Lecture 39: Register Allocation. The Memory Hierarchy. The Register Allocation Problem. Managing the Memory Hierarchy

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1 Ltur 39: Rgistr Alloation [Aapt rom nots y R. Boik an G. Nula] Topis: Mmory Hirarhy Managmnt Rgistr Alloation: Rgistr intrrn graph Graph oloring huristis Spilling Cah Managmnt Th Mmory Hirarhy Computrs mploy a varity o mmory vis, traing o apaity, prsistn, an sp (som yars ago): Dvi Ass tim Capaity Rgistrs 1 yl yts Cah yls 256KB 16MB Main mmory yls 32MB >16GB Disk M yls 10GB > 1TB Disk arm... > 3PB Last moii: W Apr 29 12:20: CS164: Ltur #39 1 Last moii: W Apr 29 12:20: CS164: Ltur #39 2 Managing th Mmory Hirarhy Programs ar writtn as i thr ar only two kins o mmory: main mmory an isk (varials an ils). Programmr is rsponsil or moving ata rom isk to mmory. Harwar is rsponsil or moving ata twn mmory an ahs Compilr is rsponsil or moving ata twn mmory an rgistrs (whih th programmr usually osn t s). Cah an rgistr sizs ar growing slowly: important to manag thm wll. Prossor sp improvs astr than mmory sp an isk sp??? Th ost o a ah miss is growing, an th wining gap is rig with mor ahs. Th Rgistr Alloation Prolm Our intrmiat o styl uss tmporaris proligatly, simpliying o gnration an optimization, ut ompliating inal translation to assmly Hn, th rgistr alloation prolm: Rwrit th intrmiat o to us wr tmporaris than thr ar mahin rgistrs So w must assign mor tmporaris to a rgistr, without hanging th program havior Last moii: W Apr 29 12:20: CS164: Ltur #39 3 Last moii: W Apr 29 12:20: CS164: Ltur #39 4

2 Consir th program a := + := a + := - 1 An Exampl assuming that assumption that a an i atr us. Thn, Can rus a atr a + Sam with tmporary atr - 1 Can alloat a,, an all to on rgistr (r1): r1 := + r1 := r1 + r1 := r1-1 Basi Rgistr Alloation Ia So in gnral, sin th valu in a a tmporary is not n or th rst o th omputation, Any st o tmporaris an shar a singl physial rgistr i at most on is aliv at any program point. This rul is asy to apply to asi loks. Gnral CFGs ar onsiraly trikir. Last moii: W Apr 29 12:20: CS164: Ltur #39 5 Last moii: W Apr 29 12:20: CS164: Ltur #39 6 Going Gloal: Alloation in CFGs (I) First stp is to omput liv varials or ah statmnt. In this xampl, assum that varial is liv at xit. {,,} {a,,} {,,} {,,,} a := + := -a := + < 0 Alloation in CFGs (II): Rgistr Intrrn Graphs Th sts in th prvious sli iniat sts o virtual rgistrs that ar simultanously aliv at all points in th program, an thror annot shar a physial rgistr. Can summariz all ths sts y onstruting an unirt graph with a no or ah virtual rgistr, an an g twn any two virtual rgistrs that appar togthr in th sam st somwhr in th program. Call this th rgistr intrrn graph (RIG). {,} := 2 * {,} {,,} {} := + > := + := - 1 > 0 {} {,,, } {,,, } {,,, } a Th RIG xtrats xatly th inormation n to haratriz lgal rgistr assignmnts Givs gloal (ovr th ntir CFG) pitur o th rgistr rquirmnts Last moii: W Apr 29 12:20: CS164: Ltur #39 7 Last moii: W Apr 29 12:20: CS164: Ltur #39 8

3 Alloation in CFGs (III): Graph Coloring Graph Coloring: Exampl A oloring o a graph is an assignmnt o olors to nos, suh that nos onnt y an g hav irnt olors. A graph is k-oloral i it has a oloring with k olors. In our prolm, olors = rgistrs. That is, I w hav k availal mahin rgistrs an our rgistr intrrn graph is k-oloral, thn th oloring givs us a rgistr assignmnt. Consir th sampl RIG: r1 r2 a r2 r3 r3 r4 Thr is no oloring with wr than 4 olors Thr ar 4-olorings o this graph Bor. Atr A: a := + A: r2 := r3 + r4 := -a r3 := -r2 := + r2 := r3 + r1 i >= 0 jump C i r1 >= 0 jump C B: := 2 * B: r1 := 2 * r2 jump D jump D C: := + C: r3 := r3 + r2 := - 1 r2 := r2-1 i <= 0 jump E i r2 <= 0 jump E D: := + D: r3 := r1 + r4 i <= jump A i r3 <= r4 jump A E: E: Last moii: W Apr 29 12:20: CS164: Ltur #39 9 Last moii: W Apr 29 12:20: CS164: Ltur #39 10 Alloation in CFGs (III): Computing Graph Colorings Th rmaining prolm is to omput a oloring or th intrrn graph. Unortunatly, this prolm is har (NP-har). No ast algorithms ar known, An sis, a oloring might not xist or a givn numr o rgistrs. For (1), w ll us huristis. Osrvation: Graph Coloring Huristi: Motivation Pik a no t with < k nighors in RIG. Eliminat t an its gs rom RIG. I th rsulting graph has a k-oloring thn so os th original graph. Rason: whatvr n k 1 olors t s nighors hav, w know w ll always al to olor t (sin thr ar k olors). Thror, liminating t annot at th oloraility o th othr nos. Last moii: W Apr 29 12:20: CS164: Ltur #39 11 Last moii: W Apr 29 12:20: CS164: Ltur #39 12

