Performance and RLC Crosstalk Driven Global Routing Ling Zhang, Tong Jing, Xianlong Hong, Jingyu Xu Jinjun Xiong, Lei He Dept. of CST, Tsinghua Univ Dept. of EE, UC, Los Angeles Speaker: Xianlong Hong

ISCAS 2004, Vancouver, Canada Outline Introduction & Previous Work Problem Formulations Our Algorithm: PO-GR Experimental Results & Discussions Conclusions 2018/12/3 ISCAS 2004, Vancouver, Canada

ISCAS 2004, Vancouver, Canada Introduction Device size shrinking and clock frequency increasing Coupling capacitance and inductance could not be ignored Longer delay and crosstalk caused by coupling effects Global routing with performance optimization becomes more important. 2018/12/3 ISCAS 2004, Vancouver, Canada

ISCAS 2004, Vancouver, Canada Previous Work(1) Noise modeling Sakurai model (T. Sakurai, C. Kobayashi, M. Node, 1993) LSK model for calculating coupling inductance (L. He, K. M. Lepak, 2000) Model for calculating noise voltage (K. M. Lepak, I. Luwandi, L. He, 2001) 2018/12/3 ISCAS 2004, Vancouver, Canada

ISCAS 2004, Vancouver, Canada Previous Work(2) Noise minimization Spacing in detailed routing phase (K. Chaudhary, A. Onozawa et al, 1993) Track permutation in detailed routing phase (T. Gao, C. L. Liu, 1996) Wire perturbation in detailed routing phase (P. Saxena, C. L. Liu, 1999) Crosstalk reduction after global routing phase (T. X. Xue, E. S. Kuh, D. F. Wang, 1997) (J. J. Xiong, J. Chen, J. Ma, L. He, 2002) Coupling capacitance crosstalk reduction in global routing phase (J. Y. Xu, T. Jing, X. L. Hong, L. Zhang, 2004, ASP-DAC) 2018/12/3 ISCAS 2004, Vancouver, Canada

ISCAS 2004, Vancouver, Canada Major Contributions An efficient crosstalk elimination algorithm based on Tabu search and shielding technology is proposed. Timing performance and routability are simultaneously considered at global routing level. By using LSK model, we take coupling inductance into consideration. 2018/12/3 ISCAS 2004, Vancouver, Canada

ISCAS 2004, Vancouver, Canada Outline Introduction & Previous Work Problem Formulations Our Algorithm: PO-GR Experimental Results & Discussions Conclusions 2018/12/3 ISCAS 2004, Vancouver, Canada

Problem Formulations(1)—Global Routing Problem GRC GRG e v 2 1 v Fig.1 Global Routing Graph(GRG) 2018/12/3 ISCAS 2004, Vancouver, Canada

Problem Formulations(2)—LSK Model Accurate calculation: Simplified calculation in LSK model: 1 K f(i) g(j) gl Ni Nj gr Wire order kij Kit for segment of net i in region t: (for all j sensitive to i) LSK, the total K value for net i: (for all t occupied by net i) Fig.2 LSK Model 2018/12/3 ISCAS 2004, Vancouver, Canada

Problem Formulations(3)—Tabu Search Outline: Step1. Select an initial solution xnow, and set Tabu list H=empty; Step2. While not meet the stop conditions do Generate a candidate list Can_N(xnow) from the neighborhood N(xnow,H) of xnow that doesn’t conflict with H; Select the best solution from Can_N(xnow):xnext; xnow=xnext; Update Tabu list H; End While Key factors: neighborhood Tabu object & Tabu length aspiration rule How to search efficiently How to choose properly How to set the reasonably 2018/12/3 ISCAS 2004, Vancouver, Canada

ISCAS 2004, Vancouver, Canada Outline Introduction & Previous Work Problem Formulations Our Algorithm: PO-GR Experimental Results & Discussions Conclusions 2018/12/3 ISCAS 2004, Vancouver, Canada

Our Algorithm: PO-GR—(1) Part 1: timing performance and routability Part 2: Crosstalk estimation and elimination Part 1 firstly generates an initial routing solution considering congestion and timing optimization Then, Part 2 eliminates the crosstalk from the solution by inserting shields and gets a mid-result Finally, regard the mid-result as input and send it to Part 1 for iterations 2018/12/3 ISCAS 2004, Vancouver, Canada

Our Algorithm: PO-GR—(2) 1. Call Part 1 to generate a minimum wire length initial solution X0 without congestion and timing violation; Call Part 2 to obtain X1 = CEE(X0); If no edge overflow in X1 then go to 4.; Else do go back to 1. to generate a new solution; Call Part 1 again to obtain congestion and timing optimized solution X2 from X1; 2. CEE 3. 4. pseudo code of PO-GR Fig.3 flow chart of PO-GR 2018/12/3 ISCAS 2004, Vancouver, Canada

Insert shield with specific method Part 2—CEE partition the LSK bound at each sink of a net into the GRG edges belonging to the source-sink paths. Insert shield with specific method Check each net to eliminate possible remnant crosstalk and delete unnecessary shields to minimize total area. Fig.4 flow chart of CEE 2018/12/3 ISCAS 2004, Vancouver, Canada

