-
Notifications
You must be signed in to change notification settings - Fork 3
/
avx_mathfun.h
715 lines (570 loc) · 22.4 KB
/
avx_mathfun.h
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
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
#pragma once
/*
AVX implementation of sin, cos, sincos, exp and log
Based on "sse_mathfun.h", by Julien Pommier
http://gruntthepeon.free.fr/ssemath/
Copyright (C) 2012 Giovanni Garberoglio
Interdisciplinary Laboratory for Computational Science (LISC)
Fondazione Bruno Kessler and University of Trento
via Sommarive, 18
I-38123 Trento (Italy)
This software is provided 'as-is', without any express or implied
warranty. In no event will the authors be held liable for any damages
arising from the use of this software.
Permission is granted to anyone to use this software for any purpose,
including commercial applications, and to alter it and redistribute it
freely, subject to the following restrictions:
1. The origin of this software must not be misrepresented; you must not
claim that you wrote the original software. If you use this software
in a product, an acknowledgment in the product documentation would be
appreciated but is not required.
2. Altered source versions must be plainly marked as such, and must not be
misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.
(this is the zlib license)
*/
#include <ATen/native/cpu/Intrinsics.h>
/* yes I know, the top of this file is quite ugly */
#if defined(__GNUC__)
# define ALIGN32_BEG __attribute__((aligned(32)))
#elif defined(_WIN32)
# define ALIGN32_BEG __declspec(align(32))
#endif
/* __m128 is ugly to write */
typedef __m256 v8sf; // vector of 8 float (avx)
typedef __m256i v8si; // vector of 8 int (avx)
typedef __m128i v4si; // vector of 8 int (avx)
#define _PI32AVX_CONST(Name, Val) \
static const ALIGN32_BEG int _pi32avx_##Name[4] = { Val, Val, Val, Val }
_PI32AVX_CONST(1, 1);
_PI32AVX_CONST(inv1, ~1);
_PI32AVX_CONST(2, 2);
_PI32AVX_CONST(4, 4);
/* declare some AVX constants -- why can't I figure a better way to do that? */
#define _PS256_CONST(Name, Val) \
static const ALIGN32_BEG float _ps256_##Name[8] = { Val, Val, Val, Val, Val, Val, Val, Val }
#define _PI32_CONST256(Name, Val) \
static const ALIGN32_BEG int _pi32_256_##Name[8] = { Val, Val, Val, Val, Val, Val, Val, Val }
#define _PS256_CONST_TYPE(Name, Type, Val) \
static const ALIGN32_BEG Type _ps256_##Name[8] = { Val, Val, Val, Val, Val, Val, Val, Val }
_PS256_CONST(1 , 1.0f);
_PS256_CONST(0p5, 0.5f);
/* the smallest non denormalized float number */
_PS256_CONST_TYPE(min_norm_pos, int, 0x00800000);
_PS256_CONST_TYPE(mant_mask, int, 0x7f800000);
_PS256_CONST_TYPE(inv_mant_mask, int, ~0x7f800000);
_PS256_CONST_TYPE(sign_mask, int, (int)0x80000000);
_PS256_CONST_TYPE(inv_sign_mask, int, ~0x80000000);
_PI32_CONST256(0, 0);
_PI32_CONST256(1, 1);
_PI32_CONST256(inv1, ~1);
