Rigorous and portable standard functions

BIT Numerical Mathematics

Volumn 41, Issue 3, 2001, Pages 540-562

  Rump, Siegfried M ^a  

^a HAMBURG UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Accuracy; Elementary standard functions; Floating point implementation

Indexed keywords

EID: 0041694320     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021971313412     Document Type: Article

References (24)

1. O. Aberth and M. Schaefer, Precise computation using range arithmetic, via C++, ACM Trans. Math. Softw., 18:4 (1992), pp. 481-491.
2. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, New York, 1968.
3. N. C. Börsken, Komplexe Kreis-Standardfunktionen, Diplomarbeit, Freiburger Intervall-Ber. 78/2, Inst. für Angewandte Mathematik, Universität Freiburg, 1978.
4. K. D. Braune, Hochgenaue Standardfunktionen für reelle und komplexe Punkte und Intervalle in beliebigen Gleitpunktrastern, Dissertation, Universität Karlsruhe, 1987.
5. R. P. Brent, A Fortran multiple-precision arithmetic package, Tech. Report, Department of Computer Science, Australian National University, Canberra, 1975.
6. R. P. Brent, J. A. Hooper, and J. M. Yohe, An AUGMENT interface for Brent's multiple precision arithmetic package, ACM Trans. Math. Software, 6:2 (1980), pp. 204-217.
7. B. M. Brown, D. K. R. McCormack, and A. Zettl, On the existence of an eigenvalue below the essential spectrum, Proc. R. Soc. Lond., 455 (1999), pp. 2229-2234.
8. J.-P. Eckmann and P. Wittwer, Computer Methods and Borel Summability Applied to Feigenbaum's Equation, Vol. 227 of Lecture Notes in Physics, Springer-Verlag, Berlin, 1985.
9. T. C. Hales, Cannonballs and honeycombs, Notices Amer. Math. Soc., 47:4 (2000), pp. 440-449.
10. N. J. Higham, Accuracy and Stability of Numerical Algorithms, SIAM, Philadelphia, PA, 1996.
11. O. Holzmann, B. Lang, and H. Schütt, Newton's constant of gravitation and verified numerical quadrature, Reliable Computing, 2:3 (1996), pp. 229-239.
12. IEEE Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Standard 754-1985, Institute of Electrical and Electronics Engineers, New York, 1985.
13. R. Klatte, U. Kulisch, M. Neaga, D. Ratz, and Ch. Ullrich, PASCAL-XSC-Sprachbeschreibung mit Beispielen, Springer-Verlag, Berlin, 1991.
14. R. Klatte, U. Kulisch, A. Wiethoff, C. Lawo, and M. Rauch, C-XSC A C++ Class Library for Extended Scientific Computing, Springer-Verlag, Berlin, 1993.
15. W. Krämer, Inverse Standardfunktionen für reelle und komplexe Intervallargumente mit a priori Fehlerabschätzung für beliebige Datenformate, Dissertation, Universität Karlsruhe, 1987.
16. W. Krämer, Die Berechnung von Standardfunktionen in Rechenanlagen, Jahrb. Überbl. Math. 1992, 1992, pp. 97-115.
17. B. Lang, Verified quadrature in determining Newton's constant of gravitation, J. Universal Computer Science, 4:1 (1998), pp. 16-24.
18. MATLAB User's Guide, Version 5, The MathWorks Inc., Natick, MA, 1997.
19. J. M. Muller, Elementary Functions, Algorithms and Implementation, Birkhäuser, Boston, MA, 1997.
20. M. Payne and R. Hanek, Radian reduction for trigonometric functions, SIGNUM Newsletter, 18 (1983), pp. 19-24.
21. S. M. Rump, Fast and parallel interval arithmetic. BIT, 39:3 (1999), pp. 539-560.
22. S. M. Rump, INTLAB - INTerval LABoratory, in Developments in Reliable Computing, T. Csendes, ed., Kluwer Academic Publishers, Dordrecht, 1999, pp. 77-104. http://www.ti3.tu-harburg.de/rump/ intlab/index.html.
23. P. T. P. Tang, Table-lookup algorithms for elementary functions and their error analysis, Tech. Report MCS-P194-1190, Argonne National Lab., January 1991.
24. W. F. Wong and E. Goto, Fast hardware-based algorithms for elementary function computations, in Proc. International Symposium on Supercomputing, Kyushu University Press, Fukuoka, Japan, 1991, pp. 56-65.