InteractiveUtils methods show incorrect method for negative powers

[BioTurboNick]

julia> @code_typed true ^ -1
CodeInfo(
1 ─ %1 = Base.slt_int(p, 0)::Bool
└──      goto #5 if not %1
2 ─ %3 = Base.not_int(x)::Bool
└──      goto #4 if not %3
3 ─      invoke Base.throw_domerr_powbysq(_2::Bool, _3::Int64)::Union{}
└──      unreachable
4 ─      nothing::Nothing
5 ┄ %8 = (p === 0)::Bool
│   %9 = Base.or_int(%8, x)::Bool
└──      goto #6
6 ─      return %9
) => Bool

# as expected
julia> a = true ^ 1; println(a, " ", typeof(a))
true Bool

# ???
julia> a = true ^ -1; println(a, " ", typeof(a))
1.0 Float64

# strangely, these forms work
julia> a = true ^ Int64(-1); println(a, " ", typeof(a))
true Bool
julia> a = true ^ -Int64(1); println(a, " ", typeof(a))
true Bool

[Seelengrab]

I think the difference to true ^ Int(1) is due to literal integer powers being handled specially during parsing - it's the only time we truly know what function to apply and since true isa Number, it gets promoted and computed as inv(true), which is 1.0. Exponentiation with literals being quasi type unstable is known.

[BioTurboNick]

Ahh interesting. Okay. Why are they handled specially?

[BioTurboNick]

So is the issue just that inv(x::Bool) = x should be defined?

Oh, I see, it's because false (0) to a negative power is Inf. I suppose the alternative is to error, but maybe that would cause more issues?

Answering my own question - 1) because it's more efficient, and 2) Needs special handling to be mathematically correct?

[BioTurboNick]

Although, I guess that leaves the question of why InteractiveUtils doesn't show the correct method lowering.

[BioTurboNick]

I guess this is a duplicate of #21014.

[Seelengrab]

It's handled specially because we can, at parse time, figure out that the exponent is negative (it's a literal after all, the type can't magically change) and thus the result will be a Float64. This makes it stable by not going through the regular ^. x^(-y) will after all always be 1/(x^y), with some edge case caveats.