_PI32_CONST256(2, 2);
_PI32_CONST256(4, 4);
_PI32_CONST256(0x7f, 0x7f);
_PS256_CONST(cephes_SQRTHF, 0.707106781186547524);
_PS256_CONST(cephes_log_p0, 7.0376836292E-2);
_PS256_CONST(cephes_log_p1, - 1.1514610310E-1);
_PS256_CONST(cephes_log_p2, 1.1676998740E-1);
_PS256_CONST(cephes_log_p3, - 1.2420140846E-1);
_PS256_CONST(cephes_log_p4, + 1.4249322787E-1);
_PS256_CONST(cephes_log_p5, - 1.6668057665E-1);
_PS256_CONST(cephes_log_p6, + 2.0000714765E-1);
_PS256_CONST(cephes_log_p7, - 2.4999993993E-1);
_PS256_CONST(cephes_log_p8, + 3.3333331174E-1);
_PS256_CONST(cephes_log_q1, -2.12194440e-4);
_PS256_CONST(cephes_log_q2, 0.693359375);
#ifndef CPU_CAPABILITY_AVX2
typedef union imm_xmm_union {
v8si imm;
v4si xmm[2];
} imm_xmm_union;
#define COPY_IMM_TO_XMM(imm_, xmm0_, xmm1_) { \
imm_xmm_union u __attribute__((aligned(32))); \
u.imm = imm_; \
xmm0_ = u.xmm[0]; \
xmm1_ = u.xmm[1]; \
}
#define COPY_XMM_TO_IMM(xmm0_, xmm1_, imm_) { \
imm_xmm_union u __attribute__((aligned(32))); \
u.xmm[0]=xmm0_; u.xmm[1]=xmm1_; imm_ = u.imm; \
}
#define AVX2_BITOP_USING_SSE2(fn) \
static inline v8si _mm256_##fn(v8si x, int a) \
{ \
/* use SSE2 instruction to perform the bitop AVX2 */ \
v4si x1, x2; \
v8si ret; \
COPY_IMM_TO_XMM(x, x1, x2); \
x1 = _mm_##fn(x1,a); \
x2 = _mm_##fn(x2,a); \
COPY_XMM_TO_IMM(x1, x2, ret); \
return(ret); \
}
#warning "Using SSE2 to perform AVX2 bitshift ops"
AVX2_BITOP_USING_SSE2(slli_epi32)
AVX2_BITOP_USING_SSE2(srli_epi32)
#define AVX2_INTOP_USING_SSE2(fn) \
static inline v8si _mm256_##fn(v8si x, v8si y) \
{ \
/* use SSE2 instructions to perform the AVX2 integer operation */ \
v4si x1, x2; \
v4si y1, y2; \
v8si ret; \
COPY_IMM_TO_XMM(x, x1, x2); \
COPY_IMM_TO_XMM(y, y1, y2); \
x1 = _mm_##fn(x1,y1); \
x2 = _mm_##fn(x2,y2); \
COPY_XMM_TO_IMM(x1, x2, ret); \
return(ret); \
}
#warning "Using SSE2 to perform AVX2 integer ops"
AVX2_INTOP_USING_SSE2(and_si128)
AVX2_INTOP_USING_SSE2(andnot_si128)
AVX2_INTOP_USING_SSE2(cmpeq_epi32)
AVX2_INTOP_USING_SSE2(sub_epi32)
AVX2_INTOP_USING_SSE2(add_epi32)
#endif /* CPU_CAPABILITY_AVX2 */
/* natural logarithm computed for 8 simultaneous float
return NaN for x <= 0
*/
inline v8sf log256_ps(v8sf x) {
v8si imm0;
v8sf one = *(v8sf*)_ps256_1;
//v8sf invalid_mask = _mm256_cmple_ps(x, _mm256_setzero_ps());
v8sf invalid_mask = _mm256_cmp_ps(x, _mm256_setzero_ps(), _CMP_LE_OS);
x = _mm256_max_ps(x, *(v8sf*)_ps256_min_norm_pos); /* cut off denormalized stuff */
// can be done with AVX2
imm0 = _mm256_srli_epi32(_mm256_castps_si256(x), 23);
/* keep only the fractional part */
x = _mm256_and_ps(x, *(v8sf*)_ps256_inv_mant_mask);
x = _mm256_or_ps(x, *(v8sf*)_ps256_0p5);
// this is again another AVX2 instruction
imm0 = _mm256_sub_epi32(imm0, *(v8si*)_pi32_256_0x7f);
v8sf e = _mm256_cvtepi32_ps(imm0);
e = _mm256_add_ps(e, one);
/* part2:
if( x < SQRTHF ) {
e -= 1;
x = x + x - 1.0;
