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Intrinsic functions are some common and important functions that are provided as a part of the Fortran language. We have already discussed some of these functions in the Arrays, Characters and String chapters.

Intrinsic functions can be categorised as −

• Numeric Functions
• Mathematical Functions
• Numeric Inquiry Functions
• Floating-Point Manipulation Functions
• Bit Manipulation Functions
• Character Functions
• Kind Functions
• Logical Functions
• Array Functions.

We have discussed the array functions in the Arrays chapter. In the following section we provide brief descriptions of all these functions from other categories.

In the function name column,

• A represents any type of numeric variable
• R represents a real or integer variable
• X and Y represent real variables
• Z represents complex variable
• W represents real or complex variable

Numeric Functions

Example

program numericFunctions
implicit none  

   ! define constants  
   ! define variables
   real :: a, b 
   complex :: z
   
   ! values for a, b 
   a = 15.2345
   b = -20.7689
   write(*,*) 'abs(a): ',abs(a),' abs(b): ',abs(b)   
   write(*,*) 'aint(a): ',aint(a),' aint(b): ',aint(b) 
   write(*,*) 'ceiling(a): ',ceiling(a),' ceiling(b): ',ceiling(b)   
   write(*,*) 'floor(a): ',floor(a),' floor(b): ',floor(b)  
   z = cmplx(a, b)
   write(*,*) 'z: ',z   
   
end program numericFunctions

When you compile and execute the above program, it produces the following result −

abs(a): 15.2344999   abs(b): 20.7688999    
aint(a): 15.0000000  aint(b): -20.0000000    
ceiling(a): 16  ceiling(b): -20
floor(a): 15  floor(b): -21
z: (15.2344999, -20.7688999)

Mathematical Functions

Example

The following program computes the horizontal and vertical position x and y respectively of a projectile after a time, t −

Where, x = u t cos a and y = u t sin a - g t2 / 2

program projectileMotion  
implicit none  

   ! define constants  
   real, parameter :: g = 9.8  
   real, parameter :: pi = 3.1415927  
   
   !define variables
   real :: a, t, u, x, y   
   
   !values for a, t, and u 
   a = 45.0
   t = 20.0
   u = 10.0
   
   ! convert angle to radians  
   a = a * pi / 180.0  
   x = u * cos(a) * t   
   y = u * sin(a) * t - 0.5 * g * t * t  
   
   write(*,*) 'x: ',x,'  y: ',y   
   
end program projectileMotion

When you compile and execute the above program, it produces the following result −

x: 141.421356  y: -1818.57861  

Numeric Inquiry Functions

These functions work with a certain model of integer and floating-point arithmetic. The functions return properties of numbers of the same kind as the variable X, which can be real and in some cases integer.

Floating-Point Manipulation Functions

Bit Manipulation Functions

Character Functions

AD

Kind Functions

Logical Function

A module is like a package where you can keep your functions and subroutines, in case you are writing a very big program, or your functions or subroutines can be used in more than one program.

Modules provide you a way of splitting your programs between multiple files.

Modules are used for −

• Packaging subprograms, data and interface blocks.
• Defining global data that can be used by more than one routine.
• Declaring variables that can be made available within any routines you choose.
• Importing a module entirely, for use, into another program or subroutine.

Syntax of a Module

A module consists of two parts −

• a specification part for statements declaration
• a contains part for subroutine and function definitions

The general form of a module is −

module name     
   

[contains [subroutine and function definitions] ] end module [name]

Using a Module into your Program

You can incorporate a module in a program or subroutine by the use statement −

use name  

Please note that

• You can add as many modules as needed, each will be in separate files and compiled separately.
• A module can be used in various different programs.
• A module can be used many times in the same program.
• The variables declared in a module specification part, are global to the module.
• The variables declared in a module become global variables in any program or routine where the module is used.
• The use statement can appear in the main program, or any other subroutine or module which uses the routines or variables declared in a particular module.

Example

The following example demonstrates the concept −

Live Demo

module constants  
implicit none 

   real, parameter :: pi = 3.1415926536  
   real, parameter :: e = 2.7182818285 
   
contains      
   subroutine show_consts()          
  print*, "Pi = ", pi          
  print*,  "e = ", e     
   end subroutine show_consts 
   
end module constants 


program module_example     
use constants      
implicit none     

   real :: x, ePowerx, area, radius 
   x = 2.0
   radius = 7.0
   ePowerx = e ** x
   area = pi * radius**2     
   
   call show_consts() 
   
   print*, "e raised to the power of 2.0 = ", ePowerx
   print*, "Area of a circle with radius 7.0 = ", area  
   
end program module_example

When you compile and execute the above program, it produces the following result −

Pi = 3.14159274    
e =  2.71828175    
e raised to the power of 2.0 = 7.38905573    
Area of a circle with radius 7.0 = 153.938049   

Accessibility of Variables and Subroutines in a Module

By default, all the variables and subroutines in a module is made available to the program that is using the module code, by the use statement.

