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.
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