EE244: Design Technology for Integrated Circuits and Systems Outline Lecture 9.2. Introduction to Behavioral Synthesis (cont.)

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1 EE244: Design Technology for Integrated Circuits and Systems Outline Lecture 9.2 Introduction to Behavioral Synthesis (cont.) Relationship to silicon compilation Stochastic Algorithms and Learning EE244 Fall Role of VHDL In general, VHDL syntax is sufficient and probably not worth re-working. In some cases VHDL goes too far. e.g. if(clk quiet for 4) A := B+1; In some cases not far enough e.g. Synchronizing elements in dataflow view. We need a Policy-of-Use for VHDL-based synthesis In-progress within the industry (e.g. Synopsys) NSF/DARPA group looking into it. International standards groups also working on some issues world wide (e.g. IEEE DATC). EE244 Fall Page 1

2 D D D D D D D Implications of Deep Submicron Languages versus Models: A Software Analogy "C" Pascal Silage f77 Lisp UDL-I VHDL Intermediate Form Hardware Intermediate Form Von Neumann Computer Hardware Implementation EE244 Fall An Alternate View of Synthesis mmake arbitrary "cut" through the logic such that the machine is partitioned. Cut line EE244 Fall Page 2

3 An Alternate View of Synthesis Ordered set of signals crossing cut represent an encoding of an abstract type Logic synthesis: For all possible independent cuts, choose an encoding of the cut (in time and "wires") such that the objective function (literal count, performance, etc.) is optimized. EE244 Fall An Alternate View of Synthesis η η Behavioral Synthesis: Given a set of abstract types (sets) at the behavioral level, encode them in terms of lower-level abstract types such that the synthesis objective is met. EE244 Fall Page 3

4 An Alternate View of Synthesis The encoding is simply a list (array?) of values for each member of the set The process is repeated until all types are encoded in terms of members of the type Boolean. EE244 Fall An Alternate View of Synthesis OPCODE: { add, sub, mult, div, and, or, xor } add: [ a, b ] sub: [ a, c ] mult: [ a, d ] div: [ b, a ] and: [ b, b ] or: [ b, c ] xor: [ b, d ] TWOBIT: { a, b, c, d } a: [ 0, 0 ] b: [ 0, 1 ] c: [ 1, 0 ] d: [ 1, 1 ] BOOLEAN: { 0, 1} add: [ 0,0,0,1 ] sub: [ 0,0,1,0 ] mult: [ 0,0,1,1 ] div: [ 0,1,0,0 ] and: [ 0,1,0,1 ] or: [ 0,1,1,0 ] xor: [ 0,1,1,1 ] EE244 Fall Page 4

5 Two Approaches to Combinational and Sequential Optimization "Bottom Up": Given a fully-encoded (Boolean) description of the problem, iteratively re-encode the machine to achieve the best result possible. "Top Down": Given an unencoded ("high-level", behavioral) description of the machine, find an encoding that achieves the best possible result. EE244 Fall An Alternate View of Synthesis: Implications Redundant Encodings: e.g One-hot for controllers; redundant arithmetic (Matsushita, ISSCC89); Wallace Tree as hierarchical encoding; Carry-Save as space-time encoding. Finite-State Machine: Special case of constrained encoding: ouput encoding of secondary outputs = input encoding of secondary inputs. EE244 Fall Page 5

6 D D D D D D D Implications of Deep Submicron Abstract Datatype Approach to Consistency: A Software Analogy VHDL Flavors Common Lisp Franz CAR, CDR CONS COND VHDL Synchronous Combinational Asynchronous Hardware Intermediate Form (The Lambda Calculus) Provides symbolic canonical form (Boolean Algebra? HOL?) sequential canonical form? EE244 Fall Simulated Annealing with Learning Introduction and Overview Training Simulated-Annealing-Based Placement Decision-Theoretic Network Partitioning EE244 Fall Page 6

