about summary refs log tree commit diff
path: root/sysdeps/ia64/fpu/s_log1p.S
blob: 8c57c4bf288a3349df5f99f70fc16c8d0b505421 (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
1095
1096
1097
1098
1099
1100
1101
1102
.file "log1p.s"


// Copyright (c) 2000 - 2005, Intel Corporation
// All rights reserved.
//
//
// 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.
// 06/29/01 Improved speed of all paths
// 05/20/02 Cleaned up namespace and sf0 syntax
// 10/02/02 Improved performance by basing on log algorithm
// 02/10/03 Reordered header: .section, .global, .proc, .align
// 04/18/03 Eliminate possible WAW dependency warning
// 03/31/05 Reformatted delimiters between data tables
//
// API
//==============================================================
// double log1p(double)
//
// log1p(x) = log(x+1)
//
// Overview of operation
//==============================================================
// Background
// ----------
//
// This algorithm is based on fact that
// log1p(x) = log(1+x) and
// log(a b) = log(a) + log(b).
// In our case we have 1+x = 2^N f, where 1 <= f < 2.
// So
//   log(1+x) = log(2^N f) = log(2^N) + log(f) = n*log(2) + log(f)
//
// To calculate log(f) we do following
//   log(f) = log(f * frcpa(f) / frcpa(f)) =
//          = log(f * frcpa(f)) + log(1/frcpa(f))
//
// According to definition of IA-64's frcpa instruction it's a
// floating point that approximates 1/f using a lookup on the
// top of 8 bits of the input number's + 1 significand with relative
// error < 2^(-8.886). So we have following
//
// |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256
//
// and
//
// log(f) = log(f * frcpa(f)) + log(1/frcpa(f)) =
//        = log(1 + r) + T
//
// The first value can be computed by polynomial P(r) approximating
// log(1 + r) on |r| < 1/256 and the second is precomputed tabular
// value defined by top 8 bit of f.
//
// Finally we have that  log(1+x) ~ (N*log(2) + T) + P(r)
//
// Note that if input argument is close to 0.0 (in our case it means
// that |x| < 1/256) we can use just polynomial approximation
// because 1+x = 2^0 * f = f = 1 + r and
// log(1+x) = log(1 + r) ~ P(r)
//
//
// Implementation
// --------------
//
// 1. |x| >= 2^(-8), and x > -1
//   InvX = frcpa(x+1)
//   r = InvX*(x+1) - 1
//   P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)),
//   all coefficients are calculated in quad and rounded to double
//   precision. A7,A6,A5,A4 are stored in memory whereas A3 and A2
//   created with setf.
//
//   N = float(n) where n is true unbiased exponent of x
//
//   T is tabular value of log(1/frcpa(x)) calculated in quad precision
//   and represented by two floating-point numbers 64-bit Thi and 32-bit Tlo.
//   To load Thi,Tlo we get bits from 55 to 62 of register format significand
//   as index and calculate two addresses
//     ad_Thi = Thi_table_base_addr + 8 * index
//     ad_Tlo = Tlo_table_base_addr + 4 * index
//
//   L1 (log(2)) is calculated in quad
//   precision and represented by two floating-point 64-bit numbers L1hi,L1lo
//   stored in memory.
//
//   And final result = ((L1hi*N + Thi) + (N*L1lo + Tlo)) + P(r)
//
//
// 2. 2^(-80) <= |x| < 2^(-8)
//   r = x
//   P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)),
//   A7,A6,A5,A4,A3,A2 are the same as in case |x| >= 1/256
//
//   And final results
//     log(1+x)   = P(r)
//
// 3. 0 < |x| < 2^(-80)
//   Although log1p(x) is basically x, we would like to preserve the inexactness
//   nature as well as consistent behavior under different rounding modes.
//   We can do this by computing the result as
//
//     log1p(x) = x - x*x
//
//
//    Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are
//          filtered and processed on special branches.
//

//
// Special values
//==============================================================
//
// log1p(-1)    = -inf            // Call error support
//
// log1p(+qnan) = +qnan
// log1p(-qnan) = -qnan
// log1p(+snan) = +qnan
// log1p(-snan) = -qnan
//
// log1p(x),x<-1= QNAN Indefinite // Call error support
// log1p(-inf)  = QNAN Indefinite
// log1p(+inf)  = +inf
// log1p(+/-0)  = +/-0
//
//
// Registers used
//==============================================================
// Floating Point registers used:
// f8, input
// f7 -> f15,  f32 -> f40
//
// General registers used:
// r8  -> r11
// r14 -> r20
//
// Predicate registers used:
// p6 -> p12

// Assembly macros
//==============================================================
GR_TAG                 = r8
GR_ad_1                = r8
GR_ad_2                = r9
GR_Exp                 = r10
GR_N                   = r11

