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
|
.file "acos.s"
// Copyright (c) 2000 - 2003 Intel Corporation
// All rights reserved.
//
// Contributed 2000 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
//==============================================================
// 02/02/00 Initial version
// 08/17/00 New and much faster algorithm.
// 08/30/00 Avoided bank conflicts on loads, shortened |x|=1 and x=0 paths,
// fixed mfb split issue stalls.
// 05/20/02 Cleaned up namespace and sf0 syntax
// 08/02/02 New and much faster algorithm II
// 02/06/03 Reordered header: .section, .global, .proc, .align
// Description
//=========================================
// The acos function computes the principal value of the arc cosine of x.
// acos(0) returns Pi/2, acos(1) returns 0, acos(-1) returns Pi.
// A doman error occurs for arguments not in the range [-1,+1].
//
// The acos function returns the arc cosine in the range [0, Pi] radians.
//
// There are 8 paths:
// 1. x = +/-0.0
// Return acos(x) = Pi/2 + x
//
// 2. 0.0 < |x| < 0.625
// Return acos(x) = Pi/2 - x - x^3 *PolA(x^2)
// where PolA(x^2) = A3 + A5*x^2 + A7*x^4 +...+ A35*x^32
//
// 3. 0.625 <=|x| < 1.0
// Return acos(x) = Pi/2 - asin(x) =
// = Pi/2 - sign(x) * ( Pi/2 - sqrt(R) * PolB(R))
// Where R = 1 - |x|,
// PolB(R) = B0 + B1*R + B2*R^2 +...+B12*R^12
//
// sqrt(R) is approximated using the following sequence:
// y0 = (1 + eps)/sqrt(R) - initial approximation by frsqrta,
// |eps| < 2^(-8)
// Then 3 iterations are used to refine the result:
// H0 = 0.5*y0
// S0 = R*y0
//
// d0 = 0.5 - H0*S0
// H1 = H0 + d0*H0
// S1 = S0 + d0*S0
//
// d1 = 0.5 - H1*S1
// H2 = H1 + d0*H1
// S2 = S1 + d0*S1
//
// d2 = 0.5 - H2*S2
// S3 = S3 + d2*S3
//
// S3 approximates sqrt(R) with enough accuracy for this algorithm
//
// So, the result should be reconstracted as follows:
// acos(x) = Pi/2 - sign(x) * (Pi/2 - S3*PolB(R))
//
// But for optimization purposes the reconstruction step is slightly
// changed:
// acos(x) = Cpi + sign(x)*PolB(R)*S2 - sign(x)*d2*S2*PolB(R)
// where Cpi = 0 if x > 0 and Cpi = Pi if x < 0
//
// 4. |x| = 1.0
// Return acos(1.0) = 0.0, acos(-1.0) = Pi
//
// 5. 1.0 < |x| <= +INF
// A doman error occurs for arguments not in the range [-1,+1]
//
// 6. x = [S,Q]NaN
// Return acos(x) = QNaN
//
// 7. x is denormal
// Return acos(x) = Pi/2 - x,
//
// 8. x is unnormal
// Normalize input in f8 and return to the very beginning of the function
//
// Registers used
//==============================================================
// Floating Point registers used:
// f8, input, output
// f6, f7, f9 -> f15, f32 -> f64
// General registers used:
// r3, r21 -> r31, r32 -> r38
// Predicate registers used:
// p0, p6 -> p14
//
// Assembly macros
//=========================================
// integer registers used
// scratch
rTblAddr = r3
rPiBy2Ptr = r21
rTmpPtr3 = r22
rDenoBound = r23
rOne = r24
rAbsXBits = r25
rHalf = r26
r0625 = r27
rSign = r28
rXBits = r29
rTmpPtr2 = r30
rTmpPtr1 = r31
// stacked
GR_SAVE_PFS = r32
GR_SAVE_B0 = r33
GR_SAVE_GP = r34
GR_Parameter_X = r35
GR_Parameter_Y = r36
GR_Parameter_RESULT = r37
