  Digital System Research has pioneered the mathematics and design for a new
class of computing machine using residue numbers. Unlike prior art, the new
breakthrough provides methods and apparatus for general purpose computation
using several new residue based fractional representations. The result is that
fractional arithmetic may be performed without carry. Additionally, fractional
operations such as addition, subtraction and multiplication of a fraction by an
integer occur in a single clock period, regardless of word size. Fractional
multiplication is of the order O(p), where p equals the number of residues.
More significantly, complex operations, such as sum of products, may be
performed in an extended format, where fractional products are performed and
summed using single clock instructions, regardless of word width, and where a
normalization operation with an execution time of the order O(p) is performed
as a final step.

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