ECE260B CSE241A Winter Placement

Transcription

1 ECE260B CSE241A Winter 2005 Placement Website: / courses/ ece260b- w05 ECE260B CSE241A Placement.1 Slides courtesy of Prof. Andrew B. Slides courtesy of Prof. Andrew B. Kahng

2 VLSI Design Flow and Physical Design Stage IO Pad Placement Power/Ground Stripes, Rings Routing Global Placement Definitions: Cell: a circuit component to be placed on the chip area. In placement, the functionality of the component is ignored. Net: specifying a subset of terminals, to connect several cells. Netlist: a set of nets which contains the connectivity information of the circuit. Detail Placement Clock Tree Synthesis and Routing Global Routing Extraction and Delay Calc. Timing Verification Detail Routing ECE260B CSE241A Placement.2

3 Placement Problem Input: A set of cells and their complete information (a cell library). Connectivity information between cells (netlist information). Output: A set of locations on the chip: one location for each cell. Goal: The cells are placed to produce a routable chip that meets timing and other constraints (e.g., low-power, noise, etc.) Challenge: The number of cells in a design is very large (> 1 million). The timing constraints are very tight. ECE260B CSE241A Placement.3

4 Optimal Relative Order: A B C ECE260B CSE241A Placement.4

5 To spread... A B C ECE260B CSE241A Placement.5

6 .. or not to spread A B C ECE260B CSE241A Placement.6

7 Place to the left A B C ECE260B CSE241A Placement.7

8 or to the right A B C ECE260B CSE241A Placement.8

9 Optimal Relative Order: A B C Without free space, the placement problem is dominated by order ECE260B CSE241A Placement.9

10 Placement Problem A bad placement A good placement ECE260B CSE241A Placement.10

11 Global and Detailed Placement In global placement, we decide the approximate locations for cells by placing cells in global bins. In detailed placement, we make some local adjustment to obtain the final nonoverlapping placement. Global Placement Detailed Placement ECE260B CSE241A Placement.11

12 Placement Footprints: Standard Cell: Data Path: IP - Floorplanning ECE260B CSE241A Placement.12

13 Placement Footprints: Core Reserved areas IO Control Mixed Data Path & sea of gates: ECE260B CSE241A Placement.13

14 Placement Footprints: Perimeter IO Area IO ECE260B CSE241A Placement.14

15 Placement objectives are subject to user constraints / design style: Hierarchical Design Constraints pin location power rail reserved layers Flat Design with Floorplan Constraints Fixed Circuits I/O Connections ECE260B CSE241A Placement.15

16 Standard Cells ECE260B CSE241A Placement.16

17 Standard Cells Power connected by abutment, placed in sea-of-rows Rarely rotated DRC clean in any combination Circuit clean (I.e. no naked T-gates, no huge input capacitances) 8,9,10+ tracks in height Metal 1 only used (hopefully) Multi-height stdcells possible Buffers: sizes, intrinsic delay steps, optimal repeater selection Special clock buffers + gates (balanced P:N) Special metastability hardened flops Cap cells (metal1 used?) Gap fillers (metal1 used?) Tie-high, tie-low ECE260B CSE241A Placement.17

18 Unconstrained Placement ECE260B CSE241A Placement.18

19 Floor planned Placement ECE260B CSE241A Placement.19

20 Placement Cube (4D) Cost Function(s) to be used Cut, wirelength, congestion, crossing,... Algorithm(s) to be used FM, Quadratic, annealing,. Granularity of the netlist Coarseness of the layout domain 2x2, 4x4,. Netlist Granularity Algorithm Cost Function Layout Coarseness An effective methodology picks the right mix from the above and knows when to switch from one to next. Most methods today are ad-hoc ECE260B CSE241A Placement.20

21 Advantages of Hierarchy Design is carved into smaller pieces that can be worked on in parallel (improved throughput) A known floor plan provides the logic design team with a large degree of placement control. A known floor plan provided early knowledge of long wires Timing closure problems can be addressed by tools, logic design, and hierarchy manipulation Late design changes can be done with minimal turmoil to the entire design ECE260B CSE241A Placement.21

22 Disadvantages of Hierarchy Results depend on the quality of the hierarchy. The logic hierarchy must be designed with Physical Design taken into account. Additional methodology requirements must be met to enable hierarchy. Ex. Pin assignment, Macro abstract management, area budgeting, floor planning, timing budgets, etc Late design changes may affect multiple components. Hierarchy allows divergent methodologies Hierarchy hinders Design Automation algorithms. They can no longer perform global optimizations. ECE260B CSE241A Placement.22

