Lecture 11: Pointer Analysis17-355/17-655/17-819: Program Analysis

Rohan Padhye and Jonathan AldrichMarch 11, 2021

* Course materials developed with Claire Le Goues

1(c) 2021 J. Aldrich, C. Le Goues, R. Padhye

Extending WHILE3ADDR with Pointers

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Consider Constant Propagation

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Need to know that line 3 changes variable z!

Consider Constant Propagation

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Points-To Analysis: May vs. Must and Strong Updates

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Pointer Analysis• Two common relations used as abstract values

o Alias analysis: (x, y) alias pairso Points-to analysis: p --> q // or sets for points-to(p)o Both have may and must versions

• Very expensive to run precisely as data-flow analysiso Lattice is 2Var x Var. Yikes!o Almost always needs to be inter-procedural

§ (even if used for intra-procedural optimizations)o Context-sensitivity is often important for adequate precision

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Andersen’s Analysis• Flow-insensitive analysis

o Considers only nodes of a CFG (i.e., instructions) and ignores all edgeso What? Yes, really.o Trades-off precision for tractabilityo Can be combined with context-sensitive techniques

• Key idea: cast as constraint-solving problemo Abstract model of memory locations and points-to sets

§ Let 𝑙𝑥 represent location of var 𝑥§ Let 𝑝 be the set of locations pointed-to by var 𝑝

o One subset constraint per instructiono Invoke constraint solver. Done!

7(c) 2021 J. Aldrich, C. Le Goues, R. Padhye

Andersen’s Analysis

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Andersen’s Analysis

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Examplex := 42y := 108q := &xif (..) p := q

elsep := &y

r = &ps = *rprint(*s)print(*q)

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Dynamic Memory Allocation?

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Dynamic Memory Allocation

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Exercise

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Efficiency• O(n) constraints• O(n) firings per copy-constraint• O(n2) firings per assign/deref-constraint• Worst-case O(n3) firings• Can be solved in O(n3) time

o McAllester [SAS’99]• O(n2) in practice

o Sridharan et al. [SAS’09]o K-sparseness property

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Field-Sensitivity

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Field-Sensitivity

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A field-insensitive approach just treats fields `.f` as dereferences `*`.

Field-Sensitive Analysis

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Field-Sensitive Analysis

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Field-Sensitive Analysis

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a := new X()b := new Y()c := new Y()a.f := ba.g := cprint(a.f)

Steensgaard’s Analysis• Problem: Quadratic-in-practice is still not ultra-scalable• Challenge: Need ~LINEAR. How?

o Solution space of pointer analysis (e.g. points-to sets) itself is O(n2).• Key idea: Use constant-space per pointer. Merge aliases and

alternates into the same equivalence class.o p can point to q or r? Let’s treat q and r as the same pseudo-var and merge

everything we know about q and r.o Points-to “sets” are basically singletons

20(c) 2021 J. Aldrich, C. Le Goues, R. Padhye

Steensgaard’s Analysis - Example

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Steensgaard’s Analysis - Example

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Steensgaard’s Analysis - Exercise

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Steensgaard’s Analysis

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Steensgaard’s Analysis

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Steensgaard’s Analysis

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• Abstract locations implemented as union-find data structureo Each union and find operation takes O(α(n)) time eacho Total algorithm running time is O(n * α(n)) ~ almost linearo Space consumption is linear

• In practice: very scalableo Millions of LoC

OOP: Dynamic Dispatch

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