Implementing Exact Calculations in Hardware

A technique for performing exact calculations it discussed. The technique uses single-modulus P arithmetic to perform calculations over the finite field of integers and the finite ring of integers. It is shown that the arithmetic operations modulo P (which obviously can be impleinented in microprocessor configurations, VLSI, and/or software) can easily be extended from the range of values of the finite field of integers, modulo P, to the finite ring of integers, modulo pN where N is afny positive integer. This technique can be used for exact calculations over the rational numbers as well as complex numbers. Examples, block diagrams, And processor arrays are presented illustrating the simplicity of these operations.