1. Robert Brayton Alan Mishchenko Niklas Een
Magic An Industrial-Strength Logic Optimization, Technology Mapping, and Formal Verification System
Robert Brayton Alan Mishchenko Niklas Een
UC Berkeley

2. Overview Motivation Big picture Problem representation Algorithms
Sequential synthesis
Combinational synthesis with choices
Technology mapping
Minimum-perturbation retiming
Experimental results
Future work

3. Motivation
ABC is a public-domain system for logic synthesis and formal verification under development at Berkeley since 2005
A successor of Espresso, MIS, SIS, VIS
The baseline version of ABC is not applicable to industrial designs because it does not support
Complex flops
Multiple clock domains
Special objects (adders, RAMs, DSPs, etc)
Standard-cell libraries
A fresh start, called Magic, was taken in Fall 2009
Includes new design database should support these
Integrates application packages for better memory/runtime

4. Big Picture Verilog, EDIF, BLIF Programmable APIs
A. Mishchenko, N. Een, R. K. Brayton, S. Jang, M. Ciesielski, and T. Daniel, "Magic: An industrial-strength logic optimization, technology mapping, and formal verification tool". Proc. IWLS'10.

5. Application Packages Framework Combinational optimization
Design database
File input / output
Programmable APIs
Combinational optimization
AIG rewriting
Choice computation
Technology mapping
Sequential optimization
Retiming
Merging equivalence nodes
Mapping with choices
Speedup
Verification
Simulation
Comb equivalence checking
Seq equivalence checking

6. “Industrial Stuff” Clock domains Complex controls of the flops
Represent clock signal in the data-base
Annotate flops with their clock-domain number in the AIG
Separate clock domains in sequential transforms
Complex controls of the flops
Use parametrized flop model
Perform elaboration of control signals if needed
Handle asynchronous reset carefully!
Industrial primitives (adders, RAMs, DSPs, etc)
Use boxes (black/white, comb/seq, merge/no_merge, etc)
Currently propagates timing information, improves quality of synthesis
Elaborate boxes for seq synthesis, but do not map them
Need better support for user-specified attributes (don’t-touch, etc)

7. Representations Netlist AIG: The main data-structure of ABC / Magic
Original / current / resulting design with “industrial stuff”
AIG: The main data-structure of ABC / Magic
Represents local / global functions
Gets synthesized / mapped / verified
Logic network
Represents the result of technology mapping
In many cases, it is convenient to represent logic network as an AIG annotated with technology primitives (LUTs, gates, etc)

8. AIG Definition and Examples
AIG is a Boolean network composed of two-input ANDs and inverters
cdab 00 01 11 10 1
F(a,b,c,d) = ab + d(ac’+bc) b c a d
6 nodes
4 levels
F(a,b,c,d) = ac’(b’d’)’ + c(a’d’)’ = ac’(b+d) + bc(a+d)
cdab 00 01 11 10 1 a c b d
7 nodes
3 levels

9. Three Simple Tricks Structural hashing Complemented edges
Makes sure AIG is in a compact form
Is applied during AIG construction
Makes each node structurally unique
Propagates constants
Complemented edges
Represents inverters as attributes on the edges
Saves memory, leads to fast uniform manipulation
Increases logic sharing using DeMorgan’s rule
Memory allocation
Uses fixed amount of memory for each node
Based on a simple custom memory manager
Allocates memory for nodes in a topological order
Optimized for traversal in the same topological order
Computes fanout information on demand a b c d
Without hashing a b c d
With hashing

10. AIG: A Unifying Representation
An underlying data structure for various computations
Representing both local and global functions
Used in rewriting, resubstitution, simulation, SAT sweeping, induction, etc
A unifying representation for the whole flow
Synthesis, mapping, verification pass around AIGs
Stored multiple structures for mapping (‘AIG with choices’)
The main functional representation in ABC
Foundation of ‘contemporary’ logic synthesis
Source of ‘signature features’ (speed, scalability, etc)

11. Sequential Synthesis
Detect, prove, and merge sequentially equivalent nodes
Seq equiv nodes are equivalent on reachable states
Special case: Comb equiv nodes are equivalent on for any state
Observations
Can be done using simulation and SAT (without BDDs)
Leads to substantial reduction for large designs (> 10% in area)
Works for large designs (10-15 minutes for 1M gates) B A B A
A. Mishchenko, M. L. Case, R. K. Brayton, and S. Jang, "Scalable and scalably-verifiable sequential synthesis", Proc. ICCAD'08.

12. Comb Synthesis With Choices
Restructure the AIG and keep track of changes
Iterate fast local AIG rewriting with a global view (via hash table)
Collect AIG snapshots and prove equivalences across them
Use equivalences (choices) during technology mapping
Observations
Leads to improved QoR after technology mapping
Successfully applied to 1M gate designs
Pre-computing AIG subgraphs for F = abc
Rewriting node A a b c A
Subgraph 1 b c a A
Subgraph 2  a b a b a c b c a c
Subgraph 1
Subgraph 2
Subgraph 3
A. Mishchenko, S. Chatterjee, and R. Brayton, "DAG-aware AIG rewriting: A fresh look at combinational logic synthesis", Proc. DAC '06.

13. Technology Mapping Customizable structural mapping with priority cuts
AIG
Mapped network
Customizable structural mapping with priority cuts
Computes a small subset of cuts without impacting the QoR
Uses structural choices
Observations
Controls QoR tradeoffs
Minimizes delay/area, wire count, switching activity, etc
Successfully applied to 1M gate designs  a b c d e f
LUT f a b c d e
Primary inputs
Primary outputs
Choice node
A. Mishchenko, S. Cho, S. Chatterjee, R. Brayton, "Combinational and sequential mapping with priority cuts", Proc. ICCAD '07.

14. Minimum-Perturbation Retiming
Reduces delay after retiming, while minimizing the number of flops moved
Produces a trade-off: delay gain vs. the number of flops moved
Handles “industrial stuff” and retimes over white boxes!
Computes new initial state after backward retiming
Allows the user to control the resources
Desired delay gain
Maximum allowed number of flops moved
Maximum area increase after retiming
Observations
Can be useful before and after placement
Can be implemented efficiently
Runs in less than a minute for 1M gates
Delay
Flops moved
S. Ray, A. Mishchenko, R. K. Brayton, S. Jang, and T. Daniel, "Minimum-perturbation retiming for delay optimization". Proc. IWLS'10.

15. Experimental Setup
Integrated Magic into an industrial FPGA synthesis flow
Experimented with the full flow, including P&R
Did not use retiming
Did not use post-placement re-synthesis
Verified by running Magic and in-house simulation tools
Experimented with 20 designs, from 175K to 648K LUT4
Two experimental runs:
“Reference” stands for the typical industrial flow without Magic
“Magic” stands for the new flow with Magic
Frontend
Magic
Backend
Design entry, high-level synthesis, quick mapping
Seq and comb synthesis, mapping, legalization
Placement, routing, design rule checking, etc

16. Experimental Results

17. Cumulative Improvements
fMAX = 11.8%
LUT count = 12.7%
FF-to-FF level = 22.3%
Register count = 9.4%
Total flow runtime = 3.1%
P&R runtime = 50%

18. Future Work Continue to improve application packages
AIG rewriting, tech-mapping, sequential synthesis, etc
Improve integration of logic and physical synthesis
Synthesis/mapping/retiming before placement
Retiming/restructuring after placement
Extend the flow to work for other technologies
Macro cells
Standard cells