softfloat/f128_sqrt.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, 2017 The Regents of the
   8 University of 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_sqrt( float128_t a )
  45 {
  46     union ui128_f128 uA;
  47     uint_fast64_t uiA64, uiA0;
  48     bool signA;
  49     int_fast32_t expA;
  50     struct uint128 sigA, uiZ;
  51     struct exp32_sig128 normExpSig;
  52     int_fast32_t expZ;
  53     uint_fast32_t sig32A, recipSqrt32, sig32Z;
  54     struct uint128 rem;
  55     uint32_t qs[3];
  56     uint_fast32_t q;
  57     uint_fast64_t x64, sig64Z;
  58     struct uint128 y, term;
  59     uint_fast64_t sigZExtra;
  60     struct uint128 sigZ;
  61     union ui128_f128 uZ;
  62
  63     /*------------------------------------------------------------------------
  64     *------------------------------------------------------------------------*/
  65     uA.f = a;
  66     uiA64 = uA.ui.v64;
  67     uiA0  = uA.ui.v0;
  68     signA = signF128UI64( uiA64 );
  69     expA  = expF128UI64( uiA64 );
  70     sigA.v64 = fracF128UI64( uiA64 );
  71     sigA.v0  = uiA0;
  72     /*------------------------------------------------------------------------
  73     *------------------------------------------------------------------------*/
  74     if ( expA == 0x7FFF ) {
  75         if ( sigA.v64 | sigA.v0 ) {
  76             uiZ = softfloat_propagateNaNF128UI( uiA64, uiA0, 0, 0 );
  77             goto uiZ;
  78         }
  79         if ( ! signA ) return a;
  80         goto invalid;
  81     }
  82     /*------------------------------------------------------------------------
  83     *------------------------------------------------------------------------*/
  84     if ( signA ) {
  85         if ( ! (expA | sigA.v64 | sigA.v0) ) return a;
  86         goto invalid;
  87     }
  88     /*------------------------------------------------------------------------
  89     *------------------------------------------------------------------------*/
  90     if ( ! expA ) {
  91         if ( ! (sigA.v64 | sigA.v0) ) return a;
  92         normExpSig = softfloat_normSubnormalF128Sig( sigA.v64, sigA.v0 );
  93         expA = normExpSig.exp;
  94         sigA = normExpSig.sig;
  95     }
  96     /*------------------------------------------------------------------------
  97     | (`sig32Z' is guaranteed to be a lower bound on the square root of
  98     | `sig32A', which makes `sig32Z' also a lower bound on the square root of
  99     | `sigA'.)
 100     *------------------------------------------------------------------------*/
 101     expZ = ((expA - 0x3FFF)>>1) + 0x3FFE;
 102     expA &= 1;
 103     sigA.v64 |= UINT64_C( 0x0001000000000000 );
 104     sig32A = sigA.v64>>17;
 105     recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A );
 106     sig32Z = ((uint_fast64_t) sig32A * recipSqrt32)>>32;
 107     if ( expA ) {
 108         sig32Z >>= 1;
 109         rem = softfloat_shortShiftLeft128( sigA.v64, sigA.v0, 12 );
 110     } else {
 111         rem = softfloat_shortShiftLeft128( sigA.v64, sigA.v0, 13 );
 112     }
 113     qs[2] = sig32Z;
 114     rem.v64 -= (uint_fast64_t) sig32Z * sig32Z;
 115     /*------------------------------------------------------------------------
 116     *------------------------------------------------------------------------*/
 117     q = ((uint32_t) (rem.v64>>2) * (uint_fast64_t) recipSqrt32)>>32;
 118     x64 = (uint_fast64_t) sig32Z<<32;
 119     sig64Z = x64 + ((uint_fast64_t) q<<3);
 120     y = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
 121     /*------------------------------------------------------------------------
 122     | (Repeating this loop is a rare occurrence.)
