Порівняльний аналіз ефективності використання дрібнозернистого та вкладеного паралелізму для збільшення пришвидшення паралельних обчислень у багатоядерних комп’ютерних системах
The article presents a comparative analysis of the effectiveness of using parallelism of varying granularity degrees in modern multicore computer systems using the most popular programming languages and libraries (such as C#, Java, C++, and OpenMP). Based on the performed comparison, the possibiliti...
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Репозитарії
System research and information technologies| _version_ | 1867334422185902080 |
|---|---|
| author | Martell, Valerii Korochkin, Aleksandr Rusanova, Olga |
| author_facet | Martell, Valerii Korochkin, Aleksandr Rusanova, Olga |
| author_institution_txt_mv | [
{
"author": "Valerii Martell",
"institution": "National Technical University of Ukraine \"Igor Sikorsky Kyiv Polytechnic Institute\", Kyiv"
},
{
"author": "Aleksandr Korochkin",
"institution": "National Technical University of Ukraine \"Igor Sikorsky Kyiv Polytechnic Institute\", Kyiv"
},
{
"author": "Olga Rusanova",
"institution": "National Technical University of Ukraine \"Igor Sikorsky Kyiv Polytechnic Institute\", Kyiv"
}
] |
| author_sort | Martell, Valerii |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
| collection | OJS |
| datestamp_date | 2022-10-17T22:12:39Z |
| description | The article presents a comparative analysis of the effectiveness of using parallelism of varying granularity degrees in modern multicore computer systems using the most popular programming languages and libraries (such as C#, Java, C++, and OpenMP). Based on the performed comparison, the possibilities of increasing the efficiency of computations in multicore computer systems by using combinations of medium- and fine-grained parallelism were also investigated. The results demonstrate the high potential efficiency of fine-grained parallelism when organizing intensive parallel computations. Based on these results, it can be argued that, in comparison with more traditional parallelization methods that use medium-grain parallelism, the use of separately fine-grained parallelism can reduce the computation time of a large mathematical problem by an average of 4%. The use of combined parallelism can reduce the computation time of such a problem to 5,5%. This reduction in execution time can be significant when performing very large computations. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2022.2.03 |
| first_indexed | 2025-07-17T10:27:42Z |
| format | Article |
| fulltext |
V. Martell, A. Korochkin, O. Rusanova, 2022
Системні дослідження та інформаційні технології, 2022, № 2 45
UDC 004.438:519.685.8
DOI: 10.20535/SRIT.2308-8893.2022.2.03
COMPARATIVE ANALYSIS OF THE EFFECTIVENESS OF
USING FINE-GRAINED AND NESTED PARALLELISM
TO INCREASE THE SPEEDUP OF PARALLEL COMPUTING
IN MULTICORE COMPUTER SYSTEMS
V. MARTELL, A. KOROCHKIN, O. RUSANOVA
Abstract. The article presents a comparative analysis of the effectiveness of using
parallelism of varying granularity degrees in modern multicore computer systems
using the most popular programming languages and libraries (such as C#, Java,
C++, and OpenMP). Based on the performed comparison, the possibilities of in-
creasing the efficiency of computations in multicore computer systems by using
combinations of medium- and fine-grained parallelism were also investigated. The
results demonstrate the high potential efficiency of fine-grained parallelism when
organizing intensive parallel computations. Based on these results, it can be argued
that, in comparison with more traditional parallelization methods that use medium-
grain parallelism, the use of separately fine-grained parallelism can reduce the com-
putation time of a large mathematical problem by an average of 4%. The use of
combined parallelism can reduce the computation time of such a problem to 5,5%.
This reduction in execution time can be significant when performing very large
computations.
Keywords: multicore computer system, core, thread, tasks, parallelism, granularity,
fork-join, speedup coefficient, fine-grained parallelism, nested parallelism, com-
bined parallelism.
INTRODUCTION
Classical von Neumann architecture is not designed for parallel computing; all
commands execute in one sequence strictly one after another. Each such individ-
ual sequence that operates on the machine at the current time is a process. ISO
9000:2000 [1] defines a process as a set of interconnected and interacting actions
that convert input data into output. A computer program in itself is only a passive
sequence of instructions, while a process is the direct execution of those instruc-
tions.
The concept of process is inextricably linked with the concept of thread. The
execution thread is the smallest unit of processing, the execution of which can be
assigned by the operating system kernel [2]. Implementation of execution threads
and processes in different operating systems differs from each other, but in most
cases, the execution thread is within the process. Multiple threads can exist within
the same process and share resources such as memory, while processes do not
share these resources. In particular, the execution thread hare process instructions
(its code) and its context (the values of the variables they have at any given time).
Thus, in the framework of von Neumann or single-core architecture, paral-
lelism is usually realized by time multiplexing: the processor switches between
different threads. This context switching is called pseudo-parallelism and usually
V. Martell, A. Korochkin, O. Rusanova
ISSN 1681–6048 System Research & Information Technologies, 2022, № 2 46
occurs often for the user to perceive the execution of threads or tasks as simulta-
neous [3]. In such systems, there are effective time schedulers in standby mode
(blocked) [4]. Scheduling is based on the principle of priorities, for example, in
most cases, some user input has a higher priority than some computations, so if
the central processor unit (CPU) receives an input signal, a priority interrupt oc-
curs and the CPU processes its, which allows the user to control most of process,
such as urgently terminate some of them.
