Announcements. Programming Project 4 due Saturday, August 18 at 11:30AM

Transcription

1 Rgistr Allotion

2 Announmnts Progrmming Projt 4 u Stury, August 18 t 11:30AM OH ll this wk. Ask qustions vi mil! Ask qustions vi Pizz! No lt sumissions.

3 Pls vlut this ours on Axss. Your k rlly mks irn.

4 Whr W Ar Sour Co Lxil Anlysis Syntx Anlysis Smnti Anlysis IR Gnrtion IR Optimiztion Co Gnrtion Optimiztion Mhin Co

5 Whr W Ar Sour Co Lxil Anlysis Syntx Anlysis Smnti Anlysis IR Gnrtion IR Optimiztion Co Gnrtion Optimiztion Mhin Co Fn-TAC-sti!

6 Whr W Ar Sour Co Lxil Anlysis Syntx Anlysis Smnti Anlysis IR Gnrtion IR Optimiztion Co Gnrtion Optimiztion Mhin Co

7 Co Gnrtion t Gln At this point, w hv optimiz IR o tht ns to onvrt into th trgt lngug (.g. ssmly, mhin o). Gol o this stg: Choos th pproprit mhin instrutions or h IR instrution. Divvy up init mhin rsours (rgistrs, hs, t.) Implmnt low-lvl tils o th runtim nvironmnt. Mhin-spii optimiztions r otn on hr, though som r trt s prt o inl optimiztion phs.

8 Ovrviw Rgistr Allotion (Toy) How to ssign vrils to initly mny rgistrs? Wht to o whn it n't on? How to o so iinty? Grg Colltion (Mony) How to tt rliml mmory? How to rlim mmory iintly?

9 Mmory Tros Thr is n normous tro twn sp n siz in mmory. SRAM is st ut vry xpnsiv: Cn kp up with prossor sps in th GHz. As o 2007, ost is $10/MB Goo luk uying 1TB o th stu! Hr isks r hp ut vry slow: As o 2012, you n uy 2TB hr riv or out $100 As o 2012, goo isk sk tims r msur in ms (out two to our million tims slowr thn prossor yl!)

10 Th Mmory Hirrhy I: Try to gt th st o ll worls y using multipl typs o mmory.

11 Th Mmory Hirrhy I: Try to gt th st o ll worls y using multipl typs o mmory. Rgistrs L1 Ch L2 Ch Min Mmory Hr Disk Ntwork

12 Th Mmory Hirrhy I: Try to gt th st o ll worls y using multipl typs o mmory. Rgistrs L1 Ch L2 Ch Min Mmory Hr Disk Ntwork 256B - 8KB 16KB 64KB 1MB - 4MB 4GB 256GB 500GB+ HUGE

13 Th Mmory Hirrhy I: Try to gt th st o ll worls y using multipl typs o mmory. Rgistrs L1 Ch L2 Ch Min Mmory Hr Disk Ntwork 256B - 8KB 16KB 64KB 1MB - 4MB 4GB 256GB 500GB+ HUGE ns 1ns 5ns 5ns 25ns 25ns 100ns 3 10ms ms

14 Th Chllngs o Co Gnrtion Almost ll progrmming lngugs xpos ors viw o th mmory hirrhy: All vrils liv in mmory. Disk n ntwork xpliitly hnl sprtly. (Intrsting xption: Stnor's Squoi progrmming lngug) Chllngs in o gnrtion: Position ojts in wy tht tks mximum vntg o th mmory hirrhy. Do so without hints rom th progrmmr.

15 Rgistrs Most mhins hv st o rgistrs, it mmory lotions tht n ss quikly, n hv omputtions prorm on thm, n xist in smll quntity. Using rgistrs intlligntly is ritil stp in ny ompilr. A goo rgistr llotor n gnrt o orrs o mgnitu ttr thn rgistr llotor.

16 Rgistr Allotion In TAC, thr r n unlimit numr o vrils. On physil mhin thr r smll numr o rgistrs: x86 hs our gnrl-purpos rgistrs n numr o spiliz rgistrs. MIPS hs twnty-our gnrl-purpos rgistrs n ight spil-purpos rgistrs. Rgistr llotion is th pross o ssigning vrils to rgistrs n mnging t trnsr in n out o rgistrs.

