1// TR1 cmath -*- C++ -*-
3// Copyright (C) 2006-2022 Free Software Foundation, Inc.
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)
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.
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.
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/>.
26 * This is a TR1 C++ Library header.
29#ifndef _GLIBCXX_TR1_CMATH
30#define _GLIBCXX_TR1_CMATH 1
32#pragma GCC system_header
36#ifdef _GLIBCXX_USE_C99_MATH_TR1
146namespace std _GLIBCXX_VISIBILITY(default)
148_GLIBCXX_BEGIN_NAMESPACE_VERSION
152#if _GLIBCXX_USE_C99_MATH_TR1
154 // Using declarations to bring names from libc's <math.h> into std::tr1.
303#if _GLIBCXX_USE_C99_MATH
304#if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC
306 /// Function template definitions [8.16.3].
307 template<typename _Tp>
308 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
312 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
313 return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
314 FP_SUBNORMAL, FP_ZERO, __type(__f));
317 template<typename _Tp>
318 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
322 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
323 return __builtin_isfinite(__type(__f));
326 template<typename _Tp>
327 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
331 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
332 return __builtin_isinf(__type(__f));
335 template<typename _Tp>
336 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
340 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
341 return __builtin_isnan(__type(__f));
344 template<typename _Tp>
345 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
349 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
350 return __builtin_isnormal(__type(__f));
353 template<typename _Tp>
354 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
358 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
359 return __builtin_signbit(__type(__f));
362 template<typename _Tp>
363 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
365 isgreater(_Tp __f1, _Tp __f2)
367 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
368 return __builtin_isgreater(__type(__f1), __type(__f2));
371 template<typename _Tp>
372 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
374 isgreaterequal(_Tp __f1, _Tp __f2)
376 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
377 return __builtin_isgreaterequal(__type(__f1), __type(__f2));
380 template<typename _Tp>
381 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
383 isless(_Tp __f1, _Tp __f2)
385 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
386 return __builtin_isless(__type(__f1), __type(__f2));
389 template<typename _Tp>
390 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
392 islessequal(_Tp __f1, _Tp __f2)
394 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
395 return __builtin_islessequal(__type(__f1), __type(__f2));
398 template<typename _Tp>
399 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
401 islessgreater(_Tp __f1, _Tp __f2)
403 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
404 return __builtin_islessgreater(__type(__f1), __type(__f2));
407 template<typename _Tp>
408 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
410 isunordered(_Tp __f1, _Tp __f2)
412 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
413 return __builtin_isunordered(__type(__f1), __type(__f2));
419#if _GLIBCXX_USE_C99_MATH_TR1
421 /** Additional overloads [8.16.4].
425 // For functions defined in C++03 the additional overloads are already
426 // declared in <cmath> so we can just re-declare them in std::tr1.
448#if __cplusplus >= 201103L
450 // Since C++11, <cmath> defines additional overloads for these functions
477 using std::nearbyint;
478 using std::nextafter;
479 using std::nexttoward;
480 using std::remainder;
489#else // __cplusplus < 201103L
491 // In C++03 we need to provide the additional overloads.
