C++ Interval Arithmetic Programming Reference

Forte Developer 7

816-2465-10

Contents

Before You Begin

Who Should Use This Book

How This Book Is Organized

What Is Not in This Book

Related Interval References

Online Resources

Web Sites

Email

Code Examples

Typographic Conventions

Shell Prompts

Accessing Forte Developer Development Tools and Man Pages

Accessing Forte Developer Compilers and Tools

Accessing Forte Developer Man Pages

Accessing Forte Developer Documentation

Product Documentation in Accessible Formats

Accessing Related Solaris Documentation

Sending Your Comments

1. Using the Interval Arithmetic Library

1.1 What Is Interval Arithmetic?

1.2 C++ Interval Support Goal: Implementation Quality

1.2.1 Quality Interval Code

1.2.2 Narrow-Width Interval Results

1.2.3 Rapidly Executing Interval Code

1.2.4 Easy-to-Use Development Environment

1.2.5 The C++ Interval Class Compilation Interface

1.2.5.1 namespace SUNW_interval

1.2.5.2 Boolean Return Values

1.2.5.3 Input and Output

1.3 Writing Interval Code for C++

1.3.1 Hello Interval World

1.3.2 interval External Representations

1.3.3 Interval Declaration and Initialization

1.3.4 interval Input/Output

1.3.5 Single-Number Input/Output

1.3.6 Arithmetic Expressions

1.3.7 interval-Specific Functions

1.3.8 Interval Versions of Standard Functions

1.4 Code Development Tools

1.4.1 Debugging Support

2. C++ Interval Arithmetic Library Reference

2.1 Character Set Notation

2.1.1 String Representation of an Interval Constant (SRIC)

2.1.2 Internal Approximation

2.2 interval Constructor

2.2.1 interval Constructor Examples

2.3 interval Arithmetic Expressions

2.4 Operators and Functions

2.4.1 Arithmetic Operators +, -, *, /

2.4.2 Power Function pow(X,n) and pow(X,Y)

2.5 Set Theoretic Functions

2.5.1 Hull: X Y or interval_hull(X,Y)

2.5.2 Intersection: XY or intersect(X,Y)

2.6 Set Relations

2.6.1 Disjoint: X Y = or disjoint(X,Y)

2.6.2 Element: r Y or in(r,Y)

2.6.3 Interior: in_interior(X,Y)

2.6.4 Proper Subset: X Y or proper_subset(X,Y)

2.6.5 Proper Superset: X Y or proper_superset(X,Y)

2.6.6 Subset: X Y or subset(X,Y)

2.6.7 Superset: X Y or superset(X,Y)

2.7 Relational Functions

2.7.1 Interval Order Relations

2.7.2 Set Relational Functions

2.7.2.1 Set-equal: X = Y or seq(X,Y)

2.7.2.2 Set-greater-or-equal: sge(X,Y)

2.7.2.3 Set-greater: sgt(X,Y)

2.7.2.4 Set-less-or-equal: sle(X,Y)

2.7.2.5 Set-less: slt(X,Y)

2.7.2.6 Set-not-equal: or sne(X,Y)

2.7.3 Certainly Relational Functions

2.7.4 Possibly Relational Functions

2.8 Input and Output

2.8.1 Input

2.8.2 Single-Number Output

2.8.3 Single-Number Input/Output and Base Conversions

2.9 Mathematical Functions

2.9.1 Inverse Tangent Function atan2(Y,X)

2.9.2 Maximum: maximum(X1,X2)

2.9.3 Minimum: minimum(X1,X2)

2.9.4 Functions That Accept Interval Arguments

2.10 Interval Types and the Standard Template Library

2.11 nvector and nmatrix Template Classes

2.11.1 nvector<T> Class

2.11.2 nmatrix<T> Class

2.12 References

Glossary

Index