From 8a5c1b0606aa5fc875e9cef9881a9e9927ee5b2a Mon Sep 17 00:00:00 2001
From: Loic Guegan <manzerberdes@gmx.com>
Date: Tue, 28 May 2019 14:03:33 +0200
Subject: Switch to ICA3PP

---
 IEEEtran.cls | 6347 ----------------------------------------------------------
 1 file changed, 6347 deletions(-)
 delete mode 100755 IEEEtran.cls

(limited to 'IEEEtran.cls')

diff --git a/IEEEtran.cls b/IEEEtran.cls
deleted file mode 100755
index 905a10c..0000000
--- a/IEEEtran.cls
+++ /dev/null
@@ -1,6347 +0,0 @@
-%%
-%% IEEEtran.cls 2015/08/26 version V1.8b
-%% 
-%% This is the IEEEtran LaTeX class for authors of the Institute of 
-%% Electrical and Electronics Engineers (IEEE) Transactions journals and
-%% conferences.
-%% 
-%% Support sites:
-%% http://www.michaelshell.org/tex/ieeetran/
-%% http://www.ctan.org/pkg/ieeetran
-%% and
-%% http://www.ieee.org/
-%%
-%% Based on the original 1993 IEEEtran.cls, but with many bug fixes
-%% and enhancements (from both JVH and MDS) over the 1996/7 version.
-%%
-%%
-%% Contributors:
-%% Gerry Murray (1993), Silvano Balemi (1993),
-%% Jon Dixon (1996), Peter N"uchter (1996),
-%% Juergen von Hagen (2000), and Michael Shell (2001-2014)
-%% 
-%% 
-%% Copyright (c) 1993-2000 by Gerry Murray, Silvano Balemi, 
-%%                         Jon Dixon, Peter N"uchter,
-%%                         Juergen von Hagen
-%%                         and
-%% Copyright (c) 2001-2015 by Michael Shell
-%%
-%% Current maintainer (V1.3 to V1.8b): Michael Shell
-%%                                     See:
-%%                                     http://www.michaelshell.org/
-%%                                     for current contact information.
-%%
-%% Special thanks to Peter Wilson (CUA) and Donald Arseneau
-%% for allowing the inclusion of the \@ifmtarg command 
-%% from their ifmtarg LaTeX package. 
-%% 
-%%*************************************************************************
-%% Legal Notice:
-%% This code is offered as-is without any warranty either expressed or
-%% implied; without even the implied warranty of MERCHANTABILITY or
-%% FITNESS FOR A PARTICULAR PURPOSE! 
-%% User assumes all risk.
-%% In no event shall the IEEE or any contributor to this code be liable for
-%% any damages or losses, including, but not limited to, incidental,
-%% consequential, or any other damages, resulting from the use or misuse
-%% of any information contained here.
-%%
-%% All comments are the opinions of their respective authors and are not
-%% necessarily endorsed by the IEEE.
-%%
-%% This work is distributed under the LaTeX Project Public License (LPPL)
-%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
-%% distributed and modified. A copy of the LPPL, version 1.3, is included
-%% in the base LaTeX documentation of all distributions of LaTeX released
-%% 2003/12/01 or later.
-%% Retain all contribution notices and credits.
-%% ** Modified files should be clearly indicated as such, including  **
-%% ** renaming them and changing author support contact information. **
-%%
-%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
-%%                    bare_conf.tex, bare_jrnl.tex, bare_conf_compsoc.tex,
-%%                    bare_jrnl_compsoc.tex
-%% 
-%% Major changes to the user interface should be indicated by an 
-%% increase in the version numbers. If a version is a beta, it will 
-%% be indicated with a BETA suffix, i.e., 1.4 BETA.
-%% Small changes can be indicated by appending letters to the version
-%% such as "IEEEtran_v14a.cls".
-%% In all cases, \Providesclass, any \typeout messages to the user,
-%% \IEEEtransversionmajor and \IEEEtransversionminor must reflect the
-%% correct version information.
-%% The changes should also be documented via source comments.
-%%*************************************************************************
-%%
-%
-% Available class options 
-% e.g., \documentclass[10pt,conference]{IEEEtran} 
-% 
-%             *** choose only one from each category ***
-%
-% 9pt, 10pt, 11pt, 12pt
-%    Sets normal font size. The default is 10pt.
-% 
-% conference, journal, technote, peerreview, peerreviewca
-%    determines format mode - conference papers, journal papers,
-%    correspondence papers (technotes), or peer review papers. The user
-%    should also select 9pt when using technote. peerreview is like
-%    journal mode, but provides for a single-column "cover" title page for
-%    anonymous peer review. The paper title (without the author names) is
-%    repeated at the top of the page after the cover page. For peer review
-%    papers, the \IEEEpeerreviewmaketitle command must be executed (will
-%    automatically be ignored for non-peerreview modes) at the place the
-%    cover page is to end, usually just after the abstract (keywords are
-%    not normally used with peer review papers). peerreviewca is like
-%    peerreview, but allows the author names to be entered and formatted
-%    as with conference mode so that author affiliation and contact
-%    information can be easily seen on the cover page.
-%    The default is journal.
-%
-% draft, draftcls, draftclsnofoot, final
-%    determines if paper is formatted as a widely spaced draft (for
-%    handwritten editor comments) or as a properly typeset final version.
-%    draftcls restricts draft mode to the class file while all other LaTeX
-%    packages (i.e., \usepackage{graphicx}) will behave as final - allows
-%    for a draft paper with visible figures, etc. draftclsnofoot is like
-%    draftcls, but does not display the date and the word "DRAFT" at the foot
-%    of the pages. If using one of the draft modes, the user will probably
-%    also want to select onecolumn.
-%    The default is final.
-%
-% letterpaper, a4paper, cspaper
-%    determines paper size: 8.5in X 11in, 210mm X 297mm or 7.875in X 10.75in.
-%    Changing the paper size in the standard journal and conference modes
-%    will not alter the typesetting of the document - only the margins will
-%    be affected. In particular, documents using the a4paper option will
-%    have reduced side margins (A4 is narrower than US letter) and a longer
-%    bottom margin (A4 is longer than US letter). For both cases, the top
-%    margins will be the same and the text will be horizontally centered.
-%    For the compsoc conference and draft modes, it is the margins that will
-%    remain constant, and thus the text area size will vary, with changes in
-%    the paper size.
-%    The cspaper option is the special ``trim'' paper size (7.875in x 10.75in)
-%    used in the actual publication of Computer Society journals. Under
-%    compsoc journal mode, this option does not alter the typesetting of the
-%    document. Authors should invoke the cspaper option only if requested to
-%    do so by the editors of the specific journal they are submitting to.
-%    For final submission to the IEEE, authors should generally use US letter 
-%    (8.5 X 11in) paper unless otherwise instructed. Note that authors should
-%    ensure that all post-processing (ps, pdf, etc.) uses the same paper
-%    specificiation as the .tex document. Problems here are by far the number
-%    one reason for incorrect margins. IEEEtran will automatically set the
-%    default paper size under pdflatex (without requiring any change to
-%    pdftex.cfg), so this issue is more important to dvips users. Fix
-%    config.ps, config.pdf, or ~/.dvipsrc for dvips, or use the
-%    dvips -t papersize option instead as needed. For the cspaper option,
-%    the corresponding dvips paper name is "ieeecs".
-%    See the testflow documentation
-%    http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/testflow
-%    for more details on dvips paper size configuration.
-%    The default is letterpaper.
-%
-% oneside, twoside
-%    determines if layout follows single sided or two sided (duplex)
-%    printing. The only notable change is with the headings at the top of
-%    the pages.
-%    The default is oneside.
-%
-% onecolumn, twocolumn
-%    determines if text is organized into one or two columns per page. One
-%    column mode is usually used only with draft papers.
-%    The default is twocolumn.
-%
-% comsoc, compsoc, transmag
-%    Use the format of the IEEE Communications Society, IEEE Computer Society
-%    or IEEE Transactions on Magnetics, respectively.
-%
-% romanappendices
-%    Use the "Appendix I" convention when numbering appendices. IEEEtran.cls
-%    now defaults to Alpha "Appendix A" convention - the opposite of what
-%    v1.6b and earlier did.
-%
-% captionsoff
-%    disables the display of the figure/table captions. Some IEEE journals
-%    request that captions be removed and figures/tables be put on pages
-%    of their own at the end of an initial paper submission. The endfloat
-%    package can be used with this class option to achieve this format.
-%
-% nofonttune
-%    turns off tuning of the font interword spacing. Maybe useful to those
-%    not using the standard Times fonts or for those who have already "tuned"
-%    their fonts.
-%    The default is to enable IEEEtran to tune font parameters.
-%
-%
-%----------
-% Available CLASSINPUTs provided (all are macros unless otherwise noted):
-% \CLASSINPUTbaselinestretch
-% \CLASSINPUTinnersidemargin
-% \CLASSINPUToutersidemargin
-% \CLASSINPUTtoptextmargin
-% \CLASSINPUTbottomtextmargin
-%
-% Available CLASSINFOs provided:
-% \ifCLASSINFOpdf                       (TeX if conditional)
-% \CLASSINFOpaperwidth                  (macro)
-% \CLASSINFOpaperheight                 (macro)
-% \CLASSINFOnormalsizebaselineskip      (length)
-% \CLASSINFOnormalsizeunitybaselineskip (length)
-%
-% Available CLASSOPTIONs provided:
-% all class option flags (TeX if conditionals) unless otherwise noted,
-% e.g., \ifCLASSOPTIONcaptionsoff
-% point size options provided as a single macro:
-% \CLASSOPTIONpt
-% which will be defined as 9, 10, 11, or 12 depending on the document's
-% normalsize point size.
-% also, class option peerreviewca implies the use of class option peerreview
-% and classoption draft implies the use of class option draftcls
-
-
-
-
-
-\ProvidesClass{IEEEtran}[2015/08/26 V1.8b by Michael Shell]
-\typeout{-- See the "IEEEtran_HOWTO" manual for usage information.}
-\typeout{-- http://www.michaelshell.org/tex/ieeetran/}
-\NeedsTeXFormat{LaTeX2e}
-
-% IEEEtran.cls version numbers, provided as of V1.3
-% These values serve as a way a .tex file can
-% determine if the new features are provided.
-% The version number of this IEEEtrans.cls can be obtained from 
-% these values. i.e., V1.4
-% KEEP THESE AS INTEGERS! i.e., NO {4a} or anything like that-
-% (no need to enumerate "a" minor changes here)
-\def\IEEEtransversionmajor{1}
-\def\IEEEtransversionminor{8}
-
-
-% hook to allow easy changeover to IEEEtran.cls/tools.sty error reporting
-\def\@IEEEclspkgerror{\ClassError{IEEEtran}}
-
-
-% These do nothing, but provide them like in article.cls
-\newif\if@restonecol
-\newif\if@titlepage
-
-
-% class option conditionals
-\newif\ifCLASSOPTIONonecolumn       \CLASSOPTIONonecolumnfalse
-\newif\ifCLASSOPTIONtwocolumn       \CLASSOPTIONtwocolumntrue
-
-\newif\ifCLASSOPTIONoneside         \CLASSOPTIONonesidetrue
-\newif\ifCLASSOPTIONtwoside         \CLASSOPTIONtwosidefalse
-
-\newif\ifCLASSOPTIONfinal           \CLASSOPTIONfinaltrue
-\newif\ifCLASSOPTIONdraft           \CLASSOPTIONdraftfalse
-\newif\ifCLASSOPTIONdraftcls        \CLASSOPTIONdraftclsfalse
-\newif\ifCLASSOPTIONdraftclsnofoot  \CLASSOPTIONdraftclsnofootfalse
-
-\newif\ifCLASSOPTIONpeerreview      \CLASSOPTIONpeerreviewfalse
-\newif\ifCLASSOPTIONpeerreviewca    \CLASSOPTIONpeerreviewcafalse
-
-\newif\ifCLASSOPTIONjournal         \CLASSOPTIONjournaltrue
-\newif\ifCLASSOPTIONconference      \CLASSOPTIONconferencefalse
-\newif\ifCLASSOPTIONtechnote        \CLASSOPTIONtechnotefalse
-
-\newif\ifCLASSOPTIONnofonttune      \CLASSOPTIONnofonttunefalse
-
-\newif\ifCLASSOPTIONcaptionsoff     \CLASSOPTIONcaptionsofffalse
-
-\newif\ifCLASSOPTIONcomsoc          \CLASSOPTIONcomsocfalse
-\newif\ifCLASSOPTIONcompsoc         \CLASSOPTIONcompsocfalse
-\newif\ifCLASSOPTIONtransmag        \CLASSOPTIONtransmagfalse
-
-\newif\ifCLASSOPTIONromanappendices \CLASSOPTIONromanappendicesfalse
-
-
-% class info conditionals
-
-% indicates if pdf (via pdflatex) output
-\newif\ifCLASSINFOpdf               \CLASSINFOpdffalse
-
-
-% V1.6b internal flag to show if using a4paper
-\newif\if@IEEEusingAfourpaper       \@IEEEusingAfourpaperfalse
-% V1.6b internal flag to show if using cspaper
-\newif\if@IEEEusingcspaper          \@IEEEusingcspaperfalse
-
-
-% IEEEtran class scratch pad registers
-% dimen
-\newdimen\@IEEEtrantmpdimenA
-\newdimen\@IEEEtrantmpdimenB
-\newdimen\@IEEEtrantmpdimenC
-% count
-\newcount\@IEEEtrantmpcountA
-\newcount\@IEEEtrantmpcountB
-\newcount\@IEEEtrantmpcountC
-% token list
-\newtoks\@IEEEtrantmptoksA
-
-% we use \CLASSOPTIONpt so that we can ID the point size (even for 9pt docs)
-% as well as LaTeX's \@ptsize to retain some compatability with some
-% external packages
-\def\@ptsize{0}
-% LaTeX does not support 9pt, so we set \@ptsize to 0 - same as that of 10pt
-\DeclareOption{9pt}{\def\CLASSOPTIONpt{9}\def\@ptsize{0}}
-\DeclareOption{10pt}{\def\CLASSOPTIONpt{10}\def\@ptsize{0}}
-\DeclareOption{11pt}{\def\CLASSOPTIONpt{11}\def\@ptsize{1}}
-\DeclareOption{12pt}{\def\CLASSOPTIONpt{12}\def\@ptsize{2}}
-
-
-
-\DeclareOption{letterpaper}{\setlength{\paperwidth}{8.5in}%
-                            \setlength{\paperheight}{11in}%
-                            \@IEEEusingAfourpaperfalse
-                            \@IEEEusingcspaperfalse
-                            \def\CLASSOPTIONpaper{letter}%
-                            \def\CLASSINFOpaperwidth{8.5in}%
-                            \def\CLASSINFOpaperheight{11in}}
-
-
-\DeclareOption{a4paper}{\setlength{\paperwidth}{210mm}%
-                        \setlength{\paperheight}{297mm}%
-                        \@IEEEusingAfourpapertrue
-                        \@IEEEusingcspaperfalse
-                        \def\CLASSOPTIONpaper{a4}%
-                        \def\CLASSINFOpaperwidth{210mm}%
-                        \def\CLASSINFOpaperheight{297mm}}
-
-% special paper option for compsoc journals
-\DeclareOption{cspaper}{\setlength{\paperwidth}{7.875in}%
-                        \setlength{\paperheight}{10.75in}%
-                        \@IEEEusingcspapertrue
-                        \@IEEEusingAfourpaperfalse
-                        \def\CLASSOPTIONpaper{ieeecs}%
-                        \def\CLASSINFOpaperwidth{7.875in}%
-                        \def\CLASSINFOpaperheight{10.75in}}
-
-\DeclareOption{oneside}{\@twosidefalse\@mparswitchfalse
-                        \CLASSOPTIONonesidetrue\CLASSOPTIONtwosidefalse}
-\DeclareOption{twoside}{\@twosidetrue\@mparswitchtrue
-                        \CLASSOPTIONtwosidetrue\CLASSOPTIONonesidefalse}
-
-\DeclareOption{onecolumn}{\CLASSOPTIONonecolumntrue\CLASSOPTIONtwocolumnfalse}
-\DeclareOption{twocolumn}{\CLASSOPTIONtwocolumntrue\CLASSOPTIONonecolumnfalse}
-
-% If the user selects draft, then this class AND any packages
-% will go into draft mode.
-\DeclareOption{draft}{\CLASSOPTIONdrafttrue\CLASSOPTIONdraftclstrue
-                      \CLASSOPTIONdraftclsnofootfalse} 
-% draftcls is for a draft mode which will not affect any packages
-% used by the document.
-\DeclareOption{draftcls}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclstrue
-                         \CLASSOPTIONdraftclsnofootfalse} 
-% draftclsnofoot is like draftcls, but without the footer.
-\DeclareOption{draftclsnofoot}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclstrue
-                               \CLASSOPTIONdraftclsnofoottrue} 
-\DeclareOption{final}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclsfalse
-                      \CLASSOPTIONdraftclsnofootfalse}
-
-\DeclareOption{journal}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse
-                        \CLASSOPTIONjournaltrue\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse}
-
-\DeclareOption{conference}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse
-                           \CLASSOPTIONjournalfalse\CLASSOPTIONconferencetrue\CLASSOPTIONtechnotefalse}
-
-\DeclareOption{technote}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse
-                         \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotetrue}
-
-\DeclareOption{peerreview}{\CLASSOPTIONpeerreviewtrue\CLASSOPTIONpeerreviewcafalse
-                           \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse}
-
-\DeclareOption{peerreviewca}{\CLASSOPTIONpeerreviewtrue\CLASSOPTIONpeerreviewcatrue
-                             \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse}
-
-\DeclareOption{nofonttune}{\CLASSOPTIONnofonttunetrue}
-
-\DeclareOption{captionsoff}{\CLASSOPTIONcaptionsofftrue}
-
-\DeclareOption{comsoc}{\CLASSOPTIONcomsoctrue\CLASSOPTIONcompsocfalse\CLASSOPTIONtransmagfalse}
-
-\DeclareOption{compsoc}{\CLASSOPTIONcomsocfalse\CLASSOPTIONcompsoctrue\CLASSOPTIONtransmagfalse}
-
-\DeclareOption{transmag}{\CLASSOPTIONtransmagtrue\CLASSOPTIONcomsocfalse\CLASSOPTIONcompsocfalse}
-
-\DeclareOption{romanappendices}{\CLASSOPTIONromanappendicestrue}
-
-
-% default to US letter paper, 10pt, twocolumn, one sided, final, journal
-\ExecuteOptions{letterpaper,10pt,twocolumn,oneside,final,journal}
-% overrride these defaults per user requests
-\ProcessOptions
-
-
-
-%% -- Command Argument Scanning Support Functions --
-
-% Sets the category codes for punctuation to their normal values.
-% For local use with argument scanning.
-\def\IEEEnormalcatcodespunct{\catcode`\!=12 \catcode`\,=12 \catcode`\:=12
-\catcode`\;=12 \catcode`\`=12 \catcode`\'=12 \catcode`\"=12 \catcode`\.=12
-\catcode`\/=12 \catcode`\?=12 \catcode`\*=12 \catcode`\+=12 \catcode`\-=12
-\catcode`\<=12 \catcode`\>=12 \catcode`\(=12 \catcode`\)=12 \catcode`\[=12
-\catcode`\]=12 \catcode`\==12 \catcode`\|=12}
-% Sets the category codes for numbers to their normal values.
-% For local use with argument scanning.
-\def\IEEEnormalcatcodesnum{\catcode`\0=12 \catcode`\1=12 \catcode`\2=12
-\catcode`\3=12 \catcode`\4=12 \catcode`\5=12 \catcode`\6=12 \catcode`\7=12
-\catcode`\8=12 \catcode`\9=12}
-% combined action of \IEEEnormalcatcodespunct and \IEEEnormalcatcodesnum
-\def\IEEEnormalcatcodes{\IEEEnormalcatcodespunct\IEEEnormalcatcodesnum}
-
-
-% usage: \@IEEEextracttoken*{}
-% \@IEEEextracttoken fully expands its argument (which it then stores in
-% \@IEEEextracttokenarg) via \edef and then the meaning of the first
-% nonbrace (but including the empty group) token found is assigned via \let
-% to \@IEEEextractedtoken as well as stored in the macro
-% \@IEEEextractedtokenmacro. Tokens that would otherwise be discarded during
-% the acquisition of the first are stored in \@IEEEextractedtokensdiscarded,
-% however their original relative brace nesting depths are not guaranteed to
-% be preserved.
-% If the argument is empty, or if a first nonbrace token does not exist (or
-% is an empty group), \@IEEEextractedtoken will be \relax and
-% \@IEEEextractedtokenmacro and \@IEEEextractedtokensdiscarded will be empty.
-%
-% For example:
-% \@IEEEextracttoken{{{ab}{cd}}{{ef}g}}
-% results in:
-%
-% \@IEEEextracttokenarg          ==> a macro containing {{ab}{cd}}{{ef}g}
-% \@IEEEextractedtoken           ==> the letter a
-% \@IEEEextractedtokenmacro      ==> a macro containing a
-% \@IEEEextractedtokensdiscarded ==> a macro containing bcd{ef}g
-%
-% the *-star form, \@IEEEextracttoken*, does not expand its argument
-% contents during processing.
-\def\@IEEEextracttoken{\@ifstar{\let\@IEEEextracttokendef=\def\@@IEEEextracttoken}{\let\@IEEEextracttokendef=\edef\@@IEEEextracttoken}}
-
-\def\@@IEEEextracttoken#1{\@IEEEextracttokendef\@IEEEextracttokenarg{#1}\relax
-\def\@IEEEextractedtokensdiscarded{}\relax % initialize to empty
-% if the macro is unchanged after being acquired as a single undelimited argument
-% with anything after it being stripped off as a delimited argument
-% we know we have one token without any enclosing braces. loop until this is true.
-\let\@IEEEextracttokencurgroup\@IEEEextracttokenarg
-\loop
-  % trap case of an empty argument as this would cause a problem with
-  % \@@@IEEEextracttoken's first (nondelimited) argument acquisition
-  \ifx\@IEEEextracttokencurgroup\@empty
-    \def\@IEEEextractedtokenmacro{}\relax
-  \else
-    \expandafter\@@@IEEEextracttoken\@IEEEextracttokencurgroup\@IEEEgeneralsequenceDELIMITER\relax
-  \fi
-  \ifx\@IEEEextractedtokenmacro\@IEEEextracttokencurgroup
-  \else
-    \let\@IEEEextracttokencurgroup=\@IEEEextractedtokenmacro
-\repeat
-% we can safely do a \let= here because there should be at most one token
-% the relax is needed to handle the case of no token found
-\expandafter\let\expandafter\@IEEEextractedtoken\@IEEEextractedtokenmacro\relax}
-
-\def\@@@IEEEextracttoken#1#2\@IEEEgeneralsequenceDELIMITER{\def\@IEEEextractedtokenmacro{#1}\relax
-\def\@@IEEEextractedtokensdiscarded{#2}\expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter
-\@IEEEextractedtokensdiscarded\expandafter\expandafter\expandafter
-{\expandafter\@@IEEEextractedtokensdiscarded\@IEEEextractedtokensdiscarded}}
-%%
-%% -- End of Command Argument Scanning Support Functions --
-
-
-
-% Computer Society conditional execution command
-\long\def\@IEEEcompsoconly#1{\relax\ifCLASSOPTIONcompsoc\relax#1\relax\fi\relax}
-% inverse
-\long\def\@IEEEnotcompsoconly#1{\relax\ifCLASSOPTIONcompsoc\else\relax#1\relax\fi\relax}
-% compsoc conference
-\long\def\@IEEEcompsocconfonly#1{\relax\ifCLASSOPTIONcompsoc\ifCLASSOPTIONconference\relax#1\relax\fi\fi\relax}
-% compsoc not conference
-\long\def\@IEEEcompsocnotconfonly#1{\relax\ifCLASSOPTIONcompsoc\ifCLASSOPTIONconference\else\relax#1\relax\fi\fi\relax}
-
-
-% comsoc verify that newtxmath, mtpro2, mt11p or mathtime has been loaded
-\def\@IEEEcomsocverifymathfont{\typeout{-- Verifying Times compatible math font.}\relax
-  \@ifpackageloaded{newtxmath}{\typeout{-- newtxmath loaded, OK.}}{\@@IEEEcomsocverifymathfont}}
-\def\@@IEEEcomsocverifymathfont{\@ifpackageloaded{mtpro2}{\typeout{-- mtpro2 loaded, OK.}}{\@@@IEEEcomsocverifymathfont}}
-\def\@@@IEEEcomsocverifymathfont{\@ifpackageloaded{mt11p}{\typeout{-- mt11p2 loaded, OK.}}{\@@@@IEEEcomsocverifymathfont}}
-\def\@@@@IEEEcomsocverifymathfont{\@ifpackageloaded{mathtime}{\typeout{-- mathtime loaded, OK.}}{\@IEEEcomsocenforcemathfont}}
-
-% comsoc, if a Times math font was not loaded by user, enforce it
-\def\@IEEEcomsocenforcemathfont{\typeout{** Times compatible math font not found, forcing.}\relax
-\IfFileExists{newtxmath.sty}{\typeout{-- Found newtxmath, loading.}\RequirePackage{newtxmath}}{\@@IEEEcomsocenforcemathfont}}
-\def\@@IEEEcomsocenforcemathfont{\IfFileExists{mtpro2.sty}{\typeout{-- Found mtpro2, loading.}\RequirePackage{mtpro2}}{\@@@IEEEcomsocenforcemathfont}}
-\def\@@@IEEEcomsocenforcemathfont{\IfFileExists{mt11p.sty}{\typeout{-- Found mt11p, loading.}\RequirePackage{mt11p}}{\@@@@IEEEcomsocenforcemathfont}}
-\def\@@@@IEEEcomsocenforcemathfont{\IfFileExists{mathtime.sty}{\typeout{-- Found mathtime, loading.}\RequirePackage{mathtime}}{\@@@@@IEEEcomsocenforcemathfont}}
-% if no acceptable Times math font package found, error with newtxmath requirement
-\def\@@@@@IEEEcomsocenforcemathfont{\typeout{** No Times compatible math font package found. newtxmath is required.}\RequirePackage{newtxmath}}
-
-
-\ifCLASSOPTIONcomsoc
-  % ensure that if newtxmath is used, the cmintegrals option is also invoked
-  \PassOptionsToPackage{cmintegrals}{newtxmath}
-  % comsoc requires a Times like math font
-  % ensure this requirement is satisfied at document start
-  \AtBeginDocument{\@IEEEcomsocverifymathfont}
-\fi
-
-
-
-% The IEEE uses Times Roman font, so we'll default to Times.
-% These three commands make up the entire times.sty package.
-\renewcommand{\sfdefault}{phv}
-\renewcommand{\rmdefault}{ptm}
-\renewcommand{\ttdefault}{pcr}
-
-% V1.7 compsoc nonconference papers, use Palatino/Palladio as the main text font,
-% not Times Roman.
-\@IEEEcompsocnotconfonly{\renewcommand{\rmdefault}{ppl}}
-
-% enable the selected main text font
-\normalfont\selectfont
-
-
-\ifCLASSOPTIONcomsoc
-  \typeout{-- Using IEEE Communications Society mode.}
-\fi
-
-\ifCLASSOPTIONcompsoc
-  \typeout{-- Using IEEE Computer Society mode.}
-\fi
-
-
-% V1.7 conference notice message hook
-\def\@IEEEconsolenoticeconference{\typeout{}%
-\typeout{** Conference Paper **}%
-\typeout{Before submitting the final camera ready copy, remember to:}%
-\typeout{}%
-\typeout{ 1. Manually equalize the lengths of two columns on the last page}%
-\typeout{ of your paper;}%
-\typeout{}%
-\typeout{ 2. Ensure that any PostScript and/or PDF output post-processing}%
-\typeout{ uses only Type 1 fonts and that every step in the generation}%
-\typeout{ process uses the appropriate paper size.}%
-\typeout{}}
-
-
-% we can send console reminder messages to the user here
-\AtEndDocument{\ifCLASSOPTIONconference\@IEEEconsolenoticeconference\fi}
-
-
-% warn about the use of single column other than for draft mode
-\ifCLASSOPTIONtwocolumn\else%
-  \ifCLASSOPTIONdraftcls\else%
-   \typeout{** ATTENTION: Single column mode is not typically used with IEEE publications.}%
-  \fi%
-\fi
-
-
-% V1.7 improved paper size setting code.
-% Set pdfpage and dvips paper sizes. Conditional tests are similar to that
-% of ifpdf.sty. Retain within {} to ensure tested macros are never altered,
-% even if only effect is to set them to \relax.
-% if \pdfoutput is undefined or equal to relax, output a dvips special
-{\@ifundefined{pdfoutput}{\AtBeginDvi{\special{papersize=\CLASSINFOpaperwidth,\CLASSINFOpaperheight}}}{%
-% pdfoutput is defined and not equal to \relax
-% check for pdfpageheight existence just in case someone sets pdfoutput
-% under non-pdflatex. If exists, set them regardless of value of \pdfoutput.
-\@ifundefined{pdfpageheight}{\relax}{\global\pdfpagewidth\paperwidth
-\global\pdfpageheight\paperheight}%
-% if using \pdfoutput=0 under pdflatex, send dvips papersize special
-\ifcase\pdfoutput
-\AtBeginDvi{\special{papersize=\CLASSINFOpaperwidth,\CLASSINFOpaperheight}}%
-\else
-% we are using pdf output, set CLASSINFOpdf flag
-\global\CLASSINFOpdftrue
-\fi}}
-
-% let the user know the selected papersize
-\typeout{-- Using \CLASSINFOpaperwidth\space x \CLASSINFOpaperheight\space
-(\CLASSOPTIONpaper)\space paper.}
-
-\ifCLASSINFOpdf
-\typeout{-- Using PDF output.}
-\else
-\typeout{-- Using DVI output.}
-\fi
-
-
-% The idea hinted here is for LaTeX to generate markleft{} and markright{}
-% automatically for you after you enter \author{}, \journal{},
-% \journaldate{}, journalvol{}, \journalnum{}, etc.
-% However, there may be some backward compatibility issues here as
-% well as some special applications for IEEEtran.cls and special issues
-% that may require the flexible \markleft{}, \markright{} and/or \markboth{}.
-% We'll leave this as an open future suggestion.
-%\newcommand{\journal}[1]{\def\@journal{#1}}
-%\def\@journal{}
-
-
-
-% pointsize values
-% used with ifx to determine the document's normal size
-\def\@IEEEptsizenine{9}
-\def\@IEEEptsizeten{10}
-\def\@IEEEptsizeeleven{11}
-\def\@IEEEptsizetwelve{12}
-
-
-
-% FONT DEFINITIONS (No sizexx.clo file needed) 
-% V1.6 revised font sizes, displayskip values and
-%      revised normalsize baselineskip to reduce underfull vbox problems
-%      on the 58pc = 696pt = 9.5in text height we want
-%      normalsize     #lines/column  baselineskip (aka leading)
-%             9pt     63             11.0476pt (truncated down)
-%            10pt     58             12pt      (exact)
-%            11pt     52             13.3846pt (truncated down)
-%            12pt     50             13.92pt   (exact)
-%
-
-% we need to store the nominal baselineskip for the given font size
-% in case baselinestretch ever changes.
-% this is a dimen, so it will not hold stretch or shrink
-\newdimen\@IEEEnormalsizeunitybaselineskip
-\@IEEEnormalsizeunitybaselineskip\baselineskip
-
-
-
-%% ******* WARNING! *******
-%%
-%% Authors should not alter font sizes, baselineskip ("leading"),
-%% margins or other spacing values in an attempt to squeeze more
-%% material on each page.
-%%
-%% The IEEE's own typesetting software will restore the correct
-%% values when re-typesetting/proofing the submitted document,
-%% possibly resulting in unexpected article over length charges.
-%%
-%% ******* WARNING! *******
-
-
-% 9pt option defaults
-\ifx\CLASSOPTIONpt\@IEEEptsizenine
-\typeout{-- This is a 9 point document.}
-\def\normalsize{\@setfontsize{\normalsize}{9}{11.0476pt}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{11.0476pt}
-\normalsize
-\abovedisplayskip 1.5ex plus 3pt minus 1pt
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0pt plus 3pt
-\belowdisplayshortskip 1.5ex plus 3pt minus 1pt
-\def\small{\@setfontsize{\small}{8.5}{10pt}}
-\def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}}
-\def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}}
-\def\tiny{\@setfontsize{\tiny}{5}{6pt}}
-% sublargesize is the same as large - 10pt
-\def\sublargesize{\@setfontsize{\sublargesize}{10}{12pt}}
-\def\large{\@setfontsize{\large}{10}{12pt}}
-\def\Large{\@setfontsize{\Large}{12}{14pt}}
-\def\LARGE{\@setfontsize{\LARGE}{14}{17pt}}
-\def\huge{\@setfontsize{\huge}{17}{20pt}}
-\def\Huge{\@setfontsize{\Huge}{20}{24pt}}
-\fi
-%
-% 10pt option defaults
-\ifx\CLASSOPTIONpt\@IEEEptsizeten
-\typeout{-- This is a 10 point document.}
-\def\normalsize{\@setfontsize{\normalsize}{10}{12.00pt}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{12pt}
-\normalsize
-\abovedisplayskip 1.5ex plus 4pt minus 2pt
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0pt plus 4pt
-\belowdisplayshortskip 1.5ex plus 4pt minus 2pt
-\def\small{\@setfontsize{\small}{9}{10pt}}
-\def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}}
-\def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}}
-\def\tiny{\@setfontsize{\tiny}{5}{6pt}}
-% sublargesize is a tad smaller than large - 11pt
-\def\sublargesize{\@setfontsize{\sublargesize}{11}{13.4pt}}
-\def\large{\@setfontsize{\large}{12}{14pt}}
-\def\Large{\@setfontsize{\Large}{14}{17pt}}
-\def\LARGE{\@setfontsize{\LARGE}{17}{20pt}}
-\def\huge{\@setfontsize{\huge}{20}{24pt}}
-\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
-\fi
-%
-% 11pt option defaults
-\ifx\CLASSOPTIONpt\@IEEEptsizeeleven
-\typeout{-- This is an 11 point document.}
-\def\normalsize{\@setfontsize{\normalsize}{11}{13.3846pt}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{13.3846pt}
-\normalsize
-\abovedisplayskip 1.5ex plus 5pt minus 3pt
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0pt plus 5pt
-\belowdisplayshortskip 1.5ex plus 5pt minus 3pt
-\def\small{\@setfontsize{\small}{10}{12pt}}
-\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}
-\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}
-\def\tiny{\@setfontsize{\tiny}{6}{7pt}}
-% sublargesize is the same as large - 12pt
-\def\sublargesize{\@setfontsize{\sublargesize}{12}{14pt}}
-\def\large{\@setfontsize{\large}{12}{14pt}}
-\def\Large{\@setfontsize{\Large}{14}{17pt}}
-\def\LARGE{\@setfontsize{\LARGE}{17}{20pt}}
-\def\huge{\@setfontsize{\huge}{20}{24pt}}
-\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
-\fi
-%
-% 12pt option defaults
-\ifx\CLASSOPTIONpt\@IEEEptsizetwelve
-\typeout{-- This is a 12 point document.}
-\def\normalsize{\@setfontsize{\normalsize}{12}{13.92pt}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{13.92pt}
-\normalsize
-\abovedisplayskip 1.5ex plus 6pt minus 4pt
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0pt plus 6pt
-\belowdisplayshortskip 1.5ex plus 6pt minus 4pt
-\def\small{\@setfontsize{\small}{10}{12pt}}
-\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}
-\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}
-\def\tiny{\@setfontsize{\tiny}{6}{7pt}}
-% sublargesize is the same as large - 14pt
-\def\sublargesize{\@setfontsize{\sublargesize}{14}{17pt}}
-\def\large{\@setfontsize{\large}{14}{17pt}}
-\def\Large{\@setfontsize{\Large}{17}{20pt}}
-\def\LARGE{\@setfontsize{\LARGE}{20}{24pt}}
-\def\huge{\@setfontsize{\huge}{22}{26pt}}
-\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
-\fi
-
-
-
-% V1.8a compsoc font sizes
-% compsoc font sizes use bp "Postscript" point units (1/72in) 
-% rather than the traditional pt (1/72.27)
-\ifCLASSOPTIONcompsoc
-% -- compsoc defaults --
-% ** will override some of these values later **
-% 9pt
-\ifx\CLASSOPTIONpt\@IEEEptsizenine
-\def\normalsize{\@setfontsize{\normalsize}{9bp}{11bp}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{11bp}
-\normalsize
-\abovedisplayskip 1.5ex plus 3bp minus 1bp
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0bp plus 3bp
-\belowdisplayshortskip 1.5ex plus 3bp minus 1bp
-\def\small{\@setfontsize{\small}{8.5bp}{10bp}}
-\def\footnotesize{\@setfontsize{\footnotesize}{8bp}{9bp}}
-\def\scriptsize{\@setfontsize{\scriptsize}{7bp}{8bp}}
-\def\tiny{\@setfontsize{\tiny}{5bp}{6bp}}
-% sublargesize is the same as large - 10bp
-\def\sublargesize{\@setfontsize{\sublargesize}{10bp}{12bp}}
-\def\large{\@setfontsize{\large}{10bp}{12bp}}
-\def\Large{\@setfontsize{\Large}{12bp}{14bp}}
-\def\LARGE{\@setfontsize{\LARGE}{14bp}{17bp}}
-\def\huge{\@setfontsize{\huge}{17bp}{20bp}}
-\def\Huge{\@setfontsize{\Huge}{20bp}{24bp}}
-\fi
-%
-% 10pt
-\ifx\CLASSOPTIONpt\@IEEEptsizeten
-\def\normalsize{\@setfontsize{\normalsize}{10bp}{12bp}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{12bp}
-\normalsize
-\abovedisplayskip 1.5ex plus 4bp minus 2bp
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0pt plus 4bp
-\belowdisplayshortskip 1.5ex plus 4bp minus 2bp
-\def\small{\@setfontsize{\small}{9bp}{10bp}}
-\def\footnotesize{\@setfontsize{\footnotesize}{8bp}{9bp}}
-\def\scriptsize{\@setfontsize{\scriptsize}{7bp}{8bp}}
-\def\tiny{\@setfontsize{\tiny}{5bp}{6bp}}
-% sublargesize is a tad smaller than large - 11bp
-\def\sublargesize{\@setfontsize{\sublargesize}{11bp}{13.5bp}}
-\def\large{\@setfontsize{\large}{12bp}{14bp}}
-\def\Large{\@setfontsize{\Large}{14bp}{17bp}}
-\def\LARGE{\@setfontsize{\LARGE}{17bp}{20bp}}
-\def\huge{\@setfontsize{\huge}{20bp}{24bp}}
-\def\Huge{\@setfontsize{\Huge}{24bp}{28bp}}
-\fi
-%
-% 11pt
-\ifx\CLASSOPTIONpt\@IEEEptsizeeleven
-\def\normalsize{\@setfontsize{\normalsize}{11bp}{13.5bp}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{13.5bp}
-\normalsize
-\abovedisplayskip 1.5ex plus 5bp minus 3bp
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0pt plus 5bp
-\belowdisplayshortskip 1.5ex plus 5bp minus 3bp
-\def\small{\@setfontsize{\small}{10bp}{12bp}}
-\def\footnotesize{\@setfontsize{\footnotesize}{9bp}{10.5bp}}
-\def\scriptsize{\@setfontsize{\scriptsize}{8bp}{9bp}}
-\def\tiny{\@setfontsize{\tiny}{6bp}{7bp}}
-% sublargesize is the same as large - 12bp
-\def\sublargesize{\@setfontsize{\sublargesize}{12bp}{14bp}}
-\def\large{\@setfontsize{\large}{12bp}{14bp}}
-\def\Large{\@setfontsize{\Large}{14bp}{17bp}}
-\def\LARGE{\@setfontsize{\LARGE}{17bp}{20bp}}
-\def\huge{\@setfontsize{\huge}{20bp}{24bp}}
-\def\Huge{\@setfontsize{\Huge}{24bp}{28bp}}
-\fi
-%
-% 12pt
-\ifx\CLASSOPTIONpt\@IEEEptsizetwelve
-\def\normalsize{\@setfontsize{\normalsize}{12bp}{14bp}}%
-\setlength{\@IEEEnormalsizeunitybaselineskip}{14bp}%
-\normalsize
-\abovedisplayskip 1.5ex plus 6bp minus 4bp
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0pt plus 6bp
-\belowdisplayshortskip 1.5ex plus 6bp minus 4bp
-\def\small{\@setfontsize{\small}{10bp}{12bp}}
-\def\footnotesize{\@setfontsize{\footnotesize}{9bp}{10.5bp}}
-\def\scriptsize{\@setfontsize{\scriptsize}{8bp}{9bp}}
-\def\tiny{\@setfontsize{\tiny}{6bp}{7bp}}
-% sublargesize is the same as large - 14bp
-\def\sublargesize{\@setfontsize{\sublargesize}{14bp}{17bp}}
-\def\large{\@setfontsize{\large}{14bp}{17bp}}
-\def\Large{\@setfontsize{\Large}{17bp}{20bp}}
-\def\LARGE{\@setfontsize{\LARGE}{20bp}{24bp}}
-\def\huge{\@setfontsize{\huge}{22bp}{26bp}}
-\def\Huge{\@setfontsize{\Huge}{24bp}{28bp}}
-\fi
-%
-% -- override defaults: compsoc journals use special normalsizes --
-\ifCLASSOPTIONconference
-% 
-% compsoc conferences
-% 9pt
-\ifx\CLASSOPTIONpt\@IEEEptsizenine
-\def\normalsize{\@setfontsize{\normalsize}{9bp}{10.8bp}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{10.8bp}
-\normalsize
-\abovedisplayskip 1.5ex plus 3bp minus 1bp
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0bp plus 3bp
-\belowdisplayshortskip 1.5ex plus 3bp minus 1bp
-\fi
-% 10pt
-\ifx\CLASSOPTIONpt\@IEEEptsizeten
-\def\normalsize{\@setfontsize{\normalsize}{10bp}{11.2bp}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{11.2bp}
-\normalsize
-\abovedisplayskip 1.5ex plus 4bp minus 2bp
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0pt plus 4bp
-\belowdisplayshortskip 1.5ex plus 4bp minus 2bp
-\fi
-% 11pt
-\ifx\CLASSOPTIONpt\@IEEEptsizeeleven
-\def\normalsize{\@setfontsize{\normalsize}{11bp}{13.2bp}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{13.2bp}
-\normalsize
-\abovedisplayskip 1.5ex plus 5bp minus 3bp
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0pt plus 5bp
-\belowdisplayshortskip 1.5ex plus 5bp minus 3bp
-\fi
-% 12pt
-\ifx\CLASSOPTIONpt\@IEEEptsizetwelve
-\def\normalsize{\@setfontsize{\normalsize}{12bp}{14.4bp}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{14.4bp}
-\normalsize
-\abovedisplayskip 1.5ex plus 6bp minus 4bp
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0pt plus 6bp
-\belowdisplayshortskip 1.5ex plus 6bp minus 4bp
-\fi
-% 
-% compsoc nonconferences
-\else
-% 9pt
-\ifx\CLASSOPTIONpt\@IEEEptsizenine
-\def\normalsize{\@setfontsize{\normalsize}{9bp}{10.8bp}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{10.8bp}
-\normalsize
-\abovedisplayskip 1.5ex plus 3bp minus 1bp
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0bp plus 3bp
-\belowdisplayshortskip 1.5ex plus 3bp minus 1bp
-\fi
-% 10pt
-\ifx\CLASSOPTIONpt\@IEEEptsizeten
-% the official spec is 9.5bp with 11.4bp leading for 10pt,
-% but measurements of proofs suggest upto 11.723bp leading
-% here we'll use 11.54bp which gives 61 lines per column
-% with the standard compsoc margins
-\def\normalsize{\@setfontsize{\normalsize}{9.5bp}{11.54bp}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{11.54bp}
-\normalsize
-\abovedisplayskip 1.5ex plus 4bp minus 2bp
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0pt plus 4bp
-\belowdisplayshortskip 1.5ex plus 4bp minus 2bp
-\fi
-% 11pt
-\ifx\CLASSOPTIONpt\@IEEEptsizeeleven
-\def\normalsize{\@setfontsize{\normalsize}{11bp}{13.2bp}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{13.2bp}
-\normalsize
-\abovedisplayskip 1.5ex plus 5bp minus 3bp
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0pt plus 5bp
-\belowdisplayshortskip 1.5ex plus 5bp minus 3bp
-\fi
-% 12pt
-\ifx\CLASSOPTIONpt\@IEEEptsizetwelve
-\def\normalsize{\@setfontsize{\normalsize}{12bp}{14.4bp}}
-\setlength{\@IEEEnormalsizeunitybaselineskip}{14.4bp}
-\normalsize
-\abovedisplayskip 1.5ex plus 6bp minus 4bp
-\belowdisplayskip \abovedisplayskip
-\abovedisplayshortskip 0pt plus 6bp
-\belowdisplayshortskip 1.5ex plus 6bp minus 4bp
-\fi
-\fi\fi
-
-
-
-
-% V1.6 The Computer Modern Fonts will issue a substitution warning for
-% 24pt titles (24.88pt is used instead, but the default and correct
-% Times font will scale exactly as needed) increase the substitution
-% tolerance to turn off this warning.
