Make sure lmul! and rmul! for Givens rotations are inlined.

[andreasnoack]

Stop using simd macro since it is not generally valid.

[Jutho]

Out of curiosity, why was simd invalid, and why is inlining necessary?

[andreasnoack]

I removed @simd because of #27482 but hadn't realized that after #27670 it is probably safe to keep them. I had to add the inline annotations because Julia's inlining heuristic didn't conder them inline worthy. However, when using SubArrays, inlining is critical because Julia will be able to avoid the creation of the SubArray in e.g. lmul!(G, view(A, :, 1:5)) only when lmul! is inlined. It made a quite big difference in https://github.com/andreasnoack/GenericLinearAlgebra.jl/blob/c24566d1588ec19e1d928b737133218bba833618/src/eigenGeneral.jl#L173.

[Jutho]

Thanks for the detailed answer. I am interested as I share your interest for writing linear algeba functions in native Julia. Forcing inlining to get rid of the subarray allocations is a nice trick, but but of course points to the deeper lying problem of not having a non-allocating view. In principle, the inliner's judgement is correct: this function contains a loop that runs over all the entries of a possibly large vector, and will therefore take significant amount of time/flops so that it should not be inlined.

[andreasnoack]

Unfortunately, the only option right now is to abuse @inline. The same is the case if you want constant propagation to work. Either you @inline everything or it is unpredictable if a constant will actually get propagated. #25303 stalled because of that.

[Jutho]

Thanks for the pointers; that's very helpful information.