Java PI Generation – Nilakantha

Java program to generate PI digits using Nilakantha series using double and BigDecimal.

After 500.000 iterations as expected it generates 16 correct decimal digits.

3.14159265358978689874902556766755878925323486328125
3.141592653589793240462643383269502884197291399375103050974944693349816400880678999026756787303333903

Main.java

import java.math.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;

// ? 2019 TheFlyingKeyboard and released under MIT License
// theflyingkeyboard.net

public class Main {

    private static final int scale = 100;

    public static void main(String[] args) {
        long iterations = 500000;

        System.out.println(new BigDecimal(nilakantha(iterations)));
        System.out.println(nilakanthaBigDecimal(iterations));
    }

    private static double nilakantha(long iterations) {
        iterations -= 1;
        double pi = 3;
        long divisorBegin = 2;
        double divisor;

        for (long i = 0; i < iterations; ++i) {
            divisor = 1.0d;
            for(long j = 0; j < 3; ++j) {
                divisor *= divisorBegin + j;
            }

            pi += i % 2 == 0 ? 4.0d / divisor : -4.0d / divisor;
            divisorBegin += 2;
        }

        return pi;
    }

    private static BigDecimal nilakanthaBigDecimal(long iterations) {
        iterations -= 1;
        BigDecimal pi = new BigDecimal(3);
        BigDecimal divisorBegin = new BigDecimal(2);
        BigDecimal divisor;

        BigDecimal one = new BigDecimal(1);
        BigDecimal two = new BigDecimal(2);
        BigDecimal four = new BigDecimal(4);
        BigDecimal minusFour = new BigDecimal(-4);
        MathContext mc = new MathContext(scale);

        for (long i = 0; i < iterations; ++i) {
            divisor = one;
            for(long j = 0; j < 3; ++j) {
                divisor = divisor.multiply(new BigDecimal(j).add(divisorBegin, mc), mc);
            }

            pi = pi.add(i % 2 == 0 ? four.divide(divisor, mc) : minusFour.divide(divisor, mc), mc);
            divisorBegin = divisorBegin.add(two, mc);
        }

        return pi;
    }
}