsmask is the logical OR of the flags to be set, e.g. + // flagsmask = INVALID_EXCEPTION | ZERO_DIVIDE_EXCEPTION | OVERFLOW_EXCEPTION + // UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION to set all five IEEE 754R + // exception flags + *pfpsf = *pfpsf | (flagsmask & BID_IEEE_FLAGS); +} +#endif + +#if DECIMAL_CALL_BY_REFERENCE +void +lowerFlags (_IDEC_flags * pflagsmask _EXC_FLAGS_PARAM) { + // *pflagsmask is the logical OR of the flags to be cleared, e.g. + // *pflagsmask =INVALID_EXCEPTION | ZERO_DIVIDE_EXCEPTION | OVERFLOW_EXCEPTION + // UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION to clear all five IEEE 754R + // exception flags + *pfpsf = *pfpsf & ~(*pflagsmask & BID_IEEE_FLAGS); +} +#else +void +lowerFlags (_IDEC_flags flagsmask _EXC_FLAGS_PARAM) { + // flagsmask is the logical OR of the flags to be cleared, e.g. + // flagsmask = INVALID_EXCEPTION | ZERO_DIVIDE_EXCEPTION | OVERFLOW_EXCEPTION + // UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION to clear all five IEEE 754R + // exception flags + *pfpsf = *pfpsf & ~(flagsmask & BID_IEEE_FLAGS); +} +#endif + +#if DECIMAL_CALL_BY_REFERENCE +void +testFlags (_IDEC_flags * praised, + _IDEC_flags * pflagsmask _EXC_FLAGS_PARAM) { + // *praised is a pointer to the result, i.e. the logical OR of the flags + // selected by *pflagsmask that are set; e.g. if + // *pflagsmask = INVALID_EXCEPTION | UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION + // and only the invalid and inexact flags are raised (set) then upon return + // *praised = INVALID_EXCEPTION | INEXACT_EXCEPTION + *praised = *pfpsf & (*pflagsmask & BID_IEEE_FLAGS); +} +#else +_IDEC_flags +testFlags (_IDEC_flags flagsmask _EXC_FLAGS_PARAM) { + _IDEC_flags raised; + // the raturn value raised is the logical OR of the flags + // selected by flagsmask, that are set; e.g. if + // flagsmask = INVALID_EXCEPTION | UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION and + // only the invalid and inexact flags are raised (set) then the return value + // is raised = INVALID_EXCEPTION | INEXACT_EXCEPTION + raised = *pfpsf & (flagsmask & BID_IEEE_FLAGS); + return (raised); +} +#endif + +#if DECIMAL_CALL_BY_REFERENCE +void +testSavedFlags (_IDEC_flags * praised, _IDEC_flags * psavedflags, + _IDEC_flags * pflagsmask) { + // *praised is a pointer to the result, i.e. the logical OR of the flags + // selected by *pflagsmask that are set in *psavedflags; e.g. if + // *pflagsmask = INVALID_EXCEPTION | UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION + // and only the invalid and inexact flags are raised (set) in *psavedflags + // then upon return *praised = INVALID_EXCEPTION | INEXACT_EXCEPTION + // Note that the flags could be saved in a global variable, but this function + // would still expect that value as an argument passed by reference + *praised = *psavedflags & (*pflagsmask & BID_IEEE_FLAGS); +} +#else +_IDEC_flags +testSavedFlags (_IDEC_flags savedflags, _IDEC_flags flagsmask) { + _IDEC_flags raised; + // the raturn value raised is the logical OR of the flags + // selected by flagsmask, that are set in savedflags; e.g. if + // flagsmask = INVALID_EXCEPTION | UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION and + // only the invalid and inexact flags are raised (set) in savedflags + // then the return value is raised = INVALID_EXCEPTION | INEXACT_EXCEPTION + // Note that the flags could be saved in a global variable, but this function + // would still expect that value as an argument passed by value + raised = savedflags & (flagsmask & BID_IEEE_FLAGS); + return (raised); +} +#endif + +#if DECIMAL_CALL_BY_REFERENCE +void +restoreFlags (_IDEC_flags * pflagsvalues, + _IDEC_flags * pflagsmask _EXC_FLAGS_PARAM) { + // restore the status flags selected by *pflagsmask to the values speciafied + // (as a logical OR) in *pflagsvalues; e.g. if + // *pflagsmask = INVALID_EXCEPTION | UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION + // and only the invalid and inexact flags are raised (set) in *pflagsvalues + // then upon return the invalid status flag will be set, the underflow status + // flag will be clear, and the inexact status flag will be set + *pfpsf = *pfpsf & ~(*pflagsmask & BID_IEEE_FLAGS); + // clear flags that have to be restored + *pfpsf = *pfpsf | (*pflagsvalues & (*pflagsmask & BID_IEEE_FLAGS)); + // restore flags +} +#else +void +restoreFlags (_IDEC_flags flagsvalues, + _IDEC_flags flagsmask _EXC_FLAGS_PARAM) { + // restore the status flags selected by flagsmask to the values speciafied + // (as a logical OR) in flagsvalues; e.g. if + // flagsmask = INVALID_EXCEPTION | UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION + // and only the invalid and inexact flags are raised (set) in flagsvalues + // then upon return the invalid status flag will be set, the underflow status + // flag will be clear, and the inexact status flag will be set + *pfpsf = *pfpsf & ~(flagsmask & BID_IEEE_FLAGS); + // clear flags that have to be restored + *pfpsf = *pfpsf | (flagsvalues & (flagsmask & BID_IEEE_FLAGS)); + // restore flags +} +#endif + +#if DECIMAL_CALL_BY_REFERENCE +void +saveFlags (_IDEC_flags * pflagsvalues, + _IDEC_flags * pflagsmask _EXC_FLAGS_PARAM) { + // return in *pflagsvalues the status flags specified (as a logical OR) in + // *pflagsmask; e.g. if + // *pflagsmask = INVALID_EXCEPTION | UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION + // and only the invalid and inexact flags are raised (set) in the status word, + // then upon return the value in *pflagsvalues will have the invalid status + // flag set, the underflow status flag clear, and the inexact status flag set + *pflagsvalues = *pfpsf & (*pflagsmask & BID_IEEE_FLAGS); +} +#else +_IDEC_flags +saveFlags (_IDEC_flags flagsmask _EXC_FLAGS_PARAM) { + _IDEC_flags flagsvalues; + // return the status flags specified (as a logical OR) in flagsmask; e.g. if + // flagsmask = INVALID_EXCEPTION | UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION + // and only the invalid and inexact flags are raised (set) in the status word, + // then the return value will have the invalid status flag set, the + // underflow status flag clear, and the inexact status flag set + flagsvalues = *pfpsf & (flagsmask & BID_IEEE_FLAGS); + return (flagsvalues); +} +#endif + +// Note the following definitions from bid_conf.h (rearranged): if the rounding +// mode is global, it has a fixed name recognized by the library functions: +// _IDEC_glbround; rnd_mode, defined as &_IDEC_glbround, can be used instead; no +// argument is passed for the rounding mode to the library functions; if the +// rounding mode is local then it is passed as an arument, by reference or by +// value, to the library functions +// +// #if DECIMAL_CALL_BY_REFERENCE +// #if !DECIMAL_GLOBAL_ROUNDING +// #define _RND_MODE_PARAM , _IDEC_round *prnd_mode +// #else +// #define _RND_MODE_PARAM +// #define rnd_mode _IDEC_glbround +// #endif +// #else +// #if !DECIMAL_GLOBAL_ROUNDING +// #define _RND_MODE_PARAM , _IDEC_round rnd_mode +// #else +// #define _RND_MODE_PARAM +// #define rnd_mode _IDEC_glbround +// #endif +// #endif + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + // #define _RND_MODE_PARAM , _IDEC_round *prnd_mode +void +getDecimalRoundingDirection (_IDEC_round * rounding_mode + _RND_MODE_PARAM) { + // returns the current rounding mode + *rounding_mode = *prnd_mode; +} +#else + // #define _RND_MODE_PARAM + // #define rnd_mode _IDEC_glbround +void +getDecimalRoundingDirection (_IDEC_round * rounding_mode + _RND_MODE_PARAM) { + // returns the current rounding mode + *rounding_mode = rnd_mode; +} +#endif +#else +#if !DECIMAL_GLOBAL_ROUNDING + // #define _RND_MODE_PARAM , _IDEC_round rnd_mode +_IDEC_round +getDecimalRoundingDirection (_IDEC_round rnd_mode) { + // returns the current rounding mode + return (rnd_mode); +} +#else + // #define _RND_MODE_PARAM + // #define rnd_mode _IDEC_glbround +_IDEC_round +getDecimalRoundingDirection (void) { + // returns the current rounding mode + return (rnd_mode); +} +#endif +#endif + +#if DECIMAL_CALL_BY_REFERENCE +#if !DECIMAL_GLOBAL_ROUNDING + // #define _RND_MODE_PARAM , _IDEC_round *prnd_mode +void +setDecimalRoundingDirection (_IDEC_round * rounding_mode + _RND_MODE_PARAM) { + // sets the current rounding mode to the value in *rounding_mode, if valid + if (*rounding_mode == ROUNDING_TO_NEAREST || + *rounding_mode == ROUNDING_DOWN || + *rounding_mode == ROUNDING_UP || + *rounding_mode == ROUNDING_TO_ZERO || + *rounding_mode == ROUNDING_TIES_AWAY) { + *prnd_mode = *rounding_mode; + } +} +#else + // #define _RND_MODE_PARAM + // #define rnd_mode _IDEC_glbround +void +setDecimalRoundingDirection (_IDEC_round * rounding_mode + ) { + // sets the global rounding mode to the value in *rounding_mode, if valid + if (*rounding_mode == ROUNDING_TO_NEAREST || + *rounding_mode == ROUNDING_DOWN || + *rounding_mode == ROUNDING_UP || + *rounding_mode == ROUNDING_TO_ZERO || + *rounding_mode == ROUNDING_TIES_AWAY) { + rnd_mode = *rounding_mode; + } +} +#endif +#else +#if !DECIMAL_GLOBAL_ROUNDING + // #define _RND_MODE_PARAM , _IDEC_round rnd_mode +_IDEC_round +setDecimalRoundingDirection (_IDEC_round rounding_mode _RND_MODE_PARAM) { + // sets the current rounding mode to the value in rounding_mode; + // however, when arguments are passed by value and the rounding mode + // is a local variable, this is not of any use + if (rounding_mode == ROUNDING_TO_NEAREST || + rounding_mode == ROUNDING_DOWN || + rounding_mode == ROUNDING_UP || + rounding_mode == ROUNDING_TO_ZERO || + rounding_mode == ROUNDING_TIES_AWAY) { + return (rounding_mode); + } + return (rnd_mode); +} +#else + // #define _RND_MODE_PARAM + // #define rnd_mode _IDEC_glbround +void +setDecimalRoundingDirection (_IDEC_round rounding_mode) { + // sets the current rounding mode to the value in rounding_mode, if valid; + if (rounding_mode == ROUNDING_TO_NEAREST || + rounding_mode == ROUNDING_DOWN || + rounding_mode == ROUNDING_UP || + rounding_mode == ROUNDING_TO_ZERO || + rounding_mode == ROUNDING_TIES_AWAY) { + rnd_mode = rounding_mode; + } +} +#endif +#endif + +#if DECIMAL_CALL_BY_REFERENCE +void +is754 (int *retval) { + *retval = 0; +} +#else +int +is754 (void) { + return 0; +} +#endif + +#if DECIMAL_CALL_BY_REFERENCE +void +is754R (int *retval) { + *retval = 1; +} +#else +int +is754R (void) { + return 1; +} +#endif diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_from_int.c b/gcc-4.4.3/libgcc/config/libbid/bid_from_int.c new file mode 100644 index 000000000..1bc41b914 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_from_int.c @@ -0,0 +1,349 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID64_round_integral_exact + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_from_int32 (UINT64 * pres, + int *px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + int x = *px; +#else +UINT64 +bid64_from_int32 (int x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT64 res; + + // if integer is negative, put the absolute value + // in the lowest 32bits of the result + if ((x & SIGNMASK32) == SIGNMASK32) { + // negative int32 + x = ~x + 1; // 2's complement of x + res = (unsigned int) x | 0xb1c0000000000000ull; + // (exp << 53)) = biased exp. is 0 + } else { // positive int32 + res = x | 0x31c0000000000000ull; // (exp << 53)) = biased exp. is 0 + } + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_from_uint32 (UINT64 * pres, unsigned int *px + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + unsigned int x = *px; +#else +UINT64 +bid64_from_uint32 (unsigned int x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT64 res; + + res = x | 0x31c0000000000000ull; // (exp << 53)) = biased exp. is 0 + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_from_int64 (UINT64 * pres, SINT64 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + SINT64 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64_from_int64 (SINT64 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 res; + UINT64 x_sign, C; + unsigned int q, ind; + int incr_exp = 0; + int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0; + int is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; + + x_sign = x & 0x8000000000000000ull; + // if the integer is negative, use the absolute value + if (x_sign) + C = ~((UINT64) x) + 1; + else + C = x; + if (C <= BID64_SIG_MAX) { // |C| <= 10^16-1 and the result is exact + if (C < 0x0020000000000000ull) { // C < 2^53 + res = x_sign | 0x31c0000000000000ull | C; + } else { // C >= 2^53 + res = + x_sign | 0x6c70000000000000ull | (C & 0x0007ffffffffffffull); + } + } else { // |C| >= 10^16 and the result may be inexact + // the smallest |C| is 10^16 which has 17 decimal digits + // the largest |C| is 0x8000000000000000 = 9223372036854775808 w/ 19 digits + if (C < 0x16345785d8a0000ull) { // x < 10^17 + q = 17; + ind = 1; // number of digits to remove for q = 17 + } else if (C < 0xde0b6b3a7640000ull) { // C < 10^18 + q = 18; + ind = 2; // number of digits to remove for q = 18 + } else { // C < 10^19 + q = 19; + ind = 3; // number of digits to remove for q = 19 + } + // overflow and underflow are not possible + // Note: performace can be improved by inlining this call + round64_2_18 ( // will work for 19 digits too if C fits in 64 bits + q, ind, C, &res, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint); + if (incr_exp) + ind++; + // set the inexact flag + if (is_inexact_lt_midpoint || is_inexact_gt_midpoint || + is_midpoint_lt_even || is_midpoint_gt_even) + *pfpsf |= INEXACT_EXCEPTION; + // general correction from RN to RA, RM, RP, RZ; result uses ind for exp + if (rnd_mode != ROUNDING_TO_NEAREST) { + if ((!x_sign + && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) + || + ((rnd_mode == ROUNDING_TIES_AWAY + || rnd_mode == ROUNDING_UP) && is_midpoint_gt_even))) + || (x_sign + && ((rnd_mode == ROUNDING_DOWN && is_inexact_lt_midpoint) + || + ((rnd_mode == ROUNDING_TIES_AWAY + || rnd_mode == ROUNDING_DOWN) + && is_midpoint_gt_even)))) { + res = res + 1; + if (res == 0x002386f26fc10000ull) { // res = 10^16 => rounding overflow + res = 0x00038d7ea4c68000ull; // 10^15 + ind = ind + 1; + } + } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) && + ((x_sign && (rnd_mode == ROUNDING_UP || + rnd_mode == ROUNDING_TO_ZERO)) || + (!x_sign && (rnd_mode == ROUNDING_DOWN || + rnd_mode == ROUNDING_TO_ZERO)))) { + res = res - 1; + // check if we crossed into the lower decade + if (res == 0x00038d7ea4c67fffull) { // 10^15 - 1 + res = 0x002386f26fc0ffffull; // 10^16 - 1 + ind = ind - 1; + } + } else { + ; // exact, the result is already correct + } + } + if (res < 0x0020000000000000ull) { // res < 2^53 + res = x_sign | (((UINT64) ind + 398) << 53) | res; + } else { // res >= 2^53 + res = + x_sign | 0x6000000000000000ull | (((UINT64) ind + 398) << 51) | + (res & 0x0007ffffffffffffull); + } + } + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_from_uint64 (UINT64 * pres, UINT64 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64_from_uint64 (UINT64 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 res; + UINT128 x128, res128; + unsigned int q, ind; + int incr_exp = 0; + int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0; + int is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; + + if (x <= BID64_SIG_MAX) { // x <= 10^16-1 and the result is exact + if (x < 0x0020000000000000ull) { // x < 2^53 + res = 0x31c0000000000000ull | x; + } else { // x >= 2^53 + res = 0x6c70000000000000ull | (x & 0x0007ffffffffffffull); + } + } else { // x >= 10^16 and the result may be inexact + // the smallest x is 10^16 which has 17 decimal digits + // the largest x is 0xffffffffffffffff = 18446744073709551615 w/ 20 digits + if (x < 0x16345785d8a0000ull) { // x < 10^17 + q = 17; + ind = 1; // number of digits to remove for q = 17 + } else if (x < 0xde0b6b3a7640000ull) { // x < 10^18 + q = 18; + ind = 2; // number of digits to remove for q = 18 + } else if (x < 0x8ac7230489e80000ull) { // x < 10^19 + q = 19; + ind = 3; // number of digits to remove for q = 19 + } else { // x < 10^20 + q = 20; + ind = 4; // number of digits to remove for q = 20 + } + // overflow and underflow are not possible + // Note: performace can be improved by inlining this call + if (q <= 19) { + round64_2_18 ( // will work for 20 digits too if x fits in 64 bits + q, ind, x, &res, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint); + } else { // q = 20 + x128.w[1] = 0x0; + x128.w[0] = x; + round128_19_38 (q, ind, x128, &res128, &incr_exp, + &is_midpoint_lt_even, &is_midpoint_gt_even, + &is_inexact_lt_midpoint, &is_inexact_gt_midpoint); + res = res128.w[0]; // res.w[1] is 0 + } + if (incr_exp) + ind++; + // set the inexact flag + if (is_inexact_lt_midpoint || is_inexact_gt_midpoint || + is_midpoint_lt_even || is_midpoint_gt_even) + *pfpsf |= INEXACT_EXCEPTION; + // general correction from RN to RA, RM, RP, RZ; result uses ind for exp + if (rnd_mode != ROUNDING_TO_NEAREST) { + if ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) || + ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_UP) + && is_midpoint_gt_even)) { + res = res + 1; + if (res == 0x002386f26fc10000ull) { // res = 10^16 => rounding overflow + res = 0x00038d7ea4c68000ull; // 10^15 + ind = ind + 1; + } + } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) && + (rnd_mode == ROUNDING_DOWN || + rnd_mode == ROUNDING_TO_ZERO)) { + res = res - 1; + // check if we crossed into the lower decade + if (res == 0x00038d7ea4c67fffull) { // 10^15 - 1 + res = 0x002386f26fc0ffffull; // 10^16 - 1 + ind = ind - 1; + } + } else { + ; // exact, the result is already correct + } + } + if (res < 0x0020000000000000ull) { // res < 2^53 + res = (((UINT64) ind + 398) << 53) | res; + } else { // res >= 2^53 + res = 0x6000000000000000ull | (((UINT64) ind + 398) << 51) | + (res & 0x0007ffffffffffffull); + } + } + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_from_int32 (UINT128 * pres, + int *px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + int x = *px; +#else +UINT128 +bid128_from_int32 (int x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 res; + + // if integer is negative, use the absolute value + if ((x & SIGNMASK32) == SIGNMASK32) { + res.w[HIGH_128W] = 0xb040000000000000ull; + res.w[LOW_128W] = ~((unsigned int) x) + 1; // 2's complement of x + } else { + res.w[HIGH_128W] = 0x3040000000000000ull; + res.w[LOW_128W] = (unsigned int) x; + } + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_from_uint32 (UINT128 * pres, unsigned int *px + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + unsigned int x = *px; +#else +UINT128 +bid128_from_uint32 (unsigned int x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + UINT128 res; + + res.w[HIGH_128W] = 0x3040000000000000ull; + res.w[LOW_128W] = x; + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_from_int64 (UINT128 * pres, SINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + SINT64 x = *px; +#else +UINT128 +bid128_from_int64 (SINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT128 res; + + // if integer is negative, use the absolute value + if ((x & SIGNMASK64) == SIGNMASK64) { + res.w[HIGH_128W] = 0xb040000000000000ull; + res.w[LOW_128W] = ~x + 1; // 2's complement of x + } else { + res.w[HIGH_128W] = 0x3040000000000000ull; + res.w[LOW_128W] = x; + } + BID_RETURN (res); +} + +#if DECIMAL_CALL_BY_REFERENCE +void +bid128_from_uint64 (UINT128 * pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT128 +bid128_from_uint64 (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT128 res; + + res.w[HIGH_128W] = 0x3040000000000000ull; + res.w[LOW_128W] = x; + BID_RETURN (res); +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_functions.h b/gcc-4.4.3/libgcc/config/libbid/bid_functions.h new file mode 100644 index 000000000..579370ae8 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_functions.h @@ -0,0 +1,3279 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#ifndef _BID_FUNCTIONS_H +#define _BID_FUNCTIONS_H + +#ifdef IN_LIBGCC2 +// When we are built as the part of the gcc runtime library, libgcc, +// we will use gcc types defined in bid_gcc_intrinsics.h. +#include "bid_gcc_intrinsics.h" + +#define ALIGN(n) __attribute__ ((aligned(n))) +#else +typedef char SINT8; +typedef unsigned char UINT8; +typedef unsigned UINT32; +typedef signed SINT32; + +#ifdef __GNUC__ +#define __int64 long long +#endif + +#if __GNUC__ || defined LINUX || defined SUNOS +typedef unsigned long long UINT64; +typedef signed long long SINT64; +#else +typedef unsigned __int64 UINT64; +typedef signed __int64 SINT64; +#endif + +#if defined _MSC_VER +#if defined _M_IX86 && !defined __INTEL_COMPILER // Win IA-32, MS compiler +#define ALIGN(n) +#else +#define ALIGN(n) __declspec(align(n)) +#endif +#else +#define ALIGN(n) __attribute__ ((aligned(n))) +#endif + +// bid_gcc_intrinsics.h will also define this. +typedef +ALIGN (16) + struct { + UINT64 w[2]; + } UINT128; +#endif + + +#if !defined _MSC_VER || defined __INTEL_COMPILER +#define __ENABLE_BINARY80__ 1 +#endif + +#ifndef HPUX_OS +#define BINARY80 long double +#define BINARY128 UINT128 +#define SQRT80 sqrtl +#else +#define BINARY80 __float80 +#define BINARY128 __float128 +#define SQRT80 sqrtw +#endif + + typedef ALIGN (16) + struct { + UINT64 w[3]; + } UINT192; + typedef ALIGN (16) + struct { + UINT64 w[4]; + } UINT256; + typedef unsigned int FPSC; // floating-point status and control + +// TYPE parameters +#define BID128_MAXDIGITS 34 +#define BID64_MAXDIGITS 16 +#define BID32_MAXDIGITS 7 + +// rounding modes +#define ROUNDING_TO_NEAREST 0x00000 +#define ROUNDING_DOWN 0x00001 +#define ROUNDING_UP 0x00002 +#define ROUNDING_TO_ZERO 0x00003 +#define ROUNDING_TIES_AWAY 0x00004 + +#define RMODE_MASK (ROUNDING_TO_NEAREST | ROUNDING_DOWN | ROUNDING_UP | ROUNDING_TO_ZERO | ROUNDING_TIES_AWAY) + +// status +#define FLAG_MASK 0x0000003f +#define BID_IEEE_FLAGS 0x0000003d +#define EXACT_STATUS 0x00000000 +#define INEXACT_EXCEPTION 0x00000020 +#define UNDERFLOW_EXCEPTION 0x00000010 +#define OVERFLOW_EXCEPTION 0x00000008 +#define ZERO_DIVIDE_EXCEPTION 0x00000004 +#define DENORMAL_EXCEPTION 0x00000002 +#define INVALID_EXCEPTION 0x00000001 + +#define MODE_MASK 0x00001f80 +#define INEXACT_MODE 0x00001000 +#define UNDERFLOW_MODE 0x00000800 +#define OVERFLOW_MODE 0x00000400 +#define ZERO_DIVIDE_MODE 0x00000200 +#define DENORMAL_MODE 0x00000100 +#define INVALID_MODE 0x00000080 + +#if defined LINUX || defined SUNOS +#define LX16 "%016llx" +#define LX "%llx" +#define LD4 "%4llu" +#define LD16 "%016lld" +#define LD "%lld" +#define LUD "%llu" +#define LUD16 "%016llu" +#define X8 "%08x" +#define X4 "%04x" + +#define FMT_LLX16 "%016llx" +#define FMT_LLX "%llx" +#define FMT_LLU4 "%4llu" +#define FMT_LLD16 "%016lld" +#define FMT_LLD "%lld" +#define FMT_LLU "%llu" +#define FMT_LLU16 "%016llu" +#define FMT_X8 "%08x" +#define FMT_X4 "%04x" +#else +#define LX16 "%016I64x" +#define LX "%I64x" +#define LD16 "%016I64d" +#define LD4 "%4I64u" +#define LD "%I64d" +#define LUD "%I64u" +#define LUD16 "%016I64u" +#define X8 "%08x" +#define X4 "%04x" + +#define FMT_LLX16 "%016I64x" +#define FMT_LLX "%I64x" +#define FMT_LLD16 "%016I64d" +#define FMT_LLU4 "%4I64u" +#define FMT_LLD "%I64d" +#define FMT_LLU "%I64u" +#define FMT_LLU16 "%016I64u" +#define FMT_X8 "%08x" +#define FMT_X4 "%04x" +#endif + +#define decNumberIsSNaN(dn) (((dn)->bits&(DECSNAN))!=0) + int __signbitf (float); + int __signbit (double); + +#define __IMFC99MACRO_( __x__, __func__ ) \ + (( sizeof( __x__ ) > sizeof( float )) \ + ? __func__( (double)(__x__) ) \ + : __func__##f( (float)(__x__) )) + +#define signbit( __x__ ) __IMFC99MACRO_( __x__, __signbit ) + +#if !defined(__INTEL_COMPILER) + +#define __fence + +#define isinf( __x__ ) __IMFC99MACRO_( __x__, __isinf ) +#define isnan( __x__ ) __IMFC99MACRO_( __x__, __isnan ) + + int __isnanf (float); + int __isnan (double); + + int __isinff (float); + int __isinf (double); + +#endif + +/* rounding modes */ +// typedef unsigned int _IDEC_round; + extern _IDEC_round _IDEC_gblround; // initialized to ROUNDING_TO_NEAREST + +/* exception flags */ +// typedef unsigned int _IDEC_flags; // could be a struct with diagnostic info + extern _IDEC_flags _IDEC_gblflags; // initialized to EXACT_STATUS + +/* exception masks */ + typedef unsigned int _IDEC_exceptionmasks; + extern _IDEC_exceptionmasks _IDEC_gblexceptionmasks; // initialized to MODE_MASK + +#if DECIMAL_ALTERNATE_EXCEPTION_HANDLING + +/* exception information */ + + typedef struct { + unsigned int inexact_result:1; + unsigned int underflow:1; + unsigned int overflow:1; + unsigned int zero_divide:1; + unsigned int invalid_operation:1; + } fpieee_exception_flags_t; + + typedef enum { + _fp_round_nearest, + _fp_round_minus_infinity, + _fp_round_plus_infinity, + _fp_round_chopped, + _fp_round_away + } fpieee_rounding_mode_t; + + typedef enum { + _fp_precision24, + _fp_precision63, + _fp_precision64, + _fp_precision7, + _fp_precision16, + _fp_precision34 + } _fpieee_precision_t; + + typedef enum { + _fp_code_unspecified, + _fp_code_add, + _fp_code_subtract, + _fp_code_multiply, + _fp_code_divide, + _fp_code_square_root, + _fp_code_compare, + _fp_code_convert, + _fp_code_convert_to_integer_neareven, + _fp_code_convert_to_integer_down, + _fp_code_convert_to_integer_up, + _fp_code_convert_to_integer_truncate, + _fp_code_convert_to_integer_nearaway, + _fp_code_fma, + _fp_code_fmin, + _fp_code_fmax, + _fp_code_famin, + _fp_code_famax, + _fp_code_round_to_integral, + _fp_code_minnum, + _fp_code_maxnum, + _fp_code_minnummag, + _fp_code_maxnummag, + _fp_code_quantize, + _fp_code_logb, + _fp_code_scaleb, + _fp_code_remainder, + _fp_code_nextup, + _fp_code_nextdown, + _fp_code_nextafter, + } fp_operation_code_t; + + typedef enum { + _fp_compare_equal, + _fp_compare_greater, + _fp_compare_less, + _fp_compare_unordered + } fpieee_compare_result_t; + + typedef enum { + _fp_format_fp32, + _fp_format_fp64, + _fp_format_fp80, + _fp_format_fp128, + _fp_format_dec_fp32, + _fp_format_dec_fp64, + _fp_format_dec_fp128, + _fp_format_i8, /* 8-bit integer */ + _fp_format_i16, /* 16-bit integer */ + _fp_format_i32, /* 32-bit integer */ + _fp_format_i64, /* 64-bit integer */ + _fp_format_u8, /* 8-bit unsigned integer */ + _fp_format_u16, /* 16-bit unsigned integer */ + _fp_format_u32, /* 32-bit unsigned integer */ + _fp_format_u64, /* 64-bit unsigned integer */ + _fp_format_compare, /* compare value format */ + _fp_format_decimal_char, /* decimal character */ + _fp_format_string /* string */ + } fpieee_format_t; + + typedef struct { + unsigned short W[5]; + } _float80_t; + + typedef struct { + unsigned int W[4]; + } _float128_t; + + typedef struct { + union { + float fp32_value; + double fp64_value; + _float80_t fp80_value; + _float128_t fp128_value; + UINT32 decfp32_value; + UINT64 decfp64_value; + UINT128 decfp128_value; + char i8_value; + short i16_value; + int i32_value; + SINT64 i64_value; + unsigned char u8_value; + unsigned short u16_value; + unsigned int u32_value; + unsigned long u64_value; + fpieee_compare_result_t compare_value; + unsigned char s[256]; + } value; + unsigned int operand_valid:1; + fpieee_format_t format:5; + } fpieee_value_t; + + typedef struct { + unsigned int rounding_mode:3; + unsigned int precision:3; + unsigned int operation:26; + fpieee_exception_flags_t cause; + fpieee_exception_flags_t enable; + fpieee_exception_flags_t status; + fpieee_value_t operand1; + fpieee_value_t operand2; + fpieee_value_t operand3; + fpieee_value_t result; + } _IDEC_excepthandling; + extern _IDEC_excepthandling _IDEC_glbexcepthandling; + +#endif + +#if DECIMAL_CALL_BY_REFERENCE + + extern void bid_to_dpd32 (UINT32 * pres, UINT32 * px); + extern void bid_to_dpd64 (UINT64 * pres, UINT64 * px); + extern void bid_to_dpd128 (UINT128 * pres, UINT128 * px); + extern void dpd_to_bid32 (UINT32 * pres, UINT32 * px); + extern void dpd_to_bid64 (UINT64 * pres, UINT64 * px); + extern void dpd_to_bid128 (UINT128 * pres, UINT128 * px); + + extern void bid128dd_add (UINT128 * pres, UINT64 * px, + UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128dq_add (UINT128 * pres, UINT64 * px, + UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128qd_add (UINT128 * pres, UINT128 * px, + UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_add (UINT128 * pres, UINT128 * px, + UINT128 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128dd_sub (UINT128 * pres, UINT64 * px, + UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128dq_sub (UINT128 * pres, UINT64 * px, + UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128qd_sub (UINT128 * pres, UINT128 * px, + UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_sub (UINT128 * pres, UINT128 * px, + UINT128 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128dd_mul (UINT128 * pres, UINT64 * px, + UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128dq_mul (UINT128 * pres, UINT64 * px, + UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128qd_mul (UINT128 * pres, UINT128 * px, + UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_mul (UINT128 * pres, UINT128 * px, + UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_div (UINT128 * pres, UINT128 * px, + UINT128 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128dd_div (UINT128 * pres, UINT64 * px, + UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128dq_div (UINT128 * pres, UINT64 * px, + UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128qd_div (UINT128 * pres, UINT128 * px, + UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_fma (UINT128 * pres, UINT128 * px, + UINT128 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128ddd_fma (UINT128 * pres, UINT64 * px, + UINT64 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128ddq_fma (UINT128 * pres, UINT64 * px, + UINT64 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128dqd_fma (UINT128 * pres, UINT64 * px, + UINT128 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128dqq_fma (UINT128 * pres, UINT64 * px, + UINT128 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128qdd_fma (UINT128 * pres, UINT128 * px, + UINT64 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128qdq_fma (UINT128 * pres, UINT128 * px, + UINT64 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128qqd_fma (UINT128 * pres, UINT128 * px, + UINT128 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + // Note: bid128qqq_fma is represented by bid128_fma + // Note: bid64ddd_fma is represented by bid64_fma + extern void bid64ddq_fma (UINT64 * pres, UINT64 * px, + UINT64 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64dqd_fma (UINT64 * pres, UINT64 * px, + UINT128 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64dqq_fma (UINT64 * pres, UINT64 * px, + UINT128 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64qdd_fma (UINT64 * pres, UINT128 * px, + UINT64 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64qdq_fma (UINT64 * pres, UINT128 * px, + UINT64 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64qqd_fma (UINT64 * pres, UINT128 * px, + UINT128 * py, UINT64 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64qqq_fma (UINT64 * pres, UINT128 * px, + UINT128 * py, UINT128 * pz + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid128_sqrt (UINT128 * pres, + UINT128 * + px _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128d_sqrt (UINT128 * pres, UINT64 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid64_add (UINT64 * pres, UINT64 * px, + UINT64 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64dq_add (UINT64 * pres, UINT64 * px, + UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64qd_add (UINT64 * pres, UINT128 * px, + UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64qq_add (UINT64 * pres, UINT128 * px, + UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_sub (UINT64 * pres, UINT64 * px, + UINT64 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64dq_sub (UINT64 * pres, UINT64 * px, + UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64qd_sub (UINT64 * pres, UINT128 * px, + UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64qq_sub (UINT64 * pres, UINT128 * px, + UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_mul (UINT64 * pres, UINT64 * px, + UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64dq_mul (UINT64 * pres, UINT64 * px, + UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64qd_mul (UINT64 * pres, UINT128 * px, + UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64qq_mul (UINT64 * pres, UINT128 * px, + UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_div (UINT64 * pres, UINT64 * px, + UINT64 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64dq_div (UINT64 * pres, UINT64 * px, + UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64qd_div (UINT64 * pres, UINT128 * px, + UINT64 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64qq_div (UINT64 * pres, UINT128 * px, + UINT128 * py + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_fma (UINT64 * pres, UINT64 * px, + UINT64 * py, + UINT64 * + pz _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_sqrt (UINT64 * pres, + UINT64 * + px _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64q_sqrt (UINT64 * pres, UINT128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid128_to_int8_rnint (char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int8_xrnint (char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int8_rninta (char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int8_xrninta (char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int8_int (char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_to_int8_xint (char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_to_int8_floor (char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int8_xfloor (char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int8_ceil (char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_to_int8_xceil (char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int16_rnint (short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int16_xrnint (short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int16_rninta (short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int16_xrninta (short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int16_int (short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_to_int16_xint (short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int16_floor (short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int16_xfloor (short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int16_ceil (short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int16_xceil (short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint8_rnint (unsigned char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint8_xrnint (unsigned char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint8_rninta (unsigned char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint8_xrninta (unsigned char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint8_int (unsigned char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_to_uint8_xint (unsigned char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint8_floor (unsigned char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint8_xfloor (unsigned char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint8_ceil (unsigned char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint8_xceil (unsigned char *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint16_rnint (unsigned short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint16_xrnint (unsigned short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint16_rninta (unsigned short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint16_xrninta (unsigned short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint16_int (unsigned short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint16_xint (unsigned short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint16_floor (unsigned short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint16_xfloor (unsigned short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint16_ceil (unsigned short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint16_xceil (unsigned short *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int32_rnint (int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int32_xrnint (int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int32_rninta (int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int32_xrninta (int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int32_int (int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_to_int32_xint (int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int32_floor (int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int32_xfloor (int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int32_ceil (int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int32_xceil (int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint32_rnint (unsigned int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint32_xrnint (unsigned int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint32_rninta (unsigned int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint32_xrninta (unsigned int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint32_int (unsigned int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint32_xint (unsigned int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint32_floor (unsigned int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint32_xfloor (unsigned int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint32_ceil (unsigned int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint32_xceil (unsigned int *pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int64_rnint (SINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int64_xrnint (SINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int64_rninta (SINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int64_xrninta (SINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int64_int (SINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_to_int64_xint (SINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int64_floor (SINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int64_xfloor (SINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int64_ceil (SINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_int64_xceil (SINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint64_rnint (UINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint64_xrnint (UINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint64_rninta (UINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint64_xrninta (UINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint64_int (UINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint64_xint (UINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint64_floor (UINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint64_xfloor (UINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint64_ceil (UINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_to_uint64_xceil (UINT64 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int32_rnint (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int32_xrnint (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int32_rninta (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int32_xrninta (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int32_int (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int32_xint (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int32_floor (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int32_xfloor (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int32_ceil (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int32_xceil (int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int8_rnint (char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int8_xrnint (char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int8_rninta (char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int8_xrninta (char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int8_int (char *pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int8_xint (char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int8_floor (char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int8_xfloor (char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int8_ceil (char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int8_xceil (char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int16_rnint (short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int16_xrnint (short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int16_rninta (short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int16_xrninta (short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int16_int (short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int16_xint (short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int16_floor (short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int16_xfloor (short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int16_ceil (short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int16_xceil (short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint8_rnint (unsigned char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint8_xrnint (unsigned char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint8_rninta (unsigned char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint8_xrninta (unsigned char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint8_int (unsigned char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_uint8_xint (unsigned char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_uint8_floor (unsigned char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint8_xfloor (unsigned char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint8_ceil (unsigned char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_uint8_xceil (unsigned char *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint16_rnint (unsigned short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint16_xrnint (unsigned short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint16_rninta (unsigned short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint16_xrninta (unsigned short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint16_int (unsigned short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_uint16_xint (unsigned short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint16_floor (unsigned short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint16_xfloor (unsigned short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint16_ceil (unsigned short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint16_xceil (unsigned short *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint32_rnint (unsigned int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint32_xrnint (unsigned int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint32_rninta (unsigned int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint32_xrninta (unsigned int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint32_int (unsigned int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_uint32_xint (unsigned int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint32_floor (unsigned int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint32_xfloor (unsigned int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint32_ceil (unsigned int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint32_xceil (unsigned int *pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int64_rnint (SINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int64_xrnint (SINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int64_rninta (SINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int64_xrninta (SINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int64_int (SINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int64_xint (SINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int64_floor (SINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int64_xfloor (SINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_int64_ceil (SINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_int64_xceil (SINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint64_rnint (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint64_xrnint (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint64_rninta (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint64_xrninta (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint64_int (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_uint64_xint (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint64_floor (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint64_xfloor (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint64_ceil (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_uint64_xceil (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern void bid64_quiet_equal (int *pres, UINT64 * px, UINT64 * py + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_quiet_greater (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_quiet_greater_equal (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_quiet_greater_unordered (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_quiet_less (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_quiet_less_equal (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_quiet_less_unordered (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_quiet_not_equal (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_quiet_not_greater (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_quiet_not_less (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_quiet_ordered (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_quiet_unordered (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_signaling_greater (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_signaling_greater_equal (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_signaling_greater_unordered (int *pres, + UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_signaling_less (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_signaling_less_equal (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_signaling_less_unordered (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_signaling_not_greater (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_signaling_not_less (int *pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern void bid128_quiet_equal (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_quiet_greater (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_quiet_greater_equal (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_quiet_greater_unordered (int *pres, + UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_quiet_less (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_quiet_less_equal (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_quiet_less_unordered (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_quiet_not_equal (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_quiet_not_greater (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_quiet_not_less (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_quiet_ordered (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_quiet_unordered (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_signaling_greater (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_signaling_greater_equal (int *pres, + UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_signaling_greater_unordered (int *pres, + UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_signaling_less (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_signaling_less_equal (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_signaling_less_unordered (int *pres, + UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_signaling_not_greater (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_signaling_not_less (int *pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern void bid64_round_integral_exact (UINT64 * pres, UINT64 * px + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_round_integral_nearest_even (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_round_integral_negative (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_round_integral_positive (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_round_integral_zero (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_round_integral_nearest_away (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern void bid128_round_integral_exact (UINT128 * pres, + UINT128 * + px _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_round_integral_nearest_even (UINT128 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_round_integral_negative (UINT128 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_round_integral_positive (UINT128 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_round_integral_zero (UINT128 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_round_integral_nearest_away (UINT128 * pres, + UINT128 * + px _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern void bid64_nextup (UINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_nextdown (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_nextafter (UINT64 * pres, UINT64 * px, + UINT64 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern void bid128_nextup (UINT128 * pres, UINT128 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_nextdown (UINT128 * pres, + UINT128 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_nextafter (UINT128 * pres, UINT128 * px, + UINT128 * + py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern void bid64_minnum (UINT64 * pres, UINT64 * px, UINT64 * py + _EXC_FLAGS_PARAM); + extern void bid64_minnum_mag (UINT64 * pres, UINT64 * px, + UINT64 * py _EXC_FLAGS_PARAM); + extern void bid64_maxnum (UINT64 * pres, UINT64 * px, UINT64 * py + _EXC_FLAGS_PARAM); + extern void bid64_maxnum_mag (UINT64 * pres, UINT64 * px, + UINT64 * py _EXC_FLAGS_PARAM); + + extern void bid128_minnum (UINT128 * pres, UINT128 * px, + UINT128 * py _EXC_FLAGS_PARAM); + extern void bid128_minnum_mag (UINT128 * pres, UINT128 * px, + UINT128 * py _EXC_FLAGS_PARAM); + extern void bid128_maxnum (UINT128 * pres, UINT128 * px, + UINT128 * py _EXC_FLAGS_PARAM); + extern void bid128_maxnum_mag (UINT128 * pres, UINT128 * px, + UINT128 * py _EXC_FLAGS_PARAM); + + extern void bid64_from_int32 (UINT64 * pres, int *px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_from_uint32 (UINT64 * pres, unsigned int *px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_from_int64 (UINT64 * pres, SINT64 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_from_uint64 (UINT64 * pres, + UINT64 * + px _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_from_int32 (UINT128 * pres, + int *px _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_from_uint32 (UINT128 * pres, + unsigned int *px _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_from_int64 (UINT128 * pres, + SINT64 * + px _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_from_uint64 (UINT128 * pres, + UINT64 * + px _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern void bid64_isSigned (int *pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_isNormal (int *pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_isSubnormal (int *pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_isFinite (int *pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_isZero (int *pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_isInf (int *pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_isSignaling (int *pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_isCanonical (int *pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_isNaN (int *pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_copy (UINT64 * pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_negate (UINT64 * pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_abs (UINT64 * pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_copySign (UINT64 * pres, UINT64 * px, UINT64 * py + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_class (int *pres, UINT64 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_sameQuantum (int *pres, UINT64 * px, UINT64 * py + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_totalOrder (int *pres, UINT64 * px, UINT64 * py + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_totalOrderMag (int *pres, UINT64 * px, + UINT64 * + py _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_radix (int *pres, + UINT64 * + px _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid128_isSigned (int *pres, UINT128 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_isNormal (int *pres, UINT128 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_isSubnormal (int *pres, UINT128 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_isFinite (int *pres, UINT128 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_isZero (int *pres, UINT128 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_isInf (int *pres, UINT128 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_isSignaling (int *pres, UINT128 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_isCanonical (int *pres, UINT128 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_isNaN (int *pres, UINT128 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_copy (UINT128 * pres, UINT128 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_negate (UINT128 * pres, UINT128 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_abs (UINT128 * pres, UINT128 * px + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_copySign (UINT128 * pres, UINT128 * px, + UINT128 * + py _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_class (int *pres, + UINT128 * + px _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_sameQuantum (int *pres, UINT128 * px, + UINT128 * + py _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_totalOrder (int *pres, UINT128 * px, + UINT128 * + py _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_totalOrderMag (int *pres, UINT128 * px, + UINT128 * + py _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid128_radix (int *pres, + UINT128 * + px _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid64_rem (UINT64 * pres, UINT64 * px, UINT64 * py + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_logb (int * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_scalb (UINT64 * pres, UINT64 * px, + int *pn _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid128_rem (UINT128 * pres, UINT128 * px, UINT128 * py + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_logb (int * pres, UINT128 * px + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_scalb (UINT128 * pres, UINT128 * px, + int *pn _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid32_to_bid64 (UINT64 * pres, + UINT32 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid32_to_bid128 (UINT128 * pres, + UINT32 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_bid128 (UINT128 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern void bid64_to_bid32 (UINT32 * pres, + UINT64 * + px _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_to_bid32 (UINT32 * pres, + UINT128 * + px _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_to_bid64 (UINT64 * pres, + UINT128 * + px _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid64_from_string (UINT64 * pres, char *ps + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid64_to_string (char *ps, UINT64 * px + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_from_string (UINT128 * pres, char *ps + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_to_string (char *str, UINT128 * px + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid64_quantize (UINT64 * pres, UINT64 * px, + UINT64 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid128_quantize (UINT128 * pres, UINT128 * px, + UINT128 * + py _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid128_to_binary32 (float *pres, UINT128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid128_to_binary64 (double *pres, UINT128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid128_to_binary80 (BINARY80 * pres, UINT128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid128_to_binary128 (BINARY128 * pres, UINT128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void binary128_to_bid32 (UINT32 * pres, BINARY128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void binary128_to_bid64 (UINT64 * pres, BINARY128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void binary128_to_bid128 (UINT128 * pres, BINARY128 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid64_to_binary32 (float *pres, UINT64 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid64_to_binary64 (double *pres, UINT64 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid64_to_binary80 (BINARY80 * pres, UINT64 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid64_to_binary128 (BINARY128 * pres, UINT64 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void binary64_to_bid32 (UINT32 * pres, double *px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void binary64_to_bid64 (UINT64 * pres, double *px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void binary64_to_bid128 (UINT128 * pres, double *px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid32_to_binary32 (float *pres, UINT32 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid32_to_binary64 (double *pres, UINT32 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid32_to_binary80 (BINARY80 * pres, UINT32 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid32_to_binary128 (BINARY128 * pres, UINT32 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void binary32_to_bid32 (UINT32 * pres, float *px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void binary32_to_bid64 (UINT64 * pres, float *px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void binary32_to_bid128 (UINT128 * pres, float *px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void binary80_to_bid32 (UINT32 * pres, BINARY80 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void binary80_to_bid64 (UINT64 * pres, BINARY80 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void binary80_to_bid128 (UINT128 * pres, BINARY80 * px + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void is754 (int *retval); + + extern void is754R (int *retval); + + extern void signalException (_IDEC_flags * + pflagsmask _EXC_FLAGS_PARAM); + + extern void lowerFlags (_IDEC_flags * pflagsmask _EXC_FLAGS_PARAM); + + extern void testFlags (_IDEC_flags * praised, + _IDEC_flags * pflagsmask _EXC_FLAGS_PARAM); + + extern void testSavedFlags (_IDEC_flags * praised, + _IDEC_flags * psavedflags, + _IDEC_flags * pflagsmask); + + extern void restoreFlags (_IDEC_flags * pflagsvalues, + _IDEC_flags * + pflagsmask _EXC_FLAGS_PARAM); + + extern void saveFlags (_IDEC_flags * pflagsvalues, + _IDEC_flags * pflagsmask _EXC_FLAGS_PARAM); + + void getDecimalRoundingDirection (_IDEC_round * + rounding_mode _RND_MODE_PARAM); + + void setDecimalRoundingDirection (_IDEC_round * + rounding_mode _RND_MODE_PARAM); + +#else + + extern UINT32 bid_to_dpd32 (UINT32 px); + extern UINT64 bid_to_dpd64 (UINT64 px); + extern UINT128 bid_to_dpd128 (UINT128 px); + extern UINT32 dpd_to_bid32 (UINT32 px); + extern UINT64 dpd_to_bid64 (UINT64 px); + extern UINT128 dpd_to_bid128 (UINT128 px); + + extern UINT128 bid128dd_add (UINT64 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128dq_add (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128qd_add (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128_add (UINT128 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128dd_sub (UINT64 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128dq_sub (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128qd_sub (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128_sub (UINT128 x, + UINT128 y _RND_MODE_PARAM + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128dd_mul (UINT64 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128dq_mul (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128qd_mul (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128_mul (UINT128 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128_div (UINT128 x, + UINT128 y _RND_MODE_PARAM + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128dd_div (UINT64 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128dq_div (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128qd_div (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128_fma (UINT128 x, UINT128 y, UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128ddd_fma (UINT64 x, UINT64 y, UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128ddq_fma (UINT64 x, UINT64 y, UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128dqd_fma (UINT64 x, UINT128 y, UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128dqq_fma (UINT64 x, UINT128 y, + UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128qdd_fma (UINT128 x, UINT64 y, UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128qdq_fma (UINT128 x, UINT64 y, + UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128qqd_fma (UINT128 x, UINT128 y, + UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + // Note: bid128qqq_fma is represented by bid128_fma + // Note: bid64ddd_fma is represented by bid64_fma + extern UINT64 bid64ddq_fma (UINT64 x, UINT64 y, + UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64dqd_fma (UINT64 x, UINT128 y, + UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64dqq_fma (UINT64 x, UINT128 y, + UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64qdd_fma (UINT128 x, UINT64 y, + UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64qdq_fma (UINT128 x, UINT64 y, + UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64qqd_fma (UINT128 x, UINT128 y, + UINT64 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64qqq_fma (UINT128 x, UINT128 y, + UINT128 z + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern UINT128 bid128_sqrt (UINT128 x _RND_MODE_PARAM + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128d_sqrt (UINT64 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern UINT64 bid64_add (UINT64 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64dq_add (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64qd_add (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64qq_add (UINT128 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64_sub (UINT64 x, + UINT64 y _RND_MODE_PARAM + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64dq_sub (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64qd_sub (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64qq_sub (UINT128 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64_mul (UINT64 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64dq_mul (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64qd_mul (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64qq_mul (UINT128 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64_div (UINT64 x, + UINT64 y _RND_MODE_PARAM + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64dq_div (UINT64 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64qd_div (UINT128 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64qq_div (UINT128 x, UINT128 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64_fma (UINT64 x, UINT64 y, + UINT64 z _RND_MODE_PARAM + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_sqrt (UINT64 x _RND_MODE_PARAM + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64q_sqrt (UINT128 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern char bid128_to_int8_rnint (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern char bid128_to_int8_xrnint (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern char bid128_to_int8_rninta (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern char bid128_to_int8_xrninta (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern char bid128_to_int8_int (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern char bid128_to_int8_xint (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern char bid128_to_int8_floor (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern char bid128_to_int8_xfloor (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern char bid128_to_int8_ceil (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern char bid128_to_int8_xceil (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid128_to_int16_rnint (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid128_to_int16_xrnint (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid128_to_int16_rninta (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid128_to_int16_xrninta (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid128_to_int16_int (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid128_to_int16_xint (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid128_to_int16_floor (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid128_to_int16_xfloor (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid128_to_int16_ceil (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid128_to_int16_xceil (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid128_to_uint8_rnint (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid128_to_uint8_xrnint (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid128_to_uint8_rninta (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid128_to_uint8_xrninta (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid128_to_uint8_int (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid128_to_uint8_xint (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid128_to_uint8_floor (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid128_to_uint8_xfloor (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid128_to_uint8_ceil (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid128_to_uint8_xceil (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid128_to_uint16_rnint (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid128_to_uint16_xrnint (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid128_to_uint16_rninta (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid128_to_uint16_xrninta (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid128_to_uint16_int (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid128_to_uint16_xint (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid128_to_uint16_floor (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid128_to_uint16_xfloor (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid128_to_uint16_ceil (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid128_to_uint16_xceil (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_to_int32_rnint (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_to_int32_xrnint (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_to_int32_rninta (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_to_int32_xrninta (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_to_int32_int (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid128_to_int32_xint (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid128_to_int32_floor (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_to_int32_xfloor (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_to_int32_ceil (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid128_to_int32_xceil (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid128_to_uint32_rnint (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid128_to_uint32_xrnint (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid128_to_uint32_rninta (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid128_to_uint32_xrninta (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid128_to_uint32_int (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid128_to_uint32_xint (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid128_to_uint32_floor (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid128_to_uint32_xfloor (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid128_to_uint32_ceil (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid128_to_uint32_xceil (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid128_to_int64_rnint (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid128_to_int64_xrnint (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid128_to_int64_rninta (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid128_to_int64_xrninta (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid128_to_int64_int (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid128_to_int64_xint (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid128_to_int64_floor (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid128_to_int64_xfloor (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid128_to_int64_ceil (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid128_to_int64_xceil (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid128_to_uint64_rnint (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid128_to_uint64_xrnint (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid128_to_uint64_rninta (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid128_to_uint64_xrninta (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid128_to_uint64_int (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid128_to_uint64_xint (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid128_to_uint64_floor (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid128_to_uint64_xfloor (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid128_to_uint64_ceil (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid128_to_uint64_xceil (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_to_int32_rnint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_to_int32_xrnint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_to_int32_rninta (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_to_int32_xrninta (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_to_int32_int (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_to_int32_xint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_to_int32_floor (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_to_int32_xfloor (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_to_int32_ceil (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_to_int32_xceil (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern char bid64_to_int8_rnint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern char bid64_to_int8_xrnint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern char bid64_to_int8_rninta (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern char bid64_to_int8_xrninta (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern char bid64_to_int8_int (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern char bid64_to_int8_xint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern char bid64_to_int8_floor (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern char bid64_to_int8_xfloor (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern char bid64_to_int8_ceil (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern char bid64_to_int8_xceil (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern short bid64_to_int16_rnint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid64_to_int16_xrnint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid64_to_int16_rninta (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid64_to_int16_xrninta (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid64_to_int16_int (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern short bid64_to_int16_xint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid64_to_int16_floor (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid64_to_int16_xfloor (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid64_to_int16_ceil (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern short bid64_to_int16_xceil (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid64_to_uint8_rnint (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid64_to_uint8_xrnint (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid64_to_uint8_rninta (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid64_to_uint8_xrninta (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid64_to_uint8_int (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid64_to_uint8_xint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid64_to_uint8_floor (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid64_to_uint8_xfloor (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid64_to_uint8_ceil (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned char bid64_to_uint8_xceil (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid64_to_uint16_rnint (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid64_to_uint16_xrnint (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid64_to_uint16_rninta (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid64_to_uint16_xrninta (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid64_to_uint16_int (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid64_to_uint16_xint (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid64_to_uint16_floor (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid64_to_uint16_xfloor (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid64_to_uint16_ceil (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned short bid64_to_uint16_xceil (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid64_to_uint32_rnint (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid64_to_uint32_xrnint (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid64_to_uint32_rninta (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid64_to_uint32_xrninta (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid64_to_uint32_int (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid64_to_uint32_xint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid64_to_uint32_floor (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid64_to_uint32_xfloor (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid64_to_uint32_ceil (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern unsigned int bid64_to_uint32_xceil (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid64_to_int64_rnint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid64_to_int64_xrnint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid64_to_int64_rninta (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid64_to_int64_xrninta (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid64_to_int64_int (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid64_to_int64_xint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid64_to_int64_floor (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid64_to_int64_xfloor (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid64_to_int64_ceil (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern SINT64 bid64_to_int64_xceil (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_to_uint64_rnint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_to_uint64_xrnint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_to_uint64_rninta (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_to_uint64_xrninta (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_to_uint64_int (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_to_uint64_xint (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_to_uint64_floor (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_to_uint64_xfloor (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_to_uint64_ceil (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_to_uint64_xceil (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern int bid64_quiet_equal (UINT64 x, UINT64 y + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_quiet_greater (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_quiet_greater_equal (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_quiet_greater_unordered (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_quiet_less (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_quiet_less_equal (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_quiet_less_unordered (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_quiet_not_equal (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_quiet_not_greater (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_quiet_not_less (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_quiet_ordered (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_quiet_unordered (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_signaling_greater (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_signaling_greater_equal (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_signaling_greater_unordered (UINT64 x, + UINT64 y + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_signaling_less (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_signaling_less_equal (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_signaling_less_unordered (UINT64 x, + UINT64 y + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_signaling_not_greater (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_signaling_not_less (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern int bid128_quiet_equal (UINT128 x, UINT128 y + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_quiet_greater (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid128_quiet_greater_equal (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_quiet_greater_unordered (UINT128 x, + UINT128 y + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_quiet_less (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid128_quiet_less_equal (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_quiet_less_unordered (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_quiet_not_equal (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_quiet_not_greater (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_quiet_not_less (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_quiet_ordered (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid128_quiet_unordered (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_signaling_greater (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_signaling_greater_equal (UINT128 x, + UINT128 y + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_signaling_greater_unordered (UINT128 x, + UINT128 y + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_signaling_less (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_signaling_less_equal (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_signaling_less_unordered (UINT128 x, + UINT128 y + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_signaling_not_greater (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_signaling_not_less (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern UINT64 bid64_round_integral_exact (UINT64 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_round_integral_nearest_even (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_round_integral_negative (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_round_integral_positive (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_round_integral_zero (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_round_integral_nearest_away (UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern UINT128 bid128_round_integral_exact (UINT128 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_round_integral_nearest_even (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_round_integral_negative (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_round_integral_positive (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_round_integral_zero (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_round_integral_nearest_away (UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern UINT64 bid64_nextup (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_nextdown (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64_nextafter (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern UINT128 bid128_nextup (UINT128 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_nextdown (UINT128 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128_nextafter (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern UINT64 bid64_minnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM); + extern UINT64 bid64_minnum_mag (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM); + extern UINT64 bid64_maxnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM); + extern UINT64 bid64_maxnum_mag (UINT64 x, + UINT64 y _EXC_FLAGS_PARAM); + + extern UINT128 bid128_minnum (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM); + extern UINT128 bid128_minnum_mag (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM); + extern UINT128 bid128_maxnum (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM); + extern UINT128 bid128_maxnum_mag (UINT128 x, + UINT128 y _EXC_FLAGS_PARAM); + + extern UINT64 bid64_from_int32 (int x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_from_uint32 (unsigned int x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_from_int64 (SINT64 x _RND_MODE_PARAM + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_from_uint64 (UINT64 _RND_MODE_PARAM + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_from_int32 (int x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_from_uint32 (unsigned int x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_from_int64 (SINT64 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_from_uint64 (UINT64 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern int bid64_isSigned (UINT64 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_isNormal (UINT64 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_isSubnormal (UINT64 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_isFinite (UINT64 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_isZero (UINT64 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_isInf (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_isSignaling (UINT64 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_isCanonical (UINT64 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_isNaN (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64_copy (UINT64 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_negate (UINT64 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_abs (UINT64 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT64 bid64_copySign (UINT64 x, + UINT64 y _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid64_class (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_sameQuantum (UINT64 x, UINT64 y + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_totalOrder (UINT64 x, UINT64 y + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_totalOrderMag (UINT64 x, UINT64 y + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_radix (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern int bid128_isSigned (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_isNormal (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_isSubnormal (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_isFinite (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_isZero (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_isInf (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_isSignaling (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_isCanonical (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_isNaN (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_copy (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_negate (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_abs (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_copySign (UINT128 x, + UINT128 y _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_class (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_sameQuantum (UINT128 x, + UINT128 y _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_totalOrder (UINT128 x, + UINT128 y _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_totalOrderMag (UINT128 x, + UINT128 y _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern int bid128_radix (UINT128 x _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern UINT64 bid64_rem (UINT64 x, UINT64 y + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid64_logb (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64_scalb (UINT64 x, + int n _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern UINT128 bid128_rem (UINT128 x, UINT128 y + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern int bid128_logb (UINT128 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + extern UINT128 bid128_scalb (UINT128 x, + int n _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern UINT64 bid32_to_bid64 (UINT32 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid32_to_bid128 (UINT32 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid64_to_bid128 (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT32 bid64_to_bid32 (UINT64 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT32 bid128_to_bid32 (UINT128 x _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid128_to_bid64 (UINT128 x _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern void bid64_to_string (char *ps, UINT64 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT64 bid64_from_string (char *ps + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern void bid128_to_string (char *str, UINT128 x + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + extern UINT128 bid128_from_string (char *ps + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern UINT64 bid64_quantize (UINT64 x, UINT64 y + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern UINT128 bid128_quantize (UINT128 x, UINT128 y + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + + extern UINT32 binary128_to_bid32 (BINARY128 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern UINT64 binary128_to_bid64 (BINARY128 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern UINT128 binary128_to_bid128 (BINARY128 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern UINT32 binary64_to_bid32 (double x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern UINT64 binary64_to_bid64 (double x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern UINT128 binary64_to_bid128 (double x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern UINT32 binary80_to_bid32 (BINARY80 