Interval package

The GNU Octave interval package for real-valued interval arithmetic.

Development status

• Completeness
• All required IEEE 1788 functions are implemented, the standard is currently in recirculation ballot phase and quite stable.
• Planned: more solvers; plotting functions
• Planned: Improvement of the user documentation
• Explain interval arithmetic concepts with examples from the package
• PDF export is broken
• Add nodes for cross references and separate HTML pages
• Quality
• Includes tests for all functions, many tests for basic functions
• No known bugs. The package is quite new and still has a small user base, so there might be hidden bugs. Also some advanced functions need more testing.
• Portability
• Runs in GNU Octave 3.8.2 and 4.0 release candidates
• Known to run under GNU/Linux, Microsoft Windows, Mac OS X and FreeBSD

Compatibility

The interval package's main goal is to be compliant with IEEE 1788, so it is compatible with other standard-conforming implementations (on the set of operations described by the standard document).

This interval package is not meant to be a replacement for INTLAB and any compatibility with it is pure coincidence. Since both are compatible with GNU Octave, they happen to agree on many function names and programs written for INTLAB may possibly run with this interval package as well. Some fundamental differences that I am currently aware of:

• INTLAB is non-free software, it grants none of the four essential freedoms of free software
• INTLAB is not conforming to IEEE 1788 and the parsing of intervals from strings uses a different format—especially for the uncertain form
• INTLAB supports intervals with complex numbers and sparse interval matrices, but no empty intervals
• INTLAB uses inferior accuracy for most arithmetic operations, because it focuses on speed
• Basic operations can be found in both packages, but the availability of special functions depends
 Code: In GNU Octave the interval package can also be run alongside INTLAB. ``` # INTLAB intervals A1 = infsup (2, 3); B1 = hull (-4, A1); C1 = midrad (0, 2); # Interval package intervals pkg load interval A2 = infsup (2, 3); B2 = hull (-4, A2); C2 = midrad (0, 2); pkg unload interval # Computation with INTLAB A1 + B1 * C1 # Computation without INTLAB A2 + B2 * C2 ```

Similar software

For C++ there is an open source interval library libieeep1788 by Marco Nehmeier (member of IEEE P1788). It aims to be standard compliant with IEEE 1788 and is designed in a modular way, supporting several interval data types and different flavors of interval arithmetic [1]. The GNU Octave interval package shares several unit tests with libieeep1788.

For C++, Pascal and Fortran there is a free interval library XSC. It is not standard compliant with IEEE 1788. Some parts of the GNU Octave interval package have been derived from C-XSC.

For MATLAB there is a popular, nonfree interval arithmetic toolbox INTLAB by Siegfried Rump. It had been free of charge for academic use in the past, but no longer is. Its origin dates back to 1999, so it is well tested and comprises a lot of functionality, especially for vector / matrix operations. INTLAB is compatible with GNU Octave since Version 9 [2].