This is the first tutorial in the "Livermore Computing Getting Started" workshop. It is intended to provide only a very quick overview of the extensive and broad topic of Parallel Computing, as a lead-in for the tutorials that follow it. As such, it covers just the very basics of parallel computing, and is intended for someone who is just becoming acquainted with the subject and who is planning to attend one or more of the other tutorials in this workshop. It is not intended to cover Parallel Programming in depth, as this would require significantly more time. The tutorial begins with a discussion on parallel computing - what it is and how it's used, followed by a discussion on concepts and terminology associated with parallel computing. The topics of parallel memory architectures and programming models are then explored. These topics are followed by a series of practical discussions on a number of the complex issues related to designing and running parallel programs. The tutorial concludes with several examples of how to parallelize simple serial programs.
Overview
What is Parallel Computing?
Serial Computing:
Traditionally, software has been written for serial
computation:
A problem is broken into a discrete series of instructions
Instructions are executed sequentially one after another
Executed on a single processor
Only one instruction may execute at any moment in time
For example:
Parallel Computing:
In the simplest sense, parallel computing is the simultaneous
use of multiple compute resources to solve a computational problem:
A problem is broken into discrete parts that can be solved concurrently
Each part is further broken down to a series of instructions
Instructions from each part execute simultaneously on different processors
An overall control/coordination mechanism is employed
For example:
The computational problem should be able to:
Be broken apart into discrete pieces of work that can be solved
simultaneously;
Execute multiple program instructions at any moment in time;
Be solved in less time with multiple compute resources than with a single
compute resource.
The compute resources are typically:
A single computer with multiple processors/cores
An arbitrary number of such computers connected by a network
Parallel Computers:
Virtually all stand-alone computers today are parallel from a hardware
perspective:
In the natural world, many complex, interrelated events are happening at the
same time, yet within a temporal sequence.
Compared to serial computing, parallel computing is much better suited for
modeling, simulating and understanding complex, real world phenomena.
For example, imagine modeling these serially:
Main Reasons:
SAVE TIME AND/OR MONEY:
In theory, throwing more resources at a task will shorten its time to
completion, with potential cost savings.
Parallel computers can be built from cheap, commodity components.
SOLVE LARGER / MORE COMPLEX PROBLEMS:
Many problems are so large and/or complex that it is impractical or
impossible to solve them on a single computer, especially given limited
computer memory.
Example: Folding@home (folding.stanford.edu)
uses over 160,000 computers globally (June, 2015)
MAKE BETTER USE OF UNDERLYING PARALLEL HARDWARE:
Modern computers, even laptops, are parallel in architecture with
multiple processors/cores.
Parallel software is specifically intended for parallel hardware with
multiple cores, threads, etc.
In most cases, serial programs run on modern computers "waste"
potential computing power.
Intel Xeon processor with 6 cores and 6 L3 cache units
The Future:
During the past 20+ years, the trends indicated by ever faster
networks, distributed systems, and multi-processor computer architectures
(even at the desktop level) clearly show
that parallelism is the future of computing.
In this same time period, there has been a greater than
500,000x
increase in supercomputer performance, with no end currently in sight.
Historically, parallel computing has been considered to be
"the high end of computing", and has been used to model difficult
problems in many areas of science and engineering:
Today, commercial applications provide an equal or greater driving
force in the development of faster computers.
These applications require the processing of large
amounts of data in sophisticated ways. For example:
"Big Data", databases, data mining
Oil exploration
Web search engines, web based business services
Medical imaging and diagnosis
Pharmaceutical design
Financial and economic modeling
Management of national and multi-national corporations
Advanced graphics and virtual reality, particularly in the entertainment
industry
Networked video and multi-media technologies
Collaborative work environments
Global Applications:
Parallel computing is now being used extensively around the world, in a
wide variety of applications.
Named after the Hungarian mathematician/genius John von Neumann who first
authored the general requirements for an electronic computer in his 1945 papers.
Also known as "stored-program computer" - both program instructions and data are
kept in electronic memory. Differs from earlier computers which were programmed
through "hard wiring".
Since then, virtually all computers have followed this basic design:
Comprised of four main components:
Memory
Control Unit
Arithmetic Logic Unit
Input/Output
Read/write, random access memory is used to store both program instructions
and data
Program instructions are coded data which tell the computer to do
something
Data is simply information to be used by the program
Control unit fetches instructions/data from memory, decodes
the instructions and then sequentially coordinates operations
to accomplish the programmed task.
Arithmetic Unit performs basic arithmetic operations
Input/Output is the interface to the human operator
John von Neumann circa 1940s (Source: LANL archives)
Well, parallel computers still follow this basic design,
just multiplied in units. The basic, fundamental architecture remains the
same.
Concepts and Terminology
Flynn's Classical Taxonomy
There are different ways to classify parallel computers. Examples available
HERE.
One of the more widely used classifications, in use since 1966, is called
Flynn's Taxonomy.
Flynn's taxonomy distinguishes multi-processor computer architectures
according
to how they can be classified along the two independent dimensions of
Instruction Stream and Data Stream.
Each of these dimensions can have only one of two possible states:
Single or Multiple.
The matrix below defines the 4 possible classifications according to Flynn:
Single Instruction, Single Data (SISD):
A serial (non-parallel) computer
Single Instruction: Only one instruction stream is
being acted on by the CPU during any one clock cycle
Single Data: Only one data stream is being used as input during any one clock cycle
Deterministic execution
This is the oldest type of computer
Examples: older generation mainframes, minicomputers, workstations and single
processor/core PCs.
UNIVAC1
IBM 360
CRAY1
CDC 7600
PDP1
Dell Laptop
Single Instruction, Multiple Data (SIMD):
A type of parallel computer
Single Instruction: All processing units execute the same instruction at any given clock cycle
Multiple Data: Each processing unit can operate on a different data
element
Best suited for specialized problems characterized by a high degree of
regularity, such as graphics/image processing.
Synchronous (lockstep) and deterministic execution
Two varieties: Processor Arrays and Vector Pipelines
Vector Pipelines: IBM 9000, Cray X-MP, Y-MP & C90, Fujitsu VP, NEC SX-2,
Hitachi S820, ETA10
Most modern computers, particularly those with graphics processor units
(GPUs) employ SIMD instructions and execution units.
ILLIAC IV
MasPar
Cray X-MP
Cray Y-MP
Thinking Machines CM-2
Cell Processor (GPU)
Multiple Instruction, Single Data (MISD):
A type of parallel computer
Multiple Instruction: Each processing unit operates on the data
independently via separate instruction streams.
Single Data: A single data stream is fed into multiple processing units.
Few (if any) actual examples of this class of parallel computer have ever
existed.
