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Baste Nesse Buanes edited comment on MATH836 at 7/31/12 5:07 PM:

FractionTestByAxiom added: Tests the Fraction class through axioms. Not intended to be a part
of a finished product, but to explore the class, looking for bugs.
was (Author: snalin):
Tests the Fraction class through axioms. Not intended to be a part of a finished product,
but to explore the class, looking for bugs.
> Fraction(double, int) constructor strange behaviour
> 
>
> Key: MATH836
> URL: https://issues.apache.org/jira/browse/MATH836
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.0
> Reporter: Baste Nesse Buanes
> Priority: Minor
> Labels: Fraction
> Attachments: FractionTestByAxiom.java, valuemaxDenominator_pairs_that_fails
>
>
> The Fraction constructor Fraction(double, int) takes a double value and a int maximal
denominator, and approximates a fraction. When the double value is a large, negative number
with many digits in the fractional part, and the maximal denominator is a big, positive integer
(in the 100'000s), two distinct bugs can manifest:
> 1: the constructor returns a positive Fraction. Calling Fraction(33655.1677817278, 371880)
returns the fraction 410517235/243036, which both has the wrong sign, and is far away from
the absolute value of the given value
> 2: the constructor does not manage to reduce the Fraction properly. Calling Fraction(43979.60679604749,
366081) returns the fraction 1651878166/256677, which should have* been reduced to 24654898/3831.
> I have, as of yet, not found a solution. The constructor looks like this:
> public Fraction(double value, int maxDenominator)
> throws FractionConversionException
> {
> this(value, 0, maxDenominator, 100);
> }
> Increasing the 100 value (max iterations) does not fix the problem for all cases. Changing
the 0value (the epsilon, maximum allowed error) to something small does not work either,
as this breaks the tests in FractionTest.
> The problem is not neccissarily that the algorithm is unable to approximate a fraction
correctly. A solution where a FractionConversionException had been thrown in each of these
examples would probably be the best solution if an improvement on the approximation algorithm
turns out to be hard to find.
> This bug has been found when trying to explore the idea of axiombased testing (http://bldl.ii.uib.no/testing.html).
Attached is a java test class FractionTestByAxiom (junit, goes into org.apache.commons.math3.fraction)
which shows these bugs through a simplified approach to this kind of testing, and a text file
describing some of the value/maxDenominator combinations which causes one of these failures.
> * It is never specified in the documentation that the Fraction class guarantees that
completely reduced rational numbers are constructed, but a comment inside the equals method
claims that "since fractions are always in lowest terms, numerators and can be compared directly
for equality", so it seems like this is the intention.

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