SINGLELEVEL PARTITIONING SUPPORT IN BOOMII

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SINGLE-LEVEL PARTITIONING SUPPORT IN BOOM-II

• Petr Fier, Hana Kubátová
• Department of Computer Science and Engineering
• Czech Technical University

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Outline

• Motivation
• Single-Level Partitioning
• Constraint-Driven Minimization
• BOOM-II Its Modifications
• Experimental Results
• Conclusions

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Motivation

• Typical logic synthesis process
• Perform two-level minimization
• Then do the decomposition, independently on the
  previous phase
• Then apply other criteria (low power, DFT)
• ?
• Two-level minimization is performed independently
  on the following phases can misguide the
  solution

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Single-Level Partitioning

• Two-level AND-OR network
• The issue limited number of inputs/outputs in
  real devices
• Solution divide the circuit into stand-alone
  blocks, while reducing number of their inputs
• In praxis, not all the inputs are needed to
  generate values of particular outputs ? it is
  possible

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Constraint-Driven Minimization

• Two-level Partitioning - divide circuit into
  blocks - keep the number of inputs minimal
• Design for Testability - reduce the cone size
• Load Balancing - divide circuit into blocks -
  reduce the number of branchings
• ???

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BOOM-II

• Heuristic two-level Boolean minimizer
• Composition of two minimizers - BOOM - FC-Min
• BOOM is suitable for functions with a large
  number of inputs
• FC-Min is suitable for functions with a large
  number of outputs
• Iterative minimization both the minimizers are
  being alternated

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BOOM-II
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BOOM CD-Search

• Generates an irredundant set of implicants
  covering the on-set of asingle-output function
• Implicants are being constructedtop-down, i.e.,
  by reducing a universal hypercube until it
  becomes an implicant- by adding literals to a
  term
• Greedy heuristic

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BOOM CD-Search

• Literals to be added to a term are being
  selected using a scoring function - frequency of
  occurrence
• For partitioning the frequency of the literal
  that is already included in the processed block
  is multiplied by theCD-Search partitioning force

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BOOM IE, IR

• Implicant Expansion - expands implicants to
  PIs - no modification
• Implicant Reduction - reduces PIs to group
  implicants - no modification

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FC-Min Find Cover

• Generates a cover of the on-set
• Determines the number of product terms in the
  solution, not their structure
• It is not dependent on input literals cannot
  be modified
• However - it strictly defines what terms would
  be shared among what output variables - it
  determines what outputs would be grouped together

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FC-Min Implicant Generation

• Generates implicants from the cover
• Purely deterministic cannot be modified

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FC-Min Implicant Expansion

• Expands implicants to reduce no. of literals
• Can be influenced - literals of variables
  included in other blocks are removed first

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CP Solution

• The essential phase
• Finds an irredundant set of implicants
• Constructs the final solution

A greedy incremental heuristic, based on a
scoring function To apply partitioning,
additional weights are assigned to the
implicants, the weights modify the scoring
function
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Experimental Results
Boolean function 50 inputs, 40 outputs, into 4
blocks
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Conclusions

• Constraint-Driven two-level minimization support
  in BOOM-II was presented
• Partitioning
• Design for testability
• Low power design