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
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
|
/*============================================================================
This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
Package, Release 3d, by John R. Hauser.
Copyright 2011, 2012, 2013, 2014, 2015, 2016 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
softfloat_mulAddF128(
uint_fast64_t uiA64,
uint_fast64_t uiA0,
uint_fast64_t uiB64,
uint_fast64_t uiB0,
uint_fast64_t uiC64,
uint_fast64_t uiC0,
uint_fast8_t op
)
{
bool signA;
int_fast32_t expA;
struct uint128 sigA;
bool signB;
int_fast32_t expB;
struct uint128 sigB;
bool signC;
int_fast32_t expC;
struct uint128 sigC;
bool signZ;
uint_fast64_t magBits;
struct uint128 uiZ;
struct exp32_sig128 normExpSig;
int_fast32_t expZ;
uint64_t sig256Z[4];
struct uint128 sigZ;
int_fast32_t shiftDist, expDiff;
struct uint128 x128;
uint64_t sig256C[4];
static uint64_t zero256[4] = INIT_UINTM4( 0, 0, 0, 0 );
uint_fast64_t sigZExtra, sig256Z0;
union ui128_f128 uZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
signA = signF128UI64( uiA64 );
expA = expF128UI64( uiA64 );
sigA.v64 = fracF128UI64( uiA64 );
sigA.v0 = uiA0;
signB = signF128UI64( uiB64 );
expB = expF128UI64( uiB64 );
sigB.v64 = fracF128UI64( uiB64 );
sigB.v0 = uiB0;
signC = signF128UI64( uiC64 ) ^ (op == softfloat_mulAdd_subC);
expC = expF128UI64( uiC64 );
sigC.v64 = fracF128UI64( uiC64 );
sigC.v0 = uiC0;
signZ = signA ^ signB ^ (op == softfloat_mulAdd_subProd);
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( expA == 0x7FFF ) {
if (
(sigA.v64 | sigA.v0) || ((expB == 0x7FFF) && (sigB.v64 | sigB.v0))
) {
goto propagateNaN_ABC;
}
magBits = expB | sigB.v64 | sigB.v0;
goto infProdArg;
}
if ( expB == 0x7FFF ) {
if ( sigB.v64 | sigB.v0 ) goto propagateNaN_ABC;
magBits = expA | sigA.v64 | sigA.v0;
goto infProdArg;
}
if ( expC == 0x7FFF ) {
if ( sigC.v64 | sigC.v0 ) {
uiZ.v64 = 0;
uiZ.v0 = 0;
goto propagateNaN_ZC;
}
uiZ.v64 = uiC64;
uiZ.v0 = uiC0;
goto uiZ;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( ! expA ) {
if ( ! (sigA.v64 | sigA.v0) ) goto zeroProd;
normExpSig = softfloat_normSubnormalF128Sig( sigA.v64, sigA.v0 );
expA = normExpSig.exp;
sigA = normExpSig.sig;
}
if ( ! expB ) {
if ( ! (sigB.v64 | sigB.v0) ) goto zeroProd;
normExpSig = softfloat_normSubnormalF128Sig( sigB.v64, sigB.v0 );
expB = normExpSig.exp;
sigB = normExpSig.sig;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
expZ = expA + expB - 0x3FFE;
sigA.v64 |= UINT64_C( 0x0001000000000000 );
sigB.v64 |= UINT64_C( 0x0001000000000000 );
sigA = softfloat_shortShiftLeft128( sigA.v64, sigA.v0, 8 );
sigB = softfloat_shortShiftLeft128( sigB.v64, sigB.v0, 15 );
softfloat_mul128To256M( sigA.v64, sigA.v0, sigB.v64, sigB.v0, sig256Z );
sigZ.v64 = sig256Z[indexWord( 4, 3 )];
