How can I find the Square Root of a Java BigInteger?

Question

Is there a library that will find the square root of a BigInteger? I want it computed offline - only once, and not inside any loop. So even computationally expensive solutio

Answer 1

As Jigar states, Newton's iteration is both quite simple to understand and to implement. I'll leave it up to others decide whether it is the most efficient algorithm or not for finding the square root of a number.

With recursion it can be done in just about two lines.

private static BigInteger newtonIteration(BigInteger n, BigInteger x0)
{
    final BigInteger x1 = n.divide(x0).add(x0).shiftRight(1);
    return x0.equals(x1)||x0.equals(x1.subtract(BigInteger.ONE)) ? x0 : newtonIteration(n, x1);
}

Where n is the number we want to find the square root of, and x0 is the number from the previous call, which will always be 1 when initiate the first call from another method. So preferably, you will complement it with something like this as well;

public static BigInteger sqrt(final BigInteger number)
{
    if(number.signum() == -1)
        throw new ArithmeticException("We can only calculate the square root of positive numbers.");
    return newtonIteration(number, BigInteger.ONE);
}