Some conceivable uses might be:
multiple frequency filters operating on a single signal stream
multiple cryptography algorithms attempting to crack a single coded
message.
Multiple Instruction, Multiple Data (MIMD):
A type of parallel computer
Multiple Instruction: Every processor may be executing a different
instruction stream
Multiple Data: Every processor may be working with a different data
stream
Execution can be synchronous or asynchronous, deterministic or
non-deterministic
Currently, the most common type of parallel computer - most modern
supercomputers fall into this category.
Examples: most current supercomputers, networked parallel computer
clusters and "grids", multi-processor SMP computers, multi-core PCs.
Note: many MIMD architectures also include SIMD execution sub-components
IBM POWER5
HP/Compaq Alphaserver
Intel IA32
AMD Opteron
Cray XT3
IBM BG/L
Concepts and Terminology
Some General Parallel Terminology
Like everything else, parallel computing has its own "jargon". Some of the
more commonly used terms associated with parallel computing are listed below.
Most of these will be discussed in more detail later.
Supercomputing / High Performance Computing (HPC)
Using the world's fastest and largest computers to solve large problems.
Node
A standalone "computer in a box". Usually comprised of multiple CPUs/processors/cores, memory, network interfaces, etc. Nodes are networked
together to comprise a supercomputer.
CPU / Socket / Processor / Core
This varies, depending upon who you talk to. In the past, a CPU (Central Processing Unit) was a singular execution component for a computer. Then, multiple CPUs were incorporated into a node. Then, individual CPUs were subdivided into multiple "cores", each being a unique execution unit. CPUs with multiple cores are sometimes called "sockets" - vendor dependent. The result is a node with multiple CPUs, each containing multiple cores. The nomenclature is confused at times. Wonder why?
Task
A logically discrete section of computational work. A task is typically a
program or program-like set of instructions that is executed by a processor.
A parallel program consists of multiple tasks running on multiple processors.
Pipelining
Breaking a task into steps performed by different processor units, with inputs streaming through, much like an assembly line; a type of parallel computing.
Shared Memory
From a strictly hardware point of view, describes a computer architecture
where all processors have direct (usually bus based) access to common
physical memory. In a programming sense, it describes a model where
parallel tasks all have the same "picture" of memory and can directly
address and access the same logical memory locations regardless
of where the physical memory actually exists.
Symmetric Multi-Processor (SMP)
Shared memory hardware architecture where multiple processors share a single address space and have equal access to all resources.
Distributed Memory
In hardware, refers to network based memory access for physical memory that
is not common. As a programming model, tasks can only logically "see"
local machine memory and must use communications to access memory on other
machines where other tasks are executing.
Communications
Parallel tasks typically need to exchange data. There are several ways this can be accomplished, such as through a shared memory bus or over a network, however the actual event of data exchange is commonly referred to as communications regardless of the method employed.
Synchronization
The coordination of parallel tasks in real time, very often associated with
communications. Often implemented by establishing a synchronization point within an application where a task may not proceed further until another task(s) reaches the same or logically equivalent point.
Synchronization usually involves waiting by at least one task, and can therefore cause a parallel application's wall clock execution time to increase.
Granularity
In parallel computing, granularity is a qualitative measure of the ratio
of computation to communication.
Coarse: relatively large amounts of computational work
are done between communication events
Fine: relatively small amounts of computational work are
done between communication events
Observed Speedup
Observed speedup of a code which has been parallelized, defined as:
wall-clock time of serial execution
-----------------------------------
wall-clock time of parallel execution
One of the simplest and most widely used indicators for a parallel program's performance.
Parallel Overhead
The amount of time required to coordinate parallel tasks, as opposed to
doing useful work. Parallel overhead can include factors such as:
Task start-up time
Synchronizations
Data communications
Software overhead imposed by parallel languages, libraries,
operating system, etc.
Task termination time
Massively Parallel
Refers to the hardware that comprises a given parallel system - having many processing elements. The meaning of "many" keeps increasing, but currently, the largest parallel computers are comprised of processing elements numbering in the hundreds of thousands to millions.
Embarrassingly Parallel
Solving many similar, but independent tasks
simultaneously; little to no need for coordination between the tasks.
Scalability
Refers to a parallel system's (hardware and/or software) ability to demonstrate a proportionate increase in parallel speedup with the addition of more resources. Factors that contribute to scalability include:
Hardware - particularly memory-cpu bandwidths and network communication
properties
Application algorithm
Parallel overhead related
Characteristics of your specific application
Concepts and Terminology
Limits and Costs of Parallel Programming
Amdahl's Law:
Amdahl's Law states that potential program
speedup is defined by the fraction of code (P) that can be parallelized:
1
speedup = --------
1 - P
If none of the code can be parallelized, P = 0 and the speedup = 1 (no
speedup).
If all of the code is parallelized, P = 1 and the speedup is
infinite (in theory).
If 50% of the code can be parallelized, maximum speedup = 2, meaning
the code will run twice as fast.
Introducing the number of processors performing the parallel fraction of
work, the relationship can be modeled by:
1
speedup = ------------
P + S
---
N
where P = parallel fraction, N = number of processors and S = serial
fraction.
It soon becomes obvious that there are limits to the scalability of
parallelism. For example:
speedup
--------------------------------
N P = .50 P = .90 P = .99
----- ------- ------- -------
10 1.82 5.26 9.17
100 1.98 9.17 50.25
1,000 1.99 9.91 90.99
10,000 1.99 9.91 99.02
100,000 1.99 9.99 99.90
However, certain problems demonstrate increased performance by increasing
the problem size. For example:
We can increase the problem size by doubling the grid dimensions and
halving the time step. This results in four times the number of grid
points and twice the number of time steps. The timings then look like:
Problems that increase the percentage of parallel time with their size
are more scalable than problems with a fixed percentage of
parallel time.
Complexity:
In general, parallel applications are much more complex than corresponding
serial applications, perhaps an order of magnitude. Not only do you have
multiple instruction streams executing at the same time, but you also have
data flowing between them.
The costs of complexity are measured in programmer time in virtually every
aspect of the software development cycle:
Design
Coding
Debugging
Tuning
Maintenance
Adhering to "good" software development practices is essential when
working with parallel applications - especially if somebody besides
you will have to work with the software.
Portability:
Thanks to standardization in several APIs, such as MPI, POSIX threads,
and OpenMP, portability issues with parallel programs are not as
serious as in years past. However...
All of the usual portability issues associated with serial programs
apply to parallel programs. For example, if you use vendor "enhancements"
to Fortran, C or C++, portability will be a problem.
Even though standards exist for several APIs, implementations will differ
in a number of details, sometimes to the point of requiring code
modifications in order to effect portability.
Operating systems can play a key role in code portability issues.
Hardware architectures are characteristically highly variable and can
affect portability.
