memmove(s+1, s, 8);

it's usually desirable that after the copy
s[2] gets what s[1] had in it, not s[0]
(and so on).  just checking the initial pointers
is fractionally cheaper than the full check for overlap, but
is enough to guarantee safety.
i did find that on 386 it was better to do the full
check because the forward copy was much faster,
and the cheap check, though safe, meant that
arbitrarily many copies ended up taking the reverse-copy path,
just because of malloc outcomes (say).

overlapped copy was used on some architectures to
set whole buffers to a value having set the first byte, but it's
otherwise not usually what's desired.