1 // Special functions -*- C++ -*- 2 3 // Copyright (C) 2006, 2007, 2008, 2009 4 // Free Software Foundation, Inc. 5 // 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) 10 // any later version. 11 // 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. 16 // 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. 20 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/>. 25 26 /** @file tr1/poly_hermite.tcc 27 * This is an internal header file, included by other library headers. 28 * You should not attempt to use it directly. 29 */ 30 31 // 32 // ISO C++ 14882 TR1: 5.2 Special functions 33 // 34 35 // Written by Edward Smith-Rowland based on: 36 // (1) Handbook of Mathematical Functions, 37 // Ed. Milton Abramowitz and Irene A. Stegun, 38 // Dover Publications, Section 22 pp. 773-802 39 40 #ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC 41 #define _GLIBCXX_TR1_POLY_HERMITE_TCC 1 42 43 namespace std 44 { 45 namespace tr1 46 { 47 48 // [5.2] Special functions 49 50 // Implementation-space details. 51 namespace __detail 52 { 53 54 /** 55 * @brief This routine returns the Hermite polynomial 56 * of order n: \f$ H_n(x) \f$ by recursion on n. 57 * 58 * The Hermite polynomial is defined by: 59 * @f[ 60 * H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2} 61 * @f] 62 * 63 * @param __n The order of the Hermite polynomial. 64 * @param __x The argument of the Hermite polynomial. 65 * @return The value of the Hermite polynomial of order n 66 * and argument x. 67 */ 68 template<typename _Tp> 69 _Tp 70 __poly_hermite_recursion(const unsigned int __n, const _Tp __x) 71 { 72 // Compute H_0. 73 _Tp __H_0 = 1; 74 if (__n == 0) 75 return __H_0; 76 77 // Compute H_1. 78 _Tp __H_1 = 2 * __x; 79 if (__n == 1) 80 return __H_1; 81 82 // Compute H_n. 83 _Tp __H_n, __H_nm1, __H_nm2; 84 unsigned int __i; 85 for (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i) 86 { 87 __H_n = 2 * (__x * __H_nm1 + (__i - 1) * __H_nm2); 88 __H_nm2 = __H_nm1; 89 __H_nm1 = __H_n; 90 } 91 92 return __H_n; 93 } 94 95 96 /** 97 * @brief This routine returns the Hermite polynomial 98 * of order n: \f$ H_n(x) \f$. 99 * 100 * The Hermite polynomial is defined by: 101 * @f[ 102 * H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2} 103 * @f] 104 * 105 * @param __n The order of the Hermite polynomial. 106 * @param __x The argument of the Hermite polynomial. 107 * @return The value of the Hermite polynomial of order n 108 * and argument x. 109 */ 110 template<typename _Tp> 111 inline _Tp 112 __poly_hermite(const unsigned int __n, const _Tp __x) 113 { 114 if (__isnan(__x)) 115 return std::numeric_limits<_Tp>::quiet_NaN(); 116 else 117 return __poly_hermite_recursion(__n, __x); 118 } 119 120 } // namespace std::tr1::__detail 121 } 122 } 123 124 #endif // _GLIBCXX_TR1_POLY_HERMITE_TCC 125
