Pointer Analysis. Pointer analysis. Pointer and Alias Analysis. Useful for what? Intraprocedural Points-to Analysis. Kinds of alias information

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1 Poer Anasis Poer anasis Oue: Wha is oer anasis Inrarocedura oer anasis Inerrocedura oer anasis Andersen and Seensgaard Poer and Aias Anasis Aiases: wo eressions ha denoe he same memor ocaion. Aiases are roduced b: oers ca-b-reference arra deg C unions Usefu for wha? Imrove he recision of anases ha require knowg wha is modified or referenced (eg cons ro, CSE ) Eimae redundan oads/sores and dead sores. := *; := *; // reace wih :=? * := ; // is * dead? Paraeizaion of code can recursive cas o quick_sor be run arae? Yes, rovided ha he reference disc regions of he arra. Idenif objecs o be racked error deecion oos.ock();.unock(); // same objec as? Kds of aias formaion Pos-o formaion (mus or ma versions) a rogram o, comue a se of airs of he form!, where os o. can reresen his formaion z a os-o grah Inrarocedura Pos-o Anasis Wan o comue ma-os-o formaion Laice: Aias airs a each rogram o, comue he se of of a airs (e 1,e 2 ) where e 1 and e 2 mus/ma reference he same memor. Sorage shae anasis a each rogram o, comue an absrac descriion of he oer srucure. 1

2 Fow funcions Fow funcions := k F := k () = := F := () = ou ou := a + b F := a+b () = := & F := & () = ou ou Fow funcions Inrarocedura Pos-o Anasis := * ou F := * () = Fow funcions: * := ou F * := () = Poers o dnamica-aocaed memor Hande saemens of he form: := new T One idea: generae a new variabe each ime he new saemen is anazed o sand for he new ocaion: Eame := new Cons := := new Cons * := := 2

3 Eame soved Wha wen wrong? := new Cons Laice fie a! We were essenia runng he rogram := := new Cons V2 V2 V2 V3 Insead, we need o summarize he fie man aocaed objecs a fie wa New Idea: roduce summar nodes, which wi sand for a whoe cass of aocaed objecs. * := V2 V2 V3 := V2 V2 V3 Wha wen wrong? Eame: For each new saemen wih abe L, roduce a summar node oc L, which sands for he memor aocaed b saemen L. Eame revisied : := new Cons := Summar nodes can use oher crierion for mergg. : := new Cons * := := Eame revisied & soved Eame revisied & soved : := new Cons Ier 1 Ier 2 Ier 3 : := new Cons Ier 1 Ier 2 Ier 3 := := : := new Cons * := := : := new Cons * := := 3

4 Arra aiasg, and oers o arras Arra deg can cause aiasg: a[i] aiases b[j] if: a aiases b and i = j a and b overa, and i = j + k, where k is he amoun of overa. Can have oers o eemens of an arra := &a[i]; ; ++; How can arras be modeed? Coud rea he whoe arra as one ocaion. Coud r o reason abou he arra de eressions: arra deendence anasis. Fieds Can summarize fieds usg er fied summar for each fied F, kee a os-o node caed F ha summarizes a ossibe vaues ha can ever be sored F Can aso use aocaion sies for each fied F, and each aocaion sie S, kee a os-o node caed (F, S) ha summarizes a ossibe vaues ha can ever be sored he fied F of objecs aocaed a sie S. Summar We jus saw: rarocedura os-o anasis handg dnamica aocaed memor handg oers o arras Bu, rarocedura oer anasis is no enough. Sharg daa srucures across muie rocedures is one he big benefis of oers: sead of assg he whoe daa srucures around, jus ass oers o hem (eg C ass b reference). So oers end u og o srucures shared across rocedures. If ou don do an erroc anasis, ou have o make conservaive assumions funcions enries and funcion cas. Conservaive aroimaion on enr Sa we don have errocedura oer anasis. Wha shoud he formaion be a he u of he foowg rocedure: goba g; void (,) { g Conservaive aroimaion on enr Here are a few souions: Inerrocedura oer anasis Ma difficu erformg errocedura oer anasis is scag goba g; void (,) { g ocaions from aoc sies rior o his vocaion,,g & ocaions from aoc sies rior o his vocaion One can use a o-down summar based aroach (Wison & Lam 95), bu even hese are hard o scae The are a ver conservaive! We can r o do beer. 4

