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\eteiri

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\subsection{\trip\ test, \etrip\ test}
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If somebody claims to have a correct implementation of \TeX, I will not
believe it until I see that {\tt TRIP.TEX} is translated properly.
I propose, in fact, that a program must meet two criteria before it
can justifiably be called \TeX: (1)~The person who wrote it must be
happy with the way it works at his or her installation; and (2)~the
program must produce the correct results from {\tt TRIP.TEX}.
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      $B07$&!%(B
\item $F$$B$GI=$7$?ItJ,$O(B0, 1, 2$B$N$I$l$+$,3JG<$5$l!$Id9f(Bbit$B$H$7$F$NLr3d$r;}$D!%(B
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\item $B0J>e$N@bL@$G$O8+$K$/$$$N$G!$$3$N(Bglue$B$,I=8=$7$F$$$kCM$r=R$Y$k$H!$0J2<$N$h(B
      $B$&$K$J$k!%(B
\[
 \begin{cases}
(1-2F)(10^{18}A_1+10^9A_2+A_3)\cdot 10^{E-32767-20},
&{\rm if}\ F\neq2;\\
{\rm NaN},&{\rm if}\ F=2.
\end{cases}
\]
$B$^$?!$(Bwidth part$B$K<B:]$K3JG<$5$l$F$$$kCM$O(B$1000(E+65536F)+A_0$$B$G$"$k!%(B

\end{enumerate}

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\begin{enumerate}
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\subsection{$BCn<h$j(B}
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\eteiri
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$B7k6I!$(B\textit{scan\_float} procedure$B$NFbIt$G4{B8$N(Bglue$B$r<h$j=P$9=j$G(B
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\subsection{$B=iEy4X?t(B}
$B<!$K!$=iEy4X?t$N<BAu$G$"$k!%4pK\E*$K$O!$4X78<0$rMQ$$$F0z?t$r(B0$B6aK5$N$"$kCM(B
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\nobreak\cite{okuc}$B$rBg$$$K;29M$K$7$?!%(B

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$B$G$"$k!%K\@a$N4X?t$N7W;;$G$O!%(B$n$$B7e$N0z?t$,M?$($i$l$?;~$K!$FbIt$G$O(B
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\paragraph{$BJ?J}:,(B (\textit{fp\_sqrt})}
$a$$B$NJ?J}:,(B$\sqrt a$$B$N7W;;$O!$J}Dx<0(B$1-a/x^2=0$$B$+$iF3$+$l$k(BNewton$BK!(B
$x_{n+1}:=(3-ax_n^2)x_n/2$$B$rMQ$$$k$3$H$K$7$?!%$3$N(BNewton$BK!$G$O(B$1/\!\sqrt
a$$B$,(B2$B<!<}B+$G7W;;$5$l!$<}B+8e(B$x_\infty$$B$K(B$a$$B$r$+$1$l$P!$(B$\sqrt a$$B$,F@$i$l(B
$B$k!%(B$a$
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$B$O!$(B$a$$B$N>e0L7e$r$$$/$D$+$H$C$?$b$N$NJ?J}:,$r1|B<(B
\nobreak\cite{okuc}$B$K:\$C$F$$$k%"%k%4%j%:%`$r;HMQ$7$F7W;;$7$?$b$N$H$7$?!%(B

$B$J$*!$$3$N4X?t$N(Bdebug$BCf$K!$$:$C$HA0$K=q$$$?!VNs$ND9$5$N=L>.!W$N4]$a=hM}(B
$B$K(Bbug$B$,8+$D$+$C$?!%860x$O(B{\bf while}\ $i<n+1$ {\bf do} ... $B$N%k!<(B
$B%W$G!$(B$i$$B$b(B$n$$B$b99?7$;$:$K2s$7$F$$$?$3$H$G$"$C$?!%$3$N$h$&$K!$=iEy4X?t$N(B
debug$BCf$K!$4{$KAH$s$@;MB'1i;;Ey$N(Bbug$B$,H/8+$5$l$k$3$H$,7k9=$"$C$?$,!$0J9_(B
$B$O$$$A$$$A$=$l$r=q$+$J$$$3$H$K$9$k!%(B

