Probability-Driven Evaluation of Lower-Part Approximation Adders

Parallel prefix adder topologies suffer from carry chains forming critical paths, limiting the performance and therefore the efficiency. We study approximation methods that offload the lower-part of calculation to an approximate unit and shorten the carry chain. We derive their accuracy models using probability theory. These models can replace Monte Carlo simulations. Furthermore, they can reveal better accuracy trade-offs without going through the RTL design, synthesis, and simulation of each unit and approximation level individually. Thus, they can eliminate the required design and simulation time and effort. After analyzing area-wise comparisons at varying number of approximated bits, we show that choosing a design that outperforms the others probabilistically also outperforms them in terms of accuracy, power, and performance trade-offs.