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(emacs-lisp-intro.info)rotate-yk-ptr remainder

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Using `%' in `rotate-yank-pointer'
..................................

   When the `kill-ring-yank-pointer' points to the beginning of the
kill ring, and the argument passed to `rotate-yank-pointer' is 1, the
`%' expression returns 1:

     (- length (length kill-ring-yank-pointer))
          => 0

therefore,

     (+ arg (- length (length kill-ring-yank-pointer)))
          => 1

and consequently:

     (% (+ arg (- length (length kill-ring-yank-pointer)))
        length)
          => 1

regardless of the value of `length'.

As a result of this, the `setq kill-ring-yank-pointer' expression
simplifies to:

     (setq kill-ring-yank-pointer (nthcdr 1 kill-ring))

What it does is now easy to understand.  Instead of pointing as it did
to the first element of the kill ring, the `kill-ring-yank-pointer' is
set to point to the second element.

   Clearly, if the argument passed to `rotate-yank-pointer' is two, then
the `kill-ring-yank-pointer' is set to `(nthcdr 2 kill-ring)'; and so
on for different values of the argument.

   Similarly, if the `kill-ring-yank-pointer' starts out pointing to
the second element of the kill ring, its length is shorter than the
length of the kill ring by 1, so the computation of the remainder is
based on the expression `(% (+ arg 1) length)'.  This means that the
`kill-ring-yank-pointer' is moved from the second element of the kill
ring to the third element if the argument passed to
`rotate-yank-pointer' is 1.