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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}

\usepackage{color}

\usepackage{rgb}

\usepackage{graphicx}

\usepackage{epsfig}

%{\color{red} Asir}

\begin{document}

\parskip 3pt

\fbox{{\huge \color{blue} We Are Efficient}}

\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} :

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

{\color{green} Parallel computing time} : $O((n\log n)/L+n\log L)$

\vskip 5pt

{\color{green} Parallel computing time} : $O((n\log n)/L+n{\color{red}\log L})$\\

No collective operations : $O((n\log n)/L+n{\color{red}L})$\\

($L$: number of processes, $n$: degree)

\vskip 8pt

\epsfxsize=17cm

\epsffile{3k.ps}

\rightline{ {\color{red} {\tt http://www.openxm.org} }}

\end{document}