Fast K-ary Reduction and Integer Gcd Algorithms
نویسنده
چکیده
The paper presents a new fast k-ary reduction for integer GCD. It enjoys powerful properties and improves on the running time of the quite similar integer GCD algorithm of Kannan et al. Our k-ary reduction also improves on Sorenson's k-ary reductionn14] and thus favorably matches We-ber's algorithmm15]. More generally, the fast k-ary reduction also provides a basic tool for almost all the best existing integer GCD algorithms.
منابع مشابه
Improvements on the accelerated integer GCD algorithm
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 O (
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Recently, Ken Weber introduced an algorithm for finding the (a, b)-pairs satisfying au+ bv ≡ 0 (mod k), with 0< |a|, |b| < √ k, where (u, k) and (v, k) are coprime. It is based on Sorenson’s and Jebelean’s “k-ary reduction” algorithms. We provide a formula for N(k), the maximal number of iterations in the loop of Weber’s GCD algorithm. 1999 Elsevier Science B.V. All rights reserved.
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