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Highly accurate tables for elementary functions. (English) Zbl 0853.65022
Based on J. E. Bresenham’s algorithm [Algorithm for computer control of a digital plotter, IBM Systems J., 25-30 (1965)], a fast method for computing accurate tables of elementary functions is proposed. Together with a polynomial approximation of a function near a table value the method provides last bit accuracy for practically all argument values with using extended precision computations. The paper proposes PASCAL program fragments for some of the usual elementary functions (trigonometric, hyperbolic, etc.).
MSC:
65D20Computation of special functions, construction of tables
65A05Tables (numerical analysis)
26-04Machine computation, programs (real functions)
26A09Elementary functions of one real variable
References:
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[5]G. H. Hardy, and E. M. Wright,An Introduction to the Theory of Numbers, Oxford, 1938.
[6]IEEE:IEEE Standard for Binary Floating-Point Arithmetic, 754–1985, New York, 1985.
[7]A. Janser and W. Luther,Der Bresenham-Algorithmus und andere graphische Grundprozeduren, in Micro-Computer Forum für Bildung und Wissenschaft Bd. 5, K. Dette, D. Haupt, and C Polze editors, Springer, Berlin, 1992, pp. 255–261.
[8]A. Janser and W. Luther,Der Bresenham-Algorithmus, Bericht Nr. SI-10, 1994, Schriftenreihe des Informatikinstituts der Gerhard-Mercator-Universität - GH Duisburg, ISSN: 09442-4164.
[9]W. Krämer,Die Berechnung von Standardfunktionen in Rechenanlagen, Jahrbuch Überblicke Mathematik 1992, S. D. Chatterji et al. editors, Vieweg, Wiesbaden, 1992, pp. 97–115.
[10]P. T. P. Tang,Table-driven implementation of the exponential function in IEEE floating-point arithmetic, ACM Trans. on Math. Software, Vol 15, No 2 (1989), pp. 144–157. · Zbl 0900.65047 · doi:10.1145/63522.214389
[11]P. T. P. Tang,Table-driven implementation of the Expm1 function in IEEE floating-point arithmetic, ACM Trans. on Math. Software, Vol 18, No 2 (1992), pp. 211–222. · Zbl 0892.65006 · doi:10.1145/146847.146928