version 1.1, 2000/07/21 08:27:11 |
version 1.2, 2000/07/22 08:11:09 |
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% $OpenXM$ |
% $OpenXM: OpenXM/doc/calc2000p/efficient.tex,v 1.1 2000/07/21 08:27:11 noro Exp $ |
\documentclass{slides} |
\documentclass{slides} |
\usepackage{color} |
\usepackage{color} |
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\usepackage{rgb} |
\usepackage{graphicx} |
\usepackage{graphicx} |
\usepackage{epsfig} |
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%{\color{red} Asir} |
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\begin{document} |
\begin{document} |
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\fbox{{\huge \color{blue} We Are Efficient}} |
\fbox{{\huge \color{blue} We Are Efficient}} |
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\noindent |
{\color {red} Real speedup by parallelism} |
{\color{red} OpenXM on MPI --- to achieve real speedup by parallelism} |
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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} |
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{\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} |
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{\color{green} ox\_collect} reduces data of all processes in the root process. |
\vskip 8pt |
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\noindent |
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{\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 |
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{\color{green} Algorithm} : FFT + Chinese Remainder |
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{\color{green} Algorithm}(Shoup) : FFT+Chinese Remainder |
{\color{green} Parallel computing time} : $O((n\log n)/L+n\log L)$ |
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{\color{green} Parallel computing time} : $O((n\log n)/L+n{\color{red}\log L})$\\ |
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No collective operations : $O((n\log n)/L+n{\color{red}L})$\\ |
($L$: number of processes, $n$: degree) |
($L$: number of processes, $n$: degree) |
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\vskip 8pt |
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\epsfxsize=17cm |
\epsfxsize=17cm |
\epsffile{3k.ps} |
\epsffile{3k.ps} |
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\rightline{ {\color{red} {\tt http://www.openxm.org} }} |
\end{document} |
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