comparing doubles properly
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() [doc.qt.nokia.com] instead.
I also found the method qFuzzyIsNull() its not in the doc, but compares the parameter with 0.0 thats exactly what i need
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 [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 [learncpp.com]
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)