} else { x = x - 1.0; }
*/
//v8sf mask = _mm256_cmplt_ps(x, *(v8sf*)_ps256_cephes_SQRTHF);
v8sf mask = _mm256_cmp_ps(x, *(v8sf*)_ps256_cephes_SQRTHF, _CMP_LT_OS);
v8sf tmp = _mm256_and_ps(x, mask);
x = _mm256_sub_ps(x, one);
e = _mm256_sub_ps(e, _mm256_and_ps(one, mask));
x = _mm256_add_ps(x, tmp);
v8sf z = _mm256_mul_ps(x,x);
v8sf y = *(v8sf*)_ps256_cephes_log_p0;
y = _mm256_mul_ps(y, x);
y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p1);
y = _mm256_mul_ps(y, x);
y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p2);
y = _mm256_mul_ps(y, x);
y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p3);
y = _mm256_mul_ps(y, x);
y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p4);
y = _mm256_mul_ps(y, x);
y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p5);
y = _mm256_mul_ps(y, x);
y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p6);
y = _mm256_mul_ps(y, x);
y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p7);
y = _mm256_mul_ps(y, x);
y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p8);
y = _mm256_mul_ps(y, x);
y = _mm256_mul_ps(y, z);
tmp = _mm256_mul_ps(e, *(v8sf*)_ps256_cephes_log_q1);
y = _mm256_add_ps(y, tmp);
tmp = _mm256_mul_ps(z, *(v8sf*)_ps256_0p5);
y = _mm256_sub_ps(y, tmp);
tmp = _mm256_mul_ps(e, *(v8sf*)_ps256_cephes_log_q2);
x = _mm256_add_ps(x, y);
x = _mm256_add_ps(x, tmp);
x = _mm256_or_ps(x, invalid_mask); // negative arg will be NAN
return x;
}
_PS256_CONST(exp_hi, 88.3762626647949f);
_PS256_CONST(exp_lo, -88.3762626647949f);
_PS256_CONST(cephes_LOG2EF, 1.44269504088896341);
_PS256_CONST(cephes_exp_C1, 0.693359375);
_PS256_CONST(cephes_exp_C2, -2.12194440e-4);
_PS256_CONST(cephes_exp_p0, 1.9875691500E-4);
_PS256_CONST(cephes_exp_p1, 1.3981999507E-3);
_PS256_CONST(cephes_exp_p2, 8.3334519073E-3);
_PS256_CONST(cephes_exp_p3, 4.1665795894E-2);
_PS256_CONST(cephes_exp_p4, 1.6666665459E-1);
_PS256_CONST(cephes_exp_p5, 5.0000001201E-1);
inline v8sf exp256_ps(v8sf x) {
v8sf tmp = _mm256_setzero_ps(), fx;
v8si imm0;
v8sf one = *(v8sf*)_ps256_1;
x = _mm256_min_ps(x, *(v8sf*)_ps256_exp_hi);
x = _mm256_max_ps(x, *(v8sf*)_ps256_exp_lo);
/* express exp(x) as exp(g + n*log(2)) */
fx = _mm256_mul_ps(x, *(v8sf*)_ps256_cephes_LOG2EF);
fx = _mm256_add_ps(fx, *(v8sf*)_ps256_0p5);
/* how to perform a floorf with SSE: just below */
//imm0 = _mm256_cvttps_epi32(fx);
//tmp = _mm256_cvtepi32_ps(imm0);
tmp = _mm256_floor_ps(fx);
/* if greater, subtract 1 */
//v8sf mask = _mm256_cmpgt_ps(tmp, fx);
v8sf mask = _mm256_cmp_ps(tmp, fx, _CMP_GT_OS);
mask = _mm256_and_ps(mask, one);
fx = _mm256_sub_ps(tmp, mask);
tmp = _mm256_mul_ps(fx, *(v8sf*)_ps256_cephes_exp_C1);
v8sf z = _mm256_mul_ps(fx, *(v8sf*)_ps256_cephes_exp_C2);
x = _mm256_sub_ps(x, tmp);
x = _mm256_sub_ps(x, z);
z = _mm256_mul_ps(x,x);
v8sf y = *(v8sf*)_ps256_cephes_exp_p0;
y = _mm256_mul_ps(y, x);
