Preface

Interval Arithmetic Programming Reference

Preface

This manual documents the intrinsic INTERVAL data types in the Sun^TM WorkShop 6 Fortran 95 compiler (f95).

Who Should Use This Book

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

What Is in This Book

This book contains the following two chapters:

Chapter 1, "Using Interval Arithmetic With f95," describes the goals for intrinsic interval support in f95 and provides code samples that interval programmers can use to learn more about the interval features in f95.

Chapter 2, "f95 Interval Reference," describes the interval language extensions to f95.

"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 f95. 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(4):: X = [2,3]

PRINT *, "X = ", X

AaBbCc123 What you type, contrasted with on-screen computer output
my_system% f95 -xia test.f95

my_system% a.out

X = [2.0,3.0]

my_system%

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 Fortran code equivalent of is X .IX. Y

AaBbCc123 Command-line placeholder: replace with a real name or value To invoke f95 with intrinsic INTERVAL support, type
my_system% f95 -xia source_file.f95
Note – Examples use math% as the system prompt.

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.
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.

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 new interval 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 f95 compiler is not the only source of support for intervals. Readers interested in other well known sources can refer to the following books:

IBM High Accuracy Arithmetic - Extended Scientific Computation (ACRITH-XSC), General Information, GC 33-6461-01 IBM Corp., 1990.
R.Klatte, U.Kulisch, M.Neaga, D.Ratz, Ch.Ullrich, PASCAL-XSC Language Reference with Examples, Springer, 1991.
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 f95, 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 regarding the use of 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

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.

Code Examples

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

/opt/SUNWspro/examples/intervalmath/docExamples

The name of each file is cen-m.f95, where n is the chapter in which the example occurs and m is the number of the example. Additional interval examples can be found in the following directory:

/opt/SUNWspro/examples/intervalmath/general

Related Non-Interval Sun WorkShop 6 Documentation

You can access documentation related to the subject matter of this book in the following ways:

Through the Internet at the docs.sun.com^sm Web site. You can search for a specific book title or you can browse by subject, document collection, or product at the following Web site:

http://docs.sun.com

Through the installed Sun WorkShop products on your local system or network. Sun WorkShop 6 HTML documents (manuals, online help, man pages, component readme files, and release notes) are available with your installed Sun WorkShop 6 products. To access the HTML documentation, do one of the following:

In any Sun WorkShop or Sun WorkShop^TM TeamWare window, choose Help About Documentation.
In your Netscape^TM Communicator 4.0 or compatible version browser, open the following file:

/opt/SUNWspro/docs/index.html

(Contact your system administrator if your Sun WorkShop software is not installed in the /opt directory.) Your browser displays an index of Sun WorkShop 6 HTML documents. To open a document in the index, click the document's title.

TABLE P-3 lists related Sun WorkShop 6 manuals by document collection.

TABLE P-3 Related Sun WorkShop 6 Documentation by Document Collection
Document Collection Document Title Description

Forte^TM Developer 6 / Sun WorkShop 6 Release Documents About Sun WorkShop 6 Documentation Describes the documentation available with this Sun WorkShop release and how to access it.

What's New in Sun WorkShop 6 Provides information about the new features in the current and previous release of Sun WorkShop.

Sun WorkShop 6 Release Notes Contains installation details and other information that was not available until immediately before the final release of Sun WorkShop 6. This document complements the information that is available in the component readme files.

Forte Developer 6 / Sun WorkShop 6 Analyzing Program Performance With Sun WorkShop 6 Explains how to use the new Sampling Collector and Sampling Analyzer (with examples and a discussion of advanced profiling topics) and includes information about the command-line analysis tool er_print, the LoopTool and LoopReport utilities, and UNIX profiling tools prof, gprof, and tcov.

Debugging a Program With dbx Provides information on using dbx commands to debug a program with references to how the same debugging operations can be performed using the Sun WorkShop Debugging window.

Introduction to Sun WorkShop Acquaints you with the basic program development features of the Sun WorkShop integrated programming environment.

Forte^TM C 6 / Sun WorkShop 6 Compilers C C User's Guide Describes the C compiler options, Sun-specific capabilities such as pragmas, the lint tool, parallelization, migration to a 64-bit operating system, and ANSI/ISO-compliant C.

