Register Allocation

1. Annotate the code below with liveness information, assuming {a,r} are live at the end.

   b = 5
   a = 2
   e = a * b
   f = a * c
   r = e + f
   a = r * r
   

   Answer:
   

             {c}
   b = 5
             {b,c}
   a = 2
             {a,b,c}
   e = a * b
             {e,a,c}
   f = a * c
             {e,f}
   r = e + f
             {r}
   a = r * r
             {a,r}
   

2. For the intermediate code and live sets from question 1, generate Spim code using three registers using the non-graph-coloring algorithm. Be sure to give the live register contents after the generated code, as seen for the first instruction.

   Answer:

   Statement	Code Generated	Register $t0	Register $t1	Register $t2
   b = 5	li $t0,5	b	-	-
   a = 2	li $t1,2	b	a	-
   e = a * b	mul $t0,$t1,$t0	e	a	-
   f = a * c	lw $t2,c mul $t2,$t1,$t2	e	-	f
   r = e + f	add $t0,$t0,$t2	r	-	-
   a = r * r	mul $t1,$t0,$t0	r	a	-
   	sw $t0,r sw $t1,a	-	-	-

3. Draw and 3-color the interference graph for the code from question 1.

   Answer:

   Graph:
   
   r ---- a --------- b
         / \         /
       /     \     /
      /        \  /
     e --------- c
      \
       \
        \
         f
   

   Can remove nodes in order: r,f,e,a,b,c (no marked spill nodes) and get colors/registers:

   (0)   (2)
   r ---- a --------- b (1)
         / \         /
       /     \     /
   (1)/        \  /
     e --------- c (0)
      \
       \
        \
         f (0)
   

4. Using the result of question 3, generate code allocating registers as assigned.

   Answer:

   Statement	Code Generated	Register $t0	Register $t1	Register $t2
   b = 5	li $t1,5	-	b	-
   a = 2	li $t2,2	-	b	a
   e = a * b	mul $t1,$t2,$t1	-	-	a
   f = a * c	lw $t0,c mul $t0,$t2,$t0	f	e	-
   r = e + f	add $t0,$t1,$t0	r	-	-
   a = r * r	mul $t2,$t0,$t0	r	-	a
   	sw $t0,r sw $t2,a	-	-	-