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Diff for /OpenXM/doc/Papers/rims-2003-12-16-ja-ohp.tex between version 1.1 and 1.10

version 1.1, 2003/12/11 05:43:37 version 1.10, 2003/12/13 02:09:30
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 % $OpenXM$  % $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  %% 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
 \documentclass{slides}  \documentclass{slides}
 \usepackage{color}  \usepackage{color}
 \usepackage{rgb}  \usepackage{rgb}
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 \def\nnn{ {\color{red} $\bullet$}\ }    %% $B;v<B(B  \def\nnn{ {\color{red} $\bullet$}\ }    %% $B;v<B(B
 \def\eee{ {\color{magenta} Example}:\ } %% $BNc(B  \def\eee{ {\color{magenta} Example}:\ } %% $BNc(B
 \def\ttt{ {\color{red} $\bullet$}\ }   %% $BDjM}(B  \def\ttt{ {\color{red} $\bullet$}\ }   %% $BDjM}(B
   \def\ppp{ {\color{blue} $\bullet$}\ }
   
 \def\pagetitle#1{ \fbox{{\color{magenta} #1 }}}  \def\pagetitle#1{ \fbox{{\color{magenta} #1 }}}
   
Line 55 
Line 57 
 \end{enumerate}  \end{enumerate}
 \newpage  \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 \\  \noindent  \quad \\
 \nnn $B?t3X$G$NJBNs7W;;(B,  \\  \ppp $B?t3X$G$NJBNs7W;;(B,  \\
 \nnn $B?t3X%=%U%H%&%(%"$NE}9g2=(B $B$^$?$O(B Conglomerate $B2=(B (A.Solomon) \\  \ppp $B?t3X%=%U%H%&%(%"$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) \\  \ppp $B?t3XE*CN<1$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 $B<B:]$K?t3X$N8&5f$d?t3X$N1~MQ$K;H$($k%Q%C%1!<%8$N3+H/(B
   
 \noindent  \quad \\  \noindent  \quad \\
 \nnn OpenXM 1.1.1 (January 24, 2000): $B:G=i$N<B83HG(B. \\  \nnn OpenXM 1.1.1 (January 24, 2000): $B:G=i$N<B83HG(B. \\
Line 99  $\Rightarrow$ {\color{red} ox\_ntl}
Line 103  $\Rightarrow$ {\color{red} ox\_ntl}
 \end{verbatim}  \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.  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)}  \rightline{$B3+H/(B: $B4d:,(B ($B>.86(B)}
Line 121  Visualization by JavaView and Povray.
Line 125  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. \\  $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.  {\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}  \begin{minipage}{10cm}
 POINTS  {\footnotesize \color{blue}
 1 0 0  \begin{verbatim}
 1 1 0  POINTS
 1 0 1  1 0 0
 1 1 1  1 1 0
 \end{verbatim} }  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 @ } \\  {\color{red} \verb@ polymake square.poly FACETS @ } \\
 $B7k2L(B:  $B7k2L(B:
Line 142  FACETS
Line 152  FACETS
 \newpage  \newpage
   
 \pagetitle{ Polymake $B$N(B OX 100, 101 $B%5!<%P2=$G2?$,LdBj$G$"$C$?$+(B?}  \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$$(B OX RFC 100 $B=`5r$N%5!<%P$r:n$k>l9g$K$O(B  $B?7$7$$(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  $B%?!<%2%C%H$H$9$k?t3X%=%U%H%&%(%"%7%9%F%`$N%=!<%9%3!<%I$K(B OX RFC 100 $BBP1~ItJ,(B
Line 157  unix $B$N(B shell ($B$d(B Windows $B$N%3%^%s%I%W%
Line 168  unix $B$N(B shell ($B$d(B Windows $B$N%3%^%s%I%W%
 $B$+$iMxMQ2DG=$J$h$&$K:n$i$l$F$$$k(B: {\color{red} $B%P%C%A=hM}BP1~%"%W%j%1!<%7%g%s(B}.  $B$+$iMxMQ2DG=$J$h$&$K:n$i$l$F$$$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$,$"$kDxEYBg$-$$7W;;$N>l9g$ODL?.;~4V$OL5;k$G$-$k(B.  $B%5!<%P$H$NDL?.$NIQEY$OLdBj$K$h$k$,$"$kDxEYBg$-$$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$$(B.  Polymake $B$OBPOCE*MxMQ$OA[Dj$7$F$*$i$:%5!<%P$N7W;;$rCfCG$7$F(B, $B:FEY3+;O$9$k$J$I$NI,MW$,$J$$(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}  $\Rightarrow$ {\tt system} $B$N6/2=HG(B {\color{blue} oxshell}
 \newpage  \newpage
   
Line 189  Oxshell $B$rMQ$$$F(B OX $B%5!<%P$r<B8=$9$k$N$,E,@Z$
Line 201  Oxshell $B$rMQ$$$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$$(B,  ($BC1=c;E;v(B, $B$7$+$7(B,  ZPG $B$N6KCW(B; unix $B$H(B windows $B0c$$(B,
 /bin/sh $B$NB8:_(B, $B%W%m%0%i%`$,BgJQFI$_$K$/$/J]<i$b$7$K$/$$(B)  /bin/sh $B$NB8:_(B, $B%W%m%0%i%`$,BgJQFI$_$K$/$/J]<i$b$7$K$/$$(B)
   
