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DAOmap: A Depth-optimal Area Optimization Mapping Algorithm for FPGA Designs Deming Chen, Jacon Cong ICCAD 2004PowerPoint Presentation

DAOmap: A Depth-optimal Area Optimization Mapping Algorithm for FPGA Designs Deming Chen, Jacon Cong ICCAD 2004

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DAOmap: A Depth-optimal Area Optimization Mapping Algorithm for FPGA Designs Deming Chen, Jacon Cong ICCAD 2004

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DAOmap: A Depth-optimal Area Optimization Mapping Algorithm for FPGA DesignsDeming Chen, Jacon Cong ICCAD 2004

Presented by: Wei Chen

K-input LUT can implement

any Boolean function of K

variables.

So called Completeness.

Given a circuit modeled as a DAG, partitioning the graph

such that every partition has not more than K inputs while

satisfying some objectives.

- A Boolean network N can be modeled as a DAG
- Input(v): the set of fanin nodes of gate v
- Cone rooted on node v (Ov) is a sub-network of N consisting of v and some of its predecessors, such that for any node w∈Ov, there is a path from w to v that lies entirely in Ov.
- A cut is partitioning (X, X’) of a cone Ov such X’ is a cone of v.
- The cut set of the cut V(X,X’) consists of the inputs of cone X’.
- Cut size is the number of elements in cut set
- The level of a node v is the length of the longest path from any PI node to v.
- The depth of a network is the largest node level in the network.
- A Boolean network is L-bounded if |input(v)| ≤L for each v.

Input(6) = {4,6}

Level(6) = 2

Depth = 2

2-bouned

1

4

2

6

5

3

A cone rooted at node 6

1

4

A cut C

2

6

Cut set (C) = {1,2,5}

Cut size(C) = 3

5

3

- A cut-enumeration-based method that consists of cut generation and cut selection.
- Cut generation/enumeration: for each node being considered, generate all the K-feasible cuts.
- Cut selection: Choose the nodes (and their best cuts) for implementation using LUTs
- Objective: Create a minimum area cover under the timing constraint (Optimal Depth).

- Guided by the following theorem:

f(K,v) represents all the K-feasible cuts rooted at node v

f(4,5) = {1,2}

f(4,6) = {3 ,4}

f(4,7) = [5 + f(4,5)][6 + f(4,6)] = {5,6}

+ {5, f(4,6)} + {f(4,5),6} + {f(4,5) + f(4,6)}

= {5,6} + {5,3,4} + {1,2,6} + {1,2,3,4}

1

5

2

7

3

6

4

- Unit delay model: each cut (LUT) on the paths represents one unit delay.
- The minimum arrive time for node v is:

0

0

1

1

1

1

1

5

5

5

1

5

2

2

2

2

0

0

7

7

7

7

3

3

3

1

0

3

0

1

6

6

6

6

4

4

4

0

4

0

Xv = the set of cuts that provides minimum arrive time

Arr_5 = 1 Arr_6 = 1 Arr_7 = 1

- The area of a cut c is calculated as:

2

4

1

3

- The area of a cut c is calculated as:

- The area of a cut c is calculated as:

2

4

1

3

2

4

1

3

- After cut enumeration, we obtain the optimal mapping depth of the network.
- Only critical paths need to use the cuts that lead to minimum delay.
- Cuts on non-critical paths can be reconstructed to search for a better solution in terms of area.

2

1

Carry out a topological order traversal starting from POs, then the inputs of the generated LUTs are iteratively mapped. The procedure continues until all the PIs are reached.

Input Sharing

Slack Distribution

Cut Probing

DAOmap is 16.02% better than CutMap in terms of LUT counts on average, and runs 24.2X faster when both are mapped with 5-LUT.

- This paper presents a technology mapping algorithm, DAOmap, for FPGA architectures to minimize chip area under timing constraints.
- Algorithm consists of Cut enumeration and Cut Selection.
- Novel heuristics has been designed to captured the mapping cost accurately with consideration of both local and global optimization information.
- Experimental results showed that DAOmap produced significant quality and run-time improvements compared to other mapping tools.