/* Copyright (C) 2007, 2009 Free Software Foundation, Inc.
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/* Copyright (C) 2007, 2009 Free Software Foundation, Inc.
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This file is part of GCC.
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This file is part of GCC.
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GCC is free software; you can redistribute it and/or modify it under
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GCC is free software; you can redistribute it and/or modify it under
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the terms of the GNU General Public License as published by the Free
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the terms of the GNU General Public License as published by the Free
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Software Foundation; either version 3, or (at your option) any later
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Software Foundation; either version 3, or (at your option) any later
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version.
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version.
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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for more details.
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Under Section 7 of GPL version 3, you are granted additional
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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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<http://www.gnu.org/licenses/>. */
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#define BID_128RES
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#define BID_128RES
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#include "bid_internal.h"
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#include "bid_internal.h"
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/*****************************************************************************
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/*****************************************************************************
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* BID128 nextup
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* BID128 nextup
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****************************************************************************/
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****************************************************************************/
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#if DECIMAL_CALL_BY_REFERENCE
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#if DECIMAL_CALL_BY_REFERENCE
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void
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void
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bid128_nextup (UINT128 * pres,
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bid128_nextup (UINT128 * pres,
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UINT128 *
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UINT128 *
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px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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UINT128 x = *px;
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#else
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#else
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UINT128
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UINT128
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bid128_nextup (UINT128 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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bid128_nextup (UINT128 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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_EXC_INFO_PARAM) {
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_EXC_INFO_PARAM) {
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#endif
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#endif
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UINT128 res;
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UINT128 res;
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UINT64 x_sign;
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UINT64 x_sign;
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UINT64 x_exp;
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UINT64 x_exp;
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int exp;
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int exp;
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BID_UI64DOUBLE tmp1;
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BID_UI64DOUBLE tmp1;
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int x_nr_bits;
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int x_nr_bits;
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int q1, ind;
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int q1, ind;
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UINT128 C1; // C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (UINT64)
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UINT128 C1; // C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (UINT64)
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BID_SWAP128 (x);
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BID_SWAP128 (x);
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// unpack the argument
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// unpack the argument
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x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
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x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
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C1.w[1] = x.w[1] & MASK_COEFF;
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C1.w[1] = x.w[1] & MASK_COEFF;
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C1.w[0] = x.w[0];
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C1.w[0] = x.w[0];
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// check for NaN or Infinity
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// check for NaN or Infinity
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if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
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if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
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// x is special
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// x is special
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if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
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if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
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// if x = NaN, then res = Q (x)
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// if x = NaN, then res = Q (x)
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// check first for non-canonical NaN payload
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// check first for non-canonical NaN payload
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if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
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if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
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(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull)
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(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull)
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&& (x.w[0] > 0x38c15b09ffffffffull))) {
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&& (x.w[0] > 0x38c15b09ffffffffull))) {
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x.w[1] = x.w[1] & 0xffffc00000000000ull;
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x.w[1] = x.w[1] & 0xffffc00000000000ull;
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x.w[0] = 0x0ull;