Resource Requirements:
The primary intent of parallel programming is to decrease execution
wall clock time, however in order to accomplish this, more CPU time
is required. For example, a parallel code that runs in 1 hour on 8
processors actually uses 8 hours of CPU time.
The amount of memory required can be greater for parallel codes than
serial codes, due to the need to replicate data and for overheads
associated with parallel support libraries and subsystems.
For short running parallel programs, there can actually be a decrease
in performance compared to a similar serial implementation. The overhead
costs associated with setting up the parallel environment, task creation,
communications and task termination can comprise a significant portion of
the total execution time for short runs.
Scalability:
Two types of scaling based on time to solution:
Strong scaling: The total problem size stays fixed as more
processors are added.
Weak scaling: The problem size per processor stays fixed as
more processors are added.
The ability of a parallel program's performance to scale is a result
of a number of interrelated factors. Simply adding more processors
is rarely the answer.
The algorithm may have inherent limits to scalability. At some point,
adding more resources causes performance to decrease. Many parallel
solutions demonstrate this characteristic at some point.
Hardware factors play a significant role in scalability. Examples:
Memory-cpu bus bandwidth on an SMP machine
Communications network bandwidth
Amount of memory available on any given machine or set of machines
Processor clock speed
Parallel support libraries and subsystems software can limit scalability
independent of your application.
Parallel Computer Memory Architectures
Shared Memory
General Characteristics:
Shared memory parallel computers vary widely, but generally have in common
the ability for all processors to access all memory as global address space.
Multiple processors can operate independently but share the same memory
resources.
Changes in a memory location effected by one processor are visible to all
other processors.
Historically, shared memory machines have been classified as
UMA and NUMA, based upon memory access times.
Uniform Memory Access (UMA):
Most commonly represented today by Symmetric Multiprocessor
(SMP) machines
Identical processors
Equal access and access times to memory
Sometimes called CC-UMA - Cache Coherent UMA.
Cache coherent means if one processor updates a location in shared
memory, all
the other processors know about the update. Cache coherency is
accomplished at the hardware level.
Non-Uniform Memory Access (NUMA):
Often made by physically linking two or more SMPs
One SMP can directly access memory of another SMP
Not all processors have equal access time to all memories
Memory access across link is slower
If cache coherency is maintained, then may also be called CC-NUMA -
Cache Coherent NUMA
Advantages:
Global address space provides a user-friendly programming perspective
to memory
Data sharing between tasks is both fast and uniform due to the proximity
of memory to CPUs
Shared Memory (UMA)
Shared Memory (NUMA)
Disadvantages:
Primary disadvantage is the lack of scalability between memory and CPUs.
Adding more CPUs can geometrically increases traffic on the shared
memory-CPU path, and for cache coherent systems, geometrically increase
traffic associated with cache/memory management.
Programmer responsibility for synchronization constructs that ensure
"correct" access of global memory.
Parallel Computer Memory Architectures
Distributed Memory
General Characteristics:
Like shared memory systems, distributed memory systems vary widely but
share a common characteristic. Distributed memory systems require a
communication network to connect inter-processor memory.
Processors have their own local memory. Memory addresses in one
processor do not map to another processor, so there is no concept of
global address space across all processors.
Because each processor has its own local memory, it operates
independently. Changes it makes to its local memory have no effect
on the memory of other processors. Hence, the concept of cache
coherency does not apply.
When a processor needs access to data in another processor, it is
usually the task of the programmer to explicitly define how and when
data is communicated. Synchronization between tasks is likewise the
programmer's responsibility.
The network "fabric" used for data transfer varies widely, though it can
be as simple as Ethernet.
Advantages:
Memory is scalable with the number of processors. Increase the number of
processors and the size of memory increases proportionately.
Each processor can rapidly access its own memory without interference
and without the overhead incurred with trying to maintain global cache
coherency.
Cost effectiveness: can use commodity, off-the-shelf processors and
networking.
Disadvantages:
The programmer is responsible for many of the details associated with
data communication between processors.
It may be difficult to map existing data structures, based on global
memory, to this memory organization.
Non-uniform memory access times - data residing on a remote node
takes longer to access than node local data.
Parallel Computer Memory Architectures
Hybrid Distributed-Shared Memory
General Characteristics:
The largest and fastest computers in the world today employ both shared
and distributed memory architectures.
The shared memory component can be a shared memory machine and/or
graphics processing units (GPU).
The distributed memory component is the networking of multiple shared memory/GPU
machines, which know only about their own memory - not the memory on another
machine. Therefore, network communications are required to move data from one
machine to another.
Current trends seem to indicate that this type of memory architecture
will continue to prevail and increase at the high end of computing for
the foreseeable future.
Advantages and Disadvantages:
Whatever is common to both shared and distributed memory architectures.
Increased scalability is an important advantage
Increased programmer complexity is an important disadvantage
Parallel Programming Models
Overview
There are several parallel programming models in common use:
Shared Memory (without threads)
Threads
Distributed Memory / Message Passing
Data Parallel
Hybrid
Single Program Multiple Data (SPMD)
Multiple Program Multiple Data (MPMD)
Parallel programming models exist as an abstraction above hardware
and memory architectures.
Although it might not seem apparent, these models are NOT specific
to a particular type of machine or memory architecture. In fact, any
of these models can (theoretically) be implemented on any underlying
hardware. Two examples from the past are discussed below.
SHARED memory model on a DISTRIBUTED memory machine: Kendall Square Research (KSR) ALLCACHE approach.
Machine memory was physically distributed across networked machines, but appeared to the user as a single shared memory global address space. Generically, this approach is referred to as "virtual shared memory".
DISTRIBUTED memory model on a SHARED memory machine: Message Passing Interface (MPI) on SGI Origin 2000. The SGI Origin 2000 employed the CC-NUMA type of shared memory architecture, where every task has direct access to global address space spread across all machines. However, the ability to send and receive messages using MPI, as is commonly done over a network of distributed memory machines, was implemented and commonly used.
Which model to use?
This is often a combination of what is available and personal
choice. There is no "best" model, although there certainly are better
implementations of some models over others.
The following sections describe each of the models mentioned above, and
also discuss some of their actual implementations.
Parallel Programming Models
Shared Memory Model (without threads)
In this programming model, processes/tasks share a common address space,
which they read and write to asynchronously.
Various mechanisms such as locks / semaphores are used to control
access to the shared memory, resolve contentions and to prevent race
conditions and deadlocks.
This is perhaps the simplest parallel programming model.
An advantage of this model from the programmer's point of view is that the
notion of data "ownership" is lacking, so there is no need to specify
explicitly the communication of data between tasks. All processes see and
have equal access to shared memory. Program development can often be
simplified.
