Fortran/Fortran procedures and functions

Functions and Subroutines

In most programs, a block of code is often re-used at several places. In order to minimize duplicating code and facilitate maintaining the code, such blocks of code should be placed within a function or subroutine. A Fortran function is similar to a mathematical function, which takes one or many parameters as inputs and returns a single output value. A Fortran subroutine is a block of code that performs some operation on the input variables, and as a result of calling the subroutine, the input variables are modified.

An expression containing a function call:

! func1 is a function defined elsewhere.
! It takes an integer as an input and returns another integer as the output.
a = func1(b)

A call to a subroutine:

! sub1 is a subroutine defined elsewhere.
! sub1 performs some operation on input variables e and f.
call sub1(e, f)
! Now e or f, or both (or neither) may be modified.

Many programming languages do not distinguish between functions and subroutines (e.g. C/C++, Python, Java). Pure functional programming languages (e.g. Haskell) only allow functions, because subroutines can, in some case, modify input variables as side-effects, which can complicate the code.

Functions are simpler than subroutines. A function must return a single value, and can be invoked from within expressions, like a write statement, inside an if declaration if (function) then, etc. A subroutine does not return a value, but can return many values via its arguments and can only be used as a stand-alone command (using the keyword call).

Function

In Fortran, one can use a function to return a value or an array of values. The following program calls a function to compute the sum of the square and the cube of an integer.

function func(i) result(j)
    integer, intent (in) :: i ! input
    integer              :: j ! output

    j = i**2 + i**3
end function

program main
    implicit none
    integer :: i
    integer :: func

    i = 3
    print *, "sum of the square and cube of", i, "is", func(i)
end program

The intent (in) attribute of argument i means that i cannot be changed inside the function and in contrast, the return value j has automatic intent (out). Note that the return type of func needs to be declared. If this is omitted, some compilers will not compile. Open64 will compile the resulting code with warning, but the behavior is ill-defined.

An alternative formulation (F77 compatible) is

      FUNCTION func_name(a, b)
          INTEGER :: func_name
          INTEGER :: a
          REAL    :: b
          func_name = (2*a)+b
          RETURN
      END FUNCTION
    
      PROGRAM cows
          IMPLICIT NONE
          INTEGER :: func_name
          PRINT *, func_name(2, 1.3)
      END PROGRAM

The return type of the func_name still needs to be declared, as above. The only difference is how the return type of func_name is referenced within func_name. In this case, the return variable has the same name as the function itself.

Recursion

Recursive functions can be declared , in a way such as the one shown below, in order for the code to compile.

recursive function fact(i) result(j)
    integer, intent (in) :: i
    integer :: j
    if (i==1) then
        j = 1
    else
        j = i * fact(i - 1)
    end if
end function fact

Subroutine

A subroutine can be used to return several values through its arguments. It is invoked with a call statement. Here is an example.

subroutine square_cube(i, isquare, icube)
    integer, intent (in)  :: i              ! input
    integer, intent (out) :: isquare, icube ! output

    isquare = i**2
    icube   = i**3
end subroutine

program main
    implicit none
    external square_cube ! external subroutine
    integer :: isq, icub

    call square_cube(4, isq, icub)
    print *, "i,i^2,i^3=", 4, isq, icub
end program

Intent

When declaring variables inside functions and subroutines that need to be passed in or out, intent may be added to the declaration. The default is no intent checking - which can allow erroneous coding to be undetected by the compiler.

intent (in) - the value of the dummy argument may be used, but not modified, within the procedure.

intent (out)- the dummy argument may be set and then modified within the procedure, and the values returned to the caller.

intent (inout) - initial values of the dummy argument may be both used and modified within the procedure, and then returned to the caller.

More on Functions vs. Subroutines

Different function result definitions

Functions can define the data type of their result in different forms: either as a separate variable or by the function name.

See the examples below

function f1(i) result (j)
  !! result's variable:  separately specified
  !! result's data type: separately specified
  integer, intent (in) :: i
  integer              :: j
  j = i + 1
end function

integer function f2(i) result (j)
  !! result's variable:  separately specified
  !! result's data type: by prefix
  integer, intent (in) :: i
  j = i + 2
end function

integer function f3(i)
  !! result's variable:  by function name
  !! result's data type: by prefix
  integer, intent(in) :: i
  f3 = i + 3
end function

function f4(i)
  !! result's variable:  by function name
  !! result's data type: separately specified
  integer, intent (in) :: i
  integer              :: f4
  f4 = i + 4
end function

program main
  implicit none
  integer :: f1, f2, f3, f4

  print *, 'f1(0)', f1(0) ! output: 1
  print *, 'f2(0)', f2(0) ! output: 2
  print *, 'f3(0)', f3(0) ! output: 3
  print *, 'f4(0)', f4(0) ! output: 4
end program

External

Procedures must be included by module use or by specifying them as external procedures. external supplies only an implicit interface which is inferior as the compiler doesn't know the number of arguments and neither their data types. Thus, it cannot yield warnings at compile time (in contrast to an explicit interface given from a module use, c.f. Fortran/OOP in Fortran).

