VLSI Placement (I)

1
VLSI Placement (I)

• Prof. Lei He
• Http//eda.ee.ucla.edu

Thanks to Chis Chu, Jason Cong, Paul Villarubia
and David Pan for contributions to slides
2
Problem formulation

• Input
• Blocks (standard cells and macros) B1, ... , Bn
• Shapes and Pin Positions for each block Bi
• Nets N1, ... , Nm
• Output
• Coordinates (xi , yi ) for block Bi.
• The total wire length is minimized.
• The area of the resulting block is minimized or
  given a fixed die
• Other consideration timing, routability, clock,
  buffering and interaction with physical synthesis

3
Placement can Make A Difference

• MCNC Benchmark circuit e64 (contains 230 4-LUT).
  Placed to a FPGA.

Random Initial Placement
Final Placement
After Detailed Routing
4
Importance of Placement

• Placement is a fundamental problem for physical
  design
• Glue of the physical synthesis
• Becomes very active again in recent years
• 9 new academic placers for WL min. since 2000
• Many other publications to handle timing,
  routability, etc.
• Reasons
• Serious interconnect issues (delay, routability,
  noise) in deep-submicron design
• Placement determines interconnect to the first
  order
• Need placement information even in early design
  stages (e.g., logic synthesis)
• Need to have a good placement solution
• Placement problem becomes significantly larger
• Cong et al. ASPDAC-03, ISPD-03, ICCAD-03 point
  out that existing placers are far from optimal,
  not scalable, and not stable

5
Placement Topic in Context

• Note that this course is on selected research
  topics, so the way we cover placement is at
  pretty high level, with some technical details
• More fundamentals about placement will be covered
  in details, at a core physical design course as
  CS258F
• Or a new core physical design course may be
  offered next year as EE298 (depending on faculty
  recruiting)

6
Benchmarking for Large-Scale Placement and Beyond
ISPD-2003

• S. N. Adya, M. C. Yildiz, I. L. Markov,
• P. G. Villarrubia, P. N. Parakh, P. H. Madden

7
Design Types

• ASICs
• Lots of fixed I/Os, few macros, millions of
  standard cells
• Placement densities 40-80 (IBM)
• Flat and hierarchical designs
• SoCs
• Many more macro blocks, cores
• Datapaths control logic
• Can have very low placement densities lt 20
• Micro-Processor (?P) Random Logic Macros(RLM)
• Hierarchical partitions are placement instances
  (5-30K)
• High placement densities 80-98 (low
  whitespace)
• Many fixed I/Os, relatively few standard cells
• Recall Partitioning w Terminals DAC99, ISPD
  99, ASPDAC00

8
Requirements for Placers

• Must handle 4-10M cells, 1000s macros
• 64 bits near-linear asymptotic complexity
• Scalable/compact design database (OpenAccess)
• Accept fixed ports/pads/pins fixed cells
• Place macros, esp. with var. aspect ratios
• Non-trivial heights and widths(e.g.,
  height2rows)
• Honor targets and limits for net length
• Respect floorplan constraints
• Handle a wide range of placement densities(from
  lt25 to 100 occupied), ICCAD 02

9

• Placement Footprints

Standard Cell
Data Path
IP - Floorplanning
10
Placement Footprints
Reserved areas
Mixed Data Path sea of gates
11
Placement Footprints
Perimeter IO
Area IO
12
Unconstrained Placement
13
Floor planned Placement
14
VLSI Global Placement Examples
bad placement
good placement
15
Major Placement Techniques

• Simulated Annealing
• Timberwolf package JSSC-85, DAC-86
• Dragon ICCAD-00
• Partitioning-Based Placement
• Capo DAC-00
• Fengshui DAC-2001
• Analytical Placement
• Gordian TCAD-91
• Kraftwerk DAC-98
• FastPlace ISPD-04
• Halls Quadratic Placement
• Genetic Algorithm

