about summary refs log tree commit diff
path: root/sysdeps/ia64/fpu/e_atan2.S
blob: 1786794e7d6a76e433acd4be1ddb5946ff0e1bf5 (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
.file "atan2.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
// 04/04/00  Unwind support added
// 08/15/00  Bundle added after call to __libm_error_support to properly
//           set [the previously overwritten] GR_Parameter_RESULT.
// 08/17/00  Changed predicate register macro-usage to direct predicate
//           names due to an assembler bug.
// 09/28/00  Updated to set invalid on SNaN inputs
// 01/19/01  Fixed flags for small results
// 04/13/01  Rescheduled to make all paths faster
// 05/20/02  Cleaned up namespace and sf0 syntax
// 08/20/02  Corrected inexact flag and directed rounding symmetry bugs
// 02/06/03  Reordered header: .section, .global, .proc, .align
// 04/17/03  Added missing mutex directive
// 12/23/03  atan2(NaN1,NaN2) now QNaN1, for consistency with atan2f, atan2l
//
// API
//==============================================================
// double atan2(double Y, double X)
//
// Overview of operation
//==============================================================
//
// The atan2 function returns values in the interval [-pi,+pi].
//
// There are two basic paths: swap true and swap false.
// atan2(Y,X) ==> atan2(V/U) where U >= V. If Y > X, we must swap.
//
// p6  swap True    |Y| > |X|
// p7  swap False   |Y| <= |X|
// p8  X+   (If swap=True p8=p9=0)
// p9  X-
//
// all the other predicates p10 thru p15 are false for the main path
//
// Simple trigonometric identities show
//   Region 1 (-45 to +45 degrees):
//         X>0, |Y|<=X, V=Y, U=X     atan2(Y,X) = sgnY * (0 + atan(V/U))
//
//   Region 2 (-90 to -45 degrees, and +45 to +90 degrees):
//         X>0, |Y|>X, V=X, U=Y      atan2(Y,X) = sgnY * (pi/2 - atan(V/U))
//
//   Region 3 (-135 to -90 degrees, and +90 to +135 degrees):
//         X<0, |Y|>X, V=X, U=Y      atan2(Y,X) = sgnY * (pi/2 + atan(V/U))
//
//   Region 4 (-180 to -135 degrees, and +135 to +180 degrees):
//         X<0, |Y|<=X, V=Y, U=X      atan2(Y,X) = sgnY * (pi - atan(V/U))
//
// So the result is always of the form atan2(Y,X) = P + sgnXY * atan(V/U)
//
// We compute atan(V/U) from the identity
//      atan(z) + atan([(V/U)-z] / [1+(V/U)z])
//      where z is a limited precision approximation (16 bits) to V/U
//
// z is calculated with the assistance of the frcpa instruction.
//
// atan(z) is calculated by a polynomial z + z^3 * p(w),  w=z^2
// where p(w) = P0+P1*w+...+P22*w^22
//
// Let d = [(V/U)-z] / [1+(V/U)z]) = (V-U*z)/(U+V*z)
//
// Approximate atan(d) by d + P0*d^3
// Let F = 1/(U+V*z) * (1-a), where |a|< 2^-8.8.
// Compute q(a) = 1 + a + ... + a^5.
// Then F*q(a) approximates the reciprocal to more than 50 bits.

// Special values
//==============================================================
//              Y                 x          Result
//             +number           +inf        +0
//             -number           +inf        -0
//             +number           -inf        +pi
//             -number           -inf        -pi
//
//             +inf              +number     +pi/2
//             -inf              +number     -pi/2
//             +inf              -number     +pi/2
//             -inf              -number     -pi/2
//
//             +inf              +inf        +pi/4
//             -inf              +inf        -pi/4
//             +inf              -inf        +3pi/4
//             -inf              -inf        -3pi/4
//
//             +1                +1          +pi/4
//             -1                +1          -pi/4
//             +1                -1          +3pi/4
//             -1                -1          -3pi/4
//
//             +number           +0          +pi/2
//             -number           +0          -pi/2
//             +number           -0          +pi/2
//             -number           -0          -pi/2
//
//             +0                +number     +0
//             -0                +number     -0
//             +0                -number     +pi
//             -0                -number     -pi
//
//             +0                +0          +0
//             -0                +0          -0
//             +0                -0          +pi
//             -0                -0          -pi
//
//            Nan             anything      quiet Y
//            Not NaN         NaN           quiet X

