1. In a system for processing arithmetic information employing a residue number system employing a modulus including a processing segment associated with said modulus, a plurality of processing stages within said segment; each processing stage including at least one map means having input states and output states representing the same residue digits, one state for each residue digit; said output states being related to the input states by MOD (P (input state), m.sub.i) where P is an integer polynomial, and m.sub.i is the modulus of the segments; and means routing the output of one map to the related input of the next map.