# HG changeset patch # User Ashwin Vishnu <avmo@kth.se> # Date 1525322387 -7200 # Thu May 03 06:39:47 2018 +0200 # Node ID 5dd3701155f41ade89eeb120cc73e33af11de371 # Parent 8622eed07b4defdda568b8fedb088f5712ca18b4 Finish code org, start performance diff --git a/fluidfft/Makefile b/fluidfft/Makefile --- a/fluidfft/Makefile +++ b/fluidfft/Makefile @@ -24,7 +24,7 @@ vimtex: # gvim $(name).tex --servername GVIM & # xterm -class GVIM -e vim $(name).tex --servername GVIM & - NVIM_LISTEN_ADDRESS=GVIM nvim-qt $(name).tex & + NVIM_LISTEN_ADDRESS=GVIM nvim-gtk $(name).tex & doit: vimtex $(name).pdf zathura $(name).pdf & diff --git a/fluidfft/Pyfig/fig_build_use.dio b/fluidfft/Pyfig/fig_build_use.dio --- a/fluidfft/Pyfig/fig_build_use.dio +++ b/fluidfft/Pyfig/fig_build_use.dio @@ -1,1 +1,1 @@ -<mxfile userAgent="Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Firefox/52.0" version="8.5.12" editor="www.draw.io" type="device"><diagram id="32c47e48-bc75-56f3-0806-9a032b4a9c3c" 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zdO?3_+`zvz9-covbMbO;a{i$KIk`c9)(hn1<^Ho?AlKhsfLy=F=P!+im-i11#LmI} zrxy@A5cH=P5IczDZ;hAdPk+BlasJs}9xfo)pRqi@JL~Uqyu5#D04~5^u>c^?pJT)e z0&@LdZFBx?WNBmi`Jcans->stKU0@Y#opeTlIuU&j{hbna{TWcHz#MK&(8nOab6G) NFE<JuorL0t{{`GQ(Ru&? diff --git a/fluidfft/fluidfft_paper.tex b/fluidfft/fluidfft_paper.tex --- a/fluidfft/fluidfft_paper.tex +++ b/fluidfft/fluidfft_paper.tex @@ -75,7 +75,7 @@ % useful for.} Free and open-source library. Python. Fast Fourier Transform, Distributed, MPI, -GPU. +GPU.% \section*{Introduction} @@ -84,17 +84,18 @@ % articles. A short comparison with software which implements similar % functionality should be included in this section. } -Fast Fourier transforms (FFT) are useful for many applications, -such as signal processing, numerical simulations and scientific computing in -general. There are many good libraries to perform FFT, in particular the -\emph{de-facto} standard FFTW. A new challenge is to efficiently scale FFT on -clusters with the memory distributed over a large number of cores. This is -imperative to solve big problems faster and when the arrays do not fit in the -memory of single computational node. A problem is that for one-dimensional FFT, -all the data has to be located in the memory of the on clusters with the memory +Fast Fourier transforms (FFT) are useful for many applications, such as signal +processing, numerical simulations and scientific computing in general. There +are many good libraries to perform FFT, in particular the \emph{de-facto} +standard FFTW.\@ A new challenge is to efficiently scale FFT on clusters with +the memory distributed over a large number of cores. This is imperative to +solve big problems faster and when the arrays do not fit in the memory of +single computational node. A problem is that for one-dimensional FFT, all the +data has to be located in the memory of the on clusters with the memory distributed over a large number of cores. A problem is that for one-dimensional -FFT, all the data has to be located in the memory of the process that perform the -FFT, so a lot of communication between processes are needed for 2D and 3D FFT. +FFT, all the data has to be located in the memory of the process that perform +the FFT, so a lot of communication between processes are needed for 2D and 3D +FFT.% There are two strategies to distribute the memory, the 1D (or \emph{slab}) decomposition and the 2D (or \emph{pencil}) decomposition. The 1D decomposition @@ -103,7 +104,7 @@ contrast, this limitation is overcome by the 2D decomposition. Some of the well-known libraries are written in C, C++ and Fortran. \libpack{FFTW} -supports MPI using 1D decomposition and hybrid parallelism using OpenMP. Other +supports MPI using 1D decomposition and hybrid parallelism using OpenMP.