1// TR1 cmath -*- C++ -*-
2
3// Copyright (C) 2006-2015 Free Software Foundation, Inc.
4//
5// This file is part of the GNU ISO C++ Library.  This library is free
6// software; you can redistribute it and/or modify it under the
7// terms of the GNU General Public License as published by the
8// Free Software Foundation; either version 3, or (at your option)
9// any later version.
10
11// This library is distributed in the hope that it will be useful,
12// but WITHOUT ANY WARRANTY; without even the implied warranty of
13// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
14// GNU General Public License for more details.
15
16// Under Section 7 of GPL version 3, you are granted additional
17// permissions described in the GCC Runtime Library Exception, version
18// 3.1, as published by the Free Software Foundation.
19
20// You should have received a copy of the GNU General Public License and
21// a copy of the GCC Runtime Library Exception along with this program;
22// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
23// <http://www.gnu.org/licenses/>.
24
25/** @file tr1/cmath
26 *  This is a TR1 C++ Library header.
27 */
28
29#ifndef _GLIBCXX_TR1_CMATH
30#define _GLIBCXX_TR1_CMATH 1
31
32#pragma GCC system_header
33
34#include <cmath>
35
36#ifdef _GLIBCXX_USE_C99_MATH_TR1
37
38#undef acosh
39#undef acoshf
40#undef acoshl
41#undef asinh
42#undef asinhf
43#undef asinhl
44#undef atanh
45#undef atanhf
46#undef atanhl
47#undef cbrt
48#undef cbrtf
49#undef cbrtl
50#undef copysign
51#undef copysignf
52#undef copysignl
53#undef erf
54#undef erff
55#undef erfl
56#undef erfc
57#undef erfcf
58#undef erfcl
59#undef exp2
60#undef exp2f
61#undef exp2l
62#undef expm1
63#undef expm1f
64#undef expm1l
65#undef fdim
66#undef fdimf
67#undef fdiml
68#undef fma
69#undef fmaf
70#undef fmal
71#undef fmax
72#undef fmaxf
73#undef fmaxl
74#undef fmin
75#undef fminf
76#undef fminl
77#undef hypot
78#undef hypotf
79#undef hypotl
80#undef ilogb
81#undef ilogbf
82#undef ilogbl
83#undef lgamma
84#undef lgammaf
85#undef lgammal
86#undef llrint
87#undef llrintf
88#undef llrintl
89#undef llround
90#undef llroundf
91#undef llroundl
92#undef log1p
93#undef log1pf
94#undef log1pl
95#undef log2
96#undef log2f
97#undef log2l
98#undef logb
99#undef logbf
100#undef logbl
101#undef lrint
102#undef lrintf
103#undef lrintl
104#undef lround
105#undef lroundf
106#undef lroundl
107#undef nan
108#undef nanf
109#undef nanl
110#undef nearbyint
111#undef nearbyintf
112#undef nearbyintl
113#undef nextafter
114#undef nextafterf
115#undef nextafterl
116#undef nexttoward
117#undef nexttowardf
118#undef nexttowardl
119#undef remainder
120#undef remainderf
121#undef remainderl
122#undef remquo
123#undef remquof
124#undef remquol
125#undef rint
126#undef rintf
127#undef rintl
128#undef round
129#undef roundf
130#undef roundl
131#undef scalbln
132#undef scalblnf
133#undef scalblnl
134#undef scalbn
135#undef scalbnf
136#undef scalbnl
137#undef tgamma
138#undef tgammaf
139#undef tgammal
140#undef trunc
141#undef truncf
142#undef truncl
143
144#endif
145
146namespace std _GLIBCXX_VISIBILITY(default)
147{
148namespace tr1
149{
150_GLIBCXX_BEGIN_NAMESPACE_VERSION
151
152#if _GLIBCXX_USE_C99_MATH_TR1
153
154  // types
155  using ::double_t;
156  using ::float_t;
157
158  // functions
159  using ::acosh;
160  using ::acoshf;
161  using ::acoshl;
162
163  using ::asinh;
164  using ::asinhf;
165  using ::asinhl;
166
167  using ::atanh;
168  using ::atanhf;
169  using ::atanhl;
170
171  using ::cbrt;
172  using ::cbrtf;
173  using ::cbrtl;
174
175  using ::copysign;
176  using ::copysignf;
177  using ::copysignl;
178
179  using ::erf;
180  using ::erff;
181  using ::erfl;
182
183  using ::erfc;
184  using ::erfcf;
185  using ::erfcl;
186
187  using ::exp2;
188  using ::exp2f;
189  using ::exp2l;
190
191  using ::expm1;
192  using ::expm1f;
193  using ::expm1l;
194
195  using ::fdim;
196  using ::fdimf;
197  using ::fdiml;
198
199  using ::fma;
200  using ::fmaf;
201  using ::fmal;
202
203  using ::fmax;
204  using ::fmaxf;
205  using ::fmaxl;
206
207  using ::fmin;
208  using ::fminf;
209  using ::fminl;
210
211  using ::hypot;
212  using ::hypotf;
213  using ::hypotl;
214
215  using ::ilogb;
216  using ::ilogbf;
217  using ::ilogbl;
218
219  using ::lgamma;
220  using ::lgammaf;
221  using ::lgammal;
222
223  using ::llrint;
224  using ::llrintf;
225  using ::llrintl;
226
227  using ::llround;
228  using ::llroundf;
229  using ::llroundl;
230
231  using ::log1p;
232  using ::log1pf;
233  using ::log1pl;
234
235  using ::log2;
236  using ::log2f;
237  using ::log2l;
238
239  using ::logb;
240  using ::logbf;
241  using ::logbl;
242
243  using ::lrint;
244  using ::lrintf;
