From b236ed46b184e7492b6950931018f9975d5f6b8b Mon Sep 17 00:00:00 2001 From: "baptiste.coudray" <baptiste.coudray@etu.hesge.ch> Date: Fri, 30 Jul 2021 20:35:38 +0200 Subject: [PATCH] First version finished --- .DS_Store | Bin 0 -> 10244 bytes src/config.yaml | 6 ++-- src/figs/dispatch_1d.png | Bin 8246 -> 8158 bytes src/figs/dispatch_2d.png | Bin 0 -> 20611 bytes src/figs/envelope_1d.png | Bin 0 -> 20622 bytes src/figs/envelope_2d.png | Bin 0 -> 31983 bytes src/figs/front-logo.graffle | Bin 0 -> 130421 bytes src/figs/front-logo.png | Bin 2526 -> 32337 bytes src/figs/lbm_result_and_speedup_gpu.png | Bin 0 -> 69858 bytes src/figs/ring.png | Bin 35764 -> 35346 bytes src/iso690.csl | 10 +++--- src/my.bib | 24 +++++--------- src/templates/default.latex | 4 +-- src/text/00-preface.md | 3 +- src/text/01-references.md | 10 +++--- src/text/02-introduction.md | 22 ++++++++----- src/text/03-programmation-parallele.md | 4 +-- src/text/04-mpi.md | 10 +++--- src/text/05-futhark.md | 26 +++++++-------- src/text/06-mpi-x-futhark.md | 33 ++++++++++++++----- src/text/07-automate-elementaire.md | 23 +++++++------ src/text/08-jeu-de-la-vie.md | 5 ++- src/text/09-lattice-boltzmann.md | 42 +++++++++++++++++++----- src/text/10-conclusion.md | 3 ++ src/text/ZZ-glossaire.tex | 1 + 25 files changed, 135 insertions(+), 91 deletions(-) create mode 100644 .DS_Store create mode 100644 src/figs/dispatch_2d.png create mode 100644 src/figs/envelope_1d.png create mode 100644 src/figs/envelope_2d.png create mode 100644 src/figs/front-logo.graffle create mode 100644 src/figs/lbm_result_and_speedup_gpu.png diff --git a/.DS_Store b/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..b13c5322ee0e46416bd402f8349b145fc58c4365 GIT binary patch literal 10244 zcmZQzU|@7AO)+F(P+(wS;9!8z0z3>@0Z1N%F(jFwBBCJk7#IW?a?%Zhlk;;6pyH#{ zXb6mkz-S1JhQMeDjE2DA3js!mlQ_5`^e8zR0;3@?8UpYT0F@7*4g!dFfVA-$8Xz=C zh=GxT0o(;(WME){X<`KR10ZTZT0v?+T0t~OD+42l1(pYEWnhGAWdwIa7#J8C1i(fy 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couverture +frontLogoLegend: "MPI x Futhark with examples" # La légende de l'image de couverture +frontLogoSourceURL: "Realized by Baptiste Coudray" # La source de l'image de couverture workTitle: "Bachelor thesis" workFor: "..." bibliography: my.bib diff --git a/src/figs/dispatch_1d.png b/src/figs/dispatch_1d.png index dbd4f7054c3ad3a6377f8fb76b4e0f897d31a48e..f22af69b233fca6fbff4f59e31b697aa92a882fe 100644 GIT binary patch delta 7524 zcmdnyaL-<`Gr-TCmrII^fq{Y7)59f*fq_Yffq`KT2NMGW!)1r`M-vsNi0Uk0W?*4p zU|<BvFfcGM1gVDzZ#<>PR4;SE)5S5Qg7NL#%00eUe;?od%tT^R&`eF0rH;%K1%ia6 zL{fb+f?jsF-44|V4r=q^o#kONebJ&$7cCblQ}t6et@n3_?awWLxAXYU=W}*{zxBK3 zoc#B#-)?1BT>E`9z5ZL(wOh~A-rU@rZeQ!-zyd-C_?dqGc@a|E)xgowP|wkE;64i% zM>EF{?}XRa)}EfGYyF^sSu1Q!#1ap|`rg3zN(xMJ!WVo_BtLkSr{CCb|L@0>$^LdP z7Bu@=KAj?Enl(iya#Q*Hd(qo+ZbmCbWj#AH^XI3hv+e8c)b)42*~BHP<)XdS{CsR( zexB1x^ZPZE*LhFTXe>B(^FaFi+HY^_H=jQiX>l@1+B|Q`dilB^iYLoLVp;a6C<uO< zwC&d|?*~h#$5}n@G2Zv@*XuK9&V<KRrXJ}K+?st|&a&vq(&=$h)pI9pe&!slQug-N 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name="online">en ligne</term> - <term name="accessed">consulté le</term> - <term name="retrieved">disponible</term> - <term name="from">à l'adresse</term> + <term name="online">online</term> + <term name="accessed">accessed on</term> + <term name="retrieved">retrieved</term> + <term name="from">from</term> </terms> </locale> <macro name="author"> diff --git a/src/my.bib b/src/my.bib index 9a9adbe..6ced782 100644 --- a/src/my.bib +++ b/src/my.bib @@ -7,7 +7,6 @@ urldate = {2021-07-22}, date = {2021-03-17}, langid = {french}, - note = {Page Version {ID}: 180967726}, file = {Snapshot:/Users/baptistecdr/Zotero/storage/GLQPSHE4/index.html:text/html}, } @@ -25,24 +24,22 @@ @inreference{noauthor_amdahls_2021, title = {Amdahl's law}, rights = {Creative Commons Attribution-{ShareAlike} License}, - url = {https://en.wikipedia.org/w/index.php?title=Amdahl%27s_law&oldid=1034193438}, + url = {https://en.wikipedia.org/w/index.php?title=Amdahl%27s_law}, booktitle = {Wikipedia}, urldate = {2021-07-22}, date = {2021-07-18}, langid = {english}, - note = {Page Version {ID}: 1034193438}, file = {Snapshot:/Users/baptistecdr/Zotero/storage/4KJVD4JN/index.html:text/html}, } @inreference{noauthor_gustafsons_2021, title = {Gustafson's law}, rights = {Creative Commons Attribution-{ShareAlike} License}, - url = {https://en.wikipedia.org/w/index.php?title=Gustafson%27s_law&oldid=1031307338}, + url = {https://en.wikipedia.org/w/index.php?title=Gustafson%27s_law}, booktitle = {Wikipedia}, urldate = {2021-07-22}, date = {2021-06-30}, langid = {english}, - note = {Page Version {ID}: 1031307338}, file = {Snapshot:/Users/baptistecdr/Zotero/storage/FGKVKJQD/index.html:text/html}, } @@ -89,60 +86,55 @@ @inreference{noauthor_jeu_2021, title = {Jeu de la vie}, rights = {Creative Commons Attribution-{ShareAlike} License}, - url = {https://fr.wikipedia.org/w/index.php?title=Jeu_de_la_vie&oldid=183190635}, + url = {https://fr.wikipedia.org/w/index.php?title=Jeu_de_la_vie}, booktitle = {Wikipédia}, urldate = {2021-07-22}, date = {2021-05-23}, langid = {french}, - note = {Page Version {ID}: 183190635}, file = {Snapshot:/Users/baptistecdr/Zotero/storage/HDKB5PPW/index.html:text/html}, } @inreference{noauthor_automate_2021, title = {Automate cellulaire}, rights = {Creative Commons Attribution-{ShareAlike} License}, - url = {https://fr.wikipedia.org/w/index.php?title=Automate_cellulaire&oldid=183026782}, + url = {https://fr.wikipedia.org/w/index.php?title=Automate_cellulaire}, booktitle = {Wikipédia}, urldate = {2021-07-22}, date = {2021-05-18}, langid = {french}, - note = {Page Version {ID}: 183026782}, file = {Snapshot:/Users/baptistecdr/Zotero/storage/L5L9W28B/index.html:text/html}, } @inreference{noauthor_programmation_2021, title = {Programmation