Publication 2013 Issue No. 12 - Dec. Abstract - Design and Implementation of an Embedded Coprocessor with Native Support for 5D, Quadruple-Based Clifford Algebra
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Design and Implementation of an Embedded Coprocessor with Native Support for 5D, Quadruple-Based Clifford Algebra
Dec. 2013 (vol. 62 no. 12)
pp. 2366-2381
 ASCII Text x Silvia Franchini, Antonio Gentile, Filippo Sorbello, Giorgio Vassallo, Salvatore Vitabile, "Design and Implementation of an Embedded Coprocessor with Native Support for 5D, Quadruple-Based Clifford Algebra," IEEE Transactions on Computers, vol. 62, no. 12, pp. 2366-2381, Dec., 2013.
 BibTex x @article{ 10.1109/TC.2012.225,author = {Silvia Franchini and Antonio Gentile and Filippo Sorbello and Giorgio Vassallo and Salvatore Vitabile},title = {Design and Implementation of an Embedded Coprocessor with Native Support for 5D, Quadruple-Based Clifford Algebra},journal ={IEEE Transactions on Computers},volume = {62},number = {12},issn = {0018-9340},year = {2013},pages = {2366-2381},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2012.225},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Design and Implementation of an Embedded Coprocessor with Native Support for 5D, Quadruple-Based Clifford AlgebraIS - 12SN - 0018-9340SP2366EP2381EPD - 2366-2381A1 - Silvia Franchini, A1 - Antonio Gentile, A1 - Filippo Sorbello, A1 - Giorgio Vassallo, A1 - Salvatore Vitabile, PY - 2013KW - Embedded systemsKW - CoprocessorsKW - Computer architectureKW - Field programmable gate arraysKW - Computational modelingKW - AlgebraKW - FPGA-based prototypingKW - Clifford algebraKW - computational geometryKW - embedded coprocessorsKW - application-specific processorsVL - 62JA - IEEE Transactions on ComputersER -
Silvia Franchini, University of Palermo, Palermo
Antonio Gentile, University of Palermo, Palermo
Filippo Sorbello, University of Palermo, Palermo
Giorgio Vassallo, University of Palermo, Palermo
Salvatore Vitabile, University of Palermo, Palermo
Geometric or Clifford algebra (CA) is a powerful mathematical tool that offers a natural and intuitive way to model geometric facts in a number of research fields, such as robotics, machine vision, and computer graphics. Operating in higher dimensional spaces, its practical use is hindered, however, by a significant computational cost, only partially addressed by dedicated software libraries and hardware/software codesigns. For low-dimensional algebras, several dedicated hardware accelerators and coprocessing architectures have been already proposed in the literature. This paper introduces the architecture of CliffordALU5, an embedded coprocessing core conceived for native execution of up to 5D CA operations. CliffordALU5 exploits a novel, hardware-oriented representation of the algebra elements that allows for faster execution of Clifford operations. In this paper, a prototype implementation of a complete system-on-chip (SOC) based on CliffordALU5 is presented. This prototype integrates an embedded processing soft-core based on the PowerPC 405 and a CliffordALU5 coprocessor on a Xilinx XUPV2P Field Programmable Gate Array (FPGA) board. Test results show a $(5{\times})$ average speedup for 4D Clifford products and a $(4{\times})$ average speedup for 5D Clifford products against the same operations in Gaigen 2, a CA software library generator running on the general-purpose PowerPC processor. This paper also presents an execution analysis of three different applications in three diverse domains, namely, inverse kinematics of a robot, optical motion capture, and raytracing, showing an average speedup between $(3{\times})$ and $(4{\times})$ with respect to the baseline Gaigen 2 implementation. Finally, a multicore approach to higher dimensional CA based on CliffordALU5 is discussed.
Index Terms:
Embedded systems,Coprocessors,Computer architecture,Field programmable gate arrays,Computational modeling,Algebra,FPGA-based prototyping,Clifford algebra,computational geometry,embedded coprocessors,application-specific processors
Citation:
Silvia Franchini, Antonio Gentile, Filippo Sorbello, Giorgio Vassallo, Salvatore Vitabile, "Design and Implementation of an Embedded Coprocessor with Native Support for 5D, Quadruple-Based Clifford Algebra," IEEE Transactions on Computers, vol. 62, no. 12, pp. 2366-2381, Dec. 2013, doi:10.1109/TC.2012.225