However, in the present stage, this approach no longer ensures compliance
with the requirements for computer systems. And with the emergence of multi-
core and multiprocessor architecture, the question arose of the organization of real
parallelism, when at the point of time each individual core or processor performs
its own thread. In multiprocessor and multi-core systems, threads or tasks can run
simultaneously, with each processor or core processing a separate thread at the
same time. The operating systems of such computers are much more complex and
voluminous because, for such architectures to function effectively, their compo-
nents must also exchange data (communicate and synchronize), and do so in a
timely, fast, and with minimal computational downtime. Planners of such operat-
ing systems plan the distribution of captures by the thread of cores both in time
and space [4]. So, even parallel threads are not all the same. In addition to the
level of their priority, you can enter another measure for them – quantitative, one
that is based on the volume of the basic unit in the program.
PROBLEM ANALYSIS AND TASK STATEMENT
Each individual elementary parallel computation in modern multi-core computer
systems (MCS) can be represented as a granule. Depending on how many such
elementary calculations (parallel within the system, but consecutive within one
thread) each thread contains, and how many communications (i.e. interruptions of
parallelism) were conducted between such threads, we can introduce the concept
of “granularity”.
Granularity is a measure of the ratio of the number of calculations performed
in a parallel problem to the number of communications [5]. The degree of granu-
larity varies from fine-grained to coarse-grained.
It should be noted that the granularity classifications available in different
sources differ slightly, especially for coarse- and medium-grained parallelism, so
the following classification will be taken as a basis in this article:
1. Coarse-grained parallelism: each parallel calculation is quite independent
of the others, and requires a relatively rare exchange of information with other
calculations. The units of parallelism are large and independent programs that
include thousands of commands [6].
2. Medium-grained parallelism: units of parallelization are individual proce-
dures that are called in separate threads and include hundreds of commands. It is
usually organized by both the programmer and the optimizing compiler. Most
general-purpose parallel computers are primarily focused on this category of par-
allelism [7].
3. Fine-grained parallelism: each parallel calculation is quite small and ele-
mentary, consists of dozens of commands. Usually, the units that are parallelized
are elements of expressions or individual iterations of a loop. They usually have
Comparative analysis of the effectiveness of using fine-grained and nested parallelism …
Системні дослідження та інформаційні технології, 2022, № 2 47
little or no relationship between the data. The amount of work associated with a
parallel task is low and the work is evenly distributed among the processors.
Hence, fine-grained parallelism facilitates load balancing [8].
The very term “fine-grained parallelism” refers to the simplicity and speed
of any computational action. A characteristic feature of fine-grained parallelism is
the approximate equality of computational intensity and data exchange. This level
of parallelism is often used by the parallelizing (vectorizing) compiler [9], as well
as recently in asynchronous programming. This work focuses on medium- and
fine-grained parallelism.
Fine-grained parallelism has a long history: it is the most “ancient” kind of
parallelism. The development of his theory took place simultaneously with the
development of the theory of successive calculations and is associated with the
name of the already mentioned John von Neumann. His theoretical model of a
calculator with fine-grained parallelism is widely known – “cellular automaton”
[10]. But, when in the process of development of computer technology there were
opportunities and capacities for the organization of full-fledged threads of me-
dium-grained and coarse-grained parallelism, there was some decline in interest in
fine-grained parallelism. However, the decline in interest changed when techno-
logical advances, on the one hand, led to the fact that medium- and coarse-grained
parallels somewhat exhausted their significant development, and on the other
hand allowed to create a unified architecture within which at different stages of
program implementation could move on parallelism of various degree of granu-
larity, i.e. on some parts of programs to use the classical mechanism of threads,
and on others fine-grained parallelisms, like tasks or parallel loops.
Against the background of renewed interest in fine-grained parallelism in
modern programming languages and libraries, along with the tools for organizing
parallel computations by creating a set of classic full-fledged medium-grain
threads, there are tools for computing within fine-grained parallelism. Most often,
these are tools for parallelizing loops or small sets of similar commands.
However, it also led to conflicts in the design stages of modern parallel
software. Currently, there are two opposing approaches to creating the architec-
ture of such software: on the one hand, you can represent the parallel part of the
program in the format of medium-grained structures (classical threads), on the
other hand, all calculations can be represented in the form of small tasks. At the
same time, if we can say that the classical concept of threads is not very suitable
for modern back-end problems, in contrast to the concept of tasks, then in the
field of high-load and intensive scientific calculations, solving classical problems
can be presented using both threads and tasks.
At the same time, given the above-described nature of parallelism in modern
MCS, as well as modern flexible tools for organizing different levels of
parallelism in languages and libraries of parallel programming, we can assume
that there is space and opportunities for effective solving of computational
problems with simultaneous use of both mechanisms. This combination is called
“Nested parallelism”.
Therefore, the purpose of this work is to research the possibilities of improv-
ing the execution time of parallel programs in MCS through the use of fine-
grained parallelism, the optimal combination of medium and fine-grained paral-
lelism (nested parallelism), as well as the use of modern software instruments of
their implementation.
V. Martell, A. Korochkin, O. Rusanova
ISSN 1681–6048 System Research & Information Technologies, 2022, № 2 48
FINE-GRAINED PARALLELISM IMPLEMENTATIONS OVERVIEW
Among the most popular languages and libraries currently used in high-load com-
puting, fine-grained parallelism tools are implemented in the OpenMP library
(which is usually used in combination with C++), Java and C# languages [11–14].
OpenMP
Fine-grained parallelism is represented by a special preprocessor directive
#pragma omp parallel for, which refers to the work-sharing directives. Such
directives are not used only for parallel code execution; they are used for the logi-
cal distribution of a group of threads to implement these control logic constructs.
