IEEE standard 754
for
binary floating-point arithmetic

Floating point numbers (Fortran's REAL*n, DOUBLE PRECISION, and COMPLEX*n, and C's float, double, and long double) are inexact representations of ideal real numbers. The operations performed on them are also necessarily inexact. What should you know when :
(a + b) + c != a + (b + c)


WWW, news, mailing lists


Books

  • Arithmétique des ordinateurs
    dans "Organisation et conception des ordinateurs : l'interface matériel/logiciel" - John L. Hennessy et David A. Patterson, Dunod, 1994

  • Arithmetic for Computers
    in "Computer Organization and Design: The Hardware/Software Interface" - John L. Hennessy and David A. Patterson, Morgan Kaufmann Publishers, 1997 -
    table of contents, slides: ps or pdf

  • Arithmétique des ordinateurs par David Goldberg
    dans "Architecture des ordinateurs : une approche quantitative" - John L. Hennessy et David A. Patterson, International Thomson Publishing, 1996 (cdd loria)

  • Computer Arithmetic by David Goldberg
    in "Computer Architecture: A Quantitative Approach" - John L. Hennessy and David A. Patterson, Morgan Kaufmann Publishers, 1995 - table of contents

  • Qualité des calculs sur ordinateur. Vers des arithmétiques plus fiables ?
    Marc Daumas et Jean-Michel Muller, Masson, 1997 (bu sciences)

  • Ingénierie du contrôle de la précision des calculs sur ordinateur
    Michèle Pichat et Jean Vignes, Technip, 1993

  • Arithmétique des ordinateurs. Opérateurs et fonctions élémentaires
    Jean-Michel Muller, Masson, 1989 (bu sciences)

  • Elementary Functions. Algorithms and Implementation
    Jean-Michel Muller, Birkhauser, 1997 (cdd loria)

  • Computer arithmetic algorithms
    Israel Koren, Prentice-Hall, 1993


    Articles

  • What Every Computer Scientist Should Know About Floating-Point Arithmetic
    David Goldberg, ACM Computing Surveys, pp. 5-48, vol. 23#1, 1991 (ACM Copyright Notice)

  • What Every Computer Scientist Should Know About Floating-Point Arithmetic
    in Sun's Numerical Computation Guide, David Goldberg, 1997 (addendum)

  • Handling floating-point exceptions in numeric programs
    John R. Hauser, ACM Transactions on Programming Languages and Systems, pp.139-174, vol. 18#2, 1996 (ACM Copyright Notice)

  • Estimation Of Round-Off Errors On Several Computers Architectures
    J. Asserrhine, J.-M. Chesneaux, and J.-L. Lamotte, Journal of Universal Computer Science, Vol. 1 No. 7, 1995 (Special Issue "Real Numbers and Computers")

  • On Properties of Floating Point Arithmetics: Numerical Stability and the Cost of Accurate Computation - Doug Preist


    William Kahan and IEEE 754


    Books in the "SGI Developer" collection about the IEEE 754 floating point standard


    SGI Man Pages about IEEE 754

    Cr, le 16/02/99


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