Iterative optimization in the polyhedral model

Abstract

High-level loop optimizations are necessary to achieve good performance over a wide variety of processors. Their performance impact can be significant because they involve in-depth program transformations that aim to sustain a balanced workload over the computational, storage, and communication resources of the target architecture. Therefore, it is mandatory that the compiler accurately models the target architecture as well as the effects of complex code restructuring. However, because optimizing compilers (1) use simplistic performance models that abstract away many of the complexities of modern architectures, (2) rely on inaccurate dependence analysis, and (3) lack frameworks to express complex interactions of transformation sequences, they typically uncover only a fraction of the peak performance available on many applications. We propose a complete iterative framework to address these issues. We rely on the polyhedral model to construct and traverse a large and expressive search space. This space encompasses only legal, distinct versions resulting from the restructuring of any static control loop nest. We first propose a feedback-driven iterative heuristic tailored to the search space properties of the polyhedral model. Though, it quickly converges to good solutions for small kernels, larger benchmarks containing higher dimensional spaces are more challenging and our heuristic misses opportunities for significant performance improvement. Thus, we introduce the use of a genetic algorithm with specialized operators that leverage the polyhedral representation of program dependences. We provide experimental evidence that the genetic algorithm effectively traverses huge optimization spaces, achieving good performance improvements on large loop nests.

The Polyhedral Model Is More Widely Applicable Than You Think

“…Compilers based on the Polyhedral model -including recent research tools like PoCC [29] or CHiLL [8] -target code parts that exactly fit the affine constraints of the model. Only loop nests with affine bounds and conditional expressions can be translated to a polyhedral representation.…”

Schedule Synthesis for Halide Pipelines through Reuse Analysis

“…PolyMage [16] is another DSL for image-processing applications that uses a dataflowlike language to describe pipelines. It employs polyhedral transformations [9,13,19] to optimize the computations performed by the functional stages of the pipeline with a grouping-then-tiling approach. More specifically, it relies on auto-tuning over various tile dimensions, which are all powers of two, to decide which stages of the pipeline will be grouped together.…”

Generating Configurable Hardware from Parallel Patterns

“…Tiling Previous work on automated loop tiling has largely focused on tiling imperative programs using polyhedral analysis [8,34]. There are many existing tools-such as Pluto [9], PoCC [35], CHiLL [14], and Polly [20]-that use polyhedral analysis to automatically tile and parallelize programs.…”