about summary refs log tree commit diff
path: root/sysdeps/ia64/fpu/s_expm1l.S
blob: a3a6e401e819d4680a9072d87ebde699572df5c5 (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
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
.file "expl_m1.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.
// 07/07/01 Improved speed of all paths
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/10/03 Reordered header: .section, .global, .proc, .align;
//          used data8 for long double table values
// 03/11/03 Improved accuracy and performance, corrected missing inexact flags
// 04/17/03 Eliminated misplaced and unused data label
// 12/15/03 Eliminated call to error support on expm1l underflow
//
//********************************************************************* 
//
// Function:   Combined expl(x) and expm1l(x), where
//                        x 
//             expl(x) = e , for double-extended precision x values
//                          x
//             expm1l(x) = e  - 1  for double-extended precision x values
//
//********************************************************************* 
//
// Resources Used:
//
//    Floating-Point Registers: f8  (Input and Return Value) 
//                              f9-f15,f32-f77 
//
//    General Purpose Registers: 
//      r14-r38
//      r35-r38 (Used to pass arguments to error handling routine)
//                                     
//    Predicate Registers:      p6-p15
//
//********************************************************************* 
//
// IEEE Special Conditions:
//
//    Denormal  fault raised on denormal inputs  
//    Overflow exceptions raised when appropriate for exp and expm1
//    Underflow exceptions raised when appropriate for exp and expm1
//    (Error Handling Routine called for overflow and Underflow)
//    Inexact raised when appropriate by algorithm 
//
//    exp(inf) = inf
//    exp(-inf) = +0
//    exp(SNaN) = QNaN
//    exp(QNaN) = QNaN
//    exp(0) = 1
//    exp(EM_special Values) = QNaN
//    exp(inf) = inf
//    expm1(-inf) = -1 
//    expm1(SNaN) = QNaN
//    expm1(QNaN) = QNaN
//    expm1(0) = 0
//    expm1(EM_special Values) = QNaN
//    
//********************************************************************* 
//
// Implementation and Algorithm Notes:
//
//  ker_exp_64( in_FR  : X,
//            out_FR : Y_hi,
//            out_FR : Y_lo,
//            out_FR : scale,
//            out_PR : Safe )
//
// On input, X is in register format
// p6 for exp,
// p7 for expm1,
//
// On output, 
//
//   scale*(Y_hi + Y_lo)  approximates  exp(X)       if exp
//   scale*(Y_hi + Y_lo)  approximates  exp(X)-1     if expm1
//
// The accuracy is sufficient for a highly accurate 64 sig.
// bit implementation.  Safe is set if there is no danger of 
// overflow/underflow when the result is composed from scale, 
// Y_hi and Y_lo. Thus, we can have a fast return if Safe is set. 
// Otherwise, one must prepare to handle the possible exception 
// appropriately.  Note that SAFE not set (false) does not mean 
// that overflow/underflow will occur; only the setting of SAFE
// guarantees the opposite.
//
// **** High Level Overview **** 
//
// The method consists of three cases.
// 
// If           |X| < Tiny	use case exp_tiny;
// else if	|X| < 2^(-m)	use case exp_small; m=12 for exp, m=7 for expm1
// else		use case exp_regular;
//
// Case exp_tiny:
//
//   1 + X     can be used to approximate exp(X) 
//   X + X^2/2 can be used to approximate exp(X) - 1
//
// Case exp_small:
//
//   Here, exp(X) and exp(X) - 1 can all be 
//   approximated by a relatively simple polynomial.
//
//   This polynomial resembles the truncated Taylor series
//
//	exp(w) = 1 + w + w^2/2! + w^3/3! + ... + w^n/n!
//
// Case exp_regular:
//
//   Here we use a table lookup method. The basic idea is that in
//   order to compute exp(X), we accurately decompose X into
//
//   X = N * log(2)/(2^12)  + r,	|r| <= log(2)/2^13.
//
//   Hence
//
//   exp(X) = 2^( N / 2^12 ) * exp(r).
//
//   The value 2^( N / 2^12 ) is obtained by simple combinations
//   of values calculated beforehand and stored in table; exp(r)
//   is approximated by a short polynomial because |r| is small.
//
//   We elaborate this method in 4 steps.
//
//   Step 1: Reduction
//
//   The value 2^12/log(2) is stored as a double-extended number
//   L_Inv.
//
//   N := round_to_nearest_integer( X * L_Inv )
//
//   The value log(2)/2^12 is stored as two numbers L_hi and L_lo so
//   that r can be computed accurately via
//
//   r := (X - N*L_hi) - N*L_lo
//
//   We pick L_hi such that N*L_hi is representable in 64 sig. bits
//   and thus the FMA   X - N*L_hi   is error free. So r is the 
//   1 rounding error from an exact reduction with respect to 
//   
//   L_hi + L_lo.
//
//   In particular, L_hi has 30 significant bit and can be stored
//   as a double-precision number; L_lo has 64 significant bits and
//   stored as a double-extended number.
//
//   Step 2: Approximation
//
//   exp(r) - 1 is approximated by a short polynomial of the form
//   
//   r + A_1 r^2 + A_2 r^3 + A_3 r^4 .
//
//   Step 3: Composition from Table Values 
//
//   The value 2^( N / 2^12 ) can be composed from a couple of tables
//   of precalculated values. First, express N as three integers
//   K, M_1, and M_2 as
//
//     N  =  K * 2^12  + M_1 * 2^6 + M_2
