More on Loop Optimization Data Flow Analysis CS 480

Make a broader goal for loop optimization General idea: – Link every assignment of a variable to the set of all places it might possibly be used – Link every use of a variable to the set of all places it might possibly have been assigned In general, a use might have several assignments, and an assign will almost always have many uses

How to do this Fundamental equation For each node: out = (in – kill) union gen Out: variables (and values) that flow out of a node In: variables (and values) that flow in to a node Kill: variables killed by a node Gen : variables (and values) generated by a node

Note that kill definition slightly different For common subscripts kill was defined as “possibly altered” For this we need to define kill as “possibly survive” X = 12 *p = 42 … If (x < b) // could use of x come from assign?

Apply equations repeatedly Apply equations to each node in the graph until nothing changes Will certainly need to do this repeated times x = 3 while (x < a) // link use of x to assignment if (b > 0) x = x + b else x = x - b

Once we have this information, what can we do with it? What is a variable that is used but never assigned to? What is a variable that is set but never used?

What about this one? max = 142 …. // lots of code, none of which changes max If (a < (max – 1)) …. // called constant propagation

Dead code elimination Can possibly discover, at compile time, that a whole section of code cannot possibly ever be executed. Think that no good programmer would ever do this?

How many people have done this? Debug = false … If (debug) { … } … Why generate code that is not executed?

Copy Propagation After X = y X and y are aliases of each other until one or the other is reassigned. Can look for common subexpressions that might not be obvious Z = (x + 42) * w G = (y + 42) * w

From previous lectures Loop invariant code (expressions with no set inside of loop) Induction variables and the resulting reduction in strength

Common subexpressions that span nodes Previously we only looked at common subexpressions within a single node What about expressions that span nodes – called available expressions A[x + 42] = 17 // subscript is common If (b < 39) a [ x + 42 ] = 18 // can be saved and reused

Or can be distributed out Or, common subexpressions can be moved back to a previous common node – called busy expressions if (a < 12) b[x + 32] = 17 Else b[x + 32] = 49 // can move subscript before if

Live-dead analysis When registers are used to hold variables (more next week) need to know when a variable is no longer being used, and can free up the register Called “live-dead analysis”

New one – polymorphism elimination Var w : window …. W = new textWindow(); …. w.draw(); // if we can ensure that w is a textwindow can probably generate faster code

Bottom line Data flow analysis, matching every variable set and every variable use, is one of the most powerful tools in the optimizer writers set of tricks