Numerical optical computing in the residue number system with outer-product lookup tables

An optical outer-product architecture is presented that performs residue arithmetic operations with position-coded lookup tables. The architecture can implement arbitrary integer-valued functions of two independent variables in a single gate delay. The outer-product configuration possesses spatial complexity (a gate count) that grows linearly with the size of the modulus, and therefore with the system's dynamic range, in contrast to traditional residue lookup tables, which have quadratic growth in spatial complexity. The use of linear arrays of sources and modulators leads to power requirements that also grow linearly with the size of the modulus.