  Depending on the parity of $n$ and the regularity of a bent function $f$ from
$\mathbb F_p^n$ to $\mathbb F_p$, $f$ can be affine on a subspace of dimension
at most $n/2$, $(n-1)/2$ or $n/2- 1$. We point out that many $p$-ary bent
functions take on this bound, and it seems not easy to find examples for which
one can show a different behaviour. This resembles the situation for Boolean
bent functions of which many are (weakly) $n/2$-normal, i.e. affine on a
$n/2$-dimensional subspace. However applying an algorithm by Canteaut et.al.,
some Boolean bent functions were shown to be not $n/2$- normal. We develop an
algorithm for testing normality for functions from $\mathbb F_p^n$ to $\mathbb
F_p$. Applying the algorithm, for some bent functions in small dimension we
show that they do not take on the bound on normality. Applying direct sum of
functions this yields bent functions with this property in infinitely many
dimensions.
