Range estimation of floating-point variables in Simulink models

Fixed-point arithmetic is widely used in embedded applications because it allows to build compact, fast and low-power application-specific integrated circuits designs. Practically, many of them are designed using model-based design tool such as Matlab/Simulink which allow simulations in floating-point representations. From such a high level simulable model, embedded system designers have to size the proper fixed-point representation. Thus, the challenge is to transform floating-point algorithms into numerical equivalent fixed-point programs. As software increases in complexity and both arithmetics do not have the same behaviors, designers need tools to help them in this task. In this article, we present a new statistical method based on Extreme Value Theory to estimate the dynamic range of program variables. We show that this model fits better than Gumbel model to the range estimation in digital signal processing applications both for linear and nonlinear systems. We present several experiments to illustrate the practical use of our approach. We show few simulations are required in order to estimate the bit-width of the bound of the range.