subroutine square_cube(i, isquare, icube)
    integer, intent (in)  :: i              ! input
    integer, intent (out) :: isquare, icube ! output

    isquare = i**2
    icube   = i**3
end subroutine

integer function pow4(i)
    integer, intent (in) :: i

    pow4 = i**4
end function

program main
    implicit none
    external square_cube    ! external subroutine (only implicit interface)
    integer :: pow4         ! external function (only implicit interface)
    integer :: i, isq, icub

    i = 5
    call square_cube(i, isq, icub)
    print '(A,4I5)', "i,i^2,i^3,i^4=", i, isq, icub, pow4(i)
end program

Pure procedures

Both functions and subroutines can modify their input variables. By necessity, subroutines modify input variables, since they do not return any output value. Functions do not have to, but are allowed, by default, to modify input variables. A function can be turned into a pure function, which does not have any side-effects through the use of the intent attribute on all input variables, and further enforced through the keyword pure. The pure keyword imposes additional restrictions, which essentially prevents the function from having any side-effects.

An example of a pure function.

pure real function square(x)
    real, intent (in) :: x

    square = x*x
end function

program main
    real :: a, b, square

    a = 2.0
    b = square(a)
    ! After invoking the square(.) pure function, we can be sure that
    ! besides assigning the output value of square(a) to b,
    ! nothing else has been changed.
end program

Keyword arguments

One can use any order of the input arguments if one specifies them by their dummy name. That is possible as long as the calling procedure has an interface block of the intended procedure (which is automatically created if one includes the function by module usage uses modules).

There is also a hybrid method where one specifies some parameters by position and the rest by their dummy name.

An example is given

real function adder(a,b,c,d)
    real, intent (in) :: a, b, c, d
    adder = a+b+c+d
end function

program main
    interface
        real function adder(a,b,c,d)
            real, intent (in) :: a, b, c, d
        end function
    end interface

    print *, adder(d=1.0, b=2.0, c=1.0, a=1.0)  ! specify each parameter by dummy name
    print *, adder(1.0, d=1.0, b=2.0, c=1.0)    ! specify some parameters by dummy names, other by position
end program

Optional arguments

Arguments can be set optional. The intrinsic function present can be used to check if a specific parameter is set.

An example is given below.

real function tester(a)
    real, intent (in), optional :: a
    if (present(a)) then
        tester = a
    else
        tester = 0.0
    end if
end function 

program main
    interface
        real function tester(a)
            real, intent (in), optional :: a
        end function 
    end interface

    print *, "[no args] tester()   :", tester()    ! yields: 0.0
    print *, "[   args] tester(1.0):", tester(1.0) ! yields: 1.0
end program

Interface block

If a procedure has another procedure as dummy argument then one has to specify its type, just as the type of other parameters. An interface block is used for this case. It consists of the procedure statement with the definitions of its arguments.

Note, that each interface block has its own scope. Thus, if one needs to access outside values one needs to explicitly load them. This can be achieved by the import, or use statements.

An example is given below.

function tester(a)
    real, intent (in) :: a
    real :: tester

    tester = 2*a + 3
end function tester

program main
    interface
        function tester(a)
            real, intent (in) :: a
            real :: tester
        end function tester
    end interface

    print *, "tester(1.0):", tester(1.0) ! yields: 5.0
end program main

Save attribute

The value of a variable can be saved in-between procedure calls by explicitly giving the save attribute.

An example is given below.

subroutine f()
    implicit none
    integer, save :: i = 0

    i = i + 1
    print *, "value i:", i
end

program main
    implicit none
    interface
        subroutine f()
            integer, save :: i = 0
        end
    end interface

    call f()  ! yields: 1
    call f()  ! yields: 2
    call f()  ! yields: 3
end program main

Generic

It is possible to create generic functions with the same name for different input arguments, similar to the abs function which works for integer, real, and complex data types.

The following example illustrates how to create a function add which adds either two integers or character strings.

module add_mod
    implicit none
    private
    public :: add

    interface add
        procedure add_int, add_char
    end interface add
contains
    pure function add_int( x, y )
        integer, intent (in) :: x, y
        integer :: add_int

        add_int = x+y
    end function add_int

    pure function add_char( x, y )
        character (len=*), intent (in) :: x, y
        character (len=len(x)+len(y)), allocatable :: add_char

        add_char = x // y
    end function add_char
end module add_mod

program main
  use add_mod
  implicit none

  print *, "add ints: ", add( 1, 2 )
  print *, "add chars: ", add("abc", "def")
end program main

Deferred

One can set type-bound procedures of an abstract type as deferred such that it needs to be reimplemented in derived types. For more information see the section on abstract types.

Elemental

One can create procedures that operate parameters of arbitrary dimension. The keyword elemental is used where one defines the operation on a single object (e.g. integer) and the general case is automatically handled.

An example for the addition of arbitrary long integer dimension is given.

pure elemental function add_int(x, y)
    integer, intent (in) :: x, y
    integer :: add_int
    add_int = x + y
end function add_int

program main
    implicit none

    interface
        pure elemental function add_int(x, y)
            integer, intent (in) :: x, y
            integer :: add_int
        end function add_int
  end interface

  print *, "add ints:", add_int(1, 2) ! yields: 3
  print *, "add arrays:", add_int([1, 2], [2, 3]) ! yields: 3   5
end program main