1. ER UCLA UCLA ICCAD: November 5, 2000 Predictable Routing 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

2. ER UCLA UCLA ICCAD: November 5, 2000OutlineOutline 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

3. ER UCLA UCLA ICCAD: November 5, 2000 Pattern 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 Routes Lower-L Routes There are many other types of patterns We focus exclusively on L-shaped patterns There are many other types of patterns We focus exclusively on L-shaped patterns

4. ER UCLA UCLA ICCAD: November 5, 2000 Maze Routing O(|E|) = all edges in Grid Graph = 275 bin edges Pattern Routing O(|A|) = edges on the bounding box = 20 bin edges Why use patterns? Faster routing Number of bin edges searched Faster routing Number of bin edges searched

5. ER UCLA UCLA ICCAD: November 5, 2000 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 via Minimum 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

6. ER UCLA UCLA ICCAD: November 5, 2000 What is Predictable Routing? 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

7. ER UCLA UCLA ICCAD: November 5, 2000 Predictable 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

8. ER UCLA UCLA ICCAD: November 5, 2000ExperimentsExperiments 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

9. ER UCLA UCLA ICCAD: November 5, 2000 Benchmark circuit information 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 nets

10. ER UCLA UCLA ICCAD: November 5, 2000 Criticality 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 nets 3. Maze route remaining nets 4. 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 nets 3. Maze route remaining nets 4. Rip up and reroute phase Do not consider the pattern routed nets SFPR focuses on pattern routing “small” critical nets

11. ER UCLA UCLA ICCAD: November 5, 2000 SFPR results 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

12. ER UCLA UCLA ICCAD: November 5, 2000 Pattern 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

13. ER UCLA UCLA ICCAD: November 5, 2000 x-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 n i 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 n i 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

14. ER UCLA UCLA ICCAD: November 5, 2000 x-Density Pattern Route Heuristic (x-DPR) The x-DPR heuristic 1. 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 heuristic 1. 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

15. ER UCLA UCLA ICCAD: November 5, 2000 x-DPR results 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

16. ER UCLA UCLA ICCAD: November 5, 2000 Wire 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

17. ER UCLA UCLA ICCAD: November 5, 2000ConclusionsConclusions 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