Unit-II

Parallel Computing

Introduction

Traditionally, software has been written for serial computation:o To be run on a single computer having a single Central Processing Unit (CPU);o A problem is broken into a discrete series of instructions.o Instructions are executed one after another.o Only one instruction may execute at any moment in time.

For example:

In the simplest sense, parallel computing is the simultaneous use of multiple computeresources to solve a computational problem:

o To be run using multiple CPUso A problem is broken into discrete parts that can be solved concurrently

o Each part is further broken down to a series of instructionso Instructions from each part execute simultaneously on different CPUs

For example:

The compute resources might be:

o A single computer with multiple processors;o An arbitrary number of computers connected by a network;o A combination of both.

The computational problem should be able to:o Be broken apart into discrete pieces of work that can be solved simultaneously;o Execute multiple program instructions at any moment in time;o Be solved in less time with multiple compute resources than with a single compute

resource.

Uses for 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 manyareas of science and engineering:

o Atmosphere, Earth, Environmento Physics - applied, nuclear, particle,

condensed matter, high pressure, fusion,photonics

o Bioscience, Biotechnology, Geneticso Chemistry, Molecular Sciences

o Geology, Seismologyo Mechanical Engineering - from

prosthetics to spacecrafto Electrical Engineering, Circuit

Design, Microelectronicso Computer Science,

Mathematics

Industrial and Commercial: Today, commercial applications provide an equal orgreater driving force in the development of faster computers. These applications requirethe processing of large amounts of data in sophisticated ways. For example:

o Databases, data miningo Oil explorationo Web search engines, web based

business serviceso Medical imaging and diagnosiso Pharmaceutical design

o Financial and economic modelingo Management of national and multi-national

corporationso Advanced graphics and virtual reality,

particularly in the entertainment industryo Networked video and multi-media

technologieso Collaborative work environments

Why Use Parallel Computing?

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 problems: Many problems are so large and/or complex that it is impracticalor impossible to solve them on a single computer, especially given limited computermemory. For example:

o "Grand Challenge" problems requiring PetaFLOPS and PetaBytes of computingresources.

o Web search engines/databases processing millions of transactions per second

Provide concurrency: A single compute resource can only do one thing at a time.Multiple computing resources can be doing many things simultaneously. For example,the Access Grid provides a global collaboration network where people from around theworld can meet and conduct work "virtually".

Use of non-local resources: Using compute resources on a wide area network, or eventhe Internet when local compute resources are scarce. For example:

o SETI@home over 1.3 million users, 3.2 million computers in nearly every countryin the world.

o Folding@home uses over 450,000 cpus globally

Limits to serial computing: Both physical and practical reasons pose significantconstraints to simply building ever faster serial computers:

o Transmission speeds - the speed of a serial computer is directly dependent uponhow fast data can move through hardware. Absolute limits are the speed of light(30 cm/nanosecond) and the transmission limit of copper wire (9 cm/nanosecond).Increasing speeds necessitate increasing proximity of processing elements.

o Limits to miniaturization - processor technology is allowing an increasing numberof transistors to be placed on a chip. However, even with molecular or atomic-levelcomponents, a limit will be reached on how small components can be.

o Economic limitations - it is increasingly expensive to make a single processorfaster. Using a larger number of moderately fast commodity processors to achievethe same (or better) performance is less expensive.

o Current computer architectures are increasingly relying upon hardware levelparallelism to improve performance: Multiple execution units Pipelined instructions Multi-core

Concepts related to parallel Computing

von Neumann Architecture

Named after the Hungarian mathematician John von Neumann who first authored thegeneral requirements for an electronic computer in his 1945 papers.

Since then, virtually all computers have followed this basic design, differing from earliercomputers which were programmed through "hard wiring".

o Comprised of four main components: Memory Control Unit Arithmetic Logic Unit Input/Output

o Read/write, random access memory is usedto store both program instructions and data Program instructions are coded data

which tell the computer to dosomething

Data is simply information to beused by the program

o Control unit fetches instructions/data frommemory, decodes the instructions and thensequentially coordinates operations toaccomplish the programmed task.

o Aritmetic Unit performs basic arithmeticoperations

o Input/Output is the interface to the humanoperator

Well, parallel computers still follow this basic design, just multiplied in units. The basic,fundamental architecture remains the same.

Flynn's Classical Taxonomy

There are different ways to classify parallel computers. For example: 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 andData. Each of these dimensions can have only one of two possible states: Single orMultiple.

The matrix below defines the 4 possible classifications according to Flynn:

S I S D

Single Instruction, Single Data

S I M D

Single Instruction, Multiple Data

M I S D

Multiple Instruction, Single Data

M I M D

Multiple Instruction, Multiple Data

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 and even today, the most common type of

computer Examples: older generation mainframes, minicomputers and

workstations; most modern day PCs.

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:

o Processor Arrays: Connection Machine CM-2, MasPar MP-1 & MP-2, ILLIAC IVo 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.

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 actual examples of this class of parallel computer have ever existed. One is the

experimental Carnegie-Mellon C.mmp computer (1971). Some conceivable uses might be:

o multiple frequency filters operating on a single signal streamo 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

Parallel Terminology

Like everything else, parallel computing has its own "jargon". Some of the more commonlyused terms associated with parallel computing are listed below. Most of these will bediscussed 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 multipleCPUs/processors/cores. 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 wereincorporated 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 containingmultiple cores. The nomenclature is confused at times. Wonder why?

Task

A logically discrete section of computational work. A task is typically a program orprogram-like set of instructions that is executed by a processor. A parallel programconsists of multiple tasks running on multiple processors.

Pipelining

Breaking a task into steps performed by different processor units, with inputs streamingthrough, much like an assembly line; a type of parallel computing.

Shared Memory

From a strictly hardware point of view, describes a computer architecture where allprocessors have direct (usually bus based) access to common physical memory. In aprogramming sense, it describes a model where parallel tasks all have the same"picture" of memory and can directly address and access the same logical memorylocations regardless of where the physical memory actually exists.

