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IEEEtran.cls
1 %% 2 %% IEEEtran.cls 2007/03/05 version V1.7a 3 %% 4 %% 5 %% This is the official IEEE LaTeX class for authors of the Institute of 6 %% Electrical and Electronics Engineers (IEEE) Transactions journals and 7 %% conferences. 8 %% 9 %% Support sites: 10 %% http://www.michaelshell.org/tex/ieeetran/ 11 %% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/ 12 %% and 13 %% http://www.ieee.org/ 14 %% 15 %% Based on the original 1993 IEEEtran.cls, but with many bug fixes 16 %% and enhancements (from both JVH and MDS) over the 1996/7 version. 17 %% 18 %% 19 %% Contributors: 20 %% Gerry Murray (1993), Silvano Balemi (1993), 21 %% Jon Dixon (1996), Peter N"uchter (1996), 22 %% Juergen von Hagen (2000), and Michael Shell (2001-2007) 23 %% 24 %% 25 %% Copyright (c) 1993-2000 by Gerry Murray, Silvano Balemi, 26 %% Jon Dixon, Peter N"uchter, 27 %% Juergen von Hagen 28 %% and 29 %% Copyright (c) 2001-2007 by Michael Shell 30 %% 31 %% Current maintainer (V1.3 to V1.7): Michael Shell 32 %% See: 33 %% http://www.michaelshell.org/ 34 %% for current contact information. 35 %% 36 %% Special thanks to Peter Wilson (CUA) and Donald Arseneau 37 %% for allowing the inclusion of the \@ifmtarg command 38 %% from their ifmtarg LaTeX package. 39 %% 40 %%************************************************************************* 41 %% Legal Notice: 42 %% This code is offered as-is without any warranty either expressed or 43 %% implied; without even the implied warranty of MERCHANTABILITY or 44 %% FITNESS FOR A PARTICULAR PURPOSE! 45 %% User assumes all risk. 46 %% In no event shall IEEE or any contributor to this code be liable for 47 %% any damages or losses, including, but not limited to, incidental, 48 %% consequential, or any other damages, resulting from the use or misuse 49 %% of any information contained here. 50 %% 51 %% All comments are the opinions of their respective authors and are not 52 %% necessarily endorsed by the IEEE. 53 %% 54 %% This work is distributed under the LaTeX Project Public License (LPPL) 55 %% ( http://www.latex-project.org/ ) version 1.3, and may be freely used, 56 %% distributed and modified. A copy of the LPPL, version 1.3, is included 57 %% in the base LaTeX documentation of all distributions of LaTeX released 58 %% 2003/12/01 or later. 59 %% Retain all contribution notices and credits. 60 %% ** Modified files should be clearly indicated as such, including ** 61 %% ** renaming them and changing author support contact information. ** 62 %% 63 %% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex, 64 %% bare_conf.tex, bare_jrnl.tex, bare_jrnl_compsoc.tex 65 %% 66 %% Major changes to the user interface should be indicated by an 67 %% increase in the version numbers. If a version is a beta, it will 68 %% be indicated with a BETA suffix, i.e., 1.4 BETA. 69 %% Small changes can be indicated by appending letters to the version 70 %% such as "IEEEtran_v14a.cls". 71 %% In all cases, \Providesclass, any \typeout messages to the user, 72 %% \IEEEtransversionmajor and \IEEEtransversionminor must reflect the 73 %% correct version information. 74 %% The changes should also be documented via source comments. 75 %%************************************************************************* 76 %% 77 % 78 % Available class options 79 % e.g., \documentclass[10pt,conference]{IEEEtran} 80 % 81 % *** choose only one from each category *** 82 % 83 % 9pt, 10pt, 11pt, 12pt 84 % Sets normal font size. The default is 10pt. 85 % 86 % conference, journal, technote, peerreview, peerreviewca 87 % determines format mode - conference papers, journal papers, 88 % correspondence papers (technotes), or peer review papers. The user 89 % should also select 9pt when using technote. peerreview is like 90 % journal mode, but provides for a single-column "cover" title page for 91 % anonymous peer review. The paper title (without the author names) is 92 % repeated at the top of the page after the cover page. For peer review 93 % papers, the \IEEEpeerreviewmaketitle command must be executed (will 94 % automatically be ignored for non-peerreview modes) at the place the 95 % cover page is to end, usually just after the abstract (keywords are 96 % not normally used with peer review papers). peerreviewca is like 97 % peerreview, but allows the author names to be entered and formatted 98 % as with conference mode so that author affiliation and contact 99 % information can be easily seen on the cover page. 100 % The default is journal. 101 % 102 % draft, draftcls, draftclsnofoot, final 103 % determines if paper is formatted as a widely spaced draft (for 104 % handwritten editor comments) or as a properly typeset final version. 105 % draftcls restricts draft mode to the class file while all other LaTeX 106 % packages (i.e., \usepackage{graphicx}) will behave as final - allows 107 % for a draft paper with visible figures, etc. draftclsnofoot is like 108 % draftcls, but does not display the date and the word "DRAFT" at the foot 109 % of the pages. If using one of the draft modes, the user will probably 110 % also want to select onecolumn. 111 % The default is final. 112 % 113 % letterpaper, a4paper 114 % determines paper size: 8.5in X 11in or 210mm X 297mm. CHANGING THE PAPER 115 % SIZE WILL NOT ALTER THE TYPESETTING OF THE DOCUMENT - ONLY THE MARGINS 116 % WILL BE AFFECTED. In particular, documents using the a4paper option will 117 % have reduced side margins (A4 is narrower than US letter) and a longer 118 % bottom margin (A4 is longer than US letter). For both cases, the top 119 % margins will be the same and the text will be horizontally centered. 120 % For final submission to IEEE, authors should use US letter (8.5 X 11in) 121 % paper. Note that authors should ensure that all post-processing 122 % (ps, pdf, etc.) uses the same paper specificiation as the .tex document. 123 % Problems here are by far the number one reason for incorrect margins. 124 % IEEEtran will automatically set the default paper size under pdflatex 125 % (without requiring a change to pdftex.cfg), so this issue is more 126 % important to dvips users. Fix config.ps, config.pdf, or ~/.dvipsrc for 127 % dvips, or use the dvips -t papersize option instead as needed. See the 128 % testflow documentation 129 % http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/testflow 130 % for more details on dvips paper size configuration. 131 % The default is letterpaper. 132 % 133 % oneside, twoside 134 % determines if layout follows single sided or two sided (duplex) 135 % printing. The only notable change is with the headings at the top of 136 % the pages. 137 % The default is oneside. 138 % 139 % onecolumn, twocolumn 140 % determines if text is organized into one or two columns per page. One 141 % column mode is usually used only with draft papers. 142 % The default is twocolumn. 143 % 144 % compsoc 145 % Use the format of the IEEE Computer Society. 146 % 147 % romanappendices 148 % Use the "Appendix I" convention when numbering appendices. IEEEtran.cls 149 % now defaults to Alpha "Appendix A" convention - the opposite of what 150 % v1.6b and earlier did. 151 % 152 % captionsoff 153 % disables the display of the figure/table captions. Some IEEE journals 154 % request that captions be removed and figures/tables be put on pages 155 % of their own at the end of an initial paper submission. The endfloat 156 % package can be used with this class option to achieve this format. 157 % 158 % nofonttune 159 % turns off tuning of the font interword spacing. Maybe useful to those 160 % not using the standard Times fonts or for those who have already "tuned" 161 % their fonts. 162 % The default is to enable IEEEtran to tune font parameters. 163 % 164 % 165 %---------- 166 % Available CLASSINPUTs provided (all are macros unless otherwise noted): 167 % \CLASSINPUTbaselinestretch 168 % \CLASSINPUTinnersidemargin 169 % \CLASSINPUToutersidemargin 170 % \CLASSINPUTtoptextmargin 171 % \CLASSINPUTbottomtextmargin 172 % 173 % Available CLASSINFOs provided: 174 % \ifCLASSINFOpdf (TeX if conditional) 175 % \CLASSINFOpaperwidth (macro) 176 % \CLASSINFOpaperheight (macro) 177 % \CLASSINFOnormalsizebaselineskip (length) 178 % \CLASSINFOnormalsizeunitybaselineskip (length) 179 % 180 % Available CLASSOPTIONs provided: 181 % all class option flags (TeX if conditionals) unless otherwise noted, 182 % e.g., \ifCLASSOPTIONcaptionsoff 183 % point size options provided as a single macro: 184 % \CLASSOPTIONpt 185 % which will be defined as 9, 10, 11, or 12 depending on the document‘s 186 % normalsize point size. 187 % also, class option peerreviewca implies the use of class option peerreview 188 % and classoption draft implies the use of class option draftcls 189 190 191 192 193 194 \ProvidesClass{IEEEtran}[2007/03/05 V1.7a by Michael Shell] 195 \typeout{-- See the "IEEEtran_HOWTO" manual for usage information.} 196 \typeout{-- http://www.michaelshell.org/tex/ieeetran/} 197 \NeedsTeXFormat{LaTeX2e} 198 199 % IEEEtran.cls version numbers, provided as of V1.3 200 % These values serve as a way a .tex file can 201 % determine if the new features are provided. 202 % The version number of this IEEEtrans.cls can be obtained from 203 % these values. i.e., V1.4 204 % KEEP THESE AS INTEGERS! i.e., NO {4a} or anything like that- 205 % (no need to enumerate "a" minor changes here) 206 \def\IEEEtransversionmajor{1} 207 \def\IEEEtransversionminor{7} 208 209 % These do nothing, but provide them like in article.cls 210 \newif\if@restonecol 211 \newif\if@titlepage 212 213 214 % class option conditionals 215 \newif\ifCLASSOPTIONonecolumn \CLASSOPTIONonecolumnfalse 216 \newif\ifCLASSOPTIONtwocolumn \CLASSOPTIONtwocolumntrue 217 218 \newif\ifCLASSOPTIONoneside \CLASSOPTIONonesidetrue 219 \newif\ifCLASSOPTIONtwoside \CLASSOPTIONtwosidefalse 220 221 \newif\ifCLASSOPTIONfinal \CLASSOPTIONfinaltrue 222 \newif\ifCLASSOPTIONdraft \CLASSOPTIONdraftfalse 223 \newif\ifCLASSOPTIONdraftcls \CLASSOPTIONdraftclsfalse 224 \newif\ifCLASSOPTIONdraftclsnofoot \CLASSOPTIONdraftclsnofootfalse 225 226 \newif\ifCLASSOPTIONpeerreview \CLASSOPTIONpeerreviewfalse 227 \newif\ifCLASSOPTIONpeerreviewca \CLASSOPTIONpeerreviewcafalse 228 229 \newif\ifCLASSOPTIONjournal \CLASSOPTIONjournaltrue 230 \newif\ifCLASSOPTIONconference \CLASSOPTIONconferencefalse 231 \newif\ifCLASSOPTIONtechnote \CLASSOPTIONtechnotefalse 232 233 \newif\ifCLASSOPTIONnofonttune \CLASSOPTIONnofonttunefalse 234 235 \newif\ifCLASSOPTIONcaptionsoff \CLASSOPTIONcaptionsofffalse 236 237 \newif\ifCLASSOPTIONcompsoc \CLASSOPTIONcompsocfalse 238 239 \newif\ifCLASSOPTIONromanappendices \CLASSOPTIONromanappendicesfalse 240 241 242 % class info conditionals 243 244 % indicates if pdf (via pdflatex) output 245 \newif\ifCLASSINFOpdf \CLASSINFOpdffalse 246 247 248 % V1.6b internal flag to show if using a4paper 249 \newif\if@IEEEusingAfourpaper \@IEEEusingAfourpaperfalse 250 251 252 253 % IEEEtran class scratch pad registers 254 % dimen 255 \newdimen\@IEEEtrantmpdimenA 256 \newdimen\@IEEEtrantmpdimenB 257 % count 258 \newcount\@IEEEtrantmpcountA 259 \newcount\@IEEEtrantmpcountB 260 % token list 261 \newtoks\@IEEEtrantmptoksA 262 263 % we use \CLASSOPTIONpt so that we can ID the point size (even for 9pt docs) 264 % as well as LaTeX‘s \@ptsize to retain some compatability with some 265 % external packages 266 \def\@ptsize{0} 267 % LaTeX does not support 9pt, so we set \@ptsize to 0 - same as that of 10pt 268 \DeclareOption{9pt}{\def\CLASSOPTIONpt{9}\def\@ptsize{0}} 269 \DeclareOption{10pt}{\def\CLASSOPTIONpt{10}\def\@ptsize{0}} 270 \DeclareOption{11pt}{\def\CLASSOPTIONpt{11}\def\@ptsize{1}} 271 \DeclareOption{12pt}{\def\CLASSOPTIONpt{12}\def\@ptsize{2}} 272 273 274 275 \DeclareOption{letterpaper}{\setlength{\paperheight}{11in}% 276 \setlength{\paperwidth}{8.5in}% 277 \@IEEEusingAfourpaperfalse 278 \def\CLASSOPTIONpaper{letter}% 279 \def\CLASSINFOpaperwidth{8.5in}% 280 \def\CLASSINFOpaperheight{11in}} 281 282 283 \DeclareOption{a4paper}{\setlength{\paperheight}{297mm}% 284 \setlength{\paperwidth}{210mm}% 285 \@IEEEusingAfourpapertrue 286 \def\CLASSOPTIONpaper{a4}% 287 \def\CLASSINFOpaperwidth{210mm}% 288 \def\CLASSINFOpaperheight{297mm}} 289 290 \DeclareOption{oneside}{\@twosidefalse\@mparswitchfalse 291 \CLASSOPTIONonesidetrue\CLASSOPTIONtwosidefalse} 292 \DeclareOption{twoside}{\@twosidetrue\@mparswitchtrue 293 \CLASSOPTIONtwosidetrue\CLASSOPTIONonesidefalse} 294 295 \DeclareOption{onecolumn}{\CLASSOPTIONonecolumntrue\CLASSOPTIONtwocolumnfalse} 296 \DeclareOption{twocolumn}{\CLASSOPTIONtwocolumntrue\CLASSOPTIONonecolumnfalse} 297 298 % If the user selects draft, then this class AND any packages 299 % will go into draft mode. 300 \DeclareOption{draft}{\CLASSOPTIONdrafttrue\CLASSOPTIONdraftclstrue 301 \CLASSOPTIONdraftclsnofootfalse} 302 % draftcls is for a draft mode which will not affect any packages 303 % used by the document. 304 \DeclareOption{draftcls}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclstrue 305 \CLASSOPTIONdraftclsnofootfalse} 306 % draftclsnofoot is like draftcls, but without the footer. 307 \DeclareOption{draftclsnofoot}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclstrue 308 \CLASSOPTIONdraftclsnofoottrue} 309 \DeclareOption{final}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclsfalse 310 \CLASSOPTIONdraftclsnofootfalse} 311 312 \DeclareOption{journal}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse 313 \CLASSOPTIONjournaltrue\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse} 314 315 \DeclareOption{conference}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse 316 \CLASSOPTIONjournalfalse\CLASSOPTIONconferencetrue\CLASSOPTIONtechnotefalse} 317 318 \DeclareOption{technote}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse 319 \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotetrue} 320 321 \DeclareOption{peerreview}{\CLASSOPTIONpeerreviewtrue\CLASSOPTIONpeerreviewcafalse 322 \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse} 323 324 \DeclareOption{peerreviewca}{\CLASSOPTIONpeerreviewtrue\CLASSOPTIONpeerreviewcatrue 325 \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse} 326 327 \DeclareOption{nofonttune}{\CLASSOPTIONnofonttunetrue} 328 329 \DeclareOption{captionsoff}{\CLASSOPTIONcaptionsofftrue} 330 331 \DeclareOption{compsoc}{\CLASSOPTIONcompsoctrue} 332 333 \DeclareOption{romanappendices}{\CLASSOPTIONromanappendicestrue} 334 335 336 % default to US letter paper, 10pt, twocolumn, one sided, final, journal 337 \ExecuteOptions{letterpaper,10pt,twocolumn,oneside,final,journal} 338 % overrride these defaults per user requests 339 \ProcessOptions 340 341 342 343 % Computer Society conditional execution command 344 \long\def\@IEEEcompsoconly#1{\relax\ifCLASSOPTIONcompsoc\relax#1\relax\fi\relax} 345 % inverse 346 \long\def\@IEEEnotcompsoconly#1{\relax\ifCLASSOPTIONcompsoc\else\relax#1\relax\fi\relax} 347 % compsoc conference 348 \long\def\@IEEEcompsocconfonly#1{\relax\ifCLASSOPTIONcompsoc\ifCLASSOPTIONconference\relax#1\relax\fi\fi\relax} 349 % compsoc not conference 350 \long\def\@IEEEcompsocnotconfonly#1{\relax\ifCLASSOPTIONcompsoc\ifCLASSOPTIONconference\else\relax#1\relax\fi\fi\relax} 351 352 353 % IEEE uses Times Roman font, so we‘ll default to Times. 354 % These three commands make up the entire times.sty package. 355 \renewcommand{\sfdefault}{phv} 356 \renewcommand{\rmdefault}{ptm} 357 \renewcommand{\ttdefault}{pcr} 358 359 \@IEEEcompsoconly{\typeout{-- Using IEEE Computer Society mode.}} 360 361 % V1.7 compsoc nonconference papers, use Palatino/Palladio as the main text font, 362 % not Times Roman. 363 \@IEEEcompsocnotconfonly{\renewcommand{\rmdefault}{ppl}} 364 365 % enable Times/Palatino main text font 366 \normalfont\selectfont 367 368 369 370 371 372 % V1.7 conference notice message hook 373 \def\@IEEEconsolenoticeconference{\typeout{}% 374 \typeout{** Conference Paper **}% 375 \typeout{Before submitting the final camera ready copy, remember to:}% 376 \typeout{}% 377 \typeout{ 1. Manually equalize the lengths of two columns on the last page}% 378 \typeout{ of your paper;}% 379 \typeout{}% 380 \typeout{ 2. Ensure that any PostScript and/or PDF output post-processing}% 381 \typeout{ uses only Type 1 fonts and that every step in the generation}% 382 \typeout{ process uses the appropriate paper size.}% 383 \typeout{}} 384 385 386 % we can send console reminder messages to the user here 387 \AtEndDocument{\ifCLASSOPTIONconference\@IEEEconsolenoticeconference\fi} 388 389 390 % warn about the use of single column other than for draft mode 391 \ifCLASSOPTIONtwocolumn\else% 392 \ifCLASSOPTIONdraftcls\else% 393 \typeout{** ATTENTION: Single column mode is not typically used with IEEE publications.}% 394 \fi% 395 \fi 396 397 398 % V1.7 improved paper size setting code. 399 % Set pdfpage and dvips paper sizes. Conditional tests are similar to that 400 % of ifpdf.sty. Retain within {} to ensure tested macros are never altered, 401 % even if only effect is to set them to \relax. 402 % if \pdfoutput is undefined or equal to relax, output a dvips special 403 {\@ifundefined{pdfoutput}{\AtBeginDvi{\special{papersize=\CLASSINFOpaperwidth,\CLASSINFOpaperheight}}}{% 404 % pdfoutput is defined and not equal to \relax 405 % check for pdfpageheight existence just in case someone sets pdfoutput 406 % under non-pdflatex. If exists, set them regardless of value of \pdfoutput. 407 \@ifundefined{pdfpageheight}{\relax}{\global\pdfpagewidth\paperwidth 408 \global\pdfpageheight\paperheight}% 409 % if using \pdfoutput=0 under pdflatex, send dvips papersize special 410 \ifcase\pdfoutput 411 \AtBeginDvi{\special{papersize=\CLASSINFOpaperwidth,\CLASSINFOpaperheight}}% 412 \else 413 % we are using pdf output, set CLASSINFOpdf flag 414 \global\CLASSINFOpdftrue 415 \fi}} 416 417 % let the user know the selected papersize 418 \typeout{-- Using \CLASSINFOpaperwidth\space x \CLASSINFOpaperheight\space 419 (\CLASSOPTIONpaper)\space paper.} 420 421 \ifCLASSINFOpdf 422 \typeout{-- Using PDF output.} 423 \else 424 \typeout{-- Using DVI output.} 425 \fi 426 427 428 % The idea hinted here is for LaTeX to generate markleft{} and markright{} 429 % automatically for you after you enter \author{}, \journal{}, 430 % \journaldate{}, journalvol{}, \journalnum{}, etc. 431 % However, there may be some backward compatibility issues here as 432 % well as some special applications for IEEEtran.cls and special issues 433 % that may require the flexible \markleft{}, \markright{} and/or \markboth{}. 434 % We‘ll leave this as an open future suggestion. 435 %\newcommand{\journal}[1]{\def\@journal{#1}} 436 %\def\@journal{} 437 438 439 440 % pointsize values 441 % used with ifx to determine the document‘s normal size 442 \def\@IEEEptsizenine{9} 443 \def\@IEEEptsizeten{10} 444 \def\@IEEEptsizeeleven{11} 445 \def\@IEEEptsizetwelve{12} 446 447 448 449 % FONT DEFINITIONS (No sizexx.clo file needed) 450 % V1.6 revised font sizes, displayskip values and 451 % revised normalsize baselineskip to reduce underfull vbox problems 452 % on the 58pc = 696pt = 9.5in text height we want 453 % normalsize #lines/column baselineskip (aka leading) 454 % 9pt 63 11.0476pt (truncated down) 455 % 10pt 58 12pt (exact) 456 % 11pt 52 13.3846pt (truncated down) 457 % 12pt 50 13.92pt (exact) 458 % 459 460 % we need to store the nominal baselineskip for the given font size 461 % in case baselinestretch ever changes. 462 % this is a dimen, so it will not hold stretch or shrink 463 \newdimen\@IEEEnormalsizeunitybaselineskip 464 \@IEEEnormalsizeunitybaselineskip\baselineskip 465 466 \ifx\CLASSOPTIONpt\@IEEEptsizenine 467 \typeout{-- This is a 9 point document.} 468 \def\normalsize{\@setfontsize{\normalsize}{9}{11.0476pt}}% 469 \setlength{\@IEEEnormalsizeunitybaselineskip}{11.0476pt}% 470 \normalsize 471 \abovedisplayskip 1.5ex plus3pt minus1pt% 472 \belowdisplayskip \abovedisplayskip% 473 \abovedisplayshortskip 0pt plus3pt% 474 \belowdisplayshortskip 1.5ex plus3pt minus1pt 475 \def\small{\@setfontsize{\small}{8.5}{10pt}} 476 \def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}} 477 \def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}} 478 \def\tiny{\@setfontsize{\tiny}{5}{6pt}} 479 % sublargesize is the same as large - 10pt 480 \def\sublargesize{\@setfontsize{\sublargesize}{10}{12pt}} 481 \def\large{\@setfontsize{\large}{10}{12pt}} 482 \def\Large{\@setfontsize{\Large}{12}{14pt}} 483 \def\LARGE{\@setfontsize{\LARGE}{14}{17pt}} 484 \def\huge{\@setfontsize{\huge}{17}{20pt}} 485 \def\Huge{\@setfontsize{\Huge}{20}{24pt}} 486 \fi 487 488 489 % Check if we have selected 10 points 490 \ifx\CLASSOPTIONpt\@IEEEptsizeten 491 \typeout{-- This is a 10 point document.} 492 \def\normalsize{\@setfontsize{\normalsize}{10}{12.00pt}}% 493 \setlength{\@IEEEnormalsizeunitybaselineskip}{12pt}% 494 \normalsize 495 \abovedisplayskip 1.5ex plus4pt minus2pt% 496 \belowdisplayskip \abovedisplayskip% 497 \abovedisplayshortskip 0pt plus4pt% 498 \belowdisplayshortskip 1.5ex plus4pt minus2pt 499 \def\small{\@setfontsize{\small}{9}{10pt}} 500 \def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}} 501 \def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}} 502 \def\tiny{\@setfontsize{\tiny}{5}{6pt}} 503 % sublargesize is a tad smaller than large - 11pt 504 \def\sublargesize{\@setfontsize{\sublargesize}{11}{13.4pt}} 505 \def\large{\@setfontsize{\large}{12}{14pt}} 506 \def\Large{\@setfontsize{\Large}{14}{17pt}} 507 \def\LARGE{\@setfontsize{\LARGE}{17}{20pt}} 508 \def\huge{\@setfontsize{\huge}{20}{24pt}} 509 \def\Huge{\@setfontsize{\Huge}{24}{28pt}} 510 \fi 511 512 513 % Check if we have selected 11 points 514 \ifx\CLASSOPTIONpt\@IEEEptsizeeleven 515 \typeout{-- This is an 11 point document.} 516 \def\normalsize{\@setfontsize{\normalsize}{11}{13.3846pt}}% 517 \setlength{\@IEEEnormalsizeunitybaselineskip}{13.3846pt}% 518 \normalsize 519 \abovedisplayskip 1.5ex plus5pt minus3pt% 520 \belowdisplayskip \abovedisplayskip% 521 \abovedisplayshortskip 0pt plus5pt% 522 \belowdisplayshortskip 1.5ex plus5pt minus3pt 523 \def\small{\@setfontsize{\small}{10}{12pt}} 524 \def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}} 525 \def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}} 526 \def\tiny{\@setfontsize{\tiny}{6}{7pt}} 527 % sublargesize is the same as large - 12pt 528 \def\sublargesize{\@setfontsize{\sublargesize}{12}{14pt}} 529 \def\large{\@setfontsize{\large}{12}{14pt}} 530 \def\Large{\@setfontsize{\Large}{14}{17pt}} 531 \def\LARGE{\@setfontsize{\LARGE}{17}{20pt}} 532 \def\huge{\@setfontsize{\huge}{20}{24pt}} 533 \def\Huge{\@setfontsize{\Huge}{24}{28pt}} 534 \fi 535 536 537 % Check if we have selected 12 points 538 \ifx\CLASSOPTIONpt\@IEEEptsizetwelve 539 \typeout{-- This is a 12 point document.} 540 \def\normalsize{\@setfontsize{\normalsize}{12}{13.92pt}}% 541 \setlength{\@IEEEnormalsizeunitybaselineskip}{13.92pt}% 542 \normalsize 543 \abovedisplayskip 1.5ex plus6pt minus4pt% 544 \belowdisplayskip \abovedisplayskip% 545 \abovedisplayshortskip 0pt plus6pt% 546 \belowdisplayshortskip 1.5ex plus6pt minus4pt 547 \def\small{\@setfontsize{\small}{10}{12pt}} 548 \def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}} 549 \def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}} 550 \def\tiny{\@setfontsize{\tiny}{6}{7pt}} 551 % sublargesize is the same as large - 14pt 552 \def\sublargesize{\@setfontsize{\sublargesize}{14}{17pt}} 553 \def\large{\@setfontsize{\large}{14}{17pt}} 554 \def\Large{\@setfontsize{\Large}{17}{20pt}} 555 \def\LARGE{\@setfontsize{\LARGE}{20}{24pt}} 556 \def\huge{\@setfontsize{\huge}{22}{26pt}} 557 \def\Huge{\@setfontsize{\Huge}{24}{28pt}} 558 \fi 559 560 561 % V1.6 The Computer Modern Fonts will issue a substitution warning for 562 % 24pt titles (24.88pt is used instead) increase the substitution 563 % tolerance to turn off this warning 564 \def\fontsubfuzz{.9pt} 565 % However, the default (and correct) Times font will scale exactly as needed. 566 567 568 % warn the user in case they forget to use the 9pt option with 569 % technote 570 \ifCLASSOPTIONtechnote% 571 \ifx\CLASSOPTIONpt\@IEEEptsizenine\else% 572 \typeout{** ATTENTION: Technotes are normally 9pt documents.}% 573 \fi% 574 \fi 575 576 577 % V1.7 578 % Improved \textunderscore to provide a much better fake _ when used with 579 % OT1 encoding. Under OT1, detect use of pcr or cmtt \ttfamily and use 580 % available true _ glyph for those two typewriter fonts. 581 \def\@IEEEstringptm{ptm} % Times Roman family 582 \def\@IEEEstringppl{ppl} % Palatino Roman family 583 \def\@IEEEstringphv{phv} % Helvetica Sans Serif family 584 \def\@IEEEstringpcr{pcr} % Courier typewriter family 585 \def\@IEEEstringcmtt{cmtt} % Computer Modern typewriter family 586 \DeclareTextCommandDefault{\textunderscore}{\leavevmode 587 \ifx\f@family\@IEEEstringpcr\string_\else 588 \ifx\f@family\@IEEEstringcmtt\string_\else 589 \ifx\f@family\@IEEEstringptm\kern 0em\vbox{\hrule\@width 0.5em\@height 0.5pt\kern -0.3ex}\else 590 \ifx\f@family\@IEEEstringppl\kern 0em\vbox{\hrule\@width 0.5em\@height 0.5pt\kern -0.3ex}\else 591 \ifx\f@family\@IEEEstringphv\kern -0.03em\vbox{\hrule\@width 0.62em\@height 0.52pt\kern -0.33ex}\kern -0.03em\else 592 \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} 593 594 595 596 597 % set the default \baselinestretch 598 \def\baselinestretch{1} 599 \ifCLASSOPTIONdraftcls 600 \def\baselinestretch{1.5}% default baselinestretch for draft modes 601 \fi 602 603 604 % process CLASSINPUT baselinestretch 605 \ifx\CLASSINPUTbaselinestretch\@IEEEundefined 606 \else 607 \edef\baselinestretch{\CLASSINPUTbaselinestretch} % user CLASSINPUT override 608 \typeout{** ATTENTION: Overriding \string\baselinestretch\space to 609 \baselinestretch\space via \string\CLASSINPUT.