Highly parallel, fast scaling of numbers in nonredundant residue arithmetic

A new approach to scaling in the nonredundant residue number system (RNS) with the use of the Chinese remainder theorem (CRT) is presented. The auxiliary scaling by M, where M is the number range, is performed in parallel with scaling by the scale factor K in order to avoid the number range overflow. The scaler design utilizes small look-up tables and multioperand (both modulo and binary) adders. The new approach does not impose restrictions on the form, size, and number of moduli n. The only proviso is that K>n. The scaling error is bounded by n and can be reduced to 1 or 1.5 if a correction circuit is employed. Hardware complexity expressed by the number of transistors is approximately one order smaller than that for the earlier design, whereas the scaler latency is similar.