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x.w[0] = 0x0ull;
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}
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}
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if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
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if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
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// set invalid flag
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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*pfpsf |= INVALID_EXCEPTION;
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// return quiet (x)
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// return quiet (x)
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res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
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res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
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res.w[0] = x.w[0];
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res.w[0] = x.w[0];
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} else { // x is QNaN
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} else { // x is QNaN
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// return x
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// return x
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res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
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res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
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res.w[0] = x.w[0];
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res.w[0] = x.w[0];
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}
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}
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} else { // x is not NaN, so it must be infinity
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} else { // x is not NaN, so it must be infinity
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if (!x_sign) { // x is +inf
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if (!x_sign) { // x is +inf
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res.w[1] = 0x7800000000000000ull; // +inf
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res.w[1] = 0x7800000000000000ull; // +inf
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res.w[0] = 0x0000000000000000ull;
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res.w[0] = 0x0000000000000000ull;
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} else { // x is -inf
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} else { // x is -inf
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res.w[1] = 0xdfffed09bead87c0ull; // -MAXFP = -999...99 * 10^emax
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res.w[1] = 0xdfffed09bead87c0ull; // -MAXFP = -999...99 * 10^emax
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res.w[0] = 0x378d8e63ffffffffull;
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res.w[0] = 0x378d8e63ffffffffull;
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}
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}
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}
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}
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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// check for non-canonical values (treated as zero)
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// check for non-canonical values (treated as zero)
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if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
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if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
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// non-canonical
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// non-canonical
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x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
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x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
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C1.w[1] = 0; // significand high
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C1.w[1] = 0; // significand high
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C1.w[0] = 0; // significand low
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C1.w[0] = 0; // significand low
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} else { // G0_G1 != 11
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} else { // G0_G1 != 11
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x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits
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x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits
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if (C1.w[1] > 0x0001ed09bead87c0ull ||
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if (C1.w[1] > 0x0001ed09bead87c0ull ||
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(C1.w[1] == 0x0001ed09bead87c0ull
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(C1.w[1] == 0x0001ed09bead87c0ull
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&& C1.w[0] > 0x378d8e63ffffffffull)) {
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&& C1.w[0] > 0x378d8e63ffffffffull)) {
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// x is non-canonical if coefficient is larger than 10^34 -1
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// x is non-canonical if coefficient is larger than 10^34 -1
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C1.w[1] = 0;
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C1.w[1] = 0;
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C1.w[0] = 0;
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C1.w[0] = 0;
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} else { // canonical
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} else { // canonical
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;
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;
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}
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}
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}
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}
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if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
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if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
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// x is +/-0
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// x is +/-0
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res.w[1] = 0x0000000000000000ull; // +1 * 10^emin
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res.w[1] = 0x0000000000000000ull; // +1 * 10^emin
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res.w[0] = 0x0000000000000001ull;
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res.w[0] = 0x0000000000000001ull;
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} else { // x is not special and is not zero
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} else { // x is not special and is not zero
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if (x.w[1] == 0x5fffed09bead87c0ull
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if (x.w[1] == 0x5fffed09bead87c0ull
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&& x.w[0] == 0x378d8e63ffffffffull) {
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&& x.w[0] == 0x378d8e63ffffffffull) {
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// x = +MAXFP = 999...99 * 10^emax
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// x = +MAXFP = 999...99 * 10^emax
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res.w[1] = 0x7800000000000000ull; // +inf
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res.w[1] = 0x7800000000000000ull; // +inf