An important disadvantage in terms of performance is that it becomes
more difficult to understand and manage data locality:
Keeping data local to the process that works on it conserves memory
accesses, cache refreshes and bus traffic that occurs when multiple
processes use the same data.
Unfortunately, controlling data locality is hard to understand and
may be beyond the control of the average user.
Implementations:
On stand-alone shared memory machines, native operating systems,
compilers and/or hardware provide support for shared memory programming.
For example, the POSIX standard provides an API for using shared memory,
and UNIX provides shared memory segments (shmget, shmat, shmctl, etc).
On distributed memory machines, memory is physically distributed
across a network of machines, but made global through specialized hardware
and software. A variety of SHMEM implementations are available:
http://en.wikipedia.org/wiki/SHMEM.
Parallel Programming Models
Threads Model
This programming model is a type of shared memory programming.
In the threads model of parallel programming, a single "heavy weight"
process can have multiple "light weight", concurrent execution paths.
For example:
The main program a.out is scheduled to run by the
native operating system. a.out loads and acquires all of the
necessary system and user resources to run. This is the "heavy weight"
process.
a.out performs some serial work, and then creates
a number of tasks (threads) that can be scheduled and run by the
operating system concurrently.
Each thread has local data, but also, shares the entire resources of
a.out. This saves the overhead associated with
replicating a program's resources for each thread ("light weight").
Each thread also benefits from a global memory view because it shares the
memory space of a.out.
A thread's work may best be described as a subroutine within
the main program. Any thread can execute any subroutine at the
same time as other threads.
Threads communicate with each other through global memory (updating
address locations). This requires synchronization constructs to ensure
that more than one thread is not updating the same global address at
any time.
Threads can come and go, but a.out remains present
to provide the necessary shared resources until the
application has completed.
Implementations:
From a programming perspective, threads implementations commonly
comprise:
A library of subroutines that are called from within
parallel source code
A set of compiler directives imbedded in either serial
or parallel source code
In both cases, the programmer is responsible for determining the
parallelism (although compilers can sometimes help).
Threaded implementations are not new in computing. Historically,
hardware vendors have implemented their own proprietary versions of
threads. These implementations differed substantially from each other
making it difficult for programmers to develop portable threaded
applications.
Unrelated standardization efforts have resulted in
two very different implementations of threads:
POSIX Threads and OpenMP.
POSIX Threads
Specified by the IEEE POSIX 1003.1c standard (1995). C Language only.
Part of Unix/Linux operating systems
Library based
Commonly referred to as Pthreads.
Very explicit parallelism; requires significant programmer attention
to detail.
OpenMP
Industry standard, jointly defined and endorsed by a group of major
computer hardware and software vendors, organizations and individuals.
Compiler directive based
Portable / multi-platform, including Unix and Windows platforms
Available in C/C++ and Fortran implementations
Can be very easy and simple to use - provides for "incremental
parallelism". Can begin with serial code.
Other threaded implementations exist, such as Microsoft's
This model demonstrates the following characteristics:
A set of tasks that use their own local memory during computation.
Multiple tasks can reside on the same physical machine and/or
across an arbitrary number of machines.
Tasks exchange data through communications by sending and
receiving messages.
Data transfer usually requires cooperative operations to be performed
by each process. For example, a send operation must have a matching
receive operation.
Implementations:
From a programming perspective, message passing implementations usually
comprise a library of subroutines. Calls to these subroutines
are imbedded in source code. The programmer is responsible for determining
all parallelism.
Historically, a variety of message passing libraries have been
available since the 1980s. These implementations differed substantially
from each other making it difficult for programmers to develop portable
applications.
In 1992, the MPI Forum was formed with the primary goal of establishing
a standard interface for message passing implementations.
Part 1 of the Message Passing Interface (MPI) was released in
1994. Part 2 (MPI-2) was released in 1996 and MPI-3 in 2012.
All MPI specifications are available on the web at
http://www.mpi-forum.org/docs/.
MPI is the "de facto" industry
standard for message passing, replacing virtually all other
message passing implementations used for production work.
MPI implementations exist for virtually all popular parallel computing
platforms. Not all implementations include everything in MPI-1, MPI-2
or MPI-3.
May also be referred to as the Partitioned Global Address Space (PGAS)
model.
The data parallel model demonstrates the following characteristics:
Address space is treated globally
Most of the parallel work focuses on performing operations on a
data set. The data set is typically organized into a common
structure, such as an array or cube.
A set of tasks work collectively on the same data structure, however,
each task works on a different partition of the same data structure.
Tasks perform the same operation on their partition of work, for
example, "add 4 to every array element".
On shared memory architectures, all tasks may have access to the data
structure through global memory.
On distributed memory architectures the data structure is split up and
resides as "chunks" in the local memory of each task.
Implementations:
Currently, there are several relatively popular, and sometimes developmental,
parallel programming implementations based on the Data Parallel / PGAS model.
Unified Parallel C (UPC): an extension to the C programming language
for SPMD parallel programming. Compiler dependent. More information:
http://upc.lbl.gov/
Global Arrays: provides a shared memory style programming environment in
the context of distributed array data structures. Public domain library with
C and Fortran77 bindings. More information:
https://en.wikipedia.org/wiki/Global_Arrays
X10: a PGAS based parallel programming language being developed by
IBM at the Thomas J. Watson Research Center. More information:
http://x10-lang.org/
Chapel: an open source parallel programming language project
being led by Cray. More information:
http://chapel.cray.com/
Parallel Programming Models
Hybrid Model
A hybrid model combines more than one of the previously described
programming models.
Currently, a common example of a hybrid model is the combination
of the message passing model (MPI) with the threads model (OpenMP).
Threads perform computationally intensive kernels using local,
on-node data
Communications between processes on different nodes occurs
over the network using MPI
This hybrid model lends itself well to the most popular (currently)
hardware environment of clustered multi/many-core machines.
Another similar and increasingly popular example of a hybrid model is
using MPI with CPU-GPU (Graphics Processing Unit) programming.
MPI tasks run on CPUs using local memory and communicating with
each other over a network.
Computationally intensive kernels are off-loaded to GPUs on-node.
Data exchange between node-local memory and GPUs uses CUDA (or something
equivalent).
Other hybrid models are common:
MPI with Pthreads
MPI with non-GPU accelerators
...
Parallel Programming Models
SPMD and MPMD
Single Program Multiple Data (SPMD):
SPMD is actually a "high level" programming model that can be
built upon any combination of the previously mentioned parallel
programming models.
SINGLE PROGRAM: All tasks execute their copy of the same program
simultaneously. This program can be threads, message passing,
data parallel or hybrid.
MULTIPLE DATA: All tasks may use different data
SPMD programs usually have the necessary logic programmed into them to
allow different tasks to branch or conditionally execute only those
parts of the program they are designed to execute. That is, tasks
do not necessarily have to execute the entire program - perhaps only a
portion of it.
