Optimized Automatic Code Generation for Geometric Algebra Based Algorithms with Ray Tracing Application

TL;DR

This paper introduces GMac, a novel geometric algebra-based code generator that efficiently produces optimized low-level code for geometric algorithms, demonstrated through a ray tracing application.

Contribution

The paper presents GMac, a new GA-based code generator that combines symbolic power with high performance and maintainability, with comparisons to similar tools.

Findings

GMac effectively generates optimized code for geometric algorithms.

GMac outperforms comparable GA-based code generators.

Application to ray tracing shows practical benefits.

Abstract

Automatic code generation for low-dimensional geometric algorithms is capable of producing efficient low-level software code through a high-level geometric domain specific language. Geometric Algebra (GA) is one of the most suitable algebraic systems for being the base for such code generator. This work presents an attempt at realizing such idea in practice. A novel GA-based geometric code generator, called GMac, is proposed. Comparisons to similar GA-based code generators are provided. The possibility of fully benefiting from the symbolic power of GA while obtaining good performance and maintainability of software implementations is illustrated through a ray tracing application.