From df62c1c110e8532b995b23540b7e3695729c0779 Mon Sep 17 00:00:00 2001 From: Jing Yu Date: Thu, 5 Nov 2009 15:11:04 -0800 Subject: Check in gcc sources for prebuilt toolchains in Eclair. --- gcc-4.3.1/libgcc/config/libbid/bid64_to_uint64.c | 2278 ++++++++++++++++++++++ 1 file changed, 2278 insertions(+) create mode 100644 gcc-4.3.1/libgcc/config/libbid/bid64_to_uint64.c (limited to 'gcc-4.3.1/libgcc/config/libbid/bid64_to_uint64.c') diff --git a/gcc-4.3.1/libgcc/config/libbid/bid64_to_uint64.c b/gcc-4.3.1/libgcc/config/libbid/bid64_to_uint64.c new file mode 100644 index 000000000..7b1d31f8d --- /dev/null +++ b/gcc-4.3.1/libgcc/config/libbid/bid64_to_uint64.c @@ -0,0 +1,2278 @@ +/* Copyright (C) 2007 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 2, or (at your option) any later +version. + +In addition to the permissions in the GNU 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 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.) + +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 COPYING. If not, write to the Free +Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA +02110-1301, USA. */ + +#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); +} -- cgit v1.2.3