softfloat/f128_rem.c

   1
   2 /*============================================================================
   3
   4 This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
   5 Package, Release 3d, by John R. Hauser.
   6
   7 Copyright 2011, 2012, 2013, 2014, 2015, 2016 The Regents of the University of
   8 California.  All rights reserved.
   9
  10 Redistribution and use in source and binary forms, with or without
  11 modification, are permitted provided that the following conditions are met:
  12
  13  1. Redistributions of source code must retain the above copyright notice,
  14     this list of conditions, and the following disclaimer.
  15
  16  2. Redistributions in binary form must reproduce the above copyright notice,
  17     this list of conditions, and the following disclaimer in the documentation
  18     and/or other materials provided with the distribution.
  19
  20  3. Neither the name of the University nor the names of its contributors may
  21     be used to endorse or promote products derived from this software without
  22     specific prior written permission.
  23
  24 THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
  25 EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
  26 WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
  27 DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
  28 DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
  29 (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  30 LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
  31 ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  32 (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  33 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  34
  35 =============================================================================*/
  36
  37 #include <stdbool.h>
  38 #include <stdint.h>
  39 #include "platform.h"
  40 #include "internals.h"
  41 #include "specialize.h"
  42 #include "softfloat.h"
  43
  44 float128_t f128_rem( float128_t a, float128_t b )
  45 {
  46     union ui128_f128 uA;
  47     uint_fast64_t uiA64, uiA0;
  48     bool signA;
  49     int_fast32_t expA;
  50     struct uint128 sigA;
  51     union ui128_f128 uB;
  52     uint_fast64_t uiB64, uiB0;
  53     int_fast32_t expB;
  54     struct uint128 sigB;
  55     struct exp32_sig128 normExpSig;
  56     struct uint128 rem;
  57     int_fast32_t expDiff;
  58     uint_fast32_t q, recip32;
  59     uint_fast64_t q64;
  60     struct uint128 term, altRem, meanRem;
  61     bool signRem;
  62     struct uint128 uiZ;
  63     union ui128_f128 uZ;
  64
  65     /*------------------------------------------------------------------------
  66     *------------------------------------------------------------------------*/
  67     uA.f = a;
  68     uiA64 = uA.ui.v64;
  69     uiA0  = uA.ui.v0;
  70     signA = signF128UI64( uiA64 );
  71     expA  = expF128UI64( uiA64 );
  72     sigA.v64 = fracF128UI64( uiA64 );
  73     sigA.v0  = uiA0;
  74     uB.f = b;
  75     uiB64 = uB.ui.v64;
  76     uiB0  = uB.ui.v0;
  77     expB  = expF128UI64( uiB64 );
  78     sigB.v64 = fracF128UI64( uiB64 );
  79     sigB.v0  = uiB0;
  80     /*------------------------------------------------------------------------
  81     *------------------------------------------------------------------------*/
  82     if ( expA == 0x7FFF ) {
  83         if (
  84             (sigA.v64 | sigA.v0) || ((expB == 0x7FFF) && (sigB.v64 | sigB.v0))
  85         ) {
  86             goto propagateNaN;
  87         }
  88         goto invalid;
  89     }
  90     if ( expB == 0x7FFF ) {
  91         if ( sigB.v64 | sigB.v0 ) goto propagateNaN;
  92         return a;
  93     }
  94     /*------------------------------------------------------------------------
  95     *------------------------------------------------------------------------*/
  96     if ( ! expB ) {
  97         if ( ! (sigB.v64 | sigB.v0) ) goto invalid;
  98         normExpSig = softfloat_normSubnormalF128Sig( sigB.v64, sigB.v0 );
  99         expB = normExpSig.exp;
 100         sigB = normExpSig.sig;