GR_signexp_x           = r14
GR_exp_mask            = r15
GR_exp_bias            = r16
GR_05                  = r17
GR_A3                  = r18
GR_Sig                 = r19
GR_Ind                 = r19
GR_exp_x               = r20


GR_SAVE_B0             = r33
GR_SAVE_PFS            = r34
GR_SAVE_GP             = r35
GR_SAVE_SP             = r36

GR_Parameter_X         = r37
GR_Parameter_Y         = r38
GR_Parameter_RESULT    = r39
GR_Parameter_TAG       = r40



FR_NormX               = f7
FR_RcpX                = f9
FR_r                   = f10
FR_r2                  = f11
FR_r4                  = f12
FR_N                   = f13
FR_Ln2hi               = f14
FR_Ln2lo               = f15

FR_A7                  = f32
FR_A6                  = f33
FR_A5                  = f34
FR_A4                  = f35
FR_A3                  = f36
FR_A2                  = f37

FR_Thi                 = f38
FR_NxLn2hipThi         = f38
FR_NxLn2pT             = f38
FR_Tlo                 = f39
FR_NxLn2lopTlo         = f39

FR_Xp1                 = f40


FR_Y                   = f1
FR_X                   = f10
FR_RESULT              = f8


// Data
//==============================================================
RODATA
.align 16

