The other day I ran into a question in Stackoverflow asking how to implement square-root calculation. I started googling it up and some implementations seemed to me very cumbersome but then I found Newton’s method which is pretty easy to implement. Translating it to Java was a matter of a few lines of code:

 
class Sqrt {
    public static void main(String[] args) {
        System.out.println(sqrt(17)); // 4.123105985575862
    }

    final static double DELTA = 0.0001;
    /**
     * Newton's method:
     *
     * X1 = X0 - f(x)/f'(x)
     * x^2 = num
     * f(x) = x^2 - num
     * f'(x) = 2*x
     *
     * X1 = X0 - (X0^2 - num) / 2*X0
     * ...
     * Xn = Xn-1 - ((Xn-1)^2 - num)/2Xn-1
     *
     * Stop condition: |num - (Xn)^2| < DELTA 
     * */ 

    public static double sqrt(double num) { 
        double x = num / 2; // starting point
        while(Math.abs(num - x * x) > DELTA) {
            x = x - ((x * x - num) / (2 * x));
        }
        return x;
    }
}