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Copied From：https://computing.llnl.gov/tutorials/parallel_comp/

 Author: Blaise Barney, Lawrence Livermore National Laboratory UCRL-MI-133316

 Abstract

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:
• Multiple functional units (L1 cache, L2 cache, branch, prefetch, decode, floating-point, graphics processing (GPU), integer, etc.)
• Multiple execution units/cores
 IBM BG/Q Compute Chip with 18 cores (PU) and 16 L2 Cache units (L2)

• Networks connect multiple stand-alone computers (nodes) to make larger parallel computer clusters.

• For example, the schematic below shows a typical LLNL parallel computer cluster:
• Each compute node is a multi-processor parallel computer in itself
• Multiple compute nodes are networked together with an Infiniband network
• Special purpose nodes, also multi-processor, are used for other purposes

• The majority of the world's large parallel computers (supercomputers) are clusters of hardware produced by a handful of (mostly) well known vendors.

Source: Top500.org

 Overview

## Why Use Parallel Computing?

The Real World is Massively Parallel:

 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: "Grand Challenge Problems" (en.wikipedia.org/wiki/Grand_Challenge) requiring PetaFLOPS and PetaBytes of computing resources.
• Example: Web search engines/databases processing millions of transactions every second

• PROVIDE CONCURRENCY:
• A single compute resource can only do one thing at a time. Multiple compute resources can do many things simultaneously.
• Example: Collaborative Networks provide a global venue where people from around the world can meet and conduct work "virtually".

• TAKE ADVANTAGE OF NON-LOCAL RESOURCES:
• Using compute resources on a wide area network, or even the Internet when local compute resources are scarce or insufficient. Two examples below, each of which has over 1.7 million contributors globally (May 2018):
• Example: SETI@home (setiathome.berkeley.edu)
• Example: Folding@home (folding.stanford.edu)

• 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 thatparallelism 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.

• The race is already on for Exascale Computing!
• Exaflop = 1018 calculations per second

Source: Top500.org

 Overview

## Who is Using Parallel Computing?

Science and Engineering:
• 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:  Atmosphere, Earth, Environment Physics - applied, nuclear, particle, condensed matter, high pressure, fusion, photonics Bioscience, Biotechnology, Genetics Chemistry, Molecular Sciences Geology, Seismology Mechanical Engineering - from prosthetics to spacecraft Electrical Engineering, Circuit Design, Microelectronics Computer Science, Mathematics Defense, Weapons

Industrial and Commercial:

• 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 Artificial Intelligence (AI) 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 Oil exploration

Global Applications:

• Parallel computing is now being used extensively around the world, in a wide variety of applications.

Source: Top500.org

 Click on images below for larger version

Source: Top500.org

 Concepts and Terminology

## von Neumann Architecture

• 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 sequentiallycoordinates 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)

• So what? Who cares?
• 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 andData 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
• Examples:
• Processor Arrays: Thinking Machines CM-2, MasPar MP-1 & MP-2, ILLIAC IV
• 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?

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.

The amount of time required to coordinate parallel tasks, as opposed to doing useful work. Parallel overhead can include factors such as:
• Synchronizations
• Data communications
• Software overhead imposed by parallel languages, libraries, operating system, etc.

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
• 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 = .95 P = .99 ----- ------- ------- ------- ------- 10 1.82 5.26 6.89 9.17 100 1.98 9.17 16.80 50.25 1,000 1.99 9.91 19.62 90.99 10,000 1.99 9.91 19.96 99.02 100,000 1.99 9.99 19.99 99.90 

"Famous" qoute: You can spend a lifetime getting 95% of your code to be parallel, and never achieve better than 20x speedup no matter how many processors you throw at it!

• However, certain problems demonstrate increased performance by increasing the problem size. For example:   2D Grid Calculations 85 seconds 85% Serial fraction 15 seconds 15% 

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:

  2D Grid Calculations 680 seconds 97.84% Serial fraction 15 seconds 2.16% 

• 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 and weak scaling.

• Strong scaling:
• The total problem size stays fixed as more processors are added.
• Goal is to run the same problem size faster
• Perfect scaling means problem is solved in 1/P time (compared to serial)

• Weak scaling:
• The problem size per processor stays fixed as more processors are added. The total problem size is proportional to the number of processors used.
• Goal is to run larger problem in same amount of time
• Perfect scaling means problem Px runs in same time as single processor run

• 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. This is a common situation with many parallel applications.

• 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)

• 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.

• 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.

• 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.

• 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:
• 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

• 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.

• 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 are common, but not discussed here:

 Parallel Programming Models

## Distributed Memory / Message Passing Model

• 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 athttp://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.

 Parallel Programming Models

## Data Parallel Model

• 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 global data structure can be split up logically and/or physically across tasks.

Implementations:

• Currently, there are several relatively popular, and sometimes developmental, parallel programming implementations based on the Data Parallel / PGAS model.

• Coarray Fortran: a small set of extensions to Fortran 95 for SPMD parallel programming. Compiler dependent. More information: https://en.wikipedia.org/wiki/Coarray_Fortran

• 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 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 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
• 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?

 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. These types of problems are often calledembarrassingly parallel - little or no communications are required. 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. 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 2-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:

• 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
• Oftentimes, the programmer has choices 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 fabric - different platforms use different networks. Some networks perform better than others. Choosing a platform with a faster network may be an option.

• 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:

• dependence exists between program statements when the order of statement execution affects the results of the program.

• 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.

Examples:

• Loop carried data dependence   DO J = MYSTART,MYEND A(J) = A(J-1) * 2.0 END DO 

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

• 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.

 Designing Parallel Programs

• 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.

• 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 - particles may migrate across task domains requiring more work for some 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 receives a new piece from the work queue.

• Ultimately, 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

• 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:

• 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:
• 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.

• For details and getting started information, see:

 Designing Parallel Programs

## Performance Analysis and Tuning

 Parallel Examples

## Array Processing

• 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 

• 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.

• 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 various ways. Consider the Monte Carlo method of approximating PI:
• Inscribe a circle with radius r in a square with side length of 2r
• The area of the circle is Πr2 and the area of the square is 4r2
• The ratio of the area of the circle to the area of the square is:
Πr2 / 4r2 = Π / 4
• If you randomly generate N points inside the square, approximately
N * Π / 4 of those points (M) should fall inside the circle.
• Π is then approximated as:
N * Π / 4 = M
Π / 4 = M / N
Π = 4 * M / N
• Note that increasing the number of points generated improves 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

• 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 CalculationParallel 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 2-D 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 

• 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 EquationParallel 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:  A(i,t+1) = (2.0 * A(i,t)) - A(i,t-1) + (c * (A(i-1,t) - (2.0 * A(i,t)) + A(i+1,t)))

where c is a constant

• Note that amplitude will depend on previous timesteps (t, t-1) and neighboring points (i-1, i+1).

• 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 EquationParallel 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 `

Example Programs:

• MPI Program in C:

• MPI Program in Fortran:

This completes the tutorial.

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Where would you like to go now?

• Author: Blaise Barney, Livermore Computing.

• A search on the WWW for "parallel programming" or "parallel computing" will yield a wide variety of information.