\paragraph{$B;X?t4X?t(B (\textit{fp\_exponent})}
$B;X?t4X?t$O(BTaylor$BE83+(B$\exp x=\sum_{i=0}^\infty x^i/i!$$B$NM-8B(B
$B9`$NItJ,OB$G7W;;$9$k!%<}B+$rB.$a$k$?$a$H!$8rBe5i?t$N7W;;$K7eMn$A$N62$l$,(B
$B$"$k$3$H$+$i!$(BTaylor$B5i?t$N7W;;$O(B$x\in[0,1]$$B$NHO0OFb$@$1$G9T$$!$0lHL$O(B
$\exp 2x=(\exp x)^2$, $\exp(-x)=1/\exp x$$B$G$=$l$K5"Ce$5$;$F$$$k!%(B

\paragraph{$B;03Q4X?t<~JU(B (\textit{fp\_tri\_hyp}, 
\textit{fp\_ceil\_floor})} 
$B$4B8CN$N$h$&$K!$;03Q4X?t$HAP6J@~4X?t$N(BTaylor$BE83+$OId9f$,0[$J$k$@$1$G$"$k!%(B
$B$5$i$K!$(B$\tan x=\sin x/\cos x$ $B$G$"$j!$(Bsin$B$NE83+$O4q?t<!$N$_$,!$(Bcos$B$NE83+(B
$B$K$O6v?t<!$N$_$,8=$l$k$N$G!$(B$\sin x$$B$H(B$\cos x$$B$r!J$"$k$$$O!$(B$\sinh x$$B$H(B
$\cosh x$$B$r!KF1;~$K7W;;$9$k$N$b0-$/$OL5$$!%(B$\cos x$, $\cosh x$$B$N(BTaylor$BE8(B
$B3+$N7W;;$G$O!$7eMn$A$rKI$0$?$a$K(B2$B<!$N9`$+$i@h$NOB$r7W;;$7$F!$$9$Y$F$N7W;;(B
$B$N8e$K(B1$B$rB-$9$H$$$&J}K!$r$H$C$?!%(B

$B$$$D$b$N$h$&$K<}B+$rB.$a$k$?$a!$;03Q4X?t$G$O0z?t$r(B$[0,\pi/4]$$B$K!$(B
$BAP6J@~4X?t$G$O0z?t$r(B$[0,1]$$B$K5"Ce$5$;$k!%;03Q4X?t$G$O!$0z?t(B$x$
$B$KBP$7$F(B$a:=x-2\pi \lfloor x/2\pi\rfloor$$B$H$7$F!$(B$a/4$$B$KBP$7$F(BTaylor$BE83+(B
$B$N7W;;$r9T$$!$(B
\[
 \sin 2x=2\sin x(\cos x-1)+2\sin x,\qquad
\cos 2x-1=-2\sin^2 x
\]
$B$r(B2$B2sMQ$$$FEz$($r7W;;$9$k!%(B\newpage

$BAP6J@~4X?t$G$O!$(B
\[
 \sinh 2x=2\sinh x(\cosh x-1)+2\sinh x,\qquad
\cosh 2x-1=2\sinh^2 x
\]
$B$rF1MM$KMQ$$$k!%(B

$B$^$?!$A0CJMn$N(B$a$$B$N<0$+$iJ,$+$k$h$&$K!$(B$\lfloor\cdot\rfloor$$B$N7W;;$,I,MW(B
$B$H$J$k!%$3$l$HF1$8$h$&$J%3!<%I$G(B$\lceil\cdot\rceil$$B$b7W;;$G$-$k$N$G!$$D(B
$B$$$G$KN><T$r9T$&(B\textit{fp\_ceil\_floor}\ procedure$B$b$3$3$G=q$$$?!%(B