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res.w[0] = 0x0000000000000000ull;
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res.w[0] = 0x0000000000000000ull;
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} else if (x.w[1] == 0x8000000000000000ull
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} else if (x.w[1] == 0x8000000000000000ull
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&& x.w[0] == 0x0000000000000001ull) {
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&& x.w[0] == 0x0000000000000001ull) {
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// x = -MINFP = 1...99 * 10^emin
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// x = -MINFP = 1...99 * 10^emin
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res.w[1] = 0x8000000000000000ull; // -0
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res.w[1] = 0x8000000000000000ull; // -0
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res.w[0] = 0x0000000000000000ull;
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res.w[0] = 0x0000000000000000ull;
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} else { // -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
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} else { // -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
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// can add/subtract 1 ulp to the significand
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// can add/subtract 1 ulp to the significand
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// Note: we could check here if x >= 10^34 to speed up the case q1 = 34
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// Note: we could check here if x >= 10^34 to speed up the case q1 = 34
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// q1 = nr. of decimal digits in x
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// q1 = nr. of decimal digits in x
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// determine first the nr. of bits in x
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// determine first the nr. of bits in x
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if (C1.w[1] == 0) {
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if (C1.w[1] == 0) {
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if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
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if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
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// split the 64-bit value in two 32-bit halves to avoid rnd errors
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// split the 64-bit value in two 32-bit halves to avoid rnd errors
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if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
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if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
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tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
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tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
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x_nr_bits =
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x_nr_bits =
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33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) -
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33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) -
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0x3ff);
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0x3ff);
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} else { // x < 2^32
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} else { // x < 2^32
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tmp1.d = (double) (C1.w[0]); // exact conversion
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tmp1.d = (double) (C1.w[0]); // exact conversion
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x_nr_bits =
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x_nr_bits =
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) -
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) -
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0x3ff);
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0x3ff);
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}
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}
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} else { // if x < 2^53
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} else { // if x < 2^53
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tmp1.d = (double) C1.w[0]; // exact conversion
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tmp1.d = (double) C1.w[0]; // exact conversion
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x_nr_bits =
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x_nr_bits =
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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}
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}
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} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
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} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
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tmp1.d = (double) C1.w[1]; // exact conversion
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tmp1.d = (double) C1.w[1]; // exact conversion
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x_nr_bits =
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x_nr_bits =
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65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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}
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}
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q1 = nr_digits[x_nr_bits - 1].digits;
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q1 = nr_digits[x_nr_bits - 1].digits;
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if (q1 == 0) {
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if (q1 == 0) {
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q1 = nr_digits[x_nr_bits - 1].digits1;
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q1 = nr_digits[x_nr_bits - 1].digits1;
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if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
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if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
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|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
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|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
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&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
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&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
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q1++;
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q1++;
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}
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}
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// if q1 < P34 then pad the significand with zeros
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// if q1 < P34 then pad the significand with zeros
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if (q1 < P34) {
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if (q1 < P34) {
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exp = (x_exp >> 49) - 6176;
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exp = (x_exp >> 49) - 6176;
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if (exp + 6176 > P34 - q1) {
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if (exp + 6176 > P34 - q1) {
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ind = P34 - q1; // 1 <= ind <= P34 - 1
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ind = P34 - q1; // 1 <= ind <= P34 - 1
