[jira] Resolved: (MATH-241) MathUtils.binomialCoefficient(n,k) fails for large results

["Phil Steitz (JIRA)" <ji...@apache.org>]

     [ https://issues.apache.org/jira/browse/MATH-241?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]

Phil Steitz resolved MATH-241.
------------------------------

    Resolution: Fixed

Applied second patch along with changes to double, log versions from first patch in r735879.  Many thanks.

> 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
>            Assignee: Phil Steitz
>             Fix For: 2.0
>
>         Attachments: binomialPatch.txt, binomialPatch_cs.txt
>
>
> 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 recursive property:
> {noformat}
>          assertEquals(MathUtils.binomialCoefficient(65,32) + MathUtils.binomialCoefficient(65,33),
>                  MathUtils.binomialCoefficient(66,33));
> {noformat}
> Or by directly using the (externally calculated and hopefully correct) expected value:
> {noformat}
>          assertEquals(7219428434016265740L, MathUtils.binomialCoefficient(66,33));
> {noformat}
> I suggest a nonrecursive test implementation along the lines of
> {code:title=MathUtilsTest.java|borderStyle=solid}
>     /**
>      * 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();
> 	}
> {code} 
> Which would allow you to test the expected values directly:
> {noformat}
>          assertEquals(binomialCoefficient(66,33), MathUtils.binomialCoefficient(66,33));
> {noformat}

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