17 Chllngs in Rgistr Allotion Rgistrs r sr. Otn sustntilly mor IR vrils thn rgistrs. N to in wy to rus rgistrs whnvr possil. Rgistrs r omplit. x86: Eh rgistr m o svrl smllr rgistrs; n't us rgistr n its onstitunt rgistrs t th sm tim. x86: Crtin instrutions must stor thir rsults in spii rgistrs; n't stor vlus thr i you wnt to us thos instrutions. MIPS: Som rgistrs rsrv or th ssmlr or oprting systm. Most rhitturs: Som rgistrs must prsrv ross untion lls.

18 Gols or Toy Introu rgistr llotion or MIPSstyl mhin: Som numr o inivisil, gnrl-purpos rgistrs. Explor thr lgorithms or rgistr llotion: Nïv ( no ) rgistr llotion. Linr sn rgistr llotion. Grph-oloring rgistr llotion.

19 An Initil Rgistr Allotor I: Stor vry vlu in min mmory, loing vlus only whn thy'r n. To gnrt o tht prorms omputtion: Gnrt lo instrutions to pull th vlus rom min mmory into rgistrs. Gnrt o to prorm th omputtion on th rgistrs. Gnrt stor instrutions to stor th rsult k into min mmory.

20 Our Rgistr Allotor In Ation

21 Our Rgistr Allotor In Ation = + ; = ; = + ;

22 Our Rgistr Allotor In Ation = + ; = ; = + ; Prm N... Prm 1 Stor p Stor r p + 4N... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20

23 Our Rgistr Allotor In Ation = + ; = ; = + ; Prm N... Prm 1 Stor p Stor r p + 4N... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20

24 Our Rgistr Allotor In Ation = + ; = ; = + ; lw $t0, -12(p) Prm N... Prm 1 Stor p Stor r p + 4N... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20

25 Our Rgistr Allotor In Ation = + ; = ; = + ; lw $t0, -12(p) lw $t1, -16(p) Prm N... Prm 1 Stor p Stor r p + 4N... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20

26 Our Rgistr Allotor In Ation = + ; = ; = + ; lw $t0, -12(p) lw $t1, -16(p) $t2, $t0, $t1 Prm N... Prm 1 Stor p Stor r p + 4N... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20

27 Our Rgistr Allotor In Ation = + ; = ; = + ; Prm N p + 4N lw $t0, -12(p) lw $t1, -16(p) $t2, $t0, $t1 sw $t2, -8(p)... Prm 1 Stor p Stor r... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20

28 Our Rgistr Allotor In Ation = + ; = ; = + ; Prm N p + 4N lw $t0, -12(p) lw $t1, -16(p) $t2, $t0, $t1 sw $t2, -8(p)... Prm 1 Stor p Stor r... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20

29 Our Rgistr Allotor In Ation = + ; = ; = + ; Prm N p + 4N lw $t0, -12(p) lw $t1, -16(p) $t2, $t0, $t1 sw $t2, -8(p)... Prm 1 Stor p Stor r... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20 lw $t0, -8(p)

30 Our Rgistr Allotor In Ation = + ; = ; = + ; Prm N p + 4N lw $t0, -12(p) lw $t1, -16(p) $t2, $t0, $t1 sw $t2, -8(p)... Prm 1 Stor p Stor r... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20 lw $t0, -8(p) sw $t0, -20(p)

31 Our Rgistr Allotor In Ation = + ; = ; = + ; Prm N p + 4N lw $t0, -12(p) lw $t1, -16(p) $t2, $t0, $t1 sw $t2, -8(p)... Prm 1 Stor p Stor r... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20 lw $t0, -8(p) sw $t0, -20(p)

32 Our Rgistr Allotor In Ation = + ; = ; = + ; Prm N p + 4N lw $t0, -12(p) lw $t1, -16(p) $t2, $t0, $t1 sw $t2, -8(p)... Prm 1 Stor p Stor r... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20 lw $t0, -8(p) sw $t0, -20(p) lw $t0, -8(p)

