%%
%% IEEEtran.cls 2007/03/05 version V1.7a
%% 
%% 
%% This is the official IEEE 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/tex-archive/macros/latex/contrib/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 (2001-2007)
%% 
%% 
%% Copyright (c) 1993-2000 by Gerry Murray, Silvano Balemi, 
%%                         Jon Dixon, Peter N"uchter,
%%                         Juergen von Hagen
%%                         and
%% Copyright (c) 2001-2007 by Michael Shell
%%
%% Current maintainer (V1.3 to V1.7): 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 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_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
%    determines paper size: 8.5in X 11in or 210mm X 297mm. CHANGING THE PAPER
%    SIZE 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 final submission to IEEE, authors should use US letter (8.5 X 11in)
%    paper. 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 a 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. 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.
%
% compsoc
%    Use the format of the IEEE Computer Society.
%
% 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}[2007/03/05 V1.7a 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{7}

% 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\ifCLASSOPTIONcompsoc         \CLASSOPTIONcompsocfalse

\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



% IEEEtran class scratch pad registers
% dimen
\newdimen\@IEEEtrantmpdimenA
\newdimen\@IEEEtrantmpdimenB
% count
\newcount\@IEEEtrantmpcountA
\newcount\@IEEEtrantmpcountB
% 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{\paperheight}{11in}%
                            \setlength{\paperwidth}{8.5in}%
                            \@IEEEusingAfourpaperfalse
                            \def\CLASSOPTIONpaper{letter}%
                            \def\CLASSINFOpaperwidth{8.5in}%
                            \def\CLASSINFOpaperheight{11in}}


\DeclareOption{a4paper}{\setlength{\paperheight}{297mm}%
                        \setlength{\paperwidth}{210mm}%
                        \@IEEEusingAfourpapertrue
                        \def\CLASSOPTIONpaper{a4}%
                        \def\CLASSINFOpaperwidth{210mm}%
                        \def\CLASSINFOpaperheight{297mm}}

\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{compsoc}{\CLASSOPTIONcompsoctrue}

\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



% 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}


% 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}

\@IEEEcompsoconly{\typeout{-- Using IEEE Computer Society mode.}}

% V1.7 compsoc nonconference papers, use Palatino/Palladio as the main text font,
% not Times Roman.
\@IEEEcompsocnotconfonly{\renewcommand{\rmdefault}{ppl}}

% enable Times/Palatino main text font
\normalfont\selectfont





% 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

\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 plus3pt minus1pt%
\belowdisplayskip \abovedisplayskip%
\abovedisplayshortskip 0pt plus3pt%
\belowdisplayshortskip 1.5ex plus3pt minus1pt
\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


% Check if we have selected 10 points
\ifx\CLASSOPTIONpt\@IEEEptsizeten
\typeout{-- This is a 10 point document.}
\def\normalsize{\@setfontsize{\normalsize}{10}{12.00pt}}%
\setlength{\@IEEEnormalsizeunitybaselineskip}{12pt}%
\normalsize
\abovedisplayskip 1.5ex plus4pt minus2pt%
\belowdisplayskip \abovedisplayskip%
\abovedisplayshortskip 0pt plus4pt%
\belowdisplayshortskip 1.5ex plus4pt minus2pt
\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


% Check if we have selected 11 points
\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 plus5pt minus3pt%
\belowdisplayskip \abovedisplayskip%
\abovedisplayshortskip 0pt plus5pt%
\belowdisplayshortskip 1.5ex plus5pt minus3pt
\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


% Check if we have selected 12 points
\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 plus6pt minus4pt%
\belowdisplayskip \abovedisplayskip%
\abovedisplayshortskip 0pt plus6pt%
\belowdisplayshortskip 1.5ex plus6pt minus4pt
\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


% V1.6 The Computer Modern Fonts will issue a substitution warning for
% 24pt titles (24.88pt is used instead) increase the substitution
% tolerance to turn off this warning
\def\fontsubfuzz{.9pt}
% However, the default (and correct) Times font will scale exactly as needed.


% 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

\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, IEEE allows for a more generous range which reduces the need
% for hyphenation, especially for two column text. Furthermore, IEEE
% tends to use a little bit more nominal space between the words.
% 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, 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}


% 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 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}



% V1.6 
% 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
% If we didn't adjust the interword spacing, 2200 might be better.
% The TeX default is 1000
\hbadness=1350
% 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


% 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

\topmargin    -49.0pt
\headheight   12pt
\headsep      0.25in

% use the normal font baselineskip
% so that \topskip is unaffected by changes in \baselinestretch
\topskip=\@IEEEnormalsizeunitybaselineskip
\textheight       58pc  % 9.63in, 696pt
% Tweak textheight to a perfect integer number of lines/page.
% The normal baselineskip for each document point size is used 
% to determine these values.
\ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=63\@IEEEnormalsizeunitybaselineskip\fi      % 63 lines/page
\ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=58\@IEEEnormalsizeunitybaselineskip\fi       % 58 lines/page
\ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=52\@IEEEnormalsizeunitybaselineskip\fi    % 52 lines/page
\ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=50\@IEEEnormalsizeunitybaselineskip\fi    % 50 lines/page


