diff options
Diffstat (limited to 'gcc-4.9/libgcc/soft-fp/op-common.h')
| -rw-r--r-- | gcc-4.9/libgcc/soft-fp/op-common.h | 1706 |
1 files changed, 1706 insertions, 0 deletions
diff --git a/gcc-4.9/libgcc/soft-fp/op-common.h b/gcc-4.9/libgcc/soft-fp/op-common.h new file mode 100644 index 000000000..6f8c1f3cb --- /dev/null +++ b/gcc-4.9/libgcc/soft-fp/op-common.h @@ -0,0 +1,1706 @@ +/* Software floating-point emulation. Common operations. + Copyright (C) 1997-2014 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Richard Henderson (rth@cygnus.com), + Jakub Jelinek (jj@ultra.linux.cz), + David S. Miller (davem@redhat.com) and + Peter Maydell (pmaydell@chiark.greenend.org.uk). + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + In addition to the permissions in the GNU Lesser General Public + License, the Free Software Foundation gives you unlimited + permission to link the compiled version of this file into + combinations with other programs, and to distribute those + combinations without any restriction coming from the use of this + file. (The Lesser General Public License restrictions do apply in + other respects; for example, they cover modification of the file, + and distribution when not linked into a combine executable.) + + The GNU C Library 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 + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define _FP_DECL(wc, X) \ + _FP_I_TYPE X##_c __attribute__ ((unused)); \ + _FP_I_TYPE X##_s __attribute__ ((unused)); \ + _FP_I_TYPE X##_e __attribute__ ((unused)); \ + _FP_FRAC_DECL_##wc (X) + +/* Test whether the qNaN bit denotes a signaling NaN. */ +#define _FP_FRAC_SNANP(fs, X) \ + ((_FP_QNANNEGATEDP) \ + ? (_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs) \ + : !(_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs)) +#define _FP_FRAC_SNANP_SEMIRAW(fs, X) \ + ((_FP_QNANNEGATEDP) \ + ? (_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs) \ + : !(_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs)) + +/* + * Finish truly unpacking a native fp value by classifying the kind + * of fp value and normalizing both the exponent and the fraction. + */ + +#define _FP_UNPACK_CANONICAL(fs, wc, X) \ + do \ + { \ + switch (X##_e) \ + { \ + default: \ + _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \ + _FP_FRAC_SLL_##wc (X, _FP_WORKBITS); \ + X##_e -= _FP_EXPBIAS_##fs; \ + X##_c = FP_CLS_NORMAL; \ + break; \ + \ + case 0: \ + if (_FP_FRAC_ZEROP_##wc (X)) \ + X##_c = FP_CLS_ZERO; \ + else \ + { \ + /* a denormalized number */ \ + _FP_I_TYPE _shift; \ + _FP_FRAC_CLZ_##wc (_shift, X); \ + _shift -= _FP_FRACXBITS_##fs; \ + _FP_FRAC_SLL_##wc (X, (_shift+_FP_WORKBITS)); \ + X##_e -= _FP_EXPBIAS_##fs - 1 + _shift; \ + X##_c = FP_CLS_NORMAL; \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + } \ + break; \ + \ + case _FP_EXPMAX_##fs: \ + if (_FP_FRAC_ZEROP_##wc (X)) \ + X##_c = FP_CLS_INF; \ + else \ + { \ + X##_c = FP_CLS_NAN; \ + /* Check for signaling NaN */ \ + if (_FP_FRAC_SNANP (fs, X)) \ + FP_SET_EXCEPTION (FP_EX_INVALID); \ + } \ + break; \ + } \ + } \ + while (0) + +/* Finish unpacking an fp value in semi-raw mode: the mantissa is + shifted by _FP_WORKBITS but the implicit MSB is not inserted and + other classification is not done. */ +#define _FP_UNPACK_SEMIRAW(fs, wc, X) _FP_FRAC_SLL_##wc (X, _FP_WORKBITS) + +/* A semi-raw value has overflowed to infinity. Adjust the mantissa + and exponent appropriately. */ +#define _FP_OVERFLOW_SEMIRAW(fs, wc, X) \ + do \ + { \ + if (FP_ROUNDMODE == FP_RND_NEAREST \ + || (FP_ROUNDMODE == FP_RND_PINF && !X##_s) \ + || (FP_ROUNDMODE == FP_RND_MINF && X##_s)) \ + { \ + X##_e = _FP_EXPMAX_##fs; \ + _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ + } \ + else \ + { \ + X##_e = _FP_EXPMAX_##fs - 1; \ + _FP_FRAC_SET_##wc (X, _FP_MAXFRAC_##wc); \ + } \ + FP_SET_EXCEPTION (FP_EX_INEXACT); \ + FP_SET_EXCEPTION (FP_EX_OVERFLOW); \ + } \ + while (0) + +/* Check for a semi-raw value being a signaling NaN and raise the + invalid exception if so. */ +#define _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X) \ + do \ + { \ + if (X##_e == _FP_EXPMAX_##fs \ + && !_FP_FRAC_ZEROP_##wc (X) \ + && _FP_FRAC_SNANP_SEMIRAW (fs, X)) \ + FP_SET_EXCEPTION (FP_EX_INVALID); \ + } \ + while (0) + +/* Choose a NaN result from an operation on two semi-raw NaN + values. */ +#define _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP) \ + do \ + { \ + /* _FP_CHOOSENAN expects raw values, so shift as required. */ \ + _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \ + _FP_FRAC_SRL_##wc (Y, _FP_WORKBITS); \ + _FP_CHOOSENAN (fs, wc, R, X, Y, OP); \ + _FP_FRAC_SLL_##wc (R, _FP_WORKBITS); \ + } \ + while (0) + +/* Make the fractional part a quiet NaN, preserving the payload + if possible, otherwise make it the canonical quiet NaN and set + the sign bit accordingly. */ +#define _FP_SETQNAN(fs, wc, X) \ + do \ + { \ + if (_FP_QNANNEGATEDP) \ + { \ + _FP_FRAC_HIGH_RAW_##fs (X) &= _FP_QNANBIT_##fs - 1; \ + if (_FP_FRAC_ZEROP_##wc (X)) \ + { \ + X##_s = _FP_NANSIGN_##fs; \ + _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \ + } \ + } \ + else \ + _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_QNANBIT_##fs; \ + } \ + while (0) +#define _FP_SETQNAN_SEMIRAW(fs, wc, X) \ + do \ + { \ + if (_FP_QNANNEGATEDP) \ + { \ + _FP_FRAC_HIGH_##fs (X) &= _FP_QNANBIT_SH_##fs - 1; \ + if (_FP_FRAC_ZEROP_##wc (X)) \ + { \ + X##_s = _FP_NANSIGN_##fs; \ + _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \ + _FP_FRAC_SLL_##wc (X, _FP_WORKBITS); \ + } \ + } \ + else \ + _FP_FRAC_HIGH_##fs (X) |= _FP_QNANBIT_SH_##fs; \ + } \ + while (0) + +/* Test whether a biased exponent is normal (not zero or maximum). */ +#define _FP_EXP_NORMAL(fs, wc, X) (((X##_e + 1) & _FP_EXPMAX_##fs) > 1) + +/* Prepare to pack an fp value in semi-raw mode: the mantissa is + rounded and shifted right, with the rounding possibly increasing + the exponent (including changing a finite value to infinity). */ +#define _FP_PACK_SEMIRAW(fs, wc, X) \ + do \ + { \ + int _FP_PACK_SEMIRAW_is_tiny \ + = X##_e == 0 && !_FP_FRAC_ZEROP_##wc (X); \ + if (_FP_TININESS_AFTER_ROUNDING \ + && _FP_PACK_SEMIRAW_is_tiny) \ + { \ + FP_DECL_##fs (_FP_PACK_SEMIRAW_T); \ + _FP_FRAC_COPY_##wc (_FP_PACK_SEMIRAW_T, X); \ + _FP_PACK_SEMIRAW_T##_s = X##_s; \ + _FP_PACK_SEMIRAW_T##_e = X##_e; \ + _FP_FRAC_SLL_##wc (_FP_PACK_SEMIRAW_T, 1); \ + _FP_ROUND (wc, _FP_PACK_SEMIRAW_T); \ + if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_SEMIRAW_T)) \ + _FP_PACK_SEMIRAW_is_tiny = 0; \ + } \ + _FP_ROUND (wc, X); \ + if (_FP_PACK_SEMIRAW_is_tiny) \ + { \ + if ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \ + || (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW)) \ + FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \ + } \ + if (_FP_FRAC_HIGH_##fs (X) \ + & (_FP_OVERFLOW_##fs >> 1)) \ + { \ + _FP_FRAC_HIGH_##fs (X) &= ~(_FP_OVERFLOW_##fs >> 1); \ + X##_e++; \ + if (X##_e == _FP_EXPMAX_##fs) \ + _FP_OVERFLOW_SEMIRAW (fs, wc, X); \ + } \ + _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \ + if (X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \ + { \ + if (!_FP_KEEPNANFRACP) \ + { \ + _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \ + X##_s = _FP_NANSIGN_##fs; \ + } \ + else \ + _FP_SETQNAN (fs, wc, X); \ + } \ + } \ + while (0) + +/* + * Before packing the bits back into the native fp result, take care + * of such mundane things as rounding and overflow. Also, for some + * kinds of fp values, the original parts may not have been fully + * extracted -- but that is ok, we can regenerate them now. + */ + +#define _FP_PACK_CANONICAL(fs, wc, X) \ + do \ + { \ + switch (X##_c) \ + { \ + case FP_CLS_NORMAL: \ + X##_e += _FP_EXPBIAS_##fs; \ + if (X##_e > 0) \ + { \ + _FP_ROUND (wc, X); \ + if (_FP_FRAC_OVERP_##wc (fs, X)) \ + { \ + _FP_FRAC_CLEAR_OVERP_##wc (fs, X); \ + X##_e++; \ + } \ + _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \ + if (X##_e >= _FP_EXPMAX_##fs) \ + { \ + /* overflow */ \ + switch (FP_ROUNDMODE) \ + { \ + case FP_RND_NEAREST: \ + X##_c = FP_CLS_INF; \ + break; \ + case FP_RND_PINF: \ + if (!X##_s) \ + X##_c = FP_CLS_INF; \ + break; \ + case FP_RND_MINF: \ + if (X##_s) \ + X##_c = FP_CLS_INF; \ + break; \ + } \ + if (X##_c == FP_CLS_INF) \ + { \ + /* Overflow to infinity */ \ + X##_e = _FP_EXPMAX_##fs; \ + _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ + } \ + else \ + { \ + /* Overflow to maximum normal */ \ + X##_e = _FP_EXPMAX_##fs - 1; \ + _FP_FRAC_SET_##wc (X, _FP_MAXFRAC_##wc); \ + } \ + FP_SET_EXCEPTION (FP_EX_OVERFLOW); \ + FP_SET_EXCEPTION (FP_EX_INEXACT); \ + } \ + } \ + else \ + { \ + /* we've got a denormalized number */ \ + int _FP_PACK_CANONICAL_is_tiny = 1; \ + if (_FP_TININESS_AFTER_ROUNDING && X##_e == 0) \ + { \ + FP_DECL_##fs (_FP_PACK_CANONICAL_T); \ + _FP_FRAC_COPY_##wc (_FP_PACK_CANONICAL_T, X); \ + _FP_PACK_CANONICAL_T##_s = X##_s; \ + _FP_PACK_CANONICAL_T##_e = X##_e; \ + _FP_ROUND (wc, _FP_PACK_CANONICAL_T); \ + if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_CANONICAL_T)) \ + _FP_PACK_CANONICAL_is_tiny = 0; \ + } \ + X##_e = -X##_e + 1; \ + if (X##_e <= _FP_WFRACBITS_##fs) \ + { \ + _FP_FRAC_SRS_##wc (X, X##_e, _FP_WFRACBITS_##fs); \ + _FP_ROUND (wc, X); \ + if (_FP_FRAC_HIGH_##fs (X) \ + & (_FP_OVERFLOW_##fs >> 1)) \ + { \ + X##_e = 1; \ + _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ + FP_SET_EXCEPTION (FP_EX_INEXACT); \ + } \ + else \ + { \ + X##_e = 0; \ + _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \ + } \ + if (_FP_PACK_CANONICAL_is_tiny \ + && ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \ + || (FP_TRAPPING_EXCEPTIONS \ + & FP_EX_UNDERFLOW))) \ + FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \ + } \ + else \ + { \ + /* underflow to zero */ \ + X##_e = 0; \ + if (!_FP_FRAC_ZEROP_##wc (X)) \ + { \ + _FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \ + _FP_ROUND (wc, X); \ + _FP_FRAC_LOW_##wc (X) >>= (_FP_WORKBITS); \ + } \ + FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \ + } \ + } \ + break; \ + \ + case FP_CLS_ZERO: \ + X##_e = 0; \ + _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ + break; \ + \ + case FP_CLS_INF: \ + X##_e = _FP_EXPMAX_##fs; \ + _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ + break; \ + \ + case FP_CLS_NAN: \ + X##_e = _FP_EXPMAX_##fs; \ + if (!_FP_KEEPNANFRACP) \ + { \ + _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \ + X##_s = _FP_NANSIGN_##fs; \ + } \ + else \ + _FP_SETQNAN (fs, wc, X); \ + break; \ + } \ + } \ + while (0) + +/* This one accepts raw argument and not cooked, returns + * 1 if X is a signaling NaN. + */ +#define _FP_ISSIGNAN(fs, wc, X) \ + ({ \ + int __ret = 0; \ + if (X##_e == _FP_EXPMAX_##fs) \ + { \ + if (!