1*af0d731bSPaulXiCao // -*- C++ -*- 2*af0d731bSPaulXiCao //===----------------------------------------------------------------------===// 3*af0d731bSPaulXiCao // 4*af0d731bSPaulXiCao // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 5*af0d731bSPaulXiCao // See https://llvm.org/LICENSE.txt for license information. 6*af0d731bSPaulXiCao // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 7*af0d731bSPaulXiCao // 8*af0d731bSPaulXiCao //===----------------------------------------------------------------------===// 9*af0d731bSPaulXiCao 10*af0d731bSPaulXiCao #ifndef _LIBCPP___MATH_SPECIAL_FUNCTIONS_H 11*af0d731bSPaulXiCao #define _LIBCPP___MATH_SPECIAL_FUNCTIONS_H 12*af0d731bSPaulXiCao 13*af0d731bSPaulXiCao #include <__config> 14*af0d731bSPaulXiCao #include <__math/copysign.h> 15*af0d731bSPaulXiCao #include <__math/traits.h> 16*af0d731bSPaulXiCao #include <__type_traits/enable_if.h> 17*af0d731bSPaulXiCao #include <__type_traits/is_integral.h> 18*af0d731bSPaulXiCao #include <limits> 19*af0d731bSPaulXiCao 20*af0d731bSPaulXiCao #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 21*af0d731bSPaulXiCao # pragma GCC system_header 22*af0d731bSPaulXiCao #endif 23*af0d731bSPaulXiCao 24*af0d731bSPaulXiCao _LIBCPP_BEGIN_NAMESPACE_STD 25*af0d731bSPaulXiCao 26*af0d731bSPaulXiCao #if _LIBCPP_STD_VER >= 17 27*af0d731bSPaulXiCao 28*af0d731bSPaulXiCao template <class _Real> 29*af0d731bSPaulXiCao _LIBCPP_HIDE_FROM_ABI _Real __hermite(unsigned __n, _Real __x) { 30*af0d731bSPaulXiCao // The Hermite polynomial H_n(x). 31*af0d731bSPaulXiCao // The implementation is based on the recurrence formula: H_{n+1}(x) = 2x H_n(x) - 2n H_{n-1}. 32*af0d731bSPaulXiCao // Press, William H., et al. Numerical recipes 3rd edition: The art of scientific computing. 33*af0d731bSPaulXiCao // Cambridge university press, 2007, p. 183. 34*af0d731bSPaulXiCao 35*af0d731bSPaulXiCao // NOLINTBEGIN(readability-identifier-naming) 36*af0d731bSPaulXiCao if (__math::isnan(__x)) 37*af0d731bSPaulXiCao return __x; 38*af0d731bSPaulXiCao 39*af0d731bSPaulXiCao _Real __H_0{1}; 40*af0d731bSPaulXiCao if (__n == 0) 41*af0d731bSPaulXiCao return __H_0; 42*af0d731bSPaulXiCao 43*af0d731bSPaulXiCao _Real __H_n_prev = __H_0; 44*af0d731bSPaulXiCao _Real __H_n = 2 * __x; 45*af0d731bSPaulXiCao for (unsigned __i = 1; __i < __n; ++__i) { 46*af0d731bSPaulXiCao _Real __H_n_next = 2 * (__x * __H_n - __i * __H_n_prev); 47*af0d731bSPaulXiCao __H_n_prev = __H_n; 48*af0d731bSPaulXiCao __H_n = __H_n_next; 49*af0d731bSPaulXiCao } 50*af0d731bSPaulXiCao 51*af0d731bSPaulXiCao if (!__math::isfinite(__H_n)) { 52*af0d731bSPaulXiCao // Overflow occured. Two possible cases: 53*af0d731bSPaulXiCao // n is odd: return infinity of the same sign as x. 54*af0d731bSPaulXiCao // n is even: return +Inf 55*af0d731bSPaulXiCao _Real __inf = std::numeric_limits<_Real>::infinity(); 56*af0d731bSPaulXiCao return (__n & 1) ? __math::copysign(__inf, __x) : __inf; 57*af0d731bSPaulXiCao } 58*af0d731bSPaulXiCao return __H_n; 59*af0d731bSPaulXiCao // NOLINTEND(readability-identifier-naming) 60*af0d731bSPaulXiCao } 61*af0d731bSPaulXiCao 62*af0d731bSPaulXiCao inline _LIBCPP_HIDE_FROM_ABI double hermite(unsigned __n, double __x) { return std::__hermite(__n, __x); } 63*af0d731bSPaulXiCao 64*af0d731bSPaulXiCao inline _LIBCPP_HIDE_FROM_ABI float hermite(unsigned __n, float __x) { 65*af0d731bSPaulXiCao // use double internally -- float is too prone to overflow! 66*af0d731bSPaulXiCao return static_cast<float>(std::hermite(__n, static_cast<double>(__x))); 67*af0d731bSPaulXiCao } 68*af0d731bSPaulXiCao 69*af0d731bSPaulXiCao inline _LIBCPP_HIDE_FROM_ABI long double hermite(unsigned __n, long double __x) { return std::__hermite(__n, __x); } 70*af0d731bSPaulXiCao 71*af0d731bSPaulXiCao inline _LIBCPP_HIDE_FROM_ABI float hermitef(unsigned __n, float __x) { return std::hermite(__n, __x); } 72*af0d731bSPaulXiCao 73*af0d731bSPaulXiCao inline _LIBCPP_HIDE_FROM_ABI long double hermitel(unsigned __n, long double __x) { return std::hermite(__n, __x); } 74*af0d731bSPaulXiCao 75*af0d731bSPaulXiCao template <class _Integer, std::enable_if_t<std::is_integral_v<_Integer>, int> = 0> 76*af0d731bSPaulXiCao _LIBCPP_HIDE_FROM_ABI double hermite(unsigned __n, _Integer __x) { 77*af0d731bSPaulXiCao return std::hermite(__n, static_cast<double>(__x)); 78*af0d731bSPaulXiCao } 79*af0d731bSPaulXiCao 80*af0d731bSPaulXiCao #endif // _LIBCPP_STD_VER >= 17 81*af0d731bSPaulXiCao 82*af0d731bSPaulXiCao _LIBCPP_END_NAMESPACE_STD 83*af0d731bSPaulXiCao 84*af0d731bSPaulXiCao #endif // _LIBCPP___MATH_SPECIAL_FUNCTIONS_H 85