Section: New Results

Polyhedral Value Analysis as Fast Abstract Interpretation

Participant : Laure Gonnord.

Together with Tobias Grosser, (ETH Zurich, Switzerland), Siddhart Bhat, (IIIT Hydrabad, India), Marcin Copik (ETH Zurich, Switzerland), Sven Verdoolaege (Polly Labs, Belgium) and Torsten Hoefler (ETH Zurich, Switzerland), we tried to bridge the gap between the well founded classical abstract interpretation techniques and their usage in production compilers.

We formulate the polyhedral value analysis (a classical algorithm in production compilers like LLVM, scalar evolution based on Presburger set as abstract interpretation), present a set of fast join operators, and show that aggressively falling back to top (rather than continuing with approximations) results in a scalable analysis. By formally describing the required analysis, we provide the necessary theoretical foundations for analysing large program systems with hundred thousands of loops and complex control flow structures at a precision high enough to cater for high-precision users such as polyhedral optimization frameworks, at a compile-time cost comparable with just compiling the application.

The paper is under redaction process.