about summary refs log tree commit diff
path: root/sysdeps/ia64/fpu/e_acosl.S
blob: 81f56e41c8c411ea7bd00b77e9c34eda93386b28 (plain) (blame)
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
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
.file "acosl.s"

// Copyright (c) 2000, 2001, Intel Corporation
// All rights reserved.
// 
// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
// 
// WARRANTY DISCLAIMER
// 
// 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://developer.intel.com/opensource.
//
// History
//==============================================================
// 2/02/00  Initial version 
// 2/07/00  Modified calculation of acos_corr to correct acosl
// 4/04/00  Unwind support added
// 8/15/00  Bundle added after call to __libm_error_support to properly
//          set [the previously overwritten] GR_Parameter_RESULT.
// 12/20/00 Set denormal flag properly.
//
// API
//==============================================================
// double-extended = acosl (double-extended)
// input  floating point f8
// output floating point f8
//
// Registers used
//==============================================================
//
// predicate registers used:
// p6 -> p12
//
// floating-point registers used:
// f8 has input, then output
// f8 -> f15, f32 ->f99
//
// general registers used:
// r32 -> r48
//
// Overview of operation
//==============================================================
// There are three paths
// 1. |x| < 2^-25                 ACOS_TINY
// 2. 2^-25 <= |x| < 1/4          ACOS_POLY
// 3. 1/4 <= |x| < 1              ACOS_ATAN

#include "libm_support.h"

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

// f8 is input, but acos_V must be put in f8
//    when __libm_atan2_reg is called, f8 must get V
// f9 gets U when __libm_atan2_reg is called


// __libm_atan2_reg returns 
// f8  = Z_hi
// f10 = Z_lo
// f11 = s_lo

acos_Z_hi = f8
acos_Z_lo = f10
acos_S_lo = f11

// When we call __libm_atan2_reg, we must save 
// the following:

acos_corr  = f12
acos_X     = f13
acos_pi_hi = f14
acos_pi_lo = f15

// The rest of the assembly macros

acos_P79                   = f32
acos_P59                   = f33
acos_P39                   = f34
acos_P19                   = f35

acos_P810                  = f36
acos_P610                  = f37
acos_P410                  = f38
acos_P210                  = f39

acos_A1                    = f41
acos_A2                    = f42
acos_A3                    = f43
acos_A4                    = f44
acos_A5                    = f45
acos_A6                    = f46
acos_A7                    = f47
acos_A8                    = f48
acos_A9                    = f49
acos_A10                   = f50

acos_X2                    = f51
acos_X4                    = f52

acos_B                     = f53
acos_Bb                    = f54
acos_A                     = f55
acos_Aa                    = f56

acos_1mA                   = f57

acos_W                     = f58
acos_Ww                    = f59

acos_y0                    = f60
acos_y1                    = f61
acos_y2                    = f62

acos_H                     = f63
acos_Hh                    = f64

acos_t1                    = f65
acos_t2                    = f66
acos_t3                    = f67
acos_t4                    = f68
acos_t5                    = f69

acos_Pseries               = f70
acos_NORM_f8               = f71
acos_ABS_NORM_f8           = f72

acos_2                     = f73
acos_P1P2                  = f74
acos_HALF                  = f75
acos_U                     = f76

acos_1mB                   = f77
acos_V                     = f78 
acos_S                     = f79

acos_BmUU                  = f80 
acos_BmUUpb                = f81 
acos_2U                    = f82
acos_1d2U                  = f83

acos_Dd                    = f84

acos_pi_by_2_hi            = f85
acos_pi_by_2_lo            = f86
acos_xmpi_by_2_lo          = f87
acos_xPmw                  = f88

acos_Uu                    = f89
acos_AmVV                  = f90 
acos_AmVVpa                = f91 

acos_2V                    = f92 
acos_1d2V                  = f93
acos_Vv                    = f94

acos_Vu                    = f95 
acos_Uv                    = f96 

acos_2_Z_hi                = f97
acos_s_lo_Z_lo             = f98
acos_result_lo             = f99

acos_Z_hi                  = f8
acos_Z_lo                  = f10
acos_s_lo                  = f11

acos_GR_17_ones            = r33
acos_GR_16_ones            = r34
acos_GR_signexp_f8         = r35
acos_GR_exp                = r36
acos_GR_true_exp           = r37
acos_GR_fffe               = r38

