Strides for Adjoint & Transpose

[mcabbott]

This adds JuliaLang/julia#35929 which updated JuliaLang/julia#29135 .

Edit: the more recently merged PR JuliaLang/julia#35929 is marked "backport 1.5". I presume that this means the VERSION cutoff used here may need to change.

[martinholters]

I'll review later, but on first glance: Needs a README entry.

[mcabbott]

Sure. If I do it after #709 then I won't have to fix clashes.

This one may need to wait for the backport anyway.

[martinholters]

LGTM. Once the backport is done and the version conditional updated accordingly, this should be good to go.

[martinholters]

Travis Linux Julia 1.0:

generalized dot #32739: Test Failed at /home/travis/build/JuliaLang/Compat.jl/test/runtests.jl:173

  Expression: dot(x, transpose(A), y) ≈ dot(x, transpose(A) * y) ≈ x' * transpose(A) * y ≈ (x' * transpose(A)) * y

   Evaluated: 0.0016273856f0 ≈ 0.0016267318f0 ≈ 0.0016271947f0 ≈ 0.0016271947f0

AV Julia latest (1.6.0-DEV.452) 32 bit:

generalized dot #32739: Test Failed at C:\projects\compat-jl\test\runtests.jl:171
  Expression: dot(x, A, y) ≈ dot(A' * x, y) ≈ x' * A * y ≈ (x' * A) * y
   Evaluated: 0.0003067404f0 ≈ 0.00030654308f0 ≈ 0.00030654308f0 ≈ 0.00030654308f0

All others pass. Does this influence the dispatch of dot in some way here? E.g., going through BLAS more often than before or something?

The inputs here are randomly generated, that might explain why it only fails sometimes, but I haven't seen this before, so most likely related to this PR.

[martinholters]

On second thought, this PR shouldn't change anything on Julia 1.6.0-DEV.452 (except for adding tests, which are not the ones failing here), so hard to blame it. But the same change in Base could lead to same problem in the here, of course.

[mcabbott]

I don't understand this at all. It's both 1.0 on Travis and master on Appveyor, on the same test. Both seem like they ought to have been identical on earlier runs of this PR.

And I can't see how strides would change dot, rand(2,2)' isa StridedArray remains false so it shouldn't dispatch differently.

[martinholters]

Running

@testset begin
    n = 10
    for iter in 1:1000000
        A = randn(Float32, n, n)
        x = rand(Float32, n)
        y = rand(Float32, n)
        @test dot(x, transpose(A), y) ≈ dot(x, transpose(A)*y) ≈ *(x', transpose(A), y) ≈ (x'*transpose(A))*y
    end
end

gives around 200 fails across different Julia versions. Seems we were just very unlucky with the latest CI run. I'll restart and if it looks better this time, this should be ready to merge. The flaky test is an orthogonal issue.