mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
synced 2024-12-23 21:25:49 +00:00
add math::bernoulli_number
add type_traits is_int, is_uint
This commit is contained in:
bolero-MURAKAMI
parent
576744f408
commit
29b9d07975
6 changed files with 395 additions and 51 deletions
231
sprout/math/bernoulli.hpp
Normal file
231
sprout/math/bernoulli.hpp
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@ -0,0 +1,231 @@
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#ifndef SPROUT_MATH_BERNOULLI_HPP
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#define SPROUT_MATH_BERNOULLI_HPP
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#include <cstddef>
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#include <stdexcept>
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#include <type_traits>
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#include <sprout/config.hpp>
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#include <sprout/array.hpp>
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namespace sprout {
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namespace math {
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namespace detail {
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template<typename T>
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struct bernoulli_numbers;
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template<>
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struct bernoulli_numbers<float> {
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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 = table_type{{
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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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};
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SPROUT_CONSTEXPR typename sprout::math::detail::bernoulli_numbers<
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float
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>::table_type sprout::math::detail::bernoulli_numbers<
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float
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>::table;
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template<>
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struct bernoulli_numbers<double> {
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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 = table_type{{
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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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};
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SPROUT_CONSTEXPR typename sprout::math::detail::bernoulli_numbers<
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double
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>::table_type sprout::math::detail::bernoulli_numbers<
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double
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>::table;
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template<>
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struct bernoulli_numbers<long double> {
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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 = table_type{{
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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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};
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SPROUT_CONSTEXPR typename sprout::math::detail::bernoulli_numbers<
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long double
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>::table_type sprout::math::detail::bernoulli_numbers<
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long double
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>::table;
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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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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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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 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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: throw std::invalid_argument("bernoulli_number(): argument limit exceeded")
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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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@ -2,20 +2,23 @@
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#define SPROUT_MATH_FACTORIAL_HPP
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#include <cstddef>
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#include <cstdint>
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#include <stdexcept>
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#include <type_traits>
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#include <sprout/config.hpp>
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#include <sprout/array.hpp>
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#include <sprout/type_traits/is_int.hpp>
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#include <sprout/type_traits/is_uint.hpp>
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namespace sprout {
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namespace math {
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namespace detail {
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template<typename T>
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template<typename T, typename Enable = void>
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struct factorials;
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template<>
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struct factorials<std::int8_t> {
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template<typename T>