The SPMD model, using message passing or hybrid programming,
is probably the most commonly used parallel programming model
for multi-node clusters.
Multiple Program Multiple Data (MPMD):
Like SPMD, MPMD is actually a "high level" programming model that can
be built upon any combination of the previously mentioned parallel
programming models.
MULTIPLE PROGRAM: Tasks may execute different programs
simultaneously. The programs can be threads, message passing,
data parallel or hybrid.
MULTIPLE DATA: All tasks may use different data
MPMD applications are not as common as SPMD applications, but may
be better suited for certain types of problems, particularly those
that lend themselves better to functional decomposition
than domain decomposition (discussed later under
Partioning).
Designing Parallel Programs
Automatic vs. Manual Parallelization
Designing and developing parallel programs has characteristically been a
very manual process. The programmer is typically responsible for
both identifying and actually implementing parallelism.
Very often, manually developing parallel codes is a time consuming,
complex, error-prone and iterative process.
For a number of years now, various tools have been available to assist
the programmer with converting serial programs into parallel programs.
The most common type of tool used to automatically parallelize a serial
program is a parallelizing compiler or pre-processor.
A parallelizing compiler generally works in two different ways:
Fully Automatic
The compiler analyzes the source code and
identifies opportunities for parallelism.
The analysis includes
identifying inhibitors to parallelism and possibly a cost
weighting on whether or not the parallelism would actually
improve performance.
Loops (do, for) are the most frequent target for
automatic parallelization.
Programmer Directed
Using "compiler directives" or possibly compiler flags,
the programmer explicitly tells the compiler how to
parallelize the code.
May be able to be used in conjunction with some degree of
automatic parallelization also.
The most common compiler generated parallelization is done using
on-node shared memory and threads (such as OpenMP).
If you are beginning with an existing serial code and have time
or budget constraints, then automatic parallelization may be
the answer. However, there are several important caveats that
apply to automatic parallelization:
Wrong results may be produced
Performance may actually degrade
Much less flexible than manual parallelization
Limited to a subset (mostly loops) of code
May actually not parallelize code if the compiler analysis suggests there
are inhibitors or the code is too complex
The remainder of this section applies to the manual method of
developing parallel codes.
Designing Parallel Programs
Understand the Problem and the Program
Undoubtedly, the first step in developing parallel software is to
first understand the problem that you wish to solve in parallel.
If you are starting with a serial program, this necessitates
understanding the existing code also.
Before spending time in an attempt to develop a parallel solution
for a problem, determine whether or not the problem is one that can
actually be parallelized.
Example of an easy to parallelize problem:
Calculate the potential energy for each of several thousand
independent conformations of a molecule.
When done, find the minimum energy conformation.
This problem is able to be solved in parallel. Each of the
molecular conformations is independently determinable.
The calculation of the minimum energy conformation is also a
parallelizable problem.
Example of a problem with little-to-no parallelism:
Calculation of the Fibonacci series (0,1,1,2,3,5,8,13,21,...) by use of
the formula:
F(n) = F(n-1) + F(n-2)
The calculation of the F(n) value uses those of both F(n-1) and F(n-2), which
must be computed first.
Identify the program's
hotspots:
Know where most of the real work is being done.
The majority of scientific and technical programs usually
accomplish most of their work in a few places.
Profilers and performance analysis tools can help here
Focus on parallelizing the hotspots and ignore those sections
of the program that account for little CPU usage.
Identify bottlenecks
in the program:
Are there areas that are disproportionately slow, or cause
parallelizable work to halt or be deferred?
For example, I/O is usually something that slows a program down.
May be possible to restructure the program or use a different
algorithm to reduce or eliminate unnecessary slow areas
Identify inhibitors to parallelism. One common class of inhibitor
is data dependence, as demonstrated by the Fibonacci sequence
above.
Investigate other algorithms if possible. This may be the single most
important consideration when designing a parallel application.
Take advantage of optimized third party parallel software and highly
optimized math libraries available from leading vendors (IBM's ESSL,
Intel's MKL, AMD's AMCL, etc.).
Designing Parallel Programs
Partitioning
One of the first steps in designing a parallel program is to break the
problem into discrete "chunks" of work that can be distributed to
multiple tasks. This is known as decomposition or partitioning.
There are two basic ways to partition computational work among parallel
tasks: domain decomposition and
functional decomposition.
Domain Decomposition:
In this type of partitioning, the data associated with a problem
is decomposed. Each parallel task then works on a portion of
the data.
There are different ways to partition data:
Functional Decomposition:
In this approach, the focus is on the computation that is to be
performed rather than on the data manipulated by the computation.
The problem is decomposed according to the work that must be done.
Each task then performs a portion of the overall work.
Functional decomposition lends itself well to problems that can be
split into different tasks. For example:
Ecosystem Modeling Each program calculates the population
of a given group, where each group's growth depends on that of its
neighbors. As time progresses, each process calculates
its current state, then exchanges information with the neighbor
populations. All tasks then progress to calculate the state at the
next time step.
Signal Processing An audio signal data set is passed
through four distinct computational filters. Each filter is a
separate process. The first segment of data must pass through the
first filter before progressing to the second. When it does, the
second segment of data passes through the first filter. By the time
the fourth segment of data is in the first filter, all four
tasks are busy.
Climate Modeling Each model component can be thought of as a separate task.
Arrows represent exchanges of data between components during
computation: the atmosphere model generates wind velocity data
that are used by the ocean model, the ocean model generates sea
surface temperature data that are used by the atmosphere model,
and so on.
Combining these two types of problem decomposition is common and natural.
Designing Parallel Programs
Communications
Who Needs Communications?
The need for communications between tasks depends upon your problem:
You DON'T need communications
Some types of problems can be decomposed and executed in parallel
with virtually no need for tasks to share data. For example, imagine an
image processing operation where every pixel in a black and white image
needs to have its color reversed. The image data can easily be
distributed to multiple tasks that then act independently of each other
to do their portion of the work.
These types of problems are often called embarrassingly
parallel
because they are so straight-forward. Very little inter-task communication
is required.
You DO need communications
Most parallel applications are not quite so simple, and do require
tasks to
share data with each other. For example, a 3-D heat diffusion problem
requires a task to know the temperatures calculated by the tasks that have
neighboring data. Changes to neighboring data has a direct effect on that
task's data.
Factors to Consider:
There are a number of important factors to consider when designing your
program's inter-task communications:
Cost of communications
Inter-task communication virtually always implies overhead.
Machine cycles and resources that could be used for computation
are instead used to package and transmit data.
Communications frequently require some type of synchronization
between tasks, which can result in tasks spending time "waiting"
instead of doing work.
