\abovedisplayskip 1.5ex plus5pt minus3pt%
\belowdisplayskip \abovedisplayskip%
\abovedisplayshortskip 0pt plus5pt%
\belowdisplayshortskip 1.5ex plus5pt minus3pt
\def\small{\@setfontsize{\small}{10}{12pt}}
\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}
\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}
\def\tiny{\@setfontsize{\tiny}{6}{7pt}}
% sublargesize is the same as large - 12pt
\def\sublargesize{\@setfontsize{\sublargesize}{12}{14pt}}
\def\large{\@setfontsize{\large}{12}{14pt}}
\def\Large{\@setfontsize{\Large}{14}{17pt}}
\def\LARGE{\@setfontsize{\LARGE}{17}{20pt}}
\def\huge{\@setfontsize{\huge}{20}{24pt}}
\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
\fi


% Check if we have selected 12 points
\ifx\@IEEEptsize\@IEEEptsizetwelve
\typeout{-- This is a 12 point document.}
\def\normalsize{\@setfontsize{\normalsize}{12}{13.92pt}}%
\setlength{\@IEEEnormalsizefontbaselineskip}{13.92pt}%
\normalsize
\abovedisplayskip 1.5ex plus6pt minus4pt%
\belowdisplayskip \abovedisplayskip%
\abovedisplayshortskip 0pt plus6pt%
\belowdisplayshortskip 1.5ex plus6pt minus4pt
\def\small{\@setfontsize{\small}{10}{12pt}}
\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}
\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}
\def\tiny{\@setfontsize{\tiny}{6}{7pt}}
% sublargesize is the same as large - 14pt
\def\sublargesize{\@setfontsize{\sublargesize}{14}{17pt}}
\def\large{\@setfontsize{\large}{14}{17pt}}
\def\Large{\@setfontsize{\Large}{17}{20pt}}
\def\LARGE{\@setfontsize{\LARGE}{20}{24pt}}
\def\huge{\@setfontsize{\huge}{22}{26pt}}
\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
\fi


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


% warn the user in case they forget to use the 9pt option with
% technote
\if@technote%
 \ifx\@IEEEptsize\@IEEEptsizenine\else%
  \typeout{** ATTENTION: Technotes are normally 9pt documents.}%
 \fi%
\fi


% set \baselinestretch
\def\baselinestretch{1}
\if@draftclsmode% draft mode uses larger than normal spacing
\def\baselinestretch{1.5} % controls line spacing for draft version
\fi                       % some people may like 1.7 or greater
                          % so that there will be even more space
                          % for hand written comments 

\normalsize % make \baselinestretch take affect


% V1.6
% store the normalsize baselineskip
\newskip\normalsizebaselineskip
\normalsizebaselineskip=\baselineskip\relax
% store the nominal value of jot
\newskip\normaljot
\normaljot=0.25\normalsizebaselineskip\relax

% set \jot
\jot=\normaljot\relax


% abstract and keywords are in \small, except 
% for 9pt docs in which they are in \footnotesize
% Since 9pt docs use an 8pt footnotesize, \small
% becomes a rather awkward 8.5pt
\let\@IEEEabskeysecsize=\small
\ifx\@IEEEptsize\@IEEEptsizenine
 \let\@IEEEabskeysecsize=\footnotesize
\fi



% V1.6, we are now going to fine tune the interword spacing
% The default interword glue for Times under TeX appears to use a
% nominal interword spacing of 25% (relative to the font size, i.e., 1em)
% a maximum of 40% and a minimum of 19%.
% For example, 10pt text uses an interword glue of:
% 
% 2.5pt plus 1.49998pt minus 0.59998pt
% 
% However, IEEE allows for a more generous range which reduces the need
% for hyphenation, especially for two column text. Furthermore, IEEE
% tends to use a little bit more nominal space between the words.
% IEEE's interword spacing percentages appear to be:
% 35% nominal
% 23% minimum
% 50% maximum
% (They may even be using a tad more for the largest fonts such as 24pt.)
% 
% for bold text, IEEE increases the spacing a little more:
% 37.5% nominal
% 23% minimum
% 55% maximum

