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version 1.5, 2003/12/12 01:30:45 version 1.7, 2003/12/12 06:05:21
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 % $OpenXM: OpenXM/doc/Papers/rims-2003-12-16-ja-ohp.tex,v 1.4 2003/12/12 01:09:50 takayama Exp $  % $OpenXM: OpenXM/doc/Papers/rims-2003-12-16-ja-ohp.tex,v 1.6 2003/12/12 01:54:05 noro Exp $
 %% xdvi -paper a4r rims-2003-12-16-ja-ohp  %% xdvi -paper a4r rims-2003-12-16-ja-ohp
 %% dvips -f -t landscape  rims-2003-12-16-ja-ohp| psnup -8 -r | lpr -Pxerox6  %% dvips -f -t landscape  rims-2003-12-16-ja-ohp| psnup -8 -r | lpr -Pxerox6
 %% dvipdfm -l rims-2003-12-16-ja-ohp  %% dvipdfm -l rims-2003-12-16-ja-ohp
Line 324  value}{\tt )}
Line 324  value}{\tt )}
 \pagetitle{4. {\color{blue} OX-RFC 102 --- $BK\3JE*$J%5!<%P4VDL?.$rMQ$$$?J,;67W;;(B}}  \pagetitle{4. {\color{blue} OX-RFC 102 --- $BK\3JE*$J%5!<%P4VDL?.$rMQ$$$?J,;67W;;(B}}
 \parskip 5pt  \parskip 5pt
   
 \rightline{$B3+H/(B: $BLnO$(B}  
   
 OX-RFC-100, 101 : master-server $B4VDL?.$rMQ$$$?J,;67W;;(B  OX-RFC-100, 101 : master-server $B4VDL?.$rMQ$$$?J,;67W;;(B
   
 OX-RFC-102 : server-server $B4VDL?.(B  OX-RFC-102 : server-server $B4VDL?.(B
Line 408  broadcast $B$9$k(B. $B3F(B server $B$N%9%?%C%/$K
Line 406  broadcast $B$9$k(B. $B3F(B server $B$N%9%?%C%/$K
 \noindent  \noindent
 \pagetitle{broadcast $B$N<jB3$-(B}  \pagetitle{broadcast $B$N<jB3$-(B}
   
 {SM\_bcast\_102} $B$N<B9T(B : $root=0$ $B$G(B, $B<1JL;R$,(B $b2^k$ ($b$ $B$O4q?t(B) $B$N(B server $B$N>l9g(B  {SM\_bcast\_102} $B$N<B9T(B
   
 \begin{enumerate}  $root=0$ $B$G(B, $B<1JL;R$,(B $b2^k$ ($b$ $B$O4q?t(B) $B$N(B server $B$NF0:n(B
 \item $B<1JL;R$,(B $(b-1)2^k$ $B$G$"$k(B server $B$+$i%G!<%?$r<u?.(B.  
 \item $B<1JL;R$,(B $b2^k+2^i$ ($i=k-1,\ldots,0$) $B$N(B server $B$K=g$K%G!<%?$rAw?.(B.  
 \end{enumerate}  
   
   \vskip\baselineskip
   \begin{tabbing}
   $data \leftarrow$ $B<1JL;R$,(B $(b-1)2^k$ $B$N(B server $B$+$i$N%G!<%?(B\\
   for \= $i=k-1$ down to $0$\\
       \> $B<1JL;R$,(B $b2^k+2^i$ $B$N(B server $B$K(B $data$ $B$rAw?.(B\\
   end for
   \end{tabbing}
   \vskip\baselineskip
 2 $B$G3d$j@Z$l$k2s?t$,B?$$<1JL;R$r;}$D(B server $B$,@h$K%G!<%?Aw?.(B  2 $B$G3d$j@Z$l$k2s?t$,B?$$<1JL;R$r;}$D(B server $B$,@h$K%G!<%?Aw?.(B
   
 $\Rightarrow$ $B%G%C%I%m%C%/$K$J$i$J$$(B  $\Rightarrow$ $B%G%C%I%m%C%/$K$J$i$J$$(B
   
 $BFHN)$J%Z%"$I$&$7$NDL?.$,F1;~$K9T$($k$J$i!"9b!9(B $\lceil \log_2 N\rceil$ $B%9%F%C%W(B  $BFHN)$J%Z%"$I$&$7$NDL?.$,F1;~$K9T$($k$J$i!"9b!9(B $\lceil \log_2 N\rceil$ $B%9%F%C%W(B
 ($N$ $B$O(B server $B$NAm?t(B) $B$G(B broadcast $B40N;(B.  ($N$ $B$O(B server $B$NAm?t(B) $B$G(B broadcast $B40N;(B.
   
