Efficient Parallel GCD Algorithms for Multicore Shared Memory Architectures

The greatest common divisor (GCD) is used for numerous applications in number theory, modular arithmetic, encryption algorithms such as RSA, random number generation, and solving linear Diophantine equations. High-performance algorithms, which are efficiently and accurately find the GCD of two integers and n (>2) integers, are needed in the modern world for many applications in science and engineering. Parallel hardware and parallel programming solve such emerging challenges that are not possible in a serial world. Modern desktop and laptop computers are equipped with multicore processors with shared memory architecture. In this paper, we develop novel efficient parallel n integers GCD algorithms for multicore shared memory architecture. The brute force, divide-and-conquer, linear recursive and finding minimum first techniques are adopted in our novel algorithms to reduce the size and the complexity of the n integers GCD problem. Various working models of OpenMP, such as the thread-centric, loop-centric and task-centric models are utilized, which promised a more natural way of exploiting and expressing regular and irregular algorithms. A comprehensive performance analysis applies to prove the efficiency of the proposed algorithms.