Is there a way to catch integer exceptions with gfortran or ifort like there is for catching floating point exceptions? 
Consider this simple program to calculate the factorial:
program factorial
  use, intrinsic :: iso_fortran_env 
  implicit none
  integer(8)          :: fac
  real(REAL64)        :: facR
  integer,parameter   :: maxOrder = 30
  integer             :: i
  fac = 1 ; facR = 1.e0_REAL64
  do i=2,maxOrder
    fac=fac*i ; facR=facR*real(i,REAL64)
    write(*,*) i, fac, facR
  enddo ! i
end program
At some point there will be an overflow - for integer(8) as shown here, it will occur at around 21. But without the calculation using floats as a reference I couldn't tell for sure...
There is nothing in the Fortran standard that deals with integer overflow. As it stands you can't even rely on integers wrapping round when a computation exceeds the maximum value representable in the chosen kind. So, while a test such as
huge(2_8)+1 < 0_8
is likely to work with most current compilers (at least the ones I have used recently) it's not guaranteed.
I am sure that neither Intel Fortran nor gfortran provide compiler-generated run-time checks for integer overflow either. I'm not sure about other compilers but I'll be (pleasantly) surprised to learn that any of them do.
I think, therefore, that you have to proceed with your current approach.
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