| |
| /*============================================================================ |
| |
| This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic |
| Package, Release 3d, by John R. Hauser. |
| |
| Copyright 2011, 2012, 2013, 2014, 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" |
| |
| #ifdef SOFTFLOAT_FAST_INT64 |
| |
| void f128M_sqrt( const float128_t *aPtr, float128_t *zPtr ) |
| { |
| |
| *zPtr = f128_sqrt( *aPtr ); |
| |
| } |
| |
| #else |
| |
| void f128M_sqrt( const float128_t *aPtr, float128_t *zPtr ) |
| { |
| const uint32_t *aWPtr; |
| uint32_t *zWPtr; |
| uint32_t uiA96; |
| bool signA; |
| int32_t rawExpA; |
| uint32_t rem[6]; |
| int32_t expA, expZ; |
| uint64_t rem64; |
| uint32_t sig32A, recipSqrt32, sig32Z, qs[3], q; |
| uint64_t sig64Z; |
| uint32_t term[5]; |
| uint64_t x64; |
| uint32_t y[5], rem32; |
| |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| aWPtr = (const uint32_t *) aPtr; |
| zWPtr = (uint32_t *) zPtr; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| uiA96 = aWPtr[indexWordHi( 4 )]; |
| signA = signF128UI96( uiA96 ); |
| rawExpA = expF128UI96( uiA96 ); |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| if ( rawExpA == 0x7FFF ) { |
| if ( |
| fracF128UI96( uiA96 ) |
| || (aWPtr[indexWord( 4, 2 )] | aWPtr[indexWord( 4, 1 )] |
| | aWPtr[indexWord( 4, 0 )]) |
| ) { |
| softfloat_propagateNaNF128M( aWPtr, 0, zWPtr ); |
| return; |
| } |
| if ( ! signA ) goto copyA; |
| goto invalid; |
| } |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| expA = softfloat_shiftNormSigF128M( aWPtr, 13 - (rawExpA & 1), rem ); |
| if ( expA == -128 ) goto copyA; |
| if ( signA ) goto invalid; |
| /*------------------------------------------------------------------------ |
| | (`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) + 0x3FFE; |
| expA &= 1; |
| rem64 = (uint64_t) rem[indexWord( 4, 3 )]<<32 | rem[indexWord( 4, 2 )]; |
| if ( expA ) { |
| if ( ! rawExpA ) { |
| softfloat_shortShiftRight128M( rem, 1, rem ); |
| rem64 >>= 1; |
| } |
| sig32A = rem64>>29; |
| } else { |
| sig32A = rem64>>30; |
| } |
| recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A ); |
| sig32Z = ((uint64_t) sig32A * recipSqrt32)>>32; |
| if ( expA ) sig32Z >>= 1; |
| qs[2] = sig32Z; |
| rem64 -= (uint64_t) sig32Z * sig32Z; |
| rem[indexWord( 4, 3 )] = rem64>>32; |
| rem[indexWord( 4, 2 )] = rem64; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| q = ((uint32_t) (rem64>>2) * (uint64_t) recipSqrt32)>>32; |
| sig64Z = ((uint64_t) sig32Z<<32) + ((uint64_t) q<<3); |
| term[indexWord( 4, 3 )] = 0; |
| term[indexWord( 4, 0 )] = 0; |
| /*------------------------------------------------------------------------ |
| | (Repeating this loop is a rare occurrence.) |
| *------------------------------------------------------------------------*/ |
| for (;;) { |
| x64 = ((uint64_t) sig32Z<<32) + sig64Z; |