Competing communication traffic can saturate the available network
bandwidth, further aggravating performance problems.
Latency vs. Bandwidth
latency is the time it takes to send a minimal (0 byte)
message from point A to point B. Commonly expressed as microseconds.
bandwidth is the amount of data that can be communicated
per unit of time. Commonly expressed as megabytes/sec or gigabytes/sec.
Sending many small messages can cause latency to dominate communication
overheads. Often it is more efficient to package small messages into a
larger message, thus increasing the effective communications bandwidth.
Visibility of communications
With the Message Passing Model, communications are explicit and
generally quite visible and under the control of the programmer.
With the Data Parallel Model, communications often occur
transparently to the programmer, particularly on distributed
memory architectures. The programmer may not even be able to
know exactly how inter-task communications are being accomplished.
Synchronous vs. asynchronous communications
Synchronous communications require some type of "handshaking"
between tasks that are sharing data. This can be explicitly
structured in code by the programmer, or it may happen at a
lower level unknown to the programmer.
Synchronous communications are often referred to as
blocking communications since other work must
wait until the communications have completed.
Asynchronous communications allow tasks to transfer data independently
from one another. For example, task 1 can prepare and send a
message to task 2, and then immediately begin doing other work.
When task 2 actually receives the data doesn't matter.
Asynchronous communications are often referred to as
non-blocking communications since other work can
be done while the communications are taking place.
Interleaving computation with communication is the single greatest
benefit for using asynchronous communications.
Scope of communications
Knowing which tasks must communicate with each other is critical during
the design stage of a parallel code. Both of the two scopings
described below can be implemented synchronously or asynchronously.
Point-to-point - involves two tasks with one task
acting as the sender/producer of data, and the other acting as
the receiver/consumer.
Collective - involves data sharing between more than
two tasks, which are often specified as being members in a common
group, or collective. Some common variations (there are more):
Efficiency of communications
Very often, the programmer will have a choice with regard to
factors that can affect communications performance. Only a
few are mentioned here.
Which implementation for a given model should be used? Using
the Message Passing Model as an
example, one MPI implementation may be faster on a given
hardware platform than another.
What type of communication operations should be used? As
mentioned previously, asynchronous communication operations
can improve overall program performance.
Network media - some platforms may offer more than one network
for communications. Which one is best?
Overhead and Complexity
Finally, realize that this is only a partial list of things to consider!!!
Designing Parallel Programs
Synchronization
Managing the sequence of work and the tasks performing it is a critical
design consideration for most parallel programs.
Can be a significant factor in program performance (or lack of it)
Often requires "serialization" of segments of the program.
Types of Synchronization:
Barrier
Usually implies that all tasks are involved
Each task performs its work until it reaches the barrier. It then
stops, or "blocks".
When the last task reaches the barrier, all tasks are synchronized.
What happens from here varies. Often, a serial section of work must
be done. In other cases, the tasks are automatically released to
continue their work.
Lock / semaphore
Can involve any number of tasks
Typically used to serialize (protect) access to global data
or a section of code. Only one task at a time may use (own) the
lock / semaphore / flag.
The first task to acquire the lock "sets" it. This task can then
safely (serially) access the protected data or code.
Other tasks can attempt to acquire the lock but must wait until the
task that owns the lock releases it.
Can be blocking or non-blocking
Synchronous communication operations
Involves only those tasks executing a communication operation
When a task performs a communication operation, some form of
coordination is required with the other task(s) participating in
the communication. For example, before a task can perform a
send operation, it must first receive an acknowledgment from the
receiving task that it is OK to send.
Discussed previously in the Communications section.
Designing Parallel Programs
Data Dependencies
Definition:
A dependence exists between program statements when
the order of statement execution affects the results of the program.
A data dependence results from multiple use of the same
location(s) in storage by different tasks.
Dependencies are important to parallel programming because they are one
of the primary inhibitors to parallelism.
The value of A(J-1) must be computed before the value of A(J),
therefore A(J) exhibits a data dependency on A(J-1).
Parallelism is inhibited.
If Task 2 has A(J) and task 1 has A(J-1),
computing the correct value of A(J) necessitates:
Distributed memory architecture - task 2 must obtain the value
of A(J-1) from task 1 after task 1 finishes its computation
Shared memory architecture - task 2 must read A(J-1) after
task 1 updates it
Loop independent data dependence
task 1 task 2
------ ------
X = 2 X = 4
. .
. .
Y = X**2 Y = X**3
As with the previous example, parallelism is inhibited.
The value of Y is dependent on:
Distributed memory architecture - if or when the value of X is
communicated between the tasks.
Shared memory architecture - which task last stores the value of X.
Although all data dependencies are important to identify when designing
parallel programs, loop carried dependencies are particularly important
since loops are possibly the most common target of parallelization efforts.
How to Handle Data Dependencies:
Distributed memory architectures - communicate required data at
synchronization points.
Shared memory architectures -synchronize read/write operations between
tasks.
Designing Parallel Programs
Load Balancing
Load balancing refers to the practice of distributing approximately equal
amounts of work among tasks
so that all tasks are kept busy all of the time.
It can be considered a minimization of task idle time.
Load balancing is important to parallel programs for performance
reasons. For example, if all tasks are subject to a barrier
synchronization point, the slowest task will determine the overall
performance.
How to Achieve Load Balance:
Equally partition the work each task receives
For array/matrix operations where each task performs similar
work, evenly distribute the data set among the tasks.
For loop iterations where the work done in each iteration
is similar, evenly distribute the iterations across the tasks.
If a heterogeneous mix of machines with varying performance
characteristics are being used, be sure to use some type of performance
analysis tool to detect any load imbalances. Adjust work accordingly.
Use dynamic work assignment
Certain classes of problems result in load imbalances even if data
is evenly distributed among tasks:
Sparse arrays - some tasks will have actual data to work on
while others have mostly "zeros".
Adaptive grid methods - some tasks may need to refine their
mesh while others don't.
N-body simulations - where some particles may migrate
to/from their original task domain to another task's; where
the particles owned by some tasks require more work than
those owned by other tasks.
When the amount of work each task will perform is intentionally
variable, or is unable to be predicted, it may be helpful to use
a scheduler - task pool approach. As each task finishes
its work, it queues to get a new piece of work.
It may become necessary to design an algorithm which detects and handles
load imbalances as they occur dynamically within the code.
Designing Parallel Programs
Granularity
Computation / Communication Ratio:
In parallel computing, granularity is a qualitative measure of the ratio
of computation to communication.
Periods of computation are typically separated from periods of
communication by synchronization events.
Fine-grain Parallelism:
Relatively small amounts of computational work are done between
communication events
Low computation to communication ratio
Facilitates load balancing
Implies high communication overhead and less opportunity for
performance enhancement
If granularity is too fine it is possible that the overhead
required for communications and synchronization between tasks
takes longer than the computation.