23 Traditional Placement Algorithms Quadratic Placement Simulated Annealing Bi-Partitioning / Quadrisection Force Directed Placement Hybrid Netlist Granularity Algorithm Cost Function Layout Coarseness ECE260B CSE241A Placement.23

24 Quadratic Placement Analytical Technique x3 x1 x2 Min [(x1-x3) 2 + (x1-x2) 2 + (x2-x4) 2 ] : F x4 δ F/δ x1 = 0; δ F/ δ x2 = 0; Ax = B A 2-1 = B = -1 2 x3 x4 x = x1 x2 ECE260B CSE241A Placement.24

25 Analytical Placement Get a solution with lots of overlap What do we do with the overlap? ECE260B CSE241A Placement.25

26 Pros and Cons of QP Pros: Cons: Very Fast Analytical Solution Can Handle Large Design Sizes Can be Used as an Initial Seed Placement Engine Can Generate Overlapped Solutions: Postprocessing Needed Not Suitable for Timing Driven Placement Not Suitable for Simultaneous Optimization of Other Aspects of Physical Design (clocks, crosstalk ) Gives Trivial Solutions without Pads (and close to trivial with pads) ECE260B CSE241A Placement.26

27 Simulated Annealing Placement Initial Placement Improved through Swaps and Moves Accept a Swap/ Move if it improves cost Accept a Swap/ Move that degrades cost under some probability conditions Cost ECE260B CSE241A Placement.27 Time

28 Pros and Cons of SA Pros: Can Reach Globally Optimal Solution (given enough time) Open Cost Function. Can Optimize Simultaneously all Aspects of Physical Design Can be Used for End Case Placement Cons: Extremely Slow Process of Reaching a Good Solution ECE260B CSE241A Placement.28

29 Bi-Partitioning/ Quadrisection ECE260B CSE241A Placement.29

30 Pros and Cons of Partitioning Based Placement Pros: More Suitable to Timing Driven Placement since it is Move Based New Innovation (hmetis) in Partitioning Algorithms have made this Extremely Fast Open Cost Function Move Based means Simultaneous Optimization of all Design Aspects Possible Cons: Not Well Understood Lots of indifferent moves May not work well with some cost functions. ECE260B CSE241A Placement.30

31 Hypergraphs in VLSI CAD Circuit netlist represented by hypergraph ECE260B CSE241A Placement.31

32 Hypergraph Partitioning in VLSI Variants directed/undirected hypergraphs weighted/unweighted vertices, edges constraints, objectives, Human-designed instances Benchmarks up to 4,000,000 vertices sparse (vertex degree 4, hyperedge size 4) small number of very large hyperedges Efficiency, flexibility: KL-FM style preferred ECE260B CSE241A Placement.32

33 Context: Top-Down VLSI Placement etc ECE260B CSE241A Placement.33

34 Context: Top-Down Placement Speed Structure 6,000 cells/minute to final detailed placement partitioning used only in top-down global placement implied partitioning runtime: 1 second for 25,000 cells, < 30 seconds for 750,000 cells tight balance constraint on total cell areas in partitions widely varying cell areas fixed terminals (pads, terminal propagation, etc.) ECE260B CSE241A Placement.34

35 Fiduccia-Mattheyses (FM) Approach Pass: start with all vertices free to move (unlocked) label each possible move with immediate change in cost that it causes (gain) iteratively select and execute a move with highest gain, lock the moving vertex (i.e., cannot move again during the pass), and update affected gains best solution seen during the pass is adopted as starting solution for next pass FM: start with some initial solution perform passes until a pass fails to improve solution quality ECE260B CSE241A Placement.35

36 Cut During One Pass (Bipartitioning) Cut Moves ECE260B CSE241A Placement.36

37 Multilevel Partitioning Clustering Refinement ECE260B CSE241A Placement.37

38 Force Directed Placement Cells are dragged by forces. Forces are generated by nets connecting cells. Longer nets generate bigger forces. Placement is obtained by either a constructive or an iterative method. i i F ij j ECE260B CSE241A Placement.38

39 Pros and Cons of Force Directed Placement Pros: Very Fast Analytical Solution Can Handle Large Design Sizes Can be Used as an Initial Seed Placement Engine The Force Cons: Not sensitive to the non-overlapping constraints Gives Trivial Solutions without Pads Not Suitable for Timing Driven Placement ECE260B CSE241A Placement.39