Symmetric Multi-Processor (SMP)

Hardware architecture where multiple processors share a single address space andaccess to all resources; shared memory computing.

Distributed Memory

In hardware, refers to network based memory access for physical memory that is notcommon. As a programming model, tasks can only logically "see" local machine memoryand must use communications to access memory on other machines where other tasksare executing.

Communications

Parallel tasks typically need to exchange data. There are several ways this can beaccomplished, such as through a shared memory bus or over a network, however theactual event of data exchange is commonly referred to as communications regardless ofthe method employed.

Synchronization

The coordination of parallel tasks in r eal time, very often associated withcommunications. Often implemented by establishing a synchronization point within anapplication where a task may not proceed further until another task(s) reaches the sameor logically equivalent point.

Synchronization usually involves waiting by at least one task, and can therefore cause aparallel application's wall clock execution time to increase.

Granularity

In parallel computing, granularity is a qualitative measure of the ratio of computation tocommunication.

Coarse: relatively large amounts of computational work are done betweencommunication events

Fine: relatively small amounts of computational work are done betweencommunication 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'sperformance.

Parallel Overhead

The amount of time required to coordinate parallel tasks, as opposed to doing usefulwork. Parallel overhead can include factors such as:

Task start-up time Synchronizations Data communications Software overhead imposed by parallel compilers, libraries, tools, operating

system, etc. Task termination time

Massively Parallel

Refers to the hardware that comprises a given parallel system - having many processors.The meaning of "many" keeps increasing, but currently, the largest parallel computerscan be comprised of processors numbering in the hundreds of thousands.

Embarrassingly Parallel

Solving many similar, but independent tasks simultaneously; little to no need forcoordination between the tasks.

Scalability

Refers to a parallel system's (hardware and/or software) ability to demonstrate aproportionate increase in parallel speedup with the addition of more processors.Factors that contribute to scalability include:

Hardware - particularly memory-cpu bandwidths and network communications Application algorithm Parallel overhead related Characteristics of your specific application and coding

Parallel Computer Memory Architectures

Shared Memory

General Characteristics:

Shared memory parallel computers vary widely, but generally have in common theability 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. Shared memory machines can be divided into two main classes based upon memory

access times: UMA and NUMA.

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 aboutthe 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

Disadvantages:

Primary disadvantage is the lack of scalability between memory and CPUs. Adding moreCPUs can geometrically increases traffic on the shared memory-CPU path, and forcache coherent systems, geometrically increase traffic associated with cache/memorymanagement.

Programmer responsibility for synchronization constructs that ensure "correct" accessof global memory.

Expense: it becomes increasingly difficult and expensive to design and produce sharedmemory machines with ever increasing numbers of processors.

Distributed Memory

General Characteristics:

Like shared memory systems, distributed memory systems vary widely but share acommon characteristic. Distributed memory systems require a communication networkto connect inter-processor memory.

Processors have their own local memory. Memory addresses in one processor do notmap to another processor, so there is no concept of global address space across allprocessors.

Because each processor has its own local memory, it operates independently. Changesit 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 ofthe 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 can be assimple as Ethernet.

Advantages:

Memory is scalable with the number of processors. Increase the number of processorsand the size of memory increases proportionately.

Each processor can rapidly access its own memory without interference and withoutthe overhead incurred with trying to maintain 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 datacommunication between processors.

It may be difficult to map existing data structures, based on global memory, to thismemory organization.

Non-uniform memory access (NUMA) times

Hybrid Distributed-Shared Memory

The largest and fastest computers in the world today employ both shared anddistributed memory architectures.

The shared memory component can be a cache coherent SMP machine and/or graphicsprocessing units (GPU).

The distributed memory component is the networking of multiple SMP/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 SMP/GPU toanother.

Current trends seem to indicate that this type of memory architecture will continue toprevail and increase at the high end of computing for the foreseeable future.

Advantages and Disadvantages: whatever is common to both shared and distributedmemory architectures.

Parallel Programming Models

Overview

There are several parallel programming models in common use:o Shared Memory (without threads)o Threadso Distributed Memory / Message Passingo Data Parallelo Hybrido Single Program Multiple Data (SPMD)o Multiple Program Multiple Data (MPMD)

Parallel programming models exist as an abstraction above hardware and memoryarchitectures.

Which model to use? This is often a combination of what is available and personalchoice. There is no "best" model, although there certainly are better implementationsof some models over others.

The following sections describe each of the models mentioned above, and also discusssome of their actual implementations.

Shared Memory Model (without threads)

In this programming model, tasks share a common address space, which they read andwrite to asynchronously.

Various mechanisms such as locks / semaphores may be used to control access to theshared memory.

An advantage of this model from the programmer's point of view is that the notion ofdata "ownership" is lacking, so there is no need to specify explicitly the communicationof data between tasks. Program development can often be simplified.

An important disadvantage in terms of performance is that it becomes more difficult tounderstand and manage data locality.

o Keeping data local to the processor that works on it conserves memory accesses,cache refreshes and bus traffic that occurs when multiple processors use thesame data.

o Unfortunately, controlling data locality is hard to understand and beyond thecontrol of the average user.

Implementations:

Native compilers and/or hardware translate user program variables into actual memoryaddresses, which are global. On stand-alone SMP machines, this is straightforward.

On distributed shared memory machines, such as the SGI Origin, memory is physicallydistributed across a network of machines, but made global through specializedhardware and software.

Threads Model

This programming model is a type of shared memory programming. In the threads model of parallel programming, a single process can have multiple,

concurrent execution paths.

Perhaps the most simple analogy thatcan be used to describe threads is theconcept of a single program thatincludes a number of subroutines:

o The main program a.out isscheduled to run by the nativeoperating system. a.out loadsand acquires all of the necessarysystem and user resources to run.

o a.out performs some serialwork, and then creates a numberof tasks (threads) that can bescheduled and run by the operating system concurrently.

o Each thread has local data, but also, shares the entire resources of a.out. Thissaves the overhead associated with replicating a program's resources for eachthread. Each thread also benefits from a global memory view because it sharesthe memory space of a.out.

o 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.

o Threads communicate with each other through global memory (updating addresslocations). This requires synchronization constructs to ensure that more than onethread is not updating the same global address at any time.

o Threads can come and go, but a.out remains present to provide the necessaryshared resources until the application has completed.

