A Binary Recursive Gcd Algorithm

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 our algorithm is very close to the one of the well-known Knuth-Sch¨onhage fast gcd algorithm; although it does not improve on its O(M(n) log n) complexity, 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.

• Type: Conference
• Year: 2004
• Where: ANTS
• Authors: Damien Stehlé, Paul Zimmermann
• Keywords: Algorithms, ANTS 2004, Binary Algorithm, Euclidean Algorithm, Time Recursive Algorithm