1. Penn ESE 535 Spring 2011 -- DeHon 1 ESE535: Electronic Design Automation Day 12: February 23, 2011 Routing 2 (Pathfinder)

2. Penn ESE 535 Spring 2011 -- DeHon 2 Today Routing –Pathfinder graph based global routing simultaneous global/detail Behavioral (C, MATLAB, …) RTL Gate Netlist Layout Masks Arch. Select Schedule FSM assign Two-level, Multilevel opt. Covering Retiming Placement Routing

3. Penn ESE 535 Spring 2011 -- DeHon 3 Global Routing Problem: Find sequence of channels for all routes –minimizing channel sizes –minimize max channel size –meeting channel capacity limits

4. Penn ESE 535 Spring 2011 -- DeHon 4 Global  Graph Graph Problem on routes through regions w

5. Penn ESE 535 Spring 2011 -- DeHon 5 Global/Detail With limited switching (e.g. FPGA) –can represent routing graph exactly

6. Penn ESE 535 Spring 2011 -- DeHon 6 Global/Detail

7. Penn ESE 535 Spring 2011 -- DeHon 7 Routing in Graph Find (shortest/available) path between source and sink –search problem (e.g. BFS, A*)

8. Penn ESE 535 Spring 2011 -- DeHon 8 Breadth First Search (BFS) Start at source src Put src node in priority queue with cost 0 –Priority queue orders by cost While (not found sink) –Pop least cost node from queue Get: current_node, current_cost –Is this sink?  found –For each outgoing edge from current_node Push destination onto queue with cost current_cost+edge_cost

9. Penn ESE 535 Spring 2011 -- DeHon 9 Easy? Finding a path is moderately easy What’s hard? Can I just iterate and pick paths?

10. Penn ESE 535 Spring 2011 -- DeHon 10 Example s1s3s2 d2d1d3 All links capacity 1 si disi di

11. Penn ESE 535 Spring 2011 -- DeHon 11 Challenge Satisfy all routes simultaneously Routes share potential resources Greedy/iterative –not know who will need which resources E.g. consider routing s3->d3 then s2->d2 then s1->d1 –i.e. resource/path choice looks arbitrary –…but earlier decisions limit flexibility for later like scheduling –order effect result s1s3s2 d2d1d3

12. Penn ESE 535 Spring 2011 -- DeHon 12 Negotiated Congestion Old idea –try once –see where we run into problems –undo problematic/blocking allocation rip-up –use that information to redirect/update costs on subsequent trials retry

13. Penn ESE 535 Spring 2011 -- DeHon 13 Negotiated Congestion Here –route signals –allow overuse –identify overuse and encourage signals to avoid reroute signals based on overuse/past congestion

14. Penn ESE 535 Spring 2011 -- DeHon 14 Basic Algorithm Route signals along minimum cost path If congestion/overuse –assign higher cost to congested resources Repeat until done

15. Penn ESE 535 Spring 2011 -- DeHon 15 Key Idea Congested paths/resources become expensive When there is freedom –future routes, with freedom to avoid congestion will avoid it When there is less freedom –must take congested routes Routes which must use congested resources will, while others will chose uncongested paths

16. Penn ESE 535 Spring 2011 -- DeHon 16 Cost Function (1) PathCost=  (link costs) LinkCost = base  f(#routes using, time) Base cost of resource –E.g. delay of resource –Encourage minimum resource usage (minimum length path, if possible) –minimizing delay = minimizing resources Congestion –penalizes (over) sharing –increase sharing penalty over time s1s3s2 d2d1d3 2 3 4 3 11 1 1 1 4 4 3 2 111 3+1+4=8

17. Penn ESE 535 Spring 2011 -- DeHon 17 Example (first order congestion) Base costs (delays) s1s3s2 d2d1d3 2 3 4 3 11 1 1 1 4 4 3 2 111 Capacity 1 1 1 1 1 1 1 1 1

