Sharp estimates for the main parameters of the Euclid Algorithm

Loïck Lhote (1) , Brigitte Vallée (1)

1 Equipe AMACC - Laboratoire GREYC - UMR6072

We provide sharp estimates for the probabilistic behaviour of the main parameters of the Euclid algorithm, and we study in par- ticular the distribution of the bit-complexity which involves two main parameters : digit–costs and length of continuants. We perform a “dy- namical analysis” which heavily uses the dynamical system underlying the Euclidean algorithm. Baladi and Vall´ee [2] have recently designed a general framework for “distributional dynamical analysis”, where they have exhibited asymptotic gaussian laws for a large class of digit–costs. However, this family contains neither the bit–complexity cost nor the length of continuants.

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

Loïck Lhote, Brigitte Vallée. Sharp estimates for the main parameters of the Euclid Algorithm. 2008. ⟨hal-00210493⟩