Exercise 5.14: Measure the number of pushes and
the maximum stack depth required to compute 
  
    n
    !
  
 for various small values of

  n
 using the factorial machine shown in Figure 5.11.  From your data
determine formulas in terms of 
  n
 for the total number of push operations
and the maximum stack depth used in computing 
  
    n
    !
  
 for any 
  
    n
    >
    1
  
. Note
that each of these is a linear function of 
  n
 and is thus determined by two
constants.  In order to get the statistics printed, you will have to augment
the factorial machine with instructions to initialize the stack and print the
statistics.  You may want to also modify the machine so that it repeatedly
reads a value for 
  n
, computes the factorial, and prints the result (as we
did for the GCD machine in Figure 5.4), so that you will not
have to repeatedly invoke get-register-contents,
set-register-contents!, and start.