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Zbl 0884.65041
Kearfott, R.Baker
Algorithm 763: INTERVAL$\sb -$ARITHMETIC: A Fortran 90 module for an interval data type. (English)
[J] ACM Trans. Math. Softw. 22, No.4, 385-392 (1996). ISSN 0098-3500

Summary: 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 $\text {INTERVAL}_- \text {ARITHMETIC}$ 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.

MSC 2000:: *65G30 Interval and finite arithmetic
65Y15 Packaged methods

Keywords: interval arithmetic; Fortran 90 module $\text {INTERVAL}\sb - \text {ARITHMETIC}$; computer arithmetic; error analysis; operator overloading; portability; automatically verified computations

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