245  using ::lrintl;
246
247  using ::lround;
248  using ::lroundf;
249  using ::lroundl;
250
251  using ::nan;
252  using ::nanf;
253  using ::nanl;
254
255  using ::nearbyint;
256  using ::nearbyintf;
257  using ::nearbyintl;
258
259  using ::nextafter;
260  using ::nextafterf;
261  using ::nextafterl;
262
263  using ::nexttoward;
264  using ::nexttowardf;
265  using ::nexttowardl;
266
267  using ::remainder;
268  using ::remainderf;
269  using ::remainderl;
270
271  using ::remquo;
272  using ::remquof;
273  using ::remquol;
274
275  using ::rint;
276  using ::rintf;
277  using ::rintl;
278
279  using ::round;
280  using ::roundf;
281  using ::roundl;
282
283  using ::scalbln;
284  using ::scalblnf;
285  using ::scalblnl;
286
287  using ::scalbn;
288  using ::scalbnf;
289  using ::scalbnl;
290
291  using ::tgamma;
292  using ::tgammaf;
293  using ::tgammal;
294
295  using ::trunc;
296  using ::truncf;
297  using ::truncl;
298
299#endif
300
301#if _GLIBCXX_USE_C99_MATH
302#if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC
303
304  /// Function template definitions [8.16.3].
305  template<typename _Tp>
306    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
307					   int>::__type
308    fpclassify(_Tp __f)
309    {
310      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
311      return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
312				  FP_SUBNORMAL, FP_ZERO, __type(__f));
313    }
314
315  template<typename _Tp>
316    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
317					   int>::__type
318    isfinite(_Tp __f)
319    {
320      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
321      return __builtin_isfinite(__type(__f));
322    }
323
324  template<typename _Tp>
325    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
326					   int>::__type
327    isinf(_Tp __f)
328    {
329      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
330      return __builtin_isinf(__type(__f));
331    }
332
333  template<typename _Tp>
334    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
335					   int>::__type
336    isnan(_Tp __f)
337    {
338      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
339      return __builtin_isnan(__type(__f));
340    }
341
342  template<typename _Tp>
343    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
344					   int>::__type
345    isnormal(_Tp __f)
346    {
347      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
348      return __builtin_isnormal(__type(__f));
349    }
350
351  template<typename _Tp>
352    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
353					   int>::__type
354    signbit(_Tp __f)
355    {
356      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
357      return __builtin_signbit(__type(__f));
358    }
359
360  template<typename _Tp>
361    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
362					   int>::__type
363    isgreater(_Tp __f1, _Tp __f2)
364    {
365      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
366      return __builtin_isgreater(__type(__f1), __type(__f2));
367    }
368
369  template<typename _Tp>
370    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
371					   int>::__type
372    isgreaterequal(_Tp __f1, _Tp __f2)
373    {
374      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
375      return __builtin_isgreaterequal(__type(__f1), __type(__f2));
376    }
377
378  template<typename _Tp>
379    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
380					   int>::__type
381    isless(_Tp __f1, _Tp __f2)
382    {
383      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
384      return __builtin_isless(__type(__f1), __type(__f2));
385    }
386
387  template<typename _Tp>
388    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
389					   int>::__type
390    islessequal(_Tp __f1, _Tp __f2)
391    {
392      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
393      return __builtin_islessequal(__type(__f1), __type(__f2));
394    }
395
396  template<typename _Tp>
397    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
398					   int>::__type
399    islessgreater(_Tp __f1, _Tp __f2)
400    {
401      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
402      return __builtin_islessgreater(__type(__f1), __type(__f2));
403    }
404
405  template<typename _Tp>
406    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
407					   int>::__type
408    isunordered(_Tp __f1, _Tp __f2)
409    {
410      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
411      return __builtin_isunordered(__type(__f1), __type(__f2));
412    }
413
414#endif
415#endif
416
417#if _GLIBCXX_USE_C99_MATH_TR1
418
419  /// Additional overloads [8.16.4].
