Abstract
The purpose of this paper is to give some insight in the construction of correct programs, especially numerical software, and in proving their correctness. After a brief survey of general program correctness axioms, the paper deals with various sets of axioms for machine arithmetic and some of its desirable features including a proposed standard for binary floating-point arithmetic. Moreover, a brief discussion is devoted to interval arithmetic. Finally, as an example of proving correctness, some algorithms for finding a zero of a real function in a real interval are considered.
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7. References
Program correctness
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Machine arithmetic
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Interval arithmetic
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Finding a real zero
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Dekker, T.J. (1982). Program correctness and machine arithmetic. In: Messina, P.C., Murli, A. (eds) Problems and Methodologies in Mathematical Software Production. Lecture Notes in Computer Science, vol 142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11603-6_3
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DOI: https://doi.org/10.1007/3-540-11603-6_3
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