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
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
|
/*============================================================================
This C source file is part of the SoftPosit Posit Arithmetic Package
by S. H. Leong (Cerlane).
Copyright 2017, 2018 A*STAR. 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 <math.h>
#ifdef SOFTPOSIT_QUAD
#include <quadmath.h>
#endif
#include "platform.h"
#include "internals.h"
#ifdef SOFTPOSIT_QUAD
void checkQuadExtraPX1TwoBits(__float128 f32, __float128 temp, bool * bitsNPlusOne, bool * bitsMore ){
temp /= 2;
if (temp<=f32){
*bitsNPlusOne = 1;
f32-=temp;
}
if (f32>0)
*bitsMore = 1;
}
uint_fast32_t convertQuadFractionPX1(__float128 f32, uint_fast16_t fracLength, bool * bitNPlusOne, bool * bitsMore ){
uint_fast32_t frac=0;
if(f32==0) return 0;
else if(f32==INFINITY) return 0x80000000;
f32 -= 1; //remove hidden bit
if (fracLength==0)
checkQuadExtraPX1TwoBits(f32, 1.0, bitNPlusOne, bitsMore);
else{
__float128 temp = 1;
while (true){
temp /= 2;
if (temp<=f32){
f32-=temp;
fracLength--;
frac = (frac<<1) + 1; //shift in one
if (f32==0){
frac <<= (uint_fast32_t)fracLength;
break;
}
if (fracLength == 0){
checkQuadExtraPX1TwoBits(f32, temp, bitNPlusOne, bitsMore);
break;
}
}
else{
frac <<= 1; //shift in a zero
fracLength--;
if (fracLength == 0){
checkQuadExtraPX1TwoBits(f32, temp, bitNPlusOne, bitsMore);
break;
}
}
}
}
return frac;
}
posit_1_t convertQuadToPX1(__float128 f32, int x){
union ui32_pX1 uZ;
bool sign, regS;
uint_fast32_t reg, frac=0;
int_fast32_t exp=0;
bool bitNPlusOne=0, bitsMore=0;
(f32>=0) ? (sign=0) : (sign=1);
if (f32 == 0 ){
uZ.ui = 0;
return uZ.p;
}
else if(f32 == INFINITY || f32 == -INFINITY || f32 == NAN){
uZ.ui = 0x80000000;
return uZ.p;
}
else if (f32 == 1) {
uZ.ui = 0x40000000;
return uZ.p;
}
else if (f32 == -1){
uZ.ui = 0xC0000000;
return uZ.p;
}
else if (f32>1 || f32<-1){
if (sign){
//Make negative numbers positive for easier computation
f32 = -f32;
}
regS = 1;
reg = 1; //because k = m-1; so need to add back 1
// minpos
if (x==32 && f32 <= 8.673617379884035e-19){
uZ.ui = 1;
}
else{
//regime
while (f32>=4){
f32 *=0.25; // f32/=4;
reg++;
}
if (f32>=2){
f32*=0.5;
exp++;
}
int fracLength = x-3-reg;
if (fracLength<0){
if (reg==x-2){
bitNPlusOne=exp;
exp=0;
}
if(f32>1) bitsMore=1;
}
else
frac = convertQuadFractionPX1 (f32, fracLength, &bitNPlusOne, &bitsMore);
if (reg==30 && frac>0){
bitsMore = 1;
frac = 0;
}
if (reg>(x-2) ){
uZ.ui=(regS) ? (0x7FFFFFFF & ((int32_t)0x80000000>>(x-1)) ): (0x1 << (32-x));
}
//rounding off fraction bits
else{
uint_fast32_t regime = 1;
if (regS) regime = ( (1<<reg)-1 ) <<1;
