Parameterized Diamond Tiling for Stencil Computations with Chapel Parallel Iterators

Abstract

Stencil computations figure prominently in the core kernels of many scientific computations, such as partial differential equation solvers. Parallel scaling of stencil computations can be significantly improved on multicore processors using advanced tiling techniques that include the time dimension, such as diamond tiling. Such techniques are difficult to include in general purpose optimizing compilers because of the need for inter-procedural pointer and array data-flow analysis, plus the need to tune scheduling strategies and tile size parameters for each pairing of stencil computation and machine. Since a fully automatic solution is problematic, we propose to provide parameterized space and time tiling iterators through libraries. Ideally, the execution schedule or tiling code will be expressed orthogonally to the computation. This supports code reuse, easier tuning, and improved programmer productivity. Chapel iterators provide this capability implicitly. We present an advanced, parameterized tiling approach that we have implemented using Chapel parallel iterators. We show how such iterators can be used by programmers in stencil computations with multiple spatial dimensions. We also demonstrate that these new iterators provide better scaling than a traditional data parallel schedule.

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