132 lines
3.8 KiB
C++
132 lines
3.8 KiB
C++
// Special functions -*- C++ -*-
|
|
|
|
// Copyright (C) 2006-2021 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 3, 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.
|
|
//
|
|
// Under Section 7 of GPL version 3, you are granted additional
|
|
// permissions described in the GCC Runtime Library Exception, version
|
|
// 3.1, as published by the Free Software Foundation.
|
|
|
|
// You should have received a copy of the GNU General Public License and
|
|
// a copy of the GCC Runtime Library Exception along with this program;
|
|
// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
|
|
// <http://www.gnu.org/licenses/>.
|
|
|
|
/** @file tr1/poly_hermite.tcc
|
|
* This is an internal header file, included by other library headers.
|
|
* Do not attempt to use it directly. @headername{tr1/cmath}
|
|
*/
|
|
|
|
//
|
|
// ISO C++ 14882 TR1: 5.2 Special functions
|
|
//
|
|
|
|
// Written by Edward Smith-Rowland based on:
|
|
// (1) Handbook of Mathematical Functions,
|
|
// Ed. Milton Abramowitz and Irene A. Stegun,
|
|
// Dover Publications, Section 22 pp. 773-802
|
|
|
|
#ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC
|
|
#define _GLIBCXX_TR1_POLY_HERMITE_TCC 1
|
|
|
|
namespace std _GLIBCXX_VISIBILITY(default)
|
|
{
|
|
_GLIBCXX_BEGIN_NAMESPACE_VERSION
|
|
|
|
#if _GLIBCXX_USE_STD_SPEC_FUNCS
|
|
#elif defined(_GLIBCXX_TR1_CMATH)
|
|
namespace tr1
|
|
{
|
|
#else
|
|
# error do not include this header directly, use <cmath> or <tr1/cmath>
|
|
#endif
|
|
// [5.2] Special functions
|
|
|
|
// Implementation-space details.
|
|
namespace __detail
|
|
{
|
|
/**
|
|
* @brief This routine returns the Hermite polynomial
|
|
* of order n: \f$ H_n(x) \f$ by recursion on n.
|
|
*
|
|
* The Hermite polynomial is defined by:
|
|
* @f[
|
|
* H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
|
|
* @f]
|
|
*
|
|
* @param __n The order of the Hermite polynomial.
|
|
* @param __x The argument of the Hermite polynomial.
|
|
* @return The value of the Hermite polynomial of order n
|
|
* and argument x.
|
|
*/
|
|
template<typename _Tp>
|
|
_Tp
|
|
__poly_hermite_recursion(unsigned int __n, _Tp __x)
|
|
{
|
|
// Compute H_0.
|
|
_Tp __H_0 = 1;
|
|
if (__n == 0)
|
|
return __H_0;
|
|
|
|
// Compute H_1.
|
|
_Tp __H_1 = 2 * __x;
|
|
if (__n == 1)
|
|
return __H_1;
|
|
|
|
// Compute H_n.
|
|
_Tp __H_n, __H_nm1, __H_nm2;
|
|
unsigned int __i;
|
|
for (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i)
|
|
{
|
|
__H_n = 2 * (__x * __H_nm1 - (__i - 1) * __H_nm2);
|
|
__H_nm2 = __H_nm1;
|
|
__H_nm1 = __H_n;
|
|
}
|
|
|
|
return __H_n;
|
|
}
|
|
|
|
|
|
/**
|
|
* @brief This routine returns the Hermite polynomial
|
|
* of order n: \f$ H_n(x) \f$.
|
|
*
|
|
* The Hermite polynomial is defined by:
|
|
* @f[
|
|
* H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
|
|
* @f]
|
|
*
|
|
* @param __n The order of the Hermite polynomial.
|
|
* @param __x The argument of the Hermite polynomial.
|
|
* @return The value of the Hermite polynomial of order n
|
|
* and argument x.
|
|
*/
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
__poly_hermite(unsigned int __n, _Tp __x)
|
|
{
|
|
if (__isnan(__x))
|
|
return std::numeric_limits<_Tp>::quiet_NaN();
|
|
else
|
|
return __poly_hermite_recursion(__n, __x);
|
|
}
|
|
} // namespace __detail
|
|
#if ! _GLIBCXX_USE_STD_SPEC_FUNCS && defined(_GLIBCXX_TR1_CMATH)
|
|
} // namespace tr1
|
|
#endif
|
|
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
|
}
|
|
|
|
#endif // _GLIBCXX_TR1_POLY_HERMITE_TCC
|