Register Allocation III. Interference Graph Allocators. Computing the Interference Graph (in MiniJava compiler)

Transcription

1 Register Alloation III Announements Reommen have interferene graph onstrution working by Monay Last leture Register alloation aross funtion alls Toay Register alloation options Interferene Graph Alloators Chaitin Briggs CS553 Leture Register Alloation III 2 CS553 Leture Register Alloation III 3 Granularity of Alloation (Renumber step in Briggs) What is alloate to registers? Variables/Temporaries Live ranges/webs (i.e., u-hains with ommon uses) Values (i.e., efinitions; same as variables with SSA) t 1 : x := 5 b 2 t 2 : y := x b 3 t 3 : x := y+1 b 4 b 1 t 6 :... x... t 4 :... x... t 5 : x := 3 Variables: 2 (x & y) Live Ranges/Web: 3 (t 1 t 2,t 4 ; t 2 t 3 ; t 3,t 5 t 6 ) Values: 4 (t 1, t 2, t 3, t 5, φ (t 3,t 5 )) What are the traeoffs? Eah alloation unit is given a symboli register name (e.g., s1, s2, et.) CS553 Leture Register Alloation III 4 Computing the Interferene Graph (in MiniJava ompiler) Use results of live variable analysis for eah flow graph noe n o for eah ef in ef(n) o for eah temp in liveout(n) o if ( not stmt(n) isa MOVE or ef!= temp ) then E E (ef, temp) CS553 Leture Register Alloation III 5 1

2 Coalesing Coalesing Logistis Move instrutions Coe generation an proue unneessary move instrutions mov t1, t2 If we an assign t1 an t2 to the same register, we an eliminate the move If t1 an t2 are not onnete in the interferene graph, oalese them into a single variable Rule When builing the interferene graph, o NOT make virtual registers interfere ue to opies. If the virtual registers s1 an s2 o not interfere an there is a opy statement s1 = s2 then s1 an s2 an be oalese. Example Problem Coalesing an inrease the number of eges an make a graph unolorable Limit oalesing to avoi unolorable graphs oalese t1 t2 t1 t2 CS553 Leture Register Alloation III 6 CS553 Leture Register Alloation III 7 Coalesing in MiniJava ompiler Currently the InterfereneGraph only has one Temp.Temp assoiate with eah noe represent eah merge noe with just one of the temps keep a separate map of representatives mappe to sets of temps also keep a map of temps mappe to their representative when rewriting the oe use the representative instea of the original temp Register Alloation: Spilling If we an t fin a k-oloring of the interferene graph Spill variables (noes) until the graph is olorable Choosing variables to spill Choose least frequently aesse variables Break ties by hoosing noes with the most onflits in the interferene graph Yes, these are heuristis! CS553 Leture Register Alloation III 8 CS553 Leture Register Alloation III 9 2

3 Weighte Interferene Graph Goal Weight(s) =! f ( r) f(r) is exeution frequeny of r " referenes r of s Stati approximation Use some reasonable sheme to rank variables One possibility Weight(s) = 1 Noes after branh: ½ weight of branh Noes in loop: 10 weight of noes outsie loop Improvement #1: Simplifiation Phase [Chaitin 81] Noes with < k neighbors are guarantee olorable Improvement over simple greey oloring algorithm Remove them from the graph first Reues the egree of the remaining noes Must spill only when all remaining noes have egree k Referre to as pessimisti spilling CS553 Leture Register Alloation III 10 CS553 Leture Register Alloation III 11 The Problem: Worst Case Assumptions Improvement #2: Optimisti Spilling [Briggs 89] Is the following graph 2-olorable? s1 s1 s4 s2 s4 s3 Clearly 2-olorable But Chaitin s algorithm leas to an immeiate blok an spill The algorithm assumes the worst ase, namely, that all neighbors will be assigne a ifferent olor CS553 Leture Register Alloation III 12 s2 s3 Some neighbors might get the same olor Noes with k neighbors might be olorable Bloking oes not imply that spilling is neessary Push bloke noes on stak (rather than plae in spill set) Chek olorability upon popping the stak, when more information is available Defer eision CS553 Leture Register Alloation III 13 3

4 Algorithm [Briggs et al. 89] while interferene graph not empty o while a noe n with < k neighbors o Remove n from the graph simplify Push n on a stak if any noes remain in the graph then { bloke with >= k eges } Pik a noe n to spill { lowest spill-ost/highest egree } Push n on stak efer eision Remove n from the graph while stak not empty o Pop noe n from stak make eision if n is olorable then Alloate n to a register else Insert spill oe for n { Store after ef; loa before use } Reonstrut interferene graph & start over CS553 Leture Register Alloation III 14 Example Attempt to 2-olor this graph (, ) Stak: b * f* a* e* * bloke noe e a f CS553 Leture Register Alloation III 15 b Weighte orer: e a f b Possible Register Alloation Design Overall algorithm: graph oloring with simplifiation Interferene graph: two temps interfere if one is efine in a stmt an the other is live out of the same stmt exeption is a MOVE statement where the temps are the soure an est Coalese: Briggs strategy oalese if new noe will have fewer than K neighbors of signifiant egree (>= K) Spill heuristi: spill the noe with the lowest weight an break ties by spilling the noe with the most ajaent eges Simplifiation: optimisti Selet: pop everything off the stak before generating spill oe Improvement #3: Live Range Splitting [Chow & Hennessy 84] Start with variables as our alloation unit When a variable an t be alloate, split it into multiple subranges for separate alloation Seletive spilling: put some subranges in registers, some in memory Insert memory operations at bounaries Why is this a goo iea? CS553 Leture Register Alloation III 16 CS553 Leture Register Alloation III 18 4

5 Improvement #4: Rematerialization [Chaitin 82]&[Briggs 84] Seletively re-ompute values rather than loaing from memory Reverse CSE Next Time Leture Instrution sheuling Easy ase Value an be ompute in single instrution, an All operans are available Examples Constants Aresses of global variables Aresses of loal variables (on stak) CS553 Leture Register Alloation III 19 CS553 Leture Register Alloation III 20 5