/* 
 * Program to approximate pi using numerical integration, starting with initial
 * number of slices and repeating with increasing number of slices until 
 * values converge (difference between successive estimates small).
 */ 
#include <stdio.h>
#include <math.h>

double estimate_pi(long slices);

int main(void) {
	long slices;
	printf("enter starting number of slices:\n"); 
	if ((scanf("%ld", &slices) != 1) || (slices <= 0)) {
		printf("not a positive number\n");
	}
	double threshold;
	printf("enter convergence threshold:\n"); 
	if ((scanf("%lf", &threshold) != 1) || (threshold <= 0)) {
		printf("not a positive number\n");
		return 1;
	}

	double previous_estimate = 0;
	double estimate = 0;

	do {
		previous_estimate = estimate;
		estimate = estimate_pi(slices);
		printf("for %ld slices, estimated pi = %.15f\n", slices, estimate);
		slices *= 2;
	} while (fabs(estimate - previous_estimate) > threshold);

	return 0;
}

double estimate_pi(long slices) {
	double sum_of_heights = 0.0;
	double width_of_slice = 1.0/slices;
	for (int i = 0; i < slices; ++i) {
		/* height = 4/(1+x*x) at the midpoint */
		double midpoint = (i + 0.5)*width_of_slice;
		sum_of_heights += 4/(1 + midpoint*midpoint);
	}
	double pi = sum_of_heights * width_of_slice;
	return pi;
}