493#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
496 { return __builtin_acoshf(__x); }
499 acosh(long double __x)
500 { return __builtin_acoshl(__x); }
503 template<typename _Tp>
504 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
507 { return __builtin_acosh(__x); }
509#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
512 { return __builtin_asinhf(__x); }
515 asinh(long double __x)
516 { return __builtin_asinhl(__x); }
519 template<typename _Tp>
520 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
523 { return __builtin_asinh(__x); }
525#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
528 { return __builtin_atanhf(__x); }
531 atanh(long double __x)
532 { return __builtin_atanhl(__x); }
535 template<typename _Tp>
536 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
539 { return __builtin_atanh(__x); }
541#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
544 { return __builtin_cbrtf(__x); }
547 cbrt(long double __x)
548 { return __builtin_cbrtl(__x); }
551 template<typename _Tp>
552 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
555 { return __builtin_cbrt(__x); }
557#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
559 copysign(float __x, float __y)
560 { return __builtin_copysignf(__x, __y); }
563 copysign(long double __x, long double __y)
564 { return __builtin_copysignl(__x, __y); }
567 template<typename _Tp, typename _Up>
568 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
569 copysign(_Tp __x, _Up __y)
571 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
572 return copysign(__type(__x), __type(__y));
575#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
578 { return __builtin_erff(__x); }
582 { return __builtin_erfl(__x); }
585 template<typename _Tp>
586 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
589 { return __builtin_erf(__x); }
591#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
594 { return __builtin_erfcf(__x); }
597 erfc(long double __x)
598 { return __builtin_erfcl(__x); }
601 template<typename _Tp>
602 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
605 { return __builtin_erfc(__x); }
607#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
610 { return __builtin_exp2f(__x); }
613 exp2(long double __x)
614 { return __builtin_exp2l(__x); }
617 template<typename _Tp>
618 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
621 { return __builtin_exp2(__x); }
623#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
626 { return __builtin_expm1f(__x); }
629 expm1(long double __x)
630 { return __builtin_expm1l(__x); }
633 template<typename _Tp>
634 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
637 { return __builtin_expm1(__x); }
639#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
641 fdim(float __x, float __y)
642 { return __builtin_fdimf(__x, __y); }
645 fdim(long double __x, long double __y)
646 { return __builtin_fdiml(__x, __y); }
649 template<typename _Tp, typename _Up>
650 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
651 fdim(_Tp __x, _Up __y)
653 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
654 return fdim(__type(__x), __type(__y));
657#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
659 fma(float __x, float __y, float __z)
660 { return __builtin_fmaf(__x, __y, __z); }
663 fma(long double __x, long double __y, long double __z)
664 { return __builtin_fmal(__x, __y, __z); }
667 template<typename _Tp, typename _Up, typename _Vp>
668 inline typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
669 fma(_Tp __x, _Up __y, _Vp __z)
671 typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type;
672 return fma(__type(__x), __type(__y), __type(__z));
675#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
677 fmax(float __x, float __y)
678 { return __builtin_fmaxf(__x, __y); }
681 fmax(long double __x, long double __y)
682 { return __builtin_fmaxl(__x, __y); }
685 template<typename _Tp, typename _Up>
686 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
687 fmax(_Tp __x, _Up __y)
689 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
690 return fmax(__type(__x), __type(__y));
693#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
695 fmin(float __x, float __y)
696 { return __builtin_fminf(__x, __y); }
699 fmin(long double __x, long double __y)
700 { return __builtin_fminl(__x, __y); }
703 template<typename _Tp, typename _Up>
704 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
705 fmin(_Tp __x, _Up __y)
707 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
708 return fmin(__type(__x), __type(__y));
711#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
713 hypot(float __x, float __y)
714 { return __builtin_hypotf(__x, __y); }
717 hypot(long double __x, long double __y)
718 { return __builtin_hypotl(__x, __y); }
721 template<typename _Tp, typename _Up>
722 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
723 hypot(_Tp __y, _Up __x)
725 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
726 return hypot(__type(__y), __type(__x));
729#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
732 { return __builtin_ilogbf(__x); }
735 ilogb(long double __x)
736 { return __builtin_ilogbl(__x); }
739 template<typename _Tp>
740 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
743 { return __builtin_ilogb(__x); }
745#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
748 { return __builtin_lgammaf(__x); }
751 lgamma(long double __x)
752 { return __builtin_lgammal(__x); }
755 template<typename _Tp>
756 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
759 { return __builtin_lgamma(__x); }
761#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
764 { return __builtin_llrintf(__x); }
767 llrint(long double __x)
768 { return __builtin_llrintl(__x); }
771 template<typename _Tp>
772 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
775 { return __builtin_llrint(__x); }
777#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
