Using integer sets for data-parallel program analysis and optimization

In this paper, we describe our experience with using an abstract integer-set framework to develop the Rice dHPF compiler, a compiler for High Performance Fortran. We present simple, yet general formulations of the major computation partitioning and communication analysis tasks as well as a number of important optimizations in terms of abstract operations on sets of integer tuples. This approach has made it possible to implement a comprehensive collection of advanced optimizations in dHPF, and to do so in the context of a more general computation partitioning model than previous compilers. One potential limitation of the approach is that the underlying class of integer set problems is fundamentally unable to represent HPF data distributions on a symbolic number of processors. We describe how we extend the approach to compile codes for a symbolic number of processors, without requiring any changes to the set formulations for the above optimizations. We show experimentally that the set representation is not a dominant factor in compile times on both small and large codes. Finally, we present preliminary performance measurements to show that the generated code achieves good speedups for a few benchmarks. Overall, we believe we are the first to demonstrate by implementation experience that it is practical to build a compiler for HPF using a general and powerful integer-set framework.