## MPFR

 swMATH ID: 3312 Software Authors: Guillaume Hanrot, Vincent Lefèvre, Patrick Pélissier, Philippe Théveny, Paul Zimmermann Description: The MPFR library is a C library for multiple-precision floating-point computations with correct rounding. MPFR has continuously been supported by the INRIA and the current main authors come from the Caramel and AriC project-teams at Loria (Nancy, France) and LIP (Lyon, France) respectively; see more on the credit page. MPFR is based on the GMP multiple-precision library. The main goal of MPFR is to provide a library for multiple-precision floating-point computation which is both efficient and has a well-defined semantics. It copies the good ideas from the ANSI/IEEE-754 standard for double-precision floating-point arithmetic (53-bit significand). MPFR is free. It is distributed under the GNU Lesser General Public License (GNU Lesser GPL), version 3 or later (2.1 or later for MPFR versions until 2.4.x). The library has been registered in France by the Agence de Protection des Programmes under the number IDDN FR 001 120020 00 R P 2000 000 10800, on 15 March 2000. This license guarantees your freedom to share and change MPFR, to make sure MPFR is free for all its users. Unlike the ordinary General Public License, the Lesser GPL enables developers of non-free programs to use MPFR in their programs. If you have written a new function for MPFR or improved an existing one, please share your work! Homepage: http://www.mpfr.org/ Programming Languages: C library Operating Systems: None Dependencies: None Keywords: reliable computing; correct rounding; IEEE 754; GNU MPFR Related Software: gmp; Mathematica; mctoolbox; SageMath; Matlab; ARPREC; MPC; INTLAB; Julia; LAPACK; MPFI; iRRAM; PARI/GP; XBLAS; Arb; Maple; Algorithm 524; Taylor; DLMF; Ada95 Cited in: 229 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Reliable computing with GNU MPFR. Zbl 1295.65148
Zimmermann, Paul
2010
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### Cited by 336 Authors

 19 Sharma, Janak Raj 14 Grau-Sánchez, Miquel 13 Noguera, Miquel 10 Rump, Siegfried Michael 6 Arora, Himani 6 Ezquerro, José Antonio 6 Graillat, Stef 6 Koch, Hans-Friedrich 6 Petković, Miodrag S. 5 Arioli, Gianni 5 Barrio, Roberto 5 Muller, Jean-Michel 5 Tsai, Chia-Cheng 5 Zimmermann, Paul 4 Argyros, Ioannis Konstantinos 4 Grau, Àngela 4 Ogita, Takeshi 4 Oishi, Shin’ichi 4 van der Hoeven, Joris 3 Balaprakash, Prasanna 3 Birattari, Mauro 3 Cuyt, Annie A. M. 3 Dorigo, Marco 3 Enge, Andreas 3 Gupta, Puneet Kumar 3 Gutiérrez, José Manuel 3 Hanrot, Guillaume 3 Hernández-Verón, Miguel Ángel 3 Hernández, Miguel Ángel 3 Johansson, Fredrik 3 Joldeş, Mioara 3 Kumar, Deepak 3 Lefèvre, Vincent 3 Rodríguez, Marcos 3 Sharma, Rajni 3 Stützle, Thomas G. 3 Wilczak, Daniel 3 Yap, Chee-Keng 2 Abad, Alberto J. 2 Backeljauw, Franky 2 Bauer, Andrej 2 Behl, Ramandeep 2 Beliakov, Gleb 2 Bertot, Yves 2 Bhalla, Sonia 2 Brauße, Franz 2 Brzeziński, Dariusz W. 2 Calleja, Renato C. 2 Celletti, Alessandra 2 Chan, Yao-ban 2 Chiba, Fumihiro 2 Cirillo, Emiliano 2 de la Llave, Rafael 2 Dena, Ángeles 2 Díaz-Barrero, José Luis 2 Donà, Pietro 2 Fousse, Laurent 2 Higham, Nicholas J. 2 Hormann, Kai 2 Jiang, Hao 2 Kalra, Nitin 2 Kapela, Tomasz 2 Kavkler, Iztok 2 Korovina, Margarita Vladimirovna 2 Kumar, Sunil 2 Lange, Marko 2 Lecerf, Grégoire 2 Leykin, Anton 2 Liao, Shijun 2 Martel, Matthieu 2 Mascarenhas, Walter F. 2 Melquiond, Guillaume 2 Ménissier-Morain, Valérie 2 Milošević, Dušan M. 2 Mörig, Marc 2 Müller, Norbert Th. 2 Petković, Ivan M. 2 Popescu, Valentina 2 Quintana-Ortí, Enrique S. 2 Revol, Nathalie 2 Rouillier, Fabrice 2 Stehlé, Damien 2 Tucker, Warwick 2 Ushijima, Teruo 2 Wang, Xiaofeng 2 Xiao, Xiaoyong 2 Yin, Hongwei 2 Yu, Jihun 2 Zgliczyński, Piotr 1 Abdulla, Ugur G. 1 Adjé, Assalé 1 Aguilar-Melchor, Carlos 1 Albrecht, Martin R. 1 Aleksandrov, P. A. 1 Alfosail, Feras K. 1 Aliaga, José Ignacio 1 Armknecht, Frederik 1 Artz, Johannes 1 Austin, Anthony P. 1 Baeza, Antonio ...and 236 more Authors
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### Cited in 92 Serials

