Sublinear parallel algorithm for computing the greatest common divisor of two integers
SIAM Journal on Computing
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
An algorithm for exact division
Journal of Symbolic Computation
A generalization of the binary GCD algorithm
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Journal of Algorithms
An analysis of Lehmer's Euclidean GCD algorithm
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Parallel implementation of the accelerated integer GCD algorithm
Journal of Symbolic Computation - Special issue on parallel symbolic computation
Improvements on the accelerated integer GCD algorithm
Information Processing Letters
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
On a parallel Lehmer-Euclid GCD algorithm
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
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Most of integer GCD algorithms use one or several basic transformations which reduce at each step the size of the inputs integers u and v. These transformations called reductions are studied in a general framework. Our investigations lead to many applications such as a new integer division and a new reduction called Modular Reduction or MR for short. This reduction is, at least theoretically, optimal on some subset of reductions, if we consider the number of bits chopped by each reductions. Although its computation is rather difficult, we suggest, as a first attempt, a weaker version which is more efficient in time. Sequential and parallel integer GCD algorithms are designed based on this new reduction and our experiments show that it performs as well as the Weber's version of the Sorenson's k-ary reduction.