/* 
 * Program to approximate pi using Monte Carlo approach:
 *
 * Simulate throwing darts at board with quarter-circle
 * inscribed in unit square, counting how many fall within
 * the quarter-circle.  The ratio of this count to the total
 * number of darts should be approximately the same as the
 * ratio of the area of the quarter-circle to the area of
 * the square -- i.e., pi/4.
 *
 * (In the code, "samples" is the number of darts.)
 */
#include <stdio.h>
#include <stdlib.h>
#include <math.h>

double estimate_pi(int seed, int samples);

int main(int argc, char * argv[]) {

    if (argc < 3) {
        printf("usage:  %s num_samples seed\n", argv[0]);
        return EXIT_FAILURE;
    }
    char *endptr;
    long samples = strtol(argv[1], &endptr, 10);
    if ((*endptr != '\0') || samples <= 0) {
        printf("invalid num_samples\n");
        return EXIT_FAILURE;
    }
    long seed = strtol(argv[2], &endptr, 10);
    if ((*endptr != '\0') || seed <= 0) {
        printf("invalid seed\n");
        return EXIT_FAILURE;
    }
    double pi = estimate_pi(seed, samples);
    printf("%ld samples, seed %ld, result %.15f, difference %.15f\n", 
            samples, seed, pi, fabs(pi-acos(-1.0)));
    return EXIT_SUCCESS;
}

double estimate_pi(int seed, int samples) {

    srand(seed);
    int count = 0;

    /* "throw" darts and count how many are inside the circle */
    for (int i = 0; i < samples; ++i) {
        double x = ((double) rand()) / ((double) RAND_MAX);
        double y = ((double) rand()) / ((double) RAND_MAX);
        if ((x*x + y*y) <= 1.0) {
            count += 1;
        }
    }
    return 4 * ((double) count) / ((double) samples);
}