| Date post: | 19-Dec-2015 |
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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 := yz := z + x
x := yz := z + y
Copy prop DAEx := yz := 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 < 0 || 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 < 0 || index >= a.length()) { throw OutOfBoundsException; } a[index] = 0;}
Another example
p := &x;*p := 5y := x + 1;
Another example
p := &x;*p := 5y := x + 1;
x := 5;*p := 3y := 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 := ...
x := ...y := ...y := ...p := ...if (...) { ... x ... x := ... ... y ...}else { ... x ... x := ... *p := ...}... x ...... y ...y := ...
y := ...
y := ...
p := ...
... x ...
x := ...
... y ...
... x ...
x := ...
*p := ...
... x ...
... 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 := ...
y := ...
p := ...
... x ...
x := ...
... y ...
... x ...
x := ...
*p := ...
... x ...
... 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
