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 Oϵ(n/logn)Oϵ(n/logn) time using at most n1+ϵn1+ϵ 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⩾vu⩾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)au+bv=gcd(u,v), are deeply linked with the order of magnitude of the rational v/uv/u and its continuants. Consequently, the computation of such coefficients is much easier.