A signed integer programmable power-of-two scaler for {2n-1, 2n, 2n+1} RNS

Scaling is used for wordlength reduction in many DSP algorithms. Variable scaler provides greater flexibility than fixed scaler and allows for more efficient utilization of the dynamic range. Programmable magnitude scaling is extremely difficult to perform in RNS, let alone scaling of signed integer. To the best of our knowledge, no programmable signed integer scaler in RNS has been reported. What make sign integer scaling challenging is that sign detection is itself a problematic operation in RNS. This paper presents an algorithm that can selectively scale a signed integer in the three moduli set RNS {2ⁿ-1, 2ⁿ, 2ⁿ+1} by a power-of-two factor. The proposed architecture can be deemed as a signed RNS extension of the unsigned integer programmable power-of-two scaler for {2ⁿ-1, 2ⁿ, 2ⁿ+1}. On average, it reduces the area and total power consumption of the unsigned version by 27.4% and 30.3% with an average delay extension of slightly less than 20% to adjust the range of a residue after magnitude scaling.