Parallelization along K-dimension (Parallel Reduction) for GEMM with small M/N and large K

[seulchanson]

Hi OpenBLAS team,

I noticed that zgemm (and other GEMM functions) falls back to single-threaded execution when M and N are small (e.g., 32) but K is extremely large (e.g., 1,000,000).

On my many-core system, this leaves most cores idle. Given the large K size, parallelizing the K-loop (via parallel reduction) should theoretically offer significant speedup. I perform the matrix partitioning (of k) externally, and then use multithreading to call zgemm, but the performance is only average.

Questions:

Does OpenBLAS currently support threading along the K-dimension for this shape?

If not, are there any plans to implement parallel reduction for large K?

My Machine Info:

Thanks!

[seulchanson]

MKL performs quite well with these types of tall and thin matrices (m and n are small, k is large), but OpenBLAS almost degrades to vectorized computation. 🥲

The context of this problem is large-scale physical simulation programs, where OpenBLAS (zgemm) is used to compute the MGS process for block-GMRES.

[ChipKerchner]

Parallelizing K can cause epsilon differences dependent on number of threads.