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 // 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 // . /** @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 or #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 _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 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