
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Vincent Lefèvre, JeanMichel Muller, Arnaud Tisserand, "Toward Correctly Rounded Transcendentals," IEEE Transactions on Computers, vol. 47, no. 11, pp. 12351243, November, 1998.  
BibTex  x  
@article{ 10.1109/12.736435, author = {Vincent Lefèvre and JeanMichel Muller and Arnaud Tisserand}, title = {Toward Correctly Rounded Transcendentals}, journal ={IEEE Transactions on Computers}, volume = {47}, number = {11}, issn = {00189340}, year = {1998}, pages = {12351243}, 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  00189340 SP1235 EP1243 EPD  12351243 A1  Vincent Lefèvre, A1  JeanMichel Muller, A1  Arnaud Tisserand, PY  1998 KW  Floatingpoint 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 doubleprecision exponential function in a small domain. These new results show that this problem can be solved, at least for the doubleprecision 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. 1,8431,846, 1988.
[2] ANSI/IEEE Std. 7541985, Binary FloatingPoint 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 multipleprecision evaluation of elementary functions,” J. ACM, vol. 23, pp. 242, 1976.
[6] M. Daumas and D.W. Matula, "Rounding of FloatingPoint Intervals," Proc. SCAN93,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. 162175, 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, UrbanaChampaign, 1970.
[9] C.B. Dunham, "Feasibility of 'Perfect' Function Evaluation," SIGNUM Newsletter, vol. 25, no. 4, pp. 2526, 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. 2645, Mar. 1991.
[11] D. Goldberg, “What Every Computer Scientist Should Know About FloatingPoint Arithmetic,” Computing Surveys, vol. 23, no. 1, pp. 548, 1991.
[12] W. Kahan, "Minimizing q*mn," 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 IEEE754," 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, AddisonWesley, Reading, Mass., 1998.
[15] D. Knuth, The Art of Computer Programming, vol. 3: Sorting and Searching. AddisonWesley, 1973.
[16] V. Lefèvre, "An Algorithm That Computes a Lower Bound on the Distance Between a Segment and z2," Research Report RR9718, LIP,École Normale Supérieure de Lyon, 1997. Available athttp://www.enslyon.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. 2342, 1996.
[20] M. Payne and R. Hanek, "Radian Reduction for Trigonometric Functions," SIGNUM Newsletter, vol. 18, pp. 1924, 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. 138145,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. 964973, Aug. 1994.
[23] R.A. Smith, "A ContinuedFraction Analysis of Trigonometric Argument Reduction," IEEE Trans. Computers, vol. 44, no. 11, pp. 1,3481,351, 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. 410423, Sept. 1991.
[25] D. Zuras, "More on Squaring and Multiplying Large Integers," IEEE Trans. Computers, vol. 43, no. 8, pp. 899908, Aug. 1994.