typeof(π/Complex64(2)) == Complex128

[ettersi]

We currently have

julia> typeof(π/Complex64(2))
Complex{Float64}

This looks like a bug to me. Compare with

julia> typeof(π*Complex64(2))
Complex{Float32}

julia> typeof(π/Float32(2))
Float32

[stevengj]

It's due to this promotion rule.

We could add a promotion rule for Complex, or we could add a more generic rule. Something like:

promote_rule(::Type{<:AbstractIrrational}, ::Type{T}) where {T<:Real} = promote_type(Float64, T)
promote_rule(::Type{S}, ::Type{T}) where {S<:AbstractIrrational,T<:Number} = promote_type(promote_type(S, real(T)), T)

so that non-Real number types use real to promote based on the real part.