Dataflow Analysis

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Challenge the future
Delft
University of
Technology
Course IN4303, 2016-2017
Compiler Construction
Guido Wachsmuth, Eelco ...

today’s lecture
Dataflow Analysis
Overview
Control flow graphs
• intermediate representation
2

today’s lecture
Dataflow Analysis
Overview
Control flow graphs
• intermediate representation
Non-local optimizations
• dea...

today’s lecture
Dataflow Analysis
Overview
Control flow graphs
• intermediate representation
Non-local optimizations
• dea...

today’s lecture
Dataflow Analysis
Overview
Control flow graphs
• intermediate representation
Non-local optimizations
• dea...

Term Rewriting
Optimizations
I
3

optimization
Dataflow Analysis
Optimizing Compilers
Fully optimizing compiler
• Opt(P) produces smallest program with same...

optimization
Dataflow Analysis
Local vs Non-Local Optimizations
Local optimizations
• peephole optimization
• constant fol...

optimization
Dataflow Analysis
Program Optimizations
Register allocation
• keep non-overlapping temporaries in same regist...

example
Dataflow Analysis
Dead Code Elimination
7
delete computation whose result will never be used
a ← 0
b ← a + 1
c ← c...

example
Dataflow Analysis
Dead Code Elimination
7
a ← 0
b ← a + 1
c ← c + b
return c
delete computation whose result will ...

example
Dataflow Analysis
Constant Propagation
8
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
return c
substitute reference to cons...

example
Dataflow Analysis
Constant Propagation
8
a ← 0
b ← 0 + 1
c ← c + b
a ← 2 * b
return c
a ← 0
b ← a + 1
c ← c + b
a ...

example
Dataflow Analysis
Constant Propagation + Folding
9
a ← 1
b ← a + 1
c ← c + b
a ← 2 * b
return c

example
Dataflow Analysis
Constant Propagation + Folding
9
a ← 0
b ← 2
c ← c + 2
a ← 4
return c
a ← 1
b ← a + 1
c ← c + b
...

example
Dataflow Analysis
Copy Propagation
10
a ← e
b ← a + 1
c ← c + b
a ← 2 * b
return c

example
Dataflow Analysis
Copy Propagation
10
a ← e
b ← e + 1
c ← c + b
a ← 2 * b
return c
a ← e
b ← a + 1
c ← c + b
a ← 2...

example
Dataflow Analysis
Common Subexpression Elimination
11
c ← a + b
d ← 1
e ← a + b
if expression is computed more tha...

example
Dataflow Analysis
Common Subexpression Elimination
11
c ← a + b
d ← 1
e ← a + b
x ← a + b
c ← x
d ← 1
e ← x
if exp...

optimization
Dataflow Analysis
Intraprocedural Global Optimization
Terminology
• Intraprocedural: within a single procedur...

Dataflow Analysis
Control-flow Graphs
II
13

quadruples
Dataflow Analysis
Intermediate Language
Store
a ← b ⊕ c
a ← b
Memory access
a ← M[b]
M[a] ← b
Functions
f(a1, …...

example
Dataflow Analysis
Control-Flow Graphs
15
a ← 0
L1: b ← a + 1
c ← c + b
a ← 2 * b
if a < N
goto L1
else
goto L2
L2:...

example
Dataflow Analysis
Control-Flow Graphs
15
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
a ← 0
L1: b ← a + 1...

terminology
Dataflow Analysis
Control-Flow Graphs
16
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c

terminology
Dataflow Analysis
Control-Flow Graphs
16
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
node

terminology
Dataflow Analysis
Control-Flow Graphs
16
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
node
in-edge

terminology
Dataflow Analysis
Control-Flow Graphs
16
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
node
in-edge
in...

terminology
Dataflow Analysis
Control-Flow Graphs
16
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
node
predecesso...

terminology
Dataflow Analysis
Control-Flow Graphs
16
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
node
predecesso...

terminology
Dataflow Analysis
Control-Flow Graphs
16
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
node
predecesso...

