1// TR1 cmath -*- C++ -*-
3// Copyright (C) 2006-2024 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
34#include <bits/requires_hosted.h> // TR1
38#ifdef _GLIBCXX_USE_C99_MATH_TR1
148namespace std _GLIBCXX_VISIBILITY(default)
150_GLIBCXX_BEGIN_NAMESPACE_VERSION
154#if _GLIBCXX_USE_C99_MATH_TR1
156 // Using declarations to bring names from libc's <math.h> into std::tr1.
305#if _GLIBCXX_USE_C99_MATH
306#if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC
308 /// Function template definitions [8.16.3].
309 template<typename _Tp>
310 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
314 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
315 return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
316 FP_SUBNORMAL, FP_ZERO, __type(__f));
319 template<typename _Tp>
320 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
324 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
325 return __builtin_isfinite(__type(__f));
328 template<typename _Tp>
329 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
333 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
334 return __builtin_isinf(__type(__f));
337 template<typename _Tp>
338 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
342 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
343 return __builtin_isnan(__type(__f));
346 template<typename _Tp>
347 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
351 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
352 return __builtin_isnormal(__type(__f));
355 template<typename _Tp>
356 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
360 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
361 return __builtin_signbit(__type(__f));
364 template<typename _Tp>
365 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
367 isgreater(_Tp __f1, _Tp __f2)
369 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
370 return __builtin_isgreater(__type(__f1), __type(__f2));
373 template<typename _Tp>
374 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
376 isgreaterequal(_Tp __f1, _Tp __f2)
378 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
379 return __builtin_isgreaterequal(__type(__f1), __type(__f2));
382 template<typename _Tp>
383 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
385 isless(_Tp __f1, _Tp __f2)
387 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
388 return __builtin_isless(__type(__f1), __type(__f2));
391 template<typename _Tp>
392 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
394 islessequal(_Tp __f1, _Tp __f2)
396 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
397 return __builtin_islessequal(__type(__f1), __type(__f2));
400 template<typename _Tp>
401 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
403 islessgreater(_Tp __f1, _Tp __f2)
405 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
406 return __builtin_islessgreater(__type(__f1), __type(__f2));
409 template<typename _Tp>
410 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
412 isunordered(_Tp __f1, _Tp __f2)
414 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
415 return __builtin_isunordered(__type(__f1), __type(__f2));
421#if _GLIBCXX_USE_C99_MATH_TR1
423 /** Additional overloads [8.16.4].
427 // For functions defined in C++03 the additional overloads are already
428 // declared in <cmath> so we can just re-declare them in std::tr1.
450#if __cplusplus >= 201103L
452 // Since C++11, <cmath> defines additional overloads for these functions
479 using std::nearbyint;
480 using std::nextafter;
481 using std::nexttoward;
482 using std::remainder;
491#else // __cplusplus < 201103L
493 // In C++03 we need to provide the additional overloads.
