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C++ Interval Arithmetic Programming Reference

Forte Developer 7



Before You Begin

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How This Book Is Organized

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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 namespace SUNW_interval Boolean Return Values 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 intervalhull Y or interval_hull(X,Y)

2.5.2 Intersection: XintersectionY or intersect(X,Y)

2.6 Set Relations

2.6.1 Disjoint: X intersectionY = empty set or disjoint(X,Y)

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

2.6.3 Interior: in_interior(X,Y)

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

2.6.5 Proper Superset: X proper super set Y or proper_superset(X,Y)

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

2.6.7 Superset: X reflex super set Y or superset(X,Y)

2.7 Relational Functions

2.7.1 Interval Order Relations

2.7.2 Set Relational Functions Set-equal: X = Y or seq(X,Y) Set-greater-or-equal: sge(X,Y) Set-greater: sgt(X,Y) Set-less-or-equal: sle(X,Y) Set-less: slt(X,Y) 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