Jean-Michel Muller's publications



 books - edition of special issues of journal and conference proceedings - articles in international journals - articles in national journals - articles in proceedings of international conferences

Recent preprints

C.-P. Jeannerod, N. Louvet, J.-M. Muller, and A. Plet,  A library for symbolic floating-point arithmetic, Nov. 2015

M. Joldes, J.-M. Muller, and V. Popescu, Tight and rigourous error bounds for basic buiding blocks of double-word arithmetic, Aug. 2016.

Books / Livres

J.-M. Muller, Arithmétique des Ordinateurs, Masson, Paris, 1989 (in French, full text available online here).

J.-C. Bajard, O. Beaumont, J.M. Chesneaux, M. Daumas, J. Erhel, D. Michelucci, J.M. Muller, B. Philippe, N. Revol, J.L. Roch and J. Vignes, Qualite des calculs sur ordinateurs,coordinated by M. Daumas and J.M. Muller, Masson, Paris, 1997 (in French).

J.-M. Muller,Elementary Functions, Algorithms and Implementation,Birkhauser Boston, 1st edition,1997. 2nd edition, 2006. 3rd edition, 2016.

J.-C. Bajard and J.-M. Muller (coordinateurs), Calcul et arithmetique des ordinateurs, Hermes (traite IC2), 2004 (in French). See contents and Introduction -- Voir la table des matières et l'introduction.

Jean-Michel Muller (coordinator), Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol, Damien Stehlé, Serge Torres, Handbook of Floating-Point Arithmetic, Birkhauser Boston, dec. 2009. 

Edition of special issues of journals and proceedings of conferences / Edition d'actes et numéros spéciaux

J.C. Bajard, D. Michelucci, J.M. Moreau and J.M. Muller, Special issue "Real Numbers and computers", Journal of Universal Computer Science, Vol.1 No .7, July 1995.

J.C. Bajard, C. Frougny, J.M. Muller and G. Villard, Special issue "Real Numbers and computers", Theoretical Computer Science, Volume 162, No 1, Aug. 1996.

T. Lang, J.M. Muller and N. Takagi, Proceedings of the 13th IEEE Symposium on Computer Arithmetic, IEEE Computer Society Press, July 1997.

N. Takagi and J.M. Muller, Special Section on Computer Arithmetic of  IEEE Transactions on Computers, Vol. 47 No 7, July 1998.

J.C. Bajard, C. Frougny and J.M. Muller, Special issue "Real Numbers and Computers", Theoretical Computer Science, Vol. 210 No 1, Jan. 1999.


D. Litaize et J.M. Muller, numéro spécial Conception et Evaluation  d'Architectures de Calculateurs, Technique et Science Informatiques, Vol. 21 No 2, 2002.

J.M. Chesneaux, C. Frougny and J.M. Muller, Special issue "Real Numbers and Computers", Theoretical Computer Science, Vol. 279 Nos 1-2, May 2002.

Peter Kornerup, Jean-Claude Bajard, Christiane Frougny and  Jean-Michel Muller, Special issue "Real Numbers and Computers", Theoretical Computer Science, Vol.  291, issue 2, Jan. 2003.

Peter Kornerup and Jean-Michel Muller (Editors), Proceedings of the 18th IEEE Symposium on Computer Arithmetic, IEEE Conference Publishing Services, June 2007.

Peter Kornerup, Paolo Montuschi, Jean-Michel Muller and Eric Schwarz, Special section on Computer Arithmetic of IEEE Transactions on Computers, Vol. 58 No 2, Feb. 2009. PDF of the introduction.

Amparo Gil, Jean-Michel Muller and J. Segura, Special issue on Numerical Software: Design, Analysis and Verification, Science of Computer Programming, Elsevier, Volume 90 Part A, 2014.

J.-M. Muller, A. Tisserand, and J. Villalba, Proceedings of the 23rd IEEE Symposium on Computer Arithmetic, IEEE Conference Publishing Services, June 2015.

J. Hormigo, J.-M. Muller, S. Oberman, N. Revol, A. Tisserand, and J. Villalba, Special issue on Computer Arithmetic, IEEE Transactions on Computers, Vol. 66, Issue 12, december 2017.

Articles in international journals / Articles dans des revues internationales

J.M. Muller, Discrete basis and computation of elementary functions, IEEE Transactions on Computers, Vol. C-35 No 9, Sept. 1985.

M. Cosnard, J.M. Muller and Y. Robert, Parallel QR decomposition of a rectangular matrix, Numerische Mathematik, Vol. 48, pp. 239-249, 1986.

A. Guyot, B. Hochet and J.M. Muller, A way to build efficient carry-skip adders, IEEE Transactions on Computers, Vol. C-36 No 10, Oct. 1987.

J. Duprat and J.M. Muller, Hardwired Polynomial evaluation, Journal of Parallel and Distributed Computing, Vol. 5, pages 291-309, June 1988.

C. Mazenc, X. Merrheim and Jean-Michel Muller, Computing functions Cos-1 and Sin-1 using Cordic, IEEE Transactions on Computers, Vol. 42 No 1, Jan. 1993.

J. Duprat and J.M. Muller, The CORDIC algorithm : new results for fast VLSI implementation, IEEE Transactions on Computers, Vol. 42 No 2, Feb. 1993.

M. Daumas, C. Mazenc and J.M. Muller, Towards a User Transparent Interval Arithmetic, Interval Computations 1994, 4, 1994, p. 46-63.

J.M. Muller, Some characterizations of functions computable in on-line arithmetic, IEEE Transactions on Computers, Vol. 43 No 6, June 1994.

