The application of core functions to residue number systems

A theory of core functions is presented, and the application of this theory to the difficult residue number system (RNS) operations is described. Potential applications for special-purpose core-based RNS processors include adaptive array processing, Kalman filtering, fast-Fourier transforms, and image processing. The theoretical developments are motivated by the assumption that look-up tables are available with some limit on the number of addresses per table. The tables are used to implement both the modular and nonmodular operations. The restriction on the number of addresses per table, in turn, places a restriction on the largest permissible modulus, because the tables used to implement the modular operations will be addressed by a pair of residues. The contents of each look-up table may be precomputed by any method, as long as the limit on address space is respected and the number of bits per address is reasonable