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Christoph Quirin Lauter

Software Engineer for Intel Corporation, member of the Numerics team

Former Ph.D. student under Florent de Dinechin, in the Arénaire project, at LIP.

Married, no children.

Research interests:

The subject of my Ph.D. thesis has been the correct rounding of elementary functions, such as exp(x), log(x), sin(x), asin(x), power(x,y), in IEEE 754 double precision.

The implementation of elementary functions faces several difficulties of different kind:

• theoretical issues as the table maker's dilemma,
• applicational problems like the computation and the proof of approximation error bounds or like the testing of exact cases,
• challenges like certifiying the behaviour of100 lines of floating-point code or
• difficulties in the (automatized) efficient implementation on current hardware.

I participated on the revision of the IEEE 754 standard that reigns floating-point arithmetic. With Florent de Dinechin and Jean-Michel Muller, I proposed the following reformulation of the chapter on elementary functions. The proposal can be found here. A second remark on the draft version 1.6.0 of january 10, 2008 can be found here.

I have done research on how the implementation and certification of a mathematical function can be automatized. Starting from this, I have been interested on safe algorithms for some high-level computation problems. As an example, let me mention the computation of the infinity norm of a composite function. Here, computation means giving an under- and, more important, an over-estimate of the unknown supremum of the function. The function itself is given as an expression tree. Its leaves are basic functions or "black-box" codes. Of course, the multi-precision evaluation of such a tree in a point or small interval is an important sub-problem. This yields directly to questions on how intermediate precision must be adapted for ensuring a faithful rounding...

I have integrated those algorithms in the software tool Sollya. Sollya is intended as a safe support for the development of elementary functions. I used then Sollya for my Metalibm project, striving to an automatic implementer for mathematical (libm) functions.

Short curriculum vitae:

• Born April, 24 1980 in Amberg, Germany
• Bavarian A-levels 1999, specialization in mathematics et french.
• Start of the studies at Technische Universität München in 2000
• Year Erasmus at École Normale Supérieure de Lyon 2002
• Internship in the Intel Numerics Group 2003
• Diploma in Computer Science (Master's) at Technische Universität München 2005
• Ph.D. thesis in the Arénaire team at École Normale Supérieure de Lyon 2005-2008
• Software Engineer for Intel Corporation in the Numerics Group since 2008

Publications:

Articles in international journals:

• Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic, with Jean-Michel Muller, Peter Kornerup, Vincent Lefèvre and Nicolas Louvet, in ACM Transactions on Mathematical Software, Vol. 37, No. 1, Article 4, January 2010, Preprint in research report 2008-15, LIP, École Normale Supérieure de Lyon, May 2008.
• An efficient rounding boundary test for pow(x,y) in double precision, with Vincent Lefèvre, in IEEE Transactions on Computers, 2009, vol. 58, 2, pages 197-207, February 2009. Preprint in research report 2007-36, LIP, École Normale Supérieure de Lyon, August 2007.
• Fast and correctly rounded logarithms in double-precision, with Florent de Dinechin and Jean-Michel Muller, in RAIRO, Theoretical Informatics and Applications, 2007, vol. 41, pages 85-102, Preprint in research report 2005-37, LIP, École Normale Supérieure de Lyon, September 2005.

Articles to appear in international journals:

• Certifying the floating-point implementation of an elementary function using Gappa, with Florent de Dinechin and Guillaume Melquiond, TCSI, Special Issue on Computer Arithmetic, to appear.

Articles in the proceedings of international conferences:

• Certified and fast computation of supremum norms of approximation errors, with Sylvain Chevillard and Mioara Joldeş, in Proceedings of the 19th IEEE Symposium on Computer Arithmetic, pages 169-176, Portland, Oregon, USA, July 2009, Preprint in research report 2008-37, LIP, École Normale Supérieure de Lyon, October 2008.
• Optimizing polynomials for floating-point implementation, with Florent de Dinechin, in Proceedings of the 8th Conference on Real Numbers and Computers, pages 7-16, Santiago de Compostela, Spain, July 2008, Preprint in research report 2008-11, LIP, École Normale Supérieure de Lyon, March 2008.
• A certified infinite norm for the implementation of elementary functions, with Sylvain Chevillard, in Proceedings of the Seventh International Conference on Quality Software, pages 153-160, Portland, Oregon, USA, October 2007, Preprint and Extended Version in research report 2007-26, LIP, École Normale Supérieure de Lyon, June 2007.
• Assisted verification of elementary functions using Gappa, with Florent de Dinechin and Guillaume Melquiond, in Proceedings of the 21st Annual ACM Symposium on Applied Computing - MCMS Track, vol. 2, pages 1318-1322, Dijon, France, April 2006, Preprint and Extended Version in research report #5683, INRIA, September 2005.