} 610 \fi 611 612 \normalsize % make \baselinestretch take affect 613 614 615 616 617 % store the normalsize baselineskip 618 \newdimen\CLASSINFOnormalsizebaselineskip 619 \CLASSINFOnormalsizebaselineskip=\baselineskip\relax 620 % and the normalsize unity (baselinestretch=1) baselineskip 621 % we could save a register by giving the user access to 622 % \@IEEEnormalsizeunitybaselineskip. However, let‘s protect 623 % its read only internal status 624 \newdimen\CLASSINFOnormalsizeunitybaselineskip 625 \CLASSINFOnormalsizeunitybaselineskip=\@IEEEnormalsizeunitybaselineskip\relax 626 % store the nominal value of jot 627 \newdimen\IEEEnormaljot 628 \IEEEnormaljot=0.25\baselineskip\relax 629 630 % set \jot 631 \jot=\IEEEnormaljot\relax 632 633 634 635 636 % V1.6, we are now going to fine tune the interword spacing 637 % The default interword glue for Times under TeX appears to use a 638 % nominal interword spacing of 25% (relative to the font size, i.e., 1em) 639 % a maximum of 40% and a minimum of 19%. 640 % For example, 10pt text uses an interword glue of: 641 % 642 % 2.5pt plus 1.49998pt minus 0.59998pt 643 % 644 % However, IEEE allows for a more generous range which reduces the need 645 % for hyphenation, especially for two column text. Furthermore, IEEE 646 % tends to use a little bit more nominal space between the words. 647 % IEEE‘s interword spacing percentages appear to be: 648 % 35% nominal 649 % 23% minimum 650 % 50% maximum 651 % (They may even be using a tad more for the largest fonts such as 24pt.) 652 % 653 % for bold text, IEEE increases the spacing a little more: 654 % 37.5% nominal 655 % 23% minimum 656 % 55% maximum 657 658 % here are the interword spacing ratios we‘ll use 659 % for medium (normal weight) 660 \def\@IEEEinterspaceratioM{0.35} 661 \def\@IEEEinterspaceMINratioM{0.23} 662 \def\@IEEEinterspaceMAXratioM{0.50} 663 664 % for bold 665 \def\@IEEEinterspaceratioB{0.375} 666 \def\@IEEEinterspaceMINratioB{0.23} 667 \def\@IEEEinterspaceMAXratioB{0.55} 668 669 670 % command to revise the interword spacing for the current font under TeX: 671 % \fontdimen2 = nominal interword space 672 % \fontdimen3 = interword stretch 673 % \fontdimen4 = interword shrink 674 % since all changes to the \fontdimen are global, we can enclose these commands 675 % in braces to confine any font attribute or length changes 676 \def\@@@IEEEsetfontdimens#1#2#3{{% 677 \setlength{\@IEEEtrantmpdimenB}{\f@size pt}% grab the font size in pt, could use 1em instead. 678 \setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}% 679 \fontdimen2\font=\@IEEEtrantmpdimenA\relax 680 \addtolength{\@IEEEtrantmpdimenA}{-#2\@IEEEtrantmpdimenB}% 681 \fontdimen3\font=-\@IEEEtrantmpdimenA\relax 682 \setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}% 683 \addtolength{\@IEEEtrantmpdimenA}{-#3\@IEEEtrantmpdimenB}% 684 \fontdimen4\font=\@IEEEtrantmpdimenA\relax}} 685 686 % revise the interword spacing for each font weight 687 \def\@@IEEEsetfontdimens{{% 688 \mdseries 689 \@@@IEEEsetfontdimens{\@IEEEinterspaceratioM}{\@IEEEinterspaceMAXratioM}{\@IEEEinterspaceMINratioM}% 690 \bfseries 691 \@@@IEEEsetfontdimens{\@IEEEinterspaceratioB}{\@IEEEinterspaceMAXratioB}{\@IEEEinterspaceMINratioB}% 692 }} 693 694 % revise the interword spacing for each font shape 695 % \slshape is not often used for IEEE work and is not altered here. The \scshape caps are 696 % already a tad too large in the free LaTeX fonts (as compared to what IEEE uses) so we 697 % won‘t alter these either. 698 \def\@IEEEsetfontdimens{{% 699 \normalfont 700 \@@IEEEsetfontdimens 701 \normalfont\itshape 702 \@@IEEEsetfontdimens 703 }} 704 705 % command to revise the interword spacing for each font size (and shape 706 % and weight). Only the \rmfamily is done here as \ttfamily uses a 707 % fixed spacing and \sffamily is not used as the main text of IEEE papers. 708 \def\@IEEEtunefonts{{\selectfont\rmfamily 709 \tiny\@IEEEsetfontdimens 710 \scriptsize\@IEEEsetfontdimens 711 \footnotesize\@IEEEsetfontdimens 712 \small\@IEEEsetfontdimens 713 \normalsize\@IEEEsetfontdimens 714 \sublargesize\@IEEEsetfontdimens 715 \large\@IEEEsetfontdimens 716 \LARGE\@IEEEsetfontdimens 717 \huge\@IEEEsetfontdimens 718 \Huge\@IEEEsetfontdimens}} 719 720 % if the nofonttune class option is not given, revise the interword spacing 721 % now - in case IEEEtran makes any default length measurements, and make 722 % sure all the default fonts are loaded 723 \ifCLASSOPTIONnofonttune\else 724 \@IEEEtunefonts 725 \fi 726 727 % and again at the start of the document in case the user loaded different fonts 728 \AtBeginDocument{\ifCLASSOPTIONnofonttune\else\@IEEEtunefonts\fi} 729 730 731 732 % V1.6 733 % LaTeX is a little to quick to use hyphenations 734 % So, we increase the penalty for their use and raise 735 % the badness level that triggers an underfull hbox 736 % warning. The author may still have to tweak things, 737 % but the appearance will be much better "right out 738 % of the box" than that under V1.5 and prior. 739 % TeX default is 50 740 \hyphenpenalty=750 741 % If we didn‘t adjust the interword spacing, 2200 might be better. 742 % The TeX default is 1000 743 \hbadness=1350 744 % IEEE does not use extra spacing after punctuation 745 \frenchspacing 746 747 % V1.7 increase this a tad to discourage equation breaks 748 \binoppenalty=1000 % default 700 749 \relpenalty=800 % default 500 750 751 752 % margin note stuff 753 \marginparsep 10pt 754 \marginparwidth 20pt 755 \marginparpush 25pt 756 757 758 % if things get too close, go ahead and let them touch 759 \lineskip 0pt 760 \normallineskip 0pt 761 \lineskiplimit 0pt 762 \normallineskiplimit 0pt 763 764 % The distance from the lower edge of the text body to the 765 % footline 766 \footskip 0.4in 767 768 % normally zero, should be relative to font height. 769 % put in a little rubber to help stop some bad breaks (underfull vboxes) 770 \parskip 0ex plus 0.2ex minus 0.1ex 771 772 \parindent 1.0em 773 774 \topmargin -49.0pt 775 \headheight 12pt 776 \headsep 0.25in 777 778 % use the normal font baselineskip 779 % so that \topskip is unaffected by changes in \baselinestretch 780 \topskip=\@IEEEnormalsizeunitybaselineskip 781 \textheight 58pc % 9.63in, 696pt 782 % Tweak textheight to a perfect integer number of lines/page. 783 % The normal baselineskip for each document point size is used 784 % to determine these values. 785 \ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=63\@IEEEnormalsizeunitybaselineskip\fi % 63 lines/page 786 \ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=58\@IEEEnormalsizeunitybaselineskip\fi % 58 lines/page 787 \ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=52\@IEEEnormalsizeunitybaselineskip\fi % 52 lines/page 788 \ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=50\@IEEEnormalsizeunitybaselineskip\fi % 50 lines/page 789 790 791 \columnsep 1pc 792 \textwidth 43pc % 2 x 21pc + 1pc = 43pc 793 794 795 % the default side margins are equal 796 \if@IEEEusingAfourpaper 797 \oddsidemargin 14.32mm 798 \evensidemargin 14.32mm 799 \else 800 \oddsidemargin 0.680in 801 \evensidemargin 0.680in 802 \fi 803 % compensate for LaTeX‘s 1in offset 804 \addtolength{\oddsidemargin}{-1in} 805 \addtolength{\evensidemargin}{-1in} 806 807 808 809 % adjust margins for conference mode 810 \ifCLASSOPTIONconference 811 \topmargin -0.25in 812 % we retain the reserved, but unused space for headers 813 \addtolength{\topmargin}{-\headheight} 814 \addtolength{\topmargin}{-\headsep} 815 \textheight 9.25in % The standard for conferences (668.4975pt) 816 % Tweak textheight to a perfect integer number of lines/page. 817 \ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=61\@IEEEnormalsizeunitybaselineskip\fi % 61 lines/page 818 \ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=56\@IEEEnormalsizeunitybaselineskip\fi % 56 lines/page 819 \ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=50\@IEEEnormalsizeunitybaselineskip\fi % 50 lines/page 820 \ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=48\@IEEEnormalsizeunitybaselineskip\fi % 48 lines/page 821 \fi 822 823 824 % compsoc conference 825 \ifCLASSOPTIONcompsoc 826 \ifCLASSOPTIONconference 827 % compsoc conference use a larger value for columnsep 828 \columnsep 0.375in 829 % compsoc conferences want 1in top margin, 1.125in bottom margin 830 \topmargin 0in 831 \addtolength{\topmargin}{-6pt}% we tweak this a tad to better comply with top of line stuff 832 % we retain the reserved, but unused space for headers 833 \addtolength{\topmargin}{-\headheight} 834 \addtolength{\topmargin}{-\headsep} 835 \textheight 8.875in % (641.39625pt) 836 % Tweak textheight to a perfect integer number of lines/page. 837 \ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=58\@IEEEnormalsizeunitybaselineskip\fi % 58 lines/page 838 \ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=53\@IEEEnormalsizeunitybaselineskip\fi % 53 lines/page 839 \ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=48\@IEEEnormalsizeunitybaselineskip\fi % 48 lines/page 840 \ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=46\@IEEEnormalsizeunitybaselineskip\fi % 46 lines/page 841 \textwidth 6.5in 842 % the default side margins are equal 843 \if@IEEEusingAfourpaper 844 \oddsidemargin 22.45mm 845 \evensidemargin 22.45mm 846 \else 847 \oddsidemargin 1in 848 \evensidemargin 1in 849 \fi 850 % compensate for LaTeX‘s 1in offset 851 \addtolength{\oddsidemargin}{-1in} 852 \addtolength{\evensidemargin}{-1in} 853 \fi\fi 854 855 856 857 % draft mode settings override that of all other modes 858 % provides a nice 1in margin all around the paper and extra 859 % space between the lines for editor‘s comments 860 \ifCLASSOPTIONdraftcls 861 % want 1in from top of paper to text 862 \setlength{\topmargin}{-\headsep}% 863 \addtolength{\topmargin}{-\headheight}% 864 % we want 1in side margins regardless of paper type 865 \oddsidemargin 0in 866 \evensidemargin 0in 867 % set the text width 868 \setlength{\textwidth}{\paperwidth}% 869 \addtolength{\textwidth}{-2.0in}% 870 \setlength{\textheight}{\paperheight}% 871 \addtolength{\textheight}{-2.0in}% 872 % digitize textheight to be an integer number of lines. 873 % this may cause the bottom margin to be off a tad 874 \addtolength{\textheight}{-1\topskip}% 875 \divide\textheight by \baselineskip% 876 \multiply\textheight by \baselineskip% 877 \addtolength{\textheight}{\topskip}% 878 \fi 879 880 881 882 % process CLASSINPUT inner/outer margin 883 % if inner margin defined, but outer margin not, set outer to inner. 884 \ifx\CLASSINPUTinnersidemargin\@IEEEundefined 885 \else 886 \ifx\CLASSINPUToutersidemargin\@IEEEundefined 887 \edef\CLASSINPUToutersidemargin{\CLASSINPUTinnersidemargin} 888 \fi 889 \fi 890 891 \ifx\CLASSINPUToutersidemargin\@IEEEundefined 892 \else 893 % if outer margin defined, but inner margin not, set inner to outer. 894 \ifx\CLASSINPUTinnersidemargin\@IEEEundefined 895 \edef\CLASSINPUTinnersidemargin{\CLASSINPUToutersidemargin} 896 \fi 897 \setlength{\oddsidemargin}{\CLASSINPUTinnersidemargin} 898 \ifCLASSOPTIONtwoside 899 \setlength{\evensidemargin}{\CLASSINPUToutersidemargin} 900 \else 901 \setlength{\evensidemargin}{\CLASSINPUTinnersidemargin} 902 \fi 903 \addtolength{\oddsidemargin}{-1in} 904 \addtolength{\evensidemargin}{-1in} 905 \setlength{\textwidth}{\paperwidth} 906 \addtolength{\textwidth}{-\CLASSINPUTinnersidemargin} 907 \addtolength{\textwidth}{-\CLASSINPUToutersidemargin} 908 \typeout{** ATTENTION: Overriding inner side margin to \CLASSINPUTinnersidemargin\space and 909 outer side margin to \CLASSINPUToutersidemargin\space via \string\CLASSINPUT.} 910 \fi 911 912 913 914 % process CLASSINPUT top/bottom text margin 915 % if toptext margin defined, but bottomtext margin not, set bottomtext to toptext margin 916 \ifx\CLASSINPUTtoptextmargin\@IEEEundefined 917 \else 918 \ifx\CLASSINPUTbottomtextmargin\@IEEEundefined 919 \edef\CLASSINPUTbottomtextmargin{\CLASSINPUTtoptextmargin} 920 \fi 921 \fi 922 923 \ifx\CLASSINPUTbottomtextmargin\@IEEEundefined 924 \else 925 % if bottomtext margin defined, but toptext margin not, set toptext to bottomtext margin 926 \ifx\CLASSINPUTtoptextmargin\@IEEEundefined 927 \edef\CLASSINPUTtoptextmargin{\CLASSINPUTbottomtextmargin} 928 \fi 929 \setlength{\topmargin}{\CLASSINPUTtoptextmargin} 930 \addtolength{\topmargin}{-1in} 931 \addtolength{\topmargin}{-\headheight} 932 \addtolength{\topmargin}{-\headsep} 933 \setlength{\textheight}{\paperheight} 934 \addtolength{\textheight}{-\CLASSINPUTtoptextmargin} 935 \addtolength{\textheight}{-\CLASSINPUTbottomtextmargin} 936 % in the default format we use the normal baselineskip as topskip 937 % we only need 0.7 of this to clear typical top text and we need 938 % an extra 0.3 spacing at the bottom for descenders. This will 939 % correct for both. 940 \addtolength{\topmargin}{-0.3\@IEEEnormalsizeunitybaselineskip} 941 \typeout{** ATTENTION: Overriding top text margin to \CLASSINPUTtoptextmargin\space and 942 bottom text margin to \CLASSINPUTbottomtextmargin\space via \string\CLASSINPUT.} 943 \fi 944 945 946 947 948 949 950 951 % LIST SPACING CONTROLS 952 953 % Controls the amount of EXTRA spacing 954 % above and below \trivlist 955 % Both \list and IED lists override this. 956 % However, \trivlist will use this as will most 957 % things built from \trivlist like the \center 958 % environment. 959 \topsep 0.5\baselineskip 960 961 % Controls the additional spacing around lists preceded 962 % or followed by blank lines. IEEE does not increase 963 % spacing before or after paragraphs so it is set to zero. 964 % \z@ is the same as zero, but faster. 965 \partopsep \z@ 966 967 % Controls the spacing between paragraphs in lists. 968 % IEEE does not increase spacing before or after paragraphs 969 % so this is also zero. 970 % With IEEEtran.cls, global changes to 971 % this value DO affect lists (but not IED lists). 972 \parsep \z@ 973 974 % Controls the extra spacing between list items. 975 % IEEE does not put extra spacing between items. 976 % With IEEEtran.cls, global changes to this value DO affect 977 % lists (but not IED lists). 978 \itemsep \z@ 979 980 % \itemindent is the amount to indent the FIRST line of a list 981 % item. It is auto set to zero within the \list environment. To alter 982 % it, you have to do so when you call the \list. 983 % However, IEEE uses this for the theorem environment 984 % There is an alternative value for this near \leftmargini below 985 \itemindent -1em 986 987 % \leftmargin, the spacing from the left margin of the main text to 988 % the left of the main body of a list item is set by \list. 989 % Hence this statement does nothing for lists. 990 % But, quote and verse do use it for indention. 991 \leftmargin 2em 992 993 % we retain this stuff from the older IEEEtran.cls so that \list 994 % will work the same way as before. However, itemize, enumerate and 995 % description (IED) could care less about what these are as they 996 % all are overridden. 997 \leftmargini 2em 998 %\itemindent 2em % Alternative values: sometimes used. 999 %\leftmargini 0em 1000 \leftmarginii 1em 1001 \leftmarginiii 1.5em 1002 \leftmarginiv 1.5em 1003 \leftmarginv 1.0em 1004 \leftmarginvi 1.0em 1005 \labelsep 0.5em 1006 \labelwidth \z@ 1007 1008 1009 % The old IEEEtran.cls behavior of \list is retained. 1010 % However, the new V1.3 IED list environments override all the 1011 % @list stuff (\@listX is called within \list for the 1012 % appropriate level just before the user‘s list_decl is called). 1013 % \topsep is now 2pt as IEEE puts a little extra space around 1014 % lists - used by those non-IED macros that depend on \list. 1015 % Note that \parsep and \itemsep are not redefined as in 1016 % the sizexx.clo \@listX (which article.cls uses) so global changes 1017 % of these values DO affect \list 1018 % 1019 \def\@listi{\leftmargin\leftmargini \topsep 2pt plus 1pt minus 1pt} 1020 \let\@listI\@listi 1021 \def\@listii{\leftmargin\leftmarginii\labelwidth\leftmarginii% 1022 \advance\labelwidth-\labelsep \topsep 2pt} 1023 \def\@listiii{\leftmargin\leftmarginiii\labelwidth\leftmarginiii% 1024 \advance\labelwidth-\labelsep \topsep 2pt} 1025 \def\@listiv{\leftmargin\leftmarginiv\labelwidth\leftmarginiv% 1026 \advance\labelwidth-\labelsep \topsep 2pt} 1027 \def\@listv{\leftmargin\leftmarginv\labelwidth\leftmarginv% 1028 \advance\labelwidth-\labelsep \topsep 2pt} 1029 \def\@listvi{\leftmargin\leftmarginvi\labelwidth\leftmarginvi% 1030 \advance\labelwidth-\labelsep \topsep 2pt} 1031 1032 1033 % IEEE uses 5) not 5. 1034 \def\labelenumi{\theenumi)} \def\theenumi{\arabic{enumi}} 1035 1036 % IEEE uses a) not (a) 1037 \def\labelenumii{\theenumii)} \def\theenumii{\alph{enumii}} 1038 1039 % IEEE uses iii) not iii. 1040 \def\labelenumiii{\theenumiii)} \def\theenumiii{\roman{enumiii}} 1041 1042 % IEEE uses A) not A. 1043 \def\labelenumiv{\theenumiv)} \def\theenumiv{\Alph{enumiv}} 1044 1045 % exactly the same as in article.cls 1046 \def\p@enumii{\theenumi} 1047 \def\p@enumiii{\theenumi(\theenumii)} 1048 \def\p@enumiv{\p@enumiii\theenumiii} 1049 1050 % itemized list label styles 1051 \def\labelitemi{$\scriptstyle\bullet$} 1052 \def\labelitemii{\textbf{--}} 1053 \def\labelitemiii{$\ast$} 1054 \def\labelitemiv{$\cdot$} 1055 1056 1057 1058 % **** V1.3 ENHANCEMENTS **** 1059 % Itemize, Enumerate and Description (IED) List Controls 1060 % *************************** 1061 % 1062 % 1063 % IEEE seems to use at least two different values by 1064 % which ITEMIZED list labels are indented to the right 1065 % For The Journal of Lightwave Technology (JLT) and The Journal 1066 % on Selected Areas in Communications (JSAC), they tend to use 1067 % an indention equal to \parindent. For Transactions on Communications 1068 % they tend to indent ITEMIZED lists a little more--- 1.3\parindent. 1069 % We‘ll provide both values here for you so that you can choose 1070 % which one you like in your document using a command such as: 1071 % setlength{\IEEEilabelindent}{\IEEEilabelindentB} 1072 \newdimen\IEEEilabelindentA 1073 \IEEEilabelindentA \parindent 1074 1075 \newdimen\IEEEilabelindentB 1076 \IEEEilabelindentB 1.3\parindent 1077 % However, we‘ll default to using \parindent 1078 % which makes more sense to me 1079 \newdimen\IEEEilabelindent 1080 \IEEEilabelindent \IEEEilabelindentA 1081 1082 1083 % This controls the default amount the enumerated list labels 1084 % are indented to the right. 1085 % Normally, this is the same as the paragraph indention 1086 \newdimen\IEEEelabelindent 1087 \IEEEelabelindent \parindent 1088 1089 % This controls the default amount the description list labels 1090 % are indented to the right. 1091 % Normally, this is the same as the paragraph indention 1092 \newdimen\IEEEdlabelindent 1093 \IEEEdlabelindent \parindent 1094 1095 % This is the value actually used within the IED lists. 1096 % The IED environments automatically set its value to 1097 % one of the three values above, so global changes do 1098 % not have any effect 1099 \newdimen\IEEElabelindent 1100 \IEEElabelindent \parindent 1101 1102 % The actual amount labels will be indented is 1103 % \IEEElabelindent multiplied by the factor below 1104 % corresponding to the level of nesting depth 1105 % This provides a means by which the user can 1106 % alter the effective \IEEElabelindent for deeper 1107 % levels 1108 % There may not be such a thing as correct "standard IEEE" 1109 % values. What IEEE actually does may depend on the specific 1110 % circumstances. 1111 % The first list level almost always has full indention. 1112 % The second levels I‘ve seen have only 75% of the normal indentation 1113 % Three level or greater nestings are very rare. I am guessing 1114 % that they don‘t use any indentation. 1115 \def\IEEElabelindentfactori{1.0} % almost always one 1116 \def\IEEElabelindentfactorii{0.75} % 0.0 or 1.0 may be used in some cases 1117 \def\IEEElabelindentfactoriii{0.0} % 0.75? 0.5? 0.0? 1118 \def\IEEElabelindentfactoriv{0.0} 1119 \def\IEEElabelindentfactorv{0.0} 1120 \def\IEEElabelindentfactorvi{0.0} 1121 1122 % value actually used within IED lists, it is auto 1123 % set to one of the 6 values above 1124 % global changes here have no effect 1125 \def\IEEElabelindentfactor{1.0} 1126 1127 % This controls the default spacing between the end of the IED 1128 % list labels and the list text, when normal text is used for 1129 % the labels. 1130 \newdimen\IEEEiednormlabelsep 1131 \IEEEiednormlabelsep 0.6em 1132 1133 % This controls the default spacing between the end of the IED 1134 % list labels and the list text, when math symbols are used for 1135 % the labels (nomenclature lists). IEEE usually increases the 1136 % spacing in these cases 1137 \newdimen\IEEEiedmathlabelsep 1138 \IEEEiedmathlabelsep 1.2em 1139 1140 % This controls the extra vertical separation put above and 1141 % below each IED list. IEEE usually puts a little extra spacing 1142 % around each list. However, this spacing is barely noticeable. 1143 \newskip\IEEEiedtopsep 1144 \IEEEiedtopsep 2pt plus 1pt minus 1pt 1145 1146 1147 % This command is executed within each IED list environment 1148 % at the beginning of the list. You can use this to set the 1149 % parameters for some/all your IED list(s) without disturbing 1150 % global parameters that affect things other than lists. 1151 % i.e., renewcommand{\IEEEiedlistdecl}{\setlength{\labelsep}{5em}} 1152 % will alter the \labelsep for the next list(s) until 1153 % \IEEEiedlistdecl is redefined. 1154 \def\IEEEiedlistdecl{\relax} 1155 1156 % This command provides an easy way to set \leftmargin based 1157 % on the \labelwidth, \labelsep and the argument \IEEElabelindent 1158 % Usage: \IEEEcalcleftmargin{width-to-indent-the-label} 1159 % output is in the \leftmargin variable, i.e., effectively: 1160 % \leftmargin = argument + \labelwidth + \labelsep 1161 % Note controlled spacing here, shield end of lines with % 1162 \def\IEEEcalcleftmargin#1{\setlength{\leftmargin}{#1}% 1163 \addtolength{\leftmargin}{\labelwidth}% 1164 \addtolength{\leftmargin}{\labelsep}} 1165 1166 % This command provides an easy way to set \labelwidth to the 1167 % width of the given text. It is the same as 1168 % \settowidth{\labelwidth}{label-text} 1169 % and useful as a shorter alternative. 1170 % Typically used to set \labelwidth to be the width 1171 % of the longest label in the list 1172 \def\IEEEsetlabelwidth#1{\settowidth{\labelwidth}{#1}} 1173 1174 % When this command is executed, IED lists will use the 1175 % IEEEiedmathlabelsep label separation rather than the normal 1176 % spacing. To have an effect, this command must be executed via 1177 % the \IEEEiedlistdecl or within the option of the IED list 1178 % environments. 1179 \def\IEEEusemathlabelsep{\setlength{\labelsep}{\IEEEiedmathlabelsep}} 1180 1181 % A flag which controls whether the IED lists automatically 1182 % calculate \leftmargin from \IEEElabelindent, \labelwidth and \labelsep 1183 % Useful if you want to specify your own \leftmargin 1184 % This flag must be set (\IEEEnocalcleftmargintrue or \IEEEnocalcleftmarginfalse) 1185 % via the \IEEEiedlistdecl or within the option of the IED list 1186 % environments to have an effect. 1187 \newif\ifIEEEnocalcleftmargin 1188 \IEEEnocalcleftmarginfalse 1189 1190 % A flag which controls whether \IEEElabelindent is multiplied by 1191 % the \IEEElabelindentfactor for each list level. 1192 % This flag must be set via the \IEEEiedlistdecl or within the option 1193 % of the IED list environments to have an effect. 