| term[indexWord( 4, 2 )] = x64>>32; |
| term[indexWord( 4, 1 )] = x64; |
| softfloat_remStep128MBy32( rem, 29, term, q, y ); |
| rem32 = y[indexWord( 4, 3 )]; |
| if ( ! (rem32 & 0x80000000) ) break; |
| --q; |
| sig64Z -= 1<<3; |
| } |
| qs[1] = q; |
| rem64 = (uint64_t) rem32<<32 | y[indexWord( 4, 2 )]; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| q = ((uint32_t) (rem64>>2) * (uint64_t) recipSqrt32)>>32; |
| if ( rem64>>34 ) q += recipSqrt32; |
| sig64Z <<= 1; |
| /*------------------------------------------------------------------------ |
| | (Repeating this loop is a rare occurrence.) |
| *------------------------------------------------------------------------*/ |
| for (;;) { |
| x64 = sig64Z + (q>>26); |
| term[indexWord( 4, 2 )] = x64>>32; |
| term[indexWord( 4, 1 )] = x64; |
| term[indexWord( 4, 0 )] = q<<6; |
| softfloat_remStep128MBy32( |
| y, 29, term, q, &rem[indexMultiwordHi( 6, 4 )] ); |
| rem32 = rem[indexWordHi( 6 )]; |
| if ( ! (rem32 & 0x80000000) ) break; |
| --q; |
| } |
| qs[0] = q; |
| rem64 = (uint64_t) rem32<<32 | rem[indexWord( 6, 4 )]; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| q = (((uint32_t) (rem64>>2) * (uint64_t) recipSqrt32)>>32) + 2; |
| if ( rem64>>34 ) q += recipSqrt32; |
| x64 = (uint64_t) q<<27; |
| y[indexWord( 5, 0 )] = x64; |
| x64 = ((uint64_t) qs[0]<<24) + (x64>>32); |
| y[indexWord( 5, 1 )] = x64; |
| x64 = ((uint64_t) qs[1]<<21) + (x64>>32); |
| y[indexWord( 5, 2 )] = x64; |
| x64 = ((uint64_t) qs[2]<<18) + (x64>>32); |
| y[indexWord( 5, 3 )] = x64; |
| y[indexWord( 5, 4 )] = x64>>32; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| if ( (q & 0xF) <= 2 ) { |
| q &= ~3; |
| y[indexWordLo( 5 )] = q<<27; |
| term[indexWord( 5, 4 )] = 0; |
| term[indexWord( 5, 3 )] = 0; |
| term[indexWord( 5, 2 )] = 0; |
| term[indexWord( 5, 1 )] = q>>6; |
| term[indexWord( 5, 0 )] = q<<26; |
| softfloat_sub160M( y, term, term ); |
| rem[indexWord( 6, 1 )] = 0; |
| rem[indexWord( 6, 0 )] = 0; |
| softfloat_remStep160MBy32( |
| &rem[indexMultiwordLo( 6, 5 )], |
| 14, |
| term, |
| q, |
| &rem[indexMultiwordLo( 6, 5 )] |
| ); |
| rem32 = rem[indexWord( 6, 4 )]; |
| if ( rem32 & 0x80000000 ) { |
| softfloat_sub1X160M( y ); |
| } else { |
| if ( |
| rem32 || rem[indexWord( 6, 0 )] || rem[indexWord( 6, 1 )] |
| || (rem[indexWord( 6, 3 )] | rem[indexWord( 6, 2 )]) |
| ) { |
| y[indexWordLo( 5 )] |= 1; |
| } |
| } |
| } |
| softfloat_roundPackMToF128M( 0, expZ, y, zWPtr ); |
| return; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| invalid: |
| softfloat_invalidF128M( zWPtr ); |
| return; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| copyA: |
| zWPtr[indexWordHi( 4 )] = uiA96; |
| zWPtr[indexWord( 4, 2 )] = aWPtr[indexWord( 4, 2 )]; |
| zWPtr[indexWord( 4, 1 )] = aWPtr[indexWord( 4, 1 )]; |
| zWPtr[indexWord( 4, 0 )] = aWPtr[indexWord( 4, 0 )]; |
| |
| } |
| |
| #endif |
| |
