%Paper: 
%From: Aaron Keith Grant <akg2@yukawa.uchicago.edu>
%Date: Thu, 1 Sep 94 22:43:28 CDT
%Date (revised): Thu, 1 Sep 94 22:57:01 CDT

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	The figures, as well as two additional files containing     %%
%%      the necessary macros, have been submitted in a separate     %%
%%      file.                                                       %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\input psfig.tex
\documentstyle[12pt,world_sci]{article}
\pagestyle{empty}
\def\PRL#1{{\em Phys.~Rev.~Lett.~}{\bf #1}}
\def\PRD#1{{\em Phys.~Rev.~}{\bf D#1}}
\def\NPB#1{{\em Nucl.~Phys.~}{\bf B#1}}
\def\PLB#1{{\em Phys.~Lett.~}{\bf B#1}}
\def\ARNPS#1{{\em Ann.~Rev.~Nucl.~Part.~Sci.~}{\bf #1}}

\def\Slash{\hskip -.6em/}
\def\Zbb{Zb\bar{b}}
\def\glb{g_L^b}
\def\grb{g_R^b}
\def\dglb{\delta g_L^b}
\def\dgrb{\delta g_R^b}
\def\ds{\delta s^2}
\def\da{\delta\alpha_s}
\def\drho{\delta\rho}
\def\seff{\sin^2\theta_{\rm eff}}
\def\sig0{\sigma_{\rm had}^0}
\def\Gamhad{\Gamma_{\rm had}}
\def\Gamb{\Gamma_{b\bar{b}}}
\def\Gamc{\Gamma_{c\bar{c}}}
\def\Game{\Gamma_{e^+e^-}}
\def\delb{\delta_b}
\def\xib{\xi_b}
\def\zetab{\zeta_b}

\def\beq{\begin{equation}}
\def\eeq{\end{equation}}
\def\beqa{\begin{eqnarray}}
\def\eeqa{\end{eqnarray}}

\begin{document}

\begin{flushleft}
Presented at the DPF'94 Meeting  \hfill  FERMILAB-CONF-94/279-T \\
Albuquerque, NM, Aug. 2--6, 1994 \hfill  EFI 94-44 \\
Proceedings to be published by World Scientific \hfill August 1994 \\
\end{flushleft}

\title{{\bf AN ANALYSIS OF NON--OBLIQUE CORRECTIONS TO\\
           THE $\Zbb$ VERTEX \\}}
\author{TATSU TAKEUCHI\thanks{Presenting author} \\
{\em Fermi National Accelerator Laboratory \\
     P.O. Box 500, Batavia, IL 60510}\\
\vspace{0.3cm}
and\\
\vspace*{0.3cm}
AARON K. GRANT and JONATHAN L. ROSNER\\
{\em Enrico Fermi Institute and Department of Physics,
University of Chicago \\
5640 S. Ellis Avenue, Chicago, IL 60637}}

\maketitle

\setlength{\baselineskip}{2.6ex}

\begin{center}
\parbox{13.0cm}
{\begin{center} ABSTRACT \end{center}
{\small \hspace*{0.3cm}
We present a model--independent analysis of the $Z b \bar b$ vertex,
with the aim of constraining contributions of new physics to the
left- and right--handed couplings of the $b$.  We find that the left--handed
coupling of the $b$ is quite narrowly constrained by present data, but that
the right--handed coupling is still largely unconstrained.}}
\end{center}


\section{Introduction}

Recently there has been increasing interest in extensions of the
Standard Model (SM) which predict sizable corrections to the $\Zbb$ vertex.
This interest is motivated in part
by the fact that a deviation from the SM prediction of
$R_b = \Gamma_{b\bar{b}}/\Gamma_{\rm had}$ has been observed at LEP.
This quantity is particularly well suited for detecting
non--SM vertex corrections
since the leading QCD corrections cancel, to leading order, in the ratio.
However, since a shift in the couplings of the $b$  will also affect
observables such as $R_Z = \Gamma_{\rm had}/\Gamma_{\ell^+\ell^-}$
and $\sigma^0_{\rm had}$,
it is important to analyze all the precision electroweak data
in a systematic fashion for possible signatures of such
corrections.


\section{Sensitivity to oblique and non--oblique corrections}

In the standard renormalization scheme where $\alpha$, $G_\mu$, and $m_Z$
are used as input to fix the theory, electroweak observables get their
dependence on oblique corrections through the $\rho$ parameter and
$\seff$.   If we denote the contribution of new physics to these
two quantities as $\drho$ and $\ds$, respectively, we have
%
\beqa
\rho  & = & [\rho]_{\rm SM} + \drho,   \cr
\seff & = & [\seff]_{\rm SM} + \ds,
\eeqa
%
where $[\cal{O}]_{\rm SM}$ denotes the Standard Model prediction of
the observable $\cal{O}$.

