Compilation Lecture 11a. Register Allocation Noam Rinetzky. Text book: Modern compiler implementation in C Andrew A.

Transcription

1 Compilation Leture 11a Text book: Modern ompiler implementation in C Andrew A. Appel Register Alloation Noam Rinetzky 1

2 Registers Dediated memory loations that an be aessed quikly, an have omputations performed on them, and

3 Registers Dediated memory loations that an be aessed quikly, an have omputations performed on them, and Usages Operands of instrutions Store temporary results Can (should) be used as loop indexes due to frequent arithmeti operation Used to manage administrative info e.g., runtime stak

4 Register alloation Number of registers is limited Need to alloate them in a lever way Using registers intelligently is a ritial step in any ompiler A good register alloator an generate ode orders of magnitude better than a bad register alloator

5 Register Alloation Mahine-agnosti optimizations Assume unbounded number of registers Expression trees Basi bloks Mahine-dependent optimization K registers Some have speial purposes Control flow graphs (global register alloation)

6 Basi Compiler Phases Soure program (string) lexial analysis Tokens syntax analysis Abstrat syntax tree semanti analysis AST + Symbol table Translate Frame Intermediate representation Instrution seletion Assembly Global Register Alloation Fin. Assembly

7 Input: Global Register Alloation Sequene of mahine instrutions ( assembly ) Unbounded number of temporary variables aka symboli registers mahine desription Output # of registers, restritions Sequene of mahine instrutions using mahine registers (assembly) Mahine registers Some MOV instrutions removed

8 Global Register Alloation Input: Sequene of mahine ode instrutions (assembly) Output Unbounded number of temporary registers Sequene of mahine ode instrutions (assembly) Mahine registers Some MOVE instrutions removed Missing prologue and epilogue

9 Computing Liveness Information Dataflow analysis (previous leture)

10 Variable Liveness A statement x = y + z defines x uses y and z A variable x is live at a program point if its value (at this point) is used at a later point y = 42 z = 73 x = y + z print(x); x undef, y live, z undef x undef, y live, z live x is live, y dead, z dead x is dead, y dead, z dead (showing state after the statement)

11 Liveness Analysis b = a + 2 = b * b b = + 1 return b * a

12 Liveness Analysis b = a + 2 = b * b b = + 1 return b * a {b, a}

13 Liveness Analysis b = a + 2 = b * b b = + 1 return b * a {a, } {b, a}

14 Liveness Analysis b = a + 2 = b * b b = + 1 return b * a {b, a} {a, } {b, a}

15 Liveness Analysis b = a + 2 = b * b b = + 1 return b * a {a} {b, a} {a, } {b, a}

16 Interferene graph onstrution (Main idea) For every node n in CFG, we have out[n] Set of temporaries live out of n Two variables interfere if they appear in the same out[n] of any node n Cannot be alloated to the same register Conversely, if two variables do not interfere with eah other, they an be assigned the same register We say they have disjoint live ranges How to assign registers to variables?

17 Interferene graph Nodes of the graph = variables Edges onnet variables that interfere with one another Nodes will be assigned a olor orresponding to the register assigned to the variable Two olors an t be next to one another in the graph

18 Results of Liveness Analysis b = a + 2 = b * b b = + 1 return b * a {a} {b, a} {a, } {b, a}

19 Interferene graph olor register b = a + 2 = b * b b = + 1 return b * a {a} {b, a} {a, } {b, a} a eax ebx b

20 Colored graph olor register b = a + 2 = b * b b = + 1 return b * a {a} {b, a} {a, } {b, a} a eax ebx b

21 Graph oloring This problem is equivalent to grapholoring, whih is NP-hard if there are at least three registers No good polynomial-time algorithms (or even good approximations!) are known for this problem We have to be ontent with a heuristi that is good enough for RIGs that arise in pratie

22 Coloring by simplifiation [Kempe 1879] How to find a k-oloring of a graph Intuition: Suppose we are trying to k-olor a graph and find a node with fewer than k edges If we delete this node from the graph and olor what remains, we an find a olor for this node if we add it bak in Reason: fewer than k neighbors d some olor must be left over

