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f128_sqrt.c
Go to the documentation of this file.
1
2/*============================================================================
3
4This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
5Package, Release 3e, by John R. Hauser.
6
7Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017 The Regents of the
8University of California. All rights reserved.
9
10Redistribution and use in source and binary forms, with or without
11modification, 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
24THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
25EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
26WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
27DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
28DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
29(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
30LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
31ON 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
33SOFTWARE, 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
45{
46 union ui128_f128 uA;
47 uint_fast64_t uiA64, uiA0;
48 bool signA;
49 int_fast32_t expA;
50 struct uint128 sigA, uiZ;
51 struct exp32_sig128 normExpSig;
52 int_fast32_t expZ;
53 uint_fast32_t sig32A, recipSqrt32, sig32Z;
54 struct uint128 rem;
55 uint32_t qs[3];
57 uint_fast64_t x64, sig64Z;
58 struct uint128 y, term;
59 uint_fast64_t sigZExtra;
60 struct uint128 sigZ;
61 union ui128_f128 uZ;
62
63 /*------------------------------------------------------------------------
64 *------------------------------------------------------------------------*/
65 uA.f = a;
66 uiA64 = uA.ui.v64;
67 uiA0 = uA.ui.v0;
68 signA = signF128UI64( uiA64 );
69 expA = expF128UI64( uiA64 );
70 sigA.v64 = fracF128UI64( uiA64 );
71 sigA.v0 = uiA0;
72 /*------------------------------------------------------------------------
73 *------------------------------------------------------------------------*/
74 if ( expA == 0x7FFF ) {
75 if ( sigA.v64 | sigA.v0 ) {
76 uiZ = softfloat_propagateNaNF128UI( uiA64, uiA0, 0, 0 );
77 goto uiZ;
78 }
79 if ( ! signA ) return a;
80 goto invalid;
81 }
82 /*------------------------------------------------------------------------
83 *------------------------------------------------------------------------*/
84 if ( signA ) {
85 if ( ! (expA | sigA.v64 | sigA.v0) ) return a;
86 goto invalid;
87 }
88 /*------------------------------------------------------------------------
89 *------------------------------------------------------------------------*/
90 if ( ! expA ) {
91 if ( ! (sigA.v64 | sigA.v0) ) return a;
92 normExpSig = softfloat_normSubnormalF128Sig( sigA.v64, sigA.v0 );
93 expA = normExpSig.exp;
94 sigA = normExpSig.sig;
95 }
96 /*------------------------------------------------------------------------
97 | (`sig32Z' is guaranteed to be a lower bound on the square root of
98 | `sig32A', which makes `sig32Z' also a lower bound on the square root of
99 | `sigA'.)
100 *------------------------------------------------------------------------*/
101 expZ = ((expA - 0x3FFF)>>1) + 0x3FFE;
102 expA &= 1;
103 sigA.v64 |= UINT64_C( 0x0001000000000000 );
104 sig32A = sigA.v64>>17;
105 recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A );
106 sig32Z = ((uint_fast64_t) sig32A * recipSqrt32)>>32;
107 if ( expA ) {
108 sig32Z >>= 1;
109 rem = softfloat_shortShiftLeft128( sigA.v64, sigA.v0, 12 );
110 } else {
111 rem = softfloat_shortShiftLeft128( sigA.v64, sigA.v0, 13 );
112 }
113 qs[2] = sig32Z;
114 rem.v64 -= (uint_fast64_t) sig32Z * sig32Z;
115 /*------------------------------------------------------------------------
116 *------------------------------------------------------------------------*/
117 q = ((uint32_t) (rem.v64>>2) * (uint_fast64_t) recipSqrt32)>>32;
118 x64 = (uint_fast64_t) sig32Z<<32;
119 sig64Z = x64 + ((uint_fast64_t) q<<3);
120 y = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
121 /*------------------------------------------------------------------------
122 | (Repeating this loop is a rare occurrence.)
123 *------------------------------------------------------------------------*/
124 for (;;) {
125 term = softfloat_mul64ByShifted32To128( x64 + sig64Z, q );
126 rem = softfloat_sub128( y.v64, y.v0, term.v64, term.v0 );
127 if ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) ) break;
128 --q;
129 sig64Z -= 1<<3;
130 }
131 qs[1] = q;
132 /*------------------------------------------------------------------------
133 *------------------------------------------------------------------------*/
134 q = ((rem.v64>>2) * recipSqrt32)>>32;
135 y = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
136 sig64Z <<= 1;
137 /*------------------------------------------------------------------------
138 | (Repeating this loop is a rare occurrence.)
