Automating the Actions of Dense Linear Algebra Experts

After decades of studying dense linear algebra (DLA) algorithms and their implementations on many hardware architectures, experts still spend a lot of time porting code to new architectures. Entire libraries are developed by experts re-applying their design knowledge repeatedly. We explore how to encode that knowledge of core algorithms and software components in the style of Design by Transformation (DxT) to generate high-performance code automatically for distributed-memory systems. We compare our performance results to that of hand-written code, our results demonstrate knowledge reuse, and we explore how proper abstractions in domain-specific languages and domain representations are essential to this work. Finally, we explain what it takes to retarget a DxT knowledge base to generate shared-memory code for some base DLA operations, using code generation to be more productive in exploring implementation ideas.