1194 \newif\ifIEEEnolabelindentfactor 1195 \IEEEnolabelindentfactorfalse 1196 1197 1198 % internal variable to indicate type of IED label 1199 % justification 1200 % 0 - left; 1 - center; 2 - right 1201 \def\@IEEEiedjustify{0} 1202 1203 1204 % commands to allow the user to control IED 1205 % label justifications. Use these commands within 1206 % the IED environment option or in the \IEEEiedlistdecl 1207 % Note that changing the normal list justifications 1208 % is nonstandard and IEEE may not like it if you do so! 1209 % I include these commands as they may be helpful to 1210 % those who are using these enhanced list controls for 1211 % other non-IEEE related LaTeX work. 1212 % itemize and enumerate automatically default to right 1213 % justification, description defaults to left. 1214 \def\IEEEiedlabeljustifyl{\def\@IEEEiedjustify{0}}%left 1215 \def\IEEEiedlabeljustifyc{\def\@IEEEiedjustify{1}}%center 1216 \def\IEEEiedlabeljustifyr{\def\@IEEEiedjustify{2}}%right 1217 1218 1219 1220 1221 % commands to save to and restore from the list parameter copies 1222 % this allows us to set all the list parameters within 1223 % the list_decl and prevent \list (and its \@list) 1224 % from overriding any of our parameters 1225 % V1.6 use \edefs instead of dimen‘s to conserve dimen registers 1226 % Note controlled spacing here, shield end of lines with % 1227 \def\@IEEEsavelistparams{\edef\@IEEEiedtopsep{\the\topsep}% 1228 \edef\@IEEEiedlabelwidth{\the\labelwidth}% 1229 \edef\@IEEEiedlabelsep{\the\labelsep}% 1230 \edef\@IEEEiedleftmargin{\the\leftmargin}% 1231 \edef\@IEEEiedpartopsep{\the\partopsep}% 1232 \edef\@IEEEiedparsep{\the\parsep}% 1233 \edef\@IEEEieditemsep{\the\itemsep}% 1234 \edef\@IEEEiedrightmargin{\the\rightmargin}% 1235 \edef\@IEEEiedlistparindent{\the\listparindent}% 1236 \edef\@IEEEieditemindent{\the\itemindent}} 1237 1238 % Note controlled spacing here 1239 \def\@IEEErestorelistparams{\topsep\@IEEEiedtopsep\relax% 1240 \labelwidth\@IEEEiedlabelwidth\relax% 1241 \labelsep\@IEEEiedlabelsep\relax% 1242 \leftmargin\@IEEEiedleftmargin\relax% 1243 \partopsep\@IEEEiedpartopsep\relax% 1244 \parsep\@IEEEiedparsep\relax% 1245 \itemsep\@IEEEieditemsep\relax% 1246 \rightmargin\@IEEEiedrightmargin\relax% 1247 \listparindent\@IEEEiedlistparindent\relax% 1248 \itemindent\@IEEEieditemindent\relax} 1249 1250 1251 % v1.6b provide original LaTeX IED list environments 1252 % note that latex.ltx defines \itemize and \enumerate, but not \description 1253 % which must be created by the base classes 1254 % save original LaTeX itemize and enumerate 1255 \let\LaTeXitemize\itemize 1256 \let\endLaTeXitemize\enditemize 1257 \let\LaTeXenumerate\enumerate 1258 \let\endLaTeXenumerate\endenumerate 1259 1260 % provide original LaTeX description environment from article.cls 1261 \newenvironment{LaTeXdescription} 1262 {\list{}{\labelwidth\z@ \itemindent-\leftmargin 1263 \let\makelabel\descriptionlabel}} 1264 {\endlist} 1265 \newcommand*\descriptionlabel[1]{\hspace\labelsep 1266 \normalfont\bfseries #1} 1267 1268 1269 % override LaTeX‘s default IED lists 1270 \def\itemize{\@IEEEitemize} 1271 \def\enditemize{\@endIEEEitemize} 1272 \def\enumerate{\@IEEEenumerate} 1273 \def\endenumerate{\@endIEEEenumerate} 1274 \def\description{\@IEEEdescription} 1275 \def\enddescription{\@endIEEEdescription} 1276 1277 % provide the user with aliases - may help those using packages that 1278 % override itemize, enumerate, or description 1279 \def\IEEEitemize{\@IEEEitemize} 1280 \def\endIEEEitemize{\@endIEEEitemize} 1281 \def\IEEEenumerate{\@IEEEenumerate} 1282 \def\endIEEEenumerate{\@endIEEEenumerate} 1283 \def\IEEEdescription{\@IEEEdescription} 1284 \def\endIEEEdescription{\@endIEEEdescription} 1285 1286 1287 % V1.6 we want to keep the IEEEtran IED list definitions as our own internal 1288 % commands so they are protected against redefinition 1289 \def\@IEEEitemize{\@ifnextchar[{\@@IEEEitemize}{\@@IEEEitemize[\relax]}} 1290 \def\@IEEEenumerate{\@ifnextchar[{\@@IEEEenumerate}{\@@IEEEenumerate[\relax]}} 1291 \def\@IEEEdescription{\@ifnextchar[{\@@IEEEdescription}{\@@IEEEdescription[\relax]}} 1292 \def\@endIEEEitemize{\endlist} 1293 \def\@endIEEEenumerate{\endlist} 1294 \def\@endIEEEdescription{\endlist} 1295 1296 1297 % DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS 1298 % AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS 1299 % IEEEtran itemized list MDS 1/2001 1300 % Note controlled spacing here, shield end of lines with % 1301 \def\@@IEEEitemize[#1]{% 1302 \ifnum\@itemdepth>3\relax\@toodeep\else% 1303 \ifnum\@listdepth>5\relax\@toodeep\else% 1304 \advance\@itemdepth\@ne% 1305 \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}% 1306 % get the labelindentfactor for this level 1307 \advance\@listdepth\@ne% we need to know what the level WILL be 1308 \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}% 1309 \advance\@listdepth-\@ne% undo our increment 1310 \def\@IEEEiedjustify{2}% right justified labels are default 1311 % set other defaults 1312 \IEEEnocalcleftmarginfalse% 1313 \IEEEnolabelindentfactorfalse% 1314 \topsep\IEEEiedtopsep% 1315 \IEEElabelindent\IEEEilabelindent% 1316 \labelsep\IEEEiednormlabelsep% 1317 \partopsep 0ex% 1318 \parsep 0ex% 1319 \itemsep 0ex% 1320 \rightmargin 0em% 1321 \listparindent 0em% 1322 \itemindent 0em% 1323 % calculate the label width 1324 % the user can override this later if 1325 % they specified a \labelwidth 1326 \settowidth{\labelwidth}{\csname labelitem\romannumeral\the\@itemdepth\endcsname}% 1327 \@IEEEsavelistparams% save our list parameters 1328 \list{\csname\@itemitem\endcsname}{% 1329 \@IEEErestorelistparams% override any list{} changes 1330 % to our globals 1331 \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel 1332 \IEEEiedlistdecl% let user alter parameters 1333 #1\relax% 1334 % If the user has requested not to use the 1335 % labelindent factor, don‘t revise \labelindent 1336 \ifIEEEnolabelindentfactor\relax% 1337 \else\IEEElabelindent=\IEEElabelindentfactor\labelindent% 1338 \fi% 1339 % Unless the user has requested otherwise, 1340 % calculate our left margin based 1341 % on \IEEElabelindent, \labelwidth and 1342 % \labelsep 1343 \ifIEEEnocalcleftmargin\relax% 1344 \else\IEEEcalcleftmargin{\IEEElabelindent}% 1345 \fi}\fi\fi}% 1346 1347 1348 % DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS 1349 % AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS 1350 % IEEEtran enumerate list MDS 1/2001 1351 % Note controlled spacing here, shield end of lines with % 1352 \def\@@IEEEenumerate[#1]{% 1353 \ifnum\@enumdepth>3\relax\@toodeep\else% 1354 \ifnum\@listdepth>5\relax\@toodeep\else% 1355 \advance\@enumdepth\@ne% 1356 \edef\@enumctr{enum\romannumeral\the\@enumdepth}% 1357 % get the labelindentfactor for this level 1358 \advance\@listdepth\@ne% we need to know what the level WILL be 1359 \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}% 1360 \advance\@listdepth-\@ne% undo our increment 1361 \def\@IEEEiedjustify{2}% right justified labels are default 1362 % set other defaults 1363 \IEEEnocalcleftmarginfalse% 1364 \IEEEnolabelindentfactorfalse% 1365 \topsep\IEEEiedtopsep% 1366 \IEEElabelindent\IEEEelabelindent% 1367 \labelsep\IEEEiednormlabelsep% 1368 \partopsep 0ex% 1369 \parsep 0ex% 1370 \itemsep 0ex% 1371 \rightmargin 0em% 1372 \listparindent 0em% 1373 \itemindent 0em% 1374 % calculate the label width 1375 % We‘ll set it to the width suitable for all labels using 1376 % normalfont 1) to 9) 1377 % The user can override this later 1378 \settowidth{\labelwidth}{9)}% 1379 \@IEEEsavelistparams% save our list parameters 1380 \list{\csname label\@enumctr\endcsname}{\usecounter{\@enumctr}% 1381 \@IEEErestorelistparams% override any list{} changes 1382 % to our globals 1383 \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel 1384 \IEEEiedlistdecl% let user alter parameters 1385 #1\relax% 1386 % If the user has requested not to use the 1387 % IEEElabelindent factor, don‘t revise \IEEElabelindent 1388 \ifIEEEnolabelindentfactor\relax% 1389 \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent% 1390 \fi% 1391 % Unless the user has requested otherwise, 1392 % calculate our left margin based 1393 % on \IEEElabelindent, \labelwidth and 1394 % \labelsep 1395 \ifIEEEnocalcleftmargin\relax% 1396 \else\IEEEcalcleftmargin{\IEEElabelindent}% 1397 \fi}\fi\fi}% 1398 1399 1400 % DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS 1401 % AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS 1402 % IEEEtran description list MDS 1/2001 1403 % Note controlled spacing here, shield end of lines with % 1404 \def\@@IEEEdescription[#1]{% 1405 \ifnum\@listdepth>5\relax\@toodeep\else% 1406 % get the labelindentfactor for this level 1407 \advance\@listdepth\@ne% we need to know what the level WILL be 1408 \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}% 1409 \advance\@listdepth-\@ne% undo our increment 1410 \def\@IEEEiedjustify{0}% left justified labels are default 1411 % set other defaults 1412 \IEEEnocalcleftmarginfalse% 1413 \IEEEnolabelindentfactorfalse% 1414 \topsep\IEEEiedtopsep% 1415 \IEEElabelindent\IEEEdlabelindent% 1416 % assume normal labelsep 1417 \labelsep\IEEEiednormlabelsep% 1418 \partopsep 0ex% 1419 \parsep 0ex% 1420 \itemsep 0ex% 1421 \rightmargin 0em% 1422 \listparindent 0em% 1423 \itemindent 0em% 1424 % Bogus label width in case the user forgets 1425 % to set it. 1426 % TIP: If you want to see what a variable‘s width is you 1427 % can use the TeX command \showthe\width-variable to 1428 % display it on the screen during compilation 1429 % (This might be helpful to know when you need to find out 1430 % which label is the widest) 1431 \settowidth{\labelwidth}{Hello}% 1432 \@IEEEsavelistparams% save our list parameters 1433 \list{}{\@IEEErestorelistparams% override any list{} changes 1434 % to our globals 1435 \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel 1436 \IEEEiedlistdecl% let user alter parameters 1437 #1\relax% 1438 % If the user has requested not to use the 1439 % labelindent factor, don‘t revise \IEEElabelindent 1440 \ifIEEEnolabelindentfactor\relax% 1441 \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent% 1442 \fi% 1443 % Unless the user has requested otherwise, 1444 % calculate our left margin based 1445 % on \IEEElabelindent, \labelwidth and 1446 % \labelsep 1447 \ifIEEEnocalcleftmargin\relax% 1448 \else\IEEEcalcleftmargin{\IEEElabelindent}\relax% 1449 \fi}\fi} 1450 1451 % v1.6b we use one makelabel that does justification as needed. 1452 \def\@IEEEiedmakelabel#1{\relax\if\@IEEEiedjustify 0\relax 1453 \makebox[\labelwidth][l]{\normalfont #1}\else 1454 \if\@IEEEiedjustify 1\relax 1455 \makebox[\labelwidth][c]{\normalfont #1}\else 1456 \makebox[\labelwidth][r]{\normalfont #1}\fi\fi} 1457 1458 1459 % VERSE and QUOTE 1460 % V1.7 define environments with newenvironment 1461 \newenvironment{verse}{\let\\=\@centercr 1462 \list{}{\itemsep\z@ \itemindent -1.5em \listparindent \itemindent 1463 \rightmargin\leftmargin\advance\leftmargin 1.5em}\item\relax} 1464 {\endlist} 1465 \newenvironment{quotation}{\list{}{\listparindent 1.5em \itemindent\listparindent 1466 \rightmargin\leftmargin \parsep 0pt plus 1pt}\item\relax} 1467 {\endlist} 1468 \newenvironment{quote}{\list{}{\rightmargin\leftmargin}\item\relax} 1469 {\endlist} 1470 1471 1472 % \titlepage 1473 % provided only for backward compatibility. \maketitle is the correct 1474 % way to create the title page. 1475 \newif\if@restonecol 1476 \def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn 1477 \else \newpage \fi \thispagestyle{empty}\c@page\z@} 1478 \def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi} 1479 1480 % standard values from article.cls 1481 \arraycolsep 5pt 1482 \arrayrulewidth .4pt 1483 \doublerulesep 2pt 1484 1485 \tabcolsep 6pt 1486 \tabbingsep 0.5em 1487 1488 1489 %% FOOTNOTES 1490 % 1491 %\skip\footins 10pt plus 4pt minus 2pt 1492 % V1.6 respond to changes in font size 1493 % space added above the footnotes (if present) 1494 \skip\footins 0.9\baselineskip plus 0.4\baselineskip minus 0.2\baselineskip 1495 1496 % V1.6, we need to make \footnotesep responsive to changes 1497 % in \baselineskip or strange spacings will result when in 1498 % draft mode. Here is a little LaTeX secret - \footnotesep 1499 % determines the height of an invisible strut that is placed 1500 % *above* the baseline of footnotes after the first. Since 1501 % LaTeX considers the space for characters to be 0.7/baselineskip 1502 % above the baseline and 0.3/baselineskip below it, we need to 1503 % use 0.7/baselineskip as a \footnotesep to maintain equal spacing 1504 % between all the lines of the footnotes. IEEE often uses a tad 1505 % more, so use 0.8\baselineskip. This slightly larger value also helps 1506 % the text to clear the footnote marks. Note that \thanks in IEEEtran 1507 % uses its own value of \footnotesep which is set in \maketitle. 1508 {\footnotesize 1509 \global\footnotesep 0.8\baselineskip} 1510 1511 1512 \skip\@mpfootins = \skip\footins 1513 \fboxsep = 3pt 1514 \fboxrule = .4pt 1515 % V1.6 use 1em, then use LaTeX2e‘s \@makefnmark 1516 % Note that IEEE normally *left* aligns the footnote marks, so we don‘t need 1517 % box resizing tricks here. 1518 \long\def\@makefntext#1{\parindent 1em\indent\hbox{\@makefnmark}#1}% V1.6 use 1em 1519 % V1.7 compsoc does not use superscipts for footnote marks 1520 \ifCLASSOPTIONcompsoc 1521 \def\@IEEEcompsocmakefnmark{\hbox{\normalfont\@thefnmark.\ }} 1522 \long\def\@makefntext#1{\parindent 1em\indent\hbox{\@IEEEcompsocmakefnmark}#1} 1523 \fi 1524 1525 % IEEE does not use footnote rules 1526 \def\footnoterule{} 1527 1528 % V1.7 for compsoc, IEEE uses a footnote rule only for \thanks. We devise a "one-shot" 1529 % system to implement this. 1530 \newif\if@IEEEenableoneshotfootnoterule 1531 \@IEEEenableoneshotfootnoterulefalse 1532 \ifCLASSOPTIONcompsoc 1533 \def\footnoterule{\relax\if@IEEEenableoneshotfootnoterule 1534 \kern-5pt 1535 \hbox to \columnwidth{\hfill\vrule width 0.5\columnwidth height 0.4pt\hfill} 1536 \kern4.6pt 1537 \global\@IEEEenableoneshotfootnoterulefalse 1538 \else 1539 \relax 1540 \fi} 1541 \fi 1542 1543 % V1.6 do not allow LaTeX to break a footnote across multiple pages 1544 \interfootnotelinepenalty=10000 1545 1546 % V1.6 discourage breaks within equations 1547 % Note that amsmath normally sets this to 10000, 1548 % but LaTeX2e normally uses 100. 1549 \interdisplaylinepenalty=2500 1550 1551 % default allows section depth up to /paragraph 1552 \setcounter{secnumdepth}{4} 1553 1554 % technotes do not allow /paragraph 1555 \ifCLASSOPTIONtechnote 1556 \setcounter{secnumdepth}{3} 1557 \fi 1558 % neither do compsoc conferences 1559 \@IEEEcompsocconfonly{\setcounter{secnumdepth}{3}} 1560 1561 1562 \newcounter{section} 1563 \newcounter{subsection}[section] 1564 \newcounter{subsubsection}[subsection] 1565 \newcounter{paragraph}[subsubsection] 1566 1567 % used only by IEEEtran‘s IEEEeqnarray as other packages may 1568 % have their own, different, implementations 1569 \newcounter{IEEEsubequation}[equation] 1570 1571 % as shown when called by user from \ref, \label and in table of contents 1572 \def\theequation{\arabic{equation}} % 1 1573 \def\theIEEEsubequation{\theequation\alph{IEEEsubequation}} % 1a (used only by IEEEtran‘s IEEEeqnarray) 1574 \ifCLASSOPTIONcompsoc 1575 % compsoc is all arabic 1576 \def\thesection{\arabic{section}} 1577 \def\thesubsection{\thesection.\arabic{subsection}} 1578 \def\thesubsubsection{\thesubsection.\arabic{subsubsection}} 1579 \def\theparagraph{\thesubsubsection.\arabic{paragraph}} 1580 \else 1581 \def\thesection{\Roman{section}} % I 1582 % V1.7, \mbox prevents breaks around - 1583 \def\thesubsection{\mbox{\thesection-\Alph{subsection}}} % I-A 1584 % V1.7 use I-A1 format used by IEEE rather than I-A.1 1585 \def\thesubsubsection{\thesubsection\arabic{subsubsection}} % I-A1 1586 \def\theparagraph{\thesubsubsection\alph{paragraph}} % I-A1a 1587 \fi 1588 1589 % From Heiko Oberdiek. Because of the \mbox in \thesubsection, we need to 1590 % tell hyperref to disable the \mbox command when making PDF bookmarks. 1591 % This done already with hyperref.sty version 6.74o and later, but 1592 % it will not hurt to do it here again for users of older versions. 1593 \@ifundefined{pdfstringdefPreHook}{\let\pdfstringdefPreHook\@empty}{}% 1594 \g@addto@macro\pdfstringdefPreHook{\let\mbox\relax} 1595 1596 1597 % Main text forms (how shown in main text headings) 1598 % V1.6, using \thesection in \thesectiondis allows changes 1599 % in the former to automatically appear in the latter 1600 \ifCLASSOPTIONcompsoc 1601 \ifCLASSOPTIONconference% compsoc conference 1602 \def\thesectiondis{\thesection.} 1603 \def\thesubsectiondis{\thesectiondis\arabic{subsection}.} 1604 \def\thesubsubsectiondis{\thesubsectiondis\arabic{subsubsection}.} 1605 \def\theparagraphdis{\thesubsubsectiondis\arabic{paragraph}.} 1606 \else% compsoc not conferencs 1607 \def\thesectiondis{\thesection} 1608 \def\thesubsectiondis{\thesectiondis.\arabic{subsection}} 1609 \def\thesubsubsectiondis{\thesubsectiondis.\arabic{subsubsection}} 1610 \def\theparagraphdis{\thesubsubsectiondis.\arabic{paragraph}} 1611 \fi 1612 \else% not compsoc 1613 \def\thesectiondis{\thesection.} % I. 1614 \def\thesubsectiondis{\Alph{subsection}.} % B. 1615 \def\thesubsubsectiondis{\arabic{subsubsection})} % 3) 1616 \def\theparagraphdis{\alph{paragraph})} % d) 1617 \fi 1618 1619 % just like LaTeX2e‘s \@eqnnum 1620 \def\theequationdis{{\normalfont \normalcolor (\theequation)}}% (1) 1621 % IEEEsubequation used only by IEEEtran‘s IEEEeqnarray 1622 \def\theIEEEsubequationdis{{\normalfont \normalcolor (\theIEEEsubequation)}}% (1a) 1623 % redirect LaTeX2e‘s equation number display and all that depend on 1624 % it, through IEEEtran‘s \theequationdis 1625 \def\@eqnnum{\theequationdis} 1626 1627 1628 1629 % V1.7 provide string macros as article.cls does 1630 \def\contentsname{Contents} 1631 \def\listfigurename{List of Figures} 1632 \def\listtablename{List of Tables} 1633 \def\refname{References} 1634 \def\indexname{Index} 1635 \def\figurename{Fig.} 1636 \def\tablename{TABLE} 1637 \@IEEEcompsocconfonly{\def\figurename{Figure}\def\tablename{Table}} 1638 \def\partname{Part} 1639 \def\appendixname{Appendix} 1640 \def\abstractname{Abstract} 1641 % IEEE specific names 1642 \def\IEEEkeywordsname{Index Terms} 1643 \def\IEEEproofname{Proof} 1644 1645 1646 % LIST OF FIGURES AND TABLES AND TABLE OF CONTENTS 1647 % 1648 \def\@pnumwidth{1.55em} 1649 \def\@tocrmarg{2.55em} 1650 \def\@dotsep{4.5} 1651 \setcounter{tocdepth}{3} 1652 1653 % adjusted some spacings here so that section numbers will not easily 1654 % collide with the section titles. 1655 % VIII; VIII-A; and VIII-A.1 are usually the worst offenders. 1656 % MDS 1/2001 1657 \def\tableofcontents{\section*{\contentsname}\@starttoc{toc}} 1658 \def\l@section#1#2{\addpenalty{\@secpenalty}\addvspace{1.0em plus 1pt}% 1659 \@tempdima 2.75em \begingroup \parindent \z@ \rightskip \@pnumwidth% 1660 \parfillskip-\@pnumwidth {\bfseries\leavevmode #1}\hfil\hbox to\@pnumwidth{\hss #2}\par% 1661 \endgroup} 1662 % argument format #1:level, #2:labelindent,#3:labelsep 1663 \def\l@subsection{\@dottedtocline{2}{2.75em}{3.75em}} 1664 \def\l@subsubsection{\@dottedtocline{3}{6.5em}{4.5em}} 1665 % must provide \l@ defs for ALL sublevels EVEN if tocdepth 1666 % is such as they will not appear in the table of contents 1667 % these defs are how TOC knows what level these things are! 1668 \def\l@paragraph{\@dottedtocline{4}{6.5em}{5.5em}} 1669 \def\l@subparagraph{\@dottedtocline{5}{6.5em}{6.5em}} 1670 \def\listoffigures{\section*{\listfigurename}\@starttoc{lof}} 1671 \def\l@figure{\@dottedtocline{1}{0em}{2.75em}} 1672 \def\listoftables{\section*{\listtablename}\@starttoc{lot}} 1673 \let\l@table\l@figure 1674 1675 1676 %% Definitions for floats 1677 %% 1678 %% Normal Floats 1679 \floatsep 1\baselineskip plus 0.2\baselineskip minus 0.2\baselineskip 1680 \textfloatsep 1.7\baselineskip plus 0.2\baselineskip minus 0.4\baselineskip 1681 \@fptop 0pt plus 1fil 1682 \@fpsep 0.75\baselineskip plus 2fil 1683 \@fpbot 0pt plus 1fil 1684 \def\topfraction{0.9} 1685 \def\bottomfraction{0.4} 1686 \def\floatpagefraction{0.8} 1687 % V1.7, let top floats approach 90% of page 1688 \def\textfraction{0.1} 1689 1690 %% Double Column Floats 1691 \dblfloatsep 1\baselineskip plus 0.2\baselineskip minus 0.2\baselineskip 1692 1693 \dbltextfloatsep 1.7\baselineskip plus 0.2\baselineskip minus 0.4\baselineskip 1694 % Note that it would be nice if the rubber here actually worked in LaTeX2e. 1695 % There is a long standing limitation in LaTeX, first discovered (to the best 1696 % of my knowledge) by Alan Jeffrey in 1992. LaTeX ignores the stretchable 1697 % portion of \dbltextfloatsep, and as a result, double column figures can and 1698 % do result in an non-integer number of lines in the main text columns with 1699 % underfull vbox errors as a consequence. A post to comp.text.tex 1700 % by Donald Arseneau confirms that this had not yet been fixed in 1998. 1701 % IEEEtran V1.6 will fix this problem for you in the titles, but it doesn‘t 1702 % protect you from other double floats. Happy vspace‘ing. 1703 1704 \@dblfptop 0pt plus 1fil 1705 \@dblfpsep 0.75\baselineskip plus 2fil 1706 \@dblfpbot 0pt plus 1fil 1707 \def\dbltopfraction{0.8} 1708 \def\dblfloatpagefraction{0.8} 1709 \setcounter{dbltopnumber}{4} 1710 1711 \intextsep 1\baselineskip plus 0.2\baselineskip minus 0.2\baselineskip 1712 \setcounter{topnumber}{2} 1713 \setcounter{bottomnumber}{2} 1714 \setcounter{totalnumber}{4} 1715 1716 1717 1718 % article class provides these, we should too. 1719 \newlength\abovecaptionskip 1720 \newlength\belowcaptionskip 1721 % but only \abovecaptionskip is used above figure captions and *below* table 1722 % captions 1723 \setlength\abovecaptionskip{0.5\baselineskip} 1724 \setlength\belowcaptionskip{0pt} 1725 % V1.6 create hooks in case the caption spacing ever needs to be 1726 % overridden by a user 1727 \def\@IEEEfigurecaptionsepspace{\vskip\abovecaptionskip\relax}% 1728 \def\@IEEEtablecaptionsepspace{\vskip\abovecaptionskip\relax}% 1729 1730 1731 % 1.6b revise caption system so that \@makecaption uses two arguments 1732 % as with LaTeX2e. Otherwise, there will be problems when using hyperref. 1733 \def\@IEEEtablestring{table} 1734 1735 \ifCLASSOPTIONcompsoc 1736 % V1.7 compsoc \@makecaption 1737 \ifCLASSOPTIONconference% compsoc conference 1738 \long\def\@makecaption#1#2{% 1739 % test if is a for a figure or table 1740 \ifx\@captype\@IEEEtablestring% 1741 % if a table, do table caption 1742 \normalsize\begin{center}{\normalfont\sffamily\normalsize {#1.}~ #2}\end{center}% 1743 \@IEEEtablecaptionsepspace 1744 % if not a table, format it as a figure 1745 \else 1746 \@IEEEfigurecaptionsepspace 1747 \setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ #2}% 1748 \ifdim \wd\@tempboxa >\hsize% 1749 % if caption is longer than a line, let it wrap around 1750 \setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ }% 1751 \parbox[t]{\hsize}{\normalfont\sffamily\normalsize \noindent\unhbox\@tempboxa#2}% 1752 % if caption is shorter than a line, center 1753 \else% 1754 \hbox to\hsize{\normalfont\sffamily\normalsize\hfil\box\@tempboxa\hfil}% 1755 \fi\fi} 1756 \else% nonconference compsoc 1757 \long\def\@makecaption#1#2{% 1758 % test if is a for a figure or table 1759 \ifx\@captype\@IEEEtablestring% 1760 % if a table, do table caption 1761 \normalsize\begin{center}{\normalfont\sffamily\normalsize #1}\\{\normalfont\sffamily\normalsize #2}\end{center}% 1762 \@IEEEtablecaptionsepspace 1763 % if not a table, format it as a figure 1764 \else 1765 \@IEEEfigurecaptionsepspace 1766 \setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ #2}% 1767 \ifdim \wd\@tempboxa >\hsize% 1768 % if caption is longer than a line, let it wrap around 1769 \setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ }% 1770 \parbox[t]{\hsize}{\normalfont\sffamily\normalsize \noindent\unhbox\@tempboxa#2}% 1771 % if caption is shorter than a line, left justify 1772 \else% 1773 \hbox to\hsize{\normalfont\sffamily\normalsize\box\@tempboxa\hfil}% 1774 \fi\fi} 1775 \fi 1776 1777 \else% traditional noncompsoc \@makecaption 1778 \long\def\@makecaption#1#2{% 1779 % test if is a for a figure or table 1780 \ifx\@captype\@IEEEtablestring% 1781 % if a table, do table caption 1782 \footnotesize\begin{center}{\normalfont\footnotesize #1}\\{\normalfont\footnotesize\scshape #2}\end{center}% 1783 \@IEEEtablecaptionsepspace 1784 % if not a table, format it as a figure 1785 \else 1786 \@IEEEfigurecaptionsepspace 1787 % 3/2001 use footnotesize, not small; use two nonbreaking spaces, not one 1788 \setbox\@tempboxa\hbox{\normalfont\footnotesize {#1.}~~ #2}% 1789 \ifdim \wd\@tempboxa >\hsize% 1790 % if caption is longer than a line, let it wrap around 1791 \setbox\@tempboxa\hbox{\normalfont\footnotesize {#1.}~~ }% 1792 \parbox[t]{\hsize}{\normalfont\footnotesize\noindent\unhbox\@tempboxa#2}% 1793 % if caption is shorter than a line, center if conference, left justify otherwise 1794 \else% 1795 \ifCLASSOPTIONconference \hbox to\hsize{\normalfont\footnotesize\hfil\box\@tempboxa\hfil}% 1796 \else \hbox to\hsize{\normalfont\footnotesize\box\@tempboxa\hfil}% 1797 \fi\fi\fi} 1798 \fi 1799 1800 1801 1802 % V1.7 disable captions class option, do so in a way that retains operation of \label 1803 % within \caption 1804 \ifCLASSOPTIONcaptionsoff 1805 \long\def\@makecaption#1#2{\vspace*{2em}\footnotesize\begin{center}{\footnotesize #1}\end{center}% 1806 \let\@IEEEtemporiglabeldefsave\label 1807 \let\@IEEEtemplabelargsave\relax 1808 \def\label##1{\gdef\@IEEEtemplabelargsave{##1}}% 1809 \setbox\@tempboxa\hbox{#2}% 1810 \let\label\@IEEEtemporiglabeldefsave 1811 \ifx\@IEEEtemplabelargsave\relax\else\label{\@IEEEtemplabelargsave}\fi} 1812 \fi 1813 1814 1815 % V1.7 define end environments with \def not \let so as to work OK with 1816 % preview-latex 1817 \newcounter{figure} 1818 \def\thefigure{\@arabic\c@figure} 1819 \def\fps@figure{tbp} 1820 \def\ftype@figure{1} 1821 \def\ext@figure{lof} 1822 \def\fnum@figure{\figurename~\thefigure} 1823 \def\figure{\@float{figure}} 1824 \def\endfigure{\end@float} 1825 \@namedef{figure*}{\@dblfloat{figure}} 1826 \@namedef{endfigure*}{\end@dblfloat} 1827 \newcounter{table} 1828 \ifCLASSOPTIONcompsoc 1829 \def\thetable{\arabic{table}} 1830 \else 1831 \def\thetable{\@Roman\c@table} 1832 \fi 1833 \def\fps@table{tbp} 1834 \def\ftype@table{2} 1835 \def\ext@table{lot} 1836 \def\fnum@table{\tablename~\thetable} 1837 % V1.6 IEEE uses 8pt text for tables 1838 % to default to footnotesize, we hack into LaTeX2e‘s \@floatboxreset and pray 1839 \def\table{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@float{table}} 1840 \def\endtable{\end@float} 1841 % v1.6b double column tables need to default to footnotesize as well. 1842 \@namedef{table*}{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@dblfloat{table}} 1843 \@namedef{endtable*}{\end@dblfloat} 1844 1845 1846 1847 1848 %% 1849 %% START OF IEEEeqnarry DEFINITIONS 1850 %% 1851 %% Inspired by the concepts, examples, and previous works of LaTeX 1852 %% coders and developers such as Donald Arseneau, Fred Bartlett, 1853 %% David Carlisle, Tony Liu, Frank Mittelbach, Piet van Oostrum, 1854 %% Roland Winkler and Mark Wooding. 