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, 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 >= 17
81
82_LIBCPP_END_NAMESPACE_STD
83
84#endif // _LIBCPP___MATH_SPECIAL_FUNCTIONS_H