-
Notifications
You must be signed in to change notification settings - Fork 2
/
sse_mathfun.h
1525 lines (1353 loc) · 43.3 KB
/
sse_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
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
/*!
@file sse_mathfun.h
SIMD (SSE1+MMX or SSE2) implementation of sin, cos, exp and log
Inspired by Intel Approximate Math library, and based on the
corresponding algorithms of the cephes math library
The default is to use the SSE1 version. If you define USE_SSE2 the
the SSE2 intrinsics will be used in place of the MMX intrinsics. Do
not expect any significant performance improvement with SSE2.
*/
/* Copyright (C) 2010,2011 RJVB - extensions */
/* Copyright (C) 2007 Julien Pommier
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)
*/
#ifndef _SSE_MATHFUN_H
#ifdef USE_SSE_AUTO
# ifdef __SSE2__
# if defined(__GNUC__)
# warning "USE_SSE2"
# endif
# define USE_SSE2
# endif
# if defined(__SSE3__) || defined(__SSSE3__)
# if defined(__GNUC__)
# warning "USE_SSE3"
# endif
# define USE_SSE2
# define USE_SSE3
# endif
# if defined(__SSE4__) || defined(__SSE4_1__) || defined(__SSE4_2__) || ((_M_IX86_FP > 1) && !defined(_M_AMD64))
# if defined(__GNUC__)
# warning "USE_SSE4"
# endif
# define USE_SSE2
# define USE_SSE3
# define USE_SSE4
# endif
#endif
#include <math.h>
#include <xmmintrin.h>
#include <emmintrin.h>
/* yes I know, the top of this file is quite ugly */
/*!
macros to obtain the required 16bit alignment
*/
#ifdef _MSC_VER /* visual c++ */
# define ALIGN16_BEG __declspec(align(16))
# define ALIGN16_END
# define inline __forceinline
#else /* gcc or icc */
# define ALIGN16_BEG
# define ALIGN16_END __attribute__((aligned(16)))
#endif
/* __m128 is ugly to write */
/*!
an SSE vector of 4 floats
*/
typedef __m128 v4sf; // vector of 4 float (sse1)
#if defined(USE_SSE3) || defined(USE_SSE4)
# define USE_SSE2
#endif
/*!
an SSE/MMX vector of 4 32bit integers
*/
#ifdef __APPLE_CC__
typedef int v4si __attribute__ ((__vector_size__ (16), __may_alias__));
#else
typedef __m128i v4si; // vector of 4 int (sse2)
#endif
// RJVB 20111028: some support for double precision semantics
/*!
an SSE2+ vector of 2 doubles
*/
typedef __m128d v2df; // vector of 2 double (sse2)
/*!
an MMX vector of 2 32bit ints
*/
typedef __m64 v2si; // vector of 2 int (mmx)
#if defined(USE_SSE3) || defined(USE_SSE4)
# define USE_SSE3
# include <pmmintrin.h>
# if defined(__SSSE3__) || (_M_IX86_FP > 1)
# include <tmmintrin.h>
# endif
#endif
#if defined(USE_SSE4)
# define USE_SSE4
# include <smmintrin.h>
#endif
#ifdef __GNUC__0
# define _MM_SET_PD(b,a) (v2df){(a),(b)}
# define _MM_SET1_PD(a) (v2df){(a),(a)}
// static inline v2df _MM_SET1_PD(double a)
// {
// return (v2df){a,a};
// }
# define _MM_SETR_PD(a,b) (v2df){(a),(b)}
# define _MM_SETZERO_PD() (v2df){0.0,0.0}
# define _MM_SET_PS(d,c,b,a) (v4sf){(a),(b),(c),(d)}
# define _MM_SET1_PS(a) (v4sf){(a),(a),(a),(a)}
// static inline v4sf _MM_SET1_PS(float a)
// {
// return (v4sf){a,a,a,a};
// }
# define _MM_SETR_PS(a,b,c,d) (v4sf){(a),(b),(c),(d)}
# define _MM_SETZERO_PS() (v4sf){0.0f,0.0f,0.0f,0.0f}
# define _MM_SETZERO_SI128() (__m128i)(__v4si){0,0,0,0}
# define _MM_SETZERO_SI64() ALIGN16_BEG (__m64 ALIGN16_END)0LL
#else
