Vincent Lefèvre's Research Pages: Computer Arithmetic

My Web Pages

My blog associated with these web pages.

• Test of mathematical functions of the standard C library on various machines.

• Linux and the extended precision on x86 processors.

• Multiplication by integer constants.

• Floating-point arithmetic test programs.

See also sipe.h (Small Integer Plus Exponent).

My Publications

You can see the list of my publications (with a link to the publication if it is available on the web) or download it in the bibtex format.

Slides

Information about the file formats of my slides.

• The table maker's dilemma, Caen, France, March 1999 (in French): PDF, gzipped PS.

• The table maker's dilemma, AOC workshop, November 2000 (in English): PDF, gzipped PS.

• The table maker's dilemma, École de Printemps Arithmétique des Ordinateurs, Prapoutel, France, March 2001 (in French): PDF, gzipped PS.

• Multiplication by an integer constant, AOC workshop, June 2001 (in French): PDF, gzipped PS.

• MPFR (software demonstration), Computability and Complexity in Analysis workshop, Málaga, Spain, July 2002 (in English): PDF, gzipped PS.

• Exhaustive tests of the elementary functions, Arinews workshop, November 2002 (in French): PDF, gzipped PS.

• Exhaustive tests of the elementary functions, journées au vert SPACES, May 2003 (in French): PDF, gzipped PS.

• Multiplication by an integer constant, lower bounds on the code length, RNC'5, École Normale Supérieure de Lyon, Lyon, France, September 2003 (in English): PDF, gzipped PS.

• Exhaustive tests of the elementary functions, Arinews workshop, November 2003 (in French): PDF, gzipped PS.

• Back on the algorithm that computes a lower bound on the distance between a segment and ℤ², Arinews workshop, May 2004 (in French): PDF, gzipped PS. Associated HTML file: example.

• Back on the algorithm that computes a lower bound on the distance between a segment and ℤ², journées au vert SPACES, June 2004 (in French): PDF, gzipped PS. Associated HTML file: example.

• The generic multiple-precision floating-point addition with correct rounding (as in the MPFR library), RNC'6, Schloß Dagstuhl, Germany, November 2004 (in English): PDF, gzipped PS.

• The Euclidean division implemented with a floating-point division and a floor, Arinews workshop, March 2005 (in French): PDF, gzipped PS.

• New results on the distance between a segment and ℤ² — application to the exact rounding, Arith'17, June 2005 (in English): PDF, gzipped PS.

• Worst cases for the exponential function in the IEEE 754r decimal64 format, JNAO, May/June 2006 (in English): PDF, gzipped PS.

• Searching for worst cases of sin(BIG) (in double precision), journées au vert SPACES, June 2006 (in French): PDF, gzipped PS.

• Searching for some worst cases for the correct rounding of the power functions in double precision, Dagstuhl Seminar 08021 Numerical Validation in Current Hardware Architectures, January 2008 (in English): PDF.

• Approximating a function f by polynomials to compute approximate successive values f(0), f(1), f(2)..., Arénaire workshop, March 2008 (in French): PDF.

• Introduction to the GNU MPFR library, CNC'2 summer school, June 2009 (in English): PDF.

• Finding worst cases for correct rounding of numerically regular math functions in fixed precision, internal communication, October 2009 (in English): PDF.

Links Related to my Work

• The Table Maker's Dilemma.

• SLZ algorithm and results.

• Projet ANR EVA-Flo: Évaluation et Validation Automatique pour le calcul Flottant.

• Arithmétique des Ordinateurs Certifiée (1999 - 2002).

• Jean-Michel Muller's home page.

• About the IEEE-754 standard, and its revision (754R / 754-2008). See also: IEEE 754-2008 errata.

• Some disasters attributable to bad numerical computing.

• The GMP library.

• The MPFR library (and also MPFR++ and MPFI). Try it online!

• The Apfloat library.

• iRRAM, exact arithmetic in C++.

• Interval Computations pages and interval arithmetic standardization.

• Exact geometric computation web site and the Core library.