package Others;

import java.lang.Math;

/**
 * Guass Legendre Algorithm
 * ref https://en.wikipedia.org/wiki/Gauss–Legendre_algorithm
 *
 * @author AKS1996
 */
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;
 }

}