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/*
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This is a Java Program to Implement Borwein Algorithm. Borwein’s algorithm is an algorithm devised by Jonathan and Peter Borwein to calculate the value of 1/π.
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*/
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/**
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** Java Program to Implement Borwein Algorithm
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**/
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import java.util.Scanner;
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/** Class Borwein **/
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public class Borwein
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{
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/** compute 1/pi **/
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public double getOneByPi(int k)
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{
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double ak = 6.0 - 4 * Math.sqrt(2);
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double yk = Math.sqrt(2) - 1.0;
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double ak1 ;
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double yk1 ;
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for (int i = 0; i < k; i++)
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{
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yk1 = (1 - Math.pow((1 - yk * yk * yk * yk),(0.25)))/(1 + Math.pow((1 - yk * yk * yk * yk),(0.25)));
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ak1 = ak * Math.pow((1 + yk1), 4) - Math.pow(2, 2 * i + 3) * yk1 * (1 + yk1 + yk1 * yk1);
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yk = yk1;
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ak = ak1;
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}
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return ak;
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}
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/** Main function **/
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public static void main (String[] args)
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{
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Scanner scan = new Scanner(System.in);
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System.out.println("Borwein 1/Pi Algorithm Test\n");
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/** Make an object of Borwein class **/
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Borwein b = new Borwein();
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System.out.println("Enter number of iterations ");
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int k = scan.nextInt();
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System.out.println("\nValue of 1/pi : "+ b.getOneByPi(k));
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}
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}
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/*
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Enter number of iterations
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5
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Value of 1/pi : 0.31830988618379075
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