% $OpenXM: OpenXM/doc/calc2000p/efficient.tex,v 1.2 2000/07/22 08:11:09 noro Exp $
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\fbox{{\huge \color{blue} We Are Efficient}}

{\color {red} Real speedup by parallelism}

Each process can communicate with any other process on {\color{green} MPI}

$\Rightarrow$ {\color{green} Collective operations} similar to \\
{\color{SeaGreen} MPI\_Bcast} and {\color{SeaGreen} MPI\_Reduce}

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{\color{red} An example} :
the product of dense univariate polynomials with 3000bit coefficients

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{\color{green} Algorithm}(Shoup) : FFT+Chinese Remainder
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{\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)

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