Static analysis of linear congruence equalities among variables of a program
TAPSOFT '91 Proceedings of the international joint conference on theory and practice of software development on Colloquium on trees in algebra and programming (CAAP '91): vol 1
Expansion and estimation of the range of nonlinear functions
Mathematics of Computation
Implementation of automatic differentiation tools
PEPM '02 Proceedings of the 2002 ACM SIGPLAN workshop on Partial evaluation and semantics-based program manipulation
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Improving the Results of Static Analyses Programs by Local Decreasing Iteration
Proceedings of the 12th Conference on Foundations of Software Technology and Theoretical Computer Science
Static Analyses of the Precision of Floating-Point Operations
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
Higher-Order and Symbolic Computation
Semantics of roundoff error propagation in finite precision calculations
Higher-Order and Symbolic Computation
The octahedron abstract domain
Science of Computer Programming
Pentagons: a weakly relational abstract domain for the efficient validation of array accesses
Proceedings of the 2008 ACM symposium on Applied computing
A Sound Floating-Point Polyhedra Abstract Domain
APLAS '08 Proceedings of the 6th Asian Symposium on Programming Languages and Systems
SubPolyhedra: A (More) Scalable Approach to Infer Linear Inequalities
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
Abstract Simulation: A Static Analysis of Simulink Models
ICESS '09 Proceedings of the 2009 International Conference on Embedded Software and Systems
The Zonotope Abstract Domain Taylor1+
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Interval Polyhedra: An Abstract Domain to Infer Interval Linear Relationships
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
Two variables per linear inequality as an abstract domain
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
An abstract domain extending difference-bound matrices with disequality constraints
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Handbook of Floating-Point Arithmetic
Handbook of Floating-Point Arithmetic
Static analysis of numerical algorithms
SAS'06 Proceedings of the 13th international conference on Static Analysis
An abstract domain to discover interval linear equalities
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Efficient strongly relational polyhedral analysis
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Compositional analysis of floating-point linear numerical filters
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
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The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floatingpoint arithmetic, which is well-known to only provide approximated results, is omnipresent in this activity. In order to validate the behaviors of numerical simulations using abstract interpretation-based static analysis, we present, theoretically and with experiments, a new partially relational abstract domain dedicated to floating-point variables. It comes from interval expansion of non-linear functions using slopes and it is able to mimic all the behaviors of the floating-point arithmetic. Hence it is adapted to prove the absence of run-time errors or to analyze the numerical precision of embedded control systems.