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Static Analysis on Floating-Point Programs Dealing with Division Operations

MG Thushara, K. Somasundaram
2019 International Journal of Advanced Computer Science and Applications  
Given a certain accuracy for the inputs of a program, the static analysis computes a safe approximation of the accuracy on the outputs.  ...  Floating point values disposes a large dynamic range. But the main pitfall is the inaccuracies that occur with floating point computations.  ...  Literature Reviews FLUCTUAT [9] is a static analyzer for analysing the errors generated from approximations of floating-point arithmetic operations on real numbers.  ... 
doi:10.14569/ijacsa.2019.0101058 fatcat:fzpix3gc5rf6jeu6fga2ypp3mi

Apron: A Library of Numerical Abstract Domains for Static Analysis [chapter]

Bertrand Jeannet, Antoine Miné
2009 Lecture Notes in Computer Science  
This article describes Apron, a freely available library dedicated to the static analysis of the numerical variables of programs by abstract interpretation.  ...  This work is supported by the INRIA project-team Abstraction common to the CNRS and theÉcole Normale Supérieure, and the ANR project ASOPT.  ...  to build many kinds of static analyses.  ... 
doi:10.1007/978-3-642-02658-4_52 fatcat:7sak2skdenatjm6jp733jji6wi

Experimental Assessment of Astrée on Safety-Critical Avionics Software [chapter]

Jean Souyris, David Delmas
2007 Lecture Notes in Computer Science  
When it analyses a program of the class for which it is specialised, Astrée is far more precise than general purpose static analysers.  ...  undefined behaviours (e.g., floating-point division by zero), no violation of the programming guidelines (e.g., arithmetic operators  ...  To avoid this kind of loss of precision, Astrée contains an Abstract domain called the "Boolean tree domain". Floating-point calculus.  ... 
doi:10.1007/978-3-540-75101-4_45 fatcat:2dazyzxedfhgzjwlgn4mon3sdi

Checking Compatibility of Bit Sizes in Floating Point Comparison Operations

Manuel Fähndrich, Francesco Logozzo
2012 Electronical Notes in Theoretical Computer Science  
We motivate, define and design a simple static analysis to check that comparisons of floating point values use compatible bit widths and thus compatible precision ranges.  ...  Precision mismatches arise due to the difference in bit widths of processor internal floating point registers (typically 80 or 64 bits) and their corresponding widths when stored in memory (64 or 32 bits  ...  For instance [4, 6, 5] present static analyses to spot the source of imprecision in floating point computa-tions.  ... 
doi:10.1016/j.entcs.2012.10.004 fatcat:b2a6al3hrjgrdit74ixdfv3woa

Towards an Industrial Use of FLUCTUAT on Safety-Critical Avionics Software [chapter]

David Delmas, Eric Goubault, Sylvie Putot, Jean Souyris, Karim Tekkal, Franck Védrine
2009 Lecture Notes in Computer Science  
Most modern safety-critical control programs, such as those embedded in fly-by-wire control systems, perform a lot of floating-point computations.  ...  FLUCTUAT is a static analyzer developed by CEA-LIST for studying the propagation of rounding errors in C programs.  ...  Static analyses may also yield infinite or abnormally large ranges or errors on output variables (the analyzer points to the main sources of errors).  ... 
doi:10.1007/978-3-642-04570-7_6 fatcat:px3rge46mrf47iemxvngyu5fn4

FORWARD AND BACKWARD STATIC ANALYSIS FOR CRITICAL NUMERICAL ACCURACY IN FLOATING POINT PROGRAMS

Somasundaram Kanagasabapathi, MG Thushara
2020 Computer Science  
Weaddress the problem of determining the minimal accuracy on the inputs and on the intermediary results of a program containing foating-point computations in order to ensure a desired accuracy on the outputs  ...  The main approach is to combine a forward and a backward static analysis, done by abstract interpretation.  ...  The IEEE754 Standard defines the semantics of the elementary operations by: x p,r y = • p,r (x * y) where p,r denotes floating-point operations (such as +, −, × or ÷) computed using the rounding mode r  ... 
doi:10.7494/csci.2020.21.2.3421 fatcat:5taz43nqgbdz7ialwvcihqcmi4

The pitfalls of verifying floating-point computations

David Monniaux
2008 ACM Transactions on Programming Languages and Systems  
Current critical systems commonly use a lot of floating-point computations, and thus the testing or static analysis of programs containing floating-point operators has become a priority.  ...  However, correctly defining the semantics of common implementations of floating-point is tricky, because semantics may change with many factors beyond source-code level, such as choices made by compilers  ...  Acknowledgements We thank Patrick Cousot, Pascal Cuoq, Jérôme Feret, David Madore, Antoine Miné and the anonymous referees for their helpful comments.  ... 
doi:10.1145/1353445.1353446 fatcat:nsle4apatrg7tcsiseeyz5c42i

Unboxed Compilation of Floating Point Arithmetic in a Dynamically Typed Language Environment [chapter]

Tobias Lindahl, Konstantinos Sagonas
2003 Lecture Notes in Computer Science  
In the context of the dynamically typed concurrent functional programming language ERLANG, we describe a simple static analysis for identifying variables containing floating point numbers, how this information  ...  of strongly typed strict functional languages on floating point intensive programs.  ...  Sincere thanks to Björn Gustavsson of the Erlang/OTP team for incorporating the floating point type analysis in the BEAM compiler and for sending us the Wings benchmarks.  ... 
doi:10.1007/3-540-44854-3_9 fatcat:jpivfivgzrbvrbbpiyitkpofaa