Crosstalk Elimination Based on Tabu Search(1) Simulated Annealing, or Tabu search? The runtime of Simulated Annealing could be very long, while with similar performance, Tabu search is much faster. 2018/12/3 ISCAS 2004, Vancouver, Canada

ISCAS 2004, Vancouver, Canada xcur: current solution; xnew: candidate in neighborhood of xcur; xtmp: best candidate; xmin: best solution ever reached; Na: maximum iteration times with no improvement; Nb: number of candidates selected from neighborhood; Nc: maximum trying times for searching one candidate; randommove(x): method of generate a candidate in neighborhood of x; cost(x): evaluation of solution x; Set the global solution in one GRG edge as initial solution xcur; Set Tabu list H=empty; a=0; c=0; While( a < Na ) tmpcost = ; b = 0; While (b < Nb ) xnew = xcur; randommove ( xnew ); If cost (xnew) is in H c++; If c < Nc, then continue; Else c = 0; If cost (xnew) < tmpcost, then xtmp = xnew; tmpcost = cost (xnew); b++; End While Insert xcur into H; xcur= xtmp; If cost (xcur) < cost (xmin), then xmin = xcur; a = 0; Else a++; Update H; 2018/12/3 ISCAS 2004, Vancouver, Canada

Crosstalk Elimination Based on Tabu Search(2) randommove(x): { swap two net randomly, move one net randomly, insert one shield randomly, remove one shield randomly } cost(x)=w1*c1 + w2*c2 + w3*c3 + w4*c4 c1: total number of nets that are adjacent to their sensitive nets; c2: total number of shields in a GRG edge; c3: summation of (Keff - Kth ) for all nets with Keff > Kth in a GRG edge; c4: total number of nets with (Keff > Kth) in a GRG edge. 2018/12/3 ISCAS 2004, Vancouver, Canada

ISCAS 2004, Vancouver, Canada Outline Introduction & Previous Work Problem Formulations Our Algorithm: PO-GR Experimental Results & Discussions Conclusions 2018/12/3 ISCAS 2004, Vancouver, Canada

ISCAS 2004, Vancouver, Canada Benchmark Data Circuits Number of nets Grids   C2 745 9  11 C5 1764 16  18 C7 2356 Technology: 0.2um Sensitivity rate: 0.5 for all nets and sensitivity matrix is random. LSK bound:1000 at each sink 2018/12/3 ISCAS 2004, Vancouver, Canada

Experimental Results(1) Circuits C2 C5 C7 Step 2 in CEE Simulated Annealing(SA) 901.97 2140.36 3748.78 Tabu search 45.75 112.87 237.80 Runtime reduction 856.22 2027.49 3510.98 Step 3 in SA 153.53 56.36 453.70 91.44 34.08 227.50 62.09 22.28 226.20 Total runtime (Step2+Step3) 1055.50 2196.72 4202.48 137.19 146.95 465.30 Total runtime reduction 918.31 2049.77 3737.18 Comparison of runtime(s) between Tabu search and Simulate Annealing 2018/12/3 ISCAS 2004, Vancouver, Canada

Experimental Results(2) Circuits C2 C5 C7 Area SA 149196 271301 342395 Tabu search 149202 273307 346393 Shield number (Sn) 158 460 589 165 501 621 Sn increment 7 41 32 Comparison of results between Tabu search and Simulated Annealing 2018/12/3 ISCAS 2004, Vancouver, Canada

Experimental Results(3) Circuits C2 C5 C7 W mode (um) (Part 1)Wire length 480350 1307456 1552916 (PO-GR) Wire length 477326 1368198 1575922 Wire length increment -0.63% 4.65% 1.48% T mode 476424 1346876 1569366 479100 1280352 1567818 0.56% -4.94% -0.10% (Part 1) Min-R -0.009243 0.012124 0.000034 (PO-GR) Min-R -0.007195 0.003439 0.001243 Comparison of results between P1 and PO-GR 2018/12/3 ISCAS 2004, Vancouver, Canada

ISCAS 2004, Vancouver, Canada Discussions Tabu search sharply decreases the runtime of step2 in CEE(about 20x speedup), and doesn’t make any bad effects on step3 in CEE(its runtime slightly decreases too). Tabu search can obtains similar results in routing area compared with SA method, while the shielding number only increases a little. Tabu search achieve 2.5x wire length reduction compared with SA. PO-GR keeps the effectiveness in timing optimization. 2018/12/3 ISCAS 2004, Vancouver, Canada

ISCAS 2004, Vancouver, Canada Outline Introduction & Previous Work Problem Formulations Our Algorithm: PO-GR Experimental Results & Discussions Conclusions 2018/12/3 ISCAS 2004, Vancouver, Canada

ISCAS 2004, Vancouver, Canada Conclusions PO-GR is able to: Take coupling inductance into consideration. Tackle coupling noise, timing performance and routability simultaneously. Efficiently eliminate crosstalk throughout the global routing phase by inserting shields and has little influence on wire length and timing performance. Preserve the good routing result and greatly decrease the running time. 2018/12/3 ISCAS 2004, Vancouver, Canada

ISCAS 2004, Vancouver, Canada THANK YOU 2018/12/3 ISCAS 2004, Vancouver, Canada