7 High-Level Goals Use principles of rationality (Bayesian probability and decision theory) to model complex problems and the use of expensive resources Use data engineering to help understand opportunities for addressing and simplifying the complexity inherent in most EDA optimization problems EE244 Fall Complexity Kinds of Complexity Computational: computational complexity or intractability. Informational: in determining relevant and missing information, and amount of information needed before work can begin. Conceptual: in terms of the depth of understanding required for the person programming the task. Organizational: in terms of the people in the task and their management. Complexity Agents Rationality The Problem! A Framework Key Principle EE244 Fall Page 7

8 Rationality Use probability and decision theory to optimize the use of an agent s constrained resources Probabilities (not just frequencies) Utilities The belief that node N will be in the 2nd partition at termination of the Fidducia and Mattheysses algorithm;during operation of a partitioning algorithm, Belief about the correlation between the size of the cut-set in the current pass, and the size of the cut-set in the final pass; Belief about whether the distance or shortest path between two cells provides some information about the cells placement during operation of a partitioning algorithm. Usual concerns in electronic design: area, timing, power, yield, etc. EE244 Fall Data Engineering Develop understanding of complex problems by visualization, analysis and optimization Information Theory Optimization Rapid Prototyping Data Engineering Learning and Statistics Visualization EE244 Fall Page 8

9 Our Proposal: Stochastic Optimizer with Learning Working Memory Complex Objective Function Stochastic Inference Engine Move Set Goals: Use incremental learning (Bayesian, etc.) to capture knowledge Use stochastic pattern recognition Train using well-characterized problems Physical design, Logic synthesis Domain-Specific Knowledge Pack Identify effective approaches to parallel implementation EE244 Fall Overall Flow of Experiment blif MIS OCT Wolfe Learning Anneal.cel result Timberwolf SC-4 Data Analysis & Visualization Matlab result Not possible to obtain TimberWolf 7 for this work, but expect to work with University of Washington on clustering project EE244 Fall Page 9

10 Selecting a Candidate Move Comparison... Model Evaluation m Choose Set Selected Move MAX(*) (β 1 p 1, β 2 p 2,, β n p n ) (p 1, p 2,, p n ), for each of m moves EE244 Fall Parameters in the Model p 1 : The Euclidian distance between two cells p 2 : The square of the distance between C 1 and the origin (0,0) (a control parameter) p 3 : The square of the distance between C 2 and the origin (0,0) (a control parameter) p 4 : The number of connections between C 1 and C 2 p 5 : The total weighted connectivity of the cells in the candidate move p 6, p 7 : Force change to weighted center of gravity Cost Function: Change in the size of the maximum net bounding-box for all nets connected to the candidate cells to be swapped EE244 Fall Page 10

11 Cost Estimate vs. TimberWolf Chip Area 0.5 Normalized Area Normalized Cost Estimate MOSAICO chip area using MSU standard-cell library vs. sum of net bounding-box lengths EE244 Fall Examples Used for Placement ID Name Cells Nets Used to train the model: 1 C C C apex i10 1,269 1,526 6 i i i i Used to test the model: 10 C C6288 1,893 1,925 EE244 Fall Page 11

12 Results for Trained Placement Trained Model Conventional Example Best Average Worst Std. Dev. Best Average Worst Std. Dev. C , , ,460 2, , , ,460 2,484 C499 77,942 83,019 89,188 1,699 92,788 98, ,230 1,984 C880 83,433 89,984 96,782 2, , , ,730 2,132 apex6 281, , ,010 4, , , ,280 4,552 i10 1,582,200 1,638,000 1,689,200 14,289 1,842,800 1,887,600 1,931,000 14,018 i6 146, , ,510 2, , , ,790 3,369 i7 199, , ,390 2, , , ,510 3,905 i8 369, , ,770 5, , , ,290 5,300 i9 156, , ,310 3, , , ,500 3,262 C , , ,720 8, , , ,450 7,148 C6288 2,199,200 2,261,600 2,337,600 19,716 2,598,100 2,658,000 2,722,700 20,667 EE244 Fall Three Approaches Comparison... Selected Move Model Evaluation Conventional Trained Untrained Annealing Model Model only one MAX(m moves) MAX( m moves) only one (β 1 p 1 +β 2 p 2 + +β n p n ) (p 1 +p 2 + +p n )/m m Choose Set m=1 m=10 m=10 EE244 Fall Page 12

