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[/] [openrisc/] [trunk/] [gnu-src/] [gcc-4.5.1/] [libgcc/] [config/] [libbid/] [bid128_add.c] - Rev 280
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/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. This file is part of GCC. GCC is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version. GCC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. Under Section 7 of GPL version 3, you are granted additional permissions described in the GCC Runtime Library Exception, version 3.1, as published by the Free Software Foundation. You should have received a copy of the GNU General Public License and a copy of the GCC Runtime Library Exception along with this program; see the files COPYING3 and COPYING.RUNTIME respectively. If not, see <http://www.gnu.org/licenses/>. */ #include "bid_internal.h" #if DECIMAL_CALL_BY_REFERENCE void bid64dq_add (UINT64 * pres, UINT64 * px, UINT128 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT64 bid64dq_add (UINT64 x, UINT128 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT64 res = 0xbaddbaddbaddbaddull; UINT128 x1; #if DECIMAL_CALL_BY_REFERENCE bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid64qq_add (&res, &x1, py _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); res = bid64qq_add (x1, y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64qd_add (UINT64 * pres, UINT128 * px, UINT64 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 y = *py; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT64 bid64qd_add (UINT128 x, UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT64 res = 0xbaddbaddbaddbaddull; UINT128 y1; #if DECIMAL_CALL_BY_REFERENCE bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid64qq_add (&res, px, &y1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); res = bid64qq_add (x, y1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64qq_add (UINT64 * pres, UINT128 * px, UINT128 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px, y = *py; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT64 bid64qq_add (UINT128 x, UINT128 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 one = { {0x0000000000000001ull, 0x3040000000000000ull} }; UINT64 res = 0xbaddbaddbaddbaddull; BID_SWAP128 (one); #if DECIMAL_CALL_BY_REFERENCE bid64qqq_fma (&res, &one, &x, &y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else res = bid64qqq_fma (one, x, y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128dd_add (UINT128 * pres, UINT64 * px, UINT64 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px, y = *py; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT128 bid128dd_add (UINT64 x, UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; UINT128 x1, y1; #if DECIMAL_CALL_BY_REFERENCE bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid128_add (&res, &x1, &y1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); res = bid128_add (x1, y1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128dq_add (UINT128 * pres, UINT64 * px, UINT128 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT128 bid128dq_add (UINT64 x, UINT128 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; UINT128 x1; #if DECIMAL_CALL_BY_REFERENCE bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid128_add (&res, &x1, py _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); res = bid128_add (x1, y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128qd_add (UINT128 * pres, UINT128 * px, UINT64 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 y = *py; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT128 bid128qd_add (UINT128 x, UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; UINT128 y1; #if DECIMAL_CALL_BY_REFERENCE bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid128_add (&res, px, &y1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); res = bid128_add (x, y1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif BID_RETURN (res); } // bid128_add stands for bid128qq_add /***************************************************************************** * BID64/BID128 sub ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64dq_sub (UINT64 * pres, UINT64 * px, UINT128 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT64 bid64dq_sub (UINT64 x, UINT128 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT64 res = 0xbaddbaddbaddbaddull; UINT128 x1; #if DECIMAL_CALL_BY_REFERENCE bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid64qq_sub (&res, &x1, py _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); res = bid64qq_sub (x1, y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64qd_sub (UINT64 * pres, UINT128 * px, UINT64 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 y = *py; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT64 bid64qd_sub (UINT128 x, UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT64 res = 0xbaddbaddbaddbaddull; UINT128 y1; #if DECIMAL_CALL_BY_REFERENCE bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid64qq_sub (&res, px, &y1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); res = bid64qq_sub (x, y1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64qq_sub (UINT64 * pres, UINT128 * px, UINT128 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px, y = *py; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT64 bid64qq_sub (UINT128 x, UINT128 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 one = { {0x0000000000000001ull, 0x3040000000000000ull} }; UINT64 res = 0xbaddbaddbaddbaddull; UINT64 y_sign; BID_SWAP128 (one); if ((y.w[HIGH_128W] & MASK_NAN) != MASK_NAN) { // y is not NAN // change its sign y_sign = y.w[HIGH_128W] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative if (y_sign) y.w[HIGH_128W] = y.w[HIGH_128W] & 0x7fffffffffffffffull; else y.w[HIGH_128W] = y.w[HIGH_128W] | 0x8000000000000000ull; } #if DECIMAL_CALL_BY_REFERENCE bid64qqq_fma (&res, &one, &x, &y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else res = bid64qqq_fma (one, x, y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128dd_sub (UINT128 * pres, UINT64 * px, UINT64 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px, y = *py; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT128 bid128dd_sub (UINT64 x, UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; UINT128 x1, y1; #if DECIMAL_CALL_BY_REFERENCE bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid128_sub (&res, &x1, &y1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); res = bid128_sub (x1, y1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128dq_sub (UINT128 * pres, UINT64 * px, UINT128 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT128 bid128dq_sub (UINT64 x, UINT128 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; UINT128 x1; #if DECIMAL_CALL_BY_REFERENCE bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid128_sub (&res, &x1, py _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); res = bid128_sub (x1, y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128qd_sub (UINT128 * pres, UINT128 * px, UINT64 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 y = *py; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT128 bid128qd_sub (UINT128 x, UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; UINT128 y1; #if DECIMAL_CALL_BY_REFERENCE bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid128_sub (&res, px, &y1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); res = bid128_sub (x, y1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128_add (UINT128 * pres, UINT128 * px, UINT128 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px, y = *py; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT128 bid128_add (UINT128 x, UINT128 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} }; UINT64 x_sign, y_sign, tmp_sign; UINT64 x_exp, y_exp, tmp_exp; // e1 = x_exp, e2 = y_exp UINT64 C1_hi, C2_hi, tmp_signif_hi; UINT64 C1_lo, C2_lo, tmp_signif_lo; // Note: C1.w[1], C1.w[0] represent C1_hi, C1_lo (all UINT64) // Note: C2.w[1], C2.w[0] represent C2_hi, C2_lo (all UINT64) UINT64 tmp64, tmp64A, tmp64B; BID_UI64DOUBLE tmp1, tmp2; int x_nr_bits, y_nr_bits; int q1, q2, delta, scale, x1, ind, shift, tmp_inexact = 0; UINT64 halfulp64; UINT128 halfulp128; UINT128 C1, C2; UINT128 ten2m1; UINT128 highf2star; // top 128 bits in f2*; low 128 bits in R256[1], R256[0] UINT256 P256, Q256, R256; int is_inexact = 0, is_midpoint_lt_even = 0, is_midpoint_gt_even = 0; int is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0; int second_pass = 0; BID_SWAP128 (x); BID_SWAP128 (y); x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative y_sign = y.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // check for NaN or Infinity if (((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) || ((y.w[1] & MASK_SPECIAL) == MASK_SPECIAL)) { // x is special or y is special if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN // check first for non-canonical NaN payload if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && (x.w[0] > 0x38c15b09ffffffffull))) { x.w[1] = x.w[1] & 0xffffc00000000000ull; x.w[0] = 0x0ull; } if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return quiet (x) res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] res.w[0] = x.w[0]; } else { // x is QNaN // return x res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] res.w[0] = x.w[0]; // if y = SNaN signal invalid exception if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; } } BID_SWAP128 (res); BID_RETURN (res); } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN // check first for non-canonical NaN payload if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) || (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) && (y.w[0] > 0x38c15b09ffffffffull))) { y.w[1] = y.w[1] & 0xffffc00000000000ull; y.w[0] = 0x0ull; } if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return quiet (y) res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16] res.w[0] = y.w[0]; } else { // y is QNaN // return y res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16] res.w[0] = y.w[0]; } BID_SWAP128 (res); BID_RETURN (res); } else { // neither x not y is NaN; at least one is infinity if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x is infinity if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y is infinity // if same sign, return either of them if ((x.w[1] & MASK_SIGN) == (y.w[1] & MASK_SIGN)) { res.w[1] = x_sign | MASK_INF; res.w[0] = 0x0ull; } else { // x and y are infinities of opposite signs // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return QNaN Indefinite res.w[1] = 0x7c00000000000000ull; res.w[0] = 0x0000000000000000ull; } } else { // y is 0 or finite // return x res.w[1] = x_sign | MASK_INF; res.w[0] = 0x0ull; } } else { // x is not NaN or infinity, so y must be infinity res.w[1] = y_sign | MASK_INF; res.w[0] = 0x0ull; } BID_SWAP128 (res); BID_RETURN (res); } } // unpack the arguments // unpack x C1_hi = x.w[1] & MASK_COEFF; C1_lo = x.w[0]; // test for non-canonical values: // - values whose encoding begins with x00, x01, or x10 and whose // coefficient is larger than 10^34 -1, or // - values whose encoding begins with x1100, x1101, x1110 (if NaNs // and infinitis were eliminated already this test is reduced to // checking for x10x) // x is not infinity; check for non-canonical values - treated as zero if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11; non-canonical x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits C1_hi = 0; // significand high C1_lo = 0; // significand low } else { // G0_G1 != 11 x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits if (C1_hi > 0x0001ed09bead87c0ull || (C1_hi == 0x0001ed09bead87c0ull && C1_lo > 0x378d8e63ffffffffull)) { // x is non-canonical if coefficient is larger than 10^34 -1 C1_hi = 0; C1_lo = 0; } else { // canonical ; } } // unpack y C2_hi = y.w[1] & MASK_COEFF; C2_lo = y.w[0]; // y is not infinity; check for non-canonical values - treated as zero if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11; non-canonical y_exp = (y.