Bibliography

Major publications by the team in recent years

[1]

M. Daumas, J.-M. Muller (editors)
Qualité des calculs sur ordinateur : vers des arithmétiques plus fiables, Masson, 1997,
http://perso.ens-lyon.fr/jean-michel.muller/livre_masson.html.

[2]

M. Daumas, L. Rideau, L. Théry.
A generic library of floating-point numbers and its application to exact computing, in: 14th International Conference on Theorem Proving in Higher Order Logics, Edinburgh, Scotland, 2001, p. 169-184,
http://perso.ens-lyon.fr/marc.daumas/SoftArith/DauRidThe01.ps.

[3]

J.-M. Muller.
Elementary functions, algorithms and implementation, Birkhauser, 1997,
http://perso.ens-lyon.fr/jean-michel.muller/book_functions.html.

Publications of the year

Books and Monographs

[4]

J.-C. Bajard, J.-M. Muller (editors)
Calcul et Arithmétique des Ordinateurs, IC 2, Hermès Science Publishing, 2004.

Doctoral dissertations and Habilitation theses

[5]

S. Boldo.
Preuves formelles en arithmétiques à virgule flottante, Ph. D. Thesis, École Normale Supérieure de Lyon, Lyon, France, November 2004.

[6]

P. Giorgi.
Algorithmique et arithmétique pour l'algèbre linéaire exacte à partir de la bibliothèque LinBox, Ph. D. Thesis, École Normale Supérieure de Lyon, Lyon, France, December 2004.

Articles in refereed journals and book chapters

[7]

B. Beckermann, G. Labahn, G. Villard.
Normal forms for general polynomial matrices, in: Journal of Symbolic Computation, to appear.

[8]

J.-L. Beuchat, J.-M. Muller.
Modulo M Multiplication-Addition: Algorithms and FPGA Implementation, in: Electronics Letters, May 2004, vol. 40, n^o 11, p. 654–655.

[9]

J.-L. Beuchat, A. Tisserand.
Opérateurs arithmétiques sur circuits FPGA, in: Calcul et arithmétique des ordinateurs, J.-C. Bajard, J.-M. Muller (editors), Traité IC2, Lavoisier, 2004, p. 109–152.

[10]

S. Boldo, M. Daumas.
A simple test qualifying the accuracy of Horner's rule for polynomials, in: Numerical Algorithms, December 2004, vol. 37, n^o 1, p. 45-60.

[11]

S. Boldo, M. Daumas.
Properties of two's complement floating point notations, in: International Journal on Software Tools for Technology Transfer, 2004, vol. 5, n^o 2-3, p. 237-246,
http://perso.ens-lyon.fr/marc.daumas/SoftArith/BolDau04a.pdf.

[12]

N. Brisebarre, D. Defour, P. Kornerup, J.-M. Muller, N. Revol.
A new range reduction algorithm, in: IEEE Transactions on Computers, to appear.

[13]

N. Brisebarre, J.-M. Muller, S. Raina.
Accelerating Correctly Rounded Floating-Point Division when the Divisor is Known in Advance, in: IEEE Transactions on Computers, August 2004, vol. 53, n^o 8, p. 1069–1072.

[14]

F. de Dinechin, A. Tisserand.
Multipartite table methods, in: IEEE Transactions on Computers, to appear.

[15]

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, 2004, vol. 37, n^o 1-4, p. 367–375no.

[16]

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.

[17]

C.-P. Jeannerod.
On matrix perturbations with minimal leading Jordan structure, in: Journal of Computational and Applied Mathematics, 2004, vol. 162(1), p. 113–132.

[18]

C.-P. Jeannerod, G. Villard.
Essentially optimal computation of the inverse of generic polynomial matrices, in: Journal of Complexity, to appear,
http://dx.doi.org/10.1016/j.jco.2004.03.005.

[19]

E. Kaltofen, G. Villard.
On the complexity of computing determinants, in: Computational Complexity, to appear.

[20]

E. Kaltofen, G. Villard.
Computing the sign or the value of the determinant of an integer matrix, a complexity survey, in: J. Comp. Applied Math, 2004, vol. 162, n^o 1, p. 133–146.

[21]

P. Koiran, N. Portier, G. Villard.
A rank theorem for Vandermonde matrices, in: Linear Algebra and its Applications, 2004, vol. 378, p. 99–107.

[22]

P. Kornerup, J.-M. Muller.
Choosing Starting Values for Certain Newton-Raphson Iterations, in: Theoretical Computer Science, to appear.

[23]

J.-M. Muller, J.-L. Nicolas, X. Roblot.
Nombre de Solutions dans une Binade de l'Equation a² + b² = c² + c (in French), in: l'Enseignement Mathématique, 2004, vol. 50, p. 147–182.

[24]

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, to appear.

[25]

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, to appear.

[26]

N. Revol, F. Rouillier.
Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library, in: Reliable Computing, 2005, vol. 11, p. 1–16.

[27]

B. D. Saunders, A. Storjohann, G. Villard.
Matrix rank certification, in: Elect. J. Linear Algebra, 2004, vol. 11, p. 16–23.

