SquareRoot.java

public class SquareRoot {
    /**
     * Estimate the sqrt via {@link #superFastSqrt(float)} then refine the accuracy
     * <p/>
     * Refines the guess onece, which should be 'good enough'
     * 
     * @param d the number to estimate
     */
    public static double fastSqrt(double d) {
        return increaseAccuracy(guessSqrt(d), 1);
    }

    /**
     * Estimate the sqrt via {@link #superFastSqrt(float)} then refine the accuracy
     * <p/>
     * Should be faster than {@link Math#sqrt(double)} with only one or two rounds of accuracy
     * 
     * @param d the number to estimate
     * @param accuracy the number of times to refine the guess
     */
    public static double fastSqrt(double d, int accuracy) {
        return increaseAccuracy(guessSqrt(d), accuracy);
    }

    /**
     * Guess the sqrt of the given number
     * <p/>
     * Uses the <href a=https://en.wikipedia.org/wiki/Fast_inverse_square_root>bit-shifting hack</href> from Quake 3
     * 
     * @param f the number to calculate
     * @return the aproxamite sqrt
     */
    public static double guessSqrt(double d) {
        return guessSqrt((float) d);
    }

    /**
     * Guess the sqrt of the given number
     * <p/>
     * Uses the <href a=https://en.wikipedia.org/wiki/Fast_inverse_square_root>bit-shifting hack</href> from Quake 3
     * 
     * @param f the number to calculate
     * @return the aproxamite sqrt
     */
    public static float guessSqrt(float f) {
        int i = Float.floatToRawIntBits(f);
        i = 0x5f3759df - (i >>> 1)
        return Float.intBitsToFloat(i);
    }

    public static double increaseAccuracy(double d, int accuracy) {
        double half = d * 0.5;
        for (int i = 0; i < accuracy; i++) {
            d *= 1.5 - (half * d * d);
        }
        return d;
    }
}