780 { return __builtin_llroundf(__x); }
783 llround(long double __x)
784 { return __builtin_llroundl(__x); }
787 template<typename _Tp>
788 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
791 { return __builtin_llround(__x); }
793#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
796 { return __builtin_log1pf(__x); }
799 log1p(long double __x)
800 { return __builtin_log1pl(__x); }
803 template<typename _Tp>
804 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
807 { return __builtin_log1p(__x); }
810#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
813 { return __builtin_log2f(__x); }
816 log2(long double __x)
817 { return __builtin_log2l(__x); }
820 template<typename _Tp>
821 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
824 { return __builtin_log2(__x); }
826#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
829 { return __builtin_logbf(__x); }
832 logb(long double __x)
833 { return __builtin_logbl(__x); }
836 template<typename _Tp>
837 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
841 return __builtin_logb(__x);
844#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
847 { return __builtin_lrintf(__x); }
850 lrint(long double __x)
851 { return __builtin_lrintl(__x); }
854 template<typename _Tp>
855 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
858 { return __builtin_lrint(__x); }
860#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
863 { return __builtin_lroundf(__x); }
866 lround(long double __x)
867 { return __builtin_lroundl(__x); }
870 template<typename _Tp>
871 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
874 { return __builtin_lround(__x); }
876#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
879 { return __builtin_nearbyintf(__x); }
882 nearbyint(long double __x)
883 { return __builtin_nearbyintl(__x); }
886 template<typename _Tp>
887 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
890 { return __builtin_nearbyint(__x); }
892#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
894 nextafter(float __x, float __y)
895 { return __builtin_nextafterf(__x, __y); }
898 nextafter(long double __x, long double __y)
899 { return __builtin_nextafterl(__x, __y); }
902 template<typename _Tp, typename _Up>
903 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
904 nextafter(_Tp __x, _Up __y)
906 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
907 return nextafter(__type(__x), __type(__y));
910#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
912 nexttoward(float __x, long double __y)
913 { return __builtin_nexttowardf(__x, __y); }
916 nexttoward(long double __x, long double __y)
917 { return __builtin_nexttowardl(__x, __y); }
920 template<typename _Tp>
921 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
923 nexttoward(_Tp __x, long double __y)
924 { return __builtin_nexttoward(__x, __y); }
926#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
928 remainder(float __x, float __y)
929 { return __builtin_remainderf(__x, __y); }
932 remainder(long double __x, long double __y)
933 { return __builtin_remainderl(__x, __y); }
936 template<typename _Tp, typename _Up>
937 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
938 remainder(_Tp __x, _Up __y)
940 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
941 return remainder(__type(__x), __type(__y));
944#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
946 remquo(float __x, float __y, int* __pquo)
947 { return __builtin_remquof(__x, __y, __pquo); }
950 remquo(long double __x, long double __y, int* __pquo)
951 { return __builtin_remquol(__x, __y, __pquo); }
954 template<typename _Tp, typename _Up>
955 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
956 remquo(_Tp __x, _Up __y, int* __pquo)
958 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
959 return remquo(__type(__x), __type(__y), __pquo);
962#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
965 { return __builtin_rintf(__x); }
968 rint(long double __x)
969 { return __builtin_rintl(__x); }
972 template<typename _Tp>
973 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
976 { return __builtin_rint(__x); }
978#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
981 { return __builtin_roundf(__x); }
984 round(long double __x)
985 { return __builtin_roundl(__x); }
988 template<typename _Tp>
989 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
992 { return __builtin_round(__x); }
994#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
996 scalbln(float __x, long __ex)
997 { return __builtin_scalblnf(__x, __ex); }
1000 scalbln(long double __x, long __ex)
1001 { return __builtin_scalblnl(__x, __ex); }
1004 template<typename _Tp>
1005 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1007 scalbln(_Tp __x, long __ex)
1008 { return __builtin_scalbln(__x, __ex); }
1010#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1012 scalbn(float __x, int __ex)
1013 { return __builtin_scalbnf(__x, __ex); }
1016 scalbn(long double __x, int __ex)
1017 { return __builtin_scalbnl(__x, __ex); }
1020 template<typename _Tp>
1021 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1023 scalbn(_Tp __x, int __ex)
1024 { return __builtin_scalbn(__x, __ex); }
1026#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1029 { return __builtin_tgammaf(__x); }
1032 tgamma(long double __x)
1033 { return __builtin_tgammal(__x); }
1036 template<typename _Tp>
1037 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1040 { return __builtin_tgamma(__x); }
1042#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1045 { return __builtin_truncf(__x); }
1048 trunc(long double __x)
1049 { return __builtin_truncl(__x); }
1052 template<typename _Tp>
1053 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1056 { return __builtin_trunc(__x); }
1058#endif // __cplusplus < 201103L
1062#endif /* _GLIBCXX_USE_C99_MATH_TR1 */
1064 // DR 550. What should the return type of pow(float,int) be?
