forked from Github_Repos/cvw
202 lines
8.6 KiB
C
202 lines
8.6 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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float128_t f128_sqrt( float128_t a )
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{
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union ui128_f128 uA;
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uint_fast64_t uiA64, uiA0;
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bool signA;
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int_fast32_t expA;
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struct uint128 sigA, uiZ;
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struct exp32_sig128 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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uint32_t qs[3];
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uint_fast32_t q;
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uint_fast64_t x64, sig64Z;
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struct uint128 y, term;
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uint_fast64_t sigZExtra;
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struct uint128 sigZ;
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union ui128_f128 uZ;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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uA.f = a;
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uiA64 = uA.ui.v64;
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uiA0 = uA.ui.v0;
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signA = signF128UI64( uiA64 );
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expA = expF128UI64( uiA64 );
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sigA.v64 = fracF128UI64( uiA64 );
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sigA.v0 = uiA0;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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if ( expA == 0x7FFF ) {
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if ( sigA.v64 | sigA.v0 ) {
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uiZ = softfloat_propagateNaNF128UI( uiA64, uiA0, 0, 0 );
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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 ( ! (expA | sigA.v64 | sigA.v0) ) 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 ( ! expA ) {
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if ( ! (sigA.v64 | sigA.v0) ) return a;
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normExpSig = softfloat_normSubnormalF128Sig( sigA.v64, sigA.v0 );
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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) + 0x3FFE;
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expA &= 1;
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sigA.v64 |= UINT64_C( 0x0001000000000000 );
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sig32A = sigA.v64>>17;
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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( sigA.v64, sigA.v0, 12 );
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} else {
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rem = softfloat_shortShiftLeft128( sigA.v64, sigA.v0, 13 );
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}
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qs[2] = sig32Z;
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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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sig64Z = x64 + ((uint_fast64_t) 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 + sig64Z, 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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sig64Z -= 1<<3;
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}
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qs[1] = q;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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q = ((rem.v64>>2) * recipSqrt32)>>32;
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y = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
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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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term = softfloat_shortShiftLeft128( 0, sig64Z, 32 );
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term = softfloat_add128( term.v64, term.v0, 0, (uint_fast64_t) q<<6 );
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term = softfloat_mul128By32( term.v64, term.v0, 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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}
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qs[0] = q;
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/*------------------------------------------------------------------------
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*------------------------------------------------------------------------*/
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q = (((rem.v64>>2) * recipSqrt32)>>32) + 2;
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sigZExtra = (uint64_t) ((uint_fast64_t) q<<59);
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term = softfloat_shortShiftLeft128( 0, qs[1], 53 );
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sigZ =
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softfloat_add128(
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(uint_fast64_t) qs[2]<<18, ((uint_fast64_t) qs[0]<<24) + (q>>5),
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term.v64, term.v0
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);
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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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sigZExtra = (uint64_t) ((uint_fast64_t) q<<59);
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y = softfloat_shortShiftLeft128( sigZ.v64, sigZ.v0, 6 );
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y.v0 |= sigZExtra>>58;
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term = softfloat_sub128( y.v64, y.v0, 0, q );
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y = softfloat_mul64ByShifted32To128( term.v0, q );
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term = softfloat_mul64ByShifted32To128( term.v64, q );
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term = softfloat_add128( term.v64, term.v0, 0, y.v64 );
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rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 20 );
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term = softfloat_sub128( term.v64, term.v0, rem.v64, rem.v0 );
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/*--------------------------------------------------------------------
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| The concatenation of `term' and `y.v0' is now the negative remainder
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| (3 words altogether).
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*--------------------------------------------------------------------*/
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if ( term.v64 & UINT64_C( 0x8000000000000000 ) ) {
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sigZExtra |= 1;
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} else {
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if ( term.v64 | term.v0 | y.v0 ) {
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if ( sigZExtra ) {
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--sigZExtra;
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} else {
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sigZ = softfloat_sub128( sigZ.v64, sigZ.v0, 0, 1 );
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sigZExtra = ~0;
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}
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}
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}
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}
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return softfloat_roundPackToF128( 0, expZ, sigZ.v64, sigZ.v0, sigZExtra );
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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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uiZ.v64 = defaultNaNF128UI64;
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uiZ.v0 = defaultNaNF128UI0;
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uiZ:
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uZ.ui = uiZ;
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return uZ.f;
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}
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