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 #ifdef SOFTFLOAT_FAST_INT64 45 46 void f128M_sqrt( const float128_t *aPtr, float128_t *zPtr ) 47 { 48 49 *zPtr = f128_sqrt( *aPtr ); 50 51 } 52 53 #else 54 55 void f128M_sqrt( const float128_t *aPtr, float128_t *zPtr ) 56 { 57 const uint32_t *aWPtr; 58 uint32_t *zWPtr; 59 uint32_t uiA96; 60 bool signA; 61 int32_t rawExpA; 62 uint32_t rem[6]; 63 int32_t expA, expZ; 64 uint64_t rem64; 65 uint32_t sig32A, recipSqrt32, sig32Z, qs[3], q; 66 uint64_t sig64Z, x64; 67 uint32_t term[5], y[5], rem32; 68 69 /*------------------------------------------------------------------------ 70 *------------------------------------------------------------------------*/ 71 aWPtr = (const uint32_t *) aPtr; 72 zWPtr = (uint32_t *) zPtr; 73 /*------------------------------------------------------------------------ 74 *------------------------------------------------------------------------*/ 75 uiA96 = aWPtr[indexWordHi( 4 )]; 76 signA = signF128UI96( uiA96 ); 77 rawExpA = expF128UI96( uiA96 ); 78 /*------------------------------------------------------------------------ 79 *------------------------------------------------------------------------*/ 80 if ( rawExpA == 0x7FFF ) { 81 if ( 82 fracF128UI96( uiA96 ) 83 || (aWPtr[indexWord( 4, 2 )] | aWPtr[indexWord( 4, 1 )] 84 | aWPtr[indexWord( 4, 0 )]) 85 ) { 86 softfloat_propagateNaNF128M( aWPtr, 0, zWPtr ); 87 return; 88 } 89 if ( ! signA ) goto copyA; 90 goto invalid; 91 } 92 /*------------------------------------------------------------------------ 93 *------------------------------------------------------------------------*/ 94 expA = softfloat_shiftNormSigF128M( aWPtr, 13 - (rawExpA & 1), rem ); 95 if ( expA == -128 ) goto copyA; 96 if ( signA ) goto invalid; 97 /*------------------------------------------------------------------------ 98 | (`sig32Z' is guaranteed to be a lower bound on the square root of 99 | `sig32A', which makes `sig32Z' also a lower bound on the square root of 100 | `sigA'.) 101 *------------------------------------------------------------------------*/ 102 expZ = ((expA - 0x3FFF)>>1) + 0x3FFE; 103 expA &= 1; 104 rem64 = (uint64_t) rem[indexWord( 4, 3 )]<<32 | rem[indexWord( 4, 2 )]; 105 if ( expA ) { 106 if ( ! rawExpA ) { 107 softfloat_shortShiftRight128M( rem, 1, rem ); 108 rem64 >>= 1; 109 } 110 sig32A = rem64>>29; 111 } else { 112 sig32A = rem64>>30; 113 } 114 recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A ); 115 sig32Z = ((uint64_t) sig32A * recipSqrt32)>>32; 116 if ( expA ) sig32Z >>= 1; 117 qs[2] = sig32Z; 118 rem64 -= (uint64_t) sig32Z * sig32Z; 119 rem[indexWord( 4, 3 )] = rem64>>32; 120 rem[indexWord( 4, 2 )] = rem64; 121 /*------------------------------------------------------------------------ 122 *------------------------------------------------------------------------*/ 123 q = ((uint32_t) (rem64>>2) * (uint64_t) recipSqrt32)>>32; 124 qs[1] = q; 125 sig64Z = ((uint64_t) sig32Z<<32) + ((uint64_t) q<<3); 126 x64 = ((uint64_t) sig32Z<<32) + sig64Z; 127 term[indexWord( 4, 3 )] = 0; 128 term[indexWord( 4, 2 )] = x64>>32; 129 term[indexWord( 4, 1 )] = x64; 130 term[indexWord( 4, 0 )] = 0; 131 softfloat_remStep128MBy32( rem, 29, term, q, y ); 132 rem64 = (uint64_t) y[indexWord( 4, 3 )]<<32 | y[indexWord( 4, 2 )]; 133 /*------------------------------------------------------------------------ 134 *------------------------------------------------------------------------*/ 135 q = ((uint32_t) (rem64>>2) * (uint64_t) recipSqrt32)>>32; 136 sig64Z <<= 1; 137 /*------------------------------------------------------------------------ 138 | (Repeating this loop is a rare occurrence.) 