J.C. Bajard, J. Duprat, S. Kla and J.M. Muller, Some operators for on-line radix-2 computations, Journal of Parallel and Distributed Computing, Vol. 22 No 2, pages 336-345, Aug. 1994.

J.C. Bajard, S.Kla and J.M. Muller, BKM: A new hardware algorithm for complex elementary functions, IEEE Transactions on Computers, Vol. 43 No 8, pages 955-963, Aug. 1994.

M. Daumas, C. Mazenc, X. Merrheim and J.M. Muller, Modular Range Reduction: a New Algorithm for Fast and Accurate Computation of the Elementary Functions, Journal of Universal Computer Science, Vol. 1 No 3, pages 162-175, March 1995.

J.M. Muller, O. Scherbyna and A. Tisserand, Semi-Logarithmic Number Systems, IEEE Transactions on Computers, Vol. 47 No 2, pages 145-151, February 1998. PDF

J.C. Bajard, L.S. Didier and J.M. Muller, A New Euclidean Division Algorithm for Residue Number Systems, Journal of VLSI Signal Processing 19, pp. 167-178, 1998.

V. Lefevre, J.M. Muller and A. Tisserand, Toward Correctly Rounded Transcendentals,   IEEE Transactions on Computers, Vol. 47 No 11, Nov. 1998.  PDF

J.M. Muller, A few results on table-based methods, Reliable Computing, Vol. 5 No 3, 1999.

A. Mignotte, J.M. Muller and O.Peyran,  Synthesis for mixed arithmetic, Design Automation for Embedded Systems, Vol. 5 No 1, pages 29-60, Feb. 2000.

M. Ercegovac, L. Imbert, D. Matula, J.M. Muller and G. Wei,  Improving Goldschmidt Division, Square Root and Square Root Reciprocal, IEEE Transactions on Computers, Vol. 49, No. 7, July 2000.PDF.

Milos Ercegovac, Tomas Lang, Jean-Michel Muller and Arnaud Tisserand, Reciprocation, Square root, Inverse Square Root,and some Elementary Functions using Small MultipliersIEEE Transactions on Computers, Vol. 49, No. 7, July 2000.  PDF.

L. Imbert, J.M. Muller and F. Rico, Radix-10 BKM Algorithm for Computing Transcendentals on Pocket Computers, Journal of VLSI Signal Processing, Vol. 25 No 2, pages 179-186, June 2000.

V. Lefevre and J.M. Muller, On-the-fly Range Reduction, Journal of VLSI Signal Processing 33, pages 31-35, Jan 2003.

J.-L. Beuchat and J.-M. Muller, Modulo M Multiplication-Addition: Algorithms and FPGA Implementation,  Electronic Letters, Vol. 40 No 11, pages 654-655, may 2004.

N. Brisebarre, J.-M. Muller and S. Raina, Accelerating Correctly Rounded Floating-PointDivision when the Divisor is Known in AdvanceIEEE Transactions on Computers, Vol. 53, No. 8, pages 1069-1072, aug. 2004.

J.M. Muller, J.L. Nicolas and X. Roblot, Nombre de solutions dans une binade de l'equation ${A^2+B^2=C^2+C}$l'Enseignement Mathématique 50, pp. 147-182, 2004.

David Defour, Guillaume Hanrot, Vincent Lefèvre, Jean-Michel Muller, Nathalie Revol and Paul Zimmermann, Proposal for a Standardization of Mathematical Function Implementation in Floating-Point ArithmeticNumerical Algorithms, vol. 37 no 1-4, pages 367-375, December 2004.

N. Brisebarre, D. Defour, P. Kornerup, J.M. Muller and N. Revol, A New Range-Reduction Algorithm, IEEE Transactions on  Computers, Vol. 54 no 3, pages 331-339, march 2005.

J.A. Pineiro, S.F. Oberman, J.-M. Muller and J.D. Bruguera, High-Speed Function Approximation using a Minimax Quadratic InterpolatorIEEE Transactions on  Computers,  Vol. 54 no 3, pages 304-318, march 2005.

P. Kornerup and J.-M. Muller, Choosing Starting Values for certain Newton-Raphson Iterations, Theoretical Computer Science, Vol. 351, pp 101-110, feb. 2006.

P. Kornerup and J.-M. Muller, Leading Guard Digits in Finite-Precision Redundant Representations,  IEEE Transactions on Computers, Vol. 55 No 5, may 2006.

N. Brisebarre, J.-M. Muller and A. Tisserand, Computing machine-efficient polynomial approximation, ACM Transactions on Mathematical Software, Vol. 32 No 2, june 2006.

N. Brisebarre, J.-M. Muller, A. Tisserand and S. Torres, Hardware Operators for Function Evaluation Using Sparse-Coefficient Polynomials, Electronic Letters, Volume 42, Issue 25, p. 1441-1442, december 2006.

N. Brisebarre and J.-M. Muller, Correct Rounding of Algebraic Functions, Theoretical Informatics and Applications, Vol. 41, pages 71-83, jan-march 2007.

F. de Dinechin, C. Lauter and J.-M. Muller, Fast and Correctly Rounded Logarithms in Double-Precision, Theoretical Informatics and Applications, Vol. 41, pages 85-102, jan-march 2007.

M.D. Ercegovac and J.-M. Muller, Complex Square Root with Operand Prescaling, Journal of VLSI Signal Processing, Vol. 49, No 1, october 2007.

N. Brisebarre and J.-M. Muller, Correctly rounded multiplication by arbitrary precision constants, IEEE Transactions on Computers, Vol. 57, No 2, pages 165-174, february 2008.

J.-L. Beuchat, T. Miyoshi, J.-M. Muller and E. Okamoto, Horner's Rule-Based Multiplication over GF(p) and GF(p^n): A Survey, International Journal of Electronics, Vol. 95 Issue 7, pages 669-685, july 2008.