# define _MM_SET_PD(b,a) _mm_setr_pd((a),(b))
# define _MM_SET1_PD(a) _mm_set1_pd((a))
# define _MM_SETR_PD(a,b) _mm_setr_pd((a),(b))
# define _MM_SETZERO_PD() _mm_setzero_pd()
# define _MM_SET_PS(d,c,b,a) _mm_setr_ps((a),(b),(c),(d))
# define _MM_SET1_PS(a) _mm_set1_ps((a))
# define _MM_SETR_PS(a,b,c,d) _mm_setr_ps((a),(b),(c),(d))
# define _MM_SETZERO_PS() _mm_setzero_ps()
# define _MM_SETZERO_SI128() _mm_setzero_si128()
# define _MM_SETZERO_SI64() _mm_setzero_si64()
#endif
#define VELEM(type,a,n) (((type*)&a)[n])
/* declare some SSE constants -- why can't I figure a better way to do that? */
#define _PS_CONST(Name, Val) \
static const ALIGN16_BEG float _ps_##Name[4] ALIGN16_END = { (const float)(Val), (const float)(Val), (const float)(Val), (const float)(Val) }
#define _PI32_CONST(Name, Val) \
static const ALIGN16_BEG int _pi32_##Name[4] ALIGN16_END = { Val, Val, Val, Val }
#define _PS_CONST_TYPE(Name, Type, Val) \
static const ALIGN16_BEG Type _ps_##Name[4] ALIGN16_END = { Val, Val, Val, Val }
#define _PD_CONST(Name, Val) \
static const ALIGN16_BEG double _pd_##Name[2] ALIGN16_END = { (const double)(Val), (const double)(Val) }
#define _PD_CONST_TYPE(Name, Type, Val) \
static const ALIGN16_BEG Type _pd_##Name[2] ALIGN16_END = { Val, Val }
#pragma mark code section
#ifdef SSE_MATHFUN_WITH_CODE
_PS_CONST(1 , 1.0f);
_PS_CONST(0p5, 0.5f);
/* the smallest non denormalized float number */
_PS_CONST_TYPE(min_norm_pos, int, 0x00800000);
_PS_CONST_TYPE(mant_mask, int, 0x7f800000);
_PS_CONST_TYPE(inv_mant_mask, int, ~0x7f800000);
_PS_CONST_TYPE(sign_mask, int, 0x80000000);
_PS_CONST_TYPE(inv_sign_mask, int, ~0x80000000);
_PI32_CONST(1, 1);
_PI32_CONST(inv1, ~1);
_PI32_CONST(2, 2);
_PI32_CONST(4, 4);
_PI32_CONST(0x7f, 0x7f);
_PS_CONST(cephes_SQRTHF, 0.707106781186547524);
_PS_CONST(cephes_log_p0, 7.0376836292E-2);
_PS_CONST(cephes_log_p1, - 1.1514610310E-1);
_PS_CONST(cephes_log_p2, 1.1676998740E-1);
_PS_CONST(cephes_log_p3, - 1.2420140846E-1);
_PS_CONST(cephes_log_p4, + 1.4249322787E-1);
_PS_CONST(cephes_log_p5, - 1.6668057665E-1);
_PS_CONST(cephes_log_p6, + 2.0000714765E-1);
_PS_CONST(cephes_log_p7, - 2.4999993993E-1);
_PS_CONST(cephes_log_p8, + 3.3333331174E-1);
_PS_CONST(cephes_log_q1, -2.12194440e-4);
_PS_CONST(cephes_log_q2, 0.693359375);
#ifdef USE_SSE2
_PD_CONST(1, 1.0);
_PD_CONST(_1, -1.0);
_PD_CONST(0p5, 0.5);
/* the smallest non denormalised float number */
// _PD_CONST_TYPE(min_norm_pos, int, 0x00800000);
// _PD_CONST_TYPE(mant_mask, int, 0x7f800000);
// _PD_CONST_TYPE(inv_mant_mask, int, ~0x7f800000);
_PD_CONST_TYPE(sign_mask, long long, 0x8000000000000000LL);
_PD_CONST_TYPE(inv_sign_mask, long long, ~0x8000000000000000LL);
#endif
#if defined (__MINGW32__)
/* the ugly part below: many versions of gcc used to be completely buggy with respect to some intrinsics
The movehl_ps is fixed in mingw 3.4.5, but I found out that all the _mm_cmp* intrinsics were completely
broken on my mingw gcc 3.4.5 ...
Note that the bug on _mm_cmp* does occur only at -O0 optimization level
*/
inline __m128 my_movehl_ps(__m128 a, const __m128 b) {
asm (
"movhlps %2,%0\n\t"
: "=x" (a)
: "0" (a), "x"(b)
);
return a; }
#warning "redefined _mm_movehl_ps (see gcc bug 21179)"
#define _mm_movehl_ps my_movehl_ps
inline __m128 my_cmplt_ps(__m128 a, const __m128 b) {
asm (
"cmpltps %2,%0\n\t"
: "=x" (a)
: "0" (a), "x"(b)
);
return a;
}
inline __m128 my_cmpgt_ps(__m128 a, const __m128 b) {
asm (
"cmpnleps %2,%0\n\t"
: "=x" (a)
: "0" (a), "x"(b)
);
return a;
}
inline __m128 my_cmpeq_ps(__m128 a, const __m128 b) {
asm (
"cmpeqps %2,%0\n\t"
: "=x" (a)
: "0" (a), "x"(b)
);
return a;
}
#warning "redefined _mm_cmpxx_ps functions..."
