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SLIDE 1

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

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SLIDE 2

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

❖✈❡r✈✐❡✇

❱❛r✐❛❜❧❡s ♠❛② ❜❡ st♦r❡❞ ✐♥ t❤❡ ♠❛✐♥ ♠❡♠♦r② ♦r ✐♥ r❡❣✐st❡rs✳ ④ ▼❛✐♥ ♠❡♠♦r② ✐s ♠✉❝❤ s❧♦✇❡r t❤❛♥ r❡❣✐st❡rs✳ ④ ❚❤❡ ♥✉♠❜❡r ♦❢ r❡❣✐st❡rs ✐s str✐❝t❧② ❧✐♠✐t❡❞✳ ❚❤❡ ❣♦❛❧ ♦❢ r❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ ✐s t♦ ❞❡❝r❡❛s❡ t❤❡ ♥✉♠❜❡r ♦❢ ♠❡♠♦r② ❛❝❝❡ss❡s ❜② ❦❡❡♣✐♥❣ ❛s ♠❛♥② ❛s ♣♦ss✐❜❧❡ ✈❛r✐❛❜❧❡s ✐♥ r❡❣✐st❡rs✳ ④ ❉❡❝✐❞❡s ✇❤✐❝❤ ✈❛❧✉❡s t♦ ❦❡❡♣ ✐♥ r❡❣✐st❡rs ❛♥❞ ✇❤✐❝❤ ✐♥ ♠❡♠♦r②✳ ④ ❆ss✐❣♥s ❝♦♥❝r❡t❡ r❡❣✐st❡rs ❢♦r ✈❛❧✉❡s ✇❤✐❝❤ ❛r❡ ❦❡♣t t❤❡r❡✳

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SLIDE 3

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

❖❜s❡r✈❛t✐♦♥s

❯s✉❛❧❧② t❤❡r❡ ❛r❡ ❧❡ss r❡❣✐st❡rs t❤❛♥ ✈❛r✐❛❜❧❡s✳ ❙✐♠✉❧t❛♥❡♦✉s❧② ❛❧✐✈❡ ✈❛r✐❛❜❧❡s ❝❛♥♥♦t ❜❡ ❛❧❧♦❝❛t❡❞ t♦ t❤❡ s❛♠❡ r❡❣✐st❡r✳ ❱❛r✐❛❜❧❡s ✇❤✐❝❤ ❧✐❢❡ t✐♠❡s ❞♦ ♥♦t ♦✈❡r❧❛♣ ❝❛♥ ❜❡ ❛❧❧♦❝❛t❡❞ t♦ t❤❡ s❛♠❡ r❡❣✐st❡r✳ ❚❤❡s❡ ❝♦♥str❛✐♥ts ❝❛♥ ❜❡ r❡♣r❡s❡♥t❡❞ ❛s ❛♥ ✐♥t❡r❢❡r❡♥❝❡ ❣r❛♣❤✿ ④ ♥♦❞❡s ❛r❡ ✈❛r✐❛❜❧❡s❀ ④ ❡❞❣❡s ❛r❡ ❜❡t✇❡❡♥ s✐♠✉❧t❛♥❡♦✉s❧② ❛❧✐✈❡ ✈❛r✐❛❜❧❡s✳ ❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ ❝❛♥ ❜❡ st❛t❡❞ ❛s ❛ ❣r❛♣❤ ❝♦❧♦r✐♥❣ ♣r♦❜❧❡♠ ♦❢ t❤❡ ✐♥t❡r❢❡r❡♥❝❡ ❣r❛♣❤ ✇✐t❤ ❦ ❝♦❧♦rs ✭▲❛✈r♦✈ ✶✾✻✷✱ ❈❤❛✐t✐♥ ✶✾✽✶✮ ④ ❦ ❂ t❤❡ ♥✉♠❜❡r ♦❢ r❡❣✐st❡rs✳

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SLIDE 4

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

{a} b = a + 2 {a,b} c = b * b {a,c} b = c + 1 {a,b} return b*a Code Live sets a b c Live ranges a b c Interference graph

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SLIDE 5

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

{a} b = a + 2 {a,b} c = b * b {a,c} b = c + 1 {a,b} return b*a Code Live sets a b c Live ranges a b c Interference graph

