Experiments on Optimizing the Performance of Stencil Codes with SPL Conqueror

A standard technique for numerically solving elliptic partial differential equations on structured grids is to discretize them, and, then, to apply an efficient geometric multi-grid solver. Unfortunately, finding the optimal choice of multi-grid components and parameter settings is challenging and existing auto-tuning techniques fail to explain performanceoptimal settings. To improve the state of the art, we explore whether recent work on optimizing configurations of product lines can be applied to the stencil-code domain. In particular, we extend the domain-independent tool SPL Conqueror in an empirical study to predict the performance-optimal configurations of three geometric multi-grid stencil codes: a program using HIPAcc, the evaluation prototype HSMGP, and a program using DUNE. For HIPAcc, we reach an prediction accuracy of 96 %, on average, measuring only 21.4 % of all configurations; we predict a configuration that is nearly optimal after measuring less than 0.3 % of all configurations. For HSMGP, we predict performance with an accuracy of 97 % including the performance-optimal configuration, while measuring 3.2 % of all configurations. For DUNE, we predict performance of all configurations with an accuracy of 86 % after measuring 3.3 % of all configurations. The performance-optimal configuration is within the 0.5 % configurations predicted to perform best.