منابع مشابه
Binary GCD algorithm
The binary GCD algorithm, also known as Stein’s algorithm, is an algorithm that computes the greatest common divisor of two nonnegative integers. Stein’s algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces division with arithmetic shifts, comparisons, and subtraction. Although the algorithm was first published by the Israeli physicist and programm...
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 کاملA 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 کامل5.2 Partial Correctness
Finally, let us calculate the bit complexity required by the algorithm. The longest messages sent by the algorithm are vectors of n values. Regarding each entry as a separate variable (since, in two of the cases, overlap and reading, they are written by diierent readers), a simple application of Lemma 7 implies that the longest message requires O(n 4). However, we can note that, in response to ...
متن کاملA Binary Recursive Gcd Algorithm
The binary algorithm is a variant of the Euclidean algorithm that performs well in practice. We present a quasi-linear time recursive algorithm that computes the greatest common divisor of two integers by simulating a slightly modified version of the binary algorithm. The structure of our algorithm is very close to the one of the well-known Knuth-Schönhage fast gcd algorithm; although it does n...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2018
ISSN: 1898-9934,1426-2630
DOI: 10.2478/forma-2018-0014