Sprout/sprout/math/bernoulli.hpp

#ifndef SPROUT_MATH_BERNOULLI_HPP
#define SPROUT_MATH_BERNOULLI_HPP

#include <cstddef>
#include <stdexcept>
#include <type_traits>
#include <sprout/config.hpp>
#include <sprout/array.hpp>

namespace sprout {
	namespace math {
		namespace detail {
			template<typename T>
			struct bernoulli_numbers;

			template<>
			struct bernoulli_numbers<float> {
			public:
				typedef float type;
			public:
				SPROUT_STATIC_CONSTEXPR std::size_t limit = 64;
			public:
				typedef sprout::array<type, limit / 2 + 1> table_type;
			public:
				SPROUT_STATIC_CONSTEXPR table_type table = table_type{{
					1.F,
					1.F / 6,
					-1.F / 30,
					1.F / 42,
					-1.F / 30,
					5.F / 66,
					-691.F / 2730,
					7.F / 6,
					-3617.F / 510,
					43867.F / 798,
					-174611.F / 330,
					854513.F / 138,
					-236364091.F / 2730,
					8553103.F / 6,
					-236364091.F / 870,
					8615841276005.F / 14322,
					-7709321041217.F / 510,
					2577687858367.F / 6,
					-26315271553053477373.F / 1919190,
					2929993913841559.F / 6,
					-261082718496449122051.F / 13530,
					1520097643918070802691.F / 1806,
					-2.783326957930102423502e22F / 690,
					5.96451111593912163278e23F / 282,
					-1.20866265222965259346e23F,
					7.500866746076964366856e24F,
					-5.038778101481068914138e26F,
					3.65287764848181233351e28F,
					-2.849876930245088222627e30F,
					2.386542749968362764465e32F,
					-2.139994925722533366581e34F,
					2.050097572347809756992e36F,
					-2.09380059113463784091e38F
				}};
			};
			SPROUT_CONSTEXPR typename sprout::math::detail::bernoulli_numbers<
				float
			>::table_type sprout::math::detail::bernoulli_numbers<
				float
			>::table;

			template<>
			struct bernoulli_numbers<double> {
			public:
				typedef double type;
			public:
				SPROUT_STATIC_CONSTEXPR std::size_t limit = 100;
			public:
				typedef sprout::array<type, limit / 2 + 1> table_type;
			public:
				SPROUT_STATIC_CONSTEXPR table_type table = table_type{{
					1.,
					1. / 6,
					-1. / 30,
					1. / 42,
					-1. / 30,
					5. / 66,
					-691. / 2730,
					7. / 6,
					-3617. / 510,
					43867. / 798,
					-174611. / 330,
					854513. / 138,
					-236364091. / 2730,
					8553103. / 6,
					-236364091. / 870,
					8615841276005. / 14322,
					-7709321041217. / 510,
					2577687858367. / 6,
					-26315271553053477373. / 1919190,
					2929993913841559. / 6,
					-261082718496449122051. / 13530,
					1520097643918070802691. / 1806,
					-2.783326957930102423502e22 / 690,
					5.96451111593912163278e23 / 282,
					-1.20866265222965259346e23,
					7.500866746076964366856e24,
					-5.038778101481068914138e26,
					3.65287764848181233351e28,
					-2.849876930245088222627e30,
					2.386542749968362764465e32,
					-2.139994925722533366581e34,
					2.050097572347809756992e36,
					-2.09380059113463784091e38,
					2.275269648846351555965e40,
					-2.62577102862395760473e42,
					3.21250821027180325182e44,
					-4.159827816679471091392e46,
					5.692069548203528002388e48,
					-8.21836294197845756923e50,
					1.250290432716699301673e53,
					-2.001558323324837027493e55,
					3.36749829153643742334e57,
					-5.947097050313544771866e59,
					1.101191032362797755956e62,
					-2.135525954525350118866e64,
					4.332889698664119241962e66,
					-9.18855282416693282262e68 ,
					2.034689677632907449346e71,
					-4.70038339580357310786e73,
					1.131804344548424927068e76,
					-2.838224957069370695926e78
				}};
			};
			SPROUT_CONSTEXPR typename sprout::math::detail::bernoulli_numbers<
				double
			>::table_type sprout::math::detail::bernoulli_numbers<
				double
			>::table;

