Joint Variable Partitioning and Bank Selection Instruction Optimization on

Embedded Systems with Multiple Memory Banks

Liu Tiantian, Minming Li, Chun Jason XueCity University of Hong Kong

2010.1.19

2

Outline of this talkOutline of this talk

Background & Related work

What the problem is? Variable partitioning & BSL insertion

How to solve the problem?For speedFor space

Experimental results

3

BackgroundBackground

88--bit microcontrollersbit microcontrollersAbout 55% of all CPUs sold in the world are 8-bit microcontrollersCan access limited memory with few buses and smaller address registers

Partitioned memory architecturePartitioned memory architectureZilog Z80 and MOS6502 series:

16 bit address registers can only addressa maximum of 64 KB memory=> support more than 64 KB memory by partitioning it into banks

Bank SwitchingBank Switching：：Only can access one bank at a time, bank registerbank register.

Bank selection instructions (Bank selection instructions (BSLsBSLs)): instructions needed to be inserted into the original programs to modify the bank register to point to the wanted bank.

Their insertions increase both code size and runtime overheadcode size and runtime overhead.

4

What we focus on?What we focus on?

to minimize the size and time overhead introduced by minimize the size and time overhead introduced by BSLsBSLs. . Speed overheadSpeed overhead (means runtime increase) minimization

Space overheadSpace overhead (means code size increase) minimization

Variable partitioningVariable partitioningCurrent techniques aim at achieving the maximum instruction level parallelism for architectures which allow multiple banks to be accessed simultaneously

BSL insertionBSL insertionCurrent compilers provide limited support to generate bank switching code optimally.

The two process are related to each other and affect the overhead.

5

Related WorkRelated WorkBSL minimization

Bernhard Scholz, Bernd Burgstaller, Jingling Xue, ”Minimal Placement of Bank Selection Instructions for Partitioned Memory Architectures,” ACM Transactions on Embedded Computing Systems (TECS), Vol. 7, No. 2: 1-32, 2008.Bernhard Scholz, Bernd Burgstaller, Jingling Xue, ”Minimizing Bank Selection Instructions for Partitioned Memory Architectures,” CASES06: 201-211, 2006.

assume the variables have already been assignedassume the variables have already been assigned to memory banks present an optimization technique that minimizes the overhead of BSLs.

Yuan Mengting, Wu Guoqing, Yu Chao, ”Optimizing Bank Selection Instructions by Using Shared Memory,” ICESS2008: 447-450, 2008.

assume the variables have already been partitionedassume the variables have already been partitioned into banks. consider using the architecture with a shared memory bank

Variable partitioning: most aim at achieving the maximum instruction level parallelism for architectures which allow multiple banks to be accessed simultaneously.

transform the variable partitioning problem to an Interference Graph (IG)to an Interference Graph (IG) or Variable Variable Independence Graph (VIG)Independence Graph (VIG) to find the parallelism between variablescombined with instruction scheduling problemscheduling problem for multi-core DSP architecturesoptimizing energy consumptionenergy consumption: try to determine when to power some banks down

There is no variable partitioning techniques for BSL overhead miThere is no variable partitioning techniques for BSL overhead minimizationnimization which is important for embedded systems with multiple memory banks.

6

Outline of this talkOutline of this talk

Background & Related work

What the problem is? Variable partitioning & BSL insertion

How to solve the problem?For speedFor space

Experimental results

7

(a) Multi-bank architecture (b) Application model: DFG

v1

v2 v3

v4 v5 v6

v8

v7

60 40320

33 27 40

402733

100

a1

a2 a4

a1

a6a3

a5

a4

8-bit micro-controller

MemoryBank 1

(B1)

MemoryBank 2

(B2)

MemoryBank k

(Bk)

Bank register

Variables: a1, a2, …, an

……

0

m-1

0

m-1

0

m-1

What the problem is? Variable partitioningWhat the problem is? Variable partitioning

BBii: a memory bank,size of m

aaii: a variable, size of 1B(aB(aii)): the memory

bank storing ai

vvii: a node, is a basic data accessing block

A(vA(vii)): the variable accessed by vi

DFGDFG: Data Flow Graph, to model an embedded application

e(ue(u, v), v): an edge, the control flow of code

w(e(uw(e(u, v)), v)): the execution frequency of e(u, v)

In the system, we have in total:k banks: B1 ,… Bk , each of size mn variables: v1 ,… vn , each of size 1k*m>=n

The n variables need to be partitioned into the k banks

8

Wha

t the

pro

blem

is?

