%%
%% IEEEtrantools.sty 2014/09/17 version V1.4
%% 
%% 
%% This package provides several popular and unique commands from the
%% IEEEtran.cls class (version 1.8a) file.
%% 
%% The provided commands include \IEEEPARstart, \IEEEitemize, \IEEEenumerate,
%% \IEEEdescription as well as the \IEEEeqnarray, \IEEEeqnarraybox family
%% of commands including support commands such as \IEEEstrut, the IEEEproof
%% environment and its support commands and the \IEEEauthorrefmark command.
%% Also provides the \bstctlcite command for the control entry types of
%% IEEEtran.bst V1.00 and later.
%% 
%% IEEEtrantools.sty should not be used with IEEEtran.cls.
%% 
%% Support sites:
%% http://www.michaelshell.org/tex/ieeetran/
%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
%%
%% 
%% Copyright (c) 2002-2014 by Michael Shell
%%                            See: http://www.michaelshell.org/
%%                            for current contact information.
%%
%%*************************************************************************
%% 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: IEEEtrantools.sty, IEEEtrantools_doc.txt
%%*************************************************************************
%%
%%
%%
%% Available package options (e.g., \usepackage[redeflists]{IEEEtrantools}
%%
%% redeflists
%%    Causes IEEEtrantools to redefine the standard itemize, enumerate and
%%    description (IED) list environments to their IEEE versions.
%%    IEEEitemize, IEEEenumerate and IEEEdescription remain available in any
%%    case. This option may not be compatible with packages that alter the
%%    standard IED list environments.
%%    
%%
%%**********************************************************************


\ProvidesPackage{IEEEtrantools}[2014/09/17 V1.4 by Michael Shell]
\typeout{-- See the "IEEEtrantools_doc.txt" manual for usage information.}
\typeout{-- http://www.michaelshell.org/tex/ieeetran/tools/}
\NeedsTeXFormat{LaTeX2e}


% If \@IEEEeqnarray is detected, error.
{\@ifundefined{@IEEEeqnarray}{\relax}{%
\PackageError{IEEEtrantools}{The IEEEtrantools package is not for use\MessageBreak
                             with classes that already provide it}%
    {Do not load IEEEtrantools - you don't need it.}%
}}


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


% define needed flags to indicate document options
\newif\if@IEEETOOLSredeflists
\global\@IEEETOOLSredeflistsfalse


% IEEEtran class scratch pad registers
% dimen
\newdimen\@IEEEtrantmpdimenA
\newdimen\@IEEEtrantmpdimenB
\newdimen\@IEEEtrantmpdimenC
% count
\newcount\@IEEEtrantmpcountA
\newcount\@IEEEtrantmpcountB
\newcount\@IEEEtrantmpcountC
% token list
\newtoks\@IEEEtrantmptoksA


% declare the options
\DeclareOption{redeflists}{\@IEEETOOLSredefliststrue}
% provide legacy support for retainorgcmds which does nothing now.
\DeclareOption{retainorgcmds}{\@IEEETOOLSredeflistsfalse}

% get and process any supplied options
\ProcessOptions


% store the nominal value of jot
\newdimen\IEEEnormaljot
\IEEEnormaljot\jot\relax
% V1.4 allow for other packages that later change \jot
\AtBeginDocument{\IEEEnormaljot\jot\relax}




%% -- Command Argument Scanning Support Functions --
%

% usage: \@IEEEstripouterbraces*{}
% \@IEEEstripouterbraces fully expands its argument (which it then stores
% in \@IEEEstripouterbracesarg) via \edef, then removes any outer enclosing
% braces, and finally stores the result in the macro
% \@IEEEstrippedouterbraces.
%
% For example:
% \@IEEEstripouterbraces{{{{ab}c}}}
% results in:
%
% \@IEEEstripouterbracesarg ==> a macro containing {{{ab}c}}
% \@IEEEstrippedouterbraces ==> a macro containing {ab}c
%
% the *-star form,\@IEEEstripouterbraces*, does not expand the argument
% contents during processing
\def\@IEEEstripouterbraces{\@ifstar{\let\@IEEEstripouterbracesdef=\def\@@IEEEstripouterbraces}{\let\@IEEEstripouterbracesdef=\edef\@@IEEEstripouterbraces}}

\def\@@IEEEstripouterbraces#1{\@IEEEstripouterbracesdef\@IEEEstripouterbracesarg{#1}\relax
% If the macro is unchanged after being acquired as a single delimited
% argument, we know we have one sequence of tokens without any enclosing
% braces. Loop until this is true.
\loop
  \expandafter\@@@IEEEstripouterbraces\@IEEEstripouterbracesarg\@IEEEgeneralsequenceDELIMITER
\ifx\@IEEEstrippedouterbraces\@IEEEstripouterbracesarg
\else
  \let\@IEEEstripouterbracesarg\@IEEEstrippedouterbraces
\repeat}

\def\@@@IEEEstripouterbraces#1\@IEEEgeneralsequenceDELIMITER{\def\@IEEEstrippedouterbraces{#1}}



% usage: \@IEEEextractgroup*{}
% \@IEEEextractgroup fully expands its argument (which it then stores in
% \@IEEEextractgrouparg) via \edef and then assigns the first "brace group"
% of tokens to the macro \@IEEEextractedgroup.
% The remaining groups, if any, are stored in the macro
% \@IEEEextractedgroupremain. If the argument does not contain the requisite
% groups, the respective macros will be defined to be empty.
% There is an asymmetry in that \@IEEEextractedgroup is stripped of its first
% outer grouping while \@IEEEextractedgroupremain retains even the outer
% grouping (if present) that originally identified it as a group.
%
% For example:
% \@IEEEextractgroup{{{ab}}{c{de}}}
% results in:
%
% \@IEEEextractgrouparg       ==> a macro containing {{ab}}{c{de}}
% \@IEEEextractedgroup        ==> a macro containing {ab}
% \@IEEEextractedgroupremain  ==> a macro containing {c{de}}
%
% The *-star form, \@IEEEextractgroup*, does not expand its argument
% contents during processing.
\def\@IEEEextractgroup{\@ifstar{\let\@IEEEextractgroupdef=\def\@@IEEEextractgroup}{\let\@IEEEextractgroupdef=\edef\@@IEEEextractgroup}}

\def\@@IEEEextractgroup#1{\@IEEEextractgroupdef\@IEEEextractgrouparg{#1}\relax
% trap the case of an empty extracted group as this would cause problems with
% \@IEEEextractgroupremain's argument acquisition
\ifx\@IEEEextractgrouparg\@empty
  \def\@IEEEextractedgroup{}\relax
  \def\@IEEEextractedgroupremain{}\relax
\else
  % We have to use some dirty tricks here. We want to insert {} around
  % whatever remains after the first group so that TeX's argument scanner
  % will preserve any originally enclosing braces as well as provide an
  % empty argument to acquire even if there isn't a second group.
  % In this first of two dirty tricks, we put a } at the end of the structure
  % we are going to extract from. The \ifnum0=`{\fi keeps TeX happy to allow
  % what would otherwise be an unbalanced macro definition for
  % \@@IEEEextractgroup to be acceptable to it.
  \ifnum0=`{\fi\expandafter\@IEEEextractgroupremain\@IEEEextractgrouparg}\relax
\fi}

% In the second part of the dirty tricks, we insert a leading { right after
% the first group is acquired, but before the remainder is. Again, the
% \ifnum0=`}\fi keeps TeX happy during definition time, but will disappear
% during run time.
\def\@IEEEextractgroupremain#1{\def\@IEEEextractedgroup{#1}\expandafter\@@IEEEextractgroupremain\expandafter{\ifnum0=`}\fi}

\def\@@IEEEextractgroupremain#1{\def\@IEEEextractedgroupremain{#1}}



% usage: \@IEEEextracttoken*{}
% \@IEEEextracttoken fully expands its argument (which it then stores in
% \@IEEEextracttokenarg) via \edef and then the meaning of the first
% nonbrace (but including the empty group) token found is assigned via \let
% to \@IEEEextractedtoken as well as stored in the macro
% \@IEEEextractedtokenmacro. Tokens that would otherwise be discarded during
% the acquisition of the first are stored in \@IEEEextractedtokensdiscarded,
% however their original relative brace nesting depths are not guaranteed to
% be preserved.
% If the argument is empty, or if a first nonbrace token does not exist (or
% is an empty group), \@IEEEextractedtoken will be \relax and
% \@IEEEextractedtokenmacro and \@IEEEextractedtokensdiscarded will be empty.
%
% For example:
% \@IEEEextracttoken{{{ab}{cd}}{{ef}g}}
% results in:
%
% \@IEEEextracttokenarg          ==> a macro containing {{ab}{cd}}{{ef}g}
% \@IEEEextractedtoken           ==> the letter a
% \@IEEEextractedtokenmacro      ==> a macro containing a
% \@IEEEextractedtokensdiscarded ==> a macro containing bcd{ef}g
%
% the *-star form, \@IEEEextracttoken*, does not expand its argument
% contents during processing.
\def\@IEEEextracttoken{\@ifstar{\let\@IEEEextracttokendef=\def\@@IEEEextracttoken}{\let\@IEEEextracttokendef=\edef\@@IEEEextracttoken}}

\def\@@IEEEextracttoken#1{\@IEEEextracttokendef\@IEEEextracttokenarg{#1}\relax
\def\@IEEEextractedtokensdiscarded{}\relax % initialize to empty
% if the macro is unchanged after being acquired as a single undelimited argument
% with anything after it being stripped off as a delimited argument
% we know we have one token without any enclosing braces. loop until this is true.
\let\@IEEEextracttokencurgroup\@IEEEextracttokenarg
\loop
  % trap case of an empty argument as this would cause a problem with
  % \@@@IEEEextracttoken's first (nondelimited) argument acquisition
  \ifx\@IEEEextracttokencurgroup\@empty
    \def\@IEEEextractedtokenmacro{}\relax
  \else
    \expandafter\@@@IEEEextracttoken\@IEEEextracttokencurgroup\@IEEEgeneralsequenceDELIMITER\relax
  \fi
  \ifx\@IEEEextractedtokenmacro\@IEEEextracttokencurgroup
  \else
    \let\@IEEEextracttokencurgroup=\@IEEEextractedtokenmacro
\repeat
% we can safely do a \let= here because there should be at most one token
% the relax is needed to handle the case of no token found
\expandafter\let\expandafter\@IEEEextractedtoken\@IEEEextractedtokenmacro\relax}

\def\@@@IEEEextracttoken#1#2\@IEEEgeneralsequenceDELIMITER{\def\@IEEEextractedtokenmacro{#1}\relax
\def\@@IEEEextractedtokensdiscarded{#2}\expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter
\@IEEEextractedtokensdiscarded\expandafter\expandafter\expandafter
{\expandafter\@@IEEEextractedtokensdiscarded\@IEEEextractedtokensdiscarded}}



% usage: \@IEEEextracttokengroups*{}
% \@IEEEextracttokengroups fully expands its argument (which it then stores
% in \@IEEEextracttokengroupsarg) and then assigns the first "brace group" of
% tokens (with the outermost braces removed) to the macro
% \@IEEEextractedfirstgroup.
% The meaning of the first nonbrace (but including the empty group) token
% within this first group is assigned via \let to \@IEEEextractedfirsttoken
% as well as stored in the macro \@IEEEextractedfirsttokenmacro. If a first
% nonbrace token does not exist (or is an empty group), these will be \relax
% and empty, respectively.  Tokens that would otherwise be discarded during
% the acquisition of the first token in the first group are stored in
% \@IEEEextractedfirsttokensdiscarded, however their original relative brace
% nesting depths are not guaranteed to be preserved.
% The first group within this first group is stored in the macro
% \@IEEEextractedfirstfirstgroup.
% Likewise for the next group after the first: \@IEEEextractednextgroup,
% \@IEEEextractednextfirstgroup, \@IEEEextractednextgroupfirsttoken,
% \@IEEEextractednextgroupfirsttokenmacro, and 
% \@IEEEextractednextfirsttokensdiscarded.
% All tokens/groups after the first group, including any enclosing braces,
% are stored in the macro \@IEEEextractedafterfirstgroupremain which will
% be empty if none exist.
%
% For example:
% \@IEEEextracttokengroups{{{ab}{cd}}{{ef}g}}
% will result in:
%
% \@IEEEextracttokengroupsarg             ==> a macro containing {{ab}{cd}}{{ef}g}
% \@IEEEextractedfirstgroup               ==> a macro containing {ab}{cd}
% \@IEEEextractedafterfirstgroupremain    ==> a macro containing {{ef}g}
% \@IEEEextractedfirsttoken               ==> the letter a
% \@IEEEextractedfirsttokenmacro          ==> a macro containing a
% \@IEEEextractedfirsttokensdiscarded     ==> a macro containing bcd
% \@IEEEextractedfirstfirstgroup          ==> a macro containing ab
% \@IEEEextractednextgroup                ==> a macro containing {ef}g
% \@IEEEextractednextfirsttoken           ==> the letter e
% \@IEEEextractednextfirsttokenmacro      ==> a macro containing e
% \@IEEEextractednextfirsttokensdiscarded ==> a macro containing fg
% \@IEEEextractednextfirstgroup           ==> a macro containing ef
%
% If given an empty argument, \@IEEEextractedfirsttoken and
% \@IEEEextractednextfirsttoken will be set to \relax
% and all the macros will be empty.
% the *-star form, \@IEEEextracttokengroups*, does not expand its argument
% contents during processing.
%
% Depends on: \@IEEEextractgroup, \@IEEEextracttoken
\def\@IEEEextracttokengroups{\@ifstar{\let\@IEEEextracttokengroupsdef=\def\@@IEEEextracttokengroups}{\let\@IEEEextracttokengroupsdef=\edef\@@IEEEextracttokengroups}}
\def\@@IEEEextracttokengroups#1{\@IEEEextracttokengroupsdef\@IEEEextracttokengroupsarg{#1}\relax
% begin extraction, these functions are safe with empty arguments
% first group
\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextracttokengroupsarg}\relax
\let\@IEEEextractedfirstgroup\@IEEEextractedgroup
\let\@IEEEextractedafterfirstgroupremain\@IEEEextractedgroupremain
\expandafter\@IEEEextracttoken\expandafter*\expandafter{\@IEEEextractedfirstgroup}\relax
\let\@IEEEextractedfirsttoken\@IEEEextractedtoken
\let\@IEEEextractedfirsttokenmacro\@IEEEextractedtokenmacro
\let\@IEEEextractedfirsttokensdiscarded\@IEEEextractedtokensdiscarded
% first first group
\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextractedfirstgroup}\relax
\let\@IEEEextractedfirstfirstgroup\@IEEEextractedgroup
% next group
\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextractedafterfirstgroupremain}\relax
\let\@IEEEextractednextgroup\@IEEEextractedgroup
\expandafter\@IEEEextracttoken\expandafter*\expandafter{\@IEEEextractednextgroup}\relax
\let\@IEEEextractednextfirsttoken\@IEEEextractedtoken
\let\@IEEEextractednextfirsttokenmacro\@IEEEextractedtokenmacro
\let\@IEEEextractednextfirsttokensdiscarded\@IEEEextractedtokensdiscarded
% next first group
\expandafter\@IEEEextractgroup\expandafter*\expandafter{\@IEEEextractednextgroup}\relax
\let\@IEEEextractednextfirstgroup\@IEEEextractedgroup}


%%
%% -- End of Command Argument Scanning Support Functions --




% -- page setup commands --

% The default sample text for calculating margins
\def\IEEEdefaultsampletext{\normalfont\normalsize gT}
\def\IEEEdefaultheadersampletext{\normalfont\normalsize T}
\def\IEEEdefaultfootersampletext{\normalfont\normalsize gT}



