Abstract Interpretation of Floating-Point Computations

Refining Abstract Interpretation-based Approximations with Constraint Solvers

Programs with floating-point computations are tricky to develop because floating-point arithmetic differs from real arithmetic and has many counterintuitive properties. A classical approach to verify such programs consists in estimating the precision of floating-point computations with respect to the same sequence of operations in an idealized semantics of real numbers. Tools like Fluctuat—base...

Utilisation de solveurs de contraintes pour réduire les approximations produites par interprétation abstraite

Programs with floating-point computations are tricky to develop because floating-point arithmetic differs from real arithmetic and has many counterintuitive properties. A classical approach to verify such programs consists in estimating the precision of floatingpoint computations with respect to the same sequence of operations in an idealized semantics of real numbers. Tools like Fluctuat—based...

Asserting the Precision of Floating-Point Computations: A Simple Abstract Interpreter

Static Analysis of Numerical Algorithms

We present a new numerical abstract domain for static analysis of the errors introduced by the approximation by floating-point arithmetic of real numbers computation, by abstract interpretation [3]. This work extends a former domain [4,8], with an implicitly relational domain for the approximation of the floating-point values of variables, based on affine arithmetic [2]. It allows us to analyze...

Static Analysis-Based Validation of Floating-Point Computations

Interpretation : principle α γ Abstraction Class of executions Concrete domain Abstract domain Widening Narrowing Post fixed−point