1 // TR1 cmath -*- C++ -*-
3 // Copyright (C) 2006, 2007, 2008, 2009, 2010, 2011
4 // Free Software Foundation, Inc.
6 // This file is part of the GNU ISO C++ Library. This library is free
7 // software; you can redistribute it and/or modify it under the
8 // terms of the GNU General Public License as published by the
9 // Free Software Foundation; either version 3, or (at your option)
12 // This library is distributed in the hope that it will be useful,
13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 // GNU General Public License for more details.
17 // Under Section 7 of GPL version 3, you are granted additional
18 // permissions described in the GCC Runtime Library Exception, version
19 // 3.1, as published by the Free Software Foundation.
21 // You should have received a copy of the GNU General Public License and
22 // a copy of the GCC Runtime Library Exception along with this program;
23 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
24 // <http://www.gnu.org/licenses/>.
27 * This is a TR1 C++ Library header.
30 #ifndef _GLIBCXX_TR1_CMATH
31 #define _GLIBCXX_TR1_CMATH 1
33 #pragma GCC system_header
37 #ifdef _GLIBCXX_USE_C99_MATH_TR1
147 namespace std _GLIBCXX_VISIBILITY(default)
151 _GLIBCXX_BEGIN_NAMESPACE_VERSION
153 #if _GLIBCXX_USE_C99_MATH_TR1
302 #if _GLIBCXX_USE_C99_MATH
303 #if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC
305 /// Function template definitions [8.16.3].
306 template<typename _Tp>
307 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
311 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
312 return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
313 FP_SUBNORMAL, FP_ZERO, __type(__f));
316 template<typename _Tp>
317 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
321 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
322 return __builtin_isfinite(__type(__f));
325 template<typename _Tp>
326 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
330 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
331 return __builtin_isinf(__type(__f));
334 template<typename _Tp>
335 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
339 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
340 return __builtin_isnan(__type(__f));
343 template<typename _Tp>
344 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
348 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
349 return __builtin_isnormal(__type(__f));
352 template<typename _Tp>
353 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
357 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
358 return __builtin_signbit(__type(__f));
361 template<typename _Tp>
362 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
364 isgreater(_Tp __f1, _Tp __f2)
366 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
367 return __builtin_isgreater(__type(__f1), __type(__f2));
370 template<typename _Tp>
371 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
373 isgreaterequal(_Tp __f1, _Tp __f2)
375 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
376 return __builtin_isgreaterequal(__type(__f1), __type(__f2));
379 template<typename _Tp>
380 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
382 isless(_Tp __f1, _Tp __f2)
384 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
385 return __builtin_isless(__type(__f1), __type(__f2));
388 template<typename _Tp>
389 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
391 islessequal(_Tp __f1, _Tp __f2)
393 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
394 return __builtin_islessequal(__type(__f1), __type(__f2));
397 template<typename _Tp>
398 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
400 islessgreater(_Tp __f1, _Tp __f2)
402 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
403 return __builtin_islessgreater(__type(__f1), __type(__f2));
406 template<typename _Tp>
407 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
409 isunordered(_Tp __f1, _Tp __f2)
411 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
412 return __builtin_isunordered(__type(__f1), __type(__f2));
418 #if _GLIBCXX_USE_C99_MATH_TR1
420 /// Additional overloads [8.16.4].
