RTL Design Flow - Computation Structures Group

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Technologies “Closed book”: gate-array standard-cell “Open book”: CMOS Domino, complex gate static CMOS LOGIC EQUATIONS TECHNOLOGY-INDEPENDENT OPTIMIZATION TECH-DEPENDENT OPTIMIZATION (MAPPING, TIMING) OPTIMIZED LOGIC NETWORK Optimizations F = ⎧ ⎨ ⎩ Factor F ⎧ F = ⎨ ⎩ f 1 = AB + AC + AD + AE + A BC D E f 2 = AB + AC + AD + AF + A BC D F f1 = AB+ ( C + D + E)+ABCDE f2 = A( B + C + D + F)+ABCDF Extract common expression ⎧ g1 = B + C + D G = ⎨ f1 ⎪ ⎩ f2 = A( g1 + E ) + A E g1 = A( g1 + F )+ A F g1 Factoring Commonality Extraction LIBRARY 5 7 Tech.-Independent Optimization Involves: Minimizing two-level logic functions. Finding common subexpressions. Substituting one expression into another. Factoring single functions. Factored versus Disjunctive forms f = ac + ad + bc + bd + ae sum-of-products or disjunctive form f = ( a + b ) ( c + d ) + ae factored form multi-level or complex gate What Does “Best” Mean? Transistor count AREA Number of circuits POWER Number of levels DELAY (Speed) Need quick estimators of area, delay and power which are also accurate 6 8
Algebraic vs. Boolean Methods Algebraic techniques view equations as polynomials and attempt to factor equations or “divide” them Do not exploit Boolean identities e.g., a a = 0 In algebraic substitution (or division) if a function f = f(a, b, c) is divided by g = g(a, b), a and b will not appear in f / g Algebraic division: O(n log n) time Boolean division: 2-level minimization required Strong (or Boolean) Division Given a function f to be strong divided by g Add an extra input to f corresponding to g, namely G and obtain function h as follows h DC = Gg+ Gg h ON = f ON − h DC Minimize h using two-level minimizer 9 11 Comparison f = ab + ac+ ba+ bc + ca + cb Algebraic factorization procedures f = a( b + c ) + a ( b + c ) + bc + cb Boolean factorization produces f = ( a + b + c ) ( a + b + c ) l = ( bf+ bf ) ( a + e)+ ae( b f + bf ) r = ( bf+ b f ) ( a + e)+ ae( b f + bf ) Algebraic substitution of l into r fails Boolean substitution r = a( el + el ) + a( el + el ) l = a( er + e r ) + a( er + er) Strong Division Example f=a bc +abc +abc +a b c g = ab+ab bc 00 01 11 10 Ga 00 01 11 10 1 x x x x x Minimization gives h = G c + G c 1 h DC = G (a b + a b) + G (a b + a b) h ON = f ON − h DC 1 x x x 1 Function h 10 12
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Page 5 and 6: Tech.-Dependent Optimization LIBRAR
Page 7 and 8: DAG Covering Sound Algorithmic appr
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Page 11 and 12: Modeling the Net’s Wire Length (x
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Page 15 and 16: Final Placement - 1 Earlier steps h
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RTL Design Flow - Computation Structures Group

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