Presentation slides for lecture 8 of course IN4303 on Compiler Construction at TU Delft.

1. Dataflow Analysis
Guido Wachsmuth
Delft
Course IN4303, 2012/13
University of
Technology Compiler Construction
Challenge the future

2. Overview
today’s lecture
control flow graphs
Dataflow Analysis 2

3. Overview
today’s lecture
control flow graphs
data flow analyses
• liveness analysis
• reaching definitions
• available expressions
Dataflow Analysis 2

4. Overview
today’s lecture
control flow graphs
data flow analyses
• liveness analysis
• reaching definitions
• available expressions
non-local optimisations
• dead code elimination
• constant & copy propagation
• common subexpression elimination
Dataflow Analysis 2

5. I
control-flow graphs
Dataflow Analysis 3

6. Intermediate language
quadruples
store jumps
a ← b ⊕ c L:
a ← b goto L
if a ⊗ b
memory access
goto L1
a ← M[b]
else
M[a] ← b
goto L2
functions
f(a1, …, an)
b ← f(a1, …, an)
Dataflow Analysis 4

7. Control-flow graphs
example
a ← 0
L1: b ← a + 1
c ← c + b
a ← 2 * b
if a < N
goto L1
else
goto L2
L2: return c
Dataflow Analysis 5

8. Control-flow graphs
example
a ← 0 a ← 0
L1: b ← a + 1
b ← a + 1
c ← c + b
a ← 2 * b c ← c + b
if a < N
goto L1 a ← 2 * b
else
if a < N
goto L2
L2: return c return c
Dataflow Analysis 5

9. Control-flow graphs
terminology
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 6

10. Control-flow graphs
terminology
a ← 0
node b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 6

11. Control-flow graphs
terminology
a ← 0
in-edge
node b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 6

12. Control-flow graphs
terminology
a ← 0
in-edge
node b ← a + 1
c ← c + b
in-edge
a ← 2 * b
if a < N
return c
Dataflow Analysis 6

13. Control-flow graphs
terminology
predecessor a ← 0
in-edge
node b ← a + 1
c ← c + b
in-edge
a ← 2 * b
predecessor if a < N
return c
Dataflow Analysis 6

14. Control-flow graphs
terminology
predecessor a ← 0
in-edge
node b ← a + 1
out-edge
c ← c + b
in-edge
a ← 2 * b
predecessor if a < N
return c
Dataflow Analysis 6

15. Control-flow graphs
terminology
predecessor a ← 0
in-edge
node b ← a + 1
out-edge
successor c ← c + b
in-edge
a ← 2 * b
predecessor if a < N
return c
Dataflow Analysis 6

16. II
liveness analysis
Dataflow Analysis 7

17. Liveness analysis
terminology
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 8

18. Liveness analysis
terminology
definition a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 8

19. Liveness analysis
terminology
definition a ← 0
usage b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 8

20. Liveness analysis
terminology
definition a ← 0
usage b ← a + 1
c ← c + b
definition a ← 2 * b
if a < N
return c
Dataflow Analysis 8

21. Liveness analysis
terminology
definition a ← 0
usage b ← a + 1
c ← c + b
definition a ← 2 * b
usage if a < N
return c
Dataflow Analysis 8

22. Liveness analysis
terminology
definition a ← 0
usage b ← a + 1
c ← c + b
definition a ← 2 * b
live-in
usage if a < N
return c
Dataflow Analysis 8

23. Liveness analysis
terminology
definition a ← 0
usage b ← a + 1
c ← c + b
definition a ← 2 * b
live-out
live-in
usage if a < N
return c
Dataflow Analysis 8

24. Liveness analysis
terminology
definition a ← 0
live-in
usage b ← a + 1
c ← c + b
definition a ← 2 * b
live-out
live-in
usage if a < N
return c
Dataflow Analysis 8

25. Liveness analysis
terminology
definition a ← 0
live-in
usage b ← a + 1
c ← c + b
definition a ← 2 * b
live-out
live-in
usage if a < N
live-out
return c
Dataflow Analysis 8

