A novel high dynamic range 4-module set {2²ⁿ⁺¹, 2²ⁿ + 1, 2ⁿ + 1, 2ⁿ − 1} whit efficient reverse converter and review improving modular multiplication''s dynamic range with this module set

摘要

In the last years, many modulus sets in the Residue Number System (RNS) for increasing Dynamic Range (DR) are presented. Hence, for achieve this goal a new 4-Moduli Set{2²ⁿ⁺¹, 2²ⁿ + l, 2ⁿ + 1, 2ⁿ−1}, and its efficient reverse converter design are introduced in this paper. This modulus set contains pair-wise relatively prime, and it offers the maximum feasible DR. New CRT-I is used to obtain a high-performance memory-less reverse converter for this modulus set. Also our modulus set can speed up internal RNS arithmetic processing, compared to the modulus set {2ⁿ − 1, 2ⁿ + 1, 2²ⁿ − 2, 2²ⁿ⁺¹ −3}. Finally, we review improving the modular multiplication with this modulus set, and its dynamic range compared with other modulus sets.