Generalize scalar indexing and implement reducedim without stagedfunctions

[timholy]

This generalizes CartesianIndex indexing to allow a construct like A[i::Int,I::CartesianIndex]. This allows one to split out the innermost loop for special treatment. We did that already for the special case of @simd, this just generalizes it in a way that allows one to exploit it for pure julia code, too.

CC @Jutho, @mbauman. Some day we probably will want to go further, and allow full getindex(A, indexes::Union(Integer, CartesianIndex)...). But for now we can't add that without generating ambiguity warnings, and I don't currently need the general case for anything.

I then used this to rewrite the algorithms in reducedim.jl without using Base.Cartesian or any staged functions, with no loss of performance. (In fact, the sum!(R2, A) case is about 15% faster.)

 julia> A = rand(10^4, 10^4);

julia> R1 = zeros(1, size(A,2));   # for reducing along dimension 1

julia> R2 = zeros(size(A,1), 1);   # for reducing along dimension 2

julia> R12 = zeros(1, 1);       # for reducing along dimensions 1 and 2

julia> @time sum!(R1, A);
elapsed time: 0.350055697 seconds (4 MB allocated)

julia> @time sum!(R2, A);
elapsed time: 0.188841453 seconds (144 bytes allocated)

julia> @time sum!(R12, A);
elapsed time: 0.128383574 seconds (144 bytes allocated)

julia> @time sum!(R1, A);
elapsed time: 0.131577355 seconds (144 bytes allocated)

julia> @time sum!(R2, A);
elapsed time: 0.18379862 seconds (144 bytes allocated)

julia> @time sum!(R12, A);
elapsed time: 0.129456885 seconds (144 bytes allocated)

julia> B = sub(A, 1:size(A,1), 1:size(A,2));  # defeat fast linear indexing

julia> Base.linearindexing(B)
Base.LinearSlow()

julia> @time sum!(R1, B);
elapsed time: 0.598274799 seconds (7 MB allocated, 3.22% gc time in 1 pauses with 1 full sweep)

julia> @time sum!(R1, B);
elapsed time: 0.125478658 seconds (144 bytes allocated)

julia> @time sum!(R2, B);
elapsed time: 0.421974903 seconds (144 bytes allocated)

julia> @time sum!(R12, B);
elapsed time: 0.125809267 seconds (144 bytes allocated)

Reference: #10310 (comment) and the comments above (this makes the "blows out of the water" comment no longer apply).

[timholy]

This is necessary to prevent a stackoverflow from size_skip1 if ndims(R) > ndims(A). I doubt that it used to be an error. I don't think there's any good reason to support it, but if others disagree, then size_skip1 needs to be a stagedfunction.

[Jutho]

The CartesianIndex changes look great to me. I have not really checked the reducedim.jl changes as I am not familiar with this code.