Buffer and FF Insertion Slides from Charles J. Alpert IBM Corp.

2 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Talk Outline Introduction Buffer insertion Van Ginneken dynamic programming Extensions Interconnect planning

3 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Simple Buffer Insertion Problem Given: Source and sink locations, sink capacitances and RATs, a buffer type, source delay rules, unit wire resistance and capacitance Buffer RAT 1 RAT 2 RAT 3 RAT 4 s0s0

4 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Simple Buffer Insertion Problem Find: Buffer locations and a routing tree such that slack at the source is minimized RAT 2 RAT 3 RAT 4 RAT 1 s0s0

5 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Slack Example RAT = 400 delay = 600 RAT = 500 delay = 350 RAT = 400 delay = 300 RAT = 500 delay = 400 slack = -200 slack = +100

6 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Elmore Delay AB C R1R1 R2R2 C1C1 C2C2

7 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Common Approaches Iteratively insert buffers Closed-form solutions (2 pin nets) Dynamic programming Simultaneous constructions

8 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Van Ginneken’s Classic Algorithm Optimal for multi-sink nets Quadratic runtime Bottom-up from sinks to source Generate list of candidates at each node At source, pick the best candidate in list

9 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Key Assumptions Given routing tree Given potential insertion points

10 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Generating Candidates (1) (2) (3)

11 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Pruning Candidates (3) (a) (b) Both (a) and (b) “look” the same to the source. Throw out the one with the worst slack (4)

12 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Candidate Example Continued (4) (5)

13 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Candidate Example Continued After pruning (5) At driver, compute which candidate maximizes slack. Result is optimal.

14 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Merging Branches Right Candidates Left Candidates

15 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Pruning Merged Branches Critical With pruning

16 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Van Ginneken Example (20,400) (30,250) (5, 220) Wire C=10,d=150 Buffer C=5, d=30 (20,400) Buffer C=5, d=50 C=5, d=30 Wire C=15,d=200 C=15,d=120 (30,250) (5, 220) (45, 50) (5, 0) (20,100) (5, 70)

17 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Van Ginneken Example Cont’d (20,400) (30,250) (5, 220) (45, 50) (5, 0) (20,100) (5, 70) (5,0) is inferior to (5,70). (45,50) is inferior to (20,100) (20,400) (30,250) (5, 220) (20,100) (5, 70) (30,10) (15, -10) Pick solution with largest slack, follow arrows to get solution Wire C=10

18 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Van Ginneken Recap Generate candidates from sinks to source Quadratic runtime Adding a buffer adds only one new candidate Merging branches additive, not multiplicative Optimal for Elmore delay model

19 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Optimal Extensions Multiple buffer types Inverters Polarity constraints Controlling buffer resources Capacitance constraints Blockage recognition Wire sizing

20 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Multiple Buffer Types (1) (2) Time complexity increases from O(n 2 ) to O(n 2 B 2 ) where B is the number of different buffer types

21 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Inverters (1) (2) Maintain a “+” and a “-” list of candidates Only merge branches with same polarity Throw out negative candidates at source

22 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Polarity Constraints Some sinks are positive, some negative Put negative sinks into “-” list “-” list “+” list

23 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Controlling Buffering Resources (C 1, q 1, 3), (C 2, q 2, 3), (C 3, q 3, 3) (C 4, q 4, 2), (C 5, q 5, 2) (C 6, q 6, 1), (C 7, q 7, 1), (C 8, q 8, 1) (C 9, q 9, 0) (C 1, q 1 ), (C 2, q 2 ), (C 3, q 3 ) (C 4, q 4 ), (C 5, q 5 ) (C 6, q 6 ), (C 7, q 7 ), (C 8, q 8 ) (C 9, q 9 ) Before, maintain list of capacitance slack pairs Now, store an array of lists, indexed by # of buffers Prune candidates with inferior cap, slack, and #buffers

24 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Buffering Resource Trade-off

25 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Capacitance Constraints Each gate g drives at most C(g) capacitance When inserting buffer g, check downstream capacitance. If bigger than C(g), throw out candidate Total cap = 500 ff

26 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Blockage Recognition Delete insertion points that run over blockages

27 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Other Extensions Simultaneous driver sizing Modeling effective capacitance Higher-order interconnect delay Slew constraints Noise constraints

28 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Driver Sizing

29 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Driver Sizing Driver behaves like buffer Pick driver with the best slack Implications upstream in timing graph Delay penalty for large input capacitance

30 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001  -Models Van Ginneken candidate: (Cap, slack) C CnCn R CfCf Replace Cap with  -model (C n, R, C f ) Total capacitance preserved: C n + C f = C R represents degree of resistive shielding

31 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Computing Gate Delay When inserting buffer, compute effective capacitance from  -model C ef f Use effective instead of lumped capacitance in gate delay equation Optimality no longer guaranteed

32 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Higher-order Interconnect Delay Moment matching with first 3 moments Previously: candidate (  -model, slack) Now: candidate (  -model, m 1, m 2, m 3 ) Given moments, compute slack on the fly Bottom-up, efficient moment computation Problem: guess slew rate

33 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Slew Constraints When inserting buffer, compute slews to gates driven by buffer If slew exceeds target, prune candidate Difficulty: unknown gate input slew Slew 300 ps Slew 350 ps ?

34 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Noise Constraints Each gate has acceptable noise threshold Compute cumulative noise for each wire via Devgan noise metric Throw out candidates that violate noise Not in production code

35 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Extensions Recap Multiple buffer types, including inverters Polarity constraints Controlling buffer resources Slew, capacitance, and noise constraints Blockage recognition Driver sizing Higher-order delay modeling Wire sizing

36 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Talk Outline Introduction Buffer insertion Van Ginneken dynamic programming Extensions Interconnect planning

37 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 What is the Problem? DSM timing closure Squeeze buffers into tight spaces Alleviate hot spots, local wire congestion Getting worse Handle wire congestion, buffering resources early Acknowledge these constraints when floorplanning

38 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Which Floorplan Is Better? Timing analysis worthless Interconnect synthesis, electrical correction, routing, extraction Days to find answer

39 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Buffer Explosion Past Number of buffers triples each generation 800K buffers in 0.05 micron technology

40 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Buffer Block Planning Create blocks between macros just for holding buffers Adjust floorplan accordingly Computing size/#/location of blocks Analyze 2-pin nets Find feasible regions Assign buffers with smallest region Combine buffers into blocks

41 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Feasible Regions feasible region

42 Optimization Strategies for Physical Synthesis and Timing ClosureICCAD-2001 Buffer Block Planning Trade-offs Goods Buffer locations flexibile Global view, buffers most difficult ones first Bads Wire congestion around blocks Don’t have timing information Some nets still cannot be buffered/routed