40 Hybrid Placement Mix-matching different placement algorithms Effective algorithms are always hybrid ECE260B CSE241A Placement.40

41 GORDIAN (quadratic + partitioning) Initial Placement min { x i x j 2 } min { y i y j 2 } Partition and Replace ECE260B CSE241A Placement.41

42 Congestion Minimization Traditional placement problem is to minimize interconnection length (wirelength) A valid placement has to be routable Congestion is important because it represents routability (lower congestion implies better routability) There is not yet enough research work on the congestion minimization problem ECE260B CSE241A Placement.42

43 Definition of Congestion Routing demand = 3 Assume routing supply is 1, overflow = 3-1 = 2 on this edge. Overflow on each edge = Routing Demand - Routing Supply (if Routing Demand > Routing Supply) 0 (otherwise) Overflow = Σ all edges overflow ECE260B CSE241A Placement.43

44 Correlation between Wirelength and Congestion Total Wirelength = Total Routing Demand ECE260B CSE241A Placement.44

45 Wirelength Congestion A congestion minimized placement A wirelength minimized placement ECE260B CSE241A Placement.45

46 Congestion Map of a Wirelength Minimized Placement Congested Spots ECE260B CSE241A Placement.46

47 Congestion MAP ECE260B CSE241A Placement.47

48 Congestion Reduction Postprocessing Reduce congestion globally by minimizing the traditional wirelength Post process the wirelength optimized placement using the congestion objective ECE260B CSE241A Placement.48

49 Congestion Reduction Postprocessing Among a variety of cost functions and methods for congestion minimization, wirelength alone followed by a post processing congestion minimization works the best and is one of the fastest. Cost functions such as a hybrid length plus congestion do not work very well. ECE260B CSE241A Placement.49

50 Cost Functions for Placement The final goal of placement is to achieve routability and meet timing constraints Constraints are very hard to use in optimization, thus we use cost functions (e.g., Wirelength) to predict our goals. We will show what happens when you try constraints directly The main challenge is a technical understanding of various cost functions and their interaction. ECE260B CSE241A Placement.50

51 Prediction What is prediction? every system has some critical cost functions: Area, wirelength, congestion, timing etc. Prediction aims at estimating values of these cost functions without having to go through the time-consuming process of full construction. Allows quick space exploration, localizes the search For example: statistical wire-load models Wirelength in placement ECE260B CSE241A Placement.51

52 Paradigms of Prediction Two fundamental paradigms statistical prediction #of two-terminal nets in all designs #of two-terminal nets with length greater than 10 in all designs constructive prediction #of two-terminal nets with length greater than 10 in this design and everything in between, e.g., #of critical two-terminal nets in a design based on statistical data and a quick inspection of the design in hand. Absolute truth or I need it to make progress SLIP (System Level Interconnect Prediction) community. ECE260B CSE241A Placement.52

53 Cost Functions for Placement Net-cut Linear wirelength Quadratic wirelength Congestion Timing Coupling Other performance related cost functions Undiscovered: crossing Netlist Granularity Algorithm Cost Function Layout Coarseness ECE260B CSE241A Placement.53

54 Net-cut Cost for Global Placement The net-cut cost is defined as the number of external nets between different global bins Minimizing net-cut in global placement tends to put highly connected cells close to each other. ECE260B CSE241A Placement.54

55 Linear Wirelength Cost (x1,y1) 1 The linear length of a net between cell 1 and cell 2 is l 12 = x1-x2 + y1-y2 2 (x2,y2) The linear wirelength cost is the summation of the linear length of all nets. ECE260B CSE241A Placement.55

56 Quadratic Wirelength Cost (x1,y1) 1 The quadratic length of a net between cell 1 and cell 2 is 12 = (x1-x2) 2 +(y1-y2) 2 l 12 2 (x2,y2) The quadratic wirelength cost is the summation of the quadratic length of all nets. ECE260B CSE241A Placement.56

57 Congestion Cost Routing demand = 3 Assume routing supply is 1, overflow = 3-1 = 2 on this edge. Overflow on each edge = Routing Demand - Routing Supply (if Routing Demand > Routing Supply) 0 (otherwise) Congestion Overflow = Σ overflow all edges ECE260B CSE241A Placement.57