% usage: \IEEEsettextwidth{inner margin}{outer margin}
% Sets \textwidth to allow the specified inner and outer margins
% for the current \paperwidth.
\def\IEEEsettextwidth#1#2{\@IEEEtrantmpdimenA\paperwidth
\@IEEEtrantmpdimenB#1\relax
\advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB
\@IEEEtrantmpdimenB#2\relax
\advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB
\textwidth\@IEEEtrantmpdimenA}



% usage: \IEEEsetsidemargin{mode: i, o, c, a}{margin/offset}
% Sets \oddsidemargin and \evensidemargin to yield the specified margin
% of the given mode.
% The available modes are:
% i = inner margin
% o = outer margin
% c = centered, with the given offset
% a = adjust the margins using the given offset
% For the offsets, positive values increase the inner margin.
% \textwidth should be set properly for the given margins before calling this
% function.
\def\IEEEsetsidemargin#1#2{\@IEEEtrantmpdimenA #2\relax
\@IEEEextracttoken{#1}\relax
% check for mode errors
\ifx\@IEEEextractedtokenmacro\@empty
  \@IEEEclspkgerror{Empty mode type in \string\IEEEsetsidemargin\space (line \the\inputlineno).\MessageBreak
  Defaulting to `i'}{Valid modes for \string\IEEEsetsidemargin\space are: i, o, c and a.}\relax
  \let\@IEEEextractedtoken=i\relax
  \def\@IEEEextractedtokenmacro{i}\relax
\else
  \ifx\@IEEEextractedtokensdiscarded\@empty\else
    \typeout{** WARNING: \string\IEEEsetsidemargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
  \fi
\fi
% handle each mode
\if\@IEEEextractedtoken a\relax
  \advance\oddsidemargin by \@IEEEtrantmpdimenA\relax
\else
\if\@IEEEextractedtoken c\relax
  \oddsidemargin\paperwidth
  \advance\oddsidemargin by -\textwidth
  \divide\oddsidemargin by 2\relax
  \advance\oddsidemargin by -1in\relax
  \advance\oddsidemargin by \@IEEEtrantmpdimenA\relax
\else
\if\@IEEEextractedtoken o\relax
  \oddsidemargin\paperwidth
  \advance\oddsidemargin by -\textwidth
  \advance\oddsidemargin by -\@IEEEtrantmpdimenA
  \advance\oddsidemargin by -1in\relax
\else
  \if\@IEEEextractedtoken i\relax
  \else
    \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsetsidemargin\space (line \the\inputlineno).\MessageBreak
    Defaulting to `i'}%
    {Valid modes for \string\IEEEsetsidemargin\space are: i, o, c  and a.}%
  \fi
  \oddsidemargin\@IEEEtrantmpdimenA
  \advance\oddsidemargin by -1in\relax
\fi\fi\fi
% odd and even side margins both mean "inner" for single sided pages
\evensidemargin\oddsidemargin
% but are mirrors of each other when twosided is in effect
\if@twoside
  \evensidemargin\paperwidth
  \advance\evensidemargin by -\textwidth
  \advance\evensidemargin by -\oddsidemargin
  % have to compensate for both the builtin 1in LaTex offset
  % and the fact we already subtracted this offset from \oddsidemargin
  \advance\evensidemargin -2in\relax
\fi}



% usage: \IEEEsettextheight[sample text]{top text margin}{bottom text margin}
% Sets \textheight based on the specified top margin and bottom margin.
% Takes into consideration \paperheight, \topskip, and (by default) the
% the actual height and depth of the \IEEEdefaultsampletext text. 
\def\IEEEsettextheight{\@ifnextchar [{\@IEEEsettextheight}{\@IEEEsettextheight[\IEEEdefaultsampletext]}}
\def\@IEEEsettextheight[#1]#2#3{\textheight\paperheight\relax
  \@IEEEtrantmpdimenA #2\relax
  \advance \textheight by -\@IEEEtrantmpdimenA% subtract top margin
  \@IEEEtrantmpdimenA #3\relax
  \advance \textheight by -\@IEEEtrantmpdimenA% subtract bottom margin
  \advance \textheight by \topskip% add \topskip
  % subtract off everything above the top, and below the bottom, baselines
  \settoheight{\@IEEEtrantmpdimenA}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance \textheight by -\@IEEEtrantmpdimenA
  \settodepth{\@IEEEtrantmpdimenA}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance \textheight by -\@IEEEtrantmpdimenA}



\newdimen\IEEEquantizedlength
\IEEEquantizedlength 0sp\relax
\newdimen\IEEEquantizedlengthdiff
\IEEEquantizedlengthdiff 0sp\relax
\def\IEEEquantizedlengthint{0}

% usage: \IEEEquantizelength{mode: d, c, i}{base unit}{length}
% Sets the length \IEEEquantizedlength to be an integer multiple of the given
% (nonzero) base unit such that \IEEEquantizedlength approximates the given
% length.
% \IEEEquantizedlengthdiff is a length equal to the difference between the
% \IEEEquantizedlength and the given length.
% \IEEEquantizedlengthint is a macro containing the integer number of base units
% in \IEEEquantizedlength.
% i.e., \IEEEquantizedlength =  \IEEEquantizedlengthint * base unit
% The mode determines how \IEEEquantizedlength is quantized:
% d = always decrease (always round down \IEEEquantizeint)
% c = use the closest match
% i = always increase (always round up \IEEEquantizeint)
% In anycase, if the given length is already quantized,
% \IEEEquantizedlengthdiff will be set to zero.
\def\IEEEquantizelength#1#2#3{\begingroup
% work in isolation so as not to externally disturb the \@IEEEtrantmp
% variables
% load the argument values indirectly via \IEEEquantizedlengthdiff
% in case the user refers to our \@IEEEtrantmpdimenX, \IEEEquantizedlength,
% etc. in the arguments. we also will work with these as counters,
% i.e., in sp units
% A has the base unit
\IEEEquantizedlengthdiff #2\relax\relax\relax\relax
\@IEEEtrantmpcountA\IEEEquantizedlengthdiff
% B has the input length
\IEEEquantizedlengthdiff #3\relax\relax\relax\relax
\@IEEEtrantmpcountB\IEEEquantizedlengthdiff
\@IEEEtrantmpdimenA\the\@IEEEtrantmpcountA sp\relax
\@IEEEtrantmpdimenB\the\@IEEEtrantmpcountB sp\relax
% \@IEEEtrantmpcountC will have the quantized int
% \IEEEquantizedlength will have the quantized length
% \@IEEEtrantmpdimenC will have the quantized diff
% initialize them to zero as this is what will be
% exported if an error occurs
\@IEEEtrantmpcountC 0\relax
\IEEEquantizedlength 0sp\relax
\@IEEEtrantmpdimenC 0sp\relax
% extract mode
\@IEEEextracttoken{#1}\relax
% check for mode errors
\ifx\@IEEEextractedtokenmacro\@empty
  \@IEEEclspkgerror{Empty mode type in \string\IEEEquantizelength\space (line \the\inputlineno).\MessageBreak
  Defaulting to `d'}{Valid modes for \string\IEEEquantizelength\space are: d, c and i.}\relax
  \let\@IEEEextractedtoken=d\relax
  \def\@IEEEextractedtokenmacro{d}\relax
\else
  \ifx\@IEEEextractedtokensdiscarded\@empty\else
    \typeout{** WARNING: \string\IEEEquantizelength\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
  \fi
\fi
% check for base unit is zero error
\ifnum\@IEEEtrantmpcountA=0\relax
\@IEEEclspkgerror{Base unit is zero in \string\IEEEquantizelength\space (line \the\inputlineno).\MessageBreak
  \string\IEEEquantizedlength\space and \string\IEEEquantizedlengthdiff\space are set to zero}{Division by zero is not allowed.}\relax
\else% base unit is nonzero
  % \@IEEEtrantmpcountC carries the number of integer units
  % in the quantized length (integer length \ base)
  \@IEEEtrantmpcountC\@IEEEtrantmpcountB\relax
  \divide\@IEEEtrantmpcountC by \@IEEEtrantmpcountA\relax
  % \IEEEquantizedlength has the (rounded down) quantized length
  % = base * int
  \IEEEquantizedlength\@IEEEtrantmpdimenA\relax
  \multiply\IEEEquantizedlength by \@IEEEtrantmpcountC\relax
  % \@IEEEtrantmpdimenC has the difference
  % = quantized length - length
  \@IEEEtrantmpdimenC\IEEEquantizedlength\relax
  \advance\@IEEEtrantmpdimenC by -\@IEEEtrantmpdimenB\relax
  % trap special case of length being already quantized
  % to avoid a roundup under i option
  \ifdim\@IEEEtrantmpdimenC=0sp\relax
  \else % length not is already quantized
    % set dimenA to carry the upper quantized (absolute value) difference:
    % quantizedlength + base - length
    \advance\@IEEEtrantmpdimenA by \IEEEquantizedlength\relax
    \advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB\relax
    % set dimenB to carry the lower quantized (absolute value) difference:
    % length - quantizedlength
    \advance\@IEEEtrantmpdimenB by -\IEEEquantizedlength\relax
    % handle each mode
    \if\@IEEEextractedtoken c\relax
      % compare upper and lower amounts, select upper if lower > upper
      \ifdim\@IEEEtrantmpdimenB>\@IEEEtrantmpdimenA\relax
        % use upper
        \advance\IEEEquantizedlength by \the\@IEEEtrantmpcountA sp\relax
        \advance\@IEEEtrantmpcountC by 1\relax
        \@IEEEtrantmpdimenC\@IEEEtrantmpdimenA
      \else% <=. uselower
        % no need to do anything for lower, use output values already setup
      \fi
    \else% not mode c
    \if\@IEEEextractedtoken i\relax
      % always round up under i mode
      \advance\IEEEquantizedlength by \the\@IEEEtrantmpcountA sp\relax
      \advance\@IEEEtrantmpcountC by 1\relax
      \@IEEEtrantmpdimenC\@IEEEtrantmpdimenA
    \else
      \if\@IEEEextractedtoken d\relax
      \else
        \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEquantizelength\space (line \the\inputlineno).\MessageBreak
        Defaulting to `d'}%
        {Valid modes for \string\IEEEquantizelength\space are: d, c, and i.}\relax
      \fi % if d
      % no need to do anything for d, use output values already setup
    \fi\fi % if i, c
  \fi % if length is already quantized
\fi% if base unit is zero
% globally assign the results to macros we use here to escape the enclosing
% group without needing to call \global on any of the \@IEEEtrantmp variables.
% \@IEEEtrantmpcountC has the quantized int
% \IEEEquantizedlength has the quantized length
% \@IEEEtrantmpdimenC has the quantized diff
\xdef\@IEEEquantizedlengthintmacro{\the\@IEEEtrantmpcountC}\relax
\@IEEEtrantmpcountC\IEEEquantizedlength\relax
\xdef\@IEEEquantizedlengthmacro{\the\@IEEEtrantmpcountC}\relax
\@IEEEtrantmpcountC\@IEEEtrantmpdimenC\relax
\xdef\@IEEEquantizedlengthdiffmacro{\the\@IEEEtrantmpcountC}\relax
\endgroup
% locally assign the outputs here from the macros
\expandafter\IEEEquantizedlength\@IEEEquantizedlengthmacro sp\relax
\expandafter\IEEEquantizedlengthdiff\@IEEEquantizedlengthdiffmacro sp\relax
\edef\IEEEquantizedlengthint{\@IEEEquantizedlengthintmacro}\relax}



\newdimen\IEEEquantizedtextheightdiff
\IEEEquantizedtextheightdiff 0sp\relax

% usage: \IEEEquantizetextheight[base unit]{mode: d, c, i}
% Sets \textheight to be an integer multiple of the current \baselineskip
% (or the optionally specified base unit) plus the first (\topskip) line.
% \IEEEquantizedtextheightdiff is a length equal to the difference between
% the new quantized and original \textheight.
% \IEEEquantizedtextheightlpc is a macro containing the integer number of
% lines per column under the quantized \textheight. i.e.,
% \textheight = \IEEEquantizedtextheightlpc * \baselineskip + \topskip
% The mode determines how \textheight is quantized:
% d = always decrease (always round down the number of lines per column)
% c = use the closest match
% i = always increase (always round up the number of lines per column)
% In anycase, if \textheight is already quantized, it will remain unchanged,
% and \IEEEquantizedtextheightdiff will be set to zero.
% Depends on: \IEEEquantizelength
\def\IEEEquantizetextheight{\@ifnextchar [{\@IEEEquantizetextheight}{\@IEEEquantizetextheight[\baselineskip]}}
\def\@IEEEquantizetextheight[#1]#2{\begingroup
% use our \IEEEquantizedtextheightdiff as a scratch pad
% we need to subtract off \topskip before quantization
\IEEEquantizedtextheightdiff\textheight
\advance\IEEEquantizedtextheightdiff by -\topskip\relax
\IEEEquantizelength{#2}{#1}{\IEEEquantizedtextheightdiff}
% add back \topskip line
\advance\IEEEquantizedlength by \topskip
\@IEEEtrantmpcountC\IEEEquantizedlengthint\relax
\advance\@IEEEtrantmpcountC by 1\relax
% globally assign the results to macros we use here to escape the enclosing
% group without needing to call \global on any of the \@IEEEtrantmp variables.
\xdef\@IEEEquantizedtextheightlpcmacro{\the\@IEEEtrantmpcountC}\relax
\@IEEEtrantmpcountC\IEEEquantizedlength\relax
\xdef\@IEEEquantizedtextheightmacro{\the\@IEEEtrantmpcountC}\relax
\@IEEEtrantmpcountC\IEEEquantizedlengthdiff\relax
\xdef\@IEEEquantizedtextheightdiffmacro{\the\@IEEEtrantmpcountC}\relax
\endgroup
% locally assign the outputs here from the macros
\textheight\@IEEEquantizedtextheightmacro sp\relax
\IEEEquantizedtextheightdiff\@IEEEquantizedtextheightdiffmacro sp\relax
\edef\IEEEquantizedtextheightlpc{\@IEEEquantizedtextheightlpcmacro}}



