Parallel Architectures

1
Chapter 2

• Parallel Architectures

2
Outline

• Some chapter references
• Brief review of complexity
• Terminology for comparisons
• Interconnection networks
• Processor arrays
• Multiprocessors
• Multicomputers
• Flynns Taxonomy moved to Chpt 1

3
Some Chapter References

• Selim Akl, The Design and Analysis of Parallel
  Algorithms, Prentice Hall, 1989 (earlier
  textbook).
• G. C. Fox, What Have We Learnt from Using Real
  Parallel Machines to Solve Real Problems?
  Technical Report C3P-522, Cal Tech, December
  1989. (Included in part in more recent books
  co-authored by Fox.)
• A. Grama, A. Gupta, G. Karypis, V. Kumar,
  Introduction to Parallel Computing, Second
  Edition, 2003 (first edition 1994), Addison
  Wesley.
• Harry Jordan, Gita Alaghband, Fundamentals of
  Parallel Processing Algorithms, Architectures,
  Languages, Prentice Hall, 2003, Ch 1, 3-5.
• F. Thomson Leighton Introduction to Parallel
  Algorithms and Architectures Arrays, Trees,
  Hypercubes 1992 Morgan Kaufmann Publishers.

4
References - continued

• Gregory Pfsiter, In Search of Clusters The
  ongoing Battle in Lowly Parallelism, 2nd Edition,
  Ch 2. (Discusses details of some serious problems
  that MIMDs incur).
• Michael Quinn, Parallel Programming in C with MPI
  and OpenMP, McGraw Hill,2004 (Current Textbook),
  Chapter 2.
• Michael Quinn, Parallel Computing Theory and
  Practice, McGraw Hill, 1994, Ch. 1,2
• Sayed H. Roosta, Parallel Processing Parallel
  Algorithms Theory and Computation, Springer
  Verlag, 2000, Chpt 1.
• Wilkinson Allen, Parallel Programming
  Techniques and Applications, Prentice Hall, 2nd
  Edition, 2005, Ch 1-2.

5
Brief Review Complexity Concepts Needed for
Comparisons

• Whenever we define a counting function, we
  usually characterize the growth rate of that
  function in terms of complexity classes.
• Technical Definition We say a function f(n) is
  in O(g(n)), if (and only if) there are positive
  constants c and n0 such that
• 0 f(n) ? cg(n) for n ? n0
• O(n) is read as big-oh of n.
• This notation can be used to separate counting
  functions into complexity classes that
  characterize the size of the count.
• We can use it for any kind of counting functions
  such as timings, bisection widths, etc.

6
Big-Oh and Asymptotic Growth Rate

• The big-Oh notation gives an upper bound on the
  (asymptotic) growth rate of a function
• The statement f(n) is O(g(n)) means that the
  growth rate of f(n) is not greater than the
  growth rate of g(n)
• We can use the big-Oh notation to rank functions
  according to their growth rate

Assume f(n) is O(g(n)) g(n) is O(f(n))
g(n) grows faster Yes No
f(n) grows faster No Yes
Same growth Yes Yes
7
Relatives of Big-Oh

• big-Omega
• f(n) is ?(g(n)) if there is a constant c gt 0
• and an integer constant n0 ? 1 such that
• f(n) ? cg(n) for n ? n0
• Intuitively, this says up to a constant factor,
  f(n) asymptotically is greater than or equal to
  g(n)
• big-Theta
• f(n) is ?(g(n)) if there are constants c gt 0 and
  c gt 0 and an integer constant n0 ? 1 such that
  0 cg(n) ? f(n) ? cg(n) for n ? n0
• Intuitively, this says up to a constant factor,
  f(n) and g(n) are asymptotically the same.
• Note These concepts are covered in algorithm
  courses

8
Relatives of Big-Oh

• little-oh
• f(n) is o(g(n)) if, for any constant c gt 0, there
  is an integer constant n0 ? 0 such that 0 ? f(n)
  lt cg(n) for n ? n0
• Intuitively, this says f(n) is, up to a constant,
  asymptotically strictly less than g(n), so f(n) ?
  ?(g(n)).
• little-omega
• f(n) is ?(g(n)) if, for any constant c gt 0, there
  is an integer constant n0 ? 0 such that f(n) gt
  cg(n) 0 for n ? n0
• Intuitively, this says f(n) is, up to a constant,
  asymptotically strictly greater than g(n), so
  f(n) ? ?(g(n)).
• These are not used as much as the earlier
  definitions, but they round out the picture.

9
Summary for Intuition for Asymptotic Notation

• big-Oh
• f(n) is O(g(n)) if f(n) is asymptotically less
  than or equal to g(n)
• big-Omega
• f(n) is ?(g(n)) if f(n) is asymptotically greater
  than or equal to g(n)
• big-Theta
• f(n) is ?(g(n)) if f(n) is asymptotically equal
  to g(n)
• little-oh
• f(n) is o(g(n)) if f(n) is asymptotically
  strictly less than g(n)
• little-omega
• f(n) is ?(g(n)) if is asymptotically strictly
  greater than g(n)

10
A CALCULUS DEFINITION OF O, ?(often easier to
use)
Definition Let f and g be functions defined on
the positive integers with nonnegative values. We
say g is in O(f) if and only if lim
g(n)/f(n) c n -gt ? for some nonnegative real
number c--- i.e. the limit exists and is not
infinite. Definition We say f is in ?(g) if and
only if f is in O(g) and g is in O(f) Note
Often use L'Hopital's Rule to calculate the
limits you need.
11
Why Asymptotic Behavior is Important

• 1) Allows us to compare counts on large sets.
• 2) Helps us understand the maximum size of input
  that can be handled in a given time, provided we
  know the environment in which we are running.
• 3) Stresses the fact that even dramatic speedups
  in hardware can not overcome the handicap of an
  asymptotically slow algorithm.

