Abstract

Computation in the residue number system allows complex operations to be separated into less complex, carry-free operations that can be processed in parallel. The use of lookup tables is one approach to performing computation in the residue number system. However, the spatial complexity of traditional lookup tables grows quadratically with the modulus and hence the dynamic range. In this paper, we present the results of an effort to build a low-complexity optical processor for performing computations in the residue number system by using outer-product lookup tables. The processor can implement arbitrary integer-valued operations by applying the correct m²-to-m mapping from the lookup table to the output. Complexity and power requirements are shown to grow slowly in comparison to traditional residue lookup tables.

© 1992 Optical Society of America