An Analytical Model for Loop Tiling Transformation

Abstract

Loop tiling is a well-known loop transformation that enhances data locality in memory hierarchy. In this paper, we initially reveal two important inefficiencies of current analytical loop tiling models and we provide the theoretical background on how current analytical models can address these inefficiencies. To this end, we propose a new analytical model which is more accurate that the existing ones. We showcase, both theoretically and experimentally, that the proposed model can accurately estimate the number of cache misses for every generated tile size and as a result more efficient tile sizes are opted. Our evaluation results provide high cache misses gains and significant performance gains over gcc compiler and Pluto tool on an x86 platform.