I. J. Anderson, A distillation algorithm for oating-point summation, SIAM J. Sci. Comput, vol.20, issue.5, p.17971806, 1999.

D. F. Bacon, S. L. Graham, and O. J. Sharp, Compiler transformations for high-performance computing, ACM Computing Surveys, vol.26, issue.4, p.345420, 1994.
DOI : 10.1145/197405.197406

H. David and . Bailey, A Fortran-90 double-double library

H. David and . Bailey, A Fortran 90-based multiprecision system, ACM Trans. Math. Softw, vol.21, issue.4, p.379387, 1995.

H. David and . Bailey, High-precision oating-point arithmetic in scientic computation, Computing in Science and Engineering, vol.7, issue.3, p.5461, 2005.

D. H. Bailey, Y. Hida, K. Jeyabalan, X. S. Li, and B. Thompson, C++/Fortran-90 arbitrary precision package

Å. Björck, Iterative renement and reliable computing, Reliable Numerical Computation, p.249266, 1990.

G. Bohlender, W. Walter, P. Kornerup, and D. W. Matula, Semantics for exact oating point operations, Proceedings : 10th IEEE Symposium on Computer Arithmetic, p.2226, 1991.

S. Boldo, Pitfalls of a full oating-point proof : example on the formal proof of the veltkamp/dekker algorithms, Third International Joint Conference on Automated Reasoning, 2006.

S. Boldo and M. Daumas, Representable correcting terms for possibly underowing oating point operations, ARITH '03 : Proceedings of the 16th IEEE Symposium on Computer Arithmetic (ARITH-16'03), p.79, 2003.

S. Boldo and J. Muller, Some Functions Computable with a Fused-Mac, 17th IEEE Symposium on Computer Arithmetic (ARITH'05)
DOI : 10.1109/ARITH.2005.39

URL : https://hal.archives-ouvertes.fr/inria-00000895

R. P. Brent, A Fortran Multiple-Precision Arithmetic Package, ACM Transactions on Mathematical Software, vol.4, issue.1, p.5770, 1978.
DOI : 10.1145/355769.355775

K. Briggs, Doubledouble oating point arithmetic

F. Chaitin-chatelin and V. Frayssé, Lectures on nite precision computations, Society for Industrial and Applied Mathematics (SIAM), 1996.

M. Cornea, J. Harrison, P. T. , and P. Tang, Scientic computing on Itanium based systems, 2002.

G. Florent-de-dinechin and . Villard, High precision numerical accuracy in physics research, Nuclear Inst. and Methods in Physics Research, p.207210, 2006.

T. J. Dekker, A oating-point technique for extending the available precision, Numer. Math, vol.18, p.224242, 1971.

J. W. Demmel and X. Li, Faster numerical algorithms via exception handling, IEEE Trans. Comput, vol.43, issue.8, p.983992, 1994.

J. Demmel, Underow and the reliability of numerical software, SIAM Journal on Scientic and Statistical Computing, vol.5, issue.4, p.887919, 1984.

J. Demmel and Y. Hida, Accurate and ecient oating point summation, SIAM Journal on Scientic Computing, vol.25, issue.4, p.12141248, 2003.

J. Demmel and Y. Hida, Fast and accurate oating point summation with application to computational geometry, Numerical Algorithms, vol.37, issue.14, p.101112, 2004.

J. Demmel, Y. Hida, W. Kahan, X. S. Li, S. Mukherjee et al., Error bounds from extra-precise iterative renement, ACM Trans. Math. Softw, vol.32, issue.2, p.325351, 2006.

T. O. Espelid, On oating-point summation, SIAM Rev, vol.37, p.603607, 1995.

S. Graillat, P. Langlois, and N. Louvet, Improving the compensated Horner scheme with a fused multiply and add, Proceedings of the 2006 ACM symposium on Applied computing , SAC '06, p.13231327, 2006.
DOI : 10.1145/1141277.1141585

A. Griewank, Evaluating derivatives : principles and techniques of algorithmic dierentiation, Society for Industrial and Applied Mathematics, 2000.
DOI : 10.1137/1.9780898717761

G. Hanrot, V. Lefèvre, P. Pélissier, and P. Zimmermann, The MPFR library

J. R. Hauser, Handling oating-point exceptions in numeric programs, ACM Trans. Program. Lang. Syst, vol.18, issue.2, p.139174, 1996.

