CAD TOOLS FOR VLSI. FLOORPLANNING Page 1 FLOORPLANNING
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1 FLOORPLANNING Page 1 FLOORPLANNING Floorplanning: taking layout information into account at early stages of the design process. BEHAVIORAL D. STRUCTURAL D. Systems Algorithms Processors Register transfers ALU s, RAM, etc. Logic Gates, flip-flops, etc. Transfer Transistors functions PHYSICAL D. Transistor layout Cell layout Module layout Floorplans Physical partitions Illustration of the floorplan-based design strategy on Gajski s Y-chart
2 FLOORPLANNING Page 2 THE FLOORPLAN-BASED DESIGN METHODOLOGY Structure is immediately translated into layout, by making estimates of the area, I/O, etc. 0 I T Y X c 1 c 2 FU 0 X I T Y c 1 c 2 FU
3 FLOORPLANNING Page 3 THE FLOORPLAN-BASED DESIGN METHODOLOGY (Continued) * A chip is essentially a two-dimensional medium; taking this aspect into account in early stages of the design helps in creating designs of good quality. * Floorplanning gives early feedback: thinking of layout at early stages may suggest valuable architectural modifications. * Floorplanning fits very well in a top-down design strategy, the stepwise refinement strategy also propagated in software design. * Floorplanning assumes however flexibility in layout design, the existence of cells that can adapt their shapes and terminal locations to the environment.
4 FLOORPLANNING Page 4 FLOORPLANNING CONCEPTS * Abutment: establishing connections between cells by putting them directly next to each other, without the necessity of routing. + I = I * Leaf cell: a cell at the lowest level of the hierarchy; it does not contain any other cell. * Composite cell: a cell that is composed of either leaf cells or composite cells. The whole chip is the highest-level composite cell. Restriction: all leaf cells and composite cells are supposed to be rectangular.
5 FLOORPLANNING Page 5 FLOORPLANNING CONCEPTS (Continued) * Slicing floorplans: a floorplan with the property that a composite cell s subcells are obtained by a horizontal or vertical bisection of the composite cell. Slicing floorplans can be represented by a slicing tree.
6 FLOORPLANNING Page 6 FLOORPLANNING CONCEPTS (Continued) * In a slicing tree, all cells (except for the toplevel cell) have a parent, and all composite cells have children. * Not all floorplans are slicing. Composite cell without the slicing property * Limiting floorplans to those that have the slicing property is reasonable: it certainly facilitates floorplanning algorithms.
7 FLOORPLANNING Page 7 SLICING TREE GENERATION The automatic generation of a slicing tree is similar to the automatic placement of cells. One could e.g. use a min-cut partitioning algorithm.
8 FLOORPLANNING Page 8 SHAPE FUNCTIONS Flexible cells imply that cells can assume different aspect ratios. * One can e.g. assume that all implementations of the cell have the same area A. The relation between the width w and the height h is: hw A, or h w A. The shape function is a hyperbola. h legal shapes w
9 FLOORPLANNING Page 9 SHAPE FUNCTIONS (Continued) * Very thin cells are not interesting and often not feasible to design. The shape function is a combination of a hyperbola and two straight lines. h w
10 FLOORPLANNING Page 10 SHAPE FUNCTIONS (Continued) * Leaf cells are built from discrete transistors: it is not realistic to assume that the shape function follows the hyperbola continuously. * In an extreme case, a cell is rigid: it can only be rotated and mirrored during floorplanning or placement. This type of cell is called an inset cell. h The shape function of a 2 4 inset cell. w
11 FLOORPLANNING Page 11 SHAPE FUNCTIONS (Continued) * In general a piecewise linear function can be used to approximate any shape function. h w * The points where the function changes its coefficient are called the break points of the piecewise linear function.
12 FLOORPLANNING Page 12 THE SHAPE FUNCTION OF COMPOSITE CELLS The shape function of a composite cell obtained by vertical abutment is the sum of the shape functions of its children cells. h f 3 f 1 f 2 f 3 f 2 f 1 w
13 FLOORPLANNING Page 13 THE SHAPE FUNCTION OF COMPOSITE CELLS (Continued) * In case of horizontal abutment, the computation of the new shape function is somewhat more complicated: f 1 3 f 1 1 f 1 2. * A choice for the minimal shape of composite cell fixes the shapes of the shapes of its children cells. minimal area of parent consequence for children s shapes
14 FLOORPLANNING Page 14 SIZING ALGORITHM FOR SLICING FLOORPLANS * The shape functions of all leaf cells are given as piecewise linear functions. * Traverse the slicing tree in order to compute the shape functions of all composite cells (bottom-up composition). * Choose the desired shape of the top-level cell; as the shape function is piecewise linear only the break points of the function need to be evaluated, when looking e.g. for the minimal area. * Propagate the consequences of the choice down to the leaf cells (top-down propagation). Note: the algorithm operates in polynomial time!
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