BSL

Inse

rtio

nW

hat t

he p

robl

em is

? B

SL In

sert

ion

Whe

n a

node

u a

nd o

ne o

f its

chi

ldre

n v

acce

ss v

aria

bles

that

are

in

diffe

rent

ban

ks, a

BS

L ne

eds

to b

e in

serte

d.Th

ere

are

thre

e po

ssib

le p

ositi

ons

to in

sert

this

BS

L:

at th

e ex

it of

nod

e u

at th

e ex

it of

nod

e u;

at e

dge

at e

dge

e(u

e(u ,

v)

, v);

at th

e en

tranc

e of

nod

e v

at th

e en

tranc

e of

nod

e v.

The

thre

e po

sitio

ns h

ave

diffe

rent

impa

cts

on s

peed

and

spa

cedi

ffere

nt im

pact

s on

spe

ed a

nd s

pace

over

head

s.

u v

u ac

cess

es a

1,a1

is s

tore

d in

B1

v ac

cess

esa2

,a2

is s

tore

d in

B2

BS

L

BS

L

BS

L

Inse

rting

at t

he e

xit o

f no

de v

3 is

not

a

good

sol

utio

n fo

r sp

eed.

Inse

rting

at t

he

entra

nce

of n

ode

v7 is

a g

ood

solu

tion

for s

pace

.

320

v 3 v 6

a 4 a 6

v 4v 5

v 6

v 7

4027

33

a 1

a 6a 4

a 3

40BSL BSL

BSL

BSL

BSL

BSL

BSL

BSL

BSL

BSL

(a)

For S

peed

(

b) F

or S

pace

9

Mot

ivat

iona

l Exa

mpl

eM

otiv

atio

nal E

xam

ple

Ass

ume

we

have

a d

ual-b

ank

arch

itect

ure

and

each

ban

k ha

s a

size

of t

hree

.

The

varia

ble

parti

tioni

ng te

chni

ques

und

er

com

paris

on a

re:

Equ

ally

par

titio

ning

acc

ordi

ng to

re

fere

nce

orde

rP

artit

ioni

ng fo

r par

alle

lism

[8]

The

prop

osed

alg

orith

ms

for s

peed

The

prop

osed

alg

orith

ms

for s

pace

v 1

v 2v 3

v 4v 5

v 6

v 8v 7

6040

320

3327

40

4027

33

100

a 1

a 2a 4

a 1

a 6a 3

a 5a 4

10

Mot

ivat

iona

l Exa

mpl

eM

otiv

atio

nal E

xam

ple --

Res

ults

Res

ults Th

e pr

opos

ed a

lgor

ithm

fo

r spa

ce a

lso

offe

rs a

n op

timal

so

lutio

n fo

r spe

ed

of 2

00 B

SL-

cycl

es

Even

for s

uch

a sm

all

exam

ple,

we

can

achi

eve

sign

ifica

nt

impr

ovem

ents

!

(a) P

artit

ion

equa

lly a

ccor

ding

to re

fere

nce

orde

r.

(b) P

artit

ion

usin

g m

etho

d in

[8].

(c)

Parti

tion

usin

g al

gorit

hm fo

r spe

ed.

(d

) Par

titio

n us

ing

algo

rithm

for s

pace

.

