Skip to main content

Implementation of a Clifford Algebra Co-Processor Design on a Field Programmable Gate Array

  • Chapter
Book cover Clifford Algebras

Part of the book series: Progress in Mathematical Physics ((PMP,volume 34))

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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.

    Google Scholar 

  2. R. Abłamowicz, B. Fauser, The CLIFFORD Home Page, math.tntech.edu/rafal/cliff5/index.html, last visited 15. Sept. 2003.

    Google Scholar 

  3. J. Browne, The GrassmannAlgebra Book Home Page, http://www.ses.swin.edu.au/hornes/browne/grassrnannalgebra/book/. last visited 15. Sept. 2003.

  4. A. Differ, The Clados Home Page, sourceforge.net/projects/clados/, last visited 15. Sept. 2003.

    Google Scholar 

  5. L. Dorst, The GABLE Home Page, carol.wins.uva.nl/~leo/GABLE/, last visited 15. Sept. 2003.

    Google Scholar 

  6. D. Fontijne, The Gaigen Home Page, carol.wins.uva.nl/~fontijne/gaigen/ last visited 15. Sept. 2003.

    Google Scholar 

  7. D. Hestenes, G. Sobczyk. Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics. Dordrecht, 1984.

    MATH  Google Scholar 

  8. K. Kommesser. The CHDL Home Page, www-li5.ti.uni-mannheim.de/fpga/?chdl/, last visited 15. Sept. 2003.

    Google Scholar 

  9. P. Leopardi, The GluCat Home Page, glucat.sourceforge.net/, last visited 15. Sept. 2003.

    Google Scholar 

  10. P. Lounesto. Clifford Algebra and Spinors. Cambridge University Press, 1997.

    Google Scholar 

  11. P. Lounesto, The CLICAL Home Page, www.helsinki.fi/~lounesto/CLICAL.htm. last visited 15. Sept. 2003.

    Google Scholar 

  12. C.B. U. Perwass, Applications ofGeometric Algebra in Computer Vision. PhD thesis, Cambridge University, 2000.

    Google Scholar 

  13. 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.

    Chapter  Google Scholar 

  14. C.B.U. Perwass, The CLU Home Page, http://www.perwass.de/cbup/clu.htrnl. last visited 15. Sept. 2003.

  15. C. Gebken, Implementierung eines Koprozessors fur geometrische Algebra aufeinem FPGA Diploma thesis, Christian-Albrechts-University Kiel, 2003.

    Google Scholar 

  16. G. Sommer, editor. Geometric Computing with Clifford Algebra. Springer Verlag, 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Birkhäuser Boston

About this chapter

Cite this chapter

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

Download citation

  • 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

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics