Có 60+ tài liệu thuộc chủ đề "tổng quan chi tiết của VLSI"
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FIGURE 18.12 Illustration of the adaptec2 circuit from the ISPD05 benchmark suite [39] where (a) shows the circuit’s fixed obstacles and I/O pads before placement and (b) shows that after the placement of cells after a single QP, many cells may become trapped (or blocked) by fixed obstacles.. So, the question arises as to what is the best method to...
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Galerkin coarsening thus defines the linear coarsening operator P T : R n → R m as the transpose of the linear interpolation operator P, as simple substitution of Equation 19.5 into Equation 19.4 yields Equation 19.6 on premultiplication by P T. By confining coarse-level iterative improvement to the perturbation e = Pe c to s, relaxation ˜ at the...
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19.3.4 R ELAXATION. Iterative improvement at each level may employ various techniques—network flows, simu- lated annealing, nonlinear programming, force-directed models—provided that it can support incorporation of complex constraints appropriate to the modeling scale at the current level.. 19.3.4.1 mPL6. In mPL5 [49] and mPL6 [39], fast numerical PDE solvers are used in a generalization of the Eisenmann–Johannes force-directed model [10,13]...
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Once a placement is legal, with all overlaps removed and logic elements properly aligned, optimizations that are traditionally classified as detailed placement can be applied. Small groups of standard cells can be shifted or reordered—these local optimizations can have a dramatic impact on wirelength. 20.1.1 N OTATION. Each net connects a subset of the cells.. For simplicity, in most cases...
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20.3.2 T ETRIS- B ASED L EGALIZATION. for i = 1 to the number of cells do best = lim sup;. for j = 1 to the number of rows do. Move cell i in L s to the row best _ row . Our example code can be made to run more quickly by only considering rows close to...
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21.1 Introduction. 21.2 Building Blocks and Classification. 21.2.1 Net Modeling. 21.2.2 Timing Analysis and Metrics. 21.2.3 Overview of Timing-Driven Placement. 21.3 Netweighting-Based Approach. 21.3.1 Static Netweighting. 21.3.1.1 Slack-Based Netweighting. 21.3.1.2 Sensitivity-Based Netweighting. 21.3.2 Dynamic Netweighting. 21.3.2.1 Incremental Timing Analysis. 21.3.2.2 Incremental Net Weighting. 21.3.2.3 Placement Implementation. 21.4 Net-Constraint-Based Approach. 21.4.1 Net-Constraint Generation. 21.4.1.1 Generating Effective NLCs. 21.4.1.2 Single-Shot NLC Generation....
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The netweight can be computed as. 0 (21.16) where. α and β set the bound of netweight changes, and control the balance between WNS and TNS 21.3.2 D YNAMIC N ETWEIGHTING. This scheme can be applied on any placement and netweighting algorithms. 21.3.2.1 Incremental Timing Analysis. S T L ( n ) l ( n ) (21.17) where. d k...
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Furthermore, because of the complexity of modern placement problems and the iterative refinement nature from global placement to detailed/legal placement, it is very important to have stability between placement iterations. The timing constraint on each pin is called delta arrival time constraint, which is defined as the difference of arrival time at this pin to the arrival time of the...
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The third approach is to balance the perimeter-degree of the partitions during the partitioning phase of the multilevel placement. Alternatively, one could satisfy both the constraints in a sequential manner by first balancing the perimeter-degree and then balancing the areas of the partitions.. 22.3 GLOBAL-PLACEMENT CONGESTION IMPROVEMENT. There have been several studies on incorporating the congestion metric during global-placement stage...
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Let WL be the total wirelength and OF be the total overflow of the current placement. The overflow is the difference between routing demand and routing supply of the bin, if demand is larger. 1 − α) WL + α OF, 0 ≤ α ≤ 1 (Figure 22.10c). S Number of. The authors found that during global placement, none of...
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FIGURE 23.4 (a) Three-dimensional grid model for a three-layer circuit and (b) its corresponding grid graph, where solid lines represent intralayer connections and dashed lines represent interlayer connections.. Here, each terminal is assumed to lie at the center of the grid cell that contains the terminal.. If a two-dimensional grid model is used (as in Figure 23.3), the routing tracks...
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FIGURE 23.17 Maze routing is applied repeatedly to find the routing solution of a net with three terminals.. This process continues until all the terminals of the net are routed. Figure 23.17 illustrates this process with an example. Here, wave expansion starts from terminal A, and it reaches terminal B (Figure 23.17a). The next wavefront is started to be expanded...
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next subsection discusses a batched variant of the I1S approach, which offers runtime improvements in practice.. 24.3.1 B ATCHED 1 - S TEINER V ARIANT. The batched 1-Steiner (B1S) variant computes MST(P, {x}) for each candidate Steiner point x ∈ H ( P ) (i.e., the Hanan grid candidate points). that is, introducing each of the two 1-Steiner points does...
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For an arbitrary instance of the group Steiner problem (with k groups), this combination yields a routing tree with simultaneous provably good bounds for both tree radius and tree cost. 24.5.6 E MPIRICAL P ERFORMANCE OF THE G ROUP S TEINER H EURISTIC. 24.6 OTHER STEINER TREE METHODS. Once it became known [48,49] that MST-improvement-based Steiner heuristics having worst-case performance...
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0 Output: Spanning tree T BRBC with r ( T BRBC. Output T BRBC = shortest paths tree of Q. FIGURE 25.2 BRBC spanning tree algorithm produces a tree T BRBC with radius at most ( 1. B., Robins, G., Sarrafzadeh, M., and Wong, C. An alternative approach to the wirelength-radius trade-offs is the AHHK algorithm [40], which integrates Prim’s...
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Input: A signal net S with source s 0 ∈ S and critical sink s c ∈ S Output: A critical-sink routing tree T over S. in the tree ( V. FIGURE 25.15 The SERT-C algorithm directly incorporates the Elmore delay formula into a greedy critical- sink routing tree construction. B., and Robins, G., Proceedings of the ACM/IEEE Design Automation...
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Rubinstein, J., Penfield, P., and Horowitz, M. IEEE Transactions Computer-Aided Design . In Proceedings of the IEEE International Conference Computer-Aided Design, Santa Clara, CA, November 1991, pp. Awerbuch, B., Baratz, A., and Peleg, D. In Proceed- ings of the ACM Symposium Principles of Distributed Computing, Quebec City, Quebec, Canada, 1990, pp. B., Robins, G., Sarrafzadeh, M., and Wong, C. In...
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26.4 VAN GINNEKEN EXTENSIONS. 26.4.1 H ANDLING L IBRARY WITH M ULTIPLE B UFFERS. Each buffer b in the buffer library has a cost W ( b. which can be measured by area or any other metric, depending on the optimization objective. With the above notations, our new problem can be formulated as follows.. However, because the domination is defined...
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and Li, Z., IEEE Trans Computer-Aided Design . and Shi, W., IEEE Trans Computer-Aided Design . If candidate α 2 is not on the convex hull of the solution set, then ρ 1,2 <. When a wire is added, only qa, ca, and ra in the root of the tree [39] or as global variables themselves [41] are updated. c...
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27.3 SIMULTANEOUS TREE CONSTRUCTION AND BUFFER INSERTION In this section, some of the methods that combine buffer insertion and topology construction are presented. The work started with the first version of the P-Tree algorithm [8] that was designed to construct timing-driven routing tree and it has seen a decade long evolution of various improvements and extensions that were building on...