23 Coloring by simplifiation [Kempe 1879] How to find a k-oloring of a graph Phase 1: Simplifiation Repeatedly simplify graph When a variable (i.e., graph node) is removed, push it on a stak Phase 2: Coloring Unwind stak and reonstrut the graph as follows: Pop variable from the stak Add it bak to the graph Color the node for that variable with a olor that it doesn t interfere with simplify olor

24 olor register eax ebx Coloring k=2 a b stak: d e

25 olor register eax ebx Coloring k=2 a b stak: d e

26 olor register eax ebx Coloring k=2 a b stak: d e e

27 olor register eax ebx Coloring k=2 a d b e stak: a e

28 olor register eax ebx Coloring k=2 a d b e stak: b a e

29 olor register eax ebx Coloring k=2 a d b e stak: d b a e

30 olor register eax ebx Coloring k=2 a d b e stak: b a e

31 olor register eax ebx Coloring k=2 a b stak: d e a e

32 olor register eax ebx Coloring k=2 a b stak: d e e

33 olor register eax ebx Coloring k=2 a b stak: d e

34 olor register eax ebx Coloring k=2 a b stak: d e

35 Failure of heuristi If the graph annot be olored, it will eventually be simplified to graph in whih every node has at least K neighbors Sometimes, the graph is still K-olorable! Finding a K-oloring in all situations is an NP-omplete problem We will have to approximate to make register alloators fast enough

36 olor register eax ebx Coloring k=2 a b stak: d e

37 olor register eax ebx Coloring k=2 Some graphs an t be olored in K olors: a b stak: d e

38 olor register eax ebx Coloring k=2 Some graphs an t be olored using K olors: a b d e a? e?

39 olor register eax ebx Coloring k=2 Some graphs an t be olored using K olors: a b d e a? e?

40 olor register eax ebx Coloring k=2 Some graphs an t be olored in K olors: a b stak: d e

41 olor register eax ebx Coloring k=2 Simplifiation gets stuk! a b stak: d e

42 Chaitin s algorithm Choose and remove an arbitrary node, marking it troublesome Use heuristis to hoose whih one When adding node bak in, it may be possible to find a valid olor Otherwise, we have to spill that node

43 Spilling Phase 3: spilling one all nodes have K or more neighbors, pik a node for spilling There are many heuristis that an be used to pik a node Try to pik node not used muh, not in inner loop Storage in ativation reord Remove it from graph We an now repeat phases 1-2 without this node Better approah rewrite ode to spill variable, reompute liveness information and try to olor again

44 olor register eax ebx Coloring k=2 Some graphs an t be olored in K olors: a d b e stak: e a d no olors left for e!

45 olor register eax ebx Coloring k=2 Some graphs an t be olored in K olors: a d b e stak: b e a d

46 olor register eax ebx Coloring k=2 Some graphs an t be olored in K olors: a d b e stak: e a d

47 olor register eax ebx Coloring k=2 Some graphs an t be olored in K olors: a b stak: a d d e

48 olor register eax ebx Coloring k=2 Some graphs an t be olored in K olors: a b stak: d d e

49 olor register eax ebx Coloring k=2 Some graphs an t be olored in K olors: a b stak: d e

50 Optimizing move instrutions Code generation produes a lot of extra mov instrutions mov t5, t9 If we an assign t5 and t9 to same register, we an get rid of the mov effetively, opy elimination at the register alloation level Idea: if t5 and t9 are not onneted in inferene graph, oalese them into a single variable; the move will be redundant Problem: oalesing nodes an make a graph un-olorable Conservative oalesing heuristi

51 Optimizing MOV instrutions Code generation produes a lot of extra mov instrutions mov t5, t9 If we an assign t5 and t9 to same register, we an get rid of the mov effetively, opy elimination at the register alloation level Idea: if t5 and t9 are not onneted in inferene graph, oalese them into a single variable; the move will be redundant Problem: oalesing nodes an make a graph un-olorable Conservative oalesing heuristi

