NEMO: A New I mplicit NEMO: A New I mplicit Connection Graph- -Based Based Gridless Gridless Connection Graph Router with Multi- -Layer Planes Layer Planes Router with Multi and Pseudo- -Tile Propagation Tile Propagation and Pseudo Hsin-Yu Chen Yih- -Lang Li Lang Li Zhi Zhi- -Da Da Lin Lin Yih Computer Science Department, ent, Computer Science Departm Faraday Tech. Corp. National Chiao- -Tung University (NCTU) Tung University (NCTU) Faraday Tech. Corp. National Chiao 1 1 ISPD 2006 San Jose 2006/4/13 2006/4/13
Outline Outline Introduction Introduction New Implicit Connection Graph-Based Router (NEMO) General-Purpose Routing Experimental Results Conclusion 2 2 ISPD 2006 San Jose 2006/4/13 2006/4/13
Why Gridless Gridless Routing ? Routing ? Why � Variable Variable- -width and variable width and variable- -space routing space routing � becomes inevitable for modern designs becomes inevitable for modern designs – Wide space and fat wire for crosstalk and delay – Wide space and fat wire for crosstalk and delay optimization optimization � Gridless Gridless routers are more flexible for variable routers are more flexible for variable- -rule rule � routing than grid- -based routers based routers routing than grid 3 3 ISPD 2006 San Jose 2006/4/13 2006/4/13
Basic Concept Concept Basic rule Half width rule Half width separation rule separation rule s w 2 × s + w Nonzero-width Model Zero-width Model 4 4 ISPD 2006 San Jose 2006/4/13 2006/4/13
I mplicit Connection I mplicit Connection Graph- -Based Router Based Router Graph I2 I1 I3 R1 R2 R3 R4 11 A I1 ...…………………… Four slices B I2 I3 R1 R2 R3 R4 B C D 2 A C D 1 0 0 1 2 ………………………………….. 16 Fast routing graph construction Efficient query data structure • J. Cong et al., “An Implicit connection graph maze (Slit tree + Interval Tree) Routing Algorithm for ECO routing,” in ISPD99 5 5 ISPD 2006 San Jose 2006/4/13 2006/4/13
I mplicit Connection I mplicit Connection Routing Graph Routing Graph 6 6 ISPD 2006 San Jose 2006/4/13 2006/4/13
Contribution of This Work Contribution of This Work � We propose a new implicit connection We propose a new implicit connection � graph- -based router with pseudo based router with pseudo- -tile tile graph extraction and propagation to extraction and propagation to – reduce the time required for query – reduce the time required for query operations operations – speed up path searching. – speed up path searching. 7 7 ISPD 2006 San Jose 2006/4/13 2006/4/13
Outline Outline Introduction New Implicit Connection Graph-Based New Implicit Connection Graph-Based Router (NEMO) Router (NEMO) General-Purpose Routing Experimental Results Conclusion 8 8 ISPD 2006 San Jose 2006/4/13 2006/4/13
Features of NEMO Features of NEMO � Multi Multi- -Plane Routing Graph Plane Routing Graph � � Tile plane but not grid plane Tile plane but not grid plane � � Non Non- -zero width wire model zero width wire model � � Pseudo Maximum (horizontally or Pseudo Maximum (horizontally or � vertically) Stripped Tile (PMT) Extraction vertically) Stripped Tile (PMT) Extraction and Propagation and Propagation � Pseudo Blockage Insertion & Gridline Pseudo Blockage Insertion & Gridline � Reduction Reduction 9 9 ISPD 2006 San Jose 2006/4/13 2006/4/13
Multi- -Plane Routing Graph Plane Routing Graph Multi : L 1 : L 2 : L 3 An 3-layer routing example L 1 L 2 L 3 10 10 ISPD 2006 San Jose 2006/4/13 2006/4/13
Why Tile, Not Grid Why Tile, Not Grid L2 Grids on adjacent Layers don’t align L1 L 1y (4) L 1y (4) L 1y (4) L 1y (4) L 1y (3) L 1y (3) L 1y (3) L 1y (3) L 1y (2) L 1y (2) L 1y (2) L 1y (2) L 1y (1) L 1y (1) L 1y (1) L 1y (1) L 1x (1) L 1x (1) L 1x (2) L 1x (2) L 1x (3) L 1x (3) L 1x L 1x (4) L 1x (1) L 1x (1) L 1x (2) L 1x (2) L 1x (3) L 1x (3) L 1x (4) L 1x (4) 11 11 ISPD 2006 San Jose 2006/4/13 2006/4/13
Non- -Zero Width Wire Model Zero Width Wire Model Non rule Half width separation rule W s W s 12 12 ISPD 2006 San Jose 2006/4/13 2006/4/13
