Java Program to Implement Borwein Algorithm

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.

Here is the source code of the Java Program to Implement Borwein Algorithm. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

```
/**
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 **  Java Program to Implement Borwein Algorithm

```
 **/
```
```
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 **/
```
```
    public double getOneByPi(int k)
```
```
    {
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        double ak = 6.0 - 4 * Math.sqrt(2);

```
        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)));

            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);

        System.out.println("Borwein 1/Pi Algorithm Test\n");

        /** 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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```
}
```

Borwein 1/Pi Algorithm Test
 
Enter number of iterations
5
 
Value of 1/pi : 0.31830988618379075

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