Although multiplication and addition can be very efficiently implemented in a Residue Number System (RNS), scaling (division by a constant) is much more computationally complex. This limitation has prevented wider adoption of RNS. In this paper, different RNS scaling schemes are surveyed and compared. It is found that scaling in RNS has been performed with the aid of conversions to and from RNS, base extensions between modulus sets, and redundant RNS channels. Recent advances in RNS scaling theory have reduced the overhead of such measures but RNS scaling still falls short of the ideal: a simple operation performed entirely within the RNS channels.
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