//
//   Where 0 <= M_1, M_2 < 2^6; and K can be positive or negative.
//   When N is represented in 2's complement, M_2 is simply the 6
//   lsb's, M_1 is the next 6, and K is simply N shifted right
//   arithmetically (sign extended) by 12 bits.
//
//   Now, 2^( N / 2^12 ) is simply  
//	
//      2^K * 2^( M_1 / 2^6 ) * 2^( M_2 / 2^12 )
//
//   Clearly, 2^K needs no tabulation. The other two values are less
//   trivial because if we store each accurately to more than working
//   precision, than its product is too expensive to calculate. We
//   use the following method.
//
//   Define two mathematical values, delta_1 and delta_2, implicitly
//   such that
//
//     T_1 = exp( [M_1 log(2)/2^6]  -  delta_1 ) 
//     T_2 = exp( [M_2 log(2)/2^12] -  delta_2 )
//
//   are representable as 24 significant bits. To illustrate the idea,
//   we show how we define delta_1: 
//
//     T_1     := round_to_24_bits( exp( M_1 log(2)/2^6 ) )
//     delta_1  = (M_1 log(2)/2^6) - log( T_1 )  
//
//   The last equality means mathematical equality. We then tabulate
//
//     W_1 := exp(delta_1) - 1
//     W_2 := exp(delta_2) - 1
//
//   Both in double precision.
//
//   From the tabulated values T_1, T_2, W_1, W_2, we compose the values
//   T and W via
//
//     T := T_1 * T_2			...exactly
//     W := W_1 + (1 + W_1)*W_2	
//
//   W approximates exp( delta ) - 1  where delta = delta_1 + delta_2.
//   The mathematical product of T and (W+1) is an accurate representation
//   of 2^(M_1/2^6) * 2^(M_2/2^12).
//
//   Step 4. Reconstruction
//
//   Finally, we can reconstruct exp(X), exp(X) - 1. 
//   Because
//
//	X = K * log(2) + (M_1*log(2)/2^6  - delta_1) 
//		       + (M_2*log(2)/2^12 - delta_2)
//		       + delta_1 + delta_2 + r 		...accurately
//   We have
//
//	exp(X) ~=~ 2^K * ( T + T*[exp(delta_1+delta_2+r) - 1] )
//	       ~=~ 2^K * ( T + T*[exp(delta + r) - 1]         )
//	       ~=~ 2^K * ( T + T*[(exp(delta)-1)  
//				 + exp(delta)*(exp(r)-1)]   )
//             ~=~ 2^K * ( T + T*( W + (1+W)*poly(r) ) )
//             ~=~ 2^K * ( Y_hi  +  Y_lo )
//
//   where Y_hi = T  and Y_lo = T*(W + (1+W)*poly(r))
//
//   For exp(X)-1, we have
//
//	exp(X)-1 ~=~ 2^K * ( Y_hi + Y_lo ) - 1
//		 ~=~ 2^K * ( Y_hi + Y_lo - 2^(-K) )
//
//   and we combine Y_hi + Y_lo - 2^(-N)  into the form of two 
//   numbers  Y_hi + Y_lo carefully.
//
//   **** Algorithm Details ****
//
//   A careful algorithm must be used to realize the mathematical ideas
//   accurately. We describe each of the three cases. We assume SAFE
//   is preset to be TRUE.
//
//   Case exp_tiny:
//
//   The important points are to ensure an accurate result under 
//   different rounding directions and a correct setting of the SAFE 
//   flag.
//
//   If expm1 is 1, then
//      SAFE  := False	...possibility of underflow
//      Scale := 1.0
//      Y_hi  := X
//      Y_lo  := 2^(-17000)
//   Else
//      Scale := 1.0
//      Y_hi  := 1.0
//      Y_lo  := X	...for different rounding modes
//   Endif
//
//   Case exp_small:
//
//   Here we compute a simple polynomial. To exploit parallelism, we split
//   the polynomial into several portions.
//
//   Let r = X 
//
//   If exp 	...i.e. exp( argument )
//
//      rsq := r * r; 
//      r4  := rsq*rsq
//      poly_lo := P_3 + r*(P_4 + r*(P_5 + r*P_6))
//      poly_hi := r + rsq*(P_1 + r*P_2)
//      Y_lo    := poly_hi + r4 * poly_lo
//      Y_hi    := 1.0
//      Scale   := 1.0
//
//   Else			...i.e. exp( argument ) - 1
//
//      rsq := r * r
//      r4  := rsq * rsq
//      poly_lo := Q_7 + r*(Q_8 + r*Q_9))
//      poly_med:= Q_3 + r*Q_4 + rsq*(Q_5 + r*Q_6)
//      poly_med:= poly_med + r4*poly_lo
//      poly_hi := Q_1 + r*Q_2
//      Y_lo    := rsq*(poly_hi +  rsq*poly_lo)
//      Y_hi    := X
//      Scale   := 1.0
//
//   Endif
//
//  Case exp_regular:
//
//  The previous description contain enough information except the
//  computation of poly and the final Y_hi and Y_lo in the case for
//  exp(X)-1.
//
//  The computation of poly for Step 2:
//
//   rsq := r*r
//   poly := r + rsq*(A_1 + r*(A_2 + r*A_3))
//
//  For the case exp(X) - 1, we need to incorporate 2^(-K) into
//  Y_hi and Y_lo at the end of Step 4.
//
//   If K > 10 then
//      Y_lo := Y_lo - 2^(-K)
//   Else
//      If K < -10 then
//	 Y_lo := Y_hi + Y_lo
//	 Y_hi := -2^(-K)
//      Else
//	 Y_hi := Y_hi - 2^(-K)
//      End If
//   End If
//
//=======================================================
// General Purpose Registers
//
GR_ad_Arg           = r14
GR_ad_A             = r15
GR_sig_inv_ln2      = r15
GR_rshf_2to51       = r16
GR_ad_PQ            = r16
GR_ad_Q             = r16
GR_signexp_x        = r17
GR_exp_x            = r17
GR_small_exp        = r18
GR_rshf             = r18
GR_exp_mask         = r19
GR_ad_W1            = r20
GR_exp_2tom51       = r20
GR_ad_W2            = r21
GR_exp_underflow    = r21
GR_M2               = r22
GR_huge_exp         = r22
GR_M1               = r23
GR_huge_signif      = r23
GR_K                = r24
GR_one              = r24
GR_minus_one        = r24
GR_exp_bias         = r25
GR_ad_Limits        = r26
GR_N_fix            = r26
GR_exp_2_mk         = r26
GR_ad_P             = r27
GR_exp_2_k          = r27
GR_big_expo_neg     = r28
GR_very_small_exp   = r29
GR_exp_half         = r29
GR_ad_T1            = r30
GR_ad_T2            = r31