			template<>
			struct bernoulli_numbers<long double> {
			public:
				typedef long double type;
			public:
				SPROUT_STATIC_CONSTEXPR std::size_t limit = 100;
			public:
				typedef sprout::array<type, limit / 2 + 1> table_type;
			public:
				SPROUT_STATIC_CONSTEXPR table_type table = table_type{{
					1.L,
					1.L / 6,
					-1.L / 30,
					1.L / 42,
					-1.L / 30,
					5.L / 66,
					-691.L / 2730,
					7.L / 6,
					-3617.L / 510,
					43867.L / 798,
					-174611.L / 330,
					854513.L / 138,
					-236364091.L / 2730,
					8553103.L / 6,
					-236364091.L / 870,
					8615841276005.L / 14322,
					-7709321041217.L / 510,
					2577687858367.L / 6,
					-26315271553053477373.L / 1919190,
					2929993913841559.L / 6,
					-261082718496449122051.L / 13530,
					1520097643918070802691.L / 1806,
					-2.783326957930102423502e22L / 690,
					5.96451111593912163278e23L / 282,
					-1.20866265222965259346e23L,
					7.500866746076964366856e24L,
					-5.038778101481068914138e26L,
					3.65287764848181233351e28L,
					-2.849876930245088222627e30L,
					2.386542749968362764465e32L,
					-2.139994925722533366581e34L,
					2.050097572347809756992e36L,
					-2.09380059113463784091e38L,
					2.275269648846351555965e40L,
					-2.62577102862395760473e42L,
					3.21250821027180325182e44L,
					-4.159827816679471091392e46L,
					5.692069548203528002388e48L,
					-8.21836294197845756923e50L,
					1.250290432716699301673e53L,
					-2.001558323324837027493e55L,
					3.36749829153643742334e57L,
					-5.947097050313544771866e59L,
					1.101191032362797755956e62L,
					-2.135525954525350118866e64L,
					4.332889698664119241962e66L,
					-9.18855282416693282262e68L,
					2.034689677632907449346e71L,
					-4.70038339580357310786e73L,
					1.131804344548424927068e76L,
					-2.838224957069370695926e78L
				}};
			};
			SPROUT_CONSTEXPR typename sprout::math::detail::bernoulli_numbers<
				long double
			>::table_type sprout::math::detail::bernoulli_numbers<
				long double
			>::table;
		}	// namespace detail
		//
		// bernoulli_number_limit
		//
		template<typename T, typename = typename std::enable_if<std::is_floating_point<T>::value>::type>
		SPROUT_CONSTEXPR std::size_t bernoulli_number_limit() {
			typedef typename std::remove_cv<T>::type type;
			return sprout::math::detail::bernoulli_numbers<type>::limit;
		}
		//
		// bernoulli_number
		//
		template<typename T, typename = typename std::enable_if<std::is_floating_point<T>::value>::type>
		SPROUT_CONSTEXPR T bernoulli_number(std::size_t x) {
			typedef typename std::remove_cv<T>::type type;
			return x <= sprout::math::bernoulli_number_limit<type>()
				? x == 1 ? type(-1) / 2
					: x % 2 ? type(0)
					: sprout::math::detail::bernoulli_numbers<type>::table[x / 2]
				: throw std::invalid_argument("bernoulli_number(): argument limit exceeded")
				;
		}
	}	// namespace math

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

#endif	// #ifndef SPROUT_MATH_BERNOULLI_HPP