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// (C) Copyright John Maddock 2006.
// (C) Copyright Matt Borland 2024.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_SPECIAL_HERMITE_HPP
#define BOOST_MATH_SPECIAL_HERMITE_HPP
#ifdef _MSC_VER
#pragma once
#endif
#include <boost/math/tools/config.hpp>
#include <boost/math/tools/promotion.hpp>
#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/math/policies/error_handling.hpp>
namespace boost{
namespace math{
// Recurrence relation for Hermite polynomials:
template <class T1, class T2, class T3>
BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T1, T2, T3>::type
hermite_next(unsigned n, T1 x, T2 Hn, T3 Hnm1)
{
using promoted_type = tools::promote_args_t<T1, T2, T3>;
return (2 * promoted_type(x) * promoted_type(Hn) - 2 * n * promoted_type(Hnm1));
}
namespace detail{
// Implement Hermite polynomials via recurrence:
template <class T>
BOOST_MATH_GPU_ENABLED T hermite_imp(unsigned n, T x)
{
T p0 = 1;
T p1 = 2 * x;
if(n == 0)
return p0;
unsigned c = 1;
while(c < n)
{
BOOST_MATH_GPU_SAFE_SWAP(p0, p1);
p1 = static_cast<T>(hermite_next(c, x, p0, p1));
++c;
}
return p1;
}
} // namespace detail
template <class T, class Policy>
BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type
hermite(unsigned n, T x, const Policy&)
{
typedef typename tools::promote_args<T>::type result_type;
typedef typename policies::evaluation<result_type, Policy>::type value_type;
return policies::checked_narrowing_cast<result_type, Policy>(detail::hermite_imp(n, static_cast<value_type>(x)), "boost::math::hermite<%1%>(unsigned, %1%)");
}
template <class T>
BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type
hermite(unsigned n, T x)
{
return boost::math::hermite(n, x, policies::policy<>());
}
} // namespace math
} // namespace boost
#endif // BOOST_MATH_SPECIAL_HERMITE_HPP
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