Many applications are error-resilient, allowing for the introduction of approximations in the calculations, as long as a certain accuracy target is met. Traditionally, fixed-point arithmetic is used to relax accuracy, by optimizing the bit-width. This arithmetic leads to important benefits in terms of delay, power and area. Lately, several hardware approximate operators were invented, seeking the same performance benefits. However, a fair comparison between the usage of this new class of operators and classical fixed-point arithmetic with careful truncation or rounding, has never been performed. In this paper, we first compare approximate and fixed-point arithmetic operators in terms of power, area and delay, as well as in terms of induced error, using many state-of-the-art metrics and by emphasizing the issue of data sizing. To perform this analysis, we developed a design exploration framework, APXPERF, which guarantees that all operators are compared using the same operating conditions. Moreover, operators are compared in several classical real-life applications leveraging relevant metrics. In this paper, we show that considering a large set of parameters, existing approximate adders and multipliers tend to be dominated by truncated or rounded fixed-point ones. For a given accuracy level and when considering the whole computation data-path, fixed-point operators are several orders of magnitude more accurate while spending less energy to execute the application. A conclusion of this study is that the entropy of careful sizing is always lower than approximate operators, since it require significantly less bits to be processed in the data-path and stored. Approximated data therefore always contain on average a greater amount of costly erroneous, useless information.
['Benjamin Barrois', 'Olivier Sentieys', 'Daniel Menard']
The hidden cost of functional approximation against careful data sizing — A case study