y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_exp_p1);
y = _mm256_mul_ps(y, x);
y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_exp_p2);
y = _mm256_mul_ps(y, x);
y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_exp_p3);
y = _mm256_mul_ps(y, x);
y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_exp_p4);
y = _mm256_mul_ps(y, x);
y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_exp_p5);
y = _mm256_mul_ps(y, z);
y = _mm256_add_ps(y, x);
y = _mm256_add_ps(y, one);
/* build 2^n */
imm0 = _mm256_cvttps_epi32(fx);
// another two AVX2 instructions
imm0 = _mm256_add_epi32(imm0, *(v8si*)_pi32_256_0x7f);
imm0 = _mm256_slli_epi32(imm0, 23);
v8sf pow2n = _mm256_castsi256_ps(imm0);
y = _mm256_mul_ps(y, pow2n);
return y;
}
_PS256_CONST(minus_cephes_DP1, -0.78515625);
_PS256_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
_PS256_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
_PS256_CONST(sincof_p0, -1.9515295891E-4);
_PS256_CONST(sincof_p1, 8.3321608736E-3);
_PS256_CONST(sincof_p2, -1.6666654611E-1);
_PS256_CONST(coscof_p0, 2.443315711809948E-005);
_PS256_CONST(coscof_p1, -1.388731625493765E-003);
_PS256_CONST(coscof_p2, 4.166664568298827E-002);
_PS256_CONST(cephes_FOPI, 1.27323954473516); // 4 / M_PI
/* evaluation of 8 sines at onces using AVX intrisics
The code is the exact rewriting of the cephes sinf function.
Precision is excellent as long as x < 8192 (I did not bother to
take into account the special handling they have for greater values
-- it does not return garbage for arguments over 8192, though, but
the extra precision is missing).
Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the
surprising but correct result.
*/
inline v8sf sin256_ps(v8sf x) { // any x
v8sf xmm1, xmm2 = _mm256_setzero_ps(), xmm3, sign_bit, y;
v8si imm0, imm2;
#ifndef CPU_CAPABILITY_AVX2
v4si imm0_1, imm0_2;
v4si imm2_1, imm2_2;
#endif
sign_bit = x;
/* take the absolute value */
x = _mm256_and_ps(x, *(v8sf*)_ps256_inv_sign_mask);
/* extract the sign bit (upper one) */
sign_bit = _mm256_and_ps(sign_bit, *(v8sf*)_ps256_sign_mask);
/* scale by 4/Pi */
y = _mm256_mul_ps(x, *(v8sf*)_ps256_cephes_FOPI);
/*
Here we start a series of integer operations, which are in the
realm of AVX2.
If we don't have AVX, let's perform them using SSE2 directives
*/
#ifdef CPU_CAPABILITY_AVX2
/* store the integer part of y in mm0 */
imm2 = _mm256_cvttps_epi32(y);
/* j=(j+1) & (~1) (see the cephes sources) */
// another two AVX2 instruction
imm2 = _mm256_add_epi32(imm2, *(v8si*)_pi32_256_1);
imm2 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_inv1);
y = _mm256_cvtepi32_ps(imm2);
/* get the swap sign flag */
imm0 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_4);
imm0 = _mm256_slli_epi32(imm0, 29);
/* get the polynom selection mask
there is one polynom for 0 <= x <= Pi/4
and another one for Pi/4<x<=Pi/2
Both branches will be computed.
