Input Distribution Aware Library of Approximate Adders Based on Memristor-Aided Logic

Memristor-aided logic (MAGIC) is one of the most popular design styles for implementing Logic-in-Memory (LiM) using memristors. MAGIC-based LiM has been shown to be useful for high throughput applications, as the same design can be mapped to multiple rows of a crossbar. The computations can be performed simultaneously on all these rows on different inputs to achieve high throughput. In recent years, approximate circuits have been extensively explored to obtain benefits in power, performance, and area for traditional CMOS designs. While these approximate circuits produce erroneous outputs, several applications can produce an acceptable quality output even with these approximations. In this work, we propose approximate circuits for MAGIC-based LiM. We have used the Ripple Carry Adder (RCA) architecture and introduced functional approximation to generate the approximate RCAs. We obtained the mapping of these approximate RCAs on the memristor crossbar using the SIMPLER MAGIC tool. We generated the Pareto-optimal designs using Gate Count and Total Cycles as design metrics against Mean Square Error and Mean Absolute Error as error metrics. We generated separate Pareto-optimal designs for three different input data distributions namely uniform, exponential, and normal data distributions.