fonctionnelle}, rights = {Creative Commons Attribution-{ShareAlike} License}, - url = {https://fr.wikipedia.org/w/index.php?title=Programmation_fonctionnelle&oldid=183271341}, + url = {https://fr.wikipedia.org/w/index.php?title=Programmation_fonctionnelle}, booktitle = {Wikipédia}, urldate = {2021-07-22}, date = {2021-05-26}, langid = {french}, - note = {Page Version {ID}: 183271341}, file = {Snapshot:/Users/baptistecdr/Zotero/storage/Z4UFD79Y/index.html:text/html}, } @inreference{noauthor_maximum_2021, title = {Maximum subarray problem}, rights = {Creative Commons Attribution-{ShareAlike} License}, - url = {https://en.wikipedia.org/w/index.php?title=Maximum_subarray_problem&oldid=1030176929}, + url = {https://en.wikipedia.org/w/index.php?title=Maximum_subarray_problem}, booktitle = {Wikipedia}, urldate = {2021-07-22}, date = {2021-06-24}, langid = {english}, - note = {Page Version {ID}: 1030176929}, file = {Snapshot:/Users/baptistecdr/Zotero/storage/LL8NK2KY/index.html:text/html}, } @inreference{noauthor_distributed_2021, title = {Distributed computing}, rights = {Creative Commons Attribution-{ShareAlike} License}, - url = {https://en.wikipedia.org/w/index.php?title=Distributed_computing&oldid=1033553148}, + url = {https://en.wikipedia.org/w/index.php?title=Distributed_computing}, booktitle = {Wikipedia}, urldate = {2021-07-23}, date = {2021-07-14}, langid = {english}, - note = {Page Version {ID}: 1033553148}, file = {Snapshot:/Users/baptistecdr/Zotero/storage/ZF8EB2I9/index.html:text/html}, } @@ -154,4 +146,4 @@ date = {2010}, langid = {english}, file = {Chapter 1 Covering Multithreading Basics (Multithreaded Programming Guide):/Users/baptistecdr/Zotero/storage/ASQQ8TRR/index.html:text/html}, -} \ No newline at end of file +} diff --git a/src/templates/default.latex b/src/templates/default.latex index a1924a1..e27f675 100644 --- a/src/templates/default.latex +++ b/src/templates/default.latex @@ -333,7 +333,7 @@ $endif$ \huge{$title$}\\ \vspace{.5cm} \IfFileExists{figs/front-logo.png}{ - \includegraphics[scale=1.2]{figs/front-logo.png}\\ + \includegraphics[scale=0.6]{figs/front-logo.png}\\ }{ \vspace{8cm} } @@ -363,7 +363,7 @@ $endif$ % Illustration URL page \vspace*{\fill} \IfFileExists{figs/front-logo.png}{ - $frontLogoLegend$ \url{$frontLogoSourceURL$} + Legend and source of the cover picture: $frontLogoLegend$ $frontLogoSourceURL$ }{ Cette page a été laissée blanche intentionnellement. } diff --git a/src/text/00-preface.md b/src/text/00-preface.md index 3c0516f..22c765d 100644 --- a/src/text/00-preface.md +++ b/src/text/00-preface.md @@ -10,8 +10,9 @@ I would like to thank the people who helped me during this project: # Abstract {-} +Today, most computers are equipped with (+^GPU). They provide more and more computing cores and have become fundamental embedded high-performance computing tools. In this context, the number of applications taking advantage of these tools seems low at first glance. The problem is that the development tools are heterogeneous, complex, and strongly dependent on the (+GPU) running the code. Futhark is an experimental, functional, and architecture agnostic language; that is why it seems relevant to study it. It allows generating code allowing a standard sequential execution (on a single-core processor), on (+GPU) (with (+CUDA) and (+OpenCL) backends), on several cores of the same processor (shared memory). To make it a tool that could be used on all high-performance platforms, it lacks support for distributed computing with (+MPI). Nous créons une librairie qui effectue la distribution d'un automate cellulaire sur plusieurs noeuds de calculs via MPI. The update of the cellular automaton is computed via the Futhark language using one of the four available backends (sequential, multicore, OpenCL, and CUDA). Pour valider notre librairie, we implement a cellular automaton in one dimension ((+SCA)), in two dimensions (Game of Life) and three dimensions ((+LBM)). Finally, with the performance tests performed, we obtain an ideal speedup in one and two dimensions with the sequential and multicore backend. With the GPU backend, we obtain an ideal speedup only when the number of tasks equals the number of GPUs. -\begin{figure} \vspace{.1cm} \begin{center} \includegraphics[width=3.72cm,height=2.4cm]{figs/front-logo.png} +\begin{figure} \vspace{.1cm} \begin{center} \includegraphics[scale=0.4]{figs/front-logo.png} \end{center} \end{figure} \begin{tabular}{ p{3cm} p{1cm} p{1cm} p{6cm} } \multicolumn{1}{l}{Candidate:}& & & \multicolumn{1}{l}{Referent teacher:}\\ \multicolumn{1}{l}{\textbf{Baptiste Coudray}} & & & \multicolumn{1}{l}{\textbf{Dr. Orestis Malaspinas}} \\ \multicolumn{1}{l}{Field of study: Information Technologies Engineering} & & & diff --git a/src/text/01-references.md b/src/text/01-references.md index e09af76..c2f3614 100644 --- a/src/text/01-references.md +++ b/src/text/01-references.md @@ -8,11 +8,11 @@ #### Reference of the URLs {-} -\begin{tabular}{ p{3cm} p{9cm} } \multicolumn{1}{l}{URL01} & -\multicolumn{1}{l}{\url{https://upload.wikimedia.org/wikipedia/commons/e/e5/Gospers_glider_gun.gif}}\\ -\multicolumn{1}{l}{URL02} & \multicolumn{1}{l}{\url{https://commons.wikimedia.org/wiki/File:AmdahlsLaw.svg}} \\ -\multicolumn{1}{l}{URL03} & \multicolumn{1}{l}{\url{https://commons.wikimedia.org/wiki/File:Gustafson.png}} \\ -\multicolumn{1}{l}{URL04} & \multicolumn{1}{l}{\url{https://commons.wikimedia.org/wiki/File:Elder_futhark.png}} \\ +\begin{tabular}{ p{3cm} p{9cm} } +\multicolumn{1}{l}{URL01} & \multicolumn{1}{l}{\url{https://commons.wikimedia.org/wiki/File:AmdahlsLaw.svg}} \\ +\multicolumn{1}{l}{URL02} & \multicolumn{1}{l}{\url{https://commons.wikimedia.org/wiki/File:Gustafson.png}} \\ +\multicolumn{1}{l}{URL03} & \multicolumn{1}{l}{\url{https://commons.wikimedia.org/wiki/File:Elder_futhark.png}} \\ +\multicolumn{1}{l}{URL04} & \multicolumn{1}{l}{\url{https://futhark-lang.org/images/mss.svg}} \\ \multicolumn{1}{l}{URL05} & \multicolumn{1}{l}{\url{https://commons.wikimedia.org/wiki/File:Gol-blinker1.png}} \\ \multicolumn{1}{l}{URL06} & \multicolumn{1}{l}{\url{https://commons.wikimedia.org/wiki/File:Gol-blinker2.png}} \\ \end{tabular} diff --git a/src/text/02-introduction.md b/src/text/02-introduction.md index f8b8713..1900e9f 100644 --- a/src/text/02-introduction.md +++ b/src/text/02-introduction.md @@ -2,26 +2,32 @@ # Introduction {-} -Today, most computers are equipped with GPUs. They provide more and more computing cores and have become fundamental embedded high-performance computing tools. In this context, the number of applications taking advantage of these tools seems low at first glance. The problem is that the development tools are heterogeneous, complex, and strongly dependent on the GPU running the code. Futhark is an experimental, functional, and architecture agnostic language; that is why it seems relevant to study it. It allows generating code allowing a standard sequential execution (on a single-core processor), on GPU (with CUDA and OpenCL backends), on several cores of the same processor (shared memory). To make it a tool that could be used on all high-performance platforms, it lacks support for distributed computing. This work aims to develop a library that can port any Futhark code to an MPI library with as little effort as possible. +Today, most computers are equipped with (+^GPU). They provide more and more computing cores and have become fundamental embedded high-performance computing tools. In this context, the number of applications taking advantage of these tools seems low at first glance. The problem is that the development tools are heterogeneous, complex, and strongly dependent on the (+GPU) running the code. Futhark is an experimental, functional, and architecture agnostic language; that is why it seems relevant to study it. It allows generating code allowing a standard sequential execution (on a single-core processor), on (+GPU) (with (+CUDA) and (+OpenCL) backends), on several cores of the same processor (shared memory). To make it a tool that could be used on all high-performance platforms, it lacks support for distributed computing. This work aims to develop a library that can port any Futhark code to an (+MPI) library with as little effort as possible. -To achieve that, we introduce the interest of parallelization --, then what is MPI and Futhark. We decide to implement a library that can parallelize cellular automaton in, one, two or three dimensions. By adding Futhark on top of MPI, the programmer will have the possibilities to compile his code in : +To achieve that, we introduce the meaning of distributed high-performance computing, then what is (+MPI) and Futhark. We decide to implement a library that can parallelize cellular automaton in, one, two or three dimensions. By adding Futhark on top of (+MPI), the programmer will have the possibilities to compile his code in : * parallelized-sequential mode, * parallelized-multicore mode, * parallelized-OpenCL mode, * parallelized-CUDA mode. -Finally, we used this library by implementing a cellular automata in each dimension, and we perform a benchmark to ensure that each cellular automata scales correctly in these four modes. +Finally, we used this library by implementing a cellular automata in each dimension: -The leading resources we used to carry out this project were Futhark and MPI user guide. We also exchanged with Futhark creator Troels Henriksen. +* a (+SCA) in one dimension, +* the Game of Life in two dimensions, +* the (+LBM) in three dimensions. + +We perform a benchmark to ensure that each cellular automata scales correctly in the four modes. + +The leading resources we used to carry out this project were Futhark and (+MPI) user guide. We also exchanged with Futhark creator Troels Henriksen. ## Working method {-} During this project, we use Git and put the source code on the Gitlab platform of HEPIA: -* https://gitedu.hesge.ch/baptiste.coudray/projet-de-bachelor - * Source code of the library with usage examples. -* https://gitedu.hesge.ch/baptiste.coudray/projet-de-semestre/-/tree/report - * Source code of this report +* Source code of the library with usage examples + * https://gitedu.hesge.ch/baptiste.coudray/projet-de-bachelor +* Source code of this report + * https://gitedu.hesge.ch/baptiste.coudray/projet-de-semestre/-/tree/report \pagebreak diff --git a/src/text/03-programmation-parallele.md b/src/text/03-programmation-parallele.md index 62cc67c..7638906 100644 --- a/src/text/03-programmation-parallele.md +++ b/src/text/03-programmation-parallele.md @@ -14,7 +14,7 @@ In parallel computing, two important laws give the theoretical speedup that can \pagebreak -\cimg{figs/amdahls-law.png}{scale=0.6}{Amdahl's law}{Source: Taken from https://commons.wikimedia.org/, ref. URL02} +\cimg{figs/amdahls-law.png}{scale=0.6}{Amdahl's law}{Source: Taken from https://commons.wikimedia.org/, ref. URL01} Amdahl's law states that the program's overall speed is limited by the code that cannot be parallelized. Indeed, there will almost always be a sequential part in a code that cannot be parallelized. There is, therefore, a relationship between the ratio of parallelizable code and the overall execution speed of the program [@noauthor_amdahls_2021]. @@ -27,7 +27,7 @@ In the graph above, we notice that if: \pagebreak -\cimg{figs/gustafson-law.png}{scale=0.75}{Gustafson–Barsis's law}{Source: Taken from https://commons.wikimedia.org/, ref. URL03} +\cimg{figs/gustafson-law.png}{scale=0.75}{Gustafson–Barsis's law}{Source: Taken from