CS2946 Reconfigurable Computing

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CS294-6Reconfigurable Computing

• Day 10
• September 24, 1998
• Interconnect Richness

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Last Thursday

• Interconnect is dominant area in spatial
  architectures
• Characterize interconnect locality/richness
• Bifurcators
• Rents Rule

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Today

• How rich should interconnect be?
• Allow full utilization?
• Model requirements and area impact
• (Remind students use microphones)

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Thursday Geometric Growth

• (F,a)-bifurcator
• F bandwidth at root
• geometric regression a at each level

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Thursday Good Model?
Log-log plot straight lines represent
geometric growth
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Rents Rule

• Long standing empirical relationship
• IO CNP
• 0?P ?1.0
• compare (F,a)-bifurcator
• a 2P
• Captures notion of locality
• some signals generated and consumed locally
• reconvergent fanout

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Today

• How rich should interconnect be?
• Allow full utilization?
• Model requirements and area impact

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Step 1 Build Architecture Model

• Assume geometric growth
• Build architecture can tune
• F, C
• a, p

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Tree of Meshes

• Tree
• Restricted internal bandwidth
• Can match to model

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Parameterize C
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Parameterize Growth
(2 1) a?2
(2 2 2 1) a2(3/4)
(2 2 1) a(22)(1/3) 2(2/3)
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Step 2 Area Model

• Need to know effect of architecture parameters on
  area (costs)
• focus on dominant components
• wires (saw on Thursday)
• switches
• logic blocks(?)

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Area Parameters

• Alogic 40Kl2
• Asw 2.5Kl2
• Wire Pitch 8l

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Switchbox Population

• Full population is excessive (see next week)
• Hypothesis linear population adequate
• still to be (dis)proven

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Cartoon VLSI Area Model
(Example artificially small for clarity)
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Larger Cartoon
1024 LUT Network
P0.67
LUT Area 3
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Effects of P (a) on Area
P0.5
P0.67
P0.75
1024 LUT Area Comparison
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Effects of P on Capacity
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Step 3 Characterize Application Requirements

• Identify representative applications.
• Today IWLS93 logic benchmarks
• How much structure there?
• How much variation among applications?

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Application Requirements
Max C7, P0.68 Avg C5, P0.72
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Benchmark Wide
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Benchmark Parameters
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Complication

• Interconnect requirements vary among applications
• Interconnect richness has large effect on area
• What is effect of architecture/application
  mismatch?
• Interconnect too rich?
• Interconnect too poor?

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Interconnect Mismatch in Theory
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Step 4 Assess Resource Impact

• Map designs to parameterized architecture
• Identify architectural resource required

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Mapping to Fixed Wire Schedule

• Easy if need less wires than Net
• If need more wires than net, must depopulate to
  meet interconnect limitations.

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Mapping to Fixed-WS

• Better results if reassociate rather than
  keeping original subtrees.

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Observation

• Dont really want a bisection of LUTs
• subtree filled to capacity by either of
• LUTs
• root bandwidth
• May be profitable to cut at some place other than
  midpoint
• not require balance condition
• Bisection should account for both LUT and
  wiring limitations

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Challenge

• Not know where to cut design into
• not knowing when wires will limit subtree
  capacity

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Brute Force Solution

• Explore all cuts
• start with all LUTs in group
• consider all balances
• try cut
• recurse

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Brute Force

• Too expensive
• Exponential work
• viable if solving same subproblems

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Simplification

• Single linear ordering
• Partitions pick split point on ordering
• Reduce to finding cost of start,end ranges
  (subtrees) within linear ordering
• Only n2 such subproblems
• Can solve with dynamic programming

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Dynamic Programming

• Start with base set of size 1
• Compute all splits of size n, from solutions to
  all problems of size n-1 or smaller
• Done when compute where to split 0,N-1

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Dynamic Programming

• Just one possible heuristic solution to this
  problem
• not optimal
• dependent on ordering
• sacrifices ability to reorder on splits to avoid
  exponential problem size
• Opportunity to find a better solution here...

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Ordering LUTs

• Another problem
• lay out gates in 1D line
• minimize sum of squared wire length
• tend to cluster connected gates together
• Is solvable mathematically for optimal
• Eigenvector of connectivity matrix
• Use this 1D ordering for our linear ordering

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Mapping Results
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Step 5 Apply Area Model

• Assess impact of resource results

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Resources x Area Model Area
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Net Area
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Picking an Optimum
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What about a single design?
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LUT Utilization predict Area?
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Summary

• Interconnect area dominates logic block area
• Interconnect requirements vary
• among designs
• within a single design
• To minimize area
• focus on using dominant resource (interconnect)
• may underuse non-dominant resources (LUTs)

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Methodology

• Architecture model (parameterized)
• Cost model
• Important task characteristics
• Mapping Algorithm
• Map to determine resources
• Apply cost model
• Digest results
• find optimum (multiple?)
• understand conflicts (avoidable?)