Novel forward and inverse PRNS converters of reduced computational complexity

This paper introduces a novel computational technique that reduces the computational complexity of forward and inverse polynomial residue number system (PRNS) conversion. By expressing the PRNS conversion procedures as a matrix-by-vector product and by properly exploiting the symmetries of the corresponding transformation matrices, it is found that the computational complexity can be reduced to half, in comparison to the direct conversion computation. In addition, in the case that the moduli are of the form m = 2/sup n/ + 1 and by means of the diminished-1 arithmetic, the complexity of the necessary processing is further reduced.