, IEEE Standard for Floating-Point Arithmetic, 2008.

V. Lefèvre, J. 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

D. , D. Sarma, and D. W. Matula, Faithful bipartite ROM reciprocal tables, 12th IEEE Symposium on Computer Arithmetic, pp.17-28, 1995.

F. De-dinechin and A. Tisserand, Multipartite table methods, IEEE Transactions on Computers, vol.54, issue.3, pp.319-330, 2005.
DOI : 10.1109/TC.2005.54

URL : https://hal.archives-ouvertes.fr/ensl-00542210

D. Defour, F. De-dinechin, and J. Muller, A new scheme for table-based evaluation of functions, Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002., pp.1608-1613, 2002.
DOI : 10.1109/ACSSC.2002.1197049

URL : https://hal.archives-ouvertes.fr/inria-00071948

, CR-Libm, a library of correctly rounded elementary functions in double-precision

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

J. Muller, Elementary Functions: Algorithms and Implementation, 2006.
URL : https://hal.archives-ouvertes.fr/ensl-00000008

V. Lefèvre, Hardest-to-round cases, ENS Lyon, Tech. Rep, 2010.

S. Chevillard, J. Harrison, M. Joldes¸, C. Joldes¸, and . Lauter, Efficient and accurate computation of upper bounds of approximation errors, Theoretical Computer Science, vol.412, issue.16, pp.1523-1543, 2011.
DOI : 10.1016/j.tcs.2010.11.052

URL : https://hal.archives-ouvertes.fr/ensl-00445343

M. H. Payne and R. N. Hanek, Radian reduction for trigonometric functions, ACM SIGNUM Newsletter, vol.18, issue.1, pp.19-24, 1983.
DOI : 10.1145/1057600.1057602

M. Daumas, C. Mazenc, X. Merrheim, and J. Muller, Modular Range Reduction: a New Algorithm for Fast and Accurate Computation of the Elementary Functions, pp.162-175, 1995.
DOI : 10.1007/978-3-642-80350-5_15

N. Brisebarre, D. Defour, P. Kornerup, J. Muller, and N. , A new range-reduction algorithm, IEEE Transactions on Computers, vol.54, issue.3, 2005.
DOI : 10.1109/TC.2005.36

URL : https://hal.archives-ouvertes.fr/ensl-00086904

F. De-dinechin and C. Q. Lauter, Optimizing polynomials for floating-point implementation, Proceedings of the 8th Conference on Real Numbers and Computers, pp.7-16, 2008.
URL : https://hal.archives-ouvertes.fr/ensl-00260563

N. Brisebarre and S. Chevillard, Efficient polynomial L-approximations, 18th IEEE Symposium on Computer Arithmetic (ARITH '07), pp.169-176, 2007.
DOI : 10.1109/ARITH.2007.17

URL : https://hal.archives-ouvertes.fr/inria-00119513

C. Mouilleron and G. Revy, Automatic Generation of Fast and Certified Code for Polynomial Evaluation, 2011 IEEE 20th Symposium on Computer Arithmetic, pp.233-242, 2011.
DOI : 10.1109/ARITH.2011.39

URL : https://hal.archives-ouvertes.fr/ensl-00531721

H. De-lassus-saintgenì-es, D. Defour, and G. Revy, Range reduction based on Pythagorean triples for trigonometric function evaluation, 2015 IEEE 26th International Conference on Application-specific Systems, Architectures and Processors (ASAP), pp.74-81, 2015.
DOI : 10.1109/ASAP.2015.7245712

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

URL : https://digital.library.unt.edu/ark:/67531/metadc1114328/m2/1/high_res_d/6133932.pdf

J. R. Shewchuk, Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates, Discrete & Computational Geometry, vol.18, issue.3, pp.305-363, 1997.
DOI : 10.1007/PL00009321

D. Defour, Cache-optimised methods for the evaluation of elementary functions Laboratoire de l'informatique du parallélisme, 2002.

