CS137: Today Electronic Design Automation Problem Parallelism - - PDF document

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CALTECH CS137 Winter2006 -- DeHon 1

CS137: Electronic Design Automation

Day 8: January 27, 2006 Cellular Placement

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Today

• Problem
• Parallelism
• Cellular Automata
• Idea
• Details

– Avoid Local Minima – Update locations

• Results
• Directions
• Primary Sources

– Wrighton&DeHon FPGA2003 – Wrighton MS Thesis 2003

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Placement

• Problem: Pick locations for all building

blocks

– minimizing energy, delay, area – really:

• minimize wire length
• minimize channel density

– surrogates:

• Minimizing squared wire length
• Minimize bounding box

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Parallelism

• What parallelism exists in placement?

– Evaluate costs of prospective moves

• One set to many perspective locations
• Many moves each to single location

– Perform moves

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Cellular Automata

• Basic idea: regular array of identical

cells with nearest-neighbor communication

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CA Model

• On each cycle:

– Each cell exchanges values with neighbors – Updates state/value based on own state and that of neighbors – E.g. Conway’s LIFE

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Cellular Automata

• Physical Advantage:

– No long wires

• Area linear in number of nodes
• Minimum delaysmall cycle time
• Good scaling properties

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System Architecture Taxonomy

(Subject to continuing refinement and embellishment)

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CA Placement

• Can we perform placement in a CA?

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Mapping

• Each cell is a physical placement

location

• State is a logical node assigned to the

cell

• Assume:

– Cell knows own location – State knows location of connected nodes

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Costs

• Assume:

– Cell knows own location – State knows location of connected nodes

• Cell computes: its cost at that location

( )

2 .

) . ( ) . (

∑

∈

−

edges g e

snk e L src e L

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Moves

• Two adjacent cells can exchange graph

nodes

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Moves

• Evaluate goodness of proposed swap

– Each cell considers impact of its graph node being in the other cell – Keep if swap reduces cost

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Move Costs

• Only really need to evaluate delta cost
• (src.x-sink.x)2
• Moving sink
• d/dx=-2 (src.x-sink.x)
• Delta move cost is linear distance

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Parallel Swaps

• Pair up and perform N/2 swaps in

parallel

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Movement

• Alternate pairings with N,S,E,W

neighbor move any directions

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Basic Idea

• Pair up PEs
• Compute impact of swaps in parallel
• Perform swaps in parallel
• Repeat until converge

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Problems/Details

• Greedy swaps local minima?
• How update location of neighbors?

– …they are moving, too

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Avoid Greedy

• Insert randomness in swaps
• Simulated Annealing
• Shake up system to get out of local

minima

• Swap if

– Randomly decide to swap – OR beneficial to swap

• Change swap thresholds over time

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Swap?

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Impact of Randomness

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Range Limiting

Eurgo, Hauck, & Sharma DAC 2005

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Local Swaps Only

• Assume there’s an ideal location
• Each node takes a biased Random Walk

away from minimum cost location

• Gives node a distribution function around the

minimum cost location

• If wander into a better “minimum cost” home,

then wanders around new centerpoint

• Decreasing temperature restricts effective

radius of walk

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Local Swap Random Walk

• Decreasing temperature restricts

effective radius of walk

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How update locations?

• Broadcast?
• Pipelined Ring?
• Send to neighbors?

– Routing network?

• Tree?
• For whom?

– Everyone? Only things moved? Only things moved a lot?

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Simple Solution: Ring

• Drop value

in ring

• Shift around

entire array

• Everyone

listens for updates

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Simple Solution: Ring

• Weakness?

– Serial – N cycles to complete – N/2 swaps in O(1) – Then O(N) to update?

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Simple Solution: Ring

• Linear update bad
• Idea: allow staleness

– Things move slowly – Estimate of position not that bad… – …and continued

• peration will

correct…

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Algorithm

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Algorithm

Update Locations

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Algorithm

Try Moves

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Quality vs. Parameters

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Iso-Quality

Pick point on Iso-Quality Curve that minimizes time

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FPGA Implementation

• Virtex E (180nm)
• 10ns cycle (100MHz)
• 150 cycles for 4-phase swap

– (~40 cycles/swap)

• 400 LUTs / Placement Engine
• Comparing

– 2.2GHz Intel Xeon (L2 512KB)

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Results

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Tuning Quality

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Scaling

• Processor cycles O(N4/3)

– VPR

• Systolic cycles

– O(N1/2) – assume geometric refinement;

O(N1/2 ) update

– O(N5/6) – mesh sort, same number of swaps as VPR (N4/3 / N1/2)

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Scaling

Also includes technology scaling

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Variations

• Update Schemes
• Cost Functions
• Larger bins than PEs

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Update Scheme: Tree

• Build Reduce Tree (H-Tree)
• Route to route in O(N1/2) time
• Route from root to leaves in O(N1/2)

times

• Pipeline
• Same bandwidth as Ring (1/cycle)
• But less staleness (only O(N1/2))

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Reducing Broadcast (Idea 1)

• Don’t update things that haven’t moved

(much)

– …or things that move and move back before broadcast

• Keep track of staleness

– How far moved from last broadcast

• Give priority to stalest data
• Max staleness wins at each tree stage

– Break ties with randomness

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Reducing Broadcast (Idea 2)

• Update locally
• Don’t need to know if someone far away

moved by 1 square

• …but need to know if near neighbor did
• Multigrid/multiscale scheme

– Only alert nodes in same subtree – When change subtrees at a level, alert all nodes underneath

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Update Scheme: Mesh Route

• Can Route a permutation in O(N1/2) time
• n a mesh
• Build mesh switching
• Make O(N) swaps
• Then take O(N1/2) time moving/updating
• Becomes full simulated annealing

– i.e. not just local swaps

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Cost Functions

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Cost Functions

• Bounding Box2 phase update

– Phase 1: alert source to location of all sinks – Phase 2: source communicates bbox extents to all sinks

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Timing

• Linear Update:

– Topological ordering of netlist – Use tree to distribute updates – Send updates in netlist order – get delay in one pass

• Mesh:

– Compute directly with dataflow-style spreading activation

• Wait for all inputs; then send output

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Bins

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Node Bins

• Keep more than one graph node per PE
• Local swap of one node from each PE

node set each step

– One with largest benefit? – Randomly select based on cost/benefit?

• Like rejectionnless annealing

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Admin

• Parallel Prefix familiarity?
• Due today: literature review
• There is class on Monday