-% 
-% V1.8a, the compsoc bp font sizes can also cause bogus font substitution
-% warnings with footnote or scriptsize math and the $\bullet$ itemized
-% list of \IEEEcompsocitemizethanks. So, increase this to 1.5pt or more.
-\def\fontsubfuzz{1.7bp}
-
-
-% warn the user in case they forget to use the 9pt option with
-% technote
-\ifCLASSOPTIONtechnote%
- \ifx\CLASSOPTIONpt\@IEEEptsizenine\else%
-  \typeout{** ATTENTION: Technotes are normally 9pt documents.}%
- \fi%
-\fi
-
-
-% V1.7
-% Improved \textunderscore to provide a much better fake _ when used with
-% OT1 encoding. Under OT1, detect use of pcr or cmtt \ttfamily and use
-% available true _ glyph for those two typewriter fonts.
-\def\@IEEEstringptm{ptm} % Times Roman family
-\def\@IEEEstringppl{ppl} % Palatino Roman family
-\def\@IEEEstringphv{phv} % Helvetica Sans Serif family
-\def\@IEEEstringpcr{pcr} % Courier typewriter family
-\def\@IEEEstringcmtt{cmtt} % Computer Modern typewriter family
-\DeclareTextCommandDefault{\textunderscore}{\leavevmode
-\ifx\f@family\@IEEEstringpcr\string_\else
-\ifx\f@family\@IEEEstringcmtt\string_\else
-\ifx\f@family\@IEEEstringptm\kern 0em\vbox{\hrule\@width 0.5em\@height 0.5pt\kern -0.3ex}\else
-\ifx\f@family\@IEEEstringppl\kern 0em\vbox{\hrule\@width 0.5em\@height 0.5pt\kern -0.3ex}\else
-\ifx\f@family\@IEEEstringphv\kern -0.03em\vbox{\hrule\@width 0.62em\@height 0.52pt\kern -0.33ex}\kern -0.03em\else
-\kern 0.09em\vbox{\hrule\@width 0.6em\@height 0.44pt\kern -0.63pt\kern -0.42ex}\kern 0.09em\fi\fi\fi\fi\fi\relax}
-
-
-
-
-% set the default \baselinestretch
-\def\baselinestretch{1}
-\ifCLASSOPTIONdraftcls
-  \def\baselinestretch{1.5}% default baselinestretch for draft modes
-\fi 
-
-
-% process CLASSINPUT baselinestretch
-\ifx\CLASSINPUTbaselinestretch\@IEEEundefined
-\else
-  \edef\baselinestretch{\CLASSINPUTbaselinestretch} % user CLASSINPUT override
-  \typeout{** ATTENTION: Overriding \string\baselinestretch\space to
-           \baselinestretch\space via \string\CLASSINPUT.}
-\fi
-
-\small\normalsize % make \baselinestretch take affect
-
-
-
-
-% store the normalsize baselineskip
-\newdimen\CLASSINFOnormalsizebaselineskip
-\CLASSINFOnormalsizebaselineskip=\baselineskip\relax
-% and the normalsize unity (baselinestretch=1) baselineskip
-% we could save a register by giving the user access to
-% \@IEEEnormalsizeunitybaselineskip. However, let's protect
-% its read only internal status
-\newdimen\CLASSINFOnormalsizeunitybaselineskip
-\CLASSINFOnormalsizeunitybaselineskip=\@IEEEnormalsizeunitybaselineskip\relax
-% store the nominal value of jot
-\newdimen\IEEEnormaljot
-\IEEEnormaljot=0.25\baselineskip\relax
-
-% set \jot
-\jot=\IEEEnormaljot\relax
-
-
-
-
-% V1.6, we are now going to fine tune the interword spacing
-% The default interword glue for Times under TeX appears to use a
-% nominal interword spacing of 25% (relative to the font size, i.e., 1em)
-% a maximum of 40% and a minimum of 19%.
-% For example, 10pt text uses an interword glue of:
-% 
-% 2.5pt plus 1.49998pt minus 0.59998pt
-% 
-% However, the IEEE allows for a more generous range which reduces the need
-% for hyphenation, especially for two column text. Furthermore, the IEEE
-% tends to use a little bit more nominal space between the words.
-% The IEEE's interword spacing percentages appear to be:
-% 35% nominal
-% 23% minimum
-% 50% maximum
-% (They may even be using a tad more for the largest fonts such as 24pt.)
-% 
-% for bold text, the IEEE increases the spacing a little more:
-% 37.5% nominal
-% 23% minimum
-% 55% maximum
-
-% here are the interword spacing ratios we'll use
-% for medium (normal weight)
-\def\@IEEEinterspaceratioM{0.35}
-\def\@IEEEinterspaceMINratioM{0.23}
-\def\@IEEEinterspaceMAXratioM{0.50}
-
-% for bold
-\def\@IEEEinterspaceratioB{0.375}
-\def\@IEEEinterspaceMINratioB{0.23}
-\def\@IEEEinterspaceMAXratioB{0.55}
-
-
-% compsoc nonconference papers use Palatino,
-% tweak settings to better match the proofs
-\ifCLASSOPTIONcompsoc
-\ifCLASSOPTIONconference\else
-% for medium (normal weight)
-\def\@IEEEinterspaceratioM{0.28}
-\def\@IEEEinterspaceMINratioM{0.21}
-\def\@IEEEinterspaceMAXratioM{0.47}
-% for bold
-\def\@IEEEinterspaceratioB{0.305}
-\def\@IEEEinterspaceMINratioB{0.21}
-\def\@IEEEinterspaceMAXratioB{0.52}
-\fi\fi
-
-
-% command to revise the interword spacing for the current font under TeX:
-% \fontdimen2 = nominal interword space
-% \fontdimen3 = interword stretch
-% \fontdimen4 = interword shrink
-% since all changes to the \fontdimen are global, we can enclose these commands
-% in braces to confine any font attribute or length changes
-\def\@@@IEEEsetfontdimens#1#2#3{{%
-\setlength{\@IEEEtrantmpdimenB}{\f@size pt}% grab the font size in pt, could use 1em instead.
-\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%
-\fontdimen2\font=\@IEEEtrantmpdimenA\relax
-\addtolength{\@IEEEtrantmpdimenA}{-#2\@IEEEtrantmpdimenB}%
-\fontdimen3\font=-\@IEEEtrantmpdimenA\relax
-\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%
-\addtolength{\@IEEEtrantmpdimenA}{-#3\@IEEEtrantmpdimenB}%
-\fontdimen4\font=\@IEEEtrantmpdimenA\relax}}
-
-% revise the interword spacing for each font weight
-\def\@@IEEEsetfontdimens{{%
-\mdseries
-\@@@IEEEsetfontdimens{\@IEEEinterspaceratioM}{\@IEEEinterspaceMAXratioM}{\@IEEEinterspaceMINratioM}%
-\bfseries
-\@@@IEEEsetfontdimens{\@IEEEinterspaceratioB}{\@IEEEinterspaceMAXratioB}{\@IEEEinterspaceMINratioB}%
-}}
-
-% revise the interword spacing for each font shape
-% \slshape is not often used for IEEE work and is not altered here. The \scshape caps are
-% already a tad too large in the free LaTeX fonts (as compared to what the IEEE uses) so we
-% won't alter these either.
-\def\@IEEEsetfontdimens{{%
-\normalfont
-\@@IEEEsetfontdimens
-\normalfont\itshape
-\@@IEEEsetfontdimens
-}}
-
-% command to revise the interword spacing for each font size (and shape
-% and weight). Only the \rmfamily is done here as \ttfamily uses a 
-% fixed spacing and \sffamily is not used as the main text of IEEE papers.
-\def\@IEEEtunefonts{{\selectfont\rmfamily
-\tiny\@IEEEsetfontdimens
-\scriptsize\@IEEEsetfontdimens
-\footnotesize\@IEEEsetfontdimens
-\small\@IEEEsetfontdimens
-\normalsize\@IEEEsetfontdimens
-\sublargesize\@IEEEsetfontdimens
-\large\@IEEEsetfontdimens
-\LARGE\@IEEEsetfontdimens
-\huge\@IEEEsetfontdimens
-\Huge\@IEEEsetfontdimens}}
-
-% if the nofonttune class option is not given, revise the interword spacing
-% now - in case IEEEtran makes any default length measurements, and make
-% sure all the default fonts are loaded
-\ifCLASSOPTIONnofonttune\else
-\@IEEEtunefonts
-\fi
-
-% and again at the start of the document in case the user loaded different fonts
-\AtBeginDocument{\ifCLASSOPTIONnofonttune\else\@IEEEtunefonts\fi}
-
-
-
-
-
-% -- V1.8a page setup commands --
-
-% The default sample text for calculating margins
-% Note that IEEE publications use \scriptsize for headers and footers.
-\def\IEEEdefaultsampletext{\normalfont\normalsize gT}
-\def\IEEEdefaultheadersampletext{\normalfont\scriptsize T}% IEEE headers default to uppercase
-\def\IEEEdefaultfootersampletext{\normalfont\scriptsize gT}
-
-
-
-% usage: \IEEEsettextwidth{inner margin}{outer margin}
-% Sets \textwidth to allow the specified inner and outer margins
-% for the current \paperwidth.
-\def\IEEEsettextwidth#1#2{\@IEEEtrantmpdimenA\paperwidth
-\@IEEEtrantmpdimenB#1\relax
-\advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB
-\@IEEEtrantmpdimenB#2\relax
-\advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB
-\textwidth\@IEEEtrantmpdimenA}
-
-
-
-% usage: \IEEEsetsidemargin{mode: i, o, c, a}{margin/offset}
-% Sets \oddsidemargin and \evensidemargin to yield the specified margin
-% of the given mode.
-% The available modes are:
-% i = inner margin
-% o = outer margin
-% c = centered, with the given offset
-% a = adjust the margins using the given offset
-% For the offsets, positive values increase the inner margin.
-% \textwidth should be set properly for the given margins before calling this
-% function.
-\def\IEEEsetsidemargin#1#2{\@IEEEtrantmpdimenA #2\relax
-\@IEEEextracttoken{#1}\relax
-% check for mode errors
-\ifx\@IEEEextractedtokenmacro\@empty
-  \@IEEEclspkgerror{Empty mode type in \string\IEEEsetsidemargin\space (line \the\inputlineno).\MessageBreak
-  Defaulting to `i'}{Valid modes for \string\IEEEsetsidemargin\space are: i, o, c and a.}\relax
-  \let\@IEEEextractedtoken=i\relax
-  \def\@IEEEextractedtokenmacro{i}\relax
-\else
-  \ifx\@IEEEextractedtokensdiscarded\@empty\else
-    \typeout{** WARNING: \string\IEEEsetsidemargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
-  \fi
-\fi
-% handle each mode
-\if\@IEEEextractedtoken a\relax
-  \advance\oddsidemargin by \@IEEEtrantmpdimenA\relax
-\else
-\if\@IEEEextractedtoken c\relax
-  \oddsidemargin\paperwidth
-  \advance\oddsidemargin by -\textwidth
-  \divide\oddsidemargin by 2\relax
-  \advance\oddsidemargin by -1in\relax
-  \advance\oddsidemargin by \@IEEEtrantmpdimenA\relax
-\else
-\if\@IEEEextractedtoken o\relax
-  \oddsidemargin\paperwidth
-  \advance\oddsidemargin by -\textwidth
-  \advance\oddsidemargin by -\@IEEEtrantmpdimenA
-  \advance\oddsidemargin by -1in\relax
-\else
-  \if\@IEEEextractedtoken i\relax
-  \else
-    \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsetsidemargin\space (line \the\inputlineno).\MessageBreak
-    Defaulting to `i'}%
-    {Valid modes for \string\IEEEsetsidemargin\space are: i, o, c  and a.}%
-  \fi
-  \oddsidemargin\@IEEEtrantmpdimenA
-  \advance\oddsidemargin by -1in\relax
-\fi\fi\fi
-% odd and even side margins both mean "inner" for single sided pages
-\evensidemargin\oddsidemargin
-% but are mirrors of each other when twosided is in effect
-\if@twoside
-  \evensidemargin\paperwidth
-  \advance\evensidemargin by -\textwidth
-  \advance\evensidemargin by -\oddsidemargin
-  % have to compensate for both the builtin 1in LaTex offset
-  % and the fact we already subtracted this offset from \oddsidemargin
-  \advance\evensidemargin -2in\relax
-\fi}
-
-
-
-% usage: \IEEEsettextheight[sample text]{top text margin}{bottom text margin}
-% Sets \textheight based on the specified top margin and bottom margin.
-% Takes into consideration \paperheight, \topskip, and (by default) the
-% the actual height and depth of the \IEEEdefaultsampletext text. 
-\def\IEEEsettextheight{\@ifnextchar [{\@IEEEsettextheight}{\@IEEEsettextheight[\IEEEdefaultsampletext]}}
-\def\@IEEEsettextheight[#1]#2#3{\textheight\paperheight\relax
-  \@IEEEtrantmpdimenA #2\relax
-  \advance \textheight by -\@IEEEtrantmpdimenA% subtract top margin
-  \@IEEEtrantmpdimenA #3\relax
-  \advance \textheight by -\@IEEEtrantmpdimenA% subtract bottom margin
-  \advance \textheight by \topskip% add \topskip
-  % subtract off everything above the top, and below the bottom, baselines
-  \settoheight{\@IEEEtrantmpdimenA}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance \textheight by -\@IEEEtrantmpdimenA
-  \settodepth{\@IEEEtrantmpdimenA}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance \textheight by -\@IEEEtrantmpdimenA}
-
-
-
-\newdimen\IEEEquantizedlength
-\IEEEquantizedlength 0sp\relax
-\newdimen\IEEEquantizedlengthdiff
-\IEEEquantizedlengthdiff 0sp\relax
-\def\IEEEquantizedlengthint{0}
-
-% usage: \IEEEquantizelength{mode: d, c, i}{base unit}{length}
-% Sets the length \IEEEquantizedlength to be an integer multiple of the given
-% (nonzero) base unit such that \IEEEquantizedlength approximates the given
-% length.
-% \IEEEquantizedlengthdiff is a length equal to the difference between the
-% \IEEEquantizedlength and the given length.
-% \IEEEquantizedlengthint is a macro containing the integer number of base units
-% in \IEEEquantizedlength.
-% i.e., \IEEEquantizedlength =  \IEEEquantizedlengthint * base unit
-% The mode determines how \IEEEquantizedlength is quantized:
-% d = always decrease (always round down \IEEEquantizeint)
-% c = use the closest match
-% i = always increase (always round up \IEEEquantizeint)
-% In anycase, if the given length is already quantized,
-% \IEEEquantizedlengthdiff will be set to zero.
-\def\IEEEquantizelength#1#2#3{\begingroup
-% work in isolation so as not to externally disturb the \@IEEEtrantmp
-% variables
-% load the argument values indirectly via \IEEEquantizedlengthdiff
-% in case the user refers to our \@IEEEtrantmpdimenX, \IEEEquantizedlength,
-% etc. in the arguments. we also will work with these as counters,
-% i.e., in sp units
-% A has the base unit
-\IEEEquantizedlengthdiff #2\relax\relax\relax\relax
-\@IEEEtrantmpcountA\IEEEquantizedlengthdiff
-% B has the input length
-\IEEEquantizedlengthdiff #3\relax\relax\relax\relax
-\@IEEEtrantmpcountB\IEEEquantizedlengthdiff
-\@IEEEtrantmpdimenA\the\@IEEEtrantmpcountA sp\relax
-\@IEEEtrantmpdimenB\the\@IEEEtrantmpcountB sp\relax
-% \@IEEEtrantmpcountC will have the quantized int
-% \IEEEquantizedlength will have the quantized length
-% \@IEEEtrantmpdimenC will have the quantized diff
-% initialize them to zero as this is what will be
-% exported if an error occurs
-\@IEEEtrantmpcountC 0\relax
-\IEEEquantizedlength 0sp\relax
-\@IEEEtrantmpdimenC 0sp\relax
-% extract mode
-\@IEEEextracttoken{#1}\relax
-% check for mode errors
-\ifx\@IEEEextractedtokenmacro\@empty
-  \@IEEEclspkgerror{Empty mode type in \string\IEEEquantizelength\space (line \the\inputlineno).\MessageBreak
-  Defaulting to `d'}{Valid modes for \string\IEEEquantizelength\space are: d, c and i.}\relax
-  \let\@IEEEextractedtoken=d\relax
-  \def\@IEEEextractedtokenmacro{d}\relax
-\else
-  \ifx\@IEEEextractedtokensdiscarded\@empty\else
-    \typeout{** WARNING: \string\IEEEquantizelength\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
-  \fi
-\fi
-% check for base unit is zero error
-\ifnum\@IEEEtrantmpcountA=0\relax
-\@IEEEclspkgerror{Base unit is zero in \string\IEEEquantizelength\space (line \the\inputlineno).\MessageBreak
-  \string\IEEEquantizedlength\space and \string\IEEEquantizedlengthdiff\space are set to zero}{Division by zero is not allowed.}\relax
-\else% base unit is nonzero
-  % \@IEEEtrantmpcountC carries the number of integer units
-  % in the quantized length (integer length \ base)
-  \@IEEEtrantmpcountC\@IEEEtrantmpcountB\relax
-  \divide\@IEEEtrantmpcountC by \@IEEEtrantmpcountA\relax
-  % \IEEEquantizedlength has the (rounded down) quantized length
-  % = base * int
-  \IEEEquantizedlength\@IEEEtrantmpdimenA\relax
-  \multiply\IEEEquantizedlength by \@IEEEtrantmpcountC\relax
-  % \@IEEEtrantmpdimenC has the difference
-  % = quantized length - length
-  \@IEEEtrantmpdimenC\IEEEquantizedlength\relax
-  \advance\@IEEEtrantmpdimenC by -\@IEEEtrantmpdimenB\relax
-  % trap special case of length being already quantized
-  % to avoid a roundup under i option
-  \ifdim\@IEEEtrantmpdimenC=0sp\relax
-  \else % length not is already quantized
-    % set dimenA to carry the upper quantized (absolute value) difference:
-    % quantizedlength + base - length
-    \advance\@IEEEtrantmpdimenA by \IEEEquantizedlength\relax
-    \advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB\relax
-    % set dimenB to carry the lower quantized (absolute value) difference:
-    % length - quantizedlength
-    \advance\@IEEEtrantmpdimenB by -\IEEEquantizedlength\relax
-    % handle each mode
-    \if\@IEEEextractedtoken c\relax
-      % compare upper and lower amounts, select upper if lower > upper
-      \ifdim\@IEEEtrantmpdimenB>\@IEEEtrantmpdimenA\relax
-        % use upper
-        \advance\IEEEquantizedlength by \the\@IEEEtrantmpcountA sp\relax
-        \advance\@IEEEtrantmpcountC by 1\relax
-        \@IEEEtrantmpdimenC\@IEEEtrantmpdimenA
-      \else% <=. uselower
-        % no need to do anything for lower, use output values already setup
-      \fi
-    \else% not mode c
-    \if\@IEEEextractedtoken i\relax
-      % always round up under i mode
-      \advance\IEEEquantizedlength by \the\@IEEEtrantmpcountA sp\relax
-      \advance\@IEEEtrantmpcountC by 1\relax
-      \@IEEEtrantmpdimenC\@IEEEtrantmpdimenA
-    \else
-      \if\@IEEEextractedtoken d\relax
-      \else
-        \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEquantizelength\space (line \the\inputlineno).\MessageBreak
-        Defaulting to `d'}%
-        {Valid modes for \string\IEEEquantizelength\space are: d, c, and i.}\relax
-      \fi % if d
-      % no need to do anything for d, use output values already setup
-    \fi\fi % if i, c
-  \fi % if length is already quantized
-\fi% if base unit is zero
-% globally assign the results to macros we use here to escape the enclosing
-% group without needing to call \global on any of the \@IEEEtrantmp variables.
-% \@IEEEtrantmpcountC has the quantized int
-% \IEEEquantizedlength has the quantized length
-% \@IEEEtrantmpdimenC has the quantized diff
-\xdef\@IEEEquantizedlengthintmacro{\the\@IEEEtrantmpcountC}\relax
-\@IEEEtrantmpcountC\IEEEquantizedlength\relax
-\xdef\@IEEEquantizedlengthmacro{\the\@IEEEtrantmpcountC}\relax
-\@IEEEtrantmpcountC\@IEEEtrantmpdimenC\relax
-\xdef\@IEEEquantizedlengthdiffmacro{\the\@IEEEtrantmpcountC}\relax
-\endgroup
-% locally assign the outputs here from the macros
-\expandafter\IEEEquantizedlength\@IEEEquantizedlengthmacro sp\relax
-\expandafter\IEEEquantizedlengthdiff\@IEEEquantizedlengthdiffmacro sp\relax
-\edef\IEEEquantizedlengthint{\@IEEEquantizedlengthintmacro}\relax}
-
-
-
-\newdimen\IEEEquantizedtextheightdiff
-\IEEEquantizedtextheightdiff 0sp\relax
-
-% usage: \IEEEquantizetextheight[base unit]{mode: d, c, i}
-% Sets \textheight to be an integer multiple of the current \baselineskip
-% (or the optionally specified base unit) plus the first (\topskip) line.
-% \IEEEquantizedtextheightdiff is a length equal to the difference between
-% the new quantized and original \textheight.
-% \IEEEquantizedtextheightlpc is a macro containing the integer number of
-% lines per column under the quantized \textheight. i.e.,
-% \textheight = \IEEEquantizedtextheightlpc * \baselineskip + \topskip
-% The mode determines how \textheight is quantized:
-% d = always decrease (always round down the number of lines per column)
-% c = use the closest match
-% i = always increase (always round up the number of lines per column)
-% In anycase, if \textheight is already quantized, it will remain unchanged,
-% and \IEEEquantizedtextheightdiff will be set to zero.
-% Depends on: \IEEEquantizelength
-\def\IEEEquantizetextheight{\@ifnextchar [{\@IEEEquantizetextheight}{\@IEEEquantizetextheight[\baselineskip]}}
-\def\@IEEEquantizetextheight[#1]#2{\begingroup
-% use our \IEEEquantizedtextheightdiff as a scratch pad
-% we need to subtract off \topskip before quantization
-\IEEEquantizedtextheightdiff\textheight
-\advance\IEEEquantizedtextheightdiff by -\topskip\relax
-\IEEEquantizelength{#2}{#1}{\IEEEquantizedtextheightdiff}
-% add back \topskip line
-\advance\IEEEquantizedlength by \topskip
-\@IEEEtrantmpcountC\IEEEquantizedlengthint\relax
-\advance\@IEEEtrantmpcountC by 1\relax
-% globally assign the results to macros we use here to escape the enclosing
-% group without needing to call \global on any of the \@IEEEtrantmp variables.
-\xdef\@IEEEquantizedtextheightlpcmacro{\the\@IEEEtrantmpcountC}\relax
-\@IEEEtrantmpcountC\IEEEquantizedlength\relax
-\xdef\@IEEEquantizedtextheightmacro{\the\@IEEEtrantmpcountC}\relax
-\@IEEEtrantmpcountC\IEEEquantizedlengthdiff\relax
-\xdef\@IEEEquantizedtextheightdiffmacro{\the\@IEEEtrantmpcountC}\relax
-\endgroup
-% locally assign the outputs here from the macros
-\textheight\@IEEEquantizedtextheightmacro sp\relax
-\IEEEquantizedtextheightdiff\@IEEEquantizedtextheightdiffmacro sp\relax
-\edef\IEEEquantizedtextheightlpc{\@IEEEquantizedtextheightlpcmacro}}
-
-
-
-% usage: \IEEEsettopmargin[sample text]{mode: t, b, c, a, q}{margin/offset}
-% Sets \topmargin based on the specified vertical margin.
-% Takes into consideration the base 1in offset, \headheight, \headsep,
-% \topskip, and (by default) the the actual height (or, for the bottom, depth)
-% of the \IEEEdefaultsampletext text.
-% The available modes are:
-% t = top margin
-% b = bottom margin
-% c = vertically centered, with the given offset
-% a = adjust the vertical margins using the given offset
-% q = adjust the margins using \IEEEquantizedtextheightdiff and the given offset
-% For the offsets, positive values increase the top margin.
-% \headheight, \headsep, \topskip and \textheight should be set properly for the
-% given margins before calling this function.
-\def\IEEEsettopmargin{\@ifnextchar [{\@IEEEsettopmargin}{\@IEEEsettopmargin[\IEEEdefaultsampletext]}}
-\def\@IEEEsettopmargin[#1]#2#3{\@IEEEtrantmpdimenA #3\relax
-\@IEEEextracttoken{#2}\relax
-% check for mode errors
-\ifx\@IEEEextractedtokenmacro\@empty
-  \@IEEEclspkgerror{Empty mode type in \string\IEEEsettopmargin\space (line \the\inputlineno).\MessageBreak
-  Defaulting to `t'}{Valid modes for \string\IEEEsettopmargin\space are: t, b, c, a and q.}\relax
-  \let\@IEEEextractedtoken=t\relax
-  \def\@IEEEextractedtokenmacro{t}\relax
-\else
-  \ifx\@IEEEextractedtokensdiscarded\@empty\else
-    \typeout{** WARNING: \string\IEEEsettopmargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
-  \fi
-\fi
-% handle each mode
-\if\@IEEEextractedtoken a\relax
-  \advance\topmargin by \@IEEEtrantmpdimenA\relax
-\else
-\if\@IEEEextractedtoken q\relax
-  % we need to adjust by half the \IEEEquantizedtextheightdiff value
-  \@IEEEtrantmpdimenB\IEEEquantizedtextheightdiff\relax
-  \divide\@IEEEtrantmpdimenB by 2\relax
-  % a positive \IEEEquantizedtextheightdiff means we need to reduce \topmargin
-  % because \textheight has been lenghtened
-  \advance\topmargin by -\@IEEEtrantmpdimenB\relax
-  \advance\topmargin by \@IEEEtrantmpdimenA\relax
-\else
-\if\@IEEEextractedtoken c\relax
-  \topmargin\paperheight
-  \advance\topmargin by -\textheight
-  % \textheight includes \topskip, but we should not count topskip whitespace here, backout
-  \advance \topmargin by \topskip
-  \settoheight{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance\topmargin by -\@IEEEtrantmpdimenB\relax
-  \settodepth{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance\topmargin by -\@IEEEtrantmpdimenB\relax
-  \divide\topmargin by 2\relax
-  \advance\topmargin by \@IEEEtrantmpdimenA\relax
-\else
-\if\@IEEEextractedtoken b\relax
-  \topmargin\paperheight
-  \advance\topmargin by -\textheight
-  % \textheight includes \topskip, but we should not count topskip whitespace here, backout
-  \advance \topmargin by \topskip
-  \settodepth{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance\topmargin by -\@IEEEtrantmpdimenB\relax
-  \advance\topmargin by -\@IEEEtrantmpdimenA\relax
-\else
-  \if\@IEEEextractedtoken t\relax
-  \else
-    \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsettopmargin\space (line \the\inputlineno).\MessageBreak
-    Defaulting to `t'}%
-    {Valid modes for \string\IEEEsettopmargin\space are: t, b, c, a and q.}\relax
-  \fi
-  \topmargin\@IEEEtrantmpdimenA\relax
-  \settoheight{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance\topmargin by \@IEEEtrantmpdimenB\relax
-\fi\fi % if t, b, c
-% convert desired top margin into actual \topmargin
-% this is not done for the q or a modes because they are only adjustments
-\advance \topmargin by -\topskip
-\advance \topmargin by -1in
-\advance \topmargin by -\headheight
-\advance \topmargin by -\headsep
-\fi\fi % if q, a
-}
-
-
-
-% usage: \IEEEsetheadermargin[header sample][text sample]{mode: t, b, c, a}{margin/offset}
-% Differentially adjusts \topmargin and \headsep (such that their sum is unchanged)
-% based on the specified header margin.
-% Takes into consideration the base 1in offset, \headheight, \topskip, and (by default)
-% the actual height (or depth) of the \IEEEdefaultheadersampletext and
-% \IEEEdefaultsampletext text.
-% The available modes are:
-% t = top margin (top of the header text to the top of the page)
-% b = bottom margin (bottom of the header text to the top of the main text)
-% c = vertically centered between the main text and the top of the page,
-%     with the given offset
-% a = adjust the vertical position using the given offset
-% For the offsets, positive values move the header downward.
-% \headheight, \headsep, \topskip and \topmargin should be set properly before
-% calling this function.
-\def\IEEEsetheadermargin{\@ifnextchar [{\@IEEEsetheadermargin}{\@IEEEsetheadermargin[\IEEEdefaultheadersampletext]}}
-\def\@IEEEsetheadermargin[#1]{\@ifnextchar [{\@@IEEEsetheadermargin[#1]}{\@@IEEEsetheadermargin[#1][\IEEEdefaultsampletext]}}
-\def\@@IEEEsetheadermargin[#1][#2]#3#4{\@IEEEtrantmpdimenA #4\relax
-\@IEEEextracttoken{#3}\relax
-% check for mode errors
-\ifx\@IEEEextractedtokenmacro\@empty
-  \@IEEEclspkgerror{Empty mode type in \string\IEEEsetheadermargin\space (line \the\inputlineno).\MessageBreak
-  Defaulting to `t'}{Valid modes for \string\IEEEsetheadermargin\space are: t, b, c, and a.}\relax
-  \let\@IEEEextractedtoken=t\relax
-  \def\@IEEEextractedtokenmacro{t}\relax
-\else
-  \ifx\@IEEEextractedtokensdiscarded\@empty\else
-    \typeout{** WARNING: \string\IEEEsetheadermargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
-  \fi
-\fi
-% handle each mode
-\if\@IEEEextractedtoken a\relax
-  % No need to do anything here and can pass through the adjustment
-  % value as is. The end adjustment of \topmargin and \headsep will
-  % do all that is needed
-\else
-\if\@IEEEextractedtoken c\relax
-  % get the bottom margin
-  \@IEEEtrantmpdimenB\headsep\relax
-  \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
-  \advance\@IEEEtrantmpdimenB by \topskip
-  \settoheight{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax
-  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
-  % at this point \@IEEEtrantmpdimenB has the actual header bottom margin
-  % subtract from it the top header margin
-  \advance\@IEEEtrantmpdimenB -1in\relax % take into consideration the system 1in offset of the top margin
-  \advance\@IEEEtrantmpdimenB by -\topmargin
-  \advance\@IEEEtrantmpdimenB by -\headheight
-  \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance\@IEEEtrantmpdimenB by \@IEEEtrantmpdimenC
-  % at this point \@IEEEtrantmpdimenB has the difference between the bottom and top margins
-  % we need to adjust by half this amount to center the header
-  \divide\@IEEEtrantmpdimenB by 2\relax
-  % and add to offset
-  \advance\@IEEEtrantmpdimenA by \@IEEEtrantmpdimenB
-\else
-\if\@IEEEextractedtoken b\relax
-  \@IEEEtrantmpdimenB\headsep\relax
-  \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
-  \advance\@IEEEtrantmpdimenB by \topskip
-  \settoheight{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax
-  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
-  % at this point \@IEEEtrantmpdimenB has the actual header bottom margin
-  % get the difference between the actual and the desired
-  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenA
-  \@IEEEtrantmpdimenA\@IEEEtrantmpdimenB
-\else
-  \if\@IEEEextractedtoken t\relax
-  \else
-    \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsetheadermargin\space (line \the\inputlineno).\MessageBreak
-    Defaulting to `t'}%
-    {Valid modes for \string\IEEEsetheadermargin\space are: t, b, c and a.}\relax
-  \fi
-  \@IEEEtrantmpdimenB 1in\relax % take into consideration the system 1in offset of the top margin
-  \advance\@IEEEtrantmpdimenB by \topmargin
-  \advance\@IEEEtrantmpdimenB by \headheight
-  \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
-  % at this point \@IEEEtrantmpdimenB has the actual header top margin
-  % get the difference between the desired and the actual
-  \advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB
-\fi\fi % if t, b, c
-\fi % if a
-% advance \topmargin by the needed amount and reduce \headsep by the same
-% so as not to disturb the location of the main text
-\advance\topmargin by \@IEEEtrantmpdimenA\relax
-\advance\headsep by -\@IEEEtrantmpdimenA\relax
-}
-
-
-
-% usage: \IEEEsetfootermargin[footer sample][text sample]{mode: t, b, c, a}{margin/offset}
-% Adjusts \footskip based on the specified footer margin.
-% Takes into consideration the base 1in offset, \paperheight, \headheight,
-% \headsep, \textheight and (by default) the actual height (or depth) of the
-% \IEEEdefaultfootersampletext and \IEEEdefaultsampletext text.
-% The available modes are:
-% t = top margin (top of the footer text to the bottom of the main text)
-% b = bottom margin (bottom of the footer text to the bottom of page)
-% c = vertically centered between the main text and the bottom of the page,
-%     with the given offset
-% a = adjust the vertical position using the given offset
-% For the offsets, positive values move the footer downward.
-% \headheight, \headsep, \topskip, \topmargin, and \textheight should be set
-% properly before calling this function.
