Declared double precision Function in F90 and return type mismatch error

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@BigNish7 ,

Note the current specification of the Fortran language. per the year 2023 ISO IEC standard revision, does not allow generic resolution of FUNCTIONs based on the characteristics (e.g., TYPE, KIND, RANK aka TKR) of the RESULT declaration. Thus in certain ordinary scenarios, the argument(s) of the function has to be used as some form of a “mold” in a “generic” interface.

In your specific case here involving “combinatorics”, the above “mold” trick will not be too “cool”.

Another option can thus be what you are first advised by @snano and tweaking it a bit to compute the numbers using the highest precision supported and making available an explicit interface for the same. The caller can then decide to scale the precision (down) as needed.

Note with modern Fortran, a suggestion will be to perform as much compile-time math as viable with your processor. A silly example is below as illustration where the factorials are computed up to a certain arbitrary limit at compile-time:

Click to see code 
module kinds_m

   integer, parameter :: SP = kind( 1E0 ) 
   integer, parameter :: DP = kind( 1D0 ) 
   integer, parameter :: QP = selected_real_kind( p=2*precision(1.0_dp) )
   integer, parameter :: MP = merge( QP, DP, QP > 0 )

end module

module Combinatorics_m

   use kinds_m, only : MP

   integer, parameter :: MAXN = 100  !<-- arbitrary "maximum"; change as suitable
   real(kind=MP), parameter :: Idx(*) = [( real(i, kind=MP), integer :: i = 1, MAXN )]
   real(kind=MP), parameter :: Factorial(*) = [( product(Idx(1:j)), integer :: j = 1, MAXN )]

contains

   elemental function n_Choose_r( n, r ) result( nCr )
      ! Argument list
      integer, intent(in) :: n
      integer, intent(in) :: r
      ! Function result
      real(kind=MP) :: nCr

      nCr = 1.0_mp
      ! Modify the checks below as appropriate
      if ( n > MAXN ) then
         ! Error Handling
         error stop "nCr calculation: n must be less than 50."
         return
      end if
      if ( r > n ) then
         ! Error Handling
         error stop "nCr calculion: n must be greater than r"
         return
      end if
      if ( r == 0 ) return
      
      nCr = factorial(n) / factorial(r) / factorial(n-r)

      return

   end function
    
end module
    use Combinatorics_m, only : n_Choose_r
    print *, " Choose(10,2) = ", n_Choose_r( 10, 2 ), "; expected is 45"
    print *, " Choose(99,9) = ", n_Choose_r( 99, 9 ), "; expected is 1731030945644."
end

Program using Intel Fortran processor on Windows 10 OS:

C:\temp>ifx /free /standard-semantics p.f
Intel(R) Fortran Compiler for applications running on Intel(R) 64, Version 2024.1.0 Build 20240308
Copyright (C) 1985-2024 Intel Corporation. All rights reserved.

Microsoft (R) Incremental Linker Version 14.36.32537.0
Copyright (C) Microsoft Corporation.  All rights reserved.

-out:p.exe
-subsystem:console
p.obj

C:\temp>p.exe
  Choose(10,2) =  45.0000000000000000000000000000000 ; expected is 45
  Choose(99,9) =  1731030945644.00000000000000000000 ; expected is 1731030945644
 .

C:\temp>
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