Calculate PI To Arbitrary Precision (Sample Java Code)

Sample Java code to calculate PI to arbitrary precision. This uses Machin’s formula: pi/4 = 4*arctan(1/5) - arctan(1/239).

Notes:
1. Run Pi with a positive integer precision value. For example to calculate PI to 10 decimal places run:
java Pi 10
2. There are other algorithms and even better ones to calculate PI too. This is just an example. I use it to load test my server.
3. Try running with 1 million (1000000) to give your server a good workout

import java.math.BigDecimal;

public class Pi {
    public static void main(String args[]) throws NumberFormatException {
        int digits = Integer.parseInt(args[0]);
        String pi = computePi(digits).toString();
        int freq[] = new int[10];
        for(int i = 0;i < 10;i++) freq[i] = 0;
        int c;
        for(int i = 0;i < pi.length();i++) {
            c = pi.charAt(i);
            if(c == '.') continue;
            c -= '0';
            freq[c]++;
        }
        for(int i = 0;i < 10;i++) {
            System.out.println("" + i + " " + freq[i]);
        }
    }
    /** constants used in pi computation */
    private static final BigDecimal FOUR = BigDecimal.valueOf(4);

    /** rounding mode to use during pi computation */
    private static final int roundingMode = BigDecimal.ROUND_HALF_EVEN;

    /**
     * Compute the value of pi to the specified number of
     * digits after the decimal point.  The value is
     * computed using Machin's formula:
     *
     *          pi/4 = 4*arctan(1/5) - arctan(1/239)
     *
     * and a power series expansion of arctan(x) to
     * sufficient precision.
     */
    public static BigDecimal computePi(int digits) {
        int scale = digits + 5;
        BigDecimal arctan1_5 = arctan(5, scale);
        BigDecimal arctan1_239 = arctan(239, scale);
        BigDecimal pi = arctan1_5.multiply(FOUR).subtract(
                                  arctan1_239).multiply(FOUR);
        return pi.setScale(digits,
                           BigDecimal.ROUND_HALF_UP);
    }
    /**
     * Compute the value, in radians, of the arctangent of
     * the inverse of the supplied integer to the specified
     * number of digits after the decimal point.  The value
     * is computed using the power series expansion for the
     * arc tangent:
     *
     * arctan(x) = x - (x^3)/3 + (x^5)/5 - (x^7)/7 +
     *     (x^9)/9 ...
     */
    public static BigDecimal arctan(int inverseX,
                                    int scale)
    {
        BigDecimal result, numer, term;
        BigDecimal invX = BigDecimal.valueOf(inverseX);
        BigDecimal invX2 =
            BigDecimal.valueOf(inverseX * inverseX);

        numer = BigDecimal.ONE.divide(invX,
                                      scale, roundingMode);

        result = numer;
        int i = 1;
        do {
            numer =
                numer.divide(invX2, scale, roundingMode);
            int denom = 2 * i + 1;
            term =
                numer.divide(BigDecimal.valueOf(denom),
                             scale, roundingMode);
            if ((i % 2) != 0) {
                result = result.subtract(term);
            } else {
                result = result.add(term);
            }
            i++;
        } while (term.compareTo(BigDecimal.ZERO) != 0);
        return result;
    }
}

Note: The code has been adapted from a java.sun example.