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits C2_hi = 0; // significand high C2_lo = 0; // significand low } else { // G0_G1 != 11 y_exp = y.w[1] & MASK_EXP; // biased and shifted left 49 bits if (C2_hi > 0x0001ed09bead87c0ull || (C2_hi == 0x0001ed09bead87c0ull && C2_lo > 0x378d8e63ffffffffull)) { // y is non-canonical if coefficient is larger than 10^34 -1 C2_hi = 0; C2_lo = 0; } else { // canonical ; } } if ((C1_hi == 0x0ull) && (C1_lo == 0x0ull)) { // x is 0 and y is not special // if y is 0 return 0 with the smaller exponent if ((C2_hi == 0x0ull) && (C2_lo == 0x0ull)) { if (x_exp < y_exp) res.w[1] = x_exp; else res.w[1] = y_exp; if (x_sign && y_sign) res.w[1] = res.w[1] | x_sign; // both negative else if (rnd_mode == ROUNDING_DOWN && x_sign != y_sign) res.w[1] = res.w[1] | 0x8000000000000000ull; // -0 // else; // res = +0 res.w[0] = 0; } else { // for 0 + y return y, with the preferred exponent if (y_exp <= x_exp) { res.w[1] = y.w[1]; res.w[0] = y.w[0]; } else { // if y_exp > x_exp // return (C2 * 10^scale) * 10^(y_exp - scale) // where scale = min (P34-q2, y_exp-x_exp) // determine q2 = nr. of decimal digits in y // determine first the nr. of bits in y (y_nr_bits) if (C2_hi == 0) { // y_bits is the nr. of bits in C2_lo if (C2_lo >= 0x0020000000000000ull) { // y >= 2^53 // split the 64-bit value in two 32-bit halves to avoid // rounding errors if (C2_lo >= 0x0000000100000000ull) { // y >= 2^32 tmp2.d = (double) (C2_lo >> 32); // exact conversion y_nr_bits = 32 + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); } else { // y < 2^32 tmp2.d = (double) (C2_lo); // exact conversion y_nr_bits = ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // if y < 2^53 tmp2.d = (double) C2_lo; // exact conversion y_nr_bits = ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // C2_hi != 0 => nr. bits = 64 + nr_bits (C2_hi) tmp2.d = (double) C2_hi; // exact conversion y_nr_bits = 64 + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); } q2 = nr_digits[y_nr_bits].digits; if (q2 == 0) { q2 = nr_digits[y_nr_bits].digits1; if (C2_hi > nr_digits[y_nr_bits].threshold_hi || (C2_hi == nr_digits[y_nr_bits].threshold_hi && C2_lo >= nr_digits[y_nr_bits].threshold_lo)) q2++; } // return (C2 * 10^scale) * 10^(y_exp - scale) // where scale = min (P34-q2, y_exp-x_exp) scale = P34 - q2; ind = (y_exp - x_exp) >> 49; if (ind < scale) scale = ind; if (scale == 0) { res.w[1] = y.w[1]; res.w[0] = y.w[0]; } else if (q2 <= 19) { // y fits in 64 bits if (scale <= 19) { // 10^scale fits in 64 bits // 64 x 64 C2_lo * ten2k64[scale] __mul_64x64_to_128MACH (res, C2_lo, ten2k64[scale]); } else { // 10^scale fits in 128 bits // 64 x 128 C2_lo * ten2k128[scale - 20] __mul_128x64_to_128 (res, C2_lo, ten2k128[scale - 20]); } } else { // y fits in 128 bits, but 10^scale must fit in 64 bits // 64 x 128 ten2k64[scale] * C2 C2.w[1] = C2_hi; C2.w[0] = C2_lo; __mul_128x64_to_128 (res, ten2k64[scale], C2); } // subtract scale from the exponent y_exp = y_exp - ((UINT64) scale << 49); res.w[1] = res.w[1] | y_sign | y_exp; } } BID_SWAP128 (res); BID_RETURN (res); } else if ((C2_hi == 0x0ull) && (C2_lo == 0x0ull)) { // y is 0 and x is not special, and not zero // for x + 0 return x, with the preferred exponent if (x_exp <= y_exp) { res.w[1] = x.w[1]; res.w[0] = x.w[0]; } else { // if x_exp > y_exp // return (C1 * 10^scale) * 10^(x_exp - scale) // where scale = min (P34-q1, x_exp-y_exp) // determine q1 = nr. of decimal digits in x // determine first the nr. of bits in x if (C1_hi == 0) { // x_bits is the nr. of bits in C1_lo if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid // rounding errors if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32 tmp1.d = (double) (C1_lo >> 32); // exact conversion x_nr_bits = 32 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } else { // x < 2^32 tmp1.d = (double) (C1_lo); // exact conversion x_nr_bits = ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // if x < 2^53 tmp1.d = (double) C1_lo; // exact conversion x_nr_bits = ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi) tmp1.d = (double) C1_hi; // exact conversion x_nr_bits = 64 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } q1 = nr_digits[x_nr_bits].digits; if (q1 == 0) { q1 = nr_digits[x_nr_bits].digits1; if (C1_hi > nr_digits[x_nr_bits].threshold_hi || (C1_hi == nr_digits[x_nr_bits].threshold_hi && C1_lo >= nr_digits[x_nr_bits].threshold_lo)) q1++; } // return (C1 * 10^scale) * 10^(x_exp - scale) // where scale = min (P34-q1, x_exp-y_exp) scale = P34 - q1; ind = (x_exp - y_exp) >> 49; if (ind < scale) scale = ind; if (scale == 0) { res.w[1] = x.w[1]; res.w[0] = x.w[0]; } else if (q1 <= 19) { // x fits in 64 bits if (scale <= 19) { // 10^scale fits in 64 bits // 64 x 64 C1_lo * ten2k64[scale] __mul_64x64_to_128MACH (res, C1_lo, ten2k64[scale]); } else { // 10^scale fits in 128 bits // 64 x 128 C1_lo * ten2k128[scale - 20] __mul_128x64_to_128 (res, C1_lo, ten2k128[scale - 20]); } } else { // x fits in 128 bits, but 10^scale must fit in 64 bits // 64 x 128 ten2k64[scale] * C1 C1.w[1] = C1_hi; C1.w[0] = C1_lo; __mul_128x64_to_128 (res, ten2k64[scale], C1); } // subtract scale from the exponent x_exp = x_exp - ((UINT64) scale << 49); res.w[1] = res.w[1] | x_sign | x_exp; } BID_SWAP128 (res); BID_RETURN (res); } else { // x and y are not canonical, not special, and are not zero // note that the result may still be zero, and then it has to have the // preferred exponent if (x_exp < y_exp) { // if exp_x < exp_y then swap x and y tmp_sign = x_sign; tmp_exp = x_exp; tmp_signif_hi = C1_hi; tmp_signif_lo = C1_lo; x_sign = y_sign; x_exp = y_exp; C1_hi = C2_hi; C1_lo = C2_lo; y_sign = tmp_sign; y_exp = tmp_exp; C2_hi = tmp_signif_hi; C2_lo = tmp_signif_lo; } // q1 = nr. of decimal digits in x // determine first the nr. of bits in x if (C1_hi == 0) { // x_bits is the nr. of bits in C1_lo if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53 //split the 64-bit value in two 32-bit halves to avoid rounding errors if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32 tmp1.d = (double) (C1_lo >> 32); // exact conversion x_nr_bits = 32 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } else { // x < 2^32 tmp1.d = (double) (C1_lo); // exact conversion x_nr_bits = ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // if x < 2^53 tmp1.d = (double) C1_lo; // exact conversion x_nr_bits = ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi) tmp1.d = (double) C1_hi; // exact conversion x_nr_bits = 64 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } q1 = nr_digits[x_nr_bits].digits; if (q1 == 0) { q1 = nr_digits[x_nr_bits].digits1; if (C1_hi > nr_digits[x_nr_bits].threshold_hi || (C1_hi == nr_digits[x_nr_bits].threshold_hi && C1_lo >= nr_digits[x_nr_bits].threshold_lo)) q1++; } // q2 = nr. of decimal digits in y // determine first the nr. of bits in y (y_nr_bits) if (C2_hi == 0) { // y_bits is the nr. of bits in C2_lo if (C2_lo >= 0x0020000000000000ull) { // y >= 2^53 //split the 64-bit value in two 32-bit halves to avoid rounding errors if (C2_lo >= 0x0000000100000000ull) { // y >= 2^32 tmp2.d = (double) (C2_lo >> 32); // exact conversion y_nr_bits = 32 + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); } else { // y < 2^32 tmp2.d = (double) (C2_lo); // exact conversion y_nr_bits = ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // if y < 2^53 tmp2.d = (double) C2_lo; // exact conversion y_nr_bits = ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // C2_hi != 0 => nr. bits = 64 + nr_bits (C2_hi) tmp2.d = (double) C2_hi; // exact conversion y_nr_bits = 64 + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff); } q2 = nr_digits[y_nr_bits].digits; if (q2 == 0) { q2 = nr_digits[y_nr_bits].digits1; if (C2_hi > nr_digits[y_nr_bits].threshold_hi || (C2_hi == nr_digits[y_nr_bits].threshold_hi && C2_lo >= nr_digits[y_nr_bits].threshold_lo)) q2++; } delta = q1 + (int) (x_exp >> 49) - q2 - (int) (y_exp >> 49); if (delta >= P34) { // round the result directly because 0 < C2 < ulp (C1 * 10^(x_exp-e2)) // n = C1 * 10^e1 or n = C1 +/- 10^(q1-P34)) * 10^e1 // the result is inexact; the preferred exponent is the least possible if (delta >= P34 + 1) { // for RN the result is the operand with the larger magnitude, // possibly scaled up by 10^(P34-q1) // an overflow cannot occur in this case (rounding to nearest) if (q1 < P34) { // scale C1 up by 10^(P34-q1) // Note: because delta >= P34+1 it is certain that // x_exp - ((UINT64)scale << 49) will stay above e_min scale = P34 - q1; if (q1 <= 19) { // C1 fits in 64 bits // 1 <= q1 <= 19 => 15 <= scale <= 33 if (scale <= 19) { // 10^scale fits in 64 bits __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); } else { // if 20 <= scale <= 33 // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where // (C1 * 10^(scale-19)) fits in 64 bits C1_lo = C1_lo * ten2k64[scale - 19]; __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); } } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits C1.w[1] = C1_hi; C1.w[0] = C1_lo; // C1 = ten2k64[P34 - q1] * C1 __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); } x_exp = x_exp - ((UINT64) scale << 49); C1_hi = C1.w[1]; C1_lo = C1.w[0]; } // some special cases arise: if delta = P34 + 1 and C1 = 10^(P34-1) // (after scaling) and x_sign != y_sign and C2 > 5*10^(q2-1) => // subtract 1 ulp // Note: do this only for rounding to nearest; for other rounding // modes the correction will be applied next if ((rnd_mode == ROUNDING_TO_NEAREST || rnd_mode == ROUNDING_TIES_AWAY) && delta == (P34 + 1) && C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b0a00000000ull && x_sign != y_sign && ((q2 <= 19 && C2_lo > midpoint64[q2 - 1]) || (q2 >= 20 && (C2_hi > midpoint128 [q2 - 20]. w[1] || (C2_hi == midpoint128 [q2 - 20]. w[1] && C2_lo > midpoint128 [q2 - 20]. w [0]))))) { // C1 = 10^34 - 1 and decrement x_exp by 1 (no underflow possible) C1_hi = 0x0001ed09bead87c0ull; C1_lo = 0x378d8e63ffffffffull; x_exp = x_exp - EXP_P1; } if (rnd_mode != ROUNDING_TO_NEAREST) { if ((rnd_mode == ROUNDING_DOWN && x_sign && y_sign) || (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) { // add 1 ulp and then check for overflow C1_lo = C1_lo + 1; if (C1_lo == 0) { // rounding overflow in the low 64 bits C1_hi = C1_hi + 1; } if (C1_hi == 0x0001ed09bead87c0ull && C1_lo == 0x378d8e6400000000ull) { // C1 = 10^34 => rounding overflow C1_hi = 0x0000314dc6448d93ull; C1_lo = 0x38c15b0a00000000ull; // 10^33 x_exp = x_exp + EXP_P1; if (x_exp == EXP_MAX_P1) { // overflow C1_hi = 0x7800000000000000ull; // +inf C1_lo = 0x0ull; x_exp = 0; // x_sign is preserved // set overflow flag (the inexact flag was set too) *pfpsf |= OVERFLOW_EXCEPTION; } } } else if ((rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) || (rnd_mode == ROUNDING_TO_ZERO && x_sign != y_sign)) { // subtract 1 ulp from C1 // Note: because delta >= P34 + 1 the result cannot be zero C1_lo = C1_lo - 1; if (C1_lo == 0xffffffffffffffffull) C1_hi = C1_hi - 1; // if the coefficient is 10^33 - 1 then make it 10^34 - 1 and // decrease the exponent by 1 (because delta >= P34 + 1 the // exponent will not become less than e_min) // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // make C1 = 10^34 - 1 C1_hi = 0x0001ed09bead87c0ull; C1_lo = 0x378d8e63ffffffffull; x_exp = x_exp - EXP_P1; } } else { ; // the result is already correct } } // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // assemble the result res.w[1] = x_sign | x_exp | C1_hi; res.w[0] = C1_lo; } else { // delta = P34 // in most cases, the smaller operand may be < or = or > 1/2 ulp of the // larger operand // however, the case C1 = 10^(q1-1) and x_sign != y_sign is special due // to accuracy loss after subtraction, and will be treated separately if (x_sign == y_sign || (q1 <= 20 && (C1_hi != 0 || C1_lo != ten2k64[q1 - 1])) || (q1 >= 21 && (C1_hi != ten2k128[q1 - 21].w[1] || C1_lo != ten2k128[q1 - 21].w[0]))) { // if x_sign == y_sign or C1 != 10^(q1-1) // compare C2 with 1/2 ulp = 5 * 10^(q2-1), the latter read from table // Note: cases q1<=19 and q1>=20 can be coalesced at some latency cost if (q2 <= 19) { // C2 and 5*10^(q2-1) both fit in 64 bits halfulp64 = midpoint64[q2 - 1]; // 5 * 10^(q2-1) if (C2_lo < halfulp64) { // n2 < 1/2 ulp (n1) // for RN the result is the operand with the larger magnitude, // possibly scaled up by 10^(P34-q1) // an overflow cannot occur in this case (rounding to nearest) if (q1 < P34) { // scale C1 up by 10^(P34-q1) // Note: because delta = P34 it is certain that // x_exp - ((UINT64)scale << 49) will stay above e_min scale = P34 - q1; if (q1 <= 19) { // C1 fits in 64 bits // 1 <= q1 <= 19 => 15 <= scale <= 33 if (scale <= 19) { // 10^scale fits in 64 bits __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); } else { // if 20 <= scale <= 33 // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where // (C1 * 10^(scale-19)) fits in 64 bits C1_lo = C1_lo * ten2k64[scale - 19]; __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); } } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits C1.w[1] = C1_hi; C1.w[0] = C1_lo; // C1 = ten2k64[P34 - q1] * C1 __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); } x_exp = x_exp - ((UINT64) scale << 49); C1_hi = C1.w[1]; C1_lo = C1.w[0]; } if (rnd_mode != ROUNDING_TO_NEAREST) { if ((rnd_mode == ROUNDING_DOWN && x_sign && y_sign) || (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) { // add 1 ulp and then check for overflow C1_lo = C1_lo + 1; if (C1_lo == 0) { // rounding overflow in the low 64 bits C1_hi = C1_hi + 1; } if (C1_hi == 0x0001ed09bead87c0ull && C1_lo == 0x378d8e6400000000ull) { // C1 = 10^34 => rounding overflow C1_hi = 0x0000314dc6448d93ull; C1_lo = 0x38c15b0a00000000ull; // 10^33 x_exp = x_exp + EXP_P1; if (x_exp == EXP_MAX_P1) { // overflow C1_hi = 0x7800000000000000ull; // +inf C1_lo = 0x0ull; x_exp = 0; // x_sign is preserved // set overflow flag (the inexact flag was set too) *pfpsf |= OVERFLOW_EXCEPTION; } } } else if ((rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) || (rnd_mode == ROUNDING_TO_ZERO && x_sign != y_sign)) { // subtract 1 ulp from C1 // Note: because delta >= P34 + 1 the result cannot be zero C1_lo = C1_lo - 1; if (C1_lo == 0xffffffffffffffffull) C1_hi = C1_hi - 1; // if the coefficient is 10^33-1 then make it 10^34-1 and // decrease the exponent by 1 (because delta >= P34 + 1 the // exponent will not become less than e_min) // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // make C1 = 10^34 - 1 C1_hi = 0x0001ed09bead87c0ull; C1_lo = 0x378d8e63ffffffffull; x_exp = x_exp - EXP_P1; } } else { ; // the result is already correct } } // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // assemble the result res.w[1] = x_sign | x_exp | C1_hi; res.w[0] = C1_lo; } else if ((C2_lo == halfulp64) && (q1 < P34 || ((C1_lo & 0x1) == 0))) { // n2 = 1/2 ulp (n1) and C1 is even // the result is the operand with the larger magnitude, // possibly scaled up by 10^(P34-q1) // an overflow cannot occur in this case (rounding to nearest) if (q1 < P34) { // scale C1 up by 10^(P34-q1) // Note: because delta = P34 it is certain that // x_exp - ((UINT64)scale << 49) will stay above e_min scale = P34 - q1; if (q1 <= 19) { // C1 fits in 64 bits // 1 <= q1 <= 19 => 15 <= scale <= 33 if (scale <= 19) { // 10^scale fits in 64 bits __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); } else { // if 20 <= scale <= 33 // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where // (C1 * 10^(scale-19)) fits in 64 bits C1_lo = C1_lo * ten2k64[scale - 19]; __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); } } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits C1.w[1] = C1_hi; C1.w[0] = C1_lo; // C1 = ten2k64[P34 - q1] * C1 __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); } x_exp = x_exp - ((UINT64) scale << 49); C1_hi = C1.w[1]; C1_lo = C1.w[0]; } if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign == y_sign && (C1_lo & 0x01)) || (rnd_mode == ROUNDING_TIES_AWAY && x_sign == y_sign) || (rnd_mode == ROUNDING_UP && !x_sign && !y_sign) || (rnd_mode == ROUNDING_DOWN && x_sign && y_sign)) { // add 1 ulp and then check for overflow C1_lo = C1_lo + 1; if (C1_lo == 0) { // rounding overflow in the low 64 bits C1_hi = C1_hi + 1; } if (C1_hi == 0x0001ed09bead87c0ull && C1_lo == 0x378d8e6400000000ull) { // C1 = 10^34 => rounding overflow C1_hi = 0x0000314dc6448d93ull; C1_lo = 0x38c15b0a00000000ull; // 10^33 x_exp = x_exp + EXP_P1; if (x_exp == EXP_MAX_P1) { // overflow C1_hi = 0x7800000000000000ull; // +inf C1_lo = 0x0ull; x_exp = 0; // x_sign is preserved // set overflow flag (the inexact flag was set too) *pfpsf |= OVERFLOW_EXCEPTION; } } } else if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign != y_sign && (C1_lo & 0x01)) || (rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) || (rnd_mode == ROUNDING_TO_ZERO && x_sign != y_sign)) { // subtract 1 ulp from C1 // Note: because delta >= P34 + 1 the result cannot be zero C1_lo = C1_lo - 1; if (C1_lo == 0xffffffffffffffffull) C1_hi = C1_hi - 1; // if the coefficient is 10^33 - 1 then make it 10^34 - 1 // and decrease the exponent by 1 (because delta >= P34 + 1 // the exponent will not become less than e_min) // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // make C1 = 10^34 - 1 C1_hi = 0x0001ed09bead87c0ull; C1_lo = 0x378d8e63ffffffffull; x_exp = x_exp - EXP_P1; } } else { ; // the result is already correct } // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // assemble the result res.w[1] = x_sign | x_exp | C1_hi; res.w[0] = C1_lo; } else { // if C2_lo > halfulp64 || // (C2_lo == halfulp64 && q1 == P34 && ((C1_lo & 0x1) == 1)), i.e. // 1/2 ulp(n1) < n2 < 1 ulp(n1) or n2 = 1/2 ulp(n1) and C1 odd // res = x+1 ulp if n1*n2 > 0 and res = x-1 ulp if n1*n2 < 0 if (q1 < P34) { // then 1 ulp = 10^(e1+q1-P34) < 10^e1 // Note: if (q1 == P34) then 1 ulp = 10^(e1+q1-P34) = 10^e1 // because q1 < P34 we must first replace C1 by // C1 * 10^(P34-q1), and must decrease the exponent by // (P34-q1) (it will still be at least e_min) scale = P34 - q1; if (q1 <= 19) { // C1 fits in 64 bits // 1 <= q1 <= 19 => 15 <= scale <= 33 if (scale <= 19) { // 10^scale fits in 64 bits __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); } else { // if 20 <= scale <= 33 // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where // (C1 * 10^(scale-19)) fits in 64 bits C1_lo = C1_lo * ten2k64[scale - 19]; __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); } } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits C1.w[1] = C1_hi; C1.w[0] = C1_lo; // C1 = ten2k64[P34 - q1] * C1 __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); } x_exp = x_exp - ((UINT64) scale << 49); C1_hi = C1.w[1]; C1_lo = C1.w[0]; // check for rounding overflow if (C1_hi == 0x0001ed09bead87c0ull && C1_lo == 0x378d8e6400000000ull) { // C1 = 10^34 => rounding overflow C1_hi = 0x0000314dc6448d93ull; C1_lo = 0x38c15b0a00000000ull; // 10^33 x_exp = x_exp + EXP_P1; } } if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign != y_sign) || (rnd_mode == ROUNDING_TIES_AWAY && x_sign != y_sign && C2_lo != halfulp64) || (rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) || (rnd_mode == ROUNDING_TO_ZERO && x_sign != y_sign)) { // the result is x - 1 // for RN n1 * n2 < 0; underflow not possible C1_lo = C1_lo - 1; if (C1_lo == 0xffffffffffffffffull) C1_hi--; // check if we crossed into the lower decade if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 C1_lo = 0x378d8e63ffffffffull; x_exp = x_exp - EXP_P1; // no underflow, because n1 >> n2 } } else if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign == y_sign) || (rnd_mode == ROUNDING_TIES_AWAY && x_sign == y_sign) || (rnd_mode == ROUNDING_DOWN && x_sign && y_sign) || (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) { // the result is x + 1 // for RN x_sign = y_sign, i.e. n1*n2 > 0 C1_lo = C1_lo + 1; if (C1_lo == 0) { // rounding overflow in the low 64 bits C1_hi = C1_hi + 1; } if (C1_hi == 0x0001ed09bead87c0ull && C1_lo == 0x378d8e6400000000ull) { // C1 = 10^34 => rounding overflow C1_hi = 0x0000314dc6448d93ull; C1_lo = 0x38c15b0a00000000ull; // 10^33 x_exp = x_exp + EXP_P1; if (x_exp == EXP_MAX_P1) { // overflow C1_hi = 0x7800000000000000ull; // +inf C1_lo = 0x0ull; x_exp = 0; // x_sign is preserved // set the overflow flag *pfpsf |= OVERFLOW_EXCEPTION; } } } else { ; // the result is x } // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // assemble the result res.w[1] = x_sign | x_exp | C1_hi; res.w[0] = C1_lo; } } else { // if q2 >= 20 then 5*10^(q2-1) and C2 (the latter in // most cases) fit only in more than 64 bits halfulp128 = midpoint128[q2 - 20]; // 5 * 10^(q2-1) if ((C2_hi < halfulp128.w[1]) || (C2_hi == halfulp128.w[1] && C2_lo < halfulp128.w[0])) { // n2 < 1/2 ulp (n1) // the result is the operand with the larger magnitude, // possibly scaled up by 10^(P34-q1) // an overflow cannot occur in this case (rounding to nearest) if (q1 < P34) { // scale C1 up by 10^(P34-q1) // Note: because delta = P34 it is certain that // x_exp - ((UINT64)scale << 49) will stay above e_min scale = P34 - q1; if (q1 <= 19) { // C1 fits in 64 bits // 1 <= q1 <= 19 => 15 <= scale <= 33 if (scale <= 19) { // 10^scale fits in 64 bits __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); } else { // if 20 <= scale <= 33 // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where // (C1 * 10^(scale-19)) fits in 64 bits C1_lo = C1_lo * ten2k64[scale - 19]; __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); } } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits C1.w[1] = C1_hi; C1.w[0] = C1_lo; // C1 = ten2k64[P34 - q1] * C1 __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); } C1_hi = C1.w[1]; C1_lo = C1.w[0]; x_exp = x_exp - ((UINT64) scale << 49); } if (rnd_mode != ROUNDING_TO_NEAREST) { if ((rnd_mode == ROUNDING_DOWN && x_sign && y_sign) || (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) { // add 1 ulp and then check for overflow C1_lo = C1_lo + 1; if (C1_lo == 0) { // rounding overflow in the low 64 bits C1_hi = C1_hi + 1; } if (C1_hi == 0x0001ed09bead87c0ull && C1_lo == 0x378d8e6400000000ull) { // C1 = 10^34 => rounding overflow C1_hi = 0x0000314dc6448d93ull; C1_lo = 0x38c15b0a00000000ull; // 10^33 x_exp = x_exp + EXP_P1; if (x_exp == EXP_MAX_P1) { // overflow C1_hi = 0x7800000000000000ull; // +inf C1_lo = 0x0ull; x_exp = 0; // x_sign is preserved // set overflow flag (the inexact flag was set too) *pfpsf |= OVERFLOW_EXCEPTION; } } } else if ((rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) || (rnd_mode == ROUNDING_TO_ZERO && x_sign != y_sign)) { // subtract 1 ulp from C1 // Note: because delta >= P34 + 1 the result cannot be zero C1_lo = C1_lo - 1; if (C1_lo == 0xffffffffffffffffull) C1_hi = C1_hi - 1; // if the coefficient is 10^33-1 then make it 10^34-1 and // decrease the exponent by 1 (because delta >= P34 + 1 the // exponent will not become less than e_min) // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // make C1 = 10^34 - 1 C1_hi = 0x0001ed09bead87c0ull; C1_lo = 0x378d8e63ffffffffull; x_exp = x_exp - EXP_P1; } } else { ; // the result is already correct } } // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // assemble the result res.w[1] = x_sign | x_exp | C1_hi; res.w[0] = C1_lo; } else if ((C2_hi == halfulp128.w[1] && C2_lo == halfulp128.w[0]) && (q1 < P34 || ((C1_lo & 0x1) == 0))) { // midpoint & lsb in C1 is 0 // n2 = 1/2 ulp (n1) and C1 is even // the result is the operand with the larger magnitude, // possibly scaled up by 10^(P34-q1) // an overflow cannot occur in this case (rounding to nearest) if (q1 < P34) { // scale C1 up by 10^(P34-q1) // Note: because delta = P34 it is certain that // x_exp - ((UINT64)scale << 49) will stay above e_min scale = P34 - q1; if (q1 <= 19) { // C1 fits in 64 bits // 1 <= q1 <= 19 => 15 <= scale <= 33 if (scale <= 19) { // 10^scale fits in 64 bits __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); } else { // if 20 <= scale <= 33 // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where // (C1 * 10^(scale-19)) fits in 64 bits C1_lo = C1_lo * ten2k64[scale - 19]; __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); } } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits C1.w[1] = C1_hi; C1.w[0] = C1_lo; // C1 = ten2k64[P34 - q1] * C1 __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); } x_exp = x_exp - ((UINT64) scale << 49); C1_hi = C1.w[1]; C1_lo = C1.w[0]; } if (rnd_mode != ROUNDING_TO_NEAREST) { if ((rnd_mode == ROUNDING_TIES_AWAY && x_sign == y_sign) || (rnd_mode == ROUNDING_UP && !y_sign)) { // add 1 ulp and then check for overflow C1_lo = C1_lo + 1; if (C1_lo == 0) { // rounding overflow in the low 64 bits C1_hi = C1_hi + 1; } if (C1_hi == 0x0001ed09bead87c0ull && C1_lo == 0x378d8e6400000000ull) { // C1 = 10^34 => rounding overflow C1_hi = 0x0000314dc6448d93ull; C1_lo = 0x38c15b0a00000000ull; // 10^33 x_exp = x_exp + EXP_P1; if (x_exp == EXP_MAX_P1) { // overflow C1_hi = 0x7800000000000000ull; // +inf C1_lo = 0x0ull; x_exp = 0; // x_sign is preserved // set overflow flag (the inexact flag was set too) *pfpsf |= OVERFLOW_EXCEPTION; } } } else if ((rnd_mode == ROUNDING_DOWN && y_sign) || (rnd_mode == ROUNDING_TO_ZERO && x_sign != y_sign)) { // subtract 1 ulp from C1 // Note: because delta >= P34 + 1 the result cannot be zero C1_lo = C1_lo - 1; if (C1_lo == 0xffffffffffffffffull) C1_hi = C1_hi - 1; // if the coefficient is 10^33 - 1 then make it 10^34 - 1 // and decrease the exponent by 1 (because delta >= P34 + 1 // the exponent will not become less than e_min) // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // make C1 = 10^34 - 1 C1_hi = 0x0001ed09bead87c0ull; C1_lo = 0x378d8e63ffffffffull; x_exp = x_exp - EXP_P1; } } else { ; // the result is already correct } } // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // assemble the result res.w[1] = x_sign | x_exp | C1_hi; res.w[0] = C1_lo; } else { // if C2 > halfulp128 || // (C2 == halfulp128 && q1 == P34 && ((C1 & 0x1) == 1)), i.e. // 1/2 ulp(n1) < n2 < 1 ulp(n1) or n2 = 1/2 ulp(n1) and C1 odd // res = x+1 ulp if n1*n2 > 0 and res = x-1 ulp if n1*n2 < 0 if (q1 < P34) { // then 1 ulp = 10^(e1+q1-P34) < 10^e1 // Note: if (q1 == P34) then 1 ulp = 10^(e1+q1-P34) = 10^e1 // because q1 < P34 we must first replace C1 by C1*10^(P34-q1), // and must decrease the exponent by (P34-q1) (it will still be // at least e_min) scale = P34 - q1; if (q1 <= 19) { // C1 fits in 64 bits // 1 <= q1 <= 19 => 15 <= scale <= 33 if (scale <= 19) { // 10^scale fits in 64 bits __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo); } else { // if 20 <= scale <= 33 // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where // (C1 * 10^(scale-19)) fits in 64 bits C1_lo = C1_lo * ten2k64[scale - 19]; __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo); } } else { //if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits C1.w[1] = C1_hi; C1.w[0] = C1_lo; // C1 = ten2k64[P34 - q1] * C1 __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1); } C1_hi = C1.w[1]; C1_lo = C1.w[0]; x_exp = x_exp - ((UINT64) scale << 49); } if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign != y_sign) || (rnd_mode == ROUNDING_TIES_AWAY && x_sign != y_sign && (C2_hi != halfulp128.w[1] || C2_lo != halfulp128.w[0])) || (rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) || (rnd_mode == ROUNDING_UP && x_sign && !y_sign) || (rnd_mode == ROUNDING_TO_ZERO && x_sign != y_sign)) { // the result is x - 1 // for RN n1 * n2 < 0; underflow not possible C1_lo = C1_lo - 1; if (C1_lo == 0xffffffffffffffffull) C1_hi--; // check if we crossed into the lower decade if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 C1_lo = 0x378d8e63ffffffffull; x_exp = x_exp - EXP_P1; // no underflow, because n1 >> n2 } } else if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign == y_sign) || (rnd_mode == ROUNDING_TIES_AWAY && x_sign == y_sign) || (rnd_mode == ROUNDING_DOWN && x_sign && y_sign) || (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) { // the result is x + 1 // for RN x_sign = y_sign, i.e. n1*n2 > 0 C1_lo = C1_lo + 1; if (C1_lo == 0) { // rounding overflow in the low 64 bits C1_hi = C1_hi + 1; } if (C1_hi == 0x0001ed09bead87c0ull && C1_lo == 0x378d8e6400000000ull) { // C1 = 10^34 => rounding overflow C1_hi = 0x0000314dc6448d93ull; C1_lo = 0x38c15b0a00000000ull; // 10^33 x_exp = x_exp + EXP_P1; if (x_exp == EXP_MAX_P1) { // overflow C1_hi = 0x7800000000000000ull; // +inf C1_lo = 0x0ull; x_exp = 0; // x_sign is preserved // set the overflow flag *pfpsf |= OVERFLOW_EXCEPTION; } } } else { ; // the result is x } // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // assemble the result res.w[1] = x_sign | x_exp | C1_hi; res.w[0] = C1_lo; } } // end q1 >= 20 // end case where C1 != 10^(q1-1) } else { // C1 = 10^(q1-1) and x_sign != y_sign // instead of C' = (C1 * 10^(e1-e2) + C2)rnd,P34 // calculate C' = C1 * 10^(e1-e2-x1) + (C2 * 10^(-x1))rnd,P34 // where x1 = q2 - 1, 0 <= x1 <= P34 - 1 // Because C1 = 10^(q1-1) and x_sign != y_sign, C' will have P34 // digits and n = C' * 10^(e2+x1) // If the result has P34+1 digits, redo the steps above with x1+1 // If the result has P34-1 digits or less, redo the steps above with // x1-1 but only if initially x1 >= 1 // NOTE: these two steps can be improved, e.g we could guess if // P34+1 or P34-1 digits will be obtained by adding/subtracting // just the top 64 bits of the two operands // The result cannot be zero, and it cannot overflow x1 = q2 - 1; // 0 <= x1 <= P34-1 // Calculate C1 * 10^(e1-e2-x1) where 1 <= e1-e2-x1 <= P34 // scale = (int)(e1 >> 49) - (int)(e2 >> 49) - x1; 0 <= scale <= P34-1 scale = P34 - q1 + 1; // scale=e1-e2-x1 = P34+1-q1; 1<=scale<=P34 // either C1 or 10^(e1-e2-x1) may not fit is 64 bits, // but their product fits with certainty in 128 bits if (scale >= 20) { //10^(e1-e2-x1) doesn't fit in 64 bits, but C1 does __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); } else { // if (scale >= 1 // if 1 <= scale <= 19 then 10^(e1-e2-x1) fits in 64 bits if (q1 <= 19) { // C1 fits in 64 bits __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); } else { // q1 >= 20 C1.w[1] = C1_hi; C1.w[0] = C1_lo; __mul_128x64_to_128 (C1, ten2k64[scale], C1); } } tmp64 = C1.w[0]; // C1.w[1], C1.w[0] contains C1 * 10^(e1-e2-x1) // now round C2 to q2-x1 = 1 decimal digit // C2' = C2 + 1/2 * 10^x1 = C2 + 5 * 10^(x1-1) ind = x1 - 1; // -1 <= ind <= P34 - 2 if (ind >= 0) { // if (x1 >= 1) C2.w[0] = C2_lo; C2.w[1] = C2_hi; if (ind <= 18) { C2.w[0] = C2.w[0] + midpoint64[ind]; if (C2.w[0] < C2_lo) C2.w[1]++; } else { // 19 <= ind <= 32 C2.w[0] = C2.w[0] + midpoint128[ind - 19].w[0]; C2.w[1] = C2.w[1] + midpoint128[ind - 19].w[1]; if (C2.w[0] < C2_lo) C2.w[1]++; } // the approximation of 10^(-x1) was rounded up to 118 bits __mul_128x128_to_256 (R256, C2, ten2mk128[ind]); // R256 = C2*, f2* // calculate C2* and f2* // C2* is actually floor(C2*) in this case // C2* and f2* need shifting and masking, as shown by // shiftright128[] and maskhigh128[] // the top Ex bits of 10^(-x1) are T* = ten2mk128trunc[ind], e.g. // if x1=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 // if (0 < f2* < 10^(-x1)) then // if floor(C1+C2*) is even then C2* = floor(C2*) - logical right // shift; C2* has p decimal digits, correct by Prop. 1) // else if floor(C1+C2*) is odd C2* = floor(C2*)-1 (logical right // shift; C2* has p decimal digits, correct by Pr. 1) // else // C2* = floor(C2*) (logical right shift; C has p decimal digits, // correct by Property 1) // n = C2* * 10^(e2+x1) if (ind <= 2) { highf2star.w[1] = 0x0; highf2star.w[0] = 0x0; // low f2* ok } else if (ind <= 21) { highf2star.w[1] = 0x0; highf2star.w[0] = R256.w[2] & maskhigh128[ind]; // low f2* ok } else { highf2star.w[1] = R256.w[3] & maskhigh128[ind]; highf2star.w[0] = R256.w[2]; // low f2* is ok } // shift right C2* by Ex-128 = shiftright128[ind] if (ind >= 3) { shift = shiftright128[ind]; if (shift < 64) { // 3 <= shift <= 63 R256.w[2] = (R256.w[2] >> shift) | (R256.w[3] << (64 - shift)); R256.w[3] = (R256.w[3] >> shift); } else { // 66 <= shift <= 102 R256.w[2] = (R256.w[3] >> (shift - 64)); R256.w[3] = 0x0ULL; } } // redundant is_inexact_lt_midpoint = 0; is_inexact_gt_midpoint = 0; is_midpoint_lt_even = 0; is_midpoint_gt_even = 0; // determine inexactness of the rounding of C2* // (cannot be followed by a second rounding) // if (0 < f2* - 1/2 < 10^(-x1)) then // the result is exact // else (if f2* - 1/2 > T* then) // the result of is inexact if (ind <= 2) { if (R256.w[1] > 0x8000000000000000ull || (R256.w[1] == 0x8000000000000000ull && R256.w[0] > 0x0ull)) { // f2* > 1/2 and the result may be exact tmp64A = R256.w[1] - 0x8000000000000000ull; // f* - 1/2 if ((tmp64A > ten2mk128trunc[ind].w[1] || (tmp64A == ten2mk128trunc[ind].w[1] && R256.w[0] >= ten2mk128trunc[ind].w[0]))) { // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // this rounding is applied to C2 only! // x_sign != y_sign is_inexact_gt_midpoint = 1; } // else the result is exact // rounding down, unless a midpoint in [ODD, EVEN] } else { // the result is inexact; f2* <= 1/2 // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // this rounding is applied to C2 only! // x_sign != y_sign is_inexact_lt_midpoint = 1; } } else if (ind <= 21) { // if 3 <= ind <= 21 if (highf2star.w[1] > 0x0 || (highf2star.w[1] == 0x0 && highf2star.w[0] > onehalf128[ind]) || (highf2star.w[1] == 0x0 && highf2star.w[0] == onehalf128[ind] && (R256.w[1] || R256.w[0]))) { // f2* > 1/2 and the result may be exact // Calculate f2* - 1/2 tmp64A = highf2star.w[0] - onehalf128[ind]; tmp64B = highf2star.w[1]; if (tmp64A > highf2star.w[0]) tmp64B--; if (tmp64B || tmp64A || R256.w[1] > ten2mk128trunc[ind].w[1] || (R256.w[1] == ten2mk128trunc[ind].w[1] && R256.w[0] > ten2mk128trunc[ind].w[0])) { // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // this rounding is applied to C2 only! // x_sign != y_sign is_inexact_gt_midpoint = 1; } // else the result is exact } else { // the result is inexact; f2* <= 1/2 // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // this rounding is applied to C2 only! // x_sign != y_sign is_inexact_lt_midpoint = 1; } } else { // if 22 <= ind <= 33 if (highf2star.w[1] > onehalf128[ind] || (highf2star.w[1] == onehalf128[ind] && (highf2star.w[0] || R256.w[1] || R256.w[0]))) { // f2* > 1/2 and the result may be exact // Calculate f2* - 1/2 // tmp64A = highf2star.w[0]; tmp64B = highf2star.w[1] - onehalf128[ind]; if (tmp64B || highf2star.w[0] || R256.w[1] > ten2mk128trunc[ind].w[1] || (R256.w[1] == ten2mk128trunc[ind].w[1] && R256.w[0] > ten2mk128trunc[ind].w[0])) { // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // this rounding is applied to C2 only! // x_sign != y_sign is_inexact_gt_midpoint = 1; } // else the result is exact } else { // the result is inexact; f2* <= 1/2 // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // this rounding is applied to C2 only! // x_sign != y_sign is_inexact_lt_midpoint = 1; } } // check for midpoints after determining inexactness if ((R256.w[1] || R256.w[0]) && (highf2star.w[1] == 0) && (highf2star.w[0] == 0) && (R256.w[1] < ten2mk128trunc[ind].w[1] || (R256.w[1] == ten2mk128trunc[ind].w[1] && R256.w[0] <= ten2mk128trunc[ind].w[0]))) { // the result is a midpoint if ((tmp64 + R256.w[2]) & 0x01) { // MP in [EVEN, ODD] // if floor(C2*) is odd C = floor(C2*) - 1; the result may be 0 R256.w[2]--; if (R256.w[2] == 0xffffffffffffffffull) R256.w[3]--; // this rounding is applied to C2 only! // x_sign != y_sign is_midpoint_lt_even = 1; is_inexact_lt_midpoint = 0; is_inexact_gt_midpoint = 0; } else { // else MP in [ODD, EVEN] // this rounding is applied to C2 only! // x_sign != y_sign is_midpoint_gt_even = 1; is_inexact_lt_midpoint = 0; is_inexact_gt_midpoint = 0; } } } else { // if (ind == -1) only when x1 = 0 R256.w[2] = C2_lo; R256.w[3] = C2_hi; is_midpoint_lt_even = 0; is_midpoint_gt_even = 0; is_inexact_lt_midpoint = 0; is_inexact_gt_midpoint = 0; } // and now subtract C1 * 10^(e1-e2-x1) - (C2 * 10^(-x1))rnd,P34 // because x_sign != y_sign this last operation is exact C1.w[0] = C1.w[0] - R256.w[2]; C1.w[1] = C1.w[1] - R256.w[3]; if (C1.w[0] > tmp64) C1.w[1]--; // borrow if (C1.w[1] >= 0x8000000000000000ull) { // negative coefficient! C1.w[0] = ~C1.w[0]; C1.w[0]++; C1.w[1] = ~C1.w[1]; if (C1.w[0] == 0x0) C1.w[1]++; tmp_sign = y_sign; // the result will have the sign of y } else { tmp_sign = x_sign; } // the difference has exactly P34 digits x_sign = tmp_sign; if (x1 >= 1) y_exp = y_exp + ((UINT64) x1 << 49); C1_hi = C1.w[1]; C1_lo = C1.w[0]; // general correction from RN to RA, RM, RP, RZ; result uses y_exp if (rnd_mode != ROUNDING_TO_NEAREST) { if ((!x_sign && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) || ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_UP) && is_midpoint_gt_even))) || (x_sign && ((rnd_mode == ROUNDING_DOWN && is_inexact_lt_midpoint) || ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_DOWN) && is_midpoint_gt_even)))) { // C1 = C1 + 1 C1_lo = C1_lo + 1; if (C1_lo == 0) { // rounding overflow in the low 64 bits C1_hi = C1_hi + 1; } if (C1_hi == 0x0001ed09bead87c0ull && C1_lo == 0x378d8e6400000000ull) { // C1 = 10^34 => rounding overflow C1_hi = 0x0000314dc6448d93ull; C1_lo = 0x38c15b0a00000000ull; // 10^33 y_exp = y_exp + EXP_P1; } } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) && ((x_sign && (rnd_mode == ROUNDING_UP || rnd_mode == ROUNDING_TO_ZERO)) || (!x_sign && (rnd_mode == ROUNDING_DOWN || rnd_mode == ROUNDING_TO_ZERO)))) { // C1 = C1 - 1 C1_lo = C1_lo - 1; if (C1_lo == 0xffffffffffffffffull) C1_hi--; // check if we crossed into the lower decade if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 C1_lo = 0x378d8e63ffffffffull; y_exp = y_exp - EXP_P1; // no underflow, because delta + q2 >= P34 + 1 } } else { ; // exact, the result is already correct } } // assemble the result res.w[1] = x_sign | y_exp | C1_hi; res.w[0] = C1_lo; } } // end delta = P34 } else { // if (|delta| <= P34 - 1) if (delta >= 0) { // if (0 <= delta <= P34 - 1) if (delta <= P34 - 1 - q2) { // calculate C' directly; the result is exact // in this case 1<=q1<=P34-1, 1<=q2<=P34-1 and 0 <= e1-e2 <= P34-2 // The coefficient of the result is C1 * 10^(e1-e2) + C2 and the // exponent is e2; either C1 or 10^(e1-e2) may not fit is 64 bits, // but their product fits with certainty in 128 bits (actually in 113) scale = delta - q1 + q2; // scale = (int)(e1 >> 49) - (int)(e2 >> 49) if (scale >= 20) { // 10^(e1-e2) does not fit in 64 bits, but C1 does __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); C1_hi = C1.w[1]; C1_lo = C1.w[0]; } else if (scale >= 1) { // if 1 <= scale <= 19 then 10^(e1-e2) fits in 64 bits if (q1 <= 19) { // C1 fits in 64 bits __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); } else { // q1 >= 20 C1.w[1] = C1_hi; C1.w[0] = C1_lo; __mul_128x64_to_128 (C1, ten2k64[scale], C1); } C1_hi = C1.w[1]; C1_lo = C1.w[0]; } else { // if (scale == 0) C1 is unchanged C1.w[0] = C1_lo; // C1.w[1] = C1_hi; } // now add C2 if (x_sign == y_sign) { // the result cannot overflow C1_lo = C1_lo + C2_lo; C1_hi = C1_hi + C2_hi; if (C1_lo < C1.w[0]) C1_hi++; } else { // if x_sign != y_sign C1_lo = C1_lo - C2_lo; C1_hi = C1_hi - C2_hi; if (C1_lo > C1.w[0]) C1_hi--; // the result can be zero, but it cannot overflow if (C1_lo == 0 && C1_hi == 0) { // assemble the result if (x_exp < y_exp) res.w[1] = x_exp; else res.w[1] = y_exp; res.w[0] = 0; if (rnd_mode == ROUNDING_DOWN) { res.w[1] |= 0x8000000000000000ull; } BID_SWAP128 (res); BID_RETURN (res); } if (C1_hi >= 0x8000000000000000ull) { // negative coefficient! C1_lo = ~C1_lo; C1_lo++; C1_hi = ~C1_hi; if (C1_lo == 0x0) C1_hi++; x_sign = y_sign; // the result will have the sign of y } } // assemble the result res.w[1] = x_sign | y_exp | C1_hi; res.w[0] = C1_lo; } else if (delta == P34 - q2) { // calculate C' directly; the result may be inexact if it requires // P34+1 decimal digits; in this case the 'cutoff' point for addition // is at the position of the lsb of C2, so 0 <= e1-e2 <= P34-1 // The coefficient of the result is C1 * 10^(e1-e2) + C2 and the // exponent is e2; either C1 or 10^(e1-e2) may not fit is 64 bits, // but their product fits with certainty in 128 bits (actually in 113) scale = delta - q1 + q2; // scale = (int)(e1 >> 49) - (int)(e2 >> 49) if (scale >= 20) { // 10^(e1-e2) does not fit in 64 bits, but C1 does __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); } else if (scale >= 1) { // if 1 <= scale <= 19 then 10^(e1-e2) fits in 64 bits if (q1 <= 19) { // C1 fits in 64 bits __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); } else { // q1 >= 20 C1.w[1] = C1_hi; C1.w[0] = C1_lo; __mul_128x64_to_128 (C1, ten2k64[scale], C1); } } else { // if (scale == 0) C1 is unchanged C1.w[1] = C1_hi; C1.w[0] = C1_lo; // only the low part is necessary } C1_hi = C1.w[1]; C1_lo = C1.w[0]; // now add C2 if (x_sign == y_sign) { // the result can overflow! C1_lo = C1_lo + C2_lo; C1_hi = C1_hi + C2_hi; if (C1_lo < C1.w[0]) C1_hi++; // test for overflow, possible only when C1 >= 10^34 if (C1_hi > 0x0001ed09bead87c0ull || (C1_hi == 0x0001ed09bead87c0ull && C1_lo >= 0x378d8e6400000000ull)) { // C1 >= 10^34 // in this case q = P34 + 1 and x = q - P34 = 1, so multiply // C'' = C'+ 5 = C1 + 5 by k1 ~ 10^(-1) calculated for P34 + 1 // decimal digits // Calculate C'' = C' + 1/2 * 10^x if (C1_lo >= 0xfffffffffffffffbull) { // low half add has carry C1_lo = C1_lo + 5; C1_hi = C1_hi + 1; } else { C1_lo = C1_lo + 5; } // the approximation of 10^(-1) was rounded up to 118 bits // 10^(-1) =~ 33333333333333333333333333333400 * 2^-129 // 10^(-1) =~ 19999999999999999999999999999a00 * 2^-128 C1.w[1] = C1_hi; C1.w[0] = C1_lo; // C'' ten2m1.w[1] = 0x1999999999999999ull; ten2m1.w[0] = 0x9999999999999a00ull; __mul_128x128_to_256 (P256, C1, ten2m1); // P256 = C*, f* // C* is actually floor(C*) in this case // the top Ex = 128 bits of 10^(-1) are // T* = 0x00199999999999999999999999999999 // if (0 < f* < 10^(-x)) then // if floor(C*) is even then C = floor(C*) - logical right // shift; C has p decimal digits, correct by Prop. 1) // else if floor(C*) is odd C = floor(C*) - 1 (logical right // shift; C has p decimal digits, correct by Pr. 1) // else // C = floor(C*) (logical right shift; C has p decimal digits, // correct by Property 1) // n = C * 10^(e2+x) if ((P256.w[1] || P256.w[0]) && (P256.w[1] < 0x1999999999999999ull || (P256.w[1] == 0x1999999999999999ull && P256.w[0] <= 0x9999999999999999ull))) { // the result is a midpoint if (P256.w[2] & 0x01) { is_midpoint_gt_even = 1; // if floor(C*) is odd C = floor(C*) - 1; the result is not 0 P256.w[2]--; if (P256.w[2] == 0xffffffffffffffffull) P256.w[3]--; } else { is_midpoint_lt_even = 1; } } // n = Cstar * 10^(e2+1) y_exp = y_exp + EXP_P1; // C* != 10^P because C* has P34 digits // check for overflow if (y_exp == EXP_MAX_P1 && (rnd_mode == ROUNDING_TO_NEAREST || rnd_mode == ROUNDING_TIES_AWAY)) { // overflow for RN res.w[1] = x_sign | 0x7800000000000000ull; // +/-inf res.w[0] = 0x0ull; // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // set the overflow flag *pfpsf |= OVERFLOW_EXCEPTION; BID_SWAP128 (res); BID_RETURN (res); } // if (0 < f* - 1/2 < 10^(-x)) then // the result of the addition is exact // else // the result of the addition is inexact if (P256.w[1] > 0x8000000000000000ull || (P256.w[1] == 0x8000000000000000ull && P256.w[0] > 0x0ull)) { // the result may be exact tmp64 = P256.w[1] - 0x8000000000000000ull; // f* - 1/2 if ((tmp64 > 0x1999999999999999ull || (tmp64 == 0x1999999999999999ull && P256.w[0] >= 0x9999999999999999ull))) { // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; is_inexact = 1; } // else the result is exact } else { // the result is inexact // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; is_inexact = 1; } C1_hi = P256.w[3]; C1_lo = P256.w[2]; if (!is_midpoint_gt_even && !is_midpoint_lt_even) { is_inexact_lt_midpoint = is_inexact && (P256.w[1] & 0x8000000000000000ull); is_inexact_gt_midpoint = is_inexact && !(P256.w[1] & 0x8000000000000000ull); } // general correction from RN to RA, RM, RP, RZ; // result uses y_exp if (rnd_mode != ROUNDING_TO_NEAREST) { if ((!x_sign && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) || ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_UP) && is_midpoint_gt_even))) || (x_sign && ((rnd_mode == ROUNDING_DOWN && is_inexact_lt_midpoint) || ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_DOWN) && is_midpoint_gt_even)))) { // C1 = C1 + 1 C1_lo = C1_lo + 1; if (C1_lo == 0) { // rounding overflow in the low 64 bits C1_hi = C1_hi + 1; } if (C1_hi == 0x0001ed09bead87c0ull && C1_lo == 0x378d8e6400000000ull) { // C1 = 10^34 => rounding overflow C1_hi = 0x0000314dc6448d93ull; C1_lo = 0x38c15b0a00000000ull; // 10^33 y_exp = y_exp + EXP_P1; } } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) && ((x_sign && (rnd_mode == ROUNDING_UP || rnd_mode == ROUNDING_TO_ZERO)) || (!x_sign && (rnd_mode == ROUNDING_DOWN || rnd_mode == ROUNDING_TO_ZERO)))) { // C1 = C1 - 1 C1_lo = C1_lo - 1; if (C1_lo == 0xffffffffffffffffull) C1_hi--; // check if we crossed into the lower decade if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 C1_lo = 0x378d8e63ffffffffull; y_exp = y_exp - EXP_P1; // no underflow, because delta + q2 >= P34 + 1 } } else { ; // exact, the result is already correct } // in all cases check for overflow (RN and RA solved already) if (y_exp == EXP_MAX_P1) { // overflow if ((rnd_mode == ROUNDING_DOWN && x_sign) || // RM and res < 0 (rnd_mode == ROUNDING_UP && !x_sign)) { // RP and res > 0 C1_hi = 0x7800000000000000ull; // +inf C1_lo = 0x0ull; } else { // RM and res > 0, RP and res < 0, or RZ C1_hi = 0x5fffed09bead87c0ull; C1_lo = 0x378d8e63ffffffffull; } y_exp = 0; // x_sign is preserved // set the inexact flag (in case the exact addition was exact) *pfpsf |= INEXACT_EXCEPTION; // set the overflow flag *pfpsf |= OVERFLOW_EXCEPTION; } } } // else if (C1 < 10^34) then C1 is the coeff.; the result is exact } else { // if x_sign != y_sign the result is exact C1_lo = C1_lo - C2_lo; C1_hi = C1_hi - C2_hi; if (C1_lo > C1.w[0]) C1_hi--; // the result can be zero, but it cannot overflow if (C1_lo == 0 && C1_hi == 0) { // assemble the result if (x_exp < y_exp) res.w[1] = x_exp; else res.w[1] = y_exp; res.w[0] = 0; if (rnd_mode == ROUNDING_DOWN) { res.w[1] |= 0x8000000000000000ull; } BID_SWAP128 (res); BID_RETURN (res); } if (C1_hi >= 0x8000000000000000ull) { // negative coefficient! C1_lo = ~C1_lo; C1_lo++; C1_hi = ~C1_hi; if (C1_lo == 0x0) C1_hi++; x_sign = y_sign; // the result will have the sign of y } } // assemble the result res.w[1] = x_sign | y_exp | C1_hi; res.w[0] = C1_lo; } else { // if (delta >= P34 + 1 - q2) // instead of C' = (C1 * 10^(e1-e2) + C2)rnd,P34 // calculate C' = C1 * 10^(e1-e2-x1) + (C2 * 10^(-x1))rnd,P34 // where x1 = q1 + e1 - e2 - P34, 1 <= x1 <= P34 - 1 // In most cases C' will have P34 digits, and n = C' * 10^(e2+x1) // If the result has P34+1 digits, redo the steps above with x1+1 // If the result has P34-1 digits or less, redo the steps above with // x1-1 but only if initially x1 >= 1 // NOTE: these two steps can be improved, e.g we could guess if // P34+1 or P34-1 digits will be obtained by adding/subtracting just // the top 64 bits of the two operands // The result cannot be zero, but it can overflow x1 = delta + q2 - P34; // 1 <= x1 <= P34-1 roundC2: // Calculate C1 * 10^(e1-e2-x1) where 0 <= e1-e2-x1 <= P34 - 1 // scale = (int)(e1 >> 49) - (int)(e2 >> 49) - x1; 0 <= scale <= P34-1 scale = delta - q1 + q2 - x1; // scale = e1 - e2 - x1 = P34 - q1 // either C1 or 10^(e1-e2-x1) may not fit is 64 bits, // but their product fits with certainty in 128 bits (actually in 113) if (scale >= 20) { //10^(e1-e2-x1) doesn't fit in 64 bits, but C1 does __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); } else if (scale >= 1) { // if 1 <= scale <= 19 then 10^(e1-e2-x1) fits in 64 bits if (q1 <= 19) { // C1 fits in 64 bits __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); } else { // q1 >= 20 C1.w[1] = C1_hi; C1.w[0] = C1_lo; __mul_128x64_to_128 (C1, ten2k64[scale], C1); } } else { // if (scale == 0) C1 is unchanged C1.w[1] = C1_hi; C1.w[0] = C1_lo; } tmp64 = C1.w[0]; // C1.w[1], C1.w[0] contains C1 * 10^(e1-e2-x1) // now round C2 to q2-x1 decimal digits, where 1<=x1<=q2-1<=P34-1 // (but if we got here a second time after x1 = x1 - 1, then // x1 >= 0; note that for x1 = 0 C2 is unchanged) // C2' = C2 + 1/2 * 10^x1 = C2 + 5 * 10^(x1-1) ind = x1 - 1; // 0 <= ind <= q2-2<=P34-2=32; but note that if x1 = 0 // during a second pass, then ind = -1 if (ind >= 0) { // if (x1 >= 1) C2.w[0] = C2_lo; C2.w[1] = C2_hi; if (ind <= 18) { C2.w[0] = C2.w[0] + midpoint64[ind]; if (C2.w[0] < C2_lo) C2.w[1]++; } else { // 19 <= ind <= 32 C2.w[0] = C2.w[0] + midpoint128[ind - 19].w[0]; C2.w[1] = C2.w[1] + midpoint128[ind - 19].w[1]; if (C2.w[0] < C2_lo) C2.w[1]++; } // the approximation of 10^(-x1) was rounded up to 118 bits __mul_128x128_to_256 (R256, C2, ten2mk128[ind]); // R256 = C2*, f2* // calculate C2* and f2* // C2* is actually floor(C2*) in this case // C2* and f2* need shifting and masking, as shown by // shiftright128[] and maskhigh128[] // the top Ex bits of 10^(-x1) are T* = ten2mk128trunc[ind], e.g. // if x1=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 // if (0 < f2* < 10^(-x1)) then // if floor(C1+C2*) is even then C2* = floor(C2*) - logical right // shift; C2* has p decimal digits, correct by Prop. 1) // else if floor(C1+C2*) is odd C2* = floor(C2*)-1 (logical right // shift; C2* has p decimal digits, correct by Pr. 1) // else // C2* = floor(C2*) (logical right shift; C has p decimal digits, // correct by Property 1) // n = C2* * 10^(e2+x1) if (ind <= 2) { highf2star.w[1] = 0x0; highf2star.w[0] = 0x0; // low f2* ok } else if (ind <= 21) { highf2star.w[1] = 0x0; highf2star.w[0] = R256.w[2] & maskhigh128[ind]; // low f2* ok } else { highf2star.w[1] = R256.w[3] & maskhigh128[ind]; highf2star.w[0] = R256.w[2]; // low f2* is ok } // shift right C2* by Ex-128 = shiftright128[ind] if (ind >= 3) { shift = shiftright128[ind]; if (shift < 64) { // 3 <= shift <= 63 R256.w[2] = (R256.w[2] >> shift) | (R256.w[3] << (64 - shift)); R256.w[3] = (R256.w[3] >> shift); } else { // 66 <= shift <= 102 R256.w[2] = (R256.w[3] >> (shift - 64)); R256.w[3] = 0x0ULL; } } if (second_pass) { is_inexact_lt_midpoint = 0; is_inexact_gt_midpoint = 0; is_midpoint_lt_even = 0; is_midpoint_gt_even = 0; } // determine inexactness of the rounding of C2* (this may be // followed by a second rounding only if we get P34+1 // decimal digits) // if (0 < f2* - 1/2 < 10^(-x1)) then // the result is exact // else (if f2* - 1/2 > T* then) // the result of is inexact if (ind <= 2) { if (R256.w[1] > 0x8000000000000000ull || (R256.w[1] == 0x8000000000000000ull && R256.w[0] > 0x0ull)) { // f2* > 1/2 and the result may be exact tmp64A = R256.w[1] - 0x8000000000000000ull; // f* - 1/2 if ((tmp64A > ten2mk128trunc[ind].w[1] || (tmp64A == ten2mk128trunc[ind].w[1] && R256.w[0] >= ten2mk128trunc[ind].w[0]))) { // set the inexact flag // *pfpsf |= INEXACT_EXCEPTION; tmp_inexact = 1; // may be set again during a second pass // this rounding is applied to C2 only! if (x_sign == y_sign) is_inexact_lt_midpoint = 1; else // if (x_sign != y_sign) is_inexact_gt_midpoint = 1; } // else the result is exact // rounding down, unless a midpoint in [ODD, EVEN] } else { // the