https://commons.wikimedia.org/, ref. URL02} Gustafson's law says that the more significant the amount of data to be processed, the more advantageous it is to use many processors. Thus, the acceleration is linear, as can be seen on the graph [@noauthor_gustafsons_2021]. On the graph, we notice, for example, that with a code that is 90% parallelized, we have a speedup of at least x100 with 120 processors, where Amdahl's law estimated a maximum speedup of x10 with 512 processors. Gustafson's law is therefore much more optimistic in terms of performance gain. diff --git a/src/text/04-mpi.md b/src/text/04-mpi.md index daa45fe..1fb0aaf 100644 --- a/src/text/04-mpi.md +++ b/src/text/04-mpi.md @@ -1,17 +1,17 @@ # Message Passing Interface -In order to realize parallel programming, the standard (+^MPI) was created in 1993-1994 to standardize the passage of messages between several computers or in a computer with several processors/cores [@noauthor_message_2021]. (+^MPI) is, therefore, a communication protocol and not a programming language. Currently, the latest version of (+^MPI) is 4.0 which approved in 2021. There are several implementations of the standard: +In order to realize parallel programming, the standard (+MPI) was created in 1993-1994 to standardize the passage of messages between several computers or in a computer with several processors/cores [@noauthor_message_2021]. (+MPI) is, therefore, a communication protocol and not a programming language. Currently, the latest version of (+MPI) is 4.0 which approved in 2021. There are several implementations of the standard: * MPICH, which support for the moment, MPI 3.1, * Open MPI, which support, for the moment, MPI 3.1 -We use Open MPI throughout this project on the cluster of the (+^HES-GE). +We use Open MPI throughout this project on the cluster of the (+HES-GE). \pagebreak ## Example -To understand the basis of (+^MPI), let us look at an example mimicking a *token ring* network [@kendall_mpi_2018]. This type of network forces a process to send a message to the message in the console, for example, only if it has the token in its possession. Moreover, once it has emitted its message, the process must transmit the token to its neighbor. +To understand the basis of (+MPI), let us look at an example mimicking a *token ring* network [@kendall_mpi_2018]. This type of network forces a process to send a message to the message in the console, for example, only if it has the token in its possession. Moreover, once it has emitted its message, the process must transmit the token to its neighbor. \cimg{figs/ring.png}{scale=0.4}{Imitation of a network in \textit{token ring}}{Source: Created by Baptiste Coudray} @@ -67,8 +67,8 @@ mpicc ring.c -o ring mpirun -n 5 ./ring ``` -To compile a (+^MPI) program, you have to go through the `mpicc` program, which is a wrapper -around (+^GCC). Indeed, `mpicc` automatically adds the correct compilation parameters to the (+^GCC) program. +To compile a (+MPI) program, you have to go through the `mpicc` program, which is a wrapper +around (+GCC). Indeed, `mpicc` automatically adds the correct compilation parameters to the (+GCC) program. Next, our compiled program must be run through `mpirun` to distribute our program to compute nodes. Finally, the `-n` parameter is used to specify the number of processes to run. ``` diff --git a/src/text/05-futhark.md b/src/text/05-futhark.md index 910c022..a16b1db 100644 --- a/src/text/05-futhark.md +++ b/src/text/05-futhark.md @@ -1,25 +1,25 @@ # Introduction to the language Futhark -\cimg{figs/futhark.png}{scale=0.60}{Futhark}{Source: Taken from https://commons.wikimedia.org/, ref. URL04} +\cimg{figs/futhark.png}{scale=0.60}{Futhark}{Source: Taken from https://commons.wikimedia.org/, ref. URL03} -Futhark is a purely functional programming language for producing parallelizable code on (+^CPU) or (+^GPU). It was designed by Troels Henriksen, Cosmin Oancea and Martin Elsman at the University of Copenhagen. +Futhark is a purely functional programming language for producing parallelizable code on (+CPU) or (+GPU). It was designed by Troels Henriksen, Cosmin Oancea and Martin Elsman at the University of Copenhagen. The main goal of Futhark is to write generic code that can compile into either: -* (+^OpenCL), -* (+^CUDA), -* multi-threaded (+^POSIX) C, +* (+OpenCL), +* (+CUDA), +* multi-threaded (+POSIX) C, * sequential C, * sequential Python. -Although a Futhark code can compile into an executable, this feature reserves for testing purposes because there is no (+^IO). Thus, the main interest is to write particular functions that you would like to speed up thanks to parallel programming and compile in library mode to use in a C program. +Although a Futhark code can compile into an executable, this feature reserves for testing purposes because there is no (+IO). Thus, the main interest is to write particular functions that you would like to speed up thanks to parallel programming and compile in library mode to use in a C program. \pagebreak -To see the performance of Futhark, Here is an example from the Futhark site that compares the resolution time of the (+^MSS) problem. The (+^MSS) problem is the task of finding a contiguous subarray with the largest sum, within a given one-dimensional array A[1...n] of numbers [@noauthor_maximum_2021]. +To see the performance of Futhark, Here is an example from the Futhark site that compares the resolution time of the (+MSS) problem. The (+MSS) problem is the task of finding a contiguous subarray with the largest sum, within a given one-dimensional array A[1...n] of numbers [@noauthor_maximum_2021]. \cimg{figs/mss_bench.png}{scale=0.35}{MSS runtime (lower is better)}{Source: Taken from https://futhark-lang.org/performance.html, ref. URL04} -This graph shows performance