C++ Interval Arithmetic Programming Reference

Preface

This manual documents the C++ interface to the C++ interval arithmetic library provided with the Sun WorkShop^TM 6 update 1 Compilers C++ (5.2).

Who Should Use This Book

This is a reference manual intended for programmers with a working knowledge of the C++ language, the Solaris^TM operating environment, and UNIX commands.

What Is in This Book

This book contains the following chapters:

Chapter 1, "Using the Interval Arithmetic Library," describes the C++ interval arithmetic support goals and provides code samples that interval programmers can use to learn more about the C++ interval features.

Chapter 2, "C++ Interval Arithmetic Library Reference," describes the C++ interval arithmetic library interface.

"Glossary" contains definitions of interval terms.

What Is Not in This Book

This book is not an introduction to intervals and does not contain derivations of the interval innovations included in the interval arithmetic C++ library. For a list of sources containing introductory interval information, see the interval arithmetic readme.

What Typographic Changes Mean

The following table describes the typographic conventions used in this book.

TABLE P-1   Typographic Conventions 

Typeface or Symbol	Meaning	Example
AaBbCc123	Code samples, the names of commands, files, and directories; on-screen computer output	interval<double>("[4, 5]"))
AaBbCc123	What you type, contrasted with on-screen computer output	math% CC -xia test.cc math% a.out x = [2.0,3.0]
AaBbCc123	Placeholders for interval language elements	The interval affirmative order relational operators op {lt, le, eq, ge, gt} are equivalent to the mathematical operators .
AaBbCc123	Variables used in equations, book titles, new words or terms, or words to be emphasized	The C++ code equivalent of is intersect(X,Y)
AaBbCc123	Command-line placeholder: replace with a real name or value	To invoke CC with class interval support, type math% CC -xia source_file.cc

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Note – Examples use math% as the system prompt.

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Shell Prompts

TABLE P-2 shows the default system prompt and superuser prompt for the C shell, Bourne shell, and Korn shell.

TABLE P-2   Shell Prompts

Shell	Prompt
C shell	%
Bourne shell and Korn shell	$
C shell, Bourne shell, and Korn shell superuser	#

Access to Sun WorkShop Development Tools

Because Sun WorkShop product components and man pages do not install into the standard /usr/bin/ and /usr/share/man directories, you must change your PATH and MANPATH environment variables to enable access to Sun WorkShop compilers and tools.

To determine if you need to set your PATH environment variable:

1. Display the current value of the PATH variable by typing:

% echo $PATH

2. Review the output for a string of paths containing /opt/SUNWspro/bin/.

If you find the paths, your PATH variable is already set to access Sun WorkShop development tools. If you do not find the paths, set your PATH environment variable by following the instructions in this section.

To determine if you need to set your MANPATH environment variable:

1. Request the workshop man page by typing:

% man workshop

2. Review the output, if any.

If the workshop(1) man page cannot be found or if the man page displayed is not for the current version of the software installed, follow the instructions in this section for setting your MANPATH environment variable.

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Note – The information in this section assumes that your Sun WorkShop 6 products were installed in the /opt directory. Contact your system administrator if your Sun WorkShop software is not installed in /opt.

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The PATH and MANPATH variables should be set in your home .cshrc file if you are using the C shell or in your home .profile file if you are using the Bourne or Korn shells:

• To use Sun WorkShop commands, add the following to your PATH variable:

  /opt/SUNWspro/bin

• To access Sun WorkShop man pages with the man command, add the following to your MANPATH variable:

  /opt/SUNWspro/man

For more information about the PATH variable, see the csh(1), sh(1), and ksh(1) man pages. For more information about the MANPATH variable, see the man(1) man page. For more information about setting your PATH and MANPATH variables to access this release, see the Sun WorkShop 6 Installation Guide or your system administrator.

Related Interval References

The interval literature is large and growing. Interval applications exist in various substantive fields. However, most interval books and journal articles either contain these algorithms, or are written for interval analysts who are developing new interval algorithms. There is not yet a book titled "Introduction to Intervals."

The Sun WorkShop 6 C++ compiler is not the only source of C++ support for intervals. Readers interested in other well known sources can refer to the following books:

• R. Klatte, U. Kulisch, A. Wiethoff, C. Lawo, M. Rauch, C-XSC Class Library for Extended Scientific Computing. Springer, 1993.
• R. Hammer, M. Hocks, U. Kulisch, D. Ratz, Numerical Toolbox for Verified Computing I, Basic Numerical Problems. Springer, 1993.

