Interval Arithmetic Programming Reference

# Contents

## 1.  Using Interval Arithmetic With f95

1.1 f95 INTERVAL Type and Interval Arithmetic Support
1.2 f95 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
1.3 Writing Interval Code for f95
1.3.1 Command-Line Options
1.3.2 Hello Interval World
1.3.3 Interval Declaration and Initialization
1.3.4 INTERVAL Input/Output
1.3.5 Single-Number Input/Output
1.3.6 Interval Statements and Expressions
1.3.7 Default Kind Type Parameter Value (KTPV)
1.3.8 Value Assignment V = expr
1.3.9 Mixed-Type Expression Evaluation
1.3.10 Arithmetic Expressions
1.3.11 Interval Order Relations
1.3.12 Intrinsic INTERVAL-Specific Functions
1.3.13 Interval Versions of Standard Intrinsic Functions
1.4 Code Development Tools
1.4.1 Debugging Support
1.4.2 Global Program Checking
1.4.3 Interval Functionality Provided in Sun Fortran Libraries
1.4.4 Porting Code and Binary Files
1.4.5 Parallelization
1.5 Error Detection
1.5.1 Known Containment Failures

## 2.  f95 Interval Reference

2.1 Fortran Extensions
2.1.1 Character Set Notation
2.1.2 INTERVAL Constants
2.1.3 Internal Approximation
2.1.4 INTERVAL Statement
2.2 Data Type and Data Items
2.2.1 Name: INTERVAL
2.2.2 Kind Type Parameter Value (KTPV)
2.2.3 INTERVAL Arrays
2.3 INTERVAL Arithmetic Expressions
2.3.1 Mixed-Mode INTERVAL Expressions
2.3.2 Value Assignment
2.3.3 Interval Command-Line Options
2.3.4 Constant Expressions
2.4 Intrinsic Operators
2.4.1 Arithmetic Operators +, -, *, /
2.5 Power Operators X**N and X**Y
2.6 Set Theoretic Operators
2.6.1 Hull: X Y or (X.IH.Y)
2.6.2 Intersection: XY or (X.IX.Y)
2.7 Set Relations
2.7.1 Disjoint: X Y = or (X .DJ. Y)
2.7.2 Element: r Y or (R.IN. Y)
2.7.3 Interior: (X .INT. Y)
2.7.4 Proper Subset: X Y or (X .PSB. Y)
2.7.5 Proper Superset: X Y or (X .PSP. Y)
2.7.6 Subset: X Y or (X .SB. Y)
2.7.7 Superset: X Y or (X .SP. Y)
2.7.8 Relational Operators
2.8 Extending Intrinsic INTERVAL Operators
2.8.1 Extended Operators with Widest-Need Evaluation
2.8.2 INTERVAL (X [,Y, KIND])
2.8.3 Specific Names for Intrinsic Generic INTERVAL Functions
2.9 INTERVAL Statements
2.9.1 Type Declaration
2.9.2 Input and Output
2.9.3 Intrinsic INTERVAL Functions
2.9.4 Mathematical Functions
2.10 References