A NEW ECO TECHNOLOGY FOR FUNCTIONAL CHANGES ANDREMOVING TIMING VIOLATIONS

Jui-Hung Hung , Yao-Kai Yeh,Yung-Sheng Tseng and Tsai-Ming Hsieh

Dept. of Information and Computer Engineering

Chung Yuan Christian University

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Outline

Introduction Problem Formulation Algorithm Experimental Results Conclusions

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Outline

Introduction Problem Formulation Algorithm Experimental Results Conclusions

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Introduction

The cost of remaking a complete photomask is very expensive, such that spare cells rewiring is a convenient way to repair the problems of functional change or timing violation.

Engineering Change Order (ECO), is an effective technique for fixing circuit functionality and timing problems after the placement stage.

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Introduction(cont.)

Spare cells are pre-injected after the placement stage and not connect to other cells, therefore we have to modify the netlist information and replace the original standard cell by spare cells.

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Introduction(cont.)

Assuming that we have to use spare cells to implement a function NAND2 whose two input nets and one output net are denoted by NET1, NET2, NET3

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Introduction(cont.)7

Introduction(cont.)

There are two main research directions ECO for functional changes ECO for timing optimizations

We can assume the ECO problem as resource allocation problem and competition among timing and functional ECO.

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Outline

Introduction Problem Formulation Algorithm Experimental Results Conclusions

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Problem Formulation(cont.)

Given: original circuit(netlist and cell placement) a set of spare cells a cell library a set of timing constraints a set of functional changes.

Our approach is to complete the functional changes by the spare cells rewiring and with the goal of minimum total wiring cost.

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Problem Formulation

Wiring cost Sum of the half perimeter of the minimum

bounding box (HPBB) of each net.

cost(i) = HPBB(i) = xspan(i)+ yspan(i)

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Outline

Introduction Problem Formulation Algorithm Experimental Results Conclusions

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Algorithm

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Algorithm(cont.)

Technology Mapping Table Generation Spare Cell Selection Matching Timing Analysis Buffer Insertion and Gate Sizing

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Algorithm(cont.)

Technology Mapping Table Generation We transform the functional change to

Boolean expression. NOR NAND DeMorgan’s Theorems Constant insertion[1]

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Technology Mapping Table Generation

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Spare Cell Selection

In spare cell selection, we regard this problem as a question of resource allocation, with timing consideration to choose spare cell combinations with smaller timing influence.

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Spare Cell Cost Estimation

Using single spare cell

: a set of nets induced by an ECO function which contains input and output nets.

: a spare cell. :The estimation of wirelength from the

spare cell S to the bounding box formed by the e.

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Spare Cell Cost Estimation(cont.) Using multiple spare cell

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Matching

When different ECO functions require the same spare cell, we need to reallocate resources until the requirement is satisfied.

We can define the “spare cell selection for functional change” problem into a resource allocation and competition among timing and functional ECO.

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Matching(cont.)

Use Hungarian Algorithm to find the better match which with minimum wiring cost in a bipartite graph.

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Timing Analysis

Apply Synopsys’s Liberty library to simulate the circuit timing.

By the two indexes of input transition time and downstream capacitance, we can calculate the gate delay time and output transition time by lookup tables.

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Timing Analysis(con’t)

The downstream capacitance calculation is defined as: Downstream components capacitance plus Downstream wire capacitance

Downstream components capacitance Total input pin capacitance of fan-out gates

Downstream wire capacitance Sum of the Manhattan distance between

current component and the downstream component multiply by the capacitance per wirelength.

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Buffer insertion and gate sizing spare cell search range

α : capacitance per unit wirelength β : a user defined value between 1 to 1.5.

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Outline

Introduction Problem Formulation Algorithm Experimental Results Conclusions

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Experimental Results28

Experimental Results29

Outline

Introduction Problem Formulation Algorithm Experimental Results Conclusions

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Conclusions

This paper present a new ECO technique for functional changes and timing optimizations simultaneously.

The experimental results show that it not only completes functional changes in a reasonable run time but also fixes most timing violation paths.

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