Affine Arithmetic and Applications to Real-Number Proving Mariano M. Moscato1 , C´esar A. Mu˜ noz2 , and Andrew P. Smith1 1

Source URL: shemesh.larc.nasa.gov

Computing DOIs00607A generalization of p-boxes to affine arithmetic Olivier Bouissou · Eric Goubault · Jean Goubault-Larrecq · Sylvie Putot

Source URL: www.lix.polytechnique.fr

A Logical Product Approach to Zonotope Intersection Khalil Ghorbal, Eric Goubault, Sylvie Putot Laboratory for the Modelling and Analysis of Interacting Systems CEA, LIST, Boˆıte 94, Gif-sur-Yvette, FFrance. fir

Source URL: www.lix.polytechnique.fr

• Geometry
• Affine geometry
• Mathematics
• Space
• Affine arithmetic
• Abstract interpretation
• Affine space
• Substitution
• Affine connection
• Morphism of algebraic varieties

Static Analysis of the Accuracy and Robustness of Finite Precision Implementations Fluctuat Eric Goubault and Sylvie Putot

Source URL: www.lix.polytechnique.fr

• Mathematics
• Affine geometry
• Numerical analysis
• Software
• Theoretical computer science
• Abstract interpretation
• Fluctuat
• Affine arithmetic
• Affine space
• Integral
• Rounding
• Matrix

Under-approximations of computations in real numbers based on generalized affine arithmetic Eric Goubault and Sylvie Putot CEA-LIST Laboratory for ModEling and Analysis of Systems in Interaction, 91191 Gif-sur-Yvette Ced

Source URL: www.lix.polytechnique.fr

• Mathematics
• Mathematical analysis
• Numerical analysis
• Geometry
• Functions and mappings
• Affine geometry
• Affine arithmetic
• Interval arithmetic
• Quasigroup
• Abstract interpretation
• Logarithm
• Derivative

Modular Static Analysis with Zonotopes Eric Goubault, Sylvie Putot, and Franck V´edrine CEA Saclay Nano-INNOV, CEA LIST, Laboratory for the Modelling and Analysis of Interacting Systems, Point Courrier 174, 91191 Gif su

Source URL: www.lix.polytechnique.fr

• Mathematics
• Affine geometry
• Affine arithmetic
• Affine space
• Lambda calculus
• Abstract interpretation
• Function

The Zonotope Abstract Domain Taylor1+ Khalil Ghorbal, Eric Goubault, and Sylvie Putot CEA, LIST, Modelisation and Analysis of Systems in Interaction, FGif-sur-Yvette Cedex, France,

Source URL: www.lix.polytechnique.fr

• Numerical analysis
• Affine geometry
• Operations research
• Affine arithmetic
• Abstract interpretation
• Semidefinite programming
• Polyhedron
• Interval arithmetic
• Fixed point

C:/rump/Publikationen/Rump_Veroeff/Affine/revised/AffineRevised.dvi

Source URL: www.ti3.tu-harburg.de

• Numerical analysis
• Limit of a function
• Affine arithmetic
• Taylor series
• Interval arithmetic
• Error function
• Affine connection
• Approximation theory

Static Analysis of Finite Precision Computations Eric Goubault and Sylvie Putot CEA LIST, Laboratory for the Modelling and Analysis of Interacting Systems, Point courrier 94, Gif-sur-Yvette, FFrance, Firstname.Las

Source URL: www.lix.polytechnique.fr

• Computer arithmetic
• Abstract interpretation
• Interval arithmetic
• Rounding
• Floating point
• Affine arithmetic
• Interval
• Function
• Limit of a function
• NaN
• Fixed-point arithmetic
• Machine epsilon

Static Analysis of the Accuracy in Control Systems : Principles and Experiments Eric Goubault1 , Sylvie Putot1 , Philippe Baufreton2 , and Jean Gassino3 1 CEA/LISTGif-sur-Yvette, {eric.goubault,sylvie.putot}@cea.

Source URL: www.lix.polytechnique.fr

• Computer arithmetic
• Abstract interpretation
• Floating point
• Interval arithmetic
• Fluctuat
• Rounding
• Infinite loop
• Affine arithmetic
• Lookup table
• Recursion
• Division algorithm
• Fixed-point arithmetic