Yilin Zhang and David Z. Pan ECE, Univ. of Texas at Austin

transcript

Timing-Driven, Over-the-Block Rectilinear Steiner Tree

Construction with Pre-Buffering and Slew Constraints

Yilin Zhang and David Z. Pan

ECE, Univ. of Texas at Austin

ISPD’ 2014

Outline

Background & MotivationTOB-RSMT

› Problem Formulation› TOB-RSMT Algorithms

Experimental ResultsConclusion

History of VLSI RSMTs

Wirelength driven: BOI, BI1S, RV-based RST, FLUTE and GeoSteiner

Obstacle-avoiding RSMT (OA-RSMT) › [Chow+, VLSI14] [Liu+, DAC12][Li+, ICCAD08]

Over-the-block RSMT (OB-RSMT) are proposed since 2012

› [Huang+, ICCAD12] [Zhang+, ICCAD12] Minimum delay routing tree (MDRT) : BA-Tree,

etc.RAT-driven RSMT: C-Tree, etc.

Limitations on Previous Timing-driven RST

Cluster nodes during bottom-up method› Such as BA-Tree and C-Tree

Clustering distance metric: › spatial and slack

Hard to find accurate slack:Some segments are not fixed yet All segments are not buffered yet

Limitations in Dealing Blocks

Completely neglect block will have slew problem› No over-the-block buffer allowed

Obstacle avoiding› More congested outside-block› Detour means more WL and worse timing

detours

Post-buffering Topology Tuning is NecessaryBuffering plays a big role in delay reduction

› Shielding effect; linear delay on long wire› But it is always placed after wiring

Change topology after buffering is fruitful!

DSB unchanged

DSA decreased Db2

Our Contributions

Use pre-buffering to find practical slack for each node in the graph

Use over-the-block routing resource to improve WL, buffering cost and timing

Apply post-buffering tuning to improve timing on critical paths with little extra cost

Outline

Problem Formulation

N = {s0,s1,s2,...,sn}, n sinks and source s0

B = {b1, b2, . . . , bm}, non-overlapping rectilinear blocks in two-dimensional space R

Buffered T(V, E) connects all the pins in N to optimize WNS with the lowest buffering cost

› V is the set of nodes › E is the set of horizontal and vertical edges.

Slew rate on every point in T within constraints› Slew mode buffering [Hu+, TCAD07]

No buffers are allowed over the blocks

Timing Models

Elmore Delay

› Peri Model + Bakoglu’s Metric

» ( 4% error [Kashyap+, ISPD03] [Bakoglu+, 90] )

Overall Algorithm

Initial timing-driven RST with Pre-buffering

Find all over-the-block slew violation and fix them

Buffering

Tune the topology according to buffering information

Buffering

Return buffered T

Initial Tree Generation with Pre-Buffering

Iterative method› Until converges or oscillates between several states

Feed back real delay to each node to find slack (criticality)

› Identified critical sinks before topology construction are real critical ones

› Practical slack on each node

Initial Tree with Pre-Buffering Flow

[Lin+, TCAD11]

Initial Tree with Pre-Buffering Example

Simple model without buffering suggests D is critical

However, with buffering, D is not critical

Now, D is inserted far from source

with less WL

Buffering-Aware Over-the-Block TD-RST

TD-RST needs over-the-block route

› Better WL, buffer resources and timing

› Replace obstacle-avoiding detours with shorter over-

the-block connection

150ps 100ps

120ps 110ps

Different with WL-driven BOB-RSMT

Original

WL driven

Move non-critical paths to save slew

Protect critical paths for timing

WL+slack

The hard problem with over-the-block is slewEach topology confines a set of inside treesUse hypothetic buffer to check if it is possible for

buffering

Slew Constraints in Buffering-Aware TD-RST

Optimization Primitives

Three optimization primitives

Parallel sliding Perpendicular sliding

EP merging[Zhang, ICCAD12]

Formulation consider slack and WL together

Formulation of Buffering-Aware TD-RST

WijCdEPit: delay

increase for every sink downstream EPi

Increase of TNS

Increase of WL

Buffer-location-based Tuning Benefits

Tuning topology after buffering benefits!

Buffering resources are costly

Improve timing without increasing buffers is

tempting

› With small amount of WL increase

We propose a way to post-tune the topology

base on buffer location information

Saturated/Un-saturated Buffers

Some buffers are “Saturated” and some are “Un-

saturated”

› Saturate: the slew reaches maximum

› Un-saturated: slew does not reach maximum

Buffer-location-based Tuning Study

Un-saturated buffer == opportunity

WL increase

Delay to A improves

Buffer-location-based Tuning Condition

Δslew = slewmax – slewcur

Lmax is the max allowed distance to relocate

› If neglecting buffer input cap, Lmax =

› If consider buffer input cap, Lmax =

Buffer-location-based Tuning Flow

Sort all sinks according to slack

Tuning

Buffered T

Return buffered T

n = n.parent

satisfy Lmax constraint ?

For each neg slack sink n

n at source?

YContinue

Buffering

Outline

Experimental Setups

C++ programming language Intel Core 3.0GHz Linux machine with 32GB

memory Gurobi Optimizer 5.10 for mathematical

optimizationRC01-RC12 are benchmarks [Feng+, ISPD06]Two sizes of buffers: 450 ohms and 850 ohms,

3.8 fF and 1.9 fF Interconnect RC from ITRS and slew constraints

Experimental Setups

SD-OARST is baseline [Lin+, TCAD11]TOB-RST-1 OA-RST with pre-bufferingTOB-RST-2 is over-the-block with pre-bufferingTOB-RST is over-the-block with pre-buffering

and post-buffering tuning

Experimental Results

TOB-RST-1 to SD-OARST › similarity of WL (buffering cost)› pre-buffering benefits the slack

TOB-RST-2 to TOB-RST-1: › 179ps on average for WNS› buffering cost and WL reduced by 6% and 5%

TOB-RST to TOB-RST-2: › 70ps in WNS on average, less than 1% more WL

Experimental Results

Outline

Conclusion

Timing-driven over-the-block rectilinear Steiner minimum tree

Use pre-buffering to find practical slack for each node

Use over-the-block routing resources to improve WL, buffering cost and timing

Apply post-buffering tuning to improve timing on critical paths with little extra cost

Significantly improve WNS for all benchmarks along with 2% less WL and 4% less buffering cost than SD-OARST

Acknowledgment

This work is supported in part by Oracle Thanks to Dr. Salim Chowdhury, Dr. Rajendran

Panda and Dr. Akshay Sharma from Oracle

Thank you!Questions?

Yilin Zhang and David Z. Pan ECE, Univ. of Texas at Austin

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