On Metrics for Comparing Routability Estimation Methods for FPGAs

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On Metrics for Comparing Routability Estimation
Methods for FPGAs

• Parivallal Kannan, Shankar Balachandran, Dinesh
  Bhatia
• Center for Integrated Circuits and Systems
• The University of Texas at Dallas
• http//www.cics.utdallas.edu/

Speaker
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Outline

• Introduction
• Routability Estimation
• fGREP and enhancements to fGREP (FPL 2001)
• RISA (ICCAD 94)
• Lous Method and enhancements (ISPD 2001)
• Rents Rule based method (TCAD 2002)
• Proposed Estimation Quality Metric
• Experimentation and Results
• Conclusion

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Introduction

• Interconnect Estimation
• Estimate the routing resource requirement of
  adesign before actually routing it
• FPGA device size is ever increasing gtgt1 mil gates
• Design Cycles are lengthy
• Multiple iterations of Placement and Routing
• Prediction of wiring requirements duringphysical
  design is essential for
• Fast design closure
• Performance
• Maximum Area utilization

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Introduction (contd.)

• FPGA design flow
• Routing resources are fixed
• Routability Estimation is more appropriate term
• If device has enough routing resources to
  satisfy an estimate, then the design is routable
• Useful Parameters
• Peak Routing Demand (Global)
• Routing Demand Distribution (Local)

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Estimation Methods

• Rents Rule
• Empirical relationship between gates and pins
• RISA (ICCAD 94)
• empirical method based on a wiring distribution
  map
• fGREP (FPL 2001)
• based on the concept of routing flexibility
• Lous Method (ISPD 2001)
• based on the ratio of number paths using a
  routing elementto total number of paths
• Other Methods
• Stochastic models (Brown et.al.), BDD based
  method(Wood et.al.)

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Estimation methods for FPGAs

• fGREP
• Designed for FPGAs
• Yang et.al (TCAD 2002)
• Rents rule based method for ASIC design flows
• Easily adaptable to FPGAs for estimating
  peakrouting demand
• Regional Estimation model may not be
  applicableto FPGAs
• RISA
• Easily adaptable to FPGAs. VPR has an
  implementation
• Lous method
• Easily adaptable to FPGAs (VLSI 2002)

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Requirements of a Good Routability Estimation
Method

• Accurate
• Estimates should conform to standard routers
• Reliable
• Should produce comparable errors over a large set
  of benchmarks
• Fast
• to be used inside other PD Methods
• Usable
• Global and Local results
• Generic
• Architecture Independence

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Preliminaries

• Generic island style FPGA architecture (VPR
  style)
• Logic blocks (L), Connection Boxes (C), Switch
  Boxes (S)
• Routing Graph of FPGA G(V,E)
• V is the set of routing channels
• E is the set of switch boxes

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fGREP

• New formulation for estimating routing demand for
  aplaced circuit.
• Based on the concept of routing flexibility
• Flexibility is the number of alternatives
  available to reacha nets terminal
• Directly operates on multi-terminal nets
• Estimates match very closely the actual routes
  produced by a detailed router (VPR, Pathfinder)
• Very Fast implementation is possible. Easy
  deployment.
• Generic - can be adapted for any FPGA
  architectureand ASIC design flows

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fGREP - Definitions

• A net nk?N, is a set of terminals, Tk?V
• Every terminal tik?Tk, exacts a routing demand
  called terminal demand on all elements in the
  net bounding box
• Terminal Demand on a routing element at a
  distance lq from a terminal tik vi, is
  proportional to the total number of routing
  elements at the same distance
• Distance is measured on the breadth-first search
  tree from a terminal
• The set of such equidistant elements form a
  level-set,

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fGREP Definitions (cont.)

• The terminal demand due to vi on vj is then,
• All the terminals of a net collectively produce a
  Net Demand. This is the terminal demand due
  to the terminal with the lowest distance from the
  routing element vj,
• Final routing demand on an element due to all the
  nets in the netlist is,

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fGREP Illustration
Level-Set Illustration
Terminal and Net Demand Illustration
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fGREP Enhancements

• fGREP runtimes are high for large high fanout
  nets
• fGREP runtime is proportional to E x T, where
  Eis the set of routing elements in the net
  bounding box and T, the set of terminals of the
  net
• Major speed-up possible by limiting the search to
  within the Zones of Influence of each terminal
• Within a zone, the net-demands are due to a
  single terminal
• The zones are the Voronoi regions of the
  terminals, within the net-bounding box

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fGREP Enhancements (contd.)

