RNS architectures for the implementation of the `diagonal function

The `diagonal function' is a new tool for performing non-modular operations in the Residue Number System (RNS). It is defined from the RNS to the integers and exploits the geometrical disposal in multi-dimensional discrete spaces of integers in residue representations. This paper presents a new class of RNS architectures for the effective implementation of the `diagonal function'. The architectures are general, since they do not impose constraints on the set of moduli, and flexible, since they can be best suited depending on specific system requirements. The superiority of the new architectures with respect to traditional approaches is shown in terms of waste of hardware and time delay.