cs294-6 reconfigurable computing day 12 october 1, 1998 interconnect population
Post on 21-Dec-2015
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TRANSCRIPT
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– 2.5K2/switch => 1.9M2
– Compare real XC4K at 1.25M2
Wires vs. Switches
• Full Population – Switch area => W2
• (4x3/2)W2
• ~15K W2
– Wire Area => W2
• 8Wx8WW2
Tradeoff
• Crossbar– N2
– 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)
– 2logb(N)-1 serial switches
• (2x2=>7, 4x4=>3)
General trend: flatter => more total switches factored => longer switch series
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 (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 (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
Constant Mapping Ratio
• Linear => CMR=1.5
• Problem is using 3rd side, can build flat concentrator with– W2/2 switches– gives CMR=1 for tree routes
Finishing Greedy Perfect Route• Tree Connections routed with:
– 2W+W2/2 switches
• Must route one remaining side as before– 3W2
• Total– 3.5W2+2W– (compare 6W2 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?