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SLIDE 6

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

{a} b = a + 2 {a,b} c = b * b {a,c} b = c + 1 {a,b} return b*a Code Live sets a b c Live ranges a b c Interference graph ❂ Register 1 (R1) ❂ Register 2 (R2) R2 = R1 + 2 R2 = R2 * R2 R2 = R2 + 1 return R2*R1

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SLIDE 7

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

❈♦♥str✉❝t✐♦♥ ♦❢ t❤❡ ✐♥t❡r❢❡r❡♥❝❡ ❣r❛♣❤

❚♦ ❜✉✐❧❞ t❤❡ ✐♥t❡r❢❡r❡♥❝❡ ❣r❛♣❤ ✇❡ ♥❡❡❞ t♦ ❞❡t❡r♠✐♥❡ ❧✐✈❡ r❛♥❣❡s ♦❢ ✈❛r✐❛❜❧❡s✳ ■♥ ❝❛s❡ ♦❢ ❧♦❝❛❧ r❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ ✐♥s✐❞❡ ❜❛s✐❝ ❜❧♦❝❦s✱ ❛❧❧ ❧✐✈❡ r❛♥❣❡s ❛r❡ ❧✐♥❡❛r✳ ✔ ❉✐s❝♦✈❡r✐♥❣ ❧✐✈❡ r❛♥❣❡s ❛♥❞ ❝❤❡❝❦✐♥❣ ✇❤❡t❤❡r t❤❡② ♦✈❡r❧❛♣ ✐s ✈❡r② ❡❛s②✳ ✘ ❱❛r✐❛❜❧❡s ❤❛✈❡ t♦ ❜❡ r❡❛❞ ❢r♦♠ t❤❡ ♠❡♠♦r② ❜❡❢♦r❡ ❡♥t❡r✐♥❣ t♦ t❤❡ ❜❛s✐❝ ❜❧♦❝❦✱ ❛♥❞ t♦ ❜❡ st♦r❡❞ t♦ t❤❡ ♠❡♠♦r② ✇❤❡♥ ❧❡❛✈✐♥❣✳ ■♥ ❝❛s❡ ♦❢ ❣❧♦❜❛❧ r❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥✱ ❧✐✈❡ r❛♥❣❡s ❢♦r♠ ❛ ✇❡❜✳ ✘ ❉✐s❝♦✈❡r✐♥❣ ❧✐✈❡ r❛♥❣❡s ✐s ♠♦r❡ ❝♦♠♣❧❡①✳ ✔ ❆❧❧♦✇s ♠♦r❡ ❡✍❝✐❡♥t ✉s❛❣❡ ♦❢ r❡❣✐st❡rs✳

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SLIDE 8

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

use x use y def x def y use x def x use x def x use y def y use x use y def x def y use x def x use x def x use y def y

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SLIDE 9

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

use x use y def x def y use x def x use x def x use y def y use x use y def x def y use x def x use x def x use y def y

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SLIDE 10

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

use x use y def x def y use x def x use x def x use y def y use x use y def x def y use x def x use x def x use y def y

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SLIDE 11

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

use x use y def x def y use x def x use x def x use y def y use x use y def x def y use x def x use x def x use y def y

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SLIDE 12

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

use x use y def x def y use x def x use x def x use y def y use x use y def x def y use x def x use x def x use y def y

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SLIDE 13

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

use x use y def x def y use x def x use x def x use y def y use x use y def x def y use x def x use x def x use y def y

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SLIDE 14

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

use x use y def x def y use x def x use x def x use y def y use x use y def x def y use x def x use x def x use y def y

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SLIDE 15

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

use x use y def x def y use x def x use x def x use y def y

s1 s2 s3 s4

❲❡❜s s1 ❛♥❞ s2 ♦✈❡r❧❛♣ ❲❡❜s s1 ❛♥❞ s4 ♦✈❡r❧❛♣

use x use y def x def y use x def x use x def x use y def y

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SLIDE 16
  • r❛♣❤ ❝♦❧♦r✐♥❣

❉❡☞♥✐t✐♦♥

❆ ❣r❛♣❤ ● ✐s ❦✲❝♦❧♦r❛❜❧❡ ✐☛ ✐ts ♥♦❞❡s ❝❛♥ ❜❡ ❧❛❜❡❧❡❞ ✇✐t❤ ✐♥t❡❣❡rs ✶ ✿ ✿ ✿ ❦ s♦ t❤❛t ♥♦ ❡❞❣❡ ✐♥ ● ❝♦♥♥❡❝ts t✇♦ ♥♦❞❡s ✇✐t❤ t❤❡ s❛♠❡ ❧❛❜❡❧✳