26. Liveness analysis
terminology
definition a ← 0 live-out
live-in
usage b ← a + 1
c ← c + b
definition a ← 2 * b
live-out
live-in
usage if a < N
live-out
return c
Dataflow Analysis 8

27. Liveness analysis
example
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 9

28. Liveness analysis
example
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 9

29. Liveness analysis
example
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 9

30. Liveness analysis
example
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 9

31. Liveness analysis
example
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 9

32. Liveness analysis
example
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 9

33. Liveness analysis
example
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 9

34. Liveness analysis
example
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 9

35. Liveness analysis
example
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 9

36. Liveness analysis
example
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 9

37. Liveness analysis
example
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 9

38. Liveness analysis
formalisation
in[n] = use[n] ∪ (out[n] - def[n])
out[n] = ∪ s∈succ[n] in[s]
1. If a variable is used at node n, then it is live-in at n.
2. If a variable is live-out but not defined at node n, it is live-in at n.
3. If a variable is live-in at node n, then it is live-out at its predecessors.
Dataflow Analysis 10

39. Liveness analysis
algorithm
for each n
in[n] ← {} ; out[n] ← {}
repeat
for each n
in'[n] = in[n] ; out'[n] = out[n]
in[n] = use[n] ∪ (out[n] - def[n])
for each s in succ[n]
out[n] = out[n] ∪ in[s]
until
for all n: in[n] = in'[n] and out[n] = out'[n]
Dataflow Analysis 11

40. Liveness analysis
example
1a ← 0 1 2 3 4 5 6 7
u d i o i o i o i o i o i o i o
2b ← a + 1
1 a a a ac c ac c ac c ac
3c ← c + b 2 a b a a bc ac bc ac bc ac bc ac bc ac bc
3 bc c bc bc b bc b bc b bc b bc bc bc bc
4a ← 2 * b
4 b a b b a b a b ac bc ac bc ac bc ac
5 if a < N 5 a a a a ac ac ac ac ac ac ac ac ac ac ac
6 c c c c c c c c
6 return c
Dataflow Analysis 12

41. Liveness analysis
example
1a ← 0 1 2 3 4 5 6 7
u d i o i o i o i o i o i o i o
2b ← a + 1
1 a a a ac c ac c ac c ac
3c ← c + b 2 a b a a bc ac bc ac bc ac bc ac bc ac bc
3 bc c bc bc b bc b bc b bc b bc bc bc bc
4a ← 2 * b
4 b a b b a b a b ac bc ac bc ac bc ac
5 if a < N 5 a a a a ac ac ac ac ac ac ac ac ac ac ac
6 c c c c c c c c
6 return c
Dataflow Analysis 12

42. Liveness analysis
example
1a ← 0 1 2 3 4 5 6 7
u d i o i o i o i o i o i o i o
2b ← a + 1
1 a a a ac c ac c ac c ac
3c ← c + b 2 a b a a bc ac bc ac bc ac bc ac bc ac bc
3 bc c bc bc b bc b bc b bc b bc bc bc bc
4a ← 2 * b
4 b a b b a b a b ac bc ac bc ac bc ac
5 if a < N 5 a a a a ac ac ac ac ac ac ac ac ac ac ac
6 c c c c c c c c
6 return c
Dataflow Analysis 12

43. Liveness analysis
example
1a ← 0 1 2 3 4 5 6 7
u d i o i o i o i o i o i o i o
2b ← a + 1
1 a a a ac c ac c ac c ac
3c ← c + b 2 a b a a bc ac bc ac bc ac bc ac bc ac bc
3 bc c bc bc b bc b bc b bc b bc bc bc bc
4a ← 2 * b
4 b a b b a b a b ac bc ac bc ac bc ac
5 if a < N 5 a a a a ac ac ac ac ac ac ac ac ac ac ac
6 c c c c c c c c
6 return c
Dataflow Analysis 12

