a simplr method for routability-driven placement

International Conference on CAD (ICCAD) 2011 1

A SimPLR Method forRoutability-driven Placement

Myung-Chul Kim†, Jin Hu†, Dong-Jin Lee and Igor L. Markov

Dept. of Computer Science and Engineering (CSE)

Dept. of Electrical Engineering and Computer Science (EECS)University of Michigan

†equal contribution


Goal of placement and routing: produce a legal, routable and high-quality solution No overlapping objects No (or very few) violations Small interconnect length

Placement and Routing Objectives

Functionality

Performance (timing, yield, power)

HPWL-drivenPlacement

optimize: half-perimeter WL

subject to: no cell overlaps

optimize: routed WL

subject to: no violations?

Routing


Routability-driven Placement Issue: Routability becoming harder due to technology advances

Routing blockages Increased number of metal layers layer-route requirements

Issue: Placer can harm routability; low HPWL regions can be hard to route

HPWL-drivenPlacement



optimize: routed WL

subject to: no violations?

Routing


Routability-driven Placement Issue: Routability becoming harder due to technology advances

Routing blockages Increased number of metal layers layer-route requirements

Issue: Placer can harm routability; low HPWL regions can be hard to route

routability information is given to placer



optimize: routed WL

subject to: no violations

RoutingRoutability-driven

Placement

consider: routability


Standard Placement FlowPlacement Instance

Converge?

Global Placement Iteration(s)

Legalization

Detailed Placement

yes

no


Routability-driven Placement FlowPlacement Instance

Converge?

optional

Initial Global Placement


Legalization

Detailed PlacementCongestion-aware

yes

no

Routability components

Routability-driven

Congestion Estimation Must be scalable (speed) and accurate (quality)

Must know how to use routability information

Early routability prediction – ability for placer to respond early and often


Prior Work

Static Rent’s Rule, pin density

Probabilistic Probabilistic wire routing, wire density

Constructive 2-d A* routing, fast global router

Congestion Estimation Approaches

During Global Placement Cell bloating, growing/shrinking regions

After Global Placement Whitespace injection, linear programming

During Detailed Placement Congestion-based objective function

Congestion-driven Optimizations in Placement

Incorporate past ideas with new techniques in integrated framework

Give the placer advance, firsthand access to tentative routesand account for technology constraints


Lookahead Legalization (LAL)

Pseudonet Insertion

Linear System Solver (CG)

Converge?no

yes Global placement iteration

SimPLR FlowPlacement Instance

Converge?

Initial Global Placement


Congestion Estimation

Legalization

Detailed Placement

yes

no

Lookahead Routing (LAR)

Routability-driven Cell Bloating

Dynamically-adjusting Target Density

Routability components

Placer-specific components

Global Placer: Global Router:Detailed Placer:

SimPLBFG-RFastPlace-DP

Congestion-aware

Routability-driven

Initial Wirelength Optimization

from congestion estimation

Contributions


• Part 1: improve runtime without sacrificing accuracy• Part 2: routing congestion (per edge) to placer congestion (per bin)

Lookahead Routing (LAR)Purpose: provides accurate and fast routability information: interconnect length and congestion (based on actual routes) Compatibility: routing grid (3-d) versus placement grid (2-d)

H layer

V layerVIA

placement bin



MST construction and simplified RRR


BFG-R-based routing

Part 1

Convert to 2.5-d grid

usage and capacity of 2.5-d edges

3-d routing instance(with raw capacities)




Report congestion to global placement

placement bin

BFG-R-based routing

Part 2

Convert to 2.5-d grid

Convert to 2-d grid

congestion of binsusage and capacity of

2.5-d edges


3-d routing instance(with raw capacities)


LAR: Single 3-d Layer (No Blockages)

Layer l

• For every routing layer l, given wire width ww(l), wire spacing ws(l)


e

LAR: Single 3-d Layer (No Blockages)

Layer l

For all edges e, define:

• normalized capacity nCap(e) =

• For every routing layer l, given wire width ww(l), wire spacing ws(l)

• For every routing edge e, given edge capacity cap(e)

cap(e)ww(l)+ ws(l)


LAR: Single 3-d Layer (With Blockages)

For all edges e, define: • Free intervals (ranges) f(e) with no routing blockage


• For every routing edge e, given edge size s(e)• Blockages take up proportionate amount of capacity (based on s(e))

routing blockagefree interval f

cap(e)ww(l)+ ws(l)Σ

f

f(e)s(e)

s(e)


For all edges e, define: • Free intervals (ranges) f(e) where no routing blockage


LAR: Single 3-d Layer ExampleGiven: ww(l) = 2, wire spacing ws(l) = 2, cap(e) = 40, s(e) = 50

81225 50


f

f(e)s(e)