 13 ACM Transactions on Mathematical Software 13 Journal of Computational and Applied Mathematics 11 Applied Mathematics and Computation 10 Numerical Algorithms 7 Mathematics of Computation 6 S$$\vec{\text{e}}$$MA Journal 5 SIAM Journal on Scientific Computing 5 Computational and Applied Mathematics 5 Communications in Nonlinear Science and Numerical Simulation 4 Computers & Mathematics with Applications 4 Numerische Mathematik 4 Engineering Analysis with Boundary Elements 3 Calcolo 3 Information and Computation 3 International Journal of Computer Mathematics 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 ETNA. Electronic Transactions on Numerical Analysis 3 International Journal of Computational Methods 2 Computer Physics Communications 2 Journal of Computational Physics 2 Journal of Mathematical Analysis and Applications 2 BIT 2 Journal of Algebra 2 Journal of Optimization Theory and Applications 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Applied Numerical Mathematics 2 Linear Algebra and its Applications 2 Celestial Mechanics and Dynamical Astronomy 2 Experimental Mathematics 2 Reliable Computing 2 Chaos 2 Journal of High Energy Physics 2 Methodology and Computing in Applied Probability 2 Mathematics in Computer Science 2 ACM Communications in Computer Algebra 2 Advances in Numerical Analysis 2 Applied Mathematics and Nonlinear Sciences 1 Classical and Quantum Gravity 1 Communications in Mathematical Physics 1 General Relativity and Gravitation 1 IMA Journal of Numerical Analysis 1 Information Processing Letters 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Fluid Mechanics 1 Journal of Statistical Physics 1 Mathematical Biosciences 1 Nonlinearity 1 Computing 1 Journal of Differential Equations 1 Mathematics and Computers in Simulation 1 Meccanica 1 Operations Research 1 Theoretical Computer Science 1 Transactions of the American Mathematical Society 1 Insurance Mathematics & Economics 1 Annals of Pure and Applied Logic 1 Physica D 1 Journal of Complexity 1 Computers & Operations Research 1 Journal of Automated Reasoning 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Scientific Computing 1 Neural Networks 1 Random Structures & Algorithms 1 Japan Journal of Industrial and Applied Mathematics 1 Computational Geometry 1 Computational Mathematics and Mathematical Physics 1 Communications in Partial Differential Equations 1 European Journal of Operational Research 1 Journal of Statistical Computation and Simulation 1 SIAM Review 1 Journal of Nonlinear Science 1 Computational Optimization and Applications 1 Journal de Théorie des Nombres de Bordeaux 1 Applicationes Mathematicae 1 Numerical Linear Algebra with Applications 1 Discrete and Continuous Dynamical Systems 1 INFORMS Journal on Computing 1 Abstract and Applied Analysis 1 Higher-Order and Symbolic Computation 1 LMS Journal of Computation and Mathematics 1 RAIRO. Theoretical Informatics and Applications 1 The Journal of Logic and Algebraic Programming 1 Information 1 Acta Numerica 1 Journal of Statistical Mechanics: Theory and Experiment 1 Algorithms 1 TWMS Journal of Pure and Applied Mathematics 1 Discrete Mathematics and its Applications 1 Matematicheskie Voprosy Kriptografii
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### Cited in 45 Fields

 159 Numerical analysis (65-XX) 33 Computer science (68-XX) 20 Number theory (11-XX) 17 Dynamical systems and ergodic theory (37-XX) 16 Approximations and expansions (41-XX) 13 Partial differential equations (35-XX) 12 Special functions (33-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 9 Operations research, mathematical programming (90-XX) 9 Information and communication theory, circuits (94-XX) 7 Real functions (26-XX) 7 Mechanics of particles and systems (70-XX) 6 Combinatorics (05-XX) 6 Ordinary differential equations (34-XX) 6 Probability theory and stochastic processes (60-XX) 5 Mathematical logic and foundations (03-XX) 5 Statistics (62-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Commutative algebra (13-XX) 4 Operator theory (47-XX) 4 Fluid mechanics (76-XX) 4 Quantum theory (81-XX) 3 Field theory and polynomials (12-XX) 3 Algebraic geometry (14-XX) 3 Topological groups, Lie groups (22-XX) 3 Functions of a complex variable (30-XX) 3 Integral equations (45-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Relativity and gravitational theory (83-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Convex and discrete geometry (52-XX) 2 Mechanics of deformable solids (74-XX) 2 Biology and other natural sciences (92-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Difference and functional equations (39-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)