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// pad with P34 - q1 zeros, until exponent = emin
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// pad with P34 - q1 zeros, until exponent = emin
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// C1 = C1 * 10^ind
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// C1 = C1 * 10^ind
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if (q1 <= 19) { // 64-bit C1
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if (q1 <= 19) { // 64-bit C1
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if (ind <= 19) { // 64-bit 10^ind and 64-bit C1
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if (ind <= 19) { // 64-bit 10^ind and 64-bit C1
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__mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]);
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__mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]);
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} else { // 128-bit 10^ind and 64-bit C1
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} else { // 128-bit 10^ind and 64-bit C1
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__mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]);
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__mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]);
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}
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}
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} else { // C1 is (most likely) 128-bit
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} else { // C1 is (most likely) 128-bit
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if (ind <= 14) { // 64-bit 10^ind and 128-bit C1 (most likely)
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if (ind <= 14) { // 64-bit 10^ind and 128-bit C1 (most likely)
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__mul_128x64_to_128 (C1, ten2k64[ind], C1);
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__mul_128x64_to_128 (C1, ten2k64[ind], C1);
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} else if (ind <= 19) { // 64-bit 10^ind and 64-bit C1 (q1 <= 19)
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} else if (ind <= 19) { // 64-bit 10^ind and 64-bit C1 (q1 <= 19)
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__mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]);
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__mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]);
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} else { // 128-bit 10^ind and 64-bit C1 (C1 must be 64-bit)
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} else { // 128-bit 10^ind and 64-bit C1 (C1 must be 64-bit)
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__mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]);
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__mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]);
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}
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}
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}
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}
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x_exp = x_exp - ((UINT64) ind << 49);
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x_exp = x_exp - ((UINT64) ind << 49);
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} else { // pad with zeros until the exponent reaches emin
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} else { // pad with zeros until the exponent reaches emin
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ind = exp + 6176;
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ind = exp + 6176;
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// C1 = C1 * 10^ind
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// C1 = C1 * 10^ind
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if (ind <= 19) { // 1 <= P34 - q1 <= 19 <=> 15 <= q1 <= 33
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if (ind <= 19) { // 1 <= P34 - q1 <= 19 <=> 15 <= q1 <= 33
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if (q1 <= 19) { // 64-bit C1, 64-bit 10^ind
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if (q1 <= 19) { // 64-bit C1, 64-bit 10^ind
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__mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]);
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__mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]);
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} else { // 20 <= q1 <= 33 => 128-bit C1, 64-bit 10^ind
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} else { // 20 <= q1 <= 33 => 128-bit C1, 64-bit 10^ind
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__mul_128x64_to_128 (C1, ten2k64[ind], C1);
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__mul_128x64_to_128 (C1, ten2k64[ind], C1);
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}
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}
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} else { // if 20 <= P34 - q1 <= 33 <=> 1 <= q1 <= 14 =>
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} else { // if 20 <= P34 - q1 <= 33 <=> 1 <= q1 <= 14 =>
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// 64-bit C1, 128-bit 10^ind
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// 64-bit C1, 128-bit 10^ind
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__mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]);
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__mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]);
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}
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}
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x_exp = EXP_MIN;
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x_exp = EXP_MIN;
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}
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}
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}
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}
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if (!x_sign) { // x > 0
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if (!x_sign) { // x > 0
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// add 1 ulp (add 1 to the significand)
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// add 1 ulp (add 1 to the significand)
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C1.w[0]++;
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C1.w[0]++;
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if (C1.w[0] == 0)
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if (C1.w[0] == 0)
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C1.w[1]++;
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C1.w[1]++;
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if (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] == 0x378d8e6400000000ull) { // if C1 = 10^34
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if (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] == 0x378d8e6400000000ull) { // if C1 = 10^34
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C1.w[1] = 0x0000314dc6448d93ull; // C1 = 10^33
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C1.w[1] = 0x0000314dc6448d93ull; // C1 = 10^33
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C1.w[0] = 0x38c15b0a00000000ull;
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C1.w[0] = 0x38c15b0a00000000ull;
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x_exp = x_exp + EXP_P1;
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x_exp = x_exp + EXP_P1;
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}
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}
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} else { // x < 0
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} else { // x < 0
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// subtract 1 ulp (subtract 1 from the significand)