// atan2(+-0/+-0) sets double error tag to 37

// Registers used
//==============================================================

// predicate registers used:
// p6 -> p15

// floating-point registers used:
// f8, f9 input
// f32 -> f119

// general registers used
// r32 -> r41

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

EXP_AD_P1                    = r33
EXP_AD_P2                    = r34
rsig_near_one                = r35


GR_SAVE_B0                   = r35
GR_SAVE_GP                   = r36
GR_SAVE_PFS                  = r37

GR_Parameter_X               = r38
GR_Parameter_Y               = r39
GR_Parameter_RESULT          = r40
atan2_GR_tag                 = r41

atan2_Y                      = f8
atan2_X                      = f9

atan2_u1_X                   = f32
atan2_u1_Y                   = f33
atan2_z2_X                   = f34
atan2_z2_Y                   = f35

atan2_two                    = f36
atan2_B1sq_Y                 = f37
atan2_z1_X                   = f38
atan2_z1_Y                   = f39
atan2_B1X                    = f40

atan2_B1Y                    = f41
atan2_wp_X                   = f42
atan2_B1sq_X                 = f43
atan2_z                      = f44
atan2_w                      = f45

atan2_P0                     = f46
atan2_P1                     = f47
atan2_P2                     = f48
atan2_P3                     = f49
atan2_P4                     = f50

atan2_P5                     = f51
atan2_P6                     = f52
atan2_P7                     = f53
atan2_P8                     = f54
atan2_P9                     = f55

atan2_P10                    = f56
atan2_P11                    = f57
atan2_P12                    = f58
atan2_P13                    = f59
atan2_P14                    = f60

atan2_P15                    = f61
atan2_P16                    = f62
atan2_P17                    = f63
atan2_P18                    = f64
atan2_P19                    = f65

atan2_P20                    = f66
atan2_P21                    = f67
atan2_P22                    = f68
atan2_tmp                    = f68
atan2_pi_by_2                = f69
atan2_sgn_pi_by_2            = f69
atan2_V13                    = f70

atan2_W11                    = f71
atan2_E                      = f72
atan2_wp_Y                   = f73
atan2_V11                    = f74
atan2_V12                    = f75

atan2_V7                     = f76
atan2_V8                     = f77
atan2_W7                     = f78
atan2_W8                     = f79
atan2_W3                     = f80

atan2_W4                     = f81
atan2_V3                     = f82
atan2_V4                     = f83
atan2_F                      = f84
atan2_gV                     = f85

atan2_V10                    = f86
atan2_zcub                   = f87
atan2_V6                     = f88
atan2_V9                     = f89
atan2_W10                    = f90

atan2_W6                     = f91
atan2_W2                     = f92
atan2_V2                     = f93
atan2_alpha                  = f94
atan2_alpha_1                = f95

atan2_gVF                    = f96
atan2_V5                     = f97
atan2_W12                    = f98
atan2_W5                     = f99
atan2_alpha_sq               = f100

atan2_Cp                     = f101
atan2_V1                     = f102
atan2_ysq                    = f103
atan2_W1                     = f104
atan2_alpha_cub              = f105

atan2_C                      = f106
atan2_xsq                    = f107
atan2_d                      = f108
atan2_A_hi                   = f109
atan2_dsq                    = f110

atan2_pd                     = f111
atan2_A_lo                   = f112
atan2_A                      = f113
atan2_Pp                     = f114
atan2_sgnY                   = f115

atan2_sig_near_one           = f116
atan2_near_one               = f116
atan2_pi                     = f117
atan2_sgn_pi                 = f117
atan2_3pi_by_4               = f118
atan2_pi_by_4                = f119


