module numbers
  ! set precision of single and double precision real and integers
  integer, parameter :: singleR = selected_real_kind(p=6,r=37)
  integer, parameter :: doubleR = selected_real_kind(p=15,r=307)
  integer, parameter :: singleI = selected_int_kind(9)
  integer, parameter :: doubleI = selected_int_kind(18)
  ! signal invalid values
  real(kind=doubleR), parameter    :: invalid_R = -1.d99
  integer(kind=singleI), parameter :: invalid_I = -1234567890
  character(len=20), parameter     :: invalid   = 'INVALID'
end module numbers