GR_SAVE_PFS                = r43
GR_SAVE_B0                 = r39
GR_SAVE_GP                 = r41

// r40 is address of table of coefficients
// r42 

GR_Parameter_X             = r44 
GR_Parameter_Y             = r45 
GR_Parameter_RESULT        = r46 
GR_Parameter_TAG                = r47 


// 2^-40:
// A true exponent of -40 is
//                    : -40 + register_bias
//                    : -28 + ffff = ffd7

// A true exponent of 1 is 
//                    : 1 + register_bias
//                    : 1 + ffff = 10000

// Data tables
//==============================================================

#ifdef _LIBC
.rodata
#else
.data
#endif

.align 16

acos_coefficients:
ASM_TYPE_DIRECTIVE(acos_coefficients,@object)
data8  0xc90fdaa22168c234, 0x00003FFF            // pi_by_2_hi
data8  0xc4c6628b80dc1cd1, 0x00003FBF            // pi_by_2_lo
data8  0xc90fdaa22168c234, 0x00004000            // pi_hi
data8  0xc4c6628b80dc1cd1, 0x00003FC0            // pi_lo

data8  0xBB08911F2013961E, 0x00003FF8            // A10
data8  0x981F1095A23A87D3, 0x00003FF8            // A9 
data8  0xBDF09C6C4177BCC6, 0x00003FF8            // A8 
data8  0xE4C3A60B049ACCEA, 0x00003FF8            // A7 
data8  0x8E2789F4E8A8F1AD, 0x00003FF9            // A6 
data8  0xB745D09B2B0E850B, 0x00003FF9            // A5 
data8  0xF8E38E3BC4C50920, 0x00003FF9            // A4 
data8  0xB6DB6DB6D89FCD81, 0x00003FFA            // A3 
data8  0x99999999999AF376, 0x00003FFB            // A2 
data8  0xAAAAAAAAAAAAAA71, 0x00003FFC            // A1
ASM_SIZE_DIRECTIVE(acos_coefficients)


.align 32
.global acosl#
ASM_TYPE_DIRECTIVE(acosl#,@function)

.section .text
.proc  acosl#
.align 32


acosl: 

// After normalizing f8, get its true exponent
{ .mfi
      alloc r32 = ar.pfs,1,11,4,0                                             
(p0)  fnorm.s1    acos_NORM_f8 = f8                                            
(p0)  mov         acos_GR_17_ones = 0x1ffff                                    
}

{ .mmi
(p0)  mov        acos_GR_16_ones = 0xffff                                     
(p0)  addl                 r40   = @ltoff(acos_coefficients), gp
      nop.i 999
}
;;

// Set denormal flag on denormal input with fcmp
{ .mfi
      ld8 r40 = [r40]
      fcmp.eq  p6,p0 = f8,f0
      nop.i 999
}
;;


// Load the constants pi_by_2 and pi.
// Each is stored as hi and lo values
// Also load the coefficients for ACOS_POLY

{ .mmi
(p0) ldfe       acos_pi_by_2_hi = [r40],16 ;;      
(p0) ldfe       acos_pi_by_2_lo = [r40],16      
     nop.i 999 ;;
}

{ .mmi
(p0) ldfe       acos_pi_hi      = [r40],16 ;;      
(p0) ldfe       acos_pi_lo      = [r40],16      
     nop.i 999 ;;
}

{ .mmi
(p0) ldfe       acos_A10        = [r40],16 ;;      
(p0) ldfe       acos_A9         = [r40],16      
     nop.i 999 ;;
}

// Take the absolute value of f8
{ .mmf
      nop.m 999
(p0)  getf.exp   acos_GR_signexp_f8  = acos_NORM_f8                           
(p0)  fmerge.s  acos_ABS_NORM_f8 = f0, acos_NORM_f8 
}

{ .mii
(p0) ldfe       acos_A8         = [r40],16      
     nop.i 999 ;;
(p0) and        acos_GR_exp         = acos_GR_signexp_f8, acos_GR_17_ones ;;    
}

// case 1: |x| < 2^-25         ==> p6   ACOS_TINY
// case 2: 2^-25 <= |x| < 2^-2 ==> p8   ACOS_POLY
// case 3: 2^-2  <= |x| < 1    ==> p9   ACOS_ATAN
// case 4: 1     <= |x|        ==> p11  ACOS_ERROR_RETURN
//  Admittedly |x| = 1 is not an error but this is where that case is
//  handled.

