C++ Interval Arithmetic Programming Reference

Contents

 Preface

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

1.3 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 U 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

2.7.3 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 References

 Glossary

 Index