mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
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804 lines
34 KiB
C++
804 lines
34 KiB
C++
/*=============================================================================
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Copyright (c) 2011-2014 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_RANDOM_BINOMIAL_DISTRIBUTION_HPP
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#define SPROUT_RANDOM_BINOMIAL_DISTRIBUTION_HPP
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#include <iosfwd>
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#include <istream>
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#include <sprout/config.hpp>
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#include <sprout/array/array.hpp>
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#include <sprout/cstdlib/abs.hpp>
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#include <sprout/math/abs.hpp>
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#include <sprout/math/log.hpp>
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#include <sprout/math/pow.hpp>
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#include <sprout/math/sqrt.hpp>
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#include <sprout/math/floor.hpp>
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#include <sprout/random/random_result.hpp>
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#include <sprout/random/uniform_01.hpp>
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#include <sprout/random/results.hpp>
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#include <sprout/assert.hpp>
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#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
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# include <sprout/workaround/recursive_function_template.hpp>
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#endif
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namespace sprout {
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namespace random {
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namespace detail {
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# define SPROUT_BINOMIAL_TABLE_DEF \
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table_type{{ \
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1, \
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1, \
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2, \
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6, \
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24, \
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120 \
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}}
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template<typename RealType>
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struct binomial_table {
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public:
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typedef sprout::array<RealType, 10> 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_BINOMIAL_TABLE_DEF)
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;
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};
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template<class RealType>
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SPROUT_CONSTEXPR_OR_CONST typename sprout::random::detail::binomial_table<RealType>::table_type
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sprout::random::detail::binomial_table<RealType>::table
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SPROUT_STATIC_CONSTEXPR_DATA_MEMBER_OUTER(SPROUT_BINOMIAL_TABLE_DEF)
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;
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# undef SPROUT_BINOMIAL_TABLE_DEF
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} // namespace detail
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//
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// binomial_distribution
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//
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template<typename IntType = int, typename RealType = double>
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class binomial_distribution {
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public:
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typedef RealType input_type;
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typedef IntType result_type;
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private:
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struct btrd_type {
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public:
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RealType r;
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RealType nr;
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RealType npq;
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RealType b;
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RealType a;
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RealType c;
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RealType alpha;
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RealType v_r;
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RealType u_rv_r;
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};
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public:
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//
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// param_type
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//
