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/*################################################################################
##
## Copyright (C) 2016-2024 Keith O'Hara
##
## This file is part of the GCE-Math C++ library.
##
## Licensed under the Apache License, Version 2.0 (the "License");
## you may not use this file except in compliance with the License.
## You may obtain a copy of the License at
##
## http://www.apache.org/licenses/LICENSE-2.0
##
## Unless required by applicable law or agreed to in writing, software
## distributed under the License is distributed on an "AS IS" BASIS,
## WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
## See the License for the specific language governing permissions and
## limitations under the License.
##
################################################################################*/
#ifndef _gcem_beta_HPP
#define _gcem_beta_HPP
#include <cmath>
#include <type_traits>
namespace gcem
{
/**
* Compile-time beta function
*
* @param a a real-valued input.
* @param b a real-valued input.
* @return the beta function using \f[ \text{B}(\alpha,\beta) := \int_0^1 t^{\alpha - 1} (1-t)^{\beta - 1} dt = \frac{\Gamma(\alpha)\Gamma(\beta)}{\Gamma(\alpha + \beta)} \f]
* where \f$ \Gamma \f$ denotes the gamma function.
*/
template<typename T1, typename T2>
constexpr
common_return_t<T1,T2>
beta(const T1 a, const T2 b)
noexcept
{
if (std::is_constant_evaluated()) {
return exp( lbeta(a,b) );
} else {
#ifdef __cpp_lib_math_special_functions
return std::beta(a, b);
#else
return exp( lbeta(a,b) );
#endif
}
}
}
#endif