#define _mm_cmplt_ps my_cmplt_ps
#define _mm_cmpgt_ps my_cmpgt_ps
#define _mm_cmpeq_ps my_cmpeq_ps
#endif
#ifndef USE_SSE2
typedef union xmm_mm_union {
__m128 xmm;
__m64 mm[2];
} xmm_mm_union;
#define COPY_XMM_TO_MM(xmm_, mm0_, mm1_) { \
xmm_mm_union u; u.xmm = xmm_; \
mm0_ = u.mm[0]; \
mm1_ = u.mm[1]; \
}
#define COPY_MM_TO_XMM(mm0_, mm1_, xmm_) { \
xmm_mm_union u; u.mm[0]=mm0_; u.mm[1]=mm1_; xmm_ = u.xmm; \
}
#endif // USE_SSE2
/*!
natural logarithm computed for 4 simultaneous float
@n
return NaN for x <= 0
*/
static inline v4sf log_ps(v4sf x)
{
v4sf e;
#ifdef USE_SSE2
v4si emm0;
#else
v2si mm0, mm1;
#endif
v4sf one = *(v4sf*)_ps_1;
v4sf invalid_mask = _mm_cmple_ps(x, _MM_SETZERO_PS());
x = _mm_max_ps(x, *(v4sf*)_ps_min_norm_pos); /* cut off denormalized stuff */
#ifndef USE_SSE2
/* part 1: x = frexpf(x, &e); */
COPY_XMM_TO_MM(x, mm0, mm1);
mm0 = _mm_srli_pi32(mm0, 23);
mm1 = _mm_srli_pi32(mm1, 23);
#else
emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);
#endif
/* keep only the fractional part */
x = _mm_and_ps(x, *(v4sf*)_ps_inv_mant_mask);
x = _mm_or_ps(x, *(v4sf*)_ps_0p5);
#ifndef USE_SSE2
/* now e=mm0:mm1 contain the really base-2 exponent */
mm0 = _mm_sub_pi32(mm0, *(v2si*)_pi32_0x7f);
mm1 = _mm_sub_pi32(mm1, *(v2si*)_pi32_0x7f);
e = _mm_cvtpi32x2_ps(mm0, mm1);
_mm_empty(); /* bye bye mmx */
#else
emm0 = _mm_sub_epi32(emm0, *(v4si*)_pi32_0x7f);
e = _mm_cvtepi32_ps(emm0);
#endif
e = _mm_add_ps(e, one);
/* part2:
if( x < SQRTHF ) {
e -= 1;
x = x + x - 1.0;
} else { x = x - 1.0; }
*/
{
v4sf z, y;
v4sf mask = _mm_cmplt_ps(x, *(v4sf*)_ps_cephes_SQRTHF);
v4sf tmp = _mm_and_ps(x, mask);
x = _mm_sub_ps(x, one);
e = _mm_sub_ps(e, _mm_and_ps(one, mask));
x = _mm_add_ps(x, tmp);
z = _mm_mul_ps(x,x);
y = *(v4sf*)_ps_cephes_log_p0;
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p1);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p2);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p3);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p4);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p5);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p6);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p7);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p8);
y = _mm_mul_ps(y, x);
y = _mm_mul_ps(y, z);
tmp = _mm_mul_ps(e, *(v4sf*)_ps_cephes_log_q1);
y = _mm_add_ps(y, tmp);
tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
y = _mm_sub_ps(y, tmp);
tmp = _mm_mul_ps(e, *(v4sf*)_ps_cephes_log_q2);
x = _mm_add_ps(x, y);
x = _mm_add_ps(x, tmp);
x = _mm_or_ps(x, invalid_mask); // negative arg will be NAN
}
return x;
}
_PS_CONST(exp_hi, 88.3762626647949f);
_PS_CONST(exp_lo, -88.3762626647949f);
_PS_CONST(cephes_LOG2EF, 1.44269504088896341);
_PS_CONST(cephes_exp_C1, 0.693359375);
_PS_CONST(cephes_exp_C2, -2.12194440e-4);
_PS_CONST(cephes_exp_p0, 1.9875691500E-4);
_PS_CONST(cephes_exp_p1, 1.3981999507E-3);
_PS_CONST(cephes_exp_p2, 8.3334519073E-3);
_PS_CONST(cephes_exp_p3, 4.1665795894E-2);
_PS_CONST(cephes_exp_p4, 1.6666665459E-1);
_PS_CONST(cephes_exp_p5, 5.0000001201E-1);
/*!