12
Recall ORDER WINS OUT(Example from Baases
Algorithms Text)
The TRS-80 Main language support BASIC -
typically a slow running interpreted language For
more details on TRS-80 see http//mate.kjsl.com/t
rs80/
The CRAY-YMP Language used in example FORTRAN- a
fast running language For more details on
CRAY-YMP see
http//ds.dial.pipex.com/town/park/abm64/CrayWWWSt
uff/Cfaqp1.htmlTOC3
13
CRAY YMP TRS-80with FORTRAN
with BASICcomplexity is 3n3
complexity is 19,500,000n
microsecond (abbr µsec) One-millionth of a
second. millisecond (abbr msec) One-thousandth of
a second.
n is 10 100 1000 2500 10000 1000000
3 microsec
200 millisec
2 sec
3 millisec
20 sec
3 sec
50 sec
50 sec
49 min
3.2 min
95 years
5.4 hours
14
Interconnection Networks

• Uses of interconnection networks
• Connect processors to shared memory
• Connect processors to each other
• Interconnection media types
• Shared medium
• Switched medium
• Different interconnection networks define
  different parallel machines.
• The interconnection networks properties
  influence the type of algorithm used for various
  machines as it affects how data is routed.

15
Shared versus Switched Media

1. With shared medium, one message is sent all
   processors listen
2. With switched medium, multiple messages are
   possible.

16
Shared Medium

• Allows only message at a time
• Messages are broadcast
• Each processor listens to every message
• Before sending a message, a processor listen
  until medium is unused
• Collisions require resending of messages
• Ethernet is an example

17
Switched Medium

• Supports point-to-point messages between pairs of
  processors
• Each processor is connected to one switch
• Advantages over shared media
• Allows multiple messages to be sent
  simultaneously
• Allows scaling of the network to accommodate the
  increase in processors

18
Switch Network Topologies

• View switched network as a graph
• Vertices processors or switches
• Edges communication paths
• Two kinds of topologies
• Direct
• Indirect

19
Direct Topology

• Ratio of switch nodes to processor nodes is 11
• Every switch node is connected to
• 1 processor node
• At least 1 other switch node

Indirect Topology

• Ratio of switch nodes to processor nodes is
  greater than 11
• Some switches simply connect to other switches

20
Terminology for Evaluating Switch Topologies

• We need to evaluate 4 characteristics of a
  network in order to help us understand their
  effectiveness in implementing efficient parallel
  algorithms on a machine with a given network.
• These are
• The diameter
• The bisection width
• The edges per node
• The constant edge length
• Well define these and see how they affect
  algorithm choice.
• Then we will investigate several different
  topologies and see how these characteristics are
  evaluated.

21
Terminology for Evaluating Switch Topologies

• Diameter Largest distance between two switch
  nodes.
• A low diameter is desirable
• It puts a lower bound on the complexity of
  parallel algorithms which requires communication
  between arbitrary pairs of nodes.

22
Terminology for Evaluating Switch Topologies

• Bisection width The minimum number of edges
  between switch nodes that must be removed in
  order to divide the network into two halves
  (within 1 node, if the number of processors is
  odd.)
• High bisection width is desirable.
• In algorithms requiring large amounts of data
  movement, the size of the data set divided by the
  bisection width puts a lower bound on the
  complexity of an algorithm,
• Actually proving what the bisection width of a
  network is can be quite difficult.

23
Terminology for Evaluating Switch Topologies

• Number of edges per node
• It is best if the maximum number of edges/node is
  a constant independent of network size, as this
  allows the processor organization to scale more
  easily to a larger number of nodes.
• Degree is the maximum number of edges per node.
• Constant edge length? (yes/no)
• Again, for scalability, it is best if the nodes
  and edges can be laid out in 3D space so that the
  maximum edge length is a constant independent of
  network size.

24
Evaluating Switch Topologies

• Many have been proposed and analyzed. We will
  consider several well known ones
• 2-D mesh
• linear network
• binary tree
• hypertree
• butterfly
• hypercube
• shuffle-exchange
• Those in yellow have been used in commercial
  parallel computers.

25
2-D Meshes
Note Circles represent switches and squares
represent processors in all these slides.
26
2-D Mesh Network

• Direct topology
• Switches arranged into a 2-D lattice or grid
• Communication allowed only between neighboring
  switches
• Torus Variant that includes wraparound
  connections between switches on edge of mesh

27
Evaluating 2-D Meshes(Assumes mesh is a square)

• n number of processors
• Diameter
• ?(n1/2)
• Places a lower bound on algorithms that require
  processing with arbitrary nodes sharing data.
• Bisection width
• ?(n1/2)
• Places a lower bound on algorithms that require
  distribution of data to all nodes.
• Max number of edges per switch
• 4 is the degree
• Constant edge length?
• Yes
• Does this scale well?
• Yes

28
Linear Network

• Switches arranged into a 1-D mesh
• Direct topology
• Corresponds to a row or column of a 2-D mesh
• Ring A variant that allows a wraparound
  connection between switches on the end.
• The linear and ring networks have many
  applications
• Essentially supports a pipeline in both
  directions
• Although these networks are very simple, they
  support many optimal algorithms.