% here are the interword spacing ratios we'll use
% for medium (normal weight)
\def\@IEEEinterspaceratioM{0.35}
\def\@IEEEinterspaceMINratioM{0.23}
\def\@IEEEinterspaceMAXratioM{0.50}

% for bold
\def\@IEEEinterspaceratioB{0.375}
\def\@IEEEinterspaceMINratioB{0.23}
\def\@IEEEinterspaceMAXratioB{0.55}


% command to revise the interword spacing for the current font under TeX:
% \fontdimen2 = nominal interword space
% \fontdimen3 = interword stretch
% \fontdimen4 = interword shrink
% since all changes to the \fontdimen are global, we can enclose these commands
% in braces to confine any font attribute or length changes
\def\@@@IEEEsetfontdimens#1#2#3{{%
\setlength{\@IEEEtrantmpdimenB}{\f@size pt}% grab the font size in pt, could use 1em instead.
\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%
\fontdimen2\font=\@IEEEtrantmpdimenA\relax
\addtolength{\@IEEEtrantmpdimenA}{-#2\@IEEEtrantmpdimenB}%
\fontdimen3\font=-\@IEEEtrantmpdimenA\relax
\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%
\addtolength{\@IEEEtrantmpdimenA}{-#3\@IEEEtrantmpdimenB}%
\fontdimen4\font=\@IEEEtrantmpdimenA\relax}}

% revise the interword spacing for each font weight
\def\@@IEEEsetfontdimens{{%
\mdseries
\@@@IEEEsetfontdimens{\@IEEEinterspaceratioM}{\@IEEEinterspaceMAXratioM}{\@IEEEinterspaceMINratioM}%
\bfseries
\@@@IEEEsetfontdimens{\@IEEEinterspaceratioB}{\@IEEEinterspaceMAXratioB}{\@IEEEinterspaceMINratioB}%
}}

% revise the interword spacing for each font shape
% \slshape is not often used for IEEE work and is not altered here. The \scshape caps are
% already a tad too large in the free LaTeX fonts (as compared to what IEEE uses) so we
% won't alter these either.
\def\@IEEEsetfontdimens{{%
\normalfont
\@@IEEEsetfontdimens
\normalfont\itshape
\@@IEEEsetfontdimens
}}

% if the nofonttune class option is not given, revise the interword spacing
% for each font size (and shape and weight). Only the \rmfamily is done here
% as \ttfamily uses a fixed spacing and \sffamily is not used as the main
% text of IEEE papers.
\def\@IEEEtunefonts{%
\if@fonttunesettings
{\selectfont\rmfamily
\tiny\@IEEEsetfontdimens
\scriptsize\@IEEEsetfontdimens
\footnotesize\@IEEEsetfontdimens
\small\@IEEEsetfontdimens
\normalsize\@IEEEsetfontdimens
\sublargesize\@IEEEsetfontdimens
\large\@IEEEsetfontdimens
\LARGE\@IEEEsetfontdimens
\huge\@IEEEsetfontdimens
\Huge\@IEEEsetfontdimens}\fi}

% if needed, revise the interword spacing now - in case IEEEtran makes any default
% length measurements, and make sure all the default fonts are loaded
\@IEEEtunefonts

% and again at the start of the document in case the user loaded different fonts
\AtBeginDocument{\@IEEEtunefonts}



% V1.6 
% LaTeX is a little to quick to use hyphenations
% So, we increase the penalty for their use and raise
% the badness level that triggers an underfull hbox
% warning. The author may still have to tweak things,
% but the appearance will be much better "right out
% of the box" than that under V1.5 and prior.
% TeX default is 50
\hyphenpenalty=750
% If we didn't adjust the interword spacing, 2200 might be better.
% The TeX default is 1000
\hbadness=1350
% IEEE does not use extra spacing after punctuation
\frenchspacing



