CAD TOOLS FOR VLSI

FLOORPLANNING Page 1

FLOORPLANNING

Floorplanning: taking layout information intoaccount at early stages of the design process.

BEHAVIORAL D.STRUCTURAL D.

PHYSICAL D.

Physical partitions

Floorplans

Module layout

Cell layout

Transistor layout

Systems

Algorithms

Register transfers

Logic

Transferfunctions

Processors

ALU’s, RAM, etc.

Gates, flip-flops, etc.

Transistors

Illustration of the floorplan-based designstrategy on Gajski’s Y-chart

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FLOORPLANNING Page 2

THE FLOORPLAN-BASEDDESIGN METHODOLOGY

Structure is immediately translated into layout,by making estimates of the area, I/O, etc.

I T Y

FU

0

X c1

c2

FU

IT

YX

c1

c2

0

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FLOORPLANNING Page 3

THE FLOORPLAN-BASEDDESIGN METHODOLOGY

(Continued)

* A chip is essentially a two-dimensional me-dium; taking this aspect into account in earlystages of the design helps in creating designsof good quality.

* Floorplanning gives early feedback: thinkingof layout at early stages may suggest valuablearchitectural modifications.

* Floorplanning fits very well in a top-downdesign strategy, the stepwise refinement strat-egy also propagated in software design.

* Floorplanning assumes however flexibility inlayout design, the existence of cells that canadapt their shapes and terminal locations tothe environment.

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FLOORPLANNING Page 4

FLOORPLANNINGCONCEPTS

* Abutment: establishing connections betweencells by putting them directly next to eachother, without the necessity of routing.

II+ =

* Leaf cell: a cell at the lowest level of the hier-archy; it does not contain any other cell.

* Composite cell: a cell that is composed of ei-ther leaf cells or composite cells. The wholechip is the highest-level composite cell.

Restriction: all leaf cells and composite cells aresupposed to be rectangular.

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FLOORPLANNING Page 5

FLOORPLANNINGCONCEPTS (Continued)

* Slicing floorplans: a floorplan with the prop-erty that a composite cell’s subcells are ob-tained by a horizontal or vertical bisection ofthe composite cell. Slicing floorplans can berepresented by a slicing tree.

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FLOORPLANNING Page 6

FLOORPLANNINGCONCEPTS (Continued)

* In a slicing tree, all cells (except for the top-level cell) have a parent, and all compositecells have children.

* Not all floorplans are slicing.

Composite cell without the slicing property

* Limiting floorplans to those that have theslicing property is reasonable: it certainly fa-cilitates floorplanning algorithms.

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FLOORPLANNING Page 7

SLICING TREEGENERATION

The automatic generation of a slicing tree is sim-ilar to the automatic placement of cells. Onecould e.g. use a min-cut partitioning algorithm.

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FLOORPLANNING Page 8

SHAPE FUNCTIONS

Flexible cells imply that cells can assume differ-ent aspect ratios.* One can e.g. assume that all implementations

of the cell have the same area A. The relationbetween the width w and the height h is:

hw� A, or h �

Aw. The shape function is a

hyperbola.

h

w

legalshapes

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FLOORPLANNING Page 9

SHAPE FUNCTIONS(Continued)

* Very thin cells are not interesting and oftennot feasible to design. The shape function isa combination of a hyperbola and two straightlines.

h

w

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FLOORPLANNING Page 10

SHAPE FUNCTIONS(Continued)

* Leaf cells are built from discrete transistors:it is not realistic to assume that the shapefunction follows the hyperbola continuously.

* In an extreme case, a cell is rigid: it can onlybe rotated and mirrored during floorplanningor placement. This type of cell is called an in-set cell.

h

w

The shape function of a 2� 4 inset cell.

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FLOORPLANNING Page 11

SHAPE FUNCTIONS(Continued)

* In general a piecewise linear function can beused to approximate any shape function.

h

w

* The points where the function changes its co-efficient are called the break points of thepiecewise linear function.

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FLOORPLANNING Page 12

THE SHAPE FUNCTIONOF COMPOSITE CELLS

The shape function of a composite cell obtainedby vertical abutment is the sum of the shapefunctions of its children cells.

h

w

f1

f2

f3

f3 � f1 � f2

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FLOORPLANNING Page 13

THE SHAPE FUNCTIONOF COMPOSITE CELLS

(Continued)

* In case of horizontal abutment, the computa-tion of the new shape function is somewhatmore complicated: f�1

3 � f�11 � f�1

2 .

* A choice for the minimal shape of compositecell fixes the shapes of the shapes of its chil-dren cells.

minimalareaof parent

consequence forchildren’s shapes

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FLOORPLANNING Page 14

SIZING ALGORITHM FORSLICING FLOORPLANS

* The shape functions of all leaf cells are givenas piecewise linear functions.

* Traverse the slicing tree in order to computethe shape functions of all composite cells(bottom-up composition).

* Choose the desired shape of the top-levelcell; as the shape function is piecewise linearonly the break points of the function need tobe evaluated, when looking e.g. for the mini-mal area.

* Propagate the consequences of the choicedown to the leaf cells (top-down propaga-tion).

Note: the algorithm operates in polynomialtime!