LOCAL_OBJECT_START(log_data)
// coefficients of polynomial approximation
data8 0x3FC2494104381A8E // A7
data8 0xBFC5556D556BBB69 // A6
data8 0x3FC999999988B5E9 // A5
data8 0xBFCFFFFFFFF6FFF5 // A4
//
// hi parts of ln(1/frcpa(1+i/256)), i=0...255
data8 0x3F60040155D5889D // 0
data8 0x3F78121214586B54 // 1
data8 0x3F841929F96832EF // 2
data8 0x3F8C317384C75F06 // 3
data8 0x3F91A6B91AC73386 // 4
data8 0x3F95BA9A5D9AC039 // 5
data8 0x3F99D2A8074325F3 // 6
data8 0x3F9D6B2725979802 // 7
data8 0x3FA0C58FA19DFAA9 // 8
data8 0x3FA2954C78CBCE1A // 9
data8 0x3FA4A94D2DA96C56 // 10
data8 0x3FA67C94F2D4BB58 // 11
data8 0x3FA85188B630F068 // 12
data8 0x3FAA6B8ABE73AF4C // 13
data8 0x3FAC441E06F72A9E // 14
data8 0x3FAE1E6713606D06 // 15
data8 0x3FAFFA6911AB9300 // 16
data8 0x3FB0EC139C5DA600 // 17
data8 0x3FB1DBD2643D190B // 18
data8 0x3FB2CC7284FE5F1C // 19
data8 0x3FB3BDF5A7D1EE64 // 20
data8 0x3FB4B05D7AA012E0 // 21
data8 0x3FB580DB7CEB5701 // 22
data8 0x3FB674F089365A79 // 23
data8 0x3FB769EF2C6B568D // 24
data8 0x3FB85FD927506A47 // 25
data8 0x3FB9335E5D594988 // 26
data8 0x3FBA2B0220C8E5F4 // 27
data8 0x3FBB0004AC1A86AB // 28
data8 0x3FBBF968769FCA10 // 29
data8 0x3FBCCFEDBFEE13A8 // 30
data8 0x3FBDA727638446A2 // 31
data8 0x3FBEA3257FE10F79 // 32
data8 0x3FBF7BE9FEDBFDE5 // 33
data8 0x3FC02AB352FF25F3 // 34
data8 0x3FC097CE579D204C // 35
data8 0x3FC1178E8227E47B // 36
data8 0x3FC185747DBECF33 // 37
data8 0x3FC1F3B925F25D41 // 38
data8 0x3FC2625D1E6DDF56 // 39
data8 0x3FC2D1610C868139 // 40
data8 0x3FC340C59741142E // 41
data8 0x3FC3B08B6757F2A9 // 42
data8 0x3FC40DFB08378003 // 43
data8 0x3FC47E74E8CA5F7C // 44
data8 0x3FC4EF51F6466DE4 // 45
data8 0x3FC56092E02BA516 // 46
data8 0x3FC5D23857CD74D4 // 47
data8 0x3FC6313A37335D76 // 48
data8 0x3FC6A399DABBD383 // 49
data8 0x3FC70337DD3CE41A // 50
data8 0x3FC77654128F6127 // 51
data8 0x3FC7E9D82A0B022D // 52
data8 0x3FC84A6B759F512E // 53
data8 0x3FC8AB47D5F5A30F // 54
data8 0x3FC91FE49096581B // 55
data8 0x3FC981634011AA75 // 56
data8 0x3FC9F6C407089664 // 57
data8 0x3FCA58E729348F43 // 58
data8 0x3FCABB55C31693AC // 59
data8 0x3FCB1E104919EFD0 // 60
data8 0x3FCB94EE93E367CA // 61
data8 0x3FCBF851C067555E // 62
data8 0x3FCC5C0254BF23A5 // 63
data8 0x3FCCC000C9DB3C52 // 64
data8 0x3FCD244D99C85673 // 65
data8 0x3FCD88E93FB2F450 // 66
data8 0x3FCDEDD437EAEF00 // 67
data8 0x3FCE530EFFE71012 // 68
data8 0x3FCEB89A1648B971 // 69
data8 0x3FCF1E75FADF9BDE // 70
data8 0x3FCF84A32EAD7C35 // 71
data8 0x3FCFEB2233EA07CD // 72
data8 0x3FD028F9C7035C1C // 73
data8 0x3FD05C8BE0D9635A // 74
data8 0x3FD085EB8F8AE797 // 75
data8 0x3FD0B9C8E32D1911 // 76
data8 0x3FD0EDD060B78080 // 77
data8 0x3FD122024CF0063F // 78
data8 0x3FD14BE2927AECD4 // 79
data8 0x3FD180618EF18ADF // 80
data8 0x3FD1B50BBE2FC63B // 81
data8 0x3FD1DF4CC7CF242D // 82
data8 0x3FD214456D0EB8D4 // 83
data8 0x3FD23EC5991EBA49 // 84
data8 0x3FD2740D9F870AFB // 85
data8 0x3FD29ECDABCDFA03 // 86
data8 0x3FD2D46602ADCCEE // 87
data8 0x3FD2FF66B04EA9D4 // 88
data8 0x3FD335504B355A37 // 89
data8 0x3FD360925EC44F5C // 90
data8 0x3FD38BF1C3337E74 // 91
data8 0x3FD3C25277333183 // 92
data8 0x3FD3EDF463C1683E // 93
data8 0x3FD419B423D5E8C7 // 94
data8 0x3FD44591E0539F48 // 95
data8 0x3FD47C9175B6F0AD // 96
data8 0x3FD4A8B341552B09 // 97
data8 0x3FD4D4F39089019F // 98
data8 0x3FD501528DA1F967 // 99
data8 0x3FD52DD06347D4F6 // 100
data8 0x3FD55A6D3C7B8A89 // 101
data8 0x3FD5925D2B112A59 // 102
data8 0x3FD5BF406B543DB1 // 103
data8 0x3FD5EC433D5C35AD // 104
data8 0x3FD61965CDB02C1E // 105
data8 0x3FD646A84935B2A1 // 106
data8 0x3FD6740ADD31DE94 // 107
data8 0x3FD6A18DB74A58C5 // 108
