mirror of
https://github.com/llvm/llvm-project.git
synced 2025-04-25 07:16:05 +00:00
af0d731b12
Implementing the Hermite polynomials which are part of C++17's mathematical special functions. The goal is to get early feedback which will make implementing the other functions easier. Integration of functions in chunks (e.g. `std::hermite` at first, then `std::laguerre`, etc.) might make sense as well (also see note on boost.math below). I started out from this abandoned merge request: https://reviews.llvm.org/D58876 . The C++23 standard defines them in-terms of `/* floating-point type */` arguments. I have not looked into that. Note, there is still an ongoing discussion on discourse whether importing boost.math is an option.
85 lines
2.8 KiB
C++
85 lines
2.8 KiB
C++
// -*- C++ -*-
|
|
//===----------------------------------------------------------------------===//
|
|
//
|
|
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
|
|
// See https://llvm.org/LICENSE.txt for license information.
|
|
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
|
|
//
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
#ifndef _LIBCPP___MATH_SPECIAL_FUNCTIONS_H
|
|
#define _LIBCPP___MATH_SPECIAL_FUNCTIONS_H
|
|
|
|
#include <__config>
|
|
#include <__math/copysign.h>
|
|
#include <__math/traits.h>
|
|
#include <__type_traits/enable_if.h>
|
|
#include <__type_traits/is_integral.h>
|
|
#include <limits>
|
|
|
|
#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
|
|
# pragma GCC system_header
|
|
#endif
|
|
|
|
_LIBCPP_BEGIN_NAMESPACE_STD
|
|
|
|
#if _LIBCPP_STD_VER >= 17
|
|
|
|
template <class _Real>
|
|
_LIBCPP_HIDE_FROM_ABI _Real __hermite(unsigned __n, _Real __x) {
|
|
// The Hermite polynomial H_n(x).
|
|
// The implementation is based on the recurrence formula: H_{n+1}(x) = 2x H_n(x) - 2n H_{n-1}.
|
|
// Press, William H., et al. Numerical recipes 3rd edition: The art of scientific computing.
|
|
// Cambridge university press, 2007, p. 183.
|
|
|
|
// NOLINTBEGIN(readability-identifier-naming)
|
|
if (__math::isnan(__x))
|
|
return __x;
|
|
|
|
_Real __H_0{1};
|
|
if (__n == 0)
|
|
return __H_0;
|
|
|
|
_Real __H_n_prev = __H_0;
|
|
_Real __H_n = 2 * __x;
|
|
for (unsigned __i = 1; __i < __n; ++__i) {
|
|
_Real __H_n_next = 2 * (__x * __H_n - __i * __H_n_prev);
|
|
__H_n_prev = __H_n;
|
|
__H_n = __H_n_next;
|
|
}
|
|
|
|
if (!__math::isfinite(__H_n)) {
|
|
// Overflow occured. Two possible cases:
|
|
// n is odd: return infinity of the same sign as x.
|
|
// n is even: return +Inf
|
|
_Real __inf = std::numeric_limits<_Real>::infinity();
|
|
return (__n & 1) ? __math::copysign(__inf, __x) : __inf;
|
|
}
|
|
return __H_n;
|
|
// NOLINTEND(readability-identifier-naming)
|
|
}
|
|
|
|
inline _LIBCPP_HIDE_FROM_ABI double hermite(unsigned __n, double __x) { return std::__hermite(__n, __x); }
|
|
|
|
inline _LIBCPP_HIDE_FROM_ABI float hermite(unsigned __n, float __x) {
|
|
// use double internally -- float is too prone to overflow!
|
|
return static_cast<float>(std::hermite(__n, static_cast<double>(__x)));
|
|
}
|
|
|
|
inline _LIBCPP_HIDE_FROM_ABI long double hermite(unsigned __n, long double __x) { return std::__hermite(__n, __x); }
|
|
|
|
inline _LIBCPP_HIDE_FROM_ABI float hermitef(unsigned __n, float __x) { return std::hermite(__n, __x); }
|
|
|
|
inline _LIBCPP_HIDE_FROM_ABI long double hermitel(unsigned __n, long double __x) { return std::hermite(__n, __x); }
|
|
|
|
template <class _Integer, std::enable_if_t<std::is_integral_v<_Integer>, int> = 0>
|
|
_LIBCPP_HIDE_FROM_ABI double hermite(unsigned __n, _Integer __x) {
|
|
return std::hermite(__n, static_cast<double>(__x));
|
|
}
|
|
|
|
#endif // _LIBCPP_STD_VER >= 17
|
|
|
|
_LIBCPP_END_NAMESPACE_STD
|
|
|
|
#endif // _LIBCPP___MATH_SPECIAL_FUNCTIONS_H
|