The left and right handed couplings of the $b$ quark to the $Z$
are given by
%\beqa
%\glb  =  [\glb]_{\rm SM} + \frac{1}{3}\,\ds + \dglb, \cr
%\grb  =  [\grb]_{\rm SM} + \frac{1}{3}\,\ds + \dgrb,
%\eeqa
\beq
\glb  =  [\glb]_{\rm SM} + \frac{1}{3}\,\ds + \dglb, ~~~
\grb  =  [\grb]_{\rm SM} + \frac{1}{3}\,\ds + \dgrb,
\eeq
where we have included possible non--oblique corrections from
new physics, $\dglb$ and $\dgrb$.
Assuming that there are no other non--oblique corrections from
new physics, we can calculate the dependence of various
observables on $\drho$, $\ds$, $\dglb$, and $\dgrb$.
It is convenient to define the following linear combinations
of $\dglb$ and $\dgrb$:
%
\beqa
\xib   & \equiv & (\cos\phi_b)\dglb - (\sin\phi_b)\dgrb,  \cr
\zetab & \equiv & (\sin\phi_b)\dglb + (\cos\phi_b)\dgrb,
\label{xizetadef}
\eeqa
where $\phi_b \equiv \tan^{-1}|\grb/\glb| \approx 0.181$.
By expanding $\Gamb$ and
$A_b \equiv [(\glb)^2-(\grb)^2]/[(\glb)^2+(\grb)^2]$
about the point $\ds=\xib=\zetab=0$,
we find
%
\beqa
\Gamb
& = & [ \Gamb ]_{\rm SM}
      \left(  1 + \drho - 1.25\,\ds  - 4.65\,\xib
      \right),  \cr
A_b
& = & [ A_b ]_{\rm SM}
      \left( 1 - 0.68\,\ds - 1.76\,\zetab
      \right).
\label{Abzeta}
\eeqa
%
All the other observables get their dependence on
$\dglb$ and $\dgrb$ through either $\Gamb$ or
$A_b$ so they will depend on either $\xib$ or $\zetab$, but not both.
The observables that depend on $\Gamb$ are:
%
\beqa
\Gamma_Z & = & [\Gamma_Z]_{\rm SM}
               \left( 1 + \drho - 1.06\,\ds - 0.71\,\xib
               \right),   \cr
\sig0 & = & [\sig0]_{\rm SM}
               \left( 1 + 0.11\,\ds + 0.41\,\xib
               \right),   \cr
R_Z \;\equiv\; \Gamma_{\rm had}/\Gamma_{\ell^+\ell^-}
    & = & [R_Z]_{\rm SM}
               \left( 1 - 0.85\,\ds - 1.02\,\xib
               \right),   \cr
R_b \;\equiv\; \Gamma_{b\bar{b}}/\Gamma_{\rm had}
    & = & [R_b]_{\rm SM}
               \left( 1 + 0.18\,\ds - 3.63\,\xib
               \right),   \cr
R_c \;\equiv\; \Gamma_{c\bar{c}}/\Gamma_{\rm had}
    & = & [R_c]_{\rm SM}
               \left( 1 - 0.35\,\ds + 1.02\,\xib
               \right).
\label{Rxidep}
\eeqa
%
Note that only $\Gamma_Z$  depends on $\drho$. All of the other
observables can be expressed as ratios of widths, so that
the $\rho$ dependence cancels
between numerator and denominator.
We will ignore $\Gamma_Z$
in the following in order to keep the number of parameters
at a manageable level.
In an analogous way, we find
%
\beq
A_{\rm FB}^b = \frac{3}{4} A_e A_b
             = [A_{\rm FB}^b]_{\rm SM}
               \left( 1 - 55.7\,\ds - 1.76\,\zetab
               \right).
\label{AFBbzeta}
\eeq
%

The relationship between our parameters and others
that have appeared in the literature is as follows.
The parameter $\epsilon_b$ introduced in Ref.~1 is
related to $\dglb$ by
%
\beq
\epsilon_b = [\epsilon_b]_{\rm SM} - 2\dglb.
\eeq
The parameters $\delta_{bV}$ and $\eta_b$ introduced in Ref.~2
are related to $\xib$ and $\zetab$ by
%
\beqa
\delta_{bV} & = & [\delta_{bV}]_{\rm SM} - 4.65\,\xib,  \cr
\eta_b      & = & [\eta_b]_{\rm SM}      - 1.76\,\zetab.
\eeqa
%

%\end{document}
%\bye

\section{Determination of $\xib$ and $\zetab$}

In order to constrain $\xib$ and $\zetab$, we must first compute nominal
Standard Model values for the various observables.  This in turn requires
that we specify nominal values for the top and Higgs masses.
In the following, we use $m_t = 175$~GeV and $m_H = 300$~GeV.
It is also necessary to specify the value of $\alpha_s$
used in computing the QCD corrections. Here we will use
$\alpha_s = 0.120 \pm 0.006$,
which is the value determined from
hadronic event shapes, jet rates, and energy correlations \cite{ALPHAS}.
We use this value rather than the $0.123 \pm 0.006$ determined using
lineshape data because it is independent of the $Z$ lineshape
parameters we will be using in this analysis.
For the top and Higgs masses given above, the Standard Model
predictions for the relevant observables are summarized in Table 1,
together with the most recent experimental determinations \cite{GLASGOW}.
The errors on $[\sig0]_{\rm SM}$ and $[R_Z]_{\rm SM}$ are due to
the uncertainty in $\alpha_s$.
\begin{table}
\begin{center}
\caption{Experimental measurements and Standard Model predictions for
	various observables}
\begin{tabular}{ccc}
\hline\hline
Observable & Experiment & SM prediction \\
\hline
$\seff$    & $0.2317\pm 0.0007$ (LEP) $0.2294\pm 0.0010$ (SLD)  & 0.2320 \\
$\sig0$    & $41.49\pm 0.12$ (nb)      & $41.43 \pm 0.03 $ \\
$R_Z$      & $20.795\pm 0.040$         & $20.74 \pm 0.04 $ \\
$R_b$      & $0.2202\pm 0.0020$        & $0.2157$          \\
$R_c$      & $0.1583\pm 0.0098$        & $0.1711$          \\
$A^b_{\rm FB}$ & $0.0967\pm 0.0038$     & $0.0957$          \\
$A_b$      &   $0.99\pm 0.14$          & $0.934$           \\
\hline
\end{tabular}
\end{center}
\end{table}

%
%\beqa
%[\seff]_{\rm SM}        & = & 0.2319             \cr
%[\sig0]_{\rm SM}        & = & 41.44   \pm  0.03  \quad({\rm nb})  \cr
%[R_Z]_{\rm SM}          & = & 20.72   \pm  0.04  \cr
%[R_b]_{\rm SM}          & = & 0.2152             \cr
%[R_c]_{\rm SM}          & = & 0.1713             \cr
%[A_{\rm FB}^b]_{\rm SM} & = & 0.0958    	 \cr
%[A_b]_{\rm SM}          & = & 0.934
%\label{SMpred}
%\eeqa
%
%
%\beqa
%\seff         & = &  0.2317 \pm 0.0007 \quad({\rm LEP}) \cr
%\seff         & = &  0.2294 \pm 0.0010 \quad({\rm SLD}) \cr
%\sig0         & = & 41.49   \pm 0.12   \quad({\rm nb})  \cr
%R_Z           & = & 20.795  \pm 0.040  \cr
%R_b           & = &  0.2202 \pm 0.0020 \cr
%R_c           & = &  0.1583 \pm 0.0098 \cr
%A_{\rm FB}^b  & = &  0.0967 \pm 0.0038 \cr
%A_b           & = &  0.99\phantom{00} \pm 0.14\phantom{00} \quad({\rm SLD})
%\label{EXP}
%\eeqa
%
The LEP value of $\seff$ is the average over the {\it leptonic}
asymmetries only;  since the $b\bar b$ asymmetries are sensitive to vertex
corrections as well as shifts in the value of $\seff$,  they should be
handled separately.


\begin{center}
\psfig{file=DPF_fig1.ps,angle=90,width=4in}
{\small {\bf Fig. 1.}  The 1--$\sigma$ limits placed on $\xib$
and $\ds$.}
\end{center}

\vspace{0.5cm}

\begin{center}
\psfig{file=DPF_fig2.ps,angle=90,width=4in}
{\small {\bf Fig. 2.}  The 1--$\sigma$ limits placed on $\zetab$ and $\ds$.}
\end{center}

The constraints imposed by the various observables are illustrated in
Figures 1 and 2.  In Fig.~1, we show the experimentally preferred
$1-\sigma$ bands
in the $\ds-\xib$ plane, and in Fig.~2 we show the corresponding figure
for the $\ds-\zetab$ plane.
%The bands illustrate the $1-\sigma$ uncertainties
%on the various constraints.