However, you can control the accessibility of module code using the private and public attributes. When you declare some variable or subroutine as private, it is not available outside the module.

Example

The following example illustrates the concept −

In the previous example, we had two module variables, e and pi. Let us make them private and observe the output −

Live Demo

module constants  
implicit none 

   real, parameter,private :: pi = 3.1415926536  
   real, parameter, private :: e = 2.7182818285 
   
contains      
   subroutine show_consts()          
  print*, "Pi = ", pi          
  print*, "e = ", e     
   end subroutine show_consts 
   
end module constants 


program module_example     
use constants      
implicit none     

   real :: x, ePowerx, area, radius 
   x = 2.0
   radius = 7.0
   ePowerx = e ** x
   area = pi * radius**2     
   
   call show_consts() 
   
   print*, "e raised to the power of 2.0 = ", ePowerx
   print*, "Area of a circle with radius 7.0 = ", area  
   
end program module_example

When you compile and execute the above program, it gives the following error message −

   ePowerx = e ** x
   1
Error: Symbol 'e' at (1) has no IMPLICIT type
main.f95:19.13:

   area = pi * radius**2     
   1
Error: Symbol 'pi' at (1) has no IMPLICIT type

Since e and pi, both are declared private, the program module_example cannot access these variables anymore.

However, other module subroutines can access them −

Live Demo

module constants  
implicit none 

   real, parameter,private :: pi = 3.1415926536  
   real, parameter, private :: e = 2.7182818285 
   
contains      
   subroutine show_consts()          
  print*, "Pi = ", pi          
  print*, "e = ", e     
   end subroutine show_consts 
   
   function ePowerx(x)result(ePx) 
   implicit none
  real::x
  real::ePx
  ePx = e ** x
   end function ePowerx
   function areaCircle(r)result(a)  
   implicit none
  real::r
  real::a
  a = pi * r**2  
   end function areaCircle
end module constants 


program module_example     
use constants      
implicit none     

   call show_consts() 
   
   Print*, "e raised to the power of 2.0 = ", ePowerx(2.0)
   print*, "Area of a circle with radius 7.0 = ", areaCircle(7.0)  
   
end program module_example

When you compile and execute the above program, it produces the following result −

Pi = 3.14159274    
e = 2.71828175    
e raised to the power of 2.0 = 7.38905573    
Area of a circle with radius 7.0 = 153.938049   

A procedure is a group of statements that perform a well-defined task and can be invoked from your program. Information (or data) is passed to the calling program, to the procedure as arguments.

There are two types of procedures −

• Functions
• Subroutines

Function

A function is a procedure that returns a single quantity. A function should not modify its arguments.

The returned quantity is known as function value, and it is denoted by the function name.

Syntax

Syntax for a function is as follows −

function name(arg1, arg2, ....)  
   

end function [name]

The following example demonstrates a function named area_of_circle. It calculates the area of a circle with radius r.

program calling_func

   real :: a
   a = area_of_circle(2.0) 
   
   Print *, "The area of a circle with radius 2.0 is"
   Print *, a
   
end program calling_func


! this function computes the area of a circle with radius r  
function area_of_circle (r)  

! function result     
implicit none      

   ! dummy arguments        
   real :: area_of_circle   
   
   ! local variables 
   real :: r     
   real :: pi
   
   pi = 4 * atan (1.0)     
   area_of_circle = pi * r**2  
   
end function area_of_circle

When you compile and execute the above program, it produces the following result −

The area of a circle with radius 2.0 is
   12.5663710   

Please note that −

• You must specify implicit none in both the main program as well as the procedure.
• The argument r in the called function is called dummy argument.

The result Option

If you want the returned value to be stored in some other name than the function name, you can use the result option.

You can specify the return variable name as −

function name(arg1, arg2, ....) result (return_var_name)  
   

Subroutine

A subroutine does not return a value, however it can modify its arguments.

Syntax

subroutine name(arg1, arg2, ....)    
   

end subroutine [name]

Calling a Subroutine

You need to invoke a subroutine using the call statement.

The following example demonstrates the definition and use of a subroutine swap, that changes the values of its arguments.