▼❛✐♥ q✉❡st✐♦♥s

❍♦✇ t♦ ☞♥❞ ❡✍❝✐❡♥t❧② ❦✲❝♦❧♦r✐♥❣ ♦❢ ❛ ❣r❛♣❤❄ ❲❤❡t❤❡r ❛♥❞ ❤♦✇ t♦ ☞♥❞ ❛♥ ♦♣t✐♠❛❧ ❝♦❧♦r✐♥❣ ✭✐❡✳ ❛ ❝♦❧♦r✐♥❣ ✇✐t❤ t❤❡ ♠✐♥✐♠✉♠ ♥✉♠❜❡r ♦❢ ❝♦❧♦rs✮❄ ❲❤❛t t♦ ❞♦ ✇❤❡♥ t❤❡r❡ ❛r❡ ♥♦t ❡♥♦✉❣❤ ❝♦❧♦rs ✭✐❡✳ r❡❣✐st❡rs✮❄

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SLIDE 17
  • r❛♣❤ ❝♦❧♦r✐♥❣

Pr♦❜❧❡♠

❚❤❡ ❣r❛♣❤ ❝♦❧♦r✐♥❣ ♣r♦❜❧❡♠ ✐s ◆P✲❝♦♠♣❧❡t❡✳

❖❜s❡r✈❛t✐♦♥s

❖♣t✐♠❛❧ ❛❧❣♦r✐t❤♠ ✇♦r❦s ✇✐t❤ ❛❧❧ ❣r❛♣❤s✳ ④ ❚❤❡ ✧✇♦rst ❝❛s❡ ❣r❛♣❤✧ ❞♦❡s♥✬t ❛♣♣❡❛r ✐♥ ♣r❛❝t✐❝❡✳ ■t ❛❧✇❛②s ☞♥❞s ❛ ♠✐♥✐♠❛❧ ❝♦❧♦r✐♥❣✳ ④ ❖❢t❡♥✱ ❛♥ ❛♣♣r♦①✐♠❛t❡ ❝♦❧♦r✐♥❣ ✐s ❡♥♦✉❣❤✳

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SLIDE 18
  • r❛♣❤ ❝♦❧♦r✐♥❣

Pr♦❜❧❡♠

❲❤❛t t♦ ❞♦ ✐❢ t❤❡ ❣r❛♣❤ ✐s ♥♦t ❦✲❝♦❧♦r❛❜❧❡❄ ■❡✳ t❤❡r❡ ✐s ♥♦t ❡♥♦✉❣❤ r❡❣✐st❡rs❄ ❍❛♣♣❡♥s ✈❡r② ♦❢t❡♥✳

❙♣✐❧❧✐♥❣

❈❤♦♦s❡ ❛ ✈❛r✐❛❜❧❡ ❛♥❞ ❦❡❡♣ ✐ts ✈❛❧✉❡s ✐♥ t❤❡ ♠❡♠♦r② ✭✐❡✳ ✐♥ t❤❡ st❛❝❦✮ ✐♥st❡❛❞ ♦❢ ❛♥ r❡❣✐st❡r✳ ④ ❚❤❡ ♣r♦❝❡ss ✐s ❝❛❧❧❡❞ s♣✐❧❧✐♥❣✳ P❧❛❝❡s ✇❤❡r❡ t❤❡ ✈❛r✐❛❜❧❡ ✐s ❛❝❝❡ss❡❞✱ ❣❡♥❡r❛t❡ ❛♥ ❡①tr❛ ❝♦❞❡ ❢♦r r❡❛❞✐♥❣ ❢r♦♠ ❛♥❞ st♦r✐♥❣ t♦ t❤❡ ♠❡♠♦r②✳