A fit to the data with $\ds$, $\xib$, and $\zetab$ as parameters,
including the correlation of -0.4 between $R_b$ and $R_c$, yields
%
\beqa
\ds    & = & -0.0009 \pm 0.0006,  \cr
\xib   & = & -0.003\phantom{0}  \pm 0.002,   \cr
\zetab & = & \phantom{-}0.018\phantom{0} \pm 0.027.
\label{ThreeDfit}
\eeqa
%
The 2--dimensional projections of the allowed regions onto the
$\ds$--$\xib$ and $\ds$--$\zetab$ planes are
shown in Figs.~3 and 4.

\begin{center}
\psfig{file=DPF_fig3.ps,angle=90,width=4in}
{\small {\bf Fig. 3.}
The 68\% and 90\% confidence limits on $\xib$ and $\ds$.
Dashed contours show the positions of the 90\% limit when only the
LEP or SLD value of $\seff$ is used.  The SM points are plotted for
$m_t = 150$, 175, and 200 GeV.  Larger $m_t$ correspond to smaller
$\ds$.}
\end{center}

\vspace{0.5cm}

\begin{center}
\psfig{file=DPF_fig4.ps,angle=90,width=4in}
{\small {\bf Fig. 4.}
The 68\% and 90\% confidence limits on $\zetab$ and $\ds$.
The meaning of the dashed contours and SM points are the same as in Fig. 3.}
\end{center}


In terms of $\dglb$ and $\dgrb$, Eq.~\ref{ThreeDfit} translates into
%
\beq
\dglb  = -0.000 \pm 0.005,~~~ \dgrb  =\phantom{-} 0.018 \pm 0.027.
\label{Results3}
\eeq
%
We see from this that the left--handed coupling of the $b$ is very tightly
constrained by present data, while the right--handed coupling is more
weakly constrained.  This leaves considerable freedom for models
containing extra right--handed gauge bosons or extended Higgs sectors, which
would tend to modify the right--handed coupling of the $b$.  It is also
important to note that many observables, in addition to $R_b$, are
sensitive to shifts in the couplings of the $b$.

\vspace{0.5cm}
{\bf \noindent Acknowledgements \hfil}
\vspace{0.4cm}

We would like to thank M. Peskin, T. Rizzo, J. Hewett,
and T. Onogi for helpful discussions.
This work was supported by
the United States Department of Energy under
Contract Number DE--AC02--76CH03000, and in part
under Grant Number DE--FG02--90ER40560.

\bibliographystyle{unsrt}
\begin{thebibliography}{9}

\bibitem{ABC}
{G.~Altarelli, R.~Barbieri, and F.~Caravaglios,
\NPB{405} (1993) 3;
\PLB{314} (1993) 357.}

\bibitem{CVR}
{A.~Blondel, A.~Djouadi, and C.~Verzegnassi,
\PLB{293} (1992) 253;
A.~Blondel and C.~Verzegnassi,
\PLB{311} (1993) 346;
D.~Comelli, C.~Verzegnassi, and F.~M.~Renard,
Report No. PM/94--04, UTS--DFT--94--02 (1994).}

\bibitem{ALPHAS}
{S.~Bethke and J.~E.~Pilcher, \ARNPS{42} (1992) 251.}

\bibitem{GLASGOW}
{D.~Schaile, results presented at the Madison Phenomenology
Conference (April 11-14 1994) Madison, Wisconsin;
A.~Blondel \emet, the LEP Electroweak Working Group,
Report No. LEPEWWG/94--02;
D.~Abbaneo \emet, the LEP Electroweak Heavy Flavors Working Group,
Report No. LEPHF/94--03.}

\end{thebibliography}
\end{document}
\bye
% Psfig/TeX 
\def\PsfigVersion{1.9}
% dvips version
%
% All psfig/tex software, documentation, and related files
% in this distribution of psfig/tex are 
% Copyright 1987, 1988, 1991 Trevor J. Darrell
%
% Permission is granted for use and non-profit distribution of psfig/tex 
% providing that this notice is clearly maintained. The right to
% distribute any portion of psfig/tex for profit or as part of any commercial
% product is specifically reserved for the author(s) of that portion.
%
% *** Feel free to make local modifications of psfig as you wish,
% *** but DO NOT post any changed or modified versions of ``psfig''
% *** directly to the net. Send them to me and I'll try to incorporate
% *** them into future versions. If you want to take the psfig code 
% *** and make a new program (subject to the copyright above), distribute it, 
% *** (and maintain it) that's fine, just don't call it psfig.
%
% Bugs and improvements to trevor@media.mit.edu.
%
% Thanks to Greg Hager (GDH) and Ned Batchelder for their contributions
% to the original version of this project.
%
% Modified by J. Daniel Smith on 9 October 1990 to accept the
% %%BoundingBox: comment with or without a space after the colon.  Stole
% file reading code from Tom Rokicki's EPSF.TEX file (see below).
%
% More modifications by J. Daniel Smith on 29 March 1991 to allow the
% the included PostScript figure to be rotated.  The amount of
% rotation is specified by the "angle=" parameter of the \psfig command.
%
% Modified by Robert Russell on June 25, 1991 to allow users to specify
% .ps filenames which don't yet exist, provided they explicitly provide
% boundingbox information via the \psfig command. Note: This will only work
% if the "file=" parameter follows all four "bb???=" parameters in the
% command. This is due to the order in which psfig interprets these params.
%
%  3 Jul 1991	JDS	check if file already read in once
%  4 Sep 1991	JDS	fixed incorrect computation of rotated
%			bounding box
% 25 Sep 1991	GVR	expanded synopsis of \psfig
% 14 Oct 1991	JDS	\fbox code from LaTeX so \psdraft works with TeX
%			changed \typeout to \ps@typeout
% 17 Oct 1991	JDS	added \psscalefirst and \psrotatefirst
%

