Challenge the future Delft University of Technology Course IN4303, 2016-2017 Compiler Construction Guido Wachsmuth, Eelco Visser Dataflow Analysis
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Challenge the future
Delft University of Technology
Course IN4303, 2016-2017 Compiler Construction
Guido Wachsmuth, Eelco Visser
Dataflow Analysis
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
• dead code elimination
• constant & copy propagation
• common subexpression elimination
2
today’s lecture
Dataflow Analysis
Overview
Control flow graphs
• intermediate representation
Non-local optimizations
• dead code elimination
• constant & copy propagation
• common subexpression elimination
Data flow analyses
• liveness analysis
• reaching definitions
• available expressions
2
today’s lecture
Dataflow Analysis
Overview
Control flow graphs
• intermediate representation
Non-local optimizations
• dead code elimination
• constant & copy propagation
• common subexpression elimination
Data flow analyses
• liveness analysis
• reaching definitions
• available expressions
Optimizations (again)
2
Term Rewriting
Optimizations
I
3
optimization
Dataflow Analysis
Optimizing Compilers
Fully optimizing compiler
• Opt(P) produces smallest program with same I/O behavior
• smallest program for non-terminating programs without I/O:Loop = (L : goto L)
• solves halting problem: Opt(Q) = Loop iff Q halts
Optimizing compiler
• produces program with same I/O behavior
• that is smaller or faster
Full employment theorem for compiler writers
• there is always a better optimizing compiler
4
optimization
Dataflow Analysis
Local vs Non-Local Optimizations
Local optimizations
• peephole optimization
• constant folding
• pattern match + rewrite
Non-local optimizations
• constant propagation
• dead-code elimination
• require information from different parts of program
5
iload 1iload 1mul
iload 1dupmul
(3 + 4) * x 7 * x
optimization
Dataflow Analysis
Program Optimizations
Register allocation
• keep non-overlapping temporaries in same register
Common-subexpression elimination
• if expression is computed more than once, eliminate one computation
Dead-code elimination
• delete computation whose result will never be used
Constant folding
• if operands of expression are constant, do computation at compile-time
And many more possible optimizations
6
example
Dataflow Analysis
Dead Code Elimination
7
delete computation whose result will never be used
a ← 0b ← a + 1c ← c + ba ← 2 * breturn c
example
Dataflow Analysis
Dead Code Elimination
7
a ← 0b ← a + 1c ← c + b
return c
delete computation whose result will never be used
a ← 0b ← a + 1c ← c + ba ← 2 * breturn c
example
Dataflow Analysis
Constant Propagation
8
a ← 0b ← a + 1c ← c + ba ← 2 * breturn c
substitute reference to constant valued variable
example
Dataflow Analysis
Constant Propagation
8
a ← 0b ← 0 + 1c ← c + ba ← 2 * breturn c
a ← 0b ← a + 1c ← c + ba ← 2 * breturn c
substitute reference to constant valued variable
example
Dataflow Analysis
Constant Propagation + Folding
9
a ← 1b ← a + 1c ← c + ba ← 2 * breturn c
example
Dataflow Analysis
Constant Propagation + Folding
9
a ← 0b ← 2c ← c + 2a ← 4return c
a ← 1b ← a + 1c ← c + ba ← 2 * breturn c
example
Dataflow Analysis
Copy Propagation
10
a ← eb ← a + 1c ← c + ba ← 2 * breturn c
example
Dataflow Analysis
Copy Propagation
10
a ← eb ← e + 1c ← c + ba ← 2 * breturn c
a ← eb ← a + 1c ← c + ba ← 2 * breturn c
example
Dataflow Analysis
Common Subexpression Elimination
11
c ← a + bd ← 1e ← a + b
if expression is computed more than once, eliminate one computation
example
Dataflow Analysis
Common Subexpression Elimination
11
c ← a + bd ← 1e ← a + b
x ← a + bc ← xd ← 1e ← x
if expression is computed more than once, eliminate one computation
optimization
Dataflow Analysis
Intraprocedural Global Optimization
Terminology
• Intraprocedural: within a single procedure or function
• Global: spans all statements with procedure
• Interprocedural: operating on several procedures at once
Recipe
• Dataflow analysis: traverse flow graph, gather information
• Transformation: modify program using information from analysis
12
Dataflow Analysis
Control-flow Graphs
II
13
quadruples
Dataflow Analysis
Intermediate Language
Store
a ← b ⊕ ca ← b
Memory access
a ← M[b]M[a] ← b
Functions
f(a1, …, an)b ← f(a1, …, an)
Jumps
L:goto Lif a ⊗ b goto L1 else goto L2
14
example
Dataflow Analysis
Control-Flow Graphs
15
a ← 0L1: b ← a + 1 c ← c + b a ← 2 * b if a < N goto L1 else goto L2L2: return c
example
Dataflow Analysis
Control-Flow Graphs
15
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
a ← 0L1: b ← a + 1 c ← c + b a ← 2 * b if a < N goto L1 else goto L2L2: 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
