A parallel extended GCD algorithm

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 (n/ logn) time using at most n1+ 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. © 2007 Elsevier B.V. All rights reserved.