% From: gvr@cs.brown.edu (George V. Reilly)
%
% \psdraft	draws an outline box, but doesn't include the figure
%		in the DVI file.  Useful for previewing.
%
% \psfull	includes the figure in the DVI file (default).
%
% \psscalefirst width= or height= specifies the size of the figure
% 		before rotation.
% \psrotatefirst (default) width= or height= specifies the size of the
% 		 figure after rotation.  Asymetric figures will
% 		 appear to shrink.
%
% \psfigurepath#1	sets the path to search for the figure
%
% \psfig
% usage: \psfig{file=, figure=, height=, width=,
%			bbllx=, bblly=, bburx=, bbury=,
%			rheight=, rwidth=, clip=, angle=, silent=}
%
%	"file" is the filename.  If no path name is specified and the
%		file is not found in the current directory,
%		it will be looked for in directory \psfigurepath.
%	"figure" is a synonym for "file".
%	By default, the width and height of the figure are taken from
%		the BoundingBox of the figure.
%	If "width" is specified, the figure is scaled so that it has
%		the specified width.  Its height changes proportionately.
%	If "height" is specified, the figure is scaled so that it has
%		the specified height.  Its width changes proportionately.
%	If both "width" and "height" are specified, the figure is scaled
%		anamorphically.
%	"bbllx", "bblly", "bburx", and "bbury" control the PostScript
%		BoundingBox.  If these four values are specified
%               *before* the "file" option, the PSFIG will not try to
%               open the PostScript file.
%	"rheight" and "rwidth" are the reserved height and width
%		of the figure, i.e., how big TeX actually thinks
%		the figure is.  They default to "width" and "height".
%	The "clip" option ensures that no portion of the figure will
%		appear outside its BoundingBox.  "clip=" is a switch and
%		takes no value, but the `=' must be present.
%	The "angle" option specifies the angle of rotation (degrees, ccw).
%	The "silent" option makes \psfig work silently.
%

% check to see if macros already loaded in (maybe some other file says
% "\input psfig") ...
\ifx\undefined\psfig\else\endinput\fi

%
% from a suggestion by eijkhout@csrd.uiuc.edu to allow
% loading as a style file. Changed to avoid problems
% with amstex per suggestion by jbence@math.ucla.edu

\let\LaTeXAtSign=\@
\let\@=\relax
\edef\psfigRestoreAt{\catcode`\@=\number\catcode`@\relax}
%\edef\psfigRestoreAt{\catcode`@=\number\catcode`@\relax}
\catcode`\@=11\relax
\newwrite\@unused
\def\ps@typeout#1{{\let\protect\string\immediate\write\@unused{#1}}}
\ps@typeout{psfig/tex \PsfigVersion}

%% Here's how you define your figure path.  Should be set up with null
%% default and a user useable definition.

\def\figurepath{./}
\def\psfigurepath#1{\edef\figurepath{#1}}

%
% @psdo control structure -- similar to Latex @for.
% I redefined these with different names so that psfig can
% be used with TeX as well as LaTeX, and so that it will not 
% be vunerable to future changes in LaTeX's internal
% control structure,
%
\def\@nnil{\@nil}
\def\@empty{}
\def\@psdonoop#1\@@#2#3{}
\def\@psdo#1:=#2\do#3{\edef\@psdotmp{#2}\ifx\@psdotmp\@empty \else
    \expandafter\@psdoloop#2,\@nil,\@nil\@@#1{#3}\fi}
\def\@psdoloop#1,#2,#3\@@#4#5{\def#4{#1}\ifx #4\@nnil \else
       #5\def#4{#2}\ifx #4\@nnil \else#5\@ipsdoloop #3\@@#4{#5}\fi\fi}
\def\@ipsdoloop#1,#2\@@#3#4{\def#3{#1}\ifx #3\@nnil 
       \let\@nextwhile=\@psdonoop \else
      #4\relax\let\@nextwhile=\@ipsdoloop\fi\@nextwhile#2\@@#3{#4}}
\def\@tpsdo#1:=#2\do#3{\xdef\@psdotmp{#2}\ifx\@psdotmp\@empty \else
    \@tpsdoloop#2\@nil\@nil\@@#1{#3}\fi}
\def\@tpsdoloop#1#2\@@#3#4{\def#3{#1}\ifx #3\@nnil 
       \let\@nextwhile=\@psdonoop \else
      #4\relax\let\@nextwhile=\@tpsdoloop\fi\@nextwhile#2\@@#3{#4}}
% 
% \fbox is defined in latex.tex; so if \fbox is undefined, assume that
% we are not in LaTeX.
% Perhaps this could be done better???
\ifx\undefined\fbox
% \fbox code from modified slightly from LaTeX
\newdimen\fboxrule
\newdimen\fboxsep
\newdimen\ps@tempdima
\newbox\ps@tempboxa
\fboxsep = 3pt
\fboxrule = .4pt
\long\def\fbox#1{\leavevmode\setbox\ps@tempboxa\hbox{#1}\ps@tempdima\fboxrule
    \advance\ps@tempdima \fboxsep \advance\ps@tempdima \dp\ps@tempboxa
   \hbox{\lower \ps@tempdima\hbox
  {\vbox{\hrule height \fboxrule
          \hbox{\vrule width \fboxrule \hskip\fboxsep
          \vbox{\vskip\fboxsep \box\ps@tempboxa\vskip\fboxsep}\hskip 
                 \fboxsep\vrule width \fboxrule}
                 \hrule height \fboxrule}}}}
\fi
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% file reading stuff from epsf.tex
%   EPSF.TEX macro file:
%   Written by Tomas Rokicki of Radical Eye Software, 29 Mar 1989.
%   Revised by Don Knuth, 3 Jan 1990.
%   Revised by Tomas Rokicki to accept bounding boxes with no
%      space after the colon, 18 Jul 1990.
%   Portions modified/removed for use in PSFIG package by
%      J. Daniel Smith, 9 October 1990.
%
\newread\ps@stream
\newif\ifnot@eof       % continue looking for the bounding box?
\newif\if@noisy        % report what you're making?
\newif\if@atend        % %%BoundingBox: has (at end) specification
\newif\if@psfile       % does this look like a PostScript file?
%
% PostScript files should start with `%!'
%
{\catcode`\%=12\global\gdef\epsf@start{%!}}
\def\epsf@PS{PS}
%
\def\epsf@getbb#1{%
%
%   The first thing we need to do is to open the
%   PostScript file, if possible.
%
\openin\ps@stream=#1
\ifeof\ps@stream\ps@typeout{Error, File #1 not found}\else
%
%   Okay, we got it. Now we'll scan lines until we find one that doesn't
%   start with %. We're looking for the bounding box comment.
%
   {\not@eoftrue \chardef\other=12
    \def\do##1{\catcode`##1=\other}\dospecials \catcode`\ =10
    \loop
       \if@psfile
	  \read\ps@stream to \epsf@fileline
       \else{
	  \obeyspaces
          \read\ps@stream to \epsf@tmp\global\let\epsf@fileline\epsf@tmp}
       \fi
       \ifeof\ps@stream\not@eoffalse\else
%
%   Check the first line for `%!'.  Issue a warning message if its not
%   there, since the file might not be a PostScript file.
%
       \if@psfile\else
       \expandafter\epsf@test\epsf@fileline:. \\%
       \fi
%
%   We check to see if the first character is a % sign;
%   if so, we look further and stop only if the line begins with
%   `%%BoundingBox:' and the `(atend)' specification was not found.
%   That is, the only way to stop is when the end of file is reached,
%   or a `%%BoundingBox: llx lly urx ury' line is found.
%
          \expandafter\epsf@aux\epsf@fileline:. \\%
       \fi
   \ifnot@eof\repeat
   }\closein\ps@stream\fi}%
%
% This tests if the file we are reading looks like a PostScript file.
%
\long\def\epsf@test#1#2#3:#4\\{\def\epsf@testit{#1#2}
			\ifx\epsf@testit\epsf@start\else
\ps@typeout{Warning! File does not start with `\epsf@start'.  It may not be a PostScript file.}
			\fi
			\@psfiletrue} % don't test after 1st line
%
%   We still need to define the tricky \epsf@aux macro. This requires
%   a couple of magic constants for comparison purposes.
%
{\catcode`\%=12\global\let\epsf@percent=%\global\def\epsf@bblit{%BoundingBox}}
%
%
%   So we're ready to check for `%BoundingBox:' and to grab the
%   values if they are found.  We continue searching if `(at end)'
%   was found after the `%BoundingBox:'.
%
\long\def\epsf@aux#1#2:#3\\{\ifx#1\epsf@percent
   \def\epsf@testit{#2}\ifx\epsf@testit\epsf@bblit
	\@atendfalse
        \epsf@atend #3 . \\%
	\if@atend	
	   \if@verbose{
		\ps@typeout{psfig: found `(atend)'; continuing search}
	   }\fi
        \else
        \epsf@grab #3 . . . \\%
        \not@eoffalse
        \global\no@bbfalse
        \fi
   \fi\fi}%
%
%   Here we grab the values and stuff them in the appropriate definitions.
%
\def\epsf@grab #1 #2 #3 #4 #5\\{%
   \global\def\epsf@llx{#1}\ifx\epsf@llx\empty
      \epsf@grab #2 #3 #4 #5 .\\\else
   \global\def\epsf@lly{#2}%
   \global\def\epsf@urx{#3}\global\def\epsf@ury{#4}\fi}%
%
% Determine if the stuff following the %%BoundingBox is `(atend)'
% J. Daniel Smith.  Copied from \epsf@grab above.
%
\def\epsf@atendlit{(atend)} 
\def\epsf@atend #1 #2 #3\\{%
   \def\epsf@tmp{#1}\ifx\epsf@tmp\empty
      \epsf@atend #2 #3 .\\\else
   \ifx\epsf@tmp\epsf@atendlit\@atendtrue\fi\fi}


