In this guide, we will discuss Fortran Numbers. Numbers in Fortran are represented by three intrinsic data types −
- Integer type
- Real type
- Complex type
Integer Type
The integer types can hold only integer values. The following example extracts the largest value that could be hold in a usual four byte integer −
program testingInt implicit none integer :: largeval print *, huge(largeval) end program testingInt
When you compile and execute the above program it produces the following result −
2147483647
Please note that the huge() function gives the largest number that can be held by the specific integer data type. You can also specify the number of bytes using the kind specifier. The following example demonstrates this −
program testingInt
implicit none
!two byte integer
integer(kind = 2) :: shortval
!four byte integer
integer(kind = 4) :: longval
!eight byte integer
integer(kind = 8) :: verylongval
!sixteen byte integer
integer(kind = 16) :: veryverylongval
!default integer
integer :: defval
print *, huge(shortval)
print *, huge(longval)
print *, huge(verylongval)
print *, huge(veryverylongval)
print *, huge(defval)
end program testingInt
When you compile and execute the above program it produces the following result −
32767 2147483647 9223372036854775807 170141183460469231731687303715884105727 2147483647
Real Type
It stores the floating point numbers, such as 2.0, 3.1415, -100.876, etc.
Traditionally there were two different real types : the default real type and double precision type.
However, Fortran 90/95 provides more control over the precision of real and integer data types through the kind specifier, which we will study shortly.
The following example shows the use of real data type −
program division implicit none ! Define real variables real :: p, q, realRes ! Define integer variables integer :: i, j, intRes ! Assigning values p = 2.0 q = 3.0 i = 2 j = 3 ! floating point division realRes = p/q intRes = i/j print *, realRes print *, intRes end program division
When you compile and execute the above program it produces the following result −
0.666666687 0
Complex Type
This is used for storing complex numbers. A complex number has two parts : the real part and the imaginary part. Two consecutive numeric storage units store these two parts.
For example, the complex number (3.0, -5.0) is equal to 3.0 – 5.0i
The generic function cmplx() creates a complex number. It produces a result who’s real and imaginary parts are single precision, irrespective of the type of the input arguments.
program createComplex implicit none integer :: i = 10 real :: x = 5.17 print *, cmplx(i, x) end program createComplex
When you compile and execute the above program it produces the following result −
(10.0000000, 5.17000008)
The following program demonstrates complex number arithmetic −
program ComplexArithmatic implicit none complex, parameter :: i = (0, 1) ! sqrt(-1) complex :: x, y, z x = (7, 8); y = (5, -7) write(*,*) i * x * y z = x + y print *, "z = x + y = ", z z = x - y print *, "z = x - y = ", z z = x * y print *, "z = x * y = ", z z = x / y print *, "z = x / y = ", z end program ComplexArithmatic
When you compile and execute the above program it produces the following result −
(9.00000000, 91.0000000) z = x + y = (12.0000000, 1.00000000) z = x - y = (2.00000000, 15.0000000) z = x * y = (91.0000000, -9.00000000) z = x / y = (-0.283783793, 1.20270276)
The Range, Precision and Size of Numbers
The range on integer numbers, the precision and the size of floating point numbers depends on the number of bits allocated to the specific data type.
The following table displays the number of bits and range for integers −
| Number of bits | Maximum value | Reason |
|---|---|---|
| 64 | 9,223,372,036,854,774,807 | (2**63)–1 |
| 32 | 2,147,483,647 | (2**31)–1 |
The following table displays the number of bits, smallest and largest value, and the precision for real numbers.
| Number of bits | Largest value | Smallest value | Precision |
|---|---|---|---|
| 64 | 0.8E+308 | 0.5E–308 | 15–18 |
| 32 | 1.7E+38 | 0.3E–38 | 6-9 |
The following examples demonstrate this −
program rangePrecision implicit none real:: x, y, z x = 1.5e+40 y = 3.73e+40 z = x * y print *, z end program rangePrecision
When you compile and execute the above program it produces the following result −
x = 1.5e+40
1
Error : Real constant overflows its kind at (1)
main.f95:5.12:
y = 3.73e+40
1
Error : Real constant overflows its kind at (1)
Now let us use a smaller number −
program rangePrecision implicit none real:: x, y, z x = 1.5e+20 y = 3.73e+20 z = x * y print *, z z = x/y print *, z end program rangePrecision
When you compile and execute the above program it produces the following result −
Infinity 0.402144760
Now let’s watch underflow −
program rangePrecision implicit none real:: x, y, z x = 1.5e-30 y = 3.73e-60 z = x * y print *, z z = x/y print *, z end program rangePrecision
When you compile and execute the above program it produces the following result −
y = 3.73e-60
1
Warning : Real constant underflows its kind at (1)
Executing the program....
$demo
0.00000000E+00
Infinity
The Kind Specifier
In scientific programming, one often needs to know the range and precision of data of the hardware platform on which the work is being done.
The intrinsic function kind() allows you to query the details of the hardware’s data representations before running a program.
program kindCheck implicit none integer :: i real :: r complex :: cp print *,' Integer ', kind(i) print *,' Real ', kind(r) print *,' Complex ', kind(cp) end program kindCheck
When you compile and execute the above program it produces the following result −
Integer 4 Real 4 Complex 4
You can also check the kind of all data types −
program checkKind implicit none integer :: i real :: r character :: c logical :: lg complex :: cp print *,' Integer ', kind(i) print *,' Real ', kind(r) print *,' Complex ', kind(cp) print *,' Character ', kind(c) print *,' Logical ', kind(lg) end program checkKind
When you compile and execute the above program it produces the following result −
Integer 4 Real 4 Complex 4 Character 1 Logical 4
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