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Published byCedric Turbin Modified over 2 years ago

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Worst case complexity of Andersen *x = y x abc y def x abc y def Worst case: N 2 per statement, so at least N 3 for the whole program. Andersen is in fact O(N 3 )

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New idea: one successor per node Make each node have only one successor. This is an invariant that we want to maintain. x a,b,c y d,e,f *x = y x a,b,c y d,e,f

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x *x = y y More general case for *x = y

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x *x = y yxyxy More general case for *x = y

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x x = *y y Handling: x = *y

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x x = *y yxyxy Handling: x = *y

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x x = y y x = &y xy Handling: x = y (what about y = x?) Handling: x = &y

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x x = y yxyxy x = &y xyx y,… xy Handling: x = y (what about y = x?) Handling: x = &y get the same for y = x

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Our favorite example, once more! S1: l := new Cons p := l S2: t := new Cons *p := t p := t 1 2 3 4 5

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Our favorite example, once more! S1: l := new Cons p := l S2: t := new Cons *p := t p := t l S1 t S2 p l S1 l p l t S2 p l S1,S2 tp 1 2 3 4 5 12 3 l S1 t S2 p 4 5

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Flow insensitive loss of precision S1: l := new Cons p := l S2: t := new Cons *p := t p := t l t S1 p S2 l t S1 p S2 l t S1 p S2 l t S1 p S2 Flow-sensitive Subset-based Flow-insensitive Subset-based l t S1 p S2 l S1,S2 tp Flow-insensitive Unification- based

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bar() { i := &a; j := &b; foo(&i); foo(&j); // i pnts to what? *i :=...; } void foo(int* p) { printf(“%d”,*p); } 1 2 3 4 Another example

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bar() { i := &a; j := &b; foo(&i); foo(&j); // i pnts to what? *i :=...; } void foo(int* p) { printf(“%d”,*p); } i a j b p i a i a j b i a j b p i,j a,b p 1 2 3 4 12 Another example 4 3

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Int fact (int n) { If (n == 0) return 1; else return n * fact (n – 1); } 5 void main () { Int Sum; : Sum = fact (5); : } Factorial Program Using Recursion.

Int fact (int n) { If (n == 0) return 1; else return n * fact (n – 1); } 5 void main () { Int Sum; : Sum = fact (5); : } Factorial Program Using Recursion.

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