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

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!