sigZ.v0 = sig256Z[indexWord( 4, 2 )];
shiftDist = 0;
if ( ! (sigZ.v64 & UINT64_C( 0x0100000000000000 )) ) {
--expZ;
shiftDist = -1;
}
if ( ! expC ) {
if ( ! (sigC.v64 | sigC.v0) ) {
shiftDist += 8;
goto sigZ;
}
normExpSig = softfloat_normSubnormalF128Sig( sigC.v64, sigC.v0 );
expC = normExpSig.exp;
sigC = normExpSig.sig;
}
sigC.v64 |= UINT64_C( 0x0001000000000000 );
sigC = softfloat_shortShiftLeft128( sigC.v64, sigC.v0, 8 );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
expDiff = expZ - expC;
if ( expDiff < 0 ) {
expZ = expC;
if ( (signZ == signC) || (expDiff < -1) ) {
shiftDist -= expDiff;
if ( shiftDist ) {
sigZ =
softfloat_shiftRightJam128( sigZ.v64, sigZ.v0, shiftDist );
}
} else {
if ( ! shiftDist ) {
x128 =
softfloat_shortShiftRight128(
sig256Z[indexWord( 4, 1 )], sig256Z[indexWord( 4, 0 )],
1
);
sig256Z[indexWord( 4, 1 )] = (sigZ.v0<<63) | x128.v64;
sig256Z[indexWord( 4, 0 )] = x128.v0;
sigZ = softfloat_shortShiftRight128( sigZ.v64, sigZ.v0, 1 );
sig256Z[indexWord( 4, 3 )] = sigZ.v64;
sig256Z[indexWord( 4, 2 )] = sigZ.v0;
}
}
} else {
if ( shiftDist ) softfloat_add256M( sig256Z, sig256Z, sig256Z );
if ( ! expDiff ) {
sigZ.v64 = sig256Z[indexWord( 4, 3 )];
sigZ.v0 = sig256Z[indexWord( 4, 2 )];
} else {
sig256C[indexWord( 4, 3 )] = sigC.v64;
sig256C[indexWord( 4, 2 )] = sigC.v0;
sig256C[indexWord( 4, 1 )] = 0;
sig256C[indexWord( 4, 0 )] = 0;
softfloat_shiftRightJam256M( sig256C, expDiff, sig256C );
}
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
shiftDist = 8;
if ( signZ == signC ) {
/*--------------------------------------------------------------------
*--------------------------------------------------------------------*/
if ( expDiff <= 0 ) {
sigZ = softfloat_add128( sigC.v64, sigC.v0, sigZ.v64, sigZ.v0 );
} else {
softfloat_add256M( sig256Z, sig256C, sig256Z );
sigZ.v64 = sig256Z[indexWord( 4, 3 )];
sigZ.v0 = sig256Z[indexWord( 4, 2 )];
}
if ( sigZ.v64 & UINT64_C( 0x0200000000000000 ) ) {
++expZ;
shiftDist = 9;
}
} else {
/*--------------------------------------------------------------------
*--------------------------------------------------------------------*/
if ( expDiff < 0 ) {
signZ = signC;
if ( expDiff < -1 ) {
sigZ =
softfloat_sub128( sigC.v64, sigC.v0, sigZ.v64, sigZ.v0 );
sigZExtra =
sig256Z[indexWord( 4, 1 )] | sig256Z[indexWord( 4, 0 )];
if ( sigZExtra ) {
sigZ = softfloat_sub128( sigZ.v64, sigZ.v0, 0, 1 );
}
if ( ! (sigZ.v64 & UINT64_C( 0x0100000000000000 )) ) {
--expZ;
shiftDist = 7;
}
goto shiftRightRoundPack;
} else {
sig256C[indexWord( 4, 3 )] = sigC.v64;
sig256C[indexWord( 4, 2 )] = sigC.v0;
sig256C[indexWord( 4, 1 )] = 0;
sig256C[indexWord( 4, 0 )] = 0;
softfloat_sub256M( sig256C, sig256Z, sig256Z );
}
} else if ( ! expDiff ) {
sigZ = softfloat_sub128( sigZ.v64, sigZ.v0, sigC.v64, sigC.v0 );
