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// Special functions -*- C++ -*- |
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// Copyright (C) 2006-2015 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/>. |
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/** @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} |
*/ |
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// |
// ISO C++ 14882 TR1: 5.2 Special functions |
// |
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// 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 |
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#ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC |
#define _GLIBCXX_TR1_POLY_HERMITE_TCC 1 |
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namespace std _GLIBCXX_VISIBILITY(default) |
{ |
namespace tr1 |
{ |
// [5.2] Special functions |
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// Implementation-space details. |
namespace __detail |
{ |
_GLIBCXX_BEGIN_NAMESPACE_VERSION |
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/** |
* @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; |
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// Compute H_1. |
_Tp __H_1 = 2 * __x; |
if (__n == 1) |
return __H_1; |
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// 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; |
} |
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return __H_n; |
} |
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/** |
* @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); |
} |
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_GLIBCXX_END_NAMESPACE_VERSION |
} // namespace std::tr1::__detail |
} |
} |
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#endif // _GLIBCXX_TR1_POLY_HERMITE_TCC |