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

Assuming IEEE 754 semantics, there are definitely some cases where you can do this. Conventional floating point number computations are exact whenever they can be, which for example includes (but is not limited to) all basic operations where the operands and the results are integers.

So if you know for a fact that you don't do anything that would result in something unrepresentable, you are fine. For example

float a = 1.0f;
float b = 1.0f;
float c = 2.0f;
assert(a + b == c); // you can safely expect this to succeed

The situation only really gets bad if you have computations with results that aren't exactly representable (or that involve operations which aren't exact) and you change the order of operations.

Note that the C++ standard itself doesn't guarantee IEEE 754 semantics, but that's what you can expect to be dealing with most of the time.