40

40

40a 1

a 6

a 5a 4B

1 B

2

a 1

a 4

a 2

a 5

a 3

a 6

S

peed

: 234

Spac

e: 4

v 1

v 2v 3

v 4v 5

v 6

v 8v 7

6032

0

3327

27

33

100

a 1

a 2a 4

a 3B

1

B2

a 1

a 2

a 3

a 4

a 6

a 5

S

peed

: 300

Spac

e: 5

v 1

v 2v 3

v 4v 5

v 6

v 8v 7

6032

0

3327

27

33

100

a 1

a 2a 4

a 3

a 1 a 5

40

4040 a 6a 4

BSL

BSL BSL

BSL

BSL

BSL

BSL

BSL

BSL

33a 3

a 1 a 5a 4B

1 B

2

a 1

a 2

a 4

a 3

a 5

a 6

S

peed

: 200

Spac

e: 4

v 1

v 2v 3

v 4v 5

v 6

v 8v 7

6032

0

27

27

33

100

a 1

a 2a 4

40

4040 a 6B

SLB

SL

BSL

BSL

320

a 3a 6

B1

B2

a 1

a 3

a 2

a 4

a 5

a 6

S

peed

: 200

Spac

e: 3

v 1

v 2v 3

v 4v 5

v 6

v 8v 7

60

3327

27

33

100

a 1

a 2a 4

a 1 a 5

40

4040

a 4

BSL

BSL

BSL

11

Out

line

of th

is ta

lkO

utlin

e of

this

talk

Bac

kgro

und

& R

elat

ed w

ork

Wha

t the

pro

blem

is?

Var

iabl

e pa

rtitio

ning

& B

SL

inse

rtion

How

to s

olve

the

prob

lem

?Fo

r spe

edFo

r spa

ce

Exp

erim

enta

l res

ults

12

For S

peed

For S

peed

-- pat

tern

spa

ttern

sN

eed

to c

onsi

der t

he e

xecu

tion

cycl

es o

f ins

erte

d co

nsid

er th

e ex

ecut

ion

cycl

es o

f ins

erte

d B

SLs

BS

Ls.

One

inse

rtion

of B

SL

may

lead

to m

any

exec

utio

ns c

ycle

s in

runt

ime.

Fo

ur b

asic

kin

ds o

f par

ent-c

hild

pat

tern

s

Pat

tern

(a).

One

to o

ne: i

nser

ting

one

BS

L at

thre

e po

sitio

ns a

re th

e sa

me.

Pat

tern

(b).

One

to o

ne w

ith s

elf-l

oops

: ins

ertin

g on

e B

SL

at p

ositi

on ②

or ③

is b

ette

r tha

n ①

. Nev

er in

serti

ng

Nev

er in

serti

ng B

SLs

BSLs

at n

odes

with

sel

fat

nod

es w

ith s

elf -- l

oop

loop

.P

atte

rn (c

). O

ne to

man

y: N

o m

atte

r whi

ch p

ositi

ons

BS

Lsar

e in

serte

d at

, th

ey w

ill be

exe

cute

d in

tota

l

BS

L-cy

cles

.P

atte

rn (d

). M

any

to o

ne: N

o m

atte

r whi

ch p

ositi

ons

BS

Lsar

e in

serte

d at

, the

y w

ill be

exe

cute

d in

tota

l

B

SL-

cycl

es.

Con

clus

ion:

afte

r par

titio

ning

, alw

ays

inse

rting

in

serti

ng B

SLs

BS

Lsat

edg

es w

hen

at e

dges

whe

n ne

eded

need

ed.

∑∈

],2[

1))

,(

(n

ii v

ve

w

[1,

1](

(,

))i

ni

nw

ev

v∈

−∑

13

For S

peed

For S

peed

-- Alg

orith

m(1

)A

lgor

ithm

(1)

An

Acc

essi

ng G

raph

(AG

)A

cces

sing

Gra

ph (A

G)G

’(V’,

E)’

is c

onst

ruct

ed to

pre

sent

the

adja

cent

acce

ssin

g re

latio

nshi

ps b

etw

een

varia

bles

.an

und

irect

ed g

raph

v’: a

nod

e re

pres

ents

a u

niqu

e va

riabl

e e’

(u’,

v’):

an e

dge

repr

esen

ts th

e ad

jace

nt a

cces

sing

rela

tions

hip

betw

een

the

two

varia

bles

u’a

ndv’

