This article [2] has some interesting details on the swinging factorial function n≀, but I can't seem to find the essay that it references: "Swing, divide and conquer the factorial", 2008.

[1] https://projecteuler.net/

[2] https://oeis.org/A000142/a000142.pdf

If it runs fast there, it will run fast everywhere, as integers are made of Lisp conses on purpose, so you can see Lisp built from itself as if they were Peano axioms:

https://www.t3x.org/zsp/

  (require 'nmath)
  (gc)
  (define (fac n)
   (fi '#1  n))
  
  (define  (fi a n)
   (or  
   (and (= n '#0) 1) 
   (and (= n '#1) a)
    (and 
    (fi
     (* a n)
     (- n '#1)
      ))))
  
  
  (fac '#10)
  (fac '#0)

    -:cat fact.l | ./zl
     zenlisp 2013-11-22 by Nils M Holm
     => :t
     => '(#125434 #5638)
     => 'fac
     => 'fi
     => '#3628800
     => '1

    zenlisp 2013-11-22 by Nils M Holm
    => :t
    => '(#125434 #5638)
    => 'fac
    => 'fi
    => :t
    + (fi #1 #10)
    + (fi #10 #9)
    + (fi #90 #8)
    + (fi #720 #7)
    + (fi #5040 #6)
    + (fi #30240 #5)
    + (fi #151200 #4)
    + (fi #604800 #3)
    + (fi #1814400 #2)
    + (fi #3628800 #1)
    => '#3628800
    + (fi #1 #0)
    => '1

Integers are not actual integers, but lists.

'#3628800 it's '(3 6 2 8 8 0 0).

Open "nmath.l" to see how are digits implemented. Base.t it's interesting too, as it explains you some functions.