29
Evaluating Linear and Ring Networks

• Diameter
• Linear n-1 or T(n)
• Ring ?n/2? or T(n)
• Bisection width
• Linear 1 or T(1)
• Ring 2 or T(1)
• Degree for switches
• 2
• Constant edge length?
• Yes
• Does this scale well?
• Yes

30
Binary Tree Network

• Indirect topology
• n 2d processor nodes, 2n-1 switches, where d
  0,1,... is the number of levels

i.e. 23 8 processors on bottom and 2(n) 1
2(8) 1 15 switches
31
Evaluating Binary Tree Network

• Diameter
• 2 log n or O(log n).
• Note- this is small
• Bisection width
• 1, the lowest possible number
• Degree
• 3
• Constant edge length?
• No
• Does this scale well?
• No

32
Hypertree Network (of degree 4 and depth 2)

• Front view 4-ary tree of height 2
• (b) Side view upside down binary tree of height
  d
• (c) Complete network

33
Hypertree Network

• Indirect topology
• Note- the degree k and the depth d must be
  specified.
• This gives from the front a k-ary tree of height
  d.
• From the side, the same network looks like an
  upside down binary tree of height d.
• Joining the front and side views yields the
  complete network.

34
Evaluating 4-ary Hypertree with Depth d

• A 4-ary hypertree has n 4d processors
• General formula for k-ary hypertree is n kd
• Diameter is 2d 2 log n
• shares the low diameter of binary tree
• Bisection width 2d1
• Note here, 2d1 23 8
• Large value - much better than binary tree
• Constant edge length?
• No
• Degree 6

35
Butterfly Network
A 23 8 processor butterfly network with 8432
switching nodes

• Indirect topology
• n 2d processornodes connectedby n(log n
  1)switching nodes

As complicated as this switching network appears
to be, it is really quite simple as it admits a
very nice routing algorithm! Wrapped Butterfly
When top and bottom ranks are merged into single
rank.
The rows are called ranks.
36
Building the 23 Butterfly Network

• There are 8 processors.
• Have 4 ranks (i.e. rows) with 8 switches per
  rank.
• Connections
• Node(i,j), for i gt 0, is connected to two nodes
  on rank i-1, namely node(i-1,j) and node(i-1,m),
  where m is the integer found by flipping the ith
  most significant bit in the binary d-bit
  representation of j.
• For example, suppose i 2 and j 3. Then node
  (2,3) is connected to node (1,3).
• To get the other connection, 3 0112. So, flip
  2nd significant bit i.e. 0012 and connect
  node(2,3) to node(1,1) --- NOTE There is an
  error on pg 32 on this example.
• Nodes connected by a cross edge from rank i to
  rank i1 have node numbers that differ only in
  their (i1) bit.

37
Why It Is Called a Butterfly Network

• Walk cycles such as node(i,j), node(i-1,j),
  node(i,m), node(i-1,m), node(i,j) where m is
  determined by the bit flipping as shown and you
  see a butterfly

38
Butterfly Network Routing
Send message from processor 2 to processor
5. Algorithm 0 means ship left 1 means ship
right. 1) 5 101. Pluck off leftmost bit 1
and send 01msg to right. 2) Pluck off leftmost
bit 0 and send 1msg to left. 3) Pluck off
leftmost bit 1 and send msg to right. Each
cross edge followed changes address by 1 bit.
39
Evaluating the Butterfly Networkwith n Processors

• Diameter
• log n
• Bisection width
• n / 2 (Likely error 32/216)
• Degree
• 4 (even for d gt 3)
• Constant edge length?
• No, grows exponentially
• as rank size decrease

On pg 442, Leighton gives ?(n / log(n)) as
the bisection width. Simply remove cross edges
between two successive levels to create bisection
cut.
40
Hypercube (also called binary n-cube)
A hypercube with n 2d processors switches
for d4
41
Hypercube (or Binary n-cube) n 2d Processors

• Direct topology
• 2 x 2 x x 2 mesh
• Number of nodes is a power of 2
• Node addresses 0, 1, , n-1
• Node i is connected to k nodes whose addresses
  differ from i in exactly one bit position.
• Example k 0111 is connected to 1111, 0011,
  0101, and 0110

42
Growing a HypercubeNote For d 4, it is called
a 4-dimensional cube.
43
Evaluating Hypercube Networkwith n 2d nodes

• Diameter
• d log n
• Bisection width
• n / 2
• Edges per node
• log n
• Constant edge length?
• No.
• The length of the longest edge increases as n
  increases.

44
Routing on the Hypercube Network

• Example Send a message from node 2 0010 to
  node 5 0101
• The nodes differ in 3 bits so the shortest path
  will be of length 3.
• One path is
• 0010 ? 0110 ?
• 0100 ? 0101
• obtained by flipping one of the differing bits at
  each step.
• Similar to butterfly

• As with the butterfly network, bit flipping
  helps you route on this network.

45
A Perfect Shuffle

• A permutation that is produced as follows is
  called a perfect shuffle
• Given a power of 2 cards, numbered 0, 1, 2, ...,
  2d -1, write the card number with d bits. By left
  rotating the bits with a wrap, we calculate the
  position of the card after the perfect shuffle.
• Example For d 3, card 5 101. Left rotating
  and wrapping gives us 011. So, card 5 goes to
  position 3. Note that card 0 000 and card 7
  111, stay in position.

46
Shuffle-exchange Network with n 2d Processors
0
1
2
3
4
5
6
7

• Direct topology
• Number of nodes is a power of 2
• Nodes have addresses 0, 1, , 2d-1
• Two outgoing links from node i
• Shuffle link to node LeftCycle(i)
• Exchange link between node i and node i1
  
• when i is even

47
Shuffle-exchange Addressing 16 processors
No arrows on line segment means it is
bidirectional. Otherwise, you must follow the
arrows. Devising a routing algorithm for this
network is interesting and will be a homework
problem.
48
Evaluating the Shuffle-exchange

• Diameter
• 2log n 1
• Edges per node
• 3
• Constant edge length?
• No
• Bisection width
• ?(n/ log n)
• Between 2n/log n and n/(2 log n)
• See Leighton pg 480

49
Two Problems with Shuffle-Exchange

• Shuffle-Exchange does not expand well
• A large shuffle-exchange network does not
  decompose well into smaller separate shuffle
  exchange networks.
• In a large shuffle-exchange network, a small
  percentage of nodes will be hot spots
• They will encounter much heavier traffic
• Above results are in dissertation of one of
  Batchers students.

