Gaspard Methodology The Y Model approach

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Gaspard MethodologyThe Y Model approach

• Models and UML profiles

Arnaud CUCCURU, phd student ModEasy meeting,
Lille, February 2005
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Outline

• Y Model overview
• Common modeling paradigms
• Application modeling
• Hardware Architecture modeling
• Association modeling

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Y model overview (1/2)
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Y overview (2/2)

• Component Oriented Modeling
• Factorization mechanisms

Y

• Expression of data dependences
• Data parallelism expression

• Resource dimensionning
• Grid modeling

• Spatial and temporal mapping of an application
  on an architecture

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Common modeling paradigms

• Component oriented modeling
• Components libraries
• Factorization mechanisms

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Common modeling paradigms Component Oriented
Modeling (1/2)

• Benefits
• Strong encapsulation (to ease reuse)
• Hierarchichal description (to handle complexity)

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Common modeling paradigms Component Oriented
Modeling (2/2)
ComponentB
InterfaceZ
InterfaceB
InterfaceB
InterfaceZ
ComponentC
InterfaceC
InterfaceC
Component Reusable design element
Connector Messages media
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Common modeling paradigms Components Libraries

• Predefined components ElementaryComponent
• No internal structure description
• Supposed to be implemented in a library

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Common modeling paradigms Factorization
mechanisms (1/4)
Metaclass ElementaryComponent
Multidimentional Cardinalities

• Definition of a repetition space
  RepetitiveComponent
• Use of multidimentional cardinalities on
  structural elements (parts and ports)
• Use of smart connectors to interconnect
  factorized elements RepetitiveConnector

Mechanisms inspired by the Array Oriented Language
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Common modeling paradigms Factorization
mechanisms (2/4)
Component
Ports
Parts
Connectors
Potential factorization
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Common modeling paradigms Factorization
mechanisms (2/4)
Component
a3 ComponentA
2

a2 ComponentA
2
3
6

a1 ComponentA
2

Ports
Potential factorization
gt Cardinalities
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Common modeling paradigms Factorization
mechanisms (2/4)
Component
a ComponentA 3
2
3
6

Potential factorization
Parts
gt Cardinalities
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Common modeling paradigms Factorization
mechanisms (2/4)
Component
RepetitiveConnector
RepetitiveConnector
a ComponentA 3
2
3
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Several informations (vectors) are associated to
Repetitive Connectors to describe connection
patterns between ports Origin, Paving, Fitting
Potential factorization
Connectors
gt RepetitiveConnector
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Common modeling paradigms Factorization
mechanisms (2/4)
RepetitiveComponent
Component
Factorization expressed In the context of a
repetitive component
RepetitiveConnector
RepetitiveConnector
a ComponentA 3
2
3
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Note A repetitive component contains a
repetition of a single part
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Common modeling paradigms Factorization
mechanisms (3/4)
Component
a3 ComponentA
1
0
5
4
2
a2 ComponentA
1
1
3
0
2
0
1
a1 ComponentA
0
1
0

• Basic idea Handle ports with cardinalities as
  arrays of ports
• Dependences can be defined between patterns
  inside ports in the boundaries, and ports of the
  repeated parts

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Common modeling paradigms Factorization
mechanisms (3/4)
Component
Origin 0 Paving 2
Origin 0 Paving 1
a3 ComponentA
1
0
5
4
2
a2 ComponentA
1
1
3
0
2
0
1
a1 ComponentA
0
1
0

• Paving vector gt identifies origin of each
  pattern inside the array of ports at the
  boundary, from a given Origin vector
• Paving limit is given by the cardinality
  associated to the repeated part (in this case 3)

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Common modeling paradigms Factorization
mechanisms (3/4)
Component
Origin 0 Paving 2
Origin 0 Paving 1
a3 ComponentA
1
2
0
5
4
2
a2 ComponentA
1
1
3
1
0
2
0
1
a1 ComponentA
0
1
0
0

• An index vector is implicitely associated to
  each repetition of the part (Coordinates in the
  repetition space)
• Origin of the pattern associated to each part
  origin index x paving

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Common modeling paradigms Factorization
mechanisms (3/4)
Component
Origin 0 Paving 2
Origin 0 Paving 1
a3 ComponentA
1
0
5
Fitting 1
Fitting
4
2
a2 ComponentA
1
1
3
0
2
0
1
a1 ComponentA
0
1
0

• Fitting vector gt determines the ports that
  belong to a given pattern inside of an array
  (from the origin of the pattern given by the
  Paving)
• Fitting limit is given by the cardinality
  associated to the ports of the repeated part

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Common modeling paradigms Factorization
mechanisms (3/4)
RepetitiveComponent
a ComponentA 3
RepetitiveConnector Origin0 Paving1 Fttin
g
RepetitiveConnector Origin0 Paving2 Fitti
ng1
2
3
6

Final compact representation
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Common modeling paradigms Factorization
mechanisms (4/4)
Metaclass ElementaryComponent
Metaclass RepetitiveComponent

• Expression of connections between repeated
  instances SelfConnector
• Connection between different points of the
  repetition space

