summaryrefslogtreecommitdiff
path: root/sysdeps/ia64/fpu/libm_sincosf.S
blob: 26e66fad6eefaccd53c62f642ecd2d810fdead7a (plain)
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
.file "libm_sincosf.s"


// Copyright (c) 2002 - 2005, Intel Corporation
// All rights reserved.
//
// Contributed 2002 by the Intel Numerics Group, Intel Corporation
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * 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.
//
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.

// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS 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 INTEL OR ITS
// 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.
//
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at
// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
// History
//==============================================================
// 02/01/02 Initial version
// 02/18/02 Large arguments processing routine is excluded.
//          External interface entry points are added
// 02/26/02 Added temporary return of results in r8, r9
// 03/13/02 Corrected restore of predicate registers
// 03/19/02 Added stack unwind around call to __libm_cisf_large
// 09/05/02 Work range is widened by reduction strengthen (2 parts of Pi/16)
// 02/10/03 Reordered header: .section, .global, .proc, .align
// 02/11/04 cisf is moved to the separate file.
// 03/31/05 Reformatted delimiters between data tables

// API
//==============================================================
// 1) void sincosf(float, float*s, float*c)
// 2) __libm_sincosf - internal LIBM function, that accepts
//    argument in f8 and returns cosine through f8, sine through f9

//
// Overview of operation
//==============================================================
//
// Step 1
// ======
// Reduce x to region -1/2*pi/2^k ===== 0 ===== +1/2*pi/2^k  where k=4
//    divide x by pi/2^k.
//    Multiply by 2^k/pi.
//    nfloat = Round result to integer (round-to-nearest)
//
// r = x -  nfloat * pi/2^k
//    Do this as (x -  nfloat * HIGH(pi/2^k)) - nfloat * LOW(pi/2^k) for increased accuracy.
//    pi/2^k is stored as two numbers that when added make pi/2^k.
//       pi/2^k = HIGH(pi/2^k) + LOW(pi/2^k)
//    HIGH part is rounded to zero, LOW - to nearest
//
// x = (nfloat * pi/2^k) + r
//    r is small enough that we can use a polynomial approximation
//    and is referred to as the reduced argument.
//
// Step 3
// ======
// Take the unreduced part and remove the multiples of 2pi.
// So nfloat = nfloat (with lower k+1 bits cleared) + lower k+1 bits
//
//    nfloat (with lower k+1 bits cleared) is a multiple of 2^(k+1)
//    N * 2^(k+1)
//    nfloat * pi/2^k = N * 2^(k+1) * pi/2^k + (lower k+1 bits) * pi/2^k
//    nfloat * pi/2^k = N * 2 * pi + (lower k+1 bits) * pi/2^k
//    nfloat * pi/2^k = N2pi + M * pi/2^k
//
//
// Sin(x) = Sin((nfloat * pi/2^k) + r)
//        = Sin(nfloat * pi/2^k) * Cos(r) + Cos(nfloat * pi/2^k) * Sin(r)
//
//          Sin(nfloat * pi/2^k) = Sin(N2pi + Mpi/2^k)
//                               = Sin(N2pi)Cos(Mpi/2^k) + Cos(N2pi)Sin(Mpi/2^k)
//                               = Sin(Mpi/2^k)
//
//          Cos(nfloat * pi/2^k) = Cos(N2pi + Mpi/2^k)
//                               = Cos(N2pi)Cos(Mpi/2^k) + Sin(N2pi)Sin(Mpi/2^k)
//                               = Cos(Mpi/2^k)
//
// Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r)
//
//
// Step 4
// ======
// 0 <= M < 2^(k+1)
// There are 2^(k+1) Sin entries in a table.
// There are 2^(k+1) Cos entries in a table.
//
// Get Sin(Mpi/2^k) and Cos(Mpi/2^k) by table lookup.
//
//
// Step 5
// ======
// Calculate Cos(r) and Sin(r) by polynomial approximation.
//
// Cos(r) = 1 + r^2 q1  + r^4 q2 = Series for Cos
// Sin(r) = r + r^3 p1  + r^5 p2 = Series for Sin
//
// and the coefficients q1, q2 and p1, p2 are stored in a table
//
//
// Calculate
// Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r)
//
// as follows
//
//    S[m] = Sin(Mpi/2^k) and C[m] = Cos(Mpi/2^k)
//    rsq = r*r
//
//
//    P = p1 + r^2p2
//    Q = q1 + r^2q2
//
//       rcub = r * rsq
//       Sin(r) = r + rcub * P
//              = r + r^3p1  + r^5p2 = Sin(r)
//
//       P =  r + rcub * P
//
//    Answer = S[m] Cos(r) + C[m] P
//
//       Cos(r) = 1 + rsq Q
//       Cos(r) = 1 + r^2 Q
//       Cos(r) = 1 + r^2 (q1 + r^2q2)
//       Cos(r) = 1 + r^2q1 + r^4q2
//
//       S[m] Cos(r) = S[m](1 + rsq Q)
//       S[m] Cos(r) = S[m] + S[m] rsq Q
//       S[m] Cos(r) = S[m] + s_rsq Q
//       Q           = S[m] + s_rsq Q
//
// Then,
//
//    Answer = Q + C[m] P