13 Performance of Trained Model: Apex Number of Solutions Trained Model Untrained Model Conventional Final Solution Cost (x10^3) EE244 Fall Percentage Improvement for Placement Example Best Average Worst C % 18% 15% C499 16% 16% 15% C880 17% 16% 14% apex6 17% 16% 15% i10 14% 13% 13% i6 17% 17% 17% i7 15% 16% 16% i8 17% 15% 14% i9 16% 17% 15% C % 16% 15% C % 15% 14% EE244 Fall Page 13

14 Variation of Parameter Model Weights with Temperature Zone 100% Relative Weight of Model Parameter 80% 60% 40% 20% 0% P2 P3 P5 P1 P6 P7 P4-20% T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 Temperature Zones EE244 Fall Netlist Partitioning Routinely used as an essential preprocessing step for placement and in routing. One standard approach used is the Fidducia and Mattheysses (FM) algorithm (related to Lin- Kernighan (LK) algorithm). While implementing Dutt and Deng s PROP 1 approach, we identified and analyzed two improvements for regular FM. 1 A Probability-Based Approach to VLSI Circuit Partitioning, Proc. ACM/IEEE Design Automation Conf., June 1996 EE244 Fall Page 14

15 Examples for Partitioning Example Nets Cells I/O s C C C C C C6288 1,925 1, biomed 5,742 6,514 0 struct 1,920 1,952 0 industry2 13,419 12,637 0 industry3 21,923 15,406 0 EE244 Fall Examples for Partitioning Example Nets Cells I/O s avq-small 22,124 21, avq-large 25,384 25, s9234 5,844 5,866 0 s ,651 8,772 0 s ,383 10,470 0 s ,828 18,148 0 s ,843 23,949 0 s ,717 20,995 0 golem 144, ,048 0 EE244 Fall Page 15

16 Netlist Partitioning node (cell) pa rtition of cost 4 net List of cells and nets Cut the cells into two parts to minimize the number of nets that contain cells in each part Is a coarse approximation to the general constraint satisfaction problem, placement, etc. EE244 Fall Dutt and Deng s PROP DAC 96 best paper Uses probabilistic argument to replace the gain heuristic with another Extensive testing shows is superior nonclustering algorithm EE244 Fall Page 16

17 FM Algorithm Repeat: move a node across the partition so as to increase cost the least, then lock the node so it stays there. Note this may cause a cost increase Until, all nodes are locked. Thus one Pass is completed. Select the intermediate partition with the least cost. Repeat additional passes until no further cost reduction. EE244 Fall Changes in Cost During FM Each segment represents one pass EE244 Fall Page 17

18 Changes in Cost During FM For all later passes seen, the minimum cost partition is always near the end or the beginning of the pass. What does the 90% of computation in the middle of the pass achieve? Is it useful? Hypothesis 1: The full FM pass is an expensive way of making a stochastic move in the space when regular hill-climbing near the current partition fails. EE244 Fall Note on Experimental Evaluation Different algorithms take different amounts of time to complete For different problems, we might have different amounts of time available to complete To do fair comparison need to time-equalize algorithms Do this using the Best-of-N wrapper: Run the algorithm N times from random initialization Return the best value from the N runs EE244 Fall Page 18