\columnsep         1pc
\textwidth        43pc   % 2 x 21pc + 1pc = 43pc
 

% the default side margins are equal
\if@IEEEusingAfourpaper 
\oddsidemargin        14.32mm
\evensidemargin       14.32mm
\else
\oddsidemargin        0.680in
\evensidemargin       0.680in
\fi
% compensate for LaTeX's 1in offset
\addtolength{\oddsidemargin}{-1in}
\addtolength{\evensidemargin}{-1in}



% adjust margins for conference mode
\ifCLASSOPTIONconference
 \topmargin        -0.25in
 % we retain the reserved, but unused space for headers
 \addtolength{\topmargin}{-\headheight}
 \addtolength{\topmargin}{-\headsep}
 \textheight        9.25in % The standard for conferences (668.4975pt)
 % Tweak textheight to a perfect integer number of lines/page.
 \ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=61\@IEEEnormalsizeunitybaselineskip\fi      % 61 lines/page
 \ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=56\@IEEEnormalsizeunitybaselineskip\fi       % 56 lines/page
 \ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=50\@IEEEnormalsizeunitybaselineskip\fi    % 50 lines/page
 \ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=48\@IEEEnormalsizeunitybaselineskip\fi    % 48 lines/page
\fi


% compsoc conference
\ifCLASSOPTIONcompsoc
\ifCLASSOPTIONconference
 % compsoc conference use a larger value for columnsep
 \columnsep 0.375in
 % compsoc conferences want 1in top margin, 1.125in bottom margin
 \topmargin        0in
 \addtolength{\topmargin}{-6pt}% we tweak this a tad to better comply with top of line stuff
 % we retain the reserved, but unused space for headers
 \addtolength{\topmargin}{-\headheight}
 \addtolength{\topmargin}{-\headsep}
 \textheight        8.875in % (641.39625pt)
 % Tweak textheight to a perfect integer number of lines/page.
 \ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=58\@IEEEnormalsizeunitybaselineskip\fi      % 58 lines/page
 \ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=53\@IEEEnormalsizeunitybaselineskip\fi       % 53 lines/page
 \ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=48\@IEEEnormalsizeunitybaselineskip\fi    % 48 lines/page
 \ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=46\@IEEEnormalsizeunitybaselineskip\fi    % 46 lines/page 
 \textwidth 6.5in
 % the default side margins are equal
 \if@IEEEusingAfourpaper 
  \oddsidemargin        22.45mm
  \evensidemargin       22.45mm
 \else
  \oddsidemargin        1in
  \evensidemargin       1in
 \fi
 % compensate for LaTeX's 1in offset
 \addtolength{\oddsidemargin}{-1in}
 \addtolength{\evensidemargin}{-1in}
\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 
  % want 1in from top of paper to text
  \setlength{\topmargin}{-\headsep}%
  \addtolength{\topmargin}{-\headheight}%
  % we want 1in side margins regardless of paper type
  \oddsidemargin      0in
  \evensidemargin     0in
  % set the text width
  \setlength{\textwidth}{\paperwidth}%
  \addtolength{\textwidth}{-2.0in}%
  \setlength{\textheight}{\paperheight}%
  \addtolength{\textheight}{-2.0in}%
  % digitize textheight to be an integer number of lines.
  % this may cause the bottom margin to be off a tad
  \addtolength{\textheight}{-1\topskip}%
  \divide\textheight  by \baselineskip%
  \multiply\textheight  by \baselineskip%
  \addtolength{\textheight}{\topskip}%
\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
  \setlength{\oddsidemargin}{\CLASSINPUTinnersidemargin}
  \ifCLASSOPTIONtwoside
    \setlength{\evensidemargin}{\CLASSINPUToutersidemargin}
  \else
    \setlength{\evensidemargin}{\CLASSINPUTinnersidemargin}
  \fi
  \addtolength{\oddsidemargin}{-1in}
  \addtolength{\evensidemargin}{-1in}
  \setlength{\textwidth}{\paperwidth}
  \addtolength{\textwidth}{-\CLASSINPUTinnersidemargin}
  \addtolength{\textwidth}{-\CLASSINPUToutersidemargin}
  \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
  \setlength{\topmargin}{\CLASSINPUTtoptextmargin}
  \addtolength{\topmargin}{-1in}
  \addtolength{\topmargin}{-\headheight}
  \addtolength{\topmargin}{-\headsep}
  \setlength{\textheight}{\paperheight}
  \addtolength{\textheight}{-\CLASSINPUTtoptextmargin}
  \addtolength{\textheight}{-\CLASSINPUTbottomtextmargin}
  % in the default format we use the normal baselineskip as topskip
  % we only need 0.7 of this to clear typical top text and we need
  % an extra 0.3 spacing at the bottom for descenders. This will
  % correct for both.
  \addtolength{\topmargin}{-0.3\@IEEEnormalsizeunitybaselineskip}
  \typeout{** ATTENTION: Overriding top text margin to \CLASSINPUTtoptextmargin\space and 
           bottom text margin to \CLASSINPUTbottomtextmargin\space via \string\CLASSINPUT.}
\fi







