How do you compare float and double while accounting for precision loss?

Be extremely careful using any of the other suggestions. It all depends on context.

I have spent a long time tracing bugs in a system that presumed a==b if |a-b|<epsilon. The underlying problems were:

1. The implicit presumption in an algorithm that if a==b and b==c then a==c.

2. Using the same epsilon for lines measured in inches and lines measured in mils (.001 inch). That is a==b but 1000a!=1000b. (This is why AlmostEqual2sComplement asks for the epsilon or max ULPS).

3. The use of the same epsilon for both the cosine of angles and the length of lines!

4. Using such a compare function to sort items in a collection. (In this case using the builtin C++ operator == for doubles produced correct results.)

Like I said: it all depends on context and the expected size of a and b.

By the way, std::numeric_limits<double>::epsilon() is the “machine epsilon”. It is the difference between 1.0 and the next value representable by a double. I guess that it could be used in the compare function but only if the expected values are less than 1. (This is in response to @cdv’s answer…)

Also, if you basically have int arithmetic in doubles (here we use doubles to hold int values in certain cases) your arithmetic will be correct. For example 4.0/2.0 will be the same as 1.0+1.0. This is as long as you do not do things that result in fractions (4.0/3.0) or do not go outside of the size of an int.