420  using std::acos;
421
422#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO
423  inline float
424  acosh(float __x)
425  { return __builtin_acoshf(__x); }
426
427  inline long double
428  acosh(long double __x)
429  { return __builtin_acoshl(__x); }
430#endif
431
432  template<typename _Tp>
433    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
434					   double>::__type
435    acosh(_Tp __x)
436    { return __builtin_acosh(__x); }
437
438  using std::asin;
439
440#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO
441  inline float
442  asinh(float __x)
443  { return __builtin_asinhf(__x); }
444
445  inline long double
446  asinh(long double __x)
447  { return __builtin_asinhl(__x); }
448#endif
449
450  template<typename _Tp>
451    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
452					   double>::__type
453    asinh(_Tp __x)
454    { return __builtin_asinh(__x); }
455
456  using std::atan;
457  using std::atan2;
458
459#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO
460  inline float
461  atanh(float __x)
462  { return __builtin_atanhf(__x); }
463
464  inline long double
465  atanh(long double __x)
466  { return __builtin_atanhl(__x); }
467#endif
468
469  template<typename _Tp>
470    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
471					   double>::__type
472    atanh(_Tp __x)
473    { return __builtin_atanh(__x); }
474
475#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO
476  inline float
477  cbrt(float __x)
478  { return __builtin_cbrtf(__x); }
479
480  inline long double
481  cbrt(long double __x)
482  { return __builtin_cbrtl(__x); }
483#endif
484
485  template<typename _Tp>
486    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
487					   double>::__type
488    cbrt(_Tp __x)
489    { return __builtin_cbrt(__x); }
490
491  using std::ceil;
492
493#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
494  inline float
495  copysign(float __x, float __y)
496  { return __builtin_copysignf(__x, __y); }
497
498  inline long double
499  copysign(long double __x, long double __y)
500  { return __builtin_copysignl(__x, __y); }
501#endif
502
503  template<typename _Tp, typename _Up>
504    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
505    copysign(_Tp __x, _Up __y)
506    {
507      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
508      return copysign(__type(__x), __type(__y));
509    }
510
511  using std::cos;
512  using std::cosh;
513
514#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
515  inline float
516  erf(float __x)
517  { return __builtin_erff(__x); }
518
519  inline long double
520  erf(long double __x)
521  { return __builtin_erfl(__x); }
522#endif
523
524  template<typename _Tp>
525    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
526					   double>::__type
527    erf(_Tp __x)
528    { return __builtin_erf(__x); }
529
530#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
531  inline float
532  erfc(float __x)
533  { return __builtin_erfcf(__x); }
534
535  inline long double
536  erfc(long double __x)
537  { return __builtin_erfcl(__x); }
538#endif
539
540  template<typename _Tp>
541    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
542					   double>::__type
543    erfc(_Tp __x)
544    { return __builtin_erfc(__x); }
545
546  using std::exp;
547
548#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
549  inline float
550  exp2(float __x)
551  { return __builtin_exp2f(__x); }
552
553  inline long double
554  exp2(long double __x)
555  { return __builtin_exp2l(__x); }
556#endif
557
558  template<typename _Tp>
559    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
560					   double>::__type
561    exp2(_Tp __x)
562    { return __builtin_exp2(__x); }
563
564#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
565  inline float
566  expm1(float __x)
567  { return __builtin_expm1f(__x); }
568
569  inline long double
570  expm1(long double __x)
571  { return __builtin_expm1l(__x); }
572#endif
573
574  template<typename _Tp>
575    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
576					   double>::__type
577    expm1(_Tp __x)
578    { return __builtin_expm1(__x); }
579
580  // Note: we deal with fabs in a special way, because an using std::fabs
581  // would bring in also the overloads for complex types, which in C++0x
582  // mode have a different return type.
583  // With __CORRECT_ISO_CPP_MATH_H_PROTO, math.h imports std::fabs in the
584  // global namespace after the declarations of the float / double / long
585  // double overloads but before the std::complex overloads.
586  using ::fabs;
587
588#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
589#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO
590  inline float
591  fabs(float __x)
592  { return __builtin_fabsf(__x); }
593
594  inline long double
595  fabs(long double __x)
596  { return __builtin_fabsl(__x); }
597#endif
598
599  template<typename _Tp>
600    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
601					   double>::__type
602    fabs(_Tp __x)
603    { return __builtin_fabs(__x); }
604#endif
605
606#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
607  inline float
608  fdim(float __x, float __y)
609  { return __builtin_fdimf(__x, __y); }
610
611  inline long double
612  fdim(long double __x, long double __y)
613  { return __builtin_fdiml(__x, __y); }
614#endif
615
616  template<typename _Tp, typename _Up>
617    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
618    fdim(_Tp __x, _Up __y)
619    {
620      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
621      return fdim(__type(__x), __type(__y));
622    }
623
624  using std::floor;
625
626#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
627  inline float
628  fma(float __x, float __y, float __z)
629  { return __builtin_fmaf(__x, __y, __z); }
630
631  inline long double
632  fma(long double __x, long double __y, long double __z)
633  { return __builtin_fmal(__x, __y, __z); }
634#endif
635
636  template<typename _Tp, typename _Up, typename _Vp>
637    inline typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
638    fma(_Tp __x, _Up __y, _Vp __z)
639    {
640      typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type;
641      return fma(__type(__x), __type(__y), __type(__z));
642    }
643
644#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
645  inline float
646  fmax(float __x, float __y)
647  { return __builtin_fmaxf(__x, __y); }
648
649  inline long double
650  fmax(long double __x, long double __y)
651  { return __builtin_fmaxl(__x, __y); }
652#endif
653
654  template<typename _Tp, typename _Up>
655    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