1855 %% I don‘t make the claim that my work here is even near their calibre. ;) 1856 1857 1858 % hook to allow easy changeover to IEEEtran.cls/tools.sty error reporting 1859 \def\@IEEEclspkgerror{\ClassError{IEEEtran}} 1860 1861 \newif\if@IEEEeqnarraystarform% flag to indicate if the environment was called as the star form 1862 \@IEEEeqnarraystarformfalse 1863 1864 \newif\if@advanceIEEEeqncolcnt% tracks if the environment should advance the col counter 1865 % allows a way to make an \IEEEeqnarraybox that can be used within an \IEEEeqnarray 1866 % used by IEEEeqnarraymulticol so that it can work properly in both 1867 \@advanceIEEEeqncolcnttrue 1868 1869 \newcount\@IEEEeqnnumcols % tracks how many IEEEeqnarray cols are defined 1870 \newcount\@IEEEeqncolcnt % tracks how many IEEEeqnarray cols the user actually used 1871 1872 1873 % The default math style used by the columns 1874 \def\IEEEeqnarraymathstyle{\displaystyle} 1875 % The default text style used by the columns 1876 % default to using the current font 1877 \def\IEEEeqnarraytextstyle{\relax} 1878 1879 % like the iedlistdecl but for \IEEEeqnarray 1880 \def\IEEEeqnarraydecl{\relax} 1881 \def\IEEEeqnarrayboxdecl{\relax} 1882 1883 % \yesnumber is the opposite of \nonumber 1884 % a novel concept with the same def as the equationarray package 1885 % However, we give IEEE versions too since some LaTeX packages such as 1886 % the MDWtools mathenv.sty redefine \nonumber to something else. 1887 \providecommand{\yesnumber}{\global\@eqnswtrue} 1888 \def\IEEEyesnumber{\global\@eqnswtrue} 1889 \def\IEEEnonumber{\global\@eqnswfalse} 1890 1891 1892 \def\IEEEyessubnumber{\global\@IEEEissubequationtrue\global\@eqnswtrue% 1893 \if@IEEEeqnarrayISinner% only do something inside an IEEEeqnarray 1894 \if@IEEElastlinewassubequation\addtocounter{equation}{-1}\else\setcounter{IEEEsubequation}{1}\fi% 1895 \def\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\fi} 1896 1897 % flag to indicate that an equation is a sub equation 1898 \newif\if@IEEEissubequation% 1899 \@IEEEissubequationfalse 1900 1901 % allows users to "push away" equations that get too close to the equation numbers 1902 \def\IEEEeqnarraynumspace{\hphantom{\if@IEEEissubequation\theIEEEsubequationdis\else\theequationdis\fi}} 1903 1904 % provides a way to span multiple columns within IEEEeqnarray environments 1905 % will consider \if@advanceIEEEeqncolcnt before globally advancing the 1906 % column counter - so as to work within \IEEEeqnarraybox 1907 % usage: \IEEEeqnarraymulticol{number cols. to span}{col type}{cell text} 1908 \long\def\IEEEeqnarraymulticol#1#2#3{\multispan{#1}% 1909 % check if column is defined 1910 \relax\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined% 1911 \csname @IEEEeqnarraycolPRE#2\endcsname#3\relax\relax\relax\relax\relax% 1912 \relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST#2\endcsname% 1913 \else% if not, error and use default type 1914 \@IEEEclspkgerror{Invalid column type "#2" in \string\IEEEeqnarraymulticol.\MessageBreak 1915 Using a default centering column instead}% 1916 {You must define IEEEeqnarray column types before use.}% 1917 \csname @IEEEeqnarraycolPRE@IEEEdefault\endcsname#3\relax\relax\relax\relax\relax% 1918 \relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST@IEEEdefault\endcsname% 1919 \fi% 1920 % advance column counter only if the IEEEeqnarray environment wants it 1921 \if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by #1\relax\fi} 1922 1923 % like \omit, but maintains track of the column counter for \IEEEeqnarray 1924 \def\IEEEeqnarrayomit{\omit\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by 1\relax\fi} 1925 1926 1927 % provides a way to define a letter referenced column type 1928 % usage: \IEEEeqnarraydefcol{col. type letter/name}{pre insertion text}{post insertion text} 1929 \def\IEEEeqnarraydefcol#1#2#3{\expandafter\def\csname @IEEEeqnarraycolPRE#1\endcsname{#2}% 1930 \expandafter\def\csname @IEEEeqnarraycolPOST#1\endcsname{#3}% 1931 \expandafter\def\csname @IEEEeqnarraycolDEF#1\endcsname{1}} 1932 1933 1934 % provides a way to define a numerically referenced inter-column glue types 1935 % usage: \IEEEeqnarraydefcolsep{col. glue number}{glue definition} 1936 \def\IEEEeqnarraydefcolsep#1#2{\expandafter\def\csname @IEEEeqnarraycolSEP\romannumeral #1\endcsname{#2}% 1937 \expandafter\def\csname @IEEEeqnarraycolSEPDEF\romannumeral #1\endcsname{1}} 1938 1939 1940 \def\@IEEEeqnarraycolisdefined{1}% just a macro for 1, used for checking undefined column types 1941 1942 1943 % expands and appends the given argument to the \@IEEEtrantmptoksA token list 1944 % used to build up the \halign preamble 1945 \def\@IEEEappendtoksA#1{\edef\@@IEEEappendtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA #1}}% 1946 \@@IEEEappendtoksA} 1947 1948 % also appends to \@IEEEtrantmptoksA, but does not expand the argument 1949 % uses \toks8 as a scratchpad register 1950 \def\@IEEEappendNOEXPANDtoksA#1{\toks8={#1}% 1951 \edef\@@IEEEappendNOEXPANDtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA\the\toks8}}% 1952 \@@IEEEappendNOEXPANDtoksA} 1953 1954 % define some common column types for the user 1955 % math 1956 \IEEEeqnarraydefcol{l}{$\IEEEeqnarraymathstyle}{$\hfil} 1957 \IEEEeqnarraydefcol{c}{\hfil$\IEEEeqnarraymathstyle}{$\hfil} 1958 \IEEEeqnarraydefcol{r}{\hfil$\IEEEeqnarraymathstyle}{$} 1959 \IEEEeqnarraydefcol{L}{$\IEEEeqnarraymathstyle{}}{{}$\hfil} 1960 \IEEEeqnarraydefcol{C}{\hfil$\IEEEeqnarraymathstyle{}}{{}$\hfil} 1961 \IEEEeqnarraydefcol{R}{\hfil$\IEEEeqnarraymathstyle{}}{{}$} 1962 % text 1963 \IEEEeqnarraydefcol{s}{\IEEEeqnarraytextstyle}{\hfil} 1964 \IEEEeqnarraydefcol{t}{\hfil\IEEEeqnarraytextstyle}{\hfil} 1965 \IEEEeqnarraydefcol{u}{\hfil\IEEEeqnarraytextstyle}{} 1966 1967 % vertical rules 1968 \IEEEeqnarraydefcol{v}{}{\vrule width\arrayrulewidth} 1969 \IEEEeqnarraydefcol{vv}{\vrule width\arrayrulewidth\hfil}{\hfil\vrule width\arrayrulewidth} 1970 \IEEEeqnarraydefcol{V}{}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth} 1971 \IEEEeqnarraydefcol{VV}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth\hfil}% 1972 {\hfil\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth} 1973 1974 % horizontal rules 1975 \IEEEeqnarraydefcol{h}{}{\leaders\hrule height\arrayrulewidth\hfil} 1976 \IEEEeqnarraydefcol{H}{}{\leaders\vbox{\hrule width\arrayrulewidth\vskip\doublerulesep\hrule width\arrayrulewidth}\hfil} 1977 1978 % plain 1979 \IEEEeqnarraydefcol{x}{}{} 1980 \IEEEeqnarraydefcol{X}{$}{$} 1981 1982 % the default column type to use in the event a column type is not defined 1983 \IEEEeqnarraydefcol{@IEEEdefault}{\hfil$\IEEEeqnarraymathstyle}{$\hfil} 1984 1985 1986 % a zero tabskip (used for "-" col types) 1987 \def\@IEEEeqnarraycolSEPzero{0pt plus 0pt minus 0pt} 1988 % a centering tabskip (used for "+" col types) 1989 \def\@IEEEeqnarraycolSEPcenter{1000pt plus 0pt minus 1000pt} 1990 1991 % top level default tabskip glues for the start, end, and inter-column 1992 % may be reset within environments not always at the top level, e.g., \IEEEeqnarraybox 1993 \edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPcenter}% default start glue 1994 \edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPcenter}% default end glue 1995 \edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue 1996 1997 1998 1999 % creates a vertical rule that extends from the bottom to the top a a cell 2000 % Provided in case other packages redefine \vline some other way. 2001 % usage: \IEEEeqnarrayvrule[rule thickness] 2002 % If no argument is provided, \arrayrulewidth will be used for the rule thickness. 2003 \newcommand\IEEEeqnarrayvrule[1][\arrayrulewidth]{\vrule\@width#1\relax} 2004 2005 % creates a blank separator row 2006 % usage: \IEEEeqnarrayseprow[separation length][font size commands] 2007 % default is \IEEEeqnarrayseprow[0.25\normalbaselineskip][\relax] 2008 % blank arguments inherit the default values 2009 % uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers 2010 \def\IEEEeqnarrayseprow{\relax\@ifnextchar[{\@IEEEeqnarrayseprow}{\@IEEEeqnarrayseprow[0.25\normalbaselineskip]}} 2011 \def\@IEEEeqnarrayseprow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprow[#1]}{\@@IEEEeqnarrayseprow[#1][\relax]}} 2012 \def\@@IEEEeqnarrayseprow[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}% 2013 \ifx\@IEEEeqnarrayseprowARGONE\@empty% 2014 % get the skip value, based on the font commands 2015 % use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3 2016 % assign within a bogus box to confine the font changes 2017 {\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}% 2018 \else% 2019 {\setbox0=\hbox{#2\relax\global\skip5=#1}}% 2020 \fi% 2021 \@IEEEeqnarrayhoptolastcolumn\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax} 2022 2023 % creates a blank separator row, but omits all the column templates 2024 % usage: \IEEEeqnarrayseprowcut[separation length][font size commands] 2025 % default is \IEEEeqnarrayseprowcut[0.25\normalbaselineskip][\relax] 2026 % blank arguments inherit the default values 2027 % uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers 2028 \def\IEEEeqnarrayseprowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols 2029 % advance column counter only if the IEEEeqnarray environment wants it 2030 \if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% 2031 \@ifnextchar[{\@IEEEeqnarrayseprowcut}{\@IEEEeqnarrayseprowcut[0.25\normalbaselineskip]}} 2032 \def\@IEEEeqnarrayseprowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprowcut[#1]}{\@@IEEEeqnarrayseprowcut[#1][\relax]}} 2033 \def\@@IEEEeqnarrayseprowcut[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}% 2034 \ifx\@IEEEeqnarrayseprowARGONE\@empty% 2035 % get the skip value, based on the font commands 2036 % use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3 2037 % assign within a bogus box to confine the font changes 2038 {\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}% 2039 \else% 2040 {\setbox0=\hbox{#2\relax\global\skip5=#1}}% 2041 \fi% 2042 \IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax} 2043 2044 2045 2046 % draws a single rule across all the columns optional 2047 % argument determines the rule width, \arrayrulewidth is the default 2048 % updates column counter as needed and turns off struts 2049 % usage: \IEEEeqnarrayrulerow[rule line thickness] 2050 \def\IEEEeqnarrayrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols 2051 % advance column counter only if the IEEEeqnarray environment wants it 2052 \if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% 2053 \@ifnextchar[{\@IEEEeqnarrayrulerow}{\@IEEEeqnarrayrulerow[\arrayrulewidth]}} 2054 \def\@IEEEeqnarrayrulerow[#1]{\leaders\hrule height#1\hfil\relax% put in our rule 2055 % turn off any struts 2056 \IEEEeqnarraystrutsize{0pt}{0pt}[\relax]\relax} 2057 2058 2059 % draws a double rule by using a single rule row, a separator row, and then 2060 % another single rule row 2061 % first optional argument determines the rule thicknesses, \arrayrulewidth is the default 2062 % second optional argument determines the rule spacing, \doublerulesep is the default 2063 % usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing] 2064 \def\IEEEeqnarraydblrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols 2065 % advance column counter only if the IEEEeqnarray environment wants it 2066 \if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% 2067 \@ifnextchar[{\@IEEEeqnarraydblrulerow}{\@IEEEeqnarraydblrulerow[\arrayrulewidth]}} 2068 \def\@IEEEeqnarraydblrulerow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerow[#1]}% 2069 {\@@IEEEeqnarraydblrulerow[#1][\doublerulesep]}} 2070 \def\@@IEEEeqnarraydblrulerow[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}% 2071 % we allow the user to say \IEEEeqnarraydblrulerow[][] 2072 \ifx\@IEEEeqnarraydblrulerowARG\@empty% 2073 \@IEEEeqnarrayrulerow[\arrayrulewidth]% 2074 \else% 2075 \@IEEEeqnarrayrulerow[#1]\relax% 2076 \fi% 2077 \def\@IEEEeqnarraydblrulerowARG{#2}% 2078 \ifx\@IEEEeqnarraydblrulerowARG\@empty% 2079 \\\IEEEeqnarrayseprow[\doublerulesep][\relax]% 2080 \else% 2081 \\\IEEEeqnarrayseprow[#2][\relax]% 2082 \fi% 2083 \\\multispan{\@IEEEeqnnumcols}% 2084 % advance column counter only if the IEEEeqnarray environment wants it 2085 \if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% 2086 \def\@IEEEeqnarraydblrulerowARG{#1}% 2087 \ifx\@IEEEeqnarraydblrulerowARG\@empty% 2088 \@IEEEeqnarrayrulerow[\arrayrulewidth]% 2089 \else% 2090 \@IEEEeqnarrayrulerow[#1]% 2091 \fi% 2092 } 2093 2094 % draws a double rule by using a single rule row, a separator (cutting) row, and then 2095 % another single rule row 2096 % first optional argument determines the rule thicknesses, \arrayrulewidth is the default 2097 % second optional argument determines the rule spacing, \doublerulesep is the default 2098 % usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing] 2099 \def\IEEEeqnarraydblrulerowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols 2100 % advance column counter only if the IEEEeqnarray environment wants it 2101 \if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% 2102 \@ifnextchar[{\@IEEEeqnarraydblrulerowcut}{\@IEEEeqnarraydblrulerowcut[\arrayrulewidth]}} 2103 \def\@IEEEeqnarraydblrulerowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerowcut[#1]}% 2104 {\@@IEEEeqnarraydblrulerowcut[#1][\doublerulesep]}} 2105 \def\@@IEEEeqnarraydblrulerowcut[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}% 2106 % we allow the user to say \IEEEeqnarraydblrulerow[][] 2107 \ifx\@IEEEeqnarraydblrulerowARG\@empty% 2108 \@IEEEeqnarrayrulerow[\arrayrulewidth]% 2109 \else% 2110 \@IEEEeqnarrayrulerow[#1]% 2111 \fi% 2112 \def\@IEEEeqnarraydblrulerowARG{#2}% 2113 \ifx\@IEEEeqnarraydblrulerowARG\@empty% 2114 \\\IEEEeqnarrayseprowcut[\doublerulesep][\relax]% 2115 \else% 2116 \\\IEEEeqnarrayseprowcut[#2][\relax]% 2117 \fi% 2118 \\\multispan{\@IEEEeqnnumcols}% 2119 % advance column counter only if the IEEEeqnarray environment wants it 2120 \if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi% 2121 \def\@IEEEeqnarraydblrulerowARG{#1}% 2122 \ifx\@IEEEeqnarraydblrulerowARG\@empty% 2123 \@IEEEeqnarrayrulerow[\arrayrulewidth]% 2124 \else% 2125 \@IEEEeqnarrayrulerow[#1]% 2126 \fi% 2127 } 2128 2129 2130 2131 % inserts a full row‘s worth of &‘s 2132 % relies on \@IEEEeqnnumcols to provide the correct number of columns 2133 % uses \@IEEEtrantmptoksA, \count0 as scratch registers 2134 \def\@IEEEeqnarrayhoptolastcolumn{\@IEEEtrantmptoksA={}\count0=1\relax% 2135 \loop% add cols if the user did not use them all 2136 \ifnum\count0<\@IEEEeqnnumcols\relax% 2137 \@IEEEappendtoksA{&}% 2138 \advance\count0 by 1\relax% update the col count 2139 \repeat% 2140 \the\@IEEEtrantmptoksA%execute the &‘s 2141 } 2142 2143 2144 2145 \newif\if@IEEEeqnarrayISinner % flag to indicate if we are within the lines 2146 \@IEEEeqnarrayISinnerfalse % of an IEEEeqnarray - after the IEEEeqnarraydecl 2147 2148 \edef\@IEEEeqnarrayTHEstrutheight{0pt} % height and depth of IEEEeqnarray struts 2149 \edef\@IEEEeqnarrayTHEstrutdepth{0pt} 2150 2151 \edef\@IEEEeqnarrayTHEmasterstrutheight{0pt} % default height and depth of 2152 \edef\@IEEEeqnarrayTHEmasterstrutdepth{0pt} % struts within an IEEEeqnarray 2153 2154 \edef\@IEEEeqnarrayTHEmasterstrutHSAVE{0pt} % saved master strut height 2155 \edef\@IEEEeqnarrayTHEmasterstrutDSAVE{0pt} % and depth 2156 2157 \newif\if@IEEEeqnarrayusemasterstrut % flag to indicate that the master strut value 2158 \@IEEEeqnarrayusemasterstruttrue % is to be used 2159 2160 2161 2162 % saves the strut height and depth of the master strut 2163 \def\@IEEEeqnarraymasterstrutsave{\relax% 2164 \expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax% 2165 \expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax% 2166 % remove stretchability 2167 \dimen0\skip0\relax% 2168 \dimen2\skip2\relax% 2169 % save values 2170 \edef\@IEEEeqnarrayTHEmasterstrutHSAVE{\the\dimen0}% 2171 \edef\@IEEEeqnarrayTHEmasterstrutDSAVE{\the\dimen2}} 2172 2173 % restores the strut height and depth of the master strut 2174 \def\@IEEEeqnarraymasterstrutrestore{\relax% 2175 \expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutHSAVE\relax% 2176 \expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutDSAVE\relax% 2177 % remove stretchability 2178 \dimen0\skip0\relax% 2179 \dimen2\skip2\relax% 2180 % restore values 2181 \edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}% 2182 \edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}} 2183 2184 2185 % globally restores the strut height and depth to the 2186 % master values and sets the master strut flag to true 2187 \def\@IEEEeqnarraystrutreset{\relax% 2188 \expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax% 2189 \expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax% 2190 % remove stretchability 2191 \dimen0\skip0\relax% 2192 \dimen2\skip2\relax% 2193 % restore values 2194 \xdef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% 2195 \xdef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% 2196 \global\@IEEEeqnarrayusemasterstruttrue} 2197 2198 2199 % if the master strut is not to be used, make the current 2200 % values of \@IEEEeqnarrayTHEstrutheight, \@IEEEeqnarrayTHEstrutdepth 2201 % and the use master strut flag, global 2202 % this allows user strut commands issued in the last column to be carried 2203 % into the isolation/strut column 2204 \def\@IEEEeqnarrayglobalizestrutstatus{\relax% 2205 \if@IEEEeqnarrayusemasterstrut\else% 2206 \xdef\@IEEEeqnarrayTHEstrutheight{\@IEEEeqnarrayTHEstrutheight}% 2207 \xdef\@IEEEeqnarrayTHEstrutdepth{\@IEEEeqnarrayTHEstrutdepth}% 2208 \global\@IEEEeqnarrayusemasterstrutfalse% 2209 \fi} 2210 2211 2212 2213 % usage: \IEEEeqnarraystrutsize{height}{depth}[font size commands] 2214 % If called outside the lines of an IEEEeqnarray, sets the height 2215 % and depth of both the master and local struts. If called inside 2216 % an IEEEeqnarray line, sets the height and depth of the local strut 2217 % only and sets the flag to indicate the use of the local strut 2218 % values. If the height or depth is left blank, 0.7\normalbaselineskip 2219 % and 0.3\normalbaselineskip will be used, respectively. 2220 % The optional argument can be used to evaluate the lengths under 2221 % a different font size and styles. If none is specified, the current 2222 % font is used. 2223 % uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2 2224 \def\IEEEeqnarraystrutsize#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsize{#1}{#2}}{\@IEEEeqnarraystrutsize{#1}{#2}[\relax]}} 2225 \def\@IEEEeqnarraystrutsize#1#2[#3]{\def\@IEEEeqnarraystrutsizeARG{#1}% 2226 \ifx\@IEEEeqnarraystrutsizeARG\@empty% 2227 {\setbox0=\hbox{#3\relax\global\skip3=0.7\normalbaselineskip}}% 2228 \skip0=\skip3\relax% 2229 \else% arg one present 2230 {\setbox0=\hbox{#3\relax\global\skip3=#1\relax}}% 2231 \skip0=\skip3\relax% 2232 \fi% if null arg 2233 \def\@IEEEeqnarraystrutsizeARG{#2}% 2234 \ifx\@IEEEeqnarraystrutsizeARG\@empty% 2235 {\setbox0=\hbox{#3\relax\global\skip3=0.3\normalbaselineskip}}% 2236 \skip2=\skip3\relax% 2237 \else% arg two present 2238 {\setbox0=\hbox{#3\relax\global\skip3=#2\relax}}% 2239 \skip2=\skip3\relax% 2240 \fi% if null arg 2241 % remove stretchability, just to be safe 2242 \dimen0\skip0\relax% 2243 \dimen2\skip2\relax% 2244 % dimen0 = height, dimen2 = depth 2245 \if@IEEEeqnarrayISinner% inner does not touch master strut size 2246 \edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% 2247 \edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% 2248 \@IEEEeqnarrayusemasterstrutfalse% do not use master 2249 \else% outer, have to set master strut too 2250 \edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}% 2251 \edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}% 2252 \edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% 2253 \edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% 2254 \@IEEEeqnarrayusemasterstruttrue% use master strut 2255 \fi} 2256 2257 2258 % usage: \IEEEeqnarraystrutsizeadd{added height}{added depth}[font size commands] 2259 % If called outside the lines of an IEEEeqnarray, adds the given height 2260 % and depth to both the master and local struts. 2261 % If called inside an IEEEeqnarray line, adds the given height and depth 2262 % to the local strut only and sets the flag to indicate the use 2263 % of the local strut values. 2264 % In both cases, if a height or depth is left blank, 0pt is used instead. 2265 % The optional argument can be used to evaluate the lengths under 2266 % a different font size and styles. If none is specified, the current 2267 % font is used. 2268 % uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2 2269 \def\IEEEeqnarraystrutsizeadd#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsizeadd{#1}{#2}}{\@IEEEeqnarraystrutsizeadd{#1}{#2}[\relax]}} 2270 \def\@IEEEeqnarraystrutsizeadd#1#2[#3]{\def\@IEEEeqnarraystrutsizearg{#1}% 2271 \ifx\@IEEEeqnarraystrutsizearg\@empty% 2272 \skip0=0pt\relax% 2273 \else% arg one present 2274 {\setbox0=\hbox{#3\relax\global\skip3=#1}}% 2275 \skip0=\skip3\relax% 2276 \fi% if null arg 2277 \def\@IEEEeqnarraystrutsizearg{#2}% 2278 \ifx\@IEEEeqnarraystrutsizearg\@empty% 2279 \skip2=0pt\relax% 2280 \else% arg two present 2281 {\setbox0=\hbox{#3\relax\global\skip3=#2}}% 2282 \skip2=\skip3\relax% 2283 \fi% if null arg 2284 % remove stretchability, just to be safe 2285 \dimen0\skip0\relax% 2286 \dimen2\skip2\relax% 2287 % dimen0 = height, dimen2 = depth 2288 \if@IEEEeqnarrayISinner% inner does not touch master strut size 2289 % get local strut size 2290 \expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax% 2291 \expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax% 2292 % add it to the user supplied values 2293 \advance\dimen0 by \skip0\relax% 2294 \advance\dimen2 by \skip2\relax% 2295 % update the local strut size 2296 \edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% 2297 \edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% 2298 \@IEEEeqnarrayusemasterstrutfalse% do not use master 2299 \else% outer, have to set master strut too 2300 % get master strut size 2301 \expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax% 2302 \expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax% 2303 % add it to the user supplied values 2304 \advance\dimen0 by \skip0\relax% 2305 \advance\dimen2 by \skip2\relax% 2306 % update the local and master strut sizes 2307 \edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}% 2308 \edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}% 2309 \edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}% 2310 \edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}% 2311 \@IEEEeqnarrayusemasterstruttrue% use master strut 2312 \fi} 2313 2314 2315 % allow user a way to see the struts 2316 \newif\ifIEEEvisiblestruts 2317 \IEEEvisiblestrutsfalse 2318 2319 % inserts an invisible strut using the master or local strut values 2320 % uses scratch registers \skip0, \skip2, \dimen0, \dimen2 2321 \def\@IEEEeqnarrayinsertstrut{\relax% 2322 \if@IEEEeqnarrayusemasterstrut 2323 % get master strut size 2324 \expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax% 2325 \expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax% 2326 \else% 2327 % get local strut size 2328 \expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax% 2329 \expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax% 2330 \fi% 2331 % remove stretchability, probably not needed 2332 \dimen0\skip0\relax% 2333 \dimen2\skip2\relax% 2334 % dimen0 = height, dimen2 = depth 2335 % allow user to see struts if desired 2336 \ifIEEEvisiblestruts% 2337 \vrule width0.2pt height\dimen0 depth\dimen2\relax% 2338 \else% 2339 \vrule width0pt height\dimen0 depth\dimen2\relax\fi} 2340 2341 2342 % creates an invisible strut, useable even outside \IEEEeqnarray 2343 % if \IEEEvisiblestrutstrue, the strut will be visible and 0.2pt wide. 2344 % usage: \IEEEstrut[height][depth][font size commands] 2345 % default is \IEEEstrut[0.7\normalbaselineskip][0.3\normalbaselineskip][\relax] 2346 % blank arguments inherit the default values 2347 % uses \dimen0, \dimen2, \skip0, \skip2 2348 \def\IEEEstrut{\relax\@ifnextchar[{\@IEEEstrut}{\@IEEEstrut[0.7\normalbaselineskip]}} 2349 \def\@IEEEstrut[#1]{\relax\@ifnextchar[{\@@IEEEstrut[#1]}{\@@IEEEstrut[#1][0.3\normalbaselineskip]}} 2350 \def\@@IEEEstrut[#1][#2]{\relax\@ifnextchar[{\@@@IEEEstrut[#1][#2]}{\@@@IEEEstrut[#1][#2][\relax]}} 2351 \def\@@@IEEEstrut[#1][#2][#3]{\mbox{#3\relax% 2352 \def\@IEEEstrutARG{#1}% 2353 \ifx\@IEEEstrutARG\@empty% 2354 \skip0=0.7\normalbaselineskip\relax% 2355 \else% 2356 \skip0=#1\relax% 2357 \fi% 2358 \def\@IEEEstrutARG{#2}% 2359 \ifx\@IEEEstrutARG\@empty% 2360 \skip2=0.3\normalbaselineskip\relax% 2361 \else% 2362 \skip2=#2\relax% 2363 \fi% 2364 % remove stretchability, probably not needed 2365 \dimen0\skip0\relax% 2366 \dimen2\skip2\relax% 2367 \ifIEEEvisiblestruts% 2368 \vrule width0.2pt height\dimen0 depth\dimen2\relax% 2369 \else% 2370 \vrule width0.0pt height\dimen0 depth\dimen2\relax\fi}} 2371 2372 2373 % enables strut mode by setting a default strut size and then zeroing the 2374 % \baselineskip, \lineskip, \lineskiplimit and \jot 2375 \def\IEEEeqnarraystrutmode{\IEEEeqnarraystrutsize{0.7\normalbaselineskip}{0.3\normalbaselineskip}[\relax]% 2376 \baselineskip=0pt\lineskip=0pt\lineskiplimit=0pt\jot=0pt} 2377 2378 2379 2380 \def\IEEEeqnarray{\@IEEEeqnarraystarformfalse\@IEEEeqnarray} 2381 \def\endIEEEeqnarray{\end@IEEEeqnarray} 2382 2383 \@namedef{IEEEeqnarray*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarray} 2384 \@namedef{endIEEEeqnarray*}{\end@IEEEeqnarray} 2385 2386 2387 % \IEEEeqnarray is an enhanced \eqnarray. 