computes e**x of the 4 floats in x
*/
static inline v4sf exp_ps(v4sf x)
{ v4sf tmp = _MM_SETZERO_PS(), fx, mask, y, z;
v4sf pow2n;
#ifdef USE_SSE2
v4si emm0;
#else
v2si mm0, mm1;
#endif
v4sf one = *(v4sf*)_ps_1;
x = _mm_min_ps(x, *(v4sf*)_ps_exp_hi);
x = _mm_max_ps(x, *(v4sf*)_ps_exp_lo);
/* express exp(x) as exp(g + n*log(2)) */
fx = _mm_mul_ps(x, *(v4sf*)_ps_cephes_LOG2EF);
fx = _mm_add_ps(fx, *(v4sf*)_ps_0p5);
/* how to perform a floorf with SSE: just below */
#ifndef USE_SSE2
/* step 1 : cast to int */
tmp = _mm_movehl_ps(tmp, fx);
mm0 = _mm_cvttps_pi32(fx);
mm1 = _mm_cvttps_pi32(tmp);
/* step 2 : cast back to float */
tmp = _mm_cvtpi32x2_ps(mm0, mm1);
#else
emm0 = _mm_cvttps_epi32(fx);
tmp = _mm_cvtepi32_ps(emm0);
#endif
/* if greater, substract 1 */
mask = _mm_cmpgt_ps(tmp, fx);
mask = _mm_and_ps(mask, one);
fx = _mm_sub_ps(tmp, mask);
tmp = _mm_mul_ps(fx, *(v4sf*)_ps_cephes_exp_C1);
z = _mm_mul_ps(fx, *(v4sf*)_ps_cephes_exp_C2);
x = _mm_sub_ps(x, tmp);
x = _mm_sub_ps(x, z);
z = _mm_mul_ps(x,x);
y = *(v4sf*)_ps_cephes_exp_p0;
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p1);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p2);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p3);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p4);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p5);
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, x);
y = _mm_add_ps(y, one);
/* build 2^n */
#ifndef USE_SSE2
z = _mm_movehl_ps(z, fx);
mm0 = _mm_cvttps_pi32(fx);
mm1 = _mm_cvttps_pi32(z);
mm0 = _mm_add_pi32(mm0, *(v2si*)_pi32_0x7f);
mm1 = _mm_add_pi32(mm1, *(v2si*)_pi32_0x7f);
mm0 = _mm_slli_pi32(mm0, 23);
mm1 = _mm_slli_pi32(mm1, 23);
COPY_MM_TO_XMM(mm0, mm1, pow2n);
_mm_empty();
#else
emm0 = _mm_cvttps_epi32(fx);
emm0 = _mm_add_epi32(emm0, *(v4si*)_pi32_0x7f);
emm0 = _mm_slli_epi32(emm0, 23);
pow2n = _mm_castsi128_ps(emm0);
#endif
y = _mm_mul_ps(y, pow2n);
return y;
}
_PS_CONST(minus_cephes_DP1, -0.78515625);
_PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
_PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
_PS_CONST(sincof_p0, -1.9515295891E-4);
_PS_CONST(sincof_p1, 8.3321608736E-3);
_PS_CONST(sincof_p2, -1.6666654611E-1);
_PS_CONST(coscof_p0, 2.443315711809948E-005);
_PS_CONST(coscof_p1, -1.388731625493765E-003);
_PS_CONST(coscof_p2, 4.166664568298827E-002);
_PS_CONST(cephes_FOPI, 1.27323954473516); // 4 / M_PI
#ifdef USE_SSE2
_PD_CONST(minus_cephes_DP1, -0.78515625);
_PD_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
_PD_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
_PD_CONST(sincof_p0, -1.9515295891E-4);
_PD_CONST(sincof_p1, 8.3321608736E-3);
_PD_CONST(sincof_p2, -1.6666654611E-1);
_PD_CONST(coscof_p0, 2.443315711809948E-005);
_PD_CONST(coscof_p1, -1.388731625493765E-003);
_PD_CONST(coscof_p2, 4.166664568298827E-002);
_PD_CONST(cephes_FOPI, 1.27323954473516); // 4 / M_PI
#endif
/*!
evaluation of 4 sines at onces, using only SSE1+MMX intrinsics so
it runs also on old athlons XPs and the pentium III of your grand
mother.
@n
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).
@n
Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the
surprising but correct result.
@n
Performance is also surprisingly good, 1.33 times faster than the
macos vsinf SSE2 function, and 1.5 times faster than the
__vrs4_sinf of amd's ACML (which is only available in 64 bits). Not
too bad for an SSE1 function (with no special tuning) !
However the latter libraries probably have a much better handling of NaN,
Inf, denormalized and other special arguments..
@n
On my core 1 duo, the execution of this function takes approximately 95 cycles.
@n
From what I have observed on the experiments with Intel AMath lib, switching to an
SSE2 version would improve the perf by only 10%.
@n
Since it is based on SSE intrinsics, it has to be compiled at -O2 to
deliver full speed.
