Don t Sit on the Fence

Transcription

1 Don t Sit on the Fence A Static Analysis Approach to Automatic Fence Insertion Or Ostrovsky April 25th 2018 Or Ostrovsky Don t Sit on the Fence April 25th / 50

2 Table of contents 1 Introduction 2 Cycles 3 Static Analysis 4 Soundness of Construction 5 Fence placement 6 Conclusion Or Ostrovsky Don t Sit on the Fence April 25th / 50

3 Table of contents 1 Introduction 2 Cycles 3 Static Analysis 4 Soundness of Construction 5 Fence placement 6 Conclusion Or Ostrovsky Don t Sit on the Fence April 25th / 50

4 Problem Programming not under SC is complicated Programmers are stupid Or Ostrovsky Don t Sit on the Fence April 25th / 50

5 Problem Programming not under SC is complicated Programmers are stupid Solution: Let the computer do it Or Ostrovsky Don t Sit on the Fence April 25th / 50

6 Problem Programming not under SC is complicated Programmers are stupid Solution: Let the computer do it Easier said than done Or Ostrovsky Don t Sit on the Fence April 25th / 50

7 Goal Simulate Sequential Consistency, using fences Automatic Optimal Or Ostrovsky Don t Sit on the Fence April 25th / 50

8 Challenges Or Ostrovsky Don t Sit on the Fence April 25th / 50

9 Challenges Correctness Optimality Scalability Compiler optimizations Or Ostrovsky Don t Sit on the Fence April 25th / 50

10 Table of contents 1 Introduction 2 Cycles 3 Static Analysis 4 Soundness of Construction 5 Fence placement 6 Conclusion Or Ostrovsky Don t Sit on the Fence April 25th / 50

11 Memory models: Recap. Operational vs. Axiomatic Different relations Program Order (po) Coherence (co)/memory Order (mo) Read From (rf) From Read (fr = rf 1 ; co) Static vs. dynamic Sequential Consistency vs. Relaxed memory models SC: acyclic(po co rf fr) Relaxed: only a subset Or Ostrovsky Don t Sit on the Fence April 25th / 50

12 Candidate execution Definition Event Wxv, Rxv Event Structure E (E, po), E = {events} Execution Witness X (co, rf, fr) Candidate Execution (E, X) Memory Model MM : {(E, X)} {true, false} Or Ostrovsky Don t Sit on the Fence April 25th / 50

13 Candidate execution Definition Event Wxv, Rxv Event Structure E (E, po), E = {events} Execution Witness X (co, rf, fr) Candidate Execution (E, X) Memory Model MM : {(E, X)} {true, false} Construction? Or Ostrovsky Don t Sit on the Fence April 25th / 50

14 Candidate execution Example Or Ostrovsky Don t Sit on the Fence April 25th / 50

15 Minimal cycles Definition MC1 Per thread: At most 2 accesses Accesses are adjacent in the cycle MC2 Per memory location: At most 3 accesses Accesses are adjacent in the cycle Or Ostrovsky Don t Sit on the Fence April 25th / 50

16 Minimality condition: MC2 Example Or Ostrovsky Don t Sit on the Fence April 25th / 50

17 Delay cycles Definition Delay is a relaxed edge of po, or rf on an architecture A (MM). Delays can be prevented using fences. Theorem A candidate execution is valid on A but not on SC if: DC1 It contains at least one cycle that has a delay. DC2 All of the cycles contain a delay. Or Ostrovsky Don t Sit on the Fence April 25th / 50

18 Critical cycles Definition CS1 At least one delay CS2 Per thread: At most 2 accesses Accesses are adjacent in the cycle To different memory locations CS3 Per memory location: At most 3 accesses Accesses are adjacent in the cycle From different threads Or Ostrovsky Don t Sit on the Fence April 25th / 50

19 Critical cycles Definition CS1 At least one delay CS2 Per thread: At most 2 accesses Accesses are adjacent in the cycle To different memory locations CS3 Per memory location: At most 3 accesses Accesses are adjacent in the cycle From different threads Or Ostrovsky Don t Sit on the Fence April 25th / 50

20 Critical cycles: proof Theorem If an execution candidate is valid on A but not on SC, then there is a cycle which satisfies: 1 Is a minimal cycle. 2 Has least one delay. 3 Accesses on the same threads are to different locations 4 Accesses to the same location are from different threads Or Ostrovsky Don t Sit on the Fence April 25th / 50

21 Table of contents 1 Introduction 2 Cycles 3 Static Analysis 4 Soundness of Construction 5 Fence placement 6 Conclusion Or Ostrovsky Don t Sit on the Fence April 25th / 50

22 Abstract Event Graph Definition Abstract Event Wx, Rx: Abstraction of events Static event set E s = {abstract events} Static Program Order po s : Abstraction of po Competing pairs cmp: Communication between threads AEG aeg (E s, po s, cmp) Or Ostrovsky Don t Sit on the Fence April 25th / 50

