\section{Introduction}
\label{ch1:1}
-Almost of the software applications are traditionally programmed as a sequential programs according to the Von Neumann report in 1993 \cite{ref50}. The structure of the
-program code is understandable by the human brain as a series of instructions that execute one after the other. From many years until a short time, the users of the sequential applications are moving their thinking towards that these applications must run faster with each new generation of microprocessors. This idea is no longer valid nowadays, because the recent release of the microprocessors have many computing units embedded in one chip and these programs are only run over one computing unit sequentially.
-Consequently, the traditional applications not have improved their performance a lot over the new architectures, whereas the new applications run faster over them in a parallel. The parallel application is executed over all the available computing units at the same time to improve its performance. Furthermore, the concurrency revolution has been referred to the drastically improvement in the performance of the new applications side by side to the new parallel architectures \cite{ref51}. Therefore, parallel applications and parallel architectures are closely tied together. It is hard to think about any of a parallel applications without thinking of the parallel hardware that executing them.
-For example, the energy consumption of the parallel system mainly depends on both of the parallel application and the parallel architecture executing this application. Indeed, the energy consumption model or any measurement system depends on many specifications, some of them are concerting the parallel platform such as the frequency of the processor, power consumption of the processor and communication model. The others are concerting the parallel application such as the computation and communication times of the application.
+Traditionally, almost of the software applications are programmed as a sequential programs according to the Von Neumann report in 1993 \cite{ref50}. The structure of the
+program code is understandable by the human brain as a series of instructions that execute one after the other. From many years until a short time, the users of the sequential applications had moved their thinking towards that these applications must run faster with each new generation of microprocessors. This idea is no longer valid nowadays, because the recent release of the microprocessors have many computing units embedded in one chip and these programs are only run over one computing unit sequentially.
+Consequently, the traditional applications not have improved their performance a lot over the new architectures, whereas the new applications run faster over them in parallel. The parallel application is executed over all the available computing units at the same time to improve its performance. Furthermore, the concurrency revolution has been referred to the drastically improvement in the performance of the new applications side by side to the new parallel architectures \cite{ref51}. Therefore, parallel applications and parallel architectures are closely tied together. It is hard to think about any of parallel applications without thinking of the parallel hardware that executing them.
+For example, the energy consumption of the parallel system mainly depends on both of the parallel application and the parallel architecture executing this application. Indeed, the energy consumption model or any measurement system depends on many specifications, some of them are concerting the parallel hardware architecture such as the frequency of the processor, power consumption of the processor and communication model. The others are concerting the parallel application such as the computation and communication times of the application.
In this work, the iterative parallel applications, which is the most popular type of the parallel applications, are interested and running them over different parallel architectures to optimize their energy consumptions is the main goal.
-As a result, this chapter is aimed to give a brief overview for a parallel hardware architectures, parallel iterative applications and the energy model from the other authors used to measure the energy consumption of these applications.
+As a result, this chapter is aimed to give a brief overview for parallel hardware architectures, parallel iterative applications and the energy model from the other authors used to measure the energy consumption of these applications.
The reminder of this chapter is organized as follows: section \ref{ch1:2} is devoted
to describe the types of parallelism and the types of the parallel platforms. It is also gives some information about the parallel programming models. Section \ref{ch1:3} explains both the synchronous and asynchronous parallel iterative methods and comparing them. Section \ref{ch1:4}, presents the well accepted energy model from the state of the art that can be used to measure the energy consumption of the parallel iterative applications when changing the frequency of the processor. Finally, section \ref{ch1:5} summaries this chapter.
\section{Parallel Computing Architectures}
\label{ch1:2}
-The process of the simultaneous application of the calculations is called the parallel computing.
+The process of the simultaneous execution of the calculations is called the parallel computing.
It has main principle refer to the ability of dividing the large problem into smaller sub-problems that can be solved at the same time \cite{ref2}.
Mainly, solving the sub-problems of the main problem in a parallel computing are carried out on multiple parallel processors.
Indeed, the parallel processors architecture is a computer system composed of many processing elements connected via network model in addition to the software tools required to make the processing units work together \cite{ref1}.
Consequently, parallel computing architecture consist of software and hardware resources.
-The hardware resources are the processing units and the memory model in addition to the network system connecting them. The software resources include the specific operating system, the programming language and the compiler, or the runtime libraries. Furthermore, parallel computing can have different levels of parallelism, which can perform in software or hardware. There are five types of parallelism as follows:
+The hardware resources are the processing units and memory model in addition to the network system connecting them. The software resources include the specific operating system, the programming language and the compiler, or the runtime libraries. Furthermore, parallel computing can have different levels of parallelism, which can perform in software or hardware. There are five types of parallelism as follows:
\begin{itemize}
-\item \textbf{Bit-level parallelism (BLP)}: The appearance of very-large-scale integration (VLSI) in 1970s has been considered the first approach towards the parallel computing. It is used to increase the number of bits in word size being processed by a processor as in the figure~\ref{fig:ch1:1}. Year after year, the number of bits is increased starting from 4-bit microprocessors reaching until 64 bit microprocessors . For example, the recent x86-64 architecture becomes the most familiar architecture nowadays. Therefore, the biggest word size is given more parallelism level and thus less instructions to be executed by the processor at the same time.