Implementations:

From a programming perspective, threads implementations commonly comprise:o A library of subroutines that are called from within parallel source codeo A set of compiler directives imbedded in either serial or parallel source code

In both cases, the programmer is responsible for determining all parallelism.

Threaded implementations are not new in computing. Historically, hardware vendorshave implemented their own proprietary versions of threads. These implementationsdiffered substantially from each other making it difficult for programmers to developportable threaded applications.

Unrelated standardization efforts have resulted in two very different implementationsof threads: POSIX Threads and OpenMP.

POSIX Threadso Library based; requires parallel coding

o Specified by the IEEE POSIX 1003.1c standard (1995).o C Language onlyo Commonly referred to as Pthreads.o Most hardware vendors now offer Pthreads in addition to their proprietary

threads implementations.o Very explicit parallelism; requires significant programmer attention to detail.

OpenMPo Compiler directive based; can use serial codeo Jointly defined and endorsed by a group of major computer hardware and

software vendors. The OpenMP Fortran API was released October 28, 1997. TheC/C++ API was released in late 1998.

o Portable / multi-platform, including Unix and Windows NT platformso Available in C/C++ and Fortran implementationso Can be very easy and simple to use - provides for "incremental parallelism"

Microsoft has its own implementation for threads, which is not related to the UNIXPOSIX standard or OpenMP.

Distributed Memory /Message Passing Model

This model demonstratesthe followingcharacteristics:

o A set of tasks thatuse their own localmemory duringcomputation.Multiple tasks canreside on the samephysical machineand/or across anarbitrary number ofmachines.

o Tasks exchange datathrough communications by sending and receiving messages.

o Data transfer usually requires cooperative operations to be performed by eachprocess. 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. Theprogrammer 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 forprogrammers to develop portable applications.

In 1992, the MPI Forum was formed with the primary goal of establishing a standardinterface for message passing implementations.

Part 1 of the Message Passing Interface (MPI) was released in 1994. Part 2 (MPI-2) wasreleased in 1996.

MPI is now the "de facto" industry standard for message passing, replacing virtually allother message passing implementations used for production work. MPIimplementations exist for virtually all popular parallel computing platforms. Not allimplementations include everything in both MPI1 and MPI2.

Data Parallel Model

The data parallel modeldemonstrates the followingcharacteristics:

o Most of the parallel workfocuses on performingoperations on a data set.The data set is typicallyorganized into a commonstructure, such as anarray or cube.

o A set of tasks workcollectively on the samedata structure, however,each task works on adifferent partition of thesame data structure.

o Tasks perform the sameoperation on their partition of work, for example, "add 4 to every arrayelement".

On shared memory architectures, all tasks may have access to the data structurethrough global memory. On distributed memory architectures the data structure is splitup and resides as "chunks" in the local memory of each task.

Implementations:

Programming with the data parallel model is usually accomplished by writing a programwith data parallel constructs. The constructs can be calls to a data parallel subroutinelibrary or, compiler directives recognized by a data parallel compiler.

Fortran 90 and 95 (F90, F95): ISO/ANSI standard extensions to Fortran 77.o Contains everything that is in Fortran 77o New source code format; additions to character seto Additions to program structure and commandso Variable additions - methods and argumentso Pointers and dynamic memory allocation addedo Array processing (arrays treated as objects) addedo Recursive and new intrinsic functions addedo Many other new features

Implementations are available for most common parallel platforms.

High Performance Fortran (HPF): Extensions to Fortran 90 to support data parallelprogramming.

o Contains everything in Fortran 90o Directives to tell compiler how to distribute data addedo Assertions that can improve optimization of generated code addedo Data parallel constructs added (now part of Fortran 95)

HPF compilers were relatively common in the 1990s, but are no longer commonlyimplemented.

Compiler Directives: Allow the programmer to specify the distribution and alignment ofdata. Fortran implementations are available for most common parallel platforms.

Distributed memory implementations of this model usually require the compiler toproduce object code with calls to a message passing library (MPI) for data distribution.All message passing is done invisibly to the programmer.

Hybrid Model

A hybrid modelcombines more thanone of the previouslydescribedprogramming models.

Currently, a commonexample of a hybridmodel is thecombination of themessage passingmodel (MPI) with thethreads model(OpenMP).

o Threads perform computationally intensive kernels using local, on-node datao Communications between processes on different nodes occurs over the network

using MPI This hybrid model lends itself well to the increasingly common hardware environment

of clustered multi/many-core machines. Another similar and increasingly popular example of a hybrid model is using MPI with

GPU (Graphics Processing Unit) programming.o GPUs perform computationally intensive kernels using local, on-node datao Communications between processes on different nodes occurs over the network

using MPI

SPMD and MPMD

Single Program Multiple Data (SPMD):

SPMD is actually a "high level"programming model that can bebuilt upon any combination ofthe previously mentioned parallelprogramming models.

SINGLE PROGRAM: All tasksexecute their copy of the sameprogram simultaneously. This program can be threads, message passing, data parallelor 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 entireprogram - perhaps only a portion of it.

The SPMD model, using message passing or hybrid programming, is probably the mostcommonly used parallel programming model for multi-node clusters.

Multiple Program Multiple Data (MPMD):

Like SPMD, MPMD is actually a"high level" programming modelthat can be built upon anycombination of the previouslymentioned parallel programmingmodels.

MULTIPLE PROGRAM: Tasks mayexecute different programs simultaneously. The programs can be threads, messagepassing, 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 tofunctional decomposition than domain decomposition (discussed later underPartioning).