-\def\IEEEsetfootermargin{\@ifnextchar [{\@IEEEsetfootermargin}{\@IEEEsetfootermargin[\IEEEdefaultfootersampletext]}}
-\def\@IEEEsetfootermargin[#1]{\@ifnextchar [{\@@IEEEsetfootermargin[#1]}{\@@IEEEsetfootermargin[#1][\IEEEdefaultsampletext]}}
-\def\@@IEEEsetfootermargin[#1][#2]#3#4{\@IEEEtrantmpdimenA #4\relax
-\@IEEEextracttoken{#3}\relax
-% check for mode errors
-\ifx\@IEEEextractedtokenmacro\@empty
-  \@IEEEclspkgerror{Empty mode type in \string\IEEEsetfootermargin\space (line \the\inputlineno).\MessageBreak
-  Defaulting to `t'}{Valid modes for \string\IEEEsetfootermargin\space are: t, b, c, and a.}\relax
-  \let\@IEEEextractedtoken=t\relax
-  \def\@IEEEextractedtokenmacro{t}\relax
-\else
-  \ifx\@IEEEextractedtokensdiscarded\@empty\else
-    \typeout{** WARNING: \string\IEEEsetfootermargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
-  \fi
-\fi
-% handle each mode
-\if\@IEEEextractedtoken a\relax
-  % No need to do anything here and can pass through the adjustment
-  % value as is. The end adjustment of \footskip will do all that
-  % is needed
-\else
-\if\@IEEEextractedtoken c\relax
-  % calculate the bottom margin
-  \@IEEEtrantmpdimenB 1in\relax % system 1in offset
-  \advance\@IEEEtrantmpdimenB\topmargin\relax
-  \advance\@IEEEtrantmpdimenB\headheight\relax
-  \advance\@IEEEtrantmpdimenB\headsep\relax
-  \advance\@IEEEtrantmpdimenB\textheight\relax
-  \advance\@IEEEtrantmpdimenB\footskip\relax
-  \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance\@IEEEtrantmpdimenC by \@IEEEtrantmpdimenB
-  \@IEEEtrantmpdimenB\paperheight
-  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
-  % at this point \@IEEEtrantmpdimenB has the actual footer bottom margin
-  % now subtract off the footer top margin
-  \advance\@IEEEtrantmpdimenB -\footskip\relax
-  \settodepth{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax
-  \advance\@IEEEtrantmpdimenB by \@IEEEtrantmpdimenC
-  \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance\@IEEEtrantmpdimenB by \@IEEEtrantmpdimenC
-  % at this point \@IEEEtrantmpdimenB has the difference between the bottom
-  % and top footer margins
-  % our adjustment must be half this value to center the footer
-  \divide\@IEEEtrantmpdimenB by 2\relax
-  % add to the offset
-  \advance\@IEEEtrantmpdimenA by \@IEEEtrantmpdimenB
-\else
-\if\@IEEEextractedtoken b\relax
-  % calculate the bottom margin
-  \@IEEEtrantmpdimenB 1in\relax % system 1in offset
-  \advance\@IEEEtrantmpdimenB\topmargin\relax
-  \advance\@IEEEtrantmpdimenB\headheight\relax
-  \advance\@IEEEtrantmpdimenB\headsep\relax
-  \advance\@IEEEtrantmpdimenB\textheight\relax
-  \advance\@IEEEtrantmpdimenB\footskip\relax
-  \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance\@IEEEtrantmpdimenC by \@IEEEtrantmpdimenB
-  \@IEEEtrantmpdimenB\paperheight
-  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
-  % at this point \@IEEEtrantmpdimenB has the actual footer bottom margin
-  % get the difference between the actual and the desired
-  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenA
-  \@IEEEtrantmpdimenA\@IEEEtrantmpdimenB
-\else
-  \if\@IEEEextractedtoken t\relax
-  \else
-    \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsetfootermargin\space (line \the\inputlineno).\MessageBreak
-    Defaulting to `t'}%
-    {Valid modes for \string\IEEEsetfootermargin\space are: t, b, c and a.}\relax
-  \fi
-  \@IEEEtrantmpdimenB\footskip\relax
-  \settodepth{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax
-  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
-  \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
-  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
-  % at this point \@IEEEtrantmpdimenB has the actual footer top margin
-  % get the difference between the desired and the actual
-  \advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB
-\fi\fi % if t, b, c
-\fi % if a
-% advance \footskip by the needed amount
-\advance\footskip by \@IEEEtrantmpdimenA\relax
-}
-
-% -- End V1.8a page setup commands --
-
-
-
-
-
-% V1.6
-% LaTeX is a little to quick to use hyphenations
-% So, we increase the penalty for their use and raise
-% the badness level that triggers an underfull hbox
-% warning. The author may still have to tweak things,
-% but the appearance will be much better "right out
-% of the box" than that under V1.5 and prior.
-% TeX default is 50
-\hyphenpenalty=750
-\ifCLASSOPTIONcompsoc
-\hyphenpenalty 500
-\fi
-% If we didn't adjust the interword spacing, 2200 might be better.
-% The TeX default is 1000
-\hbadness=1350
-% The IEEE does not use extra spacing after punctuation
-\frenchspacing
-
-% V1.7 increase this a tad to discourage equation breaks
-\binoppenalty=1000 % default 700
-\relpenalty=800     % default 500
-
-% v1.8a increase these to discourage widows and orphans
-\clubpenalty=1000          % default 150
-\widowpenalty=1000         % default 150
-\displaywidowpenalty=1000 % default  50
-
-
-% margin note stuff
-\marginparsep      10pt
-\marginparwidth    20pt
-\marginparpush     25pt
-
-
-% if things get too close, go ahead and let them touch
-\lineskip            0pt
-\normallineskip      0pt
-\lineskiplimit       0pt
-\normallineskiplimit 0pt
-
-% The distance from the lower edge of the text body to the
-% footline
-\footskip 0.4in
-
-% normally zero, should be relative to font height.
-% put in a little rubber to help stop some bad breaks (underfull vboxes)
-\parskip 0ex plus 0.2ex minus 0.1ex
-
-\parindent    1.0em
-\ifCLASSOPTIONcompsoc
-  \parindent    1.5em
-\fi
-
-\headheight   12pt
-\headsep      18pt
-% use the normal font baselineskip
-% so that \topskip is unaffected by changes in \baselinestretch
-\topskip=\@IEEEnormalsizeunitybaselineskip
-
-
-% V1.8 \maxdepth defaults to 4pt, but should be font size dependent
-\maxdepth=0.5\@IEEEnormalsizeunitybaselineskip
-\textheight       58pc  % 9.63in, 696pt
-
-% set the default top margin to 58pt
-% which results in a \topmargin of -49.59pt for 10pt documents
-\IEEEsettopmargin{t}{58pt}
-% tweak textheight to a perfect integer number of lines/column.
-% standard is: 9pt/63 lpc; 10pt/58 lpc; 11pt/52 lpc; 12pt/50 lpc
-\IEEEquantizetextheight{c}
-% tweak top margin so that the error is shared equally at the top and bottom
-\IEEEsettopmargin{q}{0sp}
-
-
-\columnsep         1pc
-\textwidth        43pc   % 2 x 21pc + 1pc = 43pc
-
-% set the default side margins to center the text
-\IEEEsetsidemargin{c}{0pt}
-
-
-% adjust margins for default conference mode
-\ifCLASSOPTIONconference
- \textheight        9.25in % The standard for conferences (668.4975pt)
- \IEEEsettopmargin{t}{0.75in}
- % tweak textheight to a perfect integer number of lines/page.
- % standard is: 9pt/61 lpc; 10pt/56 lpc; 11pt/50 lpc; 12pt/48 lpc
- \IEEEquantizetextheight{c}
- % tweak top margin so that the error is shared equally at the top and bottom
- \IEEEsettopmargin{q}{0sp}
-\fi
-
-
-% compsoc text sizes, margins and spacings
-\ifCLASSOPTIONcompsoc
- \columnsep         12bp
- % CS specs for \textwdith are 6.875in
- % \textwidth         6.875in
- % however, measurements from proofs show they are using 3.5in columns
- \textwidth         7in
- \advance\textwidth by \columnsep
- % set the side margins to center the text
- \IEEEsetsidemargin{c}{0pt}
- % top/bottom margins to center
- % could just set \textheight to 9.75in for all the different paper sizes
- % and then quantize, but we'll do it the long way here to allow for easy
- % future per-paper size adjustments
- \IEEEsettextheight{0.625in}{0.625in}% 11in - 2 * 0.625in = 9.75in is the standard text height for compsoc journals
- \IEEEsettopmargin{t}{0.625in}
- \if@IEEEusingcspaper
-   \IEEEsettextheight{0.5in}{0.5in}% 10.75in - 2 * 0.5in = 9.75in
-   \IEEEsettopmargin{t}{0.5in}
- \fi
- \if@IEEEusingAfourpaper
-   \IEEEsettextheight{24.675mm}{24.675mm}% 297mm - 2 * 24.675mm = 247.650mm (9.75in)
-   \IEEEsettopmargin{t}{24.675mm}
- \fi
- % tweak textheight to a perfect integer number of lines/page.
- % standard is: 9pt/65 lpc; 10pt/61 lpc; 11pt/53 lpc; 12pt/49 lpc
- \IEEEquantizetextheight{c}
- % tweak top margin so that the error is shared equally at the top and bottom
- \IEEEsettopmargin{q}{0sp}
-
-% compsoc conference
- \ifCLASSOPTIONconference
-  % compsoc conference use a larger value for columnsep
-  \columnsep 0.25in
-  \IEEEsettextwidth{0.75in}{0.75in}
-  % set the side margins to center the text (0.75in for letterpaper)
-  \IEEEsetsidemargin{c}{0pt}
-  % compsoc conferences want 1in top and bottom margin
-  \IEEEsettextheight{1in}{1in}
-  \IEEEsettopmargin{t}{1in}
-  % tweak textheight to a perfect integer number of lines/page.
-  % standard is: 9pt/58 lpc; 10pt/53 lpc; 11pt/48 lpc; 12pt/46 lpc
-  \IEEEquantizetextheight{c}
-  % tweak top margin so that the error is shared equally at the top and bottom
-  \IEEEsettopmargin{q}{0sp}
- \fi
-\fi
-
-
-
-% draft mode settings override that of all other modes
-% provides a nice 1in margin all around the paper and extra
-% space between the lines for editor's comments
-\ifCLASSOPTIONdraftcls
-  % we want 1in side margins regardless of paper type
-  \IEEEsettextwidth{1in}{1in}
-  \IEEEsetsidemargin{c}{0pt}
-  % want 1in top and bottom margins
-  \IEEEsettextheight{1in}{1in}
-  \IEEEsettopmargin{t}{1in}
-  % digitize textheight to be an integer number of lines.
-  % this may cause the top and bottom margins to be off a tad
-  \IEEEquantizetextheight{c}
-  % tweak top margin so that the error is shared equally at the top and bottom
-  \IEEEsettopmargin{q}{0sp}
-\fi
-
-
-
-% process CLASSINPUT inner/outer margin
-% if inner margin defined, but outer margin not, set outer to inner.
-\ifx\CLASSINPUTinnersidemargin\@IEEEundefined
-\else
-  \ifx\CLASSINPUToutersidemargin\@IEEEundefined
-    \edef\CLASSINPUToutersidemargin{\CLASSINPUTinnersidemargin}
-  \fi
-\fi
-
-\ifx\CLASSINPUToutersidemargin\@IEEEundefined
-\else
-  % if outer margin defined, but inner margin not, set inner to outer.
-  \ifx\CLASSINPUTinnersidemargin\@IEEEundefined
-    \edef\CLASSINPUTinnersidemargin{\CLASSINPUToutersidemargin}
-  \fi
-  \IEEEsettextwidth{\CLASSINPUTinnersidemargin}{\CLASSINPUToutersidemargin}
-  \IEEEsetsidemargin{i}{\CLASSINPUTinnersidemargin}
-  \typeout{** ATTENTION: Overriding inner side margin to \CLASSINPUTinnersidemargin\space and 
-           outer side margin to \CLASSINPUToutersidemargin\space via \string\CLASSINPUT.}
-\fi
-
-
-
-% process CLASSINPUT top/bottom text margin
-% if toptext margin defined, but bottomtext margin not, set bottomtext to toptext margin
-\ifx\CLASSINPUTtoptextmargin\@IEEEundefined
-\else
-  \ifx\CLASSINPUTbottomtextmargin\@IEEEundefined
-    \edef\CLASSINPUTbottomtextmargin{\CLASSINPUTtoptextmargin}
-  \fi
-\fi
-
-\ifx\CLASSINPUTbottomtextmargin\@IEEEundefined
-\else
-  % if bottomtext margin defined, but toptext margin not, set toptext to bottomtext margin
-  \ifx\CLASSINPUTtoptextmargin\@IEEEundefined
-    \edef\CLASSINPUTtoptextmargin{\CLASSINPUTbottomtextmargin}
-  \fi
-  \IEEEsettextheight{\CLASSINPUTtoptextmargin}{\CLASSINPUTbottomtextmargin}
-  \IEEEsettopmargin{t}{\CLASSINPUTtoptextmargin}
-  \typeout{** ATTENTION: Overriding top text margin to \CLASSINPUTtoptextmargin\space and 
-           bottom text margin to \CLASSINPUTbottomtextmargin\space via \string\CLASSINPUT.}
-\fi
-
-
-
-% default to center header and footer text in the margins
-\IEEEsetheadermargin{c}{0pt}
-\IEEEsetfootermargin{c}{0pt}
-
-% adjust header and footer positions for compsoc journals
-\ifCLASSOPTIONcompsoc
-  \ifCLASSOPTIONjournal
-    \IEEEsetheadermargin{b}{\@IEEEnormalsizeunitybaselineskip}
-    \IEEEsetfootermargin{t}{\@IEEEnormalsizeunitybaselineskip}
-  \fi
-\fi
-
-
-% V1.8a display lines per column info message on user's console
-\def\IEEEdisplayinfolinespercolumn{\@IEEEtrantmpdimenA=\textheight
-% topskip represents only one line even if > baselineskip
-\advance\@IEEEtrantmpdimenA by -1\topskip
-\@IEEEtrantmpcountA=\@IEEEtrantmpdimenA
-\@IEEEtrantmpcountB=\@IEEEtrantmpdimenA
-\divide\@IEEEtrantmpcountB by \baselineskip
-% need to add one line to include topskip (first) line
-\advance\@IEEEtrantmpcountB by 1
-% save lines per column value as text
-\edef\@IEEEnumlinespercolumninfotxt{\the\@IEEEtrantmpcountB}
-% backout topskip advance to allow direct \@IEEEtrantmpcountA comparison
-\advance\@IEEEtrantmpcountB by -1
-% restore value as text height (without topskip) rather than just as number of lines
-\multiply\@IEEEtrantmpcountB by \baselineskip
-% is the column height an integer number of lines per column?
-\ifnum\@IEEEtrantmpcountA=\@IEEEtrantmpcountB
-\edef\@IEEEnumlinespercolumnexactinfotxt{exact}
-\else
-\@IEEEtrantmpdimenA\@IEEEtrantmpcountA sp\relax
-\advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpcountB sp\relax
-\edef\@IEEEnumlinespercolumnexactinfotxt{approximate, difference = \the\@IEEEtrantmpdimenA}
-\fi
-\typeout{-- Lines per column: \@IEEEnumlinespercolumninfotxt\space (\@IEEEnumlinespercolumnexactinfotxt).}}
-% delay execution till start of document to allow for user changes
-\AtBeginDocument{\IEEEdisplayinfolinespercolumn}
-
-
-
-% LIST SPACING CONTROLS
-
-% Controls the amount of EXTRA spacing
-% above and below \trivlist 
-% Both \list and IED lists override this.
-% However, \trivlist will use this as will most
-% things built from \trivlist like the \center
-% environment.
-\topsep           0.5\baselineskip
-
-% Controls the additional spacing around lists preceded
-% or followed by blank lines. the IEEE does not increase
-% spacing before or after paragraphs so it is set to zero.
-% \z@ is the same as zero, but faster.
-\partopsep          \z@
-
-% Controls the spacing between paragraphs in lists. 
-% The IEEE does not increase spacing before or after paragraphs
-% so this is also zero. 
-% With IEEEtran.cls, global changes to
-% this value DO affect lists (but not IED lists).
-\parsep             \z@
-
-% Controls the extra spacing between list items. 
-% The IEEE does not put extra spacing between items.
-% With IEEEtran.cls, global changes to this value DO affect
-% lists (but not IED lists).
-\itemsep            \z@
-
-% \itemindent is the amount to indent the FIRST line of a list
-% item. It is auto set to zero within the \list environment. To alter
-% it, you have to do so when you call the \list.
-% However, the IEEE uses this for the theorem environment
-% There is an alternative value for this near \leftmargini below
-\itemindent         -1em
-
-% \leftmargin, the spacing from the left margin of the main text to
-% the left of the main body of a list item is set by \list.
-% Hence this statement does nothing for lists.
-% But, quote and verse do use it for indention.
-\leftmargin         2em
-
-% we retain this stuff from the older IEEEtran.cls so that \list
-% will work the same way as before. However, itemize, enumerate and
-% description (IED) could care less about what these are as they
-% all are overridden.
-\leftmargini        2em
-%\itemindent         2em  % Alternative values: sometimes used.
-%\leftmargini        0em
-\leftmarginii       1em
-\leftmarginiii    1.5em
-\leftmarginiv     1.5em
-\leftmarginv      1.0em
-\leftmarginvi     1.0em
-\labelsep         0.5em 
-\labelwidth         \z@
-
-
-% The old IEEEtran.cls behavior of \list is retained.
-% However, the new V1.3 IED list environments override all the
-% @list stuff (\@listX is called within \list for the
-% appropriate level just before the user's list_decl is called). 
-% \topsep is now 2pt as the IEEE puts a little extra space around
-% lists - used by those non-IED macros that depend on \list.
-% Note that \parsep and \itemsep are not redefined as in 
-% the sizexx.clo \@listX (which article.cls uses) so global changes
-% of these values DO affect \list
-% 
-\def\@listi{\leftmargin\leftmargini \topsep 2pt plus 1pt minus 1pt}
-\let\@listI\@listi
-\def\@listii{\leftmargin\leftmarginii\labelwidth\leftmarginii%
-    \advance\labelwidth-\labelsep \topsep 2pt}
-\def\@listiii{\leftmargin\leftmarginiii\labelwidth\leftmarginiii%
-    \advance\labelwidth-\labelsep \topsep 2pt}
-\def\@listiv{\leftmargin\leftmarginiv\labelwidth\leftmarginiv%
-    \advance\labelwidth-\labelsep \topsep 2pt}
-\def\@listv{\leftmargin\leftmarginv\labelwidth\leftmarginv%
-    \advance\labelwidth-\labelsep \topsep 2pt}
-\def\@listvi{\leftmargin\leftmarginvi\labelwidth\leftmarginvi%
-    \advance\labelwidth-\labelsep \topsep 2pt}
-
-
-% The IEEE uses 5) not 5.
-\def\labelenumi{\theenumi)}     \def\theenumi{\arabic{enumi}}
-
-% The IEEE uses a) not (a)
-\def\labelenumii{\theenumii)}  \def\theenumii{\alph{enumii}}
-
-% The IEEE uses iii) not iii.
-\def\labelenumiii{\theenumiii)} \def\theenumiii{\roman{enumiii}}
-
-% The IEEE uses A) not A.
-\def\labelenumiv{\theenumiv)}   \def\theenumiv{\Alph{enumiv}}
-
-% exactly the same as in article.cls
-\def\p@enumii{\theenumi}
-\def\p@enumiii{\theenumi(\theenumii)}
-\def\p@enumiv{\p@enumiii\theenumiii}
-
-% itemized list label styles
-\def\labelitemi{$\scriptstyle\bullet$}
-\def\labelitemii{\textbf{--}}
-\def\labelitemiii{$\ast$}
-\def\labelitemiv{$\cdot$}
-
-
-
-% **** V1.3 ENHANCEMENTS ****
-% Itemize, Enumerate and Description (IED) List Controls
-% ***************************
-% 
-% 
-% The IEEE seems to use at least two different values by
-% which ITEMIZED list labels are indented to the right
-% For The Journal of Lightwave Technology (JLT) and The Journal
-% on Selected Areas in Communications (JSAC), they tend to use
-% an indention equal to \parindent. For Transactions on Communications
-% they tend to indent ITEMIZED lists a little more--- 1.3\parindent.
-% We'll provide both values here for you so that you can choose 
-% which one you like in your document using a command such as:
-% setlength{\IEEEilabelindent}{\IEEEilabelindentB}
-\newdimen\IEEEilabelindentA
-\IEEEilabelindentA \parindent
-
-\newdimen\IEEEilabelindentB
-\IEEEilabelindentB 1.3\parindent
-% However, we'll default to using \parindent
-% which makes more sense to me
-\newdimen\IEEEilabelindent
-\IEEEilabelindent \IEEEilabelindentA
-
-
-% This controls the default amount the enumerated list labels
-% are indented to the right.
-% Normally, this is the same as the paragraph indention
-\newdimen\IEEEelabelindent
-\IEEEelabelindent \parindent
-
-% This controls the default amount the description list labels
-% are indented to the right.
-% Normally, this is the same as the paragraph indention
-\newdimen\IEEEdlabelindent
-\IEEEdlabelindent \parindent
-
-% This is the value actually used within the IED lists.
-% The IED environments automatically set its value to
-% one of the three values above, so global changes do 
-% not have any effect
-\newdimen\IEEElabelindent
-\IEEElabelindent \parindent
-
-% The actual amount labels will be indented is
-% \IEEElabelindent multiplied by the factor below
-% corresponding to the level of nesting depth
-% This provides a means by which the user can
-% alter the effective \IEEElabelindent for deeper
-% levels
-% There may not be such a thing as correct "standard IEEE"
-% values. What the IEEE actually does may depend on the specific
-% circumstances.
-% The first list level almost always has full indention.
-% The second levels I've seen have only 75% of the normal indentation
-% Three level or greater nestings are very rare. I am guessing
-% that they don't use any indentation.
-\def\IEEElabelindentfactori{1.0}   % almost always one
-\def\IEEElabelindentfactorii{0.75} % 0.0 or 1.0 may be used in some cases
-\def\IEEElabelindentfactoriii{0.0} % 0.75? 0.5? 0.0?
-\def\IEEElabelindentfactoriv{0.0}
-\def\IEEElabelindentfactorv{0.0}
-\def\IEEElabelindentfactorvi{0.0}
-
-% value actually used within IED lists, it is auto
-% set to one of the 6 values above
-% global changes here have no effect
-\def\IEEElabelindentfactor{1.0}
-
-% This controls the default spacing between the end of the IED
-% list labels and the list text, when normal text is used for
-% the labels.
-% compsoc uses a larger value here, but we'll set that later
-% in the class so that this code block area can be extracted
-% as-is for IEEEtrantools.sty
-\newdimen\IEEEiednormlabelsep
-\IEEEiednormlabelsep 0.6em
-
-% This controls the default spacing between the end of the IED
-% list labels and the list text, when math symbols are used for
-% the labels (nomenclature lists). The IEEE usually increases the 
-% spacing in these cases
-\newdimen\IEEEiedmathlabelsep
-\IEEEiedmathlabelsep 1.2em
-
-% This controls the extra vertical separation put above and
-% below each IED list. the IEEE usually puts a little extra spacing
-% around each list. However, this spacing is barely noticeable.
-% compsoc uses a larger value here, but we'll set that later
-% in the class so that this code block area can be extracted
-% as-is for IEEEtrantools.sty
-\newskip\IEEEiedtopsep
-\IEEEiedtopsep 2pt plus 1pt minus 1pt
-
-
-% This command is executed within each IED list environment
-% at the beginning of the list. You can use this to set the 
-% parameters for some/all your IED list(s) without disturbing 
-% global parameters that affect things other than lists.
-% i.e., renewcommand{\IEEEiedlistdecl}{\setlength{\labelsep}{5em}}
-% will alter the \labelsep for the next list(s) until 
-% \IEEEiedlistdecl is redefined. 
-\def\IEEEiedlistdecl{\relax}
-
-% This command provides an easy way to set \leftmargin based
-% on the \labelwidth, \labelsep and the argument \IEEElabelindent
-% Usage: \IEEEcalcleftmargin{width-to-indent-the-label}
-% output is in the \leftmargin variable, i.e., effectively:
-% \leftmargin = argument + \labelwidth + \labelsep
-% Note controlled spacing here, shield end of lines with %
-\def\IEEEcalcleftmargin#1{\setlength{\leftmargin}{#1}%
-\addtolength{\leftmargin}{\labelwidth}%
-\addtolength{\leftmargin}{\labelsep}}
-
-% This command provides an easy way to set \labelwidth to the
-% width of the given text. It is the same as
-% \settowidth{\labelwidth}{label-text}
-% and useful as a shorter alternative.
-% Typically used to set \labelwidth to be the width
-% of the longest label in the list
-\def\IEEEsetlabelwidth#1{\settowidth{\labelwidth}{#1}}
-
-% When this command is executed, IED lists will use the 
-% IEEEiedmathlabelsep label separation rather than the normal
-% spacing. To have an effect, this command must be executed via
-% the \IEEEiedlistdecl or within the option of the IED list
-% environments.
-\def\IEEEusemathlabelsep{\setlength{\labelsep}{\IEEEiedmathlabelsep}}
-
-% A flag which controls whether the IED lists automatically
-% calculate \leftmargin from \IEEElabelindent, \labelwidth and \labelsep
-% Useful if you want to specify your own \leftmargin
-% This flag must be set (\IEEEnocalcleftmargintrue or \IEEEnocalcleftmarginfalse) 
-% via the \IEEEiedlistdecl or within the option of the IED list
-% environments to have an effect.
-\newif\ifIEEEnocalcleftmargin
-\IEEEnocalcleftmarginfalse
-
-% A flag which controls whether \IEEElabelindent is multiplied by
-% the \IEEElabelindentfactor for each list level.
-% This flag must be set via the \IEEEiedlistdecl or within the option 
-% of the IED list environments to have an effect.
-\newif\ifIEEEnolabelindentfactor
-\IEEEnolabelindentfactorfalse
-
-
-% internal variable to indicate type of IED label
-% justification
-% 0 - left; 1 - center; 2 - right
-\def\@IEEEiedjustify{0}
-
-
-% commands to allow the user to control IED
-% label justifications. Use these commands within
-% the IED environment option or in the \IEEEiedlistdecl
-% Note that changing the normal list justifications
-% is nonstandard and the IEEE may not like it if you do so!
-% I include these commands as they may be helpful to
-% those who are using these enhanced list controls for
-% other non-IEEE related LaTeX work.
-% itemize and enumerate automatically default to right
-% justification, description defaults to left.
-\def\IEEEiedlabeljustifyl{\def\@IEEEiedjustify{0}}%left
-\def\IEEEiedlabeljustifyc{\def\@IEEEiedjustify{1}}%center
-\def\IEEEiedlabeljustifyr{\def\@IEEEiedjustify{2}}%right
-
-
-
-
-% commands to save to and restore from the list parameter copies
-% this allows us to set all the list parameters within
-% the list_decl and prevent \list (and its \@list) 
-% from overriding any of our parameters
-% V1.6 use \edefs instead of dimen's to conserve dimen registers
-% Note controlled spacing here, shield end of lines with %
-\def\@IEEEsavelistparams{\edef\@IEEEiedtopsep{\the\topsep}%
-\edef\@IEEEiedlabelwidth{\the\labelwidth}%
-\edef\@IEEEiedlabelsep{\the\labelsep}%
-\edef\@IEEEiedleftmargin{\the\leftmargin}%
-\edef\@IEEEiedpartopsep{\the\partopsep}%
-\edef\@IEEEiedparsep{\the\parsep}%
-\edef\@IEEEieditemsep{\the\itemsep}%
-\edef\@IEEEiedrightmargin{\the\rightmargin}%
-\edef\@IEEEiedlistparindent{\the\listparindent}%
-\edef\@IEEEieditemindent{\the\itemindent}}
-
-% Note controlled spacing here
-\def\@IEEErestorelistparams{\topsep\@IEEEiedtopsep\relax%
-\labelwidth\@IEEEiedlabelwidth\relax%
-\labelsep\@IEEEiedlabelsep\relax%
-\leftmargin\@IEEEiedleftmargin\relax%
-\partopsep\@IEEEiedpartopsep\relax%
-\parsep\@IEEEiedparsep\relax%
-\itemsep\@IEEEieditemsep\relax%
-\rightmargin\@IEEEiedrightmargin\relax%
-\listparindent\@IEEEiedlistparindent\relax%
-\itemindent\@IEEEieditemindent\relax}
-
-
-% v1.6b provide original LaTeX IED list environments
-% note that latex.ltx defines \itemize and \enumerate, but not \description
-% which must be created by the base classes
-% save original LaTeX itemize and enumerate
-\let\LaTeXitemize\itemize
-\let\endLaTeXitemize\enditemize
-\let\LaTeXenumerate\enumerate
-\let\endLaTeXenumerate\endenumerate
-
-% provide original LaTeX description environment from article.cls
-\newenvironment{LaTeXdescription}
-               {\list{}{\labelwidth\z@ \itemindent-\leftmargin
-                        \let\makelabel\descriptionlabel}}
-               {\endlist}
-\newcommand*\descriptionlabel[1]{\hspace\labelsep
-                                 \normalfont\bfseries #1}
-
-
-% override LaTeX's default IED lists
-\def\itemize{\@IEEEitemize}
-\def\enditemize{\@endIEEEitemize}
-\def\enumerate{\@IEEEenumerate}
-\def\endenumerate{\@endIEEEenumerate}
-\def\description{\@IEEEdescription}
-\def\enddescription{\@endIEEEdescription}
-
-% provide the user with aliases - may help those using packages that
-% override itemize, enumerate, or description
-\def\IEEEitemize{\@IEEEitemize}
-\def\endIEEEitemize{\@endIEEEitemize}
-\def\IEEEenumerate{\@IEEEenumerate}
-\def\endIEEEenumerate{\@endIEEEenumerate}
-\def\IEEEdescription{\@IEEEdescription}
-\def\endIEEEdescription{\@endIEEEdescription}
-
-
-% V1.6 we want to keep the IEEEtran IED list definitions as our own internal
-% commands so they are protected against redefinition
-\def\@IEEEitemize{\@ifnextchar[{\@@IEEEitemize}{\@@IEEEitemize[\relax]}}
-\def\@IEEEenumerate{\@ifnextchar[{\@@IEEEenumerate}{\@@IEEEenumerate[\relax]}}
-\def\@IEEEdescription{\@ifnextchar[{\@@IEEEdescription}{\@@IEEEdescription[\relax]}}
-\def\@endIEEEitemize{\endlist}
-\def\@endIEEEenumerate{\endlist}
-\def\@endIEEEdescription{\endlist}
-
-
-% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
-% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
-% IEEEtran itemized list MDS 1/2001
-% Note controlled spacing here, shield end of lines with %
-\def\@@IEEEitemize[#1]{%
-                \ifnum\@itemdepth>3\relax\@toodeep\else%
-                \ifnum\@listdepth>5\relax\@toodeep\else%
-                \advance\@itemdepth\@ne%
-                \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
-                % get the IEEElabelindentfactor for this level
-                \advance\@listdepth\@ne% we need to know what the level WILL be
-                \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
-                \advance\@listdepth-\@ne% undo our increment
-                \def\@IEEEiedjustify{2}% right justified labels are default
-                % set other defaults
-                \IEEEnocalcleftmarginfalse%
-                \IEEEnolabelindentfactorfalse%
-                \topsep\IEEEiedtopsep%
-                \IEEElabelindent\IEEEilabelindent%
-                \labelsep\IEEEiednormlabelsep%
-                \partopsep 0ex%
-                \parsep 0ex%
-                \itemsep 0ex%
-                \rightmargin 0em%
-                \listparindent 0em%
-                \itemindent 0em%
-                % calculate the label width
-                % the user can override this later if
-                % they specified a \labelwidth
-                \settowidth{\labelwidth}{\csname labelitem\romannumeral\the\@itemdepth\endcsname}%
-                \@IEEEsavelistparams% save our list parameters
-                \list{\csname\@itemitem\endcsname}{%
-                \@IEEErestorelistparams% override any list{} changes
-                                       % to our globals
-                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
-                \IEEEiedlistdecl% let user alter parameters
-                #1\relax%
-                % If the user has requested not to use the
-                % IEEElabelindent factor, don't revise \IEEElabelindent
-                \ifIEEEnolabelindentfactor\relax%
-                \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent%
-                \fi%
-                % Unless the user has requested otherwise,
-                % calculate our left margin based
-                % on \IEEElabelindent, \labelwidth and
-                % \labelsep
-                \ifIEEEnocalcleftmargin\relax%
-                \else\IEEEcalcleftmargin{\IEEElabelindent}%
-                \fi}\fi\fi}%
-
-
-% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
-% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
-% IEEEtran enumerate list MDS 1/2001
-% Note controlled spacing here, shield end of lines with %
-\def\@@IEEEenumerate[#1]{%
-                \ifnum\@enumdepth>3\relax\@toodeep\else%
-                \ifnum\@listdepth>5\relax\@toodeep\else%
-                \advance\@enumdepth\@ne%
-                \edef\@enumctr{enum\romannumeral\the\@enumdepth}%
-                % get the IEEElabelindentfactor for this level
-                \advance\@listdepth\@ne% we need to know what the level WILL be
-                \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
-                \advance\@listdepth-\@ne% undo our increment
-                \def\@IEEEiedjustify{2}% right justified labels are default
-                % set other defaults
-                \IEEEnocalcleftmarginfalse%
-                \IEEEnolabelindentfactorfalse%
-                \topsep\IEEEiedtopsep%
-                \IEEElabelindent\IEEEelabelindent%
-                \labelsep\IEEEiednormlabelsep%
-                \partopsep 0ex%
-                \parsep 0ex%
-                \itemsep 0ex%
-                \rightmargin 0em%
-                \listparindent 0em%
-                \itemindent 0em%
-                % calculate the label width
-                % We'll set it to the width suitable for all labels using
-                % normalfont 1) to 9)
-                % The user can override this later
-                \settowidth{\labelwidth}{9)}%
-                \@IEEEsavelistparams% save our list parameters
-                \list{\csname label\@enumctr\endcsname}{\usecounter{\@enumctr}%
-                \@IEEErestorelistparams% override any list{} changes
-                                       % to our globals
-                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
-                \IEEEiedlistdecl% let user alter parameters 
-                #1\relax%
-                % If the user has requested not to use the
-                % IEEElabelindent factor, don't revise \IEEElabelindent
-                \ifIEEEnolabelindentfactor\relax%
-                \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent%
-                \fi%
-                % Unless the user has requested otherwise,
-                % calculate our left margin based
-                % on \IEEElabelindent, \labelwidth and
-                % \labelsep
-                \ifIEEEnocalcleftmargin\relax%
-                \else\IEEEcalcleftmargin{\IEEElabelindent}%
-                \fi}\fi\fi}%
-
-
-% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
-% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
-% IEEEtran description list MDS 1/2001
-% Note controlled spacing here, shield end of lines with %
-\def\@@IEEEdescription[#1]{%
-                \ifnum\@listdepth>5\relax\@toodeep\else%
-                % get the IEEElabelindentfactor for this level
-                \advance\@listdepth\@ne% we need to know what the level WILL be
-                \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
-                \advance\@listdepth-\@ne% undo our increment
-                \def\@IEEEiedjustify{0}% left justified labels are default
-                % set other defaults
-                \IEEEnocalcleftmarginfalse%
-                \IEEEnolabelindentfactorfalse%
-                \topsep\IEEEiedtopsep% 
-                \IEEElabelindent\IEEEdlabelindent%
-                % assume normal labelsep
-                \labelsep\IEEEiednormlabelsep%
-                \partopsep 0ex%
-                \parsep 0ex%
-                \itemsep 0ex%
-                \rightmargin 0em%
-                \listparindent 0em%
-                \itemindent 0em%
-                % Bogus label width in case the user forgets
-                % to set it.
-                % TIP: If you want to see what a variable's width is you
-                % can use the TeX command \showthe\width-variable to 
-                % display it on the screen during compilation 
-                % (This might be helpful to know when you need to find out
-                % which label is the widest)
-                \settowidth{\labelwidth}{Hello}%
-                \@IEEEsavelistparams% save our list parameters
-                \list{}{\@IEEErestorelistparams% override any list{} changes
-                                               % to our globals
-                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
-                \IEEEiedlistdecl% let user alter parameters 
-                #1\relax%
-                % If the user has requested not to use the
-                % labelindent factor, don't revise \IEEElabelindent
-                \ifIEEEnolabelindentfactor\relax%
-                \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent%
-                \fi%
-                % Unless the user has requested otherwise,
-                % calculate our left margin based
-                % on \IEEElabelindent, \labelwidth and
-                % \labelsep
-                \ifIEEEnocalcleftmargin\relax%
-                \else\IEEEcalcleftmargin{\IEEElabelindent}\relax%
-                \fi}\fi}
-
-% v1.6b we use one makelabel that does justification as needed.
-\def\@IEEEiedmakelabel#1{\relax\if\@IEEEiedjustify 0\relax
-\makebox[\labelwidth][l]{\normalfont #1}\else
-\if\@IEEEiedjustify 1\relax
-\makebox[\labelwidth][c]{\normalfont #1}\else
-\makebox[\labelwidth][r]{\normalfont #1}\fi\fi}
-
-
-% compsoc uses a larger value for the normal labelsep
-% and also extra spacing above and below each list
-\ifCLASSOPTIONcompsoc
-  \IEEEiednormlabelsep 1.2em
-  \IEEEiedtopsep 6pt plus 3pt minus 3pt
-\fi
-
-
-% VERSE and QUOTE
-% V1.7 define environments with newenvironment
-\newenvironment{verse}{\let\\=\@centercr
-    \list{}{\itemsep\z@ \itemindent -1.5em \listparindent \itemindent
-    \rightmargin\leftmargin\advance\leftmargin 1.5em}\item\relax}
-    {\endlist}
-\newenvironment{quotation}{\list{}{\listparindent 1.5em \itemindent\listparindent
-    \rightmargin\leftmargin \parsep 0pt plus 1pt}\item\relax}
-    {\endlist}
-\newenvironment{quote}{\list{}{\rightmargin\leftmargin}\item\relax}
-    {\endlist}
-
-
-% \titlepage
-% provided only for backward compatibility. \maketitle is the correct
-% way to create the title page. 
-\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
-    \else \newpage \fi \thispagestyle{empty}\c@page\z@}
-\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}
-
-% standard values from article.cls
-\arraycolsep     5pt
-\arrayrulewidth .4pt
-\doublerulesep   2pt
-
-\tabcolsep       6pt
-\tabbingsep      0.5em
-
-
-%% FOOTNOTES
-%
-%\skip\footins 10pt plus 4pt minus 2pt
-% V1.6 respond to changes in font size
-% space added above the footnotes (if present)
-\skip\footins 0.9\baselineskip  plus 0.4\baselineskip  minus 0.2\baselineskip
-
-% V1.6, we need to make \footnotesep responsive to changes
-% in \baselineskip or strange spacings will result when in
-% draft mode. Here is a little LaTeX secret - \footnotesep
-% determines the height of an invisible strut that is placed
-% *above* the baseline of footnotes after the first. Since
-% LaTeX considers the space for characters to be 0.7\baselineskip
-% above the baseline and 0.3\baselineskip below it, we need to
-% use 0.7\baselineskip as a \footnotesep to maintain equal spacing
-% between all the lines of the footnotes. The IEEE often uses a tad
-% more, so use 0.8\baselineskip. This slightly larger value also helps
-% the text to clear the footnote marks. Note that \thanks in IEEEtran
-% uses its own value of \footnotesep which is set in \maketitle.
-{\footnotesize
-\global\footnotesep 0.8\baselineskip}
-
-
-\skip\@mpfootins = \skip\footins
-\fboxsep = 3pt
-\fboxrule = .4pt
-% V1.6 use 1em, then use LaTeX2e's \@makefnmark
-% Note that the IEEE normally *left* aligns the footnote marks, so we don't need
-% box resizing tricks here.
-\long\def\@makefntext#1{\parindent 1em\indent\hbox{\@makefnmark}#1}% V1.6 use 1em
-% V1.7 compsoc does not use superscipts for footnote marks
-\ifCLASSOPTIONcompsoc
-\def\@IEEEcompsocmakefnmark{\hbox{\normalfont\@thefnmark.\ }}
-\long\def\@makefntext#1{\parindent 1em\indent\hbox{\@IEEEcompsocmakefnmark}#1}
-\fi
-
-% The IEEE does not use footnote rules
-\def\footnoterule{}
-
-% V1.7 for compsoc, the IEEE uses a footnote rule only for \thanks. We devise a "one-shot"
-% system to implement this.
-\newif\if@IEEEenableoneshotfootnoterule
-\@IEEEenableoneshotfootnoterulefalse
-\ifCLASSOPTIONcompsoc
-\def\footnoterule{\relax\if@IEEEenableoneshotfootnoterule
-\kern-5pt
-\hbox to \columnwidth{\hfill\vrule width 0.5\columnwidth height 0.4pt\hfill}
-\kern4.6pt
-\global\@IEEEenableoneshotfootnoterulefalse
-\else
-\relax
-\fi}
-\fi
-
-% V1.6 do not allow LaTeX to break a footnote across multiple pages
-\interfootnotelinepenalty=10000
-
-% V1.6 discourage breaks within equations
-% Note that amsmath normally sets this to 10000,
-% but LaTeX2e normally uses 100.