+\item \textbf{Bit-level parallelism (BLP)}: The appearance of very-large-scale integration (VLSI) in 1970s has been considered the first approach towards the parallel computing. It is used to increase the number of bits in word size being processed by a processor as in the figure~\ref{fig:ch1:1}. For many successive years, the number of bits is increased starting from 4-bit microprocessors reaching until 64 bit microprocessors . For example, the recent x86-64 architecture becomes the most familiar architecture nowadays. Therefore, the biggest word size gives more parallelism level and thus less instructions to be executed by the processor at the same time.
\begin{figure}[h!]
\centering
\label{fig:ch1:1}
\end{figure}
-\item \textbf{Data-level parallelism (DLP)}:Data parallelism is the process of distributing the data vector between different parallel processors and each one performs the same operation on its data sub-vector. Therefore, many arithmetic operations can be performed on the same data vector in a simultaneous manner. This type of parallelism can be used in many programs, especially from the area of scientific computing. Usually, data-parallel operations are only provided for arrays operations, see figure \ref{fig:ch1:2}. As an example about the applications of this type of parallelism are the vectors multiplication, image and signal processing.
+\item \textbf{Data-level parallelism (DLP)}:Data parallelism is a process of distributing the data vector between different parallel processors and each one performs the same operations on its data sub-vector. Therefore, many arithmetic operations can be performed on the same data vector in a simultaneous manner. This type of parallelism can be used in many programs, especially from the area of scientific computing. Usually, data-parallel operations are only provided for arrays operations, for example see figure \ref{fig:ch1:2}. As an example about the applications of this type of parallelism are vectors multiplication, image and signal processing.
\begin{figure}[h!]
\centering
\item \textbf{Instruction-level parallelism (ILP)}: Generally, the sequential program composed of many instructions. These instructions can be executed in a parallel at the same time, if each of them is independent from the others. In particular, parallelism can be achieved in the instruction level by using pipeline. It means all the independent instructions of the program are overlapped the execution of each others. For example, if we have two instruction $I_1$ and $I_2$, they are independent if there is no control and data dependency between them.
In pipeline stages, the execution of each instruction is divided into multiple steps that can be overlapped with the steps of other instructions by the pipeline hardware unit.
-Figure~\ref{fig:ch1:3} demonstrates four instructions each one has four steps denoted as fetch, decode, execute and write which are implemented in a hardware units by pipeline.
+Figure~\ref{fig:ch1:3} demonstrates four instructions each one has four steps denoted as fetch, decode, execute and write, which are implemented in a hardware units by pipeline.
\begin{figure}[h!]
\centering
\item \textbf{Thread-level parallelism (TLP)}: It is also known as a task-level parallelism.
According to the Moore’s law \cite{ref9}, the processor can have a number of transistors by a double
-each two years to increase the frequency of the processor and thus its performance. Beside that, cache and main memories sizes are must increased together to satisfy this increased.
-This leads to some limits come from two main reasons, the first one is when the cache size is drastically increased leading to a larger access time. The second is related to the big increase in the number of the transistors per CPU can be increased significantly the heat dissipation. As a result, the programmers sub divided their programs into multiple tasks which can be executed in parallel over distributed processors or shared multi-cores processors to improve the performance of the program, see figure~\ref{fig:ch1:4}. Each processor can have a multiple or individual thread dedicated for each task. A thread can be defined as a part of a parallel program which shares processor resources with other threads.
+each two years to increase the frequency of the processor and thus its performance. Besides, cache and main memories sizes are must increased together to satisfy this increased.
+But, this leads to some limits come from two main reasons, the first one is when the cache size is drastically increased leading to a larger access time. The second is related to the big increase in the number of the transistors per CPU that can be increased significantly the heat dissipation. As a result, the programmers subdivided their programs into multiple tasks which can be executed in parallel over distributed processors or shared multi-cores processors to improve the performance of the program, see figure~\ref{fig:ch1:4}. Each processor can has a multiple or individual thread dedicated for each task. A thread can be defined as a part of a parallel program which shares processor resources with other threads.
\begin{figure}[h!]