\paragraph{$BBP?t4X?t<~JU(B (\textit{fp\_log\_inner}, 
\textit{fp\_log}, \textit{fp\_arc\_hyp})}
$BBP?t4X?t$O!$1|B<(B\nobreak\cite{okuc}$B$K$h$l$P(B
\[
 \frac12\log\frac{1+u}{1-u}=u+\frac{u^3}{3}+\frac{u^5}{5}
+\frac{u^7}{7}+\cdots
\]
$B$r7W;;$9$kJ}$,B.$$$H$"$k$,!$L@$i$+$KJ,$+$k$h$&$K$3$N<0$O(Barctanh$B$N(BTaylor
$BE83+<0$=$N$b$N$G$"$k!%(B$x=(1+u)/(1-u)$$B$r2r$/$H(B$u=(x-1)/(x+1)$$B$H$J$j!$$3$l(B
$B$O(B$x>0$$B$G$OC1D4A}2C$G(B$x=1$$B$N$H$-$K(B$u=0$$B$H$J$k!%EvA3<}B+$rB.$a$k$?$a$K$O(B
$|u|$$B$,>.$5$$J}$,$h$$$N$G!$(B$x$$B$r(B1$B$N6aK5$NHO0O$K5"Ce$5$;$F7W;;$r$*$3$J(B
$B$&$h$&$K$9$k!%(B
$B5"CeJ}K!$OC1=c$G!$$^$:E,@Z$J(B$10^n$$B$r3]$1$F(B$x\in [1,10)$$B$H(B
$B$5$;!$0J2<$N$h$&$K$5$i$KJQ49$9$k!'(B
\def\from{\leftarrow}
\begin{alignat*}{4}
x \in[1,1.5)&\Longrightarrow \text{\inhibitglue$B!J$=$N$^$^!K(B\inhibitglue},\qquad&
x \in[1.5,3)&\Longrightarrow x\from x/2,\\
x \in[3,6)&\Longrightarrow x\from x/4,&
x \in[6,10)&\Longrightarrow x\from x/8.
\end{alignat*}
$B$3$&$9$k$H!$(B$|u|\le 0.2$$B$H$J$j!$<}B+B.EY$O$+$J$jB.$$$b$N$HM=A[$5$l$k!%5U(B
$BJQ49$KI,MW$J(B$\log 10$, $\log 2$, $\log 4$, $\log 8$$B$K$D$$$F$O!$(B$\log 10$
$B$H(B$\log 64$$B$rDj?t$H$7$FFbIt$K;}$C$F$*$/$3$H$H$7$?!%(B

$BBP?t4X?t(B$\log x$$B$r<BAu$7$F$7$^$($P!$5UAP6J@~4X?t$O0J2<$N<0(B
$B$G7W;;2DG=$G$"$k!'(B
\begin{align*}
\mathop{\rm arcsinh} x&=\log(x+\sqrt{x^2+1}),\\
\mathop{\rm arccosh} x&=\log(x+\sqrt{x^2-1}),\qquad x\ge 1\\
\mathop{\rm arctanh} x&=\frac12\log\frac{1+x}{1-x},\qquad |x|<1
\end{align*}
$B$3$NCf$G(Barctanh$B$N<BAu$O(Blog$B$N$=$l$NFbIt$KF~$j9~$`7A$K$J$C$F$$$k$N$G!$0z?t(B
$B$,>.$5$$>l9g$K$O(B$\log x$$B$NFbIt7W;;It!JB($A!$K\@a$N:G=i$K<($7$?(BTaylor$BE83+(B
$B$N7W;;!K$K$=$N$^$^0z$-EO$7$F$7$^$&$h$&$K$7$?!%(B

