Abstract
Many modern algorithms for the transcendental functions rely on a large table of precomputed values together with a low-order polynomial to interpolate between them. In verifying such an algorithm, one is faced with the problem of bounding the error in this polynomial approximation. The most straightforward methods are based on numerical approximations, and are not prima facie reducible to a formal HOL proof. We discuss a technique for proving such results formally in HOL, via the formalization of a number of results in polynomial theory, e.g. squarefree decomposition and Sturm's theorem, and the use of a computer algebra system to compute results that are then checked in HOL. We demonstrate our method by tackling an example from the literature.
Work supported by the EPSRC grant ‘Floating Point Verification’
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© 1997 Springer-Verlag Berlin Heidelberg
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Harrison, J. (1997). Verifying the accuracy of polynomial approximations in HOL. In: Gunter, E.L., Felty, A. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1997. Lecture Notes in Computer Science, vol 1275. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028391
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DOI: https://doi.org/10.1007/BFb0028391
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Online ISBN: 978-3-540-69526-4
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