Forte^TM C++ 6 / Sun WorkShop 6 Compilers C++ C++ Library Reference Describes the C++ libraries, including C++ Standard Library, Tools.h++ class library, Sun WorkShop Memory Monitor, Iostream, and Complex.

C++ Migration Guide Provides guidance on migrating code to this version of the Sun WorkShop C++ compiler.

C++ Programming Guide Explains how to use the new features to write more efficient programs and covers templates, exception handling, runtime type identification, cast operations, performance, and multithreaded programs.

C++ User's Guide Provides information on command-line options and how to use the compiler.

Sun WorkShop Memory Monitor User's Manual Describes how the Sun WorkShop Memory Monitor solves the problems of memory management in C and C++. This manual is only available through your installed product (see /opt/SUNWspro/docs/index.html) and not at the docs.sun.com Web site.

Forte^TM for High Performance Computing 6 / Sun WorkShop 6 Compilers Fortran 77/95 Fortran Library Reference Provides details about the library routines supplied with the Fortran compiler.

Fortran Programming Guide Discusses issues relating to input/output, libraries, program analysis, debugging, and performance.

Fortran User's Guide Provides information on command-line options and how to use the compilers.

FORTRAN 77 Language Reference Provides a complete language reference.

Interval Arithmetic Programming Reference Describes the intrinsic INTERVAL data type supported by the Fortran 95 compiler.

Forte^TM TeamWare 6 / Sun WorkShop TeamWare 6 Sun WorkShop TeamWare 6 User's Guide Describes how to use the Sun WorkShop TeamWare code management tools.

Forte Developer 6 / Sun WorkShop Visual 6 Sun WorkShop Visual User's Guide Describes how to use Visual to create C++ and Java^TM graphical user interfaces.

Forte^TM / Sun Performance Library 6 Sun Performance Library Reference Discusses the optimized library of subroutines and functions used to perform computational linear algebra and fast Fourier transforms.

Sun Performance Library User's Guide Describes how to use the Sun-specific features of the Sun Performance Library, which is a collection of subroutines and functions used to solve linear algebra problems.

Numerical Computation Guide Numerical Computation Guide Describes issues regarding the numerical accuracy of floating-point computations.

Standard Library 2 Standard C++ Class Library Reference Provides details on the Standard C++ Library.

Standard C++ Library User's Guide Describes how to use the Standard C++ Library.

Tools.h++ 7 Tools.h++ Class Library Reference Provides details on the Tools.h++ class library.

Tools.h++ User's Guide Discusses use of the C++ classes for enhancing the efficiency of your programs.

TABLE P-4 describes related Solaris documentation available through the docs.sun.com Web site.

TABLE P-4 Related Solaris Documentation
Document Collection Document Title Description

Solaris Software Developer Linker and Libraries Guide Describes the operations of the Solaris link-editor and runtime linker and the objects on which they operate.

Programming Utilities Guide Provides information for developers about the special built-in programming tools that are available in the Solaris operating environment.

**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(4):: X = [2,3]` PRINT *, "X = ", X
`AaBbCc123`	What you type, contrasted with on-screen computer output	my_system`%` `f95 -xia test.f95` my_system% `a.out` X = [2.0,3.0] my_system%
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 Fortran code equivalent of is `X .IX. Y`
AaBbCc123	Command-line placeholder: replace with a real name or value	To invoke `f95` with intrinsic `INTERVAL` support, type my_system% `f95 -xia` source_file`.f95`

**TABLE P-2** Shell Prompts
Shell	Prompt
C shell	`%`
Bourne shell and Korn shell	`$`
C shell, Bourne shell, and Korn shell superuser	`#`

