Another revision: this time I check if the found parent is null before comparing
with the expanded file name by `file-equal-p` (haven't come to this case,
though). And return the relative parent when input is relative.

Current cases as in shortdoc.el:

    (file-parent-directory "/foo/bar")
    ⇒ "/foo/"
    (file-parent-directory "~")
    ⇒ "/home/"
    (file-parent-directory "/tmp/")
    ⇒ "/"
    (file-parent-directory "foo/bar")
    ⇒ "foo/"
    (file-parent-directory "foo")
    ⇒ "./"
    (file-parent-directory "/")
    ⇒ nil

Also, about the comparator to check if the input is already at top-level;
`file-equal-p` looks like the most comprehensive one, but it makes use of
`file-truename` which is reported to be slow; on the other hand for `f.el`,
`dired+.el`, just comparing two strings with `equal` is
sufficient.

So I wonder in this case, with both FILENAME and the found parent's names
expanded, we can opt to use `equal`/`string=` instead of `file-equal-p` for
better performance?

-- 
Daanturo.