history 55

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Register Allocation

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

● OH all t is !ee"#● As" $uestions %ia email&● As" $uestions %ia Pia''a&● No late submissions #

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Please e%aluate t is course on A(ess#

)our *eed+ac" really ma"es a di**erence#

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ere e Are

-e(ical Analysis

.R /eneration

Synta( Analysis

Semantic Analysis

.R O timi'ation

ode /eneration

O timi'ation

Sourceode

MachineCode

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ere e Are

.R /eneration

.R O timi'ation

ode /eneration

O timi'ation

Sourceode

MachineCode

Fan-TAC-stic!

-e(ical Analysis

Synta( Analysis

.R /eneration

Semantic Analysis

Fan-TAC-stic!

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ere e Are

-e(ical Analysis

Semantic Analysis

Synta( Analysis

.R O timi'ation

.R /eneration

ode /eneration

O timi'ation

Sourceode

MachineCode

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ode /eneration at a /lance● At t is oint, !e a%e o timi'ed .R code t at needs

to +e con%erted into t e target language 2e#g#assem+ly, mac ine code #

● /oal o* t is stage:● oose t e a ro riate mac ine instructions *or eac .R

instruction#● i%%y u *inite mac ine resources 2registers, cac es,

etc#●

.m lement lo!5le%el details o* t e runtime en%ironment#● Mac ine5s eci*ic o timi'ations are o*ten done ere,

t oug some are treated as art o* a *inalo timi'ation ase#

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O%er%ie!● Register Allocation 26oday

● Ho! to assign %aria+les to *initely manyregisters7

● at to do ! en it can t +e done7● Ho! to do so e**icienty7

● Garbage Collection 2Monday● Ho! to detect reclaima+le memory7● Ho! to reclaim memory e**iciently7

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Memory 6radeo**s● 6 ere is an enormous tradeo** +et!een speed and

size in memory#● SRAM is *ast +ut %ery e( ensi%e:

● an "ee u !it rocessor s eeds in t e /H'#● As o* 900 , cost is ;10

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6 e Memory Hierarc y● Idea : 6ry to get t e +est o* all !orlds +y

using multi le ty es o* memory#

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Registers

L1 Cache

L2 Cache

Main Memory Hard Disk

Net ork

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L1 Cache

L2 Cache


Net ork

9>?= 5 8@=

1?@= ?4@=

1M= 5 4M=

4/= 9>?/=>00/=B

H!G"

Registers

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L1 Cache

L2 Cache


Net ork

9>?= 5 8@=

1?@= ?4@=

1M= 5 4M=

4/= 9>?/=>00/=B

H!G"

0#9> 1ns

1ns >ns

>ns 9>ns

9>ns 100ns3 10ms

10 9000ms

Registers

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6 e allenges o* ode /eneration

● Almost all rogramming languages e( ose acoarse %ie! o* t e memory ierarc y:

● All %aria+les li%e in Cmemory#D●

is" and net!or" e( licitly andled se arately#● 2.nteresting e(ce tion: Stan*ord s #e$uoia

rogramming language● allenges in code generation:

● Position o+jects in a !ay t at ta"es ma(imumad%antage o* t e memory ierarc y#

● o so !it out ints *rom t e rogrammer#

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Registers● Most mac ines a%e a set o* registers ,

dedicated memory locations t at● can +e accessed $uic"ly,●

can a%e com utations er*ormed on t em, and● e(ist in small $uantity#

● Esing registers intelligently is a critical ste inany com iler#

● A good register allocator can generate code orderso* magnitude +etter t an a +ad register allocator#

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Register Allocation● .n 6A , t ere are an unlimited num+er o* %aria+les#● On a ysical mac ine t ere are a small num+er o*

registers:● (8? as *our general5 ur ose registers and a num+er o*

s eciali'ed registers#● M.PS as t!enty5*our general5 ur ose registers and

eig t s ecial5 ur ose registers#● Register allocation is t e rocess o* assigning

%aria+les to registers and managing data trans*erin and out o* registers#

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allenges in Register Allocation

● Registers are scarce #● O*ten su+stantially more .R %aria+les t an registers#● Feed to *ind a !ay to reuse registers ! ene%er ossi+le#

