/*
 * Program to estimate pi using numerical integration.
 *
 * Also illustrates looping until convergence.
 */
#include <stdio.h>
#include <math.h>

/* best(?) available value of pi, to check computed approximation */
/* surprisingly, no library-defined constant for this in standard C! */
#define M_PI acos(-1.0)

double curve(double x);
double estimate(long num_slices);

int main(void) {

	long num_slices;
	double threshold;

	printf("how many slices to start with?\n");
	if ((scanf("%ld", &num_slices) != 1) || (num_slices <= 0)){
		printf("not a positive integer\n");
		return 1;
	}
	printf("convergence threshold?\n");
	if ((scanf("%lf", &threshold) != 1) || (threshold <= 0)){
		printf("not a positive number\n");
	}

	double est = 1.0;
	double previous_est = 0.0;

	while (fabs(previous_est - est) > threshold) {
		/* save current estimate */
		previous_est = est;
		/* compute new estimate and print */
		est = estimate(num_slices);
		printf("result for %ld slices:\n%22.20f (differs from M_PI by %g)\n", 
			num_slices, est, est - M_PI);
		/* double number of slices */
		num_slices *= 2;
	}

	return 0;
}

double curve(double x) {
	return 4 / (1 + x*x) ;
}

double estimate(long num_slices) {

	double work = 0.0; /* sum of rectangle heights */
	double width = 1.0/num_slices;

	for (int i = 0; i < num_slices; ++i) {
		work += curve(width*(i+0.5));
	}
	return work * width;
}