A Binary Recursive Gcd Algorithm
Identifieur interne : 004F91 ( Hal/Checkpoint ); précédent : 004F90; suivant : 004F92A Binary Recursive Gcd Algorithm
Auteurs : Damien Stehlé [France] ; Paul Zimmermann [France]Source :
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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.
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<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>
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<sourceDesc><biblStruct><analytic><title xml:lang="en">A Binary Recursive Gcd Algorithm</title>
<author role="aut"><persName><forename type="first">Damien</forename>
<surname>Stehlé</surname>
</persName>
<email>damien.stehle@loria.fr</email>
<idno type="halAuthorId">130769</idno>
<orgName ref="#struct-364475"></orgName>
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<author role="aut"><persName><forename type="first">Paul</forename>
<surname>Zimmermann</surname>
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<meeting><title>6th International Symposium on Algorithmic Number Theory - ANTS VI</title>
<date type="start">2004</date>
<settlement>Burligton, US</settlement>
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<editor>Duncan Buell</editor>
<imprint><publisher>Springer</publisher>
<biblScope unit="serie">Lecture notes in Computer Science</biblScope>
<biblScope unit="volume">3076</biblScope>
<biblScope unit="pp">411--425</biblScope>
<date type="datePub">2004</date>
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<textClass><keywords scheme="author"><term xml:lang="en">calcul de pgcd</term>
<term xml:lang="en">quasi-linear time complexity</term>
<term xml:lang="en">gcd computation</term>
<term xml:lang="en">euclidean algorithm</term>
<term xml:lang="en">knuth-schönhage algorithm</term>
<term xml:lang="en">algorithme d'euclide</term>
<term xml:lang="en">algorithme de knuth-schönhage</term>
<term xml:lang="en">complexité quasi-linéaire</term>
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<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.</abstract>
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