The #pragma omp for directive informs that when running a loop in parallel
mode, loop iterations must be distributed between a group of threads. Execution
of the following program code:
1. int size=100; //the number of calculation iterations
2. #pragma omp parallel for
3. for(int i = 0; i < size; i++)
4. Calculations();
5. ShowResults();
in the four-processor system would happen as shown in Fig. 1. This distribution is
used by default and is called static scheduling.
Main thread
size = 100
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ShowResults()
Fig. 1. The scheme of distribution loop iterations in parallel threads using OpenMP
OpenMP also provides another, more flexible types of scheduling, such as
dynamic scheduling, runtime scheduling, and guided scheduling. The special sec-
tion is used to set up one of these modes. The following code scheme shows the
format of this section: schedule (algorithm name) num_threads (number of
iterations). This mechanism is used when different iterations perform different
amounts of work and determine whether a thread that has already completed its
iteration will be able to take over part of the work of another thread.
Comparative analysis of the effectiveness of using fine-grained and nested parallelism …
Системні дослідження та інформаційні технології, 2022, № 2 49
When writing more complex parallel programs, one of the key tasks to solve
is the problem of thread synchronization. In OpenMP, implicit barrier synchroni-
zation is at the end of each #pragma omp parallel and parallel for block. There are
also manual synchronization tools, such as barriers that can be created using the
#pragma omp barrier directive.
With writing the parallel program, the second main task that needs to be
figured out is the mutual exclusion problem, which avoids the situation so-called
“race condition”, when a large number of threads will behave unpredictable or be
blocked due to access to the same area of memory, which, for example, contains
some variable (shared resource), which used in all threads. With the large number
of threads created with the application of fine-grained parallelism, this problem is
particularly acute. OpenMP provides the ability to use special nonblocking tools
to solve the problem of mutual exclusion, such as the directive #pragma omp
atomic, as well as modifiers of the directive #pragma omp parallel for: shared,
private, firstprivate, lastprivate or reduction. Manual means of solving the
problem of mutual exclusion are represented by such constructions as locks and
critical sections.
Java
Developers are offered extremely flexible and powerful tools for implementing
fine-grained parallelism based on the Fork-Join model, realized in built-in package
java.util.concurent.
A recursive algorithm is used to implement this model in Java, which
described in the following paragraph:
1. The check on the possibility of dividing the actions of this thread into two
smaller tasks.
2. If the check is successful, the distribution is performed (Fork), by creating
new threads for each new task. In each new thread, the algorithm begins anew.
The thread that performed the distribution is blocked until both created threads
have finished their work, and then it performs the final collection of the result.
3. If the check is not successful (the limit of the so-called “grain of parallel-
ism” is reached), then the calculations are performed in this thread, after which
the connection with the generated thread occurs (Join).
This implementation contains two classes: RecursiveAction and Recur-
siveTask. When it is necessary to calculate a specific numeric value of a large
function (such as the sum of vector elements), it is better to use Recursive Task.
In the case of general operations, the results of which are not a specific number,
RecursiveAction works better. By inheriting these classes and describing the
computer’s own overload, the developer can customize the work to solve a spe-
cific problem, which is extremely effective.
An example of using the RecursiveAction class to implement fine-grained
parallelism in Java organizing a parallel loop as an example is shown in the listing
below:
1 class ParallelFor extends RecursiveAction {
2 private int from, to;
3 volatile final int GRAIN = 25;
4 public ParallelFor(int from, int to) {
5 this.from = from;
6 this.to = to;
7 }
8 protected void compute() {
V. Martell, A. Korochkin, O. Rusanova
ISSN 1681–6048 System Research & Information Technologies, 2022, № 2 50
9 int len = to ‐ from;
10 // Stop condition of main recursion
11 if (len < GRAIN)
12 work(from, to);
13 else {
14 int mid = (from + to) >>> 1;
15 ForkJoinTask<Void> parallelFor1 =
16 = new ParallelFor(from, mid).fork();
17 ForkJoinTask<Void> parallelFor2 =
18 = new ParallelFor(mid, to).fork();
19 parallelFor1.join();
20 parallelFor2.join();
21 }
22 }
23 }
24 // Parallel loop startup is performed using the invoke()
25 // method called on the instance of the ForkJoinPool class
26 ForkJoinPool pool = new ForkJoinPool();
27 pool.invoke(new ParallelFor(from, to));
The variable GRAIN determines the depth of the partition, in other words,
the amount of work, after achieving which, the thread will start to perform it,
rather than making further parallelization. The work() method may contain certain
basic parameterized calculations, which performance is expected from each Fork-
Join task after reaching the maximum depth of parallelization. For example, after
setting the initial values of the variables GRAIN = 25, from = 0, to = 100, we ob-
tain a parallel execution of the loop of 100 iterations discussed in the previous
subsection, in which each of the Fork-Join tasks will receive 25 iterations for
processing. However, unlike OpenMP, the structure of the generated threads and
their control hierarchy will be treelike, as shown in Fig. 2.
Main thread
Iterations 0-99
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Fork() Fork()
Join() Join()Join()Join()
Fig. 2. The scheme of distribution loop iterations in Fork-Join parallelization using Java
Comparative analysis of the effectiveness of using fine-grained and nested parallelism …
Системні дослідження та інформаційні технології, 2022, № 2 51
The resulting structure is more complex than the one in OpenMP. Neverthe-
less, according to the results provided in the next chapter, such an approach to
fine-grained parallelism proved to be no less effective.
C#
C# also provides the ability to implement fine-grained parallelism. All the neces-
sary functionality for this is contained by a static class Sys-
tem.Threading.Tasks.Parallel, namely by its three main methods Paral-
lel.For(), Parallel.ForEach(), Parallel.Invoke() and their various overloads.
