A Note on the Complexity of Euclidean Algorithm

Let l（a, b） denote the number of iterations of execution of Euclidean algorithm upon input data a and b with a>b>0. Li Xiaomingtgives l（a, b）<log₂（ab）. We point out that in any case this evaluation is not better than that of G. Lamé: l（a, b）<1.441log₂b+1, moreover the Lamé's depends only on the smaller one of two input data.