predictable routing

ERER UCLAUCLA

ICCAD: November 5, 2000

Predictable RoutingPredictable RoutingPredictable RoutingPredictable Routing

Ryan Kastner, Elaheh Borzorgzadeh, and Majid Sarrafzadeh

Ryan Kastner, Elaheh Borzorgzadeh, and Majid Sarrafzadeh

ER Group

Dept. of Computer Science

UCLA

Los Angeles, CA

ER Group

Dept. of Computer Science

UCLA

Los Angeles, CA

NuCAD Group

Dept. of Electrical & Computer Engineering

Northwestern University

Evanston, IL

NuCAD Group

Dept. of Electrical & Computer Engineering

Northwestern University

Evanston, IL

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OutlineOutlineOutlineOutline

Pattern Routing Predictable Routing Experiments

Smallest First Pattern Routing x-density Pattern Routing Wire length and Run time

Conclusion

Pattern Routing Predictable Routing Experiments

Smallest First Pattern Routing x-density Pattern Routing Wire length and Run time

Conclusion

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Pattern routingPattern routingPattern routingPattern routing

Use simple patterns to connect the terminals of a net Simplest pattern is single bend routing

Given a two-terminal net, single bend routes are the two distinct 1-bend routes

Sometimes called L-shaped routing

Use simple patterns to connect the terminals of a net Simplest pattern is single bend routing

Given a two-terminal net, single bend routes are the two distinct 1-bend routes

Sometimes called L-shaped routing

Upper-L RoutesLower-L Routes

There are many other types of patterns

We focus exclusively on L-shaped patternsWe focus exclusively on L-shaped patterns

There are many other types of patterns

We focus exclusively on L-shaped patternsWe focus exclusively on L-shaped patterns

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Maze Routing O(|E|) = all edges in Grid Graph = 275 bin edges Maze Routing O(|E|) = all edges in Grid Graph = 275 bin edges Pattern Routing O(|A|) = edges on the bounding box = 20 bin edges Pattern Routing O(|A|) = edges on the bounding box = 20 bin edges

Why use patterns?Why use patterns?Why use patterns?Why use patterns?

Faster routing Number of bin edges searched

Faster routing Number of bin edges searched

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Why use patterns?Why use patterns?Why use patterns?Why use patterns?

Small wire delay The route has minimum wire length Only one via introduced

Minimal interconnect resistance and capacitance Fewer number vias fewer detailed routing constraints

Small wire delay The route has minimum wire length Only one via introduced

Minimal interconnect resistance and capacitance Fewer number vias fewer detailed routing constraints

One viaOne viaMinimum lengthMinimum length

Downside – may degrade quality of routing solution Maze routing will consider every possible path L-shape routing considers 2 paths

Downside – may degrade quality of routing solution Maze routing will consider every possible path L-shape routing considers 2 paths

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What is Predictable Routing?What is Predictable Routing?What is Predictable Routing?What is Predictable Routing?

Definition: Pattern route a subset of critical nets Definition: Pattern route a subset of critical nets

Critical Nets – pattern route

Non-critical Nets – maze route

Benefits Wire planning - Organizes routing

Important routing metrics more accurately modeled a priori

Congestion

Wire length

Benefits Wire planning - Organizes routing

Important routing metrics more accurately modeled a priori

Congestion

Wire length Allows early, accurate buffer insertion and wire sizing Allows early, accurate buffer insertion and wire sizing

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Predictable RoutingPredictable RoutingPredictable RoutingPredictable Routing

Number of patterns should be small Fewer patterns higher route predictability

Number of patterns should be small Fewer patterns higher route predictability

50% chance

for upper-L

50% chance

for lower-L

Net Terminals

Steiner Point

Two-terminal Net

We focus on two-terminal nets Majority of nets are two terminal Multi-terminal nets two-terminal nets using any

Steiner Tree algorithm

We focus on two-terminal nets Majority of nets are two terminal Multi-terminal nets two-terminal nets using any

Steiner Tree algorithm

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ExperimentsExperimentsExperimentsExperiments

Focus on pattern routing “critical” nets Criticality label by high level CAD tools Criticality increasingly dependent on wire length

Goal: Show that you can pattern route critical nets without degrading the routing solution quality We focus on routability Wire length, run time considered as secondary

factors

Focus on pattern routing “critical” nets Criticality label by high level CAD tools Criticality increasingly dependent on wire length

Goal: Show that you can pattern route critical nets without degrading the routing solution quality We focus on routability Wire length, run time considered as secondary

factors

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Benchmark circuit informationBenchmark circuit informationBenchmark circuit informationBenchmark circuit information

Data file Num Cells Num Nets Num Pins Global Binsprimary1 833 1156 3303 8 x 16primary1.2 833 1156 3303 16 x 16primary2 3014 3671 12914 8 x 16primary2.2 3014 3671 12914 32 x 32avqs 21584 30038 84081 30 x 80avqs.2 21584 30038 84081 80 x 80biomed 6417 7052 22253 20 x 40biomed.2 6417 7052 22253 40 x 40struct 1888 1920 5407 20 x 16

5 MCNC standard-cell benchmark circuits Unfortunately, benchmarks provide no criticality data

5 MCNC standard-cell benchmark circuits Unfortunately, benchmarks provide no criticality data

Need to find heuristics for pattern routing small and large netsNeed to find heuristics for pattern routing small and large nets

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Criticality Heuristics - SFPRCriticality Heuristics - SFPRCriticality Heuristics - SFPRCriticality Heuristics - SFPR

Smallest-First Pattern Routing (SFPR)1. Sort two-terminal nets based on BB (smallest

to largest)2. Pattern route x% of the smallest nets3. Maze route remaining nets4. Rip up and reroute phase

