Error Metric Computation for Approximate Combinational Circuits

Abstract

In this chapter, the different algorithms to symbolically compute the error metrics of approximate combinational circuits are explained. This essentially forms the basis for the formal verification of such circuits. The error metrics introduced in the previous chapter (see Sect. 2.5) are used to quantify the approximations in the system. In the past, techniques based on statistical analysis have been proposed for the error characterization of the approximation circuits. Approaches such as Chippa et al. (Design automation conference, pp 1–9, 2013), Gupta et al. (International symposium on low power electronics and design, pp 409–414, 2011), Venkatesan et al. (International Conference on Computer Aided Design, pp 667–673, 2011) are examples. However, statistical techniques typically depend on a probabilistic error model, input vectors, and a probabilistic algorithm, which are application dependent, varying over time, and difficult to predict at the design stage. Further, a complete set of input vectors that can represent all the corner cases of the circuit operation is clearly impractical. Hence, such techniques cannot guarantee a reliable circuit operation under approximations. Since by design, approximation circuits can produce errors, it is imperative to ensure the bounds of the errors committed. Therefore, error analysis with formal guarantees is a must to the design of an approximate computing hardware. In this book, we dedicate two chapters, the current one and the next chapter, to this analysis.