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From "Christian Semrau (JIRA)" <j...@apache.org>
Subject [jira] Created: (MATH-241) MathUtils.binomialCoefficient(n,k) fails for large results
Date Fri, 16 Jan 2009 23:35:59 GMT
MathUtils.binomialCoefficient(n,k) fails for large results
----------------------------------------------------------

                 Key: MATH-241
                 URL: https://issues.apache.org/jira/browse/MATH-241
             Project: Commons Math
          Issue Type: Bug
    Affects Versions: 2.0
            Reporter: Christian Semrau


Probably due to rounding errors, MathUtils.binomialCoefficient(n,k) fails for results near
Long.MAX_VALUE.

The existence of failures can be demonstrated by testing the recursion property:

         assertEquals(MathUtils.binomialCoefficient(66,33), MathUtils.binomialCoefficient(65,32)
+ MathUtils.binomialCoefficient(65,33));


I suggest a nonrecursive test implementation along the lines of

    /**
     * Exact implementation using BigInteger and the explicit formula (n, k) == ((k-1)*...*n)
/ (1*...*(n-k))
     */
	public static long binomialCoefficient(int n, int k) {
		if (k == 0 || k == n)
			return 1;
		BigInteger result = BigInteger.ONE;
		for (int i = k + 1; i <= n; i++) {
			result = result.multiply(BigInteger.valueOf(i));
		}
		for (int i = 1; i <= n - k; i++) {
			result = result.divide(BigInteger.valueOf(i));
		}
		if (result.compareTo(BigInteger.valueOf(Long.MAX_VALUE)) > 0) {
			throw new ArithmeticException("Binomial coefficient overflow: " + n + ", " + k);
		}
		return result.longValue();
	}


Which would allow you to test the expected values directly:

         assertEquals(binomialCoefficient(66,33), MathUtils.binomialCoefficient(66,33));


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