Make scroll-{up, down} move point to {start, end} of newly visible text

[Spencer Baugh]

After I use scroll-up or scroll-down, I want to start reading the new
text on the screen.  But it's easy to lose track of where the new text
start, especially with larger values of next-screen-context-lines.

So, I would like scrolling to move point to the division between old and
new text.  Then the location of the cursor will help me keep track of
which text is new and which text is old.

Concretely, this means scroll-up should put point at the beginning of
the new text (and therefore at the end of the old text), and scroll-down
should put point at the end of the new text (and therefore at the
beginning of the old text).

Is this possible?

Alternative suggestions for how I can keep track of what text is new on
screen after scrolling are also appreciated.

I think I only want this for scroll-{up,down} and
scroll-other-window{,-down} but possibly it would make sense for other
commands which I don't know.

(I would file a bug requesting this feature, but scrolling is so
fundamental that perhaps this is already supported by some combination
of features which I don't know)