L. John, D. A. Hennessy, and . Patterson, Computer Architecture A Quantitative Approach, 2003.

Y. Hida, X. S. Li, and D. H. Bailey, Double-double and quad double package

Y. Hida, X. S. Li, and D. H. Bailey, Algorithms for quad-double precision oating point arithmetic, Proceedings of the 15th Symposium on Computer Arithmetic, p.155162, 2001.

N. J. Higham, The Accuracy of Solutions to Triangular Systems, SIAM Journal on Numerical Analysis, vol.26, issue.5, p.12521265, 1989.
DOI : 10.1137/0726070

N. J. Higham, The accuracy of oating point summation, SIAM J. Sci. Comput, vol.14, issue.4, p.783799, 1993.

N. J. Higham, Iterative renement for linear systems and LAPACK, IMA J. Numer. Anal, vol.17, issue.4, p.495509, 1997.

N. J. Higham, Accuracy and stability of numerical algorithms, Society for Industrial and Applied Mathematics (SIAM), 2002.
DOI : 10.1137/1.9780898718027

. Intel, Intel 64 an IA-32 Architectures Software Developer's Manual, 2007.

. Intel, Intel 64 and IA-32 Architectures Optimization Reference Manual, 2007.

L. Jaulin, M. Kieer, O. Didrit, and E. Walter, Applied interval analysis, 2001.
DOI : 10.1007/978-1-4471-0249-6

URL : https://hal.archives-ouvertes.fr/hal-00845131

W. Kahan, Pracniques: further remarks on reducing truncation errors, Communications of the ACM, vol.8, issue.1, 1965.
DOI : 10.1145/363707.363723

A. H. Karp and P. Markstein, High-precision division and square root, ACM Transactions on Mathematical Software, vol.23, issue.4, p.561589, 1997.
DOI : 10.1145/279232.279237

E. Donald and . Knuth, The Art of Computer Programming Seminumerical Algorithms, 1998.

U. W. Kulisch and W. L. Miranker, The arithmetic of the digital computer, SIAM Rev, vol.28, p.140, 1986.

P. Langlois, When automatic linear correction of rounding errors is exact, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.328, issue.6, p.515539, 2001.
DOI : 10.1016/S0764-4442(99)80207-9

P. Langlois, Analyse d'erreur en précision nie Outils d'analyse numérique pour l'Automatique, Traité IC2, Hermès Science, p.1952, 2002.

P. Langlois and N. Louvet, Solving triangular systems more accurately and eciently, Proceedings of the 17th IMACS World Congress, 2005.

P. Langlois and N. Louvet, How to Ensure a Faithful Polynomial Evaluation with the Compensated Horner Algorithm, 18th IEEE Symposium on Computer Arithmetic (ARITH '07), p.141149, 2007.
DOI : 10.1109/ARITH.2007.21

P. Langlois and N. Louvet, More instruction level parallelism explains the actual eciency of compensated algorithms, 2007.

P. Langlois and N. Louvet, Operator dependant compensated algorithms, Proceedings of the 12th GAMM -IMACS International Symposium on Scientic Computing, Computer Arithmetic, and Validated Numerics, 2007.

C. Li, S. Pion, and C. Yap, Recent progress in exact geometric computation, The Journal of Logic and Algebraic Programming, vol.64, issue.1, p.85111, 2005.
DOI : 10.1016/j.jlap.2004.07.006

URL : https://hal.archives-ouvertes.fr/inria-00344355

T. Thompson, D. J. Tung, and . Yoo, A reference implementation for the Extended and Mixed precision BLAS standard

T. Thompson, D. J. Tung, and . Yoo, Design, implementation and testing of extended and mixed precision BLAS, ACM Trans. Math. Software, vol.28, issue.2, p.152205, 2002.