data8 0x3FD6CF31058670EC // 109
data8 0x3FD6F180E852F0B9 // 110
data8 0x3FD71F5D71B894EF // 111
data8 0x3FD74D5AEFD66D5C // 112
data8 0x3FD77B79922BD37D // 113
data8 0x3FD7A9B9889F19E2 // 114
data8 0x3FD7D81B037EB6A6 // 115
data8 0x3FD8069E33827230 // 116
data8 0x3FD82996D3EF8BCA // 117
data8 0x3FD85855776DCBFA // 118
data8 0x3FD8873658327CCE // 119
data8 0x3FD8AA75973AB8CE // 120
data8 0x3FD8D992DC8824E4 // 121
data8 0x3FD908D2EA7D9511 // 122
data8 0x3FD92C59E79C0E56 // 123
data8 0x3FD95BD750EE3ED2 // 124
data8 0x3FD98B7811A3EE5B // 125
data8 0x3FD9AF47F33D406B // 126
data8 0x3FD9DF270C1914A7 // 127
data8 0x3FDA0325ED14FDA4 // 128
data8 0x3FDA33440224FA78 // 129
data8 0x3FDA57725E80C382 // 130
data8 0x3FDA87D0165DD199 // 131
data8 0x3FDAAC2E6C03F895 // 132
data8 0x3FDADCCC6FDF6A81 // 133
data8 0x3FDB015B3EB1E790 // 134
data8 0x3FDB323A3A635948 // 135
data8 0x3FDB56FA04462909 // 136
data8 0x3FDB881AA659BC93 // 137
data8 0x3FDBAD0BEF3DB164 // 138
data8 0x3FDBD21297781C2F // 139
data8 0x3FDC039236F08818 // 140
data8 0x3FDC28CB1E4D32FC // 141
data8 0x3FDC4E19B84723C1 // 142
data8 0x3FDC7FF9C74554C9 // 143
data8 0x3FDCA57B64E9DB05 // 144
data8 0x3FDCCB130A5CEBAF // 145
data8 0x3FDCF0C0D18F326F // 146
data8 0x3FDD232075B5A201 // 147
data8 0x3FDD490246DEFA6B // 148
data8 0x3FDD6EFA918D25CD // 149
data8 0x3FDD9509707AE52F // 150
data8 0x3FDDBB2EFE92C554 // 151
data8 0x3FDDEE2F3445E4AE // 152
data8 0x3FDE148A1A2726CD // 153
data8 0x3FDE3AFC0A49FF3F // 154
data8 0x3FDE6185206D516D // 155
data8 0x3FDE882578823D51 // 156
data8 0x3FDEAEDD2EAC990C // 157
data8 0x3FDED5AC5F436BE2 // 158
data8 0x3FDEFC9326D16AB8 // 159
data8 0x3FDF2391A21575FF // 160
data8 0x3FDF4AA7EE03192C // 161
data8 0x3FDF71D627C30BB0 // 162
data8 0x3FDF991C6CB3B379 // 163
data8 0x3FDFC07ADA69A90F // 164
data8 0x3FDFE7F18EB03D3E // 165
data8 0x3FE007C053C5002E // 166
data8 0x3FE01B942198A5A0 // 167
data8 0x3FE02F74400C64EA // 168
data8 0x3FE04360BE7603AC // 169
data8 0x3FE05759AC47FE33 // 170
data8 0x3FE06B5F1911CF51 // 171
data8 0x3FE078BF0533C568 // 172
data8 0x3FE08CD9687E7B0E // 173
data8 0x3FE0A10074CF9019 // 174
data8 0x3FE0B5343A234476 // 175
data8 0x3FE0C974C89431CD // 176
data8 0x3FE0DDC2305B9886 // 177
data8 0x3FE0EB524BAFC918 // 178
data8 0x3FE0FFB54213A475 // 179
data8 0x3FE114253DA97D9F // 180
data8 0x3FE128A24F1D9AFF // 181
data8 0x3FE1365252BF0864 // 182
data8 0x3FE14AE558B4A92D // 183
data8 0x3FE15F85A19C765B // 184
data8 0x3FE16D4D38C119FA // 185
data8 0x3FE18203C20DD133 // 186
data8 0x3FE196C7BC4B1F3A // 187
data8 0x3FE1A4A738B7A33C // 188
data8 0x3FE1B981C0C9653C // 189
data8 0x3FE1CE69E8BB106A // 190
data8 0x3FE1DC619DE06944 // 191
data8 0x3FE1F160A2AD0DA3 // 192
data8 0x3FE2066D7740737E // 193
data8 0x3FE2147DBA47A393 // 194
data8 0x3FE229A1BC5EBAC3 // 195
data8 0x3FE237C1841A502E // 196
data8 0x3FE24CFCE6F80D9A // 197
data8 0x3FE25B2C55CD5762 // 198
data8 0x3FE2707F4D5F7C40 // 199
data8 0x3FE285E0842CA383 // 200
data8 0x3FE294294708B773 // 201
data8 0x3FE2A9A2670AFF0C // 202
data8 0x3FE2B7FB2C8D1CC0 // 203
data8 0x3FE2C65A6395F5F5 // 204
data8 0x3FE2DBF557B0DF42 // 205
data8 0x3FE2EA64C3F97654 // 206
data8 0x3FE3001823684D73 // 207
data8 0x3FE30E97E9A8B5CC // 208
data8 0x3FE32463EBDD34E9 // 209
data8 0x3FE332F4314AD795 // 210
data8 0x3FE348D90E7464CF // 211
data8 0x3FE35779F8C43D6D // 212
data8 0x3FE36621961A6A99 // 213
data8 0x3FE37C299F3C366A // 214
data8 0x3FE38AE2171976E7 // 215
data8 0x3FE399A157A603E7 // 216
data8 0x3FE3AFCCFE77B9D1 // 217
data8 0x3FE3BE9D503533B5 // 218
data8 0x3FE3CD7480B4A8A2 // 219
data8 0x3FE3E3C43918F76C // 220
data8 0x3FE3F2ACB27ED6C6 // 221
