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This book constitutes the proceedings of the 10th International Workshop on Numerical Software Verification, NSV 2017, held in Heidelberg, Germany, in July 2017 - colocated with the International Workshop on Formal Methods for Rigorous Systems Engineering of Cyber-Physical Systems, RISE4CPS 2017, a one-time, invited-only event. The 3 full papers presented together with 3 short papers, 2 keynote abstracts and 4 invited abstracts were carefully reviewed and selected from numerous submissions. The NSV 2017 workshop is dedicated to the development of logical and mathematical techniques for the reasoning about programmability and reliability.

Computer science. --- Software engineering. --- Algorithms. --- Computer logic. --- Mathematical logic. --- Computer simulation. --- Computer Science. --- Logics and Meanings of Programs. --- Software Engineering. --- Algorithm Analysis and Problem Complexity. --- Mathematical Logic and Formal Languages. --- Simulation and Modeling. --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Computer science logic --- Algorism --- Computer software engineering --- Informatics --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Logic, Symbolic and mathematical --- Algebra --- Arithmetic --- Engineering --- Science --- Foundations --- Logic design. --- Computer software. --- Software, Computer --- Computer systems --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Machine theory --- Switching theory --- Computer software --- Verification --- Machine theory. --- Computer Science Logic and Foundations of Programming. --- Formal Languages and Automata Theory. --- Computer Modelling. --- Abstract automata --- Abstract machines --- Automata --- Mathematical machine theory --- Algorithms --- Recursive functions --- Robotics

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Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs. This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation. Describes the notions of specification and weakest precondition computation and their practical useShows how to tackle algorithms that extend beyond the realm of simple floating-point arithmeticIncludes real analysis and a case study about numerical analysis.

Discrete mathematics --- Computer science

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Floating-point arithmetic --- Mathematical models.