it is better to run iterative resynthesis on parts of the circuit

It Is Better to Run Iterative It Is Better to Run Iterative Resynthesis on Parts of the Resynthesis on Parts of the

CircuitCircuit

Petr Fišer, Jan SchmidtFaculty of Information Technology

Czech Technical University in Praguefiserp@fit.cvut.cz, schmidt@fit.cvut.cz

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OutlineOutline

PreliminariesIterative resynthesisMotivationCircuit resynthesis by partsExperimentsConclusions

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PreliminariesPreliminaries

Synthesis (optimization) of circuits (networks) will be discussedJust for simplicity: Combinational circuits are assumed Mapping into arbitrary 2-input gates

Cost (optimality criterion, quality) = # of gates

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Iterative ResynthesisIterative Resynthesis

Iterative resynthesis = improving the result quality by repetitive application of a single synthesis process, in order to improve the result qualityPossible assumption: the synthesis process cannot make the circuit worseNeeds not be always true

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Iterative Resynthesis in ABCIterative Resynthesis in ABC

ABC naturally supports iterative resynthesisEmphasized by “choices”Many possible processesSuggested: repeating {choice; map}Superchoice:

fraig_store; resynfraig_store; resyn2fraig_store; resyn2rsfraig_store; sharefraig_store; fraig_restore

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Iterative Resynthesis in ABCIterative Resynthesis in ABC

0 200 400 600 800 10000

500

1000

1500

2000

2500

3000

3500

4000

too_large

Gat

es

Iteration

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How Many Iterations suffice?How Many Iterations suffice?228 of IWLS’93 benchmarks examined

Iterations to converge # of cases< 20 19420 – 100 27100 – 500 4500 – 1000 1 (t481)> 1000 2 (seq, too_large)

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MotivationMotivationImagine:

e64 IWLS’93 circuit (65 inputs, 65 outputs, 649 2-input gates)

Case 1 – synthesis of the circuit, as it is:Case 1 – synthesis of the circuit, as it is: 530 gates 2.33s runtime

Case 2 – split the circuit into two halves, synthesize Case 2 – split the circuit into two halves, synthesize them separately, then merge the resultsthem separately, then merge the results

522 gates 1.73s total runtime

Where is the problem?What’s wrong?

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Circuit Resynthesis by PartsCircuit Resynthesis by Parts Resynthesize(Network N, opt) {do {

(W, NR) = Extract_Window(N, opt);W’ = resynthesize_by_ABC(W);N’ = NR W’;if (cost(N’) ≤ cost(N)) N = N’;

} while (!end());}

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Window ExtractionWindow Extraction

PI1

PI2

PI5

PI4

PI3

PO1

PO3PO2

PO4

W

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Window ExtractionWindow ExtractionConnected circuits are always extractedMethod 0 – Random selection

1. Randomly select one “pivot” gate2. Incrementally add randomly selected adjoining gates

Method 1 – Minimize_fanin1. Randomly select one “pivot” gate2. Incrementally add adjoining gates, so that the number of window primary

inputs is minimized (in a greedy way)Method 2 – Minimize_fanout

1. Randomly select one “pivot” gate2. Incrementally add adjoining gates, so that the number of window primary

outputs is minimized (in a greedy way)Method 3 – Minimize_fanin+fanout

1. Randomly select one “pivot” gate2. Incrementally add adjoining gates, so that the sum of numbers of window

primary inputs and outputs is minimized (in a greedy way)

These methods allow for arbitrary window size scaling

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Window ExtractionWindow ExtractionMethod 4 – RadiusSelect

1. Randomly select one “pivot” gate2. Add all adjoining gates (i.e., all fan-in and fan-out gates)3. For each gate in the window, do (2.), up to the given radius

Method 5 – Windowing-like selectionSimilar to the window selection algorithm in the resubstitution process in

ABC1. Randomly select one “pivot” gate2. Find the minimum level of its transitive fan-in to a given depth3. Generate transitive fan-out of the pivot, to a given depth4. For these fan-out nodes, include all transitive fan-in nodes up to the

computed level into the window

The window size is partially determined by the circuit structure

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Experimental SetupExperimental Setup

228 of IWLS’93 benchmarks processedResynthesis using ABC, using the “superchoice” script, followed by technology mapping into 2-input gatesIterated 1000-times (recall – this should be more than enough)100% circuit resynthesis yielded 19.97% improvement in the average

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Comparison of MethodsComparison of Methods

Gates (size 20%)

Time (size 20%)

Method 0 Method 1 Method 2 Method 3100

105

110

115

120

125

Gat

es

Method 0 Method 1 Method 2 Method 30

20

40

60

80

100

120

Tim

e [s

]

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Comparison of MethodsComparison of Methods

M. 4, radius 3

M. 4, radius 4

M. 4, radius 5

M. 4, radius 6

M. 4, radius 7

M. 4, radius 8

M. 4, radius 9

M. 5, depth 3

M. 5, depth 4

M. 5, depth 5

M. 5, depth 6

M. 5, depth 7

M. 5, depth 8

M. 5, depth 980

90

100

110

120

Gat

es

M. 4, radius 3

M. 4, radius 4

M. 4, radius 5

M. 4, radius 6

M. 4, radius 7

M. 4, radius 8

M. 4, radius 9

M. 5, depth 3

M. 5, depth 4

M. 5, depth 5

M. 5, depth 6

M. 5, depth 7

M. 5, depth 8

M. 5, depth 90

2

4

6

8

10

12

14

Tim

e [s

]

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ResultsResultsMethod 0 (Random select), improvement vs. ABC iterated 1000-times

10% 30% 50% 70% 90%

-6,0

-4,0

-2,0

0,0

2,0

4,0

6,0

8,0

10,0Im

prov

emen

t vs.

AB

C [%

]

Window size

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ResultsResultsMethod 4 (Radius select), improvement vs. ABC iterated 1000-times

3 4 5 6 7 8 9 10 11

-6,0

-4,0

-2,0

0,0

2,0

4,0

6,0

8,0Im

prov

emen

t vs.

ABC

[%]

Radius

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Why This Happens - Example CasesWhy This Happens - Example Cases

Behavior of one of the “good for us” circuits (e64)Method 0 (random selection)

0 100 200 300 400 500 6000

100

200

300

400

500

600

e64

Gat

es

Window size

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Why This Happens - Example CasesWhy This Happens - Example Cases

Behavior of one of the “bad for us” circuits (clip)Method 0 (random selection)

0 50 100 150 200 250 300 3500

50

100

150

200

250

300

350

clip

Gat

es

Window size

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Convergence, Maybe?Convergence, Maybe?

0 200 400 600 800 10000

100

200

300

400

500

600

700

e64

Resynthesis of 50%

Resynthesis of 100%

Gat

es

Iteration

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Convergence, Maybe?Convergence, Maybe?

0 200 400 600 800 10000

50

100

150

200

250

300

350clip

Resynthesis of 50%

Resynthesis of 100%

Gat

es

Iteration

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ConclusionsConclusions

Sometimes it is better to resynthesize circuits by parts, rather than as wholeIn cases where not, probably it is due to random fluctuations caused by random part selectionsResynthesis by parts converges slower, but yields better resultsWhy?

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QuestionsDiscussion

Stoning to death…