// Registers used
//==============================================================
// general input registers:
// r14 -> r19
// r32 -> r49

// predicate registers used:
// p6 -> p14

// floating-point registers used
// f9 -> f15
// f32 -> f100

// Assembly macros
//==============================================================

cisf_Arg                     = f8

cisf_Sin_res                 = f9
cisf_Cos_res                 = f8


cisf_NORM_f8                 = f10
cisf_W                       = f11
cisf_int_Nfloat              = f12
cisf_Nfloat                  = f13

cisf_r                       = f14
cisf_r_exact                 = f68
cisf_rsq                     = f15
cisf_rcub                    = f32

cisf_Inv_Pi_by_16            = f33
cisf_Pi_by_16_hi             = f34
cisf_Pi_by_16_lo             = f35

cisf_Inv_Pi_by_64            = f36
cisf_Pi_by_64_hi             = f37
cisf_Pi_by_64_lo             = f38


cisf_P1                      = f39
cisf_Q1                      = f40
cisf_P2                      = f41
cisf_Q2                      = f42
cisf_P3                      = f43
cisf_Q3                      = f44
cisf_P4                      = f45
cisf_Q4                      = f46

cisf_P_temp1                 = f47
cisf_P_temp2                 = f48

cisf_Q_temp1                 = f49
cisf_Q_temp2                 = f50

cisf_P                       = f51

cisf_SIG_INV_PI_BY_16_2TO61  = f52
cisf_RSHF_2TO61              = f53
cisf_RSHF                    = f54
cisf_2TOM61                  = f55
cisf_NFLOAT                  = f56
cisf_W_2TO61_RSH             = f57

cisf_tmp                     = f58

cisf_Sm_sin                  = f59
cisf_Cm_sin                  = f60

cisf_Sm_cos                  = f61
cisf_Cm_cos                  = f62

cisf_srsq_sin                = f63
cisf_srsq_cos                = f64

cisf_Q_sin                   = f65
cisf_Q_cos                   = f66
cisf_Q                       = f67

/////////////////////////////////////////////////////////////

cisf_pResSin                 = r33
cisf_pResCos                 = r34

cisf_exp_limit               = r35
cisf_r_signexp               = r36
cisf_AD_beta_table           = r37
cisf_r_sincos                = r38

cisf_r_exp                   = r39
cisf_r_17_ones               = r40

cisf_GR_sig_inv_pi_by_16     = r14
cisf_GR_rshf_2to61           = r15
cisf_GR_rshf                 = r16
cisf_GR_exp_2tom61           = r17
cisf_GR_n                    = r18

cisf_GR_n_sin                = r19
cisf_GR_m_sin                = r41
cisf_GR_32m_sin              = r41

cisf_GR_n_cos                = r42
cisf_GR_m_cos                = r43
cisf_GR_32m_cos              = r43

cisf_AD_2_sin                = r44
cisf_AD_2_cos                = r45

cisf_gr_tmp                  = r46
GR_SAVE_B0                   = r47
GR_SAVE_GP                   = r48
rB0_SAVED                    = r49
GR_SAVE_PFS                  = r50
GR_SAVE_PR                   = r51
cisf_AD_1                    = r52

