summaryrefslogtreecommitdiff
path: root/libstdc++-v3/include/tr1/cmath
blob: 21bdee8865406e6d96cd27099758d216b0478c64 (plain)
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
// TR1 cmath -*- C++ -*-

// Copyright (C) 2006, 2007, 2008, 2009, 2010, 2011
// Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.

// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.

// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.

/** @file tr1/cmath
 *  This is a TR1 C++ Library header. 
 */

#ifndef _GLIBCXX_TR1_CMATH
#define _GLIBCXX_TR1_CMATH 1

#pragma GCC system_header

#include <cmath>

#ifdef _GLIBCXX_USE_C99_MATH_TR1

#undef acosh
#undef acoshf
#undef acoshl
#undef asinh
#undef asinhf
#undef asinhl
#undef atanh
#undef atanhf
#undef atanhl
#undef cbrt
#undef cbrtf
#undef cbrtl
#undef copysign
#undef copysignf
#undef copysignl
#undef erf
#undef erff
#undef erfl
#undef erfc
#undef erfcf
#undef erfcl
#undef exp2
#undef exp2f
#undef exp2l
#undef expm1
#undef expm1f
#undef expm1l
#undef fdim
#undef fdimf
#undef fdiml
#undef fma
#undef fmaf
#undef fmal
#undef fmax
#undef fmaxf
#undef fmaxl
#undef fmin
#undef fminf
#undef fminl
#undef hypot
#undef hypotf
#undef hypotl
#undef ilogb
#undef ilogbf
#undef ilogbl
#undef lgamma
#undef lgammaf
#undef lgammal
#undef llrint
#undef llrintf
#undef llrintl
#undef llround
#undef llroundf
#undef llroundl
#undef log1p
#undef log1pf
#undef log1pl
#undef log2
#undef log2f
#undef log2l
#undef logb
#undef logbf
#undef logbl
#undef lrint
#undef lrintf
#undef lrintl
#undef lround
#undef lroundf
#undef lroundl
#undef nan
#undef nanf
#undef nanl
#undef nearbyint
#undef nearbyintf
#undef nearbyintl
#undef nextafter
#undef nextafterf
#undef nextafterl
#undef nexttoward
#undef nexttowardf
#undef nexttowardl
#undef remainder
#undef remainderf
#undef remainderl
#undef remquo
#undef remquof
#undef remquol
#undef rint
#undef rintf
#undef rintl
#undef round
#undef roundf
#undef roundl
#undef scalbln
#undef scalblnf
#undef scalblnl
#undef scalbn
#undef scalbnf
#undef scalbnl
#undef tgamma
#undef tgammaf
#undef tgammal
#undef trunc
#undef truncf
#undef truncl

#endif

namespace std _GLIBCXX_VISIBILITY(default)
{
namespace tr1
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

#if _GLIBCXX_USE_C99_MATH_TR1

  // types
  using ::double_t;
  using ::float_t;

  // functions
  using ::acosh;
  using ::acoshf;
  using ::acoshl;

  using ::asinh;
  using ::asinhf;
  using ::asinhl;

  using ::atanh;
  using ::atanhf;
  using ::atanhl;

  using ::cbrt;
  using ::cbrtf;
  using ::cbrtl;

  using ::copysign;
  using ::copysignf;
  using ::copysignl;

  using ::erf;
  using ::erff;
  using ::erfl;

  using ::erfc;
  using ::erfcf;
  using ::erfcl;

  using ::exp2;
  using ::exp2f;
  using ::exp2l;

  using ::expm1;
  using ::expm1f;
  using ::expm1l;

  using ::fdim;
  using ::fdimf;
  using ::fdiml;

  using ::fma;
  using ::fmaf;
  using ::fmal;

  using ::fmax;
  using ::fmaxf;
  using ::fmaxl;

  using ::fmin;
  using ::fminf;
  using ::fminl;

  using ::hypot;
  using ::hypotf;
  using ::hypotl;

  using ::ilogb;
  using ::ilogbf;
  using ::ilogbl;

  using ::lgamma;
  using ::lgammaf;
  using ::lgammal;

  using ::llrint;
  using ::llrintf;
  using ::llrintl;

  using ::llround;
  using ::llroundf;
  using ::llroundl;

