===================================================================
RCS file: /home/cvs/OpenXM/doc/Papers/rims-2003-12-16-ja-ohp.tex,v
retrieving revision 1.2
retrieving revision 1.10
diff -u -p -r1.2 -r1.10
--- OpenXM/doc/Papers/rims-2003-12-16-ja-ohp.tex	2003/12/11 06:00:41	1.2
+++ OpenXM/doc/Papers/rims-2003-12-16-ja-ohp.tex	2003/12/13 02:09:30	1.10
@@ -1,6 +1,7 @@
-% $OpenXM: OpenXM/doc/Papers/rims-2003-12-16-ja-ohp.tex,v 1.1 2003/12/11 05:43:37 takayama Exp $
+% $OpenXM: OpenXM/doc/Papers/rims-2003-12-16-ja-ohp.tex,v 1.9 2003/12/12 08:34:10 noro Exp $
 %% xdvi -paper a4r rims-2003-12-16-ja-ohp
 %% dvips -f -t landscape  rims-2003-12-16-ja-ohp| psnup -8 -r | lpr -Pxerox6
+%% dvipdfm -l rims-2003-12-16-ja-ohp
 \documentclass{slides}
 \usepackage{color}
 \usepackage{rgb}
@@ -20,6 +21,7 @@
 \def\nnn{ {\color{red} $\bullet$}\ }    %% $B;v<B(B
 \def\eee{ {\color{magenta} Example}:\ } %% $BNc(B
 \def\ttt{ {\color{red} $\bullet$}\ }   %% $BDjM}(B
+\def\ppp{ {\color{blue} $\bullet$}\ }
 
 \def\pagetitle#1{ \fbox{{\color{magenta} #1 }}}
 
@@ -55,11 +57,13 @@
 \end{enumerate}
 \newpage
 
+%C OpenXM $B$O(B ... $B$NN,$G$3$3$K=q$$$F$"$k$h$&$J$3$H$rL\I8$K?tG/A0$+$i(B
+%C $B%Q%C%1!<%8$N3+H/(B, $B%W%m%H%3%k$N3+H/$r$7$F$$$^$9(B.
 \noindent  \quad \\
-\nnn $B?t3X$G$NJBNs7W;;(B,  \\
-\nnn $B?t3X%=%U%H%&%(%"$NE}9g2=(B $B$^$?$O(B Conglomerate $B2=(B (A.Solomon) \\
-\nnn $B?t3XE*CN<1$N%^%M!<%8%a%s%H(B (Mathematical Knowledge Management) \\
-\nnn $B<B:]$K?t3X$N8&5f$d?t3X$N1~MQ$K;H$($k%Q%C%1!<%8$N3+H/(B 
+\ppp $B?t3X$G$NJBNs7W;;(B,  \\
+\ppp $B?t3X%=%U%H%&%(%"$NE}9g2=(B $B$^$?$O(B Conglomerate $B2=(B (A.Solomon) \\
+\ppp $B?t3XE*CN<1$N%^%M!<%8%a%s%H(B (Mathematical Knowledge Management) \\
+\ppp $B<B:]$K?t3X$N8&5f$d?t3X$N1~MQ$K;H$($k%Q%C%1!<%8$N3+H/(B 
 
 \noindent  \quad \\
 \nnn OpenXM 1.1.1 (January 24, 2000): $B:G=i$N<B83HG(B. \\
@@ -99,7 +103,7 @@ $\Rightarrow$ {\color{red} ox\_ntl}
 \end{verbatim}
 }
 
-$B<BAu$K$h$jL@$i$+$K$J$C$?$3$H(B: \\
+$B<BAu$K$h$jL@$i$+$K$J$C$?$3$H(B: \quad ox\_toolkit $B$NM-8z@-(B,
 ox\_toolkit $B$NLdBjE@$N2~A1(B, LLL $B$r$h$V$?$a$K(B CMO array $B$bI,MW(B.
 
