--- /dev/null
+%%
+%% IEEEtran.cls 2007/03/05 version V1.7a
+%%
+%%
+%% This is the official IEEE LaTeX class for authors of the Institute of
+%% Electrical and Electronics Engineers (IEEE) Transactions journals and
+%% conferences.
+%%
+%% Support sites:
+%% http://www.michaelshell.org/tex/ieeetran/
+%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
+%% and
+%% http://www.ieee.org/
+%%
+%% Based on the original 1993 IEEEtran.cls, but with many bug fixes
+%% and enhancements (from both JVH and MDS) over the 1996/7 version.
+%%
+%%
+%% Contributors:
+%% Gerry Murray (1993), Silvano Balemi (1993),
+%% Jon Dixon (1996), Peter N"uchter (1996),
+%% Juergen von Hagen (2000), and Michael Shell (2001-2007)
+%%
+%%
+%% Copyright (c) 1993-2000 by Gerry Murray, Silvano Balemi,
+%% Jon Dixon, Peter N"uchter,
+%% Juergen von Hagen
+%% and
+%% Copyright (c) 2001-2007 by Michael Shell
+%%
+%% Current maintainer (V1.3 to V1.7): Michael Shell
+%% See:
+%% http://www.michaelshell.org/
+%% for current contact information.
+%%
+%% Special thanks to Peter Wilson (CUA) and Donald Arseneau
+%% for allowing the inclusion of the \@ifmtarg command
+%% from their ifmtarg LaTeX package.
+%%
+%%*************************************************************************
+%% Legal Notice:
+%% This code is offered as-is without any warranty either expressed or
+%% implied; without even the implied warranty of MERCHANTABILITY or
+%% FITNESS FOR A PARTICULAR PURPOSE!
+%% User assumes all risk.
+%% In no event shall IEEE or any contributor to this code be liable for
+%% any damages or losses, including, but not limited to, incidental,
+%% consequential, or any other damages, resulting from the use or misuse
+%% of any information contained here.
+%%
+%% All comments are the opinions of their respective authors and are not
+%% necessarily endorsed by the IEEE.
+%%
+%% This work is distributed under the LaTeX Project Public License (LPPL)
+%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
+%% distributed and modified. A copy of the LPPL, version 1.3, is included
+%% in the base LaTeX documentation of all distributions of LaTeX released
+%% 2003/12/01 or later.
+%% Retain all contribution notices and credits.
+%% ** Modified files should be clearly indicated as such, including **
+%% ** renaming them and changing author support contact information. **
+%%
+%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
+%% bare_conf.tex, bare_jrnl.tex, bare_jrnl_compsoc.tex
+%%
+%% Major changes to the user interface should be indicated by an
+%% increase in the version numbers. If a version is a beta, it will
+%% be indicated with a BETA suffix, i.e., 1.4 BETA.
+%% Small changes can be indicated by appending letters to the version
+%% such as "IEEEtran_v14a.cls".
+%% In all cases, \Providesclass, any \typeout messages to the user,
+%% \IEEEtransversionmajor and \IEEEtransversionminor must reflect the
+%% correct version information.
+%% The changes should also be documented via source comments.
+%%*************************************************************************
+%%
+%
+% Available class options
+% e.g., \documentclass[10pt,conference]{IEEEtran}
+%
+% *** choose only one from each category ***
+%
+% 9pt, 10pt, 11pt, 12pt
+% Sets normal font size. The default is 10pt.
+%
+% conference, journal, technote, peerreview, peerreviewca
+% determines format mode - conference papers, journal papers,
+% correspondence papers (technotes), or peer review papers. The user
+% should also select 9pt when using technote. peerreview is like
+% journal mode, but provides for a single-column "cover" title page for
+% anonymous peer review. The paper title (without the author names) is
+% repeated at the top of the page after the cover page. For peer review
+% papers, the \IEEEpeerreviewmaketitle command must be executed (will
+% automatically be ignored for non-peerreview modes) at the place the
+% cover page is to end, usually just after the abstract (keywords are
+% not normally used with peer review papers). peerreviewca is like
+% peerreview, but allows the author names to be entered and formatted
+% as with conference mode so that author affiliation and contact
+% information can be easily seen on the cover page.
+% The default is journal.
+%
+% draft, draftcls, draftclsnofoot, final
+% determines if paper is formatted as a widely spaced draft (for
+% handwritten editor comments) or as a properly typeset final version.
+% draftcls restricts draft mode to the class file while all other LaTeX
+% packages (i.e., \usepackage{graphicx}) will behave as final - allows
+% for a draft paper with visible figures, etc. draftclsnofoot is like
+% draftcls, but does not display the date and the word "DRAFT" at the foot
+% of the pages. If using one of the draft modes, the user will probably
+% also want to select onecolumn.
+% The default is final.
+%
+% letterpaper, a4paper
+% determines paper size: 8.5in X 11in or 210mm X 297mm. CHANGING THE PAPER
+% SIZE WILL NOT ALTER THE TYPESETTING OF THE DOCUMENT - ONLY THE MARGINS
+% WILL BE AFFECTED. In particular, documents using the a4paper option will
+% have reduced side margins (A4 is narrower than US letter) and a longer
+% bottom margin (A4 is longer than US letter). For both cases, the top
+% margins will be the same and the text will be horizontally centered.
+% For final submission to IEEE, authors should use US letter (8.5 X 11in)
+% paper. Note that authors should ensure that all post-processing
+% (ps, pdf, etc.) uses the same paper specificiation as the .tex document.
+% Problems here are by far the number one reason for incorrect margins.
+% IEEEtran will automatically set the default paper size under pdflatex
+% (without requiring a change to pdftex.cfg), so this issue is more
+% important to dvips users. Fix config.ps, config.pdf, or ~/.dvipsrc for
+% dvips, or use the dvips -t papersize option instead as needed. See the
+% testflow documentation
+% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/testflow
+% for more details on dvips paper size configuration.
+% The default is letterpaper.
+%
+% oneside, twoside
+% determines if layout follows single sided or two sided (duplex)
+% printing. The only notable change is with the headings at the top of
+% the pages.
+% The default is oneside.
+%
+% onecolumn, twocolumn
+% determines if text is organized into one or two columns per page. One
+% column mode is usually used only with draft papers.
+% The default is twocolumn.
+%
+% compsoc
+% Use the format of the IEEE Computer Society.
+%
+% romanappendices
+% Use the "Appendix I" convention when numbering appendices. IEEEtran.cls
+% now defaults to Alpha "Appendix A" convention - the opposite of what
+% v1.6b and earlier did.
+%
+% captionsoff
+% disables the display of the figure/table captions. Some IEEE journals
+% request that captions be removed and figures/tables be put on pages
+% of their own at the end of an initial paper submission. The endfloat
+% package can be used with this class option to achieve this format.
+%
+% nofonttune
+% turns off tuning of the font interword spacing. Maybe useful to those
+% not using the standard Times fonts or for those who have already "tuned"
+% their fonts.
+% The default is to enable IEEEtran to tune font parameters.
+%
+%
+%----------
+% Available CLASSINPUTs provided (all are macros unless otherwise noted):
+% \CLASSINPUTbaselinestretch
+% \CLASSINPUTinnersidemargin
+% \CLASSINPUToutersidemargin
+% \CLASSINPUTtoptextmargin
+% \CLASSINPUTbottomtextmargin
+%
+% Available CLASSINFOs provided:
+% \ifCLASSINFOpdf (TeX if conditional)
+% \CLASSINFOpaperwidth (macro)
+% \CLASSINFOpaperheight (macro)
+% \CLASSINFOnormalsizebaselineskip (length)
+% \CLASSINFOnormalsizeunitybaselineskip (length)
+%
+% Available CLASSOPTIONs provided:
+% all class option flags (TeX if conditionals) unless otherwise noted,
+% e.g., \ifCLASSOPTIONcaptionsoff
+% point size options provided as a single macro:
+% \CLASSOPTIONpt
+% which will be defined as 9, 10, 11, or 12 depending on the document's
+% normalsize point size.
+% also, class option peerreviewca implies the use of class option peerreview
+% and classoption draft implies the use of class option draftcls
+
+
+
+
+
+\ProvidesClass{IEEEtran}[2007/03/05 V1.7a by Michael Shell]
+\typeout{-- See the "IEEEtran_HOWTO" manual for usage information.}
+\typeout{-- http://www.michaelshell.org/tex/ieeetran/}
+\NeedsTeXFormat{LaTeX2e}
+
+% IEEEtran.cls version numbers, provided as of V1.3
+% These values serve as a way a .tex file can
+% determine if the new features are provided.
+% The version number of this IEEEtrans.cls can be obtained from
+% these values. i.e., V1.4
+% KEEP THESE AS INTEGERS! i.e., NO {4a} or anything like that-
+% (no need to enumerate "a" minor changes here)
+\def\IEEEtransversionmajor{1}
+\def\IEEEtransversionminor{7}
+
+% These do nothing, but provide them like in article.cls
+\newif\if@restonecol
+\newif\if@titlepage
+
+
+% class option conditionals
+\newif\ifCLASSOPTIONonecolumn \CLASSOPTIONonecolumnfalse
+\newif\ifCLASSOPTIONtwocolumn \CLASSOPTIONtwocolumntrue
+
+\newif\ifCLASSOPTIONoneside \CLASSOPTIONonesidetrue
+\newif\ifCLASSOPTIONtwoside \CLASSOPTIONtwosidefalse
+
+\newif\ifCLASSOPTIONfinal \CLASSOPTIONfinaltrue
+\newif\ifCLASSOPTIONdraft \CLASSOPTIONdraftfalse
+\newif\ifCLASSOPTIONdraftcls \CLASSOPTIONdraftclsfalse
+\newif\ifCLASSOPTIONdraftclsnofoot \CLASSOPTIONdraftclsnofootfalse
+
+\newif\ifCLASSOPTIONpeerreview \CLASSOPTIONpeerreviewfalse
+\newif\ifCLASSOPTIONpeerreviewca \CLASSOPTIONpeerreviewcafalse
+
+\newif\ifCLASSOPTIONjournal \CLASSOPTIONjournaltrue
+\newif\ifCLASSOPTIONconference \CLASSOPTIONconferencefalse
+\newif\ifCLASSOPTIONtechnote \CLASSOPTIONtechnotefalse
+
+\newif\ifCLASSOPTIONnofonttune \CLASSOPTIONnofonttunefalse
+
+\newif\ifCLASSOPTIONcaptionsoff \CLASSOPTIONcaptionsofffalse
+
+\newif\ifCLASSOPTIONcompsoc \CLASSOPTIONcompsocfalse
+
+\newif\ifCLASSOPTIONromanappendices \CLASSOPTIONromanappendicesfalse
+
+
+% class info conditionals
+
+% indicates if pdf (via pdflatex) output
+\newif\ifCLASSINFOpdf \CLASSINFOpdffalse
+
+
+% V1.6b internal flag to show if using a4paper
+\newif\if@IEEEusingAfourpaper \@IEEEusingAfourpaperfalse
+
+
+
+% IEEEtran class scratch pad registers
+% dimen
+\newdimen\@IEEEtrantmpdimenA
+\newdimen\@IEEEtrantmpdimenB
+% count
+\newcount\@IEEEtrantmpcountA
+\newcount\@IEEEtrantmpcountB
+% token list
+\newtoks\@IEEEtrantmptoksA
+
+% we use \CLASSOPTIONpt so that we can ID the point size (even for 9pt docs)
+% as well as LaTeX's \@ptsize to retain some compatability with some
+% external packages
+\def\@ptsize{0}
+% LaTeX does not support 9pt, so we set \@ptsize to 0 - same as that of 10pt
+\DeclareOption{9pt}{\def\CLASSOPTIONpt{9}\def\@ptsize{0}}
+\DeclareOption{10pt}{\def\CLASSOPTIONpt{10}\def\@ptsize{0}}
+\DeclareOption{11pt}{\def\CLASSOPTIONpt{11}\def\@ptsize{1}}
+\DeclareOption{12pt}{\def\CLASSOPTIONpt{12}\def\@ptsize{2}}
+
+
+
+\DeclareOption{letterpaper}{\setlength{\paperheight}{11in}%
+ \setlength{\paperwidth}{8.5in}%
+ \@IEEEusingAfourpaperfalse
+ \def\CLASSOPTIONpaper{letter}%
+ \def\CLASSINFOpaperwidth{8.5in}%
+ \def\CLASSINFOpaperheight{11in}}
+
+
+\DeclareOption{a4paper}{\setlength{\paperheight}{297mm}%
+ \setlength{\paperwidth}{210mm}%
+ \@IEEEusingAfourpapertrue
+ \def\CLASSOPTIONpaper{a4}%
+ \def\CLASSINFOpaperwidth{210mm}%
+ \def\CLASSINFOpaperheight{297mm}}
+
+\DeclareOption{oneside}{\@twosidefalse\@mparswitchfalse
+ \CLASSOPTIONonesidetrue\CLASSOPTIONtwosidefalse}
+\DeclareOption{twoside}{\@twosidetrue\@mparswitchtrue
+ \CLASSOPTIONtwosidetrue\CLASSOPTIONonesidefalse}
+
+\DeclareOption{onecolumn}{\CLASSOPTIONonecolumntrue\CLASSOPTIONtwocolumnfalse}
+\DeclareOption{twocolumn}{\CLASSOPTIONtwocolumntrue\CLASSOPTIONonecolumnfalse}
+
+% If the user selects draft, then this class AND any packages
+% will go into draft mode.
+\DeclareOption{draft}{\CLASSOPTIONdrafttrue\CLASSOPTIONdraftclstrue
+ \CLASSOPTIONdraftclsnofootfalse}
+% draftcls is for a draft mode which will not affect any packages
+% used by the document.
+\DeclareOption{draftcls}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclstrue
+ \CLASSOPTIONdraftclsnofootfalse}
+% draftclsnofoot is like draftcls, but without the footer.
+\DeclareOption{draftclsnofoot}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclstrue
+ \CLASSOPTIONdraftclsnofoottrue}
+\DeclareOption{final}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclsfalse
+ \CLASSOPTIONdraftclsnofootfalse}
+
+\DeclareOption{journal}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse
+ \CLASSOPTIONjournaltrue\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse}
+
+\DeclareOption{conference}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse
+ \CLASSOPTIONjournalfalse\CLASSOPTIONconferencetrue\CLASSOPTIONtechnotefalse}
+
+\DeclareOption{technote}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse
+ \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotetrue}
+
+\DeclareOption{peerreview}{\CLASSOPTIONpeerreviewtrue\CLASSOPTIONpeerreviewcafalse
+ \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse}
+
+\DeclareOption{peerreviewca}{\CLASSOPTIONpeerreviewtrue\CLASSOPTIONpeerreviewcatrue
+ \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse}
+
+\DeclareOption{nofonttune}{\CLASSOPTIONnofonttunetrue}
+
+\DeclareOption{captionsoff}{\CLASSOPTIONcaptionsofftrue}
+
+\DeclareOption{compsoc}{\CLASSOPTIONcompsoctrue}
+
+\DeclareOption{romanappendices}{\CLASSOPTIONromanappendicestrue}
+
+
+% default to US letter paper, 10pt, twocolumn, one sided, final, journal
+\ExecuteOptions{letterpaper,10pt,twocolumn,oneside,final,journal}
+% overrride these defaults per user requests
+\ProcessOptions
+
+
+
+% Computer Society conditional execution command
+\long\def\@IEEEcompsoconly#1{\relax\ifCLASSOPTIONcompsoc\relax#1\relax\fi\relax}
+% inverse
+\long\def\@IEEEnotcompsoconly#1{\relax\ifCLASSOPTIONcompsoc\else\relax#1\relax\fi\relax}
+% compsoc conference
+\long\def\@IEEEcompsocconfonly#1{\relax\ifCLASSOPTIONcompsoc\ifCLASSOPTIONconference\relax#1\relax\fi\fi\relax}
+% compsoc not conference
+\long\def\@IEEEcompsocnotconfonly#1{\relax\ifCLASSOPTIONcompsoc\ifCLASSOPTIONconference\else\relax#1\relax\fi\fi\relax}
+
+
+% IEEE uses Times Roman font, so we'll default to Times.
+% These three commands make up the entire times.sty package.
+\renewcommand{\sfdefault}{phv}
+\renewcommand{\rmdefault}{ptm}
+\renewcommand{\ttdefault}{pcr}
+
+\@IEEEcompsoconly{\typeout{-- Using IEEE Computer Society mode.}}
+
+% V1.7 compsoc nonconference papers, use Palatino/Palladio as the main text font,
+% not Times Roman.
+\@IEEEcompsocnotconfonly{\renewcommand{\rmdefault}{ppl}}
+
+% enable Times/Palatino main text font
+\normalfont\selectfont
+
+
+
+
+
+% V1.7 conference notice message hook
+\def\@IEEEconsolenoticeconference{\typeout{}%
+\typeout{** Conference Paper **}%
+\typeout{Before submitting the final camera ready copy, remember to:}%
+\typeout{}%
+\typeout{ 1. Manually equalize the lengths of two columns on the last page}%
+\typeout{ of your paper;}%
+\typeout{}%
+\typeout{ 2. Ensure that any PostScript and/or PDF output post-processing}%
+\typeout{ uses only Type 1 fonts and that every step in the generation}%
+\typeout{ process uses the appropriate paper size.}%
+\typeout{}}
+
+
+% we can send console reminder messages to the user here
+\AtEndDocument{\ifCLASSOPTIONconference\@IEEEconsolenoticeconference\fi}
+
+
+% warn about the use of single column other than for draft mode
+\ifCLASSOPTIONtwocolumn\else%
+ \ifCLASSOPTIONdraftcls\else%
+ \typeout{** ATTENTION: Single column mode is not typically used with IEEE publications.}%
+ \fi%
+\fi
+
+
+% V1.7 improved paper size setting code.
+% Set pdfpage and dvips paper sizes. Conditional tests are similar to that
+% of ifpdf.sty. Retain within {} to ensure tested macros are never altered,
+% even if only effect is to set them to \relax.
+% if \pdfoutput is undefined or equal to relax, output a dvips special
+{\@ifundefined{pdfoutput}{\AtBeginDvi{\special{papersize=\CLASSINFOpaperwidth,\CLASSINFOpaperheight}}}{%
+% pdfoutput is defined and not equal to \relax
+% check for pdfpageheight existence just in case someone sets pdfoutput
+% under non-pdflatex. If exists, set them regardless of value of \pdfoutput.
+\@ifundefined{pdfpageheight}{\relax}{\global\pdfpagewidth\paperwidth
+\global\pdfpageheight\paperheight}%
+% if using \pdfoutput=0 under pdflatex, send dvips papersize special
+\ifcase\pdfoutput
+\AtBeginDvi{\special{papersize=\CLASSINFOpaperwidth,\CLASSINFOpaperheight}}%
+\else
+% we are using pdf output, set CLASSINFOpdf flag
+\global\CLASSINFOpdftrue
+\fi}}
+
+% let the user know the selected papersize
+\typeout{-- Using \CLASSINFOpaperwidth\space x \CLASSINFOpaperheight\space
+(\CLASSOPTIONpaper)\space paper.}
+
+\ifCLASSINFOpdf
+\typeout{-- Using PDF output.}
+\else
+\typeout{-- Using DVI output.}
+\fi
+
+
+% The idea hinted here is for LaTeX to generate markleft{} and markright{}
+% automatically for you after you enter \author{}, \journal{},
+% \journaldate{}, journalvol{}, \journalnum{}, etc.
+% However, there may be some backward compatibility issues here as
+% well as some special applications for IEEEtran.cls and special issues
+% that may require the flexible \markleft{}, \markright{} and/or \markboth{}.
+% We'll leave this as an open future suggestion.
+%\newcommand{\journal}[1]{\def\@journal{#1}}
+%\def\@journal{}
+
+
+
+% pointsize values
+% used with ifx to determine the document's normal size
+\def\@IEEEptsizenine{9}
+\def\@IEEEptsizeten{10}
+\def\@IEEEptsizeeleven{11}
+\def\@IEEEptsizetwelve{12}
+
+
+
+% FONT DEFINITIONS (No sizexx.clo file needed)
+% V1.6 revised font sizes, displayskip values and
+% revised normalsize baselineskip to reduce underfull vbox problems
+% on the 58pc = 696pt = 9.5in text height we want
+% normalsize #lines/column baselineskip (aka leading)
+% 9pt 63 11.0476pt (truncated down)
+% 10pt 58 12pt (exact)
+% 11pt 52 13.3846pt (truncated down)
+% 12pt 50 13.92pt (exact)
+%
+
+% we need to store the nominal baselineskip for the given font size
+% in case baselinestretch ever changes.
+% this is a dimen, so it will not hold stretch or shrink
+\newdimen\@IEEEnormalsizeunitybaselineskip
+\@IEEEnormalsizeunitybaselineskip\baselineskip
+
+\ifx\CLASSOPTIONpt\@IEEEptsizenine
+\typeout{-- This is a 9 point document.}
+\def\normalsize{\@setfontsize{\normalsize}{9}{11.0476pt}}%
+\setlength{\@IEEEnormalsizeunitybaselineskip}{11.0476pt}%
+\normalsize
+\abovedisplayskip 1.5ex plus3pt minus1pt%
+\belowdisplayskip \abovedisplayskip%
+\abovedisplayshortskip 0pt plus3pt%
+\belowdisplayshortskip 1.5ex plus3pt minus1pt
+\def\small{\@setfontsize{\small}{8.5}{10pt}}
+\def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}}
+\def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}}
+\def\tiny{\@setfontsize{\tiny}{5}{6pt}}
+% sublargesize is the same as large - 10pt
+\def\sublargesize{\@setfontsize{\sublargesize}{10}{12pt}}
+\def\large{\@setfontsize{\large}{10}{12pt}}
+\def\Large{\@setfontsize{\Large}{12}{14pt}}
+\def\LARGE{\@setfontsize{\LARGE}{14}{17pt}}
+\def\huge{\@setfontsize{\huge}{17}{20pt}}
+\def\Huge{\@setfontsize{\Huge}{20}{24pt}}
+\fi
+
+
+% Check if we have selected 10 points
+\ifx\CLASSOPTIONpt\@IEEEptsizeten
+\typeout{-- This is a 10 point document.}
+\def\normalsize{\@setfontsize{\normalsize}{10}{12.00pt}}%
+\setlength{\@IEEEnormalsizeunitybaselineskip}{12pt}%
+\normalsize
+\abovedisplayskip 1.5ex plus4pt minus2pt%
+\belowdisplayskip \abovedisplayskip%
+\abovedisplayshortskip 0pt plus4pt%
+\belowdisplayshortskip 1.5ex plus4pt minus2pt
+\def\small{\@setfontsize{\small}{9}{10pt}}
+\def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}}
+\def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}}
+\def\tiny{\@setfontsize{\tiny}{5}{6pt}}
+% sublargesize is a tad smaller than large - 11pt
+\def\sublargesize{\@setfontsize{\sublargesize}{11}{13.4pt}}
+\def\large{\@setfontsize{\large}{12}{14pt}}
+\def\Large{\@setfontsize{\Large}{14}{17pt}}
+\def\LARGE{\@setfontsize{\LARGE}{17}{20pt}}
+\def\huge{\@setfontsize{\huge}{20}{24pt}}
+\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
+\fi
+
+
+% Check if we have selected 11 points
+\ifx\CLASSOPTIONpt\@IEEEptsizeeleven
+\typeout{-- This is an 11 point document.}
+\def\normalsize{\@setfontsize{\normalsize}{11}{13.3846pt}}%
+\setlength{\@IEEEnormalsizeunitybaselineskip}{13.3846pt}%
+\normalsize
+\abovedisplayskip 1.5ex plus5pt minus3pt%
+\belowdisplayskip \abovedisplayskip%
+\abovedisplayshortskip 0pt plus5pt%
+\belowdisplayshortskip 1.5ex plus5pt minus3pt
+\def\small{\@setfontsize{\small}{10}{12pt}}
+\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}
+\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}
+\def\tiny{\@setfontsize{\tiny}{6}{7pt}}
+% sublargesize is the same as large - 12pt
+\def\sublargesize{\@setfontsize{\sublargesize}{12}{14pt}}
+\def\large{\@setfontsize{\large}{12}{14pt}}
+\def\Large{\@setfontsize{\Large}{14}{17pt}}
+\def\LARGE{\@setfontsize{\LARGE}{17}{20pt}}
+\def\huge{\@setfontsize{\huge}{20}{24pt}}
+\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
+\fi
+
+
+% Check if we have selected 12 points
+\ifx\CLASSOPTIONpt\@IEEEptsizetwelve
+\typeout{-- This is a 12 point document.}
+\def\normalsize{\@setfontsize{\normalsize}{12}{13.92pt}}%
+\setlength{\@IEEEnormalsizeunitybaselineskip}{13.92pt}%
+\normalsize
+\abovedisplayskip 1.5ex plus6pt minus4pt%
+\belowdisplayskip \abovedisplayskip%
+\abovedisplayshortskip 0pt plus6pt%
+\belowdisplayshortskip 1.5ex plus6pt minus4pt
+\def\small{\@setfontsize{\small}{10}{12pt}}
+\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}
+\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}
+\def\tiny{\@setfontsize{\tiny}{6}{7pt}}
+% sublargesize is the same as large - 14pt
+\def\sublargesize{\@setfontsize{\sublargesize}{14}{17pt}}
+\def\large{\@setfontsize{\large}{14}{17pt}}
+\def\Large{\@setfontsize{\Large}{17}{20pt}}
+\def\LARGE{\@setfontsize{\LARGE}{20}{24pt}}
+\def\huge{\@setfontsize{\huge}{22}{26pt}}
+\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
+\fi
+
+
+% V1.6 The Computer Modern Fonts will issue a substitution warning for
+% 24pt titles (24.88pt is used instead) increase the substitution
+% tolerance to turn off this warning
+\def\fontsubfuzz{.9pt}
+% However, the default (and correct) Times font will scale exactly as needed.
+
+
+% warn the user in case they forget to use the 9pt option with
+% technote
+\ifCLASSOPTIONtechnote%
+ \ifx\CLASSOPTIONpt\@IEEEptsizenine\else%
+ \typeout{** ATTENTION: Technotes are normally 9pt documents.}%
+ \fi%
+\fi
+
+
+% V1.7
+% Improved \textunderscore to provide a much better fake _ when used with
+% OT1 encoding. Under OT1, detect use of pcr or cmtt \ttfamily and use
+% available true _ glyph for those two typewriter fonts.
+\def\@IEEEstringptm{ptm} % Times Roman family
+\def\@IEEEstringppl{ppl} % Palatino Roman family
+\def\@IEEEstringphv{phv} % Helvetica Sans Serif family
+\def\@IEEEstringpcr{pcr} % Courier typewriter family
+\def\@IEEEstringcmtt{cmtt} % Computer Modern typewriter family
+\DeclareTextCommandDefault{\textunderscore}{\leavevmode
+\ifx\f@family\@IEEEstringpcr\string_\else
+\ifx\f@family\@IEEEstringcmtt\string_\else
+\ifx\f@family\@IEEEstringptm\kern 0em\vbox{\hrule\@width 0.5em\@height 0.5pt\kern -0.3ex}\else
+\ifx\f@family\@IEEEstringppl\kern 0em\vbox{\hrule\@width 0.5em\@height 0.5pt\kern -0.3ex}\else
+\ifx\f@family\@IEEEstringphv\kern -0.03em\vbox{\hrule\@width 0.62em\@height 0.52pt\kern -0.33ex}\kern -0.03em\else
+\kern 0.09em\vbox{\hrule\@width 0.6em\@height 0.44pt\kern -0.63pt\kern -0.42ex}\kern 0.09em\fi\fi\fi\fi\fi\relax}
+
+
+
+
+% set the default \baselinestretch
+\def\baselinestretch{1}
+\ifCLASSOPTIONdraftcls
+ \def\baselinestretch{1.5}% default baselinestretch for draft modes
+\fi
+
+
+% process CLASSINPUT baselinestretch
+\ifx\CLASSINPUTbaselinestretch\@IEEEundefined
+\else
+ \edef\baselinestretch{\CLASSINPUTbaselinestretch} % user CLASSINPUT override
+ \typeout{** ATTENTION: Overriding \string\baselinestretch\space to
+ \baselinestretch\space via \string\CLASSINPUT.}
+\fi
+
+\normalsize % make \baselinestretch take affect
+
+
+
+
+% store the normalsize baselineskip
+\newdimen\CLASSINFOnormalsizebaselineskip
+\CLASSINFOnormalsizebaselineskip=\baselineskip\relax
+% and the normalsize unity (baselinestretch=1) baselineskip
+% we could save a register by giving the user access to
+% \@IEEEnormalsizeunitybaselineskip. However, let's protect
+% its read only internal status
+\newdimen\CLASSINFOnormalsizeunitybaselineskip
+\CLASSINFOnormalsizeunitybaselineskip=\@IEEEnormalsizeunitybaselineskip\relax
+% store the nominal value of jot
+\newdimen\IEEEnormaljot
+\IEEEnormaljot=0.25\baselineskip\relax
+
+% set \jot
+\jot=\IEEEnormaljot\relax
+
+
+
+
+% V1.6, we are now going to fine tune the interword spacing
+% The default interword glue for Times under TeX appears to use a
+% nominal interword spacing of 25% (relative to the font size, i.e., 1em)
+% a maximum of 40% and a minimum of 19%.
+% For example, 10pt text uses an interword glue of:
+%
+% 2.5pt plus 1.49998pt minus 0.59998pt
+%
+% However, IEEE allows for a more generous range which reduces the need
+% for hyphenation, especially for two column text. Furthermore, IEEE
+% tends to use a little bit more nominal space between the words.
+% IEEE's interword spacing percentages appear to be:
+% 35% nominal
+% 23% minimum
+% 50% maximum
+% (They may even be using a tad more for the largest fonts such as 24pt.)
+%
+% for bold text, IEEE increases the spacing a little more:
+% 37.5% nominal
+% 23% minimum
+% 55% maximum
+
+% here are the interword spacing ratios we'll use
+% for medium (normal weight)
+\def\@IEEEinterspaceratioM{0.35}
+\def\@IEEEinterspaceMINratioM{0.23}
+\def\@IEEEinterspaceMAXratioM{0.50}
+
+% for bold
+\def\@IEEEinterspaceratioB{0.375}
+\def\@IEEEinterspaceMINratioB{0.23}
+\def\@IEEEinterspaceMAXratioB{0.55}
+
+
+% command to revise the interword spacing for the current font under TeX:
+% \fontdimen2 = nominal interword space
+% \fontdimen3 = interword stretch
+% \fontdimen4 = interword shrink
+% since all changes to the \fontdimen are global, we can enclose these commands
+% in braces to confine any font attribute or length changes
+\def\@@@IEEEsetfontdimens#1#2#3{{%
+\setlength{\@IEEEtrantmpdimenB}{\f@size pt}% grab the font size in pt, could use 1em instead.
+\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%
+\fontdimen2\font=\@IEEEtrantmpdimenA\relax
+\addtolength{\@IEEEtrantmpdimenA}{-#2\@IEEEtrantmpdimenB}%
+\fontdimen3\font=-\@IEEEtrantmpdimenA\relax
+\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%
+\addtolength{\@IEEEtrantmpdimenA}{-#3\@IEEEtrantmpdimenB}%
+\fontdimen4\font=\@IEEEtrantmpdimenA\relax}}
+
+% revise the interword spacing for each font weight
+\def\@@IEEEsetfontdimens{{%
+\mdseries
+\@@@IEEEsetfontdimens{\@IEEEinterspaceratioM}{\@IEEEinterspaceMAXratioM}{\@IEEEinterspaceMINratioM}%
+\bfseries
+\@@@IEEEsetfontdimens{\@IEEEinterspaceratioB}{\@IEEEinterspaceMAXratioB}{\@IEEEinterspaceMINratioB}%
+}}
+
+% revise the interword spacing for each font shape
+% \slshape is not often used for IEEE work and is not altered here. The \scshape caps are
+% already a tad too large in the free LaTeX fonts (as compared to what IEEE uses) so we
+% won't alter these either.
+\def\@IEEEsetfontdimens{{%
+\normalfont
+\@@IEEEsetfontdimens
+\normalfont\itshape
+\@@IEEEsetfontdimens
+}}
+
+% command to revise the interword spacing for each font size (and shape
+% and weight). Only the \rmfamily is done here as \ttfamily uses a
+% fixed spacing and \sffamily is not used as the main text of IEEE papers.
+\def\@IEEEtunefonts{{\selectfont\rmfamily
+\tiny\@IEEEsetfontdimens
+\scriptsize\@IEEEsetfontdimens
+\footnotesize\@IEEEsetfontdimens
+\small\@IEEEsetfontdimens
+\normalsize\@IEEEsetfontdimens
+\sublargesize\@IEEEsetfontdimens
+\large\@IEEEsetfontdimens
+\LARGE\@IEEEsetfontdimens
+\huge\@IEEEsetfontdimens
+\Huge\@IEEEsetfontdimens}}
+
+% if the nofonttune class option is not given, revise the interword spacing
+% now - in case IEEEtran makes any default length measurements, and make
+% sure all the default fonts are loaded
+\ifCLASSOPTIONnofonttune\else
+\@IEEEtunefonts
+\fi
+
+% and again at the start of the document in case the user loaded different fonts
+\AtBeginDocument{\ifCLASSOPTIONnofonttune\else\@IEEEtunefonts\fi}
+
+
+
+% V1.6
+% LaTeX is a little to quick to use hyphenations
+% So, we increase the penalty for their use and raise
+% the badness level that triggers an underfull hbox
+% warning. The author may still have to tweak things,
+% but the appearance will be much better "right out
+% of the box" than that under V1.5 and prior.
+% TeX default is 50
+\hyphenpenalty=750
+% If we didn't adjust the interword spacing, 2200 might be better.
+% The TeX default is 1000
+\hbadness=1350
+% IEEE does not use extra spacing after punctuation
+\frenchspacing
+
+% V1.7 increase this a tad to discourage equation breaks
+\binoppenalty=1000 % default 700
+\relpenalty=800 % default 500
+
+
+% margin note stuff
+\marginparsep 10pt
+\marginparwidth 20pt
+\marginparpush 25pt
+
+
+% if things get too close, go ahead and let them touch
+\lineskip 0pt
+\normallineskip 0pt
+\lineskiplimit 0pt
+\normallineskiplimit 0pt
+
+% The distance from the lower edge of the text body to the
+% footline
+\footskip 0.4in
+
+% normally zero, should be relative to font height.
+% put in a little rubber to help stop some bad breaks (underfull vboxes)
+\parskip 0ex plus 0.2ex minus 0.1ex
+
+\parindent 1.0em
+
+\topmargin -49.0pt
+\headheight 12pt
+\headsep 0.25in
+
+% use the normal font baselineskip
+% so that \topskip is unaffected by changes in \baselinestretch
+\topskip=\@IEEEnormalsizeunitybaselineskip
+\textheight 58pc % 9.63in, 696pt
+% Tweak textheight to a perfect integer number of lines/page.
+% The normal baselineskip for each document point size is used
+% to determine these values.
+\ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=63\@IEEEnormalsizeunitybaselineskip\fi % 63 lines/page
+\ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=58\@IEEEnormalsizeunitybaselineskip\fi % 58 lines/page
+\ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=52\@IEEEnormalsizeunitybaselineskip\fi % 52 lines/page
+\ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=50\@IEEEnormalsizeunitybaselineskip\fi % 50 lines/page
+
+
+\columnsep 1pc
+\textwidth 43pc % 2 x 21pc + 1pc = 43pc
+
+
+% the default side margins are equal
+\if@IEEEusingAfourpaper
+\oddsidemargin 14.32mm
+\evensidemargin 14.32mm
+\else
+\oddsidemargin 0.680in
+\evensidemargin 0.680in
+\fi
+% compensate for LaTeX's 1in offset
+\addtolength{\oddsidemargin}{-1in}
+\addtolength{\evensidemargin}{-1in}
+
+
+
+% adjust margins for conference mode
+\ifCLASSOPTIONconference
+ \topmargin -0.25in
+ % we retain the reserved, but unused space for headers
+ \addtolength{\topmargin}{-\headheight}
+ \addtolength{\topmargin}{-\headsep}
+ \textheight 9.25in % The standard for conferences (668.4975pt)
+ % Tweak textheight to a perfect integer number of lines/page.
+ \ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=61\@IEEEnormalsizeunitybaselineskip\fi % 61 lines/page
+ \ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=56\@IEEEnormalsizeunitybaselineskip\fi % 56 lines/page
+ \ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=50\@IEEEnormalsizeunitybaselineskip\fi % 50 lines/page
+ \ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=48\@IEEEnormalsizeunitybaselineskip\fi % 48 lines/page
+\fi
+
+
+% compsoc conference
+\ifCLASSOPTIONcompsoc
+\ifCLASSOPTIONconference
+ % compsoc conference use a larger value for columnsep
+ \columnsep 0.375in
+ % compsoc conferences want 1in top margin, 1.125in bottom margin
+ \topmargin 0in
+ \addtolength{\topmargin}{-6pt}% we tweak this a tad to better comply with top of line stuff
+ % we retain the reserved, but unused space for headers
+ \addtolength{\topmargin}{-\headheight}
+ \addtolength{\topmargin}{-\headsep}
+ \textheight 8.875in % (641.39625pt)
+ % Tweak textheight to a perfect integer number of lines/page.
+ \ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=58\@IEEEnormalsizeunitybaselineskip\fi % 58 lines/page
+ \ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=53\@IEEEnormalsizeunitybaselineskip\fi % 53 lines/page
+ \ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=48\@IEEEnormalsizeunitybaselineskip\fi % 48 lines/page
+ \ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=46\@IEEEnormalsizeunitybaselineskip\fi % 46 lines/page
+ \textwidth 6.5in
+ % the default side margins are equal
+ \if@IEEEusingAfourpaper
+ \oddsidemargin 22.45mm
+ \evensidemargin 22.45mm
+ \else
+ \oddsidemargin 1in
+ \evensidemargin 1in
+ \fi
+ % compensate for LaTeX's 1in offset
+ \addtolength{\oddsidemargin}{-1in}
+ \addtolength{\evensidemargin}{-1in}
+\fi\fi
+
+
+
+% draft mode settings override that of all other modes
+% provides a nice 1in margin all around the paper and extra
+% space between the lines for editor's comments
+\ifCLASSOPTIONdraftcls
+ % want 1in from top of paper to text
+ \setlength{\topmargin}{-\headsep}%
+ \addtolength{\topmargin}{-\headheight}%
+ % we want 1in side margins regardless of paper type
+ \oddsidemargin 0in
+ \evensidemargin 0in
+ % set the text width
+ \setlength{\textwidth}{\paperwidth}%
+ \addtolength{\textwidth}{-2.0in}%
+ \setlength{\textheight}{\paperheight}%
+ \addtolength{\textheight}{-2.0in}%
+ % digitize textheight to be an integer number of lines.
+ % this may cause the bottom margin to be off a tad
+ \addtolength{\textheight}{-1\topskip}%
+ \divide\textheight by \baselineskip%
+ \multiply\textheight by \baselineskip%
+ \addtolength{\textheight}{\topskip}%
+\fi
+
+
+
+% process CLASSINPUT inner/outer margin
+% if inner margin defined, but outer margin not, set outer to inner.
+\ifx\CLASSINPUTinnersidemargin\@IEEEundefined
+\else
+ \ifx\CLASSINPUToutersidemargin\@IEEEundefined
+ \edef\CLASSINPUToutersidemargin{\CLASSINPUTinnersidemargin}
+ \fi
+\fi
+
+\ifx\CLASSINPUToutersidemargin\@IEEEundefined
+\else
+ % if outer margin defined, but inner margin not, set inner to outer.