result is inexact; f2* <= 1/2 // set the inexact flag // *pfpsf |= INEXACT_EXCEPTION; tmp_inexact = 1; // just in case we will round a second time // rounding up, unless a midpoint in [EVEN, ODD] // this rounding is applied to C2 only! if (x_sign == y_sign) is_inexact_gt_midpoint = 1; else // if (x_sign != y_sign) is_inexact_lt_midpoint = 1; } } else if (ind <= 21) { // if 3 <= ind <= 21 if (highf2star.w[1] > 0x0 || (highf2star.w[1] == 0x0 && highf2star.w[0] > onehalf128[ind]) || (highf2star.w[1] == 0x0 && highf2star.w[0] == onehalf128[ind] && (R256.w[1] || R256.w[0]))) { // f2* > 1/2 and the result may be exact // Calculate f2* - 1/2 tmp64A = highf2star.w[0] - onehalf128[ind]; tmp64B = highf2star.w[1]; if (tmp64A > highf2star.w[0]) tmp64B--; if (tmp64B || tmp64A || R256.w[1] > ten2mk128trunc[ind].w[1] || (R256.w[1] == ten2mk128trunc[ind].w[1] && R256.w[0] > ten2mk128trunc[ind].w[0])) { // set the inexact flag // *pfpsf |= INEXACT_EXCEPTION; tmp_inexact = 1; // may be set again during a second pass // this rounding is applied to C2 only! if (x_sign == y_sign) is_inexact_lt_midpoint = 1; else // if (x_sign != y_sign) is_inexact_gt_midpoint = 1; } // else the result is exact } else { // the result is inexact; f2* <= 1/2 // set the inexact flag // *pfpsf |= INEXACT_EXCEPTION; tmp_inexact = 1; // may be set again during a second pass // rounding up, unless a midpoint in [EVEN, ODD] // this rounding is applied to C2 only! if (x_sign == y_sign) is_inexact_gt_midpoint = 1; else // if (x_sign != y_sign) is_inexact_lt_midpoint = 1; } } else { // if 22 <= ind <= 33 if (highf2star.w[1] > onehalf128[ind] || (highf2star.w[1] == onehalf128[ind] && (highf2star.w[0] || R256.w[1] || R256.w[0]))) { // f2* > 1/2 and the result may be exact // Calculate f2* - 1/2 // tmp64A = highf2star.w[0]; tmp64B = highf2star.w[1] - onehalf128[ind]; if (tmp64B || highf2star.w[0] || R256.w[1] > ten2mk128trunc[ind].w[1] || (R256.w[1] == ten2mk128trunc[ind].w[1] && R256.w[0] > ten2mk128trunc[ind].w[0])) { // set the inexact flag // *pfpsf |= INEXACT_EXCEPTION; tmp_inexact = 1; // may be set again during a second pass // this rounding is applied to C2 only! if (x_sign == y_sign) is_inexact_lt_midpoint = 1; else // if (x_sign != y_sign) is_inexact_gt_midpoint = 1; } // else the result is exact } else { // the result is inexact; f2* <= 1/2 // set the inexact flag // *pfpsf |= INEXACT_EXCEPTION; tmp_inexact = 1; // may be set again during a second pass // rounding up, unless a midpoint in [EVEN, ODD] // this rounding is applied to C2 only! if (x_sign == y_sign) is_inexact_gt_midpoint = 1; else // if (x_sign != y_sign) is_inexact_lt_midpoint = 1; } } // check for midpoints if ((R256.w[1] || R256.w[0]) && (highf2star.w[1] == 0) && (highf2star.w[0] == 0) && (R256.w[1] < ten2mk128trunc[ind].w[1] || (R256.w[1] == ten2mk128trunc[ind].w[1] && R256.w[0] <= ten2mk128trunc[ind].w[0]))) { // the result is a midpoint if ((tmp64 + R256.w[2]) & 0x01) { // MP in [EVEN, ODD] // if floor(C2*) is odd C = floor(C2*) - 1; the result may be 0 R256.w[2]--; if (R256.w[2] == 0xffffffffffffffffull) R256.w[3]--; // this rounding is applied to C2 only! if (x_sign == y_sign) is_midpoint_gt_even = 1; else // if (x_sign != y_sign) is_midpoint_lt_even = 1; is_inexact_lt_midpoint = 0; is_inexact_gt_midpoint = 0; } else { // else MP in [ODD, EVEN] // this rounding is applied to C2 only! if (x_sign == y_sign) is_midpoint_lt_even = 1; else // if (x_sign != y_sign) is_midpoint_gt_even = 1; is_inexact_lt_midpoint = 0; is_inexact_gt_midpoint = 0; } } // end if (ind >= 0) } else { // if (ind == -1); only during a 2nd pass, and when x1 = 0 R256.w[2] = C2_lo; R256.w[3] = C2_hi; tmp_inexact = 0; // to correct a possible setting to 1 from 1st pass if (second_pass) { is_midpoint_lt_even = 0; is_midpoint_gt_even = 0; is_inexact_lt_midpoint = 0; is_inexact_gt_midpoint = 0; } } // and now add/subtract C1 * 10^(e1-e2-x1) +/- (C2 * 10^(-x1))rnd,P34 if (x_sign == y_sign) { // addition; could overflow // no second pass is possible this way (only for x_sign != y_sign) C1.w[0] = C1.w[0] + R256.w[2]; C1.w[1] = C1.w[1] + R256.w[3]; if (C1.w[0] < tmp64) C1.w[1]++; // carry // if the sum has P34+1 digits, i.e. C1>=10^34 redo the calculation // with x1=x1+1 if (C1.w[1] > 0x0001ed09bead87c0ull || (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] >= 0x378d8e6400000000ull)) { // C1 >= 10^34 // chop off one more digit from the sum, but make sure there is // no double-rounding error (see table - double rounding logic) // now round C1 from P34+1 to P34 decimal digits // C1' = C1 + 1/2 * 10 = C1 + 5 if (C1.w[0] >= 0xfffffffffffffffbull) { // low half add has carry C1.w[0] = C1.w[0] + 5; C1.w[1] = C1.w[1] + 1; } else { C1.w[0] = C1.w[0] + 5; } // the approximation of 10^(-1) was rounded up to 118 bits __mul_128x128_to_256 (Q256, C1, ten2mk128[0]); // Q256 = C1*, f1* // C1* is actually floor(C1*) in this case // the top 128 bits of 10^(-1) are // T* = ten2mk128trunc[0]=0x19999999999999999999999999999999 // if (0 < f1* < 10^(-1)) then // if floor(C1*) is even then C1* = floor(C1*) - logical right // shift; C1* has p decimal digits, correct by Prop. 1) // else if floor(C1*) is odd C1* = floor(C1*) - 1 (logical right // shift; C1* has p decimal digits, correct by Pr. 1) // else // C1* = floor(C1*) (logical right shift; C has p decimal digits // correct by Property 1) // n = C1* * 10^(e2+x1+1) if ((Q256.w[1] || Q256.w[0]) && (Q256.w[1] < ten2mk128trunc[0].w[1] || (Q256.w[1] == ten2mk128trunc[0].w[1] && Q256.w[0] <= ten2mk128trunc[0].w[0]))) { // the result is a midpoint if (is_inexact_lt_midpoint) { // for the 1st rounding is_inexact_gt_midpoint = 1; is_inexact_lt_midpoint = 0; is_midpoint_gt_even = 0; is_midpoint_lt_even = 0; } else if (is_inexact_gt_midpoint) { // for the 1st rounding Q256.w[2]--; if (Q256.w[2] == 0xffffffffffffffffull) Q256.w[3]--; is_inexact_gt_midpoint = 0; is_inexact_lt_midpoint = 1; is_midpoint_gt_even = 0; is_midpoint_lt_even = 0; } else if (is_midpoint_gt_even) { // for the 1st rounding // Note: cannot have is_midpoint_lt_even is_inexact_gt_midpoint = 0; is_inexact_lt_midpoint = 1; is_midpoint_gt_even = 0; is_midpoint_lt_even = 0; } else { // the first rounding must have been exact if (Q256.w[2] & 0x01) { // MP in [EVEN, ODD] // the truncated result is correct Q256.w[2]--; if (Q256.w[2] == 0xffffffffffffffffull) Q256.w[3]--; is_inexact_gt_midpoint = 0; is_inexact_lt_midpoint = 0; is_midpoint_gt_even = 1; is_midpoint_lt_even = 0; } else { // MP in [ODD, EVEN] is_inexact_gt_midpoint = 0; is_inexact_lt_midpoint = 0; is_midpoint_gt_even = 0; is_midpoint_lt_even = 1; } } tmp_inexact = 1; // in all cases } else { // the result is not a midpoint // determine inexactness of the rounding of C1 (the sum C1+C2*) // if (0 < f1* - 1/2 < 10^(-1)) then // the result is exact // else (if f1* - 1/2 > T* then) // the result of is inexact // ind = 0 if (Q256.w[1] > 0x8000000000000000ull || (Q256.w[1] == 0x8000000000000000ull && Q256.w[0] > 0x0ull)) { // f1* > 1/2 and the result may be exact Q256.w[1] = Q256.w[1] - 0x8000000000000000ull; // f1* - 1/2 if ((Q256.w[1] > ten2mk128trunc[0].w[1] || (Q256.w[1] == ten2mk128trunc[0].w[1] && Q256.w[0] > ten2mk128trunc[0].w[0]))) { is_inexact_gt_midpoint = 0; is_inexact_lt_midpoint = 1; is_midpoint_gt_even = 0; is_midpoint_lt_even = 0; // set the inexact flag tmp_inexact = 1; // *pfpsf |= INEXACT_EXCEPTION; } else { // else the result is exact for the 2nd rounding if (tmp_inexact) { // if the previous rounding was inexact if (is_midpoint_lt_even) { is_inexact_gt_midpoint = 1; is_midpoint_lt_even = 0; } else if (is_midpoint_gt_even) { is_inexact_lt_midpoint = 1; is_midpoint_gt_even = 0; } else { ; // no change } } } // rounding down, unless a midpoint in [ODD, EVEN] } else { // the result is inexact; f1* <= 1/2 is_inexact_gt_midpoint = 1; is_inexact_lt_midpoint = 0; is_midpoint_gt_even = 0; is_midpoint_lt_even = 0; // set the inexact flag tmp_inexact = 1; // *pfpsf |= INEXACT_EXCEPTION; } } // end 'the result is not a midpoint' // n = C1 * 10^(e2+x1) C1.w[1] = Q256.w[3]; C1.w[0] = Q256.w[2]; y_exp = y_exp + ((UINT64) (x1 + 1) << 49); } else { // C1 < 10^34 // C1.w[1] and C1.w[0] already set // n = C1 * 10^(e2+x1) y_exp = y_exp + ((UINT64) x1 << 49); } // check for overflow if (y_exp == EXP_MAX_P1 && (rnd_mode == ROUNDING_TO_NEAREST || rnd_mode == ROUNDING_TIES_AWAY)) { res.w[1] = 0x7800000000000000ull | x_sign; // +/-inf res.w[0] = 0x0ull; // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // set the overflow flag *pfpsf |= OVERFLOW_EXCEPTION; BID_SWAP128 (res); BID_RETURN (res); } // else no overflow } else { // if x_sign != y_sign the result of this subtract. is exact C1.w[0] = C1.w[0] - R256.w[2]; C1.w[1] = C1.w[1] - R256.w[3]; if (C1.w[0] > tmp64) C1.w[1]--; // borrow if (C1.w[1] >= 0x8000000000000000ull) { // negative coefficient! C1.w[0] = ~C1.w[0]; C1.w[0]++; C1.w[1] = ~C1.w[1]; if (C1.w[0] == 0x0) C1.w[1]++; tmp_sign = y_sign; // the result will have the sign of y if last rnd } else { tmp_sign = x_sign; } // if the difference has P34-1 digits or less, i.e. C1 < 10^33 then // redo the calculation with x1=x1-1; // redo the calculation also if C1 = 10^33 and // (is_inexact_gt_midpoint or is_midpoint_lt_even); // (the last part should have really been // (is_inexact_lt_midpoint or is_midpoint_gt_even) from // the rounding of C2, but the position flags have been reversed) // 10^33 = 0x0000314dc6448d93 0x38c15b0a00000000 if ((C1.w[1] < 0x0000314dc6448d93ull || (C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] < 0x38c15b0a00000000ull)) || (C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] == 0x38c15b0a00000000ull && (is_inexact_gt_midpoint || is_midpoint_lt_even))) { // C1=10^33 x1 = x1 - 1; // x1 >= 0 if (x1 >= 0) { // clear position flags and tmp_inexact is_midpoint_lt_even = 0; is_midpoint_gt_even = 0; is_inexact_lt_midpoint = 0; is_inexact_gt_midpoint = 0; tmp_inexact = 0; second_pass = 1; goto roundC2; // else result has less than P34 digits } } // if the coefficient of the result is 10^34 it means that this // must be the second pass, and we are done if (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] == 0x378d8e6400000000ull) { // if C1 = 10^34 C1.w[1] = 0x0000314dc6448d93ull; // C1 = 10^33 C1.w[0] = 0x38c15b0a00000000ull; y_exp = y_exp + ((UINT64) 1 << 49); } x_sign = tmp_sign; if (x1 >= 1) y_exp = y_exp + ((UINT64) x1 << 49); // x1 = -1 is possible at the end of a second pass when the // first pass started with x1 = 1 } C1_hi = C1.w[1]; C1_lo = C1.w[0]; // general correction from RN to RA, RM, RP, RZ; result