Java fast fixed-divisor integer division.

function

	/**
	 * Computes a pair of magic numbers used to optimise integer division by a fixed
	 * divisor <code>d</code>.
	 * <p>
	 * The function is given the maximum value of the dividend <code>nmax</code> and
	 * the divisor <code>d</code>. It returns a pair of integers: the magic number
	 * <code>m</code> and a shift amount <code>p</code>.
	 * <p>
	 * To divide a dividend x by d, one multiplies x by m and then shifts the (full
	 * length) product right p bits: <code>x / d === ((x * m) >> p)</code>.
	 * <p>
	 * Described in 'Hacker's Delight' (chpt. 10).
	 * <p>
	 * x % d can be computed from z = (x * m) >> p with:
	 * <code>x % d === x - z * d</code>.
	 * 
	 * @param nmax maximum value (dividend) that will be divided
	 * @param d    constant for divisor value
	 * @return [m, p]
	 */
	private int[] magicDivision(final int nmax, final int d) {
		final int nc = (nmax / d) * d - 1;
		final int nbits = (FastMath.log2(nmax)) + 1;
		int m = 0;
		int p = 0;
		for (; p < 2 * nbits + 1; p++) {
			final int p2 = (int) FastMath.twoPow(p);
			final int z = (d - 1 - (p2 - 1) % d);
			if (p2 > nc * z) {
				m = (p2 + z) / d;
			}
		}
		return new int[] { m, p - 1 };
	}