Compiling Imperative and Object-Oriented Languages - Register Allocation

Register Allocation

Guido Wachsmuth

Delft
Course IN4303, 2012/13
University of
Technology Compiler Construction
Challenge the future

Overview
today’s lecture

interference graphs

• construction during liveness analysis

Register Allocation 2

Overview
today’s lecture

interference graphs


graph colouring

• assign registers to local variables and compiler temporaries
• store local variables and temporaries in memory


Overview
today’s lecture

interference graphs


graph colouring


coalescing

• handle move instructions


Overview
today’s lecture

interference graphs


graph colouring


coalescing

• handle move instructions

pre-coloured nodes


I
interference graphs


Recap: Liveness analysis
terminology

a ← 0

b ← a + 1

c ← c + b

a ← 2 * b

if a < N

return c


terminology

definition a ← 0

b ← a + 1

c ← c + b

a ← 2 * b

if a < N

return c


terminology

definition a ← 0

usage b ← a + 1

c ← c + b

a ← 2 * b

if a < N

return c


terminology

definition a ← 0

usage b ← a + 1

c ← c + b

definition a ← 2 * b

if a < N

return c


terminology

definition a ← 0

usage b ← a + 1

c ← c + b


usage if a < N

return c


terminology

definition a ← 0

usage b ← a + 1

c ← c + b


live-in
usage if a < N

return c


terminology

definition a ← 0

usage b ← a + 1

c ← c + b

live-out

live-in
usage if a < N

return c


terminology

definition a ← 0

live-in
usage b ← a + 1

c ← c + b

live-out

live-in
usage if a < N

return c


terminology

definition a ← 0

live-in
usage b ← a + 1

c ← c + b

live-out

live-in
usage if a < N
live-out

return c


terminology

definition a ← 0 live-out

live-in
usage b ← a + 1

c ← c + b

live-out

live-in
usage if a < N
live-out

return c


example

a ← 0

b ← a + 1

c ← c + b

a ← 2 * b

if a < N

return c


Interference graphs
example

a ← 0

b ← a + 1

c ← c + b

a ← 2 * b

if a < N

return c


Interference graphs
example

a ← 0

b ← a + 1

a b
c ← c + b

a ← 2 * b
c

if a < N

return c


II
graph colouring


Graph colouring
example

a ← 0

b ← a + 1

a b
c ← c + b

a ← 2 * b
c

if a < N

return c


Graph colouring
example

r1 ← 0

r1 ← r1 + 1

a b
r2 ← r2 + r1

r1 ← 2 * r1
c

if r1 < N

return r2


Graph colouring
steps

simplify
remove node of insignificant degree (fewer than k edges)

spill
remove node with k or more edges

select
add node, select colour


Graph colouring
example with 2 colours

a b

c


Graph colouring

a b

c

a


Graph colouring

a b

c

c

a


Graph colouring

f

e

j k b m

h g d c


Graph colouring

f

e

j k b m

h g d c g


Graph colouring

f

e

j k b m

h

h g d c g


Graph colouring

f

e

j k b m k

h

h g d c g


Graph colouring

f

e

d

j k b m k

h

h g d c g


Graph colouring

f

e j

d

j k b m k

h

h g d c g


Graph colouring

f
e

e j

d

j k b m k

h

h g d c g


Graph colouring
f
f
e

e j

d

j k b m k

h

h g d c g


Graph colouring
example with 4 colours b

f
f
e

e j

d

j k b m k

h

h g d c g


Graph colouring c


f
f
e

e j

d

j k b m k

h

h g d c g


Graph colouring

f
f
e

e j

d

j k b m k

h

h g d c g


Graph colouring
f
f
e

e j

d

j k b m k

h

h g d c g


Graph colouring

f
e

e j

d

j k b m k

h

h g d c g


Graph colouring

f

e j

d

j k b m k

h

h g d c g


Graph colouring

f

e

d

j k b m k

h

h g d c g


Graph colouring

f

e

j k b m k

h

h g d c g


Graph colouring

f

e

j k b m

h

h g d c g


Graph colouring

f

e

j k b m

h g d c g


Graph colouring

f

e

j k b m

h g d c


Optimistic colouring
steps

simplify
remove node of insignificant degree (fewer than k edges)

spill
remove node of significant degree (k or more edges)

select



d

a b

c



d

a b

c

a



d

a b

c

potential spill a



d

a b

c
c

potential spill a



d

a b

b

c
c

potential spill a


Spilling
steps

simplify
remove node of insignificant degree (less than k edges)

spill
remove node of significant degree (k or more edges)

select

actual spill

start over


Spilling

a b

c


Spilling

a b

c

potential spill a


Spilling

a b

c

c

potential spill a


Spilling

a b

c

actual spill a


Spilling
example

a ← 1

b ← a + 1

c ← b + 1

a ← c + a

return b


Spilling
example

a1 ← 1 a ← 1

M[42] ← a1
b ← a + 1

c ← b + 1

a ← c + a

return b


Spilling
example

a1 ← 1 a ← 1

M[42] ← a1
b ← a + 1 a2 ← M[42]

b ← a2 + 1
c ← b + 1

a ← c + a

return b


Spilling
example

a1 ← 1 a ← 1

M[42] ← a1
b ← a + 1 a2 ← M[42]

b ← a2 + 1
c ← b + 1
a3 ← M[42]

