Recap from last time

1. Recap from last time • Saw several examples of optimizations • Constant folding • Constant Prop • Copy Prop • Common Sub-expression Elim • Partial Redundancy Elim • Saw that a naïve CSE can undo Copy Prop

2. Another example x := y**z ... x := ...

3. Another example • Often used as a clean-up pass x := y**z ... x := ... Copy prop DAE x := y z := z + x x := y z := z + y x := y z := z + y

4. Another example if (false) { ... }

5. Another example if (false) { ... }

6. Another example • In Java: a = new int [10]; for (index = 0; index < 10; index ++) { a[index] = 100; }

7. Another example • In “lowered” Java: a = new int [10]; for (index = 0; index < 10; index ++) { if (index < 0 || index >= a.length()) { throw OutOfBoundsException; } a[index] = 0; }

8. Another example • In “lowered” Java: a = new int [10]; for (index = 0; index < 10; index ++) { if (index < 0 || index >= a.length()) { throw OutOfBoundsException; } a[index] = 0; }

9. Another example p := &x; *p := 5 y := x + 1;

10. Another example p := &x; *p := 5 y := x + 1; x := 5; *p := 3 y := x + 1; ???

11. Another example for j := 1 to N for i := 1 to M a[i] := a[i] + b[j]

12. Another example for j := 1 to N for i := 1 to M a[i] := a[i] + b[j]

13. Another example area(h,w) { return h * w } h := ...; w := 4; a := area(h,w)

14. Another example area(h,w) { return h * w } h := ...; w := 4; a := area(h,w)

15. Optimization themes • Don’t compute if you don’t have to • unused assignment elimination • Compute at compile-time if possible • constant folding, loop unrolling, inlining • Compute it as few times as possible • CSE, PRE, PDE, loop invariant code motion • Compute it as cheaply as possible • strength reduction • Enable other optimizations • constant and copy prop, pointer analysis • Compute it with as little code space as possible • unreachable code elimination

16. Dataflow analysis

17. Dataflow analysis: what is it? • A common framework for expressing algorithms that compute information about a program • Why is such a framework useful?

18. Dataflow analysis: what is it? • A common framework for expressing algorithms that compute information about a program • Why is such a framework useful? • Provides a common language, which makes it easier to: • communicate your analysis to others • compare analyses • adapt techniques from one analysis to another • reuse implementations (eg: dataflow analysis frameworks)

19. Control Flow Graphs • For now, we will use a Control Flow Graph representation of programs • each statement becomes a node • edges between nodes represent control flow • Later we will see other program representations • variations on the CFG (eg CFG with basic blocks) • other graph based representations

20. Example CFG x := ... y := ... x := ... y := ... y := ... p := ... if (...) { ... x ... x := ... ... y ... } else { ... x ... x := ... *p := ... } ... x ... ... y ... y := ... y := ... p := ... if (...) ... x ... ... x ... x := ... x := ... ... y ... *p := ... ... x ... ... x ... y := ...

21. An example DFA: reaching definitions • For each use of a variable, determine what assignments could have set the value being read from the variable • Information useful for: • performing constant and copy prop • detecting references to undefined variables • presenting “def/use chains” to the programmer • building other representations, like the DFG • Let’s try this out on an example

22. x := ... Visual sugar y := ... 1: x := ... 2: y := ... 3: y := ... 4: p := ... y := ... p := ... if (...) ... x ... 5: x := ... ... y ... ... x ... 6: x := ... 7: *p := ... ... x ... ... x ... x := ... x := ... ... y ... *p := ... ... x ... ... y ... 8: y := ... ... x ... ... x ... y := ...

23. 1: x := ... 2: y := ... 3: y := ... 4: p := ... ... x ... 5: x := ... ... y ... ... x ... 6: x := ... 7: *p := ... ... x ... ... y ... 8: y := ...

24. 1: x := ... 2: y := ... 3: y := ... 4: p := ... ... x ... 5: x := ... ... y ... ... x ... 6: x := ... 7: *p := ... ... x ... ... y ... 8: y := ...

25. Safety • When is computed info safe? • Recall intended use of this info: • performing constant and copy prop • detecting references to undefined variables • presenting “def/use chains” to the programmer • building other representations, like the DFG • Safety: • can have more bindings than the “true” answer, but can’t miss any

26. Reaching definitions generalized • DFA framework geared to computing information at each program point (edge) in the CFG • So generalize problem by stating what should be computed at each program point • For each program point in the CFG, compute the set of definitions (statements) that may reach that point • Notion of safety remains the same