% Note: iRAbot veut systématiquement une année (2009 ou 2010). @Book{ MULLER:2009:ENSL-00379167:1, title = {Handbook of Floating-Point Arithmetic}, author = {Muller, Jean-Michel and Brisebarre, Nicolas and de Dinechin, Florent and Jeannerod, Claude-Pierre and Lef{\`e}vre, Vincent and Melquiond, Guillaume and Revol, Nathalie and Stehl{\'e}, Damien and Torres, Serge}, keywords = {{F}loating-{P}oint arithmetic; computer arithmetic; arithmetic algorithms; arithmetic operators; numerical computing}, language = {{A}nglais}, affiliation = {{ARENAIRE} - {INRIA} {R}h{\^o}ne-{A}lpes / {LIP} {L}aboratoire de l'{I}nformatique du {P}arall{\'e}lisme - {INRIA} - {CNRS} : {UMR}5668 - {U}niversit{\'e} {C}laude {B}ernard - {L}yon {I} - {E}cole {N}ormale {S}up{\'e}rieure de {L}yon - {ENS} {L}yon - {L}aboratoire de l'{I}nformatique du {P}arall{\'e}lisme - {LIP} - {INRIA} - {CNRS} : {UMR}5668 - {U}niversit{\'e} {C}laude {B}ernard - {L}yon {I} - {E}cole {N}ormale {S}up{\'e}rieure de {L}yon - {ENS} {L}yon - {L}aboratoire de {R}echerche en {I}nformatique - {LRI} - {CNRS} : {UMR}8623 - {U}niversit{\'e} {P}aris {S}ud - {P}aris {XI} - {M}acquarie {U}niversity - {U}niversity of {S}ydney }, publisher = {{B}irkh\"auser {B}oston }, pages = {600 }, note = {{ACM} {G}.1.0; {G}.1.2; {G}.4; {B}.2.0; {B}.2.4; {F}.2.1., ISBN 978-0-8176-4704-9}, year = {2009}, url = {http://prunel.ccsd.cnrs.fr/ensl-00379167/en/} } @InBook{ Stehle09, author = {Damien Stehl{\'e}}, booktitle = {The LLL Algorithm, Survey and Applications, Nguyen, Phong Q.; Vall{\'ee}, Brigitte (Eds.)}, title = {Floating-point {LLL}: theoretical and practical aspects}, publisher = {Springer}, year = {2009}, series = {Information Security and Cryptography} } @Proceedings{ KORNERUP:2009:ENSL-00383561:1, title = {Special Section on Computer Arithmetic}, editor = {Kornerup, Peter and Montuschi, Paolo and Muller, Jean-Michel and Schwarz, Eric}, keywords = {computer arithmetic}, language = {{A}nglais}, affiliation = {{D}epartment of {M}athematics \& {C}omputer {S}cience - {IMADA} - {S}outhern {D}anish {U}niversity - {D}epartment of {C}omputer {E}ngineering - {P}olitecnico di {T}orino - {ARENAIRE} - {INRIA} {R}h{\^o}ne-{A}lpes / {LIP} {L}aboratoire de l'{I}nformatique du {P}arall{\'e}lisme - {INRIA} - {CNRS} : {UMR}5668 - {U}niversit{\'e} {C}laude {B}ernard - {L}yon {I} - {E}cole {N}ormale {S}up{\'e}rieure de {L}yon - {ENS} {L}yon - {L}aboratoire de l'{I}nformatique du {P}arall{\'e}lisme - {LIP} - {INRIA} - {CNRS} : {UMR}5668 - {U}niversit{\'e} {C}laude {B}ernard - {L}yon {I} - {E}cole {N}ormale {S}up{\'e}rieure de {L}yon - {ENS} {L}yon - {S}ystems and {T}echnology {D}ivision - {IBM} }, series = {{IEEE} {T}ransactions on {C}omputers }, volume = {58 }, number = {2 }, audience = {internationale }, x-proceedings={yes}, x-international-audience={yes}, month = feb, year = {2009}, url = {http://prunel.ccsd.cnrs.fr/ensl-00383561/en/} } @Misc{ MullerNumeration09, author = {Jean-Michel Muller}, title = {Exact computations with an arithmetic known to be approximate}, note = {Invited lectures (3 hours) at the conference \emph{Numeration: Mathematics and Computer Science}, CIRM, Marseille, Mar. 2009 }, year = {2009} } @Misc{ ChStVi09, author = {Xiao-Wen Chang and Damien Stehl{\'e} and Gilles Villard}, title = {Perturbation Analysis of the {QR }factor {R} in the Context of {LLL} Lattice Basis Reduction}, note = {Submitted}, year = {2009} } @Misc{ HoNo10, author = {Mark van Hoeij and Andrew Novocin}, title = {Gradual sub-lattice reduction and a new complexity for factoring polynomials}, note = {To appear