Fractional powers of nonpositive intervals containing zero

[cbilz]

^ returns the zero interval while pow returns the empty interval:

julia> using IntervalArithmetic

julia> a = interval(-1.0, 0.0)
[-1, 0]

julia> a^1.7
[0, 0]

julia> pow(a,1.7)
∅

julia> b = interval(0.0)
[0, 0]

julia> b^1.7
[0, 0]

julia> pow(b,1.7)
∅

This seems inconsistent. Does ITF1788 say what the correct result should be?

[cbilz]

I believe the standard says that interval(0.0)^1.7 should return interval(0.0), as it does. (see Table 9.1 and Case a) in 7.3)

It does not stipulate what something like interval(-1.0, 0.0)^1.7, where the interval contains negative numbers, should return. One of the suggested possibilities is to return interval(0.0). This is consistent with what sqrt(interval(-1.0, 0.0)) does.

I would suggest that pow should also return interval(0.0) in these cases.

[lucaferranti]

sorry I forgot to answer, as you figured out the ^ is currently the standard conforming behavior. ITF1788 has a (similar) test for what you're doing here.