14ff556cf6266463174770171a41cd270798b72b3Howard Hinnant//===----------------------------------------------------------------------===// 24ff556cf6266463174770171a41cd270798b72b3Howard Hinnant// 34ff556cf6266463174770171a41cd270798b72b3Howard Hinnant// The LLVM Compiler Infrastructure 44ff556cf6266463174770171a41cd270798b72b3Howard Hinnant// 5b64f8b07c104c6cc986570ac8ee0ed16a9f23976Howard Hinnant// This file is dual licensed under the MIT and the University of Illinois Open 6b64f8b07c104c6cc986570ac8ee0ed16a9f23976Howard Hinnant// Source Licenses. See LICENSE.TXT for details. 74ff556cf6266463174770171a41cd270798b72b3Howard Hinnant// 84ff556cf6266463174770171a41cd270798b72b3Howard Hinnant//===----------------------------------------------------------------------===// 9d9144e8d1783617b279146f397a6ab3defefefc4Jonathan Roelofs// 10d9144e8d1783617b279146f397a6ab3defefefc4Jonathan Roelofs// REQUIRES: long_tests 114ff556cf6266463174770171a41cd270798b72b3Howard Hinnant 124ff556cf6266463174770171a41cd270798b72b3Howard Hinnant// <random> 134ff556cf6266463174770171a41cd270798b72b3Howard Hinnant 144ff556cf6266463174770171a41cd270798b72b3Howard Hinnant// template<class IntType = int> 154ff556cf6266463174770171a41cd270798b72b3Howard Hinnant// class poisson_distribution 164ff556cf6266463174770171a41cd270798b72b3Howard Hinnant 174ff556cf6266463174770171a41cd270798b72b3Howard Hinnant// template<class _URNG> result_type operator()(_URNG& g); 184ff556cf6266463174770171a41cd270798b72b3Howard Hinnant 194ff556cf6266463174770171a41cd270798b72b3Howard Hinnant#include <random> 204ff556cf6266463174770171a41cd270798b72b3Howard Hinnant#include <cassert> 214ff556cf6266463174770171a41cd270798b72b3Howard Hinnant#include <vector> 224ff556cf6266463174770171a41cd270798b72b3Howard Hinnant#include <numeric> 234ff556cf6266463174770171a41cd270798b72b3Howard Hinnant 244ff556cf6266463174770171a41cd270798b72b3Howard Hinnanttemplate <class T> 254ff556cf6266463174770171a41cd270798b72b3Howard Hinnantinline 264ff556cf6266463174770171a41cd270798b72b3Howard HinnantT 274ff556cf6266463174770171a41cd270798b72b3Howard Hinnantsqr(T x) 284ff556cf6266463174770171a41cd270798b72b3Howard Hinnant{ 294ff556cf6266463174770171a41cd270798b72b3Howard Hinnant return x * x; 304ff556cf6266463174770171a41cd270798b72b3Howard Hinnant} 314ff556cf6266463174770171a41cd270798b72b3Howard Hinnant 324ff556cf6266463174770171a41cd270798b72b3Howard Hinnantint main() 334ff556cf6266463174770171a41cd270798b72b3Howard Hinnant{ 344ff556cf6266463174770171a41cd270798b72b3Howard Hinnant { 354ff556cf6266463174770171a41cd270798b72b3Howard Hinnant typedef std::poisson_distribution<> D; 364ff556cf6266463174770171a41cd270798b72b3Howard Hinnant typedef std::minstd_rand G; 374ff556cf6266463174770171a41cd270798b72b3Howard Hinnant G g; 384ff556cf6266463174770171a41cd270798b72b3Howard Hinnant D d(2); 394ff556cf6266463174770171a41cd270798b72b3Howard Hinnant const int N = 100000; 404ff556cf6266463174770171a41cd270798b72b3Howard Hinnant std::vector<double> u; 414ff556cf6266463174770171a41cd270798b72b3Howard Hinnant for (int i = 0; i < N; ++i) 42df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant { 43df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant D::result_type v = d(g); 44df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant assert(d.min() <= v && v <= d.max()); 45df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant u.push_back(v); 46df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant } 474ff556cf6266463174770171a41cd270798b72b3Howard Hinnant double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 484ff556cf6266463174770171a41cd270798b72b3Howard Hinnant double var = 0; 49df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double skew = 0; 50df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double kurtosis = 0; 51a2cd27094316a83e188727fe0478b5f0dfd0a055Eric Fiselier for (unsigned i = 0; i < u.size(); ++i) 52df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant { 53d6c0cf0ebdfd1d237fe7e07ab3732467dbd14c91Eric Fiselier double dbl = (u[i] - mean); 