656    fmax(_Tp __x, _Up __y)
657    {
658      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
659      return fmax(__type(__x), __type(__y));
660    }
661
662#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
663  inline float
664  fmin(float __x, float __y)
665  { return __builtin_fminf(__x, __y); }
666
667  inline long double
668  fmin(long double __x, long double __y)
669  { return __builtin_fminl(__x, __y); }
670#endif
671
672  template<typename _Tp, typename _Up>
673    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
674    fmin(_Tp __x, _Up __y)
675    {
676      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
677      return fmin(__type(__x), __type(__y));
678    }
679
680  using std::fmod;
681  using std::frexp;
682
683#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
684  inline float
685  hypot(float __x, float __y)
686  { return __builtin_hypotf(__x, __y); }
687
688  inline long double
689  hypot(long double __x, long double __y)
690  { return __builtin_hypotl(__x, __y); }
691#endif
692
693  template<typename _Tp, typename _Up>
694    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
695    hypot(_Tp __y, _Up __x)
696    {
697      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
698      return hypot(__type(__y), __type(__x));
699    }
700
701#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO
702  inline int
703  ilogb(float __x)
704  { return __builtin_ilogbf(__x); }
705
706  inline int
707  ilogb(long double __x)
708  { return __builtin_ilogbl(__x); }
709#endif
710
711  template<typename _Tp>
712    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
713					   int>::__type
714    ilogb(_Tp __x)
715    { return __builtin_ilogb(__x); }
716
717  using std::ldexp;
718
719#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
720  inline float
721  lgamma(float __x)
722  { return __builtin_lgammaf(__x); }
723
724  inline long double
725  lgamma(long double __x)
726  { return __builtin_lgammal(__x); }
727#endif
728
729  template<typename _Tp>
730    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
731					   double>::__type
732    lgamma(_Tp __x)
733    { return __builtin_lgamma(__x); }
734
735#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
736  inline long long
737  llrint(float __x)
738  { return __builtin_llrintf(__x); }
739
740  inline long long
741  llrint(long double __x)
742  { return __builtin_llrintl(__x); }
743#endif
744
745  template<typename _Tp>
746    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
747					   long long>::__type
748    llrint(_Tp __x)
749    { return __builtin_llrint(__x); }
750
751#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
752  inline long long
753  llround(float __x)
754  { return __builtin_llroundf(__x); }
755
756  inline long long
757  llround(long double __x)
758  { return __builtin_llroundl(__x); }
759#endif
760
761  template<typename _Tp>
762    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
763					   long long>::__type
764    llround(_Tp __x)
765    { return __builtin_llround(__x); }
766
767  using std::log;
768  using std::log10;
769
770#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
771  inline float
772  log1p(float __x)
773  { return __builtin_log1pf(__x); }
774
775  inline long double
776  log1p(long double __x)
777  { return __builtin_log1pl(__x); }
778#endif
779
780  template<typename _Tp>
781    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
782					   double>::__type
783    log1p(_Tp __x)
784    { return __builtin_log1p(__x); }
785
786  // DR 568.
787#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
788  inline float
789  log2(float __x)
790  { return __builtin_log2f(__x); }
791
792  inline long double
793  log2(long double __x)
794  { return __builtin_log2l(__x); }
795#endif
796
797  template<typename _Tp>
798    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
799					   double>::__type
800    log2(_Tp __x)
801    { return __builtin_log2(__x); }
802
803#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
804  inline float
805  logb(float __x)
806  { return __builtin_logbf(__x); }
807
808  inline long double
809  logb(long double __x)
810  { return __builtin_logbl(__x); }
811#endif
812
813  template<typename _Tp>
814    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
815					   double>::__type
816    logb(_Tp __x)
817    {
818      return __builtin_logb(__x);
819    }
820
821#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
822  inline long
823  lrint(float __x)
824  { return __builtin_lrintf(__x); }
825
826  inline long
827  lrint(long double __x)
828  { return __builtin_lrintl(__x); }
829#endif
830
831  template<typename _Tp>
832    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
833					   long>::__type
834    lrint(_Tp __x)
835    { return __builtin_lrint(__x); }
836
837#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
838  inline long
839  lround(float __x)
840  { return __builtin_lroundf(__x); }
841
842  inline long
843  lround(long double __x)
844  { return __builtin_lroundl(__x); }
845#endif
846
847  template<typename _Tp>
848    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
849					   long>::__type
850    lround(_Tp __x)
851    { return __builtin_lround(__x); }
852
853#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP_FP
854  inline float
855  nearbyint(float __x)
856  { return __builtin_nearbyintf(__x); }
857
858  inline long double
859  nearbyint(long double __x)
860  { return __builtin_nearbyintl(__x); }
861#endif
862
863  template<typename _Tp>
864    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
865					   double>::__type
866    nearbyint(_Tp __x)
867    { return __builtin_nearbyint(__x); }
868
869#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
870  inline float
871  nextafter(float __x, float __y)
872  { return __builtin_nextafterf(__x, __y); }
873
874  inline long double
875  nextafter(long double __x, long double __y)
876  { return __builtin_nextafterl(__x, __y); }
877#endif
878
879  template<typename _Tp, typename _Up>
880    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
881    nextafter(_Tp __x, _Up __y)
882    {
883      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
884      return nextafter(__type(__x), __type(__y));
885    }
886
887#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP_FP
888  inline float
889  nexttoward(float __x, long double __y)
890  { return __builtin_nexttowardf(__x, __y); }
891
892  inline long double
893  nexttoward(long double __x, long double __y)
894  { return __builtin_nexttowardl(__x, __y); }
895#endif
896
897  template<typename _Tp>
