Interference graph. Register Allocation. A bigger example. Units of allocation

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1 Rgistr Alloation Intrfrn graph Th prolm: assign mahin rsours (rgistrs, stak loations) to hol run-tim ata Constraint: simultanously liv ata alloat to iffrnt loations Goal: minimiz ovrha of stak loas & stors an rgistr movs Rprsnt notion of simultanously liv using intrfrn graph nos ar units of alloation n 1 is link y an g to n 2 if n 1 an n 2 ar simultanously liv at som program point symmtri, not rflxiv, not transitiv Two ajant nos must alloat to istint loations Craig Chamrs 181 CSE 501 Craig Chamrs 182 CSE 501 Units of alloation A iggr xampl What ar th units of alloation? varials? sparat f/us hains (liv rangs)? valus? i.., varials, in SSA form aftr opy propagation x := 5 a :=... :=... := a... :=... y := x x := y x... x := a := a := x := a :=... Craig Chamrs 183 CSE 501 Craig Chamrs 184 CSE 501

2 Computing intrfrn graph Alloating rgistrs using intrfrn graph Construt as si-fft of liv varials analysis akwars itrativ fa algorithm Flow funtion: intify fs & last uss LV x :=...y... : Alloating varials to k rgistrs is quivalnt to fining a k-oloring of th intrfrn graph k-oloring: olor nos of graph using up to k olors, ajant nos hav iffrnt olors optimal graph oloring: NP-omplt LV if... : Craig Chamrs 185 CSE 501 Craig Chamrs 186 CSE 501 Spilling Stati frquny stimats If an t fin k-oloring of intrfrn graph, must spill som varials to stak, until th rsulting intrfrn graph is k-oloral Whih to spill? last frquntly ass varials most onfliting varials (nos with highst out-gr) Initial no: wight = 1 Nos aftr ranh: 1/2 wight of ranh Nos in loop: 10x nos outsi loop Dynami profils oul giv ttr frquny stimats Wight intrfrn graph: wight(n) = sum ovr all rfrns (uss an fs) r of n: xution frquny of r Just n huristi ranking of varials Try to spill nos with lowst wight an highst out-gr, if for to spill Craig Chamrs 187 CSE 501 Craig Chamrs 188 CSE 501

3 Simpl gry alloation algorithm Exampl For all nos, in rasing orr of wight: try to alloat no to a rgistr, if possil if not, alloat to a stak loation Rsrv 2-3 srath rgistrs to us whn manipulating nos alloat to stak loations Wight Orr: Assum 3 rgistrs availal Craig Chamrs 189 CSE 501 Craig Chamrs 190 CSE 501 Improvmnt #1: a simplifiation phas [Chaitin 82] Ky ia: nos with < k nighors an alloat aftr all thir nighors, ut still guarant a rgistr So rmov thm from th graph first rus th gr of th rmaining nos Must rsort to spilling only whn all rmaining nos hav gr k Th algorithm whil intrfrn graph not mpty: whil thr xists a no with < k nighors: rmov it from th graph push it on a stak if all rmaining nos hav k nighors, thn lok: pik a no to spill (hoos no with lowst (spill ost/gr)) rmov no from graph a to spill st if any nos in spill st: insrt spill o for all spill nos (insrt stors aftr fs, loas for uss) ronstrut intrfrn graph, start ovr whil stak not mpty: pop no from stak alloat to rgistr Craig Chamrs 191 CSE 501 Craig Chamrs 192 CSE 501

4 Exampl Exampl Wight Orr: Wight Orr: Assum 3 rgistrs availal Assum 2 rgistrs availal Craig Chamrs 193 CSE 501 Craig Chamrs 194 CSE 501 Susumption An annoying as Twist in Chaitin s algorithm: if s x:=y, whr x & y not simultanously liv, thn mrg liv rangs & liminat all suh opis + avois gnrating o for simpl opis an introu xtra spilling D A B If alloat valus insta of varials or liv rangs, thn susumption happns impliitly C If only 2 rgistrs availal lok immiatly, must spill Craig Chamrs 195 CSE 501 Craig Chamrs 196 CSE 501

