Optimizations for intensive signal processing applications on … · 2010. 9. 6. · PhD defense Œ Calin Glitia Modeling intensive signal processing applications 9/34. Array Oriented

Optimizations for intensive signal processingapplications on Systems-on-Chip

Calin Glitia

September 6, 2010

PhD defense – Calin Glitia 1/34

Intensive signal processing

Detection systemsMultimedia

Repetitive computationsConsiderable amount of data ⇒ Multi-dimensional arrays


Modular decomposition

Data-fiow oriented modeling

Logical parallelism1 Task parallelism and pipeline2 Data parallelism

Complexity:Elementary functions assemblageComplex accesses at the data structures


Modular decomposition

Data-fiow oriented modeling

Logical parallelism1 Task parallelism and pipeline2 Data parallelismComplexity:

Elementary functions assemblageComplex accesses at the data structures


Execution platforms

Systems-on-Chip:Increase in the integrationcapacityMultiprocessors

Multiprocessor SoC


Execution platforms

Systems-on-Chip:Increase in the integrationcapacityMultiprocessors

Architecture models :Repetitive topologiesPhysical parallelism

Multiprocessor SoC

XAUI 1PHY/MAC

SerializeDeserialize

XAUI 1PHY/MAC


Flexible I/OPCIe 1PHY/MAC

Flexible I/O

UARTHPI, I2C

JTAG, SPI

PCIe 0PHY/MAC



GbE 0

GbE 1

DDR Controller 0 DDR Controller 1

DDR Controller 3 DDR Controller 2


Co-design

Application Architecture

Mapping

Code Generation


Co-design


Mapping

Code Generation

Logical parallelism Physical parallelism

Distribution

Eflcient execution


Co-design


Mapping

Code Generation

Logical parallelism Physical parallelism

Distribution

Eflcient execution

Optimizations


Outline


Mapping

Code Generation


Outline


Mapping

Code Generation

Array Oriented Language


Outline


Mapping

Code Generation


Inter repetition dependence


Outline


Mapping

Code Generation



Modeling and Analysis of Real-Time Embedded Systems


Outline


Mapping

Code Generation




High-level refactoring– data-parallel transformations– strategies


Outline


Mapping

Code Generation





Gaspard2 environment


Some of the existing languages

Data-Flow

1 Synchronous Data Flow

2 Extensions:Cyclo-Static Data FlowMulti-dimensional Synchronous Data Flow, Windowed SynchronousData FlowBoolean Data Flow, Dynamic Data Flow

3 Array-OL

Functional languages

Alpha: polyhedron, recurrence equationsSisal, Single Assignment C

PhD defense – Calin Glitia Modeling intensive signal processing applications 7/34

Some of the existing languages

Data-Flow

1 Synchronous Data Flow2 Extensions:

Cyclo-Static Data FlowMulti-dimensional Synchronous Data Flow, Windowed SynchronousData FlowBoolean Data Flow, Dynamic Data Flow

3 Array-OL

Functional languages

Alpha: polyhedron, recurrence equationsSisal, Single Assignment C


Multidimensional Synchronous DataFlow (MDSDF)

Matrix multiplication

B

(M,N)

TTransposition

(M,N,1)

(1,M,N)

Repetition

(1,1,1)

(L, 1, 1)

A

(L,M)

Repetition

(1,1,1)

(1,1,N)

Downsample

(1,M,1)

(1,1,1)

TTransposition

(L,1,N)

(L,N,1)

(0, 1, 0)

Data-fiow graph: actors consuming/producingMultiDimensional-tokensStatic analysis/scheduleLimitations: Multiple data consumptionsExtensions




B

(M,N)

T(3, 1, 2)

(M,N,1)

(1,M,N)

(1,1,1)

(L, 1, 1)

A

(L,M)

(1,1,1)

(1,1,N)

Downsample

(1,M,1)

(1,1,1)

T(1, 3, 2)

(L,1,N)

(L,N,1)

(0, 1, 0)

Data-fiow graph: actors consuming/producingMultiDimensional-tokensStatic analysis/schedule

Limitations: Multiple data consumptionsExtensions




B

(M,N)

T(3, 1, 2)

(M,N,1)

(1,M,N)

(1,1,1)

(L, 1, 1)

A

(L,M)

(1,1,1)

(1,1,N)

Downsample

(1,M,1)

(1,1,1)

T(1, 3, 2)

(L,1,N)

(L,N,1)

(0, 1, 0)

