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Recursive Bisection Placement:Feng Shui 5.0 Implementation Details
Ameya R. AgnihotriSUNY Binghamton CSD
Binghamton, NY
Satoshi OnoSUNY Binghamton CSD &University of Kitakyushu
Binghamton, NY
Patrick H. MaddenSUNY Binghamton CSD &University of Kitakyushu
Binghamton, NY
ABSTRACTIn this paper, we summarize circuit placement techniques and al-gorithms developed by the BLAC CAD research group; these havebeen integrated into our recursive bisection based placement toolfeng shui. We also briefly describe current research interests.
Catagories and Subject Descriptions: J.6 [Computer-Aided En-gineering]: CAD
General terms: Algorithms
Keywords: Placement, floorplanning, mixed block design
1. INTRODUCTIONCircuit placement is a well-studied area of physical design. Sim-
ulated annealing[13, 22, 26], recursive bisection[3, 7, 4, 2], andanalytic methods[14, 25, 8, 24] are widely used. In this paper, wesummarize research performed at Binghamton University, result-ing in improved techniques and algorithms for placement. Due tospace constraints, we describe our work briefly; a longer version ofthis paper, related publications, and binary releases of our tools areavailable on the web at http://vlsicad.cs.binghamton.edu.
The primary vehicle for testing research ideas has been our re-cursive bisection based placement tool feng shui; the overall flowof our tool is shown in Figure 1. Following the release of version5.0, development based around recursive bisection will be put onhold, as our focus is now on a new approach.
This paper is organized into four main sections; we considerglobal placement, legalization, detailed placement, and future di-rections for placement research.
2. GLOBAL PLACEMENTThe overall flow of our bisection based placement approach fol-
lows traditional methods[3, 7]. Starting from an initial circuit netlistand placement region, we repeatedly divide the logic elements us-ing a partitioner (either hMetis or MLPart). Terminal propagationnormally results in an interdependence of partitioning results for
Copyright is held by the author/owner.ISPD’05, April 3–6, 2005, San Francisco, California, USA.ACM 1-59593-021-3/05/0004.
different regions. A common approach to address the interdepen-dence is through “cycling[23, 10, 11];” a region may be partitionedmultiple times before terminal propagation becomes stable. As analternative to cycling, we investigated large-scale multi-way par-titioning in [27], using a method based on iterative deletion[18].While we were unable to eliminate cycling from our flow, and wirelength improvements were modest, using the initial partitioning so-lutions provided by iterative deletion reduced the number of cyclesneeded for convergence.
For bisection based placement, the direction of cut lines can in-fluence results considerably. Early methods for cut line selectionwere essentially ad hoc; in [28], we performed dynamic program-ming based analysis using Rent’s Rule[20]. This analysis showedthat an aspect ratio based methodology is appropriate; adjustmentof the aspect ratios used resulted in improved results for both fengshui and Capo.
The bisection approach, cycling for terminal propagation, anddifferent possible cut sequences, are illustrated in Figure 2.
While results of feng shui were good on MCNC benchmarks,pathological behavior was observed on more recent benchmarks–and in particular, the synthetic PEKO examples [6]. The degre-dation in performance was due to the narrow region problem; thisproblem was addressed in a novel way by the introduction of frac-tional cut lines[2]. Rather than aligning horizontal cut lines withrow boundaries, they are instead allowed to float freely–this re-quires a legalization step, which we describe in the next section.While the need for legalization introduced a new problem to besolved, we find that it can in fact be solved relatively easily; thenet result of fractional cut lines is roughly a 5% reduction in wirelength, and a greater degree of stability in standard cell placement.A second, and perhaps greater benefit of fractional cut lines is asimplification in placement for circuits that contain both macroblocks and standard cells. Without a constraint on row alignment orlegality during global placement, macro blocks and standard cellscan be handled simultaneously by recursive bisection[12].
