Compiler-Based Register Compiler-Based Register Name Adjustment for Low-Name Adjustment for Low-

Power Embedded ProcessorsPower Embedded Processors

Peter Petrov; Alex Orailoglu; ICCAD’03

2/19

AgendaAgenda

Introduction Mathematical Formulation Heuristic Solutions For RNA

Register PermuTation (RPT) Register PerturBation (RPB)

Experimental Results Conclusions

3/19

IntroductionIntroduction

Objective: Low-PowerLow-Power Key Point: Reduce bit transition activity

on the register index streams.

Concept: Register Name Adjustment (RNA)

4/19

ExampleExample

add r3, r2, r4 add r6, r2, r4

sub r6, r3, r5 sub r7, r6, r5

sub r3, r2, r6 sub r6, r2, r7

mul r4, r4, r5 mul r4, r4, r5

011

110

011

100

110

111

110

100

010

011

010

100

010

110

010

100

100

101

110

101

100

101

111

101

Total Bit Transitions: 7 + 4 + 5 = 16 3 + 4 + 3 = 10

5/19

AgendaAgenda

Introduction Mathematical FormulationMathematical Formulation Heuristic Solutions For RNA

Register PermuTation (RPT) Register PerturBation (RPB)

Experimental Results Conclusions

6/19

Cost FunctionCost Function

fc(rega, regb): the hamming distance between rega and regb.

l: the lth column in an instruction.

M(Pi, j): a bijective mapping function from the original reg Pi, j to a new reg index

CPMPMfl

n

ililic

3

1

1

1,1, ,cost

7/19

LiteralsLiterals LiteralsLiterals: unchangeable field in an instruction

such as an opcode or immediate oprand.

L(i, j): to record the literal positions.

ji

ji

P

PMM

,

,'

if Li, j = 0

if Li, j = 1

8/19

ExampleExample

ld r5, (r1) 0add r3, r2, r5add r4, r3, r2mul r3, r4, r3st r3, r7 (10)

v5 v1 0v3 v2 v5v4 v3 v2v3 v4 v3v3 v7 10

P =

0 0 1 0 0 0 0 0 0 0 0 0 0 0 1

L =

(v3, v4) – 3 (v4, v7) – 1 (v1, v2) – 1(v2, v3) – 2 (v5, v2) – 1(v5, v3) – 1 ( 0, v5) – 1(v3, v3) – 1 (10, v3) – 1

9/19

AgendaAgenda

Introduction Mathematical Formulation Heuristic Solutions For RNAHeuristic Solutions For RNA

Register PermuTation (RPT)Register PermuTation (RPT) Register PerturBation (RPB)Register PerturBation (RPB)

Experimental Results Conclusions

10/19

FlowFlow

RPB: Max the distribution skew of register pair occurrences

Select Vi and Vj that maximize f(eij) + f(eji)

Pick names for Vi and Vj and compute the cost

All unassigned indices tried?

All registers named?

Name Vi and Vj with min costYes

Finish

Yes

No

No

Brute-ForceTime-

Consuming

11/19

Cost Function of RPTCost Function of RPT

Cij =

jcicHefef

kcjcHjckcH

kcicHickcH

jiij

IkRkLk

IkRkLk

jj

ii

,

,,

,,

,

,

Vi Vj

eij

eji

Literali

…

Regi

…

Literalj

…

Regj

…

12/19

Register PertuBationRegister PertuBation Number of higher utilization frequency↓

Performance↑ Number of self transition↑ Performance↑

13/19

Cost Function of RPBCost Function of RPB

N

x

2

2

PN

DD ˆ

ˆ1ˆ0 DC

Maximize σto maximize the distribution skew of register pair occurrenc

es

D: the number of self-transitionsDoes larger σ impl

y larger skewness?

14/19

Register PertuBationRegister PertuBation Commutativity Transformation

Dead Register Reassignment

r1 r2, r3 r1 r2, r3r4 r1, r2 r2 r1, r2r2 r3, r4 r2 r3, r2

r1 r2, r3 r1 r2, r3r4 r1, r2 r4 r2, r1

Note: r4 must be dead after the third instruction

Note: these instructions must be commutable

Question: would the data

dependency increase?

15/19

Dead Register Dead Register ReassignmentReassignment

r1 r2 r3

1 23

4

56

7

8

r1 r2 r3

1 23

4

56

7

8

Self-Transition

16/19

AgendaAgenda

Introduction Mathematical Formulation Heuristic Solutions For RNA

Register PermuTation (RPT) Register PerturBation (RPB)

Experimental ResultsExperimental Results Conclusions

17/19

Experimental ResultsExperimental Results ˆ1ˆ

0 DC

Circuit TotalRPT RPB

Total Impr% λ(0.0) λ(0.25) λ(0.5) λ(0.75) λ(1.0) Impr%

fdct 70 58 18.09 47 46 46 46 46 34.55

ej 73,837 63,169 14.45 49,203 48,933 48,934 48,934 45,224 38.75

mmul 7,613 6,463 15.11 4,710 4,460 4,460 4,460 4,593 41.41

tri 5,929 5,400 8.92 3,490 3,489 3,489 3,489 3,335 43.76

sor 1,440 1,142 20.69 1,004 1,003 1,043 1,043 1,004 30.30

adpcm_e 20,513 15,338 25.23 15,897 15,144 15,144 15,144 14,750 28.10

adpcm_d 17,212 13,689 20.46 13,393 12,655 12,655 12,655 11,404 33.74

Does larger σ imply larger skewness?

18/19

AgendaAgenda

Introduction Mathematical Formulation Heuristic Solutions For RNA

Register PermuTation (RPT) Register PerturBation (RPB)

Experimental Results ConclusionsConclusions

19/19

ConclusionsConclusions

Minimize the bit transitions , reduce the power consumption.

RPT improves up to 25%. RPB improves up to 44%.