% usage: \IEEEsettopmargin[sample text]{mode: t, b, c, a, q}{margin/offset}
% Sets \topmargin based on the specified vertical margin.
% Takes into consideration the base 1in offset, \headheight, \headsep,
% \topskip, and (by default) the the actual height (or, for the bottom, depth)
% of the \IEEEdefaultsampletext text.
% The available modes are:
% t = top margin
% b = bottom margin
% c = vertically centered, with the given offset
% a = adjust the vertical margins using the given offset
% q = adjust the margins using \IEEEquantizedtextheightdiff and the given offset
% For the offsets, positive values increase the top margin.
% \headheight, \headsep, \topskip and \textheight should be set properly for the
% given margins before calling this function.
\def\IEEEsettopmargin{\@ifnextchar [{\@IEEEsettopmargin}{\@IEEEsettopmargin[\IEEEdefaultsampletext]}}
\def\@IEEEsettopmargin[#1]#2#3{\@IEEEtrantmpdimenA #3\relax
\@IEEEextracttoken{#2}\relax
% check for mode errors
\ifx\@IEEEextractedtokenmacro\@empty
  \@IEEEclspkgerror{Empty mode type in \string\IEEEsettopmargin\space (line \the\inputlineno).\MessageBreak
  Defaulting to `t'}{Valid modes for \string\IEEEsettopmargin\space are: t, b, c, a and q.}\relax
  \let\@IEEEextractedtoken=t\relax
  \def\@IEEEextractedtokenmacro{t}\relax
\else
  \ifx\@IEEEextractedtokensdiscarded\@empty\else
    \typeout{** WARNING: \string\IEEEsettopmargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
  \fi
\fi
% handle each mode
\if\@IEEEextractedtoken a\relax
  \advance\topmargin by \@IEEEtrantmpdimenA\relax
\else
\if\@IEEEextractedtoken q\relax
  % we need to adjust by half the \IEEEquantizedtextheightdiff value
  \@IEEEtrantmpdimenB\IEEEquantizedtextheightdiff\relax
  \divide\@IEEEtrantmpdimenB by 2\relax
  % a positive \IEEEquantizedtextheightdiff means we need to reduce \topmargin
  % because \textheight has been lenghtened
  \advance\topmargin by -\@IEEEtrantmpdimenB\relax
  \advance\topmargin by \@IEEEtrantmpdimenA\relax
\else
\if\@IEEEextractedtoken c\relax
  \topmargin\paperheight
  \advance\topmargin by -\textheight
  % \textheight includes \topskip, but we should not count topskip whitespace here, backout
  \advance \topmargin by \topskip
  \settoheight{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance\topmargin by -\@IEEEtrantmpdimenB\relax
  \settodepth{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance\topmargin by -\@IEEEtrantmpdimenB\relax
  \divide\topmargin by 2\relax
  \advance\topmargin by \@IEEEtrantmpdimenA\relax
\else
\if\@IEEEextractedtoken b\relax
  \topmargin\paperheight
  \advance\topmargin by -\textheight
  % \textheight includes \topskip, but we should not count topskip whitespace here, backout
  \advance \topmargin by \topskip
  \settodepth{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance\topmargin by -\@IEEEtrantmpdimenB\relax
  \advance\topmargin by -\@IEEEtrantmpdimenA\relax
\else
  \if\@IEEEextractedtoken t\relax
  \else
    \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsettopmargin\space (line \the\inputlineno).\MessageBreak
    Defaulting to `t'}%
    {Valid modes for \string\IEEEsettopmargin\space are: t, b, c, a and q.}\relax
  \fi
  \topmargin\@IEEEtrantmpdimenA\relax
  \settoheight{\@IEEEtrantmpdimenB}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance\topmargin by \@IEEEtrantmpdimenB\relax
\fi\fi % if t, b, c
% convert desired top margin into actual \topmargin
% this is not done for the q or a modes because they are only adjustments
\advance \topmargin by -\topskip
\advance \topmargin by -1in
\advance \topmargin by -\headheight
\advance \topmargin by -\headsep
\fi\fi % if q, a
}



% usage: \IEEEsetheadermargin[header sample][text sample]{mode: t, b, c, a}{margin/offset}
% Differentially adjusts \topmargin and \headsep (such that their sum is unchanged)
% based on the specified header margin.
% Takes into consideration the base 1in offset, \headheight, \topskip, and (by default)
% the actual height (or depth) of the \IEEEdefaultheadersampletext and
% \IEEEdefaultsampletext text.
% The available modes are:
% t = top margin (top of the header text to the top of the page)
% b = bottom margin (bottom of the header text to the top of the main text)
% c = vertically centered between the main text and the top of the page,
%     with the given offset
% a = adjust the vertical position using the given offset
% For the offsets, positive values move the header downward.
% \headheight, \headsep, \topskip and \topmargin should be set properly before
% calling this function.
\def\IEEEsetheadermargin{\@ifnextchar [{\@IEEEsetheadermargin}{\@IEEEsetheadermargin[\IEEEdefaultheadersampletext]}}
\def\@IEEEsetheadermargin[#1]{\@ifnextchar [{\@@IEEEsetheadermargin[#1]}{\@@IEEEsetheadermargin[#1][\IEEEdefaultsampletext]}}
\def\@@IEEEsetheadermargin[#1][#2]#3#4{\@IEEEtrantmpdimenA #4\relax
\@IEEEextracttoken{#3}\relax
% check for mode errors
\ifx\@IEEEextractedtokenmacro\@empty
  \@IEEEclspkgerror{Empty mode type in \string\IEEEsetheadermargin\space (line \the\inputlineno).\MessageBreak
  Defaulting to `t'}{Valid modes for \string\IEEEsetheadermargin\space are: t, b, c, and a.}\relax
  \let\@IEEEextractedtoken=t\relax
  \def\@IEEEextractedtokenmacro{t}\relax
\else
  \ifx\@IEEEextractedtokensdiscarded\@empty\else
    \typeout{** WARNING: \string\IEEEsetheadermargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
  \fi
\fi
% handle each mode
\if\@IEEEextractedtoken a\relax
  % No need to do anything here and can pass through the adjustment
  % value as is. The end adjustment of \topmargin and \headsep will
  % do all that is needed
\else
\if\@IEEEextractedtoken c\relax
  % get the bottom margin
  \@IEEEtrantmpdimenB\headsep\relax
  \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
  \advance\@IEEEtrantmpdimenB by \topskip
  \settoheight{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax
  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
  % at this point \@IEEEtrantmpdimenB has the actual header bottom margin
  % subtract from it the top header margin
  \advance\@IEEEtrantmpdimenB -1in\relax % take into consideration the system 1in offset of the top margin
  \advance\@IEEEtrantmpdimenB by -\topmargin
  \advance\@IEEEtrantmpdimenB by -\headheight
  \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance\@IEEEtrantmpdimenB by \@IEEEtrantmpdimenC
  % at this point \@IEEEtrantmpdimenB has the difference between the bottom and top margins
  % we need to adjust by half this amount to center the header
  \divide\@IEEEtrantmpdimenB by 2\relax
  % and add to offset
  \advance\@IEEEtrantmpdimenA by \@IEEEtrantmpdimenB
\else
\if\@IEEEextractedtoken b\relax
  \@IEEEtrantmpdimenB\headsep\relax
  \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
  \advance\@IEEEtrantmpdimenB by \topskip
  \settoheight{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax
  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
  % at this point \@IEEEtrantmpdimenB has the actual header bottom margin
  % get the difference between the actual and the desired
  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenA
  \@IEEEtrantmpdimenA\@IEEEtrantmpdimenB
\else
  \if\@IEEEextractedtoken t\relax
  \else
    \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsetheadermargin\space (line \the\inputlineno).\MessageBreak
    Defaulting to `t'}%
    {Valid modes for \string\IEEEsetheadermargin\space are: t, b, c and a.}\relax
  \fi
  \@IEEEtrantmpdimenB 1in\relax % take into consideration the system 1in offset of the top margin
  \advance\@IEEEtrantmpdimenB by \topmargin
  \advance\@IEEEtrantmpdimenB by \headheight
  \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
  % at this point \@IEEEtrantmpdimenB has the actual header top margin
  % get the difference between the desired and the actual
  \advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB
\fi\fi % if t, b, c
\fi % if a
% advance \topmargin by the needed amount and reduce \headsep by the same
% so as not to disturb the location of the main text
\advance\topmargin by \@IEEEtrantmpdimenA\relax
\advance\headsep by -\@IEEEtrantmpdimenA\relax
}



% usage: \IEEEsetfootermargin[footer sample][text sample]{mode: t, b, c, a}{margin/offset}
% Adjusts \footskip based on the specified footer margin.
% Takes into consideration the base 1in offset, \paperheight, \headheight,
% \headsep, \textheight and (by default) the actual height (or depth) of the
% \IEEEdefaultfootersampletext and \IEEEdefaultsampletext text.
% The available modes are:
% t = top margin (top of the footer text to the bottom of the main text)
% b = bottom margin (bottom of the footer text to the bottom of page)
% c = vertically centered between the main text and the bottom of the page,
%     with the given offset
% a = adjust the vertical position using the given offset
% For the offsets, positive values move the footer downward.
% \headheight, \headsep, \topskip, \topmargin, and \textheight should be set
% properly before calling this function.
\def\IEEEsetfootermargin{\@ifnextchar [{\@IEEEsetfootermargin}{\@IEEEsetfootermargin[\IEEEdefaultfootersampletext]}}
\def\@IEEEsetfootermargin[#1]{\@ifnextchar [{\@@IEEEsetfootermargin[#1]}{\@@IEEEsetfootermargin[#1][\IEEEdefaultsampletext]}}
\def\@@IEEEsetfootermargin[#1][#2]#3#4{\@IEEEtrantmpdimenA #4\relax
\@IEEEextracttoken{#3}\relax
% check for mode errors
\ifx\@IEEEextractedtokenmacro\@empty
  \@IEEEclspkgerror{Empty mode type in \string\IEEEsetfootermargin\space (line \the\inputlineno).\MessageBreak
  Defaulting to `t'}{Valid modes for \string\IEEEsetfootermargin\space are: t, b, c, and a.}\relax
  \let\@IEEEextractedtoken=t\relax
  \def\@IEEEextractedtokenmacro{t}\relax
\else
  \ifx\@IEEEextractedtokensdiscarded\@empty\else
    \typeout{** WARNING: \string\IEEEsetfootermargin\space mode specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
  \fi
\fi
% handle each mode
\if\@IEEEextractedtoken a\relax
  % No need to do anything here and can pass through the adjustment
  % value as is. The end adjustment of \footskip will do all that
  % is needed
\else
\if\@IEEEextractedtoken c\relax
  % calculate the bottom margin
  \@IEEEtrantmpdimenB 1in\relax % system 1in offset
  \advance\@IEEEtrantmpdimenB\topmargin\relax
  \advance\@IEEEtrantmpdimenB\headheight\relax
  \advance\@IEEEtrantmpdimenB\headsep\relax
  \advance\@IEEEtrantmpdimenB\textheight\relax
  \advance\@IEEEtrantmpdimenB\footskip\relax
  \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance\@IEEEtrantmpdimenC by \@IEEEtrantmpdimenB
  \@IEEEtrantmpdimenB\paperheight
  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
  % at this point \@IEEEtrantmpdimenB has the actual footer bottom margin
  % now subtract off the footer top margin
  \advance\@IEEEtrantmpdimenB -\footskip\relax
  \settodepth{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax
  \advance\@IEEEtrantmpdimenB by \@IEEEtrantmpdimenC
  \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance\@IEEEtrantmpdimenB by \@IEEEtrantmpdimenC
  % at this point \@IEEEtrantmpdimenB has the difference between the bottom
  % and top footer margins
  % our adjustment must be half this value to center the footer
  \divide\@IEEEtrantmpdimenB by 2\relax
  % add to the offset
  \advance\@IEEEtrantmpdimenA by \@IEEEtrantmpdimenB
\else
\if\@IEEEextractedtoken b\relax
  % calculate the bottom margin
  \@IEEEtrantmpdimenB 1in\relax % system 1in offset
  \advance\@IEEEtrantmpdimenB\topmargin\relax
  \advance\@IEEEtrantmpdimenB\headheight\relax
  \advance\@IEEEtrantmpdimenB\headsep\relax
  \advance\@IEEEtrantmpdimenB\textheight\relax
  \advance\@IEEEtrantmpdimenB\footskip\relax
  \settodepth{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance\@IEEEtrantmpdimenC by \@IEEEtrantmpdimenB
  \@IEEEtrantmpdimenB\paperheight
  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
  % at this point \@IEEEtrantmpdimenB has the actual footer bottom margin
  % get the difference between the actual and the desired
  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenA
  \@IEEEtrantmpdimenA\@IEEEtrantmpdimenB
\else
  \if\@IEEEextractedtoken t\relax
  \else
    \@IEEEclspkgerror{Unknown mode type `\@IEEEextractedtokenmacro' in \string\IEEEsetfootermargin\space (line \the\inputlineno).\MessageBreak
    Defaulting to `t'}%
    {Valid modes for \string\IEEEsetfootermargin\space are: t, b, c and a.}\relax
  \fi
  \@IEEEtrantmpdimenB\footskip\relax
  \settodepth{\@IEEEtrantmpdimenC}{\begingroup #2\relax\relax\relax\endgroup}\relax
  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
  \settoheight{\@IEEEtrantmpdimenC}{\begingroup #1\relax\relax\relax\endgroup}\relax
  \advance\@IEEEtrantmpdimenB by -\@IEEEtrantmpdimenC
  % at this point \@IEEEtrantmpdimenB has the actual footer top margin
  % get the difference between the desired and the actual
  \advance\@IEEEtrantmpdimenA by -\@IEEEtrantmpdimenB
\fi\fi % if t, b, c
\fi % if a
% advance \footskip by the needed amount
\advance\footskip by \@IEEEtrantmpdimenA\relax
}


% -- End page setup commands --




% 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
% base class should define \description
\let\LaTeXdescription\description
\let\endLaTeXdescription\enddescription


% override LaTeX's default IED lists, if the user requested it
\if@IEEETOOLSredeflists
\def\itemize{\@IEEEitemize}
\def\enditemize{\@endIEEEitemize}
\def\enumerate{\@IEEEenumerate}
\def\endenumerate{\@endIEEEenumerate}
\def\description{\@IEEEdescription}
\def\enddescription{\@endIEEEdescription}
\fi


% provide the user with the IEEE IED commands
\def\IEEEitemize{\@IEEEitemize}
\def\endIEEEitemize{\@endIEEEitemize}
\def\IEEEenumerate{\@IEEEenumerate}
\def\endIEEEenumerate{\@endIEEEenumerate}
\def\IEEEdescription{\@IEEEdescription}
\def\endIEEEdescription{\@endIEEEdescription}


% V1.6 we want to keep the IEEEtran IED list definitions as our own internal
% commands so they are protected against redefinition
\def\@IEEEitemize{\@ifnextchar[{\@@IEEEitemize}{\@@IEEEitemize[\relax]}}
\def\@IEEEenumerate{\@ifnextchar[{\@@IEEEenumerate}{\@@IEEEenumerate[\relax]}}
\def\@IEEEdescription{\@ifnextchar[{\@@IEEEdescription}{\@@IEEEdescription[\relax]}}
\def\@endIEEEitemize{\endlist}
\def\@endIEEEenumerate{\endlist}
\def\@endIEEEdescription{\endlist}


% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
% IEEEtran itemized list MDS 1/2001
% Note controlled spacing here, shield end of lines with %
\def\@@IEEEitemize[#1]{%
                \ifnum\@itemdepth>3\relax\@toodeep\else%
                \ifnum\@listdepth>5\relax\@toodeep\else%
                \advance\@itemdepth\@ne%
                \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
                % get the IEEElabelindentfactor for this level
                \advance\@listdepth\@ne% we need to know what the level WILL be
                \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
                \advance\@listdepth-\@ne% undo our increment
                \def\@IEEEiedjustify{2}% right justified labels are default
                % set other defaults
                \IEEEnocalcleftmarginfalse%
                \IEEEnolabelindentfactorfalse%
                \topsep\IEEEiedtopsep%
                \IEEElabelindent\IEEEilabelindent%
                \labelsep\IEEEiednormlabelsep%
                \partopsep 0ex%
                \parsep 0ex%
                \itemsep 0ex%
                \rightmargin 0em%
                \listparindent 0em%
                \itemindent 0em%
                % calculate the label width
                % the user can override this later if
                % they specified a \labelwidth
                \settowidth{\labelwidth}{\csname labelitem\romannumeral\the\@itemdepth\endcsname}%
                \@IEEEsavelistparams% save our list parameters
                \list{\csname\@itemitem\endcsname}{%
                \@IEEErestorelistparams% override any list{} changes
                                       % to our globals
                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
                \IEEEiedlistdecl% let user alter parameters
                #1\relax%
                % If the user has requested not to use the
                % IEEElabelindent factor, don't revise \IEEElabelindent
                \ifIEEEnolabelindentfactor\relax%
                \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent%
                \fi%
                % Unless the user has requested otherwise,
                % calculate our left margin based
                % on \IEEElabelindent, \labelwidth and
                % \labelsep
                \ifIEEEnocalcleftmargin\relax%
                \else\IEEEcalcleftmargin{\IEEElabelindent}%
                \fi}\fi\fi}%


% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
% IEEEtran enumerate list MDS 1/2001
% Note controlled spacing here, shield end of lines with %
\def\@@IEEEenumerate[#1]{%
                \ifnum\@enumdepth>3\relax\@toodeep\else%
                \ifnum\@listdepth>5\relax\@toodeep\else%
                \advance\@enumdepth\@ne%
                \edef\@enumctr{enum\romannumeral\the\@enumdepth}%
                % get the IEEElabelindentfactor for this level
                \advance\@listdepth\@ne% we need to know what the level WILL be
                \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
                \advance\@listdepth-\@ne% undo our increment
                \def\@IEEEiedjustify{2}% right justified labels are default
                % set other defaults
                \IEEEnocalcleftmarginfalse%
                \IEEEnolabelindentfactorfalse%
                \topsep\IEEEiedtopsep%
                \IEEElabelindent\IEEEelabelindent%
                \labelsep\IEEEiednormlabelsep%
                \partopsep 0ex%
                \parsep 0ex%
                \itemsep 0ex%
                \rightmargin 0em%
                \listparindent 0em%
                \itemindent 0em%
                % calculate the label width
                % We'll set it to the width suitable for all labels using
                % normalfont 1) to 9)
                % The user can override this later
                \settowidth{\labelwidth}{9)}%
                \@IEEEsavelistparams% save our list parameters
                \list{\csname label\@enumctr\endcsname}{\usecounter{\@enumctr}%
                \@IEEErestorelistparams% override any list{} changes
                                       % to our globals
                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
                \IEEEiedlistdecl% let user alter parameters 
                #1\relax%
                % If the user has requested not to use the
                % IEEElabelindent factor, don't revise \IEEElabelindent
                \ifIEEEnolabelindentfactor\relax%
                \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent%
                \fi%
                % Unless the user has requested otherwise,
                % calculate our left margin based
                % on \IEEElabelindent, \labelwidth and
                % \labelsep
                \ifIEEEnocalcleftmargin\relax%
                \else\IEEEcalcleftmargin{\IEEElabelindent}%
                \fi}\fi\fi}%


% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
% IEEEtran description list MDS 1/2001
% Note controlled spacing here, shield end of lines with %
\def\@@IEEEdescription[#1]{%
                \ifnum\@listdepth>5\relax\@toodeep\else%
                % get the IEEElabelindentfactor for this level
                \advance\@listdepth\@ne% we need to know what the level WILL be
                \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
                \advance\@listdepth-\@ne% undo our increment
                \def\@IEEEiedjustify{0}% left justified labels are default
                % set other defaults
                \IEEEnocalcleftmarginfalse%
                \IEEEnolabelindentfactorfalse%
                \topsep\IEEEiedtopsep% 
                \IEEElabelindent\IEEEdlabelindent%
                % assume normal labelsep
                \labelsep\IEEEiednormlabelsep%
                \partopsep 0ex%
                \parsep 0ex%
                \itemsep 0ex%
                \rightmargin 0em%
                \listparindent 0em%
                \itemindent 0em%
                % Bogus label width in case the user forgets
                % to set it.
                % TIP: If you want to see what a variable's width is you
                % can use the TeX command \showthe\width-variable to 
                % display it on the screen during compilation 
                % (This might be helpful to know when you need to find out
                % which label is the widest)
                \settowidth{\labelwidth}{Hello}%
                \@IEEEsavelistparams% save our list parameters
                \list{}{\@IEEErestorelistparams% override any list{} changes
                                               % to our globals
                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
                \IEEEiedlistdecl% let user alter parameters 
                #1\relax%
                % If the user has requested not to use the
                % labelindent factor, don't revise \IEEElabelindent
                \ifIEEEnolabelindentfactor\relax%
                \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent%
                \fi%
                % Unless the user has requested otherwise,
                % calculate our left margin based
                % on \IEEElabelindent, \labelwidth and
                % \labelsep
                \ifIEEEnocalcleftmargin\relax%
                \else\IEEEcalcleftmargin{\IEEElabelindent}\relax%
                \fi}\fi}

% v1.6b we use one makelabel that does justification as needed.
\def\@IEEEiedmakelabel#1{\relax\if\@IEEEiedjustify 0\relax
\makebox[\labelwidth][l]{\normalfont #1}\else
\if\@IEEEiedjustify 1\relax
\makebox[\labelwidth][c]{\normalfont #1}\else
\makebox[\labelwidth][r]{\normalfont #1}\fi\fi}









% used only by IEEEtran's IEEEeqnarray as other packages may
% have their own, different, implementations
\newcounter{IEEEsubequation}[equation]

% e.g., "1a" (used only by IEEEtran's IEEEeqnarray)
\def\theIEEEsubequation{\theequation\alph{IEEEsubequation}}
% just like LaTeX2e's \@eqnnum
\def\theequationdis{{\normalfont \normalcolor (\theequation)}}% (1)
% IEEEsubequation used only by IEEEtran's IEEEeqnarray
\def\theIEEEsubequationdis{{\normalfont \normalcolor (\theIEEEsubequation)}}% (1a)




%%
%% START OF IEEEeqnarray DEFINITIONS
%%
%% Inspired by the concepts, examples, and previous works of LaTeX 
%% coders and developers such as Donald Arseneau, Fred Bartlett, 
%% David Carlisle, Tony Liu, Frank Mittelbach, Piet van Oostrum, 
%% Roland Winkler and Mark Wooding.
%% I don't make the claim that my work here is even near their calibre. ;)


\newif\if@IEEEeqnarrayboxnojot% flag to indicate if the environment was called as the star form
\@IEEEeqnarrayboxnojotfalse

\newif\if@advanceIEEEeqncolcnt% tracks if the environment should advance the col counter
% allows a way to make an \IEEEeqnarraybox that can be used within an \IEEEeqnarray
% used by IEEEeqnarraymulticol so that it can work properly in both
\@advanceIEEEeqncolcnttrue

\newcount\@IEEEeqnnumcols % tracks how many IEEEeqnarray cols are defined
\newcount\@IEEEeqncolcnt  % tracks how many IEEEeqnarray cols the user actually used


% The default math style used by the columns
\def\IEEEeqnarraymathstyle{\displaystyle}
% The default text style used by the columns
% default to using the current font
\def\IEEEeqnarraytextstyle{\relax}

% like the iedlistdecl but for \IEEEeqnarray
\def\IEEEeqnarraydecl{\relax}
\def\IEEEeqnarrayboxdecl{\relax}



% V1.8 flags to indicate that equation numbering is to persist
\newif\if@IEEEeqnumpersist%
\@IEEEeqnumpersistfalse
\newif\if@IEEEsubeqnumpersist%
\@IEEEsubeqnumpersistfalse
%
% V1.8 flags to indicate if (sub)equation number of last line was preadvanced
\newif\if@IEEEeqnumpreadv%
\@IEEEeqnumpreadvfalse
\newif\if@IEEEsubeqnumpreadv%
\@IEEEsubeqnumpreadvfalse

\newcount\@IEEEsubeqnnumrollback% saves previous value of IEEEsubequation number in case we need to restore it

% \yesnumber is the opposite of \nonumber
% a novel concept with the same def as the equationarray package
% However, we give IEEE versions too since some LaTeX packages such as 
% the MDWtools mathenv.sty redefine \nonumber to something else.
% This command is intended for use in non-IEEEeqnarray math environments
\providecommand{\yesnumber}{\global\@eqnswtrue}


% IEEEyes/nonumber 
% V1.8 add persistant * forms
% These commands can alter the type of equation an IEEEeqnarray line is.
\def\IEEEyesnumber{\@ifstar{\global\@IEEEeqnumpersisttrue\global\@IEEEsubeqnumpersistfalse\@IEEEyesnumber}{\@IEEEyesnumber}}

\def\@IEEEyesnumber{\global\@eqnswtrue
\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray
\ifnum\c@IEEEsubequation>0\relax
   \stepcounter{equation}\setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax
   \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label
\fi
% even if we reached this eqn num via a preadv, it is legit now
\global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse
\fi}

\def\IEEEnonumber{\@ifstar{\global\@IEEEeqnumpersistfalse\global\@IEEEsubeqnumpersistfalse\global\@eqnswfalse}{\global\@eqnswfalse}}


\def\IEEEyessubnumber{\@ifstar{\global\@IEEEsubeqnumpersisttrue\@IEEEyessubnumber}{\@IEEEyessubnumber}}
%
\def\@IEEEyessubnumber{\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray
  \ifnum\c@IEEEsubequation>0\relax% if it already is a subequation, we are good to go as-is
  \else% if we are a regular equation we have to watch out for two cases
    \if@IEEEeqnumpreadv% if this equation is the result of a preadvance, backout and bump the sub eqnnum
       \global\advance\c@equation\m@ne\global\c@IEEEsubequation=\@IEEEsubeqnnumrollback\addtocounter{IEEEsubequation}{1}\relax
    \else% non-preadvanced equations just need initialization of their sub eqnnum
       \setcounter{IEEEsubequation}{1}\relax
    \fi
  \fi% fi already is subequation
  \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax
  \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label
  \global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse% no longer a preadv anymore
  \global\@eqnswtrue
\fi}


\def\IEEEnosubnumber{\@ifstar{\global\@IEEEsubeqnumpersistfalse\@IEEEnosubnumber}{\@IEEEnosubnumber}}
%
\def\@IEEEnosubnumber{\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray
  \if@eqnsw % we do nothing unless we know we will display because we play with the counters here
    % if it currently is a subequation, bump up to the next equation number and turn off the subequation
    \ifnum\c@IEEEsubequation>0\relax\addtocounter{equation}{1}\setcounter{IEEEsubequation}{0}\relax
    \fi
    \global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse% no longer a preadv anymore
    \gdef\@currentlabel{\p@equation\theequation}\relax
    \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label
  \fi
\fi}



% allows users to "push away" equations that get too close to the equation numbers
\def\IEEEeqnarraynumspace{\hphantom{\ifnum\c@IEEEsubequation>0\relax\theIEEEsubequationdis\else\theequationdis\fi}}

% provides a way to span multiple columns within IEEEeqnarray environments
% will consider \if@advanceIEEEeqncolcnt before globally advancing the
% column counter - so as to work within \IEEEeqnarraybox
% usage: \IEEEeqnarraymulticol{number cols. to span}{col type}{cell text}
\long\def\IEEEeqnarraymulticol#1#2#3{\multispan{#1}\relax
% check if column is defined for the precolumn definition
% We have to be careful here because TeX scans for & even within an \iffalse
% where it does not expand macros. So, if we used only one \ifx and a #3
% appeared in the false branch and the user inserted another alignment
% structure that uses & in the \IEEEeqnarraymulticol{}, TeX will not see that
% there is an inner alignment in the false branch yet still will see any &
% there and will think that they apply to the outer alignment resulting in an
% incomplete \ifx error.
% So, here we use separate checks for the pre and post parts in order to keep
% the #3 outside of all conditionals.
\relax\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined\relax
\csname @IEEEeqnarraycolPRE#2\endcsname
\else% if not, error and use default type
\@IEEEclspkgerror{Invalid column type "#2" in \string\IEEEeqnarraymulticol.\MessageBreak
Using a default centering column instead}%
{You must define IEEEeqnarray column types before use.}%
\csname @IEEEeqnarraycolPRE@IEEEdefault\endcsname
\fi
% The ten \relax are to help prevent misleading error messages in case a user
% accidently inserted a macro that tries to acquire additional arguments.
#3\relax\relax\relax\relax\relax\relax\relax\relax\relax\relax
% check if column is defined for the postcolumn definition
\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined\relax
\csname @IEEEeqnarraycolPOST#2\endcsname
\else% if not, use the default type
\csname @IEEEeqnarraycolPOST@IEEEdefault\endcsname
\fi
% advance column counter only if the IEEEeqnarray environment wants it
\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by #1\relax\fi}

% like \omit, but maintains track of the column counter for \IEEEeqnarray
\def\IEEEeqnarrayomit{\omit\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by 1\relax\fi}


% provides a way to define a letter referenced column type
% usage: \IEEEeqnarraydefcol{col. type letter/name}{pre insertion text}{post insertion text}
\def\IEEEeqnarraydefcol#1#2#3{\expandafter\def\csname @IEEEeqnarraycolPRE#1\endcsname{#2}%
\expandafter\def\csname @IEEEeqnarraycolPOST#1\endcsname{#3}%
\expandafter\def\csname @IEEEeqnarraycolDEF#1\endcsname{1}}


% provides a way to define a numerically referenced inter-column glue types
% usage: \IEEEeqnarraydefcolsep{col. glue number}{glue definition}
\def\IEEEeqnarraydefcolsep#1#2{\expandafter\def\csname @IEEEeqnarraycolSEP\romannumeral #1\endcsname{#2}%
\expandafter\def\csname @IEEEeqnarraycolSEPDEF\romannumeral #1\endcsname{1}}


\def\@IEEEeqnarraycolisdefined{1}% just a macro for 1, used for checking undefined column types


% expands and appends the given argument to the \@IEEEtrantmptoksA token list
% used to build up the \halign preamble
\def\@IEEEappendtoksA#1{\edef\@@IEEEappendtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA #1}}%
\@@IEEEappendtoksA}

% also appends to \@IEEEtrantmptoksA, but does not expand the argument
% uses \toks8 as a scratchpad register
\def\@IEEEappendNOEXPANDtoksA#1{\toks8={#1}%
\edef\@@IEEEappendNOEXPANDtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA\the\toks8}}%
\@@IEEEappendNOEXPANDtoksA}

% define some common column types for the user
% math
\IEEEeqnarraydefcol{l}{$\IEEEeqnarraymathstyle}{$\hfil}
\IEEEeqnarraydefcol{c}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}
\IEEEeqnarraydefcol{r}{\hfil$\IEEEeqnarraymathstyle}{$}
\IEEEeqnarraydefcol{L}{$\IEEEeqnarraymathstyle{}}{{}$\hfil}
\IEEEeqnarraydefcol{C}{\hfil$\IEEEeqnarraymathstyle{}}{{}$\hfil}
\IEEEeqnarraydefcol{R}{\hfil$\IEEEeqnarraymathstyle{}}{{}$}
% text
\IEEEeqnarraydefcol{s}{\IEEEeqnarraytextstyle}{\hfil}
\IEEEeqnarraydefcol{t}{\hfil\IEEEeqnarraytextstyle}{\hfil}
\IEEEeqnarraydefcol{u}{\hfil\IEEEeqnarraytextstyle}{}

% vertical rules
\IEEEeqnarraydefcol{v}{}{\vrule width\arrayrulewidth}
\IEEEeqnarraydefcol{vv}{\vrule width\arrayrulewidth\hfil}{\hfil\vrule width\arrayrulewidth}
\IEEEeqnarraydefcol{V}{}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}
\IEEEeqnarraydefcol{VV}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth\hfil}%
{\hfil\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}

% horizontal rules
\IEEEeqnarraydefcol{h}{}{\leaders\hrule height\arrayrulewidth\hfil}
\IEEEeqnarraydefcol{H}{}{\leaders\vbox{\hrule width\arrayrulewidth\vskip\doublerulesep\hrule width\arrayrulewidth}\hfil}

% plain
\IEEEeqnarraydefcol{x}{}{}
\IEEEeqnarraydefcol{X}{$}{$}

% the default column type to use in the event a column type is not defined
\IEEEeqnarraydefcol{@IEEEdefault}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}


% a zero tabskip (used for "-" col types)
\def\@IEEEeqnarraycolSEPzero{0pt plus 0pt minus 0pt}
% a centering tabskip (used for "+" col types)
\def\@IEEEeqnarraycolSEPcenter{1000pt plus 0pt minus 1000pt}

% top level default tabskip glues for the start, end, and inter-column
% may be reset within environments not always at the top level, e.g., \IEEEeqnarraybox
\edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPcenter}% default start glue
\edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPcenter}% default end glue
\edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue



% creates a vertical rule that extends from the bottom to the top a a cell
% Provided in case other packages redefine \vline some other way.
% usage: \IEEEeqnarrayvrule[rule thickness]
% If no argument is provided, \arrayrulewidth will be used for the rule thickness. 
\newcommand\IEEEeqnarrayvrule[1][\arrayrulewidth]{\vrule\@width#1\relax}

% creates a blank separator row
% usage: \IEEEeqnarrayseprow[separation length][font size commands]
% default is \IEEEeqnarrayseprow[0.25\normalbaselineskip][\relax]
% blank arguments inherit the default values
% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers
\def\IEEEeqnarrayseprow{\relax\@ifnextchar[{\@IEEEeqnarrayseprow}{\@IEEEeqnarrayseprow[0.25\normalbaselineskip]}}
\def\@IEEEeqnarrayseprow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprow[#1]}{\@@IEEEeqnarrayseprow[#1][\relax]}}
\def\@@IEEEeqnarrayseprow[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%
\ifx\@IEEEeqnarrayseprowARGONE\@empty%
% get the skip value, based on the font commands
% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3
% assign within a bogus box to confine the font changes
{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%
\else%
{\setbox0=\hbox{#2\relax\global\skip5=#1}}%
\fi%
\@IEEEeqnarrayhoptolastcolumn\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}

% creates a blank separator row, but omits all the column templates
% usage: \IEEEeqnarrayseprowcut[separation length][font size commands]
% default is \IEEEeqnarrayseprowcut[0.25\normalbaselineskip][\relax]
% blank arguments inherit the default values
% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers
\def\IEEEeqnarrayseprowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
% advance column counter only if the IEEEeqnarray environment wants it
\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
\@ifnextchar[{\@IEEEeqnarrayseprowcut}{\@IEEEeqnarrayseprowcut[0.25\normalbaselineskip]}}
\def\@IEEEeqnarrayseprowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprowcut[#1]}{\@@IEEEeqnarrayseprowcut[#1][\relax]}}
\def\@@IEEEeqnarrayseprowcut[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%
\ifx\@IEEEeqnarrayseprowARGONE\@empty%
% get the skip value, based on the font commands
% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3
% assign within a bogus box to confine the font changes
{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%
\else%
{\setbox0=\hbox{#2\relax\global\skip5=#1}}%
\fi%
\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}



% draws a single rule across all the columns optional
% argument determines the rule width, \arrayrulewidth is the default
% updates column counter as needed and turns off struts
% usage: \IEEEeqnarrayrulerow[rule line thickness]
\def\IEEEeqnarrayrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
% advance column counter only if the IEEEeqnarray environment wants it
\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
\@ifnextchar[{\@IEEEeqnarrayrulerow}{\@IEEEeqnarrayrulerow[\arrayrulewidth]}}
\def\@IEEEeqnarrayrulerow[#1]{\leaders\hrule height#1\hfil\relax% put in our rule 
% turn off any struts
\IEEEeqnarraystrutsize{0pt}{0pt}[\relax]\relax}


% draws a double rule by using a single rule row, a separator row, and then
% another single rule row 
% first optional argument determines the rule thicknesses, \arrayrulewidth is the default
% second optional argument determines the rule spacing, \doublerulesep is the default
% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]
\def\IEEEeqnarraydblrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
% advance column counter only if the IEEEeqnarray environment wants it
\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
\@ifnextchar[{\@IEEEeqnarraydblrulerow}{\@IEEEeqnarraydblrulerow[\arrayrulewidth]}}
\def\@IEEEeqnarraydblrulerow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerow[#1]}%
{\@@IEEEeqnarraydblrulerow[#1][\doublerulesep]}}
\def\@@IEEEeqnarraydblrulerow[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%
% we allow the user to say \IEEEeqnarraydblrulerow[][]
\ifx\@IEEEeqnarraydblrulerowARG\@empty%
\@IEEEeqnarrayrulerow[\arrayrulewidth]%
\else%
\@IEEEeqnarrayrulerow[#1]\relax%
\fi%
\def\@IEEEeqnarraydblrulerowARG{#2}%
\ifx\@IEEEeqnarraydblrulerowARG\@empty%
\\\IEEEeqnarrayseprow[\doublerulesep][\relax]%
\else%
\\\IEEEeqnarrayseprow[#2][\relax]%
\fi%
\\\multispan{\@IEEEeqnnumcols}%
% advance column counter only if the IEEEeqnarray environment wants it
\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
\def\@IEEEeqnarraydblrulerowARG{#1}%
\ifx\@IEEEeqnarraydblrulerowARG\@empty%
\@IEEEeqnarrayrulerow[\arrayrulewidth]%
\else%
\@IEEEeqnarrayrulerow[#1]%
\fi%
}

% draws a double rule by using a single rule row, a separator (cutting) row, and then
% another single rule row 
% first optional argument determines the rule thicknesses, \arrayrulewidth is the default
% second optional argument determines the rule spacing, \doublerulesep is the default
% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]
\def\IEEEeqnarraydblrulerowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
% advance column counter only if the IEEEeqnarray environment wants it
\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
\@ifnextchar[{\@IEEEeqnarraydblrulerowcut}{\@IEEEeqnarraydblrulerowcut[\arrayrulewidth]}}
\def\@IEEEeqnarraydblrulerowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerowcut[#1]}%
{\@@IEEEeqnarraydblrulerowcut[#1][\doublerulesep]}}
\def\@@IEEEeqnarraydblrulerowcut[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%
% we allow the user to say \IEEEeqnarraydblrulerow[][]
\ifx\@IEEEeqnarraydblrulerowARG\@empty%
\@IEEEeqnarrayrulerow[\arrayrulewidth]%
\else%
\@IEEEeqnarrayrulerow[#1]%
\fi%
\def\@IEEEeqnarraydblrulerowARG{#2}%
\ifx\@IEEEeqnarraydblrulerowARG\@empty%
\\\IEEEeqnarrayseprowcut[\doublerulesep][\relax]%
\else%
\\\IEEEeqnarrayseprowcut[#2][\relax]%
\fi%
\\\multispan{\@IEEEeqnnumcols}%
% advance column counter only if the IEEEeqnarray environment wants it
\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
\def\@IEEEeqnarraydblrulerowARG{#1}%
\ifx\@IEEEeqnarraydblrulerowARG\@empty%
\@IEEEeqnarrayrulerow[\arrayrulewidth]%
\else%
\@IEEEeqnarrayrulerow[#1]%
\fi%
}



% inserts a full row's worth of &'s
% relies on \@IEEEeqnnumcols to provide the correct number of columns
% uses \@IEEEtrantmptoksA, \count0 as scratch registers
\def\@IEEEeqnarrayhoptolastcolumn{\@IEEEtrantmptoksA={}\count0=1\relax%
\loop% add cols if the user did not use them all
\ifnum\count0<\@IEEEeqnnumcols\relax%
\@IEEEappendtoksA{&}%
\advance\count0 by 1\relax% update the col count
\repeat%
\the\@IEEEtrantmptoksA%execute the &'s
}



\newif\if@IEEEeqnarrayISinner % flag to indicate if we are within the lines
\@IEEEeqnarrayISinnerfalse    % of an IEEEeqnarray - after the IEEEeqnarraydecl

\edef\@IEEEeqnarrayTHEstrutheight{0pt} % height and depth of IEEEeqnarray struts
\edef\@IEEEeqnarrayTHEstrutdepth{0pt}

\edef\@IEEEeqnarrayTHEmasterstrutheight{0pt} % default height and depth of
\edef\@IEEEeqnarrayTHEmasterstrutdepth{0pt}  % struts within an IEEEeqnarray

\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{0pt} % saved master strut height
\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{0pt} % and depth

\newif\if@IEEEeqnarrayusemasterstrut % flag to indicate that the master strut value
\@IEEEeqnarrayusemasterstruttrue     % is to be used



% saves the strut height and depth of the master strut
\def\@IEEEeqnarraymasterstrutsave{\relax%
\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
% remove stretchability
\dimen0\skip0\relax%
\dimen2\skip2\relax%
% save values
\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{\the\dimen0}%
\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{\the\dimen2}}

% restores the strut height and depth of the master strut
\def\@IEEEeqnarraymasterstrutrestore{\relax%
\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutHSAVE\relax%
\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutDSAVE\relax%
% remove stretchability
\dimen0\skip0\relax%
\dimen2\skip2\relax%
% restore values
\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}}


% globally restores the strut height and depth to the 
% master values and sets the master strut flag to true
\def\@IEEEeqnarraystrutreset{\relax%
\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
% remove stretchability
\dimen0\skip0\relax%
\dimen2\skip2\relax%
% restore values
\xdef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
\xdef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
\global\@IEEEeqnarrayusemasterstruttrue}


% if the master strut is not to be used, make the current
% values of \@IEEEeqnarrayTHEstrutheight, \@IEEEeqnarrayTHEstrutdepth
% and the use master strut flag, global
% this allows user strut commands issued in the last column to be carried
% into the isolation/strut column
\def\@IEEEeqnarrayglobalizestrutstatus{\relax%
\if@IEEEeqnarrayusemasterstrut\else%
\xdef\@IEEEeqnarrayTHEstrutheight{\@IEEEeqnarrayTHEstrutheight}%
\xdef\@IEEEeqnarrayTHEstrutdepth{\@IEEEeqnarrayTHEstrutdepth}%
\global\@IEEEeqnarrayusemasterstrutfalse%
\fi}



% usage: \IEEEeqnarraystrutsize{height}{depth}[font size commands]
% If called outside the lines of an IEEEeqnarray, sets the height
% and depth of both the master and local struts. If called inside
% an IEEEeqnarray line, sets the height and depth of the local strut
% only and sets the flag to indicate the use of the local strut
% values. If the height or depth is left blank, 0.7\normalbaselineskip
% and 0.3\normalbaselineskip will be used, respectively.
% The optional argument can be used to evaluate the lengths under
% a different font size and styles. If none is specified, the current
% font is used.
% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2
\def\IEEEeqnarraystrutsize#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsize{#1}{#2}}{\@IEEEeqnarraystrutsize{#1}{#2}[\relax]}}
\def\@IEEEeqnarraystrutsize#1#2[#3]{\def\@IEEEeqnarraystrutsizeARG{#1}%
\ifx\@IEEEeqnarraystrutsizeARG\@empty%
{\setbox0=\hbox{#3\relax\global\skip3=0.7\normalbaselineskip}}%
\skip0=\skip3\relax%
\else% arg one present
{\setbox0=\hbox{#3\relax\global\skip3=#1\relax}}%
\skip0=\skip3\relax%
\fi% if null arg
\def\@IEEEeqnarraystrutsizeARG{#2}%
\ifx\@IEEEeqnarraystrutsizeARG\@empty%
{\setbox0=\hbox{#3\relax\global\skip3=0.3\normalbaselineskip}}%
\skip2=\skip3\relax%
\else% arg two present
{\setbox0=\hbox{#3\relax\global\skip3=#2\relax}}%
\skip2=\skip3\relax%
\fi% if null arg
% remove stretchability, just to be safe
\dimen0\skip0\relax%
\dimen2\skip2\relax%
% dimen0 = height, dimen2 = depth
\if@IEEEeqnarrayISinner% inner does not touch master strut size
\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
\@IEEEeqnarrayusemasterstrutfalse% do not use master
\else% outer, have to set master strut too
\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%
\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
\@IEEEeqnarrayusemasterstruttrue% use master strut
\fi}


% usage: \IEEEeqnarraystrutsizeadd{added height}{added depth}[font size commands]
% If called outside the lines of an IEEEeqnarray, adds the given height
% and depth to both the master and local struts.
% If called inside an IEEEeqnarray line, adds the given height and depth
% to the local strut only and sets the flag to indicate the use 
% of the local strut values.
% In both cases, if a height or depth is left blank, 0pt is used instead.
% The optional argument can be used to evaluate the lengths under
% a different font size and styles. If none is specified, the current
% font is used.
% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2
\def\IEEEeqnarraystrutsizeadd#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsizeadd{#1}{#2}}{\@IEEEeqnarraystrutsizeadd{#1}{#2}[\relax]}}
\def\@IEEEeqnarraystrutsizeadd#1#2[#3]{\def\@IEEEeqnarraystrutsizearg{#1}%
\ifx\@IEEEeqnarraystrutsizearg\@empty%
\skip0=0pt\relax%
\else% arg one present
{\setbox0=\hbox{#3\relax\global\skip3=#1}}%
\skip0=\skip3\relax%
\fi% if null arg
\def\@IEEEeqnarraystrutsizearg{#2}%
\ifx\@IEEEeqnarraystrutsizearg\@empty%
\skip2=0pt\relax%
\else% arg two present
{\setbox0=\hbox{#3\relax\global\skip3=#2}}%
\skip2=\skip3\relax%
\fi% if null arg
% remove stretchability, just to be safe
\dimen0\skip0\relax%
\dimen2\skip2\relax%
% dimen0 = height, dimen2 = depth
\if@IEEEeqnarrayISinner% inner does not touch master strut size
% get local strut size
\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%
\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%
% add it to the user supplied values
\advance\dimen0 by \skip0\relax%
\advance\dimen2 by \skip2\relax%
% update the local strut size
\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
\@IEEEeqnarrayusemasterstrutfalse% do not use master
\else% outer, have to set master strut too
% get master strut size
\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
% add it to the user supplied values
\advance\dimen0 by \skip0\relax%
\advance\dimen2 by \skip2\relax%
% update the local and master strut sizes
\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%
\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
\@IEEEeqnarrayusemasterstruttrue% use master strut
\fi}


% allow user a way to see the struts
\newif\ifIEEEvisiblestruts
\IEEEvisiblestrutsfalse

% inserts an invisible strut using the master or local strut values
% uses scratch registers \skip0, \skip2, \dimen0, \dimen2
\def\@IEEEeqnarrayinsertstrut{\relax%
\if@IEEEeqnarrayusemasterstrut
% get master strut size
\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
\else%
% get local strut size
\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%
\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%
\fi%
% remove stretchability, probably not needed
\dimen0\skip0\relax%
\dimen2\skip2\relax%
% dimen0 = height, dimen2 = depth
% allow user to see struts if desired
\ifIEEEvisiblestruts%
\vrule width0.2pt height\dimen0 depth\dimen2\relax%
\else%
\vrule width0pt height\dimen0 depth\dimen2\relax\fi}


% creates an invisible strut, useable even outside \IEEEeqnarray
% if \IEEEvisiblestrutstrue, the strut will be visible and 0.2pt wide. 
% usage: \IEEEstrut[height][depth][font size commands]
% default is \IEEEstrut[0.7\normalbaselineskip][0.3\normalbaselineskip][\relax]
% blank arguments inherit the default values
% uses \dimen0, \dimen2, \skip0, \skip2
\def\IEEEstrut{\relax\@ifnextchar[{\@IEEEstrut}{\@IEEEstrut[0.7\normalbaselineskip]}}
\def\@IEEEstrut[#1]{\relax\@ifnextchar[{\@@IEEEstrut[#1]}{\@@IEEEstrut[#1][0.3\normalbaselineskip]}}
\def\@@IEEEstrut[#1][#2]{\relax\@ifnextchar[{\@@@IEEEstrut[#1][#2]}{\@@@IEEEstrut[#1][#2][\relax]}}
\def\@@@IEEEstrut[#1][#2][#3]{\mbox{#3\relax%
\def\@IEEEstrutARG{#1}%
\ifx\@IEEEstrutARG\@empty%
\skip0=0.7\normalbaselineskip\relax%
\else%
\skip0=#1\relax%
\fi%
\def\@IEEEstrutARG{#2}%
\ifx\@IEEEstrutARG\@empty%
\skip2=0.3\normalbaselineskip\relax%
\else%
\skip2=#2\relax%
\fi%
% remove stretchability, probably not needed
\dimen0\skip0\relax%
\dimen2\skip2\relax%
\ifIEEEvisiblestruts%
\vrule width0.2pt height\dimen0 depth\dimen2\relax%
\else%
\vrule width0.0pt height\dimen0 depth\dimen2\relax\fi}}


