Static analyses of floating-point operations (2001)  (Make Corrections)  
Eric Goubault
Lecture Notes in Computer Science

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Abstract: Computers manipulate approximations of real numbers, called floating-point numbers. The calculations they make are accurate enough for most applications. Unfortunately, in some (catastrophic) situations, the floating-point operations lose so much precision that they quickly become irrelevant. In this article, we review some of the problems one can encounter, focussing on the IEEE754-1985 norm. We give a (sketch of a) semantics of its basic operations then abstract them (in the sense of abstract ... (Update)

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BibTeX entry:   (Update)

@article{ goubault01static,
    author = "Eric Goubault",
    title = "Static Analyses of the Precision of Floating-Point Operations",
    journal = "Lecture Notes in Computer Science",
    volume = "2126",
    pages = "234--??",
    year = "2001",
    url = "citeseer.nj.nec.com/goubault01static.html" }
Citations (may not include all citations):
1568   The Art of Computer Programming (context) - Knuth - 1973    
727   A structural approach to operational semantics (context) - Plotkin - 1981
184   Automatic discovery of linear restraints among variables of .. - Cousot, Halbwachs - 1978
99   Abstract interpretation frameworks (context) - Cousot, Cousot - 1992
87   What every computer-scientist should know about computer ari.. - Goldberg - 1991
51   Exact real computer arithmetic with continued fractions (context) - Vuillemin - 1990
38   Essentials of Pad'e approximants (context) - Baker - 1975
25   Comparing Galoi connection and wideningnarrowing approache t.. - Cousot, the et al.
19   Abstract interpretation by dynamic partitioning (context) - Bourdoncle - 1992
18   emes de transitions finis (context) - Arnold - 1992
18   Efficient chaotic iteration strategies with widenings - Bourdoncle - 1993
12   Computer Approximations (context) - Hart, Cheney et al. - 1968
11   Finite precision lexicographic continued fraction number sys.. (context) - Kornerup, Matula
10   Interprocedural abstract interpretation of block structured .. (context) - Bourdoncle - 1990
9   Efficient multiprecision floating point multiplication with .. - Krandick, Johnson - 1993
9   Lecture notes on the status of ieee standard 754 for binary .. (context) - Kahan - 1996
8   Arithm'etique des Ordinateurs (context) - Muller - 1989
7   Exploiting redundancy in bit-pipelined rational arithmetic (context) - Kornerup, Matula - 1989
6   Error analysis in computing (context) - Porte, Vignes - 1974
6   Society for Industrial and Applied Mathematics (context) - Moore, Applications et al. - 1979
6   line arithmetic unit for bit-pipelined rational arithmetic (context) - Kornerup, Matula - 1988
5   Abstract interpretation of probabilistic semantics (context) - Monniaux - 2000
4   Calculator function approximation (context) - Schelin - 1983
4   Finite-precision rational arithmetic: an arithmetic unit (context) - Kornerup, Matula - 1983
4   Improving the results of static analyses of programs by loca.. (context) - Granger - 1992
3   A stochastic arithmetic for reliable scientific computation (context) - Vignes - 1993
3   The status of investigations into computer hardware design b.. (context) - Robertson, Trivedi - 1973
2   Affine relationships between variables of a program (context) - Karr - 1976
2   a diriger des recherches, Universit (context) - Chesneaux, et et al. - 1995
2   Affine arithmetic (context) - Vincius, Andrade et al. - 1994
2   Rational approximations for special functions (context) - Clenshaw - 1974
2   Continued fractions for high-speed and high-accuracy compute.. (context) - Seidensticker - 1983
2   A domain-theoretic approach to real number computation (context) - Edalat, Sunderhauf - 1998
2   An abstract Monte-Carlo method for the analysis of probabili.. - Monniaux - 2001
2   Sur la robustesse de la m'ethode cestac (context) - Chesneaux, Vignes - 1988
1   The improbability of probabilistic error analyses for numeri.. (context) - Kahan - 1991
1   Controle et estimation stochastique des arrondis de calcul (context) - Vignes - 1987
1   Fast rounding in multiprecision floating-slash arithmetic (context) - Scott - 1989
1   ele et en ligne des fonctions arithm (context) - Kla - 1993
1   New methods for evaluating the validity of mathematical soft.. (context) - Vignes - 1978
1   An efficient stochastic method for round-off error analysis (context) - Vignes, Alt - 1985
1   Les fondements de l'arith'etique stochastique (context) - Chesneaux, Vignes - 1992
1   Le calcul sur ordinateur `a pr'ecision finie (context) - Chaitin-Chatelin - 1994
1   physics and exact real arithmetic (context) - Edalat, computation - 1997
1   Real Numbers and Computers --- Les Nombres r'eels et l'Ordin.. (context) - Bajard, Michelucci et al. - 1995
1   a toolbox for assessing the quality of numerical methods and.. (context) - Chaitin-Chatelin, Traviesas - 2000
1   Department of Computing Technical Report DOC (context) - Edalat, Potts et al. - 1997
1   An application of abstract interpretation to floating-point .. (context) - Ameur, Cros et al. - 1992
1   Computer interval arithmetic: Definition and proof of 18 cor.. (context) - Good, London - 1970
1   Petite analyse en nombres flottants (context) - Regal - 1999
1   Programming with CGAL: The example of triangulations (context) - Boissonat, Cazals et al. - 1999

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