diff --git a/day1/images/446px-Nuclear_power_plant.svg.png b/day1/images/446px-Nuclear_power_plant.svg.png deleted file mode 100644 index 0401567..0000000 Binary files a/day1/images/446px-Nuclear_power_plant.svg.png and /dev/null differ diff --git a/day1/images/Amplifier1.jpg b/day1/images/Amplifier1.jpg deleted file mode 100644 index 62850fc..0000000 Binary files a/day1/images/Amplifier1.jpg and /dev/null differ diff --git a/day1/images/Amplifier2.jpg b/day1/images/Amplifier2.jpg deleted file mode 100644 index c0f1518..0000000 Binary files a/day1/images/Amplifier2.jpg and /dev/null differ diff --git a/day1/images/Amplifier3.jpg b/day1/images/Amplifier3.jpg deleted file mode 100644 index 3dee8ec..0000000 Binary files a/day1/images/Amplifier3.jpg and /dev/null differ diff --git a/day1/images/Blue_Gene_01.jpg b/day1/images/Blue_Gene_01.jpg deleted file mode 100644 index e0f4768..0000000 Binary files a/day1/images/Blue_Gene_01.jpg and /dev/null differ diff --git a/day1/images/Fibonacci.jpg b/day1/images/Fibonacci.jpg deleted file mode 100644 index 4049d15..0000000 Binary files a/day1/images/Fibonacci.jpg and /dev/null differ diff --git a/day1/images/Fork_join.pdf b/day1/images/Fork_join.pdf deleted file mode 100644 index 0faf775..0000000 Binary files a/day1/images/Fork_join.pdf and /dev/null differ diff --git a/day1/images/Fork_join.png b/day1/images/Fork_join.png deleted file mode 100644 index ff17f5f..0000000 Binary files a/day1/images/Fork_join.png and /dev/null differ diff --git a/day1/images/Fork_join.tex b/day1/images/Fork_join.tex deleted file mode 100644 index d2e6f64..0000000 --- a/day1/images/Fork_join.tex +++ /dev/null @@ -1,84 +0,0 @@ -% Slide 104 -\begin{tikzpicture}[scale = 0.9] -\begin{scope} - -\node[anchor = east] at (0,0) {Master thread}; -\draw (0,0) -- (9.6, 0); -\draw[line width = 3pt, blue6, opacity = 0.4] (0,0) -- (9.6, 0); - -\node[anchor = south] at (2.2, 0.6) {Task 1}; -\draw[thick, fill = white] (1, -0.6) rectangle (3.4, 0.6); -\draw (1, -0.4) -- (3.4, -0.4); -\draw (1, 0.4) -- (3.4, 0.4); -\draw (1.8, 0.4) -- (1.8, -0.4); -\draw (2.6, 0.4) -- (2.6, -0.4); - -\node at (1.4, 0) {A}; -\node at (2.2, 0) {B}; -\node at (3, 0) {C}; - -\node[anchor = south] at (5.2, 0.6) {Task 2}; -\draw[thick, fill = white] (4, -0.6) rectangle (6.4, 0.6); -\draw (4, -0.4) -- (6.4, -0.4); -\draw (4, 0.4) -- (6.4, 0.4); -\draw (4.6, 0.4) -- (4.6, -0.4); -\draw (5.0, 0.4) -- (5.0, -0.4); -\draw (5.9, 0.4) -- (5.9, -0.4); - -\node at (4.3, 0) {A}; -\node at (4.8, 0) {B}; -\node at (5.45, 0) {C}; -\node at (6.15, 0) {D}; - -\node[anchor = south] at (8.2, 0.6) {Task 3}; -\draw[thick, fill = white] (7, -0.6) rectangle (9.4, 0.6); -\draw (7, -0.4) -- (9.4, -0.4); -\draw (7, 0.4) -- (9.4, 0.4); - -\draw (8.2, -0.4) -- (8.2, 0.4); -\node at (7.6, 0) {A}; -\node at (8.8, 0) {B}; -\end{scope} - -\begin{scope}[yshift = -3cm] - -\node[anchor = east] at (0,0) {Master thread}; -\draw (0,0) -- (9.6, 0); - -\node[anchor = south] at (1.7, 1.5) {\scriptsize Parallel Task 1}; -\draw[thick, fill = white] (1, -1.5) rectangle (2.4, 1.5); - -\node[anchor = south] at (3.9, 1.5) {\scriptsize Parallel Task 2}; -\draw[thick, fill = white] (3.2, -1.5) rectangle (4.6, 1.5); - -\node[anchor = south] at (6.3, 1.5) {\scriptsize Parallel Task 3}; -\draw[thick, fill = white] (5.4, -1.5) rectangle (7.2, 1.5); - -\node[draw, rectangle, minimum width = 0.8cm, minimum height = 0.8cm] (A1) at (1.7, 0.9) {A}; -\node[draw, rectangle, minimum width = 0.8cm, minimum height = 0.8cm] (B1) at (1.7, 0.0) {B}; -\node[draw, rectangle, minimum width = 0.8cm, minimum height = 0.8cm] (C1) at (1.7, -0.9) {C}; -\node[draw, rectangle, minimum width = 0.6cm, minimum height = 0.5cm] (A2) at (3.75, 1) {A}; -\node[draw, rectangle, minimum width = 0.4cm, minimum height = 0.5cm] (B2) at (3.7, 0.35) {B}; -\node[draw, rectangle, minimum width = 0.9cm, minimum height = 0.5cm] (C2) at (3.9, -0.35) {C}; -\node[draw, rectangle, minimum width = 0.5cm, minimum height = 0.5cm] (D2) at (3.725, -1) {D}; -\node[draw, rectangle, minimum width = 1.2cm, minimum height = 0.8cm] (A3) at (6.3, 0.75) {A}; -\node[draw, rectangle, minimum width = 1.2cm, minimum height = 0.8cm] (B3) at (6.3, -0.75) {B}; - -\draw[line width = 3pt, blue6, opacity = 0.4] (0,0) -- (1, 0) -- (A1.west) (A1.east) -- (2.4,0) -- (3.2, 0) -- (A2.west) (A2.east) -- (4.4, 1) -- (4.6, 0) -- (5.4, 0) -- (A3.west) (A3.east) -- (7.2, 0) -- (9.6, 0); - -\draw[dashed] (1, 0) -- (A1.west) (A1.east) -- (2.4, 0); -\draw[dashed] (1, 0) -- (B1.west) (B1.east) -- (2.4, 0); -\draw[dashed] (1, 0) -- (C1.west) (C1.east) -- (2.4, 0); - -\draw[dashed] (3.2, 0) -- (A2.west) (A2.east) -- (4.4, 1) -- (4.6, 0); -\draw[dashed] (3.2, 0) -- (B2.west) (B2.east) -- (4.4, 0.35) -- (4.6, 0); -\draw[dashed] (3.2, 0) -- (C2.west) (C2.east) -- (4.4, -0.35) -- (4.6, 0); -\draw[dashed] (3.2, 0) -- (D2.west) (D2.east) -- (4.4, -1) -- (4.6, 0); - -\draw[dashed] (5.4, 0) -- (A3.west) (A3.east) -- (7.2, 0); -\draw[dashed] (5.4, 0) -- (B3.west) (B3.east) -- (7.2, 0); - -\end{scope} - -\end{tikzpicture} - diff --git a/day1/images/SDLC.jpg b/day1/images/SDLC.jpg deleted file mode 100644 index fa27f4d..0000000 Binary files a/day1/images/SDLC.jpg and /dev/null differ diff --git a/day1/images/dhb.jpg b/day1/images/dhb.jpg deleted file mode 100644 index 1581edc..0000000 Binary files a/day1/images/dhb.jpg and /dev/null differ diff --git a/day1/images/dhb2.jpg b/day1/images/dhb2.jpg deleted file mode 100644 index 55c0128..0000000 Binary files a/day1/images/dhb2.jpg and /dev/null differ diff --git a/day1/images/execution-model-simplified.pdf b/day1/images/execution-model-simplified.pdf deleted file mode 100644 index c8915de..0000000 Binary files a/day1/images/execution-model-simplified.pdf and /dev/null differ diff --git a/day1/images/execution-model-simplified.tex b/day1/images/execution-model-simplified.tex deleted file mode 100644 index 5646ae2..0000000 --- a/day1/images/execution-model-simplified.tex +++ /dev/null @@ -1,43 +0,0 @@ -% Slide 72 -\begin{tikzpicture}[yscale = 0.7, xscale = 0.9] - -\draw[very thick, ->] (0,8.5) node[above right] {Master thread} -- (0,-1); - -\pgfmathsetmacro{\forkheight}{7} - -\foreach \x in {1, 2, ..., 5} { - \draw[blue2, ->, thick] (0,{\forkheight + 0.5}) - to[out = -90, in = 180] (0.5, \forkheight) - -- ({\x - 0.5}, \forkheight) - to[out=0, in = 90] (\x, {\forkheight-0.5}) -- (\x, {\forkheight - 2}); - - \draw[blue2, thin] (\x, {\forkheight - 2}) - to[out = -90, in = 0] ({\x - 0.5}, {\forkheight - 2.25}) - -- (0.5, {\forkheight - 2.25}) - to[out = 180, in = 90] (0, {\forkheight - 2.5}); -} - -\node[point, label={left:Fork}] at (0, {\forkheight + 0.5}) {}; -\node[point, label={left:Join}] at (0, {\forkheight - 2.5}) {}; -\node[blue2, anchor = south, yshift = 0.1cm] at (4, \forkheight) {Worker threads}; - -\pgfmathsetmacro{\forkheight}{2.5} - -\foreach \x in {1, 2, 3} { - \draw[blue2, ->, thick] (0,{\forkheight + 0.5}) - to[out = -90, in = 180] (0.5, \forkheight) - -- ({\x - 0.5}, \forkheight) - to[out=0, in = 90] (\x, {\forkheight-0.5}) -- (\x, {\forkheight - 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270 1890 4230 1890 4230 2880 270 2880 270 1890 -4 0 0 50 -1 0 12 0.0000 4 180 1290 1665 2430 Shared Memory\001 -4 0 0 50 -1 0 12 0.0000 4 15 135 3060 990 ...\001 diff --git a/day1/images/memorymodel.png b/day1/images/memorymodel.png deleted file mode 100644 index 8311ac8..0000000 Binary files a/day1/images/memorymodel.png and /dev/null differ diff --git a/day1/images/schedule-decision.pdf b/day1/images/schedule-decision.pdf deleted file mode 100644 index 92a7c4c..0000000 Binary files a/day1/images/schedule-decision.pdf and /dev/null differ diff --git a/day1/images/schedule-decision.png b/day1/images/schedule-decision.png deleted file mode 100644 index 6f3d7bc..0000000 Binary files a/day1/images/schedule-decision.png and /dev/null differ diff --git a/day1/images/schedule-decision.tex b/day1/images/schedule-decision.tex deleted file mode 100644 index facff13..0000000 --- a/day1/images/schedule-decision.tex +++ /dev/null @@ -1,16 +0,0 @@ -% Slide 97 -\begin{tikzpicture}[scale=0.8] - -\node (Start) at (0, 4) {Start}; -\node[decision] (Schedule) at (0, 2) {\texttt{schedule} \\ clause present?}; -\node[anchor = west] (DefSched) at (4, 2) {Use \textit{def-sched-var} schedule kind}; -\node[decision, inner sep = 2pt] (Runtime) at (0, -1.5) {schedule kind \\ value is \texttt{runtime}?}; -\node[anchor = west, align = left] (SchedKind) at (4, -1.5) {Use schedule kind specified\\ in \texttt{schedule} clause}; -\node[anchor = west, align = left] (RunSched) at (4, -4) {Use \textit{run-sched-var} schedule kind}; - -\draw[->] (Start) -- (Schedule); -\draw[->] (Schedule) -- node[near start, above] {No} (DefSched); -\draw[->] (Schedule) -- node[midway, right] {Yes} (Runtime); -\draw[->] (Runtime) |- node[pos = 0.83, above] {Yes} (RunSched); -\draw[->] (Runtime) -- node[near start, above] {No} (SchedKind); -\end{tikzpicture} diff --git a/day1/images/warning.png b/day1/images/warning.png deleted file mode 100644 index 05c010e..0000000 Binary files a/day1/images/warning.png and /dev/null differ diff --git a/day1/openmp.tex b/day1/openmp.tex deleted file mode 100644 index 6a1e702..0000000 --- a/day1/openmp.tex +++ /dev/null @@ -1,1729 +0,0 @@ -\section{OpenMP\\\textbf{Lecture based on specifications ver 3.1}} -%\intersec{figures/fidis} - -\subsection{Introduction} -\begin{frame} - \frametitle{Releases history, present and future} - \begin{itemize} - \item{October 1997: Fortran version 1.0 } - \item{Late 1998: C/C++ version 1.0 } - \item{June 2000: Fortran version 2.0 } - \item{April 2002: C/C++ version 2.0 } - \item{June 2005: Combined C/C++ and Fortran version 2.5 } - \item{May 2008: Combined C/C++ and Fortran version 3.0} - \item{\textbf{July 2011: Combined C/C++ and Fortran version 3.1}} - \item{July 2013: Combined C/C++ and Fortran version 4.0 } - \item{November 2015: Combined C/C++ and Fortran version 4.5 } - \end{itemize} - \addimage{day1/images/logo_OpenMP.png}{5cm}{10cm}{5cm}{} -\end{frame} - -% \subsubsection{threading concepts, terminology (OpenMP, tasking, data, implementation)} - -\begin{frame} - \frametitle{Terminology} - \begin{itemize} - \item{\textbf{thread :} an execution entity with a stack and a static memory (\textit{threadprivate memory})} - \item{\textbf{OpenMP thread :} a \textit{thread} managed by the OpenMP runtime} - \item{\textbf{thread-safe routine :} a routine that can be executed concurrently} - \item{\textbf{processor :} an HW unit on which one or more \textit{OpenMP thread} can execute} -% \item{\textbf{device :} an implementation defined logical execution engine} - \end{itemize} -\end{frame} - -\subsubsection{Models} - -\begin{frame} - \frametitle{Execution and memory models} - \begin{itemize} - \item{Execution model : fork-join} - \item{One heavy thread (process) per program (initial thread)} - \item{leightweigt threads for parallel regions. threads are assigned to cores by the OS} - \item{No implicit synchronization (except at the beginning and at the end of a parallel region)} - \item{Shared Memory with shared variables} - \item{Private Memory per thread with threadprivate variables} - \end{itemize} -\end{frame} - -\begin{frame} - \frametitle{Memory model (simplified)} - \begin{center} - {\includegraphics[width=\textwidth]{day1/images/memory-model-simplified.pdf}} - \end{center} -\end{frame} - -\begin{frame} - \frametitle{Execution model (simplified)} - \begin{center} - {\input{day1/images/execution-model-simplified.tex}} - \end{center} -\end{frame} - -\subsubsection{Remarks} - -\begin{frame} - \frametitle{OpenMP and MPI/pthreads } - \begin{itemize} - \item{\textbf{OpenMP} $\neq$ OpenMPI} - \item{All what you can do with OpenMP can be done with MPI and/or pthreads} - % \item{Memory issue} - \item{easier \textbf{BUT} data coherence/consistency} - % \item{In fact: \textbf{no} easy parallel paradigm exists} - \end{itemize} -\end{frame} - -\subsection{Directives} - -\subsubsection{format \& conditional compilation} - -\begin{frame}[containsverbatim] - \frametitle{Syntax in C} - % \begin{itemize} - % \item{OpenMP directives are written as pragmas: \texttt{\#pragma omp}} - % \item{Use the conditional compilation flag \texttt{\#if defined \_OPENMP} for the preprocessor} - % \end{itemize} - - \begin{block}{} - OpenMP directives are written as pragmas: \texttt{\#pragma omp} - \end{block} - - \begin{block}{} - Use the conditional compilation flag \texttt{\#if defined \_OPENMP} for the preprocessor - \end{block} - - Compilation using the GNU gcc compiler: -\begin{verbatim} -gcc -fopenmp ex1.c -o ex1 -\end{verbatim} - Compilation using the Intel C compiler: -\begin{verbatim} -icc -qopenmp ex1.c -o ex1 -\end{verbatim} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{Hello World in C} - - \begin{lstlisting}[language=C++,frame=lines] -#include -#include -int main(int argc, char *argv[]) { - int myrank=0; - int mysize=1; -#if defined (_OPENMP) -#pragma omp parallel default(shared) private(myrank, mysize) -{ - mysize = omp_get_num_threads(); - myrank = omp_get_thread_num(); -#endif - printf("Hello from thread %d out of %d\n", myrank, mysize); -#if defined (_OPENMP) -} -#endif - return 0; -} -\end{lstlisting} -% (Source file: \texttt{ex1.c}) -\end{frame} - -\begin{frame}[containsverbatim] - \frametitle{Syntax in Fortran 90} - % \begin{itemize} - % \item{OpenMP directives are written as comments: \texttt{!\$omp omp}} - % \item{Sentinels \texttt{!\$} are authorized for conditional compilation (preprocessor) } - % \end{itemize} - - \begin{block}{} - OpenMP directives are written as comments: \texttt{!\$omp omp} - \end{block} - \begin{block}{} - Sentinels \texttt{!\$} are authorized for conditional compilation (preprocessor) - \end{block} - - - Compilation using the GNU gfortran compiler: -\begin{verbatim} -gfortran -fopenmp ex1.f90 -o ex1 -\end{verbatim} - Compilation using the Intel Fortran compiler: -\begin{verbatim} -ifort -qopenmp ex1.f90 -o ex1 -\end{verbatim} -\end{frame} - - - -\begin{frame}[containsverbatim] - \frametitle{Hello World in Fortran 90} - - \begin{lstlisting}[language=Fortran,frame=lines] -program ex1 - implicit none - integer :: myrank, mysize -!$ integer, external :: omp_get_num_threads, omp_get_thread_num - myrank=0 - mysize=1 -!$omp parallel default(shared) private(myrank, mysize) -!$ mysize = omp_get_num_threads() -!$ myrank = omp_get_thread_num() - print *, "Hello from thread",myrank,"out of",mysize -!$omp end parallel -end program ex1 -\end{lstlisting} -% $ This comment is just for the colors in emacs... -\end{frame} - -\begin{frame}[containsverbatim] - \frametitle{Number of concurrent threads} - - The number of threads is specified in a hardcoded way ($omp\_set\_num\_threads()$) or via an environment variable. - \\~\\ - - BASH-like shells : - -\begin{verbatim} -export OMP_NUM_THREADS=4 -\end{verbatim} - - CSH-like shells : - -\begin{verbatim} -setenv OMP_NUM_THREADS 4 -\end{verbatim} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{Components of OpenMP} - \begin{itemize} - \item{Compiler directives (written as comments) that allow work sharing, synchronization and data scoping} - \item{A runtime library (libomp.so) that contains informal, data access and synchronization directives} - \item{Environment variables} - \end{itemize} -\end{frame} - - -\subsubsection{The \texttt{parallel} construct} - - -\begin{frame}[containsverbatim] - \frametitle{The \texttt{parallel} construct} - - \begin{exampleblock}{Syntax} - This is the mother of all constructs in OpenMP. It starts a parallel execution. - \begin{lstlisting}[language=C,frame=lines] -#pragma omp parallel [clause[[,] clause]...] -{ - structured-block -} -\end{lstlisting} - where \textit{clause} is one of the following: - \begin{itemize} - \item \textbf{\texttt{if}} or \textbf{\texttt{num\_threads}} : conditional clause - \item \textbf{\texttt{default(private | firstprivate | shared | none)}} : default data scoping - \item \textbf{\texttt{private(\textit{list})}}, \textbf{\texttt{firstprivate(\textit{list})}}, \textbf{\texttt{shared(\textit{list})}} or \textbf{\texttt{copyin(\textit{list})}} : data scoping - \item \textbf{\texttt{reduction(\textit{\{ operator | intrinsic\_procedure\_name \} : list})}} - \end{itemize} - \end{exampleblock} -\end{frame} - - -\begin{frame}[fragile] - \frametitle{Example : the \texttt{if} conditional clause } - - \begin{block}{The \texttt{if} clause} - A \texttt{if} test specifies if a parallel region must be executed in parallel or not: - -\begin{verbatim} -if (n<2) then - execute test(n) serial -else - execute test(n) in parallel -endif -\end{verbatim} - - \end{block} - - \begin{lstlisting}[language=C,frame=lines] -#pragma omp parallel if (n>2) - test(n); -\end{lstlisting} -\end{frame} - -\begin{frame}[containsverbatim] - \frametitle{The \texttt{if} clause [output]} - -\begin{verbatim} -vkeller@mathicsepc13:~/OpenMP/exercises/C$ ./ex3 - var = 1 : Code is executed by only one thread - Parallelized with 2 threads : 2 - Parallelized with 3 threads : 3 - Parallelized with 4 threads : 4 -\end{verbatim} - -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{Data scoping} - What is data scoping ? - \begin{itemize} - \item{most common source of errors} - \item{determine which variables are {\bf private} to a thread, which are {\bf shared} among all the threads} - \item{In case of a private variable, what is its value when entering the - parallel region {\bf firstprivate}, what is its value when leaving the - parallel region {\bf lastprivate}} - \item The default scope (if none are specified) is \textbf{shared} - \item{most difficult part of OpenMP} - \end{itemize} -\end{frame} - - -\begin{frame}[fragile] - \frametitle{The data sharing-attributes \texttt{shared} and \texttt{private}} - \begin{exampleblock}{Syntax} -These attributes determines the scope (visibility) of a single or list of variables -\begin{lstlisting}[language=C,frame=lines] -shared(list1) private(list2) -\end{lstlisting} - -\begin{itemize} -\item{The \verb+private+ attribute : the data is private to each thread and non-initiatilized. Each thread has its own copy. Example : \verb+#pragma omp parallel private(i)+} -\item{The \verb+shared+ attribute : the data is shared among all the threads. It is accessible (and non-protected) by all the threads simultaneously. Example : \verb+#pragma omp parallel shared(array)+} -\end{itemize} - -\end{exampleblock} - -\end{frame} - - - -\begin{frame}[containsverbatim] -\frametitle{The data sharing-attributes \texttt{firstprivate} and \texttt{lastprivate}} -\begin{exampleblock}{Syntax} -These clauses determines the attributes of the variables within a parallel region: -\begin{lstlisting}[language=C,frame=lines] -firstprivate(list1) lastprivate(list2) -\end{lstlisting} -\begin{itemize} -\item{The \texttt{firstprivate} like {\tt private} but initialized to the value before the parallel region} -\item{The \texttt{lastprivate} like {\tt private} but the value is updated after the parallel region} -\end{itemize} -\end{exampleblock} -%\begin{alertblock}{} -%\textbf{Fortran only !