33 Our Rgistr Allotor In Ation = + ; = ; = + ; Prm N p + 4N lw $t0, -12(p) lw $t1, -16(p) $t2, $t0, $t1 sw $t2, -8(p)... Prm 1 Stor p Stor r... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20 lw $t0, -8(p) sw $t0, -20(p) lw $t0, -8(p) lw $t1, -20(p)

34 Our Rgistr Allotor In Ation = + ; = ; = + ; Prm N p + 4N lw $t0, -12(p) lw $t1, -16(p) $t2, $t0, $t1 sw $t2, -8(p)... Prm 1 Stor p Stor r... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20 lw $t0, -8(p) sw $t0, -20(p) lw $t0, -8(p) lw $t1, -20(p) $t2, $t0, $t1

35 Our Rgistr Allotor In Ation = + ; = ; = + ; Prm N p + 4N lw $t0, -12(p) lw $t1, -16(p) $t2, $t0, $t1 sw $t2, -8(p)... Prm 1 Stor p Stor r... p + 4 p + 0 p - 4 p - 8 p - 12 p - 16 p - 20 lw $t0, -8(p) sw $t0, -20(p) lw $t0, -8(p) lw $t1, -20(p) $t2, $t0, $t1 sw $t2, -16(p)

36 Anlysis o our Allotor Disvntg: Gross iniiny. Issus unnssry los n stors y th ozn. Wsts sp on vlus tht oul stor purly in rgistrs. Esily n orr o mgnitu or two slowr thn nssry. Unptl in ny proution ompilr. Avntg: Simpliity. Cn trnslt h pi o IR irtly to ssmly s w go. Nvr n to worry out running out o rgistrs. Nvr n to worry out untion lls or spil-purpos rgistrs. Goo i you just n to gt prototyp ompilr up n running.

37 Builing Bttr Allotor Gol: Try to hol s mny vrils in rgistrs s possil. Rus mmory rs/writs. Rus totl mmory usg. W will n to rss ths qustions: Whih rgistrs o w put vrils in? Wht o w o whn w run out o rgistrs?

38 Rgistr Consistny = + = = =

39 Rgistr Consistny At h progrm point, h vril must in th sm lotion. Dos not mn tht h vril is lwys stor in th sm lotion! At h progrm point, h rgistr hols t most on liv vril. Cn ssign svrl vrils th sm rgistr i no two o thm vr will r togthr.

40 Liv Rngs n Liv Intrvls Rll: A vril is liv t prtiulr progrm point i its vlu my r ltr or it is writtn. Cn in this using glol livnss nlysis. Th liv rng or vril is th st o progrm points t whih tht vril is liv. Th liv intrvl or vril is th smllst surng o th IR o ontining ll vril's liv rngs. A proprty o th IR o, not th CFG. Lss pris thn liv rngs, ut simplr to work with.

41 Liv Rngs n Liv Intrvls

42 Liv Rngs n Liv Intrvls = + = + = + IZ Goto _L0 = + Goto _L1; _L0: = - _L1: g =

43 Liv Rngs n Liv Intrvls = + = + = + = + = + IZ Goto _L0 = + Goto _L1; = + _L0: = - _L1: g = = + = g =

44 Liv Rngs n Liv Intrvls = + = + = + = + = + IZ Goto _L0 = + Goto _L1; = + _L0: = - _L1: g = = + = g = { g }

45 Liv Rngs n Liv Intrvls = + = + = + = + = + IZ Goto _L0 = + Goto _L1; = + _L0: = - _L1: g = = + = { } g = { g }

46 Liv Rngs n Liv Intrvls = + = + = + = + = + IZ Goto _L0 = + Goto _L1; = + _L0: _L1: = - g = = + { } = { } g = { g }

47 Liv Rngs n Liv Intrvls = + = + = + = + = + IZ Goto _L0 = + Goto _L1; = + _L0: = - _L1: g = {, } = + { } = { } g = { g }

48 Liv Rngs n Liv Intrvls = + = + = + = + = + IZ Goto _L0 = + Goto _L1; = + _L0: = - _L1: g = {, } = + { } = { } { } g = { g }

49 Liv Rngs n Liv Intrvls = + = + = + = + = + IZ Goto _L0 = + Goto _L1; = + _L0: = - _L1: g = {, } = + { } {, } = { } { } g = { g }

