Error-aware Design Procedure to Implement Energy-efficient Approximate Squaring Hardware

Abstract

Background: In recent years, there has been a high demand for executing digital signal processing and machine learning applications on energy-constrained devices. Squaring is a vital arithmetic operation used in such applications. Hence, improving the energy efficiency of squaring is crucial. Objective: In this paper, a novel approximation method based on piecewise linear segmentation of the square function is proposed. Method: Two-segment, four-segment and eight-segment accurate and energy-efficient 32-bit approximate designs for squaring were implemented using this method. The proposed 2-segment approximate squaring hardware showed 12.5% maximum relative error and delivered up to 55.6% energy saving when compared with state-of-the-art approximate multipliers used for squaring. Result: The proposed 4-segment hardware achieved a maximum relative error of 3.13% with up to 46.5% energy saving. Conclusion: The proposed 8-segment design emerged as the most accurate squaring hardware with a maximum relative error of 0.78%. The comparison also revealed that the 8-segment design is the most efficient design in terms of error-area-delay-power product.