19 Stochastic FM Is a simple, strawman, stochastic variation of FM Terminology Stochastic Pass: Accept the next move off the gain bucket with probability δ, where the probability of accepting a down-hill move (if one exists) is 85%. Adaptive-Length Pass: Make regular FM pass but stop short if no improvement in cost is achieved for 200% of the length of the prefix of the last successful pass Algorithm Repeat { Perform stochastic pass of length 5% Hamming distance from current best-partition; Repeat { make adaptive-length passes } until (no improvement); Update current best-partition if last partition is superior; } Until ( Time bound reached or no improvement after 100 passes ) EE244 Fall Stochastic FM: Block Diagram Stochastic FM Stochastic pass Adaptive-length pass yes Time out? no Improvement? yes no Record cost EE244 Fall Page 19

20 Experimental Results We have extensively tested Hypothesis 1 using a number of alternative algorithms. We compared the following three algorithms: FM Half-pass FM (HP-FM: no pass is allowed more than half way) Stochastic FM (S-FM: time bound = time for 1 FM run) We compared the following two algorithms: Best-of-N FM Stochastic FM for longer runs (5 FM runs, 20 FM runs, ) EE244 Fall Comparison: FM vs HP-FM vs S-FM EE244 Fall Page 20

21 Comparison: Best-of-N FM vs long S-FM EE244 Fall Multiple Passes of FM In most practical applications, FM is run multiple times with the Best-of-N wrapper. Question: Can the current run be improved by considering previous runs? (i.e. learning) We have gathered initial data and there appears to be good opportunity to cut many runs short in later runs, and thus double the speed of Best-of-N FM. EE244 Fall Page 21

22 Visualizing Typical Passes Each run colored by final cost. Cost at end of run is correlated with cost 1/2- way through. passes passes EE244 Fall Cutoff Best-of-N FM Simple on-line adaptive model of whether the current run will yield a lower cost solution quality(pass,min-cost) = judges whether to abort run repeat (N times) { } repeat { passes of the current run } until (run terminates normally or quality(pass,min-cost) goes low); Update current best partition; EE244 Fall Page 22

23 Cutoff Best-of-N FM Cutoff best-of-x wrapper FM variant Start Continue Record best cost Runs Costs Passes Current (run, pass) fails quality test? no yes Done N runs? yes no EE244 Fall Best-of-N FM vs Cutoff Best-of-20 EE244 Fall Page 23

24 Cutoff Stochastic FM or DT-FM Decision-Theoretic FM (DTFM): Runs stochastic FM inside a cutoff best-of-n controller Is an adaptive stochastic algorithm: Adapts pass lengths during each run Learns when to abort a run early Currently uses simplistic adaptive schemes for proof-of -concept EE244 Fall DT-FM vs Best-of-N FM and PROP EE244 Fall Page 24

25 Summary DT-FM designed using Data Engineering DT-FM has an adaptive stochastic wrapper around standard FM. Currently has simple adaptive methods for proof of concept. Is comparable to the state-of-the-art PROP algorithm (Dutt & Deng, DAC 96) on all but one problem. For several O(10,000) cell problems, reconstructs best-known partition. EE244 Fall Stochastic Optimization with Learning for Complex Problems PLANS FOR 1997: Continue the development of the learning framework and evaluate incremental learning approaches (Bayesian, etc.) Apply the techniques to one or two new problems: standardcell library generation, optimal clustering for placement Evaluate the effectiveness of adaptive optimization on other problems: BDD variable sifting SPECIFIC MILESTONES AND DELIVERABLES: Complete standard-cell placement evaluation (Mar-97) Implement adaptive approach to BDD variable sifting and evaluate (Jul-97) Formulate approach to optimal clustering problem and implement prototype (Sep-97) Implement incremental learning algorithms in the framework EE244 Fall Page 25

26 Summary Complexity is a key problem in design, and data engineering can help to improve complex algorithms. We have demonstrated the use of data engineering technology can improve simple standard-cell placement and standard net-list partitioning methods by up to 20%. We have identified various opportunities for additional data engineering in optimization and adaptive computation. EE244 Fall Page 26