David Sheldon, Frank Vahid * Department of Computer Science and Engineering

Making Good Points: Application-Specific Pareto-Point Generation for Design Space Exploration using Rigorous Statistical Methods

David Sheldon, Frank Vahid*

Department of Computer Science and EngineeringUniversity of California, Riverside

*Also with the Center for Embedded Computer Systems at UC Irvine

Counterbus

W1

16 bytes4 physical lines filled when line size is 32 bytes

Off Chip Memory

Line Concatenation

[Zhang/Vahid/Najjar, ISCA 2003, ISVLSI 2003, TECS 2005]

Parameterized Component: Cache

2 of 19

127% 620% 126%

0%

20%

40%

60%

80%

100%

120%

padp

cm

crc

auto

2

bcnt bilv

bina

ry blit

brev

g3fa

x fir

pjep

g

ucbq

sort v4

2

adpc

m epic

g721

pegw

it

mpe

g

jpeg ar

t

mcf

pars

er vpr

Ave

Nor

malized

Ene

rgy)

cnv8K4W32B cnv8K1W32B cfg8Kwcwslc

40% avg savings

David Sheldon, UC Riverside 3 of 19

FPGA Systems are Often Built from Parameterized Components

Parameterized components include: Cache (e.g., size, associatively, line size)

Processors Co-processors Buses (e.g., bit width, network-on-chip structure)

uP

MPEG Enc

Cache config

config

config

config Bus

FPGADSP

config

0

2

4

6

8

10

12

14

0 20 40 60 80 100 120 140 160 180 200

Mill

ions

Thousands

Equivilent LUTs

cycl

es

520 pointsOver 10 days

~35 min per point

<1 min to execute

Remaining time was in synthesis and place and route

Microblaze Soft-Core Processor – Design Space due to Parameters

Pareto points: Points where no point exists that is better in all metrics.

Cycles

Equivalent LUTs 4 of 19


Pareto Points Differ Per Application and Per Criteria

App a2

Designer B

Platform

App a1

Time

Ener

gyTime

Ener

gy

Pareto points

Designer A

c1c2 c3

c1

c2

c3

(a)

(b)

c1 c3 ...c2


Previous Work: Parameter Interdependency graph

Platune [Givargis/Vahid 2002]: Introduced parameter interdependency graph

Edges – parameters are dependent

Nodes not connected – independent

Search dependent parameters exhaustively; compose local Pareto points into global points

Greatly reduces search space if independent parameters

Good results, 44 hours Randomized Approaches

Pareto Simulated Annealing (PSA) [Talarico 2006]

Good results, 6 hours Genetic Algorithms [Ascia 2005]

Good results, 4 hours

Platune’s Architecture

MIPSI$

D$MEM

CPU–I$ Bus

CPU–D$ Bus

$-MEM Bus

sizeassoc.linesize

sizeassoc.

codea code

code

Supply Voltage


Our Approach We developed

Design-of-Experiments (DoE)-based technique to automatically generate a parameter interdependency graph

Relieves designer of burden Technique to generate Pareto-points via parameter interdependency graph edge-weight-based algorithm

Improve speed versus Platune Called DoE-Based Pareto-Point Generator (DPG)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 2 4 6 8 10 12Time (sec)

Ener

gy (

J)

Time

Performance


Design of Experiments (DoE)

i$ size i$ assoc d$ size d$ lined$ assocm-i$code

m-i$a code

$-mcode

Supply Voltage

MIPSI$

D$MEM

CPU–I$ Bus

CPU–D$ Bus

$-MEM Bus

sizeassoc.linesize

sizeassoc.

codea code

code

Supply Voltage

2k8

8k832

BiBi

Bi

4.1

DoE generates a set of orthogonal experiments that allows for statistical analysis of the search space


DPG Algorithm Subsequent DoE analysis determines main effects of parameters

Y bar Marginal Means Plot

0

0.00002

0.00004

0.00006

0.00008

0.0001

0.00012

0.00014

0.00016

-1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1

Effect Levels

i$ size

i$ assoc

d$ size

d$ line

d$ assoc

m-i$code

m-i$a code

$-mcode

Supply Voltage

MIPSI$

D$MEM

CPU–I$ Bus

CPU–D$ Bus

$-MEM Bus

sizeassoc.linesize

sizeassoc.

codea code

code

Supply Voltage


DPG Algorithm (cont.) Compute weight of each pair of nodes Sort edges in decreasing weight

DK, (I$ assoc, CPU-I$ address code) DI, (I$ assoc, CPU I$ code) IK, (CPU-I$ code, CPU I$ address code) IQ, (CPU-I$ code, $-MEM address code) KQ, (CPU I$ address code, $-MEM address code) ...

MIPSI$

D$MEM

CPU–I$ Bus

CPU–D$ Bus

$-MEM Bus

sizeassoc.linesize

sizeassoc.

codea code

code

Supply Voltage


DPG Algorithm (cont.) Pair wise merge of nodes

Creates a sparse set of Pareto points The designer can direct the tool to fill in the regions of interest

Original Pareto pointsFilled in Pareto points

Time

Energy


Platune – Pareto Graph with Fill-in

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Time

Ener

gy

Platune

Single Factor

DoE IOT

DPG - 3 value

DPG - fill in

jpeg


Platune – Pareto Graph with Fill-in

0

0.001

0.002

0.003

0.004

0.005

0.006

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (sec)

Ener

gy (J

)

PlatuneDPG

b1_histogram

Interdependency Graph Comparison: Manual vs. Automated


jpeg b1_histogram g3fax


Platune Results

44

0

1

2

3

4

5

6

SF DoE IOT DPG Genetic PSA Platune

Run

time

in H

ours

DPG is 30x faster than Platune 2.5x faster than Genetic Algorithms

Xilinx Microblaze Soft-Core Processor

Tuned the Microblaze for various benchmarks

Exhaustive data generated for 12 benchmarks for comparison

The Microblaze also has a configurable cache, which allows for over 3,000 configurations.

For these tests we used results previously generated thus giving us only 64 configurations.


MicroblazebsFPUdiv

mulMSRPCMP


Network on Chip – Results

DPG also works on larger design spaces

DPG Scales Well


Number of Parameters

DPG Analysis Phase

Total Design Space

Percent of Design Space

6 34 64 53.13%10 67 1,024 6.54%15 136 32,768 0.42%20 234 1,048,576 0.02%25 353 33,554,432 0.001%30 497 1,073,741,824 0.00005%


Conclusion DoE-Based Pareto-Point Generation (DPG) algorithm quickly finds good Pareto Points Results were better and obtained faster than previous Platune or randomized techniques

Approach is easier to use – no designer knowledge of parameter interdependencies is needed

Useful for FPGAs as well as other parameterized systems, such as SOCs synthesized to ASICs, parameterized SOCs, etc.

Documents

David Sheldon, Frank Vahid * Department of Computer Science and Engineering