On the Virtues of Generic Programming for Symbolic Computation

  • Authors:

  • Xin Li;Marc Moreno Maza;Éric Schost

  • Affiliations:

  • University of Western Ontario, London N6A 1M8,;University of Western Ontario, London N6A 1M8,;University of Western Ontario, London N6A 1M8,

  • Venue:
  • ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
  • Year:
  • 2007

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Abstract

The purpose of this study is to measure the impact of C level code polynomial arithmetic on the performances of AXIOMhigh-level algorithms, such as polynomial factorization. More precisely, given a high-level AXIOMpackage Pparametrized by a univariate polynomial domain U, we have compared the performances of Pwhen applied to different U's, including an AXIOMwrapper for our C level code.Our experiments show that when Prelies on Ufor its univariate polynomial computations, our specialized C level code can provide a significant speed-up. For instance, the improved implementation of square-free factorization in AXIOMis 7 times faster than the one in Mapleand very close to the one in MAGMA. On the contrary, when Pdoes not rely much on the operations of Uand implements its private univariate polynomial operation, then Pcannot benefit from our highly optimized C level code. Consequently, code which is poorly generic reduces the speed-up opportunities when applied to highly efficient and specialized