50 Liv Rngs n Liv Intrvls = + = + = + = + = + IZ Goto _L0 = + _L0: Goto _L1; = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

51 Liv Rngs n Liv Intrvls = + = + = + = + = + IZ Goto _L0 _L0: = + Goto _L1; {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

52 Liv Rngs n Liv Intrvls = + = + = + = + IZ Goto _L0 = + Goto _L1; _L0: = + {,, } {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

53 Liv Rngs n Liv Intrvls = + = + = + = + IZ Goto _L0 = + Goto _L1; _L0: {,, } = + {,, } {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

54 Liv Rngs n Liv Intrvls = + = + = + IZ Goto _L0 = + Goto _L1; _L0: = + {,, } {,, } = + {,, } {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

55 Liv Rngs n Liv Intrvls = + = + = + IZ Goto _L0 = + Goto _L1; _L0: {,,, } = + {,, } {,, } = + {,, } {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

56 Liv Rngs n Liv Intrvls = + = + = + IZ Goto _L0 = + Goto _L1; _L0: {,,, } = + {,, } {,, } = + {,, } {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

57 Liv Rngs n Liv Intrvls = + = + = + IZ Goto _L0 = + Goto _L1; _L0: {,,, } = + {,, } {,, } = + {,, } {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

58 Liv Rngs n Liv Intrvls = + = + = + IZ Goto _L0 = + Goto _L1; _L0: {,,, } = + {,, } {,, } = + {,, } {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

59 Liv Rngs n Liv Intrvls = + {,,, } = + {,, } = + = + IZ Goto _L0 {,, } = + {,, } = + Goto _L1; _L0: {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

60 Liv Rngs n Liv Intrvls = + {,,, } = + {,, } = + = + IZ Goto _L0 {,, } = + {,, } = + Goto _L1; _L0: {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

61 Liv Rngs n Liv Intrvls = + {,,, } = + {,, } = + = + IZ Goto _L0 {,, } = + {,, } = + Goto _L1; _L0: {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

62 Liv Rngs n Liv Intrvls = + {,,, } = + {,, } = + = + IZ Goto _L0 {,, } = + {,, } = + Goto _L1; _L0: {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

63 Liv Rngs n Liv Intrvls = + {,,, } = + {,, } = + = + IZ Goto _L0 {,, } = + {,, } = + Goto _L1; _L0: {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

64 Liv Rngs n Liv Intrvls = + g {,,, } = + {,, } = + = + IZ Goto _L0 {,, } = + {,, } = + Goto _L1; _L0: {,, } = + {, } _L1: = - g = {, } = + { } {, } = { } { } g = { g }

65 Rgistr Allotion with Liv Intrvls Givn th liv intrvls or ll th vrils in th progrm, w n llot rgistrs using simpl gry lgorithm. g I: Trk whih rgistrs r r t h point. Whn liv intrvl gins, giv tht vril r rgistr. Whn liv intrvl ns, th rgistr is on gin r. W n't lwys it vrything into rgistr; w'll s wht o to in minut.

66 Rgistr Allotion with Liv Intrvls g

67 Rgistr Allotion with Liv Intrvls g Fr Rgistrs R 0 R 1 R 2 R 23

68 Rgistr Allotion with Liv Intrvls g Fr Rgistrs R 0 R 1 R 2 R 23

69 Rgistr Allotion with Liv Intrvls g Fr Rgistrs R 0 R 1 R 2 R 23

70 Rgistr Allotion with Liv Intrvls g Fr Rgistrs R 0 R 1 R 2 R 23

71 Rgistr Allotion with Liv Intrvls g Fr Rgistrs R 0 R 1 R 2 R 23

72 Rgistr Allotion with Liv Intrvls g Fr Rgistrs R 0 R 1 R 2 R 32

73 Rgistr Allotion with Liv Intrvls g Fr Rgistrs R 0 R 1 R 2 R 32

74 Rgistr Allotion with Liv Intrvls g Fr Rgistrs R 0 R 1 R 2 R 32

75 Rgistr Allotion with Liv Intrvls g Fr Rgistrs R 0 R 1 R 2 R 32

76 Rgistr Allotion with Liv Intrvls g Fr Rgistrs R 0 R 1 R 2 R 32

77 Rgistr Allotion with Liv Intrvls g Fr Rgistrs R 0 R 1 R 2 R 23

78 Rgistr Allotion with Liv Intrvls g Fr Rgistrs R 0 R 1 R 2 R 23

79 Rgistr Allotion with Liv Intrvls g Fr Rgistrs R 0 R 1 R 2 R 23

80 Anothr Exmpl

81 Anothr Exmpl g

82 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

83 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

84 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

85 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

86 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

87 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2 Wht o w o now?