% enables strut mode by setting a default strut size and then zeroing the
% \baselineskip, \lineskip, \lineskiplimit and \jot
\def\IEEEeqnarraystrutmode{\IEEEeqnarraystrutsize{0.7\normalbaselineskip}{0.3\normalbaselineskip}[\relax]%
\baselineskip=0pt\lineskip=0pt\lineskiplimit=0pt\jot=0pt}


% equation and subequation forms to use to setup hyperref's \@currentHref
\def\@IEEEtheHrefequation{equation.\theHequation}
\def\@IEEEtheHrefsubequation{equation.\theHequation\alph{IEEEsubequation}}


\def\IEEEeqnarray{\@IEEEeqnumpersisttrue\@IEEEsubeqnumpersistfalse\@IEEEeqnarray}
\def\endIEEEeqnarray{\end@IEEEeqnarray}

\@namedef{IEEEeqnarray*}{\@IEEEeqnumpersistfalse\@IEEEsubeqnumpersistfalse\@IEEEeqnarray}
\@namedef{endIEEEeqnarray*}{\end@IEEEeqnarray}


% \IEEEeqnarray is an enhanced \eqnarray. 
% The star form defaults to not putting equation numbers at the end of each row.
% usage: \IEEEeqnarray[decl]{cols}
\def\@IEEEeqnarray{\relax\@ifnextchar[{\@@IEEEeqnarray}{\@@IEEEeqnarray[\relax]}}
\def\@@IEEEeqnarray[#1]#2{%
   % default to showing the equation number or not based on whether or not
   % the star form was involked
   \if@IEEEeqnumpersist\global\@eqnswtrue
   \else% not the star form
   \global\@eqnswfalse
   \fi% if star form
   % provide a basic hyperref \theHequation if this has not already been setup (hyperref not loaded, or no section counter)
   \@ifundefined{theHequation}{\def\theHequation{\arabic{equation}}}{}\relax
   % provide dummy hyperref commands in case hyperref is not loaded
   \providecommand{\Hy@raisedlink}[1]{}\relax
   \providecommand{\hyper@anchorstart}[1]{}\relax
   \providecommand{\hyper@anchorend}{}\relax
   \providecommand{\@currentHref}{}\relax
   \@IEEEeqnumpreadvfalse% reset eqnpreadv flag
   \@IEEEsubeqnumpreadvfalse% reset subeqnpreadv flag
   \@IEEEeqnarrayISinnerfalse% not yet within the lines of the halign
   \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default
   \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise
   \IEEEvisiblestrutsfalse% diagnostic mode defaults to off
   % no extra space unless the user specifically requests it
   \lineskip=0pt\relax
   \lineskiplimit=0pt\relax
   \baselineskip=\normalbaselineskip\relax%
   \jot=\IEEEnormaljot\relax%
   \mathsurround\z@\relax% no extra spacing around math
   \@advanceIEEEeqncolcnttrue% advance the col counter for each col the user uses, 
                             % used in \IEEEeqnarraymulticol and in the preamble build
   %V1.8 Here we preadvance to the next equation number.
   % If the user later wants a continued subequation, we can roll back.
   \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation%
   \stepcounter{equation}\@IEEEeqnumpreadvtrue% advance equation counter before first line
   \setcounter{IEEEsubequation}{0}% no subequation yet
   \let\@IEEEcurrentlabelsave\@currentlabel% save current label as we later change it globally
   \let\@IEEEcurrentHrefsave\@currentHref% save current href label as we later change it globally
   \def\@currentlabel{\p@equation\theequation}% redefine the ref label
   \def\@currentHref{\@IEEEtheHrefequation}% setup hyperref label
   \IEEEeqnarraydecl\relax% allow a way for the user to make global overrides
   #1\relax% allow user to override defaults
   \let\\\@IEEEeqnarraycr% replace newline with one that can put in eqn. numbers
   \global\@IEEEeqncolcnt\z@% col. count = 0 for first line
   \@IEEEbuildpreamble{#2}\relax% build the preamble and put it into \@IEEEtrantmptoksA 
   % put in the column for the equation number
   \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first
   \toks0={##}%
   % advance the \@IEEEeqncolcnt for the isolation col, this helps with error checking
   \@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}%
   % add the isolation column
   \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}%
   % advance the \@IEEEeqncolcnt for the equation number col, this helps with error checking
   \@IEEEappendtoksA{&\global\advance\@IEEEeqncolcnt by 1\relax}%
   % add the equation number col to the preamble
   \@IEEEappendtoksA{\tabskip\z@skip\hb@xt@\z@\bgroup\hss\the\toks0\egroup}%
   % note \@IEEEeqnnumcols does not count the equation col or isolation col
   % set the starting tabskip glue as determined by the preamble build
   \tabskip=\@IEEEBPstartglue\relax
   % begin the display alignment
   \@IEEEeqnarrayISinnertrue% commands are now within the lines
   $$\everycr{}\halign to\displaywidth\bgroup
   % "exspand" the preamble
   \span\the\@IEEEtrantmptoksA\cr}

% enter isolation/strut column (or the next column if the user did not use
% every column), record the strut status, complete the columns, do the strut if needed,
% restore counters (to backout any equation setup for a next line that was never used)
% to their correct values and exit
\def\end@IEEEeqnarray{\@IEEEeqnarrayglobalizestrutstatus&\@@IEEEeqnarraycr\egroup
\if@IEEEsubeqnumpreadv\global\advance\c@IEEEsubequation\m@ne\fi
\if@IEEEeqnumpreadv\global\advance\c@equation\m@ne\global\c@IEEEsubequation=\@IEEEsubeqnnumrollback\fi
\global\let\@currentlabel\@IEEEcurrentlabelsave% restore current label
\global\let\@currentHref\@IEEEcurrentHrefsave% restore current href label
$$\@ignoretrue}


% IEEEeqnarray uses a modifed \\ instead of the plain \cr to
% end rows. This allows for things like \\*[vskip amount]
% These "cr" macros are modified versions of those for LaTeX2e's eqnarray
% the {\ifnum0=`} braces must be kept away from the last column to avoid
% altering spacing of its math, so we use & to advance to the next column
% as there is an isolation/strut column after the user's columns
\def\@IEEEeqnarraycr{\@IEEEeqnarrayglobalizestrutstatus&% save strut status and advance to next column
   {\ifnum0=`}\fi
   \@ifstar{%
      \global\@eqpen\@M\@IEEEeqnarrayYCR
   }{%
      \global\@eqpen\interdisplaylinepenalty \@IEEEeqnarrayYCR
   }%
}

\def\@IEEEeqnarrayYCR{\@testopt\@IEEEeqnarrayXCR\z@skip}

\def\@IEEEeqnarrayXCR[#1]{%
   \ifnum0=`{\fi}%
   \@@IEEEeqnarraycr
   \noalign{\penalty\@eqpen\vskip\jot\vskip #1\relax}}%

\def\@@IEEEeqnarraycr{\@IEEEtrantmptoksA={}% clear token register
    \advance\@IEEEeqncolcnt by -1\relax% adjust col count because of the isolation column
    \ifnum\@IEEEeqncolcnt>\@IEEEeqnnumcols\relax
    \@IEEEclspkgerror{Too many columns within the IEEEeqnarray\MessageBreak
                          environment}%
    {Use fewer \string &'s or put more columns in the IEEEeqnarray column\MessageBreak 
     specifications.}\relax%
    \else
    \loop% add cols if the user did not use them all
    \ifnum\@IEEEeqncolcnt<\@IEEEeqnnumcols\relax
    \@IEEEappendtoksA{&}%
    \advance\@IEEEeqncolcnt by 1\relax% update the col count
    \repeat
    % this number of &'s will take us the the isolation column
    \fi
    % execute the &'s
    \the\@IEEEtrantmptoksA%
    % handle the strut/isolation column
    \@IEEEeqnarrayinsertstrut% do the strut if needed
    \@IEEEeqnarraystrutreset% reset the strut system for next line or IEEEeqnarray
    &% and enter the equation number column
    \if@eqnsw% only if we display something
      \Hy@raisedlink{\hyper@anchorstart{\@currentHref}}% start a hyperref anchor
      \global\@IEEEeqnumpreadvfalse\relax% displaying an equation number means
      \global\@IEEEsubeqnumpreadvfalse\relax% the equation counters point to valid equations
      % V1.8 Here we setup the counters, currentlabel and status for what would be the *next*
      % equation line as would be the case under the current settings. However, there are two problems.
      % One problem is that there might not ever be a next line. The second problem is that the user
      % may later alter the meaning of a line with commands such as \IEEEyessubnumber. So, to handle
      % these cases we have to record the current values of the (sub)equation counters and revert back
      % to them if the next line is changed or never comes. The \if@IEEEeqnumpreadv, \if@IEEEsubeqnumpreadv
      % and \@IEEEsubeqnnumrollback stuff tracks this.
      % The logic to handle all this is surprisingly complex, but a nice feature of the approach here is
      % that the equation counters and labels remain valid for what the line would be unless a
      % \IEEEyessubnumber et al. later changes it. So, any hyperref links are always correct.
      \ifnum\c@IEEEsubequation>0\relax% handle subequation
         \theIEEEsubequationdis\relax
         \if@IEEEsubeqnumpersist% setup for default type of next line
            \stepcounter{IEEEsubequation}\global\@IEEEsubeqnumpreadvtrue\relax
            \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax
            \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label
         \else
             % if no subeqnum persist, go ahead and setup for a new equation number
             \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation
             \stepcounter{equation}\global\@IEEEeqnumpreadvtrue\relax
             \setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax
             \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label
         \fi
      \else% display a standard equation number
        \theequationdis\relax
        \setcounter{IEEEsubequation}{0}\relax% not really needed
        \if@IEEEsubeqnumpersist% setup for default type of next line
           % subequations that follow plain equations carry the same equation number e.g, 5, 5a rather than 5, 6a
           \stepcounter{IEEEsubequation}\global\@IEEEsubeqnumpreadvtrue\relax
           \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax
           \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label
         \else
             % if no subeqnum persist, go ahead and setup for a new equation number
             \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation
             \stepcounter{equation}\global\@IEEEeqnumpreadvtrue\relax
             \setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax
             \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label
         \fi
      \fi%
      \Hy@raisedlink{\hyper@anchorend}% end hyperref anchor
    \fi% fi only if we display something
    % reset the flags to indicate the default preferences of the display of equation numbers
    \if@IEEEeqnumpersist\global\@eqnswtrue\else\global\@eqnswfalse\fi
    \if@IEEEsubeqnumpersist\global\@eqnswtrue\fi% ditto for the subequation flag
    % reset the number of columns the user actually used
    \global\@IEEEeqncolcnt\z@\relax
    % the real end of the line
    \cr}





% \IEEEeqnarraybox is like \IEEEeqnarray except the box form puts everything
% inside a vtop, vbox, or vcenter box depending on the letter in the second
% optional argument (t,b,c). Vbox is the default. Unlike \IEEEeqnarray,
% equation numbers are not displayed and \IEEEeqnarraybox can be nested.
% \IEEEeqnarrayboxm is for math mode (like \array) and does not put the vbox
% within an hbox.
% \IEEEeqnarrayboxt is for text mode (like \tabular) and puts the vbox within
% a \hbox{$ $} construct.
% \IEEEeqnarraybox will auto detect whether to use \IEEEeqnarrayboxm or 
% \IEEEeqnarrayboxt depending on the math mode.
% The third optional argument specifies the width this box is to be set to -
% natural width is the default.
% The * forms do not add \jot line spacing
% usage: \IEEEeqnarraybox[decl][pos][width]{cols}
\def\IEEEeqnarrayboxm{\@IEEEeqnarrayboxnojotfalse\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}
\def\endIEEEeqnarrayboxm{\end@IEEEeqnarraybox}
\@namedef{IEEEeqnarrayboxm*}{\@IEEEeqnarrayboxnojottrue\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}
\@namedef{endIEEEeqnarrayboxm*}{\end@IEEEeqnarraybox}

\def\IEEEeqnarrayboxt{\@IEEEeqnarrayboxnojotfalse\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}
\def\endIEEEeqnarrayboxt{\end@IEEEeqnarraybox}
\@namedef{IEEEeqnarrayboxt*}{\@IEEEeqnarrayboxnojottrue\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}
\@namedef{endIEEEeqnarrayboxt*}{\end@IEEEeqnarraybox}

\def\IEEEeqnarraybox{\@IEEEeqnarrayboxnojotfalse\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%
\@IEEEeqnarraybox}
\def\endIEEEeqnarraybox{\end@IEEEeqnarraybox}

\@namedef{IEEEeqnarraybox*}{\@IEEEeqnarrayboxnojottrue\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%
\@IEEEeqnarraybox}
\@namedef{endIEEEeqnarraybox*}{\end@IEEEeqnarraybox}

% flag to indicate if the \IEEEeqnarraybox needs to put things into an hbox{$ $} 
% for \vcenter in non-math mode
\newif\if@IEEEeqnarrayboxHBOXSW%
\@IEEEeqnarrayboxHBOXSWfalse

\def\@IEEEeqnarraybox{\relax\@ifnextchar[{\@@IEEEeqnarraybox}{\@@IEEEeqnarraybox[\relax]}}
\def\@@IEEEeqnarraybox[#1]{\relax\@ifnextchar[{\@@@IEEEeqnarraybox[#1]}{\@@@IEEEeqnarraybox[#1][b]}}
\def\@@@IEEEeqnarraybox[#1][#2]{\relax\@ifnextchar[{\@@@@IEEEeqnarraybox[#1][#2]}{\@@@@IEEEeqnarraybox[#1][#2][\relax]}}

% #1 = decl; #2 = t,b,c; #3 = width, #4 = col specs
\def\@@@@IEEEeqnarraybox[#1][#2][#3]#4{\@IEEEeqnarrayISinnerfalse % not yet within the lines of the halign
   \@IEEEeqnarraymasterstrutsave% save current master strut values
   \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default
   \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise
   \IEEEvisiblestrutsfalse% diagnostic mode defaults to off
   % no extra space unless the user specifically requests it
   \lineskip=0pt\relax%
   \lineskiplimit=0pt\relax%
   \baselineskip=\normalbaselineskip\relax%
   \jot=\IEEEnormaljot\relax%
   \mathsurround\z@\relax% no extra spacing around math
   % the default end glues are zero for an \IEEEeqnarraybox
   \edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPzero}% default start glue
   \edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPzero}% default end glue
   \edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue
   \@advanceIEEEeqncolcntfalse% do not advance the col counter for each col the user uses, 
                              % used in \IEEEeqnarraymulticol and in the preamble build
   \IEEEeqnarrayboxdecl\relax% allow a way for the user to make global overrides
   #1\relax% allow user to override defaults
   \let\\\@IEEEeqnarrayboxcr% replace newline with one that allows optional spacing
   \@IEEEbuildpreamble{#4}\relax% build the preamble and put it into \@IEEEtrantmptoksA
   % add an isolation column to the preamble to stop \\'s {} from getting into the last col
   \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first
   \toks0={##}%
   % add the isolation column to the preamble
   \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}% 
   % set the starting tabskip glue as determined by the preamble build
   \tabskip=\@IEEEBPstartglue\relax
   % begin the alignment
   \everycr{}%
   % use only the very first token to determine the positioning
   \@IEEEextracttoken{#2}\relax
   \ifx\@IEEEextractedtokensdiscarded\@empty\else
     \typeout{** WARNING: IEEEeqnarraybox position specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
   \fi
   % \@IEEEextractedtoken has the first token, the rest are ignored
   % if we need to put things into and hbox and go into math mode, do so now
   \if@IEEEeqnarrayboxHBOXSW \leavevmode \hbox \bgroup $\fi%
   % use the appropriate vbox type
   \if\@IEEEextractedtoken t\relax\vtop\else\if\@IEEEextractedtoken c\relax%
   \vcenter\else\vbox\fi\fi\bgroup%
   \@IEEEeqnarrayISinnertrue% commands are now within the lines
   \ifx#3\relax\halign\else\halign to #3\relax\fi%
   \bgroup
   % "exspand" the preamble
   \span\the\@IEEEtrantmptoksA\cr}