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// subtract 1 ulp (subtract 1 from the significand)
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C1.w[0]--;
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C1.w[0]--;
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if (C1.w[0] == 0xffffffffffffffffull)
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if (C1.w[0] == 0xffffffffffffffffull)
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C1.w[1]--;
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C1.w[1]--;
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if (x_exp != 0 && C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] == 0x38c15b09ffffffffull) { // if C1 = 10^33 - 1
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if (x_exp != 0 && C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] == 0x38c15b09ffffffffull) { // if C1 = 10^33 - 1
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C1.w[1] = 0x0001ed09bead87c0ull; // C1 = 10^34 - 1
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C1.w[1] = 0x0001ed09bead87c0ull; // C1 = 10^34 - 1
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C1.w[0] = 0x378d8e63ffffffffull;
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C1.w[0] = 0x378d8e63ffffffffull;
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x_exp = x_exp - EXP_P1;
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x_exp = x_exp - EXP_P1;
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}
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}
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}
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}
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// assemble the result
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// assemble the result
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res.w[1] = x_sign | x_exp | C1.w[1];
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res.w[1] = x_sign | x_exp | C1.w[1];
|
res.w[0] = C1.w[0];
|
res.w[0] = C1.w[0];
|
} // end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
|
} // end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
|
} // end x is not special and is not zero
|
} // end x is not special and is not zero
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
|
|
/*****************************************************************************
|
/*****************************************************************************
|
* BID128 nextdown
|
* BID128 nextdown
|
****************************************************************************/
|
****************************************************************************/
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
#if DECIMAL_CALL_BY_REFERENCE
|
void
|
void
|
bid128_nextdown (UINT128 * pres,
|
bid128_nextdown (UINT128 * pres,
|
UINT128 *
|
UINT128 *
|
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
|
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
|
UINT128 x = *px;
|
UINT128 x = *px;
|
#else
|
#else
|
UINT128
|
UINT128
|
bid128_nextdown (UINT128 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
bid128_nextdown (UINT128 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
_EXC_INFO_PARAM) {
|
_EXC_INFO_PARAM) {
|
#endif
|
#endif
|
|
|
UINT128 res;
|
UINT128 res;
|
UINT64 x_sign;
|
UINT64 x_sign;
|
UINT64 x_exp;
|
UINT64 x_exp;
|
int exp;
|
int exp;
|
BID_UI64DOUBLE tmp1;
|
BID_UI64DOUBLE tmp1;
|
int x_nr_bits;
|
int x_nr_bits;
|
int q1, ind;
|
int q1, ind;
|
UINT128 C1; // C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (UINT64)
|
UINT128 C1; // C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (UINT64)
|
|
|
BID_SWAP128 (x);
|
BID_SWAP128 (x);
|
// unpack the argument
|
// unpack the argument
|
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
C1.w[1] = x.w[1] & MASK_COEFF;
|
C1.w[1] = x.w[1] & MASK_COEFF;
|
C1.w[0] = x.w[0];
|
C1.w[0] = x.w[0];
|
|
|
// check for NaN or Infinity
|
// check for NaN or Infinity
|
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
|
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
|
// x is special
|
// x is special
|
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
|
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
|
// if x = NaN, then res = Q (x)
|
// if x = NaN, then res = Q (x)
|
// check first for non-canonical NaN payload
|
// check first for non-canonical NaN payload
|
if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
|
if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
|
(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull)
|
(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull)
|
&& (x.w[0] > 0x38c15b09ffffffffull))) {
|
&& (x.w[0] > 0x38c15b09ffffffffull))) {
|
x.w[1] = x.w[1] & 0xffffc00000000000ull;
|
x.w[1] = x.w[1] & 0xffffc00000000000ull;
|
x.w[0] = 0x0ull;
|
x.w[0] = 0x0ull;
|
}
|
}
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
|
// set invalid flag
|
// set invalid flag
|
*pfpsf |= INVALID_EXCEPTION;
|
*pfpsf |= INVALID_EXCEPTION;
|
// return quiet (x)
|
// return quiet (x)
|
res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
|
res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
|
res.w[0] = x.w[0];
|
res.w[0] = x.w[0];
|
} else { // x is QNaN
|
} else { // x is QNaN
|
// return x
|
// return x
|
res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
|
res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
|
res.w[0] = x.w[0];
|
res.w[0] = x.w[0];
|
}
|
}
|
} else { // x is not NaN, so it must be infinity
|
} else { // x is not NaN, so it must be infinity
|
if (!x_sign) { // x is +inf
|
if (!x_sign) { // x is +inf
|
res.w[1] = 0x5fffed09bead87c0ull; // +MAXFP = +999...99 * 10^emax
|
res.w[1] = 0x5fffed09bead87c0ull; // +MAXFP = +999...99 * 10^emax
|
res.w[0] = 0x378d8e63ffffffffull;
|
res.w[0] = 0x378d8e63ffffffffull;
|
} else { // x is -inf
|
} else { // x is -inf
|
res.w[1] = 0xf800000000000000ull; // -inf
|
res.w[1] = 0xf800000000000000ull; // -inf
|
res.w[0] = 0x0000000000000000ull;
|
res.w[0] = 0x0000000000000000ull;
|
}
|
}
|
}
|
}
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// check for non-canonical values (treated as zero)
|
// check for non-canonical values (treated as zero)
|
if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
|
if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
|
// non-canonical
|
// non-canonical
|
x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
|
x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
|
C1.w[1] = 0; // significand high
|
C1.w[1] = 0; // significand high
|
C1.w[0] = 0; // significand low
|
C1.w[0] = 0; // significand low
|
} else { // G0_G1 != 11
|
} else { // G0_G1 != 11
|
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits
|
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits
|
if (C1.w[1] > 0x0001ed09bead87c0ull ||
|
if (C1.w[1] > 0x0001ed09bead87c0ull ||
|
(C1.w[1] == 0x0001ed09bead87c0ull
|
(C1.w[1] == 0x0001ed09bead87c0ull
|
&& C1.w[0] > 0x378d8e63ffffffffull)) {
|
&& C1.w[0] > 0x378d8e63ffffffffull)) {
|
// x is non-canonical if coefficient is larger than 10^34 -1
|
// x is non-canonical if coefficient is larger than 10^34 -1
|
C1.w[1] = 0;
|
C1.w[1] = 0;
|
C1.w[0] = 0;
|
C1.w[0] = 0;
|
} else { // canonical
|
} else { // canonical
|
;
|
;
|
}
|
}
|
}
|
}
|
|
|
if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
|
if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
|
// x is +/-0
|
// x is +/-0
|
res.w[1] = 0x8000000000000000ull; // -1 * 10^emin
|
res.w[1] = 0x8000000000000000ull; // -1 * 10^emin
|
res.w[0] = 0x0000000000000001ull;
|
res.w[0] = 0x0000000000000001ull;
|
} else { // x is not special and is not zero
|
} else { // x is not special and is not zero
|
if (x.w[1] == 0xdfffed09bead87c0ull
|
if (x.w[1] == 0xdfffed09bead87c0ull
|
&& x.w[0] == 0x378d8e63ffffffffull) {
|
&& x.w[0] == 0x378d8e63ffffffffull) {
|
// x = -MAXFP = -999...99 * 10^emax
|
// x = -MAXFP = -999...99 * 10^emax
|
res.w[1] = 0xf800000000000000ull; // -inf
|
res.w[1] = 0xf800000000000000ull; // -inf
|
res.w[0] = 0x0000000000000000ull;
|
res.w[0] = 0x0000000000000000ull;
|
