Algorithm 763: INTERVAL_ARITHMETIC: a Fortran 90 module for an interval data type

Authors:
R. Baker Kearfott
Affiliations:
Univ. of Southwestern Louisiana, Lafayette
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1996

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Abstract

Interval arithmetic is useful in automatically verified computations, that is, in computations in which the algorithm itself rigorously proves that the answer must lie within certain bounds. In addition to rigor, interval arithmetic also provides a simple and sometimes sharp method of bounding ranges of functions for global optimization and other tasks. Convenient use of interval arithmetic requires an interval data type in the programming language. Although various packages supply such a data type, previous ones are machine specific, obsolete, and unsupported, for languages other than Fortran, or commercial. The Fortran 90 module INTERVAL_ARITHMETIC provides a portable interval data type in Fortran 90. This data type is based on two double-precision real Fortran storage units. Module INTERVAL_ARTHMETIC uses the Fortran 77 library INTLIB (ACM TOMS Algorithm 737) as a supporting library. The module has been employed extensively in the author's own research.