mirror of
https://github.com/openhwgroup/cvw
synced 2025-02-11 06:05:49 +00:00
177 lines
7.3 KiB
C
177 lines
7.3 KiB
C
|
|
/*============================================================================
|
|
|
|
This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
|
|
Package, Release 3e, by John R. Hauser.
|
|
|
|
Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017 The Regents of the
|
|
University of California. All rights reserved.
|
|
|
|
Redistribution and use in source and binary forms, with or without
|
|
modification, are permitted provided that the following conditions are met:
|
|
|
|
1. Redistributions of source code must retain the above copyright notice,
|
|
this list of conditions, and the following disclaimer.
|
|
|
|
2. Redistributions in binary form must reproduce the above copyright notice,
|
|
this list of conditions, and the following disclaimer in the documentation
|
|
and/or other materials provided with the distribution.
|
|
|
|
3. Neither the name of the University nor the names of its contributors may
|
|
be used to endorse or promote products derived from this software without
|
|
specific prior written permission.
|
|
|
|
THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
|
|
EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
|
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
|
|
DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
|
|
DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
|
|
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
|
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
|
|
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
|
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
|
|
=============================================================================*/
|
|
|
|
#include <stdbool.h>
|
|
#include <stdint.h>
|
|
#include "platform.h"
|
|
#include "internals.h"
|
|
#include "specialize.h"
|
|
#include "softfloat.h"
|
|
|
|
extFloat80_t extF80_sqrt( extFloat80_t a )
|
|
{
|
|
union { struct extFloat80M s; extFloat80_t f; } uA;
|
|
uint_fast16_t uiA64;
|
|
uint_fast64_t uiA0;
|
|
bool signA;
|
|
int_fast32_t expA;
|
|
uint_fast64_t sigA;
|
|
struct uint128 uiZ;
|
|
uint_fast16_t uiZ64;
|
|
uint_fast64_t uiZ0;
|
|
struct exp32_sig64 normExpSig;
|
|
int_fast32_t expZ;
|
|
uint_fast32_t sig32A, recipSqrt32, sig32Z;
|
|
struct uint128 rem;
|
|
uint_fast64_t q, x64, sigZ;
|
|
struct uint128 y, term;
|
|
uint_fast64_t sigZExtra;
|
|
union { struct extFloat80M s; extFloat80_t f; } uZ;
|
|
|
|
/*------------------------------------------------------------------------
|
|
*------------------------------------------------------------------------*/
|
|
uA.f = a;
|
|
uiA64 = uA.s.signExp;
|
|
uiA0 = uA.s.signif;
|
|
signA = signExtF80UI64( uiA64 );
|
|
expA = expExtF80UI64( uiA64 );
|
|
sigA = uiA0;
|
|
/*------------------------------------------------------------------------
|
|
*------------------------------------------------------------------------*/
|
|
if ( expA == 0x7FFF ) {
|
|
if ( sigA & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) {
|
|
uiZ = softfloat_propagateNaNExtF80UI( uiA64, uiA0, 0, 0 );
|
|
uiZ64 = uiZ.v64;
|
|
uiZ0 = uiZ.v0;
|
|
goto uiZ;
|
|
}
|
|
if ( ! signA ) return a;
|
|
goto invalid;
|
|
}
|
|
/*------------------------------------------------------------------------
|
|
*------------------------------------------------------------------------*/
|
|
if ( signA ) {
|
|
if ( ! sigA ) goto zero;
|
|
goto invalid;
|
|
}
|
|
/*------------------------------------------------------------------------
|
|
*------------------------------------------------------------------------*/
|
|
if ( ! expA ) expA = 1;
|
|
if ( ! (sigA & UINT64_C( 0x8000000000000000 )) ) {
|
|
if ( ! sigA ) goto zero;
|
|
normExpSig = softfloat_normSubnormalExtF80Sig( sigA );
|
|
expA += normExpSig.exp;
|
|
sigA = normExpSig.sig;
|
|
}
|
|
/*------------------------------------------------------------------------
|
|
| (`sig32Z' is guaranteed to be a lower bound on the square root of
|
|
| `sig32A', which makes `sig32Z' also a lower bound on the square root of
|
|
| `sigA'.)