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SLIDE 19
  • r❛♣❤ ❝♦❧♦r✐♥❣

■❞❡❛

P✐❝❦ ❛ ♥♦❞❡ ✇✐t❝❤ ❤❛s ❞❡❣r❡❡ ❁ ❦✳ ④ ❚❤✐s ♥♦❞❡ ✐s ❦✲❝♦❧♦r❛❜❧❡✦ ❘❡♠♦✈❡ t❤❡ ♥♦❞❡ ✭❛♥❞ ❛❧❧ ✐ts ❡❞❣❡s✮ ❢r♦♠ t❤❡ ❣r❛♣❤✳ ④ ❆❧❧ ✐ts ♥❡✐❣❤❜♦✉rs ❤❛✈❡ ♥♦✇ ❞❡❣r❡❡ ❞❡❝r❡♠❡♥t❡❞ ❜② ♦♥❡✳ ④ ▼❛② r❡s✉❧t t♦ ♥❡✇ ♥♦❞❡s ✇✐t❤ ❞❡❣r❡❡ ❁ ❦✳ ■❢ ❛❧❧ ♥♦❞❡s ❤❛✈❡ ❞❡❣r❡❡ ✕ ❦✱ t❤❡♥ ♣✐❝❦ ❛ ♥♦❞❡✱ s♣✐❧❧ ✐t t♦ t❤❡ ♠❡♠♦r②✱ ❛♥❞ ❝♦♥t✐♥✉❡✳

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SLIDE 20
  • r❛♣❤ ❝♦❧♦r✐♥❣

❈❤❛✐t✐♥✬s ❛❧❣♦r✐t❤♠

✶ ❯♥t✐❧ t❤❡r❡ ❛r❡ ♥♦❞❡s ✇✐t❤ ❞❡❣r❡❡ ❁ ❦✿

④ ❝❤♦♦s❡ s✉❝❤ ♥♦❞❡ ❛♥❞ ♣✉s❤ ✐t ✐♥t♦ t❤❡ st❛❝❦❀ ④ ❞❡❧❡t❡ t❤❡ ♥♦❞❡ ❛♥❞ ❛❧❧ ✐ts ❡❞❣❡s ❢r♦♠ t❤❡ ❣r❛♣❤✳

✷ ■❢ t❤❡ ❣r❛♣❤ ✐s ♥♦♥✲❡♠♣t② ✭❛♥❞ ❛❧❧ ♥♦❞❡s ❤❛✈❡ ❞❡❣r❡❡ ✕ ❦✮✱

t❤❡♥✿ ④ ❝❤♦♦s❡ ❛ ♥♦❞❡ ✭✉s✐♥❣ s♦♠❡ ❤❡✉r✐st✐❝s✮ ❛♥❞ s♣✐❧❧ ✐t t♦ t❤❡ ♠❡♠♦r②❀ ④ ❞❡❧❡t❡ t❤❡ ♥♦❞❡ ❛♥❞ ❛❧❧ ✐ts ❡❞❣❡s ❢r♦♠ t❤❡ ❣r❛♣❤✳ ④ ✐❢ t❤✐s r❡s✉❧ts t♦ s♦♠❡ ♥♦❞❡s ✇✐t❤ ❞❡❣r❡❡ ❁ ❦✱ t❤❡♥ ❣♦ t♦ t❤❡ st❡♣ ✶❀ ④ ♦t❤❡r✇✐s❡ ❝♦♥t✐♥✉❡ ✇✐t❤ t❤❡ st❡♣ ✷✳