2388 % The star form defaults to not putting equation numbers at the end of each row. 2389 % usage: \IEEEeqnarray[decl]{cols} 2390 \def\@IEEEeqnarray{\relax\@ifnextchar[{\@@IEEEeqnarray}{\@@IEEEeqnarray[\relax]}} 2391 \def\@@IEEEeqnarray[#1]#2{% 2392 % default to showing the equation number or not based on whether or not 2393 % the star form was involked 2394 \if@IEEEeqnarraystarform\global\@eqnswfalse 2395 \else% not the star form 2396 \global\@eqnswtrue 2397 \fi% if star form 2398 \@IEEEissubequationfalse% default to no subequations 2399 \@IEEElastlinewassubequationfalse% assume last line is not a sub equation 2400 \@IEEEeqnarrayISinnerfalse% not yet within the lines of the halign 2401 \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default 2402 \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise 2403 \IEEEvisiblestrutsfalse% diagnostic mode defaults to off 2404 % no extra space unless the user specifically requests it 2405 \lineskip=0pt\relax 2406 \lineskiplimit=0pt\relax 2407 \baselineskip=\normalbaselineskip\relax% 2408 \jot=\IEEEnormaljot\relax% 2409 \mathsurround\z@\relax% no extra spacing around math 2410 \@advanceIEEEeqncolcnttrue% advance the col counter for each col the user uses, 2411 % used in \IEEEeqnarraymulticol and in the preamble build 2412 \stepcounter{equation}% advance equation counter before first line 2413 \setcounter{IEEEsubequation}{0}% no subequation yet 2414 \def\@currentlabel{\p@equation\theequation}% redefine the ref label 2415 \IEEEeqnarraydecl\relax% allow a way for the user to make global overrides 2416 #1\relax% allow user to override defaults 2417 \let\\\@IEEEeqnarraycr% replace newline with one that can put in eqn. numbers 2418 \global\@IEEEeqncolcnt\z@% col. count = 0 for first line 2419 \@IEEEbuildpreamble #2\end\relax% build the preamble and put it into \@IEEEtrantmptoksA 2420 % put in the column for the equation number 2421 \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first 2422 \toks0={##}% 2423 % advance the \@IEEEeqncolcnt for the isolation col, this helps with error checking 2424 \@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}% 2425 % add the isolation column 2426 \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}% 2427 % advance the \@IEEEeqncolcnt for the equation number col, this helps with error checking 2428 \@IEEEappendtoksA{&\global\advance\@IEEEeqncolcnt by 1\relax}% 2429 % add the equation number col to the preamble 2430 \@IEEEappendtoksA{\tabskip\z@skip\hb@xt@\z@\bgroup\hss\the\toks0\egroup}% 2431 % note \@IEEEeqnnumcols does not count the equation col or isolation col 2432 % set the starting tabskip glue as determined by the preamble build 2433 \tabskip=\@IEEEBPstartglue\relax 2434 % begin the display alignment 2435 \@IEEEeqnarrayISinnertrue% commands are now within the lines 2436 $$\everycr{}\halign to\displaywidth\bgroup 2437 % "exspand" the preamble 2438 \span\the\@IEEEtrantmptoksA\cr} 2439 2440 % enter isolation/strut column (or the next column if the user did not use 2441 % every column), record the strut status, complete the columns, do the strut if needed, 2442 % restore counters to correct values and exit 2443 \def\end@IEEEeqnarray{\@IEEEeqnarrayglobalizestrutstatus&\@@IEEEeqnarraycr\egroup% 2444 \if@IEEElastlinewassubequation\global\advance\c@IEEEsubequation\m@ne\fi% 2445 \global\advance\c@equation\m@ne% 2446 $$\@ignoretrue} 2447 2448 % need a way to remember if last line is a subequation 2449 \newif\if@IEEElastlinewassubequation% 2450 \@IEEElastlinewassubequationfalse 2451 2452 % IEEEeqnarray uses a modifed \\ instead of the plain \cr to 2453 % end rows. This allows for things like \\*[vskip amount] 2454 % This "cr" macros are modified versions those for LaTeX2e‘s eqnarray 2455 % the {\ifnum0=`} braces must be kept away from the last column to avoid 2456 % altering spacing of its math, so we use & to advance to the next column 2457 % as there is an isolation/strut column after the user‘s columns 2458 \def\@IEEEeqnarraycr{\@IEEEeqnarrayglobalizestrutstatus&% save strut status and advance to next column 2459 {\ifnum0=`}\fi 2460 \@ifstar{% 2461 \global\@eqpen\@M\@IEEEeqnarrayYCR 2462 }{% 2463 \global\@eqpen\interdisplaylinepenalty \@IEEEeqnarrayYCR 2464 }% 2465 } 2466 2467 \def\@IEEEeqnarrayYCR{\@testopt\@IEEEeqnarrayXCR\z@skip} 2468 2469 \def\@IEEEeqnarrayXCR[#1]{% 2470 \ifnum0=`{\fi}% 2471 \@@IEEEeqnarraycr 2472 \noalign{\penalty\@eqpen\vskip\jot\vskip #1\relax}}% 2473 2474 \def\@@IEEEeqnarraycr{\@IEEEtrantmptoksA={}% clear token register 2475 \advance\@IEEEeqncolcnt by -1\relax% adjust col count because of the isolation column 2476 \ifnum\@IEEEeqncolcnt>\@IEEEeqnnumcols\relax 2477 \@IEEEclspkgerror{Too many columns within the IEEEeqnarray\MessageBreak 2478 environment}% 2479 {Use fewer \string &‘s or put more columns in the IEEEeqnarry column\MessageBreak 2480 specifications.}\relax% 2481 \else 2482 \loop% add cols if the user did not use them all 2483 \ifnum\@IEEEeqncolcnt<\@IEEEeqnnumcols\relax 2484 \@IEEEappendtoksA{&}% 2485 \advance\@IEEEeqncolcnt by 1\relax% update the col count 2486 \repeat 2487 % this number of &‘s will take us the the isolation column 2488 \fi 2489 % execute the &‘s 2490 \the\@IEEEtrantmptoksA% 2491 % handle the strut/isolation column 2492 \@IEEEeqnarrayinsertstrut% do the strut if needed 2493 \@IEEEeqnarraystrutreset% reset the strut system for next line or IEEEeqnarray 2494 &% and enter the equation number column 2495 % is this line needs an equation number, display it and advance the 2496 % (sub)equation counters, record what type this line was 2497 \if@eqnsw% 2498 \if@IEEEissubequation\theIEEEsubequationdis\addtocounter{equation}{1}\stepcounter{IEEEsubequation}% 2499 \global\@IEEElastlinewassubequationtrue% 2500 \else% display a standard equation number, initialize the IEEEsubequation counter 2501 \theequationdis\stepcounter{equation}\setcounter{IEEEsubequation}{0}% 2502 \global\@IEEElastlinewassubequationfalse\fi% 2503 \fi% 2504 % reset the eqnsw flag to indicate default preference of the display of equation numbers 2505 \if@IEEEeqnarraystarform\global\@eqnswfalse\else\global\@eqnswtrue\fi 2506 \global\@IEEEissubequationfalse% reset the subequation flag 2507 % reset the number of columns the user actually used 2508 \global\@IEEEeqncolcnt\z@\relax 2509 % the real end of the line 2510 \cr} 2511 2512 2513 2514 2515 2516 % \IEEEeqnarraybox is like \IEEEeqnarray except the box form puts everything 2517 % inside a vtop, vbox, or vcenter box depending on the letter in the second 2518 % optional argument (t,b,c). Vbox is the default. Unlike \IEEEeqnarray, 2519 % equation numbers are not displayed and \IEEEeqnarraybox can be nested. 2520 % \IEEEeqnarrayboxm is for math mode (like \array) and does not put the vbox 2521 % within an hbox. 2522 % \IEEEeqnarrayboxt is for text mode (like \tabular) and puts the vbox within 2523 % a \hbox{$ $} construct. 2524 % \IEEEeqnarraybox will auto detect whether to use \IEEEeqnarrayboxm or 2525 % \IEEEeqnarrayboxt depending on the math mode. 2526 % The third optional argument specifies the width this box is to be set to - 2527 % natural width is the default. 2528 % The * forms do not add \jot line spacing 2529 % usage: \IEEEeqnarraybox[decl][pos][width]{cols} 2530 \def\IEEEeqnarrayboxm{\@IEEEeqnarraystarformfalse\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox} 2531 \def\endIEEEeqnarrayboxm{\end@IEEEeqnarraybox} 2532 \@namedef{IEEEeqnarrayboxm*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox} 2533 \@namedef{endIEEEeqnarrayboxm*}{\end@IEEEeqnarraybox} 2534 2535 \def\IEEEeqnarrayboxt{\@IEEEeqnarraystarformfalse\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox} 2536 \def\endIEEEeqnarrayboxt{\end@IEEEeqnarraybox} 2537 \@namedef{IEEEeqnarrayboxt*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox} 2538 \@namedef{endIEEEeqnarrayboxt*}{\end@IEEEeqnarraybox} 2539 2540 \def\IEEEeqnarraybox{\@IEEEeqnarraystarformfalse\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi% 2541 \@IEEEeqnarraybox} 2542 \def\endIEEEeqnarraybox{\end@IEEEeqnarraybox} 2543 2544 \@namedef{IEEEeqnarraybox*}{\@IEEEeqnarraystarformtrue\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi% 2545 \@IEEEeqnarraybox} 2546 \@namedef{endIEEEeqnarraybox*}{\end@IEEEeqnarraybox} 2547 2548 % flag to indicate if the \IEEEeqnarraybox needs to put things into an hbox{$ $} 2549 % for \vcenter in non-math mode 2550 \newif\if@IEEEeqnarrayboxHBOXSW% 2551 \@IEEEeqnarrayboxHBOXSWfalse 2552 2553 \def\@IEEEeqnarraybox{\relax\@ifnextchar[{\@@IEEEeqnarraybox}{\@@IEEEeqnarraybox[\relax]}} 2554 \def\@@IEEEeqnarraybox[#1]{\relax\@ifnextchar[{\@@@IEEEeqnarraybox[#1]}{\@@@IEEEeqnarraybox[#1][b]}} 2555 \def\@@@IEEEeqnarraybox[#1][#2]{\relax\@ifnextchar[{\@@@@IEEEeqnarraybox[#1][#2]}{\@@@@IEEEeqnarraybox[#1][#2][\relax]}} 2556 2557 % #1 = decl; #2 = t,b,c; #3 = width, #4 = col specs 2558 \def\@@@@IEEEeqnarraybox[#1][#2][#3]#4{\@IEEEeqnarrayISinnerfalse % not yet within the lines of the halign 2559 \@IEEEeqnarraymasterstrutsave% save current master strut values 2560 \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default 2561 \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise 2562 \IEEEvisiblestrutsfalse% diagnostic mode defaults to off 2563 % no extra space unless the user specifically requests it 2564 \lineskip=0pt\relax% 2565 \lineskiplimit=0pt\relax% 2566 \baselineskip=\normalbaselineskip\relax% 2567 \jot=\IEEEnormaljot\relax% 2568 \mathsurround\z@\relax% no extra spacing around math 2569 % the default end glues are zero for an \IEEEeqnarraybox 2570 \edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPzero}% default start glue 2571 \edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPzero}% default end glue 2572 \edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue 2573 \@advanceIEEEeqncolcntfalse% do not advance the col counter for each col the user uses, 2574 % used in \IEEEeqnarraymulticol and in the preamble build 2575 \IEEEeqnarrayboxdecl\relax% allow a way for the user to make global overrides 2576 #1\relax% allow user to override defaults 2577 \let\\\@IEEEeqnarrayboxcr% replace newline with one that allows optional spacing 2578 \@IEEEbuildpreamble #4\end\relax% build the preamble and put it into \@IEEEtrantmptoksA 2579 % add an isolation column to the preamble to stop \\‘s {} from getting into the last col 2580 \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first 2581 \toks0={##}% 2582 % add the isolation column to the preamble 2583 \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}% 2584 % set the starting tabskip glue as determined by the preamble build 2585 \tabskip=\@IEEEBPstartglue\relax 2586 % begin the alignment 2587 \everycr{}% 2588 % use only the very first token to determine the positioning 2589 % this stops some problems when the user uses more than one letter, 2590 % but is probably not worth the effort 2591 % \noindent is used as a delimiter 2592 \def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}% 2593 \@IEEEgrabfirstoken#2\relax\relax\noindent 2594 % \@IEEEgrabbedfirstoken has the first token, the rest are discarded 2595 % if we need to put things into and hbox and go into math mode, do so now 2596 \if@IEEEeqnarrayboxHBOXSW \leavevmode \hbox \bgroup $\fi% 2597 % use the appropriate vbox type 2598 \if\@IEEEgrabbedfirstoken t\relax\vtop\else\if\@IEEEgrabbedfirstoken c\relax% 2599 \vcenter\else\vbox\fi\fi\bgroup% 2600 \@IEEEeqnarrayISinnertrue% commands are now within the lines 2601 \ifx#3\relax\halign\else\halign to #3\relax\fi% 2602 \bgroup 2603 % "exspand" the preamble 2604 \span\the\@IEEEtrantmptoksA\cr} 2605 2606 % carry strut status and enter the isolation/strut column, 2607 % exit from math mode if needed, and exit 2608 \def\end@IEEEeqnarraybox{\@IEEEeqnarrayglobalizestrutstatus% carry strut status 2609 &% enter isolation/strut column 2610 \@IEEEeqnarrayinsertstrut% do strut if needed 2611 \@IEEEeqnarraymasterstrutrestore% restore the previous master strut values 2612 % reset the strut system for next IEEEeqnarray 2613 % (sets local strut values back to previous master strut values) 2614 \@IEEEeqnarraystrutreset% 2615 % ensure last line, exit from halign, close vbox 2616 \crcr\egroup\egroup% 2617 % exit from math mode and close hbox if needed 2618 \if@IEEEeqnarrayboxHBOXSW $\egroup\fi} 2619 2620 2621 2622 % IEEEeqnarraybox uses a modifed \\ instead of the plain \cr to 2623 % end rows. This allows for things like \\[vskip amount] 2624 % This "cr" macros are modified versions those for LaTeX2e‘s eqnarray 2625 % For IEEEeqnarraybox, \\* is the same as \2626 % the {\ifnum0=`} braces must be kept away from the last column to avoid 2627 % altering spacing of its math, so we use & to advance to the isolation/strut column 2628 % carry strut status into isolation/strut column 2629 \def\@IEEEeqnarrayboxcr{\@IEEEeqnarrayglobalizestrutstatus% carry strut status 2630 &% enter isolation/strut column 2631 \@IEEEeqnarrayinsertstrut% do strut if needed 2632 % reset the strut system for next line or IEEEeqnarray 2633 \@IEEEeqnarraystrutreset% 2634 {\ifnum0=`}\fi% 2635 \@ifstar{\@IEEEeqnarrayboxYCR}{\@IEEEeqnarrayboxYCR}} 2636 2637 % test and setup the optional argument to \\[] 2638 \def\@IEEEeqnarrayboxYCR{\@testopt\@IEEEeqnarrayboxXCR\z@skip} 2639 2640 % IEEEeqnarraybox does not automatically increase line spacing by \jot 2641 \def\@IEEEeqnarrayboxXCR[#1]{\ifnum0=`{\fi}% 2642 \cr\noalign{\if@IEEEeqnarraystarform\else\vskip\jot\fi\vskip#1\relax}} 2643 2644 2645 2646 % starts the halign preamble build 2647 \def\@IEEEbuildpreamble{\@IEEEtrantmptoksA={}% clear token register 2648 \let\@IEEEBPcurtype=u%current column type is not yet known 2649 \let\@IEEEBPprevtype=s%the previous column type was the start 2650 \let\@IEEEBPnexttype=u%next column type is not yet known 2651 % ensure these are valid 2652 \def\@IEEEBPcurglue={0pt plus 0pt minus 0pt}% 2653 \def\@IEEEBPcurcolname{@IEEEdefault}% name of current column definition 2654 % currently acquired numerically referenced glue 2655 % use a name that is easier to remember 2656 \let\@IEEEBPcurnum=\@IEEEtrantmpcountA% 2657 \@IEEEBPcurnum=0% 2658 % tracks number of columns in the preamble 2659 \@IEEEeqnnumcols=0% 2660 % record the default end glues 2661 \edef\@IEEEBPstartglue{\@IEEEeqnarraycolSEPdefaultstart}% 2662 \edef\@IEEEBPendglue{\@IEEEeqnarraycolSEPdefaultend}% 2663 % now parse the user‘s column specifications 2664 \@@IEEEbuildpreamble} 2665 2666 2667 % parses and builds the halign preamble 2668 \def\@@IEEEbuildpreamble#1#2{\let\@@nextIEEEbuildpreamble=\@@IEEEbuildpreamble% 2669 % use only the very first token to check the end 2670 % \noindent is used as a delimiter as \end can be present here 2671 \def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}% 2672 \@IEEEgrabfirstoken#1\relax\relax\noindent 2673 \ifx\@IEEEgrabbedfirstoken\end\let\@@nextIEEEbuildpreamble=\@@IEEEfinishpreamble\else% 2674 % identify current and next token type 2675 \@IEEEgetcoltype{#1}{\@IEEEBPcurtype}{1}% current, error on invalid 2676 \@IEEEgetcoltype{#2}{\@IEEEBPnexttype}{0}% next, no error on invalid next 2677 % if curtype is a glue, get the glue def 2678 \if\@IEEEBPcurtype g\@IEEEgetcurglue{#1}{\@IEEEBPcurglue}\fi% 2679 % if curtype is a column, get the column def and set the current column name 2680 \if\@IEEEBPcurtype c\@IEEEgetcurcol{#1}\fi% 2681 % if curtype is a numeral, acquire the user defined glue 2682 \if\@IEEEBPcurtype n\@IEEEprocessNcol{#1}\fi% 2683 % process the acquired glue 2684 \if\@IEEEBPcurtype g\@IEEEprocessGcol\fi% 2685 % process the acquired col 2686 \if\@IEEEBPcurtype c\@IEEEprocessCcol\fi% 2687 % ready prevtype for next col spec. 2688 \let\@IEEEBPprevtype=\@IEEEBPcurtype% 2689 % be sure and put back the future token(s) as a group 2690 \fi\@@nextIEEEbuildpreamble{#2}} 2691 2692 2693 % executed just after preamble build is completed 2694 % warn about zero cols, and if prevtype type = u, put in end tabskip glue 2695 \def\@@IEEEfinishpreamble#1{\ifnum\@IEEEeqnnumcols<1\relax 2696 \@IEEEclspkgerror{No column specifiers declared for IEEEeqnarray}% 2697 {At least one column type must be declared for each IEEEeqnarray.}% 2698 \fi%num cols less than 1 2699 %if last type undefined, set default end tabskip glue 2700 \if\@IEEEBPprevtype u\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue}\fi} 2701 2702 2703 % Identify and return the column specifier‘s type code 2704 \def\@IEEEgetcoltype#1#2#3{% 2705 % use only the very first token to determine the type 2706 % \noindent is used as a delimiter as \end can be present here 2707 \def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}% 2708 \@IEEEgrabfirstoken#1\relax\relax\noindent 2709 % \@IEEEgrabfirstoken has the first token, the rest are discarded 2710 % n = number 2711 % g = glue (any other char in catagory 12) 2712 % c = letter 2713 % e = \end 2714 % u = undefined 2715 % third argument: 0 = no error message, 1 = error on invalid char 2716 \let#2=u\relax% assume invalid until know otherwise 2717 \ifx\@IEEEgrabbedfirstoken\end\let#2=e\else 2718 \ifcat\@IEEEgrabbedfirstoken\relax\else% screen out control sequences 2719 \if0\@IEEEgrabbedfirstoken\let#2=n\else 2720 \if1\@IEEEgrabbedfirstoken\let#2=n\else 2721 \if2\@IEEEgrabbedfirstoken\let#2=n\else 2722 \if3\@IEEEgrabbedfirstoken\let#2=n\else 2723 \if4\@IEEEgrabbedfirstoken\let#2=n\else 2724 \if5\@IEEEgrabbedfirstoken\let#2=n\else 2725 \if6\@IEEEgrabbedfirstoken\let#2=n\else 2726 \if7\@IEEEgrabbedfirstoken\let#2=n\else 2727 \if8\@IEEEgrabbedfirstoken\let#2=n\else 2728 \if9\@IEEEgrabbedfirstoken\let#2=n\else 2729 \ifcat,\@IEEEgrabbedfirstoken\let#2=g\relax 2730 \else\ifcat a\@IEEEgrabbedfirstoken\let#2=c\relax\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi 2731 \if#2u\relax 2732 \if0\noexpand#3\relax\else\@IEEEclspkgerror{Invalid character in column specifications}% 2733 {Only letters, numerals and certain other symbols are allowed \MessageBreak 2734 as IEEEeqnarray column specifiers.}\fi\fi} 2735 2736 2737 % identify the current letter referenced column 2738 % if invalid, use a default column 2739 \def\@IEEEgetcurcol#1{\expandafter\ifx\csname @IEEEeqnarraycolDEF#1\endcsname\@IEEEeqnarraycolisdefined% 2740 \def\@IEEEBPcurcolname{#1}\else% invalid column name 2741 \@IEEEclspkgerror{Invalid column type "#1" in column specifications.\MessageBreak 2742 Using a default centering column instead}% 2743 {You must define IEEEeqnarray column types before use.}% 2744 \def\@IEEEBPcurcolname{@IEEEdefault}\fi} 2745 2746 2747 % identify and return the predefined (punctuation) glue value 2748 \def\@IEEEgetcurglue#1#2{% 2749 % ! = \! (neg small) -0.16667em (-3/18 em) 2750 % , = \, (small) 0.16667em ( 3/18 em) 2751 % : = \: (med) 0.22222em ( 4/18 em) 2752 % ; = \; (large) 0.27778em ( 5/18 em) 2753 % ‘ = \quad 1em 2754 % " = \qquad 2em 2755 % . = 0.5\arraycolsep 2756 % / = \arraycolsep 2757 % ? = 2\arraycolsep 2758 % * = 1fil 2759 % + = \@IEEEeqnarraycolSEPcenter 2760 % - = \@IEEEeqnarraycolSEPzero 2761 % Note that all em values are referenced to the math font (textfont2) fontdimen6 2762 % value for 1em. 2763 % 2764 % use only the very first token to determine the type 2765 % this prevents errant tokens from getting in the main text 2766 % \noindent is used as a delimiter here 2767 \def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}% 2768 \@IEEEgrabfirstoken#1\relax\relax\noindent 2769 % get the math font 1em value 2770 % LaTeX2e‘s NFSS2 does not preload the fonts, but \IEEEeqnarray needs 2771 % to gain access to the math (\textfont2) font‘s spacing parameters. 2772 % So we create a bogus box here that uses the math font to ensure 2773 % that \textfont2 is loaded and ready. If this is not done, 2774 % the \textfont2 stuff here may not work. 2775 % Thanks to Bernd Raichle for his 1997 post on this topic. 2776 {\setbox0=\hbox{$\displaystyle\relax$}}% 2777 % fontdimen6 has the width of 1em (a quad). 2778 \@IEEEtrantmpdimenA=\fontdimen6\textfont2\relax% 2779 % identify the glue value based on the first token 2780 % we discard anything after the first 2781 \if!\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=-0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else 2782 \if,\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else 2783 \if:\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.22222\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else 2784 \if;\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.27778\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else 2785 \if‘\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=1\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else 2786 \if"\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=2\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else 2787 \if.\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.5\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else 2788 \if/\@IEEEgrabbedfirstoken\edef#2{\the\arraycolsep}\else 2789 \if?\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=2\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else 2790 \if *\@IEEEgrabbedfirstoken\edef#2{0pt plus 1fil minus 0pt}\else 2791 \if+\@IEEEgrabbedfirstoken\edef#2{\@IEEEeqnarraycolSEPcenter}\else 2792 \if-\@IEEEgrabbedfirstoken\edef#2{\@IEEEeqnarraycolSEPzero}\else 2793 \edef#2{\@IEEEeqnarraycolSEPzero}% 2794 \@IEEEclspkgerror{Invalid predefined inter-column glue type "#1" in\MessageBreak 2795 column specifications. Using a default value of\MessageBreak 2796 0pt instead}% 2797 {Only !,:;‘"./?*+ and - are valid predefined glue types in the\MessageBreak 2798 IEEEeqnarray column specifications.}\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi} 2799 2800 2801 2802 % process a numerical digit from the column specification 2803 % and look up the corresponding user defined glue value 2804 % can transform current type from n to g or a as the user defined glue is acquired 2805 \def\@IEEEprocessNcol#1{\if\@IEEEBPprevtype g% 2806 \@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak 2807 specifications. Ignoring consecutive glue specifiers\MessageBreak 2808 after the first}% 2809 {You cannot have two or more glue types next to each other\MessageBreak 2810 in the IEEEeqnarray column specifications.}% 2811 \let\@IEEEBPcurtype=a% abort this glue, future digits will be discarded 2812 \@IEEEBPcurnum=0\relax% 2813 \else% if we previously aborted a glue 2814 \if\@IEEEBPprevtype a\@IEEEBPcurnum=0\let\@IEEEBPcurtype=a%maintain digit abortion 2815 \else%acquire this number 2816 % save the previous type before the numerical digits started 2817 \if\@IEEEBPprevtype n\else\let\@IEEEBPprevsavedtype=\@IEEEBPprevtype\fi% 2818 \multiply\@IEEEBPcurnum by 10\relax% 2819 \advance\@IEEEBPcurnum by #1\relax% add in number, \relax is needed to stop TeX‘s number scan 2820 \if\@IEEEBPnexttype n\else%close acquisition 2821 \expandafter\ifx\csname @IEEEeqnarraycolSEPDEF\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname\@IEEEeqnarraycolisdefined% 2822 \edef\@IEEEBPcurglue{\csname @IEEEeqnarraycolSEP\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname}% 2823 \else%user glue not defined 2824 \@IEEEclspkgerror{Invalid user defined inter-column glue type "\number\@IEEEBPcurnum" in\MessageBreak 2825 column specifications. Using a default value of\MessageBreak 2826 0pt instead}% 2827 {You must define all IEEEeqnarray numerical inter-column glue types via\MessageBreak 2828 \string\IEEEeqnarraydefcolsep \space before they are used in column specifications.}% 2829 \edef\@IEEEBPcurglue{\@IEEEeqnarraycolSEPzero}% 2830 \fi% glue defined or not 2831 \let\@IEEEBPcurtype=g% change the type to reflect the acquired glue 2832 \let\@IEEEBPprevtype=\@IEEEBPprevsavedtype% restore the prev type before this number glue 2833 \@IEEEBPcurnum=0\relax%ready for next acquisition 2834 \fi%close acquisition, get glue 2835 \fi%discard or acquire number 2836 \fi%prevtype glue or not 2837 } 2838 2839 2840 % process an acquired glue 2841 % add any acquired column/glue pair to the preamble 2842 \def\@IEEEprocessGcol{\if\@IEEEBPprevtype a\let\@IEEEBPcurtype=a%maintain previous glue abortions 2843 \else 2844 % if this is the start glue, save it, but do nothing else 2845 % as this is not used in the preamble, but before 2846 \if\@IEEEBPprevtype s\edef\@IEEEBPstartglue{\@IEEEBPcurglue}% 2847 \else%not the start glue 2848 \if\@IEEEBPprevtype g%ignore if back to back glues 2849 \@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak 2850 specifications. Ignoring consecutive glue specifiers\MessageBreak 2851 after the first}% 2852 {You cannot have two or more glue types next to each other\MessageBreak 2853 in the IEEEeqnarray column specifications.}% 2854 \let\@IEEEBPcurtype=a% abort this glue 2855 \else% not a back to back glue 2856 \if\@IEEEBPprevtype c\relax% if the previoustype was a col, add column/glue pair to preamble 2857 \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi 2858 \toks0={##}% 2859 % make preamble advance col counter if this environment needs this 2860 \if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi 2861 % insert the column defintion into the preamble, being careful not to expand 2862 % the column definition 2863 \@IEEEappendtoksA{\tabskip=\@IEEEBPcurglue}% 2864 \@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}% 2865 \@IEEEappendtoksA{\@IEEEBPcurcolname}% 2866 \@IEEEappendNOEXPANDtoksA{\endcsname}% 2867 \@IEEEappendtoksA{\the\toks0}% 2868 \@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax% 2869 \relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}% 2870 \@IEEEappendtoksA{\@IEEEBPcurcolname}% 2871 \@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax% 2872 \relax\relax\relax\relax\relax\endgroup}% 2873 \advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble 2874 \else% error: non-start glue with no pending column 2875 \@IEEEclspkgerror{Inter-column glue specifier without a prior column\MessageBreak 2876 type in the column specifications. Ignoring this glue\MessageBreak 2877 specifier}% 2878 {Except for the first and last positions, glue can be placed only\MessageBreak 2879 between column types.