|
|
*------------------------------------------------------------------------*/
|
|
expZ = ((expA - 0x3FFF)>>1) + 0x3FFF;
|
|
expA &= 1;
|
|
sig32A = sigA>>32;
|
|
recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A );
|
|
sig32Z = ((uint_fast64_t) sig32A * recipSqrt32)>>32;
|
|
if ( expA ) {
|
|
sig32Z >>= 1;
|
|
rem = softfloat_shortShiftLeft128( 0, sigA, 61 );
|
|
} else {
|
|
rem = softfloat_shortShiftLeft128( 0, sigA, 62 );
|
|
}
|
|
rem.v64 -= (uint_fast64_t) sig32Z * sig32Z;
|
|
/*------------------------------------------------------------------------
|
|
*------------------------------------------------------------------------*/
|
|
q = ((uint32_t) (rem.v64>>2) * (uint_fast64_t) recipSqrt32)>>32;
|
|
x64 = (uint_fast64_t) sig32Z<<32;
|
|
sigZ = x64 + (q<<3);
|
|
y = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
|
|
/*------------------------------------------------------------------------
|
|
| (Repeating this loop is a rare occurrence.)
|
|
*------------------------------------------------------------------------*/
|
|
for (;;) {
|
|
term = softfloat_mul64ByShifted32To128( x64 + sigZ, q );
|
|
rem = softfloat_sub128( y.v64, y.v0, term.v64, term.v0 );
|
|
if ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) ) break;
|
|
--q;
|
|
sigZ -= 1<<3;
|
|
}
|
|
/*------------------------------------------------------------------------
|
|
*------------------------------------------------------------------------*/
|
|
q = (((rem.v64>>2) * recipSqrt32)>>32) + 2;
|
|
x64 = sigZ;
|
|
sigZ = (sigZ<<1) + (q>>25);
|
|
sigZExtra = (uint64_t) (q<<39);
|
|
/*------------------------------------------------------------------------
|
|
*------------------------------------------------------------------------*/
|
|
if ( (q & 0xFFFFFF) <= 2 ) {
|
|
q &= ~(uint_fast64_t) 0xFFFF;
|
|
sigZExtra = (uint64_t) (q<<39);
|
|
term = softfloat_mul64ByShifted32To128( x64 + (q>>27), q );
|
|
x64 = (uint32_t) (q<<5) * (uint_fast64_t) (uint32_t) q;
|
|
term = softfloat_add128( term.v64, term.v0, 0, x64 );
|
|
rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 28 );
|
|
rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
|
|
if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
|
|
if ( ! sigZExtra ) --sigZ;
|
|
--sigZExtra;
|
|
} else {
|
|
if ( rem.v64 | rem.v0 ) sigZExtra |= 1;
|
|
}
|
|
}
|
|
return
|
|
softfloat_roundPackToExtF80(
|
|
0, expZ, sigZ, sigZExtra, extF80_roundingPrecision );
|
|
/*------------------------------------------------------------------------
|
|
*------------------------------------------------------------------------*/
|
|
invalid:
|
|
softfloat_raiseFlags( softfloat_flag_invalid );
|
|
uiZ64 = defaultNaNExtF80UI64;
|
|
uiZ0 = defaultNaNExtF80UI0;
|
|
goto uiZ;
|
|
/*------------------------------------------------------------------------
|
|
*------------------------------------------------------------------------*/
|
|
zero:
|
|
uiZ64 = packToExtF80UI64( signA, 0 );
|
|
uiZ0 = 0;
|
|
uiZ:
|
|
uZ.s.signExp = uiZ64;
|
|
uZ.s.signif = uiZ0;
|
|
return uZ.f;
|
|
|
|
}
|
|
|