GRAPHITE: Polyhedral Analyses and Optimizations for GCC

We present a plan to add loop nest optimizations in GCC based on polyhedral representations of loop nests. We advocate a static analysis approach based on a hierarchy of interchangeable abstractions with solvers that range from the exact solvers such as OMEGA, to faster but less precise solvers based on more coarse abstractions. The intermediate representation GRAPHITE1 (GIMPLE Represented as Polyhedra with Interchangeable Envelopes), built on GIMPLE and the natural loops, hosts the high level loop transformations. We base this presentation on the WRaP-IT project developed in the Alchemy group at INRIA Futurs and Paris-Sud University, on the PIPS compiler developed at École des mines de Paris, and on a joint work with several members of the static analysis and polyhedral compilation community in France. The main goal of this project is to bring more high level loop optimizations to GCC: loop fusion, tiling, strip mining, etc. Thanks to the 1This work was partially supported by ACI/APRON. WRaP-IT experience, we know that the polyhedral analyzes and transformations are affordable in a production compiler. A second goal of this project is to experiment with compile time reduction versus attainable precision when replacing operations on polyhedra with faster operations on more abstract domains. However, the use of a too coarse representation for computing might also result in an over approximated solution that cannot be used in subsequent computations. There exists a trade off between speed of the computation and the attainable precision that has not yet been analyzed for real world programs.