if (
! (sigZ.v64 | sigZ.v0) && ! sig256Z[indexWord( 4, 1 )]
&& ! sig256Z[indexWord( 4, 0 )]
) {
goto completeCancellation;
}
sig256Z[indexWord( 4, 3 )] = sigZ.v64;
sig256Z[indexWord( 4, 2 )] = sigZ.v0;
if ( sigZ.v64 & UINT64_C( 0x8000000000000000 ) ) {
signZ = ! signZ;
softfloat_sub256M( zero256, sig256Z, sig256Z );
}
} else {
softfloat_sub256M( sig256Z, sig256C, sig256Z );
if ( 1 < expDiff ) {
sigZ.v64 = sig256Z[indexWord( 4, 3 )];
sigZ.v0 = sig256Z[indexWord( 4, 2 )];
if ( ! (sigZ.v64 & UINT64_C( 0x0100000000000000 )) ) {
--expZ;
shiftDist = 7;
}
goto sigZ;
}
}
/*--------------------------------------------------------------------
*--------------------------------------------------------------------*/
sigZ.v64 = sig256Z[indexWord( 4, 3 )];
sigZ.v0 = sig256Z[indexWord( 4, 2 )];
sigZExtra = sig256Z[indexWord( 4, 1 )];
sig256Z0 = sig256Z[indexWord( 4, 0 )];
if ( sigZ.v64 ) {
if ( sig256Z0 ) sigZExtra |= 1;
} else {
expZ -= 64;
sigZ.v64 = sigZ.v0;
sigZ.v0 = sigZExtra;
sigZExtra = sig256Z0;
if ( ! sigZ.v64 ) {
expZ -= 64;
sigZ.v64 = sigZ.v0;
sigZ.v0 = sigZExtra;
sigZExtra = 0;
if ( ! sigZ.v64 ) {
expZ -= 64;
sigZ.v64 = sigZ.v0;
sigZ.v0 = 0;
}
}
}
shiftDist = softfloat_countLeadingZeros64( sigZ.v64 );
expZ += 7 - shiftDist;
shiftDist = 15 - shiftDist;
if ( 0 < shiftDist ) goto shiftRightRoundPack;
if ( shiftDist ) {
shiftDist = -shiftDist;
sigZ = softfloat_shortShiftLeft128( sigZ.v64, sigZ.v0, shiftDist );
x128 = softfloat_shortShiftLeft128( 0, sigZExtra, shiftDist );
sigZ.v0 |= x128.v64;
sigZExtra = x128.v0;
}
goto roundPack;
}
sigZ:
sigZExtra = sig256Z[indexWord( 4, 1 )] | sig256Z[indexWord( 4, 0 )];
shiftRightRoundPack:
sigZExtra = (uint64_t) (sigZ.v0<<(64 - shiftDist)) | (sigZExtra != 0);
sigZ = softfloat_shortShiftRight128( sigZ.v64, sigZ.v0, shiftDist );
roundPack:
return
softfloat_roundPackToF128(
signZ, expZ - 1, sigZ.v64, sigZ.v0, sigZExtra );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
propagateNaN_ABC:
uiZ = softfloat_propagateNaNF128UI( uiA64, uiA0, uiB64, uiB0 );
goto propagateNaN_ZC;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
infProdArg:
if ( magBits ) {
uiZ.v64 = packToF128UI64( signZ, 0x7FFF, 0 );
uiZ.v0 = 0;
if ( expC != 0x7FFF ) goto uiZ;
if ( sigC.v64 | sigC.v0 ) goto propagateNaN_ZC;
if ( signZ == signC ) goto uiZ;
}
softfloat_raiseFlags( softfloat_flag_invalid );
uiZ.v64 = defaultNaNF128UI64;
uiZ.v0 = defaultNaNF128UI0;
propagateNaN_ZC:
uiZ = softfloat_propagateNaNF128UI( uiZ.v64, uiZ.v0, uiC64, uiC0 );
goto uiZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
zeroProd:
uiZ.v64 = uiC64;
uiZ.v0 = uiC0;
if ( ! (expC | sigC.v64 | sigC.v0) && (signZ != signC) ) {
completeCancellation:
uiZ.v64 =
packToF128UI64(
(softfloat_roundingMode == softfloat_round_min), 0, 0 );
uiZ.v0 = 0;
}
uiZ:
uZ.ui = uiZ;
return uZ.f;
}
|
