FPL: fast Presburger arithmetic through transprecision

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