Approximation of Pi by probability

pi.c

/*
 * pi.c
 *
 * Approximation of Pi by the probability
 * of a point to fall into the circle of
 * a circumscribed square in the xy-plane.
 *
 * Inspired by Simulation Fifth Edition
 * Book by Sheldon Ross
 */

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <assert.h>

int main(int argc, char ** argv)
{
        unsigned long long nsamples, inside_cnt = 0;
        double x, y;

        srand((unsigned) time(NULL));
        assert(argc == 2);
        nsamples = atoi(argv[1]);
        assert(nsamples != 0);

        for (int i = 0; i < nsamples; ++i) {
                x = ( 2 * ((double) rand() / RAND_MAX) ) - 1;
                y = ( 2 * ((double) rand() / RAND_MAX) ) - 1;
                if (x*x + y*y <= 1)
                        ++inside_cnt;
        }

        double pi = 4 * ( (double) inside_cnt / (double) nsamples);
        printf("pi ~= %lf\n", pi);

        double nu = fabs(pi / M_PI - 1);
        printf("nu = %lf\n", nu);

        return 0;
}