Team Arénaire
Members
Overall Objectives
Scientific Foundations
Application Domains
Software
New Results
Contracts and Grants with Industry
Other Grants and Activities
Dissemination
Bibliography
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Bibliography

Major publications by the team in recent years

[1]
N. Brisebarre, J.-M. Muller, A. Tisserand.
Computing machine-efficient polynomial approximations, in: ACM Transactions on Mathematical Software, to appear.
[2]
F. de Dinechin, A. Ershov, N. Gast.
Towards the post-ultimate libm, in: 17th Symposium on Computer Arithmetic, IEEE Computer Society Press, June 2005.
[3]
F. de Dinechin, A. Tisserand.
Multipartite table methods, in: IEEE Transactions on Computers, March 2005, vol. 54, no 3, p. 319–330.
[4]
D. Defour, G. Hanrot, V. Lefèvre, J.-M. Muller, N. Revol, P. Zimmermann.
Proposal for a standardization of mathematical function implementation in floating-point arithmetic, in: Numerical Algorithms, dec 2004, vol. 37, no 1-4, p. 367–375.
[5]
J. Detrey, F. de Dinechin.
Parameterized floating-point logarithm and exponential functions for FPGAs, in: Journal of Microprocessors and Microsystems, to appear.
[6]
C.-P. Jeannerod, G. Villard.
Essentially optimal computation of the inverse of generic polynomial matrices, in: Journal of Complexity, 2005, vol. 21, no 1, p. 72–86.
[7]
E. Kaltofen, G. Villard.
On the complexity of computing determinants, in: Computational Complexity, 2005, vol. 13, no 3-4, p. 91–130.
[8]
J.-M. Muller.
Elementary Functions: Algorithms and Implementation, Second, Birkhäuser , Boston, 2006.
[9]
N. Revol, K. Makino, M. Berz.
Taylor models and floating-point arithmetic: proof that arithmetic operations are validated in COSY, in: Journal of Logic and Algebraic Programming, 2005, vol. 64, p. 135–154.
[10]
N. Revol, F. Rouillier.
Motivations for an arbitrary precision interval arithmetic and the MPFI library, in: Reliable Computing, 2005, vol. 11, no 4, p. 275–290.
[11]
A. Tisserand.
Low-Power Arithmetic Operators, in: Low Power Electronics Design, C. Piguet (editor), CRC Press, November 2004, chap. 9.

Publications of the year

Articles in refereed journals and book chapters

[12]
B. Beckermann, G. Labahn, G. Villard.
Normal forms for general polynomial matrices, in: Journal of Symbolic Computation, to appear, 2005.
[13]
N. Boullis, A. Tisserand.
Some Optimizations of Hardware Multiplication by Constant Matrices, in: IEEE Transactions on Computers, October 2005, vol. 54, no 10, p. 1271–1282.
[14]
N. Brisebarre, D. Defour, P. Kornerup, J.-M. Muller, N. Revol.
A new range reduction algorithm, in: IEEE Transactions on Computers, 2005, vol. 54, no 3, p. 331–339.
[15]
N. Brisebarre, J.-M. Muller.
Correct Rounding of Algebraic Functions, in: RAIRO Theoretical Informatics and Applications, to appear, 2005.
[16]
N. Brisebarre, G. Philibert.
Effective lower and upper bounds for the Fourier coefficients of powers of the modular invariant j, in: J. Ramanujan Math. Soc., 2005, vol. 20, no 4, p. 255–282.
[17]
A. Darte, R. Schreiber, G. Villard.
Lattice based memory allocation, in: IEEE Transactions on Computers, 2005, vol. 54, no 10, p. 1242–1257.
[18]
F. de Dinechin, C. Q. Lauter, J.-M. Muller.
Fast and correctly rounded logarithms in double-precision, in: Theoretical Informatics and Applications, to appear, 2005.
[19]
F. de Dinechin, G. Villard.
High precision numerical accuracy in physics research, in: Nuclear Inst. and Methods in Physics Research, A, to appear, 2006.
[20]
J. Detrey, F. de Dinechin.
Outils pour une comparaison sans a priori entre arithmétique logarithmique et arithmétique flottante, in: Technique et science informatiques, to appear, 2005.
[21]
P. Kornerup, J.-M. Muller.
Choosing Starting Values for Certain Newton-Raphson Iterations, in: Theoretical Computer Science, 2004.
[22]
G. Melquiond, S. Pion.
Formally certified floating-point filters for homogeneous geometric predicates, in: Theoretical Informatics and Applications, to appear, 2006.
[23]
J. A. Pineiro, S. F. Oberman, J.-M. Muller, J. D. Bruguera.
High-Speed Function Approximation using a Minimax Quadratic Interpolator, in: IEEE Transactions on Computers, 2004.

