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): 4:14:38 (2024)
 Error in ulps of the multiplication or division by a correctlyrounded function or constant in binary floatingpoint arithmetic, joint work with JeanMichel 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.39603977.
 DifferentialDifference Properties of Hypergeometric Series, joint work with Bruno Salvy, Proceedings of the American Mathematical Society 151 (2023), 26032617.
 Error analysis of some operations involved in the Fast Fourier Transform, joint work with Mioara Joldeş, JeanMichel Muller, AnaMaria 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 SilviuIoan Filip and Guillaume Hanrot, IEEE Transactions on Signal Processing, Volume 66, No 10, pages 26732684, May 2018.
 Exponential sums and correctlyrounded functions, joint work with Guillaume Hanrot and Olivier Robert, IEEE Transactions on Computers, Volume 66, No 12, pages 20442057, December 2017.
 On a twovalued 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 859871, April 2018.
 Comparison between binary and decimal floatingpoint numbers, joint work with Christoph Lauter, Marc Mezzarobba and JeanMichel Muller, IEEE Transactions on Computers, Volume 65, No 7, pages 20322044, July 2016.

(M,p,k)Friendly Points: a TableBased Method to Evaluate Trigonometric Functions, joint work with Dong Wang, JeanMichel Muller and
Miloš Ercegovac, IEEE Transactions on Circuits and Systems II: express briefs, Volume 31, No 9, pages 711715, September 2014.
 Algorithms and Arithmetic Operators
for Computing the η_{T}
Pairing in Characteristic Three,
joint work with
JeanLuc
Beuchat,
Jérémie Detrey, Eiji
Okamoto,
Masaaki Shirase and
Tsuyoshi Takagi,
IEEE Transactions on
Computers,
Vol. 57, n. 11, 2008, pages 14541468. There is an appendix to the article.

Correctly Rounded Multiplication by Arbitrary Precision
Constants,
joint work with JeanMichel
Muller,
IEEE Transactions on
Computers,
Vol. 57, n. 2, 2008, pages 165174.

Correct Rounding of Algebraic
Functions, joint work with JeanMichel
Muller, RAIRO
Theoretical Informatics and Applications,
Vol. 41, pages 7183, janmarch
2007.
 Hardware Operators for Function
Evaluation Using SparseCoefficient Polynomials,
joint work with JeanMichel
Muller,
Arnaud
Tisserand and Serge Torres,
Electronic Letters, Vol. 42, Issue 25, Dec. 2006, pages 14411442.

Computing MachineEfficient Polynomial Approximations, joint work with JeanMichel Muller and
Arnaud
Tisserand,
ACM Transactions on
Mathematical Software, Vol. 32, n. 2, Jun. 2006, pages 236256.
 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 255282.