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class param_type {
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public:
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typedef binomial_distribution distribution_type;
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private:
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IntType t_;
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RealType p_;
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public:
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SPROUT_CONSTEXPR param_type()
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: t_(1)
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, p_(0.5)
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{}
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explicit SPROUT_CONSTEXPR param_type(IntType t_arg, RealType p_arg = RealType(0.5))
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: t_((SPROUT_ASSERT(t_arg >= IntType(0)), t_arg))
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, p_((SPROUT_ASSERT(RealType(0) <= p_arg && p_arg <= RealType(1)), p_arg))
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{}
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SPROUT_CONSTEXPR IntType t() const SPROUT_NOEXCEPT {
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return t_;
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}
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SPROUT_CONSTEXPR RealType p() const SPROUT_NOEXCEPT {
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return p_;
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}
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template<typename Elem, typename Traits>
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friend SPROUT_NON_CONSTEXPR std::basic_istream<Elem, Traits>& operator>>(
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std::basic_istream<Elem, Traits>& lhs,
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param_type& rhs
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)
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{
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IntType t;
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RealType p;
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if (lhs >> t >> std::ws >> p) {
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if (t >= IntType(0) && RealType(0) <= p && p <= RealType(1)) {
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rhs.t_ = t;
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rhs.p_ = p;
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} else {
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lhs.setstate(std::ios_base::failbit);
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}
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}
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return lhs;
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}
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template<typename Elem, typename Traits>
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friend SPROUT_NON_CONSTEXPR std::basic_ostream<Elem, Traits>& operator<<(
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std::basic_ostream<Elem, Traits>& lhs,
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param_type const& rhs
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)
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{
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return lhs << rhs.t_ << " " << rhs.p_;
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}
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friend SPROUT_CONSTEXPR bool operator==(param_type const& lhs, param_type const& rhs) SPROUT_NOEXCEPT {
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return lhs.t_ == rhs.t_ && lhs.p_ == rhs.p_;
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}
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friend SPROUT_CONSTEXPR bool operator!=(param_type const& lhs, param_type const& rhs) SPROUT_NOEXCEPT {
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return !(lhs == rhs);
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}
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};
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private:
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static SPROUT_CONSTEXPR IntType init_t(IntType t) {
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return t;
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}
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static SPROUT_CONSTEXPR RealType init_p(RealType p) {
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return RealType(0.5) < p ? 1 - p : p;
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}
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static SPROUT_CONSTEXPR IntType init_m(IntType t, RealType p) {
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return static_cast<IntType>((init_t(t) + 1) * init_p(p));
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}
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static SPROUT_CONSTEXPR btrd_type
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init_btrd_6(
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IntType, RealType, RealType r, RealType nr, RealType npq,
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RealType b, RealType a, RealType c, RealType alpha, RealType v_r
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)
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{