% End of file reading stuff from epsf.tex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% trigonometry stuff from "trig.tex"
\chardef\psletter = 11 % won't conflict with \begin{letter} now...
\chardef\other = 12

\newif \ifdebug %%% turn me on to see TeX hard at work ...
\newif\ifc@mpute %%% don't need to compute some values
\c@mputetrue % but assume that we do

\let\then = \relax
\def\r@dian{pt }
\let\r@dians = \r@dian
\let\dimensionless@nit = \r@dian
\let\dimensionless@nits = \dimensionless@nit
\def\internal@nit{sp }
\let\internal@nits = \internal@nit
\newif\ifstillc@nverging
\def \Mess@ge #1{\ifdebug \then \message {#1} \fi}

{ %%% Things that need abnormal catcodes %%%
	\catcode `\@ = \psletter
	\gdef \nodimen {\expandafter \n@dimen \the \dimen}
	\gdef \term #1 #2 #3%
	       {\edef \t@ {\the #1}%%% freeze parameter 1 (count, by value)
		\edef \t@@ {\expandafter \n@dimen \the #2\r@dian}%
				   %%% freeze parameter 2 (dimen, by value)
		\t@rm {\t@} {\t@@} {#3}%
	       }
	\gdef \t@rm #1 #2 #3%
	       {{%
		\count 0 = 0
		\dimen 0 = 1 \dimensionless@nit
		\dimen 2 = #2\relax
		\Mess@ge {Calculating term #1 of \nodimen 2}%
		\loop
		\ifnum	\count 0 < #1
		\then	\advance \count 0 by 1
			\Mess@ge {Iteration \the \count 0 \space}%
			\Multiply \dimen 0 by {\dimen 2}%
			\Mess@ge {After multiplication, term = \nodimen 0}%
			\Divide \dimen 0 by {\count 0}%
			\Mess@ge {After division, term = \nodimen 0}%
		\repeat
		\Mess@ge {Final value for term #1 of 
				\nodimen 2 \space is \nodimen 0}%
		\xdef \Term {#3 = \nodimen 0 \r@dians}%
		\aftergroup \Term
	       }}
	\catcode `\p = \other
	\catcode `\t = \other
	\gdef \n@dimen #1pt{#1} %%% throw away the ``pt''
}

\def \Divide #1by #2{\divide #1 by #2} %%% just a synonym

\def \Multiply #1by #2%%% allows division of a dimen by a dimen
       {{%%% should really freeze parameter 2 (dimen, passed by value)
	\count 0 = #1\relax
	\count 2 = #2\relax
	\count 4 = 65536
	\Mess@ge {Before scaling, count 0 = \the \count 0 \space and
			count 2 = \the \count 2}%
	\ifnum	\count 0 > 32767 %%% do our best to avoid overflow
	\then	\divide \count 0 by 4
		\divide \count 4 by 4
	\else	\ifnum	\count 0 < -32767
		\then	\divide \count 0 by 4
			\divide \count 4 by 4
		\else
		\fi
	\fi
	\ifnum	\count 2 > 32767 %%% while retaining reasonable accuracy
	\then	\divide \count 2 by 4
		\divide \count 4 by 4
	\else	\ifnum	\count 2 < -32767
		\then	\divide \count 2 by 4
			\divide \count 4 by 4
		\else
		\fi
	\fi
	\multiply \count 0 by \count 2
	\divide \count 0 by \count 4
	\xdef \product {#1 = \the \count 0 \internal@nits}%
	\aftergroup \product
       }}

