Matrix-matrix multiplication is a fundamental operation of great importance to scientific computing and, increasingly, machine learning. It is a simple enough concept to be introduced in a typical high school algebra course yet in practice important enough that its implementation on computers continues to be an active research topic. This note describes a set of exercises that use this operation to illustrate how high performance can be attained on modern CPUs with hierarchical memories (multiple caches). It does so by building on the insights that underly the BLAS-like Library Instantiation Softare (BLIS) framework by exposing a simplified “sandbox” that mimics the implementation in BLIS. As such, it also becomes a vehicle for the “crowd sourcing” of the optimization of BLIS. We call this set of exercises BLISlab.

Check the tutorial for more details.

• [How to Optimize GEMM Wiki] (https://github.com/flame/how-to-optimize-gemm/wiki)
• [GEMM: From Pure C to SSE Optimized Micro Kernels] (http://apfel.mathematik.uni-ulm.de/~lehn/sghpc/gemm/)

For those of you looking for the appropriate article to cite regarding BLISlab, we recommend citing our TR:

@TechReport{FLAWN80,
  author = {Jianyu Huang and Robert A. van~de~Geijn},
  title = {{BLISlab}: A Sandbox for Optimizing {GEMM}},
  institution = {The University of Texas at Austin, Department of Computer Science},
  type = {FLAME Working Note \#80,},
  number = {TR-16-13},
  year = {2016},
  url = {http://arxiv.org/pdf/1609.00076v1.pdf}
}

This material was partially sponsored by grants from the National Science Foundation (Awards ACI-1148125/1340293 and ACI-1550493).

Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).