The MPFR Library

MPFR Links

Internal links:

• Latest release: download – documentation – bugs – changes.
• Gforge: information to use the anonymous access to the Subversion repository.
• Sample: to start with the MPFR library.
• FAQ: frequently asked questions.
• Credit: involved projects and developers.
• History: links to all MPFR versions and past events.
• Algorithms: documents describing algorithms used in MPFR.

External links on MPFR:

• Try MPFR online, thanks to Tomonori Kouya.
• Mailing-list.

Introduction

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 CACAO and Arénaire 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 mantissa).

MPFR is free. It is distributed under the GNU Lesser General Public License (GNU Lesser GPL), version 2.1 or later. 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!

Interfaces for MPFR

• The following four C++ interfaces for MPFR, very different in their design, are available:
  • MPFRCPP, written by Alexey V. Beshenov. This interface uses a modern C++ design with using of classes, templates and function objects.
  • MPFR++, developed in the Arénaire project. Warning! The version currently available (2004-02-27) is not up-to-date, is not compatible with the latest releases of MPFR and has several bugs. News from 2007-05-02: Changes have been done on this interface since, but they are not published yet.
  • The gmpfrxx C++ interface for both GMP and MPFR, written by Jon Wilkening.
  • The Debian package libmpfr-dev provides the mpfrxx.h file. However it is quite old and very limited.
• The multiple-precision arithmetic is very useful for interval arithmetic. Get a multiple-precision interval arithmetic library MPFI, based on MPFR (note: due to API and internal changes in MPFR, you should take MPFI 1.3.4-RC1 or above). This library MPFI is developed by Nathalie Revol from the Arénaire project and Fabrice Rouillier, a former SPACES member. This library implements basic operators {+,-,*,/} and the same functions as MPFR {sqrt, exp, comparison functions, etc.}, except sine and cosine functions applied on intervals. Read more explanations on Nathalie Revol's software page.
• The MPC library (alternative link), a library for multiple-precision complex arithmetic with correct rounding, based on the MPFR and GMP libraries.
• The Perl interface Math::MPFR.
• A LISP interface, written by Richard Fateman. This package also contains a FFT implementation.
• The functional programming language Ursala includes an MPFR interface.

Software Using MPFR

• The KDE calculator Abakus by Michael Pyne (supporting arbitrary precision thanks to MPFR as of version 0.90).
• The ALGLIB.NET project implements multiple-precision linear algebra using MPFR.
• The APRON library, dedicated to the static analysis of the numerical variables of a program by Abstract Interpretation.
• The numerical analysis library BNCpack can be compiled with MPFR.
• CGAL (Computational Geometry Algorithms Library).
• Gappa, a tool intended to help verifying and formally proving properties on numerical programs, by Guillaume Melquiond.
• Genius Math Tool and the GEL language, by Jiri Lebl.
• GCC: first in GFortran, then in the middle-end phase as of GCC 4.3, to resolve math functions with constant arguments. More information.
• Giac/Xcas, a free computer algebra system, by Bernard Parisse.
• The iRRAM - Exact Arithmetic in C++ implementation from Norbert Müller (University of Trier, Germany).
• The C++ continued fractions toolkit libcff by Johan Vervloet.
• Macaulay 2, a software system devoted to supporting research in algebraic geometry and commutative algebra (as of version 1.1).
• The Magma computational algebra system.
• The mpfs library, an experiment in stochastic lazy floating-point arithmetic, from Keith Briggs.
• MPFR is one of the components of SAGE.
• Sollya, a tool environment for safe floating-point code development, written by Christoph Lauter and Sylvain Chevillard in the Arénaire project.
• SXEmacs can be compiled with MPFR support (as of version 22.1.3).
• The Wcalc calculator by Kyle Wheeler (supporting arbitrary precision thanks to MPFR as of version 2.0).
• MPFR is also used by the Fluctuat tool developed and used internally at the CEA (France).

Other Related Free Software

• MAPM, a portable arbitrary precision math library in C, by Michael C. Ring.
• CoStLy, a Complex interval Standard functions Library developed by Markus Neher (Karlsruhe).
• The XSC-Languages, FI_LIB, FILIB++ and intpak software developed at University of Wuppertal (Germany).
• The Core library: a library for robust numerical and geometric computation.
• The CLN C++ library (GPL).
• The Quad-Double package by David Bailey, Yozo Hida and Sherry Li.
• The numerical difference utility from Nelson Beebe, similar to diff but for numerical files.
• The General Multiprecision PYthon project: a GMP interface for the Python language.
• The Constructive Reals Calculator from Hans Boehm.
• The xrc - exact reals in C from Keith Briggs.
• The precise computation software from Oliver Aberth.
• The RR class from NTL, which implements a smooth extension of IEEE floating point to arbitrary precision and guarantees a platform-independent behaviour.
• A continued-fraction package based on GMP, by François Balsalobre.
• SCSLib, a fast and lightweight multiple-precision library supporting the four arithmetic operations, developed in the Arénaire project; the precision (210 bits by default) is fixed at compile time. CRlibm, a correctly-rounded elementary function library.
• Sun's libmcr, a correctly-rounded library of basic double-precision transcendental elementary functions.
• The PreciseFloating (floating-point arithmetic library) project in Java, by Daniel Aioanei: directed rounding, rational arithmetic and arbitrary precision arithmetic based on regular continued fraction expansions.
• The decNumber package by Mike Cowlishaw (IBM): arbitrary-precision decimal arithmetic.
• The Intel® Decimal Floating-Point BID Library for the IEEE 754r Standard.
• The calc calculator by Landon Curt Noll. This calculator implements a rational arithmetic, with a fallback to some kind of multiple-precision fixed-point arithmetic (integer multiplied by a configurable epsilon).
• The Qalculate calculator by Niklas Knutsson, based on CLN.

Related References and Links

• The C standard: the N1124 draft and the C99 rationale (especially Section 7.12 and Annex F). New in C99.
• LIA stuff.
• The Standard Decimal Arithmetic page from Mike Cowlishaw.
• The Digital Library of Mathematical Functions project, whose aim is to develop an electronic version of the Handbook of Mathematical Functions from Abramowitz and Stegun.
• The Arithmos project from the Computer Arithmetic group, University of Antwerp, Belgium.
• The Table Maker's Dilemma page from the Arénaire project at ENS-Lyon, France.
• Mathematical constants and computation by Xavier Gourdon and Pascal Sebah.
• The Open Source for Numerics page from Intel.
• The 754R standard revision group.
• The CerPAN ANR project.
• The EVA-Flo ANR project.