I am an Inria researcher (*Chargé de Recherche*) at the Laboratoire de l'Informatique du Parallélisme (École Normale Supérieure de Lyon) in the AriC project (ex-Arénaire). I mainly work on computer arithmetic (in particular, floating-point arithmetic and correct rounding, in fixed or arbitrary precision). I also participate in standardization: IEEE 754, interval arithmetic (P1788), POSIX. I am one of the main developers of the GNU MPFR library (arbitrary-precision floating-point arithmetic with correct rounding), on which I started to work when I was at Loria.

My blog associated with these web pages.

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

Sipe (radix-2 floating-point computations in very low precisions with correct rounding).

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.

Our book Handbook of Floating-Point Arithmetic, second edition (on the publisher's site). See also this page with links and errata and the first edition.

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 ℤ

^{2}, 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 ℤ

^{2}, 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 ℤ

^{2}— 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 work session, March 2008 (in French): PDF.Introduction to the GNU MPFR library, CNC'2 summer school, June 2009 (in English): PDF.

**Errata:**The formulas on slide 15 (Simple Output) are incorrect; one needs to add 1 to both formulas. MPFR (code and documentation) was correct.Finding worst cases for correct rounding of numerically regular math functions in fixed precision, internal communication, October 2009 (in English): PDF.

Proofs by exhaustive tests in small precision, Arénaire work session, November 2009 (in English): PDF.

Hierarchical approximations of a function by polynomials in LEMA, internal communication, February 2010 (in English): PDF.

Correct rounding of mathematical functions, ENS-Lyon students' seminar, March 2010 (in English): PDF.

Hard-to-round cases, TaMaDi ANR project, October 2010 (in English): PDF.

**Errata:**On slide 11 (Function`log1p`

), the command./readres -y 58 -f hr -s dwim archres/results.l1m.-1.54.*

should be replaced by:

./readres -x 58 -f hr -s dwim archres/results.l1m.-1.54.*

and on slide 27 (Function

`log2`

), the command./readres -x 53 -f hr -s dwim archres/results.lg2.*

should be replaced by:

./readres -y 53 -f hr -s dwim archres/results.ex2.*

(these errors have no effects on the results).

Generating coefficients of approximation polynomials on sub-intervals, with guaranteed error bounds, TaMaDi ANR project, February 2011 (in French): PDF.

Introduction to the GNU MPFR library, GNU Hackers Meeting (Paris), August 2011 (in English): PDF.

**Errata:**The formulas on slide 17 (Simple Output) are incorrect; one needs to add 1 to both formulas. MPFR (code and documentation) was correct.Generating a minimal interval arithmetic based on GNU MPFR (in the context of the search for hard-to-round cases), Dagstuhl Seminar 11371 Uncertainty modeling and analysis with intervals: Foundations, tools, applications, September 2011 (in English): PDF.

Hierarchical polynomial approximation, TaMaDi ANR project, December 2011 (in English): PDF.

IEEE P1788 – Standardization of interval arithmetic, AriC (ex-Arénaire) work session, June 2012 (in English): PDF.

Floating-point arithmetic in arbitrary precision, school précision et reproductibilité en calcul numérique, March 2013 (in English, except the title slide): PDF.

**Errata:**The formulas on slide 24 (Simple Output) are incorrect; one needs to add 1 to both formulas. The GNU MPFR library (code and documentation) was correct.SIPE: Small Integer Plus Exponent, ARITH 21, April 2013 (in English): PDF.

Hard-to-round cases – Part 2, TaMaDi ANR project, October 2013 (in English): PDF.

Introduction to the GNU MPFR library, AriC (ex-Arénaire) work session, April 2014 (in English): PDF.

Correctly rounded arbitrary-precision floating-point summation, RAIM 2016, June 2016 (in English): PDF.

Correctly rounded arbitrary-precision floating-point summation, ARITH 23, July 2016 (in English): PDF.

SLZ algorithm and results (2005-11-10).

TaMaDi ANR project (2010 - 2013): Table Maker's Dilemma.

EVA-Flo ANR project (2007 - 2010):

*Évaluation et Validation Automatique pour le calcul Flottant*.Arithmétique des Ordinateurs Certifiée (1999 - 2002).

About the IEEE 754 standard / permanent archival site for the 754-2019 development. See also the IEEE 754-2019 errata and the old IEEE 754-2008 errata (non-exhaustive list).

Multiple precision / arbitrary precision:

The GMP library (integers, rational numbers).

The GNU MPFR library (floating-point arithmetic with correct rounding). Try it online! Thanks to Tomonori Kouya for this service.

The GNU MPC library (complex numbers), based on GNU MPFR.

The MPFI library (interval arithmetic), based on GNU MPFR.

The Apfloat library.

iRRAM, exact arithmetic in C++, based on GNU MPFR.

Interval Computations pages and interval arithmetic standardization.

Exact geometric computation web site and the Core library.

La Recherche Award 2013 in computer science (Peter Kornerup, Vincent Lefèvre, Nicolas Louvet, and Jean-Michel Muller). Video.

The CORE-MATH project (some mathematical functions in the binary32, binary64, binary80 and binary128 formats with correct rounding).

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