425 { return __builtin_acoshf(__x); }
428 acosh(long double __x)
429 { return __builtin_acoshl(__x); }
431 template<typename _Tp>
432 inline typename __gnu_cxx::__promote<_Tp>::__type
435 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
436 return acosh(__type(__x));
443 { return __builtin_asinhf(__x); }
446 asinh(long double __x)
447 { return __builtin_asinhl(__x); }
449 template<typename _Tp>
450 inline typename __gnu_cxx::__promote<_Tp>::__type
453 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
454 return asinh(__type(__x));
462 { return __builtin_atanhf(__x); }
465 atanh(long double __x)
466 { return __builtin_atanhl(__x); }
468 template<typename _Tp>
469 inline typename __gnu_cxx::__promote<_Tp>::__type
472 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
473 return atanh(__type(__x));
478 { return __builtin_cbrtf(__x); }
481 cbrt(long double __x)
482 { return __builtin_cbrtl(__x); }
484 template<typename _Tp>
485 inline typename __gnu_cxx::__promote<_Tp>::__type
488 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
489 return cbrt(__type(__x));
495 copysign(float __x, float __y)
496 { return __builtin_copysignf(__x, __y); }
499 copysign(long double __x, long double __y)
500 { return __builtin_copysignl(__x, __y); }
502 template<typename _Tp, typename _Up>
503 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
504 copysign(_Tp __x, _Up __y)
506 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
507 return copysign(__type(__x), __type(__y));
515 { return __builtin_erff(__x); }
519 { return __builtin_erfl(__x); }
521 template<typename _Tp>
522 inline typename __gnu_cxx::__promote<_Tp>::__type
525 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
526 return erf(__type(__x));
531 { return __builtin_erfcf(__x); }
534 erfc(long double __x)
535 { return __builtin_erfcl(__x); }
537 template<typename _Tp>
538 inline typename __gnu_cxx::__promote<_Tp>::__type
541 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
542 return erfc(__type(__x));
549 { return __builtin_exp2f(__x); }
552 exp2(long double __x)
553 { return __builtin_exp2l(__x); }
555 template<typename _Tp>
556 inline typename __gnu_cxx::__promote<_Tp>::__type
559 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
560 return exp2(__type(__x));
565 { return __builtin_expm1f(__x); }
568 expm1(long double __x)
569 { return __builtin_expm1l(__x); }
571 template<typename _Tp>
572 inline typename __gnu_cxx::__promote<_Tp>::__type
575 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
576 return expm1(__type(__x));
579 // Note: we deal with fabs in a special way, because an using std::fabs
580 // would bring in also the overloads for complex types, which in C++0x
581 // mode have a different return type.
586 { return __builtin_fabsf(__x); }
589 fabs(long double __x)
590 { return __builtin_fabsl(__x); }
592 template<typename _Tp>
593 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
596 { return __builtin_fabs(__x); }
599 fdim(float __x, float __y)
600 { return __builtin_fdimf(__x, __y); }
603 fdim(long double __x, long double __y)
604 { return __builtin_fdiml(__x, __y); }
606 template<typename _Tp, typename _Up>
607 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
608 fdim(_Tp __x, _Up __y)
610 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
611 return fdim(__type(__x), __type(__y));
617 fma(float __x, float __y, float __z)
618 { return __builtin_fmaf(__x, __y, __z); }
621 fma(long double __x, long double __y, long double __z)
622 { return __builtin_fmal(__x, __y, __z); }
624 template<typename _Tp, typename _Up, typename _Vp>
625 inline typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
626 fma(_Tp __x, _Up __y, _Vp __z)
628 typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type;
629 return fma(__type(__x), __type(__y), __type(__z));
633 fmax(float __x, float __y)
634 { return __builtin_fmaxf(__x, __y); }
637 fmax(long double __x, long double __y)
638 { return __builtin_fmaxl(__x, __y); }
640 template<typename _Tp, typename _Up>
641 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
642 fmax(_Tp __x, _Up __y)
644 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
645 return fmax(__type(__x), __type(__y));