% carry strut status and enter the isolation/strut column, 
% exit from math mode if needed, and exit
\def\end@IEEEeqnarraybox{\@IEEEeqnarrayglobalizestrutstatus% carry strut status
&% enter isolation/strut column
\@IEEEeqnarrayinsertstrut% do strut if needed
\@IEEEeqnarraymasterstrutrestore% restore the previous master strut values
% reset the strut system for next IEEEeqnarray
% (sets local strut values back to previous master strut values)
\@IEEEeqnarraystrutreset%
% ensure last line, exit from halign, close vbox
\crcr\egroup\egroup%
% exit from math mode and close hbox if needed
\if@IEEEeqnarrayboxHBOXSW $\egroup\fi}



% IEEEeqnarraybox uses a modifed \\ instead of the plain \cr to
% end rows. This allows for things like \\[vskip amount]
% This "cr" macros are modified versions those for LaTeX2e's eqnarray
% For IEEEeqnarraybox, \\* is the same as \\
% the {\ifnum0=`} braces must be kept away from the last column to avoid
% altering spacing of its math, so we use & to advance to the isolation/strut column
% carry strut status into isolation/strut column
\def\@IEEEeqnarrayboxcr{\@IEEEeqnarrayglobalizestrutstatus% carry strut status
&% enter isolation/strut column
\@IEEEeqnarrayinsertstrut% do strut if needed
% reset the strut system for next line or IEEEeqnarray
\@IEEEeqnarraystrutreset%
{\ifnum0=`}\fi%
\@ifstar{\@IEEEeqnarrayboxYCR}{\@IEEEeqnarrayboxYCR}}

% test and setup the optional argument to \\[]
\def\@IEEEeqnarrayboxYCR{\@testopt\@IEEEeqnarrayboxXCR\z@skip}

% IEEEeqnarraybox does not automatically increase line spacing by \jot
\def\@IEEEeqnarrayboxXCR[#1]{\ifnum0=`{\fi}%
\cr\noalign{\if@IEEEeqnarrayboxnojot\else\vskip\jot\fi\vskip#1\relax}}



% usage: \@IEEEbuildpreamble{column specifiers}
% starts the halign preamble build 
% the assembled preamble is put in \@IEEEtrantmptoksA
\def\@IEEEbuildpreamble#1{\@IEEEtrantmptoksA={}% clear token register
\let\@IEEEBPcurtype=u%current column type is not yet known
\let\@IEEEBPprevtype=s%the previous column type was the start
\let\@IEEEBPnexttype=u%next column type is not yet known
% ensure these are valid
\def\@IEEEBPcurglue={0pt plus 0pt minus 0pt}%
\def\@IEEEBPcurcolname{@IEEEdefault}% name of current column definition
% currently acquired numerically referenced glue
% use a name that is easier to remember
\let\@IEEEBPcurnum=\@IEEEtrantmpcountA%
\@IEEEBPcurnum=0%
% tracks number of columns in the preamble
\@IEEEeqnnumcols=0%
% record the default end glues
\edef\@IEEEBPstartglue{\@IEEEeqnarraycolSEPdefaultstart}%
\edef\@IEEEBPendglue{\@IEEEeqnarraycolSEPdefaultend}%
\edef\@IEEEedefMACRO{#1}\relax% fully expand the preamble to support macro containers
% now parse the user's column specifications
% \ignorespaces is used as a delimiter, need at least one trailing \relax because
% \@@IEEEbuildpreamble looks into the future 
\expandafter\@@IEEEbuildpreamble\@IEEEedefMACRO\ignorespaces\relax\relax}


% usage: \@@IEEEbuildpreamble{current column}{next column}
% parses and builds the halign preamble
\def\@@IEEEbuildpreamble#1#2{\let\@@nextIEEEbuildpreamble=\@@IEEEbuildpreamble%
% use only the very first token to check the end
\@IEEEextracttokengroups{#1}\relax
\ifx\@IEEEextractedfirsttoken\ignorespaces\let\@@nextIEEEbuildpreamble=\@@IEEEfinishpreamble\else%
% identify current and next token type
\@IEEEgetcoltype{#1}{\@IEEEBPcurtype}{1}% current, error on invalid
\@IEEEgetcoltype{#2}{\@IEEEBPnexttype}{0}% next, no error on invalid next
% if curtype is a glue, get the glue def
\if\@IEEEBPcurtype g\@IEEEgetcurglue{#1}{\@IEEEBPcurglue}\fi%
% if curtype is a column, get the column def and set the current column name
\if\@IEEEBPcurtype c\@IEEEgetcurcol{#1}\fi%
% if curtype is a numeral, acquire the user defined glue
\if\@IEEEBPcurtype n\@IEEEprocessNcol{#1}\fi%
% process the acquired glue 
\if\@IEEEBPcurtype g\@IEEEprocessGcol\fi%
% process the acquired col 
\if\@IEEEBPcurtype c\@IEEEprocessCcol\fi%
% ready prevtype for next col spec.
\let\@IEEEBPprevtype=\@IEEEBPcurtype%
% be sure and put back the future token(s) as a group
\fi\@@nextIEEEbuildpreamble{#2}}


% usage: \@@IEEEfinishpreamble{discarded}
% executed just after preamble build is completed
% warn about zero cols, and if prevtype type = u, put in end tabskip glue
% argument is not used
\def\@@IEEEfinishpreamble#1{\ifnum\@IEEEeqnnumcols<1\relax
\@IEEEclspkgerror{No column specifiers declared for IEEEeqnarray}%
{At least one column type must be declared for each IEEEeqnarray.}%
\fi%num cols less than 1
%if last type undefined, set default end tabskip glue
\if\@IEEEBPprevtype u\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue}\fi}


% usage: \@IEEEgetcoltype{col specifier}{\output}{error more}
% Identify and return the column specifier's type code in the given
% \output macro:
% n = number
% g = glue (any other char in catagory 12)
% c = letter
% e = \ignorespaces (end of sequence)
% u = undefined
% error mode: 0 = no error message, 1 = error on invalid char
\def\@IEEEgetcoltype#1#2#3{%
% use only the very first token to determine the type
\@IEEEextracttoken{#1}\relax
% \@IEEEextractedtoken has the first token, the rest are discarded
\let#2=u\relax% assume invalid until know otherwise
\ifx\@IEEEextractedtoken\ignorespaces\let#2=e\else
\ifcat\@IEEEextractedtoken\relax\else% screen out control sequences
\if0\@IEEEextractedtoken\let#2=n\else
\if1\@IEEEextractedtoken\let#2=n\else
\if2\@IEEEextractedtoken\let#2=n\else
\if3\@IEEEextractedtoken\let#2=n\else
\if4\@IEEEextractedtoken\let#2=n\else
\if5\@IEEEextractedtoken\let#2=n\else
\if6\@IEEEextractedtoken\let#2=n\else
\if7\@IEEEextractedtoken\let#2=n\else
\if8\@IEEEextractedtoken\let#2=n\else
\if9\@IEEEextractedtoken\let#2=n\else
\ifcat,\@IEEEextractedtoken\let#2=g\relax
\else\ifcat a\@IEEEextractedtoken\let#2=c\relax\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
\if#2u\relax
\if0\noexpand#3\relax\else\@IEEEclspkgerror{Invalid character in column specifications}%
{Only letters, numerals and certain other symbols are allowed \MessageBreak
as IEEEeqnarray column specifiers.}\fi\fi}


% usage: \@IEEEgetcurcol{col specifier}
% verify the letter referenced column exists
% and return its name in \@IEEEBPcurcolname
% if column specifier is invalid, use the default column @IEEEdefault
\def\@IEEEgetcurcol#1{\expandafter\ifx\csname @IEEEeqnarraycolDEF#1\endcsname\@IEEEeqnarraycolisdefined%
\def\@IEEEBPcurcolname{#1}\else% invalid column name
\@IEEEclspkgerror{Invalid column type "#1" in column specifications.\MessageBreak
Using a default centering column instead}%
{You must define IEEEeqnarray column types before use.}%
\def\@IEEEBPcurcolname{@IEEEdefault}\fi}


% usage: \@IEEEgetcurglue{glue specifier}{\output}
% identify the predefined (punctuation) glue value
% and return it in the given output macro
\def\@IEEEgetcurglue#1#2{%
% ! = \! (neg small)  -0.16667em (-3/18 em)
% , = \, (small)       0.16667em ( 3/18 em)
% : = \: (med)         0.22222em ( 4/18 em)
% ; = \; (large)       0.27778em ( 5/18 em)
% ' = \quad            1em
% " = \qquad           2em
% . = 0.5\arraycolsep
% / = \arraycolsep
% ? = 2\arraycolsep
% * = 1fil
% + = \@IEEEeqnarraycolSEPcenter
% - = \@IEEEeqnarraycolSEPzero
% Note that all em values are referenced to the math font (textfont2) fontdimen6
% value for 1em.
% 
% use only the very first token to determine the type
\@IEEEextracttoken{#1}\relax
\ifx\@IEEEextractedtokensdiscarded\@empty\else
  \typeout{** WARNING: IEEEeqnarray predefined inter-column glue type specifiers after the first in `\@IEEEextracttokenarg' ignored (line \the\inputlineno).}\relax
\fi
% get the math font 1em value
% LaTeX2e's NFSS2 does not preload the fonts, but \IEEEeqnarray needs
% to gain access to the math (\textfont2) font's spacing parameters.
% So we create a bogus box here that uses the math font to ensure
% that \textfont2 is loaded and ready. If this is not done,
% the \textfont2 stuff here may not work.
% Thanks to Bernd Raichle for his 1997 post on this topic.
{\setbox0=\hbox{$\displaystyle\relax$}}%
% fontdimen6 has the width of 1em (a quad).
\@IEEEtrantmpdimenA=\fontdimen6\textfont2\relax%
% identify the glue value based on the first token
% we discard anything after the first
\if!\@IEEEextractedtoken\@IEEEtrantmpdimenA=-0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
\if,\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
\if:\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.22222\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
\if;\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.27778\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
\if'\@IEEEextractedtoken\@IEEEtrantmpdimenA=1\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
\if"\@IEEEextractedtoken\@IEEEtrantmpdimenA=2\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
\if.\@IEEEextractedtoken\@IEEEtrantmpdimenA=0.5\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else
\if/\@IEEEextractedtoken\edef#2{\the\arraycolsep}\else
\if?\@IEEEextractedtoken\@IEEEtrantmpdimenA=2\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else
\if *\@IEEEextractedtoken\edef#2{0pt plus 1fil minus 0pt}\else
\if+\@IEEEextractedtoken\edef#2{\@IEEEeqnarraycolSEPcenter}\else
\if-\@IEEEextractedtoken\edef#2{\@IEEEeqnarraycolSEPzero}\else
\edef#2{\@IEEEeqnarraycolSEPzero}%
\@IEEEclspkgerror{Invalid predefined inter-column glue type "#1" in\MessageBreak
column specifications. Using a default value of\MessageBreak
0pt instead}%
{Only !,:;'"./?*+ and - are valid predefined glue types in the\MessageBreak 
IEEEeqnarray column specifications.}\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}


% usage: \@IEEEprocessNcol{digit}
% process a numerical digit from the column specification
% and look up the corresponding user defined glue value
% can transform current type from n to g or a as the user defined glue is acquired
\def\@IEEEprocessNcol#1{\if\@IEEEBPprevtype g%
\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak
specifications. Ignoring consecutive glue specifiers\MessageBreak
after the first}%
{You cannot have two or more glue types next to each other\MessageBreak 
in the IEEEeqnarray column specifications.}%
\let\@IEEEBPcurtype=a% abort this glue, future digits will be discarded
\@IEEEBPcurnum=0\relax%
\else% if we previously aborted a glue
\if\@IEEEBPprevtype a\@IEEEBPcurnum=0\let\@IEEEBPcurtype=a%maintain digit abortion
\else%acquire this number
% save the previous type before the numerical digits started
\if\@IEEEBPprevtype n\else\let\@IEEEBPprevsavedtype=\@IEEEBPprevtype\fi%
\multiply\@IEEEBPcurnum by 10\relax%
\advance\@IEEEBPcurnum by #1\relax% add in number, \relax is needed to stop TeX's number scan
\if\@IEEEBPnexttype n\else%close acquisition
\expandafter\ifx\csname @IEEEeqnarraycolSEPDEF\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname\@IEEEeqnarraycolisdefined%
\edef\@IEEEBPcurglue{\csname @IEEEeqnarraycolSEP\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname}%
\else%user glue not defined
\@IEEEclspkgerror{Invalid user defined inter-column glue type "\number\@IEEEBPcurnum" in\MessageBreak
column specifications. Using a default value of\MessageBreak
0pt instead}%
{You must define all IEEEeqnarray numerical inter-column glue types via\MessageBreak
\string\IEEEeqnarraydefcolsep \space before they are used in column specifications.}%
\edef\@IEEEBPcurglue{\@IEEEeqnarraycolSEPzero}%
\fi% glue defined or not
\let\@IEEEBPcurtype=g% change the type to reflect the acquired glue
\let\@IEEEBPprevtype=\@IEEEBPprevsavedtype% restore the prev type before this number glue
\@IEEEBPcurnum=0\relax%ready for next acquisition
\fi%close acquisition, get glue
\fi%discard or acquire number
\fi%prevtype glue or not
}


% process an acquired glue
% add any acquired column/glue pair to the preamble
\def\@IEEEprocessGcol{\if\@IEEEBPprevtype a\let\@IEEEBPcurtype=a%maintain previous glue abortions
\else
% if this is the start glue, save it, but do nothing else 
% as this is not used in the preamble, but before
\if\@IEEEBPprevtype s\edef\@IEEEBPstartglue{\@IEEEBPcurglue}%
\else%not the start glue
\if\@IEEEBPprevtype g%ignore if back to back glues
\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak
specifications. Ignoring consecutive glue specifiers\MessageBreak
after the first}%
{You cannot have two or more glue types next to each other\MessageBreak 
in the IEEEeqnarray column specifications.}%
\let\@IEEEBPcurtype=a% abort this glue
\else% not a back to back glue
\if\@IEEEBPprevtype c\relax% if the previoustype was a col, add column/glue pair to preamble
\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi
\toks0={##}%
% make preamble advance col counter if this environment needs this
\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi
% insert the column defintion into the preamble, being careful not to expand
% the column definition
\@IEEEappendtoksA{\tabskip=\@IEEEBPcurglue}%
\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}%
\@IEEEappendtoksA{\@IEEEBPcurcolname}%
\@IEEEappendNOEXPANDtoksA{\endcsname}%
\@IEEEappendtoksA{\the\toks0}%
\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax%
\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}%
\@IEEEappendtoksA{\@IEEEBPcurcolname}%
\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax%
\relax\relax\relax\relax\relax\endgroup}%
\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble
\else% error: non-start glue with no pending column
\@IEEEclspkgerror{Inter-column glue specifier without a prior column\MessageBreak
type in the column specifications. Ignoring this glue\MessageBreak 
specifier}%
{Except for the first and last positions, glue can be placed only\MessageBreak
between column types.}%
\let\@IEEEBPcurtype=a% abort this glue
\fi% previous was a column
\fi% back-to-back glues
\fi% is start column glue
\fi% prev type not a
}