} else if (x.w[1] == 0x0ull && x.w[0] == 0x0000000000000001ull) { // +MINFP
|
} else if (x.w[1] == 0x0ull && x.w[0] == 0x0000000000000001ull) { // +MINFP
|
res.w[1] = 0x0000000000000000ull; // +0
|
res.w[1] = 0x0000000000000000ull; // +0
|
res.w[0] = 0x0000000000000000ull;
|
res.w[0] = 0x0000000000000000ull;
|
} else { // -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
|
} else { // -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
|
// can add/subtract 1 ulp to the significand
|
// can add/subtract 1 ulp to the significand
|
|
|
// Note: we could check here if x >= 10^34 to speed up the case q1 = 34
|
// Note: we could check here if x >= 10^34 to speed up the case q1 = 34
|
// q1 = nr. of decimal digits in x
|
// q1 = nr. of decimal digits in x
|
// determine first the nr. of bits in x
|
// determine first the nr. of bits in x
|
if (C1.w[1] == 0) {
|
if (C1.w[1] == 0) {
|
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
|
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
|
// split the 64-bit value in two 32-bit halves to avoid rnd errors
|
// split the 64-bit value in two 32-bit halves to avoid rnd errors
|
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
|
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
|
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
|
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
|
x_nr_bits =
|
x_nr_bits =
|
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) -
|
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) -
|
0x3ff);
|
0x3ff);
|
} else { // x < 2^32
|
} else { // x < 2^32
|
tmp1.d = (double) (C1.w[0]); // exact conversion
|
tmp1.d = (double) (C1.w[0]); // exact conversion
|
x_nr_bits =
|
x_nr_bits =
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) -
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) -
|
0x3ff);
|
0x3ff);
|
}
|
}
|
} else { // if x < 2^53
|
} else { // if x < 2^53
|
tmp1.d = (double) C1.w[0]; // exact conversion
|
tmp1.d = (double) C1.w[0]; // exact conversion
|
x_nr_bits =
|
x_nr_bits =
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
}
|
}
|
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
|
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
|
tmp1.d = (double) C1.w[1]; // exact conversion
|
tmp1.d = (double) C1.w[1]; // exact conversion
|
x_nr_bits =
|
x_nr_bits =
|
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
}
|
}
|
q1 = nr_digits[x_nr_bits - 1].digits;
|
q1 = nr_digits[x_nr_bits - 1].digits;
|
if (q1 == 0) {
|
if (q1 == 0) {
|
q1 = nr_digits[x_nr_bits - 1].digits1;
|
q1 = nr_digits[x_nr_bits - 1].digits1;
|
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
|
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
|
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
|
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
|
q1++;
|
q1++;
|
}
|
}
|
// if q1 < P then pad the significand with zeros
|
// if q1 < P then pad the significand with zeros
|
if (q1 < P34) {
|
if (q1 < P34) {
|
exp = (x_exp >> 49) - 6176;
|
exp = (x_exp >> 49) - 6176;
|
if (exp + 6176 > P34 - q1) {
|
if (exp + 6176 > P34 - q1) {
|
ind = P34 - q1; // 1 <= ind <= P34 - 1
|
ind = P34 - q1; // 1 <= ind <= P34 - 1
|
// pad with P34 - q1 zeros, until exponent = emin
|
// pad with P34 - q1 zeros, until exponent = emin
|
// C1 = C1 * 10^ind
|
// C1 = C1 * 10^ind
|
if (q1 <= 19) { // 64-bit C1
|
if (q1 <= 19) { // 64-bit C1
|
if (ind <= 19) { // 64-bit 10^ind and 64-bit C1
|
if (ind <= 19) { // 64-bit 10^ind and 64-bit C1
|
__mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]);
|
__mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]);
|
} else { // 128-bit 10^ind and 64-bit C1
|
} else { // 128-bit 10^ind and 64-bit C1
|
__mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]);
|
__mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]);
|
}
|
}
|
} else { // C1 is (most likely) 128-bit
|
} else { // C1 is (most likely) 128-bit
|
if (ind <= 14) { // 64-bit 10^ind and 128-bit C1 (most likely)
|
if (ind <= 14) { // 64-bit 10^ind and 128-bit C1 (most likely)
|
__mul_128x64_to_128 (C1, ten2k64[ind], C1);
|
__mul_128x64_to_128 (C1, ten2k64[ind], C1);
|
} else if (ind <= 19) { // 64-bit 10^ind and 64-bit C1 (q1 <= 19)
|
} else if (ind <= 19) { // 64-bit 10^ind and 64-bit C1 (q1 <= 19)
|
__mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]);
|
__mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]);
|
} else { // 128-bit 10^ind and 64-bit C1 (C1 must be 64-bit)
|
} else { // 128-bit 10^ind and 64-bit C1 (C1 must be 64-bit)
|
__mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]);
|
__mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]);
|
}
|
}
|
}
|
}
|
x_exp = x_exp - ((UINT64) ind << 49);
|
x_exp = x_exp - ((UINT64) ind << 49);
|
} else { // pad with zeros until the exponent reaches emin
|
} else { // pad with zeros until the exponent reaches emin
|
ind = exp + 6176;
|
ind = exp + 6176;
|
// C1 = C1 * 10^ind
|
// C1 = C1 * 10^ind
|
if (ind <= 19) { // 1 <= P34 - q1 <= 19 <=> 15 <= q1 <= 33
|
if (ind <= 19) { // 1 <= P34 - q1 <= 19 <=> 15 <= q1 <= 33
|
if (q1 <= 19) { // 64-bit C1, 64-bit 10^ind
|
if (q1 <= 19) { // 64-bit C1, 64-bit 10^ind
|
__mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]);
|
__mul_64x64_to_128MACH (C1, C1.w[0], ten2k64[ind]);
|
} else { // 20 <= q1 <= 33 => 128-bit C1, 64-bit 10^ind
|
} else { // 20 <= q1 <= 33 => 128-bit C1, 64-bit 10^ind
|
__mul_128x64_to_128 (C1, ten2k64[ind], C1);
|
__mul_128x64_to_128 (C1, ten2k64[ind], C1);
|
}
|
}
|
} else { // if 20 <= P34 - q1 <= 33 <=> 1 <= q1 <= 14 =>
|
} else { // if 20 <= P34 - q1 <= 33 <=> 1 <= q1 <= 14 =>
|
// 64-bit C1, 128-bit 10^ind
|
// 64-bit C1, 128-bit 10^ind
|
__mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]);
|
__mul_128x64_to_128 (C1, C1.w[0], ten2k128[ind - 20]);
|
}
|
}
|
x_exp = EXP_MIN;
|
x_exp = EXP_MIN;
|
}
|
}
|
}
|
}
|
if (x_sign) { // x < 0
|
if (x_sign) { // x < 0
|
// add 1 ulp (add 1 to the significand)
|
// add 1 ulp (add 1 to the significand)
|
C1.w[0]++;
|
C1.w[0]++;
|
if (C1.w[0] == 0)
|
if (C1.w[0] == 0)
|
C1.w[1]++;
|
C1.w[1]++;
|
if (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] == 0x378d8e6400000000ull) { // if C1 = 10^34
|
if (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] == 0x378d8e6400000000ull) { // if C1 = 10^34
|
C1.w[1] = 0x0000314dc6448d93ull; // C1 = 10^33
|
C1.w[1] = 0x0000314dc6448d93ull; // C1 = 10^33
|
C1.w[0] = 0x38c15b0a00000000ull;
|
C1.w[0] = 0x38c15b0a00000000ull;
|
x_exp = x_exp + EXP_P1;
|
x_exp = x_exp + EXP_P1;
|
}
|
}
|
} else { // x > 0
|
} else { // x > 0
|
// subtract 1 ulp (subtract 1 from the significand)
|
// subtract 1 ulp (subtract 1 from the significand)
|
C1.w[0]--;
|
C1.w[0]--;
|
if (C1.w[0] == 0xffffffffffffffffull)
|
if (C1.w[0] == 0xffffffffffffffffull)
|
C1.w[1]--;
|
C1.w[1]--;
|
if (x_exp != 0 && C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] == 0x38c15b09ffffffffull) { // if C1 = 10^33 - 1
|
if (x_exp != 0 && C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] == 0x38c15b09ffffffffull) { // if C1 = 10^33 - 1
|
C1.w[1] = 0x0001ed09bead87c0ull; // C1 = 10^34 - 1
|
C1.w[1] = 0x0001ed09bead87c0ull; // C1 = 10^34 - 1
|
C1.w[0] = 0x378d8e63ffffffffull;
|
C1.w[0] = 0x378d8e63ffffffffull;
|
x_exp = x_exp - EXP_P1;
|
x_exp = x_exp - EXP_P1;
|
}
|
}
|
}
|
}
|
// assemble the result
|
// assemble the result
|
res.w[1] = x_sign | x_exp | C1.w[1];
|
res.w[1] = x_sign | x_exp | C1.w[1];
|
res.w[0] = C1.w[0];
|
res.w[0] = C1.w[0];
|
} // end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
|
} // end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
|
} // end x is not special and is not zero
|
} // end x is not special and is not zero
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
|
|
/*****************************************************************************
|
/*****************************************************************************
|
* BID128 nextafter
|
* BID128 nextafter
|
****************************************************************************/
|
****************************************************************************/
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