 101     }
 102     if ( ! expA ) {
 103         if ( ! (sigA.v64 | sigA.v0) ) return a;
 104         normExpSig = softfloat_normSubnormalF128Sig( sigA.v64, sigA.v0 );
 105         expA = normExpSig.exp;
 106         sigA = normExpSig.sig;
 107     }
 108     /*------------------------------------------------------------------------
 109     *------------------------------------------------------------------------*/
 110     sigA.v64 |= UINT64_C( 0x0001000000000000 );
 111     sigB.v64 |= UINT64_C( 0x0001000000000000 );
 112     rem = sigA;
 113     expDiff = expA - expB;
 114     if ( expDiff < 1 ) {
 115         if ( expDiff < -1 ) return a;
 116         if ( expDiff ) {
 117             --expB;
 118             sigB = softfloat_add128( sigB.v64, sigB.v0, sigB.v64, sigB.v0 );
 119             q = 0;
 120         } else {
 121             q = softfloat_le128( sigB.v64, sigB.v0, rem.v64, rem.v0 );
 122             if ( q ) {
 123                 rem = softfloat_sub128( rem.v64, rem.v0, sigB.v64, sigB.v0 );
 124             }
 125         }
 126     } else {
 127         recip32 = softfloat_approxRecip32_1( sigB.v64>>17 );
 128         expDiff -= 30;
 129         for (;;) {
 130             q64 = (uint_fast64_t) (uint32_t) (rem.v64>>19) * recip32;
 131             if ( expDiff < 0 ) break;
 132             q = (q64 + 0x80000000)>>32;
 133             rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
 134             term = softfloat_mul128By32( sigB.v64, sigB.v0, q );
 135             rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
 136             if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
 137                 rem = softfloat_add128( rem.v64, rem.v0, sigB.v64, sigB.v0 );
 138             }
 139             expDiff -= 29;
 140         }
 141         /*--------------------------------------------------------------------
 142         | (`expDiff' cannot be less than -29 here.)
 143         *--------------------------------------------------------------------*/
 144         q = (uint32_t) (q64>>32)>>(~expDiff & 31);
 145         rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, expDiff + 30 );
 146         term = softfloat_mul128By32( sigB.v64, sigB.v0, q );
 147         rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
 148         if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
 149             altRem = softfloat_add128( rem.v64, rem.v0, sigB.v64, sigB.v0 );
 150             goto selectRem;
 151         }
 152     }
 153     /*------------------------------------------------------------------------
 154     *------------------------------------------------------------------------*/
 155     do {
 156         altRem = rem;
 157         ++q;
 158         rem = softfloat_sub128( rem.v64, rem.v0, sigB.v64, sigB.v0 );
 159     } while ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) );
 160  selectRem:
 161     meanRem = softfloat_add128( rem.v64, rem.v0, altRem.v64, altRem.v0 );
 162     if (
 163         (meanRem.v64 & UINT64_C( 0x8000000000000000 ))
 164             || (! (meanRem.v64 | meanRem.v0) && (q & 1))
 165     ) {
 166         rem = altRem;
 167     }
 168     signRem = signA;
 169     if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
 170         signRem = ! signRem;
 171         rem = softfloat_sub128( 0, 0, rem.v64, rem.v0 );
 172     }
 173     return softfloat_normRoundPackToF128( signRem, expB - 1, rem.v64, rem.v0 );
 174     /*------------------------------------------------------------------------
 175     *------------------------------------------------------------------------*/
 176  propagateNaN:
 177     uiZ = softfloat_propagateNaNF128UI( uiA64, uiA0, uiB64, uiB0 );
 178     goto uiZ;
 179     /*------------------------------------------------------------------------
 180     *------------------------------------------------------------------------*/
 181  invalid:
 182     softfloat_raiseFlags( softfloat_flag_invalid );
 183     uiZ.v64 = defaultNaNF128UI64;
 184     uiZ.v0  = defaultNaNF128UI0;
 185  uiZ:
 186     uZ.ui = uiZ;
 187     return uZ.f;
 188
 189 }
 190