495#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
498 { return __builtin_acoshf(__x); }
501 acosh(long double __x)
502 { return __builtin_acoshl(__x); }
505 template<typename _Tp>
506 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
509 { return __builtin_acosh(__x); }
511#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
514 { return __builtin_asinhf(__x); }
517 asinh(long double __x)
518 { return __builtin_asinhl(__x); }
521 template<typename _Tp>
522 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
525 { return __builtin_asinh(__x); }
527#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
530 { return __builtin_atanhf(__x); }
533 atanh(long double __x)
534 { return __builtin_atanhl(__x); }
537 template<typename _Tp>
538 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
541 { return __builtin_atanh(__x); }
543#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
546 { return __builtin_cbrtf(__x); }
549 cbrt(long double __x)
550 { return __builtin_cbrtl(__x); }
553 template<typename _Tp>
554 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
557 { return __builtin_cbrt(__x); }
559#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
561 copysign(float __x, float __y)
562 { return __builtin_copysignf(__x, __y); }
565 copysign(long double __x, long double __y)
566 { return __builtin_copysignl(__x, __y); }
569 template<typename _Tp, typename _Up>
570 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
571 copysign(_Tp __x, _Up __y)
573 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
574 return copysign(__type(__x), __type(__y));
577#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
580 { return __builtin_erff(__x); }
584 { return __builtin_erfl(__x); }
587 template<typename _Tp>
588 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
591 { return __builtin_erf(__x); }
593#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
596 { return __builtin_erfcf(__x); }
599 erfc(long double __x)
600 { return __builtin_erfcl(__x); }
603 template<typename _Tp>
604 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
607 { return __builtin_erfc(__x); }
609#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
612 { return __builtin_exp2f(__x); }
615 exp2(long double __x)
616 { return __builtin_exp2l(__x); }
619 template<typename _Tp>
620 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
623 { return __builtin_exp2(__x); }
625#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
628 { return __builtin_expm1f(__x); }
631 expm1(long double __x)
632 { return __builtin_expm1l(__x); }
635 template<typename _Tp>
636 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
639 { return __builtin_expm1(__x); }
641#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
643 fdim(float __x, float __y)
644 { return __builtin_fdimf(__x, __y); }
647 fdim(long double __x, long double __y)
648 { return __builtin_fdiml(__x, __y); }
651 template<typename _Tp, typename _Up>
652 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
653 fdim(_Tp __x, _Up __y)
655 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
656 return fdim(__type(__x), __type(__y));
659#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
661 fma(float __x, float __y, float __z)
662 { return __builtin_fmaf(__x, __y, __z); }
665 fma(long double __x, long double __y, long double __z)
666 { return __builtin_fmal(__x, __y, __z); }
669 template<typename _Tp, typename _Up, typename _Vp>
670 inline typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
671 fma(_Tp __x, _Up __y, _Vp __z)
673 typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type;
674 return fma(__type(__x), __type(__y), __type(__z));
677#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
679 fmax(float __x, float __y)
680 { return __builtin_fmaxf(__x, __y); }
683 fmax(long double __x, long double __y)
684 { return __builtin_fmaxl(__x, __y); }
687 template<typename _Tp, typename _Up>
688 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
689 fmax(_Tp __x, _Up __y)
691 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
692 return fmax(__type(__x), __type(__y));
695#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
697 fmin(float __x, float __y)
698 { return __builtin_fminf(__x, __y); }
701 fmin(long double __x, long double __y)
702 { return __builtin_fminl(__x, __y); }
705 template<typename _Tp, typename _Up>
706 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
707 fmin(_Tp __x, _Up __y)
709 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
710 return fmin(__type(__x), __type(__y));
713#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
715 hypot(float __x, float __y)
716 { return __builtin_hypotf(__x, __y); }
719 hypot(long double __x, long double __y)
720 { return __builtin_hypotl(__x, __y); }
723 template<typename _Tp, typename _Up>
724 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
725 hypot(_Tp __y, _Up __x)
727 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
728 return hypot(__type(__y), __type(__x));
731#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
734 { return __builtin_ilogbf(__x); }
737 ilogb(long double __x)
738 { return __builtin_ilogbl(__x); }
741 template<typename _Tp>
742 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
745 { return __builtin_ilogb(__x); }
747#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
750 { return __builtin_lgammaf(__x); }
753 lgamma(long double __x)
754 { return __builtin_lgammal(__x); }
757 template<typename _Tp>
758 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
761 { return __builtin_lgamma(__x); }
763#pragma GCC diagnostic push
764#pragma GCC diagnostic ignored "-Wlong-long"
766#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
769 { return __builtin_llrintf(__x); }
772 llrint(long double __x)
773 { return __builtin_llrintl(__x); }
776 template<typename _Tp>
777 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
780 { return __builtin_llrint(__x); }