J.-L. Beuchat and J.-M. Muller, Automatic Generation of Modular Multipliers for FPGA Applications,  IEEE Transactions on Computers, Vol. 57 No 12, december 2008.

M. Ercegovac and Jean-Michel Muller, An Efficient Method for Evaluating Complex Polynomials, Journal of  Signal Processing Systems, Vol. 58 no 1, pages 17-27, january 2010.

P. Kornerup, C. Lauter, V. Lefèvre, N. Louvet and J.-M. Muller, Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic,  ACM Transactions on Mathematical Software, Vol. 37 no 1, january 2010.

P. Kornerup, J.-M. Muller, and A. Panhaleux, Performing Arithmetic Operations on Round-to-Nearest Representations, IEEE Transactions on Computers, Vol. 60 No 2, february 2011.

C.-P. Jeannerod, N. Louvet, J.-M. Muller and A. Panhaleux, Midpoints and exact points of some algebraic functions in floating-point arithmetic, IEEE Transactions on Computers, Vol. 60 No 2, february 2011.

S. Boldo and J.-M. Muller, Exact and Approximated error of the FMA, IEEE Transactions on Computers, Vol. 60 No 2, february 2011.

Peter Kornerup, Vincent Lefèvre, Nicolas Louvet, and Jean-Michel Muller, On the computation of correctly-rounded sums, IEEE Transactions on Computers, Vol. 61 No 3, pages 289-298, March 2012.

C.-P. Jeannerod, N. Louvet, and J.-M. Muller, Further analysis of Kahan's algorithm for 2x2 determinants, Mathematics of Computation, Vol. 82, No 284, pages 2245-2264, oct. 2013

F. de Dinechin, C. Lauter, J.-M. Muller, and S. Torres, On Ziv's rounding test, ACM Transactions on Mathematical Software, Vol. 39 No 4, 2013.

E. Martin-Dorel, G. Melquiond, and J.-M. Muller, Some issues related to double rounding, BIT Numerical Mathematics, Volume 53, Issue 4, pages 897-924, 2013.

D. Wang, J.-M. Muller, N. Brisebarre, and M. Ercegovac, (M,p,k)-Friendly Points: a Table-Based Method to Evaluate Trigonometric Functions,  IEEE Transactions on Circuits and Systems II: express briefs, Volume 31, No 9, pp 711-715, September 2014

J.-M. Muller, On the error of computing ab+cd using Cornea, Harrison and Tang's method, ACM Transactions on Mathematical Software, Vol. 41 No 2, January 2015.

S. Graillat, V. Lefèvre, and J.-M. Muller, On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic, Numerical Algorithms (first published online: DOI 10.1007/s11075-015-9967-8), Vol. 70, Issue 3, pages 653-667, November 2015.

M. Joldes, O. Marty, J.-M. Muller, and V. Popescu, Arithmetic algorithms for extended precision using floating-point expansions, IEEE Transactions on Computers, Vol. 65 No 4, pp. 1197-1210, April 2016.

N. Brisebarre, C. Lauter, M. Mezzarobba, and J.-M. Muller, Comparison between binary and decimal floating-point numbers (extended version of the ARITH-21 paper), IEEE Transactions on Computers, Vol. 65 No 7, pp. 2032-2044, July 2016.

P. Montuschi and J.-M. Muller, Modern Computer Arithmetic, Computer, Vol. 49 issue 9, page 12, September 2016.

C.-P. Jeannerod, N. Louvet, J.-M. Muller, and A. Plet, Sharp error bounds for complex floating-point inversion, Numerical Algorithms, Vol. 73 No 3, pp. 735-760, november 2016.

C.-P. Jeannerod, P. Kornerup, N. Louvet, and J.-M. Muller, Error Bounds on Complex Floating-Point Multiplication with an FMA, Mathematics of Computation, Vol. 86 No 304, pages 881-898, march 2017.

S. Boldo, S. Graillat, and J.-M. Muller, On the robustness of the 2Sum and Fast2Sum algorithms, ACM Transactions on Mathematical Software, Vol. 44 No 1, July 2017.

M. Joldes, J.-M. Muller, and V. Popescu, Tight and rigourous error bounds for basic buiding blocks of double-word arithmetic, ACM Transactions on Mathematical Software, Vol. 44 No 2, October 2017.

Chapters in books

Florent de Dinechin, Milos Ercegovac, Jean-Michel Muller and Nathalie Revol, chapter Digital Arithmetic, in Encyclopedia of Computer Science and Engineering, Benjamin W. Wah Editor, Wiley,  ISBN 978-0-471-38393-2, pages 935-948, January 2009.

Florent de Dinechin and Jean-Michel Muller, Evaluating Elementary Functions, in The Princeton Companion to Applied Mathematics, Nicholas Higham editor, Princeton University Press, ISBN 9780691150390, Sept. 2015.

Articles in national journals

J. Duprat and J.M. Muller, Ecrire les nombres autrement pour calculer plus vite, Technique et Science Informatique, Vol. 10 No 3, 1991.

J.M. Muller, Algorithmes de division pour microprocesseurs : illustration à  l'aide du << bug >> du Pentium, Technique et Science Informatiques, Vol. 14 No 8, Oct. 1995.

J.M. Muller, Ordinateurs en quete d'arithmetique ,La Recherche, No 278, Vol. 26, July-Aug. 1995.

J.M. Muller, Vers des primitives propres en arithmetique des ordinateurs, Techniques et Sciences Informatiques, Vol. 19, Jan. 2000 .

V. Lefèvre and J.M. Muller, L'erreur en Arithmétique des Ordinateurs, Le Temps des Savoirs, No 2, Octobre 2000.

D. Lavenier, D. Litaize, J.M. Muller et P. Sainrat, Et demain, quel PC ?  Techniques et Sciences Informatiques, Vol. 20, No1, 2001.

D. Defour and J.M. Muller, Evaluation des fonctions élémentaires, Réseaux et Systèmes Répartis, Vol. 13, No 4-5, 2001.

S. Boldo and J.-M. Muller, Des ordinateurs capables de calculer plus juste, La Recherche, No 492, pages 46-52, Oct. 2014.

Articles in proceedings of international conferences

M. Cosnard, A. Guyot, B. Hochet, J.M. Muller, H. Ouaouicha and E. Zysman, FELIN : An Elementary functions cruncher, Computers and computing , actes du colloque N. Gastinel... Le calcul demain (Grenoble, Dec 85), Editions MASSON and WILEY\&Sons, pp. 301--305.

M. Cosnard, M. Daoudi, J.M. Muller and Y. Robert, On parallel and systolic Givens factorizations of dense matrices, Actes du colloque Algorithmes and architectures paralleles (Luminy, France 1986), Parallel algorithms \& architectures, M. Cosnard et al. editors, Elsevier Sci. Publishers B.V (North-Holland).

M. Cosnard, J.M. Muller, Y. Robert and D. Trystram, Communication costs versus computation costs in parallel Gaussian elimination, Ibid.

M. Cosnard, A. Guyot, B. Hochet, J.M. Muller, H. Ouaouicha, P. Paul and E. Zysman, The FELIN Arithmetic coprocessor chip, 8th IEEE Symposium on Computer Arithmetic, Como, Italy, May 1987.

J.M. Muller and D. Trystram, A VLSI Architecture for the discrete Fourier transform, IFIP WG 10.3 conf. on parallel processing, Pisa, Italy, 25-27 April 1988,inParallel Processing (M. Cosnard, M.H. Barton and M. Vanneschi editors), Elsevier Sci. Publishers B.V., North-Holland, 1988.

J.M. Muller and D. Trystram, Perfect Shuffle VLSI implementation : Applications to sorting and FFT computation, CONPAR 88, Manchester, 12-16 Sept. 1988.

J.M. Muller and F. Siebert-Roch, VLSI manipulation of polynomials, Computer Algebra and Parallelism, Grenoble, 1988, in Computer algebra and parallelism, editors : J. Della Dora and J. Fitch, Academic press, 1989.

J. Duprat, Y. Herreros and J.M. Muller, Some results about On-line computation of functions, 9th IEEE symposium on Computer Arithmetic, Santa-Monica, USA, Sept. 1989.

A. Guyot, Y. Herreros and J.M. Muller, JANUS, an on-line multiplier/divider for manipulating large numbers, 9th IEEE symposium on Computer Arithmetic, Santa-Monica, USA, Sept. 1989.

A. Guyot, Y. Kusumaputri and J.M. Muller, OCAPI, a parallel arithmetic operator for very large numbers, IFIP workshop on parallel architectures on silicon, Grenoble, France, Dec 1989.

A. Guyot, Y. Herreros, J.M. Muller and G. Privat, Redundant arithmetic operators in digital signal processing applications, IFIP workshop on parallel architectures on silicon, Grenoble, France, Dec 1989.

J. Duprat and J.M. Muller, Fast VLSI implementation of CORDIC using redundancy, IFIP Workshop on Algorithms and Parallel VLSI Architectures, Pont-a-Mousson, France, 10-16 June 1990.

P. Francois and J.M. Muller, The SCALP perturbation method, 13th Imacs World Congress on Computation and Applied Mathematics, Dublin, July 1991.

C. Mazenc, X. Merrheim, J.M. Muller and S. Kla, New algorithms for parallel and on-line computation of elementary functions, SPIE's 1991 International Symposium on Optical and Optoelectronic Applied Science and Engineering, San Diego, USA, July 1991.

J.M. Muller, On-line computations : a survey and some new results, IFIP Workshop on Algorithms and Parallel VLSI Architectures, Bonas, France, June 1991.

J. Duprat, M. Fiallos-Aguilar, J.M. Muller and H.J. Yeh, Delays of On-line Floating-point operators in Borrow-Save representation, IFIP Workshop on Algorithms and Parallel VLSI Architectures, Bonas, France, June 1991.

G. Corbaz, J. Duprat, B. Hochet and J.M. Muller, Implementation of a VLSI polynomial evaluator for real-time applications, International Conference on Application-Specific Array Processors, Barcelone, Espagne, Sept. 1991.

J.C. Bajard and J.M. Muller, A New VLSI Architecture For Fast On-line Evaluation of Power Series, International Conference on Signal Processing Applications \& Technology, Boston, Nov. 1992.

J.C. Bajard, A. Guyot, J.M. Muller and A. Skaf, On-line approximation of real functions using polynomials, International Conference on Microelectronics, Mosnastir, Tunisia, Dec 1992.

X. Merrheim, J.M. Muller and H.J. Yeh, Fast evaluation of polynomials and inverses of polynomials , 11th IEEE Symposium on Computer Arithmetic, Windsor, Canada, June 1993

J.C. Bajard, S. Kla and J.M. Muller, BKM: a new hardware algorithm for complex elementary functions , 11th IEEE Symposium on Computer Arithmetic, Windsor, Canada, June 1993

J.C. Bajard, A. Guyot, J.M. Muller and A. Skaf, A VLSI circuit for on-line polynomial computing: application to exponential, trigonometric and hyperbolic functions , VLSI93, Grenoble, Sept. 1993.

J.C. Bajard, A. Guyot, J.M. Muller and A. Skaf, Design of a VLSI circuit for on-line evaluation of several elementary functions using their Taylor expansions , International Conference on Application-Specific Array Processors (ASAP93), Venice, Italy, Oct. 1993.

M. Daumas, C. Mazenc, X. Merrheim and J.M. Muller, Fast and accurate range reduction for computation of the elementary functions , 14th Imacs World Congress on Computational and Applied Mathematics, Atlanta, USA, July 1994.

M. Daumas, J.M. Muller and J. Vuillemin, Implementing on-line arithmetic on PAM, 4th International Workshop on Field Programmable Logic and Applications, Prague, Sept. 1994.

A. Guyot, J.M. Muller and A. Skaf, On-line hardware implementation for complex exponential and logarithm, ESSCIRC'94, Ulm, Germany, Sept. 1994.

A. Mignotte and J.M. Muller, Overview of synthesis and arithmetic, IFIP Workshop on Logic and Architecture Synthesis, Grenoble, Dec. 1994.

J.M. Muller, O. Scherbyna and A. Tisserand, Semi-Logarithmic number systems , 12th IEEE Symposium on Computer Arithmetic, Bath, UK, July 1995.

J.M. Muller and A. Tisserand, Towards exact rounding of theelementary functions ({Highlighted talk ), Scan -95 (Imacs / Gamm Symposium on Scientific computing, Computer  Arithmetic and Validated Numerics), Wuppertal, Germany, Sept. 1995. in Scientific Computing and ValidatedNumerics, Alefeld, Frommer & Lang Eds, Akademie Verlag, 1996.

M. Ercegovac, J.M. Muller and A. Tisserand, Fpga Implementation of Polynomial Evaluation Algorithms, SPIE Photonics East'95 Conference, Philadelphie, USA, Oct. 1995.

A.M. Nielsen and J.M. Muller, On-Line Operators for Complex Arithmetics, MPCS'96 (Second International Conference on Masssively Parallel Computing Systems), Ischia, Italy, 6--9 May 1996.

A. Mignotte, J.M. Muller and O. Peyran, Mixed Arithmetics: Introduction and Design Structure, MPCS'96 (Second International Conference on Masssively Parallel Computing Systems), Ischia, Italy,6--9 May 1996.

J.C. Bajard, L.S. Didier and J.M. Muller, A New Euclidean Division Algorithm for Residue Number Systems, ASAP'96, Chicago, USA, Aug. 1996.

Marc Daumas, Jean-Michel Muller and Arnaud Tisserand, Theoretical support for standardized elementary functions, CESA'96 (IMACS Multiconference Computational Engineering in Systems Applications), Lille, France, 9--12 July 1996.

A. Mignotte, J.M. Muller and O. Peyran, Model for Using Redundant Number Systems in Special-Purpose Architectures, CESA'96 (IMACS Multiconference Computational Engineering in Systems Applications), Lille,France, 9--12 July 1996.

A.M. Nielsen and J.M. Muller, On-line Algorithms for Computing Exponentials and Logarithms, Europar'96, Lyon,France, Aug. 1996.

V. Lefèvre, J.M. Muller  and A. Tisserand, Towards Correctly Rounded Transcendentals, 13th IEEE Symposium on Computer Arithmetic, Asilomar, USA, July 1997.

J.M. Muller, M. Daumas and A. Tisserand, Very high radix on-line arithmetic for accurate computations, 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, Berlin, Germany , Aug.  1997.

J.M. Muller, A. Tisserand and J.M. Vincent,  Asynchronous sub-logarithmic adders, 1997 IEEE Pacific Rim Conference on Communication, Computers and Signal Processing (PACRIM97), Victoria, Canada,  Aug. 1997.

Milos Ercegovac, Tomas Lang, Jean-Michel Muller and Arnaud Tisserand, Reciprocation, Square root, Inverse Square Root, and some Elementary Functions  using Small Multipliers, SPIE's International Symposium on Optical Science,  Engineering, and Instrumentation, San Diego, July 1998.

Milos Ercegovac and Jean-Michel Muller,  Fast Evaluation of Functions at  Regularly-Spaced Points, SPIE's International Symposium on Optical Science,  Engineering, and Instrumentation, San Diego, July 1998.

F. Kaess, R. Kanan, M. Declercq, A. Tisserand, J.-M. Muller, B. Hochet and J.-M. Vincent,  A Fast Encoding Architecture for High-SpeedFlash Analog-to-Digital Converters, Second International Workshop on Design and  Diagnostics of Electronic Circuits and Systems, Szczyrk, Poland,  September 2-4,  1998.

J.M. Muller,  Table methods for evaluating elementary functions: a  survey, SCAN'98, Budapest, Hungary, September 22-25, 1998.

F. Kaess, R. Kanan, M. Declercq, A. Tisserand, J.-M. Muller, B. Hochet, and  J.-M. Vincent,  Improving High-Speed Flash Analog-to-Digital Converters  Accuracy using Sum Encoding, SCAN'98,  Budapest, Hungary,  September 22-25, 1998.

V. Lefevre and  J.M. Muller, Table Methods for the Elementary Functions, SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, Denver, July 1999.

V. Lefèvre and J.M. Muller, On-the-fly Range Reduction, SPIE's International Symposium on Optical Science and Technology, San Diego, July 30-Aug. 4 2000.

M. Daumas, C. Finot and J.M. Muller, Table Based Implementation of Elementary Functions for Hundred-Bit Precision, 16th IMACS World Congress on Computational and Applied Mathematics, Lausanne, Switzerland, August 21-25, 2000.

J.M. Muller, Correctly Rounded Functions for Better Arithmetic (invited talk), 34th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, California,  Oct.29-Nov. 1, 2000

V. Lefèvre and  J.M. Muller, Worst Cases for Correct Rounding of the Elementary Functions in Double Precision, 15th IEEE Symposium on Computer Arithmetic, Vail, Colorado, June 2001.

J.A. Pineiro, J.D. Bruguera and  J.M. Muller, Faithful Powering Computation using Table Look-Up and a Fused Accumulation Tree, 15th IEEE Symposium on Computer Arithmetic, Vail, Colorado, June 2001.

T. Lang and J.M. Muller,  Bound on Run of Zeros and Ones for Algebraic Functions, 15th IEEE Symposium on Computer Arithmetic, Vail, Colorado, June 2001.

D. Defour and J.M. Muller, Correctly Rounded Exponential Function in Double Precision Arithmetic, SPIE 46th Annual Meeting International Symposium on Optical Science and Technology, San Diego, USA, July 2001.

J.A. Pineiro, J.D. Bruguera and J.M. Muller, FPGA Implementation of a Faithful Polynomial Approximation for Powering Function Computation. Proceedings of EUROMICRO Symposium on Digital System Design (DSD'2001). Warszawa, Poland, September 2001.

D. Defour, P. Kornerup, J.M. Muller and N. Revol,  A new range reduction algorithm, 35th Conference on signals, systems and computers, Pacific Grove, California, Nov. 2001.

David Defour, Florent de Dinechin et Jean-Michel Muller, A new scheme for table-based evaluation of functions, 36th Conference on signals, systems and computers, Pacific Grove, California, Nov. 2002. 

J.M. Muller,   A "Partially rounded" Small-Order Approximations for Accurate, Hardware-Oriented, Table-Based Methods, 16th IEEE Symposium on Computer Arithmetic, Santiago de Compostela, SPAIN, June 15-18, 2003.


Milos D. Ercegovac and Jean-Michel Muller, Complex Division with Prescaling of the Operands, ASAP'2003, 14th IEEE International Conference on Application-specific Systems, Architectures and Processors The Hague, The Netherlands, June 24-26, 2003.

C. Daramy, D. Defour, F. de Dinechin and J.M. Muller, CR-LIBM: a correctly rounded elementary function library, SPIE 48th Annual Meeting International Symposium on Optical Science and Technology, San Diego, USA, Aug 3-8, 2003.

Peter Kornerup and Jean-Michel Muller, Choosing Starting Values for Newton-Raphson Computation of Reciprocals, Square-Roots and Square-Root Reciprocals, RNC5, lyon, Sept. 2003.

Milos D. Ercegovac and Jean-Michel Muller, Digit-Recurrence Algorithms for Division and Square Root with Limited Precision Primitives, 37th Conference on signals, systems and computers, Pacific Grove, California, Nov. 2003.

C. Bertin,  N. Brisebarre,  B. Dupont de Dinechin, C.-P. Jeannerod,  C Monat,  J.-M. Muller, S. Raina et A. Tisserand,  A floating-point library for integer processors, SPIE 49th Annual Meeting International Symposium on Optical Science and Technology, Denver, Colorado, Aug. 2-6, 2004.

 Milos D. Ercegovac and Jean-Michel Muller,Design of a Complex Divider, SPIE 49th Annual Meeting International Symposium on Optical Science and Technology, Denver, Colorado, Aug. 2-6, 2004.

 Milos D. Ercegovac and Jean-Michel Muller,  Complex Square Root with Operand Prescaling (best paper award), ASAP'2004,  15th IEEE International Conference on Application-specific Systems, Architectures and Processors, Galveston, Texas, 27-29 sept. 2004.

Nicolas Brisebarre and Jean-Michel Muller, Functions approximable by  E-fractions, (invited talk), 38th Conference on signals, systems and computers, Pacific Grove, California, Nov. 2004.

Nicolas Brisebarre, Jean-Michel Muller and Arnaud Tisserand,  Sparse-coefficient polynomial approximations for hardware implementations,38th Conference on signals, systems and computers, Pacific Grove, California, Nov. 2004.

Nicolas Brisebarre and Jean-Michel Muller, Correctly rounded multiplication by arbitrary precision constants, 17th IEEE Symposium on Computer Arithmetic (ARITH-17), Cape Cod (MA, USA), june 2005 (supplementary material can be obtained here)

Sylvie Boldo and Jean-Michel Muller, Some functions computable with a fused-MAC, 17th IEEE Symposium on Computer Arithmetic (ARITH-17), Cape Cod (MA, USA), june 2005.

Benoit de Dinechin, Christophe Monat, Jean-Michel Muller and Arnaud Tisserand, Division by Constant for the ST100 DSP Microprocessor, 17th IEEE Symposium on Computer Arithmetic (ARITH-17), Cape Cod (MA, USA), june 2005.

Milos D. Ercegovac and Jean-Michel Muller, Variable Radix Real and Complex Digit-Recurrence Division, ASAP'2005,  16th IEEE International Conference on Application-specific Systems, Architectures and Processors, Samos, Greece, jul. 2005.

Peter Kornerup and  Jean-Michel Muller, RN-coding of numbers: definition and some properties, IMACS'2005 World Congress, Paris, jul 2005.

Jean-Luc Beuchat and Jean-Michel Muller, Multiplication Algorithms for Radix-2 RN-Codings and Two's Complement Numbers, ASAP'2005,  16th IEEE International Conference on Application-specific Systems, Architectures and Processors, Samos, Greece, jul. 2005.

Rachid Beguenane, Jean-Luc Beuchat, Jean-Michel Muller and Stéphane Simard, Modular Multiplication of Large Integers on FPGAs, 39th Conference on signals, systems and computers, Pacific Grove, California, Nov. 2005.