RODATA

.align 16
// Pi/16 parts
LOCAL_OBJECT_START(double_cisf_pi)
   data8 0xC90FDAA22168C234, 0x00003FFC // pi/16 1st part
   data8 0xC4C6628B80DC1CD1, 0x00003FBC // pi/16 2nd part
LOCAL_OBJECT_END(double_cisf_pi)

// Coefficients for polynomials
LOCAL_OBJECT_START(double_cisf_pq_k4)
   data8 0x3F810FABB668E9A2 // P2
   data8 0x3FA552E3D6DE75C9 // Q2
   data8 0xBFC555554447BC7F // P1
   data8 0xBFDFFFFFC447610A // Q1
LOCAL_OBJECT_END(double_cisf_pq_k4)

// Sincos table (S[m], C[m])
LOCAL_OBJECT_START(double_sin_cos_beta_k4)
    data8 0x0000000000000000 // sin ( 0 Pi / 16 )
    data8 0x3FF0000000000000 // cos ( 0 Pi / 16 )
//
    data8 0x3FC8F8B83C69A60B // sin ( 1 Pi / 16 )
    data8 0x3FEF6297CFF75CB0 // cos ( 1 Pi / 16 )
//
    data8 0x3FD87DE2A6AEA963 // sin ( 2 Pi / 16 )
    data8 0x3FED906BCF328D46 // cos ( 2 Pi / 16 )
//
    data8 0x3FE1C73B39AE68C8 // sin ( 3 Pi / 16 )
    data8 0x3FEA9B66290EA1A3 // cos ( 3 Pi / 16 )
//
    data8 0x3FE6A09E667F3BCD // sin ( 4 Pi / 16 )
    data8 0x3FE6A09E667F3BCD // cos ( 4 Pi / 16 )
//
    data8 0x3FEA9B66290EA1A3 // sin ( 5 Pi / 16 )
    data8 0x3FE1C73B39AE68C8 // cos ( 5 Pi / 16 )
//
    data8 0x3FED906BCF328D46 // sin ( 6 Pi / 16 )
    data8 0x3FD87DE2A6AEA963 // cos ( 6 Pi / 16 )
//
    data8 0x3FEF6297CFF75CB0 // sin ( 7 Pi / 16 )
    data8 0x3FC8F8B83C69A60B // cos ( 7 Pi / 16 )
//
    data8 0x3FF0000000000000 // sin ( 8 Pi / 16 )
    data8 0x0000000000000000 // cos ( 8 Pi / 16 )
//
    data8 0x3FEF6297CFF75CB0 // sin ( 9 Pi / 16 )
    data8 0xBFC8F8B83C69A60B // cos ( 9 Pi / 16 )
//
    data8 0x3FED906BCF328D46 // sin ( 10 Pi / 16 )
    data8 0xBFD87DE2A6AEA963 // cos ( 10 Pi / 16 )
//
    data8 0x3FEA9B66290EA1A3 // sin ( 11 Pi / 16 )
    data8 0xBFE1C73B39AE68C8 // cos ( 11 Pi / 16 )
//
    data8 0x3FE6A09E667F3BCD // sin ( 12 Pi / 16 )
    data8 0xBFE6A09E667F3BCD // cos ( 12 Pi / 16 )
//
    data8 0x3FE1C73B39AE68C8 // sin ( 13 Pi / 16 )
    data8 0xBFEA9B66290EA1A3 // cos ( 13 Pi / 16 )
//
    data8 0x3FD87DE2A6AEA963 // sin ( 14 Pi / 16 )
    data8 0xBFED906BCF328D46 // cos ( 14 Pi / 16 )
//
    data8 0x3FC8F8B83C69A60B // sin ( 15 Pi / 16 )
    data8 0xBFEF6297CFF75CB0 // cos ( 15 Pi / 16 )
//
    data8 0x0000000000000000 // sin ( 16 Pi / 16 )