Dataflow Analysis
Liveness Analysis
III
17

definition
Dataflow Analysis
Liveness Analysis
Motivation: register allocation
• intermediate code with unbounded number o...

example
Dataflow Analysis
Register Allocation
19
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c

example
Dataflow Analysis
Register Allocation
19
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
{a, b} ! r
{c} ! q

example
Dataflow Analysis
Register Allocation
19
r ← 0
r ← r + 1
q ← q + r
r ← 2 * r
if r < N
return q
a ← 0
b ← a + 1
c ←...

a ← 0
return c
if a < N
b ← a + 1
a ← 2 * b
c ← c + b
example
Dataflow Analysis
Liveness Analysis
20

a ← 0
return c
if a < N
b ← a + 1
a ← 2 * b
c ← c + b
example
Dataflow Analysis
Liveness Analysis
20

a ← 0
return c
if a < N
b ← a + 1
a ← 2 * b
c ← c + b
example
Dataflow Analysis
Liveness Analysis
20

a ← 0
return c
if a < N
b ← a + 1
a ← 2 * b
c ← c + b
example
Dataflow Analysis
Liveness Analysis
20

a ← 0
return c
if a < N
b ← a + 1
a ← 2 * b
c ← c + b
example
Dataflow Analysis
Liveness Analysis
20

a ← 0
return c
if a < N
b ← a + 1
a ← 2 * b
c ← c + b
example
Dataflow Analysis
Liveness Analysis
20

a ← 0
return c
if a < N
b ← a + 1
a ← 2 * b
c ← c + b
example
Dataflow Analysis
Liveness Analysis
20

a ← 0
return c
if a < N
b ← a + 1
a ← 2 * b
c ← c + b
example
Dataflow Analysis
Liveness Analysis
20

a ← 0
return c
if a < N
b ← a + 1
a ← 2 * b
c ← c + b
example
Dataflow Analysis
Liveness Analysis
20

a ← 0
return c
if a < N
b ← a + 1
a ← 2 * b
c ← c + b
example
Dataflow Analysis
Liveness Analysis
20

a ← 0
return c
if a < N
b ← a + 1
a ← 2 * b
c ← c + b
example
Dataflow Analysis
Liveness Analysis
20

definitions
Dataflow Analysis
Liveness Analysis
Def and use
• an assignment to a variable defines a variable
• an occurren...

terminology
Dataflow Analysis
Liveness Analysis
22
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c

terminology
Dataflow Analysis
Liveness Analysis
22
definition a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c

terminology
Dataflow Analysis
Liveness Analysis
22
usage
definition a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c

terminology
Dataflow Analysis
Liveness Analysis
22
usage
definition
definition
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < ...

terminology
Dataflow Analysis
Liveness Analysis
22
usage
definition
usage
definition
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
i...

terminology
Dataflow Analysis
Liveness Analysis
22
usage
definition
usage
definition
live-in
a ← 0
b ← a + 1
c ← c + b
a ←...

terminology
Dataflow Analysis
Liveness Analysis
22
usage
definition
usage
definition
live-in
live-out
a ← 0
b ← a + 1
c ← ...

terminology
Dataflow Analysis
Liveness Analysis
22
usage
definition
usage
definition
live-in
live-in
live-out
a ← 0
b ← a ...

terminology
Dataflow Analysis
Liveness Analysis
22
usage
definition
usage
definition
live-in
live-out
live-in
live-out
a ←...

terminology
Dataflow Analysis
Liveness Analysis
22
usage
definition
usage
definition
live-in
live-out
live-out
live-in
liv...

formalization
Dataflow Analysis
Liveness Analysis
in[n] = use[n] ∪ (out[n] - def[n])
out[n] = ∪s∈succ[n] in[s]
1. If a var...

algorithm
Dataflow Analysis
Liveness Analysis
for each n
in[n] ← {} ; out[n] ← {}
repeat
for each n
in'[n] = in[n] ; out'[...

example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
1
2
3
4
5...

example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
1
2
3
4
5...

example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
1
2
3
4
5...

example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
1
2
3
4
5...

example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
1
2
3
4
5...

example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
1
2
3
4
5...

example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
1
2
3
4
5...

example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
1
2
3
4
5...

example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
1
2
3
4
5...

optimization
Dataflow Analysis
Liveness Analysis
26
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
6
5
...

optimization
Dataflow Analysis
Liveness Analysis
26
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
6
5
...

optimization
Dataflow Analysis
Liveness Analysis
26
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
6
5
...

optimization
Dataflow Analysis
Liveness Analysis
26
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
6
5
...

optimization
Dataflow Analysis
Liveness Analysis
26
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
3
4
5
6
6
5
...

generalisation
Dataflow Analysis
Liveness Analysis
27
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c

generalisation
Dataflow Analysis
Liveness Analysis
27
kill a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c

generalisation
Dataflow Analysis
Liveness Analysis
27
gen
kill a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c

generalisation
Dataflow Analysis
Liveness Analysis
27
gen
kill
kill
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c

generalisation
Dataflow Analysis
Liveness Analysis
27
gen
kill
gen
kill
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
retur...

