/* File:       pi-c.c
 *
 * Purpose:    Estimates pi using the Madhava–Leibniz series.
 *
 * Compile:    gcc -g -Wall -o pi-c pi-c.c
 *                 (bonus: try with -O3 ?)
 * Run:        ./pi-c num-intervals
 */

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <sys/time.h>

/* We define pi here so we can check and see how accurate our computation is. */
#define PI 3.141592653589793238462643

double get_time(void)
{
    struct timeval t;
    gettimeofday(&t, NULL);
    return t.tv_sec + t.tv_usec / 1000000.0;
}

int main(int argc, char *argv[])
{
    if (argc <= 1) {
        fprintf(stderr, "Usage: %s num-intervals\n", argv[0]);
        return EXIT_FAILURE;
    }
    unsigned long long intervals = strtoull(argv[1], NULL, 10);
    printf("Intervals: %llu\n", intervals);

    double time1 = get_time();

    long double total = 0.0;
    for (unsigned long long i = 0; i < intervals; ++i) {
        if (i % 2 == 0) {
            total = total + (1.0 / ((2.0 * i) + 1));
        } else {
            total = total - (1.0 / ((2.0 * i) + 1));
        }
    }
    total = total * 4;

    double time2 = get_time();

    printf("   Result: %.20Lf\n", total);
    printf(" Accuracy: %.20Lf\n", PI - total);
    printf("     Time: %.10lf\n", time2 - time1);
}