#include <string>
using namespace std;

int i4_uniform_ab(int a, int b, int &seed);

double normal_01_cdf(double x);
double normal_01_cdf_inv(double cdf);
void normal_01_cdf_values(int &n_data, double &x, double &fx);
double normal_01_mean();
double normal_01_moment(int order);
double normal_01_pdf(double x);
double normal_01_sample(int &seed);
double normal_01_variance();

double normal_ms_cdf(double x, double mu, double sigma);
double normal_ms_cdf_inv(double cdf, double mu, double sigma);
double normal_ms_mean(double mu, double sigma);
double normal_ms_moment(int order, double mu, double sigma);
double normal_ms_moment_central(int order, double mu, double sigma);
double normal_ms_moment_central_values(int order, double mu, double sigma);
double normal_ms_moment_values(int order, double mu, double sigma);
double normal_ms_pdf(double x, double mu, double sigma);
double normal_ms_sample(double mu, double sigma, int &seed);
double normal_ms_variance(double mu, double sigma);

double r8_abs(double x);
double r8_choose(int n, int k);
double r8_factorial2(int n);
void r8_factorial2_values(int &n_data, int &n, double &f);
double r8_huge();
double r8_log_2(double x);
double r8_mop(int i);
double r8_uniform_01(int &seed);

void r8poly_print(int n, double a[], string title);
double r8poly_value_horner(int n, double a[], double x);

double *r8vec_linspace_new(int n, double a_first, double a_last);
double r8vec_max(int n, double x[]);
double r8vec_mean(int n, double x[]);
double r8vec_min(int n, double x[]);
void r8vec_print(int n, double a[], string title);
double r8vec_variance(int n, double x[]);

void timestamp();

double truncated_normal_ab_cdf(double x, double mu, double sigma, double a,
                               double b);
void truncated_normal_ab_cdf_values(int &n_data, double &mu, double &sigma,
                                    double &a, double &b, double &x,
                                    double &fx);
double truncated_normal_ab_cdf_inv(double cdf, double mu, double sigma,
                                   double a, double b);
double truncated_normal_ab_mean(double mu, double sigma, double a, double b);
double truncated_normal_ab_moment(int order, double mu, double sigma, double a,
                                  double b);
double truncated_normal_ab_pdf(double x, double mu, double sigma, double a,
                               double b);
void truncated_normal_ab_pdf_values(int &n_data, double &mu, double &sigma,
                                    double &a, double &b, double &x,
                                    double &fx);
double truncated_normal_ab_sample(double mu, double sigma, double a, double b,
                                  int &seed);
double truncated_normal_ab_variance(double mu, double sigma, double a,
                                    double b);

double truncated_normal_a_cdf(double x, double mu, double sigma, double a);
void truncated_normal_a_cdf_values(int &n_data, double &mu, double &sigma,
                                   double &a, double &x, double &fx);
double truncated_normal_a_cdf_inv(double cdf, double mu, double sigma,
                                  double a);
double truncated_normal_a_mean(double mu, double sigma, double a);
double truncated_normal_a_moment(int order, double mu, double sigma, double a);
double truncated_normal_a_pdf(double x, double mu, double sigma, double a);
void truncated_normal_a_pdf_values(int &n_data, double &mu, double &sigma,
                                   double &a, double &x, double &fx);
double truncated_normal_a_sample(double mu, double sigma, double a, int &seed);
double truncated_normal_a_variance(double mu, double sigma, double a);

double truncated_normal_b_cdf(double x, double mu, double sigma, double b);
void truncated_normal_b_cdf_values(int &n_data, double &mu, double &sigma,
                                   double &b, double &x, double &fx);
double truncated_normal_b_cdf_inv(double cdf, double mu, double sigma,
                                  double b);
double truncated_normal_b_mean(double mu, double sigma, double b);
double truncated_normal_b_moment(int order, double mu, double sigma, double b);
double truncated_normal_b_pdf(double x, double mu, double sigma, double b);
void truncated_normal_b_pdf_values(int &n_data, double &mu, double &sigma,
                                   double &b, double &x, double &fx);
double truncated_normal_b_sample(double mu, double sigma, double b, int &seed);
double truncated_normal_b_variance(double mu, double sigma, double b);