3. LEGALIZATIONTo obtain a legal placement after fractional cut based bisection,
a number of techniques were investigated.Dynamic Programming Based Legalization: our first approach
to legalization used a row-by-row dynamic programming algorithm[2].The approach minimizes displacement for cells assigned to a row,and is similar in many respects to other DP based optimization tech-niques. We are currently investigating methods to legalize multiplerows at a time, using cost functions other than cell displacement.
The method operates as follows: we first sort all cells by their
Aspect Ratio basedcut line selection [28]
Iterative Deletion [18,27]
Multi-level Partitioning
Fractional-cut basedregion adjustment [2]
Sliding WindowBranch-and-Bound
Global Placement:bisection based, with fractionalcut lines to obtain uniformarea utilization.The initial region size matchesthe total area of cells and macroblocks; partitioning attempts tosplit each region roughly in half.
Iterative deletion provides earlyterminal propagation information,which is refined through cycling.
Recent collaboration with Purdueand UCLA has shown that cutlines can be shifted to adjustplacement density without degradingwire lengths.
Optional cut line shiftingfor routability or gate sizing[16,17]
Single or Multi-rowdynamic programming(standard cell design)[2]
Greedy Tetris(mixed size)[9,15,12]
Legalization:a dynamic programming methodprovides good results for standardcell designs, while a greedy methodis used for mixed size.
Detailed Placement:Standard branch-and-boundmethods are used to optimizestandard cell locations; recentexperiments indicate a great dealof potential in this area.
Cycle (by default,
three passes).
Figure 1: Overall flow of feng shui 5.0
vertical location, based on the result of global placement. A subsetof these cells – the “highest” locations, with a total area slightlyin excess of the desired area of the cell row – are selected. Thedynamic programming formulation then assigns a cost for eitherinserting the cell into the top row (the cost being equal to displace-ment), or for deferring the legalization of the cell for a subsequentrow (the cost being equal to the distance to the next row). By pro-cessing cells from left to right, the optimal solution (for a singlerow) can be found quickly. After placing cells into the top row, theprocess moves to the next row down.
Greedy Legalization: for mixed size benchmarks, our early at-tempts to adapt our dynamic programming based method were notsatisfactory. Based on a preprint of a paper by Li and Koh[15],we began investigating a simple greedy approach; we later learnedthat a similar standard cell legalization method had previously beenpatented by Hill[9]. We extended this method to handle macroblocks, which were not addressed in the patent. The method is sur-prisingly fast, and produces excellent results in designs where thecircuit elements are distributed uniformly. On average, the place-ments produced by feng shui 2.6[12] improved wire lengths by 26%over mPG[5], and by 29% over a combination of Capo and Par-quet[1].
With fractional cut bisection, distribution for standard cells isquite uniform, making the legalization step trivial. For cases wherethe macro blocks are large and rectangular, there can be significantamounts of overlap–this results in a degredation of wire length. Weare addressing this problem in our current work.
4. DETAILED PLACEMENTWhen the PEKO[6] benchmarks were first presented, there ap-
peared to be a large gap between optimal placements and the resultsof current placement tools. The degree of suboptimality–with wirelengths being from 1.5X to more than 2.5X away from optimal–generated a flurry of interest.
Our recent research[19, 21], however, indicates that for the PEKObenchmarks, this suboptimality is almost entirely “local.” Version
(a) The overall recursive bisection approach
First cut line
Second cut line Third cut lineSubregionA
SubregionB
SubregionA1
SubregionA2
SubregionA1
SubregionA2
SubregionB1
SubregionB2
A1
A2
B1
B2
A1’
A2’
B1
B2
A1’
A2’
B1’
B2’
A1’’
A2’’
B1’
B2’
A1’’
A2’’
B1’’
B2’’
A1’’’
A2’’’
B1’’
B2’’
(b) Cycling of partitioning to address terminal propagation changes
1
2 31 2 3
1
2
3
(c) Many cut orders and directions are possible; aspect ratio works well
Figure 2: Cut line orientation and terminal propagation arekey issues in bisection based placement; our tool employs cy-cling, and aspect ratio based cut line orientation.
