Multiple Constant Multiplication: From Target Constants to Optimized Pipelined Adder Graphs

Multiple Constant Multiplication (MCM) is a ubiq-uitous problem for numerous computation-intensive applications. One efficient approach is to replace generic multipliers by multiplierless architectures based on bit-shifts and additions. The adder graphs describing the multiplierless circuits can be optimized according to various metrics. In this paper, we optimize for throughput and improve the state-of-the-art for the design of pipelined adder graphs. In contrast to existing approaches, which pipeline a posteriori or use heuristics, our solution is to optimally solve the pipelined adder graph design problem using Mixed-Integer Linear Programming (MILP). We first model the pipelining and its cost, and then incorporate it into the state-of-the-art ILP model for the MCM design. Fusing the MCM design with pipelining into a single global optimization problem exactly solved by powerful MILP solvers demonstrated clear benefits on numerous benchmarks. Moreover, mathematical modeling allows for an easily extendable tool which can adapt to evolving hardware models/metrics.