Substitute-and-simplify: A unified design paradigm for approximate and quality configurable circuits

Many applications are inherently resilient to inexactness or approximations in their underlying computations. Approximate circuit design is an emerging paradigm that exploits this inherent resilience to realize hardware implementations that are highly efficient in energy or performance. In this work, we propose Substitute-And-SIMplIfy (SASIMI), a new systematic approach to the design and synthesis of approximate circuits. The key insight behind SASIMI is to identify signal pairs in the circuit that assume the same value with high probability, and substitute one for the other. While these substitutions introduce functional approximations, if performed judiciously, they result in some logic to be eliminated from the circuit while also enabling downsizing of gates on critical paths (simplification), resulting in significant power savings. We propose an automatic synthesis framework that performs substitution and simplification iteratively, while ensuring that a user-specified quality constraint is satisfied. We extend the proposed framework to perform automatic synthesis of quality configurable circuits that can dynamically operate at different accuracy levels depending on application requirements. We used SASIMI to automatically synthesize approximate and quality configurable implementations of a wide range of arithmetic units (Adders, Multipliers, MAC), complex data paths (SAD, FFT butterfly, Euclidean distance) and ISCAS85 benchmarks, using various error metrics such as error rate and average error magnitude. The synthesized approximate circuits demonstrate power improvements of 10%–28% for tight error constraints, and 30%–60% for relaxed error constraints. The quality configurable circuits obtain between 14%–40% improvement in energy in the approximate mode, while incurring no energy overheads in the accurate mode.