Publications in Conferences and Workshops

[24]
R. Beguenane, J.-L. Beuchat, J.-M. Muller, S. Simard.
Modular Multiplication of Large Integers on FPGA, in: 39th Asilomar Conference on Signals, Systems & Computers, IEEE Signal Processing Society, November 2005.
[25]
J.-L. Beuchat, J.-M. Muller.
Multiplication Algorithms for Radix-2 RN-Codings and Two's Complement Numbers, in: Proceedings of the 16th IEEE International Conference on Application-Specific Systems, Architectures, and Processors, S. Vassiliadis, N. Dimopoulos, S. Rajopadhye (editors), IEEE Computer Society, 2005, p. 303–308.
[26]
J.-L. Beuchat, J.-M. Muller.
RN-codes : algorithmes d'addition, de multiplication et d'élévation au carré, in: SympA'2005: 10 è m e édition du SYMPosium en Architectures nouvelles de machines, April 2005, p. 73–84.
[27]
S. Boldo, G. Melquiond.
When double rounding is odd, in: Proceedings of the 17th IMACS World Congress on Computational and Applied Mathematics, Paris, France, 2005.
[28]
S. Boldo, J.-M. Muller.
Some Functions Computable with a Fused-mac, in: Proc. 17th IEEE Symposium on Computer Arithmetic (ARITH-17), Cape Cod, USA, P. Montuschi, E. Schwarz (editors), 2005, p. 52–58
http://arith17.polito.it/program.html.
[29]
N. Brisebarre, J.-M. Muller.
Correctly rounded multiplication by arbitrary precision constants, in: Proc. 17th IEEE Symposium on Computer Arithmetic (ARITH-17), IEEE Computer Society Press, June 2005.
[30]
S. Chevillard, N. Revol.
Computation of the error functions erf and erfc in arbitrary precision with correct rounding, in: 17th IMACS Conf. on Scientific Computation, Applied Math. and Simulation, Paris, France, July 2005.
[31]
M. Daumas, G. Melquiond, C. Muñoz.
Guaranteed proofs using interval arithmetic, in: Proceedings of the 17th IEEE Symposium on Computer Arithmetic, Cape Cod, Massachusetts, USA, P. Montuschi, E. Schwarz (editors), 2005, p. 188–195.
[32]
F. de Dinechin, C. Q. Lauter, G. Melquiond.
Assisted verification of elementary functions using Gappa, in: Symposium on Applied Computing, to appear, 2005.
[33]
J. Detrey, F. de Dinechin.
A Parameterizable Floating-Point Logarithm Operator for FPGAs, in: 39th Asilomar Conference on Signals, Systems & Computers, IEEE Signal Processing Society, November 2005.
[34]
J. Detrey, F. de Dinechin.
A Parameterized Floating-Point Exponential Function for FPGAs, in: IEEE International Conference on Field-Programmable Technology (FPT'05), IEEE Computer Society Press, December 2005.
[35]
J. Detrey, F. de Dinechin.
Table-based polynomials for fast hardware function evaluation, in: 16th Intl Conference on Application-specific Systems, Architectures and Processors, IEEE Computer Society Press, July 2005.
[36]
M. D. Ercegovac, J.-M. Muller, A. Tisserand.
Simple Seed Architectures for Reciprocal and Square Root Reciprocal, in: Proc. 39th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, California, U.S.A., October 2005.
[37]
C.-P. Jeannerod, S.-K. Raina, A. Tisserand.
High-Radix Floating-Point Division Algorithms for Embedded VLIW Integer Processors, in: Proc. 17th World Congress on Scientific Computation, Applied Mathematics and Simulation IMACS, Paris, France, July 2005.
[38]
P. Kornerup, J.-M. Muller.
RN-coding of numbers: definition and some properties, in: Proceedings of the 17th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation, Paris, July 2005.
[39]
G. Melquiond, S. Pion.
Formal certification of arithmetic filters for geometric predicates, in: Proceedings of the 17th IMACS World Congress on Computational and Applied Mathematics, Paris, France, 2005.
[40]
R. Michard, A. Tisserand, N. Veyrat-Charvillon.
Divgen: a divider unit generator, in: Proc. Advanced Signal Processing Algorithms, Architectures and Implementations XV, San Diego, California, U.S.A., F. T. Luk (editor), SPIE, August 2005, vol. 5910, 59100M p.
[41]
R. Michard, A. Tisserand, N. Veyrat-Charvillon.
Evaluation de polynômes et de fractions rationnelles sur FPGA avec des opérateurs à additions et décalages en grande base, in: 10ième SYMPosium en Architectures nouvelles de machines (SYMPA), Le Croisic, April 2005, p. 85–96.
[42]
R. Michard, A. Tisserand, N. Veyrat-Charvillon.
Small FPGA polynomial approximations with 3-bit coefficients and low-precision estimations of the powers of x, in: Proc. 16th International Conference on Application-specific Systems, Architectures and Processors (ASAP), Samos, Greece, S. Vassiliadis, N. Dimopoulos, S. Rajopadhye (editors), Best Paper Award, IEEE Computer Society, July 2005, p. 334–339.
[43]
R. Michard, A. Tisserand, N. Veyrat-Charvillon.
Étude statistique de l'activité de la fonction de sélection dans l'algorithme de E-méthode, in: 5ième journées d'études Faible Tension Faible Consommation (FTFC), Paris, May 2005, p. 61–65.
[44]
J.-M. Muller, A. Tisserand, B. Dupont de Dinechin, C. Monat.
Division by Constant for the ST100 DSP Microprocessor, in: Proc. 17th Symposium on Computer Arithmetic (ARITH), Cape Cod, MA., U.S.A, P. Montuschi, E. Schwarz (editors), IEEE Computer Society, June 2005, p. 124–130.
[45]
N. Revol.
Bounding roundoff errors in Taylor models arithmetic, in: 17th IMACS Conf. on Scientific Computation, Applied Math. and Simulation, Paris, France, July 2005.
[46]
A. Storjohann, G. Villard.
Computing the rank and a small nullspace basis of a polynomial matrix, in: Proc. International Symposium on Symbolic and Algebraic Computation, Beijing, China, ACM Press, July 2005, p. 309–316.
[47]
A. Tisserand.
Algorithms and Number Systems for Hardware Computer Arithmetic, in: International Symposium on Symbolic and Algebraic Computation (ISSAC), Beijing, China, Invited tutorial, July 2005.
[48]
G. Villard.
Efficient algorithms in linear algebra, 33rd Theoretical Computer Science Spring School, Computational Complexity, Montagnac-les-truffes, May 2005.