 \rightline{$B3+H/(B: $B4d:,(B ($B>.86(B)}
@@ -121,13 +125,19 @@ Visualization by JavaView and Povray.
 $BE@(B $(1,0,0)$, $(1,1,0)$, $(1,0,1)$, $(1,1,1)$ $B>e$N(B cone $B$N(B facet $B$r5a$a$h(B. \\
 {\tt polymake} $B$G$O$D$.$h$&$JF~NO%U%!%$%k(B {\tt square.poly} $B$r$^$::n@.$9$k(B.
 
-{\footnotesize \color{blue} \begin{verbatim}
-POINTS
-1 0 0
-1 1 0
-1 0 1
-1 1 1
-\end{verbatim} }
+\begin{minipage}{10cm}
+{\footnotesize \color{blue} 
+\begin{verbatim}
+POINTS 
+1 0 0 
+1 1 0 
+1 0 1 
+1 1 1 
+\end{verbatim}
+}
+\end{minipage}
+\epsfxsize=8cm
+\epsffile{rims-2003-12-16-sq.eps}
 
 {\color{red} \verb@ polymake square.poly FACETS @ } \\
 $B7k2L(B:
@@ -142,7 +152,8 @@ FACETS
 \newpage
 
 \pagetitle{ Polymake $B$N(B OX 100, 101 $B%5!<%P2=$G2?$,LdBj$G$"$C$?$+(B?}
-%todo OX 100 $B$N35N,$,I,MW$+(B?
+%C $B>\$7$$$3$H$O$3$3$K=q$$$F$k$3$H$rFI$s$G$b$i$&$3$H$K$7$F(B, $B0l8@$G$$$($P(B
+%C C $B$N30It%W%m%0%i%`8F$S=P$7%7%9%F%`%3!<%k(B system $B$N5!G=$r6/2=$7$h$&$H$$$&$3$H(B
 
 $B?7$7$$(B OX RFC 100 $B=`5r$N%5!<%P$r:n$k>l9g$K$O(B
 $B%?!<%2%C%H$H$9$k?t3X%=%U%H%&%(%"%7%9%F%`$N%=!<%9%3!<%I$K(B OX RFC 100 $BBP1~ItJ,(B
@@ -157,6 +168,7 @@ unix $B$N(B shell ($B$d(B Windows $B$N%3%^%s%I%W%
 $B$+$iMxMQ2DG=$J$h$&$K:n$i$l$F$$$k(B: {\color{red} $B%P%C%A=hM}BP1~%"%W%j%1!<%7%g%s(B}.
 $B%5!<%P$H$NDL?.$NIQEY$OLdBj$K$h$k$,$"$kDxEYBg$-$$7W;;$N>l9g$ODL?.;~4V$OL5;k$G$-$k(B.
 Polymake $B$OBPOCE*MxMQ$OA[Dj$7$F$*$i$:%5!<%P$N7W;;$rCfCG$7$F(B, $B:FEY3+;O$9$k$J$I$NI,MW$,$J$$(B.
+$\Rightarrow$ {\tt system} $B4X?t(B. $BLdBjE@(B: $B%U%!%$%k(B, OS $B$N0c$$(B, $B%W%m%;%94IM}(B
 $\Rightarrow$ {\tt system} $B$N6/2=HG(B {\color{blue} oxshell}
 \newpage
 
@@ -189,6 +201,7 @@ Oxshell $B$rMQ$$$F(B OX $B%5!<%P$r<B8=$9$k$N$,E,@Z$
 ($BC1=c;E;v(B, $B$7$+$7(B,  ZPG $B$N6KCW(B; unix $B$H(B windows $B0c$$(B,
 /bin/sh $B$NB8:_(B, $B%W%m%0%i%`$,BgJQFI$_$K$/$/J]<i$b$7$K$/$$(B)
 