649 fmin(float __x, float __y)
650 { return __builtin_fminf(__x, __y); }
653 fmin(long double __x, long double __y)
654 { return __builtin_fminl(__x, __y); }
656 template<typename _Tp, typename _Up>
657 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
658 fmin(_Tp __x, _Up __y)
660 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
661 return fmin(__type(__x), __type(__y));
668 hypot(float __x, float __y)
669 { return __builtin_hypotf(__x, __y); }
672 hypot(long double __x, long double __y)
673 { return __builtin_hypotl(__x, __y); }
675 template<typename _Tp, typename _Up>
676 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
677 hypot(_Tp __x, _Up __y)
679 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
680 return hypot(__type(__x), __type(__y));
685 { return __builtin_ilogbf(__x); }
688 ilogb(long double __x)
689 { return __builtin_ilogbl(__x); }
691 template<typename _Tp>
695 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
696 return ilogb(__type(__x));
703 { return __builtin_lgammaf(__x); }
706 lgamma(long double __x)
707 { return __builtin_lgammal(__x); }
709 template<typename _Tp>
710 inline typename __gnu_cxx::__promote<_Tp>::__type
713 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
714 return lgamma(__type(__x));
719 { return __builtin_llrintf(__x); }
722 llrint(long double __x)
723 { return __builtin_llrintl(__x); }
725 template<typename _Tp>
729 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
730 return llrint(__type(__x));
735 { return __builtin_llroundf(__x); }
738 llround(long double __x)
739 { return __builtin_llroundl(__x); }
741 template<typename _Tp>
745 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
746 return llround(__type(__x));
754 { return __builtin_log1pf(__x); }
757 log1p(long double __x)
758 { return __builtin_log1pl(__x); }
760 template<typename _Tp>
761 inline typename __gnu_cxx::__promote<_Tp>::__type
764 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
765 return log1p(__type(__x));
771 { return __builtin_log2f(__x); }
774 log2(long double __x)
775 { return __builtin_log2l(__x); }
777 template<typename _Tp>
778 inline typename __gnu_cxx::__promote<_Tp>::__type
781 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
782 return log2(__type(__x));
787 { return __builtin_logbf(__x); }
790 logb(long double __x)
791 { return __builtin_logbl(__x); }
793 template<typename _Tp>
794 inline typename __gnu_cxx::__promote<_Tp>::__type
797 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
798 return logb(__type(__x));
803 { return __builtin_lrintf(__x); }
806 lrint(long double __x)
807 { return __builtin_lrintl(__x); }
809 template<typename _Tp>
813 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
814 return lrint(__type(__x));
819 { return __builtin_lroundf(__x); }
822 lround(long double __x)
823 { return __builtin_lroundl(__x); }
825 template<typename _Tp>
829 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
830 return lround(__type(__x));
835 { return __builtin_nearbyintf(__x); }
838 nearbyint(long double __x)
839 { return __builtin_nearbyintl(__x); }
841 template<typename _Tp>
842 inline typename __gnu_cxx::__promote<_Tp>::__type
845 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
846 return nearbyint(__type(__x));
850 nextafter(float __x, float __y)
851 { return __builtin_nextafterf(__x, __y); }
854 nextafter(long double __x, long double __y)
855 { return __builtin_nextafterl(__x, __y); }
857 template<typename _Tp, typename _Up>
858 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
859 nextafter(_Tp __x, _Up __y)
861 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
862 return nextafter(__type(__x), __type(__y));
866 nexttoward(float __x, long double __y)
867 { return __builtin_nexttowardf(__x, __y); }
870 nexttoward(long double __x, long double __y)
871 { return __builtin_nexttowardl(__x, __y); }
873 template<typename _Tp>
874 inline typename __gnu_cxx::__promote<_Tp>::__type
875 nexttoward(_Tp __x, long double __y)
877 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
878 return nexttoward(__type(__x), __y);
881 // DR 550. What should the return type of pow(float,int) be?
882 // NB: C++0x and TR1 != C++03.