1065 // NB: C++11 and TR1 != C++03.
1067 // We cannot do "using std::pow;" because that would bring in unwanted
1068 // pow(*, int) overloads in C++03, with the wrong return type. Instead we
1069 // define all the necessary overloads, but the std::tr1::pow(double, double)
1070 // overload cannot be provided here, because <tr1/math.h> would add it to
1071 // the global namespace where it would clash with ::pow(double,double) from
1072 // libc (revealed by the fix of PR c++/54537).
1073 // The solution is to forward std::tr1::pow(double,double) to
1074 // std::pow(double,double) via the function template below. See
1075 // the discussion about this issue here:
1076 // http://gcc.gnu.org/ml/gcc-patches/2012-09/msg01278.html
1078#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1080 pow(float __x, float __y)
1081 { return std::pow(__x, __y); }
1084 pow(long double __x, long double __y)
1085 { return std::pow(__x, __y); }
1088 template<typename _Tp, typename _Up>
1089 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1090 pow(_Tp __x, _Up __y)
1092 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1093 return std::pow(__type(__x), __type(__y));
1096#if __cplusplus >= 201103L
1097 // We also deal with fabs in a special way, because "using std::fabs;"
1098 // could bring in C++11's std::fabs<T>(const std::complex<T>&) with a
1099 // different return type from std::tr1::fabs<T>(const std::complex<T>&).
1100 // We define the necessary overloads, except std::tr1::fabs(double) which
1101 // could clash with ::fabs(double) from libc.
1102 // The function template handles double as well as integers, forwarding
1105#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
1106#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1109 { return __builtin_fabsf(__x); }
1112 fabs(long double __x)
1113 { return __builtin_fabsl(__x); }
1117 template<typename _Tp>
1118 inline typename __gnu_cxx::__promote<_Tp>::__type
1120 { return std::fabs(__x); }
1124 // For C++03 just use std::fabs as there is no overload for std::complex<>.
1130_GLIBCXX_END_NAMESPACE_VERSION
1134 * @defgroup tr1_math_spec_func TR1 Mathematical Special Functions
1137 * A collection of advanced mathematical special functions.
1140#if _GLIBCXX_USE_STD_SPEC_FUNCS
1142namespace std _GLIBCXX_VISIBILITY(default)
1144_GLIBCXX_BEGIN_NAMESPACE_VERSION
1148 using std::assoc_laguerref;
1149 using std::assoc_laguerrel;
1150 using std::assoc_laguerre;
1152 using std::assoc_legendref;
1153 using std::assoc_legendrel;
1154 using std::assoc_legendre;
1160 using std::comp_ellint_1f;
1161 using std::comp_ellint_1l;
1162 using std::comp_ellint_1;
1164 using std::comp_ellint_2f;
1165 using std::comp_ellint_2l;
1166 using std::comp_ellint_2;
1168 using std::comp_ellint_3f;
1169 using std::comp_ellint_3l;
1170 using std::comp_ellint_3;
1172 using std::cyl_bessel_if;
1173 using std::cyl_bessel_il;
1174 using std::cyl_bessel_i;
1176 using std::cyl_bessel_jf;
1177 using std::cyl_bessel_jl;
1178 using std::cyl_bessel_j;
1180 using std::cyl_bessel_kf;
1181 using std::cyl_bessel_kl;
1182 using std::cyl_bessel_k;
1184 using std::cyl_neumannf;
1185 using std::cyl_neumannl;
1186 using std::cyl_neumann;
1188 using std::ellint_1f;
1189 using std::ellint_1l;
1190 using std::ellint_1;
1192 using std::ellint_2f;
