Dataflow Analysis Revisited - TU/etbasten/presentations/ST-Ericsson.pdf · 2009-02-19 · Dataflow...

Dataflow Analysis Revisited

Twan Basten

[email protected]

‘Knowing is not understanding.’

Charles Kettering

2 Acknowledgements

Joint work with:

• Marc Geilen

• Sander Stuijk

• AmirHossein Ghamarian

• Bart Theelen

• …

Projects:

• NWO PROMES

• EC FP6 Betsy

• EC FP7 MNEMEE

3 Overview

• Embedded Multi-media

• Analysis of Synchronous Dataflow Graphs

• Throughput Analysis

• Throughput-Storage Trade-off Analysis

• Parametric Throughput Analysis

• Scenario-aware Dataflow

• Multiprocessor System-on-Chip Design

• Looking Forward

4

Trends

Concurrency

Connectedness

Interaction

Variability

Embedded Multi-media

emb. mm throughput storage parameters mpsocs the futurescenarios

5 Embedded Multi-media






8 Approach: Models of Computation (MoCs)

functionality

concurrency

timing

energy

quality…

Basic dimensions

processing

communication

storage

functionality

concurrency

timing

energy

quality…

Aspects Derivatives

executiontime

energydissipation

perceivedquality

reconfigurationtime

…

essential for predictabilityon the interface between science and engineering


9 Essential Challenges

predictability and efficiency

… are contradictory


10 Overview








• Looking Forward

ACSD 2006

11 Synchronous Data Flow Graphs

A,1 B,2 C,22 3 1 2

2 3 1 2

1 1

1

1 1

1

1 1

1

4 2

channelratetoken

execution time

actor

Throughput: average number of actor firings over time

emb. mm throughput storage parameters

(SDFGs [Lee 1986])

mpsocs the futurescenarios

12 Self-timed Execution

• Each actor fires as soon as it can fire

• Known to maximize throughput


13 Our Throughput Analysis Method

A,1 B,2 C,22 3 1 2

2 3 1 2

1 1

1

1 1

1

1 1

1

423

4213

21

21

1

A

A

A, C

A, CB

B

B

B

A

Periodic PhaseTransient Phase

State: distribution of tokens + remaining execution times

Throughput can be calculatedfrom the periodic phase

emb. mm throughput storage parameters ACSD 2006

Efficient implementationConsider a subset of the firings of one actor only to detect a recurrent state


14 Traditional Throughput Analysis

• Convert the SDFG to a Homogeneous SDFG (HSDFG)

• Compute the throughput of the HSDFG

Disadvantage: conversion may lead to an explosionin the size of the graph

Dataflow graph H.263 decoder

HSDFG with 1190 actors

SDFG

HSDFG


15 Throughput Analysis: Our Result

1. 10-31. 10-31. 10-31. 10-3MP3 dec.

>1800>1800>180010. 10-3H.263 decoder

>1800>1800>180056. 10-3Satellite

>1800>1800>18002. 10-3Sample Rate

81. 10-381. 10-382. 10-31.10-3Modem

Young

Tarjan

Orlin

HowardDasdan

Gupta

State

Space

Runtimes of various throughput analysis methods (in seconds)

All use conversion to HSDFG


16 Conclusions Throughput Analysis

• The first method to perform throughput analysis directly on SDFGs

• Experimental results show that the state-space technique outperforms all other existing techniques

• Can be easily integrated in simulation tools


17 Overview






• Scenario-aware dataflow


• Looking Forward

DAC 2006, IEEE T on Comp 2008

18

`

5 6 7 8 9 10 110

0.05

0.1

0.15

0.2

0.25

thro

ug

hp

ut

storage

Trade-off: Storage vs. Throughput

DSP synthesis

multi-media

applications


19 Storage Distribution

• Separate memory for each channel.

• Backward channels used to model storage space.

A,1 B,2 C,22 3 1 2α β

Tokens on channels must be stored in memory.

A,1 B,2 C,22 3 1 2α β

2 3 1 2

Storage distribution ⟨α, β⟩ → ⟨4,2⟩

24


1 1

1

1 1

1

1 1

1

1 1

1

1 1

1

1 1

1


20 Problem Definition

5 6 7 8 9 10 110

0.05

0.1

0.15

0.2

0.25

thro

ug

hp

ut

distribution size

⟨⟨⟨⟨4,2⟩⟩⟩⟩⟨⟨⟨⟨6,2⟩⟩⟩⟩

⟨⟨⟨⟨6,3⟩⟩⟩⟩

⟨⟨⟨⟨7,3⟩⟩⟩⟩

⟨⟨⟨⟨5,3⟩⟩⟩⟩

Find all minimal storage distributions for any possible throughput

1 1

1

1 1

1

1 1

1

A,1 B,2 C,22 3 1 2α β


21

tk(α)

tk(β)

sp(α)

sp(β)

tk(A)

tk(α)sp(α)

Dependency Graph

A3 A4

B0

C0

A2 B1

C1C1B3B3A5B2B2A4A3

A7A6

C0C0B1B1A2B0B0A1A0

16151413121110987654321

A,1 B,2 C,2α β

cycles denotestorage

dependencies


sp - space

tk - token

2 3 1 2


22

tk(α)

tk(β)

sp(α)

sp(β)

tk(A)

tk(α)sp(α)

