path: root/libstdc++-v3/include/tr1/cmath

// TR1 cmath -*- C++ -*-

// Copyright (C) 2006, 2007 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 2, or (at your option)
// any later version.

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

// You should have received a copy of the GNU General Public License along
// with this library; see the file COPYING.  If not, write to the Free
// Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
// USA.

// As a special exception, you may use this file as part of a free software
// library without restriction.  Specifically, if other files instantiate
// templates or use macros or inline functions from this file, or you compile
// this file and link it with other files to produce an executable, this
// file does not by itself cause the resulting executable to be covered by
// the GNU General Public License.  This exception does not however
// invalidate any other reasons why the executable file might be covered by
// the GNU General Public License.

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

#ifndef _TR1_CMATH
#define _TR1_CMATH 1

#include <bits/c++config.h>
#include <bits/stl_algobase.h>
#include <limits>
#include <cmath>
#include <tr1/common.h>

#if _GLIBCXX_USE_C99_MATH_TR1

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

#endif

// namespace std::tr1
namespace std
{
_GLIBCXX_BEGIN_NAMESPACE(_GLIBCXX_TR1)

#if _GLIBCXX_USE_C99_MATH_TR1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  using ::remquo;
  using ::remquo;
  using ::remquo;

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

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

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

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

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

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

#endif

#if _GLIBCXX_USE_C99_MATH
#if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC

  /// @brief Function template definitions [8.16.3].
  //
  using std::signbit;
  
  using std::fpclassify;

  using std::isfinite;
  using std::isinf;
  using std::isnan;
  using std::isnormal;

  using std::isgreater;
  using std::isgreaterequal;
  using std::isless;
  using std::islessequal;
  using std::islessgreater;
  using std::isunordered;
#endif
#endif

#if _GLIBCXX_USE_C99_MATH_TR1

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

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

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

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

  using std::asin;

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

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

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

  using std::atan;

  // Workaround for c++/21682.
  namespace __detail
  {
    template<typename _Tp, typename _Up>
      inline typename
      __gnu_cxx::__enable_if<std::__is_floating<_Tp>::__value
                             || std::__is_floating<_Up>::__value,
			     typename std::_GLIBCXX_TR1::
			     __promote_2<_Tp, _Up>::__type>::__type
      atan2(_Tp __y, _Up __x)
      {
	typedef typename std::_GLIBCXX_TR1::__promote_2<_Tp, _Up>::__type
	  __type;
	return std::atan2(__type(__y), __type(__x));
      }
  } // namespace __detail

  using std::atan2;
  using __detail::atan2;
 
  inline float
  atanh(float __x)
  { return __builtin_atanhf(__x); }

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

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

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

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

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

  using std::ceil;

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

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

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

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

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

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

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

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

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

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

  using std::exp;

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

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

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

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

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

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

  using std::fabs;

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

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

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

  using std::floor;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  using std::ldexp;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  using std::pow;

  // DR 550.
  template<typename _Tp, typename _Up>
    inline typename __promote_2<_Tp, _Up>::__type
    pow(_Tp __x, _Up __y)
    {
      typedef typename __promote_2<_Tp, _Up>::__type __type;
      return pow(__type(__x), __type(__y));
    }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

#endif

_GLIBCXX_END_NAMESPACE
}

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

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

// namespace std::tr1
namespace std
{
_GLIBCXX_BEGIN_NAMESPACE(_GLIBCXX_TR1)

  //  5.2.1.1  Associated Laguerre polynomials.

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

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

  template<typename _Tp>
    inline typename __promote<_Tp>::__type
    assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
    {
      typedef typename __promote<_Tp>::__type __type;
      return __detail::__assoc_laguerre<__type>(__n, __m, __x);
    }


  //  5.2.1.2  Associated Legendre functions.

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

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

  template<typename _Tp>
    inline typename __promote<_Tp>::__type
    assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
    {
      typedef typename __promote<_Tp>::__type __type;
      return __detail::__assoc_legendre_p<__type>(__l, __m, __x);
    }


  //  5.2.1.3  Beta functions.

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

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

  template<typename _Tpx, typename _Tpy>
    inline typename __promote_2<_Tpx, _Tpy>::__type
    beta(_Tpx __x, _Tpy __y)
    {
      typedef typename __promote_2<_Tpx, _Tpy>::__type __type;
      return __detail::__beta<__type>(__x, __y);
    }


  //  5.2.1.4  Complete elliptic interals of the first kind.

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

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

  template<typename _Tp>
    inline typename __promote<_Tp>::__type
    comp_ellint_1(_Tp __k)
    {
      typedef typename __promote<_Tp>::__type __type;
      return __detail::__comp_ellint_1<__type>(__k);
    }


  //  5.2.1.5  Complete elliptic interals of the second kind.

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

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

  template<typename _Tp>
    inline typename __promote<_Tp>::__type
    comp_ellint_2(_Tp __k)
    {
      typedef typename __promote<_Tp>::__type __type;
      return __detail::__comp_ellint_2<__type>(__k);
    }


  //  5.2.1.6  Complete elliptic interals of the third kind.

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

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

  template<typename _Tp, typename _Tpn>
    inline typename __promote_2<_Tp, _Tpn>::__type
    comp_ellint_3(_Tp __k, _Tpn __nu)
    {
      typedef typename __promote_2<_Tp, _Tpn>::__type __type;
      return __detail::__comp_ellint_3<__type>(__k, __nu);
    }


  //  5.2.1.7  Confluent hypergeometric functions.