\centering
Sequential~execution~time = \sum_{i=1}^{N} T_i
\end{equation}
-Whereas, if the tasks are executed synchronously over multiple processing units in a parallel, the execution time of the program is the execution time of the task that has the maximum execution time (the slowest task) as follows:
+Whereas, if the tasks are executed synchronously over multiple processing units in parallel, the execution time of the program is the execution time of the task that has maximum execution time (the slowest task) as follows:
\begin{equation}
\item \textbf{Loop-level parallelism (LLP)}:
-The numerical algorithms and many other algorithms are executed iteratively the same program portion, the computations, using different forms of the loop statements allowed in the programming languages. At each iteration, the program need to scan a large data structure such as an array structure to make the arithmetic calculations. Inside the loop structure, there are many instructions, which are independent or dependent. In a sequential loop execution the $i$ iteration must be executed after the completion of $(i-1)$ iteration.
+The numerical algorithms and many other algorithms are executed iteratively the same program portion, the computations, using different forms of the loop statements allowed in the programming languages. At each iteration, the program need to scan a large data structure such as an array structure to make the arithmetic calculations. Inside the loop structure there are many instructions, which are independent or dependent. In a sequential loop execution the $i$ iteration must be executed after the completion of $(i-1)$ iteration.
While, if each iteration is independent from the others, then all the iterations are distributed over many processors to be executed in a parallel,
-for example see figure\ref{fig:ch1:5}. Thus, this type of a loop is called $parallel~loop$.
+for example see figure\ref{fig:ch1:5}. In the parallel programming languages this type of a loop is called $parallel~loop$.
\begin{figure}[h!]
\centering
The main goal behind using a parallel computers is to solve bigger problem faster.
A collection of processing elements composing them must to work together to perform the final solution of the main problem. However, many different architectures have been proposed
and classified according to the parallelism in the instruction and data
-streams. In 1966, Michel Flynn has been proposed a simple model of categorizing all computers that still useful until know \cite{ref10}. His taxonomy considered the data and the operations performed on this data to produce four types of computer systems as follows:
+streams. In 1966, Michel Flynn has been proposed a simple model of categorizing all computers that still useful until know \cite{ref10}. His taxonomy considered the data and the operations performed on these data to produce four types of computer systems as follows:
\begin{itemize}
-\item \textbf{Single instruction, single data (SISD) stream}: A single processor executes a single instruction stream executing one data stream stored in an individual memory model, see figure \ref{fig:ch1:6}. As an example of this type is the conventional sequential computer according to the Von Neumann model, it is also called the Uniprocessors.
+\item \textbf{Single instruction, single data (SISD) stream}: A single processor executes a single instruction stream executing one data stream stored in an individual memory model, see figure \ref{fig:ch1:6}. As an example of this type is the conventional sequential computer system according to the Von Neumann model, it is also called the Uniprocessors.
\begin{figure}[h!]
\centering
\includegraphics[scale=1]{fig/ch1/sisd.pdf}
\item \textbf{Single instruction, multiple data (SIMD) stream}: All the processors execute the same instructions on different data.
Each processor stores the data in its local memory, the processor communicates with each others typically via simple communication model, see figure \ref{fig:ch1:7}. Many scientific and engineering
applications are suitable to this type of parallel scheme.
-Vector and array processors are a well know examples of this type.
+Vector and array processors are well know examples of this type.
As an example about the applications executed over this architecture are the graphics processing, video compression and medical image analysis applications.
\begin{figure}[h!]
\label{fig:ch1:7}
\end{figure}
-\item \textbf{Multiple instruction, single data (MISD) stream}: Many operations from multiple processing elements are executed over the same data stream. Each processing element has its local memory to store the private multiple program instructions applied to unique global memory data stream as in figure \ref{fig:ch1:8}. While the MISD machine is not commonly used, there are some interesting uses such as the systolic arrays and dataflow machines.
+\item \textbf{Multiple instruction, single data (MISD) stream}: Many operations from multiple processing elements are executed over the same data stream. Each processing element has its local memory to store the private program instructions applied to unique global memory data stream as in figure \ref{fig:ch1:8}. While the MISD machine is not commonly used, there are some interesting uses such as the systolic arrays and dataflow machines.
\begin{figure}[h!]
\centering
At any time, different processing elements may be executing different instructions on different data fragment, see figure \ref{fig:ch1:9}. There are two types of the MIMD machines: the share memory and massage passing MIMD machines.
In the share memory architectures, a processors are communicated via a share memory model, while in the message passing architecture each processor has its own local memory and all processors communicate via communication network model. The multi-core processors, local
clusters and grid systems are an examples for the MIMD machine.
-Many of applications have conducted over this architecture
+Many applications have been conducted over this architecture
such as computer-aided design, computer-aided manufacturing, simulation, modeling, iterative applications and so on.
\begin{figure}[h!]
\begin{itemize}
\item \textbf{Multi-core processors}:
The multi-core processor is a single chip component with two or more processing units.