} -%\end{alertblock} -\end{frame} - - - - -\subsubsection[Worksharing constructs]{worksharing constructs ("subsubsections", "single", "workshare")} - - - -\begin{frame}[containsverbatim] -\frametitle{Worksharing constructs} - -\begin{block}{} -Worksharing constructs are possible in three ``flavours'' : -\begin{itemize} -\item{\textbf{\texttt{sections}} construct} -\item{\textbf{\texttt{single}} construct} -%\item{\textbf{\texttt{master}} construct} -\item{\textbf{\texttt{workshare}} construct (only in Fortran)} -\end{itemize} -\end{block} - -\end{frame} - -\begin{frame}[containsverbatim] -\frametitle{The \texttt{sections} construct} -\begin{exampleblock}{Syntax} - -\begin{lstlisting}[language=C,frame=lines] -#pragma omp [parallel] sections [clause] -{ - #pragma omp section - { - code_block - } -}\end{lstlisting} -where \textit{clause} is one of the following: -\begin{itemize} -\item{\textbf{\texttt{private(\textit{list})}}, \textbf{\texttt{firstprivate(\textit{list})}}, \textbf{\texttt{lastprivate(\textit{list})}} : data scoping} -\item{\textbf{\texttt{reduction(\textit{\{ operator | intrinsic\_procedure\_name \} : list})}} : data scoping} -\item{Each \textbf{\texttt{section}} within a \textbf{\texttt{sections}} construct is assigned to one and only one thread} -\end{itemize} -\end{exampleblock} - - -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{A \texttt{sections} construct example (Exercise)} - - -\begin{block}{Example} -\begin{verbatim} -#pragma omp parallel -#pragma omp sections -{ - #pragma omp section - do something from a thread - #pragma omp section - do something from another thread - #pragma omp section - do something from another thread -} -\end{verbatim} -\end{block} - -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{The \texttt{single} construct} - -\begin{exampleblock}{Syntax} -\begin{lstlisting}[language=C,frame=lines] -#pragma omp single [clause[[,] clause] ...] -{ - structured-block -} -\end{lstlisting} -where \textit{clause} is one of the following: -\begin{itemize} -\item{\textbf{\texttt{private(\textit{list})}}, \textbf{\texttt{firstprivate(\textit{list})}}} -\end{itemize} -\end{exampleblock} - -\begin{block}{} -Only one thread (usualy the first entering thread) executes the \textbf{\texttt{single}} region. The others wait for completion, except if the \textbf{\texttt{nowait}} clause has been activated -\end{block} - -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{The \texttt{master} construct} - -\begin{itemize} - \item{Only the master thread execute the section. It can be used in any OpenMP construct} -\end{itemize} - -\begin{lstlisting}[language=C,frame=lines] -#pragma omp parallel default(shared) -{ -... - #pragma omp master - { - printf("I am the master\n"); - } -... -} -\end{lstlisting} - -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{The \texttt{workshare} construct (\textbf{only Fortran})} -\begin{exampleblock}{Syntax} -\begin{lstlisting}[language=Fortran,frame=lines] -!$omp workshare - structured-block -!$omp end workshare [nowait] -\end{lstlisting} -The enclosed structured block must consist of only the following: -\begin{itemize} -\item{array and scalar assignements} -\item{\textbf{\texttt{FORALL}} statements and constructs} -\item{\textbf{\texttt{WHERE}} statements and constructs} -\item{\textbf{\texttt{atomic}} constructs} -\item{\textbf{\texttt{critical}} constructs} -\item{\textbf{\texttt{parallel}} constructs} -\end{itemize} -\end{exampleblock} -\end{frame} - - - -\begin{frame}[containsverbatim] -\frametitle{A \texttt{workshare} construct example} -\begin{lstlisting}[language=Fortran,frame=lines] -!$omp parallel shared(A,B) private(i,j) -!$omp workshare -forall (i=1:N, j=1:N, A(i,j).NE.0.) - A(i,j) = 3*A(i,j)/.23 + 6. - B(i,j) = A(i,j) ** 2 -end forall -!$omp end workshare -!$omp end parallel -\end{lstlisting} - -\end{frame} - - -\subsubsection[Loops]{loops} - -\begin{frame}[containsverbatim] -\frametitle{The \texttt{for} directive} - -\begin{block}{} -Parallelization of the following loop -\end{block} - -\begin{exampleblock}{Syntax} -\begin{lstlisting}[language=C,frame=lines] -#pragma omp for [clause[[,] clause] ... ] -{ - for-loop -} -\end{lstlisting} -where \textit{clause} is one of the following: -\begin{itemize} -\item{\textbf{\texttt{schedule(\textit{kind[, chunk\_size]})}}} -\item{\textbf{\texttt{collapse(\textit{n})}}} -\item{\textbf{\texttt{ordered}}} -\item{\textbf{\texttt{private(\textit{list})}}, \textbf{\texttt{firstprivate(\textit{list})}}, \textbf{\texttt{lastprivate(\textit{list})}},\texttt{reduction()} } -\end{itemize} -\end{exampleblock} -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{The \texttt{reduction(...)} clause (Exercise)} -\begin{block}{How to deal with} -\begin{verbatim} -vec = (int*) malloc (size_vec*sizeof(int)); -global_sum = 0; -for (i=0;i>$60 & $>>$60 & $>>$60 & $>>$60 \\ -\hline -with cutoff (level=10) & 27.4 & 14.5 & 7.4 & 4.1 & 3.9 \\ -\hline -for loop & 10$^{-5}$ & 10$^{-5}$ & 10$^{-5}$ & 10$^{-5}$ & 10$^{-5}$ \\ -\hline - -\end{tabular} -\end{center} -\caption{\texttt{N=45}, time is in seconds} -\end{table} - -\begin{block}{Remark} -We get a beautiful speedup by cutting off the tree search. But another simplier algorithm (for loop) performs by 6 orders of magnitude. -\end{block} -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{Tasks remarks} - -\begin{itemize} - \item{targeted for many-cores co-processors (like Intel Phi)} - \item{Can be used to solve non symetrical problems and algorithms} - \item{Avoid them on a multi-core CPU} -\end{itemize} - -\end{frame} - - - -\subsubsection[Master and Synchronization constructs]{Master and Synchronization constructs ("master", "critical", "barrier", "taskwait", "atomic", "flush", "ordered")} - - -\begin{frame} -\frametitle{Synchronization} -\begin{block}{Synchronization constructs} -Those directives are sometimes mandatory: -\begin{itemize} - \item{\texttt{master} : region is executed by the master thread only } - \item{\texttt{critical} : region is executed by only one thread at a time } - \item{\texttt{barrier} : all threads must reach this directive to continue} - \item{\texttt{taskwait} : all tasks and childs must reach this directive to continue} - \item{\texttt{atomic (read | write | update | capture)} : the associated storage location is accessed by only one thread/task at a time} - \item{\texttt{flush} : this operation makes the thread's temporary view of memory consistent with the shared memory} - \item{\texttt{ordered} : a structured block is executed in the order of the loop iterations } -\end{itemize} -\end{block} - -\end{frame} - - -%\subsubsection{Data environment \texttt{threadprivate}} -% -%\begin{frame}[containsverbatim] -%\frametitle{The \texttt{threadprivate} directive} -% -%\begin{exampleblock}{Syntax} -%The \texttt{threadprivate} directive specifies that variables are replicated, with each thread having its own copy. -%\begin{lstlisting}[language=C,frame=lines] -%#pragma omp threadprivate(list) -%\end{lstlisting} -%where \textit{list} is a comma-separated list of named variables and named common blocks -%\end{exampleblock} -%\end{frame} -% -%\begin{frame}[containsverbatim] -%\frametitle{The \texttt{threadprivate} directive} -% -%\begin{exampleblock}{Syntax} -%\begin{itemize} -%\item{The directive must appear after the declaration of listed variables/common blocks} -%\item{The values of data in the threadprivate variables of non-initial threads are guaranteed to persist between two consecutive active \texttt{parallel} regions if: -% \begin{itemize} -% \item{No nested \texttt{parallel} regions} -% \item{Number of threads for both \texttt{parallel} regions is the same} -% \item{\texttt{dyn-var} ICV is false for both \texttt{parallel} regions} -% \end{itemize} -%} -%\item{A \texttt{threadprivate} variable is affected by a \texttt{copyin} clause if it appears in the list} -%\item{A \texttt{threadprivate} variable is \textbf{NOT} affected by a \texttt{copyin} clause if it as the \texttt{allocatable} (not initially allocated) or the \texttt{pointer} (no initial association) attributes} -%\end{itemize} -%\end{exampleblock} -% -%\end{frame} - - -%\begin{frame}[containsverbatim] -%\frametitle{A \texttt{copyin} clause} -% -%\begin{exampleblock}{Properties} -%\begin{itemize} -%\item{The \texttt{copyin} clause provides a mechanism to copy the value of the master thread's \texttt{threadprivate} variable to the \texttt{threadprivate} variable of each other member of the team executing the \texttt{parallel}region. } -%\item{If the original list item has the \texttt{POINTER} attribute, each copy receives the same association status of the master thread's copy as if by pointer assignment. } -%\item{If the original list item does not have the \texttt{POINTER} attribute, each copy becomes defined with the value of the master thread's copy as if by intrinsic assignment, unless it has the allocation status of not currently allocated, in which case each copy will have the same status. } -%\end{itemize} -%\end{exampleblock} -%\end{frame} - - - - -%\begin{frame}[containsverbatim] -%\frametitle{A \texttt{copyprivate} clause} -% -%\begin{exampleblock}{Properties} -%\begin{itemize} -%\item{The \texttt{copyprivate} clause provides a mechanism to use a private variable to broadcast a value from the data environment of one implicit task to the data environments of the other implicit tasks belonging to the \texttt{parallel} region.} -%\item{To avoid race conditions, concurrent reads or updates of the list item must be synchronized with the update of the list item that occurs as a result of the \texttt{copyprivate} clause.} -%\end{itemize} -%\end{exampleblock} -%\end{frame} - - - -\subsubsection{Nesting} - -\begin{frame} -\frametitle{Nesting regions} - -\begin{exampleblock}{Nesting} -It is possible to include parallel regions in a parallel region (i.e. nesting) under restrictions (cf. sec. 2.10, p.111, \textit{OpenMP: Specifications ver. 3.1}) -\end{exampleblock} - - -\end{frame} - - - -\subsection{Runtime Library routines} - -\begin{frame} -\frametitle{Runtime Library routines} -\begin{exampleblock}{Usage} -\begin{itemize} -\item{The functions/subroutines are defined in the lib \texttt{libomp.so / libgomp.so}. Don't - forget to include \texttt{\#include }} -\item{These functions can be called anywhere in your programs} -\end{itemize} -\end{exampleblock} -\end{frame} - -\subsubsection{General purpose routines - selection} - -%\begin{frame} -%\frametitle{Runtime Library routines} -%\framesubtitle{General purpose routines} -%\begin{center} -%\begin{tabular}{|l|l|} -%\hline -% \textbf{routine} & \textbf{behavior} \\ -%\hline -%\hline -%\texttt{omp\_set\_num\_threads} & sets/gets number of threads to be used \\ -%\texttt{omp\_get\_num\_threads} & for subsequent parallel regions that \\ -% & do not specify a num\_threads clause \\ -% & by setting the value of the first \\ -%& element of the nthreads-var ICV of \\ -%& the current task \\ -%\hline -%\texttt{omp\_get\_max\_threads} & -%returns an upper bound on the number of \\ -%& threads that could be used to form a \\ -%& new team if a parallel region without a \\ -%& num\_threads clause were encountered \\ -%& after execution returns from this routine \\ -%\hline -% -%\end{tabular} -%\end{center} -% -%\end{frame} - -%\begin{frame} -%\frametitle{Runtime Library routines} -%\framesubtitle{General purpose routines} -% -%\begin{center} -%\begin{tabular}{|l|l|} -%\hline -% \textbf{routine} & \textbf{behavior} \\ -%\hline -%\hline -%\texttt{omp\_get\_thread\_num} & -%returns the thread number, within the \\ -%& current team, of the calling thread. \\ -%\hline -%\texttt{omp\_get\_num\_procs} & -%returns the number of processors \\ -%& available to the program. \\ -%\hline -%\texttt{omp\_in\_parallel} & -%returns true if the call to the routine \\ -%& is enclosed by an active parallel region \\ -%& ; otherwise, it returns false \\ -%\hline -%\texttt{omp\_set\_dynamic} & -%gets/sets the dynamic adjustment \\ -%\texttt{omp\_get\_dynamic} & -%of the number of threads available \\ -%& for the execution of subsequent \\ -%& parallel regions by getting/setting \\ -%& the value of the dyn-var ICV. \\ -%\hline -%\end{tabular} -%\end{center} -% -%\end{frame} -% -%\begin{frame} -%\frametitle{Runtime Library routines} -%\framesubtitle{General purpose routines} - -%\begin{center} -%\begin{tabular}{|l|l|} -%\hline -% \textbf{routine} & \textbf{behavior} \\ -%\hline -%\hline -%\texttt{omp\_set\_nested} & -%gets/sets nested parallelism, \\ -%\texttt{omp\_get\_nested} & -%by getting/setting the nest-var ICV. \\ -%\hline -%\texttt{omp\_set\_schedule} & -%gets/sets the schedule that is applied \\ -%\texttt{omp\_get\_schedule} & -%when runtime is used as schedule kind, \\ -%& by getting/setting the value of \\ -%& the run-sched-var ICV. \\ -%\hline -%\texttt{omp\_get\_thread\_limit} & -%returns the maximum number of \\ -%& OpenMP threads available to the \\ -%& program. \\ -%\hline -%\end{tabular} -%\end{center} -% -%\end{frame} -% -%\begin{frame} -%\frametitle{Runtime Library routines} -%\framesubtitle{General purpose routines} - -%\begin{center} -%\begin{tabular}{|l|l|} -%\hline -% \textbf{routine} & \textbf{behavior} \\ -%\hline -%\hline -%\texttt{omp\_set\_max\_active\_levels} & -%limits the number of \\ -%\texttt{omp\_get\_max\_active\_levels} & -%nested active parallel \\ -%& regions, by getting/setting \\ -%& the max-active-levels-var ICV. \\ -%\hline -%\texttt{omp\_get\_level} & -%returns the number of nested \\ -%& parallel regions enclosing the \\ -%& task that contains the call. \\ -%\hline -%\texttt{omp\_get\_ancestor\_thread\_num} & -%returns, for a given nested \\ -%& level of the current thread,\\ -%& the thread number of the \\ -%& ancestor or the current \\ -%& thread \\ -%\hline -%\end{tabular} -%\end{center} -% -%\end{frame} -% -%\begin{frame} -%\frametitle{Runtime Library routines} -%\framesubtitle{General purpose routines} - -%\begin{center} -%\begin{tabular}{|l|l|} -%\hline -% \textbf{routine} & \textbf{behavior} \\ -%\hline -%\hline -%\texttt{omp\_get\_team\_size} & -%returns, for a given nested level \\ -%& of the current thread, the size of \\ -%& the thread team to which the ancestor \\ -%& or the current thread belongs \\ -%\hline -%\texttt{omp\_get\_active\_level} & -%returns the number of nested, active \\ -%& parallel regions enclosing the task \\ -%& that contains the call. \\ -%\hline -%\texttt{omp\_in\_final} & -%returns true if the routine is executed \\ -%& in a final task region; otherwise, \\ -%& it returns false. \\ -%\hline -%\end{tabular} -%\end{center} -% -%\end{frame} - -%\subsubsection{Lock routines} -% -%\begin{frame} -%\frametitle{Runtime Library routines} -%\framesubtitle{Lock routines} -% -%\begin{block}{Remark on lock routines} -%The following routines are rarely used. They are mentionned for exhaustivity purposes -%\end{block} -% -%\begin{center} -%\begin{tabular}{|l|l|} -%\hline -% \textbf{routine} & \textbf{behavior} \\ -%\hline -%\hline -%\texttt{omp\_init\_lock} & -%initializes a simple lock \\ -%\hline -%\texttt{omp\_destroy\_lock} & -%uninitializes a simple lock \\ -%\hline -%\texttt{omp\_set\_lock} & -%waits until a simple lock is available \\ -%& and then sets it \\ -%\hline -%\texttt{omp\_unset\_lock} & -%unsets a simple lock \\ -%\hline -%\texttt{omp\_test\_lock} & -%tests a simple lock, and sets it if \\ -%& it is available \\ -%\hline -%\end{tabular} -%\end{center} -% -%\end{frame} - - - -%\subsubsection{Nestable lock routines} -% -%\begin{frame} -%\frametitle{Runtime Library routines} -%\framesubtitle{Nestable lock routines} -% -%\begin{block}{Remark on lock nestable routines} -%The following routines are rarely used. They are mentionned for exhaustivity purposes -%\end{block} -% -%\begin{center} -%\begin{tabular}{|l|l|} -%\hline -% \textbf{routine} & \textbf{behavior} \\ -%\hline -%\hline -%\texttt{omp\_init\_nest\_lock} & -%initializes a nestable lock \\ -%\hline -%\texttt{omp\_destroy\_nest\_lock} & -%uninitializes a nestable lock \\ -%\hline -%\texttt{omp\_set\_nest\_lock} & -%waits until a nestable lock is available \\ -%& and then sets it \\ -%\hline -%\texttt{omp\_unset\_nest\_lock} & -%unsets a nestable lock \\ -%\hline -%\texttt{omp\_test\_nest\_lock} & -%tests a nestable lock, and sets it if \\ -%& it is available \\ -%\hline -%\end{tabular} -%\end{center} -% -%\end{frame} - - -\subsubsection{Timing routines} - -\begin{frame} -\frametitle{Runtime Library routines} -\framesubtitle{Timing routines} - -\begin{center} -\begin{tabular}{|l|l|} -\hline - \textbf{routine} & \textbf{behavior} \\ -\hline -\hline -\texttt{omp\_get\_wtime} & -returns elapsed wall clock time in seconds. \\ -\hline -\texttt{omp\_get\_wtick} & -returns the precision of the timer used by \\ -& \texttt{omp\_get\_wtime} \\ -\hline -\end{tabular} -\end{center} - -\end{frame} - - - - - -\subsection{Environment variables} - -\begin{frame} -\frametitle{Environment variables} -\begin{exampleblock}{Usage} -\begin{itemize} -\item{Environment variables are used to set the ICVs variables} -\item{under \texttt{csh} : \texttt{setenv OMP\_VARIABLE "its-value"}} -\item{under \texttt{bash} : \texttt{export OMP\_VARIABLE="its-value"}} -\end{itemize} -\end{exampleblock} -\end{frame} - -\begin{frame} -\frametitle{Environment variables} - -\begin{center} -\begin{tabular}{|l|l|} -\hline - \textbf{variable} & \textbf{what for ?