44. Liveness analysis
example
1a ← 0 1 2 3 4 5 6 7
u d i o i o i o i o i o i o i o
2b ← a + 1
1 a a a ac c ac c ac c ac
3c ← c + b 2 a b a a bc ac bc ac bc ac bc ac bc ac bc
3 bc c bc bc b bc b bc b bc b bc bc bc bc
4a ← 2 * b
4 b a b b a b a b ac bc ac bc ac bc ac
5 if a < N 5 a a a a ac ac ac ac ac ac ac ac ac ac ac
6 c c c c c c c c
6 return c
Dataflow Analysis 12

45. Liveness analysis
example
1a ← 0 1 2 3 4 5 6 7
u d i o i o i o i o i o i o i o
2b ← a + 1
1 a a a ac c ac c ac c ac
3c ← c + b 2 a b a a bc ac bc ac bc ac bc ac bc ac bc
3 bc c bc bc b bc b bc b bc b bc bc bc bc
4a ← 2 * b
4 b a b b a b a b ac bc ac bc ac bc ac
5 if a < N 5 a a a a ac ac ac ac ac ac ac ac ac ac ac
6 c c c c c c c c
6 return c
Dataflow Analysis 12

46. Liveness analysis
example
1a ← 0 1 2 3 4 5 6 7
u d i o i o i o i o i o i o i o
2b ← a + 1
1 a a a ac c ac c ac c ac
3c ← c + b 2 a b a a bc ac bc ac bc ac bc ac bc ac bc
3 bc c bc bc b bc b bc b bc b bc bc bc bc
4a ← 2 * b
4 b a b b a b a b ac bc ac bc ac bc ac
5 if a < N 5 a a a a ac ac ac ac ac ac ac ac ac ac ac
6 c c c c c c c c
6 return c
Dataflow Analysis 12

47. Liveness analysis
example
1a ← 0 1 2 3 4 5 6 7
u d i o i o i o i o i o i o i o
2b ← a + 1
1 a a a ac c ac c ac c ac
3c ← c + b 2 a b a a bc ac bc ac bc ac bc ac bc ac bc
3 bc c bc bc b bc b bc b bc b bc bc bc bc
4a ← 2 * b
4 b a b b a b a b ac bc ac bc ac bc ac
5 if a < N 5 a a a a ac ac ac ac ac ac ac ac ac ac ac
6 c c c c c c c c
6 return c
Dataflow Analysis 12

48. Liveness analysis
example
1a ← 0 1 2 3 4 5 6 7
u d i o i o i o i o i o i o i o
2b ← a + 1
1 a a a ac c ac c ac c ac
3c ← c + b 2 a b a a bc ac bc ac bc ac bc ac bc ac bc
3 bc c bc bc b bc b bc b bc b bc bc bc bc
4a ← 2 * b
4 b a b b a b a b ac bc ac bc ac bc ac
5 if a < N 5 a a a a ac ac ac ac ac ac ac ac ac ac ac
6 c c c c c c c c
6 return c
Dataflow Analysis 12

49. Liveness analysis
optimisation
1a ← 0 1 2 3
u d o i o i o i
2b ← a + 1
6 c c c c
3c ← c + b 5 a c ac ac ac ac ac
4 b a ac bc ac bc ac bc
4a ← 2 * b
3 bc c bc bc bc bc bc bc
5 if a < N 2 a b bc ac bc ac bc ac
1 a ac a ac c ac c
6 return c
Dataflow Analysis 13

50. Liveness analysis
optimisation
1a ← 0 1 2 3
u d o i o i o i
2b ← a + 1
6 c c c c
3c ← c + b 5 a c ac ac ac ac ac
4 b a ac bc ac bc ac bc
4a ← 2 * b
3 bc c bc bc bc bc bc bc
5 if a < N 2 a b bc ac bc ac bc ac
1 a ac a ac c ac c
6 return c
Dataflow Analysis 13