{ .mii
(p0) ldfe       acos_A7         = [r40],16      
(p0) sub        acos_GR_true_exp    = acos_GR_exp, acos_GR_16_ones ;;           
(p0) cmp.ge.unc p6, p7    = -26, acos_GR_true_exp ;;                            
}

{ .mii
(p0) ldfe       acos_A6         = [r40],16      
(p7) cmp.ge.unc p8, p9    = -3,  acos_GR_true_exp ;;                            
(p9) cmp.ge.unc p10, p11  =  -1, acos_GR_true_exp                            
}

{ .mmi
(p0) ldfe       acos_A5         = [r40],16 ;;      
(p0) ldfe       acos_A4         = [r40],16      
      nop.i 999 ;;
}

{ .mmi
(p0) ldfe       acos_A3         = [r40],16 ;;      
(p0) ldfe       acos_A2         = [r40],16      
      nop.i 999 ;;
}

// ACOS_ERROR_RETURN ==> p11 is true
// case 4: |x| >= 1
{ .mib
(p0)  ldfe       acos_A1         = [r40],16      
      nop.i 999
(p11) br.spnt         L(ACOS_ERROR_RETURN) ;; 
}

// ACOS_TINY ==> p6 is true
// case 1: |x| < 2^-25
{ .mfi
      nop.m 999
(p6)  fms.s1        acos_xmpi_by_2_lo = acos_NORM_f8,f1, acos_pi_by_2_lo 
      nop.i 999 ;;
}

{ .mfb
           nop.m 999
(p6)  fms.s0         f8 = acos_pi_by_2_hi,f1, acos_xmpi_by_2_lo                
(p6)  br.ret.spnt   b0 ;;                                                   
}



// ACOS_POLY ==> p8 is true
// case 2: 2^-25 <= |x| < 2^-2                   
{ .mfi
      nop.m 999
(p8)  fms.s1        acos_W       = acos_pi_by_2_hi, f1, acos_NORM_f8     
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p8)  fma.s1        acos_X2   = f8,f8, f0                                
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p8)  fms.s1        acos_Ww      = acos_pi_by_2_hi, f1, acos_W           
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p8)  fma.s1        acos_X4   = acos_X2,acos_X2, f0                      
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p8)  fms.s1        acos_Ww      = acos_Ww, f1, acos_NORM_f8             
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p8)  fma.s1        acos_P810 = acos_X4, acos_A10, acos_A8               
      nop.i 999
}

// acos_P79  = X4*A9   + A7
// acos_P810 = X4*A10  + A8
{ .mfi
      nop.m 999
(p8)  fma.s1        acos_P79  = acos_X4, acos_A9, acos_A7                
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p8)  fma.s1        acos_Ww      = acos_Ww, f1, acos_pi_by_2_lo          
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p8)  fma.s1        acos_P610 = acos_X4, acos_P810, acos_A6              
      nop.i 999
}


// acos_P59   = X4*(X4*A9   + A7)  + A5
// acos_P610  = X4*(X4*A10  + A8)  + A6
{ .mfi
      nop.m 999
(p8)  fma.s1        acos_P59  = acos_X4, acos_P79, acos_A5               
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p8)  fma.s1        acos_P410 = acos_X4, acos_P610, acos_A4              
      nop.i 999
}

// acos_P39   = X4*(X4*(X4*A9   + A7)  + A5) + A3
// acos_P410  = X4*(X4*(X4*A10  + A8)  + A6) + A4
{ .mfi
      nop.m 999
(p8)  fma.s1        acos_P39  = acos_X4, acos_P59, acos_A3               
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p8)  fma.s1        acos_P210 = acos_X4, acos_P410, acos_A2              
      nop.i 999
}

// acos_P19   = X4*(X4*(X4*(X4*A9   + A7)  + A5) + A3) + A1 = P1
// acos_P210  = X4*(X4*(X4*(X4*A10  + A8)  + A6) + A4) + A2 = P2
{ .mfi
      nop.m 999
(p8)  fma.s1        acos_P19  = acos_X4, acos_P39, acos_A1               
      nop.i 999 ;;
}