. w

’(e’(u

’, v’

)), w

here

((

,))

we

uv

=∑

(,

)&

(((

)'&

()

')||(

()

'&(

)'))

DFG

eu

vE

Au

uA

vv

Au

vA

vu

∈=

==

=

DFG

->A

G

A va

riabl

e

w’(e

’(u’,v

’)) g

ives

the

exec

utio

n tim

es o

f the

inse

rted

BS

L if

u’an

d v’

are

in d

iffer

ent b

anks

a 1

a 2 a 3

a 4

a 5a 6

60 33

3327

40100

4067

14

For S

peed

For S

peed

-- Alg

orith

m(1

)A

lgor

ithm

(1)

The

prob

lem

bec

omes

: we

wan

t to

parti

tion

the

n no

des

into

k p

arts

parti

tion

the

n no

des

into

k p

arts

so th

at th

e si

ze o

f eac

h pa

rt do

es n

ot e

xcee

d m

and

the

tota

l wei

ght o

f th

e cr

oss

edge

s be

twee

n pa

rts a

re m

inim

ized

.

kk --ba

lanc

ed p

artit

ioni

ngba

lanc

ed p

artit

ioni

ngpr

oble

m

prov

ed to

be

an N

PN

P-- H

ard

Har

dpr

oble

mso

me

theo

retic

al w

orks

abo

ut th

is p

robl

em

A p

olyn

omia

l heu

ristic

alg

orith

m: g

reed

y

Com

bine

two

varia

bles

Com

bine

two

varia

bles

who

se c

ombi

natio

n ca

n m

axim

ize

the

spee

d sa

ving

in e

ach

itera

tion.

Th

e co

mpl

exity

is O

(n2

log

n).

B1:

a1,

a4,

a5

B2:

a2,

a3,

a6

a 1

a 2 a 3

a 4

a 5a 6

60 33

3327

40100

4067

15

Out

line

of th

is ta

lkO

utlin

e of

this

talk

Bac

kgro

und

& R

elat

ed w

ork

Wha

t the

pro

blem

is?

Var

iabl

e pa

rtitio

ning

& B

SL

inse

rtion

How

to s

olve

the

prob

lem

?Fo

r spe

edFo

r spa

ce

Exp

erim

enta

l res

ults

16

For S

pace

For S

pace

-- pat

tern

spa

ttern

s

Onl

y ca

re a

bout

the

tota

l num

ber o

f th

e to

tal n

umbe

r of B

SLs

BS

Lsin

serte

din

serte

din

to th

e or

igin

al c

ode

uppe

r bou

nd :

|V|-1

(ins

ertin

g at

ent

ranc

e w

hen

need

ed e

xcep

t roo

t).Fo

ur b

asic

kin

ds o

f par

ent-c

hild

pat

tern

s

Pat

tern

(a):

inse

rting

one

BS

L at

the

thre

e po

sitio

ns a

re th

e sa

me.

P

atte

rn (b

): in

serti

ng o

ne B

SL

at th

e th

ree

posi

tions

are

the

sam

e.P

atte

rn (c

): th

e nu

mbe

r of B

SLs

is a

t mos

t the

num

ber o

f chi

ldre

n. In

serti

ng a

t In

serti

ng a

t th

e ex

it of

the

bran

chin

g pa

rent

the

exit

of th

e br

anch

ing

pare

ntm

ay s

ave

som

e BS

Ls.

Pat

tern

(d):

at m

ost o

ne B

SL n

eeds

to b

e in

serte

d, a

nd in

serti

ng a

t the

in

serti

ng a

t the

en

tranc

e of

the

mer

ging

chi

lden

tranc

e of

the

mer

ging

chi

ld-- n

ode

node

will

alw

ays

be a

n op

timal

sol

utio

n.

