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 we prove that its bit-time complexity is still O ( n 2 ) for two n-bit integers in the worst case. Our preliminar experiments show a potential speedup for small integers. A parallel version matches the best presently known time complexity, namely O ( n / log n ) time with O ( n 1 + ϵ ) processors, for any constant ϵ > 0 .