+ \ifx\CLASSINPUTinnersidemargin\@IEEEundefined
+ \edef\CLASSINPUTinnersidemargin{\CLASSINPUToutersidemargin}
+ \fi
+ \setlength{\oddsidemargin}{\CLASSINPUTinnersidemargin}
+ \ifCLASSOPTIONtwoside
+ \setlength{\evensidemargin}{\CLASSINPUToutersidemargin}
+ \else
+ \setlength{\evensidemargin}{\CLASSINPUTinnersidemargin}
+ \fi
+ \addtolength{\oddsidemargin}{-1in}
+ \addtolength{\evensidemargin}{-1in}
+ \setlength{\textwidth}{\paperwidth}
+ \addtolength{\textwidth}{-\CLASSINPUTinnersidemargin}
+ \addtolength{\textwidth}{-\CLASSINPUToutersidemargin}
+ \typeout{** ATTENTION: Overriding inner side margin to \CLASSINPUTinnersidemargin\space and
+ outer side margin to \CLASSINPUToutersidemargin\space via \string\CLASSINPUT.}
+\fi
+
+
+
+% process CLASSINPUT top/bottom text margin
+% if toptext margin defined, but bottomtext margin not, set bottomtext to toptext margin
+\ifx\CLASSINPUTtoptextmargin\@IEEEundefined
+\else
+ \ifx\CLASSINPUTbottomtextmargin\@IEEEundefined
+ \edef\CLASSINPUTbottomtextmargin{\CLASSINPUTtoptextmargin}
+ \fi
+\fi
+
+\ifx\CLASSINPUTbottomtextmargin\@IEEEundefined
+\else
+ % if bottomtext margin defined, but toptext margin not, set toptext to bottomtext margin
+ \ifx\CLASSINPUTtoptextmargin\@IEEEundefined
+ \edef\CLASSINPUTtoptextmargin{\CLASSINPUTbottomtextmargin}
+ \fi
+ \setlength{\topmargin}{\CLASSINPUTtoptextmargin}
+ \addtolength{\topmargin}{-1in}
+ \addtolength{\topmargin}{-\headheight}
+ \addtolength{\topmargin}{-\headsep}
+ \setlength{\textheight}{\paperheight}
+ \addtolength{\textheight}{-\CLASSINPUTtoptextmargin}
+ \addtolength{\textheight}{-\CLASSINPUTbottomtextmargin}
+ % in the default format we use the normal baselineskip as topskip
+ % we only need 0.7 of this to clear typical top text and we need
+ % an extra 0.3 spacing at the bottom for descenders. This will
+ % correct for both.
+ \addtolength{\topmargin}{-0.3\@IEEEnormalsizeunitybaselineskip}
+ \typeout{** ATTENTION: Overriding top text margin to \CLASSINPUTtoptextmargin\space and
+ bottom text margin to \CLASSINPUTbottomtextmargin\space via \string\CLASSINPUT.}
+\fi
+
+
+
+
+
+
+
+% LIST SPACING CONTROLS
+
+% Controls the amount of EXTRA spacing
+% above and below \trivlist
+% Both \list and IED lists override this.
+% However, \trivlist will use this as will most
+% things built from \trivlist like the \center
+% environment.
+\topsep 0.5\baselineskip
+
+% Controls the additional spacing around lists preceded
+% or followed by blank lines. IEEE does not increase
+% spacing before or after paragraphs so it is set to zero.
+% \z@ is the same as zero, but faster.
+\partopsep \z@
+
+% Controls the spacing between paragraphs in lists.
+% IEEE does not increase spacing before or after paragraphs
+% so this is also zero.
+% With IEEEtran.cls, global changes to
+% this value DO affect lists (but not IED lists).
+\parsep \z@
+
+% Controls the extra spacing between list items.
+% IEEE does not put extra spacing between items.
+% With IEEEtran.cls, global changes to this value DO affect
+% lists (but not IED lists).
+\itemsep \z@
+
+% \itemindent is the amount to indent the FIRST line of a list
+% item. It is auto set to zero within the \list environment. To alter
+% it, you have to do so when you call the \list.
+% However, IEEE uses this for the theorem environment
+% There is an alternative value for this near \leftmargini below
+\itemindent -1em
+
+% \leftmargin, the spacing from the left margin of the main text to
+% the left of the main body of a list item is set by \list.
+% Hence this statement does nothing for lists.
+% But, quote and verse do use it for indention.
+\leftmargin 2em
+
+% we retain this stuff from the older IEEEtran.cls so that \list
+% will work the same way as before. However, itemize, enumerate and
+% description (IED) could care less about what these are as they
+% all are overridden.
+\leftmargini 2em
+%\itemindent 2em % Alternative values: sometimes used.
+%\leftmargini 0em
+\leftmarginii 1em
+\leftmarginiii 1.5em
+\leftmarginiv 1.5em
+\leftmarginv 1.0em
+\leftmarginvi 1.0em
+\labelsep 0.5em
+\labelwidth \z@
+
+
+% The old IEEEtran.cls behavior of \list is retained.
+% However, the new V1.3 IED list environments override all the
+% @list stuff (\@listX is called within \list for the
+% appropriate level just before the user's list_decl is called).
+% \topsep is now 2pt as IEEE puts a little extra space around
+% lists - used by those non-IED macros that depend on \list.
+% Note that \parsep and \itemsep are not redefined as in
+% the sizexx.clo \@listX (which article.cls uses) so global changes
+% of these values DO affect \list
+%
+\def\@listi{\leftmargin\leftmargini \topsep 2pt plus 1pt minus 1pt}
+\let\@listI\@listi
+\def\@listii{\leftmargin\leftmarginii\labelwidth\leftmarginii%
+ \advance\labelwidth-\labelsep \topsep 2pt}
+\def\@listiii{\leftmargin\leftmarginiii\labelwidth\leftmarginiii%
+ \advance\labelwidth-\labelsep \topsep 2pt}
+\def\@listiv{\leftmargin\leftmarginiv\labelwidth\leftmarginiv%
+ \advance\labelwidth-\labelsep \topsep 2pt}
+\def\@listv{\leftmargin\leftmarginv\labelwidth\leftmarginv%
+ \advance\labelwidth-\labelsep \topsep 2pt}
+\def\@listvi{\leftmargin\leftmarginvi\labelwidth\leftmarginvi%
+ \advance\labelwidth-\labelsep \topsep 2pt}
+
+
+% IEEE uses 5) not 5.
+\def\labelenumi{\theenumi)} \def\theenumi{\arabic{enumi}}
+
+% IEEE uses a) not (a)
+\def\labelenumii{\theenumii)} \def\theenumii{\alph{enumii}}
+
+% IEEE uses iii) not iii.
+\def\labelenumiii{\theenumiii)} \def\theenumiii{\roman{enumiii}}
+
+% IEEE uses A) not A.
+\def\labelenumiv{\theenumiv)} \def\theenumiv{\Alph{enumiv}}
+
+% exactly the same as in article.cls
+\def\p@enumii{\theenumi}
+\def\p@enumiii{\theenumi(\theenumii)}
+\def\p@enumiv{\p@enumiii\theenumiii}
+
+% itemized list label styles
+\def\labelitemi{$\scriptstyle\bullet$}
+\def\labelitemii{\textbf{--}}
+\def\labelitemiii{$\ast$}
+\def\labelitemiv{$\cdot$}
+
+
+
+% **** V1.3 ENHANCEMENTS ****
+% Itemize, Enumerate and Description (IED) List Controls
+% ***************************
+%
+%
+% IEEE seems to use at least two different values by
+% which ITEMIZED list labels are indented to the right
+% For The Journal of Lightwave Technology (JLT) and The Journal
+% on Selected Areas in Communications (JSAC), they tend to use
+% an indention equal to \parindent. For Transactions on Communications
+% they tend to indent ITEMIZED lists a little more--- 1.3\parindent.
+% We'll provide both values here for you so that you can choose
+% which one you like in your document using a command such as:
+% setlength{\IEEEilabelindent}{\IEEEilabelindentB}
+\newdimen\IEEEilabelindentA
+\IEEEilabelindentA \parindent
+
+\newdimen\IEEEilabelindentB
+\IEEEilabelindentB 1.3\parindent
+% However, we'll default to using \parindent
+% which makes more sense to me
+\newdimen\IEEEilabelindent
+\IEEEilabelindent \IEEEilabelindentA
+
+
+% This controls the default amount the enumerated list labels
+% are indented to the right.
+% Normally, this is the same as the paragraph indention
+\newdimen\IEEEelabelindent
+\IEEEelabelindent \parindent
+
+% This controls the default amount the description list labels
+% are indented to the right.
+% Normally, this is the same as the paragraph indention
+\newdimen\IEEEdlabelindent
+\IEEEdlabelindent \parindent
+
+% This is the value actually used within the IED lists.
+% The IED environments automatically set its value to
+% one of the three values above, so global changes do
+% not have any effect
+\newdimen\IEEElabelindent
+\IEEElabelindent \parindent
+
+% The actual amount labels will be indented is
+% \IEEElabelindent multiplied by the factor below
+% corresponding to the level of nesting depth
+% This provides a means by which the user can
+% alter the effective \IEEElabelindent for deeper
+% levels
+% There may not be such a thing as correct "standard IEEE"
+% values. What IEEE actually does may depend on the specific
+% circumstances.
+% The first list level almost always has full indention.
+% The second levels I've seen have only 75% of the normal indentation
+% Three level or greater nestings are very rare. I am guessing
+% that they don't use any indentation.
+\def\IEEElabelindentfactori{1.0} % almost always one
+\def\IEEElabelindentfactorii{0.75} % 0.0 or 1.0 may be used in some cases
+\def\IEEElabelindentfactoriii{0.0} % 0.75? 0.5? 0.0?
+\def\IEEElabelindentfactoriv{0.0}
+\def\IEEElabelindentfactorv{0.0}
+\def\IEEElabelindentfactorvi{0.0}
+
+% value actually used within IED lists, it is auto
+% set to one of the 6 values above
+% global changes here have no effect
+\def\IEEElabelindentfactor{1.0}
+
+% This controls the default spacing between the end of the IED
+% list labels and the list text, when normal text is used for
+% the labels.
+\newdimen\IEEEiednormlabelsep
+\IEEEiednormlabelsep 0.6em
+
+% This controls the default spacing between the end of the IED
+% list labels and the list text, when math symbols are used for
+% the labels (nomenclature lists). IEEE usually increases the
+% spacing in these cases
+\newdimen\IEEEiedmathlabelsep
+\IEEEiedmathlabelsep 1.2em
+
+% This controls the extra vertical separation put above and
+% below each IED list. IEEE usually puts a little extra spacing
+% around each list. However, this spacing is barely noticeable.
+\newskip\IEEEiedtopsep
+\IEEEiedtopsep 2pt plus 1pt minus 1pt
+
+
+% This command is executed within each IED list environment
+% at the beginning of the list. You can use this to set the
+% parameters for some/all your IED list(s) without disturbing
+% global parameters that affect things other than lists.
+% i.e., renewcommand{\IEEEiedlistdecl}{\setlength{\labelsep}{5em}}
+% will alter the \labelsep for the next list(s) until
+% \IEEEiedlistdecl is redefined.
+\def\IEEEiedlistdecl{\relax}
+
+% This command provides an easy way to set \leftmargin based
+% on the \labelwidth, \labelsep and the argument \IEEElabelindent
+% Usage: \IEEEcalcleftmargin{width-to-indent-the-label}
+% output is in the \leftmargin variable, i.e., effectively:
+% \leftmargin = argument + \labelwidth + \labelsep
+% Note controlled spacing here, shield end of lines with %
+\def\IEEEcalcleftmargin#1{\setlength{\leftmargin}{#1}%
+\addtolength{\leftmargin}{\labelwidth}%
+\addtolength{\leftmargin}{\labelsep}}
+
+% This command provides an easy way to set \labelwidth to the
+% width of the given text. It is the same as
+% \settowidth{\labelwidth}{label-text}
+% and useful as a shorter alternative.
+% Typically used to set \labelwidth to be the width
+% of the longest label in the list
+\def\IEEEsetlabelwidth#1{\settowidth{\labelwidth}{#1}}
+
+% When this command is executed, IED lists will use the
+% IEEEiedmathlabelsep label separation rather than the normal
+% spacing. To have an effect, this command must be executed via
+% the \IEEEiedlistdecl or within the option of the IED list
+% environments.
+\def\IEEEusemathlabelsep{\setlength{\labelsep}{\IEEEiedmathlabelsep}}
+
+% A flag which controls whether the IED lists automatically
+% calculate \leftmargin from \IEEElabelindent, \labelwidth and \labelsep
+% Useful if you want to specify your own \leftmargin
+% This flag must be set (\IEEEnocalcleftmargintrue or \IEEEnocalcleftmarginfalse)
+% via the \IEEEiedlistdecl or within the option of the IED list
+% environments to have an effect.
+\newif\ifIEEEnocalcleftmargin
+\IEEEnocalcleftmarginfalse
+
+% A flag which controls whether \IEEElabelindent is multiplied by
+% the \IEEElabelindentfactor for each list level.
+% This flag must be set via the \IEEEiedlistdecl or within the option
+% of the IED list environments to have an effect.
+\newif\ifIEEEnolabelindentfactor
+\IEEEnolabelindentfactorfalse
+
+
+% internal variable to indicate type of IED label
+% justification
+% 0 - left; 1 - center; 2 - right
+\def\@IEEEiedjustify{0}
+
+
+% commands to allow the user to control IED
+% label justifications. Use these commands within
+% the IED environment option or in the \IEEEiedlistdecl
+% Note that changing the normal list justifications
+% is nonstandard and IEEE may not like it if you do so!
+% I include these commands as they may be helpful to
+% those who are using these enhanced list controls for
+% other non-IEEE related LaTeX work.
+% itemize and enumerate automatically default to right
+% justification, description defaults to left.
+\def\IEEEiedlabeljustifyl{\def\@IEEEiedjustify{0}}%left
+\def\IEEEiedlabeljustifyc{\def\@IEEEiedjustify{1}}%center
+\def\IEEEiedlabeljustifyr{\def\@IEEEiedjustify{2}}%right
+
+
+
+
+% commands to save to and restore from the list parameter copies
+% this allows us to set all the list parameters within
+% the list_decl and prevent \list (and its \@list)
+% from overriding any of our parameters
+% V1.6 use \edefs instead of dimen's to conserve dimen registers
+% Note controlled spacing here, shield end of lines with %
+\def\@IEEEsavelistparams{\edef\@IEEEiedtopsep{\the\topsep}%
+\edef\@IEEEiedlabelwidth{\the\labelwidth}%
+\edef\@IEEEiedlabelsep{\the\labelsep}%
+\edef\@IEEEiedleftmargin{\the\leftmargin}%
+\edef\@IEEEiedpartopsep{\the\partopsep}%
+\edef\@IEEEiedparsep{\the\parsep}%
+\edef\@IEEEieditemsep{\the\itemsep}%
+\edef\@IEEEiedrightmargin{\the\rightmargin}%
+\edef\@IEEEiedlistparindent{\the\listparindent}%
+\edef\@IEEEieditemindent{\the\itemindent}}
+
+% Note controlled spacing here
+\def\@IEEErestorelistparams{\topsep\@IEEEiedtopsep\relax%
+\labelwidth\@IEEEiedlabelwidth\relax%
+\labelsep\@IEEEiedlabelsep\relax%
+\leftmargin\@IEEEiedleftmargin\relax%
+\partopsep\@IEEEiedpartopsep\relax%
+\parsep\@IEEEiedparsep\relax%
+\itemsep\@IEEEieditemsep\relax%
+\rightmargin\@IEEEiedrightmargin\relax%
+\listparindent\@IEEEiedlistparindent\relax%
+\itemindent\@IEEEieditemindent\relax}
+
+
+% v1.6b provide original LaTeX IED list environments
+% note that latex.ltx defines \itemize and \enumerate, but not \description
+% which must be created by the base classes
+% save original LaTeX itemize and enumerate
+\let\LaTeXitemize\itemize
+\let\endLaTeXitemize\enditemize
+\let\LaTeXenumerate\enumerate
+\let\endLaTeXenumerate\endenumerate
+
+% provide original LaTeX description environment from article.cls
+\newenvironment{LaTeXdescription}
+ {\list{}{\labelwidth\z@ \itemindent-\leftmargin
+ \let\makelabel\descriptionlabel}}
+ {\endlist}
+\newcommand*\descriptionlabel[1]{\hspace\labelsep
+ \normalfont\bfseries #1}
+
+
+% override LaTeX's default IED lists
+\def\itemize{\@IEEEitemize}
+\def\enditemize{\@endIEEEitemize}
+\def\enumerate{\@IEEEenumerate}
+\def\endenumerate{\@endIEEEenumerate}
+\def\description{\@IEEEdescription}
+\def\enddescription{\@endIEEEdescription}
+
+% provide the user with aliases - may help those using packages that
+% override itemize, enumerate, or description
+\def\IEEEitemize{\@IEEEitemize}
+\def\endIEEEitemize{\@endIEEEitemize}
+\def\IEEEenumerate{\@IEEEenumerate}
+\def\endIEEEenumerate{\@endIEEEenumerate}
+\def\IEEEdescription{\@IEEEdescription}
+\def\endIEEEdescription{\@endIEEEdescription}
+
+
+% V1.6 we want to keep the IEEEtran IED list definitions as our own internal
+% commands so they are protected against redefinition
+\def\@IEEEitemize{\@ifnextchar[{\@@IEEEitemize}{\@@IEEEitemize[\relax]}}
+\def\@IEEEenumerate{\@ifnextchar[{\@@IEEEenumerate}{\@@IEEEenumerate[\relax]}}
+\def\@IEEEdescription{\@ifnextchar[{\@@IEEEdescription}{\@@IEEEdescription[\relax]}}
+\def\@endIEEEitemize{\endlist}
+\def\@endIEEEenumerate{\endlist}
+\def\@endIEEEdescription{\endlist}
+
+
+% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
+% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
+% IEEEtran itemized list MDS 1/2001
+% Note controlled spacing here, shield end of lines with %
+\def\@@IEEEitemize[#1]{%
+ \ifnum\@itemdepth>3\relax\@toodeep\else%
+ \ifnum\@listdepth>5\relax\@toodeep\else%
+ \advance\@itemdepth\@ne%
+ \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
+ % get the labelindentfactor for this level
+ \advance\@listdepth\@ne% we need to know what the level WILL be
+ \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
+ \advance\@listdepth-\@ne% undo our increment
+ \def\@IEEEiedjustify{2}% right justified labels are default
+ % set other defaults
+ \IEEEnocalcleftmarginfalse%
+ \IEEEnolabelindentfactorfalse%
+ \topsep\IEEEiedtopsep%
+ \IEEElabelindent\IEEEilabelindent%
+ \labelsep\IEEEiednormlabelsep%
+ \partopsep 0ex%
+ \parsep 0ex%
+ \itemsep 0ex%
+ \rightmargin 0em%
+ \listparindent 0em%
+ \itemindent 0em%
+ % calculate the label width
+ % the user can override this later if
+ % they specified a \labelwidth
+ \settowidth{\labelwidth}{\csname labelitem\romannumeral\the\@itemdepth\endcsname}%
+ \@IEEEsavelistparams% save our list parameters
+ \list{\csname\@itemitem\endcsname}{%
+ \@IEEErestorelistparams% override any list{} changes
+ % to our globals
+ \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
+ \IEEEiedlistdecl% let user alter parameters
+ #1\relax%
+ % If the user has requested not to use the
+ % labelindent factor, don't revise \labelindent
+ \ifIEEEnolabelindentfactor\relax%
+ \else\IEEElabelindent=\IEEElabelindentfactor\labelindent%
+ \fi%
+ % Unless the user has requested otherwise,
+ % calculate our left margin based
+ % on \IEEElabelindent, \labelwidth and
+ % \labelsep
+ \ifIEEEnocalcleftmargin\relax%
+ \else\IEEEcalcleftmargin{\IEEElabelindent}%
+ \fi}\fi\fi}%
+
+
+% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
+% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
+% IEEEtran enumerate list MDS 1/2001
+% Note controlled spacing here, shield end of lines with %
+\def\@@IEEEenumerate[#1]{%
+ \ifnum\@enumdepth>3\relax\@toodeep\else%
+ \ifnum\@listdepth>5\relax\@toodeep\else%
+ \advance\@enumdepth\@ne%
+ \edef\@enumctr{enum\romannumeral\the\@enumdepth}%
+ % get the labelindentfactor for this level
+ \advance\@listdepth\@ne% we need to know what the level WILL be
+ \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
+ \advance\@listdepth-\@ne% undo our increment
+ \def\@IEEEiedjustify{2}% right justified labels are default
+ % set other defaults
+ \IEEEnocalcleftmarginfalse%
+ \IEEEnolabelindentfactorfalse%
+ \topsep\IEEEiedtopsep%
+ \IEEElabelindent\IEEEelabelindent%
+ \labelsep\IEEEiednormlabelsep%
+ \partopsep 0ex%
+ \parsep 0ex%
+ \itemsep 0ex%
+ \rightmargin 0em%
+ \listparindent 0em%
+ \itemindent 0em%
+ % calculate the label width
+ % We'll set it to the width suitable for all labels using
+ % normalfont 1) to 9)
+ % The user can override this later
+ \settowidth{\labelwidth}{9)}%
+ \@IEEEsavelistparams% save our list parameters
+ \list{\csname label\@enumctr\endcsname}{\usecounter{\@enumctr}%
+ \@IEEErestorelistparams% override any list{} changes
+ % to our globals
+ \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
+ \IEEEiedlistdecl% let user alter parameters
+ #1\relax%
+ % If the user has requested not to use the
+ % IEEElabelindent factor, don't revise \IEEElabelindent
+ \ifIEEEnolabelindentfactor\relax%
+ \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent%
+ \fi%
+ % Unless the user has requested otherwise,
+ % calculate our left margin based
+ % on \IEEElabelindent, \labelwidth and
+ % \labelsep
+ \ifIEEEnocalcleftmargin\relax%
+ \else\IEEEcalcleftmargin{\IEEElabelindent}%
+ \fi}\fi\fi}%
+
+
+% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
+% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
+% IEEEtran description list MDS 1/2001
+% Note controlled spacing here, shield end of lines with %
+\def\@@IEEEdescription[#1]{%
+ \ifnum\@listdepth>5\relax\@toodeep\else%
+ % get the labelindentfactor for this level
+ \advance\@listdepth\@ne% we need to know what the level WILL be
+ \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
+ \advance\@listdepth-\@ne% undo our increment
+ \def\@IEEEiedjustify{0}% left justified labels are default
+ % set other defaults
+ \IEEEnocalcleftmarginfalse%
+ \IEEEnolabelindentfactorfalse%
+ \topsep\IEEEiedtopsep%
+ \IEEElabelindent\IEEEdlabelindent%
+ % assume normal labelsep
+ \labelsep\IEEEiednormlabelsep%
+ \partopsep 0ex%
+ \parsep 0ex%
+ \itemsep 0ex%
+ \rightmargin 0em%
+ \listparindent 0em%
+ \itemindent 0em%
+ % Bogus label width in case the user forgets
+ % to set it.
+ % TIP: If you want to see what a variable's width is you
+ % can use the TeX command \showthe\width-variable to
+ % display it on the screen during compilation
+ % (This might be helpful to know when you need to find out
+ % which label is the widest)
+ \settowidth{\labelwidth}{Hello}%
+ \@IEEEsavelistparams% save our list parameters
+ \list{}{\@IEEErestorelistparams% override any list{} changes
+ % to our globals
+ \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
+ \IEEEiedlistdecl% let user alter parameters
+ #1\relax%
+ % If the user has requested not to use the
+ % labelindent factor, don't revise \IEEElabelindent
+ \ifIEEEnolabelindentfactor\relax%
+ \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent%
+ \fi%
+ % Unless the user has requested otherwise,
+ % calculate our left margin based
+ % on \IEEElabelindent, \labelwidth and
+ % \labelsep
+ \ifIEEEnocalcleftmargin\relax%
+ \else\IEEEcalcleftmargin{\IEEElabelindent}\relax%
+ \fi}\fi}
+
+% v1.6b we use one makelabel that does justification as needed.
+\def\@IEEEiedmakelabel#1{\relax\if\@IEEEiedjustify 0\relax
+\makebox[\labelwidth][l]{\normalfont #1}\else
+\if\@IEEEiedjustify 1\relax
+\makebox[\labelwidth][c]{\normalfont #1}\else
+\makebox[\labelwidth][r]{\normalfont #1}\fi\fi}
+
+
+% VERSE and QUOTE
+% V1.7 define environments with newenvironment
+\newenvironment{verse}{\let\\=\@centercr
+ \list{}{\itemsep\z@ \itemindent -1.5em \listparindent \itemindent
+ \rightmargin\leftmargin\advance\leftmargin 1.5em}\item\relax}
+ {\endlist}
+\newenvironment{quotation}{\list{}{\listparindent 1.5em \itemindent\listparindent
+ \rightmargin\leftmargin \parsep 0pt plus 1pt}\item\relax}
+ {\endlist}
+\newenvironment{quote}{\list{}{\rightmargin\leftmargin}\item\relax}
+ {\endlist}
+
+
+% \titlepage
+% provided only for backward compatibility. \maketitle is the correct
+% way to create the title page.
+\newif\if@restonecol
+\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
+ \else \newpage \fi \thispagestyle{empty}\c@page\z@}
+\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}
+
+% standard values from article.cls
+\arraycolsep 5pt
+\arrayrulewidth .4pt
+\doublerulesep 2pt
+
+\tabcolsep 6pt
+\tabbingsep 0.5em
+
+
+%% FOOTNOTES
+%
+%\skip\footins 10pt plus 4pt minus 2pt
+% V1.6 respond to changes in font size
+% space added above the footnotes (if present)
+\skip\footins 0.9\baselineskip plus 0.4\baselineskip minus 0.2\baselineskip
+
+% V1.6, we need to make \footnotesep responsive to changes
+% in \baselineskip or strange spacings will result when in
+% draft mode. Here is a little LaTeX secret - \footnotesep
+% determines the height of an invisible strut that is placed
+% *above* the baseline of footnotes after the first. Since
+% LaTeX considers the space for characters to be 0.7/baselineskip
+% above the baseline and 0.3/baselineskip below it, we need to
+% use 0.7/baselineskip as a \footnotesep to maintain equal spacing
+% between all the lines of the footnotes. IEEE often uses a tad
+% more, so use 0.8\baselineskip. This slightly larger value also helps
+% the text to clear the footnote marks. Note that \thanks in IEEEtran
+% uses its own value of \footnotesep which is set in \maketitle.
+{\footnotesize
+\global\footnotesep 0.8\baselineskip}
+
+
+\skip\@mpfootins = \skip\footins
+\fboxsep = 3pt
+\fboxrule = .4pt
+% V1.6 use 1em, then use LaTeX2e's \@makefnmark
+% Note that IEEE normally *left* aligns the footnote marks, so we don't need
+% box resizing tricks here.
+\long\def\@makefntext#1{\parindent 1em\indent\hbox{\@makefnmark}#1}% V1.6 use 1em
+% V1.7 compsoc does not use superscipts for footnote marks
+\ifCLASSOPTIONcompsoc
+\def\@IEEEcompsocmakefnmark{\hbox{\normalfont\@thefnmark.\ }}
+\long\def\@makefntext#1{\parindent 1em\indent\hbox{\@IEEEcompsocmakefnmark}#1}
+\fi
+
+% IEEE does not use footnote rules
+\def\footnoterule{}
+
+% V1.7 for compsoc, IEEE uses a footnote rule only for \thanks. We devise a "one-shot"
+% system to implement this.
+\newif\if@IEEEenableoneshotfootnoterule
+\@IEEEenableoneshotfootnoterulefalse
+\ifCLASSOPTIONcompsoc
+\def\footnoterule{\relax\if@IEEEenableoneshotfootnoterule
+\kern-5pt
+\hbox to \columnwidth{\hfill\vrule width 0.5\columnwidth height 0.4pt\hfill}
+\kern4.6pt
+\global\@IEEEenableoneshotfootnoterulefalse
+\else
+\relax
+\fi}
+\fi
+
+% V1.6 do not allow LaTeX to break a footnote across multiple pages
+\interfootnotelinepenalty=10000
+
+% V1.6 discourage breaks within equations
+% Note that amsmath normally sets this to 10000,
+% but LaTeX2e normally uses 100.
+\interdisplaylinepenalty=2500
+
+% default allows section depth up to /paragraph
+\setcounter{secnumdepth}{4}
+
+% technotes do not allow /paragraph
+\ifCLASSOPTIONtechnote
+ \setcounter{secnumdepth}{3}
+\fi
+% neither do compsoc conferences
+\@IEEEcompsocconfonly{\setcounter{secnumdepth}{3}}
+
+
+\newcounter{section}
+\newcounter{subsection}[section]
+\newcounter{subsubsection}[subsection]
+\newcounter{paragraph}[subsubsection]
+
+% used only by IEEEtran's IEEEeqnarray as other packages may
+% have their own, different, implementations
+\newcounter{IEEEsubequation}[equation]
+
+% as shown when called by user from \ref, \label and in table of contents
+\def\theequation{\arabic{equation}} % 1
+\def\theIEEEsubequation{\theequation\alph{IEEEsubequation}} % 1a (used only by IEEEtran's IEEEeqnarray)
+\ifCLASSOPTIONcompsoc
+% compsoc is all arabic
+\def\thesection{\arabic{section}}
+\def\thesubsection{\thesection.\arabic{subsection}}
+\def\thesubsubsection{\thesubsection.\arabic{subsubsection}}
+\def\theparagraph{\thesubsubsection.\arabic{paragraph}}
+\else
+\def\thesection{\Roman{section}} % I
+% V1.7, \mbox prevents breaks around -
+\def\thesubsection{\mbox{\thesection-\Alph{subsection}}} % I-A
+% V1.7 use I-A1 format used by IEEE rather than I-A.1
+\def\thesubsubsection{\thesubsection\arabic{subsubsection}} % I-A1
+\def\theparagraph{\thesubsubsection\alph{paragraph}} % I-A1a
+\fi
+
+% From Heiko Oberdiek. Because of the \mbox in \thesubsection, we need to
+% tell hyperref to disable the \mbox command when making PDF bookmarks.
+% This done already with hyperref.sty version 6.74o and later, but
+% it will not hurt to do it here again for users of older versions.
+\@ifundefined{pdfstringdefPreHook}{\let\pdfstringdefPreHook\@empty}{}%
+\g@addto@macro\pdfstringdefPreHook{\let\mbox\relax}
+
+
+% Main text forms (how shown in main text headings)
+% V1.6, using \thesection in \thesectiondis allows changes
+% in the former to automatically appear in the latter
+\ifCLASSOPTIONcompsoc
+ \ifCLASSOPTIONconference% compsoc conference
+ \def\thesectiondis{\thesection.}
+ \def\thesubsectiondis{\thesectiondis\arabic{subsection}.}
+ \def\thesubsubsectiondis{\thesubsectiondis\arabic{subsubsection}.}
+ \def\theparagraphdis{\thesubsubsectiondis\arabic{paragraph}.}
+ \else% compsoc not conferencs
+ \def\thesectiondis{\thesection}
+ \def\thesubsectiondis{\thesectiondis.\arabic{subsection}}
+ \def\thesubsubsectiondis{\thesubsectiondis.\arabic{subsubsection}}
+ \def\theparagraphdis{\thesubsubsectiondis.\arabic{paragraph}}
+ \fi
+\else% not compsoc
+ \def\thesectiondis{\thesection.} % I.
+ \def\thesubsectiondis{\Alph{subsection}.} % B.
+ \def\thesubsubsectiondis{\arabic{subsubsection})} % 3)
+ \def\theparagraphdis{\alph{paragraph})} % d)
+\fi
+
+% just like LaTeX2e's \@eqnnum
+\def\theequationdis{{\normalfont \normalcolor (\theequation)}}% (1)
+% IEEEsubequation used only by IEEEtran's IEEEeqnarray
+\def\theIEEEsubequationdis{{\normalfont \normalcolor (\theIEEEsubequation)}}% (1a)
+% redirect LaTeX2e's equation number display and all that depend on
+% it, through IEEEtran's \theequationdis
+\def\@eqnnum{\theequationdis}
+
+
+
+% V1.7 provide string macros as article.cls does
+\def\contentsname{Contents}
+\def\listfigurename{List of Figures}
+\def\listtablename{List of Tables}
+\def\refname{References}
+\def\indexname{Index}
+\def\figurename{Fig.}
+\def\tablename{TABLE}
+\@IEEEcompsocconfonly{\def\figurename{Figure}\def\tablename{Table}}
+\def\partname{Part}
+\def\appendixname{Appendix}
+\def\abstractname{Abstract}
+% IEEE specific names
+\def\IEEEkeywordsname{Index Terms}
+\def\IEEEproofname{Proof}
+
+
+% LIST OF FIGURES AND TABLES AND TABLE OF CONTENTS
+%
+\def\@pnumwidth{1.55em}
+\def\@tocrmarg{2.55em}
+\def\@dotsep{4.5}
+\setcounter{tocdepth}{3}
+
+% adjusted some spacings here so that section numbers will not easily
+% collide with the section titles.
+% VIII; VIII-A; and VIII-A.1 are usually the worst offenders.
+% MDS 1/2001
+\def\tableofcontents{\section*{\contentsname}\@starttoc{toc}}
+\def\l@section#1#2{\addpenalty{\@secpenalty}\addvspace{1.0em plus 1pt}%
+ \@tempdima 2.75em \begingroup \parindent \z@ \rightskip \@pnumwidth%
+ \parfillskip-\@pnumwidth {\bfseries\leavevmode #1}\hfil\hbox to\@pnumwidth{\hss #2}\par%
+ \endgroup}
+% argument format #1:level, #2:labelindent,#3:labelsep
+\def\l@subsection{\@dottedtocline{2}{2.75em}{3.75em}}
+\def\l@subsubsection{\@dottedtocline{3}{6.5em}{4.5em}}
+% must provide \l@ defs for ALL sublevels EVEN if tocdepth
+% is such as they will not appear in the table of contents
+% these defs are how TOC knows what level these things are!
+\def\l@paragraph{\@dottedtocline{4}{6.5em}{5.5em}}
+\def\l@subparagraph{\@dottedtocline{5}{6.5em}{6.5em}}
+\def\listoffigures{\section*{\listfigurename}\@starttoc{lof}}
+\def\l@figure{\@dottedtocline{1}{0em}{2.75em}}
+\def\listoftables{\section*{\listtablename}\@starttoc{lot}}
+\let\l@table\l@figure
+
+
+%% Definitions for floats
+%%
+%% Normal Floats
+\floatsep 1\baselineskip plus 0.2\baselineskip minus 0.2\baselineskip
+\textfloatsep 1.7\baselineskip plus 0.2\baselineskip minus 0.4\baselineskip
+\@fptop 0pt plus 1fil
+\@fpsep 0.75\baselineskip plus 2fil
+\@fpbot 0pt plus 1fil
+\def\topfraction{0.9}
+\def\bottomfraction{0.4}
+\def\floatpagefraction{0.8}
+% V1.7, let top floats approach 90% of page
+\def\textfraction{0.1}
+
+%% Double Column Floats
+\dblfloatsep 1\baselineskip plus 0.2\baselineskip minus 0.2\baselineskip
+
+\dbltextfloatsep 1.7\baselineskip plus 0.2\baselineskip minus 0.4\baselineskip
+% Note that it would be nice if the rubber here actually worked in LaTeX2e.
+% There is a long standing limitation in LaTeX, first discovered (to the best
+% of my knowledge) by Alan Jeffrey in 1992. LaTeX ignores the stretchable
+% portion of \dbltextfloatsep, and as a result, double column figures can and
+% do result in an non-integer number of lines in the main text columns with
+% underfull vbox errors as a consequence. A post to comp.text.tex
+% by Donald Arseneau confirms that this had not yet been fixed in 1998.
+% IEEEtran V1.6 will fix this problem for you in the titles, but it doesn't
+% protect you from other double floats. Happy vspace'ing.
+
+\@dblfptop 0pt plus 1fil
+\@dblfpsep 0.75\baselineskip plus 2fil
+\@dblfpbot 0pt plus 1fil
+\def\dbltopfraction{0.8}
+\def\dblfloatpagefraction{0.8}
+\setcounter{dbltopnumber}{4}
+
+\intextsep 1\baselineskip plus 0.2\baselineskip minus 0.2\baselineskip
+\setcounter{topnumber}{2}
+\setcounter{bottomnumber}{2}
+\setcounter{totalnumber}{4}
+
+
+
+% article class provides these, we should too.
+\newlength\abovecaptionskip
+\newlength\belowcaptionskip
+% but only \abovecaptionskip is used above figure captions and *below* table
+% captions
+\setlength\abovecaptionskip{0.5\baselineskip}
+\setlength\belowcaptionskip{0pt}
+% V1.6 create hooks in case the caption spacing ever needs to be
+% overridden by a user
+\def\@IEEEfigurecaptionsepspace{\vskip\abovecaptionskip\relax}%
+\def\@IEEEtablecaptionsepspace{\vskip\abovecaptionskip\relax}%
+
+
+% 1.6b revise caption system so that \@makecaption uses two arguments
+% as with LaTeX2e. Otherwise, there will be problems when using hyperref.
+\def\@IEEEtablestring{table}
+
+\ifCLASSOPTIONcompsoc
+% V1.7 compsoc \@makecaption
+\ifCLASSOPTIONconference% compsoc conference
+\long\def\@makecaption#1#2{%
+% test if is a for a figure or table
+\ifx\@captype\@IEEEtablestring%
+% if a table, do table caption
+\normalsize\begin{center}{\normalfont\sffamily\normalsize {#1.}~ #2}\end{center}%
+\@IEEEtablecaptionsepspace
+% if not a table, format it as a figure
+\else
+\@IEEEfigurecaptionsepspace
+\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ #2}%
+\ifdim \wd\@tempboxa >\hsize%
+% if caption is longer than a line, let it wrap around
+\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ }%
+\parbox[t]{\hsize}{\normalfont\sffamily\normalsize \noindent\unhbox\@tempboxa#2}%
+% if caption is shorter than a line, center
+\else%
+\hbox to\hsize{\normalfont\sffamily\normalsize\hfil\box\@tempboxa\hfil}%
+\fi\fi}
+\else% nonconference compsoc
+\long\def\@makecaption#1#2{%
+% test if is a for a figure or table
+\ifx\@captype\@IEEEtablestring%
+% if a table, do table caption
+\normalsize\begin{center}{\normalfont\sffamily\normalsize #1}\\{\normalfont\sffamily\normalsize #2}\end{center}%
+\@IEEEtablecaptionsepspace
+% if not a table, format it as a figure
+\else
+\@IEEEfigurecaptionsepspace
+\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ #2}%
+\ifdim \wd\@tempboxa >\hsize%
+% if caption is longer than a line, let it wrap around
+\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ }%
+\parbox[t]{\hsize}{\normalfont\sffamily\normalsize \noindent\unhbox\@tempboxa#2}%
+% if caption is shorter than a line, left justify
+\else%
+\hbox to\hsize{\normalfont\sffamily\normalsize\box\@tempboxa\hfil}%
+\fi\fi}
+\fi
+
+\else% traditional noncompsoc \@makecaption
+\long\def\@makecaption#1#2{%
+% test if is a for a figure or table
+\ifx\@captype\@IEEEtablestring%
+% if a table, do table caption
+\footnotesize\begin{center}{\normalfont\footnotesize #1}\\{\normalfont\footnotesize\scshape #2}\end{center}%
+\@IEEEtablecaptionsepspace
+% if not a table, format it as a figure
+\else
+\@IEEEfigurecaptionsepspace
+% 3/2001 use footnotesize, not small; use two nonbreaking spaces, not one
+\setbox\@tempboxa\hbox{\normalfont\footnotesize {#1.}~~ #2}%
+\ifdim \wd\@tempboxa >\hsize%
+% if caption is longer than a line, let it wrap around
+\setbox\@tempboxa\hbox{\normalfont\footnotesize {#1.}~~ }%
+\parbox[t]{\hsize}{\normalfont\footnotesize\noindent\unhbox\@tempboxa#2}%
+% if caption is shorter than a line, center if conference, left justify otherwise
+\else%
+\ifCLASSOPTIONconference \hbox to\hsize{\normalfont\footnotesize\hfil\box\@tempboxa\hfil}%
+\else \hbox to\hsize{\normalfont\footnotesize\box\@tempboxa\hfil}%
+\fi\fi\fi}
+\fi
+
+
+
+% V1.7 disable captions class option, do so in a way that retains operation of \label
+% within \caption
+\ifCLASSOPTIONcaptionsoff
+\long\def\@makecaption#1#2{\vspace*{2em}\footnotesize\begin{center}{\footnotesize #1}\end{center}%
+\let\@IEEEtemporiglabeldefsave\label
+\let\@IEEEtemplabelargsave\relax
+\def\label##1{\gdef\@IEEEtemplabelargsave{##1}}%
+\setbox\@tempboxa\hbox{#2}%
+\let\label\@IEEEtemporiglabeldefsave
+\ifx\@IEEEtemplabelargsave\relax\else\label{\@IEEEtemplabelargsave}\fi}
+\fi
+
+
+% V1.7 define end environments with \def not \let so as to work OK with
+% preview-latex
+\newcounter{figure}
+\def\thefigure{\@arabic\c@figure}
+\def\fps@figure{tbp}
+\def\ftype@figure{1}
+\def\ext@figure{lof}
+\def\fnum@figure{\figurename~\thefigure}
+\def\figure{\@float{figure}}
+\def\endfigure{\end@float}
+\@namedef{figure*}{\@dblfloat{figure}}
+\@namedef{endfigure*}{\end@dblfloat}
+\newcounter{table}
+\ifCLASSOPTIONcompsoc
+\def\thetable{\arabic{table}}
+\else
+\def\thetable{\@Roman\c@table}
+\fi
+\def\fps@table{tbp}
+\def\ftype@table{2}
+\def\ext@table{lot}
+\def\fnum@table{\tablename~\thetable}
+% V1.6 IEEE uses 8pt text for tables
+% to default to footnotesize, we hack into LaTeX2e's \@floatboxreset and pray
+\def\table{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@float{table}}
+\def\endtable{\end@float}
+% v1.6b double column tables need to default to footnotesize as well.