898    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
899					   double>::__type
900    nexttoward(_Tp __x, long double __y)
901    { return __builtin_nexttoward(__x, __y); }
902
903#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
904  inline float
905  remainder(float __x, float __y)
906  { return __builtin_remainderf(__x, __y); }
907
908  inline long double
909  remainder(long double __x, long double __y)
910  { return __builtin_remainderl(__x, __y); }
911#endif
912
913  template<typename _Tp, typename _Up>
914    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
915    remainder(_Tp __x, _Up __y)
916    {
917      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
918      return remainder(__type(__x), __type(__y));
919    }
920
921#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
922  inline float
923  remquo(float __x, float __y, int* __pquo)
924  { return __builtin_remquof(__x, __y, __pquo); }
925
926  inline long double
927  remquo(long double __x, long double __y, int* __pquo)
928  { return __builtin_remquol(__x, __y, __pquo); }
929#endif
930
931  template<typename _Tp, typename _Up>
932    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
933    remquo(_Tp __x, _Up __y, int* __pquo)
934    {
935      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
936      return remquo(__type(__x), __type(__y), __pquo);
937    }
938
939#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
940  inline float
941  rint(float __x)
942  { return __builtin_rintf(__x); }
943
944  inline long double
945  rint(long double __x)
946  { return __builtin_rintl(__x); }
947#endif
948
949  template<typename _Tp>
950    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
951					   double>::__type
952    rint(_Tp __x)
953    { return __builtin_rint(__x); }
954
955#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
956  inline float
957  round(float __x)
958  { return __builtin_roundf(__x); }
959
960  inline long double
961  round(long double __x)
962  { return __builtin_roundl(__x); }
963#endif
964
965  template<typename _Tp>
966    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
967					   double>::__type
968    round(_Tp __x)
969    { return __builtin_round(__x); }
970
971#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
972  inline float
973  scalbln(float __x, long __ex)
974  { return __builtin_scalblnf(__x, __ex); }
975
976  inline long double
977  scalbln(long double __x, long __ex)
978  { return __builtin_scalblnl(__x, __ex); }
979#endif
980
981  template<typename _Tp>
982    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
983					   double>::__type
984    scalbln(_Tp __x, long __ex)
985    { return __builtin_scalbln(__x, __ex); }
986
987#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
988  inline float
989  scalbn(float __x, int __ex)
990  { return __builtin_scalbnf(__x, __ex); }
991
992  inline long double
993  scalbn(long double __x, int __ex)
994  { return __builtin_scalbnl(__x, __ex); }
995#endif
996
997  template<typename _Tp>
998    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
999					   double>::__type
1000    scalbn(_Tp __x, int __ex)
1001    { return __builtin_scalbn(__x, __ex); }
1002
1003  using std::sin;
1004  using std::sinh;
1005  using std::sqrt;
1006  using std::tan;
1007  using std::tanh;
1008
1009#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1010  inline float
1011  tgamma(float __x)
1012  { return __builtin_tgammaf(__x); }
1013
1014  inline long double
1015  tgamma(long double __x)
1016  { return __builtin_tgammal(__x); }
1017#endif
1018
1019  template<typename _Tp>
1020    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1021					   double>::__type
1022    tgamma(_Tp __x)
1023    { return __builtin_tgamma(__x); }
1024
1025#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1026  inline float
1027  trunc(float __x)
1028  { return __builtin_truncf(__x); }
1029
1030  inline long double
1031  trunc(long double __x)
1032  { return __builtin_truncl(__x); }
1033#endif
1034
1035  template<typename _Tp>
1036    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1037					   double>::__type
1038    trunc(_Tp __x)
1039    { return __builtin_trunc(__x); }
1040
1041#endif
1042_GLIBCXX_END_NAMESPACE_VERSION
1043}
1044}
1045
1046namespace std _GLIBCXX_VISIBILITY(default)
1047{
1048namespace tr1
1049{
1050_GLIBCXX_BEGIN_NAMESPACE_VERSION
1051
1052  // DR 550. What should the return type of pow(float,int) be?
1053  // NB: C++0x and TR1 != C++03.
1054
1055  // The std::tr1::pow(double, double) overload cannot be provided
1056  // here, because it would clash with ::pow(double,double) declared
1057  // in <math.h>, if <tr1/math.h> is included at the same time (raised
1058  // by the fix of PR c++/54537). It is not possible either to use the
1059  // using-declaration 'using ::pow;' here, because if the user code
1060  // has a 'using std::pow;', it would bring the pow(*,int) averloads
1061  // in the tr1 namespace, which is undesirable. Consequently, the
1062  // solution is to forward std::tr1::pow(double,double) to
1063  // std::pow(double,double) via the templatized version below. See
1064  // the discussion about this issue here:
1065  // http://gcc.gnu.org/ml/gcc-patches/2012-09/msg01278.html
1066
1067#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1068  inline float
1069  pow(float __x, float __y)
1070  { return std::pow(__x, __y); }
1071
1072  inline long double
1073  pow(long double __x, long double __y)
1074  { return std::pow(__x, __y); }
1075#endif
1076
1077  template<typename _Tp, typename _Up>
1078    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1079    pow(_Tp __x, _Up __y)
1080    {
1081      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1082      return std::pow(__type(__x), __type(__y));
1083    }
1084
1085_GLIBCXX_END_NAMESPACE_VERSION
1086}
1087}
1088
1089#include <bits/stl_algobase.h>
1090#include <limits>
1091#include <tr1/type_traits>
1092
1093#include <tr1/gamma.tcc>
1094#include <tr1/bessel_function.tcc>
1095#include <tr1/beta_function.tcc>
1096#include <tr1/ell_integral.tcc>
1097#include <tr1/exp_integral.tcc>
1098#include <tr1/hypergeometric.tcc>
1099#include <tr1/legendre_function.tcc>
1100#include <tr1/modified_bessel_func.tcc>
1101#include <tr1/poly_hermite.tcc>
1102#include <tr1/poly_laguerre.tcc>
1103#include <tr1/riemann_zeta.tcc>
1104
1105namespace std _GLIBCXX_VISIBILITY(default)
1106{
1107namespace tr1
1108{
1109_GLIBCXX_BEGIN_NAMESPACE_VERSION
1110
1111  /**
1112   * @defgroup tr1_math_spec_func Mathematical Special Functions
1113   * @ingroup numerics
1114   *
1115   * A collection of advanced mathematical special functions.
