Fortran operator overloading based in C function

Question

I want to expose a C++ class to Fortran. From various searches, I have seen that the most direct way is to use intermediate C functions.

My question is the following: considering a simple C struct describe below and a C function call add, how can I declare a Fortran module which would declare an associated Fortran derived type and use the add function for operator overloading ?

struct my_double{  double x; }

my_double add(const my_double*, const my_double*);

The (non working) solution I came up to is something like this:

module my_module
  use iso_c_binding
  type, bind(c) :: my_double
     real(c_double) :: x
  end type my_double
  interface operator (+)
    module procedure add
  end interface operator (+)
  interface
     type(my_double) function add (v1,v2) bind ( c )
       use iso_c_binding
       type (my_double), intent(in) :: v1,v2
       type (my_double)  :: v3
    end function add
  end interface
end module my_module

Does anyone have an advice on how to make this work ?