Stencil computations are widely used from physical simulations to machine-learning. They are embarrassingly parallel and perfectly fit modern hardware such as Graphic Processing Units. Although stencil computations have been extensively studied, optimizing them for increasingly diverse hardware remains challenging. Domain Specific Languages (DSLs) have raised the programming abstraction and offer good performance. However, this places the burden on DSL implementers who have to write almost full-fledged parallelizing compilers and optimizers.Lift has recently emerged as a promising approach to achieve performance portability and is based on a small set of reusable parallel primitives that DSL or library writers can build upon. Lift's key novelty is in its encoding of optimizations as a system of extensible rewrite rules which are used to explore the optimization space. However, Lift has mostly focused on linear algebra operations and it remains to be seen whether this approach is applicable for other domains.This paper demonstrates how complex multidimensional stencil code and optimizations such as tiling are expressible using compositions of simple 1D Lift primitives. By leveraging existing Lift primitives and optimizations, we only require the addition of two primitives and one rewrite rule to do so. Our results show that this approach outperforms existing compiler approaches and hand-tuned codes.CCS Concepts • Software and its engineering → Parallel programming languages; Compilers;
Stencil computations are a widely used type of algorithm, found in applications from physical simulations to machine learning. Stencils are embarrassingly parallel, therefore fit on modern hardware such as Graphic Processing Units perfectly. Although stencil computations have been extensively studied, optimizing them for increasingly diverse hardware remains challenging. Domain-specific Languages (DSLs) have raised the programming abstraction and offer good performance; however, this method places the burden on DSL implementers to write almost full-fledged parallelizing compilers and optimizers.Lift has recently emerged as a promising approach to achieve performance portability by using a small set of reusable parallel primitives that DSL or library writers utilize. Lift's key novelty is in its encoding of optimizations as a system of extensible rewrite rules which are used to explore the optimization space.This article demonstrates how complex multi-dimensional stencil code and optimizations are expressed using compositions of simple 1D Lift primitives and rewrite rules. We introduce two optimizations that provide high performance for stencils in particular: classical overlapped tiling for multi-dimensional stencils and 2.5D tiling specifically for 3D stencils. We provide an in-depth analysis on how the tiling optimizations affects stencils of different shapes and sizes across different applications. Our experimental results show that our approach outperforms existing compiler approaches and hand-tuned codes.Extension of Conference Paper High performance stencil code generation with Lift published at CGO 2018 [22]. This paper presents an extended in-depth discussion of a real-world stencil application, the representation of a optimization specific for 3-dimensional stencils -2.5D tiling -as a rewrite rule, and additional performance results analyzing the performance characteristics of 2.5D tiling, in particular with respect to different stencil sizes and shapes.
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