● Registers are com%licated #● (8?: Gac register made o* se%eral smaller registers can t

use a register and its constituent registers at t e sametime#

● (8?: ertain instructions must store t eir results in

s eci*ic registers can t store %alues t ere i* you !ant touse t ose instructions#● M.PS: Some registers reser%ed *or t e assem+ler or

o erating system#● Most arc itectures: Some registers must +e reser%ed

across *unction calls#

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/oals *or 6oday● .ntroduce register allocation *or a M.PS5

style mac ine:● Some num+er o* indi%isi+le, general5 ur ose

registers#● G( lore t ree algorit ms *or register

allocation:●

FaI%e 2CnoD register allocation#● -inear scan register allocation#● /ra 5coloring register allocation#

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An .nitial Register Allocator● Idea : Store e%ery %alue in main memory,

loading %alues only ! en t ey re needed#● 6o generate a code t at er*orms a

com utation:● /enerate load instructions to ull t e %alues

*rom main memory into registers#● /enerate code to er*orm t e com utation

on t e registers#● /enerate store instructions to store t e

result +ac" into main memory#

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Our Register Allocator .n Action

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a = b + c;d = a;c = a + d;

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a = b + c;d = a;c = a + d;

&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)

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a = b + c;d = a;c = a + d;

&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)

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a = b + c;d = a;c = a + d;

&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)

lw $t0, -12(fp)

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a = b + c;d = a;c = a + d;

&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)

lw $t0, -12(fp)lw $t1, -16(fp)

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a = b + c;d = a;c = a + d;

&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)

lw $t0, -12(fp)lw $t1, -16(fp)add $t2, $t0, $t1

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a = b + c;d = a;c = a + d;

&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)

lw $t0, -12(fp)lw $t1, -16(fp)add $t2, $t0, $t1sw $t2, -8(fp)

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a = b + c;d = a;c = a + d;

&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)


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a = b + c;d = a;c = a + d;

&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)


lw $t0, -8(fp)

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a = b + c;d = a;c = a + d;

&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)


lw $t0, -8(fp)sw $t0, -20(fp)

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a = b + c;d = a;c = a + d;

&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)


lw $t0, -8(fp)sw $t0, -20(fp)

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a = b + c;d = a;c = a + d;

&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)


lw $t0, -8(fp)sw $t0, -20(fp)

lw $t0, -8(fp)

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a = b + c;d = a;c = a + d;

&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)


lw $t0, -8(fp)sw $t0, -20(fp)

lw $t0, -8(fp)lw $t1, -20(fp)

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a = b + c;d = a;c = a + d;

&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)


lw $t0, -8(fp)sw $t0, -20(fp)

lw $t0, -8(fp)lw $t1, -20(fp)add $t2, $t0, $t1

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a = b + c;d = a;c = a + d;


lw $t0, -8(fp)sw $t0, -20(fp)


&aram N

###

&aram 1

#tored '%

#tored ra

a b

c

d

'% ( )

'% ( *N

+++

'% ( *

'% , *

'% , -

'% , 12

'% , 1.

'% , 2)

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Analysis o* our Allocator●

isad%antage: Gross ine''iciency #● .ssues unnecessary loads and stores +y t e do'en#● astes s ace on %alues t at could +e stored urely in registers#● Gasily an order o* magnitude or t!o slo!er t an necessary#● Enacce ta+le in any roduction com iler#

● Ad%antage: #im%licity #● an translate eac iece o* .R directly to assem+ly as !e go#● Fe%er need to !orry a+out running out o* registers#● Fe%er need to !orry a+out *unction calls or s ecial5 ur ose

registers#● /ood i* you just needed to get a rototy e com iler u and

running#

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=uilding a =etter Allocator● Goal : 6ry to old as many %aria+les in

registers as ossi+le#● Reduces memory reads

● e !ill need to address t ese $uestions:● ic registers do !e ut %aria+les in7● at do !e do ! en !e run out o* registers7

