Scalable algorithms for the integer arithmetics and rational calulations in heterogeneous computation environment

Abstract

Algorithmic analysis of large-scale problems that are sensitive to rounding errorsrequires precise rational calculations in the distributed computing environment.Enhanced efficiency of the software my be gained to heterogeneous computing systems that perform local basic arithmetic operations simultaneously using large number of ultralight threads. This paper examines the scalability algorithms for basic arithmetic operations and methods of its improvement.The possibility of increasing of the software efficiency using massive parallelism in heterogeneous computing systems is described. The use of reduntant number system allows you to perform the operation of algebraic addition in constant time and to construct scalable algorithms for all basic arithmetic operations. Scalability of the basic integer arithmetic algorithms can be easily transferred to a rational arithmetic.