Residue number system scaling schemes

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, bse 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.

[1]  Fred J. Taylor,et al.  Efficient scaling in the residue number system , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[2]  Fred J. Taylor,et al.  An Autoscale Residue Multiplier , 1982, IEEE Transactions on Computers.

[3]  Maria Cristina Pinotti,et al.  Fast base extension and precise scaling in RNS for look-up table implementations , 1995, IEEE Trans. Signal Process..

[4]  Ramdas Kumaresan,et al.  A fast and accurate RNS scaling technique for high speed signal processing , 1989, IEEE Trans. Acoust. Speech Signal Process..

[5]  Richard I. Tanaka,et al.  Residue arithmetic and its applications to computer technology , 1967 .

[6]  Graham A. Jullien,et al.  Residue Number Scaling and Other Operations Using ROM Arrays , 1978, IEEE Transactions on Computers.

[7]  Zenon D. Ulman,et al.  Highly parallel, fast scaling of numbers in nonredundant residue arithmetic , 1998, IEEE Trans. Signal Process..

[8]  Neil Burgess Scaling an RNS number using the core function , 2003, Proceedings 2003 16th IEEE Symposium on Computer Arithmetic.