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Register onsistency

a = b + c

d = a d = b

e = d

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Register onsistency● At eac rogram oint, eac %aria+le

must +e in t e same location#● oes not mean t at eac %aria+le is al!ays

stored in t e same location&● At eac rogram oint, eac register

olds at most one li%e %aria+le#● an assign se%eral %aria+les t e same

register i* no t!o o* t em e%er !ill +e readtoget er#

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-i%e Ranges and -i%e .nter%als● Recall: A %aria+le is li/e at a articular rogram

oint i* its %alue may +e read later +e*ore it is!ritten#

● an *ind t is using glo+al li%eness analysis#● 6 e li/e range *or a %aria+le is t e set o* rogram

oints at ! ic t at %aria+le is li%e#● 6 e li/e inter/al *or a %aria+le is t e smallest

su+range o* t e .R code containing all a %aria+le s

li%e ranges#● A ro erty o* t e .R code, not t e J/#● -ess recise t an li%e ranges, +ut sim ler to !or" !it #

-i%e Ranges and -i%e .nter%als

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g


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g

e = d + a f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1:

g = d


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ge = d + a

f = b + c

f = f + b

d = e + f d = e – f

g = d

e = d + a f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1:

g = d


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ge = d + a

f = b + c

f = f + b

d = e + f d = e – f

g = d

{ g }

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1:

g = d


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ge = d + a

f = b + c

f = f + b

d = e + f d = e – f

{ d }g = d

{ g }

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1:

g = d


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e = d + a

f = b + c

f = f + b

d = e + f{ d }

d = e – f

{ d }g = d

{ g }

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d


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e = d + a

f = b + c

f = f + b

{ e, f }

d = e + f{ d }

d = e – f

{ d }g = d

{ g }

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d


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e = d + a

f = b + c

f = f + b

{ e, f }

d = e + f{ d }

d = e – f{ d }

{ d }g = d { g }

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d


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e = d + a

f = b + c

f = f + b

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d


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e = d + a

f = b + c

f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d


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e = d + a

f = b + c

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d


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e = d + a

f = b + c{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d


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e = d + a

{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d


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e = d + a{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d


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{ a, b, c, d }e = d + a

{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d

-i%e Ranges and -i%e .nter%als{ b d }

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{ a, b, c, d }e = d + a

{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d


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{ a, b, c, d }e = d + a

{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

a

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d


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{ a, b, c, d }e = d + a

{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

a b b

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d

-i%e Ranges and -i%e .nter%als{ a b c d }b

b

b

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{ a, b, c, d }e = d + a

{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

a bc b b

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d


b

b b

d

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{ a, b, c, d }e = d + a

{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

a bc b b bd

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d


b

b b

d

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{ a, b, c, d }e = d + a

{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

a bc b b bd

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d

-i%e Ranges and -i%e .nter%als{ a b c d }a b

cb

b b

eb

d

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{ a, b, c, d }e = d + a

{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

a bc b b be bd

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d

-i%e Ranges and -i%e .nter%als{ a, b, c, d }a b

cb

b b

eb

d b

f

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{ a, b, c, d }e = d + a

{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

a bc b b be bd bf

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d

-i%e Ranges and -i%e .nter%als{ a, b, c, d }a b

cb

b b

eb

d b

gb

f

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{ a, b, c, d }e = d + a

{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }

d = e + f{ d }

{ e, f }

d = e – f{ d }

{ d }g = d { g }

a bc b b be bd bg bf

e = d + a

f = b + c

f = f + b

IfZ e Goto _L0

d = e + f

d = e - f

Goto _L1;

_L0:

_L1: g = d

Register Allocation !it -i%e .nter%als

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g

●

/i%en t e li%e inter%als *or all t e %aria+les in t e rogram, !e canallocate registers using a sim legreedy algorit m#

