DocumentCode
2460870
Title
Comparing several GCD algorithms
Author
Jebelean, T.
Author_Institution
RISC-Linz, Austria
fYear
1993
fDate
29 Jun-2 Jul 1993
Firstpage
180
Lastpage
185
Abstract
The execution times of several algorithms for computing the GCD of arbitrary precision integers are compared. These algorithms are the known ones (Euclidean, binary, plus-minus), and the improved variants of these for multidigit computation (Lehmer and similar), as well as new algorithms introduced by the author: an improved Lehmer algorithm using two digits in partial consequence computation, and a generation of the binary algorithm using a new concept of modular conjugates. The last two algorithms prove to be the fastest of all, giving a speedup of six to eight times over the classical Euclidean scheme, and two times over the best currently known algorithms. Also, the generalized binary algorithm is suitable for systolic parallelization in a least-significant digits first pipelined manner
Keywords
digital arithmetic; pipeline arithmetic; systolic arrays; Euclidean; GCD algorithms; Lehmer; binary; improved Lehmer algorithm; least-significant digits first; modular conjugates; multidigit computation; partial consequence computation; plus-minus; precision integers; systolic parallelization; Algebra; Algorithm design and analysis; Arithmetic; Artificial intelligence; Computational Intelligence Society; Concurrent computing;
fLanguage
English
Publisher
ieee
Conference_Titel
Computer Arithmetic, 1993. Proceedings., 11th Symposium on
Conference_Location
Windsor, Ont.
Print_ISBN
0-8186-3862-1
Type
conf
DOI
10.1109/ARITH.1993.378094
Filename
378094
Link To Document