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


RODATA

.align 16

LOCAL_OBJECT_START(atan2_tb1)
data8 0xA21922DC45605EA1 ,  0x00003FFA // P11
data8 0xB199DD6D2675C40F ,  0x0000BFFA // P10
data8 0xC2F01E5DDD100DBE ,  0x00003FFA // P9
data8 0xD78F28FC2A592781 ,  0x0000BFFA // P8
data8 0xF0F03ADB3FC930D3 ,  0x00003FFA // P7
data8 0x88887EBB209E3543 ,  0x0000BFFB // P6
data8 0x9D89D7D55C3287A5 ,  0x00003FFB // P5
data8 0xBA2E8B9793955C77 ,  0x0000BFFB // P4
data8 0xE38E38E320A8A098 ,  0x00003FFB // P3
data8 0x9249249247E37913 ,  0x0000BFFC // P2
data8 0xCCCCCCCCCCC906CD ,  0x00003FFC // P1
data8 0xAAAAAAAAAAAAA8A9 ,  0x0000BFFD // P0
data8 0xC90FDAA22168C235 ,  0x00004000 // pi
LOCAL_OBJECT_END(atan2_tb1)

LOCAL_OBJECT_START(atan2_tb2)
data8 0xCE585A259BD8374C ,  0x00003FF0 // P21
data8 0x9F90FB984D8E39D0 ,  0x0000BFF3 // P20
data8 0x9D3436AABE218776 ,  0x00003FF5 // P19
data8 0xDEC343E068A6D2A8 ,  0x0000BFF6 // P18
data8 0xF396268151CFB11C ,  0x00003FF7 // P17
data8 0xD818B4BB43D84BF2 ,  0x0000BFF8 // P16
data8 0xA2270D30A90AA220 ,  0x00003FF9 // P15
data8 0xD5F4F2182E7A8725 ,  0x0000BFF9 // P14
data8 0x80D601879218B53A ,  0x00003FFA // P13
data8 0x9297B23CCFFB291F ,  0x0000BFFA // P12
data8 0xFE7E52D2A89995B3 ,  0x0000BFEC // P22
data8 0xC90FDAA22168C235 ,  0x00003FFF // pi/2
data8 0xC90FDAA22168C235 ,  0x00003FFE // pi/4
data8 0x96cbe3f9990e91a8 ,  0x00004000 // 3pi/4
LOCAL_OBJECT_END(atan2_tb2)




.section .text
GLOBAL_IEEE754_ENTRY(atan2)

{ .mfi
           alloc        r32           = ar.pfs,1,5,4,0
           frcpa.s1     atan2_u1_X,p6 = f1,atan2_X
           nop.i 999
}
{ .mfi
           addl         EXP_AD_P1   = @ltoff(atan2_tb1), gp
           fma.s1       atan2_two  = f1,f1,f1
           nop.i 999
;;
}

{ .mfi
           ld8  EXP_AD_P1 = [EXP_AD_P1]
           frcpa.s1     atan2_u1_Y,p7 = f1,atan2_Y
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_xsq  = atan2_X,atan2_X,f0
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fclass.m p10,p0 = atan2_Y, 0xc3     // Test for y=nan
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_ysq  = atan2_Y,atan2_Y,f0
           nop.i 999
}
;;

{ .mfi
           add  EXP_AD_P2 = 0xd0,EXP_AD_P1
           fclass.m p12,p0 = atan2_X, 0xc3     // Test for x nan
           nop.i 999
}
;;


