#ifndef UTILS_H
#define UTILS_H

#include <gsl/gsl_roots.h>
#include <gsl/gsl_vector.h>

#define SIGNUM(x) ((x) < 0 ? -1 : 1)

double volume_of_ball (unsigned int dimension);
double ln_volume_of_ball (unsigned int dimension);
double surface_area_of_ball (unsigned int dimension);
double ln_surface_area_of_ball (unsigned int dimension);

double angle_between_vectors (const gsl_vector* x, const gsl_vector* y);
double dot_product (const gsl_vector* x, const gsl_vector* y);
double gaussian_pdf (double x);
double gaussian_cdf (double x);

double rerror (double approx, double exact);

double bisection (gsl_function* f, double a, double b);
double bisection_rlimit (gsl_function* f, double a, double b);

#endif