1// Special functions -*- C++ -*- 
2 
3// Copyright (C) 2006-2019 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 
42namespace std _GLIBCXX_VISIBILITY(default) 
43{ 
44_GLIBCXX_BEGIN_NAMESPACE_VERSION 
45 
46#if _GLIBCXX_USE_STD_SPEC_FUNCS 
47#elif defined(_GLIBCXX_TR1_CMATH) 
48namespace 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