of a maximum segment sum implementation in Futhark and Thrust (a C++ library developed by NVIDIA for (+^GPU) programming). The sequential runtime is for Futhark code compiled to sequential (+^CPU) code and the Futhark runtime is for code compiled to (+^CUDA) [@henriksen_gotta_2021]. As we can see, the Futhark version is much faster than the sequential and Thrust versions, which justify using this language in this project. +This graph shows performance of a maximum segment sum implementation in Futhark and Thrust (a C++ library developed by NVIDIA for (+GPU) programming). The sequential runtime is for Futhark code compiled to sequential (+CPU) code and the Futhark runtime is for code compiled to (+CUDA) [@henriksen_gotta_2021]. As we can see, the Futhark version is much faster than the sequential and Thrust versions, which justify using this language in this project. \pagebreak @@ -41,13 +41,13 @@ echo 12 | ./fact To compile the Futhark code, we have to specify a backend; this one allows us to compile our code in: -* (+^OpenCL) (opencl, pyopencl), -* (+^CUDA) (cuda), -* multi-thread (+^POSIX) C (multicore), +* (+OpenCL) (opencl, pyopencl), +* (+CUDA) (cuda), +* multi-thread (+POSIX) C (multicore), * sequential C (c), * Python sequential (python). -Here we compile in (+^OpenCL) to run the program on the graphics card, and we run the program with the number 12 as the parameter. +Here we compile in (+OpenCL) to run the program on the graphics card, and we run the program with the number 12 as the parameter. ``` 479001600i32 @@ -69,7 +69,7 @@ Functions that can be used in C code must be defined with the `entry` keyword. T futhark opencl --lib fact.fut ``` -Then you have to compile the Futhark code in library mode and specify the backend. Here, the factorial program is compiled in (+^OpenCL). Finally, it generates a `fact.h` and `fact.c` file, which can be included in a C program. +Then you have to compile the Futhark code in library mode and specify the backend. Here, the factorial program is compiled in (+OpenCL). Finally, it generates a `fact.h` and `fact.c` file, which can be included in a C program. ```c #include <stdio.h> diff --git a/src/text/06-mpi-x-futhark.md b/src/text/06-mpi-x-futhark.md index fc795dd..aad7324 100644 --- a/src/text/06-mpi-x-futhark.md +++ b/src/text/06-mpi-x-futhark.md @@ -1,4 +1,4 @@ -# Automate cellulaire +# Cellular Automaton A cellular automaton consists of a regular grid of cells, each in one of a finite number of states. The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time $t = 0$) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the rule for updating the state of cells is the same for each cell and does not change over time [@noauthor_automate_2021]. @@ -44,6 +44,8 @@ In a one-dimensional Cartesian topology, we notice that the rows can communicate In a two-dimensional Cartesian topology, we notice that rows can communicate directly with their left, right, top, and bottom neighbors. When a row needs to communicate with its diagonal neighbor, we use the default communicator (`MPI_COMM_WORLD`) to communicate directly with each other without going through a neighbor. +\pagebreak + ### Three dimensions \cimg{figs/communication_3d.png}{scale=0.60}{Example of Cartesian virtual topology in three dimensions}{Source: Created by Baptiste Coudray} @@ -56,35 +58,50 @@ The cellular automaton is shared as equally possible among the available tasks t #### One dimension -\cimg{figs/futhark.png}{scale=0.60}{Example of sharing a cellular automaton in one dimension}{Source: Created by Baptiste Coudray} +\cimg{figs/dispatch_1d.png}{scale=0.60}{Example of sharing a cellular automaton in one dimension}{Source: Created by Baptiste Coudray} In this example, a cell automaton of dimension one, size 8, is split between three processes. As the division of the cellular automaton is not an integer, rank two have only two cells, unlike the others, which have three. #### Two dimensions -\cimg{figs/dispatch_1d.png}{scale=0.60}{Example of sharing a cellular automaton in two dimensions}{Source: Created by Baptiste Coudray} +\cimg{figs/dispatch_2d.png}{scale=0.60}{Example of sharing a cellular automaton in two dimensions}{Source: Created by Baptiste Coudray} In this example, the cellular automaton is in two dimensions and of size $9 \times 9$. With four tasks available, it can be separated into four sub-matrices of $3 \times 3$. #### Three dimensions In three dimensions, the cellular automaton partitioning representation is challenging to make understandable. Thus, based on the two-dimensional partitioning, each task divides the third dimension. -For example, a cellular automaton of size $4 \times 4 \times 4$, each process has a piece of size $2 \times 2 \times 2$. +For example, a cellular automaton of size $4 \times{} 4 \times{} 4$, each process has a piece of size $2 \times{} 2 \times{} 2$. ### Envelope The envelope of a chunk represents the missing neighbours of the cells at the extremities of the chunk. These missing cells are needed to compute the next iteration of the chunk of the cellular automaton that the process has. +\pagebreak + #### One dimension -\cimg{figs/dispatch_1d.png}{scale=0.60}{Example of the envelope of a chunk in one dimension}{Source: Created by Baptiste Coudray} +\cimg{figs/envelope_1d.png}{scale=0.60}{Example of the envelope of a chunk in one dimension}{Source: Created by Baptiste Coudray} -In one dimension, the Moore neighborhood of a cell includes the west-neighbor and the east-neighbor. Using the previously described one-dimensional cellular automaton, we notice that the envelope of $R_{n}$ includes the last cell of $R_{(n-1) \% N}$ and the first cell of $R_{(n+1) \% N}$. Thus, the ranks exchange data via MPI using the Cartesian virtual