Data-fiow graph: actors consuming/producingMultiDimensional-tokensStatic analysis/scheduleLimitations: Multiple data consumptionsExtensions


Array Oriented Language – principles

Similarities with other data-fiow languages

Hierarchical decomposition – task parallelismData-fiow oriented formalism – multi-dimensional data structures


B(M, N)

A(L,M)

C(L, N)

(L, N)

Line×Column multiplication(M)

(M)

(1)

Ligne×Colonne

(M)

(M)(M)

(M)

×(1)

(1)(1)

Sum

(M) (1)

Explicit data parallelism : data-parallel repetitions (“loops”)Uniform paving by sub-arraysSpace and time mixed as dimensions of the data structures






B(M, N)

A(L,M)

C(L, N)

(L, N)


(M)

(1)

Ligne×Colonne

(M)

(M)(M)

(M)

×(1)

(1)(1)

Sum

(M) (1)

Explicit data parallelism : data-parallel repetitions (“loops”)Uniform paving by sub-arrays

Space and time mixed as dimensions of the data structures






B(M, N)

A(L,M)

C(L, N)

(L, N)


(M)

(1)

Ligne×Colonne

(M)

(M)(M)

(M)

×(1)

(1)(1)

Sum

(M) (1)

Explicit data parallelism : data-parallel repetitions (“loops”)Uniform paving by sub-arraysSpace and time mixed as dimensions of the data structures


Data-parallel repetitions

Matrix multiplication: N = 3,M = 4, L = 2

(3, 4)

(4, 2)

(3, 2)

(3, 2)

(4)

(4)

(1)





Line×Column multiplications




uniformly spaced input/output patterns




DATA-PARALLEL instances




(3, 4)

(4, 2)

(3, 2)

(3, 2)

(4)

(4)

(1)

Compact representation: repetition space




(3, 4)

(4, 2)

(3, 2)

(3, 2)

(4)

(4)

(1)

F =(10

)o =

(00

)P =

(0 00 1

)

F =(01

)o =

(00

)P =

(1 00 0

)

F =( )

o =(00

)P =

(1 00 1

)

Tilers – links between input and output patterns


Uniform sub-array accesses (patterns)

Tiler

o: origin of the reference pattern

F : Fitting matrix – the shape of the tiles in the arrayP: Paving matrix – uniform spacing of the tiles

0 80

5

Formal specification:

o+ (P F) ·(ri

)mod sarray



Tiler

o: origin of the reference patternF : Fitting matrix – the shape of the tiles in the array

P: Paving matrix – uniform spacing of the tiles

0 80

5


o+ (P F) ·(ri

)mod sarray



Tiler

o: origin of the reference patternF : Fitting matrix – the shape of the tiles in the arrayP: Paving matrix – uniform spacing of the tiles

0 80

5


o+ (P F) ·(ri

)mod sarray


Common motif-based accesses

Pattern examples

0 3

0

4

0 5

0

4

0 5

0

3

0 5

0

3

0 5

0

5

Paving example

0 90

4

r =(00

) 0 904

r =(10

) 0 904

r =(20

)

0 90

4

r =(01

) 0 904

r =(11

) 0 904

r =(21

)

0 90

4

r =(02

) 0 904

r =(12

) 0 904

r =(22

)F =

(1 00 1

)spattern =

(53

)o =

(00

)sarray =

(105

)P =

(0 31 0

)srepetition =

(33

)


Summary ARRAY-OL

Specification

Data-fiow oriented visual formalismExpress the regularity of computations/data accessesExploit the parallelism

Rules that allow static analysis

Limitations

Numerical values for the multidimensional spaces/accessesCycles not allowed in the dependence graphExtension: inter-repetition dependences


Summary ARRAY-OL

Specification

Data-fiow oriented visual formalismExpress the regularity of computations/data accessesExploit the parallelismRules that allow static analysis

Limitations



Summary ARRAY-OL

Specification


Limitations

Numerical values for the multidimensional spaces/accesses

Cycles not allowed in the dependence graphExtension: inter-repetition dependences


Summary ARRAY-OL

Specification


Limitations

Numerical values for the multidimensional spaces/accessesCycles not allowed in the dependence graph

Extension: inter-repetition dependences


Summary ARRAY-OL

Specification


Limitations



Need for uniform dependences

State construction

Transfer data between different instances of the same repetition.

Examples: Sum, Integrate

Integrate – Flatten

...

...

0

+[0] +[1] +[2]...

Uniform data dependences between instances of a repetition


Need for uniform dependences

State construction

Transfer data between different instances of the same repetition.Examples: Sum, Integrate

Integrate – Flatten

...

