Designing Functions

Syntax

In addition to intrinsic functions, Fortran allows you to design your own functions. A Fortran function, or more precisely, a Fortran function subprogram, has the following syntax:

type FUNCTION  function-name (arg1, arg2, ..., argn)
   IMPLICIT  NONE
   [specification part]
   [execution part]
   [subprogram part]
END FUNCTION  function-name

Here are some elaborations of the above syntax:

The first line of a function starts with the keyword FUNCTION. Before FUNCTION, the type gives the type of the function value (i.e., INTEGER, REAL, LOGICAL and CHARACTER) and after FUNCTION is the name you assign to that function.
Following the function-name, there is a pair of parenthesis in which a number of arguments arg1, arg2, ..., argn are separated with commas. These arguments are referred to as formal arguments. Formal arguments must be variable names and cannot be expressions. Here are a examples:
1. The following is a function called Factorial. It takes only one formal argument n and returns an INTEGER as its function value.
2. The following is a function called TestSomething. It takes three formal arguments a, b and c, and returns a LOGICAL value (i.e., .TRUE. or .FALSE.) as its function value.
A function must be ended with END FUNCTION followed by the name of that function.
Between FUNCTION and END FUNCTION, there are the IMPLICIT NONE, specification part, execution part and subprogram part. These are exactly identical to that of a PROGRAM.

If a function does not need any formal argument, it can be written as

type FUNCTION  function-name ()
   IMPLICIT  NONE
   [specification part]
   [execution part]
   [subprogram part]
END FUNCTION  function-name

where arg1, arg2, ..., argn are left out. But, the pait of parenthesis must be there.

Semantics

The meaning of a function is very simple:

A function is a self-contained unit that receives some "input" from the outside world via its formal arguments, does some computations, and then returns the result with the name of the function.
Thus, since the function returns its result via the name of the function, somewhere in the function there must exist one or more assignment statements like the following:
```
function-name = expression
```
where the result of expression is stored to the name of the function.
However, the name of the function cannot appear in the right-hand side of any expression. That is, the name of the function, used as a variable name, can only appear in the left-hand side of an expression. This is an artificial restriction in this course only.
A function receives its input values from formal arguments, does computations, and saves the result in its name. When the control of execution reaches END FUNCTION, the value stored in the name of the function is returned as the function value.
To tell the function about the types of its formal arguments, all arguments must be declared with a new attribute INTENT(IN). The meaning of INTENT(IN) indicates that the function will only take the value from the formal argument and must not change its content.
Any statements that can be used in PROGRAM can also be used in a FUNCTION.