Base-62 conversion in Emacs-Lisp

(defun my-int-to-base62 (integer &optional length)
  "Convert an INTEGER to a base-62 number represented as a string.
If LENGTH is given, pad the string with leading zeroes as needed
so the result is always that long or longer."
  (let ((s "")
        (i integer))
    (while (> i 0)
      (setq s (concat (char-to-string
                       (my-int-to-base62-one-char (mod i 62))) s)
            i (/ i 62)))
    (setq length (max 1 (or length 1)))
    (if (< (length s) length)
        (setq s (concat (make-string (- length (length s)) ?0) s)))
    s))

;; Workhorse for `my-int-to-base62'
(defun my-int-to-base62-one-char (integer)
  "Convert INTEGER between 0 and 61 into one character 0..9, a..z, A..Z."
  ;; Uses chars ?0, ?A, ?a off the ASCII table.  Evaluate those symbols and you
  ;; see important gaps between the character sets:
  ;; 0-9 has codes 48 thru 57
  ;; A-Z has codes 65 thru 90
  ;; a-z has codes 97 thru 122
  ;; Why compose chars to construct the final base62 string?  It's either
  ;; that, or you make a lookup string "0123456789abcdefg...", so you're
  ;; looking something up anyway.  The ASCII table is faster.
  (cond
   ((< integer 10) (+ ?0 integer))
   ((< integer 36) (+ ?a integer -10))
   ((< integer 62) (+ ?A integer -36))
   (t (error "Input was larger than 61"))))