Parallel.For and Parallel.ForEach provide parallel execution of for and foreach
loops, respectively. The override methods presented in this class are aimed to
maximize the parameterization of parallelism, depending on the specific task be-
ing implemented.
Each method described above is based on a mechanism similar to the one
used in Java. Nonetheless, it has also been simplified with a mechanism for dele-
gating and anonymous methods. Developers are not required to manually write
the entire recursive part and the regulation of grain parallelism, this is the respon-
sibility of the execution environment. Therefore, in practice, the implementation
of fine-grained parallelism becomes extremely simple and has almost no different
from the classical single-threaded approach.
The following piece of code provides a similar parallelization to the previous
loop of a hundred iterations:
1 Parallel.For(0, 100, i => {
2 Calculation();
3 });
Although parallelization in C# occurs by the very same mechanism as in
OpenMP, through the simplifying, that assures the virtual environment of the
CLR execution, the resulting threads’ structure and their hierarchy of manage-
ment will be similar to that in the OpenMP library.
Also in C# are realized the tools for the organization of fine-grained parallel-
ism manually, similar to corresponding tools in Java. The Task class (Sys-
tem.Threading.Tasks) is responsible for this. The formed tasks can be performed
in one or more threads. The official documentation of this programming language
recommends using them primarily for asynchronous programming. In fact, the
tools for organization parallel loops in C# discussed above are high-level abstrac-
tions constructed using Tasks.
NESTED (COMBINED) PARALLELISM
This approach is based on the use of two types of parallelism in the parallel pro-
gram: medium-grained and fine-grained. The program includes a set of traditional
threads for the number of MCS cores. Each of these threads additionally imple-
ments internal (fine-grained) parallelism by creating subthreads using appropriate
Fork-Join tools. The initial number of traditional threads can be reduced in order
to provide fine-grained parallelism with free processor resources. A parallel
thread interaction scheme for such a program for the test system and the task (dis-
cussed in the next section) implemented by OpenMP tools as an example, can be
represented as shown in Fig. 3.
V. Martell, A. Korochkin, O. Rusanova
ISSN 1681–6048 System Research & Information Technologies, 2022, № 2 52
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Comparative analysis of the effectiveness of using fine-grained and nested parallelism …
Системні дослідження та інформаційні технології, 2022, № 2 53
Support for nested parallelism in OpenMP is enabled manually. There are
two ways to do this:
1. By calling omp_nested true command before compiling the program.
2. By calling omp_set_nested(1) procedure in the program code.
Both methods set the environment variable omp_nested to the value of true.
However, the second method is more preferable because it provides better port-
ability of the code, because there is no guarantee that on computers where the
code will run in the future, will be manually set the appropriate value of the vari-
able omp_nested.
Unlike OpenMP, Java and C# do not require any additional operations to ac-
tivate compiler support for nested parallelism.
EXPERIMENTAL TESTING
Selection a problem for testing
For the most transparent comparative testing, the problem of multiplying two
square matrices of large dimension ( NN * elements of 64-bit type double) was
chosen as an example of a typical problem from the field of high-load computing:
MCMBMA . (1)
Due to the large number of elementary mathematical operations, which can
be differently and in different quantities distributed between threads or tasks, the
program to solve this problem can be properly implemented using all types of
parallelism, while always maintaining high-intensity computations, with minimal
downtime for synchronization and data exchange, which is important for more
transparent comparative performance testing.
In addition, the choice of this problem for comparative testing of different
types of parallelism is also ideal in terms of its coverage of all models of data ex-
change and interaction between threads or tasks. In medium-grained parallelism,
it contains the required fragment of the copy of the shared resource (matrix MC)
between the threads. In fine-grained parallelism, there is an interaction of tasks
without copying shared resources (a direct reference to matrices elements), which
is just more typical for applied implementations of this type of parallelism. And in
nested parallelism, these two approaches of parallel interaction with shared re-
sources are combined. Therefore, it can be argued that this problem contains all
the characteristic cases that occur in solving other common mathematical prob-
lems in parallel programs.
Description of the mathematical model of the test problem
The mathematical algorithm for performing this problem (1) is reduced to N-fold
repetition of the calculation:
N
k
jkkiij cba
1
,, , (2)
where ijijij cba ,, are the corresponding elements of the ith row and jth column of
the matrices MA, MB, MC; i and j lie in the range from 1 to N .
Therefore, the total number of elementary operations that must be performed
to obtain solution (1) is equal to 3N .
V. Martell, A. Korochkin, O. Rusanova
ISSN 1681–6048 System Research & Information Technologies, 2022, № 2 54
With this in mind, the following parallel mathematical algorithm was chosen [15]:
MCMBMA HH , (3)
where H is a rounded up number equal to the quotient of the division PN / and
MAH, HMB are the corresponding rectangular matrices of dimensions H by N
elements of the matrices MA and MB [15].
It is worth noting that in this case, the variable P can be either equal to the
number of cores available in the system (medium-grained parallelism), or be less
than this number (no parallelism, some variants of nested parallelism), or signifi-
cantly larger than it (fine-grained parallelism).
Each thread implements H repetitions of the algorithm (2), while calculating
the Hth part (3) of the total program’s result.
Since this algorithm provides for frequent access to all elements of the MC
matrix from each thread, an important point is that when creating threads, each of
them gets its own instance of this matrix, which eliminates conflicts between
threads for capturing and owning shared resources. However, such copying is
valid only for medium-grained parallelism; for fine-grained and nested
parallelism, such copying does not occur.
Description of the test software and hardware complex
Testing of programs was carried out in two identical MCSs. Their main character-
istics are shown in Table 1.
T a b l e 1 . The main characteristics of the test MCSs
Hardware
Processor AMD Phenom II
Processor architecture K10
Number of cores 6
RAM capacity 8 Gb
RAM type DDR3
Sofrware
Operation system Windows 7
OpenMP version 3.1
C++ compiler MC++ (MSVC)
JVM version 1.8
.NET Framework version 4.7
The software structure is aligned
with the hardware structure (primarily
for medium-grained part of comput-
ing), and it includes both manual and
automatic scalability. The schemati-
cally formed structure of the hardware
and software test complex is shown in
Fig. 4.
The following symbols are in-
troduced into this diagram:
1. )(PE i — the processing ele-
Fig. 4. The test hardware and software
complex schematic structure
Comparative analysis of the effectiveness of using fine-grained and nested parallelism …
Системні дослідження та інформаційні технології, 2022, № 2 55
ment (processor or core). Its index corresponds to the number of this element, and
lies in the range from 1 to P inclusive, where P is the number of all processing
elements in the test system. At the software level, each physical processor ele-
ment corresponds to a software-generated thread.
2. CM — the common (shared) memory (RAM for example), to which each
processor element is connected, and with the help of which they communicate
with each other.
3. I/O - an I/O device that is connected to one of the processor elements (or
to one of the cores, since in fact the processing of I/O signals will ultimately be
processed by one of the physical cores of the system), and which provides input
of initial data and output of results.
4. MA, MB, and MC are matrices that make up the multiplication operation
(1). Moreover, the MA and MB matrices are multipliers and are entered from the
I/O device (for large dimensions, random input is used, the execution time of
which is not taken into account in the overall test result), and the MC matrix is the
result that is output by this device at the end of all calculations (the execution time
measurement is stopped just before the output).
Tests results
Table 2 shows the results of testing parallel programs for the operation of matrix
multiplication for different values of N (dimension of matrices). Presented the
execution time of programs that were built with:
using medium-grained parallelism through the thread mechanism;
using fine-grained parallelism through the parallel loops and/or fork-join
mechanisms described in the previous section;
using nested (combined) parallelism, when each thread additionally uses
parallel processing through the parallel loops and/or fork-join constructs.
Based on the actual time indicators obtained, the acceleration coefficients
(speedup coefficients) of the considered programs are calculated. The speedup
coefficient of a parallel program is the ratio of the execution time of a program
without parallelism on one computing core to the execution time of a similar pro-
gram with parallelism on P computing cores and shows how much the program
execution time is reduced in a parallel system [15]. Calculated using the
formula
pT
T
SC 1 ,
where 1T is the actual running time of the program without applying parallelism,
and pT is the actual running time of a similar program using parallelism in P
computing cores. Ideally, this coefficient is equal to the number of cores, but in
practice, this coefficient is always several tenths less than the number of cores.
This is due to the presence of other background processes in the system, which
also occupy a certain place in the kernel operation plan.
Below are graphs (Fig. 5) showing the dependence of the speedup coeffi-
cients for all three types of parallelism on the values of N.
V. Martell, A. Korochkin, O. Rusanova
ISSN 1681–6048 System Research & Information Technologies, 2022, № 2 56
Fig. 5. The dependence of the average speedup coefficients of test parallel programs on
the type of parallelism used in them, and on the software tools for its implementation:
OpenMP (via C ++) (a), Java (b) and C# (c) in solving the problem of two square matrices
multiplication
Additionally, more detailed testing of fine-grained parallelism was con-
ducted in order to identify ways to increase its efficiency. At this stage, those test
programs from the developed package were tested, which were written using only
fine-grained parallelism. Multiple measurements of the time of the multiplication
operation of two matrices with a dimension of 1500*1500 elements were per-
formed. The dependence of execution time on the number of software imple-
mented threads was checked. Fig. 6 demonstrate the detected time dependence on
the number of created tasks. More detailed results are provided in Table 2 and 3.
Fig. 6. The dependence of fine-grained parallelism execution time on the number
of created threads
Comparative analysis of the effectiveness of using fine-grained and nested parallelism …
Системні дослідження та інформаційні технології, 2022, № 2 57
T a b l e 2 . The results of testing the performance of test parallel programs de-
veloped using different types of parallelism (or without using parallelism – as a
control sample) and various software tools for its implementation in solving the
problem of two square matrices multiplication
Computing time (sec)
Medium-grained Fine-grained N
OpenMP Java C# OpenMP Java C#
516 1,7 0,2 1,2 1,6 0,2 1,1
1032 13,3 3,3 9,8 12,8 2,9 9,8
1548 46,7 14,0 35,6 45,9 12,1 34,1
2064 111,7 38,5 79,8 110,8 33,5 78,1
Computing time (sec)
Nested Non-parallel N
OpenMP Java C# OpenMP Java C#
516 1,5 0,2 1,1 7,7 8,0 5,2
1032 12,4 3,1 9,5 66,1 66,9 45,5
1548 44,9 13,0 33,8 240,6 250,2 171,4
2064 108,1 35,5 74,8 586,5 640,1 387,1
T a b l e 3 . The results of fine-grained parallelism testing in solving the problem
of two square matrices multiplication using various software tools for its im-
plementation
Computing time (sec)
Number of threads
C# Java OpenMP
2 71,309 133,944 190,618
3 55,1 101,41 125,12
4 42,099 77,393 79,894
5 37,202 60,942 68,167
6 34,222 47,532 46,157
10 34,113 45,551 47,202
12 32,841 45,117 46,011
15 31,405 44,37 45,7
20 30,404 44,33 47,196
25 30,511 43,101 46,21
30 28,329 41,9 43,15
50 27,683 40,88 43,01
CONCLUSIONS AND FUTURE WORK
The results obtained during testing showed the effectiveness of MCS in the im-
plementation of the considered mathematical problem solution by using Java and
C# languages and OpenMP library. Additionally, reduction of the programs exe-
cution time with the application of the parallelism of any degree of grain is possi-
ble (speedup coefficient values are in the range of 4,0–5,5). The best result in
terms of program execution time was obtained for the C#.
