about summary refs log tree commit diff
path: root/sysdeps/ia64/fpu/s_expm1.S
blob: 19a237990c2241f21da587878c7ff4f7a9cdd307 (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
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
.file "exp_m1.s"

// Copyright (C) 2000, 2001, Intel Corporation
// All rights reserved.
// 
// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
//
// 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://developer.intel.com/opensource.
//
// HISTORY
// 2/02/00  Initial Version 
// 4/04/00  Unwind support added
// 8/15/00  Bundle added after call to __libm_error_support to properly
//          set [the previously overwritten] GR_Parameter_RESULT.
//
// ********************************************************************* 
//
// Function:   Combined exp(x) and expm1(x), where
//                       x 
//             exp(x) = e , for double precision x values
//                         x
//             expm1(x) = e  - 1  for double precision x values
//
// ********************************************************************* 
//
// Accuracy:       Within .7 ulps for 80-bit floating point values
//                 Very accurate for double precision values
//
// ********************************************************************* 
//
// Resources Used:
//
//    Floating-Point Registers: f8  (Input and Return Value) 
//                              f9,f32-f61, f99-f102 
//
//    General Purpose Registers: 
//      r32-r61
//      r62-r65 (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,
//            in_GR  : Flag,
//            in_GR  : Expo_Range
//            out_FR : Y_hi,
//            out_FR : Y_lo,
//            out_FR : scale,
//            out_PR : Safe )
//
// On input, X is in register format and 
// Flag  = 0 for exp,
// Flag  = 1 for expm1,
//
// On output, provided X and X_cor are real numbers, then
//
//   scale*(Y_hi + Y_lo)  approximates  exp(X)       if Flag is 0
//   scale*(Y_hi + Y_lo)  approximates  exp(X)-1     if Flag is 1
//
// 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^(-6)	use case exp_small;
// else		use case exp_regular;
//
// Case exp_tiny:
//
//   1 + X     can be used to approximate exp(X) or exp(X+X_cor);
//   X + X^2/2 can be used to approximate exp(X) - 1
//
// Case exp_small:
//
//   Here, exp(X), exp(X+X_cor), and exp(X) - 1 can all be 
//   appproximated 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.
//
//   In the case Flag = 2, we further modify r by
//
//   r := r + X_cor.
//
//   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 Flag 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 Flag is not 1	...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
//      set lsb(Y_lo) to 1
//      Y_hi    := 1.0
//      Scale   := 1.0
//
//   Else			...i.e. exp( argument ) - 1
//
//      rsq := r * r
//      r4  := rsq * rsq
//      r6  := rsq * r4
//      poly_lo := r6*(Q_5 + r*(Q_6 + r*Q_7))
//      poly_hi := Q_1 + r*(Q_2 + r*(Q_3 + r*Q_4))
//      Y_lo    := rsq*poly_hi +  poly_lo
//      set lsb(Y_lo) to 1
//      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
//

#include "libm_support.h"

GR_SAVE_PFS          = r59
GR_SAVE_B0           = r60
GR_SAVE_GP           = r61

GR_Parameter_X       = r62
GR_Parameter_Y       = r63
GR_Parameter_RESULT  = r64

FR_X             = f9
FR_Y             = f1
FR_RESULT        = f99

#ifdef _LIBC
.rodata
#else
.data
#endif

.align 64 
Constants_exp_64_Arg:
ASM_TYPE_DIRECTIVE(Constants_exp_64_Arg,@object)
data4 0x5C17F0BC,0xB8AA3B29,0x0000400B,0x00000000 
data4 0x00000000,0xB17217F4,0x00003FF2,0x00000000
data4 0xF278ECE6,0xF473DE6A,0x00003FD4,0x00000000
// /* Inv_L, L_hi, L_lo */
ASM_SIZE_DIRECTIVE(Constants_exp_64_Arg)

.align 64 
Constants_exp_64_Exponents:
ASM_TYPE_DIRECTIVE(Constants_exp_64_Exponents,@object)
data4 0x0000007E,0x00000000,0xFFFFFF83,0xFFFFFFFF
data4 0x000003FE,0x00000000,0xFFFFFC03,0xFFFFFFFF
data4 0x00003FFE,0x00000000,0xFFFFC003,0xFFFFFFFF
data4 0x00003FFE,0x00000000,0xFFFFC003,0xFFFFFFFF
data4 0xFFFFFFE2,0xFFFFFFFF,0xFFFFFFC4,0xFFFFFFFF
data4 0xFFFFFFBA,0xFFFFFFFF,0xFFFFFFBA,0xFFFFFFFF
ASM_SIZE_DIRECTIVE(Constants_exp_64_Exponents)

.align 64 
Constants_exp_64_A:
ASM_TYPE_DIRECTIVE(Constants_exp_64_A,@object)
data4 0xB1B736A0,0xAAAAAAAB,0x00003FFA,0x00000000
data4 0x90CD6327,0xAAAAAAAB,0x00003FFC,0x00000000
data4 0xFFFFFFFF,0xFFFFFFFF,0x00003FFD,0x00000000
// /* Reversed */
ASM_SIZE_DIRECTIVE(Constants_exp_64_A)

