The `diagonal function´ in non-redundant residue number system

Although the `diagonal function´ of a Residue Number System has been recently introduced as a powerful tool to perform non modular operations, its implementation is generally realized using an additional modulus external to the set of system moduli. The aim of this paper is to demonstrate the usefulness of the `diagonal function´ in Non-Redundant Residue Number Systems, i.e. without extra moduli. To this purpose two techniques for magnitude comparison and sign detection are presented which use advanced implementations of the `diagonal function´ on non redundant computing architectures