binomial Function

public pure function binomial(n, r) result(c)

Compute binomial coefficient C(n,r) = n! / (r! * (n-r)!)

Calculates “n choose r” using iterative algorithm to avoid factorial overflow for large numbers. Uses int64 to handle large combinatorial values that overflow int32.

Arguments

Type IntentOptional Attributes Name
integer(kind=default_int), intent(in) :: n

Total number of items
integer(kind=default_int), intent(in) :: r

Number of items to choose

Return Value integer(kind=int64)

Binomial coefficient result


Called by

proc~~binomial~~CalledByGraph proc~binomial binomial proc~get_nfrags get_nfrags proc~get_nfrags->proc~binomial proc~run_fragmented_calculation run_fragmented_calculation proc~run_fragmented_calculation->proc~binomial proc~run_fragmented_calculation->proc~get_nfrags proc~run_calculation run_calculation proc~run_calculation->proc~run_fragmented_calculation proc~compute_energy_and_forces compute_energy_and_forces proc~compute_energy_and_forces->proc~run_calculation proc~run_multi_molecule_calculations run_multi_molecule_calculations proc~run_multi_molecule_calculations->proc~run_calculation program~main main program~main->proc~run_calculation program~main->proc~run_multi_molecule_calculations

Variables

Type Visibility Attributes Name Initial
integer(kind=default_int), private :: i

Loop counter

Source Code

   pure function binomial(n, r) result(c)
      !! Compute binomial coefficient C(n,r) = n! / (r! * (n-r)!)
      !!
      !! Calculates "n choose r" using iterative algorithm to avoid
      !! factorial overflow for large numbers.
      !! Uses int64 to handle large combinatorial values that overflow int32.
      integer(default_int), intent(in) :: n  !! Total number of items
      integer(default_int), intent(in) :: r  !! Number of items to choose
      integer(int64) :: c              !! Binomial coefficient result
      integer(default_int) :: i              !! Loop counter

      if (r == 0 .or. r == n) then
         c = 1_int64
      else if (r > n) then
         c = 0_int64
      else
         c = 1_int64
         do i = 1, r
            c = c*int(n - i + 1, int64)/int(i, int64)
         end do
      end if
   end function binomial