GR_Parameter_TAG = r38
// floating point registers used
FR_X = f10
FR_Y = f1
FR_RESULT = f8
// scratch
fXSqr = f6
fXCube = f7
fXQuadr = f9
f1pX = f10
f1mX = f11
f1pXRcp = f12
f1mXRcp = f13
fH = f14
fS = f15
// stacked
fA3 = f32
fB1 = f32
fA5 = f33
fB2 = f33
fA7 = f34
fPiBy2 = f34
fA9 = f35
fA11 = f36
fB10 = f35
fB11 = f36
fA13 = f37
fA15 = f38
fB4 = f37
fB5 = f38
fA17 = f39
fA19 = f40
fB6 = f39
fB7 = f40
fA21 = f41
fA23 = f42
fB3 = f41
fB8 = f42
fA25 = f43
fA27 = f44
fB9 = f43
fB12 = f44
fA29 = f45
fA31 = f46
fA33 = f47
fA35 = f48
fBaseP = f49
fB0 = f50
fSignedS = f51
fD = f52
fHalf = f53
fR = f54
fCloseTo1Pol = f55
fSignX = f56
fDenoBound = f57
fNormX = f58
fX8 = f59
fRSqr = f60
fRQuadr = f61
fR8 = f62
fX16 = f63
fCpi = f64
// Data tables
//==============================================================
RODATA
.align 16
LOCAL_OBJECT_START(acos_base_range_table)
// Ai: Polynomial coefficients for the acos(x), |x| < .625000
// Bi: Polynomial coefficients for the acos(x), |x| > .625000
data8 0xBFDAAB56C01AE468 //A29
data8 0x3FE1C470B76A5B2B //A31
data8 0xBFDC5FF82A0C4205 //A33
data8 0x3FC71FD88BFE93F0 //A35
data8 0xB504F333F9DE6487, 0x00003FFF //B0
data8 0xAAAAAAAAAAAAFC18, 0x00003FFC //A3
data8 0x3F9F1C71BC4A7823 //A9
data8 0x3F96E8BBAAB216B2 //A11
data8 0x3F91C4CA1F9F8A98 //A13
data8 0x3F8C9DDCEDEBE7A6 //A15
data8 0x3F877784442B1516 //A17
data8 0x3F859C0491802BA2 //A19
data8 0x9999999998C88B8F, 0x00003FFB //A5
data8 0x3F6BD7A9A660BF5E //A21
data8 0x3F9FC1659340419D //A23
data8 0xB6DB6DB798149BDF, 0x00003FFA //A7
data8 0xBFB3EF18964D3ED3 //A25
data8 0x3FCD285315542CF2 //A27
data8 0xF15BEEEFF7D2966A, 0x00003FFB //B1
data8 0x3EF0DDA376D10FB3 //B10
data8 0xBEB83CAFE05EBAC9 //B11
data8 0x3F65FFB67B513644 //B4
data8 0x3F5032FBB86A4501 //B5
data8 0x3F392162276C7CBA //B6
data8 0x3F2435949FD98BDF //B7
data8 0xD93923D7FA08341C, 0x00003FF9 //B2
data8 0x3F802995B6D90BDB //B3
data8 0x3F10DF86B341A63F //B8
data8 0xC90FDAA22168C235, 0x00003FFF // Pi/2
data8 0x3EFA3EBD6B0ECB9D //B9
data8 0x3EDE18BA080E9098 //B12
LOCAL_OBJECT_END(acos_base_range_table)
.section .text
GLOBAL_LIBM_ENTRY(acos)
acos_unnormal_back:
{ .mfi
getf.d rXBits = f8 // grab bits of input value
// set p12 = 1 if x is a NaN, denormal, or zero
fclass.m p12, p0 = f8, 0xcf
adds rSign = 1, r0
}
{ .mfi
addl rTblAddr = @ltoff(acos_base_range_table),gp
// 1 - x = 1 - |x| for positive x
fms.s1 f1mX = f1, f1, f8
addl rHalf = 0xFFFE, r0 // exponent of 1/2
}
;;
{ .mfi
addl r0625 = 0x3FE4, r0 // high 16 bits of 0.625
// set p8 = 1 if x < 0
fcmp.lt.s1 p8, p9 = f8, f0
shl rSign = rSign, 63 // sign bit
}
{ .mfi
// point to the beginning of the table
ld8 rTblAddr = [rTblAddr]
// 1 + x = 1 - |x| for negative x
fma.s1 f1pX = f1, f1, f8
adds rOne = 0x3FF, r0
}
;;
{ .mfi
andcm rAbsXBits = rXBits, rSign // bits of |x|
fmerge.s fSignX = f8, f1 // signum(x)
shl r0625 = r0625, 48 // bits of DP representation of 0.625
}
{ .mfb
setf.exp fHalf = rHalf // load A2 to FP reg
fma.s1 fXSqr = f8, f8, f0 // x^2
// branch on special path if x is a NaN, denormal, or zero
(p12) br.cond.spnt acos_special
}
;;
{ .mfi
adds rPiBy2Ptr = 272, rTblAddr
nop.f 0