    data8 0xBFF0000000000000 // cos ( 16 Pi / 16 )
//
    data8 0xBFC8F8B83C69A60B // sin ( 17 Pi / 16 )
    data8 0xBFEF6297CFF75CB0 // cos ( 17 Pi / 16 )
//
    data8 0xBFD87DE2A6AEA963 // sin ( 18 Pi / 16 )
    data8 0xBFED906BCF328D46 // cos ( 18 Pi / 16 )
//
    data8 0xBFE1C73B39AE68C8 // sin ( 19 Pi / 16 )
    data8 0xBFEA9B66290EA1A3 // cos ( 19 Pi / 16 )
//
    data8 0xBFE6A09E667F3BCD // sin ( 20 Pi / 16 )
    data8 0xBFE6A09E667F3BCD // cos ( 20 Pi / 16 )
//
    data8 0xBFEA9B66290EA1A3 // sin ( 21 Pi / 16 )
    data8 0xBFE1C73B39AE68C8 // cos ( 21 Pi / 16 )
//
    data8 0xBFED906BCF328D46 // sin ( 22 Pi / 16 )
    data8 0xBFD87DE2A6AEA963 // cos ( 22 Pi / 16 )
//
    data8 0xBFEF6297CFF75CB0 // sin ( 23 Pi / 16 )
    data8 0xBFC8F8B83C69A60B // cos ( 23 Pi / 16 )
//
    data8 0xBFF0000000000000 // sin ( 24 Pi / 16 )
    data8 0x0000000000000000 // cos ( 24 Pi / 16 )
//
    data8 0xBFEF6297CFF75CB0 // sin ( 25 Pi / 16 )
    data8 0x3FC8F8B83C69A60B // cos ( 25 Pi / 16 )
//
    data8 0xBFED906BCF328D46 // sin ( 26 Pi / 16 )
    data8 0x3FD87DE2A6AEA963 // cos ( 26 Pi / 16 )
//
    data8 0xBFEA9B66290EA1A3 // sin ( 27 Pi / 16 )
    data8 0x3FE1C73B39AE68C8 // cos ( 27 Pi / 16 )
//
    data8 0xBFE6A09E667F3BCD // sin ( 28 Pi / 16 )
    data8 0x3FE6A09E667F3BCD // cos ( 28 Pi / 16 )
//
    data8 0xBFE1C73B39AE68C8 // sin ( 29 Pi / 16 )
    data8 0x3FEA9B66290EA1A3 // cos ( 29 Pi / 16 )
//
    data8 0xBFD87DE2A6AEA963 // sin ( 30 Pi / 16 )
    data8 0x3FED906BCF328D46 // cos ( 30 Pi / 16 )
//
    data8 0xBFC8F8B83C69A60B // sin ( 31 Pi / 16 )
    data8 0x3FEF6297CFF75CB0 // cos ( 31 Pi / 16 )
//
    data8 0x0000000000000000 // sin ( 32 Pi / 16 )
    data8 0x3FF0000000000000 // cos ( 32 Pi / 16 )
LOCAL_OBJECT_END(double_sin_cos_beta_k4)

.section .text

GLOBAL_IEEE754_ENTRY(sincosf)
// cis_GR_sig_inv_pi_by_16 = significand of 16/pi
{ .mlx
      alloc         GR_SAVE_PFS              = ar.pfs, 0, 21, 0, 0
      movl          cisf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A // 16/pi signd

}
// cis_GR_rshf_2to61 = 1.1000 2^(63+63-2)
{ .mlx
      addl          cisf_AD_1           = @ltoff(double_cisf_pi), gp
      movl          cisf_GR_rshf_2to61  = 0x47b8000000000000 // 1.1 2^(63+63-2)
};;