88 Rgistr Spilling I rgistr nnot oun or vril v, w my n to spill vril. Whn vril is spill, it is stor in mmory rthr thn rgistr. Whn w n rgistr or th spill vril: Evit som xisting rgistr to mmory. Lo th vril into th rgistr. Whn on, writ th rgistr k to mmory n rlo th rgistr with its originl vlu. Spilling is slow, ut somtims nssry.

89 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2 Wht o w o now?

90 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

91 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

92 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

93 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

94 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

95 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

96 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

97 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

98 Anothr Exmpl g Fr Rgistrs R 0 R 1 R 2

99 Linr Sn Rgistr Allotion This lgorithm is ll linr sn rgistr llotion n is omprtivly nw lgorithm. Avntgs: Vry iint (tr omputing liv intrvls, runs in linr tim) Prous goo o in mny instns. Allotion stp works in on pss; n gnrt o uring itrtion. Otn us in JIT ompilrs lik Jv HotSpot. Disvntgs: Impris u to us o liv intrvls rthr thn liv rngs. Othr thniqus known to suprior in mny ss.

100 Corrtnss Proo Skth No rgistr hols two liv vrils t on: Liv intrvls r onsrvtiv pproximtions o liv rngs. No two vrils with ovrlpping liv rngs pl in th sm rgistr. At h progrm point, vry vril is in th sm lotion: All vrils ssign uniqu lotion.

101 Son-Chn Bin Pking A mor ggrssiv vrsion o linr-sn. Uss liv rngs inst o liv intrvls. I vril must spill, on't spill ll uss o it. A ltr liv rng might still it into rgistr. Rquirs inl t-low nlysis to onirm vrils r ssign onsistnt lotions. S Qulity n Sp in Linr-sn Rgistr Allotion y Tru, Hollowy, n Smith.

102 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

103 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

104 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

105 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

106 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

107 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

108 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

109 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

110 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

111 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

112 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

113 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

114 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

115 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

116 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

117 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

118 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

119 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

120 Son-Chn Bin Pking g Fr Rgistrs R 0 R 1 R 2

121 An Entirly Dirnt Approh

122 An Entirly Dirnt Approh {,,, } = + {,, } {,, } = + {,, } {,, } = + {, } {, } = + { } {, } = { } { } g = { g }

123 An Entirly Dirnt Approh {,,, } = + {,, } {,, } = + {,, } {, } = + { } {,, } = + {, } {, } = { } Wht n w inr rom ll ths vrils ing liv t this point? { } g = { g }

124 An Entirly Dirnt Approh {,,, } = + {,, } {,, } = + {,, } {,, } = + {, } {, } = + { } {, } = { } { } g = { g }

125 An Entirly Dirnt Approh {,,, } = + {,, } {,, } = + {,, } {, } = + { } {,, } = + {, } {, } = { } g { } g = { g }

126 An Entirly Dirnt Approh {,,, } = + {,, } {,, } = + {,, } {, } = + { } {,, } = + {, } {, } = { } g { } g = { g }

127 An Entirly Dirnt Approh {,,, } = + {,, } {,, } = + {,, } {, } = + { } {,, } = + {, } {, } = { } g { } g = { g }

128 An Entirly Dirnt Approh {,,, } = + {,, } {,, } = + {,, } {, } = + { } {,, } = + {, } {, } = { } g { } g = { g }

129 An Entirly Dirnt Approh {,,, } = + {,, } Rgistrs R 0 R 1 R 2 R 3 {,, } = + {,, } {, } = + { } {,, } = + {, } {, } = { } g { } g = { g }

130 An Entirly Dirnt Approh {,,, } = + {,, } Rgistrs R 0 R 1 R 2 R 3 {,, } = + {,, } {, } = + { } {,, } = + {, } {, } = { } g { } g = { g }

131 Th Rgistr Intrrn Grph Th rgistr intrrn grph (RIG) o ontrol-low grph is n unirt grph whr Eh no is vril. Thr is n g twn two vrils tht r liv t th sm progrm point. Prorm rgistr llotion y ssigning h vril irnt rgistr rom ll o its nighors. Thr's just on th...