Con

clus

ion:

for n

odes

with

mor

e th

an o

ne in

com

ing

or o

utgo

ing

node

s w

ith m

ore

than

one

inco

min

g or

out

goin

g ed

ges

edge

s , fu

rther

redu

ctio

n of

BS

Lsca

n be

ach

ieve

d w

hen

cons

ider

ing

the

inse

rting

pos

ition

s an

d va

riabl

e po

sitio

nsBSL

17

For S

pace

For S

pace

-- diff

icul

ties

diffi

culti

es

Eve

n th

ough

we

know

som

e st

rate

gies

abo

ut B

SL

inse

rtion

on

the

basi

c pa

ttern

s, th

ere

is n

o fix

ed b

est s

trate

gy li

ke w

hen

optim

izin

g fo

r spe

ed.

som

e ba

sic

patte

rns

coul

d in

terv

ene

basi

c pa

ttern

s co

uld

inte

rven

ean

d cr

eate

com

plex

pat

tern

sa

bette

r BS

L in

serti

on p

ositi

on a

lso

depe

nds

on th

e va

riabl

esde

pend

s on

the

varia

bles

’’po

sitio

nspo

sitio

ns

If a3

, a4

and

a5 a

rein

the

sam

e ba

nk,

this

met

hod

is th

e be

st s

olut

ion

But

if y

ou fi

rst

cons

ider

this

pat

tern

(d),

you

may

inse

rt a

BS

L at

th

e en

tranc

e of

v4

at fi

rst

If a3

, a4

and

a5 a

re n

ot in

the

sam

e ba

nk, a

lway

s ne

eds

thre

e B

SLs

.Th

is m

etho

d is

the

one

of

the

best

sol

utio

n

BSL

18

For S

pace

For S

pace

-- alg

orith

mal

gorit

hm

The

spac

e m

inim

izat

ion

prob

lem

is a

lso

NP

NP

-- Har

dH

ard.

Eve

n if

the

varia

bles

hav

e al

read

y be

en p

artit

ione

d in

to b

anks

, the

B

SL

inse

rting

pro

blem

is s

till N

P-H

ard.

We

prop

ose

a he

uris

tic a

lgor

ithm

:S

tep0

: Par

titio

n D

FG in

to p

atte

rns;

Ste

p1: P

artit

ion

varia

bles

usi

ng A

G;

Ste

p2: I

nser

t BS

Lsba

sed

on p

atte

rns.

19

For S

pace

For S

pace

-- alg

orith

m: S

tep

0al

gorit

hm: S

tep

0

Ste

p0. P

artit

ion

DFG

: Alg

orith

m P

CD

FG to

kee

p tra

ck o

f eac

h ba

sic

patte

rn a

nd p

artit

ion

a D

FG in

to b

asic

pat

tern

s.if

one

child

-nod

e of

v h

as in

-deg

ree(

v) >

1 th

en re

turn

FA

LSE

Ret

urn

fals

e

v 2

v 5v 4

v 1v 3

v 2

v 5v 4

v 1

v 3

Ret

urn

fals

e

Ret

urn

fals

e

v 1

v 2v 3

v 4v 5

v 6

v 8v 7

6040

320

3327

40

4027

33

100

a 1

a 2a 4

a 1

a 6

a 5a 4a 3

20

For S

pace

For S

pace

-- alg

orith

m: S

tep

1al

gorit

hm: S

tep

1

Ste

p1. P

artit

ion

varia

bles

: co

nstru

ct A

G G

’(V’,

E’)

for s

pace

Cal

cula

te e

dges

’wei

ghts

w’(e

’(u’,

v’))

:–

1. s

umm

ate

the

num

ber

sum

mat

e th

e nu

mbe

rof e

dges

who

se v

ertic

es a

cces

s u’

and

v’:

–2.

For

pat

tern

(c),

enha

nce

enha

nce

edge

s e’

(A(c

hild

x), A

(chi

ldy)

):w

’(e’(A

(chi

ldx)

, A(c

hild

y)))

+ +

; –

3. F

or p

atte

rn (d

), sl

ack

slac

ked

ges

e’(A

(par

entx

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–4.