5 Improvmnt #2: lok osn t man spill [Briggs t al. 89] Improvmnt #3: liv rang splitting Priority-Bas Coloring [Chow & Hnnssy 84] Ky ia: just aus a no has k nighors osn t man it will n to spill (nighors may gt ovrlapping olors) Algorithm: Lik Chaitin, xpt: whn rmoving lok no, just push onto stak ( optimisti spilling ) whn on rmoving nos: pop nos off stak an s if thy an alloat rally spill only if it an t alloat at this stag Ky ia: if a varial an t alloat to a rgistr, try to split it into multipl surangs that an alloat sparatly mov instrutions insrt at split points som liv rang pis in rgistrs, som in mmory sltiv spilling Othr misllanous nhanmnts Craig Chamrs 197 CSE 501 Craig Chamrs 198 CSE 501 Exampl Improvmnt #4: rmatrialization... a... 1 := := a := a... 2 := :=... 2 := Wight Orr: 2 a Ia: insta of rloaing valu from mmory, romput it insta, if romputation is hapr than rloaing Simpl stratgy: hoos rmatrialization ovr spilling, if an romput a valu in a singl instrution, an all oprans will always availal Exampls: onstants arss of gloal var arss of var in stak fram Assum 2 rgistrs availal Craig Chamrs 199 CSE 501 Craig Chamrs 200 CSE 501

6 Prforman rsults [Briggs t al. 94] E.g. For som prour: Rgistr alloation an alls Simpl approah: alling onvntions Mor sophistiat: intrproural rgistr alloation XXX spill instrutions for YYY spill instrutions aftr YYY is Z% smallr than XXX Z rangs twn -2% an 48% for optimisti spilling Z rangs twn -26% an 33% for rmatrialization Optimisti spilling a goo huristi Mix rsults for rmatrialization Craig Chamrs 201 CSE 501 Craig Chamrs 202 CSE 501 Calling onvntions Call-sav vs. allr-sav rgistrs Goals: fast alls pass k argumnts in rgistrs, rsult in rgistr languag-inpnnt support uggr, profilr, t. Prolmati languag faturs: varargs passing/rturning aggrgats rturning multipl valus xptions, stjmp/longjmp N a onvntion at alls for whih rgistrs manag y allr (allr-sav) an whih manag y all (all-sav) SPARC has harwar-sav rgistrs, too Callr-sav: allr must sav/rstor any allr-sav rgistrs liv aross alls all is fr to us ths rgistrs w/o any ovrha Call-sav: all must sav/rstor any all-sav rgistrs it uss allr is fr to us ths rgistrs, vn aross alls Harwar-sav: allr an all an us frly Craig Chamrs 203 CSE 501 Craig Chamrs 204 CSE 501

7 A prolm with all-sav rgistrs Impat on rgistr alloator Run-tim utilitis (.g. longjmp) an programming nvironmnt tools (.g. uggr) n to al to fin ontnts of rgistrs rlativ to a partiular stak fram Callr-sav rgistrs ar on stak in stak fram at known pla Call-sav rgistrs? How shoul rgistr alloator al w/ alling onvntions? Simpl: alling-onvntion-olivious rgistr alloation spill all liv allr-sav rgistrs for all, rstor aftr all sav all all-sav rgistrs at ntry, rstor at rturn Bttr: alling-onvntion-awar rgistr alloation inorporat prfrr rgistrs for formals, atuals all kills allr-sav rgistrs alloator knows to avoi ths rgistrs, sav/rstor o turns into normal spills liv-rang splitting partiularly usful to split var into for all/uring all/aftr all sgmnts ntry is f of all all-sav rgistrs, xit is us alloator knows must spill ths rgistrs if us in pro Craig Chamrs 205 CSE 501 Craig Chamrs 206 CSE 501 Exploiting alling onvntion Rih man s intrproural rgistr alloation Calling-onvntion-awar rgistr alloator an ustomiz its usag to us hapr rgistrs laf routins (try to) us only allr-sav rgistrs routins with alls us all-sav rgistrs for varials liv aross alls Alloat rgistrs aross alls to minimiz ovrlap twn allr an all sugraph Alloat gloal varials to rgistrs ovr ntir program Poor man s intrproural rgistr alloation Coul o ompil-tim intrproural rgistr alloation + gains most nfit might xpnsiv might rquir lots of rompilation aftr programming hang Or, oul o link-tim r-alloation + low ompil-tim ost + littl impat on sparat ompilation ost at link tim proaly lss fftiv Craig Chamrs 207 CSE 501 Craig Chamrs 208 CSE 501

