Update on local

.gitignore

@@ -0,0 +1,12 @@
+IEEE-conference-template-062824.pdf
+*.synctex.gz
+*.aux
+*.fdb_latexmk
+*.fls
+*.log
+*.out
+.DS_Store
+*.synctex*
+*.bbl
+*.blg
+~$*.*

IEEE-conference-template-062824.tex

@@ -0,0 +1,42 @@
+\documentclass[conference]{IEEEtran}
+\IEEEoverridecommandlockouts
+% The preceding line is only needed to identify funding in the first footnote. If that is unneeded, please comment it out.
+%Template version as of 6/27/2024
+
+\usepackage{cite}
+\usepackage{amsmath,amssymb,amsfonts}
+\usepackage{algorithmic}
+\usepackage{graphicx}
+\usepackage{textcomp}
+\usepackage{xcolor}
+\begin{document}
+
+\title{Conference Paper Title\\
+% \thanks{Identify applicable funding agency here. If none, delete this.}
+}
+
+\author{\IEEEauthorblockN{1\textsuperscript{st} Given Name Surname}
+\IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\
+\textit{name of organization (of Aff.)}\\
+City, Country \\
+email address or ORCID}
+}
+
+\maketitle
+
+\begin{abstract}
+    Abstract.
+\end{abstract}
+
+\begin{IEEEkeywords}
+keywords.
+\end{IEEEkeywords}
+
+\input{sections/Introduction.tex}
+
+\cite{ahmedInternet2024}.
+
+\bibliographystyle{ieeetr}
+\bibliography{../refs}
+
+\end{document}

IEEEtran.cls

@@ -0,0 +1,6347 @@
+%%
+%% 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!
+

main.tex

@@ -1,14 +0,0 @@
-\documentclass{article}
-\usepackage{graphicx} % Required for inserting images
-
-\title{DAC-2025}
-\author{Youngbin Kim}
-\date{September 2024}
-
-\begin{document}
-
-\maketitle
-
-\section{Introduction}
-
-\end{document}

sections/Introduction.tex

@@ -0,0 +1,2 @@
+\section{Introduction}
+Introduction.