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Rational number arithmetic by parallel p-adic algorithms

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Parallel Computation (ACPC 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 734))

Abstract

In this paper we analyze the possibility of speeding up rational number arithmetic by using a parallel p-adic approach.

Approximated p-adic arithmetic has received much attention in the last years and several contributions made this arithmetic more efficient. Moreover, p-adic arithmetic is very appropriate for parallel computations over rational numbers as it is based on the multiple homomorphic images technique and the computations are performed independently in each image.

However, to reconstruct the unique result a very time consuming algorithm (the Chinese Remainder Algorithm) has to be used. In order to improve the performance of the recovery step, we propose a specific parallel algorithm and we show that this new algorithm is faster with respect to an already existing algorithm.

To compare these algorithms we have implemented the parallel p-adic arithmetic with both of them. The analysis of the dynamic behaviour of the algorithms shows that the proposed algorithm needs a smaller amount of synchronization, yielding an efficient parallel algorithm.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Universitá “La Sapienza”, Roma, Italy

    Carla Limongelli

  2. Research Institute for Symbolic Computation (RISC-Linz), Johannes Kepler University, Linz, Austria

    Hans Wolfgang Loidl

Authors
  1. Carla Limongelli
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  2. Hans Wolfgang Loidl
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Editor information

Jens Volkert

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© 1993 Springer-Verlag Berlin Heidelberg

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Limongelli, C., Loidl, H.W. (1993). Rational number arithmetic by parallel p-adic algorithms. In: Volkert, J. (eds) Parallel Computation. ACPC 1993. Lecture Notes in Computer Science, vol 734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57314-3_7

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  • DOI: https://doi.org/10.1007/3-540-57314-3_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57314-2

  • Online ISBN: 978-3-540-48055-6

  • eBook Packages: Springer Book Archive

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