Applicability of the ECM Performance Model to Explicit ODE Methods on Current Multi-core Processors

摘要

To support the portability of efficiency when bringing an application from scientific computing to a new HPC system, autotuning techniques are promising approaches. Ideally, these approaches are able to derive an efficient implementation for a specific HPC system by applying suitable program transformations. Often, a large number of implementations results, and the most efficient of these variants should be selected. In this article, we investigate performance modelling and prediction techniques which can support the selection process. These techniques may significantly reduce the selection effort, compared to extensive runtime tests. We apply the execution-cache-memory (ECM) performance model to numerical solution methods for ordinary differential equations (ODEs). In particular, we consider the question whether it is possible to obtain a performance prediction for the resulting implementation variants to support the variant selection. We investigate the accuracy of the prediction for different ODEs and different hardware platforms and show that the prediction is able to reliably select a set of fast variants and, thus, to limit the search space for possible later empirical tuning.