NAN correctness of interval multiplication

[mkeeter]

If an interval containing 0 is multiplied by an interval that contains ±infinity, the result should be the NaN interval (because 0*inf = NaN).

[Wulfsta]

Is this strictly "contains zero", or is it only when 0 and ±inf end up at the same end of the interval? That is, (0, 1) * (-inf, 1) would be an issue, but (0, 1) * (1, inf) does not present a problem? I am asking partially for my own knowledge, since I am not sure if "multiplication" in this context simply produces another interval or is actually some other construct (but I am obviously assuming the former).

[mkeeter]

I think it should be an "interval contains zero" check.

If any pair of values in the input intervals could produce NaN, then the output interval must be (NaN, NaN); the semantics of a (NaN, NaN) interval are "could be any value, including NaN" (and non-NaN interval must not contain NaN).

For example, (0, 1) * (1, inf) can produce NaN at the 0 * inf corner, so it should return NaN.

This example is handled correctly today, but (-1, 1) * (1, inf) is not handled correctly.

[Wulfsta]

Ah, so then this does not produce another interval, but a domain of some other shape?

[mkeeter]

I'm not sure what you mean by "domain", but you can think of it as modeling

enum Interval {
    Valid { lower: NonNanF32, upper: NonNanF32 },
    Invalid,
}

where Interval::Invalid is physically stored as (NaN, NaN)