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Sprout/sprout/random/binomial_distribution.hpp
bolero-MURAKAMI 3c4a465d35 support C++14 constexpr: random distributions
2013-11-05 23:46:23 +09:00

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/*=============================================================================
Copyright (c) 2011-2013 Bolero MURAKAMI
https://github.com/bolero-MURAKAMI/Sprout
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
=============================================================================*/
#ifndef SPROUT_RANDOM_BINOMIAL_DISTRIBUTION_HPP
#define SPROUT_RANDOM_BINOMIAL_DISTRIBUTION_HPP
#include <iosfwd>
#include <istream>
#include <sprout/config.hpp>
#include <sprout/array/array.hpp>
#include <sprout/cstdlib/abs.hpp>
#include <sprout/math/abs.hpp>
#include <sprout/math/log.hpp>
#include <sprout/math/pow.hpp>
#include <sprout/math/sqrt.hpp>
#include <sprout/math/floor.hpp>
#include <sprout/random/random_result.hpp>
#include <sprout/random/uniform_01.hpp>
#include <sprout/assert.hpp>
#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
# include <sprout/workaround/recursive_function_template.hpp>
#endif
namespace sprout {
namespace random {
namespace detail {
# define SPROUT_BINOMIAL_TABLE_DEF \
table_type{{ \
1, \
1, \
2, \
6, \
24, \
120 \
}}
template<typename RealType>
struct binomial_table {
public:
typedef sprout::array<RealType, 10> table_type;
public:
SPROUT_STATIC_CONSTEXPR table_type table
SPROUT_STATIC_CONSTEXPR_DATA_MEMBER_INNER(SPROUT_BINOMIAL_TABLE_DEF)
;
};
template<class RealType>
SPROUT_CONSTEXPR_OR_CONST typename sprout::random::detail::binomial_table<RealType>::table_type
sprout::random::detail::binomial_table<RealType>::table
SPROUT_STATIC_CONSTEXPR_DATA_MEMBER_OUTER(SPROUT_BINOMIAL_TABLE_DEF)
;
# undef SPROUT_BINOMIAL_TABLE_DEF
} // namespace detail
//
// binomial_distribution
//
template<typename IntType = int, typename RealType = double>
class binomial_distribution {
public:
typedef RealType input_type;
typedef IntType result_type;
private:
struct btrd_type {
public:
RealType r;
RealType nr;
RealType npq;
RealType b;
RealType a;
RealType c;
RealType alpha;
RealType v_r;
RealType u_rv_r;
};
public:
//
// param_type
//
class param_type {
public:
typedef binomial_distribution distribution_type;
private:
IntType t_;
RealType p_;
public:
SPROUT_CONSTEXPR param_type()
: t_(1)
, p_(0.5)
{}
explicit SPROUT_CONSTEXPR param_type(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))
{}
SPROUT_CONSTEXPR IntType t() const SPROUT_NOEXCEPT {
return t_;
}
SPROUT_CONSTEXPR RealType p() const SPROUT_NOEXCEPT {
return p_;
}
template<typename Elem, typename Traits>
friend SPROUT_NON_CONSTEXPR std::basic_istream<Elem, Traits>& operator>>(
std::basic_istream<Elem, Traits>& lhs,
param_type& rhs
)
{
IntType t;
RealType p;
if (lhs >> t >> std::ws >> p) {
if (t >= IntType(0) && RealType(0) <= p && p <= RealType(1)) {
rhs.t_ = t;
rhs.p_ = p;
} else {
lhs.setstate(std::ios_base::failbit);
}
}
return lhs;
}
template<typename Elem, typename Traits>
friend SPROUT_NON_CONSTEXPR std::basic_ostream<Elem, Traits>& operator<<(
std::basic_ostream<Elem, Traits>& lhs,
param_type const& rhs
)
{
return lhs << rhs.t_ << " " << rhs.p_;
}
friend SPROUT_CONSTEXPR bool operator==(param_type const& lhs, param_type const& rhs) SPROUT_NOEXCEPT {
return lhs.t_ == rhs.t_ && lhs.p_ == rhs.p_;
}
friend SPROUT_CONSTEXPR bool operator!=(param_type const& lhs, param_type const& rhs) SPROUT_NOEXCEPT {
return !(lhs == rhs);
}
};
private:
static SPROUT_CONSTEXPR IntType init_t(IntType t) {
return t;
}
static SPROUT_CONSTEXPR RealType init_p(RealType p) {
return RealType(0.5) < p ? 1 - p : p;
}
static SPROUT_CONSTEXPR IntType init_m(IntType t, RealType p) {
return static_cast<IntType>((init_t(t) + 1) * init_p(p));
}
static SPROUT_CONSTEXPR btrd_type
init_btrd_6(
IntType, RealType, RealType r, RealType nr, RealType npq,