a4 ← c + a3 a ← c + a

M[42] ← a4
return b


Spilling
example

a ← 1

b ← a + 1

c ← b + 1

a ← c + a

return b


Spilling
example

a ← 1

b ← a + 1

b2 ← M[42] c ← b + 1

c ← b2 + 1
a ← c + a

return b


Spilling
example

a ← 1

b ← a + 1 b1 ← a + 1

M[42] ← b1
b2 ← M[42] c ← b + 1

c ← b2 + 1
a ← c + a

return b


Spilling
example

a ← 1

b ← a + 1 b1 ← a + 1

M[42] ← b1
b2 ← M[42] c ← b + 1

c ← b2 + 1
a ← c + a

return b b3 ← M[42]

return b3


coffee break


III
coalescing


Recap: graph colouring
example

f

e

j k b m

h g d c


Coalescing
better solution

f

e

j k b m

h g d c


Coalescing
coalescing nodes

f

e

j/b k m

h g c/d


Coalescing
conservative strategies

Briggs

• a/b has fewer than k neighbours of significant degree

• nodes of insignificant degree and a/b can be simplified

• remaining graph is colourable

George

• all neighbours of a of significant degree interfere also with b

• neighbours of a of insignificant degree can be simplified

• subgraph of original graph is colourable


Graph colouring
steps

simplify
remove non-move-related node of insignificant degree

coalesce

freeze
turn move-related node of insignificant degree into non-move-related

spill

select

start over


Coalescing
example

f

e

j k b m

h g d c


Coalescing
example

f

e

j k b m

h g d c g


Coalescing
example

f

e

j k b m

h

h g d c g


Coalescing
example

f

e

j k b m k

h

h g d c g


Coalescing
example

f

e

j k b m k

h

h g c/d g


Coalescing
example

f

e

j/b k m k

h

h g c/d g


Coalescing
example

f

e

c/d

j/b k m k

h

h g c/d g


Coalescing
example

f

e j/b

c/d

j/b k m k

h

h g c/d g


Coalescing
example

f
f

e j/b

c/d

j/b k m k

h

h g c/d g


Coalescing
example
m
f
f

e j/b

c/d

j/b k m k

h

h g c/d g


Coalescing
example

f
f

e j/b

c/d

j/b k m k

h

h g c/d g


Coalescing
example

f

e j/b

c/d

j/b k m k

h

h g c/d g


Coalescing
example

f

e

c/d

j/b k m k

h

h g c/d g


Coalescing
example

f

e

j/b k m k

h

h g c/d g


Coalescing
example

f

e

j/b k m

h

h g c/d g


Coalescing
example

f

e

j/b k m

h g c/d g


Coalescing
coalescing nodes

f

e

j/b k m

h g c/d


IV
pre-coloured nodes


Recap: Calling Conventions
CDECL

caller push 21
push 42
• push parameters right-to-left on the stack call
add
_f
ESP 8
• clean-up stack after call

callee

• save old BP push EBP

• initialise new BP mov
mov
EBP
EAX
ESP
[EBP + 8]
• save registers mov EDX [EBP + 12]

• return result in AX
add
pop
EAX
EBP
EDX

• restore registers ret

• restore BP


STDCALL

caller push 21
push 42
• push parameters right-to-left on the stack call _f@8

callee

• save old BP
• initialise new BP push EBP

• save registers mov
mov
EBP
EAX
ESP
[EBP + 8]
• return result in AX mov EDX [EBP + 12]

• restore registers
add
pop
EAX
EBP
EDX

• restore BP ret 8


FASTCALL

caller mov ECX 21
mov EDX 42
• passes parameters in registers call @f@8

• pushes additional parameters right-to-left on the stack
• cleans up the stack

callee
push EBP

• save old BP, initialise new BP mov
mov
EBP ESP
EAX ECX
• save registers add EAX EDX

• return result in AX
pop
ret
EBP

• restore registers
• restore BP


Pre-coloured nodes
representing registers

nodes

• register = pre-coloured node

• no simplify, no spill

• coalesce possible

edges

• all registers interfere with each other

• explicit usage of registers

• call and return instructions influence liveness


V
summary


Summary
lessons learned

How can we assign registers to local variables and temporaries?

• perform liveness analysis
• build interference graph
• colour interference graph

What to do if the graph is not colourable?

• keep local variables in memory

How to handle move instructions efficiently?

• coalesce nodes safely


Literature
learn more

Andrew W. Appel, Jens Palsberg: Modern Compiler
Implementation in Java, 2nd edition. 2002

Lal George, Andrew W. Appel: Iterative Register Coalescing.
POPL 1996

Lal George, Andrew W. Appel: Iterative Register Coalescing.
TOPLAS 18(3), 1996


Outlook
coming next

imperative and object-oriented languages

• Lecture 11: Register Allocation today
• Lecture 12: Garbage Collection Nov 13

compiler components & their generators

• Lecture 13: Scanning Nov 20
• Lecture 14: LL Parsing Dec 04
• Lecture 15: LR Parsing Dec 11

exam preparation

• Question & Answer Jan 08


copyrights


Pictures
attribution & copyrights

Slide 1:
Colors #2 by Carmelo Speltino, some rights reserved

Slide 40:
Tchibo by Dominica Williamson, some rights reserved

Slide 76:
Romantic Pigeon Date by Harald Hoyer, some rights reserved


Compiling Imperative and Object-Oriented Languages - Register Allocation

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