226 lines
8.8 KiB
C
226 lines
8.8 KiB
C
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/*============================================================================
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This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
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Package, Release 3e, by John R. Hauser.
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Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017 The Regents of the
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University of California. All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are met:
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1. Redistributions of source code must retain the above copyright notice,
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this list of conditions, and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright notice,
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this list of conditions, and the following disclaimer in the documentation
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and/or other materials provided with the distribution.
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3. Neither the name of the University nor the names of its contributors may
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be used to endorse or promote products derived from this software without
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specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
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EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
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DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
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DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
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ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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=============================================================================*/
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#include <stdbool.h>
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#include <stdint.h>
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#include "platform.h"
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#include "internals.h"
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#include "specialize.h"
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#include "softfloat.h"
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extFloat80_t extF80_rem( extFloat80_t a, extFloat80_t b )
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{
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union { struct extFloat80M s; extFloat80_t f; } uA;
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uint_fast16_t uiA64;
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uint_fast64_t uiA0;
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bool signA;
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int_fast32_t expA;
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uint_fast64_t sigA;
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union { struct extFloat80M s; extFloat80_t f; } uB;
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uint_fast16_t uiB64;
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uint_fast64_t uiB0;
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int_fast32_t expB;
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uint_fast64_t sigB;
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struct exp32_sig64 normExpSig;
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int_fast32_t expDiff;
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struct uint128 rem, shiftedSigB;
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uint_fast32_t q, recip32;
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uint_fast64_t q64;
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struct uint128 term, altRem, meanRem;
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bool signRem;
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struct uint128 uiZ;
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uint_fast16_t uiZ64;
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uint_fast64_t uiZ0;
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union { struct extFloat80M s; extFloat80_t f; } uZ;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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uA.f = a;
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uiA64 = uA.s.signExp;
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uiA0 = uA.s.signif;
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signA = signExtF80UI64( uiA64 );
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expA = expExtF80UI64( uiA64 );
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sigA = uiA0;
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uB.f = b;
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uiB64 = uB.s.signExp;
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uiB0 = uB.s.signif;
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expB = expExtF80UI64( uiB64 );
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sigB = uiB0;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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if ( expA == 0x7FFF ) {
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if (
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(sigA & UINT64_C( 0x7FFFFFFFFFFFFFFF ))
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|| ((expB == 0x7FFF) && (sigB & UINT64_C( 0x7FFFFFFFFFFFFFFF )))
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) {
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goto propagateNaN;
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}
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goto invalid;
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}
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if ( expB == 0x7FFF ) {
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if ( sigB & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) goto propagateNaN;
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/*--------------------------------------------------------------------
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| Argument b is an infinity. Doubling `expB' is an easy way to ensure
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| that `expDiff' later is less than -1, which will result in returning
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| a canonicalized version of argument a.
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*--------------------------------------------------------------------*/
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expB += expB;
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}
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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if ( ! expB ) expB = 1;
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if ( ! (sigB & UINT64_C( 0x8000000000000000 )) ) {
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if ( ! sigB ) goto invalid;
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normExpSig = softfloat_normSubnormalExtF80Sig( sigB );
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expB += normExpSig.exp;
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sigB = normExpSig.sig;
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}
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if ( ! expA ) expA = 1;
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if ( ! (sigA & UINT64_C( 0x8000000000000000 )) ) {
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if ( ! sigA ) {
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expA = 0;
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goto copyA;
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}
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normExpSig = softfloat_normSubnormalExtF80Sig( sigA );
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expA += normExpSig.exp;
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sigA = normExpSig.sig;
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}
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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expDiff = expA - expB;
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if ( expDiff < -1 ) goto copyA;
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rem = softfloat_shortShiftLeft128( 0, sigA, 32 );
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shiftedSigB = softfloat_shortShiftLeft128( 0, sigB, 32 );
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if ( expDiff < 1 ) {
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if ( expDiff ) {
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--expB;
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shiftedSigB = softfloat_shortShiftLeft128( 0, sigB, 33 );
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q = 0;
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} else {
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q = (sigB <= sigA);
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if ( q ) {
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rem =
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softfloat_sub128(
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rem.v64, rem.v0, shiftedSigB.v64, shiftedSigB.v0 );
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}
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}
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} else {
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recip32 = softfloat_approxRecip32_1( sigB>>32 );
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expDiff -= 30;
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for (;;) {
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q64 = (uint_fast64_t) (uint32_t) (rem.v64>>2) * recip32;
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if ( expDiff < 0 ) break;
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q = (q64 + 0x80000000)>>32;
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rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
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term = softfloat_mul64ByShifted32To128( sigB, q );
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rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
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if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
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rem =
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softfloat_add128(
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rem.v64, rem.v0, shiftedSigB.v64, shiftedSigB.v0 );
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}
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expDiff -= 29;
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}
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/*--------------------------------------------------------------------
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| (`expDiff' cannot be less than -29 here.)
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*--------------------------------------------------------------------*/
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q = (uint32_t) (q64>>32)>>(~expDiff & 31);
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rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, expDiff + 30 );
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term = softfloat_mul64ByShifted32To128( sigB, q );
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rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
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if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
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altRem =
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softfloat_add128(
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rem.v64, rem.v0, shiftedSigB.v64, shiftedSigB.v0 );
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goto selectRem;
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}
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}
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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do {
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altRem = rem;
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++q;
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rem =
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softfloat_sub128(
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rem.v64, rem.v0, shiftedSigB.v64, shiftedSigB.v0 );
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} while ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) );
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selectRem:
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meanRem = softfloat_add128( rem.v64, rem.v0, altRem.v64, altRem.v0 );
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if (
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(meanRem.v64 & UINT64_C( 0x8000000000000000 ))
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|| (! (meanRem.v64 | meanRem.v0) && (q & 1))
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) {
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rem = altRem;
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}
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signRem = signA;
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if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
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signRem = ! signRem;
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rem = softfloat_sub128( 0, 0, rem.v64, rem.v0 );
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}
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return
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softfloat_normRoundPackToExtF80(
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signRem, rem.v64 | rem.v0 ? expB + 32 : 0, rem.v64, rem.v0, 80 );
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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propagateNaN:
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uiZ = softfloat_propagateNaNExtF80UI( uiA64, uiA0, uiB64, uiB0 );
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uiZ64 = uiZ.v64;
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uiZ0 = uiZ.v0;
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goto uiZ;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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invalid:
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softfloat_raiseFlags( softfloat_flag_invalid );
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uiZ64 = defaultNaNExtF80UI64;
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uiZ0 = defaultNaNExtF80UI0;
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goto uiZ;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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copyA:
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if ( expA < 1 ) {
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sigA >>= 1 - expA;
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expA = 0;
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}
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uiZ64 = packToExtF80UI64( signA, expA );
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uiZ0 = sigA;
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uiZ:
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uZ.s.signExp = uiZ64;
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uZ.s.signif = uiZ0;
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return uZ.f;
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}
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