Morton ordering of 2D arrays for efficient access to hierarchical memory

Abstract

This article investigates the recursive Morton ordering of two-dimensional arrays as an efficient way to access hierarchical memory across a range of heterogeneous computer platforms, ranging from manycore devices, multicore processors, clusters and distributed environments. A brief overview of previous research in this area is given, and algorithms that make use of Morton ordering are described. These are then used to investigate the efficiency of the Morton ordering approach by performance experiments on different processors. In particular, timing results are presented for matrix multiplication, Cholesky factorization and fast Fourier transform algorithms. The use of the Morton ordering approach leads naturally to algorithms that are recursive and exposes parallelism at each level of recursion. Thus, the approach advocated in this talk not only provides convenient and efficient access to hierarchical memory but also provides a basis for exploiting parallelism.