5 Eame revisied : := new Cons := : := new Cons * := := Cos: sace: sore one fac a each rog o ime: ieraion Ier 1 Ier 2 Ier 3 New idea: sore one daafow fac Sore one daafow fac for he whoe rogram Each saemen udaes his one daafow fac use he revious fow funcions, bu now he ake he whoe rogram daafow fac, and reurn an udaed version of i. Process each saemen once, ignorg he order of he saemens This is caed a fow-sensiive anasis. Fow sensiive oer anasis Fow sensiive oer anasis : := new Cons : := new Cons := := : := new Cons : := new Cons * := := * := := Fow sensiive vs. sensiive Wha wen wrong? : := new Cons := Fow-sensiive Son Fow-sensiive Son Wha haened o he k beween and? Can do srong udaes anmore! Need o remove a he ki ses from he fow funcions. : := new Cons * := Wha haened o he sef oo on? We si have o ierae! := 5

6 Fow sensiive oer anasis: fied : := new Cons Fow sensiive oer anasis: fied This is Andersen s agorihm 94 Fa resu : := new Cons Ier 1 Ier 2 Ier 3 := : := new Cons * := := := : := new Cons * := := L2 L1 L2 Fow sensiive vs. sensiive, aga Fow sensiive oss of recision : := new Cons := : := new Cons * := := Fow-sensiive Son Fow-sensiive Son Fow sensiive anasis eads o oss of recision! ma() { := &; := &z; Fow sensiive anasis es us ha ma o o z here! However: uses ess memor (memor can be a big boeneck o runng on arge rograms) runs faser In Cass Eercise! In Cass Eercise! soved : := new Cons : := new Cons : q := new Cons : q := new Cons * = q * = q q r = &q r = &q *q = r *q = *q = r *q = r s s = r s = s = r s = *r = s *r = s 6

7 Wors case comei of Andersen New idea: one successor er node Make each node have on one successor. This is an varian ha we wan o maa. * = a b c d e f a b c d e f * = a,b,c d,e,f a,b,c d,e,f Wors case: N 2 er saemen, so a eas N 3 for he whoe rogram. Andersen is fac O(N 3 ) More genera case for * = More genera case for * = * = * = Handg: = * Handg: = * = * = * 7

8 Handg: = (wha abou =?) Handg: = (wha abou =?) = = ge he same for = Handg: = & Handg: = & = & = &, Our favorie eame, once more! Our favorie eame, once more! : := new Cons := 2 1 : := new Cons := : := new Cons 3 * := 4 : := new Cons 3 * := := 5 := 5, Fow sensiive oss of recision Anoher eame : := new Cons := : := new Cons * := := Fow-sensiive Subse-based Fow-sensiive Subse-based Fow-sensiive Unificaionbased, bar() { 1 i := &a; 2 j := &b; 3 foo(&i); 4 foo(&j); // i ns o wha? *i := ; void foo(* ) { rf( %d,*); 8

9 Anoher eame Amos ear ime bar() { 1 i := &a; 2 j := &b; 3 foo(&i); 4 foo(&j); // i ns o wha? *i := ; void foo(* ) { rf( %d,*); 1 i 2 a i a j b i a 4 j b 3 i a i,j a,b j b Time comei: O(Nα(N, N)) verse Ackermann funcion So sow-growg, i is basica ear racice For he curious: node mergg imemened usg UNION-FIND srucure, which aows se union wih amorized cos of O(α(N, N)) er o. Take CSE 202 o earn more! In Cass Eercise! In Cass Eercise! soved : := new Cons : := new Cons : q := new Cons : q := new Cons Seensgaard q,,s2 * = q * = q r s r = &q r = &q *q = r s = r *q = s = *q = r s = r *q = s = Andersen q *r = s *r = s r s Advanced Poer Anasis Combe fow-sensiive/fow-sensiive Cever daa-srucure design Cone-sensiivi 9