generalisation
Dataflow Analysis
Liveness Analysis
27
gen
kill
gen
kill
in
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
re...

generalisation
Dataflow Analysis
Liveness Analysis
27
gen
kill
gen
kill
in
out
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < ...

generalisation
Dataflow Analysis
Liveness Analysis
27
gen
kill
gen
kill
in
out
out
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if ...

generalisation
Dataflow Analysis
Liveness Analysis
27
gen
kill
gen
kill
in
out
out
in
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
...

generalisation
Dataflow Analysis
Liveness Analysis
27
gen
kill
gen
kill
in
out
out
in
out
a ← 0
b ← a + 1
c ← c + b
a ← 2 ...

gen & kill
Dataflow Analysis
Liveness Analysis
28
a ← b ⊕ c
a ← b
a ← M[b]
M[a] ← b
f(a1, …, an)
a ← f(a1, …, an)
goto L
i...

gen & kill
Dataflow Analysis
Liveness Analysis
28
a ← b ⊕ c
a ← b
a ← M[b]
M[a] ← b
f(a1, …, an)
a ← f(a1, …, an)
goto L
i...

generalisation
Dataflow Analysis
Liveness Analysis
in[n] = gen[n] ∪ (out[n] - kill[n])
out[n] = ∪s∈succ[n] in[s]
29

Dataflow Analysis
More Analyses
IV
30

definition
Dataflow Analysis
Reaching Definitions
Unambiguous definition of a
• a statement of the form (d : a ← b ⊕ c) or...

example
Dataflow Analysis
Reaching Definitions
32
a ← 5
c ← 1
if c > a
c ← c + c
goto 3
a ← c - a
1
2
3
4
5
6

gen & kill
Dataflow Analysis
Reaching Definitions
33
d: a ← b ⊕ c
d: a ← b
d: a ← M[b]
M[a] ← b
f(a1, …, an)
d: a ← f(a1, ...

gen & kill
Dataflow Analysis
Reaching Definitions
33
d: a ← b ⊕ c
d: a ← b
d: a ← M[b]
M[a] ← b
f(a1, …, an)
d: a ← f(a1, ...

formalisation
Dataflow Analysis
Reaching Definitions
in[n] = ∪p∈pred[n] out[p]
out[n] = gen[n] ∪ (in[n] - kill[n])
34

definition
Dataflow Analysis
Available Expressions
An expression (b ⊕ c) is available at node n if
• on every path from th...

example
Dataflow Analysis
Available Expressions
36
c ← a + b
d ← 1
e ← a + b
1
2
3

gen & kill
Dataflow Analysis
Available Expressions
37
d: a ← b ⊕ c
d: a ← b
d: a ← M[b]
M[a] ← b
f(a1, …, an)
d: a ← f(a1,...

gen & kill
Dataflow Analysis
Available Expressions
37
d: a ← b ⊕ c
d: a ← b
d: a ← M[b]
M[a] ← b
f(a1, …, an)
d: a ← f(a1,...

formalisation
Dataflow Analysis
Available Expressions
in[n] = ∩p∈pred[n] out[p]
out[n] = gen[n] ∪ (in[n] - kill[n])
38

definition
Dataflow Analysis
Reaching Expressions
An expression (s : a ← b ⊕ c) reaches node n if
• there is a path from s...

Dataflow Analysis
Optimizations
V
40

example
Dataflow Analysis
Dead Code Elimination
41
a ← 0
b ← a + 1
c ← c + b
return c
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
...

example
Dataflow Analysis
Common Subexpression Elimination
42
c ← a + b
d ← 1
e ← a + b
x ← a + b
c ← x
d ← 1
e ← x
consid...

example
Dataflow Analysis
Constant Propagation
43
a ← 0
b ← 0 + 1
c ← c + b
a ← 2 * b
return c
a ← 0
b ← a + 1
c ← c + b
a...

example
Dataflow Analysis
Copy Propagation
44
a ← e
b ← e + 1
c ← c + b
a ← 2 * b
return c
a ← e
b ← a + 1
c ← c + b
a ← 2...

Term Rewriting
Summary
V
45

Dataflow Analysis
Summary
Liveness analysis
• intermediate language
• control-flow graphs
• definition & algorithm
More da...

learn more
Dataflow Analysis
Literature
Andrew W. Appel, Jens Palsberg: Modern Compiler Implementation in
Java, 2nd editio...

Dataflow Analysis
Copyrights & Credits
48

Dataflow Analysis 49

copyrights
Dataflow Analysis
Pictures
Slide 1:
ink swirl by Graham Richardson, some rights reserved
Slide 25:
Seattle's Be...

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