import java.lang.Math;

/*

* author: @AKS1996

* Guass Legendre Algorithm

* ref https://en.wikipedia.org/wiki/Gauss–Legendre_algorithm

*

*/

public class GuassLegendre {

public static void main(String[] args) {

for(int i=1;i<=3;++i)

System.out.println(pi(i));

}

static double pi(int l){

/*

* l: No of loops to run

*/

double a = 1,b=Math.pow(2,-0.5),t=0.25,p=1;

for(int i=0;i<l;++i){

double temp[] = update(a,b,t,p);

a = temp[0];

b = temp[1];

t = temp[2];

p = temp[3];

}

return Math.pow(a+b, 2)/(4*t);

}

static double[] update(double a, double b, double t, double p){

double values[] = new double[4];

values[0] = (a+b)/2;

values[1] = Math.sqrt(a*b);

values[2] = t - p*Math.pow(a - values[0],2);

values[3] = 2*p;

return values;

}

}