A Binary Recursive Gcd Algorithm
Identifieur interne : 007128 ( Main/Exploration ); précédent : 007127; suivant : 007129A Binary Recursive Gcd Algorithm
Auteurs : Damien Stehlé [France] ; Paul Zimmermann [France]Source :
English descriptors
- mix :
Abstract
The binary algorithm is a variant of the Euclidean algorithm that performs well in practice. We present a quasi-linear time recursive algorithm that computes the greatest common divisor of two integers by simulating a slightly modified version of the binary algorithm. The structure of the recursive algorithm is very close to the one of the well-known Knuth-Schönhage fast gcd algorithm, but the description and the proof of correctness are significantly simpler in our case. This leads to a simplification of the implementation and to better running times.
Url:
Affiliations:
- France
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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Le document en format XML
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pgcd</term><term>complexité quasi-linéaire</term><term>euclidean algorithm</term><term>gcd computation</term><term>knuth-schönhage algorithm</term><term>quasi-linear time complexity</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">The binary algorithm is a variant of the Euclidean algorithm that performs well in practice. We present a quasi-linear time recursive algorithm that computes the greatest common divisor of two integers by simulating a slightly modified version of the binary algorithm. The structure of the recursive algorithm is very close to the one of the well-known Knuth-Schönhage fast gcd algorithm, but the description and the proof of correctness are significantly simpler in our case. This leads to a simplification of the implementation and to better running times.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Nancy</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université de Lorraine</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Stehle, Damien" sort="Stehle, Damien" uniqKey="Stehle D" first="Damien" last="Stehlé">Damien Stehlé</name></region><name sortKey="Zimmermann, Paul" sort="Zimmermann, Paul" uniqKey="Zimmermann P" first="Paul" last="Zimmermann">Paul Zimmermann</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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