CMSC 430 Practice 3

These 3-address code instructions may be used in the follow-

ing questions:

3-addr Instruction Eect

load R1 x R1

x

store x R1 x

R1

add R1 R2 R3 R1

R2+R3

sub R1 R2 R3 R1

R2-R3

mult R1 R2 R3 R1

R2 * R3

1. Optimizations

(a) How can compiler transformations improve a pro-

gram?

(b) What does the compiler need to consider when ap-

plying optimizations?

(c) What are the dierent scopes of compiler optimiza-

tions? What are the tradeos when considering

what scope of optimizations to use?

2. Local optimizations

Consider the following code.

(1) a := 1

(2) b := f + a

(3) c := a

(4) d := f + a

(5) e := f + c

(6) f := b

(7) g := f + a

(a) Build a DAG for the code.

3. Control ow analysis

For the following problems, consider this code:

<S1> a := 1

<S2> b := 2

<S3> L1: c := a + b

<S4> d := c - a

<S5> if (...) goto L3

<S6> L2: d := b * d

<S7> if (...) goto L3

<S8> d := a + b

<S9> e := e + 1

<S10> goto L2

<S11> L3: b := a + b

<S12> e := c - a

<S13> if (...) goto L1

<S14> a := b * d

<S15> b := a - d

(a) What are the basic blocks?

(b) What is the control ow graph?

(c) Depth-rst order selects nodes in the order they

are visited (start by visiting the root node) and

then recursively visiting every child of each node

(if the child has not been visited before). Note that

the order in whichchildren are visited is random.

What are all the possible results of depth-rst traver-

sal on the control ow graph?

(d) Using depth-rst order, is it possible to visit a child

before its parent? For which depth-rst ordering(s)

of the control ow graph does this occur?

(e) Postorder selects nodes (starting from root)

after

visiting every child of that node (if the child has

not been visited before). Note that the order in

whichchildren are visited is random.

What are all the possible results of Postorder traver-

sal for the control ow graph?

(f) Reverse Postorder simply reverses the no de order-

ing found by a Postorder traversal of the graph.

What are the possible Reverse Postorder traver-

sals of the control ow graph?

(g) Using Reverse Postorder, is it possible to visit a

child before its parent? Whyorwhy not?

4. Reaching denitions

Reaching denitions

for a point in the program

p

is de-

ned as the set of denitions of a variable for which there

is some path from the denition to

p

with no other def-

inition of that variable. Calculate reaching denitions

for the code in the control-ow graph problem.

(a) What is the dataow equation for REACH?

(b) In what direction is REACH calculated? I.e., do es

information ow forwards or backwards in the CFG?

(c) Calculate GEN, KILL for each basic block.

(d) What is a good initial value for REACH for each

basic block?

(e) Solve the data-ow equations in reverse Postorder.

Showyour work.

5. Livevariables

Live variables

for a point in the program

p

is dened

as the set of variables

x

for which there is some path

from

p

to a use of

x

with no denition to

x

on the path.

Calculate livevariables for the code in the control-ow

graph problem.

(a) We dene LIVE(

b

) for a basic block

b

to be the

set of live variables at the end of

b

. What is the

dataow equation for LIVE?

(b) In what direction is LIVE calculated? I.e., do es in-

formation ow forwards or backwards in the CFG?

(c) Show GEN, KILL for each basic block.

(d) What is a good initial value for LIVE for each basic

block?

(e) Solve the data-ow equations in rPostorder. Show

your work.