CSE P 501 Compilers. Register Allocation Hal Perkins Spring UW CSE P 501 Spring 2018 P-1

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1 CSE P 501 Compilrs Rgistr Allotion Hl Prkins Spring 2018 UW CSE P 501 Spring 2018 P-1

2 Agn Rgistr llotion onstrints Lol mthos Fstr ompil, slowr o, ut goo nough or lots o things (JITs, ) Glol llotion rgistr oloring UW CSE P 501 Spring 2018 P-2

3 k Intrmit o typilly ssums ininit numr o rgistrs Rl mhin hs k rgistrs vill Gols Prou orrt o tht uss k or wr rgistrs Minimiz los n stors Minimiz sp n or spill vlus Do this iintly O(n), O(n log n), my O(n 2 ) UW CSE P 501 Spring 2018 P-3

4 Rgistr Allotion Tsk At h point in th o, pik th vlus to kp in rgistrs Insrt o to mov vlus twn rgistrs n mmory No itionl trnsormtions shuling shoul hv on its jo But w will usully rrun shuling i w insrt spill o Minimiz insrt o, oth ynmilly n sttilly UW CSE P 501 Spring 2018 P-4

5 Allotion vs Assignmnt Allotion: iing whih vlus to kp in rgistrs Assignmnt: hoosing spii rgistrs or vlus Compilr must o oth UW CSE P 501 Spring 2018 P-5

6 Lol Rgistr Allotion Apply to si loks Prous nt rgistr usg insi lok But n hv iniinis t ounris twn loks Two vritions: top-own, ottom-up UW CSE P 501 Spring 2018 P-6

7 Top-own Lol Allotion Prinipl: kp most hvily us vlus in rgistrs Priority = # o tims rgistr rrn in lok I mor virtul rgistrs thn physil, Rsrv som rgistrs or vlus llot to mmory N nough to rss n lo two oprns n stor rsult Othr rgistrs it to hot vlus But r ti up or ntir lok with prtiulr vlu, vn i only n or prt o th lok UW CSE P 501 Spring 2018 P-7

8 Bottom-up Lol Allotion (1) Kp list o vill rgistrs (initilly ll rgistrs t ginning o lok) Sn th o Allot rgistr whn on is n Fr rgistr s soon s possil In x:=y op z, r y n z i thy r no longr n or lloting x UW CSE P 501 Spring 2018 P-8

9 Bottom-up Lol Allotion (2) I no rgistrs r r whn on is n or llotion: Look t vlus ssign to rgistrs in th on not n or longst orwr strth in th o Insrt o to spill th vlu to mmory n insrt o to rlo it whn n ltr I opy lry xists in mmory, no n to spill UW CSE P 501 Spring 2018 P-9

10 Lol "ottom-up" Rgistr Allotion, ; lo v2 rom mmory 2. ; lo v3 rom mmory 3. v1 = v2 + v3 4. ; lo v5, v6 rom mmory 5. v4 = v5 - v6 6. v7 = v ; lo v9 rom mmory 8. v8 = - v9 9. v10 = v6 * v4 10. v11 = v10 - v3 Still in LIR. So lots (too mny!) virtul rgistrs rquir (v2, t). Gry instrutions (1,2,4,7) lo oprns rom mmory into virtul rgistrs. W will ignor ths going orwr. Fous on mpping virtul to physil. UW CSE P 501 Spring 2018 P-10

11 Lol "ottom-up" Rgistr Allotion, 0 1. v1 = v2 + v3 2. v4 = v5 - v6 3. v7 = v v8 = - v9 5. v10 = v6 * v4 6. v11 = v10 - v3 prg vrg R1 - R2 - R3 - R4 - vrg NxtR v1 1 v2 1 v3 1 v4 2 v5 2 v6 2 v7 3 v8 4 v9 4 v10 5 v11 6 UW CSE P 501 Spring 2018 P-11