in the proceedings of {LATIN'10}}, year = {2010} } @Misc{ PuSt09, author = {Xavier Pujol and Damien Stehl{\'e}}, title = {Solving the Shortest Lattice Vector Problem in Time $2^{2.465n}$}, note = {IACR eprint}, url = {http://eprint.iacr.org/2009/605}, year = {2009} } @Article{ NGUYEN:2009:INRIA-00328629:1, title = {Low-dimensional lattice basis reduction revisited}, x-international-audience={yes}, author = {Nguyen, Phong Q. AND Stehlé, Damien}, publisher = {ACM }, journal = {ACM Transactions on Algorithms }, year = {2009}, url = {http://hal.inria.fr/inria-00328629/en/}, x-editorial-board={yes} } @Article{ NgSt09, title = {An {LLL} Algorithm with Quadratic Complexity}, x-international-audience={yes}, author = {Nguyen, Phong Q. AND Stehlé, Damien}, journal = {SIAM Journal on Computing}, year = {2009}, volume = 39, number = 3, pages = {874--903}, x-editorial-board={yes} } @Article{ MoStVi09b, author = {Ivan Morel and Damien Stehl\'e and Gilles Villard}, title = {Analyse num\'erique et r\'eduction des r\'eseaux}, note = {To appear}, journal = {Technique et Science Informatiques}, publisher = {Lavoisier}, x-international-audience={no}, x-editorial-board={yes}, year = {2010} } @Article{ ErcegovacMuller2008, author = {Milos Ercegovac and Jean-Michel Muller}, title = {An Efficient Method for Evaluating Complex Polynomials}, journal = {Journal of Signal Processing Systems}, volume = {58}, number = {1}, pages = {17--27}, x-international-audience={yes}, x-editorial-board={yes}, year = {2010} } @Article{ Kornerup2008, author = {Peter Kornerup and Christoph Quirin Lauter and Vincent Lefèvre and Nicolas Louvet and Jean-Michel Muller}, title = {Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic}, journal = {{ACM} Transactions on Mathematical Software}, volume = {37}, number = {1}, note = {To appear}, x-international-audience={yes}, x-editorial-board={yes}, x-pays = {DK}, year = {2010} } @Article{ GrLL:08, author = {Stef Graillat and {Ph}ilippe Langlois and Nicolas Louvet}, title = {Algorithms for Accurate, Validated and Fast Polynomial Evaluation}, journal = {Japan Journal of Industrial and Applied Mathematics}, note = {To appear}, x-international-audience={yes}, x-editorial-board={yes}, year = {2010} } @Article{ LauLef2009a, author = {Christoph Quirin Lauter and Vincent Lefèvre}, title = {An efficient rounding boundary test for \texttt{pow(x,y)} in double precision}, journal = {{IEEE} Transactions on Computers}, publisher = {{IEEE} Computer Society Press, Los Alamitos, CA}, volume = {58}, number = {2}, pages = {197--207}, month = feb, year = {2009}, keywords = {floating-point arithmetic,correct rounding,power function}, url = {http://doi.ieeecomputersociety.org/10.1109/TC.2008.202}, x-international-audience={yes}, x-editorial-board={yes}, doi = {10.1109/TC.2008.202} } @Article{ GrLaNg08b, author = { Stef Graillat and Jean-Luc Lamotte and Nguyen, Hong Diep }, title = {Extended precision with a rounding mode toward zero environment. Application on the {CELL} processor}, journal = {International Journal of Reliability and Safety}, note = {Special issue on "Reliable Engineering Computing"}, x-international-audience={yes}, x-editorial-board={yes}, year = {2009}, volume = {3}, number = {1/2/3}, pages = {153--173} } @Misc{JeKnMoRe09, author = {Claude-Pierre Jeannerod and Herv{\'e} Knochel and Christophe Monat and Guillaume Revy}, title = {Computing floating-point square roots via bivariate polynomial evaluation}, note = {Submitted}, year = {2009} } @TechReport{ JeLoMuPa09, author = {Claude-Pierre Jeannerod and Nicolas