V. Martell, A. Korochkin, O. Rusanova
ISSN 1681–6048 System Research & Information Technologies, 2022, № 2 58
Medium-grained parallelism showed sufficient efficiency, but had the worst
result. At the same time, the speedup achieved by OpenMP tools is constantly
increasing with the amount of data processed. While using the C# and the Java
tools, speedup remains at approximately the same level.
Using fine-grained parallelism was also effective, in which case the speedup
coefficient increases steadily with increasing data volume. This type of parallel-
ism was most effective in C#.
Furthermore, additional testing of fine-grained parallelism revealed a declin-
ing exponential dependence between the number of threads, which is allowed to
create by the program, and the time of its operation. As mentioned in Section 3,
the main reason for this is a larger number of fine-grained tasks (threads) that ac-
cess physical processing elements (cores) and shared resources, which leads to
significant downtime due to the problem of mutual exclusion. The optimal num-
ber of fine-grained tasks is in the range of 5 to 20, regardless of how it was
organized.
Nested (combined) parallelism showed its effectiveness and allowed to in-
crease speedup coefficient when it is used in C# language and OpenMP library.
Moreover, there is an increase of speedup coefficient with increasing amount of
processed data, which is one of the most important arguments for the feasibility of
this approach in the MCS.
It could be assumed that the efficiency of using nested parallelism will in-
crease with an increasing number of cores in the MCS, where:
1. There will be additional processor resources for its implementation.
2. It is possible to reduce the size of grains.
3. There will be an optimal ratio between the number of streams and sub-
threads.
Besides, the efficiency of nested parallelism implemented in OpenMP can be
improved by more efficient implementation of the powerful sub-threads manage-
ment system embedded in the library, similar to how it was done in the fork-join
model. Since the identified patterns of change in program execution time and
speedup coefficients, in general, are preserved for all considered means of orga-
nizing parallelism, it can be argued that this approach will be effective regardless
of the language or library by which it will be organized.
Therefore, it can be argued that the use of fine-grained and/or combined
(nested) parallelism in most cases is an effective approach to the implementation
of parallel computing in multi-core computer systems.
Possible directions of work continuation:
1. Testing formed hypotheses in larger and more powerful multi-core com-
puter systems.
2. Testing formed hypotheses on a number of more applied problems.
3. Check the statement about the effectiveness of fine-grained and combined
parallelism, regardless of the instruments of its organization, compared with me-
dium-grained parallelism.
From the point of view of the development of high-level instruments of fine-
grained parallelism realization in modern parallel programming languages and
libraries:
1. Adaptation of existing computational planning methods to the realities of
fine-grained and nested parallelism.
2. Adaptation of existing effective processing queue management policies to
the realities of fine-grained and nested parallelism.
Comparative analysis of the effectiveness of using fine-grained and nested parallelism …
Системні дослідження та інформаційні технології, 2022, № 2 59
REFERENCES
1. ISO 9000:2000 Quality management systems – Fundamentals and vocabulary.
Available: https://www.iso.org/standard/29280.html
2. L. Lamport, “How to Make a Multiprocessor Computer That Correctly Executes
Multiprocess Programs”, IEEE Transactions on Computers, vol. C-28, no. 9,
pp. 690–691, 1979. doi: 10.1109/TC.1979.1675439.
3. A.C. Wayne, S.J. Procter, and T.E. Anderson, “The nachos instructional operating
system”, in USENIX Winter 1993 Con-ference (USENIX Winter 1993 Conference).
San Diego, CA: USENIX Association, Jan. 1993. doi: 10.1.1.181.878.
4. B.S. Tanenbaum and H. Bos, Modern Operating Systems, 4th ed. USA: Prentice Hall
Press, 2014. doi: 10.5555/2655363.
5. J.E. Moreira, D. Schouten, and C.D. Polychronopoulos, “The performance impact of
granularity control and functional parallelism”, in Proceedings of the 8th Interna-
tional Workshop on Languages and Compilers for Parallel Computing, ser.
LCPC’95, pp. 581–597. Berlin, Heidelberg: Springer-Verlag, 1995. doi:
10.5555/645673.665710.
6. K. Hwang, Advanced Computer Architecture: Parallelism, Scalability, Programma-
bility, 1st ed. McGraw-HillHigher Education, 1992. doi: 10.5555/541880.
7. R. Miller and Q.F. Stout, Parallel Algorithms for Regular Architectures: Meshes and
Pyramids. Cambridge, Mass: MITPress, 1996. doi: 10.5555/249608.
8. B. Blaise, Introduction to Parallel Computing. [Online]. Available: https://hpc.llnl.
gov/training/tutorials/introduction-parallel-computing-tutorial/
9. J.L. Hennessy and D.A. Patterson, Computer Architecture, Fifth Edition: A Quanti-
tative Approach. Morgan Kaufmann Publishers Inc., 2011. doi: 10.5555/1999263.
10. O. Bandman, “Composing fine-grained parallel algorithms forspatial dynamics simu-
lation”, in Proceedings of the 8th International Conference on Parallel Computing
Technologies, ser. PaCT’05, pp. 99–113. Berlin, Heidelberg: Springer-Verlag,
2005. doi: 10.1007/11535294_9.
