1// Special functions -*- C++ -*-
2
3// Copyright (C) 2006-2022 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