Floating Point Stability

Question

Say I have two rational fractions a/b and c/d that are equal. a, b, c, and d can all be represented as 32 bit signed integers. if i do division with 64 bit floating point numbers will a/b == c/d always?

Answer 1

There are cases where compiler optimizations will prevent the equality from being true even if the results are guaranteed identical. The original x86 floating point operations are performed on 80-bit registers; if you compare one of those to a stored 64-bit value it will probably compare unequal.