Louvet and Jean-Michel Muller and Adrien Panhaleux}, title = {Midpoints and exact points of some algebraic functions in floating-point arithmetic}, institution = {LIP, \'Ecole Normale Sup\'erieure de Lyon}, type = {Research report}, year = {2009}, number = {ensl-00409366}, url = {http://prunel.ccsd.cnrs.fr/ensl-00409366} } @TechReport{ Chevillard2009, author = {Sylvain Chevillard}, title = {The functions erf and erfc computed with arbitrary precision}, institution = {Laboratoire de l'Informatique du Parall\'elisme (LIP)}, type = {Research report}, year = {2009}, number = {RR2009-04}, address = {46, all\'ee d'Italie, 69~364 Lyon Cedex~07}, month = jan, abstract = {The error function $\erf$ is a special function. It is widely used in statistical computations for instance, where it is also known as the standard normal cumulative probability. The complementary error function is defined as $\erfc(x)=\erf(x)-1$. In this paper, the computation of $\erf(x)$ and $\erfc(x)$ in arbitrary precision is detailed: our algorithms take as input a target precision $t'$ and deliver approximate values of $\erf(x)$ or $\erfc(x)$ with a relative error bounded by $2^{-t'}$. We study three different algorithms for evaluating $\erf$ and $\erfc$. These algorithms are completely detailed. In particular, the determination of the order of truncation, the analysis of roundoff errors and the way of choosing the working precision are presented. We implemented the three algorithms and studied experimentally what is the best algorithm to use in function of the point $x$ and the target precision $t'$.}, keywords = {error function, complementary error function, $\erf$, $\erfc$, floating-point arithmetic, arbitrary precision, multiple precision}, url = {http://prunel.ccsd.cnrs.fr/ensl-00356709} } @TechReport{ ChevillardHarrisonJoldesLauter2009, author = {Sylvain Chevillard and John Harrison and Mioara Joldes and Christoph Quirin Lauter}, title = {Efficient and accurate computation of upper bounds of approximation error s}, institution = {Laboratoire de l'Informatique du Parall\'elisme (LIP)}, type = {Research report}, year = {2009}, number = {RR2009-}, address = {46, all\'ee d'Italie, 69~364 Lyon Cedex~07}, month = dec, abstract = {For purposes of actual evaluation, mathematical functions $f$ are commonly replaced by approximation polynomials $p$. Examples include floating-point implementations of elementary functions, quadrature or more theoretical proof work involving transcendental functions. Replacing $f$ by $p$ induces an error $\epsilon = \nicefrac{p}{f} - 1$. In order to ensure the validity of the use of $p$ instead of $f$, the maximum error, i.e. the supremum norm $\ninf{\epsilon}$ must be safely bounded above. Numerical algorithms for supremum norms are efficient but cannot offer the required safety. Previous validated approaches often require tedious manual intervention. If they are automated, they have several drawbacks, such as the lack of quality guarantees. In this article a novel, automated supremum norm algorithm with \emph{a priori} quality is proposed. It focuses on the validation step and paves the way for formally certified supremum norms. Key elements are the use of intermediate approximation polynomials with bounded truncation remainder and a non-negativity test based on a Sum-of-squares expression of polynomials. The new algorithm was implemented in the tool Sollya. The article includes experimental results on real-life examples. }, keywords = {Supremum norm, approximation error, Taylor Models, Sum-of-Squares, validation, certification, formal