Oil and Water can mix! Experiences with integrating Polyhedral and AST-based Transformations

The polyhedral model is an algebraic framework for affine program representations and transformations for enhancing locality and parallelism. Compared with traditional AST-based transformation frameworks, the polyhedral model can easily handle imperfectly nested loops and complex data dependences within and across loop nests in a unified framework. On the other hand, AST-based transformation frameworks for locality and parallelism have a long history that dates back to early vectorizing and parallelizing compilers. They can be used to efficiently perform a wide range of transformations including hierarchical parametric tiling, parallel reduction, scalar replacement and unroll-and-jam, and the implemented loop transformations are more compact (with smaller code size) than polyhedral frameworks. While many members of the polyhedral and AST-based transformation camps see the two frameworks as a mutually exclusive either-or choice, our experience has been that both frameworks can be integrated in a synergistic manner. In this paper, we present our early experiences with integrating polyhedral and AST-based transformations. Our preliminary experiments demonstrate the benefits of the proposed combined approach relative to Pluto, a pure polyhedral framework for locality and parallelism optimizations.