} \\ -\hline -\hline -\texttt{OMP\_SCHEDULE} -& sets the run-sched-var ICV that specifies \\ -& the runtime schedule type and chunk size. \\ -& It can be set to any of the valid OpenMP \\ -& schedule types. \\ -\hline - -\texttt{OMP\_NUM\_THREADS} -& sets the nthreads-var ICV that specifies \\ -& the number of threads to use in parallel \\ -& regions \\ -\hline - -%\texttt{OMP\_DYNAMIC} -%& sets the dyn-var ICV that specifies the \\ -%& dynamic adjustment of threads to use for \\ -%& parallel regions. \\ - -\hline -\end{tabular} -\end{center} - -\end{frame} - -%\begin{frame} -%\frametitle{Environment variables} -% -%\begin{center} -%\begin{tabular}{|l|l|} -%\hline -% \textbf{variable} & \textbf{what for ?} \\ -%\hline -%\hline -% -%\texttt{OMP\_PROC\_BIND} -%& sets the bind-var ICV that controls whether \\ -%& threads are bound to processors \\ -% -%\hline -%\texttt{OMP\_NESTED} -%& sets the nest-var ICV that enables or disables \\ -%& nested parallelism \\ -% -%\hline -%\texttt{OMP\_STACKSIZE} -%& sets the stacksize-var ICV that specifies \\ -%& the size of the stack for threads created by \\ -%& the OpenMP implementation. \\ -% -%\hline -%\texttt{OMP\_WAIT\_POLICY} -%& sets the wait-policy-var ICV that controls \\ -%& the desired behavior of waiting threads. \\ -% -%\hline -%\end{tabular} -%\end{center} -% -%\end{frame} - -%\begin{frame} -%\frametitle{Environment variables} -% -%\begin{center} -%\begin{tabular}{|l|l|} -%\hline -% \textbf{variable} & \textbf{what for ?} \\ -%\hline -%\hline -%\texttt{OMP\_MAX\_ACTIVE\_LEVELS} -%& sets the max-active-levels-var ICV \\ -%& that controls the maximum number of \\ -%& nested active parallel regions. \\ -% -%\hline -%\texttt{OMP\_THREAD\_LIMIT} -%& sets the thread-limit-var ICV that \\ -%& controls the maximum number of \\ -%& threads participating in the OpenMP \\ -%& program. \\ -% -%\hline -%\end{tabular} -%\end{center} -% -%\end{frame} - - -\subsubsection{The apparent ``easiness'' of OpenMP} - -\begin{frame} -\frametitle{The apparent ``easiness'' of OpenMP} - -\begin{block}{} -\textit{``Compared to MPI, OpenMP is much easier''} -\end{block} - -\begin{exampleblock}{In the reality} -\begin{itemize} -\item{Parallelization of a non-appropriate algorithm} -\item{Parallelization of an unoptimized code} -\item{Race conditions in shared memory environment} -\item{Memory coherence} -\item{Compiler implementation of the OpenMP API} -\item{(Much) more threads/tasks than your machine can support} -\end{itemize} -\end{exampleblock} - -\end{frame} - - -\subsection{About affinity} - - -\begin{frame}[fragile] -\frametitle{OpenMP Thread affinity} - -\textbf{Affinity = on which core does my thread run ?} - -\begin{block}{Show and set affinity with Intel executable} -By setting the \verb+export KMP_AFFINITY=verbose,SCHEDULING+ you are able to see where the OS pin each thread -\end{block} -\begin{block}{Show and set affinity with GNU executable} -By setting the \verb+export GOMP_CPU_AFFINITY=verbose,SCHEDULING+ you are able to see where the OS pin each thread -\end{block} -\end{frame} - - - -\begin{frame}[containsverbatim] - \frametitle{OpenMP Thread affinity with compact} - \begingroup - \fontsize{6pt}{12pt}\linespread{0.5}\selectfont -\begin{verbatim} -vkeller@mathicsepc13:~$ export KMP_AFFINITY=verbose,compact -vkeller@mathicsepc13:~$ ./ex10 -OMP: Info #204: KMP_AFFINITY: decoding x2APIC ids. -OMP: Info #202: KMP_AFFINITY: Affinity capable, using global cpuid leaf 11 info -OMP: Info #154: KMP_AFFINITY: Initial OS proc set respected: {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15} -OMP: Info #156: KMP_AFFINITY: 16 available OS procs -OMP: Info #157: KMP_AFFINITY: Uniform topology -OMP: Info #179: KMP_AFFINITY: 2 packages x 4 cores/pkg x 2 threads/core (8 total cores) -OMP: Info #206: KMP_AFFINITY: OS proc to physical thread map: -OMP: Info #171: KMP_AFFINITY: OS proc 0 maps to package 0 core 0 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 8 maps to package 0 core 0 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 1 maps to package 0 core 1 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 9 maps to package 0 core 1 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 2 maps to package 0 core 9 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 10 maps to package 0 core 9 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 3 maps to package 0 core 10 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 11 maps to package 0 core 10 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 4 maps to package 1 core 0 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 12 maps to package 1 core 0 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 5 maps to package 1 core 1 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 13 maps to package 1 core 1 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 6 maps to package 1 core 9 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 14 maps to package 1 core 9 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 7 maps to package 1 core 10 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 15 maps to package 1 core 10 thread 1 -OMP: Info #144: KMP_AFFINITY: Threads may migrate across 1 innermost levels of machine -OMP: Info #147: KMP_AFFINITY: Internal thread 0 bound to OS proc set {0,8} -OMP: Info #147: KMP_AFFINITY: Internal thread 1 bound to OS proc set {0,8} -OMP: Info #147: KMP_AFFINITY: Internal thread 2 bound to OS proc set {1,9} -OMP: Info #147: KMP_AFFINITY: Internal thread 3 bound to OS proc set {1,9} - [DGEMM] Compute time [s] : 0.344645023345947 - [DGEMM] Performance [GF/s]: 0.580307233391397 - [DGEMM] Verification : 2000000000.00000 -\end{verbatim} - \endgroup -\end{frame} - - - -\begin{frame}[containsverbatim] - \frametitle{OpenMP Thread affinity with scatter} - \begingroup - \fontsize{6pt}{12pt}\linespread{0.5}\selectfont -\begin{verbatim} -vkeller@mathicsepc13:~$ export KMP_AFFINITY=verbose,scatter -vkeller@mathicsepc13:~$ ./ex10 -OMP: Info #204: KMP_AFFINITY: decoding x2APIC ids. -OMP: Info #202: KMP_AFFINITY: Affinity capable, using global cpuid leaf 11 info -OMP: Info #154: KMP_AFFINITY: Initial OS proc set respected: {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15} -OMP: Info #156: KMP_AFFINITY: 16 available OS procs -OMP: Info #157: KMP_AFFINITY: Uniform topology -OMP: Info #179: KMP_AFFINITY: 2 packages x 4 cores/pkg x 2 threads/core (8 total cores) -OMP: Info #206: KMP_AFFINITY: OS proc to physical thread map: -OMP: Info #171: KMP_AFFINITY: OS proc 0 maps to package 0 core 0 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 8 maps to package 0 core 0 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 1 maps to package 0 core 1 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 9 maps to package 0 core 1 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 2 maps to package 0 core 9 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 10 maps to package 0 core 9 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 3 maps to package 0 core 10 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 11 maps to package 0 core 10 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 4 maps to package 1 core 0 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 12 maps to package 1 core 0 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 5 maps to package 1 core 1 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 13 maps to package 1 core 1 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 6 maps to package 1 core 9 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 14 maps to package 1 core 9 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 7 maps to package 1 core 10 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 15 maps to package 1 core 10 thread 1 -OMP: Info #144: KMP_AFFINITY: Threads may migrate across 1 innermost levels of machine -OMP: Info #147: KMP_AFFINITY: Internal thread 0 bound to OS proc set {0,8} -OMP: Info #147: KMP_AFFINITY: Internal thread 1 bound to OS proc set {4,12} -OMP: Info #147: KMP_AFFINITY: Internal thread 2 bound to OS proc set {1,9} -OMP: Info #147: KMP_AFFINITY: Internal thread 3 bound to OS proc set {5,13} - [DGEMM] Compute time [s] : 0.204235076904297 - [DGEMM] Performance [GF/s]: 0.979263714301724 - [DGEMM] Verification : 2000000000.00000 -\end{verbatim} -\endgroup -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{OpenMP Thread affinity with explicit (a kind of pining)} -\begingroup - \fontsize{6pt}{12pt}\linespread{0.5}\selectfont -\begin{verbatim} -vkeller@mathicsepc13:~$ export KMP_AFFINITY='proclist=[0,2,4,6],explicit',verbose -vkeller@mathicsepc13:~$ ./ex10 -OMP: Info #204: KMP_AFFINITY: decoding x2APIC ids. -OMP: Info #202: KMP_AFFINITY: Affinity capable, using global cpuid leaf 11 info -OMP: Info #154: KMP_AFFINITY: Initial OS proc set respected: {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15} -OMP: Info #156: KMP_AFFINITY: 16 available OS procs -OMP: Info #157: KMP_AFFINITY: Uniform topology -OMP: Info #179: KMP_AFFINITY: 2 packages x 4 cores/pkg x 2 threads/core (8 total cores) -OMP: Info #206: KMP_AFFINITY: OS proc to physical thread map: -OMP: Info #171: KMP_AFFINITY: OS proc 0 maps to package 0 core 0 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 8 maps to package 0 core 0 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 1 maps to package 0 core 1 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 9 maps to package 0 core 1 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 2 maps to package 0 core 9 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 10 maps to package 0 core 9 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 3 maps to package 0 core 10 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 11 maps to package 0 core 10 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 4 maps to package 1 core 0 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 12 maps to package 1 core 0 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 5 maps to package 1 core 1 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 13 maps to package 1 core 1 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 6 maps to package 1 core 9 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 14 maps to package 1 core 9 thread 1 -OMP: Info #171: KMP_AFFINITY: OS proc 7 maps to package 1 core 10 thread 0 -OMP: Info #171: KMP_AFFINITY: OS proc 15 maps to package 1 core 10 thread 1 -OMP: Info #144: KMP_AFFINITY: Threads may migrate across 1 innermost levels of machine -OMP: Info #147: KMP_AFFINITY: Internal thread 0 bound to OS proc set {0,8} -OMP: Info #147: KMP_AFFINITY: Internal thread 3 bound to OS proc set {6,14} -OMP: Info #147: KMP_AFFINITY: Internal thread 1 bound to OS proc set {2,10} -OMP: Info #147: KMP_AFFINITY: Internal thread 2 bound to OS proc set {4,12} - [DGEMM] Compute time [s] : 0.248908042907715 - [DGEMM] Performance [GF/s]: 0.803509591990774 - [DGEMM] Verification : 2000000000.00000 -\end{verbatim} -\endgroup -\end{frame} - - - - - - -\subsubsection{``OpenMP-ization'' strategy} - - -\begin{frame} -\frametitle{``OpenMP-ization'' strategy} - -\begin{itemize} -\item {\textbf{STEP 1} : Optimize the sequential version: - \begin{itemize} - \item {Choose the best algorithm} - \item {``Help the (right) compiler''} - \item {Use the existing optimized scientific libraries} - \end{itemize} -} -\item {\textbf{STEP 2} : Parallelize it: - \begin{itemize} - \item {Identify the bottlenecks (heavy loops)} - \item {``auto-parallelization'' is rarely the best !} - \end{itemize} -} -\end{itemize} - -\begin{alertblock}{Goal} -Debugging - Profiling - Optimization cycle. Then parallelization ! -\end{alertblock} - - -\end{frame} - -\begin{frame} -\frametitle{Tricks and tips} - -\begin{block}{} -\begin{itemize} -\item{\textbf{Algorithm}: choose the ``best'' one} -%\item{\textbf{Implementation}: choose the best one (remember Fibonacci)} -\item{\textbf{cc-NUMA}: no (real) support from OpenMP side (but OS). A multi-CPU machine is not a real shared memory architecture} -\item{\textbf{False-sharing}: multiple threads write in the same cache line} -\item{\textbf{Avoid barrier}. This is trivial. Bus sometimes you can't} -\item{\textbf{Small number of tasks}. Try to reduce the number of forked tasks} -\item{\textbf{Asymetrical problem}. OpenMP is well suited for symetrical problems, even if tasks can help} -\item{\textbf{Tune the schedule}: types, chunks...} -\item{\textbf{Performance expectations}: a theoretical analysis using the simple Amdahl's law can help} -\item{\textbf{Parallelization level}: coarse (SPMD) or fine (loop) grain ?} -\end{itemize} -\end{block} - -\end{frame} - - - - -\subsection{Conclusion} - -\begin{frame} -\frametitle{A simple conclusion ...} -\begin{center} - {\includegraphics[height=2.5cm]{day1/images/warning.png}} -\begin{alertblock}{The message} - \textbf{FIRST OPTIMIZE ON ONE CORE, THEN PARALLELIZE (the right algorithm)} -\end{alertblock} - -\url{http://openmp.org/wp/openmp-compilers} - -\end{center} - -\end{frame} - - - - - -% ============================================================= -% OpenMP 4.0 -% ============================================================= - -\subsection{What's new in 4.0 ?} - - -\begin{frame}[fragile] - \frametitle{What's new with OpenMP 4.0 ?} - - \begin{itemize} - \item{ Support for new devices (\verb+Intel Phi+, \verb+GPU+,...) with \verb+omp target+. Offloading on those devices. } - \item{ Hardware agnostic} - \item{ League of threads with \verb+omp teams+ and distribute a loop over the team with \verb+omp distribute+ } - \item{ SIMD support for vectorization \verb+omp simd+ } - \item{ Task management enhancements (cancelation of a task, groups of tasks, task-to-task synchro)} - \item{ Set thread affinity with a more standard way than \verb+KMP_AFFINITY+ with the concepts of \verb+places+ (a thread, a core, a socket), \verb+policies+ (spread, close, master) and \verb+control settings+ the new clause \verb+proc_bind+} - \end{itemize} -\end{frame} - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: "../phys_743_parallel_programming" -%%% End: diff --git a/day1/optim.tex b/day1/optim.tex deleted file mode 100644 index 373f77b..0000000 --- a/day1/optim.tex +++ /dev/null @@ -1,528 +0,0 @@ -\subsection{Debugging-Profiling-Optimization-Parallelization} - -\begin{frame}[containsverbatim] - \frametitle{SDLC} - \begin{figure}[ht!] - \centering - \includegraphics[width=7cm]{day1/images/SDLC.jpg} - \end{figure} -\end{frame} - - - -\begin{frame} - \frametitle{Before you start your parallel implementation} - - \begin{itemize} - \item {\bf You have no serial code : } design your application in a parallel way from scratch - \item {\bf You have a serial code :} follow a Debugging-Profiling-Optimization cycle before any parallelization - \end{itemize} -\end{frame} - -\subsubsection{Debugging} - -\begin{frame} - \frametitle{Debugging ?} - - \begin{itemize} - \item Find and correct bugs within an application - \item Bugs can be of various nature : division by zero, buffer overflow, null pointer, infinite loops, etc.. - \item The compiler is (very) rarely able to recognize a bug at compilation time and the error is (very) rarely explicit regarding the bug ("syntax error") - \item Use standard tools like {\tt gdb} - \item A multi-threaded code can be tricky to debug (race conditions, deadlocks, etc..) - \item (Complex) tools exist for parallel debug : {\tt Totalview}, {\tt Alinea DDT} or recently {\tt Eclipse PTP} - \end{itemize} - -\end{frame} - - -\subsubsection{Profiling} - -\begin{frame} - \frametitle{Profiling ?