softfloat/source/extF80M_sqrt.c

   1
   2 /*============================================================================
   3
   4 This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
   5 Package, Release 3e, by John R. Hauser.
   6
   7 Copyright 2011, 2012, 2013, 2014, 2015, 2017 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 #ifdef SOFTFLOAT_FAST_INT64
  45
  46 void extF80M_sqrt( const extFloat80_t *aPtr, extFloat80_t *zPtr )
  47 {
  48
  49     *zPtr = extF80_sqrt( *aPtr );
  50
  51 }
  52
  53 #else
  54
  55 void extF80M_sqrt( const extFloat80_t *aPtr, extFloat80_t *zPtr )
  56 {
  57     const struct extFloat80M *aSPtr;
  58     struct extFloat80M *zSPtr;
  59     uint_fast16_t uiA64, signUI64;
  60     int32_t expA;
  61     uint64_t rem64;
  62     int32_t expZ;
  63     uint32_t rem96[3], sig32A, recipSqrt32, sig32Z, q;
  64     uint64_t sig64Z, x64;
  65     uint32_t rem32, term[4], rem[4], extSigZ[3];
  66
  67     /*------------------------------------------------------------------------
  68     *------------------------------------------------------------------------*/
  69     aSPtr = (const struct extFloat80M *) aPtr;
  70     zSPtr = (struct extFloat80M *) zPtr;
  71     /*------------------------------------------------------------------------
  72     *------------------------------------------------------------------------*/
  73     uiA64 = aSPtr->signExp;
  74     signUI64 = uiA64 & packToExtF80UI64( 1, 0 );
  75     expA = expExtF80UI64( uiA64 );
  76     rem64 = aSPtr->signif;
  77     /*------------------------------------------------------------------------
  78     *------------------------------------------------------------------------*/
  79     if ( expA == 0x7FFF ) {
  80         if ( rem64 & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) {
  81             softfloat_propagateNaNExtF80M( aSPtr, 0, zSPtr );
  82             return;
  83         }
  84         if ( signUI64 ) goto invalid;
  85         rem64 = UINT64_C( 0x8000000000000000 );
  86         goto copyA;
  87     }
  88     /*------------------------------------------------------------------------
  89     *------------------------------------------------------------------------*/
  90     if ( ! expA ) expA = 1;
  91     if ( ! (rem64 & UINT64_C( 0x8000000000000000 )) ) {
  92         if ( ! rem64 ) {
  93             uiA64 = signUI64;
  94             goto copyA;
  95         }
  96         expA += softfloat_normExtF80SigM( &rem64 );
  97     }
  98     if ( signUI64 ) goto invalid;
  99     /*------------------------------------------------------------------------
 100     *------------------------------------------------------------------------*/
 101     expZ = ((expA - 0x3FFF)>>1) + 0x3FFF;
 102     expA &= 1;
 103     softfloat_shortShiftLeft64To96M( rem64, 30 - expA, rem96 );
 104     sig32A = rem64>>32;
 105     recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A );
 106     sig32Z = ((uint64_t) sig32A * recipSqrt32)>>32;
 107     if ( expA ) sig32Z >>= 1;
 108     rem64 =
 109         ((uint64_t) rem96[indexWord( 3, 2 )]<<32 | rem96[indexWord( 3, 1 )])
 110             - (uint64_t) sig32Z * sig32Z;
 111     rem96[indexWord( 3, 2 )] = rem64>>32;
 112     rem96[indexWord( 3, 1 )] = rem64;
 113     /*------------------------------------------------------------------------
 114     *------------------------------------------------------------------------*/
 115     q = ((uint32_t) (rem64>>2) * (uint64_t) recipSqrt32)>>32;
 116     sig64Z = ((uint64_t) sig32Z<<32) + ((uint64_t) q<<3);
 117     term[indexWord( 3, 2 )] = 0;
 118     /*------------------------------------------------------------------------
 119     | (Repeating this loop is a rare occurrence.)
 120     *------------------------------------------------------------------------*/
 121     for (;;) {
 122         x64 = ((uint64_t) sig32Z<<32) + sig64Z;
 123         term[indexWord( 3, 1 )] = x64>>32;
 124         term[indexWord( 3, 0 )] = x64;
 125         softfloat_remStep96MBy32(
 126             rem96, 29, term, q, &rem[indexMultiwordHi( 4, 3 )] );
 127         rem32 = rem[indexWord( 4, 3 )];
 128         if ( ! (rem32 & 0x80000000) ) break;
 129         --q;
 130         sig64Z -= 1<<3;
 131     }
 132     rem64 = (uint64_t) rem32<<32 | rem[indexWord( 4, 2 )];
 133     /*------------------------------------------------------------------------
 134     *------------------------------------------------------------------------*/
 135     q = (((uint32_t) (rem64>>2) * (uint64_t) recipSqrt32)>>32) + 2;
 136     if ( rem64>>34 ) q += recipSqrt32;
 137     x64 = (uint64_t) q<<7;
 138     extSigZ[indexWord( 3, 0 )] = x64;
 139     x64 = (sig64Z<<1) + (x64>>32);
 140     extSigZ[indexWord( 3, 2 )] = x64>>32;
 141     extSigZ[indexWord( 3, 1 )] = x64;
 142     /*------------------------------------------------------------------------
 143     *------------------------------------------------------------------------*/
 144     if ( (q & 0xFFFFFF) <= 2 ) {
 145         q &= ~(uint32_t) 0xFFFF;
 146         extSigZ[indexWordLo( 3 )] = q<<7;
 147         x64 = sig64Z + (q>>27);
 148         term[indexWord( 4, 3 )] = 0;
 149         term[indexWord( 4, 2 )] = x64>>32;
 150         term[indexWord( 4, 1 )] = x64;
 151         term[indexWord( 4, 0 )] = q<<5;
 152         rem[indexWord( 4, 0 )] = 0;
 153         softfloat_remStep128MBy32( rem, 28, term, q, rem );
 154         q = rem[indexWordHi( 4 )];
 155         if ( q & 0x80000000 ) {
 156             softfloat_sub1X96M( extSigZ );
 157         } else {
 158             if ( q || rem[indexWord( 4, 1 )] || rem[indexWord( 4, 2 )] ) {
 159                 extSigZ[indexWordLo( 3 )] |= 1;
 160             }
 161         }
 162     }
 163     softfloat_roundPackMToExtF80M(
 164         0, expZ, extSigZ, extF80_roundingPrecision, zSPtr );
 165     return;
 166     /*------------------------------------------------------------------------
 167     *------------------------------------------------------------------------*/
 168  invalid:
 169     softfloat_invalidExtF80M( zSPtr );
 170     return;
 171     /*------------------------------------------------------------------------
 172     *------------------------------------------------------------------------*/
 173  copyA:
 174     zSPtr->signExp = uiA64;
 175     zSPtr->signif  = rem64;
 176
 177 }
 178
 179 #endif
 180