*/
imm2 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_2);
imm2 = _mm256_cmpeq_epi32(imm2,*(v8si*)_pi32_256_0);
#else
/* we use SSE2 routines to perform the integer ops */
COPY_IMM_TO_XMM(_mm256_cvttps_epi32(y),imm2_1,imm2_2);
imm2_1 = _mm_add_epi32(imm2_1, *(v4si*)_pi32avx_1);
imm2_2 = _mm_add_epi32(imm2_2, *(v4si*)_pi32avx_1);
imm2_1 = _mm_and_si128(imm2_1, *(v4si*)_pi32avx_inv1);
imm2_2 = _mm_and_si128(imm2_2, *(v4si*)_pi32avx_inv1);
COPY_XMM_TO_IMM(imm2_1,imm2_2,imm2);
y = _mm256_cvtepi32_ps(imm2);
imm0_1 = _mm_and_si128(imm2_1, *(v4si*)_pi32avx_4);
imm0_2 = _mm_and_si128(imm2_2, *(v4si*)_pi32avx_4);
imm0_1 = _mm_slli_epi32(imm0_1, 29);
imm0_2 = _mm_slli_epi32(imm0_2, 29);
COPY_XMM_TO_IMM(imm0_1, imm0_2, imm0);
imm2_1 = _mm_and_si128(imm2_1, *(v4si*)_pi32avx_2);
imm2_2 = _mm_and_si128(imm2_2, *(v4si*)_pi32avx_2);
imm2_1 = _mm_cmpeq_epi32(imm2_1, _mm_setzero_si128());
imm2_2 = _mm_cmpeq_epi32(imm2_2, _mm_setzero_si128());
COPY_XMM_TO_IMM(imm2_1, imm2_2, imm2);
#endif
v8sf swap_sign_bit = _mm256_castsi256_ps(imm0);
v8sf poly_mask = _mm256_castsi256_ps(imm2);
sign_bit = _mm256_xor_ps(sign_bit, swap_sign_bit);
/* The magic pass: "Extended precision modular arithmetic"
x = ((x - y * DP1) - y * DP2) - y * DP3; */
xmm1 = *(v8sf*)_ps256_minus_cephes_DP1;
xmm2 = *(v8sf*)_ps256_minus_cephes_DP2;
xmm3 = *(v8sf*)_ps256_minus_cephes_DP3;
xmm1 = _mm256_mul_ps(y, xmm1);
xmm2 = _mm256_mul_ps(y, xmm2);
xmm3 = _mm256_mul_ps(y, xmm3);
x = _mm256_add_ps(x, xmm1);
x = _mm256_add_ps(x, xmm2);
x = _mm256_add_ps(x, xmm3);
/* Evaluate the first polynom (0 <= x <= Pi/4) */
y = *(v8sf*)_ps256_coscof_p0;
v8sf z = _mm256_mul_ps(x,x);
y = _mm256_mul_ps(y, z);
y = _mm256_add_ps(y, *(v8sf*)_ps256_coscof_p1);
y = _mm256_mul_ps(y, z);
y = _mm256_add_ps(y, *(v8sf*)_ps256_coscof_p2);
y = _mm256_mul_ps(y, z);
y = _mm256_mul_ps(y, z);
v8sf tmp = _mm256_mul_ps(z, *(v8sf*)_ps256_0p5);
y = _mm256_sub_ps(y, tmp);
y = _mm256_add_ps(y, *(v8sf*)_ps256_1);
/* Evaluate the second polynom (Pi/4 <= x <= 0) */
v8sf y2 = *(v8sf*)_ps256_sincof_p0;
y2 = _mm256_mul_ps(y2, z);
y2 = _mm256_add_ps(y2, *(v8sf*)_ps256_sincof_p1);
y2 = _mm256_mul_ps(y2, z);
y2 = _mm256_add_ps(y2, *(v8sf*)_ps256_sincof_p2);
y2 = _mm256_mul_ps(y2, z);
y2 = _mm256_mul_ps(y2, x);
y2 = _mm256_add_ps(y2, x);
/* select the correct result from the two polynoms */
xmm3 = poly_mask;
y2 = _mm256_and_ps(xmm3, y2); //, xmm3);
y = _mm256_andnot_ps(xmm3, y);
y = _mm256_add_ps(y,y2);
/* update the sign */
y = _mm256_xor_ps(y, sign_bit);
return y;
}
/* almost the same as sin_ps */
inline v8sf cos256_ps(v8sf x) { // any x
v8sf xmm1, xmm2 = _mm256_setzero_ps(), xmm3, y;
v8si imm0, imm2;
#ifndef CPU_CAPABILITY_AVX2
v4si imm0_1, imm0_2;
v4si imm2_1, imm2_2;
#endif
/* take the absolute value */
x = _mm256_and_ps(x, *(v8sf*)_ps256_inv_sign_mask);
/* scale by 4/Pi */
y = _mm256_mul_ps(x, *(v8sf*)_ps256_cephes_FOPI);
#ifdef CPU_CAPABILITY_AVX2
/* store the integer part of y in mm0 */
imm2 = _mm256_cvttps_epi32(y);
/* j=(j+1) & (~1) (see the cephes sources) */
