/* usage only for people who do not care about licenses */
/* also it's an attempt on an algorithm that should probably
be considered public domain */

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

double find_pi (int i, bool f) {
 int    n=0;
 double a=1, b=1/sqrt(2), t=0.25, p=1, an, r;
 for (n=0; n<i; n++) {
  an = (a+b) / 2;
  b  = sqrt(a*b);
  t -= p * pow((a-an),2);
  p *= 2;
  a = an;
  r = pow ( a+b , 2 ) / (4*t) ;
  n ++ ;
  if (f) { printf ( "%d %f %f \n", n, fabs(a-b), r ) ; }
  }
 return r;
 }

int main(void) {
 printf("%f\n", find_pi(3,true));
 }