Replication Package for Article: FPL: Fast Presburger Arithmetic through Transprecision

Pitchanathan, Arjun; Ulmann, Christian; Weber, Michel; Hoefler, Torsten; Grosser, Tobias

doi:10.1145/3462302

Cited by 1 publication

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“…We have made available a replication package [Pitchanathan et al 2021] that includes a Docker image with the necessary toolchains, data, sources and scripts to reproduce the main results from our evaluation (Section 6). The package also includes our benchmark for Presburger arithmetic as used in polyhedral compilation.…”

Section: Data Availability Statementmentioning

confidence: 99%

FPL: fast Presburger arithmetic through transprecision

Pitchanathan

Ulmann

Weber

et al. 2021

Proc. ACM Program. Lang.

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Presburger arithmetic provides the mathematical core for the polyhedral compilation techniques that drive analytical cache models, loop optimization for ML and HPC, formal verification, and even hardware design. Polyhedral compilation is widely regarded as being slow due to the potentially high computational cost of the underlying Presburger libraries. Researchers typically use these libraries as powerful black-box tools, but the perceived internal complexity of these libraries, caused by the use of C as the implementation language and a focus on end-user-facing documentation, holds back broader performance-optimization efforts. With FPL, we introduce a new library for Presburger arithmetic built from the ground up in modern C++. We carefully document its internal algorithmic foundations, use lightweight C++ data structures to minimize memory management costs, and deploy transprecision computing across the entire library to effectively exploit machine integers and vector instructions. On a newly-developed comprehensive benchmark suite for Presburger arithmetic, we show a 5.4x speedup in total runtime over the state-of-the-art library isl in its default configuration and 3.6x over a variant of isl optimized with element-wise transprecision computing. We expect that the availability of a well-documented and fast Presburger library will accelerate the adoption of polyhedral compilation techniques in production compilers.

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Section: Data Availability Statementmentioning

confidence: 99%