imm2 = _mm256_add_epi32(imm2, *(v8si*)_pi32_256_1);
imm2 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_inv1);
y = _mm256_cvtepi32_ps(imm2);
imm2 = _mm256_sub_epi32(imm2, *(v8si*)_pi32_256_2);
/* get the swap sign flag */
imm0 = _mm256_andnot_si256(imm2, *(v8si*)_pi32_256_4);
imm0 = _mm256_slli_epi32(imm0, 29);
/* get the polynom selection mask */
imm2 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_2);
imm2 = _mm256_cmpeq_epi32(imm2, *(v8si*)_pi32_256_0);
#else
/* we use SSE2 routines to perform the integer ops */
COPY_IMM_TO_XMM(_mm256_cvttps_epi32(y),imm2_1,imm2_2);
imm2_1 = _mm_add_epi32(imm2_1, *(v4si*)_pi32avx_1);
imm2_2 = _mm_add_epi32(imm2_2, *(v4si*)_pi32avx_1);
imm2_1 = _mm_and_si128(imm2_1, *(v4si*)_pi32avx_inv1);
imm2_2 = _mm_and_si128(imm2_2, *(v4si*)_pi32avx_inv1);
COPY_XMM_TO_IMM(imm2_1,imm2_2,imm2);
y = _mm256_cvtepi32_ps(imm2);
imm2_1 = _mm_sub_epi32(imm2_1, *(v4si*)_pi32avx_2);
imm2_2 = _mm_sub_epi32(imm2_2, *(v4si*)_pi32avx_2);
imm0_1 = _mm_andnot_si128(imm2_1, *(v4si*)_pi32avx_4);
imm0_2 = _mm_andnot_si128(imm2_2, *(v4si*)_pi32avx_4);
imm0_1 = _mm_slli_epi32(imm0_1, 29);
imm0_2 = _mm_slli_epi32(imm0_2, 29);
COPY_XMM_TO_IMM(imm0_1, imm0_2, imm0);
imm2_1 = _mm_and_si128(imm2_1, *(v4si*)_pi32avx_2);
imm2_2 = _mm_and_si128(imm2_2, *(v4si*)_pi32avx_2);
imm2_1 = _mm_cmpeq_epi32(imm2_1, _mm_setzero_si128());
imm2_2 = _mm_cmpeq_epi32(imm2_2, _mm_setzero_si128());
COPY_XMM_TO_IMM(imm2_1, imm2_2, imm2);
#endif
v8sf sign_bit = _mm256_castsi256_ps(imm0);
v8sf poly_mask = _mm256_castsi256_ps(imm2);
/* The magic pass: "Extended precision modular arithmetic"
x = ((x - y * DP1) - y * DP2) - y * DP3; */
xmm1 = *(v8sf*)_ps256_minus_cephes_DP1;
xmm2 = *(v8sf*)_ps256_minus_cephes_DP2;
xmm3 = *(v8sf*)_ps256_minus_cephes_DP3;
xmm1 = _mm256_mul_ps(y, xmm1);
xmm2 = _mm256_mul_ps(y, xmm2);
xmm3 = _mm256_mul_ps(y, xmm3);
x = _mm256_add_ps(x, xmm1);
x = _mm256_add_ps(x, xmm2);
x = _mm256_add_ps(x, xmm3);
/* Evaluate the first polynom (0 <= x <= Pi/4) */
y = *(v8sf*)_ps256_coscof_p0;
v8sf z = _mm256_mul_ps(x,x);
y = _mm256_mul_ps(y, z);
y = _mm256_add_ps(y, *(v8sf*)_ps256_coscof_p1);
y = _mm256_mul_ps(y, z);
y = _mm256_add_ps(y, *(v8sf*)_ps256_coscof_p2);
y = _mm256_mul_ps(y, z);
y = _mm256_mul_ps(y, z);
v8sf tmp = _mm256_mul_ps(z, *(v8sf*)_ps256_0p5);
y = _mm256_sub_ps(y, tmp);
y = _mm256_add_ps(y, *(v8sf*)_ps256_1);
/* Evaluate the second polynom (Pi/4 <= x <= 0) */
v8sf y2 = *(v8sf*)_ps256_sincof_p0;
y2 = _mm256_mul_ps(y2, z);
y2 = _mm256_add_ps(y2, *(v8sf*)_ps256_sincof_p1);
y2 = _mm256_mul_ps(y2, z);
y2 = _mm256_add_ps(y2, *(v8sf*)_ps256_sincof_p2);
y2 = _mm256_mul_ps(y2, z);
y2 = _mm256_mul_ps(y2, x);
y2 = _mm256_add_ps(y2, x);
/* select the correct result from the two polynoms */
xmm3 = poly_mask;
y2 = _mm256_and_ps(xmm3, y2); //, xmm3);
y = _mm256_andnot_ps(xmm3, y);
y = _mm256_add_ps(y,y2);
/* update the sign */
y = _mm256_xor_ps(y, sign_bit);
return y;
}
/* since sin256_ps and cos256_ps are almost identical, sincos256_ps could replace both of them..
