Performance Analysis of a Scalable Algorithm for 3D Linear Transforms on Supercomputer with Intel Processors/Co-Processors

摘要

Practical realizations of 3D forward/inverse separable discretetransforms, such as Fourier transform, cosine/sine transform, etc. are frequently theprincipal limiters that prevent many practical applications from scaling to a largenumber of processors. Existing approaches, which are based primarily on 1D or 2Ddata decompositions, prevent the 3D transforms from effectively scaling to themaximum (possible/available) number of computer nodes. A highly scalableapproach to realize forward/inverse 3D transforms has been proposed. It is based ona 3D decomposition of data and geared towards a torus network of computer nodes.The proposed algorithms requires compute-and-roll time-steps, where each stepconsists of an execution of multiple GEMM operations and concurrent movement ofcubical data blocks between nearest neighbors. The aim of this paper is to present anexperimental performance study of an implementation on high performancecomputer architecture.