Is the recursive comparison against OpenBLAS using ReLAPACK or the normal(?) one? I don't remember the story on building with that or know the different algorithms.

Does Julia not use OpenBLAS at all now?

Julia defaults to OpenBLAS but libblastrampoline makes it so that `using MKL` flips it to MKL on the fly. See the JuliaCon video for more details on that (https://www.youtube.com/watch?v=t6hptekOR7s). The recursive comparison is against OpenBLAS/LAPACK and MKL, see this PR for some (older) details: https://github.com/YingboMa/RecursiveFactorization.jl/pull/2... . What it really comes down to in the end is that OpenBLAS is rather bad, and MKL is optimized for Intel CPUs but not for AMD CPUs, so when the best CPUs are now all AMD CPUs, having a new set of BLAS tools and mixing that with recursive LAPACK tools is either as good or better on most modern systems. Then we see this in practice even when we build BLAS into Sundials for 1,000 ODE chemical reaction networks (https://benchmarks.sciml.ai/html/Bio/BCR.html).

The question was whether the comparison was against OpenBLAS built with recursive LAPACK routines (not the default, I've now checked). I don't know whether that would use the same algorithm.

I don't see great attraction in "flipping" to MKL. (In general I switch BLASes by dynamic linking if necessary.) I'm puzzled by the value of "rather bad" for OpenBLAS, at least for BLAS [1], but it seemed OK against MKL for LAPACK-based R benchmarks I measured on sandybridge. That said, I don't understand why people avoid AMD's BLAS/LAPACK (BLIS/libflame with enhancements intended for merging) on AMD systems. In this context: BLIS studiously avoids Fortran for some reason, even for test the Fortran interface.

I have nothing against Julia, incidentally; I have the original Dylan book.

1. https://git.sr.ht/~fx/blis/tree/performance/docs/Performance...

It doesn't look like you're measuring factorization performance? OpenBLAS matrix-matrix multiplication is fine, it just falls apart when going to things like Cholesky and LU. Also it falls apart on smaller problems, like <100x100 cases.

> not the default, I've now checked

Whatever the Julia default build is doing, so probably not the recursive LAPACK routines then if that's how it's being built. If there's a better default that's worth an issue.

> That said, I don't understand why people avoid AMD's BLAS/LAPACK

There just isn't a BLIS wrapper into Julia right now, and it's much easier to just write new BLAS tools than to build wrappers IMO. It makes it very easy to customize to nonstandard Julia number types too. But I do think that BLIS is a great project and I would like to see it replace OpenBLAS as the default. There's been some discussion to make it as easy as MKL (https://github.com/JuliaLinearAlgebra/BLIS.jl/issues/3).

OK, no, I measured level 3 BLAS, and it sounded like a blanket dismissal of OpenBLAS. I'm surprised at it falling apart at all, but I haven't considered its LAPACK much and I value understanding from measurement. The set of R LA benchmarks I ran on sandybridge in response to theories about the Microsoft R distribution did include Cholesky. (I think the operations are a thin wrapper over LAPACK ones.) In that case OB was actually better than MKL for Cholesky with the versions I had then, so I'm puzzled. Probably I should revisit that sometime.

OB seems to me a better general default than BLIS, though its threading implementation may not be robust. BLIS is even broken on POWER9, and I don't remember whether the dynamic micro-architecture selection ever added for other than x86.

For really small matrices on x86, I'd front BLAS with libxsmm, but I don't remember where it starts winning, or know the threshold for BLIS' non-packed kernels.

Anyway, thanks for the info. I should be embarrassed never to have made time to look seriously at Julia.

Yeah no worries. You might want to join in the community at least because this kind of discussion is par for the course on the Slack. You might find a nice home here!

> though its threading implementation may not be robust

That's one of the main issues I have with it. Its poor threading behavior coupled with a bad default (https://github.com/JuliaLang/julia/issues/33409 one of my biggest pet peeve issues right now) really degrades real user performance.