11. D. Lea, “A java fork/join framework”, in Proceedings of the ACM2000 Conference
on Java Grande, ser. JAVA ’00, pp. 36–43. New York, NY, USA: Association for
Computing Machinery, 2000. doi: 10.1145/337449.337465.
12. P.E. Hadjidoukas, G.C. Philos, and V.V. Dimakopoulos, “Exploiting fine-grain
thread parallelism on multicore architectures”, Sci. Program., vol. 17, no. 4,
pp. 309–323, Dec. 2009. doi: 10.1155/2009/249651.
13. P. Czarnul, “Assessment of OpenMP master-slave implementations for selected ir-
regular parallel applications”, Electronics, vol. 10, no. 10, 2021. doi:
10.3390/electronics10101188.
14. J. Ponge, Fork and Join: Java Can Excel at Painless Parallel Programming Too!
[Online]. Available: https://www.oracle.com/technical-resources/articles/java/fork-
join.html
15. O. Rusanova and A. Korochkin, “Scheduling problems for parallel and distributed
systems”, Ada Lett., vol. XIX, no. 3, pp. 195–201, Sep. 1999. doi:
10.1145/319295.319323.
Received 15.06.2022
INFORMATION ON THE ARTICLE
Valerii V. Martell, ORCID: 0000-0002-1749-5818, National Technical University of
Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail: va-
lerii.martell@gmail.com
Aleksandr V. Korochkin, ORCID: 0000-0003-4650-2316, National Technical University
of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail:
avcora@gmail.com
V. Martell, A. Korochkin, O. Rusanova
ISSN 1681–6048 System Research & Information Technologies, 2022, № 2 60
Olga V. Rusanova, ORCID: 0000-0003-0145-3012, National Technical University of
Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail:
olga.rusanova.v@gmail.com
ПОРІВНЯЛЬНИЙ АНАЛІЗ ЕФЕКТИВНОСТІ ВИКОРИСТАННЯ
ДРІБНОЗЕРНИСТОГО ТА ВКЛАДЕНОГО ПАРАЛЕЛІЗМУ ДЛЯ ЗБІЛЬШЕННЯ
ПРИШВИДШЕННЯ ПАРАЛЕЛЬНИХ ОБЧИСЛЕНЬ У БАГАТОЯДЕРНИХ
КОМП’ЮТЕРНИХ СИСТЕМАХ / В.В. Мартелл, О.В. Корочкін, О.В. Русанова
Анотація. Подано результати порівняльного аналізу ефективності викорис-
тання паралелізму різного ступеня зернистості в сучасних багатоядерних
комп’ютерних системах з використанням найпопулярніших натепер мов про-
грамування та бібліотек (таких як C#, Java, C++ та OpenMP). Досліджено мож-
ливості підвищення ефективності обчислень у багатоядерних комп’ютерних
системах за допомогою комбінацій середньо- та дрібнозернистого паралеліз-
му. Отримані результати демонструють високу потенційну ефективність вико-
ристання дрібнозернистого паралелізму для організації інтенсивних паралель-
них обчислень. На підставі цих результатів можна стверджувати, що
порівняно з більш традиційними методами розпаралелювання, які використо-
вують паралелізм із середньою зернистістю, використання окремо дрібнозер-
нистого паралелізму може скоротити час обчислення великої тестової матема-
тичної задачі в середньому на 4% , а використання комбінованого паралелізму
— до 5,5%. Це скорочення часу виконання доцільне в разі виконання надвели-
ких обчислень.
Ключові слова: багатоядерна комп’ютерна система, ядро, потік, завдання, па-
ралелізм, зернистість, fork-join, коефіцієнт пришвидшення, дрібнозернистий
паралелізм, вкладений паралелізм, комбінований паралелізм.
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| id | journaliasakpiua-article-251975 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:27:42Z |
| publishDate | 2022 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/4f/c35689d5ed0327beb27a99ba82df4f4f.pdf |
| spelling | journaliasakpiua-article-2519752022-10-17T22:12:39Z Comparative analysis of the effectiveness of using fine-grained and nested parallelism to increase the speedup of parallel computing in multicore computer systems СРАВНИТЕЛЬНЫЙ АНАЛИЗ ЭФФЕКТИВНОСТИ ИСПОЛЬЗОВАНИЯ МЕЛКОЗЕРНИСТОГО И ВЛОЖЕННОГО ПАРАЛЛЕЛИЗМА ДЛЯ УВЕЛИЧЕНИЯ УСКОРЕНИЯ ПАРАЛЕЛЬНЫХ ВЫЧИСЛЕНИЙ В МНОГОЯДЕРНЫХ КОМПЬЮТЕРНЫХ СИСТЕМАХ Порівняльний аналіз ефективності використання дрібнозернистого та вкладеного паралелізму для збільшення пришвидшення паралельних обчислень у багатоядерних комп’ютерних системах Martell, Valerii Korochkin, Aleksandr Rusanova, Olga multicore computer system core thread tasks parallelism granularity fork-join speedup coefficient fine-grained parallelism nested parallelism combined parallelism багатоядерна комп’ютерна система ядро потік завдання паралелізм зернистість fork-join коефіцієнт пришвидшення дрібнозернистий паралелізм вкладений паралелізм комбінований паралелізм The article presents a comparative analysis of the effectiveness of using parallelism of varying granularity degrees in modern multicore computer systems using the most popular programming languages and libraries (such as C#, Java, C++, and OpenMP). Based on the performed comparison, the possibilities of increasing the efficiency of computations in multicore computer systems by using combinations of medium- and fine-grained parallelism were also investigated. The results demonstrate the high potential efficiency of fine-grained parallelism when organizing intensive parallel computations. Based on these results, it can be argued that, in comparison with more traditional parallelization methods that use medium-grain parallelism, the use of separately fine-grained parallelism can reduce the computation time of a large mathematical problem by an average of 4%. The use of combined parallelism can reduce the computation time of such a problem to 5,5%. This reduction in