...

0

+[0] +[1] +[2]...

Uniform data dependences between instances of a repetition


Uniform dependences

Integrate

(∞)(∞)

(∞)

+

pinpout

default

Inter-repetition dependence

1 Data dependence: pout→pin

2 Dependence vector inside therepetition space

3 Initial values: default link fordependences that exit therepetition space

Calin Glitia, Philippe Dumont, and Pierre Boulet.

Array-OL with delays, a domain specific specification language for multidimensionalintensive signal processing.Multidimensional Systems and Signal Processing, 2009.


Uniform dependences

Integrate

(∞)(∞)

(∞)

+

pinpout

d =(1)

default








Uniform dependences

Integrate

(∞)(∞)0

()

(∞)

+

pinpout

default








Uniform dependences

Integrate

(∞)(∞)0

()

(∞)

+

pinpout

d =(1)

default








Initial values

Initial values – default link

Same initial valueDifferent values – TilerDifferent default links – Exclusive tilers

d =(2, 0

)


Initial values


Same initial value

Different values – TilerDifferent default links – Exclusive tilers


Initial values


Same initial valueDifferent values – Tiler

Different default links – Exclusive tilers

F =( )

o =(00

)P =

(1 00 1

)


Initial values


Same initial valueDifferent values – TilerDifferent default links – Exclusive tilers

F =(1)

o =(0)

P =(4 0

)

F =(1)

o =(−4)

P =(4 0

)


Complex dependences

Dependence constructions:

Multiple default links

Multiple dependences on a repetition spaceDependences connected through the hierarchy


Complex dependences


Multiple default linksMultiple dependences on a repetition space

Dependences connected through the hierarchy


Complex dependences


Multiple default linksMultiple dependences on a repetition spaceDependences connected through the hierarchy

Dependences on the complete repetition space


Impact on the parallelism

The repetition space is split in parallel hyper-planesPipeline execution following the distance vector

Scheduling uniform loops

Alain Darte and Yves Robert.

Constructive methods for scheduling uniform loop nests.IEEE Trans. Parallel Distributed Systems, 5(8):814–822, 1994.



The repetition space is split in parallel hyper-planes

Pipeline execution following the distance vector






The repetition space is split in parallel hyper-planesPipeline execution following the distance vector





Outline


Mapping

Code Generation





Profile UML – standard OMG

Model Driven EngineeringCo-design: application, architecture, mapping

Repetitive Structure Modeling

All the ARRAY-OL concepts are includedProposed by the DaRT team


Model repeated inter-connected architecture topologies

Physical connections between architecture components

Compact expression

Cyclic uniform inter-connections


Model repeated inter-connected architecture topologies

Physical connections between architecture components

Compact expressionCyclic uniform inter-connections


Summary inter-repetition dependences

1 Expression of state constructions

2 Complex dependences through the hierarchy

3 Parallelism – pipeline

4 Repeated inter-connected architectures

+


Outline


Mapping

Code Generation



PhD defense – Calin Glitia From a high-level specification to the execution 23/34

Outline


Mapping

Code Generation






Execution

Logical space and time as mixed dimensions of multidimensionalstructure

Specification: expresses the data dependencesbetween all the data elements that transits the system

And a partial execution orderbetween all the execution of the tasks in of the system

EFFICIENT execution

Optimized code generationProjection of specification into physical space and time

Adapt a specification to the execution

High-level refactoringExecution that refiects the specification


Projection into space and time

Multi-dimensional structures

repetition spaces

⇓in space ←→

linked(trade-off)

data structures

⇓in time

Take into account the execution constraints

Data dependencesAvailable resources




repetition spaces⇓

in space

←→linked(trade-off)

data structures⇓

in time






repetition spaces⇓

in space ←→linked(trade-off)

data structures⇓

in time




Projection example

Horizontal Filter

(1920, 1080,∞) (720, 1080,∞)(240, 1080,∞)

(13) (3)

Vertical Filter

(720, 480,∞)(720, 120,∞)

(14) (4)


Projection example

Horizontal Filter

(1920, 1080,∞) (720, 1080,∞)(240, 1080,∞)

(13) (3)

Vertical Filter

(720, 480,∞)(720, 120,∞)

(14) (4)

Maximal parallelism

Memory sizeInfinite data structures – Blocking points


Projection example

Horizontal Filter

(1920, 1080,∞) (720, 1080,∞)(240, 1080,∞)

(13) (3)

Vertical Filter

(720, 480,∞)(720, 120,∞)

