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
A static analyzer for large safety-critical software
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
Validation of assembler programs for DSPs: a static analyzer
Proceedings of the 5th ACM SIGPLAN-SIGSOFT workshop on Program analysis for software tools and engineering
Semantics of roundoff error propagation in finite precision calculations
Higher-Order and Symbolic Computation
The pitfalls of verifying floating-point computations
ACM Transactions on Programming Languages and Systems (TOPLAS)
Perturbing numerical calculations for statistical analysis of floating-point program (in)stability
Proceedings of the 19th international symposium on Software testing and analysis
Checking roundoff errors using counterexample-guided narrowing
Proceedings of the IEEE/ACM international conference on Automated software engineering
An overview of semantics for the validation of numerical programs
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Mobile robot localization by multiangulation using set inversion
Robotics and Autonomous Systems
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 introduce a relational static analysis to determine the stability of the numerical errors arising inside a loop in which floating-point computations are carried out. This analysis is based on a stability test for non-linear functions and on a precise semantics for floating-point numbers that computes the propagation of the errors made at each operation. A major advantage of this approach is that higher-order error terms are not neglected. We introduce two algorithms for the analysis. The first one, less complex, only determines the global stability of the loop. The second algorithm determines which particular operation makes a loop unstable. Both algorithms have been implemented and we present some experimental results.