robust window-based multi-node technology- independent logic minimization jeff l.cobb kanupriya...
TRANSCRIPT
![Page 1: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/1.jpg)
Robust Window-based Robust Window-based Multi-node Technology-Multi-node Technology-
Independent Logic Independent Logic MinimizationMinimization
Jeff L.Cobb
Kanupriya Gulati Sunil P. Khatri
Texas Instruments, Inc. Dept. of ECE, Texas A&M University
1
![Page 2: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/2.jpg)
Overview
IntroductionBackgroundPrevious workApproachExperimental resultsConclusions
2
![Page 3: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/3.jpg)
Introduction
VLSI design flow◦HDL (Verilog, VHDL)◦Logic optimization◦Physical design
3
![Page 4: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/4.jpg)
Introduction
Purpose of logic optimization◦Reduce area◦Reduce power◦Reduce delay
Logic optimization◦Technology-independent optimization
◦Goal: reduce literal count◦Technology-dependent optimization
4
![Page 5: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/5.jpg)
BackgroundDon’t Cares
◦Logic function allowed to have 0 or 1 as possible output for a given input
ODC SDC
◦XDC: External don’t cares given5
![Page 6: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/6.jpg)
BackgroundDon’t Cares
◦Computed for one node at a time◦Cannot capture multi-node flexibility
6
xy (x+y) = xy(xy) + (x+y)(x+y) = xy+xy = x y
Goal: multi-node logic minimization◦Yields a Boolean relation◦Need to determinize this relation for solution
![Page 7: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/7.jpg)
BackgroundBoolean relations
◦Can express more than one allowed output vector for a single input vector
◦Don’t cares only express flexibility for a single output
7
![Page 8: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/8.jpg)
Terminology
8
![Page 9: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/9.jpg)
Problem Definition
9
• Implement dual-node Boolean relation-based multi-level logic minimization technique
•Goals: • Method must scale to large designs• Compare to best don’t care-based method
(single-node)
![Page 10: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/10.jpg)
Previous Work
10
• [CM77] Formulated multi-node minimization problem• No results provided
• [WW94] Multi-node minimization• Extremely large runtimes, works on very
small designs• [MB05] Single node approach, uses windowing and SAT based formulation• Used for comparison purposes
• This work: Efficient choice of nodes, window based, efficient quantification scheduling
![Page 11: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/11.jpg)
Approach
Key featuresDual node optimizationCareful node pair selectionWindow based optimization techniqueEarly quantification for efficiency
11
![Page 12: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/12.jpg)
Approach
12
![Page 13: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/13.jpg)
Node Pair Selection
Node Pair Selection
13
![Page 14: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/14.jpg)
Node Pair Selection
14
![Page 15: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/15.jpg)
Node Pair Selection
15
![Page 16: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/16.jpg)
Node Pair Selection• Compute common input ratio
• Compute common output ratio
• Select node pairs that satisfy
16
![Page 17: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/17.jpg)
Subnetwork Extraction
17
![Page 18: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/18.jpg)
Subnetwork Extraction
18
![Page 19: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/19.jpg)
Building the Relation
where
19
),...,,...,(),...,,...,(),...,,...,( 111 nixnixnix xxxfxxxfxxxfiii
![Page 20: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/20.jpg)
Quantification Scheduling
20
![Page 21: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/21.jpg)
Quantification Scheduling
21
![Page 22: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/22.jpg)
Quantification Scheduling
22
![Page 23: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/23.jpg)
Call BREL (a Boolean relation minimizer) to minimize
Returns new nodes and
Graft new nodes into
Delete original nodes
,
Endgame
23
![Page 24: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/24.jpg)
BREL
24
• BREL is a heuristic Boolean relation solver
• Solving a Boolean relation • Same as minimum cost determinization of
the relation (i.e. finding the lowest cost function which is contained in the relation)
• Branch and bound approach
![Page 25: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/25.jpg)
Experimental ResultsImplemented in SISUses CUDD ROBDD Package15 benchmark circuits from mcnc91, itc99Metric for quality: literal countPreprocessing steps:
Removes constant-valued nodesRemoves nodes that do not fanout
Merges functionally identical nodes
25
![Page 26: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/26.jpg)
Experimental Results
Parameter selection
4 parameters to node selection algorithm
Goal: Find “golden” values
26
![Page 27: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/27.jpg)
Experimental ResultsParameter:
27
![Page 28: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/28.jpg)
Experimental ResultsParameters:
: Window size
: Partners for
28
![Page 29: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/29.jpg)
Experimental Results
29
![Page 30: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/30.jpg)
Experimental ResultsParameter:
30
![Page 31: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/31.jpg)
Experimental Results
“Golden” parameter values:
Can be modified to balance quality/runtime
31
![Page 32: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/32.jpg)
Experimental Results Compared versus
12% lit. improvement
38x runtime increase But runtimes are still within 3-4 min
Low memory (#BDD nodes)
High gain (number of node pairs which givean improvement)
32
![Page 33: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/33.jpg)
Experimental Results Run after
13% lit. improvement
Both use 2x2 windows
33
![Page 34: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/34.jpg)
Experimental ResultsLimit subnetwork size τ
34
![Page 35: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/35.jpg)
Conclusions12% less literals than best DC approachRuntimes under 4 minutes for largest networkLow memory usageFurther reduce literals by 13% after running best
DC approach
Future WorkConsider 3+ nodes in relationSAT-based relation constructionAlternative to BREL
35
![Page 36: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/36.jpg)
36
Thank you!
![Page 37: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/37.jpg)
37
SAT-Sweep
![Page 38: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/38.jpg)
38
BREL
![Page 39: Robust Window-based Multi-node Technology- Independent Logic Minimization Jeff L.Cobb Kanupriya Gulati Sunil P. Khatri Texas Instruments, Inc. Dept. of](https://reader035.vdocuments.us/reader035/viewer/2022070306/5516534b550346c6758b5aa6/html5/thumbnails/39.jpg)
39
BREL