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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;

}

}