Clifford Algebra or Geometric Algebra (GA) is a simple and intuitive way to model geometric objects and their transformations. Operating in high-dimensional vector spaces with significant computational costs, the practical use of GA requires, however, dedicated software and/or hardware architectures to directly support Clifford data types and operators. In this paper, a family of embedded coprocessors for the native execution of GA operations is presented. The paper shows the evolution of the coprocessor family focusing on the latest two architectures that offer direct hardware support to up to five-dimensional Clifford operations. The proposed coprocessors exploit hardware-oriented representations of GA elements and operators properly conceived to obtain fast performing implementations. The coprocessor prototypes, implemented on Field Programmable Gate Arrays (FPGA) development boards, show significant speedups of about one order of magnitude with respect to the baseline software library Gaigen running on a general-purpose processor. The paper also presents an execution analysis of different GA-based applications, namely inverse kinematics of a robot, optical motion capture, raytracing, and medical image processing, showing good speedups with respect to the baseline general-purpose implementation.

Franchini, S., Gentile, A., Sorbello, F., Vassallo, G., Vitabile, S. (2015). A Family of Embedded Coprocessors with Native Geometric Algebra Support. In Proceedings of Sixth International Conference on Applied Geometric Algebra in Computer Science and Engineering (AGACSE 2015), S. Xambó Descamps, J. M. Parra Serra, R. González Calvet, Eds, Universitat Politecnica de Catalunya, Facultat d’Informatica de Barcelona, Barcelona, Spain. (pp. 163-172). Barcelona : S. Xambó Descamps, J. M. Parra Serra, R. González Calvet, Eds, Universitat Politecnica de Catalunya, Facultat d’Informatica de Barcelona, Barcelona, Spain.

A Family of Embedded Coprocessors with Native Geometric Algebra Support

FRANCHINI, Silvia Giuseppina;GENTILE, Antonio;SORBELLO, Filippo;VASSALLO, Giorgio;VITABILE, Salvatore
2015-01-01

Abstract

Clifford Algebra or Geometric Algebra (GA) is a simple and intuitive way to model geometric objects and their transformations. Operating in high-dimensional vector spaces with significant computational costs, the practical use of GA requires, however, dedicated software and/or hardware architectures to directly support Clifford data types and operators. In this paper, a family of embedded coprocessors for the native execution of GA operations is presented. The paper shows the evolution of the coprocessor family focusing on the latest two architectures that offer direct hardware support to up to five-dimensional Clifford operations. The proposed coprocessors exploit hardware-oriented representations of GA elements and operators properly conceived to obtain fast performing implementations. The coprocessor prototypes, implemented on Field Programmable Gate Arrays (FPGA) development boards, show significant speedups of about one order of magnitude with respect to the baseline software library Gaigen running on a general-purpose processor. The paper also presents an execution analysis of different GA-based applications, namely inverse kinematics of a robot, optical motion capture, raytracing, and medical image processing, showing good speedups with respect to the baseline general-purpose implementation.
2015
Settore ING-INF/05 - Sistemi Di Elaborazione Delle Informazioni
978-84-606-9982-8
Franchini, S., Gentile, A., Sorbello, F., Vassallo, G., Vitabile, S. (2015). A Family of Embedded Coprocessors with Native Geometric Algebra Support. In Proceedings of Sixth International Conference on Applied Geometric Algebra in Computer Science and Engineering (AGACSE 2015), S. Xambó Descamps, J. M. Parra Serra, R. González Calvet, Eds, Universitat Politecnica de Catalunya, Facultat d’Informatica de Barcelona, Barcelona, Spain. (pp. 163-172). Barcelona : S. Xambó Descamps, J. M. Parra Serra, R. González Calvet, Eds, Universitat Politecnica de Catalunya, Facultat d’Informatica de Barcelona, Barcelona, Spain.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/167505
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