782#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
785 { return __builtin_llroundf(__x); }
788 llround(long double __x)
789 { return __builtin_llroundl(__x); }
792 template<typename _Tp>
793 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
796 { return __builtin_llround(__x); }
797#pragma GCC diagnostic pop
799#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
802 { return __builtin_log1pf(__x); }
805 log1p(long double __x)
806 { return __builtin_log1pl(__x); }
809 template<typename _Tp>
810 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
813 { return __builtin_log1p(__x); }
816#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
819 { return __builtin_log2f(__x); }
822 log2(long double __x)
823 { return __builtin_log2l(__x); }
826 template<typename _Tp>
827 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
830 { return __builtin_log2(__x); }
832#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
835 { return __builtin_logbf(__x); }
838 logb(long double __x)
839 { return __builtin_logbl(__x); }
842 template<typename _Tp>
843 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
847 return __builtin_logb(__x);
850#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
853 { return __builtin_lrintf(__x); }
856 lrint(long double __x)
857 { return __builtin_lrintl(__x); }
860 template<typename _Tp>
861 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
864 { return __builtin_lrint(__x); }
866#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
869 { return __builtin_lroundf(__x); }
872 lround(long double __x)
873 { return __builtin_lroundl(__x); }
876 template<typename _Tp>
877 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
880 { return __builtin_lround(__x); }
882#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
885 { return __builtin_nearbyintf(__x); }
888 nearbyint(long double __x)
889 { return __builtin_nearbyintl(__x); }
892 template<typename _Tp>
893 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
896 { return __builtin_nearbyint(__x); }
898#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
900 nextafter(float __x, float __y)
901 { return __builtin_nextafterf(__x, __y); }
904 nextafter(long double __x, long double __y)
905 { return __builtin_nextafterl(__x, __y); }
908 template<typename _Tp, typename _Up>
909 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
910 nextafter(_Tp __x, _Up __y)
912 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
913 return nextafter(__type(__x), __type(__y));
916#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
918 nexttoward(float __x, long double __y)
919 { return __builtin_nexttowardf(__x, __y); }
922 nexttoward(long double __x, long double __y)
923 { return __builtin_nexttowardl(__x, __y); }
926 template<typename _Tp>
927 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
929 nexttoward(_Tp __x, long double __y)
930 { return __builtin_nexttoward(__x, __y); }
932#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
934 remainder(float __x, float __y)
935 { return __builtin_remainderf(__x, __y); }
938 remainder(long double __x, long double __y)
939 { return __builtin_remainderl(__x, __y); }
942 template<typename _Tp, typename _Up>
943 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
944 remainder(_Tp __x, _Up __y)
946 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
947 return remainder(__type(__x), __type(__y));
950#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
952 remquo(float __x, float __y, int* __pquo)
953 { return __builtin_remquof(__x, __y, __pquo); }
956 remquo(long double __x, long double __y, int* __pquo)
957 { return __builtin_remquol(__x, __y, __pquo); }
960 template<typename _Tp, typename _Up>
961 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
962 remquo(_Tp __x, _Up __y, int* __pquo)
964 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
965 return remquo(__type(__x), __type(__y), __pquo);
968#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
971 { return __builtin_rintf(__x); }
974 rint(long double __x)
975 { return __builtin_rintl(__x); }
978 template<typename _Tp>
979 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
982 { return __builtin_rint(__x); }
984#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
987 { return __builtin_roundf(__x); }
990 round(long double __x)
991 { return __builtin_roundl(__x); }
994 template<typename _Tp>
995 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
998 { return __builtin_round(__x); }
1000#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1002 scalbln(float __x, long __ex)
1003 { return __builtin_scalblnf(__x, __ex); }
1006 scalbln(long double __x, long __ex)
1007 { return __builtin_scalblnl(__x, __ex); }
1010 template<typename _Tp>
1011 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1013 scalbln(_Tp __x, long __ex)
1014 { return __builtin_scalbln(__x, __ex); }
1016#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1018 scalbn(float __x, int __ex)
1019 { return __builtin_scalbnf(__x, __ex); }
1022 scalbn(long double __x, int __ex)
1023 { return __builtin_scalbnl(__x, __ex); }
1026 template<typename _Tp>
1027 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1029 scalbn(_Tp __x, int __ex)
1030 { return __builtin_scalbn(__x, __ex); }
1032#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1035 { return __builtin_tgammaf(__x); }
1038 tgamma(long double __x)
1039 { return __builtin_tgammal(__x); }
1042 template<typename _Tp>
1043 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1046 { return __builtin_tgamma(__x); }
1048#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1051 { return __builtin_truncf(__x); }
1054 trunc(long double __x)
1055 { return __builtin_truncl(__x); }
1058 template<typename _Tp>
1059 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1062 { return __builtin_trunc(__x); }
1064#endif // __cplusplus < 201103L
1068#endif /* _GLIBCXX_USE_C99_MATH_TR1 */
1070 // DR 550. What should the return type of pow(float,int) be?
