Abstract

We describe algorithms for parallel matrix and vector manipulation using a novel, all-optical arithmetic and logic unit (ALU). The ALU permits repeated parallel Boolean operations on an N × N matrix. Control of the ALU is by means of an optical control unit that has its microcontrol store in a holographic ROM. The ALU includes several storage registers for use as accumulators and for storage of operands and results, and it uses holographic interconnects to accomplish several special purpose arithmetic and logical shifting operations. The algorithms to be presented include one for Boolean matrix multiplication that allows the multiplication of two N × N matrices in N machine clock cycles, a process that is O(N³). We also present an algorithm for performing arithmetic addition of N pairs of N digit integers in N + 3 machine clock cycles. The ALU can be programmed to perform arbitrary matrix and vector operations.

© 1992 Optical Society of America