uses y_exp if (rnd_mode != ROUNDING_TO_NEAREST) { if ((!x_sign && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) || ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_UP) && is_midpoint_gt_even))) || (x_sign && ((rnd_mode == ROUNDING_DOWN && is_inexact_lt_midpoint) || ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_DOWN) && is_midpoint_gt_even)))) { // C1 = C1 + 1 C1_lo = C1_lo + 1; if (C1_lo == 0) { // rounding overflow in the low 64 bits C1_hi = C1_hi + 1; } if (C1_hi == 0x0001ed09bead87c0ull && C1_lo == 0x378d8e6400000000ull) { // C1 = 10^34 => rounding overflow C1_hi = 0x0000314dc6448d93ull; C1_lo = 0x38c15b0a00000000ull; // 10^33 y_exp = y_exp + EXP_P1; } } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) && ((x_sign && (rnd_mode == ROUNDING_UP || rnd_mode == ROUNDING_TO_ZERO)) || (!x_sign && (rnd_mode == ROUNDING_DOWN || rnd_mode == ROUNDING_TO_ZERO)))) { // C1 = C1 - 1 C1_lo = C1_lo - 1; if (C1_lo == 0xffffffffffffffffull) C1_hi--; // check if we crossed into the lower decade if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 C1_lo = 0x378d8e63ffffffffull; y_exp = y_exp - EXP_P1; // no underflow, because delta + q2 >= P34 + 1 } } else { ; // exact, the result is already correct } // in all cases check for overflow (RN and RA solved already) if (y_exp == EXP_MAX_P1) { // overflow if ((rnd_mode == ROUNDING_DOWN && x_sign) || // RM and res < 0 (rnd_mode == ROUNDING_UP && !x_sign)) { // RP and res > 0 C1_hi = 0x7800000000000000ull; // +inf C1_lo = 0x0ull; } else { // RM and res > 0, RP and res < 0, or RZ C1_hi = 0x5fffed09bead87c0ull; C1_lo = 0x378d8e63ffffffffull; } y_exp = 0; // x_sign is preserved // set the inexact flag (in case the exact addition was exact) *pfpsf |= INEXACT_EXCEPTION; // set the overflow flag *pfpsf |= OVERFLOW_EXCEPTION; } } // assemble the result res.w[1] = x_sign | y_exp | C1_hi; res.w[0] = C1_lo; if (tmp_inexact) *pfpsf |= INEXACT_EXCEPTION; } } else { // if (-P34 + 1 <= delta <= -1) <=> 1 <= -delta <= P34 - 1 // NOTE: the following, up to "} else { // if x_sign != y_sign // the result is exact" is identical to "else if (delta == P34 - q2) {" // from above; also, the code is not symmetric: a+b and b+a may take // different paths (need to unify eventually!) // calculate C' = C2 + C1 * 10^(e1-e2) directly; the result may be // inexact if it requires P34 + 1 decimal digits; in either case the // 'cutoff' point for addition is at the position of the lsb of C2 // The coefficient of the result is C1 * 10^(e1-e2) + C2 and the // exponent is e2; either C1 or 10^(e1-e2) may not fit is 64 bits, // but their product fits with certainty in 128 bits (actually in 113) // Note that 0 <= e1 - e2 <= P34 - 2 // -P34 + 1 <= delta <= -1 <=> -P34 + 1 <= delta <= -1 <=> // -P34 + 1 <= q1 + e1 - q2 - e2 <= -1 <=> // q2 - q1 - P34 + 1 <= e1 - e2 <= q2 - q1 - 1 <=> // 1 - P34 - P34 + 1 <= e1-e2 <= P34 - 1 - 1 => 0 <= e1-e2 <= P34 - 2 scale = delta - q1 + q2; // scale = (int)(e1 >> 49) - (int)(e2 >> 49) if (scale >= 20) { // 10^(e1-e2) does not fit in 64 bits, but C1 does __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]); } else if (scale >= 1) { // if 1 <= scale <= 19 then 10^(e1-e2) fits in 64 bits if (q1 <= 19) { // C1 fits in 64 bits __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]); } else { // q1 >= 20 C1.w[1] = C1_hi; C1.w[0] = C1_lo; __mul_128x64_to_128 (C1, ten2k64[scale], C1); } } else { // if (scale == 0) C1 is unchanged C1.w[1] = C1_hi; C1.w[0] = C1_lo; // only the low part is necessary } C1_hi = C1.w[1]; C1_lo = C1.w[0]; // now add C2 if (x_sign == y_sign) { // the result can overflow! C1_lo = C1_lo + C2_lo; C1_hi = C1_hi + C2_hi; if (C1_lo < C1.w[0]) C1_hi++; // test for overflow, possible only when C1 >= 10^34 if (C1_hi > 0x0001ed09bead87c0ull || (C1_hi == 0x0001ed09bead87c0ull && C1_lo >= 0x378d8e6400000000ull)) { // C1 >= 10^34 // in this case q = P34 + 1 and x = q - P34 = 1, so multiply // C'' = C'+ 5 = C1 + 5 by k1 ~ 10^(-1) calculated for P34 + 1 // decimal digits // Calculate C'' = C' + 1/2 * 10^x if (C1_lo >= 0xfffffffffffffffbull) { // low half add has carry C1_lo = C1_lo + 5; C1_hi = C1_hi + 1; } else { C1_lo = C1_lo + 5; } // the approximation of 10^(-1) was rounded up to 118 bits // 10^(-1) =~ 33333333333333333333333333333400 * 2^-129 // 10^(-1) =~ 19999999999999999999999999999a00 * 2^-128 C1.w[1] = C1_hi; C1.w[0] = C1_lo; // C'' ten2m1.w[1] = 0x1999999999999999ull; ten2m1.w[0] = 0x9999999999999a00ull; __mul_128x128_to_256 (P256, C1, ten2m1); // P256 = C*, f* // C* is actually floor(C*) in this case // the top Ex = 128 bits of 10^(-1) are // T* = 0x00199999999999999999999999999999 // if (0 < f* < 10^(-x)) then // if floor(C*) is even then C = floor(C*) - logical right // shift; C has p decimal digits, correct by Prop. 1) // else if floor(C*) is odd C = floor(C*) - 1 (logical right // shift; C has p decimal digits, correct by Pr. 1) // else // C = floor(C*) (logical right shift; C has p decimal digits, // correct by Property 1) // n = C * 10^(e2+x) if ((P256.w[1] || P256.w[0]) && (P256.w[1] < 0x1999999999999999ull || (P256.w[1] == 0x1999999999999999ull && P256.w[0] <= 0x9999999999999999ull))) { // the result is a midpoint if (P256.w[2] & 0x01) { is_midpoint_gt_even = 1; // if floor(C*) is odd C = floor(C*) - 1; the result is not 0 P256.w[2]--; if (P256.w[2] == 0xffffffffffffffffull) P256.w[3]--; } else { is_midpoint_lt_even = 1; } } // n = Cstar * 10^(e2+1) y_exp = y_exp + EXP_P1; // C* != 10^P34 because C* has P34 digits // check for overflow if (y_exp == EXP_MAX_P1 && (rnd_mode == ROUNDING_TO_NEAREST || rnd_mode == ROUNDING_TIES_AWAY)) { // overflow for RN res.w[1] = x_sign | 0x7800000000000000ull; // +/-inf res.w[0] = 0x0ull; // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // set the overflow flag *pfpsf |= OVERFLOW_EXCEPTION; BID_SWAP128 (res); BID_RETURN (res); } // if (0 < f* - 1/2 < 10^(-x)) then // the result of the addition is exact // else // the result of the addition is inexact if (P256.w[1] > 0x8000000000000000ull || (P256.w[1] == 0x8000000000000000ull && P256.w[0] > 0x0ull)) { // the result may be exact tmp64 = P256.w[1] - 0x8000000000000000ull; // f* - 1/2 if ((tmp64 > 0x1999999999999999ull || (tmp64 == 0x1999999999999999ull && P256.w[0] >= 0x9999999999999999ull))) { // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; is_inexact = 1; } // else the result is exact } else { // the result is inexact // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; is_inexact = 1; } C1_hi = P256.w[3]; C1_lo = P256.w[2]; if (!is_midpoint_gt_even && !is_midpoint_lt_even) { is_inexact_lt_midpoint = is_inexact && (P256.w[1] & 0x8000000000000000ull); is_inexact_gt_midpoint = is_inexact && !(P256.w[1] & 0x8000000000000000ull); } // general correction from RN to RA, RM, RP, RZ; result uses y_exp if (rnd_mode != ROUNDING_TO_NEAREST) { if ((!x_sign && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) || ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_UP) && is_midpoint_gt_even))) || (x_sign && ((rnd_mode == ROUNDING_DOWN && is_inexact_lt_midpoint) || ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_DOWN) && is_midpoint_gt_even)))) { // C1 = C1 + 1 C1_lo = C1_lo + 1; if (C1_lo == 0) { // rounding overflow in the low 64 bits C1_hi = C1_hi + 1; } if (C1_hi == 0x0001ed09bead87c0ull && C1_lo == 0x378d8e6400000000ull) { // C1 = 10^34 => rounding overflow C1_hi = 0x0000314dc6448d93ull; C1_lo = 0x38c15b0a00000000ull; // 10^33 y_exp = y_exp + EXP_P1; } } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) && ((x_sign && (rnd_mode == ROUNDING_UP || rnd_mode == ROUNDING_TO_ZERO)) || (!x_sign && (rnd_mode == ROUNDING_DOWN || rnd_mode == ROUNDING_TO_ZERO)))) { // C1 = C1 - 1 C1_lo = C1_lo - 1; if (C1_lo == 0xffffffffffffffffull) C1_hi--; // check if we crossed into the lower decade if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) { // 10^33 - 1 C1_hi = 0x0001ed09bead87c0ull; // 10^34 - 1 C1_lo = 0x378d8e63ffffffffull; y_exp = y_exp - EXP_P1; // no underflow, because delta + q2 >= P34 + 1 } } else { ; // exact, the result is already correct } // in all cases check for overflow (RN and RA solved already) if (y_exp == EXP_MAX_P1) { // overflow if ((rnd_mode == ROUNDING_DOWN && x_sign) || // RM and res < 0 (rnd_mode == ROUNDING_UP && !x_sign)) { // RP and res > 0 C1_hi = 0x7800000000000000ull; // +inf C1_lo = 0x0ull; } else { // RM and res > 0, RP and res < 0, or RZ C1_hi = 0x5fffed09bead87c0ull; C1_lo = 0x378d8e63ffffffffull; } y_exp = 0; // x_sign is preserved // set the inexact flag (in case the exact addition was exact) *pfpsf |= INEXACT_EXCEPTION; // set the overflow flag *pfpsf |= OVERFLOW_EXCEPTION; } } } // else if (C1 < 10^34) then C1 is the coeff.; the result is exact // assemble the result res.w[1] = x_sign | y_exp | C1_hi; res.w[0] = C1_lo; } else { // if x_sign != y_sign the result is exact C1_lo = C2_lo - C1_lo; C1_hi = C2_hi - C1_hi; if (C1_lo > C2_lo) C1_hi--; if (C1_hi >= 0x8000000000000000ull) { // negative coefficient! C1_lo = ~C1_lo; C1_lo++; C1_hi = ~C1_hi; if (C1_lo == 0x0) C1_hi++; x_sign = y_sign; // the result will have the sign of y } // the result can be zero, but it cannot overflow if (C1_lo == 0 && C1_hi == 0) { // assemble the result if (x_exp < y_exp) res.w[1] = x_exp; else res.w[1] = y_exp; res.w[0] = 0; if (rnd_mode == ROUNDING_DOWN) { res.w[1] |= 0x8000000000000000ull; } BID_SWAP128 (res); BID_RETURN (res); } // assemble the result res.w[1] = y_sign | y_exp | C1_hi; res.w[0] = C1_lo; } } } BID_SWAP128 (res); BID_RETURN (res) } } // bid128_sub stands for bid128qq_sub /***************************************************************************** * BID128 sub ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid128_sub (UINT128 * pres, UINT128 * px, UINT128 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px, y = *py; #if !DECIMAL_GLOBAL_ROUNDING unsigned int rnd_mode = *prnd_mode; #endif #else UINT128 bid128_sub (UINT128 x, UINT128 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 res; UINT64 y_sign; if ((y.w[HIGH_128W] & MASK_NAN) != MASK_NAN) { // y is not NAN // change its sign y_sign = y.w[HIGH_128W] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative if (y_sign) y.w[HIGH_128W] = y.w[HIGH_128W] & 0x7fffffffffffffffull; else y.w[HIGH_128W] = y.w[HIGH_128W] | 0x8000000000000000ull; } #if DECIMAL_CALL_BY_REFERENCE bid128_add (&res, &x, &y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else res = bid128_add (x, y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif BID_RETURN (res); }
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