Target-Specific Refinement of Multigrid Codes

Abstract—This paper applies partial evaluation to stage a sten-cil code Domain-Specific Language (DSL) onto a functional and imperative programming language. Platform-specific primitives such as scheduling or vectorization, and algorithmic variants such as boundary handling are factored out into a library that make up the elements of that DSL. We show how partial evaluation can eliminate all overhead of this separation of concerns and creates code that resembles hand-crafted versions for a particular target platform. We evaluate our technique by implementing a DSL for the V-cycle multigrid iteration. Our approach generates code for AMD and NVIDIA GPUs (via SPIR and NVVM) as well as for CPUs using AVX/AVX2 alike from the same high-level DSL program. First results show that we achieve a speedup of up to 3 × on the CPU by vectorizing multigrid components and a speedup of up to 2 × on the GPU by merging the computation of multigrid components. Index Terms—Multigrid codes, partial evaluation, domain-specific language. I.