  using ::log1p;
  using ::log1pf;
  using ::log1pl;

  using ::log2;
  using ::log2f;
  using ::log2l;

  using ::logb;
  using ::logbf;
  using ::logbl;

  using ::lrint;
  using ::lrintf;
  using ::lrintl;

  using ::lround;
  using ::lroundf;
  using ::lroundl;

  using ::nan;
  using ::nanf;
  using ::nanl;

  using ::nearbyint;
  using ::nearbyintf;
  using ::nearbyintl;

  using ::nextafter;
  using ::nextafterf;
  using ::nextafterl;

  using ::nexttoward;
  using ::nexttowardf;
  using ::nexttowardl;

  using ::remainder;
  using ::remainderf;
  using ::remainderl;

  using ::remquo;
  using ::remquof;
  using ::remquol;

  using ::rint;
  using ::rintf;
  using ::rintl;

  using ::round;
  using ::roundf;
  using ::roundl;

  using ::scalbln;
  using ::scalblnf;
  using ::scalblnl;

  using ::scalbn;
  using ::scalbnf;
  using ::scalbnl;

  using ::tgamma;
  using ::tgammaf;
  using ::tgammal;

  using ::trunc;
  using ::truncf;
  using ::truncl;

#endif

#if _GLIBCXX_USE_C99_MATH
#if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC

  /// Function template definitions [8.16.3].
  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    fpclassify(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
				  FP_SUBNORMAL, FP_ZERO, __type(__f));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isfinite(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isfinite(__type(__f));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isinf(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isinf(__type(__f));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isnan(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isnan(__type(__f));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isnormal(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isnormal(__type(__f));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    signbit(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_signbit(__type(__f));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isgreater(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isgreater(__type(__f1), __type(__f2));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isgreaterequal(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isgreaterequal(__type(__f1), __type(__f2));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isless(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isless(__type(__f1), __type(__f2));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    islessequal(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_islessequal(__type(__f1), __type(__f2));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    islessgreater(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_islessgreater(__type(__f1), __type(__f2));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isunordered(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isunordered(__type(__f1), __type(__f2));
    }

#endif
#endif

#if _GLIBCXX_USE_C99_MATH_TR1

  /// Additional overloads [8.16.4].
  using std::acos;

  inline float
  acosh(float __x)
  { return __builtin_acoshf(__x); }

  inline long double
  acosh(long double __x)
  { return __builtin_acoshl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    acosh(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return acosh(__type(__x));
    }

  using std::asin;

  inline float
  asinh(float __x)
  { return __builtin_asinhf(__x); }

  inline long double
  asinh(long double __x)
  { return __builtin_asinhl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    asinh(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return asinh(__type(__x));
    }

  using std::atan;
  using std::atan2;

  inline float
  atanh(float __x)
  { return __builtin_atanhf(__x); }

  inline long double
  atanh(long double __x)
  { return __builtin_atanhl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    atanh(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return atanh(__type(__x));
    }

  inline float
  cbrt(float __x)
  { return __builtin_cbrtf(__x); }

  inline long double
  cbrt(long double __x)
  { return __builtin_cbrtl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    cbrt(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return cbrt(__type(__x));
    }

  using std::ceil;

  inline float
  copysign(float __x, float __y)
  { return __builtin_copysignf(__x, __y); }

  inline long double
  copysign(long double __x, long double __y)
  { return __builtin_copysignl(__x, __y); }

  template<typename _Tp, typename _Up>
    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    copysign(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return copysign(__type(__x), __type(__y));
    }

  using std::cos;
  using std::cosh;  

  inline float
  erf(float __x)
  { return __builtin_erff(__x); }

  inline long double
  erf(long double __x)
  { return __builtin_erfl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    erf(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return erf(__type(__x));
    }

  inline float
  erfc(float __x)
  { return __builtin_erfcf(__x); }

  inline long double
  erfc(long double __x)
  { return __builtin_erfcl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    erfc(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return erfc(__type(__x));
    }

  using std::exp;

  inline float
  exp2(float __x)
  { return __builtin_exp2f(__x); }

  inline long double
  exp2(long double __x)
  { return __builtin_exp2l(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    exp2(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return exp2(__type(__x));
    }

  inline float
  expm1(float __x)
  { return __builtin_expm1f(__x); }

  inline long double
  expm1(long double __x)
  { return __builtin_expm1l(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    expm1(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return expm1(__type(__x));
    }