Coarse-grain Parallelism:
Relatively large amounts of computational work are done between
communication/synchronization events
High computation to communication ratio
Implies more opportunity for performance increase
Harder to load balance efficiently
Which is Best?
The most efficient granularity is dependent on the algorithm and the
hardware environment in which it runs.
In most cases the overhead associated with communications and
synchronization is high relative to execution speed
so it is advantageous to have coarse granularity.
Fine-grain parallelism can help reduce overheads due to load imbalance.
Designing Parallel Programs
I/O
The Bad News:
I/O operations are generally regarded as inhibitors to parallelism.
I/O operations require orders of magnitude more time than memory operations.
Parallel I/O systems may be immature or not available for all platforms.
In an environment where all tasks see the same file space, write
operations can result in file overwriting.
Read operations can be affected by the file server's ability to handle
multiple read requests at the same time.
I/O that must be conducted over the network (NFS, non-local) can cause
severe bottlenecks and even crash file servers.
The Good News:
Parallel file systems are available. For example:
GPFS: General Parallel File System (IBM)
Lustre: for Linux clusters (Intel)
OrangeFS: Open source parallel file system follow on to Parallel Virtual
File System (PVFS)
PanFS: Panasas ActiveScale File System for Linux clusters (Panasas,
Inc.)
The parallel I/O programming interface specification for MPI has been
available since 1996 as part of MPI-2. Vendor and "free" implementations
are now commonly available.
A few pointers:
Rule #1: Reduce overall I/O as much as possible
If you have access to a parallel file system, use it.
Writing large chunks of data rather than small chunks is usually
significantly more efficient.
Fewer, larger files performs better than many small files.
Confine I/O to specific serial portions of the job, and then use
parallel communications to distribute data to parallel tasks.
For example, Task 1 could read an input file and then communicate
required data to other tasks. Likewise, Task 1 could perform
write operation after receiving required data from all other tasks.
Aggregate I/O operations across tasks - rather than having many tasks
perform I/O, have a subset of tasks perform it.
Designing Parallel Programs
Debugging
Debugging parallel codes can be incredibly difficult, particularly as codes
scale upwards.
The good news is that there are some excellent debuggers available to assist:
Threaded - pthreads and OpenMP
MPI
GPU / accelerator
Hybrid
Livermore Computing users have access to several parallel debugging tools
installed on LC's clusters:
TotalView from RogueWave Software
DDT from Allinea
Inspector from Intel
Stack Trace Analysis Tool (STAT) - locally developed
All of these tools have a learning curve associated with them - some more than
others.
This example demonstrates calculations on 2-dimensional array elements; a
function is evaluated on each array element.
The computation on each array element is independent from other array elements.
The problem is computationally intensive.
The serial program calculates one element at a time in sequential order.
Serial code could be of the form:
do j = 1,n
do i = 1,n
a(i,j) = fcn(i,j)
end do
end do
Questions to ask:
Is this problem able to be parallelized?
How would the problem be partitioned?
Are communications needed?
Are there any data dependencies?
Are there synchronization needs?
Will load balancing be a concern?
Array Processing Parallel Solution 1
The calculation of elements is independent of one another - leads to an
embarrassingly parallel solution.
Arrays elements are evenly distributed so that each process owns a portion of
the array (subarray).
Distribution scheme is chosen for efficient memory access; e.g. unit stride
(stride of 1) through the subarrays. Unit stride maximizes cache/memory usage.
Since it is desirable to have unit stride through the subarrays, the
choice of a distribution scheme depends on the programming language.
See the Block - Cyclic Distributions Diagram
for the options.
Independent calculation of array elements ensures there is no
need for communication or synchronization between tasks.
Since the amount of work is evenly distributed across processes, there should
not be load balance concerns.
After the array is distributed, each task executes the portion of the loop
corresponding to the data it owns. For example, both Fortran (column-major)
and C (row-major) block distributions are shown:
do j = mystart, myend
do i = 1, n
a(i,j) = fcn(i,j)
end do
end do
for i (i = mystart; i < myend; i++) {
for j (j = 0; j < n; j++) {
a(i,j) = fcn(i,j);
}
}
Notice that only the outer loop variables are different from the serial
solution.
One Possible Solution:
Implement as a Single Program Multiple Data (SPMD) model - every task executes
the same program.
Master process initializes array, sends info to worker processes and receives
results.
Worker process receives info, performs its share of computation and sends
results to master.
Using the Fortran storage scheme, perform block distribution of the array.
Pseudo code solution:
red highlights changes for
parallelism.
find out if I am MASTER or WORKER
if I am MASTER
initialize the array
send each WORKER info on part of array it owns
send each WORKER its portion of initial array
receive from each WORKER results
else if I am WORKER
receive from MASTER info on part of array I own
receive from MASTER my portion of initial array
# calculate my portion of array
do j = my first column,my last column
do i = 1,n
a(i,j) = fcn(i,j)
end do
end do
send MASTER results
endif
Example Programs:
MPI Program in C:
MPI Program in Fortran:
Array Processing Parallel Solution 2: Pool of Tasks
The previous array solution demonstrated static load balancing:
Each task has a fixed amount of work to do
May be significant idle time for faster or more lightly loaded
processors - slowest tasks determines overall performance.
Static load balancing is not usually a major concern if all tasks
are performing the same amount of work on identical machines.
If you have a load balance problem (some tasks work faster than
others), you may benefit by using a "pool of tasks"
scheme.
Pool of Tasks Scheme:
Two processes are employed
Master Process:
Holds pool of tasks for worker processes to do
Sends worker a task when requested
Collects results from workers
Worker Process: repeatedly does the following
Gets task from master process
Performs computation
Sends results to master
Worker processes do not know before runtime which portion of array
they will handle or how many tasks they will perform.
Dynamic load balancing occurs at run time: the faster tasks will
get more work to do.
Pseudo code solution:
red highlights changes for
parallelism.
find out if I am MASTER or WORKER
if I am MASTER
do until no more jobs
if request send to WORKER next job
else receive results from WORKER
end do
else if I am WORKER
do until no more jobs
request job from MASTER
receive from MASTER next job
calculate array element: a(i,j) = fcn(i,j)
send results to MASTER
end do
endif
Discussion:
In the above pool of tasks example, each task calculated an individual
array element as a job. The computation to communication ratio is
finely granular.
Finely granular solutions incur more communication overhead in order
to reduce task idle time.
A more optimal solution might be to distribute more work with each job.
The "right" amount of work is problem dependent.