886 remainder(float __x, float __y)
887 { return __builtin_remainderf(__x, __y); }
890 remainder(long double __x, long double __y)
891 { return __builtin_remainderl(__x, __y); }
893 template<typename _Tp, typename _Up>
894 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
895 remainder(_Tp __x, _Up __y)
897 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
898 return remainder(__type(__x), __type(__y));
902 remquo(float __x, float __y, int* __pquo)
903 { return __builtin_remquof(__x, __y, __pquo); }
906 remquo(long double __x, long double __y, int* __pquo)
907 { return __builtin_remquol(__x, __y, __pquo); }
909 template<typename _Tp, typename _Up>
910 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
911 remquo(_Tp __x, _Up __y, int* __pquo)
913 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
914 return remquo(__type(__x), __type(__y), __pquo);
919 { return __builtin_rintf(__x); }
922 rint(long double __x)
923 { return __builtin_rintl(__x); }
925 template<typename _Tp>
926 inline typename __gnu_cxx::__promote<_Tp>::__type
929 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
930 return rint(__type(__x));
935 { return __builtin_roundf(__x); }
938 round(long double __x)
939 { return __builtin_roundl(__x); }
941 template<typename _Tp>
942 inline typename __gnu_cxx::__promote<_Tp>::__type
945 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
946 return round(__type(__x));
950 scalbln(float __x, long __ex)
951 { return __builtin_scalblnf(__x, __ex); }
954 scalbln(long double __x, long __ex)
955 { return __builtin_scalblnl(__x, __ex); }
957 template<typename _Tp>
958 inline typename __gnu_cxx::__promote<_Tp>::__type
959 scalbln(_Tp __x, long __ex)
961 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
962 return scalbln(__type(__x), __ex);
966 scalbn(float __x, int __ex)
967 { return __builtin_scalbnf(__x, __ex); }
970 scalbn(long double __x, int __ex)
971 { return __builtin_scalbnl(__x, __ex); }
973 template<typename _Tp>
974 inline typename __gnu_cxx::__promote<_Tp>::__type
975 scalbn(_Tp __x, int __ex)
977 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
978 return scalbn(__type(__x), __ex);
989 { return __builtin_tgammaf(__x); }
992 tgamma(long double __x)
993 { return __builtin_tgammal(__x); }
995 template<typename _Tp>
996 inline typename __gnu_cxx::__promote<_Tp>::__type
999 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1000 return tgamma(__type(__x));
1005 { return __builtin_truncf(__x); }
1008 trunc(long double __x)
1009 { return __builtin_truncl(__x); }
1011 template<typename _Tp>
1012 inline typename __gnu_cxx::__promote<_Tp>::__type
1015 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1016 return trunc(__type(__x));
1020 _GLIBCXX_END_NAMESPACE_VERSION
1024 namespace std _GLIBCXX_VISIBILITY(default)
1028 _GLIBCXX_BEGIN_NAMESPACE_VERSION
1030 // DR 550. What should the return type of pow(float,int) be?
1031 // NB: C++0x and TR1 != C++03.
1033 pow(double __x, double __y)
1034 { return std::pow(__x, __y); }
1037 pow(float __x, float __y)
1038 { return std::pow(__x, __y); }
1041 pow(long double __x, long double __y)
1042 { return std::pow(__x, __y); }
1044 template<typename _Tp, typename _Up>
1045 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1046 pow(_Tp __x, _Up __y)
1048 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1049 return std::pow(__type(__x), __type(__y));
1052 _GLIBCXX_END_NAMESPACE_VERSION
1056 #include <bits/stl_algobase.h>
1058 #include <tr1/type_traits>
1060 #include <tr1/gamma.tcc>
1061 #include <tr1/bessel_function.tcc>
1062 #include <tr1/beta_function.tcc>
1063 #include <tr1/ell_integral.tcc>
1064 #include <tr1/exp_integral.tcc>
1065 #include <tr1/hypergeometric.tcc>
1066 #include <tr1/legendre_function.tcc>
1067 #include <tr1/modified_bessel_func.tcc>
1068 #include <tr1/poly_hermite.tcc>
1069 #include <tr1/poly_laguerre.tcc>
1070 #include <tr1/riemann_zeta.tcc>
1072 namespace std _GLIBCXX_VISIBILITY(default)
1076 _GLIBCXX_BEGIN_NAMESPACE_VERSION
1079 * @defgroup tr1_math_spec_func Mathematical Special Functions
1082 * A collection of advanced mathematical special functions.
1087 assoc_laguerref(unsigned int __n, unsigned int __m, float __x)
1088 { return __detail::__assoc_laguerre<float>(__n, __m, __x); }
1091 assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x)
1093 return __detail::__assoc_laguerre<long double>(__n, __m, __x);
1096 /// 5.2.1.1 Associated Laguerre polynomials.
