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Christoph Quirin Lauter, Vincent Lefèvre, "An Efficient Rounding Boundary Test for {\rm pow}(x, y) in Double Precision," IEEE Transactions on Computers, vol. 58, no. 2, pp. 197207, February, 2009.  
BibTex  x  
@article{ 10.1109/TC.2008.202, author = {Christoph Quirin Lauter and Vincent Lefèvre}, title = {An Efficient Rounding Boundary Test for {\rm pow}(x, y) in Double Precision}, journal ={IEEE Transactions on Computers}, volume = {58}, number = {2}, issn = {00189340}, year = {2009}, pages = {197207}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2008.202}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  An Efficient Rounding Boundary Test for {\rm pow}(x, y) in Double Precision IS  2 SN  00189340 SP197 EP207 EPD  197207 A1  Christoph Quirin Lauter, A1  Vincent Lefèvre, PY  2009 KW  Floatingpoint arithmetic KW  correct rounding KW  power function. VL  58 JA  IEEE Transactions on Computers ER   
[1] Standard 7541985 for Binary FloatingPoint Arithmetic, ANSI/IEEE, 1985.
[2] 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.
[3] J.M. Muller, Elementary Functions, Algorithms and Implementation. Birkhäuser, 1997.
[4] L. Fousse, G. Hanrot, V. Lefèvre, P. Pélissier, and P. Zimmermann, “MPFR: A MultiplePrecision Binary FloatingPoint Library with Correct Rounding,” ACM Trans. Math. Software, vol. 33, no. 2, June 2007.
[5] F. de Dinechin, A. Ershov, and N. Gast, “Towards the PostUltimate LIBM,” Proc. 17th IEEE Symp. Computer Arithmetic (ARITH17 '05), June 2005.
[6] F. de Dinechin, C.Q. Lauter, and J.M. Muller, “Fast and Correctly Rounded Logarithms in DoublePrecision,” RAIRO, Theoretical Informatics and Applications, vol. 41, pp. 85102, 2007.
[7] V. Lefèvre and J.M. Muller, “Worst Cases for Correct Rounding of the Elementary Functions in Double Precision,” Proc. 15th IEEE Symp. Computer Arithmetic (ARITH15 '01), pp. 111118, N.Burgess and L. Ciminiera, eds., http://www.ece.ucdavis. edu/acsel/arithmetic/ arith15/papersARITH15_Lefevre.pdf, 2001.
[8] CRLibm, a Library of Correctly Rounded Elementary Functions in DoublePrecision, http://lipforge.enslyon.fr/wwwcrlibm/, 2008.
[9] “Sun Microsystems,” LIBMCR, a Reference CorrectlyRounded Library of Basic DoublePrecision Transcendental Elementary Functions, http://www.sun.com/downloadproducts.xml?id=41797765 , 2008.
[10] D. Stehlé, V. Lefèvre, and P. Zimmermann, “Searching Worst Cases of a OneVariable Function Using Lattice Reduction,” IEEE Trans. Computers, vol. 54, no. 3, pp. 340346, http://csdl.computer. org/dl/trans/tc/2005/ 03t0340.pdf, Mar. 2005.
[11] The MPFR Team, The MPFR Library: Algorithms and Proofs, http://www.mpfr.orggforge.html, July 2007.
[12] G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers. Oxford Univ. Press, 1979.
[13] V. Lefèvre, “New Results on the Distance between a Segment and${\hbox{\rlap{Z}\kern 2.0pt{\hbox{Z}}}}^{2}$ . Application to the Exact Rounding,” Proc. 17th IEEE Symp. Computer Arithmetic (ARITH17 '05), pp. 6875, P. Montuschi and E. Schwarz, eds., http://arith17.polito.it/finalpaper147.pdf , June 2005.
[14] P. Kornerup, V. Lefèvre, and J.M. Muller, Computing Integer Powers in FloatingPoint Arithmetic, Laboratoire de l'Informatique du Parallélisme, Lyon, France, Research Report RR200723, http://www.vinc17.org/research/papersrr_power.pdf , May 2007.
[15] S. Boldo, Preuves Formelles en Arithmétiques à Virgule Flottante, PhD dissertation, Ecole Normale Supérieure de Lyon, http://www. enslyon.fr/LIP/Pub/Rapports/ PhD/PhD2004PhD200405.pdf, Nov. 2004.
[16] A. Feldstein and R. Goodman, “Convergence Estimates for the Distribution of Trailing Digits,” J. ACM, vol. 23, no. 2, pp. 287297, http://portal.acm.orgcitation.cfm?id=321948 , Apr. 1976.
[17] C.E. Leiserson, H. Prokop, and K.H. Randall, Using de Bruijn Sequences to Index a 1 in a Computer Word, http://supertech.csail. mit.edu/papersdebruijn.pdf , 1998.