Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
An algorithm for exact division
Journal of Symbolic Computation
A generalization of the binary GCD algorithm
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
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Information and Computation
The accelerated integer GCD algorithm
ACM Transactions on Mathematical Software (TOMS)
Parallel implementation of the accelerated integer GCD algorithm
Journal of Symbolic Computation - Special issue on parallel symbolic computation
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
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The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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On a parallel Lehmer-Euclid GCD algorithm
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Parallel volume rendering on a single-chip SIMD architecture
PVG '01 Proceedings of the IEEE 2001 symposium on parallel and large-data visualization and graphics
Towards nanocomputer architecture
CRPIT '02 Proceedings of the seventh Asia-Pacific conference on Computer systems architecture
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Parallel integer gcd algorithms and their application to polynomial gcd
Parallel integer gcd algorithms and their application to polynomial gcd
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This paper describes the first algorithm to compute the greatest common divisor (GCD) of two n-bit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A generalization of the binary GCD algorithm, in: ISSAC '93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, 1993, pp. 111-116; K. Weber, The accelerated integer GCD algorithm, ACM Trans. Math. Softw. 21 (1995) 111-122] when U and V are close to the same size, that replaces U by (U - bV)/p, where p is one of the prime moduli and b is the unique integer in the interval (- p/2, p/2) such that b ≡ UV-1 (mod p). When the algorithm is executed on a bit common CRCW PRAM with O(n log n log log log n) processors, it takes O(n) time in the worst case. A heuristic model of the average case yields O(n/log n) time on the same number of processors.