139 *------------------------------------------------------------------------*/ 140 for (;;) { 141 x64 = sig64Z + (q>>26); 142 term[indexWord( 4, 2 )] = x64>>32; 143 term[indexWord( 4, 1 )] = x64; 144 term[indexWord( 4, 0 )] = q<<6; 145 term[indexWord( 4, 3 )] = 0; 146 softfloat_remStep128MBy32( 147 y, 29, term, q, &rem[indexMultiwordHi( 6, 4 )] ); 148 rem32 = rem[indexWordHi( 6 )]; 149 if ( ! (rem32 & 0x80000000) ) break; 150 --q; 151 } 152 qs[0] = q; 153 rem64 = (uint64_t) rem32<<32 | rem[indexWord( 6, 4 )]; 154 /*------------------------------------------------------------------------ 155 *------------------------------------------------------------------------*/ 156 q = (((uint32_t) (rem64>>2) * (uint64_t) recipSqrt32)>>32) + 2; 157 x64 = (uint64_t) q<<27; 158 y[indexWord( 5, 0 )] = x64; 159 x64 = ((uint64_t) qs[0]<<24) + (x64>>32); 160 y[indexWord( 5, 1 )] = x64; 161 x64 = ((uint64_t) qs[1]<<21) + (x64>>32); 162 y[indexWord( 5, 2 )] = x64; 163 x64 = ((uint64_t) qs[2]<<18) + (x64>>32); 164 y[indexWord( 5, 3 )] = x64; 165 y[indexWord( 5, 4 )] = x64>>32; 166 /*------------------------------------------------------------------------ 167 *------------------------------------------------------------------------*/ 168 if ( (q & 0xF) <= 2 ) { 169 q &= ~3; 170 y[indexWordLo( 5 )] = q<<27; 171 term[indexWord( 5, 4 )] = 0; 172 term[indexWord( 5, 3 )] = 0; 173 term[indexWord( 5, 2 )] = 0; 174 term[indexWord( 5, 1 )] = q>>6; 175 term[indexWord( 5, 0 )] = q<<26; 176 softfloat_sub160M( y, term, term ); 177 rem[indexWord( 6, 1 )] = 0; 178 rem[indexWord( 6, 0 )] = 0; 179 softfloat_remStep160MBy32( 180 &rem[indexMultiwordLo( 6, 5 )], 181 14, 182 term, 183 q, 184 &rem[indexMultiwordLo( 6, 5 )] 185 ); 186 rem32 = rem[indexWord( 6, 4 )]; 187 if ( rem32 & 0x80000000 ) { 188 softfloat_sub1X160M( y ); 189 } else { 190 if ( 191 rem32 || rem[indexWord( 6, 0 )] || rem[indexWord( 6, 1 )] 192 || (rem[indexWord( 6, 3 )] | rem[indexWord( 6, 2 )]) 193 ) { 194 y[indexWordLo( 5 )] |= 1; 195 } 196 } 197 } 198 softfloat_roundPackMToF128M( 0, expZ, y, zWPtr ); 199 return; 200 /*------------------------------------------------------------------------ 201 *------------------------------------------------------------------------*/ 202 invalid: 203 softfloat_invalidF128M( zWPtr ); 204 return; 205 /*------------------------------------------------------------------------ 206 *------------------------------------------------------------------------*/ 207 copyA: 208 zWPtr[indexWordHi( 4 )] = uiA96; 209 zWPtr[indexWord( 4, 2 )] = aWPtr[indexWord( 4, 2 )]; 210 zWPtr[indexWord( 4, 1 )] = aWPtr[indexWord( 4, 1 )]; 211 zWPtr[indexWord( 4, 0 )] = aWPtr[indexWord( 4, 0 )]; 212 213 } 214 215 #endif 216 217