proof} } @TechReport{BOLDO:2009:INRIA-00429617:1, title = { {E}xact and {A}pproximated error of the {FMA}}, author = {{B}oldo, {S}ylvie and {M}uller, {J}ean-{M}ichel}, abstract = {{T}he fused multiply accumulate-add ({FMA}) instruction, specified by the {IEEE} 754-2008 {S}tandard for {F}loating-{P}oint {A}rithmetic, eases some calculations, and is already available on some current processors such as the {P}ower {PC} or the {I}tanium. {W}e first extend an earlier work on the computation of the exact error of an {FMA} (by giving more general conditions and providing a formal proof). {T}hen, we present a new algorithm that computes an approximation to the error of an {FMA}, and provide error bounds and a formal proof for that algorithm.}, language = {{A}nglais}, institution = {INRIA}, affiliation = {{PROVAL} - {INRIA} {S}aclay - {I}le de {F}rance - {INRIA} - {U}niversit{\'e} {P}aris {S}ud - {P}aris {XI} - {CNRS} : {UMR} - {L}aboratoire de {R}echerche en {I}nformatique - {LRI} - {CNRS} : {UMR}8623 - {U}niversit{\'e} {P}aris {S}ud - {P}aris {XI} - {L}aboratoire de l'{I}nformatique du {P}arall{\'e}lisme - {LIP} - {INRIA} - {CNRS} : {UMR}5668 - {U}niversit{\'e} {C}laude {B}ernard - {L}yon {I} - {\'E}cole normale sup{\'e}rieure de {L}yon - {ENS} {L}yon }, type = {Research report}, note = {{S}oumis {\`a} {IEEE}-{TC} }, URL = {http://hal.archives-ouvertes.fr/inria-00429617/en/}, year = {2009} } @Article{ LefevreMuller2009, author = {Vincent Lefèvre and Jean-Michel Muller}, title = {Erreurs en arithmétique des ordinateurs}, journal = {Images des mathématiques}, url = {http://images.math.cnrs.fr/Erreurs-en-arithmetique-des.html}, x-international-audience={no}, x-editorial-board={yes}, x-scientific-popularization={yes}, month = jun, year = {2009} } @InProceedings{ DinechinJoldesPasca2009, author = {de Dinechin, Florent and Joldes, Mioara and Bogdan Pasca and Guillaume Revy}, title = {Racines carr{\'e}es multiplicatives sur {FPGA}}, booktitle = {13$^{\textrm{e}}$ {SYMP}osium en Architectures nouvelles de machines ({SYMPA})}, year = 2009, address = {Toulouse}, x-international-audience={no}, x-editorial-board={yes}, x-proceedings = {yes}, note = {10 pages}, month = sep } @InProceedings{ MoStVi09a, author = "Ivan Morel and Damien Stehl\'e and Gilles Villard", title = "{H-LLL: Using Householder inside LLL}", month = aug, booktitle = {Proc. International Symposium on Symbolic and Algebraic Computation (ISSAC 2009), Seould, Korea}, publisher = {ACM Press}, pages = {271--278}, x-international-audience={yes}, x-proceedings = {yes}, year = 2009 } @InProceedings{ KeaPryRev08, author = {Kearfott, R. Baker and Pryce, John D. and Revol, Nathalie}, title = {Discussions on an Interval Arithmetic Standard at {D}agstuhl Seminar 08021}, booktitle = {{D}agstuhl Seminar on Numerical Validation in Current Hardware Architectures}, series = {Lecture Notes in Computer Science}, volume = 5492, pages = {1--6}, year = {2009}, x-pays = {US,GB}, x-international-audience={yes}, x-proceedings = {yes} } @InProceedings{ GrLaNg08, author = {Graillat, Stef and Lamotte, Jean-Luc and Nguyen, Hong Diep}, title = {Error-Free Transformation in rounding mode toward zero}, booktitle = {{D}agstuhl Seminar on Numerical Validation in Current Hardware Architectures}, series = {Lecture Notes in Computer Science}, volume = 5492, pages = {217--229}, year = {2009}, x-international-audience={yes}, x-proceedings = {yes} } @InProceedings{ JeKnMoReVi09, author = {Claude-Pierre Jeannerod and Herv\'e Knochel and Christophe Monat and Guillaume Revy