it is almost as fast, and gives you a free cosine with your sine */
inline void sincos256_ps(v8sf x, v8sf *s, v8sf *c) {
v8sf xmm1, xmm2, xmm3 = _mm256_setzero_ps(), sign_bit_sin, y;
v8si imm0, imm2, imm4;
#ifndef CPU_CAPABILITY_AVX2
v4si imm0_1, imm0_2;
v4si imm2_1, imm2_2;
v4si imm4_1, imm4_2;
#endif
sign_bit_sin = x;
/* take the absolute value */
x = _mm256_and_ps(x, *(v8sf*)_ps256_inv_sign_mask);
/* extract the sign bit (upper one) */
sign_bit_sin = _mm256_and_ps(sign_bit_sin, *(v8sf*)_ps256_sign_mask);
/* scale by 4/Pi */
y = _mm256_mul_ps(x, *(v8sf*)_ps256_cephes_FOPI);
#ifdef CPU_CAPABILITY_AVX2
/* store the integer part of y in imm2 */
imm2 = _mm256_cvttps_epi32(y);
/* j=(j+1) & (~1) (see the cephes sources) */
imm2 = _mm256_add_epi32(imm2, *(v8si*)_pi32_256_1);
imm2 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_inv1);
y = _mm256_cvtepi32_ps(imm2);
imm4 = imm2;
/* get the swap sign flag for the sine */
imm0 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_4);
imm0 = _mm256_slli_epi32(imm0, 29);
//v8sf swap_sign_bit_sin = _mm256_castsi256_ps(imm0);
/* get the polynom selection mask for the sine*/
imm2 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_2);
imm2 = _mm256_cmpeq_epi32(imm2, *(v8si*)_pi32_256_0);
//v8sf poly_mask = _mm256_castsi256_ps(imm2);
#else
/* we use SSE2 routines to perform the integer ops */
COPY_IMM_TO_XMM(_mm256_cvttps_epi32(y),imm2_1,imm2_2);
imm2_1 = _mm_add_epi32(imm2_1, *(v4si*)_pi32avx_1);
imm2_2 = _mm_add_epi32(imm2_2, *(v4si*)_pi32avx_1);
imm2_1 = _mm_and_si128(imm2_1, *(v4si*)_pi32avx_inv1);
imm2_2 = _mm_and_si128(imm2_2, *(v4si*)_pi32avx_inv1);
COPY_XMM_TO_IMM(imm2_1,imm2_2,imm2);
y = _mm256_cvtepi32_ps(imm2);
imm4_1 = imm2_1;
imm4_2 = imm2_2;
imm0_1 = _mm_and_si128(imm2_1, *(v4si*)_pi32avx_4);
imm0_2 = _mm_and_si128(imm2_2, *(v4si*)_pi32avx_4);
imm0_1 = _mm_slli_epi32(imm0_1, 29);
imm0_2 = _mm_slli_epi32(imm0_2, 29);
COPY_XMM_TO_IMM(imm0_1, imm0_2, imm0);
imm2_1 = _mm_and_si128(imm2_1, *(v4si*)_pi32avx_2);
imm2_2 = _mm_and_si128(imm2_2, *(v4si*)_pi32avx_2);
imm2_1 = _mm_cmpeq_epi32(imm2_1, _mm_setzero_si128());
imm2_2 = _mm_cmpeq_epi32(imm2_2, _mm_setzero_si128());
COPY_XMM_TO_IMM(imm2_1, imm2_2, imm2);
#endif