+\@namedef{table*}{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@dblfloat{table}}
+\@namedef{endtable*}{\end@dblfloat}
+
+
+
+
+%%
+%% START OF IEEEeqnarry DEFINITIONS
+%%
+%% Inspired by the concepts, examples, and previous works of LaTeX
+%% coders and developers such as Donald Arseneau, Fred Bartlett,
+%% David Carlisle, Tony Liu, Frank Mittelbach, Piet van Oostrum,
+%% Roland Winkler and Mark Wooding.
+%% I don't make the claim that my work here is even near their calibre. ;)
+
+
+% hook to allow easy changeover to IEEEtran.cls/tools.sty error reporting
+\def\@IEEEclspkgerror{\ClassError{IEEEtran}}
+
+\newif\if@IEEEeqnarraystarform% flag to indicate if the environment was called as the star form
+\@IEEEeqnarraystarformfalse
+
+\newif\if@advanceIEEEeqncolcnt% tracks if the environment should advance the col counter
+% allows a way to make an \IEEEeqnarraybox that can be used within an \IEEEeqnarray
+% used by IEEEeqnarraymulticol so that it can work properly in both
+\@advanceIEEEeqncolcnttrue
+
+\newcount\@IEEEeqnnumcols % tracks how many IEEEeqnarray cols are defined
+\newcount\@IEEEeqncolcnt % tracks how many IEEEeqnarray cols the user actually used
+
+
+% The default math style used by the columns
+\def\IEEEeqnarraymathstyle{\displaystyle}
+% The default text style used by the columns
+% default to using the current font
+\def\IEEEeqnarraytextstyle{\relax}
+
+% like the iedlistdecl but for \IEEEeqnarray
+\def\IEEEeqnarraydecl{\relax}
+\def\IEEEeqnarrayboxdecl{\relax}
+
+% \yesnumber is the opposite of \nonumber
+% a novel concept with the same def as the equationarray package
+% However, we give IEEE versions too since some LaTeX packages such as
+% the MDWtools mathenv.sty redefine \nonumber to something else.
+\providecommand{\yesnumber}{\global\@eqnswtrue}
+\def\IEEEyesnumber{\global\@eqnswtrue}
+\def\IEEEnonumber{\global\@eqnswfalse}
+
+
+\def\IEEEyessubnumber{\global\@IEEEissubequationtrue\global\@eqnswtrue%
+\if@IEEEeqnarrayISinner% only do something inside an IEEEeqnarray
+\if@IEEElastlinewassubequation\addtocounter{equation}{-1}\else\setcounter{IEEEsubequation}{1}\fi%
+\def\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\fi}
+
+% flag to indicate that an equation is a sub equation
+\newif\if@IEEEissubequation%
+\@IEEEissubequationfalse
+
+% allows users to "push away" equations that get too close to the equation numbers
+\def\IEEEeqnarraynumspace{\hphantom{\if@IEEEissubequation\theIEEEsubequationdis\else\theequationdis\fi}}
+
+% provides a way to span multiple columns within IEEEeqnarray environments
+% will consider \if@advanceIEEEeqncolcnt before globally advancing the
+% column counter - so as to work within \IEEEeqnarraybox
+% usage: \IEEEeqnarraymulticol{number cols. to span}{col type}{cell text}
+\long\def\IEEEeqnarraymulticol#1#2#3{\multispan{#1}%
+% check if column is defined
+\relax\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined%
+\csname @IEEEeqnarraycolPRE#2\endcsname#3\relax\relax\relax\relax\relax%
+\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST#2\endcsname%
+\else% if not, error and use default type
+\@IEEEclspkgerror{Invalid column type "#2" in \string\IEEEeqnarraymulticol.\MessageBreak
+Using a default centering column instead}%
+{You must define IEEEeqnarray column types before use.}%
+\csname @IEEEeqnarraycolPRE@IEEEdefault\endcsname#3\relax\relax\relax\relax\relax%
+\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST@IEEEdefault\endcsname%
+\fi%
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by #1\relax\fi}
+
+% like \omit, but maintains track of the column counter for \IEEEeqnarray
+\def\IEEEeqnarrayomit{\omit\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by 1\relax\fi}
+
+
+% provides a way to define a letter referenced column type
+% usage: \IEEEeqnarraydefcol{col. type letter/name}{pre insertion text}{post insertion text}
+\def\IEEEeqnarraydefcol#1#2#3{\expandafter\def\csname @IEEEeqnarraycolPRE#1\endcsname{#2}%
+\expandafter\def\csname @IEEEeqnarraycolPOST#1\endcsname{#3}%
+\expandafter\def\csname @IEEEeqnarraycolDEF#1\endcsname{1}}
+
+
+% provides a way to define a numerically referenced inter-column glue types
+% usage: \IEEEeqnarraydefcolsep{col. glue number}{glue definition}
+\def\IEEEeqnarraydefcolsep#1#2{\expandafter\def\csname @IEEEeqnarraycolSEP\romannumeral #1\endcsname{#2}%
+\expandafter\def\csname @IEEEeqnarraycolSEPDEF\romannumeral #1\endcsname{1}}
+
+
+\def\@IEEEeqnarraycolisdefined{1}% just a macro for 1, used for checking undefined column types
+
+
+% expands and appends the given argument to the \@IEEEtrantmptoksA token list
+% used to build up the \halign preamble
+\def\@IEEEappendtoksA#1{\edef\@@IEEEappendtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA #1}}%
+\@@IEEEappendtoksA}
+
+% also appends to \@IEEEtrantmptoksA, but does not expand the argument
+% uses \toks8 as a scratchpad register
+\def\@IEEEappendNOEXPANDtoksA#1{\toks8={#1}%
+\edef\@@IEEEappendNOEXPANDtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA\the\toks8}}%
+\@@IEEEappendNOEXPANDtoksA}
+
+% define some common column types for the user
+% math
+\IEEEeqnarraydefcol{l}{$\IEEEeqnarraymathstyle}{$\hfil}
+\IEEEeqnarraydefcol{c}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}
+\IEEEeqnarraydefcol{r}{\hfil$\IEEEeqnarraymathstyle}{$}
+\IEEEeqnarraydefcol{L}{$\IEEEeqnarraymathstyle{}}{{}$\hfil}
+\IEEEeqnarraydefcol{C}{\hfil$\IEEEeqnarraymathstyle{}}{{}$\hfil}
+\IEEEeqnarraydefcol{R}{\hfil$\IEEEeqnarraymathstyle{}}{{}$}
+% text
+\IEEEeqnarraydefcol{s}{\IEEEeqnarraytextstyle}{\hfil}
+\IEEEeqnarraydefcol{t}{\hfil\IEEEeqnarraytextstyle}{\hfil}
+\IEEEeqnarraydefcol{u}{\hfil\IEEEeqnarraytextstyle}{}
+
+% vertical rules
+\IEEEeqnarraydefcol{v}{}{\vrule width\arrayrulewidth}
+\IEEEeqnarraydefcol{vv}{\vrule width\arrayrulewidth\hfil}{\hfil\vrule width\arrayrulewidth}
+\IEEEeqnarraydefcol{V}{}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}
+\IEEEeqnarraydefcol{VV}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth\hfil}%
+{\hfil\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}
+
+% horizontal rules
+\IEEEeqnarraydefcol{h}{}{\leaders\hrule height\arrayrulewidth\hfil}
+\IEEEeqnarraydefcol{H}{}{\leaders\vbox{\hrule width\arrayrulewidth\vskip\doublerulesep\hrule width\arrayrulewidth}\hfil}
+
+% plain
+\IEEEeqnarraydefcol{x}{}{}
+\IEEEeqnarraydefcol{X}{$}{$}
+
+% the default column type to use in the event a column type is not defined
+\IEEEeqnarraydefcol{@IEEEdefault}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}
+
+
+% a zero tabskip (used for "-" col types)
+\def\@IEEEeqnarraycolSEPzero{0pt plus 0pt minus 0pt}
+% a centering tabskip (used for "+" col types)
+\def\@IEEEeqnarraycolSEPcenter{1000pt plus 0pt minus 1000pt}
+
+% top level default tabskip glues for the start, end, and inter-column
+% may be reset within environments not always at the top level, e.g., \IEEEeqnarraybox
+\edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPcenter}% default start glue
+\edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPcenter}% default end glue
+\edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue
+
+
+
+% creates a vertical rule that extends from the bottom to the top a a cell
+% Provided in case other packages redefine \vline some other way.
+% usage: \IEEEeqnarrayvrule[rule thickness]
+% If no argument is provided, \arrayrulewidth will be used for the rule thickness.
+\newcommand\IEEEeqnarrayvrule[1][\arrayrulewidth]{\vrule\@width#1\relax}
+
+% creates a blank separator row
+% usage: \IEEEeqnarrayseprow[separation length][font size commands]
+% default is \IEEEeqnarrayseprow[0.25\normalbaselineskip][\relax]
+% blank arguments inherit the default values
+% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers
+\def\IEEEeqnarrayseprow{\relax\@ifnextchar[{\@IEEEeqnarrayseprow}{\@IEEEeqnarrayseprow[0.25\normalbaselineskip]}}
+\def\@IEEEeqnarrayseprow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprow[#1]}{\@@IEEEeqnarrayseprow[#1][\relax]}}
+\def\@@IEEEeqnarrayseprow[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%
+\ifx\@IEEEeqnarrayseprowARGONE\@empty%
+% get the skip value, based on the font commands
+% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3
+% assign within a bogus box to confine the font changes
+{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%
+\else%
+{\setbox0=\hbox{#2\relax\global\skip5=#1}}%
+\fi%
+\@IEEEeqnarrayhoptolastcolumn\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}
+
+% creates a blank separator row, but omits all the column templates
+% usage: \IEEEeqnarrayseprowcut[separation length][font size commands]
+% default is \IEEEeqnarrayseprowcut[0.25\normalbaselineskip][\relax]
+% blank arguments inherit the default values
+% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers
+\def\IEEEeqnarrayseprowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
+\@ifnextchar[{\@IEEEeqnarrayseprowcut}{\@IEEEeqnarrayseprowcut[0.25\normalbaselineskip]}}
+\def\@IEEEeqnarrayseprowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprowcut[#1]}{\@@IEEEeqnarrayseprowcut[#1][\relax]}}
+\def\@@IEEEeqnarrayseprowcut[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%
+\ifx\@IEEEeqnarrayseprowARGONE\@empty%
+% get the skip value, based on the font commands
+% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3
+% assign within a bogus box to confine the font changes
+{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%
+\else%
+{\setbox0=\hbox{#2\relax\global\skip5=#1}}%
+\fi%
+\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}
+
+
+
+% draws a single rule across all the columns optional
+% argument determines the rule width, \arrayrulewidth is the default
+% updates column counter as needed and turns off struts
+% usage: \IEEEeqnarrayrulerow[rule line thickness]
+\def\IEEEeqnarrayrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
+\@ifnextchar[{\@IEEEeqnarrayrulerow}{\@IEEEeqnarrayrulerow[\arrayrulewidth]}}
+\def\@IEEEeqnarrayrulerow[#1]{\leaders\hrule height#1\hfil\relax% put in our rule
+% turn off any struts
+\IEEEeqnarraystrutsize{0pt}{0pt}[\relax]\relax}
+
+
+% draws a double rule by using a single rule row, a separator row, and then
+% another single rule row
+% first optional argument determines the rule thicknesses, \arrayrulewidth is the default
+% second optional argument determines the rule spacing, \doublerulesep is the default
+% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]
+\def\IEEEeqnarraydblrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
+\@ifnextchar[{\@IEEEeqnarraydblrulerow}{\@IEEEeqnarraydblrulerow[\arrayrulewidth]}}
+\def\@IEEEeqnarraydblrulerow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerow[#1]}%
+{\@@IEEEeqnarraydblrulerow[#1][\doublerulesep]}}
+\def\@@IEEEeqnarraydblrulerow[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%
+% we allow the user to say \IEEEeqnarraydblrulerow[][]
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%
+\@IEEEeqnarrayrulerow[\arrayrulewidth]%
+\else%
+\@IEEEeqnarrayrulerow[#1]\relax%
+\fi%
+\def\@IEEEeqnarraydblrulerowARG{#2}%
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%
+\\\IEEEeqnarrayseprow[\doublerulesep][\relax]%
+\else%
+\\\IEEEeqnarrayseprow[#2][\relax]%
+\fi%
+\\\multispan{\@IEEEeqnnumcols}%
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
+\def\@IEEEeqnarraydblrulerowARG{#1}%
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%
+\@IEEEeqnarrayrulerow[\arrayrulewidth]%
+\else%
+\@IEEEeqnarrayrulerow[#1]%
+\fi%
+}
+
+% draws a double rule by using a single rule row, a separator (cutting) row, and then
+% another single rule row
+% first optional argument determines the rule thicknesses, \arrayrulewidth is the default
+% second optional argument determines the rule spacing, \doublerulesep is the default
+% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]
+\def\IEEEeqnarraydblrulerowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
+\@ifnextchar[{\@IEEEeqnarraydblrulerowcut}{\@IEEEeqnarraydblrulerowcut[\arrayrulewidth]}}
+\def\@IEEEeqnarraydblrulerowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerowcut[#1]}%
+{\@@IEEEeqnarraydblrulerowcut[#1][\doublerulesep]}}
+\def\@@IEEEeqnarraydblrulerowcut[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%
+% we allow the user to say \IEEEeqnarraydblrulerow[][]
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%
+\@IEEEeqnarrayrulerow[\arrayrulewidth]%
+\else%
+\@IEEEeqnarrayrulerow[#1]%
+\fi%
+\def\@IEEEeqnarraydblrulerowARG{#2}%
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%
+\\\IEEEeqnarrayseprowcut[\doublerulesep][\relax]%
+\else%
+\\\IEEEeqnarrayseprowcut[#2][\relax]%
+\fi%
+\\\multispan{\@IEEEeqnnumcols}%
+% advance column counter only if the IEEEeqnarray environment wants it
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
+\def\@IEEEeqnarraydblrulerowARG{#1}%
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%
+\@IEEEeqnarrayrulerow[\arrayrulewidth]%
+\else%
+\@IEEEeqnarrayrulerow[#1]%
+\fi%
+}
+
+
+
+% inserts a full row's worth of &'s
+% relies on \@IEEEeqnnumcols to provide the correct number of columns
+% uses \@IEEEtrantmptoksA, \count0 as scratch registers
+\def\@IEEEeqnarrayhoptolastcolumn{\@IEEEtrantmptoksA={}\count0=1\relax%
+\loop% add cols if the user did not use them all
+\ifnum\count0<\@IEEEeqnnumcols\relax%
+\@IEEEappendtoksA{&}%
+\advance\count0 by 1\relax% update the col count
+\repeat%
+\the\@IEEEtrantmptoksA%execute the &'s
+}
+
+
+
+\newif\if@IEEEeqnarrayISinner % flag to indicate if we are within the lines
+\@IEEEeqnarrayISinnerfalse % of an IEEEeqnarray - after the IEEEeqnarraydecl
+
+\edef\@IEEEeqnarrayTHEstrutheight{0pt} % height and depth of IEEEeqnarray struts
+\edef\@IEEEeqnarrayTHEstrutdepth{0pt}
+
+\edef\@IEEEeqnarrayTHEmasterstrutheight{0pt} % default height and depth of
+\edef\@IEEEeqnarrayTHEmasterstrutdepth{0pt} % struts within an IEEEeqnarray
+
+\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{0pt} % saved master strut height
+\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{0pt} % and depth
+
+\newif\if@IEEEeqnarrayusemasterstrut % flag to indicate that the master strut value
+\@IEEEeqnarrayusemasterstruttrue % is to be used
+
+
+
+% saves the strut height and depth of the master strut
+\def\@IEEEeqnarraymasterstrutsave{\relax%
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
+% remove stretchability
+\dimen0\skip0\relax%
+\dimen2\skip2\relax%
+% save values
+\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{\the\dimen2}}
+
+% restores the strut height and depth of the master strut
+\def\@IEEEeqnarraymasterstrutrestore{\relax%
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutHSAVE\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutDSAVE\relax%
+% remove stretchability
+\dimen0\skip0\relax%
+\dimen2\skip2\relax%
+% restore values
+\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}}
+
+
+% globally restores the strut height and depth to the
+% master values and sets the master strut flag to true
+\def\@IEEEeqnarraystrutreset{\relax%
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
+% remove stretchability
+\dimen0\skip0\relax%
+\dimen2\skip2\relax%
+% restore values
+\xdef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
+\xdef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
+\global\@IEEEeqnarrayusemasterstruttrue}
+
+
+% if the master strut is not to be used, make the current
+% values of \@IEEEeqnarrayTHEstrutheight, \@IEEEeqnarrayTHEstrutdepth
+% and the use master strut flag, global
+% this allows user strut commands issued in the last column to be carried
+% into the isolation/strut column
+\def\@IEEEeqnarrayglobalizestrutstatus{\relax%
+\if@IEEEeqnarrayusemasterstrut\else%
+\xdef\@IEEEeqnarrayTHEstrutheight{\@IEEEeqnarrayTHEstrutheight}%
+\xdef\@IEEEeqnarrayTHEstrutdepth{\@IEEEeqnarrayTHEstrutdepth}%
+\global\@IEEEeqnarrayusemasterstrutfalse%
+\fi}
+
+
+
+% usage: \IEEEeqnarraystrutsize{height}{depth}[font size commands]
+% If called outside the lines of an IEEEeqnarray, sets the height
+% and depth of both the master and local struts. If called inside
+% an IEEEeqnarray line, sets the height and depth of the local strut
+% only and sets the flag to indicate the use of the local strut
+% values. If the height or depth is left blank, 0.7\normalbaselineskip
+% and 0.3\normalbaselineskip will be used, respectively.
+% The optional argument can be used to evaluate the lengths under
+% a different font size and styles. If none is specified, the current
+% font is used.
+% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2
+\def\IEEEeqnarraystrutsize#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsize{#1}{#2}}{\@IEEEeqnarraystrutsize{#1}{#2}[\relax]}}
+\def\@IEEEeqnarraystrutsize#1#2[#3]{\def\@IEEEeqnarraystrutsizeARG{#1}%
+\ifx\@IEEEeqnarraystrutsizeARG\@empty%
+{\setbox0=\hbox{#3\relax\global\skip3=0.7\normalbaselineskip}}%
+\skip0=\skip3\relax%
+\else% arg one present
+{\setbox0=\hbox{#3\relax\global\skip3=#1\relax}}%
+\skip0=\skip3\relax%
+\fi% if null arg
+\def\@IEEEeqnarraystrutsizeARG{#2}%
+\ifx\@IEEEeqnarraystrutsizeARG\@empty%
+{\setbox0=\hbox{#3\relax\global\skip3=0.3\normalbaselineskip}}%
+\skip2=\skip3\relax%
+\else% arg two present
+{\setbox0=\hbox{#3\relax\global\skip3=#2\relax}}%
+\skip2=\skip3\relax%
+\fi% if null arg
+% remove stretchability, just to be safe
+\dimen0\skip0\relax%
+\dimen2\skip2\relax%
+% dimen0 = height, dimen2 = depth
+\if@IEEEeqnarrayISinner% inner does not touch master strut size
+\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
+\@IEEEeqnarrayusemasterstrutfalse% do not use master
+\else% outer, have to set master strut too
+\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%
+\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
+\@IEEEeqnarrayusemasterstruttrue% use master strut
+\fi}
+
+
+% usage: \IEEEeqnarraystrutsizeadd{added height}{added depth}[font size commands]
+% If called outside the lines of an IEEEeqnarray, adds the given height
+% and depth to both the master and local struts.
+% If called inside an IEEEeqnarray line, adds the given height and depth
+% to the local strut only and sets the flag to indicate the use
+% of the local strut values.
+% In both cases, if a height or depth is left blank, 0pt is used instead.
+% The optional argument can be used to evaluate the lengths under
+% a different font size and styles. If none is specified, the current
+% font is used.
+% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2
+\def\IEEEeqnarraystrutsizeadd#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsizeadd{#1}{#2}}{\@IEEEeqnarraystrutsizeadd{#1}{#2}[\relax]}}
+\def\@IEEEeqnarraystrutsizeadd#1#2[#3]{\def\@IEEEeqnarraystrutsizearg{#1}%
+\ifx\@IEEEeqnarraystrutsizearg\@empty%
+\skip0=0pt\relax%
+\else% arg one present
+{\setbox0=\hbox{#3\relax\global\skip3=#1}}%
+\skip0=\skip3\relax%
+\fi% if null arg
+\def\@IEEEeqnarraystrutsizearg{#2}%
+\ifx\@IEEEeqnarraystrutsizearg\@empty%
+\skip2=0pt\relax%
+\else% arg two present
+{\setbox0=\hbox{#3\relax\global\skip3=#2}}%
+\skip2=\skip3\relax%
+\fi% if null arg
+% remove stretchability, just to be safe
+\dimen0\skip0\relax%
+\dimen2\skip2\relax%
+% dimen0 = height, dimen2 = depth
+\if@IEEEeqnarrayISinner% inner does not touch master strut size
+% get local strut size
+\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%
+% add it to the user supplied values
+\advance\dimen0 by \skip0\relax%
+\advance\dimen2 by \skip2\relax%
+% update the local strut size
+\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
+\@IEEEeqnarrayusemasterstrutfalse% do not use master
+\else% outer, have to set master strut too
+% get master strut size
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
+% add it to the user supplied values
+\advance\dimen0 by \skip0\relax%
+\advance\dimen2 by \skip2\relax%
+% update the local and master strut sizes
+\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%
+\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
+\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
+\@IEEEeqnarrayusemasterstruttrue% use master strut
+\fi}
+
+
+% allow user a way to see the struts
+\newif\ifIEEEvisiblestruts
+\IEEEvisiblestrutsfalse
+
+% inserts an invisible strut using the master or local strut values
+% uses scratch registers \skip0, \skip2, \dimen0, \dimen2
+\def\@IEEEeqnarrayinsertstrut{\relax%
+\if@IEEEeqnarrayusemasterstrut
+% get master strut size
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
+\else%
+% get local strut size
+\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%
+\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%
+\fi%
+% remove stretchability, probably not needed
+\dimen0\skip0\relax%
+\dimen2\skip2\relax%
+% dimen0 = height, dimen2 = depth
+% allow user to see struts if desired
+\ifIEEEvisiblestruts%
+\vrule width0.2pt 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}
+
+
+
+\def\IEEEeqnarray{\@IEEEeqnarraystarformfalse\@IEEEeqnarray}
+\def\endIEEEeqnarray{\end@IEEEeqnarray}
+
+\@namedef{IEEEeqnarray*}{\@IEEEeqnarraystarformtrue\@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@IEEEeqnarraystarform\global\@eqnswfalse
+ \else% not the star form
+ \global\@eqnswtrue
+ \fi% if star form
+ \@IEEEissubequationfalse% default to no subequations
+ \@IEEElastlinewassubequationfalse% assume last line is not a sub equation
+ \@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
+ \stepcounter{equation}% advance equation counter before first line
+ \setcounter{IEEEsubequation}{0}% no subequation yet
+ \def\@currentlabel{\p@equation\theequation}% redefine the ref 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\end\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
+ $$\everycr{}\halign to\displaywidth\bgroup
+ % "exspand" the preamble
+ \span\the\@IEEEtrantmptoksA\cr}
+
+% enter isolation/strut column (or the next column if the user did not use
+% every column), record the strut status, complete the columns, do the strut if needed,
+% restore counters to correct values and exit
+\def\end@IEEEeqnarray{\@IEEEeqnarrayglobalizestrutstatus&\@@IEEEeqnarraycr\egroup%
+\if@IEEElastlinewassubequation\global\advance\c@IEEEsubequation\m@ne\fi%
+\global\advance\c@equation\m@ne%
+$$\@ignoretrue}
+
+% need a way to remember if last line is a subequation
+\newif\if@IEEElastlinewassubequation%
+\@IEEElastlinewassubequationfalse
+
+% IEEEeqnarray 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
+% 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 IEEEeqnarry 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
+ % is this line needs an equation number, display it and advance the
+ % (sub)equation counters, record what type this line was
+ \if@eqnsw%
+ \if@IEEEissubequation\theIEEEsubequationdis\addtocounter{equation}{1}\stepcounter{IEEEsubequation}%
+ \global\@IEEElastlinewassubequationtrue%
+ \else% display a standard equation number, initialize the IEEEsubequation counter
+ \theequationdis\stepcounter{equation}\setcounter{IEEEsubequation}{0}%
+ \global\@IEEElastlinewassubequationfalse\fi%
+ \fi%
+ % reset the eqnsw flag to indicate default preference of the display of equation numbers
+ \if@IEEEeqnarraystarform\global\@eqnswfalse\else\global\@eqnswtrue\fi
+ \global\@IEEEissubequationfalse% reset 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{$ $} construct.
+% \IEEEeqnarraybox will auto detect whether to use \IEEEeqnarrayboxm or
+% \IEEEeqnarrayboxt depending on the math mode.
+% The third optional argument specifies the width this box is to be set to -
+% natural width is the default.
+% The * forms do not add \jot line spacing
+% usage: \IEEEeqnarraybox[decl][pos][width]{cols}
+\def\IEEEeqnarrayboxm{\@IEEEeqnarraystarformfalse\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}
+\def\endIEEEeqnarrayboxm{\end@IEEEeqnarraybox}
+\@namedef{IEEEeqnarrayboxm*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}
+\@namedef{endIEEEeqnarrayboxm*}{\end@IEEEeqnarraybox}
+
+\def\IEEEeqnarrayboxt{\@IEEEeqnarraystarformfalse\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}
+\def\endIEEEeqnarrayboxt{\end@IEEEeqnarraybox}
+\@namedef{IEEEeqnarrayboxt*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}
+\@namedef{endIEEEeqnarrayboxt*}{\end@IEEEeqnarraybox}
+
+\def\IEEEeqnarraybox{\@IEEEeqnarraystarformfalse\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%
+\@IEEEeqnarraybox}
+\def\endIEEEeqnarraybox{\end@IEEEeqnarraybox}
+
+\@namedef{IEEEeqnarraybox*}{\@IEEEeqnarraystarformtrue\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%
+\@IEEEeqnarraybox}
+\@namedef{endIEEEeqnarraybox*}{\end@IEEEeqnarraybox}
+
+% flag to indicate if the \IEEEeqnarraybox needs to put things into an hbox{$ $}
+% 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\end\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
+ % this stops some problems when the user uses more than one letter,
+ % but is probably not worth the effort
+ % \noindent is used as a delimiter
+ \def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%
+ \@IEEEgrabfirstoken#2\relax\relax\noindent
+ % \@IEEEgrabbedfirstoken has the first token, the rest are discarded
+ % 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\@IEEEgrabbedfirstoken t\relax\vtop\else\if\@IEEEgrabbedfirstoken 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@IEEEeqnarraystarform\else\vskip\jot\fi\vskip#1\relax}}
+
+
+
+% starts the halign preamble build
+\def\@IEEEbuildpreamble{\@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}%
+% now parse the user's column specifications
+\@@IEEEbuildpreamble}
+
+
+% parses and builds the halign preamble
+\def\@@IEEEbuildpreamble#1#2{\let\@@nextIEEEbuildpreamble=\@@IEEEbuildpreamble%
+% use only the very first token to check the end
+% \noindent is used as a delimiter as \end can be present here
+\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%
+\@IEEEgrabfirstoken#1\relax\relax\noindent
+\ifx\@IEEEgrabbedfirstoken\end\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}}
+
+
+% executed just after preamble build is completed
+% warn about zero cols, and if prevtype type = u, put in end tabskip glue
+\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}
+
+
+% Identify and return the column specifier's type code
+\def\@IEEEgetcoltype#1#2#3{%
+% use only the very first token to determine the type
+% \noindent is used as a delimiter as \end can be present here
+\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%
+\@IEEEgrabfirstoken#1\relax\relax\noindent
+% \@IEEEgrabfirstoken has the first token, the rest are discarded
+% n = number
+% g = glue (any other char in catagory 12)
+% c = letter
+% e = \end
+% u = undefined
+% third argument: 0 = no error message, 1 = error on invalid char
+\let#2=u\relax% assume invalid until know otherwise
+\ifx\@IEEEgrabbedfirstoken\end\let#2=e\else
+\ifcat\@IEEEgrabbedfirstoken\relax\else% screen out control sequences
+\if0\@IEEEgrabbedfirstoken\let#2=n\else
+\if1\@IEEEgrabbedfirstoken\let#2=n\else
+\if2\@IEEEgrabbedfirstoken\let#2=n\else
+\if3\@IEEEgrabbedfirstoken\let#2=n\else
+\if4\@IEEEgrabbedfirstoken\let#2=n\else
+\if5\@IEEEgrabbedfirstoken\let#2=n\else
+\if6\@IEEEgrabbedfirstoken\let#2=n\else
+\if7\@IEEEgrabbedfirstoken\let#2=n\else
+\if8\@IEEEgrabbedfirstoken\let#2=n\else
+\if9\@IEEEgrabbedfirstoken\let#2=n\else
+\ifcat,\@IEEEgrabbedfirstoken\let#2=g\relax
+\else\ifcat a\@IEEEgrabbedfirstoken\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}
+
+
+% identify the current letter referenced column
+% if invalid, use a default column
+\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}
+
+
+% identify and return the predefined (punctuation) glue value
+\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
+% this prevents errant tokens from getting in the main text
+% \noindent is used as a delimiter here
+\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%
+\@IEEEgrabfirstoken#1\relax\relax\noindent
+% 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!\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=-0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if,\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if:\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.22222\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if;\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.27778\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if'\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=1\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if"\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=2\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if.\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.5\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if/\@IEEEgrabbedfirstoken\edef#2{\the\arraycolsep}\else
+\if?\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=2\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else
+\if *\@IEEEgrabbedfirstoken\edef#2{0pt plus 1fil minus 0pt}\else
+\if+\@IEEEgrabbedfirstoken\edef#2{\@IEEEeqnarraycolSEPcenter}\else
+\if-\@IEEEgrabbedfirstoken\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}
+
+
+
+% 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 IEEEeqnarry DEFINITIONS
+%%
+
+
+
+
+% set up the running headings, this complex because of all the different
+% modes IEEEtran supports
+\if@twoside
+ \ifCLASSOPTIONtechnote
+ \def\ps@headings{%
+ \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}
+ \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}
+ \ifCLASSOPTIONdraftcls
+ \ifCLASSOPTIONdraftclsnofoot
+ \def\@oddfoot{}\def\@evenfoot{}%
+ \else
+ \def\@oddfoot{\scriptsize\@date\hfil DRAFT}
+ \def\@evenfoot{\scriptsize DRAFT\hfil\@date}
+ \fi
+ \else
+ \def\@oddfoot{}\def\@evenfoot{}
+ \fi}
+ \else % not a technote
+ \def\ps@headings{%
+ \ifCLASSOPTIONconference
+ \def\@oddhead{}
+ \def\@evenhead{}
+ \else
+ \def\@oddhead{\hbox{}\scriptsize\rightmark \hfil \thepage}
+ \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}
+ \fi
+ \ifCLASSOPTIONdraftcls
+ \def\@oddhead{\hbox{}\scriptsize\rightmark \hfil \thepage}
+ \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}
+ \ifCLASSOPTIONdraftclsnofoot
+ \def\@oddfoot{}\def\@evenfoot{}%
+ \else
+ \def\@oddfoot{\scriptsize\@date\hfil DRAFT}
+ \def\@evenfoot{\scriptsize DRAFT\hfil\@date}
+ \fi
+ \else
+ \def\@oddfoot{}\def\@evenfoot{}%
+ \fi}
+ \fi
+\else % single side
+\def\ps@headings{%
+ \ifCLASSOPTIONconference
+ \def\@oddhead{}
+ \def\@evenhead{}
+ \else
+ \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}
+ \def\@evenhead{}
+ \fi
+ \ifCLASSOPTIONdraftcls
+ \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}
+ \def\@evenhead{}
+ \ifCLASSOPTIONdraftclsnofoot
+ \def\@oddfoot{}
+ \else
+ \def\@oddfoot{\scriptsize \@date \hfil DRAFT}
+ \fi
+ \else
+ \def\@oddfoot{}
+ \fi
+ \def\@evenfoot{}}
+\fi
+
+
+% title page style
+\def\ps@IEEEtitlepagestyle{\def\@oddfoot{}\def\@evenfoot{}%
+\ifCLASSOPTIONconference
+ \def\@oddhead{}%
+ \def\@evenhead{}%
+\else
+ \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}%
+ \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}%
+\fi
+\ifCLASSOPTIONdraftcls
+ \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}%
+ \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}%
+ \ifCLASSOPTIONdraftclsnofoot\else
+ \def\@oddfoot{\scriptsize \@date\hfil DRAFT}%
+ \def\@evenfoot{\scriptsize DRAFT\hfil \@date}%
+ \fi
+\else
+ % all non-draft mode footers
+ \if@IEEEusingpubid
+ % for title pages that are using a pubid
+ % do not repeat pubid if using peer review option
+ \ifCLASSOPTIONpeerreview
+ \else
+ \footskip 0pt%
+ \ifCLASSOPTIONcompsoc
+ \def\@oddfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}%
+ \def\@evenfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}%
+ \else
+ \def\@oddfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}%
+ \def\@evenfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}%
+ \fi
+ \fi
+ \fi
+\fi}
+
+
+% peer review cover page style
+\def\ps@IEEEpeerreviewcoverpagestyle{%
+\def\@oddhead{}\def\@evenhead{}%
+\def\@oddfoot{}\def\@evenfoot{}%
+\ifCLASSOPTIONdraftcls
+ \ifCLASSOPTIONdraftclsnofoot\else
+ \def\@oddfoot{\scriptsize \@date\hfil DRAFT}%
+ \def\@evenfoot{\scriptsize DRAFT\hfil \@date}%
+ \fi
+\else
+ % non-draft mode footers
+ \if@IEEEusingpubid
+ \footskip 0pt%
+ \ifCLASSOPTIONcompsoc
+ \def\@oddfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}%
+ \def\@evenfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}%
+ \else
+ \def\@oddfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}%
+ \def\@evenfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}%
+ \fi
+ \fi
+\fi}
+
+
+% start with empty headings
+\def\rightmark{}\def\leftmark{}
+
+
+%% Defines the command for putting the header. \footernote{TEXT} is the same
+%% as \markboth{TEXT}{TEXT}.
+%% Note that all the text is forced into uppercase, if you have some text
+%% that needs to be in lower case, for instance et. al., then either manually
+%% set \leftmark and \rightmark or use \MakeLowercase{et. al.} within the
+%% arguments to \markboth.
+\def\markboth#1#2{\def\leftmark{\@IEEEcompsoconly{\sffamily}\MakeUppercase{#1}}%
+\def\rightmark{\@IEEEcompsoconly{\sffamily}\MakeUppercase{#2}}}
+\def\footernote#1{\markboth{#1}{#1}}
+
+\def\today{\ifcase\month\or
+ January\or February\or March\or April\or May\or June\or
+ July\or August\or September\or October\or November\or December\fi
+ \space\number\day, \number\year}
+
+
+
+
+%% CITATION AND BIBLIOGRAPHY COMMANDS
+%%
+%% V1.6 no longer supports the older, nonstandard \shortcite and \citename setup stuff
+%
+%
+% Modify Latex2e \@citex to separate citations with "], ["
+\def\@citex[#1]#2{%
+ \let\@citea\@empty
+ \@cite{\@for\@citeb:=#2\do
+ {\@citea\def\@citea{], [}%
+ \edef\@citeb{\expandafter\@firstofone\@citeb\@empty}%
+ \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
+ \@ifundefined{b@\@citeb}{\mbox{\reset@font\bfseries ?}%
+ \G@refundefinedtrue
+ \@latex@warning
+ {Citation `\@citeb' on page \thepage \space undefined}}%
+ {\hbox{\csname b@\@citeb\endcsname}}}}{#1}}
+
+% V1.6 we create hooks for the optional use of Donald Arseneau's
+% cite.sty package. cite.sty is "smart" and will notice that the
+% following format controls are already defined and will not
+% redefine them. The result will be the proper sorting of the
+% citation numbers and auto detection of 3 or more entry "ranges" -
+% all in IEEE style: [1], [2], [5]--[7], [12]
+% This also allows for an optional note, i.e., \cite[mynote]{..}.
+% If the \cite with note has more than one reference, the note will
+% be applied to the last of the listed references. It is generally
+% desired that if a note is given, only one reference is listed in
+% that \cite.
+% Thanks to Mr. Arseneau for providing the required format arguments
+% to produce the IEEE style.
+\def\citepunct{], [}
+\def\citedash{]--[}
+
+% V1.7 default to using same font for urls made by url.sty
+\AtBeginDocument{\csname url@samestyle\endcsname}
+
+% V1.6 class files should always provide these
+\def\newblock{\hskip .11em\@plus.33em\@minus.07em}
+\let\@openbib@code\@empty
+
+
+% Provide support for the control entries of IEEEtran.bst V1.00 and later.