topology. +In one dimension, the Moore neighborhood of a cell includes the west-neighbor and the east-neighbor. We notice that the envelope of $R_{n}$ includes the last cell of $R_{(n-1)\:\%\:N}$ and the first cell of $R_{(n+1)\:\%\:N}$. For example, the envelope for R1 is the west-neighbor (three) and the east neighbor (seven). Thus, the ranks exchange data via MPI using the Cartesian virtual topology. + +\pagebreak #### Two dimensions +\cimg{figs/envelope_2d.png}{scale=0.60}{Example of the envelope of a chunk in two dimensions}{Source: Created by Baptiste Coudray} -#### Three dimensions +Using the two-dimensional cellular automaton described above, the chunk envelope of R0 requires eight communications. This example uses a Cartesian topology of size $2\times 2$ (m\times n), the neighbors are recovered as follows: -En troisième dimension, on rajoute la profondeur de devant et la profondeur de derrière +1. `North West Neighbors` are sent by $R_{ ((y - 1)\:\%:m,\:(x - 1)\%:n) }$, +2. `North Neighbors`, are sent by $R_{ ((y - 1)\%:m,\:x) }$, +3. `North East Neighbors`, are sent by $R_{ ((y - 1)\:\%:m,\:(x + 1)\:\%:n) }$, +4. `East Neighbors`, are sent by $R_{ (y,\:(x + 1)\%:n) }$, +5. `South East Neighbors`, are sent by $R_{ ((y + 1)\:\%:m,\:(x + 1)\%:n) }$, +6. `South Neighbors`, are sent by $R_{ ((y + 1)\%:m,\:x) }$, +7. `South West Neighbors`, are sent by $R_{ ((y + 1)\%:m,\:(x - 1)\%:n) }$, +8. `West Neighbors`, are sent by $R_{ (y,\:(x - 1)\%:n) }$. + +#### Three dimensions +With a three-dimensional cellular automaton, the envelope of a chunk requires 26 MPI communications. \pagebreak diff --git a/src/text/07-automate-elementaire.md b/src/text/07-automate-elementaire.md index be174eb..cccbdca 100644 --- a/src/text/07-automate-elementaire.md +++ b/src/text/07-automate-elementaire.md @@ -2,7 +2,7 @@ The simplest non-trivial cellular automaton that can be conceived consists of a one-dimensional grid of cells that can take only two states ("0" or "1"), with a neighborhood consisting, for each cell, of itself and the two cells adjacent to it [@noauthor_automate_2021]. -There are $2^3 = 8$ possible configurations (or patterns, rules) of such a neighborhood. In order for the cellular automaton to work, it is necessary to define what the state must be at the next generation of a cell for each of these patterns. The 8 rules/configurations defined is as follows: +There are $2^3 = 8$ possible configurations (or patterns, rules) of such a neighborhood. In order for the cellular automaton to work, it is necessary to define what the state must be at the next generation of a cell for each of these patterns. The eight rules/configurations defined is as follows: | Rule n° | East neighbour state | Cell state | West neighbour state | Cell next state | |:---:|:---:|:---:|:---:|:---:| @@ -20,8 +20,7 @@ Table: Evolution rules for a cellule in a one dimensional cellular-automaton ## Example -\cimg{figs/simple_automate.png}{scale=0.5}{First state of blinker}{Source: Taken from -\url{https://commons.wikimedia.org/}, ref. URL05. Re-created by Baptiste Coudray} +\cimg{figs/simple_automate.png}{scale=0.5}{First and second state of a SCA}{Source: Created by Baptiste Coudray} Iteration 0 is the initial state and only cell two is alive. To perform the next iteration: @@ -31,7 +30,7 @@ Iteration 0 is the initial state and only cell two is alive. To perform the next ## Parallelized version -With the created library, we implement this (+^SCA) previously described. To do this, we create a Futhark `elementary.fut` file, which is used to calculate the next state of a part of the cellular automaton. +With the created library, we implement this (+SCA) previously described. To do this, we create a Futhark `elementary.fut` file, which is used to calculate the next state of a part of the cellular automaton. ``` let compute_next_elems [n] (chunk_elems :[n]i8) :[]i8 = ... @@ -82,7 +81,7 @@ Finally, a C file `main.c` is needed to create the program's entry point. We ini ## CPU Benchmark -We perform benchmarks to validate the scalability of our one-dimensional parallelization when compiling in sequential, multicore, (+^OpenCL), or (+^CUDA) mode. The benchmarks are performed on the HES-GE cluster (Baobab/Yggdrasil). +We perform benchmarks to validate the scalability of our one-dimensional parallelization when compiling in sequential, multicore, (+OpenCL), or (+CUDA) mode. The benchmarks are performed on the (+HES-GE) cluster (Baobab/Yggdrasil). The sequential and multicore benchmarks are performed as follows: * the cellular automaton is $300,000,000$ cells in size, @@ -100,7 +99,7 @@ The sequential and multicore benchmarks are performed as follows: | 32 | 20.938 [s] | ± 0.007 [s] | x31.4 | 15 | | 64 | 11.071 [s] | ± 0.024 [s] | x59.4 | 15 | | 128 | 5.316 [s] | ± 0.191 [s] | x123.7 | 15 | -Table: Results for the parallelized-sequential version of SCA +Table: Results for the parallelized-sequential version of (+SCA) | Number of tasks | Average [s] | Standard Derivation [s] | Speedup | Number of measures | |:---:|:---:|:---:|:---:|:---:| @@ -112,7 +111,7 @@ Table: Results for the parallelized-sequential version of SCA | 32 | 25.776 [s] | ± 0.725 [s] | x27.5 | 15 | | 64 | 12.506 [s] | ± 0.554 [s] | x56.7 | 15 | | 128 | 5.816 [s] | ± 0.045 [s] | x121.8 | 15 | -Table: Results for the parallelized-multicore version of SCA +Table: Results for the parallelized-multicore version of (+SCA) \pagebreak @@ -120,11 +119,11 @@ Table: Results for the parallelized-multicore version of SCA We compare the average computation time for each task and each version (sequential and multicore) on the left graph. On the right graph, we compare the ideal speedup with the parallelized-sequential and multicore version speedup. -The more we increase the number