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_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) < 1<<5 ) { 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 } 133 134