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-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
predecessor
predecessor
in-edge
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
predecessor
predecessor
in-edge
out-edge
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
predecessor
predecessor
successor
in-edge
out-edge
in-edge
Dataflow Analysis
Liveness Analysis
III
17
definition
Dataflow Analysis
Liveness Analysis
Motivation: register allocation
• intermediate code with unbounded number of temporary variables
• map to bounded number of registers
• if two variables are not ‘live’ at the same time, store in same register
Liveness
• a variable is live if it holds a value that may be needed in the future
18
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 ← c + b
a ← 2 * b
if a < N
return c
{a, b} ! r{c} ! q
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 occurrence of a variable in an expression uses that variable
• def[x] = {n | n defines x}, def[n] = {x | n defines x}
• use[x] = {n | n uses x}, use[n] = {x | n uses x}
A variable is live on an edge if
• there is a directed path from that edge to a use of the variable
• that does not go through any def
A variable is live in/out at a node
• live-in: it is live on any of the in-edges of that node
• live-out: it is live on any of the out-edges of the node
21
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 < N
return c
terminology
Dataflow Analysis
Liveness Analysis
22
usage
definition
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
usage
definition
live-in
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
terminology
Dataflow Analysis
Liveness Analysis
22
usage
definition
usage
definition
live-in
live-out
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
terminology
Dataflow Analysis
Liveness Analysis
22
usage
definition
usage
definition
live-in
live-in
live-out
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
terminology
Dataflow Analysis
Liveness Analysis
22
usage
definition
usage
definition
live-in
live-outlive-in
live-out
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
terminology
Dataflow Analysis
Liveness Analysis
22
usage
definition
usage
definition
live-in
live-out
live-outlive-in
live-out
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
formalization
Dataflow Analysis
Liveness Analysis
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
23
algorithm
Dataflow Analysis
Liveness Analysis
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]
24
example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
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6
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u
a
bc
b
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c
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
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u
a
bc
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a
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a
example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
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u
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a
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b
a
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o
a
example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
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example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
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o
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example
Dataflow Analysis
Liveness Analysis
25
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
1
2
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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
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u
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b
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o
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5
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o
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ac
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
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u
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bc
b
a
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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
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u
a
bc
b
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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
4
3
2
1
u
c
a
b
bc
a
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
4
3
2
1
u
c
a
b
bc
a
d
a
c
b
a
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
4
3
2
1
u
c
a
b
bc
a
d
a
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b
a
1
o
c
ac
bc
bc
ac
i
c
ac
bc
bc
ac
a