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return btrd_type{
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r, nr, npq,
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b, a, c, alpha, v_r,
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RealType(0.86) * v_r
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};
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}
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static SPROUT_CONSTEXPR btrd_type
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init_btrd_5(
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IntType t, RealType p, RealType r, RealType nr, RealType npq,
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RealType sqrt_npq, RealType b
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)
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{
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return init_btrd_6(
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t, p, r, nr, npq, b,
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RealType(-0.0873) + RealType(0.0248) * b + RealType(0.01) * p,
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t * p + RealType(0.5),
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(RealType(2.83) + RealType(5.1) / b) * sqrt_npq, RealType(0.92) - RealType(4.2) / b
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);
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}
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static SPROUT_CONSTEXPR btrd_type init_btrd_4(IntType t, RealType p, RealType r, RealType nr, RealType npq, RealType sqrt_npq) {
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return init_btrd_5(t, p, r, nr, npq, sqrt_npq, RealType(1.15) + RealType(2.53) * sqrt_npq);
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}
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static SPROUT_CONSTEXPR btrd_type init_btrd_3(IntType t, RealType p, RealType r, RealType nr, RealType npq) {
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return init_btrd_4(t, p, r, nr, npq, sprout::sqrt(npq));
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}
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static SPROUT_CONSTEXPR btrd_type init_btrd_2(IntType t, RealType p, RealType r) {
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return init_btrd_3(t, p, r, (t + 1) * r, t * p * (1 - p));
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}
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static SPROUT_CONSTEXPR btrd_type init_btrd_1(IntType t, RealType p) {
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return init_btrd_2(t, p, p / (1 - p));
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}
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static SPROUT_CONSTEXPR btrd_type init_btrd(IntType t, RealType p) {
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return init_btrd_1(init_t(t), init_p(p));
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}
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static SPROUT_CONSTEXPR RealType init_q_n(IntType t, RealType p) {
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return sprout::pow(1 - init_p(p), static_cast<RealType>(init_t(t)));
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}
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static SPROUT_CONSTEXPR bool init_use_inversion(IntType t, RealType p) {
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return init_m(t, p) < 11;
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}
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static SPROUT_CONSTEXPR RealType fc_1(RealType ikp1) {
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return (RealType(1) / 12 - (RealType(1) / 360 - (RealType(1) / 1260) * (ikp1 * ikp1)) * (ikp1 * ikp1)) * ikp1;
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}
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static SPROUT_CONSTEXPR RealType fc(IntType k) {
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return k < 10
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? sprout::random::detail::binomial_table<RealType>::table[k]
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: fc_1(RealType(1) / (k + 1))
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;
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}
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private:
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IntType t_;
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RealType p_;
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IntType m_;
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btrd_type btrd_;
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RealType q_n_;
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private:
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SPROUT_CONSTEXPR bool use_inversion() const {
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return m_ < 11;
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}
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template<typename Engine>
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SPROUT_CXX14_CONSTEXPR result_type
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invert(IntType t, RealType p, Engine& eng) const {
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RealType q = 1 - p;
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RealType s = p / q;
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RealType a = (t + 1) * s;
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RealType r = q_n_;