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern UINT64 binary80_to_bid64 (BINARY80 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern UINT128 binary80_to_bid128 (BINARY80 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern UINT32 binary32_to_bid32 (float x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern UINT64 binary32_to_bid64 (float x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern UINT128 binary32_to_bid128 (float x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern float bid128_to_binary32 (UINT128 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern double bid128_to_binary64 (UINT128 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern BINARY80 bid128_to_binary80 (UINT128 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern BINARY128 bid128_to_binary128 (UINT128 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern float bid64_to_binary32 (UINT64 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern double bid64_to_binary64 (UINT64 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern BINARY80 bid64_to_binary80 (UINT64 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern BINARY128 bid64_to_binary128 (UINT64 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern float bid32_to_binary32 (UINT32 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern double bid32_to_binary64 (UINT32 x + _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM); + + extern BINARY80 bid32_to_binary80 (UINT32 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern BINARY128 bid32_to_binary128 (UINT32 x + _RND_MODE_PARAM + _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM + _EXC_INFO_PARAM); + + extern int is754 (void); + + extern int is754R (void); + + extern void signalException (_IDEC_flags flagsmask + _EXC_FLAGS_PARAM); + + extern void lowerFlags (_IDEC_flags flagsmask _EXC_FLAGS_PARAM); + + extern _IDEC_flags testFlags (_IDEC_flags flagsmask + _EXC_FLAGS_PARAM); + + extern _IDEC_flags testSavedFlags (_IDEC_flags savedflags, + _IDEC_flags flagsmask); + + extern void restoreFlags (_IDEC_flags flagsvalues, + _IDEC_flags flagsmask _EXC_FLAGS_PARAM); + + extern _IDEC_flags saveFlags (_IDEC_flags flagsmask + _EXC_FLAGS_PARAM); + +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round getDecimalRoundingDirection (_IDEC_round rnd_mode); +#else + _IDEC_round getDecimalRoundingDirection (void); +#endif + +#if !DECIMAL_GLOBAL_ROUNDING + _IDEC_round setDecimalRoundingDirection (_IDEC_round + rounding_mode + _RND_MODE_PARAM); +#else + void setDecimalRoundingDirection (_IDEC_round rounding_mode); +#endif + +#endif + +// Internal Functions + + extern void + round64_2_18 (int q, + int x, + UINT64 C, + UINT64 * ptr_Cstar, + int *delta_exp, + int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint); + + extern void + round128_19_38 (int q, + int x, + UINT128 C, + UINT128 * ptr_Cstar, + int *delta_exp, + int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint); + + extern void + round192_39_57 (int q, + int x, + UINT192 C, + UINT192 * ptr_Cstar, + int *delta_exp, + int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint); + + extern void + round256_58_76 (int q, + int x, + UINT256 C, + UINT256 * ptr_Cstar, + int *delta_exp, + int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint); + +#endif + +// Prototypes for Internal Functions + + extern UINT32 bid_to_bid32 (UINT32); + extern UINT64 bid_to_bid64 (UINT64); + extern UINT128 bid_to_bid128 (UINT128); + extern UINT32 bid32_canonize (UINT32); + extern UINT64 bid64_canonize (UINT64); + extern UINT128 bid128_canonize (UINT128); diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_gcc_intrinsics.h b/gcc-4.4.3/libgcc/config/libbid/bid_gcc_intrinsics.h new file mode 100644 index 000000000..f5bd8d04a --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_gcc_intrinsics.h @@ -0,0 +1,295 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#ifndef _BID_GCC_INTRINSICS_H +#define _BID_GCC_INTRINSICS_H + +#ifdef IN_LIBGCC2 + +#include "tconfig.h" +#include "coretypes.h" +#include "tm.h" + +#ifndef LIBGCC2_WORDS_BIG_ENDIAN +#define LIBGCC2_WORDS_BIG_ENDIAN WORDS_BIG_ENDIAN +#endif + +#ifndef LIBGCC2_FLOAT_WORDS_BIG_ENDIAN +#define LIBGCC2_FLOAT_WORDS_BIG_ENDIAN LIBGCC2_WORDS_BIG_ENDIAN +#endif + +#ifndef LIBGCC2_LONG_DOUBLE_TYPE_SIZE +#define LIBGCC2_LONG_DOUBLE_TYPE_SIZE LONG_DOUBLE_TYPE_SIZE +#endif + +#ifndef LIBGCC2_HAS_XF_MODE +#define LIBGCC2_HAS_XF_MODE \ + (BITS_PER_UNIT == 8 && LIBGCC2_LONG_DOUBLE_TYPE_SIZE == 80) +#endif + +#ifndef LIBGCC2_HAS_TF_MODE +#define LIBGCC2_HAS_TF_MODE \ + (BITS_PER_UNIT == 8 && LIBGCC2_LONG_DOUBLE_TYPE_SIZE == 128) +#endif + +#ifndef BID_HAS_XF_MODE +#define BID_HAS_XF_MODE LIBGCC2_HAS_XF_MODE +#endif + +#ifndef BID_HAS_TF_MODE +#define BID_HAS_TF_MODE LIBGCC2_HAS_TF_MODE +#endif + +/* Some handy typedefs. */ + +typedef float SFtype __attribute__ ((mode (SF))); +typedef float DFtype __attribute__ ((mode (DF))); +#if LIBGCC2_HAS_XF_MODE +typedef float XFtype __attribute__ ((mode (XF))); +#endif /* LIBGCC2_HAS_XF_MODE */ +#if LIBGCC2_HAS_TF_MODE +typedef float TFtype __attribute__ ((mode (TF))); +#endif /* LIBGCC2_HAS_XF_MODE */ + +typedef int SItype __attribute__ ((mode (SI))); +typedef int DItype __attribute__ ((mode (DI))); +typedef unsigned int USItype __attribute__ ((mode (SI))); +typedef unsigned int UDItype __attribute__ ((mode (DI))); + +/* The type of the result of a decimal float comparison. This must + match `word_mode' in GCC for the target. */ + +typedef int CMPtype __attribute__ ((mode (word))); + +typedef int SINT8 __attribute__ ((mode (QI))); +typedef unsigned int UINT8 __attribute__ ((mode (QI))); +typedef USItype UINT32; +typedef SItype SINT32; +typedef UDItype UINT64; +typedef DItype SINT64; + +/* It has to be identical to the one defined in bid_functions.h. */ +typedef __attribute__ ((aligned(16))) struct +{ + UINT64 w[2]; +} UINT128; +#else /* if not IN_LIBGCC2 */ + +#ifndef BID_HAS_XF_MODE +#define BID_HAS_XF_MODE 1 +#endif + +#ifndef BID_HAS_TF_MODE +#if defined __i386__ +#define BID_HAS_TF_MODE 0 +#else +#define BID_HAS_TF_MODE 1 +#endif +#endif + +#ifndef SFtype +#define SFtype float +#endif + +#ifndef DFtype +#define DFtype double +#endif + +#if BID_HAS_XF_MODE +#ifndef XFtype +#define XFtype long double +#endif + +#endif /* IN_LIBGCC2 */ + +#if BID_HAS_TF_MODE +#ifndef TFtype +#define TFtype __float128 +#endif +#endif + +#ifndef SItype +#define SItype SINT32 +#endif + +#ifndef DItype +#define DItype SINT64 +#endif + +#ifndef USItype +#define USItype UINT32 +#endif + +#ifndef UDItype +#define UDItype UINT64 +#endif + +#ifndef CMPtype +#define CMPtype long +#endif +#endif /* IN_LIBGCC2 */ + +#if BID_HAS_GCC_DECIMAL_INTRINSICS +/* Prototypes for gcc instrinsics */ + +extern _Decimal64 __bid_adddd3 (_Decimal64, _Decimal64); +extern _Decimal64 __bid_subdd3 (_Decimal64, _Decimal64); +extern _Decimal32 __bid_addsd3 (_Decimal32, _Decimal32); +extern _Decimal32 __bid_subsd3 (_Decimal32, _Decimal32); +extern _Decimal128 __bid_addtd3 (_Decimal128, _Decimal128); +extern _Decimal128 __bid_subtd3 (_Decimal128, _Decimal128); +extern DFtype __bid_truncdddf (_Decimal64); +extern DItype __bid_fixdddi (_Decimal64); +extern _Decimal32 __bid_truncddsd2 (_Decimal64); +extern SFtype __bid_truncddsf (_Decimal64); +extern SItype __bid_fixddsi (_Decimal64); +extern _Decimal128 __bid_extendddtd2 (_Decimal64); +#if BID_HAS_TF_MODE +extern TFtype __bid_extendddtf (_Decimal64); +#endif +extern UDItype __bid_fixunsdddi (_Decimal64); +extern USItype __bid_fixunsddsi (_Decimal64); +#if BID_HAS_XF_MODE +extern XFtype __bid_extendddxf (_Decimal64); +#endif +extern _Decimal64 __bid_extenddfdd (DFtype); +extern _Decimal32 __bid_truncdfsd (DFtype); +extern _Decimal128 __bid_extenddftd (DFtype); +extern _Decimal64 __bid_floatdidd (DItype); +extern _Decimal32 __bid_floatdisd (DItype); +extern _Decimal128 __bid_floatditd (DItype); +extern _Decimal64 __bid_divdd3 (_Decimal64, _Decimal64); +extern _Decimal32 __bid_divsd3 (_Decimal32, _Decimal32); +extern _Decimal128 __bid_divtd3 (_Decimal128, _Decimal128); +extern CMPtype __bid_eqdd2 (_Decimal64, _Decimal64); +extern CMPtype __bid_eqsd2 (_Decimal32, _Decimal32); +extern CMPtype __bid_eqtd2 (_Decimal128, _Decimal128); +extern CMPtype __bid_gedd2 (_Decimal64, _Decimal64); +extern CMPtype __bid_gesd2 (_Decimal32, _Decimal32); +extern CMPtype __bid_getd2 (_Decimal128, _Decimal128); +extern CMPtype __bid_gtdd2 (_Decimal64, _Decimal64); +extern CMPtype __bid_gtsd2 (_Decimal32, _Decimal32); +extern CMPtype __bid_gttd2 (_Decimal128, _Decimal128); +extern CMPtype __bid_ledd2 (_Decimal64, _Decimal64); +extern CMPtype __bid_lesd2 (_Decimal32, _Decimal32); +extern CMPtype __bid_letd2 (_Decimal128, _Decimal128); +extern CMPtype __bid_ltdd2 (_Decimal64, _Decimal64); +extern CMPtype __bid_ltsd2 (_Decimal32, _Decimal32); +extern CMPtype __bid_lttd2 (_Decimal128, _Decimal128); +extern CMPtype __bid_nedd2 (_Decimal64, _Decimal64); +extern CMPtype __bid_nesd2 (_Decimal32, _Decimal32); +extern CMPtype __bid_netd2 (_Decimal128, _Decimal128); +extern CMPtype __bid_unorddd2 (_Decimal64, _Decimal64); +extern CMPtype __bid_unordsd2 (_Decimal32, _Decimal32); +extern CMPtype __bid_unordtd2 (_Decimal128, _Decimal128); +extern _Decimal64 __bid_muldd3 (_Decimal64, _Decimal64); +extern _Decimal32 __bid_mulsd3 (_Decimal32, _Decimal32); +extern _Decimal128 __bid_multd3 (_Decimal128, _Decimal128); +extern _Decimal64 __bid_extendsddd2 (_Decimal32); +extern DFtype __bid_extendsddf (_Decimal32); +extern DItype __bid_fixsddi (_Decimal32); +extern SFtype __bid_truncsdsf (_Decimal32); +extern SItype __bid_fixsdsi (_Decimal32); +extern _Decimal128 __bid_extendsdtd2 (_Decimal32); +#if BID_HAS_TF_MODE +extern TFtype __bid_extendsdtf (_Decimal32); +#endif +extern UDItype __bid_fixunssddi (_Decimal32); +extern USItype __bid_fixunssdsi (_Decimal32); +#if BID_HAS_XF_MODE +extern XFtype __bid_extendsdxf (_Decimal32); +#endif +extern _Decimal64 __bid_extendsfdd (SFtype); +extern _Decimal32 __bid_extendsfsd (SFtype); +extern _Decimal128 __bid_extendsftd (SFtype); +extern _Decimal64 __bid_floatsidd (SItype); +extern _Decimal32 __bid_floatsisd (SItype); +extern _Decimal128 __bid_floatsitd (SItype); +extern _Decimal64 __bid_trunctddd2 (_Decimal128); +extern DFtype __bid_trunctddf (_Decimal128); +extern DItype __bid_fixtddi (_Decimal128); +extern _Decimal32 __bid_trunctdsd2 (_Decimal128); +extern SFtype __bid_trunctdsf (_Decimal128); +extern SItype __bid_fixtdsi (_Decimal128); +#if BID_HAS_TF_MODE +extern TFtype __bid_trunctdtf (_Decimal128); +#endif +extern UDItype __bid_fixunstddi (_Decimal128); +extern USItype __bid_fixunstdsi (_Decimal128); +#if BID_HAS_XF_MODE +extern XFtype __bid_trunctdxf (_Decimal128); +#endif +#if BID_HAS_TF_MODE +extern _Decimal64 __bid_trunctfdd (TFtype); +extern _Decimal32 __bid_trunctfsd (TFtype); +extern _Decimal128 __bid_extendtftd (TFtype); +#endif +extern _Decimal64 __bid_floatunsdidd (UDItype); +extern _Decimal32 __bid_floatunsdisd (UDItype); +extern _Decimal128 __bid_floatunsditd (UDItype); +extern _Decimal64 __bid_floatunssidd (USItype); +extern _Decimal32 __bid_floatunssisd (USItype); +extern _Decimal128 __bid_floatunssitd (USItype); +#if BID_HAS_XF_MODE +extern _Decimal64 __bid_truncxfdd (XFtype); +extern _Decimal32 __bid_truncxfsd (XFtype); +extern _Decimal128 __bid_extendxftd (XFtype); +#endif +extern int isinfd32 (_Decimal32); +extern int isinfd64 (_Decimal64); +extern int isinfd128 (_Decimal128); +#endif /* BID_HAS_GCC_DECIMAL_INTRINSICS */ + +extern void __dfp_set_round (int); +extern int __dfp_get_round (void); +extern void __dfp_clear_except (void); +extern int __dfp_test_except (int); +extern void __dfp_raise_except (int); + +#if BID_HAS_GCC_DECIMAL_INTRINSICS +/* Used by gcc intrinsics. We have to define them after UINT128 + is defined. */ +union decimal32 { + _Decimal32 d; + UINT32 i; +}; + +union decimal64 { + _Decimal64 d; + UINT64 i; +}; + +union decimal128 { + _Decimal128 d; + UINT128 i; +}; + +#if BID_HAS_TF_MODE +union float128 { + TFtype f; + UINT128 i; +}; +#endif +#endif /* BID_HAS_GCC_DECIMAL_INTRINSICS */ + +#endif /* _BID_GCC_INTRINSICS_H */ diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_inline_add.h b/gcc-4.4.3/libgcc/config/libbid/bid_inline_add.h new file mode 100644 index 000000000..76246fab6 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_inline_add.h @@ -0,0 +1,1253 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +/***************************************************************************** + * + * Helper add functions (for fma) + * + * __BID_INLINE__ UINT64 get_add64( + * UINT64 sign_x, int exponent_x, UINT64 coefficient_x, + * UINT64 sign_y, int exponent_y, UINT64 coefficient_y, + * int rounding_mode) + * + * __BID_INLINE__ UINT64 get_add128( + * UINT64 sign_x, int exponent_x, UINT64 coefficient_x, + * UINT64 sign_y, int final_exponent_y, UINT128 CY, + * int extra_digits, int rounding_mode) + * + ***************************************************************************** + * + * Algorithm description: + * + * get_add64: same as BID64 add, but arguments are unpacked and there + * are no special case checks + * + * get_add128: add 64-bit coefficient to 128-bit product (which contains + * 16+extra_digits decimal digits), + * return BID64 result + * - the exponents are compared and the two coefficients are + * properly aligned for addition/subtraction + * - multiple paths are needed + * - final result exponent is calculated and the lower term is + * rounded first if necessary, to avoid manipulating + * coefficients longer than 128 bits + * + ****************************************************************************/ + +#ifndef _INLINE_BID_ADD_H_ +#define _INLINE_BID_ADD_H_ + +#include "bid_internal.h" + +#define MAX_FORMAT_DIGITS 16 +#define DECIMAL_EXPONENT_BIAS 398 +#define MASK_BINARY_EXPONENT 0x7ff0000000000000ull +#define BINARY_EXPONENT_BIAS 0x3ff +#define UPPER_EXPON_LIMIT 51 + +/////////////////////////////////////////////////////////////////////// +// +// get_add64() is essentially the same as bid_add(), except that +// the arguments are unpacked +// +////////////////////////////////////////////////////////////////////// +__BID_INLINE__ UINT64 +get_add64 (UINT64 sign_x, int exponent_x, UINT64 coefficient_x, + UINT64 sign_y, int exponent_y, UINT64 coefficient_y, + int rounding_mode, unsigned *fpsc) { + UINT128 CA, CT, CT_new; + UINT64 sign_a, sign_b, coefficient_a, coefficient_b, sign_s, sign_ab, + rem_a; + UINT64 saved_ca, saved_cb, C0_64, C64, remainder_h, T1, carry, tmp, + C64_new; + int_double tempx; + int exponent_a, exponent_b, diff_dec_expon; + int bin_expon_ca, extra_digits, amount, scale_k, scale_ca; + unsigned rmode, status; + + // sort arguments by exponent + if (exponent_x <= exponent_y) { + sign_a = sign_y; + exponent_a = exponent_y; + coefficient_a = coefficient_y; + sign_b = sign_x; + exponent_b = exponent_x; + coefficient_b = coefficient_x; + } else { + sign_a = sign_x; + exponent_a = exponent_x; + coefficient_a = coefficient_x; + sign_b = sign_y; + exponent_b = exponent_y; + coefficient_b = coefficient_y; + } + + // exponent difference + diff_dec_expon = exponent_a - exponent_b; + + /* get binary coefficients of x and y */ + + //--- get number of bits in the coefficients of x and y --- + + tempx.d = (double) coefficient_a; + bin_expon_ca = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff; + + if (!coefficient_a) { + return get_BID64 (sign_b, exponent_b, coefficient_b, rounding_mode, + fpsc); + } + if (diff_dec_expon > MAX_FORMAT_DIGITS) { + // normalize a to a 16-digit coefficient + + scale_ca = estimate_decimal_digits[bin_expon_ca]; + if (coefficient_a >= power10_table_128[scale_ca].w[0]) + scale_ca++; + + scale_k = 16 - scale_ca; + + coefficient_a *= power10_table_128[scale_k].w[0]; + + diff_dec_expon -= scale_k; + exponent_a -= scale_k; + + /* get binary coefficients of x and y */ + + //--- get number of bits in the coefficients of x and y --- + tempx.d = (double) coefficient_a; + bin_expon_ca = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff; + + if (diff_dec_expon > MAX_FORMAT_DIGITS) { +#ifdef SET_STATUS_FLAGS + if (coefficient_b) { + __set_status_flags (fpsc, INEXACT_EXCEPTION); + } +#endif + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (((rounding_mode) & 3) && coefficient_b) // not ROUNDING_TO_NEAREST + { + switch (rounding_mode) { + case ROUNDING_DOWN: + if (sign_b) { + coefficient_a -= ((((SINT64) sign_a) >> 63) | 1); + if (coefficient_a < 1000000000000000ull) { + exponent_a--; + coefficient_a = 9999999999999999ull; + } else if (coefficient_a >= 10000000000000000ull) { + exponent_a++; + coefficient_a = 1000000000000000ull; + } + } + break; + case ROUNDING_UP: + if (!sign_b) { + coefficient_a += ((((SINT64) sign_a) >> 63) | 1); + if (coefficient_a < 1000000000000000ull) { + exponent_a--; + coefficient_a = 9999999999999999ull; + } else if (coefficient_a >= 10000000000000000ull) { + exponent_a++; + coefficient_a = 1000000000000000ull; + } + } + break; + default: // RZ + if (sign_a != sign_b) { + coefficient_a--; + if (coefficient_a < 1000000000000000ull) { + exponent_a--; + coefficient_a = 9999999999999999ull; + } + } + break; + } + } else +#endif +#endif + // check special case here + if ((coefficient_a == 1000000000000000ull) + && (diff_dec_expon == MAX_FORMAT_DIGITS + 1) + && (sign_a ^ sign_b) + && (coefficient_b > 5000000000000000ull)) { + coefficient_a = 9999999999999999ull; + exponent_a--; + } + + return get_BID64 (sign_a, exponent_a, coefficient_a, + rounding_mode, fpsc); + } + } + // test whether coefficient_a*10^(exponent_a-exponent_b) may exceed 2^62 + if (bin_expon_ca + estimate_bin_expon[diff_dec_expon] < 60) { + // coefficient_a*10^(exponent_a-exponent_b)<2^63 + + // multiply by 10^(exponent_a-exponent_b) + coefficient_a *= power10_table_128[diff_dec_expon].w[0]; + + // sign mask + sign_b = ((SINT64) sign_b) >> 63; + // apply sign to coeff. of b + coefficient_b = (coefficient_b + sign_b) ^ sign_b; + + // apply sign to coefficient a + sign_a = ((SINT64) sign_a) >> 63; + coefficient_a = (coefficient_a + sign_a) ^ sign_a; + + coefficient_a += coefficient_b; + // get sign + sign_s = ((SINT64) coefficient_a) >> 63; + coefficient_a = (coefficient_a + sign_s) ^ sign_s; + sign_s &= 0x8000000000000000ull; + + // coefficient_a < 10^16 ? + if (coefficient_a < power10_table_128[MAX_FORMAT_DIGITS].w[0]) { +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rounding_mode == ROUNDING_DOWN && (!coefficient_a) + && sign_a != sign_b) + sign_s = 0x8000000000000000ull; +#endif +#endif + return get_BID64 (sign_s, exponent_b, coefficient_a, + rounding_mode, fpsc); + } + // otherwise rounding is necessary + + // already know coefficient_a<10^19 + // coefficient_a < 10^17 ? + if (coefficient_a < power10_table_128[17].w[0]) + extra_digits = 1; + else if (coefficient_a < power10_table_128[18].w[0]) + extra_digits = 2; + else + extra_digits = 3; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = rounding_mode; + if (sign_s && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#else + rmode = 0; +#endif +#else + rmode = 0; +#endif + coefficient_a += round_const_table[rmode][extra_digits]; + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_64x64_to_128 (CT, coefficient_a, + reciprocals10_64[extra_digits]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 + amount = short_recip_scale[extra_digits]; + C64 = CT.w[1] >> amount; + + } else { + // coefficient_a*10^(exponent_a-exponent_b) is large + sign_s = sign_a; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = rounding_mode; + if (sign_s && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#else + rmode = 0; +#endif +#else + rmode = 0; +#endif + + // check whether we can take faster path + scale_ca = estimate_decimal_digits[bin_expon_ca]; + + sign_ab = sign_a ^ sign_b; + sign_ab = ((SINT64) sign_ab) >> 63; + + // T1 = 10^(16-diff_dec_expon) + T1 = power10_table_128[16 - diff_dec_expon].w[0]; + + // get number of digits in coefficient_a + //P_ca = power10_table_128[scale_ca].w[0]; + //P_ca_m1 = power10_table_128[scale_ca-1].w[0]; + if (coefficient_a >= power10_table_128[scale_ca].w[0]) { + scale_ca++; + //P_ca_m1 = P_ca; + //P_ca = power10_table_128[scale_ca].w[0]; + } + + scale_k = 16 - scale_ca; + + // apply sign + //Ts = (T1 + sign_ab) ^ sign_ab; + + // test range of ca + //X = coefficient_a + Ts - P_ca_m1; + + // addition + saved_ca = coefficient_a - T1; + coefficient_a = + (SINT64) saved_ca *(SINT64) power10_table_128[scale_k].w[0]; + extra_digits = diff_dec_expon - scale_k; + + // apply sign + saved_cb = (coefficient_b + sign_ab) ^ sign_ab; + // add 10^16 and rounding constant + coefficient_b = + saved_cb + 10000000000000000ull + + round_const_table[rmode][extra_digits]; + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_64x64_to_128 (CT, coefficient_b, + reciprocals10_64[extra_digits]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 + amount = short_recip_scale[extra_digits]; + C0_64 = CT.w[1] >> amount; + + // result coefficient + C64 = C0_64 + coefficient_a; + // filter out difficult (corner) cases + // the following test is equivalent to + // ( (initial_coefficient_a + Ts) < P_ca && + // (initial_coefficient_a + Ts) > P_ca_m1 ), + // which ensures the number of digits in coefficient_a does not change + // after adding (the appropriately scaled and rounded) coefficient_b + if ((UINT64) (C64 - 1000000000000000ull - 1) > + 9000000000000000ull - 2) { + if (C64 >= 10000000000000000ull) { + // result has more than 16 digits + if (!scale_k) { + // must divide coeff_a by 10 + saved_ca = saved_ca + T1; + __mul_64x64_to_128 (CA, saved_ca, 0x3333333333333334ull); + //reciprocals10_64[1]); + coefficient_a = CA.w[1] >> 1; + rem_a = + saved_ca - (coefficient_a << 3) - (coefficient_a << 1); + coefficient_a = coefficient_a - T1; + + saved_cb += + /*90000000000000000 */ +rem_a * + power10_table_128[diff_dec_expon].w[0]; + } else + coefficient_a = + (SINT64) (saved_ca - T1 - + (T1 << 3)) * (SINT64) power10_table_128[scale_k - + 1].w[0]; + + extra_digits++; + coefficient_b = + saved_cb + 100000000000000000ull + + round_const_table[rmode][extra_digits]; + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_64x64_to_128 (CT, coefficient_b, + reciprocals10_64[extra_digits]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 + amount = short_recip_scale[extra_digits]; + C0_64 = CT.w[1] >> amount; + + // result coefficient + C64 = C0_64 + coefficient_a; + } else if (C64 <= 1000000000000000ull) { + // less than 16 digits in result + coefficient_a = + (SINT64) saved_ca *(SINT64) power10_table_128[scale_k + + 1].w[0]; + //extra_digits --; + exponent_b--; + coefficient_b = + (saved_cb << 3) + (saved_cb << 1) + 100000000000000000ull + + round_const_table[rmode][extra_digits]; + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_64x64_to_128 (CT_new, coefficient_b, + reciprocals10_64[extra_digits]); + + // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 + amount = short_recip_scale[extra_digits]; + C0_64 = CT_new.w[1] >> amount; + + // result coefficient + C64_new = C0_64 + coefficient_a; + if (C64_new < 10000000000000000ull) { + C64 = C64_new; +#ifdef SET_STATUS_FLAGS + CT = CT_new; +#endif + } else + exponent_b++; + } + + } + + } + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == 0) //ROUNDING_TO_NEAREST +#endif + if (C64 & 1) { + // check whether fractional part of initial_P/10^extra_digits + // is exactly .5 + // this is the same as fractional part of + // (initial_P + 0.5*10^extra_digits)/10^extra_digits is exactly zero + + // get remainder + remainder_h = CT.w[1] << (64 - amount); + + // test whether fractional part is 0 + if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits])) { + C64--; + } + } +#endif + +#ifdef SET_STATUS_FLAGS + status = INEXACT_EXCEPTION; + + // get remainder + remainder_h = CT.w[1] << (64 - amount); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if ((remainder_h == 0x8000000000000000ull) + && (CT.w[0] < reciprocals10_64[extra_digits])) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits])) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (tmp, carry, CT.w[0], + reciprocals10_64[extra_digits]); + if ((remainder_h >> (64 - amount)) + carry >= + (((UINT64) 1) << amount)) + status = EXACT_STATUS; + break; + } + __set_status_flags (fpsc, status); + +#endif + + return get_BID64 (sign_s, exponent_b + extra_digits, C64, + rounding_mode, fpsc); +} + + +/////////////////////////////////////////////////////////////////// +// round 128-bit coefficient and return result in BID64 format +// do not worry about midpoint cases +////////////////////////////////////////////////////////////////// +static UINT64 +__bid_simple_round64_sticky (UINT64 sign, int exponent, UINT128 P, + int extra_digits, int rounding_mode, + unsigned *fpsc) { + UINT128 Q_high, Q_low, C128; + UINT64 C64; + int amount, rmode; + + rmode = rounding_mode; +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (sign && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#endif +#endif + __add_128_64 (P, P, round_const_table[rmode][extra_digits]); + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Q_high, Q_low, P, + reciprocals10_128[extra_digits]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[extra_digits]; + __shr_128 (C128, Q_high, amount); + + C64 = __low_64 (C128); + +#ifdef SET_STATUS_FLAGS + + __set_status_flags (fpsc, INEXACT_EXCEPTION); + +#endif + + return get_BID64 (sign, exponent, C64, rounding_mode, fpsc); +} + +/////////////////////////////////////////////////////////////////// +// round 128-bit coefficient and return result in BID64 format +/////////////////////////////////////////////////////////////////// +static UINT64 +__bid_full_round64 (UINT64 sign, int exponent, UINT128 P, + int extra_digits, int rounding_mode, + unsigned *fpsc) { + UINT128 Q_high, Q_low, C128, Stemp, PU; + UINT64 remainder_h, C64, carry, CY; + int amount, amount2, rmode, status = 0; + + if (exponent < 0) { + if (exponent >= -16 && (extra_digits + exponent < 0)) { + extra_digits = -exponent; +#ifdef SET_STATUS_FLAGS + if (extra_digits > 0) { + rmode = rounding_mode; + if (sign && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + __add_128_128 (PU, P, + round_const_table_128[rmode][extra_digits]); + if (__unsigned_compare_gt_128 + (power10_table_128[extra_digits + 15], PU)) + status = UNDERFLOW_EXCEPTION; + } +#endif + } + } + + if (extra_digits > 0) { + exponent += extra_digits; + rmode = rounding_mode; + if (sign && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + __add_128_128 (P, P, round_const_table_128[rmode][extra_digits]); + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Q_high, Q_low, P, + reciprocals10_128[extra_digits]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[extra_digits]; + __shr_128_long (C128, Q_high, amount); + + C64 = __low_64 (C128); + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == 0) //ROUNDING_TO_NEAREST +#endif + if (C64 & 1) { + // check whether fractional part of initial_P/10^extra_digits + // is exactly .5 + + // get remainder + amount2 = 64 - amount; + remainder_h = 0; + remainder_h--; + remainder_h >>= amount2; + remainder_h = remainder_h & Q_high.w[0]; + + if (!remainder_h + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) { + C64--; + } + } +#endif + +#ifdef SET_STATUS_FLAGS + status |= INEXACT_EXCEPTION; + + // get remainder + remainder_h = Q_high.w[0] << (64 - amount); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if (remainder_h == 0x8000000000000000ull + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if (!remainder_h + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (Stemp.w[0], CY, Q_low.w[0], + reciprocals10_128[extra_digits].w[0]); + __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], + reciprocals10_128[extra_digits].w[1], CY); + if ((remainder_h >> (64 - amount)) + carry >= + (((UINT64) 1) << amount)) + status = EXACT_STATUS; + } + + __set_status_flags (fpsc, status); + +#endif + } else { + C64 = P.w[0]; + if (!C64) { + sign = 0; + if (rounding_mode == ROUNDING_DOWN) + sign = 0x8000000000000000ull; + } + } + return get_BID64 (sign, exponent, C64, rounding_mode, fpsc); +} + +///////////////////////////////////////////////////////////////////////////////// +// round 192-bit coefficient (P, remainder_P) and return result in BID64 format +// the lowest 64 bits (remainder_P) are used for midpoint checking only +//////////////////////////////////////////////////////////////////////////////// +static UINT64 +__bid_full_round64_remainder (UINT64 sign, int exponent, UINT128 P, + int extra_digits, UINT64 remainder_P, + int rounding_mode, unsigned *fpsc, + unsigned uf_status) { + UINT128 Q_high, Q_low, C128, Stemp; + UINT64 remainder_h, C64, carry, CY; + int amount, amount2, rmode, status = uf_status; + + rmode = rounding_mode; + if (sign && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; + if (rmode == ROUNDING_UP && remainder_P) { + P.w[0]++; + if (!P.w[0]) + P.w[1]++; + } + + if (extra_digits) { + __add_128_64 (P, P, round_const_table[rmode][extra_digits]); + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Q_high, Q_low, P, + reciprocals10_128[extra_digits]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[extra_digits]; + __shr_128 (C128, Q_high, amount); + + C64 = __low_64 (C128); + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == 0) //ROUNDING_TO_NEAREST +#endif + if (!remainder_P && (C64 & 1)) { + // check whether fractional part of initial_P/10^extra_digits + // is exactly .5 + + // get remainder + amount2 = 64 - amount; + remainder_h = 0; + remainder_h--; + remainder_h >>= amount2; + remainder_h = remainder_h & Q_high.w[0]; + + if (!remainder_h + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) { + C64--; + } + } +#endif + +#ifdef SET_STATUS_FLAGS + status |= INEXACT_EXCEPTION; + + if (!remainder_P) { + // get remainder + remainder_h = Q_high.w[0] << (64 - amount); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if (remainder_h == 0x8000000000000000ull + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if (!remainder_h + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (Stemp.w[0], CY, Q_low.w[0], + reciprocals10_128[extra_digits].w[0]); + __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], + reciprocals10_128[extra_digits].w[1], CY); + if ((remainder_h >> (64 - amount)) + carry >= + (((UINT64) 1) << amount)) + status = EXACT_STATUS; + } + } + __set_status_flags (fpsc, status); + +#endif + } else { + C64 = P.w[0]; +#ifdef SET_STATUS_FLAGS + if (remainder_P) { + __set_status_flags (fpsc, uf_status | INEXACT_EXCEPTION); + } +#endif + } + + return get_BID64 (sign, exponent + extra_digits, C64, rounding_mode, + fpsc); +} + + +/////////////////////////////////////////////////////////////////// +// get P/10^extra_digits +// result fits in 64 bits +/////////////////////////////////////////////////////////////////// +__BID_INLINE__ UINT64 +__truncate (UINT128 P, int extra_digits) +// extra_digits <= 16 +{ + UINT128 Q_high, Q_low, C128; + UINT64 C64; + int amount; + + // get P*(2^M[extra_digits])/10^extra_digits + __mul_128x128_full (Q_high, Q_low, P, + reciprocals10_128[extra_digits]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[extra_digits]; + __shr_128 (C128, Q_high, amount); + + C64 = __low_64 (C128); + + return C64; +} + + +/////////////////////////////////////////////////////////////////// +// return number of decimal digits in 128-bit value X +/////////////////////////////////////////////////////////////////// +__BID_INLINE__ int +__get_dec_digits64 (UINT128 X) { + int_double tempx; + int digits_x, bin_expon_cx; + + if (!X.w[1]) { + //--- get number of bits in the coefficients of x and y --- + tempx.d = (double) X.w[0]; + bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff; + // get number of decimal digits in the coeff_x + digits_x = estimate_decimal_digits[bin_expon_cx]; + if (X.w[0] >= power10_table_128[digits_x].w[0]) + digits_x++; + return digits_x; + } + tempx.d = (double) X.w[1]; + bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff; + // get number of decimal digits in the coeff_x + digits_x = estimate_decimal_digits[bin_expon_cx + 64]; + if (__unsigned_compare_ge_128 (X, power10_table_128[digits_x])) + digits_x++; + + return digits_x; +} + + +//////////////////////////////////////////////////////////////////////////////// +// +// add 64-bit coefficient to 128-bit coefficient, return result in BID64 format +// +//////////////////////////////////////////////////////////////////////////////// +__BID_INLINE__ UINT64 +get_add128 (UINT64 sign_x, int exponent_x, UINT64 coefficient_x, + UINT64 sign_y, int final_exponent_y, UINT128 CY, + int extra_digits, int rounding_mode, unsigned *fpsc) { + UINT128 CY_L, CX, FS, F, CT, ST, T2; + UINT64 CYh, CY0L, T, S, coefficient_y, remainder_y; + SINT64 D = 0; + int_double tempx; + int diff_dec_expon, extra_digits2, exponent_y, status; + int extra_dx, diff_dec2, bin_expon_cx, digits_x, rmode; + + // CY has more than 16 decimal digits + + exponent_y = final_exponent_y - extra_digits; + +#ifdef IEEE_ROUND_NEAREST_TIES_AWAY + rounding_mode = 0; +#endif +#ifdef IEEE_ROUND_NEAREST + rounding_mode = 0; +#endif + + if (exponent_x > exponent_y) { + // normalize x + //--- get number of bits in the coefficients of x and y --- + tempx.d = (double) coefficient_x; + bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff; + // get number of decimal digits in the coeff_x + digits_x = estimate_decimal_digits[bin_expon_cx]; + if (coefficient_x >= power10_table_128[digits_x].w[0]) + digits_x++; + + extra_dx = 16 - digits_x; + coefficient_x *= power10_table_128[extra_dx].w[0]; + if ((sign_x ^ sign_y) && (coefficient_x == 1000000000000000ull)) { + extra_dx++; + coefficient_x = 10000000000000000ull; + } + exponent_x -= extra_dx; + + if (exponent_x > exponent_y) { + + // exponent_x > exponent_y + diff_dec_expon = exponent_x - exponent_y; + + if (exponent_x <= final_exponent_y + 1) { + __mul_64x64_to_128 (CX, coefficient_x, + power10_table_128[diff_dec_expon].w[0]); + + if (sign_x == sign_y) { + __add_128_128 (CT, CY, CX); + if ((exponent_x > + final_exponent_y) /*&& (final_exponent_y>0) */ ) + extra_digits++; + if (__unsigned_compare_ge_128 + (CT, power10_table_128[16 + extra_digits])) + extra_digits++; + } else { + __sub_128_128 (CT, CY, CX); + if (((SINT64) CT.w[1]) < 0) { + CT.w[0] = 0 - CT.w[0]; + CT.w[1] = 0 - CT.w[1]; + if (CT.w[0]) + CT.w[1]--; + sign_y = sign_x; + } else if (!(CT.w[1] | CT.w[0])) { + sign_y = + (rounding_mode != + ROUNDING_DOWN) ? 0 : 0x8000000000000000ull; + } + if ((exponent_x + 1 >= + final_exponent_y) /*&& (final_exponent_y>=0) */ ) { + extra_digits = __get_dec_digits64 (CT) - 16; + if (extra_digits <= 0) { + if (!CT.w[0] && rounding_mode == ROUNDING_DOWN) + sign_y = 0x8000000000000000ull; + return get_BID64 (sign_y, exponent_y, CT.w[0], + rounding_mode, fpsc); + } + } else + if (__unsigned_compare_gt_128 + (power10_table_128[15 + extra_digits], CT)) + extra_digits--; + } + + return __bid_full_round64 (sign_y, exponent_y, CT, extra_digits, + rounding_mode, fpsc); + } + // diff_dec2+extra_digits is the number of digits to eliminate from + // argument CY + diff_dec2 = exponent_x - final_exponent_y; + + if (diff_dec2 >= 17) { +#ifndef IEEE_ROUND_NEAREST +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY + if ((rounding_mode) & 3) { + switch (rounding_mode) { + case ROUNDING_UP: + if (!sign_y) { + D = ((SINT64) (sign_x ^ sign_y)) >> 63; + D = D + D + 1; + coefficient_x += D; + } + break; + case ROUNDING_DOWN: + if (sign_y) { + D = ((SINT64) (sign_x ^ sign_y)) >> 63; + D = D + D + 1; + coefficient_x += D; + } + break; + case ROUNDING_TO_ZERO: + if (sign_y != sign_x) { + D = 0 - 1; + coefficient_x += D; + } + break; + } + if (coefficient_x < 1000000000000000ull) { + coefficient_x -= D; + coefficient_x = + D + (coefficient_x << 1) + (coefficient_x << 3); + exponent_x--; + } + } +#endif +#endif +#ifdef SET_STATUS_FLAGS + if (CY.w[1] | CY.w[0]) + __set_status_flags (fpsc, INEXACT_EXCEPTION); +#endif + return get_BID64 (sign_x, exponent_x, coefficient_x, + rounding_mode, fpsc); + } + // here exponent_x <= 16+final_exponent_y + + // truncate CY to 16 dec. digits + CYh = __truncate (CY, extra_digits); + + // get remainder + T = power10_table_128[extra_digits].w[0]; + __mul_64x64_to_64 (CY0L, CYh, T); + + remainder_y = CY.w[0] - CY0L; + + // align coeff_x, CYh + __mul_64x64_to_128 (CX, coefficient_x, + power10_table_128[diff_dec2].w[0]); + + if (sign_x == sign_y) { + __add_128_64 (CT, CX, CYh); + if (__unsigned_compare_ge_128 + (CT, power10_table_128[16 + diff_dec2])) + diff_dec2++; + } else { + if (remainder_y) + CYh++; + __sub_128_64 (CT, CX, CYh); + if (__unsigned_compare_gt_128 + (power10_table_128[15 + diff_dec2], CT)) + diff_dec2--; + } + + return __bid_full_round64_remainder (sign_x, final_exponent_y, CT, + diff_dec2, remainder_y, + rounding_mode, fpsc, 0); + } + } + // Here (exponent_x <= exponent_y) + { + diff_dec_expon = exponent_y - exponent_x; + + if (diff_dec_expon > MAX_FORMAT_DIGITS) { + rmode = rounding_mode; + + if ((sign_x ^ sign_y)) { + if (!CY.w[0]) + CY.w[1]--; + CY.w[0]--; + if (__unsigned_compare_gt_128 + (power10_table_128[15 + extra_digits], CY)) { + if (rmode & 3) { + extra_digits--; + final_exponent_y--; + } else { + CY.w[0] = 1000000000000000ull; + CY.w[1] = 0; + extra_digits = 0; + } + } + } + __scale128_10 (CY, CY); + extra_digits++; + CY.w[0] |= 1; + + return __bid_simple_round64_sticky (sign_y, final_exponent_y, CY, + extra_digits, rmode, fpsc); + } + // apply sign to coeff_x + sign_x ^= sign_y; + sign_x = ((SINT64) sign_x) >> 63; + CX.w[0] = (coefficient_x + sign_x) ^ sign_x; + CX.w[1] = sign_x; + + // check whether CY (rounded to 16 digits) and CX have + // any digits in the same position + diff_dec2 = final_exponent_y - exponent_x; + + if (diff_dec2 <= 17) { + // align CY to 10^ex + S = power10_table_128[diff_dec_expon].w[0]; + __mul_64x128_short (CY_L, S, CY); + + __add_128_128 (ST, CY_L, CX); + extra_digits2 = __get_dec_digits64 (ST) - 16; + return __bid_full_round64 (sign_y, exponent_x, ST, extra_digits2, + rounding_mode, fpsc); + } + // truncate CY to 16 dec. digits + CYh = __truncate (CY, extra_digits); + + // get remainder + T = power10_table_128[extra_digits].w[0]; + __mul_64x64_to_64 (CY0L, CYh, T); + + coefficient_y = CY.w[0] - CY0L; + // add rounding constant + rmode = rounding_mode; + if (sign_y && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (!(rmode & 3)) //ROUNDING_TO_NEAREST +#endif +#endif + { + coefficient_y += round_const_table[rmode][extra_digits]; + } + // align coefficient_y, coefficient_x + S = power10_table_128[diff_dec_expon].w[0]; + __mul_64x64_to_128 (F, coefficient_y, S); + + // fraction + __add_128_128 (FS, F, CX); + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == 0) //ROUNDING_TO_NEAREST +#endif + { + // rounding code, here RN_EVEN + // 10^(extra_digits+diff_dec_expon) + T2 = power10_table_128[diff_dec_expon + extra_digits]; + if (__unsigned_compare_gt_128 (FS, T2) + || ((CYh & 1) && __test_equal_128 (FS, T2))) { + CYh++; + __sub_128_128 (FS, FS, T2); + } + } +#endif +#ifndef IEEE_ROUND_NEAREST +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY + if (rmode == 4) //ROUNDING_TO_NEAREST +#endif + { + // rounding code, here RN_AWAY + // 10^(extra_digits+diff_dec_expon) + T2 = power10_table_128[diff_dec_expon + extra_digits]; + if (__unsigned_compare_ge_128 (FS, T2)) { + CYh++; + __sub_128_128 (FS, FS, T2); + } + } +#endif +#ifndef IEEE_ROUND_NEAREST +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY + switch (rmode) { + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if ((SINT64) FS.w[1] < 0) { + CYh--; + if (CYh < 1000000000000000ull) { + CYh = 9999999999999999ull; + final_exponent_y--; + } + } else { + T2 = power10_table_128[diff_dec_expon + extra_digits]; + if (__unsigned_compare_ge_128 (FS, T2)) { + CYh++; + __sub_128_128 (FS, FS, T2); + } + } + break; + case ROUNDING_UP: + if ((SINT64) FS.w[1] < 0) + break; + T2 = power10_table_128[diff_dec_expon + extra_digits]; + if (__unsigned_compare_gt_128 (FS, T2)) { + CYh += 2; + __sub_128_128 (FS, FS, T2); + } else if ((FS.w[1] == T2.w[1]) && (FS.w[0] == T2.w[0])) { + CYh++; + FS.w[1] = FS.w[0] = 0; + } else if (FS.w[1] | FS.w[0]) + CYh++; + break; + } +#endif +#endif + +#ifdef SET_STATUS_FLAGS + status = INEXACT_EXCEPTION; +#ifndef IEEE_ROUND_NEAREST +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY + if (!(rmode & 3)) +#endif +#endif + { + // RN modes + if ((FS.w[1] == + round_const_table_128[0][diff_dec_expon + extra_digits].w[1]) + && (FS.w[0] == + round_const_table_128[0][diff_dec_expon + + extra_digits].w[0])) + status = EXACT_STATUS; + } +#ifndef IEEE_ROUND_NEAREST +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY + else if (!FS.w[1] && !FS.w[0]) + status = EXACT_STATUS; +#endif +#endif + + __set_status_flags (fpsc, status); +#endif + + return get_BID64 (sign_y, final_exponent_y, CYh, rounding_mode, + fpsc); + } + +} + +////////////////////////////////////////////////////////////////////////// +// +// If coefficient_z is less than 16 digits long, normalize to 16 digits +// +///////////////////////////////////////////////////////////////////////// +static UINT64 +BID_normalize (UINT64 sign_z, int exponent_z, + UINT64 coefficient_z, UINT64 round_dir, int round_flag, + int rounding_mode, unsigned *fpsc) { + SINT64 D; + int_double tempx; + int digits_z, bin_expon, scale, rmode; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = rounding_mode; + if (sign_z && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#else + if (coefficient_z >= power10_table_128[15].w[0]) + return z; +#endif +#endif + + //--- get number of bits in the coefficients of x and y --- + tempx.d = (double) coefficient_z; + bin_expon = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff; + // get number of decimal digits in the coeff_x + digits_z = estimate_decimal_digits[bin_expon]; + if (coefficient_z >= power10_table_128[digits_z].w[0]) + digits_z++; + + scale = 16 - digits_z; + exponent_z -= scale; + if (exponent_z < 0) { + scale += exponent_z; + exponent_z = 0; + } + coefficient_z *= power10_table_128[scale].w[0]; + +#ifdef SET_STATUS_FLAGS + if (round_flag) { + __set_status_flags (fpsc, INEXACT_EXCEPTION); + if (coefficient_z < 1000000000000000ull) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); + else if ((coefficient_z == 1000000000000000ull) && !exponent_z + && ((SINT64) (round_dir ^ sign_z) < 0) && round_flag + && (rmode == ROUNDING_DOWN || rmode == ROUNDING_TO_ZERO)) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); + } +#endif + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (round_flag && (rmode & 3)) { + D = round_dir ^ sign_z; + + if (rmode == ROUNDING_UP) { + if (D >= 0) + coefficient_z++; + } else { + if (D < 0) + coefficient_z--; + if (coefficient_z < 1000000000000000ull && exponent_z) { + coefficient_z = 9999999999999999ull; + exponent_z--; + } + } + } +#endif +#endif + + return get_BID64 (sign_z, exponent_z, coefficient_z, rounding_mode, + fpsc); +} + + +////////////////////////////////////////////////////////////////////////// +// +// 0*10^ey + cz*10^ez, ey> 52) - 0x3ff; + scale_cz = estimate_decimal_digits[bin_expon]; + if (coefficient_z >= power10_table_128[scale_cz].w[0]) + scale_cz++; + + scale_k = 16 - scale_cz; + if (diff_expon < scale_k) + scale_k = diff_expon; + coefficient_z *= power10_table_128[scale_k].w[0]; + + return get_BID64 (sign_z, exponent_z - scale_k, coefficient_z, + *prounding_mode, fpsc); +} +#endif diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_internal.h b/gcc-4.4.3/libgcc/config/libbid/bid_internal.h new file mode 100644 index 000000000..8a3f08b3a --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_internal.h @@ -0,0 +1,2607 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#ifndef __BIDECIMAL_H +#define __BIDECIMAL_H + +#include "bid_conf.h" +#include "bid_functions.h" + +#define __BID_INLINE__ static __inline + +/********************************************************************* + * + * Logical Shift Macros + * + *********************************************************************/ + +#define __shr_128(Q, A, k) \ +{ \ + (Q).w[0] = (A).w[0] >> k; \ + (Q).w[0] |= (A).w[1] << (64-k); \ + (Q).w[1] = (A).w[1] >> k; \ +} + +#define __shr_128_long(Q, A, k) \ +{ \ + if((k)<64) { \ + (Q).w[0] = (A).w[0] >> k; \ + (Q).w[0] |= (A).w[1] << (64-k); \ + (Q).w[1] = (A).w[1] >> k; \ + } \ + else { \ + (Q).w[0] = (A).w[1]>>((k)-64); \ + (Q).w[1] = 0; \ + } \ +} + +#define __shl_128_long(Q, A, k) \ +{ \ + if((k)<64) { \ + (Q).w[1] = (A).w[1] << k; \ + (Q).w[1] |= (A).w[0] >> (64-k); \ + (Q).w[0] = (A).w[0] << k; \ + } \ + else { \ + (Q).w[1] = (A).w[0]<<((k)-64); \ + (Q).w[0] = 0; \ + } \ +} + +#define __low_64(Q) (Q).w[0] +/********************************************************************* + * + * String Macros + * + *********************************************************************/ +#define tolower_macro(x) (((unsigned char)((x)-'A')<=('Z'-'A'))?