Do not consider the pattern routed nets

SFPR focuses on pattern routing “small” critical nets

Smallest-First Pattern Routing (SFPR)1. Sort two-terminal nets based on BB (smallest

to largest)2. Pattern route x% of the smallest nets3. Maze route remaining nets4. Rip up and reroute phase

Do not consider the pattern routed nets

SFPR focuses on pattern routing “small” critical nets

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SFPR resultsSFPR resultsSFPR resultsSFPR results

Data file 0% 50% 60% 70% 80% 90%primary1 622 -8 -13 -1 -7 -2primary1.2 379 -3 -3 -3 1 -1primary2 1370 -2 -10 -11 -2 18primary2.2 665 0 -1 21 21 47avqs 3149 -109 -25 22 -53 146avqs.2 401 -9 3 -38 61 6biomed 2994 -9 14 -89 -29 -43biomed.2 15 0 0 -2 0 1struct 769 -7 -17 -13 14 89total 10364 -147 -52 -114 6 261

Percentage of pattern routed nets

Base Overflow Overflow with x% pattern routed - Base Overflow

Results are the total overflow (measure of congestion) Smaller is better (min overflow = min congestion)

70% of the “small” nets can be pattern routed

Results are the total overflow (measure of congestion) Smaller is better (min overflow = min congestion)

70% of the “small” nets can be pattern routed

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Pattern routing long netsPattern routing long netsPattern routing long netsPattern routing long nets

Pattern routing longest nets first leads to large degradation in quality of routing solution

Idea: choose long nets that are evenly distributed across the chip

x-Density routing Every edge of the grid graph has at most x nets crossing it

Pattern routing longest nets first leads to large degradation in quality of routing solution

Idea: choose long nets that are evenly distributed across the chip

x-Density routing Every edge of the grid graph has at most x nets crossing it

Example of a 1-density routing

Example of a 1-density routing

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xx-Density Routing-Density Routingxx-Density Routing-Density Routing

Formal definition – decision problem Given an integer x, a set of two-terminal nets N and a

grid graph G(V,E) Does there exist a single bend routing for every net ni

in N

1 < i < |N| such occupancy(e) x for every edge e E?

Polynomial time solvable - O(|N| log |N|) time Finding the maximum subset of nets is much

harder

Formal definition – decision problem Given an integer x, a set of two-terminal nets N and a

grid graph G(V,E) Does there exist a single bend routing for every net ni

in N

1 < i < |N| such occupancy(e) x for every edge e E?

Polynomial time solvable - O(|N| log |N|) time Finding the maximum subset of nets is much

harder

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xx-Density Pattern Route Heuristic -Density Pattern Route Heuristic ((xx-DPR)-DPR)xx-Density Pattern Route Heuristic -Density Pattern Route Heuristic ((xx-DPR)-DPR)

The x-DPR heuristic1. Find a set of x-Density routable nets

Set should be x-Density with “large” nets

2. Pattern route the x-Density nets

3. Maze route the remaining nets

4. Rip and reroute nets Do not consider the x-Density nets

The x-DPR heuristic1. Find a set of x-Density routable nets

Set should be x-Density with “large” nets

2. Pattern route the x-Density nets

3. Maze route the remaining nets

4. Rip and reroute nets Do not consider the x-Density nets

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xx-DPR results-DPR resultsxx-DPR results-DPR resultsData file base 1-density 2-density 3-density 4-density 5-densityprimary1 622 0 -10 -4 -5 7primary1.2 379 -3 4 9 22 39primary2 1321 0 4 6 3 5primary2.2 665 -3 32 30 11 42avqs 3149 -13 -20 -121 6 20avqs.2 401 22 3 -23 7 82biomed 4837 -5 -41 -52 18 -7biomed.2 47 -6 2 -4 11 6struct 769 -4 4 24 38 56total 12190 -12 -22 -135 121 250

x-density (x 3) routing does not degrade routing solution

Allows “large” nets to be routed

x-density (x 3) routing does not degrade routing solution

Allows “large” nets to be routed

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Wire length and Run timeWire length and Run timeWire length and Run timeWire length and Run time

Wire length Pattern routed (critical) nets guaranteed to have minimum wire

length Overall wire length varies over benchmarks: +5% to –10%

Run time Single Net: Pattern routing faster (lower theoretical upper

bound) Overall global routing

Pattern routing nets adds restrictions small solution space Rip up and reroute phase may take longer to find a better solution

Running time trends SFPR Small circuits – 20% worse with pattern routing SFPR Large circuits – overall runtime similar (± 5%) or better x-density – overall runtime similar (± 5%)

Wire length Pattern routed (critical) nets guaranteed to have minimum wire

length Overall wire length varies over benchmarks: +5% to –10%

Run time Single Net: Pattern routing faster (lower theoretical upper

bound) Overall global routing

Pattern routing nets adds restrictions small solution space Rip up and reroute phase may take longer to find a better solution

Running time trends SFPR Small circuits – 20% worse with pattern routing SFPR Large circuits – overall runtime similar (± 5%) or better x-density – overall runtime similar (± 5%)

Sometimes there is small degradation in wire length and run time

Sometimes there is small degradation in wire length and run time

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ConclusionsConclusionsConclusionsConclusions

We showed that you can pattern route up to 70% of small nets

We showed that you can pattern route large nets using x-density routing

We showed that pattern routing has many benefits Better prediction of routing metrics Pattern routed nets have small interconnect delay Allows early accurate buffer insertion, wire sizing and wire

planning

We showed that you can pattern route up to 70% of small nets

We showed that you can pattern route large nets using x-density routing

We showed that pattern routing has many benefits Better prediction of routing metrics Pattern routed nets have small interconnect delay Allows early accurate buffer insertion, wire sizing and wire

planning

predictable routing

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