| version 1.1, 2000/07/21 08:27:11 |
version 1.3, 2000/07/31 07:26:12 |
|
|
| % $OpenXM$ |
% $OpenXM: OpenXM/doc/calc2000p/efficient.tex,v 1.2 2000/07/22 08:11:09 noro Exp $ |
| \documentclass{slides} |
\documentclass{slides} |
| |
\topmargin -0.5cm |
| |
\textheight 9.5in |
| \usepackage{color} |
\usepackage{color} |
| |
\usepackage{rgb} |
| \usepackage{graphicx} |
\usepackage{graphicx} |
| \usepackage{epsfig} |
\usepackage{epsfig} |
| %{\color{red} Asir} |
|
| \begin{document} |
\begin{document} |
| \parskip 3pt |
\parskip 3pt |
| \fbox{{\huge \color{blue} We Are Efficient}} |
\fbox{\large \color{blue} Efficient Computation with OpenXM} |
| |
\vskip 2pt |
| |
|
| \noindent |
{\color {red} Real speedup by parallelism} |
| {\color{red} OpenXM on MPI --- to achieve real speedup by parallelism} |
|
| |
|
| A process can communicate with any other process on MPI |
Each process can communicate with any other process on {\color{green} MPI} |
| $\Rightarrow$ {\color{green} Collective operations} |
|
| |
|
| {\color{green} ox\_bcast} broadcasts data from the root process to all other |
$\Rightarrow$ {\color{green} Collective operations} similar to \\ |
| processes. |
{\color{SeaGreen} MPI\_Bcast} and {\color{SeaGreen} MPI\_Reduce} |
| |
|
| {\color{green} ox\_collect} reduces data of all processes in the root process. |
\vskip 8pt |
| |
|
| \noindent |
|
| {\color{red} An example} : |
{\color{red} An example} : |
| the product of two dense univariate polynomials with 3000bit coefficients |
the product of dense univariate polynomials with 3000bit coefficients |
| |
|
| {\color{green} Algorithm} : FFT + Chinese Remainder |
\vskip 8pt |
| |
{\color{green} Algorithm}(Shoup) : FFT+Chinese Remainder |
| |
\vskip 5pt |
| |
{\color{green} Communication cost} :\\ |
| |
\quad $O(n{\color{red}\log L})$ with collective operations\\ |
| |
\quad $O(n{\color{red}L})$ without collective operations\\ |
| |
\quad ($L$: number of processes, $n$: degree) |
| |
|
| {\color{green} Parallel computing time} : $O((n\log n)/L+n\log L)$ |
\vskip 5pt |
| |
|
| ($L$: number of processes, $n$: degree) |
|
| |
|
| \epsfxsize=17cm |
\epsfxsize=17cm |
| \epsffile{3k.ps} |
\epsffile{3k.ps} |
| |
|
| |
\rightline{ {\color{red} {\tt http://www.openxm.org} }} |
| \end{document} |
\end{document} |
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to efficient.tex CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM / doc / calc2000p