Fast and correctly rounded logarithms in double-precision
Florent de Dinechin; Christoph Lauter; Jean-Michel Muller
RAIRO - Theoretical Informatics and Applications (2007)
- Volume: 41, Issue: 1, page 85-102
- ISSN: 0988-3754
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top- CR-Libm, a library of correctly rounded elementary functions in double-precision. . URIhttp://lipforge.ens-lyon.fr/www/crlibm/
- ANSI/IEEE. Standard 754-1985 for Binary Floating-Point Arithmetic (also IEC 60559). 1985.
- Y. Bertot and P. Casteran, Interactive Theorem Proving and Program Development. Coq'Art: the Calculus of Inductive Constructions. Texts in Theoretical Computer Science, Springer Verlag (2004).
- M. Cornea, J. Harrison and P.T.P. Tang, Scientific Computing on Itanium-based Systems. Intel Press (2002).
- M. Daumas and G. Melquiond, Generating formally certified bounds on values and round-off errors, in 6th Conference on Real Numbers and Computers (2004).
- D. Defour, Cache-optimised methods for the evaluation of elementary functions. Technical Report 2002-38, LIP, École normale supérieure de Lyon (2002).
- F. de Dinechin and D. Defour, Software carry-save: A case study for instruction-level parallelism, in Seventh International Conference on Parallel Computing Technologies (September 2003).
- F. de Dinechin, D. Defour and Ch.Q. Lauter, Fast correct rounding of elementary functions in double precision using double-extended arithmetic. Technical Report 2004-10, LIP, École normale supérieure de Lyon (March 2004).
- F. de Dinechin, A. Ershov and N. Gast, Towards the post-ultimate libm, in 17th Symposium on Computer Arithmetic. IEEE Computer Society Press (June 2005).
- F. de Dinechin, Ch.Q. Lauter and G. Melquiond, Assisted verification of elementary functions using Gappa, in ACM Symposium on Applied Computing (2006).
- F. de Dinechin, C. Loirat and J.-M. Muller, A proven correctly rounded logarithm in double-precision, in RNC6, Real Numbers and Computers (November 2004).
- D. Defour, Collapsing dependent floating point operations. Technical report, DALI Research Team, LP2A, University of Perpignan, France (December 2004).
- D. Defour and F. de Dinechin, Software carry-save for fast multiple-precision algorithms, in 35th International Congress of Mathematical Software (2002).
- D. Defour, F. de Dinechin and J.-M. Muller, Correctly rounded exponential function in double precision arithmetic, in Advanced Signal Processing Algorithms, Architectures, and Implementations X (SPIE'2000) (August 2001).
- T.J. Dekker, A floating point technique for extending the available precision. Numerische Mathematik18 (1971) 224–242.
- P.M. Farmwald, High bandwidth evaluation of elementary functions, in Proceedings of the 5th IEEE Symposium on Computer Arithmetic. IEEE (1981).
- S. Gal, Computing elementary functions: A new approach for achieving high accuracy and good performance, in Accurate Scientific Computations, Lect. Notes Comput. Sci. 235 (1986) 1–16.
- D. Goldberg, What every computer scientist should know about floating-point arithmetic. ACM Computing Surveys23 (1991) 5–47.
- W. Hofschuster and W. Krämer, FI_LIB, eine schnelle und portable Funktionsbibliothek für reelle Argumente und reelle Intervalle im IEEE-double-Format. Technical Report Nr. 98/7, Institut für Wissenschaftliches Rechnen und Mathematische Modellbildung, Universität Karlsruhe (1998).
- ISO/IEC. International Standard ISO/IEC 9899:1999(E). Programming languages – C. 1999.
- R. Klatte, U. Kulisch, C. Lawo, M. Rauch and A. Wiethoff, C-XSC a C++ class library for extended scientific computing. Springer Verlag (1993).
- Ch.Q. Lauter, Basic building blocks for a triple-double intermediate format. Technical Report 2005-38, LIP, École normale supérieure de Lyon (September 2005).
- V. Lefèvre, Moyens arithmétiques pour un calcul fiable. Ph.D. Thesis, École normale supérieure de Lyon, Lyon, France (2000).
- V. Lefèvre and J.-M. Muller, Worst cases for correct rounding of the elementary functions in double precision, (2004). URIhttp://perso.ens-lyon.fr/jean-michel.muller/Intro-to-TMD.htm
- V. Lefèvre, J.M. Muller and A. Tisserand, Towards correctly rounded transcendentals. IEEE Transactions on Computers47 (1998) 1235–1243.
- IBM Accurate Portable MathLib, . URIhttp://oss.software.ibm.com/mathlib/
- P. Markstein, IA-64 and Elementary Functions: Speed and Precision. Hewlett-Packard Professional Books, Prentice Hall (2000).
- R.E. Moore, Interval analysis. Prentice Hall (1966).
- MPFR, . URIhttp://www.mpfr.org/
- J.-M. Muller, Elementary Functions, Algorithms and Implementation. Birkhauser, Boston (1997/2005).
- P.T.P. Tang, Table lookup algorithms for elementary functions and their error analysis, in 10th IEEE Symposium on Computer Arithmetic. IEEE (June 1991).
- W.F. Wong and E. Goto, Fast hardware-based algorithms for elementary function computations using rectangular multipliers. IEEE Transactions on Computers43 (1994) 278–294.
- A. Ziv, Fast evaluation of elementary mathematical functions with correctly rounded last bit. ACM Transactions on Mathematical Software17 (1991) 410–423.