50
Comparing Networks(See Table 2.1)

• All have logarithmic diameterexcept 2-D mesh
• Hypertree, butterfly, and hypercube have
  bisection width n / 2 (? Likely true only for
  n-cube)
• All have constant edges per node except hypercube
• Only 2-D mesh, linear, and ring topologies keep
  edge lengths constant as network size increases
• Shuffle-exchange is a good compromise- fixed
  number of edges per node, low diameter, good
  bisection width.
• However, negative results on preceding slide also
  need to be considered.

51
Alternate Names for SIMDs

• Recall that all active processors of a true SIMD
  computer must simultaneously access the same
  memory location.
• The value in the i-th processor can be viewed as
  the i-th component of a vector.
• SIMD machines are sometimes called vector
  computers Jordan,et.al. or processor arrays
  Quinn 94,04 based on their ability to execute
  vector and matrix operations efficiently.

52
SIMD Computers

• SIMD computers that focus on vector operations
• Support some vector and possibly matrix
  operations in hardware
• Usually limit or provide less support for
  non-vector type operations involving data in the
  vector components.
• General purpose SIMD computers
• Usually also provide some vector and possibly
  matrix operations in hardware.
• Support more traditional type operations (e.g.,
  other than for vector/matrix data types).

53
Pipelined Architectures

• Pipelined architectures are sometimes considered
  to be SIMD architectures
• See pg 37 of Textbook pg 8-9 Jordan et. al.
• Vector components are entered successively into
  first processor in pipeline.
• The i-th processor of the pipeline receives the
  output from the (i-1)th processor.
• Normal operations in each processor are much
  larger (coarser) in pipelined computers than in
  true SIMDs
• Pipelined is somewhat SIMD in nature in that
  synchronization is not required.

54
Why Processor Arrays?

• Historically, high cost of control units
• Scientific applications have data parallelism

55
Data/instruction Storage

• Front end computer
• Also called the control unit
• Holds and runs program
• Data manipulated sequentially
• Processor array
• Data manipulated in parallel

56
Processor Array Performance

• Performance work done per time unit
• Performance of processor array
• Speed of processing elements
• Utilization of processing elements

57
Performance Example 1

• 1024 processors
• Each adds a pair of integers in 1 ?sec (1
  microsecond or one millionth of second or 10-6
  second.)
• What is the performance when adding two
  1024-element vectors (one per processor)?

58
Performance Example 2

• 512 processors
• Each adds two integers in 1 ?sec
• What is the performance when adding two vectors
  of length 600?
• Since 600 gt 512, 88 processor must add two pairs
  of integers.
• The other 424 processors add only a single pair
  of integers.

59
Example of a 2-D Processor Interconnection
Network in a Processor Array
Each VLSI chip has 16 processing elements. Each
PE can simultaneously send a value to a neighbor.
PE processor element
60
SIMD Execution Style

• The traditional (SIMD, vector, processor array)
  execution style (Quinn 94, pg 62, Quinn 2004,
  pgs 37-43
• The sequential processor that broadcasts the
  commands to the rest of the processors is called
  the front end or control unit (or sometimes
  host).
• The front end is a general purpose CPU that
  stores the program and the data that is not
  manipulated in parallel.
• The front end normally executes the sequential
  portions of the program.
• Each processing element has a local memory that
  can not be directly accessed by the control unit
  or other processing elements.

61
SIMD Execution Style

• Collectively, the individual memories of the
  processing elements (PEs) store the (vector) data
  that is processed in parallel.
• When the front end encounters an instruction
  whose operand is a vector, it issues a command to
  the PEs to perform the instruction in parallel.
• Although the PEs execute in parallel, some units
  can be allowed to skip any particular
  instruction.

62
Masking on Processor Arrays

• All the processors work in lockstep except those
  that are masked out (by setting mask register).
• The conditional if-then-else is different for
  processor arrays than sequential version
• Every active processor tests to see if its data
  meets the negation of the boolean condition.
• If it does, it sets its mask bit so those
  processors will not participate in the operation
  initially.
• Next the unmasked processors, execute the THEN
  part.
• Afterwards, mask bits (for original set of active
  processors) are flipped and unmasked processors
  perform the the ELSE part.

63
if (COND) then A else B
64
if (COND) then A else B
65
if (COND) then A else B
66
SIMD Machines

• An early SIMD computer designed for vector and
  matrix processing was the Illiac IV computer
• Initial development at the University of Illinois
  1965-70
• Moved to NASA Ames, completed in 1972 but not
  fully functional until 1976.
• See Jordan et. al., pg 7 and Wikepedia
• The MPP, DAP, the Connection Machines CM-1 and
  CM-2, MasPar MP-1 and MP-2 are examples of SIMD
  computers
• See Akl pg 8-12 and Quinn, 94
• The CRAY-1 and the Cyber-205 use pipelined
  arithmetic units to support vector operations and
  are sometimes called a pipelined SIMD
• See Jordan, et al, p7, Quinn 94, pg 61-2, and
  Quinn 2004, pg37).