// acos_P1P2 = Xsq*P2 + P1
// acos_P1P2 = Xsq*(Xsq*P2 + P1)
{ .mfi
      nop.m 999
(p8)  fma.s1        acos_P1P2    = acos_X2, acos_P210, acos_P19          
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p8)  fma.s1        acos_P1P2    = acos_X2, acos_P1P2, f0                
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p8)  fms.s1        acos_xPmw    = acos_NORM_f8, acos_P1P2, acos_Ww       
      nop.i 999 ;;
}

{ .mfb
      nop.m 999
(p8)  fms.s0         f8           = acos_W, f1, acos_xPmw                 
(p8)  br.ret.spnt   b0 ;;                                                   
}


// ACOS_ATAN
// case 3: 2^-2  <= |x| < 1                      
// case 3: 2^-2  <= |x| < 1    ==> p9   ACOS_ATAN

// Step 1.1:     Get A,B and a,b
// A + a = 1- |X|
// B + b = 1+ |X|
// Note also that we will use  acos_corr (f13)
// and                         acos_W

// Step 2
// Call __libm_atan2_reg


{ .mfi
(p0)  mov    acos_GR_fffe = 0xfffe                      
(p0)  fma.s1 acos_B          = f1,f1,  acos_ABS_NORM_f8                            
(p0)  mov   GR_SAVE_B0 = b0 ;;                                
}

{ .mmf
(p0)  mov   GR_SAVE_GP = gp                                
      nop.m 999
(p0)  fms.s1 acos_A   = f1,f1,  acos_ABS_NORM_f8                            
}

{ .mfi
(p0)  setf.exp       acos_HALF = acos_GR_fffe                   
      nop.f 999
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fms.s1 acos_1mB = f1,f1, acos_B                                       
      nop.i 999 ;;
}

// We want atan2(V,U)
//   so put V in f8 and U in f9
//   but save X in acos_X

{ .mfi
      nop.m 999
(p0)  fmerge.se acos_X = f8, f8                               
      nop.i 999 ;;
}

// Step 1.2:
/////////////////////////
// Get U = sqrt(B)
/////////////////////////

{ .mfi
      nop.m 999
(p0)  frsqrta.s1     acos_y0,p8  = acos_B                                
      nop.i 999
}

{ .mfi
      nop.m 999
(p0)  fms.s1 acos_1mA = f1,f1, acos_A                                       
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1 acos_Bb  = acos_1mB,f1, acos_ABS_NORM_f8                       
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_Hh     = acos_HALF, acos_B, f0                 
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_t1     = acos_y0, acos_y0, f0                  
      nop.i 999
}

{ .mfi
      nop.m 999
(p0)  fms.s1 acos_Aa  = acos_1mA,f1, acos_ABS_NORM_f8                       
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fnma.s1        acos_t2     = acos_t1, acos_Hh, acos_HALF           
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_y1     = acos_t2, acos_y0, acos_y0             
      nop.i 999
}


// Step 1.2:
/////////////////////////
// Get V = sqrt(A)
/////////////////////////
{ .mfi
      nop.m 999
(p0)  frsqrta.s1     acos_y0,p8  = acos_A                                
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_t3     = acos_y1, acos_Hh, f0                  
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_t1     = acos_y0, acos_y0, f0                  
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fnma.s1        acos_t4     = acos_t3, acos_y1, acos_HALF           
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_y2     = acos_t4, acos_y1, acos_y1             
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_S      = acos_B, acos_y2, f0                   
      nop.i 999
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_H      = acos_y2, acos_HALF, f0                
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_t5     = acos_Hh, acos_y2, f0                  
      nop.i 999
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_Hh     = acos_HALF, acos_A, f0                 
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fnma.s1        acos_Dd     = acos_S, acos_S, acos_B                
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fnma.s1        acos_t2     = acos_t1, acos_Hh, acos_HALF           
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_U      = acos_Dd, acos_H, acos_S               
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_y1     = acos_t2, acos_y0, acos_y0             
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_2U       = acos_U, f1, acos_U                  
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_t3     = acos_y1, acos_Hh, f0                  
      nop.i 999
}