}% 2880 \let\@IEEEBPcurtype=a% abort this glue 2881 \fi% previous was a column 2882 \fi% back-to-back glues 2883 \fi% is start column glue 2884 \fi% prev type not a 2885 } 2886 2887 2888 % process an acquired letter referenced column and, if necessary, add it to the preamble 2889 \def\@IEEEprocessCcol{\if\@IEEEBPnexttype g\else 2890 \if\@IEEEBPnexttype n\else 2891 % we have a column followed by something other than a glue (or numeral glue) 2892 % so we must add this column to the preamble now 2893 \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi%col separator for those after the first 2894 \if\@IEEEBPnexttype e\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue\relax}\else%put in end glue 2895 \@IEEEappendtoksA{\tabskip=\@IEEEeqnarraycolSEPdefaultmid\relax}\fi% or default mid glue 2896 \toks0={##}% 2897 % make preamble advance col counter if this environment needs this 2898 \if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi 2899 % insert the column definition into the preamble, being careful not to expand 2900 % the column definition 2901 \@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}% 2902 \@IEEEappendtoksA{\@IEEEBPcurcolname}% 2903 \@IEEEappendNOEXPANDtoksA{\endcsname}% 2904 \@IEEEappendtoksA{\the\toks0}% 2905 \@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax% 2906 \relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}% 2907 \@IEEEappendtoksA{\@IEEEBPcurcolname}% 2908 \@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax% 2909 \relax\relax\relax\relax\relax\endgroup}% 2910 \advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble 2911 \fi%next type not numeral 2912 \fi%next type not glue 2913 } 2914 2915 2916 %% 2917 %% END OF IEEEeqnarry DEFINITIONS 2918 %% 2919 2920 2921 2922 2923 % set up the running headings, this complex because of all the different 2924 % modes IEEEtran supports 2925 \if@twoside 2926 \ifCLASSOPTIONtechnote 2927 \def\ps@headings{% 2928 \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage} 2929 \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}} 2930 \ifCLASSOPTIONdraftcls 2931 \ifCLASSOPTIONdraftclsnofoot 2932 \def\@oddfoot{}\def\@evenfoot{}% 2933 \else 2934 \def\@oddfoot{\scriptsize\@date\hfil DRAFT} 2935 \def\@evenfoot{\scriptsize DRAFT\hfil\@date} 2936 \fi 2937 \else 2938 \def\@oddfoot{}\def\@evenfoot{} 2939 \fi} 2940 \else % not a technote 2941 \def\ps@headings{% 2942 \ifCLASSOPTIONconference 2943 \def\@oddhead{} 2944 \def\@evenhead{} 2945 \else 2946 \def\@oddhead{\hbox{}\scriptsize\rightmark \hfil \thepage} 2947 \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}} 2948 \fi 2949 \ifCLASSOPTIONdraftcls 2950 \def\@oddhead{\hbox{}\scriptsize\rightmark \hfil \thepage} 2951 \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}} 2952 \ifCLASSOPTIONdraftclsnofoot 2953 \def\@oddfoot{}\def\@evenfoot{}% 2954 \else 2955 \def\@oddfoot{\scriptsize\@date\hfil DRAFT} 2956 \def\@evenfoot{\scriptsize DRAFT\hfil\@date} 2957 \fi 2958 \else 2959 \def\@oddfoot{}\def\@evenfoot{}% 2960 \fi} 2961 \fi 2962 \else % single side 2963 \def\ps@headings{% 2964 \ifCLASSOPTIONconference 2965 \def\@oddhead{} 2966 \def\@evenhead{} 2967 \else 2968 \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage} 2969 \def\@evenhead{} 2970 \fi 2971 \ifCLASSOPTIONdraftcls 2972 \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage} 2973 \def\@evenhead{} 2974 \ifCLASSOPTIONdraftclsnofoot 2975 \def\@oddfoot{} 2976 \else 2977 \def\@oddfoot{\scriptsize \@date \hfil DRAFT} 2978 \fi 2979 \else 2980 \def\@oddfoot{} 2981 \fi 2982 \def\@evenfoot{}} 2983 \fi 2984 2985 2986 % title page style 2987 \def\ps@IEEEtitlepagestyle{\def\@oddfoot{}\def\@evenfoot{}% 2988 \ifCLASSOPTIONconference 2989 \def\@oddhead{}% 2990 \def\@evenhead{}% 2991 \else 2992 \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}% 2993 \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}% 2994 \fi 2995 \ifCLASSOPTIONdraftcls 2996 \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}% 2997 \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}% 2998 \ifCLASSOPTIONdraftclsnofoot\else 2999 \def\@oddfoot{\scriptsize \@date\hfil DRAFT}% 3000 \def\@evenfoot{\scriptsize DRAFT\hfil \@date}% 3001 \fi 3002 \else 3003 % all non-draft mode footers 3004 \if@IEEEusingpubid 3005 % for title pages that are using a pubid 3006 % do not repeat pubid if using peer review option 3007 \ifCLASSOPTIONpeerreview 3008 \else 3009 \footskip 0pt% 3010 \ifCLASSOPTIONcompsoc 3011 \def\@oddfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}% 3012 \def\@evenfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}% 3013 \else 3014 \def\@oddfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}% 3015 \def\@evenfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}% 3016 \fi 3017 \fi 3018 \fi 3019 \fi} 3020 3021 3022 % peer review cover page style 3023 \def\ps@IEEEpeerreviewcoverpagestyle{% 3024 \def\@oddhead{}\def\@evenhead{}% 3025 \def\@oddfoot{}\def\@evenfoot{}% 3026 \ifCLASSOPTIONdraftcls 3027 \ifCLASSOPTIONdraftclsnofoot\else 3028 \def\@oddfoot{\scriptsize \@date\hfil DRAFT}% 3029 \def\@evenfoot{\scriptsize DRAFT\hfil \@date}% 3030 \fi 3031 \else 3032 % non-draft mode footers 3033 \if@IEEEusingpubid 3034 \footskip 0pt% 3035 \ifCLASSOPTIONcompsoc 3036 \def\@oddfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}% 3037 \def\@evenfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}% 3038 \else 3039 \def\@oddfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}% 3040 \def\@evenfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}% 3041 \fi 3042 \fi 3043 \fi} 3044 3045 3046 % start with empty headings 3047 \def\rightmark{}\def\leftmark{} 3048 3049 3050 %% Defines the command for putting the header. \footernote{TEXT} is the same 3051 %% as \markboth{TEXT}{TEXT}. 3052 %% Note that all the text is forced into uppercase, if you have some text 3053 %% that needs to be in lower case, for instance et. al., then either manually 3054 %% set \leftmark and \rightmark or use \MakeLowercase{et. al.} within the 3055 %% arguments to \markboth. 3056 \def\markboth#1#2{\def\leftmark{\@IEEEcompsoconly{\sffamily}\MakeUppercase{#1}}% 3057 \def\rightmark{\@IEEEcompsoconly{\sffamily}\MakeUppercase{#2}}} 3058 \def\footernote#1{\markboth{#1}{#1}} 3059 3060 \def\today{\ifcase\month\or 3061 January\or February\or March\or April\or May\or June\or 3062 July\or August\or September\or October\or November\or December\fi 3063 \space\number\day, \number\year} 3064 3065 3066 3067 3068 %% CITATION AND BIBLIOGRAPHY COMMANDS 3069 %% 3070 %% V1.6 no longer supports the older, nonstandard \shortcite and \citename setup stuff 3071 % 3072 % 3073 % Modify Latex2e \@citex to separate citations with "], [" 3074 \def\@citex[#1]#2{% 3075 \let\@citea\@empty 3076 \@cite{\@for\@citeb:=#2\do 3077 {\@citea\def\@citea{], [}% 3078 \edef\@citeb{\expandafter\@firstofone\@citeb\@empty}% 3079 \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi 3080 \@ifundefined{b@\@citeb}{\mbox{\reset@font\bfseries ?}% 3081 \G@refundefinedtrue 3082 \@latex@warning 3083 {Citation `\@citeb‘ on page \thepage \space undefined}}% 3084 {\hbox{\csname b@\@citeb\endcsname}}}}{#1}} 3085 3086 % V1.6 we create hooks for the optional use of Donald Arseneau‘s 3087 % cite.sty package. cite.sty is "smart" and will notice that the 3088 % following format controls are already defined and will not 3089 % redefine them. The result will be the proper sorting of the 3090 % citation numbers and auto detection of 3 or more entry "ranges" - 3091 % all in IEEE style: [1], [2], [5]--[7], [12] 3092 % This also allows for an optional note, i.e., \cite[mynote]{..}. 3093 % If the \cite with note has more than one reference, the note will 3094 % be applied to the last of the listed references. It is generally 3095 % desired that if a note is given, only one reference is listed in 3096 % that \cite. 3097 % Thanks to Mr. Arseneau for providing the required format arguments 3098 % to produce the IEEE style. 3099 \def\citepunct{], [} 3100 \def\citedash{]--[} 3101 3102 % V1.7 default to using same font for urls made by url.sty 3103 \AtBeginDocument{\csname url@samestyle\endcsname} 3104 3105 % V1.6 class files should always provide these 3106 \def\newblock{\hskip .11em\@plus.33em\@minus.07em} 3107 \let\@openbib@code\@empty 3108 3109 3110 % Provide support for the control entries of IEEEtran.bst V1.00 and later. 3111 % V1.7 optional argument allows for a different aux file to be specified in 3112 % order to handle multiple bibliographies. For example, with multibib.sty: 3113 % \newcites{sec}{Secondary Literature} 3114 % \bstctlcite[@auxoutsec]{BSTcontrolhak} 3115 \def\bstctlcite{\@ifnextchar[{\@bstctlcite}{\@bstctlcite[@auxout]}} 3116 \def\@bstctlcite[#1]#2{\@bsphack 3117 \@for\@citeb:=#2\do{% 3118 \edef\@citeb{\expandafter\@firstofone\@citeb}% 3119 \if@filesw\immediate\write\csname #1\endcsname{\string\citation{\@citeb}}\fi}% 3120 \@esphack} 3121 3122 % V1.6 provide a way for a user to execute a command just before 3123 % a given reference number - used to insert a \newpage to balance 3124 % the columns on the last page 3125 \edef\@IEEEtriggerrefnum{0} % the default of zero means that 3126 % the command is not executed 3127 \def\@IEEEtriggercmd{\newpage} 3128 3129 % allow the user to alter the triggered command 3130 \long\def\IEEEtriggercmd#1{\long\def\@IEEEtriggercmd{#1}} 3131 3132 % allow user a way to specify the reference number just before the 3133 % command is executed 3134 \def\IEEEtriggeratref#1{\@IEEEtrantmpcountA=#1% 3135 \edef\@IEEEtriggerrefnum{\the\@IEEEtrantmpcountA}}% 3136 3137 % trigger command at the given reference 3138 \def\@IEEEbibitemprefix{\@IEEEtrantmpcountA=\@IEEEtriggerrefnum\relax% 3139 \advance\@IEEEtrantmpcountA by -1\relax% 3140 \ifnum\c@enumiv=\@IEEEtrantmpcountA\relax\@IEEEtriggercmd\relax\fi} 3141 3142 3143 \def\@biblabel#1{[#1]} 3144 3145 % compsoc journals left align the reference numbers 3146 \@IEEEcompsocnotconfonly{\def\@biblabel#1{[#1]\hfill}} 3147 3148 % controls bib item spacing 3149 \def\IEEEbibitemsep{0pt plus .5pt} 3150 3151 \@IEEEcompsocconfonly{\def\IEEEbibitemsep{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}} 3152 3153 3154 \def\thebibliography#1{\section*{\refname}% 3155 \addcontentsline{toc}{section}{\refname}% 3156 % V1.6 add some rubber space here and provide a command trigger 3157 \footnotesize\@IEEEcompsocconfonly{\small}\vskip 0.3\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip% 3158 \list{\@biblabel{\@arabic\c@enumiv}}% 3159 {\settowidth\labelwidth{\@biblabel{#1}}% 3160 \leftmargin\labelwidth 3161 \advance\leftmargin\labelsep\relax 3162 \itemsep \IEEEbibitemsep\relax 3163 \usecounter{enumiv}% 3164 \let\p@enumiv\@empty 3165 \renewcommand\theenumiv{\@arabic\c@enumiv}}% 3166 \let\@IEEElatexbibitem\bibitem% 3167 \def\bibitem{\@IEEEbibitemprefix\@IEEElatexbibitem}% 3168 \def\newblock{\hskip .11em plus .33em minus .07em}% 3169 % originally: 3170 % \sloppy\clubpenalty4000\widowpenalty4000% 3171 % by adding the \interlinepenalty here, we make it more 3172 % difficult, but not impossible, for LaTeX to break within a reference. 3173 % IEEE almost never breaks a reference (but they do it more often with 3174 % technotes). You may get an underfull vbox warning around the bibliography, 3175 % but the final result will be much more like what IEEE will publish. 3176 % MDS 11/2000 3177 \ifCLASSOPTIONtechnote\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty100% 3178 \else\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty500\fi% 3179 \sfcode`\.=1000\relax} 3180 \let\endthebibliography=\endlist 3181 3182 3183 3184 3185 % TITLE PAGE COMMANDS 3186 % 3187 % 3188 % \IEEEmembership is used to produce the sublargesize italic font used to indicate author 3189 % IEEE membership. compsoc uses a large size sans slant font 3190 \def\IEEEmembership#1{{\@IEEEnotcompsoconly{\sublargesize}\normalfont\@IEEEcompsoconly{\sffamily}\textit{#1}}} 3191 3192 3193 % \IEEEauthorrefmark{} produces a footnote type symbol to indicate author affiliation. 3194 % When given an argument of 1 to 9, \IEEEauthorrefmark{} follows the standard LaTeX footnote 3195 % symbol sequence convention. However, for arguments 10 and above, \IEEEauthorrefmark{} 3196 % reverts to using lower case roman numerals, so it cannot overflow. Do note that you 3197 % cannot use \footnotemark[] in place of \IEEEauthorrefmark{} within \author as the footnote 3198 % symbols will have been turned off to prevent \thanks from creating footnote marks. 3199 % \IEEEauthorrefmark{} produces a symbol that appears to LaTeX as having zero vertical 3200 % height - this allows for a more compact line packing, but the user must ensure that 3201 % the interline spacing is large enough to prevent \IEEEauthorrefmark{} from colliding 3202 % with the text above. 3203 % V1.7 make this a robust command 3204 \DeclareRobustCommand*{\IEEEauthorrefmark}[1]{\raisebox{0pt}[0pt][0pt]{\textsuperscript{\footnotesize\ensuremath{\ifcase#1\or *\or \dagger\or \ddagger\or% 3205 \mathsection\or \mathparagraph\or \|\or **\or \dagger\dagger% 3206 \or \ddagger\ddagger \else\textsuperscript{\expandafter\romannumeral#1}\fi}}}} 3207 3208 3209 % FONT CONTROLS AND SPACINGS FOR CONFERENCE MODE AUTHOR NAME AND AFFILIATION BLOCKS 3210 % 3211 % The default font styles for the author name and affiliation blocks (confmode) 3212 \def\@IEEEauthorblockNstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\sublargesize\@IEEEcompsocconfonly{\large}} 3213 \def\@IEEEauthorblockAstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\@IEEEcompsocconfonly{\itshape}\normalsize\@IEEEcompsocconfonly{\large}} 3214 % The default if the user does not use an author block 3215 \def\@IEEEauthordefaulttextstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\sublargesize} 3216 3217 % spacing from title (or special paper notice) to author name blocks (confmode) 3218 % can be negative 3219 \def\@IEEEauthorblockconfadjspace{-0.25em} 3220 % compsoc conferences need more space here 3221 \@IEEEcompsocconfonly{\def\@IEEEauthorblockconfadjspace{0.75\@IEEEnormalsizeunitybaselineskip}} 3222 3223 % spacing between name and affiliation blocks (confmode) 3224 % This can be negative. 3225 % IEEE doesn‘t want any added spacing here, but I will leave these 3226 % controls in place in case they ever change their mind. 3227 % Personally, I like 0.75ex. 3228 %\def\@IEEEauthorblockNtopspace{0.75ex} 3229 %\def\@IEEEauthorblockAtopspace{0.75ex} 3230 \def\@IEEEauthorblockNtopspace{0.0ex} 3231 \def\@IEEEauthorblockAtopspace{0.0ex} 3232 % baseline spacing within name and affiliation blocks (confmode) 3233 % must be positive, spacings below certain values will make 3234 % the position of line of text sensitive to the contents of the 3235 % line above it i.e., whether or not the prior line has descenders, 3236 % subscripts, etc. For this reason it is a good idea to keep 3237 % these above 2.6ex 3238 \def\@IEEEauthorblockNinterlinespace{2.6ex} 3239 \def\@IEEEauthorblockAinterlinespace{2.75ex} 3240 3241 % This tracks the required strut size. 3242 % See the \@IEEEauthorhalign command for the actual default value used. 3243 \def\@IEEEauthorblockXinterlinespace{2.7ex} 3244 3245 % variables to retain font size and style across groups 3246 % values given here have no effect as they will be overwritten later 3247 \gdef\@IEEESAVESTATEfontsize{10} 3248 \gdef\@IEEESAVESTATEfontbaselineskip{12} 3249 \gdef\@IEEESAVESTATEfontencoding{OT1} 3250 \gdef\@IEEESAVESTATEfontfamily{ptm} 3251 \gdef\@IEEESAVESTATEfontseries{m} 3252 \gdef\@IEEESAVESTATEfontshape{n} 3253 3254 % saves the current font attributes 3255 \def\@IEEEcurfontSAVE{\global\let\@IEEESAVESTATEfontsize\f@size% 3256 \global\let\@IEEESAVESTATEfontbaselineskip\f@baselineskip% 3257 \global\let\@IEEESAVESTATEfontencoding\f@encoding% 3258 \global\let\@IEEESAVESTATEfontfamily\f@family% 3259 \global\let\@IEEESAVESTATEfontseries\f@series% 3260 \global\let\@IEEESAVESTATEfontshape\f@shape} 3261 3262 % restores the saved font attributes 3263 \def\@IEEEcurfontRESTORE{\fontsize{\@IEEESAVESTATEfontsize}{\@IEEESAVESTATEfontbaselineskip}% 3264 \fontencoding{\@IEEESAVESTATEfontencoding}% 3265 \fontfamily{\@IEEESAVESTATEfontfamily}% 3266 \fontseries{\@IEEESAVESTATEfontseries}% 3267 \fontshape{\@IEEESAVESTATEfontshape}% 3268 \selectfont} 3269 3270 3271 % variable to indicate if the current block is the first block in the column 3272 \newif\if@IEEEprevauthorblockincol \@IEEEprevauthorblockincolfalse 3273 3274 3275 % the command places a strut with height and depth = \@IEEEauthorblockXinterlinespace 3276 % we use this technique to have complete manual control over the spacing of the lines 3277 % within the halign environment. 3278 % We set the below baseline portion at 30%, the above 3279 % baseline portion at 70% of the total length. 3280 % Responds to changes in the document‘s \baselinestretch 3281 \def\@IEEEauthorstrutrule{\@IEEEtrantmpdimenA\@IEEEauthorblockXinterlinespace% 3282 \@IEEEtrantmpdimenA=\baselinestretch\@IEEEtrantmpdimenA% 3283 \rule[-0.3\@IEEEtrantmpdimenA]{0pt}{\@IEEEtrantmpdimenA}} 3284 3285 3286 % blocks to hold the authors‘ names and affilations. 3287 % Makes formatting easy for conferences 3288 % 3289 % use real definitions in conference mode 3290 % name block 3291 \def\IEEEauthorblockN#1{\relax\@IEEEauthorblockNstyle% set the default text style 3292 \gdef\@IEEEauthorblockXinterlinespace{0pt}% disable strut for spacer row 3293 % the \expandafter hides the \cr in conditional tex, see the array.sty docs 3294 % for details, probably not needed here as the \cr is in a macro 3295 % do a spacer row if needed 3296 \if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockNtopspaceline\fi 3297 \global\@IEEEprevauthorblockincoltrue% we now have a block in this column 3298 %restore the correct strut value 3299 \gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockNinterlinespace}% 3300 % input the author names 3301 #1% 3302 % end the row if the user did not already 3303 \crcr} 3304 % spacer row for names 3305 \def\@IEEEauthorblockNtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockNtopspace}} 3306 % 3307 % affiliation block 3308 \def\IEEEauthorblockA#1{\relax\@IEEEauthorblockAstyle% set the default text style 3309 \gdef\@IEEEauthorblockXinterlinespace{0pt}%disable strut for spacer row 3310 % the \expandafter hides the \cr in conditional tex, see the array.sty docs 3311 % for details, probably not needed here as the \cr is in a macro 3312 % do a spacer row if needed 3313 \if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockAtopspaceline\fi 3314 \global\@IEEEprevauthorblockincoltrue% we now have a block in this column 3315 %restore the correct strut value 3316 \gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockAinterlinespace}% 3317 % input the author affiliations 3318 #1% 3319 % end the row if the user did not already 3320 \crcr} 3321 % spacer row for affiliations 3322 \def\@IEEEauthorblockAtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockAtopspace}} 3323 3324 3325 % allow papers to compile even if author blocks are used in modes other 3326 % than conference or peerreviewca. For such cases, we provide dummy blocks. 3327 \ifCLASSOPTIONconference 3328 \else 3329 \ifCLASSOPTIONpeerreviewca\else 3330 % not conference or peerreviewca mode 3331 \def\IEEEauthorblockN#1{#1}% 3332 \def\IEEEauthorblockA#1{#1}% 3333 \fi 3334 \fi 3335 3336 3337 3338 % we provide our own halign so as not to have to depend on tabular 3339 \def\@IEEEauthorhalign{\@IEEEauthordefaulttextstyle% default text style 3340 \lineskip=0pt\relax% disable line spacing 3341 \lineskiplimit=0pt\relax% 3342 \baselineskip=0pt\relax% 3343 \@IEEEcurfontSAVE% save the current font 3344 \mathsurround\z@\relax% no extra spacing around math 3345 \let\\\@IEEEauthorhaligncr% replace newline with halign friendly one 3346 \tabskip=0pt\relax% no column spacing 3347 \everycr{}% ensure no problems here 3348 \@IEEEprevauthorblockincolfalse% no author blocks yet 3349 \def\@IEEEauthorblockXinterlinespace{2.7ex}% default interline space 3350 \vtop\bgroup%vtop box 3351 \halign\bgroup&\relax\hfil\@IEEEcurfontRESTORE\relax ##\relax 3352 \hfil\@IEEEcurfontSAVE\@IEEEauthorstrutrule\cr} 3353 3354 % ensure last line, exit from halign, close vbox 3355 \def\end@IEEEauthorhalign{\crcr\egroup\egroup} 3356 3357 % handle bogus star form 3358 \def\@IEEEauthorhaligncr{{\ifnum0=`}\fi\@ifstar{\@@IEEEauthorhaligncr}{\@@IEEEauthorhaligncr}} 3359 3360 % test and setup the optional argument to \\[] 3361 \def\@@IEEEauthorhaligncr{\@testopt\@@@IEEEauthorhaligncr\z@skip} 3362 3363 % end the line and do the optional spacer 3364 \def\@@@IEEEauthorhaligncr[#1]{\ifnum0=`{\fi}\cr\noalign{\vskip#1\relax}} 3365 3366 3367 3368 % flag to prevent multiple \and warning messages 3369 \newif\if@IEEEWARNand 3370 \@IEEEWARNandtrue 3371 3372 % if in conference or peerreviewca modes, we support the use of \and as \author is a 3373 % tabular environment, otherwise we warn the user that \and is invalid 3374 % outside of conference or peerreviewca modes. 3375 \def\and{\relax} % provide a bogus \and that we will then override 3376 3377 \renewcommand{\and}[1][\relax]{\if@IEEEWARNand\typeout{** WARNING: \noexpand\and is valid only 3378 when in conference or peerreviewca}\typeout{modes (line \the\inputlineno).}\fi\global\@IEEEWARNandfalse} 3379 3380 \ifCLASSOPTIONconference% 3381 \renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}% 3382 \fi 3383 \ifCLASSOPTIONpeerreviewca 3384 \renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}% 3385 \fi 3386 3387 3388 % page clearing command 3389 % based on LaTeX2e‘s \cleardoublepage, but allows different page styles 3390 % for the inserted blank pages 3391 \def\@IEEEcleardoublepage#1{\clearpage\if@twoside\ifodd\c@page\else 3392 \hbox{}\thispagestyle{#1}\newpage\if@twocolumn\hbox{}\thispagestyle{#1}\newpage\fi\fi\fi} 3393 3394 3395 % user command to invoke the title page 3396 \def\maketitle{\par% 3397 \begingroup% 3398 \normalfont% 3399 \def\thefootnote{}% the \thanks{} mark type is empty 3400 \def\footnotemark{}% and kill space from \thanks within author 3401 \let\@makefnmark\relax% V1.7, must *really* kill footnotemark to remove all \textsuperscript spacing as well. 3402 \footnotesize% equal spacing between thanks lines 3403 \footnotesep 0.7\baselineskip%see global setting of \footnotesep for more info 3404 % V1.7 disable \thanks note indention for compsoc 3405 \@IEEEcompsoconly{\long\def\@makefntext##1{\parindent 1em\noindent\hbox{\@makefnmark}##1}}% 3406 \normalsize% 3407 \ifCLASSOPTIONpeerreview 3408 \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext% 3409 \thispagestyle{IEEEpeerreviewcoverpagestyle}\@thanks% 3410 \else 3411 \if@twocolumn% 3412 \ifCLASSOPTIONtechnote% 3413 \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext% 3414 \else 3415 \twocolumn[\@maketitle\@IEEEdynamictitlevspace\@IEEEaftertitletext]% 3416 \fi 3417 \else 3418 \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext% 3419 \fi 3420 \thispagestyle{IEEEtitlepagestyle}\@thanks% 3421 \fi 3422 % pullup page for pubid if used. 3423 \if@IEEEusingpubid 3424 \enlargethispage{-\@IEEEpubidpullup}% 3425 \fi 3426 \endgroup 3427 \setcounter{footnote}{0}\let\maketitle\relax\let\@maketitle\relax 3428 \gdef\@thanks{}% 3429 % v1.6b do not clear these as we will need the title again for peer review papers 3430 % \gdef\@author{}\gdef\@title{}% 3431 \let\thanks\relax} 3432 3433 3434 3435 % V1.7 parbox to format \@IEEEcompsoctitleabstractindextext 3436 \long\def\@IEEEcompsoctitleabstractindextextbox#1{\parbox{0.915\textwidth}{#1}} 3437 3438 % formats the Title, authors names, affiliations and special paper notice 3439 % THIS IS A CONTROLLED SPACING COMMAND! Do not allow blank lines or unintentional 3440 % spaces to enter the definition - use % at the end of each line 3441 \def\@maketitle{\newpage 3442 \begin{center}% 3443 \ifCLASSOPTIONtechnote% technotes 3444 {\bfseries\large\@IEEEcompsoconly{\sffamily}\@title\par}\vskip 1.3em{\lineskip .5em\@IEEEcompsoconly{\sffamily}\@author 3445 \@IEEEspecialpapernotice\par{\@IEEEcompsoconly{\vskip 1.5em\relax 3446 \@IEEEcompsoctitleabstractindextextbox{\@IEEEcompsoctitleabstractindextext}\par 3447 \hfill\@IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax 3448 \else% not a technote 3449 \vskip0.2em{\Huge\@IEEEcompsoconly{\sffamily}\@IEEEcompsocconfonly{\normalfont\normalsize\vskip 2\@IEEEnormalsizeunitybaselineskip 3450 \bfseries\Large}\@title\par}\vskip1.0em\par% 3451 % V1.6 handle \author differently if in conference mode 3452 \ifCLASSOPTIONconference% 3453 {\@IEEEspecialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace% 3454 \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par}\relax 3455 \else% peerreviewca, peerreview or journal 3456 \ifCLASSOPTIONpeerreviewca 3457 % peerreviewca handles author names just like conference mode 3458 {\@IEEEcompsoconly{\sffamily}\@IEEEspecialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace% 3459 \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par 3460 {\@IEEEcompsoconly{\vskip 1.5em\relax 3461 \@IEEEcompsoctitleabstractindextextbox{\@IEEEcompsoctitleabstractindextext}\par\hfill 3462 \@IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax 3463 \else% journal or peerreview 3464 {\lineskip.5em\@IEEEcompsoconly{\sffamily}\sublargesize\@author\@IEEEspecialpapernotice\par 3465 {\@IEEEcompsoconly{\vskip 1.5em\relax 3466 \@IEEEcompsoctitleabstractindextextbox{\@IEEEcompsoctitleabstractindextext}\par\hfill 3467 \@IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax 3468 \fi 3469 \fi 3470 \fi\end{center}} 3471 3472 3473 3474 % V1.7 Computer Society "diamond line" which follows index terms for nonconference papers 3475 \def\@IEEEcompsocdiamondline{\vrule depth 0pt height 0.5pt width 4cm\hspace{7.5pt}% 3476 \raisebox{-3.5pt}{\fontfamily{pzd}\fontencoding{U}\fontseries{m}\fontshape{n}\fontsize{11}{12}\selectfont\char70}% 3477 \hspace{7.5pt}\vrule depth 0pt height 0.5pt width 4cm\relax} 3478 3479 % V1.7 standard LateX2e \thanks, but with \itshape under compsoc. Also make it a \long\def 3480 % We also need to trigger the one-shot footnote rule 3481 \def\@IEEEtriggeroneshotfootnoterule{\global\@IEEEenableoneshotfootnoteruletrue} 3482 3483 3484 \long\def\thanks#1{\footnotemark 3485 \protected@xdef\@thanks{\@thanks 3486 \protect\footnotetext[\the\c@footnote]{\@IEEEcompsoconly{\itshape 3487 \protect\@IEEEtriggeroneshotfootnoterule\relax}\ignorespaces#1}}} 3488 \let\@thanks\@empty 3489 3490 % V1.7 allow \author to contain \par‘s. This is needed to allow \thanks to contain \par. 3491 \long\def\author#1{\gdef\@author{#1}} 3492 3493 3494 % in addition to setting up IEEEitemize, we need to remove a baselineskip space above and 3495 % below it because \list‘s \pars introduce blank lines because of the footnote struts. 