Live Demo

program calling_func
implicit none

   real :: a, b
   a = 2.0
   b = 3.0
   
   Print *, "Before calling swap"
   Print *, "a = ", a
   Print *, "b = ", b
   
   call swap(a, b)
   
   Print *, "After calling swap"
   Print *, "a = ", a
   Print *, "b = ", b
   
end program calling_func


subroutine swap(x, y) 
implicit none

   real :: x, y, temp   
   
   temp = x  
   x = y 
   y = temp  
   
end subroutine swap

When you compile and execute the above program, it produces the following result −

Before calling swap
a = 2.00000000    
b = 3.00000000    
After calling swap
a = 3.00000000    
b = 2.00000000   

Specifying the Intent of the Arguments

The intent attribute allows you to specify the intention with which arguments are used in the procedure. The following table provides the values of the intent attribute −

The following example demonstrates the concept −

Live Demo

program calling_func
implicit none

   real :: x, y, z, disc
   
   x = 1.0
   y = 5.0
   z = 2.0
   
   call intent_example(x, y, z, disc)
   
   Print *, "The value of the discriminant is"
   Print *, disc
   
end program calling_func


subroutine intent_example (a, b, c, d)     
implicit none     

   ! dummy arguments      
   real, intent (in) :: a     
   real, intent (in) :: b      
   real, intent (in) :: c    
   real, intent (out) :: d   
   
   d = b * b - 4.0 * a * c 
   
end subroutine intent_example

When you compile and execute the above program, it produces the following result −

The value of the discriminant is
   17.0000000    

Recursive Procedures

Recursion occurs when a programming languages allows you to call a function inside the same function. It is called recursive call of the function.

When a procedure calls itself, directly or indirectly, is called a recursive procedure. You should declare this type of procedures by preceding the word recursive before its declaration.

When a function is used recursively, the result option has to be used.

Following is an example, which calculates factorial for a given number using a recursive procedure −

program calling_func
implicit none

   integer :: i, f
   i = 15
   
   Print *, "The value of factorial 15 is"
   f = myfactorial(15)
   Print *, f
   
end program calling_func

! computes the factorial of n (n!)      
recursive function myfactorial (n) result (fac)  
! function result     
implicit none     

   ! dummy arguments     
   integer :: fac     
   integer, intent (in) :: n     
   
   select case (n)         
  case (0:1)         
     fac = 1         
  case default    
     fac = n * myfactorial (n-1)  
   end select 
   
end function myfactorial

Internal Procedures

When a procedure is contained within a program, it is called the internal procedure of the program. The syntax for containing an internal procedure is as follows −

program program_name     
   implicit none         
   ! type declaration statements         
   ! executable statements    
   . . .     
   contains         
   ! internal procedures      
   . . .  
end program program_name

The following example demonstrates the concept −

program mainprog  
implicit none 

   real :: a, b 
   a = 2.0
   b = 3.0
   
   Print *, "Before calling swap"
   Print *, "a = ", a
   Print *, "b = ", b
   
   call swap(a, b)
   
   Print *, "After calling swap"
   Print *, "a = ", a
   Print *, "b = ", b
 
contains   
   subroutine swap(x, y)     
  real :: x, y, temp      
  temp = x 
  x = y  
  y = temp   
   end subroutine swap 
   
end program mainprog   

When you compile and execute the above program, it produces the following result −

Before calling swap
a = 2.00000000    
b = 3.00000000    
After calling swap
a = 3.00000000    
b = 2.00000000   

In the last chapter, you have seen how to read data from, and write data to the terminal. In this chapter you will study file input and output functionalities provided by Fortran.

You can read and write to one or more files. The OPEN, WRITE, READ and CLOSE statements allow you to achieve this.

Opening and Closing Files

Before using a file you must open the file. The open command is used to open files for reading or writing. The simplest form of the command is −

open (unit = number, file = "name").

However, the open statement may have a general form −

open (list-of-specifiers)

The following table describes the most commonly used specifiers −

After the file has been opened, it is accessed by read and write statements. Once done, it should be closed using the close statement.

The close statement has the following syntax −

close ([UNIT = ]u[,IOSTAT = ios,ERR = err,STATUS = sta])

Please note that the parameters in brackets are optional.

Example

This example demonstrates opening a new file for writing some data into the file.

program outputdata   
implicit none

   real, dimension(100) :: x, y  
   real, dimension(100) :: p, q
   integer :: i  
   
   ! data  
   do i=1,100  
  x(i) = i * 0.1 
  y(i) = sin(x(i)) * (1-cos(x(i)/3.0))  
   end do  
   
   ! output data into a file 
   open(1, file = 'data1.dat', status = 'new')  
   do i=1,100  
  write(1,*) x(i), y(i)   
   end do  
   
   close(1) 
   
end program outputdata

When the above code is compiled and executed, it creates the file data1.dat and writes the x and y array values into it. And then closes the file.

Reading from and Writing into the File

The read and write statements respectively are used for reading from and writing into a file respectively.

