Complex-float logic needs to be replicated by plans

[gaurav-arya]

The current design of AbstractFFTs.jl requires plan implementers to handle the complex-float promotion when doing *(p::MyPlan, x), e.g. as done below in the test plans here:

AbstractFFTs.jl/test/testplans.jl

Line 89 in 79789f2

Base.:*(p::TestPlan, x::AbstractArray) = mul!(similar(x, complex(float(eltype(x)))), p, x)

This would ideally be taken care of AbstractFFTs.jl just like is done for fft etc.

Edit (July 29): possibly, the right way to solve problems like this (and other ones like having to manually compute normalization in plan_inv), would be a trait. The AdjointStyle trait was recently added, whose scope was limited to enabling adjoint functionality given that inverse functionality for the plan already exists. We could add additional traits for automatically getting other functionality that is the same for e.g. all FFTs (and even parent traits that specify all additional traits together) such that downstream implementers have to implement the minimum possible functionality when the right trait exists