On the simulation of residue number systems

It is sometimes difficult to simulate on general purpose computers the performance of digital systems that use residue number systems. This paper demonstrates a new technique that makes effective use of a Fast Fourier Transform (FFT) to simulate the basic arithmetic operations required by such number systems. An algorithm for performing such operations which involves the FFT, standard programming techniques and normal arithmetic computations is presented. It is exemplified by consider operations in finite fields. The FFT size is proportional to the exponent of the size of the residue system. Thus there is a logarithmetic relationship between the number system´s size and the transform length. Favarable comparisons are given between the FFT mechanization of this approach and one employing a more conventional assembly language implementation.