Designing Parallel Programs

Automatic vs. Manual Parallelization

Designing and developing parallel programs has characteristically been a very manualprocess. The programmer is typically responsible for both identifying and actuallyimplementing 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 programmerwith converting serial programs into parallel programs. The most common type of toolused to automatically parallelize a serial program is a parallelizing compiler or pre-processor.

A parallelizing compiler generally works in two different ways:o Fully Automatic

o The compiler analyzes the source code and identifies opportunities forparallelism.

o The analysis includes identifying inhibitors to parallelism and possibly acost weighting on whether or not the parallelism would actually improveperformance.

o Loops (do, for) loops are the most frequent target for automaticparallelization.

o Programmer Directedo Using "compiler directives" or possibly compiler flags, the programmer

explicitly tells the compiler how to parallelize the code.o May be able to be used in conjunction with some degree of automatic

parallelization also. 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 importantcaveats that apply to automatic parallelization:

o Wrong results may be producedo Performance may actually degradeo Much less flexible than manual parallelizationo Limited to a subset (mostly loops) of codeo May actually not parallelize code if the 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.

Understand the Problem and the Program

Undoubtedly, the first step in developing parallel software is to first understand theproblem that you wish to solve in parallel. If you are starting with a serial program, thisnecessitates 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.

o Example of Parallelizable Problem:

Calculate the potential energy for each of several thousandindependent conformations of a molecule. When done, find theminimum energy conformation.

o This problem is able to be solved in parallel. Each of the molecular conformationsis independently determinable. The calculation of the minimum energyconformation is also a parallelizable problem.

o Example of a Non-parallelizable Problem:

Calculation of the Fibonacci series (0,1,1,2,3,5,8,13,21,...) by useof the formula:

F(n) = F(n-1) + F(n-2)

o This is a non-parallelizable problem because the calculation of the Fibonaccisequence as shown would entail dependent calculations rather than independent

ones. The calculation of the F(n) value uses those of both F(n-1) and F(n-2).These three terms cannot be calculated independently and therefore, not inparallel.

Identify the program's hotspots:o 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.o Profilers and performance analysis tools can help hereo Focus on parallelizing the hotspots and ignore those sections of the program that

account for little CPU usage. Identify bottlenecks in the program

o Are there areas that are disproportionately slow, or cause parallelizable work tohalt or be deferred? For example, I/O is usually something that slows a programdown.

o May be possible to restructure the program or use a different algorithm to reduceor eliminate unnecessary slow areas

Identify inhibitors to parallelism. One common class of inhibitor is data dependence, asdemonstrated by the Fibonacci sequence above.

Investigate other algorithms if possible. This may be the single most importantconsideration when designing a parallel application.

Take advantage of optimized third party parallel software and highly optimized mathlibraries available from leading vendors (IBM's ESSL, Intel's MKL, AMD's AMCL,etc.).

Partitioning

One of the first steps in designing a parallel program is to break the problem intodiscrete "chunks" of work that can be distributed to multiple tasks. This is known asdecomposition or partitioning.

There are two basic ways to partition computational work among parallel tasks: domaindecomposition and functional decomposition.

Domain Decomposition:

In this type of partitioning, the data associated with a problem is decomposed. Eachparallel task then works on a portion of of the data.

There are different ways to partition data: 0ne Dimensional and two Dimensional

Functional Decomposition:

In this approach, the focus is on the computation that is to be performed rather than onthe data manipulated by the computation. The problem is decomposed according to thework 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 differenttasks. For example:

Ecosystem ModelingEach program calculates the population of a given group, where each group's growthdepends on that of its neighbors. As time progresses, each process calculates its currentstate, then exchanges information with the neighbor populations. All tasks then progress

to calculate the state at the next time step.

Signal ProcessingAn audio signal data set is passed through four distinct computational filters. Each filteris a separate process. The first segment of data must pass through the first filter beforeprogressing to the second. When it does, the second segment of data passes through thefirst filter. By the time the fourth segment of data is in the first filter, all four tasks arebusy.

Climate ModelingEach model component can be thought of as a separate task. Arrows represent exchangesof data between components during computation: the atmosphere model generates windvelocity data that are used by the ocean model, the ocean model generates sea surfacetemperature data that are used by the atmosphere model, and so on.

Combining these two types of problem decomposition is common and natural.

Communications

Who Needs Communications?

The need for communications between tasks depends upon your problem:

You DON'T need communicationso Some types of problems can be decomposed and executed in parallel with

virtually no need for tasks to share data. For example, imagine an imageprocessing operation where every pixel in a black and white image needs to haveits color reversed. The image data can easily be distributed to multiple tasks thatthen act independently of each other to do their portion of the work.

o These types of problems are often called embarrassingly parallel because they areso straight-forward. Very little inter-task communication is required.

You DO need communicationso 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 toknow 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'sinter-task communications:

Cost of communicationso Inter-task communication virtually always implies overhead.o Machine cycles and resources that could be used for computation are instead used

to package and transmit data.o Communications frequently require some type of synchronization between tasks,

which can result in tasks spending time "waiting" instead of doing work.o Competing communication traffic can saturate the available network bandwidth,

further aggravating performance problems. Latency vs. Bandwidth

o latency is the time it takes to send a minimal (0 byte) message from point A topoint B. Commonly expressed as microseconds.

o bandwidth is the amount of data that can be communicated per unit of time.Commonly expressed as megabytes/sec or gigabytes/sec.

o Sending many small messages can cause latency to dominate communicationoverheads. Often it is more efficient to package small messages into a largermessage, thus increasing the effective communications bandwidth.

Visibility of communicationso With the Message Passing Model, communications are explicit and generally

quite visible and under the control of the programmer.o With the Data Parallel Model, communications often occur transparently to the

programmer, particularly on distributed memory architectures. The programmermay not even be able to know exactly how inter-task communications are beingaccomplished.

Synchronous vs. asynchronous communicationso 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.

o Synchronous communications are often referred to as blocking communicationssince other work must wait until the communications have completed.

o Asynchronous communications allow tasks to transfer data independently fromone another. For example, task 1 can prepare and send a message to task 2, andthen immediately begin doing other work. When task 2 actually receives the datadoesn't matter.

o Asynchronous communications are often referred to as non-blockingcommunications since other work can be done while the communications aretaking place.

o Interleaving computation with communication is the single greatest benefit forusing asynchronous communications.