+%C $B%"%$%G%#%"$O0l8@$G$$$($P<!$N0l9T$N$_(B.
 {\tt oxshell} $B$G$O$3$N;E;v$O<!$N(B 1 $B9T$G=q$/(B. \\
 {\color{red} \verb@[(polymake) (stringInOut://$B%9%?%C%/%^%7%sJQ?tL>(B.poly) $BF0:n(B] oxshell@}\\
 $B%9%?%C%/%^%7%s$NJQ?t$r%U%!%$%k$r$_$J$7$F$$$k(B.
@@ -197,6 +210,7 @@ Oxshell $B$rMQ$$$F(B OX $B%5!<%P$r<B8=$9$k$N$,E,@Z$
 $BNc(B: Java $B$N(B io.StringReader ( io.InputStreamReader $B$NBe$o$j(B). \\
 $BNc(B: $B%9%/%j%W%H8@8l$G$"$k(B Python
   \verb@ x=os.popen("abc","r").read(); @
+%C netscape $B$N(B plugin $B$J$I$bFbItE*$K$O;w$?%"%$%G%#%"$rMQ$$$F$$$k$H;W$o$l$k(B. 
 
 \noindent
 {\color{blue} $B?7$7$$ItJ,(B}:
@@ -224,6 +238,8 @@ lion
 
 \pagetitle{ oxshell.facets() $B$N<BAu(B, $B?t3X4X?t$N<BAuNc(B }
 
+%C $B$b$&0l$D$N%]%$%s%H$O(B tfb, OpenMath $B$NM-8z@-$N<B>Z(B.
+%C $BEv$jA0$@$,L5$/$F$O$J$i$J$$8&5f$@$C$?(B.
 \nnn $B%G!<%?JQ49$K$O(B tfb/2 ($BEDB<(B)format $B$rMxMQ(B, OpenMath $B%"!<%-%F%/%A%c$rMxMQ(B.
 {\color{blue}$B@.2L(B}: $B$=$NM-8z@-$r<B>Z$G$-$?(B.)
 %% $B$3$l$b?7$7$$E@$G$"$m$&(B.
@@ -235,7 +251,8 @@ lion
   Outputs to stdout and stderr ]
 \end{verbatim} }
 
-
+%C $B?t3XE*$K$O<!$NF05!(B.  D-module $B$N7W;;$G(B facet $B$@$;$k(B.
+%C ($B:XF#$`$D$_$N(B) $b$ function $B$r(B polytope algorithm $B$G5a$a$k=i$a$F$N<BAu(B.
 {\color{red} taka\_ahg.b(A,Idx)}(OpenXM/src/asir-contrib/packages/src/taka\_ahg.rr)
 oxshell $B$K$h$k(B polymake $B8F$S=P$75!G=$rMQ$$$??t3X4X?t(B.
 $B$3$N4X?t$O(B $B9TNs(B {\tt A} $B$KIU?o$7$?(B $BJ}8~(B {\tt Idx} $B$N$"$k(B $b$ $B4X?t$r7W;;$9$k(B.
@@ -248,6 +265,7 @@ Saito, Mutsumi; Parameter shift in normal generalized 
 
 \newpage
 
+\begin{minipage}{13cm}
 {\footnotesize
 \begin{verbatim}
 [1163]:= load("oxshell.rr");
@@ -278,8 +296,10 @@ def b(A,Idx,V) {
 }
 \end{verbatim}
 }
+\end{minipage}
+\epsfxsize=12cm
+\epsffile{rims-2003-12-16-sq2.eps}
 
-
 \rightline{$B3+H/(B: $B9b;3(B}
 \newpage
 
@@ -312,11 +332,308 @@ value}{\tt )}
 
 \noindent
 \pagetitle{4. {\color{blue} OX-RFC 102 --- $BK\3JE*$J%5!<%P4VDL?.$rMQ$$$?J,;67W;;(B}}
+\parskip 5pt
 