+% V1.7 optional argument allows for a different aux file to be specified in
+% order to handle multiple bibliographies. For example, with multibib.sty:
+% \newcites{sec}{Secondary Literature}
+% \bstctlcite[@auxoutsec]{BSTcontrolhak}
+\def\bstctlcite{\@ifnextchar[{\@bstctlcite}{\@bstctlcite[@auxout]}}
+\def\@bstctlcite[#1]#2{\@bsphack
+ \@for\@citeb:=#2\do{%
+ \edef\@citeb{\expandafter\@firstofone\@citeb}%
+ \if@filesw\immediate\write\csname #1\endcsname{\string\citation{\@citeb}}\fi}%
+ \@esphack}
+
+% V1.6 provide a way for a user to execute a command just before
+% a given reference number - used to insert a \newpage to balance
+% the columns on the last page
+\edef\@IEEEtriggerrefnum{0} % the default of zero means that
+ % the command is not executed
+\def\@IEEEtriggercmd{\newpage}
+
+% allow the user to alter the triggered command
+\long\def\IEEEtriggercmd#1{\long\def\@IEEEtriggercmd{#1}}
+
+% allow user a way to specify the reference number just before the
+% command is executed
+\def\IEEEtriggeratref#1{\@IEEEtrantmpcountA=#1%
+\edef\@IEEEtriggerrefnum{\the\@IEEEtrantmpcountA}}%
+
+% trigger command at the given reference
+\def\@IEEEbibitemprefix{\@IEEEtrantmpcountA=\@IEEEtriggerrefnum\relax%
+\advance\@IEEEtrantmpcountA by -1\relax%
+\ifnum\c@enumiv=\@IEEEtrantmpcountA\relax\@IEEEtriggercmd\relax\fi}
+
+
+\def\@biblabel#1{[#1]}
+
+% compsoc journals left align the reference numbers
+\@IEEEcompsocnotconfonly{\def\@biblabel#1{[#1]\hfill}}
+
+% controls bib item spacing
+\def\IEEEbibitemsep{0pt plus .5pt}
+
+\@IEEEcompsocconfonly{\def\IEEEbibitemsep{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}}
+
+
+\def\thebibliography#1{\section*{\refname}%
+ \addcontentsline{toc}{section}{\refname}%
+ % V1.6 add some rubber space here and provide a command trigger
+ \footnotesize\@IEEEcompsocconfonly{\small}\vskip 0.3\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip%
+ \list{\@biblabel{\@arabic\c@enumiv}}%
+ {\settowidth\labelwidth{\@biblabel{#1}}%
+ \leftmargin\labelwidth
+ \advance\leftmargin\labelsep\relax
+ \itemsep \IEEEbibitemsep\relax
+ \usecounter{enumiv}%
+ \let\p@enumiv\@empty
+ \renewcommand\theenumiv{\@arabic\c@enumiv}}%
+ \let\@IEEElatexbibitem\bibitem%
+ \def\bibitem{\@IEEEbibitemprefix\@IEEElatexbibitem}%
+\def\newblock{\hskip .11em plus .33em minus .07em}%
+% originally:
+% \sloppy\clubpenalty4000\widowpenalty4000%
+% by adding the \interlinepenalty here, we make it more
+% difficult, but not impossible, for LaTeX to break within a reference.
+% IEEE almost never breaks a reference (but they do it more often with
+% technotes). You may get an underfull vbox warning around the bibliography,
+% but the final result will be much more like what IEEE will publish.
+% MDS 11/2000
+\ifCLASSOPTIONtechnote\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty100%
+\else\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty500\fi%
+ \sfcode`\.=1000\relax}
+\let\endthebibliography=\endlist
+
+
+
+
+% TITLE PAGE COMMANDS
+%
+%
+% \IEEEmembership is used to produce the sublargesize italic font used to indicate author
+% IEEE membership. compsoc uses a large size sans slant font
+\def\IEEEmembership#1{{\@IEEEnotcompsoconly{\sublargesize}\normalfont\@IEEEcompsoconly{\sffamily}\textit{#1}}}
+
+
+% \IEEEauthorrefmark{} produces a footnote type symbol to indicate author affiliation.
+% When given an argument of 1 to 9, \IEEEauthorrefmark{} follows the standard LaTeX footnote
+% symbol sequence convention. However, for arguments 10 and above, \IEEEauthorrefmark{}
+% reverts to using lower case roman numerals, so it cannot overflow. Do note that you
+% cannot use \footnotemark[] in place of \IEEEauthorrefmark{} within \author as the footnote
+% symbols will have been turned off to prevent \thanks from creating footnote marks.
+% \IEEEauthorrefmark{} produces a symbol that appears to LaTeX as having zero vertical
+% height - this allows for a more compact line packing, but the user must ensure that
+% the interline spacing is large enough to prevent \IEEEauthorrefmark{} from colliding
+% with the text above.
+% V1.7 make this a robust command
+\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}}}}
+
+
+% FONT CONTROLS AND SPACINGS FOR CONFERENCE MODE AUTHOR NAME AND AFFILIATION BLOCKS
+%
+% The default font styles for the author name and affiliation blocks (confmode)
+\def\@IEEEauthorblockNstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\sublargesize\@IEEEcompsocconfonly{\large}}
+\def\@IEEEauthorblockAstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\@IEEEcompsocconfonly{\itshape}\normalsize\@IEEEcompsocconfonly{\large}}
+% The default if the user does not use an author block
+\def\@IEEEauthordefaulttextstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\sublargesize}
+
+% spacing from title (or special paper notice) to author name blocks (confmode)
+% can be negative
+\def\@IEEEauthorblockconfadjspace{-0.25em}
+% compsoc conferences need more space here
+\@IEEEcompsocconfonly{\def\@IEEEauthorblockconfadjspace{0.75\@IEEEnormalsizeunitybaselineskip}}
+
+% spacing between name and affiliation blocks (confmode)
+% This can be negative.
+% IEEE doesn't want any added spacing here, but I will leave these
+% controls in place in case they ever change their mind.
+% Personally, I like 0.75ex.
+%\def\@IEEEauthorblockNtopspace{0.75ex}
+%\def\@IEEEauthorblockAtopspace{0.75ex}
+\def\@IEEEauthorblockNtopspace{0.0ex}
+\def\@IEEEauthorblockAtopspace{0.0ex}
+% baseline spacing within name and affiliation blocks (confmode)
+% must be positive, spacings below certain values will make
+% the position of line of text sensitive to the contents of the
+% line above it i.e., whether or not the prior line has descenders,
+% subscripts, etc. For this reason it is a good idea to keep
+% these above 2.6ex
+\def\@IEEEauthorblockNinterlinespace{2.6ex}
+\def\@IEEEauthorblockAinterlinespace{2.75ex}
+
+% This tracks the required strut size.
+% See the \@IEEEauthorhalign command for the actual default value used.
+\def\@IEEEauthorblockXinterlinespace{2.7ex}
+
+% variables to retain font size and style across groups
+% values given here have no effect as they will be overwritten later
+\gdef\@IEEESAVESTATEfontsize{10}
+\gdef\@IEEESAVESTATEfontbaselineskip{12}
+\gdef\@IEEESAVESTATEfontencoding{OT1}
+\gdef\@IEEESAVESTATEfontfamily{ptm}
+\gdef\@IEEESAVESTATEfontseries{m}
+\gdef\@IEEESAVESTATEfontshape{n}
+
+% saves the current font attributes
+\def\@IEEEcurfontSAVE{\global\let\@IEEESAVESTATEfontsize\f@size%
+\global\let\@IEEESAVESTATEfontbaselineskip\f@baselineskip%
+\global\let\@IEEESAVESTATEfontencoding\f@encoding%
+\global\let\@IEEESAVESTATEfontfamily\f@family%
+\global\let\@IEEESAVESTATEfontseries\f@series%
+\global\let\@IEEESAVESTATEfontshape\f@shape}
+
+% restores the saved font attributes
+\def\@IEEEcurfontRESTORE{\fontsize{\@IEEESAVESTATEfontsize}{\@IEEESAVESTATEfontbaselineskip}%
+\fontencoding{\@IEEESAVESTATEfontencoding}%
+\fontfamily{\@IEEESAVESTATEfontfamily}%
+\fontseries{\@IEEESAVESTATEfontseries}%
+\fontshape{\@IEEESAVESTATEfontshape}%
+\selectfont}
+
+
+% variable to indicate if the current block is the first block in the column
+\newif\if@IEEEprevauthorblockincol \@IEEEprevauthorblockincolfalse
+
+
+% the command places a strut with height and depth = \@IEEEauthorblockXinterlinespace
+% we use this technique to have complete manual control over the spacing of the lines
+% within the halign environment.
+% We set the below baseline portion at 30%, the above
+% baseline portion at 70% of the total length.
+% Responds to changes in the document's \baselinestretch
+\def\@IEEEauthorstrutrule{\@IEEEtrantmpdimenA\@IEEEauthorblockXinterlinespace%
+\@IEEEtrantmpdimenA=\baselinestretch\@IEEEtrantmpdimenA%
+\rule[-0.3\@IEEEtrantmpdimenA]{0pt}{\@IEEEtrantmpdimenA}}
+
+
+% blocks to hold the authors' names and affilations.
+% Makes formatting easy for conferences
+%
+% use real definitions in conference mode
+% name block
+\def\IEEEauthorblockN#1{\relax\@IEEEauthorblockNstyle% set the default text style
+\gdef\@IEEEauthorblockXinterlinespace{0pt}% disable strut for spacer row
+% the \expandafter hides the \cr in conditional tex, see the array.sty docs
+% for details, probably not needed here as the \cr is in a macro
+% do a spacer row if needed
+\if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockNtopspaceline\fi
+\global\@IEEEprevauthorblockincoltrue% we now have a block in this column
+%restore the correct strut value
+\gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockNinterlinespace}%
+% input the author names
+#1%
+% end the row if the user did not already
+\crcr}
+% spacer row for names
+\def\@IEEEauthorblockNtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockNtopspace}}
+%
+% affiliation block
+\def\IEEEauthorblockA#1{\relax\@IEEEauthorblockAstyle% set the default text style
+\gdef\@IEEEauthorblockXinterlinespace{0pt}%disable strut for spacer row
+% the \expandafter hides the \cr in conditional tex, see the array.sty docs
+% for details, probably not needed here as the \cr is in a macro
+% do a spacer row if needed
+\if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockAtopspaceline\fi
+\global\@IEEEprevauthorblockincoltrue% we now have a block in this column
+%restore the correct strut value
+\gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockAinterlinespace}%
+% input the author affiliations
+#1%
+% end the row if the user did not already
+\crcr}
+% spacer row for affiliations
+\def\@IEEEauthorblockAtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockAtopspace}}
+
+
+% allow papers to compile even if author blocks are used in modes other
+% than conference or peerreviewca. For such cases, we provide dummy blocks.
+\ifCLASSOPTIONconference
+\else
+ \ifCLASSOPTIONpeerreviewca\else
+ % not conference or peerreviewca mode
+ \def\IEEEauthorblockN#1{#1}%
+ \def\IEEEauthorblockA#1{#1}%
+ \fi
+\fi
+
+
+
+% we provide our own halign so as not to have to depend on tabular
+\def\@IEEEauthorhalign{\@IEEEauthordefaulttextstyle% default text style
+ \lineskip=0pt\relax% disable line spacing
+ \lineskiplimit=0pt\relax%
+ \baselineskip=0pt\relax%
+ \@IEEEcurfontSAVE% save the current font
+ \mathsurround\z@\relax% no extra spacing around math
+ \let\\\@IEEEauthorhaligncr% replace newline with halign friendly one
+ \tabskip=0pt\relax% no column spacing
+ \everycr{}% ensure no problems here
+ \@IEEEprevauthorblockincolfalse% no author blocks yet
+ \def\@IEEEauthorblockXinterlinespace{2.7ex}% default interline space
+ \vtop\bgroup%vtop box
+ \halign\bgroup&\relax\hfil\@IEEEcurfontRESTORE\relax ##\relax
+ \hfil\@IEEEcurfontSAVE\@IEEEauthorstrutrule\cr}
+
+% ensure last line, exit from halign, close vbox
+\def\end@IEEEauthorhalign{\crcr\egroup\egroup}
+
+% handle bogus star form
+\def\@IEEEauthorhaligncr{{\ifnum0=`}\fi\@ifstar{\@@IEEEauthorhaligncr}{\@@IEEEauthorhaligncr}}
+
+% test and setup the optional argument to \\[]
+\def\@@IEEEauthorhaligncr{\@testopt\@@@IEEEauthorhaligncr\z@skip}
+
+% end the line and do the optional spacer
+\def\@@@IEEEauthorhaligncr[#1]{\ifnum0=`{\fi}\cr\noalign{\vskip#1\relax}}
+
+
+
+% flag to prevent multiple \and warning messages
+\newif\if@IEEEWARNand
+\@IEEEWARNandtrue
+
+% if in conference or peerreviewca modes, we support the use of \and as \author is a
+% tabular environment, otherwise we warn the user that \and is invalid
+% outside of conference or peerreviewca modes.
+\def\and{\relax} % provide a bogus \and that we will then override
+
+\renewcommand{\and}[1][\relax]{\if@IEEEWARNand\typeout{** WARNING: \noexpand\and is valid only
+ when in conference or peerreviewca}\typeout{modes (line \the\inputlineno).}\fi\global\@IEEEWARNandfalse}
+
+\ifCLASSOPTIONconference%
+\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%
+\fi
+\ifCLASSOPTIONpeerreviewca
+\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%
+\fi
+
+
+% page clearing command
+% based on LaTeX2e's \cleardoublepage, but allows different page styles
+% for the inserted blank pages
+\def\@IEEEcleardoublepage#1{\clearpage\if@twoside\ifodd\c@page\else
+\hbox{}\thispagestyle{#1}\newpage\if@twocolumn\hbox{}\thispagestyle{#1}\newpage\fi\fi\fi}
+
+
+% user command to invoke the title page
+\def\maketitle{\par%
+ \begingroup%
+ \normalfont%
+ \def\thefootnote{}% the \thanks{} mark type is empty
+ \def\footnotemark{}% and kill space from \thanks within author
+ \let\@makefnmark\relax% V1.7, must *really* kill footnotemark to remove all \textsuperscript spacing as well.
+ \footnotesize% equal spacing between thanks lines
+ \footnotesep 0.7\baselineskip%see global setting of \footnotesep for more info
+ % V1.7 disable \thanks note indention for compsoc
+ \@IEEEcompsoconly{\long\def\@makefntext##1{\parindent 1em\noindent\hbox{\@makefnmark}##1}}%
+ \normalsize%
+ \ifCLASSOPTIONpeerreview
+ \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
+ \thispagestyle{IEEEpeerreviewcoverpagestyle}\@thanks%
+ \else
+ \if@twocolumn%
+ \ifCLASSOPTIONtechnote%
+ \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
+ \else
+ \twocolumn[\@maketitle\@IEEEdynamictitlevspace\@IEEEaftertitletext]%
+ \fi
+ \else
+ \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
+ \fi
+ \thispagestyle{IEEEtitlepagestyle}\@thanks%
+ \fi
+ % pullup page for pubid if used.
+ \if@IEEEusingpubid
+ \enlargethispage{-\@IEEEpubidpullup}%
+ \fi
+ \endgroup
+ \setcounter{footnote}{0}\let\maketitle\relax\let\@maketitle\relax
+ \gdef\@thanks{}%
+ % v1.6b do not clear these as we will need the title again for peer review papers
+ % \gdef\@author{}\gdef\@title{}%
+ \let\thanks\relax}
+
+
+
+% V1.7 parbox to format \@IEEEcompsoctitleabstractindextext
+\long\def\@IEEEcompsoctitleabstractindextextbox#1{\parbox{0.915\textwidth}{#1}}
+
+% formats the Title, authors names, affiliations and special paper notice
+% THIS IS A CONTROLLED SPACING COMMAND! Do not allow blank lines or unintentional
+% spaces to enter the definition - use % at the end of each line
+\def\@maketitle{\newpage
+\begin{center}%
+\ifCLASSOPTIONtechnote% technotes
+ {\bfseries\large\@IEEEcompsoconly{\sffamily}\@title\par}\vskip 1.3em{\lineskip .5em\@IEEEcompsoconly{\sffamily}\@author
+ \@IEEEspecialpapernotice\par{\@IEEEcompsoconly{\vskip 1.5em\relax
+ \@IEEEcompsoctitleabstractindextextbox{\@IEEEcompsoctitleabstractindextext}\par
+ \hfill\@IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax
+\else% not a technote
+ \vskip0.2em{\Huge\@IEEEcompsoconly{\sffamily}\@IEEEcompsocconfonly{\normalfont\normalsize\vskip 2\@IEEEnormalsizeunitybaselineskip
+ \bfseries\Large}\@title\par}\vskip1.0em\par%
+ % V1.6 handle \author differently if in conference mode
+ \ifCLASSOPTIONconference%
+ {\@IEEEspecialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%
+ \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par}\relax
+ \else% peerreviewca, peerreview or journal
+ \ifCLASSOPTIONpeerreviewca
+ % peerreviewca handles author names just like conference mode
+ {\@IEEEcompsoconly{\sffamily}\@IEEEspecialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%
+ \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par
+ {\@IEEEcompsoconly{\vskip 1.5em\relax
+ \@IEEEcompsoctitleabstractindextextbox{\@IEEEcompsoctitleabstractindextext}\par\hfill
+ \@IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax
+ \else% journal or peerreview
+ {\lineskip.5em\@IEEEcompsoconly{\sffamily}\sublargesize\@author\@IEEEspecialpapernotice\par
+ {\@IEEEcompsoconly{\vskip 1.5em\relax
+ \@IEEEcompsoctitleabstractindextextbox{\@IEEEcompsoctitleabstractindextext}\par\hfill
+ \@IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax
+ \fi
+ \fi
+\fi\end{center}}
+
+
+
+% V1.7 Computer Society "diamond line" which follows index terms for nonconference papers
+\def\@IEEEcompsocdiamondline{\vrule depth 0pt height 0.5pt width 4cm\hspace{7.5pt}%
+\raisebox{-3.5pt}{\fontfamily{pzd}\fontencoding{U}\fontseries{m}\fontshape{n}\fontsize{11}{12}\selectfont\char70}%
+\hspace{7.5pt}\vrule depth 0pt height 0.5pt width 4cm\relax}
+
+% V1.7 standard LateX2e \thanks, but with \itshape under compsoc. Also make it a \long\def
+% We also need to trigger the one-shot footnote rule
+\def\@IEEEtriggeroneshotfootnoterule{\global\@IEEEenableoneshotfootnoteruletrue}
+
+
+\long\def\thanks#1{\footnotemark
+ \protected@xdef\@thanks{\@thanks
+ \protect\footnotetext[\the\c@footnote]{\@IEEEcompsoconly{\itshape
+ \protect\@IEEEtriggeroneshotfootnoterule\relax}\ignorespaces#1}}}
+\let\@thanks\@empty
+
+% V1.7 allow \author to contain \par's. This is needed to allow \thanks to contain \par.
+\long\def\author#1{\gdef\@author{#1}}
+
+
+% in addition to setting up IEEEitemize, we need to remove a baselineskip space above and
+% below it because \list's \pars introduce blank lines because of the footnote struts.
+\def\@IEEEsetupcompsocitemizelist{\def\labelitemi{$\bullet$}%
+\setlength{\IEEElabelindent}{0pt}\setlength{\parskip}{0pt}%
+\setlength{\partopsep}{0pt}\setlength{\topsep}{0.5\baselineskip}\vspace{-1\baselineskip}\relax}
+
+
+% flag for fake non-compsoc \IEEEcompsocthanksitem - prevents line break on very first item
+\newif\if@IEEEbreakcompsocthanksitem \@IEEEbreakcompsocthanksitemfalse
+
+\ifCLASSOPTIONcompsoc
+% V1.7 compsoc bullet item \thanks
+% also, we need to redefine this to destroy the argument in \@IEEEdynamictitlevspace
+\long\def\IEEEcompsocitemizethanks#1{\relax\@IEEEbreakcompsocthanksitemfalse\footnotemark
+ \protected@xdef\@thanks{\@thanks
+ \protect\footnotetext[\the\c@footnote]{\itshape\protect\@IEEEtriggeroneshotfootnoterule
+ {\let\IEEEiedlistdecl\relax\protect\begin{IEEEitemize}[\protect\@IEEEsetupcompsocitemizelist]\ignorespaces#1\relax
+ \protect\end{IEEEitemize}}\protect\vspace{-1\baselineskip}}}}
+\DeclareRobustCommand*{\IEEEcompsocthanksitem}{\item}
+\else
+% non-compsoc, allow for dual compilation via rerouting to normal \thanks
+\long\def\IEEEcompsocitemizethanks#1{\thanks{#1}}
+% redirect to "pseudo-par" \hfil\break\indent after swallowing [] from \IEEEcompsocthanksitem[]
+\DeclareRobustCommand{\IEEEcompsocthanksitem}{\@ifnextchar [{\@IEEEthanksswallowoptionalarg}%
+{\@IEEEthanksswallowoptionalarg[\relax]}}
+% be sure and break only after first item, be sure and ignore spaces after optional argument
+\def\@IEEEthanksswallowoptionalarg[#1]{\relax\if@IEEEbreakcompsocthanksitem\hfil\break
+\indent\fi\@IEEEbreakcompsocthanksitemtrue\ignorespaces}
+\fi
+
+
+% V1.6b define the \IEEEpeerreviewmaketitle as needed
+\ifCLASSOPTIONpeerreview
+\def\IEEEpeerreviewmaketitle{\@IEEEcleardoublepage{empty}%
+\ifCLASSOPTIONtwocolumn
+\twocolumn[\@IEEEpeerreviewmaketitle\@IEEEdynamictitlevspace]
+\else
+\newpage\@IEEEpeerreviewmaketitle\@IEEEstatictitlevskip
+\fi
+\thispagestyle{IEEEtitlepagestyle}}
+\else
+% \IEEEpeerreviewmaketitle does nothing if peer review option has not been selected
+\def\IEEEpeerreviewmaketitle{\relax}
+\fi
+
+% peerreview formats the repeated title like the title in journal papers.
+\def\@IEEEpeerreviewmaketitle{\begin{center}\@IEEEcompsoconly{\sffamily}%
+\normalfont\normalsize\vskip0.2em{\Huge\@title\par}\vskip1.0em\par
+\end{center}}
+
+
+
+% V1.6
+% this is a static rubber spacer between the title/authors and the main text
+% used for single column text, or when the title appears in the first column
+% of two column text (technotes).
+\def\@IEEEstatictitlevskip{{\normalfont\normalsize
+% adjust spacing to next text
+% v1.6b handle peer review papers
+\ifCLASSOPTIONpeerreview
+% for peer review papers, the same value is used for both title pages
+% regardless of the other paper modes
+ \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip
+\else
+ \ifCLASSOPTIONconference% conference
+ \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip%
+ \else%
+ \ifCLASSOPTIONtechnote% technote
+ \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip%
+ \else% journal uses more space
+ \vskip 2.5\baselineskip plus 0.75\baselineskip minus 0.375\baselineskip%
+ \fi
+ \fi
+\fi}}
+
+
+% V1.6
+% This is a dynamically determined rigid spacer between the title/authors
+% and the main text. This is used only for single column titles over two
+% column text (most common)
+% This is bit tricky because we have to ensure that the textheight of the
+% main text is an integer multiple of \baselineskip
+% otherwise underfull vbox problems may develop in the second column of the
+% text on the titlepage
+% The possible use of \IEEEpubid must also be taken into account.
+\def\@IEEEdynamictitlevspace{{%
+ % we run within a group so that all the macros can be forgotten when we are done
+ \long\def\thanks##1{\relax}%don't allow \thanks to run when we evaluate the vbox height
+ \long\def\IEEEcompsocitemizethanks##1{\relax}%don't allow \IEEEcompsocitemizethanks to run when we evaluate the vbox height
+ \normalfont\normalsize% we declare more descriptive variable names
+ \let\@IEEEmaintextheight=\@IEEEtrantmpdimenA%height of the main text columns
+ \let\@IEEEINTmaintextheight=\@IEEEtrantmpdimenB%height of the main text columns with integer # lines
+ % set the nominal and minimum values for the title spacer
+ % the dynamic algorithm will not allow the spacer size to
+ % become less than \@IEEEMINtitlevspace - instead it will be
+ % lengthened
+ % default to journal values
+ \def\@IEEENORMtitlevspace{2.5\baselineskip}%
+ \def\@IEEEMINtitlevspace{2\baselineskip}%
+ % conferences and technotes need tighter spacing
+ \ifCLASSOPTIONconference%conference
+ \def\@IEEENORMtitlevspace{1\baselineskip}%
+ \def\@IEEEMINtitlevspace{0.75\baselineskip}%
+ \fi
+ \ifCLASSOPTIONtechnote%technote
+ \def\@IEEENORMtitlevspace{1\baselineskip}%
+ \def\@IEEEMINtitlevspace{0.75\baselineskip}%
+ \fi%
+ % get the height that the title will take up
+ \ifCLASSOPTIONpeerreview
+ \settoheight{\@IEEEmaintextheight}{\vbox{\hsize\textwidth \@IEEEpeerreviewmaketitle}}%
+ \else
+ \settoheight{\@IEEEmaintextheight}{\vbox{\hsize\textwidth \@maketitle}}%
+ \fi
+ \@IEEEmaintextheight=-\@IEEEmaintextheight% title takes away from maintext, so reverse sign
+ % add the height of the page textheight
+ \advance\@IEEEmaintextheight by \textheight%
+ % correct for title pages using pubid
+ \ifCLASSOPTIONpeerreview\else
+ % peerreview papers use the pubid on the cover page only.
+ % And the cover page uses a static spacer.
+ \if@IEEEusingpubid\advance\@IEEEmaintextheight by -\@IEEEpubidpullup\fi
+ \fi%
+ % subtract off the nominal value of the title bottom spacer
+ \advance\@IEEEmaintextheight by -\@IEEENORMtitlevspace%
+ % \topskip takes away some too
+ \advance\@IEEEmaintextheight by -\topskip%
+ % calculate the column height of the main text for lines
+ % now we calculate the main text height as if holding
+ % an integer number of \normalsize lines after the first
+ % and discard any excess fractional remainder
+ % we subtracted the first line, because the first line
+ % is placed \topskip into the maintext, not \baselineskip like the
+ % rest of the lines.
+ \@IEEEINTmaintextheight=\@IEEEmaintextheight%
+ \divide\@IEEEINTmaintextheight by \baselineskip%
+ \multiply\@IEEEINTmaintextheight by \baselineskip%
+ % now we calculate how much the title spacer height will
+ % have to be reduced from nominal (\@IEEEREDUCEmaintextheight is always
+ % a positive value) so that the maintext area will contain an integer
+ % number of normal size lines
+ % we change variable names here (to avoid confusion) as we no longer
+ % need \@IEEEINTmaintextheight and can reuse its dimen register
+ \let\@IEEEREDUCEmaintextheight=\@IEEEINTmaintextheight%
+ \advance\@IEEEREDUCEmaintextheight by -\@IEEEmaintextheight%
+ \advance\@IEEEREDUCEmaintextheight by \baselineskip%
+ % this is the calculated height of the spacer
+ % we change variable names here (to avoid confusion) as we no longer
+ % need \@IEEEmaintextheight and can reuse its dimen register
+ \let\@IEEECOMPENSATElen=\@IEEEmaintextheight%
+ \@IEEECOMPENSATElen=\@IEEENORMtitlevspace% set the nominal value
+ % we go with the reduced length if it is smaller than an increase
+ \ifdim\@IEEEREDUCEmaintextheight < 0.5\baselineskip\relax%
+ \advance\@IEEECOMPENSATElen by -\@IEEEREDUCEmaintextheight%
+ % if the resulting spacer is too small back out and go with an increase instead
+ \ifdim\@IEEECOMPENSATElen<\@IEEEMINtitlevspace\relax%
+ \advance\@IEEECOMPENSATElen by \baselineskip%
+ \fi%
+ \else%
+ % go with an increase because it is closer to the nominal than a decrease
+ \advance\@IEEECOMPENSATElen by -\@IEEEREDUCEmaintextheight%
+ \advance\@IEEECOMPENSATElen by \baselineskip%
+ \fi%
+ % set the calculated rigid spacer
+ \vspace{\@IEEECOMPENSATElen}}}
+
+
+
+% V1.6
+% we allow the user access to the last part of the title area
+% useful in emergencies such as when a different spacing is needed
+% This text is NOT compensated for in the dynamic sizer.
+\let\@IEEEaftertitletext=\relax
+\long\def\IEEEaftertitletext#1{\def\@IEEEaftertitletext{#1}}
+
+% V1.7 provide a way for users to enter abstract and keywords
+% into the onecolumn title are. This text is compensated for
+% in the dynamic sizer.
+\let\@IEEEcompsoctitleabstractindextext=\relax
+\long\def\IEEEcompsoctitleabstractindextext#1{\def\@IEEEcompsoctitleabstractindextext{#1}}
+% V1.7 provide a way for users to get the \@IEEEcompsoctitleabstractindextext if
+% not in compsoc journal mode - this way abstract and keywords can be placed
+% in their conventional position if not in compsoc mode.
+\def\IEEEdisplaynotcompsoctitleabstractindextext{%
+\ifCLASSOPTIONcompsoc% display if compsoc conf
+\ifCLASSOPTIONconference\@IEEEcompsoctitleabstractindextext\fi
+\else% or if not compsoc
+\@IEEEcompsoctitleabstractindextext\fi}
+
+
+% command to allow alteration of baselinestretch, but only if the current
+% baselineskip is unity. Used to tweak the compsoc abstract and keywords line spacing.
+\def\@IEEEtweakunitybaselinestretch#1{{\def\baselinestretch{1}\selectfont
+\global\@tempskipa\baselineskip}\ifnum\@tempskipa=\baselineskip%
+\def\baselinestretch{#1}\selectfont\fi\relax}
+
+
+% abstract and keywords are in \small, except
+% for 9pt docs in which they are in \footnotesize
+% Because 9pt docs use an 8pt footnotesize, \small
+% becomes a rather awkward 8.5pt
+\def\@IEEEabskeysecsize{\small}
+\ifx\CLASSOPTIONpt\@IEEEptsizenine
+ \def\@IEEEabskeysecsize{\footnotesize}
+\fi
+
+% compsoc journals use \footnotesize, compsoc conferences use normalsize
+\@IEEEcompsoconly{\def\@IEEEabskeysecsize{\footnotesize}}
+\@IEEEcompsocconfonly{\def\@IEEEabskeysecsize{\normalsize}}
+
+
+
+
+% V1.6 have abstract and keywords strip leading spaces, pars and newlines
+% so that spacing is more tightly controlled.
+\def\abstract{\normalfont
+ \if@twocolumn
+ \@IEEEabskeysecsize\bfseries\textit{\abstractname}---\relax
+ \else
+ \begin{center}\vspace{-1.78ex}\@IEEEabskeysecsize\textbf{\abstractname}\end{center}\quotation\@IEEEabskeysecsize
+ \fi\@IEEEgobbleleadPARNLSP}
+% V1.6 IEEE wants only 1 pica from end of abstract to introduction heading when in
+% conference mode (the heading already has this much above it)
+\def\endabstract{\relax\ifCLASSOPTIONconference\vspace{0ex}\else\vspace{1.34ex}\fi\par\if@twocolumn\else\endquotation\fi
+ \normalfont\normalsize}
+
+\def\IEEEkeywords{\normalfont
+ \if@twocolumn
+ \@IEEEabskeysecsize\bfseries\textit{\IEEEkeywordsname}---\relax
+ \else
+ \begin{center}\@IEEEabskeysecsize\textbf{\IEEEkeywordsname}\end{center}\quotation\@IEEEabskeysecsize
+ \fi\@IEEEgobbleleadPARNLSP}
+\def\endIEEEkeywords{\relax\ifCLASSOPTIONtechnote\vspace{1.34ex}\else\vspace{0.67ex}\fi
+ \par\if@twocolumn\else\endquotation\fi%
+ \normalfont\normalsize}
+
+% V1.7 compsoc keywords index terms
+\ifCLASSOPTIONcompsoc
+ \ifCLASSOPTIONconference% compsoc conference
+\def\abstract{\normalfont
+ \begin{center}\@IEEEabskeysecsize\textbf{\large\abstractname}\end{center}\vskip 0.5\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip
+ \if@twocolumn\else\quotation\fi\itshape\@IEEEabskeysecsize%
+ \par\@IEEEgobbleleadPARNLSP}
+\def\IEEEkeywords{\normalfont\vskip 1.5\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip
+ \begin{center}\@IEEEabskeysecsize\textbf{\large\IEEEkeywordsname}\end{center}\vskip 0.5\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip
+ \if@twocolumn\else\quotation\fi\itshape\@IEEEabskeysecsize%
+ \par\@IEEEgobbleleadPARNLSP}
+ \else% compsoc not conference
+\def\abstract{\normalfont\@IEEEtweakunitybaselinestretch{1.15}\sffamily
+ \if@twocolumn
+ \@IEEEabskeysecsize\noindent\textbf{\abstractname}---\relax
+ \else
+ \begin{center}\vspace{-1.78ex}\@IEEEabskeysecsize\textbf{\abstractname}\end{center}\quotation\@IEEEabskeysecsize%
+ \fi\@IEEEgobbleleadPARNLSP}
+\def\IEEEkeywords{\normalfont\@IEEEtweakunitybaselinestretch{1.15}\sffamily
+ \if@twocolumn
+ \@IEEEabskeysecsize\vskip 0.5\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip\noindent
+ \textbf{\IEEEkeywordsname}---\relax
+ \else
+ \begin{center}\@IEEEabskeysecsize\textbf{\IEEEkeywordsname}\end{center}\quotation\@IEEEabskeysecsize%
+ \fi\@IEEEgobbleleadPARNLSP}
+ \fi
+\fi
+
+
+
+% gobbles all leading \, \\ and \par, upon finding first token that
+% is not a \ , \\ or a \par, it ceases and returns that token
+%
+% used to strip leading \, \\ and \par from the input
+% so that such things in the beginning of an environment will not
+% affect the formatting of the text
+\long\def\@IEEEgobbleleadPARNLSP#1{\let\@IEEEswallowthistoken=0%
+\let\@IEEEgobbleleadPARNLSPtoken#1%
+\let\@IEEEgobbleleadPARtoken=\par%
+\let\@IEEEgobbleleadNLtoken=\\%
+\let\@IEEEgobbleleadSPtoken=\ %
+\def\@IEEEgobbleleadSPMACRO{\ }%
+\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadPARtoken%
+\let\@IEEEswallowthistoken=1%
+\fi%
+\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadNLtoken%
+\let\@IEEEswallowthistoken=1%
+\fi%
+\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPtoken%
+\let\@IEEEswallowthistoken=1%
+\fi%
+% a control space will come in as a macro
+% when it is the last one on a line
+\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPMACRO%
+\let\@IEEEswallowthistoken=1%
+\fi%
+% if we have to swallow this token, do so and taste the next one
+% else spit it out and stop gobbling
+\ifx\@IEEEswallowthistoken 1\let\@IEEEnextgobbleleadPARNLSP=\@IEEEgobbleleadPARNLSP\else%
+\let\@IEEEnextgobbleleadPARNLSP=#1\fi%
+\@IEEEnextgobbleleadPARNLSP}%
+
+
+
+
+% TITLING OF SECTIONS
+\def\@IEEEsectpunct{:\ \,} % Punctuation after run-in section heading (headings which are
+ % part of the paragraphs), need little bit more than a single space
+ % spacing from section number to title
+% compsoc conferences use regular period/space punctuation
+\ifCLASSOPTIONcompsoc
+\ifCLASSOPTIONconference
+\def\@IEEEsectpunct{.\ }
+\fi\fi
+
+
+\def\@seccntformat#1{\csname the#1dis\endcsname\hskip 0.5em\relax}
+
+\ifCLASSOPTIONcompsoc
+% compsoc journals need extra spacing
+\ifCLASSOPTIONconference\else
+\def\@seccntformat#1{\csname the#1dis\endcsname\hskip 1em\relax}
+\fi\fi
+
+%v1.7 put {} after #6 to allow for some types of user font control
+%and use \@@par rather than \par
+\def\@sect#1#2#3#4#5#6[#7]#8{%
+ \ifnum #2>\c@secnumdepth
+ \let\@svsec\@empty
+ \else
+ \refstepcounter{#1}%
+ % load section label and spacer into \@svsec
+ \protected@edef\@svsec{\@seccntformat{#1}\relax}%
+ \fi%
+ \@tempskipa #5\relax
+ \ifdim \@tempskipa>\z@% tempskipa determines whether is treated as a high
+ \begingroup #6{\relax% or low level heading
+ \noindent % subsections are NOT indented
+ % print top level headings. \@svsec is label, #8 is heading title
+ % IEEE does not block indent the section title text, it flows like normal
+ {\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\@@par}}%
+ \endgroup
+ \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else
+ \protect\numberline{\csname the#1\endcsname}\fi#7}%
+ \else % printout low level headings
+ % svsechd seems to swallow the trailing space, protect it with \mbox{}
+ % got rid of sectionmark stuff
+ \def\@svsechd{#6{\hskip #3\relax\@svsec #8\@IEEEsectpunct\mbox{}}%
+ \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else
+ \protect\numberline{\csname the#1\endcsname}\fi#7}}%
+ \fi%skip down
+ \@xsect{#5}}
+
+
+% section* handler
+%v1.7 put {} after #4 to allow for some types of user font control
+%and use \@@par rather than \par
+\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax
+ \ifdim \@tempskipa>\z@
+ %\begingroup #4\@hangfrom{\hskip #1}{\interlinepenalty \@M #5\par}\endgroup
+ % IEEE does not block indent the section title text, it flows like normal
+ \begingroup \noindent #4{\relax{\hskip #1}{\interlinepenalty \@M #5\@@par}}\endgroup
+ % svsechd swallows the trailing space, protect it with \mbox{}
+ \else \def\@svsechd{#4{\hskip #1\relax #5\@IEEEsectpunct\mbox{}}}\fi
+ \@xsect{#3}}
+
+
+%% SECTION heading spacing and font
+%%
+% arguments are: #1 - sectiontype name
+% (for \@sect) #2 - section level
+% #3 - section heading indent
+% #4 - top separation (absolute value used, neg indicates not to indent main text)
+% If negative, make stretch parts negative too!
+% #5 - (absolute value used) positive: bottom separation after heading,
+% negative: amount to indent main text after heading
+% Both #4 and #5 negative means to indent main text and use negative top separation
+% #6 - font control
+% You've got to have \normalfont\normalsize in the font specs below to prevent
+% trouble when you do something like:
+% \section{Note}{\ttfamily TT-TEXT} is known to ...
+% IEEE sometimes REALLY stretches the area before a section
+% heading by up to about 0.5in. However, it may not be a good
+% idea to let LaTeX have quite this much rubber.
+\ifCLASSOPTIONconference%
+% IEEE wants section heading spacing to decrease for conference mode
+\def\section{\@startsection{section}{1}{\z@}{1.5ex plus 1.5ex minus 0.5ex}%
+{0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}%
+\def\subsection{\@startsection{subsection}{2}{\z@}{1.5ex plus 1.5ex minus 0.5ex}%
+{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%
+\else % for journals
+\def\section{\@startsection{section}{1}{\z@}{3.0ex plus 1.5ex minus 1.5ex}% V1.6 3.0ex from 3.5ex
+{0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}%
+\def\subsection{\@startsection{subsection}{2}{\z@}{3.5ex plus 1.5ex minus 1.5ex}%
+{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%
+\fi
+
+% for both journals and conferences
+% decided to put in a little rubber above the section, might help somebody
+\def\subsubsection{\@startsection{subsubsection}{3}{\parindent}{0ex plus 0.1ex minus 0.1ex}%
+{0ex}{\normalfont\normalsize\itshape}}%
+\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{0ex plus 0.1ex minus 0.1ex}%
+{0ex}{\normalfont\normalsize\itshape}}%
+
+
+% compsoc
+\ifCLASSOPTIONcompsoc
+\ifCLASSOPTIONconference
+% compsoc conference
+\def\section{\@startsection{section}{1}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}%
+{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}{\normalfont\large\bfseries}}%
+\def\subsection{\@startsection{subsection}{2}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}%
+{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}{\normalfont\sublargesize\bfseries}}%
+\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}%
+{0ex}{\normalfont\normalsize\bfseries}}%
+\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{0ex plus 0.1ex minus 0.1ex}%
+{0ex}{\normalfont\normalsize}}%
+\else% compsoc journals
+% use negative top separation as compsoc journals do not indent paragraphs after section titles
+\def\section{\@startsection{section}{1}{\z@}{-3ex plus -2ex minus -1.5ex}%
+{0.7ex plus 1ex minus 0ex}{\normalfont\large\sffamily\bfseries\scshape}}%
+% Note that subsection and smaller may not be correct for the Computer Society,
+% I have to look up an example.
