An Effective Programming of GCD Algorithms for Natural Numbers

Abstract

© 2020, Allerton Press, Inc. 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.