6.6 Interval Arithmetic

Note: Interval arithmetic is only available on SPARC platforms, currently.

The Fortran 95 compiler f95 supports intervals as an intrinsic data type. An interval is the closed compact set: [a, b] ={z | a≤ z≤ b} defined by a pair of numbers, a ≤ b. Intervals can be used to:

• Solve nonlinear problems

• Perform rigorous error analysis

• Detect sources of numerical instability

By introducing intervals as an intrinsic data type to Fortran 95, all of the applicable syntax and semantics of Fortran 95 become immediately available to the developer. Besides the INTERVAL data types, f95 includes the following interval extensions to Fortran 95:

• Three classes of INTERVAL relational operators:

  • Certainly

  • Possibly

  • Set

  Intrinsic INTERVAL-specific operators, such as INF, SUP, WID, and HULL

• INTERVAL input/output edit descriptors, including single-number input/output

• Interval extensions to arithmetic, trigonometric, and other mathematical functions

• Expression context-dependent INTERVAL constants

• Mixed-mode interval expression processing

The f95 command-line option -xinterval enables the interval arithmetic features of the compiler. See the Fortran User’s Guide.

For detailed information on interval arithmetic in Fortran 95, see the Fortran 95 Interval Arithmetic Programming Reference.