11.2.0/tr1/poly_hermite.tcc

// Special functions -*- C++ -*-

// Copyright (C) 2006-2021 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.
 *  Do not attempt to use it directly. @headername{tr1/cmath}
 */

//
// 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 _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

#if _GLIBCXX_USE_STD_SPEC_FUNCS
#elif defined(_GLIBCXX_TR1_CMATH)
namespace tr1
{
#else
# error do not include this header directly, use <cmath> or <tr1/cmath>
#endif
  // [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(unsigned int __n, _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(unsigned int __n, _Tp __x)
    {
      if (__isnan(__x))
        return std::numeric_limits<_Tp>::quiet_NaN();
      else
        return __poly_hermite_recursion(__n, __x);
    }
  } // namespace __detail
#if ! _GLIBCXX_USE_STD_SPEC_FUNCS && defined(_GLIBCXX_TR1_CMATH)
} // namespace tr1
#endif

_GLIBCXX_END_NAMESPACE_VERSION
}

#endif // _GLIBCXX_TR1_POLY_HERMITE_TCC
Revision:	1166
Committed:	Tue Oct 26 14:22:36 2021 UTC (4 years ago) by rossy
File size:	3925 byte(s)
Log Message:	Daodan: Replace MinGW build env with an up-to-date MSYS2 env
#	Content
1	// Special functions -- C++ --
2
3	// Copyright (C) 2006-2021 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