data8 0x3FE4019C2125CA93 // 222
data8 0x3FE4181061389722 // 223
data8 0x3FE42711518DF545 // 224
data8 0x3FE436194E12B6BF // 225
data8 0x3FE445285D68EA69 // 226
data8 0x3FE45BCC464C893A // 227
data8 0x3FE46AED21F117FC // 228
data8 0x3FE47A1527E8A2D3 // 229
data8 0x3FE489445EFFFCCB // 230
data8 0x3FE4A018BCB69835 // 231
data8 0x3FE4AF5A0C9D65D7 // 232
data8 0x3FE4BEA2A5BDBE87 // 233
data8 0x3FE4CDF28F10AC46 // 234
data8 0x3FE4DD49CF994058 // 235
data8 0x3FE4ECA86E64A683 // 236
data8 0x3FE503C43CD8EB68 // 237
data8 0x3FE513356667FC57 // 238
data8 0x3FE522AE0738A3D7 // 239
data8 0x3FE5322E26867857 // 240
data8 0x3FE541B5CB979809 // 241
data8 0x3FE55144FDBCBD62 // 242
data8 0x3FE560DBC45153C6 // 243
data8 0x3FE5707A26BB8C66 // 244
data8 0x3FE587F60ED5B8FF // 245
data8 0x3FE597A7977C8F31 // 246
data8 0x3FE5A760D634BB8A // 247
data8 0x3FE5B721D295F10E // 248
data8 0x3FE5C6EA94431EF9 // 249
data8 0x3FE5D6BB22EA86F5 // 250
data8 0x3FE5E6938645D38F // 251
data8 0x3FE5F673C61A2ED1 // 252
data8 0x3FE6065BEA385926 // 253
data8 0x3FE6164BFA7CC06B // 254
data8 0x3FE62643FECF9742 // 255
//
// two parts of ln(2)
data8 0x3FE62E42FEF00000,0x3DD473DE6AF278ED
//
// lo parts of ln(1/frcpa(1+i/256)), i=0...255
data4 0x20E70672 // 0
data4 0x1F60A5D0 // 1
data4 0x218EABA0 // 2
data4 0x21403104 // 3
data4 0x20E9B54E // 4
data4 0x21EE1382 // 5
data4 0x226014E3 // 6
data4 0x2095E5C9 // 7
data4 0x228BA9D4 // 8
data4 0x22932B86 // 9
data4 0x22608A57 // 10
data4 0x220209F3 // 11
data4 0x212882CC // 12
data4 0x220D46E2 // 13
data4 0x21FA4C28 // 14
data4 0x229E5BD9 // 15
data4 0x228C9838 // 16
data4 0x2311F954 // 17
data4 0x221365DF // 18
data4 0x22BD0CB3 // 19
data4 0x223D4BB7 // 20
data4 0x22A71BBE // 21
data4 0x237DB2FA // 22
data4 0x23194C9D // 23
data4 0x22EC639E // 24
data4 0x2367E669 // 25
data4 0x232E1D5F // 26
data4 0x234A639B // 27
data4 0x2365C0E0 // 28
data4 0x234646C1 // 29
data4 0x220CBF9C // 30
data4 0x22A00FD4 // 31
data4 0x2306A3F2 // 32
data4 0x23745A9B // 33
data4 0x2398D756 // 34
data4 0x23DD0B6A // 35
data4 0x23DE338B // 36
data4 0x23A222DF // 37
data4 0x223164F8 // 38
data4 0x23B4E87B // 39
data4 0x23D6CCB8 // 40
data4 0x220C2099 // 41
data4 0x21B86B67 // 42
data4 0x236D14F1 // 43
data4 0x225A923F // 44
data4 0x22748723 // 45
data4 0x22200D13 // 46
data4 0x23C296EA // 47
data4 0x2302AC38 // 48
data4 0x234B1996 // 49
data4 0x2385E298 // 50
data4 0x23175BE5 // 51
data4 0x2193F482 // 52
data4 0x23BFEA90 // 53
data4 0x23D70A0C // 54
data4 0x231CF30A // 55
data4 0x235D9E90 // 56
data4 0x221AD0CB // 57
data4 0x22FAA08B // 58
data4 0x23D29A87 // 59
data4 0x20C4B2FE // 60
data4 0x2381B8B7 // 61
data4 0x23F8D9FC // 62
data4 0x23EAAE7B // 63
data4 0x2329E8AA // 64
data4 0x23EC0322 // 65
data4 0x2357FDCB // 66
data4 0x2392A9AD // 67
data4 0x22113B02 // 68
data4 0x22DEE901 // 69
data4 0x236A6D14 // 70
data4 0x2371D33E // 71
data4 0x2146F005 // 72
data4 0x23230B06 // 73
data4 0x22F1C77D // 74
data4 0x23A89FA3 // 75
data4 0x231D1241 // 76
data4 0x244DA96C // 77
data4 0x23ECBB7D // 78
data4 0x223E42B4 // 79
data4 0x23801BC9 // 80
data4 0x23573263 // 81
data4 0x227C1158 // 82
data4 0x237BD749 // 83
data4 0x21DDBAE9 // 84
data4 0x23401735 // 85
data4 0x241D9DEE // 86
data4 0x23BC88CB // 87
data4 0x2396D5F1 // 88
data4 0x23FC89CF // 89
data4 0x2414F9A2 // 90
data4 0x2474A0F5 // 91
data4 0x24354B60 // 92
data4 0x23C1EB40 // 93
data4 0x2306DD92 // 94
data4 0x24353B6B // 95
data4 0x23CD1701 // 96
data4 0x237C7A1C // 97
data4 0x245793AA // 98
data4 0x24563695 // 99
data4 0x23C51467 // 100
data4 0x24476B68 // 101
data4 0x212585A9 // 102
data4 0x247B8293 // 103
data4 0x2446848A // 104
data4 0x246A53F8 // 105