-\interdisplaylinepenalty=2500
-
-% default allows section depth up to /paragraph
-\setcounter{secnumdepth}{4}
-
-% technotes do not allow /paragraph
-\ifCLASSOPTIONtechnote
-   \setcounter{secnumdepth}{3}
-\fi
-% neither do compsoc conferences
-\@IEEEcompsocconfonly{\setcounter{secnumdepth}{3}}
-
-
-\newcounter{section}
-\newcounter{subsection}[section]
-\newcounter{subsubsection}[subsection]
-\newcounter{paragraph}[subsubsection]
-
-% used only by IEEEtran's IEEEeqnarray as other packages may
-% have their own, different, implementations
-\newcounter{IEEEsubequation}[equation]
-
-% as shown when called by user from \ref, \label and in table of contents
-\def\theequation{\arabic{equation}}                          % 1
-\def\theIEEEsubequation{\theequation\alph{IEEEsubequation}}  % 1a (used only by IEEEtran's IEEEeqnarray)
-\ifCLASSOPTIONcompsoc
-% compsoc is all arabic
-\def\thesection{\arabic{section}}                
-\def\thesubsection{\thesection.\arabic{subsection}}
-\def\thesubsubsection{\thesubsection.\arabic{subsubsection}}
-\def\theparagraph{\thesubsubsection.\arabic{paragraph}}
-\else
-\def\thesection{\Roman{section}}                             % I
-% V1.7, \mbox prevents breaks around - 
-\def\thesubsection{\mbox{\thesection-\Alph{subsection}}}     % I-A
-% V1.7 use I-A1 format used by the IEEE rather than I-A.1
-\def\thesubsubsection{\thesubsection\arabic{subsubsection}}  % I-A1
-\def\theparagraph{\thesubsubsection\alph{paragraph}}         % I-A1a
-\fi
-
-% From Heiko Oberdiek. Because of the \mbox in \thesubsection, we need to
-% tell hyperref to disable the \mbox command when making PDF bookmarks.
-% This done already with hyperref.sty version 6.74o and later, but
-% it will not hurt to do it here again for users of older versions.
-\@ifundefined{pdfstringdefPreHook}{\let\pdfstringdefPreHook\@empty}{}%
-\g@addto@macro\pdfstringdefPreHook{\let\mbox\relax}
-
-
-% Main text forms (how shown in main text headings)
-% V1.6, using \thesection in \thesectiondis allows changes
-% in the former to automatically appear in the latter
-\ifCLASSOPTIONcompsoc
-  \ifCLASSOPTIONconference% compsoc conference
-    \def\thesectiondis{\thesection.}
-    \def\thesubsectiondis{\thesectiondis\arabic{subsection}.}
-    \def\thesubsubsectiondis{\thesubsectiondis\arabic{subsubsection}.}
-    \def\theparagraphdis{\thesubsubsectiondis\arabic{paragraph}.}
-  \else% compsoc not conferencs
-    \def\thesectiondis{\thesection}
-    \def\thesubsectiondis{\thesectiondis.\arabic{subsection}}
-    \def\thesubsubsectiondis{\thesubsectiondis.\arabic{subsubsection}}
-    \def\theparagraphdis{\thesubsubsectiondis.\arabic{paragraph}}
-  \fi
-\else% not compsoc
-  \def\thesectiondis{\thesection.}                   % I.
-  \def\thesubsectiondis{\Alph{subsection}.}          % B.
-  \def\thesubsubsectiondis{\arabic{subsubsection})}  % 3)
-  \def\theparagraphdis{\alph{paragraph})}            % d)
-\fi
-
-% just like LaTeX2e's \@eqnnum
-\def\theequationdis{{\normalfont \normalcolor (\theequation)}}% (1)
-% IEEEsubequation used only by IEEEtran's IEEEeqnarray
-\def\theIEEEsubequationdis{{\normalfont \normalcolor (\theIEEEsubequation)}}% (1a)
-% redirect LaTeX2e's equation number display and all that depend on
-% it, through IEEEtran's \theequationdis
-\def\@eqnnum{\theequationdis}
-
-
-
-% V1.7 provide string macros as article.cls does
-\def\contentsname{Contents}
-\def\listfigurename{List of Figures}
-\def\listtablename{List of Tables}
-\def\refname{References}
-\def\indexname{Index}
-\def\figurename{Fig.}
-\def\tablename{TABLE}
-\@IEEEcompsocconfonly{\def\figurename{Figure}}
-\def\partname{Part}
-\def\appendixname{Appendix}
-\def\abstractname{Abstract}
-% IEEE specific names
-\def\IEEEkeywordsname{Index Terms}
-\def\IEEEproofname{Proof}
-
-
-% LIST OF FIGURES AND TABLES AND TABLE OF CONTENTS
-%
-\def\@pnumwidth{1.55em}
-\def\@tocrmarg{2.55em}
-\def\@dotsep{4.5}
-\setcounter{tocdepth}{3}
-
-% adjusted some spacings here so that section numbers will not easily 
-% collide with the section titles. 
-% VIII; VIII-A; and VIII-A.1 are usually the worst offenders.
-% MDS 1/2001
-\def\tableofcontents{\section*{\contentsname}\@starttoc{toc}}
-\def\l@section#1#2{\addpenalty{\@secpenalty}\addvspace{1.0em plus 1pt}%
-    \@tempdima 2.75em \begingroup \parindent \z@ \rightskip \@pnumwidth%
-    \parfillskip-\@pnumwidth {\bfseries\leavevmode #1}\hfil\hbox to\@pnumwidth{\hss #2}\par%
-    \endgroup}
-% argument format #1:level, #2:labelindent,#3:labelsep
-\def\l@subsection{\@dottedtocline{2}{2.75em}{3.75em}}
-\def\l@subsubsection{\@dottedtocline{3}{6.5em}{4.5em}}
-% must provide \l@ defs for ALL sublevels EVEN if tocdepth
-% is such as they will not appear in the table of contents
-% these defs are how TOC knows what level these things are!
-\def\l@paragraph{\@dottedtocline{4}{6.5em}{5.5em}}
-\def\l@subparagraph{\@dottedtocline{5}{6.5em}{6.5em}}
-\def\listoffigures{\section*{\listfigurename}\@starttoc{lof}}
-\def\l@figure{\@dottedtocline{1}{0em}{2.75em}}
-\def\listoftables{\section*{\listtablename}\@starttoc{lot}}
-\let\l@table\l@figure
-
-
-% Definitions for floats
-%
-% Normal Floats
-% V1.8 floatsep et al. revised down by 0.15\baselineskip
-% to account for the sideeffects of \topskip compensation
-\floatsep 0.85\baselineskip plus  0.2\baselineskip minus  0.2\baselineskip
-\textfloatsep 1.55\baselineskip plus  0.2\baselineskip minus  0.4\baselineskip
-\@fptop 0pt plus 1fil
-\@fpsep 0.75\baselineskip plus 2fil
-\@fpbot 0pt plus 1fil
-\def\topfraction{0.9}
-\def\bottomfraction{0.4}
-\def\floatpagefraction{0.8}
-% V1.7, let top floats approach 90% of page
-\def\textfraction{0.1}
-
-% Double Column Floats
-\dblfloatsep 0.85\baselineskip plus  0.2\baselineskip minus  0.2\baselineskip
-
-\dbltextfloatsep 1.55\baselineskip plus  0.2\baselineskip minus  0.4\baselineskip
-% Note that it would be nice if the rubber here actually worked in LaTeX2e.
-% There is a long standing limitation in LaTeX, first discovered (to the best
-% of my knowledge) by Alan Jeffrey in 1992. LaTeX ignores the stretchable
-% portion of \dbltextfloatsep, and as a result, double column figures can and
-% do result in an non-integer number of lines in the main text columns with
-% underfull vbox errors as a consequence. A post to comp.text.tex
-% by Donald Arseneau confirms that this had not yet been fixed in 1998.
-% IEEEtran V1.6 will fix this problem for you in the titles, but it doesn't
-% protect you from other double floats. Happy vspace'ing.
-
-\@dblfptop 0pt plus 1fil
-\@dblfpsep 0.75\baselineskip plus 2fil
-\@dblfpbot 0pt plus 1fil
-\def\dbltopfraction{0.8}
-\def\dblfloatpagefraction{0.8}
-\setcounter{dbltopnumber}{4}
-
-\intextsep 0.85\baselineskip plus 0.2\baselineskip minus  0.2\baselineskip
-\setcounter{topnumber}{2}
-\setcounter{bottomnumber}{2}
-\setcounter{totalnumber}{4}
-
-
-
-% article class provides these, we should too.
-\newlength\abovecaptionskip
-\newlength\belowcaptionskip
-% but only \abovecaptionskip is used above figure captions and *below* table
-% captions
-\setlength\abovecaptionskip{0.5\baselineskip}
-% compsoc journals are a little more generous
-\ifCLASSOPTIONcompsoc\ifCLASSOPTIONjournal
-  \setlength\abovecaptionskip{0.75\baselineskip}
-\fi\fi
-\setlength\belowcaptionskip{0pt}
-% V1.6 create hooks in case the caption spacing ever needs to be
-% overridden by a user
-\def\@IEEEfigurecaptionsepspace{\vskip\abovecaptionskip\relax}%
-\def\@IEEEtablecaptionsepspace{\vskip\abovecaptionskip\relax}%
-
-
-% 1.6b revise caption system so that \@makecaption uses two arguments
-% as with LaTeX2e. Otherwise, there will be problems when using hyperref.
-\def\@IEEEtablestring{table}
-
-
-% V1.8 compensate for \topskip so top of top figures align with tops of the first lines of main text
-% here we calculate a space equal to the amount \topskip exceeds the main text height
-% we hook in at \@floatboxreset
-\def\@IEEEfiguretopskipspace{\ifdim\prevdepth=-1000pt\relax
-\setlength{\@IEEEtrantmpdimenA}{1\topskip}\relax
-\addtolength{\@IEEEtrantmpdimenA}{-0.7\@IEEEnormalsizeunitybaselineskip}\relax
-\vspace*{\@IEEEtrantmpdimenA}\fi}
-% V1.8 compensate for \topskip at the top of top tables so caption text is on main text baseline
-% use a strut set on the caption baseline within \@makecaption
-\def\@IEEEtabletopskipstrut{\ifdim\prevdepth=-1000pt\rule{0pt}{\topskip}\fi}
-% the \ifdim\prevdepth checks are always expected to be true for IEEE style float caption ordering
-% because top of figure content and top of captions in tables is the first thing on the vertical
-% list of these floats
-% thanks to Donald Arseneau for his 2000/11/11 post "Re: caption hacking" with info on this topic.
-
-
-\ifCLASSOPTIONcompsoc
-% V1.7 compsoc \@makecaption
-\ifCLASSOPTIONconference% compsoc conference
-\long\def\@makecaption#1#2{%
-% test if is a for a figure or table
-\ifx\@captype\@IEEEtablestring%
-% if a table, do table caption
-\footnotesize\bgroup\par\centering\@IEEEtabletopskipstrut{\normalfont\footnotesize {#1.}\nobreakspace\scshape #2}\par\addvspace{0.5\baselineskip}\egroup%
-\@IEEEtablecaptionsepspace
-% if not a table, format it as a figure
-\else
-\@IEEEfigurecaptionsepspace
-\setbox\@tempboxa\hbox{\normalfont\footnotesize {#1.}\nobreakspace #2}%
-\ifdim \wd\@tempboxa >\hsize%
-% if caption is longer than a line, let it wrap around
-\setbox\@tempboxa\hbox{\normalfont\footnotesize {#1.}\nobreakspace}%
-\parbox[t]{\hsize}{\normalfont\footnotesize \noindent\unhbox\@tempboxa#2}%
-% if caption is shorter than a line, center
-\else%
-\hbox to\hsize{\normalfont\footnotesize\hfil\box\@tempboxa\hfil}%
-\fi\fi}
-%
-\else% nonconference compsoc
-\long\def\@makecaption#1#2{%
-% test if is a for a figure or table
-\ifx\@captype\@IEEEtablestring%
-% if a table, do table caption
-\footnotesize\bgroup\par\centering\@IEEEtabletopskipstrut{\normalfont\sffamily\footnotesize #1}\\{\normalfont\sffamily\footnotesize #2}\par\addvspace{0.5\baselineskip}\egroup%
-\@IEEEtablecaptionsepspace
-% if not a table, format it as a figure
-\else
-\@IEEEfigurecaptionsepspace
-\setbox\@tempboxa\hbox{\normalfont\sffamily\footnotesize {#1.}\nobreakspace #2}%
-\ifdim \wd\@tempboxa >\hsize%
-% if caption is longer than a line, let it wrap around
-\setbox\@tempboxa\hbox{\normalfont\sffamily\footnotesize {#1.}\nobreakspace}%
-\parbox[t]{\hsize}{\normalfont\sffamily\footnotesize \noindent\unhbox\@tempboxa#2}%
-% if caption is shorter than a line, left justify
-\else%
-\hbox to\hsize{\normalfont\sffamily\footnotesize\box\@tempboxa\hfil}%
-\fi\fi}
-\fi
-%
-\else% traditional noncompsoc \@makecaption
-\long\def\@makecaption#1#2{%
-% test if is a for a figure or table
-\ifx\@captype\@IEEEtablestring%
-% if a table, do table caption
-\footnotesize\bgroup\par\centering\@IEEEtabletopskipstrut{\normalfont\footnotesize #1}\\{\normalfont\footnotesize\scshape #2}\par\addvspace{0.5\baselineskip}\egroup%
-\@IEEEtablecaptionsepspace
-% if not a table, format it as a figure
-\else
-\@IEEEfigurecaptionsepspace
-% 3/2001 use footnotesize, not small; use two nonbreaking spaces, not one
-\setbox\@tempboxa\hbox{\normalfont\footnotesize {#1.}\nobreakspace\nobreakspace #2}%
-\ifdim \wd\@tempboxa >\hsize%
-% if caption is longer than a line, let it wrap around
-\setbox\@tempboxa\hbox{\normalfont\footnotesize {#1.}\nobreakspace\nobreakspace}%
-\parbox[t]{\hsize}{\normalfont\footnotesize\noindent\unhbox\@tempboxa#2}%
-% if caption is shorter than a line, center if conference, left justify otherwise
-\else%
-\ifCLASSOPTIONconference \hbox to\hsize{\normalfont\footnotesize\hfil\box\@tempboxa\hfil}%
-\else \hbox to\hsize{\normalfont\footnotesize\box\@tempboxa\hfil}%
-\fi\fi\fi}
-\fi
-
-
-
-% V1.7 disable captions class option, do so in a way that retains operation of \label
-% within \caption
-\ifCLASSOPTIONcaptionsoff
-\long\def\@makecaption#1#2{\vspace*{2em}\footnotesize\bgroup\par\addvspace{0.5\baselineskip}\centering{\footnotesize #1}\par\addvspace{0.5\baselineskip}\egroup%
-\let\@IEEEtemporiglabeldefsave\label
-\let\@IEEEtemplabelargsave\relax
-\def\label##1{\gdef\@IEEEtemplabelargsave{##1}}%
-\setbox\@tempboxa\hbox{#2}%
-\let\label\@IEEEtemporiglabeldefsave
-\ifx\@IEEEtemplabelargsave\relax\else\label{\@IEEEtemplabelargsave}\fi}
-\fi
-
-
-% V1.7 define end environments with \def not \let so as to work OK with
-% preview-latex
-\newcounter{figure}
-\def\thefigure{\@arabic\c@figure}
-\def\fps@figure{tbp}
-\def\ftype@figure{1}
-\def\ext@figure{lof}
-\def\fnum@figure{\figurename\nobreakspace\thefigure}
-% V1.8 within figures add \@IEEEfiguretopskipspace compensation to LaTeX2e's \@floatboxreset
-\def\figure{\def\@floatboxreset{\reset@font\normalsize\@setminipage\@IEEEfiguretopskipspace}\@float{figure}}
-\def\endfigure{\end@float}
-% V1.8 also add \@IEEEfiguretopskipspace compensation to \figure*
-\@namedef{figure*}{\def\@floatboxreset{\reset@font\normalsize\@setminipage\@IEEEfiguretopskipspace}\@dblfloat{figure}}
-\@namedef{endfigure*}{\end@dblfloat}
-
-\newcounter{table}
-\ifCLASSOPTIONcompsoc
-\def\thetable{\arabic{table}}
-\else
-\def\thetable{\@Roman\c@table}
-\fi
-\def\fps@table{tbp}
-\def\ftype@table{2}
-\def\ext@table{lot}
-\def\fnum@table{\tablename\nobreakspace\thetable}
-% V1.6 The IEEE uses 8pt text for tables
-% within tables alter LaTeX2e's \@floatboxreset to use \footnotesize
-\def\table{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@float{table}}
-\def\endtable{\end@float}
-% v1.6b double column tables need to default to footnotesize as well.
-\@namedef{table*}{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@dblfloat{table}}
-\@namedef{endtable*}{\end@dblfloat}
-
-
-
-
-%% -- Command Argument Scanning Support Functions --
-%% V1.8a 
-
-% usage: \@IEEEstripouterbraces*{}
-% \@IEEEstripouterbraces fully expands its argument (which it then stores
-% in \@IEEEstripouterbracesarg) via \edef, then removes any outer enclosing
-% braces, and finally stores the result in the macro
-% \@IEEEstrippedouterbraces.
-%
-% For example:
-% \@IEEEstripouterbraces{{{{ab}c}}}
-% results in:
-%
-% \@IEEEstripouterbracesarg ==> a macro containing {{{ab}c}}
-% \@IEEEstrippedouterbraces ==> a macro containing {ab}c
-%
-% the *-star form,\@IEEEstripouterbraces*, does not expand the argument
-% contents during processing
-\def\@IEEEstripouterbraces{\@ifstar{\let\@IEEEstripouterbracesdef=\def\@@IEEEstripouterbraces}{\let\@IEEEstripouterbracesdef=\edef\@@IEEEstripouterbraces}}
-
-\def\@@IEEEstripouterbraces#1{\@IEEEstripouterbracesdef\@IEEEstripouterbracesarg{#1}\relax
-% If the macro is unchanged after being acquired as a single delimited
-% argument, we know we have one sequence of tokens without any enclosing
-% braces. Loop until this is true.
-\loop
-  \expandafter\@@@IEEEstripouterbraces\@IEEEstripouterbracesarg\@IEEEgeneralsequenceDELIMITER
-\ifx\@IEEEstrippedouterbraces\@IEEEstripouterbracesarg
-\else
-  \let\@IEEEstripouterbracesarg\@IEEEstrippedouterbraces
-\repeat}
-
-\def\@@@IEEEstripouterbraces#1\@IEEEgeneralsequenceDELIMITER{\def\@IEEEstrippedouterbraces{#1}}
-
-
-
-% usage: \@IEEEextractgroup*{}
-% \@IEEEextractgroup fully expands its argument (which it then stores in
-% \@IEEEextractgrouparg) via \edef and then assigns the first "brace group"
-% of tokens to the macro \@IEEEextractedgroup.
-% The remaining groups, if any, are stored in the macro
-% \@IEEEextractedgroupremain. If the argument does not contain the requisite
-% groups, the respective macros will be defined to be empty.
-% There is an asymmetry in that \@IEEEextractedgroup is stripped of its first
-% outer grouping while \@IEEEextractedgroupremain retains even the outer
-% grouping (if present) that originally identified it as a group.
-%
-% For example:
-% \@IEEEextractgroup{{{ab}}{c{de}}}
-% results in:
-%
-% \@IEEEextractgrouparg       ==> a macro containing {{ab}}{c{de}}
-% \@IEEEextractedgroup        ==> a macro containing {ab}
-% \@IEEEextractedgroupremain  ==> a macro containing {c{de}}
-%
-% The *-star form, \@IEEEextractgroup*, does not expand its argument
-% contents during processing.
-\def\@IEEEextractgroup{\@ifstar{\let\@IEEEextractgroupdef=\def\@@IEEEextractgroup}{\let\@IEEEextractgroupdef=\edef\@@IEEEextractgroup}}
-
-\def\@@IEEEextractgroup#1{\@IEEEextractgroupdef\@IEEEextractgrouparg{#1}\relax
-% trap the case of an empty extracted group as this would cause problems with
-% \@IEEEextractgroupremain's argument acquisition
-\ifx\@IEEEextractgrouparg\@empty
-  \def\@IEEEextractedgroup{}\relax
-  \def\@IEEEextractedgroupremain{}\relax
-\else
-  % We have to use some dirty tricks here. We want to insert {} around
-  % whatever remains after the first group so that TeX's argument scanner
-  % will preserve any originally enclosing braces as well as provide an
-  % empty argument to acquire even if there isn't a second group.
-  % In this first of two dirty tricks, we put a } at the end of the structure
-  % we are going to extract from. The \ifnum0=`{\fi keeps TeX happy to allow
-  % what would otherwise be an unbalanced macro definition for
-  % \@@IEEEextractgroup to be acceptable to it.
-  \ifnum0=`{\fi\expandafter\@IEEEextractgroupremain\@IEEEextractgrouparg}\relax
-\fi}
-
-% In the second part of the dirty tricks, we insert a leading { right after
-% the first group is acquired, but before the remainder is. Again, the
-% \ifnum0=`}\fi keeps TeX happy during definition time, but will disappear
-% during run time.
-\def\@IEEEextractgroupremain#1{\def\@IEEEextractedgroup{#1}\expandafter\@@IEEEextractgroupremain\expandafter{\ifnum0=`}\fi}
-
-\def\@@IEEEextractgroupremain#1{\def\@IEEEextractedgroupremain{#1}}
-
-
-
-% \@IEEEextracttoken relocated at top because margin setting commands rely on it
-
-
-
-% usage: \@IEEEextracttokengroups*{}
-% \@IEEEextracttokengroups fully expands its argument (which it then stores
-% in \@IEEEextracttokengroupsarg) and then assigns the first "brace group" of
-% tokens (with the outermost braces removed) to the macro
-% \@IEEEextractedfirstgroup.
-% The meaning of the first nonbrace (but including the empty group) token
-% within this first group is assigned via \let to \@IEEEextractedfirsttoken
-% as well as stored in the macro \@IEEEextractedfirsttokenmacro. If a first
-% nonbrace token does not exist (or is an empty group), these will be \relax
-% and empty, respectively.  Tokens that would otherwise be discarded during
-% the acquisition of the first token in the first group are stored in
-% \@IEEEextractedfirsttokensdiscarded, however their original relative brace
-% nesting depths are not guaranteed to be preserved.
-% The first group within this first group is stored in the macro
-% \@IEEEextractedfirstfirstgroup.
-% Likewise for the next group after the first: \@IEEEextractednextgroup,
-% \@IEEEextractednextfirstgroup, \@IEEEextractednextgroupfirsttoken,
-% \@IEEEextractednextgroupfirsttokenmacro, and 
-% \@IEEEextractednextfirsttokensdiscarded.
-% All tokens/groups after the first group, including any enclosing braces,
-% are stored in the macro \@IEEEextractedafterfirstgroupremain which will
-% be empty if none exist.
-%
-% For example:
-% \@IEEEextracttokengroups{{{ab}{cd}}{{ef}g}}
-% will result in:
-%
-% \@IEEEextracttokengroupsarg             ==> a macro containing {{ab}{cd}}{{ef}g}
-% \@IEEEextractedfirstgroup               ==> a macro containing {ab}{cd}
-% \@IEEEextractedafterfirstgroupremain    ==> a macro containing {{ef}g}
-% \@IEEEextractedfirsttoken               ==> the letter a
-% \@IEEEextractedfirsttokenmacro          ==> a macro containing a
-% \@IEEEextractedfirsttokensdiscarded     ==> a macro containing bcd
-% \@IEEEextractedfirstfirstgroup          ==> a macro containing ab
-% \@IEEEextractednextgroup                ==> a macro containing {ef}g
-% \@IEEEextractednextfirsttoken           ==> the letter e
-% \@IEEEextractednextfirsttokenmacro      ==> a macro containing e
-% \@IEEEextractednextfirsttokensdiscarded ==> a macro containing fg
-% \@IEEEextractednextfirstgroup           ==> a macro containing ef
-%
-% If given an empty argument, \@IEEEextractedfirsttoken and
-% \@IEEEextractednextfirsttoken will be set to \relax
-% and all the macros will be empty.
-% the *-star form, \@IEEEextracttokengroups*, does not expand its argument
-% contents during processing.
-%
-% Depends on: \@IEEEextractgroup, \@IEEEextracttoken
-\def\@IEEEextracttokengroups{\@ifstar{\let\@IEEEextracttokengroupsdef=\def\@@IEEEextracttokengroups}{\let\@IEEEextracttokengroupsdef=\edef\@@IEEEextracttokengroups}}
-\def\@@IEEEextracttokengroups#1{\@IEEEextracttokengroupsdef\@IEEEextracttokengroupsarg{#1}\relax
-% begin extraction, these functions are safe with empty arguments
-% first group
-\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextracttokengroupsarg}\relax
-\let\@IEEEextractedfirstgroup\@IEEEextractedgroup
-\let\@IEEEextractedafterfirstgroupremain\@IEEEextractedgroupremain
-\expandafter\@IEEEextracttoken\expandafter*\expandafter{\@IEEEextractedfirstgroup}\relax
-\let\@IEEEextractedfirsttoken\@IEEEextractedtoken
-\let\@IEEEextractedfirsttokenmacro\@IEEEextractedtokenmacro
-\let\@IEEEextractedfirsttokensdiscarded\@IEEEextractedtokensdiscarded
-% first first group
-\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextractedfirstgroup}\relax
-\let\@IEEEextractedfirstfirstgroup\@IEEEextractedgroup
-% next group
-\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextractedafterfirstgroupremain}\relax
-\let\@IEEEextractednextgroup\@IEEEextractedgroup
-\expandafter\@IEEEextracttoken\expandafter*\expandafter{\@IEEEextractednextgroup}\relax
-\let\@IEEEextractednextfirsttoken\@IEEEextractedtoken
-\let\@IEEEextractednextfirsttokenmacro\@IEEEextractedtokenmacro
-\let\@IEEEextractednextfirsttokensdiscarded\@IEEEextractedtokensdiscarded
-% next first group
-\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextractednextgroup}\relax
-\let\@IEEEextractednextfirstgroup\@IEEEextractedgroup}
-
-
-%% -- End of Command Argument Scanning Support Functions --
-
-
-
-
-%%
-%% START OF IEEEeqnarray DEFINITIONS
-%%
-%% Inspired by the concepts, examples, and previous works of LaTeX 
-%% coders and developers such as Donald Arseneau, Fred Bartlett, 
-%% David Carlisle, Tony Liu, Frank Mittelbach, Piet van Oostrum, 
-%% Roland Winkler and Mark Wooding.
-%% I don't make the claim that my work here is even near their calibre. ;)
-
-
-\newif\if@IEEEeqnarrayboxnojot% flag to indicate if the environment was called as the star form
-\@IEEEeqnarrayboxnojotfalse
-
-\newif\if@advanceIEEEeqncolcnt% tracks if the environment should advance the col counter
-% allows a way to make an \IEEEeqnarraybox that can be used within an \IEEEeqnarray
-% used by IEEEeqnarraymulticol so that it can work properly in both
-\@advanceIEEEeqncolcnttrue
-
-\newcount\@IEEEeqnnumcols % tracks how many IEEEeqnarray cols are defined
-\newcount\@IEEEeqncolcnt  % tracks how many IEEEeqnarray cols the user actually used
-
-
-% The default math style used by the columns
-\def\IEEEeqnarraymathstyle{\displaystyle}
-% The default text style used by the columns
-% default to using the current font
-\def\IEEEeqnarraytextstyle{\relax}
-
-% like the iedlistdecl but for \IEEEeqnarray
-\def\IEEEeqnarraydecl{\relax}
-\def\IEEEeqnarrayboxdecl{\relax}
-
-
-
-% V1.8 flags to indicate that equation numbering is to persist
-\newif\if@IEEEeqnumpersist%
-\@IEEEeqnumpersistfalse
-\newif\if@IEEEsubeqnumpersist%
-\@IEEEsubeqnumpersistfalse
-%
-% V1.8 flags to indicate if (sub)equation number of last line was preadvanced
-\newif\if@IEEEeqnumpreadv%
-\@IEEEeqnumpreadvfalse
-\newif\if@IEEEsubeqnumpreadv%
-\@IEEEsubeqnumpreadvfalse
-
-\newcount\@IEEEsubeqnnumrollback% saves previous value of IEEEsubequation number in case we need to restore it
-
-% \yesnumber is the opposite of \nonumber
-% a novel concept with the same def as the equationarray package
-% However, we give IEEE versions too since some LaTeX packages such as 
-% the MDWtools mathenv.sty redefine \nonumber to something else.
-% This command is intended for use in non-IEEEeqnarray math environments
-\providecommand{\yesnumber}{\global\@eqnswtrue}
-
-
-% IEEEyes/nonumber 
-% V1.8 add persistant * forms
-% These commands can alter the type of equation an IEEEeqnarray line is.
-\def\IEEEyesnumber{\@ifstar{\global\@IEEEeqnumpersisttrue\global\@IEEEsubeqnumpersistfalse\@IEEEyesnumber}{\@IEEEyesnumber}}
-
-\def\@IEEEyesnumber{\global\@eqnswtrue
-\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray
-\ifnum\c@IEEEsubequation>0\relax
-   \stepcounter{equation}\setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax
-   \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label
-\fi
-% even if we reached this eqn num via a preadv, it is legit now
-\global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse
-\fi}
-
-\def\IEEEnonumber{\@ifstar{\global\@IEEEeqnumpersistfalse\global\@IEEEsubeqnumpersistfalse\global\@eqnswfalse}{\global\@eqnswfalse}}
-
-
-\def\IEEEyessubnumber{\@ifstar{\global\@IEEEsubeqnumpersisttrue\@IEEEyessubnumber}{\@IEEEyessubnumber}}
-%
-\def\@IEEEyessubnumber{\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray
-  \ifnum\c@IEEEsubequation>0\relax% if it already is a subequation, we are good to go as-is
-  \else% if we are a regular equation we have to watch out for two cases
-    \if@IEEEeqnumpreadv% if this equation is the result of a preadvance, backout and bump the sub eqnnum
-       \global\advance\c@equation\m@ne\global\c@IEEEsubequation=\@IEEEsubeqnnumrollback\addtocounter{IEEEsubequation}{1}\relax
-    \else% non-preadvanced equations just need initialization of their sub eqnnum
-       \setcounter{IEEEsubequation}{1}\relax
-    \fi
-  \fi% fi already is subequation
-  \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax
-  \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label
-  \global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse% no longer a preadv anymore
-  \global\@eqnswtrue
-\fi}
-
-
-\def\IEEEnosubnumber{\@ifstar{\global\@IEEEsubeqnumpersistfalse\@IEEEnosubnumber}{\@IEEEnosubnumber}}
-%
-\def\@IEEEnosubnumber{\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray
-  \if@eqnsw % we do nothing unless we know we will display because we play with the counters here
-    % if it currently is a subequation, bump up to the next equation number and turn off the subequation
-    \ifnum\c@IEEEsubequation>0\relax\addtocounter{equation}{1}\setcounter{IEEEsubequation}{0}\relax
-    \fi
-    \global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse% no longer a preadv anymore
-    \gdef\@currentlabel{\p@equation\theequation}\relax
-    \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label
-  \fi
-\fi}
-
-
-
-% allows users to "push away" equations that get too close to the equation numbers
-\def\IEEEeqnarraynumspace{\hphantom{\ifnum\c@IEEEsubequation>0\relax\theIEEEsubequationdis\else\theequationdis\fi}}
-
-% provides a way to span multiple columns within IEEEeqnarray environments
-% will consider \if@advanceIEEEeqncolcnt before globally advancing the
-% column counter - so as to work within \IEEEeqnarraybox
-% usage: \IEEEeqnarraymulticol{number cols. to span}{col type}{cell text}
-\long\def\IEEEeqnarraymulticol#1#2#3{\multispan{#1}\relax
-% check if column is defined for the precolumn definition
-% We have to be careful here because TeX scans for & even within an \iffalse
-% where it does not expand macros. So, if we used only one \ifx and a #3
-% appeared in the false branch and the user inserted another alignment
-% structure that uses & in the \IEEEeqnarraymulticol{}, TeX will not see that
-% there is an inner alignment in the false branch yet still will see any &
-% there and will think that they apply to the outer alignment resulting in an
-% incomplete \ifx error.
-% So, here we use separate checks for the pre and post parts in order to keep
-% the #3 outside of all conditionals.
-\relax\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined\relax
-\csname @IEEEeqnarraycolPRE#2\endcsname
-\else% if not, error and use default type
-\@IEEEclspkgerror{Invalid column type "#2" in \string\IEEEeqnarraymulticol.\MessageBreak
-Using a default centering column instead}%
-{You must define IEEEeqnarray column types before use.}%
-\csname @IEEEeqnarraycolPRE@IEEEdefault\endcsname
-\fi
-% The ten \relax are to help prevent misleading error messages in case a user
-% accidently inserted a macro that tries to acquire additional arguments.
-#3\relax\relax\relax\relax\relax\relax\relax\relax\relax\relax
-% check if column is defined for the postcolumn definition
-\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined\relax
-\csname @IEEEeqnarraycolPOST#2\endcsname
-\else% if not, use the default type
-\csname @IEEEeqnarraycolPOST@IEEEdefault\endcsname
-\fi
-% advance column counter only if the IEEEeqnarray environment wants it
-\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by #1\relax\fi}
-
-% like \omit, but maintains track of the column counter for \IEEEeqnarray
-\def\IEEEeqnarrayomit{\omit\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by 1\relax\fi}
-
-
-% provides a way to define a letter referenced column type
-% usage: \IEEEeqnarraydefcol{col. type letter/name}{pre insertion text}{post insertion text}
-\def\IEEEeqnarraydefcol#1#2#3{\expandafter\def\csname @IEEEeqnarraycolPRE#1\endcsname{#2}%
-\expandafter\def\csname @IEEEeqnarraycolPOST#1\endcsname{#3}%
-\expandafter\def\csname @IEEEeqnarraycolDEF#1\endcsname{1}}
-
-
-% provides a way to define a numerically referenced inter-column glue types
-% usage: \IEEEeqnarraydefcolsep{col. glue number}{glue definition}
-\def\IEEEeqnarraydefcolsep#1#2{\expandafter\def\csname @IEEEeqnarraycolSEP\romannumeral #1\endcsname{#2}%
-\expandafter\def\csname @IEEEeqnarraycolSEPDEF\romannumeral #1\endcsname{1}}
-
-
-\def\@IEEEeqnarraycolisdefined{1}% just a macro for 1, used for checking undefined column types
-
-
-% expands and appends the given argument to the \@IEEEtrantmptoksA token list
-% used to build up the \halign preamble
-\def\@IEEEappendtoksA#1{\edef\@@IEEEappendtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA #1}}%
-\@@IEEEappendtoksA}
-
-% also appends to \@IEEEtrantmptoksA, but does not expand the argument
-% uses \toks8 as a scratchpad register
-\def\@IEEEappendNOEXPANDtoksA#1{\toks8={#1}%
-\edef\@@IEEEappendNOEXPANDtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA\the\toks8}}%
-\@@IEEEappendNOEXPANDtoksA}
-
-% define some common column types for the user
-% math
-\IEEEeqnarraydefcol{l}{$\IEEEeqnarraymathstyle}{$\hfil}
-\IEEEeqnarraydefcol{c}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}
-\IEEEeqnarraydefcol{r}{\hfil$\IEEEeqnarraymathstyle}{$}
-\IEEEeqnarraydefcol{L}{$\IEEEeqnarraymathstyle{}}{{}$\hfil}
-\IEEEeqnarraydefcol{C}{\hfil$\IEEEeqnarraymathstyle{}}{{}$\hfil}
-\IEEEeqnarraydefcol{R}{\hfil$\IEEEeqnarraymathstyle{}}{{}$}
-% text
-\IEEEeqnarraydefcol{s}{\IEEEeqnarraytextstyle}{\hfil}
-\IEEEeqnarraydefcol{t}{\hfil\IEEEeqnarraytextstyle}{\hfil}
-\IEEEeqnarraydefcol{u}{\hfil\IEEEeqnarraytextstyle}{}
-
-% vertical rules
-\IEEEeqnarraydefcol{v}{}{\vrule width\arrayrulewidth}
-\IEEEeqnarraydefcol{vv}{\vrule width\arrayrulewidth\hfil}{\hfil\vrule width\arrayrulewidth}
-\IEEEeqnarraydefcol{V}{}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}
-\IEEEeqnarraydefcol{VV}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth\hfil}%
-{\hfil\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}
-
-% horizontal rules
-\IEEEeqnarraydefcol{h}{}{\leaders\hrule height\arrayrulewidth\hfil}
-\IEEEeqnarraydefcol{H}{}{\leaders\vbox{\hrule width\arrayrulewidth\vskip\doublerulesep\hrule width\arrayrulewidth}\hfil}
-
-% plain
-\IEEEeqnarraydefcol{x}{}{}
-\IEEEeqnarraydefcol{X}{$}{$}
-
-% the default column type to use in the event a column type is not defined
-\IEEEeqnarraydefcol{@IEEEdefault}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}
-
-
-% a zero tabskip (used for "-" col types)
-\def\@IEEEeqnarraycolSEPzero{0pt plus 0pt minus 0pt}
-% a centering tabskip (used for "+" col types)
-\def\@IEEEeqnarraycolSEPcenter{1000pt plus 0pt minus 1000pt}
-
-% top level default tabskip glues for the start, end, and inter-column
-% may be reset within environments not always at the top level, e.g., \IEEEeqnarraybox
-\edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPcenter}% default start glue
-\edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPcenter}% default end glue
-\edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue
-
-
-
-% creates a vertical rule that extends from the bottom to the top a a cell
-% Provided in case other packages redefine \vline some other way.
-% usage: \IEEEeqnarrayvrule[rule thickness]
-% If no argument is provided, \arrayrulewidth will be used for the rule thickness. 
