Improvements on the accelerated integer GCD algorithm

Abstract : The present paper analyses and presents several improvements to the algorithm for finding the $(a,b)$-pairs of integers used in the $k$-ary reduction of the right-shift $k$-ary integer GCD algorithm. While the worst-case complexity of Weber's ''Accelerated integer GCD algorithm'' is $\cO\l(\log_\phi(k)^2\r)$, we show that the worst-case number of iterations of the while loop is exactly $\tfrac 12 \l\lfloor \log_{\phi}(k)\r\rfloor$, where $\phi := \tfrac 12 \l(1+\sqrt{5}\r)$.\par We suggest improvements on the average complexity of the latter algorithm and also present two new faster residual algorithms: the sequential and the parallel one. A lower bound on the probability of avoiding the while loop in our parallel residual algorithm is also given.
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  • HAL Id : hal-00911140, version 1
  • ARXIV : 1402.2266

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Sidi Mohamed Sedjelmaci, Christian Lavault. Improvements on the accelerated integer GCD algorithm. Information Processing Letters, Elsevier, 1997, 61 (1), pp.31--36. ⟨hal-00911140⟩

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