RealType b, RealType a, RealType c, RealType alpha, RealType v_r
)
{
return btrd_type{
r, nr, npq,
b, a, c, alpha, v_r,
RealType(0.86) * v_r
};
}
static SPROUT_CONSTEXPR btrd_type
init_btrd_5(
IntType t, RealType p, RealType r, RealType nr, RealType npq,
RealType sqrt_npq, RealType b
)
{
return init_btrd_6(
t, p, r, nr, npq, b,
RealType(-0.0873) + RealType(0.0248) * b + RealType(0.01) * p,
t * p + RealType(0.5),
(RealType(2.83) + RealType(5.1) / b) * sqrt_npq, RealType(0.92) - RealType(4.2) / b
);
}
static SPROUT_CONSTEXPR btrd_type init_btrd_4(IntType t, RealType p, RealType r, RealType nr, RealType npq, RealType sqrt_npq) {
return init_btrd_5(t, p, r, nr, npq, sqrt_npq, RealType(1.15) + RealType(2.53) * sqrt_npq);
}
static SPROUT_CONSTEXPR btrd_type init_btrd_3(IntType t, RealType p, RealType r, RealType nr, RealType npq) {
return init_btrd_4(t, p, r, nr, npq, sprout::sqrt(npq));
}
static SPROUT_CONSTEXPR btrd_type init_btrd_2(IntType t, RealType p, RealType r) {
return init_btrd_3(t, p, r, (t + 1) * r, t * p * (1 - p));
}
static SPROUT_CONSTEXPR btrd_type init_btrd_1(IntType t, RealType p) {
return init_btrd_2(t, p, p / (1 - p));
}
static SPROUT_CONSTEXPR btrd_type init_btrd(IntType t, RealType p) {
return init_btrd_1(init_t(t), init_p(p));
}
static SPROUT_CONSTEXPR RealType init_q_n(IntType t, RealType p) {
return sprout::pow(1 - init_p(p), static_cast<RealType>(init_t(t)));
}
static SPROUT_CONSTEXPR bool init_use_inversion(IntType t, RealType p) {
return init_m(t, p) < 11;
}
static SPROUT_CONSTEXPR RealType fc_1(RealType ikp1) {
return (RealType(1) / 12 - (RealType(1) / 360 - (RealType(1) / 1260) * (ikp1 * ikp1)) * (ikp1 * ikp1)) * ikp1;
}
static SPROUT_CONSTEXPR RealType fc(IntType k) {
return k < 10
? sprout::random::detail::binomial_table<RealType>::table[k]
: fc_1(RealType(1) / (k + 1))
;
}
private:
IntType t_;
RealType p_;
IntType m_;
btrd_type btrd_;
RealType q_n_;
private:
SPROUT_CONSTEXPR bool use_inversion() const {
return m_ < 11;
}
template<typename Engine>
SPROUT_CXX14_CONSTEXPR result_type
invert(IntType t, RealType p, Engine& eng) const {
RealType q = 1 - p;
RealType s = p / q;
RealType a = (t + 1) * s;
RealType r = q_n_;
RealType u = static_cast<RealType>(sprout::random::uniform_01<RealType>()(eng));
IntType x = 0;
while (u > r) {
u = u - r;
++x;
r = ((a / x) - s) * r;
}
return x;
}
template<typename Engine>
SPROUT_CXX14_CONSTEXPR result_type
generate(Engine& eng) const {
for (; ; ) {
RealType u = RealType();
RealType v = static_cast<RealType>(sprout::random::uniform_01<RealType>()(eng));
if (v <= btrd_.u_rv_r) {
RealType u = v / btrd_.v_r - RealType(0.43);
return static_cast<result_type>(sprout::math::floor((2 * btrd_.a / (RealType(0.5) - sprout::math::abs(u)) + btrd_.b) * u + btrd_.c));
}
if (v >= btrd_.v_r) {
u = static_cast<RealType>(sprout::random::uniform_01<RealType>()(eng)) - RealType(0.5);
} else {
u = v / btrd_.v_r - RealType(0.93);
u = ((u < 0) ? -RealType(0.5) : RealType(0.5)) - u;
v = static_cast<RealType>(sprout::random::uniform_01<RealType>()(eng)) * btrd_.v_r;
}
RealType us = RealType(0.5) - sprout::math::abs(u);
IntType k = static_cast<IntType>(sprout::math::floor((2 * btrd_.a / us + btrd_.b) * u + btrd_.c));
if (k < 0 || k > t_) {
continue;
}
v = v * btrd_.alpha / (btrd_.a / (us * us) + btrd_.b);
RealType km = sprout::math::abs(k - m_);
if (km <= 15) {
RealType f = RealType(1);
if (m_ < k) {
IntType i = m_;
do {
++i;
f = f * (btrd_.nr / i - btrd_.r);
} while (i != k);
} else if (m_ > k) {
IntType i = k;
do {
++i;
v = v * (btrd_.nr / i - btrd_.r);
} while (i != m_);
}
if (v <= f) {
return k;
} else {
continue;
}
} else {
v = sprout::math::log(v);
RealType rho = (km / btrd_.npq) * (((km / RealType(3) + RealType(0.625)) * km + RealType(1) / 6) / btrd_.npq + RealType(0.5));
RealType t = -km * km / (2 * btrd_.npq);
if (v < t - rho) {
return k;
}
if (v > t + rho) {
continue;
}
IntType nm = t_ - m_ + 1;
RealType h = (m_ + RealType(0.5)) * sprout::math::log((m_ + 1) / (btrd_.r * nm)) + fc(m_) + fc(t_ - m_);