// p10 Y NAN, quiet and return
{ .mfi
           ldfe         atan2_P11  = [EXP_AD_P1],16
           fmerge.s     atan2_sgnY = atan2_Y,f1
           nop.i 999
}
{ .mfb
           ldfe         atan2_P21  = [EXP_AD_P2],16
(p10)      fma.d.s0 f8 = atan2_X,atan2_Y,f0   // If y=nan, result quietized y
(p10)      br.ret.spnt b0        // Exit if y=nan
;;
}


{ .mfi
           ldfe         atan2_P10  = [EXP_AD_P1],16
           fma.s1       atan2_z1_X = atan2_u1_X, atan2_Y, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P20  = [EXP_AD_P2],16
           fnma.s1      atan2_B1X  = atan2_u1_X, atan2_X, atan2_two
           nop.i 999
;;
}

{ .mfi
           ldfe         atan2_P9   = [EXP_AD_P1],16
           fma.s1       atan2_z1_Y = atan2_u1_Y, atan2_X, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P19  = [EXP_AD_P2],16
           fnma.s1      atan2_B1Y  = atan2_u1_Y, atan2_Y, atan2_two
           nop.i 999
}
;;

{ .mfi
           ldfe         atan2_P8   = [EXP_AD_P1],16
           fma.s1       atan2_z2_X = atan2_u1_X, atan2_ysq, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P18  = [EXP_AD_P2],16
           fma.s1       atan2_z2_Y = atan2_u1_Y, atan2_xsq, f0
           nop.i 999
}
;;

// p10 ==> x  inf     y ?
// p11 ==> x !inf     y ?
{ .mfi
           ldfe         atan2_P7   = [EXP_AD_P1],16
           fclass.m p10,p11 = atan2_X, 0x23    // test for x inf
           nop.i 999
}
{ .mfb
           ldfe         atan2_P17  = [EXP_AD_P2],16
(p12)      fma.d.s0        f8 = atan2_X,atan2_Y,f0     // If x nan, result quiet x
(p12)      br.ret.spnt b0                 // Exit for x nan
;;
}

// p6 true if swap,    means |y| >  |x|    or ysq > xsq
// p7 true if no swap, means |x| >= |y|    or xsq >= ysq
{ .mmf
           ldfe         atan2_P6   = [EXP_AD_P1],16
           ldfe         atan2_P16  = [EXP_AD_P2],16
           fcmp.ge.s1 p7,p6    = atan2_xsq, atan2_ysq
;;
}

{ .mfi
           ldfe         atan2_P5   = [EXP_AD_P1],16
           fma.s1       atan2_wp_X   = atan2_z1_X, atan2_z1_X, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P15       = [EXP_AD_P2],16
           fma.s1       atan2_B1sq_X = atan2_B1X, atan2_B1X, f0
           nop.i 999
;;
}

{ .mfi
           ldfe         atan2_P4   = [EXP_AD_P1],16
(p6)       fma.s1       atan2_wp_Y   = atan2_z1_Y, atan2_z1_Y, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P14  = [EXP_AD_P2],16
(p6)       fma.s1       atan2_B1sq_Y = atan2_B1Y, atan2_B1Y, f0
           nop.i 999
;;
}

{ .mfi
           ldfe         atan2_P3        = [EXP_AD_P1],16
(p6)       fma.s1       atan2_E         = atan2_z2_Y, atan2_B1Y, atan2_Y
           nop.i 999
}
{ .mfi
           ldfe         atan2_P13  = [EXP_AD_P2],16
(p7)       fma.s1       atan2_E         = atan2_z2_X, atan2_B1X, atan2_X
           nop.i 999
;;
}


{ .mfi
           ldfe         atan2_P2        = [EXP_AD_P1],16
(p6)       fma.s1       atan2_z         = atan2_z1_Y, atan2_B1Y, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P12  = [EXP_AD_P2],16
(p7)       fma.s1       atan2_z         = atan2_z1_X, atan2_B1X, f0
           nop.i 999
;;
}


