Iterative Collective Loop Fusion

Abstract

Abstract. Naive code generation from high-level languages that encourage modularity can give rise to large numbers of simple loops for arraybased programs. Collective loop fusion and array contraction can be used on such codes to improve temporal locality and performance. The problem is typically formalised using a loop dependence graph (LDG), with solutions denoted by fusion partitions. Much previous work has concentrated on approaches to the abstract formulation. We present our technique called iterative collective loop fusion based on empirically evaluating different transformations, and show how it can provide speedups over existing approaches of up to 1.38. We also give results showing that applying such techniques to high-level languages can provide speedups of up to 2.45 over the original code, and outperforms an equivalent code in Fortran.

The Impact of Global Communication Latency at Extreme Scales on Krylov Methods

“…There have been various projects looking at how to combine and schedule basic KSM operations, without altering the dependency structure of the algorithms themselves, and/or the resulting performance; some examples include [5], which considers rescheduling for bandwidth reduction, and [14], which uses careful ordering of the operations of variants of the two-sided KSMs to allow scalar products to be executed at the same time as one of the matrix-vector products; this amounts to a partial pipelining approach. Our work is differs as we consider the future impact of an algorithm that does more extensive reordering.…”