On error modeling and analysis of approximate adders

Approximate adder design has drawn wide attention as it can achieve good trade-offs between computation accuracy and cost. We observe that all existing approximate adders may produce completely incorrect result with up to 100% relative error. The big errors happen when higher bits have inconsistent views on certain lower carry-ins due to long carry chain. In this paper, we build a theoretical model to efficiently estimate the error characteristics of approximate adders. Furthermore, we present a novel approximate adder design with provable relative error bound by enforcing global carry consistency in long carry chains. Experimental results validate our theoretical model and demonstrate that our design outperforms start-of-the-art approximate adders.