Chapter 5, Computing with Register Machines

Exercise 5.27


As in last exercise, let’s first see some results for various values of n:

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;;; EC-Eval input:
(factorial 1)

(total-pushes = 3 maximum-depth = 3)
;;; EC-Eval value:
ok

;;; EC-Eval input:

(total-pushes = 16 maximum-depth = 8)
;;; EC-Eval value:
1

;;; EC-Eval input:
(factorial 2)

(total-pushes = 48 maximum-depth = 13)
;;; EC-Eval value:
2

;;; EC-Eval input:
(factorial 3)

(total-pushes = 80 maximum-depth = 18)
;;; EC-Eval value:
6

;;; EC-Eval input:
(factorial 4)

(total-pushes = 112 maximum-depth = 23)
;;; EC-Eval value:
24

;;; EC-Eval input:
(factorial 5)

(total-pushes = 144 maximum-depth = 28)
;;; EC-Eval value:
120

;;; EC-Eval input:
(factorial 6)

(total-pushes = 176 maximum-depth = 33)
;;; EC-Eval value:
720

;;; EC-Eval input:

Clearly the formulae is:

and

Thus we get the following table:

  Maximum depth Number of pushes
Recursive factorial
Iterative factorial