% process an acquired letter referenced column and, if necessary, add it to the preamble
\def\@IEEEprocessCcol{\if\@IEEEBPnexttype g\else
\if\@IEEEBPnexttype n\else
% we have a column followed by something other than a glue (or numeral glue)
% so we must add this column to the preamble now
\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi%col separator for those after the first
\if\@IEEEBPnexttype e\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue\relax}\else%put in end glue
\@IEEEappendtoksA{\tabskip=\@IEEEeqnarraycolSEPdefaultmid\relax}\fi% or default mid glue
\toks0={##}%
% make preamble advance col counter if this environment needs this
\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi
% insert the column definition into the preamble, being careful not to expand
% the column definition
\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}%
\@IEEEappendtoksA{\@IEEEBPcurcolname}%
\@IEEEappendNOEXPANDtoksA{\endcsname}%
\@IEEEappendtoksA{\the\toks0}%
\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax%
\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}%
\@IEEEappendtoksA{\@IEEEBPcurcolname}%
\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax%
\relax\relax\relax\relax\relax\endgroup}%
\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble
\fi%next type not numeral
\fi%next type not glue
}


%%
%% END OF IEEEeqnarray DEFINITIONS
%%




% \IEEEPARstart
% Definition for the big two line drop cap letter at the beginning of the
% first paragraph of journal papers. The first argument is the first letter
% of the first word, the second argument is the remaining letters of the
% first word which will be rendered in upper case.
% In V1.6 this has been completely rewritten to:
% 
% 1. no longer have problems when the user begins an environment
%    within the paragraph that uses \IEEEPARstart.
% 2. auto-detect and use the current font family
% 3. revise handling of the space at the end of the first word so that
%    interword glue will now work as normal.
% 4. produce correctly aligned edges for the (two) indented lines.
% 
% We generalize things via control macros - playing with these is fun too.
% 
% For IEEEtrantools, we do not use a "@" in the names as these are user
% alterable controls.
% 
% V1.7 added more control macros to make it easy for IEEEtrantools.sty users
% to change the font style.
% 
% the number of lines that are indented to clear it
% may need to increase if using decenders
\providecommand{\IEEEPARstartDROPLINES}{2}
% minimum number of lines left on a page to allow a \@IEEEPARstart
% Does not take into consideration rubber shrink, so it tends to
% be overly cautious
\providecommand{\IEEEPARstartMINPAGELINES}{2}
% V1.7 the height of the drop cap is adjusted to match the height of this text
% in the current font (when \IEEEPARstart is called).
\providecommand{\IEEEPARstartHEIGHTTEXT}{T}
% the depth the letter is lowered below the baseline
% the height (and size) of the letter is determined by the sum
% of this value and the height of the \IEEEPARstartHEIGHTTEXT in the current
% font. It is a good idea to set this value in terms of the baselineskip
% so that it can respond to changes therein.
\providecommand{\IEEEPARstartDROPDEPTH}{1.1\baselineskip}
% V1.7 the font the drop cap will be rendered in,
% can take zero or one argument.
\providecommand{\IEEEPARstartFONTSTYLE}{\bfseries}
% V1.7 any additional, non-font related commands needed to modify
% the drop cap letter, can take zero or one argument.
\providecommand{\IEEEPARstartCAPSTYLE}{\MakeUppercase}
% V1.7 the font that will be used to render the rest of the word,
% can take zero or one argument.
\providecommand{\IEEEPARstartWORDFONTSTYLE}{\relax}
% V1.7 any additional, non-font related commands needed to modify
% the rest of the word, can take zero or one argument.
\providecommand{\IEEEPARstartWORDCAPSTYLE}{\MakeUppercase}
% This is the horizontal separation distance from the drop letter to the main text.
% Lengths that depend on the font (e.g., ex, em, etc.) will be referenced
% to the font that is active when \IEEEPARstart is called. 
\providecommand{\IEEEPARstartSEP}{0.15em}
% V1.7 horizontal offset applied to the left of the drop cap.
\providecommand{\IEEEPARstartHOFFSET}{0em}
% V1.7 Italic correction command applied at the end of the drop cap.
\providecommand{\IEEEPARstartITLCORRECT}{\/}

% width of the letter output, set globally. Can be used in \IEEEPARstartSEP
% or \IEEEPARstartHOFFSET, but not the height lengths.
\newdimen\IEEEPARstartletwidth
\IEEEPARstartletwidth 0pt\relax

% definition of \IEEEPARstart
% THIS IS A CONTROLLED SPACING AREA, DO NOT ALLOW SPACES WITHIN THESE LINES
% 
% The token \@IEEEPARstartfont will be globally defined after the first use
% of \IEEEPARstart and will be a font command which creates the big letter
% The first argument is the first letter of the first word and the second
% argument is the rest of the first word(s).
\def\IEEEPARstart#1#2{\par{%
% if this page does not have enough space, break it and lets start
% on a new one
\@IEEEtranneedspace{\IEEEPARstartMINPAGELINES\baselineskip}{\relax}%
% V1.7 move this up here in case user uses \textbf for \IEEEPARstartFONTSTYLE
% which uses command \leavevmode which causes an unwanted \indent to be issued
\noindent
% calculate the desired height of the big letter
% it extends from the top of \IEEEPARstartHEIGHTTEXT in the current font
% down to \IEEEPARstartDROPDEPTH below the current baseline
\settoheight{\@IEEEtrantmpdimenA}{\IEEEPARstartHEIGHTTEXT}%
\addtolength{\@IEEEtrantmpdimenA}{\IEEEPARstartDROPDEPTH}%
% extract the name of the current font in bold
% and place it in \@IEEEPARstartFONTNAME
\def\@IEEEPARstartGETFIRSTWORD##1 ##2\relax{##1}%
{\IEEEPARstartFONTSTYLE{\selectfont\edef\@IEEEPARstartFONTNAMESPACE{\fontname\font\space}%
\xdef\@IEEEPARstartFONTNAME{\expandafter\@IEEEPARstartGETFIRSTWORD\@IEEEPARstartFONTNAMESPACE\relax}}}%
% define a font based on this name with a point size equal to the desired
% height of the drop letter
\font\@IEEEPARstartsubfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenA\relax%
% save this value as a counter (integer) value (sp points)
\@IEEEtrantmpcountA=\@IEEEtrantmpdimenA%
% now get the height of the actual letter produced by this font size
\settoheight{\@IEEEtrantmpdimenB}{\@IEEEPARstartsubfont\IEEEPARstartCAPSTYLE{#1}}%
% If something bogus happens like the first argument is empty or the
% current font is strange, do not allow a zero height.
\ifdim\@IEEEtrantmpdimenB=0pt\relax%
\typeout{** WARNING: IEEEPARstart drop letter has zero height! (line \the\inputlineno)}%
\typeout{ Forcing the drop letter font size to 10pt.}%
\@IEEEtrantmpdimenB=10pt%
\fi%
% and store it as a counter
\@IEEEtrantmpcountB=\@IEEEtrantmpdimenB%
% Since a font size doesn't exactly correspond to the height of the capital
% letters in that font, the actual height of the letter, \@IEEEtrantmpcountB,
% will be less than that desired, \@IEEEtrantmpcountA
% we need to raise the font size, \@IEEEtrantmpdimenA 
% by \@IEEEtrantmpcountA / \@IEEEtrantmpcountB
% But, TeX doesn't have floating point division, so we have to use integer
% division. Hence the use of the counters.
% We need to reduce the denominator so that the loss of the remainder will
% have minimal affect on the accuracy of the result
\divide\@IEEEtrantmpcountB by 200%
\divide\@IEEEtrantmpcountA by \@IEEEtrantmpcountB%
% Then reequalize things when we use TeX's ability to multiply by
% floating point values
\@IEEEtrantmpdimenB=0.005\@IEEEtrantmpdimenA%
\multiply\@IEEEtrantmpdimenB by \@IEEEtrantmpcountA%
% \@IEEEPARstartfont is globaly set to the calculated font of the big letter
% We need to carry this out of the local calculation area to to create the
% big letter.
\global\font\@IEEEPARstartfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenB%
% Now set \@IEEEtrantmpdimenA to the width of the big letter
% We need to carry this out of the local calculation area to set the
% hanging indent
\settowidth{\global\@IEEEtrantmpdimenA}{\@IEEEPARstartfont
\IEEEPARstartCAPSTYLE{#1\IEEEPARstartITLCORRECT}}}%
% end of the isolated calculation environment
\global\IEEEPARstartletwidth\@IEEEtrantmpdimenA\relax%
% add in the extra clearance we want
\advance\@IEEEtrantmpdimenA by \IEEEPARstartSEP\relax%
% add in the optional offset
\advance\@IEEEtrantmpdimenA by \IEEEPARstartHOFFSET\relax%
% V1.7 don't allow negative offsets to produce negative hanging indents
\@IEEEtrantmpdimenB\@IEEEtrantmpdimenA
\ifnum\@IEEEtrantmpdimenB < 0 \@IEEEtrantmpdimenB 0pt\fi
% \@IEEEtrantmpdimenA has the width of the big letter plus the
% separation space and \@IEEEPARstartfont is the font we need to use
% Now, we make the letter and issue the hanging indent command
% The letter is placed in a box of zero width and height so that other
% text won't be displaced by it.
\hangindent\@IEEEtrantmpdimenB\hangafter=-\IEEEPARstartDROPLINES%
\makebox[0pt][l]{\hspace{-\@IEEEtrantmpdimenA}%
\raisebox{-\IEEEPARstartDROPDEPTH}[0pt][0pt]{\hspace{\IEEEPARstartHOFFSET}%
\@IEEEPARstartfont\IEEEPARstartCAPSTYLE{#1\IEEEPARstartITLCORRECT}%
\hspace{\IEEEPARstartSEP}}}%
{\IEEEPARstartWORDFONTSTYLE{\IEEEPARstartWORDCAPSTYLE{\selectfont#2}}}}






% determines if the space remaining on a given page is equal to or greater
% than the specified space of argument one
% if not, execute argument two (only if the remaining space is greater than zero)
% and issue a \newpage
% 
% example: \@IEEEtranneedspace{2in}{\vfill}
% 
% Does not take into consideration rubber shrinkage, so it tends to
% be overly cautious
% Based on an example posted by Donald Arseneau
% Note this macro uses \@IEEEtrantmpdimenB internally for calculations,
% so DO NOT PASS \@IEEEtrantmpdimenB to this routine
% if you need a dimen register, import with \@IEEEtrantmpdimenA instead
\def\@IEEEtranneedspace#1#2{\penalty-100\begingroup%shield temp variable
\@IEEEtrantmpdimenB\pagegoal\advance\@IEEEtrantmpdimenB-\pagetotal% space left
\ifdim #1>\@IEEEtrantmpdimenB\relax% not enough space left
\ifdim\@IEEEtrantmpdimenB>\z@\relax #2\fi%
\newpage%
\fi\endgroup}


% \IEEEauthorrefmark
\DeclareRobustCommand*{\IEEEauthorrefmark}[1]{\raisebox{0pt}[0pt][0pt]{\textsuperscript{\footnotesize\ensuremath{\ifcase#1\or *\or \dagger\or \ddagger\or%
    \mathsection\or \mathparagraph\or \|\or **\or \dagger\dagger%
    \or \ddagger\ddagger \else\textsuperscript{\expandafter\romannumeral#1}\fi}}}}


% V1.3 IEEEQED and IEEEproof
\def\IEEEproofname{Proof}

\def\IEEEQEDclosed{\mbox{\rule[0pt]{1.3ex}{1.3ex}}} % for a filled box
\def\IEEEQEDopen{{\setlength{\fboxsep}{0pt}\setlength{\fboxrule}{0.2pt}\fbox{\rule[0pt]{0pt}{1.3ex}\rule[0pt]{1.3ex}{0pt}}}}
\def\IEEEQED{\IEEEQEDclosed} % default to closed

%V1.8 flag to indicate if QED symbol is to be shown
\newif\if@IEEEQEDshow  \@IEEEQEDshowtrue
\def\IEEEproofindentspace{2\parindent}% V1.8 allow user to change indentation amount if desired
% v1.7 name change to avoid namespace collision with amsthm. Also add support
% for an optional argument.
\def\IEEEproof{\@ifnextchar[{\@IEEEproof}{\@IEEEproof[\IEEEproofname]}}
\def\@IEEEproof[#1]{\@IEEEQEDshowtrue\par\noindent\hspace{\IEEEproofindentspace}{\itshape #1: }}
\def\endIEEEproof{\if@IEEEQEDshow\hspace*{\fill}\nobreakspace\IEEEQED\fi\par}
% qedhere for equation environments, similar to AMS \qedhere
\def\IEEEQEDhereeqn{\global\@IEEEQEDshowfalse\eqno\let\eqno\relax\let\leqno\relax
                    \let\veqno\relax\hbox{\IEEEQED}}
% IEEE style qedhere for IEEEeqnarray and other environments
\def\IEEEQEDhere{\global\@IEEEQEDshowfalse\IEEEQED}
% command to disable QED at end of IEEEproof
\def\IEEEQEDoff{\global\@IEEEQEDshowfalse}


% Provide support for the control entries of IEEEtran.bst V1.00 and later.
% V1.7 optional argument allows for a different aux file to be specified in
% order to handle multiple bibliographies. For example, with multibib.sty:
% \newcites{sec}{Secondary Literature}
% \bstctlcite[@auxoutsec]{BSTcontrolhak}
% V1.7 I see no need for \providecommand here.
\def\bstctlcite{\@ifnextchar[{\@bstctlcite}{\@bstctlcite[@auxout]}}
\def\@bstctlcite[#1]#2{\@bsphack
  \@for\@citeb:=#2\do{%
    \edef\@citeb{\expandafter\@firstofone\@citeb}%
    \if@filesw\immediate\write\csname #1\endcsname{\string\citation{\@citeb}}\fi}%
  \@esphack}



% need a backslash character for typeout output
{\catcode`\|=0 \catcode`\\=12
|xdef|@IEEEbackslash{\}}


% hook to allow easy disabling of all legacy warnings
\def\@IEEElegacywarn#1#2{\typeout{** ATTENTION: \@IEEEbackslash #1 is deprecated (line \the\inputlineno).
Use \@IEEEbackslash #2 instead.}}


% V1.4 no longer support these legacy commands
% \def\PARstart{\@IEEElegacywarn{PARstart}{IEEEPARstart}\IEEEPARstart}
% \let\labelindent\IEEElabelindent
% \def\calcleftmargin{\@IEEElegacywarn{calcleftmargin}{IEEEcalcleftmargin}\IEEEcalcleftmargin}
% \def\setlabelwidth{\@IEEElegacywarn{setlabelwidth}{IEEEsetlabelwidth}\IEEEsetlabelwidth}
% \def\usemathlabelsep{\@IEEElegacywarn{usemathlabelsep}{IEEEusemathlabelsep}\IEEEusemathlabelsep}
% \def\iedlabeljustifyc{\@IEEElegacywarn{iedlabeljustifyc}{IEEEiedlabeljustifyc}\IEEEiedlabeljustifyc}
% \def\iedlabeljustifyl{\@IEEElegacywarn{iedlabeljustifyl}{IEEEiedlabeljustifyl}\IEEEiedlabeljustifyl}
% \def\iedlabeljustifyr{\@IEEElegacywarn{iedlabeljustifyr}{IEEEiedlabeljustifyr}\IEEEiedlabeljustifyr}


\endinput
%%%%%%%%%%%%%%%%%%%%%%%%%% End of IEEEtrantools.sty  %%%%%%%%%%%%%%%%%%%%%%
% That's all folks!