23 Abstract Event Graph Example Or Ostrovsky Don t Sit on the Fence April 25th / 50

24 AEG construction Convert C program to goto-instructions Ignore local variables Read each instruction, and update the AEG, starting from the empty graph. Semi-formally: τ[i k ;...](aeg) = τ[i k ;...](f (aeg, (i k,..., i k 1))) Or Ostrovsky Don t Sit on the Fence April 25th / 50

25 Goto instructions Example Or Ostrovsky Don t Sit on the Fence April 25th / 50

26 Transformation function Example τ[x = f (y 1,..., y k ); i](e s, po s, cmp) = let reads = {Ry 1,..., Ry k } in let writes = {Wx} in let E s = E s reads writes in let po s = po s (end(po s ) reads) (reads writes) in τ[i](e s, po s, cmp) end(x) all sink events of x Or Ostrovsky Don t Sit on the Fence April 25th / 50

27 Transformation function: cont. Example τ[start thread th; i](aeg) = let main = τ[body(th)]( ) in let local = τ[i](aeg) in let inter = τ[i]( ) in (local.e s main.e s, local.po s main.po s, local.e s inter.e s ) A B {(a, b) A B addr(a) = addr(b) (write(a) write(b))} (,, ) Or Ostrovsky Don t Sit on the Fence April 25th / 50

28 Program & AEG Example Or Ostrovsky Don t Sit on the Fence April 25th / 50

29 Event structure construction Analogous to AEG S(P) = {(E, po)}: possible event structures S(P) = σ(p)( ): σ is very much like τ Or Ostrovsky Don t Sit on the Fence April 25th / 50

30 Transformation function Example σ[lhs = rhs; i](ses) = let de = dyn evts(lhs = rhs) in let E (E, w, R) = E {w} R in let po (po, w, R) = po (end(po) R) (R {w}) in let es (es, w, R) = (E (es.e, w, R), po (es.po, w, R)) in σ[i]({es (es, w, R) es ses, (w, R) de}) dyn evts(lhs = rhs) = {(w, R)}: Set of events that can cause the statement. Example: dyn evts(x = y + z) = {(Wxv 1, {Ryv 2, Rzv 3 }) v 1 = v 2 + v 3 } Or Ostrovsky Don t Sit on the Fence April 25th / 50

31 Transformation function: cont. Example σ[start thread th; i](ses) = let local = σ[body(th)]( ) in let main = σ[i](ses) in es l local,es m main {(es l.e es m.e, es l.po es m.po)} Or Ostrovsky Don t Sit on the Fence April 25th / 50

32 AEG & ES Example Or Ostrovsky Don t Sit on the Fence April 25th / 50

33 Loops Event a might depend on itself on previous iterations In that case, duplicate loop body Or Ostrovsky Don t Sit on the Fence April 25th / 50

34 Table of contents 1 Introduction 2 Cycles 3 Static Analysis 4 Soundness of Construction 5 Fence placement 6 Conclusion Or Ostrovsky Don t Sit on the Fence April 25th / 50

35 Soundness G = aeg(p) E S(P) Are they related? Or Ostrovsky Don t Sit on the Fence April 25th / 50

36 Concretization Definition γ e (se) {e e se s.t. addr(e) = addr(e ) dir(e) = dir(e ) origin(e) = origin(e )} γ(srel) {(c 1, c 2 ) (s 1, s 2 ) srel s.t. (c 1, c 2 ) γ e ({s 1 }) γ e ({s 2 })} Theorem E 1 γ e (E s,1 ), E 2 γ e (E s,2 ) E 1 E 2 γ(e s,1 E s,2 ) Or Ostrovsky Don t Sit on the Fence April 25th / 50

37 Events and program order Theorem E S(P), G = aeg(p) E.E γ e (G.E s ), E.po γ(g.po + s ) Lemma 5.3 in the article po + is po s closure Or Ostrovsky Don t Sit on the Fence April 25th / 50

38 rf, co, and fr Theorem E S(P), X = (rf, co, fr), (E, X) is a CE, G = aeg(p) X.rfe, X.coe, X.fre γ(g.cmp) Lemma 5.4 in the article Or Ostrovsky Don t Sit on the Fence April 25th / 50

39 Soundness Theorem Let P be a program. Let E S(P), X = (rf, co, fr) an execution witness, (E, X) a candidate execution. Also, let G = aeg(p). E.po X.coi X.rfi X.fri γ(g.po + s ) X.coe X.rfe X.fre γ(g.cmp) E.E γ e (G.E s ) From the two previous theorems Or Ostrovsky Don t Sit on the Fence April 25th / 50

