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

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

Another example Often used as a clean-up pass x := y**z... x :=... x := y z := z + x x := y z := z + y Copy propDAE x := y z := z + y

Another example if (false) {... }

Another example if (false) {... }

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

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

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

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

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

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

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

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

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

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

Dataflow analysis

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

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)

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

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

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

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

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

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

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

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