execution time can be significant when performing very large computations. В статье представлены результаты сравнительного анализа эффективности использования параллелизма различной степени зернистости в современных многоядерных компьютерных системах с использованием самых популярных на сегодняшний день языков программирования и библиотек (таких как C#, Java, C++ и OpenMP). На основе проведенного сравнения исследованы возможности повышения эффективности вычислений в многоядерных компьютерных системах с помощью комбинаций средне- и мелкозернистого параллелизма. Полученные результаты показывают высокую потенциальную эффективность использования мелкозернистого параллелизма при организации интенсивных параллельных вычислений. На основе этих результатов можно утверждать, что по сравнению с более традиционными методами распараллелирования, использующими параллелизм со средней зернистостью, использование отдельно мелкозернистого параллелизма может сократить время вычисления большой тестовой математической задачи в среднем на 4%, а использование комбинированного параллелизма позволяет сократить время вычисления такой. задачи до 5,5%. Это сокращение времени выполнения может быть значительным при выполнении очень больших вычислений. Подано результати порівняльного аналізу ефективності використання паралелізму різного ступеня зернистості в сучасних багатоядерних комп’ютерних системах з використанням найпопулярніших натепер мов програмування та бібліотек (таких як C#, Java, C++ та OpenMP). Досліджено можливості підвищення ефективності обчислень у багатоядерних комп’ютерних системах за допомогою комбінацій середньо- та дрібнозернистого паралелізму. Отримані результати демонструють високу потенційну ефективність використання дрібнозернистого паралелізму для організації інтенсивних паралельних обчислень. На підставі цих результатів можна стверджувати, що порівняно з більш традиційними методами розпаралелювання, які використовують паралелізм із середньою зернистістю, використання окремо дрібнозернистого паралелізму може скоротити час обчислення великої тестової математичної задачі в середньому на 4% , а використання комбінованого паралелізму — до 5,5%. Це скорочення часу виконання доцільне в разі виконання надвеликих обчислень. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2022-08-30 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/251975 10.20535/SRIT.2308-8893.2022.2.03 System research and information technologies; No. 2 (2022); 45-60 Системные исследования и информационные технологии; № 2 (2022); 45-60 Системні дослідження та інформаційні технології; № 2 (2022); 45-60 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/251975/261590 |
| spellingShingle | багатоядерна комп’ютерна система ядро потік завдання паралелізм зернистість fork-join коефіцієнт пришвидшення дрібнозернистий паралелізм вкладений паралелізм комбінований паралелізм Martell, Valerii Korochkin, Aleksandr Rusanova, Olga Порівняльний аналіз ефективності використання дрібнозернистого та вкладеного паралелізму для збільшення пришвидшення паралельних обчислень у багатоядерних комп’ютерних системах |
| title | Порівняльний аналіз ефективності використання дрібнозернистого та вкладеного паралелізму для збільшення пришвидшення паралельних обчислень у багатоядерних комп’ютерних системах |
| title_alt | Comparative analysis of the effectiveness of using fine-grained and nested parallelism to increase the speedup of parallel computing in multicore computer systems СРАВНИТЕЛЬНЫЙ АНАЛИЗ ЭФФЕКТИВНОСТИ ИСПОЛЬЗОВАНИЯ МЕЛКОЗЕРНИСТОГО И ВЛОЖЕННОГО ПАРАЛЛЕЛИЗМА ДЛЯ УВЕЛИЧЕНИЯ УСКОРЕНИЯ ПАРАЛЕЛЬНЫХ ВЫЧИСЛЕНИЙ В МНОГОЯДЕРНЫХ КОМПЬЮТЕРНЫХ СИСТЕМАХ |
| title_full | Порівняльний аналіз ефективності використання дрібнозернистого та вкладеного паралелізму для збільшення пришвидшення паралельних обчислень у багатоядерних комп’ютерних системах |
| title_fullStr | Порівняльний аналіз ефективності використання дрібнозернистого та вкладеного паралелізму для збільшення пришвидшення паралельних обчислень у багатоядерних комп’ютерних системах |
| title_full_unstemmed | Порівняльний аналіз ефективності використання дрібнозернистого та вкладеного паралелізму для збільшення пришвидшення паралельних обчислень у багатоядерних комп’ютерних системах |
| title_short | Порівняльний аналіз ефективності використання дрібнозернистого та вкладеного паралелізму для збільшення пришвидшення паралельних обчислень у багатоядерних комп’ютерних системах |
| title_sort | порівняльний аналіз ефективності використання дрібнозернистого та вкладеного паралелізму для збільшення пришвидшення паралельних обчислень у багатоядерних комп’ютерних системах |
| topic | багатоядерна комп’ютерна система ядро потік завдання паралелізм зернистість fork-join коефіцієнт пришвидшення дрібнозернистий паралелізм вкладений паралелізм комбінований паралелізм |
| topic_facet | multicore computer system core thread tasks parallelism granularity fork-join speedup coefficient fine-grained parallelism nested parallelism combined parallelism багатоядерна комп’ютерна система ядро потік завдання паралелізм зернистість fork-join коефіцієнт пришвидшення дрібнозернистий паралелізм вкладений паралелізм комбінований паралелізм |
| url | https://journal.iasa.kpi.ua/article/view/251975 |
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