// Step 1.3: 
// sqrt(A + a) = V + v
// sqrt(B + b) = U + u

/////////////////////////
// Get u
/////////////////////////

// acos_BmUU   = B - UU
// acos_BmUUpb = (B - UU) + b

{ .mfi
      nop.m 999
(p0)  fnma.s1        acos_BmUU     = acos_U, acos_U, acos_B              
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)   fmerge.se f9 = acos_U, acos_U                           
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fnma.s1        acos_t4     = acos_t3, acos_y1, acos_HALF           
      nop.i 999 ;;
}

// acos_1d2U = frcpa(2U)
{ .mfi
      nop.m 999
(p0)  frcpa.s1       acos_1d2U,p9  = f1, acos_2U                         
      nop.i 999
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_BmUUpb   = acos_BmUU, f1, acos_Bb              
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_y2     = acos_t4, acos_y1, acos_y1             
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
// acos_Uu = ((B - UU) + b) * frcpa(2U)
(p0)  fma.s1         acos_Uu       = acos_BmUUpb, acos_1d2U, f0          
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_S      = acos_A, acos_y2, f0                   
      nop.i 999
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_H      = acos_y2, acos_HALF, f0                
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_t5     = acos_Hh, acos_y2, f0                  
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fnma.s1        acos_Dd     = acos_S, acos_S, acos_A                
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_V      = acos_Dd, acos_H, acos_S               
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_2V       = acos_V, f1, acos_V                  
      nop.i 999
}

// Step 3
/////////////////////////
// Calculate the correction, acos_corr
/////////////////////////
// acos_corr = U*v - (V*u)

{ .mfi
      nop.m 999
(p0)  fma.s1  acos_Vu   = acos_V,acos_Uu, f0                  
      nop.i 999 ;;
}

/////////////////////////
// Get v
/////////////////////////
// acos_AmVV   = A - VV
// acos_AmVVpa = (A - VV) + a

{ .mfi
      nop.m 999
(p0)  fnma.s1        acos_AmVV     = acos_V, acos_V, acos_A              
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)   fmerge.se f8 = acos_V, acos_V                           
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)  fma.s1         acos_AmVVpa   = acos_AmVV, f1, acos_Aa              
      nop.i 999 ;;
}

// acos_1d2V = frcpa(2V)
{ .mfi
      nop.m 999
(p0)  frcpa.s1       acos_1d2V,p9  = f1, acos_2V                         
      nop.i 999 ;;
}

// acos_Vv = ((A - VV) + a) * frcpa(2V)
{ .mfi
      nop.m 999
(p0)  fma.s1         acos_Vv       = acos_AmVVpa, acos_1d2V, f0          
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p0)   fma.s1  acos_Uv   = acos_U,acos_Vv, f0                  
      nop.i 999 ;;
}


.endp acosl#
ASM_SIZE_DIRECTIVE(acosl#)


.proc __libm_callout
__libm_callout:
.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
{ .mfb
      nop.m 999
(p0)   fms.s1  acos_corr = acos_Uv,f1, acos_Vu                 
(p0)   br.call.sptk.many  b0=__libm_atan2_reg# ;;                        
}


// p6 ==> X is negative
// p7 ==> x is positive
// We know that |X| >= 1/4

{ .mfi
(p0)   mov gp              = GR_SAVE_GP                           
(p0)   fcmp.lt.unc   p6,p7 = acos_X , f0                       
(p0)   mov b0              = GR_SAVE_B0 ;;                           
}

// acos_2_Z_hi    = 2 * acos_Z_hi
// acos_s_lo_Z_lo = s_lo * Z_lo

{ .mfi
       nop.m 999
(p0)   fma.s1  acos_2_Z_hi      = acos_Z_hi, f1, acos_Z_hi               
(p0)   mov ar.pfs               = GR_SAVE_PFS                                     
}

{ .mfi
      nop.m 999
(p0)   fma.s1  acos_s_lo_Z_lo   = acos_s_lo, acos_Z_lo, f0               
      nop.i 999 ;;
}

// 2 is a constant needed later
{ .mfi
      nop.m 999
(p0)  fma.s1     acos_2 = f1,f1,f1                             
      nop.i 999 ;;
}

// X >= 1/4
// acos_result_lo = 2(s_lo * Z_lo) - corr
// f8             = (2*Z_hi) + (2(s_lo * Z_lo) - corr)

{ .mfi
      nop.m 999
(p7)   fma.s1  acos_result_lo     = acos_s_lo_Z_lo, acos_2, acos_corr      
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p7)  fma.s0   f8                 = acos_2_Z_hi, f1, acos_result_lo        
      nop.i 999
}

