An overview of high-performance computing using the residue number system

A residue number system (RNS) is a non-positional number system, an alternative to a binary representation of numbers. In RNS, a large integer is represented as a set of smaller numbers, which are the remainders (“residues”) of dividing its original value by some moduli. An exciting feature of the RNS is that addition, subtraction, and multiplication with each residue are performed independently, which provides parallel, carry-free, and high-speed computer arithmetic. On the other hand, non-modular operations that require estimating the magnitude of a number by its residues are challenging to implement in RNS since there is no parallel form for them