and Gilles Villard}, title = {A new binary floating-point division algorithm and its software implementation on the {ST231} processor}, month = jun, year = {2009}, booktitle = {Proceedings of the 19th {IEEE} Symposium on Computer Arithmetic (ARITH-19)}, x-international-audience={yes}, x-proceedings={yes}, pages = {95--103}, address = {Portland, OR} } @InProceedings{ DORMIANI:2009:ENSL-00379147:1, title = {Design and Implementation of a Radix-4 Complex Division Unit with Prescaling}, author = {Dormiani, Pouya and Ercegovac, Milos and Muller, Jean-Michel}, abstract = {{W}e present a design and implementation of a radix-4 complex division unit with prescaling of the operands. {S}pecifically, we extend the treatment of the residual bound and errors due to the use of truncated redundant representation. {T}he requirements for prescaling tables are simplified and a detailed specification of the table design is given. {A}ll principal components used in the design are described and the proposed optimizations are explained. {T}he target platform for implementation was an {A}ltera {S}tratix {II} {FPGA} [15] for which we report timing and area requirements. {F}or a precision of 36 bits, the implementation uses 1093 {ALUT}s, achieving a latency of 97ns. {T}he maximum clock frequency is 268.53 {MH}z.}, keywords = {computer arithmetic; complex arithmetic; division; digit-recurrence algorithms; prescaling}, language = {{A}nglais}, affiliation = {{D}igital {A}rithmetic and {R}econfigurable {A}rchitecture {L}aboratory - {U}niversity of {C}alifornia at {L}os {A}ngeles - {ARENAIRE} - {INRIA} {R}h{\^o}ne-{A}lpes / {LIP} {L}aboratoire de l'{I}nformatique du {P}arall{\'e}lisme - {INRIA} - {CNRS} : {UMR}5668 - {U}niversit{\'e} {C}laude {B}ernard - {L}yon {I} - {E}cole {N}ormale {S}up{\'e}rieure de {L}yon - {ENS} {L}yon - {L}aboratoire de l'{I}nformatique du {P}arall{\'e}lisme - {LIP} - {INRIA} - {CNRS} : {UMR}5668 - {U}niversit{\'e} {C}laude {B}ernard - {L}yon {I} - {E}cole {N}ormale {S}up{\'e}rieure de {L}yon - {ENS} {L}yon }, booktitle = {{P}roceedings of the 20th {IEEE} {I}nternational {C}onference on {A}pplication-specific {S}ystems, {A}rchitectures and {P}rocessors ({ASAP} 2009)}, publisher = {{IEEE} {C}omputer {S}ociety }, address = {{B}oston, U.S.A.}, audience = {internationale }, x-international-audience={yes}, x-proceedings = {yes}, note = {9 pages}, year = {2009}, url = {http://prunel.ccsd.cnrs.fr/ensl-00379147/en/} } @InProceedings{ KORNERUP:2009:INRIA-00367584:2, title = {On the Computation of Correctly-Rounded Sums}, author = {Kornerup, Peter and Lef{\`e}vre, Vincent and Louvet, Nicolas and Muller, Jean-Michel}, abstract = {{T}his paper presents a study of some basic blocks needed in the design of floating-point summation algorithms. {I}n particular, we show that among the set of the algorithms with no comparisons performing only floating-point additions/subtractions, the 2{S}um algorithm introduced by {K}nuth is minimal, both in terms of number of operations and depth of the dependency graph. {U}nder reasonable conditions, we also prove that no algorithms performing only round-to-nearest additions/subtractions exist to compute the round-to-nearest sum of at least three floating-point numbers. {S}tarting from an algorithm due to {B}oldo and {M}elquiond, we also present new results about the computation of the correctly-rounded sum of three floating-point numbers.