1. Electrical and Computer Engineering Archana Rengaraj ABC Logic Synthesis basics ECE 667 Synthesis and Verification of Digital Systems Spring 2011

2. 2 Electrical and Computer Engineering Overview  Introduction Previous synthesis methods  ABC synthesis  And-Inverter Graphs (AIG) representation AIG canonicity and redundancy AIG construction  NPN equivalence  AIG transformations Rewriting ABC commands  Summary

3. 3 Electrical and Computer Engineering Introduction  Synthesis of a design Conversion of abstract form of desired circuit behavior into a form of logic gates  Processing combinational logic before technology mapping technology independent optimization  Technology dependent optimization Synthesis targeting ASICs and FPGAs

4. 4 Electrical and Computer Engineering SIS Synthesis  Previous systems for logic synthesis and optimization: SIS, VIS – Verification Interacting with Synthesis, MVSIS - Multi valued SIS  Drawbacks of these systems Cannot integrate technology mapping and retiming Inefficient for large circuits Areas of improvement quality and runtime of synthesis and verification

5. 5 Electrical and Computer Engineering SIS Synthesis algorithm  Traditional combinational synthesis steps sweep – removing redundant nodes eliminate, resubstitute - finding better logic boundaries fast_extract – detect shared logic simplify, full_simplify – optimization of nodes

6. 6 Electrical and Computer Engineering ABC synthesis  Representing logic in terms of And Inverter Graphs (AIG)  Difference from SIS systems simple data structure: Two-input ANDs and Inverters Transformation of network done by rewriting AIGs  Advantages: scalable, faster, uniformity in computation, better quality after technology mapping

7. 7 Electrical and Computer Engineering ABC applications  synthesis and verification  combinational and sequential synthesis  combinational and sequential equivalence checking

8. 8 Electrical and Computer Engineering And-Inverter Graphs representation Boolean network converted to AIG using De Morgan law AIG NAND – Inv representation f = (x1’.x3’)’. x2 f = [(x1.x2)’.(x2.x3)’]’ f = x1*x2 + x2*x3

9. 9 Electrical and Computer Engineering AIG canonicity  AIGs are not canonical same function represented by two functionally equivalent AIGs with different structures BDDs – canonical for same variable ordering

10. 10 Electrical and Computer Engineering AIG redundancy  function represented by a redundant graph with nodes A and B representing the same function Perfectly valid AIG BDDs – no redundancy

11. 11 Electrical and Computer Engineering AIG attributes  AIG size is number of AND nodes in it.  Number of logic levels is number of AND-gates on the longest path from a primary input to a primary output The inverters are ignored when counting nodes and logic levels

12. 12 Electrical and Computer Engineering AIG construction  SOP representation of a function - it can be factored which can then be converted into AIGs f=x1.x2 + x2.x3 => f = [(x1.x2)’.(x2.x3)’]’  Circuit representation of a multi-output Boolean function - the multi-output AIG is constructed for each Primary Output of the circuit

13. 13 Electrical and Computer Engineering Definitions  Cut set of nodes of network, called leaves each path from PIs to n passes through at least one leaf  K-feasible cut if the number of leaves does not exceed K  Cut function of an AIG node n, f n (x) A boolean function of the logic cone rooted in node n and expressed in terms of the cut leaves of the AIG.  Structural hashing (command: strash) during AIG construction, no two AND gates should have identical pairs of incoming edges to detect and merge isomorphic circuit structures AIG not canonical, it contains sub-graphs, which are canonical

14. 14 Electrical and Computer Engineering NPN equivalence  F and G are NPN equivalent if F can be derived from G by selectively complementing the inputs (N), permuting the inputs (P), and optionally complementing the output (N) eg1: F1 = (a.b).c’ F2 = (a.c’).b NPN equivalent