-\newcommand\IEEEeqnarrayvrule[1][\arrayrulewidth]{\vrule\@width#1\relax}
-
-% creates a blank separator row
-% usage: \IEEEeqnarrayseprow[separation length][font size commands]
-% default is \IEEEeqnarrayseprow[0.25\normalbaselineskip][\relax]
-% blank arguments inherit the default values
-% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers
-\def\IEEEeqnarrayseprow{\relax\@ifnextchar[{\@IEEEeqnarrayseprow}{\@IEEEeqnarrayseprow[0.25\normalbaselineskip]}}
-\def\@IEEEeqnarrayseprow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprow[#1]}{\@@IEEEeqnarrayseprow[#1][\relax]}}
-\def\@@IEEEeqnarrayseprow[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%
-\ifx\@IEEEeqnarrayseprowARGONE\@empty%
-% get the skip value, based on the font commands
-% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3
-% assign within a bogus box to confine the font changes
-{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%
-\else%
-{\setbox0=\hbox{#2\relax\global\skip5=#1}}%
-\fi%
-\@IEEEeqnarrayhoptolastcolumn\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}
-
-% creates a blank separator row, but omits all the column templates
-% usage: \IEEEeqnarrayseprowcut[separation length][font size commands]
-% default is \IEEEeqnarrayseprowcut[0.25\normalbaselineskip][\relax]
-% blank arguments inherit the default values
-% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers
-\def\IEEEeqnarrayseprowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
-% advance column counter only if the IEEEeqnarray environment wants it
-\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
-\@ifnextchar[{\@IEEEeqnarrayseprowcut}{\@IEEEeqnarrayseprowcut[0.25\normalbaselineskip]}}
-\def\@IEEEeqnarrayseprowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprowcut[#1]}{\@@IEEEeqnarrayseprowcut[#1][\relax]}}
-\def\@@IEEEeqnarrayseprowcut[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%
-\ifx\@IEEEeqnarrayseprowARGONE\@empty%
-% get the skip value, based on the font commands
-% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3
-% assign within a bogus box to confine the font changes
-{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%
-\else%
-{\setbox0=\hbox{#2\relax\global\skip5=#1}}%
-\fi%
-\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}
-
-
-
-% draws a single rule across all the columns optional
-% argument determines the rule width, \arrayrulewidth is the default
-% updates column counter as needed and turns off struts
-% usage: \IEEEeqnarrayrulerow[rule line thickness]
-\def\IEEEeqnarrayrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
-% advance column counter only if the IEEEeqnarray environment wants it
-\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
-\@ifnextchar[{\@IEEEeqnarrayrulerow}{\@IEEEeqnarrayrulerow[\arrayrulewidth]}}
-\def\@IEEEeqnarrayrulerow[#1]{\leaders\hrule height#1\hfil\relax% put in our rule 
-% turn off any struts
-\IEEEeqnarraystrutsize{0pt}{0pt}[\relax]\relax}
-
-
-% draws a double rule by using a single rule row, a separator row, and then
-% another single rule row 
-% first optional argument determines the rule thicknesses, \arrayrulewidth is the default
-% second optional argument determines the rule spacing, \doublerulesep is the default
-% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]
-\def\IEEEeqnarraydblrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
-% advance column counter only if the IEEEeqnarray environment wants it
-\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
-\@ifnextchar[{\@IEEEeqnarraydblrulerow}{\@IEEEeqnarraydblrulerow[\arrayrulewidth]}}
-\def\@IEEEeqnarraydblrulerow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerow[#1]}%
-{\@@IEEEeqnarraydblrulerow[#1][\doublerulesep]}}
-\def\@@IEEEeqnarraydblrulerow[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%
-% we allow the user to say \IEEEeqnarraydblrulerow[][]
-\ifx\@IEEEeqnarraydblrulerowARG\@empty%
-\@IEEEeqnarrayrulerow[\arrayrulewidth]%
-\else%
-\@IEEEeqnarrayrulerow[#1]\relax%
-\fi%
-\def\@IEEEeqnarraydblrulerowARG{#2}%
-\ifx\@IEEEeqnarraydblrulerowARG\@empty%
-\\\IEEEeqnarrayseprow[\doublerulesep][\relax]%
-\else%
-\\\IEEEeqnarrayseprow[#2][\relax]%
-\fi%
-\\\multispan{\@IEEEeqnnumcols}%
-% advance column counter only if the IEEEeqnarray environment wants it
-\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
-\def\@IEEEeqnarraydblrulerowARG{#1}%
-\ifx\@IEEEeqnarraydblrulerowARG\@empty%
-\@IEEEeqnarrayrulerow[\arrayrulewidth]%
-\else%
-\@IEEEeqnarrayrulerow[#1]%
-\fi%
-}
-
-% draws a double rule by using a single rule row, a separator (cutting) row, and then
-% another single rule row 
-% first optional argument determines the rule thicknesses, \arrayrulewidth is the default
-% second optional argument determines the rule spacing, \doublerulesep is the default
-% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]
-\def\IEEEeqnarraydblrulerowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
-% advance column counter only if the IEEEeqnarray environment wants it
-\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
-\@ifnextchar[{\@IEEEeqnarraydblrulerowcut}{\@IEEEeqnarraydblrulerowcut[\arrayrulewidth]}}
-\def\@IEEEeqnarraydblrulerowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerowcut[#1]}%
-{\@@IEEEeqnarraydblrulerowcut[#1][\doublerulesep]}}
-\def\@@IEEEeqnarraydblrulerowcut[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%
-% we allow the user to say \IEEEeqnarraydblrulerow[][]
-\ifx\@IEEEeqnarraydblrulerowARG\@empty%
-\@IEEEeqnarrayrulerow[\arrayrulewidth]%
-\else%
-\@IEEEeqnarrayrulerow[#1]%
-\fi%
-\def\@IEEEeqnarraydblrulerowARG{#2}%
-\ifx\@IEEEeqnarraydblrulerowARG\@empty%
-\\\IEEEeqnarrayseprowcut[\doublerulesep][\relax]%
-\else%
-\\\IEEEeqnarrayseprowcut[#2][\relax]%
-\fi%
-\\\multispan{\@IEEEeqnnumcols}%
-% advance column counter only if the IEEEeqnarray environment wants it
-\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
-\def\@IEEEeqnarraydblrulerowARG{#1}%
-\ifx\@IEEEeqnarraydblrulerowARG\@empty%
-\@IEEEeqnarrayrulerow[\arrayrulewidth]%
-\else%
-\@IEEEeqnarrayrulerow[#1]%
-\fi%
-}
-
-
-
-% inserts a full row's worth of &'s
-% relies on \@IEEEeqnnumcols to provide the correct number of columns
-% uses \@IEEEtrantmptoksA, \count0 as scratch registers
-\def\@IEEEeqnarrayhoptolastcolumn{\@IEEEtrantmptoksA={}\count0=1\relax%
-\loop% add cols if the user did not use them all
-\ifnum\count0<\@IEEEeqnnumcols\relax%
-\@IEEEappendtoksA{&}%
-\advance\count0 by 1\relax% update the col count
-\repeat%
-\the\@IEEEtrantmptoksA%execute the &'s
-}
-
-
-
-\newif\if@IEEEeqnarrayISinner % flag to indicate if we are within the lines
-\@IEEEeqnarrayISinnerfalse    % of an IEEEeqnarray - after the IEEEeqnarraydecl
-
-\edef\@IEEEeqnarrayTHEstrutheight{0pt} % height and depth of IEEEeqnarray struts
-\edef\@IEEEeqnarrayTHEstrutdepth{0pt}
-
-\edef\@IEEEeqnarrayTHEmasterstrutheight{0pt} % default height and depth of
-\edef\@IEEEeqnarrayTHEmasterstrutdepth{0pt}  % struts within an IEEEeqnarray
-
-\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{0pt} % saved master strut height
-\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{0pt} % and depth
-
-\newif\if@IEEEeqnarrayusemasterstrut % flag to indicate that the master strut value
-\@IEEEeqnarrayusemasterstruttrue     % is to be used
-
-
-
-% saves the strut height and depth of the master strut
-\def\@IEEEeqnarraymasterstrutsave{\relax%
-\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
-\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
-% remove stretchability
-\dimen0\skip0\relax%
-\dimen2\skip2\relax%
-% save values
-\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{\the\dimen0}%
-\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{\the\dimen2}}
-
-% restores the strut height and depth of the master strut
-\def\@IEEEeqnarraymasterstrutrestore{\relax%
-\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutHSAVE\relax%
-\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutDSAVE\relax%
-% remove stretchability
-\dimen0\skip0\relax%
-\dimen2\skip2\relax%
-% restore values
-\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
-\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}}
-
-
-% globally restores the strut height and depth to the 
-% master values and sets the master strut flag to true
-\def\@IEEEeqnarraystrutreset{\relax%
-\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
-\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
-% remove stretchability
-\dimen0\skip0\relax%
-\dimen2\skip2\relax%
-% restore values
-\xdef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
-\xdef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
-\global\@IEEEeqnarrayusemasterstruttrue}
-
-
-% if the master strut is not to be used, make the current
-% values of \@IEEEeqnarrayTHEstrutheight, \@IEEEeqnarrayTHEstrutdepth
-% and the use master strut flag, global
-% this allows user strut commands issued in the last column to be carried
-% into the isolation/strut column
-\def\@IEEEeqnarrayglobalizestrutstatus{\relax%
-\if@IEEEeqnarrayusemasterstrut\else%
-\xdef\@IEEEeqnarrayTHEstrutheight{\@IEEEeqnarrayTHEstrutheight}%
-\xdef\@IEEEeqnarrayTHEstrutdepth{\@IEEEeqnarrayTHEstrutdepth}%
-\global\@IEEEeqnarrayusemasterstrutfalse%
-\fi}
-
-
-
-% usage: \IEEEeqnarraystrutsize{height}{depth}[font size commands]
-% If called outside the lines of an IEEEeqnarray, sets the height
-% and depth of both the master and local struts. If called inside
-% an IEEEeqnarray line, sets the height and depth of the local strut
-% only and sets the flag to indicate the use of the local strut
-% values. If the height or depth is left blank, 0.7\normalbaselineskip
-% and 0.3\normalbaselineskip will be used, respectively.
-% The optional argument can be used to evaluate the lengths under
-% a different font size and styles. If none is specified, the current
-% font is used.
-% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2
-\def\IEEEeqnarraystrutsize#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsize{#1}{#2}}{\@IEEEeqnarraystrutsize{#1}{#2}[\relax]}}
-\def\@IEEEeqnarraystrutsize#1#2[#3]{\def\@IEEEeqnarraystrutsizeARG{#1}%
-\ifx\@IEEEeqnarraystrutsizeARG\@empty%
-{\setbox0=\hbox{#3\relax\global\skip3=0.7\normalbaselineskip}}%
-\skip0=\skip3\relax%
-\else% arg one present
-{\setbox0=\hbox{#3\relax\global\skip3=#1\relax}}%
-\skip0=\skip3\relax%
-\fi% if null arg
-\def\@IEEEeqnarraystrutsizeARG{#2}%
-\ifx\@IEEEeqnarraystrutsizeARG\@empty%
-{\setbox0=\hbox{#3\relax\global\skip3=0.3\normalbaselineskip}}%
-\skip2=\skip3\relax%
-\else% arg two present
-{\setbox0=\hbox{#3\relax\global\skip3=#2\relax}}%
-\skip2=\skip3\relax%
-\fi% if null arg
-% remove stretchability, just to be safe
-\dimen0\skip0\relax%
-\dimen2\skip2\relax%
-% dimen0 = height, dimen2 = depth
-\if@IEEEeqnarrayISinner% inner does not touch master strut size
-\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
-\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
-\@IEEEeqnarrayusemasterstrutfalse% do not use master
-\else% outer, have to set master strut too
-\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
-\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%
-\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
-\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
-\@IEEEeqnarrayusemasterstruttrue% use master strut
-\fi}
-
-
-% usage: \IEEEeqnarraystrutsizeadd{added height}{added depth}[font size commands]
-% If called outside the lines of an IEEEeqnarray, adds the given height
-% and depth to both the master and local struts.
-% If called inside an IEEEeqnarray line, adds the given height and depth
-% to the local strut only and sets the flag to indicate the use 
-% of the local strut values.
-% In both cases, if a height or depth is left blank, 0pt is used instead.
-% The optional argument can be used to evaluate the lengths under
-% a different font size and styles. If none is specified, the current
-% font is used.
-% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2
-\def\IEEEeqnarraystrutsizeadd#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsizeadd{#1}{#2}}{\@IEEEeqnarraystrutsizeadd{#1}{#2}[\relax]}}
-\def\@IEEEeqnarraystrutsizeadd#1#2[#3]{\def\@IEEEeqnarraystrutsizearg{#1}%
-\ifx\@IEEEeqnarraystrutsizearg\@empty%
-\skip0=0pt\relax%
-\else% arg one present
-{\setbox0=\hbox{#3\relax\global\skip3=#1}}%
-\skip0=\skip3\relax%
-\fi% if null arg
-\def\@IEEEeqnarraystrutsizearg{#2}%
-\ifx\@IEEEeqnarraystrutsizearg\@empty%
-\skip2=0pt\relax%
-\else% arg two present
-{\setbox0=\hbox{#3\relax\global\skip3=#2}}%
-\skip2=\skip3\relax%
-\fi% if null arg
-% remove stretchability, just to be safe
-\dimen0\skip0\relax%
-\dimen2\skip2\relax%
-% dimen0 = height, dimen2 = depth
-\if@IEEEeqnarrayISinner% inner does not touch master strut size
-% get local strut size
-\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%
-\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%
-% add it to the user supplied values
-\advance\dimen0 by \skip0\relax%
-\advance\dimen2 by \skip2\relax%
-% update the local strut size
-\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
-\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
-\@IEEEeqnarrayusemasterstrutfalse% do not use master
-\else% outer, have to set master strut too
-% get master strut size
-\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
-\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
-% add it to the user supplied values
-\advance\dimen0 by \skip0\relax%
-\advance\dimen2 by \skip2\relax%
-% update the local and master strut sizes
-\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
-\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%
-\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
-\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
-\@IEEEeqnarrayusemasterstruttrue% use master strut
-\fi}
-
-
-% allow user a way to see the struts
-\newif\ifIEEEvisiblestruts
-\IEEEvisiblestrutsfalse
-
-% inserts an invisible strut using the master or local strut values
-% uses scratch registers \skip0, \skip2, \dimen0, \dimen2
-\def\@IEEEeqnarrayinsertstrut{\relax%
-\if@IEEEeqnarrayusemasterstrut
-% get master strut size
-\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
-\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
-\else%
-% get local strut size
-\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%
-\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%
-\fi%
-% remove stretchability, probably not needed
-\dimen0\skip0\relax%
-\dimen2\skip2\relax%
-% dimen0 = height, dimen2 = depth
-% allow user to see struts if desired
-\ifIEEEvisiblestruts%
-\vrule width0.2pt height\dimen0 depth\dimen2\relax%
-\else%
-\vrule width0pt height\dimen0 depth\dimen2\relax\fi}
-
-
-% creates an invisible strut, useable even outside \IEEEeqnarray
-% if \IEEEvisiblestrutstrue, the strut will be visible and 0.2pt wide. 
-% usage: \IEEEstrut[height][depth][font size commands]
-% default is \IEEEstrut[0.7\normalbaselineskip][0.3\normalbaselineskip][\relax]
-% blank arguments inherit the default values
-% uses \dimen0, \dimen2, \skip0, \skip2
-\def\IEEEstrut{\relax\@ifnextchar[{\@IEEEstrut}{\@IEEEstrut[0.7\normalbaselineskip]}}
-\def\@IEEEstrut[#1]{\relax\@ifnextchar[{\@@IEEEstrut[#1]}{\@@IEEEstrut[#1][0.3\normalbaselineskip]}}
-\def\@@IEEEstrut[#1][#2]{\relax\@ifnextchar[{\@@@IEEEstrut[#1][#2]}{\@@@IEEEstrut[#1][#2][\relax]}}
-\def\@@@IEEEstrut[#1][#2][#3]{\mbox{#3\relax%
-\def\@IEEEstrutARG{#1}%
-\ifx\@IEEEstrutARG\@empty%
-\skip0=0.7\normalbaselineskip\relax%
-\else%
-\skip0=#1\relax%
-\fi%
-\def\@IEEEstrutARG{#2}%
-\ifx\@IEEEstrutARG\@empty%
-\skip2=0.3\normalbaselineskip\relax%
-\else%
-\skip2=#2\relax%
-\fi%
-% remove stretchability, probably not needed
-\dimen0\skip0\relax%
-\dimen2\skip2\relax%
-\ifIEEEvisiblestruts%
-\vrule width0.2pt height\dimen0 depth\dimen2\relax%
-\else%
-\vrule width0.0pt height\dimen0 depth\dimen2\relax\fi}}
-
-
-% enables strut mode by setting a default strut size and then zeroing the
-% \baselineskip, \lineskip, \lineskiplimit and \jot
-\def\IEEEeqnarraystrutmode{\IEEEeqnarraystrutsize{0.7\normalbaselineskip}{0.3\normalbaselineskip}[\relax]%
-\baselineskip=0pt\lineskip=0pt\lineskiplimit=0pt\jot=0pt}
-
-
-% equation and subequation forms to use to setup hyperref's \@currentHref
-\def\@IEEEtheHrefequation{equation.\theHequation}
-\def\@IEEEtheHrefsubequation{equation.\theHequation\alph{IEEEsubequation}}
-
-
-\def\IEEEeqnarray{\@IEEEeqnumpersisttrue\@IEEEsubeqnumpersistfalse\@IEEEeqnarray}
-\def\endIEEEeqnarray{\end@IEEEeqnarray}
-
-\@namedef{IEEEeqnarray*}{\@IEEEeqnumpersistfalse\@IEEEsubeqnumpersistfalse\@IEEEeqnarray}
-\@namedef{endIEEEeqnarray*}{\end@IEEEeqnarray}
-
-
-% \IEEEeqnarray is an enhanced \eqnarray. 
-% The star form defaults to not putting equation numbers at the end of each row.
-% usage: \IEEEeqnarray[decl]{cols}
-\def\@IEEEeqnarray{\relax\@ifnextchar[{\@@IEEEeqnarray}{\@@IEEEeqnarray[\relax]}}
-% We have to be careful here to normalize catcodes just before acquiring the
-% cols as that specification may contain punctuation which could be subject
-% to document catcode changes.
-\def\@@IEEEeqnarray[#1]{\begingroup\IEEEnormalcatcodes\@@@IEEEeqnarray[#1]}
-\def\@@@IEEEeqnarray[#1]#2{\endgroup
-   % default to showing the equation number or not based on whether or not
-   % the star form was involked
-   \if@IEEEeqnumpersist\global\@eqnswtrue
-   \else% not the star form
-   \global\@eqnswfalse
-   \fi% if star form
-   % provide a basic hyperref \theHequation if this has not already been setup (hyperref not loaded, or no section counter)
-   \@ifundefined{theHequation}{\def\theHequation{\arabic{equation}}}{}\relax
-   % provide dummy hyperref commands in case hyperref is not loaded
-   \providecommand{\Hy@raisedlink}[1]{}\relax
-   \providecommand{\hyper@anchorstart}[1]{}\relax
-   \providecommand{\hyper@anchorend}{}\relax
-   \providecommand{\@currentHref}{}\relax
-   \@IEEEeqnumpreadvfalse% reset eqnpreadv flag
-   \@IEEEsubeqnumpreadvfalse% reset subeqnpreadv flag
-   \@IEEEeqnarrayISinnerfalse% not yet within the lines of the halign
-   \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default
-   \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise
-   \IEEEvisiblestrutsfalse% diagnostic mode defaults to off
-   % no extra space unless the user specifically requests it
-   \lineskip=0pt\relax
-   \lineskiplimit=0pt\relax
-   \baselineskip=\normalbaselineskip\relax%
-   \jot=\IEEEnormaljot\relax%
-   \mathsurround\z@\relax% no extra spacing around math
-   \@advanceIEEEeqncolcnttrue% advance the col counter for each col the user uses, 
-                             % used in \IEEEeqnarraymulticol and in the preamble build
-   %V1.8 Here we preadvance to the next equation number.
-   % If the user later wants a continued subequation, we can roll back.
-   \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation%
-   \stepcounter{equation}\@IEEEeqnumpreadvtrue% advance equation counter before first line
-   \setcounter{IEEEsubequation}{0}% no subequation yet
-   \let\@IEEEcurrentlabelsave\@currentlabel% save current label as we later change it globally
-   \let\@IEEEcurrentHrefsave\@currentHref% save current href label as we later change it globally
-   \def\@currentlabel{\p@equation\theequation}% redefine the ref label
-   \def\@currentHref{\@IEEEtheHrefequation}% setup hyperref label
-   \IEEEeqnarraydecl\relax% allow a way for the user to make global overrides
-   #1\relax% allow user to override defaults
-   \let\\\@IEEEeqnarraycr% replace newline with one that can put in eqn. numbers
-   \global\@IEEEeqncolcnt\z@% col. count = 0 for first line
-   \@IEEEbuildpreamble{#2}\relax% build the preamble and put it into \@IEEEtrantmptoksA 
-   % put in the column for the equation number
-   \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first
-   \toks0={##}%
-   % advance the \@IEEEeqncolcnt for the isolation col, this helps with error checking
-   \@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}%
-   % add the isolation column
-   \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}%
-   % advance the \@IEEEeqncolcnt for the equation number col, this helps with error checking
-   \@IEEEappendtoksA{&\global\advance\@IEEEeqncolcnt by 1\relax}%
-   % add the equation number col to the preamble
-   \@IEEEappendtoksA{\tabskip\z@skip\hb@xt@\z@\bgroup\hss\the\toks0\egroup}%
-   % note \@IEEEeqnnumcols does not count the equation col or isolation col
-   % set the starting tabskip glue as determined by the preamble build
-   \tabskip=\@IEEEBPstartglue\relax
-   % begin the display alignment
-   \@IEEEeqnarrayISinnertrue% commands are now within the lines
-   $$\everycr{}\halign to\displaywidth\bgroup
-   % "exspand" the preamble
-   \span\the\@IEEEtrantmptoksA\cr}
-
-% enter isolation/strut column (or the next column if the user did not use
-% every column), record the strut status, complete the columns, do the strut if needed,
-% restore counters (to backout any equation setup for a next line that was never used)
-% to their correct values and exit
-\def\end@IEEEeqnarray{\@IEEEeqnarrayglobalizestrutstatus&\@@IEEEeqnarraycr\egroup
-\if@IEEEsubeqnumpreadv\global\advance\c@IEEEsubequation\m@ne\fi
-\if@IEEEeqnumpreadv\global\advance\c@equation\m@ne\global\c@IEEEsubequation=\@IEEEsubeqnnumrollback\fi
-\global\let\@currentlabel\@IEEEcurrentlabelsave% restore current label
-\global\let\@currentHref\@IEEEcurrentHrefsave% restore current href label
-$$\@ignoretrue}
-
-
-% IEEEeqnarray uses a modifed \\ instead of the plain \cr to
-% end rows. This allows for things like \\*[vskip amount]
-% These "cr" macros are modified versions of those for LaTeX2e's eqnarray
-% the {\ifnum0=`} braces must be kept away from the last column to avoid
-% altering spacing of its math, so we use & to advance to the next column
-% as there is an isolation/strut column after the user's columns
-\def\@IEEEeqnarraycr{\@IEEEeqnarrayglobalizestrutstatus&% save strut status and advance to next column
-   {\ifnum0=`}\fi
-   \@ifstar{%
-      \global\@eqpen\@M\@IEEEeqnarrayYCR
-   }{%
-      \global\@eqpen\interdisplaylinepenalty \@IEEEeqnarrayYCR
-   }%
-}
-
-\def\@IEEEeqnarrayYCR{\@testopt\@IEEEeqnarrayXCR\z@skip}
-
-\def\@IEEEeqnarrayXCR[#1]{%
-   \ifnum0=`{\fi}%
-   \@@IEEEeqnarraycr
-   \noalign{\penalty\@eqpen\vskip\jot\vskip #1\relax}}%
-
-\def\@@IEEEeqnarraycr{\@IEEEtrantmptoksA={}% clear token register
-    \advance\@IEEEeqncolcnt by -1\relax% adjust col count because of the isolation column
-    \ifnum\@IEEEeqncolcnt>\@IEEEeqnnumcols\relax
-    \@IEEEclspkgerror{Too many columns within the IEEEeqnarray\MessageBreak
-                          environment}%
-    {Use fewer \string &'s or put more columns in the IEEEeqnarray column\MessageBreak 
-     specifications.}\relax%
-    \else
-    \loop% add cols if the user did not use them all
-    \ifnum\@IEEEeqncolcnt<\@IEEEeqnnumcols\relax
-    \@IEEEappendtoksA{&}%
-    \advance\@IEEEeqncolcnt by 1\relax% update the col count
-    \repeat
-    % this number of &'s will take us the the isolation column
-    \fi
-    % execute the &'s
-    \the\@IEEEtrantmptoksA%
-    % handle the strut/isolation column
-    \@IEEEeqnarrayinsertstrut% do the strut if needed
-    \@IEEEeqnarraystrutreset% reset the strut system for next line or IEEEeqnarray
-    &% and enter the equation number column
-    \if@eqnsw% only if we display something
-      \Hy@raisedlink{\hyper@anchorstart{\@currentHref}}% start a hyperref anchor
-      \global\@IEEEeqnumpreadvfalse\relax% displaying an equation number means
-      \global\@IEEEsubeqnumpreadvfalse\relax% the equation counters point to valid equations
-      % V1.8 Here we setup the counters, currentlabel and status for what would be the *next*
-      % equation line as would be the case under the current settings. However, there are two problems.
-      % One problem is that there might not ever be a next line. The second problem is that the user
-      % may later alter the meaning of a line with commands such as \IEEEyessubnumber. So, to handle
-      % these cases we have to record the current values of the (sub)equation counters and revert back
-      % to them if the next line is changed or never comes. The \if@IEEEeqnumpreadv, \if@IEEEsubeqnumpreadv
-      % and \@IEEEsubeqnnumrollback stuff tracks this.
-      % The logic to handle all this is surprisingly complex, but a nice feature of the approach here is
-      % that the equation counters and labels remain valid for what the line would be unless a
-      % \IEEEyessubnumber et al. later changes it. So, any hyperref links are always correct.
-      \ifnum\c@IEEEsubequation>0\relax% handle subequation
-         \theIEEEsubequationdis\relax
-         \if@IEEEsubeqnumpersist% setup for default type of next line
-            \stepcounter{IEEEsubequation}\global\@IEEEsubeqnumpreadvtrue\relax
-            \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax
-            \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label
-         \else
-             % if no subeqnum persist, go ahead and setup for a new equation number
-             \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation
-             \stepcounter{equation}\global\@IEEEeqnumpreadvtrue\relax
-             \setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax
-             \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label
-         \fi
-      \else% display a standard equation number
-        \theequationdis\relax
-        \setcounter{IEEEsubequation}{0}\relax% not really needed
-        \if@IEEEsubeqnumpersist% setup for default type of next line
-           % subequations that follow plain equations carry the same equation number e.g, 5, 5a rather than 5, 6a
-           \stepcounter{IEEEsubequation}\global\@IEEEsubeqnumpreadvtrue\relax
-           \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax
-           \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label
-         \else
-             % if no subeqnum persist, go ahead and setup for a new equation number
-             \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation
-             \stepcounter{equation}\global\@IEEEeqnumpreadvtrue\relax
-             \setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax
-             \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label
-         \fi
-      \fi%
-      \Hy@raisedlink{\hyper@anchorend}% end hyperref anchor
-    \fi% fi only if we display something
-    % reset the flags to indicate the default preferences of the display of equation numbers
-    \if@IEEEeqnumpersist\global\@eqnswtrue\else\global\@eqnswfalse\fi
-    \if@IEEEsubeqnumpersist\global\@eqnswtrue\fi% ditto for the subequation flag
-    % reset the number of columns the user actually used
-    \global\@IEEEeqncolcnt\z@\relax
-    % the real end of the line
-    \cr}
-
-
-
-
-
-% \IEEEeqnarraybox is like \IEEEeqnarray except the box form puts everything
-% inside a vtop, vbox, or vcenter box depending on the letter in the second
-% optional argument (t,b,c). Vbox is the default. Unlike \IEEEeqnarray,
-% equation numbers are not displayed and \IEEEeqnarraybox can be nested.
-% \IEEEeqnarrayboxm is for math mode (like \array) and does not put the vbox
-% within an hbox.
-% \IEEEeqnarrayboxt is for text mode (like \tabular) and puts the vbox within
-% a \hbox{$ $} construct.
-% \IEEEeqnarraybox will auto detect whether to use \IEEEeqnarrayboxm or 
-% \IEEEeqnarrayboxt depending on the math mode.
-% The third optional argument specifies the width this box is to be set to -
-% natural width is the default.
-% The * forms do not add \jot line spacing
-% usage: \IEEEeqnarraybox[decl][pos][width]{cols}
-\def\IEEEeqnarrayboxm{\@IEEEeqnarrayboxnojotfalse\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}
-\def\endIEEEeqnarrayboxm{\end@IEEEeqnarraybox}
-\@namedef{IEEEeqnarrayboxm*}{\@IEEEeqnarrayboxnojottrue\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}
-\@namedef{endIEEEeqnarrayboxm*}{\end@IEEEeqnarraybox}
-
-\def\IEEEeqnarrayboxt{\@IEEEeqnarrayboxnojotfalse\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}
-\def\endIEEEeqnarrayboxt{\end@IEEEeqnarraybox}
-\@namedef{IEEEeqnarrayboxt*}{\@IEEEeqnarrayboxnojottrue\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}
-\@namedef{endIEEEeqnarrayboxt*}{\end@IEEEeqnarraybox}
-
-\def\IEEEeqnarraybox{\@IEEEeqnarrayboxnojotfalse\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%
-\@IEEEeqnarraybox}
-\def\endIEEEeqnarraybox{\end@IEEEeqnarraybox}
-
-\@namedef{IEEEeqnarraybox*}{\@IEEEeqnarrayboxnojottrue\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%
-\@IEEEeqnarraybox}
-\@namedef{endIEEEeqnarraybox*}{\end@IEEEeqnarraybox}
-
-% flag to indicate if the \IEEEeqnarraybox needs to put things into an hbox{$ $} 
-% for \vcenter in non-math mode
-\newif\if@IEEEeqnarrayboxHBOXSW%
-\@IEEEeqnarrayboxHBOXSWfalse
-
-\def\@IEEEeqnarraybox{\relax\@ifnextchar[{\@@IEEEeqnarraybox}{\@@IEEEeqnarraybox[\relax]}}
-% We have to be careful here to normalize catcodes just before acquiring the
-% cols as that specification may contain punctuation which could be subject
-% to document catcode changes.
-\def\@@IEEEeqnarraybox[#1]{\relax\begingroup\IEEEnormalcatcodes\@ifnextchar[{\@@@IEEEeqnarraybox[#1]}{\@@@IEEEeqnarraybox[#1][b]}}
-\def\@@@IEEEeqnarraybox[#1][#2]{\relax\@ifnextchar[{\@@@@IEEEeqnarraybox[#1][#2]}{\@@@@IEEEeqnarraybox[#1][#2][\relax]}}
-
-% #1 = decl; #2 = t,b,c; #3 = width, #4 = col specs
-\def\@@@@IEEEeqnarraybox[#1][#2][#3]#4{\endgroup\@IEEEeqnarrayISinnerfalse % not yet within the lines of the halign
-   \@IEEEeqnarraymasterstrutsave% save current master strut values
-   \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default
-   \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise
-   \IEEEvisiblestrutsfalse% diagnostic mode defaults to off
-   % no extra space unless the user specifically requests it
-   \lineskip=0pt\relax%
-   \lineskiplimit=0pt\relax%
-   \baselineskip=\normalbaselineskip\relax%
-   \jot=\IEEEnormaljot\relax%
-   \mathsurround\z@\relax% no extra spacing around math
-   % the default end glues are zero for an \IEEEeqnarraybox
-   \edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPzero}% default start glue
-   \edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPzero}% default end glue
-   \edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue
-   \@advanceIEEEeqncolcntfalse% do not advance the col counter for each col the user uses, 
-                              % used in \IEEEeqnarraymulticol and in the preamble build
-   \IEEEeqnarrayboxdecl\relax% allow a way for the user to make global overrides
-   #1\relax% allow user to override defaults
-   \let\\\@IEEEeqnarrayboxcr% replace newline with one that allows optional spacing
-   \@IEEEbuildpreamble{#4}\relax% build the preamble and put it into \@IEEEtrantmptoksA
-   % add an isolation column to the preamble to stop \\'s {} from getting into the last col
-   \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first
-   \toks0={##}%
-   % add the isolation column to the preamble
-   \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}% 
-   % set the starting tabskip glue as determined by the preamble build
-   \tabskip=\@IEEEBPstartglue\relax
-   % begin the alignment
-   \everycr{}%
-   % use only the very first token to determine the positioning
-   \@IEEEextracttoken{#2}\relax
-   \ifx\@IEEEextractedtokensdiscarded\@empty\else
-     \typeout{** WARNING: IEEEeqnarraybox position specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
-   \fi
-   % \@IEEEextractedtoken has the first token, the rest are ignored
-   % if we need to put things into and hbox and go into math mode, do so now
-   \if@IEEEeqnarrayboxHBOXSW \leavevmode \hbox \bgroup $\fi%
-   % use the appropriate vbox type
-   \if\@IEEEextractedtoken t\relax\vtop\else\if\@IEEEextractedtoken c\relax%
-   \vcenter\else\vbox\fi\fi\bgroup%
-   \@IEEEeqnarrayISinnertrue% commands are now within the lines
-   \ifx#3\relax\halign\else\halign to #3\relax\fi%
-   \bgroup
-   % "exspand" the preamble
-   \span\the\@IEEEtrantmptoksA\cr}
-
-% carry strut status and enter the isolation/strut column, 
-% exit from math mode if needed, and exit
-\def\end@IEEEeqnarraybox{\@IEEEeqnarrayglobalizestrutstatus% carry strut status
-&% enter isolation/strut column
-\@IEEEeqnarrayinsertstrut% do strut if needed
-\@IEEEeqnarraymasterstrutrestore% restore the previous master strut values
-% reset the strut system for next IEEEeqnarray
-% (sets local strut values back to previous master strut values)
-\@IEEEeqnarraystrutreset%
-% ensure last line, exit from halign, close vbox
-\crcr\egroup\egroup%
-% exit from math mode and close hbox if needed
-\if@IEEEeqnarrayboxHBOXSW $\egroup\fi}
-
-
-
-% IEEEeqnarraybox uses a modifed \\ instead of the plain \cr to
-% end rows. This allows for things like \\[vskip amount]
-% This "cr" macros are modified versions those for LaTeX2e's eqnarray
-% For IEEEeqnarraybox, \\* is the same as \\
-% the {\ifnum0=`} braces must be kept away from the last column to avoid
-% altering spacing of its math, so we use & to advance to the isolation/strut column
-% carry strut status into isolation/strut column
-\def\@IEEEeqnarrayboxcr{\@IEEEeqnarrayglobalizestrutstatus% carry strut status
-&% enter isolation/strut column
-\@IEEEeqnarrayinsertstrut% do strut if needed
-% reset the strut system for next line or IEEEeqnarray
-\@IEEEeqnarraystrutreset%
-{\ifnum0=`}\fi%
-\@ifstar{\@IEEEeqnarrayboxYCR}{\@IEEEeqnarrayboxYCR}}
-
-% test and setup the optional argument to \\[]
-\def\@IEEEeqnarrayboxYCR{\@testopt\@IEEEeqnarrayboxXCR\z@skip}
-
-% IEEEeqnarraybox does not automatically increase line spacing by \jot
-\def\@IEEEeqnarrayboxXCR[#1]{\ifnum0=`{\fi}%
-\cr\noalign{\if@IEEEeqnarrayboxnojot\else\vskip\jot\fi\vskip#1\relax}}
-
-
-
-% usage: \@IEEEbuildpreamble{column specifiers}
-% starts the halign preamble build 
-% the assembled preamble is put in \@IEEEtrantmptoksA
-\def\@IEEEbuildpreamble#1{\@IEEEtrantmptoksA={}% clear token register
-\let\@IEEEBPcurtype=u%current column type is not yet known
-\let\@IEEEBPprevtype=s%the previous column type was the start
-\let\@IEEEBPnexttype=u%next column type is not yet known
-% ensure these are valid
-\def\@IEEEBPcurglue={0pt plus 0pt minus 0pt}%
-\def\@IEEEBPcurcolname{@IEEEdefault}% name of current column definition
-% currently acquired numerically referenced glue
-% use a name that is easier to remember
-\let\@IEEEBPcurnum=\@IEEEtrantmpcountA%
-\@IEEEBPcurnum=0%
-% tracks number of columns in the preamble
-\@IEEEeqnnumcols=0%
-% record the default end glues
-\edef\@IEEEBPstartglue{\@IEEEeqnarraycolSEPdefaultstart}%
-\edef\@IEEEBPendglue{\@IEEEeqnarraycolSEPdefaultend}%
-\edef\@IEEEedefMACRO{#1}\relax% fully expand the preamble to support macro containers
-% now parse the user's column specifications
-% \ignorespaces is used as a delimiter, need at least one trailing \relax because
-% \@@IEEEbuildpreamble looks into the future 
-\expandafter\@@IEEEbuildpreamble\@IEEEedefMACRO\ignorespaces\relax\relax}
-
-
-% usage: \@@IEEEbuildpreamble{current column}{next column}
-% parses and builds the halign preamble
-\def\@@IEEEbuildpreamble#1#2{\let\@@nextIEEEbuildpreamble=\@@IEEEbuildpreamble%
-% use only the very first token to check the end
-\@IEEEextracttokengroups{#1}\relax
-\ifx\@IEEEextractedfirsttoken\ignorespaces\let\@@nextIEEEbuildpreamble=\@@IEEEfinishpreamble\else%
-% identify current and next token type
-\@IEEEgetcoltype{#1}{\@IEEEBPcurtype}{1}% current, error on invalid
-\@IEEEgetcoltype{#2}{\@IEEEBPnexttype}{0}% next, no error on invalid next
-% if curtype is a glue, get the glue def
-\if\@IEEEBPcurtype g\@IEEEgetcurglue{#1}{\@IEEEBPcurglue}\fi%
-% if curtype is a column, get the column def and set the current column name
-\if\@IEEEBPcurtype c\@IEEEgetcurcol{#1}\fi%
-% if curtype is a numeral, acquire the user defined glue
-\if\@IEEEBPcurtype n\@IEEEprocessNcol{#1}\fi%
-% process the acquired glue 
-\if\@IEEEBPcurtype g\@IEEEprocessGcol\fi%
-% process the acquired col 
-\if\@IEEEBPcurtype c\@IEEEprocessCcol\fi%
-% ready prevtype for next col spec.
-\let\@IEEEBPprevtype=\@IEEEBPcurtype%
-% be sure and put back the future token(s) as a group
-\fi\@@nextIEEEbuildpreamble{#2}}
-
-
-% usage: \@@IEEEfinishpreamble{discarded}
-% executed just after preamble build is completed
-% warn about zero cols, and if prevtype type = u, put in end tabskip glue
-% argument is not used
-\def\@@IEEEfinishpreamble#1{\ifnum\@IEEEeqnnumcols<1\relax
-\@IEEEclspkgerror{No column specifiers declared for IEEEeqnarray}%
-{At least one column type must be declared for each IEEEeqnarray.}%
-\fi%num cols less than 1
-%if last type undefined, set default end tabskip glue
-\if\@IEEEBPprevtype u\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue}\fi}
-
-
-% usage: \@IEEEgetcoltype{col specifier}{\output}{error more}
-% Identify and return the column specifier's type code in the given
-% \output macro:
-% n = number
-% g = glue (any other char in catagory 12)
-% c = letter
-% e = \ignorespaces (end of sequence)
-% u = undefined
-% error mode: 0 = no error message, 1 = error on invalid char
-\def\@IEEEgetcoltype#1#2#3{%
-% use only the very first token to determine the type
-\@IEEEextracttoken{#1}\relax
-% \@IEEEextractedtoken has the first token, the rest are discarded
-\let#2=u\relax% assume invalid until know otherwise
-\ifx\@IEEEextractedtoken\ignorespaces\let#2=e\else
-\ifcat\@IEEEextractedtoken\relax\else% screen out control sequences
-\if0\@IEEEextractedtoken\let#2=n\else
-\if1\@IEEEextractedtoken\let#2=n\else
-\if2\@IEEEextractedtoken\let#2=n\else
-\if3\@IEEEextractedtoken\let#2=n\else
-\if4\@IEEEextractedtoken\let#2=n\else
-\if5\@IEEEextractedtoken\let#2=n\else
-\if6\@IEEEextractedtoken\let#2=n\else
-\if7\@IEEEextractedtoken\let#2=n\else
-\if8\@IEEEextractedtoken\let#2=n\else
-\if9\@IEEEextractedtoken\let#2=n\else
-\ifcat,\@IEEEextractedtoken\let#2=g\relax
-\else\ifcat a\@IEEEextractedtoken\let#2=c\relax\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
-\if#2u\relax
-\if0\noexpand#3\relax\else\@IEEEclspkgerror{Invalid character in column specifications}%
-{Only letters, numerals and certain other symbols are allowed \MessageBreak
-as IEEEeqnarray column specifiers.}\fi\fi}
-
-
-% usage: \@IEEEgetcurcol{col specifier}
-% verify the letter referenced column exists
-% and return its name in \@IEEEBPcurcolname
-% if column specifier is invalid, use the default column @IEEEdefault
-\def\@IEEEgetcurcol#1{\expandafter\ifx\csname @IEEEeqnarraycolDEF#1\endcsname\@IEEEeqnarraycolisdefined%
-\def\@IEEEBPcurcolname{#1}\else% invalid column name
-\@IEEEclspkgerror{Invalid column type "#1" in column specifications.\MessageBreak
-Using a default centering column instead}%
-{You must define IEEEeqnarray column types before use.}%
-\def\@IEEEBPcurcolname{@IEEEdefault}\fi}
-
-
-% usage: \@IEEEgetcurglue{glue specifier}{\output}
-% identify the predefined (punctuation) glue value
-% and return it in the given output macro
-\def\@IEEEgetcurglue#1#2{%
-% ! = \! (neg small)  -0.16667em (-3/18 em)
-% , = \, (small)       0.16667em ( 3/18 em)
-% : = \: (med)         0.22222em ( 4/18 em)
-% ; = \; (large)       0.27778em ( 5/18 em)
-% ' = \quad            1em
-% " = \qquad           2em
-% . = 0.5\arraycolsep
-% / = \arraycolsep
-% ? = 2\arraycolsep
-% * = 1fil
-% + = \@IEEEeqnarraycolSEPcenter
-% - = \@IEEEeqnarraycolSEPzero
-% Note that all em values are referenced to the math font (textfont2) fontdimen6
-% value for 1em.
-% 
-% use only the very first token to determine the type
-\@IEEEextracttoken{#1}\relax
-\ifx\@IEEEextractedtokensdiscarded\@empty\else
-  \typeout{** WARNING: IEEEeqnarray predefined inter-column glue type specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
-\fi
-% get the math font 1em value
-% LaTeX2e's NFSS2 does not preload the fonts, but \IEEEeqnarray needs
-% to gain access to the math (\textfont2) font's spacing parameters.