1193 using std::ellint_2l;
1194 using std::ellint_2;
1196 using std::ellint_3f;
1197 using std::ellint_3l;
1198 using std::ellint_3;
1204 using std::hermitef;
1205 using std::hermitel;
1208 using std::laguerref;
1209 using std::laguerrel;
1210 using std::laguerre;
1212 using std::legendref;
1213 using std::legendrel;
1214 using std::legendre;
1216 using std::riemann_zetaf;
1217 using std::riemann_zetal;
1218 using std::riemann_zeta;
1220 using std::sph_besself;
1221 using std::sph_bessell;
1222 using std::sph_bessel;
1224 using std::sph_legendref;
1225 using std::sph_legendrel;
1226 using std::sph_legendre;
1228 using std::sph_neumannf;
1229 using std::sph_neumannl;
1230 using std::sph_neumann;
1233_GLIBCXX_END_NAMESPACE_VERSION
1236#else // ! _GLIBCXX_USE_STD_SPEC_FUNCS
1238#include <bits/stl_algobase.h>
1240#include <tr1/type_traits>
1242#include <tr1/gamma.tcc>
1243#include <tr1/bessel_function.tcc>
1244#include <tr1/beta_function.tcc>
1245#include <tr1/ell_integral.tcc>
1246#include <tr1/exp_integral.tcc>
1247#include <tr1/legendre_function.tcc>
1248#include <tr1/modified_bessel_func.tcc>
1249#include <tr1/poly_hermite.tcc>
1250#include <tr1/poly_laguerre.tcc>
1251#include <tr1/riemann_zeta.tcc>
1253namespace std _GLIBCXX_VISIBILITY(default)
1255_GLIBCXX_BEGIN_NAMESPACE_VERSION
1258 /** @addtogroup tr1_math_spec_func
1263 assoc_laguerref(unsigned int __n, unsigned int __m, float __x)
1264 { return __detail::__assoc_laguerre<float>(__n, __m, __x); }
1267 assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x)
1269 return __detail::__assoc_laguerre<long double>(__n, __m, __x);
1272 /// 5.2.1.1 Associated Laguerre polynomials.
1273 template<typename _Tp>
1274 inline typename __gnu_cxx::__promote<_Tp>::__type
1275 assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
1277 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1278 return __detail::__assoc_laguerre<__type>(__n, __m, __x);
1282 assoc_legendref(unsigned int __l, unsigned int __m, float __x)
1283 { return __detail::__assoc_legendre_p<float>(__l, __m, __x); }
1286 assoc_legendrel(unsigned int __l, unsigned int __m, long double __x)
1287 { return __detail::__assoc_legendre_p<long double>(__l, __m, __x); }
1289 /// 5.2.1.2 Associated Legendre functions.
1290 template<typename _Tp>
1291 inline typename __gnu_cxx::__promote<_Tp>::__type
1292 assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
1294 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1295 return __detail::__assoc_legendre_p<__type>(__l, __m, __x);
1299 betaf(float __x, float __y)
1300 { return __detail::__beta<float>(__x, __y); }
1303 betal(long double __x, long double __y)
1304 { return __detail::__beta<long double>(__x, __y); }
1306 /// 5.2.1.3 Beta functions.
1307 template<typename _Tpx, typename _Tpy>
1308 inline typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type
1309 beta(_Tpx __x, _Tpy __y)
1311 typedef typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type __type;
1312 return __detail::__beta<__type>(__x, __y);
1316 comp_ellint_1f(float __k)
1317 { return __detail::__comp_ellint_1<float>(__k); }
1320 comp_ellint_1l(long double __k)
1321 { return __detail::__comp_ellint_1<long double>(__k); }
1323 /// 5.2.1.4 Complete elliptic integrals of the first kind.
