Shape Analysis. Mooly Sagiv

Transcription

1 Shape Aalysis Mooly Sagiv

2 ... ad also Uiversiy of Wiscosi F. DiMaio D. Gopa A. Logiov T. Reps IBM Research J. Field H. Koloder M. Rodeh E. Yahav Microsof Research J. Berdie B. Cook G. Ramaligam Uiversiy of Massachuses N. Immerma B. Hesse Iria B. Jeae Tel-Aviv Uiversiy D. Ami I. Bogudlov G. Arold G. Erez N. Dor T. Lev-Ami R. Maevich R. Shaham A. Rabiovich N. Riezky G. Yorsh A. Warshavsky Uiversiä des Saarlades J. Bauer R. Biber R. Wilhelm

3 Shape Aalysis [Joes ad Muchick 1981] Deermie he possible shapes of a dyamically allocaed daa srucure a a give program poi

4 Programs ad Properies Dyamically allocaed memory Recursive daa srucures Recursive procedures Cocurrecy Memory safey Preservaio of Daa srucure ivarias Parial correcess Termiaio Liearizabiliy

5 Oulie Shape absracios i a ushell Compuig rasformers Heap decomposiio

6 Represeig Cocree Sores by Logical Srucures Parameric vocabulary Heap Locaios Idividuals Program variables Uary relaios Fields Biary relaios

7 Represeig Cocree Sores by Logical Srucures U = {u1, u2, u3, u4, u5} = {u1}, p = {u3} = {<u1, u2>, <u2, u3>, <u3, u4>, <u4, u5>} r = {u1, u2, u3, u4, u5} r p = {u3, u4, u5} r r r r r u1 u2 u3 u4 u5 p r p r p r p

8 Represeig Absrac Sores by 3-Valued Logical Srucures A joi semi-laice: = 1/2 {0, 1, ½} values for relaios

9 Caoical Absracio r r r r r r u1 u2 u3 u4 u5 u6 p r p r p r r r r a 1 a 2 a 3 a 4 p r p r p

10 Caoical Absracios as Formulas [Yorsh 03, Kucak 04, Wies 07 ] r r r r a 1 a 2 a 3 v: ((v) r (v) p(v) r p (v)) ( (v) r (v) p() r p (v)) ( (v) r (v) p(v) r p (v)) ( (v) r (v) p(v) r p (v))) r p p a 4 r p v:r (v) w: (w) *(w, v) v:r p (v) w: p(w) *(w, v) 10

11 Caoical Absracio Limied form of quaified ivarias quaifier aleraio oly i isrumeaio No a saic memory pariio The same memory locaio ca be represeed by differe absrac odes i differe shape graphs

12 Mos Precise Absrac Trasformer [Couso, Couso POPL 1979] τ γ α τ #

13 Parial Cocreizaio τ τ #

14 Parial Cocreizaio τ # τ #

15 y y. Bes Trasformer ( = ) Cocree Semaics y y. γ caoical absracio y y y

16 Parial Cocreizaio based Trasformer ( = ) y y Absrac Semaics y y γ caoical absracio y y y

17 Parial Cocreizaio Employed i oher shape aalysis algorihms [Disefao, TACAS 06, Eva, SAS 07, POPL 08] Soudess is immediae Ca eve guaraee precisio uder cerai codiios [Lev-Ami, VMCAI 07] Locally refie he absrac domai per saeme

18 Heap Decomposiio for Cocurre Shape Aalysis Joi work wih R. Maevich T. Lev-Ami Tel Aviv Uiversiy G. Ramaligam MSR Idia J. Berdie MSR Cambridge

19 Mai Resuls New parameric absracio for heaps Heap decomposiio + Caresia produc Epoeial sae space reducio Implemeaio i HeDec (Geeralizes TVLA) Heap Decomposiio + Caoical absracio Used o prove ieresig properies of heapmaipulaig programs wih fie-graied parallelism Liearizabiliy

20 Treiber s No-blockig Sack [1] void push(sack *S, daa_ype v) { [2] Node * = alloc(sizeof(node)); [3] ->d = v; [4] do { [5] Node * = S->Top; [6] -> = ; [7] } while (!CAS(&S->Top,,)); [8] } [9] daa_ype pop(sack *S){ [10] do { [11] Node * = S->Top; [12] if ( == NULL) [13] reur EMPTY; [14] Node *s = ->; [15] daa_ype r = s->d; [16] } while (!CAS(&S->Top,,s)); [17] reur r; [18] }

21 Full Sae r1 r4 pc=7 Top pc=16 s pc=7 r2 s pc=16 r3

22 Sub-saes r1 pc=7 Top r2 pc=7 Top Top s r3 pc=16 Top s r4 pc=16

23 Caresia Produc of Sub-saes Top r1 pc=7 r2 pc=7 s r3 pc=16 s r4 r1 pc=7 r2 pc=7 s pc=16 r3 Top Top Top Top Top s r3 pc=16 Top Top pc=16

24 Empirical Resuls Epoeial ime/space reducio No-blockig sack + liearizabiliy ime (sec.) umber of saes Decomp Full umber of hreads umber of hreads

25 ad More iformaio from hp://

26 Thak you Couso for Esablishig he righ midse Galois Coecios Semaic reducios Domai cosrucors

27 Summary Shape aalysis is a ieresig absrac ierpreaio problem Hadles ubouded memory Parially disjucive absracios Parial cocreizaio is useful for rasformers Heap decomposiio is useful for scalabiliy Geeralizes hread-modular aalysis Limied forms of quaified ivarias ca be uilized o prove ieresig properies