58 Cost Functions for Placement Various cost functions (and a mix of them) have been used in practice to model/estimate routability and timing We have a good feel for what each cost function is capable of doing We need to understand the interaction among cost functions ECE260B CSE241A Placement.58

59 Congestion Minimization and Congestion vs Wirelength Congestion is important because it closely represents routability (especially at lower-levels of granularity) Congestion is not well understood Ad-hoc techniques have been kind-of working since congestion has never been severe It has been observed that length minimization tends to reduce congestion. Goal: Reduce congestion in placement (willing to sacrifice wirelength a little bit). ECE260B CSE241A Placement.59

60 Correlation between Wirelength and Congestion Total Wirelength = Total Routing Demand ECE260B CSE241A Placement.60

61 Wirelength Congestion A congestion minimized placement A wirelength minimized placement ECE260B CSE241A Placement.61

62 Congestion Map of a Wirelength Minimized Placement Congested Spots ECE260B CSE241A Placement.62

63 Different Routing Models for modeling congestion Bounding box router: fast but inaccurate. Real router: accurate but slow. A bounding box router can be used in placement if it produces correlated routing results with the real router. Note: For different cost functions, answer might be different (e.g., for coupling, only a detailed router can answer). ECE260B CSE241A Placement.63

64 Different Routing Models A bounding box routing model A MST+shortest_path routing model ECE260B CSE241A Placement.64

65 Objective Functions Used in Congestion Minimization WL: Standard total wirelength objective. Ovrflw: Total overflow in a placement (a direct congestion cost). Hybrid: (1- α)wl + α Ovrflw QL: A quadratic plus linear objective. LQ: A linear plus quadratic objective. LkAhd: A modified overflow cost. (1- αt )WL + α T Ovrflw: A time changing hybrid objective which let the cost function gradually change from wirelength to overflow as optimization proceeds. ECE260B CSE241A Placement.65

66 Post Processing to Reduce Congestion Reduce congestion globally by minimizing the traditional wirelength Post process the wirelength optimized placement using the congestion objective ECE260B CSE241A Placement.66

67 Post Processing Heuristics Greedy cell-centric algorithm: Greedily move cells around and greedily accept moves. Flow-based cell-centric algorithm: Use a flow-based approach to move cells. Net-centric algorithm: Move nets with bigger contributions to the congestion first. ECE260B CSE241A Placement.67

68 Greedy Cell-centric Heuristic ECE260B CSE241A Placement.68

69 Flow-based Cell-centric Heuristic Cell Nodes Bin Nodes ECE260B CSE241A Placement.69

70 Net-centric Heuristic ECE260B CSE241A Placement.70

71 From Global Placement to Detailed Placement Global Placement: Assuming all the cells are placed at the centers of global bins. Detailed Placement: Cells are placed without overlapping. ECE260B CSE241A Placement.71

72 Correlation Between Global and Detailed Placement WL g : Wirelength optimized global placement. CON g : Wirelength optimized detailed placement. WL d : Congestion optimized global placement. CON d : Congestion optimized detailed placement. Conclusion: Congestion at detailed placement level is correlated with congestion at global placement level. Thus reducing congestion in global placement helps reduce congestion in final detailed placement. ECE260B CSE241A Placement.72

73 Congestion Wirelength minimization can minimize congestion globally. A post processing congestion minimization following wirelength minimization works the best to reduce congestion in placement. A number of congestion-related cost functions were tested, including a hybrid length plus congestion (commonly believed to be very effective). Experiments prove that they do not work very well. Net-centric post processing techniques are very effective to minimize congestion. Congestion at the global placement level, correlates well with congestion of detailed placement. ECE260B CSE241A Placement.73

74 Shapes of Cost Functions net-cut cost wirelength congestion Solution Space ECE260B CSE241A Placement.74

75 Relationships Between the Three Cost Functions: The net-cut objective function is more smooth than the wirelength objective function The wirelength objective function is more smooth than the congestion objective function Local minimas of these three objectives are in the same neighborhood. ECE260B CSE241A Placement.75

76 Crossing: A routability estimator? Replace each crossing with a gate A planar netlist Easy to place ECE260B CSE241A Placement.76

77 Timing Cost Critical Path Delay of the circuit is defined as the longest delay among all possible paths from primary inputs to primary outputs. Interconnection delay becomes more and more important in deep sub-micron regime. ECE260B CSE241A Placement.77