12 Lol "ottom-up" Rgistr Allotion, 1 1. v1 = v2 + v3 2. v4 = v5 - v6 3. v7 = v v8 = - v9 5. v10 = v6 * v4 6. v11 = v10 - v3 prg vrg R1 v2 R2 v3 R3 v1 R4 - R3 = R1 + R2 vrg NxtR v1 1 v2 1 3 v3 1 6 v4 2 v5 2 v6 2 v7 3 v8 4 v9 4 v10 5 v11 6 UW CSE P 501 Spring 2018 P-12

13 Lol "ottom-up" Rgistr Allotion, 2 1. v1 = v2 + v3 2. v4 = v5 - v6 3. v7 = v v8 = - v9 5. v10 = v6 * v4 6. v11 = v10 - v3 prg vrg R1 v2 R2 v3 v4 R3 v1 v6 R4 v5 R3 = R1 + R2 ; spill R3 ; spill R2? - no - still ln R2 = R4 - R3 vrg NxtR v1 v2 3 v3 6 v4 2 5 v5 2 v6 2 5 v7 3 v8 4 v9 4 v10 5 v11 6 UW CSE P 501 Spring 2018 P-13

14 Lol "ottom-up" Rgistr Allotion, 3 1. v1 = v2 + v3 2. v4 = v5 - v6 3. v7 = v v8 = - v9 5. v10 = v6 * v4 6. v11 = v10 - v3 prg vrg R1 v2 R2 v4 R3 v6 R4 v5 v7 R3 = R1 + R2 ; spill R3 ; spill R2? - no! R2 = R4 - R3 ; spill R4? - no! R4 = R1-29 An so on... vrg NxtR v1 v2 3 v3 6 v4 5 v5 v6 5 v7 3 v8 4 v9 4 v10 5 v11 6 UW CSE P 501 Spring 2018 P-14

15 Bottom-Up Allotor Invnt out on pr Shlon Bst, 1955, or Fortrn I Lslo Bly, 1965, or nlyzing pging lgorithms Willim Hrrison, 1975, ECS ompilr work Chris Frsr, 1989, LCC ompilr Vinnzo Lirtor, 1997, Rutgrs Will rinvnt gin, no out Mny rgumnts or optimlity o this UW CSE P 501 Spring 2018 P-15

16 Glol Rgistr Allotion y Grph Coloring How to onvrt th ininit squn o tmporry t rrns, t1, t2, into ssignmnts to init numr o tul rgistrs Gol: Us vill rgistrs with minimum spilling Prolm: Minimizing th numr o rgistrs is NP-omplt it is quivlnt to hromti numr minimum olors n to olor nos o grph so no g onnts sm olor UW CSE P 501 Spring 2018 Q-16

17 Bgin With Dt Flow Grph prour-wi rgistr llotion only liv vrils rquir rgistr storg tlow nlysis: vril is liv t no N i th vlu it hols is us on som pth urthr own th ontrol-low grph; othrwis it is two vrils(vlus) intrr whn thir liv rngs ovrlp UW CSE P 501 Spring 2018 Q-17

18 Liv Vril Anlysis := r(); := r(); := r(); := r(); := r(); := r(); := + *; := + *; i ( < 10 ) thn := +8; < 10 print(); ls := +8; := 10; := 10; print(); := + ; print(); := + ; print(); i print(); print(); UW CSE P 501 Spring 2018 Q-18

19 Rgistr Intrrn Grph := r(); := r(); := r(); := + *; < 10 := +8; := 10; print(); := + ; print(); print(); UW CSE P 501 Spring 2018 Q-19

20 Grph Coloring NP omplt prolm Huristi: olor sy nos lst in no N with lowst gr rmov N rom th grph olor th simplii grph st olor o N to th irst olor tht is not us y ny o N s nighors Bsis u to Chitin (1982), rin y Briggs (1992) UW CSE P 501 Spring 2018 Q-20

