Non-Modular Operations of the Residue Number System: Functions for Computing

This chapter introduces the problem of non-modular operations in the Residue Number System (RNS) and presents some recent approaches for their effective implementation. The approaches are based on specific functions defined from the RNS to the Integers that show mathematical properties useful to support the implementation of non-modular operations, like magnitude comparison and residue-to-binary conversion. In particular, two different functions defined from the RNS to the Integers are discussed: the ‘diagonal functions’ and the ‘quotient functions’. Through the paper the new implementations of non-modular operations in the RNS are described and their effectiveness is analysed with respect to traditional techniques in the literature.

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