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 } 189 190