3496 \def\@IEEEsetupcompsocitemizelist{\def\labelitemi{$\bullet$}% 3497 \setlength{\IEEElabelindent}{0pt}\setlength{\parskip}{0pt}% 3498 \setlength{\partopsep}{0pt}\setlength{\topsep}{0.5\baselineskip}\vspace{-1\baselineskip}\relax} 3499 3500 3501 % flag for fake non-compsoc \IEEEcompsocthanksitem - prevents line break on very first item 3502 \newif\if@IEEEbreakcompsocthanksitem \@IEEEbreakcompsocthanksitemfalse 3503 3504 \ifCLASSOPTIONcompsoc 3505 % V1.7 compsoc bullet item \thanks 3506 % also, we need to redefine this to destroy the argument in \@IEEEdynamictitlevspace 3507 \long\def\IEEEcompsocitemizethanks#1{\relax\@IEEEbreakcompsocthanksitemfalse\footnotemark 3508 \protected@xdef\@thanks{\@thanks 3509 \protect\footnotetext[\the\c@footnote]{\itshape\protect\@IEEEtriggeroneshotfootnoterule 3510 {\let\IEEEiedlistdecl\relax\protect\begin{IEEEitemize}[\protect\@IEEEsetupcompsocitemizelist]\ignorespaces#1\relax 3511 \protect\end{IEEEitemize}}\protect\vspace{-1\baselineskip}}}} 3512 \DeclareRobustCommand*{\IEEEcompsocthanksitem}{\item} 3513 \else 3514 % non-compsoc, allow for dual compilation via rerouting to normal \thanks 3515 \long\def\IEEEcompsocitemizethanks#1{\thanks{#1}} 3516 % redirect to "pseudo-par" \hfil\break\indent after swallowing [] from \IEEEcompsocthanksitem[] 3517 \DeclareRobustCommand{\IEEEcompsocthanksitem}{\@ifnextchar [{\@IEEEthanksswallowoptionalarg}% 3518 {\@IEEEthanksswallowoptionalarg[\relax]}} 3519 % be sure and break only after first item, be sure and ignore spaces after optional argument 3520 \def\@IEEEthanksswallowoptionalarg[#1]{\relax\if@IEEEbreakcompsocthanksitem\hfil\break 3521 \indent\fi\@IEEEbreakcompsocthanksitemtrue\ignorespaces} 3522 \fi 3523 3524 3525 % V1.6b define the \IEEEpeerreviewmaketitle as needed 3526 \ifCLASSOPTIONpeerreview 3527 \def\IEEEpeerreviewmaketitle{\@IEEEcleardoublepage{empty}% 3528 \ifCLASSOPTIONtwocolumn 3529 \twocolumn[\@IEEEpeerreviewmaketitle\@IEEEdynamictitlevspace] 3530 \else 3531 \newpage\@IEEEpeerreviewmaketitle\@IEEEstatictitlevskip 3532 \fi 3533 \thispagestyle{IEEEtitlepagestyle}} 3534 \else 3535 % \IEEEpeerreviewmaketitle does nothing if peer review option has not been selected 3536 \def\IEEEpeerreviewmaketitle{\relax} 3537 \fi 3538 3539 % peerreview formats the repeated title like the title in journal papers. 3540 \def\@IEEEpeerreviewmaketitle{\begin{center}\@IEEEcompsoconly{\sffamily}% 3541 \normalfont\normalsize\vskip0.2em{\Huge\@title\par}\vskip1.0em\par 3542 \end{center}} 3543 3544 3545 3546 % V1.6 3547 % this is a static rubber spacer between the title/authors and the main text 3548 % used for single column text, or when the title appears in the first column 3549 % of two column text (technotes). 3550 \def\@IEEEstatictitlevskip{{\normalfont\normalsize 3551 % adjust spacing to next text 3552 % v1.6b handle peer review papers 3553 \ifCLASSOPTIONpeerreview 3554 % for peer review papers, the same value is used for both title pages 3555 % regardless of the other paper modes 3556 \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip 3557 \else 3558 \ifCLASSOPTIONconference% conference 3559 \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip% 3560 \else% 3561 \ifCLASSOPTIONtechnote% technote 3562 \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip% 3563 \else% journal uses more space 3564 \vskip 2.5\baselineskip plus 0.75\baselineskip minus 0.375\baselineskip% 3565 \fi 3566 \fi 3567 \fi}} 3568 3569 3570 % V1.6 3571 % This is a dynamically determined rigid spacer between the title/authors 3572 % and the main text. This is used only for single column titles over two 3573 % column text (most common) 3574 % This is bit tricky because we have to ensure that the textheight of the 3575 % main text is an integer multiple of \baselineskip 3576 % otherwise underfull vbox problems may develop in the second column of the 3577 % text on the titlepage 3578 % The possible use of \IEEEpubid must also be taken into account. 3579 \def\@IEEEdynamictitlevspace{{% 3580 % we run within a group so that all the macros can be forgotten when we are done 3581 \long\def\thanks##1{\relax}%don‘t allow \thanks to run when we evaluate the vbox height 3582 \long\def\IEEEcompsocitemizethanks##1{\relax}%don‘t allow \IEEEcompsocitemizethanks to run when we evaluate the vbox height 3583 \normalfont\normalsize% we declare more descriptive variable names 3584 \let\@IEEEmaintextheight=\@IEEEtrantmpdimenA%height of the main text columns 3585 \let\@IEEEINTmaintextheight=\@IEEEtrantmpdimenB%height of the main text columns with integer # lines 3586 % set the nominal and minimum values for the title spacer 3587 % the dynamic algorithm will not allow the spacer size to 3588 % become less than \@IEEEMINtitlevspace - instead it will be 3589 % lengthened 3590 % default to journal values 3591 \def\@IEEENORMtitlevspace{2.5\baselineskip}% 3592 \def\@IEEEMINtitlevspace{2\baselineskip}% 3593 % conferences and technotes need tighter spacing 3594 \ifCLASSOPTIONconference%conference 3595 \def\@IEEENORMtitlevspace{1\baselineskip}% 3596 \def\@IEEEMINtitlevspace{0.75\baselineskip}% 3597 \fi 3598 \ifCLASSOPTIONtechnote%technote 3599 \def\@IEEENORMtitlevspace{1\baselineskip}% 3600 \def\@IEEEMINtitlevspace{0.75\baselineskip}% 3601 \fi% 3602 % get the height that the title will take up 3603 \ifCLASSOPTIONpeerreview 3604 \settoheight{\@IEEEmaintextheight}{\vbox{\hsize\textwidth \@IEEEpeerreviewmaketitle}}% 3605 \else 3606 \settoheight{\@IEEEmaintextheight}{\vbox{\hsize\textwidth \@maketitle}}% 3607 \fi 3608 \@IEEEmaintextheight=-\@IEEEmaintextheight% title takes away from maintext, so reverse sign 3609 % add the height of the page textheight 3610 \advance\@IEEEmaintextheight by \textheight% 3611 % correct for title pages using pubid 3612 \ifCLASSOPTIONpeerreview\else 3613 % peerreview papers use the pubid on the cover page only. 3614 % And the cover page uses a static spacer. 3615 \if@IEEEusingpubid\advance\@IEEEmaintextheight by -\@IEEEpubidpullup\fi 3616 \fi% 3617 % subtract off the nominal value of the title bottom spacer 3618 \advance\@IEEEmaintextheight by -\@IEEENORMtitlevspace% 3619 % \topskip takes away some too 3620 \advance\@IEEEmaintextheight by -\topskip% 3621 % calculate the column height of the main text for lines 3622 % now we calculate the main text height as if holding 3623 % an integer number of \normalsize lines after the first 3624 % and discard any excess fractional remainder 3625 % we subtracted the first line, because the first line 3626 % is placed \topskip into the maintext, not \baselineskip like the 3627 % rest of the lines. 3628 \@IEEEINTmaintextheight=\@IEEEmaintextheight% 3629 \divide\@IEEEINTmaintextheight by \baselineskip% 3630 \multiply\@IEEEINTmaintextheight by \baselineskip% 3631 % now we calculate how much the title spacer height will 3632 % have to be reduced from nominal (\@IEEEREDUCEmaintextheight is always 3633 % a positive value) so that the maintext area will contain an integer 3634 % number of normal size lines 3635 % we change variable names here (to avoid confusion) as we no longer 3636 % need \@IEEEINTmaintextheight and can reuse its dimen register 3637 \let\@IEEEREDUCEmaintextheight=\@IEEEINTmaintextheight% 3638 \advance\@IEEEREDUCEmaintextheight by -\@IEEEmaintextheight% 3639 \advance\@IEEEREDUCEmaintextheight by \baselineskip% 3640 % this is the calculated height of the spacer 3641 % we change variable names here (to avoid confusion) as we no longer 3642 % need \@IEEEmaintextheight and can reuse its dimen register 3643 \let\@IEEECOMPENSATElen=\@IEEEmaintextheight% 3644 \@IEEECOMPENSATElen=\@IEEENORMtitlevspace% set the nominal value 3645 % we go with the reduced length if it is smaller than an increase 3646 \ifdim\@IEEEREDUCEmaintextheight < 0.5\baselineskip\relax% 3647 \advance\@IEEECOMPENSATElen by -\@IEEEREDUCEmaintextheight% 3648 % if the resulting spacer is too small back out and go with an increase instead 3649 \ifdim\@IEEECOMPENSATElen<\@IEEEMINtitlevspace\relax% 3650 \advance\@IEEECOMPENSATElen by \baselineskip% 3651 \fi% 3652 \else% 3653 % go with an increase because it is closer to the nominal than a decrease 3654 \advance\@IEEECOMPENSATElen by -\@IEEEREDUCEmaintextheight% 3655 \advance\@IEEECOMPENSATElen by \baselineskip% 3656 \fi% 3657 % set the calculated rigid spacer 3658 \vspace{\@IEEECOMPENSATElen}}} 3659 3660 3661 3662 % V1.6 3663 % we allow the user access to the last part of the title area 3664 % useful in emergencies such as when a different spacing is needed 3665 % This text is NOT compensated for in the dynamic sizer. 3666 \let\@IEEEaftertitletext=\relax 3667 \long\def\IEEEaftertitletext#1{\def\@IEEEaftertitletext{#1}} 3668 3669 % V1.7 provide a way for users to enter abstract and keywords 3670 % into the onecolumn title are. This text is compensated for 3671 % in the dynamic sizer. 3672 \let\@IEEEcompsoctitleabstractindextext=\relax 3673 \long\def\IEEEcompsoctitleabstractindextext#1{\def\@IEEEcompsoctitleabstractindextext{#1}} 3674 % V1.7 provide a way for users to get the \@IEEEcompsoctitleabstractindextext if 3675 % not in compsoc journal mode - this way abstract and keywords can be placed 3676 % in their conventional position if not in compsoc mode. 3677 \def\IEEEdisplaynotcompsoctitleabstractindextext{% 3678 \ifCLASSOPTIONcompsoc% display if compsoc conf 3679 \ifCLASSOPTIONconference\@IEEEcompsoctitleabstractindextext\fi 3680 \else% or if not compsoc 3681 \@IEEEcompsoctitleabstractindextext\fi} 3682 3683 3684 % command to allow alteration of baselinestretch, but only if the current 3685 % baselineskip is unity. Used to tweak the compsoc abstract and keywords line spacing. 3686 \def\@IEEEtweakunitybaselinestretch#1{{\def\baselinestretch{1}\selectfont 3687 \global\@tempskipa\baselineskip}\ifnum\@tempskipa=\baselineskip% 3688 \def\baselinestretch{#1}\selectfont\fi\relax} 3689 3690 3691 % abstract and keywords are in \small, except 3692 % for 9pt docs in which they are in \footnotesize 3693 % Because 9pt docs use an 8pt footnotesize, \small 3694 % becomes a rather awkward 8.5pt 3695 \def\@IEEEabskeysecsize{\small} 3696 \ifx\CLASSOPTIONpt\@IEEEptsizenine 3697 \def\@IEEEabskeysecsize{\footnotesize} 3698 \fi 3699 3700 % compsoc journals use \footnotesize, compsoc conferences use normalsize 3701 \@IEEEcompsoconly{\def\@IEEEabskeysecsize{\footnotesize}} 3702 \@IEEEcompsocconfonly{\def\@IEEEabskeysecsize{\normalsize}} 3703 3704 3705 3706 3707 % V1.6 have abstract and keywords strip leading spaces, pars and newlines 3708 % so that spacing is more tightly controlled. 3709 \def\abstract{\normalfont 3710 \if@twocolumn 3711 \@IEEEabskeysecsize\bfseries\textit{\abstractname}---\relax 3712 \else 3713 \begin{center}\vspace{-1.78ex}\@IEEEabskeysecsize\textbf{\abstractname}\end{center}\quotation\@IEEEabskeysecsize 3714 \fi\@IEEEgobbleleadPARNLSP} 3715 % V1.6 IEEE wants only 1 pica from end of abstract to introduction heading when in 3716 % conference mode (the heading already has this much above it) 3717 \def\endabstract{\relax\ifCLASSOPTIONconference\vspace{0ex}\else\vspace{1.34ex}\fi\par\if@twocolumn\else\endquotation\fi 3718 \normalfont\normalsize} 3719 3720 \def\IEEEkeywords{\normalfont 3721 \if@twocolumn 3722 \@IEEEabskeysecsize\bfseries\textit{\IEEEkeywordsname}---\relax 3723 \else 3724 \begin{center}\@IEEEabskeysecsize\textbf{\IEEEkeywordsname}\end{center}\quotation\@IEEEabskeysecsize 3725 \fi\@IEEEgobbleleadPARNLSP} 3726 \def\endIEEEkeywords{\relax\ifCLASSOPTIONtechnote\vspace{1.34ex}\else\vspace{0.67ex}\fi 3727 \par\if@twocolumn\else\endquotation\fi% 3728 \normalfont\normalsize} 3729 3730 % V1.7 compsoc keywords index terms 3731 \ifCLASSOPTIONcompsoc 3732 \ifCLASSOPTIONconference% compsoc conference 3733 \def\abstract{\normalfont 3734 \begin{center}\@IEEEabskeysecsize\textbf{\large\abstractname}\end{center}\vskip 0.5\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip 3735 \if@twocolumn\else\quotation\fi\itshape\@IEEEabskeysecsize% 3736 \par\@IEEEgobbleleadPARNLSP} 3737 \def\IEEEkeywords{\normalfont\vskip 1.5\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip 3738 \begin{center}\@IEEEabskeysecsize\textbf{\large\IEEEkeywordsname}\end{center}\vskip 0.5\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip 3739 \if@twocolumn\else\quotation\fi\itshape\@IEEEabskeysecsize% 3740 \par\@IEEEgobbleleadPARNLSP} 3741 \else% compsoc not conference 3742 \def\abstract{\normalfont\@IEEEtweakunitybaselinestretch{1.15}\sffamily 3743 \if@twocolumn 3744 \@IEEEabskeysecsize\noindent\textbf{\abstractname}---\relax 3745 \else 3746 \begin{center}\vspace{-1.78ex}\@IEEEabskeysecsize\textbf{\abstractname}\end{center}\quotation\@IEEEabskeysecsize% 3747 \fi\@IEEEgobbleleadPARNLSP} 3748 \def\IEEEkeywords{\normalfont\@IEEEtweakunitybaselinestretch{1.15}\sffamily 3749 \if@twocolumn 3750 \@IEEEabskeysecsize\vskip 0.5\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip\noindent 3751 \textbf{\IEEEkeywordsname}---\relax 3752 \else 3753 \begin{center}\@IEEEabskeysecsize\textbf{\IEEEkeywordsname}\end{center}\quotation\@IEEEabskeysecsize% 3754 \fi\@IEEEgobbleleadPARNLSP} 3755 \fi 3756 \fi 3757 3758 3759 3760 % gobbles all leading \, \\ and \par, upon finding first token that 3761 % is not a \ , \\ or a \par, it ceases and returns that token 3762 % 3763 % used to strip leading \, \\ and \par from the input 3764 % so that such things in the beginning of an environment will not 3765 % affect the formatting of the text 3766 \long\def\@IEEEgobbleleadPARNLSP#1{\let\@IEEEswallowthistoken=0% 3767 \let\@IEEEgobbleleadPARNLSPtoken#1% 3768 \let\@IEEEgobbleleadPARtoken=\par% 3769 \let\@IEEEgobbleleadNLtoken=\\% 3770 \let\@IEEEgobbleleadSPtoken=\ % 3771 \def\@IEEEgobbleleadSPMACRO{\ }% 3772 \ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadPARtoken% 3773 \let\@IEEEswallowthistoken=1% 3774 \fi% 3775 \ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadNLtoken% 3776 \let\@IEEEswallowthistoken=1% 3777 \fi% 3778 \ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPtoken% 3779 \let\@IEEEswallowthistoken=1% 3780 \fi% 3781 % a control space will come in as a macro 3782 % when it is the last one on a line 3783 \ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPMACRO% 3784 \let\@IEEEswallowthistoken=1% 3785 \fi% 3786 % if we have to swallow this token, do so and taste the next one 3787 % else spit it out and stop gobbling 3788 \ifx\@IEEEswallowthistoken 1\let\@IEEEnextgobbleleadPARNLSP=\@IEEEgobbleleadPARNLSP\else% 3789 \let\@IEEEnextgobbleleadPARNLSP=#1\fi% 3790 \@IEEEnextgobbleleadPARNLSP}% 3791 3792 3793 3794 3795 % TITLING OF SECTIONS 3796 \def\@IEEEsectpunct{:\ \,} % Punctuation after run-in section heading (headings which are 3797 % part of the paragraphs), need little bit more than a single space 3798 % spacing from section number to title 3799 % compsoc conferences use regular period/space punctuation 3800 \ifCLASSOPTIONcompsoc 3801 \ifCLASSOPTIONconference 3802 \def\@IEEEsectpunct{.\ } 3803 \fi\fi 3804 3805 3806 \def\@seccntformat#1{\csname the#1dis\endcsname\hskip 0.5em\relax} 3807 3808 \ifCLASSOPTIONcompsoc 3809 % compsoc journals need extra spacing 3810 \ifCLASSOPTIONconference\else 3811 \def\@seccntformat#1{\csname the#1dis\endcsname\hskip 1em\relax} 3812 \fi\fi 3813 3814 %v1.7 put {} after #6 to allow for some types of user font control 3815 %and use \@@par rather than \par 3816 \def\@sect#1#2#3#4#5#6[#7]#8{% 3817 \ifnum #2>\c@secnumdepth 3818 \let\@svsec\@empty 3819 \else 3820 \refstepcounter{#1}% 3821 % load section label and spacer into \@svsec 3822 \protected@edef\@svsec{\@seccntformat{#1}\relax}% 3823 \fi% 3824 \@tempskipa #5\relax 3825 \ifdim \@tempskipa>\z@% tempskipa determines whether is treated as a high 3826 \begingroup #6{\relax% or low level heading 3827 \noindent % subsections are NOT indented 3828 % print top level headings. \@svsec is label, #8 is heading title 3829 % IEEE does not block indent the section title text, it flows like normal 3830 {\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\@@par}}% 3831 \endgroup 3832 \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else 3833 \protect\numberline{\csname the#1\endcsname}\fi#7}% 3834 \else % printout low level headings 3835 % svsechd seems to swallow the trailing space, protect it with \mbox{} 3836 % got rid of sectionmark stuff 3837 \def\@svsechd{#6{\hskip #3\relax\@svsec #8\@IEEEsectpunct\mbox{}}% 3838 \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else 3839 \protect\numberline{\csname the#1\endcsname}\fi#7}}% 3840 \fi%skip down 3841 \@xsect{#5}} 3842 3843 3844 % section* handler 3845 %v1.7 put {} after #4 to allow for some types of user font control 3846 %and use \@@par rather than \par 3847 \def\@ssect#1#2#3#4#5{\@tempskipa #3\relax 3848 \ifdim \@tempskipa>\z@ 3849 %\begingroup #4\@hangfrom{\hskip #1}{\interlinepenalty \@M #5\par}\endgroup 3850 % IEEE does not block indent the section title text, it flows like normal 3851 \begingroup \noindent #4{\relax{\hskip #1}{\interlinepenalty \@M #5\@@par}}\endgroup 3852 % svsechd swallows the trailing space, protect it with \mbox{} 3853 \else \def\@svsechd{#4{\hskip #1\relax #5\@IEEEsectpunct\mbox{}}}\fi 3854 \@xsect{#3}} 3855 3856 3857 %% SECTION heading spacing and font 3858 %% 3859 % arguments are: #1 - sectiontype name 3860 % (for \@sect) #2 - section level 3861 % #3 - section heading indent 3862 % #4 - top separation (absolute value used, neg indicates not to indent main text) 3863 % If negative, make stretch parts negative too! 3864 % #5 - (absolute value used) positive: bottom separation after heading, 3865 % negative: amount to indent main text after heading 3866 % Both #4 and #5 negative means to indent main text and use negative top separation 3867 % #6 - font control 3868 % You‘ve got to have \normalfont\normalsize in the font specs below to prevent 3869 % trouble when you do something like: 3870 % \section{Note}{\ttfamily TT-TEXT} is known to ... 3871 % IEEE sometimes REALLY stretches the area before a section 3872 % heading by up to about 0.5in. However, it may not be a good 3873 % idea to let LaTeX have quite this much rubber. 3874 \ifCLASSOPTIONconference% 3875 % IEEE wants section heading spacing to decrease for conference mode 3876 \def\section{\@startsection{section}{1}{\z@}{1.5ex plus 1.5ex minus 0.5ex}% 3877 {0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}% 3878 \def\subsection{\@startsection{subsection}{2}{\z@}{1.5ex plus 1.5ex minus 0.5ex}% 3879 {0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}% 3880 \else % for journals 3881 \def\section{\@startsection{section}{1}{\z@}{3.0ex plus 1.5ex minus 1.5ex}% V1.6 3.0ex from 3.5ex 3882 {0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}% 3883 \def\subsection{\@startsection{subsection}{2}{\z@}{3.5ex plus 1.5ex minus 1.5ex}% 3884 {0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}% 3885 \fi 3886 3887 % for both journals and conferences 3888 % decided to put in a little rubber above the section, might help somebody 3889 \def\subsubsection{\@startsection{subsubsection}{3}{\parindent}{0ex plus 0.1ex minus 0.1ex}% 3890 {0ex}{\normalfont\normalsize\itshape}}% 3891 \def\paragraph{\@startsection{paragraph}{4}{2\parindent}{0ex plus 0.1ex minus 0.1ex}% 3892 {0ex}{\normalfont\normalsize\itshape}}% 3893 3894 3895 % compsoc 3896 \ifCLASSOPTIONcompsoc 3897 \ifCLASSOPTIONconference 3898 % compsoc conference 3899 \def\section{\@startsection{section}{1}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}% 3900 {1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}{\normalfont\large\bfseries}}% 3901 \def\subsection{\@startsection{subsection}{2}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}% 3902 {1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}{\normalfont\sublargesize\bfseries}}% 3903 \def\subsubsection{\@startsection{subsubsection}{3}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}% 3904 {0ex}{\normalfont\normalsize\bfseries}}% 3905 \def\paragraph{\@startsection{paragraph}{4}{2\parindent}{0ex plus 0.1ex minus 0.1ex}% 3906 {0ex}{\normalfont\normalsize}}% 3907 \else% compsoc journals 3908 % use negative top separation as compsoc journals do not indent paragraphs after section titles 3909 \def\section{\@startsection{section}{1}{\z@}{-3ex plus -2ex minus -1.5ex}% 3910 {0.7ex plus 1ex minus 0ex}{\normalfont\large\sffamily\bfseries\scshape}}% 3911 % Note that subsection and smaller may not be correct for the Computer Society, 3912 % I have to look up an example. 3913 \def\subsection{\@startsection{subsection}{2}{\z@}{-3.5ex plus -1.5ex minus -1.5ex}% 3914 {0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\sffamily\bfseries}}% 3915 \def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-2.5ex plus -1ex minus -1ex}% 3916 {0.5ex plus 0.5ex minus 0ex}{\normalfont\normalsize\sffamily\itshape}}% 3917 \def\paragraph{\@startsection{paragraph}{4}{2\parindent}{-0ex plus -0.1ex minus -0.1ex}% 3918 {0ex}{\normalfont\normalsize}}% 3919 \fi\fi 3920 3921 3922 3923 3924 %% ENVIRONMENTS 3925 % "box" symbols at end of proofs 3926 \def\IEEEQEDclosed{\mbox{\rule[0pt]{1.3ex}{1.3ex}}} % for a filled box 3927 % V1.6 some journals use an open box instead that will just fit around a closed one 3928 \def\IEEEQEDopen{{\setlength{\fboxsep}{0pt}\setlength{\fboxrule}{0.2pt}\fbox{\rule[0pt]{0pt}{1.3ex}\rule[0pt]{1.3ex}{0pt}}}} 3929 \ifCLASSOPTIONcompsoc 3930 \def\IEEEQED{\IEEEQEDopen} % default to open for compsoc 3931 \else 3932 \def\IEEEQED{\IEEEQEDclosed} % otherwise default to closed 3933 \fi 3934 3935 % v1.7 name change to avoid namespace collision with amsthm. Also add support 3936 % for an optional argument. 3937 \def\IEEEproof{\@ifnextchar[{\@IEEEproof}{\@IEEEproof[\IEEEproofname]}} 3938 \def\@IEEEproof[#1]{\par\noindent\hspace{2em}{\itshape #1: }} 3939 \def\endIEEEproof{\hspace*{\fill}~\IEEEQED\par} 3940 3941 3942 %\itemindent is set to \z@ by list, so define new temporary variable 3943 \newdimen\@IEEEtmpitemindent 3944 \def\@begintheorem#1#2{\@IEEEtmpitemindent\itemindent\topsep 0pt\rmfamily\trivlist% 3945 \item[\hskip \labelsep{\indent\itshape #1\ #2:}]\itemindent\@IEEEtmpitemindent} 3946 \def\@opargbegintheorem#1#2#3{\@IEEEtmpitemindent\itemindent\topsep 0pt\rmfamily \trivlist% 3947 % V1.6 IEEE is back to using () around theorem names which are also in italics 3948 % Thanks to Christian Peel for reporting this. 3949 \item[\hskip\labelsep{\indent\itshape #1\ #2\ (#3):}]\itemindent\@IEEEtmpitemindent} 3950 % V1.7 remove bogus \unskip that caused equations in theorems to collide with 3951 % lines below. 3952 \def\@endtheorem{\endtrivlist} 3953 3954 % V1.6 3955 % display command for the section the theorem is in - so that \thesection 3956 % is not used as this will be in Roman numerals when we want arabic. 3957 % LaTeX2e uses \def\@thmcounter#1{\noexpand\arabic{#1}} for the theorem number 3958 % (second part) display and \def\@thmcountersep{.} as a separator. 3959 % V1.7 intercept calls to the section counter and reroute to \@IEEEthmcounterinsection 3960 % to allow \appendix(ices} to override as needed. 3961 % 3962 % special handler for sections, allows appendix(ices) to override 3963 \gdef\@IEEEthmcounterinsection#1{\arabic{#1}} 3964 % string macro 3965 \edef\@IEEEstringsection{section} 3966 3967 % redefine the #1#2[#3] form of newtheorem to use a hook to \@IEEEthmcounterinsection 3968 % if section in_counter is used 3969 \def\@xnthm#1#2[#3]{% 3970 \expandafter\@ifdefinable\csname #1\endcsname 3971 {\@definecounter{#1}\@newctr{#1}[#3]% 3972 \edef\@IEEEstringtmp{#3} 3973 \ifx\@IEEEstringtmp\@IEEEstringsection 3974 \expandafter\xdef\csname the#1\endcsname{% 3975 \noexpand\@IEEEthmcounterinsection{#3}\@thmcountersep 3976 \@thmcounter{#1}}% 3977 \else 3978 \expandafter\xdef\csname the#1\endcsname{% 3979 \expandafter\noexpand\csname the#3\endcsname \@thmcountersep 3980 \@thmcounter{#1}}% 3981 \fi 3982 \global\@namedef{#1}{\@thm{#1}{#2}}% 3983 \global\@namedef{end#1}{\@endtheorem}}} 3984 3985 3986 3987 %% SET UP THE DEFAULT PAGESTYLE 3988 \ps@headings 3989 \pagenumbering{arabic} 3990 3991 % normally the page counter starts at 1 3992 \setcounter{page}{1} 3993 % however, for peerreview the cover sheet is page 0 or page -1 3994 % (for duplex printing) 3995 \ifCLASSOPTIONpeerreview 3996 \if@twoside 3997 \setcounter{page}{-1} 3998 \else 3999 \setcounter{page}{0} 4000 \fi 4001 \fi 4002 4003 % standard book class behavior - let bottom line float up and down as 4004 % needed when single sided 4005 \ifCLASSOPTIONtwoside\else\raggedbottom\fi 4006 % if two column - turn on twocolumn, allow word spacings to stretch more and 4007 % enforce a rigid position for the last lines 4008 \ifCLASSOPTIONtwocolumn 4009 % the peer review option delays invoking twocolumn 4010 \ifCLASSOPTIONpeerreview\else 4011 \twocolumn 4012 \fi 4013 \sloppy 4014 \flushbottom 4015 \fi 4016 4017 4018 4019 4020 % \APPENDIX and \APPENDICES definitions 4021 4022 % This is the \@ifmtarg command from the LaTeX ifmtarg package 4023 % by Peter Wilson (CUA) and Donald Arseneau 4024 % \@ifmtarg is used to determine if an argument to a command 4025 % is present or not. 4026 % For instance: 4027 % \@ifmtarg{#1}{\typeout{empty}}{\typeout{has something}} 4028 % \@ifmtarg is used with our redefined \section command if 4029 % \appendices is invoked. 