177 lines
7.3 KiB
C
177 lines
7.3 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_sqrt( extFloat80_t a )
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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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struct uint128 uiZ;
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uint_fast16_t uiZ64;
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uint_fast64_t uiZ0;
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struct exp32_sig64 normExpSig;
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int_fast32_t expZ;
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uint_fast32_t sig32A, recipSqrt32, sig32Z;
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struct uint128 rem;
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uint_fast64_t q, x64, sigZ;
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struct uint128 y, term;
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uint_fast64_t sigZExtra;
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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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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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if ( expA == 0x7FFF ) {
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if ( sigA & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) {
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uiZ = softfloat_propagateNaNExtF80UI( uiA64, uiA0, 0, 0 );
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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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if ( ! signA ) return a;
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goto invalid;
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}
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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if ( signA ) {
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if ( ! sigA ) goto zero;
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goto invalid;
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}
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/*------------------------------------------------------------------------
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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 ) goto zero;
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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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| (`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) + 0x3FFF;
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expA &= 1;
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sig32A = sigA>>32;
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recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A );
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sig32Z = ((uint_fast64_t) sig32A * recipSqrt32)>>32;
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if ( expA ) {
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sig32Z >>= 1;
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rem = softfloat_shortShiftLeft128( 0, sigA, 61 );
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} else {
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rem = softfloat_shortShiftLeft128( 0, sigA, 62 );
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}
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rem.v64 -= (uint_fast64_t) sig32Z * sig32Z;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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q = ((uint32_t) (rem.v64>>2) * (uint_fast64_t) recipSqrt32)>>32;
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x64 = (uint_fast64_t) sig32Z<<32;
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sigZ = x64 + (q<<3);
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y = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
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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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term = softfloat_mul64ByShifted32To128( x64 + sigZ, q );
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rem = softfloat_sub128( y.v64, y.v0, term.v64, term.v0 );
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if ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) ) break;
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--q;
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sigZ -= 1<<3;
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}
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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q = (((rem.v64>>2) * recipSqrt32)>>32) + 2;
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x64 = sigZ;
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sigZ = (sigZ<<1) + (q>>25);
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sigZExtra = (uint64_t) (q<<39);
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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if ( (q & 0xFFFFFF) <= 2 ) {
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q &= ~(uint_fast64_t) 0xFFFF;
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sigZExtra = (uint64_t) (q<<39);
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term = softfloat_mul64ByShifted32To128( x64 + (q>>27), q );
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x64 = (uint32_t) (q<<5) * (uint_fast64_t) (uint32_t) q;
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term = softfloat_add128( term.v64, term.v0, 0, x64 );
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rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 28 );
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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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if ( ! sigZExtra ) --sigZ;
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--sigZExtra;
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} else {
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if ( rem.v64 | rem.v0 ) sigZExtra |= 1;
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}
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}
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return
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softfloat_roundPackToExtF80(
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0, expZ, sigZ, sigZExtra, extF80_roundingPrecision );
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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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zero:
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uiZ64 = packToExtF80UI64( signA, 0 );
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uiZ0 = 0;
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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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