67
SIMD Machines

• Quinn 1994, pg 63-67 discusses the CM-2
  Connection Machine (with 64K PEs) and a smaller
  updated CM-200.
• Professor Batcher was the chief architect for the
  STARAN and the MPP (Massively Parallel Processor)
  and an advisor for the ASPRO
• ASPRO is a small second generation STARAN used by
  the Navy in the spy planes.
• Professor Batcher is best known architecturally
  for the MPP, which is at the Smithsonian
  Institute currently displayed at a D.C. airport.

68
Todays SIMDs

• Many SIMDs are being embedded in sequential
  machines.
• Others are being build as part of hybrid
  architectures.
• Others are being build as special purpose
  machines, although some of them could classify as
  general purpose.
• Much of the recent work with SIMD architectures
  is proprietary.
• Often the fact that a parallel computer is SIMD
  is not mentioned by company building them.

69
A Company Building Inexpensive SIMD

• ClearSpeed is producing a COTS (commodity off the
  shelf) SIMD Board
• WorldScape is developing defense and commercial
  applications for this computer.
• Not a traditional SIMD as the hardware doesnt
  synchronize every step.
• Hardware design supports efficient
  synchronization
• This machine is programmed like a SIMD.
• The U.S. Navy has observed that their machines
  process radar a magnitude faster than others.
• There is quite a bit of information about this at
  www.wscape.com and www.clearspeed.com

70
An Example of a Hybrid SIMD

• Embedded Massively Parallel Accelerators

• Other accelerators Decypher, Biocellerator,
  GeneMatcher2, Kestrel, SAMBA, P-NAC, Splash-2,
  BioScan
• (This and next three slides are due to Prabhakar
  R. Gudla (U of Maryland) at a CMSC 838T
  Presentation, 4/23/2003.)

71
Hybrid Architecture

• combines SIMD and MIMD paradigm within a parallel
  architecture ? Hybrid Computer

72
Architecture of Systola 1024

• Instruction Systolic Array
• 32 ? 32 mesh of processing elements
• wavefront instruction execution

73
SIMDs Embedded in SISDs

• Intel's Pentium 4 included what they call MMX
  technology to gain a significant performance
  boost
• IBM and Motorola incorporated the technology into
  their G4 PowerPC chip in what they call their
  Velocity Engine.
• Both MMX technology and the Velocity Engine are
  the chip manufacturer's name for their
  proprietary SIMD processors and parallel
  extensions to their operating code.
• This same approach is used by NVidia and Evans
  Sutherland to dramatically accelerate graphics
  rendering.

74
Special Purpose SIMDs in the Bioinformatics Arena

• Parcel
• Acquired by Celera Genomics in 2000
• Products include the sequence supercomputer
  GeneMatcher, which has a high throughput sequence
  analysis capability
• Supports over a million processors
• GeneMatcher was used by Celera in their race with
  U.S. government to complete the description of
  the human genome sequencing
• TimeLogic, Inc
• Has DeCypher, a reconfigurable SIMD

75
Advantages of SIMDs

• Reference Roosta, pg 10
• Less hardware than MIMDs as they have only one
  control unit.
• Control units are complex.
• Less memory needed than MIMD
• Only one copy of the instructions need to be
  stored
• Allows more data to be stored in memory.
• Less startup time in communicating between PEs.

76
Advantages of SIMDs (cont)

• Single instruction stream and synchronization of
  PEs make SIMD applications easier to program,
  understand, debug.
• Similar to sequential programming
• Control flow operations and scalar operations can
  be executed on the control unit while PEs are
  executing other instructions.
• MIMD architectures require explicit
  synchronization primitives, which create a
  substantial amount of additional overhead.

77
Advantages of SIMDs (cont)

• During a communication operation between PEs,
• PEs send data to a neighboring PE in parallel and
  in lock step
• No need to create a header with routing
  information as routing is determined by program
  steps.
• the entire communication operation is executed
  synchronously
• SIMDs are deterministic have much more
  predictable running time.
• Can normally compute a tight (worst case) upper
  bound for the time for communications operations.
• Less complex hardware in SIMD since no message
  decoder is needed in the PEs
• MIMDs need a message decoder in each PE.

78
SIMD Shortcomings(with some rebuttals)

• Claims are from our textbook i.e., Quinn 2004.
• Similar statements are found in Grama, et. al.
• Claim 1 Not all problems are data-parallel
• While true, most problems seem to have a data
  parallel solution.
• In Fox, et.al., the observation was made in
  their study of large parallel applications at
  national labs, that most were data parallel by
  nature, but often had points where significant
  branching occurred.

79
SIMD Shortcomings(with some rebuttals)

• Claim 2 Speed drops for conditionally executed
  branches
• MIMDs processors can execute multiple branches
  concurrently.
• For an if-then-else statement with execution
  times for the then and else parts being
  roughly equal, about ½ of the SIMD processors are
  idle during its execution
• With additional branching, the average number of
  inactive processors can become even higher.
• With SIMDs, only one of these branches can be
  executed at a time.
• This reason justifies the study of multiple SIMDs
  (or MSIMDs).

80
SIMD Shortcomings(with some rebuttals)

• Claim 2 (cont) Speed drops for conditionally
  executed code
• In Fox, et.al., the observation was made that
  for the real applications surveyed, the MAXIMUM
  number of active branches at any point in time
  was about 8.
• The cost of the extremely simple processors used
  in a SIMD are extremely low
• Programmers used to worry about full utilization
  of memory but stopped this after memory cost
  became insignificant overall.

81
SIMD Shortcomings(with some rebuttals)

• Claim 3 Dont adapt to multiple users well.
• This is true to some degree for all parallel
  computers.
• If usage of a parallel processor is dedicated to
  a important problem, it is probably best not to
  risk compromising its performance by sharing
• This reason also justifies the study of multiple
  SIMDs (or MSIMD).
• SIMD architecture has not received the attention
  that MIMD has received and can greatly benefit
  from further research.

