Fast reduction and composition of binary quadratic forms
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Journal of Algorithms
The accelerated integer GCD algorithm
ACM Transactions on Mathematical Software (TOMS)
A double-digit Lehmer-Euclid algorithm for finding the GCD of long integers
Journal of Symbolic Computation - Special issue on design and implementation of symbolic computation systems
A Comparative Study of Algorithms for Computing Continued Fractions of Algebraic Numbers
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Asymptotically Fast GCD Computation in Z[i]
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Acceleration of Euclidean algorithm and extensions
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
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Subquadratic divide-and-conquer algorithms for computing the greatest common divisor have been studied for a couple of decades. The integer case has been notoriously difficult, with the need for “backup steps” in various forms. This paper explains why backup steps are necessary for algorithms based directly on the quotient sequence, and proposes a robustness criterion that can be used to construct a “half-gcd” algorithm without any backup steps.