?. Phl and ?. Log1pz, Phl ? P ) + d e l t a 6

?. Logtabpolyhl and ?. Log1pzptab, Logihm ? L o g i r ) + ( Phl ? Log1pZ ) + d e l t a 7

?. Loghm and ?. Log, Log2edhm ? Log2E ) + ( LogTabPolyhl ? Log1pZpTab ) + d e l t a 5

\. Polywithsquarehml and ?. Polywithsquare, PolyWithSquare i n [?1b ?137 ,1b?137] 156 /\ ( Polyhml ? Poly ) / Poly i n [?1b ?134 ,1b?134, Logyhml ? Logy ) / Logy i n [?1b ?128, pp.1-128

\. Loghml and ?. Logover, Logover i n [?1b ?123 ,1b?123, Log2hml ? MLog2 ) / MLog2 i n [?1b ?126 ,1b?126] 160 /\ ( Logihml ? MLogi ) / MLogi i n [?1b ?159, pp.1-159

A. Ieee, Standard 754-1985 for binary floating-point arithmetic, 1985.

A. Baker, Transcendental Number Theory, 1975.
DOI : 10.1017/CBO9780511565977

S. Boldo and M. Daumas, A mechanically-validated technique for extending the available precision, Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.No.01CH37256), 2001.
DOI : 10.1109/ACSSC.2001.987700

M. Cornea, J. Harrison, and P. T. Tang, Scientific Computing on Itanium-based Systems, 2002.

M. Daumas and C. Moreau-finot, Exponential: implementation trade-offs for hundred bit precision, Real Numbers and Computers, pp.61-74, 2000.

F. De-dinechin and D. Defour, Software carry-save: A case study for instruction-level parallelism, Seventh International Conference on Parallel Computing Technologies, 2003.

F. De-dinechin, D. Defour, and C. Lauter, Fast correct rounding of elementary functions in double precision using double-extended arithmetic, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00071446

F. De-dinechin, A. Ershov, and N. Gast, Towards the Post-Ultimate libm, 17th IEEE Symposium on Computer Arithmetic (ARITH'05), pp.288-295, 2005.
DOI : 10.1109/ARITH.2005.46
URL : https://hal.archives-ouvertes.fr/inria-00070636

F. De-dinechin, C. Q. Lauter, and G. Melquiond, Assisted verification of elementary functions using Gappa Extended version available as LIP research report RR2005-43, ACM Symposium on Applied Computing, pp.2005-2048, 2006.

D. Defour and F. De-dinechin, SOFTWARE CARRY-SAVE FOR FAST MULTIPLE-PRECISION ALGORITHMS, Mathematical Software, 2002.
DOI : 10.1142/9789812777171_0004

D. Defour, G. Hanrot, V. Lefèvre, J. Muller, N. Revol et al., Proposal for a standardization of mathematical function implementations in floating-point arithmetic. Numerical algorithms, pp.1-4367, 2004.

J. Theodorus and . Dekker, A floating point technique for extending the available precision, Numerische Mathematik, vol.18, issue.3, pp.224-242, 1971.

P. M. Farmwald, High bandwidth evaluation of elementary functions, 1981 IEEE 5th Symposium on Computer Arithmetic (ARITH)
DOI : 10.1109/ARITH.1981.6159271

S. Gal, Computing elementary functions: A new approach for achieving high accuracy and good performance, Accurate Scientific Computations, pp.1-16, 1986.
DOI : 10.1007/3-540-16798-6_1

D. Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Computing Surveys, vol.23, issue.1, pp.5-47, 1991.
DOI : 10.1145/103162.103163
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.7712

J. Harrison, T. Kubaska, S. Story, and P. T. Tang, The computation of transcendental functions on the IA-64 architecture, Intel Technology Journal, p.4, 1999.

R. Klatte, U. Kulisch, C. Lawo, M. Rauch, and A. Wiethoff, C-XSC a C++ class library for extended scientific computing, 1993.

D. Knuth, The Art of Computer Programming, 1973.

P. Kornerup, . Ch, V. Lauter, N. Lefèvre, J. Louvet et al., Computing correctly rounded integer powers in floating-point arithmetic, ACM Transactions on Mathematical Software, vol.37, issue.1, 2008.
DOI : 10.1145/1644001.1644005
URL : https://hal.archives-ouvertes.fr/inria-00388501

. Ch, V. Lauter, and . Lefèvre, An efficient rounding boundary test for pow(x,y) in double precision, 2007.

. Q. Ch and . Lauter, Basic building blocks for a triple-double intermediate format, 2005.

V. Lefèvre, J. M. Muller, and A. Tisserand, Toward correctly rounded transcendentals, IEEE Transactions on Computers, vol.47, issue.11, pp.1235-1243, 1998.
DOI : 10.1109/12.736435

V. Lefvre, Moyens arithmétiques pour un calcul fiable, 2000.

R. Li, P. Markstein, J. P. Okada, and J. W. Thomas, The libm library and floating-point arithmetic for HP-UX on Itanium, 2001.

P. Markstein, IA-64 and Elementary Functions : Speed and Precision. Hewlett-Packard Professional Books, 2000.

G. Melquiond, Gappa -génération automatique de preuves de propriétés arithmétiques

R. E. Moore, Interval analysis, 1966.

J. Muller, Elementary Functions, Algorithms and Implementation, 1997.
URL : https://hal.archives-ouvertes.fr/ensl-00000008

K. C. Ng, Argument reduction for huge arguments: Good to the last bit, 1992.

D. Stehlé, Algorithmique de la rduction de rseaux et application la recherche de pires cas pour l'arrondi de fonctions mathmatiques, 2006.

P. H. Sterbenz, Floating point computation, 1974.

P. T. Tang, Table-lookup algorithms for elementary functions and their error analysis, [1991] Proceedings 10th IEEE Symposium on Computer Arithmetic, pp.232-236, 1991.
DOI : 10.1109/ARITH.1991.145565

W. F. Wong and E. Goto, Fast hardware-based algorithms for elementary function computations using rectangular multipliers, IEEE Transactions on Computers, vol.43, issue.3, pp.278-294, 1994.
DOI : 10.1109/12.272429

A. Ziv, Fast evaluation of elementary mathematical functions with correctly rounded last bit, ACM Transactions on Mathematical Software, vol.17, issue.3, pp.410-423, 1991.
DOI : 10.1145/114697.116813