Isupov
METHODS OF BASIC NON-MODULAR OPERATIONS
IN MODULAR ARITHMETIC USING INTERVAL
POSITIONAL CHARACTERISTICS
Abstract. <...> Residue Number Systems (RNS) and modular arithmetic
enable independent processing of individual bits of numbers and find their application in many strategically important areas of science, such as cryptography, digital
signal processing, high-precision calculations, etc. <...> It is known that the main problem of the efficient use of RNS is the complexity of non-modular operations that require assessement of the positional values of modular numbers. <...> The purpose of the
study is a theoretical and scientific grounding of a new method of basic nonmodular operations in modular arithmetic (comparison, sign determination, overflow detection), which is based on the calculation and analysis of interval positional
characteristics of modular numbers. <...> This method is characterized by its simplicity
and allows to get reliable evaluation of the relative positional magnitude of a modular number asymptotically fast. <...> To solve the problem of the
effective defenition of the relative positional value of a number represented in the residue number system, the Chinese Remainder Theorem has been used. <...> The reliability of
results of non-modular operations is proved by the fundamentals of Interval Analysis. <...> A new method of the definition of non-modular comparisons in residue number systems, sign determination and overflow detection based on the calculation and
analysis of interval characteristics of modular numbers has been suggested. <...> Key words: residue number system, non-modular operation, comparison, sign determination, overflow detection, interval positional characteristic, interval analysis. <...> Под системой счисления в остаточных классах понимается такая система, в которой целое число x∈[0 <...>