{ .mfi
           ldfe         atan2_P1        = [EXP_AD_P1],16
           fcmp.eq.s0  p14,p15=atan2_X,atan2_Y  // Dummy for denorm and invalid
           nop.i 999
}
{ .mlx
           ldfe         atan2_P22       = [EXP_AD_P2],16
           movl         rsig_near_one = 0x8000000000000001 // signif near 1.0
;;
}


// p12 ==> x  inf     y inf
// p13 ==> x  inf     y !inf
{ .mmf
           ldfe         atan2_P0        = [EXP_AD_P1],16
           ldfe         atan2_pi_by_2   = [EXP_AD_P2],16
(p10)      fclass.m.unc p12,p13 = atan2_Y, 0x23  // x inf, test if y inf
;;
}

{ .mfi
           ldfe         atan2_pi        = [EXP_AD_P1],16
(p6)       fma.s1       atan2_w         = atan2_wp_Y, atan2_B1sq_Y,f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_pi_by_4       = [EXP_AD_P2],16
(p7)       fma.s1       atan2_w         = atan2_wp_X, atan2_B1sq_X,f0
           nop.i 999
;;
}

{ .mfi
           ldfe         atan2_3pi_by_4       = [EXP_AD_P2],16
(p11)      fclass.m.unc p9,p0 = atan2_Y, 0x23  // x not inf, test if y inf
           nop.i 999
;;
}

{ .mfi
           setf.sig      atan2_sig_near_one = rsig_near_one
(p12)      fcmp.gt.unc.s1 p10,p11 = atan2_X,f0 // x inf, y inf, test if x +inf
           nop.i 999
}
{ .mfi
           nop.m 999
(p6)       fnma.s1       atan2_gV        = atan2_Y, atan2_z, atan2_X
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           frcpa.s1     atan2_F,p0     = f1, atan2_E
           nop.i 999
}
{ .mfi
           nop.m 999
(p7)       fnma.s1       atan2_gV        = atan2_X, atan2_z, atan2_Y
           nop.i 999
;;
}

// p13 ==> x  inf     y !inf
{ .mfi
           nop.m 999
(p13)      fcmp.gt.unc.s1 p14,p15 = atan2_X,f0 // x inf, y !inf, test if x +inf
           nop.i 999
}
{ .mfb
           nop.m 999
(p9)       fma.d.s0  f8 = atan2_sgnY, atan2_pi_by_2, f0  // +-pi/2 if x !inf, y inf
(p9)       br.ret.spnt b0      // exit if x not inf, y inf, result is +-pi/2
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_V13       = atan2_w, atan2_P11, atan2_P10
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_W11       = atan2_w, atan2_P21, atan2_P20
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_V11       = atan2_w, atan2_P9, atan2_P8
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_V12       = atan2_w, atan2_w, f0
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_V8        = atan2_w, atan2_P7 , atan2_P6
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_W8        = atan2_w, atan2_P19, atan2_P18
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fnma.s1      atan2_alpha     = atan2_E, atan2_F, f1
           nop.i 999
}
{ .mfi
           nop.m 999
           fnma.s1      atan2_alpha_1   = atan2_E, atan2_F, atan2_two
           nop.i 999
;;
}


{ .mfi
           nop.m 999
           fma.s1       atan2_V7        = atan2_w, atan2_P5 , atan2_P4
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_W7        = atan2_w, atan2_P17, atan2_P16
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_V4        = atan2_w, atan2_P3 , atan2_P2
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_W4        = atan2_w, atan2_P15, atan2_P14
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_V3        = atan2_w, atan2_P1 , atan2_P0
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_W3        = atan2_w, atan2_P13, atan2_P12
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_V10       = atan2_V12, atan2_V13, atan2_V11
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_gVF       = atan2_gV, atan2_F, f0
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_alpha_sq  = atan2_alpha, atan2_alpha, f0
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_Cp        = atan2_alpha, atan2_alpha_1, f1
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_V9        = atan2_V12, atan2_V12, f0
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_W10       = atan2_V12, atan2_P22 , atan2_W11
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_V6        = atan2_V12, atan2_V8 , atan2_V7
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_W6        = atan2_V12, atan2_W8 , atan2_W7
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_V2        = atan2_V12, atan2_V4 , atan2_V3
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_W2        = atan2_V12, atan2_W4  , atan2_W3
           nop.i 999
;;
}