Daisy - Framework for Analysis and Optimization of Numerical Programs (Tool Paper) [chapter]

Eva Darulova, Anastasiia Izycheva, Fariha Nasir, Fabian Ritter, Heiko Becker, Robert Bastian
2018 Lecture Notes in Computer Science  
This paper presents a new framework, called Daisy, which provides in a single tool the main building blocks for accuracy analysis of floating-point and fixed-point computations which have emerged from  ...  Automated techniques for analysis and optimization of finite-precision computations have recently garnered significant interest. Most of these were, however, developed independently.  ...  Static analyses usually use this abstraction of floating-point arithmetic, as bit-precise reasoning does not scale, and furthermore is unsuitable for computing roundoff errors w.r.t. continuous real-valued  ... 
doi:10.1007/978-3-319-89960-2_15 fatcat:ktavggsosfh5zihqco7rtcolou

Refining Abstract Interpretation Based Value Analysis with Constraint Programming Techniques [chapter]

Olivier Ponsini, Claude Michel, Michel Rueher
2012 Lecture Notes in Computer Science  
precise than Fluctuat, a state-of-the-art static analyser.  ...  However, real and floating-point computation models are different: for the same sequence of operations, floating-point numbers do not behave identically to real numbers.  ...  The authors gratefully acknowledge Sylvie Putot,Éric Goubault and Franck Védrine for their advice and help on using Fluctuat.  ... 
doi:10.1007/978-3-642-33558-7_43 fatcat:e2l2xakg4vf2xj422fzz426lpi

FPU-Supported Running Error Analysis

T. Zahradnický, R. Lórencz
2010 Acta Polytechnica  
One of such a-posteriori analysis – running error analysis – uses expressions consisting of two parts; one generates the error and the other propagates input errors to the output.  ...  A-posteriori forward rounding error analyses tend to give sharper error estimates than a-priori ones, as they use actual data quantities.  ...  Definition 1 Let F t ⊂ Q be a binary floating point set with a precision of t, where Q denotes the rational number set.  ... 
doaj:6bb9b0cf88f04c62918d1c958a16a798 fatcat:scdv3xwbbbdexoqgrmel4xnyv4

Automatically adapting programs for mixed-precision floating-point computation

Michael O. Lam, Jeffrey K. Hollingsworth, Bronis R. de Supinski, Matthew P. Legendre
2013 Proceedings of the 27th international ACM conference on International conference on supercomputing - ICS '13  
As scientific computation continues to scale, efficient use of floating-point arithmetic processors is critical.  ...  This framework allows developers to explore mixed-precision configurations without modifying their source code, and it enables automatic analysis of floating-point precision.  ...  our use of the SuperLU library.  ... 
doi:10.1145/2464996.2465018 dblp:conf/ics/LamHSL13 fatcat:n4rrmzs4hjdxzio4wkjg6r23ci

Numerical program analysis and testing

Zheng Gao
2014 Proceedings of the 22nd ACM SIGSOFT International Symposium on Foundations of Software Engineering - FSE 2014  
By assisting developers in the production of numerical software, it improves the quality and productivity of software development.  ...  The research depends on numerical analysis and lies in the intersection of software engineering and program analysis.  ...  Goubault first applied affine arithmetic to abstract interpretation in 2001 [12] , intending to statically analysing the precision of numerical values with acceptable accuracy.  ... 
doi:10.1145/2635868.2666603 dblp:conf/sigsoft/Gao14 fatcat:kga2xtkwvvfz7iipn2u2r5medi

Verifying floating-point programs with constraint programming and abstract interpretation techniques

Olivier Ponsini, Claude Michel, Michel Rueher
2014 Automated Software Engineering : An International Journal  
This hybrid approach benefits of the strong points of abstract interpretation and constraint programming techniques, and thus, it is more effective than static analysers and constraint solvers, when used  ...  We compared the efficiency of the system we developed-named RAICP-with state-of-the-art static analyzers: RAICP produces substantially more precise approximations and is able to check program properties  ...  Acknowledgements The authors gratefully acknowledge Sylvie Putot,Éric Goubault and Franck Védrine for their advice and help on using FLUCTUAT.  ... 
doi:10.1007/s10515-014-0154-2 fatcat:5jp5yqpswjd3xipkxnfyev33be

Towards program optimization through automated analysis of numerical precision

Michael D. Linderman, Matthew Ho, David L. Dill, Teresa H. Meng, Garry P. Nolan
2010 Proceedings of the 8th annual IEEE/ ACM international symposium on Code generation and optimization - CGO '10  
., GPUs, there can be such a large performance difference that using reduced precision is effectively a requirement. The tradeoff is that the accuracy of the computation will be compromised.  ...  We present several case study applications that demonstrate the effectiveness of these techniques and the performance benefits that can be achieved with rigorous precision analysis.  ...  In addition we would like to thank James Balfour, and the anonymous reviewers whose valuable feedback has helped the authors greatly improve the quality of this paper.  ... 
doi:10.1145/1772954.1772987 pmid:28804690 pmcid:PMC5552069 dblp:conf/cgo/LindermanHDMN10 fatcat:zuncavs23vgfpkeypbs7h2diru
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