21 Apply Huristi UW CSE P 501 Spring 2018 Q-21

22 Apply Huristi UW CSE P 501 Spring 2018 Q-22

23 Apply Huristi UW CSE P 501 Spring 2018 Q-23

24 Apply Huristi UW CSE P 501 Spring 2018 Q-24

25 Continu UW CSE P 501 Spring 2018 Q-25

26 Continu UW CSE P 501 Spring 2018 Q-26

27 Continu UW CSE P 501 Spring 2018 Q-27

28 Continu UW CSE P 501 Spring 2018 Q-28

29 Continu UW CSE P 501 Spring 2018 Q-29

30 Continu UW CSE P 501 Spring 2018 Q-30

31 Continu UW CSE P 501 Spring 2018 Q-31

32 Continu UW CSE P 501 Spring 2018 Q-32

33 Continu UW CSE P 501 Spring 2018 Q-33

34 Finl Assignmnt := r(); := r(); := r(); := + *; i ( < 10 ) thn := +8; print(); ls := 10; := + ; print(); i print(); UW CSE P 501 Spring 2018 Q-34

35 Som Grph Coloring Issus My run out o rgistrs Solution: insrt spill o n rllot Spil-purpos n it rgistrs Exmpls: untion rturn rgistr, untion rgumnt rgistrs, rgistrs rquir or prtiulr instrutions Solution: pr-olor som nos to or llotion to prtiulr rgistr UW CSE P 501 Spring 2018 Q-35

36 Glol Rgistr Allotion (or rl) Grph oloring is th stnr thniqu, ut Nos r liv rngs not vrils Us ontrol n tlow (tully SSA) grphs to riv intrrn grph Eg twn (t1,t2) whn liv rngs t1 n t2 nnot ssign to th sm rgistr Most ommonly, t1 n t2 r oth liv t th sm tim Cn lso us to xprss onstrints out rgistrs, t. Thn olor th nos in th grph Two nos onnt y n g my not hv sm olor (i.., nnot llot to sm rgistr) I mor thn k olors r n, insrt spill o UW CSE P 501 Spring 2018 P-36

37 Liv Rngs (1) A liv rng is th st o initions n uss tht r rlt us thy low togthr Evry inition n rh vry us Evry us tht inition n rh is in th sm liv rng UW CSE P 501 Spring 2018 P-37

38 Liv Rngs (2) Th i rlis on th notion o livnss, ut not th sm s ithr th st o vrils or st o vlus Evry vlu is prt o som liv rng, vn nonymous tmporris Sm nm my prt o svrl irnt liv rngs UW CSE P 501 Spring 2018 P-38

39 Liv Rngs: Exmpl 1. loi rp 2. loi rp, 0 rw 3. loi 2 r2 4. loi rp,xost rx 5. loi rp,yost ry 6. loi rp,zost rz 7. mult rw, r2 rw 8. mult rw, rx rw 9. mult rw, ry rw 10. mult rw, rz rw 11. stori rw rp, 0 Rgistr Intrvl rp [1,11] rw [2,7] rw [7,8] rw [8,9] rw [9,10] rw [10,11] r2 [3,7] rx [4,8] ry [5,9] rz [6,10] UW CSE P 501 Spring 2018 P-39

40 Coloring y Simpliition Linr-tim pproximtion tht gnrlly givs goo rsults 1. Buil: Construt th intrrn grph 2. Simpliy: Color th grph y rptly simpliition 3. Spill: I simpliy nnot ru th grph ompltly, mrk som no or spilling 4. Slt: Assign olors to nos in th grph UW CSE P 501 Spring 2018 P-40

41 1. Buil Construt th intrrn grph Fin liv rngs SSA! Buil SSA orm o IR Eh SSA nm is initilly singlton st A F-untion mns orm th union o th sts tht inlus thos nms (union-in lgorithm) Rsulting sts rprsnt liv rngs Eithr rwrit o to us liv rng nms or kp mpping twn SSA nms n liv-rng nms UW CSE P 501 Spring 2018 P-41