18. Penn ESE 535 Spring 2011 -- DeHon 18 Example (first order congestion) s1s3s2 d2d1d3 2 3 4 3 11 1 1 1 4 4 3 2 Base costs (delays) 1 1 1 Capacity All, individual routes prefer middle; create congestion. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

19. Penn ESE 535 Spring 2011 -- DeHon 19 Example (first order congestion) s1s3s2 d2d1d3 2 3 4 3 11 1 1 1 4 4 3 2 Base costs (delays) 1 1 1 Capacity Reroute, avoid congestion. 1 1 1 1

20. Penn ESE 535 Spring 2011 -- DeHon 20 Example (need for history) Base costs (delays) Capacity Need to redirect uncongested paths; how encourage? s1s2 d2d1 2 11 s3 d3 1 s4 d4 22 1 1 1 1 2 1 1 1 2 1 1

21. Penn ESE 535 Spring 2011 -- DeHon 21 Example (need for history) Cannot route s3  d3 s1s2 d2d1 22 2 11 1 1 s3 d3 1 1 2 1 1 1 Local congestion alone won’t drive in right directions. Both paths equal cost …neither resolves problem. May ping-pong back and forth. (can imagine longer chain like this) s4 d4 1 1 2 1 1 1

22. Penn ESE 535 Spring 2011 -- DeHon 22 Cost Function (2) Cost = (base + history)*f(#resources,time) History –avoid resources with history of congestion

23. Penn ESE 535 Spring 2011 -- DeHon 23 Example (need for history) S3  d3 and s4  d4 initially ping-pong Builds up congestion history on path 3 and 4 Eventually makes path 3 and 4 more expensive than path 1; …resolves conflict…  Adaptive cost scheme. s1s2 d2d1 22 2 11 1 1 s3 d3 1 1 2 1 1 1 s4 d4 1 2 1 1

24. Delay Penn ESE 535 Spring 2011 -- DeHon 24

25. Penn ESE 535 Spring 2011 -- DeHon 25 What about delay? Existing formulation uses delay to reduces resources, but doesn’t directly treat Want: –prioritize critical path elements for shorter delay –allow nodes with slack to take longer paths

26. Penn ESE 535 Spring 2011 -- DeHon 26 Cost Function (Delay) Cost= –(1-W(edge))*delay + W(edge) *congest –congest as before (base+history)*f(#signals,time) W(edge) = Slack(edge)/Dmax –0 for edge on critical path –>0 for paths with slack Use W(edge) to order routes Update critical path and W each round

27. Penn ESE 535 Spring 2011 -- DeHon 27 Cost Function (Delay) Cost= –(1-W(edge))*delay + W(edge) *congest –congest as before (base+history)*f(#signals,time) W(edge) = Slack(edge)/D max What happens if multiple slack 0 nets contend for edge? W(edge)=Max(minW,Slack(edge)/D max ) –minW > 0

28. VPR If doesn’t uncongest, weight congestion more Cost= (1-W(e))*delay + W(e) *PF (iter) *congest PF=Pressure Factor Eventually congest dominates delay Penn ESE 535 Spring 2011 -- DeHon 28

29. VPR Pressure Factor Converges quickly But may “freeze” with higher delay than necessary Netlist Shuffle experiment Penn ESE 535 Spring 2011 -- DeHon 29 [Rubin / FPGA 2011]

30. VPR Pressure Factor Tuning Penn ESE 535 Spring 2011 -- DeHon 30 [Raphael Rubin 2010]

31. Alternate Delay Approach Believe pathfinder can resolve congestion Pathfinder has trouble mixing delay and congestion Idea: Turn delay problem into congestion problem –Reject paths that are too long –All signals compete only for resources that will allow them to meet their timing goals Penn ESE 535 Spring 2011 -- DeHon 31