GR_SAVE_PFS         = r32
GR_SAVE_B0          = r33
GR_SAVE_GP          = r34
GR_Parameter_X      = r35
GR_Parameter_Y      = r36
GR_Parameter_RESULT = r37
GR_Parameter_TAG    = r38 

// Floating Point Registers
//
FR_norm_x           = f9
FR_RSHF_2TO51       = f10
FR_INV_LN2_2TO63    = f11
FR_W_2TO51_RSH      = f12
FR_2TOM51           = f13
FR_RSHF             = f14
FR_Y_hi             = f34
FR_Y_lo             = f35
FR_scale            = f36
FR_tmp              = f37
FR_float_N          = f38
FR_N_signif         = f39
FR_L_hi             = f40
FR_L_lo             = f41
FR_r                = f42
FR_W1               = f43
FR_T1               = f44
FR_W2               = f45
FR_T2               = f46
FR_W1_p1            = f47
FR_rsq              = f48
FR_A2               = f49
FR_r4               = f50
FR_A3               = f51
FR_poly             = f52
FR_T                = f53
FR_W                = f54
FR_Wp1              = f55
FR_p21              = f59
FR_p210             = f59
FR_p65              = f60
FR_p654             = f60
FR_p6543            = f60
FR_2_mk             = f61
FR_P4Q7             = f61
FR_P4               = f61
FR_Q7               = f61
FR_P3Q6             = f62
FR_P3               = f62
FR_Q6               = f62
FR_q65              = f62
FR_q6543            = f62
FR_P2Q5             = f63
FR_P2               = f63
FR_Q5               = f63
FR_P1Q4             = f64
FR_P1               = f64
FR_Q4               = f64
FR_q43              = f64
FR_Q3               = f65
FR_Q2               = f66
FR_q21              = f66
FR_Q1               = f67
FR_A1               = f68
FR_P6Q9             = f68
FR_P6               = f68
FR_Q9               = f68
FR_P5Q8             = f69
FR_P5               = f69
FR_Q8               = f69
FR_q987             = f69
FR_q98              = f69
FR_q9876543         = f69
FR_min_oflow_x      = f70
FR_huge_exp         = f70
FR_zero_uflow_x     = f71
FR_huge_signif      = f71
FR_huge             = f72
FR_small            = f72
FR_half             = f73
FR_T_scale          = f74
FR_result_lo        = f75
FR_W_T_scale        = f76
FR_Wp1_T_scale      = f77
FR_ftz              = f77
FR_half_x           = f77
//

FR_X                = f9
FR_Y                = f0
FR_RESULT           = f15

// ************* DO NOT CHANGE ORDER OF THESE TABLES ********************

// double-extended 1/ln(2)
// 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88
// 3fff b8aa 3b29 5c17 f0bc 
// For speed the significand will be loaded directly with a movl and setf.sig
//   and the exponent will be bias+63 instead of bias+0.  Thus subsequent
//   computations need to scale appropriately.
// The constant 2^12/ln(2) is needed for the computation of N.  This is also 
//   obtained by scaling the computations.
//
// Two shifting constants are loaded directly with movl and setf.d. 
//   1. RSHF_2TO51 = 1.1000..00 * 2^(63-12) 
//        This constant is added to x*1/ln2 to shift the integer part of
//        x*2^12/ln2 into the rightmost bits of the significand.
//        The result of this fma is N_signif.
//   2. RSHF       = 1.1000..00 * 2^(63) 
//        This constant is subtracted from N_signif * 2^(-51) to give
//        the integer part of N, N_fix, as a floating-point number.
//        The result of this fms is float_N.

RODATA
.align 64 
LOCAL_OBJECT_START(Constants_exp_64_Arg)
//data8 0xB8AA3B295C17F0BC,0x0000400B // Inv_L = 2^12/log(2)
data8 0xB17217F400000000,0x00003FF2 // L_hi = hi part log(2)/2^12
data8 0xF473DE6AF278ECE6,0x00003FD4 // L_lo = lo part log(2)/2^12
LOCAL_OBJECT_END(Constants_exp_64_Arg)

LOCAL_OBJECT_START(Constants_exp_64_Limits)
data8 0xb17217f7d1cf79ac,0x0000400c // Smallest long dbl oflow x
data8 0xb220000000000000,0x0000c00c // Small long dbl uflow zero x
LOCAL_OBJECT_END(Constants_exp_64_Limits)

LOCAL_OBJECT_START(Constants_exp_64_A)
data8 0xAAAAAAABB1B736A0,0x00003FFA // A3
data8 0xAAAAAAAB90CD6327,0x00003FFC // A2
data8 0xFFFFFFFFFFFFFFFF,0x00003FFD // A1
LOCAL_OBJECT_END(Constants_exp_64_A)

LOCAL_OBJECT_START(Constants_exp_64_P)
data8 0xD00D6C8143914A8A,0x00003FF2 // P6
data8 0xB60BC4AC30304B30,0x00003FF5 // P5
data8 0x888888887474C518,0x00003FF8 // P4
data8 0xAAAAAAAA8DAE729D,0x00003FFA // P3
data8 0xAAAAAAAAAAAAAF61,0x00003FFC // P2
data8 0x80000000000004C7,0x00003FFE // P1
LOCAL_OBJECT_END(Constants_exp_64_P)

LOCAL_OBJECT_START(Constants_exp_64_Q)
data8 0x93F2AC5F7471F32E, 0x00003FE9 // Q9
data8 0xB8DA0F3550B3E764, 0x00003FEC // Q8
data8 0xD00D00D0028E89C4, 0x00003FEF // Q7
data8 0xD00D00DAEB8C4E91, 0x00003FF2 // Q6
data8 0xB60B60B60B60B6F5, 0x00003FF5 // Q5
data8 0x888888888886CC23, 0x00003FF8 // Q4
data8 0xAAAAAAAAAAAAAAAB, 0x00003FFA // Q3
data8 0xAAAAAAAAAAAAAAAB, 0x00003FFC // Q2
data8 0x8000000000000000, 0x00003FFE // Q1
LOCAL_OBJECT_END(Constants_exp_64_Q)

LOCAL_OBJECT_START(Constants_exp_64_T1)
data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29 
data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5 
data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC
data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D
data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA
data4 0x3F9EF532,0x3FA0B051,0x3FA27043,0x3FA43516
data4 0x3FA5FED7,0x3FA7CD94,0x3FA9A15B,0x3FAB7A3A
data4 0x3FAD583F,0x3FAF3B79,0x3FB123F6,0x3FB311C4
data4 0x3FB504F3,0x3FB6FD92,0x3FB8FBAF,0x3FBAFF5B
data4 0x3FBD08A4,0x3FBF179A,0x3FC12C4D,0x3FC346CD
data4 0x3FC5672A,0x3FC78D75,0x3FC9B9BE,0x3FCBEC15
data4 0x3FCE248C,0x3FD06334,0x3FD2A81E,0x3FD4F35B
data4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5
data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396A
data4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177
data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0C
LOCAL_OBJECT_END(Constants_exp_64_T1)