1071 // NB: C++11 and TR1 != C++03.
1073 // We cannot do "using std::pow;" because that would bring in unwanted
1074 // pow(*, int) overloads in C++03, with the wrong return type. Instead we
1075 // define all the necessary overloads, but the std::tr1::pow(double, double)
1076 // overload cannot be provided here, because <tr1/math.h> would add it to
1077 // the global namespace where it would clash with ::pow(double,double) from
1078 // libc (revealed by the fix of PR c++/54537).
1079 // The solution is to forward std::tr1::pow(double,double) to
1080 // std::pow(double,double) via the function template below. See
1081 // the discussion about this issue here:
1082 // http://gcc.gnu.org/ml/gcc-patches/2012-09/msg01278.html
1084#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1086 pow(float __x, float __y)
1087 { return std::pow(__x, __y); }
1090 pow(long double __x, long double __y)
1091 { return std::pow(__x, __y); }
1094 template<typename _Tp, typename _Up>
1095 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1096 pow(_Tp __x, _Up __y)
1098 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1099 return std::pow(__type(__x), __type(__y));
1102#if __cplusplus >= 201103L
1103 // We also deal with fabs in a special way, because "using std::fabs;"
1104 // could bring in C++11's std::fabs<T>(const std::complex<T>&) with a
1105 // different return type from std::tr1::fabs<T>(const std::complex<T>&).
1106 // We define the necessary overloads, except std::tr1::fabs(double) which
1107 // could clash with ::fabs(double) from libc.
1108 // The function template handles double as well as integers, forwarding
1111#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
1112#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1115 { return __builtin_fabsf(__x); }
1118 fabs(long double __x)
1119 { return __builtin_fabsl(__x); }
1123 template<typename _Tp>
1124 inline typename __gnu_cxx::__promote<_Tp>::__type
1126 { return std::fabs(__x); }
1130 // For C++03 just use std::fabs as there is no overload for std::complex<>.
1136_GLIBCXX_END_NAMESPACE_VERSION
1140 * @defgroup tr1_math_spec_func TR1 Mathematical Special Functions
1143 * A collection of advanced mathematical special functions.
1146#if _GLIBCXX_USE_STD_SPEC_FUNCS
1148namespace std _GLIBCXX_VISIBILITY(default)
1150_GLIBCXX_BEGIN_NAMESPACE_VERSION
1154 using std::assoc_laguerref;
1155 using std::assoc_laguerrel;
1156 using std::assoc_laguerre;
1158 using std::assoc_legendref;
1159 using std::assoc_legendrel;
1160 using std::assoc_legendre;
1166 using std::comp_ellint_1f;
1167 using std::comp_ellint_1l;
1168 using std::comp_ellint_1;
1170 using std::comp_ellint_2f;
1171 using std::comp_ellint_2l;
1172 using std::comp_ellint_2;
1174 using std::comp_ellint_3f;
1175 using std::comp_ellint_3l;
1176 using std::comp_ellint_3;
1178 using std::cyl_bessel_if;
1179 using std::cyl_bessel_il;
1180 using std::cyl_bessel_i;
1182 using std::cyl_bessel_jf;
1183 using std::cyl_bessel_jl;
1184 using std::cyl_bessel_j;
1186 using std::cyl_bessel_kf;
1187 using std::cyl_bessel_kl;
1188 using std::cyl_bessel_k;
1190 using std::cyl_neumannf;
1191 using std::cyl_neumannl;
1192 using std::cyl_neumann;
1194 using std::ellint_1f;
1195 using std::ellint_1l;
1196 using std::ellint_1;
1198 using std::ellint_2f;