● .dea: 6rac" ! ic registers are *reeat eac oint#

● en a li%e inter%al +egins, gi%et at %aria+le a *ree register#

● en a li%e inter%al ends, t eregister is once again *ree#

●

e can t al!ays *it e%eryt ing intoa register !e ll see ! at do to in aminute#

a bc b b e bd bg bf


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ga bc b b be bd bg bf


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ga bc b b be bd bg bf

R ) R 1 R 2R ) R 1 R 20ree Registers

R 2R


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a bc b b be bd bg bf

R ) R 1 R 2R ) R 1 R 20ree Registers

R 2R


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R )a bc b b be bd bg bf

R ) R 1 R 2R 1 R 20ree Registers

R 2R


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R 1R )a bc b b be bd bg bf

R ) R 1 R 2R 20ree Registers

R 2R


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R 2R 1R )a bc b b be bd bg bf

R ) R 1 R 20ree Registers

R 2R


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R R 2R 1R )a bc b b be bd bg bf

R ) R 1 R 20ree Registers

R 2


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R ) R R 2R 1R )a bc b b be bd bg bf

R 1 R 20ree Registers

R 2


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R )R ) R R 2R 1a bc b b be bd bg bf

R 1 R 20ree Registers

R 2


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R 2R )R ) R R 2R 1a bc b b be bd bg bf

R 10ree Registers

R 2


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R 2R 2R )R ) R R 1a bc b b be bd bg bf

R 10ree Registers

R 2


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R 2R ) R 1 R 2R 2R ) R R 1

a bc b b be bd bg bf 0ree Registers


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R ) R 2R ) R 1 R 2R 2 R R 1



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R ) R 2R ) R 1 R 2R 2 R R 1


Anot er G(am le

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Anot er G(am le

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b b ba bg be bfc bd

Anot er G(am le

b

f

d 0 R i

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R ) R 1 R 2

b b ba bg be bfc bd

R ) R 1 R 2

0ree Registers

Anot er G(am leb

bb

b

b

b

fb

d

0 R i

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R )R )

b b ba bg be bfc bd

R 1 R 2R 1 R 2

0ree Registers

Anot er G(am leb

bb

b

b

b

fb

d

0 R i t

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R )R )

b b ba bg be bfc bd

R 1 R 2R 1 R 2

0ree Registers

Anot er G(am leb

bb

b

gb

b

fb

d

0ree Registers

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R 1R )R )

b b ba bg be bfc bd

R 1 R 2R 2

0ree Registers

Anot er G(am leb

bb

a b

gb

e b

fc b

d 0ree Registers

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R 2R 1R )R )

b b ba bg be bfc bd

R 1 R 2

0ree Registers

Anot er G(am leb

bb

a b

gb

e b

fc b

d 0ree Registers

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R 2R 1R )R )

b b ba bg be bfc bd

R 1 R 2

0ree Registers

What do we donow?

Register S illing

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●

.* a register cannot +e *ound *or a %aria+lev

, !emay need to s%ill a %aria+le#● en a %aria+le is s illed, it is stored in memory

rat er t an a register#●

en !e need a register *or t e s illed %aria+le:● G%ict some e(isting register to memory#● -oad t e %aria+le into t e register#● en done, !rite t e register +ac" to memory and

reload t e register !it its original %alue#● S illing is slo!, +ut sometimes necessary#

Anot er G(am leb

bb

a b

gb

e b

fc b

d 0ree Registers

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R 2R 1R )R )

b b ba bg be bfc bd

R 1 R 2

0ree Registers

What do we donow?

Anot er G(am leb

bb

a b

gb

e b

fc b

d 0ree Registers

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R ) R 2R 1R )

b b ba bg be bfc bd

R 1 R 2

0ree Registers

Anot er G(am leb

bb

a b

gb

e b

fc b

d 0ree Registers

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R )R ) R 2R 1

b b ba bg be bfc bd

R 1 R 2

0ree Registers

Anot er G(am le b

b b

a b

g b

e b

fc b

d 0ree Registers

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R 2R )R ) R 2R 1

ba ge fc d

R 1

0ree Registers

Anot er G(am le b

b b

a b

g b

e b

fc b

d 0ree Registers

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R 2R 2R )R ) R 1

gd

R 1

g

Anot er G(am le b

b b

a b

g b

e b

fc b

d 0ree Registers

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R ) R 2R 2R ) R 1

g

R 1

g

Anot er G(am le b

b b

a b

g b

e b

fc b

d 0ree Registers

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R )R ) R 2R 2R 1

g

R 1

g

Anot er G(am le b

b b

a b

g b

e b

fc b

d 0ree Registers

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R 1R )R ) R 2R 2R 1

g g

Anot er G(am le b

b b

a b

g b

e b

fc b

d 0ree Registers

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R 1R 1R )R ) R 2R 2

Anot er G(am le b

b b

a b

g b

e b

fc b

d 0ree Registers

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R 1R 1R )R ) R 2R 2

-inear Scan Register Allocation

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● 6 is algorit m is called linear scan register allocation and is a com arati%ely ne! algorit m#

