# The accelerated integer GCD algorithm

@article{Weber1995TheAI, title={The accelerated integer GCD algorithm}, author={Kenneth Weber}, journal={ACM Trans. Math. Softw.}, year={1995}, volume={21}, pages={111-122} }

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…

## 59 Citations

New Modified Euclidean and Binary Greatest Common Divisor Algorithm

- Computer Science, Mathematics
- 2016

The implementation results show that the iteration required to compute GCD using ModEB algorithm are substantially less as compared to different GCD algorithms, and the worst case time complexity of the proposed algorithm is O(n2) with respect to the bit-time complexity for two n-bit integers.

Systolic Algorithms for Long Integer GCD Computation

- Computer ScienceCONPAR
- 1994

A word-level generalization which is suitable for systolic parallelization on multiprocessor architectures and more suitable to least-significant digits first arithmetic algorithms than Leiserson conversion lemma is found.

Parallel Implementation of the Accelerated Integer GCD Algorithm

- Computer ScienceJ. Symb. Comput.
- 1996

A parallel implementation of the accelerated algorithm for the Sequent Balance, a shared-memory multiprocessor, that displays speed-ups of 1.6, 2.5, 3.4 and 4.0 using 2, 4, 8 and 16 processors, respectively.

Asymptotically Fast GCD Computation in Z[i]

- Computer Science, MathematicsANTS
- 2000

An asymptotically fast algorithm for the computation of the greatest common divisor (GCD) of two Gaussian integers based on a controlled Euclidean descent that achieves a time bound of O(n(\rm log ~\it n)^{2} \rm log~ log~ \it n)\) bit operations for operands bounded by 2 n in absolute value.

A novel fast hybrid GCD computation algorithm

- Computer Science
- 2014

We propose a novel algorithm for integer's greatest common divisor GCD computation that hybridises both Euclidian and binary algorithms according to a new schema, in order to accelerate the GCD…

Designing systolic arrays for integer GCD computation

- Computer ScienceProceedings of IEEE International Conference on Application Specific Array Processors (ASSAP'94)
- 1994

Experiments using field programmable gate arrays demonstrate the possibility of speeding-up long integer arithmetic by two orders of magnitude by implementing this algorithm in dedicated hardware.

On acceleration of the k-ary GCD Algorithm

- Computer Science, MathematicsIOP Conference Series: Materials Science and Engineering
- 2019

It is shown that a small modification of Sorenson’s Algorithm gives a sufficient acceleration of its work, useful for applications using the GCD operation like calculations in finite fields, generation of Cryptography keys etc.

High Speed Modular Divider Based on GCD Algorithm

- Computer Science, MathematicsICICS
- 2007

The conventional GCD algorithm is extended to radix-4 to increase the efficiency of algorithm the number of comparisons is reduced and the algorithm enables very fast computation of division over GF(2m).

On Schönhage's algorithm and subquadratic integer gcd computation

- Computer Science, MathematicsMath. Comput.
- 2008

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.

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