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An Effective Programming of GCD Algorithms for Natural Numbers
Russian Mathematics ( IF 0.5 ) Pub Date : 2020-08-06 , DOI: 10.3103/s1066369x20060018 Arkan Mohammed Al Halidi , Sh. T. Ishmukhametov
Russian Mathematics ( IF 0.5 ) Pub Date : 2020-08-06 , DOI: 10.3103/s1066369x20060018 Arkan Mohammed Al Halidi , Sh. T. Ishmukhametov
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.
中文翻译:
GCD自然数算法的有效编程
我们基于近似k进制算法研究了自然数的GCD算法的加速问题。我们建议一种新的近似算法实现方案,以确保约简系数ρ = A i / B i的值等于或超过k,其中k是计算的调节参数,不超过计算机字的大小。这种方法确保了我们的算法相对于经典欧几里得算法的显着优势。
更新日期:2020-08-06
中文翻译:
GCD自然数算法的有效编程
我们基于近似k进制算法研究了自然数的GCD算法的加速问题。我们建议一种新的近似算法实现方案,以确保约简系数ρ = A i / B i的值等于或超过k,其中k是计算的调节参数,不超过计算机字的大小。这种方法确保了我们的算法相对于经典欧几里得算法的显着优势。