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 = A_i/B_i 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：

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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。