Comparing doubles properly



  • Hi,

    i have a problem with a piece of code:

    @qreal a = 0.0f;
    Q_ASSERT(qAbs(a) == 0)@

    this causes sometimes to throw the assert, and sometimes not. but why? in my real there is a value like 6.0*10^-311 so its almost 0 but it is not 0, so the assert is right. but why isn't it 0 when i initialized it with 0?



  • This is due to limited precision of floating point numbers. Use "qFuzzyCompare()":http://doc.qt.nokia.com/4.7-snapshot/qtglobal.html#qFuzzyCompare-2 instead.



  • thanks.

    I also found the method qFuzzyIsNull() its not in the doc, but compares the parameter with 0.0 thats exactly what i need



  • @qreal a = 0.0f;
    Q_ASSERT(qAbs(a) < 1e-8 && qAbs(a) > 0.0f)@

    Comparing to real number to zero is almost not possible in reality, but if you dare, you could also try this:

    @qreal a = 0.0f;
    Q_ASSERT(qAbs(a) == 0.0f)@



  • [quote author="Jupiter" date="1319709690"]thanks.

    I also found the method qFuzzyIsNull() its not in the doc, but compares the parameter with 0.0 thats exactly what i need[/quote]

    qFuzzyIsNull is declared internal in the sources. Usually that's for a reason...

    You might want to open a request to make it officially public in the "bug tracker":https://bugreports.qt.nokia.com though.



  • I guess this is the reason:

    "Donald Knuth a famous computer scientist, suggested the following method in his book “The Art of Computer Programming, Volume II: Seminumerical Algorithms (Addison-Wesley, 1969)”:
    @
    bool IsEqual(double dX, double dY)
    {
    const double dEpsilon = 0.000001; // or some other small number
    return fabs(dX - dY) <= dEpsilon * fabs(dX);
    }
    @
    dEpsilon is a very small value (eg. 0.000001) that is used to help define what “close enough” is. fabs() is a function in the standard library (#include <cmath>) that returns the absolute value of it’s double parameter.[...]"

    "look at this link for more details":http://www.learncpp.com/cpp-tutorial/35-relational-operators-comparisons/

    You surely just solved, but maybe it could be useful for someone else....



  • The epsilon method is useful, but with a fixed epsilon, it will only work properly for a certain range of values.

    This is why qFuzzyCompare uses a variable epsilon, depending on the values compared. However, when getting very close to zero, the epsilon becomes zero as well, and it's no longer a fuzzyCompare.

    I solved this by writing a wrapper that checks whether both compared values are very close to zero, then add a fixed amount (e.g. 1.0) to both of them. That way, the qFuzzyCompare I call internally never sees values that are close to zero, and works.

    One word of warning: When using a fuzzy compare, expect that a value can both be equal and greater/lesser.
    For example, when you first have

    @if (fuzzyIsEqual(a, b)@

    but later realize that all you need is a > b, you might think that you no longer need a fuzzyCompare. Of course you can replace the code with

    @if (a > b)@

    but this will not trigger in cases when the previous code did, and might cause unexpected results.

    Better, in this case to do a
    @if (fuzzyIsGreaterOrEqual(a, b)@

    (which of course you have to write yourself first)


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