A low-cost approach for determining the impact of Functional Approximation

Approximate Computing (AxC) trades off between the level of accuracy required by the user and the actual precision provided by the computing system to achieve several optimizations such as performance improvement, energy, and area reduction etc.. Several AxC techniques have been proposed so far in the literature. They work at different abstraction level and propose both hardware and software implementations. The common issue of all existing approaches is the lack of a methodology to estimate the impact of a given AxC technique on the application-level accuracy. In this paper, we propose a probabilistic approach to predict the relation between component-level functional approximation and application-level accuracy. Experimental results on a set of benchmark application show that the proposed approach is able to estimate the approximation error with good accuracy and very low computation time

Analytical approach for numerical accuracy estimation of fixed-point systems based on smooth operations

Abstract—In embedded systems using fixed-point arithmetic, converting applications into fixed-point representations requires a fast and efficient accuracy evaluation. This paper presents a new analytical approach to determine an estimation of the numerical accuracy of a fixed-point system, which is accurate and valid for all systems formulated with smooth operations (e.g. additions, subtractions, multiplications and divisions). The mathematical expression of the system output noise power is determined using matrices to obtain more compact expressions. The proposed approach is based on the determination of the timevarying impulse-response of the system. To speedup computation of the expressions, the impulse response is modelled using a linear prediction approach. The approach is illustrated in the general case of time-varying recursive systems by the Least Mean Square (LMS) algorithm example. Experiments on various and representative applications show the fixedpoint accuracy estimation quality of the proposed approach. Moreover, the approach using the linear-prediction approximation is very fast even for recursive systems. A significant speed-up compared to the best known accuracy evaluation approaches is measured even for the most complex benchmarks. Index Terms—Fixed-point arithmetic, quantization noises, adaptive filters, accuracy evaluation I