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RealType u = static_cast<RealType>(sprout::random::uniform_01<RealType>()(eng));
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IntType x = 0;
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while (u > r) {
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u = u - r;
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++x;
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r = ((a / x) - s) * r;
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}
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return x;
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}
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template<typename Engine>
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SPROUT_CXX14_CONSTEXPR result_type
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generate(Engine& eng) const {
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for (; ; ) {
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RealType u = RealType();
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RealType v = static_cast<RealType>(sprout::random::uniform_01<RealType>()(eng));
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if (v <= btrd_.u_rv_r) {
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RealType u = v / btrd_.v_r - RealType(0.43);
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return static_cast<result_type>(sprout::math::floor((2 * btrd_.a / (RealType(0.5) - sprout::math::abs(u)) + btrd_.b) * u + btrd_.c));
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}
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if (v >= btrd_.v_r) {
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u = static_cast<RealType>(sprout::random::uniform_01<RealType>()(eng)) - RealType(0.5);
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} else {
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u = v / btrd_.v_r - RealType(0.93);
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u = ((u < 0) ? -RealType(0.5) : RealType(0.5)) - u;
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v = static_cast<RealType>(sprout::random::uniform_01<RealType>()(eng)) * btrd_.v_r;
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}
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RealType us = RealType(0.5) - sprout::math::abs(u);
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IntType k = static_cast<IntType>(sprout::math::floor((2 * btrd_.a / us + btrd_.b) * u + btrd_.c));
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if (k < 0 || k > t_) {
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continue;
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}
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v = v * btrd_.alpha / (btrd_.a / (us * us) + btrd_.b);
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RealType km = sprout::math::abs(k - m_);
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if (km <= 15) {
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RealType f = RealType(1);
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if (m_ < k) {
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IntType i = m_;
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do {
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++i;
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f = f * (btrd_.nr / i - btrd_.r);
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} while (i != k);
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} else if (m_ > k) {
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IntType i = k;
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do {
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++i;
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v = v * (btrd_.nr / i - btrd_.r);
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} while (i != m_);
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}
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if (v <= f) {
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return k;
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} else {
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continue;
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}
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} else {
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v = sprout::math::log(v);
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RealType rho = (km / btrd_.npq) * (((km / RealType(3) + RealType(0.625)) * km + RealType(1) / 6) / btrd_.npq + RealType(0.5));
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RealType t = -km * km / (2 * btrd_.npq);
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if (v < t - rho) {
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return k;
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}
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if (v > t + rho) {
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continue;
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}
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IntType nm = t_ - m_ + 1;
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RealType h = (m_ + RealType(0.5)) * sprout::math::log((m_ + 1) / (btrd_.r * nm)) + fc(m_) + fc(t_ - m_);
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IntType nk = t_ - k + 1;
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if (v <= h + (t_ + 1) * sprout::math::log(static_cast<RealType>(nm) / nk)
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+ (k + RealType(0.5)) * sprout::math::log(nk * btrd_.r / (k + 1)) - fc(k) - fc(t_ - k)