\@ Other libraries, now implement the 2D decomposition: \libpack{pfft}, \libpack{p3dfft}, \libpack{2decomp\&FFT} and so on. These libraries rely on MPI for the communications between processes, are optimized for supercomputers and scales well @@ -184,10 +185,11 @@ In the present article, we shall start by describe the implementation of \fluidpack{fft} including its design aspects, the code organization. Thereafter, we shall compare the performance of different classes in -\fluidpack{fft} in two high performance computing clusters, and describe -microbenchmarks of the critical functions in . Finally, we show how we test -and maintain the quality of the code base through continuous integration and -mention some possible applications of \fluidpack{fft}. +\fluidpack{fft} in two high performance computing clusters, and also describe +using microbenchmarks how a Python function can be optimized to be as fast as +Fortran. Finally, we show how we test and maintain the quality of the code +base through continuous integration and mention some possible applications of +\fluidpack{fft}. \section*{Implementation and architecture} @@ -211,20 +213,6 @@ \subsection*{C++ API} -The C++ API is implemented as a hierarchy of classes as shown in -Fig.~\ref{fig:classes}. By utilizing inheritance the classes share the same -function names and syntax defined in the \emph{base} classes. Some examples of -such functions are: - -\begin{itemize} - - -\begin{itemize} - \item \codeinline{are\_parameters\_bad}: Verifies whether the global array - shape cannot be decomposed with the number of MPI processes available. If - the parameters are compatible returns \codeinline{false}. -\end{itemize} - \begin{figure}[htp] \centering \includegraphics[width=\linewidth]{Pyfig/fig_classes} @@ -234,7 +222,44 @@ }\label{fig:classes} \end{figure} -Let us illustrate with a trivial example, in which we initialize the FFT with a +The C++ API is implemented as a hierarchy of classes as shown in +Fig.~\ref{fig:classes}. +% +The naming convention used for the classes (\codeinline{<Type of +FFT>With<Name of Library>}) is a cue for how these are function internally. +% +By utilizing inheritance the classes share the same function names and syntax +defined in the \emph{base} classes, shown in white boxes in +Fig.~\ref{fig:classes}. Some examples of such functions are: + +\begin{itemize} + \item \codeinline{alloc\_array\_X}: Allocates array to store a physical array + with real datatype for the current process. + \item \codeinline{alloc\_array\_K}: Allocates array to store a spectral array + with complex datatype for the current process. + \item \codeinline{init\_array\_X\_random}: Allocates and initializes a physical + array with random values. + \item \codeinline{test}: Run tests for a class by comparing mean and mean energy + values in an array before and after a set of \codeinline{fft} and + \codeinline{ifft} calls. + \item \codeinline{bench}: Benchmark the \codeinline{fft} and + \codeinline{ifft} methods for certain number of iterations. +\end{itemize} + +Remaining methods which are specific to a library are defined in the +corresponding child classes, depicted in coloured boxes in +Fig.~\ref{fig:classes}, for example: + +\begin{itemize} + \item \codeinline{are\_parameters\_bad}: Verifies whether the global array + shape can be decomposed with the number of MPI processes available or not. + If the parameters are compatible returns \codeinline{false}. This method is + called prior to initializing the class. + \item \codeinline{fft} and \codeinline{ifft}: Forward and inverse FFT + methods. +\end{itemize} + +Let us illustrate with a trivial example, wherein we initialize the FFT with a random physical array, and perform a \codeinline{fft} and \codeinline{ifft} operation. \begin{minted}[fontsize=\footnotesize]{cpp} @@ -245,8 +270,7 @@ // #include <fft3dmpi_with_p3dfft.h> #include <mpi.h> -int main(int argc, char **argv) -{ +int main(int argc, char **argv) { int N0 = N1 = N2 = 32; // MPI-related int nb_procs = 4; @@ -259,33 +283,33 @@ FFT3DMPIWithFFTWMPI3D o(N0, N1, N2); // FFT3DMPIWithP3DFFT o(N0, N1, N2); - o.init_array_X_random(array_X); // Initialize the physical array with random values - o.alloc_array_K(array_K); // Allocate the spectral array in memory - o.fft(array_X, array_K); // Forward FFT - o.ifft(array_K, array_X) // Inverse FFT + o.init_array_X_random(array_X); + o.alloc_array_K(array_K); + o.fft(array_X, array_K); + o.ifft(array_K, array_X); MPI_Finalize(); return 0; } \end{minted} -As suggested in the comments, to switch the FFT library and the user only needs to -change the header file and the class name. Another added advantage is that the -user does not need to worry about the domain decomposition to declare and allocate -the arrays. A few more helper functions are available with the FFT classes, such -as functions to compute the mean value and energies in the array. These are -illustrated with examples in the documentation.\footnote{ +As suggested in the comments above, to switch the FFT library and the user only +needs to change the header file and the class name. Another added advantage is +that the user does not need to worry about the domain decomposition to declare +and allocate the arrays. A few more helper functions are available with the FFT +classes, such as functions to compute the mean value and energies in the array. +These are illustrated with examples in the documentation.\footnote{% \url{https://fluidfft.readthedocs.io/en/latest/examples/cpp.html}}. Detailed information related to the C++ classes and its member functions can be -found in the online documentation\footnote{ +found in the online documentation\footnote{% \url{https://fluidfft.readthedocs.io/en/latest/doxygen/index.html}}. \subsection*{Python API} Similar to other packages in the FluidDyn project, \fluidpack{fft} also uses an -object-oriented approach to implement the FFT classes. +object-oriented approach to implement the FFT libraries. % -This is in contrast with the approach taken by \pack{numpy.fft} and \pack -{scipy.fftpack}, wherein the user has to figure out from the documentation the +This is in contrast with the approach taken by \pack{numpy.fft} and \pack{% +scipy.fftpack}, wherein the user has to figure out from the documentation the procedure to design the input values and to use the return values while using the FFT and inverse FFT functions. The Python API wraps all the functionalities of its C++ counterpart and offers a more richer experience through an accompanying @@ -330,98 +354,148 @@ A parallelized version of the above code will work out of the box, simply by replacing the FFT class with an MPI-based FFT class, for eg. -\codeinline{fft2d.with\_fftwmpi2d}. Even if one finds the available methods -in the operator class to be lacking one can inherit the class and create a -new method, for instance using the wavenumber arrays, \codeinline{oper.KX} -and \codeinline{oper.KY}. Arguably, a similar implementation with other -available packages would require the know-how on how FFT arrays are allocated -in the memory, normalized, decomposed in parallel and so on. A more detailed -introduction on how to use \fluidpack{fft} and available functions can be -found in the -tutorials\footnote{\url{https://fluidfft.readthedocs.io/en/latest/tutorials.html}}. +\codeinline{fft2d.with\_fftwmpi2d}. Even if one finds the available methods in +the operator class to be lacking one can inherit the class and create a new +method, for instance using the wavenumber arrays, \codeinline{oper.KX} and +\codeinline{oper.KY}. Arguably, a similar implementation with other available +packages would require the know-how on how FFT arrays are allocated in the +memory, normalized, decomposed in parallel and so on. A more detailed +introduction on how to use \fluidpack{fft} and available functions can be found +in the +tutorials\footnote{\url{% + https://fluidfft.readthedocs.io/en/latest/tutorials.html}}. +Thus, we have demonstrated how, by using \fluidpack{fft}, a developer can +easily switch between FFT libraries. +% Let us now turn our attention to how the code is organized. We shall also describe -how the source code is built, and linked with the supported FFT libraries. +how the source code is built, and linked with the supported libraries. \subsection*{Code organization} -These classes unify the supported libraries by sharing method -names. This forms an API with which, a developer can easily switch between -FFT libraries, and not be dependent on simply one implementation. - -Layers: -\begin{itemize} - -\item One C++ class per method forming a hierarchy of C++ classes as shown in -Fig.