 123     *------------------------------------------------------------------------*/
 124     for (;;) {
 125         term = softfloat_mul64ByShifted32To128( x64 + sig64Z, q );
 126         rem = softfloat_sub128( y.v64, y.v0, term.v64, term.v0 );
 127         if ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) ) break;
 128         --q;
 129         sig64Z -= 1<<3;
 130     }
 131     qs[1] = q;
 132     /*------------------------------------------------------------------------
 133     *------------------------------------------------------------------------*/
 134     q = ((rem.v64>>2) * recipSqrt32)>>32;
 135     y = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
 136     sig64Z <<= 1;
 137     /*------------------------------------------------------------------------
 138     | (Repeating this loop is a rare occurrence.)
 139     *------------------------------------------------------------------------*/
 140     for (;;) {
 141         term = softfloat_shortShiftLeft128( 0, sig64Z, 32 );
 142         term = softfloat_add128( term.v64, term.v0, 0, (uint_fast64_t) q<<6 );
 143         term = softfloat_mul128By32( term.v64, term.v0, q );
 144         rem = softfloat_sub128( y.v64, y.v0, term.v64, term.v0 );
 145         if ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) ) break;
 146         --q;
 147     }
 148     qs[0] = q;
 149     /*------------------------------------------------------------------------
 150     *------------------------------------------------------------------------*/
 151     q = (((rem.v64>>2) * recipSqrt32)>>32) + 2;
 152     sigZExtra = (uint64_t) ((uint_fast64_t) q<<59);
 153     term = softfloat_shortShiftLeft128( 0, qs[1], 53 );
 154     sigZ =
 155         softfloat_add128(
 156             (uint_fast64_t) qs[2]<<18, ((uint_fast64_t) qs[0]<<24) + (q>>5),
 157             term.v64, term.v0
 158         );
 159     /*------------------------------------------------------------------------
 160     *------------------------------------------------------------------------*/
 161     if ( (q & 0xF) <= 2 ) {
 162         q &= ~3;
 163         sigZExtra = (uint64_t) ((uint_fast64_t) q<<59);
 164         y = softfloat_shortShiftLeft128( sigZ.v64, sigZ.v0, 6 );
 165         y.v0 |= sigZExtra>>58;
 166         term = softfloat_sub128( y.v64, y.v0, 0, q );
 167         y    = softfloat_mul64ByShifted32To128( term.v0,  q );
 168         term = softfloat_mul64ByShifted32To128( term.v64, q );
 169         term = softfloat_add128( term.v64, term.v0, 0, y.v64 );
 170         rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 20 );
 171         term = softfloat_sub128( term.v64, term.v0, rem.v64, rem.v0 );
 172         /*--------------------------------------------------------------------
 173         | The concatenation of `term' and `y.v0' is now the negative remainder
 174         | (3 words altogether).
 175         *--------------------------------------------------------------------*/
 176         if ( term.v64 & UINT64_C( 0x8000000000000000 ) ) {
 177             sigZExtra |= 1;
 178         } else {
 179             if ( term.v64 | term.v0 | y.v0 ) {
 180                 if ( sigZExtra ) {
 181                     --sigZExtra;
 182                 } else {
 183                     sigZ = softfloat_sub128( sigZ.v64, sigZ.v0, 0, 1 );
 184                     sigZExtra = ~0;
 185                 }
 186             }
 187         }
 188     }
 189     return softfloat_roundPackToF128( 0, expZ, sigZ.v64, sigZ.v0, sigZExtra );
 190     /*------------------------------------------------------------------------
 191     *------------------------------------------------------------------------*/
 192  invalid:
 193     softfloat_raiseFlags( softfloat_flag_invalid );
 194     uiZ.v64 = defaultNaNF128UI64;
 195     uiZ.v0  = defaultNaNF128UI0;
 196  uiZ:
 197     uZ.ui = uiZ;
 198     return uZ.f;
 199
 200 }
 201