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.