Abstract Dependency Graph

A3 A4

B0

C0

A2 B1

tk(α) tk(β)

sp(β)

tk(A)

sp(α)

A B C

abstract dependency graph contains all storage

dependencies


23 Design-Space Exploration Algorithm

Given an SDFG G with storage distribution δ

1. Compute throughput and abstract dependency graph ∆ for G with δ

2. For each channel c with a storage dependency in ∆

3. Create new storage distribution by enlarging c

4. Repeat steps 1-2

All minimal storage distributions are found

when starting from storage distribution ⟨0,...,0⟩


24 Experimental Results

2ms

3

3

16

1/132

12

1/137

12

13

MP3

53min

3254

3254

8006

1/10000

4753

1/21876

3

4

H.263

7ms

2

2

1544

0.23

1542

0.18

26

22

Satellite

1msExec. time

5#Distributions

4#Pareto points

10Distr. size

1/4Max throughput

6Distr. size

1/7min throughput > 0

2#channels

3#actors

Example

Approximation

increase buffers with n times the minimal step size


25 Conclusions Trade-off Analysis

• Exact minimum memory requirements for any possible throughput.

• Technique to search space of storage distributions efficiently.

• Experiments show feasibility of the approach.

• Technique can be combined with heuristics to prune the search space if necessary.


26 Overview








• Looking Forward

27 Parametric Throughput Analysis

H.263 decoder

throughput expression

(max {593 IQ + 594 IDCT + MC, VLD + 594 IQ + 593 IDCT})-1

Divide and Conquer: divide space in throughput regions

Parametric actor execution times

emb. mm throughput storage parameters DATE 2008mpsocs the futurescenarios

28 Overview








• Looking Forward

29 Scenario-aware H.263 Decoder Model

1

1VLD IDCT

RCMCFD1

1

3

1 1

1

1

1

11

1 e

ddd

a

bc c

Detector

Kernel

Parameterized

rate

Control channelData

channel

Tokens

I P99 P99

P0

...

1

Fixed rate

Rate I Px P0

a 0 1 0

b 0 x 0

c 99 x 1

d 1 1 0

e 99 x 0

Execution time

VLDP0 0

others 40

IDCTP0 0

others 17

MC

I, P0 0

P30 90

P40 145

P50 190

P60 235

P70 265

P80 310

P99 390

RC

I 350

P0 0

P30, P40, P50 250

P60 300

P70, P80, P99 320

FD All 0

x={30,40,50,60,70,80,99}

mpsocs the futurescenariosemb. mm throughput storage parameters

(FSM-based Scenario-Aware DataFlow (SADF))

MEMOCODE 2006

30 Scenario-aware Performance Analysis

• SDF-based throughput analysis considers worst-case actor times

• Scenario-aware throughput analysis considers worst-case actor times per scenario, but it must consider scenario transitions

• Analyzing all scenario transitions separately can be avoided

• Separate scenario transitions with an invariant reference schedule

• For every scenario, our method allows to compute the bound on the completion time of an iteration

mpsocs the futurescenariosemb. mm throughput storage parameters Marc Geilen

31 Overview








• Looking Forward

32

Huffman

Req.

Req.

Reorder

Reorder

Stereo

Antialias

Hybrid

Synth.

Antialias

Hybrid

Synth.

Freq.Inv.

Subb.

Inv.

Freq.Inv.

Subb.

Inv.

+

NI

CAP3

t4

R R

M

NI

CAP2

t5

M

R R

M

CAP1

t1

NI

M

CAP2

t2

NI

R

NI

CAP1

t6

M

R

M

CAP3

t3

NI

SDF-based MP-SoC Compilation

PhD Sander Stuijkmpsocs the futurescenariosemb. mm throughput storage parameters

33


SDF-based MP-SoC Compilation

PhD Sander Stuijk

(4 steps)

(2 steps)

(4 steps)

(3 steps)

34 Horizon: Scenario-aware Flow

extract application

model

keep trade-offs

select operating

point and switch

dynamically


35 SDF3 Toolkit

www.es.ele.tue.nl/sdf3


36 Overview








• Looking Forward

37 Dataflow MoCs Expressiveness Hierarchy

RPN: Reactive Process Networks

KPN: Kahn Process Networks

DF: DataFlow

DDF: Dynamic DF

BDF: Boolean DF

CSDF: Cyclo-Static DF

SDF: Synchronous DF

HSDF: Homogeneous SDF

• BDF and larger: turing complete

• Better notions of expressivenessneeded


38 Challenges

• Suitable notions of expressivity

• Expressivity while maintaining analyzability and synthesizability

• Abstraction without loosing accuracy

• Composability and compositionality

• MoCs for non-functional aspects

• Unification of MoCs

• Multi-objective trade-off analysis

• Parametric analysis

• Model-driven design and synthesis flows

• Model-driven run-time systems


39 Thank you !

More info: www.es.ele.tue.nl/~tbasten/

Questions ?

‘An understanding of the natural world and what's in it

is a source of not only a great curiosity but great fulfillment.’

David Attenborough

Dataflow Analysis Revisited - TU/etbasten/presentations/ST-Ericsson.pdf · 2009-02-19 · Dataflow...

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