public static double binomialCoefficientLog(final int n, final int k)
        throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException {
        CombinatoricsUtils.checkBinomial(n, k);
        if ((n == k) || (k == 0)) {
            return 0;
        }
        if ((k == 1) || (k == n - 1)) {
            return FastMath.log(n);
        }

        /*
         * For values small enough to do exact integer computation,
         * return the log of the exact value
         */
        if (n < 67) {
            return FastMath.log(binomialCoefficient(n,k));
        }

        /*
         * Return the log of binomialCoefficientDouble for values that will not
         * overflow binomialCoefficientDouble
         */
        if (n < 1030) {
            return FastMath.log(binomialCoefficientDouble(n, k));
        }

        if (k > n / 2) {
            return binomialCoefficientLog(n, n - k);
        }

        /*
         * Sum logs for values that could overflow
         */
        double logSum = 0;

        // n!/(n-k)!
        for (int i = n - k + 1; i <= n; i++) {
            logSum += FastMath.log(i);
        }

        // divide by k!
        for (int i = 2; i <= k; i++) {
            logSum -= FastMath.log(i);
        }

        return logSum;
    }