Floating Point Numbers#

The default representation of floating point numbers is using single precision (usually 32 bits / 4 bytes). For most applications a higher precision is required. For this purpose a custom kind parameter can be defined. The recommended way of defining kind parameters is to use

integer, parameter :: dp = selected_real_kind(15)

For many purposes it also suffices to directly infer the kind parameter from a literal like here

integer, parameter :: dp = kind(0.0d0)

or to rename the imported kind parameter from the iso_fortran_env module

use, intrinsic :: iso_fortran_env, only : dp => real64

For some insightful thoughts on kind parameters see Doctor Fortran in it takes all KINDs.

It is recommended to have a central module to define kind parameters and include them with use as necessary. An example for such a module is given with

!> Numerical storage size parameters for real and integer values
module kind_parameter
   implicit none

   !> Single precision real numbers, 6 digits, range 10⁻³⁷ to 10³⁷-1; 32 bits
   integer, parameter :: sp = selected_real_kind(6, 37)
   !> Double precision real numbers, 15 digits, range 10⁻³⁰⁷ to 10³⁰⁷-1; 64 bits
   integer, parameter :: dp = selected_real_kind(15, 307)
   !> Quadruple precision real numbers, 33 digits, range 10⁻⁴⁹³¹ to 10⁴⁹³¹-1; 128 bits
   integer, parameter :: qp = selected_real_kind(33, 4931)

   !> Char length for integers, range -2⁷ to 2⁷-1; 8 bits
   integer, parameter :: i1 = selected_int_kind(2)
   !> Short length for integers, range -2¹⁵ to 2¹⁵-1; 16 bits
   integer, parameter :: i2 = selected_int_kind(4)
   !> Length of default integers, range -2³¹ to 2³¹-1; 32 bits
   integer, parameter :: i4 = selected_int_kind(9)
   !> Long length for integers, range -2⁶³ to 2⁶³-1; 64 bits
   integer, parameter :: i8 = selected_int_kind(18)

end module kind_parameter

Floating point constants should always be declared including a kind parameter suffix:

real(dp) :: a, b, c
a = 1.0_dp
b = 3.5_dp
c = 1.34e8_dp

It is safe to assign integers to floating point numbers without losing accuracy:

real(dp) :: a
a = 3

In order to impose floating point division (as opposed to integer division 3/4 equal to 0), one can convert the integer to a floating point number by:

real(dp) :: a
a = real(3, dp) / 4  ! 'a' is equal to 0.75_dp

or simply separate the integer division with multiplication by 1.0_dp

real(dp) :: a
a = 3 * 1.0_dp / 4  ! 'a' is equal to 0.75_dp

To print floating point numbers without losing precision use the unlimited format specifier (g0) or the exponential representation (es24.16e3), which will give you 17 significant digits of printout.