+OX-RFC-100, 101 : master-server $B4VDL?.$rMQ$$$?J,;67W;;(B
 
-\rightline{$B3+H/(B: $BLnO$(B}
+OX-RFC-102 : server-server $B4VDL?.(B
+
+\underline{$BL\I8(B} : $BK\3JE*J,;6JBNs7W;;$r2DG=$K$9$k$3$H(B
+
+\underline{$B1~MQNc(B}
+\begin{itemize}
+\item broadcast $B$r8zN(2=$9$k(B
+
+N $B8D$N(B server $B$X$N(B broadcast $B$,(B $O(\log_2 N)$ $B$G$G$-$k(B
+
+\item LU $BJ,2r$NJ,;6JBNs7W;;(B
+
+ScaLAPACK $BIw$K(B, $B9TNs$rJ,;6J];}$7$FJBNs7W;;(B
+\end{itemize}
+
+\underline{$B;EMM(B}
+
+MPI-2 $B$N(B, $BF0E*%W%m%;%9@8@.(B, $B%W%m%;%9%0%k!<%W4V(B broadcast $B$N;EMM$r(B
+$B;29M$K$9$k(B.  {\tt http://www-unix.mcs.anl.gov/mpi}
+
+\underline{$B?7$7$$E@(B}
+
+OX RFC 100 $B$rA0Ds(B $\Rightarrow$ $B%G!<%?7?$N4IM}$NI,MW$,$J$$(B,
+100 $B$NCfCG%W%m%H%3%k$N3HD%(B,
+$B$J$I(BMPI $B$h$jMF0W$KMxMQ2DG=(B. 
+%C $B$^$?(B, $B%7%9%F%`$N@_7W$G4sM?$G$-$J$/$F$b(B, $B<BNc$G$NM-8z@-(B, $B$"$kFCDj$NLdBj$G$N(B
+%C $B@_7W$N2~A1Ey$r9M$($k(B.  $B2f!9$O(B Shoup $B$N(B $B%"%k%4%j%:%`$,8zN(NI$/<BAu$G$-$k(B
+%C $B$3$H$r<($7$?(B.
+
+
 \newpage
 
