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An Effective Programming of GCD Algorithms for Natural Numbers

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Abstract

We study the problem of acceleration of GCD algorithms for natural numbers based on the approximating k-ary algorithm. We suggest a new scheme of the approximating algorithm implementation ensuring the value of the reduction coefficient ρ = Ai/Bi equal or exceeding k where k is a regulated parameter of computation not exceeding the size of a computer word. This approach ensures a significant advantage of our algorithm against the classical Euclidean algorithm.

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Funding

This work was carried out as part of the development program of the Scientific and Educational Mathematical Center of the Volga Federal District, agreement no. 075-02-2020-1478.

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Authors and Affiliations

  1. Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008, Russia

    Arkan Mohammed Al Halidi & Sh. T. Ishmukhametov

Authors
  1. Arkan Mohammed Al Halidi
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  2. Sh. T. Ishmukhametov
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Corresponding authors

Correspondence to Arkan Mohammed Al Halidi or Sh. T. Ishmukhametov.

Additional information

Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 6, pp. 3–8.

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Al Halidi, A.M., Ishmukhametov, S.T. An Effective Programming of GCD Algorithms for Natural Numbers. Russ Math. 64, 1–5 (2020). https://doi.org/10.3103/S1066369X20060018

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  • DOI: https://doi.org/10.3103/S1066369X20060018

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