Some Properties of SSA

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Some Properties of SSA

• Mooly Sagiv

2
Outline

• Why is it called Static Single Assignment form
• What does it buy us?
• How much does it cost us?
• Open questions

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Static Single Assignment

• Every variable is assigned once
• But in loops a variable will be assigned many
  times

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An Acyclic Example
x ? x 2 x gt 0
x ? x 1
x ? x 4 x gt 0
x ? x 3
x ? x 6
x ? x 5
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A Cyclic Example
i 1 j 1 k 0 while (k lt 0) if (j lt 0)
j i k k 1 else j k k
k 2 return j
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What does it buy us?

• Compact representation of DU chains
• Convert imperative into functional style
• Extended basic blocks
• Allows flow-insensitive analysis

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How much does it cost

• Code size
• Worst case the extra number of assignments is
  quadratic
• For programs with while-do and if-then-else
  linear
• In practice linear
• Construction of SSA

8
Open Questions

• Dealing with pointers
• When is it useful?
• Is it really needed?
• Can we choose an appropriate data structure in
  the iterative data flow algorithm instead

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Conditional Constant Propagation

• Conditions with constant values can be
  interpreted to improve precision
• A more precise solution is obtained
  optimistically

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char Red red char Yellow
yellow char Orange orange main()
FRUIT snack VARIETY t1 SHAPE t2 COLOR
t3 t1 APPLE t2 ROUND switch (t1)
case APPLE t3 Red
break
case BANANA t3Yellow
break case
ORANGE t3Orange printf(s\n, t3
)
main() printf(s\n, red)
red
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char Red red char Yellow
yellow char Orange orange main()
FRUIT snack VARIETY t1 SHAPE t2 COLOR
t3 t1 APPLE t2 ROUND switch (t1)
case APPLE t3 Red
break
case BANANA t3Yellow
break case
ORANGE t3Orange printf(s\n, t3)
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Iterative Data-Flow Algorithm
Input a flow graph G(N,E,r) An
init value Init A montonic function
FB for every B in N Output For every N
in(N) Initializatio in(Entry) Init
for each node B in N-Entry do
in(B) ? WL N -
Entry Iteration while WL ! do
Select and remove an B from WL
out FB(in(B))
For all B in succ(B) such that in(B) ! in(B)
?out do
in(B) in(B) ? out
WL WL ?B
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Iterative Data-Flow Algorithm
Input a flow graph G(N,E,r) An
init value Init A montonic function
FB for every B in N Output For every N
in(N) Initializatio in(Entry) Init
for each node B in N-Entry do
in(B) ? WL
Entry Iteration while WL ! do
Select and remove an B from WL
out FB(in(B))
For all B in succ(B) such that
in(B) ! in(B) ?out do
in(B) in(B) ? out
WL
WL ?B
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char Red red char Yellow
yellow char Orange orange main()
FRUIT snack VARIETY t1 SHAPE t2 COLOR
t3 t1 APPLE t2 ROUND switch (t1)
case APPLE t3 Red
break
case BANANA t3Yellow
break case
ORANGE t3Orange printf(s\n, t3)
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Conditional Constant Propagation

• initialize the worklist to the entry node
• mark all edges as not executable
• repeat until the worklist is empty
• select and remove a node from the worklist
• if it is an assignment then mark the successor
  edge as executable
• if it is a test then symbolically evaluate the
  test and mark the enabled successor edges as
  executable
• if test evaluates to true or ? mark true edge
  executable
• if test evaluates to false or ? mark false edge
  executable
• update the value of all the variables at the
  entry and exit of this node
• if there are changes then add all successors
  reachable from the node with edges marked
  executable to the worklist

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Sparse Conditional Constant

• bring the program in SSA form
• initialize the analysis information
• all variables are mapped to ?
• all flow edges are marked as not executable
• initialize the two worklists
• Flow-Worklist contains all edges of the flow
  graph with the entry node as source
• SSA-Worklist is empty

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• repeat until both worklists are empty
• select and remove an edge from one of the
  worklists
• if it is a flow edge then
• if the edge is not marked executable then
• mark it executable
• if the target of the edge is a f-node then call
  visit-f
• if it is the first time the node is visited (only
  one incoming flow edge is marked executable) and
  it is a normal node then call visit-instr
• if it is an SSA edge then
• if the target of the edge is a f-node then call
  visit-f
• if it is a normal node and at least one of the
  flow edges entering the node are marked
  executable then call visit-instr

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• visit-f (the node is a f-node)
• the assigned variable is given a value that is
  the join the values of the arguments with
  incoming edges marked executable
• visit-instr (the node is a normal
  node)
• determine the value of the expression of the node
  and update the variable in case of an assignment
• if there are changes then
• if the node is an assignment then add all SSA
  edges with source at the target of the current
  edge to the SSA-worklist
• if the node is a test then add all relevant flow
  edges to the Flow-worklist and mark them
  executable
• if test evaluates to true or ? add true edge
• if test evaluates to false or ? add false edge