A Fortran 90-based multiprecision system, ACM Transactions on Mathematical Software, vol.21, issue.4, pp.379-387, 1995. ,
DOI : 10.1145/212066.212075
The doubledouble library, 1998. ,
Brook for GPUs: Stream computing on graphics hardware, Proceedings of SIGGRAPH 2004, pp.777-786, 2004. ,
Floating point specials on the GPU, 2005. ,
Software Carry-Save: A Case Study for Instruction-Level Parallelism, 7th conference on parallel computing technologies, 2003. ,
DOI : 10.1007/978-3-540-45145-7_18
A floating-point technique for extending the available precision, Numerische Mathematik, vol.5, issue.3, pp.224-242, 1971. ,
DOI : 10.1007/BF01397083
GNU multiple precision arithmetic library ,
The Cg Tutorial: The Definitive Guide to Programmable Real- Time Graphics, 2003. ,
Accelerating double precision fem simulations with GPUs, Proceedings of ASIM 2005 -18th Symposium on Simulation Technique, 2005. ,
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
Algorithms for quad-double precision floating point arithmetic, Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001, pp.155-162, 2001. ,
DOI : 10.1109/ARITH.2001.930115
GPU floating-point paranoia, ACM Workshop on General Purpose Computing on Graphics Processors, p.8, 2004. ,
The Art of Computer Programming Seminumerical Algorithms, 1998. ,
Basic building blocks for a triple-double intermediate format, 2005. ,
URL : https://hal.archives-ouvertes.fr/inria-00070314
A high-performance area-efficient multifunction interpolator, Proceedings of the 17th IEEE Symposium on Computer Arithmetic (Cap Cod, USA), pp.272-279, 2005. ,
Algorithms for arbitrary precision floating point arithmetic, [1991] Proceedings 10th IEEE Symposium on Computer Arithmetic, pp.132-144, 1991. ,
DOI : 10.1109/ARITH.1991.145549
Adaptive precision floating-point arithmetic and fast robust geometric predicates, Discrete and Computational Geometry, pp.305-363, 1997. ,
Virtual 16 bit precise operations on rgba8 textures, Proceedings of Vision, Modeling, and Visualization, pp.171-178, 2002. ,
Computable analysis and differential equations, Intuitionism and Proof Theory Studies in Logic and the Foundations of Mathematics, pp.47-52, 1970. ,
The failure in computable analysis of a classical existence theorem for differential equations Constructive Analysis Theory of Ordinary Differential Equations, Proc. Amer. Math. Soc. Computational Complexity of Real Functions. Birkhäuser, vol.30, pp.151-156, 1955. ,
A computable ordinary differential equation which possesses no computable solution, Annals of Mathematical Logic, vol.17, issue.1-2, pp.61-90, 1979. ,
DOI : 10.1016/0003-4843(79)90021-4
The wave equation with computable initial data such that its unique solution is not computable, Advances in Mathematics, vol.39, issue.3, pp.215-239, 1981. ,
DOI : 10.1016/0001-8708(81)90001-3
Computability in Analysis and Physics, 1989. ,
AN EFFECTIVE CAUCHY-PEANO EXISTENCE THEOREM FOR UNIQUE SOLUTIONS, International Journal of Foundations of Computer Science, vol.07, issue.02, pp.151-160, 1996. ,
DOI : 10.1142/S0129054196000129
On computable numbers, with an application to the Entscheidungsproblem, Proc. London Math. Soc, pp.230-265, 1936. ,
Computable Analysis: an Introduction, 2000. ,
Is wave propagation computable or can wave computers beat the Turing machine? Proc, pp.312-332, 2002. ,
Binary and decimal adder unit, US Patent no US6292819, 2001. ,
The IBM z900 decimal arithmetic unit, Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.No.01CH37256), pp.1335-1339, 2001. ,