5.0 of feng shui supports a graphical user interface that can displayplacements in variety of ways. For the “pixmap” display method, agraphical image is mapped onto the cells of a reference placement,and then the cells are rearranged to match placements produced byother tools.
In Figure 3, we show the feng shui 5.0 interface displaying theoptimal placement for PEKO01, with an image of one of the au-thors mapped to the cells. Below this are rearrangements of cellsto match the results of the recursive bisection engine of feng shui,a structural placement technique[19] also included in feng shui,and the results of the tools mPL [6], Dragon[26], Capo[4], andKraftwerk[8]. While the images are rotated or stretched, it is clearthat the “global” placements of all tools are quite good–and thus,the bulk of observed suboptimality is “local.” Despite the lack ofexternal pads, the placement of the analytic tool Kraftwerk also dis-plays a recognizable pattern.
The detailed placement engine of feng shui is based on sliding-window branch-and-bound optimization. Optimal rearrangementsof small groups of cells – usually 6 or fewer – are found repeatedly.The images in Figure 3 show that while the placement results are“close” to optimal, the windows used for detail placement are notlarge enough to eliminate the small scale suboptimality.
For this reason, we are currently exploring methods to performoptimal placement for windows that are much larger than 6 ele-ments. A method based on branch-and-price integer linear pro-gramming[21] has been developed, and can solve problems withup to 100 cells; at present, however, the method is too slow to beused across an entire design, and this has not yet been fully inte-grated into the feng shui code base.
5. FUTURE DIRECTIONSThe research focus of the group has moved away from recur-
sive bisection. Observations made with PEKO benchmarks suggestthat from a global perspective, results from annealing, analytic, andbisection are surprisingly similar. While there are many groups
feng shui 5.0 GUI with an image mapped tothe optimal placement of PEKO01
Dragon placement
Capo placement
Kraftwerk placement(not legalized)
mPL placementfeng shui structuralmode placement
feng shui recursivebisection placement
Figure 3: The feng shui 5.0 user interface, displaying an imagemapped onto the optimal placement of PEKO01. By rearrang-ing the cells to match the results of other placement tools, itis clear that a great deal of placement suboptimality for thesebenchmarks is “local” in nature.
working on traditional global placement methods, only relativelymarginal improvements seem likely–thus, we are investigating afundamentally new global placement approach.
Our new approach attempts to extract structure by topologicalanalysis of a circuit[19]. This works extremely well on the PEKObenchmarks, where our results are now within 22% of optimal. Webelieve that the method can be extended to more realistic structures–and that to address rising interconnect delay, future circuit struc-tures will transition towards more “PEKO-like” topologies.
We are also actively pursuing incremental placement techniques[16, 17]. To facilitate convergence of physical synthesis, we stronglybelieve that transforming an existing placement to support sizingand inserted buffers is superior to attempting to gain stability in aseparate run of the placement tools. Our work on placement legal-ization complements this. With our white space allocation meth-ods, cut line shifting, and an improvement on the cell shifting tech-nique presented in [24], we are able to regain placement legalitywithout wide changes to net lengths.
Finally, we are actively pursuing the integration of physical de-sign steps into a cohesive optimization approach. The global anddetail routing methods developed by the group are currently inte-grated into the development version of feng shui, and will likelybe released publicly in the summer of 2005. The next release mayalso feature a novel delay analysis approach, as well as support forSynopsys PowerARC delay libraries. We expect to have our gatesizing and buffer insertion methods fully integrated shortly.Acknowledgements: a number of students have worked on fengshui. In particular, Prof. Mehmet Can Yildiz is responsible fora large portion of the early work. Ateen Khatkhate and UdayanDeshpande influenced the development of the mixed size place-ment approach. We actively collaborate with our colleagues at Pur-due, Dr. Cheng-Kok Koh, and his student Chen Li; they have beeninstrumental in the development of both the mixed size legalizationstrategy, and the incremental placement techniques. The researchperformed by the group would not have been possible without thegenerous support of IBM, Intel, SRC, NYSTAR/MDC, IEEC, andthe SUNY Binghamton Research Foundation.
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