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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https://hal.inria.fr/inria-00071533
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Submitted on : Tuesday, May 23, 2006 - 5:52:49 PM
Last modification on : Thursday, January 11, 2018 - 6:20:00 AM
Long-term archiving on : Sunday, April 4, 2010 - 10:23:11 PM

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  • HAL Id : inria-00071533, version 1

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Damien Stehlé, Paul Zimmermann. A Binary Recursive Gcd Algorithm. [Research Report] RR-5050, INRIA. 2002. ⟨inria-00071533⟩

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