High-Precision Software Directory

Update: 2006-06-06


This web site (see software package links below) contains the LBNL double-double precision, quad-double precision and arbitrary precision (also termed "multiprecision" or "multiple precision") software, which has been written over a period of several years by David H. Bailey (LBNL), Yozo Hida (U.C. Berkeley), Karthik Jeyabalan (LBNL), Xiaoye S. Li (LBNL) and Brandon Thompson (formerly of U.C. Berkeley, now at Stanford). This software is provided for research use only. Incorporating this software in any commercial product requires a license agreement. This software is not warranted by the authors, the University of California or the Lawrence Berkeley National Laboratory. This work was supported in part by the Director, Office of Science, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy under contract number DE-AC03-76SF00098. Please send any comments or bug reports to Bailey (see website below). Here are links to some of the authors' websites:

  • Bailey's website
  • Li's website
  • Hida's website

    • Software packages

    Software and documentation are provided in five zipped tar files, as shown below. On many systems, browsers can automatically unzip, untar and install the individual files in directories. On Unix systems, first download the respective file, say xxx.tar.gz, then type "gunzip xxx.tar.gz" and "tar xfv xxx.tar". Each package includes a "readme" file, which contain detailed information on compiling and running the programs, as well as some technical documentation and usage information.
  • ARPREC (C++/Fortran-90 arbitrary precision package) arprec.tar.gz (version date 2006-06-06)
    Before installing, please see the "release notes" in the README file.
    This package supports a flexible, arbitrarily high level of numeric precision -- the equivalent of hundreds or even thousands of decimal digits (up to approximately ten million digits if needed). Special routines are provided for extra-high precision (above 1000 digits). The entire library is written in C++. High-precision real, integer and complex datatypes are supported. Both C++ and Fortran-90 translation modules modules are also provided that permit one to convert an existing C++ or Fortran-90 program to use the library with only minor changes to the source code. In most cases only the type statements and (in the case of Fortran-90 programs) read/write statements need be changed. Six implementations of PSLQ (one-, two- and three-level, regular and multi-pair) are included, as well as three high-precision quadrature programs. New users are encouraged to use this package.
    This verion of the ARPREC package now includes "The Experimental Mathematician's Toolkit", which is available as the program "mathtool" in the subdirectory "toolkit". This is a complete interactive high-precision arithmetic computing environment. One enters expressions in a Mathematica-style syntax, and the operations are performed using the ARPREC package, with a level of precision that can be set from 100 to 1000 decimal digit accuracy. Variables and vector arrays can be defined and referenced. This program supports all basic arithmetic operations, common transcendental and combinatorial functions, multi-pair PSLQ (one-, two- or three-level versions), high-precision quadrature, i.e. numeric integration (Gaussian, error function or tanh-sinh), and summation of series.

  • MPFUN90 (Fortran-90 arbitrary precision package) mpfun90.tar.gz (version date 2006-01-23)
    This package is similar to the ARPREC package, except that it is written exclusively in Fortran-90 (i.e., no C++). As with the ARPREC package, Fortran-90 translation modules are also provided that permit one to convert an existing Fortran-90 program to use the library with only minor changes to the source code. The MPFUN90 package was recently revamped and improved to be completely compatible, at the Fortran user level, with the ARPREC package. In other words, a high-level Fortran-90 user program that works with the MPFUN90 software should also work with the ARPREC package. For instance, the F90 quadrature and PSLQ programs mentioned above that are included with the ARPREC package also work with MPFUN90, and are included in the MPFUN90 package. In addition, the Experimental Mathematician's Toolkit now works with MPFUN package as well.

  • QD (double-double and quad double package) qd.tar.gz (version date 2006-01-23)
    This package supports both a double-double datatype (approx. 32 decimal digits) and a quad-double datatype (approx. 64 decimal digits). The computational library is written in C++. Both C++ and Fortran-90 high-level language interfaces are provided to permit one to use convert an existing C++ or Fortran-90 program to use the library with only minor changes to the source code. In most cases only a few type statements and (for Fortran-90 programs) read/write statements need to be changed. PSLQ and numerical quadrature programs are included.

  • DDFUN90 (Fortran-90 double-double package) ddfun90.tar.gz (version date 2005-03-11) This package contains software for performing double-double arithmetic (approximately 32 decimal digits). It is similar to the qd package above in functionality, and in fact, an application program written for one should be compatible with the other. However this is entirely written in Fortran-90.

  • DSFUN90 (Fortran-90 double-single package) dsfun90.tar.gz (version date 2005-03-11) This package contains software for performing double-single arithmetic (approximately 15 decimal digits). It is entirely written in Fortran-90. It is targeted to systems, such as game systems, that do not support IEEE 64-bit floating-point arithmetic.

  • MPFUN77 (Fortran-77 arbitrary precision package) mpfun77.tar.gz
    This package supports an arbitrarily high level of numeric precision -- the equivalent of hundreds or even thousands of decimal digits (up to approximately ten million digits if needed). Special routines are provided for extra-high precision (above 1000 digits). High-precision real, integer and complex datatypes are supported. A translator program is also provided that permits one to convert an existing Fortran-77 program to use the library, by inserting special comments in the source code. This package is now considered obsolete, and is no longer actively supported. New users are strongly encouraged to use either the mpfun-90 package or (preferably) the new ARPREC package.

  • RANDOM (Fortran-90 pseudo-random number generator based on normal number paper) random.tar.gz (version date 2004-08-10)
    This file contains a Fortran-90 pseudo-random number generator, based on the recently discovered class of provably normal numbers -- see paper "Random Generators and Normal Numbers", by DHB and Richard Crandall, in the papers directory. In particular, subroutine bcnrand generates a sequence of IEEE 64-bit floating-point numbers uniformly in (0,1), with period (if parameters are properly selected) = 2x3^32 = 3.7060404e15. It is completely self-contained -- the required double-double arithmetic subroutines are included in the Fortran-90 source file. The bcnrand routine is designed for simple parallelization, yielding the same overall sequence as with a one-processor program. Also included here is a memory-testing program based on the bcnrand generator.