82
SIMD Shortcomings(with some rebuttals)

• Claim 4 Do not scale down well to starter
  systems that are affordable.
• This point is arguable and its truth is likely
  to vary rapidly over time
• ClearSpeed currently sells a very economical SIMD
  board that plugs into a PC.

83
SIMD Shortcomings(with some rebuttals)

• Claim 5 Requires customized VLSI for processors
  and expense of control units in PCs has dropped.
• Reliance on COTS (Commodity, off-the-shelf parts)
  has dropped the price of MIMDS
• Expense of PCs (with control units) has dropped
  significantly
• However, reliance on COTS has fueled the success
  of low level parallelism provided by clusters
  and restricted new innovative parallel
  architecture research for well over a decade.

84
SIMD Shortcomings(with some rebuttals)

• Claim 5 (cont.)
• There is strong evidence that the period of
  continual dramatic increases in speed of PCs and
  clusters is ending.
• Continued rapid increases in parallel performance
  in the future will be necessary in order to solve
  important problems that are beyond our current
  capabilities
• Additionally, with the appearance of the very
  economical COTS SIMDs, this claim no longer
  appears to be relevant.

85
Multiprocessors

• Multiprocessor multiple-CPU computer with a
  shared memory
• Same address on two different CPUs refers to the
  same memory location
• Avoids three cited criticisms for SIMDs
• Can be built from commodity CPUs
• Naturally support multiple users
• Maintain efficiency in conditional code

86
Centralized Multiprocessor
87
Centralized Multiprocessor

• Straightforward extension of uniprocessor
• Add CPUs to bus
• All processors share same primary memory
• Memory access time same for all CPUs
• Uniform memory access (UMA) multiprocessor
• Also called a symmetrical multiprocessor (SMP)

88
Private and Shared Data

• Private data items used only by a single
  processor
• Shared data values used by multiple processors
• In a centralized multiprocessor (i.e. SMP),
  processors communicate via shared data values

89
Problems Associated with Shared Data

• The cache coherence problem
• Replicating data across multiple caches reduces
  contention among processors for shared data
  values.
• But - how can we ensure different processors have
  the same value for same address?
• The cache coherence problem is when an obsolete
  value is still stored in a processors cache.

90
Write Invalidate Protocol

• Most common solution to cache coherency
• Each CPUs cache controller monitors (snoops) the
  bus identifies which cache blocks are requested
  by other CPUs.
• A PE gains exclusive control of data item before
  performing write.
• Before write occurs, all other copies of data
  item cached by other PEs are invalidated.
• When any other CPU tries to read a memory
  location from an invalidated cache block,
• a cache miss occurs
• It has to retrieve updated data from memory

91
Cache-coherence Problem
Memory
7
X
92
Cache-coherence Problem
Memory
Read from memory is not a problem.
7
X
7
93
Cache-coherence Problem
Memory
7
X
7
7
94
Cache-coherence Problem
Write to main memory is a problem.
Memory
2
X
2
7
95
Write Invalidate Protocol
A cache control monitor snoops the bus to
see which cache block is being requested by
other processors.
7
X
7
7
96
Write Invalidate Protocol
7
X
Intent to write X
7
7
Before a write can occur, all copies of data at
that address are declared invalid.
97
Write Invalidate Protocol
7
X
Intent to write X
7
98
Write Invalidate Protocol
When another processor tries to read from this
location in cache, it receives a cache miss error
and will have to refresh from main memory.
2
X
2
99
Synchronization Required for Shared Data

• Mutual exclusion
• Definition At most one process can be engaged in
  an activity at any time.
• Example Only one processor can write to the
  same address in main memory at the same time.
• We say that process must mutually exclude all
  others while it performs this write.
• Barrier synchronization
• Definition Guarantees that no process will
  proceed beyond a designated point (called the
  barrier) until every process reaches that point.

100
Distributed Multiprocessor

• Distributes primary memory among processors
• Increase aggregate memory bandwidth and lower
  average memory access time
• Allows greater number of processors
• Also called non-uniform memory access (NUMA)
  multiprocessor
• Local memory access time is fast
• Non-local memory access time can vary
• Distributed memories have one logical address
  space

101
Distributed Multiprocessors
102
Cache Coherence

• Some NUMA multiprocessors do not support it in
  hardware
• Only instructions and private data are stored in
  cache
• Policy creates a large memory access time
  variance
• Implementation more difficult
• No shared memory bus to snoop
• Directory-based protocol needed

103
Directory-based Protocol

• Distributed directory contains information about
  cacheable memory blocks
• One directory entry for each cache block
• Each entry has
• Sharing status
• Which processors have copies

104
Sharing Status

• Uncached -- (denoted by U)
• Block not in any processors cache
• Shared (denoted by S)
• Cached by one or more processors
• Read only
• Exclusive (denoted by E)
• Cached by exactly one processor
• Processor has written to block
• Copy in memory is obsolete