data4 0x246E496D // 106
data4 0x23ED1D36 // 107
data4 0x2314C258 // 108
data4 0x233244A7 // 109
data4 0x245B7AF0 // 110
data4 0x24247130 // 111
data4 0x22D67B38 // 112
data4 0x2449F620 // 113
data4 0x23BBC8B8 // 114
data4 0x237D3BA0 // 115
data4 0x245E8F13 // 116
data4 0x2435573F // 117
data4 0x242DE666 // 118
data4 0x2463BC10 // 119
data4 0x2466587D // 120
data4 0x2408144B // 121
data4 0x2405F0E5 // 122
data4 0x22381CFF // 123
data4 0x24154F9B // 124
data4 0x23A4E96E // 125
data4 0x24052967 // 126
data4 0x2406963F // 127
data4 0x23F7D3CB // 128
data4 0x2448AFF4 // 129
data4 0x24657A21 // 130
data4 0x22FBC230 // 131
data4 0x243C8DEA // 132
data4 0x225DC4B7 // 133
data4 0x23496EBF // 134
data4 0x237C2B2B // 135
data4 0x23A4A5B1 // 136
data4 0x2394E9D1 // 137
data4 0x244BC950 // 138
data4 0x23C7448F // 139
data4 0x2404A1AD // 140
data4 0x246511D5 // 141
data4 0x24246526 // 142
data4 0x23111F57 // 143
data4 0x22868951 // 144
data4 0x243EB77F // 145
data4 0x239F3DFF // 146
data4 0x23089666 // 147
data4 0x23EBFA6A // 148
data4 0x23C51312 // 149
data4 0x23E1DD5E // 150
data4 0x232C0944 // 151
data4 0x246A741F // 152
data4 0x2414DF8D // 153
data4 0x247B5546 // 154
data4 0x2415C980 // 155
data4 0x24324ABD // 156
data4 0x234EB5E5 // 157
data4 0x2465E43E // 158
data4 0x242840D1 // 159
data4 0x24444057 // 160
data4 0x245E56F0 // 161
data4 0x21AE30F8 // 162
data4 0x23FB3283 // 163
data4 0x247A4D07 // 164
data4 0x22AE314D // 165
data4 0x246B7727 // 166
data4 0x24EAD526 // 167
data4 0x24B41DC9 // 168
data4 0x24EE8062 // 169
data4 0x24A0C7C4 // 170
data4 0x24E8DA67 // 171
data4 0x231120F7 // 172
data4 0x24401FFB // 173
data4 0x2412DD09 // 174
data4 0x248C131A // 175
data4 0x24C0A7CE // 176
data4 0x243DD4C8 // 177
data4 0x24457FEB // 178
data4 0x24DEEFBB // 179
data4 0x243C70AE // 180
data4 0x23E7A6FA // 181
data4 0x24C2D311 // 182
data4 0x23026255 // 183
data4 0x2437C9B9 // 184
data4 0x246BA847 // 185
data4 0x2420B448 // 186
data4 0x24C4CF5A // 187
data4 0x242C4981 // 188
data4 0x24DE1525 // 189
data4 0x24F5CC33 // 190
data4 0x235A85DA // 191
data4 0x24A0B64F // 192
data4 0x244BA0A4 // 193
data4 0x24AAF30A // 194
data4 0x244C86F9 // 195
data4 0x246D5B82 // 196
data4 0x24529347 // 197
data4 0x240DD008 // 198
data4 0x24E98790 // 199
data4 0x2489B0CE // 200
data4 0x22BC29AC // 201
data4 0x23F37C7A // 202
data4 0x24987FE8 // 203
data4 0x22AFE20B // 204
data4 0x24C8D7C2 // 205
data4 0x24B28B7D // 206
data4 0x23B6B271 // 207
data4 0x24C77CB6 // 208
data4 0x24EF1DCA // 209
data4 0x24A4F0AC // 210
data4 0x24CF113E // 211
data4 0x2496BBAB // 212
data4 0x23C7CC8A // 213
data4 0x23AE3961 // 214
data4 0x2410A895 // 215
data4 0x23CE3114 // 216
data4 0x2308247D // 217
data4 0x240045E9 // 218
data4 0x24974F60 // 219
data4 0x242CB39F // 220
data4 0x24AB8D69 // 221
data4 0x23436788 // 222
data4 0x24305E9E // 223
data4 0x243E71A9 // 224
data4 0x23C2A6B3 // 225
data4 0x23FFE6CF // 226
data4 0x2322D801 // 227
data4 0x24515F21 // 228
data4 0x2412A0D6 // 229
data4 0x24E60D44 // 230
data4 0x240D9251 // 231
data4 0x247076E2 // 232
data4 0x229B101B // 233
data4 0x247B12DE // 234
data4 0x244B9127 // 235
data4 0x2499EC42 // 236
data4 0x21FC3963 // 237
data4 0x23E53266 // 238
data4 0x24CE102D // 239
data4 0x23CC45D2 // 240
data4 0x2333171D // 241
data4 0x246B3533 // 242
data4 0x24931129 // 243
data4 0x24405FFA // 244
data4 0x24CF464D // 245
data4 0x237095CD // 246
data4 0x24F86CBD // 247
data4 0x24E2D84B // 248
data4 0x21ACBB44 // 249
data4 0x24F43A8C // 250
data4 0x249DB931 // 251
data4 0x24A385EF // 252
data4 0x238B1279 // 253
data4 0x2436213E // 254
data4 0x24F18A3B // 255
LOCAL_OBJECT_END(log_data)


