|
| This Article | ||
| ||
| Share | ||
| Bibliographic References | ||
| Add to: | ||
| | ||
| Search | ||
| ||
| ASCII Text | x | ||
| Vincent Lefèvre, Jean-Michel Muller, Arnaud Tisserand, "Toward Correctly Rounded Transcendentals," IEEE Transactions on Computers, vol. 47, no. 11, pp. 1235-1243, November, 1998. | |||
| BibTex | x | ||
| @article{ 10.1109/12.736435, author = {Vincent Lefèvre and Jean-Michel Muller and Arnaud Tisserand}, title = {Toward Correctly Rounded Transcendentals}, journal ={IEEE Transactions on Computers}, volume = {47}, number = {11}, issn = {0018-9340}, year = {1998}, pages = {1235-1243}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.736435}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - Toward Correctly Rounded Transcendentals IS - 11 SN - 0018-9340 SP1235 EP1243 EPD - 1235-1243 A1 - Vincent Lefèvre, A1 - Jean-Michel Muller, A1 - Arnaud Tisserand, PY - 1998 KW - Floating-point arithmetic KW - rounding KW - elementary functions KW - Table Maker's Dilemma. VL - 47 JA - IEEE Transactions on Computers ER - | |||
Abstract—The Table Maker's Dilemma is the problem of always getting correctly rounded results when computing the elementary functions. After a brief presentation of this problem, we present new developments that have helped us to solve this problem for the double-precision exponential function in a small domain. These new results show that this problem can be solved, at least for the double-precision format, for the most usual functions.
[1] W. Jone and C. Papachristou,“On partitioning for pseudo exhaustive testing of VLSI circuits,” Int’l Symp. Circuits and Systems, pp. 1,843-1,846, 1988.
[2] ANSI/IEEE Std. 754-1985, Binary Floating-Point Arithmetic, IEEE Press, Piscataway, N.J., 1985 (also called ISO/IEC 559).
[3] G.A. Baker, Essentials of PadéApproximants.New York: Academic Press, 1975.
[4] V. Berthé, "Three Distance Theorems and Combinatorics on Words," technical report, Institut de Mathématiques de Luminy, Marseille, France, 1997.
[5] R.P. Brent,“Fast multiple-precision evaluation of elementary functions,” J. ACM, vol. 23, pp. 242, 1976.
[6] M. Daumas and D.W. Matula, "Rounding of Floating-Point Intervals," Proc. SCAN-93,Vienna, Austria, June 1993.
[7] M. Daumas, C. Mazenc, X. Merrheim, and J.M. Muller, "Modular Range Reduction: A New Algorithm for Fast and Accurate Computation of the Elementary Functions," J. Universal Computer Science, vol. 1, no. 3, pp. 162-175, Mar. 1995.
[8] B. DeLugish, "A Class of Algorithms for Automatic Evaluation of Functions and Computations in a Digital Computer," PhD thesis, Dept. of Computer Science, Univ. of Illi nois, Urbana-Champaign, 1970.
[9] C.B. Dunham, "Feasibility of 'Perfect' Function Evaluation," SIGNUM Newsletter, vol. 25, no. 4, pp. 25-26, Oct. 1990.
[10] S. Gal and B. Bachelis, "An Accurate Elementary Mathematical Library for the IEEE Floating Point Standard," ACM Trans. Math. Software, vol. 17, pp. 26-45, Mar. 1991.
[11] D. Goldberg, “What Every Computer Scientist Should Know About Floating-Point Arithmetic,” Computing Surveys, vol. 23, no. 1, pp. 5-48, 1991.
[12] W. Kahan, "Minimizing q*m-n," Text accessible electronically athttp://www.ee.binghatom.edu/faculty/phatakhttp:/ /http.cs.berkeley.edu~wkahan/. At the beginning of the file "nearpi.c," 1983.
[13] W. Kahan, "Lecture Notes on the Status of IEEE-754," Postscript file accessible electronically through the Internet at the addresshttp://http.cs.berkeley.edu/~wkahan/ieee754status ieee754.ps, 1996.
[14] D. Knuth, The Art of Computer Programming, Vol. 2, Addison-Wesley, Reading, Mass., 1998.
[15] D. Knuth, The Art of Computer Programming, vol. 3: Sorting and Searching. Addison-Wesley, 1973.
[16] V. Lefèvre, "An Algorithm That Computes a Lower Bound on the Distance Between a Segment and z2," Research Report RR97-18, LIP,École Normale Supérieure de Lyon, 1997. Available athttp://www.ens-lyon.fr/LIPresearch_reports.us.html .
[17] J.M. Muller and A. Tisserand, "Towards Exact Rounding of the Elementary Functions," Scientific Computing and Validated Numerics (Proc. SCAN '95), G. Alefeld, A. Frommer, and B. Lang, eds., Wuppertal, Germany, 1996.
[18] J.M. Muller, Elementary Functions. Algorithms and Implementation. Birkhauser, 1997.
[19] Y.V. Nesterenko and M. Waldschmidt, "On the Approximation of the Values of Exponential Function and Logarithm by Algebraic Numbers (in Russian)," Mat. Zapiski, vol. 2, pp. 23-42, 1996.
[20] M. Payne and R. Hanek, "Radian Reduction for Trigonometric Functions," SIGNUM Newsletter, vol. 18, pp. 19-24, 1983.
[21] M. Schulte and E.E. Swartzlander, "Exact Rounding of Certain Elementary Functions," Proc. 11th IEEE Symp. Computer Arithmetic, E.E. Swartzlander, M.J. Irwin, and G. Jullien, eds., pp. 138-145,Windsor, Canada, June 1993.
[22] M.J. Schulte and E.E. Swartzlander Jr., Hardware Designs for Exactly Rounded Elementary Functions IEEE Trans. Computers, vol. 43, no. 8, pp. 964-973, Aug. 1994.
[23] R.A. Smith, "A Continued-Fraction Analysis of Trigonometric Argument Reduction," IEEE Trans. Computers, vol. 44, no. 11, pp. 1,348-1,351, Nov. 1995.
[24] A. Ziv, "Fast Evaluation of Elementary Mathematical Functions with Correctly Rounded Last Bit," ACM Trans. Math. Software, vol. 17, no. 3, pp. 410-423, Sept. 1991.
[25] D. Zuras, "More on Squaring and Multiplying Large Integers," IEEE Trans. Computers, vol. 43, no. 8, pp. 899-908, Aug. 1994.

