Geometric Algebra Computing for Heterogeneous Systems

• Published in: Advances in applied Clifford algebras Vol. 27; no. 1; pp. 599 - 620
• Main Authors: Hildenbrand, D., Albert, J., Charrier, P., Steinmetz, Chr
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.03.2017; Springer Nature B.V
• Subjects: Algebra; Applications of Mathematics; C (programming language); Complexity; Computation; Mathematical and Computational Physics; Mathematical Methods in Physics; Physics; Physics and Astronomy; Programming languages; Proving; Software; Theoretical; C++ AMP; Secondary 00A00; Gaalop; Ray tracer; Primary 99Z99; Geometric Algebra Computing
• ISSN: 0188-7009; 1661-4909
• DOI: 10.1007/s00006-016-0694-6

Starting from the situation 15 years ago with a great gap between the low symbolic complexity on the one hand and the high numeric complexity of coding in Geometric Algebra on the other hand, this paper reviews some applications showing, that, in the meantime, this gap could be closed, especially for CPUs. Today, the use of Geometric Algebra in engineering applications relies heavily on the availability of software solutions for the new heterogeneous computing architectures. While most of the Geometric Algebra tools are restricted to CPU focused programming languages, in this paper, we introduce the new Gaalop (Geometric Algebra al gorithms op timizer) Precompiler for heterogeneous systems (CPUs, GPUs, FPGAs, DSPs ...) based on the programming language C++ AMP (Accelerated Massive Parallelism) of the HSA (Heterogeneous System Architecture) Foundation. As a proof-of-concept we present a raytracing application together with some computing details and first performance results.