1116   * @{
1117   */
1118
1119  inline float
1120  assoc_laguerref(unsigned int __n, unsigned int __m, float __x)
1121  { return __detail::__assoc_laguerre<float>(__n, __m, __x); }
1122
1123  inline long double
1124  assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x)
1125  {
1126    return __detail::__assoc_laguerre<long double>(__n, __m, __x);
1127  }
1128
1129  ///  5.2.1.1  Associated Laguerre polynomials.
1130  template<typename _Tp>
1131    inline typename __gnu_cxx::__promote<_Tp>::__type
1132    assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
1133    {
1134      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1135      return __detail::__assoc_laguerre<__type>(__n, __m, __x);
1136    }
1137
1138  inline float
1139  assoc_legendref(unsigned int __l, unsigned int __m, float __x)
1140  { return __detail::__assoc_legendre_p<float>(__l, __m, __x); }
1141
1142  inline long double
1143  assoc_legendrel(unsigned int __l, unsigned int __m, long double __x)
1144  { return __detail::__assoc_legendre_p<long double>(__l, __m, __x); }
1145
1146  ///  5.2.1.2  Associated Legendre functions.
1147  template<typename _Tp>
1148    inline typename __gnu_cxx::__promote<_Tp>::__type
1149    assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
1150    {
1151      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1152      return __detail::__assoc_legendre_p<__type>(__l, __m, __x);
1153    }
1154
1155  inline float
1156  betaf(float __x, float __y)
1157  { return __detail::__beta<float>(__x, __y); }
1158
1159  inline long double
1160  betal(long double __x, long double __y)
1161  { return __detail::__beta<long double>(__x, __y); }
1162
1163  ///  5.2.1.3  Beta functions.
1164  template<typename _Tpx, typename _Tpy>
1165    inline typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type
1166    beta(_Tpx __x, _Tpy __y)
1167    {
1168      typedef typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type __type;
1169      return __detail::__beta<__type>(__x, __y);
1170    }
1171
1172  inline float
1173  comp_ellint_1f(float __k)
1174  { return __detail::__comp_ellint_1<float>(__k); }
1175
1176  inline long double
1177  comp_ellint_1l(long double __k)
1178  { return __detail::__comp_ellint_1<long double>(__k); }
1179
1180  ///  5.2.1.4  Complete elliptic integrals of the first kind.
1181  template<typename _Tp>
1182    inline typename __gnu_cxx::__promote<_Tp>::__type
1183    comp_ellint_1(_Tp __k)
1184    {
1185      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1186      return __detail::__comp_ellint_1<__type>(__k);
1187    }
1188
1189  inline float
1190  comp_ellint_2f(float __k)
1191  { return __detail::__comp_ellint_2<float>(__k); }
1192
1193  inline long double
1194  comp_ellint_2l(long double __k)
1195  { return __detail::__comp_ellint_2<long double>(__k); }
1196
1197  ///  5.2.1.5  Complete elliptic integrals of the second kind.
1198  template<typename _Tp>
1199    inline typename __gnu_cxx::__promote<_Tp>::__type
1200    comp_ellint_2(_Tp __k)
1201    {
1202      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1203      return __detail::__comp_ellint_2<__type>(__k);
1204    }
1205
1206  inline float
1207  comp_ellint_3f(float __k, float __nu)
1208  { return __detail::__comp_ellint_3<float>(__k, __nu); }
1209
1210  inline long double
1211  comp_ellint_3l(long double __k, long double __nu)
1212  { return __detail::__comp_ellint_3<long double>(__k, __nu); }
1213
1214  ///  5.2.1.6  Complete elliptic integrals of the third kind.
1215  template<typename _Tp, typename _Tpn>
1216    inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type
1217    comp_ellint_3(_Tp __k, _Tpn __nu)
1218    {
1219      typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type;
1220      return __detail::__comp_ellint_3<__type>(__k, __nu);
1221    }
1222
1223  inline float
1224  conf_hypergf(float __a, float __c, float __x)
1225  { return __detail::__conf_hyperg<float>(__a, __c, __x); }
1226
1227  inline long double
1228  conf_hypergl(long double __a, long double __c, long double __x)
1229  { return __detail::__conf_hyperg<long double>(__a, __c, __x); }
1230
1231  ///  5.2.1.7  Confluent hypergeometric functions.
