/*
 * Calculate the Gregory-Leibniz sum: 
 *
 * sum_{k=0}^\infty (-1)^k/(2k + 1) = M_PI/4
 */

#include <stdio.h>
#include <math.h>

#define N 10000000
#define NREP 10

double gregory(long n) 
{
    double s = 0., sign = 1.;
    long k;

    for (k = 0; k <= n; k++) 
    {
        s += sign/((double) 2*k + 1);
        sign = -sign;
    }
    return(s);
}

int main(void) 
{
    double s;
    int k;
    long n = N;

    for (k = 0; k <= NREP; k++) 
    {
        s = gregory(n);
        printf("%20ld   %20.14f   %20.14f\n", n, s, M_PI/4. - s);
        n *= 2;
    }

    return(0);
}