$B$7$+$7!$$3$N<0$G$O(B$x\simeq 0$$B$G$"$k$H$-!$(B$x+\sqrt{x^2+1}\simeq 1$$B$H$J$k(B
$B$N$G7eMn$A$,H/@8$9$k!%$=$3$G!$(B$x$$B$NM-8z7e?t$,(B$3n$$B$G$"$k$H$-!$(B
$|x|<10^{-n-5}$$B$G$"$l$P!$<!$N(BTaylor$BE83+<0$rMQ$$$F(Barcsinh$B$r7W;;$9$k$3$H$K$7(B
$B$?!'(B
\[
\mathop{\rm arcsinh} x=x-\frac{x^3}6+\frac{3x^5}{40}-\cdots.
\]
\paragraph{$B5U;03Q4X?t(B (\textit{fp\_arc\_tri})}
$B5U;03Q4X?t$OB?2A$@$,!$>o<1E*$K9M$($l$P(B$\arcsin x$, $\arctan x\in
[-\pi/2,\pi/2]$, $\arccos x\in[0,\pi]$$B$H$9$k$N$,E,Ev$@$m$&!%(B$\arcsin
x=\arctan (x/\!\sqrt{1-x^2})$$B$G$"$k$+$i!$(B$\arctan x$$B$@$17W;;$9$l$P$h$$$,!$(B
$B$3$l$O$$$D$b$N$h$&$K5i?tE83+(B
\[
 \arctan x=\sum_{n} \frac{(-1)^nx^{2n+1}}{2n+1},\qquad |x|\le 1
\]
$B$rMQ$$$k!%(B$\arctan x=\pi/2 - \arctan x^{-1}$, $\arctan x=\pi/4 - \arctan
((1-x)/(1+x))$$B$rMQ$$$l$P!$(B$|x|\le \tan \pi/8=\sqrt 2-1=0.414\cdots$$B$^$G(B
$B$G$-$F!$<}B+$OJ]>Z$5$l$k!%(B
\paragraph{$B$Y$->h(B (\textit{fp\_pow\_int})}
$B0lHL$K$O(B$a^b$$B$N7W;;$O(B$\exp(b\log a)$$B$H$9$l$P$h$$$,!$$=$l$G$O(B$(-2)^5$$B$J$I(B
$B$N(B$a\in[-\infty,0)$, $b\in\mathbb Z\setminus\mathbb N$$B$N$H$-$,7W;;$G$-$J(B
$B$$!%$3$N$?$a!$;X?tItJ,$,@0?t$N$H$-$NN_>h$r7W;;$9$k4X?t(B
\textit{fp\_pow\_int}$B$r:n$C$?!%J}?K$O1|B<(B\nobreak\cite{okuc}$B$K=>$$!$Nc$($P(B$b=1701$$B$N(B
$B$H$-$O!$(B$1701=1024+512+128+32+4+1$$B$G$"$k$+$i!$(B$x_0:=a$, $x_{n+1}:=x_n^2$
$B$H$7$?$H$-!$(B$a^b=x_0x_2x_5x_7x_9x_{10}$$B$H$7$F5a$a$l$PNI$$!%(B

$B5$$K$J$k$N$O(B$0^0$$B$N07$$$@$,!$K\Mh$O(BNaN$B$H$9$k$N$,@5Ev$J07$$$G$"$m$&!%$7$+(B
$B$7!$$3$3$G$O<jH4$-$7!$(B\textit{fp\_pow}$B$G$b(B\textit{fp\_pow\_int}$B$G$b(B1$B$H$7(B
$B$?!%8e$+$i9M$($?$j8+$D$1$?$j$7$?$3$8$D$1$r(B3$B$D$P$+$j!'(B
\begin{itemize}
\item $a^b=\exp(b\log a)$$B$rL5M}$d$j(B$a=b=0$$B$N(B
$B$H$-$K$bE,MQ$7$F!$(B``$0^0=\exp(0\log 0)=\exp(0\cdot -\infty)=\exp 0=1$''$B!%(B
\item $m^n=\#\{f\colon n\longrightarrow m\}$$B$G$"$k(B\footnote{$B=89gO@E*Dj5A$K=>$$!$(B
$m=\{0,1,\ldots,m-1\}$$B$H$7$F9M$($F$$$k!%(B}$B$+$i!$(B
$0^0=\#\{f\colon0\longrightarrow 0\}=\#\{f\colon
\emptyset\longrightarrow\emptyset\}=1$$B$H$J$k!%(B
\item $BFs9`DjM}(B$(1+m)^n=\sum_{i=0}^n {n\choose i}m^i$$B$r(B$m=n=0$$B$N$H$-@.N)(B
      $B$5$;$k$?$a$KI,MW!%(B
\end{itemize}

