Abstract
An application of interval arithmetic to software testing is described, which has its main importance for embedded systems, in particular safety critical systems. Interval arithmetic allows the full range of input data to be tested and derives predictions about possible variable range violation at runtime. Furthermore, due to a combination with an automatic differentiation-like calculus, it is possible to determine for each variable a sufficient number of digits which shall kept during calculation in order to prevent any serious cancellation.
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References
Alefeld, G.; Herzberger, J.: Introduction to Interval Computation. Academic Press, New York (1983)
Bauch, H. ET AL.: Intervallmathematik. BSB B.G. Teubner Verlagsgesellschaft, Leibzig (1987)
Kearfott, R.B.; Du, K.: The Cluster Problem in Multivariate Global Optimization. J. of Global Optimization 5, pp 253–265 (1994)
Kearfott, R.B.: A review of techniques in the verified solution of constrained global optimization problems, in: Applications of Interval Computations, ed. by R.B. Kearfott and V. Kreinovich, Kluwer Academic Publishers, Dordrecht, pp 23–59 (1996)
Kedem, G.: Automatic Differentiation of Computer Programs. ACM Trans. Math. Software 6, Nr. 2, pp 150–165 (1980)
Moore,R.: Interval Analysis. Prentice Hall, Englewood Cliffs, New York (1966)
Ratschek, H.; Rokne, J.: Computer Methods for the Range of Functions. Ellis Horwood, Chichester (1984)
Richman, P.L.: Automatic Error Analysis for Determining Precision. Comm. ACM 15, Nr. 9, pp 813–817 (1972)
Schumacher, G.: Genauigkeitsfragen bei algebraisch-numerischen Algorithmen auf Skalarund Vektorrechnern. Ph.D. Thesis, Universität Karlsruhe (1989)
Schumacher, G.; Musch, K.: Specification of a Test Case Generator for Ranges of Data. Deliverable T3/3/2, ESPRIT Project No 23920, OMI/SAFE (1998)
Schumacher, G.: Computer Aided Numerical Analysis. To appear 2000.
Skelboe, S.: Computation of rational functions. BIT 14, pp 87–95 (1974)
Tienari, M.: On the Control of Floating-Point Mantissa Length in Iterative Computations, in: Proc. of the Intern. Computing Symposium, ed. by A. Günter et al., North Holland, pp 315–322 (1974)
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© 1999 Springer Science+Business Media Dordrecht
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Musch, K., Schumacher, G. (1999). Interval Analysis for Embedded Systems. In: Csendes, T. (eds) Developments in Reliable Computing. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1247-7_12
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DOI: https://doi.org/10.1007/978-94-017-1247-7_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5350-3
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