Rigorous Floating-Point Round-Off Error Analysis in PRECiSA 4.0

Abstract Small round-off errors in safety-critical systems can lead to catastrophic consequences. In this context, determining if the result computed by a floating-point program is accurate enough with respect to its ideal real-number counterpart is essential. This paper presents PRECiSA 4.0, a tool that rigorously estimates the accumulated round-off error of a floating-point program. PRECiSA 4.0 combines static analysis, optimization techniques, and theorem proving to provide a modular approach for computing a provably correct round-off error estimation. PRECiSA 4.0 adds several features to previous versions of the tool that enhance its applicability and performance. These features include support for data collections such as lists, records, and tuples; support for recursion schemas; an updated floating-point formalization that closely characterizes the IEEE-754 standard; an efficient and modular analysis of function calls that improves the performances for large programs; and a new user interface integrated into Visual Studio Code.