1097 template<typename _Tp>
1098 inline typename __gnu_cxx::__promote<_Tp>::__type
1099 assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
1101 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1102 return __detail::__assoc_laguerre<__type>(__n, __m, __x);
1106 assoc_legendref(unsigned int __l, unsigned int __m, float __x)
1107 { return __detail::__assoc_legendre_p<float>(__l, __m, __x); }
1110 assoc_legendrel(unsigned int __l, unsigned int __m, long double __x)
1111 { return __detail::__assoc_legendre_p<long double>(__l, __m, __x); }
1113 /// 5.2.1.2 Associated Legendre functions.
1114 template<typename _Tp>
1115 inline typename __gnu_cxx::__promote<_Tp>::__type
1116 assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
1118 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1119 return __detail::__assoc_legendre_p<__type>(__l, __m, __x);
1123 betaf(float __x, float __y)
1124 { return __detail::__beta<float>(__x, __y); }
1127 betal(long double __x, long double __y)
1128 { return __detail::__beta<long double>(__x, __y); }
1130 /// 5.2.1.3 Beta functions.
1131 template<typename _Tpx, typename _Tpy>
1132 inline typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type
1133 beta(_Tpx __x, _Tpy __y)
1135 typedef typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type __type;
1136 return __detail::__beta<__type>(__x, __y);
1140 comp_ellint_1f(float __k)
1141 { return __detail::__comp_ellint_1<float>(__k); }
1144 comp_ellint_1l(long double __k)
1145 { return __detail::__comp_ellint_1<long double>(__k); }
1147 /// 5.2.1.4 Complete elliptic integrals of the first kind.
1148 template<typename _Tp>
1149 inline typename __gnu_cxx::__promote<_Tp>::__type
1150 comp_ellint_1(_Tp __k)
1152 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1153 return __detail::__comp_ellint_1<__type>(__k);
1157 comp_ellint_2f(float __k)
1158 { return __detail::__comp_ellint_2<float>(__k); }
1161 comp_ellint_2l(long double __k)
1162 { return __detail::__comp_ellint_2<long double>(__k); }
1164 /// 5.2.1.5 Complete elliptic integrals of the second kind.
1165 template<typename _Tp>
1166 inline typename __gnu_cxx::__promote<_Tp>::__type
1167 comp_ellint_2(_Tp __k)
1169 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1170 return __detail::__comp_ellint_2<__type>(__k);
1174 comp_ellint_3f(float __k, float __nu)
1175 { return __detail::__comp_ellint_3<float>(__k, __nu); }
1178 comp_ellint_3l(long double __k, long double __nu)
1179 { return __detail::__comp_ellint_3<long double>(__k, __nu); }
1181 /// 5.2.1.6 Complete elliptic integrals of the third kind.
1182 template<typename _Tp, typename _Tpn>
1183 inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type
1184 comp_ellint_3(_Tp __k, _Tpn __nu)
1186 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type;
1187 return __detail::__comp_ellint_3<__type>(__k, __nu);
1191 conf_hypergf(float __a, float __c, float __x)
1192 { return __detail::__conf_hyperg<float>(__a, __c, __x); }
1195 conf_hypergl(long double __a, long double __c, long double __x)
1196 { return __detail::__conf_hyperg<long double>(__a, __c, __x); }
1198 /// 5.2.1.7 Confluent hypergeometric functions.
1199 template<typename _Tpa, typename _Tpc, typename _Tp>
1200 inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type
1201 conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
1203 typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type;
1204 return __detail::__conf_hyperg<__type>(__a, __c, __x);
1208 cyl_bessel_if(float __nu, float __x)
1209 { return __detail::__cyl_bessel_i<float>(__nu, __x); }
1212 cyl_bessel_il(long double __nu, long double __x)
1213 { return __detail::__cyl_bessel_i<long double>(__nu, __x); }
1215 /// 5.2.1.8 Regular modified cylindrical Bessel functions.
1216 template<typename _Tpnu, typename _Tp>
1217 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1218 cyl_bessel_i(_Tpnu __nu, _Tp __x)
1220 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1221 return __detail::__cyl_bessel_i<__type>(__nu, __x);
1225 cyl_bessel_jf(float __nu, float __x)
1226 { return __detail::__cyl_bessel_j<float>(__nu, __x); }
1229 cyl_bessel_jl(long double __nu, long double __x)
1230 { return __detail::__cyl_bessel_j<long double>(__nu, __x); }
1232 /// 5.2.1.9 Cylindrical Bessel functions (of the first kind).