.align 64 
Constants_exp_64_P:
ASM_TYPE_DIRECTIVE(Constants_exp_64_P,@object)
data4 0x43914A8A,0xD00D6C81,0x00003FF2,0x00000000
data4 0x30304B30,0xB60BC4AC,0x00003FF5,0x00000000
data4 0x7474C518,0x88888888,0x00003FF8,0x00000000
data4 0x8DAE729D,0xAAAAAAAA,0x00003FFA,0x00000000
data4 0xAAAAAF61,0xAAAAAAAA,0x00003FFC,0x00000000
data4 0x000004C7,0x80000000,0x00003FFE,0x00000000 
// /* Reversed */
ASM_SIZE_DIRECTIVE(Constants_exp_64_P)

.align 64 
Constants_exp_64_Q:
ASM_TYPE_DIRECTIVE(Constants_exp_64_Q,@object)
data4 0xA49EF6CA,0xD00D56F7,0x00003FEF,0x00000000
data4 0x1C63493D,0xD00D59AB,0x00003FF2,0x00000000
data4 0xFB50CDD2,0xB60B60B5,0x00003FF5,0x00000000
data4 0x7BA68DC8,0x88888888,0x00003FF8,0x00000000
data4 0xAAAAAC8D,0xAAAAAAAA,0x00003FFA,0x00000000
data4 0xAAAAACCA,0xAAAAAAAA,0x00003FFC,0x00000000
data4 0x00000000,0x80000000,0x00003FFE,0x00000000 
// /* Reversed */
ASM_SIZE_DIRECTIVE(Constants_exp_64_Q)

.align 64 
Constants_exp_64_T1:
ASM_TYPE_DIRECTIVE(Constants_exp_64_T1,@object)
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
ASM_SIZE_DIRECTIVE(Constants_exp_64_T1)

.align 64 
Constants_exp_64_T2:
ASM_TYPE_DIRECTIVE(Constants_exp_64_T2,@object)
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
ASM_SIZE_DIRECTIVE(Constants_exp_64_T2)

.align 64 
Constants_exp_64_W1:
ASM_TYPE_DIRECTIVE(Constants_exp_64_W1,@object)
data4 0x00000000,0x00000000,0x171EC4B4,0xBE384454
data4 0x4AA72766,0xBE694741,0xD42518F8,0xBE5D32B6
data4 0x3A319149,0x3E68D96D,0x62415F36,0xBE68F4DA
data4 0xC9C86A3B,0xBE6DDA2F,0xF49228FE,0x3E6B2E50
data4 0x1188B886,0xBE49C0C2,0x1A4C2F1F,0x3E64BFC2
data4 0x2CB98B54,0xBE6A2FBB,0x9A55D329,0x3E5DC5DE
data4 0x39A7AACE,0x3E696490,0x5C66DBA5,0x3E54728B
data4 0xBA1C7D7D,0xBE62B0DB,0x09F1AF5F,0x3E576E04
data4 0x1A0DD6A1,0x3E612500,0x795FBDEF,0xBE66A419
data4 0xE1BD41FC,0xBE5CDE8C,0xEA54964F,0xBE621376
data4 0x476E76EE,0x3E6370BE,0x3427EB92,0x3E390D1A 
data4 0x2BF82BF8,0x3E1336DE,0xD0F7BD9E,0xBE5FF1CB 
data4 0x0CEB09DD,0xBE60A355,0x0980F30D,0xBE5CA37E 
data4 0x4C082D25,0xBE5C541B,0x3B467D29,0xBE5BBECA 
data4 0xB9D946C5,0xBE400D8A,0x07ED374A,0xBE5E2A08 
data4 0x365C8B0A,0xBE66CB28,0xD3403BCA,0x3E3AAD5B 
data4 0xC7EA21E0,0x3E526055,0xE72880D6,0xBE442C75 
data4 0x85222A43,0x3E58B2BB,0x522C42BF,0xBE5AAB79 
data4 0x469DC2BC,0xBE605CB4,0xA48C40DC,0xBE589FA7 
data4 0x1AA42614,0xBE51C214,0xC37293F4,0xBE48D087 
data4 0xA2D673E0,0x3E367A1C,0x114F7A38,0xBE51BEBB 
data4 0x661A4B48,0xBE6348E5,0x1D3B9962,0xBDF52643  
data4 0x35A78A53,0x3E3A3B5E,0x1CECD788,0xBE46C46C 
data4 0x7857D689,0xBE60B7EC,0xD14F1AD7,0xBE594D3D 
data4 0x4C9A8F60,0xBE4F9C30,0x02DFF9D2,0xBE521873 
data4 0x55E6D68F,0xBE5E4C88,0x667F3DC4,0xBE62140F 
data4 0x3BF88747,0xBE36961B,0xC96EC6AA,0x3E602861 
data4 0xD57FD718,0xBE3B5151,0xFC4A627B,0x3E561CD0 
data4 0xCA913FEA,0xBE3A5217,0x9A5D193A,0x3E40A3CC 
data4 0x10A9C312,0xBE5AB713,0xC5F57719,0x3E4FDADB 
data4 0xDBDF59D5,0x3E361428,0x61B4180D,0x3E5DB5DB 
data4 0x7408D856,0xBE42AD5F,0x31B2B707,0x3E2A3148 
ASM_SIZE_DIRECTIVE(Constants_exp_64_W1)

