mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
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269 lines
8.5 KiB
C++
269 lines
8.5 KiB
C++
/*=============================================================================
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Copyright (c) 2011-2016 Bolero MURAKAMI
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https://github.com/bolero-MURAKAMI/Sprout
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================*/
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#ifndef SPROUT_MATH_BERNOULLI_HPP
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#define SPROUT_MATH_BERNOULLI_HPP
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#include <type_traits>
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#include <sprout/config.hpp>
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#include <sprout/workaround/std/cstddef.hpp>
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#include <sprout/array/array.hpp>
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#include <sprout/assert.hpp>
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namespace sprout {
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namespace math {
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namespace detail {
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# define SPROUT_BERNOULLI_TABLE_DEF_FLOAT \
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{{ \
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1.F, \
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1.F / 6, \
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-1.F / 30, \
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1.F / 42, \
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-1.F / 30, \
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5.F / 66, \
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-691.F / 2730, \
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7.F / 6, \
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-3617.F / 510, \
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43867.F / 798, \
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-174611.F / 330, \
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854513.F / 138, \
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-236364091.F / 2730, \
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8553103.F / 6, \
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-236364091.F / 870, \
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8615841276005.F / 14322, \
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-7709321041217.F / 510, \
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2577687858367.F / 6, \
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-26315271553053477373.F / 1919190, \
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2929993913841559.F / 6, \
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-261082718496449122051.F / 13530, \
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1520097643918070802691.F / 1806, \
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-2.783326957930102423502e22F / 690, \
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5.96451111593912163278e23F / 282, \
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-1.20866265222965259346e23F, \
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7.500866746076964366856e24F, \
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-5.038778101481068914138e26F, \
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3.65287764848181233351e28F, \
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-2.849876930245088222627e30F, \
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2.386542749968362764465e32F, \
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-2.139994925722533366581e34F, \
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2.050097572347809756992e36F, \
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-2.09380059113463784091e38F \
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}}
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# define SPROUT_BERNOULLI_TABLE_DEF_DOUBLE \
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{{ \
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1., \
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1. / 6, \
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-1. / 30, \
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1. / 42, \
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-1. / 30, \
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5. / 66, \
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-691. / 2730, \
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7. / 6, \
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-3617. / 510, \
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43867. / 798, \
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-174611. / 330, \
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854513. / 138, \
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-236364091. / 2730, \
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8553103. / 6, \
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-236364091. / 870, \
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8615841276005. / 14322, \
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-7709321041217. / 510, \
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2577687858367. / 6, \
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-26315271553053477373. / 1919190, \
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2929993913841559. / 6, \
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-261082718496449122051. / 13530, \
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1520097643918070802691. / 1806, \
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-2.783326957930102423502e22 / 690, \
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5.96451111593912163278e23 / 282, \
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-1.20866265222965259346e23, \
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7.500866746076964366856e24, \
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-5.038778101481068914138e26, \
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3.65287764848181233351e28, \
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-2.849876930245088222627e30, \
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2.386542749968362764465e32, \
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-2.139994925722533366581e34, \
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2.050097572347809756992e36, \
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-2.09380059113463784091e38, \
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2.275269648846351555965e40, \
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-2.62577102862395760473e42, \
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3.21250821027180325182e44, \
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-4.159827816679471091392e46, \
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5.692069548203528002388e48, \
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-8.21836294197845756923e50, \
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1.250290432716699301673e53, \
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-2.001558323324837027493e55, \
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3.36749829153643742334e57, \
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-5.947097050313544771866e59, \
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1.101191032362797755956e62, \
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-2.135525954525350118866e64, \
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4.332889698664119241962e66, \
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-9.18855282416693282262e68, \
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2.034689677632907449346e71, \
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-4.70038339580357310786e73, \
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1.131804344548424927068e76, \
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-2.838224957069370695926e78 \
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}}
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# define SPROUT_BERNOULLI_TABLE_DEF_LONG_DOUBLE \
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{{ \
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1.L, \
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1.L / 6, \
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-1.L / 30, \
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1.L / 42, \
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-1.L / 30, \
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5.L / 66, \
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-691.L / 2730, \
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7.L / 6, \
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-3617.L / 510, \
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43867.L / 798, \
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-174611.L / 330, \
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854513.L / 138, \
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-236364091.L / 2730, \
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8553103.L / 6, \
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-236364091.L / 870, \
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8615841276005.L / 14322, \
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-7709321041217.L / 510, \
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2577687858367.L / 6, \
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-26315271553053477373.L / 1919190, \
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2929993913841559.L / 6, \
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-261082718496449122051.L / 13530, \
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1520097643918070802691.L / 1806, \
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-2.783326957930102423502e22L / 690, \
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5.96451111593912163278e23L / 282, \
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-1.20866265222965259346e23L, \
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7.500866746076964366856e24L, \
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-5.038778101481068914138e26L, \
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3.65287764848181233351e28L, \