   %C $B%"%$%G%#%"$O0l8@$G$$$($P<!$N0l9T$N$_(B.
 {\tt oxshell} $B$G$O$3$N;E;v$O<!$N(B 1 $B9T$G=q$/(B. \\  {\tt oxshell} $B$G$O$3$N;E;v$O<!$N(B 1 $B9T$G=q$/(B. \\
 {\color{red} \verb@[(polymake) (stringInOut://$B%9%?%C%/%^%7%sJQ?tL>(B.poly) $BF0:n(B] oxshell@}\\  {\color{red} \verb@[(polymake) (stringInOut://$B%9%?%C%/%^%7%sJQ?tL>(B.poly) $BF0:n(B] oxshell@}\\
 $B%9%?%C%/%^%7%s$NJQ?t$r%U%!%$%k$r$_$J$7$F$$$k(B.  $B%9%?%C%/%^%7%s$NJQ?t$r%U%!%$%k$r$_$J$7$F$$$k(B.
Line 197  Oxshell $B$rMQ$$$F(B OX $B%5!<%P$r<B8=$9$k$N$,E,@Z$
Line 210  Oxshell $B$rMQ$$$F(B OX $B%5!<%P$r<B8=$9$k$N$,E,@Z$
 $BNc(B: Java $B$N(B io.StringReader ( io.InputStreamReader $B$NBe$o$j(B). \\  $BNc(B: Java $B$N(B io.StringReader ( io.InputStreamReader $B$NBe$o$j(B). \\
 $BNc(B: $B%9%/%j%W%H8@8l$G$"$k(B Python  $BNc(B: $B%9%/%j%W%H8@8l$G$"$k(B Python
   \verb@ x=os.popen("abc","r").read(); @    \verb@ x=os.popen("abc","r").read(); @
   %C netscape $B$N(B plugin $B$J$I$bFbItE*$K$O;w$?%"%$%G%#%"$rMQ$$$F$$$k$H;W$o$l$k(B.
   
 \noindent  \noindent
 {\color{blue} $B?7$7$$ItJ,(B}:  {\color{blue} $B?7$7$$ItJ,(B}:
Line 224  lion
Line 238  lion
   
 \pagetitle{ oxshell.facets() $B$N<BAu(B, $B?t3X4X?t$N<BAuNc(B }  \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$$8&5f$@$C$?(B.
 \nnn $B%G!<%?JQ49$K$O(B tfb/2 ($BEDB<(B)format $B$rMxMQ(B, OpenMath $B%"!<%-%F%/%A%c$rMxMQ(B.  \nnn $B%G!<%?JQ49$K$O(B tfb/2 ($BEDB<(B)format $B$rMxMQ(B, OpenMath $B%"!<%-%F%/%A%c$rMxMQ(B.
 {\color{blue}$B@.2L(B}: $B$=$NM-8z@-$r<B>Z$G$-$?(B.)  {\color{blue}$B@.2L(B}: $B$=$NM-8z@-$r<B>Z$G$-$?(B.)
 %% $B$3$l$b?7$7$$E@$G$"$m$&(B.  %% $B$3$l$b?7$7$$E@$G$"$m$&(B.
Line 235  lion
Line 251  lion
   Outputs to stdout and stderr ]    Outputs to stdout and stderr ]
 \end{verbatim} }  \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)  {\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$$$??t3X4X?t(B.  oxshell $B$K$h$k(B polymake $B8F$S=P$75!G=$rMQ$$$??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.  $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.
Line 248  Saito, Mutsumi; Parameter shift in normal generalized 
Line 265  Saito, Mutsumi; Parameter shift in normal generalized 
   
 \newpage  \newpage
   
   \begin{minipage}{13cm}
 {\footnotesize  {\footnotesize
 \begin{verbatim}  \begin{verbatim}
 [1163]:= load("oxshell.rr");  [1163]:= load("oxshell.rr");
 [1164]:= load("taka_ahg.rr");  [1164]:= load("taka_ahg.rr");
 [1165]:=  A=[[1,0,0],[1,1,0],[1,0,1],[1,1,1],[1,2,0]];  [1165]:=  A=[[1,0,0],[1,1,0],[1,0,1],[1,1,1],[1,2,0]];
 [1166]:= fctr(taka_ahg.b(A,4,[s1,s2,s3]));  [1166]:= fctr(taka_ahg.b(A,0,[s1,s2,s3]));
 [[1,1],[s1+2*s2,2],[s1+2*s2-1,1]]  [[1,1],[s1-s3,1],[2*s1-s2-s3,1],[2*s1-s2-s3-1,1]]
 \end{verbatim}  \end{verbatim}
   
 \begin{verbatim}  \begin{verbatim}
Line 278  def b(A,Idx,V) {
Line 296  def b(A,Idx,V) {
 }  }
 \end{verbatim}  \end{verbatim}
 }  }
   \end{minipage}
   \epsfxsize=12cm
   \epsffile{rims-2003-12-16-sq2.eps}
   
   
 \rightline{$B3+H/(B: $B9b;3(B}  \rightline{$B3+H/(B: $B9b;3(B}
 \newpage  \newpage
   
Line 312  value}{\tt )}
Line 332  value}{\tt )}
   
 \noindent  \noindent
 \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
   
   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  \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}  \end{document}
   
 %%$Id$ at misc-2003/12/RIMS  
   
   %%$Id$ at misc-2003/12/RIMS
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