Some Arbitrary Precision/Multiple Precision/Exact Arithmetic Systems

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Here is a list of packages/libraries that are capable of performing arbitrary precision arithmetic on elementary real functions. They implement different ideas and approaches to arbitrary precision/multiple precision/exact real arithmetic. A direct comparison of some or preferably all of the softwares listed below --- to the extent that such comparison is possible--- will provide a good understanding of the state of the art in the field of exact real arithmetic (see Exact Real Arithmetic Systems, Results of Competition ^[1], Software Demonstration at the Fifth Workshop on Computability and Complexity in Analysis ^[2], Comparison of other software to MPFR, Floating point benches and SIAM 100-digit challenge^[3]).
The list is by no means complete and may contain some inconsistencies, because the author of this page didn't examine all the systems listed here. Any comment for improving the list is welcome.
-- Milad Niqui.

Aberth: (Precise Numerical Methods Using C++), by Oliver Aberth
apfloat: (a C++ High Performance Arbitrary Precision Arithmetic Package), by Mikko Tommila
Arithmos: (a reliable integrated computational environment), by CANT group at University of Antwerp
Bignum: (an infinite-precision function library for Miranda and Haskell), by Martin Guy
CLN: (a library for efficient computations with all kinds of numbers in arbitrary precision), by Bruno Haible and Richy Kreckel
Core library : (robust numerical and geometric computation), by Chee Yap, Zilin Du, Vikram Sharma, Sylvain Pion, Hervé Brönnimann
Calc: (the GNU Emacs calculator which can do arbitrary precision arithmetic), by Dave Gillespie
calc: (an interactive calculator which provides for easy large numeric calculations, but which also can be easily programmed for difficult or long calculations), by David I. Bell et al.
CRCalc: (this is a calculator that operates on constructive real numbers.), by Hans-J. Böhm
Creal: (exact real arithmetic, from the PhD thesis of Valérie Ménissier-Morain), by Jean-Christophe Filliâtre
Few Digits : (a collection of Haskell modules that implement exact real arithmetic), by Russell O’Connor
GMP: (GNU Multiple Precision Arithmetic Library, the fastest bignum library on the planet!),
GNU bc: (an arbitrary precision numeric processing language), by Philip A. Nelson
GNU Octave: (a high-level language, primarily intended for numerical computation), by John W. Eaton.
HFLOAT: (fast computations with extreme precision), by Jörg Arndt
ICReals: (computing a required absolute precision from a stream of linear fractional transformations), by Lindsay Errington, Marko Krznarić, Reinhold Heckmann, Abbas Edalat, Martin Escardo, Peter Potts and Philipp Sünderhauf
iRRAM: (exact reals with an iterative approach), by Norbert Müller
iRRAM with Continued Fractions: (a C++ package that combines Norbert Müller's approach to real computation, iRRAM, with the Continued Fraction algorithms for elementary functions developed), by Abbas Edalat and Marko Krznarić
Kelsey: (exact numerical computation via symbolic computation), by Tom Kelsey^[4]
libmplite: (C++ wrapper around the MPFR library for multi-precision floating point arithmetic), by Johan Vervloet
LiDIA: (a C++ Library For Computational Number Theory), by LiDIA-Group at TU Darsmtadt
Maxima: (Maxima - a sophisticated computer algebra system), William Schelter et al.
MAP:(an implementation of exact arithmetic on a representation of computable real numbers as Fast Binary Cauchy Sequnces), by David Lester
MAPM: (a portable arbitrary precision math library in C), by Michael C. Ring
Mmxlib: (a C++ core library for a new computer algebra system under development), by Joris van der Hoeven
MPC: (a library for multiprecision complex arithmetic with exact rounding, based on the MPFR and GNU MP libraries), by Paul Zimmermann, Patrick Pélissier and Andreas Enge
mpdist: (High-Precision Software Directory), by David H. Bailey, Yozo Hida, Karthik Jeyabalan, Xiaoye S. Li and Brandon Thompson
MPFI: (a multiple precision interval arithmetic library based on MPFR), by Nathalie Revol and Fabrice Rouillier
MPFR: (reliable floating point numbers), by PolKA and SPACES projects at INRIA Lorraine and LORIA
MPFR++: (a C++ interface to MPFR), by Nathalie Revol
mpfun++: (multiple precision floating point Computation Package in C++), by Siddhartha Chatterjee
PARI/GP: (a package that contains a large number of useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions), by Henri Cohen, Karim Belabas et al.
RealLib: (a package whose primary aim is to be efficient and to avoid the huge overheads usually associated with real number computations.), by Branimir Lambov
XRC: (exact reals with an approach using lazy evaluation), by Keith Briggs
XSC Languages: (Scientific Computing with Validation, Arithmetic Requirements, Hardware Solution and Language Support), by Institute of Applied Mathematics at University of Karlsruhe and WRSWT-Group at University of Wuppertal
yacas: (a general purpose easy to use Computer Algebra System built on top of its own programming language), by Ayal Pinkus et al.

There are some commercial softwares as well, that are capable of performing arbitrary precision numerical computations. Although some of them are not intended to be used numerically (rather symbolically), the notable ones are:

Footnotes

[1] Event held as part of CCA2000.
[2] Event held as part of CCA2002.
[3] In the January/February 2002 issue of SIAM News an interesting challenge was posed by Prof. Lloyd N. Trefethen. Many people participated in the challenge, leading to twenty prize winners. The results of the challenge were announced in an article the July/August 2002 issue of SIAM News, where the original challenger expressed the fact that he had misjudged the difficulty of the challenge and he did not expect to receive so many correct answers. There was a book (mathscinet review) written about solving the challenges that are solved using C, PARI/GP, MATLAB, INTLAB and Mathematica. The challenge and the book were discussed in Science.
[4] This package participated in ^[1]. The package itself could not be found on the web.
[5] The source code is available for private use but the package is based on MATLAB.