LOCAL_OBJECT_START(Constants_exp_64_T2)
data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4 
data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7 
data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E 
data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349 
data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987 
data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA 
data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610 
data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A 
data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8 
data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA 
data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50 
data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA 
data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07 
data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269 
data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE 
data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37
LOCAL_OBJECT_END(Constants_exp_64_T2)

LOCAL_OBJECT_START(Constants_exp_64_W1)
data8 0x0000000000000000, 0xBE384454171EC4B4
data8 0xBE6947414AA72766, 0xBE5D32B6D42518F8
data8 0x3E68D96D3A319149, 0xBE68F4DA62415F36
data8 0xBE6DDA2FC9C86A3B, 0x3E6B2E50F49228FE
data8 0xBE49C0C21188B886, 0x3E64BFC21A4C2F1F
data8 0xBE6A2FBB2CB98B54, 0x3E5DC5DE9A55D329
data8 0x3E69649039A7AACE, 0x3E54728B5C66DBA5
data8 0xBE62B0DBBA1C7D7D, 0x3E576E0409F1AF5F
data8 0x3E6125001A0DD6A1, 0xBE66A419795FBDEF
data8 0xBE5CDE8CE1BD41FC, 0xBE621376EA54964F
data8 0x3E6370BE476E76EE, 0x3E390D1A3427EB92
data8 0x3E1336DE2BF82BF8, 0xBE5FF1CBD0F7BD9E
data8 0xBE60A3550CEB09DD, 0xBE5CA37E0980F30D
data8 0xBE5C541B4C082D25, 0xBE5BBECA3B467D29
data8 0xBE400D8AB9D946C5, 0xBE5E2A0807ED374A
data8 0xBE66CB28365C8B0A, 0x3E3AAD5BD3403BCA
data8 0x3E526055C7EA21E0, 0xBE442C75E72880D6
data8 0x3E58B2BB85222A43, 0xBE5AAB79522C42BF
data8 0xBE605CB4469DC2BC, 0xBE589FA7A48C40DC
data8 0xBE51C2141AA42614, 0xBE48D087C37293F4
data8 0x3E367A1CA2D673E0, 0xBE51BEBB114F7A38
data8 0xBE6348E5661A4B48, 0xBDF526431D3B9962
data8 0x3E3A3B5E35A78A53, 0xBE46C46C1CECD788
data8 0xBE60B7EC7857D689, 0xBE594D3DD14F1AD7
data8 0xBE4F9C304C9A8F60, 0xBE52187302DFF9D2
data8 0xBE5E4C8855E6D68F, 0xBE62140F667F3DC4
data8 0xBE36961B3BF88747, 0x3E602861C96EC6AA
data8 0xBE3B5151D57FD718, 0x3E561CD0FC4A627B
data8 0xBE3A5217CA913FEA, 0x3E40A3CC9A5D193A
data8 0xBE5AB71310A9C312, 0x3E4FDADBC5F57719
data8 0x3E361428DBDF59D5, 0x3E5DB5DB61B4180D
data8 0xBE42AD5F7408D856, 0x3E2A314831B2B707
LOCAL_OBJECT_END(Constants_exp_64_W1)

LOCAL_OBJECT_START(Constants_exp_64_W2)
data8 0x0000000000000000, 0xBE641F2537A3D7A2
data8 0xBE68DD57AD028C40, 0xBE5C77D8F212B1B6
data8 0x3E57878F1BA5B070, 0xBE55A36A2ECAE6FE
data8 0xBE620608569DFA3B, 0xBE53B50EA6D300A3
data8 0x3E5B5EF2223F8F2C, 0xBE56A0D9D6DE0DF4
data8 0xBE64EEF3EAE28F51, 0xBE5E5AE2367EA80B
data8 0x3E47CB1A5FCBC02D, 0xBE656BA09BDAFEB7
data8 0x3E6E70C6805AFEE7, 0xBE6E0509A3415EBA
data8 0xBE56856B49BFF529, 0x3E66DD3300508651
data8 0x3E51165FC114BC13, 0x3E53333DC453290F
data8 0x3E6A072B05539FDA, 0xBE47CD877C0A7696
data8 0xBE668BF4EB05C6D9, 0xBE67C3E36AE86C93
data8 0xBE533904D0B3E84B, 0x3E63E8D9556B53CE
data8 0x3E212C8963A98DC8, 0xBE33138F032A7A22
data8 0x3E530FA9BC584008, 0xBE6ADF82CCB93C97
data8 0x3E5F91138370EA39, 0x3E5443A4FB6A05D8
data8 0x3E63DACD181FEE7A, 0xBE62B29DF0F67DEC
data8 0x3E65C4833DDE6307, 0x3E5BF030D40A24C1
data8 0x3E658B8F14E437BE, 0xBE631C29ED98B6C7
data8 0x3E6335D204CF7C71, 0x3E529EEDE954A79D
data8 0x3E5D9257F64A2FB8, 0xBE6BED1B854ED06C
data8 0x3E5096F6D71405CB, 0xBE3D4893ACB9FDF5
data8 0xBDFEB15801B68349, 0x3E628D35C6A463B9
data8 0xBE559725ADE45917, 0xBE68C29C042FC476
data8 0xBE67593B01E511FA, 0xBE4A4313398801ED
data8 0x3E699571DA7C3300, 0x3E5349BE08062A9E
data8 0x3E5229C4755BB28E, 0x3E67E42677A1F80D
data8 0xBE52B33F6B69C352, 0xBE6B3550084DA57F
data8 0xBE6DB03FD1D09A20, 0xBE60CBC42161B2C1
data8 0x3E56ED9C78A2B771, 0xBE508E319D0FA795
data8 0xBE59482AFD1A54E9, 0xBE2A17CEB07FD23E
data8 0x3E68BF5C17365712, 0x3E3956F9B3785569
LOCAL_OBJECT_END(Constants_exp_64_W2)


.section .text

GLOBAL_IEEE754_ENTRY(expm1l)