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struct factorials<T, typename std::enable_if<sprout::is_int<T>::value && sizeof(T) == 1>::type> {
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public:
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typedef std::int8_t type;
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typedef T type;
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public:
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SPROUT_STATIC_CONSTEXPR std::size_t limit = 5;
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public:
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@ -30,11 +33,17 @@ namespace sprout {
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120
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}};
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};
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<std::int8_t>::table_type sprout::math::detail::factorials<std::int8_t>::table;
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template<>
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struct factorials<std::uint8_t> {
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template<typename T>
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_int<T>::value && sizeof(T) == 1>::type
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>::table_type sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_int<T>::value && sizeof(T) == 1>::type
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>::table;
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template<typename T>
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struct factorials<T, typename std::enable_if<sprout::is_uint<T>::value && sizeof(T) == 1>::type> {
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public:
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typedef std::uint8_t type;
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typedef T type;
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public:
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SPROUT_STATIC_CONSTEXPR std::size_t limit = 5;
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public:
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@ -49,11 +58,17 @@ namespace sprout {
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120
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}};
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};
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<std::uint8_t>::table_type sprout::math::detail::factorials<std::uint8_t>::table;
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template<>
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struct factorials<std::int16_t> {
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template<typename T>
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_uint<T>::value && sizeof(T) == 1>::type
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>::table_type sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_uint<T>::value && sizeof(T) == 1>::type
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>::table;
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template<typename T>
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struct factorials<T, typename std::enable_if<sprout::is_int<T>::value && sizeof(T) == 2>::type> {
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public:
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typedef std::int16_t type;
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typedef T type;
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public:
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SPROUT_STATIC_CONSTEXPR std::size_t limit = 7;
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public:
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@ -70,11 +85,17 @@ namespace sprout {
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5040
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}};
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};
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<std::int16_t>::table_type sprout::math::detail::factorials<std::int16_t>::table;
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template<>
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struct factorials<std::uint16_t> {
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template<typename T>
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_int<T>::value && sizeof(T) == 2>::type
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>::table_type sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_int<T>::value && sizeof(T) == 2>::type
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>::table;
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template<typename T>
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struct factorials<T, typename std::enable_if<sprout::is_uint<T>::value && sizeof(T) == 2>::type> {
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public:
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typedef std::uint16_t type;
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typedef T type;
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public:
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SPROUT_STATIC_CONSTEXPR std::size_t limit = 8;
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public:
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@ -92,11 +113,17 @@ namespace sprout {
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40320
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}};
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};
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<std::uint16_t>::table_type sprout::math::detail::factorials<std::uint16_t>::table;
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template<>
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struct factorials<std::int32_t> {
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template<typename T>
