Team Arénaire

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

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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