Research reports:

• Efficient and accurate computation of upper bounds of approximation errors, with Sylvain Chevillard, John Harrison and Mioara Joldeş, Research report 2010-2, LIP, CNRS/ENS Lyon/INRIA/Université de Lyon, INRIA, LORIA, CACAO project and Intel Corporation, Hillsboro, Oregon, USA, January 2010. Article submitted to Theoretical Computer Science; Special Issue on Symbolic and Numeric Computation, 2009.
• Certifying floating-point implementations using Gappa, with Florent de Dinechin and Guillaume Melquiond, Research report arXiv: 0801.0523, LIP, CNRS/ENS Lyon/INRIA/Université de Lyon, January 2008.
• Exact and mid-point rounding cases of power(x,y), Research report 2006-46, LIP, École Normale Supérieure de Lyon, December 2006.
• Basic building blocks for a triple-double intermediate format, Research report RR-5702, INRIA, September 2005.
• Fast correct rounding of elementary functions in double precision using double-extended arithmetic, with Florent de Dinechin and David Defour, Research report 2004-10, LIP, École Normale Supérieure de Lyon, March 2004.
• A correctly rounded implementation of the exponential function on the Intel Itanium architecture, Research report RR-5024, INRIA, December 2003.

Master's and Ph.D. thesis:

• Arrondi correct de fonctions mathématiques - Fonctions univariées et bivariées, certification et automatisation, Thèse de doctorat, École Normale Supérieure de Lyon, October 2008.
• Effective evaluation of correctly rounded elementary functions using triple-double intermediate representation, Master's thesis, Technische Universität München, Faculty of Computer Science, September 2005.
• Ressourcenmanagement über drahtgebundene und drahtlose LAN, Thesis for a development project, Technische Universität München, Chair for Communication Networks, 2004.

Presentations and Workshops:

• Sollya - a numerical software tool for the semi-automatic implementation of efficient correctly rounded mathematical functions, presentation on invitation for the conference ACA 2008, Hagenberg, Austria, July 2008, Abstract.
• Quand les boucles deviennent des polynômes ou l'implantation automatique de fonctions, Presentation at the RAIM 2008 days, Lille, France, June 2008, Slides.
• Vers une implémentation automatique de fonctions libm, Presentation for the EVA-Flo project, Perpignan, France, October 2007, Slides.
• Advancements in (cr)libm development, Presentation for Intel Portland, Portland, Orgeon, USA, October 2007, Slides.
• Towards automatic generation of elementary functions, Presentation for the russian team in the Intel Numerics Group, Nizhny Novgorod, Russia, August 2007, Slides.
• Automatisation du contrôle de précision et de la preuve pour les formats double-double et triple-double, Workshop of the CACAO project, LORIA, Nancy, France, January 2007, Abstract.
• A Survey of Multiple-Precision Using Floating-Point Arithmetic, Fourth International Workshop on Taylor Methods, Boca Raton, Florida, USA, December 2006, Abstract, Slides.
• Certified infinite norm using interval arithmetic, with Sylvain Chevillard, 12th GAMM - IMACS International Symposion on Scientific Computing, Computer Arithmetic and Validated Numerics, Duisburg, Germany, September 2006, Abstract.
• Normes infinies certifiées par l'arithmétique d'intervalles, Journées Nationales d'Arithmétique des Ordinateurs 2006, May-June 2006, Slides.
• Correctly rounding elementary functions using triple-double intermediate representation, Journées Arinews, Perpignan, France, November 2005, Slides.

Miscellaneous:

• Users' manual for the Sollya tool, Release 1.1, with Sylvain Chevillard, Nicolas Jourdan and Mioara Joldeş, Users' manual.

Developped open source software:

• CR-LIBM, with Florent de Dinechin, David Defour et al.: a library of correct rounding elementary functions in double precision
• Sollya, with Sylvain Chevillard: a tool for manipulating data in the automatized implementation of elementary functions. Documentation is available here.
• Metalibm: a tool for the automatic implementation of mathematical (libm) functions.

Teaching:

• exercises in Parallel Numerics, Master Computer Science in Engineering, Technische Universität München
• exercises in Compiler Design, Master course, ENS Lyon
• exercises in Term Rewriting, Bachelor course, ENS Lyon
• exercises in Algorithms for Arithmetic 2007, Master course, ENS Lyon
• exercises in Architecture, Systems, Networks, Bachelor course, ENS Lyon
• exercises in Arithmetic 2008, Master course, ENS Lyon

Contact:

Last update: 05/08/2010.