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International Conference of the Austrian Center for Parallel Computation

ACPC 1991: Parallel Computation pp 369–384Cite as

On the multi-threaded computation of modular polynomial greatest common divisors

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 591))

Abstract

We present a parallelization of the Brown-Collins algorithm in the PARSAC-2 Computer Algebra system, and we describe the design of our S- threads parallelization environment. PARSAC-2 is a parallel extension of SAC-2 built upon multiple threads of control provided by S-threads. The Brown-Collins algorithm computes the g.c.d. and its co-factors of two polynomials in Zp[x 1,..., x r], r ≥ 2, by first reducing the problem to multiple g.c.d. calculations of modular homomorphic images (MHI) in Zp[x 2,..., x r ], and then recovering the result by interpolation. After studying timings of the SAC-2 implementation, we first parallelize the interpolation algorithm, and then we parallelize the main MHI loop by executing the modular g.c.d. computations concurrently. We determine speed-up's and speed-up efficiencies over a wide range of polynomials.

This material is based upon work supported by the National Science Foundation under Award No. CCR-9009396.

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Authors and Affiliations

  1. Department of Computer and Information Science, The Ohio State University, 43210-1277, Columbus, OH, USA

    Wolfgang Küchlin

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  1. Wolfgang Küchlin
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Hans P. Zima

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© 1992 Springer-Verlag Berlin Heidelberg

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Küchlin, W. (1992). On the multi-threaded computation of modular polynomial greatest common divisors. In: Zima, H.P. (eds) Parallel Computation. ACPC 1991. Lecture Notes in Computer Science, vol 591. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55437-8_93

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  • DOI: https://doi.org/10.1007/3-540-55437-8_93

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55437-0

  • Online ISBN: 978-3-540-47073-1

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