1324 template<typename _Tp>
1325 inline typename __gnu_cxx::__promote<_Tp>::__type
1326 comp_ellint_1(_Tp __k)
1328 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1329 return __detail::__comp_ellint_1<__type>(__k);
1333 comp_ellint_2f(float __k)
1334 { return __detail::__comp_ellint_2<float>(__k); }
1337 comp_ellint_2l(long double __k)
1338 { return __detail::__comp_ellint_2<long double>(__k); }
1340 /// 5.2.1.5 Complete elliptic integrals of the second kind.
1341 template<typename _Tp>
1342 inline typename __gnu_cxx::__promote<_Tp>::__type
1343 comp_ellint_2(_Tp __k)
1345 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1346 return __detail::__comp_ellint_2<__type>(__k);
1350 comp_ellint_3f(float __k, float __nu)
1351 { return __detail::__comp_ellint_3<float>(__k, __nu); }
1354 comp_ellint_3l(long double __k, long double __nu)
1355 { return __detail::__comp_ellint_3<long double>(__k, __nu); }
1357 /// 5.2.1.6 Complete elliptic integrals of the third kind.
1358 template<typename _Tp, typename _Tpn>
1359 inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type
1360 comp_ellint_3(_Tp __k, _Tpn __nu)
1362 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type;
1363 return __detail::__comp_ellint_3<__type>(__k, __nu);
1367 cyl_bessel_if(float __nu, float __x)
1368 { return __detail::__cyl_bessel_i<float>(__nu, __x); }
1371 cyl_bessel_il(long double __nu, long double __x)
1372 { return __detail::__cyl_bessel_i<long double>(__nu, __x); }
1374 /// 5.2.1.8 Regular modified cylindrical Bessel functions.
1375 template<typename _Tpnu, typename _Tp>
1376 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1377 cyl_bessel_i(_Tpnu __nu, _Tp __x)
1379 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1380 return __detail::__cyl_bessel_i<__type>(__nu, __x);
1384 cyl_bessel_jf(float __nu, float __x)
1385 { return __detail::__cyl_bessel_j<float>(__nu, __x); }
1388 cyl_bessel_jl(long double __nu, long double __x)
1389 { return __detail::__cyl_bessel_j<long double>(__nu, __x); }
1391 /// 5.2.1.9 Cylindrical Bessel functions (of the first kind).
1392 template<typename _Tpnu, typename _Tp>
1393 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1394 cyl_bessel_j(_Tpnu __nu, _Tp __x)
1396 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1397 return __detail::__cyl_bessel_j<__type>(__nu, __x);
1401 cyl_bessel_kf(float __nu, float __x)
1402 { return __detail::__cyl_bessel_k<float>(__nu, __x); }
1405 cyl_bessel_kl(long double __nu, long double __x)
1406 { return __detail::__cyl_bessel_k<long double>(__nu, __x); }
1408 /// 5.2.1.10 Irregular modified cylindrical Bessel functions.
1409 template<typename _Tpnu, typename _Tp>
1410 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1411 cyl_bessel_k(_Tpnu __nu, _Tp __x)
1413 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1414 return __detail::__cyl_bessel_k<__type>(__nu, __x);
1418 cyl_neumannf(float __nu, float __x)
1419 { return __detail::__cyl_neumann_n<float>(__nu, __x); }
1422 cyl_neumannl(long double __nu, long double __x)
1423 { return __detail::__cyl_neumann_n<long double>(__nu, __x); }
1425 /// 5.2.1.11 Cylindrical Neumann functions.
1426 template<typename _Tpnu, typename _Tp>
1427 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1428 cyl_neumann(_Tpnu __nu, _Tp __x)
1430 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1431 return __detail::__cyl_neumann_n<__type>(__nu, __x);
1435 ellint_1f(float __k, float __phi)
1436 { return __detail::__ellint_1<float>(__k, __phi); }
1439 ellint_1l(long double __k, long double __phi)
1440 { return __detail::__ellint_1<long double>(__k, __phi); }
1442 /// 5.2.1.12 Incomplete elliptic integrals of the first kind.