1199 using std::ellint_2l;
1200 using std::ellint_2;
1202 using std::ellint_3f;
1203 using std::ellint_3l;
1204 using std::ellint_3;
1210 using std::hermitef;
1211 using std::hermitel;
1214 using std::laguerref;
1215 using std::laguerrel;
1216 using std::laguerre;
1218 using std::legendref;
1219 using std::legendrel;
1220 using std::legendre;
1222 using std::riemann_zetaf;
1223 using std::riemann_zetal;
1224 using std::riemann_zeta;
1226 using std::sph_besself;
1227 using std::sph_bessell;
1228 using std::sph_bessel;
1230 using std::sph_legendref;
1231 using std::sph_legendrel;
1232 using std::sph_legendre;
1234 using std::sph_neumannf;
1235 using std::sph_neumannl;
1236 using std::sph_neumann;
1239_GLIBCXX_END_NAMESPACE_VERSION
1242#else // ! _GLIBCXX_USE_STD_SPEC_FUNCS
1244#include <bits/stl_algobase.h>
1246#include <tr1/type_traits>
1248#include <tr1/gamma.tcc>
1249#include <tr1/bessel_function.tcc>
1250#include <tr1/beta_function.tcc>
1251#include <tr1/ell_integral.tcc>
1252#include <tr1/exp_integral.tcc>
1253#include <tr1/legendre_function.tcc>
1254#include <tr1/modified_bessel_func.tcc>
1255#include <tr1/poly_hermite.tcc>
1256#include <tr1/poly_laguerre.tcc>
1257#include <tr1/riemann_zeta.tcc>
1259namespace std _GLIBCXX_VISIBILITY(default)
1261_GLIBCXX_BEGIN_NAMESPACE_VERSION
1264 /** @addtogroup tr1_math_spec_func
1269 assoc_laguerref(unsigned int __n, unsigned int __m, float __x)
1270 { return __detail::__assoc_laguerre<float>(__n, __m, __x); }
1273 assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x)
1275 return __detail::__assoc_laguerre<long double>(__n, __m, __x);
1278 /// 5.2.1.1 Associated Laguerre polynomials.
1279 template<typename _Tp>
1280 inline typename __gnu_cxx::__promote<_Tp>::__type
1281 assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
1283 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1284 return __detail::__assoc_laguerre<__type>(__n, __m, __x);
1288 assoc_legendref(unsigned int __l, unsigned int __m, float __x)
1289 { return __detail::__assoc_legendre_p<float>(__l, __m, __x); }
1292 assoc_legendrel(unsigned int __l, unsigned int __m, long double __x)
1293 { return __detail::__assoc_legendre_p<long double>(__l, __m, __x); }
1295 /// 5.2.1.2 Associated Legendre functions.
1296 template<typename _Tp>
1297 inline typename __gnu_cxx::__promote<_Tp>::__type
1298 assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
1300 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1301 return __detail::__assoc_legendre_p<__type>(__l, __m, __x);
1305 betaf(float __x, float __y)
1306 { return __detail::__beta<float>(__x, __y); }
1309 betal(long double __x, long double __y)
1310 { return __detail::__beta<long double>(__x, __y); }
1312 /// 5.2.1.3 Beta functions.
1313 template<typename _Tpx, typename _Tpy>
1314 inline typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type
1315 beta(_Tpx __x, _Tpy __y)
1317 typedef typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type __type;
1318 return __detail::__beta<__type>(__x, __y);
1322 comp_ellint_1f(float __k)
1323 { return __detail::__comp_ellint_1<float>(__k); }
1326 comp_ellint_1l(long double __k)
1327 { return __detail::__comp_ellint_1<long double>(__k); }
1329 /// 5.2.1.4 Complete elliptic integrals of the first kind.
