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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-exception7//8//===----------------------------------------------------------------------===//9 10#ifndef _LIBCPP___MATH_SPECIAL_FUNCTIONS_H11#define _LIBCPP___MATH_SPECIAL_FUNCTIONS_H12 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_header22#endif23 24_LIBCPP_BEGIN_NAMESPACE_STD25 26#if _LIBCPP_STD_VER >= 1727 28template <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 +Inf55 _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 62inline _LIBCPP_HIDE_FROM_ABI double hermite(unsigned __n, double __x) { return std::__hermite(__n, __x); }63 64inline _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 69inline _LIBCPP_HIDE_FROM_ABI long double hermite(unsigned __n, long double __x) { return std::__hermite(__n, __x); }70 71inline _LIBCPP_HIDE_FROM_ABI float hermitef(unsigned __n, float __x) { return std::hermite(__n, __x); }72 73inline _LIBCPP_HIDE_FROM_ABI long double hermitel(unsigned __n, long double __x) { return std::hermite(__n, __x); }74 75template <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 >= 1781 82_LIBCPP_END_NAMESPACE_STD83 84#endif // _LIBCPP___MATH_SPECIAL_FUNCTIONS_H85