132 Th On Cth This prolm is quivlnt to grpholoring, whih is NP-hr i thr r t lst thr rgistrs. No goo polynomil-tim lgorithms (or vn goo pproximtions!) r known or this prolm. W hv to ontnt with huristi tht is goo nough or RIGs tht ris in prti.

133 Th On Cth to Th On Cth

134 Th On Cth to Th On Cth I you n igur out wy to ssign rgistrs to ritrry RIGs, you'v just provn P = NP n will gt $1,000,000 hk rom th Cly Mthmtis Institut.

135 Th On Cth to Th On Cth I you n igur out wy to ssign rgistrs to ritrry RIGs, you'v just provn P = NP n will gt $1,000,000 hk rom th Cly Mthmtis Institut.

136 Bttling NP-Hrnss

137 Chitin's Algorithm Intuition: Suppos w r trying to k-olor grph n in no with wr thn k gs. I w lt this no rom th grph n olor wht rmins, w n in olor or this no i w it k in. Rson: With wr thn k nighors, som olor must lt ovr. Algorithm: Fin no with wr thn k outgoing gs. Rmov it rom th grph. Rursivly olor th rst o th grph. A th no k in. Assign it vli olor.

138 Chitin's Algorithm

139 Chitin's Algorithm g

140 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

141 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

142 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

143 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

144 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

145 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

146 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

147 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

148 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

149 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

150 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

151 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

152 Chitin's Algorithm g g Rgistrs R 0 R 1 R 2 R 3

153 Chitin's Algorithm g g Rgistrs R 0 R 1 R 2 R 3

154 Chitin's Algorithm g g Rgistrs R 0 R 1 R 2 R 3

155 Chitin's Algorithm g g Rgistrs R 0 R 1 R 2 R 3

156 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

157 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

158 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

159 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

160 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

161 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

162 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

163 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

164 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

165 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

166 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

167 Chitin's Algorithm g Rgistrs R 0 R 1 R 2 R 3

168 On Prolm Wht i w n't in no with wr thn k nighors? Choos n rmov n ritrry no, mrking it troulsom. Us huristis to hoos whih on. Whn ing no k in, it my possil to in vli olor. Othrwis, w hv to spill tht no.

169 Chitin's Algorithm Rlo g Rgistrs R 0 R 1 R 2

170 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

171 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

172 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

173 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

174 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

175 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

176 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

177 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

178 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

179 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

180 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

181 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

182 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

183 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

184 Chitin's Algorithm Rlo g g Rgistrs R 0 R 1 R 2

185 Chitin's Algorithm Rlo (spill) g g Rgistrs R 0 R 1 R 2

186 Chitin's Algorithm Rlo (spill) g g Rgistrs R 0 R 1 R 2

187 Chitin's Algorithm Rlo (spill) g g Rgistrs R 0 R 1 R 2

188 Chitin's Algorithm Rlo (spill) g g Rgistrs R 0 R 1 R 2

189 Chitin's Algorithm Rlo (spill) g g Rgistrs R 0 R 1 R 2

190 Chitin's Algorithm Rlo (spill) g Rgistrs R 0 R 1 R 2

191 Chitin's Algorithm Rlo (spill) g Rgistrs R 0 R 1 R 2

192 A Smrtr Algorithm {,,, } = + {,, } Rgistrs R 0 R 1 R 2 {,, } = + {,, } {,, } = + {, } g (spill) {, } = + { } {, } = { } { } g = { g }

193 A Smrtr Algorithm {,,, } = + {,, } Rgistrs R 0 R 1 R 2 {,, } = + {,, } {,, } = + {, } g (spill) {, } = + { } {, } = { } { } g = { g }

194 A Smrtr Algorithm {,,, } = + {,, } Rgistrs R 0 R 1 R 2 {,, } = + {,, } {,, } = + {, } g (spill) {, } ' = + { ' } {, } ' = { ' } { ' } g = ' { g }

