I. Floorplanning with Fixed Modules Fixed modules only, no rotation - - PowerPoint PPT Presentation

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I. Floorplanning with Fixed Modules Fixed modules only, no rotation - - PowerPoint PPT Presentation

Oct 13, 2022 261 likes •502 views

I. Floorplanning with Fixed Modules Fixed modules only, no rotation allowed m 1 (4,5), m 2 (3,7), m 3 (6,4), m 4 (7,7) Practical Problems in VLSI Physical Design ILP Floorplanning (1/22) ILP Formulation Practical Problems in VLSI

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Practical Problems in VLSI Physical Design ILP Floorplanning (1/22)

Fixed modules only, no rotation allowed

m1 (4,5), m2 (3,7), m3 (6,4), m4 (7,7)

  • I. Floorplanning with Fixed Modules
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Practical Problems in VLSI Physical Design ILP Floorplanning (2/22)

ILP Formulation

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Practical Problems in VLSI Physical Design ILP Floorplanning (3/22)

Non-Overlapping Constraints (cont)

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Practical Problems in VLSI Physical Design ILP Floorplanning (4/22)

Additional Constraints

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Practical Problems in VLSI Physical Design ILP Floorplanning (5/22)

Solutions

Using GLPK we get the following solutions:

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Practical Problems in VLSI Physical Design ILP Floorplanning (6/22)

Final Floorplan

Why the non-optimality?

Due to linear approximation of area objective (= y*) Chip width/height constraints also affected In fact, our ILP solution (y* = 12) is optimal under these

conditions.

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Practical Problems in VLSI Physical Design ILP Floorplanning (7/22)

  • II. Floorplanning with Rotation

Fixed modules, rotation allowed

Fixed modules: m1 (4,5), m2 (3,7), m3 (6,4), m4 (7,7) Need 4 more binary variables for rotation: z1, z2, z3, z4 We use M = max{W,H} = 23

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Practical Problems in VLSI Physical Design ILP Floorplanning (8/22)

ILP Formulation

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Practical Problems in VLSI Physical Design ILP Floorplanning (9/22)

Non-Overlapping Constraints (cont)

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Practical Problems in VLSI Physical Design ILP Floorplanning (10/22)

Non-Overlapping Constraints (cont)

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Practical Problems in VLSI Physical Design ILP Floorplanning (11/22)

Additional Constraints

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Practical Problems in VLSI Physical Design ILP Floorplanning (12/22)

Solutions

Using GLPK we get the following solutions:

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Practical Problems in VLSI Physical Design ILP Floorplanning (13/22)

  • III. Floorplanning with Flexible Modules

2 Fixed modules:

m1 (4,5), m2 (3,7) (rotation allowed)

2 Flexible modules:

m3: area = 24, aspect ratio [0.5, 2] m4: area = 49, aspect ratio [0.3, 2.5]

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Practical Problems in VLSI Physical Design ILP Floorplanning (14/22)

Linear Approximation

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Practical Problems in VLSI Physical Design ILP Floorplanning (15/22)

Linear Approximation (cont)

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Practical Problems in VLSI Physical Design ILP Floorplanning (16/22)

Upper Bound of Chip Dimension

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Practical Problems in VLSI Physical Design ILP Floorplanning (17/22)

Non-Overlap Constraint

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Practical Problems in VLSI Physical Design ILP Floorplanning (18/22)

Non-Overlap Constraint (cont)

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Practical Problems in VLSI Physical Design ILP Floorplanning (19/22)

More Constraints

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Practical Problems in VLSI Physical Design ILP Floorplanning (20/22)

Solutions

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Practical Problems in VLSI Physical Design ILP Floorplanning (21/22)

Comparison

Fixed modules only = 12 × 12 Rotation allowed = 11 × 11 Flexible modules used = 10.46 × 10.32

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Practical Problems in VLSI Physical Design ILP Floorplanning (22/22)

Approximation Error and Overlap

Due to linear approximation

Approximated area of m3 = 3.46 × 5.2 = 17.99 (actually 24) Approximated area of m4 = 3.83 × 7.32 = 28.04 (actually 49) Real area of m3 = 3.46 × 6.94 = 24 Real area of m4 = 3.83 × 12.79 = 49 Floorplan area increases, overlap occurs