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CSE 242A Integrated Circuit Layout Automation Lecture 5: Placement Winter 2009 Chung-Kuan Cheng
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Placement Formulation ½ perimeter of min bounding box Single trunk (v or h) Spanning tree Steiner tree
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Layout Area Rectilinear Area Block Shapes Single row height: width=1~2 or even hunderds Multiple rows Donuts
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Formulation: Constraints Groups: A set of cells to be placed within X & Y distance Regions: If a cell is attached to a region, it needs to be placed within the specified area. Sites: Each slot has a type. Each cell is specified by types on its area. The types have to be matched for a correct placement.
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IO Placement
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Placement Formulation Quadratic Assignment (NP Complete) Linear Assignment
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Placement Methods Analytical Method Constructive Method Iterative Method
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Analytical Method: QPlace (RAMP) Resistive Analog Module Placement ab c d a b c d
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Analytical Method (Obj)
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Analytical Method: Obj
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Analytical Method Constraints Sum x i = c 1 Sum x i 2 = c 2 Sum x i 3 = c 3 Sum x i n = c n
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Repulsive Force i j If i & j are not connected By density
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Constructive Method Input: Seeds X, Unplaced set V-X Pick a cell in in V-X with strongest connection to X Place i at a location so that partial cost is minimized Adv: Fast, Simple, Flexible Dis: Quality of the Results
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Iterative Improvement Given an initial placement A. Find the best pair to swap B. Find the best sequence to swap A D B C A B C D
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Iterative Method Target zone of each component i: Count from left. Each a e or b e is counted once, Target zone = Region between |N| and |N|+1.
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Simulated Annealing
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SA Cost Function
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Window Size, Temperature, & acceptance ratio
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Local Placement abcd Choose k cells Find the opt sequence of the k cells Find a larger set of cells Derive the opt matching (Ignore the relation between the k cells)
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Performance Driven Placement Replication a xb a x x b Gate Sizing, Buffer Insertion
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Pin Swapping a b c acb
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