Scope of communicationso 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 beimplemented synchronously or asynchronously.

o Point-to-point - involves two tasks with one task acting as the sender/producer ofdata, and the other acting as the receiver/consumer.

o Collective - involves data sharing between more than two tasks, which are often

specified as being members in a common group, or collective. Some commonvariations (there are more):

Efficiency of communicationso Very often, the programmer will have a choice with regard to factors that can

affect communications performance. Only a few are mentioned here.o 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 givenhardware platform than another.

o What type of communication operations should be used? As mentionedpreviously, asynchronous communication operations can improve overall programperformance.

o Network media - some platforms may offer more than one network forcommunications. Which one is best?

Overhead and Complexity Finally, realize that this is only a partial list of things to consider!!!

Synchronization

Types of Synchronization:

Barriero Usually implies that all tasks are involvedo Each task performs its work until it reaches the barrier. It then stops, or "blocks".o When the last task reaches the barrier, all tasks are synchronized.o 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 / semaphoreo Can involve any number of taskso 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.o The first task to acquire the lock "sets" it. This task can then safely (serially)

access the protected data or code.o Other tasks can attempt to acquire the lock but must wait until the task that owns

the lock releases it.o Can be blocking or non-blocking

Synchronous communication operationso Involves only those tasks executing a communication operationo 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 anacknowledgment from the receiving task that it is OK to send.

o Discussed previously in the Communications section.

Data Dependencies

Definition:

A dependence exists between program statements when the order of statement executionaffects the results of the program.

A data dependence results from multiple use of the same location(s) in storage bydifferent tasks.

Dependencies are important to parallel programming because they are one of theprimary inhibitors to parallelism.

Examples:

Loop carried data dependence

DO 500 J = MYSTART,MYENDA(J) = A(J-1) * 2.0

500 CONTINUE

The value of A(J-1) must be computed before the value of A(J), therefore A(J) exhibits adata 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:

o Distributed memory architecture - task 2 must obtain the value of A(J-1) from task1 after task 1 finishes its computation

o 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:

o Distributed memory architecture - if or when the value of X is communicatedbetween the tasks.

o 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 possiblythe most common target of parallelization efforts.

How to Handle Data Dependencies:

Distributed memory architectures - communicate required data at synchronizationpoints.

Shared memory architectures -synchronize read/write operations between tasks.

Load Balancing

Load balancing refers to the practice of distributing work among tasks so that all tasksare 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 determinethe overall performance.

How to Achieve Load Balance:

Equally partition the work each task receiveso For array/matrix operations where each task performs similar work, evenly

distribute the data set among the tasks.o For loop iterations where the work done in each iteration is similar, evenly

distribute the iterations across the tasks.o 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 anyload imbalances. Adjust work accordingly.

Use dynamic work assignmento Certain classes of problems result in load imbalances even if data is evenly

distributed among tasks:o Sparse arrays - some tasks will have actual data to work on while others

have mostly "zeros".o Adaptive grid methods - some tasks may need to refine their mesh while

others don't.o N-body simulations - where some particles may migrate to/from their

original task domain to another task's; where the particles owned by sometasks require more work than those owned by other tasks.

o When the amount of work each task will perform is intentionally variable, or isunable 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.

o It may become necessary to design an algorithm which detects and handles loadimbalances as they occur dynamically within the code.

Granularity

Computation / Communication Ratio:

In parallel computing, granularity is a qualitative measure of the ratio of computation tocommunication.

Periods of computation are typically separated from periods of communication bysynchronization events.

Fine-grain Parallelism:

Relatively small amounts of computational work are done between communicationevents

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 betweencommunication/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 hardwareenvironment in which it runs.

In most cases the overhead associated with communications and synchronization is highrelative to execution speed so it is advantageous to have coarse granularity.

Fine-grain parallelism can help reduce overheads due to load imbalance.

I/O

The Bad News:

I/O operations are generally regarded as inhibitors to parallelism 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:o GPFS: General Parallel File System for AIX (IBM)o Lustre: for Linux clusters (Oracle)o PVFS/PVFS2: Parallel Virtual File System for Linux clusters

(Clemson/Argonne/Ohio State/others)o PanFS: Panasas ActiveScale File System for Linux clusters (Panasas, Inc.)o HP SFS: HP StorageWorks Scalable File Share. Lustre based parallel file system

(Global File System for Linux) product from HP 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:

o Rule #1: Reduce overall I/O as much as possibleo If you have access to a parallel file system, investigate using it.o Writing large chunks of data rather than small packets is usually significantly

more efficient.o 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 couldread an input file and then communicate required data to other tasks. Likewise,Task 1 could perform write operation after receiving required data from all othertasks.

o Use local, on-node file space for I/O if possible. For example, each node mayhave /tmp filespace which can used. This is usually much more efficient thanperforming I/O over the network to one's home directory.

Limits and Costs of Parallel Programming

Amdahl's Law:

Amdahl's Law states that potentialprogram speedup is defined by thefraction of code (P) that can beparallelized:

1speedup = -----

---1 -

P

If none of the code can beparallelized, P = 0 and the speedup =1 (no speedup).

If all of the code is parallelized, P = 1and the speedup is infinite (intheory).

If 50% of the code can beparallelized, maximum speedup = 2,meaning the code will run twice asfast.

Introducing the number of processorsperforming the parallel fraction ofwork, the relationship can bemodeled by:

1speedup = -----

-------P

+ S---N

where P = parallel fraction, N =number of processors and S = serial

fraction.

It soon becomes obvious that thereare limits to the scalability ofparallelism. For example:

speedup----------

----------------------N P = .50

P = .90 P = .99----- -------

------- -------10 1.82

5.26 9.17100 1.98

9.17 50.251000 1.99

9.91 90.9910000 1.99

9.91 99.02100000 1.999.99 99.90

However, certain problems demonstrate increased performance by increasing theproblem 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 timestep. This results in four times the number of grid points and twice the number of timesteps. 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 scalablethan problems with a fixed percentage of parallel time.

