A New Residue Number System with 5-Moduli Set: {22q, 2q±3, 2q±1}
HamidReza Ahmadifar, Ghassem Jaberipur · The Computer Journal · 2014
Residue number system (RNS) parameterized moduli sets almost always contain a power-of-two modulo (e.g. 2iq), where the corresponding computation channel and residue generator are the most efficient when compared with other non-power-of-two moduli (e.g. 2jq ± δ). Furthermore, inclusion of a power-of-two modulo leads to efficient use of the new Chinese remainder theorem for reverse conversion. However, few reverse conversion schemes and modulo-(2q±3) arithmetic operators have been recently reported for ℱ={2q ± 3, 2q ± 1}, where it appears that devising similar reverse conversion schemes for the more useful 5-moduli set ℱ⋃ {2iq} is too challenging that no such moduli set has been yet proposed. Therefore, we propose the arithmetically balanced moduli set 𝒫 = {22q, 2q ± 3, 2q ± 1} and study the corresponding problems of binary to RNS conversion and the reverse, where adder-only solutions (with neither costly read-only-memories nor multipliers) are presented. We state and prove some lemmas and theorems to obtain at the required infinite geometric series to express the multiplicative inverses as power-of-two polynomials. Different groupings of moduli are investigated and more feasible cases are set aside for realization of four reverse converters showing cost/speed trade-off that are evaluated analytically and by synthesis. Both forward and reverse converters are designed and implemented via multi-operand addition realized via fast parallel architectures.