_FP_FRAC_ZEROP_##wc (X) \ + && _FP_FRAC_SNANP (fs, X)) \ + __ret = 1; \ + } \ + __ret; \ + }) + + + + + +/* Addition on semi-raw values. */ +#define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \ + do \ + { \ + if (X##_s == Y##_s) \ + { \ + /* Addition. */ \ + R##_s = X##_s; \ + int ediff = X##_e - Y##_e; \ + if (ediff > 0) \ + { \ + R##_e = X##_e; \ + if (Y##_e == 0) \ + { \ + /* Y is zero or denormalized. */ \ + if (_FP_FRAC_ZEROP_##wc (Y)) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ + _FP_FRAC_COPY_##wc (R, X); \ + goto add_done; \ + } \ + else \ + { \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + ediff--; \ + if (ediff == 0) \ + { \ + _FP_FRAC_ADD_##wc (R, X, Y); \ + goto add3; \ + } \ + if (X##_e == _FP_EXPMAX_##fs) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ + _FP_FRAC_COPY_##wc (R, X); \ + goto add_done; \ + } \ + goto add1; \ + } \ + } \ + else if (X##_e == _FP_EXPMAX_##fs) \ + { \ + /* X is NaN or Inf, Y is normal. */ \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ + _FP_FRAC_COPY_##wc (R, X); \ + goto add_done; \ + } \ + \ + /* Insert implicit MSB of Y. */ \ + _FP_FRAC_HIGH_##fs (Y) |= _FP_IMPLBIT_SH_##fs; \ + \ + add1: \ + /* Shift the mantissa of Y to the right EDIFF steps; \ + remember to account later for the implicit MSB of X. */ \ + if (ediff <= _FP_WFRACBITS_##fs) \ + _FP_FRAC_SRS_##wc (Y, ediff, _FP_WFRACBITS_##fs); \ + else if (!_FP_FRAC_ZEROP_##wc (Y)) \ + _FP_FRAC_SET_##wc (Y, _FP_MINFRAC_##wc); \ + _FP_FRAC_ADD_##wc (R, X, Y); \ + } \ + else if (ediff < 0) \ + { \ + ediff = -ediff; \ + R##_e = Y##_e; \ + if (X##_e == 0) \ + { \ + /* X is zero or denormalized. */ \ + if (_FP_FRAC_ZEROP_##wc (X)) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ + _FP_FRAC_COPY_##wc (R, Y); \ + goto add_done; \ + } \ + else \ + { \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + ediff--; \ + if (ediff == 0) \ + { \ + _FP_FRAC_ADD_##wc (R, Y, X); \ + goto add3; \ + } \ + if (Y##_e == _FP_EXPMAX_##fs) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ + _FP_FRAC_COPY_##wc (R, Y); \ + goto add_done; \ + } \ + goto add2; \ + } \ + } \ + else if (Y##_e == _FP_EXPMAX_##fs) \ + { \ + /* Y is NaN or Inf, X is normal. */ \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ + _FP_FRAC_COPY_##wc (R, Y); \ + goto add_done; \ + } \ + \ + /* Insert implicit MSB of X. */ \ + _FP_FRAC_HIGH_##fs (X) |= _FP_IMPLBIT_SH_##fs; \ + \ + add2: \ + /* Shift the mantissa of X to the right EDIFF steps; \ + remember to account later for the implicit MSB of Y. */ \ + if (ediff <= _FP_WFRACBITS_##fs) \ + _FP_FRAC_SRS_##wc (X, ediff, _FP_WFRACBITS_##fs); \ + else if (!_FP_FRAC_ZEROP_##wc (X)) \ + _FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \ + _FP_FRAC_ADD_##wc (R, Y, X); \ + } \ + else \ + { \ + /* ediff == 0. */ \ + if (!_FP_EXP_NORMAL (fs, wc, X)) \ + { \ + if (X##_e == 0) \ + { \ + /* X and Y are zero or denormalized. */ \ + R##_e = 0; \ + if (_FP_FRAC_ZEROP_##wc (X)) \ + { \ + if (!_FP_FRAC_ZEROP_##wc (Y)) \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + _FP_FRAC_COPY_##wc (R, Y); \ + goto add_done; \ + } \ + else if (_FP_FRAC_ZEROP_##wc (Y)) \ + { \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + _FP_FRAC_COPY_##wc (R, X); \ + goto add_done; \ + } \ + else \ + { \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + _FP_FRAC_ADD_##wc (R, X, Y); \ + if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \ + { \ + /* Normalized result. */ \ + _FP_FRAC_HIGH_##fs (R) \ + &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \ + R##_e = 1; \ + } \ + goto add_done; \ + } \ + } \ + else \ + { \ + /* X and Y are NaN or Inf. */ \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ + R##_e = _FP_EXPMAX_##fs; \ + if (_FP_FRAC_ZEROP_##wc (X)) \ + _FP_FRAC_COPY_##wc (R, Y); \ + else if (_FP_FRAC_ZEROP_##wc (Y)) \ + _FP_FRAC_COPY_##wc (R, X); \ + else \ + _FP_CHOOSENAN_SEMIRAW (fs, wc, R, X, Y, OP); \ + goto add_done; \ + } \ + } \ + /* The exponents of X and Y, both normal, are equal. The \ + implicit MSBs will always add to increase the \ + exponent. */ \ + _FP_FRAC_ADD_##wc (R, X, Y); \ + R##_e = X##_e + 1; \ + _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \ + if (R##_e == _FP_EXPMAX_##fs) \ + /* Overflow to infinity (depending on rounding mode). */ \ + _FP_OVERFLOW_SEMIRAW (fs, wc, R); \ + goto add_done; \ + } \ + add3: \ + if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \ + { \ + /* Overflow. */ \ + _FP_FRAC_HIGH_##fs (R) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \ + R##_e++; \ + _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \ + if (R##_e == _FP_EXPMAX_##fs) \ + /* Overflow to infinity (depending on rounding mode). */ \ + _FP_OVERFLOW_SEMIRAW (fs, wc, R); \ + } \ + add_done: ; \ + } \ + else \ + { \ + /* Subtraction. */ \ + int ediff = X##_e - Y##_e; \ + if (ediff > 0) \ + { \ + R##_e = X##_e; \ + R##_s = X##_s; \ + if (Y##_e == 0) \ + { \ + /* Y is zero or denormalized. */ \ + if (_FP_FRAC_ZEROP_##wc (Y)) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ + _FP_FRAC_COPY_##wc (R, X); \ + goto sub_done; \ + } \ + else \ + { \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + ediff--; \ + if (ediff == 0) \ + { \ + _FP_FRAC_SUB_##wc (R, X, Y); \ + goto sub3; \ + } \ + if (X##_e == _FP_EXPMAX_##fs) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ + _FP_FRAC_COPY_##wc (R, X); \ + goto sub_done; \ + } \ + goto sub1; \ + } \ + } \ + else if (X##_e == _FP_EXPMAX_##fs) \ + { \ + /* X is NaN or Inf, Y is normal. */ \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ + _FP_FRAC_COPY_##wc (R, X); \ + goto sub_done; \ + } \ + \ + /* Insert implicit MSB of Y. */ \ + _FP_FRAC_HIGH_##fs (Y) |= _FP_IMPLBIT_SH_##fs; \ + \ + sub1: \ + /* Shift the mantissa of Y to the right EDIFF steps; \ + remember to account later for the implicit MSB of X. */ \ + if (ediff <= _FP_WFRACBITS_##fs) \ + _FP_FRAC_SRS_##wc (Y, ediff, _FP_WFRACBITS_##fs); \ + else if (!_FP_FRAC_ZEROP_##wc (Y)) \ + _FP_FRAC_SET_##wc (Y, _FP_MINFRAC_##wc); \ + _FP_FRAC_SUB_##wc (R, X, Y); \ + } \ + else if (ediff < 0) \ + { \ + ediff = -ediff; \ + R##_e = Y##_e; \ + R##_s = Y##_s; \ + if (X##_e == 0) \ + { \ + /* X is zero or denormalized. */ \ + if (_FP_FRAC_ZEROP_##wc (X)) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ + _FP_FRAC_COPY_##wc (R, Y); \ + goto sub_done; \ + } \ + else \ + { \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + ediff--; \ + if (ediff == 0) \ + { \ + _FP_FRAC_SUB_##wc (R, Y, X); \ + goto sub3; \ + } \ + if (Y##_e == _FP_EXPMAX_##fs) \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ + _FP_FRAC_COPY_##wc (R, Y); \ + goto sub_done; \ + } \ + goto sub2; \ + } \ + } \ + else if (Y##_e == _FP_EXPMAX_##fs) \ + { \ + /* Y is NaN or Inf, X is normal. */ \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ + _FP_FRAC_COPY_##wc (R, Y); \ + goto sub_done; \ + } \ + \ + /* Insert implicit MSB of X. */ \ + _FP_FRAC_HIGH_##fs (X) |= _FP_IMPLBIT_SH_##fs; \ + \ + sub2: \ + /* Shift the mantissa of X to the right EDIFF steps; \ + remember to account later for the implicit MSB of Y. */ \ + if (ediff <= _FP_WFRACBITS_##fs) \ + _FP_FRAC_SRS_##wc (X, ediff, _FP_WFRACBITS_##fs); \ + else if (!_FP_FRAC_ZEROP_##wc (X)) \ + _FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \ + _FP_FRAC_SUB_##wc (R, Y, X); \ + } \ + else \ + { \ + /* ediff == 0. */ \ + if (!_FP_EXP_NORMAL (fs, wc, X)) \ + { \ + if (X##_e == 0) \ + { \ + /* X and Y are zero or denormalized. */ \ + R##_e = 0; \ + if (_FP_FRAC_ZEROP_##wc (X)) \ + { \ + _FP_FRAC_COPY_##wc (R, Y); \ + if (_FP_FRAC_ZEROP_##wc (Y)) \ + R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ + else \ + { \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + R##_s = Y##_s; \ + } \ + goto sub_done; \ + } \ + else if (_FP_FRAC_ZEROP_##wc (Y)) \ + { \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + _FP_FRAC_COPY_##wc (R, X); \ + R##_s = X##_s; \ + goto sub_done; \ + } \ + else \ + { \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + _FP_FRAC_SUB_##wc (R, X, Y); \ + R##_s = X##_s; \ + if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \ + { \ + /* |X| < |Y|, negate result. */ \ + _FP_FRAC_SUB_##wc (R, Y, X); \ + R##_s = Y##_s; \ + } \ + else if (_FP_FRAC_ZEROP_##wc (R)) \ + R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ + goto sub_done; \ + } \ + } \ + else \ + { \ + /* X and Y are NaN or Inf, of opposite signs. */ \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \ + _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \ + R##_e = _FP_EXPMAX_##fs; \ + if (_FP_FRAC_ZEROP_##wc (X)) \ + { \ + if (_FP_FRAC_ZEROP_##wc (Y)) \ + { \ + /* Inf - Inf. */ \ + R##_s = _FP_NANSIGN_##fs; \ + _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ + _FP_FRAC_SLL_##wc (R, _FP_WORKBITS); \ + FP_SET_EXCEPTION (FP_EX_INVALID); \ + } \ + else \ + { \ + /* Inf - NaN. */ \ + R##_s = Y##_s; \ + _FP_FRAC_COPY_##wc (R, Y); \ + } \ + } \ + else \ + { \ + if (_FP_FRAC_ZEROP_##wc (Y)) \ + { \ + /* NaN - Inf. */ \ + R##_s = X##_s; \ + _FP_FRAC_COPY_##wc (R, X); \ + } \ + else \ + { \ + /* NaN - NaN. */ \ + _FP_CHOOSENAN_SEMIRAW (fs, wc, R, X, Y, OP); \ + } \ + } \ + goto sub_done; \ + } \ + } \ + /* The exponents of X and Y, both normal, are equal. The \ + implicit MSBs cancel. */ \ + R##_e = X##_e; \ + _FP_FRAC_SUB_##wc (R, X, Y); \ + R##_s = X##_s; \ + if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \ + { \ + /* |X| < |Y|, negate result. */ \ + _FP_FRAC_SUB_##wc (R, Y, X); \ + R##_s = Y##_s; \ + } \ + else if (_FP_FRAC_ZEROP_##wc (R)) \ + { \ + R##_e = 0; \ + R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ + goto sub_done; \ + } \ + goto norm; \ + } \ + sub3: \ + if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \ + { \ + int diff; \ + /* Carry into most significant bit of larger one of X and Y, \ + canceling it; renormalize. */ \ + _FP_FRAC_HIGH_##fs (R) &= _FP_IMPLBIT_SH_##fs - 1; \ + norm: \ + _FP_FRAC_CLZ_##wc (diff, R); \ + diff -= _FP_WFRACXBITS_##fs; \ + _FP_FRAC_SLL_##wc (R, diff); \ + if (R##_e <= diff) \ + { \ + /* R is denormalized. */ \ + diff = diff - R##_e + 1; \ + _FP_FRAC_SRS_##wc (R, diff, _FP_WFRACBITS_##fs); \ + R##_e = 0; \ + } \ + else \ + { \ + R##_e -= diff; \ + _FP_FRAC_HIGH_##fs (R) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \ + } \ + } \ + sub_done: ; \ + } \ + } \ + while (0) + +#define _FP_ADD(fs, wc, R, X, Y) _FP_ADD_INTERNAL (fs, wc, R, X, Y, '+') +#define _FP_SUB(fs, wc, R, X, Y) \ + do \ + { \ + if (!(Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \ + Y##_s ^= 1; \ + _FP_ADD_INTERNAL (fs, wc, R, X, Y, '-'); \ + } \ + while (0) + + +/* + * Main negation routine. The input value is raw. + */ + +#define _FP_NEG(fs, wc, R, X) \ + do \ + { \ + _FP_FRAC_COPY_##wc (R, X); \ + R##_e = X##_e; \ + R##_s = 1 ^ X##_s; \ + } \ + while (0) + + +/* + * Main multiplication routine. The input values should be cooked. + */ + +#define _FP_MUL(fs, wc, R, X, Y) \ + do \ + { \ + R##_s = X##_s ^ Y##_s; \ + R##_e = X##_e + Y##_e + 1; \ + switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \ + { \ + case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \ + R##_c = FP_CLS_NORMAL; \ + \ + _FP_MUL_MEAT_##fs (R, X, Y); \ + \ + if (_FP_FRAC_OVERP_##wc (fs, R)) \ + _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \ + else \ + R##_e--; \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \ + _FP_CHOOSENAN (fs, wc, R, X, Y, '*'); \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \ + R##_s = X##_s; \ + \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \ + _FP_FRAC_COPY_##wc (R, X); \ + R##_c = X##_c; \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \ + R##_s = Y##_s; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \ + case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \ + _FP_FRAC_COPY_##wc (R, Y); \ + R##_c = Y##_c; \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \ + R##_s = _FP_NANSIGN_##fs; \ + R##_c = FP_CLS_NAN; \ + _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ + FP_SET_EXCEPTION (FP_EX_INVALID); \ + break; \ + \ + default: \ + abort (); \ + } \ + } \ + while (0) + + +/* Fused multiply-add. The input values should be cooked. */ + +#define _FP_FMA(fs, wc, dwc, R, X, Y, Z) \ + do \ + { \ + FP_DECL_##fs (T); \ + T##_s = X##_s ^ Y##_s; \ + T##_e = X##_e + Y##_e + 1; \ + switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \ + { \ + case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \ + switch (Z##_c) \ + { \ + case FP_CLS_INF: \ + case FP_CLS_NAN: \ + R##_s = Z##_s; \ + _FP_FRAC_COPY_##wc (R, Z); \ + R##_c = Z##_c; \ + break; \ + \ + case FP_CLS_ZERO: \ + R##_c = FP_CLS_NORMAL; \ + R##_s = T##_s; \ + R##_e = T##_e; \ + \ + _FP_MUL_MEAT_##fs (R, X, Y); \ + \ + if (_FP_FRAC_OVERP_##wc (fs, R)) \ + _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \ + else \ + R##_e--; \ + break; \ + \ + case FP_CLS_NORMAL:; \ + _FP_FRAC_DECL_##dwc (TD); \ + _FP_FRAC_DECL_##dwc (ZD); \ + _FP_FRAC_DECL_##dwc (RD); \ + _FP_MUL_MEAT_DW_##fs (TD, X, Y); \ + R##_e = T##_e; \ + int tsh = _FP_FRAC_HIGHBIT_DW_##dwc (fs, TD) == 0; \ + T##_e -= tsh; \ + int ediff = T##_e - Z##_e; \ + if (ediff >= 0) \ + { \ + int shift = _FP_WFRACBITS_##fs - tsh - ediff; \ + if (shift <= -_FP_WFRACBITS_##fs) \ + _FP_FRAC_SET_##dwc (ZD, _FP_MINFRAC_##dwc); \ + else \ + { \ + _FP_FRAC_COPY_##dwc##_##wc (ZD, Z); \ + if (shift < 0) \ + _FP_FRAC_SRS_##dwc (ZD, -shift, \ + _FP_WFRACBITS_DW_##fs); \ + else if (shift > 0) \ + _FP_FRAC_SLL_##dwc (ZD, shift); \ + } \ + R##_s = T##_s; \ + if (T##_s == Z##_s) \ + _FP_FRAC_ADD_##dwc (RD, TD, ZD); \ + else \ + { \ + _FP_FRAC_SUB_##dwc (RD, TD, ZD); \ + if (_FP_FRAC_NEGP_##dwc (RD)) \ + { \ + R##_s = Z##_s; \ + _FP_FRAC_SUB_##dwc (RD, ZD, TD); \ + } \ + } \ + } \ + else \ + { \ + R##_e = Z##_e; \ + R##_s = Z##_s; \ + _FP_FRAC_COPY_##dwc##_##wc (ZD, Z); \ + _FP_FRAC_SLL_##dwc (ZD, _FP_WFRACBITS_##fs); \ + int shift = -ediff - tsh; \ + if (shift >= _FP_WFRACBITS_DW_##fs) \ + _FP_FRAC_SET_##dwc (TD, _FP_MINFRAC_##dwc); \ + else if (shift > 0) \ + _FP_FRAC_SRS_##dwc (TD, shift, \ + _FP_WFRACBITS_DW_##fs); \ + if (Z##_s == T##_s) \ + _FP_FRAC_ADD_##dwc (RD, ZD, TD); \ + else \ + _FP_FRAC_SUB_##dwc (RD, ZD, TD); \ + } \ + if (_FP_FRAC_ZEROP_##dwc (RD)) \ + { \ + if (T##_s == Z##_s) \ + R##_s = Z##_s; \ + else \ + R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ + _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \ + R##_c = FP_CLS_ZERO; \ + } \ + else \ + { \ + int rlz; \ + _FP_FRAC_CLZ_##dwc (rlz, RD); \ + rlz -= _FP_WFRACXBITS_DW_##fs; \ + R##_e -= rlz; \ + int shift = _FP_WFRACBITS_##fs - rlz; \ + if (shift > 0) \ + _FP_FRAC_SRS_##dwc (RD, shift, \ + _FP_WFRACBITS_DW_##fs); \ + else if (shift < 0) \ + _FP_FRAC_SLL_##dwc (RD, -shift); \ + _FP_FRAC_COPY_##wc##_##dwc (R, RD); \ + R##_c = FP_CLS_NORMAL; \ + } \ + break; \ + } \ + goto done_fma; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \ + _FP_CHOOSENAN (fs, wc, T, X, Y, '*'); \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \ + T##_s = X##_s; \ + \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \ + _FP_FRAC_COPY_##wc (T, X); \ + T##_c = X##_c; \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \ + T##_s = Y##_s; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \ + case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \ + _FP_FRAC_COPY_##wc (T, Y); \ + T##_c = Y##_c; \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \ + T##_s = _FP_NANSIGN_##fs; \ + T##_c = FP_CLS_NAN; \ + _FP_FRAC_SET_##wc (T, _FP_NANFRAC_##fs); \ + FP_SET_EXCEPTION (FP_EX_INVALID); \ + break; \ + \ + default: \ + abort (); \ + } \ + \ + /* T = X * Y is zero, infinity or NaN. */ \ + switch (_FP_CLS_COMBINE (T##_c, Z##_c)) \ + { \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \ + _FP_CHOOSENAN (fs, wc, R, T, Z, '+'); \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \ + R##_s = T##_s; \ + _FP_FRAC_COPY_##wc (R, T); \ + R##_c = T##_c; \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \ + R##_s = Z##_s; \ + _FP_FRAC_COPY_##wc (R, Z); \ + R##_c = Z##_c; \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \ + if (T##_s == Z##_s) \ + { \ + R##_s = Z##_s; \ + _FP_FRAC_COPY_##wc (R, Z); \ + R##_c = Z##_c; \ + } \ + else \ + { \ + R##_s = _FP_NANSIGN_##fs; \ + R##_c = FP_CLS_NAN; \ + _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ + FP_SET_EXCEPTION (FP_EX_INVALID); \ + } \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \ + if (T##_s == Z##_s) \ + R##_s = Z##_s; \ + else \ + R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ + _FP_FRAC_COPY_##wc (R, Z); \ + R##_c = Z##_c; \ + break; \ + \ + default: \ + abort (); \ + } \ + done_fma: ; \ + } \ + while (0) + + +/* + * Main division routine. The input values should be cooked. + */ + +#define _FP_DIV(fs, wc, R, X, Y) \ + do \ + { \ + R##_s = X##_s ^ Y##_s; \ + R##_e = X##_e - Y##_e; \ + switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \ + { \ + case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \ + R##_c = FP_CLS_NORMAL; \ + \ + _FP_DIV_MEAT_##fs (R, X, Y); \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \ + _FP_CHOOSENAN (fs, wc, R, X, Y, '/'); \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \ + case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \ + R##_s = X##_s; \ + _FP_FRAC_COPY_##wc (R, X); \ + R##_c = X##_c; \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \ + R##_s = Y##_s; \ + _FP_FRAC_COPY_##wc (R, Y); \ + R##_c = Y##_c; \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \ + R##_c = FP_CLS_ZERO; \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \ + FP_SET_EXCEPTION (FP_EX_DIVZERO); \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \ + R##_c = FP_CLS_INF; \ + break; \ + \ + case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \ + case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \ + R##_s = _FP_NANSIGN_##fs; \ + R##_c = FP_CLS_NAN; \ + _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ + FP_SET_EXCEPTION (FP_EX_INVALID); \ + break; \ + \ + default: \ + abort (); \ + } \ + } \ + while (0) + + +/* + * Main differential comparison routine. The inputs should be raw not + * cooked. The return is -1,0,1 for normal values, 2 otherwise. + */ + +#define _FP_CMP(fs, wc, ret, X, Y, un) \ + do \ + { \ + /* NANs are unordered */ \ + if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \ + || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \ + { \ + ret = un; \ + } \ + else \ + { \ + int __is_zero_x; \ + int __is_zero_y; \ + \ + __is_zero_x = (!X##_e && _FP_FRAC_ZEROP_##wc (X)) ? 1 : 0; \ + __is_zero_y = (!Y##_e && _FP_FRAC_ZEROP_##wc (Y)) ? 1 : 0; \ + \ + if (__is_zero_x && __is_zero_y) \ + ret = 0; \ + else if (__is_zero_x) \ + ret = Y##_s ? 1 : -1; \ + else if (__is_zero_y) \ + ret = X##_s ? -1 : 1; \ + else if (X##_s != Y##_s) \ + ret = X##_s ? -1 : 1; \ + else if (X##_e > Y##_e) \ + ret = X##_s ? -1 : 1; \ + else if (X##_e < Y##_e) \ + ret = X##_s ? 1 : -1; \ + else if (_FP_FRAC_GT_##wc (X, Y)) \ + ret = X##_s ? -1 : 1; \ + else if (_FP_FRAC_GT_##wc (Y, X)) \ + ret = X##_s ? 1 : -1; \ + else \ + ret = 0; \ + } \ + } \ + while (0) + + +/* Simplification for strict equality. */ + +#define _FP_CMP_EQ(fs, wc, ret, X, Y) \ + do \ + { \ + /* NANs are unordered */ \ + if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \ + || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \ + { \ + ret = 1; \ + } \ + else \ + { \ + ret = !(X##_e == Y##_e \ + && _FP_FRAC_EQ_##wc (X, Y) \ + && (X##_s == Y##_s || (!X##_e && _FP_FRAC_ZEROP_##wc (X)))); \ + } \ + } \ + while (0) + +/* Version to test unordered. */ + +#define _FP_CMP_UNORD(fs, wc, ret, X, Y) \ + do \ + { \ + ret = ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \ + || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))); \ + } \ + while (0) + +/* + * Main square root routine. The input value should be cooked. + */ + +#define _FP_SQRT(fs, wc, R, X) \ + do \ + { \ + _FP_FRAC_DECL_##wc (T); \ + _FP_FRAC_DECL_##wc (S); \ + _FP_W_TYPE q; \ + switch (X##_c) \ + { \ + case FP_CLS_NAN: \ + _FP_FRAC_COPY_##wc (R, X); \ + R##_s = X##_s; \ + R##_c = FP_CLS_NAN; \ + break; \ + case FP_CLS_INF: \ + if (X##_s) \ + { \ + R##_s = _FP_NANSIGN_##fs; \ + R##_c = FP_CLS_NAN; /* NAN */ \ + _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ + FP_SET_EXCEPTION (FP_EX_INVALID); \ + } \ + else \ + { \ + R##_s = 0; \ + R##_c = FP_CLS_INF; /* sqrt(+inf) = +inf */ \ + } \ + break; \ + case FP_CLS_ZERO: \ + R##_s = X##_s; \ + R##_c = FP_CLS_ZERO; /* sqrt(+-0) = +-0 */ \ + break; \ + case FP_CLS_NORMAL: \ + R##_s = 0; \ + if (X##_s) \ + { \ + R##_c = FP_CLS_NAN; /* NAN */ \ + R##_s = _FP_NANSIGN_##fs; \ + _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \ + FP_SET_EXCEPTION (FP_EX_INVALID); \ + break; \ + } \ + R##_c = FP_CLS_NORMAL; \ + if (X##_e & 1) \ + _FP_FRAC_SLL_##wc (X, 1); \ + R##_e = X##_e >> 1; \ + _FP_FRAC_SET_##wc (S, _FP_ZEROFRAC_##wc); \ + _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \ + q = _FP_OVERFLOW_##fs >> 1; \ + _FP_SQRT_MEAT_##wc (R, S, T, X, q); \ + } \ + } \ + while (0) + +/* + * Convert from FP to integer. Input is raw. + */ + +/* RSIGNED can have following values: + * 0: the number is required to be 0..