78 Timing Analysis L A T C H L A T C H How do we get the delay numbers on the gate/ interconnect? ECE260B CSE241A Placement.78

79 Approaches Budgeting In accurate information Fast Path Analysis Most accurate information Very slow Path analysis with infrequent path substitution Somewhere in between ECE260B CSE241A Placement.79

80 Timing Metrics How do we assess the change in a delay due to a potential move during physical design? Whether it is channel routing or area routing, the problem is the same translate geometrical change into delay change ECE260B CSE241A Placement.80

81 Others costs: Coupling Cost Hard to model during placement Can run a global router in the middle of placement Even at the global routing level it is hard to model it Avoid it ECE260B CSE241A Placement.81

82 Coupling Solutions Once we have some metrics for coupling, we can calculate sensitivities, and optimize the physical design... Noisy region Extra space Grounded Shields Quiet region Segregation Spacing Shielding ECE260B CSE241A Placement.82

83 Other Performance Costs Power usage of the chip. Weighted nets Dual voltages (severe constraint on placement) Very little known about these cost functions and their interaction with other cost functions Fundamental research is needed to shed some light on the structure of them ECE260B CSE241A Placement.83

84 Netlist Granularity: Problem Size and Solution Space Size The most challenging part of the placement problem is to solve a huge system within given amount of time We need to effectively reduce the size of the solution space and/or reduce the problem size Netlist clustering: Edge extraction in the netlist Netlist Granularity Algorithm Layout Coarseness Cost Function ECE260B CSE241A Placement.84

85 Layout Coarsening Reduce Solution Space Edge extraction in the solution space Only simple things have been tried GP, DP (Twolf) 2x1, 2x2,. Coarsen only easy parts Netlist Granularity Algorithm Layout Coarseness Cost Function ECE260B CSE241A Placement.85

86 Incremental Placement Given an optimal placement for a given netlist, how to construct optimal placements for netlists modified from the given netlist. Very little research in this area. Different type of incremental changes (in one region, or all over) Methods to use How global should the method be An extremely important problem. ECE260B CSE241A Placement.86

87 Incremental Placement A placement move changes the interconnect capacitance and resistance of the associated net A net topology approximation is required to estimate these changes ECE260B CSE241A Placement.87

88 Placynthesis Algorithms resizing buffering cloning restructuring ECE260B CSE241A Placement.88

89 Many other Design Metrics: Power Supply and Total Power Vdd Vt power Source: The Incredible Shrinking Transistor, Yuan Taur, T. J. Watson Research Center, IBM, IEEE Spectrum, July 1999 ECE260B CSE241A Placement.89

90 Dual Voltages: A harder problem Layout synthesis with dual voltages: major geometric constraints feedthrough V H V L GND V H H L V L L H IN OUT ECE260B CSE241A Placement.90 H -- High Voltage Block L -- Low Voltage Block Layout Structure Cell Library with Dual Power Rails GND

91 Placement References C. J. Alpert, T. Chan, D. J.-H. Huang, I. Markov, and K. Yan, Quadratic Placement Revisited,Proc. 34th IEEE/ACM Design Automation Conference, 1997, pp C. J. Alpert, J.-H Huang, and A. B. Kahng, Multilevel Circuit Partitioning, Proc. 34th IEEE/ACM Design Automation Conference, 1997, pp U. Brenner, and A. Rohe, An Effective Congestion Driven Placement Framework, International Symposium on Physical Design 2002, pp A. E. Caldwell, A. B. Kahng, and I.L. Markov, Can Recursive Bisection Alone Produce Routable Placements,Proc. 37th IEEE/ACM Design Automation Conference, 2000, pp M.A. Breuer, Min-Cut Placement, J. Design Automation and Fault Tolerant Computing, I(4), 1997, pp J. Vygen, Algorithms for Large-Scale Flat Placement, Proc. 34th IEEE/ACM Design Automation Conference, 1988,pp H. Eisenmann and F. M. Johannes, Generic Global Placement and Floorplanning, Proc. 35th IEEE/ACM Design Automation Conference, 1998, pp S.-L. Ou and M. Pedram, Timing Driven Placement Based on Partitioning with Dynamic Cut-Net Control, Proc. 37th IEEE/ACM Design Automation Conference, 2000, pp C.M. Fiduccia and R.M. Mattheyses, A linear time heuristic for improving network partitions, Proc. ACM/IEEE Design Automation Conference. (1982) pp ECE260B CSE241A Placement.91