● Ad%antages:● Kery e**icient 2a*ter com uting li%e inter%als, runs in linear

time● Produces good code in many instances#● Allocation ste !or"s in one ass can generate code during

iteration#● O*ten used in L.6 com ilers li"e La%a HotS ot#

● isad%antages:● .m recise due to use o* li%e inter/als rat er t an li%e ranges #● Ot er tec ni$ues "no!n to +e su erior in many cases#

orrectness Proo* S"etc

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●

Fo register olds t!o li%e %aria+les atonce:● -i%e inter%als are conser%ati%e

a ro(imations o* li%e ranges#● Fo t!o %aria+les !it o%erla ing li%e

ranges laced in t e same register#● At eac rogram oint, e%ery %aria+le is

in t e same location:● All %aria+les assigned a uni$ue location#

Second5 ance =in Pac"ing

A i% % i * li 5 #

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● A more aggressi%e %ersion o* linear5scan#● Eses li%e ranges instead o* li%e inter/als #● .* a %aria+le must +e s illed, don t s ill all uses

o* it#● A later li%e range mig t still *it into a register#

● Re$uires a *inal data5*lo! analysis to con*irm %aria+les are assigned consistent locations#

● See C uality and S eed in -inear5scan Register AllocationD +y 6rau+, Hollo!ay, and Smit #

Second5 ance =in Pac"ing b

b b

a b

g b

e b

fc b

d

0ree Registers

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R )

R )

R 1

R 2

R 1

R 2


b b

a b

g b

e b

fc b

d

0ree Registers

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R )

R )

R 1

R 2

R 1

R 2

R


b b

a b

g b

e b

fc b

d R R R

R R0ree Registers

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R )

R )

R 1

R 2

R 1

R 2

RR


b b

a b

g b

e b

fc b

d R R R

R0ree Registers

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R 1

R )

R )

R 1

R 2

R 2

RRR


b b

a b

g b

e b

fc b

d R R R

0ree Registers

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R 2

R 1

R )

R )

R 1

R 2

RRR


b b

a b

g b

e b

fc b

d R R R

0ree Registers

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R 2

R 1

R )

R )

R 1

R 2

R RR

R


b b

a b

g b

e b

fc b

d R R

0ree Registers

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R )

R 2

R 1

R )

R 1

R 2

R

R RR


b b

a b

g b

e b

fc b

d R R

0ree Registers

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R )

R )

R 2

R 1

R 1

R 2

RR

RR

R R


b b

a b

g b

e b

fc b

d 0ree Registers

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R 2

R 1

R 1

R )

R )

R 2

R

RR

RR

R


b b

a b

g b

e b

fc b

d 0ree Registers

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R 2

R 2

R 1

R 1

R )

R )

R R

RRR

R


b b

a b

g b

e b

fc b

d 0ree Registers

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R 1

R 2

R 2

R 1

R )

R )

R

R R

RR

R


b b

a b

g b

e b

fc b

d 0ree Registers

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R 1

R 1

R 2

R 2

R )

R )

R

R R

RR

R


b b

a b

g b

e b

fc b

d 0ree Registers

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R 1

R 1

R 2

R 2

R )

R )

R

R R

R R

R


b b

a b

g b

e b

fc b

d 0ree Registers

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11 22))

R

R R

R R

R


b b

a b

g b

e b

fc b

d 0ree Registers

8/16/2019 History 55

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11 22))

R

R R

R R

R


b b

a b

g b

e b

fc b

d 0ree Registers

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11 22))

R ) R 1

R 1 R 2

R 2R )


b b

a b

g b

e b

fc b

d 0ree Registers

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) 11 22)

