Answers to Self-Study Questions

Test Yourself #1

Part (a):

          +-------------------------------+
	  |  Enter                        |
          +-------------------------------+
	                   |
			   v
          +-------------------------------+
	  | L1:                           |
          |   read a                      |
          |   read x                      |
          |   ans = 1                     |
	  |   goto L2                     |
          +-------------------------------+
	                   |
			   v
          +-------------------------------+
	  | L2:                           |
          |   if (x > 0)                  |---------+
	  |   then goto L3                |         |
	  |   else goto L4                |<--+     |
          +-------------------------------+   |     |
	                   |                  |     |
			   v                  |     |
          +-------------------------------+   |     |
	  | L3:                           |   |     |
          |   ans = ans * a               |   |     |
          |   x = x - 1                   |---+     |
	  |   goto L2                     |         |
          +-------------------------------+         |
					            |
			       +--------------------+
			       |
			       |
			       v
          +-------------------------------+
	  | L4:                           |
          |   print ans                   |
	  |   goto Exit                   |         
          +-------------------------------+
			       |
			       v
          +-------------------------------+
	  |  Exit:                        |
	  |    return                     |
          +-------------------------------+

Part (b): Here is the trace of the execution of the PE algorithm.

Stmt S	Current bb	vs	Emitted Code
			<L1, (2)>
read a	L1	2	read a
read x
ans = 1			ans = 1
goto L2
if (x > 0) then goto L3 else goto L4	L2
ans = ans * a	L3		ans = ans * a
x = x - 1		1
goto L2
if (x > 0) then goto L3 else goto L4	L2
ans = ans * a	L3		ans = ans * a
x = x - 1		0
goto L2
if (x > 0) then goto L3 else goto L4	L2
print ans	L4		print ans

And here is the residual program:

read a
ans = 1
ans = ans * a
ans = ans * a
print ans

Test Yourself #2 and #3

Here is the CFG for the example program (in its high-level form), and the PDG for the high-level form.

Here is the low-level version of the program shown in its CFG form:

Assuming that the initial classification of the inputs is

Dynamic: array
Static: len (value = 3)

Dynamic: array, item, result
Static: len, n

Here is a trace of the PE algorithm:

Stmt S	Current bb	vs	Emitted Code
			<L1,(len:3, n:0)>
read array	L1	vs0 = (len:3, n:0)	read array
read len
n=0
result = 0			result = 0
goto L2
if (n < len) then goto L3 else goto L7	L2	vs0
item = array[n]	L3		item = array[0]
if(even(item)) then goto L4 else goto L5			if(even(item)) then goto <L4,vs0> else goto <L5, vs0>
			<L4, vs0>
result = result + item	L4	vs0	result = result + item
goto L6
n = n+1	L6	vs1 = (len:3,n:1)
goto L2
if (n < len) then goto L3 else goto L7	L2	vs1
item = array[n]	L3		item = array[1]
if(even(item)) then goto L4 else goto L5			if(even(item)) then goto <L4,vs1> else goto <L5, vs1>
			<L5, vs0>
result = result - item	L5	vs0	result = result - item
goto L6
n =n + 1	L6	vs1
goto L2
if (n < len) then goto L3 else goto L7	L2	vs1
item = array[n]	L3		item = array[1]
if(even(item)) then goto L4 else goto L5			if(even(item)) then goto <L4,vs2> else goto <L5, vs2>
			<L4,vs1>
result=result+item	L4	vs1	result = result + item
goto L6
n = n + 1	L6	vs2 = (len:3, n:2)
goto L2
if (n < len) then goto L3 else goto L7	L2	vs2
item = array[n]	L3	vs2	item = array[2]
if(even(item)) then goto L4 else goto L5			if(even(item)) then goto <L4,vs2> else goto <L5, vs2>
			<L5,vs1>
result = result - item	L5	vs1	result = result - item
goto L6
n = n + 1	L6	vs2
goto L2
if (n < len) then goto L3 else goto L7	L2	vs2
item = array[n]	L3	vs2	item = array[2]
if(even(item)) then goto L4 else goto L5			if(even(item)) then goto <L4,vs2> else goto <L5, vs2>
			<L4,vs2>
result = result + item	L4	vs2	result = result + item
goto L6
n =n + 1	L6	vs3 = (len:3,n:3)
goto L2
if (n < len) then goto L3 else goto L7	L2	vs3
print result	L7		print result
return			return
			<L5,vs2>
result = result - item	L5	vs2	result = result - item
goto L6
n =n + 1	L6	vs3
goto L2
if (n < len) then goto L3 else goto L7	L2	vs3
print result	L7		print result
return			return

And here is the residual program:

<L1, (len:3, n:0)>:
  read array
  result = 0
  item = array[0]
  if (even(item)) then goto <L4, (len:3, n:0)> else goto <L5, (len:3, n:0)>
<L4, (len:3, n:0>:
  result = result + item
  item = array[1]
  if (even(item)) then goto <L4, (len:3, n:1)> else goto <L5, (len:3, n:1)>
<L5, (len:3, n:0)>:
  result = result - item
  item = array[1]
  if (even(item)) then goto <L4, (len:3, n:2)> else goto <L5, (len:3, n:2)>
<L4, (len:3, n:1>:
  result = result + item
  item = array[2]
  if (even(item)) then goto <L4, (len:3, n:2)> else goto <L5, (len:3, n:2)>
<L5, (len:3, n:1)>:
  result = result - item
  item = array[2]
  if (even(item)) then goto <L4, (len:3, n:2)> else goto <L5, (len:3, n:2)>
<L4, (len:3, n:2>:
  result = result + item
  print result
  return
<L5, (len:3, n:2)>:
  result = result - item
  print result
  return