// p8 ==> y   0     x?
// p9 ==> y  !0     x?
{ .mfi
           nop.m 999
           fclass.m p8,p9 = atan2_Y, 0x07  // Test for y=0
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_zcub      = atan2_z, atan2_w, f0
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_alpha_cub = atan2_alpha, atan2_alpha_sq, f0
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_C         = atan2_gVF, atan2_Cp, f0
           nop.i 999
;;
}

// p12 ==>  y0     x0
// p13 ==>  y0     x!0
{ .mfi
           nop.m 999
(p8)       fclass.m.unc p12,p13 = atan2_X, 0x07  // y=0, test if x is 0
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_W12       = atan2_V9, atan2_V9, f0
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_V5        = atan2_V9, atan2_V10, atan2_V6
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_W5        = atan2_V9, atan2_W10, atan2_W6
           nop.i 999
;;
}


// p9 ==>  y!0    x0
{ .mfi
           nop.m 999
(p9)       fclass.m.unc p9,p0 = atan2_X, 0x07  // y not 0, test if x is 0
           nop.i 999
}
// p10 ==> X +INF, Y +-INF
{ .mfb
           nop.m 999
(p10)      fma.d.s0       f8 = atan2_sgnY, atan2_pi_by_4, f0 // x=+inf, y=inf
(p10)      br.ret.spnt b0          // Exit for x=+inf, y=inf, result is +-pi/4
;;
}

.pred.rel "mutex",p11,p14
{ .mfi
           nop.m 999
(p14)      fmerge.s    f8 = atan2_sgnY, f0 // x=+inf, y !inf, result +-0
           nop.i 999
}
// p11 ==> X -INF, Y +-INF
{ .mfb
           nop.m 999
(p11)      fma.d.s0       f8 = atan2_sgnY, atan2_3pi_by_4, f0 // x=-inf, y=inf
(p11)      br.ret.spnt b0          // Exit for x=-inf, y=inf, result is +-3pi/4
;;
}

{ .mfi
           nop.m 999
(p13)      fcmp.gt.unc.s1 p10,p11 = atan2_X,f0 // x not 0, y=0, test if x>0
           nop.i 999
}
{ .mfb
           nop.m 999
           fma.s1       atan2_d         = atan2_alpha_cub, atan2_C, atan2_C
(p14)      br.ret.spnt b0         // Exit if x=+inf, y !inf, result +-0
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_W12       = atan2_V9, atan2_W12, f0
           nop.i 999
}
{ .mfb
           nop.m 999
(p9)       fma.d.s0       f8 = atan2_sgnY, atan2_pi_by_2, f0 // x=0, y not 0
(p9)       br.ret.spnt b0      // Exit if x=0 and y not 0, result is +-pi/2
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_V1        = atan2_V9, atan2_V5, atan2_V2
           nop.i 999
}
{ .mfb
           nop.m 999
           fma.s1       atan2_W1        = atan2_V9, atan2_W5, atan2_W2
(p12)      br.spnt ATAN2_ERROR            // Branch if x=0 and y=0
;;
}

{ .mfi
           nop.m 999
(p10)      fmerge.s     f8              = atan2_sgnY, f0  // +-0 if x>0, y=0
           nop.i 999
}
{ .mfb
           nop.m 999
(p11)      fma.d.s0        f8 = atan2_sgnY, atan2_pi, f0 // +-pi if x<0, y=0
(p13)      br.ret.spnt b0      // Exit if x!0 and y=0
;;
}


{ .mfi
           nop.m 999
           fma.s1       atan2_pd        = atan2_P0, atan2_d, f0
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_dsq       = atan2_d, atan2_d, f0
           nop.i 999
;;
}


