The Mixed Binary Euclid Algorithm

We present a new GCD algorithm for two integers that combines both the Euclidean and the binary gcd approaches. We give its worst case time analysis and prove that its bit-time complexity is still O(n) for two n-bit integers. However, our preliminar experiments show that it is very fast for small integers. A parallel version of this algorithm matches the best presently known time complexity, namely O( n logn ) time with n 1+ , for any constant > 0.