105
Directory-based Protocol - step1
106
X has value 7 step 2
Interconnection Network
Bit Vector
X
U 0 0 0
Directories
7
X
Memories
Caches
107
CPU 0 Reads X step 3
Interconnection Network
X
U 0 0 0
Directories
7
X
Memories
Caches
108
CPU 0 Reads X step 4
Interconnection Network
X
S 1 0 0
Directories
7
X
Memories
Caches
109
CPU 0 Reads X step 5
Interconnection Network
X
S 1 0 0
Directories
Memories
Caches
110
CPU 2 Reads X step 6
Interconnection Network
X
S 1 0 0
Directories
Memories
Caches
111
CPU 2 Reads X step 7
Interconnection Network
X
S 1 0 1
Directories
Memories
Caches
112
CPU 2 Reads X step 8
Interconnection Network
X
S 1 0 1
Directories
Memories
Caches
113
CPU 0 Writes 6 to X step 9
Interconnection Network
Write Miss
X
S 1 0 1
Directories
Memories
Caches
114
CPU 0 Writes 6 to X step 10
Interconnection Network
X
S 1 0 1
Directories
Invalidate
Memories
Caches
115
CPU 0 Writes 6 to X step 11
Interconnection Network
X
E 1 0 0
Directories
Memories
Caches
6
X
116
CPU 1 Reads X step 12
Interconnection Network
Read Miss
X
E 1 0 0
Directories
Memories
Caches
117
CPU 1 Reads X step 13
Interconnection Network
Switch to Shared
X
E 1 0 0
Directories
Memories
Caches
118
CPU 1 Reads X step 14
Interconnection Network
X
E 1 0 0
Directories
Memories
Caches
119
CPU 1 Reads X step 15
Interconnection Network
X
S 1 1 0
Directories
Memories
Caches
120
CPU 2 Writes 5 to X step 16
Interconnection Network
X
S 1 1 0
Directories
Memories
Write Miss
Caches
121
CPU 2 Writes 5 to X - step 17
Interconnection Network
Invalidate
X
S 1 1 0
Directories
Memories
Caches
122
CPU 2 Writes 5 to X step 18
Interconnection Network
X
E 0 0 1
Directories
Memories
5
X
Caches
123
CPU 0 Writes 4 to X step 19
Interconnection Network
X
E 0 0 1
Directories
Memories
Caches
124
CPU 0 Writes 4 to X step 20
Interconnection Network
X
E 1 0 0
Directories
Memories
Take Away
Caches
125
CPU 0 Writes 4 to X step 21
Interconnection Network
X
E 0 1 0
Directories
Memories
Caches
126
CPU 0 Writes 4 to X step 22
Interconnection Network
X
E 1 0 0
Directories
Memories
Caches
127
CPU 0 Writes 4 to X step 23
Interconnection Network
X
E 1 0 0
Directories
Creates cache block storage for X
Memories
Caches
128
CPU 0 Writes 4 to X step 24
Interconnection Network
X
E 1 0 0
Directories
Memories
Caches
4
X
129
CPU 0 Writes Back X Block step 25
Interconnection Network
Data Write Back
X
E 1 0 0
Directories
Memories
Caches
130
CPU 0 flushes cache block X step 26
Interconnection Network
X
U 0 0 0
Directories
Memories
Caches
131
Characteristics of Multiprocessors

• Interprocessor communication is done in the
  memory interface by read and write instructions
• Memory may be physically distributed and the
  reads and writes from different processors may
  take different time.
• Congestion and hotspots in the interconnection
  network may occur.
• Memory latency (i.e., time to complete a read or
  write) may be long and variable.
• Most messages through the bus or interconnection
  network are the size of single memory words.
• Randomization of requests may be used to reduce
  the probability of collisions.

132
Multicomputers

• Distributed memory multiple-CPU computer
• Same address on different processors refers to
  different physical memory locations
• Processors interact through message passing

133
Typically, Two Flavors of Multicomputers

• Commercial multicomputers
• Custom switch network
• Low latency (the time it takes to send a
  message).
• High bandwidth (data path width) across
  processors
• Commodity clusters
• Mass produced computers, switches and other
  equipment
• Use low cost components
• Message latency is higher
• Communications bandwidth is lower

134
Multicomputer Communication

• Processors are connected by an interconnection
  network
• Each processor has a local memory and can only
  access its own local memory
• Data is passed between processors using messages,
  as required by the program
• Data movement across the network is also
  asynchronous
• A common approach is to use MPI to handling
  message passing

135
Multicomputer Communications (cont)

• Multicomputers can be scaled to larger sizes much
  easier than multiprocessors.
• The amount of data transmissions between
  processors have a huge impact on the performance
• The distribution of the data among the processors
  is a very important factor in the performance
  efficiency.

136
Message-Passing Advantages

• No problem with simultaneous access to data.
• Allows different PCs to operate on the same data
  independently.
• Allows PCs on a network to be easily upgraded
  when faster processors become available.

137
Disadvantages of Message-Passing

• Programmers must make explicit message-passing
  calls in the code
• This is low-level programming and is error prone.
• Data is not shared but copied, which increases
  the total data size.
• Data Integrity
• Difficulty in maintaining correctness of multiple
  copies of data item.

138
Some Interconnection Network Terminology (1/2)

• References Wilkinson, et. al. Grama, et. al.
  Also, earlier slides on architecture networks.
• A link is the connection between two nodes.
• A switch that enables packets to be routed
  through the node to other nodes without
  disturbing the processor is assumed.
• The link between two nodes can be either
  bidirectional or use two directional links .
• Can assume either one wire that carries one bit
  or parallel wires (one wire for each bit in
  word).
• The above choices do not have a major impact on
  the concepts presented in this course.

139
Network Terminology (2/2)

• The bandwidth is the number of bits that can be
  transmitted in unit time (i.e., bits per second).
• The network latency is the time required to
  transfer a message through the network.
• The communication latency is the total time
  required to send a message, including software
  overhead and interface delay.
• The message latency or startup time is the time
  required to send a zero-length message.
• Includes software hardware overhead, such as
• Choosing a route
• packing and unpacking the message

140
Circuit Switching Message Passing

• Technique establishes a path and allows the
  entire message to transfer uninterrupted.
• Similar to telephone connection that is held
  until the end of the call.
• Links used are not available to other messages
  until the transfer is complete.
• Latency (message transfer time) If the length of
  control packet sent to establish path is small
  wrt (with respect to) the message length, the
  latency is essentially
• the constant L/B, where L is message length and B
  is bandwidth.