{ .mfi
      ld8           cisf_AD_1           = [cisf_AD_1]
      fnorm.s1      cisf_NORM_f8        = cisf_Arg
      cmp.eq        p13, p14            = r0, r0 // p13 set for sincos
}
// cis_GR_exp_2tom61 = exponent of scaling factor 2^-61
{ .mib
      mov           cisf_GR_exp_2tom61  = 0xffff-61
      nop.i         0
      br.cond.sptk  _CISF_COMMON
};;
GLOBAL_IEEE754_END(sincosf)

GLOBAL_LIBM_ENTRY(__libm_sincosf)
{ .mlx
// cisf_GR_sig_inv_pi_by_16 = significand of 16/pi
      alloc         GR_SAVE_PFS              = ar.pfs,0,21,0,0
      movl          cisf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A
}
// cisf_GR_rshf_2to61 = 1.1000 2^(63+63-2)
{ .mlx
      addl          cisf_AD_1           = @ltoff(double_cisf_pi), gp
      movl          cisf_GR_rshf_2to61  = 0x47b8000000000000
};;

// p14 set for __libm_sincos and cis
{ .mfi
      ld8           cisf_AD_1           = [cisf_AD_1]
      fnorm.s1      cisf_NORM_f8        = cisf_Arg
      cmp.eq        p14, p13            = r0, r0
}
// cisf_GR_exp_2tom61 = exponent of scaling factor 2^-61
{ .mib
      mov           cisf_GR_exp_2tom61  = 0xffff-61
      nop.i         0
      nop.b         0
};;

_CISF_COMMON:
//  Form two constants we need
//  16/pi * 2^-2 * 2^63, scaled by 2^61 since we just loaded the significand
//  1.1000...000 * 2^(63+63-2) to right shift int(W) into the low significand
//  fcmp used to set denormal, and invalid on snans
{ .mfi
      setf.sig      cisf_SIG_INV_PI_BY_16_2TO61 = cisf_GR_sig_inv_pi_by_16
      fclass.m      p6,p0                       = cisf_Arg, 0xe7//if x=0,inf,nan
      addl          cisf_gr_tmp                 = -1, r0
}
// cisf_GR_rshf = 1.1000 2^63 for right shift
{ .mlx
      setf.d        cisf_RSHF_2TO61     = cisf_GR_rshf_2to61
      movl          cisf_GR_rshf        = 0x43e8000000000000
};;

//  Form another constant
//  2^-61 for scaling Nfloat
//  0x10017 is register_bias + 24.
//  So if f8 >= 2^24, go to large args routine
{ .mmi
      getf.exp      cisf_r_signexp      = cisf_Arg
      setf.exp      cisf_2TOM61         = cisf_GR_exp_2tom61
      mov           cisf_exp_limit      = 0x10017
};;

// Load the two pieces of pi/16
// Form another constant
//  1.1000...000 * 2^63, the right shift constant
{ .mmb
      ldfe          cisf_Pi_by_16_hi    = [cisf_AD_1],16
      setf.d        cisf_RSHF           = cisf_GR_rshf
(p6)  br.cond.spnt  _CISF_SPECIAL_ARGS
};;

{ .mmi
      ldfe          cisf_Pi_by_16_lo    = [cisf_AD_1],16
      setf.sig      cisf_tmp            = cisf_gr_tmp //constant for inexact set
      nop.i         0
};;

// Start loading P, Q coefficients
{ .mmi
      ldfpd         cisf_P2,cisf_Q2     = [cisf_AD_1],16
      nop.m         0
      dep.z         cisf_r_exp          = cisf_r_signexp, 0, 17
};;

// p10 is true if we must call routines to handle larger arguments
// p10 is true if f8 exp is >= 0x10017
{ .mmb
      ldfpd         cisf_P1,cisf_Q1     = [cisf_AD_1], 16
      cmp.ge        p10, p0             = cisf_r_exp, cisf_exp_limit
(p10) br.cond.spnt  _CISF_LARGE_ARGS    // go to |x| >= 2^24 path
};;