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)
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{
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return k;
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} else {
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continue;
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}
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}
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}
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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invert_4(Engine const& eng, RealType u, RealType q, RealType s, RealType a, RealType r, IntType x = 0) const {
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return u > r
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? invert_4(eng, u - r, q, s, a, ((a / (x + 1)) - s) * r, x + 1)
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: sprout::random::random_result<Engine, binomial_distribution>(x, eng, *this)
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;
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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invert_3(IntType t, Engine const& eng, RealType u, RealType q, RealType s) const {
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return invert_4(eng, u, q, s, (t + 1) * s, q_n_);
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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invert_2(IntType t, RealType p, Engine const& eng, RealType u, RealType q) const {
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return invert_3(t, eng, u, q, p / q);
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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invert_1(IntType t, RealType p, Engine const& eng, RealType u) const {
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return invert_2(t, p, eng, u, 1 - p);
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}
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template<typename Engine, typename Random>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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invert_0(IntType t, RealType p, Random const& rnd) const {
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return invert_1(t, p, sprout::random::next(rnd).engine(), sprout::random::result(rnd));
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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invert(IntType t, RealType p, Engine const& eng) const {
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return invert_0<Engine>(t, p, sprout::random::uniform_01<RealType>()(eng));
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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invert2_0(IntType t, sprout::random::random_result<Engine, binomial_distribution> const& rnd) const {
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return sprout::random::random_result<Engine, binomial_distribution>(
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t - sprout::random::result(rnd),
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sprout::random::next(rnd).engine(),
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sprout::random::next(rnd).distribution()
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);
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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invert2(IntType t, RealType p, Engine const& eng) const {
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return invert2_0<Engine>(t, invert(t, p, eng));
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}
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#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
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template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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generate_10(Engine const& eng, RealType v, IntType k, IntType nm, RealType h, IntType nk) const {
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return v <= h + (t_ + 1) * sprout::math::log(static_cast<RealType>(nm) / nk)
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+ (k + RealType(0.5)) * sprout::math::log(nk * btrd_.r / (k + 1)) - fc(k) - fc(t_ - k)
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? sprout::random::random_result<Engine, binomial_distribution>(k, eng, *this)
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: generate<D + 1>(eng)
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;
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}
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template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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generate_10(Engine const&, RealType, IntType, IntType, RealType, IntType) const {
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return sprout::throw_recursive_function_template_instantiation_exeeded();
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}
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template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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generate_9(Engine const& eng, RealType v, IntType k, IntType nm) const {
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return generate_10<D + 1>(
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eng, v, k, nm, (m_ + RealType(0.5)) * sprout::math::log((m_ + 1) / (btrd_.r * nm)) + fc(m_) + fc(t_ - m_), t_ - k + 1
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);
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}
