1 // Special functions -*- C++ -*- 2 3 // Copyright (C) 2006-2018 Free Software Foundation, Inc. 4 // 5 // This file is part of the GNU ISO C++ Library. This library is free 6 // software; you can redistribute it and/or modify it under the 7 // terms of the GNU General Public License as published by the 8 // Free Software Foundation; either version 3, or (at your option) 9 // any later version. 10 // 11 // This library is distributed in the hope that it will be useful, 12 // but WITHOUT ANY WARRANTY; without even the implied warranty of 13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 // GNU General Public License for more details. 15 // 16 // Under Section 7 of GPL version 3, you are granted additional 17 // permissions described in the GCC Runtime Library Exception, version 18 // 3.1, as published by the Free Software Foundation. 19 20 // You should have received a copy of the GNU General Public License and 21 // a copy of the GCC Runtime Library Exception along with this program; 22 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 23 // <http://www.gnu.org/licenses/>. 24 25 /** @file tr1/poly_hermite.tcc 26 * This is an internal header file, included by other library headers. 27 * Do not attempt to use it directly. @headername{tr1/cmath} 28 */ 29 30 // 31 // ISO C++ 14882 TR1: 5.2 Special functions 32 // 33 34 // Written by Edward Smith-Rowland based on: 35 // (1) Handbook of Mathematical Functions, 36 // Ed. Milton Abramowitz and Irene A. Stegun, 37 // Dover Publications, Section 22 pp. 773-802 38 39 #ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC 40 #define _GLIBCXX_TR1_POLY_HERMITE_TCC 1 41 42 namespace std _GLIBCXX_VISIBILITY(default) 43 { 44 _GLIBCXX_BEGIN_NAMESPACE_VERSION 45 46 #if _GLIBCXX_USE_STD_SPEC_FUNCS 47 #elif defined(_GLIBCXX_TR1_CMATH) 48 namespace tr1 49 { 50 #else 51 # error do not include this header directly, use <cmath> or <tr1/cmath> 52 #endif 53 // [5.2] Special functions 54 55 // Implementation-space details. 56 namespace __detail 57 { 58 /** 59 * @brief This routine returns the Hermite polynomial 60 * of order n: \f$ H_n(x) \f$ by recursion on n. 61 * 62 * The Hermite polynomial is defined by: 63 * @f[ 64 * H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2} 65 * @f] 66 * 67 * @param __n The order of the Hermite polynomial. 68 * @param __x The argument of the Hermite polynomial. 69 * @return The value of the Hermite polynomial of order n 70 * and argument x. 71 */ 72 template<typename _Tp> 73 _Tp 74 __poly_hermite_recursion(unsigned int __n, _Tp __x) 75 { 76 // Compute H_0. 77 _Tp __H_0 = 1; 78 if (__n == 0) 79 return __H_0; 80 81 // Compute H_1. 82 _Tp __H_1 = 2 * __x; 83 if (__n == 1) 84 return __H_1; 85 86 // Compute H_n. 87 _Tp __H_n, __H_nm1, __H_nm2; 88 unsigned int __i; 89 for (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i) 90 { 91 __H_n = 2 * (__x * __H_nm1 - (__i - 1) * __H_nm2); 92 __H_nm2 = __H_nm1; 93 __H_nm1 = __H_n; 94 } 95 96 return __H_n; 97 } 98 99 100 /** 101 * @brief This routine returns the Hermite polynomial 102 * of order n: \f$ H_n(x) \f$. 103 * 104 * The Hermite polynomial is defined by: 105 * @f[ 106 * H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2} 107 * @f] 108 * 109 * @param __n The order of the Hermite polynomial. 110 * @param __x The argument of the Hermite polynomial. 111 * @return The value of the Hermite polynomial of order n 112 * and argument x. 113 */ 114 template<typename _Tp> 115 inline _Tp 116 __poly_hermite(unsigned int __n, _Tp __x) 117 { 118 if (__isnan(__x)) 119 return std::numeric_limits<_Tp>::quiet_NaN(); 120 else 121 return __poly_hermite_recursion(__n, __x); 122 } 123 } // namespace __detail 124 #if ! _GLIBCXX_USE_STD_SPEC_FUNCS && defined(_GLIBCXX_TR1_CMATH) 125 } // namespace tr1 126 #endif 127 128 _GLIBCXX_END_NAMESPACE_VERSION 129 } 130 131 #endif // _GLIBCXX_TR1_POLY_HERMITE_TCC 132