High-Performance Global Routing with Fast Overflow Reduction Huang-Yu Chen, Chin-Hsiung Hsu, and Yao-Wen Chang National Taiwan University Taiwan 2 Outline Introduction Preliminary Routing flow of NTUgr Multiple forbidden-regions expansion Critical nets rerouting selection Look-ahead historical cost increment Experimental results Conclusions 3 Outline Introduction Preliminary Routing flow of NTUgr Multiple forbidden-regions expansion Critical nets rerouting selection Look-ahead historical cost increment Experimental results Conclusions 4 Global Routing Problem Global routing Global routing is the first stage to tackle modern VLSI routing challenges Connect pins of each net in the global routing graph: global tile node A global tile node represents a tile (global cell) global edge A global edge models the relationship between adjacent tiles Overflow of a global edge: the amount of routing demand that exceeds the given capacity Tile Tile boundary Global tile node Global edge 5 Objectives of Global Routing Major objectives: minimize the total overflow minimize the maximum overflow Minor objectives: minimize the total wirelength minimize running time 6 Outline Introduction Preliminary Routing flow of NTUgr Multiple forbidden-regions expansion Critical nets rerouting selection Look-ahead historical cost increment Experimental results Conclusions 7 State-of-the-art Global Routers Archer [ICCAD07] BoxRouter [ICCAD07] FastRoute [ICCAD06, ASPDAC07, TCAD08] FGR [ICCAD07] NTHU-Route [ASPDAC08, ICCAD08] INR Those routers adopt INR (Iteratively Negotiation-based Rip-up/rerouting) to effectively reduce overflows 8 INR (Iteratively Negotiation-based Rip-up/rerouting) Proposed in PathFinder [McMurchie and Ebeling, FPGA95] Spreads the congested wires iteratively At the (i)-th iteration, the cost of a global edge e: b e : base cost of using e, p e : # of nets passing e, h e (i) : historical cost on e, INR may get stuck as the number of iterations increases [Ozdal, ICCAD07] [Gao et al., ASPDAC08] 9 Contributions NTUgr NTUgr --- a high-quality global router The 2 nd place of ISPD 2008 Global Routing Contest 3D Benchmark 3D 2D capacity mapping Enhanced 2D routing 2D 3D layer assignment 3D routing result Prerouting Initial Routing Iterative Forbidden-region Rip-up/rerouting (IFR) 10 Outline Introduction Preliminary Routing flow of NTUgr Multiple forbidden-regions expansion Critical nets rerouting selection Look-ahead historical cost increment Experimental results Conclusions 11 The Routing Flow 3D Benchmark 3D 2D capacity mapping Enhanced 2D routing 2D 3D layer assignment 3D routing result PreroutingPrerouting Initial Routing Iterative Forbidden-region Rip-up/rerouting (IFR) 12 Prerouting 1.Congestion-hotspot historical cost pre-increment Identify the high-pin-density tiles (#pin exceeds total tile capacity) Increase the historical cost lying around these tiles by 10 To avoid other nets passing through these congested tiles 2.Small bounding-box area routing Route the less-flexibility nets with smaller bounding-box area Prerouting of newblue3 (49.22% routed nets, overflows) 13 The Routing Flow 3D Benchmark 3D 2D capacity mapping Enhanced 2D routing 2D 3D layer assignment 3D routing result Prerouting Initial Routing Iterative Forbidden-region Rip-up/rerouting (IFR) 14 Initial Routing The first stage completing all nets in the whole chip iterative monotonic routing Apply iterative monotonic routing until the overflow improvement is less than 5%, cf. the previous iteration Initial routing of newblue3 (100% routed nets, overflows) 15 The Routing Flow 3D Benchmark 3D 2D capacity mapping Enhanced 2D routing 2D 3D layer assignment 3D routing result Prerouting Initial Routing Iterative Forbidden-region Rip-up/rerouting (IFR) 16 An enhanced flow over the traditional INR Perform iteratively until no overflow or timeout Iterative Forbidden-region Rip-up/rerouting (IFR) Critical nets rerouting selection Look-ahead historical cost increment Multiple forbidden regions expansion No overflow or timeout No overflow or timeout N Y IFR: 17 Outline Introduction Preliminary Routing flow of NTUgr Multiple forbidden-regions expansion Critical nets rerouting selection