uZ.ui = ((uint32_t) (regime) << (30-reg)) + ((uint32_t) (exp)<< (29-reg)) + ((uint32_t)(frac<<(32-x)));
//uZ.ui = ((uint32_t) (regime) << (30-reg)) + ((uint32_t) exp ) + ((uint32_t)(frac<<(32-x)));
//minpos
if (uZ.ui==0 && frac>0){
uZ.ui = 0x1 << (32-x);
}
if (bitNPlusOne)
uZ.ui += ( ((uZ.ui>>(32-x)) & 0x1) | bitsMore ) << (32-x);
}
if (sign) uZ.ui = -uZ.ui & 0xFFFFFFFF;
}
}
else if (f32 < 1 || f32 > -1 ){
if (sign){
//Make negative numbers positive for easier computation
f32 = -f32;
}
regS = 0;
reg = 0;
//regime
while (f32<1){
f32 *= 4;
reg++;
}
if (f32>=2){
f32*=0.5;
exp++;
}
int fracLength = x-3-reg;
if (fracLength<0){
if (reg==x-2){
bitNPlusOne=exp;
exp=0;
}
if(f32>1) bitsMore=1;
}
else
frac = convertQuadFractionPX1 (f32, fracLength, &bitNPlusOne, &bitsMore);
if (reg==30 && frac>0){
bitsMore = 1;
frac = 0;
}
if (reg>(x-2) ){
uZ.ui=(regS) ? (0x7FFFFFFF & ((int32_t)0x80000000>>(x-1)) ): (0x1 << (32-x));
}
//rounding off fraction bits
else{
uint_fast32_t regime = 1;
if (regS) regime = ( (1<<reg)-1 ) <<1;
uZ.ui = ((uint32_t) (regime) << (30-reg)) + ((uint32_t) (exp)<< (29-reg)) + ((uint32_t)(frac<<(32-x)));
//uZ.ui = ((uint32_t) (regime) << (30-reg)) + ((uint32_t) exp ) + ((uint32_t)(frac<<(32-x)));
//minpos
if (uZ.ui==0 && frac>0){
uZ.ui = 0x1 << (32-x);
}
if (bitNPlusOne)
uZ.ui += ( ((uZ.ui>>(32-x)) & 0x1) | bitsMore ) << (32-x);
}
if (sign) uZ.ui = -uZ.ui & 0xFFFFFFFF;
}
else {
//NaR - for NaN, INF and all other combinations
uZ.ui = 0x80000000;
}
return uZ.p;
}
#endif
void checkExtraPX1TwoBits(double f32, double temp, bool * bitsNPlusOne, bool * bitsMore ){
temp /= 2;
if (temp<=f32){
*bitsNPlusOne = 1;
f32-=temp;
}
if (f32>0)
*bitsMore = 1;
}
uint_fast32_t convertFractionPX1(double f32, uint_fast16_t fracLength, bool * bitsNPlusOne, bool * bitsMore ){
uint_fast32_t frac=0;
if(f32==0) return 0;
else if(f32==INFINITY) return 0x80000000;
f32 -= 1; //remove hidden bit
if (fracLength==0)
checkExtraPX1TwoBits(f32, 1.0, bitsNPlusOne, bitsMore);
else{
double temp = 1;
while (true){
temp /= 2;
if (temp<=f32){
f32-=temp;
fracLength--;
frac = (frac<<1) + 1; //shift in one
if (f32==0){
frac <<= (uint_fast16_t)fracLength;
break;
}
if (fracLength == 0){
checkExtraPX1TwoBits(f32, temp, bitsNPlusOne, bitsMore);
break;
}
}
else{
frac <<= 1; //shift in a zero
fracLength--;
if (fracLength == 0){
checkExtraPX1TwoBits(f32, temp, bitsNPlusOne, bitsMore);
break;
}
}
}
}
return frac;
}
posit_1_t convertDoubleToPX1(double f32, int x){
union ui32_pX1 uZ;
bool sign, regS;
uint_fast32_t reg, frac=0;
int_fast32_t exp=0;
bool bitNPlusOne=0, bitsMore=0;
(f32>=0) ? (sign=0) : (sign=1);
if (f32 == 0 ){
uZ.ui = 0;
return uZ.p;
}
else if(f32 == INFINITY || f32 == -INFINITY || f32 == NAN){