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-2.849876930245088222627e30L, \
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2.386542749968362764465e32L, \
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-2.139994925722533366581e34L, \
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2.050097572347809756992e36L, \
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-2.09380059113463784091e38L, \
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2.275269648846351555965e40L, \
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-2.62577102862395760473e42L, \
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3.21250821027180325182e44L, \
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-4.159827816679471091392e46L, \
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5.692069548203528002388e48L, \
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-8.21836294197845756923e50L, \
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1.250290432716699301673e53L, \
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-2.001558323324837027493e55L, \
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3.36749829153643742334e57L, \
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-5.947097050313544771866e59L, \
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1.101191032362797755956e62L, \
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-2.135525954525350118866e64L, \
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4.332889698664119241962e66L, \
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-9.18855282416693282262e68L, \
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2.034689677632907449346e71L, \
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-4.70038339580357310786e73L, \
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1.131804344548424927068e76L, \
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-2.838224957069370695926e78L \
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}}
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template<typename T, typename X = void>
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struct bernoulli_numbers;
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template<typename X>
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struct bernoulli_numbers<float, X> {
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public:
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typedef float type;
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public:
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SPROUT_STATIC_CONSTEXPR std::size_t limit = 64;
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public:
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typedef sprout::array<type, limit / 2 + 1> table_type;
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public:
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SPROUT_STATIC_CONSTEXPR table_type table
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SPROUT_STATIC_CONSTEXPR_DATA_MEMBER_INNER(SPROUT_BERNOULLI_TABLE_DEF_FLOAT)
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;
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};
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template<typename X>
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SPROUT_CONSTEXPR_OR_CONST std::size_t sprout::math::detail::bernoulli_numbers<
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float, X
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>::limit;
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template<typename X>
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SPROUT_CONSTEXPR_OR_CONST typename sprout::math::detail::bernoulli_numbers<
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float, X
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>::table_type sprout::math::detail::bernoulli_numbers<
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float, X
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>::table SPROUT_STATIC_CONSTEXPR_DATA_MEMBER_OUTER(SPROUT_BERNOULLI_TABLE_DEF_FLOAT);
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template<typename X>
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struct bernoulli_numbers<double, X> {
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public:
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typedef double type;
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public:
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SPROUT_STATIC_CONSTEXPR std::size_t limit = 100;
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public:
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typedef sprout::array<type, limit / 2 + 1> table_type;
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public:
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SPROUT_STATIC_CONSTEXPR table_type table
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SPROUT_STATIC_CONSTEXPR_DATA_MEMBER_INNER(SPROUT_BERNOULLI_TABLE_DEF_DOUBLE)
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;
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};
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template<typename X>
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SPROUT_CONSTEXPR_OR_CONST std::size_t sprout::math::detail::bernoulli_numbers<
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double, X
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>::limit;
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template<typename X>
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SPROUT_CONSTEXPR_OR_CONST typename sprout::math::detail::bernoulli_numbers<
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double, X
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>::table_type sprout::math::detail::bernoulli_numbers<
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double, X
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>::table SPROUT_STATIC_CONSTEXPR_DATA_MEMBER_OUTER(SPROUT_BERNOULLI_TABLE_DEF_DOUBLE);
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template<typename X>
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struct bernoulli_numbers<long double, X> {
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public:
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typedef long double type;
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public:
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SPROUT_STATIC_CONSTEXPR std::size_t limit = 100;
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public:
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typedef sprout::array<type, limit / 2 + 1> table_type;
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public:
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SPROUT_STATIC_CONSTEXPR table_type table
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SPROUT_STATIC_CONSTEXPR_DATA_MEMBER_INNER(SPROUT_BERNOULLI_TABLE_DEF_LONG_DOUBLE)
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;
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};
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template<typename X>
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SPROUT_CONSTEXPR_OR_CONST std::size_t sprout::math::detail::bernoulli_numbers<
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long double, X
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>::limit;
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template<typename X>
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SPROUT_CONSTEXPR_OR_CONST typename sprout::math::detail::bernoulli_numbers<
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long double, X
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>::table_type sprout::math::detail::bernoulli_numbers<
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long double, X
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>::table SPROUT_STATIC_CONSTEXPR_DATA_MEMBER_OUTER(SPROUT_BERNOULLI_TABLE_DEF_LONG_DOUBLE);
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# undef SPROUT_BERNOULLI_TABLE_DEF_FLOAT
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# undef SPROUT_BERNOULLI_TABLE_DEF_DOUBLE
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# undef SPROUT_BERNOULLI_TABLE_DEF_LONG_DOUBLE
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} // namespace detail
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//
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// bernoulli_number_limit
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//
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template<typename T, typename = typename std::enable_if<std::is_floating_point<T>::value>::type>
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inline SPROUT_CONSTEXPR std::size_t bernoulli_number_limit() {
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typedef typename std::remove_cv<T>::type type;
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return sprout::math::detail::bernoulli_numbers<type>::limit;
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}
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//
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// bernoulli_number
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//
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template<typename T, typename = typename std::enable_if<std::is_floating_point<T>::value>::type>
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inline SPROUT_CONSTEXPR T bernoulli_number(std::size_t x) {
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typedef typename std::remove_cv<T>::type type;
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return SPROUT_ASSERT(x <= sprout::math::bernoulli_number_limit<type>()),
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x == 1 ? type(-1) / 2
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: x % 2 ? type(0)
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: sprout::math::detail::bernoulli_numbers<type>::table[x / 2]
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;
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}
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} // namespace math
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using sprout::math::bernoulli_number;
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} // namespace sprout
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#endif // #ifndef SPROUT_MATH_BERNOULLI_HPP
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