CS294-6 Reconfigurable Computing Day 12 October 1, 1998 Interconnect Population

Today Costs of full population Tradeoffs Building Blocks Empirical Evidence

Symmetric

Symmetric Wire Channels IO  N P Bisection BW  N P W  N P-0.5 –N if p<0.5 W  log(N) –P=0.5

XC4K (Commercial Symmetric)

Symmetric Full Population For simplicity: XC4K –8 short –4 double –Two sides with 6 connections –=> 10x10 switchbox + 2x (12x6) C-boxes –2x12x6 + 4x10x30/2 = 744 switches –2.5K 2 /switch => 1.9M 2 –Compare real XC4K at 1.25M 2

Wires vs. Switches Full Population –Switch area => W 2 (4x3/2)W 2 ~15K  W 2 –Wire Area => W 2 8 Wx8 W   W 2

Avoidable? How can we avoid N 2 switches?

Switching Problem Connect any permutation of N sources to N sinks: –Crossbar: N 2 switches

Benes Network Routes any permutation O(Nlog(N)) switches

Tradeoff Crossbar –N 2 –N=16 => 256 –single serial switch Benes –2log(N)-1 stages –N/2 2x2’s per stage –4 switches/2x2 –4Nlog(N)-2N –N=16 => 224 –(w/ 4x4s, 192) –2log b (N)-1 serial switches (2x2=>7, 4x4=>3) General trend: flatter => more total switches factored => longer switch series

Concentrators Select M signals from N –(N>M) Crossbar –NxM

Concentrators Order of outputs often not important –(e.g. LUT inputs) Limit “crossbar” population to: –M x (N-M+1)

Switchboxes Goal: route an input to an output on a different side –doesn’t matter which output …as long as output can route on to destination

Switchboxes Intro: 4 x (3W=>W) –6W 2 (push: does order matter?)

Switchboxes (Linear Population) Connect –each wire –on each side –to a single connection on each destination side Linear total switch population –Switches = (3x4xW)/2 = 6W

Switchboxes (Xilinx/Diamond) Linear -- connect to same corresponding channel each side

Switchboxes (Universal) Linear Principle: Supports all sets of simultaneous connection requests up to channel width limits for switchbox –connection request: N-S, S-W, etc.

Switchbox (domain schemes) Asymptotically: Universal route 25% more connection sets than Diamond (strict superset)

Enough? Universal switch guarantees each switch is locally routable –if all four sides are unconstrained But, routing one universal switch places constraints on connections –not guarantee a whole set of connections can be routed

Mapping Ratio Partial schemes –=> switching limitations may prevent use of some channels As a result, need more channels to detail route than implied by global route –(counting wires in each channel segment) Mapping Ratio –Detail Routing Channels / Global Channels

Lack of CMR for domain schemes Two negative results from UCSB –Any domain scheme (diamond, universal) is: NP-complete in detailed routing –figuring out which channels/switches to use –reduce graph coloring to domain routing No Constant Mapping Ratio (CMR)

Toronto Experiments Review Fig 5 and 6 and Table 2 from –Rose and Brown JSSC v26n3p277, mar91 Recommendations: –3-4 connections per wire in switchbox (linear schemes = 3) this is pre-discovery of universal switchbox –input switch population 79-90% commensurate with M choose N structure

CMR->“Perfect” Switchboxes Universal was complete if unconstrained –Hybrid idea: build assuming one (or more) sides are unconstrained –get to use linear switches on these sides fully populate constrained sides tighten guaranteed routing bound

Greedy Routing Architecture

Constant Mapping Ratio Linear => CMR=1.5 Problem is using 3rd side, can build flat concentrator with –W 2 /2 switches –gives CMR=1 for tree routes

Finishing Greedy Perfect Route Tree Connections routed with: –2W+W 2 /2 switches Must route one remaining side as before –3W 2 Total –3.5W 2 +2W –(compare 6W 2 intro) Use Benes for constrained sides –O(Wlog(W))

Summary Even with limited switching schemes we’ve explored, full population appears untenable. Full population often more than really need. Can we define switching structures with “nice” routing properties, reasonable number of switches, and reasonable delay?

Summary (2) Empirical evidence that “linear” populations are adequate –routing challenge rises from lack of guarantees –better theory as to why adequate? –slight changes improve guarantees, ease of route?