LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
An axiomatic basis for computer programming
Communications of the ACM
Pracniques: further remarks on reducing truncation errors
Communications of the ACM
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Trading Off Parallelism and Numerical Stability
Trading Off Parallelism and Numerical Stability
Assisted verification of elementary functions using Gappa
Proceedings of the 2006 ACM symposium on Applied computing
PetaBricks: a language and compiler for algorithmic choice
Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation
Combining Coq and Gappa for Certifying Floating-Point Programs
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Automatic algorithm configuration based on local search
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
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
Towards program optimization through automated analysis of numerical precision
Proceedings of the 8th annual IEEE/ACM international symposium on Code generation and optimization
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Finite precision bit-width allocation using SAT-modulo theory
Proceedings of the Conference on Design, Automation and Test in Europe
CORAL: solving complex constraints for symbolic pathfinder
NFM'11 Proceedings of the Third international conference on NASA Formal methods
Trustworthy numerical computation in Scala
Proceedings of the 2011 ACM international conference on Object oriented programming systems languages and applications
Flocq: A Unified Library for Proving Floating-Point Algorithms in Coq
ARITH '11 Proceedings of the 2011 IEEE 20th Symposium on Computer Arithmetic
A dynamic program analysis to find floating-point accuracy problems
Proceedings of the 33rd ACM SIGPLAN conference on Programming Language Design and Implementation
Parametric flows: automated behavior equivalencing for symbolic analysis of races in CUDA programs
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Symbolic execution for software testing: three decades later
Communications of the ACM
Automatic detection of floating-point exceptions
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Dynamic floating-point cancellation detection
Parallel Computing
Automatically adapting programs for mixed-precision floating-point computation
Proceedings of the 27th international ACM conference on International conference on supercomputing
Numerical Reproducibility and Accuracy at ExaScale
ARITH '13 Proceedings of the 2013 IEEE 21st Symposium on Computer Arithmetic
Precimonious: tuning assistant for floating-point precision
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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Tools for floating-point error estimation are fundamental to program understanding and optimization. In this paper, we focus on tools for determining the input settings to a floating point routine that maximizes its result error. Such tools can help support activities such as precision allocation, performance optimization, and auto-tuning. We benchmark current abstraction-based precision analysis methods, and show that they often do not work at scale, or generate highly pessimistic error estimates, often caused by non-linear operators or complex input constraints that define the set of legal inputs. We show that while concrete-testing-based error estimation methods based on maintaining shadow values at higher precision can search out higher error-inducing inputs, suit able heuristic search guidance is key to finding higher errors. We develop a heuristic search algorithm called Binary Guided Random Testing (BGRT). In 45 of the 48 total benchmarks, including many real-world routines, BGRT returns higher guaranteed errors. We also evaluate BGRT against two other heuristic search methods called ILS and PSO, obtaining better results.