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GAPPCO: An Easy to Configure Geometric Algebra Coprocessor Based on GAPP Programs

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Abstract

Because of the high numeric complexity of Geometric Algebra, its use in engineering applications relies heavily on tools and devices for efficient implementations. In this article, we present a novel hardware design for a Geometric Algebra coprocessor, called GAPPCO, which is based on Geometric Algebra Parallelism Programs (GAPP). GAPPCO is a design for a coprocessor combining the advantages of optimizing software with a configurable hardware able to implement arbitrary Geometric Algebra algorithms. The idea is to have a fixed hardware easily and fast to be configured for different algorithms. We describe the new hardware design together with the complete tool chain for its configuration.

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References

  1. Franchini, S., Gentile, A., Grimaudo, M., Hung, C.A., Impastato, S., Sorbello, F., Vassallo, G., Vitabile, S.: A sliced coprocessor for native Clifford algebra operations. In: Proceedings of the 10th IEEE Euromicro Conference on Digital System Design—Architectures, Methods and Tools (DSD 2007), pp. 436–439 (2007)

  2. Franchini, S., Gentile, A., Sorbello, F., Vassallo, G., Vitabile, S.: An embedded, fpga-based computer graphics coprocessor with native geometric algebra support. Integr. VLSI J. 42(3), 346–355 (2009)

    Article  MATH  Google Scholar 

  3. Franchini, S., Gentile, A., Sorbello, F., Vassallo, G., Vitabile, S.: Fixed-size quadruples for a new, hardware-oriented representation of the 4d clifford algebra. Adv. Appl. Clifford Algebras 21(2), 315–340 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Franchini, S., Gentile, A., Sorbello, F., Vassallo, G., Vitabile, S.: Design space exploration of parallel embedded architectures for native clifford algebra operations. IEEE Des. Test Comput. 29(3), 60–69 (2012)

    Article  MATH  Google Scholar 

  5. Franchini, S., Gentile, A., Sorbello, F., Vassallo, G., Vitabile, S.: Design and implementation of an embedded coprocessor with native support for 5d, quadruple-based clifford algebra. IEEE Trans. Comput. 62(12), 2366–2381 (2013)

    Article  MathSciNet  Google Scholar 

  6. Franchini, S., Gentile, A., Sorbello, F., Vassallo, G., Vitabile, S.: Conformalalu: a conformal geometric algebra coprocessor for medical image processing. IEEE Trans. Comput. 64(4), 955–970 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. Franchini, S., Gentile, A., Sorbello, F., Vassallo, G., Vitabile, S.: Embedded coprocessors for native execution of geometric algebra operations. Adv. Appl. Clifford Algebras (2016). doi:10.1007/s00006-016-0662-1

  8. Gentile, Antonio, Segreto, Salvatore, Sorbello, Filippo, Vassallo, Giorgio, Vitabile, Salvatore, Vullo, Vincenzo: Cliffosor, an innovative FPGA-based architecture for geometric algebra. ERSA 2005, 211–217 (2005)

    Google Scholar 

  9. Hestenes, D.: Old wine in new bottles: a new algebraic framework for computational geometry. In: Bayro-Corrochano, E., Sobczyk, G., editors. Geometric Algebra with Applications in Science and Engineering. Birkhäuser, Basel (2001)

  10. Hildenbrand, D.: Foundations of Geometric Algebra Computing. Springer, Berlin (2013)

  11. Hildenbrand, D., Albert, J., Charrier, P., Steinmetz, C.: Geometric algebra computing for heterogeneous systems. Adv. Appl. Clifford Algebras (2016). doi:10.1007/s00006-016-0694-6

  12. Hildenbrand, D., Charrier, P., Steinmetz, C., Pitt, J.: Gaalop Home Page (2015). http://www.gaalop.de

  13. Li, H., Hestenes, H., Rockwood, A.: Generalized homogeneous coordinates for computational geometry. In: Sommer, G., editor. Geometric Computing with Clifford Algebra, pp. 27–59. Springer, Berlin (2001)

  14. Mishra, B., Wilson, P.R.: Color edge detection hardware based on geometric algebra. In: European Conference on Visual Media Production (CVMP) (2006)

  15. Perwass, C.: The CLU Home Page (2010). http://www.clucalc.info

  16. Perwass, C., Gebken, C., Sommer, G.: Implementation of a Clifford algebra co-processor design on a field programmable gate array. In: Ablamowicz, R., editor. Clifford Algebras: Application to Mathematics, Physics, and Engineering. Progress in Mathematical Physics. 6th International Conference on Clifford Algebras and Applications, Cookeville, TN, pp. 561–575. Birkhäuser, Basel (2003)

  17. Steinmetz, C.: Optimizing a geometric algebra compiler for parallel architectures using a table-based approach. In: Bachelor Thesis TU Darmstadt (2011)

  18. Stock, F., Hildenbrand, D., Koch, A.: FPGA-accelerated color edge detection using a geometric-algebra-to-verilog compiler, Finland. In: Symposium on System on Chip (SoC), Tampere (2013)

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Hildenbrand, D., Franchini, S., Gentile, A. et al. GAPPCO: An Easy to Configure Geometric Algebra Coprocessor Based on GAPP Programs. Adv. Appl. Clifford Algebras 27, 2115–2132 (2017). https://doi.org/10.1007/s00006-016-0755-x

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  • DOI: https://doi.org/10.1007/s00006-016-0755-x

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