} - - Where do I spend most of the time ? - - \begin{itemize} - \item (good) using tools like {\tt gprof} or {\tt Intel Amplifier} - \item (bad) ``by hand'' using timings and {\tt printf}'s - \end{itemize} -\end{frame} - -\begin{frame} - \frametitle{Profiling ?} - - What should be profiled ? - - \begin{itemize} - \item TTS (Time To Solution) - \item best usage of resources (storage, memory, etc..) - \item behavior of the application to scale - \item ... - \end{itemize} -\end{frame} - - - -\begin{frame}[containsverbatim] - \frametitle{Profiling : an example with gprof} - - \begin{itemize} - \item {{\bf MiniFE as test application} - \begin{itemize} - \item 3D implicit finite-elements on an unstructured mesh - \item mini-application written in C++ - \item \url{http://www.mantevo.org} - \end{itemize} - } - \item compile with {\tt -pg -g -O3 -ftree-vectorize} - \item run it. It should produce a {\tt gmon.out} file - \item then profile it {\tt gprof miniFE.x} - \end{itemize} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{Profiling : an example with gprof} - - Size : ($128~x~128~x~128$) - -\begin{Verbatim}[fontsize=\tiny] -Flat profile: - -Each sample counts as 0.01 seconds. -% cumulative self self total - time seconds seconds calls s/call s/call name - 62.15 2.61 2.61 1 2.61 2.61 void miniFE::cg_solve - 8.57 2.97 0.36 2 0.18 0.18 void miniFE::impose_dirichlet - 5.71 3.21 0.24 7471812 0.00 0.00 int miniFE::find_row_for_id - 5.71 3.45 0.24 274625 0.00 0.00 void miniFE::Hex8::diffusionMatrix_symm - 4.76 3.65 0.20 274625 0.00 0.00 void miniFE::sum_in_symm_elem_matrix - 2.62 3.76 0.11 2197000 0.00 0.00 void miniFE::Hex8::gradients_and_invJ_and_detJ - 1.90 3.84 0.08 274625 0.00 0.00 void miniFE::get_elem_nodes_and_coords - 1.90 3.92 0.08 1 0.08 0.08 int miniFE::verify_solution - 1.67 3.99 0.07 2197000 0.00 0.00 void miniFE::Hex8::gradients_and_detJ - 0.95 4.03 0.04 274625 0.00 0.00 void miniFE::Hex8::sourceVector - 0.95 4.07 0.04 1 0.04 0.04 void miniFE::make_local_matrix - 0.71 4.10 0.03 1 0.03 0.03 std::vector::_M_fill_insert - 0.71 4.13 0.03 1649773 0.00 0.00 miniFE::mytimer() - 0.71 4.16 0.03 1 0.03 0.31 int miniFE::generate_matrix_structure - 0.48 4.18 0.02 1 0.02 0.03 void miniFE::create_map_id_to_row - 0.24 4.19 0.01 8 0.00 0.00 void miniFE::get_ids - 0.24 4.20 0.01 1 0.01 0.27 void miniFE::init_matrix - 0.00 4.20 0.00 270400 0.00 0.00 void sort_if_needed - 0.00 4.20 0.00 33282 0.00 0.00 std::_Rb_tree - -... -\end{Verbatim} -\end{frame} - - -\begin{frame} - \frametitle{Profiling : an example with gprof} - - What do we learn ? - - \begin{itemize} - \item 62.15 \% of the time is spent in the solver (Conjugate Gradient) - \item 8.57 \% is spent in imposing the boundary conditions - \item etc.. - \item with that specific problem size ($128~x~128~x~128$). Is that similar with a larger/smaller one ? - \end{itemize} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{Profiling : an example with gprof} - - Smaller ($16~x~16~x~16$) - -\begin{Verbatim}[fontsize=\tiny] -Flat profile: - -Each sample counts as 0.01 seconds. -% cumulative self self total - time seconds seconds calls ms/call ms/call name -100.01 0.01 0.01 1 10.00 10.00 void miniFE::cg_solve - 0.00 0.01 0.00 18605 0.00 0.00 int miniFE::find_row_for_id - 0.00 0.01 0.00 5832 0.00 0.00 void miniFE::Hex8::gradients_and_detJ - 0.00 0.01 0.00 5832 0.00 0.00 void miniFE::Hex8::gradients_and_invJ_and_detJ - 0.00 0.01 0.00 4907 0.00 0.00 miniFE::mytimer() - 0.00 0.01 0.00 729 0.00 0.00 void sort_if_needed - 0.00 0.01 0.00 729 0.00 0.00 void miniFE::sum_in_symm_elem_matrix - 0.00 0.01 0.00 729 0.00 0.00 void miniFE::get_elem_nodes_and_coords - 0.00 0.01 0.00 729 0.00 0.00 void miniFE::Hex8::sourceVector - 0.00 0.01 0.00 729 0.00 0.00 void miniFE::Hex8::diffusionMatrix_symm - 0.00 0.01 0.00 578 0.00 0.00 std::_Rb_tree -#include -#define up 10 -int main() { - int i,n; - n = 0; - for (i = 0; i < up; i++){ - n = n + 1; - } - return 0; -} -\end{lstlisting} - -\url{https://gcc.godbolt.org/} - -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{Preprocessor ({\tt gcc -E})} -\begin{verbatim} -(...) -# 1 "/usr/include/x86_64-linux-gnu/bits/stdlib-float.h" 1 3 4 -# 956 "/usr/include/stdlib.h" 2 3 4 -# 968 "/usr/include/stdlib.h" 3 4 - -# 3 "very-simple.c" 2 - -int main() { - int i,n; - n = 0; - for (i = 0;i < 10; i++){ - n = n + 1; - } - return 0; -} -\end{verbatim} -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{Compiler ({\tt gcc -S})} -\begin{verbatim} -main: -.LFB2: - pushq %rbp - movq %rsp, %rbp - movl $0, -8(%rbp) - movl $0, -4(%rbp) - jmp .L2 -.L3: - addl $1, -8(%rbp) - addl $1, -4(%rbp) -.L2: - cmpl $9, -4(%rbp) - jle .L3 - movl $0, %eax - popq %rbp - ret -\end{verbatim} -\end{frame} - - - -\begin{frame}[containsverbatim] -\frametitle{Assembler ({\tt gcc -c})} -\begin{verbatim} - 0: 55 push %rbp - 1: 48 89 e5 mov %rsp,%rbp - 4: c7 45 f8 00 00 00 00 movl $0x0,-0x8(%rbp) - b: c7 45 fc 00 00 00 00 movl $0x0,-0x4(%rbp) - 12: eb 08 jmp 1c - 14: 83 45 f8 01 addl $0x1,-0x8(%rbp) - 18: 83 45 fc 01 addl $0x1,-0x4(%rbp) - 1c: 83 7d fc 09 cmpl $0x9,-0x4(%rbp) - 20: 7e f2 jle 14 - 22: b8 00 00 00 00 mov $0x0,%eax - 27: 5d pop %rbp - 28: c3 retq -\end{verbatim} -(using {\tt objdump -d file.o}) -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{Linker ({\tt gcc -o})} -\begin{alertblock}{} -This last stage produces the actual executable (by linking against external libraries if required) -\end{alertblock} -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{All stages in one command} - -\begin{itemize} - \item In real life, it is very unusual that one go through all the stages separatly. - \item The two main phases are {\bf compilation} ({\tt gcc -c}) and {\bf linking} ({\tt gcc -o}) -\end{itemize} - -\begin{verbatim} -vkeller@deneb1:~]$ gcc -c file1.c -o file1.o -vkeller@deneb1:~]$ gcc -c file2.c -o file2.o -vkeller@deneb1:~]$ gcc file1.o file2.o -o app.exe -vkeller@deneb1:~]$ ./app.exe -\end{verbatim} - -\begin{itemize} - \item or both at once : -\end{itemize} - -\begin{verbatim} -vkeller@deneb1:~]$ gcc file1.c file2.c -o app.exe -vkeller@deneb1:~]$ ./app.exe -\end{verbatim} -\end{frame} - -\begin{frame} -\frametitle{But ...} - -\begin{itemize} - \item complexity whith multiple files - \item dependencies - \item need for a more complex tool : {\tt Makefiles} ! -\end{itemize} -\end{frame} - - -\subsection{Makefile} - -\begin{frame} -\frametitle{About Makefiles} - -\begin{itemize} - \item a {\tt Makefile} is nothing but a {\bf recipe} on how to produce an executable - \begin{itemize} - \item what to compile ? - \item how to compile ? - \item what to link ? - \item how to link ? - \end{itemize} - \item useful for large projects or for testing purpose - \item full (re)usage of {\tt variables} - \item The usual name is {\tt Makefile} or {\tt makefile} or specified when calling {\tt make -f special.makefile} -\end{itemize} -\end{frame} - -\begin{frame}[containsverbatim] -\frametitle{What is contained in a Makefile ?} -As an example -\begin{itemize} - \item a source file {\tt poisson.c} to compile - \item you want to produce two executable versions : - \begin{itemize} - \item non-optimized with debug information - \item optimized - \end{itemize} - \item with the GNU compiler -\end{itemize} - -\begin{verbatim} -gcc -O0 -g poisson.c -lm -o p-gcc-debug.exe -gcc -O3 -ftree-vectorize poisson.c -lm -o p-gcc-optim.exe -\end{verbatim} -\end{frame} - -\begin{frame}[containsverbatim] -\frametitle{What is contained in a Makefile ?} -\begin{verbatim} -CC = gcc -CFLAGS = -O3 -ftree-vectorize -LDFLAGS = -lm - -all: p-gcc-optim.exe - -.o.c: - $(CC) -c $(CFLAGS) $(OBJ) $< -OBJ = poisson.o - -p-gcc-optim.exe: - $(CC) $(LDFLAGS) $(OBJ) -o $@ - -clean: - rm -f *.o p-gcc-optim.exe -\end{verbatim} -\end{frame} - -\begin{frame}[containsverbatim] -\frametitle{How to use the Makefile ?} - -to get the optimized version : -\begin{verbatim} -make -\end{verbatim} - -to get the non-optimized with debug information version : -\begin{verbatim} -make CFLAGS="-O0 -g" -\end{verbatim} - -Optimized version with the Intel compiler ? -\begin{verbatim} -make CC=icc CFLAGS="-O3 -xHost" LDFLAGS="" -\end{verbatim} - -or by editing the variables {\tt CC}, {\tt CFLAGS} and {\tt LDFLAGS} in the Makefile. - -\end{frame} - - -\subsection{Optimization flags} - - -\begin{frame} -\frametitle{Compiler optimization} - -\begin{itemize} - \item Different levels of optimization - \begin{itemize} - \item instructions level - \item datatype level - \item global level (inter-procedural optimization or ''IPO'') - \item loops level - \item machine code optimization - \end{itemize} - \item it is possible to optimize at each level - \item {\bf Optimization by compiler can lead to semantic changes} thus wrong results ! -\end{itemize} - -\end{frame} - - -\begin{frame} -\frametitle{Compiler optimization} - -\begin{itemize} - \item {\tt gcc -O0} no optimization - \item {\tt gcc -O1} ''the compiler tries to reduce code size and execution time'' - \item {\tt gcc -O2} ''performs nearly all supported optimizations that do not involve a space-speed tradeoff'' - \item {\tt gcc -O3} ''optimize yet more. It is -O2 plus others''. Warning: this can change the code semantics. - \item {\tt gcc -Ofast} ''Disregard strict standards compliance.'' - \item {\tt gcc -ftree-vectorize} ''perform vectorization on trees enables all -O3 optimizations plus -ffast-math'' -\end{itemize} - -\end{frame} - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: "../phys_743_parallel_programming" -%%% End: diff --git a/day2/images/Eratosthene.png b/day2/images/Eratosthene.png deleted file mode 100644 index b2dfe62..0000000 Binary files a/day2/images/Eratosthene.png and /dev/null differ diff --git a/day2/images/beowulf-hardware.tex b/day2/images/beowulf-hardware.tex deleted file mode 100644 index 58f85c7..0000000 --- a/day2/images/beowulf-hardware.tex +++ /dev/null @@ -1,33 +0,0 @@ -\begin{tikzpicture}[node distance=8mm, -node/.append style={xshift=5mm}, -master/.append style={yshift=-.6cm}, -switch/.append style={yshift=-1cm}, -internet/.append style={yshift = -1cm} -] - -\tikzstyle{sample} = [-,thin] - - \node (node0) [node] 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a/day2/images/compilation-stages.fig.bak +++ /dev/null @@ -1,31 +0,0 @@ -#FIG 3.2 Produced by xfig version 3.2.5c -Landscape -Center -Metric -A4 -100.00 -Single --2 -1200 2 -2 4 0 2 0 7 50 -1 -1 0.000 0 0 7 0 0 5 - 3060 1305 1170 1305 1170 675 3060 675 3060 1305 -2 1 0 2 1 7 50 -1 -1 0.000 0 0 -1 1 0 2 - 2 1 1.00 60.00 120.00 - 2070 1350 2070 1890 -2 4 0 2 0 7 50 -1 -1 0.000 0 0 7 0 0 5 - 3060 2565 1170 2565 1170 1935 3060 1935 3060 2565 -2 1 0 2 1 7 50 -1 -1 0.000 0 0 -1 1 0 2 - 2 1 1.00 60.00 120.00 - 2070 2610 2070 3150 -2 4 0 2 0 7 50 -1 -1 0.000 0 0 7 0 0 5 - 3060 3825 1170 3825 1170 3195 3060 3195 3060 3825 -2 1 0 2 1 7 50 -1 -1 0.000 0 0 -1 1 0 2 - 2 1 1.00 60.00 120.00 - 2070 3870 2070 4410 -2 4 0 2 0 7 50 -1 -1 0.000 0 0 7 0 0 5 - 3060 5085 1170 5085 1170 4455 3060 4455 3060 5085 -4 0 0 50 -1 0 12 0.0000 4 180 1590 1350 1125 gcc -E file.c -o file.i\001 -4 0 0 50 -1 2 12 0.0000 4 180 1125 1530 900 Preprocessor\001 -4 0 0 50 -1 2 12 0.0000 4 180 1125 1530 4680 Preprocessor\001 -4 0 0 50 -1 2 12 0.0000 4 180 1125 1530 3420 Preprocessor\001 -4 0 0 50 -1 2 12 0.0000 4 180 1125 1530 2160 Preprocessor\001 diff --git a/day2/images/compilation.tex b/day2/images/compilation.tex deleted file mode 100644 index 2e3ce48..0000000 --- a/day2/images/compilation.tex +++ /dev/null @@ -1,328 +0,0 @@ -\subsection{Compilation remainder} - -\begin{frame} -\frametitle{Compilation remainder} - -\begin{itemize} - \item understanding the different compilation phases - \item what are {\tt Makefiles} ? - \item what happen to the application when using the different optimization flags ? -\end{itemize} - -\end{frame} - -\subsection{Back to the roots} - -\begin{frame} -\frametitle{{\tt 00111001011100110111...}} - -{\bf Back to the roots} - -\begin{itemize} -% \item a computer (in fact a processor or a CPU) understands nothing but {\bf ON} and {\bf OFF} (one or zero) - \item a computer (in fact a processor or a CPU) understands nothing but {\bf ON} and {\bf OFF} ({\tt 1} or {\tt 0}) - \item There is a 4-stages process to transform a {\bf source code} from a programming language into {\it something} which is understandable by the processor (the {\bf Machine Code}) -\end{itemize} - -\end{frame} - - -\begin{frame} -\frametitle{Programming languages} - -Different programming languages : - -\begin{itemize} - \item {\bf C/C++} or {\bf Fortran} are high level compiled languages -% \item {\bf Matlab}, {\bf Python}, {\bf R} are high level interpreted languages -\end{itemize} - -they are {\bf human readable} % and with a {\bf high level of abstraction} - -\begin{itemize} - \item The {\bf assembly language} (depending on the CPU) is a {\bf low level language} -\end{itemize} - -difficult to read. It calls only CPU instructions like a LOAD, a jump or a numerical operation. - -\begin{itemize} - \item the {\bf machine code} (depending on the CPU) is the only {\bf language understandable by the processor} -\end{itemize} - -\end{frame} - -\begin{frame} -\frametitle{Compilation} -\begin{alertblock}{Question} -How to produce machine code out of high-level language ? For instance from a {\tt C} source code ? -\end{alertblock} -\end{frame} - -\begin{frame} -\frametitle{Punch cards} -\begin{center} -{\includegraphics[width=11cm]{Day2/images/punch-card.jpg}} -\end{center} -\end{frame} - -\begin{frame} -\frametitle{Modern days : with a compiler} -\begin{center} -{\input{Day2/images/compilation_stages.tex}} -\end{center} -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{Example with a C source} -\begin{lstlisting}[language=C,frame=lines] -#include -#include -#define up 10 -int main() { - int i,n; - n = 0; - for (i = 0; i < up; i++){ - n = n + 1; - } - return 0; -} -\end{lstlisting} - -\url{https://gcc.godbolt.org/} - -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{Preprocessor ({\tt gcc -E})} -\begin{verbatim} -(...) -# 1 "/usr/include/x86_64-linux-gnu/bits/stdlib-float.h" 1 3 4 -# 956 "/usr/include/stdlib.h" 2 3 4 -# 968 "/usr/include/stdlib.h" 3 4 - -# 3 "very-simple.c" 2 - -int main() { - int i,n; - n = 0; - for (i = 0;i < 10; i++){ - n = n + 1; - } - return 0; -} -\end{verbatim} -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{Compiler ({\tt gcc -S})} -\begin{verbatim} -main: -.LFB2: - pushq %rbp - movq %rsp, %rbp - movl $0, -8(%rbp) - movl $0, -4(%rbp) - jmp .L2 -.L3: - addl $1, -8(%rbp) - addl $1, -4(%rbp) -.L2: - cmpl $9, -4(%rbp) - jle .L3 - movl $0, %eax - popq %rbp - ret -\end{verbatim} -\end{frame} - - - -\begin{frame}[containsverbatim] -\frametitle{Assembler ({\tt gcc -c})} -\begin{verbatim} - 0: 55 push %rbp - 1: 48 89 e5 mov %rsp,%rbp - 4: c7 45 f8 00 00 00 00 movl $0x0,-0x8(%rbp) - b: c7 45 fc 00 00 00 00 movl $0x0,-0x4(%rbp) - 12: eb 08 jmp 1c - 14: 83 45 f8 01 addl $0x1,-0x8(%rbp) - 18: 83 45 fc 01 addl $0x1,-0x4(%rbp) - 1c: 83 7d fc 09 cmpl $0x9,-0x4(%rbp) - 20: 7e f2 jle 14 - 22: b8 00 00 00 00 mov $0x0,%eax - 27: 5d pop %rbp - 28: c3 retq -\end{verbatim} -(using {\tt objdump -d file.o}) -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{Linker ({\tt gcc -o})} -\begin{alertblock}{} -This last stage produces the actual executable (by linking against external libraries if required) -\end{alertblock} -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{All stages in one command} - -\begin{itemize} - \item In real life, it is very unusual that one go through all the stages separatly. - \item The two main phases are {\bf compilation} ({\tt gcc -c}) and {\bf linking} ({\tt gcc -o}) -\end{itemize} - -\begin{verbatim} -vkeller@deneb1:~]$ gcc -c file1.c -o file1.o -vkeller@deneb1:~]$ gcc -c file2.c -o file2.o -vkeller@deneb1:~]$ gcc file1.o file2.o -o app.exe -vkeller@deneb1:~]$ ./app.exe -\end{verbatim} - -\begin{itemize} - \item or both at once : -\end{itemize} - -\begin{verbatim} -vkeller@deneb1:~]$ gcc file1.c file2.c -o app.exe -vkeller@deneb1:~]$ ./app.exe -\end{verbatim} -\end{frame} - -\begin{frame} -\frametitle{But ...} - -\begin{itemize} - \item complexity whith multiple files - \item dependencies - \item need for a more complex tool : {\tt Makefiles} ! -\end{itemize} -\end{frame} - - -\subsection{Makefile} - -\begin{frame} -\frametitle{About Makefiles} - -\begin{itemize} - \item a {\tt Makefile} is nothing but a {\bf recipe} on how to produce an executable - \begin{itemize} - \item what to compile ? - \item how to compile ? - \item what to link ? - \item how to link ? - \end{itemize} - \item useful for large projects or for testing purpose - \item full (re)usage of {\tt variables} - \item The usual name is {\tt Makefile} or {\tt makefile} or specified when calling {\tt make -f special.makefile} -\end{itemize} -\end{frame} - -\begin{frame}[containsverbatim] -\frametitle{What is contained in a Makefile ?