/*
 * Program to estimate pi using numerical integration, revised to demonstrate
 * more-general routine to perform numerical integration.
 */
#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 curve1(double x);
double curve2(double x);
/* estimated area under curve specified by "fcn" from a to b */
double estimate(double a, double b, long num_slices, double (*fcn)(double x));

int main(void) {

	long num_slices;

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

	double pi_est = estimate(0.0, 1.0, num_slices, curve1);
	printf("result for %ld slices:\n%22.20f (differs from M_PI by %g)\n", 
			num_slices, pi_est, pi_est - M_PI);

	double tryit = estimate(10.0, 20.0, num_slices, curve2);
	printf("result of integrating x*x from 0 to 10, %ld slices:\n%22.20f\n",
			num_slices, tryit);

	return 0;
}

double curve1(double x) {
	return 4 / (1 + x*x) ;
}

double curve2(double x) {
	return x*x;
}

double estimate(double a, double b, long num_slices, double (*fcn)(double x)) {

	double work = 0.0; /* sum of rectangle heights */
	double width = (b-a)/num_slices;

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