A Binary Recursive Gcd Algorithm

Damien Stehlé 1 Paul Zimmermann 1
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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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Conference papers
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https://hal.inria.fr/inria-00100175
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Submitted on : Tuesday, September 26, 2006 - 10:15:09 AM
Last modification on : Thursday, January 11, 2018 - 6:20:00 AM

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Damien Stehlé, Paul Zimmermann. A Binary Recursive Gcd Algorithm. 6th International Symposium on Algorithmic Number Theory - ANTS VI, 2004, Burligton, US, pp.411--425. ⟨inria-00100175⟩

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