text: //===----------------------------------------------------------------------===//
  //
  //                     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
  
  // <random>
  
  // template<class RealType = double>
  // class lognormal_distribution
  
  // template<class _URNG> result_type operator()(_URNG& g);
  
  #include <random>
  #include <cassert>
  #include <vector>
  #include <numeric>
  
  template <class T>
  inline
  T
  sqr(T x)
  {
      return x * x;
  }
  
  void
  test1()
  {
      typedef std::lognormal_distribution<> D;
      typedef std::mt19937 G;
      G g;
      D d(-1./8192, 0.015625);
      const int N = 1000000;
      std::vector<D::result_type> u;
      for (int i = 0; i < N; ++i)
      {
          D::result_type v = d(g);
          assert(v > 0);
          u.push_back(v);
      }
      double mean = std::accumulate(u.begin(), u.end(), 0.0) / 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 = std::exp(d.m() + sqr(d.s())/2);
      double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s()));
      double x_skew = (std::exp(sqr(d.s())) + 2) *
            std::sqrt((std::exp(sqr(d.s())) - 1));
      double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) +
                        3*std::exp(2*sqr(d.s())) - 6;
      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) < 0.05);
      assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.25);
  }
  
  void
  test2()
  {
      typedef std::lognormal_distribution<> D;
      typedef std::mt19937 G;
      G g;
      D d(-1./32, 0.25);
      const int N = 1000000;
      std::vector<D::result_type> u;
      for (int i = 0; i < N; ++i)
      {
          D::result_type v = d(g);
          assert(v > 0);
          u.push_back(v);
      }
      double mean = std::accumulate(u.begin(), u.end(), 0.0) / 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 = std::exp(d.m() + sqr(d.s())/2);
      double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s()));
      double x_skew = (std::exp(sqr(d.s())) + 2) *
            std::sqrt((std::exp(sqr(d.s())) - 1));
      double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) +
                        3*std::exp(2*sqr(d.s())) - 6;
      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::lognormal_distribution<> D;
      typedef std::mt19937 G;
      G g;
      D d(-1./8, 0.5);
      const int N = 1000000;
      std::vector<D::result_type> u;
      for (int i = 0; i < N; ++i)
      {
          D::result_type v = d(g);
          assert(v > 0);
          u.push_back(v);
      }
      double mean = std::accumulate(u.begin(), u.end(), 0.0) / 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 = std::exp(d.m() + sqr(d.s())/2);
      double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s()));
      double x_skew = (std::exp(sqr(d.s())) + 2) *
            std::sqrt((std::exp(sqr(d.s())) - 1));
      double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) +
                        3*std::exp(2*sqr(d.s())) - 6;
      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) < 0.05);
  }
  
  void
  test4()
  {
      typedef std::lognormal_distribution<> D;
      typedef std::mt19937 G;
      G g;
      D d;
      const int N = 1000000;
      std::vector<D::result_type> u;
      for (int i = 0; i < N; ++i)
      {
          D::result_type v = d(g);
          assert(v > 0);
          u.push_back(v);
      }
      double mean = std::accumulate(u.begin(), u.end(), 0.0) / 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 = std::exp(d.m() + sqr(d.s())/2);
      double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s()));
      double x_skew = (std::exp(sqr(d.s())) + 2) *
            std::sqrt((std::exp(sqr(d.s())) - 1));
      double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) +
                        3*std::exp(2*sqr(d.s())) - 6;
      assert(std::abs((mean - x_mean) / x_mean) < 0.01);
      assert(std::abs((var - x_var) / x_var) < 0.02);
      assert(std::abs((skew - x_skew) / x_skew) < 0.08);
      assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.4);
  }
  
  void
  test5()
  {
      typedef std::lognormal_distribution<> D;
      typedef std::mt19937 G;
      G g;
      D d(-0.78125, 1.25);
      const int N = 1000000;
      std::vector<D::result_type> u;
      for (int i = 0; i < N; ++i)
      {
          D::result_type v = d(g);
          assert(v > 0);
          u.push_back(v);
      }
      double mean = std::accumulate(u.begin(), u.end(), 0.0) / 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 = std::exp(d.m() + sqr(d.s())/2);
      double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s()));
      double x_skew = (std::exp(sqr(d.s())) + 2) *
            std::sqrt((std::exp(sqr(d.s())) - 1));
      double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) +
                        3*std::exp(2*sqr(d.s())) - 6;
      assert(std::abs((mean - x_mean) / x_mean) < 0.01);
      assert(std::abs((var - x_var) / x_var) < 0.04);
      assert(std::abs((skew - x_skew) / x_skew) < 0.2);
      assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.7);
  }
  
  int main()
  {
      test1();
      test2();
      test3();
      test4();
      test5();
  }
  