import java.math.BigDecimal;
import static java.math.BigDecimal.*;
/**
*
* @author Juergen
*/
public class MyPi {
private static final BigDecimal TWO = new BigDecimal(2);
private static final BigDecimal FOUR = new BigDecimal(4);
public static void main(String[] args) {
System.out.println(pi(100));
}
// Gauss-Legendre Algorithm
public static BigDecimal pi(final int SCALE) {
BigDecimal a = ONE;
BigDecimal b = ONE.divide(sqrt(TWO, SCALE), SCALE, ROUND_HALF_UP);
BigDecimal t = new BigDecimal(0.25);
BigDecimal x = ONE;
BigDecimal y;
while (!a.equals(b)) {
y = a;
a = a.add(b).divide(TWO, SCALE, ROUND_HALF_UP);
b = sqrt(b.multiply(y), SCALE);
t = t.subtract(x.multiply(y.subtract(a).multiply(y.subtract(a))));
x = x.multiply(TWO);
}
return a.add(b).multiply(a.add(b)).divide(t.multiply(FOUR), SCALE, ROUND_HALF_UP);
}
// the Babylonian square root method (Newton's method)
public static BigDecimal sqrt(BigDecimal A, final int SCALE) {
BigDecimal x0 = new BigDecimal("0");
BigDecimal x1 = new BigDecimal(Math.sqrt(A.doubleValue()));
while (!x0.equals(x1)) {
x0 = x1;
x1 = A.divide(x0, SCALE, ROUND_HALF_UP);
x1 = x1.add(x0);
x1 = x1.divide(TWO, SCALE, ROUND_HALF_UP);
}
return x1;
}
}