54d6c0cf0ebdfd1d237fe7e07ab3732467dbd14c91Eric Fiselier double d2 = sqr(dbl); 55df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant var += d2; 56d6c0cf0ebdfd1d237fe7e07ab3732467dbd14c91Eric Fiselier skew += dbl * d2; 57df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant kurtosis += d2 * d2; 58df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant } 594ff556cf6266463174770171a41cd270798b72b3Howard Hinnant var /= u.size(); 60df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double dev = std::sqrt(var); 61df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant skew /= u.size() * dev * var; 62df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant kurtosis /= u.size() * var * var; 63df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant kurtosis -= 3; 644ff556cf6266463174770171a41cd270798b72b3Howard Hinnant double x_mean = d.mean(); 654ff556cf6266463174770171a41cd270798b72b3Howard Hinnant double x_var = d.mean(); 66df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double x_skew = 1 / std::sqrt(x_var); 67df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double x_kurtosis = 1 / x_var; 68d6d1171f2c3f254582ae1d5b9e14cea0ea8e701bHoward Hinnant assert(std::abs((mean - x_mean) / x_mean) < 0.01); 69d6d1171f2c3f254582ae1d5b9e14cea0ea8e701bHoward Hinnant assert(std::abs((var - x_var) / x_var) < 0.01); 70d6d1171f2c3f254582ae1d5b9e14cea0ea8e701bHoward Hinnant assert(std::abs((skew - x_skew) / x_skew) < 0.01); 71d6d1171f2c3f254582ae1d5b9e14cea0ea8e701bHoward Hinnant assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); 724ff556cf6266463174770171a41cd270798b72b3Howard Hinnant } 734ff556cf6266463174770171a41cd270798b72b3Howard Hinnant { 744ff556cf6266463174770171a41cd270798b72b3Howard Hinnant typedef std::poisson_distribution<> D; 754ff556cf6266463174770171a41cd270798b72b3Howard Hinnant typedef std::minstd_rand G; 764ff556cf6266463174770171a41cd270798b72b3Howard Hinnant G g; 774ff556cf6266463174770171a41cd270798b72b3Howard Hinnant D d(0.75); 784ff556cf6266463174770171a41cd270798b72b3Howard Hinnant const int N = 100000; 794ff556cf6266463174770171a41cd270798b72b3Howard Hinnant std::vector<double> u; 804ff556cf6266463174770171a41cd270798b72b3Howard Hinnant for (int i = 0; i < N; ++i) 81df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant { 82df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant D::result_type v = d(g); 83df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant assert(d.min() <= v && v <= d.max()); 84df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant u.push_back(v); 85df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant } 864ff556cf6266463174770171a41cd270798b72b3Howard Hinnant double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 874ff556cf6266463174770171a41cd270798b72b3Howard Hinnant double var = 0; 88df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double skew = 0; 89df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double kurtosis = 0; 90a2cd27094316a83e188727fe0478b5f0dfd0a055Eric Fiselier for (unsigned i = 0; i < u.size(); ++i) 91df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant { 92d6c0cf0ebdfd1d237fe7e07ab3732467dbd14c91Eric Fiselier double dbl = (u[i] - mean); 93d6c0cf0ebdfd1d237fe7e07ab3732467dbd14c91Eric Fiselier double d2 = sqr(dbl); 94df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant var += d2; 95d6c0cf0ebdfd1d237fe7e07ab3732467dbd14c91Eric Fiselier skew += dbl * d2; 96df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant kurtosis += d2 * d2; 97df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant } 984ff556cf6266463174770171a41cd270798b72b3Howard Hinnant var /= u.size(); 99df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double dev = std::sqrt(var); 100df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant skew /= u.size() * dev * var; 101df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant kurtosis /= u.size() * var * var; 102df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant kurtosis -= 3; 1034ff556cf6266463174770171a41cd270798b72b3Howard Hinnant double x_mean = d.mean(); 