*/
static inline v4sf sin_ps(v4sf x)
{ // any x
v4sf xmm1, xmm2 = _MM_SETZERO_PS(), xmm3, sign_bit, y, y2, z, tmp;
v4sf swap_sign_bit, poly_mask;
#ifdef USE_SSE2
v4si emm0, emm2;
#else
v2si mm0, mm1, mm2, mm3;
#endif
sign_bit = x;
/* take the absolute value */
x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
/* extract the sign bit (upper one) */
sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
/* scale by 4/Pi */
y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
//printf("plop:"); print4(y);
#ifdef USE_SSE2
/* store the integer part of y in mm0 */
emm2 = _mm_cvttps_epi32(y);
/* j=(j+1) & (~1) (see the cephes sources) */
emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
y = _mm_cvtepi32_ps(emm2);
/* get the swap sign flag */
emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
emm0 = _mm_slli_epi32(emm0, 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.
*/
emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
emm2 = _mm_cmpeq_epi32(emm2, _MM_SETZERO_SI128());
swap_sign_bit = _mm_castsi128_ps(emm0);
poly_mask = _mm_castsi128_ps(emm2);
sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
#else
/* store the integer part of y in mm0:mm1 */
xmm2 = _mm_movehl_ps(xmm2, y);
mm2 = _mm_cvttps_pi32(y);
mm3 = _mm_cvttps_pi32(xmm2);
/* j=(j+1) & (~1) (see the cephes sources) */
mm2 = _mm_add_pi32(mm2, *(v2si*)_pi32_1);
mm3 = _mm_add_pi32(mm3, *(v2si*)_pi32_1);
mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_inv1);
mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_inv1);
y = _mm_cvtpi32x2_ps(mm2, mm3);
/* get the swap sign flag */
mm0 = _mm_and_si64(mm2, *(v2si*)_pi32_4);
mm1 = _mm_and_si64(mm3, *(v2si*)_pi32_4);
mm0 = _mm_slli_pi32(mm0, 29);
mm1 = _mm_slli_pi32(mm1, 29);
/* get the polynom selection mask */
mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_2);
mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_2);
mm2 = _mm_cmpeq_pi32(mm2, _MM_SETZERO_SI64());
mm3 = _mm_cmpeq_pi32(mm3, _MM_SETZERO_SI64());
COPY_MM_TO_XMM(mm0, mm1, swap_sign_bit);
COPY_MM_TO_XMM(mm2, mm3, poly_mask);
sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
_mm_empty(); /* good-bye mmx */
#endif
/* The magic pass: "Extended precision modular arithmetic"
x = ((x - y * DP1) - y * DP2) - y * DP3; */
xmm1 = *(v4sf*)_ps_minus_cephes_DP1;
xmm2 = *(v4sf*)_ps_minus_cephes_DP2;
xmm3 = *(v4sf*)_ps_minus_cephes_DP3;
xmm1 = _mm_mul_ps(y, xmm1);
xmm2 = _mm_mul_ps(y, xmm2);
xmm3 = _mm_mul_ps(y, xmm3);
x = _mm_add_ps(x, xmm1);
x = _mm_add_ps(x, xmm2);
x = _mm_add_ps(x, xmm3);
/* Evaluate the first polynom (0 <= x <= Pi/4) */
y = *(v4sf*)_ps_coscof_p0;
z = _mm_mul_ps(x,x);
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p1);
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p2);
y = _mm_mul_ps(y, z);
y = _mm_mul_ps(y, z);
tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
y = _mm_sub_ps(y, tmp);
y = _mm_add_ps(y, *(v4sf*)_ps_1);
/* Evaluate the second polynom (Pi/4 <= x <= 0) */
y2 = *(v4sf*)_ps_sincof_p0;
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
y2 = _mm_mul_ps(y2, z);
y2 = _mm_mul_ps(y2, x);
y2 = _mm_add_ps(y2, x);
/* select the correct result from the two polynoms */
xmm3 = poly_mask;
y2 = _mm_and_ps(xmm3, y2); //, xmm3);
y = _mm_andnot_ps(xmm3, y);
y = _mm_add_ps(y,y2);
/* update the sign */
y = _mm_xor_ps(y, sign_bit);
return y;
}
/*!