// acos_result_lo = (pi_lo - corr)
// acos_result_lo = (pi_lo - corr) + acos_Ww 
{ .mfi
      nop.m 999
(p6)  fms.s1  acos_result_lo     = acos_pi_lo, f1, acos_corr              
      nop.i 999 ;;
}

// X <= -1/4
// acos_W = pi_hi - 2 * Z_hi
{ .mfi
      nop.m 999
(p6)  fnma.s1 acos_W             = acos_2, acos_Z_hi, acos_pi_hi          
      nop.i 999 ;;
}

// acos_Ww = pi_hi - W
// acos_Ww = (pi_hi - W) + (2 * Z_hi)
{ .mfi
      nop.m 999
(p6)  fms.s1  acos_Ww            = acos_pi_hi, f1, acos_W                 
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p6)   fms.s1  acos_Ww            = acos_Ww, f1, acos_2_Z_hi               
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p6)   fma.s1  acos_result_lo     = acos_result_lo, f1, acos_Ww            
      nop.i 999 ;;
}

// acos_Z_lo = ((pi_lo - corr) + acos_Ww) - 2 * (s_lo * Z_lo)
{ .mfi
      nop.m 999
(p6)  fnma.s1  acos_Z_lo          = acos_s_lo_Z_lo, acos_2, acos_result_lo 
      nop.i 999 ;;
}

{ .mfb
      nop.m 999
(p6)  fma.s0   f8                  = acos_W, f1, acos_Z_lo                
(p0)  br.ret.sptk   b0 ;;                          
}
.endp __libm_callout
ASM_SIZE_DIRECTIVE(__libm_callout)

.proc SPECIAL
SPECIAL:
L(ACOS_NAN): 
{ .mfb
      nop.m 999
(p0)  fma.s0 f8 = f8,f1,f0                       
(p0)  br.ret.sptk   b0 ;;                          
}

L(ACOS_ERROR_RETURN): 
// Save ar.pfs, b0, and gp; restore on exit

// qnan snan inf norm     unorm 0 -+
// 1    1    0   0        0     0 11 = 0xc3

// Coming in as X = +- 1
// What should we return?

// If X is 1, return (sign of X)pi/2


{ .mfi
      nop.m 999
(p0)  fcmp.eq.unc p6,p7 = acos_ABS_NORM_f8,f1              
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p6)  fcmp.lt.unc p8,p9 = f8,f0                            
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
(p8)  fma.s0 f8          = acos_pi_hi, f1, acos_pi_lo       
      nop.i 999
}

{ .mfb
      nop.m 999
(p9)  fmerge.s    f8 = f8,f0                               
(p6)  br.ret.spnt   b0 ;;                                     
}

// If X is a NAN, leave
{ .mfi
      nop.m 999
(p0)  fclass.m.unc p12,p0 = f8, 0xc3            
      nop.i 999 ;;
}

{ .mfb
      nop.m 999
(p12) fma.s0 f8 = f8,f1,f0                       
(p12) br.ret.spnt   b0 ;;                          
}

{ .mfi
(p0)   mov   GR_Parameter_TAG = 57 
(p0)   frcpa f10, p6 = f0, f0
nop.i 999
};;

.endp SPECIAL
ASM_SIZE_DIRECTIVE(SPECIAL)

.proc __libm_error_region
__libm_error_region:
.prologue
// (1)
{ .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
};;


// (2)
{ .mmi
        stfe [GR_Parameter_Y] = f1,16         // 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
// (3)
{ .mib
        stfe [GR_Parameter_X] = f8              // Store Parameter 1 on stack
        add   GR_Parameter_RESULT = 0,GR_Parameter_Y
        nop.b 0                                 // Parameter 3 address
}
{ .mib
        stfe [GR_Parameter_Y] = f10             // 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
        nop.m 0
        nop.m 0
        add   GR_Parameter_RESULT = 48,sp
};;

// (4)
{ .mmi
        ldfe  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
};;

.endp __libm_error_region
ASM_SIZE_DIRECTIVE(__libm_error_region)

.type   __libm_error_support#,@function
.global __libm_error_support#

.type   __libm_atan2_reg#,@function
.global __libm_atan2_reg#