1044ff556cf6266463174770171a41cd270798b72b3Howard Hinnant double x_var = d.mean(); 105df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double x_skew = 1 / std::sqrt(x_var); 106df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double x_kurtosis = 1 / x_var; 107d6d1171f2c3f254582ae1d5b9e14cea0ea8e701bHoward Hinnant assert(std::abs((mean - x_mean) / x_mean) < 0.01); 108d6d1171f2c3f254582ae1d5b9e14cea0ea8e701bHoward Hinnant assert(std::abs((var - x_var) / x_var) < 0.01); 109d6d1171f2c3f254582ae1d5b9e14cea0ea8e701bHoward Hinnant assert(std::abs((skew - x_skew) / x_skew) < 0.01); 110d6d1171f2c3f254582ae1d5b9e14cea0ea8e701bHoward Hinnant assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04); 1114ff556cf6266463174770171a41cd270798b72b3Howard Hinnant } 1124ff556cf6266463174770171a41cd270798b72b3Howard Hinnant { 1134ff556cf6266463174770171a41cd270798b72b3Howard Hinnant typedef std::poisson_distribution<> D; 114df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant typedef std::mt19937 G; 1154ff556cf6266463174770171a41cd270798b72b3Howard Hinnant G g; 1164ff556cf6266463174770171a41cd270798b72b3Howard Hinnant D d(20); 117df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant const int N = 1000000; 1184ff556cf6266463174770171a41cd270798b72b3Howard Hinnant std::vector<double> u; 1194ff556cf6266463174770171a41cd270798b72b3Howard Hinnant for (int i = 0; i < N; ++i) 120df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant { 121df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant D::result_type v = d(g); 122df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant assert(d.min() <= v && v <= d.max()); 123df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant u.push_back(v); 124df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant } 1254ff556cf6266463174770171a41cd270798b72b3Howard Hinnant double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 1264ff556cf6266463174770171a41cd270798b72b3Howard Hinnant double var = 0; 127df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double skew = 0; 128df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double kurtosis = 0; 129a2cd27094316a83e188727fe0478b5f0dfd0a055Eric Fiselier for (unsigned i = 0; i < u.size(); ++i) 130df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant { 131d6c0cf0ebdfd1d237fe7e07ab3732467dbd14c91Eric Fiselier double dbl = (u[i] - mean); 132d6c0cf0ebdfd1d237fe7e07ab3732467dbd14c91Eric Fiselier double d2 = sqr(dbl); 133df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant var += d2; 134d6c0cf0ebdfd1d237fe7e07ab3732467dbd14c91Eric Fiselier skew += dbl * d2; 135df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant kurtosis += d2 * d2; 136df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant } 1374ff556cf6266463174770171a41cd270798b72b3Howard Hinnant var /= u.size(); 138df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double dev = std::sqrt(var); 139df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant skew /= u.size() * dev * var; 140df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant kurtosis /= u.size() * var * var; 141df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant kurtosis -= 3; 1424ff556cf6266463174770171a41cd270798b72b3Howard Hinnant double x_mean = d.mean(); 1434ff556cf6266463174770171a41cd270798b72b3Howard Hinnant double x_var = d.mean(); 144df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double x_skew = 1 / std::sqrt(x_var); 145df40dc6c1a8ca0bf00fb6aec030f69042f61d974Howard Hinnant double x_kurtosis = 1 / x_var; 146d6d1171f2c3f254582ae1d5b9e14cea0ea8e701bHoward Hinnant assert(std::abs((mean - x_mean) / x_mean) < 0.01); 147d6d1171f2c3f254582ae1d5b9e14cea0ea8e701bHoward Hinnant assert(std::abs((var - x_var) / x_var) < 0.01); 148d6d1171f2c3f254582ae1d5b9e14cea0ea8e701bHoward Hinnant assert(std::abs((skew - x_skew) / x_skew) < 0.01); 149d6d1171f2c3f254582ae1d5b9e14cea0ea8e701bHoward Hinnant assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); 1504ff556cf6266463174770171a41cd270798b72b3Howard Hinnant } 1514ff556cf6266463174770171a41cd270798b72b3Howard Hinnant} 152