{ .mfi
           nop.m 999
           fmerge.se    atan2_near_one = f1, atan2_sig_near_one // Const ~1.0
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_Pp        = atan2_W12, atan2_W1, atan2_V1
           nop.i 999
;;
}

// p8 true if no swap and X positive
// p9 true if no swap and X negative
// both are false is swap is true
{ .mfi
           nop.m 999
(p7)       fcmp.ge.unc.s1 p8,p9    = atan2_X,f0
           nop.i 999
}
{ .mfb
           nop.m 999
(p15)      fma.d.s0        f8              = atan2_sgnY, atan2_pi, f0
(p15)      br.ret.spnt b0         // Exit if x=-inf, y !inf, result +-pi
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_sgn_pi_by_2 = atan2_pi_by_2, atan2_sgnY, f0
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_A_lo      = atan2_pd, atan2_dsq, atan2_d
           nop.i 999
;;
}


{ .mfi
           nop.m 999
           fma.s1       atan2_sgn_pi = atan2_pi, atan2_sgnY, f0
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_A_hi      = atan2_zcub, atan2_Pp, atan2_z
           nop.i 999
;;
}


// For |Y| <= |X| and X > 0, force inexact in case A_lo is zero
{ .mfi
           nop.m 999
(p8)       fmpy.s0      atan2_tmp       = atan2_P22, atan2_P22
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fma.s1       atan2_A         = atan2_A_hi, f1, atan2_A_lo
           nop.i 999
}
// For |Y| <= |X| and X > 0, result is A_hi + A_lo
{ .mfi
           nop.m 999
(p8)       fma.d.s0       f8         = atan2_A_hi, f1, atan2_A_lo
           nop.i 999
;;
}

.pred.rel "mutex",p6,p9
// We perturb A by multiplying by 1.0+1ulp as we produce the result
// in order to get symmetrically rounded results in directed rounding modes.
// If we don't do this, there are a few cases where the trailing 11 bits of
// the significand of the result, before converting to double, are zero.  These
// cases do not round symmetrically in round to +infinity or round to -infinity.
// The perturbation also insures that the inexact flag is set.
// For |Y| > |X|, result is  +- pi/2 - (A_hi + A_lo)
{ .mfi
           nop.m 999
(p6)       fnma.d.s0      f8        = atan2_A, atan2_near_one, atan2_sgn_pi_by_2
           nop.i 999
}
// For |Y| <= |X|, and X < 0, result is  +- pi + (A_hi + A_lo)
{ .mfb
           nop.m 999
(p9)       fma.d.s0        f8        = atan2_A, atan2_near_one, atan2_sgn_pi
           br.ret.sptk  b0
;;
}

ATAN2_ERROR:
// Here if x=0 and y=0
{ .mfi
          nop.m 999
          fclass.m p10,p11       = atan2_X,0x05  // Test if x=+0
          nop.i 999
}
;;

{ .mfi
          mov        atan2_GR_tag     = 37
(p10)     fmerge.s     f10             = atan2_sgnY, f0 // x=+0, y=0
          nop.i 999
}
{ .mfi
          nop.m 999
(p11)     fma.d.s0        f10            = atan2_sgnY, atan2_pi, f0 // x=-0, y=0
          nop.i 999
;;
}
GLOBAL_IEEE754_END(atan2)
libm_alias_double_other (__atan2, atan2)


LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
// (1)
{ .mfi
        add   GR_Parameter_Y=-32,sp             // Parameter 2 value
        nop.f 999
.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
        stfd [GR_Parameter_Y] = f8,16         // 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
        stfd [GR_Parameter_X] = f9            // STORE Parameter 1 on stack
        add   GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
        nop.b 0
}
{ .mib
        stfd [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
        add   GR_Parameter_RESULT = 48,sp
        nop.m 0
        nop.i 0
};;

// (4)
{ .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#