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

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

  template<typename _Tpa, typename _Tpc, typename _Tp>
    inline typename __promote_3<_Tpa, _Tpc, _Tp>::__type
    conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
    {
      typedef typename __promote_3<_Tpa, _Tpc, _Tp>::__type __type;
      return __detail::__conf_hyperg<__type>(__a, __c, __x);
    }


  //  5.2.1.8  Regular modified cylindrical Bessel functions.

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

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

  template<typename _Tpnu, typename _Tp>
    inline typename __promote_2<_Tpnu, _Tp>::__type
    cyl_bessel_i(_Tpnu __nu, _Tp __x)
    {
      typedef typename __promote_2<_Tpnu, _Tp>::__type __type;
      return __detail::__cyl_bessel_i<__type>(__nu, __x);
    }


  //  5.2.1.9  Cylindrical Bessel functions (of the first kind).

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

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

  template<typename _Tpnu, typename _Tp>
    inline typename __promote_2<_Tpnu, _Tp>::__type
    cyl_bessel_j(_Tpnu __nu, _Tp __x)
    {
      typedef typename __promote_2<_Tpnu, _Tp>::__type __type;
      return __detail::__cyl_bessel_j<__type>(__nu, __x);
    }


  //  5.2.1.10  Irregular modified cylindrical Bessel functions.

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

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

  template<typename _Tpnu, typename _Tp>
    inline typename __promote_2<_Tpnu, _Tp>::__type
    cyl_bessel_k(_Tpnu __nu, _Tp __x)
    {
      typedef typename __promote_2<_Tpnu, _Tp>::__type __type;
      return __detail::__cyl_bessel_k<__type>(__nu, __x);
    }


  //  5.2.1.11  Cylindrical Neumann functions.

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

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

  template<typename _Tpnu, typename _Tp>
    inline typename __promote_2<_Tpnu, _Tp>::__type
    cyl_neumann(_Tpnu __nu, _Tp __x)
    {
      typedef typename __promote_2<_Tpnu, _Tp>::__type __type;
      return __detail::__cyl_neumann_n<__type>(__nu, __x);
    }


  //  5.2.1.12  Incomplete elliptic interals of the first kind.

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

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

  template<typename _Tp, typename _Tpp>
    inline typename __promote_2<_Tp, _Tpp>::__type
    ellint_1(_Tp __k, _Tpp __phi)
    {
      typedef typename __promote_2<_Tp, _Tpp>::__type __type;
      return __detail::__ellint_1<__type>(__k, __phi);
    }


  //  5.2.1.13  Incomplete elliptic interals of the second kind.

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

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

  template<typename _Tp, typename _Tpp>
    inline typename __promote_2<_Tp, _Tpp>::__type
    ellint_2(_Tp __k, _Tpp __phi)
    {
      typedef typename __promote_2<_Tp, _Tpp>::__type __type;
      return __detail::__ellint_2<__type>(__k, __phi);
    }


  //  5.2.1.14  Incomplete elliptic interals of the third kind.

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

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

  template<typename _Tp, typename _Tpn, typename _Tpp>
    inline typename __promote_3<_Tp, _Tpn, _Tpp>::__type
    ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
    {
      typedef typename __promote_3<_Tp, _Tpn, _Tpp>::__type __type;
      return __detail::__ellint_3<__type>(__k, __nu, __phi);
    }


  //  5.2.1.15  Exponential integrals.

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

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

  template<typename _Tp>
    inline typename __promote<_Tp>::__type
    expint(_Tp __x)
    {
      typedef typename __promote<_Tp>::__type __type;
      return __detail::__expint<__type>(__x);
    }


  //  5.2.1.16  Hermite polynomials.

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

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

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


  //  5.2.1.17  Hypergeometric functions.

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

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

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


  //  5.2.1.18  Laguerre polynomials.

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

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

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


  //  5.2.1.19  Legendre polynomials.

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

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

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


  //  5.2.1.20  Riemann zeta function.

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

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

  template<typename _Tp>
    inline typename __promote<_Tp>::__type
    riemann_zeta(_Tp __x)
    {
      typedef typename __promote<_Tp>::__type __type;
      return __detail::__riemann_zeta<__type>(__x);
    }


  //  5.2.1.21  Spherical Bessel functions.

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

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

  template<typename _Tp>
    inline typename __promote<_Tp>::__type
    sph_bessel(unsigned int __n, _Tp __x)
    {
      typedef typename __promote<_Tp>::__type __type;
      return __detail::__sph_bessel<__type>(__n, __x);
    }


  //  5.2.1.22  Spherical associated Legendre functions.

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

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

  template<typename _Tp>
    inline typename __promote<_Tp>::__type
    sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
    {
      typedef typename __promote<_Tp>::__type __type;
      return __detail::__sph_legendre<__type>(__l, __m, __theta);
    }


  //  5.2.1.23  Spherical Neumann functions.

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

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

  template<typename _Tp>
    inline typename __promote<_Tp>::__type
    sph_neumann(unsigned int __n, _Tp __x)
    {
      typedef typename __promote<_Tp>::__type __type;
      return __detail::__sph_neumann<__type>(__n, __x);
    }

  /* @} */ // group tr1_math_spec_func

_GLIBCXX_END_NAMESPACE
}

#endif