-These processing units are called cores, which connected with each other via main memory model as in the figure \ref{fig:ch1:10}. Each individual core has its cache memory to store its data and execute different data or instructions stream in a parallel. Moreover, each core can have one or more threads to execute a specific programming task as shown in the thread-level parallelism. Historically, the multi-cores of the CPU began as two-core processors, with the number of cores approximately doubling with each semiconductor process generation \cite{ref12}. The very quick improvements in the performance and thus the increase in the number of cores is devoted in a graphical processing unit (GPU). A current exemplar of GPU is the NVIDIA GeForce TITAN Z with 5700 cores in 2015 \cite{ref17}. While the general-purpose microprocessors (CPU) has less number of the cores, for example the TILE-MX processor from Tilera has 100 cores in the same year \cite{ref16}.
+These processing units are called cores, which connected with each other via main memory model as in the figure \ref{fig:ch1:10}. Each individual core has its cache memory to store its data and execute different data or instructions stream in parallel. Moreover, each core can have one or more threads to execute a specific programming task as shown in the thread-level parallelism. Historically, the multi-cores of the CPU began as two-core processors, with increase in the number of cores approximately by double with each semiconductor process generation \cite{ref12}. The very quick improvements in the performance and thus the increase in the number of cores is devoted in graphical processing unit (GPU). A current exemplar of GPU is the NVIDIA GeForce TITAN Z with 5700 cores in 2015 \cite{ref17}. While the general-purpose microprocessors (CPU) has less number of the cores, for example the TILE-MX processor from Tilera has 100 cores in the same year \cite{ref16}.
For more details about the multi-core processors see \cite{ref15}.
\begin{figure}[h!]
\item \textbf{Local Cluster}:
is generally collection of independent computers that are connected
to each other via standard network switches and cables, which is a high speed
-local area networks (LAN) with low latency and big bandwidth. Moreover, each node is distributed from each other and it is communicated with other nodes using distributed massage passing model. All the nodes in the cluster must be controlled by one node called the master node, which is a specific node handles the scheduling and management of the other nodes as shown in the figure \ref{fig:ch1:11}. Usually, the hardware specifications of all nodes are homogeneous in term of the computing power and memory and it is also called tightly-coupled fashion. Also, each computing node in the cluster has the same copy of the operating system. See \cite{ref18, ref19} for more information about the cluster and its applications.
+local area networks (LAN) with low latency and big bandwidth. Moreover, each node is distributed from each other and it communicates with other nodes using distributed massage passing model. All the nodes in the cluster must be controlled by one node called the master node, which is a specific node uses to handle the scheduling and management of the other nodes as shown in the figure \ref{fig:ch1:11}. Usually, the hardware specifications of all nodes are homogeneous in term of the computing power and memory and thus it is called tightly-coupled fashion. Also, each computing node in the cluster has the same copy of the operating system. See \cite{ref18, ref19} for more information about the cluster and its applications.
\begin{figure}[h!]
\centering
\item \textbf{Grid (Distributed clusters)}:
Grid is a collection of local computing clusters from different sites connected via wide area network (WAN), which can be appeared virtually to the benefit users as a complete computing system \cite{ref20}.
-In particular, different local clusters composing the grid are geographically far away from each others. Usually, each local cluster composed from homogeneous nodes, which are different from the nodes of the others cluster located in different sites. These nodes can be different in the hardware and software specifications such as the computing power, memory, operating system, local network latency and bandwidth. Figure \ref{fig:ch1:12} presents an example of the grid composed from three heterogeneous local clusters located in a different sites which are connected throw wide area network. Furthermore, the grid can be referred to an infrastructure applies the integration and the collaboration by using a collection of different computers, networks, databases servers , and scientific devices belong to many companies and universities. Therefore, wide heterogeneous computing resources are allowed to many users simultaneously. While the only bottleneck of the grid is the high latency communications between the nodes from different sites. The grid is also called the loosely-coupled fashion platform. However, the fault tolerance is required to guarantee the process of sending and receiving the messages between the computing nodes and thus keeps all the messages from the lost.
+In particular, different local clusters composing the grid are geographically far away from each others. Usually, each local cluster composed from homogeneous nodes, which are different from the nodes of the others cluster located in different sites. These nodes can be different in the hardware and software specifications such as the computing power, memory, operating system, local network latency and bandwidth. Figure \ref{fig:ch1:12} presents an example of the grid composed of three heterogeneous local clusters located in different sites which are connected throw wide area network. Furthermore, the grid can be referred to an infrastructure applies the integration and the collaboration by using a collection of different computers, networks, databases servers and scientific devices belong to many companies and universities. Therefore, wide heterogeneous computing resources are allowed to many users simultaneously. While the only bottleneck of the grid is the high latency communications between the nodes from different sites. The grid is also called the loosely-coupled fashion platform. However, the fault tolerance is required to guarantee the process of sending and receiving the messages between the computing nodes and thus keeps all the messages from the lost.
\begin{figure}[h!]
