A Sliced Coprocessor for Native Clifford Algebra Operations

Abstract

Computer graphics applications require efficient tools to model geometric objects. The traditional approach based on compute-intensive matrix calculations is error-prone due to a lack of integration between geometric reasoning and matrix-based algorithms. Clifford algebra offers a solution to these issues since it permits specification of geometry at a coordinate-free level. The best way to exploit the symbolic computing power of geometric (Clifford) algebra is supporting its data types and operators directly in hardware. This paper outlines the architecture of S-CliffoSor (Sliced Clifford coprocessor), a parallelizable embedded coprocessor that executes native Clifford algebra operations. S-CliffoSor is a sliced coprocessor that can be replicated for parallel execution of concurrent Clifford operations. A single slice has been designed, implemented and tested on the Celoxica Inc. RC1000 board. The experimental results show the potential to achieve a 3times speedup for Clifford sums and 4times speedup for Clifford products compared to against the analogous operations in the software library generator GAIGEN.

DOI: 10.1109/DSD.2007.4341505

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Cite this paper

@article{Franchini2007ASC, title={A Sliced Coprocessor for Native Clifford Algebra Operations}, author={Silvia Franchini and Antonio Gentile and M. Grimaudo and C. A. Hung and Sandro Impastato and Filippo Sorbello and Giorgio Vassallo and Salvatore Vitabile}, journal={10th Euromicro Conference on Digital System Design Architectures, Methods and Tools (DSD 2007)}, year={2007}, pages={436-439} }