Complexity:

In general, parallel applications are much more complex than corresponding serialapplications, perhaps an order of magnitude. Not only do you have multiple instructionstreams 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 ofthe software development cycle:

o Designo Codingo Debuggingo Tuningo Maintenance

Adhering to "good" software development practices is essential when when workingwith parallel applications - especially if somebody besides you will have to work withthe software.

Portability:

Thanks to standardization in several APIs, such as MPI, POSIX threads, HPF andOpenMP, 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 parallelprograms. 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 ofdetails, sometimes to the point of requiring code modifications in order to effectportability.

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 parallelcode 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, dueto the need to replicate data and for overheads associated with parallel support librariesand subsystems.

For short running parallel programs, there can actually be a decrease in performancecompared to a similar serial implementation. The overhead costs associated with settingup the parallel environment, task creation, communications and task termination cancomprise a significant portion of the total execution time for short runs.

Scalability:

The ability of a parallel program's performance to scale is a result of a number ofinterrelated factors. Simply adding more machines is rarely the answer.

The algorithm may have inherent limits to scalability. At some point, adding moreresources causes performance to decrease. Most parallel solutions demonstrate thischaracteristic at some point.

Hardware factors play a significant role in scalability. Examples:o Memory-cpu bus bandwidth on an SMP machineo Communications network bandwidtho Amount of memory available on any given machine or set of machineso Processor clock speed

Parallel support libraries and subsystems software can limit scalability independent ofyour application.

Performance Analysis and Tuning

As with debugging, monitoring and analyzing parallel program execution is significantlymore of a challenge than for serial programs.

A number of parallel tools for execution monitoring and program analysis are available. Some are quite useful; some are cross-platform also. Some starting points:

o LC's "Supported Software and Computing Tools" web pages at:computing.llnl.gov/code/content/software_tools.php

o A dated, but potentially useful LC whitepaper on the subject of "HighPerformance Tools and Technologies" describes a large number of tools, and anumber of performance related topics applicable to code developers. Find it at:computing.llnl.gov/tutorials/performance_tools/HighPerformanceToolsTechnologiesLC.pdf.

o Performance Analysis Tools Tutorial Work remains to be done, particularly in the area of scalability.

Parallel Examples

Array Processing

This example demonstrates calculations on 2-dimensional array elements, with thecomputation on each array element beingindependent from other array elements.

The serial program calculates one element at atime in sequential order.

Serial code could be of the form:

do j = 1,ndo i = 1,na(i,j) = fcn(i,j)

end doend do

The calculation of elements is independent ofone another - leads to an embarrassingly parallelsituation.

The problem should be computationallyintensive.

Array ProcessingParallel Solution 1

Arrays elements are distributed so that eachprocessor owns a portion of an array (subarray).

Independent calculation of array elementsensures there is no need for communicationbetween tasks.

Distribution scheme is chosen by other criteria,e.g. unit stride (stride of 1) through thesubarrays. Unit stride maximizes cache/memoryusage.

Since it is desirable to have unit stride throughthe subarrays, the choice of a distributionscheme depends on the programming language.See the Block - Cyclic Distributions Diagramfor the options.

After the array is distributed, each task executesthe portion of the loop corresponding to the data

it owns. For example, with Fortran blockdistribution:

do j = mystart, myenddo i = 1,na(i,j) = fcn(i,j)

end doend do

Notice that only the outer loop variables aredifferent from the serial solution.

One Possible Solution:

Implement as a Single Program Multiple Data (SPMD) model. 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.

Methodical Design of Parallel AlgorithmsThere is no simple recipe for designing parallel algorithms. However, it can

benefited from a methodological approach that maximizes the range of options, thatprovides mechanisms for evaluating alternatives, and that reduces the cost ofbacktracking from wrong choices. The design methodology allows the programmer tofocus on machine-independent issues such as concurrency in the early stage ofdesign process, and machine-special aspects of design are delayed until late in thedesign process. As suggested by Ian Foster, this methodology organizes the designprocess into four distinct stages [12]: partitioning communication agglomeration mapping

The first two stages seek to develop concurrent and scalable algorithms, and the lasttwo stages focus on locality and performance-related issues as summarized below:PartitioningIt refers to decomposing of the computational activities and the data on which itoperates into several small tasks. The decomposition of the data associated with aproblem is known as domain/data decomposition, and the decomposition of

computation into disjoint tasks is known as functional decomposition.CommunicationIt focuses on the flow of information and coordination among the tasks that arecreated during the partitioning stage. The nature of the problem and thedecomposition method determine the communication pattern among thesecooperative tasks of a parallel program. The four popular communication patternscommonly used in parallel programs are: local/global, structured/unstructured,static/dynamic, and synchronous/asynchronous.Agglomeration

In this stage, the tasks and communication structure defined in the first two stages areevaluated in terms of performance requirements and implementation costs. Ifrequired, tasks are grouped into larger tasks to improve performance or to reducedevelopment costs. Also, individual communications may be bundled into a supercommunication. This will help in reducing communication costs by increasingcomputation and communication granularity, gaining flexibility in terms of scalabilityand mapping decisions, and reducing software-engineering costs.MappingIt is concerned with assigning each task to a processor such that it maximizesutilization of system resources (such as CPU) while minimizing the communicationcosts. Mapping decisions can be taken statically (at compile-time/before programexecution) or dynamically at runtime by load-balancing methods as discussed inVolume 1 of this book [8] and Chapter 17.Several grand challenging applications have been built using the above method-ology (refer to Part III, Algorithms and Applications, for further details on thedevelopment of real-life applications using the above methodology).1.7 Parallel Programming ParadigmsIt has been widely recognized that parallel applications can be classi_ed into somewell de_ned programming paradigms. A few programming paradigms are used re-peatedly to develop many parallel programs. Each paradigm is a class of algorithmsthat have the same control structure [19].Experience to date suggests that there are a relatively small number of para-digms underlying most parallel programs [7]. The choice of paradigm is determinedby the available parallel computing resources and by the type of parallelism inher-ent in the problem. The computing resources may de_ne the level of granularitythat can be e_ciently supported on the system. The type of parallelism reectsSection 1.7 Parallel Programming Paradigms 17the structure of either the application or the data and both types may exist in dif-ferent parts of the same application. Parallelism arising from the structure of theapplication is named as functional parallelism. In this case, di_erent parts of theprogram can perform di_erent tasks in a concurrent and cooperative manner. Butparallelism may also be found in the structure of the data. This type of parallelismallows the execution of parallel processes with identical operation but on di_erent