= 10nCap(A) =


81225

edge A5050

402 + 2

50


f

f(e)s(e)




= 10nCap(A) =


81225

edge A5050

402 + 2

50

= 0nCap(B) =0

5040

2 + 2edge B


f

f(e)s(e)




= 10nCap(A) =


81225

edge A5050

402 + 2

50

= 0nCap(B) =0

5040

2 + 2edge B

= 5nCap(C) =2550

402 + 2

edge C


f

f(e)s(e)




nCap(C) =

nCap(D) =

= 10nCap(A) =


81225

edge A5050

402 + 2

50

= 0nCap(B) =0

5040

2 + 2edge B

= 52550

402 + 2

edge C

edge D 1250

402 + 2

+ 850

402 + 2


f

f(e)s(e)

= 2.6 + 1.4 = 3


LAR: 3-d Grid to 2.5-d Grid

3-d Routing Grid 2.5-d Routing Grid




V1

Vk

V




H1

Hm

H


nCap(eV) = nCap(eV ) + … + nCap(eV )nCap(eV ) , … , nCap(eV )



eVk

eV1eV

1 k 1 k


nCap(eH ) , … , nCap(eH ) nCap(eH) = nCap(eH ) + … + nCap(eH )



eH m

eH 1eH

1 m1 m

nCap(eV) = nCap(eV ) + … + nCap(eV )nCap(eV ) , … , nCap(eV )1 k 1 k


nCap(eH ) , … , nCap(eH ) nCap(eH) = nCap(eH ) + … + nCap(eH )nUsage(eH) = 1 for every routed net in eH



1 m1 m

nCap(eV) = nCap(eV ) + … + nCap(eV )nUsage(eV) = 1 for every routed net in eV

nCap(eV ) , … , nCap(eV )1 k 1 k


BFG-R-based routing

After 2.5-d Grid Construction


LAR: 2.5-d Grid to 2-d Grid

Routing Grid Placement Grid




V

H P




nUsage(bottom)

nUsage(top)nCap(top)

nCap(bottom)

top

bottom




nUsage(bottom)

nUsage(top)nCap(top)

nCap(bottom)

top

bottom

left right nUsage(right)nUsage(left)

nCap(left)nCap(right)



C(g) = Usage(g)

Cap(g)

Congestion of gCap(g) = nCap(left) + nCap(right) + nCap(top) + nCap(bottom)

Usage(g) = max(nCap(left), nUsage(left)) + max(nCap(right), nUsage(right)) + max(nCap(top), nUsage(top)) + max(nCap(bottom), nUsage(bottom))

If at least one of the neighboring edges is congested, then the bin g is considered congested

left right

top

bottom

global placement bin g


For all cells c in congested bin g, cell bloating is based on: • cell properties: connectivity deg(c), size width(c) • progress: history* H(c), congestion C(g) *Number of times the cell has been in a congested bin

• routed solution properties:

• design usage

• difficulty to route

Routability-driven Cell BloatingPurpose: coercing cell locations and relieve local routing congestion

Σe

OF(e)

Σe

nCap(e)d =

relatively insensitive to quality

based on Lookahead Routing

OF(e) = max(0, nUsage(e) – nCap(e))

Σg

Usage(g)Cap(g)r =



α and β derived from numerical regressionsbut not benchmark specific tuning

Design(r,d) = max(0, α · r · d + β)Routing Solution-dependent Function

Incorporate routability properties in classical congestion-driven cell bloating formulation (e.g., CRISP) based on routed design vs. constant

max(width(c) + 1, 1 + Design(r,d) · H(c) · C(g) · deg(c))

For every (moveable) cell c in congested bin g, bloat by:



Unnecessarily high target density leads to better HPWL, but may also cause routing failures

Lower target density may increase the overall routed wirelength, which would lead to longer detours.

Dynamically-adjusting Target DensityPurpose: preserves overall solution quality (from cell bloating); encourages cells in uncongested areas to stay close

Trades off between routability and wirelength (quality)

Finding the best target density remains an open problem


Dynamically-adjusting Target DensityTarget density is based on: • design bounding box: area(D)• cells’ bounding box: moveable cells area(Cm), fixed cells area(Cf)• progress: constant φ increases when LAR reports an increase in WL

min(95%, )area(Cm)

area(D) – area(Cf)+ φ

For uncongested areas, cells do not spread as much

Target Density


Ex: Lookahead Legalization

Lookahead Legalization (LAL) regulates local cell density to meet the given target utilization.


Ex: Lookahead Routing

Lookahead Routing (LAR) estimates regions with routing congestion.


Ex: Routability-driven Cell Bloating

Cells in congested regions are bloated


Ex: LAL Without Target Density Control

Subsequent LAL regulates local cell density


Ex: LAL With Target Density Control

Target density control allows more packing in uncongested regions.


