Improvements on the accelerated integer GCD algorithm

نویسندگان

  • Sidi Mohamed Sedjelmaci
  • Christian Lavault
چکیده

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 (

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

The Accelerated Euclidean Algorithm

We propose a new GCD algorithm called Accelerated Euclidean Algorithm, or AEA for short, which matches the O(n log n log log n) time complexity of the Schönhage algorithm for n-bit inputs. This new GCD algorithm is designed for both integers and polynomials. We only focus our study to the integer case, the polynomial case is currently addressed [3]. The algorithm is based on a half-gcd like pro...

متن کامل

Fast K-ary Reduction and Integer Gcd Algorithms

The paper presents a new fast k-ary reduction for integer GCD. It enjoys powerful properties and improves on the running time of the quite similar integer GCD algorithm of Kannan et al. Our k-ary reduction also improves on Sorenson's k-ary reductionn14] and thus favorably matches We-ber's algorithmm15]. More generally, the fast k-ary reduction also provides a basic tool for almost all the best ...

متن کامل

GCDHEU: 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 کامل

Parallel 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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Inf. Process. Lett.

دوره 61  شماره 

صفحات  -

تاریخ انتشار 1997