1330 template<typename _Tp>
1331 inline typename __gnu_cxx::__promote<_Tp>::__type
1332 comp_ellint_1(_Tp __k)
1334 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1335 return __detail::__comp_ellint_1<__type>(__k);
1339 comp_ellint_2f(float __k)
1340 { return __detail::__comp_ellint_2<float>(__k); }
1343 comp_ellint_2l(long double __k)
1344 { return __detail::__comp_ellint_2<long double>(__k); }
1346 /// 5.2.1.5 Complete elliptic integrals of the second kind.
1347 template<typename _Tp>
1348 inline typename __gnu_cxx::__promote<_Tp>::__type
1349 comp_ellint_2(_Tp __k)
1351 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1352 return __detail::__comp_ellint_2<__type>(__k);
1356 comp_ellint_3f(float __k, float __nu)
1357 { return __detail::__comp_ellint_3<float>(__k, __nu); }
1360 comp_ellint_3l(long double __k, long double __nu)
1361 { return __detail::__comp_ellint_3<long double>(__k, __nu); }
1363 /// 5.2.1.6 Complete elliptic integrals of the third kind.
1364 template<typename _Tp, typename _Tpn>
1365 inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type
1366 comp_ellint_3(_Tp __k, _Tpn __nu)
1368 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type;
1369 return __detail::__comp_ellint_3<__type>(__k, __nu);
1373 cyl_bessel_if(float __nu, float __x)
1374 { return __detail::__cyl_bessel_i<float>(__nu, __x); }
1377 cyl_bessel_il(long double __nu, long double __x)
1378 { return __detail::__cyl_bessel_i<long double>(__nu, __x); }
1380 /// 5.2.1.8 Regular modified cylindrical Bessel functions.
1381 template<typename _Tpnu, typename _Tp>
1382 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1383 cyl_bessel_i(_Tpnu __nu, _Tp __x)
1385 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1386 return __detail::__cyl_bessel_i<__type>(__nu, __x);
1390 cyl_bessel_jf(float __nu, float __x)
1391 { return __detail::__cyl_bessel_j<float>(__nu, __x); }
1394 cyl_bessel_jl(long double __nu, long double __x)
1395 { return __detail::__cyl_bessel_j<long double>(__nu, __x); }
1397 /// 5.2.1.9 Cylindrical Bessel functions (of the first kind).
1398 template<typename _Tpnu, typename _Tp>
1399 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1400 cyl_bessel_j(_Tpnu __nu, _Tp __x)
1402 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1403 return __detail::__cyl_bessel_j<__type>(__nu, __x);
1407 cyl_bessel_kf(float __nu, float __x)
1408 { return __detail::__cyl_bessel_k<float>(__nu, __x); }
1411 cyl_bessel_kl(long double __nu, long double __x)
1412 { return __detail::__cyl_bessel_k<long double>(__nu, __x); }
1414 /// 5.2.1.10 Irregular modified cylindrical Bessel functions.
1415 template<typename _Tpnu, typename _Tp>
1416 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1417 cyl_bessel_k(_Tpnu __nu, _Tp __x)
1419 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1420 return __detail::__cyl_bessel_k<__type>(__nu, __x);
1424 cyl_neumannf(float __nu, float __x)
1425 { return __detail::__cyl_neumann_n<float>(__nu, __x); }
1428 cyl_neumannl(long double __nu, long double __x)
1429 { return __detail::__cyl_neumann_n<long double>(__nu, __x); }
1431 /// 5.2.1.11 Cylindrical Neumann functions.
1432 template<typename _Tpnu, typename _Tp>
1433 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1434 cyl_neumann(_Tpnu __nu, _Tp __x)
1436 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1437 return __detail::__cyl_neumann_n<__type>(__nu, __x);
1441 ellint_1f(float __k, float __phi)
1442 { return __detail::__ellint_1<float>(__k, __phi); }
1445 ellint_1l(long double __k, long double __phi)
1446 { return __detail::__ellint_1<long double>(__k, __phi); }
1448 /// 5.2.1.12 Incomplete elliptic integrals of the first kind.
