Geodesic
An effective programming of GCD Algorithms for natural numbers
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2020), pp. 3-8

Voir la notice de l'article provenant de la source Math-Net.Ru

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 algorithm implementation ensuring the value of the reduction coefficient $\rho=A_i/B_i$ at a stage of the procedure equal or exceeding $k$ where $k$ is a regulating parameter of computation not exceeding the size a computer word. This ensures a significant advantage of our algorithm against the classical Euclidean algorithm.
Keywords: greatest common divisor, Euclidian GCD Algorithm, $k$-ary Algorithm, approximating $k$-ary Algorithm. 
@article{IVM_2020_6_a0,
     author = {Al Halidi Arkan Mohammed and Sh. T. Ishmukhametov},
     title = {An effective programming of {GCD} {Algorithms} for natural numbers},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--8},
     publisher = {mathdoc},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_6_a0/}
}
TY  - JOUR
AU  - Al Halidi Arkan Mohammed
AU  - Sh. T. Ishmukhametov
TI  - An effective programming of GCD Algorithms for natural numbers
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2020
SP  - 3
EP  - 8
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2020_6_a0/
LA  - ru
ID  - IVM_2020_6_a0
ER  - 
%0 Journal Article
%A Al Halidi Arkan Mohammed
%A Sh. T. Ishmukhametov
%T An effective programming of GCD Algorithms for natural numbers
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2020
%P 3-8
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2020_6_a0/
%G ru
%F IVM_2020_6_a0
Al Halidi Arkan Mohammed; Sh. T. Ishmukhametov. An effective programming of GCD Algorithms for natural numbers. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2020), pp. 3-8. http://geodesic.mathdoc.fr/item/IVM_2020_6_a0/