Interval Arithmetic - Implementations

Implementations

There are many software packages that permit the development of numerical applications using interval arithmetic. These are usually provided in the form of program libraries. There are also C++ and Fortran compilers that handle interval data types and suitable operations as a language extension, so interval arithmetic is supported directly.

Since 1967 Extensions for Scientific Computation (XSC) have been developed in the University of Karlsruhe for various programming languages, such as C++, Fortran and Pascal. The first platform was a Zuse Z 23, for which a new interval data type with appropriate elementary operators was made available. There followed in 1976 Pascal-SC, a Pascal variant on a Zilog Z80 which it made possible to create fast complicated routines for automated result verification. Then came the Fortran 77-based ACRITH XSC for the System/370 architecture, which was later delivered by IBM. Starting from 1991 one could produce code for C compilers with Pascal-XSC; a year later the C++ class library supported C-XSC on many different computer systems. In 1997 all XSC variants were made available under the GNU General Public License. At the beginning of 2000 C-XSC 2.0 was released under the leadership of the working group for scientific computation at the Bergische University of Wuppertal, in order to correspond to the improved C++ standard.

Another C++-class library was created in 1993 at the Hamburg University of Technology called Profil/BIAS (Programmer's Runtime Optimized Fast Interval Library, Basic Interval Arithmetic), which made the usual interval operations more user friendly. It emphasized the efficient use of hardware, portability and independence of a particular presentation of intervals.

The Boost collection of C++ libraries contains a template class for intervals. Its authors are aiming to have interval arithmetic in the standard C++ language.

Gaol is another C++ interval arithmetic library that is unique in that it offers the relational interval operators used in interval constraint programming.

The Frink programming language has an implementation of interval arithmetic which can handle arbitrary-precision numbers. Programs written in Frink can use intervals without rewriting or recompilation.

In addition computer algebra systems, such as Mathematica, Maple and MuPAD, can handle intervals. There is a Matlab extension Intlab which builds on BLAS routines, as well as the Toolbox b4m which makes a Profil/BIAS interface. Moreover, the Software Euler Math Toolbox includes an interval arithmetic.