Sprout/sprout/math/tgamma.hpp

/*=============================================================================
  Copyright (c) 2011-2014 Bolero MURAKAMI
  https://github.com/bolero-MURAKAMI/Sprout

  Distributed under 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 SPROUT_MATH_TGAMMA_HPP
#define SPROUT_MATH_TGAMMA_HPP

#include <cstddef>
#include <type_traits>
#include <sprout/config.hpp>
#include <sprout/limits.hpp>
#include <sprout/math/detail/config.hpp>
#include <sprout/math/detail/float_compute.hpp>
#include <sprout/math/isnan.hpp>
#include <sprout/math/copysign.hpp>
#include <sprout/math/factorial.hpp>
#include <sprout/math/iround.hpp>
#include <sprout/math/is_integer.hpp>
#include <sprout/algorithm/clamp.hpp>
#include <sprout/type_traits/enabler_if.hpp>
#include HDR_ALGORITHM_MIN_MAX_SSCRISK_CEL_OR_SPROUT

namespace sprout {
	namespace math {
		namespace detail {
#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
			inline SPROUT_CONSTEXPR float
			builtin_tgamma(float x) {
				return __builtin_tgammaf(x);
			}
			inline SPROUT_CONSTEXPR double
			builtin_tgamma(double x) {
				return __builtin_tgamma(x);
			}
			inline SPROUT_CONSTEXPR long double
			builtin_tgamma(long double x) {
				return __builtin_tgammal(x);
			}
#endif

			template<typename T>
			inline SPROUT_CONSTEXPR T
			tgamma_impl_y(T w) {
				return ((((((((((((
					-1.99542863674e-7 * w + 1.337767384067e-6) * w
					- 2.591225267689e-6) * w - 1.7545539395205e-5) * w
					+ 1.45596568617526e-4) * w - 3.60837876648255e-4) * w
					- 8.04329819255744e-4) * w + 0.008023273027855346) * w
					- 0.017645244547851414) * w - 0.024552490005641278) * w
					+ 0.19109110138763841) * w - 0.233093736421782878) * w
					- 0.422784335098466784) * w + 0.99999999999999999
					;
			}
			template<typename T>
			inline SPROUT_CONSTEXPR T
			tgamma_impl_t_pos(T x, std::size_t n, std::size_t last) {
				return last - n == 1
					? x - static_cast<T>(n)
					: sprout::math::detail::tgamma_impl_t_pos(x, n, n + (last - n) / 2)
						* sprout::math::detail::tgamma_impl_t_pos(x, n + (last - n) / 2, last)
					;
			}
			template<typename T>
			inline SPROUT_CONSTEXPR T
			tgamma_impl_t_neg(T x, std::size_t n, std::size_t last) {
				return last - n == 1
					? x + static_cast<T>(n)
					: sprout::math::detail::tgamma_impl_t_neg(x, n, n + (last - n) / 2)
						* sprout::math::detail::tgamma_impl_t_neg(x, n + (last - n) / 2, last)
					;
			}
			template<typename T>
			inline SPROUT_CONSTEXPR T
			tgamma_impl_t_pos_rec(T x, std::size_t n, std::size_t last) {
				return last - n == 1
					? T(1) / (x - static_cast<T>(n))
					: sprout::math::detail::tgamma_impl_t_pos_rec(x, n, n + (last - n) / 2)
						* sprout::math::detail::tgamma_impl_t_pos_rec(x, n + (last - n) / 2, last)
					;
			}
			template<typename T>
			inline SPROUT_CONSTEXPR T
			tgamma_impl_t_neg_rec(T x, std::size_t n, std::size_t last) {
				return last - n == 1
					? T(1) / (x + static_cast<T>(n))
					: sprout::math::detail::tgamma_impl_t_neg_rec(x, n, n + (last - n) / 2)
						* sprout::math::detail::tgamma_impl_t_neg_rec(x, n + (last - n) / 2, last)
					;
			}
			template<typename T>
			inline SPROUT_CONSTEXPR T
			tgamma_impl_2_pos_rec(T x, T y, T t) {
				return t == 0 ? sprout::numeric_limits<T>::infinity()
					: (x - T(1)) / y / t
					;
			}
			template<typename T>
			inline SPROUT_CONSTEXPR T
			tgamma_impl_1(T x, int n) {
				return n == 1 ? (x - T(1)) / sprout::math::detail::tgamma_impl_y(x - (n + 2))
					: n == 0 ? T(1) / sprout::math::detail::tgamma_impl_y(x - (n + 2))
					: n == static_cast<int>(sprout::math::factorial_limit<T>())
						? sprout::math::detail::tgamma_impl_2_pos_rec(x, sprout::math::detail::tgamma_impl_y(x - (n + 2)), sprout::math::detail::tgamma_impl_t_pos_rec(x, 2, n + 1))
					: n == -static_cast<int>(sprout::math::factorial_limit<T>())
						? T(1) / sprout::math::detail::tgamma_impl_y(x - (n + 2)) * sprout::math::detail::tgamma_impl_t_neg_rec(x, 0, -n)
					: n > 1 ? (x - T(1)) / sprout::math::detail::tgamma_impl_y(x - (n + 2)) * sprout::math::detail::tgamma_impl_t_pos(x, 2, n + 1)
					: T(1) / sprout::math::detail::tgamma_impl_y(x - (n + 2)) / sprout::math::detail::tgamma_impl_t_neg(x, 0, -n)
					;
			}
			template<typename T>
			inline SPROUT_CONSTEXPR T
			tgamma_impl(T x) {
				return sprout::math::detail::tgamma_impl_1(
					x,
					sprout::clamp(
						sprout::math::iround(x - T(2)),
						-static_cast<int>(sprout::math::factorial_limit<T>()),
						static_cast<int>(sprout::math::factorial_limit<T>())
						)
					);
			}
		}	// namespace detail
		//
		// tgamma
		//
		// issue:
		//	[ !(SPROUT_USE_BUILTIN_CMATH_FUNCTION || SPROUT_USE_BUILTIN_COPYSIGN_FUNCTION) ]
		//	tgamma(-0) returns -<2D><> .
		//		# returns +<2B><> . ( same as tgamma(+0) )
		//
		template<
			typename FloatType,
			typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
		>
		inline SPROUT_CONSTEXPR FloatType
		tgamma(FloatType x) {
			return sprout::math::isnan(x) ? x
				: x == 0 ? sprout::math::copysign(sprout::numeric_limits<FloatType>::infinity(), x)
				: x == -sprout::numeric_limits<FloatType>::infinity() ? -sprout::numeric_limits<FloatType>::quiet_NaN()
				: x == sprout::numeric_limits<FloatType>::infinity() ? sprout::numeric_limits<FloatType>::infinity()
				: x < 0 && sprout::math::is_integer(x) ? sprout::numeric_limits<FloatType>::quiet_NaN()
#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
				: sprout::math::detail::builtin_tgamma(x)
#else
				: static_cast<FloatType>(sprout::math::detail::tgamma_impl(static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(x)))
#endif
				;
		}

		template<
			typename IntType,
			typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
		>
		inline SPROUT_CONSTEXPR double
		tgamma(IntType x) {
			return sprout::math::tgamma(static_cast<double>(x));
		}
	}	// namespace math

	using sprout::math::tgamma;
}	// namespace sprout

#endif	// #ifndef SPROUT_MATH_TGAMMA_HPP