[chrisseaton]

> Computers are finite state, floating point numbers are not.

No, floating point numbers are finite state. That’s the whole point behind this discussion. There are only so many possible floating point numbers representable in so many bits.

I never understand this confusion - you have finite memory - with this you can only represent a finite set of real numbers. So of course all the real numbers can’t be mapped directly.

[caf]

I understand the confusion. It occurs when people haven't fully grokked that floating point numbers generally use binary representation, and that the set of numbers that can be represented with a finite number of decimal digits is distinct from the set of numbers that can be represented with a finite number of binary digits. People generally know that they can't write down the decimal value of 1÷3 exactly - they just haven't considered that for the same reason you can't write down the binary value of 1÷10 exactly either.

This confusion is also helped along by the fact that the input and output of such numbers is generally still done in decimal, often rounded, that both decimal and binary can exactly represent the integers with a finite number of digits, and that the set of numbers exactly representable with in a finite decimal expansion is a superset of those exactly representable in a finite binary expansion (since 2 is a factor of 10).

[worik]

Sigh

The representation means that 2.9999999999 = 3.00000000

I am not confused. You cannot use equality in floating point. Why is anybody surprised by that? That is my point

(I did say floating point before when I ment real. A bit confused!)

[caf]

Don't sigh melodramatically at me.

I wasn't saying you were confused, I was saying I believe I understand how the general confusion around the whole issue arises.

(If decimal floating point had been commonly used instead of binary, the same class of issues would still exist, but I don't think people would be nearly so surprised by them).

[slavik81]

> You cannot use equality in floating point.

Sure you can. 1.0 + 2.0 == 3.0. There's a lot of gotchas, but it is possible to make useful comparisons.

[worik]

No it does not, no it is not possible to use equality comparisons usefully in FP arithmetic

[slavik81]

If that were true, they wouldn't have defined the equality operators for floating point types. Some numbers are exactly representable and some numbers are not [1]. It's difficult, but you can in fact reason about the exact results of floating point calculations. https://news.ycombinator.com/item?id=1847462