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
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 +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
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, x: 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, x: 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