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)
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
Modern computer algebra
On a parallel Lehmer-Euclid GCD algorithm
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
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A new parallel extended GCD algorithm is proposed. It matches the best existing parallel integer GCD algorithms of Sorenson and Chor and Goldreich, since it can be achieved in O"@e(n/logn) time using at most n^1^+^@e processors on CRCW PRAM. Sorenson and Chor and Goldreich both use a modular approach which consider the least significant bits. By contrast, our algorithm only deals with the leading bits of the integers u and v, with u=v. This approach is more suitable for extended GCD algorithms since the coefficients of the extended version a and b, such that au+bv=gcd(u,v), are deeply linked with the order of magnitude of the rational v/u and its continuants. Consequently, the computation of such coefficients is much easier.