\centering
the parallel programming languages are divided into two main types,
which is the shared and the distributed programming models. Moreover, these two types are divided into two subcategories according to the support level for the number of computing units composing them.
Figure \ref{fig:ch1:14} presents this classification hierarchy of the parallel programming
-models. It is also show three parallel languages examples for each subcategory.
+models. It is also showed three parallel languages examples for each subcategory.
\begin{figure}[h!]
popular implementations of MPI dedicated for grid computing. It is used
as an extended version for MPI, which implements a fault tolerance
\cite{ref52}. In this work, both of MPI and MPICH programming libraries
- are used for programming our algorithms and applications which called
- inside both Fortran and C programming languages.
+ have used for programming our algorithms and applications which called
+ inside both of Fortran and C programming languages.
\item \textbf{PVM} \cite{ref25} is for Parallel Virtual Machine, which is a collection
- of software tools and libraries to allows users working over a
+ of software tools and libraries to allow users working over a
heterogeneous set of machines to operate as a single high performance
parallel platform. It is dedicated for a group of machine that are
distributed and heterogeneous in the operating system environments.
communication model which is applied effectively over distributed memory architectures.
The primary goal of using
BLACS is mapping a liner set or processors or any distributed machines into
- a two dimensional array or grid, which is offer an easy tool for building a
+ a two dimensional array or grid, which offers an easy tool for building a
linear algebra applications.
\end{itemize}
\begin{itemize}
\item \textbf{Gridsolve} \cite{ref28} is the first middleware for grid and
high performance computing that offers a good tool to solve a complex
- scientific applications using distinct distributed machines. It applied the
+ scientific applications using distinct distributed machines. It applies the
fault tolerance and load balancing features to ensure the reliability of the
applications when running over a geographically distributed resources.
It works with different programming languages such as C,C++, Java and Fortran.
shared memory parallel programs. It can be used with programming languages such
as C, C++ and Fortran to support different types of shared memory platforms
such as multi-core processors.
- OpenMP implements multi-threading, which is a method of parallel programming
+ OpenMP uses multi-threading, which is a method of parallel programming
that organized by using master thread to control a set of slave threads. Each
thread can be executed in parallel by allocating it to a processor.
Moreover, OpenMP can be used with MPI to support hybrid platforms that have
\item \textbf{Cilk} \cite{ref13,ref35} is a linguistic and runtime technology for algorithmic
multi-threaded programming originally developed at MIT.
It is allowed the programmer to focus on building the program in a structural way
- to discover the inherent parallelism. Many specification are used in Cilk
+ to discover the inherent parallelism. Many specifications are used in Cilk
such as the load balancing, synchronization and communication protocols.
The difference between OpenMP and TBB, is the latter uses a task-based scheduling
mechanism. Furthermore, TBB is more popular with C++ programming language than
others languages. It is designed to work with any compiler environments, and thus
- it is easily ported to a new platform. Consequently, TBB has been ported to a
+ it is easily ported to a new platform. Hence, TBB has been ported to a
different types of operating systems and processors. While, it has limited
support to vector processing architecture and then it connected with OpenMP
and Cilk to support this platform.
\item \textbf{GPU programming models}
\begin{itemize}
\item \textbf{CUDA} \cite{ref37} Modern graphical processing units (GPUs) have been increasing chip-level
- parallelism. Current NVIDIA GPUs are many-core processor having thousands
+ parallelism. Current NVIDIA GPUs are many-cores processor having thousands
of core. According to this massively cores parallelism, the NVIDIA in 2007 developed
a parallel programming language called CUDA , which is for Compute Unified Device
Architecture. A CUDA program has two parts, the first one is called a host which is a
set of threads that execute sequentially over the CPU. The second part is called the
- kernels, which are a set of a threads that can be executed in a parallel over the GPU.
+ kernels, which are a set of threads that can be executed in parallel over the GPU.
\item \textbf{OpenCL}\cite{ref38} is for Open Computing Language. It is a parallel
programming language dedicated for heterogeneous platform composed
- of CPUs and GPUs. The first release is initially developed by Apple
+ of CPUs and GPUs. The first release initially developed by Apple
in 2008. Functions executed on an OpenCL device is called kernel,
which can be portably executes on any computing hardware such as CPU or GPU cores.
- This parallel programming language can support the homogeneous shared memory
- platforms and the multi-core processors, by using one core for control
+ This parallel programming language supports the homogeneous shared memory
+ platforms and the multi-core processors by using one core for control
and the others for computing.
\item \textbf{HLSL} \cite{ref39} is for High Level Shading Language, is the shader
\end{equation}
Where $A$ is a two dimensional matrix of size $N \times N$, $x$ is the unknown vector,
-and $b$ is a vector of constant, each of size $N$ . There are two types of solution methods for solving this linear system.
