Improving Voltage Assignment byOutlier Detection and Incremental Placement

Huaizhi Wu* and Martin D.F. Wong*** Atoptech, Inc.

** University of Illinois at Urbana-ChampaignDAC 2007

Outline

Introduction Motivation Outlier Detection Incremental Placement Experimental Results Conclusions

Outline

Introduction Motivation Outlier Detection Incremental Placement Experimental Results Conclusions

Introduction

Multi-Supply Voltage (MSV) Higher voltage on critical paths for performance Lower voltage on other paths for power saving

Complex power supply system Higher design cost Level shifters need to be inserted between low-Vd

d and high-Vdd cells Grouping cells into Voltage Islands

Each Voltage Island has a single supply voltage

Design Flow

Outline

Introduction Motivation Outlier Detection Incremental Placement Experimental Results Conclusions

Motivation

Outliers The few distant high voltage cells Cause disproportinately expensive penalty to the f

inal Voltage Island grouping

w/ outliers w/o outliers

outliers

Modified Design Flow

Outline

Introduction Motivation Outlier Detection Incremental Placement Experimental Results Conclusions

UncapacitatedFacility Location Problem

c10,8

f8

Nji ijijNi ii xcyf,

Njiyx

Njixy

Njx

iij

iji

Ni ij

,,0,

,,

,1..ts

Min

LP-relaxation

Nj j

Nji

Nif

Njic

ijj

iNj ij

ijijj

,,0,

,

,,

..ts

Max

Dual program

Primal-Dual Schema

Start with (at time 0) primal solution x, y=0: no facilities open, no clients

connected dual solution α, β=0: zero budget for each client

Iteration Uniformly increase budgets (αj) of clients Allocate the budgets towards facility opening cost

s and connection costs

Primal-Dual Schema (Cont.)

for unconnected client j and unpaid for facility i Client j starts paying facility i βij starts growing

for facility i Facility i is paid for Each unconnected client j paying facility i is conne

cted, and client j stops paying any facility for unconnected client j and paid for fa

cility i Client j is connected and stops paying any facility

NifiNj ij ,Njic ijijj ,, Nji0ijj ,,,

ijj c

iNj ij f

ijj c

Example:Facility Location Algorithm

t = c8,9 = 20

t = c0,5 = 37

t = 0

t = 72

t = c0,7 = 77

t = 110

t = c8,10 = 122

ijiji EucDistc200f ,

Outlier Detection Problem

Input A set N of n nodes A number nr relatively small A distance L relatively large

Output All outlier nodes r r is among a set , The distance between any node and

is at least L

NN r rr nN

rNj

rNNj \

Algorithm

Let user specify an upper limit l on the total number of outliers

Instead of terminating the Prima-Dual stage after all clients are connected

Terminate the stage when the number of unconnected clients becomes no more than l

The unconnected clients are detected as outliers

Outlier Detectionvs. Parameter Setting

Parameter Settingfor Outlier detection

The facility cost fi should neither too large nor to small

For the inputs of the problem A set N of n nodes A number nr A distance L

Let , where is a small constant

0cLnf ri 0c0

Outline

Introduction Motivation Outlier Detection Incremental Placement Experimental Results Conclusions

Incremental Placement

To eliminate outliers Improve timing on the critical paths containing the

outliers Find these paths

Force voltage reduction on the outliers, update all slacks

Find all paths with negative slacks

Example:Eliminating Outliers

Outlier

Setting Placement Constraints

Adding additional net weights Let the pure timing driven placer pay more attentio

n on those nets Increasing cell delays

Select the outlier cells and the low-Vdd cells on the selected paths

For those selected cells, use their delays under low-Vdd in timing analysis

For the rest of cells, use the delays under high-Vdd

Example:Eliminating Outliers (contd.)

C1C3

C5

Outlier

C1C3

C5

Timing Analysis

Force Voltage Reduction

Outline

Introduction Motivation Outlier Detection Incremental Placement Experimental Results Conclusions

Experimental Results:Snap Shots

Low High

After7 voltage islands & 7.85 unit power

Before7 voltage islands & 9.37 unit power

Experimental Results:Outlier Detection

314 nodes, 8 outliers 1182 nodes, 8 outliers

Experimental Results

Comparison on Different Design

Running Time

Outline

Introduction Motivation Outlier Detection Incremental Placement Experimental Results Conclusions

Conclusions

They proposed an incremental flow with consideration of outliers to improve voltage assignment

Reduce the number of Voltage Islands