GCDHEU: Heuristic polynomial GCD algorithm based on integer GCD computation
Journal of Symbolic Computation
A shift-remainder GCD algorithm
Proceedings of the 5th international conference, AAECC-5 on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
An algorithm for exact division
Journal of Symbolic Computation
A generalization of the binary GCD algorithm
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Journal of Algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A p-adic algorithm for univariate partial fractions
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Parallel integer gcd algorithms and their application to polynomial gcd
Parallel integer gcd algorithms and their application to polynomial gcd
Practical integer division with Karatsuba complexity
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Computation of replicable functions on Risa/Asir
PASCO '97 Proceedings of the second international symposium on Parallel symbolic computation
CALYPSO: a computer algebra library for parallel symbolic computation
PASCO '97 Proceedings of the second international symposium on Parallel symbolic computation
FPGA Implementation of an Extended Binary GCD Algorithm for Systolic Reduction of Rational Numbers
FPL '00 Proceedings of the The Roadmap to Reconfigurable Computing, 10th International Workshop on Field-Programmable Logic and Applications
Computer algebra handbook
A modular integer GCD algorithm
Journal of Algorithms
Modular inverse algorithms without multiplications for cryptographic applications
EURASIP Journal on Embedded Systems
ACM Communications in Computer Algebra
A modular integer GCD algorithm
Journal of Algorithms
High speed modular divider based on GCD algorithm
ICICS'07 Proceedings of the 9th international conference on Information and communications security
Crympix: cryptographic multiprecision library
ISCIS'05 Proceedings of the 20th international conference on Computer and Information Sciences
Robust HGCD with no backup steps
ICMS'06 Proceedings of the Second international conference on Mathematical Software
A novel fast hybrid GCD computation algorithm
International Journal of Computing Science and Mathematics
| Hi-index | 0.00 |
Since the greatest common divisor (GCD) of two integers is a basic arithmetic operation used in many mathematical software systems, new algorithms for its computation are of widespread interest. The accelerated integer GCD algorithm discussed here is based on a reduction step proposed by Sorenson (k-ary reduction), coupled with the dmod operation similar to Norton's smod. Some practical limitations of Sorenson's reduction have been eliminated. Worst-case complexity is still O(n2) for n-bit input, but actual implementations given input about 4096 bits long perform over 5.5 times as fast as the binary GCD on one computer architecture having a multiply instruction. Independent research by Jebelean points to the same conclusions.