1443 template<typename _Tp, typename _Tpp>
1444 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
1445 ellint_1(_Tp __k, _Tpp __phi)
1447 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
1448 return __detail::__ellint_1<__type>(__k, __phi);
1452 ellint_2f(float __k, float __phi)
1453 { return __detail::__ellint_2<float>(__k, __phi); }
1456 ellint_2l(long double __k, long double __phi)
1457 { return __detail::__ellint_2<long double>(__k, __phi); }
1459 /// 5.2.1.13 Incomplete elliptic integrals of the second kind.
1460 template<typename _Tp, typename _Tpp>
1461 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
1462 ellint_2(_Tp __k, _Tpp __phi)
1464 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
1465 return __detail::__ellint_2<__type>(__k, __phi);
1469 ellint_3f(float __k, float __nu, float __phi)
1470 { return __detail::__ellint_3<float>(__k, __nu, __phi); }
1473 ellint_3l(long double __k, long double __nu, long double __phi)
1474 { return __detail::__ellint_3<long double>(__k, __nu, __phi); }
1476 /// 5.2.1.14 Incomplete elliptic integrals of the third kind.
1477 template<typename _Tp, typename _Tpn, typename _Tpp>
1478 inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type
1479 ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
1481 typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type;
1482 return __detail::__ellint_3<__type>(__k, __nu, __phi);
1487 { return __detail::__expint<float>(__x); }
1490 expintl(long double __x)
1491 { return __detail::__expint<long double>(__x); }
1493 /// 5.2.1.15 Exponential integrals.
1494 template<typename _Tp>
1495 inline typename __gnu_cxx::__promote<_Tp>::__type
1498 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1499 return __detail::__expint<__type>(__x);
1503 hermitef(unsigned int __n, float __x)
1504 { return __detail::__poly_hermite<float>(__n, __x); }
1507 hermitel(unsigned int __n, long double __x)
1508 { return __detail::__poly_hermite<long double>(__n, __x); }
1510 /// 5.2.1.16 Hermite polynomials.
1511 template<typename _Tp>
1512 inline typename __gnu_cxx::__promote<_Tp>::__type
1513 hermite(unsigned int __n, _Tp __x)
1515 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1516 return __detail::__poly_hermite<__type>(__n, __x);
1520 laguerref(unsigned int __n, float __x)
1521 { return __detail::__laguerre<float>(__n, __x); }
1524 laguerrel(unsigned int __n, long double __x)
1525 { return __detail::__laguerre<long double>(__n, __x); }
1527 /// 5.2.1.18 Laguerre polynomials.
1528 template<typename _Tp>
1529 inline typename __gnu_cxx::__promote<_Tp>::__type
1530 laguerre(unsigned int __n, _Tp __x)
1532 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1533 return __detail::__laguerre<__type>(__n, __x);
1537 legendref(unsigned int __n, float __x)
1538 { return __detail::__poly_legendre_p<float>(__n, __x); }
1541 legendrel(unsigned int __n, long double __x)
1542 { return __detail::__poly_legendre_p<long double>(__n, __x); }
1544 /// 5.2.1.19 Legendre polynomials.
1545 template<typename _Tp>
1546 inline typename __gnu_cxx::__promote<_Tp>::__type
1547 legendre(unsigned int __n, _Tp __x)
1549 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1550 return __detail::__poly_legendre_p<__type>(__n, __x);
1554 riemann_zetaf(float __x)
1555 { return __detail::__riemann_zeta<float>(__x); }
1558 riemann_zetal(long double __x)
1559 { return __detail::__riemann_zeta<long double>(__x); }
1561 /// 5.2.1.20 Riemann zeta function.
1562 template<typename _Tp>
1563 inline typename __gnu_cxx::__promote<_Tp>::__type
1564 riemann_zeta(_Tp __x)
1566 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1567 return __detail::__riemann_zeta<__type>(__x);
1571 sph_besself(unsigned int __n, float __x)
1572 { return __detail::__sph_bessel<float>(__n, __x); }
1575 sph_bessell(unsigned int __n, long double __x)
1576 { return __detail::__sph_bessel<long double>(__n, __x); }
1578 /// 5.2.1.21 Spherical Bessel functions.