139 *------------------------------------------------------------------------*/
140 for (;;) {
141 term = softfloat_shortShiftLeft128( 0, sig64Z, 32 );
142 term = softfloat_add128( term.v64, term.v0, 0, (uint_fast64_t) q<<6 );
143 term = softfloat_mul128By32( term.v64, term.v0, q );
144 rem = softfloat_sub128( y.v64, y.v0, term.v64, term.v0 );
145 if ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) ) break;
146 --q;
147 }
148 qs[0] = q;
149 /*------------------------------------------------------------------------
150 *------------------------------------------------------------------------*/
151 q = (((rem.v64>>2) * recipSqrt32)>>32) + 2;
152 sigZExtra = (uint64_t) ((uint_fast64_t) q<<59);
153 term = softfloat_shortShiftLeft128( 0, qs[1], 53 );
154 sigZ =
156 (uint_fast64_t) qs[2]<<18, ((uint_fast64_t) qs[0]<<24) + (q>>5),
157 term.v64, term.v0
158 );
159 /*------------------------------------------------------------------------
160 *------------------------------------------------------------------------*/
161 if ( (q & 0xF) <= 2 ) {
162 q &= ~3;
163 sigZExtra = (uint64_t) ((uint_fast64_t) q<<59);
164 y = softfloat_shortShiftLeft128( sigZ.v64, sigZ.v0, 6 );
165 y.v0 |= sigZExtra>>58;
166 term = softfloat_sub128( y.v64, y.v0, 0, q );
167 y = softfloat_mul64ByShifted32To128( term.v0, q );
168 term = softfloat_mul64ByShifted32To128( term.v64, q );
169 term = softfloat_add128( term.v64, term.v0, 0, y.v64 );
170 rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 20 );
171 term = softfloat_sub128( term.v64, term.v0, rem.v64, rem.v0 );
172 /*--------------------------------------------------------------------
173 | The concatenation of `term' and `y.v0' is now the negative remainder
174 | (3 words altogether).
175 *--------------------------------------------------------------------*/
176 if ( term.v64 & UINT64_C( 0x8000000000000000 ) ) {
177 sigZExtra |= 1;
178 } else {
179 if ( term.v64 | term.v0 | y.v0 ) {
180 if ( sigZExtra ) {
181 --sigZExtra;
182 } else {
183 sigZ = softfloat_sub128( sigZ.v64, sigZ.v0, 0, 1 );
184 sigZExtra = ~0;
185 }
186 }
187 }
188 }
189 return softfloat_roundPackToF128( 0, expZ, sigZ.v64, sigZ.v0, sigZExtra );
190 /*------------------------------------------------------------------------
191 *------------------------------------------------------------------------*/
192 invalid:
194 uiZ.v64 = defaultNaNF128UI64;
195 uiZ.v0 = defaultNaNF128UI0;
196 uiZ:
197 uZ.ui = uiZ;
198 return uZ.f;
199
200}
201
const GenericPointer< typename T::ValueType > T2 T::AllocatorType & a
Definition pointer.h:1181
struct uint128 softfloat_propagateNaNF128UI(uint_fast64_t uiA64, uint_fast64_t uiA0, uint_fast64_t uiB64, uint_fast64_t uiB0)
void softfloat_raiseFlags(uint_fast8_t flags)
#define defaultNaNF128UI64
Definition specialize.h:337
#define defaultNaNF128UI0
Definition specialize.h:339
float128_t f128_sqrt(float128_t a)
Definition f128_sqrt.c:44
uint32_t softfloat_approxRecipSqrt32_1(unsigned int oddExpA, uint32_t a)
@ softfloat_flag_invalid
Definition softfloat.h:89
struct uint128 softfloat_add128(uint64_t a64, uint64_t a0, uint64_t b64, uint64_t b0)
Definition s_add128.c:44
struct uint128 softfloat_mul128By32(uint64_t a64, uint64_t a0, uint32_t b)
struct uint128 softfloat_mul64ByShifted32To128(uint64_t a, uint32_t b)
struct exp32_sig128 softfloat_normSubnormalF128Sig(uint_fast64_t sig64, uint_fast64_t sig0)
float128_t softfloat_roundPackToF128(bool sign, int_fast32_t exp, uint_fast64_t sig64, uint_fast64_t sig0, uint_fast64_t sigExtra)
struct uint128 softfloat_shortShiftLeft128(uint64_t a64, uint64_t a0, uint_fast8_t dist)
struct uint128 softfloat_sub128(uint64_t a64, uint64_t a0, uint64_t b64, uint64_t b0)
Definition s_sub128.c:44
unsigned int uint32_t
Definition stdint.h:126
uint64_t uint_fast64_t
Definition stdint.h:157
#define UINT64_C(val)
Definition stdint.h:284
uint32_t uint_fast32_t
Definition stdint.h:156
int32_t int_fast32_t
Definition stdint.h:152
unsigned __int64 uint64_t
Definition stdint.h:136