#if DECIMAL_CALL_BY_REFERENCE
|
void
|
void
|
bid128_nextafter (UINT128 * pres, UINT128 * px,
|
bid128_nextafter (UINT128 * pres, UINT128 * px,
|
UINT128 *
|
UINT128 *
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM)
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM)
|
{
|
{
|
UINT128 x = *px;
|
UINT128 x = *px;
|
UINT128 y = *py;
|
UINT128 y = *py;
|
UINT128 xnswp = *px;
|
UINT128 xnswp = *px;
|
UINT128 ynswp = *py;
|
UINT128 ynswp = *py;
|
#else
|
#else
|
UINT128
|
UINT128
|
bid128_nextafter (UINT128 x,
|
bid128_nextafter (UINT128 x,
|
UINT128 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
UINT128 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
_EXC_INFO_PARAM) {
|
_EXC_INFO_PARAM) {
|
UINT128 xnswp = x;
|
UINT128 xnswp = x;
|
UINT128 ynswp = y;
|
UINT128 ynswp = y;
|
#endif
|
#endif
|
|
|
UINT128 res;
|
UINT128 res;
|
UINT128 tmp1, tmp2, tmp3;
|
UINT128 tmp1, tmp2, tmp3;
|
FPSC tmp_fpsf = 0; // dummy fpsf for calls to comparison functions
|
FPSC tmp_fpsf = 0; // dummy fpsf for calls to comparison functions
|
int res1, res2;
|
int res1, res2;
|
UINT64 x_exp;
|
UINT64 x_exp;
|
|
|
|
|
BID_SWAP128 (x);
|
BID_SWAP128 (x);
|
BID_SWAP128 (y);
|
BID_SWAP128 (y);
|
// check for NaNs
|
// check for NaNs
|
if (((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL)
|
if (((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL)
|
|| ((y.w[1] & MASK_SPECIAL) == MASK_SPECIAL)) {
|
|| ((y.w[1] & MASK_SPECIAL) == MASK_SPECIAL)) {
|
// x is special or y is special
|
// x is special or y is special
|
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
|
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
|
// if x = NaN, then res = Q (x)
|
// if x = NaN, then res = Q (x)
|
// check first for non-canonical NaN payload
|
// check first for non-canonical NaN payload
|
if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
|
if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
|
(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull)
|
(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull)
|
&& (x.w[0] > 0x38c15b09ffffffffull))) {
|
&& (x.w[0] > 0x38c15b09ffffffffull))) {
|
x.w[1] = x.w[1] & 0xffffc00000000000ull;
|
x.w[1] = x.w[1] & 0xffffc00000000000ull;
|
x.w[0] = 0x0ull;
|
x.w[0] = 0x0ull;
|
}
|
}
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
|
// set invalid flag
|
// set invalid flag
|
*pfpsf |= INVALID_EXCEPTION;
|
*pfpsf |= INVALID_EXCEPTION;
|
// return quiet (x)
|
// return quiet (x)
|
res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
|
res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
|
res.w[0] = x.w[0];
|
res.w[0] = x.w[0];
|
} else { // x is QNaN
|
} else { // x is QNaN
|
// return x
|
// return x
|
res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
|
res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
|
res.w[0] = x.w[0];
|
res.w[0] = x.w[0];
|
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
|
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
|
// set invalid flag
|
// set invalid flag
|
*pfpsf |= INVALID_EXCEPTION;
|
*pfpsf |= INVALID_EXCEPTION;
|
}
|
}
|
}
|
}
|
BID_RETURN (res)
|
BID_RETURN (res)
|
} else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
|
} else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
|
// if x = NaN, then res = Q (x)
|
// if x = NaN, then res = Q (x)
|
// check first for non-canonical NaN payload
|
// check first for non-canonical NaN payload
|
if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
|
if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
|
(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull)
|
(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull)
|
&& (y.w[0] > 0x38c15b09ffffffffull))) {
|
&& (y.w[0] > 0x38c15b09ffffffffull))) {
|
y.w[1] = y.w[1] & 0xffffc00000000000ull;
|
y.w[1] = y.w[1] & 0xffffc00000000000ull;
|
y.w[0] = 0x0ull;
|
y.w[0] = 0x0ull;
|
}
|
}
|
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
|
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
|
// set invalid flag
|
// set invalid flag
|
*pfpsf |= INVALID_EXCEPTION;
|
*pfpsf |= INVALID_EXCEPTION;
|
// return quiet (x)
|
// return quiet (x)
|
res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
|
res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
|
res.w[0] = y.w[0];
|
res.w[0] = y.w[0];
|
} else { // x is QNaN
|
} else { // x is QNaN
|
// return x
|
// return x
|
res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
|
res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
|
res.w[0] = y.w[0];
|
res.w[0] = y.w[0];
|
}
|
}
|
BID_RETURN (res)
|
BID_RETURN (res)
|
} else { // at least one is infinity
|
} else { // at least one is infinity
|
if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
|
if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
|
x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
|
x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
|
x.w[0] = 0x0ull;
|
x.w[0] = 0x0ull;
|
}
|
}
|
if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
|
if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
|
y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
|
y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
|
y.w[0] = 0x0ull;
|
y.w[0] = 0x0ull;
|
}
|
}
|
}
|
}
|
}
|
}
|
// neither x nor y is NaN
|
// neither x nor y is NaN
|
|
|
// if not infinity, check for non-canonical values x (treated as zero)
|
// if not infinity, check for non-canonical values x (treated as zero)
|
if ((x.w[1] & MASK_ANY_INF) != MASK_INF) { // x != inf
|
if ((x.w[1] & MASK_ANY_INF) != MASK_INF) { // x != inf
|
if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
|
if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
|
// non-canonical
|
// non-canonical
|
x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
|
x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
|
x.w[1] = (x.w[1] & MASK_SIGN) | x_exp;
|
x.w[1] = (x.w[1] & MASK_SIGN) | x_exp;
|
x.w[0] = 0x0ull;
|
x.w[0] = 0x0ull;
|
} else { // G0_G1 != 11
|
} else { // G0_G1 != 11
|
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits
|
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits
|
if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
|
if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
|
((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
|
((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
|
&& x.w[0] > 0x378d8e63ffffffffull)) {
|
&& x.w[0] > 0x378d8e63ffffffffull)) {
|
// x is non-canonical if coefficient is larger than 10^34 -1
|
// x is non-canonical if coefficient is larger than 10^34 -1
|
x.w[1] = (x.w[1] & MASK_SIGN) | x_exp;
|
x.w[1] = (x.w[1] & MASK_SIGN) | x_exp;
|
x.w[0] = 0x0ull;
|
x.w[0] = 0x0ull;
|
} else { // canonical
|
} else { // canonical
|
;
|
;
|
}
|
}
|
}
|
}
|
}
|
}
|
// no need to check for non-canonical y
|
// no need to check for non-canonical y
|
|
|
// neither x nor y is NaN
|
// neither x nor y is NaN
|
tmp_fpsf = *pfpsf; // save fpsf
|
tmp_fpsf = *pfpsf; // save fpsf
|
#if DECIMAL_CALL_BY_REFERENCE
|
#if DECIMAL_CALL_BY_REFERENCE
|
bid128_quiet_equal (&res1, &xnswp,
|
bid128_quiet_equal (&res1, &xnswp,
|
&ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
&ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
_EXC_INFO_ARG);
|
_EXC_INFO_ARG);
|
bid128_quiet_greater (&res2, &xnswp,
|
bid128_quiet_greater (&res2, &xnswp,
|
&ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
&ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
_EXC_INFO_ARG);
|
_EXC_INFO_ARG);
|
#else
|
#else
|
res1 =
|
res1 =
|
bid128_quiet_equal (xnswp,
|
bid128_quiet_equal (xnswp,
|
ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
_EXC_INFO_ARG);
|
_EXC_INFO_ARG);
|
res2 =
|
res2 =
|
bid128_quiet_greater (xnswp,
|
bid128_quiet_greater (xnswp,
|
ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
_EXC_INFO_ARG);
|
_EXC_INFO_ARG);
|
#endif
|
#endif
|
*pfpsf = tmp_fpsf; // restore fpsf
|
*pfpsf = tmp_fpsf; // restore fpsf
|
|
|
if (res1) { // x = y
|
if (res1) { // x = y
|
// return x with the sign of y
|
// return x with the sign of y
|
res.w[1] =
|
res.w[1] =
|
(x.w[1] & 0x7fffffffffffffffull) | (y.
