Calling BLAS and negative step views

[ghost]

M = [2. 3.; 0. 0.] 
a = [1.,2.,3.]

v = view(a,3:-1:2)
@test M * v ≈ M * Vector(v)

should pass but fails
Evaluated: [9.0, 0.0] ≈ [12.0, 0.0]

Found while looking at #768, present on a recent 1.7.0-DEV, and 1.4.1.

Looking at LinearAlgebra/blas.jl, it seems there might be more functions which do not correctly handle negative stride yet, that is, the case of a StridedVector being a SubArray.

For the above example, there should be a fix similar to PR JuliaLang/julia#39751. If so, one should probably add an inline function computing the pointer to the first element (in the sense of having the lowest address in memory) of a StridedVector, and use this function when BLAS.dgemv is called for StridedVectors (and make the change from JuliaLang/julia#39751 use this function, too/take the code from there).

Warning: This is based on the assumption that the step size can be negative in the BLAS function.
Reading dgemv.f, I got the impression that negative strides are supported for dgemv in OpenBLAS StridedVector's.
Also page 40 of blas-report.pdf sounds like other BLAS functions should support negative stride for vectors.

[mbauman]

What is the BLAS story on negative strides? Is there a consistent one? A quick search hit this SO question which I had apparently already seen and upvoted at some point in the past.

Good point! I have edited the description to focus on this specific case. (However, my impression from a quick look at the report linked above is that vectors with negative stride might be fine for some other BLAS functions, too. I don't know how closely various implementations comply to the report.)

[vitorn]

Another example of this problem with negative stride (using Julia 1.6.3):

using LinearAlgebra
h = [1.0, 2.0]
x = [1.0, 2.0, 3.0]
xv = view(x, 2 : -1 : 1)
dot(h, xv) 
7.0

but

dot(h, x[2 : -1 : 1])
4.0

If at least one of the vectors has only integer elements, the result is correct.

The problem also happens if you use h'*xv, without loading LinearAlgebra.

[N5N3]

Should be fixed after JuliaLang/julia#42957.