How to correctly and standardly compare floats?

Question

Every time I start a new project and when I need to compare some float or double variables I write the code like this one:

if (fabs(prev.min[i] - cur->min[i]) < 0.000001 &&     fabs(prev.max[i] - cur->max[i]) < 0.000001) {         continue; } 

Then I want to get rid of these magic variables 0.000001(and 0.00000000001 for double) and fabs, so I write an inline function and some defines:

#define FLOAT_TOL 0.000001 

So I wonder if there is any standard way of doing this? May be some standard header file? It would be also nice to have float and double limits(min and max values)

Answer 1

From The Floating-Point Guide:

This is a bad way to do it because a fixed epsilon chosen because it “looks small” could actually be way too large when the numbers being compared are very small as well. The comparison would return “true” for numbers that are quite different. And when the numbers are very large, the epsilon could end up being smaller than the smallest rounding error, so that the comparison always returns “false”.

The problem with the "magic number" here is not that it's hardcoded but that it's "magic": you didn't really have a reason for choosing 0.000001 over 0.000005 or 0.0000000000001, did you? Note that float can approximately represent the latter and still smaller values - it's just about 7 decimals of precision after the first nonzero digit!

If you're going to use a fixed epsilon, you should really choose it according to the requirements of the particular piece of code where you use it. The alternative is to use a relative error margin (see link at the top for details) or, even better, or compare the floats as integers.

Answer 2

The Standard provides an epsilon value. It's in <limits> and you can access the value by std::numeric_limits<float>::epsilon and std::numeric_limits<double>::epsilon. There are other values in there, but I didn't check what exactly is.