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

Editor: Ronald Boisvert Author:

R. Baker KearfottAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 22, Issue 4

Pages 385 - 392

https://doi.org/10.1145/235815.235816

Published: 01 December 1996 Publication History

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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.

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References

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

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Reviews

Reviewer: Jesse Louis Barlow

Interval arithmetic has generated a large volume of papers and software. A number of software packages are listed in the bibliography of this paper, which proposes an improvement to the INTLIB package of Kearfott et al.<__?__Pub Fmt interword-space>[1]. The author identifies an interesting problem with the INTLIB package and proposes an appropriate solution. The problem is that, for a task as simple as computing a polynomial of an interval, users are forced to write programs that are difficult to understand. This problem is a result of the limitations of Fortran 77. An appropriate solution is the development of a Fortran 90 module that allows for the development of an interval data type with appropriate software support. As an example, the author shows how to evaluate the polynomial f x =x 4+x 3 +x in INTLIB and with the module INTERVAL_ARITHMETIC. The INTLIB code discourages readers from wanting to write a program for a more complex problem. The code using the Fortran 90 module is elegant and transparent. The module supports the standard arithmetic expressions +, ?, *, /, SQRT, LOG, and EXP, and the usual trigonometric and hyperbolic functions. Instructions for i<__?__Pub Caret>nstallation and use of the module are provided.

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 22, Issue 4

Dec. 1996

116 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/235815

Editor:
Ronald Boisvert
National Institute of Standards and Technology, Guithersburg, MD

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 December 1996

Published in TOMS Volume 22, Issue 4

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Richthammer VFassnacht FGlaß M(2020)Search-space Decomposition for System-level Design Space Exploration of Embedded SystemsACM Transactions on Design Automation of Electronic Systems10.1145/336938825:2(1-32)Online publication date: 10-Jan-2020
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Karusala NHoleman IAnderson R(2019)Engaging Identity, Assets, and Constraints in Designing for ResilienceProceedings of the ACM on Human-Computer Interaction10.1145/33593153:CSCW(1-23)Online publication date: 7-Nov-2019
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Abstract

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References

Cited By

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Recommendations

Algorithm 737: INTLIB—a portable Fortran 77 interval standard-function library

Bypassing portability pitfalls of high-level low-level programming

On the Design of a Microcode Compiler for a Machine-Independent High-Level Language

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