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On Parallelizing the Clifford Algebra Product for CLIFFORD

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Abstract

We present, as a proof of concept, a way to parallelize the Clifford product in Cℓ p,q for a diagonalized quadratic form as a new procedure cmulWpar in the CLIFFORD package for Maple ® . The procedure uses a new Threads module available under Maple 15 (and later) and a new CLIFFORD procedure cmulW which computes the Clifford product of any two Grassmann monomials in Cℓ p,q with a help of Walsh functions. We benchmark cmulWpar and compare it to two other procedures cmulNUM and cmulRS from CLIFFORD. We comment on how to improve cmulWpar by taking advantage of multi-core processors and multithreading available in modern processors.

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Authors and Affiliations

  1. Department of Mathematics, Tennessee Technological University, Box 5054, Cookeville, TN, 38505, U.S.A.

    Rafał Abłamowicz

  2. The University of Birmingham, School of Computer Science, Edgbaston-Birmingham, B15 2TT, England

    Bertfried Fauser

Authors
  1. Rafał Abłamowicz
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  2. Bertfried Fauser
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Correspondence to Rafał Abłamowicz.

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Abłamowicz, R., Fauser, B. On Parallelizing the Clifford Algebra Product for CLIFFORD . Adv. Appl. Clifford Algebras 24, 553–567 (2014). https://doi.org/10.1007/s00006-014-0445-5

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  • DOI: https://doi.org/10.1007/s00006-014-0445-5

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