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List:       jakarta-commons-dev
Subject:    [jira] [Created] (MATH-836) Fraction(double, int) constructor strange behaviour
From:       "Baste Nesse Buanes (JIRA)" <jira () apache ! org>
Date:       2012-07-31 17:04:35
Message-ID: 746498769.122158.1343754275356.JavaMail.jiratomcat () issues-vm
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Baste Nesse Buanes created MATH-836:
---------------------------------------

             Summary: Fraction(double, int) constructor strange behaviour
                 Key: MATH-836
                 URL: https://issues.apache.org/jira/browse/MATH-836
             Project: Commons Math
          Issue Type: Bug
    Affects Versions: 3.0
            Reporter: Baste Nesse Buanes
            Priority: Minor


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 0-value (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 axiom-based 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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