((x)-'A'+'a'):(x)) +/********************************************************************* + * + * Compare Macros + * + *********************************************************************/ +// greater than +// return 0 if A<=B +// non-zero if A>B +#define __unsigned_compare_gt_128(A, B) \ + ((A.w[1]>B.w[1]) || ((A.w[1]==B.w[1]) && (A.w[0]>B.w[0]))) +// greater-or-equal +#define __unsigned_compare_ge_128(A, B) \ + ((A.w[1]>B.w[1]) || ((A.w[1]==B.w[1]) && (A.w[0]>=B.w[0]))) +#define __test_equal_128(A, B) (((A).w[1]==(B).w[1]) && ((A).w[0]==(B).w[0])) +// tighten exponent range +#define __tight_bin_range_128(bp, P, bin_expon) \ +{ \ +UINT64 M; \ + M = 1; \ + (bp) = (bin_expon); \ + if((bp)<63) { \ + M <<= ((bp)+1); \ + if((P).w[0] >= M) (bp)++; } \ + else if((bp)>64) { \ + M <<= ((bp)+1-64); \ + if(((P).w[1]>M) ||((P).w[1]==M && (P).w[0]))\ + (bp)++; } \ + else if((P).w[1]) (bp)++; \ +} +/********************************************************************* + * + * Add/Subtract Macros + * + *********************************************************************/ +// add 64-bit value to 128-bit +#define __add_128_64(R128, A128, B64) \ +{ \ +UINT64 R64H; \ + R64H = (A128).w[1]; \ + (R128).w[0] = (B64) + (A128).w[0]; \ + if((R128).w[0] < (B64)) \ + R64H ++; \ + (R128).w[1] = R64H; \ +} +// subtract 64-bit value from 128-bit +#define __sub_128_64(R128, A128, B64) \ +{ \ +UINT64 R64H; \ + R64H = (A128).w[1]; \ + if((A128).w[0] < (B64)) \ + R64H --; \ + (R128).w[1] = R64H; \ + (R128).w[0] = (A128).w[0] - (B64); \ +} +// add 128-bit value to 128-bit +// assume no carry-out +#define __add_128_128(R128, A128, B128) \ +{ \ +UINT128 Q128; \ + Q128.w[1] = (A128).w[1]+(B128).w[1]; \ + Q128.w[0] = (B128).w[0] + (A128).w[0]; \ + if(Q128.w[0] < (B128).w[0]) \ + Q128.w[1] ++; \ + (R128).w[1] = Q128.w[1]; \ + (R128).w[0] = Q128.w[0]; \ +} +#define __sub_128_128(R128, A128, B128) \ +{ \ +UINT128 Q128; \ + Q128.w[1] = (A128).w[1]-(B128).w[1]; \ + Q128.w[0] = (A128).w[0] - (B128).w[0]; \ + if((A128).w[0] < (B128).w[0]) \ + Q128.w[1] --; \ + (R128).w[1] = Q128.w[1]; \ + (R128).w[0] = Q128.w[0]; \ +} +#define __add_carry_out(S, CY, X, Y) \ +{ \ +UINT64 X1=X; \ + S = X + Y; \ + CY = (SX1) ? 1 : 0; \ +} +#define __sub_borrow_in_out(S, CY, X, Y, CI) \ +{ \ +UINT64 X1, X0=X; \ + X1 = X - CI; \ + S = X1 - Y; \ + CY = ((S>X1) || (X1>X0)) ? 1 : 0; \ +} +// increment C128 and check for rounding overflow: +// if (C_128) = 10^34 then (C_128) = 10^33 and increment the exponent +#define INCREMENT(C_128, exp) \ +{ \ + C_128.w[0]++; \ + if (C_128.w[0] == 0) C_128.w[1]++; \ + if (C_128.w[1] == 0x0001ed09bead87c0ull && \ + C_128.w[0] == 0x378d8e6400000000ull) { \ + exp++; \ + C_128.w[1] = 0x0000314dc6448d93ull; \ + C_128.w[0] = 0x38c15b0a00000000ull; \ + } \ +} +// decrement C128 and check for rounding underflow, but only at the +// boundary: if C_128 = 10^33 - 1 and exp > 0 then C_128 = 10^34 - 1 +// and decrement the exponent +#define DECREMENT(C_128, exp) \ +{ \ + C_128.w[0]--; \ + if (C_128.w[0] == 0xffffffffffffffffull) C_128.w[1]--; \ + if (C_128.w[1] == 0x0000314dc6448d93ull && \ + C_128.w[0] == 0x38c15b09ffffffffull && exp > 0) { \ + exp--; \ + C_128.w[1] = 0x0001ed09bead87c0ull; \ + C_128.w[0] = 0x378d8e63ffffffffull; \ + } \ +} + + /********************************************************************* + * + * Multiply Macros + * + *********************************************************************/ +#define __mul_64x64_to_64(P64, CX, CY) (P64) = (CX) * (CY) +/*************************************** + * Signed, Full 64x64-bit Multiply + ***************************************/ +#define __imul_64x64_to_128(P, CX, CY) \ +{ \ +UINT64 SX, SY; \ + __mul_64x64_to_128(P, CX, CY); \ + \ + SX = ((SINT64)(CX))>>63; \ + SY = ((SINT64)(CY))>>63; \ + SX &= CY; SY &= CX; \ + \ + (P).w[1] = (P).w[1] - SX - SY; \ +} +/*************************************** + * Signed, Full 64x128-bit Multiply + ***************************************/ +#define __imul_64x128_full(Ph, Ql, A, B) \ +{ \ +UINT128 ALBL, ALBH, QM2, QM; \ + \ + __imul_64x64_to_128(ALBH, (A), (B).w[1]); \ + __imul_64x64_to_128(ALBL, (A), (B).w[0]); \ + \ + (Ql).w[0] = ALBL.w[0]; \ + QM.w[0] = ALBL.w[1]; \ + QM.w[1] = ((SINT64)ALBL.w[1])>>63; \ + __add_128_128(QM2, ALBH, QM); \ + (Ql).w[1] = QM2.w[0]; \ + Ph = QM2.w[1]; \ +} +/***************************************************** + * Unsigned Multiply Macros + *****************************************************/ +// get full 64x64bit product +// +#define __mul_64x64_to_128(P, CX, CY) \ +{ \ +UINT64 CXH, CXL, CYH,CYL,PL,PH,PM,PM2;\ + CXH = (CX) >> 32; \ + CXL = (UINT32)(CX); \ + CYH = (CY) >> 32; \ + CYL = (UINT32)(CY); \ + \ + PM = CXH*CYL; \ + PH = CXH*CYH; \ + PL = CXL*CYL; \ + PM2 = CXL*CYH; \ + PH += (PM>>32); \ + PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ + \ + (P).w[1] = PH + (PM>>32); \ + (P).w[0] = (PM<<32)+(UINT32)PL; \ +} +// get full 64x64bit product +// Note: +// This macro is used for CX < 2^61, CY < 2^61 +// +#define __mul_64x64_to_128_fast(P, CX, CY) \ +{ \ +UINT64 CXH, CXL, CYH, CYL, PL, PH, PM; \ + CXH = (CX) >> 32; \ + CXL = (UINT32)(CX); \ + CYH = (CY) >> 32; \ + CYL = (UINT32)(CY); \ + \ + PM = CXH*CYL; \ + PL = CXL*CYL; \ + PH = CXH*CYH; \ + PM += CXL*CYH; \ + PM += (PL>>32); \ + \ + (P).w[1] = PH + (PM>>32); \ + (P).w[0] = (PM<<32)+(UINT32)PL; \ +} +// used for CX< 2^60 +#define __sqr64_fast(P, CX) \ +{ \ +UINT64 CXH, CXL, PL, PH, PM; \ + CXH = (CX) >> 32; \ + CXL = (UINT32)(CX); \ + \ + PM = CXH*CXL; \ + PL = CXL*CXL; \ + PH = CXH*CXH; \ + PM += PM; \ + PM += (PL>>32); \ + \ + (P).w[1] = PH + (PM>>32); \ + (P).w[0] = (PM<<32)+(UINT32)PL; \ +} +// get full 64x64bit product +// Note: +// This implementation is used for CX < 2^61, CY < 2^61 +// +#define __mul_64x64_to_64_high_fast(P, CX, CY) \ +{ \ +UINT64 CXH, CXL, CYH, CYL, PL, PH, PM; \ + CXH = (CX) >> 32; \ + CXL = (UINT32)(CX); \ + CYH = (CY) >> 32; \ + CYL = (UINT32)(CY); \ + \ + PM = CXH*CYL; \ + PL = CXL*CYL; \ + PH = CXH*CYH; \ + PM += CXL*CYH; \ + PM += (PL>>32); \ + \ + (P) = PH + (PM>>32); \ +} +// get full 64x64bit product +// +#define __mul_64x64_to_128_full(P, CX, CY) \ +{ \ +UINT64 CXH, CXL, CYH,CYL,PL,PH,PM,PM2;\ + CXH = (CX) >> 32; \ + CXL = (UINT32)(CX); \ + CYH = (CY) >> 32; \ + CYL = (UINT32)(CY); \ + \ + PM = CXH*CYL; \ + PH = CXH*CYH; \ + PL = CXL*CYL; \ + PM2 = CXL*CYH; \ + PH += (PM>>32); \ + PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ + \ + (P).w[1] = PH + (PM>>32); \ + (P).w[0] = (PM<<32)+(UINT32)PL; \ +} +#define __mul_128x128_high(Q, A, B) \ +{ \ +UINT128 ALBL, ALBH, AHBL, AHBH, QM, QM2; \ + \ + __mul_64x64_to_128(ALBH, (A).w[0], (B).w[1]); \ + __mul_64x64_to_128(AHBL, (B).w[0], (A).w[1]); \ + __mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \ + __mul_64x64_to_128(AHBH, (A).w[1],(B).w[1]); \ + \ + __add_128_128(QM, ALBH, AHBL); \ + __add_128_64(QM2, QM, ALBL.w[1]); \ + __add_128_64((Q), AHBH, QM2.w[1]); \ +} +#define __mul_128x128_full(Qh, Ql, A, B) \ +{ \ +UINT128 ALBL, ALBH, AHBL, AHBH, QM, QM2; \ + \ + __mul_64x64_to_128(ALBH, (A).w[0], (B).w[1]); \ + __mul_64x64_to_128(AHBL, (B).w[0], (A).w[1]); \ + __mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \ + __mul_64x64_to_128(AHBH, (A).w[1],(B).w[1]); \ + \ + __add_128_128(QM, ALBH, AHBL); \ + (Ql).w[0] = ALBL.w[0]; \ + __add_128_64(QM2, QM, ALBL.w[1]); \ + __add_128_64((Qh), AHBH, QM2.w[1]); \ + (Ql).w[1] = QM2.w[0]; \ +} +#define __mul_128x128_low(Ql, A, B) \ +{ \ +UINT128 ALBL; \ +UINT64 QM64; \ + \ + __mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \ + QM64 = (B).w[0]*(A).w[1] + (A).w[0]*(B).w[1]; \ + \ + (Ql).w[0] = ALBL.w[0]; \ + (Ql).w[1] = QM64 + ALBL.w[1]; \ +} +#define __mul_64x128_low(Ql, A, B) \ +{ \ + UINT128 ALBL, ALBH, QM2; \ + __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ + __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ + (Ql).w[0] = ALBL.w[0]; \ + __add_128_64(QM2, ALBH, ALBL.w[1]); \ + (Ql).w[1] = QM2.w[0]; \ +} +#define __mul_64x128_full(Ph, Ql, A, B) \ +{ \ +UINT128 ALBL, ALBH, QM2; \ + \ + __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ + __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ + \ + (Ql).w[0] = ALBL.w[0]; \ + __add_128_64(QM2, ALBH, ALBL.w[1]); \ + (Ql).w[1] = QM2.w[0]; \ + Ph = QM2.w[1]; \ +} +#define __mul_64x128_to_192(Q, A, B) \ +{ \ +UINT128 ALBL, ALBH, QM2; \ + \ + __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ + __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ + \ + (Q).w[0] = ALBL.w[0]; \ + __add_128_64(QM2, ALBH, ALBL.w[1]); \ + (Q).w[1] = QM2.w[0]; \ + (Q).w[2] = QM2.w[1]; \ +} +#define __mul_64x128_to192(Q, A, B) \ +{ \ +UINT128 ALBL, ALBH, QM2; \ + \ + __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ + __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ + \ + (Q).w[0] = ALBL.w[0]; \ + __add_128_64(QM2, ALBH, ALBL.w[1]); \ + (Q).w[1] = QM2.w[0]; \ + (Q).w[2] = QM2.w[1]; \ +} +#define __mul_128x128_to_256(P256, A, B) \ +{ \ +UINT128 Qll, Qlh; \ +UINT64 Phl, Phh, CY1, CY2; \ + \ + __mul_64x128_full(Phl, Qll, A.w[0], B); \ + __mul_64x128_full(Phh, Qlh, A.w[1], B); \ + (P256).w[0] = Qll.w[0]; \ + __add_carry_out((P256).w[1],CY1, Qlh.w[0], Qll.w[1]); \ + __add_carry_in_out((P256).w[2],CY2, Qlh.w[1], Phl, CY1); \ + (P256).w[3] = Phh + CY2; \ +} +// +// For better performance, will check A.w[1] against 0, +// but not B.w[1] +// Use this macro accordingly +#define __mul_128x128_to_256_check_A(P256, A, B) \ +{ \ +UINT128 Qll, Qlh; \ +UINT64 Phl, Phh, CY1, CY2; \ + \ + __mul_64x128_full(Phl, Qll, A.w[0], B); \ + (P256).w[0] = Qll.w[0]; \ + if(A.w[1]) { \ + __mul_64x128_full(Phh, Qlh, A.w[1], B); \ + __add_carry_out((P256).w[1],CY1, Qlh.w[0], Qll.w[1]); \ + __add_carry_in_out((P256).w[2],CY2, Qlh.w[1], Phl, CY1); \ + (P256).w[3] = Phh + CY2; } \ + else { \ + (P256).w[1] = Qll.w[1]; \ + (P256).w[2] = Phl; \ + (P256).w[3] = 0; } \ +} +#define __mul_64x192_to_256(lP, lA, lB) \ +{ \ +UINT128 lP0,lP1,lP2; \ +UINT64 lC; \ + __mul_64x64_to_128(lP0, lA, (lB).w[0]); \ + __mul_64x64_to_128(lP1, lA, (lB).w[1]); \ + __mul_64x64_to_128(lP2, lA, (lB).w[2]); \ + (lP).w[0] = lP0.w[0]; \ + __add_carry_out((lP).w[1],lC,lP1.w[0],lP0.w[1]); \ + __add_carry_in_out((lP).w[2],lC,lP2.w[0],lP1.w[1],lC); \ + (lP).w[3] = lP2.w[1] + lC; \ +} +#define __mul_64x256_to_320(P, A, B) \ +{ \ +UINT128 lP0,lP1,lP2,lP3; \ +UINT64 lC; \ + __mul_64x64_to_128(lP0, A, (B).w[0]); \ + __mul_64x64_to_128(lP1, A, (B).w[1]); \ + __mul_64x64_to_128(lP2, A, (B).w[2]); \ + __mul_64x64_to_128(lP3, A, (B).w[3]); \ + (P).w[0] = lP0.w[0]; \ + __add_carry_out((P).w[1],lC,lP1.w[0],lP0.w[1]); \ + __add_carry_in_out((P).w[2],lC,lP2.w[0],lP1.w[1],lC); \ + __add_carry_in_out((P).w[3],lC,lP3.w[0],lP2.w[1],lC); \ + (P).w[4] = lP3.w[1] + lC; \ +} +#define __mul_192x192_to_384(P, A, B) \ +{ \ +UINT256 P0,P1,P2; \ +UINT64 CY; \ + __mul_64x192_to_256(P0, (A).w[0], B); \ + __mul_64x192_to_256(P1, (A).w[1], B); \ + __mul_64x192_to_256(P2, (A).w[2], B); \ + (P).w[0] = P0.w[0]; \ + __add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]); \ + __add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \ + __add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \ + (P).w[4] = P1.w[3] + CY; \ + __add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]); \ + __add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY); \ + __add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY); \ + (P).w[5] = P2.w[3] + CY; \ +} +#define __mul_64x320_to_384(P, A, B) \ +{ \ +UINT128 lP0,lP1,lP2,lP3,lP4; \ +UINT64 lC; \ + __mul_64x64_to_128(lP0, A, (B).w[0]); \ + __mul_64x64_to_128(lP1, A, (B).w[1]); \ + __mul_64x64_to_128(lP2, A, (B).w[2]); \ + __mul_64x64_to_128(lP3, A, (B).w[3]); \ + __mul_64x64_to_128(lP4, A, (B).w[4]); \ + (P).w[0] = lP0.w[0]; \ + __add_carry_out((P).w[1],lC,lP1.w[0],lP0.w[1]); \ + __add_carry_in_out((P).w[2],lC,lP2.w[0],lP1.w[1],lC); \ + __add_carry_in_out((P).w[3],lC,lP3.w[0],lP2.w[1],lC); \ + __add_carry_in_out((P).w[4],lC,lP4.w[0],lP3.w[1],lC); \ + (P).w[5] = lP4.w[1] + lC; \ +} +// A*A +// Full 128x128-bit product +#define __sqr128_to_256(P256, A) \ +{ \ +UINT128 Qll, Qlh, Qhh; \ +UINT64 TMP_C1, TMP_C2; \ + \ + __mul_64x64_to_128(Qhh, A.w[1], A.w[1]); \ + __mul_64x64_to_128(Qlh, A.w[0], A.w[1]); \ + Qhh.w[1] += (Qlh.w[1]>>63); \ + Qlh.w[1] = (Qlh.w[1]+Qlh.w[1])|(Qlh.w[0]>>63); \ + Qlh.w[0] += Qlh.w[0]; \ + __mul_64x64_to_128(Qll, A.w[0], A.w[0]); \ + \ + __add_carry_out((P256).w[1],TMP_C1, Qlh.w[0], Qll.w[1]); \ + (P256).w[0] = Qll.w[0]; \ + __add_carry_in_out((P256).w[2],TMP_C2, Qlh.w[1], Qhh.w[0], TMP_C1); \ + (P256).w[3] = Qhh.w[1]+TMP_C2; \ +} +#define __mul_128x128_to_256_low_high(PQh, PQl, A, B) \ +{ \ +UINT128 Qll, Qlh; \ +UINT64 Phl, Phh, C1, C2; \ + \ + __mul_64x128_full(Phl, Qll, A.w[0], B); \ + __mul_64x128_full(Phh, Qlh, A.w[1], B); \ + (PQl).w[0] = Qll.w[0]; \ + __add_carry_out((PQl).w[1],C1, Qlh.w[0], Qll.w[1]); \ + __add_carry_in_out((PQh).w[0],C2, Qlh.w[1], Phl, C1); \ + (PQh).w[1] = Phh + C2; \ +} +#define __mul_256x256_to_512(P, A, B) \ +{ \ +UINT512 P0,P1,P2,P3; \ +UINT64 CY; \ + __mul_64x256_to_320(P0, (A).w[0], B); \ + __mul_64x256_to_320(P1, (A).w[1], B); \ + __mul_64x256_to_320(P2, (A).w[2], B); \ + __mul_64x256_to_320(P3, (A).w[3], B); \ + (P).w[0] = P0.w[0]; \ + __add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]); \ + __add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \ + __add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \ + __add_carry_in_out((P).w[4],CY,P1.w[3],P0.w[4],CY); \ + (P).w[5] = P1.w[4] + CY; \ + __add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]); \ + __add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY); \ + __add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY); \ + __add_carry_in_out((P).w[5],CY,P2.w[3],(P).w[5],CY); \ + (P).w[6] = P2.w[4] + CY; \ + __add_carry_out((P).w[3],CY,P3.w[0],(P).w[3]); \ + __add_carry_in_out((P).w[4],CY,P3.w[1],(P).w[4],CY); \ + __add_carry_in_out((P).w[5],CY,P3.w[2],(P).w[5],CY); \ + __add_carry_in_out((P).w[6],CY,P3.w[3],(P).w[6],CY); \ + (P).w[7] = P3.w[4] + CY; \ +} +#define __mul_192x256_to_448(P, A, B) \ +{ \ +UINT512 P0,P1,P2; \ +UINT64 CY; \ + __mul_64x256_to_320(P0, (A).w[0], B); \ + __mul_64x256_to_320(P1, (A).w[1], B); \ + __mul_64x256_to_320(P2, (A).w[2], B); \ + (P).w[0] = P0.w[0]; \ + __add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]); \ + __add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY); \ + __add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY); \ + __add_carry_in_out((P).w[4],CY,P1.w[3],P0.w[4],CY); \ + (P).w[5] = P1.w[4] + CY; \ + __add_carry_out((P).w[2],CY,P2.w[0],(P).w[2]); \ + __add_carry_in_out((P).w[3],CY,P2.w[1],(P).w[3],CY); \ + __add_carry_in_out((P).w[4],CY,P2.w[2],(P).w[4],CY); \ + __add_carry_in_out((P).w[5],CY,P2.w[3],(P).w[5],CY); \ + (P).w[6] = P2.w[4] + CY; \ +} +#define __mul_320x320_to_640(P, A, B) \ +{ \ +UINT512 P0,P1,P2,P3; \ +UINT64 CY; \ + __mul_256x256_to_512((P), (A), B); \ + __mul_64x256_to_320(P1, (A).w[4], B); \ + __mul_64x256_to_320(P2, (B).w[4], A); \ + __mul_64x64_to_128(P3, (A).w[4], (B).w[4]); \ + __add_carry_out((P0).w[0],CY,P1.w[0],P2.w[0]); \ + __add_carry_in_out((P0).w[1],CY,P1.w[1],P2.w[1],CY); \ + __add_carry_in_out((P0).w[2],CY,P1.w[2],P2.w[2],CY); \ + __add_carry_in_out((P0).w[3],CY,P1.w[3],P2.w[3],CY); \ + __add_carry_in_out((P0).w[4],CY,P1.w[4],P2.w[4],CY); \ + P3.w[1] += CY; \ + __add_carry_out((P).w[4],CY,(P).w[4],P0.w[0]); \ + __add_carry_in_out((P).w[5],CY,(P).w[5],P0.w[1],CY); \ + __add_carry_in_out((P).w[6],CY,(P).w[6],P0.w[2],CY); \ + __add_carry_in_out((P).w[7],CY,(P).w[7],P0.w[3],CY); \ + __add_carry_in_out((P).w[8],CY,P3.w[0],P0.w[4],CY); \ + (P).w[9] = P3.w[1] + CY; \ +} +#define __mul_384x384_to_768(P, A, B) \ +{ \ +UINT512 P0,P1,P2,P3; \ +UINT64 CY; \ + __mul_320x320_to_640((P), (A), B); \ + __mul_64x320_to_384(P1, (A).w[5], B); \ + __mul_64x320_to_384(P2, (B).w[5], A); \ + __mul_64x64_to_128(P3, (A).w[5], (B).w[5]); \ + __add_carry_out((P0).w[0],CY,P1.w[0],P2.w[0]); \ + __add_carry_in_out((P0).w[1],CY,P1.w[1],P2.w[1],CY); \ + __add_carry_in_out((P0).w[2],CY,P1.w[2],P2.w[2],CY); \ + __add_carry_in_out((P0).w[3],CY,P1.w[3],P2.w[3],CY); \ + __add_carry_in_out((P0).w[4],CY,P1.w[4],P2.w[4],CY); \ + __add_carry_in_out((P0).w[5],CY,P1.w[5],P2.w[5],CY); \ + P3.w[1] += CY; \ + __add_carry_out((P).w[5],CY,(P).w[5],P0.w[0]); \ + __add_carry_in_out((P).w[6],CY,(P).w[6],P0.w[1],CY); \ + __add_carry_in_out((P).w[7],CY,(P).w[7],P0.w[2],CY); \ + __add_carry_in_out((P).w[8],CY,(P).w[8],P0.w[3],CY); \ + __add_carry_in_out((P).w[9],CY,(P).w[9],P0.w[4],CY); \ + __add_carry_in_out((P).w[10],CY,P3.w[0],P0.w[5],CY); \ + (P).w[11] = P3.w[1] + CY; \ +} +#define __mul_64x128_short(Ql, A, B) \ +{ \ +UINT64 ALBH_L; \ + \ + __mul_64x64_to_64(ALBH_L, (A),(B).w[1]); \ + __mul_64x64_to_128((Ql), (A), (B).w[0]); \ + \ + (Ql).w[1] += ALBH_L; \ +} +#define __scale128_10(D,_TMP) \ +{ \ +UINT128 _TMP2,_TMP8; \ + _TMP2.w[1] = (_TMP.w[1]<<1)|(_TMP.w[0]>>63); \ + _TMP2.w[0] = _TMP.w[0]<<1; \ + _TMP8.w[1] = (_TMP.w[1]<<3)|(_TMP.w[0]>>61); \ + _TMP8.w[0] = _TMP.w[0]<<3; \ + __add_128_128(D, _TMP2, _TMP8); \ +} +// 64x64-bit product +#define __mul_64x64_to_128MACH(P128, CX64, CY64) \ +{ \ + UINT64 CXH,CXL,CYH,CYL,PL,PH,PM,PM2; \ + CXH = (CX64) >> 32; \ + CXL = (UINT32)(CX64); \ + CYH = (CY64) >> 32; \ + CYL = (UINT32)(CY64); \ + PM = CXH*CYL; \ + PH = CXH*CYH; \ + PL = CXL*CYL; \ + PM2 = CXL*CYH; \ + PH += (PM>>32); \ + PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ + (P128).w[1] = PH + (PM>>32); \ + (P128).w[0] = (PM<<32)+(UINT32)PL; \ +} +// 64x64-bit product +#define __mul_64x64_to_128HIGH(P64, CX64, CY64) \ +{ \ + UINT64 CXH,CXL,CYH,CYL,PL,PH,PM,PM2; \ + CXH = (CX64) >> 32; \ + CXL = (UINT32)(CX64); \ + CYH = (CY64) >> 32; \ + CYL = (UINT32)(CY64); \ + PM = CXH*CYL; \ + PH = CXH*CYH; \ + PL = CXL*CYL; \ + PM2 = CXL*CYH; \ + PH += (PM>>32); \ + PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \ + P64 = PH + (PM>>32); \ +} +#define __mul_128x64_to_128(Q128, A64, B128) \ +{ \ + UINT64 ALBH_L; \ + ALBH_L = (A64) * (B128).w[1]; \ + __mul_64x64_to_128MACH((Q128), (A64), (B128).w[0]); \ + (Q128).w[1] += ALBH_L; \ +} +// might simplify by calculating just QM2.w[0] +#define __mul_64x128_to_128(Ql, A, B) \ +{ \ + UINT128 ALBL, ALBH, QM2; \ + __mul_64x64_to_128(ALBH, (A), (B).w[1]); \ + __mul_64x64_to_128(ALBL, (A), (B).w[0]); \ + (Ql).w[0] = ALBL.w[0]; \ + __add_128_64(QM2, ALBH, ALBL.w[1]); \ + (Ql).w[1] = QM2.w[0]; \ +} +/********************************************************************* + * + * BID Pack/Unpack Macros + * + *********************************************************************/ +///////////////////////////////////////// +// BID64 definitions +//////////////////////////////////////// +#define DECIMAL_MAX_EXPON_64 767 +#define DECIMAL_EXPONENT_BIAS 398 +#define MAX_FORMAT_DIGITS 16 +///////////////////////////////////////// +// BID128 definitions +//////////////////////////////////////// +#define DECIMAL_MAX_EXPON_128 12287 +#define DECIMAL_EXPONENT_BIAS_128 6176 +#define MAX_FORMAT_DIGITS_128 34 +///////////////////////////////////////// +// BID32 definitions +//////////////////////////////////////// +#define DECIMAL_MAX_EXPON_32 191 +#define DECIMAL_EXPONENT_BIAS_32 101 +#define MAX_FORMAT_DIGITS_32 7 +//////////////////////////////////////// +// Constant Definitions +/////////////////////////////////////// +#define SPECIAL_ENCODING_MASK64 0x6000000000000000ull +#define INFINITY_MASK64 0x7800000000000000ull +#define SINFINITY_MASK64 0xf800000000000000ull +#define SSNAN_MASK64 0xfc00000000000000ull +#define NAN_MASK64 0x7c00000000000000ull +#define SNAN_MASK64 0x7e00000000000000ull +#define QUIET_MASK64 0xfdffffffffffffffull +#define LARGE_COEFF_MASK64 0x0007ffffffffffffull +#define LARGE_COEFF_HIGH_BIT64 0x0020000000000000ull +#define SMALL_COEFF_MASK64 0x001fffffffffffffull +#define EXPONENT_MASK64 0x3ff +#define EXPONENT_SHIFT_LARGE64 51 +#define EXPONENT_SHIFT_SMALL64 53 +#define LARGEST_BID64 0x77fb86f26fc0ffffull +#define SMALLEST_BID64 0xf7fb86f26fc0ffffull +#define SMALL_COEFF_MASK128 0x0001ffffffffffffull +#define LARGE_COEFF_MASK128 0x00007fffffffffffull +#define EXPONENT_MASK128 0x3fff +#define LARGEST_BID128_HIGH 0x5fffed09bead87c0ull +#define LARGEST_BID128_LOW 0x378d8e63ffffffffull +#define SPECIAL_ENCODING_MASK32 0x60000000ul +#define INFINITY_MASK32 0x78000000ul +#define LARGE_COEFF_MASK32 0x007ffffful +#define LARGE_COEFF_HIGH_BIT32 0x00800000ul +#define SMALL_COEFF_MASK32 0x001ffffful +#define EXPONENT_MASK32 0xff +#define LARGEST_BID32 0x77f8967f +#define NAN_MASK32 0x7c000000 +#define SNAN_MASK32 0x7e000000 +#define MASK_BINARY_EXPONENT 0x7ff0000000000000ull +#define BINARY_EXPONENT_BIAS 0x3ff +#define UPPER_EXPON_LIMIT 51 +// data needed for BID pack/unpack macros +extern UINT64 round_const_table[][19]; +extern UINT128 reciprocals10_128[]; +extern int recip_scale[]; +extern UINT128 power10_table_128[]; +extern int estimate_decimal_digits[]; +extern int estimate_bin_expon[]; +extern UINT64 power10_index_binexp[]; +extern int short_recip_scale[]; +extern UINT64 reciprocals10_64[]; +extern UINT128 power10_index_binexp_128[]; +extern UINT128 round_const_table_128[][36]; + + +////////////////////////////////////////////// +// Status Flag Handling +///////////////////////////////////////////// +#define __set_status_flags(fpsc, status) *(fpsc) |= status +#define is_inexact(fpsc) ((*(fpsc))&INEXACT_EXCEPTION) + +__BID_INLINE__ UINT64 +unpack_BID64 (UINT64 * psign_x, int *pexponent_x, + UINT64 * pcoefficient_x, UINT64 x) { + UINT64 tmp, coeff; + + *psign_x = x & 0x8000000000000000ull; + + if ((x & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64) { + // special encodings + // coefficient + coeff = (x & LARGE_COEFF_MASK64) | LARGE_COEFF_HIGH_BIT64; + + if ((x & INFINITY_MASK64) == INFINITY_MASK64) { + *pexponent_x = 0; + *pcoefficient_x = x & 0xfe03ffffffffffffull; + if ((x & 0x0003ffffffffffffull) >= 1000000000000000ull) + *pcoefficient_x = x & 0xfe00000000000000ull; + if ((x & NAN_MASK64) == INFINITY_MASK64) + *pcoefficient_x = x & SINFINITY_MASK64; + return 0; // NaN or Infinity + } + // check for non-canonical values + if (coeff >= 10000000000000000ull) + coeff = 0; + *pcoefficient_x = coeff; + // get exponent + tmp = x >> EXPONENT_SHIFT_LARGE64; + *pexponent_x = (int) (tmp & EXPONENT_MASK64); + return coeff; + } + // exponent + tmp = x >> EXPONENT_SHIFT_SMALL64; + *pexponent_x = (int) (tmp & EXPONENT_MASK64); + // coefficient + *pcoefficient_x = (x & SMALL_COEFF_MASK64); + + return *pcoefficient_x; +} + +// +// BID64 pack macro (general form) +// +__BID_INLINE__ UINT64 +get_BID64 (UINT64 sgn, int expon, UINT64 coeff, int rmode, + unsigned *fpsc) { + UINT128 Stemp, Q_low; + UINT64 QH, r, mask, C64, remainder_h, CY, carry; + int extra_digits, amount, amount2; + unsigned status; + + if (coeff > 9999999999999999ull) { + expon++; + coeff = 1000000000000000ull; + } + // check for possible underflow/overflow + if (((unsigned) expon) >= 3 * 256) { + if (expon < 0) { + // underflow + if (expon + MAX_FORMAT_DIGITS < 0) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (fpsc, + UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); +#endif +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == ROUNDING_DOWN && sgn) + return 0x8000000000000001ull; + if (rmode == ROUNDING_UP && !sgn) + return 1ull; +#endif +#endif + // result is 0 + return sgn; + } +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (sgn && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#endif +#endif + // get digits to be shifted out + extra_digits = -expon; + coeff += round_const_table[rmode][extra_digits]; + + // get coeff*(2^M[extra_digits])/10^extra_digits + __mul_64x128_full (QH, Q_low, coeff, + reciprocals10_128[extra_digits]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[extra_digits]; + + C64 = QH >> amount; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == 0) //ROUNDING_TO_NEAREST +#endif + if (C64 & 1) { + // check whether fractional part of initial_P/10^extra_digits is exactly .5 + + // get remainder + amount2 = 64 - amount; + remainder_h = 0; + remainder_h--; + remainder_h >>= amount2; + remainder_h = remainder_h & QH; + + if (!remainder_h + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) { + C64--; + } + } +#endif + +#ifdef SET_STATUS_FLAGS + + if (is_inexact (fpsc)) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); + else { + status = INEXACT_EXCEPTION; + // get remainder + remainder_h = QH << (64 - amount); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if (remainder_h == 0x8000000000000000ull + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if (!remainder_h + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (Stemp.w[0], CY, Q_low.w[0], + reciprocals10_128[extra_digits].w[0]); + __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], + reciprocals10_128[extra_digits].w[1], CY); + if ((remainder_h >> (64 - amount)) + carry >= + (((UINT64) 1) << amount)) + status = EXACT_STATUS; + } + + if (status != EXACT_STATUS) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); + } + +#endif + + return sgn | C64; + } + while (coeff < 1000000000000000ull && expon >= 3 * 256) { + expon--; + coeff = (coeff << 3) + (coeff << 1); + } + if (expon > DECIMAL_MAX_EXPON_64) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); +#endif + // overflow + r = sgn | INFINITY_MASK64; + switch (rmode) { + case ROUNDING_DOWN: + if (!sgn) + r = LARGEST_BID64; + break; + case ROUNDING_TO_ZERO: + r = sgn | LARGEST_BID64; + break; + case ROUNDING_UP: + // round up + if (sgn) + r = SMALLEST_BID64; + } + return r; + } + } + + mask = 1; + mask <<= EXPONENT_SHIFT_SMALL64; + + // check whether coefficient fits in 10*5+3 bits + if (coeff < mask) { + r = expon; + r <<= EXPONENT_SHIFT_SMALL64; + r |= (coeff | sgn); + return r; + } + // special format + + // eliminate the case coeff==10^16 after rounding + if (coeff == 10000000000000000ull) { + r = expon + 1; + r <<= EXPONENT_SHIFT_SMALL64; + r |= (1000000000000000ull | sgn); + return r; + } + + r = expon; + r <<= EXPONENT_SHIFT_LARGE64; + r |= (sgn | SPECIAL_ENCODING_MASK64); + // add coeff, without leading bits + mask = (mask >> 2) - 1; + coeff &= mask; + r |= coeff; + + return r; +} + + + + +// +// No overflow/underflow checking +// +__BID_INLINE__ UINT64 +fast_get_BID64 (UINT64 sgn, int expon, UINT64 coeff) { + UINT64 r, mask; + + mask = 1; + mask <<= EXPONENT_SHIFT_SMALL64; + + // check whether coefficient fits in 10*5+3 bits + if (coeff < mask) { + r = expon; + r <<= EXPONENT_SHIFT_SMALL64; + r |= (coeff | sgn); + return r; + } + // special format + + // eliminate the case coeff==10^16 after rounding + if (coeff == 10000000000000000ull) { + r = expon + 1; + r <<= EXPONENT_SHIFT_SMALL64; + r |= (1000000000000000ull | sgn); + return r; + } + + r = expon; + r <<= EXPONENT_SHIFT_LARGE64; + r |= (sgn | SPECIAL_ENCODING_MASK64); + // add coeff, without leading bits + mask = (mask >> 2) - 1; + coeff &= mask; + r |= coeff; + + return r; +} + + +// +// no underflow checking +// +__BID_INLINE__ UINT64 +fast_get_BID64_check_OF (UINT64 sgn, int expon, UINT64 coeff, int rmode, + unsigned *fpsc) { + UINT64 r, mask; + + if (((unsigned) expon) >= 3 * 256 - 1) { + if ((expon == 3 * 256 - 1) && coeff == 10000000000000000ull) { + expon = 3 * 256; + coeff = 1000000000000000ull; + } + + if (((unsigned) expon) >= 3 * 256) { + while (coeff < 1000000000000000ull && expon >= 3 * 256) { + expon--; + coeff = (coeff << 3) + (coeff << 1); + } + if (expon > DECIMAL_MAX_EXPON_64) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (fpsc, + OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); +#endif + // overflow + r = sgn | INFINITY_MASK64; + switch (rmode) { + case ROUNDING_DOWN: + if (!sgn) + r = LARGEST_BID64; + break; + case ROUNDING_TO_ZERO: + r = sgn | LARGEST_BID64; + break; + case ROUNDING_UP: + // round up + if (sgn) + r = SMALLEST_BID64; + } + return r; + } + } + } + + mask = 1; + mask <<= EXPONENT_SHIFT_SMALL64; + + // check whether coefficient fits in 10*5+3 bits + if (coeff < mask) { + r = expon; + r <<= EXPONENT_SHIFT_SMALL64; + r |= (coeff | sgn); + return r; + } + // special format + + // eliminate the case coeff==10^16 after rounding + if (coeff == 10000000000000000ull) { + r = expon + 1; + r <<= EXPONENT_SHIFT_SMALL64; + r |= (1000000000000000ull | sgn); + return r; + } + + r = expon; + r <<= EXPONENT_SHIFT_LARGE64; + r |= (sgn | SPECIAL_ENCODING_MASK64); + // add coeff, without leading bits + mask = (mask >> 2) - 1; + coeff &= mask; + r |= coeff; + + return r; +} + + +// +// No overflow/underflow checking +// or checking for coefficients equal to 10^16 (after rounding) +// +__BID_INLINE__ UINT64 +very_fast_get_BID64 (UINT64 sgn, int expon, UINT64 coeff) { + UINT64 r, mask; + + mask = 1; + mask <<= EXPONENT_SHIFT_SMALL64; + + // check whether coefficient fits in 10*5+3 bits + if (coeff < mask) { + r = expon; + r <<= EXPONENT_SHIFT_SMALL64; + r |= (coeff | sgn); + return r; + } + // special format + r = expon; + r <<= EXPONENT_SHIFT_LARGE64; + r |= (sgn | SPECIAL_ENCODING_MASK64); + // add coeff, without leading bits + mask = (mask >> 2) - 1; + coeff &= mask; + r |= coeff; + + return r; +} + +// +// No overflow/underflow checking or checking for coefficients above 2^53 +// +__BID_INLINE__ UINT64 +very_fast_get_BID64_small_mantissa (UINT64 sgn, int expon, UINT64 coeff) { + // no UF/OF + UINT64 r; + + r = expon; + r <<= EXPONENT_SHIFT_SMALL64; + r |= (coeff | sgn); + return r; +} + + +// +// This pack macro is used when underflow is known to occur +// +__BID_INLINE__ UINT64 +get_BID64_UF (UINT64 sgn, int expon, UINT64 coeff, UINT64 R, int rmode, + unsigned *fpsc) { + UINT128 C128, Q_low, Stemp; + UINT64 C64, remainder_h, QH, carry, CY; + int extra_digits, amount, amount2; + unsigned status; + + // underflow + if (expon + MAX_FORMAT_DIGITS < 0) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); +#endif +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == ROUNDING_DOWN && sgn) + return 0x8000000000000001ull; + if (rmode == ROUNDING_UP && !sgn) + return 1ull; +#endif +#endif + // result is 0 + return sgn; + } + // 10*coeff + coeff = (coeff << 3) + (coeff << 1); +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (sgn && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#endif +#endif + if (R) + coeff |= 1; + // get digits to be shifted out + extra_digits = 1 - expon; + C128.w[0] = coeff + round_const_table[rmode][extra_digits]; + + // get coeff*(2^M[extra_digits])/10^extra_digits + __mul_64x128_full (QH, Q_low, C128.w[0], + reciprocals10_128[extra_digits]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[extra_digits]; + + C64 = QH >> amount; + //__shr_128(C128, Q_high, amount); + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == 0) //ROUNDING_TO_NEAREST +#endif + if (C64 & 1) { + // check whether fractional part of initial_P/10^extra_digits is exactly .5 + + // get remainder + amount2 = 64 - amount; + remainder_h = 0; + remainder_h--; + remainder_h >>= amount2; + remainder_h = remainder_h & QH; + + if (!remainder_h + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) { + C64--; + } + } +#endif + +#ifdef SET_STATUS_FLAGS + + if (is_inexact (fpsc)) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); + else { + status = INEXACT_EXCEPTION; + // get remainder + remainder_h = QH << (64 - amount); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if (remainder_h == 0x8000000000000000ull + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if (!remainder_h + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (Stemp.w[0], CY, Q_low.w[0], + reciprocals10_128[extra_digits].w[0]); + __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], + reciprocals10_128[extra_digits].w[1], CY); + if ((remainder_h >> (64 - amount)) + carry >= + (((UINT64) 1) << amount)) + status = EXACT_STATUS; + } + + if (status != EXACT_STATUS) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); + } + +#endif + + return sgn | C64; + +} + + + +// +// This pack macro doesnot check for coefficients above 2^53 +// +__BID_INLINE__ UINT64 +get_BID64_small_mantissa (UINT64 sgn, int expon, UINT64 coeff, + int rmode, unsigned *fpsc) { + UINT128 C128, Q_low, Stemp; + UINT64 r, mask, C64, remainder_h, QH, carry, CY; + int extra_digits, amount, amount2; + unsigned status; + + // check for possible underflow/overflow + if (((unsigned) expon) >= 3 * 256) { + if (expon < 0) { + // underflow + if (expon + MAX_FORMAT_DIGITS < 0) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (fpsc, + UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); +#endif +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == ROUNDING_DOWN && sgn) + return 0x8000000000000001ull; + if (rmode == ROUNDING_UP && !sgn) + return 1ull; +#endif +#endif + // result is 0 + return sgn; + } +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (sgn && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#endif +#endif + // get digits to be shifted out + extra_digits = -expon; + C128.w[0] = coeff + round_const_table[rmode][extra_digits]; + + // get coeff*(2^M[extra_digits])/10^extra_digits + __mul_64x128_full (QH, Q_low, C128.w[0], + reciprocals10_128[extra_digits]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = recip_scale[extra_digits]; + + C64 = QH >> amount; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == 0) //ROUNDING_TO_NEAREST +#endif + if (C64 & 1) { + // check whether fractional part of initial_P/10^extra_digits is exactly .5 + + // get remainder + amount2 = 64 - amount; + remainder_h = 0; + remainder_h--; + remainder_h >>= amount2; + remainder_h = remainder_h & QH; + + if (!remainder_h + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) { + C64--; + } + } +#endif + +#ifdef SET_STATUS_FLAGS + + if (is_inexact (fpsc)) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); + else { + status = INEXACT_EXCEPTION; + // get remainder + remainder_h = QH << (64 - amount); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if (remainder_h == 0x8000000000000000ull + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if (!remainder_h + && (Q_low.w[1] < reciprocals10_128[extra_digits].w[1] + || (Q_low.w[1] == reciprocals10_128[extra_digits].w[1] + && Q_low.w[0] < + reciprocals10_128[extra_digits].w[0]))) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (Stemp.w[0], CY, Q_low.w[0], + reciprocals10_128[extra_digits].w[0]); + __add_carry_in_out (Stemp.w[1], carry, Q_low.w[1], + reciprocals10_128[extra_digits].w[1], CY); + if ((remainder_h >> (64 - amount)) + carry >= + (((UINT64) 1) << amount)) + status = EXACT_STATUS; + } + + if (status != EXACT_STATUS) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); + } + +#endif + + return sgn | C64; + } + + while (coeff < 1000000000000000ull && expon >= 3 * 256) { + expon--; + coeff = (coeff << 3) + (coeff << 1); + } + if (expon > DECIMAL_MAX_EXPON_64) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); +#endif + // overflow + r = sgn | INFINITY_MASK64; + switch (rmode) { + case ROUNDING_DOWN: + if (!sgn) + r = LARGEST_BID64; + break; + case ROUNDING_TO_ZERO: + r = sgn | LARGEST_BID64; + break; + case ROUNDING_UP: + // round up + if (sgn) + r = SMALLEST_BID64; + } + return r; + } else { + mask = 1; + mask <<= EXPONENT_SHIFT_SMALL64; + if (coeff >= mask) { + r = expon; + r <<= EXPONENT_SHIFT_LARGE64; + r |= (sgn | SPECIAL_ENCODING_MASK64); + // add coeff, without leading bits + mask = (mask >> 2) - 1; + coeff &= mask; + r |= coeff; + return r; + } + } + } + + r = expon; + r <<= EXPONENT_SHIFT_SMALL64; + r |= (coeff | sgn); + + return r; +} + + +/***************************************************************************** +* +* BID128 pack/unpack macros +* +*****************************************************************************/ + +// +// Macro for handling BID128 underflow +// sticky bit given as additional argument +// +__BID_INLINE__ UINT128 * +handle_UF_128_rem (UINT128 * pres, UINT64 sgn, int expon, UINT128 CQ, + UINT64 R, unsigned *prounding_mode, unsigned *fpsc) { + UINT128 T128, TP128, Qh, Ql, Qh1, Stemp, Tmp, Tmp1, CQ2, CQ8; + UINT64 carry, CY; + int ed2, amount; + unsigned rmode, status; + + // UF occurs + if (expon + MAX_FORMAT_DIGITS_128 < 0) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); +#endif + pres->w[1] = sgn; + pres->w[0] = 0; +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if ((sgn && *prounding_mode == ROUNDING_DOWN) + || (!sgn && *prounding_mode == ROUNDING_UP)) + pres->w[0] = 1ull; +#endif +#endif + return pres; + } + // CQ *= 10 + CQ2.w[1] = (CQ.w[1] << 1) | (CQ.w[0] >> 63); + CQ2.w[0] = CQ.w[0] << 1; + CQ8.w[1] = (CQ.w[1] << 3) | (CQ.w[0] >> 61); + CQ8.w[0] = CQ.w[0] << 3; + __add_128_128 (CQ, CQ2, CQ8); + + // add remainder + if (R) + CQ.w[0] |= 1; + + ed2 = 1 - expon; + // add rounding constant to CQ +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = *prounding_mode; + if (sgn && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#else + rmode = 0; +#endif +#else + rmode = 0; +#endif + T128 = round_const_table_128[rmode][ed2]; + __add_carry_out (CQ.w[0], carry, T128.w[0], CQ.w[0]); + CQ.w[1] = CQ.w[1] + T128.w[1] + carry; + + TP128 = reciprocals10_128[ed2]; + __mul_128x128_full (Qh, Ql, CQ, TP128); + amount = recip_scale[ed2]; + + if (amount >= 64) { + CQ.w[0] = Qh.w[1] >> (amount - 64); + CQ.w[1] = 0; + } else { + __shr_128 (CQ, Qh, amount); + } + + expon = 0; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (!(*prounding_mode)) +#endif + if (CQ.w[0] & 1) { + // check whether fractional part of initial_P/10^ed1 is exactly .5 + + // get remainder + __shl_128_long (Qh1, Qh, (128 - amount)); + + if (!Qh1.w[1] && !Qh1.w[0] + && (Ql.w[1] < reciprocals10_128[ed2].w[1] + || (Ql.w[1] == reciprocals10_128[ed2].w[1] + && Ql.w[0] < reciprocals10_128[ed2].w[0]))) { + CQ.w[0]--; + } + } +#endif + +#ifdef SET_STATUS_FLAGS + + if (is_inexact (fpsc)) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); + else { + status = INEXACT_EXCEPTION; + // get remainder + __shl_128_long (Qh1, Qh, (128 - amount)); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if (Qh1.w[1] == 0x8000000000000000ull && (!Qh1.w[0]) + && (Ql.w[1] < reciprocals10_128[ed2].w[1] + || (Ql.w[1] == reciprocals10_128[ed2].w[1] + && Ql.w[0] < reciprocals10_128[ed2].w[0]))) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if ((!Qh1.w[1]) && (!Qh1.w[0]) + && (Ql.w[1] < reciprocals10_128[ed2].w[1] + || (Ql.w[1] == reciprocals10_128[ed2].w[1] + && Ql.w[0] < reciprocals10_128[ed2].w[0]))) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (Stemp.w[0], CY, Ql.w[0], + reciprocals10_128[ed2].w[0]); + __add_carry_in_out (Stemp.w[1], carry, Ql.w[1], + reciprocals10_128[ed2].w[1], CY); + __shr_128_long (Qh, Qh1, (128 - amount)); + Tmp.w[0] = 1; + Tmp.w[1] = 0; + __shl_128_long (Tmp1, Tmp, amount); + Qh.w[0] += carry; + if (Qh.w[0] < carry) + Qh.w[1]++; + if (__unsigned_compare_ge_128 (Qh, Tmp1)) + status = EXACT_STATUS; + } + + if (status != EXACT_STATUS) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); + } + +#endif + + pres->w[1] = sgn | CQ.w[1]; + pres->w[0] = CQ.w[0]; + + return pres; + +} + + +// +// Macro for handling BID128 underflow +// +__BID_INLINE__ UINT128 * +handle_UF_128 (UINT128 * pres, UINT64 sgn, int expon, UINT128 CQ, + unsigned *prounding_mode, unsigned *fpsc) { + UINT128 T128, TP128, Qh, Ql, Qh1, Stemp, Tmp, Tmp1; + UINT64 carry, CY; + int ed2, amount; + unsigned rmode, status; + + // UF occurs + if (expon + MAX_FORMAT_DIGITS_128 < 0) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); +#endif + pres->w[1] = sgn; + pres->w[0] = 0; +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if ((sgn && *prounding_mode == ROUNDING_DOWN) + || (!sgn && *prounding_mode == ROUNDING_UP)) + pres->w[0] = 1ull; +#endif +#endif + return pres; + } + + ed2 = 0 - expon; + // add rounding constant to CQ +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + rmode = *prounding_mode; + if (sgn && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#else + rmode = 0; +#endif +#else + rmode = 0; +#endif + + T128 = round_const_table_128[rmode][ed2]; + __add_carry_out (CQ.w[0], carry, T128.w[0], CQ.w[0]); + CQ.w[1] = CQ.w[1] + T128.w[1] + carry; + + TP128 = reciprocals10_128[ed2]; + __mul_128x128_full (Qh, Ql, CQ, TP128); + amount = recip_scale[ed2]; + + if (amount >= 64) { + CQ.w[0] = Qh.w[1] >> (amount - 64); + CQ.w[1] = 0; + } else { + __shr_128 (CQ, Qh, amount); + } + + expon = 0; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (!(*prounding_mode)) +#endif + if (CQ.w[0] & 1) { + // check whether fractional part of initial_P/10^ed1 is exactly .5 + + // get remainder + __shl_128_long (Qh1, Qh, (128 - amount)); + + if (!Qh1.w[1] && !Qh1.w[0] + && (Ql.w[1] < reciprocals10_128[ed2].w[1] + || (Ql.w[1] == reciprocals10_128[ed2].w[1] + && Ql.w[0] < reciprocals10_128[ed2].w[0]))) { + CQ.w[0]--; + } + } +#endif + +#ifdef SET_STATUS_FLAGS + + if (is_inexact (fpsc)) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); + else { + status = INEXACT_EXCEPTION; + // get remainder + __shl_128_long (Qh1, Qh, (128 - amount)); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if (Qh1.w[1] == 0x8000000000000000ull && (!Qh1.w[0]) + && (Ql.w[1] < reciprocals10_128[ed2].w[1] + || (Ql.w[1] == reciprocals10_128[ed2].w[1] + && Ql.w[0] < reciprocals10_128[ed2].w[0]))) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if ((!Qh1.w[1]) && (!Qh1.w[0]) + && (Ql.w[1] < reciprocals10_128[ed2].w[1] + || (Ql.w[1] == reciprocals10_128[ed2].w[1] + && Ql.w[0] < reciprocals10_128[ed2].w[0]))) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (Stemp.w[0], CY, Ql.w[0], + reciprocals10_128[ed2].w[0]); + __add_carry_in_out (Stemp.w[1], carry, Ql.w[1], + reciprocals10_128[ed2].w[1], CY); + __shr_128_long (Qh, Qh1, (128 - amount)); + Tmp.w[0] = 1; + Tmp.w[1] = 0; + __shl_128_long (Tmp1, Tmp, amount); + Qh.w[0] += carry; + if (Qh.w[0] < carry) + Qh.w[1]++; + if (__unsigned_compare_ge_128 (Qh, Tmp1)) + status = EXACT_STATUS; + } + + if (status != EXACT_STATUS) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); + } + +#endif + + pres->w[1] = sgn | CQ.w[1]; + pres->w[0] = CQ.w[0]; + + return pres; + +} + + + +// +// BID128 unpack, input passed by value +// +__BID_INLINE__ UINT64 +unpack_BID128_value (UINT64 * psign_x, int *pexponent_x, + UINT128 * pcoefficient_x, UINT128 x) { + UINT128 coeff, T33, T34; + UINT64 ex; + + *psign_x = (x.w[1]) & 0x8000000000000000ull; + + // special encodings + if ((x.w[1] & INFINITY_MASK64) >= SPECIAL_ENCODING_MASK64) { + if ((x.w[1] & INFINITY_MASK64) < INFINITY_MASK64) { + // non-canonical input + pcoefficient_x->w[0] = 0; + pcoefficient_x->w[1] = 0; + ex = (x.w[1]) >> 47; + *pexponent_x = ((int) ex) & EXPONENT_MASK128; + return 0; + } + // 10^33 + T33 = power10_table_128[33]; + /*coeff.w[0] = x.w[0]; + coeff.w[1] = (x.w[1]) & LARGE_COEFF_MASK128; + pcoefficient_x->w[0] = x.w[0]; + pcoefficient_x->w[1] = x.w[1]; + if (__unsigned_compare_ge_128 (coeff, T33)) // non-canonical + pcoefficient_x->w[1] &= (~LARGE_COEFF_MASK128); */ + + pcoefficient_x->w[0] = x.w[0]; + pcoefficient_x->w[1] = (x.w[1]) & 0x00003fffffffffffull; + if (__unsigned_compare_ge_128 ((*pcoefficient_x), T33)) // non-canonical + { + pcoefficient_x->w[1] = (x.w[1]) & 0xfe00000000000000ull; + pcoefficient_x->w[0] = 0; + } else + pcoefficient_x->w[1] = (x.w[1]) & 0xfe003fffffffffffull; + if ((x.w[1] & NAN_MASK64) == INFINITY_MASK64) { + pcoefficient_x->w[0] = 0; + pcoefficient_x->w[1] = x.w[1] & SINFINITY_MASK64; + } + *pexponent_x = 0; + return 0; // NaN or Infinity + } + + coeff.w[0] = x.w[0]; + coeff.w[1] = (x.w[1]) & SMALL_COEFF_MASK128; + + // 10^34 + T34 = power10_table_128[34]; + // check for non-canonical values + if (__unsigned_compare_ge_128 (coeff, T34)) + coeff.w[0] = coeff.w[1] = 0; + + pcoefficient_x->w[0] = coeff.w[0]; + pcoefficient_x->w[1] = coeff.w[1]; + + ex = (x.w[1]) >> 49; + *pexponent_x = ((int) ex) & EXPONENT_MASK128; + + return coeff.w[0] | coeff.w[1]; +} + + +// +// BID128 unpack, input pased by reference +// +__BID_INLINE__ UINT64 +unpack_BID128 (UINT64 * psign_x, int *pexponent_x, + UINT128 * pcoefficient_x, UINT128 * px) { + UINT128 coeff, T33, T34; + UINT64 ex; + + *psign_x = (px->w[1]) & 0x8000000000000000ull; + + // special encodings + if ((px->w[1] & INFINITY_MASK64) >= SPECIAL_ENCODING_MASK64) { + if ((px->w[1] & INFINITY_MASK64) < INFINITY_MASK64) { + // non-canonical input + pcoefficient_x->w[0] = 0; + pcoefficient_x->w[1] = 0; + ex = (px->w[1]) >> 47; + *pexponent_x = ((int) ex) & EXPONENT_MASK128; + return 0; + } + // 10^33 + T33 = power10_table_128[33]; + coeff.w[0] = px->w[0]; + coeff.w[1] = (px->w[1]) & LARGE_COEFF_MASK128; + pcoefficient_x->w[0] = px->w[0]; + pcoefficient_x->w[1] = px->w[1]; + if (__unsigned_compare_ge_128 (coeff, T33)) { // non-canonical + pcoefficient_x->w[1] &= (~LARGE_COEFF_MASK128); + pcoefficient_x->w[0] = 0; + } + *pexponent_x = 0; + return 0; // NaN or Infinity + } + + coeff.w[0] = px->w[0]; + coeff.w[1] = (px->w[1]) & SMALL_COEFF_MASK128; + + // 10^34 + T34 = power10_table_128[34]; + // check for non-canonical values + if (__unsigned_compare_ge_128 (coeff, T34)) + coeff.w[0] = coeff.w[1] = 0; + + pcoefficient_x->w[0] = coeff.w[0]; + pcoefficient_x->w[1] = coeff.w[1]; + + ex = (px->w[1]) >> 49; + *pexponent_x = ((int) ex) & EXPONENT_MASK128; + + return coeff.w[0] | coeff.w[1]; +} + +// +// Pack macro checks for overflow, but not underflow +// +__BID_INLINE__ UINT128 * +get_BID128_very_fast_OF (UINT128 * pres, UINT64 sgn, int expon, + UINT128 coeff, unsigned *prounding_mode, + unsigned *fpsc) { + UINT128 T; + UINT64 tmp, tmp2; + + if ((unsigned) expon > DECIMAL_MAX_EXPON_128) { + + if (expon - MAX_FORMAT_DIGITS_128 <= DECIMAL_MAX_EXPON_128) { + T = power10_table_128[MAX_FORMAT_DIGITS_128 - 1]; + while (__unsigned_compare_gt_128 (T, coeff) + && expon > DECIMAL_MAX_EXPON_128) { + coeff.w[1] = + (coeff.w[1] << 3) + (coeff.w[1] << 1) + (coeff.w[0] >> 61) + + (coeff.w[0] >> 63); + tmp2 = coeff.w[0] << 3; + coeff.w[0] = (coeff.w[0] << 1) + tmp2; + if (coeff.w[0] < tmp2) + coeff.w[1]++; + + expon--; + } + } + if ((unsigned) expon > DECIMAL_MAX_EXPON_128) { + // OF +#ifdef SET_STATUS_FLAGS + __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); +#endif +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (*prounding_mode == ROUNDING_TO_ZERO + || (sgn && *prounding_mode == ROUNDING_UP) || (!sgn + && + *prounding_mode + == + ROUNDING_DOWN)) + { + pres->w[1] = sgn | LARGEST_BID128_HIGH; + pres->w[0] = LARGEST_BID128_LOW; + } else +#endif +#endif + { + pres->w[1] = sgn | INFINITY_MASK64; + pres->w[0] = 0; + } + return pres; + } + } + + pres->w[0] = coeff.w[0]; + tmp = expon; + tmp <<= 49; + pres->w[1] = sgn | tmp | coeff.w[1]; + + return pres; +} + + +// +// No overflow/underflow checks +// No checking for coefficient == 10^34 (rounding artifact) +// +__BID_INLINE__ UINT128 * +get_BID128_very_fast (UINT128 * pres, UINT64 sgn, int expon, + UINT128 coeff) { + UINT64 tmp; + + pres->w[0] = coeff.w[0]; + tmp = expon; + tmp <<= 49; + pres->w[1] = sgn | tmp | coeff.w[1]; + + return pres; +} + +// +// No overflow/underflow checks +// +__BID_INLINE__ UINT128 * +get_BID128_fast (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff) { + UINT64 tmp; + + // coeff==10^34? + if (coeff.w[1] == 0x0001ed09bead87c0ull + && coeff.w[0] == 0x378d8e6400000000ull) { + expon++; + // set coefficient to 10^33 + coeff.w[1] = 0x0000314dc6448d93ull; + coeff.w[0] = 0x38c15b0a00000000ull; + } + + pres->w[0] = coeff.w[0]; + tmp = expon; + tmp <<= 49; + pres->w[1] = sgn | tmp | coeff.w[1]; + + return pres; +} + +// +// General BID128 pack macro +// +__BID_INLINE__ UINT128 * +get_BID128 (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff, + unsigned *prounding_mode, unsigned *fpsc) { + UINT128 T; + UINT64 tmp, tmp2; + + // coeff==10^34? + if (coeff.w[1] == 0x0001ed09bead87c0ull + && coeff.w[0] == 0x378d8e6400000000ull) { + expon++; + // set coefficient to 10^33 + coeff.w[1] = 0x0000314dc6448d93ull; + coeff.w[0] = 0x38c15b0a00000000ull; + } + // check OF, UF + if (expon < 0 || expon > DECIMAL_MAX_EXPON_128) { + // check UF + if (expon < 0) { + return handle_UF_128 (pres, sgn, expon, coeff, prounding_mode, + fpsc); + } + + if (expon - MAX_FORMAT_DIGITS_128 <= DECIMAL_MAX_EXPON_128) { + T = power10_table_128[MAX_FORMAT_DIGITS_128 - 1]; + while (__unsigned_compare_gt_128 (T, coeff) + && expon > DECIMAL_MAX_EXPON_128) { + coeff.w[1] = + (coeff.w[1] << 3) + (coeff.w[1] << 1) + (coeff.w[0] >> 61) + + (coeff.w[0] >> 63); + tmp2 = coeff.w[0] << 3; + coeff.w[0] = (coeff.w[0] << 1) + tmp2; + if (coeff.w[0] < tmp2) + coeff.w[1]++; + + expon--; + } + } + if (expon > DECIMAL_MAX_EXPON_128) { + if (!(coeff.w[1] | coeff.w[0])) { + pres->w[1] = sgn | (((UINT64) DECIMAL_MAX_EXPON_128) << 49); + pres->w[0] = 0; + return pres; + } + // OF +#ifdef SET_STATUS_FLAGS + __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); +#endif +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (*prounding_mode == ROUNDING_TO_ZERO + || (sgn && *prounding_mode == ROUNDING_UP) || (!sgn + && + *prounding_mode + == + ROUNDING_DOWN)) + { + pres->w[1] = sgn | LARGEST_BID128_HIGH; + pres->w[0] = LARGEST_BID128_LOW; + } else +#endif +#endif + { + pres->w[1] = sgn | INFINITY_MASK64; + pres->w[0] = 0; + } + return pres; + } + } + + pres->w[0] = coeff.w[0]; + tmp = expon; + tmp <<= 49; + pres->w[1] = sgn | tmp | coeff.w[1]; + + return pres; +} + + +// +// Macro used for conversions from string +// (no additional arguments given for rounding mode, status flags) +// +__BID_INLINE__ UINT128 * +get_BID128_string (UINT128 * pres, UINT64 sgn, int expon, UINT128 coeff) { + UINT128 D2, D8; + UINT64 tmp; + unsigned rmode = 0, status; + + // coeff==10^34? + if (coeff.w[1] == 0x0001ed09bead87c0ull + && coeff.w[0] == 0x378d8e6400000000ull) { + expon++; + // set coefficient to 10^33 + coeff.w[1] = 0x0000314dc6448d93ull; + coeff.w[0] = 0x38c15b0a00000000ull; + } + // check OF, UF + if ((unsigned) expon > DECIMAL_MAX_EXPON_128) { + // check UF + if (expon < 0) + return handle_UF_128 (pres, sgn, expon, coeff, &rmode, &status); + + // OF + + if (expon < DECIMAL_MAX_EXPON_128 + 34) { + while (expon > DECIMAL_MAX_EXPON_128 && + (coeff.w[1] < power10_table_128[33].w[1] || + (coeff.w[1] == power10_table_128[33].w[1] + && coeff.w[0] < power10_table_128[33].w[0]))) { + D2.w[1] = (coeff.w[1] << 1) | (coeff.w[0] >> 63); + D2.w[0] = coeff.w[0] << 1; + D8.w[1] = (coeff.w[1] << 3) | (coeff.w[0] >> 61); + D8.w[0] = coeff.w[0] << 3; + + __add_128_128 (coeff, D2, D8); + expon--; + } + } else if (!(coeff.w[0] | coeff.w[1])) + expon = DECIMAL_MAX_EXPON_128; + + if (expon > DECIMAL_MAX_EXPON_128) { + pres->w[1] = sgn | INFINITY_MASK64; + pres->w[0] = 0; + switch (rmode) { + case ROUNDING_DOWN: + if (!sgn) { + pres->w[1] = LARGEST_BID128_HIGH; + pres->w[0] = LARGEST_BID128_LOW; + } + break; + case ROUNDING_TO_ZERO: + pres->w[1] = sgn | LARGEST_BID128_HIGH; + pres->w[0] = LARGEST_BID128_LOW; + break; + case ROUNDING_UP: + // round up + if (sgn) { + pres->w[1] = sgn | LARGEST_BID128_HIGH; + pres->w[0] = LARGEST_BID128_LOW; + } + break; + } + + return pres; + } + } + + pres->w[0] = coeff.w[0]; + tmp = expon; + tmp <<= 49; + pres->w[1] = sgn | tmp | coeff.w[1]; + + return pres; +} + + + +/***************************************************************************** +* +* BID32 pack/unpack macros +* +*****************************************************************************/ + + +__BID_INLINE__ UINT32 +unpack_BID32 (UINT32 * psign_x, int *pexponent_x, + UINT32 * pcoefficient_x, UINT32 x) { + UINT32 tmp; + + *psign_x = x & 0x80000000; + + if ((x & SPECIAL_ENCODING_MASK32) == SPECIAL_ENCODING_MASK32) { + // special encodings + if ((x & INFINITY_MASK32) == INFINITY_MASK32) { + *pcoefficient_x = x & 0xfe0fffff; + if ((x & 0x000fffff) >= 1000000) + *pcoefficient_x = x & 0xfe000000; + if ((x & NAN_MASK32) == INFINITY_MASK32) + *pcoefficient_x = x & 0xf8000000; + *pexponent_x = 0; + return 0; // NaN or Infinity + } + // coefficient + *pcoefficient_x = (x & SMALL_COEFF_MASK32) | LARGE_COEFF_HIGH_BIT32; + // check for non-canonical value + if (*pcoefficient_x >= 10000000) + *pcoefficient_x = 0; + // get exponent + tmp = x >> 21; + *pexponent_x = tmp & EXPONENT_MASK32; + return 1; + } + // exponent + tmp = x >> 23; + *pexponent_x = tmp & EXPONENT_MASK32; + // coefficient + *pcoefficient_x = (x & LARGE_COEFF_MASK32); + + return *pcoefficient_x; +} + +// +// General pack macro for BID32 +// +__BID_INLINE__ UINT32 +get_BID32 (UINT32 sgn, int expon, UINT64 coeff, int rmode, + unsigned *fpsc) { + UINT128 Q; + UINT64 C64, remainder_h, carry, Stemp; + UINT32 r, mask; + int extra_digits, amount, amount2; + unsigned status; + + if (coeff > 9999999ull) { + expon++; + coeff = 1000000ull; + } + // check for possible underflow/overflow + if (((unsigned) expon) > DECIMAL_MAX_EXPON_32) { + if (expon < 0) { + // underflow + if (expon + MAX_FORMAT_DIGITS_32 < 0) { +#ifdef SET_STATUS_FLAGS + __set_status_flags (fpsc, + UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION); +#endif +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == ROUNDING_DOWN && sgn) + return 0x80000001; + if (rmode == ROUNDING_UP && !sgn) + return 1; +#endif +#endif + // result is 0 + return sgn; + } + // get digits to be shifted out +#ifdef IEEE_ROUND_NEAREST_TIES_AWAY + rmode = 0; +#endif +#ifdef IEEE_ROUND_NEAREST + rmode = 0; +#endif +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (sgn && (unsigned) (rmode - 1) < 2) + rmode = 3 - rmode; +#endif +#endif + + extra_digits = -expon; + coeff += round_const_table[rmode][extra_digits]; + + // get coeff*(2^M[extra_digits])/10^extra_digits + __mul_64x64_to_128 (Q, coeff, reciprocals10_64[extra_digits]); + + // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 + amount = short_recip_scale[extra_digits]; + + C64 = Q.w[1] >> amount; + +#ifndef IEEE_ROUND_NEAREST_TIES_AWAY +#ifndef IEEE_ROUND_NEAREST + if (rmode == 0) //ROUNDING_TO_NEAREST +#endif + if (C64 & 1) { + // check whether fractional part of initial_P/10^extra_digits is exactly .5 + + // get remainder + amount2 = 64 - amount; + remainder_h = 0; + remainder_h--; + remainder_h >>= amount2; + remainder_h = remainder_h & Q.w[1]; + + if (!remainder_h && (Q.w[0] < reciprocals10_64[extra_digits])) { + C64--; + } + } +#endif + +#ifdef SET_STATUS_FLAGS + + if (is_inexact (fpsc)) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION); + else { + status = INEXACT_EXCEPTION; + // get remainder + remainder_h = Q.w[1] << (64 - amount); + + switch (rmode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // test whether fractional part is 0 + if (remainder_h == 0x8000000000000000ull + && (Q.w[0] < reciprocals10_64[extra_digits])) + status = EXACT_STATUS; + break; + case ROUNDING_DOWN: + case ROUNDING_TO_ZERO: + if (!remainder_h && (Q.w[0] < reciprocals10_64[extra_digits])) + status = EXACT_STATUS; + break; + default: + // round up + __add_carry_out (Stemp, carry, Q.w[0], + reciprocals10_64[extra_digits]); + if ((remainder_h >> (64 - amount)) + carry >= + (((UINT64) 1) << amount)) + status = EXACT_STATUS; + } + + if (status != EXACT_STATUS) + __set_status_flags (fpsc, UNDERFLOW_EXCEPTION | status); + } + +#endif + + return sgn | (UINT32) C64; + } + + while (coeff < 1000000 && expon > DECIMAL_MAX_EXPON_32) { + coeff = (coeff << 3) + (coeff << 1); + expon--; + } + if (((unsigned) expon) > DECIMAL_MAX_EXPON_32) { + __set_status_flags (fpsc, OVERFLOW_EXCEPTION | INEXACT_EXCEPTION); + // overflow + r = sgn | INFINITY_MASK32; + switch (rmode) { + case ROUNDING_DOWN: + if (!sgn) + r = LARGEST_BID32; + break; + case ROUNDING_TO_ZERO: + r = sgn | LARGEST_BID32; + break; + case ROUNDING_UP: + // round up + if (sgn) + r = sgn | LARGEST_BID32; + } + return r; + } + } + + mask = 1 << 23; + + // check whether coefficient fits in DECIMAL_COEFF_FIT bits + if (coeff < mask) { + r = expon; + r <<= 23; + r |= ((UINT32) coeff | sgn); + return r; + } + // special format + + r = expon; + r <<= 21; + r |= (sgn | SPECIAL_ENCODING_MASK32); + // add coeff, without leading bits + mask = (1 << 21) - 1; + r |= (((UINT32) coeff) & mask); + + return r; +} + + + +// +// no overflow/underflow checks +// +__BID_INLINE__ UINT32 +very_fast_get_BID32 (UINT32 sgn, int expon, UINT32 coeff) { + UINT32 r, mask; + + mask = 1 << 23; + + // check whether coefficient fits in 10*2+3 bits + if (coeff < mask) { + r = expon; + r <<= 23; + r |= (coeff | sgn); + return r; + } + // special format + r = expon; + r <<= 21; + r |= (sgn | SPECIAL_ENCODING_MASK32); + // add coeff, without leading bits + mask = (1 << 21) - 1; + coeff &= mask; + r |= coeff; + + return r; +} + + + +/************************************************************* + * + *************************************************************/ +typedef +ALIGN (16) + struct { + UINT64 w[6]; + } UINT384; + typedef ALIGN (16) + struct { + UINT64 w[8]; + } UINT512; + +// #define P 34 +#define MASK_STEERING_BITS 0x6000000000000000ull +#define MASK_BINARY_EXPONENT1 0x7fe0000000000000ull +#define MASK_BINARY_SIG1 0x001fffffffffffffull +#define MASK_BINARY_EXPONENT2 0x1ff8000000000000ull + //used to take G[2:w+3] (sec 3.3) +#define MASK_BINARY_SIG2 0x0007ffffffffffffull + //used to mask out G4:T0 (sec 3.3) +#define MASK_BINARY_OR2 0x0020000000000000ull + //used to prefix 8+G4 to T (sec 3.3) +#define UPPER_EXPON_LIMIT 51 +#define MASK_EXP 0x7ffe000000000000ull +#define MASK_SPECIAL 0x7800000000000000ull +#define MASK_NAN 0x7c00000000000000ull +#define MASK_SNAN 0x7e00000000000000ull +#define MASK_ANY_INF 0x7c00000000000000ull +#define MASK_INF 0x7800000000000000ull +#define MASK_SIGN 0x8000000000000000ull +#define MASK_COEFF 0x0001ffffffffffffull +#define BIN_EXP_BIAS (0x1820ull << 49) + +#define EXP_MIN 0x0000000000000000ull + // EXP_MIN = (-6176 + 6176) << 49 +#define EXP_MAX 0x5ffe000000000000ull + // EXP_MAX = (6111 + 6176) << 49 +#define EXP_MAX_P1 0x6000000000000000ull + // EXP_MAX + 1 = (6111 + 6176 + 1) << 49 +#define EXP_P1 0x0002000000000000ull + // EXP_ P1= 1 << 49 +#define expmin -6176 + // min unbiased exponent +#define expmax 6111 + // max unbiased exponent +#define expmin16 -398 + // min unbiased exponent +#define expmax16 369 + // max unbiased exponent + +#define SIGNMASK32 0x80000000 +#define BID64_SIG_MAX 0x002386F26FC0ffffull +#define SIGNMASK64 0x8000000000000000ull + +// typedef unsigned int FPSC; // floating-point status and control + // bit31: + // bit30: + // bit29: + // bit28: + // bit27: + // bit26: + // bit25: + // bit24: + // bit23: + // bit22: + // bit21: + // bit20: + // bit19: + // bit18: + // bit17: + // bit16: + // bit15: + // bit14: RC:2 + // bit13: RC:1 + // bit12: RC:0 + // bit11: PM + // bit10: UM + // bit9: OM + // bit8: ZM + // bit7: DM + // bit6: IM + // bit5: PE + // bit4: UE + // bit3: OE + // bit2: ZE + // bit1: DE + // bit0: IE + +#define ROUNDING_MODE_MASK 0x00007000 + + typedef struct _DEC_DIGITS { + unsigned int digits; + UINT64 threshold_hi; + UINT64 threshold_lo; + unsigned int digits1; + } DEC_DIGITS; + + extern DEC_DIGITS nr_digits[]; + extern UINT64 midpoint64[]; + extern UINT128 midpoint128[]; + extern UINT192 midpoint192[]; + extern UINT256 midpoint256[]; + extern UINT64 ten2k64[]; + extern UINT128 ten2k128[]; + extern UINT256 ten2k256[]; + extern UINT128 ten2mk128[]; + extern UINT64 ten2mk64[]; + extern UINT128 ten2mk128trunc[]; + extern int shiftright128[]; + extern UINT64 maskhigh128[]; + extern UINT64 maskhigh128M[]; + extern UINT64 maskhigh192M[]; + extern UINT64 maskhigh256M[]; + extern UINT64 onehalf128[]; + extern UINT64 onehalf128M[]; + extern UINT64 onehalf192M[]; + extern UINT64 onehalf256M[]; + extern UINT128 ten2mk128M[]; + extern UINT128 ten2mk128truncM[]; + extern UINT192 ten2mk192truncM[]; + extern UINT256 ten2mk256truncM[]; + extern int shiftright128M[]; + extern int shiftright192M[]; + extern int shiftright256M[]; + extern UINT192 ten2mk192M[]; + extern UINT256 ten2mk256M[]; + extern unsigned char char_table2[]; + extern unsigned char char_table3[]; + + extern UINT64 ten2m3k64[]; + extern unsigned int shift_ten2m3k64[]; + extern UINT128 ten2m3k128[]; + extern unsigned int shift_ten2m3k128[]; + + + +/*************************************************************************** + *************** TABLES FOR GENERAL ROUNDING FUNCTIONS ********************* + ***************************************************************************/ + + extern UINT64 Kx64[]; + extern unsigned int Ex64m64[]; + extern UINT64 half64[]; + extern UINT64 mask64[]; + extern UINT64 ten2mxtrunc64[]; + + extern UINT128 Kx128[]; + extern unsigned int Ex128m128[]; + extern UINT64 half128[]; + extern UINT64 mask128[]; + extern UINT128 ten2mxtrunc128[]; + + extern UINT192 Kx192[]; + extern unsigned int Ex192m192[]; + extern UINT64 half192[]; + extern UINT64 mask192[]; + extern UINT192 ten2mxtrunc192[]; + + extern UINT256 Kx256[]; + extern unsigned int Ex256m256[]; + extern UINT64 half256[]; + extern UINT64 mask256[]; + extern UINT256 ten2mxtrunc256[]; + + typedef union __bid64_128 { + UINT64 b64; + UINT128 b128; + } BID64_128; + + BID64_128 bid_fma (unsigned int P0, + BID64_128 x1, unsigned int P1, + BID64_128 y1, unsigned int P2, + BID64_128 z1, unsigned int P3, + unsigned int rnd_mode, FPSC * fpsc); + +#define P16 16 +#define P34 34 + + union __int_double { + UINT64 i; + double d; + }; + typedef union __int_double int_double; + + + union __int_float { + UINT32 i; + float d; + }; + typedef union __int_float int_float; + +#define SWAP(A,B,T) {\ + T = A; \ + A = B; \ + B = T; \ +} + +// this macro will find coefficient_x to be in [2^A, 2^(A+1) ) +// ie it knows that it is A bits long +#define NUMBITS(A, coefficient_x, tempx){\ + temp_x.d=(float)coefficient_x;\ + A=((tempx.i >>23) & EXPONENT_MASK32) - 0x7f;\ +} + + enum class_types { + signalingNaN, + quietNaN, + negativeInfinity, + negativeNormal, + negativeSubnormal, + negativeZero, + positiveZero, + positiveSubnormal, + positiveNormal, + positiveInfinity + }; + + typedef union { + UINT64 ui64; + double d; + } BID_UI64DOUBLE; + +#endif diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_round.c b/gcc-4.4.3/libgcc/config/libbid/bid_round.c new file mode 100644 index 000000000..64afdbef1 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_round.c @@ -0,0 +1,1049 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +/***************************************************************************** + * + * BID64 encoding: + * **************************************** + * 63 62 53 52 0 + * |---|------------------|--------------| + * | S | Biased Exp (E) | Coeff (c) | + * |---|------------------|--------------| + * + * bias = 398 + * number = (-1)^s * 10^(E-398) * c + * coefficient range - 0 to (2^53)-1 + * COEFF_MAX = 2^53-1 = 9007199254740991 + * + ***************************************************************************** + * + * BID128 encoding: + * 1-bit sign + * 14-bit biased exponent in [0x21, 0x3020] = [33, 12320] + * unbiased exponent in [-6176, 6111]; exponent bias = 6176 + * 113-bit unsigned binary integer coefficient (49-bit high + 64-bit low) + * Note: 10^34-1 ~ 2^112.945555... < 2^113 => coefficient fits in 113 bits + * + * Note: assume invalid encodings are not passed to this function + * + * Round a number C with q decimal digits, represented as a binary integer + * to q - x digits. Six different routines are provided for different values + * of q. The maximum value of q used in the library is q = 3 * P - 1 where + * P = 16 or P = 34 (so q <= 111 decimal digits). + * The partitioning is based on the following, where Kx is the scaled + * integer representing the value of 10^(-x) rounded up to a number of bits + * sufficient to ensure correct rounding: + * + * -------------------------------------------------------------------------- + * q x max. value of a max number min. number + * of bits in C of bits in Kx + * -------------------------------------------------------------------------- + * + * GROUP 1: 64 bits + * round64_2_18 () + * + * 2 [1,1] 10^1 - 1 < 2^3.33 4 4 + * ... ... ... ... ... + * 18 [1,17] 10^18 - 1 < 2^59.80 60 61 + * + * GROUP 2: 128 bits + * round128_19_38 () + * + * 19 [1,18] 10^19 - 1 < 2^63.11 64 65 + * 20 [1,19] 10^20 - 1 < 2^66.44 67 68 + * ... ... ... ... ... + * 38 [1,37] 10^38 - 1 < 2^126.24 127 128 + * + * GROUP 3: 192 bits + * round192_39_57 () + * + * 39 [1,38] 10^39 - 1 < 2^129.56 130 131 + * ... ... ... ... ... + * 57 [1,56] 10^57 - 1 < 2^189.35 190 191 + * + * GROUP 4: 256 bits + * round256_58_76 () + * + * 58 [1,57] 10^58 - 1 < 2^192.68 193 194 + * ... ... ... ... ... + * 76 [1,75] 10^76 - 1 < 2^252.47 253 254 + * + * GROUP 5: 320 bits + * round320_77_96 () + * + * 77 [1,76] 10^77 - 1 < 2^255.79 256 257 + * 78 [1,77] 10^78 - 1 < 2^259.12 260 261 + * ... ... ... ... ... + * 96 [1,95] 10^96 - 1 < 2^318.91 319 320 + * + * GROUP 6: 384 bits + * round384_97_115 () + * + * 97 [1,96] 10^97 - 1 < 2^322.23 323 324 + * ... ... ... ... ... + * 115 [1,114] 10^115 - 1 < 2^382.03 383 384 + * + ****************************************************************************/ + +#include "bid_internal.h" + +void +round64_2_18 (int q, + int x, + UINT64 C, + UINT64 * ptr_Cstar, + int *incr_exp, + int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint) { + + UINT128 P128; + UINT128 fstar; + UINT64 Cstar; + UINT64 tmp64; + int shift; + int ind; + + // Note: + // In round128_2_18() positive numbers with 2 <= q <= 18 will be + // rounded to nearest only for 1 <= x <= 3: + // x = 1 or x = 2 when q = 17 + // x = 2 or x = 3 when q = 18 + // However, for generality and possible uses outside the frame of IEEE 754R + // this implementation works for 1 <= x <= q - 1 + + // assume *ptr_is_midpoint_lt_even, *ptr_is_midpoint_gt_even, + // *ptr_is_inexact_lt_midpoint, and *ptr_is_inexact_gt_midpoint are + // initialized to 0 by the caller + + // round a number C with q decimal digits, 2 <= q <= 18 + // to q - x digits, 1 <= x <= 17 + // C = C + 1/2 * 10^x where the result C fits in 64 bits + // (because the largest value is 999999999999999999 + 50000000000000000 = + // 0x0e92596fd628ffff, which fits in 60 bits) + ind = x - 1; // 0 <= ind <= 16 + C = C + midpoint64[ind]; + // kx ~= 10^(-x), kx = Kx64[ind] * 2^(-Ex), 0 <= ind <= 16 + // P128 = (C + 1/2 * 10^x) * kx * 2^Ex = (C + 1/2 * 10^x) * Kx + // the approximation kx of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128MACH (P128, C, Kx64[ind]); + // calculate C* = floor (P128) and f* + // Cstar = P128 >> Ex + // fstar = low Ex bits of P128 + shift = Ex64m64[ind]; // in [3, 56] + Cstar = P128.w[1] >> shift; + fstar.w[1] = P128.w[1] & mask64[ind]; + fstar.w[0] = P128.w[0]; + // the top Ex bits of 10^(-x) are T* = ten2mxtrunc64[ind], e.g. + // if x=1, T*=ten2mxtrunc64[0]=0xcccccccccccccccc + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has q - x decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has q - x decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has q - x decimal digits, + // correct by Property 1) + // in the caling function n = C* * 10^(e+x) + + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (fstar.w[1] > half64[ind] || + (fstar.w[1] == half64[ind] && fstar.w[0])) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[1] - half64[ind]; + if (tmp64 || fstar.w[0] > ten2mxtrunc64[ind]) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + // check for midpoints (could do this before determining inexactness) + if (fstar.w[1] == 0 && fstar.w[0] <= ten2mxtrunc64[ind]) { + // the result is a midpoint + if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result may be 0 + Cstar--; // Cstar is now even + *ptr_is_midpoint_gt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + *ptr_is_midpoint_lt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } + } + // check for rounding overflow, which occurs if Cstar = 10^(q-x) + ind = q - x; // 1 <= ind <= q - 1 + if (Cstar == ten2k64[ind]) { // if Cstar = 10^(q-x) + Cstar = ten2k64[ind - 1]; // Cstar = 10^(q-x-1) + *incr_exp = 1; + } else { // 10^33 <= Cstar <= 10^34 - 1 + *incr_exp = 0; + } + *ptr_Cstar = Cstar; +} + + +void +round128_19_38 (int q, + int x, + UINT128 C, + UINT128 * ptr_Cstar, + int *incr_exp, + int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint) { + + UINT256 P256; + UINT256 fstar; + UINT128 Cstar; + UINT64 tmp64; + int shift; + int ind; + + // Note: + // In round128_19_38() positive numbers with 19 <= q <= 38 will be + // rounded to nearest only for 1 <= x <= 23: + // x = 3 or x = 4 when q = 19 + // x = 4 or x = 5 when q = 20 + // ... + // x = 18 or x = 19 when q = 34 + // x = 1 or x = 2 or x = 19 or x = 20 when q = 35 + // x = 2 or x = 3 or x = 20 or x = 21 when q = 36 + // x = 3 or x = 4 or x = 21 or x = 22 when q = 37 + // x = 4 or x = 5 or x = 22 or x = 23 when q = 38 + // However, for generality and possible uses outside the frame of IEEE 754R + // this implementation works for 1 <= x <= q - 1 + + // assume *ptr_is_midpoint_lt_even, *ptr_is_midpoint_gt_even, + // *ptr_is_inexact_lt_midpoint, and *ptr_is_inexact_gt_midpoint are + // initialized to 0 by the caller + + // round a number C with q decimal digits, 19 <= q <= 38 + // to q - x digits, 1 <= x <= 37 + // C = C + 1/2 * 10^x where the result C fits in 128 bits + // (because the largest value is 99999999999999999999999999999999999999 + + // 5000000000000000000000000000000000000 = + // 0x4efe43b0c573e7e68a043d8fffffffff, which fits is 127 bits) + + ind = x - 1; // 0 <= ind <= 36 + if (ind <= 18) { // if 0 <= ind <= 18 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint64[ind]; + if (C.w[0] < tmp64) + C.w[1]++; + } else { // if 19 <= ind <= 37 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint128[ind - 19].w[0]; + if (C.w[0] < tmp64) { + C.w[1]++; + } + C.w[1] = C.w[1] + midpoint128[ind - 19].w[1]; + } + // kx ~= 10^(-x), kx = Kx128[ind] * 2^(-Ex), 0 <= ind <= 36 + // P256 = (C + 1/2 * 10^x) * kx * 2^Ex = (C + 1/2 * 10^x) * Kx + // the approximation kx of 10^(-x) was rounded up to 128 bits + __mul_128x128_to_256 (P256, C, Kx128[ind]); + // calculate C* = floor (P256) and f* + // Cstar = P256 >> Ex + // fstar = low Ex bits of P256 + shift = Ex128m128[ind]; // in [2, 63] but have to consider two cases + if (ind <= 18) { // if 0 <= ind <= 18 + Cstar.w[0] = (P256.w[2] >> shift) | (P256.w[3] << (64 - shift)); + Cstar.w[1] = (P256.w[3] >> shift); + fstar.w[0] = P256.w[0]; + fstar.w[1] = P256.w[1]; + fstar.w[2] = P256.w[2] & mask128[ind]; + fstar.w[3] = 0x0ULL; + } else { // if 19 <= ind <= 37 + Cstar.w[0] = P256.w[3] >> shift; + Cstar.w[1] = 0x0ULL; + fstar.w[0] = P256.w[0]; + fstar.w[1] = P256.w[1]; + fstar.w[2] = P256.w[2]; + fstar.w[3] = P256.w[3] & mask128[ind]; + } + // the top Ex bits of 10^(-x) are T* = ten2mxtrunc64[ind], e.g. + // if x=1, T*=ten2mxtrunc128[0]=0xcccccccccccccccccccccccccccccccc + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has q - x decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has q - x decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has q - x decimal digits, + // correct by Property 1) + // in the caling function n = C* * 10^(e+x) + + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind <= 18) { // if 0 <= ind <= 18 + if (fstar.w[2] > half128[ind] || + (fstar.w[2] == half128[ind] && (fstar.w[1] || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[2] - half128[ind]; + if (tmp64 || fstar.w[1] > ten2mxtrunc128[ind].w[1] || (fstar.w[1] == ten2mxtrunc128[ind].w[1] && fstar.w[0] > ten2mxtrunc128[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } else { // if 19 <= ind <= 37 + if (fstar.w[3] > half128[ind] || (fstar.w[3] == half128[ind] && + (fstar.w[2] || fstar.w[1] + || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[3] - half128[ind]; + if (tmp64 || fstar.w[2] || fstar.w[1] > ten2mxtrunc128[ind].w[1] || (fstar.w[1] == ten2mxtrunc128[ind].w[1] && fstar.w[0] > ten2mxtrunc128[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } + // check for midpoints (could do this before determining inexactness) + if (fstar.w[3] == 0 && fstar.w[2] == 0 && + (fstar.w[1] < ten2mxtrunc128[ind].w[1] || + (fstar.w[1] == ten2mxtrunc128[ind].w[1] && + fstar.w[0] <= ten2mxtrunc128[ind].w[0]))) { + // the result is a midpoint + if (Cstar.w[0] & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result may be 0 + Cstar.w[0]--; // Cstar is now even + if (Cstar.w[0] == 0xffffffffffffffffULL) { + Cstar.w[1]--; + } + *ptr_is_midpoint_gt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + *ptr_is_midpoint_lt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } + } + // check for rounding overflow, which occurs if Cstar = 10^(q-x) + ind = q - x; // 1 <= ind <= q - 1 + if (ind <= 19) { + if (Cstar.w[1] == 0x0ULL && Cstar.w[0] == ten2k64[ind]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k64[ind - 1]; // Cstar = 10^(q-x-1) + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind == 20) { + // if ind = 20 + if (Cstar.w[1] == ten2k128[0].w[1] + && Cstar.w[0] == ten2k128[0].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k64[19]; // Cstar = 10^(q-x-1) + Cstar.w[1] = 0x0ULL; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else { // if 21 <= ind <= 37 + if (Cstar.w[1] == ten2k128[ind - 20].w[1] && + Cstar.w[0] == ten2k128[ind - 20].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k128[ind - 21].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k128[ind - 21].w[1]; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } + ptr_Cstar->w[1] = Cstar.w[1]; + ptr_Cstar->w[0] = Cstar.w[0]; +} + + +void +round192_39_57 (int q, + int x, + UINT192 C, + UINT192 * ptr_Cstar, + int *incr_exp, + int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint) { + + UINT384 P384; + UINT384 fstar; + UINT192 Cstar; + UINT64 tmp64; + int shift; + int ind; + + // Note: + // In round192_39_57() positive numbers with 39 <= q <= 57 will be + // rounded to nearest only for 5 <= x <= 42: + // x = 23 or x = 24 or x = 5 or x = 6 when q = 39 + // x = 24 or x = 25 or x = 6 or x = 7 when q = 40 + // ... + // x = 41 or x = 42 or x = 23 or x = 24 when q = 57 + // However, for generality and possible uses outside the frame of IEEE 754R + // this implementation works for 1 <= x <= q - 1 + + // assume *ptr_is_midpoint_lt_even, *ptr_is_midpoint_gt_even, + // *ptr_is_inexact_lt_midpoint, and *ptr_is_inexact_gt_midpoint are + // initialized to 0 by the caller + + // round a number C with q decimal digits, 39 <= q <= 57 + // to q - x digits, 1 <= x <= 56 + // C = C + 1/2 * 10^x where the result C fits in 192 bits + // (because the largest value is + // 999999999999999999999999999999999999999999999999999999999 + + // 50000000000000000000000000000000000000000000000000000000 = + // 0x2ad282f212a1da846afdaf18c034ff09da7fffffffffffff, which fits in 190 bits) + ind = x - 1; // 0 <= ind <= 55 + if (ind <= 18) { // if 0 <= ind <= 18 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint64[ind]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0) { + C.w[2]++; + } + } + } else if (ind <= 37) { // if 19 <= ind <= 37 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint128[ind - 19].w[0]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0) { + C.w[2]++; + } + } + tmp64 = C.w[1]; + C.w[1] = C.w[1] + midpoint128[ind - 19].w[1]; + if (C.w[1] < tmp64) { + C.w[2]++; + } + } else { // if 38 <= ind <= 57 (actually ind <= 55) + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint192[ind - 38].w[0]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0ull) { + C.w[2]++; + } + } + tmp64 = C.w[1]; + C.w[1] = C.w[1] + midpoint192[ind - 38].w[1]; + if (C.w[1] < tmp64) { + C.w[2]++; + } + C.w[2] = C.w[2] + midpoint192[ind - 38].w[2]; + } + // kx ~= 10^(-x), kx = Kx192[ind] * 2^(-Ex), 0 <= ind <= 55 + // P384 = (C + 1/2 * 10^x) * kx * 2^Ex = (C + 1/2 * 10^x) * Kx + // the approximation kx of 10^(-x) was rounded up to 192 bits + __mul_192x192_to_384 (P384, C, Kx192[ind]); + // calculate C* = floor (P384) and f* + // Cstar = P384 >> Ex + // fstar = low Ex bits of P384 + shift = Ex192m192[ind]; // in [1, 63] but have to consider three cases + if (ind <= 18) { // if 0 <= ind <= 18 + Cstar.w[2] = (P384.w[5] >> shift); + Cstar.w[1] = (P384.w[5] << (64 - shift)) | (P384.w[4] >> shift); + Cstar.w[0] = (P384.w[4] << (64 - shift)) | (P384.w[3] >> shift); + fstar.w[5] = 0x0ULL; + fstar.w[4] = 0x0ULL; + fstar.w[3] = P384.w[3] & mask192[ind]; + fstar.w[2] = P384.w[2]; + fstar.w[1] = P384.w[1]; + fstar.w[0] = P384.w[0]; + } else if (ind <= 37) { // if 19 <= ind <= 37 + Cstar.w[2] = 0x0ULL; + Cstar.w[1] = P384.w[5] >> shift; + Cstar.w[0] = (P384.w[5] << (64 - shift)) | (P384.w[4] >> shift); + fstar.w[5] = 0x0ULL; + fstar.w[4] = P384.w[4] & mask192[ind]; + fstar.w[3] = P384.w[3]; + fstar.w[2] = P384.w[2]; + fstar.w[1] = P384.w[1]; + fstar.w[0] = P384.w[0]; + } else { // if 38 <= ind <= 57 + Cstar.w[2] = 0x0ULL; + Cstar.w[1] = 0x0ULL; + Cstar.w[0] = P384.w[5] >> shift; + fstar.w[5] = P384.w[5] & mask192[ind]; + fstar.w[4] = P384.w[4]; + fstar.w[3] = P384.w[3]; + fstar.w[2] = P384.w[2]; + fstar.w[1] = P384.w[1]; + fstar.w[0] = P384.w[0]; + } + + // the top Ex bits of 10^(-x) are T* = ten2mxtrunc192[ind], e.g. if x=1, + // T*=ten2mxtrunc192[0]=0xcccccccccccccccccccccccccccccccccccccccccccccccc + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has q - x decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has q - x decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has q - x decimal digits, + // correct by Property 1) + // in the caling function n = C* * 10^(e+x) + + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind <= 18) { // if 0 <= ind <= 18 + if (fstar.w[3] > half192[ind] || (fstar.w[3] == half192[ind] && + (fstar.w[2] || fstar.w[1] + || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[3] - half192[ind]; + if (tmp64 || fstar.w[2] > ten2mxtrunc192[ind].w[2] || (fstar.w[2] == ten2mxtrunc192[ind].w[2] && fstar.w[1] > ten2mxtrunc192[ind].w[1]) || (fstar.w[2] == ten2mxtrunc192[ind].w[2] && fstar.w[1] == ten2mxtrunc192[ind].w[1] && fstar.w[0] > ten2mxtrunc192[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } else if (ind <= 37) { // if 19 <= ind <= 37 + if (fstar.w[4] > half192[ind] || (fstar.w[4] == half192[ind] && + (fstar.w[3] || fstar.w[2] + || fstar.w[1] || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[4] - half192[ind]; + if (tmp64 || fstar.w[3] || fstar.w[2] > ten2mxtrunc192[ind].w[2] || (fstar.w[2] == ten2mxtrunc192[ind].w[2] && fstar.w[1] > ten2mxtrunc192[ind].w[1]) || (fstar.w[2] == ten2mxtrunc192[ind].w[2] && fstar.w[1] == ten2mxtrunc192[ind].w[1] && fstar.w[0] > ten2mxtrunc192[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } else { // if 38 <= ind <= 55 + if (fstar.w[5] > half192[ind] || (fstar.w[5] == half192[ind] && + (fstar.w[4] || fstar.w[3] + || fstar.w[2] || fstar.w[1] + || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[5] - half192[ind]; + if (tmp64 || fstar.w[4] || fstar.w[3] || fstar.w[2] > ten2mxtrunc192[ind].w[2] || (fstar.w[2] == ten2mxtrunc192[ind].w[2] && fstar.w[1] > ten2mxtrunc192[ind].w[1]) || (fstar.w[2] == ten2mxtrunc192[ind].w[2] && fstar.w[1] == ten2mxtrunc192[ind].w[1] && fstar.w[0] > ten2mxtrunc192[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } + // check for midpoints (could do this before determining inexactness) + if (fstar.w[5] == 0 && fstar.w[4] == 0 && fstar.w[3] == 0 && + (fstar.w[2] < ten2mxtrunc192[ind].w[2] || + (fstar.w[2] == ten2mxtrunc192[ind].w[2] && + fstar.w[1] < ten2mxtrunc192[ind].w[1]) || + (fstar.w[2] == ten2mxtrunc192[ind].w[2] && + fstar.w[1] == ten2mxtrunc192[ind].w[1] && + fstar.w[0] <= ten2mxtrunc192[ind].w[0]))) { + // the result is a midpoint + if (Cstar.w[0] & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result may be 0 + Cstar.w[0]--; // Cstar is now even + if (Cstar.w[0] == 0xffffffffffffffffULL) { + Cstar.w[1]--; + if (Cstar.w[1] == 0xffffffffffffffffULL) { + Cstar.w[2]--; + } + } + *ptr_is_midpoint_gt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + *ptr_is_midpoint_lt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } + } + // check for rounding overflow, which occurs if Cstar = 10^(q-x) + ind = q - x; // 1 <= ind <= q - 1 + if (ind <= 19) { + if (Cstar.w[2] == 0x0ULL && Cstar.w[1] == 0x0ULL && + Cstar.w[0] == ten2k64[ind]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k64[ind - 1]; // Cstar = 10^(q-x-1) + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind == 20) { + // if ind = 20 + if (Cstar.w[2] == 0x0ULL && Cstar.w[1] == ten2k128[0].w[1] && + Cstar.w[0] == ten2k128[0].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k64[19]; // Cstar = 10^(q-x-1) + Cstar.w[1] = 0x0ULL; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind <= 38) { // if 21 <= ind <= 38 + if (Cstar.w[2] == 0x0ULL && Cstar.w[1] == ten2k128[ind - 20].w[1] && + Cstar.w[0] == ten2k128[ind - 20].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k128[ind - 21].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k128[ind - 21].w[1]; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind == 39) { + if (Cstar.w[2] == ten2k256[0].w[2] && Cstar.w[1] == ten2k256[0].w[1] + && Cstar.w[0] == ten2k256[0].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k128[18].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k128[18].w[1]; + Cstar.w[2] = 0x0ULL; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else { // if 40 <= ind <= 56 + if (Cstar.w[2] == ten2k256[ind - 39].w[2] && + Cstar.w[1] == ten2k256[ind - 39].w[1] && + Cstar.w[0] == ten2k256[ind - 39].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k256[ind - 40].