[enhancement]: Ship a correctly rounded threaded OpenBLAS as an Artifact

[orkolorko]

Feature description

I think it would be a good idea to ship a version of OpenBLAS with the CONSISTENT_FPCSR=1 flag enabled together with the library as an Artifact, or compile during installation.

The main reason is that the system (or Julia) OpenBLAS distribution may not have this flag enabled.
While Julia may be started with only 1 thread, unless explicitly stated, OpenBLAS may run with multiple thread enabled and have different rounding modes on each thread.

Currently, a fix that allows consistent rounding is to call Julia with the

OPENBLAS_NUM_THREADS=1

but this affects performance.

See
Julia Threads + BLAS Threads
Using directed rounding in Octave/Matlab

[lucaferranti]

Hi @orkolorko , apologies for the delay in answering.

This sounds very interesting!

Exploiting BLAS multithreading is also what makes Rump multiplication algorithm faster. We can use matrix multiplication as a benchmark to see how this affects performance