\def\r@duce{\ifdim\dimen0 > 90\r@dian \then   % sin(x+90) = sin(180-x)
		\multiply\dimen0 by -1
		\advance\dimen0 by 180\r@dian
		\r@duce
	    \else \ifdim\dimen0 < -90\r@dian \then  % sin(-x) = sin(360+x)
		\advance\dimen0 by 360\r@dian
		\r@duce
		\fi
	    \fi}

\def\Sine#1%
       {{%
	\dimen 0 = #1 \r@dian
	\r@duce
	\ifdim\dimen0 = -90\r@dian \then
	   \dimen4 = -1\r@dian
	   \c@mputefalse
	\fi
	\ifdim\dimen0 = 90\r@dian \then
	   \dimen4 = 1\r@dian
	   \c@mputefalse
	\fi
	\ifdim\dimen0 = 0\r@dian \then
	   \dimen4 = 0\r@dian
	   \c@mputefalse
	\fi
%
	\ifc@mpute \then
        	% convert degrees to radians
		\divide\dimen0 by 180
		\dimen0=3.141592654\dimen0
%
		\dimen 2 = 3.1415926535897963\r@dian %%% a well-known constant
		\divide\dimen 2 by 2 %%% we only deal with -pi/2 : pi/2
		\Mess@ge {Sin: calculating Sin of \nodimen 0}%
		\count 0 = 1 %%% see power-series expansion for sine
		\dimen 2 = 1 \r@dian %%% ditto
		\dimen 4 = 0 \r@dian %%% ditto
		\loop
			\ifnum	\dimen 2 = 0 %%% then we've done
			\then	\stillc@nvergingfalse 
			\else	\stillc@nvergingtrue
			\fi
			\ifstillc@nverging %%% then calculate next term
			\then	\term {\count 0} {\dimen 0} {\dimen 2}%
				\advance \count 0 by 2
				\count 2 = \count 0
				\divide \count 2 by 2
				\ifodd	\count 2 %%% signs alternate
				\then	\advance \dimen 4 by \dimen 2
				\else	\advance \dimen 4 by -\dimen 2
				\fi
		\repeat
	\fi		
			\xdef \sine {\nodimen 4}%
       }}

% Now the Cosine can be calculated easily by calling \Sine
\def\Cosine#1{\ifx\sine\UnDefined\edef\Savesine{\relax}\else
		             \edef\Savesine{\sine}\fi
	{\dimen0=#1\r@dian\advance\dimen0 by 90\r@dian
	 \Sine{\nodimen 0}
	 \xdef\cosine{\sine}
	 \xdef\sine{\Savesine}}}	      
% end of trig stuff
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\psdraft{
	\def\@psdraft{0}
	%\ps@typeout{draft level now is \@psdraft \space . }
}
\def\psfull{
	\def\@psdraft{100}
	%\ps@typeout{draft level now is \@psdraft \space . }
}

\psfull

\newif\if@scalefirst
\def\psscalefirst{\@scalefirsttrue}
\def\psrotatefirst{\@scalefirstfalse}
\psrotatefirst

\newif\if@draftbox
\def\psnodraftbox{
	\@draftboxfalse
}
\def\psdraftbox{
	\@draftboxtrue
}
\@draftboxtrue

\newif\if@prologfile
\newif\if@postlogfile
\def\pssilent{
	\@noisyfalse
}
\def\psnoisy{
	\@noisytrue
}
\psnoisy
%%% These are for the option list.
%%% A specification of the form a = b maps to calling \@p@@sa{b}
\newif\if@bbllx
\newif\if@bblly
\newif\if@bburx
\newif\if@bbury
\newif\if@height
\newif\if@width
\newif\if@rheight
\newif\if@rwidth
\newif\if@angle
\newif\if@clip
\newif\if@verbose
\def\@p@@sclip#1{\@cliptrue}


\newif\if@decmpr

%%% GDH 7/26/87 -- changed so that it first looks in the local directory,
%%% then in a specified global directory for the ps file.
%%% RPR 6/25/91 -- changed so that it defaults to user-supplied name if
%%% boundingbox info is specified, assuming graphic will be created by
%%% print time.
%%% TJD 10/19/91 -- added bbfile vs. file distinction, and @decmpr flag

\def\@p@@sfigure#1{\def\@p@sfile{null}\def\@p@sbbfile{null}
	        \openin1=#1.bb
		\ifeof1\closein1
	        	\openin1=\figurepath#1.bb
			\ifeof1\closein1
			        \openin1=#1
				\ifeof1\closein1%
				       \openin1=\figurepath#1
					\ifeof1
					   \ps@typeout{Error, File #1 not found}
						\if@bbllx\if@bblly
				   		\if@bburx\if@bbury
			      				\def\@p@sfile{#1}%
			      				\def\@p@sbbfile{#1}%
							\@decmprfalse
				  	   	\fi\fi\fi\fi
					\else\closein1
				    		\def\@p@sfile{\figurepath#1}%
				    		\def\@p@sbbfile{\figurepath#1}%
						\@decmprfalse
	                       		\fi%
			 	\else\closein1%
					\def\@p@sfile{#1}
					\def\@p@sbbfile{#1}
					\@decmprfalse
			 	\fi
			\else
				\def\@p@sfile{\figurepath#1}
				\def\@p@sbbfile{\figurepath#1.bb}
				\@decmprtrue
			\fi
		\else
			\def\@p@sfile{#1}
			\def\@p@sbbfile{#1.bb}
			\@decmprtrue
		\fi}