// cisf_W          = x * cisf_Inv_Pi_by_16
// Multiply x by scaled 16/pi and add large const to shift integer part of W to
//   rightmost bits of significand
{ .mfi
      nop.m  0
      fma.s1 cisf_W_2TO61_RSH = cisf_NORM_f8,cisf_SIG_INV_PI_BY_16_2TO61,cisf_RSHF_2TO61
      nop.i  0
};;

// cisf_NFLOAT = Round_Int_Nearest(cisf_W)
{ .mfi
      nop.m         0
      fms.s1        cisf_NFLOAT         = cisf_W_2TO61_RSH,cisf_2TOM61,cisf_RSHF
      nop.i         0
};;

// N = (int)cisf_int_Nfloat
{ .mfi
      getf.sig      cisf_GR_n           = cisf_W_2TO61_RSH
      nop.f         0
      nop.i         0
};;

// Add 2^(k-1) (which is in cisf_r_sincos) to N
// cisf_r = -cisf_Nfloat * cisf_Pi_by_16_hi + x
// cisf_r = cisf_r -cisf_Nfloat * cisf_Pi_by_16_lo
{ .mfi
      add     cisf_GR_n_cos = 0x8, cisf_GR_n
      fnma.s1 cisf_r        = cisf_NFLOAT, cisf_Pi_by_16_hi, cisf_NORM_f8
      nop.i   0
};;

//Get M (least k+1 bits of N)
{ .mmi
      and           cisf_GR_m_sin       = 0x1f,cisf_GR_n
      and           cisf_GR_m_cos       = 0x1f,cisf_GR_n_cos
      nop.i         0
};;

{ .mmi
      shladd        cisf_AD_2_cos       = cisf_GR_m_cos,4, cisf_AD_1
      shladd        cisf_AD_2_sin       = cisf_GR_m_sin,4, cisf_AD_1
      nop.i         0
};;

// den. input to set uflow
{ .mmf
      ldfpd         cisf_Sm_sin, cisf_Cm_sin = [cisf_AD_2_sin]
      ldfpd         cisf_Sm_cos, cisf_Cm_cos = [cisf_AD_2_cos]
      fclass.m.unc  p10,p0                   = cisf_Arg,0x0b
};;

{ .mfi
      nop.m         0
      fma.s1        cisf_rsq            = cisf_r, cisf_r,   f0  // get r^2
      nop.i         0
}
{ .mfi
      nop.m         0
      fmpy.s0       cisf_tmp            = cisf_tmp,cisf_tmp // inexact flag
      nop.i         0
};;

{ .mmf
      nop.m         0
      nop.m         0
      fnma.s1       cisf_r_exact        = cisf_NFLOAT, cisf_Pi_by_16_lo, cisf_r
};;

{ .mfi
      nop.m         0
      fma.s1        cisf_P              = cisf_rsq, cisf_P2, cisf_P1
      nop.i         0
}
{ .mfi
      nop.m         0
      fma.s1        cisf_Q              = cisf_rsq, cisf_Q2, cisf_Q1
      nop.i         0
};;

{ .mfi
      nop.m         0
      fmpy.s1       cisf_rcub           = cisf_r_exact, cisf_rsq // get r^3
      nop.i         0
};;

{ .mfi
      nop.m         0
      fmpy.s1       cisf_srsq_sin       = cisf_Sm_sin,cisf_rsq
      nop.i         0
}
{ .mfi
      nop.m         0
      fmpy.s1       cisf_srsq_cos       = cisf_Sm_cos,cisf_rsq
      nop.i         0
};;

{ .mfi
      nop.m         0
      fma.s1        cisf_P              = cisf_rcub,cisf_P,cisf_r_exact
      nop.i         0
};;

{ .mfi
      nop.m         0
      fma.s1        cisf_Q_sin          = cisf_srsq_sin,cisf_Q, cisf_Sm_sin
      nop.i         0
}
{ .mfi
      nop.m         0
      fma.s1        cisf_Q_cos          = cisf_srsq_cos,cisf_Q, cisf_Sm_cos
      nop.i         0
};;

