229 lines
9.0 KiB
C
229 lines
9.0 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, 2017 The Regents of the University of
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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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#ifdef SOFTFLOAT_FAST_INT64
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void f128M_sqrt( const float128_t *aPtr, float128_t *zPtr )
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{
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*zPtr = f128_sqrt( *aPtr );
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}
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#else
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void f128M_sqrt( const float128_t *aPtr, float128_t *zPtr )
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{
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const uint32_t *aWPtr;
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uint32_t *zWPtr;
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uint32_t uiA96;
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bool signA;
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int32_t rawExpA;
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uint32_t rem[6];
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int32_t expA, expZ;
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uint64_t rem64;
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uint32_t sig32A, recipSqrt32, sig32Z, qs[3], q;
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uint64_t sig64Z;
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uint32_t term[5];
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uint64_t x64;
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uint32_t y[5], rem32;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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aWPtr = (const uint32_t *) aPtr;
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zWPtr = (uint32_t *) zPtr;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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uiA96 = aWPtr[indexWordHi( 4 )];
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signA = signF128UI96( uiA96 );
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rawExpA = expF128UI96( uiA96 );
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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if ( rawExpA == 0x7FFF ) {
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if (
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fracF128UI96( uiA96 )
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|| (aWPtr[indexWord( 4, 2 )] | aWPtr[indexWord( 4, 1 )]
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| aWPtr[indexWord( 4, 0 )])
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) {
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softfloat_propagateNaNF128M( aWPtr, 0, zWPtr );
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return;
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}
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if ( ! signA ) goto copyA;
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goto invalid;
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}
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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expA = softfloat_shiftNormSigF128M( aWPtr, 13 - (rawExpA & 1), rem );
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if ( expA == -128 ) goto copyA;
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if ( signA ) goto invalid;
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/*------------------------------------------------------------------------
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| (`sig32Z' is guaranteed to be a lower bound on the square root of
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| `sig32A', which makes `sig32Z' also a lower bound on the square root of
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| `sigA'.)
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*------------------------------------------------------------------------*/
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expZ = ((expA - 0x3FFF)>>1) + 0x3FFE;
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expA &= 1;
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rem64 = (uint64_t) rem[indexWord( 4, 3 )]<<32 | rem[indexWord( 4, 2 )];
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if ( expA ) {
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if ( ! rawExpA ) {
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softfloat_shortShiftRight128M( rem, 1, rem );
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rem64 >>= 1;
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}
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sig32A = rem64>>29;
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} else {
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sig32A = rem64>>30;
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}
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recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A );
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sig32Z = ((uint64_t) sig32A * recipSqrt32)>>32;
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if ( expA ) sig32Z >>= 1;
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qs[2] = sig32Z;
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rem64 -= (uint64_t) sig32Z * sig32Z;
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rem[indexWord( 4, 3 )] = rem64>>32;
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rem[indexWord( 4, 2 )] = rem64;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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q = ((uint32_t) (rem64>>2) * (uint64_t) recipSqrt32)>>32;
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sig64Z = ((uint64_t) sig32Z<<32) + ((uint64_t) q<<3);
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term[indexWord( 4, 3 )] = 0;
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term[indexWord( 4, 0 )] = 0;
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/*------------------------------------------------------------------------
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| (Repeating this loop is a rare occurrence.)
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*------------------------------------------------------------------------*/
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for (;;) {
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x64 = ((uint64_t) sig32Z<<32) + sig64Z;
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term[indexWord( 4, 2 )] = x64>>32;
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term[indexWord( 4, 1 )] = x64;
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softfloat_remStep128MBy32( rem, 29, term, q, y );
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rem32 = y[indexWord( 4, 3 )];
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if ( ! (rem32 & 0x80000000) ) break;
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--q;
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sig64Z -= 1<<3;
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}
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qs[1] = q;
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rem64 = (uint64_t) rem32<<32 | y[indexWord( 4, 2 )];
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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q = ((uint32_t) (rem64>>2) * (uint64_t) recipSqrt32)>>32;
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if ( rem64>>34 ) q += recipSqrt32;
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sig64Z <<= 1;
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/*------------------------------------------------------------------------
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| (Repeating this loop is a rare occurrence.)
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*------------------------------------------------------------------------*/
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for (;;) {
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x64 = sig64Z + (q>>26);
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term[indexWord( 4, 2 )] = x64>>32;
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term[indexWord( 4, 1 )] = x64;
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term[indexWord( 4, 0 )] = q<<6;
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softfloat_remStep128MBy32(
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y, 29, term, q, &rem[indexMultiwordHi( 6, 4 )] );
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rem32 = rem[indexWordHi( 6 )];
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if ( ! (rem32 & 0x80000000) ) break;
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--q;
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}
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qs[0] = q;
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rem64 = (uint64_t) rem32<<32 | rem[indexWord( 6, 4 )];
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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q = (((uint32_t) (rem64>>2) * (uint64_t) recipSqrt32)>>32) + 2;
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if ( rem64>>34 ) q += recipSqrt32;
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x64 = (uint64_t) q<<27;
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y[indexWord( 5, 0 )] = x64;
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x64 = ((uint64_t) qs[0]<<24) + (x64>>32);
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y[indexWord( 5, 1 )] = x64;
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x64 = ((uint64_t) qs[1]<<21) + (x64>>32);
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y[indexWord( 5, 2 )] = x64;
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x64 = ((uint64_t) qs[2]<<18) + (x64>>32);
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y[indexWord( 5, 3 )] = x64;
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y[indexWord( 5, 4 )] = x64>>32;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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if ( (q & 0xF) <= 2 ) {
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q &= ~3;
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y[indexWordLo( 5 )] = q<<27;
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term[indexWord( 5, 4 )] = 0;
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term[indexWord( 5, 3 )] = 0;
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term[indexWord( 5, 2 )] = 0;
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term[indexWord( 5, 1 )] = q>>6;
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term[indexWord( 5, 0 )] = q<<26;
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softfloat_sub160M( y, term, term );
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rem[indexWord( 6, 1 )] = 0;
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rem[indexWord( 6, 0 )] = 0;
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softfloat_remStep160MBy32(
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&rem[indexMultiwordLo( 6, 5 )],
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14,
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term,
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q,
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&rem[indexMultiwordLo( 6, 5 )]
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);
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rem32 = rem[indexWord( 6, 4 )];
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if ( rem32 & 0x80000000 ) {
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softfloat_sub1X160M( y );
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} else {
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if (
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rem32 || rem[indexWord( 6, 0 )] || rem[indexWord( 6, 1 )]
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|| (rem[indexWord( 6, 3 )] | rem[indexWord( 6, 2 )])
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) {
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y[indexWordLo( 5 )] |= 1;
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}
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}
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}
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softfloat_roundPackMToF128M( 0, expZ, y, zWPtr );
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return;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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invalid:
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softfloat_invalidF128M( zWPtr );
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return;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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copyA:
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zWPtr[indexWordHi( 4 )] = uiA96;
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zWPtr[indexWord( 4, 2 )] = aWPtr[indexWord( 4, 2 )];
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zWPtr[indexWord( 4, 1 )] = aWPtr[indexWord( 4, 1 )];
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zWPtr[indexWord( 4, 0 )] = aWPtr[indexWord( 4, 0 )];
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}
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#endif
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