Optimal Common Sub-Expression Elimination Algorithm of Multiple Constant Multiplications with a Logic Depth Constraint

In the context of multiple constant multiplication (MCM) design, we propose a novel common sub-expression elimination (CSE) algorithm that models the optimal synthesis of coefficients into a 0-1 mixedinteger linear programming (MILP) problem with a user-defined generic logic depth constraint. We also propose an efficient solution space, which combines all minimal signed digit (MSD) representations and the shifted sum (difference) of coefficients. In the examples we demonstrate, the combination of the proposed algorithm and solution space gives a better solution comparing to existing algorithms. key words: common sub-expression sharing, multiple constant multiplications, mixed-integer linear programming