1233 template<typename _Tpnu, typename _Tp>
1234 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1235 cyl_bessel_j(_Tpnu __nu, _Tp __x)
1237 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1238 return __detail::__cyl_bessel_j<__type>(__nu, __x);
1242 cyl_bessel_kf(float __nu, float __x)
1243 { return __detail::__cyl_bessel_k<float>(__nu, __x); }
1246 cyl_bessel_kl(long double __nu, long double __x)
1247 { return __detail::__cyl_bessel_k<long double>(__nu, __x); }
1249 /// 5.2.1.10 Irregular modified cylindrical Bessel functions.
1250 template<typename _Tpnu, typename _Tp>
1251 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1252 cyl_bessel_k(_Tpnu __nu, _Tp __x)
1254 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1255 return __detail::__cyl_bessel_k<__type>(__nu, __x);
1259 cyl_neumannf(float __nu, float __x)
1260 { return __detail::__cyl_neumann_n<float>(__nu, __x); }
1263 cyl_neumannl(long double __nu, long double __x)
1264 { return __detail::__cyl_neumann_n<long double>(__nu, __x); }
1266 /// 5.2.1.11 Cylindrical Neumann functions.
1267 template<typename _Tpnu, typename _Tp>
1268 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1269 cyl_neumann(_Tpnu __nu, _Tp __x)
1271 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1272 return __detail::__cyl_neumann_n<__type>(__nu, __x);
1276 ellint_1f(float __k, float __phi)
1277 { return __detail::__ellint_1<float>(__k, __phi); }
1280 ellint_1l(long double __k, long double __phi)
1281 { return __detail::__ellint_1<long double>(__k, __phi); }
1283 /// 5.2.1.12 Incomplete elliptic integrals of the first kind.
1284 template<typename _Tp, typename _Tpp>
1285 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
1286 ellint_1(_Tp __k, _Tpp __phi)
1288 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
1289 return __detail::__ellint_1<__type>(__k, __phi);
1293 ellint_2f(float __k, float __phi)
1294 { return __detail::__ellint_2<float>(__k, __phi); }
1297 ellint_2l(long double __k, long double __phi)
1298 { return __detail::__ellint_2<long double>(__k, __phi); }
1300 /// 5.2.1.13 Incomplete elliptic integrals of the second kind.
1301 template<typename _Tp, typename _Tpp>
1302 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
1303 ellint_2(_Tp __k, _Tpp __phi)
1305 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
1306 return __detail::__ellint_2<__type>(__k, __phi);
1310 ellint_3f(float __k, float __nu, float __phi)
1311 { return __detail::__ellint_3<float>(__k, __nu, __phi); }
1314 ellint_3l(long double __k, long double __nu, long double __phi)
1315 { return __detail::__ellint_3<long double>(__k, __nu, __phi); }
1317 /// 5.2.1.14 Incomplete elliptic integrals of the third kind.
1318 template<typename _Tp, typename _Tpn, typename _Tpp>
1319 inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type
1320 ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
1322 typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type;
1323 return __detail::__ellint_3<__type>(__k, __nu, __phi);
1328 { return __detail::__expint<float>(__x); }
1331 expintl(long double __x)
1332 { return __detail::__expint<long double>(__x); }
1334 /// 5.2.1.15 Exponential integrals.
1335 template<typename _Tp>
1336 inline typename __gnu_cxx::__promote<_Tp>::__type
1339 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1340 return __detail::__expint<__type>(__x);
1344 hermitef(unsigned int __n, float __x)
1345 { return __detail::__poly_hermite<float>(__n, __x); }
1348 hermitel(unsigned int __n, long double __x)
1349 { return __detail::__poly_hermite<long double>(__n, __x); }
1351 /// 5.2.1.16 Hermite polynomials.
