Displaying similar documents to “On-line evaluation of powers using Euclid's algorithm”

Efficient computation of addition chains

F. Bergeron, J. Berstel, S. Brlek (1994)

Journal de théorie des nombres de Bordeaux

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The aim of this paper is to present a unifying approach to the computation of short addition chains. Our method is based upon continued fraction expansions. Most of the popular methods for the generation of addition chains, such as the binary method, the factor method, etc..., fit in our framework. However, we present new and better algorithms. We give a general upper bound for the complexity of continued fraction methods, as a function of a chosen strategy, thus the total number of...

Digits and continuants in euclidean algorithms. Ergodic versus tauberian theorems

Brigitte Vallée (2000)

Journal de théorie des nombres de Bordeaux

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We obtain new results regarding the precise average-case analysis of the main quantities that intervene in algorithms of a broad Euclidean type. We develop a general framework for the analysis of such algorithms, where the average-case complexity of an algorithm is related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithms. The methods rely on properties of transfer operators suitably adapted from dynamical systems theory...