The accuracy estimation of the interval-positional characteristic in residue number system

Abstract

Residue Number System (RNS) provides the ability to increase performance for some types of algorithms through parallel data presentation. When implementing high-performance computing algorithms on this basis, an important issue is the effective implementation of non-modular operations, including determining the sign of a number, comparing numbers, determining overflow, dividing numbers, etc. One of the mechanisms for the effective implementation of non-modular operations is the use of positional characteristics, among which one can distinguish an approximate method that has low computational complexity in comparison with other approaches. However, the use of the approximate method can lead to errors in the calculation process in order to increase productivity, which affects the correctness of the results of the calculation of a non-modular operation. For eliminate this drawback, an interval-positional characteristic is used. The article examines the question of the necessary accuracy of the calculation of the interval-positional characteristic. A sufficient condition is proved that ensures the correctness of the calculation of the interval-positional characteristic