//===----------------------------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// REQUIRES: long_tests
// <random>
// template<class IntType = int>
// class binomial_distribution
// template<class _URNG> result_type operator()(_URNG& g);
#include <cassert>
#include <cstdint>
#include <numeric>
#include <random>
#include <type_traits>
#include <vector>
#include "test_macros.h"
template <class T>
T sqr(T x) {
return x * x;
}
template <class T>
void test1() {
typedef std::binomial_distribution<T> D;
typedef std::mt19937_64 G;
G g;
D d(5, .75);
const int N = 1000000;
std::vector<typename D::result_type> u;
for (int i = 0; i < N; ++i)
{
typename D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
}
template <class T>
void test2() {
typedef std::binomial_distribution<T> D;
typedef std::mt19937 G;
G g;
D d(30, .03125);
const int N = 100000;
std::vector<typename D::result_type> u;
for (int i = 0; i < N; ++i)
{
typename D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
}
template <class T>
void test3() {
typedef std::binomial_distribution<T> D;
typedef std::mt19937 G;
G g;
D d(40, .25);
const int N = 100000;
std::vector<typename D::result_type> u;
for (int i = 0; i < N; ++i)
{
typename D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.07);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 2.0);
}
template <class T>
void test4() {
typedef std::binomial_distribution<T> D;
typedef std::mt19937 G;
G g;
D d(40, 0);
const int N = 100000;
std::vector<typename D::result_type> u;
for (int i = 0; i < N; ++i)
{
typename D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
// In this case:
// skew computes to 0./0. == nan
// kurtosis computes to 0./0. == nan
// x_skew == inf
// x_kurtosis == inf
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(mean == x_mean);
assert(var == x_var);
// assert(skew == x_skew);
(void)skew; (void)x_skew;
// assert(kurtosis == x_kurtosis);
(void)kurtosis; (void)x_kurtosis;
}
template <class T>
void test5() {
typedef std::binomial_distribution<T> D;
typedef std::mt19937 G;
G g;
D d(40, 1);
const int N = 100000;
std::vector<typename D::result_type> u;
for (int i = 0; i < N; ++i)
{
typename D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
// In this case:
// skew computes to 0./0. == nan
// kurtosis computes to 0./0. == nan
// x_skew == -inf
// x_kurtosis == inf
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(mean == x_mean);
assert(var == x_var);
// assert(skew == x_skew);
(void)skew; (void)x_skew;
// assert(kurtosis == x_kurtosis);
(void)kurtosis; (void)x_kurtosis;
}
template <class T>
void test6() {
typedef std::binomial_distribution<T> D;
typedef std::mt19937 G;
G g;
D d(127, 0.5);
const int N = 100000;
std::vector<typename D::result_type> u;
for (int i = 0; i < N; ++i)
{
typename D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs(skew - x_skew) < 0.02);
assert(std::abs(kurtosis - x_kurtosis) < 0.03);
}
template <class T>
void test7() {
typedef std::binomial_distribution<T> D;
typedef std::mt19937 G;
G g;
D d(1, 0.5);
const int N = 100000;
std::vector<typename D::result_type> u;
for (int i = 0; i < N; ++i)
{
typename D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs(skew - x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
}
template <class T>
void test8() {
const int N = 100000;
std::mt19937 gen1;
std::mt19937 gen2;
using UnsignedT = typename std::make_unsigned<T>::type;
std::binomial_distribution<T> dist1(5, 0.1);
std::binomial_distribution<UnsignedT> dist2(5, 0.1);
for (int i = 0; i < N; ++i) {
T r1 = dist1(gen1);
UnsignedT r2 = dist2(gen2);
assert(r1 >= 0);
assert(static_cast<UnsignedT>(r1) == r2);
}
}
template <class T>
void test9() {
typedef std::binomial_distribution<T> D;
typedef std::mt19937 G;
G g;
D d(0, 0.005);
const int N = 100000;
std::vector<typename D::result_type> u;
for (int i = 0; i < N; ++i)
{
typename D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
// In this case:
// skew computes to 0./0. == nan
// kurtosis computes to 0./0. == nan
// x_skew == inf
// x_kurtosis == inf
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(mean == x_mean);
assert(var == x_var);
// assert(skew == x_skew);
(void)skew; (void)x_skew;
// assert(kurtosis == x_kurtosis);
(void)kurtosis; (void)x_kurtosis;
}
template <class T>
void test10() {
typedef std::binomial_distribution<T> D;
typedef std::mt19937 G;
G g;
D d(0, 0);
const int N = 100000;
std::vector<typename D::result_type> u;
for (int i = 0; i < N; ++i)
{
typename D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
// In this case:
// skew computes to 0./0. == nan
// kurtosis computes to 0./0. == nan
// x_skew == inf
// x_kurtosis == inf
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(mean == x_mean);
assert(var == x_var);
// assert(skew == x_skew);
(void)skew; (void)x_skew;
// assert(kurtosis == x_kurtosis);
(void)kurtosis; (void)x_kurtosis;
}
template <class T>
void test11() {
typedef std::binomial_distribution<T> D;
typedef std::mt19937 G;
G g;
D d(0, 1);
const int N = 100000;
std::vector<typename D::result_type> u;
for (int i = 0; i < N; ++i)
{
typename D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
// In this case:
// skew computes to 0./0. == nan
// kurtosis computes to 0./0. == nan
// x_skew == -inf
// x_kurtosis == inf
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(mean == x_mean);
assert(var == x_var);
// assert(skew == x_skew);
(void)skew; (void)x_skew;
// assert(kurtosis == x_kurtosis);
(void)kurtosis; (void)x_kurtosis;
}
template <class T>
void tests() {
test1<T>();
test2<T>();
test3<T>();
test4<T>();
test5<T>();
test6<T>();
test7<T>();
test8<T>();
test9<T>();
test10<T>();
test11<T>();
}
int main(int, char**) {
tests<short>();
tests<int>();
tests<long>();
tests<long long>();
tests<unsigned short>();
tests<unsigned int>();
tests<unsigned long>();
tests<unsigned long long>();
#if defined(_LIBCPP_VERSION) // extension
tests<std::int8_t>();
tests<std::uint8_t>();
#if !defined(TEST_HAS_NO_INT128)
tests<__int128_t>();
tests<__uint128_t>();
#endif
#endif
return 0;
}
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