`(-Inf)^-1` inconsistency for `Float64`

[nsajko]

using Test

@testset "inconsistency, possible bug" begin
    @testset "T: $T" for T ∈ (Float16, Float32, Float64, BigFloat)
        @testset "literal `-1`" begin
            @test -0.0 === Float64(T(-Inf)^-1)
        end
        @testset "`Int(-1)`" begin
            @test -0.0 === Float64(T(-Inf)^Int(-1))
        end
    end
end

It fails only for T === Float64, and only in the non-literal case:

Test Summary:               | Pass  Fail  Total  Time
inconsistency, possible bug |    7     1      8  1.8s
  T: Float16                |    2            2  0.0s
  T: Float32                |    2            2  0.0s
  T: Float64                |    1     1      2  1.8s
    literal `-1`            |    1            1  0.0s
    `Int(-1)`               |          1      1  1.8s
  T: BigFloat               |    2            2  0.0s
ERROR: Some tests did not pass: 7 passed, 1 failed, 0 errored, 0 broken.

The reason why the sign of the zero might matter here is perhaps that the zero with negative sign is the identity element for addition in IEEE 754 floating-point. It's suspicious that there's an "odd one out" here, in any case.