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template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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generate_9(Engine const&, RealType, IntType, IntType) const {
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return sprout::throw_recursive_function_template_instantiation_exeeded();
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}
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template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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generate_8(Engine const& eng, RealType v, IntType k, RealType rho, RealType t) const {
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return v < t - rho ? sprout::random::random_result<Engine, binomial_distribution>(k, eng, *this)
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: v > t + rho ? generate<D + 1>(eng)
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: generate_9<D + 1>(eng, v, k, t_ - m_ + 1)
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;
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}
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template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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generate_8(Engine const&, RealType, IntType, RealType, RealType) const {
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return sprout::throw_recursive_function_template_instantiation_exeeded();
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}
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template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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generate_7_3(Engine const& eng, RealType v, IntType k, RealType f) const {
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return v <= f
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? sprout::random::random_result<Engine, binomial_distribution>(k, eng, *this)
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: generate<D + 1>(eng)
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;
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}
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template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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generate_7_3(Engine const&, RealType, IntType, RealType) const {
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return sprout::throw_recursive_function_template_instantiation_exeeded();
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}
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template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
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generate_7_2(Engine const& eng, RealType v, IntType k, RealType f, IntType i) const {
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return i != k
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? generate_7_2<D + 1>(eng, v * (btrd_.nr / (i + 1) - btrd_.r), k, f, i + 1)
|
|
: generate_7_3<D + 1>(eng, v, k, f)
|
|
;
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_7_2(Engine const&, RealType, IntType, RealType, IntType) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_7_1(Engine const& eng, RealType v, IntType k, RealType f, IntType i) const {
|
|
return i != k
|
|
? generate_7_1<D + 1>(eng, v, k, f * (btrd_.nr / (i + 1) - btrd_.r), i + 1)
|
|
: generate_7_3<D + 1>(eng, v, k, f)
|
|
;
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_7_1(Engine const&, RealType, IntType, RealType, IntType) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_7(Engine const& eng, RealType v, IntType k, RealType f = RealType(1)) const {
|
|
return m_ < k ? generate_7_1<D + 1>(eng, v, k, f * (btrd_.nr / (m_ + 1) - btrd_.r), m_ + 1)
|
|
: m_ > k ? generate_7_2<D + 1>(eng, v * (btrd_.nr / (k + 1) - btrd_.r), k, f, k + 1)
|
|
: generate_7_3<D + 1>(eng, v, k, f)
|
|
;
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_7(Engine const&, RealType, IntType, RealType = RealType(1)) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_6(Engine const& eng, RealType v, IntType k, RealType km) const {
|
|
return km <= 15
|
|
? generate_7<D + 1>(eng, v, k)
|
|
: generate_8<D + 1>(
|
|
eng, sprout::math::log(v), k,
|
|
(km / btrd_.npq) * (((km / RealType(3) + RealType(0.625)) * km + RealType(1) / 6) / btrd_.npq + RealType(0.5)),
|
|
-km * km / (2 * btrd_.npq))
|
|
;
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_6(Engine const&, RealType, IntType, RealType) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_5(Engine const& eng, RealType v, RealType us, IntType k) const {
|
|
return k < 0 || k > t_
|
|
? generate<D + 1>(eng)
|
|
: generate_6<D + 1>(eng, v * btrd_.alpha / (btrd_.a / (us * us) + btrd_.b), k, sprout::abs(k - m_))
|
|
;
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_5(Engine const&, RealType, RealType, IntType) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_4(Engine const& eng, RealType v, RealType u, RealType us) const {
|
|
return generate_5<D + 1>(eng, v, us, static_cast<IntType>(sprout::math::floor((2 * btrd_.a / us + btrd_.b) * u + btrd_.c)));
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_4(Engine const&, RealType, RealType, RealType) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_3(Engine const& eng, RealType v, RealType u) const {
|
|
return generate_4<D + 1>(eng, v, u, 0.5 - sprout::abs(u));
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_3(Engine const&, RealType, RealType) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<int D, typename Engine, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_2(Random const& rnd, RealType v) const {