DOI : 10.1109/ACSSC.2001.987708
The design of the fixed point unit for the z990 microprocessor, Proceedins of the 14th ACM Great Lakes symposium on VLSI , GLSVLSI '04, pp.364-367, 2004. ,
DOI : 10.1145/988952.989040
Custom S/390 G5 and G6 microprocessors, IBM Journal of Research and Development, vol.43, issue.5.6, pp.671-680, 1999. ,
DOI : 10.1147/rd.435.0671
Decimal floating-point: algorism for computers, 16th IEEE Symposium on Computer Arithmetic, 2003. Proceedings., pp.104-111, 2003. ,
DOI : 10.1109/ARITH.2003.1207666
Combined binary/decimal adder unit, 1999. ,
Draft revision of the IEEE Standard for Floating?Point Arithmetic, 2006. ,
A family of adders, Proceedings of the 15 th IEEE Symposium on Computer Arithmetic, pp.277-284, 2001. ,
A 4-GHz 130-nm address generation unit with 32-bit sparse-tree adder core, IEEE Journal of Solid-State Circuits, vol.38, issue.5, pp.689-695, 2003. ,
DOI : 10.1109/JSSC.2003.810056
High Speed Decimal Addition, IEEE Transactions on Computers, vol.20, issue.8, pp.862-866, 1971. ,
DOI : 10.1109/T-C.1971.223362
Logical Effort: Designing Fast CMOS Circuits, 1999. ,
A 64-bit Decimal Floating-Point Adder (extended version), Proceedings of the IEEE Computer Society Annual Symposium on VLSI, pp.297-298, 2004. ,
Elementary Functions, Algorithms and Implementation, 1997. ,
URL : https://hal.archives-ouvertes.fr/ensl-00000008
A new range-reduction algorithm, IEEE Transactions on Computers, vol.54, issue.3, pp.331-339, 2005. ,
DOI : 10.1109/TC.2005.36
URL : https://hal.archives-ouvertes.fr/ensl-00086904
Software Manual for the Elementary Functions, N. J, 1980. ,
Modular Range Reduction: a New Algorithm for Fast and Accurate Computation of the Elementary Functions, J. Universal Computer Science, vol.1, pp.162-175, 1995. ,
DOI : 10.1007/978-3-642-80350-5_15
Radian reduction for trigonometric functions, ACM SIGNUM Newsletter, vol.18, issue.1, pp.19-24, 1983. ,
DOI : 10.1145/1057600.1057602
Double-residue modular range reduction for floating-point hardware implementations, IEEE Transactions on Computers, vol.55, issue.3, pp.254-267, 2006. ,
DOI : 10.1109/TC.2006.38
Diseño de arquitecturas CORDIC multidimensionales, 1995. ,
Digital Arithmetic, 2004. ,
Shortest paths for disc obstacles is computable, 21st ACM Symp. on Comp. Geometry, pp.116-125, 2005. ,
3D shape recognition and reconstruction based on line element geometry, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1, pp.1532-1538, 2005. ,
DOI : 10.1109/ICCV.2005.2
An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers, Izvestiya: Mathematics, vol.62, issue.4, pp.723-772, 1998. ,
DOI : 10.1070/IM1998v062n04ABEH000190
Interpolation of helical patches by kinematic rational B??zier patches, Computers & Graphics, vol.14, issue.2, pp.275-280, 1990. ,
DOI : 10.1016/0097-8493(90)90038-Y
On the ???piano movers??? problem. II. General techniques for computing topological properties of real algebraic manifolds, Advances in Applied Mathematics, vol.4, issue.3, pp.298-351, 1983. ,
DOI : 10.1016/0196-8858(83)90014-3
Solid Modeling, Handbook of Computer Aided Geometric Design, 2002. ,
DOI : 10.1016/B978-044451104-1/50021-6
Transcendence measures for exponentials and logarithms, Journal of the Australian Mathematical Society, vol.28, issue.04, pp.445-465, 1978. ,
DOI : 10.1007/BF01361554
Diophantine Approximation on Linear Algebraic Groups, Series of Comprehensive Studies in Mathematics, vol.326, 2000. ,
DOI : 10.1007/978-3-662-11569-5
