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Simple block partitioning, usually 4x4, with the full ordinary algorithm per block. This is the most numerically-stable and parallel.

https://developer.nvidia.com/blog/cutlass-linear-algebra-cud...

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However, on recent CPUs 4x4 is small for the innermost block size of the non-trivial hierarchy you need. You can see examples under https://github.com/flame/blis/tree/master/config with an a priori procedure for determining them in https://www.cs.utexas.edu/users/flame/pubs/TOMS-BLIS-Analyti... (but compare with what's actually used for SKX, in particular). OpenBLAS will normally be similar, though it may come out somewhat faster, but it's easier to see in BLIS.

and the most cache-friendly

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