| |
| /*============================================================================ |
| |
| 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, 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_rem( extFloat80_t a, extFloat80_t b ) |
| { |
| 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; |
| union { struct extFloat80M s; extFloat80_t f; } uB; |
| uint_fast16_t uiB64; |
| uint_fast64_t uiB0; |
| int_fast32_t expB; |
| uint_fast64_t sigB; |
| struct exp32_sig64 normExpSig; |
| int_fast32_t expDiff; |
| struct uint128 rem, shiftedSigB; |
| uint_fast32_t q, recip32; |
| uint_fast64_t q64; |
| struct uint128 term, altRem, meanRem; |
| bool signRem; |
| struct uint128 uiZ; |
| uint_fast16_t uiZ64; |
| uint_fast64_t uiZ0; |
| 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; |
| uB.f = b; |
| uiB64 = uB.s.signExp; |
| uiB0 = uB.s.signif; |
| expB = expExtF80UI64( uiB64 ); |
| sigB = uiB0; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| if ( expA == 0x7FFF ) { |
| if ( |
| (sigA & UINT64_C( 0x7FFFFFFFFFFFFFFF )) |
| || ((expB == 0x7FFF) && (sigB & UINT64_C( 0x7FFFFFFFFFFFFFFF ))) |
| ) { |
| goto propagateNaN; |
| } |
| goto invalid; |
| } |
| if ( expB == 0x7FFF ) { |
| if ( sigB & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) goto propagateNaN; |
| /*-------------------------------------------------------------------- |
| | Argument b is an infinity. Doubling `expB' is an easy way to ensure |
| | that `expDiff' later is less than -1, which will result in returning |
| | a canonicalized version of argument a. |
| *--------------------------------------------------------------------*/ |
| expB += expB; |
| } |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| if ( ! expB ) expB = 1; |
| if ( ! (sigB & UINT64_C( 0x8000000000000000 )) ) { |
| if ( ! sigB ) goto invalid; |
| normExpSig = softfloat_normSubnormalExtF80Sig( sigB ); |
| expB += normExpSig.exp; |
| sigB = normExpSig.sig; |
| } |
| if ( ! expA ) expA = 1; |
| if ( ! (sigA & UINT64_C( 0x8000000000000000 )) ) { |
| if ( ! sigA ) { |
| expA = 0; |
| goto copyA; |
| } |
| normExpSig = softfloat_normSubnormalExtF80Sig( sigA ); |
| expA += normExpSig.exp; |
| sigA = normExpSig.sig; |
| } |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| expDiff = expA - expB; |
| if ( expDiff < -1 ) goto copyA; |
| rem = softfloat_shortShiftLeft128( 0, sigA, 32 ); |
| shiftedSigB = softfloat_shortShiftLeft128( 0, sigB, 32 ); |
| if ( expDiff < 1 ) { |
| if ( expDiff ) { |
| --expB; |
| shiftedSigB = softfloat_shortShiftLeft128( 0, sigB, 33 ); |
| q = 0; |
| } else { |
| q = (sigB <= sigA); |
| if ( q ) { |
| rem = |
| softfloat_sub128( |
| rem.v64, rem.v0, shiftedSigB.v64, shiftedSigB.v0 ); |
| } |
| } |
| } else { |
| recip32 = softfloat_approxRecip32_1( sigB>>32 ); |
| expDiff -= 30; |
| for (;;) { |
| q64 = (uint_fast64_t) (uint32_t) (rem.v64>>2) * recip32; |
| if ( expDiff < 0 ) break; |
| q = (q64 + 0x80000000)>>32; |
| rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 ); |
| term = softfloat_mul64ByShifted32To128( sigB, q ); |
| rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 ); |
| if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) { |
| rem = |
| softfloat_add128( |
| rem.v64, rem.v0, shiftedSigB.v64, shiftedSigB.v0 ); |
| } |
| expDiff -= 29; |
| } |
| /*-------------------------------------------------------------------- |
| | (`expDiff' cannot be less than -29 here.) |
| *--------------------------------------------------------------------*/ |
| q = (uint32_t) (q64>>32)>>(~expDiff & 31); |
| rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, expDiff + 30 ); |
| term = softfloat_mul64ByShifted32To128( sigB, q ); |
| rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 ); |
| if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) { |
| altRem = |
| softfloat_add128( |
| rem.v64, rem.v0, shiftedSigB.v64, shiftedSigB.v0 ); |
| goto selectRem; |
| } |
| } |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| do { |
| altRem = rem; |
| ++q; |
| rem = |
| softfloat_sub128( |
| rem.v64, rem.v0, shiftedSigB.v64, shiftedSigB.v0 ); |
| } while ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) ); |
| selectRem: |
| meanRem = softfloat_add128( rem.v64, rem.v0, altRem.v64, altRem.v0 ); |
| if ( |
| (meanRem.v64 & UINT64_C( 0x8000000000000000 )) |
| || (! (meanRem.v64 | meanRem.v0) && (q & 1)) |
| ) { |
| rem = altRem; |
| } |
| signRem = signA; |
| if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) { |
| signRem = ! signRem; |
| rem = softfloat_sub128( 0, 0, rem.v64, rem.v0 ); |
| } |
| return |
| softfloat_normRoundPackToExtF80( |
| signRem, rem.v64 | rem.v0 ? expB + 32 : 0, rem.v64, rem.v0, 80 ); |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| propagateNaN: |
| uiZ = softfloat_propagateNaNExtF80UI( uiA64, uiA0, uiB64, uiB0 ); |
| uiZ64 = uiZ.v64; |
| uiZ0 = uiZ.v0; |
| goto uiZ; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| invalid: |
| softfloat_raiseFlags( softfloat_flag_invalid ); |
| uiZ64 = defaultNaNExtF80UI64; |
| uiZ0 = defaultNaNExtF80UI0; |
| goto uiZ; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| copyA: |
| if ( expA < 1 ) { |
| sigA >>= 1 - expA; |
| expA = 0; |
| } |
| uiZ64 = packToExtF80UI64( signA, expA ); |
| uiZ0 = sigA; |
| uiZ: |
| uZ.s.signExp = uiZ64; |
| uZ.s.signif = uiZ0; |
| return uZ.f; |
| |
| } |
| |