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prop

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titio

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expe

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pa

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the

sam

eba

nk

21

For S

pace

For S

pace

-- alg

orith

m: S

tep

2al

gorit

hm: S

tep

2

Ste

p2. I

nser

t BS

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base

d on

pat

tern

s

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ach

basi

c pa

ttern

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ach

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c pa

ttern

, gi

ve it

an

optim

al in

serti

on s

olut

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r pat

tern

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nd (d

): in

sert

one

BS

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entra

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of th

e ch

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if ne

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;

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atte

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sed

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r the

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at th

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the

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r eac

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node

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need

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r the

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of p

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BS

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entra

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BS

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xy

22

Out

line

of th

is ta

lkO

utlin

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this

talk

Bac

kgro

und

& R

elat

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ork

Wha

t the

pro

blem

is?

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iabl

e pa

rtitio

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& B

SL

inse

rtion

How

to s

olve

the

prob

lem

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r spe

edFo

r spa

ce

Exp

erim

enta

l res

ults

23

Expe

rimen

tsEx

perim

ents

-- ben

chm

arks

benc

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urfo

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anks

ba

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arch

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is u

sed

for b

ench

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no

mor

e th

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nei

ght

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arch

itect

ure

for t

he o

ther

s.

24

Expe

rimen

tsEx

perim

ents

-- res

ults

re

sults

for s

peed

for s

peed

The

parti

tioni

ng te

chni

ques

und

er c

ompa

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are

:

(a) e

qual

lyeq

ually

parti

tioni

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ccor

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to re

fere

nce

orde

r,

(b) a

par

alle

lpa

ralle

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titio

ning

met

hod

[8],

(c) e

qual

ly p

artit

ioni

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ith s

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k ba

nk a

djus

tmen

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, (d

) the

pro

pose

d al

gorit

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r spe

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This

met

hod

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rs th

e w

orst

solu

tions

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met

hod

achi

eves

2-

16%

ove

rhea

dre

duct

ion

Our

met

hod

achi

eves

19-

29%

over

head

redu

ctio

n

25

Expe

rimen

tsEx

perim

ents

-- res

ults

re

sults

for s

pace

for s

pace

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pace

, diff

eren

t BS

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acem

ent m

etho

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re a

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com

pare

d,

beca

use

they

als

o af

fect

the

solu

tions

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SL

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art

Par

titio

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(a)

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titio

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titio

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AG

Opt

[2][3

]Ba

sis

Par

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[8]

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ptB

SL

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redA

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Opt

BS

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Opt

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Our

sV

PA

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is m

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the

wor

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lutio

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met

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eves

2-

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rhea

dre

duct

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Eve

n co

mbi

ned

with

the

optim

al B

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plac

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t, th

e ot

her

parti

tioni

ng a

lgor

ithm

sst

ill ca

nnot

obt

ain

bette

r res

ults

than

the

prop

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alg

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m

can

obta

in th

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st s

olut

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for s

ome

case

s

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y 2%

wor

seth

an th

e op

timal

solu

tions

.

26

Con

clus

ion

Con

clus

ion

Arc

hite

ctur

e: 88

-- bit

mic

robi

t mic

ro-- c

ontro

llers

cont

rolle

rs&

par

titio

ned

bank

s &

ban

k &

par

titio

ned

bank

s &

ban

k sw

itchi

ngsw

itchi

ng

Obj

ectiv

e: m

inim

ize

the

size

and

tim

e ov

erhe

ads

over

head

sin

trodu

ced

by B

SLs

Thro

ugh:

opt

imiz

ing

the

varia

ble

parti

tioni

ngva

riabl

e pa

rtitio

ning

in d

iffer

ent b

anks

and

elab

orat

ely

plac

ing

plac

ing

BS

LsB

SLs

in p

rogr

ams.

NP

-Har

d pr

oble

ms

Diff

eren

t pos

ition

s to

inse

rt B

SLs

Diff

eren

t pat

tern

s

Heu

ristic

alg

orith

ms

are

prop

osed

.

Futu

re w

ork

Com

bini

ng m

ultip

le o

bjec

tives

Spe

cial

cas

es: o

ptim

al s

olut

ions

Than

ks!

Than

ks!

Q &

AQ

& A