.align 64 
Constants_exp_64_W2:
ASM_TYPE_DIRECTIVE(Constants_exp_64_W2,@object)
data4 0x00000000,0x00000000,0x37A3D7A2,0xBE641F25 
data4 0xAD028C40,0xBE68DD57,0xF212B1B6,0xBE5C77D8 
data4 0x1BA5B070,0x3E57878F,0x2ECAE6FE,0xBE55A36A 
data4 0x569DFA3B,0xBE620608,0xA6D300A3,0xBE53B50E 
data4 0x223F8F2C,0x3E5B5EF2,0xD6DE0DF4,0xBE56A0D9 
data4 0xEAE28F51,0xBE64EEF3,0x367EA80B,0xBE5E5AE2 
data4 0x5FCBC02D,0x3E47CB1A,0x9BDAFEB7,0xBE656BA0 
data4 0x805AFEE7,0x3E6E70C6,0xA3415EBA,0xBE6E0509 
data4 0x49BFF529,0xBE56856B,0x00508651,0x3E66DD33 
data4 0xC114BC13,0x3E51165F,0xC453290F,0x3E53333D 
data4 0x05539FDA,0x3E6A072B,0x7C0A7696,0xBE47CD87 
data4 0xEB05C6D9,0xBE668BF4,0x6AE86C93,0xBE67C3E3 
data4 0xD0B3E84B,0xBE533904,0x556B53CE,0x3E63E8D9 
data4 0x63A98DC8,0x3E212C89,0x032A7A22,0xBE33138F 
data4 0xBC584008,0x3E530FA9,0xCCB93C97,0xBE6ADF82 
data4 0x8370EA39,0x3E5F9113,0xFB6A05D8,0x3E5443A4 
data4 0x181FEE7A,0x3E63DACD,0xF0F67DEC,0xBE62B29D 
data4 0x3DDE6307,0x3E65C483,0xD40A24C1,0x3E5BF030  
data4 0x14E437BE,0x3E658B8F,0xED98B6C7,0xBE631C29 
data4 0x04CF7C71,0x3E6335D2,0xE954A79D,0x3E529EED 
data4 0xF64A2FB8,0x3E5D9257,0x854ED06C,0xBE6BED1B 
data4 0xD71405CB,0x3E5096F6,0xACB9FDF5,0xBE3D4893 
data4 0x01B68349,0xBDFEB158,0xC6A463B9,0x3E628D35 
data4 0xADE45917,0xBE559725,0x042FC476,0xBE68C29C 
data4 0x01E511FA,0xBE67593B,0x398801ED,0xBE4A4313 
data4 0xDA7C3300,0x3E699571,0x08062A9E,0x3E5349BE 
data4 0x755BB28E,0x3E5229C4,0x77A1F80D,0x3E67E426 
data4 0x6B69C352,0xBE52B33F,0x084DA57F,0xBE6B3550 
data4 0xD1D09A20,0xBE6DB03F,0x2161B2C1,0xBE60CBC4 
data4 0x78A2B771,0x3E56ED9C,0x9D0FA795,0xBE508E31 
data4 0xFD1A54E9,0xBE59482A,0xB07FD23E,0xBE2A17CE 
data4 0x17365712,0x3E68BF5C,0xB3785569,0x3E3956F9
ASM_SIZE_DIRECTIVE(Constants_exp_64_W2)

.section .text
.proc expm1#
.global expm1#
.align 64 

expm1: 
#ifdef _LIBC
.global __expm1#
__expm1:
#endif


{ .mii
      alloc r32 = ar.pfs,0,30,4,0
(p0)  add r33 = 1, r0  
(p0)  cmp.eq.unc  p7, p0 =  r0, r0 
}
;;


//
//    Set p7 true for expm1
//    Set Flag = r33 = 1 for expm1
//    These are really no longer necesary, but are a remnant 
//       when this file had multiple entry points.
//       They should be carefully removed



{ .mfi
(p0)  add r32 = 1,r0  
(p0)  fnorm.s1 f9 = f8 
      nop.i 999
}


{ .mfi
      nop.m 999
(p0)  fclass.m.unc p6, p8 =  f8, 0x1E7 
      nop.i 999
}

{ .mfi
      nop.m 999
(p0)  fclass.nm.unc p9, p0 =  f8, 0x1FF 
      nop.i 999
}

{ .mfi
	nop.m 999
(p0)  mov f36 = f1 
	nop.i 999 ;;
}

//     
//    Identify NatVals, NaNs, Infs, and Zeros. 
//    Identify EM unsupporteds. 
//    Save special input registers 
//
//    Create FR_X_cor      = 0.0 
//           GR_Flag       = 0 
//           GR_Expo_Range = 1
//           FR_Scale      = 1.0
//

