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On Modulus Replication for Residue Arithmetic Computations of Complex Inner Products
August 1990 (vol. 39 no. 8)
pp. 1065-1076

A technique is presented for coding weighted magnitude components (e.g. bits) of numbers directly into polynomial residue rings, such that repeated use may be made of the same set of moduli to effectively increase the dynamic range of the computation. This effectively limits the requirement for large sets of relatively prime moduli, For practical computations over quadratic residue rings, at least 6-bit moduli have to be considered. It is shown that 5-bit moduli can be effectively used for large dynamic range computations.

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Index Terms:
modulus replication; residue arithmetic computations; complex inner products; coding; weighted magnitude components; bits; polynomial residue rings; quadratic residue rings; 6-bit moduli; 5-bit moduli; dynamic range computations; decoding; digital arithmetic; number theory.
N.M. Wigley, G.A. Jullien, "On Modulus Replication for Residue Arithmetic Computations of Complex Inner Products," IEEE Transactions on Computers, vol. 39, no. 8, pp. 1065-1076, Aug. 1990, doi:10.1109/12.57045
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