I wish to repeat that under Fortran 77 all program units are
essentially on the same level, even if the main program logically is
superior to the subroutines and functions that are called, and even though
you could write a call map that looks like a tree. In reality the
`BLOCK `
`DATA ` is on a higher level and all the other program units are on the
same level, from the Fortran system viewpoint with the main
program just a little above. The exception is the so-called statement
functions with definitions that have to be first in a program unit
directly after the specification and are internal to that unit and
therefore is on a logically lower level. Regrettably, the normal
Fortran programmer does not use statement functions.

The above means that all routine names are on the same logical level, that means that two different routines, and two different parts of a big program are not permitted to have the same name. Quite often numerical and graphical libraries include thousands of functions and subroutines, and each routine name has to have at most six characters in the name under old Fortran standards. Therefore, it is very strong risk of a conflict of names. This problem could be partially solved by the old statement functions, since these are internal to the respective unit, and therefore different statement functions can have the same name if they are in different units. The disadvantage is that they can only treat what is in only one program line. But they can call each other in such a way that a later statement function can call an earlier statement function, but of course not the opposite.

Now internal
functions and internal subroutines are added, giving a
greater flexibility. They are specified at the end of each program
unit (but not in the `BLOCK DATA `) after the new command
`CONTAINS ` and
before the `END`. An internal subprogram can have access to the same
variables as the unit it belongs to including the possibility to call
its other internal subprograms. It is written as an ordinary
subprogram, but it is not permitted to have any internal functions or
subroutines.

Usual subroutines and functions are as earlier external subroutines and external functions, but there is now a greater reason for this name (that is calling them external) than earlier, since now you have also internal subprograms. Earlier you only had the built in (intrinsic) as an alternative. In addition, the number of intrinsic functions has increased very much, and a few intrinsic subroutines have been added.

In the specification of variables for subprograms we can for every
argument now give its `INTENT ` as `IN, OUT `
or `INOUT`.
If `IN ` is valid, then
the actual argument can be an expression like `X+Y ` or
`SIN(X) ` or a
constant like 37, since the value is only to be transferred to the
subprogram, but a new value is not to be returned to the calling unit.
The variables in this case may not be assigned a new value in the
subprogram. If `OUT ` is valid, on the other hand, the actual argument
has to be a variable. At entry to the subprogram the variable is at
this stage considered to be not defined. The third case covers both
possibilities, one value on input and another on output, or possibly
the same value. Also in this case the actual argument has to be a
variable. If a variable has a pointer attribute then `INTENT ` may not be
given. The implementation of `INTENT ` is not yet complete in all
compilers.

One use for the new program unit `MODULE ` is to take care of global
data and then it replaces the `BLOCK DATA`, the other use is to make a
package of new data type. As a rather large example I try to give a
package for interval arithmetic. For each value `X` then you have an
interval `(X_lower; X_upper)`. At the use of the package you want to
give only the variable name `X ` when you mean the interval. The
variable `X` is then supposed to be a new data type, interval. The
following is on the file `interval_arithmetics.f90 `
or `intv_ari.f90`.

MODULE INTERVAL_ARITHMETICS TYPE INTERVAL REAL LOWER, UPPER END TYPE INTERVAL INTERFACE OPERATOR (+) MODULE PROCEDURE INTERVAL_ADDITION END INTERFACE INTERFACE OPERATOR (-) MODULE PROCEDURE INTERVAL_SUBTRACTION END INTERFACE INTERFACE OPERATOR (*) MODULE PROCEDURE INTERVAL_MULTIPLICATION END INTERFACE INTERFACE OPERATOR (/) MODULE PROCEDURE INTERVAL_DIVISION END INTERFACE CONTAINS FUNCTION INTERVAL_ADDITION(A, B) TYPE(INTERVAL), INTENT(IN) :: A, B TYPE(INTERVAL) :: INTERVAL_ADDITION INTERVAL_ADDITION%LOWER = A%LOWER + B%LOWER INTERVAL_ADDITION%UPPER = A%UPPER + B%UPPER END FUNCTION INTERVAL_ADDITION FUNCTION INTERVAL_SUBTRACTION(A, B) TYPE(INTERVAL), INTENT(IN) :: A, B TYPE (INTERVAL) :: INTERVAL_SUBTRACTION INTERVAL_SUBTRACTION%LOWER = A%LOWER - B%UPPER INTERVAL_SUBTRACTION%UPPER = A%UPPER - B%LOWER END FUNCTION INTERVAL_SUBTRACTION FUNCTION INTERVAL_MULTIPLICATION(A, B) ! POSITIVE NUMBERS ASSUMED TYPE(INTERVAL), INTENT(IN) :: A, B TYPE (INTERVAL) :: INTERVAL_MULTIPLICATION INTERVAL_MULTIPLICATION%LOWER = A%LOWER * B%LOWER INTERVAL_MULTIPLICATION%UPPER = A%UPPER * B%UPPER END FUNCTION INTERVAL_MULTIPLICATION FUNCTION INTERVAL_DIVISION(A, B) ! POSITIVE NUMBERS ASSUMED TYPE(INTERVAL), INTENT(IN) :: A, B TYPE(INTERVAL) :: INTERVAL_DIVISION INTERVAL_DIVISION%LOWER = A%LOWER / B%UPPER INTERVAL_DIVISION%UPPER = A%UPPER / B%LOWER END FUNCTION INTERVAL_DIVISION END MODULE INTERVAL_ARITHMETICSAt the compilation of the above the file

USE module_name, ONLY : list_of_chosen_routinesThe following is an example of a very simple main program for the test of interval arithmetics. It is from the file

USE INTERVAL_ARITHMETICS IMPLICIT NONE TYPE (INTERVAL) :: A, B, C, D, E, F A%LOWER = 6.9 A%UPPER = 7.1 B%LOWER = 10.9 B%UPPER = 11.1 WRITE (*,*) A, B C = A + B D = A - B E = A * B F = A / B WRITE (*,*) C, D WRITE (*,*) E, F ENDRunning this program on a Sun-computer with the NAG compiler follows:

% f90 interval_arithmetics.f90 interval.f90 interval_arithmetics.f90: interval.f90: % a.out 6.9000001 7.0999999 10.8999996 11.1000004 17.7999992 18.2000008 -4.2000003 -3.7999997 75.2099991 78.8100052 0.6216216 0.6513762 % exitWe compiled with the compiler

In a module some concepts can be defined as `PRIVATE`, which means
that the program units outside of this module are not able to use this
concept. Sometimes an explicit `PUBLIC ` declaration is used, normally
`PUBLIC ` is default. Giving the following statements

PRIVATE PUBLIC :: VAR1it follows that all variables except

INTEGER :: IVAR PRIVATE :: IVARor as an attribute

INTEGER, PRIVATE :: IVARand the corresponding for

Solution.

(7.2) Complement the modules so that the package makes a
suitable error message when it
divides with an interval that contains zero.

Solution.

(7.3) Complement also so that the local rounding error at the
operation is handled. (This is not the case at the moment.)

Solution.

Last modified: 30 August 1996