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 |