} -As an example -\begin{itemize} - \item a source file {\tt poisson.c} to compile - \item you want to produce two executable versions : - \begin{itemize} - \item non-optimized with debug information - \item optimized - \end{itemize} - \item with the GNU compiler -\end{itemize} - -\begin{verbatim} -gcc -O0 -g poisson.c -lm -o p-gcc-debug.exe -gcc -O3 -ftree-vectorize poisson.c -lm -o p-gcc-optim.exe -\end{verbatim} -\end{frame} - -\begin{frame}[containsverbatim] -\frametitle{What is contained in a Makefile ?} -\begin{verbatim} -CC = gcc -CFLAGS = -O3 -ftree-vectorize -LDFLAGS = -lm - -all: p-gcc-optim.exe - -.o.c: - $(CC) -c $(CFLAGS) $(OBJ) $< -OBJ = poisson.o - -p-gcc-optim.exe: - $(CC) $(LDFLAGS) $(OBJ) -o $@ - -clean: - rm -f *.o p-gcc-optim.exe -\end{verbatim} -\end{frame} - -\begin{frame}[containsverbatim] -\frametitle{How to use the Makefile ?} - -to get the optimized version : -\begin{verbatim} -make -\end{verbatim} - -to get the non-optimized with debug information version : -\begin{verbatim} -make CFLAGS="-O0 -g" -\end{verbatim} - -Optimized version with the Intel compiler ? -\begin{verbatim} -make CC=icc CFLAGS="-O3 -xHost" LDFLAGS="" -\end{verbatim} - -or by editing the variables {\tt CC}, {\tt CFLAGS} and {\tt LDFLAGS} in the Makefile. - -\end{frame} - - -\subsection{Optimization flags} - - -\begin{frame} -\frametitle{Compiler optimization} - -\begin{itemize} - \item Different levels of optimization - \begin{itemize} - \item instructions level - \item datatype level - \item global level (inter-procedural optimization or ''IPO'') - \item loops level - \item machine code optimization - \end{itemize} - \item it is possible to optimize at each level - \item {\bf Optimization by compiler can lead to semantic changes} thus wrong results ! -\end{itemize} - -\end{frame} - - -\begin{frame} -\frametitle{Compiler optimization} - -\begin{itemize} - \item {\tt gcc -O0} no optimization - \item {\tt gcc -O1} ''the compiler tries to reduce code size and execution time'' - \item {\tt gcc -O2} ''performs nearly all supported optimizations that do not involve a space-speed tradeoff'' - \item {\tt gcc -O3} ''optimize yet more. It is -O2 plus others''. Warning: this can change the code semantics. - \item {\tt gcc -Ofast} ''Disregard strict standards compliance.'' - \item {\tt gcc -ftree-vectorize} ''perform vectorization on trees enables all -O3 optimizations plus -ffast-math'' -\end{itemize} - -\end{frame} - - - - - diff --git a/day2/images/compilation_stages.pdf b/day2/images/compilation_stages.pdf deleted file mode 100644 index 8e675e1..0000000 Binary files a/day2/images/compilation_stages.pdf and /dev/null differ diff --git a/day2/images/compilation_stages.tex b/day2/images/compilation_stages.tex deleted file mode 100644 index 2f5a1e3..0000000 --- a/day2/images/compilation_stages.tex +++ /dev/null @@ -1,17 +0,0 @@ -% Slide 34 -\begin{tikzpicture} - -\node[stage] (Preproc) at (0,0) {\stagename{Preprocessor} \texttt{gcc -E file.c -o file.i}}; -\node[stage] (Compiler) at (0,-2) {\stagename{Compiler} \texttt{gcc -S file.i -o file.s}}; -\node[stage] (Assembler) at (0,-4) {\stagename{Assembler} \texttt{gcc -c file.s -o file.o}}; -\node[stage] (Linker) at (0,-6) {\stagename{Linker} \texttt{gcc file.o -lexample -o file}}; - -\node[stage highlight, right of = Assembler, yshift = -1cm, xshift = 5cm, minimum width = 4cm] (Lib) {\stagename{External library} libexample.so}; - - -\draw[->] (Preproc) -- (Compiler); -\draw[->] (Compiler) -- (Assembler); -\draw[->] (Assembler) -- (Linker); -\draw[->, dashed] (Lib.west) -- (Linker.east); - -\end{tikzpicture} diff --git a/day2/images/dijkstras.gif b/day2/images/dijkstras.gif deleted file mode 100644 index acfb1ba..0000000 Binary files a/day2/images/dijkstras.gif and /dev/null differ diff --git a/day2/images/dijkstras.png b/day2/images/dijkstras.png deleted file mode 100644 index 08ee7da..0000000 Binary files a/day2/images/dijkstras.png and /dev/null differ diff --git a/day2/images/distributed-memory.tex b/day2/images/distributed-memory.tex deleted file mode 100644 index 83861e1..0000000 --- a/day2/images/distributed-memory.tex +++ /dev/null @@ -1,22 +0,0 @@ -% Slide 41 -\begin{tikzpicture}[node distance=8mm, -dots/.style={ - font=\sffamily, - xshift=5mm, - minimum width=1cm -}, -node split/.append style = {xshift=5mm} -] - -\tikzstyle{sample} = [-,thin] - - \node (node0) [node split,] {$P_0$ \nodepart{second} $M_0$}; - \node (node1) [node split,right of=node0] {$P_1$ \nodepart{second} $M_1$}; - \node (dots) [dots,right of=node1] {$\ldots$}; - \node (nodeN) [node split,right of=dots] {$P_N$ \nodepart{second} $M_N$}; - \node (switch) [switch,below of=node1, xshift=6mm, yshift=-1cm] {network or switch}; - -\path[sample] (node0.south) edge[out=-60,in=120] (switch.north); -\path[sample] (node1.south) edge[out=-60,in=120] (switch.north); -\path[sample] (nodeN.south) edge[out=-60,in=120] (switch.north); -\end{tikzpicture} diff --git a/day2/images/distributed.png b/day2/images/distributed.png deleted file mode 100644 index c2f4b87..0000000 Binary files a/day2/images/distributed.png and /dev/null differ diff --git a/day2/images/fft.png b/day2/images/fft.png deleted file mode 100644 index 293ec8d..0000000 Binary files a/day2/images/fft.png and /dev/null differ diff --git a/day2/images/gameoflife.png b/day2/images/gameoflife.png deleted file mode 100644 index c145ef4..0000000 Binary files a/day2/images/gameoflife.png and /dev/null differ diff --git a/day2/images/julia.png b/day2/images/julia.png deleted file mode 100644 index 2572e00..0000000 Binary files a/day2/images/julia.png and /dev/null differ diff --git a/day2/images/julia2.png b/day2/images/julia2.png deleted file mode 100644 index 379a63f..0000000 Binary files a/day2/images/julia2.png and /dev/null differ diff --git a/day2/images/mandelbrot.jpg b/day2/images/mandelbrot.jpg deleted file mode 100644 index e35842e..0000000 Binary files a/day2/images/mandelbrot.jpg and /dev/null differ diff --git a/day2/images/nbody.png b/day2/images/nbody.png deleted file mode 100644 index abea4b2..0000000 Binary files a/day2/images/nbody.png and /dev/null differ diff --git a/day2/images/projects-presentation.tex b/day2/images/projects-presentation.tex deleted file mode 100644 index 71cb784..0000000 --- a/day2/images/projects-presentation.tex +++ /dev/null @@ -1,381 +0,0 @@ -\subsection{Introduction} -\begin{frame}[containsverbatim] -\frametitle{Parallelization mini-projects} - -\begin{itemize} - \item{60 hours of personal work} - \item{Individual (for some hard problems : binom)} - \item{We propose subjects but \textbf{you can propose yours !}} - \item{MPI or CUDA (OpenMP/hybrid/MPI-IO are a plus)} -\end{itemize} - -%\begin{alertblock}{Blabla} -%\begin{alertblock}{Blabla} -%\begin{block}{Blabla} -%\end{block} - -Important dates : - -\begin{center} -\begin{tabular}{ | l | l |} -\hline -\textbf{Deliverable} & \textbf{Due date} \\ -\hline -Fixing topic & May 2, 2016 \\ -\hline -Theoretical Analysis & May 15, 2016 \\ -\hline -Final Report & June 5, 2016 \\ -\hline -Exam (15' pres + 15' Q\&A) & June 23, 2016 8:15-18:00 \\ -&and June 24, 2016 8:15-18:00 \\ -\hline -\end{tabular} -\end{center} - -(all at 11:59 pm. CEST) - -\end{frame} - - - - -\subsection{Julia set} -\begin{frame}[containsverbatim] -\frametitle{Julia set} -\begin{center} -\includegraphics[width=5.0cm]{Day2/images/julia2.png} -\end{center} -\begin{block}{Problem description} -The Julia set is the set of points of the complex plan $z = a + b i$ such that the suite -$$ -z_{(n+1)} = z_n^2 + c -$$ -remains bounded when $n \rightarrow \infty$. $c$ is a constant. -\end{block} -\end{frame} -\begin{frame}[containsverbatim] -\frametitle{Julia set} -\begin{block}{Important remarks} -\begin{itemize} - \item{load balancing} -\end{itemize} -\end{block} -\end{frame} - - - -\subsection{Mandelbrot set} -\begin{frame}[containsverbatim] -\frametitle{Mandelbrodt set} -\begin{center} -\includegraphics[width=3.0cm]{Day2/images/mandelbrot.jpg} -\end{center} -\begin{block}{Problem description} -The Mandelbrot set is the set of complex numbers $c$ obtained by the quadratic recurrence equation : -$$ -\left\{ \begin{array}{r} - z_0 = 0 \\ - z_{(n+1)} = z_n^2 + c - \end{array} \right. -$$ -such the suite does not diverge when $n \rightarrow \infty$. -\end{block} -\end{frame} -\begin{frame}[containsverbatim] -\frametitle{Mandelbrodt set} -\begin{block}{Important remarks} -\begin{itemize} - \item{load balancing} - \item{a \textit{colored plot} is obtained by coloring the points with the number of steps required to reach the cut-off value $r_{max}$ value (usually $r_{max} = 2$)} - \item{Mandelbrot set is considered as a ``map'' of all the Julia sets because it uses a different $c$ at each $z$.} -\end{itemize} -\end{block} -\end{frame} - - - - -\subsection{Traveling Salesman Problem} -\begin{frame}[containsverbatim] -\frametitle{Traveling Salesman Problem} -\begin{center} -\includegraphics[width=4.0cm]{Day2/images/tsp.png} -\\ -{\tiny Figure credit: David Applegate, Robert Bixby, Vasek Chvatal and William Cook.} -\end{center} -\begin{block}{Problem description} -Let us have an undirected weighted graph where : cities are the vertices, the edges are the paths, the weight a distance between two cities. The TSP solution is the shortest path starting and finishing at the same vertice and by visiting all the other vertices one and only one time. -\end{block} -\end{frame} -\begin{frame}[containsverbatim] -\frametitle{Traveling Salesman Problem} -\begin{block}{Important remarks} -\begin{itemize} - \item{load balancing} - \item{tree construction} -\end{itemize} -\end{block} -\end{frame} - - - - -\subsection{N-queens problem} -\begin{frame}[containsverbatim] -\frametitle{N queens problem} -\begin{center} -\includegraphics[width=4.0cm]{Day2/images/queen.jpg} -\end{center} -\begin{block}{Problem description} -The N-queens problem is the problem of placing $N$ queens on an $N \times N$ board ($N>3$) so that no queen see each other. A queen can move on its row, its column and its diagonals. -\end{block} -\end{frame} -%\begin{frame}[containsverbatim] -%\frametitle{n queens problem} -%\begin{block}{Important remarks} -%\begin{itemize} -% \item{tree construction} -% \item{} -%\end{itemize} -%\end{block} -%\end{frame} - - - - -\subsection{FFT} -\begin{frame}[containsverbatim] -\frametitle{FFT with Cooley-Tukey} -\begin{center} -\includegraphics[width=4.0cm]{Day2/images/fft.png} -\end{center} -\begin{block}{Problem description} -The Fast Fourier Transform (FFT) Cooley-Tukey algorithm computes the Discrete Fourier Transform (DFT) of a sequence recursively by a devide-and-conquer approach. The radix-2 decimation in time divides a DFT of size $N$ into two interleaved DFT of size $N/2$. -\end{block} -\end{frame} -%\begin{frame}[containsverbatim] -%\frametitle{FFT with Cooley-Tukey} -%A DFT is described as : -%$$ -%X_k = \sum_{n=0}^{N-1} x_n e^{- \frac{2 \pi i}{N} n k} -%$$ -%which can be rearranged as : -%$$ -%X_k = \sum_{m=0}^{N/2-1} x_{2m} e^{- \frac{2 \pi i}{N/2} (2m) k} + e^{- \frac{2 \pi i}{N} k} \sum_{m=0}^{N/2-1} x_{2m+1} e^{- \frac{2 \pi i}{N/2} m k} -%$$ -%in other words : the even and the odd parts of $X_k$ : -%$$ -%X_k = E_k + e^{- \frac{2 \pi i}{N}k} O_k -%$$ -%\end{frame} -%\begin{frame}[containsverbatim] -%\frametitle{FFT with Cooley-Tukey} -%Therefore: -%$$ -%X_k = \left\{ \begin{array}{ll} -% E_k + e^{- \frac{2 \pi i}{N/2}k} O_k & \text{for}~~ 0 \leq k < N/2\\ -% E_{k-N/2} + e^{- \frac{2 \pi i}{N/2}k} O_{k-N/2} &\text{for}~~ N/2 \leq k < N. -% \end{array} \right. -%$$ -%we also know that : -%$$ -%e^{- \frac{2 \pi i}{N}(k+ N/2)} = - e^{- \frac{2 \pi i}{N}k} -%$$ -%thus for $0 \leq k < \frac{N}{2}$ : -%$$ -%\begin{array}{ll} -%X_k & = E_k + e^{- \frac{2 \pi i}{N}k} O_k \\ -%X_{k+\frac{N}{2}} & = E_k - e^{- \frac{2 \pi i}{N}k} O_k -%\end{array} -%$$ -%\end{frame} -%\begin{frame}[containsverbatim] -%\frametitle{FFT with Cooley-Tukey} -%The DFT of length $N$ is then described in terms of two DFT of size $\frac{N}{2}$. The same process is applied recursively until $N=2$. -%\end{frame} -\begin{frame}[containsverbatim] -\frametitle{FFT with Cooley-Tukey} -\begin{block}{Important remarks} -\begin{itemize} - \item{Complexity !} - \item{$x_k$ reordering before devide-and-conquer} - \item{Large size numbers $N = 2^t$ with $t$ as ``large'' as possible} - \item{You can choose other algorithms than Cooley-Tukey} -\end{itemize} -\end{block} -\end{frame} - - - - -\subsection{Minimum spanning tree} -\begin{frame}[containsverbatim] -\frametitle{Minimum Spanning Tree} -\begin{center} -\includegraphics[width=4.0cm]{Day2/images/spanning.png} -\end{center} -\begin{block}{Problem description} -A minimum spanning tree is a spanning tree of a connected, undirected and weighted graph. It connects all the vertices together with the minimal total weighting for its edges -\end{block} -\end{frame} -\begin{frame}[containsverbatim] -\frametitle{Minimum Spanning Tree} -\begin{block}{Important remarks} -\begin{itemize} - \item{Parallelize Boruka's algorithm} - \item{Complexity !} -\end{itemize} -\end{block} -\end{frame} - - - - -\subsection{Dijkstra's algorithm} -\begin{frame}[containsverbatim] -\frametitle{Dijkstra's algorithm} -\begin{center} -\includegraphics[width=4.0cm]{Day2/images/dijkstras.png} -\end{center} -\begin{block}{Problem description} -Dijkstra's algorithm is an algorithm for finding the shortest paths between nodes in a graph. It can be used for finding the shortest paths from a single node to a single destination node by stopping the algorithm once the shortest path to the destination node has been determined -\end{block} -\end{frame} -%\begin{frame}[containsverbatim] -%\frametitle{Dijkstra's algorithm} -%\begin{block}{Important remarks} -%\begin{itemize} -% \item{parallelization of the tree} -%\end{itemize} -%\end{block} -%\end{frame} - - - - - -\subsection{N-body simulation} -\begin{frame}[containsverbatim] -\frametitle{N-body simulation} -\begin{center} -\includegraphics[width=3.0cm]{Day2/images/nbody.png} -\end{center} -\begin{block}{Problem description} -The n-body problem aims at simulating a dynamical system of particles under the influence of physical forces. We'll restrain on the gravity field applied on celestial bodies: -$$ -F_{ij} = \frac{G m_i m_j (q_j - q_i)}{||q_j - q_i||} -$$ -where $G$ is the gravitational constant, $m_i$ and $m_j$ the masses of the $i$-th and $j$-th bodies and $q_i$ and $q_j$ their positions. -\end{block} -\end{frame} -\begin{frame}[containsverbatim] -\frametitle{N-body simulation} -\begin{block}{Important remarks} -\begin{itemize} - \item{brute force will not be accepted} - \item{2D or 3D} - \item{non-uniform initial distribution must be tested to stress the application} - \item{how to handle collisions and ``lost bodies in the far space''} -\end{itemize} -\end{block} -\end{frame} - - - -\subsection{Sieve of Eratosthenes} -\begin{frame}[containsverbatim] -\frametitle{Sieve of Eratosthenes} -\begin{center} -\includegraphics[width=3.0cm]{Day2/images/Eratosthene.png} -\end{center} -\begin{block}{Problem description} -Find all the prime numbers $p$ such $p < N$ where $N$ is very large. Enumerate all the multiples of $p$ by counting to $N$ in incerements of $p$ and mark them as ``non-primes''. Do that to $\sqrt{N}$. The list of $p_i$ are all the primes between $p=2$ to $p=\sqrt{N}$. -\end{block} -\end{frame} -\begin{frame}[containsverbatim] -\frametitle{Sieve of Eratosthenes} -\begin{block}{Important remarks} -\begin{itemize} - \item{load balancing} - \item{Handling very large numbers} - \item{alternative : Sieve of Atkin} -\end{itemize} -\end{block} -\end{frame} - - - - - -\subsection{Game of Life} -\begin{frame}[containsverbatim] -\frametitle{Game of Life} -\begin{center} -\includegraphics[width=3.0cm]{Day2/images/gameoflife.png} -\end{center} -\begin{block}{Problem description} -The game of life is a cellular automaton with simple elements: a cell $c_i$ can be dead ($c_i = 0$) or alive ($c_i = 1$). At each time step, the following rules are applied : -\begin{itemize} - \item {if $c_i = 1$ and its neighbours are 0, 1 or 4 living cells, then $c_{i+1} = 0$} - \item {if $c_i = 1$ and its neighbours are 2 or 3 living cells, then $c_{i+1} = 1$} - \item {if $c_i = 0$ and its neighbours are exactly 3 living cells, then $c_{i+1} = 1$} -\end{itemize} -\end{block} -\end{frame} -\begin{frame}[containsverbatim] -\frametitle{Game of Life} -\begin{block}{Important remarks} -\begin{itemize} - \item{as this problem is very close to Poisson, we'll accept only non-standard subdomain decomposition (topology)} -\end{itemize} -\end{block} -\end{frame} - - - - -\subsection{Jacobi iterative method} -\begin{frame}[containsverbatim] -\frametitle{Jacobi iterative method} -\begin{block}{Problem description} -The Jacobi method solves a linear system $Ax = b$ iteratively: -$$ -A = D + R -$$ -where D is the diagonal matrix of $A$ and $R$ the rest. The solution $x_{(k+1)}$ is obtained with: -$$ -x_{(k+1)} = D^{-1} ( b - R x_k) -$$ -where $x_k$ is the $k$-th iteration of $x$ -\end{block} -\end{frame} - - - -\subsection{Gauss-Seidel iterative method} -\begin{frame}[containsverbatim] -\frametitle{Gauss-Seidel iterative method} -\begin{block}{Problem description} -The Gauss-Seidel