Metaclass RepetitiveConnector
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Common modeling paradigms Factorization
mechanisms (4/4)
Component
a3 ComponentA
prov
req
a2 ComponentA
prov
req
a1 ComponentA
prov
req

• Example Ring topology
• Each instance is able to communicate with its
  neighbour

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Common modeling paradigms Factorization
mechanisms (4/4)
RepetitiveComponent
a ComponentA 3
prov
req
SelfConnector RepetitionSpaceDependance
1 Modulo true

• Factorization of parts in the context of a
  RepetitiveComponent
• Connection between points of the repetition
  space Connection between different instances of
  the repeated part gt SelfConnector

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Common modeling paradigms Factorization
mechanisms (4/4)
RepetitiveComponent
2 1 mod 3
a3 ComponentA
a2 ComponentA
a1 ComponentA
2
1
0
prov
req
prov
req
prov
req
1 1 mod 3
0 1 mod 3

• index of the neighbour index
  RepititionSpaceDependence mod RepetitionSpace
  size (i.e. Cardinality of the repeated part)

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Application modeling

• Data Parallelism expression
• Spatial and temporal dimensions unification
• Inter-repetition dependences

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Application modeling

• AppComponent Function
• Ports Data handled (mainly multidimentional
  arrays)
• Connectors Data dependencies
• gt Expression of applications via expression of
  Data dependencies

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Application modelingData parallelism expression
(1/2)
array
array
pattern
pattern

• Example Computations on a 4x4 array to produce
  a 2x2
• Input and output arrays can be decomposed into
  patterns

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Application modeling Data parallelism
expression (1/2)
1,1
array
array
0,1
1,0
Origin 0,0 Paving 2,0,0,2 Fitting
1,0,0,1
Origin 0,0 Paving 1,0,0,1 Fitting
,
0,0

• Example Computations on a 4x4 array to produce
  a 2x2
• Input and output arrays can be decomposed into
  patterns
• Each pattern can be computed independently
  Potential Data Parallelism
• gt Represented with the common factorization
  mechanisms

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Application modelingData parallelism expression
(2/2)
array
array
pattern
pattern
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Application modelingData parallelism expression
(2/2)
RepetitiveComponent
array
array
pattern
pattern
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Application modelingData parallelism expression
(2/2)
RepetitiveComponent
array
array
pattern
pattern
p Part
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Application modelingData parallelism expression
(2/2)
RepetitiveComponent
p Part
4,4
2,2

2,2
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Application modelingData parallelism expression
(2/2)
RepetitiveComponent
RepetitiveConnector
RepetitiveConnector
p Part 2,2
4,4
2,2

2,2
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Application modeling Spatial and Temporal
dimensions unification (1/2)
Infinite vector
Infinite vector

• Example Signal processing application Infinite
  stream of data consumed and produced
• Idea Infinite stream Infinite dimension of an
  Array
• Spatial and temporal dimension in an array
• gt Modeling of time and space dependences with
  the same formalism

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Application modelingSpatial and Temporal
dimensions unification (2/2)
RepetitiveComponent
RepetitiveConnector
RepetitiveConnector
p Part
Origin 0 Paving 1 Fitting
Origin 0 Paving 1 Fitting




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Application modeling Inter repetition
dependences (1/2)

• Inter repetition dependences

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Application modelingInter repetition
dependences (2/2)
RepetitiveComponent
RepetitiveConnector
RepetitiveConnector
p Part 3
Origin 0 Paving 1 Fitting
Origin 0 Paving 1 Fitting
3
1
1
3
SelfConnector RepetitionSpaceDependance
1 Modulo false
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Hardware Architecture modeling

• Resources classification
• Complex connection patterns expression
• Grid topologies modeling

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Hardware Architecture modeling

• HwComponent Hardware resource

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Hardware Architecture modeling Resources
classification

• Passive to support data. Example RAM, ROM, SAM
• Active able to read or write in passive
  resources, with or without modifications, and to
  sequence operations. Example CPU, DMA.
• Interconnect interconnection between passive and
  active elements, or active and active. Example
  Bus, static/dynamic interconnection networks,

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Hardware Architecture modeling Complex
connection patterns (1/2)
CompoundHwComponent Omega8x8
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Hardware Architecture modeling Complex
connection patterns (2/2)
HwRepetitiveComponent OmegaStage
Crossbar2x2 2,2
RepetitiveConnector
RepetitiveConnector
8
2
2
8
origin 0 paving 2,2 fitting 1
origin 0 paving 4,1 fitting 2
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Hardware Architecture modeling Grid topologies
modeling (1/2)

• Example 4x4 cyclic grid of communicating PEs

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Hardware Architecture modeling Grid topologies
modeling (2/2)
HwRepetitiveComponent CyclicGrid4x4
SelfConnector RepetitionSpaceDependance
1,0 Modulo true
pe PE 4,4
SelfConnector RepetitionSpaceDependance
1,0 Modulo true

• Example 4x4 cyclic grid of communicating PEs

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Association modeling

• In progress

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Association modeling

• Association distribution scheduling
• distribution spatial mapping
• code on active (and passive)
• data on passive
• communications on paths
• scheduling temporal mapping
• for tasks
• memory allocation