{ .mfb
	nop.m 999
(p0)  mov f32 = f0 
(p6)  br.cond.spnt EXP_64_SPECIAL ;; 
}

{ .mib
	nop.m 999
	nop.i 999
(p9)  br.cond.spnt EXP_64_UNSUPPORTED ;; 
}

//     
//    Branch out for special input values 
//     

{ .mfi
(p0)  cmp.ne.unc p12, p13 = 0x01, r33
(p0)  fcmp.lt.unc.s0 p9,p0 =  f8, f0 
(p0)  cmp.eq.unc  p15, p0 =  r0, r0 
}

//     
//    Raise possible denormal operand exception 
//    Normalize x 
//     
//    This function computes exp( x  + x_cor) 
//    Input  FR 1: FR_X            
//    Input  FR 2: FR_X_cor  
//    Input  GR 1: GR_Flag  
//    Input  GR 2: GR_Expo_Range  
//    Output FR 3: FR_Y_hi  
//    Output FR 4: FR_Y_lo  
//    Output FR 5: FR_Scale  
//    Output PR 1: PR_Safe  

//
//    Prepare to load constants
//    Set Safe = True
//

{ .mmi
(p0)  addl           r34   = @ltoff(Constants_exp_64_Arg#), gp
(p0)  addl           r40   = @ltoff(Constants_exp_64_W1#),  gp
(p0)  addl           r41   = @ltoff(Constants_exp_64_W2#),  gp
}
;;

{ .mmi
      ld8 r34 = [r34]
      ld8 r40 = [r40]
(p0)  addl           r50   = @ltoff(Constants_exp_64_T1#),  gp
}
;;


{ .mmi
      ld8 r41  = [r41]
(p0)  ldfe f37 = [r34],16 
(p0)  addl           r51   = @ltoff(Constants_exp_64_T2#),  gp
}
;;

//
//    N = fcvt.fx(float_N)
//    Set p14 if -6 > expo_X 
//


//
//    Bias = 0x0FFFF
//    expo_X = expo_X and Mask  
//

//
//    Load L_lo
//    Set p10 if 14 < expo_X 
//

{ .mmi
      ld8  r50 = [r50]
(p0)  ldfe f40 = [r34],16 
      nop.i 999
}
;;

{ .mlx
	nop.m 999
(p0)  movl r58 = 0x0FFFF 
}
;;

//
//    Load W2_ptr
//    Branch to SMALL is expo_X < -6
//

//
//    float_N = X * L_Inv
//    expo_X = exponent of X
//    Mask = 0x1FFFF
//

{ .mmi
      ld8  r51 = [r51]
(p0)  ldfe f41 = [r34],16 
}
;;

{ .mlx
(p0)  addl           r34   = @ltoff(Constants_exp_64_Exponents#),  gp
(p0)  movl r39 = 0x1FFFF
}
;;

{ .mmi
      ld8  r34 = [r34]
(p0)  getf.exp r37 = f9 
      nop.i 999
}
;;

{ .mii
      nop.m 999
      nop.i 999 
(p0)  and  r37 = r37, r39 ;;  
}

{ .mmi
(p0)  sub r37 = r37, r58 ;;  
(p0)  cmp.gt.unc  p14, p0 =  -6, r37 
(p0)  cmp.lt.unc  p10, p0 =  14, r37 ;; 
}

{ .mfi
	nop.m 999
//
//    Load L_inv 
//    Set p12 true for Flag = 0 (exp)
//    Set p13 true for Flag = 1 (expm1)
//
(p0)  fmpy.s1 f38 = f9, f37 
	nop.i 999 ;;
}

{ .mfb
	nop.m 999
//
//    Load L_hi
//    expo_X = expo_X - Bias
//    get W1_ptr      
//
(p0)  fcvt.fx.s1 f39 = f38
(p14) br.cond.spnt EXP_SMALL ;; 
}

{ .mib
	nop.m 999
	nop.i 999
(p10) br.cond.spnt EXP_HUGE ;; 
}

{ .mmi
(p0)  shladd r34 = r32,4,r34 
(p0)  addl           r35   = @ltoff(Constants_exp_64_A#), gp
      nop.i 999
}
;;

{ .mmi
      ld8  r35 = [r35]
      nop.m 999
      nop.i 999
}
;;

//
//    Load T_1,T_2
//

{ .mmb
(p0)  ldfe f51 = [r35],16 
(p0)  ld8 r45 = [r34],8
	nop.b 999 ;;
}
//    
//    Set Safe = True  if k >= big_expo_neg  
//    Set Safe = False if k < big_expo_neg  
//    

{ .mmb
(p0)  ldfe f49 = [r35],16 
(p0)  ld8 r48 = [r34],0
	nop.b 999 ;;
}

{ .mfi
	nop.m 999
//
//    Branch to HUGE is expo_X > 14 
//
(p0)  fcvt.xf f38 = f39 
	nop.i 999 ;;
}