% we want to maintain textheight as an integer multiple of
% \baselineskip.  Keep \topsep in with this game plan too.
\topskip=\baselineskip
% set sizes and margins
% Book typesetting is a world where point and pica (12pt) reign supreme.
% IEEE textwidth is 21 pica. They have a colsep of 1 pica.
% V1.6 conference mode margins
\if@confmode
 \topmargin        -0.25in
 \textheight        9.25in % The standard for conferences
  % However, we will adjust this a  tad so that an integer number
  % of lines will always fit on each page
  % The baselineskip (leading) for each document point size is used 
  % to determine these values
  % rounded up an extra 0.1pt or so to prevent trouble with any rounding errors
 \ifx\@IEEEptsize\@IEEEptsizenine\textheight=674.0pt\fi      %9.3261in  61 lines/page
 \ifx\@IEEEptsize\@IEEEptsizeten\textheight=672.1pt\fi       %9.2998in  56 lines/page
 \ifx\@IEEEptsize\@IEEEptsizeeleven\textheight=669.3pt\fi   %9.2611in  50 lines/page
 \ifx\@IEEEptsize\@IEEEptsizetwelve\textheight=668.3pt\fi   %9.2473in  48 lines/page
\else
 \topmargin        -49.0pt
 \textheight        58pc % = 9.63in or 696pt
\fi


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


% IEEE MARGIN INFO and new \overrideIEEEmargins command
% V1.6 revised margins again
% IEEE wants the side margins to be equal under both US letter
% and A4 paper
% 
% However, for those of you who need to bind copies of your work
% (for review distribution, etc.) the \overrideIEEEmargins
% command will shift the text a tad away from the binding
% edge.
% 
%


% the default side margins are equal
\oddsidemargin    \@IEEEmarginE
\addtolength{\oddsidemargin}{-1in}% compensate for LaTeX's 1in offset
\evensidemargin   \@IEEEmarginE
\addtolength{\evensidemargin}{-1in}% compensate for LaTeX's 1in offset

% execute \overrideIEEEmargins in the preamble to make the side margin
% near the spine slightly wider so that the paper will be much more 
% agreeable to being bound.  \overrideIEEEmargins will have no effect
% when in draft or draftcls mode.
\def\overrideIEEEmargins{\if@draftclsmode\relax\else%
 \typeout{** ATTENTION: Overriding IEEE standard margins (line \the\inputlineno).}%
 \if@twoside
  % for double sided, odd pages have the bound side on the left
  % make this the wide margin
  \oddsidemargin\@IEEEmarginW
  % and even pages have the narrow margin on the left
  % as they are bound on the right
  % evensidemargin is to be the narrow margin
  % calculate the narrow margin and set evensidemargin
  \setlength{\evensidemargin}{\paperwidth}%
  \addtolength{\evensidemargin}{-\@IEEEmarginW}%
  \addtolength{\evensidemargin}{-\textwidth}%
 \else
  % for single sided the bound side is always on the left
  % make this the wide margin
  \oddsidemargin\@IEEEmarginW
  \evensidemargin\@IEEEmarginW
 \fi
 \addtolength{\oddsidemargin}{-1.0in}%  compensate for LaTeX's 1in offset
 \addtolength{\evensidemargin}{-1.0in}%
\fi}


\parindent        1.0em

% conference papers do not have headers, other papers need
% to reserve space for them
\if@confmode
\headsep          0in
\headheight       0in
\else
\headsep          0.25in
\headheight       12pt
\fi

% V1.6, if things get too close, go ahead and let them touch
\lineskip            0pt
\normallineskip      0pt
\lineskiplimit       0pt
\normallineskiplimit 0pt


% The distance from the lower edge of the text body to the
% footline
\footskip 0.4in

% normally zero, should be relative to font height.
% put in a little rubber to help stop some bad breaks (underfull vboxes)
\parskip 0ex plus 0.2ex minus 0.1ex