//
//    Set p7 true for expm1, p6 false
//    

{ .mlx
      getf.exp GR_signexp_x = f8  // Get sign and exponent of x, redo if unorm
      movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc  // significand of 1/ln2
}
{ .mlx
      addl GR_ad_Arg = @ltoff(Constants_exp_64_Arg#),gp  
      movl GR_rshf_2to51 = 0x4718000000000000 // 1.10000 2^(63+51)
}
;;

{ .mfi
      ld8  GR_ad_Arg = [GR_ad_Arg]       // Point to Arg table
      fclass.m p8, p0 =  f8, 0x1E7       // Test x for natval, nan, inf, zero
      cmp.eq  p7, p6 =  r0, r0 
}
{ .mfb
      mov GR_exp_half = 0x0FFFE          // Exponent of 0.5, for very small path
      fnorm.s1 FR_norm_x = f8            // Normalize x
      br.cond.sptk exp_continue 
}
;;

GLOBAL_IEEE754_END(expm1l)


GLOBAL_IEEE754_ENTRY(expl)
//
//    Set p7 false for exp, p6 true
//    
{ .mlx
      getf.exp GR_signexp_x = f8  // Get sign and exponent of x, redo if unorm
      movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc  // significand of 1/ln2
}
{ .mlx
      addl GR_ad_Arg = @ltoff(Constants_exp_64_Arg#),gp  
      movl GR_rshf_2to51 = 0x4718000000000000 // 1.10000 2^(63+51)
}
;;

{ .mfi
      ld8  GR_ad_Arg = [GR_ad_Arg]       // Point to Arg table
      fclass.m p8, p0 =  f8, 0x1E7       // Test x for natval, nan, inf, zero
      cmp.eq  p6, p7 =  r0, r0
}
{ .mfi
      mov GR_exp_half = 0x0FFFE          // Exponent of 0.5, for very small path
      fnorm.s1 FR_norm_x = f8            // Normalize x
      nop.i 999
}
;;

exp_continue: 
// Form two constants we need
//  1/ln2 * 2^63  to compute  w = x * 1/ln2 * 128 
//  1.1000..000 * 2^(63+63-12) to right shift int(N) into the significand

{ .mfi
      setf.sig  FR_INV_LN2_2TO63 = GR_sig_inv_ln2 // form 1/ln2 * 2^63
      fclass.nm.unc p9, p0 =  f8, 0x1FF  // Test x for unsupported
      mov GR_exp_2tom51 = 0xffff-51
}
{ .mlx
      setf.d  FR_RSHF_2TO51 = GR_rshf_2to51 // Form const 1.1000 * 2^(63+51)
      movl GR_rshf = 0x43e8000000000000  // 1.10000 2^63 for right shift
}
;;

{ .mfi
      setf.exp FR_half = GR_exp_half     // Form 0.5 for very small path
      fma.s1 FR_scale = f1,f1,f0         // Scale = 1.0
      mov GR_exp_bias = 0x0FFFF          // Set exponent bias
}
{ .mib
      add GR_ad_Limits = 0x20, GR_ad_Arg // Point to Limits table
      mov GR_exp_mask = 0x1FFFF          // Form exponent mask
(p8)  br.cond.spnt EXP_64_SPECIAL        // Branch if natval, nan, inf, zero
}
;;

{ .mfi
      setf.exp FR_2TOM51 = GR_exp_2tom51 // Form 2^-51 for scaling float_N
      nop.f 999
      add GR_ad_A = 0x40, GR_ad_Arg      // Point to A table
}
{ .mib
      setf.d  FR_RSHF = GR_rshf          // Form right shift const 1.1000 * 2^63
      add GR_ad_T1 = 0x160, GR_ad_Arg    // Point to T1 table
(p9)  br.cond.spnt EXP_64_UNSUPPORTED    // Branch if unsupported
}
;;

.pred.rel "mutex",p6,p7
{ .mfi
      ldfe FR_L_hi = [GR_ad_Arg],16      // Get L_hi
      fcmp.eq.s0 p9,p0 =  f8, f0         // Dummy op to flag denormals
(p6)  add GR_ad_PQ = 0x30, GR_ad_A       // Point to P table for exp
}
{ .mfi
      ldfe FR_min_oflow_x = [GR_ad_Limits],16 // Get min x to cause overflow
      fmpy.s1 FR_rsq = f8, f8            // rsq = x * x for small path
(p7)  add GR_ad_PQ = 0x90, GR_ad_A       // Point to Q table for expm1
};;

{ .mmi
      ldfe FR_L_lo = [GR_ad_Arg],16      // Get L_lo
      ldfe FR_zero_uflow_x = [GR_ad_Limits],16 // Get x for zero uflow result
      add GR_ad_W1 = 0x200, GR_ad_T1     // Point to W1 table
}
;;

{ .mfi
      ldfe FR_P6Q9 = [GR_ad_PQ],16       // P6(exp) or Q9(expm1) for small path
      mov FR_r = FR_norm_x               // r = X for small path
      mov GR_very_small_exp = -60        // Exponent of x for very small path
}
{ .mfi
      add GR_ad_W2 = 0x400, GR_ad_T1     // Point to W2 table
      nop.f 999
(p7)  mov GR_small_exp = -7              // Exponent of x for small path expm1
}
;;

{ .mmi
      ldfe FR_P5Q8 = [GR_ad_PQ],16       // P5(exp) or Q8(expm1) for small path
      and  GR_exp_x = GR_signexp_x, GR_exp_mask
(p6)  mov GR_small_exp = -12             // Exponent of x for small path exp
}
;;

// N_signif = X * Inv_log2_by_2^12
// By adding 1.10...0*2^63 we shift and get round_int(N_signif) in significand.
// We actually add 1.10...0*2^51 to X * Inv_log2 to do the same thing.
{ .mfi
      ldfe FR_P4Q7 = [GR_ad_PQ],16       // P4(exp) or Q7(expm1) for small path
      fma.s1 FR_N_signif = FR_norm_x, FR_INV_LN2_2TO63, FR_RSHF_2TO51
      nop.i 999
}
{ .mfi
      sub GR_exp_x = GR_exp_x, GR_exp_bias // Get exponent
      fmpy.s1 FR_r4 = FR_rsq, FR_rsq     // Form r4 for small path
      cmp.eq.unc  p15, p0 =  r0, r0      // Set Safe as default
}
;;

