Tiling for Dynamic Scheduling

Tiling is a key transformation used for coarsening the granularity of parallelism and improving locality. It is known that current stateof-the-art compiler approaches for tiling affine loop nests make use of sufficient, i.e., conservative conditions for the validity of tiling. These conservative conditions, which are used for static scheduling, miss tiling schemes for which the tile schedule is not easy to describe statically. However, the partial order of the tiles can be expressed using dependence relations which can be used for dynamic scheduling at runtime. Another set of opportunities are missed due to the classic reason that finding valid tiling hyperplanes is often harder than checking whether a given tiling is valid. Though the conservative conditions for validity of tiling have worked in practice on a large number of codes, we show that they fail to find the desired tiling in several cases – some of these have dependence patterns similar to real world problems and applications. We then look at ways to improve current techniques to address this issue. To quantify the potential of the improved techniques, we manually tile two dynamic programming algorithms – the Floyd-Warshall algorithm, and Zuker’s RNA secondary structure prediction and report their performance on a shared memory multicore. Our 3-d tiled dynamically scheduled implementation of Zuker’s algorithm outperforms an optimized multi-core implementation GTfold by a factor of 2.38. Such a 3-d tiling was possible only by reasoning with more precise validity conditions.