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k256[ind - 40].w[1]; + Cstar.w[2] = ten2k256[ind - 40].w[2]; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } + ptr_Cstar->w[2] = Cstar.w[2]; + ptr_Cstar->w[1] = Cstar.w[1]; + ptr_Cstar->w[0] = Cstar.w[0]; +} + + +void +round256_58_76 (int q, + int x, + UINT256 C, + UINT256 * ptr_Cstar, + int *incr_exp, + int *ptr_is_midpoint_lt_even, + int *ptr_is_midpoint_gt_even, + int *ptr_is_inexact_lt_midpoint, + int *ptr_is_inexact_gt_midpoint) { + + UINT512 P512; + UINT512 fstar; + UINT256 Cstar; + UINT64 tmp64; + int shift; + int ind; + + // Note: + // In round256_58_76() positive numbers with 58 <= q <= 76 will be + // rounded to nearest only for 24 <= x <= 61: + // x = 42 or x = 43 or x = 24 or x = 25 when q = 58 + // x = 43 or x = 44 or x = 25 or x = 26 when q = 59 + // ... + // x = 60 or x = 61 or x = 42 or x = 43 when q = 76 + // However, for generality and possible uses outside the frame of IEEE 754R + // this implementation works for 1 <= x <= q - 1 + + // assume *ptr_is_midpoint_lt_even, *ptr_is_midpoint_gt_even, + // *ptr_is_inexact_lt_midpoint, and *ptr_is_inexact_gt_midpoint are + // initialized to 0 by the caller + + // round a number C with q decimal digits, 58 <= q <= 76 + // to q - x digits, 1 <= x <= 75 + // C = C + 1/2 * 10^x where the result C fits in 256 bits + // (because the largest value is 9999999999999999999999999999999999999999 + // 999999999999999999999999999999999999 + 500000000000000000000000000 + // 000000000000000000000000000000000000000000000000 = + // 0x1736ca15d27a56cae15cf0e7b403d1f2bd6ebb0a50dc83ffffffffffffffffff, + // which fits in 253 bits) + ind = x - 1; // 0 <= ind <= 74 + if (ind <= 18) { // if 0 <= ind <= 18 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint64[ind]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + } + } else if (ind <= 37) { // if 19 <= ind <= 37 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint128[ind - 19].w[0]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + } + tmp64 = C.w[1]; + C.w[1] = C.w[1] + midpoint128[ind - 19].w[1]; + if (C.w[1] < tmp64) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + } else if (ind <= 57) { // if 38 <= ind <= 57 + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint192[ind - 38].w[0]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0ull) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + } + tmp64 = C.w[1]; + C.w[1] = C.w[1] + midpoint192[ind - 38].w[1]; + if (C.w[1] < tmp64) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + tmp64 = C.w[2]; + C.w[2] = C.w[2] + midpoint192[ind - 38].w[2]; + if (C.w[2] < tmp64) { + C.w[3]++; + } + } else { // if 58 <= ind <= 76 (actually 58 <= ind <= 74) + tmp64 = C.w[0]; + C.w[0] = C.w[0] + midpoint256[ind - 58].w[0]; + if (C.w[0] < tmp64) { + C.w[1]++; + if (C.w[1] == 0x0ull) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + } + tmp64 = C.w[1]; + C.w[1] = C.w[1] + midpoint256[ind - 58].w[1]; + if (C.w[1] < tmp64) { + C.w[2]++; + if (C.w[2] == 0x0) { + C.w[3]++; + } + } + tmp64 = C.w[2]; + C.w[2] = C.w[2] + midpoint256[ind - 58].w[2]; + if (C.w[2] < tmp64) { + C.w[3]++; + } + C.w[3] = C.w[3] + midpoint256[ind - 58].w[3]; + } + // kx ~= 10^(-x), kx = Kx256[ind] * 2^(-Ex), 0 <= ind <= 74 + // P512 = (C + 1/2 * 10^x) * kx * 2^Ex = (C + 1/2 * 10^x) * Kx + // the approximation kx of 10^(-x) was rounded up to 192 bits + __mul_256x256_to_512 (P512, C, Kx256[ind]); + // calculate C* = floor (P512) and f* + // Cstar = P512 >> Ex + // fstar = low Ex bits of P512 + shift = Ex256m256[ind]; // in [0, 63] but have to consider four cases + if (ind <= 18) { // if 0 <= ind <= 18 + Cstar.w[3] = (P512.w[7] >> shift); + Cstar.w[2] = (P512.w[7] << (64 - shift)) | (P512.w[6] >> shift); + Cstar.w[1] = (P512.w[6] << (64 - shift)) | (P512.w[5] >> shift); + Cstar.w[0] = (P512.w[5] << (64 - shift)) | (P512.w[4] >> shift); + fstar.w[7] = 0x0ULL; + fstar.w[6] = 0x0ULL; + fstar.w[5] = 0x0ULL; + fstar.w[4] = P512.w[4] & mask256[ind]; + fstar.w[3] = P512.w[3]; + fstar.w[2] = P512.w[2]; + fstar.w[1] = P512.w[1]; + fstar.w[0] = P512.w[0]; + } else if (ind <= 37) { // if 19 <= ind <= 37 + Cstar.w[3] = 0x0ULL; + Cstar.w[2] = P512.w[7] >> shift; + Cstar.w[1] = (P512.w[7] << (64 - shift)) | (P512.w[6] >> shift); + Cstar.w[0] = (P512.w[6] << (64 - shift)) | (P512.w[5] >> shift); + fstar.w[7] = 0x0ULL; + fstar.w[6] = 0x0ULL; + fstar.w[5] = P512.w[5] & mask256[ind]; + fstar.w[4] = P512.w[4]; + fstar.w[3] = P512.w[3]; + fstar.w[2] = P512.w[2]; + fstar.w[1] = P512.w[1]; + fstar.w[0] = P512.w[0]; + } else if (ind <= 56) { // if 38 <= ind <= 56 + Cstar.w[3] = 0x0ULL; + Cstar.w[2] = 0x0ULL; + Cstar.w[1] = P512.w[7] >> shift; + Cstar.w[0] = (P512.w[7] << (64 - shift)) | (P512.w[6] >> shift); + fstar.w[7] = 0x0ULL; + fstar.w[6] = P512.w[6] & mask256[ind]; + fstar.w[5] = P512.w[5]; + fstar.w[4] = P512.w[4]; + fstar.w[3] = P512.w[3]; + fstar.w[2] = P512.w[2]; + fstar.w[1] = P512.w[1]; + fstar.w[0] = P512.w[0]; + } else if (ind == 57) { + Cstar.w[3] = 0x0ULL; + Cstar.w[2] = 0x0ULL; + Cstar.w[1] = 0x0ULL; + Cstar.w[0] = P512.w[7]; + fstar.w[7] = 0x0ULL; + fstar.w[6] = P512.w[6]; + fstar.w[5] = P512.w[5]; + fstar.w[4] = P512.w[4]; + fstar.w[3] = P512.w[3]; + fstar.w[2] = P512.w[2]; + fstar.w[1] = P512.w[1]; + fstar.w[0] = P512.w[0]; + } else { // if 58 <= ind <= 74 + Cstar.w[3] = 0x0ULL; + Cstar.w[2] = 0x0ULL; + Cstar.w[1] = 0x0ULL; + Cstar.w[0] = P512.w[7] >> shift; + fstar.w[7] = P512.w[7] & mask256[ind]; + fstar.w[6] = P512.w[6]; + fstar.w[5] = P512.w[5]; + fstar.w[4] = P512.w[4]; + fstar.w[3] = P512.w[3]; + fstar.w[2] = P512.w[2]; + fstar.w[1] = P512.w[1]; + fstar.w[0] = P512.w[0]; + } + + // the top Ex bits of 10^(-x) are T* = ten2mxtrunc256[ind], e.g. if x=1, + // T*=ten2mxtrunc256[0]= + // 0xcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has q - x decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has q - x decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has q - x decimal digits, + // correct by Property 1) + // in the caling function n = C* * 10^(e+x) + + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind <= 18) { // if 0 <= ind <= 18 + if (fstar.w[4] > half256[ind] || (fstar.w[4] == half256[ind] && + (fstar.w[3] || fstar.w[2] + || fstar.w[1] || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[4] - half256[ind]; + if (tmp64 || fstar.w[3] > ten2mxtrunc256[ind].w[2] || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] > ten2mxtrunc256[ind].w[2]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] > ten2mxtrunc256[ind].w[1]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] == ten2mxtrunc256[ind].w[1] && fstar.w[0] > ten2mxtrunc256[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } else if (ind <= 37) { // if 19 <= ind <= 37 + if (fstar.w[5] > half256[ind] || (fstar.w[5] == half256[ind] && + (fstar.w[4] || fstar.w[3] + || fstar.w[2] || fstar.w[1] + || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[5] - half256[ind]; + if (tmp64 || fstar.w[4] || fstar.w[3] > ten2mxtrunc256[ind].w[3] || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] > ten2mxtrunc256[ind].w[2]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] > ten2mxtrunc256[ind].w[1]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] == ten2mxtrunc256[ind].w[1] && fstar.w[0] > ten2mxtrunc256[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } else if (ind <= 57) { // if 38 <= ind <= 57 + if (fstar.w[6] > half256[ind] || (fstar.w[6] == half256[ind] && + (fstar.w[5] || fstar.w[4] + || fstar.w[3] || fstar.w[2] + || fstar.w[1] || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[6] - half256[ind]; + if (tmp64 || fstar.w[5] || fstar.w[4] || fstar.w[3] > ten2mxtrunc256[ind].w[3] || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] > ten2mxtrunc256[ind].w[2]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] > ten2mxtrunc256[ind].w[1]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] == ten2mxtrunc256[ind].w[1] && fstar.w[0] > ten2mxtrunc256[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } else { // if 58 <= ind <= 74 + if (fstar.w[7] > half256[ind] || (fstar.w[7] == half256[ind] && + (fstar.w[6] || fstar.w[5] + || fstar.w[4] || fstar.w[3] + || fstar.w[2] || fstar.w[1] + || fstar.w[0]))) { + // f* > 1/2 and the result may be exact + // Calculate f* - 1/2 + tmp64 = fstar.w[7] - half256[ind]; + if (tmp64 || fstar.w[6] || fstar.w[5] || fstar.w[4] || fstar.w[3] > ten2mxtrunc256[ind].w[3] || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] > ten2mxtrunc256[ind].w[2]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] > ten2mxtrunc256[ind].w[1]) || (fstar.w[3] == ten2mxtrunc256[ind].w[3] && fstar.w[2] == ten2mxtrunc256[ind].w[2] && fstar.w[1] == ten2mxtrunc256[ind].w[1] && fstar.w[0] > ten2mxtrunc256[ind].w[0])) { // f* - 1/2 > 10^(-x) + *ptr_is_inexact_lt_midpoint = 1; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + *ptr_is_inexact_gt_midpoint = 1; + } + } + // check for midpoints (could do this before determining inexactness) + if (fstar.w[7] == 0 && fstar.w[6] == 0 && + fstar.w[5] == 0 && fstar.w[4] == 0 && + (fstar.w[3] < ten2mxtrunc256[ind].w[3] || + (fstar.w[3] == ten2mxtrunc256[ind].w[3] && + fstar.w[2] < ten2mxtrunc256[ind].w[2]) || + (fstar.w[3] == ten2mxtrunc256[ind].w[3] && + fstar.w[2] == ten2mxtrunc256[ind].w[2] && + fstar.w[1] < ten2mxtrunc256[ind].w[1]) || + (fstar.w[3] == ten2mxtrunc256[ind].w[3] && + fstar.w[2] == ten2mxtrunc256[ind].w[2] && + fstar.w[1] == ten2mxtrunc256[ind].w[1] && + fstar.w[0] <= ten2mxtrunc256[ind].w[0]))) { + // the result is a midpoint + if (Cstar.w[0] & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + // if floor(C*) is odd C = floor(C*) - 1; the result may be 0 + Cstar.w[0]--; // Cstar is now even + if (Cstar.w[0] == 0xffffffffffffffffULL) { + Cstar.w[1]--; + if (Cstar.w[1] == 0xffffffffffffffffULL) { + Cstar.w[2]--; + if (Cstar.w[2] == 0xffffffffffffffffULL) { + Cstar.w[3]--; + } + } + } + *ptr_is_midpoint_gt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } else { // else MP in [ODD, EVEN] + *ptr_is_midpoint_lt_even = 1; + *ptr_is_inexact_lt_midpoint = 0; + *ptr_is_inexact_gt_midpoint = 0; + } + } + // check for rounding overflow, which occurs if Cstar = 10^(q-x) + ind = q - x; // 1 <= ind <= q - 1 + if (ind <= 19) { + if (Cstar.w[3] == 0x0ULL && Cstar.w[2] == 0x0ULL && + Cstar.w[1] == 0x0ULL && Cstar.w[0] == ten2k64[ind]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k64[ind - 1]; // Cstar = 10^(q-x-1) + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind == 20) { + // if ind = 20 + if (Cstar.w[3] == 0x0ULL && Cstar.w[2] == 0x0ULL && + Cstar.w[1] == ten2k128[0].w[1] + && Cstar.w[0] == ten2k128[0].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k64[19]; // Cstar = 10^(q-x-1) + Cstar.w[1] = 0x0ULL; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind <= 38) { // if 21 <= ind <= 38 + if (Cstar.w[3] == 0x0ULL && Cstar.w[2] == 0x0ULL && + Cstar.w[1] == ten2k128[ind - 20].w[1] && + Cstar.w[0] == ten2k128[ind - 20].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k128[ind - 21].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k128[ind - 21].w[1]; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind == 39) { + if (Cstar.w[3] == 0x0ULL && Cstar.w[2] == ten2k256[0].w[2] && + Cstar.w[1] == ten2k256[0].w[1] + && Cstar.w[0] == ten2k256[0].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k128[18].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k128[18].w[1]; + Cstar.w[2] = 0x0ULL; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } else if (ind <= 57) { // if 40 <= ind <= 57 + if (Cstar.w[3] == 0x0ULL && Cstar.w[2] == ten2k256[ind - 39].w[2] && + Cstar.w[1] == ten2k256[ind - 39].w[1] && + Cstar.w[0] == ten2k256[ind - 39].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k256[ind - 40].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k256[ind - 40].w[1]; + Cstar.w[2] = ten2k256[ind - 40].w[2]; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + // else if (ind == 58) is not needed becauae we do not have ten2k192[] yet + } else { // if 58 <= ind <= 77 (actually 58 <= ind <= 74) + if (Cstar.w[3] == ten2k256[ind - 39].w[3] && + Cstar.w[2] == ten2k256[ind - 39].w[2] && + Cstar.w[1] == ten2k256[ind - 39].w[1] && + Cstar.w[0] == ten2k256[ind - 39].w[0]) { + // if Cstar = 10^(q-x) + Cstar.w[0] = ten2k256[ind - 40].w[0]; // Cstar = 10^(q-x-1) + Cstar.w[1] = ten2k256[ind - 40].w[1]; + Cstar.w[2] = ten2k256[ind - 40].w[2]; + Cstar.w[3] = ten2k256[ind - 40].w[3]; + *incr_exp = 1; + } else { + *incr_exp = 0; + } + } + ptr_Cstar->w[3] = Cstar.w[3]; + ptr_Cstar->w[2] = Cstar.w[2]; + ptr_Cstar->w[1] = Cstar.w[1]; + ptr_Cstar->w[0] = Cstar.w[0]; + +} diff --git a/gcc-4.4.3/libgcc/config/libbid/bid_sqrt_macros.h b/gcc-4.4.3/libgcc/config/libbid/bid_sqrt_macros.h new file mode 100644 index 000000000..19150a227 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/libbid/bid_sqrt_macros.h @@ -0,0 +1,331 @@ +/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +. */ + +#ifndef _SQRT_MACROS_H_ +#define _SQRT_MACROS_H_ + +#define FENCE __fence + +#if DOUBLE_EXTENDED_ON + +extern BINARY80 SQRT80 (BINARY80); + + +__BID_INLINE__ UINT64 +short_sqrt128 (UINT128 A10) { + BINARY80 lx, ly, l64; + int_float f64; + + // 2^64 + f64.i = 0x5f800000; + l64 = (BINARY80) f64.d; + lx = (BINARY80) A10.w[1] * l64 + (BINARY80) A10.w[0]; + ly = SQRT80 (lx); + return (UINT64) ly; +} + + +__BID_INLINE__ void +long_sqrt128 (UINT128 * pCS, UINT256 C256) { + UINT256 C4; + UINT128 CS; + UINT64 X; + SINT64 SE; + BINARY80 l64, lm64, l128, lxL, lx, ly, lS, lSH, lSL, lE, l3, l2, + l1, l0, lp, lCl; + int_float fx, f64, fm64; + int *ple = (int *) &lx; + + // 2^64 + f64.i = 0x5f800000; + l64 = (BINARY80) f64.d; + + l128 = l64 * l64; + lx = l3 = (BINARY80) C256.w[3] * l64 * l128; + l2 = (BINARY80) C256.w[2] * l128; + lx = FENCE (lx + l2); + l1 = (BINARY80) C256.w[1] * l64; + lx = FENCE (lx + l1); + l0 = (BINARY80) C256.w[0]; + lx = FENCE (lx + l0); + // sqrt(C256) + lS = SQRT80 (lx); + + // get coefficient + // 2^(-64) + fm64.i = 0x1f800000; + lm64 = (BINARY80) fm64.d; + CS.w[1] = (UINT64) (lS * lm64); + CS.w[0] = (UINT64) (lS - (BINARY80) CS.w[1] * l64); + + /////////////////////////////////////// + // CAUTION! + // little endian code only + // add solution for big endian + ////////////////////////////////////// + lSH = lS; + *((UINT64 *) & lSH) &= 0xffffffff00000000ull; + + // correction for C256 rounding + lCl = FENCE (l3 - lx); + lCl = FENCE (lCl + l2); + lCl = FENCE (lCl + l1); + lCl = FENCE (lCl + l0); + + lSL = lS - lSH; + + ////////////////////////////////////////// + // Watch for compiler re-ordering + // + ///////////////////////////////////////// + // C256-S^2 + lxL = FENCE (lx - lSH * lSH); + lp = lSH * lSL; + lp += lp; + lxL = FENCE (lxL - lp); + lSL *= lSL; + lxL = FENCE (lxL - lSL); + lCl += lxL; + + // correction term + lE = lCl / (lS + lS); + + // get low part of coefficient + X = CS.w[0]; + if (lCl >= 0) { + SE = (SINT64) (lE); + CS.w[0] += SE; + if (CS.w[0] < X) + CS.w[1]++; + } else { + SE = (SINT64) (-lE); + CS.w[0] -= SE; + if (CS.w[0] > X) + CS.w[1]--; + } + + pCS->w[0] = CS.w[0]; + pCS->w[1] = CS.w[1]; +} + +#else + +extern double sqrt (double); + +__BID_INLINE__ UINT64 +short_sqrt128 (UINT128 A10) { + UINT256 ARS, ARS0, AE0, AE, S; + + UINT64 MY, ES, CY; + double lx, l64; + int_double f64, ly; + int ey, k; + + // 2^64 + f64.i = 0x43f0000000000000ull; + l64 = f64.d; + lx = (double) A10.w[1] * l64 + (double) A10.w[0]; + ly.d = 1.0 / sqrt (lx); + + MY = (ly.i & 0x000fffffffffffffull) | 0x0010000000000000ull; + ey = 0x3ff - (ly.i >> 52); + + // A10*RS^2 + __mul_64x128_to_192 (ARS0, MY, A10); + __mul_64x192_to_256 (ARS, MY, ARS0); + + // shr by 2*ey+40, to get a 64-bit value + k = (ey << 1) + 104 - 64; + if (k >= 128) { + if (k > 128) + ES = (ARS.w[2] >> (k - 128)) | (ARS.w[3] << (192 - k)); + else + ES = ARS.w[2]; + } else { + if (k >= 64) { + ARS.w[0] = ARS.w[1]; + ARS.w[1] = ARS.w[2]; + k -= 64; + } + if (k) { + __shr_128 (ARS, ARS, k); + } + ES = ARS.w[0]; + } + + ES = ((SINT64) ES) >> 1; + + if (((SINT64) ES) < 0) { + ES = -ES; + + // A*RS*eps (scaled by 2^64) + __mul_64x192_to_256 (AE0, ES, ARS0); + + AE.w[0] = AE0.w[1]; + AE.w[1] = AE0.w[2]; + AE.w[2] = AE0.w[3]; + + __add_carry_out (S.w[0], CY, ARS0.w[0], AE.w[0]); + __add_carry_in_out (S.w[1], CY, ARS0.w[1], AE.w[1], CY); + S.w[2] = ARS0.w[2] + AE.w[2] + CY; + } else { + // A*RS*eps (scaled by 2^64) + __mul_64x192_to_256 (AE0, ES, ARS0); + + AE.w[0] = AE0.w[1]; + AE.w[1] = AE0.w[2]; + AE.w[2] = AE0.w[3]; + + __sub_borrow_out (S.w[0], CY, ARS0.w[0], AE.w[0]); + __sub_borrow_in_out (S.w[1], CY, ARS0.w[1], AE.w[1], CY); + S.w[2] = ARS0.w[2] - AE.w[2] - CY; + } + + k = ey + 51; + + if (k >= 64) { + if (k >= 128) { + S.w[0] = S.w[2]; + S.w[1] = 0; + k -= 128; + } else { + S.w[0] = S.w[1]; + S.w[1] = S.w[2]; + } + k -= 64; + } + if (k) { + __shr_128 (S, S, k); + } + + + return (UINT64) ((S.w[0] + 1) >> 1); + +} + + + +__BID_INLINE__ void +long_sqrt128 (UINT128 * pCS, UINT256 C256) { + UINT512 ARS0, ARS; + UINT256 ARS00, AE, AE2, S; + UINT128 ES, ES2, ARS1; + UINT64 ES32, CY, MY; + double l64, l128, lx, l2, l1, l0; + int_double f64, ly; + int ey, k, k2; + + // 2^64 + f64.i = 0x43f0000000000000ull; + l64 = f64.d; + + l128 = l64 * l64; + lx = (double) C256.w[3] * l64 * l128; + l2 = (double) C256.w[2] * l128; + lx = FENCE (lx + l2); + l1 = (double) C256.w[1] * l64; + lx = FENCE (lx + l1); + l0 = (double) C256.w[0]; + lx = FENCE (lx + l0); + // sqrt(C256) + ly.d = 1.0 / sqrt (lx); + + MY = (ly.i & 0x000fffffffffffffull) | 0x0010000000000000ull; + ey = 0x3ff - (ly.i >> 52); + + // A10*RS^2, scaled by 2^(2*ey+104) + __mul_64x256_to_320 (ARS0, MY, C256); + __mul_64x320_to_384 (ARS, MY, ARS0); + + // shr by k=(2*ey+104)-128 + // expect k is in the range (192, 256) if result in [10^33, 10^34) + // apply an additional signed shift by 1 at the same time (to get eps=eps0/2) + k = (ey << 1) + 104 - 128 - 192; + k2 = 64 - k; + ES.w[0] = (ARS.w[3] >> (k + 1)) | (ARS.w[4] << (k2 - 1)); + ES.w[1] = (ARS.w[4] >> k) | (ARS.w[5] << k2); + ES.w[1] = ((SINT64) ES.w[1]) >> 1; + + // A*RS >> 192 (for error term computation) + ARS1.w[0] = ARS0.w[3]; + ARS1.w[1] = ARS0.w[4]; + + // A*RS>>64 + ARS00.w[0] = ARS0.w[1]; + ARS00.w[1] = ARS0.w[2]; + ARS00.w[2] = ARS0.w[3]; + ARS00.w[3] = ARS0.w[4]; + + if (((SINT64) ES.w[1]) < 0) { + ES.w[0] = -ES.w[0]; + ES.w[1] = -ES.w[1]; + if (ES.w[0]) + ES.w[1]--; + + // A*RS*eps + __mul_128x128_to_256 (AE, ES, ARS1); + + __add_carry_out (S.w[0], CY, ARS00.w[0], AE.w[0]); + __add_carry_in_out (S.w[1], CY, ARS00.w[1], AE.w[1], CY); + __add_carry_in_out (S.w[2], CY, ARS00.w[2], AE.w[2], CY); + S.w[3] = ARS00.w[3] + AE.w[3] + CY; + } else { + // A*RS*eps + __mul_128x128_to_256 (AE, ES, ARS1); + + __sub_borrow_out (S.w[0], CY, ARS00.w[0], AE.w[0]); + __sub_borrow_in_out (S.w[1], CY, ARS00.w[1], AE.w[1], CY); + __sub_borrow_in_out (S.w[2], CY, ARS00.w[2], AE.w[2], CY); + S.w[3] = ARS00.w[3] - AE.w[3] - CY; + } + + // 3/2*eps^2, scaled by 2^128 + ES32 = ES.w[1] + (ES.w[1] >> 1); + __mul_64x64_to_128 (ES2, ES32, ES.w[1]); + // A*RS*3/2*eps^2 + __mul_128x128_to_256 (AE2, ES2, ARS1); + + // result, scaled by 2^(ey+52-64) + __add_carry_out (S.w[0], CY, S.w[0], AE2.w[0]); + __add_carry_in_out (S.w[1], CY, S.w[1], AE2.w[1], CY); + __add_carry_in_out (S.w[2], CY, S.w[2], AE2.w[2], CY); + S.w[3] = S.w[3] + AE2.w[3] + CY; + + // k in (0, 64) + k = ey + 51 - 128; + k2 = 64 - k; + S.w[0] = (S.w[1] >> k) | (S.w[2] << k2); + S.w[1] = (S.w[2] >> k) | (S.w[3] << k2); + + // round to nearest + S.w[0]++; + if (!S.w[0]) + S.w[1]++; + + pCS->w[0] = (S.w[1] << 63) | (S.w[0] >> 1); + pCS->w[1] = S.w[1] >> 1; + +} + +#endif +#endif diff --git a/gcc-4.4.3/libgcc/config/rs6000/t-darwin b/gcc-4.4.3/libgcc/config/rs6000/t-darwin new file mode 100644 index 000000000..0afe837b4 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/rs6000/t-darwin @@ -0,0 +1 @@ +SHLIB_VERPFX = $(gcc_srcdir)/config/rs6000/darwin-libgcc diff --git a/gcc-4.4.3/libgcc/config/rs6000/t-ldbl128 b/gcc-4.4.3/libgcc/config/rs6000/t-ldbl128 new file mode 100644 index 000000000..bdd62f3cd --- /dev/null +++ b/gcc-4.4.3/libgcc/config/rs6000/t-ldbl128 @@ -0,0 +1,3 @@ +SHLIB_MAPFILES += $(gcc_srcdir)/config/rs6000/libgcc-ppc-glibc.ver + +HOST_LIBGCC2_CFLAGS += -mlong-double-128 diff --git a/gcc-4.4.3/libgcc/config/rs6000/t-ppccomm b/gcc-4.4.3/libgcc/config/rs6000/t-ppccomm new file mode 100644 index 000000000..1a711ebdb --- /dev/null +++ b/gcc-4.4.3/libgcc/config/rs6000/t-ppccomm @@ -0,0 +1,103 @@ +LIB2ADD_ST += crtsavfpr.S crtresfpr.S \ + crtsavgpr.S crtresgpr.S \ + crtresxfpr.S crtresxgpr.S \ + e500crtres32gpr.S \ + e500crtres64gpr.S \ + e500crtres64gprctr.S \ + e500crtrest32gpr.S \ + e500crtrest64gpr.S \ + e500crtresx32gpr.S \ + e500crtresx64gpr.S \ + e500crtsav32gpr.S \ + e500crtsav64gpr.S \ + e500crtsav64gprctr.S \ + e500crtsavg32gpr.S \ + e500crtsavg64gpr.S \ + e500crtsavg64gprctr.S + +EXTRA_PARTS += ecrti$(objext) ecrtn$(objext) ncrti$(objext) ncrtn$(objext) + +# We build {e,n}crti.o and {e,n}crtn.o, which serve to add begin and +# end labels to all of the special sections used when we link using gcc. + +# Assemble startup files. +ecrti.S: $(gcc_srcdir)/config/rs6000/eabi-ci.asm + cat $(gcc_srcdir)/config/rs6000/eabi-ci.asm >ecrti.S + +ecrtn.S: $(gcc_srcdir)/config/rs6000/eabi-cn.asm + cat $(gcc_srcdir)/config/rs6000/eabi-cn.asm >ecrtn.S + +ncrti.S: $(gcc_srcdir)/config/rs6000/sol-ci.asm + cat $(gcc_srcdir)/config/rs6000/sol-ci.asm >ncrti.S + +ncrtn.S: $(gcc_srcdir)/config/rs6000/sol-cn.asm + cat $(gcc_srcdir)/config/rs6000/sol-cn.asm >ncrtn.S + +crtsavfpr.S: $(gcc_srcdir)/config/rs6000/crtsavfpr.asm + cat $(gcc_srcdir)/config/rs6000/crtsavfpr.asm >crtsavfpr.S + +crtresfpr.S: $(gcc_srcdir)/config/rs6000/crtresfpr.asm + cat $(gcc_srcdir)/config/rs6000/crtresfpr.asm >crtresfpr.S + +crtsavgpr.S: $(gcc_srcdir)/config/rs6000/crtsavgpr.asm + cat $(gcc_srcdir)/config/rs6000/crtsavgpr.asm >crtsavgpr.S + +crtresgpr.S: $(gcc_srcdir)/config/rs6000/crtresgpr.asm + cat $(gcc_srcdir)/config/rs6000/crtresgpr.asm >crtresgpr.S + +crtresxfpr.S: $(gcc_srcdir)/config/rs6000/crtresxfpr.asm + cat $(gcc_srcdir)/config/rs6000/crtresxfpr.asm >crtresxfpr.S + +crtresxgpr.S: $(gcc_srcdir)/config/rs6000/crtresxgpr.asm + cat $(gcc_srcdir)/config/rs6000/crtresxgpr.asm >crtresxgpr.S + +e500crtres32gpr.S: $(gcc_srcdir)/config/rs6000/e500crtres32gpr.asm + cat $(gcc_srcdir)/config/rs6000/e500crtres32gpr.asm >e500crtres32gpr.S + +e500crtres64gpr.S: $(gcc_srcdir)/config/rs6000/e500crtres64gpr.asm + cat $(gcc_srcdir)/config/rs6000/e500crtres64gpr.asm >e500crtres64gpr.S + +e500crtres64gprctr.S: $(gcc_srcdir)/config/rs6000/e500crtres64gprctr.asm + cat $(gcc_srcdir)/config/rs6000/e500crtres64gprctr.asm >e500crtres64gprctr.S + +e500crtrest32gpr.S: $(gcc_srcdir)/config/rs6000/e500crtrest32gpr.asm + cat $(gcc_srcdir)/config/rs6000/e500crtrest32gpr.asm >e500crtrest32gpr.S + +e500crtrest64gpr.S: $(gcc_srcdir)/config/rs6000/e500crtrest64gpr.asm + cat $(gcc_srcdir)/config/rs6000/e500crtrest64gpr.asm >e500crtrest64gpr.S + +e500crtresx32gpr.S: $(gcc_srcdir)/config/rs6000/e500crtresx32gpr.asm + cat $(gcc_srcdir)/config/rs6000/e500crtresx32gpr.asm >e500crtresx32gpr.S + +e500crtresx64gpr.S: $(gcc_srcdir)/config/rs6000/e500crtresx64gpr.asm + cat $(gcc_srcdir)/config/rs6000/e500crtresx64gpr.asm >e500crtresx64gpr.S + +e500crtsav32gpr.S: $(gcc_srcdir)/config/rs6000/e500crtsav32gpr.asm + cat $(gcc_srcdir)/config/rs6000/e500crtsav32gpr.asm >e500crtsav32gpr.S + +e500crtsav64gpr.S: $(gcc_srcdir)/config/rs6000/e500crtsav64gpr.asm + cat $(gcc_srcdir)/config/rs6000/e500crtsav64gpr.asm >e500crtsav64gpr.S + +e500crtsav64gprctr.S: $(gcc_srcdir)/config/rs6000/e500crtsav64gprctr.asm + cat $(gcc_srcdir)/config/rs6000/e500crtsav64gprctr.asm >e500crtsav64gprctr.S + +e500crtsavg32gpr.S: $(gcc_srcdir)/config/rs6000/e500crtsavg32gpr.asm + cat $(gcc_srcdir)/config/rs6000/e500crtsavg32gpr.asm >e500crtsavg32gpr.S + +e500crtsavg64gpr.S: $(gcc_srcdir)/config/rs6000/e500crtsavg64gpr.asm + cat $(gcc_srcdir)/config/rs6000/e500crtsavg64gpr.asm >e500crtsavg64gpr.S + +e500crtsavg64gprctr.S: $(gcc_srcdir)/config/rs6000/e500crtsavg64gprctr.asm + cat $(gcc_srcdir)/config/rs6000/e500crtsavg64gprctr.asm >e500crtsavg64gprctr.S + +ecrti$(objext): ecrti.S + $(crt_compile) -c ecrti.S + +ecrtn$(objext): ecrtn.S + $(crt_compile) -c ecrtn.S + +ncrti$(objext): ncrti.S + $(crt_compile) -c ncrti.S + +ncrtn$(objext): ncrtn.S + $(crt_compile) -c ncrtn.S diff --git a/gcc-4.4.3/libgcc/config/sh/t-linux b/gcc-4.4.3/libgcc/config/sh/t-linux new file mode 100644 index 000000000..be0b12824 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/sh/t-linux @@ -0,0 +1,37 @@ +HOST_LIBGCC2_CFLAGS = -fpic -DNO_FPSCR_VALUES + +# Override t-slibgcc-elf-ver to export some libgcc symbols with +# the symbol versions that glibc used, and hide some lib1func +# routines which should not be called via PLT. We have to create +# the list from scratch. +SHLIB_MAPFILES = \ + $(gcc_srcdir)/libgcc-std.ver \ + $(gcc_srcdir)/config/sh/libgcc-excl.ver \ + $(gcc_srcdir)/config/sh/libgcc-glibc.ver + +# Override SHLIB_LINK and SHLIB_INSTALL to use linker script +# libgcc_s.so. +SHLIB_LINK = $(CC) $(LIBGCC2_CFLAGS) -shared -nodefaultlibs \ + -Wl,--soname=@shlib_base_name@.so.1 \ + -Wl,--version-script=@shlib_map_file@ \ + -o @multilib_dir@/@shlib_base_name@.so.1.tmp @multilib_flags@ \ + @shlib_objs@ -lc && \ + rm -f @multilib_dir@/@shlib_base_name@.so && \ + if [ -f @multilib_dir@/@shlib_base_name@.so.1 ]; then \ + mv -f @multilib_dir@/@shlib_base_name@.so.1 \ + @multilib_dir@/@shlib_base_name@.so.1.backup; \ + else true; fi && \ + mv @multilib_dir@/@shlib_base_name@.so.1.tmp \ + @multilib_dir@/@shlib_base_name@.so.1 && \ + (echo "/* GNU ld script"; \ + echo " Use the shared library, but some functions are only in"; \ + echo " the static library. */"; \ + echo "GROUP ( @shlib_base_name@.so.1 libgcc.a )" \ + ) > @multilib_dir@/@shlib_base_name@.so +SHLIB_INSTALL = \ + $(mkinstalldirs) $(DESTDIR)$(slibdir)@shlib_slibdir_qual@; \ + $(INSTALL_DATA) @multilib_dir@/@shlib_base_name@.so.1 \ + $(DESTDIR)$(slibdir)@shlib_slibdir_qual@/@shlib_base_name@.so.1; \ + rm -f $(DESTDIR)$(slibdir)@shlib_slibdir_qual@/@shlib_base_name@.so; \ + $(INSTALL_DATA) @multilib_dir@/@shlib_base_name@.so \ + $(DESTDIR)$(slibdir)@shlib_slibdir_qual@/@shlib_base_name@.so diff --git a/gcc-4.4.3/libgcc/config/sparc/t-crtfm b/gcc-4.4.3/libgcc/config/sparc/t-crtfm new file mode 100644 index 000000000..d6d616f17 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/sparc/t-crtfm @@ -0,0 +1,2 @@ +crtfastmath.o: $(gcc_srcdir)/config/sparc/crtfastmath.c + $(gcc_compile) -c $(gcc_srcdir)/config/sparc/crtfastmath.c diff --git a/gcc-4.4.3/libgcc/config/t-slibgcc-darwin b/gcc-4.4.3/libgcc/config/t-slibgcc-darwin new file mode 100644 index 000000000..3dd172367 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/t-slibgcc-darwin @@ -0,0 +1,122 @@ +# Build a shared libgcc library with the darwin linker. +SHLIB_SOVERSION = 1 +SHLIB_VERSTRING = -compatibility_version $(SHLIB_SOVERSION) -current_version $(SHLIB_SOVERSION).0 +SHLIB_EXT = .dylib +SHLIB_SUFFIX = `if test @multilib_dir@ = ppc64 ; then echo _@multilib_dir@ ; fi` +SHLIB_INSTALL_NAME = @shlib_base_name@$(SHLIB_SUFFIX).$(SHLIB_SOVERSION)$(SHLIB_EXT) +SHLIB_SONAME = @shlib_base_name@.$(SHLIB_SOVERSION)$(SHLIB_EXT) +SHLIB_SOLINK = @shlib_base_name@.so +SHLIB_MAP = @shlib_map_file@ +SHLIB_OBJS = @shlib_objs@ +SHLIB_DIR = @multilib_dir@ +SHLIB_LC = -lc + +# Darwin only searches in /usr/lib for shared libraries, not in subdirectories, +# so the libgcc variants have different names not different locations. +# Note that this version is used for the loader, not the linker; the linker +# uses the stub versions named by the versioned members of $(INSTALL_FILES). +SHLIB_LINK = $(CC) $(LIBGCC2_CFLAGS) -dynamiclib -nodefaultlibs \ + -install_name @shlib_slibdir@/$(SHLIB_INSTALL_NAME) \ + -single_module -o $(SHLIB_DIR)/$(SHLIB_SONAME).tmp \ + -Wl,-exported_symbols_list,$(SHLIB_MAP) \ + $(SHLIB_VERSTRING) \ + @multilib_flags@ $(SHLIB_OBJS) $(SHLIB_LC) + +SHLIB_MKMAP = $(gcc_srcdir)/mkmap-flat.awk +SHLIB_MKMAP_OPTS = -v leading_underscore=1 +SHLIB_MAPFILES += $(gcc_srcdir)/libgcc-std.ver + +INSTALL_FILES=libgcc_s.10.4.dylib libgcc_s.10.5.dylib libgcc_s.1.dylib + +# For the toplevel multilib, build a fat archive including all the multilibs. +ifeq ($(MULTIBUILDTOP),) + +SHLIB_INSTALL = \ + $(mkinstalldirs) $(DESTDIR)$(slibdir); \ + $(INSTALL_DATA) $(SHLIB_SONAME) \ + $(DESTDIR)$(slibdir)/$(SHLIB_SONAME) + +ifeq ($(enable_shared),yes) +all: $(INSTALL_FILES) +install-leaf: install-darwin-libgcc-stubs +endif + +# In order to support -mmacosx-version-min, you need to have multiple +# different libgcc_s libraries that actually get linked against, one for +# each system version supported. They are 'stub' libraries that +# contain no code, just a list of exported symbols. +# The actual use of the libraries is controlled by REAL_LIBGCC_SPEC. +# +# This assumes each multilib corresponds to a different architecture. +libgcc_s.%.dylib : $(SHLIB_VERPFX).%.ver libgcc_s$(SHLIB_EXT) all-multi + $(STRIP) -o $(@)_T \ + -s $(SHLIB_VERPFX).$(*).ver -c -u \ + ./libgcc_s.$(SHLIB_SOVERSION)$(SHLIB_EXT).tmp + MLIBS=`$(CC) --print-multi-lib \ + | sed -e 's/;.*$$//' -e '/^\.$$/d'` ; \ + for mlib in $$MLIBS ; do \ + $(STRIP) -o $(@)_T$${mlib} \ + -s $(SHLIB_VERPFX).$(*).ver -c -u \ + ../$${mlib}/libgcc/$${mlib}/libgcc_s.$(SHLIB_SOVERSION)$(SHLIB_EXT).tmp || exit 1 ; \ + done + $(LIPO) -output $@ -create $(@)_T* + rm $(@)_T* + +libgcc_s.$(SHLIB_SOVERSION)$(SHLIB_EXT): all-multi libgcc_s$(SHLIB_EXT) \ + libgcc_s.10.4.dylib libgcc_s.10.5.dylib + cp libgcc_s.$(SHLIB_SOVERSION)$(SHLIB_EXT).tmp \ + ./libgcc_s.$(SHLIB_SOVERSION)$(SHLIB_EXT)_T_ || exit 1 ; \ + MLIBS=`$(CC) --print-multi-lib \ + | sed -e 's/;.*$$//' -e '/^\.$$/d'` ; \ + for mlib in $$MLIBS ; do \ + cp ../$${mlib}/libgcc/$${mlib}/libgcc_s.$(SHLIB_SOVERSION)$(SHLIB_EXT).tmp \ + ./libgcc_s.$(SHLIB_SOVERSION)$(SHLIB_EXT)_T_$${mlib} || exit 1 ; \ + done + $(LIPO) -output libgcc_s.$(SHLIB_SOVERSION)$(SHLIB_EXT) \ + -create libgcc_s.$(SHLIB_SOVERSION)$(SHLIB_EXT)_T* + rm libgcc_s.$(SHLIB_SOVERSION)$(SHLIB_EXT)_T* + +install-darwin-libgcc-stubs : $(INSTALL_FILES) + $(mkinstalldirs) $(DESTDIR)$(slibdir) + for d in $(INSTALL_FILES) ; do \ + $(INSTALL_DATA) $$d $(DESTDIR)$(slibdir)/$$d || exit 1 ; \ + done + if [ -f $(DESTDIR)$(slibdir)/libgcc_s_ppc64.1.dylib ]; then \ + rm -f $(DESTDIR)$(slibdir)/libgcc_s_ppc64.1.dylib; \ + else true; fi + $(LN_S) libgcc_s.1.dylib \ + $(DESTDIR)$(slibdir)/libgcc_s_ppc64.1.dylib + if [ -f $(DESTDIR)$(slibdir)/libgcc_s_x86_64.1.dylib ]; then \ + rm -f $(DESTDIR)$(slibdir)/libgcc_s_x86_64.1.dylib; \ + else true; fi + $(LN_S) libgcc_s.1.dylib \ + $(DESTDIR)$(slibdir)/libgcc_s_x86_64.1.dylib + +else + +# Do not install shared libraries for any other multilibs. Unless +# we're putting them in the gcc directory during a build, for +# compatibility with the pre-top-level layout. In that case we +# need symlinks. +SHLIB_INSTALL = + +ifeq ($(enable_shared),yes) +all: install-darwin-libgcc-links +endif + +install-darwin-libgcc-links: + $(mkinstalldirs) $(gcc_objdir)$(MULTISUBDIR) + for file in $(INSTALL_FILES); do \ + rm -f $(gcc_objdir)$(MULTISUBDIR)/$$file; \ + $(LN_S) ../$$file $(gcc_objdir)$(MULTISUBDIR)/; \ + done + + rm -f $(gcc_objdir)$(MULTISUBDIR)/libgcc_s_x86_64.1.dylib + $(LN_S) libgcc_s.1.dylib \ + $(gcc_objdir)$(MULTISUBDIR)/libgcc_s_x86_64.1.dylib + + rm -f $(gcc_objdir)$(MULTISUBDIR)/libgcc_s_ppc64.1.dylib + $(LN_S) libgcc_s.1.dylib \ + $(gcc_objdir)$(MULTISUBDIR)/libgcc_s_ppc64.1.dylib + +endif diff --git a/gcc-4.4.3/libgcc/config/t-softfp b/gcc-4.4.3/libgcc/config/t-softfp new file mode 100644 index 000000000..5d67da017 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/t-softfp @@ -0,0 +1,14 @@ +# Disable missing prototype and type limit warnings. The prototypes +# for the functions in the soft-fp files have not been brought across +# from glibc. + +# cfr. srcdirify in gcc/Makefile.in +soft-fp-files = $(filter $(gcc_srcdir)/config/soft-fp/%, $(LIB2ADD)) \ + $(filter $(gcc_objdir)/config/soft-fp/%, $(LIB2ADD)) + +soft-fp-objects-base = $(basename $(notdir $(soft-fp-files))) + +soft-fp-objects = $(addsuffix $(objext), $(soft-fp-objects-base)) \ + $(addsuffix _s$(objext), $(soft-fp-objects-base)) + +$(soft-fp-objects) : INTERNAL_CFLAGS += -Wno-missing-prototypes -Wno-type-limits diff --git a/gcc-4.4.3/libgcc/config/t-tls b/gcc-4.4.3/libgcc/config/t-tls new file mode 100644 index 000000000..405128f78 --- /dev/null +++ b/gcc-4.4.3/libgcc/config/t-tls @@ -0,0 +1,2 @@ +# Use thread-local storage +INTERNAL_CFLAGS += -DUSE_TLS diff --git a/gcc-4.4.3/libgcc/configure b/gcc-4.4.3/libgcc/configure new file mode 100644 index 000000000..6315ecd5c --- /dev/null +++ b/gcc-4.4.3/libgcc/configure @@ -0,0 +1,4665 @@ +#! /bin/sh +# Guess values for system-dependent variables and create Makefiles. +# Generated by GNU Autoconf 2.59 for GNU C Runtime Library 1.0. +# +# Copyright (C) 2003 Free Software Foundation, Inc. +# This configure script is free software; the Free Software Foundation +# gives unlimited permission to copy, distribute and modify it. +## --------------------- ## +## M4sh Initialization. ## +## --------------------- ## + +# Be Bourne compatible +if test -n "${ZSH_VERSION+set}" && (emulate sh) >/dev/null 2>&1; then + emulate sh + NULLCMD=: + # Zsh 3.x and 4.x performs word splitting on ${1+"$@"}, which + # is contrary to our usage. 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Invocation command line was + + $ $0 $@ + +_ACEOF +{ +cat <<_ASUNAME +## --------- ## +## Platform. ## +## --------- ## + +hostname = `(hostname || uname -n) 2>/dev/null | sed 1q` +uname -m = `(uname -m) 2>/dev/null || echo unknown` +uname -r = `(uname -r) 2>/dev/null || echo unknown` +uname -s = `(uname -s) 2>/dev/null || echo unknown` +uname -v = `(uname -v) 2>/dev/null || echo unknown` + +/usr/bin/uname -p = `(/usr/bin/uname -p) 2>/dev/null || echo unknown` +/bin/uname -X = `(/bin/uname -X) 2>/dev/null || echo unknown` + +/bin/arch = `(/bin/arch) 2>/dev/null || echo unknown` +/usr/bin/arch -k = `(/usr/bin/arch -k) 2>/dev/null || echo unknown` +/usr/convex/getsysinfo = `(/usr/convex/getsysinfo) 2>/dev/null || echo unknown` +hostinfo = `(hostinfo) 2>/dev/null || echo unknown` +/bin/machine = `(/bin/machine) 2>/dev/null || echo unknown` +/usr/bin/oslevel = `(/usr/bin/oslevel) 2>/dev/null || echo unknown` +/bin/universe = `(/bin/universe) 2>/dev/null || echo unknown` + +_ASUNAME + +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + echo "PATH: $as_dir" +done + +} >&5 + +cat >&5 <<_ACEOF + + +## ----------- ## +## Core tests. ## +## ----------- ## + +_ACEOF + + +# Keep a trace of the command line. +# Strip out --no-create and --no-recursion so they do not pile up. +# Strip out --silent because we don't want to record it for future runs. +# Also quote any args containing shell meta-characters. +# Make two passes to allow for proper duplicate-argument suppression. +ac_configure_args= +ac_configure_args0= +ac_configure_args1= +ac_sep= +ac_must_keep_next=false +for ac_pass in 1 2 +do + for ac_arg + do + case $ac_arg in + -no-create | --no-c* | -n | -no-recursion | --no-r*) continue ;; + -q | -quiet | --quiet | --quie | --qui | --qu | --q \ + | -silent | --silent | --silen | --sile | --sil) + continue ;; + *" "*|*" "*|*[\[\]\~\#\$\^\&\*\(\)\{\}\\\|\;\<\>\?\"\']*) + ac_arg=`echo "$ac_arg" | sed "s/'/'\\\\\\\\''/g"` ;; + esac + case $ac_pass in + 1) ac_configure_args0="$ac_configure_args0 '$ac_arg'" ;; + 2) + ac_configure_args1="$ac_configure_args1 '$ac_arg'" + if test $ac_must_keep_next = true; then + ac_must_keep_next=false # Got value, back to normal. + else + case $ac_arg in + *=* | --config-cache | -C | -disable-* | --disable-* \ + | -enable-* | --enable-* | -gas | --g* | -nfp | --nf* \ + | -q | -quiet | --q* | -silent | --sil* | -v | -verb* \ + | -with-* | --with-* | -without-* | --without-* | --x) + case "$ac_configure_args0 " in + "$ac_configure_args1"*" '$ac_arg' "* ) continue ;; + esac + ;; + -* ) ac_must_keep_next=true ;; + esac + fi + ac_configure_args="$ac_configure_args$ac_sep'$ac_arg'" + # Get rid of the leading space. + ac_sep=" " + ;; + esac + done +done +$as_unset ac_configure_args0 || test "${ac_configure_args0+set}" != set || { ac_configure_args0=; export ac_configure_args0; } +$as_unset ac_configure_args1 || test "${ac_configure_args1+set}" != set || { ac_configure_args1=; export ac_configure_args1; } + +# When interrupted or exit'd, cleanup temporary files, and complete +# config.log. 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"$ac_site_file" + fi +done + +if test -r "$cache_file"; then + # Some versions of bash will fail to source /dev/null (special + # files actually), so we avoid doing that. + if test -f "$cache_file"; then + { echo "$as_me:$LINENO: loading cache $cache_file" >&5 +echo "$as_me: loading cache $cache_file" >&6;} + case $cache_file in + [\\/]* | ?:[\\/]* ) . $cache_file;; + *) . ./$cache_file;; + esac + fi +else + { echo "$as_me:$LINENO: creating cache $cache_file" >&5 +echo "$as_me: creating cache $cache_file" >&6;} + >$cache_file +fi + +# Check that the precious variables saved in the cache have kept the same +# value. +ac_cache_corrupted=false +for ac_var in `(set) 2>&1 | + sed -n 's/^ac_env_\([a-zA-Z_0-9]*\)_set=.*/\1/p'`; do + eval ac_old_set=\$ac_cv_env_${ac_var}_set + eval ac_new_set=\$ac_env_${ac_var}_set + eval ac_old_val="\$ac_cv_env_${ac_var}_value" + eval ac_new_val="\$ac_env_${ac_var}_value" + case $ac_old_set,$ac_new_set in + set,) + { echo "$as_me:$LINENO: error: \`$ac_var' was set to \`$ac_old_val' in the previous run" >&5 +echo "$as_me: error: \`$ac_var' was set to \`$ac_old_val' in the previous run" >&2;} + ac_cache_corrupted=: ;; + ,set) + { echo "$as_me:$LINENO: error: \`$ac_var' was not set in the previous run" >&5 +echo "$as_me: error: \`$ac_var' was not set in the previous run" >&2;} + ac_cache_corrupted=: ;; + ,);; + *) + if test "x$ac_old_val" != "x$ac_new_val"; then + # differences in whitespace do not lead to failure. + ac_old_val_w=`echo x $ac_old_val` + ac_new_val_w=`echo x $ac_new_val` + if test "$ac_old_val_w" != "$ac_new_val_w"; then + { echo "$as_me:$LINENO: error: \`$ac_var' has changed since the previous run:" >&5 +echo "$as_me: error: \`$ac_var' has changed since the previous run:" >&2;} + ac_cache_corrupted=: + else + { echo "$as_me:$LINENO: warning: ignoring whitespace changes in \`$ac_var' since the previous run:" >&5 +echo "$as_me: warning: ignoring whitespace changes in \`$ac_var' since the previous run:" >&2;} + eval $ac_var=\$ac_old_val + fi + { echo "$as_me:$LINENO: former value: \`$ac_old_val'" >&5 +echo "$as_me: former value: \`$ac_old_val'" >&2;} + { echo "$as_me:$LINENO: current value: \`$ac_new_val'" >&5 +echo "$as_me: current value: \`$ac_new_val'" >&2;} + fi;; + esac + # Pass precious variables to config.status. + if test "$ac_new_set" = set; then + case $ac_new_val in + *" "*|*" "*|*[\[\]\~\#\$\^\&\*\(\)\{\}\\\|\;\<\>\?\"\']*) + ac_arg=$ac_var=`echo "$ac_new_val" | sed "s/'/'\\\\\\\\''/g"` ;; + *) ac_arg=$ac_var=$ac_new_val ;; + esac + case " $ac_configure_args " in + *" '$ac_arg' "*) ;; # Avoid dups. Use of quotes ensures accuracy. + *) ac_configure_args="$ac_configure_args '$ac_arg'" ;; + esac + fi +done +if $ac_cache_corrupted; then + { echo "$as_me:$LINENO: error: in \`$ac_pwd':" >&5 +echo "$as_me: error: in \`$ac_pwd':" >&2;} + { echo "$as_me:$LINENO: error: changes in the environment can compromise the build" >&5 +echo "$as_me: error: changes in the environment can compromise the build" >&2;} + { { echo "$as_me:$LINENO: error: run \`make distclean' and/or \`rm $cache_file' and start over" >&5 +echo "$as_me: error: run \`make distclean' and/or \`rm $cache_file' and start over" >&2;} + { (exit 1); exit 1; }; } +fi + +ac_ext=c +ac_cpp='$CPP $CPPFLAGS' +ac_compile='$CC -c $CFLAGS $CPPFLAGS conftest.$ac_ext >&5' +ac_link='$CC -o conftest$ac_exeext $CFLAGS $CPPFLAGS $LDFLAGS conftest.$ac_ext $LIBS >&5' +ac_compiler_gnu=$ac_cv_c_compiler_gnu + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +# Check whether --with-target-subdir or --without-target-subdir was given. +if test "${with_target_subdir+set}" = set; then + withval="$with_target_subdir" + +fi; + +# Check whether --with-cross-host or --without-cross-host was given. +if test "${with_cross_host+set}" = set; then + withval="$with_cross_host" + +fi; + +# Check whether --with-ld or --without-ld was given. +if test "${with_ld+set}" = set; then + withval="$with_ld" + +fi; + +if test "${srcdir}" = "."; then + if test -n "${with_build_subdir}"; then + libgcc_topdir="${srcdir}/../.." + with_target_subdir= + elif test -z "${with_target_subdir}"; then + libgcc_topdir="${srcdir}/.." + else + if test "${with_target_subdir}" != "."; then + libgcc_topdir="${srcdir}/${with_multisrctop}../.." + else + libgcc_topdir="${srcdir}/${with_multisrctop}.." + fi + fi +else + libgcc_topdir="${srcdir}/.." +fi + +ac_aux_dir= +for ac_dir in $libgcc_topdir $srcdir/$libgcc_topdir; do + if test -f $ac_dir/install-sh; then + ac_aux_dir=$ac_dir + ac_install_sh="$ac_aux_dir/install-sh -c" + break + elif test -f $ac_dir/install.sh; then + ac_aux_dir=$ac_dir + ac_install_sh="$ac_aux_dir/install.sh -c" + break + elif test -f $ac_dir/shtool; then + ac_aux_dir=$ac_dir + ac_install_sh="$ac_aux_dir/shtool install -c" + break + fi +done +if test -z "$ac_aux_dir"; then + { { echo "$as_me:$LINENO: error: cannot find install-sh or install.sh in $libgcc_topdir $srcdir/$libgcc_topdir" >&5 +echo "$as_me: error: cannot find install-sh or install.sh in $libgcc_topdir $srcdir/$libgcc_topdir" >&2;} + { (exit 1); exit 1; }; } +fi +ac_config_guess="$SHELL $ac_aux_dir/config.guess" +ac_config_sub="$SHELL $ac_aux_dir/config.sub" +ac_configure="$SHELL $ac_aux_dir/configure" # This should be Cygnus configure. + + +# Check whether --enable-shared or --disable-shared was given. +if test "${enable_shared+set}" = set; then + enableval="$enable_shared" + + case $enable_shared in + yes | no) ;; + *) + enable_shared=no + IFS="${IFS= }"; ac_save_ifs="$IFS"; IFS="${IFS}:," + for pkg in $enableval; do + if test "X$pkg" = "Xgcc" || test "X$pkg" = "Xlibgcc"; then + enable_shared=yes + fi + done + IFS="$ac_save_ifs" + ;; + esac + +else + enable_shared=yes +fi; + + +echo "$as_me:$LINENO: checking for --enable-version-specific-runtime-libs" >&5 +echo $ECHO_N "checking for --enable-version-specific-runtime-libs... $ECHO_C" >&6 +# Check whether --enable-version-specific-runtime-libs or --disable-version-specific-runtime-libs was given. +if test "${enable_version_specific_runtime_libs+set}" = set; then + enableval="$enable_version_specific_runtime_libs" + case "$enableval" in + yes) version_specific_libs=yes ;; + no) version_specific_libs=no ;; + *) { { echo "$as_me:$LINENO: error: Unknown argument to enable/disable version-specific libs" >&5 +echo "$as_me: error: Unknown argument to enable/disable version-specific libs" >&2;} + { (exit 1); exit 1; }; };; + esac +else + version_specific_libs=no +fi; +echo "$as_me:$LINENO: result: $version_specific_libs" >&5 +echo "${ECHO_T}$version_specific_libs" >&6 + + +# Check whether --with-slibdir or --without-slibdir was given. +if test "${with_slibdir+set}" = set; then + withval="$with_slibdir" + slibdir="$with_slibdir" +else + if test "${version_specific_libs}" = yes; then + slibdir='$(libsubdir)' +elif test -n "$with_cross_host" && test x"$with_cross_host" != x"no"; then + slibdir='$(exec_prefix)/$(host_noncanonical)/lib' +else + slibdir='$(libdir)' +fi +fi; + + +# Find a good install program. We prefer a C program (faster), +# so one script is as good as another. But avoid the broken or +# incompatible versions: +# SysV /etc/install, /usr/sbin/install +# SunOS /usr/etc/install +# IRIX /sbin/install +# AIX /bin/install +# AmigaOS /C/install, which installs bootblocks on floppy discs +# AIX 4 /usr/bin/installbsd, which doesn't work without a -g flag +# AFS /usr/afsws/bin/install, which mishandles nonexistent args +# SVR4 /usr/ucb/install, which tries to use the nonexistent group "staff" +# OS/2's system install, which has a completely different semantic +# ./install, which can be erroneously created by make from ./install.sh. +echo "$as_me:$LINENO: checking for a BSD-compatible install" >&5 +echo $ECHO_N "checking for a BSD-compatible install... $ECHO_C" >&6 +if test -z "$INSTALL"; then +if test "${ac_cv_path_install+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + # Account for people who put trailing slashes in PATH elements. +case $as_dir/ in + ./ | .// | /cC/* | \ + /etc/* | /usr/sbin/* | /usr/etc/* | /sbin/* | /usr/afsws/bin/* | \ + ?:\\/os2\\/install\\/* | ?:\\/OS2\\/INSTALL\\/* | \ + /usr/ucb/* ) ;; + *) + # OSF1 and SCO ODT 3.0 have their own names for install. + # Don't use installbsd from OSF since it installs stuff as root + # by default. + for ac_prog in ginstall scoinst install; do + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_prog$ac_exec_ext"; then + if test $ac_prog = install && + grep dspmsg "$as_dir/$ac_prog$ac_exec_ext" >/dev/null 2>&1; then + # AIX install. It has an incompatible calling convention. + : + elif test $ac_prog = install && + grep pwplus "$as_dir/$ac_prog$ac_exec_ext" >/dev/null 2>&1; then + # program-specific install script used by HP pwplus--don't use. + : + else + ac_cv_path_install="$as_dir/$ac_prog$ac_exec_ext -c" + break 3 + fi + fi + done + done + ;; +esac +done + + +fi + if test "${ac_cv_path_install+set}" = set; then + INSTALL=$ac_cv_path_install + else + # As a last resort, use the slow shell script. We don't cache a + # path for INSTALL within a source directory, because that will + # break other packages using the cache if that directory is + # removed, or if the path is relative. + INSTALL=$ac_install_sh + fi +fi +echo "$as_me:$LINENO: result: $INSTALL" >&5 +echo "${ECHO_T}$INSTALL" >&6 + +# Use test -z because SunOS4 sh mishandles braces in ${var-val}. +# It thinks the first close brace ends the variable substitution. +test -z "$INSTALL_PROGRAM" && INSTALL_PROGRAM='${INSTALL}' + +test -z "$INSTALL_SCRIPT" && INSTALL_SCRIPT='${INSTALL}' + +test -z "$INSTALL_DATA" && INSTALL_DATA='${INSTALL} -m 644' + + +for ac_prog in gawk mawk nawk awk +do + # Extract the first word of "$ac_prog", so it can be a program name with args. +set dummy $ac_prog; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_AWK+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$AWK"; then + ac_cv_prog_AWK="$AWK" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_AWK="$ac_prog" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +AWK=$ac_cv_prog_AWK +if test -n "$AWK"; then + echo "$as_me:$LINENO: result: $AWK" >&5 +echo "${ECHO_T}$AWK" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + + test -n "$AWK" && break +done + +# We need awk; bail out if it's missing. +case ${AWK} in + "") { { echo "$as_me:$LINENO: error: can't build without awk, bailing out" >&5 +echo "$as_me: error: can't build without awk, bailing out" >&2;} + { (exit 1); exit 1; }; } ;; +esac + +# Make sure we can run config.sub. +$ac_config_sub sun4 >/dev/null 2>&1 || + { { echo "$as_me:$LINENO: error: cannot run $ac_config_sub" >&5 +echo "$as_me: error: cannot run $ac_config_sub" >&2;} + { (exit 1); exit 1; }; } + +echo "$as_me:$LINENO: checking build system type" >&5 +echo $ECHO_N "checking build system type... $ECHO_C" >&6 +if test "${ac_cv_build+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + ac_cv_build_alias=$build_alias +test -z "$ac_cv_build_alias" && + ac_cv_build_alias=`$ac_config_guess` +test -z "$ac_cv_build_alias" && + { { echo "$as_me:$LINENO: error: cannot guess build type; you must specify one" >&5 +echo "$as_me: error: cannot guess build type; you must specify one" >&2;} + { (exit 1); exit 1; }; } +ac_cv_build=`$ac_config_sub $ac_cv_build_alias` || + { { echo "$as_me:$LINENO: error: $ac_config_sub $ac_cv_build_alias failed" >&5 +echo "$as_me: error: $ac_config_sub $ac_cv_build_alias failed" >&2;} + { (exit 1); exit 1; }; } + +fi +echo "$as_me:$LINENO: result: $ac_cv_build" >&5 +echo "${ECHO_T}$ac_cv_build" >&6 +build=$ac_cv_build +build_cpu=`echo $ac_cv_build | sed 's/^\([^-]*\)-\([^-]*\)-\(.