[28]

A. Tisserand.
Low Power Electronics Design, CRC Press, 2004, chap. Low-Power Arithmetic Operators.

Publications in Conferences and Workshops

[29]

C. Bertin, N. Brisebarre, B. D. de Dinechin, C.-P. Jeannerod, C. Monat, J.-M. Muller, S.-K. Raina, A. Tisserand.
A floating-point library for integer processors, in: Proceedings of SPIE's 49th Annual Meeting, Denver, Colorado, U.S.A., August 2004.

[30]

S. Boldo.
Bridging the gap between formal specification and bit-level floating-point arithmetic, in: Proceedings of the 6th Conference on Real Numbers and Computers, Schloss Dagstuhl, Germany, November 2004, p. 22-36.

[31]

N. Brisebarre, J.-M. Muller.
Functions Approximable by E-Fractions, in: Proc. 38th IEEE Conference on Signals, Systems and Computers, IEEE, November 2004.

[32]

N. Brisebarre, J.-M. Muller, A. Tisserand.
Sparse-Coefficient Polynomial Approximations for Hardware Implementations, in: Proc. 38th IEEE Conference on Signals, Systems and Computers, IEEE, November 2004.

[33]

M. Daumas, G. Melquiond.
Generating formally certified bounds on values and round-off errors, in: 6th Conference on Real Numbers and Computers, Schloss Dagstuhl, Germany, November 2004, p. 55–70.

[34]

F. de Dinechin, C. Loirat, J.-M. Muller.
A proven correctly rounded logarithm in double-precision, in: RNC6, Real Numbers and Computers, Schloss Dagstuhl, Germany, November 2004.

[35]

J. Detrey, F. de Dinechin.
Second Order Function Approximation Using a Single Multiplication on FPGAs, in: 14th Intl Conference on Field-Programmable Logic and Applications, Antwerp, Belgium, Improved version of Inria Research report 5140 available, LNCS 3203, August 2004, p. 221-230,
http://www.inria.fr/rrrt/rr-5140.html.

[36]

J.-G. Dumas, P. Giorgi, C. Pernet.
FFPACK: Finite Field Linear Algebra Package, in: Proc. International Symposium on Symbolic and Algebraic Computation, Santander, Spain, ACM Press, July 2004, p. 119–126.

[37]

M. D. Ercegovac, J.-M. Muller.
Complex Square Root with Operand Prescaling (best paper award), in: Proc. 15th IEEE International Conference on Application-Specific Systems, Architectures and Processors, Galveston, Texas, IEEE Computer Society Press, September 2004.

[38]

M. Grimmer, K. Petras, N. Revol.
Multiple Precision Interval Packages: Comparing Different Approaches, in: Lecture Notes in Computer Science, 2004, vol. 2991, p. 64–90,
http://www.inria.fr/rrrt/rr-4841.html.

[39]

N. Revol.
Convergent linear recurrences (with scalar coefficients) with divergent interval simulations, in: SCAN 2004 (11th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics), Fukuoka, Japan, 2004.

[40]

G. Villard.
Lattice based memory allocation (invited talk), in: Mathematics of Computer Algebra and Analysis, Waterloo, Ontario, Canada, May 2004.

Internal Reports

[41]

J.-L. Beuchat.
A Family of Modulo (2ⁿ + 1) Multipliers, Research report, Institut National de Recherche en Informatique et en Automatique, September 2004, n^o 5316.

[42]

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, n^o 5158,
http://www.inria.fr/rrrt/rr-5158.html.

[43]

S. Boldo, G. Melquiond.
When double rounding is odd, Research report, Laboratoire de l'Informatique du Parallélisme, École Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, November 2004, n^o 2004–48.

[44]

S. Boldo, J.-M. Muller.
Some Functions Computable with a Fused Mac, submitted to the 17th IEEE Symposium on Computer Arithmetic, INRIA, October 2004, n^o 5320,
http://www.inria.fr/rrrt/rr-5320.html.

[45]

N. Brisebarre, J.-M. Muller.
Correctly rounded multiplication by arbitrary precision constants, submitted to the 17th IEEE Symposium on Computer Arithmetic, INRIA, November 2004, n^o 5354,
http://www.inria.fr/rrrt/rr-5354.html.

[46]

N. Brisebarre, J.-M. Muller, A. Tisserand.
Computing machine-efficient polynomial approximations, submitted, 2004,
http://perso.ens-lyon.fr/jean-michel.muller/publications.html.

[47]

A. Darte, R. Schreiber, G. Villard.
Lattice based memory allocation, Research report, Laboratoire de l'Informatique du Parallélisme, École Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, April 2004, n^o 2004-23,
http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-23.ps.gz.

[48]

F. de Dinechin, D. Defour, C. Lauter.
Fast correct rounding of elementary functions in double precision using double-extended arithmetic, Submitted to TOMS., INRIA, March 2004, n^o 5137,
http://www.inria.fr/rrrt/rr-5137.html.

[49]

F. de Dinechin, N. Gast.
Towards the post-ultimate libm, Submitted to Arith'17, INRIA, November 2004, n^o 5367,
http://www.inria.fr/rrrt/rr-5367.html.