v8sf swap_sign_bit_sin = _mm256_castsi256_ps(imm0);
v8sf poly_mask = _mm256_castsi256_ps(imm2);
/* The magic pass: "Extended precision modular arithmetic"
x = ((x - y * DP1) - y * DP2) - y * DP3; */
xmm1 = *(v8sf*)_ps256_minus_cephes_DP1;
xmm2 = *(v8sf*)_ps256_minus_cephes_DP2;
xmm3 = *(v8sf*)_ps256_minus_cephes_DP3;
xmm1 = _mm256_mul_ps(y, xmm1);
xmm2 = _mm256_mul_ps(y, xmm2);
xmm3 = _mm256_mul_ps(y, xmm3);
x = _mm256_add_ps(x, xmm1);
x = _mm256_add_ps(x, xmm2);
x = _mm256_add_ps(x, xmm3);
#ifdef CPU_CAPABILITY_AVX2
imm4 = _mm256_sub_epi32(imm4, *(v8si*)_pi32_256_2);
imm4 = _mm256_andnot_si256(imm4, *(v8si*)_pi32_256_4);
imm4 = _mm256_slli_epi32(imm4, 29);
#else
imm4_1 = _mm_sub_epi32(imm4_1, *(v4si*)_pi32avx_2);
imm4_2 = _mm_sub_epi32(imm4_2, *(v4si*)_pi32avx_2);
imm4_1 = _mm_andnot_si128(imm4_1, *(v4si*)_pi32avx_4);
imm4_2 = _mm_andnot_si128(imm4_2, *(v4si*)_pi32avx_4);
imm4_1 = _mm_slli_epi32(imm4_1, 29);
imm4_2 = _mm_slli_epi32(imm4_2, 29);
COPY_XMM_TO_IMM(imm4_1, imm4_2, imm4);
#endif
v8sf sign_bit_cos = _mm256_castsi256_ps(imm4);
sign_bit_sin = _mm256_xor_ps(sign_bit_sin, swap_sign_bit_sin);
/* Evaluate the first polynom (0 <= x <= Pi/4) */
v8sf z = _mm256_mul_ps(x,x);
y = *(v8sf*)_ps256_coscof_p0;
y = _mm256_mul_ps(y, z);
y = _mm256_add_ps(y, *(v8sf*)_ps256_coscof_p1);
y = _mm256_mul_ps(y, z);
y = _mm256_add_ps(y, *(v8sf*)_ps256_coscof_p2);
y = _mm256_mul_ps(y, z);
y = _mm256_mul_ps(y, z);
v8sf tmp = _mm256_mul_ps(z, *(v8sf*)_ps256_0p5);
y = _mm256_sub_ps(y, tmp);
y = _mm256_add_ps(y, *(v8sf*)_ps256_1);
/* Evaluate the second polynom (Pi/4 <= x <= 0) */
v8sf y2 = *(v8sf*)_ps256_sincof_p0;
y2 = _mm256_mul_ps(y2, z);
y2 = _mm256_add_ps(y2, *(v8sf*)_ps256_sincof_p1);
y2 = _mm256_mul_ps(y2, z);
y2 = _mm256_add_ps(y2, *(v8sf*)_ps256_sincof_p2);
y2 = _mm256_mul_ps(y2, z);
y2 = _mm256_mul_ps(y2, x);
y2 = _mm256_add_ps(y2, x);
/* select the correct result from the two polynoms */
xmm3 = poly_mask;
v8sf ysin2 = _mm256_and_ps(xmm3, y2);
v8sf ysin1 = _mm256_andnot_ps(xmm3, y);
y2 = _mm256_sub_ps(y2,ysin2);
y = _mm256_sub_ps(y, ysin1);
xmm1 = _mm256_add_ps(ysin1,ysin2);
xmm2 = _mm256_add_ps(y,y2);
/* update the sign */
*s = _mm256_xor_ps(xmm1, sign_bit_sin);
*c = _mm256_xor_ps(xmm2, sign_bit_cos);
}