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_uint<T>::value && sizeof(T) == 2>::type
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>::table_type sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_uint<T>::value && sizeof(T) == 2>::type
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>::table;
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template<typename T>
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struct factorials<T, typename std::enable_if<sprout::is_int<T>::value && sizeof(T) == 4>::type> {
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public:
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typedef std::int32_t type;
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typedef T type;
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public:
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SPROUT_STATIC_CONSTEXPR std::size_t limit = 11;
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public:
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@ -117,11 +144,17 @@ namespace sprout {
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39916800
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}};
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};
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<std::int32_t>::table_type sprout::math::detail::factorials<std::int32_t>::table;
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template<>
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struct factorials<std::uint32_t> {
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template<typename T>
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_int<T>::value && sizeof(T) == 4>::type
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>::table_type sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_int<T>::value && sizeof(T) == 4>::type
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>::table;
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template<typename T>
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struct factorials<T, typename std::enable_if<sprout::is_uint<T>::value && sizeof(T) == 4>::type> {
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public:
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typedef std::uint32_t type;
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typedef T type;
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public:
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SPROUT_STATIC_CONSTEXPR std::size_t limit = 11;
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public:
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@ -142,11 +175,17 @@ namespace sprout {
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39916800
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}};
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};
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<std::uint32_t>::table_type sprout::math::detail::factorials<std::uint32_t>::table;
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template<>
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struct factorials<std::int64_t> {
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template<typename T>
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_uint<T>::value && sizeof(T) == 4>::type
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>::table_type sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_uint<T>::value && sizeof(T) == 4>::type
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>::table;
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template<typename T>
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struct factorials<T, typename std::enable_if<sprout::is_int<T>::value && sizeof(T) == 8>::type> {
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public:
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typedef std::int64_t type;
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typedef T type;
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public:
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SPROUT_STATIC_CONSTEXPR std::size_t limit = 20;
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public:
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@ -176,11 +215,17 @@ namespace sprout {
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INT64_C(2432902008176640000)
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}};
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};
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<std::int64_t>::table_type sprout::math::detail::factorials<std::int64_t>::table;
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template<>
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struct factorials<std::uint64_t> {
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template<typename T>
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SPROUT_CONSTEXPR typename sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_int<T>::value && sizeof(T) == 8>::type
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>::table_type sprout::math::detail::factorials<
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T, typename std::enable_if<sprout::is_int<T>::value && sizeof(T) == 8>::type
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>::table;
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||||
template<typename T>
|
||||
struct factorials<T, typename std::enable_if<sprout::is_uint<T>::value && sizeof(T) == 8>::type> {
|
||||
public:
|
||||
typedef std::uint64_t type;
|
||||
typedef T type;
|
||||
public:
|
||||
SPROUT_STATIC_CONSTEXPR std::size_t limit = 20;
|
||||
public:
|
||||
|
|
@ -210,11 +255,17 @@ namespace sprout {
|
|||
UINT64_C(2432902008176640000)
|
||||
}};
|
||||
};
|
||||
SPROUT_CONSTEXPR typename sprout::math::detail::factorials<std::uint64_t>::table_type sprout::math::detail::factorials<std::uint64_t>::table;
|
||||
template<>
|
||||
struct factorials<float> {
|
||||
template<typename T>
