Implementation of energy-efficient approximate multiplier with guaranteed worst case relative error

Existing design methods for approximate multipliers typically rely on exhaustive simulation to determine the approximation error. However, this approach is not tractable for complex designs. In this paper, a two-dimensional piecewise linear approximation method for multiplication that formally guarantees the maximum error is proposed. Based on this method, a design procedure to implement energy-efficient approximate multipliers is also proposed. Three 32-bit unsigned approximate multipliers with guaranteed maximum errors of 12.5%, 3.13% and 0.78% were realized using the design procedure. The efficiencies of the proposed designs were evaluated by comparing their parameters with that of the exact and state-of-the-art approximate multipliers. The proposed designs deliver up to 91.8% (62.1%) energy saving when compared with that of exact (approximate) multipliers. The effectiveness of the approximate multipliers was also assessed in an image smoothening application.