+\def\subsection{\@startsection{subsection}{2}{\z@}{-3.5ex plus -1.5ex minus -1.5ex}%
+{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\sffamily\bfseries}}%
+\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-2.5ex plus -1ex minus -1ex}%
+{0.5ex plus 0.5ex minus 0ex}{\normalfont\normalsize\sffamily\itshape}}%
+\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{-0ex plus -0.1ex minus -0.1ex}%
+{0ex}{\normalfont\normalsize}}%
+\fi\fi
+
+
+
+
+%% ENVIRONMENTS
+% "box" symbols at end of proofs
+\def\IEEEQEDclosed{\mbox{\rule[0pt]{1.3ex}{1.3ex}}} % for a filled box
+% V1.6 some journals use an open box instead that will just fit around a closed one
+\def\IEEEQEDopen{{\setlength{\fboxsep}{0pt}\setlength{\fboxrule}{0.2pt}\fbox{\rule[0pt]{0pt}{1.3ex}\rule[0pt]{1.3ex}{0pt}}}}
+\ifCLASSOPTIONcompsoc
+\def\IEEEQED{\IEEEQEDopen} % default to open for compsoc
+\else
+\def\IEEEQED{\IEEEQEDclosed} % otherwise default to closed
+\fi
+
+% v1.7 name change to avoid namespace collision with amsthm. Also add support
+% for an optional argument.
+\def\IEEEproof{\@ifnextchar[{\@IEEEproof}{\@IEEEproof[\IEEEproofname]}}
+\def\@IEEEproof[#1]{\par\noindent\hspace{2em}{\itshape #1: }}
+\def\endIEEEproof{\hspace*{\fill}~\IEEEQED\par}
+
+
+%\itemindent is set to \z@ by list, so define new temporary variable
+\newdimen\@IEEEtmpitemindent
+\def\@begintheorem#1#2{\@IEEEtmpitemindent\itemindent\topsep 0pt\rmfamily\trivlist%
+ \item[\hskip \labelsep{\indent\itshape #1\ #2:}]\itemindent\@IEEEtmpitemindent}
+\def\@opargbegintheorem#1#2#3{\@IEEEtmpitemindent\itemindent\topsep 0pt\rmfamily \trivlist%
+% V1.6 IEEE is back to using () around theorem names which are also in italics
+% Thanks to Christian Peel for reporting this.
+ \item[\hskip\labelsep{\indent\itshape #1\ #2\ (#3):}]\itemindent\@IEEEtmpitemindent}
+% V1.7 remove bogus \unskip that caused equations in theorems to collide with
+% lines below.
+\def\@endtheorem{\endtrivlist}
+
+% V1.6
+% display command for the section the theorem is in - so that \thesection
+% is not used as this will be in Roman numerals when we want arabic.
+% LaTeX2e uses \def\@thmcounter#1{\noexpand\arabic{#1}} for the theorem number
+% (second part) display and \def\@thmcountersep{.} as a separator.
+% V1.7 intercept calls to the section counter and reroute to \@IEEEthmcounterinsection
+% to allow \appendix(ices} to override as needed.
+%
+% special handler for sections, allows appendix(ices) to override
+\gdef\@IEEEthmcounterinsection#1{\arabic{#1}}
+% string macro
+\edef\@IEEEstringsection{section}
+
+% redefine the #1#2[#3] form of newtheorem to use a hook to \@IEEEthmcounterinsection
+% if section in_counter is used
+\def\@xnthm#1#2[#3]{%
+ \expandafter\@ifdefinable\csname #1\endcsname
+ {\@definecounter{#1}\@newctr{#1}[#3]%
+ \edef\@IEEEstringtmp{#3}
+ \ifx\@IEEEstringtmp\@IEEEstringsection
+ \expandafter\xdef\csname the#1\endcsname{%
+ \noexpand\@IEEEthmcounterinsection{#3}\@thmcountersep
+ \@thmcounter{#1}}%
+ \else
+ \expandafter\xdef\csname the#1\endcsname{%
+ \expandafter\noexpand\csname the#3\endcsname \@thmcountersep
+ \@thmcounter{#1}}%
+ \fi
+ \global\@namedef{#1}{\@thm{#1}{#2}}%
+ \global\@namedef{end#1}{\@endtheorem}}}
+
+
+
+%% SET UP THE DEFAULT PAGESTYLE
+\ps@headings
+\pagenumbering{arabic}
+
+% normally the page counter starts at 1
+\setcounter{page}{1}
+% however, for peerreview the cover sheet is page 0 or page -1
+% (for duplex printing)
+\ifCLASSOPTIONpeerreview
+ \if@twoside
+ \setcounter{page}{-1}
+ \else
+ \setcounter{page}{0}
+ \fi
+\fi
+
+% standard book class behavior - let bottom line float up and down as
+% needed when single sided
+\ifCLASSOPTIONtwoside\else\raggedbottom\fi
+% if two column - turn on twocolumn, allow word spacings to stretch more and
+% enforce a rigid position for the last lines
+\ifCLASSOPTIONtwocolumn
+% the peer review option delays invoking twocolumn
+ \ifCLASSOPTIONpeerreview\else
+ \twocolumn
+ \fi
+\sloppy
+\flushbottom
+\fi
+
+
+
+
+% \APPENDIX and \APPENDICES definitions
+
+% This is the \@ifmtarg command from the LaTeX ifmtarg package
+% by Peter Wilson (CUA) and Donald Arseneau
+% \@ifmtarg is used to determine if an argument to a command
+% is present or not.
+% For instance:
+% \@ifmtarg{#1}{\typeout{empty}}{\typeout{has something}}
+% \@ifmtarg is used with our redefined \section command if
+% \appendices is invoked.
+% The command \section will behave slightly differently depending
+% on whether the user specifies a title:
+% \section{My appendix title}
+% or not:
+% \section{}
+% This way, we can eliminate the blank lines where the title
+% would be, and the unneeded : after Appendix in the table of
+% contents
+\begingroup
+\catcode`\Q=3
+\long\gdef\@ifmtarg#1{\@xifmtarg#1QQ\@secondoftwo\@firstoftwo\@nil}
+\long\gdef\@xifmtarg#1#2Q#3#4#5\@nil{#4}
+\endgroup
+% end of \@ifmtarg defs
+
+
+% V1.7
+% command that allows the one time saving of the original definition
+% of section to \@IEEEappendixsavesection for \appendix or \appendices
+% we don't save \section here as it may be redefined later by other
+% packages (hyperref.sty, etc.)
+\def\@IEEEsaveoriginalsectiononce{\let\@IEEEappendixsavesection\section
+\let\@IEEEsaveoriginalsectiononce\relax}
+
+% neat trick to grab and process the argument from \section{argument}
+% we process differently if the user invoked \section{} with no
+% argument (title)
+% note we reroute the call to the old \section*
+\def\@IEEEprocessthesectionargument#1{%
+\@ifmtarg{#1}{%
+\@IEEEappendixsavesection*{\appendixname~\thesectiondis}%
+\addcontentsline{toc}{section}{\appendixname~\thesection}}{%
+\@IEEEappendixsavesection*{\appendixname~\thesectiondis \\* #1}%
+\addcontentsline{toc}{section}{\appendixname~\thesection: #1}}}
+
+% we use this if the user calls \section{} after
+% \appendix-- which has no meaning. So, we ignore the
+% command and its argument. Then, warn the user.
+\def\@IEEEdestroythesectionargument#1{\typeout{** WARNING: Ignoring useless
+\protect\section\space in Appendix (line \the\inputlineno).}}
+
+
+% remember \thesection forms will be displayed in \ref calls
+% and in the Table of Contents.
+% The \sectiondis form is used in the actual heading itself
+
+% appendix command for one single appendix
+% normally has no heading. However, if you want a
+% heading, you can do so via the optional argument:
+% \appendix[Optional Heading]
+\def\appendix{\relax}
+\renewcommand{\appendix}[1][]{\@IEEEsaveoriginalsectiononce\par
+ % v1.6 keep hyperref's identifiers unique
+ \gdef\theHsection{Appendix.A}%
+ % v1.6 adjust hyperref's string name for the section
+ \xdef\Hy@chapapp{appendix}%
+ \setcounter{section}{0}%
+ \setcounter{subsection}{0}%
+ \setcounter{subsubsection}{0}%
+ \setcounter{paragraph}{0}%
+ \gdef\thesection{A}%
+ \gdef\thesectiondis{}%
+ \gdef\thesubsection{\Alph{subsection}}%
+ \gdef\@IEEEthmcounterinsection##1{A}
+ \refstepcounter{section}% update the \ref counter
+ \@ifmtarg{#1}{\@IEEEappendixsavesection*{\appendixname}%
+ \addcontentsline{toc}{section}{\appendixname}}{%
+ \@IEEEappendixsavesection*{\appendixname~\\* #1}%
+ \addcontentsline{toc}{section}{\appendixname: #1}}%
+ % redefine \section command for appendix
+ % leave \section* as is
+ \def\section{\@ifstar{\@IEEEappendixsavesection*}{%
+ \@IEEEdestroythesectionargument}}% throw out the argument
+ % of the normal form
+}
+
+
+
+% appendices command for multiple appendices
+% user then calls \section with an argument (possibly empty) to
+% declare the individual appendices
+\def\appendices{\@IEEEsaveoriginalsectiononce\par
+ % v1.6 keep hyperref's identifiers unique
+ \gdef\theHsection{Appendix.\Alph{section}}%
+ % v1.6 adjust hyperref's string name for the section
+ \xdef\Hy@chapapp{appendix}%
+ \setcounter{section}{-1}% we want \refstepcounter to use section 0
+ \setcounter{subsection}{0}%
+ \setcounter{subsubsection}{0}%
+ \setcounter{paragraph}{0}%
+ \ifCLASSOPTIONromanappendices%
+ \gdef\thesection{\Roman{section}}%
+ \gdef\thesectiondis{\Roman{section}}%
+ \@IEEEcompsocconfonly{\gdef\thesectiondis{\Roman{section}.}}%
+ \gdef\@IEEEthmcounterinsection##1{A\arabic{##1}}
+ \else%
+ \gdef\thesection{\Alph{section}}%
+ \gdef\thesectiondis{\Alph{section}}%
+ \@IEEEcompsocconfonly{\gdef\thesectiondis{\Alph{section}.}}%
+ \gdef\@IEEEthmcounterinsection##1{\Alph{##1}}
+ \fi%
+ \refstepcounter{section}% update the \ref counter
+ \setcounter{section}{0}% NEXT \section will be the FIRST appendix
+ % redefine \section command for appendices
+ % leave \section* as is
+ \def\section{\@ifstar{\@IEEEappendixsavesection*}{% process the *-form
+ \refstepcounter{section}% or is a new section so,
+ \@IEEEprocessthesectionargument}}% process the argument
+ % of the normal form
+}
+
+
+
+% \IEEEPARstart
+% Definition for the big two line drop cap letter at the beginning of the
+% first paragraph of journal papers. The first argument is the first letter
+% of the first word, the second argument is the remaining letters of the
+% first word which will be rendered in upper case.
+% In V1.6 this has been completely rewritten to:
+%
+% 1. no longer have problems when the user begins an environment
+% within the paragraph that uses \IEEEPARstart.
+% 2. auto-detect and use the current font family
+% 3. revise handling of the space at the end of the first word so that
+% interword glue will now work as normal.
+% 4. produce correctly aligned edges for the (two) indented lines.
+%
+% We generalize things via control macros - playing with these is fun too.
+%
+% V1.7 added more control macros to make it easy for IEEEtrantools.sty users
+% to change the font style.
+%
+% the number of lines that are indented to clear it
+% may need to increase if using decenders
+\def\@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
+\def\@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).
+\def\@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.
+\def\@IEEEPARstartDROPDEPTH{1.1\baselineskip}
+% V1.7 the font the drop cap will be rendered in,
+% can take zero or one argument.
+\def\@IEEEPARstartFONTSTYLE{\bfseries}
+% V1.7 any additional, non-font related commands needed to modify
+% the drop cap letter, can take zero or one argument.
+\def\@IEEEPARstartCAPSTYLE{\MakeUppercase}
+% V1.7 the font that will be used to render the rest of the word,
+% can take zero or one argument.
+\def\@IEEEPARstartWORDFONTSTYLE{\relax}
+% V1.7 any additional, non-font related commands needed to modify
+% the rest of the word, can take zero or one argument.
+\def\@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.
+\def\@IEEEPARstartSEP{0.15em}
+% V1.7 horizontal offset applied to the left of the drop cap.
+\def\@IEEEPARstartHOFFSET{0em}
+% V1.7 Italic correction command applied at the end of the drop cap.
+\def\@IEEEPARstartITLCORRECT{\/}
+
+% V1.7 compoc uses nonbold drop cap and small caps word style
+\ifCLASSOPTIONcompsoc
+\def\@IEEEPARstartFONTSTYLE{\mdseries}
+\def\@IEEEPARstartWORDFONTSTYLE{\scshape}
+\def\@IEEEPARstartWORDCAPSTYLE{\relax}
+\fi
+
+% 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
+% add in the extra clearance we want
+\advance\@IEEEtrantmpdimenA by \@IEEEPARstartSEP\relax%
+% add in the optional offset
+\advance\@IEEEtrantmpdimenA by \@IEEEPARstartHOFFSET\relax%
+% V1.7 don't allow negative offsets to produce negative hanging indents
+\@IEEEtrantmpdimenB\@IEEEtrantmpdimenA
+\ifnum\@IEEEtrantmpdimenB < 0 \@IEEEtrantmpdimenB 0pt\fi
+% \@IEEEtrantmpdimenA has the width of the big letter plus the
+% separation space and \@IEEEPARstartfont is the font we need to use
+% Now, we make the letter and issue the hanging indent command
+% The letter is placed in a box of zero width and height so that other
+% text won't be displaced by it.
+\hangindent\@IEEEtrantmpdimenB\hangafter=-\@IEEEPARstartDROPLINES%
+\makebox[0pt][l]{\hspace{-\@IEEEtrantmpdimenA}%
+\raisebox{-\@IEEEPARstartDROPDEPTH}[0pt][0pt]{\hspace{\@IEEEPARstartHOFFSET}%
+\@IEEEPARstartfont\@IEEEPARstartCAPSTYLE{#1\@IEEEPARstartITLCORRECT}%
+\hspace{\@IEEEPARstartSEP}}}%
+{\@IEEEPARstartWORDFONTSTYLE{\@IEEEPARstartWORDCAPSTYLE{\selectfont#2}}}}
+
+
+
+
+
+
+% determines if the space remaining on a given page is equal to or greater
+% than the specified space of argument one
+% if not, execute argument two (only if the remaining space is greater than zero)
+% and issue a \newpage
+%
+% example: \@IEEEtranneedspace{2in}{\vfill}
+%
+% Does not take into consideration rubber shrinkage, so it tends to
+% be overly cautious
+% Based on an example posted by Donald Arseneau
+% Note this macro uses \@IEEEtrantmpdimenB internally for calculations,
+% so DO NOT PASS \@IEEEtrantmpdimenB to this routine
+% if you need a dimen register, import with \@IEEEtrantmpdimenA instead
+\def\@IEEEtranneedspace#1#2{\penalty-100\begingroup%shield temp variable
+\@IEEEtrantmpdimenB\pagegoal\advance\@IEEEtrantmpdimenB-\pagetotal% space left
+\ifdim #1>\@IEEEtrantmpdimenB\relax% not enough space left
+\ifdim\@IEEEtrantmpdimenB>\z@\relax #2\fi%
+\newpage%
+\fi\endgroup}
+
+
+
+% IEEEbiography ENVIRONMENT
+% Allows user to enter biography leaving place for picture (adapts to font size)
+% As of V1.5, a new optional argument allows you to have a real graphic!
+% V1.5 and later also fixes the "colliding biographies" which could happen when a
+% biography's text was shorter than the space for the photo.
+% MDS 7/2001
+% V1.6 prevent multiple biographies from making multiple TOC entries
+\newif\if@IEEEbiographyTOCentrynotmade
+\global\@IEEEbiographyTOCentrynotmadetrue
+
+% biography counter so hyperref can jump directly to the biographies
+% and not just the previous section
+\newcounter{IEEEbiography}
+\setcounter{IEEEbiography}{0}
+
+% photo area size
+\def\@IEEEBIOphotowidth{1.0in} % width of the biography photo area
+\def\@IEEEBIOphotodepth{1.25in} % depth (height) of the biography photo area
+% area cleared for photo
+\def\@IEEEBIOhangwidth{1.14in} % width cleared for the biography photo area
+\def\@IEEEBIOhangdepth{1.25in} % depth cleared for the biography photo area
+ % actual depth will be a multiple of
+ % \baselineskip, rounded up
+\def\@IEEEBIOskipN{4\baselineskip}% nominal value of the vskip above the biography
+
+\newenvironment{IEEEbiography}[2][]{\normalfont\@IEEEcompsoconly{\sffamily}\footnotesize%
+\unitlength 1in\parskip=0pt\par\parindent 1em\interlinepenalty500%
+% we need enough space to support the hanging indent
+% the nominal value of the spacer
+% and one extra line for good measure
+\@IEEEtrantmpdimenA=\@IEEEBIOhangdepth%
+\advance\@IEEEtrantmpdimenA by \@IEEEBIOskipN%
+\advance\@IEEEtrantmpdimenA by 1\baselineskip%
+% if this page does not have enough space, break it and lets start
+% with a new one
+\@IEEEtranneedspace{\@IEEEtrantmpdimenA}{\relax}%
+% nominal spacer can strech, not shrink use 1fil so user can out stretch with \vfill
+\vskip \@IEEEBIOskipN plus 1fil minus 0\baselineskip%
+% the default box for where the photo goes
+\def\@IEEEtempbiographybox{{\setlength{\fboxsep}{0pt}\framebox{%
+\begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}\centering PLACE\\ PHOTO\\ HERE \end{minipage}}}}%
+%
+% detect if the optional argument was supplied, this requires the
+% \@ifmtarg command as defined in the appendix section above
+% and if so, override the default box with what they want
+\@ifmtarg{#1}{\relax}{\def\@IEEEtempbiographybox{\mbox{\begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}%
+\centering%
+#1%
+\end{minipage}}}}% end if optional argument supplied
+% Make an entry into the table of contents only if we have not done so before
+\if@IEEEbiographyTOCentrynotmade%
+% link labels to the biography counter so hyperref will jump
+% to the biography, not the previous section
+\setcounter{IEEEbiography}{-1}%
+\refstepcounter{IEEEbiography}%
+\addcontentsline{toc}{section}{Biographies}%
+\global\@IEEEbiographyTOCentrynotmadefalse%
+\fi%
+% one more biography
+\refstepcounter{IEEEbiography}%
+% Make an entry for this name into the table of contents
+\addcontentsline{toc}{subsection}{#2}%
+% V1.6 properly handle if a new paragraph should occur while the
+% hanging indent is still active. Do this by redefining \par so
+% that it will not start a new paragraph. (But it will appear to the
+% user as if it did.) Also, strip any leading pars, newlines, or spaces.
+\let\@IEEEBIOORGparCMD=\par% save the original \par command
+\edef\par{\hfil\break\indent}% the new \par will not be a "real" \par
+\settoheight{\@IEEEtrantmpdimenA}{\@IEEEtempbiographybox}% get height of biography box
+\@IEEEtrantmpdimenB=\@IEEEBIOhangdepth%
+\@IEEEtrantmpcountA=\@IEEEtrantmpdimenB% countA has the hang depth
+\divide\@IEEEtrantmpcountA by \baselineskip% calculates lines needed to produce the hang depth
+\advance\@IEEEtrantmpcountA by 1% ensure we overestimate
+% set the hanging indent
+\hangindent\@IEEEBIOhangwidth%
+\hangafter-\@IEEEtrantmpcountA%
+% reference the top of the photo area to the top of a capital T
+\settoheight{\@IEEEtrantmpdimenB}{\mbox{T}}%
+% set the photo box, give it zero width and height so as not to disturb anything
+\noindent\makebox[0pt][l]{\hspace{-\@IEEEBIOhangwidth}\raisebox{\@IEEEtrantmpdimenB}[0pt][0pt]{%
+\raisebox{-\@IEEEBIOphotodepth}[0pt][0pt]{\@IEEEtempbiographybox}}}%
+% now place the author name and begin the bio text
+\noindent\textbf{#2\ }\@IEEEgobbleleadPARNLSP}{\relax\let\par=\@IEEEBIOORGparCMD\par%
+% 7/2001 V1.5 detect when the biography text is shorter than the photo area
+% and pad the unused area - preventing a collision from the next biography entry
+% MDS
+\ifnum \prevgraf <\@IEEEtrantmpcountA\relax% detect when the biography text is shorter than the photo
+ \advance\@IEEEtrantmpcountA by -\prevgraf% calculate how many lines we need to pad
+ \advance\@IEEEtrantmpcountA by -1\relax% we compensate for the fact that we indented an extra line
+ \@IEEEtrantmpdimenA=\baselineskip% calculate the length of the padding
+ \multiply\@IEEEtrantmpdimenA by \@IEEEtrantmpcountA%
+ \noindent\rule{0pt}{\@IEEEtrantmpdimenA}% insert an invisible support strut
+\fi%
+\par\normalfont}
+
+
+
+% V1.6
+% added biography without a photo environment
+\newenvironment{IEEEbiographynophoto}[1]{%
+% Make an entry into the table of contents only if we have not done so before
+\if@IEEEbiographyTOCentrynotmade%
+% link labels to the biography counter so hyperref will jump
+% to the biography, not the previous section
+\setcounter{IEEEbiography}{-1}%
+\refstepcounter{IEEEbiography}%
+\addcontentsline{toc}{section}{Biographies}%
+\global\@IEEEbiographyTOCentrynotmadefalse%
+\fi%
+% one more biography
+\refstepcounter{IEEEbiography}%
+% Make an entry for this name into the table of contents
+\addcontentsline{toc}{subsection}{#1}%
+\normalfont\@IEEEcompsoconly{\sffamily}\footnotesize\interlinepenalty500%
+\vskip 4\baselineskip plus 1fil minus 0\baselineskip%
+\parskip=0pt\par%
+\noindent\textbf{#1\ }\@IEEEgobbleleadPARNLSP}{\relax\par\normalfont}
+
+
+% provide the user with some old font commands
+% got this from article.cls
+\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
+\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
+\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
+\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
+\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
+\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
+\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
+\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal}
+\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal}
+
+
+% SPECIAL PAPER NOTICE COMMANDS
+%
+% holds the special notice text
+\def\@IEEEspecialpapernotice{\relax}
+
+% for special papers, like invited papers, the user can do:
+% \IEEEspecialpapernotice{(Invited Paper)} before \maketitle
+\def\IEEEspecialpapernotice#1{\ifCLASSOPTIONconference%
+\def\@IEEEspecialpapernotice{{\sublargesize\textit{#1}\vspace*{1em}}}%
+\else%
+\def\@IEEEspecialpapernotice{{\\*[1.5ex]\sublargesize\textit{#1}}\vspace*{-2ex}}%
+\fi}
+
+
+
+
+% PUBLISHER ID COMMANDS
+% to insert a publisher's ID footer
+% V1.6 \IEEEpubid has been changed so that the change in page size and style
+% occurs in \maketitle. \IEEEpubid must now be issued prior to \maketitle
+% use \IEEEpubidadjcol as before - in the second column of the title page
+% These changes allow \maketitle to take the reduced page height into
+% consideration when dynamically setting the space between the author
+% names and the maintext.
+%
+% the amount the main text is pulled up to make room for the
+% publisher's ID footer
+% IEEE uses about 1.3\baselineskip for journals,
+% dynamic title spacing will clean up the fraction
+\def\@IEEEpubidpullup{1.3\baselineskip}
+\ifCLASSOPTIONtechnote
+% for technotes it must be an integer of baselineskip as there can be no
+% dynamic title spacing for two column mode technotes (the title is in the
+% in first column) and we should maintain an integer number of lines in the
+% second column
+% There are some examples (such as older issues of "Transactions on
+% Information Theory") in which IEEE really pulls the text off the ID for
+% technotes - about 0.55in (or 4\baselineskip). We'll use 2\baselineskip
+% and call it even.
+\def\@IEEEpubidpullup{2\baselineskip}
+\fi
+
+% V1.7 compsoc does not use a pullup
+\ifCLASSOPTIONcompsoc
+\def\@IEEEpubidpullup{0pt}
+\fi
+
+% holds the ID text
+\def\@IEEEpubid{\relax}
+
+% flag so \maketitle can tell if \IEEEpubid was called
+\newif\if@IEEEusingpubid
+\global\@IEEEusingpubidfalse
+% issue this command in the page to have the ID at the bottom
+% V1.6 use before \maketitle
+\def\IEEEpubid#1{\def\@IEEEpubid{#1}\global\@IEEEusingpubidtrue}
+
+
+% command which will pull up (shorten) the column it is executed in
+% to make room for the publisher ID. Place in the second column of
+% the title page when using \IEEEpubid
+% Is smart enough not to do anything when in single column text or
+% if the user hasn't called \IEEEpubid
+% currently needed in for the second column of a page with the
+% publisher ID. If not needed in future releases, please provide this
+% command and define it as \relax for backward compatibility
+% v1.6b do not allow command to operate if the peer review option has been
+% selected because \IEEEpubidadjcol will not be on the cover page.
+% V1.7 do nothing if compsoc
+\def\IEEEpubidadjcol{\ifCLASSOPTIONcompsoc\else\ifCLASSOPTIONpeerreview\else
+\if@twocolumn\if@IEEEusingpubid\enlargethispage{-\@IEEEpubidpullup}\fi\fi\fi\fi}
+
+% Special thanks to Peter Wilson, Daniel Luecking, and the other
+% gurus at comp.text.tex, for helping me to understand how best to
+% implement the IEEEpubid command in LaTeX.
+
+
+
+%% Lockout some commands under various conditions
+
+% general purpose bit bucket
+\newsavebox{\@IEEEtranrubishbin}
+
+% flags to prevent multiple warning messages
+\newif\if@IEEEWARNthanks
+\newif\if@IEEEWARNIEEEPARstart
+\newif\if@IEEEWARNIEEEbiography
+\newif\if@IEEEWARNIEEEbiographynophoto
+\newif\if@IEEEWARNIEEEpubid
+\newif\if@IEEEWARNIEEEpubidadjcol
+\newif\if@IEEEWARNIEEEmembership
+\newif\if@IEEEWARNIEEEaftertitletext
+\@IEEEWARNthankstrue
+\@IEEEWARNIEEEPARstarttrue
+\@IEEEWARNIEEEbiographytrue
+\@IEEEWARNIEEEbiographynophototrue
+\@IEEEWARNIEEEpubidtrue
+\@IEEEWARNIEEEpubidadjcoltrue
+\@IEEEWARNIEEEmembershiptrue
+\@IEEEWARNIEEEaftertitletexttrue
+
+
+%% Lockout some commands when in various modes, but allow them to be restored if needed
+%%
+% save commands which might be locked out
+% so that the user can later restore them if needed
+\let\@IEEESAVECMDthanks\thanks
+\let\@IEEESAVECMDIEEEPARstart\IEEEPARstart
+\let\@IEEESAVECMDIEEEbiography\IEEEbiography
+\let\@IEEESAVECMDendIEEEbiography\endIEEEbiography
+\let\@IEEESAVECMDIEEEbiographynophoto\IEEEbiographynophoto
+\let\@IEEESAVECMDendIEEEbiographynophoto\endIEEEbiographynophoto
+\let\@IEEESAVECMDIEEEpubid\IEEEpubid
+\let\@IEEESAVECMDIEEEpubidadjcol\IEEEpubidadjcol
+\let\@IEEESAVECMDIEEEmembership\IEEEmembership
+\let\@IEEESAVECMDIEEEaftertitletext\IEEEaftertitletext
+
+
+% disable \IEEEPARstart when in draft mode
+% This may have originally been done because the pre-V1.6 drop letter
+% algorithm had problems with a non-unity baselinestretch
+% At any rate, it seems too formal to have a drop letter in a draft
+% paper.
+\ifCLASSOPTIONdraftcls
+\def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** ATTENTION: \noexpand\IEEEPARstart
+ is disabled in draft mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse}
+\fi
+% and for technotes
+\ifCLASSOPTIONtechnote
+\def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** WARNING: \noexpand\IEEEPARstart
+ is locked out for technotes (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse}
+\fi
+
+
+% lockout unneeded commands when in conference mode
+\ifCLASSOPTIONconference
+% when locked out, \thanks, \IEEEbiography, \IEEEbiographynophoto, \IEEEpubid,
+% \IEEEmembership and \IEEEaftertitletext will all swallow their given text.
+% \IEEEPARstart will output a normal character instead
+% warn the user about these commands only once to prevent the console screen
+% from filling up with redundant messages
+\def\thanks#1{\if@IEEEWARNthanks\typeout{** WARNING: \noexpand\thanks
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNthanksfalse}
+\def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** WARNING: \noexpand\IEEEPARstart
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse}
+
+
+% LaTeX treats environments and commands with optional arguments differently.
+% the actual ("internal") command is stored as \\commandname
+% (accessed via \csname\string\commandname\endcsname )
+% the "external" command \commandname is a macro with code to determine
+% whether or not the optional argument is presented and to provide the
+% default if it is absent. So, in order to save and restore such a command
+% we would have to save and restore \\commandname as well. But, if LaTeX
+% ever changes the way it names the internal names, the trick would break.
+% Instead let us just define a new environment so that the internal
+% name can be left undisturbed.
+\newenvironment{@IEEEbogusbiography}[2][]{\if@IEEEWARNIEEEbiography\typeout{** WARNING: \noexpand\IEEEbiography
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEbiographyfalse%
+\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}
+% and make biography point to our bogus biography
+\let\IEEEbiography=\@IEEEbogusbiography
+\let\endIEEEbiography=\end@IEEEbogusbiography
+
+\renewenvironment{IEEEbiographynophoto}[1]{\if@IEEEWARNIEEEbiographynophoto\typeout{** WARNING: \noexpand\IEEEbiographynophoto
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEbiographynophotofalse%
+\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}
+
+\def\IEEEpubid#1{\if@IEEEWARNIEEEpubid\typeout{** WARNING: \noexpand\IEEEpubid
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEpubidfalse}
+\def\IEEEpubidadjcol{\if@IEEEWARNIEEEpubidadjcol\typeout{** WARNING: \noexpand\IEEEpubidadjcol
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEpubidadjcolfalse}
+\def\IEEEmembership#1{\if@IEEEWARNIEEEmembership\typeout{** WARNING: \noexpand\IEEEmembership
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEmembershipfalse}
+\def\IEEEaftertitletext#1{\if@IEEEWARNIEEEaftertitletext\typeout{** WARNING: \noexpand\IEEEaftertitletext
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEaftertitletextfalse}
+\fi
+
+
+% provide a way to restore the commands that are locked out
+\def\IEEEoverridecommandlockouts{%
+\typeout{** ATTENTION: Overriding command lockouts (line \the\inputlineno).}%
+\let\thanks\@IEEESAVECMDthanks%
+\let\IEEEPARstart\@IEEESAVECMDIEEEPARstart%
+\let\IEEEbiography\@IEEESAVECMDIEEEbiography%
+\let\endIEEEbiography\@IEEESAVECMDendIEEEbiography%
+\let\IEEEbiographynophoto\@IEEESAVECMDIEEEbiographynophoto%
+\let\endIEEEbiographynophoto\@IEEESAVECMDendIEEEbiographynophoto%
+\let\IEEEpubid\@IEEESAVECMDIEEEpubid%
+\let\IEEEpubidadjcol\@IEEESAVECMDIEEEpubidadjcol%
+\let\IEEEmembership\@IEEESAVECMDIEEEmembership%
+\let\IEEEaftertitletext\@IEEESAVECMDIEEEaftertitletext}
+
+
+
+% need a backslash character for typeout output
+{\catcode`\|=0 \catcode`\\=12
+|xdef|@IEEEbackslash{\}}
+
+
+% hook to allow easy disabling of all legacy warnings
+\def\@IEEElegacywarn#1#2{\typeout{** ATTENTION: \@IEEEbackslash #1 is deprecated (line \the\inputlineno).
+Use \@IEEEbackslash #2 instead.}}
+
+
+% provide for legacy commands
+\def\authorblockA{\@IEEElegacywarn{authorblockA}{IEEEauthorblockA}\IEEEauthorblockA}
+\def\authorblockN{\@IEEElegacywarn{authorblockN}{IEEEauthorblockN}\IEEEauthorblockN}
+\def\authorrefmark{\@IEEElegacywarn{authorrefmark}{IEEEauthorrefmark}\IEEEauthorrefmark}
+\def\PARstart{\@IEEElegacywarn{PARstart}{IEEEPARstart}\IEEEPARstart}
+\def\pubid{\@IEEElegacywarn{pubid}{IEEEpubid}\IEEEpubid}
+\def\pubidadjcol{\@IEEElegacywarn{pubidadjcol}{IEEEpubidadjcol}\IEEEpubidadjcol}
+\def\QED{\@IEEElegacywarn{QED}{IEEEQED}\IEEEQED}
+\def\QEDclosed{\@IEEElegacywarn{QEDclosed}{IEEEQEDclosed}\IEEEQEDclosed}
+\def\QEDopen{\@IEEElegacywarn{QEDopen}{IEEEQEDopen}\IEEEQEDopen}
+\def\specialpapernotice{\@IEEElegacywarn{specialpapernotice}{IEEEspecialpapernotice}\IEEEspecialpapernotice}
+
+
+
+% provide for legacy environments
+\def\biography{\@IEEElegacywarn{biography}{IEEEbiography}\IEEEbiography}
+\def\biographynophoto{\@IEEElegacywarn{biographynophoto}{IEEEbiographynophoto}\IEEEbiographynophoto}
+\def\keywords{\@IEEElegacywarn{keywords}{IEEEkeywords}\IEEEkeywords}
+\def\endbiography{\endIEEEbiography}
+\def\endbiographynophoto{\endIEEEbiographynophoto}
+\def\endkeywords{\endIEEEkeywords}
+
+
+% provide for legacy IED commands/lengths when possible
+\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}
+
+
+
+% let \proof use the IEEEtran version even after amsthm is loaded
+% \proof is now deprecated in favor of \IEEEproof
+\AtBeginDocument{\def\proof{\@IEEElegacywarn{proof}{IEEEproof}\IEEEproof}\def\endproof{\endIEEEproof}}
+
+% V1.7 \overrideIEEEmargins is no longer supported.
+\def\overrideIEEEmargins{%
+\typeout{** WARNING: \string\overrideIEEEmargins \space no longer supported (line \the\inputlineno).}%
+\typeout{** Use the \string\CLASSINPUTinnersidemargin, \string\CLASSINPUToutersidemargin \space controls instead.}}
+
+
+\endinput
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End of IEEEtran.cls %%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% That's all folks!