shl rOne = rOne, 52 // bits of 1.0
}
{ .mfi
adds rTmpPtr1 = 16, rTblAddr
nop.f 0
// set p6 = 1 if |x| < 0.625
cmp.lt p6, p7 = rAbsXBits, r0625
}
;;
{ .mfi
ldfpd fA29, fA31 = [rTblAddr] // A29, fA31
// 1 - x = 1 - |x| for positive x
(p9) fms.s1 fR = f1, f1, f8
// point to coefficient of "near 1" polynomial
(p7) adds rTmpPtr2 = 176, rTblAddr
}
{ .mfi
ldfpd fA33, fA35 = [rTmpPtr1], 16 // A33, fA35
// 1 + x = 1 - |x| for negative x
(p8) fma.s1 fR = f1, f1, f8
(p6) adds rTmpPtr2 = 48, rTblAddr
}
;;
{ .mfi
ldfe fB0 = [rTmpPtr1], 16 // B0
nop.f 0
nop.i 0
}
{ .mib
adds rTmpPtr3 = 16, rTmpPtr2
// set p10 = 1 if |x| = 1.0
cmp.eq p10, p0 = rAbsXBits, rOne
// branch on special path for |x| = 1.0
(p10) br.cond.spnt acos_abs_1
}
;;
{ .mfi
ldfe fA3 = [rTmpPtr2], 48 // A3 or B1
nop.f 0
adds rTmpPtr1 = 64, rTmpPtr3
}
{ .mib
ldfpd fA9, fA11 = [rTmpPtr3], 16 // A9, A11 or B10, B11
// set p11 = 1 if |x| > 1.0
cmp.gt p11, p0 = rAbsXBits, rOne
// branch on special path for |x| > 1.0
(p11) br.cond.spnt acos_abs_gt_1
}
;;
{ .mfi
ldfpd fA17, fA19 = [rTmpPtr2], 16 // A17, A19 or B6, B7
// initial approximation of 1 / sqrt(1 - x)
frsqrta.s1 f1mXRcp, p0 = f1mX
nop.i 0
}
{ .mfi
ldfpd fA13, fA15 = [rTmpPtr3] // A13, A15 or B4, B5
fma.s1 fXCube = fXSqr, f8, f0 // x^3
nop.i 0
}
;;
{ .mfi
ldfe fA5 = [rTmpPtr2], 48 // A5 or B2
// initial approximation of 1 / sqrt(1 + x)
frsqrta.s1 f1pXRcp, p0 = f1pX
nop.i 0
}
{ .mfi
ldfpd fA21, fA23 = [rTmpPtr1], 16 // A21, A23 or B3, B8
fma.s1 fXQuadr = fXSqr, fXSqr, f0 // x^4
nop.i 0
}
;;
{ .mfi
ldfe fA7 = [rTmpPtr1] // A7 or Pi/2
fma.s1 fRSqr = fR, fR, f0 // R^2
nop.i 0
}
{ .mfb
ldfpd fA25, fA27 = [rTmpPtr2] // A25, A27 or B9, B12
nop.f 0
(p6) br.cond.spnt acos_base_range;
}
;;
{ .mfi
nop.m 0
(p9) fma.s1 fH = fHalf, f1mXRcp, f0 // H0 for x > 0
nop.i 0
}
{ .mfi
nop.m 0
(p9) fma.s1 fS = f1mX, f1mXRcp, f0 // S0 for x > 0
nop.i 0
}
;;
{ .mfi
nop.m 0
(p8) fma.s1 fH = fHalf, f1pXRcp, f0 // H0 for x < 0
nop.i 0
}
{ .mfi
nop.m 0
(p8) fma.s1 fS = f1pX, f1pXRcp, f0 // S0 for x > 0
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fRQuadr = fRSqr, fRSqr, f0 // R^4
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fB11 = fB11, fR, fB10
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fB1 = fB1, fR, fB0
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fB5 = fB5, fR, fB4
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fB7 = fB7, fR, fB6
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fB3 = fB3, fR, fB2
nop.i 0
}
;;
{ .mfi
nop.m 0
fnma.s1 fD = fH, fS, fHalf // d0 = 1/2 - H0*S0
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fR8 = fRQuadr, fRQuadr, f0 // R^4
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fB9 = fB9, fR, fB8
nop.i 0
}
;;
{.mfi
nop.m 0
fma.s1 fB12 = fB12, fRSqr, fB11
nop.i 0
}
{.mfi
nop.m 0
fma.s1 fB7 = fB7, fRSqr, fB5
nop.i 0
}
;;
{.mfi
nop.m 0
fma.s1 fB3 = fB3, fRSqr, fB1
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fH = fH, fD, fH // H1 = H0 + H0*d0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fS = fS, fD, fS // S1 = S0 + S0*d0
nop.i 0
}
;;
{.mfi
nop.m 0
(p9) fma.s1 fCpi = f1, f0, f0 // Cpi = 0 if x > 0
nop.i 0
}
{ .mfi
nop.m 0