15. 15 Electrical and Computer Engineering NPN equivalence contd. eg2: f1 = x1x2’x3 + x2x3’ + x4 f2 = x1’x2’x3 + x2’x3 + x4 f3 = x1x2x3 + x2’x3’ + x4’ NPN equivalent f1 and f2 not N-equivalent f1 and f3 are N-equivalent - f1 and f3 can be transformed into each other by complementing x2, x4  Representatives of each class can be transformed into each other by complementing their inputs  But no transformation between representatives of different classes

16. 16 Electrical and Computer Engineering NPN equivalence - applications  Applications Balanced form (delay) to long form (area) AIG reduction removal of redundant nodes and equivalent cones ASIC standard cell mapping FRAIGING: Functionally Reduced AIGs

17. 17 Electrical and Computer Engineering Overview  Introduction Previous synthesis methods  ABC synthesis  And-Inverter Graphs (AIG) representation AIG canonicity and redundancy AIG construction  NPN equivalence  AIG transformations Rewriting ABC commands  Summary

18. 18 Electrical and Computer Engineering AIG transformation - Rewriting  Rewriting- technique to reduce AIG size by choosing AIG sub graphs rooted at a node and replacing with pre-computed smaller subgraphs, preserving functionality at root node

19. 19 Electrical and Computer Engineering AIG rewriting basics  Selectively collapse, refactor and balance  Collapse – elimination f = (g).c’ g = a.b => f = (a.b). c’ Refactor iterative collapsing and refactoring of logic cones in the AIG to reduce the number of AIG nodes and number of logic levels  Balance creates a second AIG from an input AIG, having minimum delay (number of logic levels)  Synthesis based on AIGs Alternating DAG aware AIG rewriting and algebraic AIG balancing

20. 20 Electrical and Computer Engineering AIG rewriting algorithm

21. 21 Electrical and Computer Engineering AIG rewriting variation Refactoring  compute one large cut for each AIG node  replace AIG structure of the cut by a factored form of the cut function  Accept change if there is a decrease or no change in number of nodes Cost function  AIG rewriting - total number of AIG nodes and the maximum number of AIG levels  SIS methods - total number of literals in the factored forms

22. 22 Electrical and Computer Engineering AIG rewriting - advantages  Not much hand-tuning and trial and error  Complexity of logic given by AIG nodes or levels  An implementation of synthesis flow takes person- weeks Orders of magnitude faster  AIG rewriting leads to better quality than those offered by MVSIS and SIS AIG rewriting is local, fast, can be applied many times No longer local rewriting – better quality  Scalability - applicable to large examples

23. 23 Electrical and Computer Engineering AIG rewriting - applications  Applications formal verification design complexity estimation equivalence checking hardware emulation

24. 24 Electrical and Computer Engineering ABC rewriting script  resyn2 - rewriting script  Performs ten passes on the network b – Balance rw – rewrite rf – refactor b rw rwz – rewrite with switch enabling zero-cost replacements b rfz - refactor with switch enabling zero-cost replacements rwz b

25. 25 Electrical and Computer Engineering ABC commands – logic synthesis  resyn, resyn2, and resyn2rs – logic synthesis scripts  strash Structural hashing - standard alias st  renode recreates node boundaries in AIG by using command renode standard alias ren

26. 26 Electrical and Computer Engineering ABC commands contd.  share and sharedsd scripts for logic sharing extraction  rr Performs redundancy removal for AIGs

27. 27 Electrical and Computer Engineering Summary  Synthesis done using ABC represents network in terms of a simpler data structure - AIGs  Performs combinational synthesis, mapping, and verification  faster  Better quality of results after technology mapping  Scalable for large designs

28. 28 Electrical and Computer Engineering References [1] Alan Mishchenko, Satrajit Chatterjee, Robert Brayton, “DAG-Aware AIG Rewriting”, DAC 2006, July 24–28, 2006, San Francisco, California, USA. [2] Alan Mishchenko, “A New Enhanced Approach to Technology Mapping”. [3] Alan Mishchenko, Satrajit Chatterjee, Roland Jiang, Robert Brayton, “FRAIGs: A Unifying Representation for Logic Synthesis and Verification”.

29. 29 Electrical and Computer Engineering Thank you