+\noindent
+\pagetitle{server $B$N5/F0(B, server $B4VDL?.O)$N3+@_(B}
+
+server $B$O(B OX RFC-100, 101 $B$K$h$j5/F0$9$k(B. $B$3$NDL?.O)$K0J2<$N(B SM
+$B%3%^%s%I$rAw$k(B.
+
+\begin{itemize}
+\item {\tt SM\_set\_rank\_102} $nserver$ $rank$
+
+server $B$K(B, $B%0%k!<%WFb$N(B server $B$NAm?t(B $nserver$ $B$H(B, $B$=$NCf$G$N(B
+$B<1JL;R(B $rank$ ($0 \le rank \le nserver$) $B$rDLCN$9$k(B.
+
+\item {\tt SM\_tcp\_accept\_102} $port$ $peer$
+
+$B%]!<%HHV9f(B $port$ $B$N(B TCP $B%]!<%H$G(B, bind, listen, accept $B$r<B9T(B
+$B$7$F(B connect $B$rBT$D(B. $BDL?.$,@.N)$7$?$i(B, byte order negotiation
+$B$r9T$$(B, $BAj<j@h%F!<%V%k$KEPO?$9$k(B.
+
+\item {\tt SM\_tcp\_connect\_102} $peerhost$ $port$ $peer$
+
+$B%[%9%H(B $peerhost$ $B$N%]!<%HHV9f(B $port$ $B$N(B TCP $B%]!<%H$K(B connect $B$9$k(B. 
+$BDL?.$,@.N)$7$?$i(B, byte order negotiation $B$r9T$$(B, $BAj<j@h%F!<%V%k$KEPO?(B
+$B$9$k(B.
+
+\end{itemize}
+
+\newpage
+
+\noindent
+\pagetitle{server $B4VDL?.(B, broadcast, reduction}
+
+server $B4VDL?.$O(B, $BAj8_$N?.Mj$K4p$E$-9T$&(B --- $BAw$j<j$,Aw?.$7$?$i(B, $B<u$1<j$O(B
+$B$A$c$s$H<u?.F0:n$KF~$k$3$H(B
+
+$B%G!<%?$O(B OX $B%?%0IU$-$G(B --- {\tt OX\_SYNC\_BALL} $B$K$h$kDL?.O)%j%;%C%H$KI,MW(B
+
+$B0J2<$N(B SM $B%3%^%s%I$O(B collective $BA`:n$G$"$k(B. $B$9$J$o$A(B, $BF10l0z?t$G(B
+$B%0%k!<%WFb$NA4$F$N(B server $B$G<B9T$5$l$J$1$l$P$$$1$J$$(B.
+
+\begin{itemize}
+\item {\tt SM\_bcast\_102} $root$
+
+$B<1JL;R(B $root$ $B$N(B server $B$N%9%?%C%/>e$N%G!<%?$r(B pop $B$7(B, $B%0%k!<%WFb$K(B
+broadcast $B$9$k(B. $B3F(B server $B$N%9%?%C%/$K(B broadcast $B$5$l$?%G!<%?$,(B push
+$B$5$l$k(B.
+
+\item {\tt SM\_reduce\_102} $root$ $opname$
+
+$B3F(B server $B$N%9%?%C%/>e$N%G!<%?$,(B pop $B$5$l(B, $opname$ $B$G;XDj$5$l$k(B
+$BFs9`1i;;(B($B7k9gB'$,I,MW(B) $B$r=g$K9T$$(B, $B7k2L$r(B $root$ $B$G;XDj$5$l$k(B server
+$B$N%9%?%C%/$K(B push $B$9$k(B. $BB>$N(B server $B$K$O(B $0$ $B$,(B push 
+$B$5$l$k(B.
+\end{itemize}
+
+\newpage
+
+\noindent
+\pagetitle{broadcast $B$N<jB3$-(B}
+
+{SM\_bcast\_102} $B$N<B9T(B 
+
+$root=0$ $B$G(B, $B<1JL;R$,(B $b2^k$ ($b$ $B$O4q?t(B) $B$N(B server $B$NF0:n(B
+
+\vskip\baselineskip
+\begin{tabbing}
+$data \leftarrow$ $B<1JL;R$,(B $(b-1)2^k$ $B$N(B server $B$+$i$N%G!<%?(B\\
+for \= $i=k-1$ down to $0$\\
+    \> $B<1JL;R$,(B $b2^k+2^i$ $B$N(B server $B$K(B $data$ $B$rAw?.(B\\
+end for
+\end{tabbing}
+\vskip\baselineskip
+2 $B$G3d$j@Z$l$k2s?t$,B?$$<1JL;R$r;}$D(B server $B$,@h$K%G!<%?Aw?.(B
+
+$\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
+($N$ $B$O(B server $B$NAm?t(B) $B$G(B broadcast $B40N;(B.
+
+\newpage
+
+%C $B:YIt$O>JN,(B. $B$"$H$G(B 16 $B8D$N%5!<%P$N<BNc$G@bL@(B.
+\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
+
+%C $B$3$l$O%*%j%8%J%k(B.
+\noindent
+\pagetitle{$B%(%i!<=hM}(B}
+
+master-server $B4VDL?.O)$O(B, OX RFC-100 $B$G5,Dj$5$l$F$$$k(B.
+
+server-server $B4VDL?.O)$r6u$K$9$k$?$a$N(B, $B<1JL;R(B $i$ $B$N(B server $B$G$NA`:n(B
+
+\begin{tabbing}
+for \= $j = 0$ \= to $i-1$ do\\
+    \> do\\
