Analysis of Floorplanning Algorithm in EDA Tools

1. Analysis of Floorplanning Algorithm in EDA Tools By: RENISHKUMAR V. LADANI M.TECH-2003, DA-IICT GANDHINAGAR GUIDE: PROF. ASHOK AMIN CO-GUIDE: PROF. AMIT BHATT

2. Floorplanning in context of VLSI physical Design • Bottom-up methodology • Top-down methedology:FLOORPLAN-BASED DESIGN METHODOLOGY

3. Floorplanning in context of VLSI physical Design • Bottom-up methodology • May leads to poor utilization of the chip area and excessive wiring • Top-down methedology:FLOORPLAN-BASED DESIGN METHODOLOGY • It advocates that layout aspects should be taken into account in all design stages. • Advantege: • Gives early feed back • Suggests valuable architectural modifications • Estimates the whole chip area • Estimates wire length • Estimates delay and congestion due to wiring

4. Floorplan Example

5. Floorplanning Problem • Input to the floorplanning problem: • A set of blocks, hard of soft • Pin locations of hard blocks • A netlist (interconnect pattern) • Output expected from the floorplanning problem: • Shapes of soft blocks • Position of each blocks in final layout • Objectives: • Minimize area • Reduce wirelengths • Maximize routability (minimize congestion) • Delay of critical path • Noise, heat dissipation, etc.

6. The Cost Function Cost = *Atot + *Wtot Where, Atot= Total area of the packing. Wtot= Total wire length of packing.  and  = User specified constant. • Exact wire length of each net is not known until routing is done and also pin positions are not known yet for soft blocks • Two ways of wire length estimation • center-to-center estimation • half-perimeter estimation Wire length Estimation

7. Some Constraints in Floorplanning • Preplaced constraint • Boundary constraint • Range constraint • Note that in floorplanning some times L-shaped, U-shaped blocks are being considered in addition to rectangular blocks. Floorplan Sizing: A optimization problem in Floorplanning The availability of flexible blocks implies the possibility of having different shapes for the same hardware units. Its therefore possible to choose a suitable shape for each flexible blocks such that the resulting floorplan is optimal in some sense (e.g. minimal area).

8. Floorplanning Concepts and Approaches to Problem • The floorplan problem is known to be NP-complete • Various heuristic approaches • Simulated Annealing (SA) • Genetic Algorithm (GA) • Hybrid approach(SAGA: simulated annealing and genetic algorithm) • These algorithms depend on representation of feasible solution space • Classification of representation: • Slicing floorplan representation • Non-slicing floorplan representation

9. Slicing Structure • Rectangular Dissection: Subdivision of a given rectangle by a finite # of horizontal and vertical line segments into a finite # of non-overlapping rectangles. • Slicing structure: A rectangular dissection that can be obtained by repetitively subdividing rectangles horizontally or vertically. • Slicing tree: A binary tree, where each internal node represents a vertical cut line or horizontal cut line, and each leaf a basic rectangle. • Polish expression: Expression obtained Post order traversal of slicing tree. (16+35*2+74+**) Wong and Liu proposed an algorithm based on simulated annealing for slicing floorplan designs using a normalized polish expression(extension of polish expression) to represent a slicing structure.

10. Non-Slicing Structure • Not all floorplans are slicing • If the basic rectangles corresponding to leaf nodes in slicing structures can not be obtained by recursive cutting rectangles into smaller rectangles then the floorplan has non-slicing structure • Non-Slicing Floorplan Representation • Sequence Pair(SP) • Bounded Slicing Grid (BSG) • O-tree • Transitive Closure Graph (TCG) • Corner Block List (CBL) • B* Trees • Generalized Polish Expression(GPE)

11. Simulated annealing 01 Temperature = Intial Temperature; 02 Current placement = Random initial placement; 03 Current score = Score( Current placement); 04 While equilibrium at temperature not reached Do 05 Selected component = Select (at random); 06 Trail placement = Move (selected component); 07 Trail score = Score (trail placement); 08 If trail score < current score then 09 Current score = trial score; 10 Current placement = trail placement; 11 else 12 if uniform random(0,1) < e-(trail score – current score)/temperature then 13 Current score = trial score; 14 Current placement = trail placement; 15 temperature = temperature * Alpha; // alpha ~ 0.95 Well-known high performance optimization technique for combinatorial problems

12. Comparisons between slicing and non-slicing approach • Slicing representation • Advantages: • Smaller encoding cost and solution space bringing faster runtime for packing • Flexible to deal with hard, preplaced, soft and rectilinear blocks • Disadvantages: • Optimal solution might not be in the solution space of slicing structure • Non-slicing representation • Advantages: • Optimal solution might be achieved. • Disadvantages: • Needs more evaluating runtime for packing

13. Representation SP Fast-SP BSG O-tree B*-tree CBL TCG GPE Is P-admissible? Yes Yes Yes No No No Yes Yes Need sequence encoding? Yes Yes No Yes No Yes No No Constraint graphs for packing? Yes Yes Yes Yes No Yes No No Solution space size n!2 n!2 2n(n+2) O(n!22n-2 /n1.5) O(n!23n-3 /n1.5) O(n!23n-3 /n1.5) N!2 - Runtime for packing O(n2) O(n lg n lg n) O(n2) O(n) O(n) O(n) O(n2) O(n) Number of bits to describe floorplan 2n[lg n] 2n[lg n] - 2n+n[lg n] 6n+n[lg n] 3n+n[lg n] - - State-of-art in floorplan representations Table 1: Properties of representations. Here, n is the number of modules in the placement.

14. State-of-art in floorplan representations Table 2: Comparisons for runtime and area requirements among O-TREE, B*-TREE, CBL, SP and TCG based on genetic and simulated annealing algorithms. (NA: NOT AVAILABLE) It is important to note that GPE achieves area utilization compared to previous Fast-SP and Enhance O-tree.

15. GPE: Generalized Polish Expression • New and easy representation for VLSI floorplan • Effectively inherits the useful property of Normalized Polish Expression for slicing structure • Present non-slicing floorplan • The time complexity to transform a GPE to a corresponding placement is O(n).

16. Future planning Note sizing means handling soft(flexible) blocks while floorplanning. • Floorplan sizing can be done optimally and efficiently for slicing floorplans • “Shape Curve Computation” used for sizing flexible blocks • Sizing algorithm runs in polynomial time • Floorplan sizing can be done optimally but not efficiently for some slicing non-slicing floorplans, which are using Constraints Graph for packing such as SP, Fast-SP, O-tree and B-tree. • GPE a new representation for non-slicing floorplans, which has achieved promising result in area utilization as compared to Fast-SP and O-tree. • Since its inherits properties from polish expression for which sizing (shaping for soft blocks) can be done in polynomial time, it raises hopes that with GPE sizing can be done in less time then timing required by sizing for Non slicing floorplans. • Study for handling soft(flexible) blocks has been not carried out.

17. Thanks Question and Answer