Accurate clock mesh sizing via sequential quadratic programming
This presentation is the property of its rightful owner.
Sponsored Links
1 / 26

Accurate Clock Mesh Sizing via Sequential Quadratic Programming PowerPoint PPT Presentation


  • 74 Views
  • Uploaded on
  • Presentation posted in: General

Accurate Clock Mesh Sizing via Sequential Quadratic Programming. Venkata Rajesh Mekala, Yifang Liu, Xiaoji Ye, Jiang Hu, Peng Li Department of ECE, Texas A&M University From ISPD’10. Systematic way - Sequential Quadratic Programming (SQP).

Download Presentation

Accurate Clock Mesh Sizing via Sequential Quadratic Programming

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Accurate clock mesh sizing via sequential quadratic programming

Accurate Clock Mesh Sizing via Sequential Quadratic Programming

Venkata Rajesh Mekala, Yifang Liu, Xiaoji Ye, Jiang Hu, Peng Li

Department of ECE, Texas A&M University

From ISPD’10


Systematic way sequential quadratic programming sqp

Systematic way - Sequential Quadratic Programming (SQP)

  • One of the most popular and robust algorithms for nonlinear continuous optimization

  • Mathematical theory based


Definitions about sqp

Definitions about SQP

  • Original problem

  • Lagrangian function

  • Jacobian


Optimality condition in one dimensional problem

Optimality condition in one dimensional problem

  • Optimal solution will exist in f’(x)=0 and f’’(x)>0


Optimality condition in sqp

Optimality condition in SQP

  • Karush-Kuhn-Tucker (KKT) conditions

  • Second order optimality condition

    is positive definite

    H means Hessian matrix


How to solve

How to solve?

  • In one dimensional problem

    • Newton’s method

  • In SQP


Result in qp form

Result in QP form


Outline

Outline

  • Introduction

  • Problem formulation

  • SQP for clock network sizing

  • Sensitivity analysis

  • Algorithm overview

  • Experimental results and Conclusions


Introduction

Introduction

  • Why clock mesh?

    • Uniform, low skew clock distribution

    • Better tolerance to On-Chip Variation (OCV)


Introduction cont

Introduction (cont.)

  • Disadvantages

    • Larger area (metal resources)

    • Higher power consumption

    • Sophisticated delay model is hard to analyze highly coupled structure


Previous works

Previous works

  • Using clock tree networks

    • Moment-based sensitivity analysis

      • restricted in clock tree

    • SQP under a power budget

      • Inaccurate

    • Divide and Conquer using SLP

      • applies only to clock tree


Previous works cont

Previous works (cont.)

  • Using non-clock tree networks

    • Crosslinks

      • difficult to extend to a mesh

    • Clock mesh


Our contributions

Our Contributions

  • Adopt a current-source based gate modeling approach to speed up the accurate analysis

  • Develop efficient adjoint sensitivity analysis to provide desirable info

  • First clock mesh sizing using systematic solution search and accurate delay model


Problem formulation

Problem formulation

  • Given a CDN consisting of a clock mesh driven by a clock tree

  • Minimize power consumption while meeting skew constraints by sizing the mesh

  • Power dissipation is approximated by mesh area

  • Skew is presented in a delay variance form


Formulae and terms

Formulae and terms

  • I: set of interconnect in the mesh

  • xi: size of element i

  • wi: area of ith element

  • S: set of sinks

  • Dj: propaagation delay from clock tree root to sink j


Model of a clock mesh

π model of a clock mesh


Sqp for clock network sizing

SQP for clock network sizing

  • Use QP solver to solve


Quasi newton approximation of hessian

Quasi-Newton approximation of Hessian

  • Using BFGS method

    where


Sensitivity analysis

Sensitivity analysis


Linearize the original circuit

Linearize the original circuit

  • Using linearized compact gate model

  • Kirchhoff CL

    and VL


Algorithm overview

Algorithm overview


Experimental results

Experimental results

  • The benchmarks are taken from ISPD and ISCAS. The BPTM 65-nm technology transistor models have been used


Table of results

Table of results


Area skew tradeoff by varying delta

Area-skew tradeoff by varying delta


Runtime of cmssqp

Runtime of CMSSQP


Conclusions

Conclusions

  • Can easily extend for sizing buffers and mesh element simultaneously

  • Achieve up to 33% area reduction

  • Robust in dealing with any complex clock mesh network


  • Login