A SnapOn Placement Tool

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A Snap-OnPlacement Tool

• Israel Waldman

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Introduction
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What does placement mean?

• In the chip design process, after a circuit
  designer implements the RTL as a set of
  interconnected gates, we go to layout design
• placement putting 100s of millions of
  transistors in a very small area according to
  architectural and electrical specifications(timing
  , power, reliability etc.),
• routing connecting them.

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What is the goal of placement?

• The goal of placement in VLSI physical design is
  to produce a chip layout with optimized area and
  routability which also satisfies timing
  constraints.

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What are we talking about?

• In this paper I will tell you about a new
  placement tool, called snapon, which is based on
  multilevel hierarchical placement method.
• It has a topdown framework that combines
  existing packages and techniques, with some
  additional ideas.
• Experiments results show the strength of this new
  placement tool, it produces very good results on
  all the benchmarks.

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The classical problem

• According to what cost function the final
  placement will done

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The classical solutions
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The net-cut approach

• Net An electrical connection which connects
  several cells(e.g. AND-cell ADDER-cell etc.),
  gates or transistors together.
• Given a partitioning, a net n is not cut if and
  only if all of its terminals are located in the
  same part.
• The net-cut at a given hierarchical level is
  defined as the total number of cut nets.

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Net-cut approach cont.

• In this method, the original circuit is
  partitioned into several tightly connected
  subcircuits.
• The partitioning criteria is minimizing the
  net-cut cost.
• The final placement will be based on that
  partitioning with addition of local placement to
  produce a legal layout.

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Wirelength

• In this method the criteria for placement is
  minimizing the total wirelength.
• In order to prevent all the cells from being
  placed in the same place (zero total wirelength),
  a balancing constraint is imposed.
• Not in the same place
• Enable routability
• Again, some local adjustments will be done to
  produce a legal layout.

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Solving techniques

• There are two main techniques to solve
• problems involving cost function such as
• the placement problem
• 1)Simulated annealing
• 2)Quadratic programming

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Some mathematical notations

• The placement problem is a combinatorial
  optimization problemA problem that involves the
  search for a optimum(maximum or minimum) of a
  cost function.
• The solution space of the placement problem grows
  exponentially with the size of the problem(NP
  complete).
• Hence, this problem is solved approximately by
  heuristic algorithmsAlgorithms that makes
  compromise trading off low computational cost
  for an approximation to the globally optimal
  solution.

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Mathematical notations cont.

• Most of the heuristic algorithms are greedy.
• They start searching the solution from an
  arbitrary initial solution.
• Then, from all the solutions that can be reached
  from the current solution, the solution with the
  lowest cost will become the current solution, and
  so on.
• There are two major drawbacks to terminating at
  local minimum
• 1)There is no way to determine the
  solutions proximity to the
• global minimum.
  
  
• 2)The quality of the result is depend upon
  the initial solution.

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Mathematical notations cont.

• To solve this problem we should use hill
  climbing.
• Randomizing algorithms have this property.
• A randomizing algorithm can accept a neighbor of
  the current solution as the next solution,
  regardless of its cost, by that we could escape
  from terminating at local minimum.

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Simulated annealing

• For a number of problems such as standard-cell
  placement, Simulated annealing has proven to be
  the best known algorithm in terms of solution
  quality (measured by cost function e.g.
  wirelength).
• The SA algorithm functions like a pure
  randomizing algorithm early in the run, slowly
  switching over to a pure greedy algorithm by the
  end of the run.

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Simulated annealing cont.

• However, the major drawback of the SA paradigm is
  its sometimes extremely high computational cost.

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Quadratic programming

• In the quadratic assignment problem we are given
  a set of N objects, which have to be placed in N
  or more sites.
• Each pair of objects has its traffic intensity,
  and each pair of sites has its traffic cost (e.g.
  distance).
• The assignment solution should produce the
  minimum total cost.

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Quadratic programming cont.

• In the placement problem we can choose our sites
  to be pre-specified locations on our layout area,
  our objects to be cells or sub-circuits, our
  traffic intensities to be the number of wires
  required between components, and our distances to
  be the inter-site wire length required.
• The quadratic algorithm is a combinatorial
  algorithm which uses heuristics, hence its
  computational cost isnt high.

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What is a top-down framework?
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Top-down framework

• Since the top-down hierarchical methodology is
  one of the most effective way to solve the
  placement problem of large circuits, we use it as
  the basis for our snap-on placement tool.
• Our methodology will be a typical top-down
  hierarchical methodology placement approach which
  is based on recursive circuit partitioning.

