Automated Synthesis of Commutative Approximate Arithmetic Operators

Approximate computing, leveraging the inherent resilience to errors, emerges as a promising strategy for reducing power consumption in digital systems. The primary objective of this paper is to introduce an efficient method based on Cartesian Genetic Programming for designing approximate arithmetic circuits with commutative property. Specifically, this work focuses on the design of 8-bit approximate multipliers and 32-bit approximate adders, both serving as foundational components for hardware accelerators in neural networks. We have identified that while the design of commutative approximate adders poses no issues for evolution, the design of commutative approximate multipliers represents a challenging problem causing the commonly used CGP stuck at highly sub-optimal solutions. In response to this challenge, we propose a novel application-specific mutation operator. This operator significantly enhances the efficiency of the search process, enabling the discovery of solutions that were previously unreachable. The achieved results revealed that imposing the requirement for a commutative property does not substantially compromise the quality-error trade-offs of the obtained approximate circuits, making the resulting Pareto front comparable to that of unconstrained designs.