`%` `echo $PATH`

`%` `man workshop`

**TABLE P-3** Related Sun WorkShop 6 Documentation by Document Collection
Document Collection	Document Title	Description
Forte^TM Developer 6 / Sun WorkShop 6 Release Documents	About Sun WorkShop 6 Documentation	Describes the documentation available with this Sun WorkShop release and how to access it.
	What's New in Sun WorkShop 6	Provides information about the new features in the current and previous release of Sun WorkShop.
	Sun WorkShop 6 Release Notes	Contains installation details and other information that was not available until immediately before the final release of Sun WorkShop 6. This document complements the information that is available in the component readme files.
Forte Developer 6 / Sun WorkShop 6	Analyzing Program Performance With Sun WorkShop 6	Explains how to use the new Sampling Collector and Sampling Analyzer (with examples and a discussion of advanced profiling topics) and includes information about the command-line analysis tool `er_print`, the LoopTool and LoopReport utilities, and UNIX profiling tools `prof`, `gprof`, and `tcov`.
	Debugging a Program With dbx	Provides information on using dbx commands to debug a program with references to how the same debugging operations can be performed using the Sun WorkShop Debugging window.
	Introduction to Sun WorkShop	Acquaints you with the basic program development features of the Sun WorkShop integrated programming environment.
Forte^TM C 6 / Sun WorkShop 6 Compilers C	C User's Guide	Describes the C compiler options, Sun-specific capabilities such as pragmas, the `lint` tool, parallelization, migration to a 64-bit operating system, and ANSI/ISO-compliant C.
Forte^TM C++ 6 / Sun WorkShop 6 Compilers C++	C++ Library Reference	Describes the C++ libraries, including C++ Standard Library, Tools.h++ class library, Sun WorkShop Memory Monitor, Iostream, and Complex.
	C++ Migration Guide	Provides guidance on migrating code to this version of the Sun WorkShop C++ compiler.
	C++ Programming Guide	Explains how to use the new features to write more efficient programs and covers templates, exception handling, runtime type identification, cast operations, performance, and multithreaded programs.
	C++ User's Guide	Provides information on command-line options and how to use the compiler.
	Sun WorkShop Memory Monitor User's Manual	Describes how the Sun WorkShop Memory Monitor solves the problems of memory management in C and C++. This manual is only available through your installed product (see `/opt/SUNWspro/docs/index.html`) and not at the `docs.sun.com` Web site.
Forte^TM for High Performance Computing 6 / Sun WorkShop 6 Compilers Fortran 77/95	Fortran Library Reference	Provides details about the library routines supplied with the Fortran compiler.
	Fortran Programming Guide	Discusses issues relating to input/output, libraries, program analysis, debugging, and performance.
	Fortran User's Guide	Provides information on command-line options and how to use the compilers.
	FORTRAN 77 Language Reference	Provides a complete language reference.
	Interval Arithmetic Programming Reference	Describes the intrinsic `INTERVAL` data type supported by the Fortran 95 compiler.
Forte^TM TeamWare 6 / Sun WorkShop TeamWare 6	Sun WorkShop TeamWare 6 User's Guide	Describes how to use the Sun WorkShop TeamWare code management tools.
Forte Developer 6 / Sun WorkShop Visual 6	Sun WorkShop Visual User's Guide	Describes how to use Visual to create C++ and Java^TM graphical user interfaces.
Forte^TM / Sun Performance Library 6	Sun Performance Library Reference	Discusses the optimized library of subroutines and functions used to perform computational linear algebra and fast Fourier transforms.
	Sun Performance Library User's Guide	Describes how to use the Sun-specific features of the Sun Performance Library, which is a collection of subroutines and functions used to solve linear algebra problems.
Numerical Computation Guide	Numerical Computation Guide	Describes issues regarding the numerical accuracy of floating-point computations.
Standard Library 2	Standard C++ Class Library Reference	Provides details on the Standard C++ Library.
	Standard C++ Library User's Guide	Describes how to use the Standard C++ Library.
Tools.h++ 7	Tools.h++ Class Library Reference	Provides details on the `Tools.h++` class library.
	Tools.h++ User's Guide	Discusses use of the C++ classes for enhancing the efficiency of your programs.

**TABLE P-4** Related Solaris Documentation
Document Collection	Document Title	Description
Solaris Software Developer	Linker and Libraries Guide	Describes the operations of the Solaris link-editor and runtime linker and the objects on which they operate.
	Programming Utilities Guide	Provides information for developers about the special built-in programming tools that are available in the Solaris operating environment.

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