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Geometric Algebra Computing for Heterogeneous Systems

Hildenbrand, Dietmar and Albert, Justin and Charrier, Patrick and Steinmetz, Christian (2017):
Geometric Algebra Computing for Heterogeneous Systems.
In: Advances in Applied Clifford Algebras, Springer International Publishing, pp. 599-620, 27, (1), ISSN 1661-4909, [Online-Edition: http://dx.doi.org/10.1007/s00006-016-0694-6],
[Article]

Abstract

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 algorithms optimizer) 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.

Item Type: Article
Erschienen: 2017
Creators: Hildenbrand, Dietmar and Albert, Justin and Charrier, Patrick and Steinmetz, Christian
Title: Geometric Algebra Computing for Heterogeneous Systems
Language: English
Abstract:

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 algorithms optimizer) 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.

Journal or Publication Title: Advances in Applied Clifford Algebras
Volume: 27
Number: 1
Publisher: Springer International Publishing
Divisions: 20 Department of Computer Science
Date Deposited: 30 Mar 2017 06:48
Official URL: http://dx.doi.org/10.1007/s00006-016-0694-6
Alternative Abstract:
Alternative abstract Language
Ausgehend von der Situation vor 15 Jahren, die durch eine große Lücke zwischen der geringen symbolischen Komplexität auf der einen Seite und der hohen numerischen Komplexität der Kodierung in Geometrischer Algebra auf der anderen Seite gekennzeichnet ist, bespricht dieses Paper einige Anwendungen, die zeigen, dass in der Zwischenzeit diese Lücke geschlossen werden konnte, vor allem für CPUs. Heutzutage ist die Nutzung der Geometrischen Algebra in technischen Anwendungen stark auf die Verfügbarkeit von Softwarelösungen für neue heterogene Berechnungsarchitekturen angewiesen. Während viele Geometrische Algebra Werkzeuge auf CPU fokussierte Programmiersprachen beschränkt sind, wird in diesem Paper der neue Gaalop (Geometric Algebra algorithms optimizer) Präcompiler für heterogene Systeme (CPUs, GPUs, FPGAs, DSPs, …), basierend auf der Programmiersprache C++ AMP (Accelerated Massive Parallelism) der HSA (Heterogeneous System Architecture) Foundation, eingeführt. Als Nachweis der Machbarkeit wird eine Raytracing Anwendung zusammen mit einigen Berechnungsdetails und ersten Performanzergebnissen aufgezeigt.German
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