Propagation of Roundoff Errors in Finite Precision Computations: A Semantics Approach
ESOP '02 Proceedings of the 11th European Symposium on Programming Languages and Systems
Asserting the Precision of Floating-Point Computations: A Simple Abstract Interpreter
ESOP '02 Proceedings of the 11th European Symposium on Programming Languages and Systems
Static Analyses of the Precision of Floating-Point Operations
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
A static analyzer for large safety-critical software
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
Higher-Order and Symbolic Computation
Efficient strongly relational polyhedral analysis
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Efficient SAT-based bounded model checking for software verification
Theoretical Computer Science
The Zonotope Abstract Domain Taylor1+
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Floats and Ropes: A Case Study for Formal Numerical Program Verification
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Proving the Correctness of the Implementation of a Control-Command Algorithm
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
Refining the control structure of loops using static analysis
EMSOFT '09 Proceedings of the seventh ACM international conference on Embedded software
Towards an Industrial Use of FLUCTUAT on Safety-Critical Avionics Software
FMICS '09 Proceedings of the 14th International Workshop on Formal Methods for Industrial Critical Systems
Static analysis by policy iteration on relational domains
ESOP'07 Proceedings of the 16th European conference on Programming
Static analysis of the accuracy in control systems: principles and experiments
FMICS'07 Proceedings of the 12th international conference on Formal methods for industrial critical systems
Perturbing numerical calculations for statistical analysis of floating-point program (in)stability
Proceedings of the 19th international symposium on Software testing and analysis
LEMA: towards a language for reliable arithmetic
ACM Communications in Computer Algebra
Checking roundoff errors using counterexample-guided narrowing
Proceedings of the IEEE/ACM international conference on Automated software engineering
Test Case Generation for Adequacy of Floating-point to Fixed-point Conversion
Electronic Notes in Theoretical Computer Science (ENTCS)
Interval slopes as a numerical abstract domain for floating-point variables
SAS'10 Proceedings of the 17th international conference on Static analysis
Static analysis of finite precision computations
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
A logical product approach to zonotope intersection
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Donut domains: efficient non-convex domains for abstract interpretation
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
Numeric bounds analysis with conflict-driven learning
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Acceleration of the abstract fixpoint computation in numerical program analysis
Journal of Symbolic Computation
Under-approximations of computations in real numbers based on generalized affine arithmetic
SAS'07 Proceedings of the 14th international conference on Static Analysis
Semantics-based transformation of arithmetic expressions
SAS'07 Proceedings of the 14th international conference on Static Analysis
Program analysis using symbolic ranges
SAS'07 Proceedings of the 14th international conference on Static Analysis
Refining abstract interpretation based value analysis with constraint programming techniques
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Efficient probabilistic model checking of systems with ranged probabilities
RP'12 Proceedings of the 6th international conference on Reachability Problems
Modular static analysis with zonotopes
SAS'12 Proceedings of the 19th international conference on Static Analysis
Automatic detection of floating-point exceptions
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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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 non trivial numerical computations, that no other abstract domain we know of can analyze with such precise results, such as linear recursive filters of different orders, Newton methods for solving non-linear equations, polynomial iterations, conjugate gradient algorithms.