141
Store-and-forward Packet Switching

• Message is divided into packets of information
• Each packet includes source and destination
  addresses.
• Packets can not exceed a fixed, maximum size
  (e.g., 1000 byte).
• A packet is stored in a node in a buffer until it
  can move to the next node.

142
Packet Switching (cont)

• At each node, the designation information is
  looked at and used to select which node to
  forward the packet to.
• Routing algorithms (often probabilistic) are used
  to avoid hot spots and to minimize traffic jams.
• Significant latency is created by storing each
  packet in each node it reaches.
• Latency increases linearly with the length of the
  route.

143
Virtual Cut-Through Package Switching

• Used to reduce the latency.
• Allows packet to pass through a node without
  being stored, if the outgoing link is available.
• If complete path is available, a message can
  immediately move from source to destination..

144
Wormhole Routing

• Alternate to store-and-forward packet routing
• A message is divided into small units called
  flits (flow control units).
• Flits are 1-2 bytes in size.
• Can be transferred in parallel on links with
  multiple wires.
• Only head of flit is initially transferred when
  the next link becomes available.

145
Wormhole Routing (cont)

• As each flit moves forward, the next flit can
  move forward.
• The entire path must be reserved for a message as
  these packets pull each other along (like cars of
  a train).
• Request/acknowledge bit messages are required to
  coordinate these pull-along moves.
• See Wilkinson, et. al.
• Latency If the head of the flit is very small
  compared to the length of the message, then the
  latency is essentially the constant L/B, with L
  the message length and B the link bandwidth.

146
Deadlock

• Routing algorithms needed to find a path between
  the nodes.
• Adaptive routing algorithms choose different
  paths, depending on traffic conditions.
• Livelock is a deadlock-type situation where a
  packet continues to go around the network,
  without ever reaching its destination.
• Deadlock No packet can be forwarded because they
  are blocked by other stored packets waiting to be
  forwarded.

147
Asymmetric Multicomputers

• Has a front-end that interacts with users and I/O
  devices.
• Processors in back end are used for computation.
• Programming similar to SIMDs (i.e., processor
  arrays)
• Common with early multicomputers
• Examples of asymmetrical multicomputers given in
  textbook.

148
Asymmetrical MC Advantages

• Back-end processors dedicated to parallel
  computations ? Easier to understand, model, tune
  performance
• Only a simple back-end operating system needed ?
  Easy for a vendor to create

149
Asymmetrical MC Disadvantages

• Front-end computer is a single point of failure
• Single front-end computer limits scalability of
  system
• Primitive operating system in back-end processors
  makes debugging difficult
• Every application requires development of both
  front-end and back-end program

150
Symmetric Multicomputers

• Every computer executes the same operating system
  and has identical functionality.
• Users may log into any computer to edit or
  compile their programs.
• Any or all computers may be involved in the
  execution of their program.
• During execution of programs, every PE executes
  the same program.
• When only one PE should execute an operation, an
  if statement is used to select the PE.

151
Symmetric Multicomputers
152
Symmetrical MC Advantages

• Alleviate performance bottleneck caused by single
  front-end computer
• Better support for debugging
• Every processor executes same program

153
Symmetrical MC Disadvantages

• More difficult to maintain illusion of single
  parallel computer
• No simple way to balance program development
  workload among processors
• More difficult to achieve high performance when
  multiple processes run on each processor
• Details on next slide

154
Symmetric MC Disadvantages (cont)

• (cont.) More difficult to achieve high
  performance when multiple processes run on each
  processor
• Processes on same processor compete for same
  resources
• CPU Cycles
• Cache space
• Memory bandwidth
• Increased cache misses
• Cache is PE oriented instead of process
  oriented

155
Best Model for Commodity Cluster

• Full-Fledged operating system (e.g., Linux)
  desirable
• Feature of symmetric multicomputer
• Desirable to increase cache hits
• Favors having only a single user process on each
  PE
• Favors most nodes being off-limits for program
  development
• Need fast network
• Keep program development users off networks and
  have them access front-end by another path.
• Reserve interconnection network to usage by
  parallel processes
• Overall, a mixed model may be best for commodity
  clusters

156
Ideal Commodity Cluster Features

• Co-located computers
• Computers dedicated to running a single process
  at a time to lower cache misses
• Accessible only from the network
• No keyboards or displays
• Users access front-end by another route.
• Identical operating systems
• Identical local disk images
• Administered as an entity

157
ParPar Cluster, A Mixed Model

• Mixed model
• Incorporates both asymetrical and symetrical
  designs.

158
Network of Workstations

• Dispersed computers
• Typically located on users desks
• First priority response time for person at the
  keyboard
• Parallel jobs wait in background and run with
  spare CPU cycles are available.
• Different operating systems
• Different local images
• Checkpointing and restarting important
• Typically connected by ethernet
• Too slow for commodity network usage

159
A Commodity Cluster vs Network of Workstations

• A commodity cluster contains components of local
  area networks
• Commodity computers
• Switches
• A network of workstations is a dispersed
  collection of computers
• Distributed hetergeneous computers
• Located on primary users desks
• Unused cycles available for parallel use
• Example SETI project

160
Summary

• Commercial parallel computers appearedin 1980s
• Multiple-CPU computers now dominate
• Small-scale Centralized multiprocessors
• Large-scale Distributed memory architectures
• Multiprocessors
• Multicomputers