+    \>         \>$data$ $\leftarrow$ $B<1JL;R(B $j$ $B$N(B server $B$+$i$N(B OX $B%G!<%?(B\\
+    \> while $data \neq$ {\tt OX\_SYNC\_BALL}\\
+end for\\
+for $j = i+1$ to $nserver-1$ do\\
+    \> {\tt OX\_SYNC\_BALL} $B$r(B $B<1JL;R(B $j$ $B$N(B server $B$KAw?.(B\\
+end for
+\end{tabbing}
+
+master-server $B%j%;%C%H8e(B : $B3F(B server $B$O%3%^%s%IBT$A>uBV(B
+
+$\Rightarrow$ $B<!$N(B SM $B%3%^%s%I$r3F(B server $B$KAw?.$9$l$P$h$$(B
+
+\begin{itemize}
+\item {\tt SM\_reset\_102} ($B0z?t$J$7(B, collective)
+\end{itemize}
+
+\newpage
+
+\noindent
+\pagetitle{Asir (master) $B>e$G$N(B API}
+
+\begin{itemize}
+\item {\tt ox\_set\_rank\_102($Server$,$Nserver$,$Rank$)}
+
+$Server$ $B$K(B {\tt SM\_set\_rank\_102} $B$rAw$k(B.
+
+\item {\tt ox\_tcp\_accept\_102($Server$,$Port$,$Rank$)}
+
+$Server$ $B$K(B {\tt SM\_tcp\_accept\_102} $B$rAw$k(B.
+
+\item {\tt ox\_tcp\_connect\_102($Server$,$Host$,$Port$,$Rank$)}
+
+$Server$ $B$K(B {\tt SM\_tcp\_connect\_102} $B$rAw$k(B.
+
+\item {\tt ox\_reset\_102($Server$)} (collective)
+
+$Server$ $B$K(B {\tt SM\_reset\_102} $B$rAw$k(B
+
+\end{itemize}
+
+\newpage
+
+\noindent
+\pagetitle{Asir (server) $B>e$G$N(B API}
+
+\begin{itemize}
+\item {\tt ox\_send\_102($Rank$,$Data$)}
+
+$B<1JL;R(B $Rank$ $B$N(B server $B$K(B $Data$ $B$r(B OX $B%G!<%?$H$7$FAw?.$9$k(B.
+$B<1JL;R(B $Rank$ $B$N(B server $B$OBP1~$9$k<u?.$r3+;O$7$J$1$l$P$J$i$J$$(B.
+
+\item {\tt ox\_recv\_102($Rank$)}
+
+$B<1JL;R(B $Rank$ $B$N(B server $B$+$i(B OX $B%G!<%?$r<u?.$9$k(B.
+$B<1JL;R(B $Rank$ $B$N(B server $B$OBP1~$9$kAw?.$r3+;O$7$J$1$l$P$J$i$J$$(B.
+
+\item {\tt ox\_bcast\_102($Root$[,$Data$])} (collective)
+
+$B<1JL;R(B $Root$ $B$N(B server $B$r(B root $B$H$7$F(B, $B%0%k!<%WFb$G(B broadcast $B$9$k(B.
+$Data$ $B$,;XDj$5$l$?>l9g(B, $B%9%?%C%/$K%W%C%7%e$5$l$k(B.
+$B<1JL;R$,(B $Root$ $B$KEy$7$$(B server $B$G(B, $B%9%?%C%/(B
+$B$+$i%G!<%?$,%]%C%W$5$l(B, $B$=$N%G!<%?$,(B, $B3F8F$S=P$7$NLa$jCM$H$J$k(B.
+
+\item {\tt ox\_reduce\_102($Root$,$Operation$[,$Data$])} (collective)
+
+$B%0%k!<%WFb$N3F(B server $B$N%9%?%C%/$+$i%]%C%W$7$?%G!<%?$KBP$7(B
+$Operation$ $B$G;XDj$5$l$kFs9`1i;;$r9T$$(B,
+$B7k2L$r(B $Root$ $B$G;XDj$5$l$k(B server $B$G$N4X?t8F$S=P$7$NLa$jCM$H$7$F(B
+$BJV$9(B.
+$Data$ $B$,;XDj$5$l$?>l9g(B, $B%9%?%C%/$K%W%C%7%e$7$F$+$i>e5-$NA`:n$r(B
+$B<B9T$9$k(B. $Root$ $B0J30$N(B server $B$G$NLa$jCM$O(B 0 $B$G$"$k(B.
+\end{itemize}
+
+
+\newpage
+
+\noindent
+\pagetitle{$B<B9TNc(B : $B0lJQ?tB?9`<0$N@Q(B (master $BB&(B)}
+
+\begin{verbatim}
+def d_mul(F1,F2)
+{
+    Procs = getopt(proc);
+    /* process $B;XDj$,$J$$>l9g$K$O(B, $B<+J,$G7W;;(B */
+    if ( type(Procs) == -1 ) return umul(F1,F2);
+    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)   /* Shoup's algorithm */
+{
+    /* 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}
 
-%%$Id: rims-2003-12-16-ja-ohp.tex,v 1.2 2003/12/11 06:00:41 takayama Exp $ at misc-2003/12/RIMS
\ No newline at end of file
+%%$Id: rims-2003-12-16-ja-ohp.tex,v 1.10 2003/12/13 02:09:30 takayama Exp $ at misc-2003/12/RIMS