1 // SPDX-License-Identifier: BSD-3-Clause
2
3 /*============================================================================
4
5 This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
6 Package, Release 3a, by John R. Hauser.
7
8 Copyright 2011, 2012, 2013, 2014 The Regents of the University of California.
9 All rights reserved.
10
11 Redistribution and use in source and binary forms, with or without
12 modification, are permitted provided that the following conditions are met:
13
14 1. Redistributions of source code must retain the above copyright notice,
15 this list of conditions, and the following disclaimer.
16
17 2. Redistributions in binary form must reproduce the above copyright notice,
18 this list of conditions, and the following disclaimer in the documentation
19 and/or other materials provided with the distribution.
20
21 3. Neither the name of the University nor the names of its contributors may
22 be used to endorse or promote products derived from this software without
23 specific prior written permission.
24
25 THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
26 EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
27 WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
28 DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
29 DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
30 (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
31 LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
32 ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
33 (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
34 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
35
36 =============================================================================*/
37
38 #include <stdbool.h>
39 #include <stdint.h>
40 #include "platform.h"
41 #include "internals.h"
42 #include "specialize.h"
43 #include "softfloat.h"
44
f64_sqrt(float64_t a)45 float64_t f64_sqrt( float64_t a )
46 {
47 union ui64_f64 uA;
48 uint_fast64_t uiA;
49 bool signA;
50 int_fast16_t expA;
51 uint_fast64_t sigA, uiZ;
52 struct exp16_sig64 normExpSig;
53 int_fast16_t expZ;
54 uint32_t sig32A, recipSqrt32, sig32Z;
55 uint_fast64_t rem;
56 uint32_t q;
57 uint_fast64_t sigZ, shiftedSigZ;
58 union ui64_f64 uZ;
59
60 /*------------------------------------------------------------------------
61 *------------------------------------------------------------------------*/
62 uA.f = a;
63 uiA = uA.ui;
64 signA = signF64UI( uiA );
65 expA = expF64UI( uiA );
66 sigA = fracF64UI( uiA );
67 /*------------------------------------------------------------------------
68 *------------------------------------------------------------------------*/
69 if ( expA == 0x7FF ) {
70 if ( sigA ) {
71 uiZ = softfloat_propagateNaNF64UI( uiA, 0 );
72 goto uiZ;
73 }
74 if ( ! signA ) return a;
75 goto invalid;
76 }
77 /*------------------------------------------------------------------------
78 *------------------------------------------------------------------------*/
79 if ( signA ) {
80 if ( ! (expA | sigA) ) return a;
81 goto invalid;
82 }
83 /*------------------------------------------------------------------------
84 *------------------------------------------------------------------------*/
85 if ( ! expA ) {
86 if ( ! sigA ) return a;
87 normExpSig = softfloat_normSubnormalF64Sig( sigA );
88 expA = normExpSig.exp;
89 sigA = normExpSig.sig;
90 }
91 /*------------------------------------------------------------------------
92 | (`sig32Z' is guaranteed to be a lower bound on the square root of
93 | `sig32A', which makes `sig32Z' also a lower bound on the square root of
94 | `sigA'.)
95 *------------------------------------------------------------------------*/
96 expZ = ((expA - 0x3FF)>>1) + 0x3FE;
97 expA &= 1;
98 sigA |= UINT64_C( 0x0010000000000000 );
99 sig32A = sigA>>21;
100 recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A );
101 sig32Z = ((uint_fast64_t) sig32A * recipSqrt32)>>32;
102 if ( expA ) {
103 sigA <<= 8;
104 sig32Z >>= 1;
105 } else {
106 sigA <<= 9;
107 }
108 rem = sigA - (uint_fast64_t) sig32Z * sig32Z;
109 q = ((uint32_t) (rem>>2) * (uint_fast64_t) recipSqrt32)>>32;
110 sigZ = ((uint_fast64_t) sig32Z<<32 | 1<<5) + ((uint_fast64_t) q<<3);
111 /*------------------------------------------------------------------------
112 *------------------------------------------------------------------------*/
113 if ( (sigZ & 0x1FF) < 1<<5 ) {
114 sigZ &= ~(uint_fast64_t) 0x3F;
115 shiftedSigZ = sigZ>>6;
116 rem = (sigA<<52) - shiftedSigZ * shiftedSigZ;
117 if ( rem & UINT64_C( 0x8000000000000000 ) ) {
118 --sigZ;
119 } else {
120 if ( rem ) sigZ |= 1;
121 }
122 }
123 return softfloat_roundPackToF64( 0, expZ, sigZ );
124 /*------------------------------------------------------------------------
125 *------------------------------------------------------------------------*/
126 invalid:
127 softfloat_raiseFlags( softfloat_flag_invalid );
128 uiZ = defaultNaNF64UI;
129 uiZ:
130 uZ.ui = uiZ;
131 return uZ.f;
132
133 }
134
135