1579 template<typename _Tp>
1580 inline typename __gnu_cxx::__promote<_Tp>::__type
1581 sph_bessel(unsigned int __n, _Tp __x)
1583 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1584 return __detail::__sph_bessel<__type>(__n, __x);
1588 sph_legendref(unsigned int __l, unsigned int __m, float __theta)
1589 { return __detail::__sph_legendre<float>(__l, __m, __theta); }
1592 sph_legendrel(unsigned int __l, unsigned int __m, long double __theta)
1593 { return __detail::__sph_legendre<long double>(__l, __m, __theta); }
1595 /// 5.2.1.22 Spherical associated Legendre functions.
1596 template<typename _Tp>
1597 inline typename __gnu_cxx::__promote<_Tp>::__type
1598 sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
1600 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1601 return __detail::__sph_legendre<__type>(__l, __m, __theta);
1605 sph_neumannf(unsigned int __n, float __x)
1606 { return __detail::__sph_neumann<float>(__n, __x); }
1609 sph_neumannl(unsigned int __n, long double __x)
1610 { return __detail::__sph_neumann<long double>(__n, __x); }
1612 /// 5.2.1.23 Spherical Neumann functions.
1613 template<typename _Tp>
1614 inline typename __gnu_cxx::__promote<_Tp>::__type
1615 sph_neumann(unsigned int __n, _Tp __x)
1617 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1618 return __detail::__sph_neumann<__type>(__n, __x);
1621 /// @} tr1_math_spec_func
1625_GLIBCXX_END_NAMESPACE_VERSION
1628#endif // _GLIBCXX_USE_STD_SPEC_FUNCS
1630#if _GLIBCXX_USE_STD_SPEC_FUNCS && !defined(__STRICT_ANSI__)
1631namespace std _GLIBCXX_VISIBILITY(default)
1633_GLIBCXX_BEGIN_NAMESPACE_VERSION
1637 using __gnu_cxx::conf_hypergf;
1638 using __gnu_cxx::conf_hypergl;
1639 using __gnu_cxx::conf_hyperg;
1641 using __gnu_cxx::hypergf;
1642 using __gnu_cxx::hypergl;
1643 using __gnu_cxx::hyperg;
1646_GLIBCXX_END_NAMESPACE_VERSION
1649#else // ! (_GLIBCXX_USE_STD_SPEC_FUNCS && !defined(__STRICT_ANSI__))
1651#include <bits/stl_algobase.h>
1653#include <tr1/type_traits>
1655#include <tr1/hypergeometric.tcc>
1657namespace std _GLIBCXX_VISIBILITY(default)
1659_GLIBCXX_BEGIN_NAMESPACE_VERSION
1663 /** @addtogroup tr1_math_spec_func
1668 conf_hypergf(float __a, float __c, float __x)
1669 { return __detail::__conf_hyperg<float>(__a, __c, __x); }
1672 conf_hypergl(long double __a, long double __c, long double __x)
1673 { return __detail::__conf_hyperg<long double>(__a, __c, __x); }
1675 /// 5.2.1.7 Confluent hypergeometric functions.
1676 template<typename _Tpa, typename _Tpc, typename _Tp>
1677 inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type
1678 conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
1680 typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type;
1681 return __detail::__conf_hyperg<__type>(__a, __c, __x);
1685 hypergf(float __a, float __b, float __c, float __x)
1686 { return __detail::__hyperg<float>(__a, __b, __c, __x); }
1689 hypergl(long double __a, long double __b, long double __c, long double __x)
1690 { return __detail::__hyperg<long double>(__a, __b, __c, __x); }
1692 /// 5.2.1.17 Hypergeometric functions.
1693 template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp>
1694 inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type
1695 hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
1697 typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type;
1698 return __detail::__hyperg<__type>(__a, __b, __c, __x);
1701 /// @} tr1_math_spec_func
1705_GLIBCXX_END_NAMESPACE_VERSION
1707#endif // _GLIBCXX_USE_STD_SPEC_FUNCS && !defined(__STRICT_ANSI__)
1709#endif // _GLIBCXX_TR1_CMATH