✸ ❙✉❝❝❡ss✐✈❡❧② ♣♦♣ ♥♦❞❡s ♦☛ t❤❡ st❛❝❦ ❛♥❞ ❝♦❧♦r t❤❡♠ ✐♥ t❤❡

❧♦✇❡st ❝♦❧♦r ♥♦t ✉s❡❞ ❜② s♦♠❡ ♥❡✐❣❤❜♦r✳

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SLIDE 21

❈❤❛✐t✐♥✬s ❛❧❣♦r✐t❤♠

❊①❛♠♣❧❡✿

Stack 1 2 3 4 5

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SLIDE 22

❈❤❛✐t✐♥✬s ❛❧❣♦r✐t❤♠

❊①❛♠♣❧❡✿

Stack 1 2 3 4 5 1

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SLIDE 23

❈❤❛✐t✐♥✬s ❛❧❣♦r✐t❤♠

❊①❛♠♣❧❡✿

Stack 1 2 3 4 5 1 2

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SLIDE 24

❈❤❛✐t✐♥✬s ❛❧❣♦r✐t❤♠

❊①❛♠♣❧❡✿

Stack 1 2 3 4 5 1 2 4

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SLIDE 25

❈❤❛✐t✐♥✬s ❛❧❣♦r✐t❤♠

❊①❛♠♣❧❡✿

Stack 1 2 3 4 5 1 2 4 3

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SLIDE 26

❈❤❛✐t✐♥✬s ❛❧❣♦r✐t❤♠

❊①❛♠♣❧❡✿

Stack 1 2 3 4 5 Colors 1 2 4 3 5

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SLIDE 27

❈❤❛✐t✐♥✬s ❛❧❣♦r✐t❤♠

❊①❛♠♣❧❡✿

Stack 1 2 3 4 5 Colors 1 2 4 3

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SLIDE 28

❈❤❛✐t✐♥✬s ❛❧❣♦r✐t❤♠

❊①❛♠♣❧❡✿

Stack 1 2 3 4 5 Colors 1 2 4

slide-29
SLIDE 29

❈❤❛✐t✐♥✬s ❛❧❣♦r✐t❤♠

❊①❛♠♣❧❡✿

Stack 1 2 3 4 5 Colors 1 2

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SLIDE 30

❈❤❛✐t✐♥✬s ❛❧❣♦r✐t❤♠

❊①❛♠♣❧❡✿

Stack 1 2 3 4 5 Colors 1

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SLIDE 31

❈❤❛✐t✐♥✬s ❛❧❣♦r✐t❤♠

❊①❛♠♣❧❡✿

Stack 1 2 3 4 5 Colors

slide-32
SLIDE 32
  • r❛♣❤ ❝♦❧♦r✐♥❣

❖♣t✐♠✐st✐❝ ❝♦❧♦r✐♥❣ ✭❇r✐❣❣s ❡t ❛❧✮

■❢ ❛❧❧ ♥♦❞❡s ❤❛✈❡ ❛ ❞❡❣r❡❡ ✕ ❦✱ t❤❡♥ ✐♥st❡❛❞ ♦❢ s♣✐❧❧✐♥❣ ♦r❞❡r t❤❡ ♥♦❞❡s ❛♥❞ ♣✉s❤ t❤❡♠ ✐♥t♦ st❛❝❦✳ ④ ❲❤❡♥ t❛❦✐♥❣ ♥♦❞❡s ❜❛❝❦ ❢r♦♠ t❤❡ st❛❝❦ t❤❡② ♠❛② st✐❧❧ ❜❡ ❝♦❧♦r❛❜❧❡✦ ❚❤❡ ❢♦❧❧♦✇✐♥❣ ❣r❛♣❤ ✐s ✷✲❝♦❧♦r❛❜❧❡✿

1 2 3 4

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SLIDE 33
  • r❛♣❤ ❝♦❧♦r✐♥❣

❖♣t✐♠✐st✐❝ ❝♦❧♦r✐♥❣ ✭❇r✐❣❣s ❡t ❛❧✮

■❢ ❛❧❧ ♥♦❞❡s ❤❛✈❡ ❛ ❞❡❣r❡❡ ✕ ❦✱ t❤❡♥ ✐♥st❡❛❞ ♦❢ s♣✐❧❧✐♥❣ ♦r❞❡r t❤❡ ♥♦❞❡s ❛♥❞ ♣✉s❤ t❤❡♠ ✐♥t♦ st❛❝❦✳ ④ ❲❤❡♥ t❛❦✐♥❣ ♥♦❞❡s ❜❛❝❦ ❢r♦♠ t❤❡ st❛❝❦ t❤❡② ♠❛② st✐❧❧ ❜❡ ❝♦❧♦r❛❜❧❡✦ ❚❤❡ ❢♦❧❧♦✇✐♥❣ ❣r❛♣❤ ✐s ✷✲❝♦❧♦r❛❜❧❡✿

1 2 3 4

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SLIDE 34
  • r❛♣❤ ❝♦❧♦r✐♥❣

❈❤❛✐t✐♥✲❇r✐❣❣s✬✐ ❛❧❣♦r✐t❤♠

✶ ❯♥t✐❧ t❤❡r❡ ❛r❡ ♥♦❞❡s ✇✐t❤ ❞❡❣r❡❡ ❁ ❦✿

④ ❝❤♦♦s❡ s✉❝❤ ♥♦❞❡ ❛♥❞ ♣✉s❤ ✐t ✐♥t♦ t❤❡ st❛❝❦❀ ④ ❞❡❧❡t❡ t❤❡ ♥♦❞❡ ❛♥❞ ❛❧❧ ✐ts ❡❞❣❡s ❢r♦♠ t❤❡ ❣r❛♣❤✳