S. Linnainmaa, Software for doubled-precision oating-point computations, ACM Trans. Math. Softw, vol.7, issue.3, p.272283, 1981.

P. Linz, Accurate oating-point summation, Commun. ACM, vol.13, issue.6, p.361362, 1970.

A. Michael and . Malcolm, On accurate oating-point summation

P. Markstein, IA-64 and elementary functions : speed and precision, 2000.

J. Michael and M. , A comparison of methods for accurate summation, SIGSAM Bull, vol.38, issue.1, p.17, 2004.

B. Cleve and . Moler, Iterative renement in oating point, J. ACM, vol.14, issue.2, p.316321, 1967.

O. Møller, Note on quasi double-precision, BIT, vol.8, issue.5, p.251255, 1965.
DOI : 10.1007/BF01937505

O. Møller, Quasi double-precision in oating point addition, BIT, vol.5, issue.1, p.3750, 1965.

J. Muller, Elementary functions : algorithms and implementation, 2006.
URL : https://hal.archives-ouvertes.fr/ensl-00000008

A. Neumaier, Rundungsfehleranalyse Einiger Verfahren Zur Summation Endlicher Summen. (German) [Rounding error analysis of a method for summation of nite sums, Zeitschrift für Angewandte Mathematik und Mechanik, p.3951, 1974.

Y. Nievergelt, Scalar fused multiply-add instructions produce oating-point matrix arithmetic provably accurate to the penultimate digit, ACM Trans. Math. Softw, vol.29, issue.1, p.2748, 2003.

Y. Nievergelt, Analysis and applications of Priest's distillation, ACM Transactions on Mathematical Software, vol.30, issue.4, p.402433, 2004.
DOI : 10.1145/1039813.1039815

T. Ogita, S. M. Rump, and S. Oishi, Accurate Sum and Dot Product, SIAM Journal on Scientific Computing, vol.26, issue.6, p.19551988, 2005.
DOI : 10.1137/030601818

T. Ogita, S. M. Rump, and S. Oishi, Veried solution of linear systems without directed rounding, 2005.

T. Ohta, T. Ogita, S. M. Rump, and S. Oishi, Numerical method for dense linear systems with arbitrarily ill-conditioned matrices, Proceedings of International Symposium on Nonlinear Theory and its Applications, p.745748, 2005.

I. Shin, S. M. Oishi, and . Rump, Fast verication of solutions of matrix equations, Numerische Mathematik, vol.90, issue.4, p.755773, 2002.

M. A. Overton, Numerical Computing with IEEE Floating-Point Arithmetic, 2001.
DOI : 10.1137/1.9780898718072

K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, and S. M. Rump, Numerical method for dense linear systems with arbitrariliy ill-conditioned matrices, Proceedings of International Symposium on Nonlinear Theory and its Applications, p.749752, 2005.

K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, and S. M. Rump, A method of obtaining veried solutions for linear systems suited for Java, J. Comput. Appl. Math, vol.199, issue.2, p.337344, 2006.

J. M. Peña, On the multivariate Horner scheme, SIAM Journal on Numerical Analysis, vol.37, issue.4, p.11861197, 2000.

M. Pichat, Correction d'une somme en arithmétique à virgule ottante, Numerische Mathematik, vol.19, p.400406, 1972.

M. Pichat, Contributions à l'étude des erreurs d'arrondi en arithmétique à virgule ottante, 1976.

M. Pichat and J. Vignes, Ingénierie du contrôle de la précision des calculs sur ordinateur, Editions Technip, 1993.

D. M. Priest, Algorithms for arbitrary precision oating point arithmetic, Proceedings of the 10th IEEE Symposium on Computer Arithmetic (Arith-10), p.132144, 1991.

D. M. Priest, On Properties of Floating Point Arithmetics : Numerical Stability and the Cost of Accurate Computations, 1992.

