6533b829fe1ef96bd128a52d

RESEARCH PRODUCT

Embedded Coprocessors for Native Execution of Geometric Algebra Operations

Silvia FranchiniSalvatore VitabileGiorgio VassalloAntonio GentileFilippo Sorbello

subject

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniTheoretical computer scienceCoprocessorInverse kinematicsbusiness.industryApplied MathematicsClifford algebraGeometric algebra Embedded coprocessors Application-specific processors FPGA-based prototyping.02 engineering and technologyParallel computingData type020202 computer hardware & architectureGeometric algebraSoftware0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processingField-programmable gate arraybusinessVector spaceMathematics

description

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 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 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.

yearjournalcountryeditionlanguage
2016-04-09Advances in Applied Clifford Algebras
https://doi.org/10.1007/s00006-016-0662-1