  The Coulomb-nuclear interference (CNI) has recently been used by the TOTEM
Collaboration to analyse proton-proton elastic-scattering data from the LHC and
to draw physics conclusions. This paper will present an eikonal calculation of
the CNI effects performed to all orders of the fine structure constant,
$\alpha$. This calculation will be used as a reference to benchmark several
widely-used CNI formulae and to verify several recent claims by other authors.
