Comparing IEEE floats and doubles for equality

Question

What is the best method for comparing IEEE floats and doubles for equality? I have heard of several methods, but I wanted to see what the community thought.

Answer 1

It rather depends on what you are doing with them. A fixed-point type with the same range as an IEEE float would be many many times slower (and many times larger).

Okay, but if I want a infinitesimally small bit-resolution then it's back to my original point: == and != have no meaning in the context of such a problem.

An int lets me express ~10^9 values (regardless of the range) which seems like enough for any situation where I would care about two of them being equal. And if that's not enough, use a 64-bit OS and you've got about 10^19 distinct values.

I can express values a range of 0 to 10^200 (for example) in an int, it is just the bit-resolution that suffers (resolution would be greater than 1, but, again, no application has that sort of range as well as that sort of resolution).

To summarize, I think in all cases one either is representing a continuum of values, in which case != and == are irrelevant, or one is representing a fixed set of values, which can be mapped to an int (or a another fixed-precision type).