+and $b$ is a vector of constant, each of size $N$. There are two types of solution methods for solving this linear system.
The first method is called \textbf{Direct methods}, which is a finite number of steps depending on the
size of the linear system to give the exact solution. If the problem size is very big this methods are expensive or their
solutions are impossible in some cases. The second type is called \textbf{Iterative methods}, which is computed
\end{algorithm}
-The sequential iterative algorithm at each iteration computes the value of the relative error, which is called the residual that denoted as $R$. This error value is the maximum difference between the data components of vectors of the last two successive iterations as follows:
+The sequential iterative algorithm at each iteration computes the value of the relative error, which is called the residual that denoted as $R$. This error value is the maximum difference between the data components of the vectors of the last two successive iterations as follows:
\begin{equation}
\label{eq:res}
\subsection{Synchronous Parallel Iterative method}
\label{ch1:3:1}
The sequential iterative algorithm \ref{sia}, can be parallelized by executing it on many computing units. To solve this algorithm on $M$ computing units, first the elements of the problem vector $X$ must be subdivided into $M$ sub-vectors, $X^k=(X_1^k,\dots,X_M^k)$.
-Each sub-vector can be solved independently one computing units as follows:
+Each sub-vector can be solved independently on one computing unit as follows:
\begin{equation}
\label{eq:subvector}
\end{algorithm}
-
-
-
-The algorithm \ref{spia}, represents the synchronous parallel iterative algorithm. In contrast to
-sequential iterative algorithm, algorithm \ref{spia}, stops its iterations when the convergence condition is satisfied. It computes the residual value $R$ as follows:
+The algorithm \ref{spia}, represents the synchronous parallel iterative algorithm. Similarly to
+the sequential iterative algorithm \ref{spia}, this algorithm stops its iterations when the convergence condition is satisfied and it computes the residual value $R$ as follows:
\begin{equation}
\label{eq:res_syn}
R = \max_{i=1, \dots, M} (\max_{j=1, \dots, m}\abs{X_{ij}^{(k+1)} - X_{ij}^k})
\end{equation}
This algorithm need to satisfy some convergence condition which is called the global convergence condition. In order to detect the global convergence overall computing units, first we need to compute
-at each iteration the local residual and store it in the local variable at the computing unit $i$. Then at the end of each iteration, all the local residuals from $M$ computing units must be reduce to one maximum value represented by the global residual, which is represent the global maximum errors overall maximum local errors from $M$ computing units. Where $m$ is the size of the $i$ sub-vector.
+at each iteration the local residual and store it in the local variable at the computing unit $i$. Then at the end of each iteration, all the local residuals from $M$ computing units must be reduced to one maximum value represented by the global residual, which represents the global maximum errors overall maximum local errors from $M$ computing units. Where $m$ is the size of the $i$ sub-vector.
For example, in MPI this operation is directly applied using a high level communication procedure called \textit{AllReduce}. The goal of this communication procedure is to apply the reduction operation on all local variables computed by the computing units.
\end{figure}
-In synchronous iterative algorithm, computing processors needs to communicate with each other to
+In synchronous iterative algorithm, computing processors needs to communicate with each others to
exchange data at each iteration. Algorithm \ref{spia} can be used synchronous iterations and synchronous communications and denoted as \textbf{SISC} model. At each iteration, the computing processor waits until
-it has receive all the data computed at the previous iteration from the other processors to perform the next iteration. This type of communication model used if there are a dependencies between the parallel tasks. Figure \ref{fig:ch1:15}, shows that using SICS model in a heterogeneous platform may results in a big periods of the idle times represented by the white dashed spaces between two successive iterations. Indeed, this happens when the fast computing processor waits for the slow ones to finish their iterations to be able to synchronously send its data to them. This operation is wasted a big amount of the computing power of the faster processors and thus their energy consumptions. The increased in the level of the heterogeneity between the computing powers of the computing processors may increased propositionally these idle times.
-For this reason, this algorithm is effectively implemented over a local cluster where a high speed local network is exist to reduce these idle times.
+it has receive all the data computed at the previous iteration from the other processors to perform the next iteration. This type of communication model uses if there are a dependencies between the parallel tasks. Figure \ref{fig:ch1:15}, shows that using SICS model in a heterogeneous platform may results in a big periods of the idle times represented by the white dashed spaces between two successive iterations. Indeed, this happens when the fast computing processor waits for the slow ones to finish their iterations to be able to synchronously send its data to them. This operation wastes a big amount of the computing power of the faster processors and thus their energy consumptions. The increased in the level of the heterogeneity between the computing powers of the computing processors may increased propositionally these idle times.
+Accordingly, this algorithm is effectively implemented over a local cluster where a high speed local network is used to reduce these idle times.
\begin{figure}[h!]
