| //===----------------------------------------------------------------------===// |
| // |
| // 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 <random> |
| #include <numeric> |
| #include <vector> |
| #include <cassert> |
| |
| #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) < 0.04); |
| } |
| |
| 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) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); |
| } |
| |
| 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) < 0.03); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3); |
| } |
| |
| 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) < 0.01); |
| } |
| |
| 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<int8_t>(); |
| tests<uint8_t>(); |
| #if !defined(TEST_HAS_NO_INT128) |
| tests<__int128_t>(); |
| tests<__uint128_t>(); |
| #endif |
| #endif |
| |
| return 0; |
| } |