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) O ? ( n / log n ) time using at most n1+? n 1 + ? 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 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) a u + b v = gcd ( u , v ) , are deeply linked with the order of magnitude of the rational v/u v / u and its continuants. Consequently, the computation of such coefficients is much easier.
extended gcd algorithm integer greatest common divisor (gcd) parallel gcd algorithm complexity analysis number theory