(2^rsize)-1, if not, NV is set plus + * the result is either 0 or (2^rsize)-1 depending on the sign in such + * case. + * 1: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, + * NV is set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 + * depending on the sign in such case. + * -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is + * set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 + * depending on the sign in such case. + */ +#define _FP_TO_INT(fs, wc, r, X, rsize, rsigned) \ + do \ + { \ + if (X##_e < _FP_EXPBIAS_##fs) \ + { \ + r = 0; \ + if (X##_e == 0) \ + { \ + if (!_FP_FRAC_ZEROP_##wc (X)) \ + { \ + FP_SET_EXCEPTION (FP_EX_INEXACT); \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + } \ + } \ + else \ + FP_SET_EXCEPTION (FP_EX_INEXACT); \ + } \ + else if (X##_e >= _FP_EXPBIAS_##fs + rsize - (rsigned > 0 || X##_s) \ + || (!rsigned && X##_s)) \ + { \ + /* Overflow or converting to the most negative integer. */ \ + if (rsigned) \ + { \ + r = 1; \ + r <<= rsize - 1; \ + r -= 1 - X##_s; \ + } else { \ + r = 0; \ + if (!X##_s) \ + r = ~r; \ + } \ + \ + if (rsigned && X##_s && X##_e == _FP_EXPBIAS_##fs + rsize - 1) \ + { \ + /* Possibly converting to most negative integer; check the \ + mantissa. */ \ + int inexact = 0; \ + (void) ((_FP_FRACBITS_##fs > rsize) \ + ? ({ \ + _FP_FRAC_SRST_##wc (X, inexact, \ + _FP_FRACBITS_##fs - rsize, \ + _FP_FRACBITS_##fs); \ + 0; \ + }) \ + : 0); \ + if (!_FP_FRAC_ZEROP_##wc (X)) \ + FP_SET_EXCEPTION (FP_EX_INVALID); \ + else if (inexact) \ + FP_SET_EXCEPTION (FP_EX_INEXACT); \ + } \ + else \ + FP_SET_EXCEPTION (FP_EX_INVALID); \ + } \ + else \ + { \ + _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \ + if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \ + { \ + _FP_FRAC_ASSEMBLE_##wc (r, X, rsize); \ + r <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \ + } \ + else \ + { \ + int inexact; \ + _FP_FRAC_SRST_##wc (X, inexact, \ + (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \ + - X##_e), \ + _FP_FRACBITS_##fs); \ + if (inexact) \ + FP_SET_EXCEPTION (FP_EX_INEXACT); \ + _FP_FRAC_ASSEMBLE_##wc (r, X, rsize); \ + } \ + if (rsigned && X##_s) \ + r = -r; \ + } \ + } \ + while (0) + +/* Convert integer to fp. Output is raw. RTYPE is unsigned even if + input is signed. */ +#define _FP_FROM_INT(fs, wc, X, r, rsize, rtype) \ + do \ + { \ + if (r) \ + { \ + rtype ur_; \ + \ + if ((X##_s = (r < 0))) \ + r = -(rtype) r; \ + \ + ur_ = (rtype) r; \ + (void) ((rsize <= _FP_W_TYPE_SIZE) \ + ? ({ \ + int lz_; \ + __FP_CLZ (lz_, (_FP_W_TYPE) ur_); \ + X##_e = _FP_EXPBIAS_##fs + _FP_W_TYPE_SIZE - 1 - lz_; \ + }) \ + : ((rsize <= 2 * _FP_W_TYPE_SIZE) \ + ? ({ \ + int lz_; \ + __FP_CLZ_2 (lz_, \ + (_FP_W_TYPE) (ur_ >> _FP_W_TYPE_SIZE), \ + (_FP_W_TYPE) ur_); \ + X##_e = (_FP_EXPBIAS_##fs + 2 * _FP_W_TYPE_SIZE - 1 \ + - lz_); \ + }) \ + : (abort (), 0))); \ + \ + if (rsize - 1 + _FP_EXPBIAS_##fs >= _FP_EXPMAX_##fs \ + && X##_e >= _FP_EXPMAX_##fs) \ + { \ + /* Exponent too big; overflow to infinity. (May also \ + happen after rounding below.) */ \ + _FP_OVERFLOW_SEMIRAW (fs, wc, X); \ + goto pack_semiraw; \ + } \ + \ + if (rsize <= _FP_FRACBITS_##fs \ + || X##_e < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs) \ + { \ + /* Exactly representable; shift left. */ \ + _FP_FRAC_DISASSEMBLE_##wc (X, ur_, rsize); \ + if (_FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1 - X##_e > 0) \ + _FP_FRAC_SLL_##wc (X, (_FP_EXPBIAS_##fs \ + + _FP_FRACBITS_##fs - 1 - X##_e)); \ + } \ + else \ + { \ + /* More bits in integer than in floating type; need to \ + round. */ \ + if (_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 < X##_e) \ + ur_ = ((ur_ >> (X##_e - _FP_EXPBIAS_##fs \ + - _FP_WFRACBITS_##fs + 1)) \ + | ((ur_ << (rsize - (X##_e - _FP_EXPBIAS_##fs \ + - _FP_WFRACBITS_##fs + 1))) \ + != 0)); \ + _FP_FRAC_DISASSEMBLE_##wc (X, ur_, rsize); \ + if ((_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 - X##_e) > 0) \ + _FP_FRAC_SLL_##wc (X, (_FP_EXPBIAS_##fs \ + + _FP_WFRACBITS_##fs - 1 - X##_e)); \ + _FP_FRAC_HIGH_##fs (X) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \ + pack_semiraw: \ + _FP_PACK_SEMIRAW (fs, wc, X); \ + } \ + } \ + else \ + { \ + X##_s = 0; \ + X##_e = 0; \ + _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \ + } \ + } \ + while (0) + + +/* Extend from a narrower floating-point format to a wider one. Input + and output are raw. */ +#define FP_EXTEND(dfs, sfs, dwc, swc, D, S) \ + do \ + { \ + if (_FP_FRACBITS_##dfs < _FP_FRACBITS_##sfs \ + || (_FP_EXPMAX_##dfs - _FP_EXPBIAS_##dfs \ + < _FP_EXPMAX_##sfs - _FP_EXPBIAS_##sfs) \ + || (_FP_EXPBIAS_##dfs < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1 \ + && _FP_EXPBIAS_##dfs != _FP_EXPBIAS_##sfs)) \ + abort (); \ + D##_s = S##_s; \ + _FP_FRAC_COPY_##dwc##_##swc (D, S); \ + if (_FP_EXP_NORMAL (sfs, swc, S)) \ + { \ + D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \ + _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs - _FP_FRACBITS_##sfs)); \ + } \ + else \ + { \ + if (S##_e == 0) \ + { \ + if (_FP_FRAC_ZEROP_##swc (S)) \ + D##_e = 0; \ + else if (_FP_EXPBIAS_##dfs \ + < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1) \ + { \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \ + - _FP_FRACBITS_##sfs)); \ + D##_e = 0; \ + } \ + else \ + { \ + int _lz; \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + _FP_FRAC_CLZ_##swc (_lz, S); \ + _FP_FRAC_SLL_##dwc (D, \ + _lz + _FP_FRACBITS_##dfs \ + - _FP_FRACTBITS_##sfs); \ + D##_e = (_FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs + 1 \ + + _FP_FRACXBITS_##sfs - _lz); \ + } \ + } \ + else \ + { \ + D##_e = _FP_EXPMAX_##dfs; \ + if (!