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, 2015 The Regents of the University of
9 California. 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
extF80_sqrt(extFloat80_t a)45 extFloat80_t extF80_sqrt( extFloat80_t a )
46 {
47 union { struct extFloat80M s; extFloat80_t f; } uA;
48 uint_fast16_t uiA64;
49 uint_fast64_t uiA0;
50 bool signA;
51 int_fast32_t expA;
52 uint_fast64_t sigA;
53 struct uint128 uiZ;
54 uint_fast16_t uiZ64;
55 uint_fast64_t uiZ0;
56 struct exp32_sig64 normExpSig;
57 int_fast32_t expZ;
58 uint_fast32_t sig32A, recipSqrt32, sig32Z;
59 struct uint128 rem;
60 uint_fast64_t q, sigZ, x64;
61 struct uint128 term;
62 uint_fast64_t sigZExtra;
63 union { struct extFloat80M s; extFloat80_t f; } uZ;
64
65 /*------------------------------------------------------------------------
66 *------------------------------------------------------------------------*/
67 uA.f = a;
68 uiA64 = uA.s.signExp;
69 uiA0 = uA.s.signif;
70 signA = signExtF80UI64( uiA64 );
71 expA = expExtF80UI64( uiA64 );
72 sigA = uiA0;
73 /*------------------------------------------------------------------------
74 *------------------------------------------------------------------------*/
75 if ( expA == 0x7FFF ) {
76 if ( sigA & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) {
77 uiZ = softfloat_propagateNaNExtF80UI( uiA64, uiA0, 0, 0 );
78 uiZ64 = uiZ.v64;
79 uiZ0 = uiZ.v0;
80 goto uiZ;
81 }
82 if ( ! signA ) return a;
83 goto invalid;
84 }
85 /*------------------------------------------------------------------------
86 *------------------------------------------------------------------------*/
87 if ( signA ) {
88 if ( ! sigA ) goto zero;
89 goto invalid;
90 }
91 /*------------------------------------------------------------------------
92 *------------------------------------------------------------------------*/
93 if ( ! expA ) expA = 1;
94 if ( ! (sigA & UINT64_C( 0x8000000000000000 )) ) {
95 if ( ! sigA ) goto zero;
96 normExpSig = softfloat_normSubnormalExtF80Sig( sigA );
97 expA += normExpSig.exp;
98 sigA = normExpSig.sig;
99 }
100 /*------------------------------------------------------------------------
101 | (`sig32Z' is guaranteed to be a lower bound on the square root of
102 | `sig32A', which makes `sig32Z' also a lower bound on the square root of
103 | `sigA'.)
104 *------------------------------------------------------------------------*/
105 expZ = ((expA - 0x3FFF)>>1) + 0x3FFF;
106 expA &= 1;
107 sig32A = sigA>>32;
108 recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A );
109 sig32Z = ((uint_fast64_t) sig32A * recipSqrt32)>>32;
110 if ( expA ) {
111 sig32Z >>= 1;
112 rem = softfloat_shortShiftLeft128( 0, sigA, 61 );
113 } else {
114 rem = softfloat_shortShiftLeft128( 0, sigA, 62 );
115 }
116 rem.v64 -= (uint_fast64_t) sig32Z * sig32Z;
117 /*------------------------------------------------------------------------
118 *------------------------------------------------------------------------*/
119 q = ((uint_fast64_t) (uint32_t) (rem.v64>>2) * recipSqrt32)>>32;
120 sigZ = ((uint_fast64_t) sig32Z<<32) + (q<<3);
121 x64 = ((uint_fast64_t) sig32Z<<32) + sigZ;
122 term = softfloat_mul64ByShifted32To128( x64, q );
123 rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
124 rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
125 /*------------------------------------------------------------------------
126 *------------------------------------------------------------------------*/
127 q = (((uint_fast64_t) (uint32_t) (rem.v64>>2) * recipSqrt32)>>32) + 2;
128 x64 = sigZ;
129 sigZ = (sigZ<<1) + (q>>25);
130 sigZExtra = (uint64_t) (q<<39);
131 /*------------------------------------------------------------------------
132 *------------------------------------------------------------------------*/
133 if ( (q & 0xFFFFFF) <= 2 ) {
134 q &= ~(uint_fast64_t) 0xFFFF;
135 sigZExtra = (uint64_t) (q<<39);
136 term = softfloat_mul64ByShifted32To128( x64 + (q>>27), q );
137 x64 = (uint_fast64_t) (uint32_t) (q<<5) * (uint32_t) q;
138 term = softfloat_add128( term.v64, term.v0, 0, x64 );
139 rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 28 );
140 rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
141 if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
142 if ( ! sigZExtra ) --sigZ;
143 --sigZExtra;
144 } else {
145 if ( rem.v64 | rem.v0 ) sigZExtra |= 1;
146 }
147 }
148 return
149 softfloat_roundPackToExtF80(
150 0, expZ, sigZ, sigZExtra, extF80_roundingPrecision );
151 /*------------------------------------------------------------------------
152 *------------------------------------------------------------------------*/
153 invalid:
154 softfloat_raiseFlags( softfloat_flag_invalid );
155 uiZ64 = defaultNaNExtF80UI64;
156 uiZ0 = defaultNaNExtF80UI0;
157 goto uiZ;
158 /*------------------------------------------------------------------------
159 *------------------------------------------------------------------------*/
160 zero:
161 uiZ64 = packToExtF80UI64( signA, 0 );
162 uiZ0 = 0;
163 uiZ:
164 uZ.s.signExp = uiZ64;
165 uZ.s.signif = uiZ0;
166 return uZ.f;
167
168 }
169
170