40 Static critical cycles Theorem Let E S(P), X = (rf, co, fr), G = aeg(p). If (E, X) contains a critical cycle c = c 0,..., c n 1, then there is a cycle d = d 0,..., d n 1 in G so that: {c i } γ e ({d i }) {(c i, c i+1 mod n )} γ({(d i, d i+1 mod n )}) Looking for cycles in G will find all cycles in (E, X) Any cycle detection algorithm will do. Or Ostrovsky Don t Sit on the Fence April 25th / 50

41 Static critical cycles Example Or Ostrovsky Don t Sit on the Fence April 25th / 50

42 Static critical cycles Example a, b 1, d, e, f Or Ostrovsky Don t Sit on the Fence April 25th / 50

43 Table of contents 1 Introduction 2 Cycles 3 Static Analysis 4 Soundness of Construction 5 Fence placement 6 Conclusion Or Ostrovsky Don t Sit on the Fence April 25th / 50

44 Considerations We have a list of cycles C = {C 1,..., C n }. Now what? Or Ostrovsky Don t Sit on the Fence April 25th / 50

45 Considerations We have a list of cycles C = {C 1,..., C n }. Now what? Delays Fence types, locations & costs Different for each architecture Or Ostrovsky Don t Sit on the Fence April 25th / 50

46 Problem parameters Input: aeg(es, po s, cmp) C = {C1,..., C n } T = {f, lwf, cf, dp}, cost : T N 1 placements(c) po s T 1 Constrains 1 Output: (l, t) placements(c), t l {0, 1} Cost function: Rough estimation of cost Minimize (l,t) placements(c) t l cost(t) Problems? 1 Architecture dependent Or Ostrovsky Don t Sit on the Fence April 25th / 50

47 Constraints Every delay needs to be fenced Each type of delay can be handled by different types of fences A fence can participate in multiple delays Any of condition:... 1 Promises the problem is satisfiable Trust the cost function Or Ostrovsky Don t Sit on the Fence April 25th / 50

48 TSO delays & fences One type of fence f Only powr delays Or Ostrovsky Don t Sit on the Fence April 25th / 50

49 AEG in TSO Example Or Ostrovsky Don t Sit on the Fence April 25th / 50

50 AEG in TSO Example Not that bad, right? Or Ostrovsky Don t Sit on the Fence April 25th / 50

51 Power: delays & fences Delays powr, poww, porw, porr f Can solve delays in po + s. between(x, y) {(e 1, e 2 ) po s (x, e 1 ), (e 2, y) po s } lwf Same as f, but unsuitable for powr violations. dp Applies only to delays in po s Or Ostrovsky Don t Sit on the Fence April 25th / 50

52 Power: placement & constraints Exact definition of placements(c): placements(c) {(l, dp) l delays(c)} For each d delays(c) {(l, t) t T \ {dp}, l between(delays(c))} {(l, t) t {f, lwf}, l po s (C)} If d powr then e between(d) f e 1 If d poww then e between(d) (f e + lwf e ) 1 If d porw porr then dpd + e between(d) (f e + lwf e ) 1... Or Ostrovsky Don t Sit on the Fence April 25th / 50

53 Power: placement & constraints Exact definition of placements(c): placements(c) {(l, dp) l delays(c)} For each d delays(c) {(l, t) t T \ {dp}, l between(delays(c))} {(l, t) t {f, lwf}, l po s (C)} If d powr then e between(d) f e 1 If d poww then e between(d) (f e + lwf e ) 1 If d porw porr then dpd + e between(d) (f e + lwf e ) 1... How to solve? ILP Or Ostrovsky Don t Sit on the Fence April 25th / 50

54 AEG & ILP Example Or Ostrovsky Don t Sit on the Fence April 25th / 50

55 Table of contents 1 Introduction 2 Cycles 3 Static Analysis 4 Soundness of Construction 5 Fence placement 6 Conclusion Or Ostrovsky Don t Sit on the Fence April 25th / 50

56 Evaluation Measure how well did we do? Or Ostrovsky Don t Sit on the Fence April 25th / 50

57 Evaluation Measure how well did we do? Relative overhead Compared to other tools Different architectures Or Ostrovsky Don t Sit on the Fence April 25th / 50

58 Evaluation Measure how well did we do? Relative overhead Compared to other tools Different architectures Musketeer,Pensieve,Visual Studio, after Each access, after Heap accesses Or Ostrovsky Don t Sit on the Fence April 25th / 50

59 Conclusion Define critical cycles Discover them using static analysis Prove the static analysis is sound Find the best way to place fences Or Ostrovsky Don t Sit on the Fence April 25th / 50

60 Excluded topics Related works Pointer analysis Most of the conversion technicalities Some architecture specifics Implementation & performance (mostly) Or Ostrovsky Don t Sit on the Fence April 25th / 50

61 Questions? Or Ostrovsky Don t Sit on the Fence April 25th / 50