package Others;

/**
 * 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;
  }
}