51. Liveness analysis
optimisation
1a ← 0 1 2 3
u d o i o i o i
2b ← a + 1
6 c c c c
3c ← c + b 5 a c ac ac ac ac ac
4 b a ac bc ac bc ac bc
4a ← 2 * b
3 bc c bc bc bc bc bc bc
5 if a < N 2 a b bc ac bc ac bc ac
1 a ac a ac c ac c
6 return c
Dataflow Analysis 13

52. Liveness analysis
optimisation
1a ← 0 1 2 3
u d o i o i o i
2b ← a + 1
6 c c c c
3c ← c + b 5 a c ac ac ac ac ac
4 b a ac bc ac bc ac bc
4a ← 2 * b
3 bc c bc bc bc bc bc bc
5 if a < N 2 a b bc ac bc ac bc ac
1 a ac a ac c ac c
6 return c
Dataflow Analysis 13

53. Liveness analysis
optimisation
1a ← 0 1 2 3
u d o i o i o i
2b ← a + 1
6 c c c c
3c ← c + b 5 a c ac ac ac ac ac
4 b a ac bc ac bc ac bc
4a ← 2 * b
3 bc c bc bc bc bc bc bc
5 if a < N 2 a b bc ac bc ac bc ac
1 a ac a ac c ac c
6 return c
Dataflow Analysis 13

54. Liveness analysis
generalisation
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 14

55. Liveness analysis
generalisation
kill a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 14

56. Liveness analysis
generalisation
kill a ← 0
gen b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
Dataflow Analysis 14

57. Liveness analysis
generalisation
kill a ← 0
gen b ← a + 1
c ← c + b
kill a ← 2 * b
if a < N
return c
Dataflow Analysis 14

58. Liveness analysis
generalisation
kill a ← 0
gen b ← a + 1
c ← c + b
kill a ← 2 * b
gen if a < N
return c
Dataflow Analysis 14

59. Liveness analysis
generalisation
kill a ← 0
in
gen b ← a + 1
c ← c + b
kill a ← 2 * b
gen if a < N
return c
Dataflow Analysis 14

60. Liveness analysis
generalisation
kill a ← 0 out
in
gen b ← a + 1
c ← c + b
kill a ← 2 * b
gen if a < N
return c
Dataflow Analysis 14

61. Liveness analysis
generalisation
kill a ← 0 out
in
gen b ← a + 1
c ← c + b
kill a ← 2 * b
gen if a < N
out
return c
Dataflow Analysis 14

62. Liveness analysis
generalisation
kill a ← 0 out
in
gen b ← a + 1
c ← c + b
kill a ← 2 * b
in
gen if a < N
out
return c
Dataflow Analysis 14

63. Liveness analysis
generalisation
kill a ← 0 out
in
gen b ← a + 1
c ← c + b
kill a ← 2 * b
out
in
gen if a < N
out
return c
Dataflow Analysis 14

64. Liveness analysis
gen & kill
gen kill
a ← b ⊕ c {b,c} {a}
a ← b {b} {a}
a ← M[b] {b} {a}
M[a] ← b {a,b}
f(a1, …, an) {a1,…,an}
a ← f(a1, …, an) {a1,…,an} {a}
goto L
if a ⊗ b {a,b}
Dataflow Analysis 15

65. Liveness analysis
gen & kill
gen kill
a ← b ⊕ c {b,c} {a}
a ← b {b} {a}
a ← M[b] {b} {a}
M[a] ← b {a,b}
f(a1, …, an) {a1,…,an}
a ← f(a1, …, an) {a1,…,an} {a}
goto L
if a ⊗ b {a,b}
Dataflow Analysis 15

