https://gcc.gnu.org/bugzilla/show_bug.cgi?id=64138

--- Comment #7 from Dominique d'Humieres <dominiq at lps dot ens.fr> ---
I was sure to have seen discussions about such issues: pr33997 and 

https://groups.google.com/forum/#!msg/comp.lang.fortran/GIcxE7GM1ek/aP7eJpQ-T7QJ

AFAIU the discussions, the relevant point for this PR is

> (b) A nonoptional non-passed-object dummy argument whose name
> is such that either the other procedure has no dummy argument
> with that name or the dummy argument with that name is distinguishable
> with it.

Along this line I have renamed num to num1 and z1 to z2 in c_sub_rc

       module complex_number_module
        implicit none

        integer, parameter :: loc_real_precision = 8

        type complex_number
          real(kind=loc_real_precision) :: real_part, imag_part
        end type complex_number

        interface c_sub
          module procedure c_sub_cc,    &      ! z1 - z2
                           c_sub_cr,    &      ! z1 - num, where num is a real
number
                           c_sub_rc            ! num - z1, where num is a real
number
        end interface

 contains
! --------------------------------------------------------------------------
        type (complex_number) function c_sub_cc (z1, z2)

        type (complex_number), intent(in) :: z1, z2

        c_sub_cc%real_part = z1%real_part - z2%real_part
        c_sub_cc%imag_part = z1%imag_part - z2%imag_part

        end function c_sub_cc

! --------------------------------------------------------------------------
        type (complex_number) function c_sub_cr (z1, num)

        type (complex_number),     intent(in) :: z1
        real(kind=loc_real_precision), intent(in) :: num

        c_sub_cr%real_part = z1%real_part - num
        c_sub_cr%imag_part = z1%imag_part

        end function c_sub_cr

! --------------------------------------------------------------------------
        type (complex_number) function c_sub_rc (num1, z2)

        type (complex_number),     intent(in) :: z2
        real(kind=loc_real_precision), intent(in) :: num1

        c_sub_rc%real_part = num1 - z2%real_part
        c_sub_rc%imag_part = - z2%imag_part

        end function c_sub_rc

      end module complex_number_module

program foo
  use complex_number_module
  type(complex_number) a, b
  real(loc_real_precision) x
  a%real_part = 1
  a%imag_part = 2
  x = 3
  b = c_sub(a, x); print '(A,2F5.1)', 'a-x = ', b%real_part, b%imag_part
  b = c_sub(x, a); print '(A,2F5.1)', 'x-a = ', b%real_part, b%imag_part
  b = c_sub(z1=a, num=x); print '(A,2F5.1)', 'a-x = ', b%real_part, b%imag_part
  b = c_sub(num=x,z1=a); print '(A,2F5.1)', 'a-x = ', b%real_part, b%imag_part
  b = c_sub(num1=x,z2=a); print '(A,2F5.1)', 'x-a = ', b%real_part, b%imag_part
end program foo

This made the code to compile and if I am not mistaken to produce the correct
result

a-x =  -2.0  2.0
x-a =   2.0 -2.0
a-x =  -2.0  2.0
a-x =  -2.0  2.0
x-a =   2.0 -2.0


Out of curiosity why do want to handle complex numbers through types while they
are perfectly handled in Fortran by kinds?

To conclude I think this PR should be closed as INVALID.

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