Parallel Examples
PI Calculation
The value of PI can be calculated in a number of ways. Consider the
following method of approximating PI
Inscribe a circle in a square
Randomly generate points in the square
Determine the number of points in the square that are also in the circle
Let r be the number of points in the circle divided by the number of
points in the square
PI ~ 4 r
Note that the more points generated, the better the approximation
Serial pseudo code for this procedure:
npoints = 10000
circle_count = 0
do j = 1,npoints
generate 2 random numbers between 0 and 1
xcoordinate = random1
ycoordinate = random2
if (xcoordinate, ycoordinate) inside circle
then circle_count = circle_count + 1
end do
PI = 4.0*circle_count/npoints
The problem is computationally intensive - most of the time is spent executing
the loop
Questions to ask:
Is this problem able to be parallelized?
How would the problem be partitioned?
Are communications needed?
Are there any data dependencies?
Are there synchronization needs?
Will load balancing be a concern?
PI Calculation Parallel Solution
Another problem that's easy to parallelize:
All point calculations are independent; no data dependencies
Work can be evenly divided; no load balance concerns
No need for communication or synchronization between tasks
Parallel strategy:
Divide the loop into equal portions that can be executed by the pool of tasks
Each task independently performs its work
A SPMD model is used
One task acts as the master to collect results and compute the value of PI
Pseudo code solution:
red highlights changes for
parallelism.
npoints = 10000
circle_count = 0
p = number of tasks
num = npoints/p
find out if I am MASTER or WORKER
do j = 1,num
generate 2 random numbers between 0 and 1
xcoordinate = random1
ycoordinate = random2
if (xcoordinate, ycoordinate) inside circle
then circle_count = circle_count + 1
end do
if I am MASTER
receive from WORKERS their circle_counts
compute PI (use MASTER and WORKER calculations)
else if I am WORKER
send to MASTER circle_count
endif
Example Programs:
MPI Program in C:
MPI Program in Fortran:
Parallel Examples
Simple Heat Equation
Most problems in parallel computing require communication among the tasks.
A number of common problems require communication with "neighbor" tasks.
The heat equation describes the temperature change over time,
given initial temperature distribution and boundary conditions.
A finite differencing scheme is employed to solve the heat equation numerically
on a square region.
The elements of a 2-dimensional array represent the temperature at
points on the square.
The initial temperature is zero on the boundaries and high in the middle.
The boundary temperature is held at zero.
A time stepping algorithm is used.
The calculation of an element is dependent upon neighbor element
values:
A serial program would contain code like:
do iy = 2, ny - 1
do ix = 2, nx - 1
u2(ix, iy) = u1(ix, iy) +
cx * (u1(ix+1,iy) + u1(ix-1,iy) - 2.*u1(ix,iy)) +
cy * (u1(ix,iy+1) + u1(ix,iy-1) - 2.*u1(ix,iy))
end do
end do
Questions to ask:
Is this problem able to be parallelized?
How would the problem be partitioned?
Are communications needed?
Are there any data dependencies?
Are there synchronization needs?
Will load balancing be a concern?
Simple Heat Equation Parallel Solution
This problem is more challenging, since there data dependencies, which require
communications and synchronization.
The entire array is partitioned and distributed as subarrays to all
tasks. Each task owns an equal portion of the total array.
Because the amount of work is equal, load balancing should not be a concern
Determine data dependencies:
interior
elements belonging to a task are independent of other tasks
border
elements are dependent upon
a neighbor task's data, necessitating communication.
Implement as an SPMD model:
Master process sends initial info to workers, and then waits
to collect results from all workers
Worker processes calculate solution within specified number of time steps,
communicating as necessary with neighbor processes
Pseudo code solution:
red highlights changes for parallelism.
find out if I am MASTER or WORKER
if I am MASTER
initialize array
send each WORKER starting info and subarray
receive results from each WORKER
else if I am WORKER
receive from MASTER starting info and subarray
# Perform time steps
do t = 1, nsteps
update time
send neighbors my border info
receive from neighbors their border info
update my portion of solution array
end do
send MASTER results
endif
Example Programs:
MPI Program in C:
MPI Program in Fortran:
Parallel Examples
1-D Wave Equation
In this example, the amplitude along a uniform, vibrating string is
calculated after a specified amount of time has elapsed.
The calculation involves:
the amplitude on the y axis
i as the position index along the x axis
node points imposed along the string
update of the amplitude at discrete time steps.
The equation to be solved is the one-dimensional wave equation:
Note that amplitude will depend on previous timesteps (t, t-1) and
neighboring points (i-1, i+1).
Questions to ask:
Is this problem able to be parallelized?
How would the problem be partitioned?
Are communications needed?
Are there any data dependencies?
Are there synchronization needs?
Will load balancing be a concern?
1-D Wave Equation Parallel Solution
This is another example of a problem involving data dependencies. A parallel
solution will involve communications and synchronization.
The entire amplitude array is partitioned and distributed as subarrays to all
tasks. Each task owns an equal portion of the total array.
Load balancing: all points require equal work, so the points should
be divided equally
A block decomposition would have the work partitioned into the number
of tasks as chunks, allowing each task to own mostly contiguous data points.
Communication need only occur on data borders. The larger the block size
the less the communication.
Implement as an SPMD model:
Master process sends initial info to workers, and then waits
to collect results from all workers
Worker processes calculate solution within specified number of time steps,
communicating as necessary with neighbor processes
Pseudo code solution:
red highlights changes for parallelism.
find out number of tasks and task identities
#Identify left and right neighbors
left_neighbor = mytaskid - 1
right_neighbor = mytaskid +1
if mytaskid = first then left_neigbor = last
if mytaskid = last then right_neighbor = first
find out if I am MASTER or WORKER
if I am MASTER
initialize array
send each WORKER starting info and subarray
else if I am WORKER`
receive starting info and subarray from MASTER
endif
#Perform time steps
#In this example the master participates in calculations
do t = 1, nsteps
send left endpoint to left neighbor
receive left endpoint from right neighbor
send right endpoint to right neighbor
receive right endpoint from left neighbor
#Update points along line
do i = 1, npoints
newval(i) = (2.0 * values(i)) - oldval(i)
+ (sqtau * (values(i-1) - (2.0 * values(i)) + values(i+1)))
end do
end do
#Collect results and write to file
if I am MASTER
receive results from each WORKER
write results to file
else if I am WORKER
send results to MASTER
endif
Photos/Graphics have been
created by the author, created by other LLNL employees,
obtained from non-copyrighted, government or public domain (such as
http://commons.wikimedia.org/) sources,
or used with the permission of authors from other presentations and
web pages.
History: These materials have evolved from the following
sources, which are no longer maintained or available.
Tutorials located in the Maui High Performance Computing Center's
"SP Parallel Programming Workshop".
Tutorials located at the Cornell Theory Center's "Education and
Training" web page.
Serial Computing:
