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Publications and Research Works

Articles in international journals

• Efficient and Validated Numerical Evaluation of Abelian Integrals, joint work with Florent Bréhard, Mioara Joldeş and Warwick Tucker, ACM Transactions on Mathematical Software, 50(1): 4:1-4:38 (2024)
• Error in ulps of the multiplication or division by a correctly-rounded function or constant in binary floating-point arithmetic, joint work with Jean-Michel Muller and Joris Picot, IEEE Transactions on Emerging Topics in Computing.
• Approximation speed of quantized vs. unquantized ReLU neural networks and beyond, joint work with Antoine Gonon, Rémi Gribonval and Elisa Riccietti, IEEE Transactions on Information Theory, 2023, 69 (6), pp.3960-3977.
• Differential-Difference Properties of Hypergeometric Series, joint work with Bruno Salvy, Proceedings of the American Mathematical Society 151 (2023), 2603-2617.
• Error analysis of some operations involved in the Fast Fourier Transform, joint work with Mioara Joldeş, Jean-Michel Muller, Ana-Maria Naneş and Joris Picot, ACM Transactions on Mathematical Software, Vol. 46, Issue 2, May 2020, Article n. 11.
• Validated and numerically efficient Chebyshev spectral methods for linear ordinary differential equations, joint work with Florent Bréhard and Mioara Joldeş, ACM Transactions on Mathematical Software, Vol. 44, Issue 4, Aug. 2018, Article n. 44.
• A lattice basis reduction approach for the design of finite wordlength FIR filters, joint work with Silviu-Ioan Filip and Guillaume Hanrot, IEEE Transactions on Signal Processing, Volume 66, No 10, pages 2673-2684, May 2018.
• Exponential sums and correctly-rounded functions, joint work with Guillaume Hanrot and Olivier Robert, IEEE Transactions on Computers, Volume 66, No 12, pages 2044-2057, December 2017.
• On a two-valued sequence and related continued fractions in power series fields, joint work with Bill Allombert and Alain Lasjaunias, The Ramanujan Journal, Volume 45, Issue 3, pp 859-871, April 2018.
• Comparison between binary and decimal floating-point numbers, joint work with Christoph Lauter, Marc Mezzarobba and Jean-Michel Muller, IEEE Transactions on Computers, Volume 65, No 7, pages 2032-2044, July 2016.
• (M,p,k)-Friendly Points: a Table-Based Method to Evaluate Trigonometric Functions, joint work with Dong Wang, Jean-Michel Muller and Miloš Ercegovac, IEEE Transactions on Circuits and Systems II: express briefs, Volume 31, No 9, pages 711-715, September 2014.
• Algorithms and Arithmetic Operators for Computing the η_T Pairing in Characteristic Three, joint work with Jean-Luc Beuchat, Jérémie Detrey, Eiji Okamoto, Masaaki Shirase and Tsuyoshi Takagi, IEEE Transactions on Computers, Vol. 57, n. 11, 2008, pages 1454-1468. There is an appendix to the article.
• Correctly Rounded Multiplication by Arbitrary Precision Constants, joint work with Jean-Michel Muller, IEEE Transactions on Computers, Vol. 57, n. 2, 2008, pages 165-174.
• Correct Rounding of Algebraic Functions, joint work with Jean-Michel Muller, RAIRO Theoretical Informatics and Applications, Vol. 41, pages 71-83, jan-march 2007.
• Hardware Operators for Function Evaluation Using Sparse-Coefficient Polynomials, joint work with Jean-Michel Muller, Arnaud Tisserand and Serge Torres, Electronic Letters, Vol. 42, Issue 25, Dec. 2006, pages 1441-1442.
• Computing Machine-Efficient Polynomial Approximations, joint work with Jean-Michel Muller and Arnaud Tisserand, ACM Transactions on Mathematical Software, Vol. 32, n. 2, Jun. 2006, pages 236-256.
• Effective Lower and Upper Bounds for the Fourier Coefficients of Powers of the Modular Invariant j, joint work with Georges Philibert, Journal of the Ramanujan Mathematical Society, Vol. 20., n. 4, Dec. 2005, pages 255-282.
• A New Range Reduction Algorithm, joint work with David Defour, Peter Kornerup, Jean-Michel Muller and Nathalie Revol, IEEE Transactions on Computers, Vol. 54, n. 3, 2005, pages 331-339.
• Accelerating Correctly Rounded Floating-Point Division when the Divisor is Known in Advance, joint work with Jean-Michel Muller and Saurabh Kumar Raina, IEEE Transactions on Computers, Vol. 53, n. 8, 2004, pages 1069-1072.
• Irrationality Measures of log 2 and π/ √ 3 , Experimental Mathematics, 10-1, 2001, pages 35-52.
• Sur les fonctions entières à double pas récurrent, joint work with Laurent Habsieger, Annales de l'Institut Fourier, 49-2, 1999, pages 653-671.

Articles in proceedings of international conferences

• A path-norm toolkit for modern networks: consequences, promises and challenges, joint work with Antoine Gonon, Rémi Gribonval and Elisa Riccietti, to appear in the proceedings of the Twelfth International Conference on Learning Representations (ICLR 2024).
• Towards Machine-Efficient Rational L^∞-Approximations of Mathematical Functions, joint work with Silviu-Ioan Filip, Proceedings of the 30th IEEE Symposium on Computer Arithmetic (ARITH-30), Portland (Oregon, USA), pages 119-126, 2023.
• Testing The Sharpness of Known Error Bounds on The Fast Fourier Transform, joint work with Jean-Michel Muller and Joris Picot, Proceedings of the 30th IEEE Symposium on Computer Arithmetic (ARITH-30), Portland (Oregon, USA), pages 89-92, 2023.
• A High Throughput Polynomial and Rational Function Approximations Evaluator, joint work with George A. Constantinides, Miloš Ercegovac, Silviu-Ioan Filip, Matei Istoan and Jean-Michel Muller, proceedings of the 25th IEEE Symposium on Computer Arithmetic (ARITH-25), pages 99-106, Amherst (MA, USA), June 2018.
• Comparison between binary64 and decimal64 floating-point numbers, joint work with Christoph Lauter, Marc Mezzarobba and Jean-Michel Muller, proceedings of the 21st IEEE Symposium on Computer Arithmetic (ARITH-21), pages 145-152, Austin (Texas, USA), April 2013.
• (M,p,k)-friendly points: a table-based method for trigonometric function evaluation, joint work with Miloš Ercegovac and Jean-Michel Muller, 23rd IEEE Conference on Application-Specific Systems, Architectures and Processors (ASAP'2012), pages 46-52, Delft (The Netherlands), July 2012.
• Rigorous Polynomial Approximation using Taylor Models in Coq, joint work with Mioara Joldeş, Érik Martin-Dorel, Micaela Mayero, Jean-Michel Muller, Ioana Paşca, Laurence Rideau and Laurent Théry, 4th NASA Formal Methods Symposium (NFM 2012), pages 85-99, Norfolk (VA, USA), April 2012.
• Augmented precision square roots, 2-D norms, and discussion on correctly rounding √ x²+y² , joint work with Mioara Joldeş, Peter Kornerup, Érik Martin-Dorel and Jean-Michel Muller, 20th IEEE Symposium on Computer Arithmetic (ARITH-20), pages 20-23, Tübingen (Germany), July 2011.
• Chebyshev interpolation polynomial-based tools for rigorous computing, joint work with Mioara Joldeş, Proceedings of the 35th International Symposium on Symbolic and Algebraic Computation (ISSAC 2010), pages 147-154, Munich (Germany), July 2010. https://hal.archives-ouvertes.fr/ensl-00472509.
• Implementing Decimal Floating-Point Arithmetic through Binary: some Suggestions (poster presentation), joint work with Miloš Ercegovac, Nicolas Louvet, Érik Martin-Dorel, Jean-Michel Muller and Adrien Panhaleux, Proc. 21st IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP'2010), pages 317-320, Rennes, France, July 7-9, 2010.
• A Comparison between Hardware Accelerators for the Modified Tate Pairing over F_2^m and F_3^m, joint work with Jean-Luc Beuchat, Jérémie Detrey, Eiji Okamoto and Francisco Rodríguez-Henríquez, Second International Conference on Pairing-based Cryptography (Pairing'08), Lecture Notes in Computer Science n. 5209. Egham, United Kingdom, September 2008, 297-315. Springer-Verlag. Cryptology ePrint Archive, Report 2008/115, 2007. A slightly older but more complete version is available here.
• An Efficient Method for Evaluating Polynomial and Rational Function Approximations, joint work with Sylvain Chevillard, Miloš Ercegovac, Jean-Michel Muller and Serge Torres, 19th IEEE Conference on Application-Specific Systems, Architectures and Processors (ASAP'2008), Leuven (Belgium), pages 245-250, July 2008.
• Integer and Floating-Point Constant Multipliers for FPGAs, joint work with Florent de Dinechin and Jean-Michel Muller, 19th IEEE Conference on Application-Specific Systems, Architectures and Processors (ASAP'2008), Leuven (Belgium), pages 239-244, July 2008.
• Arithmetic Operators for Pairing-Based Cryptography, joint work with Jean-Luc Beuchat, Jérémie Detrey and Eiji Okamoto. In P. Paillier and I. Verbauwhede, editors, Proceedings of CHES 2007, number 4727 of Lecture Notes in Computer Science, pages 239-255, 2007. Springer. Cryptology ePrint Archive, Report 2007/091, 2007.
• A Coprocessor for the Final Exponentiation of the η_T Pairing in Characteristic Three, joint work with Jean-Luc Beuchat, Eiji Okamoto, Masaaki Shirase, Tsuyoshi Takagi. In C. Carlet and B. Sunar, editors, Proceedings of Waifi 2007, number 4547 of Lecture Notes in Computer Science, pages 25-39, 2007. Springer. Cryptology ePrint Archive, Report 2007/045, 2007.
• Floating-Point L²-Approximations, joint work with Guillaume Hanrot, 18th IEEE Symposium on Computer Arithmetic (ARITH-18), Montpellier (France), pages 177-184, June 2007. Download it from http://hal.inria.fr/inria-00119254.
• Efficient Polynomial L^∞-Approximations, joint work with Sylvain Chevillard, 18th IEEE Symposium on Computer Arithmetic (ARITH-18), Montpellier (France), pages 169-176, June 2007. Download it from http://hal.inria.fr/inria-00119513.
• Correctly Rounded Multiplication by Arbitrary Precision Constants, joint work with Jean-Michel Muller, 17th IEEE Symposium on Computer Arithmetic (ARITH-17), Cape Cod (MA, USA), pages 13-20, June 2005.
• Functions Approximable by E-fractions, joint work with Jean-Michel Muller, Proc. 38th Conference on signals, systems and computers, Pacific Grove, California, U.S.A., pages 1341-1344, Nov. 2004.
• Sparse-coefficient Polynomial Approximations for Hardware Implementations, joint work with Jean-Michel Muller and Arnaud Tisserand, Proc. 38th Conference on Signals, Systems and Computers, Pacific Grove, California, U.S.A., pages 532-535, Nov. 2004.

Articles under submission, reseach reports, work in progress

• An Algorithm for Finding Entire Solutions of Systems of Difference Equations, LIP Research Report RR2003-53.
• High-Throughput Hardware Architecture for the SWIFFT / SWIFFTX Hash Functions, joint work with Tamas Györfi, Guillaume Hanrot and Octavian Creț, Cryptology ePrint Archive, Report 2012/343.
• Automatic generation of hardware FIR filters from a frequency domain specification, joint work with Silviu-Ioan Filip, Matei Istoan and Florent de Dinechin.
• Integer points close to a transcendental curve and correctly-rounded evaluation of a function, joint work with Guillaume Hanrot, submitted.
• Correctly-rounded evaluation of a function: why, how, and at what cost?, joint work with Guillaume Hanrot, Jean-Michel Muller and Paul Zimmermann, submitted.
• Path-metrics, pruning and generalization, joint work with Antoine Gonon, Rémi Gribonval and Elisa Riccietti, submitted.

Others

• Une étude de deux problèmes diophantiens, PhD (thèse de doctorat) in Pure Mathematics, defended on September 25th, 1998, at Université Bordeaux I.
• Un peu de théorie des nombres et de calcul formel au service de l'arithmétique des ordinateurs, "Habilitation à diriger les recherches" in Computer Science, defended on September 5th, 2017, at École Normale Supérieure de Lyon.
• The Pasrec package. Pasrec is a Maple package whose aim is the solving of some difference equations systems.
• Writing of the Leçon de Mathématiques d'Aujourd'hui ``Fonctions modulaires et transcendance'' given by Michel Waldschmidt on November 30th, 1996, at Bordeaux. Éditions Cassini, Leçons de mathématiques d'aujourd'hui, volume 2, Le Sel et le Fer, numéro 12 (2003), leçon 5, 167-196.