(p8) fma.s1 fCpi = fPiBy2, f1, fPiBy2 // Cpi = Pi if x < 0
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fB12 = fB12, fRSqr, fB9
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fB7 = fB7, fRQuadr, fB3
nop.i 0
}
;;
{.mfi
nop.m 0
fnma.s1 fD = fH, fS, fHalf // d1 = 1/2 - H1*S1
nop.i 0
}
{ .mfi
nop.m 0
fnma.s1 fSignedS = fSignX, fS, f0 // -signum(x)*S1
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fCloseTo1Pol = fB12, fR8, fB7
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fH = fH, fD, fH // H2 = H1 + H1*d1
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fS = fS, fD, fS // S2 = S1 + S1*d1
nop.i 0
}
;;
{ .mfi
nop.m 0
// -signum(x)* S2 = -signum(x)*(S1 + S1*d1)
fma.s1 fSignedS = fSignedS, fD, fSignedS
nop.i 0
}
;;
{.mfi
nop.m 0
fnma.s1 fD = fH, fS, fHalf // d2 = 1/2 - H2*S2
nop.i 0
}
;;
{ .mfi
nop.m 0
// Cpi + signum(x)*PolB*S2
fnma.s1 fCpi = fSignedS, fCloseTo1Pol, fCpi
nop.i 0
}
{ .mfi
nop.m 0
// signum(x)*PolB * S2
fnma.s1 fCloseTo1Pol = fSignedS, fCloseTo1Pol, f0
nop.i 0
}
;;
{ .mfb
nop.m 0
// final result for 0.625 <= |x| < 1
fma.d.s0 f8 = fCloseTo1Pol, fD, fCpi
// exit here for 0.625 <= |x| < 1
br.ret.sptk b0
}
;;
// here if |x| < 0.625
.align 32
acos_base_range:
{ .mfi
ldfe fCpi = [rPiBy2Ptr] // Pi/2
fma.s1 fA33 = fA33, fXSqr, fA31
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fA15 = fA15, fXSqr, fA13
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fA29 = fA29, fXSqr, fA27
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fA25 = fA25, fXSqr, fA23
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fA21 = fA21, fXSqr, fA19
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fA9 = fA9, fXSqr, fA7
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fA5 = fA5, fXSqr, fA3
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fA35 = fA35, fXQuadr, fA33
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fA17 = fA17, fXQuadr, fA15
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fX8 = fXQuadr, fXQuadr, f0 // x^8
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fA25 = fA25, fXQuadr, fA21
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fA9 = fA9, fXQuadr, fA5
nop.i 0
}
;;
{ .mfi
nop.m 0
fms.s1 fCpi = fCpi, f1, f8 // Pi/2 - x
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fA35 = fA35, fXQuadr, fA29
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fA17 = fA17, fXSqr, fA11
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fX16 = fX8, fX8, f0 // x^16
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fA35 = fA35, fX8, fA25
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fA17 = fA17, fX8, fA9
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fBaseP = fA35, fX16, fA17
nop.i 0
}
;;
{ .mfb
nop.m 0
// final result for |x| < 0.625
fnma.d.s0 f8 = fBaseP, fXCube, fCpi
// exit here for |x| < 0.625 path
br.ret.sptk b0
}
;;
// here if |x| = 1
// acos(1) = 0
// acos(-1) = Pi
.align 32
acos_abs_1:
{ .mfi
ldfe fPiBy2 = [rPiBy2Ptr] // Pi/2
nop.f 0
nop.i 0
}
;;
.pred.rel "mutex", p8, p9
{ .mfi
nop.m 0
// result for x = 1.0
(p9) fma.d.s0 f8 = f1, f0, f0 // 0.0
nop.i 0
}
{.mfb
nop.m 0
// result for x = -1.0
