Probabilistic Error Analysis of Approximate Recursive Multipliers - 2017


Approximate multipliers are gaining importance in energy-economical computing and require careful error analysis. In this paper, we tend to gift the error chance analysis for recursive approximate multipliers with approximate partial product. Since these multipliers are created from smaller approximate multiplier building blocks, we tend to propose to derive the error likelihood in an arbitrary bit-width multiplier from the probabilistic model of the essential building block and therefore the probability distributions of inputs. The analysis relies on common features of recursive multipliers identified by fastidiously learning the behavioral model of state-of-the-art styles. By building additional upon the analysis, Likelihood Mass Function (PMF) of error is computed by individually considering all potential error cases and their inter-dependencies. We any discuss the generalizations for approximate adder trees, signed multipliers, squarers and constant multipliers. The proposed analysis is validated by applying it to many state-of-the-art approximate multipliers and comparing with corresponding simulation results. The results show that the proposed analysis serves as a good tool for predicting, evaluating and comparing the accuracy of various multipliers. Results show that for the bulk of the recursive multipliers, we have a tendency to get accurate error performance analysis. We also predict the multipliers' performance in a picture processing application to demonstrate its practical significance.

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