16
Outline

• Wire length driven placement
• Main methods
• Simulated Annealing
• Gate-Array Timberwolf package
• Standard-Cell Timberwolf package, Dragon
• Partition-based methods
• Analytical methods
• Timing and congestion consideration
• Newer trends

17
Simulated Annealing Based Placement
( I ) The Timberwolf Placement and Routing
Package, Sechen, Sangiovanni IEEE Journal of
Solid-State Circuits, vol SC-20, No. 2(1985)
510-522 Timber wolf 3.2 A New Standard Cell
Placement and Global Routing Package Sechen,
Sangiovanni, 23rd DAC, 1986, 432-439

• Timber wolf
• Stage 1
• Modules are moved between different rows as well
  as within the same row
• modules overlaps are allowed
• when the temperature is reduced below a certain
  value, stage 2 begins
• Stage 2
• Remove overlaps
• Annealing process continues, but only
  interchanges adjacent modules within the same row

18
Solution Space
All possible arrangements of modules into rows
possibly with overlaps
19
Neighboring Solutions
Three types of moves
M1 Displace a module to a new location
M2 Interchange two
modules
M3 Change the orientation of a module
Axis of reflections
1 2
2 1
1 2
3 4
3 4
3 4
20
Move Selection

• Timber wolf first try to select a move betwee M1
  and M2
• Prob(M1)4/5
• Prob(M2)1/5
• If a move of type M1 is chosen ( for certain
  module) and it is rejected, then a move of type
  M3 (for the same module) will be chosen with
  probability 1/10
• Restriction on
• How far a module can be displaced
• What pairs of modules can be interchanged

M1 Displacement M2 Interchange M3 Reflection
21
Move Restriction

• Range Limiter
• At the beginning, R is very large, big enough to
  contain the whole chip
• Window size shrinks slowly as the temperature
  decreases. In fact, height and width of R ?
  log(T)
• Stage 2 begins when window size are so small that
  no inter-row modules interchanges are possible

Rectangular window R
22
Cost Function
net i
Y C1C2C3
hi
å
b
w
a

)
(


h
C
wi
1
i
i
i
i
i
ai, bi are horizontal and vertical weights,
respectively ai 1, bi 1 ?1/2 perimeter of
bounding box

• Critical nets Increase both ai and bi
• Double metal technology Over-the-cell routing is
  possible. Fewer feed through cells are needed
• ?vertical wirings are cheaper than horizontal
  wirings . use smaller vertical weights i.e. bilt
  ai

23
Cost Function (Contd)
C2 Penalty function for module overlaps
O(i,j) amount of overlaps in the X-dimension
between modules i and j a
offset parameter to ensure C2 ? 0 when T ? 0
(
)
å
2


a
j
i
O
C
)
,
(
2
¹
j
i
C3 Penalty function that controls the row
lengths Desired row length d( r ) l(
r ) sum of the widths of the modules in row r
å
-

b
r
d
r
l
C
)
(
)
(
3
r
24
Annealing Schedule

• Tk r(k)T k-1 k 1, 2, 3, .
• r(k) increase from 0.8 to max value 0.94 and then
  decrease to 0.1
• At each temperature, a total number of Kn
  attempts is made
• n number of modules
• K user specified constant

25
Dragon2000 Standard-Cell Placement Tool for
Large Industry Circuits

• M. Wang, X. Yang, and M. Sarrafzadeh,
• ICCAD-2000
• pages 260-263

26
Main Idea

• Simulated annealing based
• 1.9x faster than iTools 1.4.0 (commerical version
  of TimberWolf)
• Comparable wirelength to iTools (i.e., very good)
• Performs better for larger circuits
• Still very slow compared with than other
  approaches
• Also shown to have good routability
• Top-down hierarchical approach
• hMetis to recursively quadrisect into 4h bins at
  level h
• Swapping of bins at each level by SA to minimize
  WL
• Terminates when each bin contains lt 7 cells
• Then swap single cells locally to further
  minimize WL
• Detailed placement is done by greedy algorithm