195 A Smrtr Algorithm {,,, } = + {,, } Rgistrs R 0 R 1 R 2 {,, } = + {,, } {,, } = + {, } g (spill) ' {, } ' = + { ' } {, } ' = { ' } { ' } g = ' { g }

196 Anothr Exmpl

197 Anothr Exmpl

198 Anothr Exmpl Rgistrs R 0 R 1 R 2

199 Anothr Exmpl Rgistrs R 0 R 1 R 2

200 Anothr Exmpl Rgistrs R 0 R 1 R 2

201 Anothr Exmpl Rgistrs R 0 R 1 R 2

202 Anothr Exmpl Rgistrs R 0 R 1 R 2

203 Anothr Exmpl Rgistrs R 0 R 1 R 2

204 Anothr Exmpl Rgistrs R 0 R 1 R 2

205 Anothr Exmpl Rgistrs R 0 R 1 R 2

206 Anothr Exmpl Rgistrs R 0 R 1 R 2

207 Anothr Exmpl Rgistrs R 0 R 1 R 2

208 Anothr Exmpl Rgistrs R 0 R 1 R 2

209 Anothr Exmpl Rgistrs R 0 R 1 R 2

210 Anothr Exmpl Rgistrs R 0 R 1 R 2

211 Anothr Exmpl Rgistrs R 0 R 1 R 2

212 Anothr Exmpl Rgistrs R 0 R 1 R 2

213 Anothr Exmpl Rgistrs R 0 R 1 R 2

214 Anothr Exmpl Rgistrs R 0 R 1 R 2

215 Anothr Exmpl Rgistrs R 0 R 1 R 2

216 Anothr Exmpl Rgistrs R 0 R 1 R 2

217 Anothr Exmpl Rgistrs R 0 R 1 R 2

218 Anothr Exmpl Rgistrs R 0 R 1 R 2

219 Anothr Exmpl Rgistrs R 0 R 1 R 2

220 Anothr Exmpl Rgistrs R 0 R 1 R 2

221 Anothr Exmpl Rgistrs R 0 R 1 R 2

222 Anothr Exmpl Rgistrs R 0 R 1 R 2

223 Anothr Exmpl Rgistrs R 0 R 1 R 2

224 Anothr Exmpl Rgistrs R 0 R 1 R 2

225 Anothr Exmpl Rgistrs R 0 R 1 R 2

226 Anothr Exmpl Rgistrs R 0 R 1 R 2

227 Anothr Exmpl (spill) Rgistrs R 0 R 1 R 2

228 Anothr Exmpl (spill) Rgistrs R 0 R 1 R 2

229 Anothr Exmpl (spill) (spill) Rgistrs R 0 R 1 R 2

230 Chitin's Algorithm Avntgs: For mny ontrol-low grphs, ins n xllnt ssignmnt o vrils to rgistrs. Whn istinguishing vrils y us, prous pris RIG. Otn us in proution ompilrs lik GCC. Disvntgs: Cor pproh s on th NP-hr grph oloring prolm. Huristi my prou pthologilly worst-s ssignmnts.

231 Corrtnss Proo Skth No two vrils liv t som point r ssign th sm rgistr. For y grph oloring. At ny progrm point h vril is lwys in on lotion. Automti i w ssign h vril on rgistr. Rquirs w triks i w sprt y us s.

232 Improvmnts to th Algorithm Choos wht to spill intlligntly. Us huristis (lst-ommonly us, grtst improvmnt, t.) to trmin wht to spill. Hnl spilling intlligntly. Whn spilling vril, romput th RIG s on th spill n us nw oloring to in rgistr.

233 Summry o Rgistr Allotion Critil stp in ll optimizing ompilrs. Th linr sn lgorithm uss liv intrvls to grily ssign vrils to rgistrs. Otn us in JIT ompilrs u to iiny. Chitin's lgorithm uss th rgistr intrrn grph (s on liv rngs) n grph oloring to ssign rgistrs. Th sis or th thniqu us in GCC.

234 Nxt Tim Grg Colltion Rrn Counting Mrk-n-Swp Stop-n-Copy Inrmntl Colltors