Polyhedral Code Generation in the Real World

Abstract

Abstract. The polyhedral model is known to be a powerful framework to reason about high level loop transformations. Recent developments in optimizing compilers broke some generally accepted ideas about the limitations of this model. First, thanks to advances in dependence analysis for irregular access patterns, its applicability which was supposed to be limited to very simple loop nests has been extended to wide code regions. Then, new algorithms made it possible to compute the target code for hundreds of statements while this code generation step was expected not to be scalable. Such theoretical advances and new software tools allowed actors from both academia and industry to study more complex and realistic cases. Unfortunately, despite strong optimization potential of a given transformation for e.g., parallelism or data locality, code generation may still be challenging or result in high control overhead. This paper presents scalable code generation methods that make possible the application of increasingly complex program transformations. By studying the transformations themselves, we show how it is possible to benefit from their properties to dramatically improve both code generation quality and space/time complexity, with respect to the best stateof-the-art code generation tool. In addition, we build on these improvements to present a new algorithm improving generated code performance for strided domains and reindexed schedules.

Mapping the FDTD Application to Many-Core Chip Architectures

“…Recent research on iteration space representation such as the polyhedron model [22] can be used to describe code transformations as convex polyhedrons in a multidimensional iteration space. The work on the polyhedron model is orthogonal to the technique presented here.…”

Iterative optimization in the polyhedral model

“…Efficient algorithms and tools now exist to generate target code from a polyhedral representation with multidimensional affine schedules. Recent work by Vasilache et al [112,111] and by Reservoir Labs [77] improved these algorithms to scale up to thousands of statements. All along this thesis, we use the state-of-the art code generator CLOOG [10] to perform the code generation task.…”

Towards effective automatic parallelization for multicore systems

“…Our source-to-source transformation system prototype pendence analysis [15,14,31] and code generation [23,20] in the polyhedral model, but the approaches suffered from scalability challenges. Recent advances in dependence analysis and more importantly in code generation [32,5,38] have solved many of these problems resulting in the polyhedral techniques being applied to code representative of real applications like the spec2000fp benchmarks. But a significant limitation has been the absence of a scalable and practical approach for automatic transformation for parallelization and locality.…”

“…Significant advances were made by Quilleré et al [32] and more recently by Bastoul et al and Vasilache et al [5,38], resulting in a powerful open-source code generator, CLooG [10]. Our tiled code generation scheme uses Ancourt and Irigoin's classic approach [3] to specify domains with fixed tile sizes and shape information, but combines it with CLooG's support for scattering functions to allow generation of tiled code for multiple domains under transformations obtained from our theoretical framework.…”