+
--- /dev/null
+(TeX-add-style-hook "new"
+ (lambda ()
+ (LaTeX-add-bibliographies
+ "biblio")
+ (LaTeX-add-labels
+ "sec:intro"
+ "fig:SIAC"
+ "fig:AIAC"
+ "sec:jacep2p"
+ "sec:archijaceP2P"
+ "fig:jaceP2P-v2"
+ "sec:benef"
+ "fig:pbdistclust"
+ "tab:benef"
+ "sec:pb"
+ "sec:pbmodel"
+ "sec:pbmodelapp"
+ "fig:tig"
+ "sec:pbmodelarchi"
+ "sec:pbmodelmapping"
+ "eq:et"
+ "eq:ettask"
+ "sec:pbrw"
+ "sec:aiacmapping"
+ "sec:specAIACmapping"
+ "sec:qmmodif"
+ "alg:qmmodified"
+ "sec:expe"
+ "sec:cg"
+ "fig:multisplit"
+ "fig:tigcg"
+ "sec:g5k"
+ "fig:g5ksite"
+ "sec:othermaping"
+ "sec:sma"
+ "alg:sma"
+ "sec:edgcutalgo"
+ "alg:edgecuts"
+ "sec:experiments"
+ "sec:xphetero"
+ "tab:exph1E"
+ "tab:exph1F"
+ "tab:exph2E"
+ "tab:exph2F"
+ "sec:xpvariation"
+ "tab:expparams"
+ "sec:conclu"
+ "sec:merci")
+ (TeX-add-symbols
+ '("myitemize" 1))
+ (TeX-run-style-hooks
+ "url"
+ "cite"
+ "algorithm2e"
+ "ruled"
+ "vlined"
+ "hyperref"
+ "graphicx"
+ "pdftex"
+ "final"
+ "babel"
+ "english"
+ "vmargin"
+ "amsfonts"
+ "amsmath"
+ "color"
+ "lmodern"
+ "inputenc"
+ "utf8x"
+ "ucs"
+ "fontenc"
+ "T1"
+ "latex2e"
+ "IEEEtran10"
+ "IEEEtran"
+ "conference"
+ "compsoc"
+ "a4paper")))
+
--- /dev/null
+@inproceedings{minimax,
+ author = {S. Kumar and
+ S. K. Das and
+ Rupak Biswas},
+ title = {Graph Partitioning for Parallel Applications in Heterogeneous
+ Grid Environments},
+ booktitle = {IPDPS},
+ year = {2002},
+}
+
+@inproceedings{fastmap,
+ author = {S. Sanyal and
+ A. Jain and
+ S. K. Das and
+ Rupak Biswas},
+ title = {A Hierarchical and Distributed Approach for Mapping Large
+ Applications to Heterogeneous Grids Using Genetic Algorithms},
+ booktitle = {CLUSTER},
+ year = {2003},
+ pages = {496-499},
+}
+
+
+@article{metis,
+ author = {G. Karypis and
+ V. Kumar},
+ title = {A Fast and High Quality Multilevel Scheme for Partioning Irregular Graphs},
+ journal = {SIAM Journal on Scientific Computing},
+ year = {1998},
+ number = {1},
+ volume = {20},
+ pages = {359-392}
+
+}
+
+
+@manual{chaco,
+ author = {B. Hendrickson and
+ R. W. Leland},
+ title = {The Chaco User's Guide},
+ organization = {Sandia National Laboratory},
+ address = {Albuquerque},
+ year = {1995}
+}
+
+@phdthesis{qm_these,
+ author = {P. Phinjaroenphan},
+ title = {An Efficient, Pratical, Portable Mapping Technique on Computational Grids},
+ school = {School of Computer Science and Information technology Science, Engineering and Technology Portfolio, RMIT University},
+ year = {2006}
+}
+
+@inproceedings{qm_papier,
+ author = {P. Phinjaroenphan and
+ S. Bevinakoppa and
+ P. Zeephongsekul},
+ title = {A Heuristic Algorithm for Mapping Parallel Applications
+ on Computational Grids},
+ booktitle = {EGC},
+ year = {2005},
+ pages = {1086-1096},
+}
+
+
+@article{cholesky-cg,
+ AUTHOR = "Hoole, S.R.H." ,
+ TITLE = "Optimal design, inverse problems and parallel computers",
+ JOURNAL = "IEEE Transactions on Magentics",
+ VOLUME = "27",
+ NUMBER = "5",
+ PAGES = "4146-4149",
+ MONTH = "September",
+ YEAR = "1991"
+}
+
+@conference{lu,
+ AUTHOR = "G. von Laszewski and M. Parashar and A.G. Mohamed and G.C. Fox" ,
+ TITLE = "On the parallelization of blocked LU factorization algorithms on distributed memory architectures" ,
+ BOOKTITLE = "Supercomputing" ,
+ MONTH = "November" ,
+ PAGES = "170-179",
+ YEAR = "1992"
+}
+
+@inbook{cg,
+ AUTHOR = "J. K. Reid (Ed)",
+ TITLE = "On the method of conjugate gradients for the solution of large sparse systems of linear equations",
+ PUBLISHER = "Academic Press Inc",
+ PAGES = "231-254",
+ MONTH = "March",
+ YEAR = "1971"
+}
+
+@inbook{book_raph,
+ AUTHOR = "J. Bahi and S. Contassot-Vivier and R. Couturier",
+ TITLE = "Parallel Iterative Algorithms: from Sequential to Grid Computing",
+ CHAPTER = "Asynchronous Iterations",
+ PAGES = "124-131",
+ publisher = {Chapman \& Hall/CRC},
+ series = {Numerical Analysis \& Scientific Computating},
+ volume = 1,
+ year = 2007,
+ note = {},
+}
+
+@inproceedings{jaceP2P-v2,
+ author = {J.-C. Charr and
+ R. Couturier and
+ D. Laiymani},
+ title = {JACEP2P-V2: A Fully Decentralized and Fault Tolerant Environment
+ for Executing Parallel Iterative Asynchronous Applications
+ on Volatile Distributed Architectures},
+ booktitle = {GPC},
+ year = {2009},
+ pages = {446-458},
+}
+
+@techreport{nas,
+ AUTHOR = "D. Bailey and E. Barszcz and J. Barton and D. Browning and R. Carter and L. Dagun and R. Fatoohi and S. Fineberg and P. Frederickson and T. Lasinski and R. Schreiber and H. Simon and V. venkatakrishnan and S. Weeratunga",
+ TITLE = "The {NAS} {P}arallel {B}enchmarks",
+ NUMBER = "RNR-94-007",
+ INSTITUTION = "The Numerical Aerodynamic Simalation Program of NASA",
+ MONTH = "March",
+ YEAR = "1994"
+}
+
+@misc{g5k,
+ AUTHOR = {},
+ TITLE = {Grid'5000},
+ NOTE = {http://www.grid5000.fr}
+}
+
+@misc{mtj,
+ author = {},
+ title = {\mbox{Matrix~Toolkit~Java}},
+ note = {http://code.google.com/p/matrix-toolkits-java/}
+}
+
+@article{conv_dec,
+ author = {J.-C. Charr and R. Couturier and D. Laiymani},
+ title = {A Fault Tolerant and Decentralized Convergence Detection Algorithm for Asynchronous Iterative Algorithms},
+ journal = {The journal of Supercomputing},
+ pages = {},
+ volume = {},
+ number = {},
+ publisher = {Springer},
+ year = {2009},
+ note = {Accepted manuscript. To appear.}
+}
+
+@article{farhat,
+ title = {A simple and efficient automatic fem domain decomposer},
+ journal = {Computers \& Structures},
+ volume = {28},
+ number = {5},
+ pages = {579 - 602},
+ year = {1988},
+ note = {},
+ issn = {0045-7949},
+ author = {C. Farhat}
+}
+
+@article{bcvc06:ij,
+ author = "J. Bahi and S. Contassot-Vivier and R. Couturier",
+ title = "Performance comparison of parallel programming environments
+ for implementing {AIAC} algorithms",
+ journal = "Journal of Supercomputing",
+ pages = "227--244",
+ volume = "35",
+ number = "3",
+ year = "2006"
+}
+
+@article{pagrid,
+ author = {S. Huang and
+ E. E. Aubanel and
+ V. C. Bhavsar},
+ title = {PaGrid: A Mesh Partitioner for Computational Grids},
+ journal = {J. Grid Comput.},
+ volume = {4},
+ number = {1},
+ year = {2006},
+ pages = {71-88},
+}
+
+@article{dag4,
+ author = {H. Topcuouglu and S. Hariri and M. Wu},
+ title = {Performance-Effective and Low-Complexity Task Scheduling for Heterogeneous Computing},
+ journal = {IEEE Trans. Parallel Distrib. Syst.},
+ volume = {13},
+ number = {3},
+ year = {2002},
+ issn = {1045-9219},
+ pages = {260--274},
+ publisher = {IEEE Press},
+ address = {Piscataway, NJ, USA},
+ }
+@article{dag3,
+author = {Y.-K. Kwok and I. Ahmad},
+title = {Dynamic Critical-Path Scheduling: An Effective Technique for Allocating Task Graphs to Multiprocessors},
+journal ={IEEE Transactions on Parallel and Distributed Systems},
+volume = {7},
+number = {5},
+issn = {1045-9219},
+year = {1996},
+pages = {506-521},
+publisher = {IEEE Computer Society},
+address = {Los Alamitos, CA, USA},
+}
+@book{dag2,
+ author = {V. Sarkar},
+ title = {Partitioning and Scheduling Parallel Programs for Multiprocessors},
+ year = {1989},
+ isbn = {0262691302},
+ publisher = {MIT Press},
+ address = {Cambridge, MA, USA},
+ }
+
+@article{dag1,
+ author = {T. Yang and
+ A. Gerasoulis},
+ title = {DSC: Scheduling Parallel Tasks on an Unbounded Number of
+ Processors},
+ journal = {IEEE Trans. Parallel Distrib. Syst.},
+ volume = {5},
+ number = {9},
+ year = {1994},
+ pages = {951-967},
+}
+
+@inproceedings{tig1,
+ author = {D. L. Long and
+ L. A. Clarke},
+ title = {Task Interaction Graphs for Concurrency Analysis},
+ booktitle = {ICSE},
+ year = {1989},
+ pages = {44-52},
+}
+
+@techreport{tig2,
+ author = {D. L. Long L. A. and Clarke},
+ title = {Task Interaction Graph: An Intermediate Representation for Concurrency},
+ year = {1988},
+ institution = {University of Massachusetts},
+ address = {Amherst, MA, USA},
+}
+
+@Book{npcomp,
+ author = {M. Garey and D. Johnson},
+ title = {Computer and Intractability : a guide to the Theory of NP-Completness},
+ publisher = {W.H. Freeman \& Co},
+ year = 1979
+}
+
+@inproceedings{largescale,
+ author = {J.-C. Charr and
+ R. Couturier and
+ D. Laiymani},
+ title = {Parallel numerical asynchronous iterative algorithms: Large
+ scale experimentations},
+ booktitle = {IPDPS},
+ year = {2009},
+ pages = {1-8},
+}
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+/col18 {0.560 0.000 0.000 srgb} bind def
+/col19 {0.690 0.000 0.000 srgb} bind def
+/col20 {0.820 0.000 0.000 srgb} bind def
+/col21 {0.560 0.000 0.560 srgb} bind def
+/col22 {0.690 0.000 0.690 srgb} bind def
+/col23 {0.820 0.000 0.820 srgb} bind def
+/col24 {0.500 0.190 0.000 srgb} bind def
+/col25 {0.630 0.250 0.000 srgb} bind def
+/col26 {0.750 0.380 0.000 srgb} bind def
+/col27 {1.000 0.500 0.500 srgb} bind def
+/col28 {1.000 0.630 0.630 srgb} bind def
+/col29 {1.000 0.750 0.750 srgb} bind def
+/col30 {1.000 0.880 0.880 srgb} bind def
+/col31 {1.000 0.840 0.000 srgb} bind def
+
+end
+
+% This junk string is used by the show operators
+/PATsstr 1 string def
+/PATawidthshow { % cx cy cchar rx ry string
+ % Loop over each character in the string
+ { % cx cy cchar rx ry char
+ % Show the character
+ dup % cx cy cchar rx ry char char
+ PATsstr dup 0 4 -1 roll put % cx cy cchar rx ry char (char)
+ false charpath % cx cy cchar rx ry char
+ /clip load PATdraw
+ % Move past the character (charpath modified the
+ % current point)
+ currentpoint % cx cy cchar rx ry char x y
+ newpath
+ moveto % cx cy cchar rx ry char
+ % Reposition by cx,cy if the character in the string is cchar
+ 3 index eq { % cx cy cchar rx ry
+ 4 index 4 index rmoveto
+ } if
+ % Reposition all characters by rx ry
+ 2 copy rmoveto % cx cy cchar rx ry
+ } forall
+ pop pop pop pop pop % -
+ currentpoint
+ newpath
+ moveto
+} bind def
+/PATcg {
+ 7 dict dup begin
+ /lw currentlinewidth def
+ /lc currentlinecap def
+ /lj currentlinejoin def
+ /ml currentmiterlimit def
+ /ds [ currentdash ] def
+ /cc [ currentrgbcolor ] def
+ /cm matrix currentmatrix def
+ end
+} bind def
+% PATdraw - calculates the boundaries of the object and
+% fills it with the current pattern
+/PATdraw { % proc
+ save exch
+ PATpcalc % proc nw nh px py
+ 5 -1 roll exec % nw nh px py
+ newpath
+ PATfill % -
+ restore
+} bind def
+% PATfill - performs the tiling for the shape
+/PATfill { % nw nh px py PATfill -
+ PATDict /CurrentPattern get dup begin
+ setfont
+ % Set the coordinate system to Pattern Space
+ PatternGState PATsg
+ % Set the color for uncolored pattezns
+ PaintType 2 eq { PATDict /PColor get PATsc } if
+ % Create the string for showing
+ 3 index string % nw nh px py str
+ % Loop for each of the pattern sources
+ 0 1 Multi 1 sub { % nw nh px py str source
+ % Move to the starting location
+ 3 index 3 index % nw nh px py str source px py
+ moveto % nw nh px py str source
+ % For multiple sources, set the appropriate color
+ Multi 1 ne { dup PC exch get PATsc } if
+ % Set the appropriate string for the source
+ 0 1 7 index 1 sub { 2 index exch 2 index put } for pop
+ % Loop over the number of vertical cells
+ 3 index % nw nh px py str nh
+ { % nw nh px py str
+ currentpoint % nw nh px py str cx cy
+ 2 index oldshow % nw nh px py str cx cy
+ YStep add moveto % nw nh px py str
+ } repeat % nw nh px py str
+ } for
+ 5 { pop } repeat
+ end
+} bind def
+
+% PATkshow - kshow with the current pattezn
+/PATkshow { % proc string
+ exch bind % string proc
+ 1 index 0 get % string proc char
+ % Loop over all but the last character in the string
+ 0 1 4 index length 2 sub {
+ % string proc char idx
+ % Find the n+1th character in the string
+ 3 index exch 1 add get % string proc char char+1
+ exch 2 copy % strinq proc char+1 char char+1 char
+ % Now show the nth character
+ PATsstr dup 0 4 -1 roll put % string proc chr+1 chr chr+1 (chr)
+ false charpath % string proc char+1 char char+1
+ /clip load PATdraw
+ % Move past the character (charpath modified the current point)
+ currentpoint newpath moveto
+ % Execute the user proc (should consume char and char+1)
+ mark 3 1 roll % string proc char+1 mark char char+1
+ 4 index exec % string proc char+1 mark...
+ cleartomark % string proc char+1
+ } for
+ % Now display the last character
+ PATsstr dup 0 4 -1 roll put % string proc (char+1)
+ false charpath % string proc
+ /clip load PATdraw
+ neewath
+ pop pop % -
+} bind def
+% PATmp - the makepattern equivalent
+/PATmp { % patdict patmtx PATmp patinstance
+ exch dup length 7 add % We will add 6 new entries plus 1 FID
+ dict copy % Create a new dictionary
+ begin
+ % Matrix to install when painting the pattern
+ TilingType PATtcalc
+ /PatternGState PATcg def
+ PatternGState /cm 3 -1 roll put
+ % Check for multi pattern sources (Level 1 fast color patterns)
+ currentdict /Multi known not { /Multi 1 def } if
+ % Font dictionary definitions
+ /FontType 3 def
+ % Create a dummy encoding vector
+ /Encoding 256 array def
+ 3 string 0 1 255 {
+ Encoding exch dup 3 index cvs cvn put } for pop
+ /FontMatrix matrix def
+ /FontBBox BBox def
+ /BuildChar {
+ mark 3 1 roll % mark dict char
+ exch begin
+ Multi 1 ne {PaintData exch get}{pop} ifelse % mark [paintdata]
+ PaintType 2 eq Multi 1 ne or
+ { XStep 0 FontBBox aload pop setcachedevice }
+ { XStep 0 setcharwidth } ifelse
+ currentdict % mark [paintdata] dict
+ /PaintProc load % mark [paintdata] dict paintproc
+ end
+ gsave
+ false PATredef exec true PATredef
+ grestore
+ cleartomark % -
+ } bind def
+ currentdict
+ end % newdict
+ /foo exch % /foo newlict
+ definefont % newfont
+} bind def
+% PATpcalc - calculates the starting point and width/height
+% of the tile fill for the shape
+/PATpcalc { % - PATpcalc nw nh px py
+ PATDict /CurrentPattern get begin
+ gsave
+ % Set up the coordinate system to Pattern Space
+ % and lock down pattern
+ PatternGState /cm get setmatrix
+ BBox aload pop pop pop translate
+ % Determine the bounding box of the shape
+ pathbbox % llx lly urx ury
+ grestore
+ % Determine (nw, nh) the # of cells to paint width and height
+ PatHeight div ceiling % llx lly urx qh
+ 4 1 roll % qh llx lly urx
+ PatWidth div ceiling % qh llx lly qw
+ 4 1 roll % qw qh llx lly
+ PatHeight div floor % qw qh llx ph
+ 4 1 roll % ph qw qh llx
+ PatWidth div floor % ph qw qh pw
+ 4 1 roll % pw ph qw qh
+ 2 index sub cvi abs % pw ph qs qh-ph
+ exch 3 index sub cvi abs exch % pw ph nw=qw-pw nh=qh-ph
+ % Determine the starting point of the pattern fill
+ %(px, py)
+ 4 2 roll % nw nh pw ph
+ PatHeight mul % nw nh pw py
+ exch % nw nh py pw
+ PatWidth mul exch % nw nh px py
+ end
+} bind def
+
+% Save the original routines so that we can use them later on
+/oldfill /fill load def
+/oldeofill /eofill load def
+/oldstroke /stroke load def
+/oldshow /show load def
+/oldashow /ashow load def
+/oldwidthshow /widthshow load def
+/oldawidthshow /awidthshow load def
+/oldkshow /kshow load def
+
+% These defs are necessary so that subsequent procs don't bind in
+% the originals
+/fill { oldfill } bind def
+/eofill { oldeofill } bind def
+/stroke { oldstroke } bind def
+/show { oldshow } bind def
+/ashow { oldashow } bind def
+/widthshow { oldwidthshow } bind def
+/awidthshow { oldawidthshow } bind def
+/kshow { oldkshow } bind def
+/PATredef {
+ MyAppDict begin
+ {
+ /fill { /clip load PATdraw newpath } bind def
+ /eofill { /eoclip load PATdraw newpath } bind def
+ /stroke { PATstroke } bind def
+ /show { 0 0 null 0 0 6 -1 roll PATawidthshow } bind def
+ /ashow { 0 0 null 6 3 roll PATawidthshow }
+ bind def
+ /widthshow { 0 0 3 -1 roll PATawidthshow }
+ bind def
+ /awidthshow { PATawidthshow } bind def
+ /kshow { PATkshow } bind def
+ } {
+ /fill { oldfill } bind def
+ /eofill { oldeofill } bind def
+ /stroke { oldstroke } bind def
+ /show { oldshow } bind def
+ /ashow { oldashow } bind def
+ /widthshow { oldwidthshow } bind def
+ /awidthshow { oldawidthshow } bind def
+ /kshow { oldkshow } bind def
+ } ifelse
+ end
+} bind def
+false PATredef
+% Conditionally define setcmykcolor if not available
+/setcmykcolor where { pop } {
+ /setcmykcolor {
+ 1 sub 4 1 roll
+ 3 {
+ 3 index add neg dup 0 lt { pop 0 } if 3 1 roll
+ } repeat
+ setrgbcolor - pop
+ } bind def
+} ifelse
+/PATsc { % colorarray
+ aload length % c1 ... cn length
+ dup 1 eq { pop setgray } { 3 eq { setrgbcolor } { setcmykcolor
+ } ifelse } ifelse
+} bind def
+/PATsg { % dict
+ begin
+ lw setlinewidth
+ lc setlinecap
+ lj setlinejoin
+ ml setmiterlimit
+ ds aload pop setdash
+ cc aload pop setrgbcolor
+ cm setmatrix
+ end
+} bind def
+
+/PATDict 3 dict def
+/PATsp {
+ true PATredef
+ PATDict begin
+ /CurrentPattern exch def
+ % If it's an uncolored pattern, save the color
+ CurrentPattern /PaintType get 2 eq {
+ /PColor exch def
+ } if
+ /CColor [ currentrgbcolor ] def
+ end
+} bind def
+% PATstroke - stroke with the current pattern
+/PATstroke {
+ countdictstack
+ save
+ mark
+ {
+ currentpoint strokepath moveto
+ PATpcalc % proc nw nh px py
+ clip newpath PATfill
+ } stopped {
+ (*** PATstroke Warning: Path is too complex, stroking
+ with gray) =
+ cleartomark
+ restore
+ countdictstack exch sub dup 0 gt
+ { { end } repeat } { pop } ifelse
+ gsave 0.5 setgray oldstroke grestore
+ } { pop restore pop } ifelse
+ newpath
+} bind def
+/PATtcalc { % modmtx tilingtype PATtcalc tilematrix
+ % Note: tiling types 2 and 3 are not supported
+ gsave
+ exch concat % tilingtype
+ matrix currentmatrix exch % cmtx tilingtype
+ % Tiling type 1 and 3: constant spacing
+ 2 ne {
+ % Distort the pattern so that it occupies
+ % an integral number of device pixels
+ dup 4 get exch dup 5 get exch % tx ty cmtx
+ XStep 0 dtransform
+ round exch round exch % tx ty cmtx dx.x dx.y
+ XStep div exch XStep div exch % tx ty cmtx a b
+ 0 YStep dtransform
+ round exch round exch % tx ty cmtx a b dy.x dy.y
+ YStep div exch YStep div exch % tx ty cmtx a b c d
+ 7 -3 roll astore % { a b c d tx ty }
+ } if
+ grestore
+} bind def
+/PATusp {
+ false PATredef
+ PATDict begin
+ CColor PATsc
+ end
+} bind def
+
+% vertical lines
+11 dict begin
+/PaintType 1 def
+/PatternType 1 def
+/TilingType 1 def
+/BBox [0 0 1 1] def
+/XStep 1 def
+/YStep 1 def
+/PatWidth 1 def
+/PatHeight 1 def
+/Multi 2 def
+/PaintData [
+ { clippath } bind
+ { 8 16 true [ 8 0 0 -16 0 16 ]
+ {<11111111111111111111111111111111>}
+ imagemask } bind
+] def
+/PaintProc {
+ pop
+ exec fill
+} def
+currentdict
+end
+/P10 exch def
+
+/cp {closepath} bind def
+/ef {eofill} bind def
+/gr {grestore} bind def
+/gs {gsave} bind def
+/sa {save} bind def
+/rs {restore} bind def
+/l {lineto} bind def
+/m {moveto} bind def
+/rm {rmoveto} bind def
+/n {newpath} bind def
+/s {stroke} bind def
+/sh {show} bind def
+/slc {setlinecap} bind def
+/slj {setlinejoin} bind def
+/slw {setlinewidth} bind def
+/srgb {setrgbcolor} bind def
+/rot {rotate} bind def
+/sc {scale} bind def
+/sd {setdash} bind def
+/ff {findfont} bind def
+/sf {setfont} bind def
+/scf {scalefont} bind def
+/sw {stringwidth} bind def
+/tr {translate} bind def
+/tnt {dup dup currentrgbcolor
+ 4 -2 roll dup 1 exch sub 3 -1 roll mul add
+ 4 -2 roll dup 1 exch sub 3 -1 roll mul add
+ 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb}
+ bind def
+/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul
+ 4 -2 roll mul srgb} bind def
+ /DrawEllipse {
+ /endangle exch def
+ /startangle exch def
+ /yrad exch def
+ /xrad exch def
+ /y exch def
+ /x exch def
+ /savematrix mtrx currentmatrix def
+ x y tr xrad yrad sc 0 0 1 startangle endangle arc
+ closepath
+ savematrix setmatrix
+ } def
+
+/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def
+/$F2psEnd {$F2psEnteredState restore end} def
+
+/pageheader {
+save
+newpath 0 218 moveto 0 0 lineto 338 0 lineto 338 218 lineto closepath clip newpath
+-152.3 295.7 translate
+1 -1 scale
+$F2psBegin
+10 setmiterlimit
+0 slj 0 slc
+ 0.06299 0.06299 sc
+} bind def
+/pagefooter {
+$F2psEnd
+restore
+} bind def
+%%EndProlog
+pageheader
+%
+% Fig objects follow
+%
+%
+% here starts figure with depth 50
+% Arc
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+ gr
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+% Ellipse
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+
+% Ellipse
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+
+% Ellipse
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+
+% Ellipse
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+
+% Ellipse
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+
+% Ellipse
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+
+% Ellipse
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+% Ellipse
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+% Ellipse
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+% Ellipse
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+% Ellipse
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+% Polyline
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--- /dev/null
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--- /dev/null
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--- /dev/null
+%!PS-Adobe-2.0 EPSF-2.0
+%%Title: dist_clust.fig
+%%Creator: fig2dev Version 3.2 Patchlevel 5a
+%%CreationDate: Fri Dec 4 09:17:26 2009
+%%BoundingBox: 0 0 423 288
+%Magnification: 1.0000
+%%EndComments
+%%BeginProlog
+/MyAppDict 100 dict dup begin def
+/$F2psDict 200 dict def
+$F2psDict begin
+$F2psDict /mtrx matrix put
+/col-1 {0 setgray} bind def
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+
+end
+
+% This junk string is used by the show operators
+/PATsstr 1 string def
+/PATawidthshow { % cx cy cchar rx ry string
+ % Loop over each character in the string
+ { % cx cy cchar rx ry char
+ % Show the character
+ dup % cx cy cchar rx ry char char
+ PATsstr dup 0 4 -1 roll put % cx cy cchar rx ry char (char)
+ false charpath % cx cy cchar rx ry char
+ /clip load PATdraw
+ % Move past the character (charpath modified the
+ % current point)
+ currentpoint % cx cy cchar rx ry char x y
+ newpath
+ moveto % cx cy cchar rx ry char
+ % Reposition by cx,cy if the character in the string is cchar
+ 3 index eq { % cx cy cchar rx ry
+ 4 index 4 index rmoveto
+ } if
+ % Reposition all characters by rx ry
+ 2 copy rmoveto % cx cy cchar rx ry
+ } forall
+ pop pop pop pop pop % -
+ currentpoint
+ newpath
+ moveto
+} bind def
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+ /lw currentlinewidth def
+ /lc currentlinecap def
+ /lj currentlinejoin def
+ /ml currentmiterlimit def
+ /ds [ currentdash ] def
+ /cc [ currentrgbcolor ] def
+ /cm matrix currentmatrix def
+ end
+} bind def
+% PATdraw - calculates the boundaries of the object and
+% fills it with the current pattern
+/PATdraw { % proc
+ save exch
+ PATpcalc % proc nw nh px py
+ 5 -1 roll exec % nw nh px py
+ newpath
+ PATfill % -
+ restore
+} bind def
+% PATfill - performs the tiling for the shape
+/PATfill { % nw nh px py PATfill -
+ PATDict /CurrentPattern get dup begin
+ setfont
+ % Set the coordinate system to Pattern Space
+ PatternGState PATsg
+ % Set the color for uncolored pattezns
+ PaintType 2 eq { PATDict /PColor get PATsc } if
+ % Create the string for showing
+ 3 index string % nw nh px py str
+ % Loop for each of the pattern sources
+ 0 1 Multi 1 sub { % nw nh px py str source
+ % Move to the starting location
+ 3 index 3 index % nw nh px py str source px py
+ moveto % nw nh px py str source
+ % For multiple sources, set the appropriate color
+ Multi 1 ne { dup PC exch get PATsc } if
+ % Set the appropriate string for the source
+ 0 1 7 index 1 sub { 2 index exch 2 index put } for pop
+ % Loop over the number of vertical cells
+ 3 index % nw nh px py str nh
+ { % nw nh px py str
+ currentpoint % nw nh px py str cx cy
+ 2 index oldshow % nw nh px py str cx cy
+ YStep add moveto % nw nh px py str
+ } repeat % nw nh px py str
+ } for
+ 5 { pop } repeat
+ end
+} bind def
+
+% PATkshow - kshow with the current pattezn
+/PATkshow { % proc string
+ exch bind % string proc
+ 1 index 0 get % string proc char
+ % Loop over all but the last character in the string
+ 0 1 4 index length 2 sub {
+ % string proc char idx
+ % Find the n+1th character in the string
+ 3 index exch 1 add get % string proc char char+1
+ exch 2 copy % strinq proc char+1 char char+1 char
+ % Now show the nth character
+ PATsstr dup 0 4 -1 roll put % string proc chr+1 chr chr+1 (chr)
+ false charpath % string proc char+1 char char+1
+ /clip load PATdraw
+ % Move past the character (charpath modified the current point)
+ currentpoint newpath moveto
+ % Execute the user proc (should consume char and char+1)
+ mark 3 1 roll % string proc char+1 mark char char+1
+ 4 index exec % string proc char+1 mark...
+ cleartomark % string proc char+1
+ } for
+ % Now display the last character
+ PATsstr dup 0 4 -1 roll put % string proc (char+1)
+ false charpath % string proc
+ /clip load PATdraw
+ neewath
+ pop pop % -
+} bind def
+% PATmp - the makepattern equivalent
+/PATmp { % patdict patmtx PATmp patinstance
+ exch dup length 7 add % We will add 6 new entries plus 1 FID
+ dict copy % Create a new dictionary
+ begin
+ % Matrix to install when painting the pattern
+ TilingType PATtcalc
+ /PatternGState PATcg def
+ PatternGState /cm 3 -1 roll put
+ % Check for multi pattern sources (Level 1 fast color patterns)
+ currentdict /Multi known not { /Multi 1 def } if
+ % Font dictionary definitions
+ /FontType 3 def
+ % Create a dummy encoding vector
+ /Encoding 256 array def
+ 3 string 0 1 255 {
+ Encoding exch dup 3 index cvs cvn put } for pop
+ /FontMatrix matrix def
+ /FontBBox BBox def
+ /BuildChar {
+ mark 3 1 roll % mark dict char
+ exch begin
+ Multi 1 ne {PaintData exch get}{pop} ifelse % mark [paintdata]
+ PaintType 2 eq Multi 1 ne or
+ { XStep 0 FontBBox aload pop setcachedevice }
+ { XStep 0 setcharwidth } ifelse
+ currentdict % mark [paintdata] dict
+ /PaintProc load % mark [paintdata] dict paintproc
+ end
+ gsave
+ false PATredef exec true PATredef
+ grestore
+ cleartomark % -
+ } bind def
+ currentdict
+ end % newdict
+ /foo exch % /foo newlict
+ definefont % newfont
+} bind def
+% PATpcalc - calculates the starting point and width/height
+% of the tile fill for the shape
+/PATpcalc { % - PATpcalc nw nh px py
+ PATDict /CurrentPattern get begin
+ gsave
+ % Set up the coordinate system to Pattern Space
+ % and lock down pattern
+ PatternGState /cm get setmatrix
+ BBox aload pop pop pop translate
+ % Determine the bounding box of the shape
+ pathbbox % llx lly urx ury
+ grestore
+ % Determine (nw, nh) the # of cells to paint width and height
+ PatHeight div ceiling % llx lly urx qh
+ 4 1 roll % qh llx lly urx
+ PatWidth div ceiling % qh llx lly qw
+ 4 1 roll % qw qh llx lly
+ PatHeight div floor % qw qh llx ph
+ 4 1 roll % ph qw qh llx
+ PatWidth div floor % ph qw qh pw
+ 4 1 roll % pw ph qw qh
+ 2 index sub cvi abs % pw ph qs qh-ph
+ exch 3 index sub cvi abs exch % pw ph nw=qw-pw nh=qh-ph
+ % Determine the starting point of the pattern fill
+ %(px, py)
+ 4 2 roll % nw nh pw ph
+ PatHeight mul % nw nh pw py
+ exch % nw nh py pw
+ PatWidth mul exch % nw nh px py
+ end
+} bind def
+
+% Save the original routines so that we can use them later on
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+/oldeofill /eofill load def
+/oldstroke /stroke load def
+/oldshow /show load def
+/oldashow /ashow load def
+/oldwidthshow /widthshow load def
+/oldawidthshow /awidthshow load def
+/oldkshow /kshow load def
+
+% These defs are necessary so that subsequent procs don't bind in
+% the originals
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+/eofill { oldeofill } bind def
+/stroke { oldstroke } bind def
+/show { oldshow } bind def
+/ashow { oldashow } bind def
+/widthshow { oldwidthshow } bind def
+/awidthshow { oldawidthshow } bind def
+/kshow { oldkshow } bind def
+/PATredef {
+ MyAppDict begin
+ {
+ /fill { /clip load PATdraw newpath } bind def
+ /eofill { /eoclip load PATdraw newpath } bind def
+ /stroke { PATstroke } bind def
+ /show { 0 0 null 0 0 6 -1 roll PATawidthshow } bind def
+ /ashow { 0 0 null 6 3 roll PATawidthshow }
+ bind def
+ /widthshow { 0 0 3 -1 roll PATawidthshow }
+ bind def
+ /awidthshow { PATawidthshow } bind def
+ /kshow { PATkshow } bind def
+ } {
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+ /eofill { oldeofill } bind def
+ /stroke { oldstroke } bind def
+ /show { oldshow } bind def
+ /ashow { oldashow } bind def
+ /widthshow { oldwidthshow } bind def
+ /awidthshow { oldawidthshow } bind def
+ /kshow { oldkshow } bind def
+ } ifelse
+ end
+} bind def
+false PATredef
+% Conditionally define setcmykcolor if not available
+/setcmykcolor where { pop } {
+ /setcmykcolor {
+ 1 sub 4 1 roll
+ 3 {
+ 3 index add neg dup 0 lt { pop 0 } if 3 1 roll
+ } repeat
+ setrgbcolor - pop
+ } bind def
+} ifelse
+/PATsc { % colorarray
+ aload length % c1 ... cn length
+ dup 1 eq { pop setgray } { 3 eq { setrgbcolor } { setcmykcolor
+ } ifelse } ifelse
+} bind def
+/PATsg { % dict
+ begin
+ lw setlinewidth
+ lc setlinecap
+ lj setlinejoin
+ ml setmiterlimit
+ ds aload pop setdash
+ cc aload pop setrgbcolor
+ cm setmatrix
+ end
+} bind def
+
+/PATDict 3 dict def
+/PATsp {
+ true PATredef
+ PATDict begin
+ /CurrentPattern exch def
+ % If it's an uncolored pattern, save the color
+ CurrentPattern /PaintType get 2 eq {
+ /PColor exch def
+ } if
+ /CColor [ currentrgbcolor ] def
+ end
+} bind def
+% PATstroke - stroke with the current pattern
+/PATstroke {
+ countdictstack
+ save
+ mark
+ {
+ currentpoint strokepath moveto
+ PATpcalc % proc nw nh px py
+ clip newpath PATfill
+ } stopped {
+ (*** PATstroke Warning: Path is too complex, stroking
+ with gray) =
+ cleartomark
+ restore
+ countdictstack exch sub dup 0 gt
+ { { end } repeat } { pop } ifelse
+ gsave 0.5 setgray oldstroke grestore
+ } { pop restore pop } ifelse
+ newpath
+} bind def
+/PATtcalc { % modmtx tilingtype PATtcalc tilematrix
+ % Note: tiling types 2 and 3 are not supported
+ gsave
+ exch concat % tilingtype
+ matrix currentmatrix exch % cmtx tilingtype
+ % Tiling type 1 and 3: constant spacing
+ 2 ne {
+ % Distort the pattern so that it occupies
+ % an integral number of device pixels
+ dup 4 get exch dup 5 get exch % tx ty cmtx
+ XStep 0 dtransform
+ round exch round exch % tx ty cmtx dx.x dx.y
+ XStep div exch XStep div exch % tx ty cmtx a b
+ 0 YStep dtransform
+ round exch round exch % tx ty cmtx a b dy.x dy.y
+ YStep div exch YStep div exch % tx ty cmtx a b c d
+ 7 -3 roll astore % { a b c d tx ty }
+ } if
+ grestore
+} bind def
+/PATusp {
+ false PATredef
+ PATDict begin
+ CColor PATsc
+ end
+} bind def
+
+% crosshatch45
+11 dict begin
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+/PatternType 1 def
+/TilingType 1 def
+/BBox [0 0 1 1] def
+/XStep 1 def
+/YStep 1 def
+/PatWidth 1 def
+/PatHeight 1 def
+/Multi 2 def
+/PaintData [
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+ { 20 20 true [ 20 0 0 -20 0 20 ]
+ {<8020004050102088201104400a02800401000a02
+ 8011044020882040501080200040501020882011
+ 04400a02800401000a0280110440208820405010>}
+ imagemask } bind
+] def
+/PaintProc {
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+ exec fill
+} def
+currentdict
+end
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+
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+/rs {restore} bind def
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+/rm {rmoveto} bind def
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+/slw {setlinewidth} bind def
+/srgb {setrgbcolor} bind def
+/rot {rotate} bind def
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+/ff {findfont} bind def
+/sf {setfont} bind def
+/scf {scalefont} bind def
+/sw {stringwidth} bind def
+/tr {translate} bind def
+/tnt {dup dup currentrgbcolor
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+ 4 -2 roll dup 1 exch sub 3 -1 roll mul add
+ 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb}
+ bind def
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+ 4 -2 roll mul srgb} bind def
+ /DrawEllipse {
+ /endangle exch def
+ /startangle exch def
+ /yrad exch def
+ /xrad exch def
+ /y exch def
+ /x exch def
+ /savematrix mtrx currentmatrix def
+ x y tr xrad yrad sc 0 0 1 startangle endangle arc
+ closepath
+ savematrix setmatrix
+ } def
+
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+/$F2psEnd {$F2psEnteredState restore end} def
+
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+} bind def
+/pagefooter {
+$F2psEnd
+restore
+} bind def
+%%EndProlog
+pageheader
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+% here ends figure;
+pagefooter
+showpage
+%%Trailer
+end
+%EOF
--- /dev/null
+#FIG 3.2 Produced by xfig version 3.2.5a
+Landscape
+Center
+Metric
+A4
+100.00
+Single
+-2
+1200 2
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+6 6840 3240 8010 3825
+# Desktop tower
+# Drawn by Dirko van Schalkwyk
+6 7106 3240 7470 3825
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+ 0.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
+ 0.000
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+ 0.000
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+ 0.000 0.000
+-6
+# Desktop tower
+# Drawn by Dirko van Schalkwyk
+6 7376 3240 7740 3825
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+ 0.000
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+ 0.000 0.000
+-6
+# Desktop tower
+# Drawn by Dirko van Schalkwyk
+6 7646 3240 8010 3825
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+-6
+# Desktop tower
+# Drawn by Dirko van Schalkwyk
+6 7601 2205 7965 2790
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+-6
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+4 0 0 50 -1 2 13 0.0000 4 150 690 6930 5085 clusters\001
+4 0 0 50 -1 2 13 0.0000 4 195 1350 6930 4860 Site containing\001
+4 0 0 50 -1 2 13 0.0000 4 195 1935 6930 5760 High latency network\001
+4 0 0 50 -1 2 13 0.0000 4 195 1875 6930 5445 Low latency network\001
--- /dev/null
+#FIG 3.2 Produced by xfig version 3.2.5a
+Landscape
+Center
+Metric
+A4
+100.00
+Single
+-2
+1200 2
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+0 33 #eff8ff
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+6 6840 3240 8010 3825
+# Desktop tower
+# Drawn by Dirko van Schalkwyk
+6 7106 3240 7470 3825
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+-6
+# Desktop tower
+# Drawn by Dirko van Schalkwyk
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+# Desktop tower
+# Drawn by Dirko van Schalkwyk
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+-6
+# Desktop tower
+# Drawn by Dirko van Schalkwyk
+6 6881 3240 7245 3825
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+\bibcite{lu}{2}
+\bibcite{cg}{3}
+\bibcite{book_raph}{4}
+\bibcite{bcvc06:ij}{5}
+\bibcite{jaceP2P-v2}{6}
+\bibcite{g5k}{7}
+\bibcite{dag1}{8}
+\bibcite{dag2}{9}
+\bibcite{dag3}{10}
+\bibcite{dag4}{11}
+\bibcite{tig1}{12}
+\bibcite{tig2}{13}
+\bibcite{npcomp}{14}
+\bibcite{metis}{15}
+\bibcite{chaco}{16}
+\bibcite{pagrid}{17}
+\bibcite{fastmap}{18}
+\bibcite{minimax}{19}
+\bibcite{qm_these}{20}
+\bibcite{nas}{21}
+\bibcite{mtj}{22}
+\bibcite{largescale}{23}
+\bibcite{farhat}{24}
+\@writefile{toc}{\contentsline {section}{References}{12}{section*.2}}
--- /dev/null
+\begin{thebibliography}{10}
+
+\bibitem{cholesky-cg}
+S.R.H. Hoole.
+\newblock Optimal design, inverse problems and parallel computers.
+\newblock {\em IEEE Transactions on Magentics}, 27(5):4146--4149, September
+ 1991.
+
+\bibitem{lu}
+G.~von Laszewski, M.~Parashar, A.G. Mohamed, and G.C. Fox.
+\newblock On the parallelization of blocked lu factorization algorithms on
+ distributed memory architectures.
+\newblock In {\em Supercomputing}, pages 170--179, November 1992.
+
+\bibitem{cg}
+J.~K.~Reid (Ed).
+\newblock {\em On the method of conjugate gradients for the solution of large
+ sparse systems of linear equations}, pages 231--254.
+\newblock Academic Press Inc, March 1971.
+
+\bibitem{book_raph}
+J.~Bahi, S.~Contassot-Vivier, and R.~Couturier.
+\newblock {\em Parallel Iterative Algorithms: from Sequential to Grid
+ Computing}, volume~1 of {\em Numerical Analysis \& Scientific Computating},
+ chapter Asynchronous Iterations, pages 124--131.
+\newblock Chapman \& Hall/CRC, 2007.
+
+\bibitem{bcvc06:ij}
+J.~Bahi, S.~Contassot-Vivier, and R.~Couturier.
+\newblock Performance comparison of parallel programming environments for
+ implementing {AIAC} algorithms.
+\newblock {\em Journal of Supercomputing}, 35(3):227--244, 2006.
+
+\bibitem{jaceP2P-v2}
+J.-C. Charr, R.~Couturier, and D.~Laiymani.
+\newblock Jacep2p-v2: A fully decentralized and fault tolerant environment for
+ executing parallel iterative asynchronous applications on volatile
+ distributed architectures.
+\newblock In {\em GPC}, pages 446--458, 2009.
+
+\bibitem{g5k}
+Grid'5000.
+\newblock http://www.grid5000.fr.
+
+\bibitem{dag1}
+T.~Yang and A.~Gerasoulis.
+\newblock Dsc: Scheduling parallel tasks on an unbounded number of processors.
+\newblock {\em IEEE Trans. Parallel Distrib. Syst.}, 5(9):951--967, 1994.
+
+\bibitem{dag2}
+V.~Sarkar.
+\newblock {\em Partitioning and Scheduling Parallel Programs for
+ Multiprocessors}.
+\newblock MIT Press, Cambridge, MA, USA, 1989.
+
+\bibitem{dag3}
+Y.-K. Kwok and I.~Ahmad.
+\newblock Dynamic critical-path scheduling: An effective technique for
+ allocating task graphs to multiprocessors.
+\newblock {\em IEEE Transactions on Parallel and Distributed Systems},
+ 7(5):506--521, 1996.
+
+\bibitem{dag4}
+H.~Topcuouglu, S.~Hariri, and M.~Wu.
+\newblock Performance-effective and low-complexity task scheduling for
+ heterogeneous computing.
+\newblock {\em IEEE Trans. Parallel Distrib. Syst.}, 13(3):260--274, 2002.