R )

R ) R 1

R 1 R 2

R 2


b b

a b

g b

e b

fc b

d 0ree Registers

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)) 11 22

R )

R ) R 1

R 1 R 2

R 2


b b

a b

g b

e b

fc b

d 0ree Registers

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))

An Gntirely i**erent A roac

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An Gntirely i**erent A roac{ a, b, c, d }

e = d + a{ b, c, e }

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{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }d = e + f

{ d }

{ e, f }d = e – f

{ d }

{ d }g = d { g }


e = d + a{ b, c, e }

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{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }d = e + f

{ d }

{ e, f }d = e – f

{ d }

{ d }g = d { g }

What can we infer fromall these variables being

live at this point?


e = d + a{ b, c, e }

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{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }d = e + f

{ d }

{ e, f }d = e – f

{ d }

{ d }g = d { g }

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e = d + a{ b, c, e }

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{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }d = e + f

{ d }

{ e, f }d = e – f

{ d }

{ d }g = d { g }

a

b c

d

e

f

g


e = d + a{ b, c, e }

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{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }d = e + f

{ d }

{ e, f }d = e – f

{ d }

{ d }g = d { g }

a

b c

d

e

f

g

8/16/2019 History 55

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e = d + a{ b, c, e }

{ b }

R ) R 1 R 2

R ) R 1 R 2Registers

R

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{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }d = e + f

{ d }

{ e, f }d = e – f

{ d }

{ d }g = d { g }

a

b c

d

e

f

g

An Gntirely i**erent A roac{ a, b, c, d }e = d + a

{ b, c, e }

{ b c e }

R ) R 1 R 2


R

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{ b, c, e }f = b + c

{ b, e, f}

{ b, e, f }f = f + b{ e, f }

{ e, f }d = e + f

{ d }

{ e, f }d = e – f

{ d }

{ d }g = d { g }

a

b c

d

e

f

g

6 e Register .nter*erence /ra

● 6 e register inter'erence gra%h 2R./ o*t l5*l ! i di t d

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a control5*lo! gra is an undirected gra! ere

● Gac node is a %aria+le#●

6 ere is an edge +et!een t!o %aria+les t atare li%e at t e same rogram oint#● Per*orm register allocation +y assigning

eac %aria+le a di**erent register *rom all o*

its neig +ors#● 6 ere s just one catc ###

6 e One atc● 6 is ro+lem is e$ui%alent to gra%h,

l i g ! i i N& h d i* t

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coloring , ! ic is N&,hard i* t ere areat least t ree registers#

● Fo good olynomial5time algorit ms 2or

e%en good a ro(imations& are "no!n*or t is ro+lem#

● e a%e to +e content !it a euristic

t at is good enoug *or R./s t at arise inractice#

6 e One atc to 6 e One atc

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.* you can *igure out a !ay to assignregisters to ar+itrary R./s, you %e just

ro%en & N N& and !ill get a 13)))3)))check *rom t e lay Mat ematics

.nstitute#


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.* you can *igure out a !ay to assignregisters to ar+itrary R./s, you %e just

ro%en & N N& and !ill get a 13)))3)))check *rom t e lay Mat ematics

.nstitute#

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=attling N& 5Hardness

aitin s Algorit m● .ntuition:

●

Su ose !e are trying to k5color a gra and *ind a node!it * ! t k dg #

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Su ose !e are trying to k5color a gra and ind a node!it *e!er t an k edges#● .* !e delete t is node *rom t e gra and color ! at

remains, !e can *ind a color *or t is node i* !e add it +ac"in#

● Reason: it *e!er t an k neig +ors, some color must +ele*t o%er#

● Algorit m:● Jind a node !it *e!er t an k outgoing edges#●

Remo%e it *rom t e gra #● Recursi%ely color t e rest o* t e gra #● Add t e node +ac" in#● Assign it a %alid color#