{ .mmi
      ldfe FR_P3Q6 = [GR_ad_PQ],16       // P3(exp) or Q6(expm1) for small path
      cmp.lt  p14, p0 =  GR_exp_x, GR_very_small_exp // Is |x| < 2^-60?
      nop.i 999
}
;;

{ .mfi
      ldfe FR_P2Q5 = [GR_ad_PQ],16       // P2(exp) or Q5(expm1) for small path
      fmpy.s1 FR_half_x = FR_half, FR_norm_x // 0.5 * x for very small path
      cmp.lt  p13, p0 =  GR_exp_x, GR_small_exp // Is |x| < 2^-m?
}
{ .mib
      nop.m 999
      nop.i 999
(p14) br.cond.spnt EXP_VERY_SMALL        // Branch if |x| < 2^-60
}
;;

{ .mfi
      ldfe FR_A3 = [GR_ad_A],16          // Get A3 for normal path
      fcmp.ge.s1 p10,p0 = FR_norm_x, FR_min_oflow_x // Will result overflow?
      mov GR_big_expo_neg = -16381       // -0x3ffd
}
{ .mfb
      ldfe FR_P1Q4 = [GR_ad_PQ],16       // P1(exp) or Q4(expm1) for small path
      nop.f 999
(p13) br.cond.spnt EXP_SMALL             // Branch if |x| < 2^-m
                                         // m=12 for exp, m=7 for expm1
}
;;

// Now we are on the main path for |x| >= 2^-m, m=12 for exp, m=7 for expm1
//
// float_N = round_int(N_signif) 
// The signficand of N_signif contains the rounded integer part of X * 2^12/ln2,
// as a twos complement number in the lower bits (that is, it may be negative).
// That twos complement number (called N) is put into GR_N.

// Since N_signif is scaled by 2^51, it must be multiplied by 2^-51
// before the shift constant 1.10000 * 2^63 is subtracted to yield float_N.
// Thus, float_N contains the floating point version of N


{ .mfi
      ldfe FR_A2 = [GR_ad_A],16          // Get A2 for main path
      fcmp.lt.s1 p11,p0 = FR_norm_x, FR_zero_uflow_x // Certain zero, uflow?
      add GR_ad_T2 = 0x100, GR_ad_T1     // Point to T2 table
}
{ .mfi
      nop.m 999
      fms.s1 FR_float_N = FR_N_signif, FR_2TOM51, FR_RSHF // Form float_N
      nop.i 999
}
;;

{ .mbb
      getf.sig GR_N_fix = FR_N_signif    // Get N from significand
(p10) br.cond.spnt  EXP_OVERFLOW         // Branch if result will overflow
(p11) br.cond.spnt  EXP_CERTAIN_UNDERFLOW_ZERO // Branch if certain zero, uflow
}
;;

{ .mfi
      ldfe FR_A1 = [GR_ad_A],16          // Get A1 for main path
      fnma.s1 FR_r = FR_L_hi, FR_float_N, FR_norm_x  // r = -L_hi * float_N + x
      extr.u GR_M1 = GR_N_fix, 6, 6      // Extract index M_1
}
{ .mfi
      and GR_M2 = 0x3f, GR_N_fix         // Extract index M_2
      nop.f 999
      nop.i 999
}
;;

// N_fix is only correct up to 50 bits because of our right shift technique.
// Actually in the normal path we will have restricted K to about 14 bits.
// Somewhat arbitrarily we extract 32 bits.
{ .mfi
      shladd GR_ad_W1 = GR_M1,3,GR_ad_W1 // Point to W1
      nop.f 999
      extr GR_K = GR_N_fix, 12, 32       // Extract limited range K
}
{ .mfi
      shladd GR_ad_T1 = GR_M1,2,GR_ad_T1 // Point to T1
      nop.f 999
      shladd GR_ad_T2 = GR_M2,2,GR_ad_T2 // Point to T2
}
;;

{ .mmi
      ldfs  FR_T1 = [GR_ad_T1],0         // Get T1
      ldfd  FR_W1 = [GR_ad_W1],0         // Get W1
      add GR_exp_2_k = GR_exp_bias, GR_K // Form exponent of 2^k
}
;;

{ .mmi
      ldfs  FR_T2 = [GR_ad_T2],0         // Get T2
      shladd GR_ad_W2 = GR_M2,3,GR_ad_W2 // Point to W2
      sub GR_exp_2_mk = GR_exp_bias, GR_K // Form exponent of 2^-k
}
;;

{ .mmf
      ldfd  FR_W2 = [GR_ad_W2],0         // Get W2
      setf.exp FR_scale = GR_exp_2_k     // Set scale = 2^k
      fnma.s1 FR_r = FR_L_lo, FR_float_N, FR_r // r = -L_lo * float_N + r
}
;;

{ .mfi
      setf.exp FR_2_mk = GR_exp_2_mk     // Form 2^-k
      fma.s1 FR_poly = FR_r, FR_A3, FR_A2 // poly = r * A3 + A2
      cmp.lt p8,p15 = GR_K,GR_big_expo_neg // Set Safe if K > big_expo_neg
}
{ .mfi
      nop.m 999
      fmpy.s1 FR_rsq = FR_r, FR_r         // rsq = r * r
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fmpy.s1 FR_T = FR_T1, FR_T2         // T = T1 * T2
      nop.i 999
}
{ .mfi
      nop.m 999
      fadd.s1 FR_W1_p1 = FR_W1, f1        // W1_p1 = W1 + 1.0
      nop.i 999
}
;;

{ .mfi
(p7)  cmp.lt.unc  p8, p9 =  10, GR_K       // If expm1, set p8 if K > 10 
      fma.s1 FR_poly = FR_r, FR_poly, FR_A1 // poly = r * poly + A1
      nop.i 999
}
;;