  // Note: we deal with fabs in a special way, because an using std::fabs
  // would bring in also the overloads for complex types, which in C++0x
  // mode have a different return type.
  using ::fabs;

  inline float
  fabs(float __x)
  { return __builtin_fabsf(__x); }

  inline long double
  fabs(long double __x)
  { return __builtin_fabsl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    fabs(_Tp __x)
    { return __builtin_fabs(__x); }

  inline float
  fdim(float __x, float __y)
  { return __builtin_fdimf(__x, __y); }

  inline long double
  fdim(long double __x, long double __y)
  { return __builtin_fdiml(__x, __y); }

  template<typename _Tp, typename _Up>
    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    fdim(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return fdim(__type(__x), __type(__y));
    }

  using std::floor;

  inline float
  fma(float __x, float __y, float __z)
  { return __builtin_fmaf(__x, __y, __z); }

  inline long double
  fma(long double __x, long double __y, long double __z)
  { return __builtin_fmal(__x, __y, __z); }

  template<typename _Tp, typename _Up, typename _Vp>
    inline typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
    fma(_Tp __x, _Up __y, _Vp __z)
    {
      typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type;
      return fma(__type(__x), __type(__y), __type(__z));
    }

  inline float
  fmax(float __x, float __y)
  { return __builtin_fmaxf(__x, __y); }

  inline long double
  fmax(long double __x, long double __y)
  { return __builtin_fmaxl(__x, __y); }

  template<typename _Tp, typename _Up>
    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    fmax(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return fmax(__type(__x), __type(__y));
    }

  inline float
  fmin(float __x, float __y)
  { return __builtin_fminf(__x, __y); }

  inline long double
  fmin(long double __x, long double __y)
  { return __builtin_fminl(__x, __y); }

  template<typename _Tp, typename _Up>
    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    fmin(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return fmin(__type(__x), __type(__y));
    }

  using std::fmod;
  using std::frexp;

  inline float
  hypot(float __x, float __y)
  { return __builtin_hypotf(__x, __y); }

  inline long double
  hypot(long double __x, long double __y)
  { return __builtin_hypotl(__x, __y); }

  template<typename _Tp, typename _Up>
    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    hypot(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return hypot(__type(__x), __type(__y));
    }

  inline int
  ilogb(float __x)
  { return __builtin_ilogbf(__x); }

  inline int
  ilogb(long double __x)
  { return __builtin_ilogbl(__x); }

  template<typename _Tp>
    inline int
    ilogb(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return ilogb(__type(__x));
    }

  using std::ldexp;

  inline float
  lgamma(float __x)
  { return __builtin_lgammaf(__x); }

  inline long double
  lgamma(long double __x)
  { return __builtin_lgammal(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    lgamma(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return lgamma(__type(__x));
    }

  inline long long
  llrint(float __x)
  { return __builtin_llrintf(__x); }

  inline long long
  llrint(long double __x)
  { return __builtin_llrintl(__x); }

  template<typename _Tp>
    inline long long
    llrint(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return llrint(__type(__x));
    }

  inline long long
  llround(float __x)
  { return __builtin_llroundf(__x); }

  inline long long
  llround(long double __x)
  { return __builtin_llroundl(__x); }

  template<typename _Tp>
    inline long long
    llround(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return llround(__type(__x));
    }

  using std::log;
  using std::log10;

  inline float
  log1p(float __x)
  { return __builtin_log1pf(__x); }

  inline long double
  log1p(long double __x)
  { return __builtin_log1pl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    log1p(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return log1p(__type(__x));
    }

