Global Register Allocation

Transcription

1 Ltur Outlin Glol Rgistr Allotion Mmory Hirrhy Mngmnt Rgistr Allotion vi Grph Coloring Rgistr intrrn grph Grph oloring huristis Spilling Ch Mngmnt 2 Th Mmory Hirrhy Rgistrs 1 yl yts Ch 3 yls 256k-16M Min mmory yls 512M-64G Disk 0.5-5M yls 10G-1T Mnging th Mmory Hirrhy Progrms r writtn s i thr r only two kins o mmory: min mmory n isk Progrmmr is rsponsil or moving t rom isk to mmory (.g., il I/O) Hrwr is rsponsil or moving t twn mmory n hs Compilr is rsponsil or moving t twn mmory n rgistrs 3 4

2 Currnt Trns Powr usg limits Siz n sp o rgistrs/hs Sp o prossors Improvs str thn mmory sp (n isk sp) Th ost o h miss is growing Th wining gp twn prossors n mmory is rig with mor lvls o hs It is vry importnt to: Mng rgistrs proprly Mng hs proprly Compilrs r goo t mnging rgistrs Th Rgistr Allotion Prolm Rll tht intrmit o uss s mny tmporris s nssry This omplits inl trnsltion to ssmly But simpliis o gnrtion n optimiztion Typil intrmit o uss too mny tmporris Th rgistr llotion prolm: Rwrit th intrmit o to us t most s mny tmporris s thr r mhin rgistrs Mtho: Assign multipl tmporris to rgistr But without hnging th progrm hvior 5 6 History Rgistr llotion is s ol s intrmit o Rgistr llotion ws us in th originl FORTRAN ompilr in th 50s Vry ru lgorithms A rkthrough ws not hiv until 1980 Rgistr llotion shm s on grph oloring Rltivly simpl, glol, n works wll in prti An Exmpl Consir th progrm := + := + := - 1 with th ssumption tht n i tr us Tmporry n rus tr + Sm with tmporry tr - 1 Cn llot,, n ll to on rgistr (r 1 ): r 1 := r 2 + r 3 r 1 := r 1 + r 4 r 1 := r

3 Bsi Rgistr Allotion I Th vlu in tmporry is not n or th rst o th omputtion A tmporry n rus Bsi rul: Tmporris t 1 n t 2 n shr th sm rgistr i t ll points in th progrm t most on o t 1 or t 2 is liv! Algorithm: Prt I Comput liv vrils or h progrm point: {,,} {,,} {,} := 2 * {,} := + := - := + {,} := + := - 1 {,,,} {,,} {,,,} := + {,} {} 9 10 Th Rgistr Intrrn Grph Rgistr Intrrn Grph: Exmpl Two tmporris tht r liv simultnously nnot llot in th sm rgistr W onstrut n unirt grph with A no or h tmporry An g twn t 1 n t 2 i thy r liv simultnously t som point in th progrm For our xmpl: This is th rgistr intrrn grph (RIG) Two tmporris n llot to th sm rgistr i thr is no g onnting thm E.g., n nnot in th sm rgistr E.g., n n in th sm rgistr 11 12

4 Rgistr Intrrn Grph: Proprtis It xtrts xtly th inormtion n to hrtriz lgl rgistr ssignmnts It givs glol (i.., ovr th ntir low grph) pitur o th rgistr rquirmnts Atr RIG onstrution, th rgistr llotion lgorithm is rhittur inpnnt Grph Coloring: Dinitions A oloring o grph is n ssignmnt o olors to nos, suh tht nos onnt y n g hv irnt olors A grph is k-olorl i it hs oloring with k olors Rgistr Allotion Through Grph Coloring In our prolm, olors = rgistrs W n to ssign olors (rgistrs) to grph nos (tmporris) Lt k = numr o mhin rgistrs Grph Coloring: Exmpl Consir th xmpl RIG r 1 r 2 r 3 I th RIG is k-olorl thn thr is rgistr ssignmnt tht uss no mor thn k rgistrs r 2 Thr is no oloring with lss thn 4 olors Thr r vrious 4-olorings o this grph r 3 r

5 Grph Coloring: Exmpl Unr this oloring th o oms: r 2 := r 3 + r 4 r 3 := -r 2 r 2 := r 3 + r 1 r 1 := 2 * r 2 r 3 := r 3 + r 2 r 2 := r 2-1 Computing Grph Colorings Th rmining prolm is how to omput oloring or th intrrn grph But: (1) Computtionlly this prolm is NP-hr: No iint lgorithms r known (2) A oloring might not xist or givn numr o rgistrs r 3 := r 1 + r 4 Th solution to (1) is to us huristis W will onsir th othr prolm ltr Grph Coloring Huristi Osrvtion: Pik no t with wr thn k nighors in RIG Elimint t n its gs rom RIG I th rsulting grph hs k-oloring thn so os th originl grph Why: Lt 1,, n th olors ssign to th nighors o t in th ru grph Sin n < k w n pik som olor or t tht is irnt rom thos o its nighors Grph Coloring Simpliition Huristi Th ollowing works wll in prti: Pik no t with wr thn k nighors Put t on stk n rmov it rom th RIG Rpt until th grph hs on no Thn strt ssigning olors to nos on th stk (strting with th lst no ) At h stp pik olor irnt rom thos ssign to lry olor nighors 19 20