{ .mfi
(p7)  cmp.eq  p15, p0 =  r0, r0            // If expm1, set Safe flag
      fma.s1 FR_T_scale = FR_T, FR_scale, f0 // T_scale = T * scale
(p9)  cmp.gt.unc  p9, p10 =  -10, GR_K     // If expm1, set p9 if K < -10
                                           // If expm1, set p10 if -10<=K<=10
}
{ .mfi
      nop.m 999
      fma.s1 FR_W = FR_W2, FR_W1_p1, FR_W1 // W = W2 * (W1+1.0) + W1
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      mov FR_Y_hi = FR_T                   // Assume Y_hi = T
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fma.s1 FR_poly = FR_rsq, FR_poly, FR_r // poly = rsq * poly + r
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fma.s1 FR_Wp1_T_scale = FR_W, FR_T_scale, FR_T_scale // (W+1)*T*scale
      nop.i 999
}
{ .mfi
      nop.m 999
      fma.s1 FR_W_T_scale = FR_W, FR_T_scale, f0 // W*T*scale
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p9)  fsub.s1 FR_Y_hi = f0, FR_2_mk      // If expm1, if K < -10 set Y_hi
      nop.i 999
}
{ .mfi
      nop.m 999
(p10) fsub.s1 FR_Y_hi = FR_T, FR_2_mk    // If expm1, if |K|<=10 set Y_hi
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fma.s1 FR_result_lo = FR_Wp1_T_scale, FR_poly, FR_W_T_scale
      nop.i 999
}
;;

.pred.rel "mutex",p8,p9
// If K > 10 adjust result_lo = result_lo - scale * 2^-k
// If |K| <= 10 adjust result_lo = result_lo + scale * T
{ .mfi
      nop.m 999
(p8)  fnma.s1 FR_result_lo = FR_scale, FR_2_mk, FR_result_lo // If K > 10
      nop.i 999
}
{ .mfi
      nop.m 999
(p9)  fma.s1 FR_result_lo = FR_T_scale, f1, FR_result_lo // If |K| <= 10
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fmpy.s0 FR_tmp = FR_A1, FR_A1         // Dummy op to set inexact
      nop.i 999
}
{ .mfb
      nop.m 999
(p15) fma.s0 f8 = FR_Y_hi, FR_scale, FR_result_lo  // Safe result
(p15) br.ret.sptk b0                        // Safe exit for normal path
}
;;

// Here if unsafe, will only be here for exp with K < big_expo_neg
{ .mfb
      nop.m 999
      fma.s0 FR_RESULT = FR_Y_hi, FR_scale, FR_result_lo  // Prelim result
      br.cond.sptk EXP_POSSIBLE_UNDERFLOW  // Branch to unsafe code
}
;;

 
EXP_SMALL: 
// Here if 2^-60 < |x| < 2^-m, m=12 for exp, m=7 for expm1
{ .mfi
(p7)  ldfe FR_Q3 = [GR_ad_Q],16          // Get Q3 for small path, if expm1
(p6)  fma.s1 FR_p65 = FR_P6, FR_r, FR_P5  // If exp, p65 = P6 * r + P5
      nop.i 999
}
{ .mfi
      mov GR_minus_one = -1
(p7)  fma.s1 FR_q98 = FR_Q9, FR_r, FR_Q8  // If expm1, q98 = Q9 * r + Q8
      nop.i 999
}
;;

{ .mfi
(p7)  ldfe FR_Q2 = [GR_ad_Q],16           // Get Q2 for small path, if expm1
(p7)  fma.s1 FR_q65 = FR_Q6, FR_r, FR_Q5  // If expm1, q65 = Q6 * r + Q5
      nop.i 999
}
;;

{ .mfi
      setf.sig FR_tmp = GR_minus_one      // Create value to force inexact
(p6)  fma.s1 FR_p21 = FR_P2, FR_r, FR_P1  // If exp, p21 = P2 * r + P1
      nop.i 999
}
{ .mfi
(p7)  ldfe FR_Q1 = [GR_ad_Q],16           // Get Q1 for small path, if expm1
(p7)  fma.s1 FR_q43 = FR_Q4, FR_r, FR_Q3  // If expm1, q43 = Q4 * r + Q3
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fma.s1 FR_p654 = FR_p65, FR_r, FR_P4 // If exp, p654 = p65 * r + P4
      nop.i 999
}
{ .mfi
      nop.m 999
(p7)  fma.s1 FR_q987 = FR_q98, FR_r, FR_Q7 // If expm1, q987 = q98 * r + Q7
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p7)  fma.s1 FR_q21 = FR_Q2, FR_r, FR_Q1  // If expm1, q21 = Q2 * r + Q1
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fma.s1 FR_p210 = FR_p21, FR_rsq, FR_r // If exp, p210 = p21 * r + P0
      nop.i 999
}
{ .mfi
      nop.m 999
(p7)  fma.s1 FR_q6543 = FR_q65, FR_rsq, FR_q43 // If expm1, q6543 = q65*r2+q43
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fma.s1 FR_p6543 = FR_p654, FR_r, FR_P3 // If exp, p6543 = p654 * r + P3
      nop.i 999
}
{ .mfi
      nop.m 999
(p7)  fma.s1 FR_q9876543 = FR_q987, FR_r4, FR_q6543 // If expm1, q9876543 = ...
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fma.s1 FR_Y_lo = FR_p6543, FR_r4, FR_p210 // If exp, form Y_lo
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p7)  fma.s1 FR_Y_lo = FR_q9876543, FR_rsq, FR_q21 // If expm1, form Y_lo
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fmpy.s0  FR_tmp = FR_tmp, FR_tmp   // Dummy op to set inexact
      nop.i 999
}
;;

.pred.rel "mutex",p6,p7
{ .mfi
      nop.m 999
(p6)  fma.s0 f8 = FR_Y_lo, f1, f1          // If exp, result = 1 + Y_lo
      nop.i 999
}
{ .mfb
      nop.m 999
(p7)  fma.s0 f8 = FR_Y_lo, FR_rsq, FR_norm_x // If expm1, result = Y_lo*r2+x
      br.ret.sptk  b0                      // Exit for 2^-60 <= |x| < 2^-m
                                           // m=12 for exp, m=7 for expm1
}
;;


EXP_VERY_SMALL: 
//
// Here if 0 < |x| < 2^-60
// If exp, result = 1.0 + x
// If expm1, result = x +x*x/2, but have to check for possible underflow
//

{ .mfi
(p7)  mov GR_exp_underflow = -16381        // Exponent for possible underflow
(p6)  fadd.s0 f8 = f1, FR_norm_x           // If exp, result = 1+x
      nop.i 999
}
{ .mfi
      nop.m 999
(p7)  fmpy.s1 FR_result_lo = FR_half_x, FR_norm_x  // If expm1 result_lo = x*x/2
      nop.i 999
}
;;

