Program units and procedures

by Michael Metcalf / CERN CN-AS

In order to discuss this topic we need some definitions. In logical terms, an executable program consists of one main program and zero or more subprograms (or procedures) - these do something. Subprograms are either functions or subroutines, which are either external, internal or module subroutines. (External subroutines are what we know from FORTRAN 77.)

From an organizational point of view, however, a complete program consists of program units. These are either main programs, external subprograms or modules and can be separately compiled.

An internal subprogram is one contained in another (at a maximum of one level of nesting) and provides a replacement for the statement function:

     SUBROUTINE outer
        REAL x, y
        :
     CONTAINS
        SUBROUTINE inner
           REAL y
           y = x + 1.
           :
        END SUBROUTINE inner     ! SUBROUTINE mandatory
     END SUBROUTINE outer

We say that outer is the host of inner, and that inner obtains access to entities in outer by host association (e.g. to x), whereas y is a local variable to inner.

The scope of a named entity is a scoping unit, here outer less inner, and inner.

The names of program units and external procedures are global, and the names of implied-DO variables have a scope of the statement that contains them.

Modules are used to package

global data (replaces COMMON and BLOCK DATA);
type definitions (themselves a scoping unit);
subprograms (which among other things replaces the use of ENTRY);
interface blocks (another scoping unit, see next article);
namelist groups (later in the series).

An example of a module containing a type defition, interface block and function subprogram is:

     MODULE interval_arithmetic
        TYPE interval
           REAL lower, upper
        END TYPE interval
        INTERFACE OPERATOR(+)
           MODULE PROCEDURE add_intervals
        END INTERFACE
        :
     CONTAINS
        FUNCTION add_intervals(a,b)
           TYPE(interval) add_intervals, a, b
           add_intervals%lower = a%lower + b%lower
           add_intervals%upper = a%upper + b%upper
        END FUNCTION add_intervals             ! FUNCTION mandatory
        :
     END MODULE interval_arithmetic

and the simple statement

     USE interval_arithmetic

provides use association to all the module's entities. Module subprograms may, in turn, contain internal subprograms.

Arguments

We may specify the intent of dummy arguments:

     SUBROUTINE shuffle (ncards, cards)
        INTEGER, INTENT(IN)  :: ncards
        INTEGER, INTENT(OUT), DIMENSION(ncards) :: cards

Also, INOUT is possible: here the actual argument must be a variable (unlike the default case where it may be a constant).

Arguments may be optional:

     SUBROUTINE mincon(n, f, x, upper, lower, equalities,     &
                inequalities, convex, xstart)
        REAL, OPTIONAL, DIMENSION :: upper, lower
        :

allows us to call mincon by

        CALL mincon (n, f, x, upper)
        :
        IF (PRESENT(lower)) THEN   ! test for presence of actual argument
        :

Arguments may be keyword rather than positional (which come first):

        CALL mincon(n, f, x, equalities=0, xstart=x0)

Optional and keyword arguments are handled by interface blocks.

Interface blocks

Any reference to an internal or module subprogram is through an interface that is 'explicit' (that is, the compiler can see all the details). A reference to an external (or dummy) procedure is usually 'implicit' (the compiler assumes the details). However, we can provide an explicit interface in this case too. It is a copy of the header, specifications and END statement of the procedure concerned, either placed in a module or inserted directly:

     REAL FUNCTION minimum(a, b, func)
! returns the minimum value of the function func(x)
! in the interval (a,b)
        REAL, INTENT(in) :: a, b
        INTERFACE
           REAL FUNCTION func(x)
              REAL, INTENT(IN) :: x
           END FUNCTION func
        END INTERFACE
        REAL f,x
        :
        f = func(x)   ! invocation of the user function.
        :
     END FUNCTION minimum

An interface block is obligatory for:

optional and keyword arguments;
POINTER and TARGET arguments (see later article);
POINTER function result (later);
new-style array arguments and array functions (later).

Placed in a module, it allows full checks at compile time between actual and dummy arguments.

Overloading and generic interfaces

Interface blocks provide the mechanism by which we are able to define generic names for specific procedures:

     INTERFACE gamma                   ! generic name
        FUNCTION sgamma(X)             ! specific name
           REAL (SELECTED_REAL_KIND( 6)) sgamma, x
        END
        FUNCTION DGAMMA(X)             ! specific name
           REAL (SELECTED_REAL_KIND(12)) dgamma, x
        END
     END INTERFACE

where a given set of specific names corresponding to a generic name must all be of functions or all of subroutines. If this interface is within a module, then it is simply

     INTERFACE gamma
        MODULE PROCEDURE sgamma, dgamma
     END INTERFACE

We can use existing names, e.g. SIN, and the compiler sorts out the correct association.

We have already seen the use of interface blocks for defined operators and assignment (see Part 3).

Recursion

Indirect recursion is useful for multi-dimensional integration. For

     volume = integrate(fy, ybounds)

We might have

     RECURSIVE FUNCTION integrate(f, bounds)
        ! Integrate f(x) from bounds(1) to bounds(2)
        REAL integrate
        INTERFACE
           FUNCTION f(x)
              REAL f, x
           END FUNCTION f
        END INTERFACE
        REAL, DIMENSION(2), INTENT(IN) :: bounds
        :
     END FUNCTION integrate

and to integrate f(x, y) over a rectangle:

     FUNCTION fy(y)
        USE func           ! module func contains function f
        REAL fy, y
        yval = y
        fy = integrate(f, xbounds)
     END

Direct recursion is when a procedure calls itself, as in

     RECURSIVE FUNCTION factorial(n) RESULT(res)
        INTEGER res, n
        IF(n.EQ.1) THEN
           res = 1
        ELSE
           res = n*factorial(n-1)
        END IF
     END

Here, we note the RESULT clause and termination test.