|
||||
SPROUT_CONSTEXPR typename sprout::math::detail::factorials<
|
||||
T, typename std::enable_if<sprout::is_uint<T>::value && sizeof(T) == 8>::type
|
||||
>::table_type sprout::math::detail::factorials<
|
||||
T, typename std::enable_if<sprout::is_uint<T>::value && sizeof(T) == 8>::type
|
||||
>::table;
|
||||
|
||||
template<typename T>
|
||||
struct factorials<T, typename std::enable_if<std::is_same<T, float>::value>::type> {
|
||||
public:
|
||||
typedef float type;
|
||||
typedef T type;
|
||||
public:
|
||||
SPROUT_STATIC_CONSTEXPR std::size_t limit = 34;
|
||||
public:
|
||||
|
|
@ -258,11 +309,17 @@ namespace sprout {
|
|||
0.29523279903960414084761860964352e39F
|
||||
}};
|
||||
};
|
||||
SPROUT_CONSTEXPR typename sprout::math::detail::factorials<float>::table_type sprout::math::detail::factorials<float>::table;
|
||||
template<>
|
||||
struct factorials<double> {
|
||||
template<typename T>
|
||||
SPROUT_CONSTEXPR typename sprout::math::detail::factorials<
|
||||
T, typename std::enable_if<std::is_same<T, float>::value>::type
|
||||
>::table_type sprout::math::detail::factorials<
|
||||
T, typename std::enable_if<std::is_same<T, float>::value>::type
|
||||
>::table;
|
||||
|
||||
template<typename T>
|
||||
struct factorials<T, typename std::enable_if<std::is_same<T, double>::value>::type> {
|
||||
public:
|
||||
typedef double type;
|
||||
typedef T type;
|
||||
public:
|
||||
SPROUT_STATIC_CONSTEXPR std::size_t limit = 170;
|
||||
public:
|
||||
|
|
@ -442,11 +499,17 @@ namespace sprout {
|
|||
0.7257415615307998967396728211129263114717e307
|
||||
}};
|
||||
};
|
||||
SPROUT_CONSTEXPR typename sprout::math::detail::factorials<double>::table_type sprout::math::detail::factorials<double>::table;
|
||||
template<>
|
||||
struct factorials<long double> {
|
||||
template<typename T>
|
||||
SPROUT_CONSTEXPR typename sprout::math::detail::factorials<
|
||||
T, typename std::enable_if<std::is_same<T, double>::value>::type
|
||||
>::table_type sprout::math::detail::factorials<
|
||||
T, typename std::enable_if<std::is_same<T, double>::value>::type
|
||||
>::table;
|
||||
|
||||
template<typename T>
|
||||
struct factorials<T, typename std::enable_if<std::is_same<T, long double>::value>::type> {
|
||||
public:
|
||||
typedef long double type;
|
||||
typedef T type;
|
||||
public:
|
||||
SPROUT_STATIC_CONSTEXPR std::size_t limit = 170;
|
||||
public:
|
||||
|
|
@ -626,22 +689,29 @@ namespace sprout {
|
|||
0.7257415615307998967396728211129263114717e307L
|
||||
}};
|
||||
};
|
||||
SPROUT_CONSTEXPR typename sprout::math::detail::factorials<long double>::table_type sprout::math::detail::factorials<long double>::table;
|
||||
template<typename T>
|
||||
SPROUT_CONSTEXPR typename sprout::math::detail::factorials<
|
||||
T, typename std::enable_if<std::is_same<T, long double>::value>::type
|
||||
>::table_type sprout::math::detail::factorials<
|
||||
T, typename std::enable_if<std::is_same<T, long double>::value>::type
|
||||
>::table;
|
||||
} // namespace detail
|
||||
//
|
||||
// factorial_limit
|
||||
//
|
||||
template<typename T>
|
||||
template<typename T, typename = typename std::enable_if<std::is_arithmetic<T>::value>::type>
|
||||
SPROUT_CONSTEXPR std::size_t factorial_limit() {
|
||||
return sprout::math::detail::factorials<T>::limit;
|
||||
typedef typename std::remove_cv<T>::type type;
|
||||
return sprout::math::detail::factorials<type>::limit;
|
||||
}
|
||||
//
|
||||
// factorial
|
||||
//
|
||||
template<typename T>
|
||||
template<typename T, typename = typename std::enable_if<std::is_arithmetic<T>::value>::type>
|
||||
SPROUT_CONSTEXPR T factorial(std::size_t x) {
|
||||
return x <= sprout::math::factorial_limit<T>()
|
||||
? sprout::math::detail::factorials<T>::table[x]
|
||||
typedef typename std::remove_cv<T>::type type;
|
||||
return x <= sprout::math::factorial_limit<type>()
|
||||
? sprout::math::detail::factorials<type>::table[x]
|
||||
: throw std::invalid_argument("factorial(): argument limit exceeded")
|
||||
;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -9,5 +9,6 @@
|
|||
#include <sprout/math/power.hpp>
|
||||
#include <sprout/math/operations.hpp>
|
||||
#include <sprout/math/factorial.hpp>
|
||||
#include <sprout/math/bernoulli.hpp>
|
||||
|
||||
#endif // #ifndef SPROUT_MATH_FUNCTIONS_HPP
|
||||
|
|
|
|||
|
|
@ -2,6 +2,8 @@
|
|||
#define SPROUT_TYPE_TRAITS_HPP
|
||||
|
||||
#include <sprout/config.hpp>
|
||||
#include <sprout/type_traits/is_int.hpp>
|
||||
#include <sprout/type_traits/is_uint.hpp>
|
||||
#include <sprout/type_traits/lvalue_reference.hpp>
|
||||
#include <sprout/type_traits/const_reference.hpp>
|
||||
#include <sprout/type_traits/has_xxx.hpp>
|
||||
|
|
|
|||
20
sprout/type_traits/is_int.hpp
Normal file
20
sprout/type_traits/is_int.hpp
Normal file
|
|
@ -0,0 +1,20 @@
|
|||
#ifndef SPROUT_TYPE_TRAITS_IS_INT_HPP
|
||||
#define SPROUT_TYPE_TRAITS_IS_INT_HPP
|
||||
|
||||
#include <type_traits>
|
||||
#include <sprout/config.hpp>
|
||||
|
||||
namespace sprout {
|
||||
//
|
||||
// is_int
|
||||
//
|
||||
template<typename T>
|
||||
struct is_int
|
||||
: public std::integral_constant<
|
||||
bool,
|
||||
std::is_integral<T>::value && std::is_signed<T>::value
|
||||
>
|
||||
{};
|
||||
} // namespace sprout
|
||||
|
||||
#endif // #ifndef SPROUT_TYPE_TRAITS_IS_INT_HPP
|
||||
20
sprout/type_traits/is_uint.hpp
Normal file
20
sprout/type_traits/is_uint.hpp
Normal file
|
|
@ -0,0 +1,20 @@
|
|||
#ifndef SPROUT_TYPE_TRAITS_IS_UINT_HPP
|
||||
#define SPROUT_TYPE_TRAITS_IS_UINT_HPP
|
||||
|
||||
#include <type_traits>
|
||||
#include <sprout/config.hpp>
|
||||
|
||||
namespace sprout {
|
||||
//
|
||||
// is_uint
|
||||
//
|
||||
template<typename T>
|
||||
struct is_uint
|
||||
: public std::integral_constant<
|
||||
bool,
|
||||
std::is_integral<T>::value && std::is_unsigned<T>::value
|
||||
>
|
||||
{};
|
||||
} // namespace sprout
|
||||
|
||||
#endif // #ifndef SPROUT_TYPE_TRAITS_IS_UINT_HPP
|
||||
Loading…
Reference in a new issue