  // DR 568.
  inline float
  log2(float __x)
  { return __builtin_log2f(__x); }

  inline long double
  log2(long double __x)
  { return __builtin_log2l(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    log2(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return log2(__type(__x));
    }

  inline float
  logb(float __x)
  { return __builtin_logbf(__x); }

  inline long double
  logb(long double __x)
  { return __builtin_logbl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    logb(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return logb(__type(__x));
    }

  inline long
  lrint(float __x)
  { return __builtin_lrintf(__x); }

  inline long
  lrint(long double __x)
  { return __builtin_lrintl(__x); }

  template<typename _Tp>
    inline long
    lrint(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return lrint(__type(__x));
    }

  inline long
  lround(float __x)
  { return __builtin_lroundf(__x); }

  inline long
  lround(long double __x)
  { return __builtin_lroundl(__x); }

  template<typename _Tp>
    inline long
    lround(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return lround(__type(__x));
    }

  inline float
  nearbyint(float __x)
  { return __builtin_nearbyintf(__x); }

  inline long double
  nearbyint(long double __x)
  { return __builtin_nearbyintl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    nearbyint(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return nearbyint(__type(__x));
    }

  inline float
  nextafter(float __x, float __y)
  { return __builtin_nextafterf(__x, __y); }

  inline long double
  nextafter(long double __x, long double __y)
  { return __builtin_nextafterl(__x, __y); }

  template<typename _Tp, typename _Up>
    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    nextafter(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return nextafter(__type(__x), __type(__y));
    }

  inline float
  nexttoward(float __x, long double __y)
  { return __builtin_nexttowardf(__x, __y); }

  inline long double
  nexttoward(long double __x, long double __y)
  { return __builtin_nexttowardl(__x, __y); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    nexttoward(_Tp __x, long double __y)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return nexttoward(__type(__x), __y);
    }

  // DR 550. What should the return type of pow(float,int) be?
  // NB: C++0x and TR1 != C++03.
  //   using std::pow;

  inline float
  remainder(float __x, float __y)
  { return __builtin_remainderf(__x, __y); }

  inline long double
  remainder(long double __x, long double __y)
  { return __builtin_remainderl(__x, __y); }

  template<typename _Tp, typename _Up>
    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    remainder(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return remainder(__type(__x), __type(__y));
    }

  inline float
  remquo(float __x, float __y, int* __pquo)
  { return __builtin_remquof(__x, __y, __pquo); }

  inline long double
  remquo(long double __x, long double __y, int* __pquo)
  { return __builtin_remquol(__x, __y, __pquo); }

  template<typename _Tp, typename _Up>
    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    remquo(_Tp __x, _Up __y, int* __pquo)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return remquo(__type(__x), __type(__y), __pquo);
    }

  inline float
  rint(float __x)
  { return __builtin_rintf(__x); }

  inline long double
  rint(long double __x)
  { return __builtin_rintl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    rint(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return rint(__type(__x));
    }

  inline float
  round(float __x)
  { return __builtin_roundf(__x); }

  inline long double
  round(long double __x)
  { return __builtin_roundl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    round(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return round(__type(__x));
    }

  inline float
  scalbln(float __x, long __ex)
  { return __builtin_scalblnf(__x, __ex); }

  inline long double
  scalbln(long double __x, long __ex)
  { return __builtin_scalblnl(__x, __ex); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    scalbln(_Tp __x, long __ex)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return scalbln(__type(__x), __ex);
    }
 
  inline float
  scalbn(float __x, int __ex)
  { return __builtin_scalbnf(__x, __ex); }

  inline long double
  scalbn(long double __x, int __ex)
  { return __builtin_scalbnl(__x, __ex); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    scalbn(_Tp __x, int __ex)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return scalbn(__type(__x), __ex);
    }

  using std::sin;
  using std::sinh;
  using std::sqrt;
  using std::tan;
  using std::tanh;

  inline float
  tgamma(float __x)
  { return __builtin_tgammaf(__x); }

  inline long double
  tgamma(long double __x)
  { return __builtin_tgammal(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    tgamma(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return tgamma(__type(__x));
    }
 
  inline float
  trunc(float __x)
  { return __builtin_truncf(__x); }

  inline long double
  trunc(long double __x)
  { return __builtin_truncl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type 
    trunc(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return trunc(__type(__x));
    }

#endif
_GLIBCXX_END_NAMESPACE_VERSION
}
}

namespace std _GLIBCXX_VISIBILITY(default)
{
namespace tr1
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