parts of the data.1.7.1 Choice of ParadigmsMost of the typical distributed computing applications are based on the very pop-ular client/server paradigm. In this paradigm, the processes usually communicatethrough Remote Procedure Calls (RPCs), but there is no inherent parallelism inthis sort of applications. They are instead used to support distributed services, andthus we do not consider this paradigm in the parallel computing area.In the world of parallel computing there are several authors which present aparadigm classi_cation. Not all of them propose exactly the same one, but we cancreate a superset of the paradigms detected in parallel applications.For instance, in [22], a theoretical classi_cation of parallel programs is presentedand broken into three classes of parallelism:1. processor farms, which are based on replication of independent jobs;2. geometric decomposition, based on the parallelisation of data structures; and3. algorithmic parallelism, which results in the use of data ow.Another classi_cation was presented in [19]. The author studied several parallelapplications and identi_ed the following set of paradigms:1. pipelining and ring-based applications;2. divide and conquer;3. master/slave; and4. cellular automata applications, which are based on data parallelism.The author of [23] also proposed a very appropriate classi_cation. The problemswere divided into a few decomposition techniques, namely:1. Geometric decomposition: the problem domain is broken up into smaller do-mains and each process executes the algorithm on each part of it.2. Iterative decomposition: some applications are based on loop execution whereeach iteration can be done in an independent way. This approach is imple-mented through a central queue of runnable tasks, and thus corresponds tothe task-farming paradigm.18 Parallel Programming Models and Paradigms Chapter 13. Recursive decomposition: this strategy starts by breaking the original probleminto several subproblems and solving these in a parallel way. It clearly corre-sponds to a divide and conquer approach.4. Speculative decomposition: some problems can use a speculative decompositionapproach: N solution techniques are tried simultaneously, and (N-1) of themare thrown away as soon as the _rst one returns a plausible answer. In somecases this could result optimistically in a shorter overall execution time.5. Functional decomposition: the application is broken down into many distinctphases, where each phase executes a di_erent algorithm within the same prob-lem. The most used topology is the process pipelining.In [15], a somewhat di_erent classi_cation was presented based on the temporalstructure of the problems. The applications were thus divided into:

1. synchronous problems, which correspond to regular computations on regulardata domains;2. loosely synchronous problems, that are typi_ed by iterative calculations ongeometrically irregular data domains;3. asynchronous problems, which are characterized by functional parallelism thatis irregular in space and time; and4. embarrassingly parallel applications, which correspond to the independentexecution of disconnected components of the same program.Synchronous and loosely synchronous problems present a somehow di_erent syn-chronization structure, but both rely on data decomposition techniques. Accordingto an extensive analysis of 84 real applications presented in [14], it was estimatedthat these two classes of problems dominated scienti_c and engineering applicationsbeing used in 76 percent of the applications. Asynchronous problems, which arefor instance represented by event-driven simulations, represented 10 percent of thestudied problems. Finally, embarrassingly parallel applications that correspond tothe master/slave model, accounted for 14 percent of the applications.The most systematic de_nition of paradigms and application templates was pre-sented in [6]. It describes a generic tuple of factors which fully characterizes a par-allel algorithm including: process properties (structure, topology and execution),interaction properties, and data properties (partitioning and placement). That clas-si_cation included most of the paradigms referred so far, albeit described in deeperdetail.To summarize, the following paradigms are popularly used in parallel program-ming:_ Task-Farming (or Master/Slave)_ Single Program Multiple Data (SPMD)Section 1.7 Parallel Programming Paradigms 19_ Data Pipelining_ Divide and Conquer_ Speculative Parallelism1.7.2 Task-Farming (or Master/Slave)The task-farming paradigm consists of two entities: master and multiple slaves. Themaster is responsible for decomposing the problem into small tasks (and distributesthese tasks among a farm of slave processes), as well as for gathering the partialresults in order to produce the _nal result of the computation. The slave processesexecute in a very simple cycle: get a message with the task, process the task, andsend the result to the master. Usually, the communication takes place only betweenthe master and the slaves.Task-farming may either use static load-balancing or dynamic load-balancing.In the _rst case, the distribution of tasks is all performed at the beginning of thecomputation, which allows the master to participate in the computation after eachslave has been allocated a fraction of the work. The allocation of tasks can be done