66. Liveness analysis
generalisation
in[n] = gen[n] ∪ (out[n] - kill[n])
out[n] = ∪ s∈succ[n] in[s]
Dataflow Analysis 16

67. coffee break
Dataflow Analysis 17

68. III
more analyses
Dataflow Analysis 18

69. More analyses
reaching definitions
1a ← 5
2c ← 1
3 if c > a
4c ← c + c
5 goto 3
6a ← c - a
Dataflow Analysis 19

70. Reaching definitions
gen & kill
gen kill
d: a ← b ⊕ c {d} defs(a)-{d}
d: a ← b {d} defs(a)-{d}
d: a ← M[b] {d} defs(a)-{d}
M[a] ← b
f(a1, …, an)
d: a ← f(a1, …, an) {d} defs(a)-{d}
goto L
if a ⊗ b
Dataflow Analysis 20

71. Reaching definitions
gen & kill
gen kill
d: a ← b ⊕ c {d} defs(a)-{d}
d: a ← b {d} defs(a)-{d}
d: a ← M[b] {d} defs(a)-{d}
M[a] ← b
f(a1, …, an)
d: a ← f(a1, …, an) {d} defs(a)-{d}
goto L
if a ⊗ b
Dataflow Analysis 20

72. Reaching definitions
formalisation
in[n] = ∪
p∈pred[n] out[p]
out[n] = gen[n] ∪ (in[n] - kill[n])
Dataflow Analysis 21

73. More analyses
available expressions
1c ← a + b
2d ← 1
3e ← a + b
Dataflow Analysis 22

74. Available expressions
gen & kill
gen kill
d: a ← b ⊕ c {b⊕c}-kill exps(a)
d: a ← b
d: a ← M[b] {M[b]}-kill exps(a)
M[a] ← b exps(M[_])
f(a1, …, an) exps(M[_])
d: a ← f(a1, …, an) exps(M[_]) ∪ exps(a)
goto L
if a ⊗ b
Dataflow Analysis 23

75. Available expressions
gen & kill
gen kill
d: a ← b ⊕ c {b⊕c}-kill exps(a)
d: a ← b
d: a ← M[b] {M[b]}-kill exps(a)
M[a] ← b exps(M[_])
f(a1, …, an) exps(M[_])
d: a ← f(a1, …, an) exps(M[_]) ∪ exps(a)
goto L
if a ⊗ b
Dataflow Analysis 23

76. Available expressions
formalisation
in[n] = ∩
p∈pred[n] out[p]
out[n] = gen[n] ∪ (in[n] - kill[n])
Dataflow Analysis 24

77. IV
optimisations
Term Rewriting 25

78. Dead code elimination
example
a ← 0 a ← 0
b ← a + 1 b ← a + 1
c ← c + b c ← c + b
a ← 2 * b return c
return c
Dataflow Analysis 26

79. Constant propagation
example
a ← 0 a ← 0
b ← a + 1 b ← 0 + 1
c ← c + b c ← c + b
a ← 2 * b a ← 2 * b
return c return c
Dataflow Analysis 27

80. Copy propagation
example
a ← e a ← e
b ← a + 1 b ← e + 1
c ← c + b c ← c + b
a ← 2 * b a ← 2 * b
return c return c
Dataflow Analysis 28

81. Common subexpression elimination
example
c ← a + b x ← a + b
d ← 1 c ← x
e ← a + b d ← 1
e ← x
Dataflow Analysis 29

82. V
summary
Term Rewriting 30

83. Summary
lessons learned
liveness analysis
• intermediate language
• control-flow graphs
• definition & algorithm
more dataflow analyses
• reaching definitions
• available expressions
optimisations
Dataflow Analysis 31

84. Literature
learn more
Andrew W. Appel, Jens Palsberg: Modern Compiler
Implementation in Java, 2nd edition. 2002
Dataflow Analysis 32

85. copyrights & credits
Dataflow Analysis 33

86. Dataflow Analysis 34

87. Pictures
copyrights
Slide 1:
ink swirl by Graham Richardson, some rights reserved
Slide 25:
Seattle's Best Coffee by Dominica Williamson, some rights reserved
Slide 32:
Animal Ark Reno by Joel Riley, some rights reserved
Dataflow Analysis 35