~\ref{fig:classes}. - -\item Cython wrappers of the C++ classes with their unit test functions. The -Cython \codeinline{.pyx} and \codeinline{.pxd} files are produced from -template files (specialized for the 2d and 3d cases) using the template -library \href{http://www.makotemplates.org/}{\pack{mako}}. - -\item Python operators classes (2d and 3d) to write code independently of the -library used for the computation of the FFT + their unit test functions. - -\item Pythran functions to speedup critical code. We will show in the -following subsection that we reach the performance of the equivalent Fortran -code. - -\item command-line utilities (\codeinline{fluidfft-bench} and -\codeinline{fluidfft-bench-analysis}). - -\end{itemize} - \begin{figure}[htp] \centering - \includegraphics[width=\linewidth]{Pyfig/fig_build_use} + \includegraphics[width=0.96\linewidth]{Pyfig/fig_build_use} \caption{Flowchart illustrating how the C++ and Python API are built and used for one particular class, viz. \codeinline{FFT2DMPIWithFFTWMPI2D}. The dotted arrows in C++ part stand for include statements, demonstrating the class hierarchy and in the Python part indicate how different codes are imported. On the bottom, a smaller flowchart demonstrates how to use the API by writing user code. - } - \label{fig:build_use} + }\label{fig:build_use} \end{figure} +The internal architecture of \fluidpack{fft} can be visualized as layers. +Through Fig.~\ref{fig:build_use}, we can see how these layers are linked together +forming the API for C++ and Python development. For simplicity, only one FFT +class is depicted in the figure, namely \codeinline{FFT2DMPIWithFFTWMPI2D}, +which wraps \libpack{FFTW}'s parallelized 2D FFT implementation. The C++ API is +accessed by importing the appropriate header file and building the user code +with a Makefile, an example of which is available \href{% + https://fluidfft.readthedocs.io/en/latest/examples/cpp.html}{% + in the documentation}. + +The Python API is built automatically when \fluidpack{fft} is +installed\footnote{% +\href{https://fluidfft.readthedocs.io/en/latest/install.html}{Detailed steps +for installation} are provided in the documentation} +% +which executes the script \codeinline{setup.py}. It first generates the Cython +source code as a pair \codeinline{.pyx} and \codeinline{.pxd} files defining a +class wrapping its C++ counterpart\footnote{Uses an approach similar to + guidelines titled \href{% + https://cython.readthedocs.io/en/latest/src/userguide/wrapping_CPlusPlus.html}{% +``Using C++ in Cython''}}. +% +The Cython files are produced from template files (specialized for the 2D and +3D cases) using the template library \mako. +% +Thereafter, \pack{cython} generates C++ code with necessary Python bindings, +which are then built in the form of extensions or dynamic libraries importable +in pure Python code. All the built extensions are then installed as a Python +package \fluidpack{fft}. + +A helper function \codeinline{fluidfft.import\_fft\_class} is provided with the +package to simply import the FFT class. However, it is more convenient and +recommended to use an operator class, as described in the example for Python +API.\@ Although the operator classes can function as pure Python code, some of +its critical methods can be optimized, if \pack{pythran} is available during +installation of \fluidpack{fft}. We will show towards the end of this section +that by using \pack{pythran}, we reach the performance of the equivalent +Fortran code. + +To summarize, \fluidpack{fft} consists of the following layers: +\begin{itemize} + +\item One C++ class per method derived from a hierarchy of C++ classes as shown + in Fig.~\ref{fig:classes}. + +\item Cython wrappers of the C++ classes with their unit test cases. + +\item Python operators classes (2D and 3D) to write code independently of the + library used for the computation of the FFT and with some mathematical helper + methods. These classes are accompanied by unit test cases. + +\item Pythran functions to speedup critical methods in the Python operators + classes. + +\end{itemize} + +Command-line utilities (\codeinline{fluidfft-bench} and +\codeinline{fluidfft-bench-analysis}) are also provided with the +\fluidpack{fft} installation to run benchmarks and plot the results. In the +next subsection, we shall look at some results by making use of these +utilities on two computing clusters. + \subsection*{Performance} -\subsubsection*{Scalability analysis using \codeinline{fluidfft-bench}} +\subsubsection*{Scalability tests using \codeinline{fluidfft-bench}} % Simple!! Few cases. Few clusters. Figures obtained with % fluidfft-bench-analysis +For every FFT classes available for the resolution and for the two tasks +forward and inverse FFT, three different functions are used and compared (see +the legend in subsequent figures): + +\begin{itemize} + +\item \codeinline{fft\_cpp}, \codeinline{ifft\_cpp} (continuous lines): + benchmark of the C++ function from the C++ code. An array (technically, a + pointer) is passed as an argument to store the result. No memory allocation + is performed inside the functions. + +\item \codeinline{fft\_as\_arg}, \codeinline{ifft\_as\_arg} (dashed lines): + benchmark of a Python method from Python. Similar to the C++ code, the second + argument of this method is an array to contain the result of the transform, + so no memory allocation is needed. + +\item \codeinline{fft\_return}, \codeinline{ifft\_return} (dotted lines): + benchmark of a Python method from Python. No array is provided to the + function to contain the result, and therefore a numpy array is created and + then returned by the function. + +\end{itemize} + +The results\footnote{\url{% +https://bitbucket.org/fluiddyn/fluidfft-bench-results}} are then plotted using +\codeinline{fluidfft-bench-analysis}. + + \paragraph{Benchmarks on Occigen} -Occigen is a GENCI-CINES HPC cluster +\href{https://www.top500.org/system/178465}{Occigen} is a GENCI-CINES HPC +cluster. -https://www.top500.org/system/178465 \begin{figure}[htp] \centering \includegraphics[width=\linewidth]{tmp/fig_occigen_384x1152x1152} -\caption{Speedup computed from the median of the elapsed times for 3d fft +\caption{Speedup computed from the median of the elapsed times for 3D fft (384$\times$1152$\times$1152, left: fft and right: ifft) on Occigen.} \label{fig:occigen384x1152x1152} \end{figure} -For every FFT classes available for the resolution and for the two tasks fft and -ifft, three functions are used and compared (see the legends): - -\begin{itemize} -\item ``fft\_cpp'' (continuous lines): benchmark of the C++ function from the C++ -code. No memory allocation. - -\item ``fft\_as\_arg'' (dashed lines): benchmark of a Python method -\codeinline{fft\_as\_arg} from Python. As for the C++ code, the second -argument of this method is an array to contain the result of the transform, so -no memory allocation is needed. - -\item "fft\_return" (dotted lines): benchmark of a Python method -\codeinline{fft} from Python. No array is provided to the function to contain -the result so a numpy array is created and then returned by the function. -\end{itemize} The fastest methods are fftw1d (which is limited to 96 cores) and p3dfft. @@ -436,7 +510,7 @@ \begin{figure}[htp] \centering \includegraphics[width=\linewidth]{tmp/fig_occigen_1152x1152x1152} -\caption{Speedup computed from the median of the elapsed times for 3d fft +\caption{Speedup computed from the median of the elapsed times for 3D fft (1152$\times$1152$\times$1152, left: fft and right: ifft) on Occigen.} \label{fig:occigen1152x1152x1152} \end{figure} @@ -455,7 +529,7 @@ \begin{figure}[htp] \centering \includegraphics[width=\linewidth]{tmp/fig_beskow_384x1152x1152} -\caption{Speedup computed from the median of the elapsed times for 3d fft +\caption{Speedup computed from the median of the elapsed times for 3D fft (384$\times$1152$\times$1152, left: fft and right: ifft) on Beskow.} \label{fig:beskow384x1152x1152} \end{figure} @@ -463,7 +537,7 @@ \begin{figure}[htp] \centering \includegraphics[width=\linewidth]{tmp/fig_beskow_1152x1152x1152} -\caption{Speedup computed from the median of the elapsed times for 3d fft +\caption{Speedup computed from the median of the elapsed times for 3D fft (1152$\times$1152$\times$1152, left: fft and right: ifft) on Beskow.} \label{fig:beskow1152x1152x1152} \end{figure} diff --git a/jors.cls b/jors.cls --- a/jors.cls +++ b/jors.cls @@ -112,7 +112,8 @@ \newcommand{\scipy}{\codeinline{scipy}\xspace} \newcommand{\pack}[1]{\codeinline{#1}\xspace} -% Override the PyPI url by using the optional 2nd argument + +\newcommand{\mako}{\href{http://www.makotemplates.org/}{\pack{mako}}} \newcommand{\libpack}[2][]{% \ifstrequal{#2}{FFTW}{%