(sed.info)tail

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4.13 Printing the Last Lines
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Printing the last N lines rather than the first is more complex but
indeed possible.  N is encoded in the second line, before the bang
character.

   This script is similar to the `tac' script in that it keeps the
final output in the hold space and prints it at the end:

     #!/usr/bin/sed -nf

     1! {; H; g; }
     1,10 !s/[^\n]*\n//
     $p
     h

   Mainly, the scripts keeps a window of 10 lines and slides it by
adding a line and deleting the oldest (the substitution command on the
second line works like a `D' command but does not restart the loop).

   The "sliding window" technique is a very powerful way to write
efficient and complex `sed' scripts, because commands like `P' would
require a lot of work if implemented manually.

   To introduce the technique, which is fully demonstrated in the rest
of this chapter and is based on the `N', `P' and `D' commands, here is
an implementation of `tail' using a simple "sliding window."

   This looks complicated but in fact the working is the same as the
last script: after we have kicked in the appropriate number of lines,
however, we stop using the hold space to keep inter-line state, and
instead use `N' and `D' to slide pattern space by one line:

     #!/usr/bin/sed -f

     1h
     2,10 {; H; g; }
     $q
     1,9d
     N
     D

   Note how the first, second and fourth line are inactive after the
first ten lines of input.  After that, all the script does is: exiting
on the last line of input, appending the next input line to pattern
space, and removing the first line.