An Intermediate Representation for Expressing and Optimizing Computations in Lattice Quantum Chromodynamics

Abstract

The field of Lattice Quantum Chromodynamics faces massive scaling problems because of the large iteration spaces of the sums required which scale with the factorial of the number of atoms represented. The LQCD IR and rewrite system from this thesis allows tackling these scaling problems quicker and more effectively. The IR allows representing both mathematical concepts such as products and sums as well as algorithmic concepts such as precomputations. Our system requires minimal code to initialize the naive algorithm and apply effective rewrites to increase performance. This development time speedup allows trying various approaches with ease. The rewrite system allows correctness to be maintained at each step while being able to drastically change the algorithmic approach in search of better asymptotic bounds. Our approaches lead to up to 5x speedups and at worse 2x slowdowns for our most important problem, but with a better development cycle, requiring only 100s of SLOC compared to 1000s of SLOC.