A New Range Reduction Algorithm, joint work with
David Defour,
Peter Kornerup,
JeanMichel
Muller and Nathalie Revol,
IEEE Transactions on Computers,
Vol. 54, n. 3, 2005, pages 331339.
 Accelerating Correctly Rounded
FloatingPoint Division when the Divisor is
Known in Advance, joint work with JeanMichel Muller and
Saurabh Kumar Raina, IEEE Transactions on
Computers, Vol. 53, n. 8, 2004, pages 10691072.
 Irrationality Measures of log 2
and
π/
√ 3 , Experimental Mathematics, 101,
2001, pages 3552.
 Sur les fonctions entières
à double pas récurrent, joint work with Laurent Habsieger,
Annales de l'Institut Fourier, 492, 1999, pages 653671.
Articles in proceedings of international conferences
 A pathnorm 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 MachineEfficient Rational L^{∞}Approximations of Mathematical Functions, joint work with SilviuIoan Filip, Proceedings of the 30th IEEE Symposium on Computer Arithmetic (ARITH30), Portland (Oregon, USA), pages 119126, 2023.
 Testing The Sharpness of Known Error Bounds on The Fast Fourier Transform, joint work with JeanMichel Muller and Joris Picot, Proceedings of the 30th IEEE Symposium on Computer Arithmetic (ARITH30), Portland (Oregon, USA), pages 8992, 2023.
 A High Throughput Polynomial and Rational Function Approximations Evaluator, joint work with
George A. Constantinides, Miloš Ercegovac, SilviuIoan Filip, Matei Istoan and JeanMichel Muller, proceedings of the 25th IEEE Symposium on Computer Arithmetic (ARITH25), pages 99106, Amherst (MA, USA), June 2018.
 Comparison between binary64 and decimal64 floatingpoint numbers, joint work with Christoph Lauter, Marc Mezzarobba and JeanMichel Muller, proceedings of the 21st IEEE Symposium on Computer Arithmetic (ARITH21), pages 145152, Austin (Texas, USA), April 2013.
 (M,p,k)friendly points: a tablebased method for trigonometric function evaluation, joint work with Miloš Ercegovac and JeanMichel Muller, 23rd IEEE Conference on ApplicationSpecific Systems, Architectures and Processors (ASAP'2012), pages 4652, Delft (The Netherlands), July 2012.
 Rigorous Polynomial Approximation using Taylor Models in Coq, joint work with Mioara Joldeş, Érik MartinDorel, Micaela Mayero, JeanMichel Muller, Ioana Paşca, Laurence Rideau and Laurent Théry, 4th NASA Formal Methods Symposium (NFM 2012), pages 8599, Norfolk (VA, USA), April 2012.
 Augmented precision square roots, 2D
norms, and discussion on correctly rounding
√ x^{2}+y^{2} , joint work
with Mioara
Joldeş,
Peter Kornerup, Érik MartinDorel and JeanMichel Muller, 20th IEEE Symposium on Computer Arithmetic (ARITH20), pages 2023, Tübingen (Germany), July 2011.
 Chebyshev interpolation
polynomialbased tools for rigorous computing,
joint work with Mioara
Joldeş, Proceedings of the 35th
International Symposium on Symbolic and Algebraic Computation
(ISSAC 2010), pages 147154,
Munich (Germany), July 2010.
https://hal.archivesouvertes.fr/ensl00472509.
 Implementing Decimal
FloatingPoint Arithmetic through Binary: some Suggestions (poster presentation),
joint work with
Miloš Ercegovac,
Nicolas Louvet,
Érik MartinDorel,
JeanMichel Muller
and
Adrien Panhaleux,
Proc. 21st IEEE International Conference on Applicationspecific
Systems, Architectures and Processors (ASAP'2010), pages 317320,
Rennes, France, July 79, 2010.
 A Comparison between Hardware Accelerators for the Modified Tate
Pairing over F_{2m} and F_{3m},
joint work with
JeanLuc
Beuchat,
Jérémie Detrey, Eiji
Okamoto
and
Francisco RodríguezHenríquez,
Second International Conference on Pairingbased Cryptography
(Pairing'08), Lecture Notes in Computer Science n. 5209. Egham,
United Kingdom, September 2008, 297315. SpringerVerlag.
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,
JeanMichel
Muller and
Serge Torres,
19th IEEE Conference on ApplicationSpecific Systems, Architectures
and Processors (ASAP'2008), Leuven (Belgium), pages 245250, July 2008.
 Integer and FloatingPoint Constant
Multipliers for FPGAs, joint work with
Florent de
Dinechin and
JeanMichel
Muller,
19th IEEE Conference on ApplicationSpecific Systems, Architectures
and Processors (ASAP'2008), Leuven (Belgium), pages 239244, July 2008.
 Arithmetic Operators for PairingBased Cryptography,
joint work with
JeanLuc 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 239255, 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
JeanLuc 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 2539, 2007. Springer.
Cryptology ePrint Archive, Report 2007/045, 2007.
 FloatingPoint L^{2}Approximations,
joint work with
Guillaume
Hanrot, 18th IEEE
Symposium on Computer Arithmetic (ARITH18), Montpellier (France),
pages 177184, June 2007. Download it from
http://hal.inria.fr/inria00119254.
 Efficient Polynomial
L^{∞}Approximations, joint work with Sylvain
Chevillard,
18th IEEE Symposium on Computer Arithmetic
(ARITH18), Montpellier (France), pages 169176, June 2007. Download it from
http://hal.inria.fr/inria00119513.
 Correctly Rounded Multiplication by Arbitrary Precision Constants, joint work with JeanMichel
Muller, 17th IEEE Symposium on Computer Arithmetic (ARITH17),
Cape Cod (MA, USA), pages 1320, June 2005.

Functions Approximable by
Efractions, joint work with JeanMichel
Muller, Proc.
38th Conference on signals, systems and computers,
Pacific Grove, California, U.S.A., pages 13411344, Nov. 2004.

Sparsecoefficient Polynomial
Approximations for Hardware Implementations, joint work with
JeanMichel Muller and
Arnaud
Tisserand, Proc.
38th Conference on Signals, Systems and Computers,
Pacific Grove, California, U.S.A., pages 532535, Nov. 2004.
Articles under submission, reseach reports, work in progress
 An Algorithm for Finding Entire Solutions of Systems of Difference Equations, LIP Research Report RR200353.
 HighThroughput 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 SilviuIoan Filip, Matei Istoan and Florent de Dinechin.

Integer points close to a transcendental curve and correctlyrounded evaluation of a function,
joint work with
Guillaume
Hanrot, submitted.

Correctlyrounded evaluation of a function: why, how, and at what cost?, joint work with Guillaume Hanrot, JeanMichel Muller and Paul Zimmermann, submitted.
 Pathmetrics, 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, 167196.
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