4 Graph Coloring Huristi Th ollowing works wll in prati: Pik a no t with < k nighors. Push t on a stak an rmov it rom th RIG. Rpat until th graph has no nos. Thn start popping nos rom th stak an aing thm ak to th graph, assigning olors to ah as w go (starting with th last no a). At ah stp, w know w an pik a olor irnt rom thos assign to alray olor nighors, y th osrvation on th last sli. Exampl o Using th Huristi (I) Start with our sampl RIG an with k = 4: a Stak: [] Now rmov a an thn, giving Stak: [, a] (top on lt) Now all nos hav < 4 nighors; rmov. Stak is [,,,,, a]. Last moii: W Apr 29 12:20: CS164: Ltur #39 13 Last moii: W Apr 29 12:20: CS164: Ltur #39 14 Graph Coloring Exampl (2) Now w assign olors...r,...rgistrs to:,,,,, a in that orr. At ah stp, guarant thr s a r rgistr. a r2 r1 r3 Spilling What i uring simpliiation w gt to a stat whr all nos hav k or mor nighors? Exampl: try to in a 3-oloring o th RIG w v n using. Atr rmoving a, w gt r2 r3 r4...an now w ar stuk, sin all nos hav 3 nighors. So, pik a no as a aniat or spilling, that is, to rsi in mmory. Last moii: W Apr 29 12:20: CS164: Ltur #39 15 Last moii: W Apr 29 12:20: CS164: Ltur #39 16

5 Exampl o Spilling Assum that is pik as a aniat. Whn w rmov it rom th graph: Exampl o Spilling (II) On th assignmnt phas w gt to th point whn w hav to assign a olor to Somtims, it just happns that among th 4 nighors o w us < 3 olors (optimisti oloring)...?? r3 Simpliiation now sus. W n up with th stak [,,,,, a ]...ut not this tim. r2 r3 r4 Last moii: W Apr 29 12:20: CS164: Ltur #39 17 Last moii: W Apr 29 12:20: CS164: Ltur #39 18 Exampl o Spilling (III) Romputing Livnss Inormation Sin optimisti oloring ail w must spill rgistr : Alloat a mmory loation all it a as th hom o (typially in th urrnt stak ram). Bor ah opration that uss, insrt := *a Atr ah opration that ins (assigns to), insrt {,,X} {a,,x} {,,X} {,,} {,,,X} a := + := -a := *a := + < 0 *a := This givs us: A: a := + C: := + := -a := - 1 := *a i <= 0 jump E := + := *a i >= 0 jump C D: := + B: := 2 * i <= jump A *a := E: jump D {,} {,} := 2 * *a := {, X} {,} {,,X} {} := *a := + > := + := - 1 > 0 {} {,,, X} {,,, X} {,,, X} Last moii: W Apr 29 12:20: CS164: Ltur #39 19 Last moii: W Apr 29 12:20: CS164: Ltur #39 20

6 A Nw RIG Th nw livnss inormation is almost as or, xpt that that is liv only Btwn an := *a an th nxt instrution, an Btwn a stor, a an th pring instrution. That is, spilling rus th liv rang o, an thus th rgistrs it intrrs with, giving us this RIG: a What to Spill? In gnral, aitional spills might rquir to allow a oloring. Th triky part is iing what to spill. Possil huristis: Spill tmporaris with most onlits Spill tmporaris with w initions an uss Avoi spilling in innr loops An this graph is 3-oloral (lt to th rar). Last moii: W Apr 29 12:20: CS164: Ltur #39 21 Last moii: W Apr 29 12:20: CS164: Ltur #39 22 Cahs Compilrs ar vry goo at managing rgistrs (muh ttr than programmrs: th C rgistr laration is rally osolt). Cahs ar anothr mattr. Th prolm is still lt to programmrs, an it is still an opn qustion whthr ompilrs an o muh in gnral to improv prorman But thy an (an a w o) prorm som simpl ah optimization Consir th loop Cah Optimization or(j = 1; j < 10; j += 1) or(i = 1; i < ; i += 1) a[i] *= [i] Why os this hav trril ah prorman? On th othr han, or(i = 1; i < ; i += 1) or(j = 1; j < 10; j += 1) a[i] *= [i] omputs th sam thing, ut with muh ttr (possily 10x) prorman [again why?]. Compilrs an o this: loop intrhang. Last moii: W Apr 29 12:20: CS164: Ltur #39 23 Last moii: W Apr 29 12:20: CS164: Ltur #39 24

7 Cah Optimization (II) Othr kins o mmory layout isions possil, suh as paing rows o a matrix with xtra yts to avoi ah onlits whn travrsing a olumn (or row in FORTRAN) o a matrix. [Why might that hlp?] Prthing instrutions on som harwar an inorm ah o antiipat utur mmory ths so that thy an pro in paralll. Again, it is possil or ompilrs to supply ths to a limit xtnt. Summary Both aus it ass o gnration, gratly improvs prorman,anausitisiiultorprogrammrstooitorthmslvs, rgistr alloation is a must hav optimization in proution ompilrs or stanar proural languags. Graph oloring is a powrul rgistr alloation shm that ompilrs an apply automatially Goo ah managmnt oul giv vn largr payos, ut so ar is iiult. Last moii: W Apr 29 12:20: CS164: Ltur #39 25 Last moii: W Apr 29 12:20: CS164: Ltur #39 26