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Pattern routing Outline Predictable Routing
College of St. Joseph, US has reference to this Academic Journal, Predictable Routing Ryan Kastner, Elaheh Borzorgzadeh, in addition to Majid Sarrafzadeh ER Group Dept. of Computer Science UCLA Los Angeles, CA NuCAD Group Dept. of Electrical & Computer Engineering Northwestern University Evanston, IL Outline Pattern Routing Predictable Routing Experiments Smallest First Pattern Routing x-density Pattern Routing Wire length in addition to Run time Conclusion Pattern routing Use simple patterns so that 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 There are many other types of patterns We focus exclusively on L-shaped patterns
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Why use patterns? Faster routing Number of bin edges searched Maze Routing O(|E|) = all edges in Grid Graph = 275 bin edges Why use patterns? Small wire delay The route has minimum wire length Only one via introduced Minimal interconnect resistance in addition to capacitance Fewer number vias ? fewer detailed routing constraints Downside ? may degrade quality of routing solution Maze routing will consider every possible path L-shape routing considers 2 paths 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
Predictable Routing Number of patterns should be small Fewer patterns ? higher route predictability 50% chance in consideration of upper-L 50% chance in consideration of lower-L Experiments 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 Benchmark circuit information 5 MCNC standard-cell benchmark circuits Unfortunately, benchmarks provide no criticality data Need so that find heuristics in consideration of pattern routing small in addition to large nets
Criticality Heuristics – SFPR Smallest-First Pattern Routing (SFPR) Sort two-terminal nets based on BB (smallest so that largest) Pattern route x% of the smallest nets Maze route remaining nets Rip up in addition to reroute phase Do not consider the pattern routed nets SFPR focuses on pattern routing ?small? critical nets SFPR results Results are the total overflow (measure of congestion) Smaller is better (min overflow = min congestion) 70% of the ?small? nets can be pattern routed Pattern routing long nets Pattern routing longest nets first leads so that 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
x-Density Routing Formal definition ? decision problem Given an integer x, a set of two-terminal nets N in addition to a grid graph G(V,E) Does there exist a single bend routing in consideration of every net ni in N 1 < i < |N| such occupancy(e) ? x in consideration of every edge e ? E? Polynomial time solvable - O(|N| log |N|) time Finding the maximum subset of nets is much harder x-Density Pattern Route Heuristic (x-DPR) The x-DPR heuristic Find a set of x-Density routable nets Set should be x-Density alongside ?large? nets Pattern route the x-Density nets Maze route the remaining nets Rip in addition to reroute nets Do not consider the x-Density nets x-DPR results x-density (x ? 3) routing does not degrade routing solution Allows ?large? nets so that be routed Wire length in addition to Run time Wire length Pattern routed (critical) nets guaranteed so that have minimum wire length Overall wire length varies over benchmarks: +5% so that ?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 in addition to reroute phase may take longer so that find a better solution Running time trends SFPR Small circuits ? 20% worse alongside pattern routing SFPR Large circuits ? overall runtime similar (ñ 5%) or better x-density ? overall runtime similar (ñ 5%) Sometimes there is small degradation in wire length in addition to run time Conclusions We showed that you can pattern route up so that 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 in addition to wire planning
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