{ .mfi
(p7)  cmp.lt.unc p0, p8 = GR_exp_x, GR_exp_underflow // Unsafe if expm1 x small
(p7)  mov FR_Y_hi = FR_norm_x              // If expm1, Y_hi = x
(p7)  cmp.lt p0, p15 = GR_exp_x, GR_exp_underflow // Unsafe if expm1 x small
}
;;

{ .mfb
      nop.m 999
(p8)  fma.s0 f8 = FR_norm_x, f1, FR_result_lo // If expm1, result=x+x*x/2
(p15) br.ret.sptk b0                       // If Safe, exit
}
;;

// Here if expm1 and 0 < |x| < 2^-16381;  may be possible underflow
{ .mfb
      nop.m 999
      fma.s0 FR_RESULT = FR_Y_hi, FR_scale, FR_result_lo // Prelim result
      br.cond.sptk EXP_POSSIBLE_UNDERFLOW  // Branch to unsafe code
}
;;

EXP_CERTAIN_UNDERFLOW_ZERO:
// Here if x < zero_uflow_x
// For exp, set result to tiny+0.0 and set I, U, and branch to error handling
// For expm1, set result to tiny-1.0 and set I, and exit
{ .mmi
      alloc GR_SAVE_PFS = ar.pfs,0,3,4,0
      nop.m 999
      mov GR_one = 1
}
;;

{ .mmi
      setf.exp FR_small = GR_one               // Form small value
      nop.m 999
(p6)  mov GR_Parameter_TAG = 13                // Error tag for exp underflow
}
;;

{ .mfi
      nop.m 999
      fmerge.s FR_X = f8,f8                    // Save x for error call
      nop.i 999
}
;;

.pred.rel "mutex",p6,p7
{ .mfb
      nop.m 999
(p6)  fma.s0 FR_RESULT = FR_small, FR_small, f0 // If exp, set I,U, tiny result
(p6)  br.cond.sptk __libm_error_region          // If exp, go to error handling
}
{ .mfb
      nop.m 999
(p7)  fms.s0 f8 = FR_small, FR_small, f1        // If expm1, set I, result -1.0
(p7)  br.ret.sptk  b0                           // If expm1, exit
}
;;
     
  
EXP_OVERFLOW:
// Here if x >= min_oflow_x
{ .mmi
      alloc GR_SAVE_PFS = ar.pfs,0,3,4,0
      mov GR_huge_exp = 0x1fffe
      nop.i 999
}
{ .mfi
      mov GR_huge_signif = -0x1
      nop.f 999
(p6)  mov GR_Parameter_TAG = 12                // Error tag for exp overflow
}
;;

{ .mmf
      setf.exp FR_huge_exp = GR_huge_exp       // Create huge value
      setf.sig FR_huge_signif = GR_huge_signif // Create huge value
      fmerge.s FR_X = f8,f8                    // Save x for error call
}
;;

{ .mfi
      nop.m 999
      fmerge.se FR_huge = FR_huge_exp, FR_huge_signif
(p7)  mov GR_Parameter_TAG = 39                // Error tag for expm1 overflow
}
;;

{ .mfb
      nop.m 999
      fma.s0 FR_RESULT = FR_huge, FR_huge, FR_huge // Force I, O, and Inf
      br.cond.sptk __libm_error_region         // Branch to error handling
}
;;



EXP_POSSIBLE_UNDERFLOW:
// Here if exp and zero_uflow_x < x < about -11356 [where k < -16381]
// Here if expm1 and |x| < 2^-16381
{ .mfi
      alloc GR_SAVE_PFS = ar.pfs,0,3,4,0
      fsetc.s2 0x7F,0x41                   // Set FTZ and disable traps
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fma.s2 FR_ftz = FR_Y_hi, FR_scale, FR_result_lo   // Result with FTZ
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fsetc.s2 0x7F,0x40                   // Disable traps (set s2 default)
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fclass.m.unc p11, p0 = FR_ftz, 0x00F // If exp, FTZ result denorm or zero?
      nop.i 999
}
;;

{ .mfb
(p11) mov   GR_Parameter_TAG = 13             // exp underflow
      fmerge.s FR_X = f8,f8                   // Save x for error call
(p11) br.cond.spnt __libm_error_region        // Branch on exp underflow
}
;;

{ .mfb
      nop.m 999
      mov   f8     = FR_RESULT                // Was safe after all
      br.ret.sptk   b0
}
;;


EXP_64_SPECIAL: 
// Here if x natval, nan, inf, zero
// If x natval, +inf, or if expm1 and x zero, just return x.
// The other cases must be tested for, and results set.
// These cases do not generate exceptions.
{ .mfi
      nop.m 999
      fclass.m p8, p0 =  f8, 0x0c3            // Is x nan?
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fclass.m.unc p13, p0 =  f8, 0x007       // If exp, is x zero?
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fclass.m.unc p11, p0 =  f8, 0x022       // If exp, is x -inf?
      nop.i 999
}
{ .mfi
      nop.m 999
(p8)  fadd.s0 f8 = f8, f1                     // If x nan, result quietized x
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p7)  fclass.m.unc p10, p0 =  f8, 0x022       // If expm1, is x -inf?
      nop.i 999
}
{ .mfi
      nop.m 999
(p13) fadd.s0 f8 = f0, f1                     // If exp and x zero, result 1.0
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p11) mov f8 = f0                             // If exp and x -inf, result 0
      nop.i 999
}
;;

{ .mfb
      nop.m 999
(p10) fsub.s1 f8 = f0, f1                     // If expm1, x -inf, result -1.0
      br.ret.sptk b0                          // Exit special cases
}
;;


EXP_64_UNSUPPORTED: 
// Here if x unsupported type
{ .mfb
      nop.m 999
      fmpy.s0 f8 = f8, f0                     // Return nan
      br.ret.sptk   b0
}
;;

GLOBAL_IEEE754_END(expl)

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
        stfe [GR_Parameter_Y] = FR_Y,16         // Save 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
        stfe [GR_Parameter_X] = FR_X            // Store Parameter 1 on stack
        add   GR_Parameter_RESULT = 0,GR_Parameter_Y
        nop.b 0                                 // Parameter 3 address
}
{ .mib
        stfe [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
        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
};;
LOCAL_LIBM_END(__libm_error_region#)

.type   __libm_error_support#,@function
.global __libm_error_support#