Robust geometric computation, Handbook of Discrete and Computational Geometry, chapter 41, pp.927-952, 2004. ,
Standard 754-1985 for Binary Floating-Point Arithmetic (also IEC 60559), 1985. ,
Standard Functions for Real and Complex Point and Interval Arguments with Dynamic Accuracy, Scientific Computation with automatic result verification, pp.159-184, 1988. ,
DOI : 10.1007/978-3-7091-6957-5_15
Scientific Computing on Itanium-based Systems, 2002. ,
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
Assisted verification of elementary functions, 2005. ,
URL : https://hal.archives-ouvertes.fr/inria-00070330
Fast and correctly rounded logarithms in double-precision, Theoretical Informatics and Applications, 2006. ,
DOI : 10.1051/ita:2007003
URL : https://hal.archives-ouvertes.fr/inria-00070331
Interval Mathematical Library Based on Chebyshev and Taylor Series Expansion, Reliable Computing, vol.11, issue.5, pp.359-367, 2005. ,
DOI : 10.1007/s11155-005-0042-3
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
Floating point verification in HOL light: The exponential function, 1997. ,
DOI : 10.1007/BFb0000475
FI LIB, eine schnelle und portable Funktionsbibliothek für reelle Argumente und reelle Intervalle im IEEE-double-Format, 1998. ,
Inverse Standard Functions for Real and Complex Point and Interval Arguments with Dynamic Accuracy, Scientific Computation with automatic result verification, pp.185-211, 1988. ,
DOI : 10.1007/978-3-7091-6957-5_16
Toward correctly rounded transcendentals, IEEE Transactions on Computers, vol.47, issue.11, pp.1235-1243, 1998. ,
DOI : 10.1109/12.736435
The libm library and floating-point arithmetic for HP-UX on Itanium, 2001. ,
IA-64 and Elementary Functions: Speed and Precision. Hewlett-Packard Professional Books, 2000. ,
Elementary Functions, Algorithms and Implementation, 1997. ,
URL : https://hal.archives-ouvertes.fr/ensl-00000008
Fast table-driven algorithms for interval elementary functions, Proceedings 13th IEEE Sympsoium on Computer Arithmetic, pp.168-174, 1997. ,
DOI : 10.1109/ARITH.1997.614892
Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library, Workshop on Validated Computing, pp.155-161, 2002. ,
DOI : 10.1007/s11155-005-6891-y
URL : https://hal.archives-ouvertes.fr/inria-00100985
Rigorous and portable standard functions, BIT Numerical Mathematics, vol.41, issue.3, 2001. ,
New algorithms for improved transcendental functions on IA-64, Proceedings 14th IEEE Symposium on Computer Arithmetic (Cat. No.99CB36336), pp.4-11, 1999. ,
DOI : 10.1109/ARITH.1999.762822
Table-driven implementation of the exponential function in IEEE floating-point arithmetic, ACM Transactions on Mathematical Software, vol.15, issue.2, pp.144-157, 1989. ,
DOI : 10.1145/63522.214389
Table-driven implementation of the logarithm function in IEEE floating-point arithmetic, ACM Transactions on Mathematical Software, vol.16, issue.4, pp.378-400, 1990. ,
DOI : 10.1145/98267.98294
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
An Overview of Floating-Point Support and Math Library on the Intel Xscale TM Architecture, Proc. 16th IEEE Symposium on Computer Arithmetic, pp.122-128, 2003. ,
A floating-point technique for extending the available precision, Numerische Mathematik, vol.5, issue.3, pp.224-242 ,
DOI : 10.1007/BF01397083
Table-driven Implementation of the Logarithm Function in IEEE Floating-Point Arithmetic, ACM Transactions on Mathematical Software, vol.16, issue.4, pp.378-400, 1990. ,