\label{fig:ch1:16}
\end{figure}
-The communications of the synchronous iterative algorithm can be implemented asynchronously. Therefore, this algorithm is called the synchronous iteration and asynchronous
+Furthermore, the communications of the synchronous iterative algorithm can be implemented asynchronously. Therefore, this algorithm is called the synchronous iteration and asynchronous
communication algorithm and denoted as \textbf{SIAC} algorithm. The main principle of this algorithm is to use a synchronized iterations while exchanging the data between the computing units asynchronously.
Moreover, each computing unit not has to wait for its neighbours to receive the data messages
-that its has sent, while it only waits for receiving the data from them. This can be implemented in SISC algorithm by replacing the synchronous send of the messages by asynchronous ones and keeps
+that its has sent, while it only waits for receiving the data from them. This can be implemented in SISC algorithm programmed in MPI by replacing the synchronous send of the messages by asynchronous ones and keeps
the synchronous receive of the data messages. The only advantage of this technique is to reduce the idle times between the iterations by making the communications to overlap partially
with computations, see figure \ref{fig:ch1:16}. The idle times are not totally eliminated because the
-fast computing nodes have to wait for slow ones to send their data messages.
+fast computing nodes still have to wait for slow ones to send their data messages.
Both of the SISC and SIAC algorithms are not tolerate to the loss of data messages. Consequently, if one node is crashed, all the other computing nodes are blocked together and all the system is crashed.
\label{ch1:3:2}
The asynchronous iterations mean that all processors perform their iterations without considering the works of the other processors. Each processor not has to wait for receiving
the data messages from the others processors and continue computing the next iteration depending on its own data received at a specific time. While all processors not have to wait
-for data delivery from each other, there are not existence for the idle times at all between the iterations, see figure \ref{fig:ch1:17}. As shown in this figure, the fast processors can perform more iterations than the others at the same time.
-The asynchronous iterative algorithm uses asynchronous communications and called \textbf{AIAC} algorithm. As same as in SISC algorithm, the AIAC algorithm subdivides the global Vectors $X$ into $M$ sub-vectors between the computing units. The main different between the two algorithm is that these $M$ sub-vectors are not updated at each iteration in the AIAC algorithm because both of the iterations and communications are asynchronous.
-However, there are two mechanisms to update the data vectors in AIAC algorithm:
+for data delivery from each other, there are not existence for the idle times at all between the iterations as in figure \ref{fig:ch1:17}. This figure indicates that the fast processors can perform more iterations than the others at the same time.
+Hence, the asynchronous iterative algorithm uses asynchronous communications is called \textbf{AIAC} algorithm. Likewise the SISC algorithm, the AIAC algorithm subdivides the global Vectors $X$ into $M$ sub-vectors between the computing units. The main different between the two algorithm is that these $M$ sub-vectors are not updated at each iteration in the AIAC algorithm because both of the iterations and communications are asynchronous.
+However, there are two mechanisms to update the data vectors in AIAC algorithm as follows:
\begin{itemize}
\item The local vectors can be updated randomly on the order of $M$ computing units.
This leads to some of these local vectors to not update at a certain time.
\begin{itemize}
\item It prevents the existence of the idle times because each processor not has to wait
- for the others to receive the data messages. Then, no idle times between each two
+ for the others to receive the data messages. Then, there is no idle times between each two
successive iterations.
-\item Less sensitive for the heterogeneous communications and nodes' computing powers. In a
+\item Less sensitive for the heterogeneous communications and nodes' computing powers. In
heterogeneous platform, the fast nodes not have to wait for the slow ones and so it
performs more iterations than them. While in the traditional synchronous iterative
methods, the fast computing nodes perform the same number of iterations as the slow ones
independently.
\item In the distributed grid architecture, the local clusters from different sites are
- connected via slow network with a high latency. The use of the AIAC model reduces the
- delay of sending the data message over such slow network link and thus the performance
+ connected via slow network with a high latency. On the other hand, the use of the AIAC model
+ reduces the delay of sending the data message over such slow network link and thus the performance
of the applications is improved.
\end{itemize}
application is perform infinity number of iterations and then all of the system
is crash.
-\item The application of the asynchronous iterative method requires more iterations compared
+\item The application of an asynchronous iterative method requires more iterations compared
to the synchronous ones to converge when it is executed over the local cluster.
The increase in the number of the iterations may increases proportionally
the execution time of the application.
iterative methods in \cite{ref44,ref45}.
In our works, we are interested to implement both of a synchronous and asynchronous
-iterative methods for solving different problems over local homogeneous cluster, local heterogeneous cluster and distributed grid. Then, the process of optimizing their energy consumptions and performance is the main objective of this work as shown in the coming chapters.
+iterative methods for solving different problems over local homogeneous cluster, local heterogeneous cluster and distributed grid. Accordingly, the process of optimizing their energy consumptions and performance is the main objective of this work as shown in the next chapters.