[50]

J. Detrey, F. de Dinechin.
A tool for unbiased comparison between logarithmic and floating-point arithmetic, Research report, Laboratoire de l'Informatique du Parallélisme, École Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, March 2004, n^o 2004–31.

[51]

J. Detrey, F. de Dinechin.
Table-based polynomials for fast hardware function evaluation, Submitted to Arith'17., LIP, November 2004, n^o RR2004-52.

[52]

P. Kornerup, J.-M. Muller.
RN-Codings of Numbers: definition and some properties, Technical report, LIP, ENS-Lyon, 2004, n^o 2004-44.

[53]

A. Storjohann, G. Villard.
Computing the rank and a small nullspace basis of a polynomial matrix, Research report, Laboratoire de l'Informatique du Parallélisme, École Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, 2004.

Miscellaneous

[54]

S. Chevillard, N. Revol.
Computation of the error functions erf and erfc in arbitrary precision with correct rounding, 2004, Submitted to the 17th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation, Paris, July 2005.

[55]

N. Dessart.
Arithmétique par intervalles, résolution de systèmes linéaires et précision, Mémoire de DEA, École Normale Supérieure de Lyon, Lyon, France, 2004,
http://www.ens-lyon.fr/LIP/Pub/Rapports/DEA/DEA2004/DEA2004-04.pdf.

[56]

G. Melquiond, S. Pion.
Formal certification of arithmetic filters for geometric predicates, 2004, Submitted to the 17th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation, Paris, July 2005.

[57]

N. Revol.
Bounding roundoff errors in Taylor models arithmetic, 2004, Submitted to the 17th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation, Paris, July 2005.

[58]

The Arénaire Project.
CR-Libm, A library of correctly rounded elementary functions in double-precision, 2004,
http://lipforge.ens-lyon.fr/projects/crlibm/.

[59]

N. Veyrat-Charvillon.
Algorithmes de multiplication pour circuits asynchrones, Mémoire de DEA, École Normale Supérieure de Lyon, Lyon, France, 2004,
http://www.ens-lyon.fr/LIP/Pub/Rapports/DEA/DEA2004/DEA2004-02.pdf.

References in notes

[60]

W. R. Adrion, M. A. Branstad, J. C. Cherniavsky.
Validation, verification and testing of computer software, in: ACM Computing Surveys, 1982, vol. 14, n^o 2, p. 159-192,
http://www.acm.org/pubs/articles/journals/surveys/1982-14-2/p159-adrion/p159-adrion.pdf.

[61]

P. Bürgisser, M. Clausen, M. Shokrollahi.
Algebraic Complexity Theory, Volume 315, Grundlehren der mathematischen Wissenschaften, (Chapter 16), Springer-Verlag, 1997.

[62]

J. T. Coonen.
Specification for a proposed standard for floating point arithmetic, Memorandum, University of California, Berkeley, 1978, n^o ERL M78/72.

[63]

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, n^o 2248, p. 157–174.

[64]

M. D. Ercegovac.
A general hardware-oriented method for evaluation of functions and computations in a digital computer, in: IEEE Transactions on Computers, July 1977, vol. C-26, n^o 7, p. 667–680.

[65]

P. Giorgi, C. Jeannerod, G. Villard.
On the complexity of polynomial matrix computations, in: Proc. Int. Symp. Symb. and Alg. Comput., Philadelphia, PE, USA, ACM Press, August 2003, p. 135–142.

[66]

D. Goldberg.
What every computer scientist should know about floating point arithmetic, in: ACM Computing Surveys, 1991, vol. 23, n^o 1, p. 5-47.

[67]

G. Huet, G. Kahn, C. Paulin-Mohring.
The Coq Proof Assistant: A Tutorial: Version 6.1, Technical Report, Inria, 1997, n^o 204,
http://www.inria.fr/rrrt/rt-0204.html.

[68]

E. Kaltofen.
Challenges of symbolic computation: my favorite open problems, in: J. Symbolic Computation, 2000, vol. 29, n^o 6, p. 891–919.

[69]

C. K. Koç, C. Y. Hung.
Carry-save adders for computing the product AB modulo N, in: Electronics Letters, June 1990, vol. 26, n^o 13, p. 899–900.

[70]

K. Makino, M. Berz.
Higher order verified inclusions of multidimensional systems by Taylor models, in: Nonlinear Analysis, 2001, vol. 47, p. 3503–3514.

[71]

T. Mulders, A. Storjohann.
Certified dense linear system solving, in: J. Symb. Comput., 2004, vol. 37, n^o 4, p. 485–510.

[72]

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.

[73]

J. R. Shewchuk.
Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates, in: Discrete and Computational Geometry, 1997, vol. 18, p. 305-363,
http://link.springer.de/link/service/journals/00454/papers97/18n3p305.pdf.

[74]

A. Wrzyszcz, D. Milford.
A New Modulo 2^a + 1 Multiplier, in: Proceedings of the IEEE International Conference on Computer Design: VLSI in Computers and Processors, 1993, p. 614–617.