once or in a cyclic way. Figure 1.4 presents a schematic representation of this _rstapproach.The other way is to use a dynamically load-balanced master/slave paradigm,which can be more suitable when the number of tasks exceeds the number of avail-able processors, or when the number of tasks is unknown at the start of the ap-plication, or when the execution times are not predictable, or when we are dealingwith unbalanced problems. An important feature of dynamic load-balancing is theability of the application to adapt itself to changing conditions of the system, notjust the load of the processors, but also a possible recon_guration of the systemresources. Due to this characteristic, this paradigm can respond quite well to thefailure of some processors, which simpli_es the creation of robust applications thatare capable of surviving the loss of slaves or even the master.At an extreme, this paradigm can also enclose some applications that are basedon a trivial decomposition approach: the sequential algorithm is executed simulta-neously on di_erent processors but with di_erent data inputs. In such applicationsthere are no dependencies between di_erent runs so there is no need for communi-cation or coordination between the processes.This paradigm can achieve high computational speedups and an interesting de-gree of scalability. However, for a large number of processors the centralized controlof the master process can become a bottleneck to the applications. It is, however,possible to enhance the scalability of the paradigm by extending the single masterto a set of masters, each of them controlling a di_erent group of process slaves.1.7.3 Single-Program Multiple-Data (SPMD)The SPMD paradigm is the most commonly used paradigm. Each process executesbasically the same piece of code but on a di_erent part of the data. This involves20 Parallel Programming Models and Paradigms Chapter 1Masterdistribute tasksSlave 1 Slave 2 Slave 3 Slave 4TerminateCollectResultscommunicationsFigure 1.4 A static master/slave structure.the splitting of application data among the available processors. This type of par-allelism is also referred to as geometric parallelism, domain decomposition, or dataparallelism. Figure 1.5 presents a schematic representation of this paradigm.Many physical problems have an underlying regular geometric structure, withspatially limited interactions. This homogeneity allows the data to be distributeduniformly across the processors, where each one will be responsible for a de_nedspatial area. Processors communicate with neighbouring processors and the com-munication load will be proportional to the size of the boundary of the element,

while the computation load will be proportional to the volume of the element. Itmay also be required to perform some global synchronization periodically amongall the processes. The communication pattern is usually highly structured and ex-tremely predictable. The data may initially be self-generated by each process ormay be read from the disk during the initialization stage.SPMD applications can be very e_cient if the data is well distributed by theprocesses and the system is homogeneous. If the processes present di_erent work-loads or capabilities, then the paradigm requires the support of some load-balancingscheme able to adapt the data distribution layout during run-time execution.This paradigm is highly sensitive to the loss of some process. Usually, the lossSection 1.7 Parallel Programming Paradigms 21of a single process is enough to cause a deadlock in the calculation in which noneof the processes can advance beyond a global synchronization point.Distribute DataCalculate Calculate Calculate CalculateExchange Exchange Exchange ExchangeCalculate Calculate Calculate CalculateCollect ResultsFigure 1.5 Basic structure of a SPMD program.1.7.4 Data PipeliningThis is a more _ne-grained parallelism, which is based on a functional decompositionapproach: the tasks of the algorithm, which are capable of concurrent operation,are identi_ed and each processor executes a small part of the total algorithm. Thepipeline is one of the simplest and most popular functional decomposition para-digms. Figure 1.6 presents the structure of this model.Processes are organized in a pipeline { each process corresponds to a stage of thepipeline and is responsible for a particular task. The communication pattern canbe very simple since the data ows between the adjacent stages of the pipeline. Forthis reason, this type of parallelism is also sometimes referred to as data ow paral-lelism. The communication may be completely asynchronous. The e_ciency of thisparadigm is directly dependent on the ability to balance the load across the stagesof the pipeline. The robustness of this paradigm against recon_gurations of thesystem can be achieved by providing multiple independent paths across the stages.This paradigm is often used in data reduction or image processing applications.1.7.5 Divide and ConquerThe divide and conquer approach is well known in sequential algorithm develop-ment. A problem is divided up into two or more subproblems. Each of thesesubproblems is solved independently and their results are combined to give the _-nal result. Often, the smaller problems are just smaller instances of the original22 Parallel Programming Models and Paradigms Chapter 1Process 1 Process 2 Process 3Phase A Phase B Phase C

Input OutputFigure 1.6 Data pipeline structure.problem, giving rise to a recursive solution. Processing may be required to dividethe original problem or to combine the results of the subproblems. In parallel divideand conquer, the subproblems can be solved at the same time, given su_cient par-allelism. The splitting and recombining process also makes use of some parallelism,but these operations require some process communication. However, because thesubproblems are independent, no communication is necessary between processesworking on di_erent subproblems.We can identify three generic computational operations for divide and conquer:split, compute, and join. The application is organized in a sort of virtual tree: someof the processes create subtasks and have to combine the results of those to producean aggregate result. The tasks are actually computed by the compute processes atthe leaf nodes of the virtual tree. Figure 1.7 presents this execution.main problemsub-problemssplitjoinFigure 1.7 Divide and conquer as a virtual tree.The task-farming paradigm can be seen as a slightly modi_ed, degenerated formof divide and conquer; i.e., where problem decomposition is performed before tasksare submitted, the split and join operations is only done by the master process andSection 1.8 Programming Skeletons and Templates 23all the other processes are only responsible for the computation.In the divide and conquer model, tasks may be generated during runtime andmay be added to a single job queue on the manager processor or distributed throughseveral job queues across the system.The programming paradigms can be mainly characterized by two factors: de-composition and distribution of the parallelism. For instance, in geometric paral-lelism both the decomposition and distribution are static. The same happens withthe functional decomposition and distribution of data pipelining. In task farm-ing, the work is statically decomposed but dynamically distributed. Finally, in thedivide and conquer paradigm both decomposition and distribution are dynamic.1.7.6 Speculative ParallelismThis paradigm is employed when it is quite di_cult to obtain parallelism throughany one of the previous paradigms. Some problems have complex datadependencies,which reduces the possibilities of exploiting the parallel execution. In these cases,an appropriate solution is to execute the problem in small parts but use somespeculation or optimistic execution to facilitate the parallelism.In some asynchronous problems, like discrete-event simulation [17], the systemwill attempt the look-ahead execution of related activities in an optimistic assump-

tion that such concurrent executions do not violate the consistency of the problemexecution. Sometimes they do, and in such cases it is necessary to rollback to someprevious consistent state of the application.Another use of this paradigm is to employ di_erent algorithms for the sameproblem; the _rst one to give the _nal solution is the one that is chosen.1.7.7 Hybrid ModelsThe boundaries between the paradigms can sometimes be fuzzy and, in some ap-plications, there could be the need to mix elements of di_erent paradigms. Hybridmethods that include more than one basic paradigm are usually observed in somelarge-scale parallel applications. These are situations where it makes sense to mix

data and task parallelism simultaneously or in di_erent parts of the same program.