Wield behavior of multiple dispatch

General Usage
1

In Julia 1.8.3. Given the following two type signatures.

(x::AbstractFloat, y::Number)
(x::Union{Float64, ComplexF64}, y::Union{Float64, ComplexF64})

I would expect there being an ambiguity error if the input type is (::Float64, ::Float64).

But

julia> FloatAndComplex64 = Union{Float64, ComplexF64}
Union{Float64, ComplexF64}

julia> begin
               function roughly_equal(x::AbstractFloat, y::Number)
                       @info "(::AbstractFloat, ::Number)"
                       -10 * eps(x) < x - y < 10 * eps(x)
               end
               function roughly_equal(x::Union{Float64, ComplexF64}, y::Union{Float64, ComplexF64})
                       @info "(::Union{Float64, ComplexF64}, ::Union{Float64, ComplexF64})"
                       abs(x - y) < 10 * eps(y)
               end
       end
roughly_equal (generic function with 4 methods)

julia> roughly_equal(3.0, 3.0)
[ Info: (::Union{Float64, ComplexF64}, ::Union{Float64, ComplexF64})
true
2

The rules for multiple dispatch are quite complex. Apparently, here the compiler ranks a union of concrete types higher than abstract types.

1 Like
3

Yes, the compiler considers the union to be more specific.

julia> Base.morespecific(Union{Float64, ComplexF64}, AbstractFloat)
true

julia> Base.morespecific(Union{Float64, ComplexF64}, Number)
true
4 Likes
4

On second thought, this can be understood using set theory: The union of concrete types is a subset of the abstract type because the abstract type includes any additional concrete subtype that is not included in the union.

5

Yeah, it makes sense. But it turns out the union of abstract types can also more concrete

julia> Base.morespecific(Union{AbstractFloat, Complex}, Real)
true
6

I gotta be honest that one makes no sense to me.

It also works with Union{Int, AbstractString} and Number.

7

This argument only applies to y:

julia> Union{Float64, ComplexF64} <: Number
true

But it does not hold for x:

julia> Union{Float64, ComplexF64} <: AbstractFloat
false
2 Likes