aitin s Algorit m

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aitin s Algorit m

b c

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a

b c

d e

g f

aitin s Algorit m

b c

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a

b c

d e

g f

R ) R 1 R 2R ) R 1 R 2Registers

R

aitin s Algorit m

b c

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a d e

g f


R

aitin s Algorit m

b c

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a d e

g f


R

c

aitin s Algorit m

b c

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a d e

g f


R

c

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aitin s Algorit m

b c

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a d e

g f


R

c b

aitin s Algorit m

b c

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a d e

g f


R

c b

aitin s Algorit m

b c

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a d e

g f


R

c b

aitin s Algorit m

b c

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a d e

g f


R

c b

d

aitin s Algorit m

b c

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a d e

g f


R

c b

d

aitin s Algorit m

b c

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a d e

g f


R

c b

d e

aitin s Algorit m

b c

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a d e

g f


R

c b

d ea

aitin s Algorit m

b c

g

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a d e

g f


R

c b

d ea

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aitin s Algorit m

b c

g

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a d e

g f


R

c b

d ea

aitin s Algorit m

b c

g

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a d e

g f


R

c b

d ea

aitin s Algorit m

b c

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a d e

g f


R

c b

d ea

aitin s Algorit m

b c

a

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a d e

g f


R

c b

d ea

aitin s Algorit m

b c

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a d e

g f


R

c b

d e

aitin s Algorit m

b c

8/16/2019 History 55

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a d e

g f


R

c b

d e

8/16/2019 History 55

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aitin s Algorit m

b c

8/16/2019 History 55

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a d e

g f

R ) R 1 R 2R ) R 1 R 2Registers R

c b

d

aitin s Algorit m

b c

8/16/2019 History 55

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a d e

g f


c b

aitin s Algorit m

b c

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a d e

g f


c b

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aitin s Algorit m

b c

8/16/2019 History 55

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a d e

g f


c

aitin s Algorit m

b c

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a d e

g f


aitin s Algorit m

b c

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a d e

g f


One Pro+lem● at i* !e can t *ind a node !it *e!er

t an k neig +ors7● oose and remo%e an ar+itrary node

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oose and remo%e an ar+itrary node,mar"ing it Ctrou+lesome#D

●

Ese euristics to c oose ! ic one#● en adding node +ac" in, it may +e

ossi+le to *ind a %alid color#●

Ot er!ise, !e a%e to s ill t at node#

aitin s Algorit m Reloaded

a

b c

d

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a d

e

f

g



a

b c

d

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a d

e

f


gg


a

b c

d

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f

a d

e


gg f


a

b c

d

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e

f

a d


gg f

e

d


a

b c

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d

e

f

a


gg f

ed

c

d


a

b

c

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d

e

f

a


gg f

ed

c

d


a

b

c b

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d

e

f

a


gg f

ed

c

d


a

b

c b

a

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d

e

f

a


gg f

ed

c

d


a

b

dc

b

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e

f


gg f

ed

c

d


a

b

dc

b

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e

f


gg f

ed

c

d


a

b

dc

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e

f


gg f

ed

c

d


a

b

dc

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e

f


gg f

ed

d


a

b

d

c

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e

f


gg f

ed

d


a

b

d

c

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e

f


gg f

ed

d


a

b

c

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e

f


gg f

e

d


a

b

c

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e

f


gg f

e

d


a

b

d

c

( spilled )

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e

f


gg f

e

d


a

b

d

c

( spilled )

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f


gg fe

d


a

b

d

c

( spilled )

8/16/2019 History 55

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f


gg fe

d


a

b

d

c

( spilled )

8/16/2019 History 55

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f


gg e

d


a

b

d

c

( spilled )

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f


gg e

d


a

b

d

c

( spilled )

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f


g e

d


a

b

d

c

( spilled )

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f


g e

A Smarter Algorit m{ a, b, c, d }

e = d + a{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

R ) R 1 R 2


d a

b

d

c

( spilled )

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{ b, e, f }f = f + b{ e, f }

{ e, f }d = e + f

{ d }

{ e, f }d = e – f

{ d }

{ d }g = d { g }

f

g e

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e = d + a{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

R ) R 1 R 2


d a

b

d

c

( spilled )

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{ b, e, f }f = f + b{ e, f }