-% So we create a bogus box here that uses the math font to ensure
-% that \textfont2 is loaded and ready. If this is not done,
-% the \textfont2 stuff here may not work.
-% Thanks to Bernd Raichle for his 1997 post on this topic.
-{\setbox0=\hbox{$\displaystyle\relax$}}%
-% fontdimen6 has the width of 1em (a quad).
-\@IEEEtrantmpdimenA=\fontdimen6\textfont2\relax%
-% identify the glue value based on the first token
-% we discard anything after the first
-\if!\@IEEEextractedtoken\@IEEEtrantmpdimenA=-0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
-\if,\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
-\if:\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.22222\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
-\if;\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.27778\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
-\if'\@IEEEextractedtoken\@IEEEtrantmpdimenA=1\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
-\if"\@IEEEextractedtoken\@IEEEtrantmpdimenA=2\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
-\if.\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.5\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else
-\if/\@IEEEextractedtoken\edef#2{\the\arraycolsep}\else
-\if?\@IEEEextractedtoken\@IEEEtrantmpdimenA=2\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else
-\if *\@IEEEextractedtoken\edef#2{0pt plus 1fil minus 0pt}\else
-\if+\@IEEEextractedtoken\edef#2{\@IEEEeqnarraycolSEPcenter}\else
-\if-\@IEEEextractedtoken\edef#2{\@IEEEeqnarraycolSEPzero}\else
-\edef#2{\@IEEEeqnarraycolSEPzero}%
-\@IEEEclspkgerror{Invalid predefined inter-column glue type "#1" in\MessageBreak
-column specifications. Using a default value of\MessageBreak
-0pt instead}%
-{Only !,:;'"./?*+ and - are valid predefined glue types in the\MessageBreak 
-IEEEeqnarray column specifications.}\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}
-
-
-% usage: \@IEEEprocessNcol{digit}
-% process a numerical digit from the column specification
-% and look up the corresponding user defined glue value
-% can transform current type from n to g or a as the user defined glue is acquired
-\def\@IEEEprocessNcol#1{\if\@IEEEBPprevtype g%
-\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak
-specifications. Ignoring consecutive glue specifiers\MessageBreak
-after the first}%
-{You cannot have two or more glue types next to each other\MessageBreak 
-in the IEEEeqnarray column specifications.}%
-\let\@IEEEBPcurtype=a% abort this glue, future digits will be discarded
-\@IEEEBPcurnum=0\relax%
-\else% if we previously aborted a glue
-\if\@IEEEBPprevtype a\@IEEEBPcurnum=0\let\@IEEEBPcurtype=a%maintain digit abortion
-\else%acquire this number
-% save the previous type before the numerical digits started
-\if\@IEEEBPprevtype n\else\let\@IEEEBPprevsavedtype=\@IEEEBPprevtype\fi%
-\multiply\@IEEEBPcurnum by 10\relax%
-\advance\@IEEEBPcurnum by #1\relax% add in number, \relax is needed to stop TeX's number scan
-\if\@IEEEBPnexttype n\else%close acquisition
-\expandafter\ifx\csname @IEEEeqnarraycolSEPDEF\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname\@IEEEeqnarraycolisdefined%
-\edef\@IEEEBPcurglue{\csname @IEEEeqnarraycolSEP\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname}%
-\else%user glue not defined
-\@IEEEclspkgerror{Invalid user defined inter-column glue type "\number\@IEEEBPcurnum" in\MessageBreak
-column specifications. Using a default value of\MessageBreak
-0pt instead}%
-{You must define all IEEEeqnarray numerical inter-column glue types via\MessageBreak
-\string\IEEEeqnarraydefcolsep \space before they are used in column specifications.}%
-\edef\@IEEEBPcurglue{\@IEEEeqnarraycolSEPzero}%
-\fi% glue defined or not
-\let\@IEEEBPcurtype=g% change the type to reflect the acquired glue
-\let\@IEEEBPprevtype=\@IEEEBPprevsavedtype% restore the prev type before this number glue
-\@IEEEBPcurnum=0\relax%ready for next acquisition
-\fi%close acquisition, get glue
-\fi%discard or acquire number
-\fi%prevtype glue or not
-}
-
-
-% process an acquired glue
-% add any acquired column/glue pair to the preamble
-\def\@IEEEprocessGcol{\if\@IEEEBPprevtype a\let\@IEEEBPcurtype=a%maintain previous glue abortions
-\else
-% if this is the start glue, save it, but do nothing else 
-% as this is not used in the preamble, but before
-\if\@IEEEBPprevtype s\edef\@IEEEBPstartglue{\@IEEEBPcurglue}%
-\else%not the start glue
-\if\@IEEEBPprevtype g%ignore if back to back glues
-\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak
-specifications. Ignoring consecutive glue specifiers\MessageBreak
-after the first}%
-{You cannot have two or more glue types next to each other\MessageBreak 
-in the IEEEeqnarray column specifications.}%
-\let\@IEEEBPcurtype=a% abort this glue
-\else% not a back to back glue
-\if\@IEEEBPprevtype c\relax% if the previoustype was a col, add column/glue pair to preamble
-\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi
-\toks0={##}%
-% make preamble advance col counter if this environment needs this
-\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi
-% insert the column defintion into the preamble, being careful not to expand
-% the column definition
-\@IEEEappendtoksA{\tabskip=\@IEEEBPcurglue}%
-\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}%
-\@IEEEappendtoksA{\@IEEEBPcurcolname}%
-\@IEEEappendNOEXPANDtoksA{\endcsname}%
-\@IEEEappendtoksA{\the\toks0}%
-\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax%
-\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}%
-\@IEEEappendtoksA{\@IEEEBPcurcolname}%
-\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax%
-\relax\relax\relax\relax\relax\endgroup}%
-\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble
-\else% error: non-start glue with no pending column
-\@IEEEclspkgerror{Inter-column glue specifier without a prior column\MessageBreak
-type in the column specifications. Ignoring this glue\MessageBreak 
-specifier}%
-{Except for the first and last positions, glue can be placed only\MessageBreak
-between column types.}%
-\let\@IEEEBPcurtype=a% abort this glue
-\fi% previous was a column
-\fi% back-to-back glues
-\fi% is start column glue
-\fi% prev type not a
-}
-
-
-% process an acquired letter referenced column and, if necessary, add it to the preamble
-\def\@IEEEprocessCcol{\if\@IEEEBPnexttype g\else
-\if\@IEEEBPnexttype n\else
-% we have a column followed by something other than a glue (or numeral glue)
-% so we must add this column to the preamble now
-\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi%col separator for those after the first
-\if\@IEEEBPnexttype e\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue\relax}\else%put in end glue
-\@IEEEappendtoksA{\tabskip=\@IEEEeqnarraycolSEPdefaultmid\relax}\fi% or default mid glue
-\toks0={##}%
-% make preamble advance col counter if this environment needs this
-\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi
-% insert the column definition into the preamble, being careful not to expand
-% the column definition
-\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}%
-\@IEEEappendtoksA{\@IEEEBPcurcolname}%
-\@IEEEappendNOEXPANDtoksA{\endcsname}%
-\@IEEEappendtoksA{\the\toks0}%
-\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax%
-\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}%
-\@IEEEappendtoksA{\@IEEEBPcurcolname}%
-\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax%
-\relax\relax\relax\relax\relax\endgroup}%
-\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble
-\fi%next type not numeral
-\fi%next type not glue
-}
-
-
-%%
-%% END OF IEEEeqnarray DEFINITIONS
-%%
-
-
-
-
-
-% set up the running headers and footers
-%
-% header and footer font and size specifications
-\def\@IEEEheaderstyle{\normalfont\scriptsize}
-\def\@IEEEfooterstyle{\normalfont\scriptsize}
-%
-% compsoc uses sans-serif headers and footers
-\ifCLASSOPTIONcompsoc
-  \def\@IEEEheaderstyle{\normalfont\sffamily\scriptsize}
-  \def\@IEEEfooterstyle{\normalfont\sffamily\scriptsize}
-\fi
-
-
-% standard page style, ps@headings
-\def\ps@headings{% default to standard twoside headers, no footers
-% will change later if the mode requires otherwise
-\def\@oddhead{\hbox{}\@IEEEheaderstyle\rightmark\hfil\thepage}\relax
-\def\@evenhead{\@IEEEheaderstyle\thepage\hfil\leftmark\hbox{}}\relax
-\let\@oddfoot\@empty
-\let\@evenfoot\@empty
-\ifCLASSOPTIONtechnote
-  % technote twoside
-  \def\@oddhead{\hbox{}\@IEEEheaderstyle\leftmark\hfil\thepage}\relax
-  \def\@evenhead{\@IEEEheaderstyle\thepage\hfil\leftmark\hbox{}}\relax
-\fi
-\ifCLASSOPTIONdraftcls
-  % draft footers
-  \def\@oddfoot{\@IEEEfooterstyle\@date\hfil DRAFT}\relax
-  \def\@evenfoot{\@IEEEfooterstyle DRAFT\hfil\@date}\relax
-\fi
-% oneside
-\if@twoside\else
-  % standard one side headers
-  \def\@oddhead{\hbox{}\@IEEEheaderstyle\leftmark\hfil\thepage}\relax
-  \let\@evenhead\@empty
-  \ifCLASSOPTIONdraftcls
-    % oneside draft footers
-    \def\@oddfoot{\@IEEEfooterstyle\@date\hfil DRAFT}\relax
-    \let\@evenfoot\@empty
-  \fi
-\fi
-% turn off headers for conferences
-\ifCLASSOPTIONconference
-  \let\@oddhead\@empty
-  \let\@evenhead\@empty
-\fi
-% turn off footers for draftclsnofoot
-\ifCLASSOPTIONdraftclsnofoot
-  \let\@oddfoot\@empty
-  \let\@evenfoot\@empty
-\fi}
-
-
-% title page style, ps@IEEEtitlepagestyle
-\def\ps@IEEEtitlepagestyle{% default title page headers, no footers
-\def\@oddhead{\hbox{}\@IEEEheaderstyle\leftmark\hfil\thepage}\relax
-\def\@evenhead{\@IEEEheaderstyle\thepage\hfil\leftmark\hbox{}}\relax
-\let\@oddfoot\@empty
-\let\@evenfoot\@empty
-% will change later if the mode requires otherwise
-\ifCLASSOPTIONdraftcls
-  % draft footers
-  \ifCLASSOPTIONdraftclsnofoot\else
-    % but only if not draftclsnofoot
-    \def\@oddfoot{\@IEEEfooterstyle\@date\hfil DRAFT}\relax
-    \def\@evenfoot{\@IEEEfooterstyle DRAFT\hfil\@date}\relax
-  \fi
-\else
-  % all nondraft mode footers
-  \if@IEEEusingpubid
-    % for title pages that are using a pubid
-    % do not repeat pubid on the title page if using a peer review cover page
-    \ifCLASSOPTIONpeerreview\else
-      % for noncompsoc papers, the pubid uses footnotesize and
-      % is at the same vertical position as where the last baseline would normally be
-      \def\@oddfoot{\hbox{}\hss\@IEEEfooterstyle\footnotesize\raisebox{\footskip}[0pt][0pt]{\@IEEEpubid}\hss\hbox{}}\relax
-      \def\@evenfoot{\hbox{}\hss\@IEEEfooterstyle\footnotesize\raisebox{\footskip}[0pt][0pt]{\@IEEEpubid}\hss\hbox{}}\relax
-      \ifCLASSOPTIONcompsoc
-        % for compsoc papers, the pubid is at the same vertical position as the normal footer
-        \def\@oddfoot{\hbox{}\hss\@IEEEfooterstyle\raisebox{0pt}[0pt][0pt]{\@IEEEpubid}\hss\hbox{}}\relax
-        \def\@evenfoot{\hbox{}\hss\@IEEEfooterstyle\raisebox{0pt}[0pt][0pt]{\@IEEEpubid}\hss\hbox{}}\relax
-      \fi
-    \fi
-  \fi
-\fi
-% turn off headers for conferences
-\ifCLASSOPTIONconference
-  \let\@oddhead\@empty
-  \let\@evenhead\@empty
-\fi}
-
-
-% peer review cover page style, ps@IEEEpeerreviewcoverpagestyle
-\def\ps@IEEEpeerreviewcoverpagestyle{% default peer review cover no headers, no footers
-\let\@oddhead\@empty
-\let\@evenhead\@empty
-\let\@oddfoot\@empty
-\let\@evenfoot\@empty
-% will change later if the mode requires otherwise
-\ifCLASSOPTIONdraftcls
-  % draft footers
-  \ifCLASSOPTIONdraftclsnofoot\else
-    % but only if not draftclsnofoot
-    \def\@oddfoot{\@IEEEfooterstyle\@date\hfil DRAFT}\relax
-    \def\@evenfoot{\@IEEEfooterstyle DRAFT\hfil\@date}\relax
-  \fi
-\else
-  % all nondraft mode footers
-  \if@IEEEusingpubid
-    % for peer review cover pages that are using a pubid
-    % for noncompsoc papers, the pubid uses footnotesize and
-    % is at the same vertical position as where the last baseline would normally be
-    \def\@oddfoot{\hbox{}\hss\@IEEEfooterstyle\footnotesize\raisebox{\footskip}[0pt][0pt]{\@IEEEpubid}\hss\hbox{}}\relax
-    \def\@evenfoot{\hbox{}\hss\@IEEEfooterstyle\footnotesize\raisebox{\footskip}[0pt][0pt]{\@IEEEpubid}\hss\hbox{}}\relax
-    \ifCLASSOPTIONcompsoc
-      % for compsoc papers, the pubid is at the same vertical position as the normal footer
-      \def\@oddfoot{\hbox{}\hss\@IEEEfooterstyle\raisebox{0pt}[0pt][0pt]{\@IEEEpubid}\hss\hbox{}}\relax
-      \def\@evenfoot{\hbox{}\hss\@IEEEfooterstyle\raisebox{0pt}[0pt][0pt]{\@IEEEpubid}\hss\hbox{}}\relax
-    \fi
-  \fi
-\fi}
-
-
-
-%% Defines the command for putting the header.
-%% Note that all the text is forced into uppercase, if you have some text
-%% that needs to be in lower case, for instance et. al., then either manually
-%% set \leftmark and \rightmark or use \MakeLowercase{et. al.} within the
-%% arguments to \markboth.
-%% V1.7b add \protect to work with Babel
-\def\markboth#1#2{\def\leftmark{\MakeUppercase{\protect#1}}%
-\def\rightmark{\MakeUppercase{\protect#2}}}
-
-\def\today{\ifcase\month\or
-    January\or February\or March\or April\or May\or June\or
-    July\or August\or September\or October\or November\or December\fi
-    \space\number\day, \number\year}
-
-
-
-
-%% CITATION AND BIBLIOGRAPHY COMMANDS
-%% 
-%% V1.6 no longer supports the older, nonstandard \shortcite and \citename setup stuff
-% 
-% 
-% Modify Latex2e \@citex to separate citations with "], ["
-\def\@citex[#1]#2{%
-  \let\@citea\@empty
-  \@cite{\@for\@citeb:=#2\do
-    {\@citea\def\@citea{], [}%
-     \edef\@citeb{\expandafter\@firstofone\@citeb\@empty}%
-     \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
-     \@ifundefined{b@\@citeb}{\mbox{\reset@font\bfseries ?}%
-       \G@refundefinedtrue
-       \@latex@warning
-         {Citation `\@citeb' on page \thepage \space undefined}}%
-       {\hbox{\csname b@\@citeb\endcsname}}}}{#1}}
-
-% V1.6 we create hooks for the optional use of Donald Arseneau's
-% cite.sty package. cite.sty is "smart" and will notice that the
-% following format controls are already defined and will not
-% redefine them. The result will be the proper sorting of the
-% citation numbers and auto detection of 3 or more entry "ranges" -
-% all in IEEE style:  [1], [2], [5]--[7], [12]
-% This also allows for an optional note, i.e., \cite[mynote]{..}.
-% If the \cite with note has more than one reference, the note will
-% be applied to the last of the listed references. It is generally
-% desired that if a note is given, only one reference is listed in
-% that \cite.
-% Thanks to Mr. Arseneau for providing the required format arguments
-% to produce the IEEE style.
-\def\citepunct{], [}
-\def\citedash{]--[}
-
-% V1.7 default to using same font for urls made by url.sty
-\AtBeginDocument{\csname url@samestyle\endcsname}
-
-% V1.6 class files should always provide these
-\def\newblock{\hskip .11em\@plus.33em\@minus.07em}
-\let\@openbib@code\@empty
-% V1.8b article.cls is now providing these too
-% we do not use \@mkboth, nor alter the page style
-\newenvironment{theindex}
-               {\if@twocolumn
-                  \@restonecolfalse
-                \else
-                  \@restonecoltrue
-                \fi
-                \twocolumn[\section*{\indexname}]%
-                \parindent\z@
-                \parskip\z@ \@plus .3\p@\relax
-                \columnseprule \z@
-                \columnsep 35\p@
-                \let\item\@idxitem}
-               {\if@restonecol\onecolumn\else\clearpage\fi}
-\newcommand\@idxitem{\par\hangindent 40\p@}
-\newcommand\subitem{\@idxitem \hspace*{20\p@}}
-\newcommand\subsubitem{\@idxitem \hspace*{30\p@}}
-\newcommand\indexspace{\par \vskip 10\p@ \@plus5\p@ \@minus3\p@\relax}
-
-
-
-% Provide support for the control entries of IEEEtran.bst V1.00 and later.
-% V1.7 optional argument allows for a different aux file to be specified in
-% order to handle multiple bibliographies. For example, with multibib.sty:
-% \newcites{sec}{Secondary Literature}
-% \bstctlcite[@auxoutsec]{BSTcontrolhak}
-\def\bstctlcite{\@ifnextchar[{\@bstctlcite}{\@bstctlcite[@auxout]}}
-\def\@bstctlcite[#1]#2{\@bsphack
-  \@for\@citeb:=#2\do{%
-    \edef\@citeb{\expandafter\@firstofone\@citeb}%
-    \if@filesw\immediate\write\csname #1\endcsname{\string\citation{\@citeb}}\fi}%
-  \@esphack}
-
-% \IEEEnoauxwrite{} allows for citations that do not add to or affect
-% the order of the existing citation list. Can be useful for \cite
-% within \thanks{}.
-\DeclareRobustCommand{\IEEEnoauxwrite}[1]{\relax
-\if@filesw
-\@fileswfalse
-#1\relax\relax\relax\relax\relax
-\@fileswtrue
-\else
-#1\relax\relax\relax\relax\relax
-\fi}
-
-% V1.6 provide a way for a user to execute a command just before 
-% a given reference number - used to insert a \newpage to balance
-% the columns on the last page
-\edef\@IEEEtriggerrefnum{0}   % the default of zero means that
-                              % the command is not executed
-\def\@IEEEtriggercmd{\newpage}
-
-% allow the user to alter the triggered command
-\long\def\IEEEtriggercmd#1{\long\def\@IEEEtriggercmd{#1}}
-
-% allow user a way to specify the reference number just before the
-% command is executed
-\def\IEEEtriggeratref#1{\@IEEEtrantmpcountA=#1%
-\edef\@IEEEtriggerrefnum{\the\@IEEEtrantmpcountA}}%
-
-% trigger command at the given reference
-\def\@IEEEbibitemprefix{\@IEEEtrantmpcountA=\@IEEEtriggerrefnum\relax%
-\advance\@IEEEtrantmpcountA by -1\relax%
-\ifnum\c@enumiv=\@IEEEtrantmpcountA\relax\@IEEEtriggercmd\relax\fi}
-
-
-\def\@biblabel#1{[#1]}
-
-% compsoc journals and conferences left align the reference numbers
-\@IEEEcompsoconly{\def\@biblabel#1{[#1]\hfill}}
-
-% controls bib item spacing
-\def\IEEEbibitemsep{0pt plus .5pt}
-
-\@IEEEcompsocconfonly{\def\IEEEbibitemsep{0.5\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}}
-
-
-\def\thebibliography#1{\section*{\refname}%
-    \addcontentsline{toc}{section}{\refname}%
-    % V1.6 add some rubber space here and provide a command trigger
-    \footnotesize\vskip 0.3\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip%
-    \list{\@biblabel{\@arabic\c@enumiv}}%
-    {\settowidth\labelwidth{\@biblabel{#1}}%
-    \leftmargin\labelwidth
-    \advance\leftmargin\labelsep\relax
-    \itemsep \IEEEbibitemsep\relax
-    \usecounter{enumiv}%
-    \let\p@enumiv\@empty
-    \renewcommand\theenumiv{\@arabic\c@enumiv}}%
-    \let\@IEEElatexbibitem\bibitem%
-    \def\bibitem{\@IEEEbibitemprefix\@IEEElatexbibitem}%
-\def\newblock{\hskip .11em plus .33em minus .07em}%
-% originally:
-%   \sloppy\clubpenalty4000\widowpenalty4000%
-% by adding the \interlinepenalty here, we make it more
-% difficult, but not impossible, for LaTeX to break within a reference.
-% The IEEE almost never breaks a reference (but they do it more often with
-% technotes). You may get an underfull vbox warning around the bibliography, 
-% but the final result will be much more like what the IEEE will publish. 
-% MDS 11/2000
-\ifCLASSOPTIONtechnote\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty100%
-\else\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty500\fi%
-    \sfcode`\.=1000\relax}
-\let\endthebibliography=\endlist
-
-
-
-
-% TITLE PAGE COMMANDS
-% 
-% 
-% \IEEEmembership is used to produce the sublargesize italic font used to indicate author 
-% IEEE membership. compsoc uses a large size sans slant font
-\def\IEEEmembership#1{{\@IEEEnotcompsoconly{\sublargesize}\normalfont\@IEEEcompsoconly{\sffamily}\textit{#1}}}
- 
-
-% \IEEEauthorrefmark{} produces a footnote type symbol to indicate author affiliation.
-% When given an argument of 1 to 9, \IEEEauthorrefmark{} follows the standard LaTeX footnote
-% symbol sequence convention. However, for arguments 10 and above, \IEEEauthorrefmark{} 
-% reverts to using lower case roman numerals, so it cannot overflow. Do note that you 
-% cannot use \footnotemark[] in place of \IEEEauthorrefmark{} within \author as the footnote
-% symbols will have been turned off to prevent \thanks from creating footnote marks.
-% \IEEEauthorrefmark{} produces a symbol that appears to LaTeX as having zero vertical
-% height - this allows for a more compact line packing, but the user must ensure that
-% the interline spacing is large enough to prevent \IEEEauthorrefmark{} from colliding
-% with the text above.
-% V1.7 make this a robust command
-% V1.8 transmag uses an arabic author affiliation symbol
-\ifCLASSOPTIONtransmag
-\DeclareRobustCommand*{\IEEEauthorrefmark}[1]{\raisebox{0pt}[0pt][0pt]{\textsuperscript{\footnotesize #1}}}
-\else
-\DeclareRobustCommand*{\IEEEauthorrefmark}[1]{\raisebox{0pt}[0pt][0pt]{\textsuperscript{\footnotesize\ensuremath{\ifcase#1\or *\or \dagger\or \ddagger\or%
-    \mathsection\or \mathparagraph\or \|\or **\or \dagger\dagger%
-    \or \ddagger\ddagger \else\textsuperscript{\expandafter\romannumeral#1}\fi}}}}
-\fi
-
-
-% FONT CONTROLS AND SPACINGS FOR CONFERENCE MODE AUTHOR NAME AND AFFILIATION BLOCKS
-% 
-% The default font styles for the author name and affiliation blocks (confmode)
-\def\@IEEEauthorblockNstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\sublargesize}
-\def\@IEEEauthorblockAstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\@IEEEcompsocconfonly{\itshape}\normalsize}
-% The default if the user does not use an author block
-\def\@IEEEauthordefaulttextstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\sublargesize}
-
-% adjustment spacing from title (or special paper notice) to author name blocks (confmode)
-% can be negative
-\def\@IEEEauthorblockconfadjspace{-0.25em}
-% compsoc conferences need more space here
-\@IEEEcompsocconfonly{\def\@IEEEauthorblockconfadjspace{0.75\@IEEEnormalsizeunitybaselineskip}}
-
-% spacing between name and affiliation blocks (confmode)
-% This can be negative.
-% The IEEE doesn't want any added spacing here, but I will leave these
-% controls in place in case they ever change their mind.
-% Personally, I like 0.75ex.
-%\def\@IEEEauthorblockNtopspace{0.75ex}
-%\def\@IEEEauthorblockAtopspace{0.75ex}
-\def\@IEEEauthorblockNtopspace{0.0ex}
-\def\@IEEEauthorblockAtopspace{0.0ex}
-\ifCLASSOPTIONtransmag
-% transmag uses one line of space above first affiliation block
-\def\@IEEEauthorblockAtopspace{1\@IEEEnormalsizeunitybaselineskip}
-\fi
-
-% baseline spacing within name and affiliation blocks (confmode)
-% must be positive, spacings below certain values will make 
-% the position of line of text sensitive to the contents of the
-% line above it i.e., whether or not the prior line has descenders, 
-% subscripts, etc. For this reason it is a good idea to keep
-% these above 2.6ex
-\def\@IEEEauthorblockNinterlinespace{2.6ex}
-\def\@IEEEauthorblockAinterlinespace{2.75ex}
-
-% This tracks the required strut size.
-% See the \@IEEEauthorhalign command for the actual default value used.
-\def\@IEEEauthorblockXinterlinespace{2.7ex}
-
-% variables to retain font size and style across groups
-% values given here have no effect as they will be overwritten later
-\gdef\@IEEESAVESTATEfontsize{10}
-\gdef\@IEEESAVESTATEfontbaselineskip{12}
-\gdef\@IEEESAVESTATEfontencoding{OT1}
-\gdef\@IEEESAVESTATEfontfamily{ptm}
-\gdef\@IEEESAVESTATEfontseries{m}
-\gdef\@IEEESAVESTATEfontshape{n}
-
-% saves the current font attributes
-\def\@IEEEcurfontSAVE{\global\let\@IEEESAVESTATEfontsize\f@size%
-\global\let\@IEEESAVESTATEfontbaselineskip\f@baselineskip%
-\global\let\@IEEESAVESTATEfontencoding\f@encoding%
-\global\let\@IEEESAVESTATEfontfamily\f@family%
-\global\let\@IEEESAVESTATEfontseries\f@series%
-\global\let\@IEEESAVESTATEfontshape\f@shape}
-
-% restores the saved font attributes
-\def\@IEEEcurfontRESTORE{\fontsize{\@IEEESAVESTATEfontsize}{\@IEEESAVESTATEfontbaselineskip}%
-\fontencoding{\@IEEESAVESTATEfontencoding}%
-\fontfamily{\@IEEESAVESTATEfontfamily}%
-\fontseries{\@IEEESAVESTATEfontseries}%
-\fontshape{\@IEEESAVESTATEfontshape}%
-\selectfont}
-
-
-% variable to indicate if the current block is the first block in the column
-\newif\if@IEEEprevauthorblockincol   \@IEEEprevauthorblockincolfalse
-
-
-% the command places a strut with height and depth = \@IEEEauthorblockXinterlinespace
-% we use this technique to have complete manual control over the spacing of the lines
-% within the halign environment.
-% We set the below baseline portion at 30%, the above
-% baseline portion at 70% of the total length.
-% Responds to changes in the document's \baselinestretch
-\def\@IEEEauthorstrutrule{\@IEEEtrantmpdimenA\@IEEEauthorblockXinterlinespace%
-\@IEEEtrantmpdimenA=\baselinestretch\@IEEEtrantmpdimenA%
-\rule[-0.3\@IEEEtrantmpdimenA]{0pt}{\@IEEEtrantmpdimenA}}
-
-
-% blocks to hold the authors' names and affilations. 
-% Makes formatting easy for conferences
-%
-% use real definitions in conference mode
-% name block
-\def\IEEEauthorblockN#1{\relax\@IEEEauthorblockNstyle% set the default text style
-\gdef\@IEEEauthorblockXinterlinespace{0pt}% disable strut for spacer row
-% the \expandafter hides the \cr in conditional tex, see the array.sty docs
-% for details, probably not needed here as the \cr is in a macro
-% do a spacer row if needed
-\if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockNtopspaceline\fi
-\global\@IEEEprevauthorblockincoltrue% we now have a block in this column
-%restore the correct strut value
-\gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockNinterlinespace}%
-% input the author names
-#1%
-% end the row if the user did not already
-\crcr}
-% spacer row for names
-\def\@IEEEauthorblockNtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockNtopspace}}
-%
-% affiliation block
-\def\IEEEauthorblockA#1{\relax\@IEEEauthorblockAstyle% set the default text style
-\gdef\@IEEEauthorblockXinterlinespace{0pt}%disable strut for spacer row
-% the \expandafter hides the \cr in conditional tex, see the array.sty docs
-% for details, probably not needed here as the \cr is in a macro
-% do a spacer row if needed
-\if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockAtopspaceline\fi
-\global\@IEEEprevauthorblockincoltrue% we now have a block in this column
-%restore the correct strut value
-\gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockAinterlinespace}%
-% input the author affiliations
-#1%
-% end the row if the user did not already
-\crcr
-% V1.8 transmag does not use any additional affiliation spacing after the first author
-\ifCLASSOPTIONtransmag\gdef\@IEEEauthorblockAtopspace{0pt}\fi}
-
-% spacer row for affiliations
-\def\@IEEEauthorblockAtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockAtopspace}}
-
-
-% allow papers to compile even if author blocks are used in modes other
-% than conference or peerreviewca. For such cases, we provide dummy blocks.
-\ifCLASSOPTIONconference
-\else
-   \ifCLASSOPTIONpeerreviewca\else
-      % not conference, peerreviewca or transmag mode
-      \ifCLASSOPTIONtransmag\else
-         \def\IEEEauthorblockN#1{#1}%
-         \def\IEEEauthorblockA#1{#1}%
-      \fi
-   \fi
-\fi
-
-
-
-% we provide our own halign so as not to have to depend on tabular
-\def\@IEEEauthorhalign{\@IEEEauthordefaulttextstyle% default text style
-   \lineskip=0pt\relax% disable line spacing
-   \lineskiplimit=0pt\relax%
-   \baselineskip=0pt\relax%
-   \@IEEEcurfontSAVE% save the current font
-   \mathsurround\z@\relax% no extra spacing around math
-   \let\\\@IEEEauthorhaligncr% replace newline with halign friendly one
-   \tabskip=0pt\relax% no column spacing
-   \everycr{}% ensure no problems here
-   \@IEEEprevauthorblockincolfalse% no author blocks yet
-   \def\@IEEEauthorblockXinterlinespace{2.7ex}% default interline space
-   \vtop\bgroup%vtop box
-   \halign\bgroup&\relax\hfil\@IEEEcurfontRESTORE\relax ##\relax
-   \hfil\@IEEEcurfontSAVE\@IEEEauthorstrutrule\cr}
-
-% ensure last line, exit from halign, close vbox
-\def\end@IEEEauthorhalign{\crcr\egroup\egroup}
-
-% handle bogus star form
-\def\@IEEEauthorhaligncr{{\ifnum0=`}\fi\@ifstar{\@@IEEEauthorhaligncr}{\@@IEEEauthorhaligncr}}
-
-% test and setup the optional argument to \\[]
-\def\@@IEEEauthorhaligncr{\@testopt\@@@IEEEauthorhaligncr\z@skip}
-
-% end the line and do the optional spacer
-\def\@@@IEEEauthorhaligncr[#1]{\ifnum0=`{\fi}\cr\noalign{\vskip#1\relax}}
-
-
-
-% flag to prevent multiple \and warning messages
-\newif\if@IEEEWARNand
-\@IEEEWARNandtrue
-
-% if in conference or peerreviewca modes, we support the use of \and as \author is a
-% tabular environment, otherwise we warn the user that \and is invalid
-% outside of conference or peerreviewca modes.
-\def\and{\relax} % provide a bogus \and that we will then override
-
-\renewcommand{\and}[1][\relax]{\if@IEEEWARNand\typeout{** WARNING: \noexpand\and is valid only
-                               when in conference or peerreviewca}\typeout{modes (line \the\inputlineno).}\fi\global\@IEEEWARNandfalse}
-
-\ifCLASSOPTIONconference%
-\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%
-\fi
-\ifCLASSOPTIONpeerreviewca
-\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%
-\fi
-% V1.8 transmag uses conference author format
-\ifCLASSOPTIONtransmag
-\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%
-\fi
-
-% page clearing command
-% based on LaTeX2e's \cleardoublepage, but allows different page styles
-% for the inserted blank pages
-\def\@IEEEcleardoublepage#1{\clearpage\if@twoside\ifodd\c@page\else
-\hbox{}\thispagestyle{#1}\newpage\if@twocolumn\hbox{}\thispagestyle{#1}\newpage\fi\fi\fi}
-
-% V1.8b hooks to allow adjustment of space above title
-\def\IEEEtitletopspace{0.5\baselineskip}
-% an added extra amount to allow for adjustment/offset
-\def\IEEEtitletopspaceextra{0pt}
-
-% user command to invoke the title page
-\def\maketitle{\par%
-  \begingroup%
-  \normalfont%
-  \def\thefootnote{}%  the \thanks{} mark type is empty
-  \def\footnotemark{}% and kill space from \thanks within author
-  \let\@makefnmark\relax% V1.7, must *really* kill footnotemark to remove all \textsuperscript spacing as well.
-  \footnotesize%       equal spacing between thanks lines
-  \footnotesep 0.7\baselineskip%see global setting of \footnotesep for more info
-  % V1.7 disable \thanks note indention for compsoc
-  \@IEEEcompsoconly{\long\def\@makefntext##1{\parindent 1em\noindent\hbox{\@makefnmark}##1}}%
-  \normalsize%
-  \ifCLASSOPTIONpeerreview
-     \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
-     \thispagestyle{IEEEpeerreviewcoverpagestyle}\@thanks%
-  \else
-     \if@twocolumn%
-        \ifCLASSOPTIONtechnote%
-           \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
-        \else
-           \twocolumn[{\IEEEquantizevspace{\@maketitle}[\IEEEquantizedisabletitlecmds]{0pt}[-\topskip]{\baselineskip}{\@IEEENORMtitlevspace}{\@IEEEMINtitlevspace}\@IEEEaftertitletext}]%
-        \fi
-     \else
-        \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
-     \fi
-     \thispagestyle{IEEEtitlepagestyle}\@thanks%
-  \fi
-  % pullup page for pubid if used.
-  \if@IEEEusingpubid
-     \enlargethispage{-\@IEEEpubidpullup}%
-  \fi 
-  \endgroup
-  \setcounter{footnote}{0}\let\maketitle\relax\let\@maketitle\relax
-  \gdef\@thanks{}%
-  % v1.6b do not clear these as we will need the title again for peer review papers
-  % \gdef\@author{}\gdef\@title{}%
-  \let\thanks\relax}
-
-
-% V1.8 parbox to format \@IEEEtitleabstractindextext
-\long\def\@IEEEtitleabstractindextextbox#1{\parbox{1\textwidth}{#1}}
-% V1.8 compsoc is partial width
-\ifCLASSOPTIONcompsoc
-% comparison with proofs suggests it's in the range of 92.1-92.3%
-\long\def\@IEEEtitleabstractindextextbox#1{\parbox{0.922\textwidth}{\@IEEEcompsocnotconfonly{\rightskip\@flushglue\leftskip\z@skip}#1}}
-\fi
-
-% formats the Title, authors names, affiliations and special paper notice
-% THIS IS A CONTROLLED SPACING COMMAND! Do not allow blank lines or unintentional
-% spaces to enter the definition - use % at the end of each line
-\def\@maketitle{\newpage
-\bgroup\par\vskip\IEEEtitletopspace\vskip\IEEEtitletopspaceextra\centering%
-\ifCLASSOPTIONtechnote% technotes, V1.8a abstract and index terms are not treated differently for compsoc technotes
-   {\bfseries\large\@IEEEcompsoconly{\Large\sffamily}\@title\par}\vskip 1.3em{\lineskip .5em\@IEEEcompsoconly{\large\sffamily}\@author
-   \@IEEEspecialpapernotice\par}\relax
-\else% not a technote
-   \vskip0.2em{\Huge\ifCLASSOPTIONtransmag\bfseries\LARGE\fi\@IEEEcompsoconly{\sffamily}\@IEEEcompsocconfonly{\normalfont\normalsize\vskip 2\@IEEEnormalsizeunitybaselineskip
-   \bfseries\Large}\@IEEEcompsocnotconfonly{\vskip 0.75\@IEEEnormalsizeunitybaselineskip}\@title\par}\relax
-   \@IEEEcompsocnotconfonly{\vskip 0.5\@IEEEnormalsizeunitybaselineskip}\vskip1.0em\par%
-   % V1.6 handle \author differently if in conference mode
-   \ifCLASSOPTIONconference%
-      {\@IEEEspecialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%
-       \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par}\relax
-   \else% peerreviewca, peerreview or journal
-      \ifCLASSOPTIONpeerreviewca
-         % peerreviewca handles author names just like conference mode
-         {\@IEEEcompsoconly{\sffamily}\@IEEEspecialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%
-          \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par
-          {\@IEEEcompsoconly{\vskip 1.5em\relax
-           \@IEEEtitleabstractindextextbox{\@IEEEtitleabstractindextext}\par\noindent\hfill
-           \IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax
-      \else% journal, peerreview or transmag
-         \ifCLASSOPTIONtransmag
-            % transmag also handles author names just like conference mode
-            % it also uses \@IEEEtitleabstractindextex, but with one line less
-            % space above, and one more below
-           {\@IEEEspecialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%
-            \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par
-           {\vspace{0.5\baselineskip}\relax\@IEEEtitleabstractindextextbox{\@IEEEtitleabstractindextext}\vspace{-1\baselineskip}\par}}\relax
-         \else% journal or peerreview
-           {\lineskip.5em\@IEEEcompsoconly{\sffamily}\sublargesize\@author\@IEEEspecialpapernotice\par
-           {\@IEEEcompsoconly{\vskip 1.5em\relax
-            \@IEEEtitleabstractindextextbox{\@IEEEtitleabstractindextext}\par\noindent\hfill
-            \IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax
-         \fi
-      \fi
-   \fi
-\fi\par\addvspace{0.5\baselineskip}\egroup}
-
-
-% V1.7 Computer Society "diamond line" which follows index terms for nonconference papers
-% V1.8a full width diamond line for single column use
-\def\@IEEEcompsocdiamondlinei{\vrule depth 0pt height 0.5pt width 4cm\nobreak\hspace{7.5pt}\nobreak
-\raisebox{-3.5pt}{\fontfamily{pzd}\fontencoding{U}\fontseries{m}\fontshape{n}\fontsize{11}{12}\selectfont\char70}\nobreak
-\hspace{7.5pt}\nobreak\vrule depth 0pt height 0.5pt width 4cm\relax}
-% V1.8a narrower width diamond line for double column use
-\def\@IEEEcompsocdiamondlineii{\vrule depth 0pt height 0.5pt width 2.5cm\nobreak\hspace{7.5pt}\nobreak
-\raisebox{-3.5pt}{\fontfamily{pzd}\fontencoding{U}\fontseries{m}\fontshape{n}\fontsize{11}{12}\selectfont\char70}\nobreak
-\hspace{7.5pt}\nobreak\vrule depth 0pt height 0.5pt width 2.5cm\relax}
-% V1.8a bare core without rules to base a last resort on for very narrow linewidths
-\def\@IEEEcompsocdiamondlineiii{\mbox{}\nobreak\hspace{7.5pt}\nobreak
-\raisebox{-3.5pt}{\fontfamily{pzd}\fontencoding{U}\fontseries{m}\fontshape{n}\fontsize{11}{12}\selectfont\char70}\nobreak
-\hspace{7.5pt}\nobreak\mbox{}\relax}
-
-% V1.8a allow \IEEEcompsocdiamondline to adjust for different linewidths.