Milos Ercegovac, Jean-Michel Muller and Arnaud Tisserand, Simple Seed Architectures for Reciprocal and Square-Root Reciprocal, 39th Conference on signals, systems and computers, Pacific Grove, California, Nov. 2005.

Jean-Michel Muller, Generating functions at compile-time (invited talk), 40th Conference on signals, systems and computers, Pacific Grove, California, Nov. 2006.

Milos Ercegovac and Jean-Michel Muller, Arithmetic Processor for Solving Tri-Diagonal Systems of Linear Equations, 40th Conference on signals, systems and computers, Pacific Grove, California, Nov. 2006.

Milos Ercegovac and Jean-Michel Muller, A Hardware-Oriented Method for Evaluating ComplexPolynomials, 18th IEEE Conference on Application-Specific Systems, Architectures and Processors (ASAP'2007), Montreal, Canada, jul. 2007.

Milos Ercegovac and Jean-Michel Muller, Complex Multiply-Add and Other Related Operators, SPIE Conf. Advanced Signal Processing Algorithms, Architectures and Implementation XVII, San Diego, California, Aug. 26-27, 2007.

Peter Kornerup, Vincent Lefevre and Jean-Michel Muller, Computing Integer Powers in Floating-Point Arithmetic, 41th Conference on signals, systems and computers, Pacific Grove, California, Nov. 2007.

Nicolas Brisebarre, Sylvain Chevillard, Milos Ercegovac, Jean-Michel Muller and Serge Torres, An efficient Method for Evaluating Polynomial and Rational Function Approximations, 19th IEEE Conference on Application-Specific Systems, Architectures and Processors (ASAP'2008), Leuven, Belgium, July 2-4, 2008.

Nicolas Brisebarre, Florent de Dinechin and Jean-Michel Muller, Integer and Floating-Point Constant Multipliers for FPGAs, 19th IEEE Conference on Application-Specific Systems, Architectures and Processors (ASAP'2008), Leuven, Belgium, July 2-4, 2008.

Peter Kornerup, Vincent Lefèvre, Nicolas Louvet, and Jean-Michel Muller, On the computation of correctly-rounded sums, 19th IEEE Symposium on Computer Arithmetic (ARITH-19), Portland, Oregon, USA, June 8-10, 2009.

Pouya Dormiani, Milos Ercegovac and Jean-Michel Muller, Design and Implementation of a Radix-4 Complex Division Unit with Prescaling, 20th IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP'09), Boston, USA, July 7-9, 2009.

Pouya Dormiani, Milos Ercegovac and Jean-Michel Muller, Low Precision Table Based Complex Reciprocal Approximation, 43rd Conference on signals, systems and computers, Pacific Grove, California, Nov. 2009.

Nicolas Louvet, Jean-Michel Muller and Adrien Panhaleux, Newton-Raphson Algorithms for Floating-Point Division Using an FMA, 21st IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP'2010), pages 200-207, Rennes, France, July 7-9, 2010.

Nicolas Brisebarre, Milos Ercegovac, Nicolas Louvet, Erik Martin-Dorel, Jean-Michel Muller, and Adrien Panhaleux, Implementing Decimal Floating-Point Arithmetic through Binary: some Suggestions (poster presentation), Proc. 21st IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP'2010), pages 317-320, Rennes, France, July 7-9, 2010.

Christian Bertin, Claude-Pierre Jeannerod, Jingyan Jourdan-Lu, Hervé Knochel, Christophe Monat, Christophe Mouilleron, Jean-Michel Muller, and Guillaume Revy, Techniques and tools for implementing IEEE 754 floating-point arithmetic on VLIW integer processors, PASCO'2010, Grenoble, France, 21-23 July 2010.

Nicolas Brisebarre, Mioara Joldes, Peter Kornerup, Erik Martin-Dorel and Jean-Michel Muller, Augmented precision square roots, 2-D norms, and discussion on correctly rounding sqrt(x^2+y^2), 20th IEEE Symposium on Computer Arithmetic (Arith-20), Tuebingen, Germany, July 25-27, 2011.

Florent de Dinechin, Jean-Michel Muller, Bogdan Pasca and Alexandru Plesco, An FPGA architecture for solving the Table Maker's Dilemma, Proc.22nd IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP'2011), Santa Monica, USA, Sept. 2011, Best paper award.

N. Brisebarre, M. Joldes, E. Martin-Dorel, M. Mayero, J.-M. Muller, I. Pasca, L. Rideau, and L. Théry, Rigorous Polynomial Approximation Using Taylor Models in Coq, Proc. NFM 2012, The 4th NASA Formal Methods Symposium (LNCS No 7226), Norfolk, Virginia, USA, April 3-5, 2012.

Nicolas Brisebarre, Milos Ercegovac, and Jean-Michel Muller, (M,p,k)-friendly points: a table-based method for trigonometric function evaluation, Proc.23rd IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP'2012), Delft, The Netherlands, 9-11 juillet 2012.

N. Brisebarre, C. Lauter, M. Mezzarobba, and J.-M. Muller, Comparison between binary64 and decimal64 floating-point numbers, 21st IEEE Symposium on Computer Arithmetic, Austin, TX, USA, April 7-10, 2013.

C.-P. Jeannerod, N. Louvet, and J.-M. Muller, On the componentwise accuracy of complex floating-point division with an FMA, 21st IEEE Symposium on Computer Arithmetic, Austin, TX, USA, April 7-10, 2013.

J.-M. Muller, Avoiding double roundings in scaled Newton-Raphson division (invited talk), Proceedings of the Asilomar Conference on Signals, Systems, and Computers, Pacific grove, CA, USA, Nov. 3-6, 2013.

