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Flow insensitivity and imprecision

Flow insensitivity and imprecision. If you ignore flow, then you lose precision. main() { x := &y; ... x := &z; }. Flow insensitive analysis tells us that x may point to z here!. But, insensitivity may alleviate two bottlenecks: (1) space : mem exhausted by large programs

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Flow insensitivity and imprecision

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  1. Flow insensitivity and imprecision If you ignore flow, then you lose precision. main() { x := &y; ... x := &z; } Flow insensitive analysis tells us that x may point to z here! But, insensitivity may alleviate two bottlenecks: (1) space : mem exhausted by large programs (2) time : need speed for JIT or edit , compile loop

  2. Andersen’s : worst case complexity Worst case: N2 per statement at least N3 for the whole program Andersen’s is in fact O(N3) x y x y *x = y a b c d e f a b c d e f

  3. New idea: one successor per node Each node can point to at most one “thing”. “Thing” : everything a var may point to. x y x y *x = y a,b,c d,e,f a,b,c d,e,f

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

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

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

  7. More general case for x = *y Handling: x = *y x y x = *y

  8. More general case for x = *y Handling: x = *y x y x y x = *y

  9. x y x y x y x = *y More general case for x = *y Handling: x = *y

  10. More general case for x = y Handling: x = y x y x = y

  11. More general case for x = y Handling: x = y x y x y x = y

  12. x y x y x y x = y More general case for x = y Handling: x = y

  13. x y x y x y x = y More general case for x = y Handling: x = y (what about y = x?)

  14. x y x y x y x = y More general case for x = y Handling: x = y (what about y = x?) same result for y = x !

  15. More general case for x = &y Handling: x = &y x y x = &y

  16. More general case for x = &y Handling: x = &y x y x y x = &y

  17. More general case for x = &y Handling: x = &y x y x y x x = &y y,…

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

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

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

  21. Another example 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

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

  23. Steensgaard and beyond Well engineered implementation of Steensgaard: 2.1 MLOC in 1 minute (Word97) One Level Flow (Das PLDI 00) extension to Steensgaard achieves higher precision 2.1 MLOC in 2 minutes (Word 97)

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