Digital Optics for Numerical Computing: The Residue Number System for Numerical Optical Computing

The use of Residue Number System RNS in performing high accuracy numerical computing with digital optics is investigated. The analysis is focused on the position coded residue representation and the Look Up Table LUT approach to arithmetic operations. Two approaches to reducing the total number of LUT entries the spatial complexity proposed by Boeing Aerospace Corp. and Westinghouse are studied. Analytical expressions for the spatial complexity, time complexity, and element complexity as a function of the modulus are derived for the two approaches in performing the standard operations of multiplication, addition and for the multiply-accumulate unit. The report thus provides a hardware-independent method of studying the trade-offs between these two major approaches to RNS optical computing. Hardware options for optical implementations of interconnects and nonlinear switching elements are outlined. The intimate relation between the algorithms, architectures and the hardware and their combined impact on the system performance is outlined suggesting directions for future work.