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CS553 Lecture Generalizing Data-flow Analysis 1
Generalizing Data-flow Analysis
! Announcements
-! Read Section 9.3 in the book ! Today -! Other types of data-flow analysis -! Reaching definitions, available expressions, reaching constants -! Abstracting data-flow analysis What’s common among the different analyses? 1 a =.. .; 2 b =.. .; 3 for (.. .) { 4 x = a + b; 5... 6 } To determine whether it’s legal to move statement 4 out of the loop, we need to ensure that there are no reaching definitions of a or b inside the loop
Reaching Definitions
! Definition
-! A definition (statement) d of a variable v reaches node n if there is a path from d to n such that v is not redefined along that path ! Uses of reaching definitions -! Build use/def chains -! Constant propagation -! Loop invariant code motion d v :=... n Reaching definitions of a and b d x := 5 n (^) f(x) Does this def of x reach n? can we replace n with f(5)? ! def[v]
CS553 Lecture Generalizing Data-flow Analysis 3 ! Defining Gen and Kill for various statement types ! statement Gen[s] Kill[s] ! s: t = b op c {s} def[t] – {s} ! s: t = M[b] {s} def[t] – {s} ! s: M[a] = b {} {} ! s: if a op b goto L {} {} statement Gen[s] Kill[s] s: goto L {} {} s: L: {} {} s: f(a,…) {} {} s: t=f(a, …) {s} def[t] – {s}
Computing Reaching Definitions
! Assumption
-! At most one definition per node -! We can refer to definitions by their node “number” ! Gen[n]: Definitions that are generated by node n (at most one) Kill[n]: Definitions that are killed by node n
A Better Formulation of Reaching Definitions
! Problem
-! Reaching definitions gives you a set of definitions (nodes) -! Doesn’t tell you what variable is defined -! Expensive to find definitions of variable v ! Solution -! Reformulate to include variable e.g., Use a set of (var, def) pairs a (^) x= b y= n (^) in[n] = {(x,a),(y,b),...}
CS553 Lecture Generalizing Data-flow Analysis 7
Available Expressions for CSE
! How is this information useful? ! Common Subexpression Elimination (CSE)
- !If an expression is available at a point where it is evaluated, it need not be recomputed ! Example (^3) c := 4 * i (^2) i := i + 1 t := 4 * i b := t (^1) i := j t := 4 * i a := t (^3) c := t (^1) i := j a := 4 * i (^2) i := i + 1 b := 4 * i guaranteed or possible forward or backward variables, definitions, ... universal or empty set due to semantics of stmt what is removed from set due to semantics of stmt what is added to set how sets from two control paths compose ! Must or may Information ! Direction ! Flow values ! Initial guess ! Kill ! Gen ! Merge
Aspects of Data-flow Analysis
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Must vs. May Information
! Must information
-! Implies a guarantee ! May information -! Identifies possibilities !!!!!!! !May Must safe overly large set overly small set desired information small set large set Gen add everything that add only facts that are might be true guaranteed to be true Kill remove only facts that remove everything that are guaranteed to be true might be false merge union intersection initial guess empty set universal set Liveness? Available expressions?
Reaching Definitions: Must or May Analysis?
! Consider uses of reaching definitions d x = 5 n (^) f(x) We need to know if d’ might reach node n d’ x = 4
CS553 Lecture Generalizing Data-flow Analysis 13
Reaching Constants Example
! Must or may info? ! Direction? ! Initial guess?
Reality Check!
! Some definitions and uses are ambiguous
-! We can’t tell whether or what variable is involved e.g., *p = x; / what variable are we assigning?! / -! Unambiguous assignments are called strong updates -! Ambiguous assignments are called weak updates ! Solutions -! Be conservative -! Sometimes we assume that it could be everything e.g., Defining *p (generating reaching definitions) -! Sometimes we assume that it is nothing e.g., Defining *p (killing reaching definitions) -! Try to figure it out: alias/pointer analysis (more later)
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Side Effects
! What happens at function calls?
-! For example, the call foo(&x) might use or define -! any local or heap variable x that has been passed by address/reference -! any global variable ! Solution -! How do we handle this for liveness used for register allocation? -! In general -! Be conservative: assume all globals and all vars passed by address/ reference may be used and/or modified -! Or Figure it out: calculate side effects (example of an interprocedural analysis)
Concepts
Data-flow analyses are distinguished by
-! Flow values (initial guess, type) -! May/must -! Direction -! Gen -! Kill -! Merge ! Complication -! Ambiguous references (strong/weak updates) -! Side effects