}, keywords = {floating-point arithmetic; summation algorithms; correct rounding; 2{S}um and {F}ast2{S}um algorithms}, language = {{A}nglais}, affiliation = {{D}epartment of {M}athematics and {C}omputer {S}cience - {IMADA} - {U}niversity of {S}outhern {D}enmark - {ARENAIRE} - {INRIA} {R}h{\^o}ne-{A}lpes / {LIP} {L}aboratoire de l'{I}nformatique du {P}arall{\'e}lisme - {INRIA} - {CNRS} : {UMR}5668 - {U}niversit{\'e} {C}laude {B}ernard - {L}yon {I} - {\'E}cole {N}ormale {S}up{\'e}rieure de {L}yon - {ENS} {L}yon }, booktitle = {19th {IEEE} {S}ymposium on {C}omputer {A}rithmetic (ARITH-19)}, address = {{P}ortland, {O}regon, U.S.A.}, audience = {internationale }, x-international-audience={yes}, x-proceedings={yes}, x-pays = {DK}, year = {2009}, pages = {155-160}, url = {http://hal.inria.fr/inria-00367584/en/} } @InProceedings{ ChevillardJoldesLauter2008, author = {Sylvain Chevillard and Mioara Joldes and Christoph Quirin Lauter}, title = {Certified and fast computation of supremum norms of approximation errors}, abstract = {In many numerical programs there is a need for a high-quality floa ting-point approximation of useful functions $f$, such as such as $\exp$, $\sin$, $\erf$. % One of the basic bricks in this process consists in computing a fast and certified bounding of approximation errors. In fact, the request is to determine the maximum error between a function f: R -> R, and a polynomial p, which approximates the function over an interval. In the actual implementation, the function is replaced by a polynomial $p$, leading to an approximation error (absolute or relative) $\epsilon = p-f$ or $\epsilon = \nicefrac{p}{f}-1$. The tight yet certain bounding of this error is an important step towards safe implementations. The main difficulty of this problem is due to the fact that this approxi mation error is very small and the difference $p-f$ is highly cancellating. In consequence, previous approaches for computing the supremum norm in this degenerate case, have proven to be either unsafe, not sufficient ly tight or too tedious in manual work. We present a safe and fast algorithm that computes a tight lower and upper bound for the supremum norms of approximation errors. The algorith m is based on a combination of several techniques, including enhanced interval arithmetic, automatic differentiation and isolation of the roots of a polynomial. We have implemented our algorithm and timings on several examples are given.%This combination of tools allows us to overcome the cancellation effects and to safely implement this algorithm in a software tool.}, keywords = {supremum norm, approximation error, certified computation, element ary function, interval arithmetic, automatic differentiation, roots isolatio n technique}, booktitle = {19th {IEEE} {S}ymposium on {C}omputer {A}rithmetic (ARITH-19)}, address = {{P}ortland, {O}regon, U.S.A.}, audience = {internationale }, x-international-audience={yes}, x-proceedings={yes}, year = {2009}, pages = {169--176}, url = {http://prunel.ccsd.cnrs.fr/ensl-00334545/} } @InProceedings{DEDINECHIN:2009:ENSL-00379154:2, title = {{G}enerating high-performance custom floating-point pipelines}, author = {de {D}inechin, {F}lorent and {K}lein, {C}ristian and {P}asca, {B}ogdan}, abstract = {{C}ustom operators, working at custom precisions, are a key ingredient to fully exploit the {FPGA} flexibility advantage for high-performance computing. {U}nfortunately, such operators are costly to design, and application designers tend to rely on less efficient off-the-shelf operators. {T}o address this issue, an open-source architecture generator framework is introduced. {I}ts salient features are an easy learning curve from {VHDL}, the ability to embedd arbitrary synthesisable {VHDL} code, portability to mainstream {FPGA} targets from {X}ilinx and {A}ltera, automatic management of complex pipelines with support for frequency-directed pipeline, automatic test-bench generation. {T}his generator is presented around the simple example of a collision detector, which it significantly improves in accuracy, {DSP} count, logic usage, frequency and latency with respect to an implementation using standard floating-point operators.