IntType nk = t_ - k + 1;
if (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)
)
{
return k;
} else {
continue;
}
}
}
}
template<typename Engine>
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
invert_4(Engine const& eng, RealType u, RealType q, RealType s, RealType a, RealType r, IntType x = 0) const {
return u > r
? invert_4(eng, u - r, q, s, a, ((a / (x + 1)) - s) * r, x + 1)
: sprout::random::random_result<Engine, binomial_distribution>(x, eng, *this)
;
}
template<typename Engine>
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
invert_3(IntType t, Engine const& eng, RealType u, RealType q, RealType s) const {
return invert_4(eng, u, q, s, (t + 1) * s, q_n_);
}
template<typename Engine>
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
invert_2(IntType t, RealType p, Engine const& eng, RealType u, RealType q) const {
return invert_3(t, eng, u, q, p / q);
}
template<typename Engine>
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
invert_1(IntType t, RealType p, Engine const& eng, RealType u) const {
return invert_2(t, p, eng, u, 1 - p);
}
template<typename Engine, typename Random>
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
invert_0(IntType t, RealType p, Random const& rnd) const {
return invert_1(t, p, rnd.engine(), rnd.result());
}
template<typename Engine>
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
invert(IntType t, RealType p, Engine const& eng) const {
return invert_0<Engine>(t, p, sprout::random::uniform_01<RealType>()(eng));
}
template<typename Engine>
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
invert2_0(IntType t, sprout::random::random_result<Engine, binomial_distribution> const& rnd) const {
return sprout::random::random_result<Engine, binomial_distribution>(t - rnd.result(), rnd.engine(), rnd.distribution());
}
template<typename Engine>
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
invert2(IntType t, RealType p, Engine const& eng) const {
return invert2_0<Engine>(t, invert(t, p, eng));
}
#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
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<D + 1>(eng)
;
}
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
generate_10(Engine const&, RealType, IntType, 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_9(Engine const& eng, RealType v, IntType k, IntType nm) const {
return generate_10<D + 1>(
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<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
generate_9(Engine const&, RealType, IntType, 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_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<D + 1>(eng)
: generate_9<D + 1>(eng, v, k, t_ - m_ + 1)
;
}
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
generate_8(Engine const&, RealType, IntType, 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_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<D + 1>(eng)
;
}
template<int D, typename Engine, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution>
generate_7_3(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_7_2(Engine const& eng, RealType v, IntType k, RealType f, IntType i) const {
return i != k
? 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>(
rnd.engine(), v,
rnd.result() - RealType(0.5)
)
: generate_3<D + 1>(
rnd.engine(), rnd.result() * 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>(rnd.engine(), rnd.result());
}
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(
rnd.engine(),
v,
rnd.result() - RealType(0.5)
)
: generate_3(
rnd.engine(),
rnd.result() * 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(rnd.engine(), rnd.result());
}
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 - rnd.result(), rnd.engine(), 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_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
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