-% Use \@IEEEcompsocdiamondlinei if its width is less than 0.66\linewidth (0.487 nominal for single column)
-% if not, fall back to \@IEEEcompsocdiamondlineii if its width is less than 0.75\linewidth (0.659 nominal for double column)
-% if all else fails, try to make a custom diamondline based on the abnormally narrow linewidth
-\def\IEEEcompsocdiamondline{\settowidth{\@IEEEtrantmpdimenA}{\@IEEEcompsocdiamondlinei}\relax
-\ifdim\@IEEEtrantmpdimenA<0.66\linewidth\relax\@IEEEcompsocdiamondlinei\relax
-\else
-\settowidth{\@IEEEtrantmpdimenA}{\@IEEEcompsocdiamondlineii}\relax
-\ifdim\@IEEEtrantmpdimenA<0.75\linewidth\relax\@IEEEcompsocdiamondlineii\relax
-\else
-\settowidth{\@IEEEtrantmpdimenA}{\@IEEEcompsocdiamondlineiii}\relax
-\@IEEEtrantmpdimenB=\linewidth\relax
-\addtolength{\@IEEEtrantmpdimenB}{-1\@IEEEtrantmpdimenA}\relax
-\vrule depth 0pt height 0.5pt width 0.33\@IEEEtrantmpdimenB\@IEEEcompsocdiamondlineiii\vrule depth 0pt height 0.5pt width 0.33\@IEEEtrantmpdimenB\relax
-\fi\fi}
-
-
-% V1.7 standard LateX2e \thanks, but with \itshape under compsoc. Also make it a \long\def
-% We also need to trigger the one-shot footnote rule
-\def\@IEEEtriggeroneshotfootnoterule{\global\@IEEEenableoneshotfootnoteruletrue}
-
-
-\long\def\thanks#1{\footnotemark
-    \protected@xdef\@thanks{\@thanks
-        \protect\footnotetext[\the\c@footnote]{\@IEEEcompsoconly{\itshape
-        \protect\@IEEEtriggeroneshotfootnoterule\relax}\ignorespaces#1}}}
-\let\@thanks\@empty
-
-
-% V1.7 allow \author to contain \par's. This is needed to allow \thanks to contain \par.
-\long\def\author#1{\gdef\@author{#1}}
-
-
-% in addition to setting up IEEEitemize, we need to remove a baselineskip space above and
-% below it because \list's \pars introduce blank lines because of the footnote struts.
-\def\@IEEEsetupcompsocitemizelist{\def\labelitemi{$\bullet$}%
-\setlength{\IEEElabelindent}{0pt}\setlength{\labelsep}{1.2em}\setlength{\parskip}{0pt}%
-\setlength{\partopsep}{0pt}\setlength{\topsep}{0.5\baselineskip}\vspace{-1\baselineskip}\relax}
-
-
-% flag for fake non-compsoc \IEEEcompsocthanksitem - prevents line break on very first item
-\newif\if@IEEEbreakcompsocthanksitem \@IEEEbreakcompsocthanksitemfalse
-
-\ifCLASSOPTIONcompsoc
-% V1.7 compsoc bullet item \thanks
-% also, we need to redefine this to destroy the argument in \IEEEquantizevspace
-\long\def\IEEEcompsocitemizethanks#1{\relax\@IEEEbreakcompsocthanksitemfalse\footnotemark
-    \protected@xdef\@thanks{\@thanks
-        \protect\footnotetext[\the\c@footnote]{\itshape\protect\@IEEEtriggeroneshotfootnoterule
-        {\let\IEEEiedlistdecl\relax\protect\begin{IEEEitemize}[\protect\@IEEEsetupcompsocitemizelist]\ignorespaces#1\relax
-        \protect\end{IEEEitemize}}\protect\vspace{-1\baselineskip}}}}
-\DeclareRobustCommand*{\IEEEcompsocthanksitem}{\item}
-\else
-% non-compsoc, allow for dual compilation via rerouting to normal \thanks
-\long\def\IEEEcompsocitemizethanks#1{\thanks{#1}}
-% redirect to "pseudo-par" \hfil\break\indent after swallowing [] from \IEEEcompsocthanksitem[]
-\DeclareRobustCommand{\IEEEcompsocthanksitem}{\@ifnextchar [{\@IEEEthanksswallowoptionalarg}%
-{\@IEEEthanksswallowoptionalarg[\relax]}}
-% be sure and break only after first item, be sure and ignore spaces after optional argument
-\def\@IEEEthanksswallowoptionalarg[#1]{\relax\if@IEEEbreakcompsocthanksitem\hfil\break
-\indent\fi\@IEEEbreakcompsocthanksitemtrue\ignorespaces}
-\fi
-
-
-% V1.6b define the \IEEEpeerreviewmaketitle as needed
-\ifCLASSOPTIONpeerreview
-\def\IEEEpeerreviewmaketitle{\@IEEEcleardoublepage{empty}%
-\ifCLASSOPTIONtwocolumn
-\twocolumn[{\IEEEquantizevspace{\@IEEEpeerreviewmaketitle}[\IEEEquantizedisabletitlecmds]{0pt}[-\topskip]{\baselineskip}{\@IEEENORMtitlevspace}{\@IEEEMINtitlevspace}}]
-\else
-\newpage\@IEEEpeerreviewmaketitle\@IEEEstatictitlevskip
-\fi
-\thispagestyle{IEEEtitlepagestyle}}
-\else
-% \IEEEpeerreviewmaketitle does nothing if peer review option has not been selected
-\def\IEEEpeerreviewmaketitle{\relax}
-\fi
-
-% peerreview formats the repeated title like the title in journal papers.
-\def\@IEEEpeerreviewmaketitle{\bgroup\par\addvspace{0.5\baselineskip}\centering\@IEEEcompsoconly{\sffamily}%
-\normalfont\normalsize\vskip0.2em{\Huge\@title\par}\vskip1.0em\par
-\par\addvspace{0.5\baselineskip}\egroup}
-
-
-
-% V1.6 
-% this is a static rubber spacer between the title/authors and the main text
-% used for single column text, or when the title appears in the first column
-% of two column text (technotes). 
-\def\@IEEEstatictitlevskip{{\normalfont\normalsize
-% adjust spacing to next text
-% v1.6b handle peer review papers
-\ifCLASSOPTIONpeerreview
-% for peer review papers, the same value is used for both title pages
-% regardless of the other paper modes
-   \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip
-\else
-   \ifCLASSOPTIONconference% conference
-      \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip%
-   \else%
-      \ifCLASSOPTIONtechnote% technote
-         \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip%
-      \else% journal uses more space
-         \vskip 2.5\baselineskip plus 0.75\baselineskip minus 0.375\baselineskip%
-      \fi
-   \fi
-\fi}}
-
-
-% set the nominal and minimum values for the quantized title spacer
-% the quantization algorithm will not allow the spacer size to
-% become less than \@IEEEMINtitlevspace - instead it will be lengthened
-% default to journal values
-\def\@IEEENORMtitlevspace{2.5\baselineskip}
-\def\@IEEEMINtitlevspace{2\baselineskip}
-% conferences and technotes need tighter spacing
-\ifCLASSOPTIONconference% conference
-  \def\@IEEENORMtitlevspace{1\baselineskip}
-  \def\@IEEEMINtitlevspace{0.75\baselineskip}
-\fi
-\ifCLASSOPTIONtechnote% technote
-  \def\@IEEENORMtitlevspace{1\baselineskip}
-  \def\@IEEEMINtitlevspace{0.75\baselineskip}
-\fi
-
-
-% V1.8a
-\def\IEEEquantizevspace{\begingroup\@ifstar{\@IEEEquantizevspacestarformtrue\@IEEEquantizevspace}{\@IEEEquantizevspacestarformfalse\@IEEEquantizevspace}}
-% \IEEEquantizevspace[output dimen register]{object}[object decl]
-%                    {top baselineskip}
-%                    [offset][prevdepth][lineskip limit][lineskip]
-%                    {unit height}{nominal vspace}{minimum vspace}
-%
-% Calculates and creates the vspace needed to make the combined height with
-% the given object an integer multiple of the given unit height. This command
-% is more general than the older \@IEEEdynamictitlevspace it replaces.
-%
-% The star form has no effect at present, but is reserved for future use.
-%
-% If the optional argument [output dimen register] is given, the calculated
-% vspace height is stored in the given output dimen (or skip) register
-% and no other action is taken, otherwise the object followed by a vspace*
-% of the appropriate height is evaluated/output.
-%
-% The optional object decl (declarations) is code that is evaluated just
-% before the object's height is evaluated. Its intented purpose is to allow
-% for the alteration or disabling of code within the object during internal
-% height evaluation (e.g., \long\def\thanks#1{\relax} ).
-% This special code is not invoked if/when the object is rendered at the end.
-%
-% The nominal vspace is the target value of the added vspace and the minimum
-% vspace is the lower allowed limit. The vspacer will be the value that achieves
-% integral overall height, in terms of the given unit height, that is closest
-% to the nominal vspace and that is not less than the specified minimum vspace.
-%
-% The line spacing algorithm of TeX is somewhat involved and requires special
-% care with regard to the first line of a vertical list (which is indicated
-% when \prevdepth is -1000pt or less). top baselineskip specifies the
-% baselineskip or topskip used prior to the object. If the height of the
-% first line of the object is greater than the given top baselineskip, then
-% the top baselineskip is subtracted from the height of the first line and
-% that difference is considered along with the rest of the object height
-% (because the object will be shifted down by an amount = 
-% top line height - top baselineskip). Otherwise, the height of the first line
-% of the object is ignored as far as the calculations are concerned.
-% This algorithm is adequate for objects that appear at the top of a page
-% (e.g., titles) where \topskip spacing is used.
-%
-% However, as explained on page 78 of the TeXbook, interline spacing is more
-% complex when \baselineskip is being used (indicated by \prevdepth > 
-% -1000pt). The four optional parameters offset, prevdepth, lineskip limit and
-% lineskip are assumed to be equal to be 0pt, \prevdepth, \lineskiplimit and
-% \lineskip, respectively, if they are omitted.
-%
-% The prevdepth is the depth of the line before the object, the lineskip limit
-% specifies how close the top of the object can come to the bottom of the
-% previous line before \baselineskip is ignored and \lineskip is inserted
-% between the object and the line above it. Lineskip does not come into
-% play unless the first line of the object is high enough to "get too close"
-% (as specified by lineskiplimit) to the line before it. The the prevdepth,
-% lineskip limit, and lineskip optional parameters are not needed for the
-% first object/line on a page (i.e., prevdepth <= -1000pt) where the simplier
-% \topskip spacing rules are in effect.
-%
-% Offset is a manual adjustment that is added to the height calculations of
-% object irrespective of the value of \prevdepth. It is useful when the top
-% baselineskip will result in a noninteger unit height object placement even
-% if the object itself has integral height. e.g., a footnotesize baselineskip
-% is used before the object, thus an offset of, say -3pt, can be given as a
-% correction.
-
-% Common combinations of these parameters include:
-%
-% top baselineskip:   (and default values for offset, prevdepth, etc.)
-% \topskip            % for objects that appear at the top of a page
-% \maxdimen           % always ignore the height of the top line
-% 0pt                 % always consider any positive height of the top line
-%
-% for objects to appear inline in normal text:
-% top baselineskip = \baselineskip
-%
-% set prevdepth = -1000pt and top baselineskip = 0pt to consider the
-% overall height of the object without any other external skip
-% consideration
-
-\newif\if@IEEEquantizevspacestarform       % flag to indicate star form
-\newif\if@IEEEquantizevspaceuseoutdimenreg % flag to indicate output dimen register is to be used
-% Use our own private registers because the object could contain a
-% structure that uses the existing tmp scratch pad registers
-\newdimen\@IEEEquantizeheightA
-\newdimen\@IEEEquantizeheightB
-\newdimen\@IEEEquantizeheightC
-\newdimen\@IEEEquantizeprevdepth % need to save this early as can change
-\newcount\@IEEEquantizemultiple
-\newbox\@IEEEquantizeboxA
-
-
-\def\@IEEEquantizevspace{\@ifnextchar [{\@IEEEquantizevspaceuseoutdimenregtrue\@@IEEEquantizevspace}{\@IEEEquantizevspaceuseoutdimenregfalse\@@IEEEquantizevspace[]}}
-
-
-\long\def\@@IEEEquantizevspace[#1]#2{\relax
-% acquire and store
-% #1 optional output dimen register
-% #2 object
-\edef\@IEEEquantizeoutdimenreg{#1}\relax
-% allow for object specifications that contain parameters
-\@IEEEtrantmptoksA={#2}\relax
-\long\edef\@IEEEquantizeobject{\the\@IEEEtrantmptoksA}\relax
-\@ifnextchar [{\@@@IEEEquantizevspace}{\@@@IEEEquantizevspace[\relax]}}
-
-\long\def\@@@IEEEquantizevspace[#1]#2{\relax
-% acquire and store
-% [#1] optional object decl, is \relax if not given by user
-% #2 top baselineskip
-% allow for object decl specifications that have parameters
-\@IEEEtrantmptoksA={#1}\relax
-\long\edef\@IEEEquantizeobjectdecl{\the\@IEEEtrantmptoksA}\relax
-\edef\@IEEEquantizetopbaselineskip{#2}\ivIEEEquantizevspace}
-
-% acquire optional argument set and store
-% [offset][prevdepth][lineskip limit][lineskip]
-\def\ivIEEEquantizevspace{\@ifnextchar [{\@vIEEEquantizevspace}{\@vIEEEquantizevspace[0pt]}}
-\def\@vIEEEquantizevspace[#1]{\edef\@IEEEquantizeoffset{#1}\@ifnextchar [{\@viIEEEquantizevspace}{\@viIEEEquantizevspace[\prevdepth]}}
-\def\@viIEEEquantizevspace[#1]{\@IEEEquantizeprevdepth=#1\relax\@ifnextchar [{\@viiIEEEquantizevspace}{\@viiIEEEquantizevspace[\lineskiplimit]}}
-\def\@viiIEEEquantizevspace[#1]{\edef\@IEEEquantizelineskiplimit{#1}\@ifnextchar [{\@viiiIEEEquantizevspace}{\@viiiIEEEquantizevspace[\lineskip]}}
-\def\@viiiIEEEquantizevspace[#1]{\edef\@IEEEquantizelineskip{#1}\@ixIEEEquantizevspace}
-
-% main routine
-\def\@ixIEEEquantizevspace#1#2#3{\relax
-\edef\@IEEEquantizeunitheight{#1}\relax
-\edef\@IEEEquantizenomvspace{#2}\relax
-\edef\@IEEEquantizeminvspace{#3}\relax
-% \@IEEEquantizeoutdimenreg
-% \@IEEEquantizeobject
-% \@IEEEquantizeobjectdecl
-% \@IEEEquantizetopbaselineskip
-% \@IEEEquantizeoffset
-% \@IEEEquantizeprevdepth
-% \@IEEEquantizelineskiplimit
-% \@IEEEquantizelineskip
-% \@IEEEquantizeunitheight
-% \@IEEEquantizenomvspace
-% \@IEEEquantizeminvspace
-% get overall height of object
-\setbox\@IEEEquantizeboxA\vbox{\begingroup\@IEEEquantizeobjectdecl\@IEEEquantizeobject\relax\endgroup}\relax
-\@IEEEquantizeheightA\ht\@IEEEquantizeboxA\relax
-% get height of first line of object
-\setbox\@IEEEquantizeboxA\vtop{\begingroup\@IEEEquantizeobjectdecl\@IEEEquantizeobject\relax\endgroup}\relax
-\@IEEEquantizeheightB\ht\@IEEEquantizeboxA\relax
-\ifdim\@IEEEquantizeprevdepth>-1000pt\relax % prevdepth > -1000pf means full baselineskip\lineskip rules in effect
-% lineskip spacing rule takes effect if height of top line > baselineskip - prevdepth - lineskiplimit, 
-% otherwise the baselineskip rule is in effect and the height of the first line does not matter at all.
-\@IEEEquantizeheightC=\@IEEEquantizetopbaselineskip\relax
-\advance\@IEEEquantizeheightC-\@IEEEquantizeprevdepth\relax
-\advance\@IEEEquantizeheightC-\@IEEEquantizelineskiplimit\relax % this works even though \@IEEEquantizelineskiplimit is a macro because TeX allows --10pt notation
-\ifdim\@IEEEquantizeheightB>\@IEEEquantizeheightC\relax
-% lineskip spacing rule is in effect i.e., the object is going to be shifted down relative to the
-% baselineskip set position by its top line height (already a part of the total height) + prevdepth + lineskip - baselineskip
-\advance\@IEEEquantizeheightA\@IEEEquantizeprevdepth\relax
-\advance\@IEEEquantizeheightA\@IEEEquantizelineskip\relax
-\advance\@IEEEquantizeheightA-\@IEEEquantizetopbaselineskip\relax
-\else
-% height of first line <= \@IEEEquantizetopbaselineskip - \@IEEEquantizeprevdepth - \@IEEEquantizelineskiplimit
-% standard baselineskip rules are in effect, so don't consider height of first line
-\advance\@IEEEquantizeheightA-\@IEEEquantizeheightB\relax
-\fi
-%
-\else % prevdepth <= -1000pt, simplier \topskip type rules in effect
-\ifdim\@IEEEquantizeheightB>\@IEEEquantizetopbaselineskip
-% height of top line (already included in the total height) in excess of
-% baselineskip is the amount it will be downshifted
-\advance\@IEEEquantizeheightA-\@IEEEquantizetopbaselineskip\relax
-\else
-% height of first line is irrelevant, remove it
-\advance\@IEEEquantizeheightA-\@IEEEquantizeheightB\relax
-\fi
-\fi % prevdepth <= -1000pt
-%
-% adjust height for any manual offset
-\advance\@IEEEquantizeheightA\@IEEEquantizeoffset\relax
-% add in nominal spacer
-\advance\@IEEEquantizeheightA\@IEEEquantizenomvspace\relax
-% check for nonzero unitheight
-\@IEEEquantizeheightB=\@IEEEquantizeunitheight\relax
-\ifnum\@IEEEquantizeheightB=0\relax
-\@IEEEclspkgerror{IEEEquantizevspace unit height cannot be zero. Assuming 10pt.}%
-{Division by zero is not allowed.}
-\@IEEEquantizeheightB=10pt\relax
-\fi
-% get integer number of lines
-\@IEEEquantizemultiple=\@IEEEquantizeheightA\relax
-\divide\@IEEEquantizemultiple\@IEEEquantizeheightB\relax
-% set A to contain the excess height over the \@IEEEquantizemultiple of lines
-% A = height - multiple*unitheight
-\@IEEEquantizeheightC\@IEEEquantizeheightB\relax
-\multiply\@IEEEquantizeheightC\@IEEEquantizemultiple\relax
-\advance\@IEEEquantizeheightA-\@IEEEquantizeheightC\relax
-% set B to contain the height short of \@IEEEquantizemultiple+1 of lines
-% B = unitheight - A
-\advance\@IEEEquantizeheightB-\@IEEEquantizeheightA\relax
-% choose A or B based on which is closer
-\@IEEEquantizeheightC\@IEEEquantizenomvspace\relax
-\ifdim\@IEEEquantizeheightA<\@IEEEquantizeheightB\relax
-% C = nomvspace - A, go with lower
-\advance\@IEEEquantizeheightC-\@IEEEquantizeheightA\relax
-\else
-% C = nomvspace + B, go with upper
-\advance\@IEEEquantizeheightC\@IEEEquantizeheightB\relax
-\fi
-% if violate lower bound, use next integer bound
-\ifdim\@IEEEquantizeheightC<\@IEEEquantizeminvspace\relax
-% A + B = unitheight
-\advance\@IEEEquantizeheightC\@IEEEquantizeheightA\relax
-\advance\@IEEEquantizeheightC\@IEEEquantizeheightB\relax
-\fi
-% export object and spacer outside of group
-\global\let\@IEEEquantizeobjectout\@IEEEquantizeobject\relax
-\global\@IEEEquantizeheightC\@IEEEquantizeheightC\relax
-\endgroup
-\if@IEEEquantizevspaceuseoutdimenreg
-\@IEEEquantizeoutdimenreg=\@IEEEquantizeheightC\relax
-\else
-\@IEEEquantizeobjectout\relax
-\vskip\@IEEEquantizeheightC\relax
-\fi}
-
-
-% user command to disable all global assignments, possible use within object decl
-\def\IEEEquantizedisableglobal{\let\global\relax
-\let\gdef\def
-\let\xdef\edef}
-% user command to allow for the disabling of \thanks and other commands, possible use within object decl
-\def\IEEEquantizedisabletitlecmds{\long\def\thanks##1{\relax}\relax
-\long\def\IEEEcompsocitemizethanks##1{\relax}\def\newpage{\relax}}
-
-
-
-
-
-% V1.6
-% we allow the user access to the last part of the title area
-% useful in emergencies such as when a different spacing is needed
-% This text is NOT compensated for in the dynamic sizer.
-\let\@IEEEaftertitletext=\relax
-\long\def\IEEEaftertitletext#1{\def\@IEEEaftertitletext{#1}}
-
-
-% V1.7 provide a way for users to enter abstract and keywords
-% into the onecolumn title are. This text is compensated for
-% in the dynamic sizer.
-\let\@IEEEtitleabstractindextext=\relax
-\long\def\IEEEtitleabstractindextext#1{\def\@IEEEtitleabstractindextext{#1}}
-
-% V1.7 provide a way for users to get the \@IEEEtitleabstractindextext if
-% not in compsoc or transmag journal mode - this way abstract and keywords
-% can still be placed in their conventional position if not in those modes.
-\def\IEEEdisplaynontitleabstractindextext{%
-% display for all conference formats
-\ifCLASSOPTIONconference\@IEEEtitleabstractindextext\relax
-\else% non-conferences
-  % V1.8a display for all technotes
-  \ifCLASSOPTIONtechnote\@IEEEtitleabstractindextext\relax
-  % V1.8a add diamond line after abstract and index terms for compsoc technotes
-  \@IEEEcompsoconly{\noindent\hfill\IEEEcompsocdiamondline\hfill\hbox{}\par}\relax
-  \else % non-conferences and non-technotes
-    \ifCLASSOPTIONcompsoc% display if not compsoc and not transmag
-    \else
-      \ifCLASSOPTIONtransmag
-      \else% not compsoc journal nor transmag journal
-         \@IEEEtitleabstractindextext\relax
-      \fi
-    \fi
-  \fi
-\fi}
-
-
-% command to allow alteration of baselinestretch, but only if the current
-% baselineskip is unity. Used to tweak the compsoc abstract and keywords line spacing.
-\def\@IEEEtweakunitybaselinestretch#1{{\def\baselinestretch{1}\selectfont
-\global\@tempskipa\baselineskip}\ifnum\@tempskipa=\baselineskip%
-\def\baselinestretch{#1}\selectfont\fi\relax}
-
-
-% abstract and keywords are in \small, except 
-% for 9pt docs in which they are in \footnotesize
-% Because 9pt docs use an 8pt footnotesize, \small
-% becomes a rather awkward 8.5pt
-\def\@IEEEabskeysecsize{\small}
-\ifx\CLASSOPTIONpt\@IEEEptsizenine
- \def\@IEEEabskeysecsize{\footnotesize}
-\fi
-
-% compsoc journals use \footnotesize, compsoc conferences use normalsize
-\@IEEEcompsoconly{\def\@IEEEabskeysecsize{\footnotesize}}
-\@IEEEcompsocconfonly{\def\@IEEEabskeysecsize{\small}}
-
-
-% V1.6 have abstract and keywords strip leading spaces, pars and newlines
-% so that spacing is more tightly controlled.
-\def\abstract{\normalfont
-    \if@twocolumn
-      \@IEEEabskeysecsize\bfseries\textit{\abstractname}---\relax
-    \else
-      \bgroup\par\addvspace{0.5\baselineskip}\centering\vspace{-1.78ex}\@IEEEabskeysecsize\textbf{\abstractname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize
-    \fi\@IEEEgobbleleadPARNLSP}
-% V1.6 The IEEE wants only 1 pica from end of abstract to introduction heading when in 
-% conference mode (the heading already has this much above it)
-\def\endabstract{\relax\ifCLASSOPTIONconference\vspace{0ex}\else\vspace{1.34ex}\fi\par\if@twocolumn\else\endquotation\fi
-    \normalfont\normalsize}
-
-\def\IEEEkeywords{\normalfont
-    \if@twocolumn
-      \@IEEEabskeysecsize\bfseries\textit{\IEEEkeywordsname}---\relax
-    \else
-      \bgroup\par\addvspace{0.5\baselineskip}\centering\@IEEEabskeysecsize\textbf{\IEEEkeywordsname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize
-    \fi\@IEEEgobbleleadPARNLSP}
-\def\endIEEEkeywords{\relax\ifCLASSOPTIONtechnote\vspace{1.34ex}\else\vspace{0.67ex}\fi
-    \par\if@twocolumn\else\endquotation\fi%
-    \normalfont\normalsize}
-
-% V1.7 compsoc keywords index terms
-\ifCLASSOPTIONcompsoc
-  \ifCLASSOPTIONconference% compsoc conference
-\def\abstract{\normalfont\@IEEEtweakunitybaselinestretch{1.15}\bfseries
-    \if@twocolumn
-      \@IEEEabskeysecsize\noindent\textit{\abstractname}---\relax
-    \else
-      \bgroup\par\addvspace{0.5\baselineskip}\centering\vspace{-1.78ex}\@IEEEabskeysecsize\textbf{\abstractname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize%
-    \fi\@IEEEgobbleleadPARNLSP}
-\def\IEEEkeywords{\normalfont\@IEEEtweakunitybaselinestretch{1.15}\bfseries
-    \if@twocolumn
-      \@IEEEabskeysecsize\vskip 0.5\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip\noindent
-      \textit{\IEEEkeywordsname}---\relax
-    \else
-      \bgroup\par\addvspace{0.5\baselineskip}\centering\@IEEEabskeysecsize\textbf{\IEEEkeywordsname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize%
-    \fi\@IEEEgobbleleadPARNLSP}
-  \else% compsoc not conference
-\def\abstract{\normalfont\@IEEEtweakunitybaselinestretch{1.15}\sffamily
-    \if@twocolumn
-      \@IEEEabskeysecsize\noindent\textbf{\abstractname}---\relax
-    \else
-      \bgroup\par\addvspace{0.5\baselineskip}\centering\vspace{-1.78ex}\@IEEEabskeysecsize\textbf{\abstractname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize%
-    \fi\@IEEEgobbleleadPARNLSP}
-\def\IEEEkeywords{\normalfont\@IEEEtweakunitybaselinestretch{1.15}\sffamily
-    \if@twocolumn
-      \@IEEEabskeysecsize\vskip 0.5\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip\noindent
-      \textbf{\IEEEkeywordsname}---\relax
-    \else
-      \bgroup\par\addvspace{0.5\baselineskip}\centering\@IEEEabskeysecsize\textbf{\IEEEkeywordsname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize%
-    \fi\@IEEEgobbleleadPARNLSP}
-  \fi
-\fi
-
-% V1.8 transmag keywords index terms
-% no abstract name, use indentation
-\ifCLASSOPTIONtransmag
-\def\abstract{\normalfont\parindent 1em\relax
-    \if@twocolumn
-      \@IEEEabskeysecsize\bfseries\indent
-    \else
-      \bgroup\par\addvspace{0.5\baselineskip}\centering\vspace{-1.78ex}\@IEEEabskeysecsize
-      \textbf{\abstractname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize
-    \fi\@IEEEgobbleleadPARNLSP}
-
-\def\IEEEkeywords{\normalfont\parindent 1em\relax
-    \if@twocolumn
-      \@IEEEabskeysecsize\vspace{1\baselineskip}\bfseries\indent\textit{\IEEEkeywordsname}---\relax
-    \else
-      \bgroup\par\vspace{1\baselineskip}\centering\@IEEEabskeysecsize
-      \textbf{\IEEEkeywordsname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize
-    \fi\@IEEEgobbleleadPARNLSP}
-\fi
-
-
-
-% gobbles all leading \, \\ and \par, upon finding first token that
-% is not a \ , \\ or a \par, it ceases and returns that token
-% 
-% used to strip leading \, \\ and \par from the input
-% so that such things in the beginning of an environment will not
-% affect the formatting of the text
-\long\def\@IEEEgobbleleadPARNLSP#1{\let\@IEEEswallowthistoken=0%
-\let\@IEEEgobbleleadPARNLSPtoken#1%
-\let\@IEEEgobbleleadPARtoken=\par%
-\let\@IEEEgobbleleadNLtoken=\\%
-\let\@IEEEgobbleleadSPtoken=\ %
-\def\@IEEEgobbleleadSPMACRO{\ }%
-\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadPARtoken%
-\let\@IEEEswallowthistoken=1%
-\fi%
-\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadNLtoken%
-\let\@IEEEswallowthistoken=1%
-\fi%
-\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPtoken%
-\let\@IEEEswallowthistoken=1%
-\fi%
-% a control space will come in as a macro
-% when it is the last one on a line
-\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPMACRO%
-\let\@IEEEswallowthistoken=1%
-\fi%
-% if we have to swallow this token, do so and taste the next one
-% else spit it out and stop gobbling
-\ifx\@IEEEswallowthistoken 1\let\@IEEEnextgobbleleadPARNLSP=\@IEEEgobbleleadPARNLSP\else%
-\let\@IEEEnextgobbleleadPARNLSP=#1\fi%
-\@IEEEnextgobbleleadPARNLSP}%
-
-
-
-
-% TITLING OF SECTIONS
-\def\@IEEEsectpunct{:\ \,}  % Punctuation after run-in section heading  (headings which are
-                            % part of the paragraphs), need little bit more than a single space
-                            % spacing from section number to title
-% compsoc conferences use regular period/space punctuation
-\ifCLASSOPTIONcompsoc
-\ifCLASSOPTIONconference
-\def\@IEEEsectpunct{.\ }
-\fi\fi
-
-
-\def\@seccntformat#1{\csname the#1dis\endcsname\hskip 0.5em\relax}
-
-\ifCLASSOPTIONcompsoc
-% compsoc journals need extra spacing
-\ifCLASSOPTIONconference\else
-\def\@seccntformat#1{\csname the#1dis\endcsname\hskip 1em\relax}
-\fi\fi
-
-%v1.7 put {} after #6 to allow for some types of user font control
-%and use \@@par rather than \par
-\def\@sect#1#2#3#4#5#6[#7]#8{%
-  \ifnum #2>\c@secnumdepth
-     \let\@svsec\@empty
-  \else
-     \refstepcounter{#1}%
-     % load section label and spacer into \@svsec
-     \protected@edef\@svsec{\@seccntformat{#1}\relax}%
-  \fi%
-  \@tempskipa #5\relax
-  \ifdim \@tempskipa>\z@% tempskipa determines whether is treated as a high
-     \begingroup #6{\relax% or low level heading
-      \noindent % subsections are NOT indented
-       % print top level headings. \@svsec is label, #8 is heading title
-       % The IEEE does not block indent the section title text, it flows like normal
-       {\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\@@par}}%
-     \endgroup
-     \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else
-               \protect\numberline{\csname the#1\endcsname}\fi#7}%
-  \else % printout low level headings
-     % svsechd seems to swallow the trailing space, protect it with \mbox{}
-     % got rid of sectionmark stuff
-     \def\@svsechd{#6{\hskip #3\relax\@svsec #8\@IEEEsectpunct\mbox{}}%
-     \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else
-               \protect\numberline{\csname the#1\endcsname}\fi#7}}%
-  \fi%skip down
-  \@xsect{#5}}
-
-
-% section* handler
-%v1.7 put {} after #4 to allow for some types of user font control
-%and use \@@par rather than \par
-\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax
-  \ifdim \@tempskipa>\z@
-     %\begingroup #4\@hangfrom{\hskip #1}{\interlinepenalty \@M #5\par}\endgroup
-     % The IEEE does not block indent the section title text, it flows like normal
-     \begingroup \noindent #4{\relax{\hskip #1}{\interlinepenalty \@M #5\@@par}}\endgroup
-  % svsechd swallows the trailing space, protect it with \mbox{}
-  \else \def\@svsechd{#4{\hskip #1\relax #5\@IEEEsectpunct\mbox{}}}\fi
-  \@xsect{#3}}
-
-
-%% SECTION heading spacing and font
-%%
-% arguments are: #1 - sectiontype name
-% (for \@sect)   #2 - section level
-%                #3 - section heading indent
-%                #4 - top separation (absolute value used, neg indicates not to indent main text)
-%                     If negative, make stretch parts negative too!
-%                #5 - (absolute value used) positive: bottom separation after heading,
-%                      negative: amount to indent main text after heading
-%                Both #4 and #5 negative means to indent main text and use negative top separation
-%                #6 - font control
-% You've got to have \normalfont\normalsize in the font specs below to prevent
-% trouble when you do something like:
-% \section{Note}{\ttfamily TT-TEXT} is known to ... 
-% The IEEE sometimes REALLY stretches the area before a section
-% heading by up to about 0.5in. However, it may not be a good
-% idea to let LaTeX have quite this much rubber.
-\ifCLASSOPTIONconference%
-% The IEEE wants section heading spacing to decrease for conference mode
-\def\section{\@startsection{section}{1}{\z@}{1.5ex plus 1.5ex minus 0.5ex}%
-{0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}%
-\def\subsection{\@startsection{subsection}{2}{\z@}{1.5ex plus 1.5ex minus 0.5ex}%
-{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%
-\else % for journals
-\def\section{\@startsection{section}{1}{\z@}{3.0ex plus 1.5ex minus 1.5ex}% V1.6 3.0ex from 3.5ex
-{0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}%
-\def\subsection{\@startsection{subsection}{2}{\z@}{3.5ex plus 1.5ex minus 1.5ex}%
-{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%
-\fi
-
-% for both journals and conferences
-% decided to put in a little rubber above the section, might help somebody
-\def\subsubsection{\@startsection{subsubsection}{3}{\parindent}{0ex plus 0.1ex minus 0.1ex}%
-{0ex}{\normalfont\normalsize\itshape}}%
-\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{0ex plus 0.1ex minus 0.1ex}%
-{0ex}{\normalfont\normalsize\itshape}}%
-
-
-% compsoc
-\ifCLASSOPTIONcompsoc
-\ifCLASSOPTIONconference
-% compsoc conference
-\def\section{\@startsection{section}{1}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}%
-{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}{\normalfont\large\bfseries}}%
-\def\subsection{\@startsection{subsection}{2}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}%
-{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}{\normalfont\sublargesize\bfseries}}%
-\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}%
-{0ex}{\normalfont\normalsize\bfseries}}%
-\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{0ex plus 0.1ex minus 0.1ex}%
-{0ex}{\normalfont\normalsize}}%
-\else% compsoc journals
-% use negative top separation as compsoc journals do not indent paragraphs after section titles
-\def\section{\@startsection{section}{1}{\z@}{-3.5ex plus -2ex minus -1.5ex}%
-{0.7ex plus 1ex minus 0ex}{\normalfont\sublargesize\sffamily\bfseries\scshape}}%
-% Note that subsection and smaller may not be correct for the Computer Society,
-% I have to look up an example.
-\def\subsection{\@startsection{subsection}{2}{\z@}{-3.5ex plus -1.5ex minus -1.5ex}%
-{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\sffamily\bfseries}}%
-\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-2.5ex plus -1ex minus -1ex}%
-{0.5ex plus 0.5ex minus 0ex}{\normalfont\normalsize\sffamily\itshape}}%
-\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{-0ex plus -0.1ex minus -0.1ex}%
-{0ex}{\normalfont\normalsize}}%
-\fi\fi
-
-% transmag
-\ifCLASSOPTIONtransmag
-\def\subsection{\@startsection{subsection}{2}{0.75\parindent}{3.5ex plus 1.5ex minus 1.5ex}%
-{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%
-\def\subsubsection{\@startsection{subsubsection}{3}{1.25\parindent}{0.1ex plus 0.1ex minus 0.1ex}%
-{0.1ex}{\normalfont\normalsize\itshape}}%
-\fi
-
-
-% V1.8a provide for a raised line Introduction section for use with Computer
-% Society papers. We have to remove any spacing glue after the section
-% heading and then remove the blank line for the new paragraph after it.
-% LaTeX's section handler alters \everypar and we need to propogate those
-% changes outside of the \parbox lest there be spacing problems at the top
-% of the next section.
-\def\IEEEraisesectionheading#1{\noindent\raisebox{1.5\baselineskip}[0pt][0pt]{\parbox[b]{\columnwidth}{#1\unskip\global\everypar=\everypar}}\vspace{-1\baselineskip}\vspace{-\parskip}\par}
-
-
-
-%% ENVIRONMENTS
-% "box" symbols at end of proofs
-\def\IEEEQEDclosed{\mbox{\rule[0pt]{1.3ex}{1.3ex}}} % for a filled box
-% V1.6 some journals use an open box instead that will just fit around a closed one
-\def\IEEEQEDopen{{\setlength{\fboxsep}{0pt}\setlength{\fboxrule}{0.2pt}\fbox{\rule[0pt]{0pt}{1.3ex}\rule[0pt]{1.3ex}{0pt}}}}
-\ifCLASSOPTIONcompsoc
-\def\IEEEQED{\IEEEQEDopen}   % default to open for compsoc
-\else
-\def\IEEEQED{\IEEEQEDclosed} % otherwise default to closed
-\fi
-
-%V1.8 flag to indicate if QED symbol is to be shown
-\newif\if@IEEEQEDshow  \@IEEEQEDshowtrue
-\def\IEEEproofindentspace{2\parindent}% V1.8 allow user to change indentation amount if desired
-% v1.7 name change to avoid namespace collision with amsthm. Also add support
-% for an optional argument.
-\def\IEEEproof{\@ifnextchar[{\@IEEEproof}{\@IEEEproof[\IEEEproofname]}}
-\def\@IEEEproof[#1]{\@IEEEQEDshowtrue\par\noindent\hspace{\IEEEproofindentspace}{\itshape #1: }}
-\def\endIEEEproof{\if@IEEEQEDshow\hspace*{\fill}\nobreakspace\IEEEQED\fi\par}
-% qedhere for equation environments, similar to AMS \qedhere
-\def\IEEEQEDhereeqn{\global\@IEEEQEDshowfalse\eqno\let\eqno\relax\let\leqno\relax
-                    \let\veqno\relax\hbox{\IEEEQED}}
-% IEEE style qedhere for IEEEeqnarray and other environments
-\def\IEEEQEDhere{\global\@IEEEQEDshowfalse\IEEEQED}
-% command to disable QED at end of IEEEproof
-\def\IEEEQEDoff{\global\@IEEEQEDshowfalse}
-
-
-%\itemindent is set to \z@ by list, so define new temporary variable
-\newdimen\@IEEEtmpitemindent
-
-\ifCLASSOPTIONcompsoc
-% V1.8a compsoc uses bold theorem titles, a period instead of a colon, vertical spacing, and hanging indentation
-% V1.8 allow long theorem names to break across lines.
-% Thanks to Miquel Payaro for reporting this.
-\def\@begintheorem#1#2{\@IEEEtmpitemindent\itemindent\relax
-    \topsep 0.2\@IEEEnormalsizeunitybaselineskip plus 0.26\@IEEEnormalsizeunitybaselineskip minus 0.05\@IEEEnormalsizeunitybaselineskip
-    \rmfamily\trivlist\hangindent\parindent%
-    \item[]\textit{\bfseries\noindent #1\ #2.} \itemindent\@IEEEtmpitemindent\relax}
-\def\@opargbegintheorem#1#2#3{\@IEEEtmpitemindent\itemindent\relax
-\topsep 0.2\@IEEEnormalsizeunitybaselineskip plus 0.26\@IEEEnormalsizeunitybaselineskip minus 0.05\@IEEEnormalsizeunitybaselineskip
-\rmfamily\trivlist\hangindent\parindent%
-% V1.6 The IEEE is back to using () around theorem names which are also in italics
-% Thanks to Christian Peel for reporting this.
-    \item[]\textit{\bfseries\noindent #1\ #2\ (#3).} \itemindent\@IEEEtmpitemindent\relax}
-% V1.7 remove bogus \unskip that caused equations in theorems to collide with
-% lines below.
-\def\@endtheorem{\endtrivlist\vskip 0.25\@IEEEnormalsizeunitybaselineskip plus 0.26\@IEEEnormalsizeunitybaselineskip minus 0.05\@IEEEnormalsizeunitybaselineskip}
-\else
-%
-% noncompsoc
-% 
-% V1.8 allow long theorem names to break across lines.
-% Thanks to Miquel Payaro for reporting this.