(14) (4)

Pipeline

Execution Order


Projection example

(1920, 1080,∞) (720, 480,∞)

(240, 120,∞)

Horizontal Filtre

(14, 13) (3, 14)

(14)

(13) (3)

Vertical Filter

(3, 4)

(3)

(14) (4)

Fusion of successive repetitions

Minimize the arrays – macro-patternsDistribution of the common repetitionEach processor its macro-patterns in memory


Projection example

(1920, 1080,∞) (720, 480,∞)

(240, 120,∞)

Horizontal Filtre

(14, 13) (3, 14)

(14)

(13) (3)

Vertical Filter

(3, 4)

(3)

(14) (4)

Re-computations

When intermediate values are consumed by multiple repetitionsTrade-off

Recompute valuesKeep in memory – increase of memory size


High-level transformations

Adapt a specification to execution

change the granularity of the repetitionsarray sizes reductions

“High-level” loop transformations

repetition = visual representation of data-parallel loop nestfusion, change paving, tiling, collapse, . . .

Calin Glitia and Pierre Boulet.

High level loop transformations for multidimensional signal processing embeddedapplications.In International Symposium on Systems, Architectures, Modeling, and Simulation(SAMOS VIII), Samos, Greece, July 2008.


Optimization strategies – memory size reduction

r1

r2 r3 r4 r5

r6

r7

MAXIMAL reduction of the intermediate arrays



r1

r2 r3 r4 r5

r6

r7

MAXIMAL reduction of the intermediate arraysFusion of multiple repetitions

Minimizes only the last intermediate arrayRe-computations!



r1

r2 r3 r4 r5

r6

r7

MAXIMAL reduction of the intermediate arraysFusion of multiple repetitions

Minimizes only the last intermediate arrayRe-computations!

Complete fusion?Too much re-computationsLimited array reduction



r1

r2 r3 r4 r5

r6

r7


Strategy that limits the re-computationsusing result from complete fusion and two-by-two fusionswhere re-computations are introduces and minimal achievable arrayreduction



r1

r2 r3 r4 r5

r6

r7

r14r67

r12


Repetitions Repetitions Re-computations Reduction factorbefore fusion after fusion (product) of the output arrays8× 128× 96

96×

119×(10× 81

)80× 801

9.29 1228.8

119× 96 1 9680× 80× 96 1 96

96 1 1128× 96× 80 128× 96× 80 1 1119× 128× 96 128× 96×

(1191

)1 12288

128× 96 1 1



r1

r2 r3 r4 r5

r6

r7

r14r67

r12


Calin Glitia, Pierre Boulet, Éric Lenormand, and Michel Barreteau.

Repetitive model refactoring strategy for the design space exploration of intensivesignal processing applications.Journal of Systems Architecture, Special Issue: Hardware/Software CoDesign.


And the inter-repetition dependences?

Why ?

To allow the use of the refactoring tools on models with uniformdependences

Typically: ⇒

Algorithm

The global accesses and dependences MUST remain unchangedAutomatically compute new dependences after a transformation

Calin Glitia and Pierre Boulet.

Interaction between inter-repetition dependences and high-level transformations inarray-ol.In Conference on Design and Architectures for Signal and Image Processing (DASIP2009), Sophia Antipolis, France, September 2009.


Outline


Mapping

Code Generation





PhD defense – Calin Glitia Gaspard2 – co-design environment for SoC 30/34

Outline


Mapping

Code Generation








SoC visual co-design

1 allows modeling, simulation and code generation of SoC2 approach Model Driven Engineering3 Subset of the MARTE UML profile


Gaspard2 conception fiow

high-level specification

inter-repetitiondependencesrefactoring tools:implementation andintegration

MDE contributions toGaspard2

specializations

code generation


Gaspard2 conception fiow

high-level specificationinter-repetitiondependencesrefactoring tools:implementation andintegration

MDE contributions toGaspard2

specializations

code generation


Conclusion


Mapping

Code Generation

PhD defense – Calin Glitia Conclusion 33/34

Conclusion


Mapping

Code Generation



Perspectives

. . .


Modeling intensive signal processing applicationsSpecification languagesArray Oriented LanguageModeling uniform dependences – contribution

From a high-level specification to the executionData-parallel transformationsOptimization strategies

Gaspard2 – co-design environment for SoCConclusion

Documents

Optimizations for intensive signal processing applications on … · 2010. 9. 6. · PhD defense Œ Calin Glitia Modeling intensive signal processing applications 9/34. Array Oriented