1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
|
/*============================================================================
This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
Package, Release 3e, by John R. Hauser.
Copyright 2011, 2012, 2013, 2014 The Regents of the University of California.
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice,
this list of conditions, and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
this list of conditions, and the following disclaimer in the documentation
and/or other materials provided with the distribution.
3. Neither the name of the University nor the names of its contributors may
be used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
=============================================================================*/
#include <stdbool.h>
#include <stdint.h>
#include "platform.h"
#include "internals.h"
#include "specialize.h"
#include "softfloat.h"
float128_t f128_div( float128_t a, float128_t b )
{
union ui128_f128 uA;
uint_fast64_t uiA64, uiA0;
bool signA;
int_fast32_t expA;
struct uint128 sigA;
union ui128_f128 uB;
uint_fast64_t uiB64, uiB0;
bool signB;
int_fast32_t expB;
struct uint128 sigB;
bool signZ;
struct exp32_sig128 normExpSig;
int_fast32_t expZ;
struct uint128 rem;
uint_fast32_t recip32;
int ix;
uint_fast64_t q64;
uint_fast32_t q;
struct uint128 term;
uint_fast32_t qs[3];
uint_fast64_t sigZExtra;
struct uint128 sigZ, uiZ;
union ui128_f128 uZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
uA.f = a;
uiA64 = uA.ui.v64;
uiA0 = uA.ui.v0;
signA = signF128UI64( uiA64 );
expA = expF128UI64( uiA64 );
sigA.v64 = fracF128UI64( uiA64 );
sigA.v0 = uiA0;
uB.f = b;
uiB64 = uB.ui.v64;
uiB0 = uB.ui.v0;
signB = signF128UI64( uiB64 );
expB = expF128UI64( uiB64 );
sigB.v64 = fracF128UI64( uiB64 );
sigB.v0 = uiB0;
signZ = signA ^ signB;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( expA == 0x7FFF ) {
if ( sigA.v64 | sigA.v0 ) goto propagateNaN;
if ( expB == 0x7FFF ) {
if ( sigB.v64 | sigB.v0 ) goto propagateNaN;
goto invalid;
}
goto infinity;
}
if ( expB == 0x7FFF ) {
if ( sigB.v64 | sigB.v0 ) goto propagateNaN;
goto zero;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( ! expB ) {
if ( ! (sigB.v64 | sigB.v0) ) {
if ( ! (expA | sigA.v64 | sigA.v0) ) goto invalid;
softfloat_raiseFlags( softfloat_flag_infinite );
goto infinity;
}
normExpSig = softfloat_normSubnormalF128Sig( sigB.v64, sigB.v0 );
expB = normExpSig.exp;
sigB = normExpSig.sig;
}
if ( ! expA ) {
if ( ! (sigA.v64 | sigA.v0) ) goto zero;
normExpSig = softfloat_normSubnormalF128Sig( sigA.v64, sigA.v0 );
expA = normExpSig.exp;
sigA = normExpSig.sig;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
expZ = expA - expB + 0x3FFE;
sigA.v64 |= UINT64_C( 0x0001000000000000 );
sigB.v64 |= UINT64_C( 0x0001000000000000 );
rem = sigA;
if ( softfloat_lt128( sigA.v64, sigA.v0, sigB.v64, sigB.v0 ) ) {
--expZ;
rem = softfloat_add128( sigA.v64, sigA.v0, sigA.v64, sigA.v0 );
}
recip32 = softfloat_approxRecip32_1( sigB.v64>>17 );
ix = 3;
for (;;) {
q64 = (uint_fast64_t) (uint32_t) (rem.v64>>19) * recip32;
q = (q64 + 0x80000000)>>32;
--ix;
if ( ix < 0 ) break;
rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
term = softfloat_mul128By32( sigB.v64, sigB.v0, q );
rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
--q;
rem = softfloat_add128( rem.v64, rem.v0, sigB.v64, sigB.v0 );
}
qs[ix] = q;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( ((q + 1) & 7) < 2 ) {
rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
term = softfloat_mul128By32( sigB.v64, sigB.v0, q );
rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
--q;
rem = softfloat_add128( rem.v64, rem.v0, sigB.v64, sigB.v0 );
} else if ( softfloat_le128( sigB.v64, sigB.v0, rem.v64, rem.v0 ) ) {
++q;
rem = softfloat_sub128( rem.v64, rem.v0, sigB.v64, sigB.v0 );
}
if ( rem.v64 | rem.v0 ) q |= 1;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
sigZExtra = (uint64_t) ((uint_fast64_t) q<<60);
term = softfloat_shortShiftLeft128( 0, qs[1], 54 );
sigZ =
softfloat_add128(
(uint_fast64_t) qs[2]<<19, ((uint_fast64_t) qs[0]<<25) + (q>>4),
term.v64, term.v0
);
return
softfloat_roundPackToF128( signZ, expZ, sigZ.v64, sigZ.v0, sigZExtra );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
propagateNaN:
uiZ = softfloat_propagateNaNF128UI( uiA64, uiA0, uiB64, uiB0 );
goto uiZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
invalid:
softfloat_raiseFlags( softfloat_flag_invalid );
uiZ.v64 = defaultNaNF128UI64;
uiZ.v0 = defaultNaNF128UI0;
goto uiZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
infinity:
uiZ.v64 = packToF128UI64( signZ, 0x7FFF, 0 );
goto uiZ0;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
zero:
uiZ.v64 = packToF128UI64( signZ, 0, 0 );
uiZ0:
uiZ.v0 = 0;
uiZ:
uZ.ui = uiZ;
return uZ.f;
}
|
