Floating point equality

Question

It is common knowledge that one has to be careful when comparing floating point values. Usually, instead of using ==, we use some epsilon or ULP based equality test

Answer 1

Case (a) fails if a == b == 0.0. In this case, the operation yields NaN, and by definition (IEEE, not C) NaN ≠ NaN.

Cases (b) and (c) can fail in parallel computation when floating-point round modes (or other computation modes) are changed in the middle of this thread's execution. Seen this one in practice, unfortunately.

Case (d) can be different because the compiler (on some machine) may choose to constant-fold the computation of 5.0f/3.0f and replace it with the constant result (of unspecified precision), whereas a/b must be computed at runtime on the target machine (which might be radically different). In fact, intermediate calculations may be performed in arbitrary precision. I've seen differences on old Intel architectures when intermediate computation was performed in 80-bit floating-point, a format that the language didn't even directly support.