  // DR 550. What should the return type of pow(float,int) be?
  // NB: C++0x and TR1 != C++03.
  inline double
  pow(double __x, double __y)
  { return std::pow(__x, __y); }

  inline float
  pow(float __x, float __y)
  { return std::pow(__x, __y); }

  inline long double
  pow(long double __x, long double __y)
  { return std::pow(__x, __y); }

  template<typename _Tp, typename _Up>
    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    pow(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return std::pow(__type(__x), __type(__y));
    }

_GLIBCXX_END_NAMESPACE_VERSION
}
}

#include <bits/stl_algobase.h>
#include <limits>
#include <tr1/type_traits>

#include <tr1/gamma.tcc>
#include <tr1/bessel_function.tcc>
#include <tr1/beta_function.tcc>
#include <tr1/ell_integral.tcc>
#include <tr1/exp_integral.tcc>
#include <tr1/hypergeometric.tcc>
#include <tr1/legendre_function.tcc>
#include <tr1/modified_bessel_func.tcc>
#include <tr1/poly_hermite.tcc>
#include <tr1/poly_laguerre.tcc>
#include <tr1/riemann_zeta.tcc>

namespace std _GLIBCXX_VISIBILITY(default)
{
namespace tr1
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

  /**
   * @defgroup tr1_math_spec_func Mathematical Special Functions
   * @ingroup numerics
   *
   * A collection of advanced mathematical special functions.
   * @{
   */

  inline float
  assoc_laguerref(unsigned int __n, unsigned int __m, float __x)
  { return __detail::__assoc_laguerre<float>(__n, __m, __x); }

  inline long double
  assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x)
  {
    return __detail::__assoc_laguerre<long double>(__n, __m, __x);
  }

  ///  5.2.1.1  Associated Laguerre polynomials.
  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __detail::__assoc_laguerre<__type>(__n, __m, __x);
    }

  inline float
  assoc_legendref(unsigned int __l, unsigned int __m, float __x)
  { return __detail::__assoc_legendre_p<float>(__l, __m, __x); }

  inline long double
  assoc_legendrel(unsigned int __l, unsigned int __m, long double __x)
  { return __detail::__assoc_legendre_p<long double>(__l, __m, __x); }

  ///  5.2.1.2  Associated Legendre functions.
  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __detail::__assoc_legendre_p<__type>(__l, __m, __x);
    }

  inline float
  betaf(float __x, float __y)
  { return __detail::__beta<float>(__x, __y); }

  inline long double
  betal(long double __x, long double __y)
  { return __detail::__beta<long double>(__x, __y); }

  ///  5.2.1.3  Beta functions.
  template<typename _Tpx, typename _Tpy>
    inline typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type
    beta(_Tpx __x, _Tpy __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type __type;
      return __detail::__beta<__type>(__x, __y);
    }

  inline float
  comp_ellint_1f(float __k)
  { return __detail::__comp_ellint_1<float>(__k); }

  inline long double
  comp_ellint_1l(long double __k)
  { return __detail::__comp_ellint_1<long double>(__k); }

  ///  5.2.1.4  Complete elliptic integrals of the first kind.
  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    comp_ellint_1(_Tp __k)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __detail::__comp_ellint_1<__type>(__k);
    }

  inline float
  comp_ellint_2f(float __k)
  { return __detail::__comp_ellint_2<float>(__k); }

  inline long double
  comp_ellint_2l(long double __k)
  { return __detail::__comp_ellint_2<long double>(__k); }

  ///  5.2.1.5  Complete elliptic integrals of the second kind.
  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    comp_ellint_2(_Tp __k)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __detail::__comp_ellint_2<__type>(__k);
    }

  inline float
  comp_ellint_3f(float __k, float __nu)
  { return __detail::__comp_ellint_3<float>(__k, __nu); }

  inline long double
  comp_ellint_3l(long double __k, long double __nu)
  { return __detail::__comp_ellint_3<long double>(__k, __nu); }

  ///  5.2.1.6  Complete elliptic integrals of the third kind.
  template<typename _Tp, typename _Tpn>
    inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type
    comp_ellint_3(_Tp __k, _Tpn __nu)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type;
      return __detail::__comp_ellint_3<__type>(__k, __nu);
    }

  inline float
  conf_hypergf(float __a, float __c, float __x)
  { return __detail::__conf_hyperg<float>(__a, __c, __x); }

  inline long double
  conf_hypergl(long double __a, long double __c, long double __x)
  { return __detail::__conf_hyperg<long double>(__a, __c, __x); }