method solves a linear system $Ax = b$ iteratively: -$$ -A = L + U -$$ -where $L$ is the lower triangular elements of $A$ and $U$ the strict upper elements of $A$. The solution $x_{(k+1)}$ is obtained with: -$$ -x_{(k+1)} = L^{-1} ( b - U x_k) -$$ -where $x_k$ is the $k$-th iteration of $x$ -\end{block} -\end{frame} - - - - -%\subsection{Shallow Water Equation I\&II} -%\begin{frame}[containsverbatim] -%\frametitle{Shallow Water Equation I\&II} - - -%\end{frame} - diff --git a/day2/images/punch-card-original.jpg b/day2/images/punch-card-original.jpg deleted file mode 100644 index 17c1baf..0000000 Binary files a/day2/images/punch-card-original.jpg and /dev/null differ diff --git a/day2/images/punch-card.jpg b/day2/images/punch-card.jpg deleted file mode 100644 index bf1fe47..0000000 Binary files a/day2/images/punch-card.jpg and /dev/null differ diff --git a/day2/images/queen.jpg b/day2/images/queen.jpg deleted file mode 100644 index a76d0d4..0000000 Binary files a/day2/images/queen.jpg and /dev/null differ diff --git a/day2/images/shared-memory.tex b/day2/images/shared-memory.tex deleted file mode 100644 index 8086f67..0000000 --- a/day2/images/shared-memory.tex +++ /dev/null @@ -1,27 +0,0 @@ -\begin{tikzpicture}[node distance=8mm, -dots/.style={ - font=\sffamily, - xshift=5mm, - minimum width=1cm -}, -node/.append style = {xshift=5mm}, -memory/.append style = {yshift=-.25cm}, -] -\tikzstyle{sample} = [-,thin] -\tikzstyle{mem} = [-,thick] - \node (node0) [node] {$P_0$}; - \node (node1) [node,right of=node0 ] {$P_1$}; - \node (dots) [dots,right of=node1 ] {$\ldots$}; - \node (nodeN) [node,right of=dots ] {$P_N$}; - \node (switch) [switch,below of=node1, xshift=6mm, yshift=-.35cm] {interconnect}; - - \node (memory) [memory,below of=switch] {memory}; - -\path[sample] (node0.south) edge[out=-60,in=120,looseness=0.8] (switch.north); -\path[sample] (node1.south) edge[out=-60,in=120] (switch.north); -\path[sample] (nodeN.south) edge[out=-120,in=120,looseness=0.8] (switch.north); - -\path[mem] (memory.north) edge (switch.south); - - -\end{tikzpicture} diff --git a/day2/images/spanning.png b/day2/images/spanning.png deleted file mode 100644 index 3bd6019..0000000 Binary files a/day2/images/spanning.png and /dev/null differ diff --git a/day2/images/tsp.gif b/day2/images/tsp.gif deleted file mode 100644 index 47a1175..0000000 Binary files a/day2/images/tsp.gif and /dev/null differ diff --git a/day2/images/tsp.png b/day2/images/tsp.png deleted file mode 100644 index a7e2c10..0000000 Binary files a/day2/images/tsp.png and /dev/null differ diff --git a/day2/mpi-basics.tex b/day2/mpi-basics.tex deleted file mode 100644 index ffa3b03..0000000 --- a/day2/mpi-basics.tex +++ /dev/null @@ -1,585 +0,0 @@ -\subsection{Introduction} - -\begin{frame} - \frametitle{What will we learn today ?} - \begin{itemize} - \item {The distributed memory programming paradigm MPI} - \item {Point-to-Point communications} - \item {Collective communications} - \item {Synchronizations} - \end{itemize} -\end{frame} - - -\begin{frame} - \frametitle{Reminder} - \begin{center} - % \includegraphics[width=8cm]{day2/images/distributed.png} - % {\includegraphics[width=\textwidth]{day2/images/distributed-memory.pdf}} - \input{day2/images/distributed-memory} - \end{center} -\end{frame} - -\begin{frame} - \frametitle{Goals and scope of MPI} - \begin{itemize} - \item {Provide a source-code portability} - \item {efficiency across different architectures} - \item {easier debugging} - \item {parallel I/O} - \end{itemize} -\end{frame} - -\begin{frame}[containsverbatim] - \frametitle{MPI} - \begin{itemize} - \item {Run multiple instances of the same program : \verb+"mpirun -np p myApp myArgs"+ starts \verb+p+ instances of the program \verb+"myApp myArgs"+} - \item {Instances exchange information by sending messages to each other} - \item {Communications take place within a \verb+communicator+ : a set of processes indexed from $0$ to $communicatorSize-1$. A special communicator named \verb+MPI_COMM_WORLD+ contains all the processes} - \end{itemize} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{Hello World} - - \begin{lstlisting}[language=C,frame=lines] - int main(int argc, char *argv[]){ - int size, rank; - MPI_Init(&argc, &argv); - MPI_Comm_size(MPI_COMM_WORLD, &size); - MPI_Comm_rank(MPI_COMM_WORLD, &rank); - - printf("I'm process %d out of %d\n", rank, size); - - MPI_Finalize(); - } - \end{lstlisting} - \begin{itemize} - \item{Compile with \verb+mpicc hello.c -o hello+} - \item{Run with \verb+mpirun -np 4 ./hello+} - \end{itemize} -\end{frame} - - -\subsection{One-to-One communications} - -\begin{frame}[containsverbatim] - \frametitle{Types of communications in MPI} - \begin{itemize} - \item {Point-to-Point (One-to-One)} - \item {Collectives (One-to-All, All-to-One, All-to-All)} - \item {One-sided (One-to...)} - \item {Blocking and Non-Blocking of all types} - \end{itemize} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{MPI\_Send() and MPI\_Recv()} - \begin{itemize} - \item {\verb+MPI_Send(buf, count, datatype, destination, +\\ \verb+ tag, communicator)+} - \item {\verb+MPI_Recv(buf, count, datatype, source, + \\ \verb+ tag, communicator, status)+} - \item {Sends (receives) \verb+count+ elements of type \verb+datatype+ to (from) \verb+destination+ (\verb+source+) buffer \verb+buf+.} - \item {{\bf Each send must be matched by a receive!} - \begin{itemize} - \item{You must know \verb+source+, \verb+tag+, \verb+communicator+ and size (\verb+count+ * \verb+sizeof(datatype)+) of incoming message} - \item{If you don’t know, use \verb+MPI_Probe+ / \verb+MPI_Iprobe+ to get that information} - \end{itemize} - } - \end{itemize} - \textcolor{red}{Mismatches cause race conditions or deadlocks} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{ping.c} - \begin{lstlisting}[language=C,frame=lines] - int main(int argc, char *argv[]) { - int rank, size; - int buf[100]; - MPI_Status status; - MPI_Init(&argc, &argv); - MPI_Comm_rank(MPI_COMM_WORLD, &rank); - MPI_Comm_size(MPI_COMM_WORLD, &size); - if (rank == 0) { - MPI_Send(buf, 100, MPI_INT, 1, 0, MPI_COMM_WORLD); - } else { - MPI_Recv(buf, 100, MPI_INT, 0, 0, MPI_COMM_WORLD,&status); - } - MPI_Finalize(); - } - \end{lstlisting} - -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{watch out for deadlocks !} - \begin{itemize} - \item{ping.c runs ok with 2 processes : \\ - \begin{tabular}{ c c c } - \underline{Process 0} & & \underline{Process 1} \\ - send(1,0) & $\longrightarrow$ & recv(0,0) \\ - finalize() & & finalize() \\ - \end{tabular} - } - \item{Deadlock if more than two processes : \\ - \begin{tabular}{ c c c c c} - \underline{Process 0} & & \underline{Process 1} & & \underline{Process 2} \\ - send(1,0) & $\longrightarrow$ & recv(0,0) & & recv(0,0) \\ - finalize() & & finalize() \\ - \end{tabular} - } - \end{itemize} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{ping$\_$correct.c} - \begin{lstlisting}[language=C,frame=lines] - int main(int argc, char *argv[]) { - int rank, size; - int buf[100]; - MPI_Status status; - MPI_Init(&argc, &argv); - MPI_Comm_rank(MPI_COMM_WORLD, &rank); - MPI_Comm_size(MPI_COMM_WORLD, &size); - if (rank == 0) { - MPI_Send(buf, 100, MPI_INT, 1, 0, MPI_COMM_WORLD); - } else if (rank==1) { - MPI_Recv(buf, 100, MPI_INT, 0, 0, MPI_COMM_WORLD,&status); - } - MPI_Finalize(); - } - \end{lstlisting} -\end{frame} - -\begin{frame}[containsverbatim] - \frametitle{Blocking point-to-point communications} - \begin{itemize} - \item {\verb+MPI_Send+ : Returns when buffer can be reused} - \item {\verb+MPI_Ssend+ : (S for Synchronous) : returns when other end posted matching recv} - \item {\verb+MPI_Recv+ : Returns when message has been received } - \item {\verb+MPI_Sendrecv+ : Sends and receive within the same call to avoid deadlocks} - \item {\verb+MPI_Bsend+ : (B for Buffer) : returns immediately, send buffer can be reused immediately } - \item {\verb+MPI_Rsend+ : (R for Ready) : returns only when the send buffer can be safely reused} - \item {\verb+MPI_Sendrecv_replace+ : sends, receive and replace buffer values using only one buffer} - \end{itemize} -\end{frame} - - - -\begin{frame}[containsverbatim] - \frametitle{Non-Blocking point-to-point communications} - \begin{itemize} - \item {\verb+MPI_Isend+ and \verb+MPI_Irecv+ : Do not wait for message to be buffered send/recv. Fills an additional \verb+MPI_Request+ parameter that identifies the request} - \item {Do not use / modify / delete buffers until request completed} - \item {Wait calls block until request(s) completed : - \begin{itemize} - \item {\verb+MPI_Wait(request, status)+} - \item {\verb+MPI_Waitall(count, array_of_requests,+\\ \verb+ array_of_statuses)+} - \end{itemize} - } - \item {\verb+MPI_Issend+ : Non-blocking version of \verb+MPI_Ssend+} - \item {\verb+MPI_Ibsend+ : Non-blocking version of \verb+MPI_Bsend+} - \item {\verb+MPI_Irsend+ : Non-blocking version of \verb+MPI_Rsend+} - \end{itemize} -\end{frame} - -% \begin{frame}[containsverbatim] -% \frametitle{MPI$\_$Request} -% -% An $MPI\_Request$ object has different purposes; -% -% \begin{itemize} - % \item {The $MPI\_Send$ and $MPI\_Recv$ requests: internally identified as requests with specific types ($MPIR\_SEND$ and $MPIR\_RECV$} - % \item {Persistent communication operations : they look like sends and receives, but are actually different from an implementation perspective} - % \item {An $MPI\_Request$ is used to represent an operation, such as a nonblocking send, at several different stages of completion. The state of the operation is encoded within the request} - % \item {} - % \end{itemize} - % \end{frame} - - - -\begin{frame}[containsverbatim] - \frametitle{Non-Blocking point-to-point communications (cont'd)} - - Playing with \verb+MPI_Request+ - - \begin{itemize} - \item {\verb+MPI_Waitsome+ : Waits for an MPI request to complete } - \item {\verb+MPI_Waitany+ : Waits for any specified MPI Request to complete } - \item {\verb+MPI_Test+ : Tests for the completion of a request } - \item {\verb+MPI_Testall+ : Tests for the completion of all previously initiated requests } - \item {\verb+MPI_Testany+ : Tests for completion of any previously initiated requests } - \item {\verb+MPI_Testsome+ : Tests for some given requests to complete } - \end{itemize} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{iping.c} - \begin{lstlisting}[language=C,frame=lines] - int main(int argc, char *argv[]) { - int rank; - int buf[100]; - MPI_Request request; - MPI_Status status; - MPI_Init(&argc, &argv); - MPI_Comm_rank(MPI_COMM_WORLD, &rank); - if (rank == 0) - MPI_Isend(buf, 100, MPI_INT, 1, 0,MPI_COMM_WORLD, &request); - else if (rank == 1) - MPI_Irecv(buf, 100, MPI_INT, 0, 0,MPI_COMM_WORLD, &request); - MPI_Wait(&request, &status); - MPI_Finalize(); - } - \end{lstlisting} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{exchange.c} - Process 0 and 1 exchange the content of their buffer with non-blocking \label{call} - \begin{lstlisting}[language=C,frame=lines] - if (rank == 0) { - MPI_Isend(buf1, 10, MPI_INT, 1, 0, MPI_COMM_WORLD, &request); - MPI_Recv(buf2, 10, MPI_INT, 1, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE); - }else if (rank == 1){ - MPI_Isend(buf1, 10, MPI_INT, 0, 0, MPI_COMM_WORLD, &request); - MPI_Recv(buf2, 10, MPI_INT, 0, 0,MPI_COMM_WORLD, MPI_STATUS_IGNORE); - } - - MPI_Wait(&request, &status); - memcpy(buf1, buf2, 10*sizeof(int)); - \end{lstlisting} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{exchange$\_$sendrecv.c} - Process 0 and 1 exchange the content of their buffer with sendrecv() - \begin{lstlisting}[language=C,frame=lines] - if (rank == 0) { - MPI_Sendrecv(buf1, 10, MPI_INT, 1, 0, buf2, 10, MPI_INT, 1, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE); - } else if (rank == 1) { - MPI_Sendrecv(buf1, 10, MPI_INT, 0, 0, buf2, 10, MPI_INT, 0, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE); - } - - memcpy(buf1, buf2, 10*sizeof(int)); - \end{lstlisting} -\end{frame} - -\begin{frame}[containsverbatim] - \frametitle{exchange$\_$sendrecv$\_$replace.c} - Process 0 and 1 exchange the content of their buffer with sendrecv$\_$replace() - \begin{lstlisting}[language=C,frame=lines] - if (rank == 0){ - MPI_Sendrecv_replace(buf1, 10, MPI_INT, 1, 0, 1, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE); - } else if (rank == 1) { - MPI_Sendrecv_replace(buf1, 10, MPI_INT, 0, 0, 0, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE); - } - \end{lstlisting} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{Wildcard receives} - MPI$\_$ANY$\_$SOURCE and MPI$\_$ANY$\_$TAG are wildcards : - \begin{lstlisting}[language=C,frame=lines] - switch(rank) { - case 0: MPI_Send(..., 1, 0, ...); break; - case 1: - MPI_Recv(..., MPI_ANY_SOURCE, MPI_ANY_TAG, ...); - MPI_Recv(..., MPI_ANY_SOURCE, MPI_ANY_TAG, ...); - break; - case 2: MPI_Send(..., 1, 1, ...); break; - } - \end{lstlisting} - leads to : \\ - - \begin{tabular}{ c c c c c} - \underline{Process 0} & & \underline{Process 1} & & \underline{Process 2} \\ - send(1,0) & $\longrightarrow$ & recv(*,*) & $\longleftarrow$ & send(1,1) \\ - & $\searrow$ & recv(*,*) & $\swarrow$ & \\ - \end{tabular} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{MPI$\_$Barrier(communicator)} - Returns when all processes in communicator have joined - \begin{lstlisting}[language=C,frame=lines] - switch(rank) { - case 0: - MPI_Send(..., dest = 1, tag = 0, ...); - MPI_Barrier(MPI_COMM_WORLD); break; - case 1: - MPI_Recv(..., MPI_ANY_SOURCE, MPI_ANY_TAG, ...); - MPI_Barrier(MPI_COMM_WORLD); - MPI_Recv(..., MPI_ANY_SOURCE, MPI_ANY_TAG, ...); break; - case 2: - MPI_Barrier(MPI_COMM_WORLD); - MPI_Send(..., src = 1, tag = 1, ...); break; - }\end{lstlisting} -\end{frame} - -\begin{frame}[containsverbatim] - \frametitle{MPI$\_$Barrier(communicator) (cont'd)} - MPI$\_$ANY$\_$SOURCE and MPI$\_$ANY$\_$TAG are wildcards : - - \begin{tabular}{ c c c c c} - \underline{Process 0} & & \underline{Process 1} & & \underline{Process 2} \\ - send(1,0) & $\longrightarrow$ & recv(*,*) & & \\ - \hline - {\bf barrier} & & {\bf barrier} & & {\bf barrier} \\ - \hline - & & recv(*,*) & $\longleftarrow$ & send(1,1) \\ - \end{tabular} - - Order of calls on process 1 is important - - \begin{itemize} - \item{recv -- barrier -- recv \textcolor{green}{correct}} - \item{barrier -- recv -- recv \textcolor{orange}{message race or deadlock (depends on msg size)}} - \item{recv -- recv -- barrier \textcolor{red}{deadlock}} - \end{itemize} -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{\textcolor{orange}{barrier -- recv -- recv}} - - \begin{tabular}{ c c c c c} - \underline{Process 0} & & \underline{Process 1} & & \underline{Process 2} \\ - send(1,0) & $\longrightarrow$ & & & \\ - & $\searrow$ & & & \\ - \hline - {\bf barrier} & & {\bf barrier} & & {\bf barrier} \\ - \hline - & & recv(*,*) & $\longleftarrow$ & send(1,1) \\ - & & recv(*,*) & $\swarrow$ & \\ - \end{tabular} - - Order of calls on process 1 is important - - \begin{itemize} - \item{recv -- barrier -- recv \textcolor{green}{correct}} - \item{barrier -- recv -- recv \textcolor{orange}{message race or deadlock (depends on msg size)}} - \item{recv -- recv -- barrier \textcolor{red}{deadlock}} - \end{itemize} -\end{frame} - -\begin{frame}[containsverbatim] - \frametitle{\textcolor{red}{recv -- recv -- barrier}} - - \begin{tabular}{ c c c c c} - \underline{Process 0} & & \underline{Process 1} & & \underline{Process 2} \\ - send(1,0) & $\longrightarrow$ & & & \\ - & & recv(*,0) & & \\ - & & recv(2,*) & & \\ - \hline - {\bf barrier} & & \textcolor{red}{{\bf barrier}} & & {\bf barrier} \\ - \hline - & & & $\longleftarrow$ & \textcolor{red}{send(1,1)} \\ - \end{tabular} - - Process 1 never enters the barrier since its second recv is never matched -\end{frame} - - -\subsection{Collective communications} - - -\begin{frame}[containsverbatim] - \frametitle{Collective communications} - - \begin{center} - \input{day2/images/collectives.tex} - \end{center} - -\end{frame} - - - -\begin{frame}[containsverbatim] - \frametitle{Collective communications} - - \begin{itemize} - \item{\verb+MPI_Bcast+ : Sends the same data to every process} - \item{\verb+MPI_Scatter+ : Sends pieces of a buffer to every process of the communicator} - \item{\verb+MPI_Gather+ : Retrieves pieces of data from every process} - \item{\verb+MPI_Allgather+ : All pieces retrieved by all processes} - \item{\verb+MPI_Reduce+ : Performs a reduction operation (\verb+MPI_SUM+, ...) across all nodes. E.g. dot product on distributed vectors} - \item{\verb+MPI_Allreduce+ : Result distributed to all processes } - \item{\verb+MPI_Alltoall+ : Sends all data to all processes} - \item{{\bf Every process of the communicator must participate}. Parameters must match. Mismatches cause race conditions or deadlocks} - \end{itemize} - -\end{frame} - - -\begin{frame}[containsverbatim] - \frametitle{Receiving image parts in order} - \begin{lstlisting}[language=C,frame=lines] - /* Generate image parts */ - ... - /* Each process sends */ - MPI_Isend(imgPart, partSize, MPI_BYTE, 0, 0, MPI_COMM_WORLD, &request); - - // Process 0 receives all parts into buf - if (rank == 0){ - char *buf = malloc(nProcs*partSize); - for (int i=0; i3$) so that no queen see each other. A queen can move on its row, its column and its diagonals. -\end{block} -\end{frame} -%\begin{frame}[containsverbatim] -%\frametitle{n queens problem} -%\begin{block}{Important remarks} -%\begin{itemize} -% \item{tree construction} -% \item{} -%\end{itemize} -%\end{block} -%\end{frame} - - - - -\subsection{FFT} -\begin{frame}[containsverbatim] -\frametitle{FFT with Cooley-Tukey} -\begin{center} -\includegraphics[width=4.0cm]{day2/images/fft.png} -\end{center} -\begin{block}{Problem description} -The Fast Fourier Transform (FFT) Cooley-Tukey algorithm computes the Discrete Fourier Transform (DFT) of a sequence recursively by a devide-and-conquer approach. The radix-2 decimation in time divides a DFT of size $N$ into two interleaved DFT of size $N/2$. -\end{block} -\end{frame} -%\begin{frame}[containsverbatim] -%\frametitle{FFT with Cooley-Tukey} -%A DFT is described as : -%$$ -%X_k = \sum_{n=0}^{N-1} x_n e^{- \frac{2 \pi i}{N} n k} -%$$ -%which can be rearranged as : -%$$ -%X_k = \sum_{m=0}^{N/2-1} x_{2m} e^{- \frac{2 \pi i}{N/2} (2m) k} + e^{- \frac{2 \pi i}{N} k} \sum_{m=0}^{N/2-1} x_{2m+1} e^{- \frac{2 \pi i}{N/2} m k} -%$$ -%in other words : the even and the odd parts of $X_k$ : -%$$ -%X_k = E_k + e^{- \frac{2 \pi i}{N}k} O_k -%$$ -%\end{frame} -%\begin{frame}[containsverbatim] -%\frametitle{FFT with Cooley-Tukey} -%Therefore: -%$$ -%X_k = \left\{ \begin{array}{ll} -% E_k + e^{- \frac{2 \pi i}{N/2}k} O_k & \text{for}~~ 0 \leq k < N/2\\ -% E_{k-N/2} + e^{- \frac{2 \pi i}{N/2}k} O_{k-N/2} &\text{for}~~ N/2 \leq k < N. -% \end{array} \right. -%$$ -%we also know that : -%$$ -%e^{- \frac{2 \pi i}{N}(k+ N/2)} = - e^{- \frac{2 \pi i}{N}k} -%$$ -%thus for $0 \leq k < \frac{N}{2}$ : -%$$ -%\begin{array}{ll} -%X_k & = E_k + e^{- \frac{2 \pi i}{N}k} O_k \\ -%X_{k+\frac{N}{2}} & = E_k - e^{- \frac{2 \pi i}{N}k} O_k -%\end{array} -%$$ -%\end{frame} -%\begin{frame}[containsverbatim] -%\frametitle{FFT with Cooley-Tukey} -%The DFT of length $N$ is then described in terms of two DFT of size $\frac{N}{2}$. The same process is applied recursively until $N=2$. -%\end{frame} -\begin{frame}[containsverbatim] -\frametitle{FFT with Cooley-Tukey} -\begin{block}{Important remarks} -\begin{itemize} - \item{Complexity !