\section{The energy consumption model of the parallel applications }
The dynamic voltage and frequency scaling technique (\textbf{DVFS}) is a process that is allowed in modern processors to reduce the dynamic
power by scaling down the voltage and frequency. Its main objective is to
-reduce the overall energy consumption~\cite{ref77}. The operational frequency $F$
+reduce the overall energy consumption of the CPU~\cite{ref77}. The operational frequency $F$
depends linearly on the supply voltage $V$ as follows:
\begin{equation}
\label{eq:v}
\end{equation}
-Therefore, the energy consumption of the individual task running over one processor can be computed as follows:
+Therefore, the energy consumption of the individual task running over one processor
+is the sum of both static and dynamic energies that can be computed as follows:
\begin{equation}
\label{eq:Eind}
E_{ind} = E_{dynNew} + E_{static} = S^{-2} \cdot P_{dyn} \cdot T + S \cdot P_{static} \cdot T
\hfill
\end{equation}
-Where $N$ is the number of parallel nodes, $T_i$ for $i=1,\dots,N$ are
+Where $N$ is the number of parallel tasks, $T_i$ for $i=1,\dots,N$ are
the execution times of the sorted tasks. Therefore, $T1$ is
the time of the slowest task, and $S_1$ its scaling factor which should be the
highest because they are proportional to the time values $T_i$.
\item It is not well adapted to a heterogeneous architectures when there are different
types of the processors, which are consumed different dynamic and static powers. Then, this model is
not able to measured the energy consumption of all the parallel system because it depends on
- one value of the static and dynamic powers.
+ one value for each of the static and dynamic powers.
\end{itemize}
Therefore, one of the more important goals of this work is to develop an energy models that
-take into account the communication times in addition to computation times to modelize and measure the energy consumptions of the parallel iterative methods. These models are dedicated to all parallel architectures such as the homogeneous and heterogeneous platforms, which are local or distributed computing clusters.
+take into account the communication times in addition to computation times to modelize and measure the energy consumptions of the parallel iterative methods. These models are dedicated to all parallel architectures such as the homogeneous and heterogeneous platforms, which may be local or distributed computing clusters.
\section{Conclusion}
\label{ch1:5}
-In this chapter, we have presented different types of parallelism levels that can be implemented in software and hardware techniques. Furthermore, the types of the parallel architectures are demonstrated and classified according to how the computing units are connected to a memory model.
+In this chapter, we have presented three sections for describing the parallel hardware architectures, parallel iterative applications and the energy consumption model used to measure the energies of these applications.
+In the first section, different types of parallelism levels that can be implemented in software and hardware techniques have explained. Furthermore, the types of the parallel architectures are demonstrated and classified according to how the computing units are connected to a memory model.
Both of the shared and distributed platforms are demonstrated and depending on them we have categorized the parallel programming models.
-The two types of parallel iterative methods, the synchronous and asynchronous iterative methods, are described. The synchronous iterative methods are well implemented over local homogeneous cluster with a high speed network link, while the asynchronous iterative methods are more conventional to implement over the distributed heterogeneous clusters.
-The energy optimization of running these two types of the parallel iterative methods over distributed platforms is the objective of this work. Consequently, the energy consumption model used for measuring the energy consumption of the parallel applications from the related literature is described. This model cannot be used for all types of parallel architectures. Indeed, it assumes measuring the dynamic power during both communication and computation times, while the processor involved remains idle during the communication times and only consumes the static power. Moreover, it is not well adapted to the heterogeneous architectures when there are different types of the processors, which are consumed different dynamic and static powers.
+In the second section, we have described the two types of parallel iterative methods, the synchronous and asynchronous iterative methods. The synchronous iterative methods are well implemented over local homogeneous cluster with a high speed network link, while the asynchronous iterative methods are more conventional to implement over the distributed heterogeneous clusters.
+Finally in the third section, the energy consumption model used for measuring the energy consumption of the parallel applications from the related literature is described. This model cannot be used for all types of parallel architectures. Indeed, it assumes measuring the dynamic power during both of the communication and computation times, while the processor involved remains idle during the communication times and only consumes the static power. Moreover, it is not well adapted to the heterogeneous architectures when there are different types of the processors, which are consumed different dynamic and static powers.
-However, in the next chapters of this thesis a new energy consumption models are developed, which they use for modeling and measuring the energy consumptions by a parallel iterative methods running on both homogeneous and heterogeneous architectures.
+However, in the next chapters of this thesis a new energy consumption models are developed, which they use for modeling and measuring the energy consumptions by a parallel iterative methods running on both homogeneous and heterogeneous architectures. Furthermore, these energies model use in a methods for optimizing both of the energy consumption and the performance of the iterative message passing applications.
\ No newline at end of file
