But my point was that saying floating point was somehow a magical non-deterministic beast is incorrect, and saying == shouldn't be allowed because of that is incorrect. Pretty much the same arguments can be made for integer arithmetic (after all x/y is undefined behavior if it overflows or y is zero even for integers, and just as with floating point you need to understand the behavior of arithmetic)
In contrast, the result of basic floating point operations is not. You may live in a world were you use a single cpu type, and a single OS, and a single compiler, in which case, it might appear to you as defined. But anyone involved in some portability across multiple systems know how improbable it is to rely on floating point for anything exact. Actually, don't. ever.
For anything which requires exact results, use integer instead.
Things that differ: bit wise representation for non-ieee formats. Things that don’t differ: numeric result.
Basically for any arithmetic operation, with a given significand and exponent size in some rounding mode, there is a single correct result. Different implementations do not produce different results.
x86 is extremely popular and 80 bit long doubles using the old FPU model can introduce weirdness on that platform. And yes, reducing the 80 bit long doubles to 64 bits after every operation significantly impacts performance. Or used to.