27
Outline

• Wire length driven placement
• Main methods
• Simulated Annealing
• Gate-Array Timberwolf package
• Standard-Cell Timberwolf package, Grover, Dragon
• Partition-based methods
• Analytical methods
• Timing and congestion consideration
• Newer trends

28
Partition based methods

• Partitioning methods
• FM
• Multilevel techniques, e.g., hMetis
• Two academic open source placement tools
• Capo (UCLA/UCSD/Michigan) multilevel FM
• Feng-shui (SUNY Binghamton) use hMetis
• Pros and cons
• Fast
• Not stable

29
Partitioning-based Approach

• Try to group closely connected modules together.
• Repeatly divide a circuit into subcircuits such
  that the cut value is minimized.
• Also, the placement region is partitioned (by
  cutlines) accordingly.
• Each subcircuit is assigned to one partition of
  the placement region.
• Note Also called min-cut placement approach.

30
An Example
Cutline
Circuit
Placement
31
Variations

• There are many variations in the
  partitioning-based approach. They are different
  in
• The objective function used.
• The partitioning algorithm used.
• The selection of cutlines.

32

• Partitioning

Objective
Given a set of interconnected blocks, produce two
sets that are of equal size, and such that the
number of nets connecting the two sets is
minimized.
33

• FM Partitioning

Initial Random Placement
list_of_sets entire_chip while(any_set_has_2_or
_more_objects(list_of_sets)) for_each_set_in(lis
t_of_sets) partition_it() / each time
through this loop the number of / / sets in
the list doubles.
/
After Cut 1
After Cut 2
34

• FM Partitioning

Moves are made based on object gain.
Object Gain The amount of change in cut
crossings that will occur
if an object is moved from
its current partition into the other partition
-1
2
0
- each object is assigned a gain - objects are
put into a sorted gain list - the object with
the highest gain from the smaller of the two
sides is selected and moved. - the moved object
is "locked" - gains of "touched" objects are
recomputed - gain lists are resorted
0
-1
0
-2
0
0
-2
-1
1
-1
1
35
FM Partitioning
-1
2
0
0
-1
0
-2
0
0
-2
-1
1
-1
1
36
-1
-2
-2
0
-1
-2
-2
0
0
-2
-1
1
-1
1
37
-1
-2
-2
0
-1
-2
-2
0
0
-2
-1
1
1
-1
38
-1
-2
-2
0
-1
-2
-2
0
0
-2
-1
1
1
-1
39
-1
-2
-2
0
-1
-2
-2
0
-2
-2
1
-1
-1
-1
40
-1
-2
-2
-1
-2
0
-2
0
-2
-2
1
-1
-1
-1
41
-1
-2
-2
-1
-2
-2
0
0
-2
-2
1
-1
-1
-1
42
-1
-2
-2
1
-2
-2
0
-2
-2
-2
1
-1
-1
-1
43
-1
-2
-2
1
-2
-2
0
-2
-2
-2
1
-1
-1
-1
44
-1
-2
-2
1
-2
-2
0
-2
-2
1
-2
-1
-1
-1
45
-1
-2
-2
1
-2
-2
0
-1
-2
-2
-2
-3
-1
-1
46
-1
-2
-2
1
-2
-2
0
-1
-2
-2
-2
-3
-1
-1
47
-1
-2
-2
1
-2
-2
0
-1
-2
-2
-2
-3
-1
-1
48
-1
-2
-2
-1
-2
-2
-2
-1
-2
-2
-2
-3
-1
-1
49
Breuers Cutline Selection Schemes

• M.A. Breuer, Min-Cut Placement, J.
  Design Automation and Fault-Tolerant Computing
  1(4)343-382, Oct. 1977.
• M.A. Breuer, A Class of Min-Cut Placement
  Algorithms, DAC 1977,
• pages 284-290.

50
of Nets Across a Cutline

• For any cutline c, let v(c) be the total number
  of nets cut by c.
• v(c) gives a lower bound on the number of tracks
  along cutline c.
• Useful in standard-cell or gate-array layout.