For a list of technical reports that establish the foundation for the interval innovations implemented in class interval, see References. See the Interval Arithmetic Readme for the location of the online versions of these references.

Online Resources

Additional interval information is available at various web sites and email mailing lists. For a list of online resources, refer to the interval arithmetic readme.

Web Sites

A detailed bibliography and interval FAQ can be obtained online at the URLs listed in the interval arithmetic readme.

Email

To discuss interval arithmetic issues or ask questions about using interval arithmetic, a mailing list has been constructed. Anyone can send questions to this list. Refer to the interval arithmetic readme for instructions on how to subscribe to this mailing list.

To report a suspected interval error, send email to the following address:

sun-dp-comments@Sun.COM

Include the following text in the Subject line of the email message:

WORKSHOP "6.0 mm/dd/yy" Interval

where mm/dd/yy is the month, day, and year of the message.

Code Examples

All code examples in this book are contained in the following directory:

http://www.sun.com/forte/cplusplus/interval

The name of each file is cen-m.cc, where n is the chapter in which the example occurs and m is the number of the example. Additional interval examples are also provided in this directory.

Related Non-Interval Sun WorkShop 6 Documentation

For more information about this product, see the following sources. (The names of our development tools have changed from Sun WorkShop^TM to Forte^TM Developer products; you might see both product names used.)

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Note – If your Sun WorkShop 6 update 1 software is not installed in the /opt directory, ask your system administrator for the equivalent path on your system.

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• Man pages and readmes. This documentation describes the new features, performance enhancements, problems and workarounds, and software corrections in this Sun WorkShop 6 update 1 release.

  You can access these documents in HTML on your local system or network by pointing your browser to file:/opt/SUNWspro/docs/index.html.

• The Sun WorkShop and Sun WorkShop TeamWare online help. The online help has been updated for the new features in this Sun WorkShop 6 update 1 release.

  You can access the online help on your local system or network by pointing your browser to file:/opt/SUNWspro/docs/index.html. You can access the online help from the Help menu in the Sun WorkShop products.

• What's New in Sun WorkShop 6 update 1. This book describes the new features in this Sun WorkShop 6 update 1 release and in the Sun WorkShop 6 release.

  You can access this book on your local system or network by pointing your browser to file:/opt/SUNWspro/docs/index.html. You can also access it by pointing your browser to http://docs.sun.com and searching for the Forte Developer 6 update 1 collection.

• Sun WorkShop 6 manuals. These manuals were provided with Sun WorkShop 6. Information in the Sun WorkShop 6 update 1 man pages, readmes, and online help supersedes information in the Sun WorkShop 6 manuals.

  You can access the manuals on your local system or network by pointing your browser to the Sun WorkShop 6 update 1 Documentation Index (file:/opt/SUNWspro/docs/index.html). You can also access them by pointing your browser to http://docs.sun.com and searching for the Forte C, Forte C++, Forte for High Performance Computing, and Forte TeamWare products.

  The following Sun WorkShop manuals are only accessible on your local system or network (by pointing your browser to file:/opt/SUNWspro/docs/index.html) and not through http://docs.sun.com:

  
  
  • Sun WorkShop Memory Monitor User's Manual
    
  • Standard C++ Class Library Reference
    
  • Standard C++ Library User's Guide
    
  • Tools.h++ Class Library Reference
    
  • Tools.h++ User's Guide
    
  • Sun Performance Library Reference
• Sun WorkShop 6 update 1 supplements. The supplements provide more detailed information on some of the major new features in this Sun WorkShop 6 update 1 release.

  You can access the supplements by pointing your browser to http://docs.sun.com and searching for the Forte Developer 6 update 1 collection.

• Sun WorkShop 6 update 1 Release Notes. These notes provide installation-related and late-breaking information about this Sun WorkShop 6 update 1 release. Information in the release notes supersedes information in any of the other documentation.

  The release notes are available as a text file on the Forte Developer 6 update 1 CD at /cdrom/devpro_v8n1_platform/release_notes.txt. They are also available in HTML on the Forte Developer Products Hot News page by pointing your browser at http://www.sun.com/forte/developer/hotnews.html.