// Code
//==============================================================

.section .text
GLOBAL_IEEE754_ENTRY(log1p)
{ .mfi
      getf.exp      GR_signexp_x = f8 // if x is unorm then must recompute
      fadd.s1       FR_Xp1 = f8, f1       // Form 1+x
      mov           GR_05 = 0xfffe
}
{ .mlx
      addl          GR_ad_1 = @ltoff(log_data),gp
      movl          GR_A3 = 0x3fd5555555555557 // double precision memory
                                               // representation of A3
}
;;

{ .mfi
      ld8           GR_ad_1 = [GR_ad_1]
      fclass.m      p8,p0 = f8,0xb // Is x unorm?
      mov           GR_exp_mask = 0x1ffff
}
{ .mfi
      nop.m         0
      fnorm.s1      FR_NormX = f8              // Normalize x
      mov           GR_exp_bias = 0xffff
}
;;

{ .mfi
      setf.exp      FR_A2 = GR_05 // create A2 = 0.5
      fclass.m      p9,p0 = f8,0x1E1 // is x NaN, NaT or +Inf?
      nop.i         0
}
{ .mib
      setf.d        FR_A3 = GR_A3 // create A3
      add           GR_ad_2 = 16,GR_ad_1 // address of A5,A4
(p8)  br.cond.spnt  log1p_unorm          // Branch if x=unorm
}
;;

log1p_common:
{ .mfi
      nop.m         0
      frcpa.s1      FR_RcpX,p0 = f1,FR_Xp1
      nop.i         0
}
{ .mfb
      nop.m         0
(p9)  fma.d.s0      f8 = f8,f1,f0 // set V-flag
(p9)  br.ret.spnt   b0 // exit for NaN, NaT and +Inf
}
;;

{ .mfi
      getf.exp      GR_Exp = FR_Xp1            // signexp of x+1
      fclass.m      p10,p0 = FR_Xp1,0x3A // is 1+x < 0?
      and           GR_exp_x = GR_exp_mask, GR_signexp_x // biased exponent of x
}
{ .mfi
      ldfpd         FR_A7,FR_A6 = [GR_ad_1]
      nop.f         0
      nop.i         0
}
;;

{ .mfi
      getf.sig      GR_Sig = FR_Xp1 // get significand to calculate index
                                    // for Thi,Tlo if |x| >= 2^-8
      fcmp.eq.s1    p12,p0 = f8,f0     // is x equal to 0?
      sub           GR_exp_x = GR_exp_x, GR_exp_bias // true exponent of x
}
;;

{ .mfi
      sub           GR_N = GR_Exp,GR_exp_bias // true exponent of x+1
      fcmp.eq.s1    p11,p0 = FR_Xp1,f0     // is x = -1?
      cmp.gt        p6,p7 = -8, GR_exp_x  // Is |x| < 2^-8
}
{ .mfb
      ldfpd         FR_A5,FR_A4 = [GR_ad_2],16
      nop.f         0
(p10) br.cond.spnt  log1p_lt_minus_1   // jump if x < -1
}
;;

// p6 is true if |x| < 1/256
// p7 is true if |x| >= 1/256
.pred.rel "mutex",p6,p7
{ .mfi
(p7)  add           GR_ad_1 = 0x820,GR_ad_1 // address of log(2) parts
(p6)  fms.s1        FR_r = f8,f1,f0 // range reduction for |x|<1/256
(p6)  cmp.gt.unc    p10,p0 = -80, GR_exp_x  // Is |x| < 2^-80
}
{ .mfb
(p7)  setf.sig      FR_N = GR_N // copy unbiased exponent of x to the
                                // significand field of FR_N
(p7)  fms.s1        FR_r = FR_RcpX,FR_Xp1,f1 // range reduction for |x|>=1/256
(p12) br.ret.spnt   b0 // exit for x=0, return x
}
;;

{ .mib
(p7)  ldfpd         FR_Ln2hi,FR_Ln2lo = [GR_ad_1],16
(p7)  extr.u        GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index
(p11) br.cond.spnt  log1p_eq_minus_1 // jump if x = -1
}
;;

{ .mmf
(p7)  shladd        GR_ad_2 = GR_Ind,3,GR_ad_2 // address of Thi
(p7)  shladd        GR_ad_1 = GR_Ind,2,GR_ad_1 // address of Tlo
(p10) fnma.d.s0     f8 = f8,f8,f8   // If |x| very small, result=x-x*x
}
;;

