softfloat/f64_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, 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 float64_t f64_sqrt( float64_t a )
  45 {
  46     union ui64_f64 uA;
  47     uint_fast64_t uiA;
  48     bool signA;
  49     int_fast16_t expA;
  50     uint_fast64_t sigA, uiZ;
  51     struct exp16_sig64 normExpSig;
  52     int_fast16_t expZ;
  53     uint32_t sig32A, recipSqrt32, sig32Z;
  54     uint_fast64_t rem;
  55     uint32_t q;
  56     uint_fast64_t sigZ, shiftedSigZ;
  57     union ui64_f64 uZ;
  58
  59     /*------------------------------------------------------------------------
  60     *------------------------------------------------------------------------*/
  61     uA.f = a;
  62     uiA = uA.ui;
  63     signA = signF64UI( uiA );
  64     expA  = expF64UI( uiA );
  65     sigA  = fracF64UI( uiA );
  66     /*------------------------------------------------------------------------
  67     *------------------------------------------------------------------------*/
  68     if ( expA == 0x7FF ) {
  69         if ( sigA ) {
  70             uiZ = softfloat_propagateNaNF64UI( uiA, 0 );
  71             goto uiZ;
  72         }
  73         if ( ! signA ) return a;
  74         goto invalid;
  75     }
  76     /*------------------------------------------------------------------------
  77     *------------------------------------------------------------------------*/
  78     if ( signA ) {
  79         if ( ! (expA | sigA) ) return a;
  80         goto invalid;
  81     }
  82     /*------------------------------------------------------------------------
  83     *------------------------------------------------------------------------*/
  84     if ( ! expA ) {
  85         if ( ! sigA ) return a;
  86         normExpSig = softfloat_normSubnormalF64Sig( sigA );
  87         expA = normExpSig.exp;
  88         sigA = normExpSig.sig;
  89     }
  90     /*------------------------------------------------------------------------
  91     | (`sig32Z' is guaranteed to be a lower bound on the square root of
  92     | `sig32A', which makes `sig32Z' also a lower bound on the square root of
  93     | `sigA'.)
  94     *------------------------------------------------------------------------*/
  95     expZ = ((expA - 0x3FF)>>1) + 0x3FE;
  96     expA &= 1;
  97     sigA |= UINT64_C( 0x0010000000000000 );
  98     sig32A = sigA>>21;
  99     recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A );
 100     sig32Z = ((uint_fast64_t) sig32A * recipSqrt32)>>32;
 101     if ( expA ) {
 102         sigA <<= 8;
 103         sig32Z >>= 1;
 104     } else {
 105         sigA <<= 9;
 106     }
 107     rem = sigA - (uint_fast64_t) sig32Z * sig32Z;
 108     q = ((uint32_t) (rem>>2) * (uint_fast64_t) recipSqrt32)>>32;
 109     sigZ = ((uint_fast64_t) sig32Z<<32 | 1<<5) + ((uint_fast64_t) q<<3);
 110     /*------------------------------------------------------------------------
 111     *------------------------------------------------------------------------*/
 112     if ( (sigZ & 0x1FF) < 0x22 ) {
 113         sigZ &= ~(uint_fast64_t) 0x3F;
 114         shiftedSigZ = sigZ>>6;
 115         rem = (sigA<<52) - shiftedSigZ * shiftedSigZ;
 116         if ( rem & UINT64_C( 0x8000000000000000 ) ) {
 117             --sigZ;
 118         } else {
 119             if ( rem ) sigZ |= 1;
 120         }
 121     }
 122     return softfloat_roundPackToF64( 0, expZ, sigZ );
 123     /*------------------------------------------------------------------------
 124     *------------------------------------------------------------------------*/
 125  invalid:
 126     softfloat_raiseFlags( softfloat_flag_invalid );
 127     uiZ = defaultNaNF64UI;
 128  uiZ:
 129     uZ.ui = uiZ;
 130     return uZ.f;
 131
 132 }
 133