% 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. 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. 
% 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. 
% 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, 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 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}


% IEEE uses 5) not 5.
\def\labelenumi{\theenumi)}     \def\theenumi{\arabic{enumi}}

% IEEE uses a) not (a)
\def\labelenumii{\theenumii)}  \def\theenumii{\alph{enumii}}

% IEEE uses iii) not iii.
\def\labelenumiii{\theenumiii)} \def\theenumiii{\roman{enumiii}}

% 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
% ***************************
% 
% 
% 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 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.
\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). 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. IEEE usually puts a little extra spacing
% around each list. However, this spacing is barely noticeable.
\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 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 labelindentfactor 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
                % labelindent factor, don't revise \labelindent
                \ifIEEEnolabelindentfactor\relax%
                \else\IEEElabelindent=\IEEElabelindentfactor\labelindent%
                \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 labelindentfactor 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 labelindentfactor 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}


% 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. 
\newif\if@restonecol
\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. 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 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

% IEEE does not use footnote rules
\def\footnoterule{}

% V1.7 for compsoc, 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 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\tablename{Table}}
\def\partname{Part}
\def\appendixname{Appendix}
\def\abstractname{Abstract}
% IEEE specific names
\def\IEEEkeywordsname{Keywords}
\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
\floatsep 1\baselineskip plus  0.2\baselineskip minus  0.2\baselineskip
\textfloatsep 1.7\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 1\baselineskip plus  0.2\baselineskip minus  0.2\baselineskip

\dbltextfloatsep 1.7\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 1\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}
\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}

\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
\normalsize\begin{center}{\normalfont\sffamily\normalsize {#1.}~ #2}\end{center}%
\@IEEEtablecaptionsepspace
% if not a table, format it as a figure
\else
\@IEEEfigurecaptionsepspace
\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ #2}%
\ifdim \wd\@tempboxa >\hsize%
% if caption is longer than a line, let it wrap around
\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ }%
\parbox[t]{\hsize}{\normalfont\sffamily\normalsize \noindent\unhbox\@tempboxa#2}%
% if caption is shorter than a line, center
\else%
\hbox to\hsize{\normalfont\sffamily\normalsize\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
\normalsize\begin{center}{\normalfont\sffamily\normalsize #1}\\{\normalfont\sffamily\normalsize #2}\end{center}%
\@IEEEtablecaptionsepspace
% if not a table, format it as a figure
\else
\@IEEEfigurecaptionsepspace
\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ #2}%
\ifdim \wd\@tempboxa >\hsize%
% if caption is longer than a line, let it wrap around
\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ }%
\parbox[t]{\hsize}{\normalfont\sffamily\normalsize \noindent\unhbox\@tempboxa#2}%
% if caption is shorter than a line, left justify
\else%
\hbox to\hsize{\normalfont\sffamily\normalsize\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\begin{center}{\normalfont\footnotesize #1}\\{\normalfont\footnotesize\scshape #2}\end{center}%
\@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.}~~ #2}%
\ifdim \wd\@tempboxa >\hsize%
% if caption is longer than a line, let it wrap around
\setbox\@tempboxa\hbox{\normalfont\footnotesize {#1.}~~ }%
\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\begin{center}{\footnotesize #1}\end{center}%
\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~\thefigure}
\def\figure{\@float{figure}}
\def\endfigure{\end@float}
\@namedef{figure*}{\@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~\thetable}
% V1.6 IEEE uses 8pt text for tables
% to default to footnotesize, we hack into LaTeX2e's \@floatboxreset and pray
\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}




%%
%% START OF IEEEeqnarry 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. ;)


% hook to allow easy changeover to IEEEtran.cls/tools.sty error reporting
\def\@IEEEclspkgerror{\ClassError{IEEEtran}}

\newif\if@IEEEeqnarraystarform% flag to indicate if the environment was called as the star form
\@IEEEeqnarraystarformfalse

\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}

% \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.
\providecommand{\yesnumber}{\global\@eqnswtrue}
\def\IEEEyesnumber{\global\@eqnswtrue}
\def\IEEEnonumber{\global\@eqnswfalse}


\def\IEEEyessubnumber{\global\@IEEEissubequationtrue\global\@eqnswtrue%
\if@IEEEeqnarrayISinner% only do something inside an IEEEeqnarray
\if@IEEElastlinewassubequation\addtocounter{equation}{-1}\else\setcounter{IEEEsubequation}{1}\fi%
\def\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\fi}

% flag to indicate that an equation is a sub equation
\newif\if@IEEEissubequation%
\@IEEEissubequationfalse

% allows users to "push away" equations that get too close to the equation numbers
\def\IEEEeqnarraynumspace{\hphantom{\if@IEEEissubequation\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}%
% check if column is defined
\relax\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined%
\csname @IEEEeqnarraycolPRE#2\endcsname#3\relax\relax\relax\relax\relax%
\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST#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#3\relax\relax\relax\relax\relax%
\relax\relax\relax\relax\relax\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 hei