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Modular Arithmetic Using Low Order Redundant Bases
May 1997 (vol. 46 no. 5)
pp. 611-616

AbstractN-digit, radix-α bases are proposed for VLSI implementation of redundant arithmetic, mod m, where

$$\Big\langle {\alpha ^N} \Big\rangle _m=\pm 1, \Big\langle {\alpha ^j} \Big\rangle _m\ne \pm 1,$$

for 0 < j < N and m is prime. These bases simplify arithmetic overflow and are well suited to redundant arithmetic. The representations provide competitive, multiplierless T-point Number Theoretic Transforms, mod m, where T | N or T | 2N.

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Index Terms:
Modular arithmetic, redundant number systems, number theoretic transforms, residue and polynomial number systems.
M.g. Parker, M. Benaissa, "Modular Arithmetic Using Low Order Redundant Bases," IEEE Transactions on Computers, vol. 46, no. 5, pp. 611-616, May 1997, doi:10.1109/12.589237
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