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## PowerPoint Slideshow about ' FPGA Intra-cluster Routing Crossbar Design' - rianna

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### FPGA Intra-cluster Routing Crossbar Design

### Generating Highly Routable Sparse Crossbars for PLDs

### Using Sparse Crossbars within LUT Clusters

### Designing Efficient Input Interconnect Blocks for LUT Clusters Using Counting and Entropy

### A 65nm flash-based FPGA fabric optimized for low cost and power

Dr. Philip Brisk

Department of Computer Science and Engineering

University of California, Riverside

CS 223

Guy Lemieux, Paul Leventis, David Lewis

International Symposium on FPGAs, 2000

Fully Populated Crossbar

- Full capacity – can connect as many signals as the number of outputs
- Flexibility – Can connect any input to any output

Full-capacity Minimal Crossbars

- Full capacity
- Reduced Flexibility: you lose the ability to connect any input to any output

- p = m(m – n + 1) switches

Perfect and Sparse Crossbars

- Perfect crossbars
- Can disjointly route any m-sized subset of the n inputs to the m outputs
- Both full and full-capacity minimal crossbars are perfect
- Sparse crossbars
- Has p < m(m – n + 1) switches
- Cannot be perfect

Evaluation Challenge

- How “routable” is a given crossbar?
- Build an FPGA, map 20+ applications, observe results
- Slow, highly subject to the application mix
- Monte Carlo Test
- Generate random test vectors
- Route each test vector on the crossbar (network flow)
- Report number of successes as a percentage
- A highly routable sparse crossbar has a >= 95% success rate

Hall’s Theorm

- Given a bipartite graph G = (V, E)
- X, Y are the bipartite independent sets of G

G has a matching of X onto Y if and only if

N(v) is the set of neighbors of vertex v

N(S) is the set of neighbors of all vertices in S

- Leverage Hall’s Theorem to generate routable sparse crossbars!

Practical Issues

- Cannot enumerate all subsets of m inputs
- N(x) should be approximately equal for all input vertices x in X
- Otherwise, any subset containing a large number of low-degree vertices is unlikely to be routable
- N(y) should be approximately equal for all output vertices y in Y
- Symmetric argument

Hamming Distance and Coding Theory

- Represent N(v) as a bitvectorbv
- bv[i] = 1 if v fans out to Oi
- Hamming Distance
- d(bv1, bv2)
- Strategy
- Maximize d(bvi, bvj) for every pair of distinct vertices vi and vj

Switch Placement Optimizer

- Start with initial switch placement
- Generate random swap of switch positions
- Accept the swap if there is an improvement
- Otherwise, reject the swap
- Stop after a fixed number of swap candidates (e.g., 10K) fails to find an improvement
- Objective is to minimize:

Example

Identical Hamming costs before and after the swap

Before: cannot route {1, 2, 3}

After: reduces Hamming costs

Guy Lemieux, David Lewis

International Symposium on FPGAs, 2001

Five Questions

- Will depopulation save area, require greater routing area, or create unroutable architectures?
- Will depopulation reduce or increase routing delays?
- What amount of depopulation is reasonable?
- How much area or delay reduction can be attained, if any?
- What are the other effects of depopulating the cluster?

WenyiFeng and SinanKaptanoglu

ACM Transactions on Reconfigurable Technology and Systems (TRETS), 1(1): article #6, March, 2008

Note: Paper is from Actel (now Microsemi)

Routing Requirement Vector (RRV)

- An ordered list of N subsets containing K distinct signals
- The ith subset is K distinct signals to route to the ith K-LUT
- Total number of RRVs for the crossbar:

M inputs

KN outputs

Entropy of an Intra-cluster Routing Crossbar

- H = lg(# routable RRVs)
- Accounts for equivalence of LUT inputs
- Why Entropy?
- # routable RRVs is huge
- Minimum number of configuration bits to program the crossbar
- Inversely correlated with usage of global routing muxes (details omitted)
- If we reduce the routability of the crossbar, we will end up programming more global routing muxes to compensate for the entropy loss

Theorem

- Let P and L be the number of muxes and switches in a crossbar
- The entropy is at most Plg(L/P)
- The entropy per switch is at most log(L/P) / (L/P)
- These bounds are achieved only when each mux has size L/P and each configuration realizes a unique RRV
- Proof omitted because I DO NOT HATE YOU!

What are we doing here?

- Lemieux and Lewis
- Routability: Monte Carlo simulations
- Area: Count switches
- Feng and Kaptanoglu
- Routability: Crossbar entropy
- Area: Entropy per switch
- Caveat: Focus only on crossbars where we can count routable, non-redundant RRVs!

Type-1 Crossbar

- 1-level
- L2 muxes are driven directly by crossbar input signals
- #routable RRVs depends on L2 crossbar topology
- Not area-efficient due to big L2 muxes
- Xilinx Virtex-style

Type-2 Crossbar

- 2-level
- L1 is sparsely populated
- L2 is fully populated
- Fully populated L2 reduces area efficiency
- VPR
- Fc,indetermines L1 population density

Type-3 Crossbar

- 2-level, Partitioned
- L1 partition Pi only drives L2 partition Oi
- From input m to LUT input n, all paths go through muxes in Pi and Oi exclusively
- #Routable RRVs is the product of #Routable RRVs for each disjoint sub-crossbar

Proposed Type-3 Crossbar and Generation Algorithm

- Each sub-crossbar is Type-2
- Can count #routable RRVs (Details omitted)

The Bottom Line…

- Who cares…
- Theoretical properties are cute
- Actel/Microsemi did not use these crossbars in their FPGAs
- Practical observation…
- The cheaper you make the intra-cluster routing crossbar, the more expensive the global routing…

Jonathan W. Greene, et al.

International Symposium on FPGAs, 2011

Note: Paper is from Microsemi

(Feng and Kaptanoglu are co-authors)

Corporate Secrets Divulged

- They used a Clos Network
- Three parameters: m, n, r

Clos Network Properties

- Used when the physical circuit switching needs to exceed the capacity of the largest feasible single crossbar
- Much cheaper than a fully populated nxn crossbar

Strict-sense Nonblocking Clos Network(m >2n – 1)

- An unused input on an ingress switch can always be connected to an unused output on an egress switch, without reconfiguration!

RearrangeablyNonblocking Clos Network(m > n)

- An unused input on an ingress switch can always be connected to an unused output on an egress switch, but reconfiguration may be necessary!

Recursive Clos Network Design

- Scalable to any ODD number of stages
- Replace center crossbar with a 3-stage Clos Network

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