|
|
return v >= btrd_.v_r
|
|
? generate_3<D + 1>(
|
|
sprout::random::next(rnd).engine(), v,
|
|
sprout::random::result(rnd) - RealType(0.5)
|
|
)
|
|
: generate_3<D + 1>(
|
|
sprout::random::next(rnd).engine(), sprout::random::result(rnd) * btrd_.v_r,
|
|
((v / btrd_.v_r - RealType(0.93)) < 0 ? RealType(-0.5) : RealType(0.5)) - (v / btrd_.v_r - RealType(0.93))
|
|
)
|
|
;
|
|
}
|
|
template<int D, typename Engine, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_2(Random const&, RealType) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_1_1(Engine const& eng, RealType u) const {
|
|
return sprout::random::random_result<Engine, binomial_distribution>(
|
|
static_cast<IntType>(sprout::math::floor((2 * btrd_.a / (RealType(0.5) - sprout::abs(u)) + btrd_.b) * u + btrd_.c)),
|
|
eng, *this
|
|
);
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_1_1(Engine const&, RealType) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_1(Engine const& eng, RealType v) const {
|
|
return v <= btrd_.u_rv_r
|
|
? generate_1_1<D + 1>(eng, v / btrd_.v_r - RealType(0.43))
|
|
: generate_2<D + 1, Engine>(sprout::random::uniform_01<RealType>()(eng), v)
|
|
;
|
|
}
|
|
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_1(Engine const&, RealType) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<int D, typename Engine, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_0(Random const& rnd) const {
|
|
return generate_1<D + 1>(sprout::random::next(rnd).engine(), sprout::random::result(rnd));
|
|
}
|
|
template<int D, typename Engine, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_0(Random const&) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<int D = 16, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate(Engine const& eng) const {
|
|
return generate_0<D + 1, Engine>(sprout::random::uniform_01<RealType>()(eng));
|
|
}
|
|
template<int D = 16, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate(Engine const&) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
#else
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_10(Engine const& eng, RealType v, IntType k, IntType nm, RealType h, IntType nk) const {
|
|
return v <= h + (t_ + 1) * sprout::math::log(static_cast<RealType>(nm) / nk)
|
|
+ (k + RealType(0.5)) * sprout::math::log(nk * btrd_.r / (k + 1)) - fc(k) - fc(t_ - k)
|
|
? sprout::random::random_result<Engine, binomial_distribution>(k, eng, *this)
|
|
: generate(eng)
|
|
;
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_9(Engine const& eng, RealType v, IntType k, IntType nm) const {
|
|
return generate_10(
|
|
eng, v, k, nm, (m_ + RealType(0.5)) * sprout::math::log((m_ + 1) / (btrd_.r * nm)) + fc(m_) + fc(t_ - m_), t_ - k + 1
|
|
);
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_8(Engine const& eng, RealType v, IntType k, RealType rho, RealType t) const {
|
|
return v < t - rho ? sprout::random::random_result<Engine, binomial_distribution>(k, eng, *this)
|
|
: v > t + rho ? generate(eng)
|
|
: generate_9(eng, v, k, t_ - m_ + 1)
|
|
;
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_7_3(Engine const& eng, RealType v, IntType k, RealType f) const {
|
|
return v <= f
|
|
? sprout::random::random_result<Engine, binomial_distribution>(k, eng, *this)
|
|
: generate(eng)
|
|
;
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_7_2(Engine const& eng, RealType v, IntType k, RealType f, IntType i) const {
|
|
return i != k
|
|
? generate_7_2(eng, v * (btrd_.nr / (i + 1) - btrd_.r), k, f, i + 1)
|
|
: generate_7_3(eng, v, k, f)
|
|
;
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_7_1(Engine const& eng, RealType v, IntType k, RealType f, IntType i) const {
|
|
return i != k
|
|
? generate_7_1(eng, v, k, f * (btrd_.nr / (i + 1) - btrd_.r), i + 1)
|
|
: generate_7_3(eng, v, k, f)
|
|
;
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_7(Engine const& eng, RealType v, IntType k, RealType f = RealType(1)) const {
|
|
return m_ < k ? generate_7_1(eng, v, k, f * (btrd_.nr / (m_ + 1) - btrd_.r), m_ + 1)
|
|
: m_ > k ? generate_7_2(eng, v * (btrd_.nr / (k + 1) - btrd_.r), k, f, k + 1)
|
|
: generate_7_3(eng, v, k, f)
|
|
;
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_6(Engine const& eng, RealType v, IntType k, RealType km) const {
|
|
return km <= 15
|
|
? generate_7(eng, v, k)
|
|
: generate_8(
|
|
eng, sprout::math::log(v), k,
|
|
(km / btrd_.npq) * (((km / RealType(3.0) + RealType(0.625)) * km + RealType(1.0) / 6) / btrd_.npq + RealType(0.5)),
|
|
-km * km / (2 * btrd_.npq))
|
|
;
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_5(Engine const& eng, RealType v, RealType, RealType us, IntType k) const {
|
|
return k < 0 || k > t_
|
|
? generate(eng)
|
|
: generate_6(eng, v * btrd_.alpha / (btrd_.a / (us * us) + btrd_.b), k, sprout::abs(k - m_))
|
|
;
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_4(Engine const& eng, RealType v, RealType u, RealType us) const {
|
|
return generate_5(eng, v, u, us, static_cast<IntType>(sprout::math::floor((2 * btrd_.a / us + btrd_.b) * u + btrd_.c)));
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_3(Engine const& eng, RealType v, RealType u) const {
|
|
return generate_4(eng, v, u, 0.5 - sprout::abs(u));
|
|
}
|
|
template<typename Engine, typename Random>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_2(Random const& rnd, RealType v) const {
|
|
return v >= btrd_.v_r
|
|
? generate_3(
|
|
sprout::random::next(rnd).engine(),
|
|
v,
|
|
sprout::random::result(rnd) - RealType(0.5)
|
|
)
|
|
: generate_3(
