/*
 * estimate pi using Monte Carlo method:
 * simulate throwing "darts" into a board with a quarter-circle 
 *   of radius 1 set in a square of size 1
 * ratio of darts that fall inside the quarter-circle to total
 *   number of darts approximates ratio of areas -- i.e., pi/4.
 * input is number of "samples" (darts) and "seed" for PRNG
 */
#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
#include <math.h>
/* copied from not-strictly-standard part of math.h */
#define M_PI		3.14159265358979323846

int main(void) {
	int samples;
	int seed;
	printf("how many samples?  maximum %d\n", INT_MAX);
	if ((scanf("%d", &samples) != 1) || (samples <= 0)) {
		printf("invalid input\n");
		return EXIT_FAILURE;
	}
	printf("seed for RNG?  maximum %d\n", INT_MAX);
	if ((scanf("%d", &seed) != 1) || (seed <= 0)) {
		printf("invalid input\n");
		return EXIT_FAILURE;
	}

	srand((unsigned int) seed);
	int count = 0;
	double x, y;
	for (int i = 0; i < samples; ++i) {
		x = (double) rand() / (double) (RAND_MAX);
		y = (double) rand() / (double) (RAND_MAX);
		if ((x*x + y*y) <= 1.0)
			++count;
	}
	double pi = 4.0 * (double) count / (double) samples;

	printf("results with %d samples, seed %d:\n", samples, seed);
	printf("computed pi = %g  (%17.15f)\n",pi, pi);
	printf("difference between computed pi and math.h M_PI = %17.15f\n", 
			fabs(pi - M_PI));
	return EXIT_SUCCESS;
}