Progress of SimPL: SUPERBLUE12

0e+0

2e+8

4e+8

6e+8

8e+8

1e+9

0 10 20 30 40 500

2

4

6

8

10

12

14

16

18

HW

PL

Iteration Number

Scal

ed O

verfl

ow p

er B

in

Legal solution

Roughly Legalized Solution

Quadratic Placement


Progress of SimPLR: SUPERBLUE12

0e+0

2e+8

4e+8

6e+8

8e+8

1e+9

0 10 20 30 40 500

2

4

6

8

10

12

14

16

18

HW

PL

Iteration Number

Scal

ed O

verfl

ow p

er B

in

Legal solution

Roughly Legalized Solution

Quadratic Placement

Lookahead Routing


Congestion-aware Detailed PlacementPurpose: preserves (and improves) routability and quality of placement

Follows traditional HPWL-driven DP, but does not hurt routability

Traditional WL-driven detailed placement may pack cells in areas that are difficult to route(congestion-unaware)

Prohibit moves that harm routability Changing objective function could harm HPWL Maintains routability moves cells out of congested regions


Congestion-aware Detailed PlacementWithin FastPlace-DP, modify cell swapping to be congestion-awareFor every (moveable) cell c, define:• optimal region R(c)• benefit of swapping with other cell c’ in R(c) bswap

• benefit of moving (swapping) with empty space in R(c) bmove


Congestion-aware Detailed Placement

Condition Operation

&& bswap ≥ bmove ?uncongested(c) uncongested(c’)

Within FastPlace-DP, modify cell swapping to be congestion-awareFor every (moveable) cell c, define:• optimal region R(c)• benefit of swapping with other cell c’ in R(c) bswap


swap(c, c’, bswap > 0) :move(c, R(c), bmove > 0)


congested(c) uncongested(c’)


Condition Operation


&&




move(c, R(c))




Condition Operation

&& bswap ≥ bmove ? swap(c, c’, bswap > 0) :move(c, R(c), bmove > 0)

move(c, R(c))

uncongested(c) uncongested(c’)

&&

uncongested(c) congested(c’)&& swap(c, c’, deg(c) < deg(c’))

For every (moveable) cell c, define:• optimal region R(c)• benefit of swapping with other cell c’ in R(c) bswap


Within FastPlace-DP, modify cell swapping to be congestion-aware




Condition Operation


&&

uncongested(c) congested(c’)&& swap(c, c’, deg(c) < deg(c’))

congested(c’)&&congested(c) C(c) > C(c’) ? swap(c, c’, deg(c) > deg(c’)) :swap(c, c’, deg(c) < deg(c’))




move(c, R(c))


Empirical Results: SimPL, Contest

HPWL-driven placement: Average of 3.81x better overflow (7 of 8 best)

Routability-driven placement: Average of 2.04x better overflow (8 of 8 best)at the cost of 4% routed wirelength

with 1% better routed wirelength


Empirical Total OF Results: ICCAD 2011Benchmark Ripple NTUPlace4* SimPLR

SUPERBLUE1 90 3222 0

SUPERBLUE2 730544 670480 740050

SUPERBLUE4 75540 85062 18444

SUPERBLUE5 128054 69820 121894

SUPERBLUE10 646300 583336 567780

SUPERBLUE12 547954 705012 181350

SUPERBLUE15 60222 42362 49286

SUPERBLUE18 38176 9996 21020

Total 2226880 2166390 1699824

1.31x 1.27x 1.0x*NTUPlace use 8 processors for cGrip,

whereas Ripple and SimPLR use 4


Empirical Results: Ca-DP

Average of 18% better overflow (7 of 8 best)at the cost of 1% in routed wirelength


Conclusions New routability-driven placement: SimPLR

Based on fast, effective SimPL placer (ICCAD 2010) Congestion maps based on actual routes (not

probabilistic);this is not too slow

Faithful representation of 3-d routes by 2-d congest. maps Accurate formulas for cell expansion based on congestion Preserve solution and ensure stability of global placement

Effective at improving routability Very strong results on the ISPD 2011 Routability-driven

Placement benchmarks


Thank you!

Any Questions?


Backup Slides


Empirical Results: Extended timeouts


Final Product: SUPERBLUE15

ISPD 2011 Routability-driven Contest (Best)

SimPLR


Conclusions New routability-driven placement: SimPLR

Integration of global routing into global placement Congestion-aware detailed placement

Effective at improving routability Best results on the ISPD 2011 Routability-driven

Placement benchmarks

Open problem: target density adjustment

a simplr method for routability-driven placement

Documents

cad iccad

ofteninternational conference

routed wlsubject

halfperimeter wlsubject

routability low hpwl

goal of placement

placer advance

jin hu