of tasks, the more the execution time is reduced. Thus, the parallelized-sequential or multicore version speedup follows the curve of the ideal speedup. +The more we increase the number of tasks, the more the execution time is reduced. Thus, the parallelized-sequential or multicore version speedup follows the curve of the ideal speedup. We can see that concurrent computing does not provide a significant performance gain over sequential computing. ## GPU Benchmark -The (+^OpenCL) and (+^CUDA) benchmarks are performed as follows: +The (+OpenCL) and (+CUDA) benchmarks are performed as follows: * the cellular automaton has $300'000'000$ cells, * the number of tasks varies between $2^0$ and $2^6$. @@ -143,7 +142,7 @@ The (+^OpenCL) and (+^CUDA) benchmarks are performed as follows: | 16 | 8 | 31.675 [s] | ± 0.056 [s] | x5.2 | 15 | | 32 | 8 | 43.65 [s] | ± 0.102 [s] | x3.8 | 15 | | 64 | 8 | 67.096 [s] | ± 0.118 [s] | x2.5 | 15 | -Table: Results for the parallelized-OpenCL version of SCA +Table: Results for the parallelized-OpenCL version of (+SCA) | Number of tasks | Number of GPUs | Average [s] | Standard Derivation [s] | Speedup | Number of measures | |:---:|:---:|:---:|:---:|:---:|:---:| @@ -154,12 +153,12 @@ Table: Results for the parallelized-OpenCL version of SCA | 16 | 8 | 30.749 [s] | ± 0.069 [s] | x5.2 | 15 | | 32 | 8 | 42.352 [s] | ± 0.117 [s] | x3.8 | 15 | | 64 | 8 | 65.228 [s] | ± 0.042 [s] | x2.5 | 15 | -Table: Results for the parallelized-CUDA version of SCA +Table: Results for the parallelized-CUDA version of (+SCA) \pagebreak \cimg{figs/elem_result_and_speedup_gpu.png}{width=\linewidth}{Benchmarks of the SCA in parallelized-OpenCL/CUDA}{Source: Realized by Baptiste Coudray} -With this performance test, we notice that the computation time is essentially the same in OpenCL as in CUDA. Moreover, the parallelization follows the ideal speedup curve when the number of processes equals the number of graphics cards. However, when the eight graphics cards are shared, the speedup in OpenCL/CUDA crashes, and the computation time increases. +With this performance test, we notice that the computation time is essentially the same in (+OpenCL) as in (+CUDA). Moreover, the parallelization follows the ideal speedup curve when the number of processes equals the number of graphics cards. However, when the eight graphics cards are shared, the speedup in (+OpenCL)/(+CUDA) crashes, and the computation time increases. Moreover, we notice that parallel computation is up to four times faster than sequential/concurrent computation when executing with a single task/graphical card. \pagebreak diff --git a/src/text/08-jeu-de-la-vie.md b/src/text/08-jeu-de-la-vie.md index 7b41a76..a90e597 100644 --- a/src/text/08-jeu-de-la-vie.md +++ b/src/text/08-jeu-de-la-vie.md @@ -9,8 +9,7 @@ The Game of Life is a zero-player game designed by John Horton Conway in 1970. I ## Example -\cimg{figs/gol_blinker1.png}{scale=0.40}{First state of blinker}{Source: Taken from -\url{https://commons.wikimedia.org/}, ref. URL05. Re-created by Baptiste Coudray} +\cimg{figs/gol_blinker1.png}{scale=0.40}{First state of blinker}{Source: Taken from \url{https://commons.wikimedia.org/}, ref. URL05. Re-created by Baptiste Coudray} \pagebreak @@ -108,6 +107,6 @@ Table: Results for the parallelized-CUDA version of Game of Life \cimg{figs/gol_result_and_speedup_gpu.png}{width=\linewidth}{Benchmarks of the game of life in parallelized-OpenCL/CUDA}{Source: Realized by Baptiste Coudray} -With this performance test, we notice that the computation time is essentially the same in OpenCL as in CUDA. Moreover, the parallelization follows the ideal speedup curve when the number of processes equals the number of graphics cards. However, when the eight graphics cards are shared, the speedup in OpenCL/CUDA stabilize, and the computation time increases ($+7 [s]$ between eight tasks and 64 tasks). +With this performance test, we notice that the computation time is essentially the same in OpenCL as in CUDA. Moreover, the parallelization follows the ideal speedup curve when the number of processes equals the number of graphics cards. However, when the eight graphics cards are shared, the speedup in OpenCL/CUDA stabilize, and the computation time increases ($+7\:[s]$ between eight tasks and 64 tasks). \pagebreak diff --git a/src/text/09-lattice-boltzmann.md b/src/text/09-lattice-boltzmann.md index 053d173..0c33cbc 100644 --- a/src/text/09-lattice-boltzmann.md +++ b/src/text/09-lattice-boltzmann.md @@ -1,4 +1,4 @@ -# Lattice-Boltzmann +# Lattice-Boltzmann Method "_The lattice Boltzmann method (LBM) has established itself in the past decades as a valuable approach to Computational Fluid Dynamics (CFD). It is commonly used to model time-dependent, incompressible or compressible flows in a @@ -10,11 +10,11 @@ fundamental research, as it keeps the cycle between the elaboration of a theory ## Parallelized version -We create the lattice-Boltzmann method with our library to test it with a three-dimensional cellular automaton. +We implement the Lattice-Boltzmann Method with our library to test it with a three-dimensional cellular automaton. ## CPU Benchmark -We perform benchmarks to validate the scalability of our three-dimensional parallelization when compiling in sequential, multicore, (+^OpenCL), or (+^CUDA) mode. The benchmarks are performed on the (+^HES-GE) cluster (Baobab/Yggdrasil). +We perform benchmarks to validate the scalability of our three-dimensional parallelization when compiling in sequential, multicore, (+OpenCL), or (+CUDA) mode. The benchmarks are performed on the (+HES-GE) cluster (Baobab/Yggdrasil). The sequential and multicore benchmarks are performed as follows: * the cellular automaton is $27'000'000$ cells in size, @@ -32,7 +32,7 @@ The sequential and multicore benchmarks are performed as follows: | 32 | 41.04 [s] | ± 1.59 [s] | x17.4 | 15 | | 64 | 22.188 [s] | ± 0.321 [s] | x32.3 | 15 | | 128 | 17.415 [s] | ± 4.956 [s] | x41.1 | 15 | -Table: Results for the parallelized-sequential version of Lattice-Boltzmann +Table: Results for the parallelized-sequential version of (+LBM) | Number of tasks | Average [s] | Standard Derivation [s] | Speedup | Number of measures | |:---:|:---:|:---:|:---:|:---:| @@ -44,17 +44,17 @@ Table: Results for the parallelized-sequential version of Lattice-Boltzmann | 32 | 46.285 [s] | ± 0.138 [s] | x15.0 | 15 | | 64 | 24.059 [s] | ± 0.061 [s] | x28.9 | 15 | | 128 | 16.614 [s] | ± 1.088 [s] | x41.9 | 15 | -Table: Results for the parallelized-multicore version of Lattice-Boltzmann +Table: Results for the parallelized-multicore version of (+LBM) \pagebreak -\cimg{figs/lbm_result_and_speedup_cpu.png}{width=\linewidth}{Benchmarks of the lattice-Boltzmann method in parallelized-sequential/multicore}{Source: Realized by Baptiste Coudray} +\cimg{figs/lbm_result_and_speedup_cpu.png}{width=\linewidth}{Benchmarks of the LBM in parallelized-sequential/multicore}{Source: Realized by Baptiste Coudray} -Contrairement aux benchmarks précédents, les speedups ne suivent pas la courbe du speedup idéal. En effet, que ce soit en sequential ou en multicore, nous obtenons un speedup maximal avec 128 tâches de x41 alors qu'on espérait avoir un speedup de x128. +Contrary to the previous benchmarks, the speedups do not follow the ideal speedup curve. Indeed, whether in sequential or multicore, we obtain a maximum speedup with 128 tasks of x41 when we were hoping to have a speedup of x128. ## GPU Benchmark -The (+^OpenCL) and (+^CUDA) benchmarks are performed as follows: +The (+OpenCL) and (+CUDA) benchmarks are performed as follows: * the cellular automaton has $27'000'000$ cells, * the number of tasks varies between $2^0$ and $2^6$. @@ -62,4 +62,30 @@ The (+^OpenCL) and (+^CUDA) benchmarks are performed as follows: * the iteration is computed $3'000$ times. * From $2^0$ to $2^3$ tasks, an NVIDIA GeForce RTX 3090 is allocated for each task; beyond that, the eight graphics cards are shared equally among the ranks. +| Number of tasks | Number of GPUs | Average [s] | Standard Derivation [s] | Speedup | Number of measures | +|:---:|:---:|:---:|:---:|:---:|:---:| +| 1 | 1 | 210.347 [s] | ± 0.096 [s] | x1.0 | 15 | +| 2 | 2 | 99.677 [s] | ± 0.038 [s] | x2.1 | 15 | +| 4 | 4 | 40.71 [s] | ± 0.076 [s] | x5.2 | 15 | +| 8 | 8 | 20.8 [s] | ± 0.031 [s] | x10.1 | 15 | +| 16 | 8 | 22.88 [s] | ± 0.064 [s] | x9.2 | 15 | +| 32 | 8 | 22.47 [s] | ± 0.036 [s] | x9.4 | 15 | +| 64 | 8 | 23.848 [s] | ± 0.035 [s] | x8.8 | 15 | +Table: Results for the parallelized-OpenCL version of (+LBM) + +| Number of tasks | Number of GPUs | Average [s] | Standard Derivation [s] | Speedup | Number of measures | +|:---:|:---:|:---:|:---:|:---:|:---:| +| 1 | 1 | 207.683 [s] | ± 0.249 [s] | x1.0 | 15 | +| 2 | 2 | 99.177 [s] | ± 0.056 [s] | x2.1 | 15 | +| 4 | 4 | 40.24 [s] | ± 0.074 [s] | x5.2 | 15 | +| 8 | 8 | 20.459 [s] | ± 0.037 [s] | x10.2 | 15 | +| 16 | 8 | 22.837 [s] | ± 0.037 [s] | x9.1 | 15 | +| 32 | 8 | 22.361 [s] | ± 0.024 [s] | x9.3 | 15 | +| 64 | 8 | 23.688 [s] | ± 0.051 [s] | x8.8 | 15 | +Table: Results for the parallelized-CUDA version of (+LBM) + +\cimg{figs/lbm_result_and_speedup_gpu.png}{width=\linewidth}{Benchmarks of the LBM in parallelized-OpenCL/CUDA}{Source: Realized by Baptiste Coudray} + +Like the other benchmarks, there is very little difference between the OpenCL and CUDA versions (computation time and speedup). We get a more than ideal speedup with 2, 4, and 8 tasks/GPUs (x2.1, x5.2, and x10.2, respectively). When several tasks use the same graphics card, the computation time stabilizes at 22 seconds, and the speedup stops increasing. + \pagebreak diff --git a/src/text/10-conclusion.md b/src/text/10-conclusion.md index e2c5c98..26013bb 100644 --- a/src/text/10-conclusion.md +++ b/src/text/10-conclusion.md @@ -1,3 +1,6 @@ # Conclusion +In this project, we created a library allowing to distribute a one, two or three dimensional cellular automaton on several computation nodes via MPI. Thanks to the different Futhark backends, the update of the cellular automaton can be done in sequential, concurrent or parallel computation. Thus, we compared these different modes by implementing a cellular automaton in one dimension ((+SCA)), in two dimensions (Game of Life) and in three dimensions ((+LBM)). Benchmarks for each backend were performed to verify the scalability of the library. We obtained ideal speedups with the cellular automata in one and two dimensions and with the use of the sequential and multicore Futhark backend. With these two backends and a three-dimensional cellular automaton, we had a maximum speedup of x41 with 128 tasks. Concerning the OpenCL and CUDA backends, they show no difference in performance between them. For the three cellular automata, the speedup is ideal only when the number of tasks is equal to the number of GPUs. +Finally, the library can be improved in order to obtain an ideal speedup in three dimensions with the CPU backends. Moreover, the addition of a load balancing of the graphic cards to obtain better performances when there are more tasks than GPUs, and the support of the Von Neumann neighborhood to manage other cellular automata. + \pagebreak diff --git a/src/text/ZZ-glossaire.tex b/src/text/ZZ-glossaire.tex index 2e0da74..4de72d9 100644 --- a/src/text/ZZ-glossaire.tex +++ b/src/text/ZZ-glossaire.tex @@ -16,3 +16,4 @@ \newacronym{IO}{I/O}{Input/Output} \newacronym{MSS}{MSS}{Maximum Segment Sum} \newacronym{SCA}{SCA}{Simple Cellular Automaton} +\newacronym{LBM}{LBM}{Lattice-Boltzmann Method} -- GitLab