Abstract
We present the design of a Clifford algebra co-processor and its implementation on a Field Programmable Gate Array (FPGA). To the best of our knowledge this is the first such design developed. The design is scalable in both the Clifford algebra dimension and the bit width of the numerical factors. Both aspects are only limited by the hardware resources. Furthermore, the signature of the underlying vector space can be changed without reconfiguring the FPGA. High calculation speeds are achieved through a pipeline architecture.
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References
R. Abłamowicz, Clifford algebra computations with Maple, in Clifford (Geometric) Algebras Banff, Alberta Canada, 1995, Ed. W.E. Baylis, Birkhäuser, Boston, 1996, pp. 463–501.
R. Abłamowicz, B. Fauser, The CLIFFORD Home Page, math.tntech.edu/rafal/cliff5/index.html, last visited 15. Sept. 2003.
J. Browne, The GrassmannAlgebra Book Home Page, http://www.ses.swin.edu.au/hornes/browne/grassrnannalgebra/book/. last visited 15. Sept. 2003.
A. Differ, The Clados Home Page, sourceforge.net/projects/clados/, last visited 15. Sept. 2003.
L. Dorst, The GABLE Home Page, carol.wins.uva.nl/~leo/GABLE/, last visited 15. Sept. 2003.
D. Fontijne, The Gaigen Home Page, carol.wins.uva.nl/~fontijne/gaigen/ last visited 15. Sept. 2003.
D. Hestenes, G. Sobczyk. Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics. Dordrecht, 1984.
K. Kommesser. The CHDL Home Page, www-li5.ti.uni-mannheim.de/fpga/?chdl/, last visited 15. Sept. 2003.
P. Leopardi, The GluCat Home Page, glucat.sourceforge.net/, last visited 15. Sept. 2003.
P. Lounesto. Clifford Algebra and Spinors. Cambridge University Press, 1997.
P. Lounesto, The CLICAL Home Page, www.helsinki.fi/~lounesto/CLICAL.htm. last visited 15. Sept. 2003.
C.B. U. Perwass, Applications ofGeometric Algebra in Computer Vision. PhD thesis, Cambridge University, 2000.
C.B.U. Perwass, G. Sommer, Numerical evaluation of versors with Clifford algebra, in Applications of Geometric Algebra in Computer Science and Engineering Eds. Leo Dorst, Chris Doran, Joan Lasenby, Birkhäuser, 2002, pp. 341–349.
C.B.U. Perwass, The CLU Home Page, http://www.perwass.de/cbup/clu.htrnl. last visited 15. Sept. 2003.
C. Gebken, Implementierung eines Koprozessors fur geometrische Algebra aufeinem FPGA Diploma thesis, Christian-Albrechts-University Kiel, 2003.
G. Sommer, editor. Geometric Computing with Clifford Algebra. Springer Verlag, 2001.
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Perwass, C., Gebken, C., Sommer, G. (2004). Implementation of a Clifford Algebra Co-Processor Design on a Field Programmable Gate Array. In: Abłamowicz, R. (eds) Clifford Algebras. Progress in Mathematical Physics, vol 34. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2044-2_35
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DOI: https://doi.org/10.1007/978-1-4612-2044-2_35
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3525-1
Online ISBN: 978-1-4612-2044-2
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