Article,
A study of the Behavior of Floating-Point Errors
(2024)
Abstract
The dangers of programs performing floating-point computations are well known. This is due to numerical reliability issues resulting from rounding errors arising during the computations. In general, these round-off errors are neglected because they are small. However, they can be accumulated and propagated and lead to faulty execution and failures. Typically, in critical embedded systems scenario, these faults may cause dramatic damages (eg. failures of Ariane 5 launch and Patriot Rocket mission). The ufp (unit in the first place) and ulp (unit in the last place) functions are used to estimate maximum value of round-off errors. In this paper, the idea consists in studying the behavior of round-off errors, checking their numerical stability using a set of constraints and ensuring that the computation results of round-off errors do not become larger when solving constraints about the ufp and ulp values.