Array Program Transformation with Loo.py by Example: High-Order Finite Elements

TL;DR

This paper demonstrates how Loo.py can transform real-world Fortran code into high-performance GPU kernels through various code transformations, showcasing its effectiveness for high-order finite element computations.

Contribution

It introduces a systematic transformation process from Fortran subroutines to GPU kernels using Loo.py, highlighting novel mechanized code conversion techniques.

Findings

Achieved kernel fusion, vectorization, and parallelization.

Demonstrated significant performance improvements.

Validated transformations on real-world weather model code.

Abstract

To concisely and effectively demonstrate the capabilities of our program transformation system Loo.py, we examine a transformation path from two real-world Fortran subroutines as found in a weather model to a single high-performance computational kernel suitable for execution on modern GPU hardware. Along the transformation path, we encounter kernel fusion, vectorization, prefetch- ing, parallelization, and algorithmic changes achieved by mechanized conversion between imperative and functional/substitution- based code, among a number more. We conclude with performance results that demonstrate the effects and support the effectiveness of the applied transformations.