Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)]

[Antoon Pardon]

Op 20-07-16 om 07:42 schreef Steven D'Aprano:
> Floating point maths is hard, thinking carefully about what you are doing and 
> whether it is appropriate to use == or a fuzzy almost-equal comparison, or if 
> equality is the right way at all.
>
> "But thinking is hard, can't you just tell me the answer?"
>
> No. But I can give some guidelines:
>
> Floating point arithmetic is deterministic, it doesn't just randomly mix in 
> error out of spite or malice. So in principle, you can always estimate the 
> rounding error from any calculation -- and sometimes there is none.

I would like to see a practical example of such an outcome.

> Arithmetic on integer-values (e.g. 1.0) is always exact, up to a limit of 
> either 2**53 or approximately 1e53, I forget which. (That's why most Javascript 
> programmers fail to notice that they don't have an integer type.) So long as 
> you're using operations that only produce integer values from integer arguments 
> (such as + - * // but not / ) then all calculations are exact. It is a waste of 
> time to do:
>
> x = 2.0
> y = x*1002.0
> is_equal(y, 2004.0, 1e-16)
>
> when you can just do y == 2004.0.

But why perforem integer arithmetics in floats, isn't that a waste of time too?
I really see no reason to use floats if you know all your results will be integers.

-- 
Antoon.