CR-LIBM A Library of Correctly Rounded Elementary Functions in Double-Precision, 2006. ,
Microsoft Visual C++ Floating-Point Optimization, 2004. ,
Representation of unit range numbers, Conference Record of the Thirty-Ninth Asilomar Conference onSignals, Systems and Computers, 2005., 2005. ,
DOI : 10.1109/ACSSC.2005.1599943
Derivation of the relative errors for the sunity representation, Appendix, 2006. ,
IA-64 and Elementary functions, 2000. ,
Elementary Functions. Algorithms and Implementations, Ed. Birkhäuser, 1997. ,
URL : https://hal.archives-ouvertes.fr/ensl-00989001
A Regular Layout for Parallel Adders, Waterloo Maple Inc. Maple 9.01. (2003) References [Swa80]. [KM05] P. Kornerup and J.-M. Muller. RN-Coding of Numbers: Definition and some Properties Proc. IMACS'2005, pp.31260-264236, 1951. ,
An IEEE Compliant Floating-Point Adder that Conforms with the Pipelined Packet-Forwarding Paradigm, IEEE Transactions on Computers J. E. Volder. The CORDIC Trigonometric Computing Technique. IRE Transactions on Electronic Computers Computer Arithmetic, vol.49, issue.18, pp.33-47330, 1959. ,
A Test for Correctly Rounded SQRT, manuscript at the URL http ,
p-adic Analysis, and Zeta-Functions, Graduate Texts in Mathematics, vol.58, 1984. ,
Towards correctly rounded transcendentals, IEEE Transactions on Computers, issue.11, pp.47-1235, 1998. ,
IA-64 and Elementary Functions: Speed and Precision, Hewlett-Packard Professional Books, 2000. ,
Number-theoretic test generation for directed rounding, IEEE Transactions on Computers, vol.49, issue.7, pp.651-658, 2000. ,
DOI : 10.1109/12.863034
Berkeley test suite ,
A Fortran-90 double-double library Available at URL = http, 2001. ,
Some Functions Computable with a Fused-Mac, 17th IEEE Symposium on Computer Arithmetic (ARITH'05), 2005. ,
DOI : 10.1109/ARITH.2005.39
URL : https://hal.archives-ouvertes.fr/inria-00000895
Design, implementation and testing of extended and mixed precision BLAS, ACM Trans. Math. Softw, vol.28, issue.2, pp.152-205, 2002. ,
IA-64 and elementary functions. Speed and precision. Hewlett-Packard Professionnal Books, 2000. ,
Accurate Sum and Dot Product, SIAM Journal on Scientific Computing, vol.26, issue.6, pp.1955-1988, 2005. ,
DOI : 10.1137/030601818
Correction d'une somme en arithmetique a virgule flottante, Numerische Mathematik, vol.19, issue.5, pp.400-406, 1972. ,
DOI : 10.1007/BF01404922
Checking Whether Floating Point Division is Correctly Rounded, monograph, Proc. 13 th IEEE Symposium on Computer Arithmetic. IEEE, pp.132-137, 1987. ,
A p-Bit Model of Binary Floating Point Division and Square Root with Emphasis on Extremal Rounding Boundaries, Ph. D. Dissertation, 2002. ,
Number Theoretic Foundations of Binary Floating Point Division with Rounding, Proceedings: Fourth Real Numbers and Computers, pp.39-60, 2000. ,
Generation and analysis of hard to round cases for binary floating point division, Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001, pp.119-127, 2001. ,
DOI : 10.1109/ARITH.2001.930111
A p??p bit fraction model of binary floating point division and extremal rounding cases, Theoretical Computer Science, vol.291, issue.2, pp.159-182, 2003. ,
DOI : 10.1016/S0304-3975(02)00224-4
A Formal Method and Efficient Traversal Algorithm for Generating Testbenches for Verification of IEEE Standard Floating Point Division " , DATE 06 Number-Theoretic Test Generation for Directed Rounding Gal's Accurate Tables Method Revisited, Proc. 17 th IEEE Symposium on Computer Arithmetic, pp.1134-1138, 2000. ,