} - \item{$x_k$ reordering before devide-and-conquer} - \item{Large size numbers $N = 2^t$ with $t$ as ``large'' as possible} - \item{You can choose other algorithms than Cooley-Tukey} -\end{itemize} -\end{block} -\end{frame} - - - - -\subsection{Minimum spanning tree} -\begin{frame}[containsverbatim] -\frametitle{Minimum Spanning Tree} -\begin{center} -\includegraphics[width=4.0cm]{day2/images/spanning.png} -\end{center} -\begin{block}{Problem description} -A minimum spanning tree is a spanning tree of a connected, undirected and weighted graph. It connects all the vertices together with the minimal total weighting for its edges -\end{block} -\end{frame} -\begin{frame}[containsverbatim] -\frametitle{Minimum Spanning Tree} -\begin{block}{Important remarks} -\begin{itemize} - \item{Parallelize Boruka's algorithm} - \item{Complexity !} -\end{itemize} -\end{block} -\end{frame} - - - - -\subsection{Dijkstra's algorithm} -\begin{frame}[containsverbatim] -\frametitle{Dijkstra's algorithm} -\begin{center} -\includegraphics[width=4.0cm]{day2/images/dijkstras.png} -\end{center} -\begin{block}{Problem description} -Dijkstra's algorithm is an algorithm for finding the shortest paths between nodes in a graph. It can be used for finding the shortest paths from a single node to a single destination node by stopping the algorithm once the shortest path to the destination node has been determined -\end{block} -\end{frame} -%\begin{frame}[containsverbatim] -%\frametitle{Dijkstra's algorithm} -%\begin{block}{Important remarks} -%\begin{itemize} -% \item{parallelization of the tree} -%\end{itemize} -%\end{block} -%\end{frame} - - - - - -\subsection{N-body simulation} -\begin{frame}[containsverbatim] -\frametitle{N-body simulation} -\begin{center} -\includegraphics[width=3.0cm]{day2/images/nbody.png} -\end{center} -\begin{block}{Problem description} -The n-body problem aims at simulating a dynamical system of particles under the influence of physical forces. We'll restrain on the gravity field applied on celestial bodies: -$$ -F_{ij} = \frac{G m_i m_j (q_j - q_i)}{||q_j - q_i||} -$$ -where $G$ is the gravitational constant, $m_i$ and $m_j$ the masses of the $i$-th and $j$-th bodies and $q_i$ and $q_j$ their positions. -\end{block} -\end{frame} -\begin{frame}[containsverbatim] -\frametitle{N-body simulation} -\begin{block}{Important remarks} -\begin{itemize} - \item{brute force will not be accepted} - \item{2D or 3D} - \item{non-uniform initial distribution must be tested to stress the application} - \item{how to handle collisions and ``lost bodies in the far space''} -\end{itemize} -\end{block} -\end{frame} - - - -\subsection{Sieve of Eratosthenes} -\begin{frame}[containsverbatim] -\frametitle{Sieve of Eratosthenes} -\begin{center} -\includegraphics[width=3.0cm]{day2/images/Eratosthene.png} -\end{center} -\begin{block}{Problem description} -Find all the prime numbers $p$ such $p < N$ where $N$ is very large. Enumerate all the multiples of $p$ by counting to $N$ in incerements of $p$ and mark them as ``non-primes''. Do that to $\sqrt{N}$. The list of $p_i$ are all the primes between $p=2$ to $p=\sqrt{N}$. -\end{block} -\end{frame} -\begin{frame}[containsverbatim] -\frametitle{Sieve of Eratosthenes} -\begin{block}{Important remarks} -\begin{itemize} - \item{load balancing} - \item{Handling very large numbers} - \item{alternative : Sieve of Atkin} -\end{itemize} -\end{block} -\end{frame} - - - - - -\subsection{Game of Life} -\begin{frame}[containsverbatim] -\frametitle{Game of Life} -\begin{center} -\includegraphics[width=3.0cm]{day2/images/gameoflife.png} -\end{center} -\begin{block}{Problem description} -The game of life is a cellular automaton with simple elements: a cell $c_i$ can be dead ($c_i = 0$) or alive ($c_i = 1$). At each time step, the following rules are applied : -\begin{itemize} - \item {if $c_i = 1$ and its neighbours are 0, 1 or 4 living cells, then $c_{i+1} = 0$} - \item {if $c_i = 1$ and its neighbours are 2 or 3 living cells, then $c_{i+1} = 1$} - \item {if $c_i = 0$ and its neighbours are exactly 3 living cells, then $c_{i+1} = 1$} -\end{itemize} -\end{block} -\end{frame} -\begin{frame}[containsverbatim] -\frametitle{Game of Life} -\begin{block}{Important remarks} -\begin{itemize} - \item{as this problem is very close to Poisson, we'll accept only non-standard subdomain decomposition (topology)} -\end{itemize} -\end{block} -\end{frame} - - - - -\subsection{Jacobi iterative method} -\begin{frame}[containsverbatim] -\frametitle{Jacobi iterative method} -\begin{block}{Problem description} -The Jacobi method solves a linear system $Ax = b$ iteratively: -$$ -A = D + R -$$ -where D is the diagonal matrix of $A$ and $R$ the rest. The solution $x_{(k+1)}$ is obtained with: -$$ -x_{(k+1)} = D^{-1} ( b - R x_k) -$$ -where $x_k$ is the $k$-th iteration of $x$ -\end{block} -\end{frame} - - - -\subsection{Gauss-Seidel iterative method} -\begin{frame}[containsverbatim] -\frametitle{Gauss-Seidel iterative method} -\begin{block}{Problem description} -The Gauss-Seidel method solves a linear system $Ax = b$ iteratively: -$$ -A = L + U -$$ -where $L$ is the lower triangular elements of $A$ and $U$ the strict upper elements of $A$. The solution $x_{(k+1)}$ is obtained with: -$$ -x_{(k+1)} = L^{-1} ( b - U x_k) -$$ -where $x_k$ is the $k$-th iteration of $x$ -\end{block} -\end{frame} - - - - -%\subsection{Shallow Water Equation I\&II} -%\begin{frame}[containsverbatim] -%\frametitle{Shallow Water Equation I\&II} - - -%\end{frame} - diff --git a/day3/images/displacements.eps b/day3/images/displacements.eps deleted file mode 100644 index e8a3845..0000000 --- a/day3/images/displacements.eps +++ /dev/null @@ -1,3051 +0,0 @@ -%!PS-Adobe-3.0 EPSF-3.0 -%%Creator: GIMP PostScript file plugin V 1.17 by Peter Kirchgessner -%%Title: displacements.eps -%%CreationDate: Mon Mar 30 17:40:30 2015 -%%DocumentData: Clean7Bit -%%LanguageLevel: 2 -%%Pages: 1 -%%BoundingBox: 14 14 985 367 -%%EndComments -%%BeginProlog -% Use own dictionary to avoid conflicts -10 dict begin -%%EndProlog -%%Page: 1 1 -% Translate for offset -14.173228346456694 14.173228346456694 translate -% Translate to begin of first scanline -0 352.4210526315789 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a/day3/images/topology.pdf b/day3/images/topology.pdf deleted file mode 100644 index 3bcccab..0000000 Binary files a/day3/images/topology.pdf and /dev/null differ diff --git a/day3/images/topology.tex b/day3/images/topology.tex deleted file mode 100644 index db3c9bb..0000000 --- a/day3/images/topology.tex +++ /dev/null @@ -1,13 +0,0 @@ -% Slide 231 - -\begin{tikzpicture} - -\draw[thick, step = 1.5cm] (0,0) grid (4.5, 3); -\node at (2.25, -0.3) {dims[1] = 3}; -\node[anchor = west] at (4.8, 1.5) {dims[0] = 2}; - -\draw[<->, xshift = -0.15cm] (0,0) -- node[midway, left] {n} (0, 3); -\draw[<->, yshift = 0.15cm] (0,3) -- node[midway, above] {m} (4.5, 3); - - -\end{tikzpicture} diff --git a/day3/mpi-advanced.tex b/day3/mpi-advanced.tex deleted file mode 100644 index 9395f53..0000000 --- a/day3/mpi-advanced.tex +++ /dev/null @@ -1,987 +0,0 @@ -\subsection{Introduction} - -\begin{frame}[containsverbatim] - \frametitle{What will we learn today ?} - \begin{itemize} - \item {Advanced \verb+MPI_Types+, MPI communicators and groups (MPI 1.0)} - \item {Persistent communications (MPI 2.0)} - \item {One-sided communications (RMA) (MPI 2.0 and MPI 3.0)} - \item {Dynamic process management (MPI 2.0)} - \item {Parallel I/O (MPI 2.0)} - \item {Non-blocking collectives (MPI 3.0)} - \end{itemize} -\end{frame} - - -\subsection{Advanced MPI$\_$Types} - - -\begin{frame}[containsverbatim] -\frametitle{Basic MPI datatypes (C)} - -\begin{center} -\begin{tabular}{ | l | l | } - \hline - \textbf{C datatype} & \textbf{MPI datatype} \\ - \hline - \hline - signed char & MPI$\_$CHAR\\ - signed short int & MPI$\_$SHORT\\ - signed int & MPI$\_$INT \\ - signed long int & MPI$\_$LONG \\ - unsigned char & MPI$\_$UNSIGNED$\_$CHAR\\ - unsigned short int & MPI$\_$UNSIGNED$\_$SHORT\\ - unsigned long int & MPI$\_$UNSIGNED$\_$LONG\\ - unsigned int & MPI$\_$UNSIGNED\\ - float & MPI$\_$FLOAT\\ - double & MPI$\_$DOUBLE\\ - long double & MPI$\_$LONG$\_$DOUBLE\\ - \hline - \end{tabular} -\end{center} -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{Basic MPI datatypes (FORTRAN)} - -\begin{center} -\begin{tabular}{ | l | l | } - \hline - \textbf{FORTRAN datatype} & \textbf{MPI datatype} \\ - \hline - \hline - INTEGER & MPI$\_$INTEGER\\ - REAL & MPI$\_$REAL\\ - REAL*8 & MPI$\_$REAL8\\ - DOUBLE PRECISION & MPI$\_$DOUBLE$\_$PRECISION\\ - COMPLEX & MPI$\_$COMPLEX\\ - LOGICAL & MPI$\_$LOGICAL\\ - CHARACTER & MPI$\_$CHARACTER \\ - \hline - \end{tabular} -\end{center} -\end{frame} - -\begin{frame}[containsverbatim] -\frametitle{Derived MPI datatypes} - -OK. That is perfect when all the data are of the same type (integers, floats, characters, etc..). But how to send a structure using MPI ? - -\begin{lstlisting}[language=C,frame=lines] -struct { - int x; int y; - double vx; double vy; - float mass; -} particle; -particle p = {1,2,0.3,0.4,1.0}; -MPI_Send(p, ...); -\end{lstlisting} -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{Derived MPI datatypes} -\begin{itemize} - \item Definition of \textbf{new} datatypes by grouping basic MPI datatypes - \item It is possible to group \begin{itemize} \item data from different types \item group non-contiguous data \end{itemize} - \item A derived datatype is defined in three steps : \begin{itemize} \item construct the type \item commit it to the system \item free it \end{itemize} -\end{itemize} - -\end{frame} - - - -\begin{frame}[containsverbatim] -\frametitle{Derived MPI datatypes} -\begin{itemize} - \item \verb+MPI_Type_contiguous+ Produces a new data type by making copies of an existing data type. - \item \verb+MPI_Type_vector+, Similar to contiguous, but allows for regular gaps (stride) in the displacements - \item \verb+MPI_Type_indexed+, An array of displacements of the input data type is provided as the map for the new data type. - \item \verb+MPI_Type_create_struct+ The new data type is formed according to completely defined map of the component data types. - \item \verb+MPI_Type_extent+ Returns the size in bytes of the specified data type. - \item \verb+MPI_Type_commit+ Commits new datatype to the system. - \item \verb+MPI_Type_free+ Deallocates the specified datatype object. -\end{itemize} - -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{MPI$\_$Type$\_$struct example} - -\begin{lstlisting}[language=C,frame=lines] -struct { int a; char b; } foo; -MPI_Datatype newtype; -blen[0] = 1; indices[0] = 0; oldtypes[0] = MPI_INT; -blen[1] = 1; indices[1] = &foo.b - &foo; oldtypes[1] = MPI_CHAR; -blen[2] = 1; indices[2] = sizeof(foo); oldtypes[2] = MPI_UB; -MPI_Type_create_struct( 3, blen, indices, oldtypes, &newtype ); -MPI_Commit(&newtype); -foo f = {1,'z'}; -MPI_Send(&f, 1, newtype, 0, 100, MPI_COMM_WORLD );) -MPI_Type_free( &newtype ); -\end{lstlisting} -The MPI datatype \texttt{newtype} is a structure that contains \texttt{\{foo, sizeof(foo)\}} -%\begin{lstlisting}[language=C,frame=lines] -%int blocklens[7]; -%MPI_Datatype myparticle; -%MPI_Datatype old_types[5]; -%old_types[0] = MPI_INT; old_types[1] = MPI_INT; -%old_types[2] = MPI_DOUBLE; old_types[3] = MPI_DOUBLE; -%old_types[4] = MPI_FLOAT; -%blocklens[0] = 1; blocklens[1] = 1; blocklens[2] = 1; -%blocklens[3] = 1; blocklens[4] = 1; -%MPI_Address( &particle.x, &indices[0] ); MPI_Address( &particle.y, &indices[1] ); -%MPI_Address( &particle.vx, &indices[2] ); MPI_Address( &particle.vy, &indices[3] ); -%MPI_Address( &particle.mass, &indices[4] ); -%MPI_Type_struct( 5, blocklens, indices, old_types, &myparticle ); -%MPI_Send( &p, 1, myparticle, 0, 100, MPI_COMM_WORLD ); -%MPI_Type_free( &myparticle ); -%\end{lstlisting} - -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{Pack/Unpack data} -\begin{itemize} - \item { Instead of creating a new datatype, it is possible to pack and unpack data of different types } - \item { Less good than MPI derived datatypes in terms of memory usage and performance } - \item { ``just like a streaming'' } - \item { \verb+int MPI_Pack(const void *inbuf, int incount, +\\\verb+MPI_Datatype datatype, void *outbuf, int outsize,+\\\verb+ int *position, MPI_Comm comm)+} - \item { \verb+int MPI_Unpack(const void *inbuf, int insize,+\\\verb+ int *position, void *outbuf, int outcount, +\\\verb+MPI_Datatype datatype, MPI_Comm comm)+} -\end{itemize} -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{Pack/Unpack data} -\begin{lstlisting}[language=C,frame=lines] -int x; float a, int position=0; -char buffer[100]; -if (myrank==0) - MPI_Pack(&a, 1, MPI_FLOAT, buffer, 100, &position, MPI_COMM_WORLD) - MPI_Pack(&x, 1, MPI_INT, buffer, 100, &position, MPI_COMM_WORLD) - MPI_Send(buffer, 100, MPI_PACKED, 1, 999, MPI_COMM_WORLD); -}else if (myrank==1) { - MPI_Recv(buffer, 1000, MPI_PACKED, 0, 999, MPI_COMM_WORLD, status) - MPI_Unpack(buffer, 100, &position, &a, 1, MPI_FLOAT, MPI_COMM_WORLD); - MPI_Unpack(buffer, 100, &position, &x, 1, MPI_INT, MPI_COMM_WORLD); -} -\end{lstlisting} -\end{frame} - - -\subsection{MPI communicators and groups} - - - -\begin{frame}[containsverbatim] -\frametitle{MPI Groups and Communicators} -MPI Groups : -\begin{itemize} - \item {ordered set of processes} - \item {each process has an unique ID (rank within the group) and can belong to several different groups} - \item {a group can be used to create a new communicator} -\end{itemize} -MPI Communicators : -\begin{itemize} - \item {A group of processes} - \item {encapsulate the communications between the belonging processes} - \item {An MPI communication can take place only with a communicator (not a group)} -\end{itemize} -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{MPI Groups and Communicators} -\begin{center} -\input{day3/images/group-comm.tex} -\end{center} -\end{frame} - - - -\begin{frame}[containsverbatim] -\frametitle{Create a new communicator} - -%\begin{lstlisting}[language=C,frame=lines] -%main(int argc, char *argv[]) { -% int myrank, new_rank, sendbuf, recvbuf, mysize, -% MPI_Group old_grp, new_grp; -% MPI_Comm new_comm; -% MPI_Init(&argc,&argv); -% MPI_Comm_rank(MPI_COMM_WORLD, &rank); -% MPI_Comm_size(MPI_COMM_WORLD, &size); -% MPI_Comm_group(MPI_COMM_WORLD, &old_group); -% if (rank < NPROCS/2) { -% MPI_Group_incl(old_grp, size/2, ranks1, &new_grp); -% } else { -% MPI_Group_incl(old_grp, size/2, ranks2, &new_grp); -% } -% MPI_Comm_create(MPI_COMM_WORLD,new_group,&new_comm); -% MPI_Group_rank (new_group, &new_rank); -% printf("rank= %d newrank= %d recvbuf= %d\n",rank,new_rank,recvbuf); -% MPI_Finalize(); -%} -%\end{lstlisting} - - -\begin{lstlisting}[language=C,frame=lines] - MPI_Init(&argc,&argv); - MPI_Comm_rank(MPI_COMM_WORLD, &rank); - MPI_Comm_size(MPI_COMM_WORLD, &size); - MPI_Comm_group(MPI_COMM_WORLD, &old_g); - int nbr_g1 = 5; - ranks1 = (int*) malloc(nbr_g1*sizeof(int)); - ranks2 = (int*) malloc((size-nbr_g1)*sizeof(int)); - for (i=0;i 