{ .mfi
(p0)  getf.sig r52 = f39 
	nop.f 999
	nop.i 999 ;;
}

{ .mii
	nop.m 999
(p0)  extr.u r43 = r52, 6, 6 ;;  
//
//    r = r - float_N * L_lo
//    K = extr(N_fix,12,52)
//
(p0)  shladd r40 = r43,3,r40 ;; 
}

{ .mfi
(p0)  shladd r50 = r43,2,r50 
(p0)  fnma.s1 f42 = f40, f38, f9 
//
//    float_N = float(N)
//    N_fix = signficand N 
//
(p0)  extr.u r42 = r52, 0, 6  
}

{ .mmi
(p0)  ldfd  f43 = [r40],0 ;; 
(p0)  shladd r41 = r42,3,r41 
(p0)  shladd r51 = r42,2,r51 
}
//
//    W_1_p1 = 1 + W_1
//

{ .mmi
(p0)  ldfs  f44 = [r50],0 ;; 
(p0)  ldfd  f45 = [r41],0 
//
//    M_2 = extr(N_fix,0,6)
//    M_1 = extr(N_fix,6,6)
//    r = X - float_N * L_hi
//
(p0)  extr r44 = r52, 12, 52  
}

{ .mmi
(p0)  ldfs  f46 = [r51],0 ;; 
(p0)  sub r46 = r58, r44  
(p0)  cmp.gt.unc  p8, p15 =  r44, r45 
}
//    
//    W = W_1 + W_1_p1*W_2 
//    Load  A_2 
//    Bias_m_K = Bias - K
//

{ .mii
(p0)  ldfe f40 = [r35],16 
//
//    load A_1
//    poly = A_2 + r*A_3 
//    rsq = r * r  
//    neg_2_mK = exponent of Bias_m_k
//
(p0)  add r47 = r58, r44 ;;  
//    
//    Set Safe = True  if k <= big_expo_pos  
//    Set Safe = False  if k >  big_expo_pos  
//    Load A_3
//    
(p15) cmp.lt p8,p15 = r44,r48 ;;
}

{ .mmf
(p0)  setf.exp f61 = r46 
//    
//    Bias_p + K = Bias + K
//    T = T_1 * T_2
//    
(p0)  setf.exp f36 = r47 
(p0)  fnma.s1 f42 = f41, f38, f42 ;; 
}

{ .mfi
	nop.m 999
//
//    Load W_1,W_2
//    Load big_exp_pos, load big_exp_neg
//
(p0)  fadd.s1 f47 = f43, f1 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p0)  fma.s1 f52 = f42, f51, f49 
	nop.i 999
}

{ .mfi
	nop.m 999
(p0)  fmpy.s1 f48 = f42, f42 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p0)  fmpy.s1 f53 = f44, f46 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p0)  fma.s1 f54 = f45, f47, f43 
	nop.i 999
}

{ .mfi
	nop.m 999
(p0)  fneg f61 =  f61 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p0)  fma.s1 f52 = f42, f52, f40 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p0)  fadd.s1 f55 = f54, f1 
	nop.i 999
}

{ .mfi
	nop.m 999
//
//    W + Wp1 * poly     
// 
(p0)  mov f34 = f53 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
//
//    A_1 + r * poly 
//    Scale = setf_exp(Bias_p_k) 
//
(p0)  fma.s1 f52 = f48, f52, f42 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
//
//    poly = r + rsq(A_1 + r*poly) 
//    Wp1 = 1 + W
//    neg_2_mK = -neg_2_mK
//
(p0)  fma.s1 f35 = f55, f52, f54
	nop.i 999 ;;
}

{ .mfb
	nop.m 999
(p0)  fmpy.s1 f35 = f35, f53 
//   
//    Y_hi = T
//    Y_lo = T * (W + Wp1*poly)
//
(p12) br.cond.sptk EXP_MAIN ;; 
}
//
//    Branch if exp(x)  
//    Continue for exp(x-1)
//

{ .mii
(p0)  cmp.lt.unc  p12, p13 =  10, r44 
	nop.i 999 ;;
//
//    Set p12 if 10 < K, Else p13 
//
(p13) cmp.gt.unc  p13, p14 =  -10, r44 ;; 
}
//
//    K > 10:  Y_lo = Y_lo + neg_2_mK
//    K <=10:  Set p13 if -10 > K, Else set p14 
//

{ .mfi
(p13) cmp.eq  p15, p0 =  r0, r0 
(p14) fadd.s1 f34 = f61, f34 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p12) fadd.s1 f35 = f35, f61 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p13) fadd.s1 f35 = f35, f34 
	nop.i 999
}

{ .mfb
	nop.m 999
//
//    K <= 10 and K < -10, Set Safe = True
//    K <= 10 and K < 10,   Y_lo = Y_hi + Y_lo 
//    K <= 10 and K > =-10, Y_hi = Y_hi + neg_2_mk 
// 
(p13) mov f34 = f61 
(p0)  br.cond.sptk EXP_MAIN ;; 
}
EXP_SMALL: 

{ .mmi
(p12)  addl           r35   = @ltoff(Constants_exp_64_P#), gp
(p0)   addl           r34   = @ltoff(Constants_exp_64_Exponents#), gp
      nop.i 999
}
;;

{ .mmi
(p12) ld8 r35 = [r35]
      ld8 r34 = [r34]
      nop.i 999
}
;;


{ .mmi
(p13)  addl           r35   = @ltoff(Constants_exp_64_Q#), gp
       nop.m 999
       nop.i 999
}
;;


// 
//    Return
//    K <= 10 and K < 10,   Y_hi = neg_2_mk 
// 
//    /*******************************************************/
//    /*********** Branch EXP_SMALL  *************************/
//    /*******************************************************/

{ .mfi
(p13) ld8 r35 = [r35]
(p0)  mov f42 = f9 
(p0)  add r34 = 0x48,r34  
}
;;

//
//    Flag = 0
//    r4 = rsq * rsq
//

{ .mfi
(p0)  ld8 r49 =[r34],0
	nop.f 999
	nop.i 999 ;;
}

{ .mii
	nop.m 999
	nop.i 999 ;;
//
//    Flag = 1
//
(p0)  cmp.lt.unc  p14, p0 =  r37, r49 ;; 
}

{ .mfi
	nop.m 999
//
//    r = X
//
(p0)  fmpy.s1 f48 = f42, f42 
	nop.i 999 ;;
}

{ .mfb
	nop.m 999
//
//    rsq = r * r
//
(p0)  fmpy.s1 f50 = f48, f48 
//
//    Is input very small?
//
(p14) br.cond.spnt EXP_VERY_SMALL ;; 
}
//
//    Flag_not1: Y_hi = 1.0
//    Flag is 1: r6 = rsq * r4
//

{ .mfi
(p12) ldfe f52 = [r35],16 
(p12) mov f34 = f1 
(p0)  add r53 = 0x1,r0 ;;  
}

{ .mfi
(p13) ldfe f51 = [r35],16 
//
//    Flag_not_1: Y_lo = poly_hi + r4 * poly_lo
//
(p13) mov f34 = f9 
	nop.i 999 ;;
}

{ .mmf
(p12) ldfe f53 = [r35],16 
//
//    For Flag_not_1, Y_hi = X
//    Scale = 1
//    Create 0x000...01
//
(p0)  setf.sig f37 = r53 
(p0)  mov f36 = f1 ;; 
}

{ .mmi
(p13) ldfe f52 = [r35],16 ;; 
(p12) ldfe f54 = [r35],16 
	nop.i 999 ;;
}

{ .mfi
(p13) ldfe f53 = [r35],16 
(p13) fmpy.s1 f58 = f48, f50 
	nop.i 999 ;;
}
//
//    Flag_not1: poly_lo = P_5 + r*P_6
//    Flag_1: poly_lo = Q_6 + r*Q_7
//

{ .mmi
(p13) ldfe f54 = [r35],16 ;; 
(p12) ldfe f55 = [r35],16 
	nop.i 999 ;;
}

{ .mmi
(p12) ldfe f56 = [r35],16 ;; 
(p13) ldfe f55 = [r35],16 
	nop.i 999 ;;
}

{ .mmi
(p12) ldfe f57 = [r35],0 ;; 
(p13) ldfe f56 = [r35],16 
	nop.i 999 ;;
}

{ .mfi
(p13) ldfe f57 = [r35],0 
	nop.f 999
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
//
//    For  Flag_not_1, load p5,p6,p1,p2
//    Else load p5,p6,p1,p2
//
(p12) fma.s1 f60 = f52, f42, f53 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p13) fma.s1 f60 = f51, f42, f52 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p12) fma.s1 f60 = f60, f42, f54 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p12) fma.s1 f59 = f56, f42, f57 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p13) fma.s1 f60 = f42, f60, f53 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p12) fma.s1 f59 = f59, f48, f42 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
//
//    Flag_1: poly_lo = Q_5 + r*(Q_6 + r*Q_7) 
//    Flag_not1: poly_lo = P_4 + r*(P_5 + r*P_6)
//    Flag_not1: poly_hi = (P_1 + r*P_2)
//
(p13) fmpy.s1 f60 = f60, f58 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p12) fma.s1 f60 = f60, f42, f55 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
//
//    Flag_1: poly_lo = r6 *(Q_5 + ....)
//    Flag_not1: poly_hi =  r + rsq *(P_1 + r*P_2)
//
(p12) fma.s1 f35 = f60, f50, f59 
	nop.i 999
}

{ .mfi
	nop.m 999
(p13) fma.s1 f59 = f54, f42, f55 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
//
//    Flag_not1: Y_lo = rsq* poly_hi + poly_lo 
//    Flag_1: poly_lo = rsq* poly_hi + poly_lo 
//
(p13) fma.s1 f59 = f59, f42, f56 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
//
//    Flag_not_1: (P_1 + r*P_2) 
//
(p13) fma.s1 f59 = f59, f42, f57 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
//
//    Flag_not_1: poly_hi = r + rsq * (P_1 + r*P_2) 
//
(p13) fma.s1 f35 = f59, f48, f60 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
//
//    Create 0.000...01
//
(p0)  for f37 = f35, f37 
	nop.i 999 ;;
}

{ .mfb
	nop.m 999
//
//    Set lsb of Y_lo to 1
//
(p0)  fmerge.se f35 = f35,f37 
(p0)  br.cond.sptk EXP_MAIN ;; 
}
EXP_VERY_SMALL: 

{ .mmi
      nop.m 999
(p13) addl r34 = @ltoff(Constants_exp_64_Exponents#),gp 
      nop.i 999;;
}

{ .mfi
(p13) ld8  r34 = [r34];
(p12) mov f35 = f9 
      nop.i 999 ;;
}

{ .mfb
	nop.m 999
(p12) mov f34 = f1 
(p12) br.cond.sptk EXP_MAIN ;; 
}

{ .mlx
(p13) add  r34 = 8,r34 
(p13) movl r39 = 0x0FFFE ;; 
}
//
//    Load big_exp_neg 
//    Create 1/2's exponent
//

{ .mii
(p13) setf.exp f56 = r39 
(p13) shladd r34 = r32,4,r34 ;;  
	nop.i 999
}
//
//    Negative exponents are stored after positive
//

{ .mfi
(p13) ld8 r45 = [r34],0
//
//    Y_hi = x
//    Scale = 1
//
(p13) fmpy.s1 f35 = f9, f9 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
//
//    Reset Safe if necessary 
//    Create 1/2
//
(p13) mov f34 = f9 
	nop.i 999 ;;
}

{ .mfi
(p13) cmp.lt.unc  p0, p15 =  r37, r45 
(p13) mov f36 = f1 
	nop.i 999 ;;
}

{ .mfb
	nop.m 999
//
//    Y_lo = x * x
//
(p13) fmpy.s1 f35 = f35, f56 
//
//    Y_lo = x*x/2 
//
(p13) br.cond.sptk EXP_MAIN ;; 
}
EXP_HUGE: 

{ .mfi
	nop.m 999
(p0)  fcmp.gt.unc.s1 p14, p0 =  f9, f0 
	nop.i 999
}

{ .mlx
	nop.m 999
(p0)  movl r39 = 0x15DC0 ;; 
}

{ .mfi
(p14) setf.exp f34 = r39 
(p14) mov f35 = f1 
(p14) cmp.eq  p0, p15 =  r0, r0 ;; 
}

{ .mfb
	nop.m 999
(p14) mov f36 = f34 
//
//    If x > 0, Set Safe = False
//    If x > 0, Y_hi = 2**(24,000)
//    If x > 0, Y_lo = 1.0
//    If x > 0, Scale = 2**(24,000)
//
(p14) br.cond.sptk EXP_MAIN ;; 
}

{ .mlx
	nop.m 999
(p12) movl r39 = 0xA240 
}

{ .mlx
	nop.m 999
(p12) movl r38 = 0xA1DC ;; 
}

{ .mmb
(p13) cmp.eq  p15, p14 =  r0, r0 
(p12) setf.exp f34 = r39 
	nop.b 999 ;;
}

{ .mlx
(p12) setf.exp f35 = r38 
(p13) movl r39 = 0xFF9C 
}

{ .mfi
	nop.m 999
(p13) fsub.s1 f34 = f0, f1
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p12) mov f36 = f34 
(p12) cmp.eq  p0, p15 =  r0, r0 ;; 
}

{ .mfi
(p13) setf.exp f35 = r39 
(p13) mov f36 = f1 
	nop.i 999 ;;
}
EXP_MAIN: 

{ .mfi
(p0)  cmp.ne.unc p12, p0 = 0x01, r33
(p0)  fmpy.s1 f101 = f36, f35 
	nop.i 999 ;;
}

{ .mfb
	nop.m 999
(p0)  fma.d.s0 f99 = f34, f36, f101 
(p15)  br.cond.sptk EXP_64_RETURN;;
}

{ .mfi
	nop.m 999
(p0)  fsetc.s3 0x7F,0x01
	nop.i 999
}

{ .mlx
	nop.m 999
(p0)  movl r50 = 0x000000000103FF ;;
}
//    
//    S0 user supplied status
//    S2 user supplied status + WRE + TD  (Overflows) 
//    S3 user supplied status + RZ + TD   (Underflows) 
//    
//    
//    If (Safe) is true, then
//        Compute result using user supplied status field.
//        No overflow or underflow here, but perhaps inexact.
//        Return
//    Else
//       Determine if overflow or underflow  was raised.
//       Fetch +/- overflow threshold for IEEE single, double,
//       double extended   
//    

{ .mfi
(p0)  setf.exp f60 = r50
(p0)  fma.d.s3 f102 = f34, f36, f101 
	nop.i 999
}

{ .mfi
	nop.m 999
(p0)  fsetc.s3 0x7F,0x40 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
//
//    For Safe, no need to check for over/under. 
//    For expm1, handle errors like exp. 
//
(p0)  fsetc.s2 0x7F,0x42
	nop.i 999;;
}

{ .mfi
	nop.m 999
(p0)  fma.d.s2 f100 = f34, f36, f101 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p0)  fsetc.s2 0x7F,0x40 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p7)  fclass.m.unc   p12, p0 =  f102, 0x00F
	nop.i 999
}

{ .mfi
	nop.m 999
(p0)  fclass.m.unc   p11, p0 =  f102, 0x00F
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p7)  fcmp.ge.unc.s1 p10, p0 =  f100, f60
	nop.i 999
}

{ .mfi
	nop.m 999
//    
//    Create largest double exponent + 1.
//    Create smallest double exponent - 1.
//    
(p0)  fcmp.ge.unc.s1 p8, p0 =  f100, f60
	nop.i 999 ;;
}
//    
//    fcmp:   resultS2 >= + overflow threshold  -> set (a) if true
//    fcmp:   resultS2 <= - overflow threshold  -> set (b) if true
//    fclass: resultS3 is denorm/unorm/0        -> set (d) if true
//    

{ .mib
(p10) mov   r65 = 41
	nop.i 999
(p10) br.cond.sptk __libm_error_region ;;
}

{ .mib
(p8)  mov   r65 = 14
	nop.i 999
(p8)  br.cond.sptk __libm_error_region ;;
}
//    
//    Report that exp overflowed
//    

{ .mib
(p12) mov   r65 = 42
	nop.i 999
(p12) br.cond.sptk __libm_error_region ;;
}

{ .mib
(p11) mov   r65 = 15
	nop.i 999
(p11) br.cond.sptk __libm_error_region ;;
}

{ .mib
	nop.m 999
	nop.i 999
//    
//    Report that exp underflowed
//    
(p0)  br.cond.sptk EXP_64_RETURN;;
}
EXP_64_SPECIAL: 

{ .mfi
	nop.m 999
(p0)  fclass.m.unc p6,  p0 =  f8, 0x0c3 
	nop.i 999
}

{ .mfi
	nop.m 999
(p0)  fclass.m.unc p13, p8 =  f8, 0x007 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p7)  fclass.m.unc p14, p0 =  f8, 0x007 
	nop.i 999
}

{ .mfi
	nop.m 999
(p0)  fclass.m.unc p12, p9 =  f8, 0x021 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p0)  fclass.m.unc p11, p0 =  f8, 0x022 
	nop.i 999
}

{ .mfi
	nop.m 999
(p7)  fclass.m.unc p10, p0 =  f8, 0x022 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
//    
//    Identify +/- 0, Inf, or -Inf 
//    Generate the right kind of NaN.
//    
(p13) fadd.d.s0 f99 = f0, f1 
	nop.i 999 ;;
}

{ .mfi
	nop.m 999
(p14) mov f99 = f8 
	nop.i 999 ;;
}

{ .mfb
	nop.m 999
(p6)  fadd.d.s0 f99 = f8, f1 
//    
//    exp(+/-0) = 1 
//    expm1(+/-0) = +/-0 
//    No exceptions raised
//    
(p6)  br.cond.sptk EXP_64_RETURN;;
}

{ .mib
	nop.m 999
	nop.i 999
(p14)  br.cond.sptk EXP_64_RETURN;;
}

{ .mfi
	nop.m 999
(p11) mov f99 = f0 
	nop.i 999 ;;
}

{ .mfb
	nop.m 999
(p10) fsub.d.s1 f99 = f0, f1 
//    
//    exp(-Inf) = 0 
//    expm1(-Inf) = -1 
//    No exceptions raised.
//    
(p10)  br.cond.sptk EXP_64_RETURN;;
}

{ .mfb
	nop.m 999
(p12) fmpy.d.s1 f99 = f8, f1 
//    
//    exp(+Inf) = Inf 
//    No exceptions raised.
//    
(p0)  br.cond.sptk EXP_64_RETURN;;
}


EXP_64_UNSUPPORTED: 

{ .mfb
       nop.m 999
(p0)  fmpy.d.s0 f99 = f8, f0 
      nop.b 0;;
}

EXP_64_RETURN:
{ .mfb
      nop.m 999
(p0)  mov   f8     = f99
(p0)  br.ret.sptk   b0
}
.endp expm1
ASM_SIZE_DIRECTIVE(expm1)

.proc __libm_error_region
__libm_error_region:
.prologue
// (1)
{ .mfi
        add   GR_Parameter_Y=-32,sp             // Parameter 2 value
        nop.f 0
.save   ar.pfs,GR_SAVE_PFS
        mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs
}
{ .mfi
.fframe 64
        add sp=-64,sp                          // Create new stack
        nop.f 0
        mov GR_SAVE_GP=gp                      // Save gp
};;

// (2)
{ .mmi
        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
// (3)
{ .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
        nop.m 0
        nop.m 0
        add   GR_Parameter_RESULT = 48,sp
};;

// (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
};;

.endp __libm_error_region
ASM_SIZE_DIRECTIVE(__libm_error_region)


.type   __libm_error_support#,@function
.global __libm_error_support#