\subsection{$B9bB.2=(B}
$B0l1~0J>e$K5s$2$?4X?t$N<BAu$O9T$C$?$,!$$3$l$i$N4X?t$O1i;;$NESCf7P2a$,5a$^(B
$B$kEY$KF0E*3NJ](B/$B2rJ|$r9T$C$F$*$j!$(Barcsin$B$r5a$a$k$@$1$G(B800$B2s0J>e$NF0E*3NJ](B
$B$r9T$C$F$$$?!%$3$l$OB.EYE*$KHs>o$KITMx$G$"$k$N$G!$$G$-$k8B$jF0E*3NJ]$r9T(B
$B$o$:$K$9$`$h$&$K=q$-D>$9I,MW$,$"$C$?!%(B

$BJ}?K$H$7$F$O<!$NDL$j$G$"$k!'3F1i;;$G$O!$EvA30z?t$H7k2L$r3JG<$9$k$?$a$NNN(B
$B0h$H!$0l;~NN0h$,I,MW$K$J$k$,!$0z?t$NM-8z7e?t$,!J$D$^$j!$0z?t$rI=8=$9$k$N(B
$B$KI,MW$J%a%b%jNN0h$NNL$,!K$o$+$C$F$$$l$P!$0l;~NN0h$NBg$-$5$O$=$3$+$i7W;;(B
$B$9$k$3$H$,$G$-$k!%85!9$N8F$S=P$785$O(B\textit{do\_float\_operation}$B$H$$$&(B1
$B$D$N(Bprocedure$B$G$"$k(B\footnote{$B$3$3$G(B\TeX $B$N%3%^%s%I$GEO$5$l$?1i;;;XNa$,:G(B
$B=*E*$K<B9T$5$l!$7k2L$rI=8=$9$k(Bglue$B$,F@$i$l$k!%(B}$B!%$h$C$F!$I,MW$J0l;~NN0h$N>e8B$,(B
$B$o$+$k$N$G!$1i;;$r<B:]$K8F$S=P$9A0$KE,Ev$J=j$G3NJ]$7$F$*$1$PNI$$!%(B

$B1i;;$N<oN`$K$h$C$F0l;~NN0h$NNL$O<!$NMM$K$J$C$?!'(B
\jdAline[c](1){\small\tabrowsep=0.5zw%\setbox0=\hbox{fp}\advance\tabrowsep-\dp0
\btabular{c/lrr/r}\vline
\emph{$B1i;;(B}&\multicolumn{1}{c}{\emph{procedure$BL>(B}}&%
\emph{$B!!0z?t!!(B}&\emph{$B!!JV$jCM!!(B}&%
\multicolumn{1}{c}{\emph{$B0l;~NN0h(B}}\\\hline
$+$, $-$&\textit{fp\_add\_or\_sub}&$n$, $n$&$n$&$n+3$\\
$\cdot$&\textit{fp\_mul}&$m$, $n$&$m$&$m+n+3$\\
$/$&\textit{fp\_div}&$n$, $n$&$n$&$5n+15$\\
$/$ (short)&\textit{fp\_short\_div}&$n$&$n$&$2n+10$\\
$a^2$&\textit{fp\_square}&$n$&$n$&$2n+3$\\
$\lfloor\cdot\rfloor$, $\lceil\cdot\rceil$%
    &\textit{fp\_ceil\_floor}&$n$&$n$&$n+3$\\\hline
\smash{$\sqrt{\hskip0.5zw}$}&\textit{fp\_sqrt}&$n$&$n$&$4n+32$\\
$\exp$&\textit{fp\_exponent}&$n$&$n$&$4n+32$\\
$\sin$, $\cosh$ etc.&\textit{fp\_tri\_hyp}&$n$&$n+5$&$5n+40$\\
$\log$$B!JFbIt!K(B&\textit{fp\_log\_inner}&$n$&$n$&$4n+12$\\
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\eteiri
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\section{$BIUO?(B}
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\texttt{eptex.p}\ar[rr]^-{\rm Web2C}&&\text{{\tt tex1.c}\ etc.}%
\ar[rr]^-{\text{C compiler}}&&\texttt{eptex}\\
&&&\texttt{pconvert.diff}\ar[u]_-{\text{patch to {\tt pconvert}}}&
\texttt{ep1.diff}\ar[r]^-{\rm patch}&\\
&&&&&\hbox to 0zw{\hss\texttt{ptexextra.c} etc.\hss}\ar[uu]
}\ 
\end{center}
\end{adjustvboxheight}