V. Lefevre and J. M. Muller, Worst cases for correct rounding of the elementary functions in double precision, Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001, pp.111-118, 2001.
DOI : 10.1109/ARITH.2001.930110

URL : https://hal.archives-ouvertes.fr/inria-00100547

, Worst cases for correct rounding of the elementary functions in double precision, 2003.

S. Gal, Computing elementary functions: A new approach for achieving high accuracy and good performance, " in Accurate Scientific Computations, ser, Lecture Notes in Computer Science, vol.235, pp.1-16, 1986.
DOI : 10.1007/3-540-16798-6_1

S. Gal and B. Bachelis, An accurate elementary mathematical library for the IEEE floating point standard, ACM Transactions on Mathematical Software, vol.17, issue.1, pp.26-45, 1991.
DOI : 10.1145/103147.103151

D. Stehlé and P. Zimmermann, Gal's Accurate Tables Method Revisited, 17th IEEE Symposium on Computer Arithmetic (ARITH'05), pp.257-264, 2005.
DOI : 10.1109/ARITH.2005.24

N. Brisebarre, M. D. Ercegovac, and J. Muller, (M, p, k)-Friendly Points: A Table-Based Method for Trigonometric Function Evaluation, 2012 IEEE 23rd International Conference on Application-Specific Systems, Architectures and Processors, pp.46-52, 2012.
DOI : 10.1109/ASAP.2012.17

URL : https://hal.archives-ouvertes.fr/ensl-00759912

D. Wang, J. Muller, N. Brisebarre, and M. D. Ercegovac, (M, p, k)-friendly points: A table-based method to evaluate trigonometric functions, IEEE Transactions on Circuits and Systems, issue.9, pp.61-711, 2014.

G. W. Reitwiesner, Binary Arithmetic, Advances in, pp.231-308, 1960.
DOI : 10.1016/S0065-2458(08)60610-5

, Sierpí nski, Pythagorean triangles, Graduate School of Science, 1962.

S. Chevillard, M. Joldes¸, C. Joldes¸, and . Lauter, Sollya: An Environment for the Development of Numerical Codes, Lecture Notes in Computer Science, K. Fukuda, J. van der Hoeven, vol.6327, pp.28-31, 2010.
DOI : 10.1007/978-3-642-15582-6_5

URL : https://hal.archives-ouvertes.fr/hal-00761644

J. Conway and R. Guy, The Book of Numbers, ser. Copernicus Series, 1998.

P. Shiu, The Shapes and Sizes of Pythagorean Triangles, The Mathematical Gazette, vol.67, issue.439, pp.33-38, 1983.
DOI : 10.2307/3617358

F. J. Barning, On pythagorean and quasi-pythagorean triangles and a generation process with the help of unimodular matrices, Dutch) Math. Centrum Amsterdam Afd. Zuivere Wisk. ZW-001, 1963.

A. Hall, 232. Genealogy of Pythagorean Triads, The Mathematical Gazette, vol.54, issue.390, pp.377-379, 1970.
DOI : 10.2307/3613860

H. L. Price, The Pythagorean Tree: A New Species ArXiv eprints, 1988.

A. V. Vella, When is n a member of a pythagorean triple, The Mathematical Gazette, pp.102-105, 2003.

A. H. Beiler, Recreations in the theory of numbers: The queen of mathematics entertains, 1964.

J. Muller, N. Brisebarre, F. De-dinechin, C. Jeannerod, V. Lefèvre et al., Handbook of Floating-Point Arithmetic, 2010.
URL : https://hal.archives-ouvertes.fr/ensl-00379167

C. Q. Lauter, Basic building blocks for a triple-double intermediate format, Inria, Research Report, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00070314

, Arrondi correct de fonctions mathématiques -fonctions univariées et bivariées, certification et automatisation, 2008.

A. Fässler, Multiple Pythagorean Number Triples, The American Mathematical Monthly, vol.32, issue.6, pp.505-517, 1991.
DOI : 10.2140/pjm.1955.5.73