{ e, f }d = e + f

{ d }

{ e, f }d = e – f

{ d }

{ d }g = d{ g }

f

g e


e = d + a{ b, c, e }

{ b, c, e }f = b + c

{ b, e, f}

R ) R 1 R 2


d a

b

d

c

d

d ( spilled )

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{ b, e, f }f = f + b

{ e, f }

{ e, f }d = e + f

{ d }

{ e, f }d = e – f

{ d }

{ d }g = d{ g }

e

g d

f

Anot er G(am le

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Anot er G(am le

a

b c

d

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a d

ef

Anot er G(am le

a

b c

d

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a d

ef


a

Anot er G(am le

b c

d

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a d

ef


a

c

a

Anot er G(am le

b

d

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ef


ac

c

a

Anot er G(am le

b

d

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ef


ac

b

c

a

Anot er G(am le

b

d

be

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ef


ac

b

c

a

Anot er G(am le

b

d

bef

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ef


ac

b

c

a

Anot er G(am le

b

d

befd

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ef


ac

b

c

a

Anot er G(am le

b

d

bef

8/16/2019 History 55

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ef


ac

b

c

a

Anot er G(am le

b

d

bef

8/16/2019 History 55

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ef


ac

b

c

a

Anot er G(am le

b

d

be

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ef


ac

b

c

a

Anot er G(am le

b

d

be

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ef


ac

b

c

a

Anot er G(am le

b

d

b

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ef


ac

b

c

a

Anot er G(am le

b

d

b

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ef


ac

b

c

a

Anot er G(am le

d

b

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ef


ac

c

a

Anot er G(am le

d

b

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ef


ac

c

a

Anot er G(am le

d

b

8/16/2019 History 55

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ef


a

c

a

Anot er G(am le

d

b

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ef


a

c

a

Anot er G(am le

d

b

8/16/2019 History 55

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ef


c

a

Anot er G(am le

d

b

8/16/2019 History 55

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ef


c

a

Anot er G(am le

b

d

befd

8/16/2019 History 55

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ef


ac

c

a

Anot er G(am le

b

d

bef

8/16/2019 History 55

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ef


ac

c

a

Anot er G(am le

b

d

bef

8/16/2019 History 55

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ef


ac

c

a

Anot er G(am le

b

d

be

8/16/2019 History 55

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ef


ac

c

a

Anot er G(am le

b

d

be

8/16/2019 History 55

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ef


ac

c

a

Anot er G(am le

b

d

b

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f


ace

c

a

Anot er G(am le

b

d

b

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f


ace

c

a

Anot er G(am le

b

d

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f


ac

e

8/16/2019 History 55

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c

a

Anot er G(am le

b

d

8/16/2019 History 55

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f


ae

8/16/2019 History 55

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c

a

Anot er G(am le

b

d

(spilled)

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f


e

c

a

Anot er G(am le

b

d

(spilled)

(spilled)

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f


e

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orrectness Proo* S"etc● Fo t!o %aria+les li%e at some oint are

assigned t e same register#● Jorced +y gra coloring#

● At any rogram oint eac %aria+le isal!ays in one location#

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y● Automatic i* !e assign eac %aria+le one

register#● Re$uires a *e! tric"s i* !e se arate +y use

case#

.m ro%ements to t e Algorit m● oose ! at to s ill intelligently#

●

Ese euristics 2least5commonly used,greatest im ro%ement, etc# to determine! at to s ill#

● Handle s illing intelligently#

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● en s illing a %aria+le, recom ute t e R./+ased on t e s ill and use a ne! coloring to*ind a register#

Summary o* Register Allocation● ritical ste in all o timi'ing com ilers#●

6 e linear scan algorit m uses li/einter/als to greedily assign %aria+les toregisters#

● O*ten used in L.6 com ilers due to e**iciency#

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● Chaitin4s algorithm uses t e registerinter'erence gra%h 2+ased on li/e rangesand gra%h coloring to assign registers#

● 6 e +asis *or t e tec ni$ue used in / #

Fe(t 6ime● Garbage Collection

●

Re*erence ounting● Mar"5and5S!ee● Sto 5and5 o y● .ncremental ollectors

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.ncremental ollectors

history 55

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