Optimize real matrix * complex vector by reinterpreting as real

[jishnub]

julia> M = rand(Float32, 1000, 1000); V = rand(ComplexF32, size(M,2))

julia> C32_1 = @btime $M * $V; # current master
  714.915 μs (1 allocation: 7.94 KiB)

julia> Revise.track(LinearAlgebra)

julia> C32_2 = @btime $M * $V; # this PR
  342.096 μs (1 allocation: 7.94 KiB)

julia> C32_1 ≈ C32_2
true

and similarly for Float64. Currently this hits generic_matvecmul!, which is presumably slow.

I had also tried to add a similar method for real matrix * complex matrix, but for some reason that I don't understand this makes BLAS.gemm! (consequently M1 * M2) worse. I have removed that method from this PR.

Sorry about the numerous whitespace changes introduced by the VSCode plugin, however hopefully these will improve readability. I haven't figured out how to disable this.

[dkarrasch]

Sorry about the numerous whitespace changes introduced by the VSCode plugin, however hopefully these will improve readability. I haven't figured out how to disable this.

You could commit only the relevant changes and leave all others outside the PR. It's quite challenging finding the new code.

Is this ready now? The code part looks good to me, so do you think there is something left untested?

[jishnub]

I think it's ready, as I've rebased it on #44027 which is fairly well tested. Further tests for strides are perhaps not necessary in this PR.

Apologies for the whitespace again. Perhaps in the future I'll sequester whitespace changes in a single commit, which would make code changes easier to find.