Image redundant wire identification
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Image redundant wire identification. Speaker: Yung-chih Chen. Outline. Introduction Previous work Possible approach Future work. == img != function. 0 0 1 1 0 1 0 1. 0 0 1 1 0 1 0 1. 0 1. 0 1. 0 0 1 0 1 1. Image eq. 0 0 1 0 1 1. Introduction. Image equivalence.

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Image redundant wire identification

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Image redundant wire identification

Image redundant wire identification

Speaker: Yung-chih Chen


Outline

Outline

  • Introduction

  • Previous work

  • Possible approach

  • Future work


Introduction

==img

!=function

0 0 1 1

0 1 0 1

0 0 1 1

0 1 0 1

0 1

0 1

0 0 1

0 1 1

Image eq.

0 0 1

0 1 1

Introduction

  • Image equivalence

Image redundant wire


Random simulation flow chat

Random simulation flow chat

Legal Vectors

Reference

Model

Constraint

circuit

Optimized

constraint

circuit

Output

Comparator

Random

Vector

Generator

Design

Under

Verification

(DUV)

Coverage Feedback


Problem formulation

circuit

DUV

Optimized

Circuit

DUV

optimize

Problem formulation

  • Input

    • A constraint circuit A’

  • Output

    • A optimized constraint circuit B’

  • Objective

    • Size of B’ << size of A’

    • B’ ==img A’


Previous work

Previous work

  • Remove tree structure

  • Use the rewiring technique to construct tree structure

  • Characteristic BDD

  • Circuit partition


Remove tree structure

Tree structure

No multiple fanouts

Replace the tree structure by a primary input

Remove tree structure


Rewiring technique

Rewiring technique

optimize


Characteristic bdd

y1

y1

y2

y2

Smoothing

all input

y2

x1

x1

1

0

x2

x2

1

0

Characteristic BDD

  • Use characteristic BDD and smoothing technique to verify image equivalence

1: legal output

0: illegal output


Remove primary input

Remove primary input

  • Assign constant value to PI to reduce circuit (cofactor)

  • Check

    • If Fxi=0 ==img org circuit, then we set constant 0 to PI xi, and optimize circuit.

    • If Fxi=1 ==img org circuit, then we set constant 1 to PI xi, and optimize circuit.


Example

x

y

y

c

x

x

c

image

b

y

y

b

b

a

a

cofactor

c=0

x

1

1

0

0

y

y

1

0

b

b

b

Image eq.

a

a

image

1

0

Example

Order: x < y < c < b < a

a

b

c

x

y

a

b

x

y


Circuit partition

Vertical partition

horizontal partition

mixed partition

Circuit partition

  • For each circuit, we can do vertical partition or horizontal partition into some subcircuit


Summary

Summary

  • Remove tree structure

  • Use the rewiring technique to construct tree structure

  • Characteristic BDD

    • Iteratively remove PIs

  • Circuit partition


Possible approach

Possible approach

  • Algorithm for image redundant wires identification

  • Iteratively remove PIs


Example 1 2

Example (1/2)

optimize


Example 2 2

Example (2/2)

optimize


Image redundant wire identification

Idea

  • Img of F = Img of Fxi=0∪ Img of Fxi=1

  • If Img of Fxi=0≤ Img of Fxi=1, then we set xi=1 and optimize the circuit

  • If Img of Fxi=1≤ Img of Fxi=0, then we set xi=0 and optimize the circuit


Image redundant wire identification

Idea

  • Img of Fxi=0 =

    Img of Fxi=0, X-xi=A∪ Img of Fxi=0, X-xi=B

  • Img of Fxi=1 =

    Img of Fxi=1, X-xi=A∪ Img of Fxi=1, X-xi=B

  • Img of Fxi=0, X-xi=B= Img of Fxi=1, X-xi=B?

A is the set of X-xi such that the effect xi can be propagated to POs

B is the set of X-xi such that the effect xi cannot be propagated to POs


Future work

Future work

  • Propose an algorithm for image redundant PIs identification

    • Analyze Img of Fxi=0and Img of Fxi=1


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