bug#55395: What does (1 2 3 . #2) mean?

["Mattias Engdegård" <mattiase@acm.org>]

What, exactly, does the #N print notation mean (with print-circle=nil)?

Let's define (rho LEAD LOOP) as the iota list that has a loop LOOP long after LEAD initial elements:

(defun rho (lead loop)
  (let ((l (number-sequence 1 (+ lead loop))))
    (setcdr (nthcdr (+ lead loop -1) l) (nthcdr lead l))
    l))

Then we have:

(rho 0 1) => (1 . #0)
(rho 0 2) => (1 2 1 2 . #2)
(rho 0 3) => (1 2 3 1 2 . #2)
(rho 0 4) => (1 2 3 4 1 2 3 4 1 2 . #5)
(rho 0 5) => (1 2 3 4 5 1 2 3 4 5 1 . #5)
(rho 1 4) => (1 2 3 4 5 2 3 4 5 2 . #5)
(rho 4 1) => (1 2 3 4 5 5 5 . #3)

and so on. The pattern is not obvious to me.

It may have made more sense before the switch of cycle-detection algorithm from Floyd to Brent. This can be fixed by hand-coding the list iteration and explicitly remembering the index of the tortoise, but would that be correct? What's the spec?

If #N means 'Nth object from the top along the path to the current object, starting at 0' then we should have

(rho 2 3) => (1 2 3 4 5 . #2)
(list (rho 2 3)) => ((1 2 3 4 5 . #3))

ie, adding the print depth to the index in the list. Do you agree?