 \newpage  \newpage
   
 \noindent  \noindent
   \pagetitle{reduction $B$N<jB3$-(B}
   
   {SM\_reduce\_102} $B$N<B9T(B
   
   server $B?t(B $N$, $root=0$ $B$G(B, $B<1JL;R$,(B $b$ $B$N(B server $B$NF0:n(B
   
   $B<j;}$A$N%G!<%?$r(B $data$ $B$H$9$k(B
   
   \vskip\baselineskip
   \begin{tabbing}
   for \= $i=0$ to $\lfloor \log_2 N \rfloor$\\
       \> if \= ( $b$ $B$K(B $2^i$ $B$N(B bit $B$,$"$k(B) then\\
       \>    \> $B<1JL;R(B $b-2^i$ $B$N(B server $B$K(B $data$ $B$rAw?.$7$F=*N;(B\\
       \> else if ( $b+2^i < N$ ) then \\
       \>     \> $data_0 \leftarrow$ $B<1JL;R(B $b+2^i$ $B$N(B server $B$+$i$N%G!<%?(B\\
       \>      \> $data \leftarrow data$ $B$H(B $data_0$ $B$NFs9`1i;;7k2L(B \\
       \> end if\\
   end for
   \end{tabbing}
   \vskip\baselineskip
   
   $B$3$N>l9g$b(B, $BFHN)$J%Z%"$I$&$7$NDL?.$,F1;~$K9T$($k$J$i!"9b!9(B $\lceil \log_2 N\rceil$ $B%9%F%C%W(B
   ($N$ $B$O(B server $B$NAm?t(B) $B$G(B reduction $B40N;(B. $B7k2L$O(B root $B$K;D$k(B.
   \newpage
   
   \noindent
   \pagetitle{broadcast $B;~$N%G!<%?$NN.$l(B}
   
   
   $N=16$, $root=0$ $B$N>l9g(B
   
   \begin{center}
   \begin{tabular}{|c|c|c|c|}
   step 1 & step 2 & step 3 & step 4 \\ \hline
   $0\rightarrow 8$&$0\rightarrow 4$ &$0\rightarrow 2$  &$0\rightarrow 1$ \\
                   &$8\rightarrow 12$&$8\rightarrow 10$  &$8\rightarrow 9$ \\
                   &                 &$4\rightarrow 6$ &$4\rightarrow 5$ \\
                   &                 &$12\rightarrow 14$&$12\rightarrow 13$ \\
                   &                 &                  &$2\rightarrow 3$ \\
                   &                 &                  &$10\rightarrow 11$ \\
                   &                 &                  &$6\rightarrow 7$ \\
                   &                 &                  &$14\rightarrow 15$
   \end{tabular}
   \end{center}
   
   reduction $B$N>l9g(B, $B%G!<%?$NN.$l$O5U$K$J$k(B (step 4 $\rightarrow$ step 1,
   $BLp0u$,5U(B)
   \newpage
   
   \noindent
 \pagetitle{$B%(%i!<=hM}(B}  \pagetitle{$B%(%i!<=hM}(B}
   
 master-server $B4VDL?.O)$O(B, OX RFC-100 $B$G5,Dj$5$l$F$$$k(B.  master-server $B4VDL?.O)$O(B, OX RFC-100 $B$G5,Dj$5$l$F$$$k(B.
Line 510  $Data$ $B$,;XDj$5$l$?>l9g(B, $B%9%?%C%/$K%W%C%7%e$7
Line 564  $Data$ $B$,;XDj$5$l$?>l9g(B, $B%9%?%C%/$K%W%C%7%e$7
 \newpage  \newpage
   
 \noindent  \noindent
 \pagetitle{$B%Q%U%)!<%^%s%9(B}  \pagetitle{$B<B9TNc(B : $B0lJQ?tB?9`<0$N@Q(B (master $BB&(B)}
   
   \begin{verbatim}
   def d_mul(F1,F2)
   {
       Procs = getopt(proc);
       if ( !var(F1) || !var(F2) ) return F1*F2;
       NP = length(Procs);
       /* $B0z?t$r(B server 0 $B$KAw$k(B */
       ox_push_cmo(0,[F1,F2]);
       /* $B3F(B server $B$K(B, server 0 $B$r(B root $B$H$7$F;E;v$r;O$a$k$h$&0MMj(B */
       for ( I = 0; I < NP; I++ )
           ox_cmo_rpc(I,"d_mul_main",0);
       /* server 0 $B$+$i7k2L$r<u$1<h$k(B */
       R = ox_pop_cmo(0);
       return R;
   }
   \end{verbatim}
   
   \newpage
   
   \noindent
   \pagetitle{$B<B9TNc(B : $B0lJQ?tB?9`<0$N@Q(B (server $BB&(B; collective)}
   \begin{verbatim}
   def d_mul_main(Root)
   {
       /* server $B$NAm?t(B, $B<+J,$N(B id $B$rCN$k(B */
       Id = ox_get_rank_102(); NP = Id[0]; Rank = Id[1];
       /* Root $B$K$"$k0z?t$r(B broadcast $B$G6&M-(B */
       Arg = ox_bcast_102(Root); F1 = Arg[0]; F2 = Arg[1];
       L = setup_modarrays(F1,F2,NP);
       Marray = L[0]; MIarray = L[1]; M = L[2];
       R = umul_chrem(F1,F2,MIarray[Rank],Marray[Rank],M);
       Arg = 0; F1 = 0; F2 = 0;
       /* $B3F(B server $B$N7k2L$rB-$79g$o$;$F(B, Root $B$KCV$/(B */
       R = ox_reduce_102(Root,"+",R);
       /* Root $B$N$_(B, $B7k2L$r(B normalize $B$9$k(B */
       if ( Rank == Root )
           R = uadj_coef(R%M,M,ishift(M,1));
       return R;
   }
   \end{verbatim}
   
   \rightline{$B3+H/(B: $BLnO$(B}
   
 \end{document}  \end{document}
   
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