What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
A stochastic arithmetic for reliable scientific computation
Mathematics and Computers in Simulation
Handling floating-point exceptions in numeric programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
Rigorous error analysis of numerical algorithms via symbolic computations
Journal of Symbolic Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Toward Correctly Rounded Transcendentals
IEEE Transactions on Computers
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Implementation of automatic differentiation tools
PEPM '02 Proceedings of the 2002 ACM SIGPLAN workshop on Partial evaluation and semantics-based program manipulation
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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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 Analysis of the Numerical Stability of Loops
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Solving Constraints over Floating-Point Numbers
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Representable Correcting Terms for Possibly Underflowing Floating Point Operations
ARITH '03 Proceedings of the 16th IEEE Symposium on Computer Arithmetic (ARITH-16'03)
The pitfalls of verifying floating-point computations
ACM Transactions on Programming Languages and Systems (TOPLAS)
Program transformation for numerical precision
Proceedings of the 2009 ACM SIGPLAN workshop on Partial evaluation and program manipulation
Enhancing the implementation of mathematical formulas for fixed-point and floating-point arithmetics
Formal Methods in System Design
Towards program optimization through automated analysis of numerical precision
Proceedings of the 8th annual IEEE/ACM international symposium on Code generation and optimization
Accuracy versus time: a case study with summation algorithms
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Checking roundoff errors using counterexample-guided narrowing
Proceedings of the IEEE/ACM international conference on Automated software engineering
Interval slopes as a numerical abstract domain for floating-point variables
SAS'10 Proceedings of the 17th international conference on Static analysis
Semantics-based transformation of arithmetic expressions
SAS'07 Proceedings of the 14th 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
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We introduce a concrete semantics for floating-point operations which describes the propagation of roundoff errors throughout a calculation. This semantics is used to assert the correctness of a static analysis which can be straightforwardly derived from it.In our model, every elementary operation introduces a new first order error term, which is later propagated and combined with other error terms, yielding higher order error terms. The semantics is parameterized by the maximal order of error to be examined and verifies whether higher order errors actually are negligible. We consider also coarser semantics computing the contribution, to the final error, of the errors due to some intermediate computations. As a result, we obtain a family of semantics and we show that the less precise ones are abstractions of the more precise ones.