32. Outlaw Long Paths Issue: Critical path may go through multiple gates –Contain more than one gate  gate path –How allocate slack among paths? Penn ESE 535 Spring 2011 -- DeHon 32 Target 12 Gate 1 Manhattan hop 1

33. Outlaw Long Paths Issue: Critical path may go through multiple gates –Contain more than one gate  gate path –How allocate slack among paths? Penn ESE 535 Spring 2011 -- DeHon 33 Target 12 Gate 1 Manhattan hop 1

34. Outlaw Long Paths Issue: Critical path may go through multiple gates –Contain more than one gate  gate path –How allocate slack among paths? Penn ESE 535 Spring 2011 -- DeHon 34 1234 5678 9 Target 12 Gate 1 Manhattan hop 1 Total Slack?

35. Slack Budgeting Divide slack among the paths –Slack of 3 –Example: give slack 1 to first link 2 to second Penn ESE 535 Spring 2011 -- DeHon 35 [So / FPGA 2008] 1234 5678 9

36. Slack Budgeting Divide slack among the paths Each net now has delay target Reject any path exceeding delay target Reduce to congestion negotiation Penn ESE 535 Spring 2011 -- DeHon 36 [So / FPGA 2008] 5 6

37. Slack Budgeting Can often find lower delay routes that VPR Takes 10x as long –Mostly in slack budgeting Solution depends on slack budget –Not exploiting full freedom to re-allocate slack among links Penn ESE 535 Spring 2011 -- DeHon 37 [So / FPGA 2008]

38. Delay Target Routing Similar high-level idea Just set target for Pathfinder cost –Rather than allowing to float Penn ESE 535 Spring 2011 -- DeHon 38

39. Delay Target Cost= (1-W(edge))*delay + W(edge) *congest W(edge) = Slack(edge)/D target –Previously: denominate was D max Compute Slack based on D target –can be negative W(edge)=Max(minW,Slack(edge)/D target ) –minW > 0 Penn ESE 535 Spring 2011 -- DeHon 39

40. Delay Target Routing Does allow slack to be used on any of the gate  gate connections on path –…but not being that deliberate/efficient about the allocation Doesn’t require time for slack allocation Penn ESE 535 Spring 2011 -- DeHon 40

41. Delay Target Routing Penn ESE 535 Spring 2011 -- DeHon 41 [Rubin / FPGA 2011]

42. Delay Target Routing Less sensitive to initial conditions Penn ESE 535 Spring 2011 -- DeHon 42 [Rubin / FPGA 2011]

43. Rerouting Penn ESE 535 Spring 2011 -- DeHon 43

44. Penn ESE 535 Spring 2011 -- DeHon 44 Rerouting Default: reroute everything Can get away rerouting only congested nodes –if keep routes in place –history force into new tracks causing greedy/uncongested routes to be rerouted

45. Penn ESE 535 Spring 2011 -- DeHon 45 Rerouting Effect of only reroute congested? –maybe more iterations (not reroute a signal until congested) –less time –Convergence? Faster? … prevent convergence? –? Hurt quality? (not see strong case for) –…but might hurt delay quality Maybe followup rerouting everything once clear up congestion?

46. Penn ESE 535 Spring 2011 -- DeHon 46 Run Time? Route |E| edges Each path search O(|E graph |) worst case –…generally less Iterations?

47. Penn ESE 535 Spring 2011 -- DeHon 47 Quality and Runtime Experiment For Synthetic netlists on HSRA –Expect to be worst-case problems Congestion only –Quality = # channels Number of individual route trials limited (measured) as multiple of nets in design –(not measuring work per route trial)