}, keywords = {architecture generator; floating-point; pipeline; computer arithmetic}, language = {{A}nglais}, affiliation = {{ARENAIRE} - {INRIA} {R}h{\^o}ne-{A}lpes / {LIP} {L}aboratoire de l'{I}nformatique du {P}arall{\'e}lisme - {INRIA} - {CNRS} : {UMR}5668 - {U}niversit{\'e} {C}laude {B}ernard - {L}yon {I} - {E}cole {N}ormale {S}up{\'e}rieure de {L}yon - {ENS} {L}yon - {L}aboratoire de l'{I}nformatique du {P}arall{\'e}lisme - {LIP} - {INRIA} - {CNRS} : {UMR}5668 - {U}niversit{\'e} {C}laude {B}ernard - {L}yon {I} - {E}cole {N}ormale {S}up{\'e}rieure de {L}yon - {ENS} {L}yon }, booktitle = {{P}roceedings of the 19th {I}nternational {C}onference on {F}ield {P}rogrammable {L}ogic and {A}pplications}, publisher = {{IEEE} }, audience = {internationale }, day = 31, month = aug, year = 2009, x-international-audience = {yes}, x-proceedings = {yes}, note = {6 pages}, url = {http://prunel.ccsd.cnrs.fr/ensl-00379154/en/} } @InProceedings{ DEDINECHIN:2009:ENSL-00356421:1, title = {{L}arge multipliers with less {DSP} blocks}, author = {de {D}inechin, {F}lorent and {P}asca, {B}ogdan}, abstract = {{R}ecent computing-oriented {FPGA}s feature {DSP} blocks including small embedded multipliers. {A} large integer multiplier, for instance for a double-precision floating-point multiplier, consumes many of these {DSP} blocks. {T}his article studies three non-standard implementation techniques of large multipliers: the {K}aratsuba-{O}fman algorithm, non-standard multiplier tiling, and specialized squarers. {T}hey allow for large multipliers working at the peak frequency of the {DSP} blocks while reducing the {DSP} block usage. {T}heir overhead in term of logic resources, if any, is much lower than that of emulating embedded multipliers. {T}heir latency overhead, if any, is very small. {C}omplete algorithmic descriptions are provided, carefully mapped on recent {X}ilinx and {A}ltera devices, and validated by synthesis results.}, keywords = {{FPGA};reconfigurable computing;integer multiplier;{K}aratsuba-{O}fman}, language = {{A}nglais}, affiliation = {{ARENAIRE} - {INRIA} {R}h{\^o}ne-{A}lpes / {LIP} {L}aboratoire de l'{I}nformatique du {P}arall{\'e}lisme - {INRIA} - {CNRS} : {UMR}5668 - {U}niversit{\'e} {C}laude {B}ernard - {L}yon {I} - {E}cole {N}ormale {S}up{\'e}rieure de {L}yon - {ENS} {L}yon }, booktitle = {{P}roceedings of the 19th {I}nternational {C}onference on {F}ield {P}rogrammable {L}ogic and {A}pplications}, publisher = {{IEEE} }, audience = {internationale }, x-international-audience = {yes}, x-proceedings = {yes}, note = {9 pages}, day = 31, month = aug, year = 2009, url = {http://prunel.ccsd.cnrs.fr/ensl-00356421/en/} } @InProceedings{DORMIANI2:2009, title = { Low Precision Table Based Complex Reciprocal Approximation}, author = {Dormiani, Pouya and Ercegovac, Milos and Muller, Jean-Michel}, keywords = {computer arithmetic; complex arithmetic; division; digit-recurrence algorithms; prescaling}, language = {{A}nglais}, affiliation = {{D}igital {A}rithmetic and {R}econfigurable {A}rchitecture {L}aboratory - {U}niversity of {C}alifornia at {L}os {A}ngeles - {ARENAIRE} - {INRIA} {R}h{\^o}ne-{A}lpes / {LIP} {L}aboratoire de l'{I}nformatique du {P}arall{\'e}lisme - {INRIA} - {CNRS} : {UMR}5668 - {U}niversit{\'e} {C}laude {B}ernard - {L}yon {I} - {E}cole {N}ormale {S}up{\'e}rieure de {L}yon - {ENS} {L}yon - {L}aboratoire de l'{I}nformatique du {P}arall{\'e}lisme - {LIP} - {INRIA} - {CNRS} : {UMR}5668 - {U}niversit{\'e} {C}laude {B}ernard - {L}yon {I} - {E}cole {N}ormale {S}up{\'e}rieure de {L}yon - {ENS} {L}yon }, booktitle = {{P}roceedings of the 43rd Asilomar Conference on signals, systems and computers}, address = {Pacific Grove, California, USA}, audience = {internationale }, x-international-audience={yes}, x-proceedings = {yes}, note = {5 pages}, month = nov, year = {2009} } @InProceedings{JeRe:2009, title = {Optimizing correctly-rounded reciprocal square roots for embedded {VLIW} cores}, author = {Jeannerod, Claude-Pierre and Revy, Guillaume}, booktitle = {{P}roceedings of the 43rd Asilomar Conference on signals, systems and computers}, address = {Pacific Grove, California, USA}, audience = {internationale }, x-international-audience={yes}, x-proceedings = {yes}, note = {5 pages}, month = nov, year = {2009} } @Misc{ JeMoVi09, author = {Claude-Pierre Jeannerod and Christophe Mouilleron and Gilles Villard}, title = {Extending {Cardinal}'s algorithm to a broader class of structured matrices}, howpublished = {Poster at ISSAC 2009}, x-international-audience={yes}, month = jul, year = {2009} } @PhDThesis{ Chevillard-Thesis, title = {Évaluation efficace de fonctions numériques - Outils et exemples}, author = {Chevillard, Sylvain}, school = {{\'E}cole {N}ormale {S}up{\'e}rieure de {Lyon}, France}, year = {2009}, month = jul, day = {6} } @PhDThesis{ Revy-Thesis, title = {Implementation of binary floating-point arithmetic on integer processors: polynomial evaluation-based algorithms and certified code generation}, author = {Revy, Guillaume}, school = {Universit{\'e} de Lyon - {\'E}cole normale sup\'erieure de {Lyon}, France}, month = dec, year = {2009} } @Misc{KLTZ2009a, AUTHOR = {Kaveh R. Ghazi and Vincent Lefèvre and Philippe Théveny and Paul Zimmermann}, TITLE = {Why and how to use arbitrary precision}, NOTE = {Submitted to \emph{Computing in Science and Engineering}}, YEAR = {2009} } @Misc{NgRe09, AUTHOR = {Nguyen, Hong Diep and Revol, Nathalie}, TITLE = {Solving and Certifying a Linear System}, NOTE = {Submitted to \emph{Reliable Computing}}, YEAR = {2009} } @inproceedings{SSTX09, author = {Damien Stehl{\'e} and Ron Steinfeld and Keisuke Tanaka and Keita Xagawa}, booktitle = {Proceedings of Asiacrypt 2009}, title = {Efficient Public-Key Encryption Based on Ideal Lattices (extended abstract)}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, volume = {5912}, pages = {617--635}, year = 2009, x-international-audience={yes}, x-proceedings = {yes}, url = {http://dx.doi.org/10.1007/978-3-642-10366-7_36} } @Article{Chevillard09, author = {Sylvain Chevillard}, title = {The functions erf and erfc computed with arbitrary precision}, journal = {Information and Computation}, url = {http://prunel.ccsd.cnrs.fr/ensl-00356709}, x-international-audience={yes}, x-editorial-board={yes}, year = {2010}, note = {accepted with the status major revision} } @inproceedings{NgRe-SWIM09, author = {Nguyen, Hong Diep and Revol, Nathalie}, title = {Relaxed method to certify the solution of a linear system}, x-international-audience={yes}, x-proceedings = {no}, booktitle = {SWIM'09 (Small Workshop on Interval Methods )}, year = 2009, address = {Lausanne, Switzerland}, month = jun }