✷ ■❢ t❤❡ ❣r❛♣❤ ✐s ♥♦♥✲❡♠♣t② ✭❛♥❞ ❛❧❧ ♥♦❞❡s ❤❛✈❡ ❞❡❣r❡❡ ✕ ❦✮✱

t❤❡♥✿ ④ ❝❤♦♦s❡ ❛ ♥♦❞❡✱ ♣✉s❤ ✐t ✐♥t♦ t❤❡ st❛❝❦✱ ❛♥❞ ❞❡❧❡t❡ ✐t ✭t♦❣❡t❤❡r ✇✐t❤ ❡❞❣❡s✮ ❢r♦♠ t❤❡ ❣r❛♣❤❀ ④ ✐❢ t❤✐s r❡s✉❧ts t♦ s♦♠❡ ♥♦❞❡s ✇✐t❤ ❞❡❣r❡❡ ❁ ❦✱ t❤❡♥ ❣♦ t♦ t❤❡ st❡♣ ✶❀ ④ ♦t❤❡r✇✐s❡ ❝♦♥t✐♥✉❡ ✇✐t❤ t❤❡ st❡♣ ✷✳

✸ P♦♣ ❛ ♥♦❞❡ ❢r♦♠ t❤❡ st❛❝❦ ❛♥❞ ❝♦❧♦r ✐t ❜② t❤❡ ❧❡❛st ❢r❡❡

❝♦❧♦r✳ ④ ■❢ t❤❡ ✐s ♥♦ ❢r❡❡ ❝♦❧♦rs✱ t❤❡♥ ❝❤♦♦s❡ ❛♥ ✉♥❝♦❧♦r❡❞ ♥♦❞❡✱ s♣✐❧❧ ✐t ✐♥t♦ t❤❡ ♠❡♠♦r②✱ ❛♥❞ ❣♦ t♦ t❤❡ st❡♣ ✶✳

slide-35
SLIDE 35
  • r❛♣❤ ❝♦❧♦r✐♥❣

❙♣✐❧❧✐♥❣ ❤❡✉r✐st✐❝s

❈❤♦♦s✐♥❣ ❛ ♥♦❞❡ ❢♦r s♣✐❧❧✐♥❣ ✐s ❛ ❝r✐t✐❝❛❧ ❢♦r ❡✍❝✐❡♥❝②✳ ❈❤❛✐t✐♥✬s ❤❡✉r✐st✐❝s✿ ④ t♦ ♠✐♥✐♠✐③❡ t❤❡ ✈❛❧✉❡ ♦❢

❝♦st ❞❡❣r❡❡ ✱ ✇❤❡r❡ ❝♦st ✐s ❛ s♣✐❧❧✐♥❣

❝♦st ❛♥❞ ❞❡❣r❡❡ ✐s ❛ ❝✉rr❡♥t ❞❡❣r❡❡ ♦❢ t❤❡ ♥♦❞❡❀ ④ ✐❡✳ ❝❤♦♦s❡ ❢♦r s♣✐❧❧✐♥❣ ❛ ✧❝❤❡❛♣❡st✧ ♣♦ss✐❜❧❡ ♥♦❞❡ ✇❤✐❝❤ ❞❡❝r❡❛s❡s t❤❡ ❞❡❣r❡❡ ♦❢ ♠♦st ♦t❤❡r ♥♦❞❡s✳ ❆❧t❡r♥❛t✐✈❡ ♣♦♣✉❧❛r ♠❡tr✐❝s✿

❝♦st ❞❡❣r❡❡✷ ✳

❱❛r✐❛t✐♦♥s✿ ④ s♣✐❧❧✐♥❣ ♦❢ ✐♥t❡r❢❡r❡♥❝❡ r❡❣✐♦♥s❀ ④ ♣❛rt✐t✐♦♥✐♥❣ ♦❢ ❧✐✈❡ r❛♥❣❡s❀ ④ r❡♠❛t❡r✐❛❧✐③❛t✐♦♥✳