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ICS 252 Introduction to Computer Design

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Presentation on theme: "ICS 252 Introduction to Computer Design"— Presentation transcript:

1 ICS 252 Introduction to Computer Design
Multi-level Logic Optimization Fall 2006 Eli Bozorgzadeh Computer Science Department-UCI

2 Multi-level logic optimization
Representation Optimization Goal: area/delay Algorithmic: algebraic, Boolean Rule-based methods Examples of transformations Fall 2006 ICS 252-Intro to Computer Design

3 ICS 252-Intro to Computer Design
Motivation Multiple-level networks: Semi-custom libraries. Gates versus macros (PLAs): More flexibility. Better performance. Applicable to a variety of designs. ©GDM Fall 2006 ICS 252-Intro to Computer Design

4 ICS 252-Intro to Computer Design
Circuit Modeling Logic network: Interconnection of logic functions. Hybrid structural/behavioral model. Bound (mapped) networks: Interconnection of logic gates. Structural model. ©GDM Fall 2006 ICS 252-Intro to Computer Design

5 Multi-level vs. Two-level
PLA Control logic Constrained layout Highly automatic Technology independent Slower Multi valued function Input,output, state encoding Multi-level All logic General Automatic Partially tech dependent Can be faster Fall 2006 ICS 252-Intro to Computer Design

6 Example of bound network
q y c va vp vx vb vc vq vy ©GDM Fall 2006 ICS 252-Intro to Computer Design

7 ICS 252-Intro to Computer Design
Example of network ©GDM Fall 2006 ICS 252-Intro to Computer Design

8 ICS 252-Intro to Computer Design
Example of network a v=a’d+bd+c’d+ae’ w b x p=ce+de r=p+a’ s=r+b’ c t=ac+bd+bc+bd+e y d z e q=a+b u=q’c+qc’+qc ©GDM Fall 2006 ICS 252-Intro to Computer Design

9 ICS 252-Intro to Computer Design
Network optimization Minimize area (power) Subject to delay constraint Minimize maximum delay Subject to area (power) constraint Minimize power consumption Maximize testability ©GDM Fall 2006 ICS 252-Intro to Computer Design

10 ICS 252-Intro to Computer Design
Estimation Area: Number of literals Number of functions/gates Delay Number of stages Refined gate delay models paths ©GDM Fall 2006 ICS 252-Intro to Computer Design

11 ICS 252-Intro to Computer Design
Problem analysis Multi-level optimization is hard Exact models Exponential complexity Impractical Approximate methods Heuristics algorithms Rule-based methods ©GDM Fall 2006 ICS 252-Intro to Computer Design

12 Strategies for optimization
Improve circuit step by step Circuit transformation Preserve network behavior Methods differ in Types of transformations Selection and order of transformations ©GDM Fall 2006 ICS 252-Intro to Computer Design

13 ICS 252-Intro to Computer Design
Eliminate Eliminate one function from the network Perform variable substitution Example: s = r + b’; r = p + a’; s = p + a’ + b’; ©GDM Fall 2006 ICS 252-Intro to Computer Design

14 ICS 252-Intro to Computer Design
Example a v=a’d+bd+c’d+ae’ w b x p=ce+de s=p+a’+b’ c t=ac+bd+bc+bd+e y d z e q=a+b u=q’c+qc’+qc ©GDM Fall 2006 ICS 252-Intro to Computer Design

15 ICS 252-Intro to Computer Design
decomposition Break one function into smaller ones Introduce new vertices in the network Example ©GDM Fall 2006 ICS 252-Intro to Computer Design

16 ICS 252-Intro to Computer Design
Example v=a’+b+c’ V=jd+ae’ a w b p=ce+de r=p+a’ x s=r+b’ c t=ac+bd+bc+bd+e y d z q=a+b u=q’c+qc’+qc e ©GDM Fall 2006 ICS 252-Intro to Computer Design

17 ICS 252-Intro to Computer Design
Example extraction Find a common sub-expression of two or more expressions Extract sub-expression as new function Introduce new vertex in the network Example ©GDM Fall 2006 ICS 252-Intro to Computer Design

18 ICS 252-Intro to Computer Design
Example a v=a’d+bd+c’d+ae’ w b x p=ke r=p+a’ s=r+b’ c K=c+d t=ka+kb+e y d q=a+b u=q’c+qc’+qc z e ©GDM Fall 2006 ICS 252-Intro to Computer Design

19 ICS 252-Intro to Computer Design
Simplification Simplify a local function Example ©GDM Fall 2006 ICS 252-Intro to Computer Design

20 ICS 252-Intro to Computer Design
Example a v=a’d+bd+c’d+ae’ w b x p=ce+de r=p+a’ s=r+b’ c t=ac+bd+bc+bd+e y d z e q=a+b u=q+c ©GDM Fall 2006 ICS 252-Intro to Computer Design

21 ICS 252-Intro to Computer Design
substitution Simplify a local function by using an additional input that was not previously in its support set. Example ©GDM Fall 2006 ICS 252-Intro to Computer Design

22 ICS 252-Intro to Computer Design
Example a v=a’d+bd+c’d+ae’ w b x p=ke r=p+a’ s=r+b’ c K=c+d t=ka+kb+e y d q=a+b u=q’c+qc’+qc z e ©GDM Fall 2006 ICS 252-Intro to Computer Design

23 ICS 252-Intro to Computer Design
Example a v=a’d+bd+c’d+ae’ w b x p=ke r=p+a’ s=r+b’ c K=c+d t=kq+e y d q=a+b u=q’c+qc’+qc z e ©GDM Fall 2006 ICS 252-Intro to Computer Design

24 Optimization approaches
Algorithmic approach Define an algorithm for each transformation Algorithm is an operator on the network Rule-based approach Rule-data base Set of pattern pairs Pattern replacement by rules ©GDM Fall 2006 ICS 252-Intro to Computer Design

25 ICS 252-Intro to Computer Design
Algorithmic approach Each operator has well-defined properties Heuristic methods Weak optimality Sequence of operators Defined by scripts in SIS Based on experience ©GDM Fall 2006 ICS 252-Intro to Computer Design

26 Example of script in SIS
sweep; eliminate -1 simplify –m nocomp eliminate -1 sweep; eliminate 5 resub –a fx resub –a;sweep… ©GDM Fall 2006 ICS 252-Intro to Computer Design

27 Boolean and algebraic methods
Boolean methods Exploit properties of logic functions Use don’t care conditions Complex Algebraic methods View functions as polynomials Exploit properties of polynomial algebra Simpler, faster but weaker ©GDM Fall 2006 ICS 252-Intro to Computer Design

28 ICS 252-Intro to Computer Design
summary Multilevel logic synthesis is performed by step-wise transformations Algorithms are based on both the Boolean and the algebraic models Rule-based ©GDM Fall 2006 ICS 252-Intro to Computer Design

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