52 Coalesing MOVs an be removed if the soure and the target share the same register The soure and the target of the move an be merged into a single node (unifying the sets of neighbors) May require more registers Conservative Coalesing Merge nodes only if the resulting node has fewer than K

53 Constrained Moves A instrution T S is onstrained if S and T interfere May happen after oalesing X Y Y Z X Y Z Constrained MOVs are not oalesed

54 Constrained Moves A instrution T S is onstrained if S and T interfere May happen after oalesing X Y X,Y Y Z Z Constrained MOVs are not oalesed

55 Constrained Moves A instrution T S is onstrained if S and T interfere May happen after oalesing X Y X,Y Y Z Z Constrained MOVs are not oalesed

56 Handling preolored nodes Some variables are pre-assigned to registers Eg: mul on x86/pentium uses eax; defines eax, edx Eg: all on x86/pentium Defines (trashes) aller-save registers eax, ex, edx To properly alloate registers, treat these register uses as speial temporary variables and enter into interferene graph as preolored nodes

57 Handling preolored nodes Simplify. Never remove a pre-olored node it already has a olor, i.e., it is a given register Coloring. One simplified graph is all olored nodes, add other nodes bak in and olor them using preolored nodes as starting point

58 Pre-Colored Nodes Some registers in the intermediate language are preolored: orrespond to real registers (stak-pointer, frame-pointer, parameters, ) Cannot be Simplified, Coalesed, or Spilled infinite degree Interfered with eah other But normal temporaries an be oalesed into pre-olored registers Register alloation is ompleted when all the nodes are pre-olored

59 Caller-Save and Callee-Save Registers allee-save-registers (MIPS 16-23) Saved by the allee when modified Values are automatially preserved aross alls aller-save-registers Saved by the aller when needed Values are not automatially preserved Usually the arhiteture defines aller-save and alleesave registers Separate ompilation Interoperability between ode produed by different ompilers/languages But ompilers an deide when to use aller/allee registers

60 Caller-Save vs. Callee-Save Registers int foo(int a) { int b=a+1; f1(); g1(b); return(b+2); } void bar (int y) { int x=y+1; f2(y); g2(2); }

61 Saving Callee-Save Registers enter: def(r 7 ) enter: def(r 7 ) t 231 r 7 exit: use(r 7 ) r 7 t 231 exit: use(r 7 )

62 Graph Coloring with Coalesing Build: Construt the interferene graph Simplify: Reursively remove non-mov nodes with less than K neighbors; Push removed nodes into stak Coalese: Conservatively merge unonstrained MOV related nodes with fewer than K heavy neighbors Freeze: Give-Up Coalesing on some MOV related nodes with low degree of interferene edges Speial ase: merged node has less than k neighbors All non-mov related nodes are heavy Potential-Spill: Spill some nodes and remove nodes Push removed nodes into stak Selet: Assign atual registers (from simplify/spill stak) Atual-Spill: Spill some potential spills and repeat the proess

63 A Complete Example Callee-saved registers Caller-saved registers

64 A Complete Example

65 A Complete Example Spill a & e Deg. of r1,ae,d < K r2 & b (Alt: ae+r1)

66 A Complete Example ae & r1 (Alt: ) pop freeze r 1 ae-d Simplify d (Alt: ae+r1) pop d d d

67 A Complete Example 1&r3, 2 &r3 a&e, b&r2

68 A Complete Example ae & r1 Simplify d Pop d d opt gen ode

69 Interproedural Alloation Alloate registers to multiple proedures Potential saving aller/allee save registers Parameter passing Return values But may inrease ompilation ost Funtion inline an help

70 Summary Two Register Alloation Methods Loal of every IR tree Simultaneous instrution seletion and register alloation Optimal (under ertain onditions) Global of every funtion Missing Applied after instrution seletion Performs well for mahines with many registers Can handle instrution level parallelism Interproedural alloation

71 The End