(p8) fma.d.s0 f8 = fPiBy2, f1, fPiBy2 // Pi
// exit here for |x| = 1.0
br.ret.sptk b0
}
;;
// here if x is a NaN, denormal, or zero
.align 32
acos_special:
{ .mfi
// point to Pi/2
adds rPiBy2Ptr = 272, rTblAddr
// set p12 = 1 if x is a NaN
fclass.m p12, p0 = f8, 0xc3
nop.i 0
}
{ .mlx
nop.m 0
// smallest positive DP normalized number
movl rDenoBound = 0x0010000000000000
}
;;
{ .mfi
ldfe fPiBy2 = [rPiBy2Ptr] // Pi/2
// set p13 = 1 if x = 0.0
fclass.m p13, p0 = f8, 0x07
nop.i 0
}
{ .mfi
nop.m 0
fnorm.s1 fNormX = f8
nop.i 0
}
;;
{ .mfb
// load smallest normal to FP reg
setf.d fDenoBound = rDenoBound
// answer if x is a NaN
(p12) fma.d.s0 f8 = f8,f1,f0
// exit here if x is a NaN
(p12) br.ret.spnt b0
}
;;
{ .mfi
nop.m 0
// absolute value of normalized x
fmerge.s fNormX = f1, fNormX
nop.i 0
}
;;
{ .mfb
nop.m 0
// final result for x = 0
(p13) fma.d.s0 f8 = fPiBy2, f1, f8
// exit here if x = 0.0
(p13) br.ret.spnt b0
}
;;
// if we still here then x is denormal or unnormal
{ .mfi
nop.m 0
// set p14 = 1 if normalized x is greater than or
// equal to the smallest denormalized value
// So, if p14 is set to 1 it means that we deal with
// unnormal rather than with "true" denormal
fcmp.ge.s1 p14, p0 = fNormX, fDenoBound
nop.i 0
}
;;
{ .mfi
nop.m 0
(p14) fcmp.eq.s0 p6, p0 = f8, f0 // Set D flag if x unnormal
nop.i 0
}
{ .mfb
nop.m 0
// normalize unnormal input
(p14) fnorm.s1 f8 = f8
// return to the main path
(p14) br.cond.sptk acos_unnormal_back
}
;;
// if we still here it means that input is "true" denormal
{ .mfb
nop.m 0
// final result if x is denormal
fms.d.s0 f8 = fPiBy2, f1, f8 // Pi/2 - x
// exit here if x is denormal
br.ret.sptk b0
}
;;
// here if |x| > 1.0
// error handler should be called
.align 32
acos_abs_gt_1:
{ .mfi
alloc r32 = ar.pfs, 0, 3, 4, 0 // get some registers
fmerge.s FR_X = f8,f8
nop.i 0
}
{ .mfb
mov GR_Parameter_TAG = 58 // error code
frcpa.s0 FR_RESULT, p0 = f0,f0
// call error handler routine
br.cond.sptk __libm_error_region
}
;;
GLOBAL_LIBM_END(acos)
LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
{ .mfi
add GR_Parameter_Y=-32,sp // Parameter 2 value
nop.f 0
.save ar.pfs,GR_SAVE_PFS
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
}
{ .mfi
.fframe 64
add sp=-64,sp // Create new stack
nop.f 0
mov GR_SAVE_GP=gp // Save gp
};;
{ .mmi
stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
add GR_Parameter_X = 16,sp // Parameter 1 address
.save b0, GR_SAVE_B0
mov GR_SAVE_B0=b0 // Save b0
};;
.body
{ .mib
stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
nop.b 0
}
{ .mib
stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
add GR_Parameter_Y = -16,GR_Parameter_Y
br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi
add GR_Parameter_RESULT = 48,sp
nop.m 0
nop.i 0
};;
{ .mmi
ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
.restore sp
add sp = 64,sp // Restore stack pointer
mov b0 = GR_SAVE_B0 // Restore return address
};;
{ .mib
mov gp = GR_SAVE_GP // Restore gp
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
br.ret.sptk b0 // Return
};;
LOCAL_LIBM_END(__libm_error_region)
.type __libm_error_support#,@function
.global __libm_error_support#
|
