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#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 lower_incomplete_gamma (double s, double x);
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 gprate (double start, double last, unsigned int n);
double gpterm (double a, double r, int n);
double bisection (gsl_function* f, double a, double b);
double bisection_rlimit (gsl_function* f, double a, double b);
#endif
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