منابع مشابه
A modular integer GCD algorithm
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 Algebr...
متن کاملGCDHEU: Heuristic Polynomial GCD Algorithm Based on Integer GCD Computation
A heuristic algorithm, GCDHEU, is described for polynomial GCD computation over the integers. The algorithm is based on evaluation at a single large integer value (for each variable), integer GCD computation, and a single-point interpolation scheme. Timing comparisons show that this algorithm is very efficient for most univariate problems and it is also the algorithm of choice for many problems...
متن کاملParallel Implementation of Schönhage's Integer GCD Algorithm
We present a parallel implementation of Schönhage’s integer GCD algorithm on distributed memory architectures. Results are generalized for the extended GCD algorithm. Experiments on sequential architectures show that Schönhage’s algorithm overcomes other GCD algorithms implemented in two well known multiple-precision packages for input sizes larger than about 50000 bytes. In the extended case t...
متن کاملImprovements on the accelerated integer GCD algorithm
The present paper analyses and presents several improvements to the algorithm for finding the (a, b)-pairs of integers used in the k-ary reduction of the right-shift k-ary integer GCD algorithm. While the worst-case complexity of Weber’s “Accelerated integer GCD algorithm” is O (
متن کاملOptimizing and Parallelizing Brown’s Modular GCD Algorithm
Consider the multivariate polynomial problem over the integers; that is, Gcd(A,B) where A,B ∈ Z[x1, x2, . . . xn]. We can solve this problem by solving the related Gcd problem in Zp[x1, x2, . . . xn] for several primes p, and then reconstructing the solution in the integers using Chinese Remaindering. The question we address in this paper is how fast can we solve the problem Gcd(A,B) in Zp[x1, ...
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ژورنال
عنوان ژورنال: Journal of Algorithms
سال: 2005
ISSN: 0196-6774
DOI: 10.1016/j.jalgor.2004.06.006