+
+\bibitem{tig1}
+D.~L. Long and L.~A. Clarke.
+\newblock Task interaction graphs for concurrency analysis.
+\newblock In {\em ICSE}, pages 44--52, 1989.
+
+\bibitem{tig2}
+D.~L. Long~L. A. and Clarke.
+\newblock Task interaction graph: An intermediate representation for
+ concurrency.
+\newblock Technical report, University of Massachusetts, Amherst, MA, USA,
+ 1988.
+
+\bibitem{npcomp}
+M.~Garey and D.~Johnson.
+\newblock {\em Computer and Intractability : a guide to the Theory of
+ NP-Completness}.
+\newblock W.H. Freeman \& Co, 1979.
+
+\bibitem{metis}
+G.~Karypis and V.~Kumar.
+\newblock A fast and high quality multilevel scheme for partioning irregular
+ graphs.
+\newblock {\em SIAM Journal on Scientific Computing}, 20(1):359--392, 1998.
+
+\bibitem{chaco}
+B.~Hendrickson and R.~W. Leland.
+\newblock {\em The Chaco User's Guide}.
+\newblock Sandia National Laboratory, Albuquerque, 1995.
+
+\bibitem{pagrid}
+S.~Huang, E.~E. Aubanel, and V.~C. Bhavsar.
+\newblock Pagrid: A mesh partitioner for computational grids.
+\newblock {\em J. Grid Comput.}, 4(1):71--88, 2006.
+
+\bibitem{fastmap}
+S.~Sanyal, A.~Jain, S.~K. Das, and Rupak Biswas.
+\newblock A hierarchical and distributed approach for mapping large
+ applications to heterogeneous grids using genetic algorithms.
+\newblock In {\em CLUSTER}, pages 496--499, 2003.
+
+\bibitem{minimax}
+S.~Kumar, S.~K. Das, and Rupak Biswas.
+\newblock Graph partitioning for parallel applications in heterogeneous grid
+ environments.
+\newblock In {\em IPDPS}, 2002.
+
+\bibitem{qm_these}
+P.~Phinjaroenphan.
+\newblock {\em An Efficient, Pratical, Portable Mapping Technique on
+ Computational Grids}.
+\newblock PhD thesis, School of Computer Science and Information technology
+ Science, Engineering and Technology Portfolio, RMIT University, 2006.
+
+\bibitem{nas}
+D.~Bailey, E.~Barszcz, J.~Barton, D.~Browning, R.~Carter, L.~Dagun, R.~Fatoohi,
+ S.~Fineberg, P.~Frederickson, T.~Lasinski, R.~Schreiber, H.~Simon,
+ V.~venkatakrishnan, and S.~Weeratunga.
+\newblock The {NAS} {P}arallel {B}enchmarks.
+\newblock Technical Report RNR-94-007, The Numerical Aerodynamic Simalation
+ Program of NASA, March 1994.
+
+\bibitem{mtj}
+\mbox{Matrix~Toolkit~Java}.
+\newblock http://code.google.com/p/matrix-toolkits-java/.
+
+\bibitem{largescale}
+J.-C. Charr, R.~Couturier, and D.~Laiymani.
+\newblock Parallel numerical asynchronous iterative algorithms: Large scale
+ experimentations.
+\newblock In {\em IPDPS}, pages 1--8, 2009.
+
+\bibitem{farhat}
+C.~Farhat.
+\newblock A simple and efficient automatic fem domain decomposer.
+\newblock {\em Computers \& Structures}, 28(5):579 -- 602, 1988.
+
+\end{thebibliography}
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--- /dev/null
+\BOOKMARK [1][-]{section.1}{Introduction}{}
+\BOOKMARK [1][-]{section.2}{JaceP2P-V2}{}
+\BOOKMARK [2][-]{subsection.2.1}{Architecture}{section.2}
+\BOOKMARK [2][-]{subsection.2.2}{Benefits of mapping}{section.2}
+\BOOKMARK [1][-]{section.3}{Problem description}{}
+\BOOKMARK [2][-]{subsection.3.1}{Model formalization}{section.3}
+\BOOKMARK [3][-]{subsubsection.3.1.1}{Application modeling}{subsection.3.1}
+\BOOKMARK [3][-]{subsubsection.3.1.2}{Architecture modeling}{subsection.3.1}
+\BOOKMARK [3][-]{subsubsection.3.1.3}{Mapping functions}{subsection.3.1}
+\BOOKMARK [2][-]{subsection.3.2}{Related work}{section.3}
+\BOOKMARK [1][-]{section.4}{AIAC mapping}{}
+\BOOKMARK [2][-]{subsection.4.1}{Specificities of the AIAC mapping problem}{section.4}
+\BOOKMARK [2][-]{subsection.4.2}{AIAC Quick-quality Map}{section.4}
+\BOOKMARK [1][-]{section.5}{Experimentation}{}
+\BOOKMARK [2][-]{subsection.5.1}{The NAS Parallel Benchmark Kernel CG}{section.5}
+\BOOKMARK [2][-]{subsection.5.2}{The Grid'5000 platform}{section.5}
+\BOOKMARK [2][-]{subsection.5.3}{Other mapping algorithms}{section.5}
+\BOOKMARK [3][-]{subsubsection.5.3.1}{A Simple Mapping algorithm}{subsection.5.3}
+\BOOKMARK [3][-]{subsubsection.5.3.2}{Edge-cuts optimization}{subsection.5.3}
+\BOOKMARK [2][-]{subsection.5.4}{Experiments}{section.5}
+\BOOKMARK [3][-]{subsubsection.5.4.1}{About heterogeneity}{subsection.5.4}
+\BOOKMARK [3][-]{subsubsection.5.4.2}{Parameters variation}{subsection.5.4}
+\BOOKMARK [1][-]{section.6}{Conclusion and future works}{}
+\BOOKMARK [1][-]{section*.2}{References}{}
--- /dev/null
+%% Version PDSEC
+\documentclass[conference,compsoc,a4paper]{IEEEtran}
+
+%% Pour Ingrid
+%\documentclass[conference,compsoc,a4paper,onecolumn]{IEEEtran}
+%\documentclass[compsoc,a4paper,oneside]{IEEEtran}
+
+\usepackage[T1]{fontenc}
+\usepackage{ucs}
+\usepackage[utf8x]{inputenc}
+\usepackage{lmodern}
+\usepackage{color}
+%% Jolis entetes %%
+%\usepackage[Glenn]{fncychap}
+\usepackage{amsmath}
+%\usepackage{amsthm}
+\usepackage{amsfonts}
+%\usepackage{graphicx}
+%\usepackage{xspace}
+% Definition des marges
+\usepackage{vmargin}
+\setpapersize[portrait]{A4}
+
+\usepackage[english]{babel}
+% Extension pour les graphiques EPS
+%\usepackage[dvips]{graphicx}
+\usepackage[pdftex,final]{graphicx}
+% Extension pour les liens intra-documents (tagged PDF)
+% et l'affichage correct des URL (commande \url{http://example.com})
+\usepackage{hyperref}
+% Extension pour que plus de titres apparaissent dans la table des matieres
+% (table des matieres, bibliographie, index).
+%\usepackage{tocbibind}
+%\newcommand{\tabledesmatieres}{
+% \setlength{\parskip}{0ex} % suppression de l'espace entre les paragraphes
+% \tableofcontents
+% \espacementnormal
+%}
+%\NoAutoSpaceBeforeFDP
+%\author{Sébastien Miquée}
+
+\usepackage[ruled,vlined]{algorithm2e}
+\usepackage{cite}
+
+\newcommand{\myitemize}[1]
+{
+\begin{itemize}
+\itemsep=#1pt
+}
+
+%
+\ifCLASSINFOpdf
+ \usepackage[pdftex]{graphicx}
+ \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
+\else
+\fi
+
+% *** PDF, URL AND HYPERLINK PACKAGES ***
+%
+\usepackage{url}
+
+
+\title{Mapping Asynchronous Iterative Applications on Heterogeneous
+ Distributed Architectures}
+
+\author{
+\IEEEauthorblockN{Raphaël Couturier \hspace{10pt} David Laiymani
+ \hspace{10pt} Sébastien Miquée}
+
+\IEEEauthorblockA{Laboratoire d'Informatique de Franche-Comté
+ (LIFC)\\
+ University of Franche-Comté\\
+ IUT de Belfort-Montbéliard,2 Rue Engel Gros, BP 27, 90016 Belfort,
+ France\\
+ % Tel.: +33-3-84587782 \hspace{20pt} Fax: +33-3-84587781\\
+Email:
+\{raphael.couturier,david.laiymani,sebastien.miquee\}@univ-fcomte.fr}
+
+%\thanks{This work was supported by the European Interreg IV From-P2P project.}
+}
+
+%% Permet de réactiver le \thanks
+\IEEEoverridecommandlockouts
+
+\date{}
+\begin{document}
+
+%% left, top, right, bottom
+\setmargrb{20mm}{15mm}{20mm}{15mm}
+
+\IEEEcompsoctitleabstractindextext
+
+\maketitle
+
+
+\begin{abstract}
+ To design parallel numerical algorithms on large scale distributed
+ and heterogeneous platforms, the asynchronous iteration model (AIAC)
+ may be an efficient solution. This class of algorithm is very
+ suitable since it enables communication/computation overlapping and
+ it suppresses all synchronizations between computation nodes. Since
+ target architectures are composed of more than one thousand
+ heterogeneous nodes connected through heterogeneous networks, the
+ need for mapping algorithms is crucial. In this paper, we propose a
+ new mapping algorithm dedicated to the AIAC model. To evaluate our
+ mapping algorithm we first implemented it in the JaceP2P programming
+ and executing environment dedicated to AIAC applications. Then we
+ conducted a set of experiments on the Grid'5000 testbed with more
+ than 700 computing cores and with a real and typical AIAC
+ application based on the NAS parallel benchmarks. Results are very
+ encouraging and show that the use of our algorithm brings an
+ important gain in term of execution time (about $40\%$).\\
+
+% To design parallel and distributed applications on heterogeneous
+% distributed architectures, the asynchronous iteration model may be
+% an efficient solution. Such architectures contain various computing
+% nodes connected by heterogeneous links. Nowadays, these
+% architectures offer users too many computing nodes as they need, so
+% a choice should be done, which is called ``tasks mapping''. In this
+% paper we propose a comparison between different mapping algorithms,
+% in order to evaluate mapping needs of the asynchronous iteration
+% model on this kind of architectures. To do our experiments we used a
+% middleware, JaceP2P-V2, which allows users to design asynchronous
+% iterative applications and execute them on distributed
+% architectures, in which we added a mapping library.\\
+
+ \textup{\small \textbf{Keywords:} Mapping algorithms, Distributed
+ clusters, Parallel iterative asynchronous algorithms, Heterogeneous
+ architectures.}
+\end{abstract}
+
+
+\IEEEpeerreviewmaketitle
+
+%\begin{keywords}
+% Mapping algorithms, Distributed clusters, Parallel iterative
+% asynchronous algorithms, Heterogeneous architectures.
+%\end{keywords}
+
+\section{Introduction}
+\label{sec:intro}
+
+Nowadays scientists of many domains, like climatic simulation or
+biological research, need great and powerful architectures to compute
+their large applications. Distributed clusters architectures, which
+are part of the grid architecture, are one of the best architectures
+used to solve such applications with an acceptable execution
+time. These architectures provide a lot of heterogeneous computing
+nodes interconnected by a high performance network, but even with the
+greatest efforts of their maintainers, there are latency and
+computation capacity differences between clusters of each site.
+
+In order to efficiently use this massive
+distributed computation power, numerous numerical algorithms have been
+elaborated. These algorithms can be broadly classified into two
+categories:
+
+\myitemize{5}
+\item \textbf{Direct methods}, which give the exact solution of the
+ problem using a finite number of operations
+ (e.g. Cholesky\cite{cholesky-cg}, LU\cite{lu},etc). However, these
+ methods cannot be applied to all kinds of numerical problems. In
+ general, they are not well adapted to very large problems.
+\item \textbf{Iterative methods}, that repeat the same instructions
+ until a desired approximation of the solution is reached -- we say
+ that the algorithm has converged. Iterative algorithms constitute
+ the only known approach to solving some kinds of problems and they
+ are easier to parallelize than direct methods. The Jacobi or
+ Conjugate Gradient\cite{cg} algorithms are examples of such
+ iterative methods.
+\end{itemize}
+
+
+In the rest of this paper we only focus on iterative methods. Now to
+parallelize this kind of algorithm, two classes of parallel iterative
+models can be described:
+
+\myitemize{5}
+
+\begin{figure}[h!]
+ \vspace{0.1cm}
+ \centering
+ \includegraphics[width=7.4cm]{images/ISCA}
+ \caption{Two processors computing in the Synchronous Iteration - Asynchronous Communication (SIAC) model}
+ \label{fig:SIAC}
+\end{figure}
+
+\item \textbf{The synchronous iteration model}. In this model, as can
+ be seen on Figure \ref{fig:SIAC}, after each iteration (represented
+ by a filled rectangle), a node sends its results to its neighbors
+ and waits for the reception of all dependency messages from its
+ neighbors to start the next iteration. This results in large idle
+ times (represented by spaces between each iteration) and is
+ equivalent to a global synchronization of nodes after each
+ iteration. These synchronizations can strongly penalize the overall
+ performances of the application particularly in case of large scale
+ platforms with high latency network. Furthermore, if a message is
+ lost, its receiver will wait forever for this message and the
+ application will be blocked. In the same way, if a machine falls
+ down, all the computation will be blocked.
+
+\begin{figure}[h!]
+ \vspace{0.1cm}
+ \centering
+ \includegraphics[width=7.4cm]{images/IACA}
+ \caption{Two processors computing in the Asynchronous Iteration - Asynchronous Communication (AIAC) model}
+ \label{fig:AIAC}
+\end{figure}
+
+
+\item \textbf{The asynchronous iteration model}. In this
+ model\cite{book_raph}, as can be seen on Figure \ref{fig:AIAC}, after
+ each iteration, a node sends its results to its neighbors and starts
+ immediately the next iteration with the last received data. These
+ data could be data from previous iterations, because last data are
+ not arrived in time or neighbors have not finish their current
+ iteration. The receiving and sending mechanisms are asynchronous and
+ nodes do not have to wait for the reception of dependency messages
+ from their neighbors. Consequently, there is no more idle time
+ between two iterations. Furthermore, this model is tolerant to
+ messages loss and even if a node dies, the remaining nodes continue
+ the computation, with the last data the failed node
+ sent. Unfortunately, the asynchronous iteration model generally
+ requires more iterations than the synchronous one to converge to the
+ solution.
+
+ This class of algorithms is very suitable in a distributed clusters
+ computing context because it suppresses all synchronizations between
+ computation nodes, tolerates messages loss and enables the
+ overlapping of communications by computations. Interested readers
+ might consult \cite{bcvc06:ij} for a precise classification and
+ comparison of parallel iterative algorithms. In this way, several
+ experiments \cite{bcvc06:ij} show the relevance of the AIAC
+ algorithms in the context of distributed clusters with high latency
+ between clusters. These works underline the good adaptability of
+ AIAC algorithms to network and processor heterogeneity.
+\end{itemize}
+
+As we aim to solve very large problems on heterogeneous distributed
+architectures, in the rest of this study we only focus on the
+asynchronous iteration model. In order to efficiently use such
+algorithms on distributed clusters architectures, it is essential to
+map the tasks of the application to the best sub-sets of nodes of the
+target architecture. This mapping procedure must take into account
+parameters such as network heterogeneity, computing nodes
+heterogeneity and tasks heterogeneity in order to minimize the overall
+execution time of the application.
+%we have to select
+%sets of computing nodes, which can improve applications execution
+%time. Indeed, as there are more available nodes as we need on such
+%architectures, it is important to select appropriate computing nodes,
+%due to their heterogeneity at computation power as well as relying
+%network.
+To the best of our knowledge, there exits no algorithm which
+specifically addresses the mapping of AIAC applications on distributed
+architectures. The aim of this paper is to propose a new mapping
+algorithm dedicated to AIAC applications and to implement it into a
+real large scale computing platform, JaceP2P-V2. Experiments conducted
+on the Grid'5000 testbed with more than 400 computing cores show that
+this new algorithm allows to enhance the performances of JaceP2P-V2 of
+about $40\%$ for a real and typical AIAC application.
+
+%this mapping problem. Our aim is to evaluate the
+%more common approaches to solve this problem, by using several mapping
+%algorithms implemented in a real large scale computing platform,
+%JaceP2P-V2, on a true distributed clusters architecture.\\
+
+The rest of this paper is organized as follows. Section
+\ref{sec:jacep2p} presents the JaceP2P-V2 middleware. We focus here on
+one of the main drawbacks of this platform: its lack of an efficient
+mapping strategy. Section \ref{sec:pb} presents our mapping problem
+and quotes existing issues to address it. Section
+\ref{sec:aiacmapping} describes the specificities of the AIAC model
+and details the main solution we propose to address the AIAC mapping
+problem. In section \ref{sec:expe} we describe the experiments we have
+conducted, with their different components and results. These results
+were conducted on the Grid'5000 testbed with more than 400 computing
+cores and show an important gain (about $40\%$) of the overall
+execution time for a typical AIAC application, i.e. based on the NAS
+Parallel Benchmark. Finally, we give some concluding remarks and plan
+our future work in section \ref{sec:conclu}.
+
+
+\section{JaceP2P-V2}
+\label{sec:jacep2p}
+
+JaceP2P-V2\cite{jaceP2P-v2} is a distributed platform implemented
+using the Java programming language and dedicated to developing and
+executing parallel iterative asynchronous applications. JaceP2P-V2
+executes parallel iterative asynchronous applications with
+dependencies between computing nodes. In addition, JaceP2P is fault
+tolerant which allows it to execute parallel applications over
+volatile environments and even for stable environments like local
+clusters, it offers a safer and crash free platform. To our knowledge
+this is the only platform dedicated to designing and executing AIAC
+algorithms.
+
+\subsection{Architecture}
+\label{sec:archijaceP2P}
+
+In this section we describe the JaceP2P-V2 environment. As can be seen
+on Figure \ref{fig:jaceP2P-v2}, which shows its architecture, this
+platform is composed of three main entities:
+
+\begin{figure}[h!]
+ \vspace{0.1cm}
+ \centering
+ \includegraphics[width=7.4cm]{images/JACEP2P-V2}
+ \caption{The JaceP2P-V2 architecture}
+ \label{fig:jaceP2P-v2}
+\end{figure}
+
+\myitemize{5}
+\item The first entity is the ``super-node'' (represented by a big
+ circle in figure \ref{fig:jaceP2P-v2}). Super-nodes form a circular
+ network and store, in registers, the identifiers of all the
+ computing nodes that are connected to the platform and that are not
+ executing any application.
+% Each super-node has a status table containing the
+% number of connected computing nodes to each super-node and all the
+% super-nodes share a ``token'' that is passed successively from a
+% super-node to the next one. Once a super-node has the token, it
+% computes the average number of computing nodes connected to a
+% super-node ($avg$) using the status table. If $avg$ is lower than
+% the number of computing nodes connected to it, then it sends the
+% identifiers of the extra computing nodes to the super-nodes that
+% have the number of computing nodes connected to them less than
+% $avg$. If the number of computing nodes connected to it has changed,
+% it broadcasts the information to all the super-nodes in the
+% platform. Finally, it passes the token to the next super node. This
+% distribution reduces the load of the super-nodes.
+ A super-node regularly receives heartbeat messages (represented by
+ doted lines in figure \ref{fig:jaceP2P-v2}) from the computing nodes
+ connected to it. If a super-node does not receive a heartbeat
+ message from a computing node for a given period of time, it
+ declares that this computing node is dead and deletes its identifier
+ from the register.
+
+\item The second entity is the ``spawner'' (represented by a square in
+ figure \ref{fig:jaceP2P-v2}). When a user wants to execute a
+ parallel application that requires $N$ computing nodes, he or she
+ launches a spawner. The spawner contacts a super-node to reserve the
+ $N$ computing nodes plus some extra nodes. When the spawner receives
+ the list of nodes from the super-node, it transforms the extra
+ nodes into spawners (for fault tolerance and scalability reasons)
+ and stores the identifiers of the rest of the nodes in its own
+ register. Once the extra nodes are transformed into spawners, they
+ form a circular network and they receive the register containing the
+ identifiers of the computing nodes. Then each spawner becomes
+ responsible for a subgroup of computing nodes, starts the tasks on
+ the computing nodes under its command and sends a specific register
+ to them.
+% So each
+% computing node receives a specific register that only contains the
+% identifiers of the daemons it interacts with and that depends on the
+% application being executed. These specific registers reduce the
+% number of messages sent by the spawners to update the register of
+% the daemons after a daemon crashes because usually a small number of
+% daemons is affected by this crash.
+ If the spawner receives a message from a computing node informing
+ that one of its neighbors is fallen, it fetches a new one from the
+ super-node in order to replace the dead one. The spawner initializes
+ the new daemon, which retrieves the last backup (see next paragraph)
+ of the dead node and continues the computing task from that
+ checkpoint.
+
+\item The third entity is the ``daemon'', or the computing node,
+ (represented in figure \ref{fig:jaceP2P-v2} by a hashed small circle
+ if it is idle and by a white small circle if it is executing an
+ application). Once launched, it connects to a super-node and waits
+ for a task to execute. Once they begin executing an application they
+ form a circular network which is only used in the failure detection
+ mechanism. Each daemon can communicate directly with the daemons
+ whose identifiers are in its register. At the end of a task, the
+ daemons reconnect to a super-node.
+\end{itemize}
+
+To be able to execute asynchronous iterative applications, JaceP2P-V2
+has an asynchronous messaging mechanism and to resist daemons'
+failures, it implements a distributed backup mechanism called the
+uncoordinated distributed checkpointing. This method allows daemons to
+save their data on neighboring daemons without any user
+intervention. The asynchronous nature of the application allows two
+daemons to execute two different iterations, thus each daemon saves
+its status without synchronizing with other daemons. This
+decentralized procedure allows the platform to be very scalable, with
+no weak points and does not require a secure and stable station for
+backups. Moreover, since the AIAC model is tolerant to messages loss,
+if a daemon dies, the other computing nodes continue their tasks and
+are not affected by this failure.
+% The application convergence detection is done by daemons, using the
+% decentralized global convergence detection algorithm presented in
+% \cite{conv_dec}. It consists of two phases: the detection phase and
+% the verification phase. This algorithm aims to detect efficiently
+% the global convergence of asynchronous iterative parallel algorithms
+% on distributed architectures.
+For more details on the JaceP2P-V2 platform, readers can refer to
+\cite{jaceP2P-v2}.
+
+\subsection{Benefits of mapping}
+\label{sec:benef}
+
+In the JaceP2P-V2 environment, presented in the previous section,
+there is no effective mapping solution. Indeed, when a user wants to
+launch an application, the spawner emits a request to the super-node,
+which is in charge of available daemons. Basically, the super-node
+returns the amount of requested computing nodes by choosing in its own
+list.
+%,
+%if there are sufficient daemons connected on it, or in other
+%super-nodes lists, in addition of its one.
+In this method, the super-node only cares about the amount of
+requested nodes, it returns in general nodes in the order of their
+connection to the platform -- there is no specific selection.
+Distributed architectures such as distributed clusters, as can be seen
+on Figure \ref{fig:pbdistclust}, are often composed of heterogeneous
+clusters linked via heterogeneous networks with high latencies and
+bandwidths. As an example the Grid'5000\cite{g5k} testbed is composed
+of 23 clusters spread over 9 sites. Those clusters are heterogeneous,
+with computing powers starting from bi-cores at 2GHz to
+bi-quadri-cores at 2.83GHz with 2Go of memory for the first one to 8Go
+for the second. Links relying clusters are 10Gb/s capable, but as many
+researchers use this platform, high latencies appear in links between
+sites.
+%In the targeted architectures, which are distributed clusters, each
+%cluster provides a fixed number of homogeneous computing nodes --
+%computing nodes are heterogeneous from a cluster to another. Figure
+%\ref{fig:pbdistclust} represents such an architecture, in which we can
+%see different sites containing several heterogeneous clusters. Each
+%cluster is relied by high speed network with clusters in the same site
+%and in others. We note that the architecture may not be represented by
+%a full connected graph, as some sites are not directly connected to
+%some others. The Grid'5000 testbed, described in section
+%\ref{sec:g5k}, is an example of such a distributed clusters
+%architecture. Though there are efficient links relying each site, a
+%residual latency continues to exist, at local clusters (in the same
+%site) as well as distant clusters (from two distinct sites), and can
+%penalize performances.
+
+\begin{figure}[ht!]
+ \centering
+ \includegraphics[width=7.8cm]{images/dist_clust}
+ \caption{A distributed clusters architecture}
+ \label{fig:pbdistclust}
+\end{figure}
+
+
+With such an architecture, it could be
+efficient to assign tasks communicating with each other on the same
+cluster, in order to improve communications. But, as we use very large
+problems, it is quite impossible to find clusters containing as many
+computing nodes as requested. So we have to dispatch tasks over
+several clusters. That implies to deal with heterogeneity in clusters
+computing power and heterogeneity in network. We should make a
+trade-off between both components in order to take the best part
+of each one to improve the overall performances.
+%The
+%literature in high performance computing has broadly demonstrated the
+%benefits of mapping solutions on the applications execution time.
+
+In order to check if a tasks mapping algorithm would provide
+performances improvement in JaceP2P-V2 environment, we have evaluated
+the contributions of a simple mapping algorithm, which is described in
+section \ref{sec:sma}. These experiments used the NPB Kernel CG
+application described in section \ref{sec:cg}, with two problem sizes
+(the given problem sizes are the sides sizes of square matrices used)
+and using a distributed clusters architecture composed of 102
+computing nodes, representing 320 computing cores, spread over 5
+clusters in 5 sites. The results of these experiments are given in
+Table \ref{tab:benef}.
+
+\renewcommand{\arraystretch}{1.5}
+
+\begin{table}[h!]
+ \centering
+ \begin{tabular}{|c|c|c|}
+ \hline
+ Problem size&$550,000$&$5,000,000$\\
+ \hline
+ Execution Time (without mapping)&141s&129s\\
+ Execution Time (with mapping)&97s&81s\\
+ \hline
+ Gains&$31\%$&$37\%$\\
+ \hline
+ \end{tabular}
+ \caption{Effects of a simple tasks
+ mapping algorithm on application's execution time}
+ \label{tab:benef}
+\end{table}
+
+As can be seen in Table \ref{tab:benef}, the effects of a
+simple tasks mapping algorithm are significant.
+%Moreover, we can see
+%that are scalable with the application's size, which demonstrates the
+%real needs of the platform for a such algorithm.
+This encouraged us to look further for better task mapping
+algorithms. In the next section, we describe the specificities of our
+model and issues which can be exploited.
+
+\section{Problem description}
+\label{sec:pb}
+
+In this section we describe the AIAC mapping problem. We first
+formalize the different elements we should take into consideration:
+the application, the targeted architecture and the objectives
+functions of the mapping. We also give a state of the art about
+considered kinds of mapping algorithms.
+
+\subsection{Model formalization}
+\label{sec:pbmodel}
+
+In this section the models of the applications and architectures we
+used are given, with the objectives functions of the mapping
+algorithms.
+
+\subsubsection{Application modeling}
+\label{sec:pbmodelapp}
+
+In high performance computing, when we want to improve the global
+execution time of parallel applications we have to make an efficient
+assignation of tasks to computing nodes. Usually, to assign tasks of
+parallel applications to computing nodes, scheduling algorithms are
+used. These algorithms often represent the application by a graph,
+called DAG \cite{dag1,dag2,dag3,dag4} (Directed Acyclic Graph). In
+this graph, each task is represented by a vertex which is relied to
+others by edges, which represent dependencies and communications
+between tasks. This means that some tasks could not start before other
+ones finish their computation and send their results. As exposed in
+the introduction, in the AIAC model, there is no precedence between
+tasks.
+
+Indeed, with the AIAC model, all tasks compute in parallel at the same
+time. As communications are asynchronous, there is no synchronization
+and no precedence. During an iteration, each task does its job and
+sends results to its neighbors and continues with the next
+iteration. If a task receives new data from its dependencies, it
+includes them and the computation continues with these new data. If
+not all dependencies data, or none, are received before starting the
+computation of the next iteration, old data are used instead. Tasks
+are not blocked on dependencies. Nevertheless regularly receiving new
+data allows tasks to converge more quickly. So, it appears that DAG
+are not appropriate to modeling AIAC applications. TIG\cite{tig1,
+ tig2} (Task Interaction Graph) are more appropriate.
+%That is why we use the
+%TIG\cite{tig1, tig2} (Task Interaction Graph) model instead of DAG,
+%which allows to modeling application using tasks and their
+%communication dependencies. Figure \ref{fig:tig} gives an example of a
+%TIG.
+
+\begin{figure}[h!]
+ \centering
+ \includegraphics[width=5cm]{images/tig}
+ \caption{An example of a TIG of a nine tasks application}
+ \label{fig:tig}
+\end{figure}
+
+In the TIG model, a parallel program is represented by a graph
+%, as can
+%be seen in Figure \ref{fig:tig}. This graph
+$GT(V,E)$, where $V = \{V_1,V_2,\dots V_v\}$ is the set of $|V|$
+vertices and $E \subset V \times V$ is the set of undirectional edges
+(see Figure \ref{fig:tig}). The vertices represent tasks and the edges
+represent the mutual communication among tasks. A function $ET : V
+\rightarrow R^+$ gives the computation cost of tasks and $CT : E
+\rightarrow R^+$ gives the communication cost for message passing on
+edges. We define $v = |V|$, $ET(V_i) = e_i$ and $CT(V_i,V_j) =
+c_{ij}$. For example, in Figure \ref{fig:tig}, \mbox{$e_0$ = 10} and $c_{01}
+= 2$, $c_{03} = 2$ and $c_{04} = 2$. Tasks in TIG exchange information
+during their execution and there is no precedence relationship among
+tasks; each task cooperates with its neighbors. This model is used to
+represent applications, where tasks are considered to be executed
+simultaneously. Temporal dependencies in the execution of tasks are
+not explicitly addressed: all the tasks are considered simultaneously
+executable and communications can take place at any time during the
+computation. That is why vertices and edges are labeled with weights
+describing computational and communication costs.\\
+
+
+\subsubsection{Architecture modeling}
+\label{sec:pbmodelarchi}
+
+As TIG models the application, we have to model the targeted
+architecture. A distributed clusters architecture can be modeled by a
+three-level-graph. The levels are \textit{architecture} (a), in our
+study it is the Grid'5000 grid, \textit{cluster} (c) and computing
+node (n) levels. Figure \ref{fig:pbdistclust} in section
+\ref{sec:benef} shows such a model. Let $GG(N,L)$ be a graph
+representing a distributed clusters architecture, where $N =
+\{N_1,N_2,\dots N_n\}$ is the set of $|N|$ vertices and $L$ is the set
+of undirectional edges. The vertices represent the computing nodes and
+the edges represent the links between them. An edge $L_i \in L$ is an
+unordered pair $(N_x,N_y) \in N$, representing a communication link
+between nodes $x$ and $y$. Let be $|C|$ the number of clusters in the
+architecture containing computing nodes. A function $WN : N
+\rightarrow R^+$ gives the computational power of nodes and $WL : L
+\rightarrow R^+$ gives the communication latency of links. We define
+$WN(N_i) = wn_i$ and $WL(L_i,L_j) = wl_{ij}$.
+
+An architecture with a three-level-graph is specified according as
+follows. All computing nodes are in the same node level. When
+computing nodes can communicate to one another with the same
+communication latency, they can be grouped into the same cluster. In
+addition, like in the Grid'5000 testbed, if computing nodes seemly
+have the same computational power with a low communication latency, a
+cluster of these nodes can be defined. All participating clusters,
+including computing nodes, are in the same architecture level and
+communicate through the architecture network.\\
+
+
+\subsubsection{Mapping functions}
+\label{sec:pbmodelmapping}
+
+After having described the two graphs used to model the application
+and the architecture, this section defines our objectives.
+
+When a parallel application $App$, represented by a graph $GT$, is
+mapped on a distributed clusters architecture, represented by a graph
+$GG$, the execution time of the application, $ET(App)$, can be defined
+as the execution time of the slowest task.
+%In the AIAC model, tasks
+%have, in general, seemly the same work and communication loads; so the
+%difference on execution time depends on the executing machines.
+Indeed an application ends when all the tasks have detected
+convergence and have reached the desired approximation of the
+solution, that is why the execution time of the application depends on
+the slowest task.
+%, this converges last.
+We define
+\begin{equation}
+ \label{eq:et}
+ ET(App) = \max_{i=1 \dots v} ( ET(V_i) )
+\end{equation}
+
+where the
+%$ET(V_s)$ is the execution time of the slowest task $V_s$. The
+execution time of each task $i$ \mbox{($i=1 \dots v$)}, $ET(V_i)$ is
+given by
+\begin{equation}
+ \label{eq:ettask}
+ ET(V_i) = \frac{e_i}{wn_i} + \sum_{j \in J} c_{ij} \cdot wl_{ij}
+\end{equation}
+
+where $e_i$ is the computational cost of $V_i$, $wn_i$ is the
+computational power of the node $N_i$ on which $V_i$ is mapped, $J$
+represents the neighbors set of $V_i$, $c_{ij}$ is the amount of
+communications between $V_i$ and $V_j$, and $wn_{ij}$ is the link
+latency between the computing nodes on which are mapped $V_i$ and
+$V_j$.
+%Note that in the AIAC model, we only consider for $e_i$ the
+%cost of an only one iteration, as we cannot determine in advance the
+%amount of iterations a task should complete to converge.
+We underline here that in the AIAC model, it is impossible to predict
+the number of iterations of a task. So it is difficult to evaluate a
+priori the cost $e_i$ of a task. In the remainder, we approximate
+$e_i$ by the cost of one iteration.
+
+The mapping problem is similar to the classical graph partitioning and
+task assignment problem \cite{npcomp}, and is thus NP-complete.
+%The
+%generalization of this problem by considering both heterogeneous tasks
+%graph and architecture graph makes the problem more complex.
+%The JaceP2P-V2 platform is design to execute parallel asynchronous
+%iterative application on heterogeneous distributed architectures, so
+%it has to launch applications on a variety of computing nodes relying
+%by non-uniform links. As demonstrates in the previous section, it does
+%not map efficiently tasks on nodes and the overall performances can be
+%strongly penalize by this lack of mapping. Indeed, if the
+%heterogeneity degree of the architecture used is high, it can be
+%possible to have two neighbors tasks executing on two foreign
+%computing nodes, that penalizes communications between these tasks,
+%that increase the execution time. With the same mining, it is
+%interesting to have similar computing nodes, in order to have seemly
+%the same iteration execution time that allows to converge more
+%quickly. We can conclude that JaceP2P-V2 needs an algorithm to
+%efficiently map tasks on computing nodes.
+%
+%%As we use parallel distributed algorithms on distributed
+%%architectures, we have to efficiently map tasks on computing nodes, in
+%%order to obtain best performances and the slowest execution time of
+%%the application.
+%There exist many scheduling and mapping algorithms in the literature,
+%and the research is active in this domain. A first approach is to use
+%one the numerous scheduling algorithms, but our model does not fit
+%with them. Indeed, a scheduling implies that we have tasks which are
+%depending on others, more precisely that some tasks cannot start
+%computation before having received data from other tasks, which are
+%called precedences, or ``strong dependencies''. This class of
+%algorithms uses a well known application's representation: the DAG
+%(Direct Acyclic Graph). This model cannot be used with our
+%problematic. Indeed, in asynchronous iterative applications, all the
+%tasks are executed in the same time, in parallel; there is no
+%precedence. So we have to look at another way, which is the ``tasks
+%mapping''.
+%
+%The second approach is to use a tasks mapping algorithm, which only
+%aims to map tasks on nodes, following a metric, to minimize the
+%application's execution time. To determine which class of tasks
+%mapping algorithms we should consider, it is important to draw up a
+%list of which information we have in hands. When an application using
+%the asynchronous iteration model is run, the number of iterations to
+%converge to the solution is unpredictable and change from a run to
+%another. So, we cannot give a good approximation of the execution time
+%of a task, but we can retrieve an estimation of the computational
+%amount of a task (plus de détails ?). In addition, as the asynchronous
+%iteration model based algorithms are able to provide to applications
+%the message lost tolerance, we cannot exactly quantify the amount of
+%communications in an application; some algorithms can converge with
+%receiving only few dependencies messages. One application's
+%representation which fit perfectly with our model is the TIG (Task
+%Interaction Graph), which only considers relations between tasks --
+%the only thing which is predictable in our model. The figure
+%\ref{fig:tig} presents an example of a TIG.
+%
+%
+%
+%On figure \ref{fig:tig} we can see an application with 6 tasks, in
+%which each task is in relation with tasks of previous and next rank,
+%with two exceptions, the first and the last tasks, which can
+%eventually be in relation, depending of the application. This is a
+%commonly scheme in asynchronous iteration model; in general, tasks are
+%in relation with some others which previous and next ranks, but in
+%some cases, dependencies are more complex.
+
+\subsection{Related work}
+\label{sec:pbrw}
+
+%In the previous section we have determined that we need to use TIG
+%model based mapping algorithms to address our problem.
+In the literature of the TIG mapping, we can find many algorithms,
+which can be divided into two categories:
+
+\myitemize{5}
+\item \textbf{Edge-cuts optimization}. The aim of this class of
+ algorithms is to minimize the use of the penalizing links between
+ clusters. As tasks are depending on neighbors, which are called here
+ dependencies, the goal is to choose nodes which distance, in term of
+ network, is small, to improve communications between tasks. Here we
+ can cite Metis\cite{metis}, Chaco\cite{chaco} and
+ PaGrid\cite{pagrid} which are libraries containing such kind of
+ algorithms. The main drawback of edge-cuts algorithms is that they
+ do not tackle the computing nodes heterogeneity issues. They only
+ focus on communication overheads.
+% The figure \ref{fig:edge} shows
+% that the optimization is on edges of communications, which are
+% circled in red.
+%
+% \begin{figure}[h!]
+% \centering
+% \includegraphics[width=3.5cm]{images/edgecut}
+% \caption{The edge-cuts optimization}
+% \label{fig:edge}
+% \end{figure}
+\item \textbf{Execution time optimization}. The aim of these
+ algorithms is to minimize the whole execution time of the
+ application. They look for nodes which can provide the small
+ execution time of tasks using their computational power. Here we can
+ cite FastMap\cite{fastmap} and MiniMax\cite{minimax} as such kind of
+ algorithms. QM\cite{qm_these} is also an algorithm of this category,
+ but it aims to find for each task the node which can provide the
+ best execution time. QM works at the task level,
+ whereas others work at the application level.\\
+% The figure
+% \ref{fig:et} shows that the optimization is on tasks, which are
+% circled in red.\\
+%
+% \begin{figure}[h!]
+% \centering
+% \includegraphics[width=3.5cm]{images/exectime}
+% \caption{The execution time optimization}
+% \label{fig:et}
+% \end{figure}
+\end{itemize}
+
+The two classes of algorithms may fit with our goals, because in our
+model we have both the computational power of nodes and communication
+costs may influence the applications performances.
+
+Nevertheless, to the best of our knowledge, none of the existing
+algorithms take into consideration the specificities of the AIAC model
+(see next section).
+%specifically address the AIAC mapping problem.
+%As the existing mapping algorithms are not designed to fit
+%with the AIAC mapping problem.
+
+\section{AIAC mapping}
+\label{sec:aiacmapping}
+
+In this section we present the specificities of the AIAC model, which
+are interesting in the mapping problem, and the solution we propose:
+the AIAC QM algorithm, which is an extended version of the QM
+algorithm.
