Lecture Outline. Memory Hierarchy Management. Register Allocation. Register Allocation. Lecture 19. Cache Management. The Memory Hierarchy

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1 Ltur Outlin Mmory Hirrhy Mngmnt Rgistr Allotion Ltur 19 Rgistr Allotion Rgistr intrrn grph Grph oloring huristis Spilling Ch Mngmnt Pro. Boik CS 164 Ltur 17 1 Pro. Boik CS 164 Ltur 17 2 Th Mmory Hirrhy Rgistrs 1 yl yts Ch 3 yls 256k-1M Min mmory yls 32M-1G 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 Pro. Boik CS 164 Ltur 17 3 Pro. Boik CS 164 Ltur 17 4 Currnt Trns Ch n rgistr sizs r growing slowly Prossor sp improvs str thn mmory sp n isk sp Th ost o h miss is growing Th wining gp is rig with mor hs It is vry importnt to: Mng rgistrs proprly Mng hs proprly Compilrs r goo t mnging rgistrs Pro. Boik CS 164 Ltur 17 5 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 wr tmporris thn thr r mhin rgistrs Mtho: ssign mor tmporris to rgistr But without hnging th progrm hvior Pro. Boik CS 164 Ltur 17 6

2 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 whn Chitin invnt rgistr llotion shm s on grph oloring Rltivly simpl, glol n works wll in prti Pro. Boik CS 164 Ltur 17 7 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 1 := r 1 + r 1 := r 1-1 Pro. Boik CS 164 Ltur 17 8 Bsi Rgistr Allotion I Algorithm: Prt 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 ny point in th progrm t most on o t 1 or t 2 is liv! Pro. Boik CS 164 Ltur 17 9 Comput liv vrils or h point: := + {,,} {,,} := - {,,} := + {,,,} {,} := + := 2 * {,,,} := - 1 {,} {,} := + {} {} Pro. Boik CS 164 Ltur Th Rgistr Intrrn Grph Two tmporris tht r liv simultnously nnot llot in th sm rgistr W onstrut n unirt grph A no or h tmporry An g twn t 1 n t 2 i thy r liv simultnously t som point in th progrm This is th rgistr intrrn grph (RIG) Two tmporris n llot to th sm rgistr i thr is no g onnting thm Pro. Boik CS 164 Ltur Rgistr Intrrn Grph. Exmpl. For our xmpl: E.g., n nnot in th sm rgistr E.g., n n in th sm rgistr Pro. Boik CS 164 Ltur 17 12

3 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 Pro. Boik CS 164 Ltur Pro. Boik CS 164 Ltur 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 I th RIG is k-olorl thn thr is rgistr ssignmnt tht uss no mor thn k rgistrs Pro. Boik CS 164 Ltur Grph Coloring. Exmpl. Consir th xmpl RIG r 1 Thr is no oloring with lss thn 4 olors Thr r 4-olorings o this grph r 4 Pro. Boik CS 164 Ltur Grph Coloring. Exmpl. Unr this oloring th o oms: := + r 4 := - := + r 1 r 1 := 2 * := + := -1 := r 1 + r 4 Computing Grph Colorings Th rmining prolm is to omput oloring or th intrrn grph But: 1. This prolm is vry hr (NP-hr). No iint lgorithms r known. 2. A oloring might not xist or givn numr or rgistrs Th solution to (1) is to us huristis W ll onsir ltr th othr prolm Pro. Boik CS 164 Ltur Pro. Boik CS 164 Ltur 17 18

4 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 Huristi Th ollowing works wll in prti: Pik no t with wr thn k nighors Push 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 Pro. Boik CS 164 Ltur Pro. Boik CS 164 Ltur Grph Coloring Exmpl (1) Strt with th RIG n with k = 4: Stk: {} Rmov n thn Grph Coloring Exmpl (2) Now ll nos hv wr thn 4 nighors n n rmov:,,, Stk: {, } Pro. Boik CS 164 Ltur Pro. Boik CS 164 Ltur Grph Coloring Exmpl (2) Strt ssigning olors to:,,,,, r 1 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: r 4 Pro. Boik CS 164 Ltur Pro. Boik CS 164 Ltur 17 24

5 Wht i th Huristi Fils? Rmov n gt stuk (s shown low) Pik no s 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:,,, Pro. Boik CS 164 Ltur Pro. Boik CS 164 Ltur Wht i th Huristi Fils? Spilling 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? r2 r3 Pro. Boik CS 164 Ltur r 1 Sin optimisti oloring il w must spill tmporry 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, Pro. Boik CS 164 Ltur Spilling. Exmpl. Romputing Livnss Inormtion This is th nw o tr spilling := 2 * stor, := + := - := lo := + := lo := + := + := - 1 Pro. Boik CS 164 Ltur Th nw livnss inormtion tr spilling: := + {,,} {,,} := - {,,} := lo := + {,,} {,,,} {,} {,} {,} := 2 * stor, {,} {} {,} := lo := + := + := - 1 {} {,,,} Pro. Boik CS 164 Ltur 17 30

6 Romputing Livnss Inormtion Th nw livnss inormtion is lmost s or is liv only Btwn := lo n th nxt instrution Btwn stor, n th pring instr. Spilling rus th liv rng o An thus rus its intrrns Whih rsult in wr nighors in RIG or Pro. Boik CS 164 Ltur Romput RIG Atr Spilling Th only hngs r in rmoving som o th gs o th spill no In our s still intrrs only with n An th rsulting RIG is 3-olorl Pro. Boik CS 164 Ltur Spilling (Cont.) Aitionl spills might rquir or oloring is oun Th triky prt is iing wht to spill Possil huristis: Spill tmporris with most onlits Spill tmporris with w initions n uss Avoi spilling in innr loops Any huristi is orrt 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 Pro. Boik CS 164 Ltur Pro. Boik CS 164 Ltur 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 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 Pro. Boik CS 164 Ltur Pro. Boik CS 164 Ltur 17 36

7 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 shms Rgistr llotion is mor omplit or CISC mhins Pro. Boik CS 164 Ltur 17 37