*\)$/\1/'` +build_vendor=`echo $ac_cv_build | sed 's/^\([^-]*\)-\([^-]*\)-\(.*\)$/\2/'` +build_os=`echo $ac_cv_build | sed 's/^\([^-]*\)-\([^-]*\)-\(.*\)$/\3/'` + + +echo "$as_me:$LINENO: checking host system type" >&5 +echo $ECHO_N "checking host system type... $ECHO_C" >&6 +if test "${ac_cv_host+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + ac_cv_host_alias=$host_alias +test -z "$ac_cv_host_alias" && + ac_cv_host_alias=$ac_cv_build_alias +ac_cv_host=`$ac_config_sub $ac_cv_host_alias` || + { { echo "$as_me:$LINENO: error: $ac_config_sub $ac_cv_host_alias failed" >&5 +echo "$as_me: error: $ac_config_sub $ac_cv_host_alias failed" >&2;} + { (exit 1); exit 1; }; } + +fi +echo "$as_me:$LINENO: result: $ac_cv_host" >&5 +echo "${ECHO_T}$ac_cv_host" >&6 +host=$ac_cv_host +host_cpu=`echo $ac_cv_host | sed 's/^\([^-]*\)-\([^-]*\)-\(.*\)$/\1/'` +host_vendor=`echo $ac_cv_host | sed 's/^\([^-]*\)-\([^-]*\)-\(.*\)$/\2/'` +host_os=`echo $ac_cv_host | sed 's/^\([^-]*\)-\([^-]*\)-\(.*\)$/\3/'` + + + case ${build_alias} in + "") build_noncanonical=${build} ;; + *) build_noncanonical=${build_alias} ;; +esac + + case ${host_alias} in + "") host_noncanonical=${build_noncanonical} ;; + *) host_noncanonical=${host_alias} ;; +esac + + + + case ${target_alias} in + "") target_noncanonical=${host_noncanonical} ;; + *) target_noncanonical=${target_alias} ;; +esac + + +# post-stage1 host modules use a different CC_FOR_BUILD so, in order to +# have matching libraries, they should use host libraries: Makefile.tpl +# arranges to pass --with-build-libsubdir=$(HOST_SUBDIR). +# However, they still use the build modules, because the corresponding +# host modules (e.g. bison) are only built for the host when bootstrap +# finishes. So: +# - build_subdir is where we find build modules, and never changes. +# - build_libsubdir is where we find build libraries, and can be overridden. + +# Prefix 'build-' so this never conflicts with target_subdir. +build_subdir="build-${build_noncanonical}" + +# Check whether --with-build-libsubdir or --without-build-libsubdir was given. +if test "${with_build_libsubdir+set}" = set; then + withval="$with_build_libsubdir" + build_libsubdir="$withval" +else + build_libsubdir="$build_subdir" +fi; +# --srcdir=. covers the toplevel, while "test -d" covers the subdirectories +if ( test $srcdir = . && test -d gcc ) \ + || test -d $srcdir/../host-${host_noncanonical}; then + host_subdir="host-${host_noncanonical}" +else + host_subdir=. +fi +# No prefix. +target_subdir=${target_noncanonical} + + +if test -n "$ac_tool_prefix"; then + # Extract the first word of "${ac_tool_prefix}ar", so it can be a program name with args. +set dummy ${ac_tool_prefix}ar; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_AR+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$AR"; then + ac_cv_prog_AR="$AR" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_AR="${ac_tool_prefix}ar" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +AR=$ac_cv_prog_AR +if test -n "$AR"; then + echo "$as_me:$LINENO: result: $AR" >&5 +echo "${ECHO_T}$AR" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + +fi +if test -z "$ac_cv_prog_AR"; then + ac_ct_AR=$AR + # Extract the first word of "ar", so it can be a program name with args. +set dummy ar; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_ac_ct_AR+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$ac_ct_AR"; then + ac_cv_prog_ac_ct_AR="$ac_ct_AR" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_ac_ct_AR="ar" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +ac_ct_AR=$ac_cv_prog_ac_ct_AR +if test -n "$ac_ct_AR"; then + echo "$as_me:$LINENO: result: $ac_ct_AR" >&5 +echo "${ECHO_T}$ac_ct_AR" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + + AR=$ac_ct_AR +else + AR="$ac_cv_prog_AR" +fi + +if test -n "$ac_tool_prefix"; then + # Extract the first word of "${ac_tool_prefix}lipo", so it can be a program name with args. +set dummy ${ac_tool_prefix}lipo; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_LIPO+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$LIPO"; then + ac_cv_prog_LIPO="$LIPO" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_LIPO="${ac_tool_prefix}lipo" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +LIPO=$ac_cv_prog_LIPO +if test -n "$LIPO"; then + echo "$as_me:$LINENO: result: $LIPO" >&5 +echo "${ECHO_T}$LIPO" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + +fi +if test -z "$ac_cv_prog_LIPO"; then + ac_ct_LIPO=$LIPO + # Extract the first word of "lipo", so it can be a program name with args. +set dummy lipo; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_ac_ct_LIPO+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$ac_ct_LIPO"; then + ac_cv_prog_ac_ct_LIPO="$ac_ct_LIPO" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_ac_ct_LIPO="lipo" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + + test -z "$ac_cv_prog_ac_ct_LIPO" && ac_cv_prog_ac_ct_LIPO=":" +fi +fi +ac_ct_LIPO=$ac_cv_prog_ac_ct_LIPO +if test -n "$ac_ct_LIPO"; then + echo "$as_me:$LINENO: result: $ac_ct_LIPO" >&5 +echo "${ECHO_T}$ac_ct_LIPO" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + + LIPO=$ac_ct_LIPO +else + LIPO="$ac_cv_prog_LIPO" +fi + +if test -n "$ac_tool_prefix"; then + # Extract the first word of "${ac_tool_prefix}nm", so it can be a program name with args. +set dummy ${ac_tool_prefix}nm; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_NM+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$NM"; then + ac_cv_prog_NM="$NM" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_NM="${ac_tool_prefix}nm" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +NM=$ac_cv_prog_NM +if test -n "$NM"; then + echo "$as_me:$LINENO: result: $NM" >&5 +echo "${ECHO_T}$NM" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + +fi +if test -z "$ac_cv_prog_NM"; then + ac_ct_NM=$NM + # Extract the first word of "nm", so it can be a program name with args. +set dummy nm; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_ac_ct_NM+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$ac_ct_NM"; then + ac_cv_prog_ac_ct_NM="$ac_ct_NM" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_ac_ct_NM="nm" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +ac_ct_NM=$ac_cv_prog_ac_ct_NM +if test -n "$ac_ct_NM"; then + echo "$as_me:$LINENO: result: $ac_ct_NM" >&5 +echo "${ECHO_T}$ac_ct_NM" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + + NM=$ac_ct_NM +else + NM="$ac_cv_prog_NM" +fi + +if test -n "$ac_tool_prefix"; then + # Extract the first word of "${ac_tool_prefix}ranlib", so it can be a program name with args. +set dummy ${ac_tool_prefix}ranlib; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_RANLIB+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$RANLIB"; then + ac_cv_prog_RANLIB="$RANLIB" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_RANLIB="${ac_tool_prefix}ranlib" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +RANLIB=$ac_cv_prog_RANLIB +if test -n "$RANLIB"; then + echo "$as_me:$LINENO: result: $RANLIB" >&5 +echo "${ECHO_T}$RANLIB" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + +fi +if test -z "$ac_cv_prog_RANLIB"; then + ac_ct_RANLIB=$RANLIB + # Extract the first word of "ranlib", so it can be a program name with args. +set dummy ranlib; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_ac_ct_RANLIB+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$ac_ct_RANLIB"; then + ac_cv_prog_ac_ct_RANLIB="$ac_ct_RANLIB" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_ac_ct_RANLIB="ranlib" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + + test -z "$ac_cv_prog_ac_ct_RANLIB" && ac_cv_prog_ac_ct_RANLIB=":" +fi +fi +ac_ct_RANLIB=$ac_cv_prog_ac_ct_RANLIB +if test -n "$ac_ct_RANLIB"; then + echo "$as_me:$LINENO: result: $ac_ct_RANLIB" >&5 +echo "${ECHO_T}$ac_ct_RANLIB" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + + RANLIB=$ac_ct_RANLIB +else + RANLIB="$ac_cv_prog_RANLIB" +fi + +if test -n "$ac_tool_prefix"; then + # Extract the first word of "${ac_tool_prefix}strip", so it can be a program name with args. +set dummy ${ac_tool_prefix}strip; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_STRIP+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$STRIP"; then + ac_cv_prog_STRIP="$STRIP" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_STRIP="${ac_tool_prefix}strip" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +STRIP=$ac_cv_prog_STRIP +if test -n "$STRIP"; then + echo "$as_me:$LINENO: result: $STRIP" >&5 +echo "${ECHO_T}$STRIP" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + +fi +if test -z "$ac_cv_prog_STRIP"; then + ac_ct_STRIP=$STRIP + # Extract the first word of "strip", so it can be a program name with args. +set dummy strip; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_ac_ct_STRIP+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$ac_ct_STRIP"; then + ac_cv_prog_ac_ct_STRIP="$ac_ct_STRIP" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_ac_ct_STRIP="strip" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + + test -z "$ac_cv_prog_ac_ct_STRIP" && ac_cv_prog_ac_ct_STRIP=":" +fi +fi +ac_ct_STRIP=$ac_cv_prog_ac_ct_STRIP +if test -n "$ac_ct_STRIP"; then + echo "$as_me:$LINENO: result: $ac_ct_STRIP" >&5 +echo "${ECHO_T}$ac_ct_STRIP" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + + STRIP=$ac_ct_STRIP +else + STRIP="$ac_cv_prog_STRIP" +fi + +echo "$as_me:$LINENO: checking whether ln -s works" >&5 +echo $ECHO_N "checking whether ln -s works... $ECHO_C" >&6 +LN_S=$as_ln_s +if test "$LN_S" = "ln -s"; then + echo "$as_me:$LINENO: result: yes" >&5 +echo "${ECHO_T}yes" >&6 +else + echo "$as_me:$LINENO: result: no, using $LN_S" >&5 +echo "${ECHO_T}no, using $LN_S" >&6 +fi + + + +ac_ext=c +ac_cpp='$CPP $CPPFLAGS' +ac_compile='$CC -c $CFLAGS $CPPFLAGS conftest.$ac_ext >&5' +ac_link='$CC -o conftest$ac_exeext $CFLAGS $CPPFLAGS $LDFLAGS conftest.$ac_ext $LIBS >&5' +ac_compiler_gnu=$ac_cv_c_compiler_gnu +if test -n "$ac_tool_prefix"; then + # Extract the first word of "${ac_tool_prefix}gcc", so it can be a program name with args. +set dummy ${ac_tool_prefix}gcc; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_CC+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$CC"; then + ac_cv_prog_CC="$CC" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_CC="${ac_tool_prefix}gcc" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +CC=$ac_cv_prog_CC +if test -n "$CC"; then + echo "$as_me:$LINENO: result: $CC" >&5 +echo "${ECHO_T}$CC" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + +fi +if test -z "$ac_cv_prog_CC"; then + ac_ct_CC=$CC + # Extract the first word of "gcc", so it can be a program name with args. +set dummy gcc; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_ac_ct_CC+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$ac_ct_CC"; then + ac_cv_prog_ac_ct_CC="$ac_ct_CC" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_ac_ct_CC="gcc" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +ac_ct_CC=$ac_cv_prog_ac_ct_CC +if test -n "$ac_ct_CC"; then + echo "$as_me:$LINENO: result: $ac_ct_CC" >&5 +echo "${ECHO_T}$ac_ct_CC" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + + CC=$ac_ct_CC +else + CC="$ac_cv_prog_CC" +fi + +if test -z "$CC"; then + if test -n "$ac_tool_prefix"; then + # Extract the first word of "${ac_tool_prefix}cc", so it can be a program name with args. +set dummy ${ac_tool_prefix}cc; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_CC+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$CC"; then + ac_cv_prog_CC="$CC" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_CC="${ac_tool_prefix}cc" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +CC=$ac_cv_prog_CC +if test -n "$CC"; then + echo "$as_me:$LINENO: result: $CC" >&5 +echo "${ECHO_T}$CC" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + +fi +if test -z "$ac_cv_prog_CC"; then + ac_ct_CC=$CC + # Extract the first word of "cc", so it can be a program name with args. +set dummy cc; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_ac_ct_CC+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$ac_ct_CC"; then + ac_cv_prog_ac_ct_CC="$ac_ct_CC" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_ac_ct_CC="cc" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +ac_ct_CC=$ac_cv_prog_ac_ct_CC +if test -n "$ac_ct_CC"; then + echo "$as_me:$LINENO: result: $ac_ct_CC" >&5 +echo "${ECHO_T}$ac_ct_CC" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + + CC=$ac_ct_CC +else + CC="$ac_cv_prog_CC" +fi + +fi +if test -z "$CC"; then + # Extract the first word of "cc", so it can be a program name with args. +set dummy cc; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_CC+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$CC"; then + ac_cv_prog_CC="$CC" # Let the user override the test. +else + ac_prog_rejected=no +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + if test "$as_dir/$ac_word$ac_exec_ext" = "/usr/ucb/cc"; then + ac_prog_rejected=yes + continue + fi + ac_cv_prog_CC="cc" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +if test $ac_prog_rejected = yes; then + # We found a bogon in the path, so make sure we never use it. + set dummy $ac_cv_prog_CC + shift + if test $# != 0; then + # We chose a different compiler from the bogus one. + # However, it has the same basename, so the bogon will be chosen + # first if we set CC to just the basename; use the full file name. + shift + ac_cv_prog_CC="$as_dir/$ac_word${1+' '}$@" + fi +fi +fi +fi +CC=$ac_cv_prog_CC +if test -n "$CC"; then + echo "$as_me:$LINENO: result: $CC" >&5 +echo "${ECHO_T}$CC" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + +fi +if test -z "$CC"; then + if test -n "$ac_tool_prefix"; then + for ac_prog in cl + do + # Extract the first word of "$ac_tool_prefix$ac_prog", so it can be a program name with args. +set dummy $ac_tool_prefix$ac_prog; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_CC+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$CC"; then + ac_cv_prog_CC="$CC" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_CC="$ac_tool_prefix$ac_prog" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +CC=$ac_cv_prog_CC +if test -n "$CC"; then + echo "$as_me:$LINENO: result: $CC" >&5 +echo "${ECHO_T}$CC" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + + test -n "$CC" && break + done +fi +if test -z "$CC"; then + ac_ct_CC=$CC + for ac_prog in cl +do + # Extract the first word of "$ac_prog", so it can be a program name with args. +set dummy $ac_prog; ac_word=$2 +echo "$as_me:$LINENO: checking for $ac_word" >&5 +echo $ECHO_N "checking for $ac_word... $ECHO_C" >&6 +if test "${ac_cv_prog_ac_ct_CC+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + if test -n "$ac_ct_CC"; then + ac_cv_prog_ac_ct_CC="$ac_ct_CC" # Let the user override the test. +else +as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for ac_exec_ext in '' $ac_executable_extensions; do + if $as_executable_p "$as_dir/$ac_word$ac_exec_ext"; then + ac_cv_prog_ac_ct_CC="$ac_prog" + echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 + break 2 + fi +done +done + +fi +fi +ac_ct_CC=$ac_cv_prog_ac_ct_CC +if test -n "$ac_ct_CC"; then + echo "$as_me:$LINENO: result: $ac_ct_CC" >&5 +echo "${ECHO_T}$ac_ct_CC" >&6 +else + echo "$as_me:$LINENO: result: no" >&5 +echo "${ECHO_T}no" >&6 +fi + + test -n "$ac_ct_CC" && break +done + + CC=$ac_ct_CC +fi + +fi + + +test -z "$CC" && { { echo "$as_me:$LINENO: error: in \`$ac_pwd':" >&5 +echo "$as_me: error: in \`$ac_pwd':" >&2;} +{ { echo "$as_me:$LINENO: error: no acceptable C compiler found in \$PATH +See \`config.log' for more details." >&5 +echo "$as_me: error: no acceptable C compiler found in \$PATH +See \`config.log' for more details." >&2;} + { (exit 1); exit 1; }; }; } + +# Provide some information about the compiler. +echo "$as_me:$LINENO:" \ + "checking for C compiler version" >&5 +ac_compiler=`set X $ac_compile; echo $2` +{ (eval echo "$as_me:$LINENO: \"$ac_compiler --version &5\"") >&5 + (eval $ac_compiler --version &5) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } +{ (eval echo "$as_me:$LINENO: \"$ac_compiler -v &5\"") >&5 + (eval $ac_compiler -v &5) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } +{ (eval echo "$as_me:$LINENO: \"$ac_compiler -V &5\"") >&5 + (eval $ac_compiler -V &5) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } + +cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ + +int +main () +{ + + ; + return 0; +} +_ACEOF +# FIXME: Cleanup? +if { (eval echo "$as_me:$LINENO: \"$ac_link\"") >&5 + (eval $ac_link) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; then + gcc_no_link=no +else + gcc_no_link=yes +fi + +if test x$gcc_no_link = xyes; then + # Setting cross_compile will disable run tests; it will + # also disable AC_CHECK_FILE but that's generally + # correct if we can't link. + cross_compiling=yes + EXEEXT= +else + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ + +int +main () +{ + + ; + return 0; +} +_ACEOF +ac_clean_files_save=$ac_clean_files +ac_clean_files="$ac_clean_files a.out a.exe b.out" +# Try to create an executable without -o first, disregard a.out. +# It will help us diagnose broken compilers, and finding out an intuition +# of exeext. +echo "$as_me:$LINENO: checking for C compiler default output file name" >&5 +echo $ECHO_N "checking for C compiler default output file name... $ECHO_C" >&6 +ac_link_default=`echo "$ac_link" | sed 's/ -o *conftest[^ ]*//'` +if { (eval echo "$as_me:$LINENO: \"$ac_link_default\"") >&5 + (eval $ac_link_default) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; then + # Find the output, starting from the most likely. This scheme is +# not robust to junk in `.', hence go to wildcards (a.*) only as a last +# resort. + +# Be careful to initialize this variable, since it used to be cached. +# Otherwise an old cache value of `no' led to `EXEEXT = no' in a Makefile. +ac_cv_exeext= +# b.out is created by i960 compilers. +for ac_file in a_out.exe a.exe conftest.exe a.out conftest a.* conftest.* b.out +do + test -f "$ac_file" || continue + case $ac_file in + *.$ac_ext | *.xcoff | *.tds | *.d | *.pdb | *.xSYM | *.bb | *.bbg | *.o | *.obj ) + ;; + conftest.$ac_ext ) + # This is the source file. + ;; + [ab].out ) + # We found the default executable, but exeext='' is most + # certainly right. + break;; + *.* ) + ac_cv_exeext=`expr "$ac_file" : '[^.]*\(\..*\)'` + # FIXME: I believe we export ac_cv_exeext for Libtool, + # but it would be cool to find out if it's true. Does anybody + # maintain Libtool? --akim. + export ac_cv_exeext + break;; + * ) + break;; + esac +done +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +{ { echo "$as_me:$LINENO: error: in \`$ac_pwd':" >&5 +echo "$as_me: error: in \`$ac_pwd':" >&2;} +{ { echo "$as_me:$LINENO: error: C compiler cannot create executables +See \`config.log' for more details." >&5 +echo "$as_me: error: C compiler cannot create executables +See \`config.log' for more details." >&2;} + { (exit 77); exit 77; }; }; } +fi + +ac_exeext=$ac_cv_exeext +echo "$as_me:$LINENO: result: $ac_file" >&5 +echo "${ECHO_T}$ac_file" >&6 + +# Check the compiler produces executables we can run. If not, either +# the compiler is broken, or we cross compile. +echo "$as_me:$LINENO: checking whether the C compiler works" >&5 +echo $ECHO_N "checking whether the C compiler works... $ECHO_C" >&6 +# FIXME: These cross compiler hacks should be removed for Autoconf 3.0 +# If not cross compiling, check that we can run a simple program. +if test "$cross_compiling" != yes; then + if { ac_try='./$ac_file' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + cross_compiling=no + else + if test "$cross_compiling" = maybe; then + cross_compiling=yes + else + { { echo "$as_me:$LINENO: error: in \`$ac_pwd':" >&5 +echo "$as_me: error: in \`$ac_pwd':" >&2;} +{ { echo "$as_me:$LINENO: error: cannot run C compiled programs. +If you meant to cross compile, use \`--host'. +See \`config.log' for more details." >&5 +echo "$as_me: error: cannot run C compiled programs. +If you meant to cross compile, use \`--host'. +See \`config.log' for more details." >&2;} + { (exit 1); exit 1; }; }; } + fi + fi +fi +echo "$as_me:$LINENO: result: yes" >&5 +echo "${ECHO_T}yes" >&6 + +rm -f a.out a.exe conftest$ac_cv_exeext b.out +ac_clean_files=$ac_clean_files_save +# Check the compiler produces executables we can run. If not, either +# the compiler is broken, or we cross compile. +echo "$as_me:$LINENO: checking whether we are cross compiling" >&5 +echo $ECHO_N "checking whether we are cross compiling... $ECHO_C" >&6 +echo "$as_me:$LINENO: result: $cross_compiling" >&5 +echo "${ECHO_T}$cross_compiling" >&6 + +echo "$as_me:$LINENO: checking for suffix of executables" >&5 +echo $ECHO_N "checking for suffix of executables... $ECHO_C" >&6 +if { (eval echo "$as_me:$LINENO: \"$ac_link\"") >&5 + (eval $ac_link) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; then + # If both `conftest.exe' and `conftest' are `present' (well, observable) +# catch `conftest.exe'. For instance with Cygwin, `ls conftest' will +# work properly (i.e., refer to `conftest.exe'), while it won't with +# `rm'. +for ac_file in conftest.exe conftest conftest.*; do + test -f "$ac_file" || continue + case $ac_file in + *.$ac_ext | *.xcoff | *.tds | *.d | *.pdb | *.xSYM | *.bb | *.bbg | *.o | *.obj ) ;; + *.* ) ac_cv_exeext=`expr "$ac_file" : '[^.]*\(\..*\)'` + export ac_cv_exeext + break;; + * ) break;; + esac +done +else + { { echo "$as_me:$LINENO: error: in \`$ac_pwd':" >&5 +echo "$as_me: error: in \`$ac_pwd':" >&2;} +{ { echo "$as_me:$LINENO: error: cannot compute suffix of executables: cannot compile and link +See \`config.log' for more details." >&5 +echo "$as_me: error: cannot compute suffix of executables: cannot compile and link +See \`config.log' for more details." >&2;} + { (exit 1); exit 1; }; }; } +fi + +rm -f conftest$ac_cv_exeext +echo "$as_me:$LINENO: result: $ac_cv_exeext" >&5 +echo "${ECHO_T}$ac_cv_exeext" >&6 + +rm -f conftest.$ac_ext +EXEEXT=$ac_cv_exeext +ac_exeext=$EXEEXT +fi +echo "$as_me:$LINENO: checking for suffix of object files" >&5 +echo $ECHO_N "checking for suffix of object files... $ECHO_C" >&6 +if test "${ac_cv_objext+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ + +int +main () +{ + + ; + return 0; +} +_ACEOF +rm -f conftest.o conftest.obj +if { (eval echo "$as_me:$LINENO: \"$ac_compile\"") >&5 + (eval $ac_compile) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; then + for ac_file in `(ls conftest.o conftest.obj; ls conftest.*) 2>/dev/null`; do + case $ac_file in + *.$ac_ext | *.xcoff | *.tds | *.d | *.pdb | *.xSYM | *.bb | *.bbg ) ;; + *) ac_cv_objext=`expr "$ac_file" : '.*\.\(.*\)'` + break;; + esac +done +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +{ { echo "$as_me:$LINENO: error: in \`$ac_pwd':" >&5 +echo "$as_me: error: in \`$ac_pwd':" >&2;} +{ { echo "$as_me:$LINENO: error: cannot compute suffix of object files: cannot compile +See \`config.log' for more details." >&5 +echo "$as_me: error: cannot compute suffix of object files: cannot compile +See \`config.log' for more details." >&2;} + { (exit 1); exit 1; }; }; } +fi + +rm -f conftest.$ac_cv_objext conftest.$ac_ext +fi +echo "$as_me:$LINENO: result: $ac_cv_objext" >&5 +echo "${ECHO_T}$ac_cv_objext" >&6 +OBJEXT=$ac_cv_objext +ac_objext=$OBJEXT +echo "$as_me:$LINENO: checking whether we are using the GNU C compiler" >&5 +echo $ECHO_N "checking whether we are using the GNU C compiler... $ECHO_C" >&6 +if test "${ac_cv_c_compiler_gnu+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ + +int +main () +{ +#ifndef __GNUC__ + choke me +#endif + + ; + return 0; +} +_ACEOF +rm -f conftest.$ac_objext +if { (eval echo "$as_me:$LINENO: \"$ac_compile\"") >&5 + (eval $ac_compile) 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && + { ac_try='test -z "$ac_c_werror_flag" + || test ! -s conftest.err' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; } && + { ac_try='test -s conftest.$ac_objext' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + ac_compiler_gnu=yes +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +ac_compiler_gnu=no +fi +rm -f conftest.err conftest.$ac_objext conftest.$ac_ext +ac_cv_c_compiler_gnu=$ac_compiler_gnu + +fi +echo "$as_me:$LINENO: result: $ac_cv_c_compiler_gnu" >&5 +echo "${ECHO_T}$ac_cv_c_compiler_gnu" >&6 +GCC=`test $ac_compiler_gnu = yes && echo yes` +ac_test_CFLAGS=${CFLAGS+set} +ac_save_CFLAGS=$CFLAGS +CFLAGS="-g" +echo "$as_me:$LINENO: checking whether $CC accepts -g" >&5 +echo $ECHO_N "checking whether $CC accepts -g... $ECHO_C" >&6 +if test "${ac_cv_prog_cc_g+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ + +int +main () +{ + + ; + return 0; +} +_ACEOF +rm -f conftest.$ac_objext +if { (eval echo "$as_me:$LINENO: \"$ac_compile\"") >&5 + (eval $ac_compile) 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && + { ac_try='test -z "$ac_c_werror_flag" + || test ! -s conftest.err' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; } && + { ac_try='test -s conftest.$ac_objext' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + ac_cv_prog_cc_g=yes +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +ac_cv_prog_cc_g=no +fi +rm -f conftest.err conftest.$ac_objext conftest.$ac_ext +fi +echo "$as_me:$LINENO: result: $ac_cv_prog_cc_g" >&5 +echo "${ECHO_T}$ac_cv_prog_cc_g" >&6 +if test "$ac_test_CFLAGS" = set; then + CFLAGS=$ac_save_CFLAGS +elif test $ac_cv_prog_cc_g = yes; then + if test "$GCC" = yes; then + CFLAGS="-g -O2" + else + CFLAGS="-g" + fi +else + if test "$GCC" = yes; then + CFLAGS="-O2" + else + CFLAGS= + fi +fi +echo "$as_me:$LINENO: checking for $CC option to accept ANSI C" >&5 +echo $ECHO_N "checking for $CC option to accept ANSI C... $ECHO_C" >&6 +if test "${ac_cv_prog_cc_stdc+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + ac_cv_prog_cc_stdc=no +ac_save_CC=$CC +cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ +#include +#include +#include +#include +/* Most of the following tests are stolen from RCS 5.7's src/conf.sh. */ +struct buf { int x; }; +FILE * (*rcsopen) (struct buf *, struct stat *, int); +static char *e (p, i) + char **p; + int i; +{ + return p[i]; +} +static char *f (char * (*g) (char **, int), char **p, ...) +{ + char *s; + va_list v; + va_start (v,p); + s = g (p, va_arg (v,int)); + va_end (v); + return s; +} + +/* OSF 4.0 Compaq cc is some sort of almost-ANSI by default. It has + function prototypes and stuff, but not '\xHH' hex character constants. + These don't provoke an error unfortunately, instead are silently treated + as 'x'. The following induces an error, until -std1 is added to get + proper ANSI mode. Curiously '\x00'!='x' always comes out true, for an + array size at least. It's necessary to write '\x00'==0 to get something + that's true only with -std1. */ +int osf4_cc_array ['\x00' == 0 ? 1 : -1]; + +int test (int i, double x); +struct s1 {int (*f) (int a);}; +struct s2 {int (*f) (double a);}; +int pairnames (int, char **, FILE *(*)(struct buf *, struct stat *, int), int, int); +int argc; +char **argv; +int +main () +{ +return f (e, argv, 0) != argv[0] || f (e, argv, 1) != argv[1]; + ; + return 0; +} +_ACEOF +# Don't try gcc -ansi; that turns off useful extensions and +# breaks some systems' header files. +# AIX -qlanglvl=ansi +# Ultrix and OSF/1 -std1 +# HP-UX 10.20 and later -Ae +# HP-UX older versions -Aa -D_HPUX_SOURCE +# SVR4 -Xc -D__EXTENSIONS__ +for ac_arg in "" -qlanglvl=ansi -std1 -Ae "-Aa -D_HPUX_SOURCE" "-Xc -D__EXTENSIONS__" +do + CC="$ac_save_CC $ac_arg" + rm -f conftest.$ac_objext +if { (eval echo "$as_me:$LINENO: \"$ac_compile\"") >&5 + (eval $ac_compile) 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && + { ac_try='test -z "$ac_c_werror_flag" + || test ! -s conftest.err' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; } && + { ac_try='test -s conftest.$ac_objext' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + ac_cv_prog_cc_stdc=$ac_arg +break +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +fi +rm -f conftest.err conftest.$ac_objext +done +rm -f conftest.$ac_ext conftest.$ac_objext +CC=$ac_save_CC + +fi + +case "x$ac_cv_prog_cc_stdc" in + x|xno) + echo "$as_me:$LINENO: result: none needed" >&5 +echo "${ECHO_T}none needed" >&6 ;; + *) + echo "$as_me:$LINENO: result: $ac_cv_prog_cc_stdc" >&5 +echo "${ECHO_T}$ac_cv_prog_cc_stdc" >&6 + CC="$CC $ac_cv_prog_cc_stdc" ;; +esac + +# Some people use a C++ compiler to compile C. Since we use `exit', +# in C++ we need to declare it. In case someone uses the same compiler +# for both compiling C and C++ we need to have the C++ compiler decide +# the declaration of exit, since it's the most demanding environment. +cat >conftest.$ac_ext <<_ACEOF +#ifndef __cplusplus + choke me +#endif +_ACEOF +rm -f conftest.$ac_objext +if { (eval echo "$as_me:$LINENO: \"$ac_compile\"") >&5 + (eval $ac_compile) 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && + { ac_try='test -z "$ac_c_werror_flag" + || test ! -s conftest.err' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; } && + { ac_try='test -s conftest.$ac_objext' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + for ac_declaration in \ + '' \ + 'extern "C" void std::exit (int) throw (); using std::exit;' \ + 'extern "C" void std::exit (int); using std::exit;' \ + 'extern "C" void exit (int) throw ();' \ + 'extern "C" void exit (int);' \ + 'void exit (int);' +do + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ +$ac_declaration +#include +int +main () +{ +exit (42); + ; + return 0; +} +_ACEOF +rm -f conftest.$ac_objext +if { (eval echo "$as_me:$LINENO: \"$ac_compile\"") >&5 + (eval $ac_compile) 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && + { ac_try='test -z "$ac_c_werror_flag" + || test ! -s conftest.err' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; } && + { ac_try='test -s conftest.$ac_objext' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + : +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +continue +fi +rm -f conftest.err conftest.$ac_objext conftest.$ac_ext + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ +$ac_declaration +int +main () +{ +exit (42); + ; + return 0; +} +_ACEOF +rm -f conftest.$ac_objext +if { (eval echo "$as_me:$LINENO: \"$ac_compile\"") >&5 + (eval $ac_compile) 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && + { ac_try='test -z "$ac_c_werror_flag" + || test ! -s conftest.err' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; } && + { ac_try='test -s conftest.$ac_objext' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + break +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +fi +rm -f conftest.err conftest.$ac_objext conftest.$ac_ext +done +rm -f conftest* +if test -n "$ac_declaration"; then + echo '#ifdef __cplusplus' >>confdefs.h + echo $ac_declaration >>confdefs.h + echo '#endif' >>confdefs.h +fi + +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +fi +rm -f conftest.err conftest.$ac_objext conftest.$ac_ext +ac_ext=c +ac_cpp='$CPP $CPPFLAGS' +ac_compile='$CC -c $CFLAGS $CPPFLAGS conftest.$ac_ext >&5' +ac_link='$CC -o conftest$ac_exeext $CFLAGS $CPPFLAGS $LDFLAGS conftest.$ac_ext $LIBS >&5' +ac_compiler_gnu=$ac_cv_c_compiler_gnu + +ac_ext=c +ac_cpp='$CPP $CPPFLAGS' +ac_compile='$CC -c $CFLAGS $CPPFLAGS conftest.$ac_ext >&5' +ac_link='$CC -o conftest$ac_exeext $CFLAGS $CPPFLAGS $LDFLAGS conftest.$ac_ext $LIBS >&5' +ac_compiler_gnu=$ac_cv_c_compiler_gnu +echo "$as_me:$LINENO: checking how to run the C preprocessor" >&5 +echo $ECHO_N "checking how to run the C preprocessor... $ECHO_C" >&6 +# On Suns, sometimes $CPP names a directory. +if test -n "$CPP" && test -d "$CPP"; then + CPP= +fi +if test -z "$CPP"; then + if test "${ac_cv_prog_CPP+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + # Double quotes because CPP needs to be expanded + for CPP in "$CC -E" "$CC -E -traditional-cpp" "/lib/cpp" + do + ac_preproc_ok=false +for ac_c_preproc_warn_flag in '' yes +do + # Use a header file that comes with gcc, so configuring glibc + # with a fresh cross-compiler works. + # Prefer to if __STDC__ is defined, since + # exists even on freestanding compilers. + # On the NeXT, cc -E runs the code through the compiler's parser, + # not just through cpp. "Syntax error" is here to catch this case. + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ +#ifdef __STDC__ +# include +#else +# include +#endif + Syntax error +_ACEOF +if { (eval echo "$as_me:$LINENO: \"$ac_cpp conftest.$ac_ext\"") >&5 + (eval $ac_cpp conftest.$ac_ext) 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } >/dev/null; then + if test -s conftest.err; then + ac_cpp_err=$ac_c_preproc_warn_flag + ac_cpp_err=$ac_cpp_err$ac_c_werror_flag + else + ac_cpp_err= + fi +else + ac_cpp_err=yes +fi +if test -z "$ac_cpp_err"; then + : +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + + # Broken: fails on valid input. +continue +fi +rm -f conftest.err conftest.$ac_ext + + # OK, works on sane cases. Now check whether non-existent headers + # can be detected and how. + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ +#include +_ACEOF +if { (eval echo "$as_me:$LINENO: \"$ac_cpp conftest.$ac_ext\"") >&5 + (eval $ac_cpp conftest.$ac_ext) 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } >/dev/null; then + if test -s conftest.err; then + ac_cpp_err=$ac_c_preproc_warn_flag + ac_cpp_err=$ac_cpp_err$ac_c_werror_flag + else + ac_cpp_err= + fi +else + ac_cpp_err=yes +fi +if test -z "$ac_cpp_err"; then + # Broken: success on invalid input. +continue +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + + # Passes both tests. +ac_preproc_ok=: +break +fi +rm -f conftest.err conftest.$ac_ext + +done +# Because of `break', _AC_PREPROC_IFELSE's cleaning code was skipped. +rm -f conftest.err conftest.$ac_ext +if $ac_preproc_ok; then + break +fi + + done + ac_cv_prog_CPP=$CPP + +fi + CPP=$ac_cv_prog_CPP +else + ac_cv_prog_CPP=$CPP +fi +echo "$as_me:$LINENO: result: $CPP" >&5 +echo "${ECHO_T}$CPP" >&6 +ac_preproc_ok=false +for ac_c_preproc_warn_flag in '' yes +do + # Use a header file that comes with gcc, so configuring glibc + # with a fresh cross-compiler works. + # Prefer to if __STDC__ is defined, since + # exists even on freestanding compilers. + # On the NeXT, cc -E runs the code through the compiler's parser, + # not just through cpp. "Syntax error" is here to catch this case. + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ +#ifdef __STDC__ +# include +#else +# include +#endif + Syntax error +_ACEOF +if { (eval echo "$as_me:$LINENO: \"$ac_cpp conftest.$ac_ext\"") >&5 + (eval $ac_cpp conftest.$ac_ext) 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } >/dev/null; then + if test -s conftest.err; then + ac_cpp_err=$ac_c_preproc_warn_flag + ac_cpp_err=$ac_cpp_err$ac_c_werror_flag + else + ac_cpp_err= + fi +else + ac_cpp_err=yes +fi +if test -z "$ac_cpp_err"; then + : +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + + # Broken: fails on valid input. +continue +fi +rm -f conftest.err conftest.$ac_ext + + # OK, works on sane cases. Now check whether non-existent headers + # can be detected and how. + cat >conftest.$ac_ext <<_ACEOF +/* confdefs.h. */ +_ACEOF +cat confdefs.h >>conftest.$ac_ext +cat >>conftest.$ac_ext <<_ACEOF +/* end confdefs.h. */ +#include +_ACEOF +if { (eval echo "$as_me:$LINENO: \"$ac_cpp conftest.$ac_ext\"") >&5 + (eval $ac_cpp conftest.$ac_ext) 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } >/dev/null; then + if test -s conftest.err; then + ac_cpp_err=$ac_c_preproc_warn_flag + ac_cpp_err=$ac_cpp_err$ac_c_werror_flag + else + ac_cpp_err= + fi +else + ac_cpp_err=yes +fi +if test -z "$ac_cpp_err"; then + # Broken: success on invalid input. +continue +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + + # Passes both tests. +ac_preproc_ok=: +break +fi +rm -f conftest.err conftest.$ac_ext + +done +# Because of `break', _AC_PREPROC_IFELSE's cleaning code was skipped. +rm -f conftest.err conftest.$ac_ext +if $ac_preproc_ok; then + : +else + { { echo "$as_me:$LINENO: error: in \`$ac_pwd':" >&5 +echo "$as_me: error: in \`$ac_pwd':" >&2;} +{ { echo "$as_me:$LINENO: error: C preprocessor \"$CPP\" fails sanity check +See \`config.log' for more details." >&5 +echo "$as_me: error: C preprocessor \"$CPP\" fails sanity check +See \`config.log' for more details." >&2;} + { (exit 1); exit 1; }; }; } +fi + +ac_ext=c +ac_cpp='$CPP $CPPFLAGS' +ac_compile='$CC -c $CFLAGS $CPPFLAGS conftest.$ac_ext >&5' +ac_link='$CC -o conftest$ac_exeext $CFLAGS $CPPFLAGS $LDFLAGS conftest.$ac_ext $LIBS >&5' +ac_compiler_gnu=$ac_cv_c_compiler_gnu + + +ac_c_preproc_warn_flag=yes + +# Check for decimal float support. + +echo "$as_me:$LINENO: checking whether decimal floating point is supported" >&5 +echo $ECHO_N "checking whether decimal floating point is supported... $ECHO_C" >&6 +if test "${libgcc_cv_dfp+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + cat >conftest.$ac_ext <<_ACEOF +_Decimal32 x; +_ACEOF +rm -f conftest.$ac_objext +if { (eval echo "$as_me:$LINENO: \"$ac_compile\"") >&5 + (eval $ac_compile) 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && + { ac_try='test -z "$ac_c_werror_flag" + || test ! -s conftest.err' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; } && + { ac_try='test -s conftest.$ac_objext' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + libgcc_cv_dfp=yes +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +libgcc_cv_dfp=no +fi +rm -f conftest.err conftest.$ac_objext conftest.$ac_ext +fi +echo "$as_me:$LINENO: result: $libgcc_cv_dfp" >&5 +echo "${ECHO_T}$libgcc_cv_dfp" >&6 +decimal_float=$libgcc_cv_dfp + + +# Check whether --enable-decimal-float or --disable-decimal-float was given. +if test "${enable_decimal_float+set}" = set; then + enableval="$enable_decimal_float" + + case $enable_decimal_float in + yes | no | bid | dpd) ;; + *) { { echo "$as_me:$LINENO: error: '$enable_decimal_float' is an invalid value for --enable-decimal-float. +Valid choices are 'yes', 'bid', 'dpd', and 'no'." >&5 +echo "$as_me: error: '$enable_decimal_float' is an invalid value for --enable-decimal-float. +Valid choices are 'yes', 'bid', 'dpd', and 'no'." >&2;} + { (exit 1); exit 1; }; } ;; + esac + +else + + case $host in + powerpc*-*-linux* | i?86*-*-linux* | x86_64*-*-linux*) + enable_decimal_float=yes + ;; + *) + enable_decimal_float=no + ;; + esac + +fi; + +# x86's use BID format instead of DPD +if test x$enable_decimal_float = xyes; then + case $host in + i?86*-*-linux* | x86_64*-*-linux*) + enable_decimal_float=bid + ;; + *) + enable_decimal_float=dpd + ;; + esac +fi + + +# Check for fixed-point support. +echo "$as_me:$LINENO: checking whether fixed-point is supported" >&5 +echo $ECHO_N "checking whether fixed-point is supported... $ECHO_C" >&6 +if test "${libgcc_cv_fixed_point+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + cat >conftest.$ac_ext <<_ACEOF +_Sat _Fract x; +_ACEOF +rm -f conftest.$ac_objext +if { (eval echo "$as_me:$LINENO: \"$ac_compile\"") >&5 + (eval $ac_compile) 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && + { ac_try='test -z "$ac_c_werror_flag" + || test ! -s conftest.err' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; } && + { ac_try='test -s conftest.$ac_objext' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + libgcc_cv_fixed_point=yes +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +libgcc_cv_fixed_point=no +fi +rm -f conftest.err conftest.$ac_objext conftest.$ac_ext +fi +echo "$as_me:$LINENO: result: $libgcc_cv_fixed_point" >&5 +echo "${ECHO_T}$libgcc_cv_fixed_point" >&6 +fixed_point=$libgcc_cv_fixed_point + + +# Check 32bit or 64bit for x86. +case ${host} in +i?86*-*-* | x86_64*-*-*) + cat > conftest.c < conftest.s <&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + # configure expects config files in libgcc/config, so need a relative + # path here. + tmake_file="${tmake_file} ../../gcc/config/i386/t-crtstuff" + fi + ;; +esac + +# Check for visibility support. This is after config.host so that +# we can check for asm_hidden_op. +echo "$as_me:$LINENO: checking for __attribute__((visibility(\"hidden\")))" >&5 +echo $ECHO_N "checking for __attribute__((visibility(\"hidden\")))... $ECHO_C" >&6 +if test "${libgcc_cv_hidden_visibility_attribute+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + + echo 'int __attribute__ ((visibility ("hidden"))) foo (void) { return 1; }' > conftest.c + libgcc_cv_hidden_visibility_attribute=no + if { ac_try='${CC-cc} -Werror -S conftest.c -o conftest.s 1>&5' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + if grep "\\$asm_hidden_op.*foo" conftest.s >/dev/null; then + libgcc_cv_hidden_visibility_attribute=yes + fi + fi + rm -f conftest.* + +fi +echo "$as_me:$LINENO: result: $libgcc_cv_hidden_visibility_attribute" >&5 +echo "${ECHO_T}$libgcc_cv_hidden_visibility_attribute" >&6 + +if test $libgcc_cv_hidden_visibility_attribute = yes; then + vis_hide='-fvisibility=hidden -DHIDE_EXPORTS' +else + vis_hide= +fi + + +# See if we have thread-local storage. We can only test assembler +# sicne link-time and run-time tests require the newly built +# gcc, which can't be used to build executable due to that libgcc +# is yet to be built here. + + # Check whether --enable-tls or --disable-tls was given. +if test "${enable_tls+set}" = set; then + enableval="$enable_tls" + + case "$enableval" in + yes|no) ;; + *) { { echo "$as_me:$LINENO: error: Argument to enable/disable tls must be yes or no" >&5 +echo "$as_me: error: Argument to enable/disable tls must be yes or no" >&2;} + { (exit 1); exit 1; }; } ;; + esac + +else + enable_tls=yes +fi; + + echo "$as_me:$LINENO: checking whether the target assembler supports thread-local storage" >&5 +echo $ECHO_N "checking whether the target assembler supports thread-local storage... $ECHO_C" >&6 +if test "${gcc_cv_have_cc_tls+set}" = set; then + echo $ECHO_N "(cached) $ECHO_C" >&6 +else + + cat >conftest.$ac_ext <<_ACEOF +__thread int a; int b; int main() { return a = b; } +_ACEOF +rm -f conftest.$ac_objext +if { (eval echo "$as_me:$LINENO: \"$ac_compile\"") >&5 + (eval $ac_compile) 2>conftest.er1 + ac_status=$? + grep -v '^ *+' conftest.er1 >conftest.err + rm -f conftest.er1 + cat conftest.err >&5 + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); } && + { ac_try='test -z "$ac_c_werror_flag" + || test ! -s conftest.err' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; } && + { ac_try='test -s conftest.$ac_objext' + { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 + (eval $ac_try) 2>&5 + ac_status=$? + echo "$as_me:$LINENO: \$? = $ac_status" >&5 + (exit $ac_status); }; }; then + gcc_cv_have_cc_tls=yes +else + echo "$as_me: failed program was:" >&5 +sed 's/^/| /' conftest.$ac_ext >&5 + +gcc_cv_have_cc_tls=no +fi +rm -f conftest.err conftest.$ac_objext conftest.$ac_ext + +fi +echo "$as_me:$LINENO: result: $gcc_cv_have_cc_tls" >&5 +echo "${ECHO_T}$gcc_cv_have_cc_tls" >&6 +set_have_cc_tls= +if test "$enable_tls $gcc_cv_have_cc_tls" = "yes yes"; then + set_have_cc_tls="-DHAVE_CC_TLS" +fi + + +# Conditionalize the makefile for this target machine. +tmake_file_= +for f in ${tmake_file} +do + if test -f ${srcdir}/config/$f + then + tmake_file_="${tmake_file_} \$(srcdir)/config/$f" + fi +done +tmake_file="${tmake_file_}" + + +# Substitute configuration variables + + + +# We need multilib support. + ac_config_files="$ac_config_files Makefile" + + ac_config_commands="$ac_config_commands default" + +cat >confcache <<\_ACEOF +# This file is a shell script that caches the results of configure +# tests run on this system so they can be shared between configure +# scripts and configure runs, see configure's option --config-cache. +# It is not useful on other systems. If it contains results you don't +# want to keep, you may remove or edit it. +# +# config.status only pays attention to the cache file if you give it +# the --recheck option to rerun configure. +# +# `ac_cv_env_foo' variables (set or unset) will be overridden when +# loading this file, other *unset* `ac_cv_foo' will be assigned the +# following values. + +_ACEOF + +# The following way of writing the cache mishandles newlines in values, +# but we know of no workaround that is simple, portable, and efficient. +# So, don't put newlines in cache variables' values. +# Ultrix sh set writes to stderr and can't be redirected directly, +# and sets the high bit in the cache file unless we assign to the vars. +{ + (set) 2>&1 | + case `(ac_space=' '; set | grep ac_space) 2>&1` in + *ac_space=\ *) + # `set' does not quote correctly, so add quotes (double-quote + # substitution turns \\\\ into \\, and sed turns \\ into \). + sed -n \ + "s/'/'\\\\''/g; + s/^\\([_$as_cr_alnum]*_cv_[_$as_cr_alnum]*\\)=\\(.*\\)/\\1='\\2'/p" + ;; + *) + # `set' quotes correctly as required by POSIX, so do not add quotes. + sed -n \ + "s/^\\([_$as_cr_alnum]*_cv_[_$as_cr_alnum]*\\)=\\(.*\\)/\\1=\\2/p" + ;; + esac; +} | + sed ' + t clear + : clear + s/^\([^=]*\)=\(.*[{}].*\)$/test "${\1+set}" = set || &/ + t end + /^ac_cv_env/!s/^\([^=]*\)=\(.*\)$/\1=${\1=\2}/ + : end' >>confcache +if diff $cache_file confcache >/dev/null 2>&1; then :; else + if test -w $cache_file; then + test "x$cache_file" != "x/dev/null" && echo "updating cache $cache_file" + cat confcache >$cache_file + else + echo "not updating unwritable cache $cache_file" + fi +fi +rm -f confcache + +test "x$prefix" = xNONE && prefix=$ac_default_prefix +# Let make expand exec_prefix. +test "x$exec_prefix" = xNONE && exec_prefix='${prefix}' + +# VPATH may cause trouble with some makes, so we remove $(srcdir), +# ${srcdir} and @srcdir@ from VPATH if srcdir is ".", strip leading and +# trailing colons and then remove the whole line if VPATH becomes empty +# (actually we leave an empty line to preserve line numbers). +if test "x$srcdir" = x.; then + ac_vpsub='/^[ ]*VPATH[ ]*=/{ +s/:*\$(srcdir):*/:/; +s/:*\${srcdir}:*/:/; +s/:*@srcdir@:*/:/; +s/^\([^=]*=[ ]*\):*/\1/; +s/:*$//; +s/^[^=]*=[ ]*$//; +}' +fi + +# Transform confdefs.h into DEFS. +# Protect against shell expansion while executing Makefile rules. +# Protect against Makefile macro expansion. +# +# If the first sed substitution is executed (which looks for macros that +# take arguments), then we branch to the quote section. Otherwise, +# look for a macro that doesn't take arguments. +cat >confdef2opt.sed <<\_ACEOF +t clear +: clear +s,^[ ]*#[ ]*define[ ][ ]*\([^ (][^ (]*([^)]*)\)[ ]*\(.*\),-D\1=\2,g +t quote +s,^[ ]*#[ ]*define[ ][ ]*\([^ ][^ ]*\)[ ]*\(.*\),-D\1=\2,g +t quote +d +: quote +s,[ `~#$^&*(){}\\|;'"<>?],\\&,g +s,\[,\\&,g +s,\],\\&,g +s,\$,$$,g +p +_ACEOF +# We use echo to avoid assuming a particular line-breaking character. +# The extra dot is to prevent the shell from consuming trailing +# line-breaks from the sub-command output. A line-break within +# single-quotes doesn't work because, if this script is created in a +# platform that uses two characters for line-breaks (e.g., DOS), tr +# would break. +ac_LF_and_DOT=`echo; echo .` +DEFS=`sed -n -f confdef2opt.sed confdefs.h | tr "$ac_LF_and_DOT" ' .'` +rm -f confdef2opt.sed + + +ac_libobjs= +ac_ltlibobjs= +for ac_i in : $LIBOBJS; do test "x$ac_i" = x: && continue + # 1. Remove the extension, and $U if already installed. + ac_i=`echo "$ac_i" | + sed 's/\$U\././;s/\.o$//;s/\.obj$//'` + # 2. Add them. + ac_libobjs="$ac_libobjs $ac_i\$U.$ac_objext" + ac_ltlibobjs="$ac_ltlibobjs $ac_i"'$U.lo' +done +LIBOBJS=$ac_libobjs + +LTLIBOBJS=$ac_ltlibobjs + + + +: ${CONFIG_STATUS=./config.status} +ac_clean_files_save=$ac_clean_files +ac_clean_files="$ac_clean_files $CONFIG_STATUS" +{ echo "$as_me:$LINENO: creating $CONFIG_STATUS" >&5 +echo "$as_me: creating $CONFIG_STATUS" >&6;} +cat >$CONFIG_STATUS <<_ACEOF +#! $SHELL +# Generated by $as_me. +# Run this file to recreate the current configuration. +# Compiler output produced by configure, useful for debugging +# configure, is in config.log if it exists. + +debug=false +ac_cs_recheck=false +ac_cs_silent=false +SHELL=\${CONFIG_SHELL-$SHELL} +_ACEOF + +cat >>$CONFIG_STATUS <<\_ACEOF +## --------------------- ## +## M4sh Initialization. ## +## --------------------- ## + +# Be Bourne compatible +if test -n "${ZSH_VERSION+set}" && (emulate sh) >/dev/null 2>&1; then + emulate sh + NULLCMD=: + # Zsh 3.x and 4.x performs word splitting on ${1+"$@"}, which + # is contrary to our usage. Disable this feature. + alias -g '${1+"$@"}'='"$@"' +elif test -n "${BASH_VERSION+set}" && (set -o posix) >/dev/null 2>&1; then + set -o posix +fi +DUALCASE=1; export DUALCASE # for MKS sh + +# Support unset when possible. +if ( (MAIL=60; unset MAIL) || exit) >/dev/null 2>&1; then + as_unset=unset +else + as_unset=false +fi + + +# Work around bugs in pre-3.0 UWIN ksh. +$as_unset ENV MAIL MAILPATH +PS1='$ ' +PS2='> ' +PS4='+ ' + +# NLS nuisances. +for as_var in \ + LANG LANGUAGE LC_ADDRESS LC_ALL LC_COLLATE LC_CTYPE LC_IDENTIFICATION \ + LC_MEASUREMENT LC_MESSAGES LC_MONETARY LC_NAME LC_NUMERIC LC_PAPER \ + LC_TELEPHONE LC_TIME +do + if (set +x; test -z "`(eval $as_var=C; export $as_var) 2>&1`"); then + eval $as_var=C; export $as_var + else + $as_unset $as_var + fi +done + +# Required to use basename. +if expr a : '\(a\)' >/dev/null 2>&1; then + as_expr=expr +else + as_expr=false +fi + +if (basename /) >/dev/null 2>&1 && test "X`basename / 2>&1`" = "X/"; then + as_basename=basename +else + as_basename=false +fi + + +# Name of the executable. +as_me=`$as_basename "$0" || +$as_expr X/"$0" : '.*/\([^/][^/]*\)/*$' \| \ + X"$0" : 'X\(//\)$' \| \ + X"$0" : 'X\(/\)$' \| \ + . : '\(.\)' 2>/dev/null || +echo X/"$0" | + sed '/^.*\/\([^/][^/]*\)\/*$/{ s//\1/; q; } + /^X\/\(\/\/\)$/{ s//\1/; q; } + /^X\/\(\/\).*/{ s//\1/; q; } + s/.*/./; q'` + + +# PATH needs CR, and LINENO needs CR and PATH. +# Avoid depending upon Character Ranges. +as_cr_letters='abcdefghijklmnopqrstuvwxyz' +as_cr_LETTERS='ABCDEFGHIJKLMNOPQRSTUVWXYZ' +as_cr_Letters=$as_cr_letters$as_cr_LETTERS +as_cr_digits='0123456789' +as_cr_alnum=$as_cr_Letters$as_cr_digits + +# The user is always right. +if test "${PATH_SEPARATOR+set}" != set; then + echo "#! /bin/sh" >conf$$.sh + echo "exit 0" >>conf$$.sh + chmod +x conf$$.sh + if (PATH="/nonexistent;."; conf$$.sh) >/dev/null 2>&1; then + PATH_SEPARATOR=';' + else + PATH_SEPARATOR=: + fi + rm -f conf$$.sh +fi + + + as_lineno_1=$LINENO + as_lineno_2=$LINENO + as_lineno_3=`(expr $as_lineno_1 + 1) 2>/dev/null` + test "x$as_lineno_1" != "x$as_lineno_2" && + test "x$as_lineno_3" = "x$as_lineno_2" || { + # Find who we are. Look in the path if we contain no path at all + # relative or not. + case $0 in + *[\\/]* ) as_myself=$0 ;; + *) as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in $PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + test -r "$as_dir/$0" && as_myself=$as_dir/$0 && break +done + + ;; + esac + # We did not find ourselves, most probably we were run as `sh COMMAND' + # in which case we are not to be found in the path. + if test "x$as_myself" = x; then + as_myself=$0 + fi + if test ! -f "$as_myself"; then + { { echo "$as_me:$LINENO: error: cannot find myself; rerun with an absolute path" >&5 +echo "$as_me: error: cannot find myself; rerun with an absolute path" >&2;} + { (exit 1); exit 1; }; } + fi + case $CONFIG_SHELL in + '') + as_save_IFS=$IFS; IFS=$PATH_SEPARATOR +for as_dir in /bin$PATH_SEPARATOR/usr/bin$PATH_SEPARATOR$PATH +do + IFS=$as_save_IFS + test -z "$as_dir" && as_dir=. + for as_base in sh bash ksh sh5; do + case $as_dir in + /*) + if ("$as_dir/$as_base" -c ' + as_lineno_1=$LINENO + as_lineno_2=$LINENO + as_lineno_3=`(expr $as_lineno_1 + 1) 2>/dev/null` + test "x$as_lineno_1" != "x$as_lineno_2" && + test "x$as_lineno_3" = "x$as_lineno_2" ') 2>/dev/null; then + $as_unset BASH_ENV || test "${BASH_ENV+set}" != set || { BASH_ENV=; export BASH_ENV; } + $as_unset ENV || test "${ENV+set}" != set || { ENV=; export ENV; } + CONFIG_SHELL=$as_dir/$as_base + export CONFIG_SHELL + exec "$CONFIG_SHELL" "$0" ${1+"$@"} + fi;; + esac + done +done +;; + esac + + # Create $as_me.lineno as a copy of $as_myself, but with $LINENO + # uniformly replaced by the line number. The first 'sed' inserts a + # line-number line before each line; the second 'sed' does the real + # work. The second script uses 'N' to pair each line-number line + # with the numbered line, and appends trailing '-' during + # substitution so that $LINENO is not a special case at line end. + # (Raja R Harinath suggested sed '=', and Paul Eggert wrote the + # second 'sed' script. Blame Lee E. McMahon for sed's syntax. :-) + sed '=' <$as_myself | + sed ' + N + s,$,-, + : loop + s,^\(['$as_cr_digits']*\)\(.*\)[$]LINENO\([^'$as_cr_alnum'_]\),\1\2\1\3, + t loop + s,-$,, + s,^['$as_cr_digits']*\n,, + ' >$as_me.lineno && + chmod +x $as_me.lineno || + { { echo "$as_me:$LINENO: error: cannot create $as_me.lineno; rerun with a POSIX shell" >&5 +echo "$as_me: error: cannot create $as_me.lineno; rerun with a POSIX shell" >&2;} + { (exit 1); exit 1; }; } + + # Don't try to exec as it changes $[0], causing all sort of problems + # (the dirname of $[0] is not the place where we might find the + # original and so on. Autoconf is especially sensible to this). + . ./$as_me.lineno + # Exit status is that of the last command. + exit +} + + +case `echo "testing\c"; echo 1,2,3`,`echo -n testing; echo 1,2,3` in + *c*,-n*) ECHO_N= ECHO_C=' +' ECHO_T=' ' ;; + *c*,* ) ECHO_N=-n ECHO_C= ECHO_T= ;; + *) ECHO_N= ECHO_C='\c' ECHO_T= ;; +esac + +if expr a : '\(a\)' >/dev/null 2>&1; then + as_expr=expr +else + as_expr=false +fi + +rm -f conf$$ conf$$.exe conf$$.file +echo >conf$$.file +if ln -s conf$$.file conf$$ 2>/dev/null; then + # We could just check for DJGPP; but this test a) works b) is more generic + # and c) will remain valid once DJGPP supports symlinks (DJGPP 2.04). + if test -f conf$$.exe; then + # Don't use ln at all; we don't have any links + as_ln_s='cp -p' + else + as_ln_s='ln -s' + fi +elif ln conf$$.file conf$$ 2>/dev/null; then + as_ln_s=ln +else + as_ln_s='cp -p' +fi +rm -f conf$$ conf$$.exe conf$$.file + +if mkdir -p . 2>/dev/null; then + as_mkdir_p=: +else + test -d ./-p && rmdir ./-p + as_mkdir_p=false +fi + +as_executable_p="test -f" + +# Sed expression to map a string onto a valid CPP name. +as_tr_cpp="eval sed 'y%*$as_cr_letters%P$as_cr_LETTERS%;s%[^_$as_cr_alnum]%_%g'" + +# Sed expression to map a string onto a valid variable name. +as_tr_sh="eval sed 'y%*+%pp%;s%[^_$as_cr_alnum]%_%g'" + + +# IFS +# We need space, tab and new line, in precisely that order. +as_nl=' +' +IFS=" $as_nl" + +# CDPATH. +$as_unset CDPATH + +exec 6>&1 + +# Open the log real soon, to keep \$[0] and so on meaningful, and to +# report actual input values of CONFIG_FILES etc. instead of their +# values after options handling. Logging --version etc. is OK. +exec 5>>config.log +{ + echo + sed 'h;s/./-/g;s/^.../## /;s/...$/ ##/;p;x;p;x' <<_ASBOX +## Running $as_me. ## +_ASBOX +} >&5 +cat >&5 <<_CSEOF + +This file was extended by GNU C Runtime Library $as_me 1.0, which was +generated by GNU Autoconf 2.59. Invocation command line was + + CONFIG_FILES = $CONFIG_FILES + CONFIG_HEADERS = $CONFIG_HEADERS + CONFIG_LINKS = $CONFIG_LINKS + CONFIG_COMMANDS = $CONFIG_COMMANDS + $ $0 $@ + +_CSEOF +echo "on `(hostname || uname -n) 2>/dev/null | sed 1q`" >&5 +echo >&5 +_ACEOF + +# Files that config.status was made for. +if test -n "$ac_config_files"; then + echo "config_files=\"$ac_config_files\"" >>$CONFIG_STATUS +fi + +if test -n "$ac_config_headers"; then + echo "config_headers=\"$ac_config_headers\"" >>$CONFIG_STATUS +fi + +if test -n "$ac_config_links"; then + echo "config_links=\"$ac_config_links\"" >>$CONFIG_STATUS +fi + +if test -n "$ac_config_commands"; then + echo "config_commands=\"$ac_config_commands\"" >>$CONFIG_STATUS +fi + +cat >>$CONFIG_STATUS <<\_ACEOF + +ac_cs_usage="\ +\`$as_me' instantiates files from templates according to the +current configuration. + +Usage: $0 [OPTIONS] [FILE]... + + -h, --help print this help, then exit + -V, --version print version number, then exit + -q, --quiet do not print progress messages + -d, --debug don't remove temporary files + --recheck update $as_me by reconfiguring in the same conditions + --file=FILE[:TEMPLATE] + instantiate the configuration file FILE + +Configuration files: +$config_files + +Configuration commands: +$config_commands + +Report bugs to ." +_ACEOF + +cat >>$CONFIG_STATUS <<_ACEOF +ac_cs_version="\\ +GNU C Runtime Library config.status 1.0 +configured by $0, generated by GNU Autoconf 2.59, + with options \\"`echo "$ac_configure_args" | sed 's/[\\""\`\$]/\\\\&/g'`\\" + +Copyright (C) 2003 Free Software Foundation, Inc. +This config.status script is free software; the Free Software Foundation +gives unlimited permission to copy, distribute and modify it." +srcdir=$srcdir +INSTALL="$INSTALL" +_ACEOF + +cat >>$CONFIG_STATUS <<\_ACEOF +# If no file are specified by the user, then we need to provide default +# value. By we need to know if files were specified by the user. +ac_need_defaults=: +while test $# != 0 +do + case $1 in + --*=*) + ac_option=`expr "x$1" : 'x\([^=]*\)='` + ac_optarg=`expr "x$1" : 'x[^=]*=\(.*\)'` + ac_shift=: + ;; + -*) + ac_option=$1 + ac_optarg=$2 + ac_shift=shift + ;; + *) # This is not an option, so the user has probably given explicit + # arguments. + ac_option=$1 + ac_need_defaults=false;; + esac + + case $ac_option in + # Handling of the options. +_ACEOF +cat >>$CONFIG_STATUS <<\_ACEOF + -recheck | --recheck | --rechec | --reche | --rech | --rec | --re | --r) + ac_cs_recheck=: ;; + --version | --vers* | -V ) + echo "$ac_cs_version"; exit 0 ;; + --he | --h) + # Conflict between --help and --header + { { echo "$as_me:$LINENO: error: ambiguous option: $1 +Try \`$0 --help' for more information." >&5 +echo "$as_me: error: ambiguous option: $1 +Try \`$0 --help' for more information." >&2;} + { (exit 1); exit 1; }; };; + --help | --hel | -h ) + echo "$ac_cs_usage"; exit 0 ;; + --debug | --d* | -d ) + debug=: ;; + --file | --fil | --fi | --f ) + $ac_shift + CONFIG_FILES="$CONFIG_FILES $ac_optarg" + ac_need_defaults=false;; + --header | --heade | --head | --hea ) + $ac_shift + CONFIG_HEADERS="$CONFIG_HEADERS $ac_optarg" + ac_need_defaults=false;; + -q | -quiet | --quiet | --quie | --qui | --qu | --q \ + | -silent | --silent | --silen | --sile | --sil | --si | --s) + ac_cs_silent=: ;; + + # This is an error. + -*) { { echo "$as_me:$LINENO: error: unrecognized option: $1 +Try \`$0 --help' for more information." >&5 +echo "$as_me: error: unrecognized option: $1 +Try \`$0 --help' for more information." >&2;} + { (exit 1); exit 1; }; } ;; + + *) ac_config_targets="$ac_config_targets $1" ;; + + esac + shift +done + +ac_configure_extra_args= + +if $ac_cs_silent; then + exec 6>/dev/null + ac_configure_extra_args="$ac_configure_extra_args --silent" +fi + +_ACEOF +cat >>$CONFIG_STATUS <<_ACEOF +if \$ac_cs_recheck; then + echo "running $SHELL $0 " $ac_configure_args \$ac_configure_extra_args " --no-create --no-recursion" >&6 + exec $SHELL $0 $ac_configure_args \$ac_configure_extra_args --no-create --no-recursion +fi + +_ACEOF + +cat >>$CONFIG_STATUS <<_ACEOF +# +# INIT-COMMANDS section. +# + +srcdir=${srcdir} +host=${host} +with_target_subdir=${with_target_subdir} +with_multisubdir=${with_multisubdir} +ac_configure_args="--enable-multilib ${ac_configure_args}" +CONFIG_SHELL=${CONFIG_SHELL-/bin/sh} +libgcc_topdir=${libgcc_topdir} +CC="${CC}" + + +_ACEOF + + + +cat >>$CONFIG_STATUS <<\_ACEOF +for ac_config_target in $ac_config_targets +do + case "$ac_config_target" in + # Handling of arguments. + "Makefile" ) CONFIG_FILES="$CONFIG_FILES Makefile" ;; + "default" ) CONFIG_COMMANDS="$CONFIG_COMMANDS default" ;; + *) { { echo "$as_me:$LINENO: error: invalid argument: $ac_config_target" >&5 +echo "$as_me: error: invalid argument: $ac_config_target" >&2;} + { (exit 1); exit 1; }; };; + esac +done + +# If the user did not use the arguments to specify the items to instantiate, +# then the envvar interface is used. Set only those that are not. +# We use the long form for the default assignment because of an extremely +# bizarre bug on SunOS 4.1.3. +if $ac_need_defaults; then + test "${CONFIG_FILES+set}" = set || CONFIG_FILES=$config_files + test "${CONFIG_COMMANDS+set}" = set || CONFIG_COMMANDS=$config_commands +fi + +# Have a temporary directory for convenience. Make it in the build tree +# simply because there is no reason to put it here, and in addition, +# creating and moving files from /tmp can sometimes cause problems. +# Create a temporary directory, and hook for its removal unless debugging. +$debug || +{ + trap 'exit_status=$?; rm -rf $tmp && exit $exit_status' 0 + trap '{ (exit 1); exit 1; }' 1 2 13 15 +} + +# Create a (secure) tmp directory for tmp files. + +{ + tmp=`(umask 077 && mktemp -d -q "./confstatXXXXXX") 2>/dev/null` && + test -n "$tmp" && test -d "$tmp" +} || +{ + tmp=./confstat$$-$RANDOM + (umask 077 && mkdir $tmp) +} || +{ + echo "$me: cannot create a temporary directory in ." >&2 + { (exit 1); exit 1; } +} + +_ACEOF + +cat >>$CONFIG_STATUS <<_ACEOF + +# +# CONFIG_FILES section. +# + +# No need to generate the scripts if there are no CONFIG_FILES. +# This happens for instance when ./config.status config.h +if test -n "\$CONFIG_FILES"; then + # Protect against being on the right side of a sed subst in config.status. + sed 's/,@/@@/; s/@,/@@/; s/,;t t\$/@;t t/; /@;t t\$/s/[\\\\&,]/\\\\&/g; + s/@@/,@/; s/@@/@,/; s/@;t t\$/,;t t/' >\$tmp/subs.sed <<\\CEOF +s,@SHELL@,$SHELL,;t t +s,@PATH_SEPARATOR@,$PATH_SEPARATOR,;t t +s,@PACKAGE_NAME@,$PACKAGE_NAME,;t t +s,@PACKAGE_TARNAME@,$PACKAGE_TARNAME,;t t +s,@PACKAGE_VERSION@,$PACKAGE_VERSION,;t t +s,@PACKAGE_STRING@,$PACKAGE_STRING,;t t +s,@PACKAGE_BUGREPORT@,$PACKAGE_BUGREPORT,;t t +s,@exec_prefix@,$exec_prefix,;t t +s,@prefix@,$prefix,;t t +s,@program_transform_name@,$program_transform_name,;t t +s,@bindir@,$bindir,;t t +s,@sbindir@,$sbindir,;t t +s,@libexecdir@,$libexecdir,;t t +s,@datadir@,$datadir,;t t +s,@sysconfdir@,$sysconfdir,;t t +s,@sharedstatedir@,$sharedstatedir,;t t +s,@localstatedir@,$localstatedir,;t t +s,@libdir@,$libdir,;t t +s,@includedir@,$includedir,;t t +s,@oldincludedir@,$oldincludedir,;t t +s,@infodir@,$infodir,;t t +s,@mandir@,$mandir,;t t +s,@build_alias@,$build_alias,;t t +s,@host_alias@,$host_alias,;t t +s,@target_alias@,$target_alias,;t t +s,@DEFS@,$DEFS,;t t +s,@ECHO_C@,$ECHO_C,;t t +s,@ECHO_N@,$ECHO_N,;t t +s,@ECHO_T@,$ECHO_T,;t t +s,@LIBS@,$LIBS,;t t +s,@libgcc_topdir@,$libgcc_topdir,;t t +s,@enable_shared@,$enable_shared,;t t +s,@slibdir@,$slibdir,;t t +s,@INSTALL_PROGRAM@,$INSTALL_PROGRAM,;t t +s,@INSTALL_SCRIPT@,$INSTALL_SCRIPT,;t t +s,@INSTALL_DATA@,$INSTALL_DATA,;t t +s,@AWK@,$AWK,;t t +s,@build@,$build,;t t +s,@build_cpu@,$build_cpu,;t t +s,@build_vendor@,$build_vendor,;t t +s,@build_os@,$build_os,;t t +s,@host@,$host,;t t +s,@host_cpu@,$host_cpu,;t t +s,@host_vendor@,$host_vendor,;t t +s,@host_os@,$host_os,;t t +s,@host_noncanonical@,$host_noncanonical,;t t +s,@build_libsubdir@,$build_libsubdir,;t t +s,@build_subdir@,$build_subdir,;t t +s,@host_subdir@,$host_subdir,;t t +s,@target_subdir@,$target_subdir,;t t +s,@AR@,$AR,;t t +s,@ac_ct_AR@,$ac_ct_AR,;t t +s,@LIPO@,$LIPO,;t t +s,@ac_ct_LIPO@,$ac_ct_LIPO,;t t +s,@NM@,$NM,;t t +s,@ac_ct_NM@,$ac_ct_NM,;t t +s,@RANLIB@,$RANLIB,;t t +s,@ac_ct_RANLIB@,$ac_ct_RANLIB,;t t +s,@STRIP@,$STRIP,;t t +s,@ac_ct_STRIP@,$ac_ct_STRIP,;t t +s,@LN_S@,$LN_S,;t t +s,@CC@,$CC,;t t +s,@CFLAGS@,$CFLAGS,;t t +s,@LDFLAGS@,$LDFLAGS,;t t +s,@CPPFLAGS@,$CPPFLAGS,;t t +s,@ac_ct_CC@,$ac_ct_CC,;t t +s,@EXEEXT@,$EXEEXT,;t t +s,@OBJEXT@,$OBJEXT,;t t +s,@CPP@,$CPP,;t t +s,@decimal_float@,$decimal_float,;t t +s,@enable_decimal_float@,$enable_decimal_float,;t t +s,@fixed_point@,$fixed_point,;t t +s,@vis_hide@,$vis_hide,;t t +s,@set_have_cc_tls@,$set_have_cc_tls,;t t +s,@tmake_file@,$tmake_file,;t t +s,@extra_parts@,$extra_parts,;t t +s,@asm_hidden_op@,$asm_hidden_op,;t t +s,@LIBOBJS@,$LIBOBJS,;t t +s,@LTLIBOBJS@,$LTLIBOBJS,;t t +CEOF + +_ACEOF + + cat >>$CONFIG_STATUS <<\_ACEOF + # Split the substitutions into bite-sized pieces for seds with + # small command number limits, like on Digital OSF/1 and HP-UX. + ac_max_sed_lines=48 + ac_sed_frag=1 # Number of current file. + ac_beg=1 # First line for current file. + ac_end=$ac_max_sed_lines # Line after last line for current file. + ac_more_lines=: + ac_sed_cmds= + while $ac_more_lines; do + if test $ac_beg -gt 1; then + sed "1,${ac_beg}d; ${ac_end}q" $tmp/subs.sed >$tmp/subs.frag + else + sed "${ac_end}q" $tmp/subs.sed >$tmp/subs.frag + fi + if test ! 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Generated by config.status. */ + if test x"$ac_file" = x-; then + configure_input= + else + configure_input="$ac_file. " + fi + configure_input=$configure_input"Generated from `echo $ac_file_in | + sed 's,.*/,,'` by configure." + + # First look for the input files in the build tree, otherwise in the + # src tree. + ac_file_inputs=`IFS=: + for f in $ac_file_in; do + case $f in + -) echo $tmp/stdin ;; + [\\/$]*) + # Absolute (can't be DOS-style, as IFS=:) + test -f "$f" || { { echo "$as_me:$LINENO: error: cannot find input file: $f" >&5 +echo "$as_me: error: cannot find input file: $f" >&2;} + { (exit 1); exit 1; }; } + echo "$f";; + *) # Relative + if test -f "$f"; then + # Build tree + echo "$f" + elif test -f "$srcdir/$f"; then + # Source tree + echo "$srcdir/$f" + else + # /dev/null tree + { { echo "$as_me:$LINENO: error: cannot find input file: $f" >&5 +echo "$as_me: error: cannot find input file: $f" >&2;} + { (exit 1); exit 1; }; } + fi;; + esac + done` || { (exit 1); exit 1; } +_ACEOF +cat >>$CONFIG_STATUS <<_ACEOF + sed "$ac_vpsub +$extrasub +_ACEOF +cat >>$CONFIG_STATUS <<\_ACEOF +:t +/@[a-zA-Z_][a-zA-Z_0-9]*@/!b +s,@configure_input@,$configure_input,;t t +s,@srcdir@,$ac_srcdir,;t t +s,@abs_srcdir@,$ac_abs_srcdir,;t t +s,@top_srcdir@,$ac_top_srcdir,;t t +s,@abs_top_srcdir@,$ac_abs_top_srcdir,;t t +s,@builddir@,$ac_builddir,;t t +s,@abs_builddir@,$ac_abs_builddir,;t t +s,@top_builddir@,$ac_top_builddir,;t t +s,@abs_top_builddir@,$ac_abs_top_builddir,;t t +s,@INSTALL@,$ac_INSTALL,;t t +" $ac_file_inputs | (eval "$ac_sed_cmds") >$tmp/out + rm -f $tmp/stdin + if test x"$ac_file" != x-; then + mv $tmp/out $ac_file + else + cat $tmp/out + rm -f $tmp/out + fi + +done +_ACEOF +cat >>$CONFIG_STATUS <<\_ACEOF + +# +# CONFIG_COMMANDS section. +# +for ac_file in : $CONFIG_COMMANDS; do test "x$ac_file" = x: && continue + ac_dest=`echo "$ac_file" | sed 's,:.*,,'` + ac_source=`echo "$ac_file" | sed 's,[^:]*:,,'` + ac_dir=`(dirname "$ac_dest") 2>/dev/null || +$as_expr X"$ac_dest" : 'X\(.*[^/]\)//*[^/][^/]*/*$' \| \ + X"$ac_dest" : 'X\(//\)[^/]' \| \ + X"$ac_dest" : 'X\(//\)$' \| \ + X"$ac_dest" : 'X\(/\)' \| \ + . : '\(.\)' 2>/dev/null || +echo X"$ac_dest" | + sed '/^X\(.*[^/]\)\/\/*[^/][^/]*\/*$/{ s//\1/; q; } + /^X\(\/\/\)[^/].*/{ s//\1/; q; } + /^X\(\/\/\)$/{ s//\1/; q; } + /^X\(\/\).*/{ s//\1/; q; } + s/.*/./; q'` + { if $as_mkdir_p; then + mkdir -p "$ac_dir" + else + as_dir="$ac_dir" + as_dirs= + while test ! -d "$as_dir"; do + as_dirs="$as_dir $as_dirs" + as_dir=`(dirname "$as_dir") 2>/dev/null || +$as_expr X"$as_dir" : 'X\(.*[^/]\)//*[^/][^/]*/*$' \| \ + X"$as_dir" : 'X\(//\)[^/]' \| \ + X"$as_dir" : 'X\(//\)$' \| \ + X"$as_dir" : 'X\(/\)' \| \ + . : '\(.\)' 2>/dev/null || +echo X"$as_dir" | + sed '/^X\(.*[^/]\)\/\/*[^/][^/]*\/*$/{ s//\1/; q; } + /^X\(\/\/\)[^/].*/{ s//\1/; q; } + /^X\(\/\/\)$/{ s//\1/; q; } + /^X\(\/\).*/{ s//\1/; q; } + s/.*/./; q'` + done + test ! -n "$as_dirs" || mkdir $as_dirs + fi || { { echo "$as_me:$LINENO: error: cannot create directory \"$ac_dir\"" >&5 +echo "$as_me: error: cannot create directory \"$ac_dir\"" >&2;} + { (exit 1); exit 1; }; }; } + + ac_builddir=. + +if test "$ac_dir" != .; then + ac_dir_suffix=/`echo "$ac_dir" | sed 's,^\.[\\/],,'` + # A "../" for each directory in $ac_dir_suffix. + ac_top_builddir=`echo "$ac_dir_suffix" | sed 's,/[^\\/]*,../,g'` +else + ac_dir_suffix= ac_top_builddir= +fi + +case $srcdir in + .) # No --srcdir option. We are building in place. + ac_srcdir=. + if test -z "$ac_top_builddir"; then + ac_top_srcdir=. + else + ac_top_srcdir=`echo $ac_top_builddir | sed 's,/$,,'` + fi ;; + [\\/]* | ?:[\\/]* ) # Absolute path. + ac_srcdir=$srcdir$ac_dir_suffix; + ac_top_srcdir=$srcdir ;; + *) # Relative path. + ac_srcdir=$ac_top_builddir$srcdir$ac_dir_suffix + ac_top_srcdir=$ac_top_builddir$srcdir ;; +esac + +# Do not use `cd foo && pwd` to compute absolute paths, because +# the directories may not exist. +case `pwd` in +.) ac_abs_builddir="$ac_dir";; +*) + case "$ac_dir" in + .) ac_abs_builddir=`pwd`;; + [\\/]* | ?:[\\/]* ) ac_abs_builddir="$ac_dir";; + *) ac_abs_builddir=`pwd`/"$ac_dir";; + esac;; +esac +case $ac_abs_builddir in +.) ac_abs_top_builddir=${ac_top_builddir}.;; +*) + case ${ac_top_builddir}. in + .) ac_abs_top_builddir=$ac_abs_builddir;; + [\\/]* | ?:[\\/]* ) ac_abs_top_builddir=${ac_top_builddir}.;; + *) ac_abs_top_builddir=$ac_abs_builddir/${ac_top_builddir}.;; + esac;; +esac +case $ac_abs_builddir in +.) ac_abs_srcdir=$ac_srcdir;; +*) + case $ac_srcdir in + .) ac_abs_srcdir=$ac_abs_builddir;; + [\\/]* | ?:[\\/]* ) ac_abs_srcdir=$ac_srcdir;; + *) ac_abs_srcdir=$ac_abs_builddir/$ac_srcdir;; + esac;; +esac +case $ac_abs_builddir in +.) ac_abs_top_srcdir=$ac_top_srcdir;; +*) + case $ac_top_srcdir in + .) ac_abs_top_srcdir=$ac_abs_builddir;; + [\\/]* | ?:[\\/]* ) ac_abs_top_srcdir=$ac_top_srcdir;; + *) ac_abs_top_srcdir=$ac_abs_builddir/$ac_top_srcdir;; + esac;; +esac + + + { echo "$as_me:$LINENO: executing $ac_dest commands" >&5 +echo "$as_me: executing $ac_dest commands" >&6;} + case $ac_dest in + default ) test -z "$CONFIG_HEADERS" || echo timestamp > stamp-h +if test -n "$CONFIG_FILES"; then + # FIXME: We shouldn't need to set ac_file + ac_file=Makefile + . ${libgcc_topdir}/config-ml.in +fi ;; + esac +done +_ACEOF + +cat >>$CONFIG_STATUS <<\_ACEOF + +{ (exit 0); exit 0; } +_ACEOF +chmod +x $CONFIG_STATUS +ac_clean_files=$ac_clean_files_save + + +# configure is writing to config.log, and then calls config.status. +# config.status does its own redirection, appending to config.log. +# Unfortunately, on DOS this fails, as config.log is still kept open +# by configure, so config.status won't be able to write to it; its +# output is simply discarded. So we exec the FD to /dev/null, +# effectively closing config.log, so it can be properly (re)opened and +# appended to by config.status. When coming back to configure, we +# need to make the FD available again. +if test "$no_create" != yes; then + ac_cs_success=: + ac_config_status_args= + test "$silent" = yes && + ac_config_status_args="$ac_config_status_args --quiet" + exec 5>/dev/null + $SHELL $CONFIG_STATUS $ac_config_status_args || ac_cs_success=false + exec 5>>config.log + # Use ||, not &&, to avoid exiting from the if with $? = 1, which + # would make configure fail if this is the last instruction. + $ac_cs_success || { (exit 1); exit 1; } +fi + diff --git a/gcc-4.4.3/libgcc/configure.ac b/gcc-4.4.3/libgcc/configure.ac new file mode 100644 index 000000000..d48bccce0 --- /dev/null +++ b/gcc-4.4.3/libgcc/configure.ac @@ -0,0 +1,260 @@ +dnl Process this file with autoconf to produce a configure script. + +sinclude(../config/enable.m4) +sinclude(../config/tls.m4) +sinclude(../config/acx.m4) +sinclude(../config/no-executables.m4) +sinclude(../config/override.m4) + +AC_PREREQ(2.59) +AC_INIT([GNU C Runtime Library], 1.0,,[libgcc]) +AC_CONFIG_SRCDIR([static-object.mk]) + +AC_ARG_WITH(target-subdir, +[ --with-target-subdir=SUBDIR Configuring in a subdirectory for target]) +AC_ARG_WITH(cross-host, +[ --with-cross-host=HOST Configuring with a cross compiler]) +AC_ARG_WITH(ld, +[ --with-ld arrange to use the specified ld (full pathname)]) + +if test "${srcdir}" = "."; then + if test -n "${with_build_subdir}"; then + libgcc_topdir="${srcdir}/../.." + with_target_subdir= + elif test -z "${with_target_subdir}"; then + libgcc_topdir="${srcdir}/.." + else + if test "${with_target_subdir}" != "."; then + libgcc_topdir="${srcdir}/${with_multisrctop}../.." + else + libgcc_topdir="${srcdir}/${with_multisrctop}.." + fi + fi +else + libgcc_topdir="${srcdir}/.." +fi +AC_SUBST(libgcc_topdir) +AC_CONFIG_AUX_DIR($libgcc_topdir) + +AC_ARG_ENABLE(shared, +[ --disable-shared don't provide a shared libgcc], +[ + case $enable_shared in + yes | no) ;; + *) + enable_shared=no + IFS="${IFS= }"; ac_save_ifs="$IFS"; IFS="${IFS}:," + for pkg in $enableval; do + if test "X$pkg" = "Xgcc" || test "X$pkg" = "Xlibgcc"; then + enable_shared=yes + fi + done + IFS="$ac_save_ifs" + ;; + esac +], [enable_shared=yes]) +AC_SUBST(enable_shared) + +AC_MSG_CHECKING([for --enable-version-specific-runtime-libs]) +AC_ARG_ENABLE(version-specific-runtime-libs, +[ --enable-version-specific-runtime-libs Specify that runtime libraries should be installed in a compiler-specific directory ], +[case "$enableval" in + yes) version_specific_libs=yes ;; + no) version_specific_libs=no ;; + *) AC_MSG_ERROR([Unknown argument to enable/disable version-specific libs]);; + esac], +[version_specific_libs=no]) +AC_MSG_RESULT($version_specific_libs) + +AC_ARG_WITH(slibdir, +[ --with-slibdir=DIR shared libraries in DIR [LIBDIR]], +slibdir="$with_slibdir", +if test "${version_specific_libs}" = yes; then + slibdir='$(libsubdir)' +elif test -n "$with_cross_host" && test x"$with_cross_host" != x"no"; then + slibdir='$(exec_prefix)/$(host_noncanonical)/lib' +else + slibdir='$(libdir)' +fi) +AC_SUBST(slibdir) + +AC_PROG_INSTALL + +AC_PROG_AWK +# We need awk; bail out if it's missing. +case ${AWK} in + "") AC_MSG_ERROR([can't build without awk, bailing out]) ;; +esac + +AC_CANONICAL_HOST +ACX_NONCANONICAL_HOST +GCC_TOPLEV_SUBDIRS + +dnl These must be called before AM_PROG_LIBTOOL, because it may want +dnl to call AC_CHECK_PROG. +AC_CHECK_TOOL(AR, ar) +AC_CHECK_TOOL(LIPO, lipo, :) +AC_CHECK_TOOL(NM, nm) +AC_CHECK_TOOL(RANLIB, ranlib, :) +AC_CHECK_TOOL(STRIP, strip, :) +AC_PROG_LN_S + +GCC_NO_EXECUTABLES +AC_PROG_CC +AC_PROG_CPP_WERROR + +# Check for decimal float support. +AC_CACHE_CHECK([whether decimal floating point is supported], [libgcc_cv_dfp], + [AC_COMPILE_IFELSE([_Decimal32 x;], [libgcc_cv_dfp=yes], + [libgcc_cv_dfp=no])]) +decimal_float=$libgcc_cv_dfp +AC_SUBST(decimal_float) + +AC_ARG_ENABLE(decimal-float, +[ --enable-decimal-float={no,yes,bid,dpd} + enable decimal float extension to C. Selecting 'bid' + or 'dpd' choses which decimal floating point format + to use], +[ + case $enable_decimal_float in + yes | no | bid | dpd) ;; + *) AC_MSG_ERROR(['$enable_decimal_float' is an invalid value for --enable-decimal-float. +Valid choices are 'yes', 'bid', 'dpd', and 'no'.]) ;; + esac +], +[ + case $host in + powerpc*-*-linux* | i?86*-*-linux* | x86_64*-*-linux*) + enable_decimal_float=yes + ;; + *) + enable_decimal_float=no + ;; + esac +]) + +# x86's use BID format instead of DPD +if test x$enable_decimal_float = xyes; then + case $host in + i?86*-*-linux* | x86_64*-*-linux*) + enable_decimal_float=bid + ;; + *) + enable_decimal_float=dpd + ;; + esac +fi +AC_SUBST(enable_decimal_float) + +# Check for fixed-point support. +AC_CACHE_CHECK([whether fixed-point is supported], [libgcc_cv_fixed_point], + [AC_COMPILE_IFELSE([_Sat _Fract x;], [libgcc_cv_fixed_point=yes], + [libgcc_cv_fixed_point=no])]) +fixed_point=$libgcc_cv_fixed_point +AC_SUBST(fixed_point) + +# Check 32bit or 64bit for x86. +case ${host} in +i?86*-*-* | x86_64*-*-*) + cat > conftest.c < conftest.s <&AS_MESSAGE_LOG_FD); then + # configure expects config files in libgcc/config, so need a relative + # path here. + tmake_file="${tmake_file} ../../gcc/config/i386/t-crtstuff" + fi + ;; +esac + +# Check for visibility support. This is after config.host so that +# we can check for asm_hidden_op. +AC_CACHE_CHECK([for __attribute__((visibility("hidden")))], + libgcc_cv_hidden_visibility_attribute, [ + echo 'int __attribute__ ((visibility ("hidden"))) foo (void) { return 1; }' > conftest.c + libgcc_cv_hidden_visibility_attribute=no + if AC_TRY_COMMAND(${CC-cc} -Werror -S conftest.c -o conftest.s 1>&AS_MESSAGE_LOG_FD); then + if grep "\\$asm_hidden_op.*foo" conftest.s >/dev/null; then + libgcc_cv_hidden_visibility_attribute=yes + fi + fi + rm -f conftest.* + ]) + +if test $libgcc_cv_hidden_visibility_attribute = yes; then + vis_hide='-fvisibility=hidden -DHIDE_EXPORTS' +else + vis_hide= +fi +AC_SUBST(vis_hide) + +# See if we have thread-local storage. We can only test assembler +# sicne link-time and run-time tests require the newly built +# gcc, which can't be used to build executable due to that libgcc +# is yet to be built here. +GCC_CHECK_CC_TLS +set_have_cc_tls= +if test "$enable_tls $gcc_cv_have_cc_tls" = "yes yes"; then + set_have_cc_tls="-DHAVE_CC_TLS" +fi +AC_SUBST(set_have_cc_tls) + +# Conditionalize the makefile for this target machine. +tmake_file_= +for f in ${tmake_file} +do + if test -f ${srcdir}/config/$f + then + tmake_file_="${tmake_file_} \$(srcdir)/config/$f" + fi +done +tmake_file="${tmake_file_}" +AC_SUBST(tmake_file) + +# Substitute configuration variables +AC_SUBST(extra_parts) +AC_SUBST(asm_hidden_op) + +# We need multilib support. +AC_CONFIG_FILES([Makefile]) +AC_CONFIG_COMMANDS([default], + [[test -z "$CONFIG_HEADERS" || echo timestamp > stamp-h +if test -n "$CONFIG_FILES"; then + # FIXME: We shouldn't need to set ac_file + ac_file=Makefile + . ${libgcc_topdir}/config-ml.in +fi]], +[[srcdir=${srcdir} +host=${host} +with_target_subdir=${with_target_subdir} +with_multisubdir=${with_multisubdir} +ac_configure_args="--enable-multilib ${ac_configure_args}" +CONFIG_SHELL=${CONFIG_SHELL-/bin/sh} +libgcc_topdir=${libgcc_topdir} +CC="${CC}" +]]) +AC_OUTPUT diff --git a/gcc-4.4.3/libgcc/empty.mk b/gcc-4.4.3/libgcc/empty.mk new file mode 100644 index 000000000..7b1d97b8b --- /dev/null +++ b/gcc-4.4.3/libgcc/empty.mk @@ -0,0 +1,2 @@ +# Empty. This file exists to suppress errors in the parent Makefile +# when a variable (e.g. LIB2ADD) is empty. diff --git a/gcc-4.4.3/libgcc/fixed-obj.mk b/gcc-4.4.3/libgcc/fixed-obj.mk new file mode 100644 index 000000000..3c7c2f317 --- /dev/null +++ b/gcc-4.4.3/libgcc/fixed-obj.mk @@ -0,0 +1,31 @@ +# This file is included several times in a row, once for each element of +# $(iter-items). On each inclusion, we advance $o to the next element. +# $(iter-labels) and $(iter-from) and $(iter-to) are also advanced. + +o := $(firstword $(iter-items)) +iter-items := $(filter-out $o,$(iter-items)) + +$o-label := $(firstword $(iter-labels)) +iter-labels := $(wordlist 2,$(words $(iter-labels)),$(iter-labels)) + +$o-from := $(firstword $(iter-from)) +iter-from := $(wordlist 2,$(words $(iter-from)),$(iter-from)) + +$o-to := $(firstword $(iter-to)) +iter-to := $(wordlist 2,$(words $(iter-to)),$(iter-to)) + +ifeq ($($o-from),$($o-to)) +$o-opt := -D$($o-from)_MODE +else +$o-opt := -DFROM_$($o-from) -DTO_$($o-to) +endif + +#$(info $o$(objext): -DL$($o-label) $($o-opt)) + +$o$(objext): %$(objext): $(gcc_srcdir)/config/fixed-bit.c + $(gcc_compile) -DL$($*-label) $($*-opt) -c $(gcc_srcdir)/config/fixed-bit.c $(vis_hide) + +ifeq ($(enable_shared),yes) +$(o)_s$(objext): %_s$(objext): $(gcc_srcdir)/config/fixed-bit.c + $(gcc_s_compile) -DL$($*-label) $($*-opt) -c $(gcc_srcdir)/config/fixed-bit.c +endif diff --git a/gcc-4.4.3/libgcc/gen-fixed.sh b/gcc-4.4.3/libgcc/gen-fixed.sh new file mode 100644 index 000000000..774996110 --- /dev/null +++ b/gcc-4.4.3/libgcc/gen-fixed.sh @@ -0,0 +1,105 @@ +#!/bin/sh + +# Worker script for libgcc/Makefile.in +# Generate lists of fixed-point labels, funcs, modes, from, to. +# Usage: +# gen-fixed.sh arith labels +# gen-fixed.sh arith funcs +# gen-fixed.sh arith modes +# gen-fixed.sh conv labels +# gen-fixed.sh conv funcs +# gen-fixed.sh conv from +# gen-fixed.sh conv to + +fixed_sfract_modes="QQ HQ SQ DQ TQ HA SA DA TA" +fixed_ufract_modes="UQQ UHQ USQ UDQ UTQ UHA USA UDA UTA" +fixed_fract_modes="$fixed_sfract_modes $fixed_ufract_modes" + +fixed_signed_modes="QI HI SI DI TI SF DF" +fixed_unsigned_modes="UQI UHI USI UDI UTI" + +fixed_func_names="_add _sub _neg _mul _mulhelper _divhelper _ashl _ashlhelper _cmp _saturate1 _saturate2" +fixed_sfunc_names="_ssadd _sssub _ssneg _ssmul _ssdiv _div _ssashl _ashr" +fixed_ufunc_names="_usadd _ussub _usneg _usmul _usdiv _udiv _usashl _lshr" + +# emit the function information +# $1 = output type selector +# $2 = base function name +# $3 = from mode +# $4 = to mode +emit () +{ + if [ "$3" != "$4" ]; then + case "$1" in + labels) + echo $2 ;; + from | modes) + echo $3 ;; + to) + echo $4 ;; + funcs) + echo $2$3$4 ;; + esac + fi +} + +case "$1" in + arith) + for n in $fixed_func_names; do + for m in $fixed_fract_modes; do + emit $2 $n $m + done + done + + for n in $fixed_sfunc_names; do + for m in $fixed_sfract_modes; do + emit $2 $n $m + done + done + + for n in $fixed_ufunc_names; do + for m in $fixed_ufract_modes; do + emit $2 $n $m + done + done + ;; + + conv) + for f in $fixed_fract_modes; do + for t in $fixed_fract_modes $fixed_signed_modes; do + emit $2 _fract $f $t + done + done + + for f in $fixed_signed_modes; do + for t in $fixed_fract_modes; do + emit $2 _fract $f $t + done + done + + for f in $fixed_fract_modes $fixed_signed_modes; do + for t in $fixed_fract_modes; do + emit $2 _satfract $f $t + done + done + + for f in $fixed_fract_modes; do + for t in $fixed_unsigned_modes; do + emit $2 _fractuns $f $t + done + done + + for f in $fixed_unsigned_modes; do + for t in $fixed_fract_modes; do + emit $2 _fractuns $f $t + done + done + + for f in $fixed_unsigned_modes; do + for t in $fixed_fract_modes; do + emit $2 _satfractuns $f $t + done + done + ;; + +esac diff --git a/gcc-4.4.3/libgcc/gstdint.h b/gcc-4.4.3/libgcc/gstdint.h new file mode 100644 index 000000000..4d61c3184 --- /dev/null +++ b/gcc-4.4.3/libgcc/gstdint.h @@ -0,0 +1,6 @@ +/* This header is only for use of libdecnumber built as part of + libgcc. The targets supported for decimal floating point have + ; libdecnumber uses GCC_HEADER_STDINT only for the sake + of the host. */ + +#include diff --git a/gcc-4.4.3/libgcc/shared-object.mk b/gcc-4.4.3/libgcc/shared-object.mk new file mode 100644 index 000000000..65171b6aa --- /dev/null +++ b/gcc-4.4.3/libgcc/shared-object.mk @@ -0,0 +1,34 @@ +# This file is included several times in a row, once for each element of +# $(iter-items). On each inclusion, we advance $o to the next element. + +o := $(firstword $(iter-items)) +iter-items := $(filter-out $o,$(iter-items)) + +base := $(basename $(notdir $o)) + +ifeq ($(suffix $o),.c) + +$(base)$(objext): $o + $(gcc_compile) $(c_flags) -c $< $(vis_hide) + +$(base)_s$(objext): $o + $(gcc_s_compile) $(c_flags) -c $< + +else + +ifneq ($(suffix $o),.S) +ifneq ($(suffix $o),.asm) +$(error Unsupported file type: $o) +endif +endif + +$(base)$(objext): $o $(base).vis + $(gcc_compile) -c -xassembler-with-cpp -include $*.vis $< + +$(base).vis: $(base)_s$(objext) + $(gen-hide-list) + +$(base)_s$(objext): $o + $(gcc_s_compile) -c -xassembler-with-cpp $< + +endif diff --git a/gcc-4.4.3/libgcc/siditi-object.mk b/gcc-4.4.3/libgcc/siditi-object.mk new file mode 100644 index 000000000..69df8338f --- /dev/null +++ b/gcc-4.4.3/libgcc/siditi-object.mk @@ -0,0 +1,22 @@ +# This file is included several times in a row, once for each element of +# $(iter-items). On each inclusion, we advance $o to the next element. +# $(iter-labels) and $(iter-sizes) are also advanced. + +o := $(firstword $(iter-items)) +iter-items := $(filter-out $o,$(iter-items)) + +$o-label := $(firstword $(iter-labels)) +iter-labels := $(wordlist 2,$(words $(iter-labels)),$(iter-labels)) + +$o-size := $(firstword $(iter-sizes)) +iter-sizes := $(wordlist 2,$(words $(iter-sizes)),$(iter-sizes)) + +$o$(objext): %$(objext): $(gcc_srcdir)/libgcc2.c + $(gcc_compile) -DL$($*-label) -c $(gcc_srcdir)/libgcc2.c $(vis_hide) \ + -DLIBGCC2_UNITS_PER_WORD=$($*-size) + +ifeq ($(enable_shared),yes) +$(o)_s$(objext): %_s$(objext): $(gcc_srcdir)/libgcc2.c + $(gcc_s_compile) -DL$($*-label) -c $(gcc_srcdir)/libgcc2.c \ + -DLIBGCC2_UNITS_PER_WORD=$($*-size) +endif diff --git a/gcc-4.4.3/libgcc/static-object.mk b/gcc-4.4.3/libgcc/static-object.mk new file mode 100644 index 000000000..ab75d3288 --- /dev/null +++ b/gcc-4.4.3/libgcc/static-object.mk @@ -0,0 +1,25 @@ +# This file is included several times in a row, once for each element of +# $(iter-items). On each inclusion, we advance $o to the next element. + +o := $(firstword $(iter-items)) +iter-items := $(filter-out $o,$(iter-items)) + +base := $(basename $(notdir $o)) + +ifeq ($(suffix $o),.c) + +$(base)$(objext): $o + $(gcc_compile) $(c_flags) -c $< $(vis_hide) + +else + +ifneq ($(suffix $o),.S) +ifneq ($(suffix $o),.asm) +$(error Unsupported file type: $o) +endif +endif + +$(base)$(objext): $o + $(gcc_compile) -c -xassembler-with-cpp $< + +endif -- cgit v1.2.3