softfloat/f64_rem.c

   1
   2 /*============================================================================
   3
   4 This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
   5 Package, Release 3a, by John R. Hauser.
   6
   7 Copyright 2011, 2012, 2013, 2014 The Regents of the University of California.
   8 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 float64_t f64_rem( float64_t a, float64_t b )
  45 {
  46     union ui64_f64 uA;
  47     uint_fast64_t uiA;
  48     bool signA;
  49     int_fast16_t expA;
  50     uint_fast64_t sigA;
  51     union ui64_f64 uB;
  52     uint_fast64_t uiB;
  53     int_fast16_t expB;
  54     uint_fast64_t sigB;
  55     struct exp16_sig64 normExpSig;
  56     uint64_t rem;
  57     int_fast16_t expDiff;
  58     uint32_t q, recip32;
  59     uint_fast64_t q64;
  60     uint64_t altRem, meanRem;
  61     bool signRem;
  62     uint_fast64_t uiZ;
  63     union ui64_f64 uZ;
  64
  65     /*------------------------------------------------------------------------
  66     *------------------------------------------------------------------------*/
  67     uA.f = a;
  68     uiA = uA.ui;
  69     signA = signF64UI( uiA );
  70     expA  = expF64UI( uiA );
  71     sigA  = fracF64UI( uiA );
  72     uB.f = b;
  73     uiB = uB.ui;
  74     expB = expF64UI( uiB );
  75     sigB = fracF64UI( uiB );
  76     /*------------------------------------------------------------------------
  77     *------------------------------------------------------------------------*/
  78     if ( expA == 0x7FF ) {
  79         if ( sigA || ((expB == 0x7FF) && sigB) ) goto propagateNaN;
  80         goto invalid;
  81     }
  82     if ( expB == 0x7FF ) {
  83         if ( sigB ) goto propagateNaN;
  84         return a;
  85     }
  86     /*------------------------------------------------------------------------
  87     *------------------------------------------------------------------------*/
  88     if ( expA < expB - 1 ) return a;
  89     /*------------------------------------------------------------------------
  90     *------------------------------------------------------------------------*/
  91     if ( ! expB ) {
  92         if ( ! sigB ) goto invalid;
  93         normExpSig = softfloat_normSubnormalF64Sig( sigB );
  94         expB = normExpSig.exp;
  95         sigB = normExpSig.sig;
  96     }
  97     if ( ! expA ) {
  98         if ( ! sigA ) return a;
  99         normExpSig = softfloat_normSubnormalF64Sig( sigA );
 100         expA = normExpSig.exp;
 101         sigA = normExpSig.sig;
 102     }
 103     /*------------------------------------------------------------------------
 104     *------------------------------------------------------------------------*/
 105     rem = sigA | UINT64_C( 0x0010000000000000 );
 106     sigB |= UINT64_C( 0x0010000000000000 );
 107     expDiff = expA - expB;
 108     if ( expDiff < 1 ) {
 109         if ( expDiff < -1 ) return a;
 110         sigB <<= 9;
 111         if ( expDiff ) {
 112             rem <<= 8;
 113             q = 0;
 114         } else {
 115             rem <<= 9;
 116             q = (sigB <= rem);
 117             if ( q ) rem -= sigB;
 118         }
 119     } else {
 120         recip32 = softfloat_approxRecip32_1( sigB>>21 );
 121         /*--------------------------------------------------------------------
 122         | Changing the shift of `rem' here requires also changing the initial
 123         | subtraction from `expDiff'.
 124         *--------------------------------------------------------------------*/
 125         rem <<= 9;
 126         expDiff -= 30;
 127         /*--------------------------------------------------------------------
 128         | The scale of `sigB' affects how many bits are obtained during each
 129         | cycle of the loop.  Currently this is 29 bits per loop iteration,
 130         | the maximum possible.
 131         *--------------------------------------------------------------------*/
 132         sigB <<= 9;
 133         for (;;) {
 134             q64 = (uint32_t) (rem>>32) * (uint_fast64_t) recip32;
 135             if ( expDiff < 0 ) break;
 136             q = (q64 + 0x80000000)>>32;
 137 #ifdef SOFTFLOAT_FAST_INT64
 138             rem <<= 29;
 139 #else
 140             rem = (uint_fast64_t) (uint32_t) (rem>>3)<<32;
 141 #endif
 142             rem -= q * (uint64_t) sigB;
 143             if ( rem & UINT64_C( 0x8000000000000000 ) ) rem += sigB;
 144             expDiff -= 29;
 145         }
 146         /*--------------------------------------------------------------------
 147         | (`expDiff' cannot be less than -29 here.)
 148         *--------------------------------------------------------------------*/
 149         q = (uint32_t) (q64>>32)>>(~expDiff & 31);
 150         rem = (rem<<(expDiff + 30)) - q * (uint64_t) sigB;
 151         if ( rem & UINT64_C( 0x8000000000000000 ) ) {
 152             altRem = rem + sigB;
 153             goto selectRem;
 154         }
 155     }
 156     /*------------------------------------------------------------------------
 157     *------------------------------------------------------------------------*/
 158     do {
 159         altRem = rem;
 160         ++q;
 161         rem -= sigB;
 162     } while ( ! (rem & UINT64_C( 0x8000000000000000 )) );
 163  selectRem:
 164     meanRem = rem + altRem;
 165     if (
 166         (meanRem & UINT64_C( 0x8000000000000000 )) || (! meanRem && (q & 1))
 167     ) {
 168         rem = altRem;
 169     }
 170     signRem = signA;
 171     if ( rem & UINT64_C( 0x8000000000000000 ) ) {
 172         signRem = ! signRem;
 173         rem = -rem;
 174     }
 175     return softfloat_normRoundPackToF64( signRem, expB, rem );
 176     /*------------------------------------------------------------------------
 177     *------------------------------------------------------------------------*/
 178  propagateNaN:
 179     uiZ = softfloat_propagateNaNF64UI( uiA, uiB );
 180     goto uiZ;
 181  invalid:
 182     softfloat_raiseFlags( softfloat_flag_invalid );
 183     uiZ = defaultNaNF64UI;
 184  uiZ:
 185     uZ.ui = uiZ;
 186     return uZ.f;
 187
 188 }
 189