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❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥

❘❡❣✐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❡✳

❘❡❣✐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✳

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ a b c { a } a b = a + 2 { a,b } c = b * b { a,c } c b = c + 1 b { a,b } return b*a Live ranges Interference graph Code Live sets

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ a b c { a } a b = a + 2 { a,b } c = b * b { a,c } c b = c + 1 b { a,b } return b*a Live ranges Interference graph Code Live sets

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ a b c { a } a b = a + 2 { a,b } c = b * b { a,c } c b = c + 1 b { a,b } return b*a Live ranges Interference graph Code Live sets R2 = R1 + 2 ❂ Register 1 ( R1 ) R2 = R2 * R2 ❂ Register 2 ( R2 ) R2 = R2 + 1 return R2*R1

❘❡❣✐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✳

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ def y def y def x def x def x def x use y use y def y def y use x use x use x use x use y use y def x def x use x use x

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ def y def y def x def x def x def x use y use y def y def y use x use x use x use x use y use y def x def x use x use x

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ def y def y def x def x def x def x use y use y def y def y use x use x use x use x use y use y def x def x use x use x

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ def y def y def x def x def x def x use y use y def y def y use x use x use x use x use y use y def x def x use x use x

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ def y def y def x def x def x def x use y use y def y def y use x use x use x use x use y use y def x def x use x use x

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ def y def y def x def x def x def x use y use y def y def y use x use x use x use x use y use y def x def x use x use x

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ def y def y def x def x def x def x use y use y def y def y use x use x use x use x use y use y def x def x use x use x

❘❡❣✐st❡r ❛❧❧♦❝❛t✐♦♥ ❲❡❜s s1 ❛♥❞ s2 ♦✈❡r❧❛♣ ❲❡❜s s1 ❛♥❞ s4 ♦✈❡r❧❛♣ def y def y s4 def x def x def x def x use y use y def y def y s1 s2 use x use x use x use x use y use y def x def x s3 use x use x

●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✮❄

●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 ❡♥♦✉❣❤✳

●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✳

●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✐♥✉❡✳