6 Grph Coloring Exmpl (1) Strt with th RIG n with k = 4: Grph Coloring Exmpl (2) Strt with th RIG n with k = 4: Stk: {} Stk: {} Rmov Rmov Grph Coloring Exmpl (3) Now ll nos hv wr thn 4 nighors n n rmov:,,, Stk: {, } Grph Coloring Exmpl (4) Strt ssigning olors to:,,,,, r 1 r 2 r 2 r 3 r 4 r

7 Wht i th Huristi Fils? Wht i uring simpliition w gt to stt whr ll nos hv k or mor nighors? Exmpl: try to in 3-oloring o th RIG: Wht i th Huristi Fils? Rmov n gt stuk (s shown low) Pik no s possil nit or spilling A spill tmporry livs is mmory Assum tht is pik s nit Wht i th Huristi Fils? Rmov n ontinu th simpliition Simpliition now sus:,,, Wht i th Huristi Fils? On th ssignmnt phs w gt to th point whn w hv to ssign olor to W hop tht mong th 4 nighors o w us lss thn 3 olors optimisti oloring? r 3 r 2 r 1 r

8 Spilling Sin optimisti oloring il, w must spill tmporry (tul spill) W must llot mmory lotion s th hom o Typilly this is in th urrnt stk rm Cll this rss Bor h oprtion tht uss, insrt := lo Atr h oprtion tht ins, insrt stor, Spilling: Exmpl This is th nw o tr spilling := 2 * stor, := + := - := lo := + := lo := + := + := Romputing Livnss Inormtion Th nw livnss inormtion tr spilling: Romputing Livnss Inormtion Nw livnss inormtion is lmost s or {,,} {,,} {,,} {,} := + := - := lo := + {,,} {,,,} is liv only Btwn := lo n th nxt instrution Btwn stor, n th pring instrution {,} {,} := 2 * stor, {,} {,} := lo := + := + := - 1 {,,,} {,} Spilling rus th liv rng o An thus rus its intrrns Whih rsults in wr RIG nighors or {} 31 32

9 Romput RIG Atr Spilling Th only hngs r in rmoving som o th gs o th spill no In our s now intrrs only with n An now th rsulting RIG is 3-olorl Spilling Nots Aitionl spills might rquir or oloring is oun Th triky prt is iing wht to spill r2 r2 r2 r3 r3 r1 Possil huristis: Spill tmporris with most onlits Spill tmporris with w initions n uss Avoi spilling in innr loops Any huristi is orrt Prolor Nos Prolor nos r nos whih r priori oun to tul mhin rgistrs Ths nos r usully us or som spii (tim-ritil) purpos,.g.: or th rm pointr or th irst N rgumnts (N=2,3,4,5) Prolor Nos (Cont.) For h olor, thr shoul only on prolor no with tht olor; ll prolor nos usully intrr with h othr W n giv n orinry tmporry th sm olor s prolor no s long s it os not intrr with it Howvr, w nnot simpliy or spill prolor nos; w thus trt thm s hving ininit gr 35 36

10 Ets o Glol Rgistr Allotion Rution in % or MIPS C Compilr totl slr Progrm yls los/stors los/stors oyr i y nro om ups s Go Mn Mnging Chs Compilrs r vry goo t mnging rgistrs Muh ttr thn progrmmr oul Compilrs r not goo t mnging hs This prolm is still lt to progrmmrs It is still n opn qustion whthr ompilr n o nything gnrl to improv prormn Compilrs n, n w o, prorm som simpl h optimiztion Ch Optimiztion Consir th loop or (j = 1; j < 10; j++) or (i = 1; i < 1000; i++) [i] *= [i] This progrm hs trril h prormn Why? Ch Optimiztion (Cont.) Consir now th progrm: or (i = 1; i < 1000; i++) or (j = 1; j < 10; j++) [i] *= [i] Computs th sm thing But with muh ttr h hvior Might tully mor thn 10x str A ompilr n prorm this optimiztion ll loop intrhng 39 40

11 Conlusions Rgistr llotion is must hv optimiztion in most ompilrs: Bus intrmit o uss too mny tmporris Bus it mks ig irn in prormn Grph oloring is powrul rgistr llotion shm (with mny vritions on th huristis) Rgistr llotion is mor omplit or CISC mhins 41