Often as the most important arithmetic modules in a processor, adders, multipliers, and dividers determine the performance and energy efficiency of many computing tasks. The demand of higher speed and power efficiency, as well as the feature of error resilience in many applications (e.g., multimedia, recognition, and data analytics), have driven the development of approximate arithmetic design. In this article, a review and classification are presented for the current designs of approximate arithmetic circuits including adders, multipliers, and dividers. A comprehensive and comparative evaluation of their error and circuit characteristics is performed for understanding the features of various designs. By using approximate multipliers and adders, the circuit for an image processing application consumes as little as 47% of the power and 36% of the power-delay product of an accurate design while achieving similar image processing quality. Improvements in delay, power, and area are obtained for the detection of differences in images by using approximate dividers.

Approximate adders have been considered as a potential alternative for error-tolerant applications to trade off some accuracy for gains in other circuit-based metrics, such as power, area and delay. Existing approximate adder designs have shown substantial advantages in improving many of these operational features. However, the error characteristics of the approximate adders still remain an issue that is not very well understood. A simulation-based method requires both programming efforts and a time-consuming execution for evaluating the effect of errors. This method becomes particularly expensive when dealing with various sizes and types of approximate adders. In this paper, a framework based on analytical models is proposed for evaluating the error characteristics of approximate adders. Error features such as the error rate and the mean error distance are obtained using this framework without developing functional models of the approximate adders for time-consuming simulation. As an example, the estimate of peak signal-to-noise ratios (PSNRs) in image processing is considered to show the potential application of the proposed analysis. This analytical framework provides an efficient method to evaluate various designs of approximate adders for meeting different figures of merit in error-tolerant applications.

Approximate circuits have been considered for error-tolerant applications that can tolerate some loss of accuracy with improved performance and energy efficiency. Multipliers are key arithmetic circuits in many such applications such as digital signal processing (DSP). In this paper, a novel approximate multiplier with a lower power consumption and a shorter critical path than traditional multipliers is proposed for high-performance DSP applications. This multiplier leverages a newly-designed approximate adder that limits its carry propagation to the nearest neighbors for fast partial product accumulation. Different levels of accuracy can be achieved through a configurable error recovery by using different numbers of most significant bits (MSBs) for error reduction. The approximate multiplier has a low mean error distance, i.e., most of the errors are not significant in magnitude. Compared to the Wallace multiplier, a 16-bit approximate multiplier implemented in a 28nm CMOS process shows a reduction in delay and power of 20% and up to 69%, respectively. It is shown that by utilizing an appropriate error recovery, the proposed approximate multiplier achieves similar processing accuracy as traditional exact multipliers but with significant improvements in power and performance.