Improving residue number system multiplication with more balanced moduli sets and enhanced modular arithmetic structures

Residue number systems (RNS) are non-weighted systems that allow to perform addition, subtraction and multiplication operations concurrently and independently on each residue. The triple moduli set {2" - 1, 2", 2" + 1} and its respective extensions have gained unprecedent importance in RNS, mainly because of the simplicity of the arithmetic units for the individual channels and also of the converters to and from RNS. However, there is neither a perfect balance between the various elements of this moduli set nor an exact equivalence in the complexity of the individual arithmetic units for each individual residue. Two complementary approaches have been proposed to improve the efficiency of RNS based on this type of moduli sets: enhancing multipliers modulo 2" + 1, which perform the most complex arithmetic operation, and overloading the binary channel in order to obtain a more balanced moduli set. Experimental results show that, when applied together, these techniques can improve the efficiency of the multipliers up to 32%.