almost the same as sin_ps
*/
static inline v4sf cos_ps(v4sf x)
{ // any x
v4sf xmm1, xmm2 = _MM_SETZERO_PS(), xmm3, y, y2, z, sign_bit, poly_mask, tmp;
#ifdef USE_SSE2
v4si emm0, emm2;
#else
v2si mm0, mm1, mm2, mm3;
#endif
/* take the absolute value */
x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
/* scale by 4/Pi */
y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
#ifdef USE_SSE2
/* store the integer part of y in mm0 */
emm2 = _mm_cvttps_epi32(y);
/* j=(j+1) & (~1) (see the cephes sources) */
emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
y = _mm_cvtepi32_ps(emm2);
emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
/* get the swap sign flag */
emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
emm0 = _mm_slli_epi32(emm0, 29);
/* get the polynom selection mask */
emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
emm2 = _mm_cmpeq_epi32(emm2, _MM_SETZERO_SI128());
sign_bit = _mm_castsi128_ps(emm0);
poly_mask = _mm_castsi128_ps(emm2);
#else
/* store the integer part of y in mm0:mm1 */
xmm2 = _mm_movehl_ps(xmm2, y);
mm2 = _mm_cvttps_pi32(y);
mm3 = _mm_cvttps_pi32(xmm2);
/* j=(j+1) & (~1) (see the cephes sources) */
mm2 = _mm_add_pi32(mm2, *(v2si*)_pi32_1);
mm3 = _mm_add_pi32(mm3, *(v2si*)_pi32_1);
mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_inv1);
mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_inv1);
y = _mm_cvtpi32x2_ps(mm2, mm3);
mm2 = _mm_sub_pi32(mm2, *(v2si*)_pi32_2);
mm3 = _mm_sub_pi32(mm3, *(v2si*)_pi32_2);
/* get the swap sign flag in mm0:mm1 and the
polynom selection mask in mm2:mm3 */
mm0 = _mm_andnot_si64(mm2, *(v2si*)_pi32_4);
mm1 = _mm_andnot_si64(mm3, *(v2si*)_pi32_4);
mm0 = _mm_slli_pi32(mm0, 29);
mm1 = _mm_slli_pi32(mm1, 29);
mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_2);
mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_2);
mm2 = _mm_cmpeq_pi32(mm2, _MM_SETZERO_SI64());
mm3 = _mm_cmpeq_pi32(mm3, _MM_SETZERO_SI64());
COPY_MM_TO_XMM(mm0, mm1, sign_bit);
COPY_MM_TO_XMM(mm2, mm3, poly_mask);
_mm_empty(); /* good-bye mmx */
#endif
/* The magic pass: "Extended precision modular arithmetic"
x = ((x - y * DP1) - y * DP2) - y * DP3; */
xmm1 = *(v4sf*)_ps_minus_cephes_DP1;
xmm2 = *(v4sf*)_ps_minus_cephes_DP2;
xmm3 = *(v4sf*)_ps_minus_cephes_DP3;
xmm1 = _mm_mul_ps(y, xmm1);
xmm2 = _mm_mul_ps(y, xmm2);
xmm3 = _mm_mul_ps(y, xmm3);
x = _mm_add_ps(x, xmm1);
x = _mm_add_ps(x, xmm2);
x = _mm_add_ps(x, xmm3);
/* Evaluate the first polynom (0 <= x <= Pi/4) */
y = *(v4sf*)_ps_coscof_p0;
z = _mm_mul_ps(x,x);
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p1);
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p2);
y = _mm_mul_ps(y, z);
y = _mm_mul_ps(y, z);
tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
y = _mm_sub_ps(y, tmp);
y = _mm_add_ps(y, *(v4sf*)_ps_1);
/* Evaluate the second polynom (Pi/4 <= x <= 0) */
y2 = *(v4sf*)_ps_sincof_p0;
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
y2 = _mm_mul_ps(y2, z);
y2 = _mm_mul_ps(y2, x);
y2 = _mm_add_ps(y2, x);
/* select the correct result from the two polynoms */
xmm3 = poly_mask;
y2 = _mm_and_ps(xmm3, y2); //, xmm3);
y = _mm_andnot_ps(xmm3, y);
y = _mm_add_ps(y,y2);
/* update the sign */
y = _mm_xor_ps(y, sign_bit);
return y;
}
/*!
since sin_ps and cos_ps are almost identical, sincos_ps could replace both of them..
it is almost as fast, and gives you a free cosine with your sine
*/
static inline void sincos_ps(v4sf x, v4sf *s, v4sf *c)
{ v4sf xmm1, xmm2, sign_bit_sin, y, y2, z, swap_sign_bit_sin, poly_mask;
v4sf sign_bit_cos;
#ifdef USE_SSE2
v4si emm2;
#else