8 Wall s link-tim rgistr alloator [Wall 86] Compilr os loal alloation + planning for linkr gnrats all graph info gnrats varial usag info for ah pro gnrats rgistr ations xut y linkr if varial alloat to rgistr Linkr os intrproural alloation & paths ompil o trmins intrfrn graph among varials piks st aitional varials to alloat to rgistrs xuts rgistr ations for thos vars to path ompil o Rgistr ations Dsri hangs to o if givn var alloat to a rgistr OPx(var): rpla opran x with rg alloat to var RESULT(var): rpla rsult with rg alloat to var (var): lt instrution if var alloat to a rg Us: for ah varial var r := loa var: (var) rk := ri op rj: OP1(var) if var loa into ri, OP2(var) if var loa into rj, RESULT(var) if var stor from rk, stor var := r: (var) Craig Chamrs 209 CSE 501 Craig Chamrs 210 CSE 501 Exampl A prolm Sour o: w = (x + y) * z; rgistr ations original o x y z w r1 := loa x r2 := loa y r3 := r1 + r2 OP1 OP2 r4 := loa z r5 := r3 * r4 OP2 RESULT stor w := r5 What if loa valu is still liv aftr an ovrwriting stor? Exampl: w = y++ * z; original o r1 := loa y r2 := r1 + 1 stor y := r2 r2 := loa z OP1, RESULT rgistr ations y z w r1 := r1 * r2 OP1 OP2 RESULT stor w := r1 Ths rgistr ations ar rokn, if y in a rgistr! ry := ry + 1 r2 := loa z r1 := ry * r2 // ry ras upat y valu, not original stor w := r1 Craig Chamrs 211 CSE 501 Craig Chamrs 212 CSE 501

9 Solution Link-tim oprations N two mor ations: LOAD(var): rpla loa with mov from rg holing var STORE(var): rpla stor with mov to rg holing var Us LOAD(var) insta of (var) if var is stor into whil rsult of loa is still liv Us STORE(var) insta of (var) if rhs is stor into mor than on varial Exampl: w = x = y++ * z; original o r1 := loa y r2 := r1 + 1 stor y := r2 r2 := loa z rgistr ations x y z w LOAD RESULT r1 := r1 * r2 OP2 RESULT stor x := r1 STORE OP1 stor w := r1 Construt wight all graph from ompilr tals wights an om from stati stimats or profil info ah pro annotat with list of us loal vars Travrs all graph ottom-up, assigning loals to groups (a kin of intrfrn graph) no simultanously-liv loals in sam group ah gloal in its own group group wight y sum of mmrs wights rursion & inirt alls pos ompliations Alloat groups to rgistrs in rasing orr of wight Run rgistr ations uring o rloation to improv o Craig Chamrs 213 CSE 501 Craig Chamrs 214 CSE 501 Exampl Possil improvmnts Call graph: v11,v12 v5, g1 v9, v10 v3,v4,g1,g2 v6, v7, v8 v1,v2, g1 Us ral profil ata to onstrut wights Do intraproural rgistr alloation at ompil-tim Trak livnss info for vars at ah all sit Trak intraproural intrfrn graph Us ral intrfrn graph to run link-tim alloation Groups: Craig Chamrs 215 CSE 501 Craig Chamrs 216 CSE 501

10 Rsults DECWRL Titan RISC prossor: 64 rgistrs Basi xprimnt: loal ompil-tim alloation uss 8 rgistrs intrproural link-tim alloator uss 52 rgistrs simpl stati frquny stimats smallish nhmark programs 10-25% sp-up ovr loal alloation alon Small improvmnts (0-6%) with ral profil ata Small improvmnts (0-5%) if us intraproural alloation too mor pronoun for largr, ral nhmarks Lss nfit if fwr rgistrs availal for gloal alloation.g. 5-20% for 8 gloal rgistrs Link-tim + loal ttr than intraproural rgistr alloation Craig Chamrs 217 CSE 501