  In this work, we establish the Freidlin--Wentzell large deviations principle
(LDP) of the stochastic Cahn--Hilliard equation with small noise, which implies
the one-point LDP. Further, we give the one-point LDP of the spatial finite
difference method (FDM) for the stochastic Cahn--Hilliard equation. Our main
result is the convergence of the one-point large deviations rate function
(LDRF) of the spatial FDM, which is about the asymptotical limit of a
parametric variational problem. The main idea for proving the convergence of
the LDRF of the spatial FDM is via the $\Gamma$-convergence of objective
functions, which relies on the qualitative analysis of skeleton equations of
the original equation and the numerical method. In order to overcome the
difficulty that the drift coefficient is not one-side Lipschitz, we use the
equivalent characterization of the skeleton equation of the spatial FDM and the
discrete interpolation inequality to obtain the uniform boundedness of the
solution to the underlying skeleton equation. This plays an important role in
deriving the $\Gamma$-convergence of objective functions.