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
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5
4
3
2
1
u
c
a
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a
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i
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2
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i
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bc
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c
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
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2
1
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c
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a
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i
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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
return c
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
return c
generalisation
Dataflow Analysis
Liveness Analysis
27
gen
kill
gen
kill
in
outa ← 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
in
out
out
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
in
out
outin
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
in
out
outin
out
a ← 0
b ← a + 1
c ← c + b
a ← 2 * b
if a < N
return c
gen & kill
Dataflow Analysis
Liveness Analysis
28
a ← b ⊕ ca ← ba ← M[b]M[a] ← b
f(a1, …, an)a ← f(a1, …, an)goto L
if a ⊗ b
gen
{b,c}{b}{b}{a,b}
{a1,…,an}{a1,…,an}
{a,b}
gen & kill
Dataflow Analysis
Liveness Analysis
28
a ← b ⊕ ca ← ba ← M[b]M[a] ← b
f(a1, …, an)a ← f(a1, …, an)goto L
if a ⊗ b
gen
{b,c}{b}{b}{a,b}
{a1,…,an}{a1,…,an}
{a,b}
kill
{a}{a}{a}
{a}
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 (d : a ← M[x])
Definition d reaches statement u if
• there is some path in control-flow graph from d to u
• that does not contain an unambiguous definition of a
Used in
• constant propagation
31
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 ⊕ cd: a ← bd: a ← M[b]M[a] ← b
f(a1, …, an)d: a ← f(a1, …, an)goto L
if a ⊗ b
gen
{d}{d}{d}
{d}
defs(a) : all definitions of a
gen & kill
Dataflow Analysis
Reaching Definitions
33
d: a ← b ⊕ cd: a ← bd: a ← M[b]M[a] ← b
f(a1, …, an)d: a ← f(a1, …, an)goto L
if a ⊗ b
gen
{d}{d}{d}
{d}
kill
defs(a)-{d}defs(a)-{d}defs(a)-{d}
defs(a)-{d}
defs(a) : all definitions of a
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 the entry node to node n
• (b ⊕ c) is computed at least once, and
• there are no definitions of b or c since most recent occurrence of (b ⊕ c) on that path
Used in
• common-subexpression elimination
35
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 ⊕ cd: a ← bd: a ← M[b]M[a] ← b
f(a1, …, an)d: a ← f(a1, …, an)goto L
if a ⊗ b
gen
{b⊕c}-kill
{M[b]}-kill
gen & kill
Dataflow Analysis
Available Expressions
37
d: a ← b ⊕ cd: a ← bd: a ← M[b]M[a] ← b
f(a1, …, an)d: a ← f(a1, …, an)goto L
if a ⊗ b
gen
{b⊕c}-kill
{M[b]}-kill
kill
exps(a)
exps(a)exps(M[_])
exps(M[_])exps(M[_]) ∪ exps(a)
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 to n
• that does not go through assignment to b or c
• or through any computation of (b ⊕ c)
Used in
• common-subexpression elimination
39
Dataflow Analysis
Optimizations
V
40
example
Dataflow Analysis
Dead Code Elimination
41
a ← 0b ← a + 1c ← c + b
return c
a ← 0b ← a + 1c ← c + ba ← 2 * breturn c
consider: (s : a ← b ⊕ c) or (s : a ← M[x]) if a is not live-out at s transform: remove s
example
Dataflow Analysis
Common Subexpression Elimination
42
c ← a + bd ← 1e ← a + b
x ← a + bc ← xd ← 1e ← x
consider: (n : a ← b ⊕ c) reaches (s : d ← b ⊕ c) path from n to s does not compute b ⊕ c or define b or c e is a fresh variabletransform: n : a ← b ⊕ c n’ : e ← a … s : d ← e
example
Dataflow Analysis
Constant Propagation
43
a ← 0b ← 0 + 1c ← c + ba ← 2 * breturn c
a ← 0b ← a + 1c ← c + ba ← 2 * breturn c
consider: (d : a ← c) & (n : e ← a ⊕ b)if c is constant & (d reaches n) & (no other def of a reaches n)transform: (n : e ← a ⊕ b) => (n : e ← c ⊕ b)
example
Dataflow Analysis
Copy Propagation
44
a ← eb ← e + 1c ← c + ba ← 2 * breturn c
a ← eb ← a + 1c ← c + ba ← 2 * breturn c
consider: (d : a ← z) & (n : e ← a ⊕ b)if z is a variable & (d reaches n) & (no other def of a reaches n) & (no def of z on path from d to n)transform: (n : e ← a ⊕ b) => (n : e ← z ⊕ b)
Term Rewriting
Summary
V
45
Dataflow Analysis
Summary
Liveness analysis
• intermediate language
• control-flow graphs
• definition & algorithm
More dataflow analyses
• reaching definitions
• available expressions
Optimizations
46
learn more
Dataflow Analysis
Literature
Andrew W. Appel, Jens Palsberg: Modern Compiler Implementation in Java, 2nd edition. 2002
47
Dataflow Analysis
Copyrights & Credits
48
copyrights
Dataflow Analysis
Pictures
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
50
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