A Binary Recursive Gcd Algorithm

Damien Stehlé (1) , Paul Zimmermann (1)

1 SPACES - Solving problems through algebraic computation and efficient software

The binary algorithm is a variant of the Euclidean algorithm that performs well in practice. We present a quasi-linear time recursive algorithm that computes the greatest common divisor of two integers by simulating a slightly modified version of the binary algorithm. The structure of the recursive algorithm is very close to the one of the well-known Knuth-Schönhage fast gcd algorithm, but the description and the proof of correctness are significantly simpler in our case. This leads to a simplification of the implementation and to better running times.

Mots clés: quasi-linear time complexity; calcul de pgcd; gcd computation; euclidean algorithm; knuth-schönhage algorithm; algorithme d'euclide; algorithme de knuth-schönhage; complexité quasi-linéaire

Domaines: Autre [cs.OH]

Damien Stehlé, Paul Zimmermann. A Binary Recursive Gcd Algorithm. 6th International Symposium on Algorithmic Number Theory - ANTS VI, 2004, Burligton, US, pp.411--425. ⟨inria-00100175⟩