C2: VLSI CAD Tools Problems and Algorithms

C2:C2: VLSI CAD Tools VLSI CAD Tools Problems and AlgorithmsProblems and Algorithms

Marcelo JohannMarcelo Johann

EAMTA 2006EAMTA 2006

EAMTA 2006 - Marcelo Johann - C21.2

OutlineOutlineFIRST PART

• Tools and CAD• The Placement Problem• The Routing Problem•Complexity, Graphs and Optimization

SECOND PART•Routing Algorithms• Placement Algorithms• Interconnections•Methodology Aspects


OutlineOutlineTHIRD PART

• Layout Compaction• Logic Synthesis, BDDs• Technology Mapping• Simmulation vs Formal Verification• Voltage Drop by Random Walks

FOURTH PART•High-Level Synthesis•CDFG, Allocation, Scheduling, Generation


ToolsToolsA long time ago we discovered the first tools…


ToolsTools…tools started to get more sophisticated…


ToolsTools…more sophisticated and complex…


ToolsTools…and then came VLSI CAD tools!


ToolsToolsDesigners use CAD tools to make Chips


ToolsToolsAnd there is a chain of tools that make tools.

g++g++STLSTL

MathCSEE

CEEE


ToolsTools

g++g++STLSTL

MathCSEE

CEEE

EEPhyChe

ProgrammingAlgorithmsGraph TheoryOptimization

VLSI Design

Foundry


But why CAD tools???But why CAD tools???

• Complexity

> 100.000.000 xtores

• Efficiency

– Effort, + productivity


Cresc

imen

to d

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cado

Desaparecimento do M

ercado

perd

a

atraso

tempo

rece

itaTime to Market


Design FlowDesign Flow

Projetista faz descrição inicial (ex:VHDL) e usa um método, um conjunto de operações com ferramentas para obter o circuito

• Síntese de alto-nível;

• Síntese Lógica;

• Síntese Física:

Placement

Routing


The Routing ProblemThe Routing Problem

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.


The Placement ProblemThe Placement Problem

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.



a b c d e f

g h i j k l

But why this way?



a

b c

d

e f

g

h

ij

k

l

And not this way?


The Placement ProblemThe Placement ProblemBecause in some dispositions cells to connect are a lot closer



a

b c

d

e f

g

h

ij

k

l

12 !

Ok. Lets see how many options we have…

That’s479.001.600

for a circuit with only 12 cells!!!

The Placement The Placement ProblemProblem


Algorithms and DataAlgorithms and Data

Algorithm Sequence of steps to solve a problem• Fundamental area of math and CS theory

Data Sctructures The way data is organized is as important as

an algorithm in order to efficiently solve a problem

• Fundamental area of applied CS;


Graph TheoryGraph TheoryGraph A Set and a set or Pairs

Relation Each pair elementbelongs to the other set

Function There is a single element fromone set associated to each elementof the first set


Circuito representado por um grafo G=(V,E)

v1

v2

v3 v4

v5

v6

v7

v8

v9

componentes

redes

RepresentationRepresentation


A Placement AlgorithmA Placement Algorithm

SA512.ppt


The Routing ProblemThe Routing Problem

+ =

Back again… After placement• Lets see how we can add connections to the

cells so that we build a real circuit

• Switch to Glauco’s Routing Intro - part 1


The Maze RouterThe Maze Router


The Maze RouterThe Maze Router


Maze RouterMaze Router’s expansion’s expansion g++void print(void);int bfs(int source, int target) { queue<int> q; q.push(source); while (!q.empty()) { int n = q.front(); q.pop(); if (n==target)

return 1; if (Space[n] != 'X')

{Space[n] = 'X';print();getchar();q.push(WEST(n));q.push(EAST(n));q.push(NORTH(n));q.push(SOUTH(n));}

} return 0; }

#include <iostream>#include <queue>using namespace std;#define SIDE 20#define PLACE(x,y) ((y)*SIDE+(x))#define WEST(n) (n-1)#define EAST(n) (n+1)#define NORTH(n) (n-SIDE)#define SOUTH(n) (n+SIDE)char Space[SIDE*SIDE];void init (void) { for (int i=0; i<SIDE*SIDE; ++i) Space[i] = ' '; for (int i=0; i<SIDE; ++i) { Space[PLACE(i,0)] = 'X'; Space[PLACE(i,SIDE-1)] = 'X'; Space[PLACE(0,i)] = 'X'; Space[PLACE(SIDE-1,i)] = 'X'; } for (int i=3; i<SIDE-3; ++i) Space[PLACE(i,10)] = 'X'; }


Maze RouterMaze Router’s tracking’s tracking g++typedef pair<int,int> Ref;

char Expansion[SIDE*SIDE];char Taken[SIDE*SIDE];

int bfs(int source, int target) { queue<Ref> q; q.push(Ref(source,0)); while (!q.empty()) { int n = q.front().first; int p = q.front().second; q.pop(); if (n==target)

return 1; if (Expansion[n] == 0 &&

Taken[n] == ' '){Expansion[n] = p;q.push(Ref(WEST(n),n));. . . }

} return 0; }

1-You have to store the node and where it came from in the queue using a pair<int,int>

2-Instead of Space, use Expansion[n] to store where the nodes came from and Taken to represent obstacles and routes

4-Write backtrack(t,s) from target to source following Expansion[n]


Solution SpaceSolution SpaceMethods to find a valid solutionCombinatorial Optimazation Algorithms• Key areas of Computer Science

http://www.rci.rutgers.edu/~cfs/305_html/ProblemSolving_Planning/TOH3DiskSol.html


ComplexityComplexityfunção n = 2 n = 6 n = 10 n = 20 n = 102 n = 103 n = 106

n 2 6 10 20 102 103 106

3n 6 18 30 60 3 * 102 3 * 103 3 * 106

n log10 n 0.6 4.7 10 26 2 * 102 3 * 103 6 * 106

n2 4 36 102 4 * 102 104 106 1012

n3 8 216 103 8 * 103 106 109 1018

2n 4 64 103 106 1030 10301 > 10500

n! 2 720 3 * 106 2 * 1018 9 * 10157 > 10500 > 10500


Complexity vs SpeedComplexity vs Speed

Both are important in practice

Complexity• When the problem’s instance size increases

Speed• When the problem’s instance size is

bounded


AlgorithmsAlgorithms• Exact Algorithms• Heuristic and Meta-Heuristic Algorithms• Randomized Algorithms


Graphs RepresentationGraphs RepresentationAdjacency Matrix• Tells which pair is connectedList of Edges• Enumarates each pairList of Neighbors• Is a vector of listsGenerating function• A successor operatorDedicated• Uses implicit graph structure

C2:C2: VLSI CAD Tools VLSI CAD Tools Problems and AlgorithmsProblems and Algorithms

EAMTA 2006EAMTA 2006

Marcelo JohannMarcelo Johann

[email protected]

www.inf.ufrgs.br/~johann

Part 1 ends

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C2: VLSI CAD Tools Problems and Algorithms