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 //===----------------------------------------------------------------------===// // // The LLVM Compiler Infrastructure // // This file is dual licensed under the MIT and the University of Illinois Open // Source Licenses. See LICENSE.TXT for details. // //===----------------------------------------------------------------------===// // // REQUIRES: long_tests // // template // class geometric_distribution // template result_type operator()(_URNG& g); #include #include #include #include template inline T sqr(T x) { return x * x; } struct Eng : std::mt19937 { using Base = std::mt19937; using Base::Base; }; void test_small_inputs() { Eng engine; std::geometric_distribution distribution(5.45361e-311); for (auto i=0; i < 1000; ++i) { volatile auto res = distribution(engine); ((void)res); } } void test1() { typedef std::geometric_distribution<> D; typedef std::mt19937 G; G g; D d(.03125); const int N = 1000000; std::vector u; for (int i = 0; i < N; ++i) { 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 = (1 - d.p()) / d.p(); double x_var = x_mean / d.p(); double x_skew = (2 - d.p()) / std::sqrt((1 - d.p())); double x_kurtosis = 6 + sqr(d.p()) / (1 - d.p()); 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); } void test2() { typedef std::geometric_distribution<> D; typedef std::mt19937 G; G g; D d(0.05); const int N = 1000000; std::vector u; for (int i = 0; i < N; ++i) { 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 = (1 - d.p()) / d.p(); double x_var = x_mean / d.p(); double x_skew = (2 - d.p()) / std::sqrt((1 - d.p())); double x_kurtosis = 6 + sqr(d.p()) / (1 - d.p()); 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) < 0.03); } void test3() { typedef std::geometric_distribution<> D; typedef std::minstd_rand G; G g; D d(.25); const int N = 1000000; std::vector u; for (int i = 0; i < N; ++i) { 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 = (1 - d.p()) / d.p(); double x_var = x_mean / d.p(); double x_skew = (2 - d.p()) / std::sqrt((1 - d.p())); double x_kurtosis = 6 + sqr(d.p()) / (1 - d.p()); 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) < 0.02); } void test4() { typedef std::geometric_distribution<> D; typedef std::mt19937 G; G g; D d(0.5); const int N = 1000000; std::vector u; for (int i = 0; i < N; ++i) { 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 = (1 - d.p()) / d.p(); double x_var = x_mean / d.p(); double x_skew = (2 - d.p()) / std::sqrt((1 - d.p())); double x_kurtosis = 6 + sqr(d.p()) / (1 - d.p()); 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) < 0.02); } void test5() { typedef std::geometric_distribution<> D; typedef std::mt19937 G; G g; D d(0.75); const int N = 1000000; std::vector u; for (int i = 0; i < N; ++i) { 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 = (1 - d.p()) / d.p(); double x_var = x_mean / d.p(); double x_skew = (2 - d.p()) / std::sqrt((1 - d.p())); double x_kurtosis = 6 + sqr(d.p()) / (1 - d.p()); 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) < 0.02); } void test6() { typedef std::geometric_distribution<> D; typedef std::mt19937 G; G g; D d(0.96875); const int N = 1000000; std::vector u; for (int i = 0; i < N; ++i) { 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 = (1 - d.p()) / d.p(); double x_var = x_mean / d.p(); double x_skew = (2 - d.p()) / std::sqrt((1 - d.p())); double x_kurtosis = 6 + sqr(d.p()) / (1 - d.p()); 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) < 0.02); } int main() { test1(); test2(); test3(); test4(); test5(); test6(); test_small_inputs(); }