A Multifunctional Unit for Designing Efficient RNS-Based Datapaths

Inter-modulo operations are the most time consuming and costly operations of the residue number system (RNS), and one of the main obstacles to applying RNS in practice to the design of computing devices, namely for signed integer arithmetic. In this paper, we derive simplified and unified mathematical formulations for inter-modulo operations, such as sign detection, magnitude comparison, scaling signed integers, and signed reverse conversion, grounded on the pillars of reverse conversion. These formulations, which cover a whole range of sets, with 3 to 5 moduli, are used to design components that when integrated allow the design of efficient complete multifunctional units, reusing blocks to perform several RNS intermodulo operations. Not only have the proposed individual components been compared with related art, but a configuration of the proposed multifunctional unit has also been implemented in application specific integrated circuits. Experimental results show that the multifunctional unit is significantly more area and power effective than the other solutions proposed in the state of the art, and the performance of the individual components compare well with dedicated ones. The novel multifunctional units are thus a further step toward the integration of RNS systems on constrained systems.