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
• Articles
• William Kahan and IEEE 754
• Books in the "SGI Developer" collection
• Man Pages about IEEE 754

• Numeric-interest mailing list page - validgh
• comp.arch.arithmetic

• www.validgh.com Home Page - David G. Hough
• Some links related to computer arithmetic - J.-M. Muller - ENS Lyon
• The Table Maker's Dilemma - LIP - ENS
• The Object-Oriented Numerics Page - Todd Veldhuizen - Canada

• Numerical Computation Guide - Sun Microsystems - 1997 (local 1996: html and postscript)

• UCB test of IEEE 754 arithmetic - David G. Hough - 1995 (netlib)
• A program for testing IEEE Decimal-binary Conversion (paper) - Vern Paxon, 1991 (ftp.ee.lbl.gov)

• The CADNA software - LIP6 - Université Paris 6
• Etude de la stabilité numérique du code OPA avec CADNA - IPSL/LIP6 (postscript)
• AQUARELS : atelier de qualité numérique - SIMULOG

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")

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William Kahan and IEEE 754

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• Documents relating to IEEE standard 754 for binary floating-point arithmetic - William Kahan - Berkeley

• An Interview with the Old Man of Floating-Point - 20 Feb. 1998

• Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic - 31 May 1996
• What can you learn about Floating-Point Arithmetic in One Hour ? - 8 Feb. 1996
• The Baleful Effect of Computer Benchmarks upon Applied Mathematics, Physics and Chemistry - 11 June 1996
• How JAVA's Floating-Point Hurts Everyone Everywhere - 1 March 1998

• The Baleful Effect of Computer Languages and Benchmarks upon Applied Mathematics, Physics and Chemistry - 15 July 1997
• The Improbability of PROBABILISTIC ERROR ANALYSES for Numerical Computations - 28 Feb. 1996
• Beastly Numbers - 13 Jan. 1996

• How to Test Whether SQRT is Rounded Correctly - 31 May 1996
• SRTEST is a Fortran/DOS program for testing accuracy of floating-point division - 15 March 1995

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

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• MIPSpro 64-Bit Porting Guide: Floating Point Optimizations
• MIPSpro 64-bit Porting Guide: Extended MIPS Floating-Point Architecture
• MIPSpro 64-bit Porting Guide: Hardware Changes

• MIPSpro Compiler Tuning: Controlling Floating Point Optimization
• Network Programming Guide: XDR Data Types Floating Points

• MIPSpro Assembly Language: Underflow Exception
• C Manual: Floating Point (F.3.6)
• MIPSpro Fortran 77: Alignment, Size, and Value Ranges
• MIPSpro Fortran 90: Numeric Precision
• Fortran Reference Manual: Intrinsic procedures to support IEEE floating-point arithmetic

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SGI Man Pages about IEEE 754

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• Fortan 90 functions
• C functions
• User Comands

16/02/99

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