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