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A Min-area Solution to Performance and RLC Crosstalk Driven Global Routing Problem

A Min-area Solution to Performance and RLC Crosstalk Driven Global Routing Problem. Tong Jing, Ling Zhang, Jinghong Liang Jingyu Xu, Xianlong Hong Jinjun Xiong, Lei He CS&T Department EE Department

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A Min-area Solution to Performance and RLC Crosstalk Driven Global Routing Problem

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  1. A Min-area Solution to Performance and RLC Crosstalk DrivenGlobal Routing Problem Tong Jing, Ling Zhang, Jinghong Liang Jingyu Xu, Xianlong Hong Jinjun Xiong, Lei He CS&T Department EE Department Tsinghua University UCLA Beijing 100084, China Los Angeles, CA, USA Speaker: Jinghong Liang

  2. Outline 1. Introduction 2. Preliminaries 3. Our Work (AT-PO-GR Algorithm) 4. Experimental Results & Discussions 5. Conclusions ASP-DAC2005, Shanghai, China

  3. Backgrounds Coupling effects and crosstalk VLSI / ULSI • Global routing plays an important role in very/ultra large scale integrated circuits (VLSI/ULSI) physical design • The progress in VLSI/ULSI enables system-on-a-chip (SOC) integration instead of system-on-a-board (SOB) integration • Chip design is with greatly shrinking of geometries and giga-hertz clock frequencies • All these advances enable us to get high-performance chips • However, one of the great concerns is coupling effects and crosstalk • Crosstalk elimination has become a challenge to global routing System-On-a-Chip (SOC) Clock frequency increases • New challenge to global routing ASP-DAC2005, Shanghai, China

  4. Previous Work (1) The existing works can be divided into three categories • Noise modeling • [T. Sakurai, S. Kobayashi, and M. Node. ISCAS, 1991] Derived expressions for a coupling capacitance and a crosstalk voltage height • [L. He and K. M. Lepak. ISPD, 2000] Declared that on-chip inductance, especially mutual inductance, should be considered for high-performance interconnect design and presented the effective coupling model, called the Keffmodel ASP-DAC2005, Shanghai, China

  5. Previous Work (2) • Noise minimization • [T. X. Xue, E. S. Kuh. IEEE Trans on CAD, 1997] Described a two-pass algorithm including region-based crosstalk risk estimation and crosstalk reduction • [H. Zhou and D. F. Wong. IEEE Trans on CAD, 1999 ] Presenteda cost function taking crosstalk into consideration, and is used during the phase of constructing the routing tree • [J. J. Xiong and L. He. IEEE Trans on CAD, 2004] Proposed a three-phase algorithm based on crosstalk budgeting, simultaneous shield insertion and net ordering (SINO), and local refinement ASP-DAC2005, Shanghai, China

  6. Previous Work (3) • Simultaneous noise minimization and performance optimization • [L. Zhang, T. Jing, X. L. Hong, J. Y. Xu, J. J. Xiong, L.He. ASICON, 2003]----(PO-GR) • [J. Y. Xu, X. L. Hong, T. Jing, L. Zhang, J. Gu. ASP-DAC, 2004] Both proposed performance optimization global routing algorithms considering crosstalk reduction. The former mainly focuses on coupling capacitance and uses spacing method. The latter considers coupling inductance and is based on shield insertion • [L. Zhang, T. Jing, X. L. Hong, J. Y. Xu, J. J. Xiong, L.He. ISCAS, 2004]----(T-PO-GR) Presented an efficient RLC crosstalk reduction algorithm ASP-DAC2005, Shanghai, China

  7. Outline 1. Introduction 2. Preliminaries 3. Our Work (AT-PO-GR Algorithm) 4. Experimental Results & Discussions 5. Conclusions ASP-DAC2005, Shanghai, China

  8. Global Routing Problem • With the progress in multi-layer routing technology, routing area is a whole chip plane • A net can be specified as a set of nodes in global routing graph (GRG) • The problem of routing a net can be described as a rectilinear Steiner minimal tree (RSMT) problem of specified nodes in GRG. ASP-DAC2005, Shanghai, China

  9. GRC 1 e GRG v 1 v 2 Global Routing Graph (GRG) ASP-DAC2005, Shanghai, China

  10. K 1 g(j) Kij f(i) Wire order Nj gr gl Ni LSK Model for RLC Crosstalk Estimation • Different from earlier noise model Sakurai, the LSK model considers coupling inductance between adjacent and non-adjacent sensitive nets Fast computation of Ki,j: The total amount of inductive coupling induced on Nit: For all net segments Njt that are sensitive to Nit ASP-DAC2005, Shanghai, China

  11. Tabu Search The basic idea of this technology is simple, which records and taboos the local minimum points that have been reached so as to avoid getting stuck at these points and finds out new search ways that could lead to the global minimum point eventually. Select an initial solution xnow, and set Tabu list H = empty; While not meet the stop conditions do Generate a candidate list from the neighborhood of xnow that does not conflict with H; Select the best solution xnextfrom the candidate list; xnow= xnext; Update Tabu list H; End While There are 3 key factors in Tabu search: tabu object, tabu length, and aspiration rule ASP-DAC2005, Shanghai, China

  12. Outline 1. Introduction 2. Preliminaries 3. Our Work (AT-PO-GR Algorithm) 4. Experimental Results & Discussions 5. Conclusions ASP-DAC2005, Shanghai, China

  13. Our Main Contributions Goal: Reduce the final routing area by means of improving the gross algorithm based on holistic optimization • The main contribution of this paper is a min-area solution to performance and RLC crosstalk driven global routing problem • The proposed algorithm can achieve smaller routing area and fewer shields under the same design constraints, yet use less running time ASP-DAC2005, Shanghai, China