S. M. Rump, Algorithms for computing validated results, Computer Algebra Handbook, p.110112, 2003.

S. M. Rump, 10. Computer-Assisted Proofs and Self-Validating Methods, Handbook on Acuracy and Reliability in Scientic Computation, 2005.
DOI : 10.1137/1.9780898718157.ch10

S. M. Rump and S. Oishi, Super-fast validated solution of linear systems, Journal of Computational and Applied Mathematics, vol.199, issue.2, p.199206, 2006.
DOI : 10.1016/j.cam.2005.07.038

S. M. Rump, T. Ogita, and S. Oishi, Accurate oating-point summation, 2006.

J. R. Shewchuk, Robust adaptive oating-point geometric predicates, SCG '96 : Proceedings of the twelfth annual symposium on Computational geometry, p.141150, 1996.

J. R. Shewchuk, Adaptive precision oating-point arithmetic and fast robust geometric predicates, Discrete and Computational Geometry, p.305363, 1997.

J. H. Wilkinson, Rounding Errors in Algebraic Processes, 1963.

Y. Zhu and W. Hayes, Fast, guaranteed-accurate sums of many oatingpoint numbers, RNC7 : Proceedings of the 7th Conference on Real Numbers and Computers, p.1122, 2006.

Y. Zhu, J. Yong, and G. Zheng, A new distillation algorithm for oating-point summation, SIAM Journal on Scientic Computing, vol.26, issue.6, p.20662078, 2005.

H. Annexe, . Ch, H. Ch, . Ch, and . Ch, Annexes Performances de CompHorner et DDHorner Environnement I : Intel Pentium 4, 3.00GHz, gcc 4.1.2, unité ottante x87 Nombre de cycles Temps d'exécution normalisé deg

I. Environnement, . Ch, H. Ch, . Ch, and . Ch, Intel Pentium 4, 3.00GHz, gcc 4.1.2, unité ottante SSE Nombre de cycles Temps d'exécution normalisé deg

I. Environnement, . Ch, H. Ch, . Ch, and . Ch, Intel Pentium 4, 3.00GHz, icc 9.1, unité ottante x87 Nombre de cycles Temps d'exécution normalisé deg

I. Environnement, . Ch, H. Ch, . Ch, and . Ch, Intel Pentium 4, 3.00GHz, icc 9.1, unité ottante SSE Nombre de cycles Temps d'exécution normalisé deg

V. Environnement, . Ch, H. Ch, . Ch, and . Ch, AMD Athlon 64 3200+, 2GHz, gcc 4.1.2, unité ottante SSE Nombre de cycles Temps d'exécution normalisé deg

V. Environnement, Intel Itanium 2, 1.5 GHz, gcc 4

. Annexe, Annexes Performances de CompHorner en présence d'un FMA Environnement VI : Intel Itanium 2, 1.5 GHz, gcc 4

. Annexe, Annexes Performances de CompHorner4

I. Environnement, Intel Pentium 4, 3.00GHz, gcc 4.1.2, unité ottante x87 Nombre de cycles Temps d'exécution normalisé deg H CH 4

I. Environnement, Intel Pentium 4, 3.00GHz, gcc 4.1.2, unité ottante SSE Nombre de cycles Temps d'exécution normalisé deg H CH 4

I. Environnement, Intel Pentium 4, 3.00GHz, icc 9.1, unité ottante x87 Nombre de cycles Temps d'exécution normalisé deg H CH 4

I. Environnement, Intel Pentium 4, 3.00GHz, icc 9.1, unité ottante SSE Nombre de cycles Temps d'exécution normalisé deg H CH 4

V. Environnement, AMD Athlon 64 3200+, 2GHz, gcc 4.1.2, unité ottante SSE Nombre de cycles Temps d'exécution normalisé deg H CH 4

V. Environnement, Intel Itanium 2, 1.5 GHz, gcc 4

. Annexe, Annexes Performances de CompTRSV Environnement II : Intel Pentium 4, 3.00GHz, gcc 4.1.2, unité ottante SSE n TRSV CompTRSV BLAS_dtrsv_x n TRSV CompTRSV