42 1. Buil Us tlow inormtion to uil intrrn grph Nos = liv rngs A n g in th grph or h pir o liv rngs tht ovrlp But wth opy oprtions. MOV ri rj os not rt intrrn twn ri, rj sin thy n th sm rgistr i th rngs o not othrwis intrr UW CSE P 501 Spring 2018 P-42

43 2. Simpliy Huristi: Assum w hv K rgistrs Fin no m with wr thn K nighors Rmov m rom th grph. I th rsulting grph n olor, thn so n th originl grph (th nighors o m hv t most K-1 olors mong thm) Rpt y rmoving n pushing on stk ll nos with gr lss thn K Eh simpliition rss othr no grs my mk mor simpliitions possil UW CSE P 501 Spring 2018 P-43

44 3. Spill I simpliy stops us ll nos hv gr k, mrk som no or spilling This no is in mmory uring xution \ Spill no no longr intrrs with rmining nos, ruing thir gr. Continu y rmoving spill no n push on th stk (optimisti hop tht spill no os not intrr with rmining nos Briggs llotor) UW CSE P 501 Spring 2018 P-44

45 3. Spill Spill isions shoul s on osts o spilling irnt vlus Issus Arss omputtion n or spill Cost o mmory oprtion Estimt xution rquny (.g., innr loops irst) UW CSE P 501 Spring 2018 P-45

46 4. Slt Assign nos to olors in th grph: Strt with mpty grph Ruil originl grph y rptly ing no rom top o th stk (Whn w o this, thr must olor or it i it in t rprsnt potntil spill pik irnt olor rom ny jnt no) Whn potntil spill no is popp it my not olorl (nighors my hv k olors lry). This is n tul spill. UW CSE P 501 Spring 2018 P-46

47 5. Strt Ovr I Slt phs nnot olor som no (must potntil spill no), los or h us n stors tr h inition Crts nw tmporris with tiny liv rngs Rpt rom ginning Itrt until Simpliy sus In prti oupl o itrtions r nough UW CSE P 501 Spring 2018 P-47

48 Colsing Liv Rngs I: i two liv rngs r onnt y opy oprtion (MOV ri rj) ut o not othrwis intrr, thn th liv rngs n ols (omin) Rwrit ll rrns to rj to us ri Rmov th opy instrution Thn n to ix up intrrn grph UW CSE P 501 Spring 2018 P-48

49 Colsing Avntgs? Mks th o smllr, str (no opy oprtion) Shrinks st o liv rngs Rus th gr o ny liv rng tht intrr with oth liv rngs ri, rj But: olsing two liv rngs n prvnt olsing o othrs, so orring mttrs Bst: Cols most rquntly xut rngs irst (.g., innr loops) Cn hv sustntil pyo o it! UW CSE P 501 Spring 2018 P-49

50 Ovrll Strutur Mor Colsing Possil Fin liv rngs Buil int. grph Cols Spill Costs Fin Coloring No Spills Spills Insrt Spills UW CSE P 501 Spring 2018 P-50

51 Complitions N to l with irrgulritis in th rgistr st Som oprtions rquir it rgistrs (iiv in x86, split rss/t rgistrs in M68k n othrs), rgistr ovrlp (AH, AL, AX, EAX, RAX) in x86 n x86-64 Rgistr onvntions lik untion rsults, us o rgistrs ross lls, t. Mol y proloring nos, ing onstrints in th grph, t. UW CSE P 501 Spring 2018 P-51

52 Grph Rprsnttion Th intrrn grph rprsnttion rivs th tim n sp rquirmnts or th llotor (n my th ompilr) Not unknown to hv O(5K) nos n O(1M) gs Dul rprsnttion works st Tringulr it mtrix or iint ss to intrrn inormtion Vtor o jny vtors or iint ss to no nighors UW CSE P 501 Spring 2018 P-52

53 An Tht s It Moulo ll th piky tils, tht is UW CSE P 501 Spring 2018 P-53