CS 132 Fall 2004, Final Solution
================================

Question 1
----------
Symboltable:

  Name | Information
  ----------------------
    B  | superclass: <none>
       | fields:  Name Type
       |            f    B
       | methods: Name Information
       |            m    args:   Name Type
       |                           a   int
       |                 result type: void
       |                 locals: <none>
    C  | superclass: B
       | fields:  Name Type
       |            g    C
       | methods: Name Information
       |            m    args:   Name Type
       |                           a   int
       |                 result type: void
       |                 locals: Name Type
       |                           j   int
       |            p    args:   <none>
       |                 result type: int
       |                 locals: <none>

Question 2
----------
Heap layout for a C-object:       /-----\
                              --->| mt ------->/---\
                                  |  f  |      | m |
                                  |  g  |      | p |
                                  \-----/      \___/

Piglet code for the body of the method m in class C:

// TEMP 0 : this
// TEMP 1 : a
// TEMP 2 : j
// TEMP 100 : the result of the translation of new B()
// TEMP 101 : the method table to for B-object
// TEMP 102 : the method table for the object to call
// TEMP 103 : the procedure name to call
// TEMP 104 : dummy variable to allow the grammar

C_m[2]
BEGIN
  MOVE TEMP 2 1
  CJUMP  LT 0 TEMP 1   ELSE
  MOVE TEMP 2   PLUS TEMP 1 1

  HSTORE TEMP 0
    4
    BEGIN
      MOVE TEMP 101 HALLOCATE 4
      HSTORE TEMP 101 0 B_m
      MOVE TEMP 100 HALLOCATE 8
      HSTORE TEMP 100 0 TEMP 101
      HSTORE TEMP 100 4 0
      HSTORE TEMP 100 8 0
    RETURN TEMP 100
    END

  HLOAD TEMP 102 TEMP 0 0
  HLOAD TEMP 103 TEMP 102 0
  MOVE TEMP 104 CALL TEMP 103 ( TEMP 0   MINUS TIMES TEMP 2 TEMP 1 1  )
  JUMP ENDD
ELSE   HSTORE TEMP 0 8 TEMP 0
ENDD   NOOP
  RETURN 0
END


Question 3
----------

A MIPS stack layout for the method m in class C:

  /-----------\
  |   this    |
  |     a     |
  |  ret addr |
  |     j     |
  |  TEMP 3   |
  |  TEMP 4   |
  |  TEMP 5   |
  |  TEMP 6   |
  |  callee   |
  |    save   |
  |    regs   |
  \-----------/

Hopefully this and a can be passed in the a-registers,
and hopefully register allocation will take care of allocating
TEMP 3-6 in registers.  Similarly, we may be able to pass
the ret addr in the ra-register.

Question 4
----------

      y |
        >
         i = 0
    i y |
        >
         a = 1
  a i y |
        >
         if y < 0 then goto L1
    a y |        |
        >        | a i
         i = y   |
    a i |        |
        >        >
    L1:  a = a + i <
    a i |            \
        >            | a i
         i = i + 1   |
    a i |            |
        >            |
         if i < 100 then goto L1
      a |
        >
         return a

Question 5
----------
Colored interference graph:

   ___________
  /           \
  |            |
  | d(1)     a(1)
  |  |  \   / 
  \  |   b(2)
   \ |  / | \ 
    c(3)  |  f(4)
     |  \ |  / |
     |   e(1)  |
     |         |
     \_________/

The program after register allocation:

      r1 = 1
      r2 = 10
      r3 = 9 + r1
      r1 = r1 + r3
      r1 = r3 + r1
      r4 = r2 + 8
      r3 = r4 + r1
      r4 = r1 + r3
      r2 = r3 + 5
      return r2+r4

Question 6
----------
Three registers:
      a:1
      b:2
      c:3
      a expires 
      d:1
      d expires
      e:1
      f spilled

      r1 = 1
      r2 = 10
      r3 = 9 + r1
      r1 = r1 + r3
      r1 = r3 + r1
       f = r2 + 8
      r3 =  f + r1
       f = r1 + r3
      r2 = r3 + 5
      return r2+f

Two registers:
      a:1
      b:2
      b spilled  // because b's live range ends last
      c:2 
      a expires
      d:1
      d expires
      e:1
      f:spilled

      s1 = 1
       b = 10
      s2 =  9 + s1
      s1 = s1 + s2
      s1 = s2 + s1
       f =  b + 8
      s2 =  f + s1
       f = s1 + s2
       b = s2 + 5
      return b+f