Topic
Lehmer's GCD algorithm
About: Lehmer's GCD algorithm is a research topic. Over the lifetime, 145 publications have been published within this topic receiving 2755 citations.
Papers published on a yearly basis
Papers
TL;DR: New systolic arrays that can lead to efricient VLSI solutions to both the G CD problem and the extended GCD problem are described.
Abstract: The problem of finding a greatest common divisor (GCD) of any two nonzero polynomials is fundamental to algebraic and symbolic computations, as well as to the decoder implementation for a variety of error-correcting codes. This paper describes new systolic arrays that can lead to efricient VLSI solutions to both the GCD problem and the extended GCD problem.
134 citations
TL;DR: It is shown that sequential versions of both algorithms take Θ( n 2 /log n ) bit operations in the worst case to compute the GCD of two n -bit integers, which compares favorably to the Euclidean and both binary algorithms, which takes Θ ( n 2 ) time.
101 citations
TL;DR: A new subquadratic left-to-right GCD algorithm, inspired by Schonhage's algorithm for reduction of binary quadratic forms, is described, which runs slightly faster than earlier algorithms, and is much simpler to implement.
Abstract: We describe a new subquadratic left-to-right GCD algorithm, inspired by Schonhage's algorithm for reduction of binary quadratic forms, and compare it to the first subquadratic GCD algorithm discovered by Knuth and Schonhage, and to the binary recursive GCD algorithm of Stehle and Zimmer-mann. The new GCD algorithm runs slightly faster than earlier algorithms, and it is much simpler to implement. The key idea is to use a stop condition for HGCD that is based not on the size of the remainders, but on the size of the next difference. This subtle change is sufficient to eliminate the back-up steps that are necessary in all previous subquadratic left-to-right GCD algorithms. The subquadratic GCD algorithms all have the same asymptotic running time, O(n(log n)(2) log log n).
67 citations
1 Aug 1993
TL;DR: A generalization of the binary algorithm for operation at ‘word level’ by using a new concept of ‘modular conjugates’ computes the GCD of multiprecision integers two times faster than Lehmer–Euclid method.
Abstract: A generalization of the binary algorithm for operation at ‘word level” by using a new concept of ‘modular conjugates” computes the GCD of multiprecision integers two times faster than Lehmer–Euclid method. Most importantly, however, the new algorithm is suitable for systolic parallelization, in ‘least-significant digits jirst” pipelined manner and for aggregation with other systolic algorithms for the arithmetic of multiprecision rational numbers.
60 citations
Journal Article•
TL;DR: In this article, the conditions générales d'utilisation (http://www.compositio.nl/) implique l'accord avec les conditions generales de utilisation, i.e., usage commerciale ou impression systématique, constitutive of an infraction pénale.
Abstract: © Foundation Compositio Mathematica, 1994, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
59 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 3 |
| 2016 | 8 |
| 2015 | 5 |
| 2014 | 4 |
| 2013 | 6 |
| 2012 | 4 |