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

Here's a solution that does not use BigInteger.multiply or BigInteger.divide:

    private static final BigInteger ZERO  = BigInteger.ZERO;
    private static final BigInteger ONE   = BigInteger.ONE;
    private static final BigInteger TWO   = BigInteger.valueOf(2);
    private static final BigInteger THREE = BigInteger.valueOf(3);

    /**
     * This method computes sqrt(n) in O(n.bitLength()) time,
     * and computes it exactly. By "exactly", I mean it returns
     * not only the (floor of the) square root s, but also the
     * remainder r, such that r >= 0, n = s^2 + r, and
     * n < (s + 1)^2.
     *
     * @param n The argument n, as described above.
     *
     * @return An array of two values, where the first element
     *         of the array is s and the second is r, as
     *         described above.
     *
     * @throws IllegalArgumentException if n is not nonnegative.
     */
    public static BigInteger[] sqrt(BigInteger n) {
        if (n == null || n.signum() < 0) {
            throw new IllegalArgumentException();
        }

        int bl = n.bitLength();
        if ((bl & 1) != 0) {
            ++ bl;
        }

        BigInteger s = ZERO;
        BigInteger r = ZERO;

        while (bl >= 2) {
            s = s.shiftLeft(1);

            BigInteger crumb = n.testBit(-- bl)
                                ? (n.testBit(-- bl) ? THREE : TWO)
                                : (n.testBit(-- bl) ? ONE : ZERO);
            r = r.shiftLeft(2).add(crumb);

            BigInteger d = s.shiftLeft(1);
            if (d.compareTo(r) < 0) {
                s = s.add(ONE);
                r = r.subtract(d).subtract(ONE);
            }
        }

        assert r.signum() >= 0;
        assert n.equals(s.multiply(s).add(r));
        assert n.compareTo(s.add(ONE).multiply(s.add(ONE))) < 0;

        return new BigInteger[] {s, r};
    }