\def\@p@@sfile#1{\@p@@sfigure{#1}}

\def\@p@@sbbllx#1{
		%\ps@typeout{bbllx is #1}
		\@bbllxtrue
		\dimen100=#1
		\edef\@p@sbbllx{\number\dimen100}
}
\def\@p@@sbblly#1{
		%\ps@typeout{bblly is #1}
		\@bbllytrue
		\dimen100=#1
		\edef\@p@sbblly{\number\dimen100}
}
\def\@p@@sbburx#1{
		%\ps@typeout{bburx is #1}
		\@bburxtrue
		\dimen100=#1
		\edef\@p@sbburx{\number\dimen100}
}
\def\@p@@sbbury#1{
		%\ps@typeout{bbury is #1}
		\@bburytrue
		\dimen100=#1
		\edef\@p@sbbury{\number\dimen100}
}
\def\@p@@sheight#1{
		\@heighttrue
		\dimen100=#1
   		\edef\@p@sheight{\number\dimen100}
		%\ps@typeout{Height is \@p@sheight}
}
\def\@p@@swidth#1{
		%\ps@typeout{Width is #1}
		\@widthtrue
		\dimen100=#1
		\edef\@p@swidth{\number\dimen100}
}
\def\@p@@srheight#1{
		%\ps@typeout{Reserved height is #1}
		\@rheighttrue
		\dimen100=#1
		\edef\@p@srheight{\number\dimen100}
}
\def\@p@@srwidth#1{
		%\ps@typeout{Reserved width is #1}
		\@rwidthtrue
		\dimen100=#1
		\edef\@p@srwidth{\number\dimen100}
}
\def\@p@@sangle#1{
		%\ps@typeout{Rotation is #1}
		\@angletrue
%		\dimen100=#1
		\edef\@p@sangle{#1} %\number\dimen100}
}
\def\@p@@ssilent#1{ 
		\@verbosefalse
}
\def\@p@@sprolog#1{\@prologfiletrue\def\@prologfileval{#1}}
\def\@p@@spostlog#1{\@postlogfiletrue\def\@postlogfileval{#1}}
\def\@cs@name#1{\csname #1\endcsname}
\def\@setparms#1=#2,{\@cs@name{@p@@s#1}{#2}}
%
% initialize the defaults (size the size of the figure)
%
\def\ps@init@parms{
		\@bbllxfalse \@bbllyfalse
		\@bburxfalse \@bburyfalse
		\@heightfalse \@widthfalse
		\@rheightfalse \@rwidthfalse
		\def\@p@sbbllx{}\def\@p@sbblly{}
		\def\@p@sbburx{}\def\@p@sbbury{}
		\def\@p@sheight{}\def\@p@swidth{}
		\def\@p@srheight{}\def\@p@srwidth{}
		\def\@p@sangle{0}
		\def\@p@sfile{} \def\@p@sbbfile{}
		\def\@p@scost{10}
		\def\@sc{}
		\@prologfilefalse
		\@postlogfilefalse
		\@clipfalse
		\if@noisy
			\@verbosetrue
		\else
			\@verbosefalse
		\fi
}
%
% Go through the options setting things up.
%
\def\parse@ps@parms#1{
	 	\@psdo\@psfiga:=#1\do
		   {\expandafter\@setparms\@psfiga,}}
%
% Compute bb height and width
%
\newif\ifno@bb
\def\bb@missing{
	\if@verbose{
		\ps@typeout{psfig: searching \@p@sbbfile \space  for bounding box}
	}\fi
	\no@bbtrue
	\epsf@getbb{\@p@sbbfile}
        \ifno@bb \else \bb@cull\epsf@llx\epsf@lly\epsf@urx\epsf@ury\fi
}	
\def\bb@cull#1#2#3#4{
	\dimen100=#1 bp\edef\@p@sbbllx{\number\dimen100}
	\dimen100=#2 bp\edef\@p@sbblly{\number\dimen100}
	\dimen100=#3 bp\edef\@p@sbburx{\number\dimen100}
	\dimen100=#4 bp\edef\@p@sbbury{\number\dimen100}
	\no@bbfalse
}
% rotate point (#1,#2) about (0,0).
% The sine and cosine of the angle are already stored in \sine and
% \cosine.  The result is placed in (\p@intvaluex, \p@intvaluey).
\newdimen\p@intvaluex
\newdimen\p@intvaluey
\def\rotate@#1#2{{\dimen0=#1 sp\dimen1=#2 sp
%            	calculate x' = x \cos\theta - y \sin\theta
		  \global\p@intvaluex=\cosine\dimen0
		  \dimen3=\sine\dimen1
		  \global\advance\p@intvaluex by -\dimen3
% 		calculate y' = x \sin\theta + y \cos\theta
		  \global\p@intvaluey=\sine\dimen0
		  \dimen3=\cosine\dimen1
		  \global\advance\p@intvaluey by \dimen3
		  }}
\def\compute@bb{
		\no@bbfalse
		\if@bbllx \else \no@bbtrue \fi
		\if@bblly \else \no@bbtrue \fi
		\if@bburx \else \no@bbtrue \fi
		\if@bbury \else \no@bbtrue \fi
		\ifno@bb \bb@missing \fi
		\ifno@bb \ps@typeout{FATAL ERROR: no bb supplied or found}
			\no-bb-error
		\fi
		%
%\ps@typeout{BB: \@p@sbbllx, \@p@sbblly, \@p@sbburx, \@p@sbbury} 
%
% store height/width of original (unrotated) bounding box
		\count203=\@p@sbburx
		\count204=\@p@sbbury
		\advance\count203 by -\@p@sbbllx
		\advance\count204 by -\@p@sbblly
		\edef\ps@bbw{\number\count203}
		\edef\ps@bbh{\number\count204}
		%\ps@typeout{ psbbh = \ps@bbh, psbbw = \ps@bbw }
		\if@angle 
			\Sine{\@p@sangle}\Cosine{\@p@sangle}
	        	{\dimen100=\maxdimen\xdef\r@p@sbbllx{\number\dimen100}
					    \xdef\r@p@sbblly{\number\dimen100}
			                    \xdef\r@p@sbburx{-\number\dimen100}
					    \xdef\r@p@sbbury{-\number\dimen100}}
%
% Need to rotate all four points and take the X-Y extremes of the new
% points as the new bounding box.
                        \def\minmaxtest{
			   \ifnum\number\p@intvaluex<\r@p@sbbllx
			      \xdef\r@p@sbbllx{\number\p@intvaluex}\fi
			   \ifnum\number\p@intvaluex>\r@p@sbburx
			      \xdef\r@p@sbburx{\number\p@intvaluex}\fi
			   \ifnum\number\p@intvaluey<\r@p@sbblly
			      \xdef\r@p@sbblly{\number\p@intvaluey}\fi
			   \ifnum\number\p@intvaluey>\r@p@sbbury
			      \xdef\r@p@sbbury{\number\p@intvaluey}\fi
			   }
%			lower left
			\rotate@{\@p@sbbllx}{\@p@sbblly}
			\minmaxtest
%			upper left
			\rotate@{\@p@sbbllx}{\@p@sbbury}
			\minmaxtest
%			lower right
			\rotate@{\@p@sbburx}{\@p@sbblly}
			\minmaxtest
%			upper right
			\rotate@{\@p@sbburx}{\@p@sbbury}
			\minmaxtest
			\edef\@p@sbbllx{\r@p@sbbllx}\edef\@p@sbblly{\r@p@sbblly}
			\edef\@p@sbburx{\r@p@sbburx}\edef\@p@sbbury{\r@p@sbbury}
%\ps@typeout{rotated BB: \r@p@sbbllx, \r@p@sbblly, \r@p@sbburx, \r@p@sbbury}
		\fi
		\count203=\@p@sbburx
		\count204=\@p@sbbury
		\advance\count203 by -\@p@sbbllx
		\advance\count204 by -\@p@sbblly
		\edef\@bbw{\number\count203}
		\edef\@bbh{\number\count204}
		%\ps@typeout{ bbh = \@bbh, bbw = \@bbw }
}
%
% \in@hundreds performs #1 * (#2 / #3) correct to the hundreds,
%	then leaves the result in @result
%
\def\in@hundreds#1#2#3{\count240=#2 \count241=#3
		     \count100=\count240	% 100 is first digit #2/#3
		     \divide\count100 by \count241
		     \count101=\count100
		     \multiply\count101 by \count241
		     \advance\count240 by -\count101
		     \multiply\count240 by 10
		     \count101=\count240	%101 is second digit of #2/#3
		     \divide\count101 by \count241
		     \count102=\count101
		     \multiply\count102 by \count241
		     \advance\count240 by -\count102
		     \multiply\count240 by 10
		     \count102=\count240	% 102 is the third digit
		     \divide\count102 by \count241
		     \count200=#1\count205=0
		     \count201=\count200
			\multiply\count201 by \count100
		 	\advance\count205 by \count201
		     \count201=\count200
			\divide\count201 by 10
			\multiply\count201 by \count101
			\advance\count205 by \count201
			%
		     \count201=\count200
			\divide\count201 by 100
			\multiply\count201 by \count102
			\advance\count205 by \count201
			%
		     \edef\@result{\number\count205}
}
\def\compute@wfromh{
		% computing : width = height * (bbw / bbh)
		\in@hundreds{\@p@sheight}{\@bbw}{\@bbh}
		%\ps@typeout{ \@p@sheight * \@bbw / \@bbh, = \@result }
		\edef\@p@swidth{\@result}
		%\ps@typeout{w from h: width is \@p@swidth}
}
\def\compute@hfromw{
		% computing : height = width * (bbh / bbw)
	        \in@hundreds{\@p@swidth}{\@bbh}{\@bbw}
		%\ps@typeout{ \@p@swidth * \@bbh / \@bbw = \@result }
		\edef\@p@sheight{\@result}
		%\ps@typeout{h from w : height is \@p@sheight}
}
\def\compute@handw{
		\if@height 
			\if@width
			\else
				\compute@wfromh
			\fi
		\else 
			\if@width
				\compute@hfromw
			\else
				\edef\@p@sheight{\@bbh}
				\edef\@p@swidth{\@bbw}
			\fi
		\fi
}
\def\compute@resv{
		\if@rheight \else \edef\@p@srheight{\@p@sheight} \fi
		\if@rwidth \else \edef\@p@srwidth{\@p@swidth} \fi
		%\ps@typeout{rheight = \@p@srheight, rwidth = \@p@srwidth}
}
%		
% Compute any missing values
\def\compute@sizes{
	\compute@bb
	\if@scalefirst\if@angle
% at this point the bounding box has been adjsuted correctly for
% rotation.  PSFIG does all of its scaling using \@bbh and \@bbw.  If
% a width= or height= was specified along with \psscalefirst, then the
% width=/height= value needs to be adjusted to match the new (rotated)
% bounding box size (specifed in \@bbw and \@bbh).
%    \ps@bbw       width=
%    -------  =  ---------- 
%    \@bbw       new width=
% so `new width=' = (width= * \@bbw) / \ps@bbw; where \ps@bbw is the
% width of the original (unrotated) bounding box.
	\if@width
	   \in@hundreds{\@p@swidth}{\@bbw}{\ps@bbw}
	   \edef\@p@swidth{\@result}
	\fi
	\if@height
	   \in@hundreds{\@p@sheight}{\@bbh}{\ps@bbh}
	   \edef\@p@sheight{\@result}
	\fi
	\fi\fi
	\compute@handw
	\compute@resv}