1232  template<typename _Tpa, typename _Tpc, typename _Tp>
1233    inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type
1234    conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
1235    {
1236      typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type;
1237      return __detail::__conf_hyperg<__type>(__a, __c, __x);
1238    }
1239
1240  inline float
1241  cyl_bessel_if(float __nu, float __x)
1242  { return __detail::__cyl_bessel_i<float>(__nu, __x); }
1243
1244  inline long double
1245  cyl_bessel_il(long double __nu, long double __x)
1246  { return __detail::__cyl_bessel_i<long double>(__nu, __x); }
1247
1248  ///  5.2.1.8  Regular modified cylindrical Bessel functions.
1249  template<typename _Tpnu, typename _Tp>
1250    inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1251    cyl_bessel_i(_Tpnu __nu, _Tp __x)
1252    {
1253      typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1254      return __detail::__cyl_bessel_i<__type>(__nu, __x);
1255    }
1256
1257  inline float
1258  cyl_bessel_jf(float __nu, float __x)
1259  { return __detail::__cyl_bessel_j<float>(__nu, __x); }
1260
1261  inline long double
1262  cyl_bessel_jl(long double __nu, long double __x)
1263  { return __detail::__cyl_bessel_j<long double>(__nu, __x); }
1264
1265  ///  5.2.1.9  Cylindrical Bessel functions (of the first kind).
1266  template<typename _Tpnu, typename _Tp>
1267    inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1268    cyl_bessel_j(_Tpnu __nu, _Tp __x)
1269    {
1270      typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1271      return __detail::__cyl_bessel_j<__type>(__nu, __x);
1272    }
1273
1274  inline float
1275  cyl_bessel_kf(float __nu, float __x)
1276  { return __detail::__cyl_bessel_k<float>(__nu, __x); }
1277
1278  inline long double
1279  cyl_bessel_kl(long double __nu, long double __x)
1280  { return __detail::__cyl_bessel_k<long double>(__nu, __x); }
1281
1282  ///  5.2.1.10  Irregular modified cylindrical Bessel functions.
1283  template<typename _Tpnu, typename _Tp>
1284    inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1285    cyl_bessel_k(_Tpnu __nu, _Tp __x)
1286    {
1287      typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1288      return __detail::__cyl_bessel_k<__type>(__nu, __x);
1289    }
1290
1291  inline float
1292  cyl_neumannf(float __nu, float __x)
1293  { return __detail::__cyl_neumann_n<float>(__nu, __x); }
1294
1295  inline long double
1296  cyl_neumannl(long double __nu, long double __x)
1297  { return __detail::__cyl_neumann_n<long double>(__nu, __x); }
1298
1299  ///  5.2.1.11  Cylindrical Neumann functions.
1300  template<typename _Tpnu, typename _Tp>
1301    inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1302    cyl_neumann(_Tpnu __nu, _Tp __x)
1303    {
1304      typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1305      return __detail::__cyl_neumann_n<__type>(__nu, __x);
1306    }
1307
1308  inline float
1309  ellint_1f(float __k, float __phi)
1310  { return __detail::__ellint_1<float>(__k, __phi); }
1311
1312  inline long double
1313  ellint_1l(long double __k, long double __phi)
1314  { return __detail::__ellint_1<long double>(__k, __phi); }
1315
1316  ///  5.2.1.12  Incomplete elliptic integrals of the first kind.
1317  template<typename _Tp, typename _Tpp>
1318    inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
1319    ellint_1(_Tp __k, _Tpp __phi)
1320    {
1321      typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
1322      return __detail::__ellint_1<__type>(__k, __phi);
1323    }
1324
1325  inline float
1326  ellint_2f(float __k, float __phi)
1327  { return __detail::__ellint_2<float>(__k, __phi); }
1328
1329  inline long double
1330  ellint_2l(long double __k, long double __phi)
1331  { return __detail::__ellint_2<long double>(__k, __phi); }
1332
1333  ///  5.2.1.13  Incomplete elliptic integrals of the second kind.
1334  template<typename _Tp, typename _Tpp>
1335    inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
1336    ellint_2(_Tp __k, _Tpp __phi)
1337    {
1338      typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
1339      return __detail::__ellint_2<__type>(__k, __phi);
1340    }
1341
1342  inline float
1343  ellint_3f(float __k, float __nu, float __phi)
1344  { return __detail::__ellint_3<float>(__k, __nu, __phi); }
1345
1346  inline long double
1347  ellint_3l(long double __k, long double __nu, long double __phi)
1348  { return __detail::__ellint_3<long double>(__k, __nu, __phi); }
1349
1350  ///  5.2.1.14  Incomplete elliptic integrals of the third kind.
1351  template<typename _Tp, typename _Tpn, typename _Tpp>
1352    inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type
1353    ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
1354    {
1355      typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type;
1356      return __detail::__ellint_3<__type>(__k, __nu, __phi);
1357    }
1358
1359  inline float
1360  expintf(float __x)
1361  { return __detail::__expint<float>(__x); }
1362
1363  inline long double
1364  expintl(long double __x)
1365  { return __detail::__expint<long double>(__x); }
1366
1367  ///  5.2.1.15  Exponential integrals.
1368  template<typename _Tp>
1369    inline typename __gnu_cxx::__promote<_Tp>::__type
1370    expint(_Tp __x)
1371    {
1372      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1373      return __detail::__expint<__type>(__x);
1374    }
1375
1376  inline float
1377  hermitef(unsigned int __n, float __x)
1378  { return __detail::__poly_hermite<float>(__n, __x); }
1379
1380  inline long double
1381  hermitel(unsigned int __n, long double __x)
1382  { return __detail::__poly_hermite<long double>(__n, __x); }
1383
1384  ///  5.2.1.16  Hermite polynomials.
1385  template<typename _Tp>
1386    inline typename __gnu_cxx::__promote<_Tp>::__type
1387    hermite(unsigned int __n, _Tp __x)
1388    {
1389      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1390      return __detail::__poly_hermite<__type>(__n, __x);
1391    }
1392
1393  inline float
1394  hypergf(float __a, float __b, float __c, float __x)
1395  { return __detail::__hyperg<float>(__a, __b, __c, __x); }
1396
1397  inline long double
1398  hypergl(long double __a, long double __b, long double __c, long double __x)
1399  { return __detail::__hyperg<long double>(__a, __b, __c, __x); }
1400
1401  ///  5.2.1.17  Hypergeometric functions.
1402  template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp>
1403    inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type
1404    hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
1405    {
1406      typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type;
1407      return __detail::__hyperg<__type>(__a, __b, __c, __x);
1408    }
1409
1410  inline float
1411  laguerref(unsigned int __n, float __x)
1412  { return __detail::__laguerre<float>(__n, __x); }
1413
1414  inline long double
1415  laguerrel(unsigned int __n, long double __x)
1416  { return __detail::__laguerre<long double>(__n, __x); }
1417
1418  ///  5.2.1.18  Laguerre polynomials.
1419  template<typename _Tp>
1420    inline typename __gnu_cxx::__promote<_Tp>::__type
1421    laguerre(unsigned int __n, _Tp __x)
1422    {
1423      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1424      return __detail::__laguerre<__type>(__n, __x);
1425    }
1426
1427  inline float
1428  legendref(unsigned int __n, float __x)
1429  { return __detail::__poly_legendre_p<float>(__n, __x); }
1430
1431  inline long double
1432  legendrel(unsigned int __n, long double __x)
1433  { return __detail::__poly_legendre_p<long double>(__n, __x); }
1434
1435  ///  5.2.1.19  Legendre polynomials.
1436  template<typename _Tp>
1437    inline typename __gnu_cxx::__promote<_Tp>::__type
1438    legendre(unsigned int __n, _Tp __x)
1439    {
1440      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1441      return __detail::__poly_legendre_p<__type>(__n, __x);
1442    }
1443
1444  inline float
1445  riemann_zetaf(float __x)
1446  { return __detail::__riemann_zeta<float>(__x); }
1447
1448  inline long double
1449  riemann_zetal(long double __x)
1450  { return __detail::__riemann_zeta<long double>(__x); }
1451
1452  ///  5.2.1.20  Riemann zeta function.
1453  template<typename _Tp>
1454    inline typename __gnu_cxx::__promote<_Tp>::__type
1455    riemann_zeta(_Tp __x)
1456    {
1457      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1458      return __detail::__riemann_zeta<__type>(__x);
1459    }
1460
1461  inline float
1462  sph_besself(unsigned int __n, float __x)
1463  { return __detail::__sph_bessel<float>(__n, __x); }
1464
1465  inline long double
1466  sph_bessell(unsigned int __n, long double __x)
1467  { return __detail::__sph_bessel<long double>(__n, __x); }
1468
1469  ///  5.2.1.21  Spherical Bessel functions.
1470  template<typename _Tp>
1471    inline typename __gnu_cxx::__promote<_Tp>::__type
1472    sph_bessel(unsigned int __n, _Tp __x)
1473    {
1474      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1475      return __detail::__sph_bessel<__type>(__n, __x);
1476    }
1477
1478  inline float
1479  sph_legendref(unsigned int __l, unsigned int __m, float __theta)
1480  { return __detail::__sph_legendre<float>(__l, __m, __theta); }
1481
1482  inline long double
1483  sph_legendrel(unsigned int __l, unsigned int __m, long double __theta)
1484  { return __detail::__sph_legendre<long double>(__l, __m, __theta); }
1485
1486  ///  5.2.1.22  Spherical associated Legendre functions.
1487  template<typename _Tp>
1488    inline typename __gnu_cxx::__promote<_Tp>::__type
1489    sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
1490    {
1491      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1492      return __detail::__sph_legendre<__type>(__l, __m, __theta);
1493    }
1494
1495  inline float
1496  sph_neumannf(unsigned int __n, float __x)
1497  { return __detail::__sph_neumann<float>(__n, __x); }
1498
1499  inline long double
1500  sph_neumannl(unsigned int __n, long double __x)
1501  { return __detail::__sph_neumann<long double>(__n, __x); }
1502
1503  ///  5.2.1.23  Spherical Neumann functions.
1504  template<typename _Tp>
1505    inline typename __gnu_cxx::__promote<_Tp>::__type
1506    sph_neumann(unsigned int __n, _Tp __x)
1507    {
1508      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1509      return __detail::__sph_neumann<__type>(__n, __x);
1510    }
1511
1512  /* @} */ // tr1_math_spec_func
1513_GLIBCXX_END_NAMESPACE_VERSION
1514}
1515}
1516
1517#endif // _GLIBCXX_TR1_CMATH
1518