|
|
sprout::random::next(rnd).engine(),
|
|
sprout::random::result(rnd) * btrd_.v_r,
|
|
((v / btrd_.v_r - RealType(0.93)) < 0 ? RealType(-0.5) : RealType(0.5)) - (v / btrd_.v_r - RealType(0.93))
|
|
)
|
|
;
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_1_1(Engine const& eng, RealType u) const {
|
|
return sprout::random::random_result<Engine, binomial_distribution>(
|
|
static_cast<IntType>(sprout::math::floor((2 * btrd_.a / (RealType(0.5) - sprout::abs(u)) + btrd_.b) * u + btrd_.c)),
|
|
eng,
|
|
*this
|
|
);
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_1(Engine const& eng, RealType v) const {
|
|
return v <= btrd_.u_rv_r
|
|
? generate_1_1(eng, v / btrd_.v_r - RealType(0.43))
|
|
: generate_2<Engine>(sprout::random::uniform_01<RealType>()(eng), v)
|
|
;
|
|
}
|
|
template<typename Engine, typename Random>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate_0(Random const& rnd) const {
|
|
return generate_1(sprout::random::next(rnd).engine(), sprout::random::result(rnd));
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate(Engine const& eng) const {
|
|
return generate_0<Engine>(sprout::random::uniform_01<RealType>()(eng));
|
|
}
|
|
#endif
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate2_0(IntType t, sprout::random::random_result<Engine, binomial_distribution> const& rnd) const {
|
|
return sprout::random::random_result<Engine, binomial_distribution>(
|
|
t - sprout::random::result(rnd),
|
|
sprout::random::next(rnd).engine(),
|
|
sprout::random::next(rnd).distribution()
|
|
);
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
|
|
generate2(IntType t, Engine const& eng) const {
|
|
return generate2_0<Engine>(t, generate(eng));
|
|
}
|
|
SPROUT_CXX14_CONSTEXPR void init() {
|
|
m_ = init_m(t_, p_);
|
|
if (use_inversion()) {
|
|
q_n_ = init_q_n(t_, p_);
|
|
} else {
|
|
btrd_ = init_btrd(t_, p_);
|
|
}
|
|
}
|
|
public:
|
|
SPROUT_CONSTEXPR binomial_distribution()
|
|
: t_(1)
|
|
, p_(RealType(0.5))
|
|
, m_(init_m(1, RealType(0.5)))
|
|
, btrd_(!init_use_inversion(1, RealType(0.5)) ? init_btrd(1, RealType(0.5)) : btrd_type())
|
|
, q_n_(init_use_inversion(1, RealType(0.5)) ? init_q_n(1, RealType(0.5)) : RealType())
|
|
{}
|
|
explicit SPROUT_CONSTEXPR binomial_distribution(IntType t_arg, RealType p_arg = RealType(0.5))
|
|
: t_((SPROUT_ASSERT(t_arg >= IntType(0)), t_arg))
|
|
, p_((SPROUT_ASSERT(RealType(0) <= p_arg && p_arg <= RealType(1)), p_arg))
|
|
, m_(init_m(t_arg, p_arg))
|
|
, btrd_(!init_use_inversion(t_arg, p_arg) ? init_btrd(t_arg, p_arg) : btrd_type())
|
|
, q_n_(init_use_inversion(t_arg, p_arg) ? init_q_n(t_arg, p_arg) : RealType())
|
|
{}
|
|
explicit SPROUT_CONSTEXPR binomial_distribution(param_type const& parm)
|
|
: t_(parm.t())
|
|
, p_(parm.p())
|
|
, m_(init_m(parm.t(), parm.p()))
|
|
, btrd_(!init_use_inversion(parm.t(), parm.p()) ? init_btrd(parm.t(), parm.p()) : btrd_type())
|
|
, q_n_(init_use_inversion(parm.t(), parm.p()) ? init_q_n(parm.t(), parm.p()) : RealType())
|
|
{}
|
|
SPROUT_CONSTEXPR result_type t() const SPROUT_NOEXCEPT {
|
|
return t_;
|
|
}
|
|
SPROUT_CONSTEXPR result_type p() const SPROUT_NOEXCEPT {
|
|
return p_;
|
|
}
|
|
SPROUT_CONSTEXPR result_type min() const SPROUT_NOEXCEPT {
|
|
return 0;
|
|
}
|
|
SPROUT_CONSTEXPR result_type max() const SPROUT_NOEXCEPT {
|
|
return t_;
|
|
}
|
|
SPROUT_CXX14_CONSTEXPR void reset() SPROUT_NOEXCEPT {}
|
|
SPROUT_CONSTEXPR param_type param() const SPROUT_NOEXCEPT {
|
|
return param_type(t_, p_);
|
|
}
|
|
SPROUT_CXX14_CONSTEXPR void param(param_type const& parm) {
|
|
t_ = parm.t();
|
|
p_ = parm.p();
|
|
init();
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CXX14_CONSTEXPR result_type operator()(Engine& eng) const {
|
|
return use_inversion() ? RealType(0.5) < p_
|
|
? t_ - invert(t_, 1 - p_, eng)
|
|
: invert(t_, p_, eng)
|
|
: RealType(0.5) < p_ ? t_ - generate(eng)
|
|
: generate(eng)
|
|
;
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> const operator()(Engine const& eng) const {
|
|
return use_inversion() ? RealType(0.5) < p_
|
|
? invert2(t_, 1 - p_, eng)
|
|
: invert(t_, p_, eng)
|
|
: RealType(0.5) < p_ ? generate2(t_, eng)
|
|
: generate(eng)
|
|
;
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CXX14_CONSTEXPR result_type operator()(Engine& eng, param_type const& parm) const {
|
|
return binomial_distribution(parm)(eng);
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> const operator()(Engine const& eng, param_type const& parm) const {
|
|
return binomial_distribution(parm)(eng);
|
|
}
|
|
template<typename Elem, typename Traits>
|
|
friend SPROUT_NON_CONSTEXPR std::basic_istream<Elem, Traits>& operator>>(
|
|
std::basic_istream<Elem, Traits>& lhs,
|
|
binomial_distribution& rhs
|
|
)
|
|
{
|
|
param_type parm;
|
|
if (lhs >> parm) {
|
|
rhs.param(parm);
|
|
}
|
|
return lhs;
|
|
}
|
|
template<typename Elem, typename Traits>
|
|
friend SPROUT_NON_CONSTEXPR std::basic_ostream<Elem, Traits>& operator<<(
|
|
std::basic_ostream<Elem, Traits>& lhs,
|
|
binomial_distribution const& rhs
|
|
)
|
|
{
|
|
return lhs << rhs.param();
|
|
}
|
|
friend SPROUT_CONSTEXPR bool operator==(binomial_distribution const& lhs, binomial_distribution const& rhs) SPROUT_NOEXCEPT {
|
|
return lhs.param() == rhs.param();
|
|
}
|
|
friend SPROUT_CONSTEXPR bool operator!=(binomial_distribution const& lhs, binomial_distribution const& rhs) SPROUT_NOEXCEPT {
|
|
return !(lhs == rhs);
|
|
}
|
|
};
|
|
} // namespace random
|
|
|
|
using sprout::random::binomial_distribution;
|
|
} // namespace sprout
|
|
|
|
#endif // #ifndef SPROUT_RANDOM_BINOMIAL_DISTRIBUTION_HPP
|