Cutline c
v(c) 2
51
Three Objective Functions

• Total Net-Cut Min. Sall cutline c v(c)
• Equivalent to min. total half-perimeter wire
  length.
• Min. Max Cut Value Min. Max.all cutline c v(c)
• Minimizing channel widths of standard-cell or
  gate-array placement.
• Sequential Cutline Consider cutlines
  sequentially, minimize cut value with respect to
  constraints imposed by previous cuts.

52
Two Cutline Styles

• Cut Oriented Min-Cut Placement
• Use the same cutlines for all sub-regions.
• Realize the sequential objective function.
• Block Oriented Min-Cut Placement
• Different sub-regions have seperate cutlines.
• More flexible.

1
2
2a
1
2b
53
3 Cutline Selection Schemes

• Suppose we want to partition as follows
• Question Which cutline to use first?
• 3 Cutline Selection Schemes
• Quadratic Placement Procedure.
• Bisection Placement Procedure.
• Slice/Bisection.

54
Quadrature Placement Procedure
3a
1
3b
4a
2
4b

• Very suitable for circuits with high routing
  density in the centre.

55
Bisection Placement Procedure
3a
2a
3b
1
3c
2b
3d
5a
4
5b
6a
6b
6c
6d

• Good for standard-cell placement.

56
Slice/Bisection Procedure
1
2
3
4
5
6
7
9a
8
9b
10a
10b
10c
10d

• Most suitable when there is a high interconnect
  density at the periphery.

57
Terminal Propagation Algorithm by Dunlop and
Kernighan

• A Procedure for Placement of
• Standard-Cell VLSI Circuits,
• TCAD, 4(1)92-98, Jan. 1985.

58
Problem of Partitioning Subcircuits
A
B
B
B
A
A
Cost of these 2 partitionings are not the same.
59
Terminal Propagation

• Need to consider nets connecting to external
  terminals or other modules as well.
• Do partitioning in a breath-first manner (i.e.,
  finish all higher-level partitioning first).

The Dummy Terminal will try to pull B to the top
partition.
Dummy Terminal
A
A
B
A
B
B
60
Dunlop and Kernighans Algorithm

• Block-Oriented Quadrature Placement.
• Partition until each region contains 6 cells.
• Need to assign cells to rows after partitioning.

Row 1
1
1
1,2
1,2
Row 2
2
2
2
2
Row 3
3,4
3,4
3
3
Row 4
4
4
4,3
4,3
61
Can Recursive Bisection Alone Produce Routable
Placement?(Name of placer Capo)

• Andrew Caldwell, Andrew Kahng, and Igor Markov
• DAC-2000

62
Capo Overview

• Standard cell placement, Fixed-die context
• Pure recursive bisectioning placer
• Several minor techniques to produce good
  bisections
• Produce good results mainly because
• Improvement in mincut bisection using multi-level
  idea in the past few years
• Pay attention to details in implementation
• Implementation with good interface (LEF/DEF and
  GSRC bookshelf) available on web

63
Capo Approach

• Recursive bisection framework
• Multi-level FM for instances with gt200 cells
• Flat FM for instances with 35-200 cells
• Branch-and-bound for instances with lt35 cells
• Careful handling partitioning tolerance
• Uncorking Prevent large cells from blocking
  smaller cells to move
• Repartitioning Several FM calls with decreasing
  tolerance
• Block splitting heuristics Higher tolerance for
  vertical cut
• Hierarchical tolerance computation Instance with
  more whitespace can have a bigger partitioning
  tolerance

64

• Partitioning

Pros - very fast - great quality - scales nearly
linearly with problem size Cons - non-trivial
to implement - very directed algorithm, but this
limits the ability to deal with miscellaneous
constraints
65
Summary for Partition Based Placement

• Improvement in mincut partitioning are conducive
  to better wirelength and congestion
• Routable placements can be produced in most cases
  without explicit congestion management
• Explicit congestion control may still be useful
  in some cases
• Better weighted wirelength often implies better
  routed wirelength, but not always