uZ.ui = 0x80000000;
return uZ.p;
}
else if (f32 == 1) {
uZ.ui = 0x40000000;
return uZ.p;
}
else if (f32 == -1){
uZ.ui = 0xC0000000;
return uZ.p;
}
else if (f32>1 || f32<-1){
if (sign){
//Make negative numbers positive for easier computation
f32 = -f32;
}
regS = 1;
reg = 1; //because k = m-1; so need to add back 1
// minpos
if (x==32 && f32 <= 8.673617379884035e-19){
uZ.ui = 1;
}
else{
//regime
while (f32>=4){
f32 *=0.25; // f32/=4;
reg++;
}
if (f32>=2){
f32*=0.5;
exp++;
}
//printf("reg: %d, exp: %d f32: %.26lf\n", reg, exp, f32);
int fracLength = x-3-reg;
if (fracLength<0){
if (reg==x-2){
bitNPlusOne=exp;
exp=0;
}
if(f32>1) bitsMore=1;
}
else
frac = convertFractionPX1(f32, fracLength, &bitNPlusOne, &bitsMore);
if (reg==30 && frac>0){
bitsMore = 1;
frac = 0;
}
if (reg>(x-2) ){
uZ.ui=(regS) ? (0x7FFFFFFF & ((int32_t)0x80000000>>(x-1)) ): (0x1 << (32-x));
}
//rounding off fraction bits
else{
uint_fast32_t regime = 1;
if (regS) regime = ( (1<<reg)-1 ) <<1;
//printf("reg: %d, exp: %d bitNPlusOne: %d bitsMore: %d\n", reg, exp, bitNPlusOne, bitsMore);
//printBinary(®ime, 32);
uZ.ui = ((uint32_t) (regime) << (30-reg)) + ((uint32_t) (exp)<< (29-reg)) + ((uint32_t)(frac<<(32-x)));
//uZ.ui = ((uint32_t) (regime) << (30-reg)) + ((uint32_t) exp ) + ((uint32_t)(frac<<(32-x)));
//minpos
if (uZ.ui==0 && frac>0){
uZ.ui = 0x1 << (32-x);
}
//printBinary(&uZ.ui, 32);
//uint32_t tt = (uZ.ui>>(32-x));
//printBinary(&tt, 32);
if (bitNPlusOne)
uZ.ui += ( ((uZ.ui>>(32-x)) & 0x1) | bitsMore ) << (32-x);
}
if (sign) uZ.ui = -uZ.ui & 0xFFFFFFFF;
}
}
else if (f32 < 1 || f32 > -1 ){
if (sign){
//Make negative numbers positive for easier computation
f32 = -f32;
}
regS = 0;
reg = 0;
//regime
while (f32<1){
f32 *= 4;
reg++;
}
if (f32>=2){
f32*=0.5;
exp++;
}
int fracLength = x-3-reg;
if (fracLength<0){
if (reg==x-2){
bitNPlusOne=exp;
exp=0;
}
if(f32>1) bitsMore=1;
}
else
frac = convertFractionPX1 (f32, fracLength, &bitNPlusOne, &bitsMore);
if (reg==30 && frac>0){
bitsMore = 1;
frac = 0;
}
if (reg>(x-2) ){
uZ.ui=(regS) ? (0x7FFFFFFF & ((int32_t)0x80000000>>(x-1)) ): (0x1 << (32-x));
}
//rounding off fraction bits
else{
uint_fast32_t regime = 1;
if (regS) regime = ( (1<<reg)-1 ) <<1;
uZ.ui = ((uint32_t) (regime) << (30-reg)) + ((uint32_t) (exp)<< (29-reg)) + ((uint32_t)(frac<<(32-x)));
//uZ.ui = ((uint32_t) (regime) << (30-reg)) + ((uint32_t) exp ) + ((uint32_t)(frac<<(32-x)));
//minpos
if (uZ.ui==0 && frac>0){
uZ.ui = 0x1 << (32-x);
}
if (bitNPlusOne)
uZ.ui += ( ((uZ.ui>>(32-x)) & 0x1) | bitsMore ) << (32-x);
}
if (sign) uZ.ui = -uZ.ui & 0xFFFFFFFF;
}
else {
//NaR - for NaN, INF and all other combinations
uZ.ui = 0x80000000;
}
return uZ.p;
}
|