  14. Problem Formulation Let Then we have Minimize Subject to: (1) (2) (3) • Formula(1) is the congestion constraint, which forbids the overflow on each GRG edge • Formula(2) guarantees the actual delay value from source i to sink j, T(i, j), is no more than the given timing constraint TD (i, j) • Formula(3) sets the upper bound of LSK, , for each source sink pair ij. ASP-DAC2005, Shanghai, China

  15. The Main Flow of AT-PO-GR Use Grrandom() to get an initial solution X0 It considers congestion and timing issues Use CtkEst() to budget and estimate crosstalk in X0 Iterate Grrandom(X0) to rip-up X0 so as to reduce its crosstalk, and get a good mid-solution Xtemp Use Gr(Xtemp) to reduce wire length, congestion, and delay Get a solution X1 Use CtkEli() toeliminate crosstalk in X1 by means of shield insertion and changing net orders Get the final resultX2 ASP-DAC2005, Shanghai, China

  16. Use Grrandom() to get an initial solution X0 A new cost formula of GRG edge taking crosstalk into account is used as follows , (4) where ctis the capacity of edge t, ftis the number of used tracks in edge t, δ is a small real number that validates formula (4) while ctis 0, is the actual congestion of edge t, K is a large integer used as the penalty factor, wt is the weighted cost of edge t, and nvtis the number of net segments in edge t that violate crosstalk constraint. Considering possible shield may be inserted due to these net segments, we add nvt in such that these edges tend to become more congested. Then, nets crossing such edges will have higher cost and thus it will be avoided. ASP-DAC2005, Shanghai, China

  17. Use CtkEst() to budget and estimate crosstalk in X0 Firstly, Where is the crosstalk bound at sink pij for net Nj len is the total length from the source pioto sink pij. Secondly, having got , CtkEst() computes actual Kitwith LSK model. At last, we can obtain Kslack for each source-sink pair ij. Kslack has the following definition. ASP-DAC2005, Shanghai, China

  18. Use Gr(Xtemp) to get a solution X1 • Gr() include 3 different strategies: stochastic optimization, deterministic optimization, and local enumeration optimization strategy. • Grrandom() only uses stochastic optimization strategy. Transition from a local minimum point ASP-DAC2005, Shanghai, China

  19. Use CtkEli() to eliminate crosstalk in X1 by means of shield insertion and changing net orders • Firstly, insert shields in each GRG region so that the crosstalk of most regions is within the given bound • Secondly, insert shield in those regions which have possible remnant crosstalk, so that crosstalk is completely eliminated • Finally, delete unnecessary shields so that the final area is minimized ASP-DAC2005, Shanghai, China

  20. Pseudo code of AT-PO-GR ASP-DAC2005, Shanghai, China

  21. Outline 1. Introduction 2. Preliminaries 3. Our Work (AT-PO-GR Algorithm) 4. Experimental Results & Discussions 5. Conclusions ASP-DAC2005, Shanghai, China

  22. Experimental Environments • Platform Hardware: sun V880 fire workstation Software: gcc2.9.1, solaris5.8 • Benchmark Data • Parameters Setting • LSK bound at each sink is set to be 1000 • Na=350, Nb=20, Nc=10, and Tabu length=3 ASP-DAC2005, Shanghai, China

  23. In Comparison with Typical Algorithms (1)PO-GR[L. Zhang, T. Jing, X. L. Hong, 2003] is the first algorithm to study inductance coupling noise, timing performance and routability simultaneously at global routing level. It uses SA algorithm in its crosstalk elimination. (2)T-PO-GR[L. Zhang, T. Jing, X. L. Hong, 2004] runs much faster than PO-GR with the similar routing results. But the routing area and shield number in T-PO-GR are comparably larger than those in PO-GR • We will compare our AT-PO-GR with the above algorithms focusing on area, running time, etc. ASP-DAC2005, Shanghai, China

  24. The comparison of wire length, running time, and routing area between AT-PO-GR and PO-GR ASP-DAC2005, Shanghai, China

  25. The comparison of wire length, running time, and routing area between AT-PO-GR and T-PO-GR ASP-DAC2005, Shanghai, China

  26. Discussions • Grrandom() can reduce crosstalk violation number（2%-7% ） • The runtime of AT-PO-GR is no more than 5% of that of PO-GR • AT-PO-GR can reduce wire length by more than 4% compared with PO-GR • Running time of AT-PO-GR is about half of that of T-PO-GR • The wire length of AT-PO-GR is shorter than that of T-PO-GR • AT-PO-GR also gets improvements in area and shield number compared with T-PO-GR ASP-DAC2005, Shanghai, China

  27. Outline 1. Introduction 2. Preliminaries 3. Our Work (AT-PO-GR Algorithm) 4. Experimental Results & Discussions 5. Conclusions ASP-DAC2005, Shanghai, China

  28. Conclusions • A min-area solution to performance and RLC crosstalk driven global routing problem has been presented in this paper • The experimental results have shown that this algorithm is able to: (i) obtain routing solutions with less routing area compared with typical existing works (ii) preserve good routing results and greatly decrease running time compared with typical existing works ASP-DAC2005, Shanghai, China

  29. Future Work • As our future work, we plan to find more specific methods to construct the Steiner tree set for crosstalk minimization, and better strategies for crosstalk budgeting ASP-DAC2005, Shanghai, China

  30. Thank you! Jinghong Liang(梁敬弘) Dept . of CST, Tsinghua Univ. Beijing 100084, P. R. China Tel.: +86-10-62785428 Fax: +86-10-62781489 E-mail: liangjh03@mails.tsinghua.edu.cn ASP-DAC2005, Shanghai, China

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