100})} -\end{itemize} - -\begin{center} -\input{day3/images/gatherv.tex} -\end{center} - -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{``v-version'' of \texttt{MPI$\_$Gather} : \texttt{MPI$\_$Gatherv}} -\begin{lstlisting}[language=C,frame=lines] -MPI_Comm comm; -int gsize,sendarray[100]; -int root, *rbuf, stride; -int *displs,i,*rcounts; -... -MPI_Comm_size(comm, &gsize); -rbuf = (int *)malloc(gsize*stride*sizeof(int)); -displs = (int *)malloc(gsize*sizeof(int)); -rcounts = (int *)malloc(gsize*sizeof(int)); -for (i=0; i 100})} -\end{itemize} - -\begin{center} -\input{day3/images/scatterv.tex} -\end{center} - -\end{frame} - - -\begin{frame}[containsverbatim] -\frametitle{``v-version'' of \texttt{MPI$\_$Scatter} : \texttt{MPI$\_$Scatterv}} -\begin{lstlisting}[language=C,frame=lines] -MPI_Comm comm; -int gsize,*sendbuf; -int root, rbuf[100], i, *displs, *scounts; -... -MPI_Comm_size(comm, &gsize); -sendbuf = (int *)malloc(gsize*stride*sizeof(int)); -... -displs = (int *)malloc(gsize*sizeof(int)); -scounts = (int *)malloc(gsize*sizeof(int)); -for (i=0; i} \\ \cxxinline{MPI_CXX_DOUBLE_COMPLEX} & \cxxinline{std::complex} \\ \cxxinline{MPI_CXX_LONG_DOUBLE_COMPLEX} & \cxxinline{std::complex}\\ \bottomrule \end{tabular} \end{minipage} \hspace{1.8cm} \begin{minipage}{.3\linewidth} \small \begin{tabular}{ll} \toprule MPI datatype & C datatype\\ \midrule \cxxinline{MPI_AINT} & \cxxinline{MPI_Aint} \\ \cxxinline{MPI_OFFSET} & \cxxinline{MPI_Offset} \\ \cxxinline{MPI_COUNT} & \cxxinline{MPI_Count} \\ \cxxinline{MPI_BYTE} & \\ \cxxinline{MPI_PACKED} & \\ \bottomrule \end{tabular} \end{minipage} \end{frame} \note{ \begin{itemize} \item \cxxinline{MPI_CHAR} is a printable character where \cxxinline{MPI_BYTE} is a type of exactly 8bit not printable as a character \item \cxxinline{MPI_PACKED} for pack/unpacked \end{itemize} } \begin{frame}[fragile] \frametitle{Derived Datatypes} \framesubtitle{Arrays} \begin{cxxcode}{Syntax} int MPI_Type_contiguous(int count, MPI_Datatype oldtype, MPI_Datatype *newtype); int MPI_Type_vector(int count, int blocklength, int stride, MPI_Datatype oldtype, MPI_Datatype *newtype); \end{cxxcode} \begin{itemize} \item array of contiguous array or with strided blocks of same type \item \cxxinline{count}: number of repetition (blocks) \item \cxxinline{blocklength}: number of element per block \item \cxxinline{stride}: number of element between start of each block \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Derived Datatypes} \framesubtitle{Array variants} \begin{itemize} \item \cxxinline{MPI_Type_create_hvector}: same as \cxxinline{MPI_Type_vector} with \cxxinline{stride} expressed in bytes \item \cxxinline{MPI_Type_create_indexed_block} same as \cxxinline{MPI_Type_vector} with array of and \cxxinline{displacements} \item \cxxinline{MPI_Type_create_hindexed_block}: same as \cxxinline{MPI_Type_create_indexed_block} with \cxxinline{displacements} in bytes \item \cxxinline{MPI_Type_indexed}: same as \cxxinline{MPI_Type_create_indexed_block} with arrays of \cxxinline{blocklengths} \item \cxxinline{MPI_Type_create_hindexed}: same as \cxxinline{MPI_Type_indexed} with \cxxinline{displacements} in bytes \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Derived Datatypes} \framesubtitle{Structures} \begin{cxxcode}{Syntax} int MPI_Type_create_struct(int count, const int array_of_blocklengths[], const MPI_Aint array_of_displacements[], const MPI_Datatype array_of_types[], MPI_Datatype *newtype) \end{cxxcode} \begin{itemize} \item \cxxinline{count}: number of repetition (blocks) \item \cxxinline{array_of_blocklengths}: sizes per block \item \cxxinline{array_of_displacements}: displacements between blocks in bytes \item \cxxinline{array_of_types}: types contained in each blocks \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Derived Datatypes} \framesubtitle{Usefull helper functions} \begin{itemize} \item \cxxinline{MPI_Get_address}: get the address of a variable \item \cxxinline{MPI_Aint_diff}: get the difference between 2 addresses \item \cxxinline{MPI_Aint_add}: get the sum of 2 addresses \item \cxxinline{MPI_Type_size}: get the size of a datatype \item \cxxinline{MPI_Get_type_extent}: get the lower bound and the extent of a type \item \cxxinline{MPI_Type_create_resized}: reset the lower bound and the extent of a type \end{itemize} \end{frame} \note{ \begin{itemize} \item Prefer \cxxinline{MPI_Get_address} over \& \item extent could be badly set then not possible to communicate multiple objects of same datatype \end{itemize} } \begin{frame}[fragile] \frametitle{Derived Datatypes} \framesubtitle{Commit/free} \begin{cxxcode}{Syntax} int MPI_Type_commit(MPI_Datatype *datatype); int MPI_Type_free(MPI_Datatype *datatype); \end{cxxcode} \begin{itemize} \item new datatypes should be committed before being usable in communications \item committed types need to be freed once not used anymore \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Derived Datatypes} \framesubtitle{Example} \cxxfile[title={mpi/datatypes.cc}, minted options app={ firstline=13, lastline=41, fontsize=\tiny}]{examples/mpi/datatypes.cc} \end{frame} \begin{frame}[fragile, exercise] \frametitle{Derived Datatypes} \framesubtitle{Send lines in poisson code} \begin{itemize} \item Create a \cxxinline{MPI_Datatype line_t} representing a line of data \item Exchange data of type \cxxinline{line_t} instead of \cxxinline{MPI_FLOAT} \end{itemize} \end{frame} \subsection{Pack/Unpack} \begin{frame}[fragile] \frametitle{Pack/Unpack} \framesubtitle{Pack} \begin{cxxcode}{Syntax} int MPI_Pack(const void *inbuf, int incount, MPI_Datatype datatype, void *outbuf, int outsize, int *position, MPI_Comm comm); \end{cxxcode} \begin{itemize} \item \cxxinline{inbuf}, \cxxinline{incount}, \cxxinline{datatype} correspond to the description of data to pack \item \cxxinline{outbuf}, \cxxinline{outsize} description of the buffer where to pack \item \cxxinline{position} current position in the packing buffer \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Pack/Unpack} \framesubtitle{Unpack} \begin{cxxcode}{Syntax} int MPI_Unpack(const void *inbuf, int insize, int *position, void *outbuf, int outcount, MPI_Datatype datatype, MPI_Comm comm); \end{cxxcode} \begin{itemize} \item \cxxinline{inbuf}, \cxxinline{incount}, description of the buffer from which to unpack \item \cxxinline{position} current position in the unpacking buffer \item \cxxinline{outbuf}, \cxxinline{outsize}, and \cxxinline{datatype} correspond to the description of data to unpack \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Pack/Unpack} \framesubtitle{Example} \cxxfile[title={mpi/pack\_unpack.cc}, minted options app={ firstline=26, lastline=39 }]{examples/mpi/pack_unpack.cc} \end{frame} \subsection{Groups and Communicator} \begin{frame}[containsverbatim] \frametitle{Groups and Communicators} \begin{itemize} \item a \code{communicator}: \begin{itemize} \item Encapsulate a \code{context}, a \code{group}, a \code{virtual topology} and \code{attributes} \item Two kinds \code{intra-communicator} and \code{inter-communicator} \end{itemize} \item a \code{group}: \begin{itemize} \item ordered set of processes \item each process has an unique ID (rank within the group) and can belong to several different groups \item a group can be used to create a new communicator \end{itemize} \end{itemize} \end{frame} \note{ \begin{itemize} \item \code{intra} communications inside a group \item \code{inter} communications between groups \end{itemize} } \begin{frame}[containsverbatim] \frametitle{Groups and Communicators} \framesubtitle{Creating new communicators} \begin{itemize} \item duplicating or splitting an existing one \cxxinline{MPI_Comm_dup}, \cxxinline{MPI_Comm_split} \item creating communicator from a group \cxxinline{MPI_Comm_create}, \cxxinline{MPI_Comm_create_group} \item need to create groups \begin{itemize} \item from a communicator \cxxinline{MPI_Comm_group} \item boolean operations \cxxinline{MPI_Group_union}, \cxxinline{MPI_Group_intersection}, \cxxinline{MPI_Group_difference} \item specifying ranks \cxxinline{MPI_Group_incl}, \cxxinline{MPI_Group_excl} \end{itemize} \item destroy created objects \cxxinline{MPI_Comm_free}, \cxxinline{MPI_Group_free} \end{itemize} \end{frame} \subsection{Virutal Topologies} \begin{frame} \frametitle{Virtual Topologies} \framesubtitle{} \begin{itemize} \item potential performance gain by mapping process to hardware \item helps for program readability \item types of topologies: Cartesian, Graph, Distributed Graph \item collective communication on neighborhoods \end{itemize} \end{frame} \note{ Details only on the cartesian on } \begin{frame}[fragile] \frametitle{Virtual Topologies} \framesubtitle{Cartesian topology} \begin{cxxcode}{Syntax} int MPI_Cart_create(MPI_Comm comm_old, int ndims, const int dims[], const int periods[], int reorder, MPI_Comm *comm_cart); \end{cxxcode} \begin{itemize} \item create a communicator with cartesian information \item convenient functions: \begin{itemize} \item \cxxinline{MPI_Dims_create} helps creating balanced distribution of process \item \cxxinline{MPI_Cart_shift} helps determining neighboors \item \cxxinline{MPI_Cart_rank} get the rank based on coordinates \item \cxxinline{MPI_Cart_coords} get coordinates based on rank \end{itemize} \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Virtual topology} \framesubtitle{Neighborhoods collective} \begin{itemize} \item \cxxinline{MPI_Neighbor_allgather} assuming we are on process with rank $i$, gather data from all rank $j$ if edge $(j, i)$ exists and send same data to all $j$ where edge $(i,j)$ exists \item \cxxinline{MPI_Neighbor_alltoall} compare to allgather, sends different data to all $j$ process \item vector variant are available \code{v} \item immediate variant are available \code{I} \item persistent variant are available \code{\_init} \item \cxxinline{MPI_Neighbor_alltoall} as one in all flavors the \code{w}, different datatypes are echanged with all neighbors \end{itemize} \end{frame} \begin{frame}[exercise, fragile] \frametitle{Virtual topology} \framesubtitle{} \begin{itemize} \item Rewrite the parallelism using a cartesian communicator \item Use neighbor collective communications \end{itemize} \end{frame} \subsection{Parallel I/O} \begin{frame}[containsverbatim] \frametitle{Parallel I/O overview} \begin{itemize} \item I/O is often (if not always) the main bottleneck in a parallel application \item MPI provides a mechanism to read/write in parallel \end{itemize} \begin{center} \input{src/mpi/figures/parallelFS.tex} \end{center} \end{frame} \begin{frame}[containsverbatim] \frametitle{Introducing remarks} \begin{itemize} \item MPI IO API works on your desktop/laptop \item Most of the large HPC systems have a \textbf{parallel file system} (like GPFS, Lustre, \emph{etc}.) \item If the file is distributed smartly on a parallel file system: performance increases \item MPI IO offers a high-level API to access a distributed file (no needs to implement complex POSIX calls) \item \textbf{does not work with ASCII files} \item Most of the standard file format support MPI IO (\emph{e.g}. HDF5, NetCDF, \emph{etc}..) \end{itemize} \end{frame} \begin{frame}[containsverbatim] \frametitle{Poisson so far} \begin{center} \input{src/mpi/figures/sofar.tex} \end{center} \end{frame} \begin{frame}[containsverbatim] \frametitle{Poisson ideal} \begin{center} \input{src/mpi/figures/sogoal.tex} \end{center} \end{frame} \begin{frame}[fragile] \frametitle{Open/Close a file in parallel} \begin{cxxcode}{Syntax} int MPI_File_open(MPI_Comm comm, const char *filename, int amode, MPI_Info info, MPI_File *fh); int MPI_File_close(MPI_File *fh); \end{cxxcode} \begin{itemize} \item \cxxinline{comm}: the communicator that contains the writing/reading MPI processes \item \cxxinline{filename}: a file name \item \cxxinline{amode}: file access mode, \cxxinline{MPI_MODE_RDONLY}, \cxxinline{MPI_MODE_WRONLY}, \cxxinline{MPI_MODE_RDWR}, \cxxinline{MPI_MODE_CREATE}, \emph{e.t.c.} \item \cxxinline{info}: file info object (\cxxinline{MPI_INFO_NULL} is a valid info) \item \cxxinline{fh}: file handle \end{itemize} \textbf{Collective calls !!} \end{frame} \begin{frame}[containsverbatim] \frametitle{Parallel IO} \framesubtitle{Terminology} \begin{itemize} \item \code{etype} is the elementary type of the data of the parallel accessed file \item \code{offset} is a position in the file in term of multiple of etypes \item \code{displacement} of a position within the file is the number of bytes from the beginning of the file \end{itemize} \begin{center} \includegraphics{src/mpi/figures/offset} %\input{day3/images/offset.tex} \end{center} \end{frame} \begin{frame}[containsverbatim] \frametitle{Parallel IO} \framesubtitle{Simple independent read/write} \begin{cxxcode}{Syntax} int MPI_File_read_at(MPI_File fh, MPI_Offset offset, void *buf, int count, MPI_Datatype datatype, MPI_Status *status); int MPI_File_write_at(MPI_File fh, MPI_Offset offset, const void *buf, int count, MPI_Datatype datatype, MPI_Status *status); \end{cxxcode} \begin{itemize} \item Can be used from a single (or group) of processes \item \cxxinline{offset} must be specified in the \cxxinline{buf} buffer \item \cxxinline{count} elements of type \cxxinline{datatype} are written \end{itemize} \end{frame} \begin{frame}[containsverbatim] \frametitle{Parallel IO} \framesubtitle{\code{view} by each process} \begin{cxxcode}{Syntax} int MPI_File_set_view(MPI_File fh, MPI_Offset disp, MPI_Datatype etype, MPI_Datatype filetype, const char *datarep, MPI_Info info); int MPI_File_get_view(MPI_File fh, MPI_Offset *disp, MPI_Datatype *etype, MPI_Datatype *filetype, char *datarep); \end{cxxcode} \begin{itemize} \item initially, each process view the file as a linear byte stream and each process views data in its own native representation \item \cxxinline{disp} is the displacement (defines the beginning of the data of the file that belongs to the process) in byte \item \cxxinline{etype} is the unit of data access and positioning \item \cxxinline{filetype} is a single \cxxinline{etype} of a multiple of it \end{itemize} \end{frame} -\begin{frame}[containsverbatim] +\begin{frame}[b,containsverbatim] \frametitle{Parallel IO} \frametitle{Setting up a \code{view}} \begin{center} - \input{day3/images/displacements.tex} + \addimage[width=12cm]{\FIGREP/displacements}{2cm}{2cm} \end{center} (source : MPI 2.2 specifications) \end{frame} \begin{frame}[containsverbatim] \frametitle{Parallel IO} \framesubtitle{Simple independent read/write without offset} \begin{cxxcode}{Syntax} int MPI_File_read(MPI_File fh, void *buf, int count, MPI_Datatype datatype, MPI_Status *status); int MPI_File_write(MPI_File fh, const void *buf, int count, MPI_Datatype datatype, MPI_Status *status); \end{cxxcode} \end{frame} \begin{frame}[containsverbatim] \frametitle{Parallel IO} \framesubtitle{Collective read/write with/without offset} \begin{cxxcode}{Syntax} int MPI_File_write_all(MPI_File fh, const void *buf, int count, MPI_Datatype datatype, MPI_Status *status); int MPI_File_read_all(MPI_File fh, void *buf, int count, MPI_Datatype datatype, MPI_Status *status); \end{cxxcode} \end{frame} \subsection{One Sided} \begin{frame}[containsverbatim] \frametitle{What we did not view} \begin{itemize} \item One Sided communications \begin{itemize} \item \cxxinline{MPI_Put}, \cxxinline{MPI_Get} \item \cxxinline{MPI_Win_*} \item shared memory \end{itemize} \item Process management \begin{itemize} \item \cxxinline{MPI_Comm_spawn} \item Communications on inter-communicators \end{itemize} \end{itemize} \end{frame} \begin{frame}[fragile,t] \frametitle{Parallelization of the poisson code} \begin{minipage}{.45\linewidth} \centering \begin{overprint} \only<1>{\includegraphics[width=.8\linewidth]{\FIGREP/grid_2D_1}} \only<2>{\includegraphics[width=.8\linewidth]{\FIGREP/grid_2D_2}} \only<3>{\includegraphics[width=.8\linewidth]{\FIGREP/grid_2D_3}} \only<4->{\includegraphics[width=.8\linewidth]{\FIGREP/grid_2D_4}} \end{overprint} \end{minipage} \begin{minipage}{.45\linewidth} \begin{overprint} \onslide<1> \begin{itemize} \item Parallelize the Poisson 2D problem using the Messages Passing Interface (MPI) \end{itemize} \onslide<2> \begin{itemize} \item This time, we want to make a 2D domain decomposition using Cartesian topology \item Use \code{MPI\_Dims\_create} and \code{MPI\_Cart\_create} to create a Cratesian topology \end{itemize} \onslide<3> \begin{itemize} \item The $p$ processes are split into $(p_{x}, p_{y})$ to make the Cartesian grid \item Each domain has size $(N/p_{x}, N/p_{y})$ (1 per process) \item Use \code{MPI\_Cart\_shift} to find the neighboring domains \end{itemize} \onslide<4> \begin{itemize} \item Adding \emph{ghost} lines before and after \item Use the \emph{ghost} lines to receive the missing local data \item You will need to define a new \textit{matrix column} datatype and update the \textit{matrix line} datatype \end{itemize} \onslide<5> \begin{itemize} \item Use the \code{MPI\_neighbor\_alltoallw} routine \item You can use the number of iteration as a check \item Remove the \cxxinline{dump()} function to start \end{itemize} \end{overprint} \end{minipage} \end{frame} %%% Local Variables: %%% mode: latex %%% TeX-master: "../../phys_743_parallel_programming" %%% End: