//===----------------------------------------------------------------------===//
//
// 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 RealType = double>
// class uniform_real_distribution
// template<class _URNG> result_type operator()(_URNG& g);
#include <random>
#include <cassert>
#include <cmath>
#include <cstddef>
#include <numeric>
#include <vector>
#include "test_macros.h"
template <class T>
inline
T
sqr(T x)
{
return x * x;
}
int main(int, char**)
{
{
typedef std::uniform_real_distribution<> D;
typedef std::minstd_rand0 G;
G g;
D d;
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.a() <= v && v < d.b());
u.push_back(v);
}
D::result_type mean = std::accumulate(u.begin(), u.end(),
D::result_type(0)) / u.size();
D::result_type var = 0;
D::result_type skew = 0;
D::result_type kurtosis = 0;
for (std::size_t i = 0; i < u.size(); ++i)
{
D::result_type dbl = (u[i] - mean);
D::result_type d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
D::result_type dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
D::result_type x_mean = (d.a() + d.b()) / 2;
D::result_type x_var = sqr(d.b() - d.a()) / 12;
D::result_type x_skew = 0;
D::result_type x_kurtosis = -6./5;
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);
}
{
typedef std::uniform_real_distribution<> D;
typedef std::minstd_rand G;
G g;
D d;
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.a() <= v && v < d.b());
u.push_back(v);
}
D::result_type mean = std::accumulate(u.begin(), u.end(),
D::result_type(0)) / u.size();
D::result_type var = 0;
D::result_type skew = 0;
D::result_type kurtosis = 0;
for (std::size_t i = 0; i < u.size(); ++i)
{
D::result_type dbl = (u[i] - mean);
D::result_type d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
D::result_type dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
D::result_type x_mean = (d.a() + d.b()) / 2;
D::result_type x_var = sqr(d.b() - d.a()) / 12;
D::result_type x_skew = 0;
D::result_type x_kurtosis = -6./5;
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);
}
{
typedef std::uniform_real_distribution<> D;
typedef std::mt19937 G;
G g;
D d;
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.a() <= v && v < d.b());
u.push_back(v);
}
D::result_type mean = std::accumulate(u.begin(), u.end(),
D::result_type(0)) / u.size();
D::result_type var = 0;
D::result_type skew = 0;
D::result_type kurtosis = 0;
for (std::size_t i = 0; i < u.size(); ++i)
{
D::result_type dbl = (u[i] - mean);
D::result_type d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
D::result_type dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
D::result_type x_mean = (d.a() + d.b()) / 2;
D::result_type x_var = sqr(d.b() - d.a()) / 12;
D::result_type x_skew = 0;
D::result_type x_kurtosis = -6./5;
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);
}
{
typedef std::uniform_real_distribution<> D;
typedef std::mt19937_64 G;
G g;
D d;
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.a() <= v && v < d.b());
u.push_back(v);
}
D::result_type mean = std::accumulate(u.begin(), u.end(),
D::result_type(0)) / u.size();
D::result_type var = 0;
D::result_type skew = 0;
D::result_type kurtosis = 0;
for (std::size_t i = 0; i < u.size(); ++i)
{
D::result_type dbl = (u[i] - mean);
D::result_type d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
D::result_type dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
D::result_type x_mean = (d.a() + d.b()) / 2;
D::result_type x_var = sqr(d.b() - d.a()) / 12;
D::result_type x_skew = 0;
D::result_type x_kurtosis = -6./5;
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);
}
{
typedef std::uniform_real_distribution<> D;
typedef std::ranlux24_base G;
G g;
D d;
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.a() <= v && v < d.b());
u.push_back(v);
}
D::result_type mean = std::accumulate(u.begin(), u.end(),
D::result_type(0)) / u.size();
D::result_type var = 0;
D::result_type skew = 0;
D::result_type kurtosis = 0;
for (std::size_t i = 0; i < u.size(); ++i)
{
D::result_type dbl = (u[i] - mean);
D::result_type d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
D::result_type dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
D::result_type x_mean = (d.a() + d.b()) / 2;
D::result_type x_var = sqr(d.b() - d.a()) / 12;
D::result_type x_skew = 0;
D::result_type x_kurtosis = -6./5;
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) / x_kurtosis) < 0.01);
}
{
typedef std::uniform_real_distribution<> D;
typedef std::ranlux48_base G;
G g;
D d;
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.a() <= v && v < d.b());
u.push_back(v);
}
D::result_type mean = std::accumulate(u.begin(), u.end(),
D::result_type(0)) / u.size();
D::result_type var = 0;
D::result_type skew = 0;
D::result_type kurtosis = 0;
for (std::size_t i = 0; i < u.size(); ++i)
{
D::result_type dbl = (u[i] - mean);
D::result_type d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
D::result_type dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
D::result_type x_mean = (d.a() + d.b()) / 2;
D::result_type x_var = sqr(d.b() - d.a()) / 12;
D::result_type x_skew = 0;
D::result_type x_kurtosis = -6./5;
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);
}
{
typedef std::uniform_real_distribution<> D;
typedef std::ranlux24 G;
G g;
D d;
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.a() <= v && v < d.b());
u.push_back(v);
}
D::result_type mean = std::accumulate(u.begin(), u.end(),
D::result_type(0)) / u.size();
D::result_type var = 0;
D::result_type skew = 0;
D::result_type kurtosis = 0;
for (std::size_t i = 0; i < u.size(); ++i)
{
D::result_type dbl = (u[i] - mean);
D::result_type d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
D::result_type dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
D::result_type x_mean = (d.a() + d.b()) / 2;
D::result_type x_var = sqr(d.b() - d.a()) / 12;
D::result_type x_skew = 0;
D::result_type x_kurtosis = -6./5;
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);
}
{
typedef std::uniform_real_distribution<> D;
typedef std::ranlux48 G;
G g;
D d;
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.a() <= v && v < d.b());
u.push_back(v);
}
D::result_type mean = std::accumulate(u.begin(), u.end(),
D::result_type(0)) / u.size();
D::result_type var = 0;
D::result_type skew = 0;
D::result_type kurtosis = 0;
for (std::size_t i = 0; i < u.size(); ++i)
{
D::result_type dbl = (u[i] - mean);
D::result_type d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
D::result_type dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
D::result_type x_mean = (d.a() + d.b()) / 2;
D::result_type x_var = sqr(d.b() - d.a()) / 12;
D::result_type x_skew = 0;
D::result_type x_kurtosis = -6./5;
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);
}
{
typedef std::uniform_real_distribution<> D;
typedef std::knuth_b G;
G g;
D d;
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.a() <= v && v < d.b());
u.push_back(v);
}
D::result_type mean = std::accumulate(u.begin(), u.end(),
D::result_type(0)) / u.size();
D::result_type var = 0;
D::result_type skew = 0;
D::result_type kurtosis = 0;
for (std::size_t i = 0; i < u.size(); ++i)
{
D::result_type dbl = (u[i] - mean);
D::result_type d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
D::result_type dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
D::result_type x_mean = (d.a() + d.b()) / 2;
D::result_type x_var = sqr(d.b() - d.a()) / 12;
D::result_type x_skew = 0;
D::result_type x_kurtosis = -6./5;
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);
}
{
typedef std::uniform_real_distribution<> D;
typedef std::minstd_rand G;
G g;
D d(-1, 1);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.a() <= v && v < d.b());
u.push_back(v);
}
D::result_type mean = std::accumulate(u.begin(), u.end(),
D::result_type(0)) / u.size();
D::result_type var = 0;
D::result_type skew = 0;
D::result_type kurtosis = 0;
for (std::size_t i = 0; i < u.size(); ++i)
{
D::result_type dbl = (u[i] - mean);
D::result_type d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
D::result_type dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
D::result_type x_mean = (d.a() + d.b()) / 2;
D::result_type x_var = sqr(d.b() - d.a()) / 12;
D::result_type x_skew = 0;
D::result_type x_kurtosis = -6./5;
assert(std::abs(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);
}
{
typedef std::uniform_real_distribution<> D;
typedef std::minstd_rand G;
G g;
D d(5.5, 25);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.a() <= v && v < d.b());
u.push_back(v);
}
D::result_type mean = std::accumulate(u.begin(), u.end(),
D::result_type(0)) / u.size();
D::result_type var = 0;
D::result_type skew = 0;
D::result_type kurtosis = 0;
for (std::size_t i = 0; i < u.size(); ++i)
{
D::result_type dbl = (u[i] - mean);
D::result_type d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
D::result_type dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
D::result_type x_mean = (d.a() + d.b()) / 2;
D::result_type x_var = sqr(d.b() - d.a()) / 12;
D::result_type x_skew = 0;
D::result_type x_kurtosis = -6./5;
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);
}
return 0;
}
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