O. Kupriianova, C. Lauter, and J.-M. Muller, Radix-Conversion for IEEE 754-2008 Mixed Radix Floating-Point Arithmetic (poster presentation), Proceedings of the Asilomar Conference on Signals, Systems, and Computers, Pacific grove, CA, USA, Nov. 3-6, 2013.

M. Joldes, J.-M. Muller, and V. Popescu, On the computation of the reciprocal of floating-point expansions using an adapted Newton-Raphson iteration, Proc.25th IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP'2014), Zurich, Switzerland, July 18-20, 2014.

N. Brunie, F. de Dinechin, J. Le Maire, and J.-M. Muller, Computing the floating-point logarithm with fixed-point operations, Proceedings of the 23rd IEEE Symposium on Computer Arithmetic, Santa Clara, CA, USA, July 10-13, 2016.

J.-M. Muller, V. Popescu, and P. Tang, A new multiplication algorithm for extended precision using floating-point expansions, Proceedings of the 23rd IEEE Symposium on Computer Arithmetic, Santa Clara, CA, USA, July 10-13, 2016.

S. Collange, M. Joldes, J.-M. Muller, and V. Popescu, Parallel floating-point expansions for extended-precision GPU computations, Proceedings of ASAP'2016, 27th Annual IEEE International Conference on Application-specific Systems, Architectures and Processors, London, UK, June 6-8, 2016.

M. Joldes, J.-M. Muller, V. Popescu, and J.-M. Muller, CAMPARY: Cuda Multiple Precision Arithmetic Library and Applications, Mathematical Software–ICMS 2016: 5th International Conference, Berlin, Germany, July 11-14, 2016, Proceedings. Vol. 9725. Springer, 2016.

C.-P. Jeannerod, J.-M. Muller, A. Plet. The Classical Relative Error Bounds for Computing sqrt(a^2+b^2) and c/sqrt(a^2+b^2) in Binary Floating-Point Arithmetic are Asymptotically Optimal, 24th IEEE Symposium on Computer Arithmetic (ARITH-24), London, UK, July  24-26, 2017. Slides.

M. Joldes, J.-M. Muller and V. Popescu, Implementation and performance evaluation of an extended precision floating-point arithmetic library for high-accuracy semi-definite programming, 24th IEEE Symposium on Computer Arithmetic (ARITH-24), London, UK, July  24-26, 2017.

S. Boldo, M. Joldes, J.-M. Muller, and V. Popescu, Formal Verification of a Floating-Point Expansion Renormalization Algorithm, 8th International Conference on Interactive Theorem Proving (ITP'2017), Brasilia, Brasil, 26-29 Sept. 2017.

A. Blot, J.-M. Muller, and L. Théry, Formal Correctness of Comparison Algorithms Between Binary64 and Decimal64 Floating-Point Numbers, International Workshop on Numerical Software Verification (NSV 2017),  Lecture Notes in Computer Science  (LNCS, volume 10381), pp 25-37, 2017.




Recent conferences without proceedings

Nicolas Brisebarre, Mioara Joldes, Erik Martin-Dorel, Micaela Mayero, Jean-Michel Muller, Ioana Pasca, Laurence Rideau and Laurent Théry, Certified Polynomial Approximation for solving the Table Maker's Dilemma, Types 2001, Bergen, Norway, Sept. 8-11 2011.

Jean-Michel Muller, Exact computations with an arithmetic known to be approximate (invited talk), MaGiX@LiX 2011, Ecole Polytechnique, Sept. 2011

Jean-Michel Muller, Faire compter les ordinateurs : quels algorithmes ? Comment faire des calculs "exacts" avec une arithmétique approchée ? Comment ne pas écrire des arithmétiques fausses ? (invited talk), Journées nationales de l'APMEP (Association des Professeurs de Mathématiques de l'Enseignement Public), Grenoble, 24 octobre 2011.

Jean-Michel Muller, Invited talk, Some issues related to double roundings, in the satellite workshop  SIAM'2012 Conference on Applied Linear Algebra, Valence, Spain, June 22, 2012.

Jean-Michel Muller, Invited talk, On Kahan's algorithm for the accurate computation of 2x2 determinants, Workshop on Numerical Software, Santander, Spain, July 6, 2012.

Jean-Michel Muller, Invited talk, Proof of Properties in Floating-Point Arithmetic, LMS computer science colloquium "Verification and Numerical Algorithms", London, November 13, 2012.

Jean-Michel Muller, Invited talk, Proof of Properties in Floating-Point Arithmetic, Continuity, Computability, Constructivity ? From Logic to Algorithms (CCC 2013), Swansea University/Gregynog, UK, 26-30 June 2013.

Jean-Michel Muller, Une petite histoire de l'arithmétique virgule flottante, Journées RAIM, 18-20 novembre 2013.

Jean-Michel Muller, Virgule flottante: la lente convergence vers la rigueur, Math & Computer Science Seminar, Paris 6 Univ., Dec. 2, 2013

Slides for the INVA'2014 conference (Tokyo and Kyoto, March 2014):  On complex multiplication and division with an FMA, and On the maximum relative error when computing x^n in floating-point arithmetic.

Jean-Michel Muller, Invited talk, Getting tight error bounds in floating-point arithmetic: illustration with complex functions, and the real x^n function, Workshop NSV: Numerical Software Verification (part of the Vienna Summer of Logic), Vienna, Austria, July 2014.

Algorithmes arithmétiques: j'apprends à compter aux ordinateurs, présentation aux Soirées mathématiques de Lyon, 24 mars 2014.

My recent co-authors

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Last modification: Feb. 6, 2017