1352 template<typename _Tp>
1353 inline typename __gnu_cxx::__promote<_Tp>::__type
1354 hermite(unsigned int __n, _Tp __x)
1356 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1357 return __detail::__poly_hermite<__type>(__n, __x);
1361 hypergf(float __a, float __b, float __c, float __x)
1362 { return __detail::__hyperg<float>(__a, __b, __c, __x); }
1365 hypergl(long double __a, long double __b, long double __c, long double __x)
1366 { return __detail::__hyperg<long double>(__a, __b, __c, __x); }
1368 /// 5.2.1.17 Hypergeometric functions.
1369 template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp>
1370 inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type
1371 hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
1373 typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type;
1374 return __detail::__hyperg<__type>(__a, __b, __c, __x);
1378 laguerref(unsigned int __n, float __x)
1379 { return __detail::__laguerre<float>(__n, __x); }
1382 laguerrel(unsigned int __n, long double __x)
1383 { return __detail::__laguerre<long double>(__n, __x); }
1385 /// 5.2.1.18 Laguerre polynomials.
1386 template<typename _Tp>
1387 inline typename __gnu_cxx::__promote<_Tp>::__type
1388 laguerre(unsigned int __n, _Tp __x)
1390 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1391 return __detail::__laguerre<__type>(__n, __x);
1395 legendref(unsigned int __n, float __x)
1396 { return __detail::__poly_legendre_p<float>(__n, __x); }
1399 legendrel(unsigned int __n, long double __x)
1400 { return __detail::__poly_legendre_p<long double>(__n, __x); }
1402 /// 5.2.1.19 Legendre polynomials.
1403 template<typename _Tp>
1404 inline typename __gnu_cxx::__promote<_Tp>::__type
1405 legendre(unsigned int __n, _Tp __x)
1407 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1408 return __detail::__poly_legendre_p<__type>(__n, __x);
1412 riemann_zetaf(float __x)
1413 { return __detail::__riemann_zeta<float>(__x); }
1416 riemann_zetal(long double __x)
1417 { return __detail::__riemann_zeta<long double>(__x); }
1419 /// 5.2.1.20 Riemann zeta function.
1420 template<typename _Tp>
1421 inline typename __gnu_cxx::__promote<_Tp>::__type
1422 riemann_zeta(_Tp __x)
1424 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1425 return __detail::__riemann_zeta<__type>(__x);
1429 sph_besself(unsigned int __n, float __x)
1430 { return __detail::__sph_bessel<float>(__n, __x); }
1433 sph_bessell(unsigned int __n, long double __x)
1434 { return __detail::__sph_bessel<long double>(__n, __x); }
1436 /// 5.2.1.21 Spherical Bessel functions.
1437 template<typename _Tp>
1438 inline typename __gnu_cxx::__promote<_Tp>::__type
1439 sph_bessel(unsigned int __n, _Tp __x)
1441 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1442 return __detail::__sph_bessel<__type>(__n, __x);
1446 sph_legendref(unsigned int __l, unsigned int __m, float __theta)
1447 { return __detail::__sph_legendre<float>(__l, __m, __theta); }
1450 sph_legendrel(unsigned int __l, unsigned int __m, long double __theta)
1451 { return __detail::__sph_legendre<long double>(__l, __m, __theta); }
1453 /// 5.2.1.22 Spherical associated Legendre functions.
1454 template<typename _Tp>
1455 inline typename __gnu_cxx::__promote<_Tp>::__type
1456 sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
1458 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1459 return __detail::__sph_legendre<__type>(__l, __m, __theta);
1463 sph_neumannf(unsigned int __n, float __x)
1464 { return __detail::__sph_neumann<float>(__n, __x); }
1467 sph_neumannl(unsigned int __n, long double __x)
1468 { return __detail::__sph_neumann<long double>(__n, __x); }
1470 /// 5.2.1.23 Spherical Neumann functions.
1471 template<typename _Tp>
1472 inline typename __gnu_cxx::__promote<_Tp>::__type
1473 sph_neumann(unsigned int __n, _Tp __x)
1475 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1476 return __detail::__sph_neumann<__type>(__n, __x);
1479 /* @} */ // tr1_math_spec_func
1480 _GLIBCXX_END_NAMESPACE_VERSION
1484 #endif // _GLIBCXX_TR1_CMATH