1449 template<typename _Tp, typename _Tpp>
1450 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
1451 ellint_1(_Tp __k, _Tpp __phi)
1453 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
1454 return __detail::__ellint_1<__type>(__k, __phi);
1458 ellint_2f(float __k, float __phi)
1459 { return __detail::__ellint_2<float>(__k, __phi); }
1462 ellint_2l(long double __k, long double __phi)
1463 { return __detail::__ellint_2<long double>(__k, __phi); }
1465 /// 5.2.1.13 Incomplete elliptic integrals of the second kind.
1466 template<typename _Tp, typename _Tpp>
1467 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
1468 ellint_2(_Tp __k, _Tpp __phi)
1470 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
1471 return __detail::__ellint_2<__type>(__k, __phi);
1475 ellint_3f(float __k, float __nu, float __phi)
1476 { return __detail::__ellint_3<float>(__k, __nu, __phi); }
1479 ellint_3l(long double __k, long double __nu, long double __phi)
1480 { return __detail::__ellint_3<long double>(__k, __nu, __phi); }
1482 /// 5.2.1.14 Incomplete elliptic integrals of the third kind.
1483 template<typename _Tp, typename _Tpn, typename _Tpp>
1484 inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type
1485 ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
1487 typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type;
1488 return __detail::__ellint_3<__type>(__k, __nu, __phi);
1493 { return __detail::__expint<float>(__x); }
1496 expintl(long double __x)
1497 { return __detail::__expint<long double>(__x); }
1499 /// 5.2.1.15 Exponential integrals.
1500 template<typename _Tp>
1501 inline typename __gnu_cxx::__promote<_Tp>::__type
1504 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1505 return __detail::__expint<__type>(__x);
1509 hermitef(unsigned int __n, float __x)
1510 { return __detail::__poly_hermite<float>(__n, __x); }
1513 hermitel(unsigned int __n, long double __x)
1514 { return __detail::__poly_hermite<long double>(__n, __x); }
1516 /// 5.2.1.16 Hermite polynomials.
1517 template<typename _Tp>
1518 inline typename __gnu_cxx::__promote<_Tp>::__type
1519 hermite(unsigned int __n, _Tp __x)
1521 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1522 return __detail::__poly_hermite<__type>(__n, __x);
1526 laguerref(unsigned int __n, float __x)
1527 { return __detail::__laguerre<float>(__n, __x); }
1530 laguerrel(unsigned int __n, long double __x)
1531 { return __detail::__laguerre<long double>(__n, __x); }
1533 /// 5.2.1.18 Laguerre polynomials.
1534 template<typename _Tp>
1535 inline typename __gnu_cxx::__promote<_Tp>::__type
1536 laguerre(unsigned int __n, _Tp __x)
1538 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1539 return __detail::__laguerre<__type>(__n, __x);
1543 legendref(unsigned int __n, float __x)
1544 { return __detail::__poly_legendre_p<float>(__n, __x); }
1547 legendrel(unsigned int __n, long double __x)
1548 { return __detail::__poly_legendre_p<long double>(__n, __x); }
1550 /// 5.2.1.19 Legendre polynomials.
1551 template<typename _Tp>
1552 inline typename __gnu_cxx::__promote<_Tp>::__type
1553 legendre(unsigned int __n, _Tp __x)
1555 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1556 return __detail::__poly_legendre_p<__type>(__n, __x);
1560 riemann_zetaf(float __x)
1561 { return __detail::__riemann_zeta<float>(__x); }
1564 riemann_zetal(long double __x)
1565 { return __detail::__riemann_zeta<long double>(__x); }
1567 /// 5.2.1.20 Riemann zeta function.
1568 template<typename _Tp>
1569 inline typename __gnu_cxx::__promote<_Tp>::__type
1570 riemann_zeta(_Tp __x)
1572 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1573 return __detail::__riemann_zeta<__type>(__x);
1577 sph_besself(unsigned int __n, float __x)
1578 { return __detail::__sph_bessel<float>(__n, __x); }
1581 sph_bessell(unsigned int __n, long double __x)
1582 { return __detail::__sph_bessel<long double>(__n, __x); }
1584 /// 5.2.1.21 Spherical Bessel functions.
