1. Recap from last time We were trying to do Common Subexpression Elimination Compute expressions that are available at each program point

2. Recap from last time X := Y op Z in out F X := Y op Z (in) = in – { X ! * } – { * !... X... } [ { X ! Y op Z | X  Y Æ X  Z} X := Y in out F X := Y (in) = in – { X ! * } – { * !... X... } [ { X ! E | Y ! E 2 in }

3. Example

4. Problems z := j * 4 is not optimized to z := x, even though x contains the value j * 4 m := b + a is not optimized to m := i, even i contains a + b w := 4 * m it not optimized to w := x, even though x contains the value 4 *m

5. Problems: more abstractly Available expressions overly sensitive to name choices, operand orderings, renamings, assignments Use SSA: distinct values have distinct names Do copy prop before running available exprs Adopt canonical form for commutative ops

6. Example in SSA X := Y op Z in out F X := Y op Z (in) = X :=  (Y,Z) in 0 out F X := Y (in 0, in 1 ) = in 1

7. Example in SSA X := Y op Z in out F X := Y op Z (in) = in [ { X ! Y op Z } X :=  (Y,Z) in 0 out F X := Y (in 0, in 1 ) = (in 0 Å in 1 ) [ { X ! E | Y ! E 2 in 0 Æ Z ! E 2 in 1 } in 1

8. Example in SSA

10. What about pointers?

11. Option 1: don’t use SSA for point-to memory Option 2: insert copies between SSA vars and real vars

12. SSA helps us with CSE Let’s see what else SSA can help us with Loop-invariant code motion

13. Two steps: analysis and transformations Step1: find invariant computations in loop –invariant: computes same result each time evaluated Step 2: move them outside loop –to top if used within loop: code hoisting –to bottom if used after loop: code sinking

14. Example

16. Detecting loop invariants An expression is invariant in a loop L iff: (base cases) –it’s a constant –it’s a variable use, all of whose defs are outside of L (inductive cases) –it’s a pure computation all of whose args are loop- invariant –it’s a variable use with only one reaching def, and the rhs of that def is loop-invariant

17. Computing loop invariants Option 1: iterative dataflow analysis –optimistically assume all expressions loop-invariant, and propagate Option 2: build def/use chains –follow chains to identify and propagate invariant expressions Option 3: SSA –like option 2, but using SSA instead of ef/use chains

18. Example using def/use chains An expression is invariant in a loop L iff: (base cases) –it’s a constant –it’s a variable use, all of whose defs are outside of L (inductive cases) –it’s a pure computation all of whose args are loop-invariant –it’s a variable use with only one reaching def, and the rhs of that def is loop-invariant

19. Example using def/use chains An expression is invariant in a loop L iff: (base cases) –it’s a constant –it’s a variable use, all of whose defs are outside of L (inductive cases) –it’s a pure computation all of whose args are loop-invariant –it’s a variable use with only one reaching def, and the rhs of that def is loop-invariant

20. Loop invariant detection using SSA An expression is invariant in a loop L iff: (base cases) –it’s a constant –it’s a variable use, all of whose single defs are outside of L (inductive cases) –it’s a pure computation all of whose args are loop- invariant –it’s a variable use whose single reaching def, and the rhs of that def is loop-invariant  functions are not pure

21. Example using SSA An expression is invariant in a loop L iff: (base cases) –it’s a constant –it’s a variable use, all of whose single defs are outside of L (inductive cases) –it’s a pure computation all of whose args are loop-invariant –it’s a variable use whose single reaching def, and the rhs of that def is loop-invariant  functions are not pure

22. Example using SSA and preheader An expression is invariant in a loop L iff: (base cases) –it’s a constant –it’s a variable use, all of whose single defs are outside of L (inductive cases) –it’s a pure computation all of whose args are loop-invariant –it’s a variable use whose single reaching def, and the rhs of that def is loop-invariant  functions are not pure

23. Code motion

24. Example

25. Lesson from example: domination restriction

26. Domination restriction in for loops

28. Avoiding domination restriction

29. Another example

30. Data dependence restriction

31. Avoiding data restriction

32. Representing control dependencies We’ve seen SSA, a way to encode data dependencies better than just def/use chains –makes CSE easier –makes loop invariant detection easier –makes code motion easier Now we move on to looking at how to encode control dependencies

33. Control Dependences A node (basic block) Y is control-dependent on another X iff X determines whether Y executes –there exists a path from X to Y s.t. every node in the path other than X and Y is post-dominated by Y –X is not post-dominated by Y

34. Control Dependences A node (basic block) Y is control-dependent on another X iff X determines whether Y executes –there exists a path from X to Y s.t. every node in the path other than X and Y is post-dominated by Y –X is not post-dominated by Y

35. Example

37. Control Dependence Graph Control dependence graph: Y descendent of X iff Y is control dependent on X –label each child edge with required condition –group all children with same condition under region node Program dependence graph: super-impose dataflow graph (in SSA form or not) on top of the control dependence graph

38. Example

40. Another example

43. Summary so far Dataflow analysis –flow functions, lattice theoretic framework, optimistic iterative analysis, MOP Advanced Program Representations –SSA, CDG, PDG, code motion Next: dealing with procedures

44. Interprocedural analyses and optimizations

45. Costs of procedure calls Up until now, we treated calls conservatively: –make the flow function for call nodes return top –start iterative analysis with incoming edge of the CFG set to top –This leads to less precise results: “lost-precision” cost Calls also incur a direct runtime cost –cost of call, return, argument & result passing, stack frame maintainance –“direct runtime” cost

46. Addressing costs of procedure calls Technique 1: try to get rid of calls, using inlining and other techniques Technique 2: interprocedural analysis, for calls that are left

47. Inlining Replace call with body of callee Turn parameter- and result-passing into assignments –do copy prop to eliminate copies Manage variable scoping correctly –rename variables where appropriate

48. Program representation for inlining Call graph –nodes are procedures –edges are calls, labelled by invocation counts/frequency Hard cases for builing call graph –calls to/from external routines –calls through pointers, function values, messages Where in the compiler should inlining be performed?

49. Inlining pros and cons (discussion)

50. Inlining pros and cons Pros –eliminate overhead of call/return sequence –eliminate overhead of passing args & returning results –can optimize callee in context of caller and vice versa Cons –can increase compiled code space requirements –can slow down compilation –recursion? Virtual inlining: simulate inlining during analysis of caller, but don’t actually perform the inlining

51. Which calls to inline (discussion) What affects the decision as to which calls to inline?

52. Which calls to inline What affects the decision as to which calls to inline? –size of caller and callee (easy to compute size before inlining, but what about size after inlining?) –frequency of call (static estimates or dynamic profiles) –call sites where callee benefits most from optimization (not clear how to quantify) –programmer annotations (if so, annotate procedure or call site? Also, should the compiler really listen to the programmer?)