- The representable values are so dense near zero that there will be less practical difference between strict equality and approximate equality. Strict equality would be theoretically significant if you found it, but not really necessary to check for. You'll see mostly false negatives.
- The representable values are so sparse far away from zero that strict equality isn't really valuable theoretically or practically. You'll see mostly false positives.
So perhaps there is a region (the location and size of it depending on what you're modelling), where strict equality is just likely enough that you need to check for it, AND that the ULP at that point is meaningful for your application. But philosophically, in that situation, are you really comparing them for equality, or does your epsilon just happen to be zero? Would it be better to interpret your question as: are there situations where you want to check for strict equality no matter what either of the values are?
- The representable values are so dense near zero that there will be less practical difference between strict equality and approximate equality. Strict equality would be theoretically significant if you found it, but not really necessary to check for. You'll see mostly false negatives.
- The representable values are so sparse far away from zero that strict equality isn't really valuable theoretically or practically. You'll see mostly false positives.
So perhaps there is a region (the location and size of it depending on what you're modelling), where strict equality is just likely enough that you need to check for it, AND that the ULP at that point is meaningful for your application. But philosophically, in that situation, are you really comparing them for equality, or does your epsilon just happen to be zero? Would it be better to interpret your question as: are there situations where you want to check for strict equality no matter what either of the values are?