# 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 â€“ 5.0i

The generic function cmplx() creates a complex number. It produces a result whoâ€™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 bitsMaximum valueReason
64 9,223,372,036,854,774,807 (2**63)â€“1
32 2,147,483,647 (2**31)â€“1

The following table displays the number of bits, smallest and largest value, and the precision for real numbers.

Number of bitsLargest valueSmallest valuePrecision
64 0.8E+308 0.5Eâ€“308 15â€“18
32 1.7E+38 0.3Eâ€“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 letâ€™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 hardwareâ€™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*1 :: 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
```

Source: www.tutorialspoint.com