Comparing doubles properly

[Jupiter]

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?

[lgeyer]

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.

[Jupiter]

thanks.

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

[ardhitama]

@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)@

[goetz]

[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.

[Al79]

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....

[Asperamanca]

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)