|
(x.w[1] & 0x7fffffffffffffffull) | (y.
|
w[1] & 0x8000000000000000ull);
|
w[1] & 0x8000000000000000ull);
|
res.w[0] = x.w[0];
|
res.w[0] = x.w[0];
|
} else if (res2) { // x > y
|
} else if (res2) { // x > y
|
#if DECIMAL_CALL_BY_REFERENCE
|
#if DECIMAL_CALL_BY_REFERENCE
|
bid128_nextdown (&res,
|
bid128_nextdown (&res,
|
&xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
&xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
_EXC_INFO_ARG);
|
_EXC_INFO_ARG);
|
#else
|
#else
|
res =
|
res =
|
bid128_nextdown (xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
bid128_nextdown (xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
_EXC_INFO_ARG);
|
_EXC_INFO_ARG);
|
#endif
|
#endif
|
BID_SWAP128 (res);
|
BID_SWAP128 (res);
|
} else { // x < y
|
} else { // x < y
|
#if DECIMAL_CALL_BY_REFERENCE
|
#if DECIMAL_CALL_BY_REFERENCE
|
bid128_nextup (&res,
|
bid128_nextup (&res,
|
&xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
&xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
#else
|
#else
|
res =
|
res =
|
bid128_nextup (xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
bid128_nextup (xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
#endif
|
#endif
|
BID_SWAP128 (res);
|
BID_SWAP128 (res);
|
}
|
}
|
// if the operand x is finite but the result is infinite, signal
|
// if the operand x is finite but the result is infinite, signal
|
// overflow and inexact
|
// overflow and inexact
|
if (((x.w[1] & MASK_SPECIAL) != MASK_SPECIAL)
|
if (((x.w[1] & MASK_SPECIAL) != MASK_SPECIAL)
|
&& ((res.w[1] & MASK_SPECIAL) == MASK_SPECIAL)) {
|
&& ((res.w[1] & MASK_SPECIAL) == MASK_SPECIAL)) {
|
// set the inexact flag
|
// set the inexact flag
|
*pfpsf |= INEXACT_EXCEPTION;
|
*pfpsf |= INEXACT_EXCEPTION;
|
// set the overflow flag
|
// set the overflow flag
|
*pfpsf |= OVERFLOW_EXCEPTION;
|
*pfpsf |= OVERFLOW_EXCEPTION;
|
}
|
}
|
// if the result is in (-10^emin, 10^emin), and is different from the
|
// if the result is in (-10^emin, 10^emin), and is different from the
|
// operand x, signal underflow and inexact
|
// operand x, signal underflow and inexact
|
tmp1.w[HIGH_128W] = 0x0000314dc6448d93ull;
|
tmp1.w[HIGH_128W] = 0x0000314dc6448d93ull;
|
tmp1.w[LOW_128W] = 0x38c15b0a00000000ull; // +100...0[34] * 10^emin
|
tmp1.w[LOW_128W] = 0x38c15b0a00000000ull; // +100...0[34] * 10^emin
|
tmp2.w[HIGH_128W] = res.w[1] & 0x7fffffffffffffffull;
|
tmp2.w[HIGH_128W] = res.w[1] & 0x7fffffffffffffffull;
|
tmp2.w[LOW_128W] = res.w[0];
|
tmp2.w[LOW_128W] = res.w[0];
|
tmp3.w[HIGH_128W] = res.w[1];
|
tmp3.w[HIGH_128W] = res.w[1];
|
tmp3.w[LOW_128W] = res.w[0];
|
tmp3.w[LOW_128W] = res.w[0];
|
tmp_fpsf = *pfpsf; // save fpsf
|
tmp_fpsf = *pfpsf; // save fpsf
|
#if DECIMAL_CALL_BY_REFERENCE
|
#if DECIMAL_CALL_BY_REFERENCE
|
bid128_quiet_greater (&res1, &tmp1,
|
bid128_quiet_greater (&res1, &tmp1,
|
&tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
&tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
_EXC_INFO_ARG);
|
_EXC_INFO_ARG);
|
bid128_quiet_not_equal (&res2, &xnswp,
|
bid128_quiet_not_equal (&res2, &xnswp,
|
&tmp3 _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
&tmp3 _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
_EXC_INFO_ARG);
|
_EXC_INFO_ARG);
|
#else
|
#else
|
res1 =
|
res1 =
|
bid128_quiet_greater (tmp1,
|
bid128_quiet_greater (tmp1,
|
tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
_EXC_INFO_ARG);
|
_EXC_INFO_ARG);
|
res2 =
|
res2 =
|
bid128_quiet_not_equal (xnswp,
|
bid128_quiet_not_equal (xnswp,
|
tmp3 _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
tmp3 _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
_EXC_INFO_ARG);
|
_EXC_INFO_ARG);
|
#endif
|
#endif
|
*pfpsf = tmp_fpsf; // restore fpsf
|
*pfpsf = tmp_fpsf; // restore fpsf
|
if (res1 && res2) {
|
if (res1 && res2) {
|
// set the inexact flag
|
// set the inexact flag
|
*pfpsf |= INEXACT_EXCEPTION;
|
*pfpsf |= INEXACT_EXCEPTION;
|
// set the underflow flag
|
// set the underflow flag
|
*pfpsf |= UNDERFLOW_EXCEPTION;
|
*pfpsf |= UNDERFLOW_EXCEPTION;
|
}
|
}
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
|
|