+
+\subsection{Specificities of the AIAC mapping problem}
+\label{sec:specAIACmapping}
+
+An important point to take into consideration in the AIAC model is
+that we do not allow the execution of multiple tasks on the same
+computing node. This comes from the fact that the targeted
+architectures are volatile distributed environments. Assigning
+multiple tasks to a node provides a fall of performances when this
+node fails. Indeed we should redeploy all of the tasks from this node
+to another one, using last saves, which implies to search a new
+available computing node, transfer saves to it and restart the
+computation from this point (which could be far from this just before
+the failure).
+
+Nevertheless, in order to benefit of multi-cores architectures, we use
+a task level parallelism by running multi-threaded sequential solver
+for example.
+%In addition, it is more simple and efficient to parallelize at the
+%task level using, as an example with the CG application, a
+%multi-threaded linear solver, which benefits of the multi-cores
+%architecture of computing nodes.
+
+Another important point in the AIAC model is that we should take into
+account precisely the locality issue. This comes from the fact that in
+this model, the faster and more frequently a task receives its
+dependencies, the faster it converges. Moreover, as the JaceP2P-V2
+environment is fault tolerant and tasks save checkpoints on their
+neighbors, it is more efficient to save on near nodes than on far
+ones.
+
+
+%As our problem is on task mapping, only considering the dependency
+%relations between tasks, with a part of consideration on task weight,
+%we should use TIG (\textit{task interaction graph}) mapping model.
+
+%\section{Mapping algorithms}
+%\label{sec:mapalgo}
+
+\subsection{AIAC Quick-quality Map}
+\label{sec:qmmodif}
+
+%After having describe the different kinds of mapping algorithms which
+%can be found in the literature, we now present the three algorithms we
+%use to do mapping in the JaceP2P-V2 environment.
+
+We present here the solution we propose, called \textit{AIAC QM
+ algorithm}, to address the AIAC mapping problem. We decided to
+improve the \textit{Quick-quality Map} (QM) algorithm since it is one
+of the most accurate to address the TIG mapping problem.
+%
+%\subsection{Modified Quick-quality Map}
+%\label{sec:modifiedqm}
+%
+%As the previous algorithm describe in section \ref{sec:sma} showed
+%that mapping provides a significant increase of applications
+%performances (which can be seen in the section \ref{sec:experiments}),
+%we decide to try another mapping algorithm, which is a modified
+%version of the \textit{Quick-quality Map} (QM) algorithm.
+%
+%
+%As explained in section \ref{sec:pb}, the asynchronous iteration model
+%is specific, as it is not a good solution to map many tasks on the
+%same node. This is why QM has been modified to take into account these
+%characteristics.
+% Indeed, originally QM tries to map many tasks on the
+%same node to improve the execution time of tasks by decreasing
+%communications costs. This solution can be good if communications
+%between tasks are heavy and if we consider that computing nodes are
+%stable and are not volatile. As
+
+%, we have modified some parts
+%of it to fit with our constraints. This was an opportunity to be taken
+%to insert a little part of ``edge-cuts'' optimization, as in our model
+%communications have to be taken into account.
+In its original version, this algorithm aims at privileging the
+computational power of nodes. Indeed, its aim is to find the more
+powerful node to map a task on. Moreover, a part of this algorithm is
+designed to map multiple tasks on the same node, in order to improve
+local communications. This solution can be efficient if communications
+between tasks are heavy and if we consider that computing nodes are
+stable and not volatile. This last point is in contradiction with
+our model, as we authorize only the execution of one task on a single
+node -- this allows to lose only the work of a single task in case of
+node's fault, with a low cost on restarting mechanism. Instead
+assigning multiple tasks on the same computing node, our mapping
+algorithm tries to keep tasks locality, to improve communications, by
+trying to assign tasks to computing nodes in the neighborhood
+of which their neighbors are mapped on.
+
+The pseudo-code of AIAC QM is given in Algorithm \ref{alg:qmmodified}.
+
+\SetAlgoSkip{}
+\begin{algorithm}
+ \SetLine
+ \dontprintsemicolon
+
+ \KwIn{Sets of tasks and computing nodes}
+ \KwOut{Mapping of tasks to nodes}
+
+ \BlankLine
+
+ sort nodes by descending power\;
+ map tasks in order on nodes\;
+ set all tasks \textit{moveable}\;
+ $r \leftarrow 1$\;
+
+ \BlankLine
+
+ \While{one task is moveable}{
+ \For{each task $t_{i}$ $\&\&$ $t_{i}$ is moveable }{
+ $n_{c} \leftarrow$ current node of $t_{i}$\;
+ $n_{n} \leftarrow t_{i}$\;
+
+ \BlankLine
+
+ \For{$k = 0 ; k < \frac{f \cdot n}{r} ; k++$}{
+ select random node $n_{r}$ in $[0,\frac{n}{r}]$\;
+ \If{ET($t_{i}$,$n_{r}$) $<$ ET($t_{i}$,$n_{n}$)}{
+ $n_{n} \leftarrow n_{r} $\;
+ }
+ }
+
+ \BlankLine
+
+ \For{each node $n_{v}$ near $dep(t_{i})$}{
+ \If{ET($t_{i}$,$n_{v}$) $<$ ET($t_{i}$,$n_{n}$)}{
+ $n_{n} \leftarrow n_{v} $\;
+ }
+ }
+
+ \BlankLine
+
+ \If{$n_{n} \neq n_{c}$}{
+ map $t_{i}$ on $n_{n}$\;
+ update ET of $t_{i}$ and dep($t_{i}$)\;
+ }
+ }
+
+ \BlankLine
+
+ set $t_i$ not moveable\;
+ $r \leftarrow r+1$ if all tasks have been considered\;
+ }
+
+ \caption{The AIAC QM}
+ \label{alg:qmmodified}
+\end{algorithm}
+%\vspace{-0.5cm}
+
+All nodes are first sorted in descending order according to their
+computation power, and all tasks are mapped on these nodes according
+to their identifier (they are also marked as ``moveable'', that means
+that each task can be moved from a node to another). As in the
+original QM algorithm, AIAC QM keeps track of the \textit{number of
+ rounds} $r$ ($r > 0$), that all tasks have been searched for a
+better node. This allows to reduce at each round the number of
+considered nodes. While there is at least one moveable task, it
+performs for each moveable task the search for a better node. It
+chooses a set of nodes, $\frac{f \cdot n}{r}$, where $f$ is defined as
+the search factor and $n$ is the number of nodes. $r$ and $f
+\in ]0,1]$ control the portion of nodes that will be considered where
+more numerous the rounds are, the less the considered nodes will
+be. Then the algorithm estimates the execution time $ET(v)$ of the
+task on each node. If it is smaller than the current node on which the
+task is mapped on, this node becomes the new potential node for
+task $t_i$.
+
+After having randomly searched for a new node, the AIAC QM tries to
+map the task on nodes that are neighbors of nodes of which the
+dependencies of $t_i$ are mapped on. This is one of the major
+modification to the original QM algorithm. It introduces a little part
+of ``edge-cuts'' optimization. In the original version, it tries to
+map the task $t_i$ on the same node of one as its dependencies. As
+explain in \ref{sec:specAIACmapping}, this is not an acceptable
+solution in our case. Instead, the algorithm now searches to map task
+$t_i$ on nodes which are near the ones its dependencies are mapped
+on. This search requires a parameter which indicates the maximum
+distance at which nodes should be from the node of dependencies of
+$t_i$.
+
+At the end of the algorithm, if a new node is found, $t_i$ is mapped
+on and its execution time is updated and $t_i$ is set to ``not
+moveable''. The execution time of each of its dependencies is also
+updated, and if this new execution time is higher than the previous,
+the task is set to ``moveable''. And finally, if all tasks have been
+considered in this round, $r$ is incremented.
+
+The complexity of the AIAC QM algorithm is about $O(n^2 \cdot
+t \cdot ln(r))$. This complexity is the same as the original
+(details are given in \cite{qm_these}, with a an increase of a factor
+$n$, corresponding to the edge-cuts part.
+
+\section{Experimentation}
+\label{sec:expe}
+
+We now describe the experiments we have conducted and their
+components, to evaluate the effects of the AIAC QM algorithm on
+application execution time.
+
+\subsection{The NAS Parallel Benchmark Kernel CG}
+\label{sec:cg}
+
+We used the ``Kernel CG'' of the NAS Parallel Benchmarks (NPB)
+\cite{nas} to evaluate the performances of the mapping
+algorithm. This benchmark is designed to be used on large
+architectures, because it tests communications over latency networks,
+by processing unstructured matrix vector multiplication. In this
+benchmark, a Conjugate Gradient is used to compute an approximation of
+the smallest eigenvalue of a large, sparse and symmetric positive
+definite matrix, by the inverse power method. In our tests, the whole
+matrix contains nonzero values, in order to stress more
+communications. As the Conjugate Gradient method cannot be executed
+with the asynchronous iteration model we have replaced it by another
+method called the multisplitting method. This latter supports the
+asynchronous iterative model.
+
+
+With the multisplitting algorithm, the $A$ matrix is split into
+horizontal rectangle parts, as Figure \ref{fig:multisplit} shows. Each
+of these parts is affected to a processor -- so the size of data
+depends on the matrix size but also on the number of participating
+nodes. In this way, a processor is in charge of computing its $X Sub$
+part by solving the following subsystem: $ASub \times XSub = BSub -
+DepLeft \times XLeft - DepRight \times XRight$
+
+After solving $XSub$, the result must be sent to other
+processors which depend on it.
+
+\begin{figure}[h!]
+ \centering
+ \includegraphics[width=7.4cm]{images/multisplit}
+ \caption{Data decomposition for the multisplitting method
+ implementation}
+ \label{fig:multisplit}
+\end{figure}
+
+The multisplitting method can be decomposed into four phases:
+\begin{enumerate}
+\itemsep=5pt
+\item \textbf{Data decomposition}. In this phase, data are allocated
+ to each processor assuming the decomposition exposed on figure
+ \ref{fig:multisplit}. Then, each processor iterates until converge
+ on the following.
+\item \textbf{Computation}. At the beginning of the computation, each
+ processor computes
+ $BLoc = BSub - DepLeft \times XLeft - DepRight \times XRight$. Then,
+ it solves $ASub \times XSub = BLoc$ by using a
+ multi-threaded sequential version of the Conjugate Gradient method.
+\item \textbf{Data exchange}. Each processor sends its $XSub$
+ part to its neighbors. Here, the neighborhood is closely related
+ to the density of the $A$ matrix. Clearly, a dense matrix implies an
+ \textit{all-to-all} communication scheme while a matrix with a low
+ bandwidth reduces the density of the communication scheme.
+\item \textbf{Convergence detection} Each processor computes its local
+ convergence and sends it to a server node. When this one detects
+ that each processor has converged, it stops the whole computation
+ process.
+\end{enumerate}
+
+%It can be pointed out here that it is possible to modify the data
+%decomposition in order to obtain non disjoint rectangle matrices. This
+%property of multisplitting methods, called \textit{overlapping}, can
+%bring significant improvements to convergence speed, but it is not the
+%aim of this paper.
+For more details about this method, interested readers are invited to
+see \cite{book_raph}. In our benchmark, the sequential solver part of
+the multisplitting method is the Conjugate Gradient, using the
+MTJ\cite{mtj} library. Its implementation is multi-threaded, so it
+benefits from multi-core processors.
+
+We point out here that this benchmark is a typical AIAC
+application. The general form of the TIG for this application is given
+by Figure \ref{fig:tigcg}.
+
+\begin{figure}[h!]
+ \centering
+ \includegraphics[width=8cm]{images/tigcg2}
+ \caption{Part of the form of the TIG representing an instance of the
+ NAS Kernel CG application}
+ \label{fig:tigcg}
+\end{figure}
+
+This figure shows 6 tasks, which are represented by a circle in which
+the identifier of the task is given. In our study, we consider that
+the computational costs of tasks are approximately the same and that the
+communications costs also the same (this comes from the difficulty to
+evaluate real costs in the AIAC model).
+% The computational cost of a task is given by the number on the top
+% left-hand side of each circle (for example the cost of task 31 is
+% 1000). Communications between tasks are represented by edges on
+% which the amount of communication is given (for example, the
+% communication cost between tasks 29 and 30 is about 30).
+Doted lines represent communications with tasks which are not
+represented on the figure. We can see here that each task has four
+neighbors (the two previous and the two next). This amount of
+neighbors is directly related to the bandwidth of the matrix (in this
+example the bandwidth is very small). For more details about the
+influence of the bandwidth on the amount of neighbors, interested
+readers are invited to see \cite{largescale}.
+
+For our experiments the bandwidth of matrices has been reduced in
+order to limit the dependencies and we fixed it to $35,000$. This
+bandwidth size generates, according to the problem's size, between 10
+and 25 neighbors per tasks.
+
+\subsection{The Grid'5000 platform}
+\label{sec:g5k}
+
+The platform used for our tests, called Grid’5000\cite{g5k}, is a
+French nationwide experimental set of clusters which provides a
+configurable and controllable instrument. We can find many clusters
+with different kinds of computers with various specifications and
+software.
+
+\begin{figure}[h!]
+ \centering
+ \includegraphics[height=6.5cm]{images/g5k-noms}
+ \caption{The Grid'5000 sites map}
+ \label{fig:g5ksite}
+\end{figure}
+
+Clusters are spread over 9 sites, as can be seen on Figure
+\ref{fig:g5ksite}, and the computing power represents more than 5000
+computing cores interconnected by the ``Renater'' network. This
+network is the national network for research and education; it
+provides a large bandwidth with high latency. Intra-clusters networks
+present small bandwidth and low latencies.
+
+
+\subsection{Other mapping algorithms}
+\label{sec:othermaping}
+
+In this section we present the two other mapping algorithms we used
+in our experiments to compare the performances of the AIAC QM
+algorithm. The first one was used to evaluate the benefits of a
+mapping solution in section \ref{sec:benef}. The second one was used
+to show the differences between the two mapping class, the ``execution
+time'' and the ``edge-cuts'' optimizations, as it is a fully edge-cut
+optimization based mapping algorithm.
+
+\subsubsection{A Simple Mapping algorithm}
+\label{sec:sma}
+
+%As mentioned in section \ref{sec:pb}, the asynchronous iteration model
+%has some specificities which distinguishes it from other classical model
+%for the mapping.
+%
+%The first thing we have done was to be sure that a mapping algorithm
+%would enhance applications performances.
+The \textit{Simple Mapping algorithm} (SMa) was designed to
+show the benefits of a mapping algorithm in the JaceP2P-V2 platform.
+%The text of the \textit{Simple Mapping} if given by
+Algorithm \ref{alg:sma} gives the pseudo-code of the \textit{Simple
+ Mapping algorithm}.
+%, in which we can see that it is very simple, with a complexity in $O(n^
+%2)$ resulting from sort methods.
+
+
+\SetAlgoSkip{}
+\begin{algorithm}
+ \SetLine
+ \dontprintsemicolon
+ \KwIn{Sets of tasks and computing nodes}
+ \KwOut{Mapping of tasks to nodes}
+
+ \BlankLine
+
+ sort computing nodes by cluster\;
+ sort clusters by size, from higher to lower\;
+ map tasks in order on sorted clusters\;
+ \caption{The Simple Mapping algorithm}
+ \label{alg:sma}
+\end{algorithm}
+
+
+%The aim of this algorithm is to do similarly to a very simple
+%edge-cuts optimization algorithm. To do that
+The algorithm puts each node in a cluster entity.
+%, which is given for now by the convention name of nodes
+%on Grid'5000 (for example azur-3.sophia.grid500.fr is the node 3 of
+%the azur cluster in the sophia site).
+Then it sorts clusters by their size, from the higher to the lower.
+%; this operation is the part which
+%is inspired by edge-cuts optimization based algorithms.
+Finally, all tasks are mapped in order on the sorted clusters; each
+task is assigned to a particular computing node of the chosen cluster.
+
+%Though this algorithm is trivial, it allows AIAC applications to run faster
+%on distributed clusters architectures, with a gain over $30\%$ on
+%execution, as experiments described in section \ref{sec:benef}.
+
+\subsubsection{Edge-cuts optimization}
+\label{sec:edgcutalgo}
+
+As explained in section \ref{sec:pb}, the asynchronous iteration model
+is so specific and unpredictable that we would like to evaluate the
+second kind of mapping algorithm, which aims to optimize the
+``edge-cuts''.
+%Multilevel partitioning algorithms such as Metis and
+%Chaco fail to address the limitations imposed by heterogeneity in the
+%underlying targeted system. They assume that computing nodes and
+%network relying them are homogeneous. This is not corresponding to our
+%execution environment, which is fully heterogeneous. These methods are
+%based on ``graph growing'' (GGP) and/or ``greedy graph growing''
+%(GGGP) algorithms which aim to divide tasks into two, or for some
+%algorithm a power of two, partitions. In our case, we do not know in
+%advance the number of partitions we need. Indeed, it depends on the
+%amount of nodes in each cluster and on the number of tasks.
+%
+%As GGP and GGGP algorithms seems to be efficient in specific cases, it
+%could be interesting to adapt one to our model, in order to evaluate a
+%real edge-cuts optimization algorithm.
+We choose the Farhat's algorithm\cite{farhat}, which has the ability
+to divide the graph into any number of partitions, thereby avoiding
+recursive bisection.
+%Therefore its running execution time is
+%independent of the desired number of subsections.
+
+The adapted version of this algorithm, Farhat's Edge-Cut (F-EC),
+evaluated in the JaceP2P-V2 environment is described in Algorithm
+\ref{alg:edgecuts}.
+
+\SetAlgoSkip{}
+\begin{algorithm}
+ \SetLine
+ \dontprintsemicolon
+
+ \KwIn{Sets of tasks and computing nodes}
+ \KwOut{Mapping of tasks to nodes}
+
+ \BlankLine
+
+
+ sort nodes by cluster\;
+ $lTasks \leftarrow$ sort tasks by dep degree\;
+ $changeCluster \leftarrow$ true\;
+ $cTasks \leftarrow$ empty;
+
+ \BlankLine
+
+ \While{one task is not mapped}{
+ \If{$changeCluster$}{
+ $curCluster \leftarrow$ nextCluster()\;
+ $places \leftarrow$ size($curCluster$)\;
+ $changeCluster \leftarrow$ false\;
+ $mTasks \leftarrow$ empty\;
+ }
+
+ \BlankLine
+
+ \If{no task in cTasks}{
+ $cTasks \leftarrow$ first task from $lTasks$\;
+ }
+
+ \BlankLine
+
+ $curTask \leftarrow$ first task in $cTasks$\;
+
+ \BlankLine
+
+ \eIf{$( 1 + $dep(curTask)~$\cdot~\delta) <= places)$}{
+ remove $curTask$ from $cTasks$\;
+ add $curTask$ in $mTasks$\;
+ $places \leftarrow places - 1$\;
+ add dep(curTask) in cTasks\;
+ }{
+ $changeCluster$ $\leftarrow$ true\;
+ associate $mTasks$ with $curCluster$\;
+ }
+ }
+
+ \caption{The Fahrat's Edge-Cut algorithm}
+ \label{alg:edgecuts}
+\end{algorithm}
+
+This algorithm aims to do a ``clusterization'' of the tasks. First, it
+groups computing nodes in clusters, which are sorted according to
+their number of nodes, from the higher to the lower. Tasks are ordered
+following their dependency degree, starting from the higher to the
+lower. Tasks in the top of the list have a higher priority to be
+mapped. Next, the algorithm tries to map on each cluster the maximum
+number of tasks. To map a task on a cluster, the algorithm evaluates
+if there is enough place to map the task and some of its
+dependencies. This amount of dependencies is fixed by a factor
+$\delta$, which is a parameter of the algorithm. In the positive case,
+the task is mapped on the current cluster and its dependencies become
+priority tasks to be mapped. This allows to keep the focus on the
+communicating tasks locality.
+%All computing nodes are first grouped in clusters.
+%%, using their full
+%%qualified name -- for now, no criteria is used to sort clusters, such
+%%are their power or size.
+%Next, tasks are inserted in a list $lTasks$, sorted in descending
+%according to their dependency degree. This allows to map tasks with
+%their dependencies to improve communications. Next begins the main
+%mapping loop.
+%
+%While not all tasks have been mapped the algorithm do the
+%following. First, at the beginning, it chooses the first available
+%cluster to be the current cluster to map tasks on, and sets the
+%variable $places$ to its size, in number of computing nodes, and
+%create a new tasks' list $mTasks$. During the execution of the
+%algorithm, passing in this block means that there is no more node
+%available in the current cluster, so it has to choose the next
+%cluster. Next, it looks in $cTasks$, which is a tasks list containing
+%tasks which are in instance to be mapped. If $cTasks$ is empty it
+%takes the first available task in $lTasks$ -- at the beginning it
+%takes the first one, which has the higher dependency degree.
+%
+%Next, it takes the first task in $cTasks$ to try to map it on the
+%current cluster. The task is mapped on if there is enough available
+%computing nodes on the current cluster. This amount of node
+%corresponds to $1 + dep( curTask ) \cdot \delta$, which represents the
+%task plus the amount of its dependencies multiplied by a ``local
+%dependency factor'' $\delta$, which indicates how many dependencies
+%must be a least with $curTask$ on the same cluster. If the task could
+%be mapped on this cluster, $curTask$ is added in $mTasks$, which is a
+%tasks' list containing tasks which are currently mapped on current
+%cluster, and removed it from $cTasks$. The number of available nodes,
+%$places$, is decremented, and the dependencies of $curTask$ are added
+%to $cTasks$. This list is sorted in the same way as $lTasks$, indeed
+%tasks are added according to their dependency degree, from the higher
+%to the lower. Otherwise, if there is not enough or no more nodes
+%available in the cluster, it has to change the current cluster, so it
+%associates the current cluster and list of tasks mapped on, $mTasks$.
+
+
+\subsection{Experiments}
+\label{sec:experiments}
+
+After having described the different components of the experiments, we
+now present the impacts of the AIAC QM mapping on applications running
+with JaceP2P-V2 on a heterogeneous distributed clusters
+architecture. In the following, we note ``heterogeneity degree'' the
+degree of heterogeneity of distributed clusters; it is the ratio
+between the average and the standard deviation of the computing nodes
+power. This heterogeneity degree may vary from 0, nodes are
+homogeneous, to 10, nodes are totally heterogeneous. In these
+experiments, we consider that there is no computing nodes fault during
+applications execution.
+
+The application used to realize these experiments is the KernelCG of
+the NAS parallel benchmark, in the multi-splitting version. Two
+problem sizes were used: one using a matrix of size $550,000$ (named
+``class E'') using 64 computing nodes and the other using a matrix of
+size $5,000,000$ (named ``class F'') using 128 nodes.
+%
+%Figure
+%\ref{fig:tigcg} shows a part of a TIG of this application.
+%
+%\begin{figure}[h!]
+% \centering
+%
+% \label{fig:tigcg}
+%\end{figure}
+
+
+
+\subsubsection{About heterogeneity}
+\label{sec:xphetero}
+
+The first experiments concern the study of the impact of the
+heterogeneity of the computing nodes on the mapping
+results. Heterogeneity takes an important place in the high
+performance computing on grid, all the more so when using the
+asynchronous iteration model.
+
+As mapping algorithms take in parameter a factor of research (for AIAC
+QM) and the amount of local dependencies (for F-EC), we fixed both to
+$50\%$. That means for AIAC QM that at each round the amount of
+considering nodes would be divided by two, and for F-EC that each task
+requires half of its dependencies on the same local cluster.
+
+Four experiments were done using four architectures having different
+heterogeneity degrees -- in two architectures computing nodes are more
+heterogeneous than in the others. In these experiments, we did not
+affect the networks heterogeneity, because of the difficulty to
+disturb and control network on Grid'5000; by default, networks are
+already quite heterogeneous. We needed more than 200 computing nodes
+to execute our application because of the small capacity of some
+clusters to execute the largest problems (there is not enough memory).
+
+The first architecture, Arc1.1, was composed of 113 computing nodes
+representing 440 computing cores, spread over 5 clusters in 4
+sites. In Arc1.1 we used bi-cores (2 clusters), quadri-cores (2
+clusters) and bi-quadri-cores (1 cluster) machines. Its heterogeneity
+degree value is 6.43. This architecture was used to run class E of the CG
+application using 64 computing nodes. The second architecture, Arc1.2,
+used to execute class F of the CG application, using 128 computing
+nodes, was composed of 213 computing nodes representing 840 computing
+cores, with a heterogeneity degree of 6.49. This architecture was
+spread on the same clusters and sites as Arc1.1. The results of the
+experiments on Arc1.1 and Arc1.2 are given in Table \ref{tab:exph1E}
+and Table \ref{tab:exph1F}, which give the gains in execution time obtained
+in comparison to the version without mapping.
+
+%\vspace{0.2cm}
+
+\renewcommand{\arraystretch}{1.5}
+
+\begin{table}[h!]
+ \centering
+ \begin{tabular}[h!]{|c||c|c|c|c|}
+ \hline
+ Algorithm& None&SMa & AIAC QM & F-EC \\
+ \hline
+ \hline
+ Execution time&150s&110s&101s&90s\\
+ \hline
+% Gains&--&$27\%$&$33\%$&\textcolor{blue}{$40\%$}\\
+ Gains&--&$27\%$&$33\%$&$40\%$\\
+ \hline
+ \end{tabular}
+ \caption{Gains in time of the execution of the class E of the CG
+ application on Arc1.1 using 64 computing nodes, with mapping
+ algorithms}
+ \label{tab:exph1E}
+ \vspace*{-0.3cm}
+\end{table}
+
+%\vspace{-0.5cm}
+
+\renewcommand{\arraystretch}{1.5}
+
+\begin{table}[h!]
+ \centering
+ \begin{tabular}[h!]{|c||c|c|c|c|}
+ \hline
+ Algorithm& None &SMa & AIAC QM & F-EC \\
+ \hline
+ \hline
+ Execution time&403s&265s&250s&218s\\
+ \hline
+% Gains&--&$34\%$&$38\%$&\textcolor{blue}{$46\%$}\\
+ Gains&--&$34\%$&$38\%$&$46\%$\\
+ \hline
+ \end{tabular}
+ \caption{Gains in time of the execution of the class F of the CG
+ application on Arc1.2 using 128 computing nodes, with mapping
+ algorithms}
+ \label{tab:exph1F}
+ \vspace*{-0.3cm}
+\end{table}
+
+At first, we can see that the Simple Mapping algorithm, though it is
+simple, provides a significant improvement of application execution
+time. This highlights that JaceP2P-V2 really needs a mapping algorithm
+in order to be more efficient. Then, we can see that the F-EC and the
+AIAC QM algorithms provide a better mapping than the Simple Mapping
+algorithms, we can see a significant difference between both
+algorithms. This comes from the homogeneity of clusters. In this case,
+the F-EC algorithm is more efficient since the minimization of the
+communications becomes more important than the tackle of the
+computational power heterogeneity problem.
+%Indeed, it is more benefic for ta becomes more important than the
+%tacklebecomes more important than the
+%tackle sks to have locally their
+%dependencies, which allows to improve communications, in case of
+%computing nodes are more homogeneous -- communications are more
+%important than computing power (that is why the F-EC algorithm is more
+%efficient).
+The effect is that tasks do less iterations as they
+receive more frequently updated data from their neighbors. In
+addition, as tasks and their dependencies are on the same cluster,
+communications are improved, but also as computations take
+approximately the same time, the amount of iterations is reduce and
+the algorithm can converge more quickly.
+
+Another important positive point is that gains are scalable, which allows
+to foresee big improvements for very large applications.\\
+
+The third architecture, Arc2.1, was composed of 112 computing nodes,
+representing 394 computing cores, spread over 5 clusters in 5
+sites. In this architecture we used bi-cores (3 clusters),
+quadri-cores (1 cluster) and bi-quadri-cores (1 cluster) machines. Its
+heterogeneity degree's value is 8.41. This architecture was used to run
+class E of the CG application, using 64 computing nodes. The fourth
+architecture, Arc2.2, used to execute class F of the CG
+application, using 128 computing nodes, was composed of 212 computing
+nodes representing 754 computing cores, with a degree of heterogeneity
+of 8.44. This architecture was spread on the same clusters and sites
+as Arc2.1. The results of the experiments on Arc2.1 and Arc2.2 are
+given in Table \ref{tab:exph2E} and Table \ref{tab:exph2F}, which give the
+gains in execution time obtained in comparison to the version without
+mapping.
+
+%\vspace{0.2cm}
+
+\renewcommand{\arraystretch}{1.5}
+
+\begin{table}[h!]
+ \centering
+ \begin{tabular}[h!]{|c||c|c|c|c|}
+ \hline
+ Algorithm&None& SMa & AIAC QM & F-EC \\
+ \hline
+ \hline
+ Execution time&498s&341s&273s&385s\\
+ \hline
+% Gains&$32\%$&\textcolor{blue}{$45\%$}&\textcolor{red}{$23\%$}\\
+ Gains&--&$32\%$&$45\%$&$23\%$\\
+ \hline
+ \end{tabular}
+ \caption{Gains in time of the execution of the class E of the CG
+ application on Arc2.1 using 64 computing nodes, with mapping
+ algorithms}
+ \label{tab:exph2E}
+ \vspace*{-0.3cm}
+\end{table}
+
+\renewcommand{\arraystretch}{1.5}
+
+\begin{table}[h!]
+ \centering
+ \begin{tabular}[h!]{|c||c|c|c|c|}
+ \hline
+ Algorithm& None&SMa & AIAC QM & F-EC \\
+ \hline
+ \hline
+ Execution time&943s&594s&453s&660s\\
+ \hline
+% Gains&$37\%$&\textcolor{blue}{$52\%$}&\textcolor{red}{$30\%$}\\
+ Gains&--&$37\%$&$52\%$&$30\%$\\
+ \hline
+ \end{tabular}
+ \caption{Gains in time of the execution of the class F of the CG
+ application on Arc2.2 using 128 computing nodes, with mapping
+ algorithms}
+ \label{tab:exph2F}
+ \vspace*{-0.3cm}
+\end{table}
+
+To begin with, these experiments confirm that a mapping algorithm is
+needed and that improvements are always scalable. Then, we can see
+that the F-EC algorithm falls in performances and AIAC QM is
+improved. What is surprising is that the Simple Mapping algorithm is
+better than F-EC. This can be explained by the fact that as computing
+nodes are quite heterogeneous, computations are not the same, so it is
+not significant to map dependencies close to tasks. In this case, the
+most important is the power of computing nodes. So, in this kind of
+architecture, it is more efficient to choose the best computing nodes
+to compute iterations more quickly and to improve the convergence
+detection.
+
+Here, it is important to note that the AIAC QM algorithm offers a gain
+of about $50\%$ on the execution time, that is to say that the
+application takes half of the execution time than without mapping.
+
+\subsubsection{Parameters variation}
+\label{sec:xpvariation}
+
+After having evaluated mapping algorithms on the heterogeneity of
+distributed clusters, we now propose to change the parameters of AIAC
+QM and F-EC algorithms, in order to determine which values are the
+most accurate.
+
+To do these experiments, we used an architecture composed of 122
+computing nodes representing 506 computing cores, spread over 5
+clusters in 5 sites. In this architecture we used bi-cores (2
+clusters), quadri-cores (2 clusters) and bi-quadri-cores (1 cluster)
+machines. Its heterogeneity degree value is 4.98.
+%, which means that
+%computing nodes power is very heterogeneous.
+
+The parameters of each algorithm, $f$ (the search factor) for
+AIAC QM and $\delta$ (the amount of local dependencies) for F-EC,
+varied both with values $10\%$, $50\%$ and $90\%$. We used the CG
+multi-splitting application on 64 computing nodes. The results of
+these experiments are given in Table \ref{tab:expparams}. Results
+exposed in this table represent the gains in execution time provided
+by each algorithm with different parameters values.
+
+%\vspace{0.2cm}
+\renewcommand{\arraystretch}{1.5}
+
+\begin{table}[h!]
+ \centering
+ \begin{tabular}[h!]{|c||c|c|c|}
+ \hline
+ Parameters& $10\%$ & $50\%$ & $90\%$ \\
+ \hline
+ \hline
+% Simple & \multicolumn{3}{c|}{\textcolor{blue}{$39\%$}}\\
+ SMa & \multicolumn{3}{c|}{$30\%$}\\
+ \hline
+% AIAC QM & $35\%$ & \textcolor{blue}{$41\%$} & $35\%$ \\
+ AIAC QM & $30\%$ & $32\%$ & $30\%$ \\
+ \hline
+% F-EC & $39\%$ & $35\%$ & \textcolor{blue}{$45\%$} \\
+ F-EC & $40\%$ & $37\%$ & $45\%$ \\
+ \hline
+ \end{tabular}
+% \caption{Parameters variations using a $500'000$ problem size on an
+% architecture of 5.37 heterogeneity degree}
+ \caption{Gains in execution time with mapping algorithms parameters
+ variations using the class E of the CG application using 64
+ computing nodes}
+% \vspace*{-0.4cm}
+ \label{tab:expparams}
+% \vspace*{-0.9cm}
+\end{table}
+
+%First of all, we can see that the Simple mapping provides the same
+%order of performances, as shown in the precedent section, so it is
+%not affected by the heterogeneity degree. Secondly,
+For the AIAC QM algorithm, we can note that the best value for its
+parameter $f$ is about $50\%$, but its impact is not big enough to
+indicate a specific configuration.
+% With a low heterogeneity degree, this mapping algorithm provides a
+% good performances improvement.
+Finally, and this is not surprising, the F-EC algorithm is more
+efficient with a factor $\delta$ near $100\%$, which directly comes
+from its aim. But we can see that it is more efficient to have a
+factor around $10\%$ than having one around $50\%$.
+
+We can note here, with a lower heterogeneity degree than in previous
+experiments, gains are lower and the difference between AIAC QM and
+F-EC (with parameters at $50\%$) is lower. It can be explained as the
+fact that more the heterogeneity degree tends to 0 more computing
+nodes are the same, so a mapping solution will not be efficient,
+except one only optimizing network latency.
+%These experiments show that the impact of parameters values does not
+%well influence the AIAC QM, whereas it is very important for the F-EC
+%algorithm.
+
+%\section{Discussion}
+%\label{sec:discussion}
+%
+%In this paper three algorithms for mapping asynchronous iterative
+%applications on heterogeneous distributed architectures are described.
+%This approach is relatively new, so we had to study related works. We
+%assume in our model that the amount of computation, the computational
+%cost of each task, cannot be known in advance, and it is the same
+%about communications. Two mains class of algorithms are mainly used,
+%the ``execution time'' and the ``edge-cuts'' optimizations, with a
+%newer preference fort the first one. Indeed, the efficiency of second
+%one is criticized for its objectives, invoking the fact that these
+%algorithms do not optimize the right metric. It is true in a broad
+%spectrum of mapping domains, but we have shown that in our case, it
+%could be an efficient solution, depending on the architecture
+%heterogeneity.
+%
+%As each experiment takes a lot of time and the Grid'5000 platform is
+%shared by many researchers, we could not conducted as many experiments
+%as we wanted and as we need to purpose an exhaustive view of this part
+%of the mapping domain. We cannot design a more general state of the
+%mapping of asynchronous iterative applications on distributed
+%architectures, but we can draw the main lines of future works.
+%%, by
+%%giving the first stones at the building of this specific part of the
+%%mapping domain.
+%
+%We have shown that the heterogeneity in computing nodes power takes an
+%important part in an efficient mapping algorithm. This parameter and
+%probably the heterogeneity in network should really be more taken into
+%consideration. Maybe a good solution consists in designing of mapping
+%algorithms giving more important priority to one or to the other
+%optimization objectives. This leads to design a novel algorithm, which
+%takes into account the different points discussed in this paper, which
+%would probably be an hybrid algorithm, efficient with our model on the
+%targeted architectures.
+
+\section{Conclusion and future works}
+\label{sec:conclu}
+
+In this paper we have presented
+%three algorithms to address the
+%mapping problem for asynchronous iterative applications in
+%heterogeneous distributed architectures. As the asynchronous iteration
+%model is very specific, it was not clear of which kind of mapping
+%algorithm should be efficient on such a problem. The two main
+%approaches given in the literature, the ``execution time'' and the
+%``edge-cuts'' optimization algorithms, have been evaluated on
+%different architectures, with different heterogeneity degrees.
+%% These architectures varied in their
+%%heterogeneity, to evaluate the algorithms.
+%
+%%We proposed three mapping algorithms for the JaceP2P-V2
+%%environment. The first is a simple way mapping, the Simple Mapping
+%%algorithm, which always provides a good and stable improvement of
+%%performances on all kinds of architectures.
+%We propose
+a specific mapping algorithm for the AIAC model, called AIAC QM. This
+algorithm is based on the execution time optimization but it also
+includes a small degree of edge-cuts optimization. Experiments on a
+real large scale architecture of a typical AIAC application show that
+the AIAC QM mapping algorithm is efficient on architectures with a
+high heterogeneity degree. This can be explained by the fact that all
+iteration computations are quite different, for our example, and the
+convergence is more quickly detected as the more powerful computing
+nodes progress in the computation. The F-EC algorithm, which is based
+on the ``edge-cuts'' optimization, is meanwhile efficient on
+architectures with a low heterogeneity degree. This can be explained
+by the fact that in such an environment, it is more accurate for a
+task to have its dependencies locally on the same cluster in order to
+have efficient communications and to allow iterations to be computed
+together, which improves the convergence detection speed.
+Experiments we conducted have shown gains in execution time up to
+$50\%$, which denotes a division by 2 of this execution time, for a
+typical AIAC application on more than 700 computing cores.
+%Experiments have shown that
+%the importance of the parameter of both algorithms, AIAC QM and F-EC,
+%is not so essential for the first one, instead it is very critical for
+%the second one, but we cannot be sure that it is true all the time on
+%all kinds of architectures; it maybe depends on the heterogeneity
+%degree of the network.
+As we did not influence the network's heterogeneity,
+% as we did for the computational power of nodes,
+the evaluation of the network impact on the
+application execution time would be one of our next work.
+
+%For now, these three mapping algorithms are implemented in an
+%additional library for the JaceP2P-V2 environment. The results
+%presented in this paper show that a mapping algorithm allows to
+%improve applications performances, but as the executing architectures
+%should have a variety of heterogeneity degree, we have to find a
+%compromise between the two approaches in order to have an efficient
+%mapping algorithm on all kinds of architectures. In the future, we
+%would like to design an efficient mapping algorithm to improve the
+%execution of asynchronous iteration applications on heterogeneous
+%distributed architectures. As the algorithm should be integrated in
+%the JaceP2P-V2 environment, which is fully decentralized and fault
+%tolerant, the new mapping algorithm should have also these
+%characteristics, in order to retrieve a fully decentralized and fault
+%tolerant environment.
+Our future works concern the amelioration of the AIAC QM algorithm, in
+order to improve it on homogeneous distributed architectures. As the
+F-EC mapping algorithm is efficient on such architectures, we will
+give a more important consideration to the edge-cuts part of AIAC
+QM. Another important point is to take into consideration the fault
+tolerance problem. In this study we have realized our experiments
+without computing node fault, which is not the real case. We have to
+take into account the AIAC QM algorithm about this important
+parameter. First we have to efficiently choose new nodes to replace
+failed ones. Secondly, as we do checkpointing to save tasks' states,
+we have to efficiently choose backup nodes not to fall in case
+a whole cluster fails, as we save on neighbors (which are
+in general on the same cluster for communication efficiency reasons),
+an important part of the application is lost and we cannot restart
+this part; so the whole application fails. A trade-off should be done
+by having some saving nodes in external clusters.
+
+\section*{Acknowledgements}
+
+\label{sec:merci}
+
+This work was supported by the European Interreg IV From-P2P project
+and the region of Franche-Comté.
+
+Experiments presented in this paper were carried out using the
+Grid'5000\cite{g5k} experimental testbed, being developed under the
+INRIA ALADDIN development action with support from CNRS, RENATER and
+several Universities as well as other funding bodies.
+
+
+\bibliographystyle{unsrt}
+%\nocite{*}
+\bibliography{biblio}
+
+
+\end{document}
+
+%% %%