Internal Reports

[49]
S. Boldo, C. Muñoz.
A formalization of floating-point numbers in PVS, Technical report, National Institute for Aerospace, 2005.
[50]
H. Brönnimann, G. Melquiond, S. Pion.
A Proposal to add Interval Arithmetic to the C++ Standard Library, Technical report, C++ standardization committee, 2005, no 5646
http://www.inria.fr/rrrt/rr-5646.html.
[51]
C.-P. Jeannerod, G. Villard.
Asymptotically fast polynomial matrix algorithms for multivariable systems, Research report, Laboratoire de l'Informatique du Parallélisme , ÉNS Lyon, August 2005, no ccsd-00008211, ArXiv cs.SC/0505030
http://hal.ccsd.cnrs.fr/ccsd-00008211.
[52]
C. Q. Lauter.
Basic building blocks for a triple-double intermediate format, Technical report, LIP, September 2005, no RR2005-38
http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2005/RR2005-38.pdf.
[53]
C. Pernet, A. Rondepierre, G. Villard.
Computing the Kalman form, Research report, IMAG , Grenoble, October 2005, no ccsd-00009558, ArXiv cs.SC/0510014
http://hal.ccsd.cnrs.fr/ccsd-00009558.

References in notes

[54]
J.-L. Beuchat, N. Sendrier, A. Tisserand, G. Villard.
FPGA Implementation of a Recently Published Signature Scheme, Research report, Institut National de Recherche en Informatique et en Automatique, March 2004, no 5158
http://www.inria.fr/rrrt/rr-5158.html.
[55]
N. Courtois, M. Finiasz, N. Sendrier.
How to achieve a McEliece-based Digital Signature Scheme, in: Advances in Cryptology – ASIACRYPT 2001, C. Boyd (editor), Lecture Notes in Computer Science, Springer, 2001, no 2248, p. 157–174.
[56]
D. Goldberg.
What every computer scientist should know about floating-point arithmetic, in: ACM Computing Surveys, 1991, vol. 23, no 1, p. 5-47
http://www.acm.org/pubs/articles/journals/surveys/1991-23-1/p5-goldberg/p5-goldberg.pdf.
[57]
O. Herrmann.
Über die Berechnung der Fourierkoeffizienten der Funktion j( $ \tau$) , in: J. Reine Angew. Math., 1975, vol. 274/275, p. 187–195.
[58]
G. Huet, G. Kahn, C. Paulin-Mohring.
The Coq Proof Assistant: A Tutorial: Version 6.1, Technical Report, Inria, 1997, no 204
http://www.inria.fr/rrrt/rt-0204.html.
[59]
E. Kaltofen.
Challenges of symbolic computation: my favorite open problems, in: J. Symbolic Computation, 2000, vol. 29, no 6, p. 891–919.
[60]
K. Mahler.
On the coefficients of transformation polynomials for the modular function, in: Bull. Austral. Math. Soc., 1974, vol. 10, p. 197–218.
[61]
P. L. Montgomery.
Modular Multiplication without Trial Division, in: Mathematics of Computation, April 1985, vol. 44, no 170, p. 519–521.
[62]
T. Ogita, S. Rump, S. Oishi.
Accurate Sum and Dot Product, in: SIAM Journal on Scientific Computing (SISC), 2005, vol. 26, no 6, p. 1955–1988.
[63]
S. Owre, J. M. Rushby, N. Shankar.
PVS: a Prototype Verification System, in: 11th International Conference on Automated Deduction, Saratoga, New-York, D. Kapur (editor), Springer-Verlag, 1992, p. 748-752
http://pvs.csl.sri.com/papers/cade92-pvs/cade92-pvs.ps.
[64]
J.-P. Serre.
Cours d'arithmétique, P.U.F., 1970.
[65]
J. R. Shewchuk.
Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates, in: Discrete and Computational Geometry, 1997, vol. 18, p. 305-363.

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