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Top-down framework cont.

• This methodology repeatedly divides a given
  circuit into sub circuits to optimize a given
  partitioning objective.
• At each level, the given layout area is
  partitioned in both horizontal and vertical
  direction (global bins).
• Each subcircuit is assigned to a partition
  (global bin).
• Recursive partitioning is repeated until each
  subcircuit contains a small number of cells.

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• In each hierarchical level i , the placement
  
• problem is to put cells into mini global
• bins while minimizing a certain placement
• cost ( usually the total wirelength ).

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A new snapon placement tool
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Merging existing tools

• What does it mean?
• - At the coarser placement levels, net-cut is
  chosen as the optimization objective to rapidly
  get an initial placement.
• - Later on, wirelength becomes the optimization
  objective till the end of the global placement
  procedure.

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Why should we merge?

• The netcut cost which is used in the
  partitioning problem is globally consistent with
  the wirelength cost in the placement problem.
• The partitioning problem is much easier problem
  then the placement problem. A leading partitioner
  can be faster than a good placement tool.
• Placement experiments showed that minimizing
  netcut in each hierarchical level positively
  affects the wirelength quality of final solution.
  

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How do we merge?

• The difference between the netcut and the
  wirelength
• objective is the cost of external nets. The
  more the external
• nets, the bigger difference between these two
  objectives.
• It was empirically found that if more than
  20-30 nets are external, net-cut is no longer a
  good objective in order to minimize wirelength.
• Conclusion
• - At each hierarchical level, we will
  decide
• whether we should consider wirelength
  by
• looking at the net-cut ratio at this
  level.

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When to stop global placement?

• Overlaps between cells exist in global placement
  since all the cells within the same global bin
  are initially placed at the bins center.
• After global placement, final placement procedure
  will be applied
• to remove these overlaps and make the
  placement legal.
• Obviously, the smaller the average number of
  cells in each global
• bin, the less effort the final placer will
  spend, on the other hand, stopping the global
  placement too late is not good either.
• Experiments shows that appropriate stopping point
  is where
• Navg is between 3-6.

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SummaryA workflow based on the above
techniques
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The framework of snap-on placement tool

• Partitioning package

Input circuit
Control Unit
Simulated annealing package
Circuit Placement Databox
Cost Evaluator
Other packages
Output placement
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Control unit workflow

• At the coarser placement level, netcut is chosen
  as the optimization objective to rapidly get an
  initial placement. We use proven partitioning
  software hMetis to minimize netcut.
• When the topdown flow reaches a certain level in
  which the number of external nets occupies
  20-30 of the number of total nets, simulated
  annealing begins to minimize wirelength on two
  dimensional placement plane.

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Control unit workflow cont.

• This global placement stage ends when the stop
  criterion is satisfied, i.e., the average number
  of cells per global bin is less than a certain
  number.
• Finally, the achieved global placement is refined
  by the final placer to generate a legal placement
  as the ultimate solution.

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Advantages

• The workflow utilizes both netcut and wirelength
  minimizing steps.
• Partitioning ensures that cells with high
  connectivity are put into the same cluster while
  annealing drives clusters to their appropriate
  locations.

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Results
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Results

• We use hMetis partitioning package to minimize
  netcut and use simulated annealing to minimize
  the wirelength in global placement stage. As the
  final placer, we use the tool NRG.
• Total wirelength(WL) is measured in meters and
  running time(Time) in seconds.
• We compared the results of this approach with the
  stateofart university placement tools,
  TimberWolf v7.0 and the best known quadratic
  placement .

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Results table
TW 7.0 Quadratic
Ours
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Results cont.

• This new tool produces comparable or better
  results than TimberWolf on all of MCNC
  benchmarks, it achieves much better wirelength
  (23.5) result than TimberWolf v7.0 on benchmark
  avql.
• Its results are also comparable with one of the
  leadingedge quadratic placement tools- Force
  Quadratic method, on most of benchmarks, except
  avqs on which our approach is inferior.

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What have we learned?

• The placement problem was introduced to you.
• We learned about two different mathematical
  techniques to solve this problem Simulated
  annealing and Quadratic programming.
• We learned about two different optimization
  approaches to solve this problem wirelength and
  net-cut.
• We have learned about a new placement tool which
  is based on top down hierarchical workflow and
  combines these two approaches to achieve
  impressive results.