1585 template<typename _Tp>
1586 inline typename __gnu_cxx::__promote<_Tp>::__type
1587 sph_bessel(unsigned int __n, _Tp __x)
1589 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1590 return __detail::__sph_bessel<__type>(__n, __x);
1594 sph_legendref(unsigned int __l, unsigned int __m, float __theta)
1595 { return __detail::__sph_legendre<float>(__l, __m, __theta); }
1598 sph_legendrel(unsigned int __l, unsigned int __m, long double __theta)
1599 { return __detail::__sph_legendre<long double>(__l, __m, __theta); }
1601 /// 5.2.1.22 Spherical associated Legendre functions.
1602 template<typename _Tp>
1603 inline typename __gnu_cxx::__promote<_Tp>::__type
1604 sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
1606 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1607 return __detail::__sph_legendre<__type>(__l, __m, __theta);
1611 sph_neumannf(unsigned int __n, float __x)
1612 { return __detail::__sph_neumann<float>(__n, __x); }
1615 sph_neumannl(unsigned int __n, long double __x)
1616 { return __detail::__sph_neumann<long double>(__n, __x); }
1618 /// 5.2.1.23 Spherical Neumann functions.
1619 template<typename _Tp>
1620 inline typename __gnu_cxx::__promote<_Tp>::__type
1621 sph_neumann(unsigned int __n, _Tp __x)
1623 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1624 return __detail::__sph_neumann<__type>(__n, __x);
1627 /// @} tr1_math_spec_func
1631_GLIBCXX_END_NAMESPACE_VERSION
1634#endif // _GLIBCXX_USE_STD_SPEC_FUNCS
1636#if _GLIBCXX_USE_STD_SPEC_FUNCS && !defined(__STRICT_ANSI__)
1637namespace std _GLIBCXX_VISIBILITY(default)
1639_GLIBCXX_BEGIN_NAMESPACE_VERSION
1643 using __gnu_cxx::conf_hypergf;
1644 using __gnu_cxx::conf_hypergl;
1645 using __gnu_cxx::conf_hyperg;
1647 using __gnu_cxx::hypergf;
1648 using __gnu_cxx::hypergl;
1649 using __gnu_cxx::hyperg;
1652_GLIBCXX_END_NAMESPACE_VERSION
1655#else // ! (_GLIBCXX_USE_STD_SPEC_FUNCS && !defined(__STRICT_ANSI__))
1657#include <bits/stl_algobase.h>
1659#include <tr1/type_traits>
1661#include <tr1/hypergeometric.tcc>
1663namespace std _GLIBCXX_VISIBILITY(default)
1665_GLIBCXX_BEGIN_NAMESPACE_VERSION
1669 /** @addtogroup tr1_math_spec_func
1674 conf_hypergf(float __a, float __c, float __x)
1675 { return __detail::__conf_hyperg<float>(__a, __c, __x); }
1678 conf_hypergl(long double __a, long double __c, long double __x)
1679 { return __detail::__conf_hyperg<long double>(__a, __c, __x); }
1681 /// 5.2.1.7 Confluent hypergeometric functions.
1682 template<typename _Tpa, typename _Tpc, typename _Tp>
1683 inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type
1684 conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
1686 typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type;
1687 return __detail::__conf_hyperg<__type>(__a, __c, __x);
1691 hypergf(float __a, float __b, float __c, float __x)
1692 { return __detail::__hyperg<float>(__a, __b, __c, __x); }
1695 hypergl(long double __a, long double __b, long double __c, long double __x)
1696 { return __detail::__hyperg<long double>(__a, __b, __c, __x); }
1698 /// 5.2.1.17 Hypergeometric functions.
1699 template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp>
1700 inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type
1701 hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
1703 typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type;
1704 return __detail::__hyperg<__type>(__a, __b, __c, __x);
1707 /// @} tr1_math_spec_func
1711_GLIBCXX_END_NAMESPACE_VERSION
1713#endif // _GLIBCXX_USE_STD_SPEC_FUNCS && !defined(__STRICT_ANSI__)
1715#endif // _GLIBCXX_TR1_CMATH