Optimizing Performance of Stencil Code with SPL Conqueror

A standard technique to numerically solve elliptic partial differential equations on structured grids is to discretize them via finite differences and then to apply an efficient geometric multi-grid solver. Unfortunately, finding the optimal choice of multi-grid components and parameters is challenging and platform dependent, especially, in cases where domain knowledge is incomplete. Auto-tuning is a viable alternative, but faces the problem of large configuration spaces and feature interactions. To improve the state of the art, we explore whether recent work on configuration optimization in product lines can be applied to the stencil-code domain. In particular, we extend and use the domain-independent tool SPL Conqueror in a series of experiments to predict the performance-optimal configurations of two geometric multigrid codes: a program using the HIPA framework and an evaluation prototype called HSMGP. For HIPA, we can predict the performance of all configurations with an accuracy of 98 %, on average, when measuring 57.5 % of the configurations, and we are able to predict a configuration that is close to the optimal one after measuring only less than 4 % of all configurations. For HSMGP, we can predict the performance with an accuracy of 88 % when measuring 11 % of all configurations.