  ///  5.2.1.7  Confluent hypergeometric functions.
  template<typename _Tpa, typename _Tpc, typename _Tp>
    inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type
    conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
    {
      typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type;
      return __detail::__conf_hyperg<__type>(__a, __c, __x);
    }

  inline float
  cyl_bessel_if(float __nu, float __x)
  { return __detail::__cyl_bessel_i<float>(__nu, __x); }

  inline long double
  cyl_bessel_il(long double __nu, long double __x)
  { return __detail::__cyl_bessel_i<long double>(__nu, __x); }

  ///  5.2.1.8  Regular modified cylindrical Bessel functions.
  template<typename _Tpnu, typename _Tp>
    inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
    cyl_bessel_i(_Tpnu __nu, _Tp __x)
    {
      typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
      return __detail::__cyl_bessel_i<__type>(__nu, __x);
    }

  inline float
  cyl_bessel_jf(float __nu, float __x)
  { return __detail::__cyl_bessel_j<float>(__nu, __x); }

  inline long double
  cyl_bessel_jl(long double __nu, long double __x)
  { return __detail::__cyl_bessel_j<long double>(__nu, __x); }

  ///  5.2.1.9  Cylindrical Bessel functions (of the first kind).
  template<typename _Tpnu, typename _Tp>
    inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
    cyl_bessel_j(_Tpnu __nu, _Tp __x)
    {
      typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
      return __detail::__cyl_bessel_j<__type>(__nu, __x);
    }

  inline float
  cyl_bessel_kf(float __nu, float __x)
  { return __detail::__cyl_bessel_k<float>(__nu, __x); }

  inline long double
  cyl_bessel_kl(long double __nu, long double __x)
  { return __detail::__cyl_bessel_k<long double>(__nu, __x); }

  ///  5.2.1.10  Irregular modified cylindrical Bessel functions.
  template<typename _Tpnu, typename _Tp>
    inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
    cyl_bessel_k(_Tpnu __nu, _Tp __x)
    {
      typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
      return __detail::__cyl_bessel_k<__type>(__nu, __x);
    }

  inline float
  cyl_neumannf(float __nu, float __x)
  { return __detail::__cyl_neumann_n<float>(__nu, __x); }

  inline long double
  cyl_neumannl(long double __nu, long double __x)
  { return __detail::__cyl_neumann_n<long double>(__nu, __x); }

  ///  5.2.1.11  Cylindrical Neumann functions.
  template<typename _Tpnu, typename _Tp>
    inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
    cyl_neumann(_Tpnu __nu, _Tp __x)
    {
      typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
      return __detail::__cyl_neumann_n<__type>(__nu, __x);
    }

  inline float
  ellint_1f(float __k, float __phi)
  { return __detail::__ellint_1<float>(__k, __phi); }

  inline long double
  ellint_1l(long double __k, long double __phi)
  { return __detail::__ellint_1<long double>(__k, __phi); }

  ///  5.2.1.12  Incomplete elliptic integrals of the first kind.
  template<typename _Tp, typename _Tpp>
    inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
    ellint_1(_Tp __k, _Tpp __phi)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
      return __detail::__ellint_1<__type>(__k, __phi);
    }

  inline float
  ellint_2f(float __k, float __phi)
  { return __detail::__ellint_2<float>(__k, __phi); }

  inline long double
  ellint_2l(long double __k, long double __phi)
  { return __detail::__ellint_2<long double>(__k, __phi); }

  ///  5.2.1.13  Incomplete elliptic integrals of the second kind.
  template<typename _Tp, typename _Tpp>
    inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
    ellint_2(_Tp __k, _Tpp __phi)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
      return __detail::__ellint_2<__type>(__k, __phi);
    }

  inline float
  ellint_3f(float __k, float __nu, float __phi)
  { return __detail::__ellint_3<float>(__k, __nu, __phi); }

  inline long double
  ellint_3l(long double __k, long double __nu, long double __phi)
  { return __detail::__ellint_3<long double>(__k, __nu, __phi); }

