Some Properties of SSA

1. 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

3. Static Single Assignment • Every variable is assigned once • But in loops a variable will be assigned many times

4. An Acyclic Example x  x + 2 x > 0 x  x + 1 x  x + 4 x > 0 x  x + 3 x  x + 6 x  x + 5

5. A Cyclic Example i = 1; j = 1; k = 0 while (k < 0) { if (j < 0) { j = i; k = k + 1; } else { j = k ; k = k + 2 } } return j

6. What does it buy us? • Compact representation of DU chains • Convert “imperative” into “functional” style • Extended basic blocks • Allows flow-insensitive analysis

7. 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

9. Conditional Constant Propagation • Conditions with constant values can be interpreted to improve precision • A more precise solution is obtained “optimistically”

10. 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: t3=Yellow; break; case ORANGE: t3=Orange; }} printf(“%s\n”, t3 );} main() { printf(“%s\n”, “red”);} “red”

11. 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: t3=Yellow; break; case ORANGE: t3=Orange; }} printf(“%s\n”, t3);}

12. Iterative Data-Flow Algorithm Input:aflow 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’}

13. Iterative Data-Flow Algorithm Input:aflow 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’}

14. 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: t3=Yellow; break; case ORANGE: t3=Orange; }} printf(“%s\n”, t3);}

15. 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

16. 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

17. 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

18. 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 markedexecutable • 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