{ .mmb
(p7)  ldfd          FR_Thi = [GR_ad_2]
(p7)  ldfs          FR_Tlo = [GR_ad_1]
(p10) br.ret.spnt   b0                   // Exit if |x| < 2^(-80)
}
;;

{ .mfi
      nop.m         0
      fma.s1        FR_r2 = FR_r,FR_r,f0 // r^2
      nop.i         0
}
{ .mfi
      nop.m         0
      fms.s1        FR_A2 = FR_A3,FR_r,FR_A2 // A3*r+A2
      nop.i         0
}
;;

{ .mfi
      nop.m         0
      fma.s1        FR_A6 = FR_A7,FR_r,FR_A6 // A7*r+A6
      nop.i         0
}
{ .mfi
      nop.m         0
      fma.s1        FR_A4 = FR_A5,FR_r,FR_A4 // A5*r+A4
      nop.i         0
}
;;

{ .mfi
      nop.m         0
(p7)  fcvt.xf       FR_N = FR_N
      nop.i         0
}
;;

{ .mfi
      nop.m         0
      fma.s1        FR_r4 = FR_r2,FR_r2,f0 // r^4
      nop.i         0
}
{ .mfi
      nop.m         0
      // (A3*r+A2)*r^2+r
      fma.s1        FR_A2 = FR_A2,FR_r2,FR_r
      nop.i         0
}
;;

{ .mfi
      nop.m         0
      // (A7*r+A6)*r^2+(A5*r+A4)
      fma.s1        FR_A4 = FR_A6,FR_r2,FR_A4
      nop.i         0
}
;;

{ .mfi
      nop.m         0
      // N*Ln2hi+Thi
(p7)  fma.s1        FR_NxLn2hipThi = FR_N,FR_Ln2hi,FR_Thi
      nop.i         0
}
{ .mfi
      nop.m         0
      // N*Ln2lo+Tlo
(p7)  fma.s1        FR_NxLn2lopTlo = FR_N,FR_Ln2lo,FR_Tlo
      nop.i         0
}
;;

{ .mfi
      nop.m         0
(p7)  fma.s1        f8 = FR_A4,FR_r4,FR_A2 // P(r) if |x| >= 1/256
      nop.i         0
}
{ .mfi
      nop.m         0
      // (N*Ln2hi+Thi) + (N*Ln2lo+Tlo)
(p7)  fma.s1        FR_NxLn2pT = FR_NxLn2hipThi,f1,FR_NxLn2lopTlo
      nop.i         0
}
;;

.pred.rel "mutex",p6,p7
{ .mfi
      nop.m         0
(p6)  fma.d.s0      f8 = FR_A4,FR_r4,FR_A2 // result if 2^(-80) <= |x| < 1/256
      nop.i         0
}
{ .mfb
      nop.m         0
(p7)  fma.d.s0      f8 = f8,f1,FR_NxLn2pT  // result if |x| >= 1/256
      br.ret.sptk   b0                     // Exit if |x| >= 2^(-80)
}
;;

.align 32
log1p_unorm:
// Here if x=unorm
{ .mfb
      getf.exp      GR_signexp_x = FR_NormX // recompute biased exponent
      nop.f         0
      br.cond.sptk  log1p_common
}
;;

.align 32
log1p_eq_minus_1:
// Here if x=-1
{ .mfi
      nop.m         0
      fmerge.s      FR_X = f8,f8 // keep input argument for subsequent
                                 // call of __libm_error_support#
      nop.i         0
}
;;

{ .mfi
      mov           GR_TAG = 140  // set libm error in case of log1p(-1).
      frcpa.s0      f8,p0 = f8,f0 // log1p(-1) should be equal to -INF.
                                      // We can get it using frcpa because it
                                      // sets result to the IEEE-754 mandated
                                      // quotient of f8/f0.
      nop.i         0
}
{ .mib
      nop.m         0
      nop.i         0
      br.cond.sptk  log_libm_err
}
;;

.align 32
log1p_lt_minus_1:
// Here if x < -1
{ .mfi
      nop.m         0
      fmerge.s      FR_X = f8,f8
      nop.i         0
}
;;

{ .mfi
      mov           GR_TAG = 141  // set libm error in case of x < -1.
      frcpa.s0      f8,p0 = f0,f0 // log1p(x) x < -1 should be equal to NaN.
                                  // We can get it using frcpa because it
                                  // sets result to the IEEE-754 mandated
                                  // quotient of f0/f0 i.e. NaN.
      nop.i         0
}
;;

.align 32
log_libm_err:
{ .mmi
      alloc         r32 = ar.pfs,1,4,4,0
      mov           GR_Parameter_TAG = GR_TAG
      nop.i         0
}
;;

GLOBAL_IEEE754_END(log1p)
libm_alias_double_other (__log1p, log1p)


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#