Look-ahead historical cost increment Experimental results Conclusions 18 forbidden regions At each iteration of IFR, new forbidden regions are constructed from the most congested regions Initially contains two adjacent tiles w.r.t. the most congested edge Expand the region until the average congestion of each boundary is smaller than a threshold (overlap is allowed) Apply a special cost metric for nets in forbidden regions Introducing new overflows within these regions is almost forbidden by incurring a large penalty Multiple Forbidden-Regions Construction Forbidden-region routing of adaptec5 19 Cost Considering Forbidden Regions The cost function of a global edge e: (penalized base cost of e) 20 Region Propagation Leveling Applied when # of overflows stops decreasing (get stuck at the local optima) Stop creating new forbidden regions Expand all forbidden regions at the previous iteration simultaneously Forbidden-region routing of bigblue3 (i)-th iteration(i+1)-th iteration(i+2)-th iterationfinal iteration 21 Final Expansion of Forbidden Regions Applied when # of overflows < 0.5% of initial overflow Expand the forbidden region to the whole routing graph to quickly reduce the remaining overflows IFR w/ final expansion IFR w/o final expansion Traditional INR Overflow reduction of adaptec5 22 Comparisons of Congested Regions BoxRouterNTHU-Route 1.0NTUgr (Ours) TerminologyBoxCongested regionForbidden region ShapeRectangular Rectilinear # of regionsSingle boxSingle regionMultiple regions Objective Performing progressive ILP Selecting rerouting nets Performing different cost functions Simultaneous expansion No Yes 23 Outline Introduction Preliminary Routing flow of NTUgr Multiple forbidden-regions expansion Critical nets rerouting selection Look-ahead historical cost increment Experimental results Conclusions 24 Critical Nets Rerouting Selection To speed up the rip-up/rerouting process critical nets Only rip-up/reroute the critical nets in each iteration The critical nets are those nets with overflows or small remaining capacity: 25 Outline Introduction Preliminary Routing flow of NTUgr Multiple forbidden-regions expansion Critical nets rerouting selection Look-ahead historical cost increment Experimental results Conclusions 26 near-overflow global edges For the near-overflow global edges (those edges would have overflow if more N demands are added), increase their historical cost in advance Setting N = 1 in NTUgr results in better quality and with about 2x runtime speedup Look-Ahead Historical Cost Increment 27 Outline Introduction Preliminary Routing flow of NTUgr Multiple forbidden-regions expansion Critical nets rerouting selection Look-ahead historical cost increment Experimental results Conclusions 28 Results on ISPD08 Benchmarks Compared with the winners of ISPD08 global routing contest Runtime is averagely the same with NTHU-Route 2.0 (for the ten overflow-free cases for the three routers) Overflow is better than FastRoute 3.0 The best solution in the literature! 29 Effects of Look-Ahead Historical Cost Increment Achieved 1.94x speed up and better overflow reduction with similar total wirelength 30 Outline Introduction Preliminary Routing flow of NTUgr Multiple forbidden-regions expansion Critical nets rerouting selection Look-ahead historical cost increment Experimental results Conclusions 31 Conclusions NTUgr--- a high-quality global router for overflow reduction 1.Prerouting Congestion-hotspot historical cost pre-increment Small bounding-box area routing 2.Initial iterative monotonic routing 3.Iterative forbidden-region rip-up/rerouting (IFR) Multiple forbidden-regions expansion Look-ahead historical cost increment Critical nets rerouting selection Have achieved good results in terms of both overflow and runtime for the new ISPD08 benchmarks 32 Conclusions and Future Work A dummy fill algorithm considering both gradient minimization and coupling constraints Achieve more balanced metal density distribution with fewer dummy features and an acceptable timing overhead Future work: integration of gradient minimization and coupling constraints Simultaneously minimize the gradient and the coupling capacitance Thank You! Huang-Yu Chen