Authors: Bryan Marker, Don Batory, and Robert van de Geijn

Engineering high-performance scientific computing software requires deep knowledge about the target hardware architecture (e.g. distributed-memory cluster) and the algorithms being implemented. We focus on the dense linear algebra (DLA) kernels on which such software is often based for portability and performance. DLA libraries are composed of common operations used by software engineers and are tailored for target architectures. Few experts can implement such libraries well, and these experts end up going through a lot of repetitive engineering efforts to support all operations and architectures. This is monotonous and can lead to errors or missed optimizations. We demonstrate how a new approach to software engineering, Design by Transformation (DxT), can be used to encode expert domain knowledge as code transformations. High-performance distributed-memory implementations of DLA operations can then be mechanically or automatically generated. The Elemental library for distributed memory dense matrix computations is used as a motivating target.