Scalability of Algorithms for Arithmetic Operations in Radix Notation∗

We consider precise rational-fractional calculations for distributed computing environments with an MPI interface for the algorithmic analysis of large-scale problems sensitive to rounding errors in their software implementation. We can achieve additional software efficacy through applying heterogeneous computer systems that execute, in parallel, local arithmetic operations with large numbers on several threads. Also, we investigate scalability of the algorithms for basic arithmetic operations and methods for increasing their speed. We demonstrate that increased efficacy can be achieved of software for integer arithmetic operations by applying mass parallelism in heterogeneous computational environments. We propose a redundant radix notation for the construction of well-scaled algorithms for executing basic integer arithmetic operations. Scalability of the algorithms for integer arithmetic operations in the radix notation is easily extended to rationalfractional arithmetic.