Java/src/main/java/com/thealgorithms/others/GaussLegendre.java

package com.thealgorithms.others;

/**
 * Gauss Legendre Algorithm ref
 * https://en.wikipedia.org/wiki/Gauss–Legendre_algorithm
 *
 * @author AKS1996
 */
public final class GaussLegendre {
    private GaussLegendre() {
    }

    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;
        double b = Math.pow(2, -0.5);
        double t = 0.25;
        double 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;
    }
}