Register Allocation. Goal: replace temporary variable accesses by register accesses Why? Constraints:
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1 Rgistr Allotion Gol: rpl tmporry vril sss y rgistr sss Why? Constrints: Fix st of rgistrs Two simultnously liv vrils nnot llot to th sm rgistr A vril is liv if it will us gin for ing rfin.
2 1. Intify Liv Vril Rngs Bsi rul: Tmporris t1 n t2 n shr th sm rgistr if t ny point in th progrm t most on of t1 or t2 is liv!
3 Rgistr Intrfrn Grph
4 Wht is th Rgistr Infrn Grph for this xmpl?
5 Rgistr Intrfrn Grph 1. Wht nnot ssign sm rgistr? 2. Wht n ssign th sm rgistr?
6 Your Turn Writ own th liv vrils ftr h sttmnt." Hint: Strt t th ottom. Instrutions Liv vrs = + 2 = * = + 1 rturn *
7 Liv Vrils Instrutions Liv vrs = + 2 = * = + 1 rturn *,
8 Liv Vrils Instrutions Liv vrs = + 2 = * = + 1 rturn *,,
9 Liv Vrils Instrutions Liv vrs = + 2 = * = + 1 rturn *,,,
10 Instrutions Liv vrs = + 2, = *, = + 1, rturn * Liv Vrils
11 Intrfrn grph n Rgistr Allotion Nos of th grph = vrils Egs onnt vrils tht intrfr with on nothr Nos will ssign olor orrsponing to th rgistr ssign to th vril Two olors n t nxt to on nothr in th grph
12 Rgistr Allotion = Grph Coloring
13 Coloring th RIG olor rgistr Instrutions Liv vrs = + 2, = *, = + 1, rturn * R1 R2
14 Coloring th RIG olor rgistr Instrutions Liv vrs = + 2, = *, = + 1, rturn * R1 R2
15 How to o th Grph oloring Qustions: Cn w ffiintly fin oloring of th grph whnvr possil? Cn w ffiintly fin th optimum oloring of th grph? How o w hoos rgistrs to voi mov instrutions? Wht o w o whn thr rn t nough olors (rgistrs) to olor th grph?
16 Coloring grph Kmp s lgorithm [1879] for fining K- oloring of grph Assum K=3 Stp 1 (simplify): fin no with t most K-1 gs n rmov from th grph (with its gs). (Rmmr this no on stk for ltr stgs.)
17 Coloring grph On oloring is foun for th simplr grph, w n lwys olor th no w sv on th stk Stp 2 (olor): whn th simplifi sugrph hs n olor, k th no on th top of th stk n ssign it olor not tkn y on of th jnt nos
18 Coloring with K=2 olor rgistr R1 R2 stk:
19 Coloring olor rgistr R1 R2 stk:
20 Coloring olor rgistr R1 R2 stk:
21 Coloring olor rgistr R1 R2 stk:
22 Coloring olor rgistr R1 R2 stk:
23 Coloring olor rgistr R1 R2 stk:
24 Coloring olor rgistr R1 R2 stk:
25 Coloring olor rgistr R1 R2 stk:
26 Coloring olor rgistr R1 R2 stk:
27 Coloring olor rgistr R1 R2 stk:
28 Coloring olor rgistr R1 R2 stk:
29 Filur If th grph nnot olor, it will vntully simplifi to grph in whih vry no hs t lst K nighors Somtims, th grph is still K-olorl! Fining K-oloring in ll situtions is n NP-omplt prolm W will hv to pproximt to mk rgistr llotors fst nough
30 Coloring with K=2 olor rgistr R1 R2 stk:
31 Coloring olor rgistr R1 R2 stk: ll nos hv 2 nighours!
32 Coloring olor rgistr R1 R2 stk:
33 Coloring olor rgistr R1 R2 stk:
34 Coloring olor rgistr R1 R2 stk:
35 Coloring olor rgistr R1 R2 stk:
36 Coloring olor rgistr R1 R2 stk:
37 Coloring olor rgistr R1 R2 stk:
38 Coloring olor rgistr R1 R2 stk: W got luky!
39 Try to Color this with 4 olors? " 3 olors?
40 On Possil 4 oloring
41 Th o woul look lik this
42 Coloring with K=2 olor rgistr R1 R2 Som grphs n t olor in K olors: stk:
43 Coloring olor rgistr R1 R2 Som grphs n t olor in K olors: stk:
44 Coloring olor rgistr R1 R2 Som grphs n t olor in K olors: stk:
45 Coloring olor rgistr R1 R2 Som grphs n t olor in K olors: stk: no olors lft for!
46 Spilling Stp 3 (spilling): on ll nos hv K or mor nighors, pik no for spilling Stor on th stk Thr r mny huristis tht n us to pik no E.g., not in n innr loop
47 Spilling: Insrting Co
48 Exmpl
49 Romputing Vril Livnss
50 Romput th RIG ftr spilling This is 3-olorl!
51 Ovrll Algorithm Simplify Livnss Mrk possil spills Color & tt tul spills Rwrit o to implmnt tul spills
52 Summry Rgistr llotion hs thr mjor prts Livnss nlysis Grph oloring Progrm trnsformtion (spilling) For mor informtion, hptr in Appl
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