Generalizing run-time tiling with the loop chain abstraction

Many scientific applications are organized in a data parallel way: as sequences of parallel and/or reduction loops. This exposes parallelism well, but does not convert data reuse between loops into data locality. This paper focuses on this issue in parallel loops whose loop-to-loop dependence structure is data-dependent due to indirect references such as A[B[i]]. Such references are a common occurrence in sparse matrix computations, molecular dynamics simulations, and unstructured-mesh computational fluid dynamics (CFD). Previously, sparse tiling approaches were developed for individual benchmarks to group iterations across such loops to improve data locality. These approaches were shown to benefit applications such as moldyn, Gauss-Seidel, and the sparse matrix powers kernel, however the run-time routines for performing sparse tiling were hand coded per application. In this paper, we present a generalized full sparse tiling algorithm that uses the newly developed loop chain abstraction as input, improves inter-loop data locality, and creates a task graph to expose shared-memory parallelism at runtime. We evaluate the overhead and performance impact of the generalized full sparse tiling algorithm on two codes: a sparse Jacobi iterative solver and the Airfoil CFD benchmark.