GNU MPFR in the World

Publications Citing MPFR

If you have published a scientific publication citing MPFR, and you want it to be mentioned here, please tell us.

Books

• Modern Computer Arithmetic, Richard Brent and Paul Zimmermann, 2006-2010.
• Handbook of Floating-Point Arithmetic, Jean-Michel Muller, Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol, Damien Stehlé and Serge Torres, 2009.

PhD Theses

• Arnaud Fontaine. Classification d'ARN codants et d'ARN non-codants, 2009.
• Bogdan Pasca. High-performance floating-point computing on reconfigurable circuits, 2011.
• Mioara Joldeş. Rigorous Polynomial Approximations and Applications, 2011.
• Marc Mezzarobba. Autour de l'évaluation numérique des fonctions D-finies, 2011.
• Christophe Mouilleron. Efficient computation with structured matrices and arithmetic expressions, 2011.

Articles

• Paul Zimmermann. MPFR : vers un calcul flottant correct ?, Interstices, 2005.
• David H. Bailey. High-Precision Floating-Point Arithmetic in Scientific Computation, Computing in Science and Engineering, 2005.
• Florent de Dinechin, Alexey V. Ershov and Nicolas Gast. Towards the Post-Ultimate libm, 17th IEEE Symposium on Computer Arithmetic (ARITH), 2005.
• Vincent Lefèvre. New Results on the Distance Between a Segment and Z². Application to the Exact Rounding, 17th IEEE Symposium on Computer Arithmetic (ARITH), 2005.
• Andrej Bauer and Iztok Kavkler. Implementing Real Numbers With RZ, 4th International Conference on Computability and Complexity in Analysis (CCA 2007), 2008.
• Vincent Lefèvre, Damien Stehlé and Paul Zimmermann. Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format, Reliable Implementation of Real Number Algorithms: Theory and Practice, 2008.
• Chee K. Yap and Jihun Yu. Foundations of Exact Rounding, 3rd Workshop on Algorithms and Computation (WALCOM), 2009.
• Christoph Quirin Lauter and Vincent Lefèvre. An Efficient Rounding Boundary Test for pow(x,y) in Double Precision, IEEE Transactions on Computers, 2009.
• Fumihiro Chiba and Teruo Ushijima. Exponential decay of errors of a fundamental solution method applied to a reduced wave problem in the exterior region of a disc, Journal of Computational and Applied Mathematics, 2009.
• Peter Kornerup, Vincent Lefèvre, Nicolas Louvet and Jean-Michel Muller. On the Computation of Correctly-Rounded Sums, 19th IEEE Symposium on Computer Arithmetic (ARITH), 2009.
• Fumihiro Chiba and Teruo Ushijima. Computation of the scattering amplitude for a scattering wave produced by a disc, Journal of Computational and Applied Mathematics, 2009.
• Kaveh R. Ghazi, Vincent Lefèvre, Philippe Théveny and Paul Zimmermann. Why and How to Use Arbitrary Precision, Computing in Science and Engineering, 2010.
• Vincent Lefèvre, Philippe Théveny, Florent de Dinechin, Claude-Pierre Jeannerod, Christophe Mouilleron, David Pfannholzer and Nathalie Revol. LEMA: towards a language for reliable arithmetic, ACM Communications in Computer Algebra (Emerging Trends Papers accepted for PLMMS 2010), 2010.
• Burçin Eröcal and William Stein. The Sage Project: Unifying Free Mathematical Software to Create a Viable Alternative to Magma, Maple, Mathematica and MATLAB, 3rd International Congress on Mathematical Software (ICMS), 2010.
• Paul Zimmermann. Reliable Computing with GNU MPFR, 3rd International Congress on Mathematical Software (ICMS), 2010.
• Marc Mörig. Deferring Dag Construction by Storing Sums of Floats Speeds-Up Exact Decision Computations Based on Expression Dags, 3rd International Congress on Mathematical Software (ICMS), 2010.
• Jihun Yu, Chee Yap, Zilin Du, Sylvain Pion and Hervé Brönnimann. The Design of Core 2: A Library for Exact Numeric Computation in Geometry and Algebra, 3rd International Congress on Mathematical Software (ICMS), 2010.
• Grégoire Lecerf. Mathemagix: Towards Large Scale Programming for Symbolic and Certified Numeric Computations, 3rd International Congress on Mathematical Software (ICMS), 2010.
• Guillaume Hanrot, Bruno Martin and Gérald Tenenbaum. Constantes de Turán-Kubilius friables: une étude numérique, Experiment. Math., Volume 19, Issue 3, pages 345-361, 2010.
• Claude-Pierre Jeannerod, Hervé Knochel, Christophe Monat and Guillaume Revy. Computing floating-point square roots via bivariate polynomial evaluation, IEEE Transactions on Computers, 2011.
• Peter Kornerup, Vincent Lefèvre, Nicolas Louvet and Jean-Michel Muller. On the Computation of Correctly-Rounded Sums, IEEE Transactions on Computers, 2011.
• Hong Diep Nguyen and Nathalie Revol. Solving and Certifying the Solution of a Linear System, Reliable Computing, 2011.
• Florent de Dinechin, Jean-Michel Muller, Bogdan Pasca and Alexandru Plesco. An FPGA architecture for solving the Table Maker's Dilemma, IEEE International Conference on Application-Specific Systems, Architectures and Processors (ASAP), 2011.
• Eric Wajnberg. Multi-objective behavioural mechanisms are adopted by foraging animals to achieve several optimality goals simultaneously, Journal of Animal Ecology, Volume 81, Issue 2, pages 503-511, 2012.
• David H. Bailey, Roberto Barrio, and Jonathan M. Borwein. High-precision computation: Mathematical physics and dynamics [preprint], Applied Mathematics and Computation, vol. 218, 2012.
• Tomonori Kouya. A Highly Efficient Implementation of Multiple Precision Sparse Matrix-Vector Multiplication and its Application to Product-Type Krylov Subspace Methods, International Journal of Numerical Methods and Applications, Volume 7, Issue 2, pages 107-119, 2012.
• Charles F. F. Karney. Sampling exactly from the normal distribution, 2013.

Other Information About MPFR

Note: This section does not contain links to MPFR interfaces and to software using MPFR as they are already on the MPFR home page.

• MPFR on Wikipedia.
• In January 2009, using MPFR, Keith Briggs found a new worst approximable pair (new record) in the problem of constructing an explicit pair of irrationals with sup-norm simultaneous approximation constant as large as possible.
• In July 2010, J. Buethe, J. Franke, A. Jost and T. Kleinjung found that the number of primes below 10²⁴ is 18435599767349200867866, using MPFR amongst various libraries.
• In 2011, with a new algorithm implemented in FLINT, which uses among others MPFR, Fredrik Johansson was able to compute p(10¹⁹), the number of partitions of 10¹⁹: slides.

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