They have the following syntax −

read ([UNIT = ]u, [FMT = ]fmt, IOSTAT = ios, ERR = err, END = s)
write([UNIT = ]u, [FMT = ]fmt, IOSTAT = ios, ERR = err, END = s)

Most of the specifiers have already been discussed in the above table.

The END = s specifier is a statement label where the program jumps, when it reaches end-of-file.

Example

This example demonstrates reading from and writing into a file.

In this program we read from the file, we created in the last example, data1.dat, and display it on screen.

Live Demo

program outputdata   
implicit none   

   real, dimension(100) :: x, y  
   real, dimension(100) :: p, q
   integer :: i  
   
   ! data  
   do i = 1,100  
  x(i) = i * 0.1 
  y(i) = sin(x(i)) * (1-cos(x(i)/3.0))  
   end do  
   
   ! output data into a file 
   open(1, file = 'data1.dat', status='new')  
   do i = 1,100  
  write(1,*) x(i), y(i)   
   end do  
   close(1) 

   ! opening the file for reading
   open (2, file = 'data1.dat', status = 'old')

   do i = 1,100  
  read(2,*) p(i), q(i)
   end do 
   
   close(2)
   
   do i = 1,100  
  write(*,*) p(i), q(i)
   end do 
   
end program outputdata

When the above code is compiled and executed, it produces the following result −

0.100000001  5.54589933E-05
0.200000003  4.41325130E-04
0.300000012  1.47636665E-03
0.400000006  3.45637114E-03
0.500000000  6.64328877E-03
0.600000024  1.12552457E-02
0.699999988  1.74576249E-02
0.800000012  2.53552198E-02
0.900000036  3.49861123E-02
1.00000000   4.63171229E-02
1.10000002   5.92407547E-02
1.20000005   7.35742599E-02
1.30000007   8.90605897E-02
1.39999998   0.105371222    
1.50000000   0.122110792    
1.60000002   0.138823599    
1.70000005   0.155002072    
1.80000007   0.170096487    
1.89999998   0.183526158    
2.00000000   0.194692180    
2.10000014   0.202990443    
2.20000005   0.207826138    
2.29999995   0.208628103    
2.40000010   0.204863414    
2.50000000   0.196052119    
2.60000014   0.181780845    
2.70000005   0.161716297    
2.79999995   0.135617107    
2.90000010   0.103344671    
3.00000000   6.48725405E-02
3.10000014   2.02930309E-02
3.20000005  -3.01767997E-02
3.29999995  -8.61928314E-02
3.40000010  -0.147283033    
3.50000000  -0.212848678    
3.60000014  -0.282169819    
3.70000005  -0.354410470    
3.79999995  -0.428629100    
3.90000010  -0.503789663    
4.00000000  -0.578774154    
4.09999990  -0.652400017    
4.20000029  -0.723436713    
4.30000019  -0.790623367    
4.40000010  -0.852691114    
4.50000000  -0.908382416    
4.59999990  -0.956472993    
4.70000029  -0.995793998    
4.80000019  -1.02525222    
4.90000010  -1.04385209    
5.00000000  -1.05071592    
5.09999990  -1.04510069    
5.20000029  -1.02641726    
5.30000019  -0.994243503    
5.40000010  -0.948338211    
5.50000000  -0.888650239    
5.59999990  -0.815326691    
5.70000029  -0.728716135    
5.80000019  -0.629372001    
5.90000010  -0.518047631    
6.00000000  -0.395693362    
6.09999990  -0.263447165    
6.20000029  -0.122622721    
6.30000019   2.53026206E-02
6.40000010   0.178709000    
6.50000000   0.335851669    
6.59999990   0.494883657    
6.70000029   0.653881252    
6.80000019   0.810866773    
6.90000010   0.963840425    
7.00000000   1.11080539    
7.09999990   1.24979746    
7.20000029   1.37891412    
7.30000019   1.49633956    
7.40000010   1.60037732    
7.50000000   1.68947268    
7.59999990   1.76223695    
7.70000029   1.81747139    
7.80000019   1.85418403    
7.90000010   1.87160957    
8.00000000   1.86922085    
8.10000038   1.84674001    
8.19999981   1.80414569    
8.30000019   1.74167395    
8.40000057   1.65982044    
8.50000000   1.55933595    
8.60000038   1.44121361    
8.69999981   1.30668485    
8.80000019   1.15719533    
8.90000057   0.994394958    
9.00000000   0.820112705    
9.10000038   0.636327863    
9.19999981   0.445154816    
9.30000019   0.248800844    
9.40000057   4.95488606E-02
9.50000000  -0.150278628    
9.60000038  -0.348357052    
9.69999981  -0.542378068    
9.80000019  -0.730095863    
9.90000057  -0.909344316    
10.0000000  -1.07807255