58. Enhancing Range Analysis in Software Design Models by Detecting Floating-Point Absorption and Cancellation

Floating-point subtleties are often overlooked by software developers, but they can have considerable impact over critical systems which make extensive manipulations of real numbers. This work presents a method for detecting floating-point absorption and cancellation when performing variable range analysis in design models. Employing this method as early as in the design phase permits cheaper detection and treatment of such floating-point anomalies. Our method works by analyzing sums and subtractions in a model and verifying if, given two variable ranges, there are sub-ranges of them on which absorption and cancellation can occur. We also provide the number of canceled bits for each sub-range in order to permit better assessment of the impact of each detected cancellation. We implemented our method in a range analysis tool that operates over SCADE models: results are presented in an HTML report and cancellations are depicted in graphs. This method can be used for early design analysis or as a basis for more complex, end-to-end numerical precision verification.