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Diffstat (limited to 'gcc-4.4.3/libstdc++-v3/include/tr1/poly_hermite.tcc')
| -rw-r--r-- | gcc-4.4.3/libstdc++-v3/include/tr1/poly_hermite.tcc | 124 |
1 files changed, 124 insertions, 0 deletions
diff --git a/gcc-4.4.3/libstdc++-v3/include/tr1/poly_hermite.tcc b/gcc-4.4.3/libstdc++-v3/include/tr1/poly_hermite.tcc new file mode 100644 index 000000000..d4825a31e --- /dev/null +++ b/gcc-4.4.3/libstdc++-v3/include/tr1/poly_hermite.tcc @@ -0,0 +1,124 @@ +// Special functions -*- C++ -*- + +// Copyright (C) 2006, 2007, 2008, 2009 +// 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. + * You should not attempt to use it directly. + */ + +// +// 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 +{ +namespace tr1 +{ + + // [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(const unsigned int __n, const _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(const unsigned int __n, const _Tp __x) + { + if (__isnan(__x)) + return std::numeric_limits<_Tp>::quiet_NaN(); + else + return __poly_hermite_recursion(__n, __x); + } + + } // namespace std::tr1::__detail +} +} + +#endif // _GLIBCXX_TR1_POLY_HERMITE_TCC |