Methods and tools for fast and reliable processing of integer data of state information systems using a non-positional number system in the residual classes system

Abstract

A characteristic feature of an industrial society is the development and use of new, progressive information technologies based on the widespread use of superproductive and reliable dual-use computer systems and components (CSC). The development and improvement of over-productive and reliable dual-purpose CSC is a strategically important and topical issue and is under the special control of the heads of states and governments of the advanced countries of the world. Today, there are a number of areas of science and technology, where there is a need for fast, reliable and high-precision integer arithmetic calculations: arithmetic operations on integers and polynomials; integer linear programming; operations on numbers and sets; solution of multidimensional NP-complete problems; implementation of routing algorithms; multiplication of vectors and matrices; the problem of the Fourier transform and its application; neural network data processing systems; tasks for military purposes; digital signal processing; digital image processing; cryptographic transformations; highly-precise integer arithmetic; the solution of problems related to the space research; highly-precise digital-to-analog and analog-to-digital conversions (Krasnobayev, Koshman, & Mavrina, 2014, р. 969).