Task/Channel Model

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Task/Channel Model
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Fosters Design Methodology

• Partitioning
• Communication
• Agglomeration
• Mapping

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Fosters Methodology
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Example Domain Decompositions
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Example Functional Decomposition
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Agglomeration Can Improve Performance

• Eliminate communication between primitive tasks
  agglomerated into consolidated task
• Combine groups of sending and receiving tasks

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Mapping Example
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Case Studies

• Boundary value problem
• Finding the maximum
• The n-body problem
• Adding data input

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Boundary Value Problem
Ice water
Rod
Insulation
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Rod Cools as Time Progresses
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Finite Difference Approximation
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Agglomeration and Mapping
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Sequential execution time

• ? time to update element
• n number of elements
• m number of iterations
• Sequential execution time m (n-1) ?

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Parallel Execution Time

• p number of processors
• ? message latency
• Parallel execution time m(??(n-1)/p?2?)

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Finding the Maximum Error
6.25
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Reduction

• Given associative operator ?
• a0 ? a1 ? a2 ? ? an-1
• Examples
• Add
• Multiply
• And, Or
• Maximum, Minimum

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Parallel Reduction Evolution
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Parallel Reduction Evolution
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Parallel Reduction Evolution
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Binomial Trees
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Finding Global Sum
4
2
0
7
-3
5
-6
-3
8
1
2
3
-4
4
6
-1
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Finding Global Sum
1
7
-6
4
4
5
8
2
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Finding Global Sum
8
-2
9
10
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Finding Global Sum
17
8
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Finding Global Sum
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Agglomeration
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Agglomeration
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The n-body Problem
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The n-body Problem
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Partitioning

• Domain partitioning
• Assume one task per particle
• Task has particles position, velocity vector
• Iteration
• Get positions of all other particles
• Compute new position, velocity

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Gather
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All-gather
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Complete Graph for All-gather
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Hypercube for All-gather
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Communication Time
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Adding Data Input
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Scatter
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Scatter in log p Steps
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