48. Penn ESE 535 Spring 2011 -- DeHon 48 Quality: fixed runtime

49. Penn ESE 535 Spring 2011 -- DeHon 49 Quality Target

50. Penn ESE 535 Spring 2011 -- DeHon 50 Quality vs. Time

51. Penn ESE 535 Spring 2011 -- DeHon 51 Conclusions? Iterations increases with N Quality degrade as we scale?

52. Penn ESE 535 Spring 2011 -- DeHon 52 Techniques to Accelerate (already in use in data just shown)

53. Penn ESE 535 Spring 2011 -- DeHon 53 Search Ordering Default: breadth first search for shortest –O(total-paths) –O(N p ) for HSRA Alternately: use A*: –estimated costs/path length, prune candidates earlier –can be more depth first (search promising paths as long as know can’t be worse)

54. Penn ESE 535 Spring 2011 -- DeHon 54 BFS  A* Start at source Put src node in priority queue with cost 0 –Priority queue orders by cost –Cost =  (path so far) + min path to dest While (not found sink) –Pop least cost node from queue Get: current_node, current_cost –Is this sink?  found –For each outgoing edge Push destination onto queue with cost current_cost+edge_cost

55. Penn ESE 535 Spring 2011 -- DeHon 55 BFS vs. A*

56. Penn ESE 535 Spring 2011 -- DeHon 56 Single-side, Directed (A*) Only expand search windows as prove necessary to have longer route.

57. Penn ESE 535 Spring 2011 -- DeHon 57 Search: one-side vs. two-sides One-side vs. Two-sides

58. Penn ESE 535 Spring 2011 -- DeHon 58 Searching In general: –greedy/depth first searching find a path faster may be more expensive – (not least delay, congest cost) –tradeoff by weighting estimated delay on remaining path vs. cost to this point control greediness of router –More greedy is faster at cost of less optimal paths (wider channels) 40% W  10x time reduction [Tessier/thesis’98]

59. Penn ESE 535 Spring 2011 -- DeHon 59 Searching Use A* like search –Always expanded (deepen) along shortest …as long as can prove no other path will dominate –Uncongested: takes O(path-length) time –Worst-case reduces to breadth-first O(total-paths) O(N p ) for HSRA

60. Penn ESE 535 Spring 2011 -- DeHon 60 Domain Negotiation For Conventional FPGAs (and many networks) –path freedom bushy in middle low on endpoints

61. Penn ESE 535 Spring 2011 -- DeHon 61 Mesh Expand 1 2 4 4 2

62. Penn ESE 535 Spring 2011 -- DeHon 62 Multistage/Benes Switches in all paths 0000 to 1111

63. Penn ESE 535 Spring 2011 -- DeHon 63 Conventional FPGA Domains Called: subset disjoint

64. Penn ESE 535 Spring 2011 -- DeHon 64 Conventional FPGA Domains Called: subset disjoint

65. Penn ESE 535 Spring 2011 -- DeHon 65 Domain Routing No point in searching along an entire path from source Just to find it’s heavily congested at sink (SRC) sink

66. Penn ESE 535 Spring 2011 -- DeHon 66 HSRA Domains

67. Penn ESE 535 Spring 2011 -- DeHon 67 Domain Negotiation Path bottlenecks exist at both endpoints Most critical place for congestion Most efficient: work search from both ends –more limiting in A* search –focus on paths with least (no) congestion on endpoints first –FPGAs -- picking “domain” first –otherwise paths may look equally good up to end (little pruning)

68. Penn ESE 535 Spring 2011 -- DeHon 68 Summary Finding short path easy/well known Complication: need to route set of signals –who gets which path? –Arbitrary decisions earlier limit options later Idea: iterate/relax using congestion history –update path costs based on congestion Cost adaptive to route –reroute with new costs Accommodate delay and congestion

69. Penn ESE 535 Spring 2011 -- DeHon 69 Admin No class next Monday 2/28 –work on assign 4 Reading for next Wednesday online Assignment 4 due Wed. 3/2 Andre away Monday and Tuesday

70. Penn ESE 535 Spring 2011 -- DeHon 70 Big Ideas Exploit freedom Technique: –Graph algorithms (BFS, DFS) –Search techniques: A* –Iterative improvement/relaxation –Adaptive cost refinement