Abstract

In this document, we are concerned with the effects of data layouts for nonsquare processor meshes on the implementation of common dense linear algebra kernels such as matrix-matrix multiplication, LU factorizations, or eigenvalue solvers. In particular, we address ease of programming and tunability of the resulting software. We introduce a generalization of the torus wrap data layout that results in a decoupling of "local" and "global" data layout view. As a result, it allows for intuitive programming of linear algebra algorithms and for tuning of the algorithm for a particular mesh aspect ratio or machine characteristics. This layout is as simple as the proposed HPF layout but, in our opinion, enhances ease of programming as well as ease of performance tuning. We emphasize that we do not advocate that all users need be concerned with these issues. We do, however, believe, that for the foreseeable future "assembler coding" (as message-passing code is likely to be viewed from a HPF pro...

Citations