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 time-varying 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 repre-sentative applications show the fixed-point 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—Accuracy evaluation, adaptive filters, fixed-point arithmetic, quantization noises. I