v2si mm0, mm1, mm2, mm3, mm4, mm5;
#endif
sign_bit_sin = x;
/* take the absolute value */
x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
/* extract the sign bit (upper one) */
sign_bit_sin = _mm_and_ps(sign_bit_sin, *(v4sf*)_ps_sign_mask);
/* scale by 4/Pi */
y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
#ifdef USE_SSE2
/* store the integer part of y in emm2 */
emm2 = _mm_cvttps_epi32(y);
/* j=(j+1) & (~1) (see the cephes sources) */
// emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
// emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
emm2 = _mm_and_si128( _mm_add_epi32( _mm_cvttps_epi32(y), *(v4si*)_pi32_1 ), *(v4si*)_pi32_inv1 );
y = _mm_cvtepi32_ps(emm2);
/* get the swap sign flag for the sine */
// emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
// emm0 = _mm_slli_epi32(emm0, 29);
// swap_sign_bit_sin = _mm_castsi128_ps(emm0);
swap_sign_bit_sin = _mm_castsi128_ps( _mm_slli_epi32( _mm_and_si128(emm2, *(v4si*)_pi32_4), 29) );
/* get the polynom selection mask for the sine*/
// emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
// emm2 = _mm_cmpeq_epi32(emm2, _MM_SETZERO_SI128());
// poly_mask = _mm_castsi128_ps(emm2);
poly_mask = _mm_castsi128_ps( _mm_cmpeq_epi32( _mm_and_si128(emm2, *(v4si*)_pi32_2), _MM_SETZERO_SI128()) );
#else
{ v4sf xmm3 = _MM_SETZERO_PS();
/* store the integer part of y in mm2:mm3 */
xmm3 = _mm_movehl_ps(xmm3, y);
mm2 = _mm_cvttps_pi32(y);
mm3 = _mm_cvttps_pi32(xmm3);
/* j=(j+1) & (~1) (see the cephes sources) */
mm2 = _mm_add_pi32(mm2, *(v2si*)_pi32_1);
mm3 = _mm_add_pi32(mm3, *(v2si*)_pi32_1);
mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_inv1);
mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_inv1);
y = _mm_cvtpi32x2_ps(mm2, mm3);
mm4 = mm2;
mm5 = mm3;
/* get the swap sign flag for the sine */
mm0 = _mm_and_si64(mm2, *(v2si*)_pi32_4);
mm1 = _mm_and_si64(mm3, *(v2si*)_pi32_4);
mm0 = _mm_slli_pi32(mm0, 29);
mm1 = _mm_slli_pi32(mm1, 29);
COPY_MM_TO_XMM(mm0, mm1, swap_sign_bit_sin);
/* get the polynom selection mask for the sine */
mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_2);
mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_2);
mm2 = _mm_cmpeq_pi32(mm2, _MM_SETZERO_SI64());
mm3 = _mm_cmpeq_pi32(mm3, _MM_SETZERO_SI64());
COPY_MM_TO_XMM(mm2, mm3, poly_mask);
}
#endif
/* The magic pass: "Extended precision modular arithmetic"
x = ((x - y * DP1) - y * DP2) - y * DP3; */
#ifdef __GNUC__
x += y * ( *(v4sf*)_ps_minus_cephes_DP1 + *(v4sf*)_ps_minus_cephes_DP2 + *(v4sf*)_ps_minus_cephes_DP3 );
#else
// xmm1 = *(v4sf*)_ps_minus_cephes_DP1;
// xmm2 = *(v4sf*)_ps_minus_cephes_DP2;
// xmm3 = *(v4sf*)_ps_minus_cephes_DP3;
// xmm1 = _mm_mul_ps(y, xmm1);
// xmm2 = _mm_mul_ps(y, xmm2);
// xmm3 = _mm_mul_ps(y, xmm3);
// x = _mm_add_ps(x, xmm1);
// x = _mm_add_ps(x, xmm2);
// x = _mm_add_ps(x, xmm3);
x = _mm_add_ps( x, _mm_mul_ps( y, _mm_add_ps( _mm_add_ps(*(v4sf*)_ps_minus_cephes_DP1, *(v4sf*)_ps_minus_cephes_DP2),
*(v4sf*)_ps_minus_cephes_DP3 ) ) );
#endif
#ifdef USE_SSE2
// emm4 = _mm_sub_epi32(emm4, *(v4si*)_pi32_2);
// emm4 = _mm_andnot_si128(emm4, *(v4si*)_pi32_4);
// emm4 = _mm_slli_epi32(emm4, 29);
// sign_bit_cos = _mm_castsi128_ps(emm4);
sign_bit_cos = _mm_castsi128_ps( _mm_slli_epi32( _mm_andnot_si128( _mm_sub_epi32(emm2, *(v4si*)_pi32_2), *(v4si*)_pi32_4), 29) );
#else
/* get the sign flag for the cosine */
mm4 = _mm_sub_pi32(mm4, *(v2si*)_pi32_2);
mm5 = _mm_sub_pi32(mm5, *(v2si*)_pi32_2);
mm4 = _mm_andnot_si64(mm4, *(v2si*)_pi32_4);
mm5 = _mm_andnot_si64(mm5, *(v2si*)_pi32_4);
mm4 = _mm_slli_pi32(mm4, 29);