  ///  5.2.1.14  Incomplete elliptic integrals of the third kind.
  template<typename _Tp, typename _Tpn, typename _Tpp>
    inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type
    ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
    {
      typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type;
      return __detail::__ellint_3<__type>(__k, __nu, __phi);
    }

  inline float
  expintf(float __x)
  { return __detail::__expint<float>(__x); }

  inline long double
  expintl(long double __x)
  { return __detail::__expint<long double>(__x); }

  ///  5.2.1.15  Exponential integrals.
  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    expint(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __detail::__expint<__type>(__x);
    }

  inline float
  hermitef(unsigned int __n, float __x)
  { return __detail::__poly_hermite<float>(__n, __x); }

  inline long double
  hermitel(unsigned int __n, long double __x)
  { return __detail::__poly_hermite<long double>(__n, __x); }

  ///  5.2.1.16  Hermite polynomials.
  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    hermite(unsigned int __n, _Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __detail::__poly_hermite<__type>(__n, __x);
    }

  inline float
  hypergf(float __a, float __b, float __c, float __x)
  { return __detail::__hyperg<float>(__a, __b, __c, __x); }

  inline long double
  hypergl(long double __a, long double __b, long double __c, long double __x)
  { return __detail::__hyperg<long double>(__a, __b, __c, __x); }

  ///  5.2.1.17  Hypergeometric functions.
  template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp>
    inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type
    hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
    {
      typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type;
      return __detail::__hyperg<__type>(__a, __b, __c, __x);
    }

  inline float
  laguerref(unsigned int __n, float __x)
  { return __detail::__laguerre<float>(__n, __x); }

  inline long double
  laguerrel(unsigned int __n, long double __x)
  { return __detail::__laguerre<long double>(__n, __x); }

  ///  5.2.1.18  Laguerre polynomials.
  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    laguerre(unsigned int __n, _Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __detail::__laguerre<__type>(__n, __x);
    }

  inline float
  legendref(unsigned int __n, float __x)
  { return __detail::__poly_legendre_p<float>(__n, __x); }

  inline long double
  legendrel(unsigned int __n, long double __x)
  { return __detail::__poly_legendre_p<long double>(__n, __x); }

  ///  5.2.1.19  Legendre polynomials.
  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    legendre(unsigned int __n, _Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __detail::__poly_legendre_p<__type>(__n, __x);
    }

  inline float
  riemann_zetaf(float __x)
  { return __detail::__riemann_zeta<float>(__x); }

  inline long double
  riemann_zetal(long double __x)
  { return __detail::__riemann_zeta<long double>(__x); }

  ///  5.2.1.20  Riemann zeta function.
  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    riemann_zeta(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __detail::__riemann_zeta<__type>(__x);
    }

  inline float
  sph_besself(unsigned int __n, float __x)
  { return __detail::__sph_bessel<float>(__n, __x); }

  inline long double
  sph_bessell(unsigned int __n, long double __x)
  { return __detail::__sph_bessel<long double>(__n, __x); }

  ///  5.2.1.21  Spherical Bessel functions.
  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    sph_bessel(unsigned int __n, _Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __detail::__sph_bessel<__type>(__n, __x);
    }

  inline float
  sph_legendref(unsigned int __l, unsigned int __m, float __theta)
  { return __detail::__sph_legendre<float>(__l, __m, __theta); }

  inline long double
  sph_legendrel(unsigned int __l, unsigned int __m, long double __theta)
  { return __detail::__sph_legendre<long double>(__l, __m, __theta); }

  ///  5.2.1.22  Spherical associated Legendre functions.
  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __detail::__sph_legendre<__type>(__l, __m, __theta);
    }

  inline float
  sph_neumannf(unsigned int __n, float __x)
  { return __detail::__sph_neumann<float>(__n, __x); }

  inline long double
  sph_neumannl(unsigned int __n, long double __x)
  { return __detail::__sph_neumann<long double>(__n, __x); }

  ///  5.2.1.23  Spherical Neumann functions.
  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    sph_neumann(unsigned int __n, _Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __detail::__sph_neumann<__type>(__n, __x);
    }

  /* @} */ // tr1_math_spec_func
_GLIBCXX_END_NAMESPACE_VERSION
}
}

#endif // _GLIBCXX_TR1_CMATH