What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
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
The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations (Software, Environments, and Tools)
Formal Verification of Floating-Point Programs
ARITH '07 Proceedings of the 18th IEEE Symposium on Computer Arithmetic
The pitfalls of verifying floating-point computations
ACM Transactions on Programming Languages and Systems (TOPLAS)
The Zonotope Abstract Domain Taylor1+
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
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 of the accuracy in control systems: principles and experiments
FMICS'07 Proceedings of the 12th international conference on Formal methods for industrial critical systems
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
A logical product approach to zonotope intersection
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Symbolic methods to enhance the precision of numerical abstract domains
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Formal verification of hybrid systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Trustworthy numerical computation in Scala
Proceedings of the 2011 ACM international conference on Object oriented programming systems languages and applications
A generic ellipsoid abstract domain for linear time invariant systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
A dynamic program analysis to find floating-point accuracy problems
Proceedings of the 33rd ACM SIGPLAN conference on Programming Language Design and Implementation
A bit too precise? bounded verification of quantized digital filters
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
An Accurate Join for Zonotopes, Preserving Affine Input/Output Relations
Electronic Notes in Theoretical Computer Science (ENTCS)
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
Mobile robot localization by multiangulation using set inversion
Robotics and Autonomous Systems
Modular static analysis with zonotopes
SAS'12 Proceedings of the 19th international conference on Static Analysis
A new abstract domain for the representation of mathematically equivalent expressions
SAS'12 Proceedings of the 19th international conference on Static Analysis
On-the-fly detection of instability problems in floating-point program execution
Proceedings of the 2013 ACM SIGPLAN international conference on Object oriented programming systems languages & applications
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We define several abstract semantics for the static analysis of finite precision computations, that bound not only the ranges of values taken by numerical variables of a program, but also the difference with the result of the same sequence of operations in an idealized real number semantics. These domains point out with more or less detail (control point, block, function for instance) sources of numerical errors in the program and the way they were propagated by further computations, thus allowing to evaluate not only the rounding error, but also sensitivity to inputs or parameters of the program. We describe two classes of abstractions, a non relational one based on intervals, and a weakly relational one based on parametrized zonotopic abstract domains called affine sets, especially well suited for sensitivity analysis and test generation. These abstract domains are implemented in the Fluctuat static analyzer, and we finally present some experiments.