mm5 = _mm_slli_pi32(mm5, 29);
COPY_MM_TO_XMM(mm4, mm5, sign_bit_cos);
_mm_empty(); /* good-bye mmx */
#endif
sign_bit_sin = _mm_xor_ps(sign_bit_sin, swap_sign_bit_sin);
/* Evaluate the first polynom (0 <= x <= Pi/4) */
#ifdef __GNUC__
z = x * x;
y = ( ( ( (*(v4sf*)_ps_coscof_p0) * z + *(v4sf*)_ps_coscof_p1 ) * z + *(v4sf*)_ps_coscof_p2 ) * z
- *(v4sf*)_ps_0p5 ) * z + *(v4sf*)_ps_1;
#else
z = _mm_mul_ps(x,x);
// y = *(v4sf*)_ps_coscof_p0;
//
// y = _mm_mul_ps(y, z);
// y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p1);
// y = _mm_mul_ps(y, z);
// y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p2);
// y = _mm_mul_ps(y, z);
// y = _mm_mul_ps(y, z);
// tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
// y = _mm_sub_ps(y, tmp);
// y = _mm_add_ps(y, *(v4sf*)_ps_1);
y = _mm_add_ps(
_mm_mul_ps(
_mm_sub_ps(
_mm_mul_ps(
_mm_add_ps(
_mm_mul_ps(
_mm_add_ps(
_mm_mul_ps(*(v4sf*)_ps_coscof_p0, z),
*(v4sf*)_ps_coscof_p1 ),
z ),
*(v4sf*)_ps_coscof_p2 ),
z ),
*(v4sf*)_ps_0p5 ),
z ),
*(v4sf*)_ps_1 );
#endif
/* Evaluate the second polynom (Pi/4 <= x <= 0) */
#ifdef __GNUC__
y2 = ( ( ( ( ((*(v4sf*)_ps_sincof_p0) * z ) + *(v4sf*)_ps_sincof_p1 ) * z ) + *(v4sf*)_ps_sincof_p2 ) * z
+ *(v4sf*)_ps_1 ) * x;
#else
// y2 = *(v4sf*)_ps_sincof_p0;
// y2 = _mm_mul_ps(y2, z);
// y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
// y2 = _mm_mul_ps(y2, z);
// y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
// y2 = _mm_mul_ps(y2, z);
// y2 = _mm_mul_ps(y2, x);
// y2 = _mm_add_ps(y2, x);
y2 = _mm_mul_ps(
_mm_add_ps(
_mm_mul_ps(
_mm_add_ps(
_mm_mul_ps(
_mm_add_ps(
_mm_mul_ps(*(v4sf*)_ps_sincof_p0, z ),
*(v4sf*)_ps_sincof_p1 ),
z ),
*(v4sf*)_ps_sincof_p2 ),
z ),
*(v4sf*)_ps_1 ),
x );
#endif
/* select the correct result from the two polynoms */
{
#if defined(__GNUC__0) && !defined(__MINGW32__)
// less precise results
xmm1 = _mm_andnot_ps( poly_mask, y) + (poly_mask & y2);
xmm2 = y + y2 - xmm1;
/* update the sign */
*s = xmm1 | sign_bit_sin;
*c = xmm2 | sign_bit_cos;
#else
// v4sf ysin2 = _mm_and_ps( poly_mask, y2);
// v4sf ysin1 = _mm_andnot_ps( poly_mask, y);
// y2 = _mm_sub_ps(y2,ysin2);
// y = _mm_sub_ps(y, ysin1);
//
// xmm1 = _mm_add_ps(ysin1,ysin2);
// xmm2 = _mm_add_ps(y,y2);
xmm1 = _mm_add_ps( _mm_andnot_ps( poly_mask, y), _mm_and_ps(poly_mask, y2) );
xmm2 = _mm_sub_ps( _mm_add_ps( y, y2 ), xmm1 );
/* update the sign */
*s = _mm_xor_ps(xmm1, sign_bit_sin);
*c = _mm_xor_ps(xmm2, sign_bit_cos);
#endif
}
}
#ifdef USE_SSE2
/*!
computes sine and cosine of the 2 doubles in x
*/
static inline void sincos_pd(v2df x, v2df *s, v2df *c)
{ v2df xmm1, xmm2, sign_bit_sin, y, y2, z, swap_sign_bit_sin, poly_mask;
v2df sign_bit_cos;
v4si emm2;
sign_bit_sin = x;
/* take the absolute value */
x = _mm_and_pd(x, *(v2df*)_pd_inv_sign_mask);
/* extract the sign bit (upper one) */
sign_bit_sin = _mm_and_pd(sign_bit_sin, *(v2df*)_pd_sign_mask);
/* scale by 4/Pi */
y = _mm_mul_pd(x, *(v2df*)_pd_cephes_FOPI);
/* store the integer part of y in emm2 */
emm2 = _mm_cvttpd_epi32(y);
/* j=(j+1) & (~1) (see the cephes sources) */
emm2 = _mm_and_si128( _mm_add_epi64( _mm_cvttpd_epi32(y), *(v4si*)_pi32_1 ), *(v4si*)_pi32_inv1 );
y = _mm_cvtepi32_pd(emm2);
/* get the swap sign flag for the sine */
{ v4sf sss = _mm_castsi128_ps( _mm_slli_epi32( _mm_and_si128(emm2, *(v4si*)_pi32_4), 29) );
float *fsss = ((float*)&sss);
swap_sign_bit_sin = _MM_SETR_PD( fsss[0], fsss[1] );
}
/* get the polynom selection mask for the sine*/
{ v4sf pm = _mm_castsi128_ps( _mm_cmpeq_epi32( _mm_and_si128(emm2, *(v4si*)_pi32_2), _MM_SETZERO_SI128()) );