Tiling Optimizations for Stencil Computations Using Rewrite Rules in L ift

Abstract

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.

Code Generation for Room Acoustics Simulations with Complex Boundary Conditions

“…Previous studies [8], [9] have shown that LIFT produces comparable results for basic frequency-independent boundary handling room acoustics simulations. Figure 4 shows LIFT performing comparably with a hand-optimized reference IV.…”

“…This paper adds support for complex boundary conditions in the intermediate representation of the LIFT data-parallel language and code generator. LIFT has been shown to produce high performance code for simple stencils [8], [9]. By making only a few small additions to the code generator and its intermediate language, support for complex boundary conditions as found in 3D wave-based room acoustics simulations is provided.…”

Pattern-based Programming Abstractions for Heterogeneous Parallel Computing

“…This language can be targeted by other high-level pattern frameworks. Lift contains the data-parallel patterns mapSeq, a map transformation; reduceSeq, a reduction; id, the identity transform, and iterate, which composes a function with itself a spe- Extensions and optimizations to Lift for stencil computations [148] have been carried out without using a specific stencil pattern often seen in other pattern frameworks (such as MapOverlap in SkePU), demonstrating the strength of composing small building blocks which encode both computation and data layout.…”

From functional to imperative: combining destination-passing style and views

“…A stencil computation updates a multiple-dimension data grid given a fixed pattern based on the neighboring value. Prior works have shown they can be represented [11,24] using primitives 𝑆𝑙𝑖𝑑𝑒 and 𝑃𝑎𝑑. The implementation from this paper uses the primitive 𝐶𝑜𝑛𝑐𝑎𝑡 to implement 𝑃𝑎𝑑.…”

“…3Add adds three vectors with 2 24 elements each into one. Both hybrid and all-views method use source view to ensure that no intermediate data array is produced.…”