// If den. arg, force underflow to be set
{ .mfi
      nop.m         0
(p10) fmpy.s.s0     cisf_tmp            = cisf_Arg,cisf_Arg
      nop.i         0
};;

//Final sin
{ .mfi
      nop.m         0
      fma.s.s0      cisf_Sin_res        = cisf_Cm_sin, cisf_P, cisf_Q_sin
      nop.i         0
}
//Final cos
{ .mfb
      nop.m         0
      fma.s.s0      cisf_Cos_res    = cisf_Cm_cos, cisf_P, cisf_Q_cos
(p14) br.cond.sptk  _CISF_RETURN //com. exit for __libm_sincos and cis main path
};;

{ .mmb
      stfs          [cisf_pResSin]      = cisf_Sin_res
      stfs          [cisf_pResCos]      = cisf_Cos_res
      br.ret.sptk   b0 // common exit for sincos main path
};;

_CISF_SPECIAL_ARGS:
// sinf(+/-0) = +/-0
// sinf(Inf)  = NaN
// sinf(NaN)  = NaN
{ .mfi
      nop.m         999
      fma.s.s0      cisf_Sin_res        = cisf_Arg, f0, f0 // sinf(+/-0,NaN,Inf)
      nop.i         999
};;

// cosf(+/-0) = 1.0
// cosf(Inf)  = NaN
// cosf(NaN)  = NaN
{ .mfb
      nop.m         999
      fma.s.s0      cisf_Cos_res        = cisf_Arg, f0, f1 // cosf(+/-0,NaN,Inf)
(p14) br.cond.sptk  _CISF_RETURN //spec exit for __libm_sincos and cis main path
};;

{ .mmb
      stfs          [cisf_pResSin]      = cisf_Sin_res
      stfs          [cisf_pResCos]      = cisf_Cos_res
      br.ret.sptk   b0 // special exit for sincos main path
};;

 // exit for sincos
 // NOTE! r8 and r9 used only because of compiler issue
 // connected with float point complex function arguments pass
 // After fix of this issue this operations can be deleted
_CISF_RETURN:
{ .mmb
      getf.s        r8                  = cisf_Cos_res
      getf.s        r9                  = cisf_Sin_res
      br.ret.sptk   b0 // exit for sincos
};;
GLOBAL_LIBM_END(__libm_sincosf)

////  |x| > 2^24 path  ///////
.proc _CISF_LARGE_ARGS
_CISF_LARGE_ARGS:
.prologue
{ .mfi
      nop.m         0
      nop.f         0
.save ar.pfs, GR_SAVE_PFS
      mov           GR_SAVE_PFS         = ar.pfs
};;

{ .mfi
      mov           GR_SAVE_GP          = gp
      nop.f         0
.save b0, GR_SAVE_B0
      mov           GR_SAVE_B0          = b0
};;

.body
// Call of huge arguments sincos
{ .mib
      nop.m         0
      mov           GR_SAVE_PR          = pr
      br.call.sptk  b0                  = __libm_sincos_large
};;

{ .mfi
      mov           gp                  = GR_SAVE_GP
      nop.f         0
      mov           pr                  = GR_SAVE_PR, 0x1fffe
}
;;

{ .mfi
      nop.m         0
      nop.f         0
      mov           b0                  = GR_SAVE_B0
}
;;

{ .mfi
      nop.m         0
      fma.s.s0      cisf_Cos_res        = cisf_Cos_res, f1, f0
      mov           ar.pfs              = GR_SAVE_PFS
}
// exit for |x| > 2^24 path (__libm_sincos and cis)
{ .mfb
      nop.m         0
      fma.s.s0      cisf_Sin_res        = cisf_Sin_res, f1, f0
(p14) br.cond.sptk  _CISF_RETURN
};;

{ .mmb
      stfs          [cisf_pResSin]      = cisf_Sin_res
      stfs          [cisf_pResCos]      = cisf_Cos_res
      br.ret.sptk   b0 // exit for sincos |x| > 2^24 path
};;

.endp _CISF_LARGE_ARGS

.type   __libm_sincos_large#,@function
.global __libm_sincos_large#