Should We Code Differently When Using Approximate Circuits

The design of approximate arithmetic circuits is driven by the trade-off between output quality and reduction in energy, delay and/or area. These approximate arithmetic circuits may violate basic algebraic properties because of the introduction of approximation in their designs for some input combinations. The violation of algebraic properties makes the output of the approximate circuits dependent on the order of the inputs. In this paper, we investigate whether this violation can be used to increase the output quality of applications implemented using approximate circuits. We make the following observations. First, commutative property violation is specific to the design of the approximate circuit. Second, the resulting output error depends on the order of the inputs applied to the approximate circuits. Third, error-resilient image processing applications also tend to show the difference in outputs based on input data order. For instance, in mean filtering application, we observe an average PSNR (SSIM) of 35.91dB (0.955) for X + Y and 27.62dB (0.874) for Y + X. Based on the observations, we propose that prior knowledge of application can be used to reorder the input data to increase output quality.