Temporal Logic Replication for Dynamically Reconfigurable FPGA Partitioning

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Temporal Logic Replication for Dynamically
Reconfigurable FPGA Partitioning

• Wai-Kei Mak
• Dept. of Computer Science and Engineering
• University of South Florida
• Evangeline F.Y. Young
• Dept. of Computer Science and Engineering
• The Chinese University of Hong Kong

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Outline

• Dynamically reconfigurable FPGA
• Temporal partitioning Conventional
  partitioning?
• Temporal logic replication
• What?
• Why?
• How?
• Experimental results
• Conclusions

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Dynamically Reconfigurable FPGA

• Store multiple contexts on chip.
• Reuse logic blocks and wire segments dynamically.
• The contexts stored can correspond to the
  multiple stages of a large circuit.

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Temporal Circuit Partitioning

• Temporal partitioning
• multiple stages execute sequentially
• Spatial partitioning
• multiple components execute concurrently

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Temporal Logic Replication

• Can reduce buffering requirement.
• Effectively utilize available slack logic
  capacity.

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Temporal Constraints

• For a net n (v1, v2, , vp),
• require s(v1) ? s(vj), j2,,p, if v1 is a
  combinational node

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Temporal Constraints (Contd)

• require s(vj) ? s(v1), j2,,p, if v1 is a
  flip-flop node

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Temporal Partitioning with Replication

• Problem Partition given circuit into pre-defined
  stages satisfying all temporal constraints.
• Objective Minimize buffers required between
  stages.
• Proposal Utilize available slack logic capacity
  to reduce signal buffering.
• Solution An effective 2-step approach.

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2-Step Approach

• Step 1 Compute a temporal partition w/o
  replication.
• Step 2 Repeatedly identify the bottleneck stage
  and apply replication for that stage.

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Advantages of 2-Step Approach

• Will not replicate unnecessarily.
• All temporal constraints are already satisfied
  when replicating.

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Min-Area Min-Cut Replication

• Let stage i be the bottleneck stage.
• Min-Cut Replication
• Compute a subset of nodes Ri in stage i for
  replication into stage i1 to maximally reduce
  the communication cost at stage i.
• Min-Area Min-Cut Replication
• Compute a minimum subset of nodes Ri in stage i
  for replication into stage i1 to maximally
  reduce the communication cost at stage i.

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Optimal Solution for Min-Area Min-Cut Replication
Let Vi set of nodes in stage i.

• Observation 1
• The min-cut replication problem can be solved by
  computing a minimum cut (Vi-Ri,Ri) in stage i.
• Observation 2
• The min-area min-cut replication problem can be
  solved by computing a minimum cut (Vi-Ri,Ri) in
  stage i s.t. Ri is minimized.

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Example

• A pre-partition

Computing a minimum cut in stage 2

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Example (Contd)

• Computed R2 j

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Network Modeling

• Need to ensure that
• cut size buffer requirement
• For a net (v1, v2, , vp),

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The Case of Limited Slack Logic Capacity

• The solution of min-area min-cut replication
  suffices if slack logic capacity is sufficiently
  large.
• Otherwise, Ri exceeds the slack, then use a
  heuristic to reduce Ri.
• Use a repeated max-flow min-cut heuristic to
  gradually reduce Ri (so cut size is only
  increased gradually).
• H. Yang, D.F. Wong, Efficient Network Flow based
  Min-Cut Balanced Partitioning, ICCAD94.

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Algorithm

• Input Stage area bound A.
• 1. Network modeling for bottleneck stage i.
• 2. Compute min-cut (Vi-Ri,Ri) s.t. Ri is
  minimized.
• 3. If Vi1Ri ? A, stop and return Ri.
• 4. Collapse a node in Ri with all nodes in
• Vi-Ri, goto 2.

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Experimental Results
Circuit buf w/o rep. buf w/ rep. Imprv. Rep.
C3540 198 194 2.02 0.48
C5315 140 129 7.86 0.67
C6288 83 63 24.10 4.41
C7552 210 176 16.19 3.12
S13207 688 669 2.76 2.54
S15850 761 699 8.15 3.59
S35932 2729 2636 3.41 2.48
S38417 2194 2104 4.10 0.63
S38584 2280 2137 6.27 0.98
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Conclusions

• Proposed temporal logic replication to reduce
  buffering requirement in DRFPGA partitioning.
• Presented an effective 2-step approach.
• Formulated and optimally solved the min-area
  min-cut replication problem.
• Extended to case of limited slack logic capacity.
• In the paper, a new timing-driven temporal
  partitioning algorithm was introduced to compute
  pre-partition.