Subprogram Attributes
Subprograms can be defined with attributes for particular conditions or behaviors. They can call themeselves, or operate elementwise on arrays.
Pure and Elemental Procedures
PURE Functions
Side effects should be avoided in functions. Fortran offers subroutines to handle situations where changes to the parameters make sense. The programmer can declare a function PURE to tell the compiler it is free of side effects. Pure functions must declare all parameters INTENT(IN).
Subroutines may also be PURE. They may change their parameters but must declare those as INTENT(OUT). INTENT(INOUT) is not permitted for PURE subroutines.
There are strict rules for PURE procedures.
 PURE procedures must have an interface.
 Any additional procedures they call must also be PURE.
 Neither PURE functions nor PURE subroutines are permitted to
 Alter any accessible global variables (e.g. from CONTAINS);
 Perform any IO – this can make debugging inconvenient;
 SAVE any variables;
 Contain any STOP statement. RETURN is permitted.
PURE FUNCTION myfunc(x)
INTEGER ::myfunc
REAL, INTENT(IN) :: x
Since there is PURE, there is also IMPURE, so that the programmer is explicit about the presence of side effects.
ELEMENTAL Procedures
PURE procedures were intended for automatic parallelization. However, a particularly useful derivative is the ELEMENTAL procedure. ELEMENTAL procedures operate elementwise on arrays. All ELEMENTAL procedures must obey the rules for PURE procedures. In addition, all arguments must be scalars.
ELEMENTAL FUNCTION f2c(tempF)
REAL :: f2c
REAL, INTENT(IN) ::tempF
f2c=(tempF32.)/1.8
END FUNCTION
Using ELEMENTAL Procedures
An elemental procedure can be called for any arrays as long as they conform to the requirements for all operations in the procedure. Each array element is modified by the procedure appropriately. The procedure can also be called as a normal scalar function.
PROGRAM elements
REAL ::tempF,tempC
REAL, DIMENSION(100) ::tempFs,tempCs
REAL, DIMENSION(10,10)::dataF,dataC
INTERFACE
ELEMENTAL FUNCTION f2c(tempF)
REAL :: f2c
REAL, INTENT(IN) ::tempF
END FUNCTION
END INTERFACE
! Set up tempFs somehow
tempC= f2c(tempF)
tempCs= f2c(tempFs)
dataC= f2c(dataF)
END PROGRAM
Like PURE procedures, ELEMENTAL procedures must have an interface.
Starting with Fortran 2008, it was recognized that the restrictions of PURE were sometimes unnecessary and detrimental to developing ELEMENTAL procedures, which have many uses for which PURE is irrelevant. They may thus be declared
IMPURE ELEMENTAL myfunc(x)
Absent IMPURE, the procedure must obey the rules for PURE.
RECURSIVE Procedures
Recursive procedures call themselves. This may seem impossible, but the compiler sets up multiple copies, usually in a section of memory called the stack. Without some care in implementing the algorithm, recursion can lead to stack overflow. Even worse, a recursive procedure must have a stopping condition or the result is infinite recursion, at least until the stack overflows and the executable or even the whole computer crashes.
Most recursive algorithms have an interative (while loop) equivalent, which may perform better, but the recursive algorithm may be simpler and easier to understand.
Both functions and subroutines can be RECURSIVE. Up to the F2008 standard, recursive functions require a RESULT clause. Recursive subroutines do not support RESULT and do not require it. Starting with the F2018 standard, the default is for subprograms to be assumed RECURSIVE, so the keyword will no longer be required unless a compiler option is used to change the default behavior. Another keyword NON_RECURSIVE can be used to make a subprogram explicitly iterative.
One of the most famous examples of a recursive algorithm is the Fibonnaci sequence. To compute the Nth number in the sequence, we can use
$$ F_0 = 0 $$ $$ F_1 = 1 $$ $$ F_{N}=F_{N1}+F_{N2} $$
program fibonnaci
implicit none
integer :: n
interface
integer function ifib(n)
implicit none
integer, intent(in) :: n
end function
recursive function rfib(n) result(fib)
implicit none
integer :: fib
integer, intent(in) :: n
end function
end interface
write(*,'(a)',advance='no') "Please enter an integer >=0:"
read(*,*) n
print *, ifib(n), rfib(n)
end program
integer function ifib(n)
! Iterative
implicit none
integer, intent(in) :: n
integer :: nm1, nm2, nval
integer :: i
if (n < 0) then
write(*,*) "Illegal term number."
ifib=1
return
endif
nm1=0
nm2=1
if (n==0) then
ifib=nm1
return
else if (n==1) then
ifib=nm2
return
else
do i=1,n
nval=nm1+nm2
nm2=nm1
nm1=nval
enddo
ifib=nval
endif
end function
recursive function rfib(n) result(fib)
! recursive, F2003 standard
implicit none
integer :: fib
integer, intent(in) :: n
integer :: nm1, nm2, nval
integer :: i
if (n < 0) then
write(*,*) "Illegal term number."
fib=1
return
endif
nm1=0
nm2=1
if (n==0) then
fib=nm1
return
else if (n==1) then
fib=nm2
return
else
fib=rfib(n1)+rfib(n2)
endif
end function
Exercise

Write an elemental function that accepts a single parameter as an angle in degrees and converts it to radians.

Write a program that computes the radian equivalent of 0 to 90 degrees in increments of 5 degrees. Print the output. Do it with a loop, and then by creating a onedimensional array of angles and passing it to the function.
Example Solution
program deg2rad
implicit none
real :: dtheta,rtheta
real :: start_val,end_val,incr
real, dimension(:), allocatable :: degrees,rads
real :: angle
integer :: n,nvals
interface
elemental real function deg_to_rad(theta)
implicit none
real, intent(in) :: theta
end function
end interface
dtheta=15.
rtheta=deg_to_rad(dtheta)
print *, "An angle of ",dtheta," in degrees is ",rtheta," radians."
start_val=0.
end_val =90.
incr =5.
nvals=90./incr+1
! Loop
do n=1,nvals
angle=start_val+incr*(n1)
write(*,'(f12.4,x,f12.4)') angle,deg_to_rad(angle)
enddo
! Array
degrees=[(start_val+incr*(n1),n=1,nvals)]
rads=deg_to_rad(degrees)
print *, rads
end program
elemental real function deg_to_rad(theta)
implicit none
real, intent(in) :: theta
real :: pi
pi =4.0*atan(1.0)
deg_to_rad=theta*pi/(180)
end function