• Problems with zoning
• fGREP needs the cardinality of the level-set, to
  calculate the demands
• Zoning will result in clipping and fragmenting of
  the search wave-front
• Terminal T1, wave-front is fragmented to W1, W2,
  W3, W4
• Simple Solution
• Maintain complete wave-front as long as at-least
  one routing-element is within the terminals zone
  of influence
• Perform search in parallel from all terminals of
  a net

• Up-to 30X speedup over fGREP was obtained by
  this method.

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RISA Chang (ICCAD 94)

• Empirically determined net-weights q are
  applied to all routing elements in a nets
  bounding box
• For a M pin net, the net-weight q is calculated
  froma Wiring Distribution Map (WDM)
• WDM is obtained by adding up and normalizing the
  demands due to optimal Steiner trees generated
  over K sets ofM random points (K very large)
• Mean value of the WDM is the net-weight q of a
  M terminal net
• Authors provide the values for the net-weights
  for 1 ? M ? 50. Values for larger M can be found
  by a linear regression process.

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RISA (contd.)

• Expression for the routing demand on a region Ri
  (W,L), due toa net nk (net b-box X,Y) with an
  overlap of (w,l) is,
• For the FPGA architecture, WLwl1. Hence the
  demands are,
• Total routing demand on a routing-element is then
  the sum of each nets routing demand

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Lous Method Lou et.al.(ISPD 2001)

• For a 2-terminal net, analytically calculate the
  total number of paths and the number of paths
  using a particular routing element
• Routing demand on a routing element is the ratio
  of the number of paths incident on the element to
  the total number of paths
• A M terminal net (M gt 2) has to be decomposed
  into 2-terminal segments
• Authors propose MST or RST decomposition
• Authors dont know how to handle segment
  overlaps. They suggest a simple addition of the
  demands, where the bounding boxes overlap.

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Lous Method Enhancements

• Most of the error is produced in the regions
  where the bounding boxes of the 2-terminal
  segments overlap

• We propose a simple solution
• use the Maximum of the demands due to
  theoverlapping regions
• Up-to 103 better estimates compared to the
  original method (compared with a detailed router)

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Rents Rule Yang et.al (TCAD 2002)

• Empirical relationship between number of blocks B
  and the number of pins P,
• r is the rents exponent
• Tb is the avg number of interconnections per
  block
• Recursively partition a circuit to get the
  cutsets. Find out rents exponent as the slope of
  the log-log plot of number of cells and nets in
  the partitions.
• The Peak Routing Demand is then given by,

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Estimation Quality Metric

• No uniform reporting methods for interconnect
  estimation research
• RISA reports the method being used in a
  placementmethod and reports the congestion
  obtained with andwithout using RISA
• Yang et.al (TCAD2002) compare peak estimates with
  aL-shaped Global router, which is but an
  approximationto a router
• Lou et.al. (ISPD2001) just report the congestion
  map obtained by using Lous method
• No comparison with well known detailed/global
  routers
• Impossible to ascertain the relative merits of
  estimation methods
• For CAD deployment, the accuracy, reliability and
  runtime requirements of estimation methods MUST
  be known.

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Est. Quality Metric (contd.)

• Quality Metric should be based on well
  knownstate-of-the-art detailed routers and be
  easily reproduced
• PathFinder (FPGA95), available with VPR
• Free for research and source code available
• Or at-least use a standard commercial router
• Four parameters as adequate quality metrics
• Peak Demand Error (W)
• Mean of regional errors (?)
• Standard deviation of the regional errors (?)
• Runtimes on standard benchmarks (t)

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Est. Quality Metric (contd.)

• Peak Estimation Error
• quick Figure of Merit for the global estimation
  quality
• Mean of Regional Estimation Errors
• Correlation of local estimates
• Standard Deviation of Regional Estimation Errors
• quick Figure of Merit for the distribution of
  local estimation errors
• Runtimes
• duh !

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Results - Peak Demand Runtime
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Results Mean and Std Deviation of Errors
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Results - Illustration

• fGREP2 is the most reliable
• RISA is the fastest, followed by fGREP2

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Conclusion

• Implemented all the routability estimation
  methods
• Proposed enhancements to fGREP andLous method,
  resulting in significantlybetter results
• Proposed a simple yet effective Estimation
  Quality Metric
• Showed that RISA is the fastest while fGREP is
  the most accurate and reliable.

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Thank You !