%
% \psfig
% usage : \psfig{file=, height=, width=, bbllx=, bblly=, bburx=, bbury=,
%			rheight=, rwidth=, clip=}
%
% "clip=" is a switch and takes no value, but the `=' must be present.
\def\psfig#1{\vbox {
	% do a zero width hard space so that a single
	% \psfig in a centering enviornment will behave nicely
	%{\setbox0=\hbox{\ }\ \hskip-\wd0}
	%
	\ps@init@parms
	\parse@ps@parms{#1}
	\compute@sizes
	%
	\ifnum\@p@scost<\@psdraft{
		%
		\special{ps::[begin] 	\@p@swidth \space \@p@sheight \space
				\@p@sbbllx \space \@p@sbblly \space
				\@p@sbburx \space \@p@sbbury \space
				startTexFig \space }
		\if@angle
			\special {ps:: \@p@sangle \space rotate \space} 
		\fi
		\if@clip{
			\if@verbose{
				\ps@typeout{(clip)}
			}\fi
			\special{ps:: doclip \space }
		}\fi
		\if@prologfile
		    \special{ps: plotfile \@prologfileval \space } \fi
		\if@decmpr{
			\if@verbose{
				\ps@typeout{psfig: including \@p@sfile.Z \space }
			}\fi
			\special{ps: plotfile "`zcat \@p@sfile.Z" \space }
		}\else{
			\if@verbose{
				\ps@typeout{psfig: including \@p@sfile \space }
			}\fi
			\special{ps: plotfile \@p@sfile \space }
		}\fi
		\if@postlogfile
		    \special{ps: plotfile \@postlogfileval \space } \fi
		\special{ps::[end] endTexFig \space }
		% Create the vbox to reserve the space for the figure.
		\vbox to \@p@srheight sp{
		% 1/92 TJD Changed from "true sp" to "sp" for magnification.
			\hbox to \@p@srwidth sp{
				\hss
			}
		\vss
		}
	}\else{
		% draft figure, just reserve the space and print the
		% path name.
		\if@draftbox{		
			% Verbose draft: print file name in box
			\hbox{\frame{\vbox to \@p@srheight sp{
			\vss
			\hbox to \@p@srwidth sp{ \hss \@p@sfile \hss }
			\vss
			}}}
		}\else{
			% Non-verbose draft
			\vbox to \@p@srheight sp{
			\vss
			\hbox to \@p@srwidth sp{\hss}
			\vss
			}
		}\fi	



	}\fi
}}
\psfigRestoreAt
\let\@=\LaTeXAtSign




