On RNS with VLSI-friendly diagonal function

Residue number system (RNS) is a promising tool for improving performance in various areas of modern science and technology. Recently were published number of papers on the use of Diagonal Function for problematic RNS operations implementation. The main conclusion of those works is the assertion that the Diagonal Function (DF) does not give an advantages over Chinese Remainder Theorem in general case. The main difficulty in the use of the DF in VLSI is the implementation of modulo Sum of Quotients (SQ) operations. In this paper we have decided to consider the problem of RNS constructing with VLSI-friendly DF. We analyzed the cases where SQ takes one of three forms 2ⁿ, 2ⁿ −1 or 2ⁿ +1. In this paper we shows the methods of RNS construction with SQ forms 2ⁿ, 2ⁿ −1 and 2ⁿ +1.