Described herein is a generalized optimal reduction scheme for reducing an array modulo a constant. The constant modulo operation calculates a result for array of bits xi, width n modulo an odd positive integer constant d, (e.g., x[n:0] mod d). Circuitry to perform such operation can be configured to compress the array of bits xi, width n into an array of bits yi width m. The techniques described herein enable the design of optimal circuitry via iterative exploration of all potential reduction strategies that are available given the input constraints.