-\def\@begintheorem#1#2{\@IEEEtmpitemindent\itemindent\relax\topsep 0pt\rmfamily\trivlist%
-    \item[]\textit{\indent #1\ #2:} \itemindent\@IEEEtmpitemindent\relax}
-\def\@opargbegintheorem#1#2#3{\@IEEEtmpitemindent\itemindent\relax\topsep 0pt\rmfamily \trivlist%
-% V1.6 The IEEE is back to using () around theorem names which are also in italics
-% Thanks to Christian Peel for reporting this.
-    \item[]\textit{\indent #1\ #2\ (#3):} \itemindent\@IEEEtmpitemindent\relax}
-% V1.7 remove bogus \unskip that caused equations in theorems to collide with
-% lines below.
-\def\@endtheorem{\endtrivlist}
-\fi
-
-
-
-% V1.6
-% display command for the section the theorem is in - so that \thesection
-% is not used as this will be in Roman numerals when we want arabic.
-% LaTeX2e uses \def\@thmcounter#1{\noexpand\arabic{#1}} for the theorem number
-% (second part) display and \def\@thmcountersep{.} as a separator.
-% V1.7 intercept calls to the section counter and reroute to \@IEEEthmcounterinsection
-% to allow \appendix(ices} to override as needed.
-%
-% special handler for sections, allows appendix(ices) to override
-\gdef\@IEEEthmcounterinsection#1{\arabic{#1}}
-% string macro
-\edef\@IEEEstringsection{section}
-
-% redefine the #1#2[#3] form of newtheorem to use a hook to \@IEEEthmcounterinsection
-% if section in_counter is used
-\def\@xnthm#1#2[#3]{%
-  \expandafter\@ifdefinable\csname #1\endcsname
-    {\@definecounter{#1}\@newctr{#1}[#3]%
-     \edef\@IEEEstringtmp{#3}
-     \ifx\@IEEEstringtmp\@IEEEstringsection
-     \expandafter\xdef\csname the#1\endcsname{%
-     \noexpand\@IEEEthmcounterinsection{#3}\@thmcountersep
-          \@thmcounter{#1}}%
-     \else
-     \expandafter\xdef\csname the#1\endcsname{%
-       \expandafter\noexpand\csname the#3\endcsname \@thmcountersep
-          \@thmcounter{#1}}%
-     \fi
-     \global\@namedef{#1}{\@thm{#1}{#2}}%
-     \global\@namedef{end#1}{\@endtheorem}}}
-
-
-
-%% SET UP THE DEFAULT PAGESTYLE
-\pagestyle{headings}
-\pagenumbering{arabic}
-
-% normally the page counter starts at 1
-\setcounter{page}{1}
-% however, for peerreview the cover sheet is page 0 or page -1
-% (for duplex printing)
-\ifCLASSOPTIONpeerreview
-   \if@twoside
-      \setcounter{page}{-1}
-   \else
-      \setcounter{page}{0}
-   \fi
-\fi
-
-% standard book class behavior - let bottom line float up and down as
-% needed when single sided
-\ifCLASSOPTIONtwoside\else\raggedbottom\fi
-% if two column - turn on twocolumn, allow word spacings to stretch more and
-% enforce a rigid position for the last lines
-\ifCLASSOPTIONtwocolumn
-% the peer review option delays invoking twocolumn
-   \ifCLASSOPTIONpeerreview\else
-      \twocolumn
-   \fi
-\sloppy 
-\flushbottom
-\fi
-
-
-
-
-% \APPENDIX and \APPENDICES definitions
-
-% This is the \@ifmtarg command from the LaTeX ifmtarg package
-% by Peter Wilson (CUA) and Donald Arseneau
-% \@ifmtarg is used to determine if an argument to a command
-% is present or not.
-% For instance:
-% \@ifmtarg{#1}{\typeout{empty}}{\typeout{has something}}
-% \@ifmtarg is used with our redefined \section command if
-% \appendices is invoked.
-% The command \section will behave slightly differently depending
-% on whether the user specifies a title: 
-% \section{My appendix title}
-% or not:
-% \section{}
-% This way, we can eliminate the blank lines where the title
-% would be, and the unneeded : after Appendix in the table of
-% contents 
-\begingroup
-\catcode`\Q=3
-\long\gdef\@ifmtarg#1{\@xifmtarg#1QQ\@secondoftwo\@firstoftwo\@nil}
-\long\gdef\@xifmtarg#1#2Q#3#4#5\@nil{#4}
-\endgroup
-% end of \@ifmtarg defs
-
-
-% V1.7
-% command that allows the one time saving of the original definition
-% of section to \@IEEEappendixsavesection for \appendix or \appendices 
-% we don't save \section here as it may be redefined later by other
-% packages (hyperref.sty, etc.)
-\def\@IEEEsaveoriginalsectiononce{\let\@IEEEappendixsavesection\section
-\let\@IEEEsaveoriginalsectiononce\relax}
-
-% neat trick to grab and process the argument from \section{argument}
-% we process differently if the user invoked \section{} with no
-% argument (title)
-% note we reroute the call to the old \section*
-\def\@IEEEprocessthesectionargument#1{%
-\@ifmtarg{#1}{%
-\@IEEEappendixsavesection*{\appendixname\nobreakspace\thesectiondis}%
-\addcontentsline{toc}{section}{\appendixname\nobreakspace\thesection}}{%
-\@IEEEappendixsavesection*{\appendixname\nobreakspace\thesectiondis\\* #1}%
-\addcontentsline{toc}{section}{\appendixname\nobreakspace\thesection: #1}}}
-
-% we use this if the user calls \section{} after
-% \appendix-- which has no meaning. So, we ignore the
-% command and its argument. Then, warn the user.
-\def\@IEEEdestroythesectionargument#1{\typeout{** WARNING: Ignoring useless
-\protect\section\space in Appendix (line \the\inputlineno).}}
-
-
-% remember \thesection forms will be displayed in \ref calls
-% and in the Table of Contents.
-% The \sectiondis form is used in the actual heading itself
-
-% appendix command for one single appendix
-% normally has no heading. However, if you want a 
-% heading, you can do so via the optional argument:
-% \appendix[Optional Heading]
-\def\appendix{\relax}
-\renewcommand{\appendix}[1][]{\@IEEEsaveoriginalsectiononce\par
-    % v1.6 keep hyperref's identifiers unique
-    \gdef\theHsection{Appendix.A}%
-    % v1.6 adjust hyperref's string name for the section
-    \xdef\Hy@chapapp{appendix}%
-    \setcounter{section}{0}%
-    \setcounter{subsection}{0}%
-    \setcounter{subsubsection}{0}%
-    \setcounter{paragraph}{0}%
-    \gdef\thesection{A}%
-    \gdef\thesectiondis{}% 
-    \gdef\thesubsection{\Alph{subsection}}%
-    \gdef\@IEEEthmcounterinsection##1{A}
-    \refstepcounter{section}% update the \ref counter
-    \@ifmtarg{#1}{\@IEEEappendixsavesection*{\appendixname}%
-                  \addcontentsline{toc}{section}{\appendixname}}{%
-             \@IEEEappendixsavesection*{\appendixname\nobreakspace\\* #1}%
-             \addcontentsline{toc}{section}{\appendixname: #1}}%
-    % redefine \section command for appendix
-    % leave \section* as is
-    \def\section{\@ifstar{\@IEEEappendixsavesection*}{%
-                    \@IEEEdestroythesectionargument}}% throw out the argument
-                                                     % of the normal form
-}
-
-
-
-% appendices command for multiple appendices
-% user then calls \section with an argument (possibly empty) to
-% declare the individual appendices
-\def\appendices{\@IEEEsaveoriginalsectiononce\par
-    % v1.6 keep hyperref's identifiers unique
-    \gdef\theHsection{Appendix.\Alph{section}}%
-    % v1.6 adjust hyperref's string name for the section
-    \xdef\Hy@chapapp{appendix}%
-    \setcounter{section}{-1}% we want \refstepcounter to use section 0
-    \setcounter{subsection}{0}%
-    \setcounter{subsubsection}{0}%
-    \setcounter{paragraph}{0}%
-    \ifCLASSOPTIONromanappendices%
-    \gdef\thesection{\Roman{section}}%
-    \gdef\thesectiondis{\Roman{section}}%
-    \@IEEEcompsocconfonly{\gdef\thesectiondis{\Roman{section}.}}%
-    \gdef\@IEEEthmcounterinsection##1{A\arabic{##1}}
-    \else%
-    \gdef\thesection{\Alph{section}}%
-    \gdef\thesectiondis{\Alph{section}}%
-    \@IEEEcompsocconfonly{\gdef\thesectiondis{\Alph{section}.}}%
-    \gdef\@IEEEthmcounterinsection##1{\Alph{##1}}
-    \fi%
-    \refstepcounter{section}% update the \ref counter
-    \setcounter{section}{0}% NEXT \section will be the FIRST appendix
-    % redefine \section command for appendices
-    % leave \section* as is
-    \def\section{\@ifstar{\@IEEEappendixsavesection*}{% process the *-form
-                    \refstepcounter{section}% or is a new section so,
-                    \@IEEEprocessthesectionargument}}% process the argument 
-                                                 % of the normal form
-}
-
-
-
-% V1.7 compoc uses nonbold drop cap and small caps word style
-\ifCLASSOPTIONcompsoc
-  \def\IEEEPARstartFONTSTYLE{\mdseries}
-  \def\IEEEPARstartWORDFONTSTYLE{\scshape}
-  \def\IEEEPARstartWORDCAPSTYLE{\relax}
-\fi
-%
-%
-% \IEEEPARstart
-% Definition for the big two line drop cap letter at the beginning of the
-% first paragraph of journal papers. The first argument is the first letter
-% of the first word, the second argument is the remaining letters of the
-% first word which will be rendered in upper case.
-% In V1.6 this has been completely rewritten to:
-% 
-% 1. no longer have problems when the user begins an environment
-%    within the paragraph that uses \IEEEPARstart.
-% 2. auto-detect and use the current font family
-% 3. revise handling of the space at the end of the first word so that
-%    interword glue will now work as normal.
-% 4. produce correctly aligned edges for the (two) indented lines.
-% 
-% We generalize things via control macros - playing with these is fun too.
-% 
-% V1.7 added more control macros to make it easy for IEEEtrantools.sty users
-% to change the font style.
-% 
-% the number of lines that are indented to clear it
-% may need to increase if using decenders
-\providecommand{\IEEEPARstartDROPLINES}{2}
-% minimum number of lines left on a page to allow a \@IEEEPARstart
-% Does not take into consideration rubber shrink, so it tends to
-% be overly cautious
-\providecommand{\IEEEPARstartMINPAGELINES}{2}
-% V1.7 the height of the drop cap is adjusted to match the height of this text
-% in the current font (when \IEEEPARstart is called).
-\providecommand{\IEEEPARstartHEIGHTTEXT}{T}
-% the depth the letter is lowered below the baseline
-% the height (and size) of the letter is determined by the sum
-% of this value and the height of the \IEEEPARstartHEIGHTTEXT in the current
-% font. It is a good idea to set this value in terms of the baselineskip
-% so that it can respond to changes therein.
-\providecommand{\IEEEPARstartDROPDEPTH}{1.1\baselineskip}
-% V1.7 the font the drop cap will be rendered in,
-% can take zero or one argument.
-\providecommand{\IEEEPARstartFONTSTYLE}{\bfseries}
-% V1.7 any additional, non-font related commands needed to modify
-% the drop cap letter, can take zero or one argument.
-\providecommand{\IEEEPARstartCAPSTYLE}{\MakeUppercase}
-% V1.7 the font that will be used to render the rest of the word,
-% can take zero or one argument.
-\providecommand{\IEEEPARstartWORDFONTSTYLE}{\relax}
-% V1.7 any additional, non-font related commands needed to modify
-% the rest of the word, can take zero or one argument.
-\providecommand{\IEEEPARstartWORDCAPSTYLE}{\MakeUppercase}
-% This is the horizontal separation distance from the drop letter to the main text.
-% Lengths that depend on the font (e.g., ex, em, etc.) will be referenced
-% to the font that is active when \IEEEPARstart is called. 
-\providecommand{\IEEEPARstartSEP}{0.15em}
-% V1.7 horizontal offset applied to the left of the drop cap.
-\providecommand{\IEEEPARstartHOFFSET}{0em}
-% V1.7 Italic correction command applied at the end of the drop cap.
-\providecommand{\IEEEPARstartITLCORRECT}{\/}
-
-% width of the letter output, set globally. Can be used in \IEEEPARstartSEP
-% or \IEEEPARstartHOFFSET, but not the height lengths.
-\newdimen\IEEEPARstartletwidth
-\IEEEPARstartletwidth 0pt\relax
-
-% definition of \IEEEPARstart
-% THIS IS A CONTROLLED SPACING AREA, DO NOT ALLOW SPACES WITHIN THESE LINES
-% 
-% The token \@IEEEPARstartfont will be globally defined after the first use
-% of \IEEEPARstart and will be a font command which creates the big letter
-% The first argument is the first letter of the first word and the second
-% argument is the rest of the first word(s).
-\def\IEEEPARstart#1#2{\par{%
-% if this page does not have enough space, break it and lets start
-% on a new one
-\@IEEEtranneedspace{\IEEEPARstartMINPAGELINES\baselineskip}{\relax}%
-% V1.7 move this up here in case user uses \textbf for \IEEEPARstartFONTSTYLE
-% which uses command \leavevmode which causes an unwanted \indent to be issued
-\noindent
-% calculate the desired height of the big letter
-% it extends from the top of \IEEEPARstartHEIGHTTEXT in the current font
-% down to \IEEEPARstartDROPDEPTH below the current baseline
-\settoheight{\@IEEEtrantmpdimenA}{\IEEEPARstartHEIGHTTEXT}%
-\addtolength{\@IEEEtrantmpdimenA}{\IEEEPARstartDROPDEPTH}%
-% extract the name of the current font in bold
-% and place it in \@IEEEPARstartFONTNAME
-\def\@IEEEPARstartGETFIRSTWORD##1 ##2\relax{##1}%
-{\IEEEPARstartFONTSTYLE{\selectfont\edef\@IEEEPARstartFONTNAMESPACE{\fontname\font\space}%
-\xdef\@IEEEPARstartFONTNAME{\expandafter\@IEEEPARstartGETFIRSTWORD\@IEEEPARstartFONTNAMESPACE\relax}}}%
-% define a font based on this name with a point size equal to the desired
-% height of the drop letter
-\font\@IEEEPARstartsubfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenA\relax%
-% save this value as a counter (integer) value (sp points)
-\@IEEEtrantmpcountA=\@IEEEtrantmpdimenA%
-% now get the height of the actual letter produced by this font size
-\settoheight{\@IEEEtrantmpdimenB}{\@IEEEPARstartsubfont\IEEEPARstartCAPSTYLE{#1}}%
-% If something bogus happens like the first argument is empty or the
-% current font is strange, do not allow a zero height.
-\ifdim\@IEEEtrantmpdimenB=0pt\relax%
-\typeout{** WARNING: IEEEPARstart drop letter has zero height! (line \the\inputlineno)}%
-\typeout{ Forcing the drop letter font size to 10pt.}%
-\@IEEEtrantmpdimenB=10pt%
-\fi%
-% and store it as a counter
-\@IEEEtrantmpcountB=\@IEEEtrantmpdimenB%
-% Since a font size doesn't exactly correspond to the height of the capital
-% letters in that font, the actual height of the letter, \@IEEEtrantmpcountB,
-% will be less than that desired, \@IEEEtrantmpcountA
-% we need to raise the font size, \@IEEEtrantmpdimenA 
-% by \@IEEEtrantmpcountA / \@IEEEtrantmpcountB
-% But, TeX doesn't have floating point division, so we have to use integer
-% division. Hence the use of the counters.
-% We need to reduce the denominator so that the loss of the remainder will
-% have minimal affect on the accuracy of the result
-\divide\@IEEEtrantmpcountB by 200%
-\divide\@IEEEtrantmpcountA by \@IEEEtrantmpcountB%
-% Then reequalize things when we use TeX's ability to multiply by
-% floating point values
-\@IEEEtrantmpdimenB=0.005\@IEEEtrantmpdimenA%
-\multiply\@IEEEtrantmpdimenB by \@IEEEtrantmpcountA%
-% \@IEEEPARstartfont is globaly set to the calculated font of the big letter
-% We need to carry this out of the local calculation area to to create the
-% big letter.
-\global\font\@IEEEPARstartfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenB%
-% Now set \@IEEEtrantmpdimenA to the width of the big letter
-% We need to carry this out of the local calculation area to set the
-% hanging indent
-\settowidth{\global\@IEEEtrantmpdimenA}{\@IEEEPARstartfont
-\IEEEPARstartCAPSTYLE{#1\IEEEPARstartITLCORRECT}}}%
-% end of the isolated calculation environment
-\global\IEEEPARstartletwidth\@IEEEtrantmpdimenA\relax%
-% add in the extra clearance we want
-\advance\@IEEEtrantmpdimenA by \IEEEPARstartSEP\relax%
-% add in the optional offset
-\advance\@IEEEtrantmpdimenA by \IEEEPARstartHOFFSET\relax%
-% V1.7 don't allow negative offsets to produce negative hanging indents
-\@IEEEtrantmpdimenB\@IEEEtrantmpdimenA
-\ifnum\@IEEEtrantmpdimenB < 0 \@IEEEtrantmpdimenB 0pt\fi
-% \@IEEEtrantmpdimenA has the width of the big letter plus the
-% separation space and \@IEEEPARstartfont is the font we need to use
-% Now, we make the letter and issue the hanging indent command
-% The letter is placed in a box of zero width and height so that other
-% text won't be displaced by it.
-\hangindent\@IEEEtrantmpdimenB\hangafter=-\IEEEPARstartDROPLINES%
-\makebox[0pt][l]{\hspace{-\@IEEEtrantmpdimenA}%
-\raisebox{-\IEEEPARstartDROPDEPTH}[0pt][0pt]{\hspace{\IEEEPARstartHOFFSET}%
-\@IEEEPARstartfont\IEEEPARstartCAPSTYLE{#1\IEEEPARstartITLCORRECT}%
-\hspace{\IEEEPARstartSEP}}}%
-{\IEEEPARstartWORDFONTSTYLE{\IEEEPARstartWORDCAPSTYLE{\selectfont#2}}}}
-
-
-
-
-% determines if the space remaining on a given page is equal to or greater
-% than the specified space of argument one
-% if not, execute argument two (only if the remaining space is greater than zero)
-% and issue a \newpage
-% 
-% example: \@IEEEtranneedspace{2in}{\vfill}
-% 
-% Does not take into consideration rubber shrinkage, so it tends to
-% be overly cautious
-% Based on an example posted by Donald Arseneau
-% Note this macro uses \@IEEEtrantmpdimenB internally for calculations,
-% so DO NOT PASS \@IEEEtrantmpdimenB to this routine
-% if you need a dimen register, import with \@IEEEtrantmpdimenA instead
-\def\@IEEEtranneedspace#1#2{\penalty-100\begingroup%shield temp variable
-\@IEEEtrantmpdimenB\pagegoal\advance\@IEEEtrantmpdimenB-\pagetotal% space left
-\ifdim #1>\@IEEEtrantmpdimenB\relax% not enough space left
-\ifdim\@IEEEtrantmpdimenB>\z@\relax #2\fi%
-\newpage%
-\fi\endgroup}
-
-
-
-% IEEEbiography ENVIRONMENT
-% Allows user to enter biography leaving place for picture (adapts to font size)
-% As of V1.5, a new optional argument allows you to have a real graphic!
-% V1.5 and later also fixes the "colliding biographies" which could happen when a 
-% biography's text was shorter than the space for the photo.
-% MDS 7/2001
-% V1.6 prevent multiple biographies from making multiple TOC entries
-\newif\if@IEEEbiographyTOCentrynotmade
-\global\@IEEEbiographyTOCentrynotmadetrue
-
-% biography counter so hyperref can jump directly to the biographies
-% and not just the previous section
-\newcounter{IEEEbiography}
-\setcounter{IEEEbiography}{0}
-
-% photo area size
-\def\@IEEEBIOphotowidth{1.0in}    % width of the biography photo area
-\def\@IEEEBIOphotodepth{1.25in}   % depth (height) of the biography photo area
-% area cleared for photo
-\def\@IEEEBIOhangwidth{1.14in}    % width cleared for the biography photo area
-\def\@IEEEBIOhangdepth{1.25in}    % depth cleared for the biography photo area
-                                  % actual depth will be a multiple of 
-                                  % \baselineskip, rounded up
-\def\@IEEEBIOskipN{4\baselineskip}% nominal value of the vskip above the biography
-
-\newenvironment{IEEEbiography}[2][]{\normalfont\@IEEEcompsoconly{\sffamily}\footnotesize%
-\unitlength 1in\parskip=0pt\par\parindent 1em\interlinepenalty500%
-% we need enough space to support the hanging indent
-% the nominal value of the spacer
-% and one extra line for good measure
-\@IEEEtrantmpdimenA=\@IEEEBIOhangdepth%
-\advance\@IEEEtrantmpdimenA by \@IEEEBIOskipN%
-\advance\@IEEEtrantmpdimenA by 1\baselineskip%
-% if this page does not have enough space, break it and lets start
-% with a new one
-\@IEEEtranneedspace{\@IEEEtrantmpdimenA}{\relax}%
-% nominal spacer can strech, not shrink use 1fil so user can out stretch with \vfill
-\vskip \@IEEEBIOskipN plus 1fil minus 0\baselineskip%
-% the default box for where the photo goes
-\def\@IEEEtempbiographybox{{\setlength{\fboxsep}{0pt}\framebox{%
-\begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}\centering PLACE\\ PHOTO\\ HERE \end{minipage}}}}%
-%
-% detect if the optional argument was supplied, this requires the
-% \@ifmtarg command as defined in the appendix section above
-% and if so, override the default box with what they want
-\@ifmtarg{#1}{\relax}{\def\@IEEEtempbiographybox{\mbox{\begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}%
-\centering%
-#1%
-\end{minipage}}}}% end if optional argument supplied
-% Make an entry into the table of contents only if we have not done so before
-\if@IEEEbiographyTOCentrynotmade%
-% link labels to the biography counter so hyperref will jump
-% to the biography, not the previous section
-\setcounter{IEEEbiography}{-1}%
-\refstepcounter{IEEEbiography}%
-\addcontentsline{toc}{section}{Biographies}%
-\global\@IEEEbiographyTOCentrynotmadefalse%
-\fi%
-% one more biography
-\refstepcounter{IEEEbiography}%
-% Make an entry for this name into the table of contents 
-\addcontentsline{toc}{subsection}{#2}%
-% V1.6 properly handle if a new paragraph should occur while the
-% hanging indent is still active. Do this by redefining \par so
-% that it will not start a new paragraph. (But it will appear to the
-% user as if it did.) Also, strip any leading pars, newlines, or spaces.
-\let\@IEEEBIOORGparCMD=\par% save the original \par command
-\edef\par{\hfil\break\indent}% the new \par will not be a "real" \par
-\settoheight{\@IEEEtrantmpdimenA}{\@IEEEtempbiographybox}% get height of biography box
-\@IEEEtrantmpdimenB=\@IEEEBIOhangdepth%
-\@IEEEtrantmpcountA=\@IEEEtrantmpdimenB% countA has the hang depth
-\divide\@IEEEtrantmpcountA by \baselineskip%  calculates lines needed to produce the hang depth
-\advance\@IEEEtrantmpcountA by 1% ensure we overestimate
-% set the hanging indent
-\hangindent\@IEEEBIOhangwidth%
-\hangafter-\@IEEEtrantmpcountA%
-% reference the top of the photo area to the top of a capital T
-\settoheight{\@IEEEtrantmpdimenB}{\mbox{T}}%
-% set the photo box, give it zero width and height so as not to disturb anything
-\noindent\makebox[0pt][l]{\hspace{-\@IEEEBIOhangwidth}\raisebox{\@IEEEtrantmpdimenB}[0pt][0pt]{%
-\raisebox{-\@IEEEBIOphotodepth}[0pt][0pt]{\@IEEEtempbiographybox}}}%
-% now place the author name and begin the bio text
-\noindent\textbf{#2\ }\@IEEEgobbleleadPARNLSP}{\relax\let\par=\@IEEEBIOORGparCMD\par%
-% 7/2001 V1.5 detect when the biography text is shorter than the photo area
-% and pad the unused area - preventing a collision from the next biography entry
-% MDS
-\ifnum \prevgraf <\@IEEEtrantmpcountA\relax% detect when the biography text is shorter than the photo
-    \advance\@IEEEtrantmpcountA by -\prevgraf% calculate how many lines we need to pad
-    \advance\@IEEEtrantmpcountA by -1\relax% we compensate for the fact that we indented an extra line
-    \@IEEEtrantmpdimenA=\baselineskip% calculate the length of the padding
-    \multiply\@IEEEtrantmpdimenA by \@IEEEtrantmpcountA%
-    \noindent\rule{0pt}{\@IEEEtrantmpdimenA}% insert an invisible support strut
-\fi%
-\par\normalfont}
-
-
-
-% V1.6
-% added biography without a photo environment
-\newenvironment{IEEEbiographynophoto}[1]{%
-% Make an entry into the table of contents only if we have not done so before
-\if@IEEEbiographyTOCentrynotmade%
-% link labels to the biography counter so hyperref will jump
-% to the biography, not the previous section
-\setcounter{IEEEbiography}{-1}%
-\refstepcounter{IEEEbiography}%
-\addcontentsline{toc}{section}{Biographies}%
-\global\@IEEEbiographyTOCentrynotmadefalse%
-\fi%
-% one more biography
-\refstepcounter{IEEEbiography}%
-% Make an entry for this name into the table of contents 
-\addcontentsline{toc}{subsection}{#1}%
-\normalfont\@IEEEcompsoconly{\sffamily}\footnotesize\interlinepenalty500%
-\vskip 4\baselineskip plus 1fil minus 0\baselineskip%
-\parskip=0pt\par%
-\noindent\textbf{#1\ }\@IEEEgobbleleadPARNLSP}{\relax\par\normalfont}
-
-
-% provide the user with some old font commands
-% got this from article.cls
-\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
-\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
-\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
-\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
-\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
-\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
-\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
-\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal}
-\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal}
-
-
-% SPECIAL PAPER NOTICE COMMANDS
-% 
-% holds the special notice text
-\def\@IEEEspecialpapernotice{\relax}
- 
-% for special papers, like invited papers, the user can do:
-% \IEEEspecialpapernotice{(Invited Paper)} before \maketitle
-\def\IEEEspecialpapernotice#1{\ifCLASSOPTIONconference%
-\def\@IEEEspecialpapernotice{{\sublargesize\textit{#1}\vspace*{1em}}}%
-\else%
-\def\@IEEEspecialpapernotice{{\\*[1.5ex]\sublargesize\textit{#1}}\vspace*{-2ex}}%
-\fi}
-
-
-
-
-% PUBLISHER ID COMMANDS
-% to insert a publisher's ID footer
-% V1.6 \IEEEpubid has been changed so that the change in page size and style
-% occurs in \maketitle. \IEEEpubid must now be issued prior to \maketitle
-% use \IEEEpubidadjcol as before - in the second column of the title page
-% These changes allow \maketitle to take the reduced page height into
-% consideration when dynamically setting the space between the author 
-% names and the maintext.
-%
-% the amount the main text is pulled up to make room for the
-% publisher's ID footer
-% The IEEE uses about 1.3\baselineskip for journals, 
-% dynamic title spacing will clean up the fraction
-\def\@IEEEpubidpullup{1.3\baselineskip}
-\ifCLASSOPTIONtechnote
-% for technotes it must be an integer of baselineskip as there can be no
-% dynamic title spacing for two column mode technotes (the title is in the
-% in first column) and we should maintain an integer number of lines in the
-% second column
-% There are some examples (such as older issues of "Transactions on
-% Information Theory") in which the IEEE really pulls the text off the ID for
-% technotes - about 0.55in (or 4\baselineskip). We'll use 2\baselineskip
-% and call it even.
-\def\@IEEEpubidpullup{2\baselineskip}
-\fi
-
-% V1.7 compsoc does not use a pullup
-\ifCLASSOPTIONcompsoc
-\def\@IEEEpubidpullup{0pt}
-\fi
-
-% holds the ID text
-\def\@IEEEpubid{\relax}
-
-% flag so \maketitle can tell if \IEEEpubid was called
-\newif\if@IEEEusingpubid
-\global\@IEEEusingpubidfalse
-% issue this command in the page to have the ID at the bottom
-% V1.6 use before \maketitle
-\def\IEEEpubid#1{\def\@IEEEpubid{#1}\global\@IEEEusingpubidtrue}
-
-
-% command which will pull up (shorten) the column it is executed in
-% to make room for the publisher ID. Place in the second column of
-% the title page when using \IEEEpubid
-% Is smart enough not to do anything when in single column text or
-% if the user hasn't called \IEEEpubid
-% currently needed in for the second column of a page with the
-% publisher ID. If not needed in future releases, please provide this
-% command and define it as \relax for backward compatibility
-% v1.6b do not allow command to operate if the peer review option has been 
-% selected because \IEEEpubidadjcol will not be on the cover page.
-% V1.7 do nothing if compsoc
-\def\IEEEpubidadjcol{\ifCLASSOPTIONcompsoc\else\ifCLASSOPTIONpeerreview\else
-\if@twocolumn\if@IEEEusingpubid\enlargethispage{-\@IEEEpubidpullup}\fi\fi\fi\fi}
-
-% Special thanks to Peter Wilson, Daniel Luecking, and the other
-% gurus at comp.text.tex, for helping me to understand how best to
-% implement the IEEEpubid command in LaTeX.
-
-
-
-%% Lockout some commands under various conditions
-
-% general purpose bit bucket
-\newsavebox{\@IEEEtranrubishbin}
-
-% flags to prevent multiple warning messages
-\newif\if@IEEEWARNthanks
-\newif\if@IEEEWARNIEEEPARstart
-\newif\if@IEEEWARNIEEEbiography
-\newif\if@IEEEWARNIEEEbiographynophoto
-\newif\if@IEEEWARNIEEEpubid
-\newif\if@IEEEWARNIEEEpubidadjcol
-\newif\if@IEEEWARNIEEEmembership
-\newif\if@IEEEWARNIEEEaftertitletext
-\@IEEEWARNthankstrue
-\@IEEEWARNIEEEPARstarttrue
-\@IEEEWARNIEEEbiographytrue
-\@IEEEWARNIEEEbiographynophototrue
-\@IEEEWARNIEEEpubidtrue
-\@IEEEWARNIEEEpubidadjcoltrue
-\@IEEEWARNIEEEmembershiptrue
-\@IEEEWARNIEEEaftertitletexttrue
-
-
-%% Lockout some commands when in various modes, but allow them to be restored if needed
-%%
-% save commands which might be locked out
-% so that the user can later restore them if needed
-\let\@IEEESAVECMDthanks\thanks
-\let\@IEEESAVECMDIEEEPARstart\IEEEPARstart
-\let\@IEEESAVECMDIEEEbiography\IEEEbiography
-\let\@IEEESAVECMDendIEEEbiography\endIEEEbiography
-\let\@IEEESAVECMDIEEEbiographynophoto\IEEEbiographynophoto
-\let\@IEEESAVECMDendIEEEbiographynophoto\endIEEEbiographynophoto
-\let\@IEEESAVECMDIEEEpubid\IEEEpubid
-\let\@IEEESAVECMDIEEEpubidadjcol\IEEEpubidadjcol
-\let\@IEEESAVECMDIEEEmembership\IEEEmembership
-\let\@IEEESAVECMDIEEEaftertitletext\IEEEaftertitletext
-
-
-% disable \IEEEPARstart when in draft mode
-% This may have originally been done because the pre-V1.6 drop letter
-% algorithm had problems with a non-unity baselinestretch
-% At any rate, it seems too formal to have a drop letter in a draft
-% paper.
-\ifCLASSOPTIONdraftcls
-\def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** ATTENTION: \noexpand\IEEEPARstart
- is disabled in draft mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse}
-\fi
-% and for technotes
-\ifCLASSOPTIONtechnote
-\def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** WARNING: \noexpand\IEEEPARstart
- is locked out for technotes (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse}
-\fi
-
-
-% lockout unneeded commands when in conference mode
-\ifCLASSOPTIONconference
-% when locked out, \thanks, \IEEEbiography, \IEEEbiographynophoto, \IEEEpubid,
-% \IEEEmembership and \IEEEaftertitletext will all swallow their given text. 
-% \IEEEPARstart will output a normal character instead
-% warn the user about these commands only once to prevent the console screen
-% from filling up with redundant messages
-\def\thanks#1{\if@IEEEWARNthanks\typeout{** WARNING: \noexpand\thanks
- is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNthanksfalse}
-\def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** WARNING: \noexpand\IEEEPARstart
- is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse}
-
-
-% LaTeX treats environments and commands with optional arguments differently.
-% the actual ("internal") command is stored as \\commandname 
-% (accessed via \csname\string\commandname\endcsname )
-% the "external" command \commandname is a macro with code to determine
-% whether or not the optional argument is presented and to provide the 
-% default if it is absent. So, in order to save and restore such a command
-% we would have to save and restore \\commandname as well. But, if LaTeX
-% ever changes the way it names the internal names, the trick would break.
-% Instead let us just define a new environment so that the internal
-% name can be left undisturbed.
-\newenvironment{@IEEEbogusbiography}[2][]{\if@IEEEWARNIEEEbiography\typeout{** WARNING: \noexpand\IEEEbiography
- is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEbiographyfalse%
-\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}
-% and make biography point to our bogus biography
-\let\IEEEbiography=\@IEEEbogusbiography
-\let\endIEEEbiography=\end@IEEEbogusbiography
-
-\renewenvironment{IEEEbiographynophoto}[1]{\if@IEEEWARNIEEEbiographynophoto\typeout{** WARNING: \noexpand\IEEEbiographynophoto
- is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEbiographynophotofalse%
-\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}
-
-\def\IEEEpubid#1{\if@IEEEWARNIEEEpubid\typeout{** WARNING: \noexpand\IEEEpubid 
- is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEpubidfalse}
-\def\IEEEpubidadjcol{\if@IEEEWARNIEEEpubidadjcol\typeout{** WARNING: \noexpand\IEEEpubidadjcol
- is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEpubidadjcolfalse}
-\def\IEEEmembership#1{\if@IEEEWARNIEEEmembership\typeout{** WARNING: \noexpand\IEEEmembership
- is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEmembershipfalse}
-\def\IEEEaftertitletext#1{\if@IEEEWARNIEEEaftertitletext\typeout{** WARNING: \noexpand\IEEEaftertitletext
- is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEaftertitletextfalse}
-\fi
-
-
-% provide a way to restore the commands that are locked out
-\def\IEEEoverridecommandlockouts{%
-\typeout{** ATTENTION: Overriding command lockouts (line \the\inputlineno).}%
-\let\thanks\@IEEESAVECMDthanks%
-\let\IEEEPARstart\@IEEESAVECMDIEEEPARstart%
-\let\IEEEbiography\@IEEESAVECMDIEEEbiography%
-\let\endIEEEbiography\@IEEESAVECMDendIEEEbiography%
-\let\IEEEbiographynophoto\@IEEESAVECMDIEEEbiographynophoto%
-\let\endIEEEbiographynophoto\@IEEESAVECMDendIEEEbiographynophoto%
-\let\IEEEpubid\@IEEESAVECMDIEEEpubid%
-\let\IEEEpubidadjcol\@IEEESAVECMDIEEEpubidadjcol%
-\let\IEEEmembership\@IEEESAVECMDIEEEmembership%
-\let\IEEEaftertitletext\@IEEESAVECMDIEEEaftertitletext}
-
-
-
-% need a backslash character for typeout output
-{\catcode`\|=0 \catcode`\\=12
-|xdef|@IEEEbackslash{\}}
-
-
-% hook to allow easy disabling of all legacy warnings
-\def\@IEEElegacywarn#1#2{\typeout{** ATTENTION: \@IEEEbackslash #1 is deprecated (line \the\inputlineno).
-Use \@IEEEbackslash #2 instead.}}
-
-
-% provide some legacy IEEEtran commands
-\def\IEEEcompsoctitleabstractindextext{\@IEEElegacywarn{IEEEcompsoctitleabstractindextext}{IEEEtitleabstractindextext}\IEEEtitleabstractindextext}
-\def\IEEEdisplaynotcompsoctitleabstractindextext{\@IEEElegacywarn{IEEEdisplaynotcompsoctitleabstractindextext}{IEEEdisplaynontitleabstractindextext}\IEEEdisplaynontitleabstractindextext}
-% provide some legacy IEEEtran environments
-
-
-% V1.8a no more support for these legacy commands
-%\def\authorblockA{\@IEEElegacywarn{authorblockA}{IEEEauthorblockA}\IEEEauthorblockA}
-%\def\authorblockN{\@IEEElegacywarn{authorblockN}{IEEEauthorblockN}\IEEEauthorblockN}
-%\def\authorrefmark{\@IEEElegacywarn{authorrefmark}{IEEEauthorrefmark}\IEEEauthorrefmark}
-%\def\PARstart{\@IEEElegacywarn{PARstart}{IEEEPARstart}\IEEEPARstart}
-%\def\pubid{\@IEEElegacywarn{pubid}{IEEEpubid}\IEEEpubid}
-%\def\pubidadjcol{\@IEEElegacywarn{pubidadjcol}{IEEEpubidadjcol}\IEEEpubidadjcol}
-%\def\specialpapernotice{\@IEEElegacywarn{specialpapernotice}{IEEEspecialpapernotice}\IEEEspecialpapernotice}
-% and environments
-%\def\keywords{\@IEEElegacywarn{keywords}{IEEEkeywords}\IEEEkeywords}
-%\def\endkeywords{\endIEEEkeywords}
-% V1.8 no more support for legacy IED list commands
-%\let\labelindent\IEEElabelindent
-%\def\calcleftmargin{\@IEEElegacywarn{calcleftmargin}{IEEEcalcleftmargin}\IEEEcalcleftmargin}
-%\def\setlabelwidth{\@IEEElegacywarn{setlabelwidth}{IEEEsetlabelwidth}\IEEEsetlabelwidth}
-%\def\usemathlabelsep{\@IEEElegacywarn{usemathlabelsep}{IEEEusemathlabelsep}\IEEEusemathlabelsep}
-%\def\iedlabeljustifyc{\@IEEElegacywarn{iedlabeljustifyc}{IEEEiedlabeljustifyc}\IEEEiedlabeljustifyc}
-%\def\iedlabeljustifyl{\@IEEElegacywarn{iedlabeljustifyl}{IEEEiedlabeljustifyl}\IEEEiedlabeljustifyl}
-%\def\iedlabeljustifyr{\@IEEElegacywarn{iedlabeljustifyr}{IEEEiedlabeljustifyr}\IEEEiedlabeljustifyr}
-% V1.8 no more support for QED and proof stuff
-%\def\QED{\@IEEElegacywarn{QED}{IEEEQED}\IEEEQED}
-%\def\QEDclosed{\@IEEElegacywarn{QEDclosed}{IEEEQEDclosed}\IEEEQEDclosed}
-%\def\QEDopen{\@IEEElegacywarn{QEDopen}{IEEEQEDopen}\IEEEQEDopen}
-%\AtBeginDocument{\def\proof{\@IEEElegacywarn{proof}{IEEEproof}\IEEEproof}\def\endproof{\endIEEEproof}}
-% V1.8 no longer support biography or biographynophoto
-%\def\biography{\@IEEElegacywarn{biography}{IEEEbiography}\IEEEbiography}
-%\def\biographynophoto{\@IEEElegacywarn{biographynophoto}{IEEEbiographynophoto}\IEEEbiographynophoto}
-%\def\endbiography{\endIEEEbiography}
-%\def\endbiographynophoto{\endIEEEbiographynophoto}
-% V1.7 and later no longer supports \overrideIEEEmargins
-%\def\overrideIEEEmargins{%
-%\typeout{** WARNING: \string\overrideIEEEmargins \space no longer supported (line \the\inputlineno).}%
-%\typeout{** Use the \string\CLASSINPUTinnersidemargin, \string\CLASSINPUToutersidemargin \space controls instead.}}
-
-\endinput
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End of IEEEtran.cls  %%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% That's all folks!
-
-- 
cgit v1.2.3