\subsection{\WEB $B$N<BNc!'(B\texttt{ks1.web}}
$B$3$N%U%!%$%k$,$"$k%G%#%l%/%H%j!$$b$7$/$O8x3+>l=j$K$"$k(B{\tt ks1.web}$B$O!$KM(B
$B$,7W;;?t3X(BI$B$N%l%]!<%H$K=q$$$?(BCarmichael$B?t$rC5:w$9$k%W%m%0%i%`!J(B{\tt
ks1.f90}, Fortran 90$B!K$r(B\WEB $B$KK]Lu$7$?$b$N$G$"$k!%(B

$B$3$3$G$O!$!JK\Mh$N(B\WEB $B$G$OF|K\8l$,DL$i$J$$$N$G!K>>;3$5$s$NF|K\8lHG(B
WEB~\cite{jpweb}$B$r;H$o$;$F$b$i$&$3$H$K$7$?!%$3$NF|K\8lHG(B\WEB $B$K$h$k(B
{\tt jtangle}, {\tt jweave}$B%3%^%s%I$,$=$l$>$l(B{\tt tangle}, {\tt weave}$B$N(B
$BBe$o$j$H$J$k!%(B

$BKM$O(BPascal$B$N%3%s%Q%$%i$r=j;}$7$F$$$J$+$C$?$N$G!$(BWeb2C$B$rMxMQ$7$F%3%s%Q(B
$B%$%k$r9T$C$?!%(B
\begin{adjustvboxheight}
\narrowbaselines\small
\begin{verbatim}
  [h7k doc]$ web2cdir=/home/h7k/ks2/texk/web2c/web2c
  [h7k doc]$ cat $web2cdir/common.defines $web2cdir/texmf.defines ks1.p|$web2cdir/
  web2c -t -hks1-a.h -cks1 |$web2cdir/fixwrites > ks1.c
  [h7k doc]$ gcc -o ks1 ks1.c
\end{verbatim}
\end{adjustvboxheight}
{\tt jtangle}, {\tt jweave}$B%3%^%s%I$G$G$-$?(B{\tt ks1.p}, {\tt ks1.tex}$B$d!$(B
$B>e$N$h$&$K(BC$B8@8l$KJQ49$7$FF@$i$l$?(B{\tt ks1.c}, {\tt ks1.h}$B$bF1$8%G%#%l%/(B
$B%H%j$KCV$$$F$*$$$?!%(B
$B$J$*!$(B{\tt ks1-a.h}$B$H$$$&$N$O(BWeb2C$B$,EG$/(BC$B%=!<%9$r(B
$B$-$A$s$H%3%s%Q%$%k$G$-$k$h$&$K$9$k$?$a$N:G>.8B$N@_Dj$G$"$k!%(B


\newpage
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	$B=t!9!W!%(B\\
\verb+http://www.matsuand.com/downloads/texread/texread3.pdf+
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	$B$k!%(B\\%
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$B!X>pJs=hM}%7%j!<%:(B2$B!!(BPASCAL$B!!86=qBh(B4
	$BHG!Y!$G]Iw4[!$(B1981
\bibitem{mppack} $BJ?;3(B $B90!$9b@:EY7W;;%W%m%0%i%`(BMPPACK 1.0$B!%(B
\verb+http://phase.hpcc.jp/phase/mppack/+
\bibitem{okuc} $B1|B<(B $B@2I'!$!X(BC$B8@8l$K$h$k:G?7%"%k%4%j%:%`<-E5!Y!$5;=QI>O@(B
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$B!J?tM}(B266$B!J3XIt@8MQ95$(<<!K$K7k9=;DIt$,$"$kLOMM!%!K(B
\bibitem{okupt} $B1|B<(B $B@2I'!$!V(BpTeX$B$X$NDs0F$b$I$-!W!$(B2008.1.4$B!%(B\\
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\end{thebibliography}

\end{document}