_FP_FRAC_ZEROP_##swc (S)) \ + { \ + if (_FP_FRAC_SNANP (sfs, S)) \ + FP_SET_EXCEPTION (FP_EX_INVALID); \ + _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \ + - _FP_FRACBITS_##sfs)); \ + _FP_SETQNAN (dfs, dwc, D); \ + } \ + } \ + } \ + } \ + while (0) + +/* Truncate from a wider floating-point format to a narrower one. + Input and output are semi-raw. */ +#define FP_TRUNC(dfs, sfs, dwc, swc, D, S) \ + do \ + { \ + if (_FP_FRACBITS_##sfs < _FP_FRACBITS_##dfs \ + || (_FP_EXPBIAS_##sfs < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1 \ + && _FP_EXPBIAS_##sfs != _FP_EXPBIAS_##dfs)) \ + abort (); \ + D##_s = S##_s; \ + if (_FP_EXP_NORMAL (sfs, swc, S)) \ + { \ + D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \ + if (D##_e >= _FP_EXPMAX_##dfs) \ + _FP_OVERFLOW_SEMIRAW (dfs, dwc, D); \ + else \ + { \ + if (D##_e <= 0) \ + { \ + if (D##_e < 1 - _FP_FRACBITS_##dfs) \ + { \ + _FP_FRAC_SET_##swc (S, _FP_ZEROFRAC_##swc); \ + _FP_FRAC_LOW_##swc (S) |= 1; \ + } \ + else \ + { \ + _FP_FRAC_HIGH_##sfs (S) |= _FP_IMPLBIT_SH_##sfs; \ + _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \ + - _FP_WFRACBITS_##dfs \ + + 1 - D##_e), \ + _FP_WFRACBITS_##sfs); \ + } \ + D##_e = 0; \ + } \ + else \ + _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \ + - _FP_WFRACBITS_##dfs), \ + _FP_WFRACBITS_##sfs); \ + _FP_FRAC_COPY_##dwc##_##swc (D, S); \ + } \ + } \ + else \ + { \ + if (S##_e == 0) \ + { \ + D##_e = 0; \ + if (_FP_FRAC_ZEROP_##swc (S)) \ + _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \ + else \ + { \ + FP_SET_EXCEPTION (FP_EX_DENORM); \ + if (_FP_EXPBIAS_##sfs \ + < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1) \ + { \ + _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \ + - _FP_WFRACBITS_##dfs), \ + _FP_WFRACBITS_##sfs); \ + _FP_FRAC_COPY_##dwc##_##swc (D, S); \ + } \ + else \ + { \ + _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \ + _FP_FRAC_LOW_##dwc (D) |= 1; \ + } \ + } \ + } \ + else \ + { \ + D##_e = _FP_EXPMAX_##dfs; \ + if (_FP_FRAC_ZEROP_##swc (S)) \ + _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \ + else \ + { \ + _FP_CHECK_SIGNAN_SEMIRAW (sfs, swc, S); \ + _FP_FRAC_SRL_##swc (S, (_FP_WFRACBITS_##sfs \ + - _FP_WFRACBITS_##dfs)); \ + _FP_FRAC_COPY_##dwc##_##swc (D, S); \ + /* Semi-raw NaN must have all workbits cleared. */ \ + _FP_FRAC_LOW_##dwc (D) \ + &= ~(_FP_W_TYPE) ((1 << _FP_WORKBITS) - 1); \ + _FP_SETQNAN_SEMIRAW (dfs, dwc, D); \ + } \ + } \ + } \ + } \ + while (0) + +/* + * Helper primitives. + */ + +/* Count leading zeros in a word. */ + +#ifndef __FP_CLZ +/* GCC 3.4 and later provide the builtins for us. */ +# define __FP_CLZ(r, x) \ + do \ + { \ + if (sizeof (_FP_W_TYPE) == sizeof (unsigned int)) \ + r = __builtin_clz (x); \ + else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long)) \ + r = __builtin_clzl (x); \ + else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long long)) \ + r = __builtin_clzll (x); \ + else \ + abort (); \ + } \ + while (0) +#endif /* ndef __FP_CLZ */ + +#define _FP_DIV_HELP_imm(q, r, n, d) \ + do \ + { \ + q = n / d, r = n % d; \ + } \ + while (0) + + +/* A restoring bit-by-bit division primitive. */ + +#define _FP_DIV_MEAT_N_loop(fs, wc, R, X, Y) \ + do \ + { \ + int count = _FP_WFRACBITS_##fs; \ + _FP_FRAC_DECL_##wc (u); \ + _FP_FRAC_DECL_##wc (v); \ + _FP_FRAC_COPY_##wc (u, X); \ + _FP_FRAC_COPY_##wc (v, Y); \ + _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \ + /* Normalize U and V. */ \ + _FP_FRAC_SLL_##wc (u, _FP_WFRACXBITS_##fs); \ + _FP_FRAC_SLL_##wc (v, _FP_WFRACXBITS_##fs); \ + /* First round. Since the operands are normalized, either the \ + first or second bit will be set in the fraction. Produce a \ + normalized result by checking which and adjusting the loop \ + count and exponent accordingly. */ \ + if (_FP_FRAC_GE_1 (u, v)) \ + { \ + _FP_FRAC_SUB_##wc (u, u, v); \ + _FP_FRAC_LOW_##wc (R) |= 1; \ + count--; \ + } \ + else \ + R##_e--; \ + /* Subsequent rounds. */ \ + do \ + { \ + int msb = (_FP_WS_TYPE) _FP_FRAC_HIGH_##wc (u) < 0; \ + _FP_FRAC_SLL_##wc (u, 1); \ + _FP_FRAC_SLL_##wc (R, 1); \ + if (msb || _FP_FRAC_GE_1 (u, v)) \ + { \ + _FP_FRAC_SUB_##wc (u, u, v); \ + _FP_FRAC_LOW_##wc (R) |= 1; \ + } \ + } \ + while (--count > 0); \ + /* If there's anything left in U, the result is inexact. */ \ + _FP_FRAC_LOW_##wc (R) |= !_FP_FRAC_ZEROP_##wc (u); \ + } \ + while (0) + +#define _FP_DIV_MEAT_1_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 1, R, X, Y) +#define _FP_DIV_MEAT_2_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 2, R, X, Y) +#define _FP_DIV_MEAT_4_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 4, R, X, Y) |