Multi- -Layer Routing Layer Routing Multi Layer 1 L 1y (4) L 2y (4) T(1,1) T(2,1) CA 1x L 1x (1) L 1x (2) L 1x (3) L 1x (4) L 1y (3) L 2y (3) T(1,2) CA 2x L 2x (1) L 2x (2) L 2x (3) L 2x (4) L 1y (2) T(1,1) T(1,2) T(2,1) T(1,1) CA 1y L 1y (1) L 1y (2) L 1y (3) L 1y (4) L 2y (2) L 1y (1) CA 2y A L 1x (4) L 1x (1) L 1x (2) L 2y (1) L 2y (2) L 2y (3) L 2y (4) L 1x (3) L 2y (1) L 2x (1) L 2x (4) L 2x (2) L 2x (3) Layer 2: T(1,1), T(2,1), T(3,1) Layer 2 T(1,2), T(2,2), T(3,2) 13 13 ISPD 2006 San Jose 2006/4/13 2006/4/13
Path Search by PMT Path Search by PMT Maximum horizontally stripped B A T1 T2 14 14 ISPD 2006 San Jose 2006/4/13 2006/4/13
PMT Extraction – – Tile Query Tile Query PMT Extraction L L L R R R Point query : obstacle B L B R Three Cut lines three internal nodes L L L R R R A A C B LA LB LC 15 15 ISPD 2006 San Jose 2006/4/13 2006/4/13
16 16 – Merging Merging PMT Extraction – ISPD 2006 San Jose PMT Extraction 5 7 7 7 5 6 4 4 4 5 D P1 P3 P3 2 2 2 2 2 C P1 P1 P2 2006/4/13 2006/4/13 3 3 1 1 B P2 P2 P3 3 1 1 3 A Y X Z
Outline Outline Introduction New Implicit Connection Graph-Based Router (NEMO) General-purpose Routing General-purpose Routing Experimental Results Conclusion 17 17 ISPD 2006 San Jose 2006/4/13 2006/4/13
Routing Flow Routing Flow Decompose multi-terminal Decompose multi-terminal net routing into multiple net routing into multiple 2-pin net routing 2-pin net routing Perform congestion-driven Perform congestion-driven global routing global routing Complete point-to-point Complete point-to-point Rip up and Rerouting Rip up and Rerouting detailed routing detailed routing 18 18 ISPD 2006 San Jose 2006/4/13 2006/4/13
19 19 Pseudo Block I nsertion Pseudo Block I nsertion : blockage T T ISPD 2006 San Jose P A T H : global path S S B A G O L L 2006/4/13 2006/4/13
Gridline Reduction Gridline Reduction Active blockages Global path S S S S T T T T Idle blockages 20 20 ISPD 2006 San Jose 2006/4/13 2006/4/13
Outline Outline Introduction New Implicit Connection Graph-Based Router (NEMO) Full-Chip Routing Experimental Results Experimental Results Conclusion 21 21 ISPD 2006 San Jose 2006/4/13 2006/4/13
Experimental Results – – Experimental Results Point- -to to- -point Routing point Routing Point Table 1. Statistics of the design under the test Test Case Rectangles Chip Dimension Test Case Rectangles Chip Dimension x × × y (um ) y (um ) x Met2 Met3 Met2 Met3 D1 5,106 3,720 470.00 × × 455.00 455.00 D1 5,106 3,720 470.00 D2 1,649,866 1,018,221 7320.00 × × 7320.00 7320.00 D2 1,649,866 1,018,221 7320.00 Table 2. Point-to-point routing results for the circuit D1 Cong et al. ISPD99 NEMO Cong et al. ISPD99 NEMO µ m) µ m) WL ( µ WL ( µ #Via Time (s) #Via Time (s) SU WL ( m) #Via Time (s) WL ( m) #Via Time (s) SU TEST1 539.50 10 0.719 539.50 10 0.109 6.6 TEST1 539.50 10 0.719 539.50 10 0.109 6.6 TEST2 382.20 6 0.515 382.20 6 0.047 10.96 TEST2 382.20 6 0.515 382.20 6 0.047 10.96 TEST3 419.50 12 0.532 419.50 12 0.063 8.44 TEST3 419.50 12 0.532 419.50 12 0.063 8.44 TEST4 527.50 8 0.734 527.50 8 0.078 9.41 TEST4 527.50 8 0.734 527.50 8 0.078 9.41 TEST5 649.00 8 0.922 649.00 8 0.094 9.81 TEST5 649.00 8 0.922 649.00 8 0.094 9.81 9 22 22 ISPD 2006 San Jose 2006/4/13 2006/4/13
Experimental Results – – Experimental Results Point- -to to- -point Routing point Routing Point Table 3. Point-to-point routing results for the circuit D2 Cong et al. ISPD99 NEMO Cong et al. ISPD99 NEMO WL ( µ µ m) WL ( µ µ m) #Via Time (s) #Via Time (s) SU m) #Via Time (s) m) #Via Time (s) SU WL ( WL ( TEST1 4997.00 238 73 4997.00 238 5 14.6 TEST1 4997.00 238 73 4997.00 238 5 14.6 TEST2 9478.00 366 170 9478.00 366 38 4.47 TEST2 9478.00 366 170 9478.00 366 38 4.47 TEST3 8299.00 246 96 8299.00 246 6 16 TEST3 8299.00 246 96 8299.00 246 6 16 TEST4 TEST4 11794.00 11794.00 446 446 127 127 11794.00 11794.00 446 446 11 11 11.55 11.55 TEST5 12391.00 458 166 12375.00 490 25 6.64 TEST5 12391.00 458 166 12375.00 490 25 6.64 TEST6 TEST6 10212.00 10212.00 374 374 109 109 10212.00 10212.00 374 374 8 8 13.63 13.63 TEST7 TEST7 11538.00 11538.00 410 410 134 134 11538.00 11538.00 410 410 11 11 12.18 12.18 TEST8 TEST8 15413.00 15413.00 180 180 329 329 15413.00 15413.00 180 180 72 72 4.57 4.57 10 23 23 ISPD 2006 San Jose 2006/4/13 2006/4/13
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