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FPGA Intra-cluster Routing Crossbar Design

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FPGA Intra-cluster Routing Crossbar Design

Dr. Philip Brisk

Department of Computer Science and Engineering

University of California, Riverside

CS 223

Generating Highly Routable Sparse Crossbars for PLDs

Guy Lemieux, Paul Leventis, David Lewis

International Symposium on FPGAs, 2000

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

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

- p = m(m – n + 1) switches

- Area savings is minimal if n >> m

…

- 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

O1

I1

O2

I2

O1

I3

O3

O2

O3

O4

I4

I5

O4

I1

I3

I4

I2

I5

I6

I6

- 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

- Build an FPGA, map 20+ applications, observe results

- 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

- X, Y are the bipartite independent sets of G

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

- 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

- 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

- 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:

Identical Hamming costs before and after the swap

Before: cannot route {1, 2, 3}

After: reduces Hamming costs

Using Sparse Crossbars within LUT Clusters

Guy Lemieux, David Lewis

International Symposium on FPGAs, 2001

- 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?

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

WenyiFeng and SinanKaptanoglu

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

Note: Paper is from Actel (now Microsemi)

312 Configurations

256 Configurations

784 Configurations

- 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

- 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

intra-cluster

crossbar

global routing

- 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!

- 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!

- 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

- 2-level
- L1 is sparsely populated
- L2 is fully populated

- Fully populated L2 reduces area efficiency
- VPR
- Fc,indetermines L1 population density

- 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

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

- 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…

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

Jonathan W. Greene, et al.

International Symposium on FPGAs, 2011

Note: Paper is from Microsemi

(Feng and Kaptanoglu are co-authors)

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

- 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

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

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

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