Towards the post-ultimate libm

Proceedings - Symposium on Computer Arithmetic

Volumn , Issue , 2005, Pages 288-296

  De Dinechin, Florent ^a   Ershov, Alexey V ^b   Gast, Nicolas ^c  

^a UNIVERSITÉ DE LYON   (France)

^b INTEL CORPORATION   (United States)

^c ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; PROGRAM PROCESSORS; STORAGE ALLOCATION (COMPUTER);

ELEMENTARY FUNCTIONS; MATHEMATICAL LIBRARY; OVERHEAD;

DIGITAL ARITHMETIC;

EID: 27944494862     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (24)

1. CR-Libm, a library of correctly rounded elementary functions in double-precision. http://lipforge.ens-lyon.fr/www/crlibm/.
2. Test of mathematical functions of the standard C library, http://www.vinc17.org/research/testlibm/.
3. ANSI/IEEE. Standard 754-1985 for binary floating-point arithmetic, 1985.
4. F. de Dinechin, D. Defour, and C. Lauter. Fast correct rounding of elementary functions in double precision using double-extended arithmetic. Technical Report 2004-10, LIP, École Normale Supérieure de Lyon, Mar. 2004.
5. F. de Dinechin and N. Gast. Towards the post-ultimate libm. Technical Report 2004-47, LIP, École Normale Supérieure de Lyon, Nov. 2004. Available at http://www.ens-lyon.fr/LIP/Pub/ Rapports/RR/RR2004/RR2004-47.pdf.
6. F. de Dinechin, C. Loirat, and J.-M. Muller. A proven correctly rounded logarithm in double-precision. In RNC6, Real Numbers and Computers, Schloss Dagstuhl, Germany, Nov. 2004.
7. D. Defour and F. de Dinechin. Software carry-save for fast multiple-precision algorithms. In 35th International Congress of Mathematical Software, Beijing, China, 2002.
8. D. Defour, G. Hanrot, V. Lefèvre, J.-M. Muller, N. Revol, and P. Zimmermann. Proposal for a standardization of mathematical function implementations in floating-point arithmetic. Numerical algorithms, 37(1-4): 367-375, Jan. 2004.
9. T. J. Dekker. A floating point technique for extending the available precision. Numerische Mathematik, 18(3):224-242, 1971.
10. P. M. Farmwald. High bandwidth evaluation of elementary functions. In Proceedings of the 5th IEEE Symposium on Computer Arithmetic. IEEE Computer Society Press, 1981.
11. S. Gal. Computing elementary functions: A new approach for achieving high accuracy and good performance. In Accurate Scientific Computations, LNCS 235, pages 1-16. Springer Verlag, 1986.
12. J. Harrison, T. Kubaska, S. Story, and P. Tang. The computation of transcendental functions on the IA-64 architecture. Intel Technology Journal, Q4, 1999.
13. R. Klatte, U. Kulisch, C. Lawo, M. Rauch, and A. Wiethoff. C-XSC a C++ class library for extended scientific computing. Springer Verlag, 1993.
14. D. Knuth. The Art of Computer Programming, volume 2. Addison Wesley, Reading, MA, 1973.
15. V. Lefèvre and J.-M. Muller. Worst cases for correct rounding of the elementary functions in double precision. http://perso.ens-lyon.fr/jean- michel.muller/Intro-to-TMD.htm, 2004.
16. R.-C. Li, P. Markstein, J. P. Okada, and J. W. Thomas. The libm library and floating-point arithmetic for HP-UX on Itanium. Technical report, Hewlett-Packard company, april 2001.
17. IBM Accurate Portable MathLib. http://oss.software.ibm.com/mathlib/.
18. P. Markstein. IA-64 and Elementary Functions : Speed and Precision. Hewlett-Packard Professional Books. Prentice Hall, 2000. ISBN: 0130183482.
19. P. Markstein. A fast quad precision elementary function library for Itanium. In Real Numbers and Computers, pages 5-12, Lyon, France, 2003.
20. R. Moore. Interval analysis. Prentice Hall, 1966.
21. GNU MPFR. http://www.mpfr.org/.
22. J.-M. Muller. Elementary Functions, Algorithms and Implementation. Birkhauser, Boston, 1997.
23. P. T. P. Tang. Table lookup algorithms for elementary functions and their error analysis. In P. Kornerup and D. W. Matula, editors, Proceedings of the 10th IEEE Symposium on Computer Arithmetic, pages 232-236, Grenoble, France, June 1991. IEEE Computer Society Press.
24. A. Ziv. Fast evaluation of elementary mathematical functions with correctly rounded last bit. ACM Transactions on Mathematical Software, 17(3):410-423, Sept. 1991.