Analysis of fast versions of the euclid algorithm

Eda Cesaratto (1) , Julien Clément (1) , Benoît Daireaux (1) , Loïck Lhote (1) , Véronique Maume-Deschamps (1) , Brigitte Vallée (1)

1 Equipe AMACC - Laboratoire GREYC - UMR6072

There exist fast variants of the gcd algorithm which are all based on principles due to Knuth and Sch¨onhage. On inputs of size n, these algorithms use a Divide and Conquer approach, perform FFT multiplications and stop the recursion at a depth slightly smaller than lg n. A rough estimate of the worst-case complexity of these fast versions provides the bound O(n(log n)2 log log n).

Domaines: Algorithme et structure de données [cs.DS]

Eda Cesaratto, Julien Clément, Benoît Daireaux, Loïck Lhote, Véronique Maume-Deschamps, et al.. Analysis of fast versions of the euclid algorithm. 2008. ⟨hal-00211424⟩