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freebsd
GitHub Repository: freebsd/freebsd-src
 Path: blob/main/contrib/llvm-project/libcxx/include/__math/special_functions.h
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// -*- C++ -*-

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//===----------------------------------------------------------------------===//

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//

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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.

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// See https://llvm.org/LICENSE.txt for license information.

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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception

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//

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//===----------------------------------------------------------------------===//

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#ifndef _LIBCPP___MATH_SPECIAL_FUNCTIONS_H

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#define _LIBCPP___MATH_SPECIAL_FUNCTIONS_H

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#include <__config>

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#include <__math/copysign.h>

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#include <__math/traits.h>

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#include <__type_traits/enable_if.h>

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#include <__type_traits/is_integral.h>

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#include <limits>

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#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)

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#  pragma GCC system_header

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#endif

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_LIBCPP_BEGIN_NAMESPACE_STD

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#if _LIBCPP_STD_VER >= 17

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template <class _Real>

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_LIBCPP_HIDE_FROM_ABI _Real __hermite(unsigned __n, _Real __x) {

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  // The Hermite polynomial H_n(x).

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  // The implementation is based on the recurrence formula: H_{n+1}(x) = 2x H_n(x) - 2n H_{n-1}.

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  // Press, William H., et al. Numerical recipes 3rd edition: The art of scientific computing.

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  // Cambridge university press, 2007, p. 183.

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  // NOLINTBEGIN(readability-identifier-naming)

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  if (__math::isnan(__x))

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    return __x;

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  _Real __H_0{1};

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  if (__n == 0)

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    return __H_0;

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  _Real __H_n_prev = __H_0;

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  _Real __H_n      = 2 * __x;

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  for (unsigned __i = 1; __i < __n; ++__i) {

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    _Real __H_n_next = 2 * (__x * __H_n - __i * __H_n_prev);

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    __H_n_prev       = __H_n;

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    __H_n            = __H_n_next;

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  }

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  if (!__math::isfinite(__H_n)) {

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    // Overflow occured. Two possible cases:

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    //    n is odd:  return infinity of the same sign as x.

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    //    n is even: return +Inf

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    _Real __inf = std::numeric_limits<_Real>::infinity();

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    return (__n & 1) ? __math::copysign(__inf, __x) : __inf;

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  }

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  return __H_n;

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  // NOLINTEND(readability-identifier-naming)

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}

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inline _LIBCPP_HIDE_FROM_ABI double hermite(unsigned __n, double __x) { return std::__hermite(__n, __x); }

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inline _LIBCPP_HIDE_FROM_ABI float hermite(unsigned __n, float __x) {

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  // use double internally -- float is too prone to overflow!

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  return static_cast<float>(std::hermite(__n, static_cast<double>(__x)));

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}

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inline _LIBCPP_HIDE_FROM_ABI long double hermite(unsigned __n, long double __x) { return std::__hermite(__n, __x); }

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inline _LIBCPP_HIDE_FROM_ABI float hermitef(unsigned __n, float __x) { return std::hermite(__n, __x); }

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inline _LIBCPP_HIDE_FROM_ABI long double hermitel(unsigned __n, long double __x) { return std::hermite(__n, __x); }

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template <class _Integer, std::enable_if_t<std::is_integral_v<_Integer>, int> = 0>

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_LIBCPP_HIDE_FROM_ABI double hermite(unsigned __n, _Integer __x) {

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  return std::hermite(__n, static_cast<double>(__x));

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}

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#endif // _LIBCPP_STD_VER >= 17

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_LIBCPP_END_NAMESPACE_STD

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#endif // _LIBCPP___MATH_SPECIAL_FUNCTIONS_H

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