4030 % The command \section will behave slightly differently depending 4031 % on whether the user specifies a title: 4032 % \section{My appendix title} 4033 % or not: 4034 % \section{} 4035 % This way, we can eliminate the blank lines where the title 4036 % would be, and the unneeded : after Appendix in the table of 4037 % contents 4038 \begingroup 4039 \catcode`\Q=3 4040 \long\gdef\@ifmtarg#1{\@xifmtarg#1QQ\@secondoftwo\@firstoftwo\@nil} 4041 \long\gdef\@xifmtarg#1#2Q#3#4#5\@nil{#4} 4042 \endgroup 4043 % end of \@ifmtarg defs 4044 4045 4046 % V1.7 4047 % command that allows the one time saving of the original definition 4048 % of section to \@IEEEappendixsavesection for \appendix or \appendices 4049 % we don‘t save \section here as it may be redefined later by other 4050 % packages (hyperref.sty, etc.) 4051 \def\@IEEEsaveoriginalsectiononce{\let\@IEEEappendixsavesection\section 4052 \let\@IEEEsaveoriginalsectiononce\relax} 4053 4054 % neat trick to grab and process the argument from \section{argument} 4055 % we process differently if the user invoked \section{} with no 4056 % argument (title) 4057 % note we reroute the call to the old \section* 4058 \def\@IEEEprocessthesectionargument#1{% 4059 \@ifmtarg{#1}{% 4060 \@IEEEappendixsavesection*{\appendixname~\thesectiondis}% 4061 \addcontentsline{toc}{section}{\appendixname~\thesection}}{% 4062 \@IEEEappendixsavesection*{\appendixname~\thesectiondis \\* #1}% 4063 \addcontentsline{toc}{section}{\appendixname~\thesection: #1}}} 4064 4065 % we use this if the user calls \section{} after 4066 % \appendix-- which has no meaning. So, we ignore the 4067 % command and its argument. Then, warn the user. 4068 \def\@IEEEdestroythesectionargument#1{\typeout{** WARNING: Ignoring useless 4069 \protect\section\space in Appendix (line \the\inputlineno).}} 4070 4071 4072 % remember \thesection forms will be displayed in \ref calls 4073 % and in the Table of Contents. 4074 % The \sectiondis form is used in the actual heading itself 4075 4076 % appendix command for one single appendix 4077 % normally has no heading. However, if you want a 4078 % heading, you can do so via the optional argument: 4079 % \appendix[Optional Heading] 4080 \def\appendix{\relax} 4081 \renewcommand{\appendix}[1][]{\@IEEEsaveoriginalsectiononce\par 4082 % v1.6 keep hyperref‘s identifiers unique 4083 \gdef\theHsection{Appendix.A}% 4084 % v1.6 adjust hyperref‘s string name for the section 4085 \xdef\Hy@chapapp{appendix}% 4086 \setcounter{section}{0}% 4087 \setcounter{subsection}{0}% 4088 \setcounter{subsubsection}{0}% 4089 \setcounter{paragraph}{0}% 4090 \gdef\thesection{A}% 4091 \gdef\thesectiondis{}% 4092 \gdef\thesubsection{\Alph{subsection}}% 4093 \gdef\@IEEEthmcounterinsection##1{A} 4094 \refstepcounter{section}% update the \ref counter 4095 \@ifmtarg{#1}{\@IEEEappendixsavesection*{\appendixname}% 4096 \addcontentsline{toc}{section}{\appendixname}}{% 4097 \@IEEEappendixsavesection*{\appendixname~\\* #1}% 4098 \addcontentsline{toc}{section}{\appendixname: #1}}% 4099 % redefine \section command for appendix 4100 % leave \section* as is 4101 \def\section{\@ifstar{\@IEEEappendixsavesection*}{% 4102 \@IEEEdestroythesectionargument}}% throw out the argument 4103 % of the normal form 4104 } 4105 4106 4107 4108 % appendices command for multiple appendices 4109 % user then calls \section with an argument (possibly empty) to 4110 % declare the individual appendices 4111 \def\appendices{\@IEEEsaveoriginalsectiononce\par 4112 % v1.6 keep hyperref‘s identifiers unique 4113 \gdef\theHsection{Appendix.\Alph{section}}% 4114 % v1.6 adjust hyperref‘s string name for the section 4115 \xdef\Hy@chapapp{appendix}% 4116 \setcounter{section}{-1}% we want \refstepcounter to use section 0 4117 \setcounter{subsection}{0}% 4118 \setcounter{subsubsection}{0}% 4119 \setcounter{paragraph}{0}% 4120 \ifCLASSOPTIONromanappendices% 4121 \gdef\thesection{\Roman{section}}% 4122 \gdef\thesectiondis{\Roman{section}}% 4123 \@IEEEcompsocconfonly{\gdef\thesectiondis{\Roman{section}.}}% 4124 \gdef\@IEEEthmcounterinsection##1{A\arabic{##1}} 4125 \else% 4126 \gdef\thesection{\Alph{section}}% 4127 \gdef\thesectiondis{\Alph{section}}% 4128 \@IEEEcompsocconfonly{\gdef\thesectiondis{\Alph{section}.}}% 4129 \gdef\@IEEEthmcounterinsection##1{\Alph{##1}} 4130 \fi% 4131 \refstepcounter{section}% update the \ref counter 4132 \setcounter{section}{0}% NEXT \section will be the FIRST appendix 4133 % redefine \section command for appendices 4134 % leave \section* as is 4135 \def\section{\@ifstar{\@IEEEappendixsavesection*}{% process the *-form 4136 \refstepcounter{section}% or is a new section so, 4137 \@IEEEprocessthesectionargument}}% process the argument 4138 % of the normal form 4139 } 4140 4141 4142 4143 % \IEEEPARstart 4144 % Definition for the big two line drop cap letter at the beginning of the 4145 % first paragraph of journal papers. The first argument is the first letter 4146 % of the first word, the second argument is the remaining letters of the 4147 % first word which will be rendered in upper case. 4148 % In V1.6 this has been completely rewritten to: 4149 % 4150 % 1. no longer have problems when the user begins an environment 4151 % within the paragraph that uses \IEEEPARstart. 4152 % 2. auto-detect and use the current font family 4153 % 3. revise handling of the space at the end of the first word so that 4154 % interword glue will now work as normal. 4155 % 4. produce correctly aligned edges for the (two) indented lines. 4156 % 4157 % We generalize things via control macros - playing with these is fun too. 4158 % 4159 % V1.7 added more control macros to make it easy for IEEEtrantools.sty users 4160 % to change the font style. 4161 % 4162 % the number of lines that are indented to clear it 4163 % may need to increase if using decenders 4164 \def\@IEEEPARstartDROPLINES{2} 4165 % minimum number of lines left on a page to allow a \@IEEEPARstart 4166 % Does not take into consideration rubber shrink, so it tends to 4167 % be overly cautious 4168 \def\@IEEEPARstartMINPAGELINES{2} 4169 % V1.7 the height of the drop cap is adjusted to match the height of this text 4170 % in the current font (when \IEEEPARstart is called). 4171 \def\@IEEEPARstartHEIGHTTEXT{T} 4172 % the depth the letter is lowered below the baseline 4173 % the height (and size) of the letter is determined by the sum 4174 % of this value and the height of the \@IEEEPARstartHEIGHTTEXT in the current 4175 % font. It is a good idea to set this value in terms of the baselineskip 4176 % so that it can respond to changes therein. 4177 \def\@IEEEPARstartDROPDEPTH{1.1\baselineskip} 4178 % V1.7 the font the drop cap will be rendered in, 4179 % can take zero or one argument. 4180 \def\@IEEEPARstartFONTSTYLE{\bfseries} 4181 % V1.7 any additional, non-font related commands needed to modify 4182 % the drop cap letter, can take zero or one argument. 4183 \def\@IEEEPARstartCAPSTYLE{\MakeUppercase} 4184 % V1.7 the font that will be used to render the rest of the word, 4185 % can take zero or one argument. 4186 \def\@IEEEPARstartWORDFONTSTYLE{\relax} 4187 % V1.7 any additional, non-font related commands needed to modify 4188 % the rest of the word, can take zero or one argument. 4189 \def\@IEEEPARstartWORDCAPSTYLE{\MakeUppercase} 4190 % This is the horizontal separation distance from the drop letter to the main text. 4191 % Lengths that depend on the font (e.g., ex, em, etc.) will be referenced 4192 % to the font that is active when \IEEEPARstart is called. 4193 \def\@IEEEPARstartSEP{0.15em} 4194 % V1.7 horizontal offset applied to the left of the drop cap. 4195 \def\@IEEEPARstartHOFFSET{0em} 4196 % V1.7 Italic correction command applied at the end of the drop cap. 4197 \def\@IEEEPARstartITLCORRECT{\/} 4198 4199 % V1.7 compoc uses nonbold drop cap and small caps word style 4200 \ifCLASSOPTIONcompsoc 4201 \def\@IEEEPARstartFONTSTYLE{\mdseries} 4202 \def\@IEEEPARstartWORDFONTSTYLE{\scshape} 4203 \def\@IEEEPARstartWORDCAPSTYLE{\relax} 4204 \fi 4205 4206 % definition of \IEEEPARstart 4207 % THIS IS A CONTROLLED SPACING AREA, DO NOT ALLOW SPACES WITHIN THESE LINES 4208 % 4209 % The token \@IEEEPARstartfont will be globally defined after the first use 4210 % of \IEEEPARstart and will be a font command which creates the big letter 4211 % The first argument is the first letter of the first word and the second 4212 % argument is the rest of the first word(s). 4213 \def\IEEEPARstart#1#2{\par{% 4214 % if this page does not have enough space, break it and lets start 4215 % on a new one 4216 \@IEEEtranneedspace{\@IEEEPARstartMINPAGELINES\baselineskip}{\relax}% 4217 % V1.7 move this up here in case user uses \textbf for \@IEEEPARstartFONTSTYLE 4218 % which uses command \leavevmode which causes an unwanted \indent to be issued 4219 \noindent 4220 % calculate the desired height of the big letter 4221 % it extends from the top of \@IEEEPARstartHEIGHTTEXT in the current font 4222 % down to \@IEEEPARstartDROPDEPTH below the current baseline 4223 \settoheight{\@IEEEtrantmpdimenA}{\@IEEEPARstartHEIGHTTEXT}% 4224 \addtolength{\@IEEEtrantmpdimenA}{\@IEEEPARstartDROPDEPTH}% 4225 % extract the name of the current font in bold 4226 % and place it in \@IEEEPARstartFONTNAME 4227 \def\@IEEEPARstartGETFIRSTWORD##1 ##2\relax{##1}% 4228 {\@IEEEPARstartFONTSTYLE{\selectfont\edef\@IEEEPARstartFONTNAMESPACE{\fontname\font\space}% 4229 \xdef\@IEEEPARstartFONTNAME{\expandafter\@IEEEPARstartGETFIRSTWORD\@IEEEPARstartFONTNAMESPACE\relax}}}% 4230 % define a font based on this name with a point size equal to the desired 4231 % height of the drop letter 4232 \font\@IEEEPARstartsubfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenA\relax% 4233 % save this value as a counter (integer) value (sp points) 4234 \@IEEEtrantmpcountA=\@IEEEtrantmpdimenA% 4235 % now get the height of the actual letter produced by this font size 4236 \settoheight{\@IEEEtrantmpdimenB}{\@IEEEPARstartsubfont\@IEEEPARstartCAPSTYLE{#1}}% 4237 % If something bogus happens like the first argument is empty or the 4238 % current font is strange, do not allow a zero height. 4239 \ifdim\@IEEEtrantmpdimenB=0pt\relax% 4240 \typeout{** WARNING: IEEEPARstart drop letter has zero height! (line \the\inputlineno)}% 4241 \typeout{ Forcing the drop letter font size to 10pt.}% 4242 \@IEEEtrantmpdimenB=10pt% 4243 \fi% 4244 % and store it as a counter 4245 \@IEEEtrantmpcountB=\@IEEEtrantmpdimenB% 4246 % Since a font size doesn‘t exactly correspond to the height of the capital 4247 % letters in that font, the actual height of the letter, \@IEEEtrantmpcountB, 4248 % will be less than that desired, \@IEEEtrantmpcountA 4249 % we need to raise the font size, \@IEEEtrantmpdimenA 4250 % by \@IEEEtrantmpcountA / \@IEEEtrantmpcountB 4251 % But, TeX doesn‘t have floating point division, so we have to use integer 4252 % division. Hence the use of the counters. 4253 % We need to reduce the denominator so that the loss of the remainder will 4254 % have minimal affect on the accuracy of the result 4255 \divide\@IEEEtrantmpcountB by 200% 4256 \divide\@IEEEtrantmpcountA by \@IEEEtrantmpcountB% 4257 % Then reequalize things when we use TeX‘s ability to multiply by 4258 % floating point values 4259 \@IEEEtrantmpdimenB=0.005\@IEEEtrantmpdimenA% 4260 \multiply\@IEEEtrantmpdimenB by \@IEEEtrantmpcountA% 4261 % \@IEEEPARstartfont is globaly set to the calculated font of the big letter 4262 % We need to carry this out of the local calculation area to to create the 4263 % big letter. 4264 \global\font\@IEEEPARstartfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenB% 4265 % Now set \@IEEEtrantmpdimenA to the width of the big letter 4266 % We need to carry this out of the local calculation area to set the 4267 % hanging indent 4268 \settowidth{\global\@IEEEtrantmpdimenA}{\@IEEEPARstartfont 4269 \@IEEEPARstartCAPSTYLE{#1\@IEEEPARstartITLCORRECT}}}% 4270 % end of the isolated calculation environment 4271 % add in the extra clearance we want 4272 \advance\@IEEEtrantmpdimenA by \@IEEEPARstartSEP\relax% 4273 % add in the optional offset 4274 \advance\@IEEEtrantmpdimenA by \@IEEEPARstartHOFFSET\relax% 4275 % V1.7 don‘t allow negative offsets to produce negative hanging indents 4276 \@IEEEtrantmpdimenB\@IEEEtrantmpdimenA 4277 \ifnum\@IEEEtrantmpdimenB < 0 \@IEEEtrantmpdimenB 0pt\fi 4278 % \@IEEEtrantmpdimenA has the width of the big letter plus the 4279 % separation space and \@IEEEPARstartfont is the font we need to use 4280 % Now, we make the letter and issue the hanging indent command 4281 % The letter is placed in a box of zero width and height so that other 4282 % text won‘t be displaced by it. 4283 \hangindent\@IEEEtrantmpdimenB\hangafter=-\@IEEEPARstartDROPLINES% 4284 \makebox[0pt][l]{\hspace{-\@IEEEtrantmpdimenA}% 4285 \raisebox{-\@IEEEPARstartDROPDEPTH}[0pt][0pt]{\hspace{\@IEEEPARstartHOFFSET}% 4286 \@IEEEPARstartfont\@IEEEPARstartCAPSTYLE{#1\@IEEEPARstartITLCORRECT}% 4287 \hspace{\@IEEEPARstartSEP}}}% 4288 {\@IEEEPARstartWORDFONTSTYLE{\@IEEEPARstartWORDCAPSTYLE{\selectfont#2}}}} 4289 4290 4291 4292 4293 4294 4295 % determines if the space remaining on a given page is equal to or greater 4296 % than the specified space of argument one 4297 % if not, execute argument two (only if the remaining space is greater than zero) 4298 % and issue a \newpage 4299 % 4300 % example: \@IEEEtranneedspace{2in}{\vfill} 4301 % 4302 % Does not take into consideration rubber shrinkage, so it tends to 4303 % be overly cautious 4304 % Based on an example posted by Donald Arseneau 4305 % Note this macro uses \@IEEEtrantmpdimenB internally for calculations, 4306 % so DO NOT PASS \@IEEEtrantmpdimenB to this routine 4307 % if you need a dimen register, import with \@IEEEtrantmpdimenA instead 4308 \def\@IEEEtranneedspace#1#2{\penalty-100\begingroup%shield temp variable 4309 \@IEEEtrantmpdimenB\pagegoal\advance\@IEEEtrantmpdimenB-\pagetotal% space left 4310 \ifdim #1>\@IEEEtrantmpdimenB\relax% not enough space left 4311 \ifdim\@IEEEtrantmpdimenB>\z@\relax #2\fi% 4312 \newpage% 4313 \fi\endgroup} 4314 4315 4316 4317 % IEEEbiography ENVIRONMENT 4318 % Allows user to enter biography leaving place for picture (adapts to font size) 4319 % As of V1.5, a new optional argument allows you to have a real graphic! 4320 % V1.5 and later also fixes the "colliding biographies" which could happen when a 4321 % biography‘s text was shorter than the space for the photo. 4322 % MDS 7/2001 4323 % V1.6 prevent multiple biographies from making multiple TOC entries 4324 \newif\if@IEEEbiographyTOCentrynotmade 4325 \global\@IEEEbiographyTOCentrynotmadetrue 4326 4327 % biography counter so hyperref can jump directly to the biographies 4328 % and not just the previous section 4329 \newcounter{IEEEbiography} 4330 \setcounter{IEEEbiography}{0} 4331 4332 % photo area size 4333 \def\@IEEEBIOphotowidth{1.0in} % width of the biography photo area 4334 \def\@IEEEBIOphotodepth{1.25in} % depth (height) of the biography photo area 4335 % area cleared for photo 4336 \def\@IEEEBIOhangwidth{1.14in} % width cleared for the biography photo area 4337 \def\@IEEEBIOhangdepth{1.25in} % depth cleared for the biography photo area 4338 % actual depth will be a multiple of 4339 % \baselineskip, rounded up 4340 \def\@IEEEBIOskipN{4\baselineskip}% nominal value of the vskip above the biography 4341 4342 \newenvironment{IEEEbiography}[2][]{\normalfont\@IEEEcompsoconly{\sffamily}\footnotesize% 4343 \unitlength 1in\parskip=0pt\par\parindent 1em\interlinepenalty500% 4344 % we need enough space to support the hanging indent 4345 % the nominal value of the spacer 4346 % and one extra line for good measure 4347 \@IEEEtrantmpdimenA=\@IEEEBIOhangdepth% 4348 \advance\@IEEEtrantmpdimenA by \@IEEEBIOskipN% 4349 \advance\@IEEEtrantmpdimenA by 1\baselineskip% 4350 % if this page does not have enough space, break it and lets start 4351 % with a new one 4352 \@IEEEtranneedspace{\@IEEEtrantmpdimenA}{\relax}% 4353 % nominal spacer can strech, not shrink use 1fil so user can out stretch with \vfill 4354 \vskip \@IEEEBIOskipN plus 1fil minus 0\baselineskip% 4355 % the default box for where the photo goes 4356 \def\@IEEEtempbiographybox{{\setlength{\fboxsep}{0pt}\framebox{% 4357 \begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}\centering PLACE\\ PHOTO\\ HERE \end{minipage}}}}% 4358 % 4359 % detect if the optional argument was supplied, this requires the 4360 % \@ifmtarg command as defined in the appendix section above 4361 % and if so, override the default box with what they want 4362 \@ifmtarg{#1}{\relax}{\def\@IEEEtempbiographybox{\mbox{\begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}% 4363 \centering% 4364 #1% 4365 \end{minipage}}}}% end if optional argument supplied 4366 % Make an entry into the table of contents only if we have not done so before 4367 \if@IEEEbiographyTOCentrynotmade% 4368 % link labels to the biography counter so hyperref will jump 4369 % to the biography, not the previous section 4370 \setcounter{IEEEbiography}{-1}% 4371 \refstepcounter{IEEEbiography}% 4372 \addcontentsline{toc}{section}{Biographies}% 4373 \global\@IEEEbiographyTOCentrynotmadefalse% 4374 \fi% 4375 % one more biography 4376 \refstepcounter{IEEEbiography}% 4377 % Make an entry for this name into the table of contents 4378 \addcontentsline{toc}{subsection}{#2}% 4379 % V1.6 properly handle if a new paragraph should occur while the 4380 % hanging indent is still active. Do this by redefining \par so 4381 % that it will not start a new paragraph. (But it will appear to the 4382 % user as if it did.) Also, strip any leading pars, newlines, or spaces. 4383 \let\@IEEEBIOORGparCMD=\par% save the original \par command 4384 \edef\par{\hfil\break\indent}% the new \par will not be a "real" \par 4385 \settoheight{\@IEEEtrantmpdimenA}{\@IEEEtempbiographybox}% get height of biography box 4386 \@IEEEtrantmpdimenB=\@IEEEBIOhangdepth% 4387 \@IEEEtrantmpcountA=\@IEEEtrantmpdimenB% countA has the hang depth 4388 \divide\@IEEEtrantmpcountA by \baselineskip% calculates lines needed to produce the hang depth 4389 \advance\@IEEEtrantmpcountA by 1% ensure we overestimate 4390 % set the hanging indent 4391 \hangindent\@IEEEBIOhangwidth% 4392 \hangafter-\@IEEEtrantmpcountA% 4393 % reference the top of the photo area to the top of a capital T 4394 \settoheight{\@IEEEtrantmpdimenB}{\mbox{T}}% 4395 % set the photo box, give it zero width and height so as not to disturb anything 4396 \noindent\makebox[0pt][l]{\hspace{-\@IEEEBIOhangwidth}\raisebox{\@IEEEtrantmpdimenB}[0pt][0pt]{% 4397 \raisebox{-\@IEEEBIOphotodepth}[0pt][0pt]{\@IEEEtempbiographybox}}}% 4398 % now place the author name and begin the bio text 4399 \noindent\textbf{#2\ }\@IEEEgobbleleadPARNLSP}{\relax\let\par=\@IEEEBIOORGparCMD\par% 4400 % 7/2001 V1.5 detect when the biography text is shorter than the photo area 4401 % and pad the unused area - preventing a collision from the next biography entry 4402 % MDS 4403 \ifnum \prevgraf <\@IEEEtrantmpcountA\relax% detect when the biography text is shorter than the photo 4404 \advance\@IEEEtrantmpcountA by -\prevgraf% calculate how many lines we need to pad 4405 \advance\@IEEEtrantmpcountA by -1\relax% we compensate for the fact that we indented an extra line 4406 \@IEEEtrantmpdimenA=\baselineskip% calculate the length of the padding 4407 \multiply\@IEEEtrantmpdimenA by \@IEEEtrantmpcountA% 4408 \noindent\rule{0pt}{\@IEEEtrantmpdimenA}% insert an invisible support strut 4409 \fi% 4410 \par\normalfont} 4411 4412 4413 4414 % V1.6 4415 % added biography without a photo environment 4416 \newenvironment{IEEEbiographynophoto}[1]{% 4417 % Make an entry into the table of contents only if we have not done so before 4418 \if@IEEEbiographyTOCentrynotmade% 4419 % link labels to the biography counter so hyperref will jump 4420 % to the biography, not the previous section 4421 \setcounter{IEEEbiography}{-1}% 4422 \refstepcounter{IEEEbiography}% 4423 \addcontentsline{toc}{section}{Biographies}% 4424 \global\@IEEEbiographyTOCentrynotmadefalse% 4425 \fi% 4426 % one more biography 4427 \refstepcounter{IEEEbiography}% 4428 % Make an entry for this name into the table of contents 4429 \addcontentsline{toc}{subsection}{#1}% 4430 \normalfont\@IEEEcompsoconly{\sffamily}\footnotesize\interlinepenalty500% 4431 \vskip 4\baselineskip plus 1fil minus 0\baselineskip% 4432 \parskip=0pt\par% 4433 \noindent\textbf{#1\ }\@IEEEgobbleleadPARNLSP}{\relax\par\normalfont} 4434 4435 4436 % provide the user with some old font commands 4437 % got this from article.cls 4438 \DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm} 4439 \DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf} 4440 \DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt} 4441 \DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} 4442 \DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit} 4443 \DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl} 4444 \DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc} 4445 \DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal} 4446 \DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal} 4447 4448 4449 % SPECIAL PAPER NOTICE COMMANDS 4450 % 4451 % holds the special notice text 4452 \def\@IEEEspecialpapernotice{\relax} 4453 4454 % for special papers, like invited papers, the user can do: 4455 % \IEEEspecialpapernotice{(Invited Paper)} before \maketitle 4456 \def\IEEEspecialpapernotice#1{\ifCLASSOPTIONconference% 4457 \def\@IEEEspecialpapernotice{{\sublargesize\textit{#1}\vspace*{1em}}}% 4458 \else% 4459 \def\@IEEEspecialpapernotice{{\\*[1.5ex]\sublargesize\textit{#1}}\vspace*{-2ex}}% 4460 \fi} 4461 4462 4463 4464 4465 % PUBLISHER ID COMMANDS 4466 % to insert a publisher‘s ID footer 4467 % V1.6 \IEEEpubid has been changed so that the change in page size and style 4468 % occurs in \maketitle. \IEEEpubid must now be issued prior to \maketitle 4469 % use \IEEEpubidadjcol as before - in the second column of the title page 4470 % These changes allow \maketitle to take the reduced page height into 4471 % consideration when dynamically setting the space between the author 4472 % names and the maintext. 4473 % 4474 % the amount the main text is pulled up to make room for the 4475 % publisher‘s ID footer 4476 % IEEE uses about 1.3\baselineskip for journals, 4477 % dynamic title spacing will clean up the fraction 4478 \def\@IEEEpubidpullup{1.3\baselineskip} 4479 \ifCLASSOPTIONtechnote 4480 % for technotes it must be an integer of baselineskip as there can be no 4481 % dynamic title spacing for two column mode technotes (the title is in the 4482 % in first column) and we should maintain an integer number of lines in the 4483 % second column 4484 % There are some examples (such as older issues of "Transactions on 4485 % Information Theory") in which IEEE really pulls the text off the ID for 4486 % technotes - about 0.55in (or 4\baselineskip). We‘ll use 2\baselineskip 4487 % and call it even. 4488 \def\@IEEEpubidpullup{2\baselineskip} 4489 \fi 4490 4491 % V1.7 compsoc does not use a pullup 4492 \ifCLASSOPTIONcompsoc 4493 \def\@IEEEpubidpullup{0pt} 4494 \fi 4495 4496 % holds the ID text 4497 \def\@IEEEpubid{\relax} 4498 4499 % flag so \maketitle can tell if \IEEEpubid was called 4500 \newif\if@IEEEusingpubid 4501 \global\@IEEEusingpubidfalse 4502 % issue this command in the page to have the ID at the bottom 4503 % V1.6 use before \maketitle 4504 \def\IEEEpubid#1{\def\@IEEEpubid{#1}\global\@IEEEusingpubidtrue} 4505 4506 4507 % command which will pull up (shorten) the column it is executed in 4508 % to make room for the publisher ID. Place in the second column of 4509 % the title page when using \IEEEpubid 4510 % Is smart enough not to do anything when in single column text or 4511 % if the user hasn‘t called \IEEEpubid 4512 % currently needed in for the second column of a page with the 4513 % publisher ID. If not needed in future releases, please provide this 4514 % command and define it as \relax for backward compatibility 4515 % v1.6b do not allow command to operate if the peer review option has been 4516 % selected because \IEEEpubidadjcol will not be on the cover page. 4517 % V1.7 do nothing if compsoc 4518 \def\IEEEpubidadjcol{\ifCLASSOPTIONcompsoc\else\ifCLASSOPTIONpeerreview\else 4519 \if@twocolumn\if@IEEEusingpubid\enlargethispage{-\@IEEEpubidpullup}\fi\fi\fi\fi} 4520 4521 % Special thanks to Peter Wilson, Daniel Luecking, and the other 4522 % gurus at comp.text.tex, for helping me to understand how best to 4523 % implement the IEEEpubid command in LaTeX. 4524 4525 4526 4527 %% Lockout some commands under various conditions 4528 4529 % general purpose bit bucket 4530 \newsavebox{\@IEEEtranrubishbin} 4531 4532 % flags to prevent multiple warning messages 4533 \newif\if@IEEEWARNthanks 4534 \newif\if@IEEEWARNIEEEPARstart 4535 \newif\if@IEEEWARNIEEEbiography 4536 \newif\if@IEEEWARNIEEEbiographynophoto 4537 \newif\if@IEEEWARNIEEEpubid 4538 \newif\if@IEEEWARNIEEEpubidadjcol 4539 \newif\if@IEEEWARNIEEEmembership 4540 \newif\if@IEEEWARNIEEEaftertitletext 4541 \@IEEEWARNthankstrue 4542 \@IEEEWARNIEEEPARstarttrue 4543 \@IEEEWARNIEEEbiographytrue 4544 \@IEEEWARNIEEEbiographynophototrue 4545 \@IEEEWARNIEEEpubidtrue 4546 \@IEEEWARNIEEEpubidadjcoltrue 4547 \@IEEEWARNIEEEmembershiptrue 4548 \@IEEEWARNIEEEaftertitletexttrue 4549 4550 4551 %% Lockout some commands when in various modes, but allow them to be restored if needed 4552 %% 4553 % save commands which might be locked out 4554 % so that the user can later restore them if needed 4555 \let\@IEEESAVECMDthanks\thanks 4556 \let\@IEEESAVECMDIEEEPARstart\IEEEPARstart 4557 \let\@IEEESAVECMDIEEEbiography\IEEEbiography 4558 \let\@IEEESAVECMDendIEEEbiography\endIEEEbiography 4559 \let\@IEEESAVECMDIEEEbiographynophoto\IEEEbiographynophoto 4560 \let\@IEEESAVECMDendIEEEbiographynophoto\endIEEEbiographynophoto 4561 \let\@IEEESAVECMDIEEEpubid\IEEEpubid 4562 \let\@IEEESAVECMDIEEEpubidadjcol\IEEEpubidadjcol 4563 \let\@IEEESAVECMDIEEEmembership\IEEEmembership 4564 \let\@IEEESAVECMDIEEEaftertitletext\IEEEaftertitletext 4565 4566 4567 % disable \IEEEPARstart when in draft mode 4568 % This may have originally been done because the pre-V1.6 drop letter 4569 % algorithm had problems with a non-unity baselinestretch 4570 % At any rate, it seems too formal to have a drop letter in a draft 4571 % paper. 4572 \ifCLASSOPTIONdraftcls 4573 \def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** ATTENTION: \noexpand\IEEEPARstart 4574 is disabled in draft mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse} 4575 \fi 4576 % and for technotes 4577 \ifCLASSOPTIONtechnote 4578 \def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** WARNING: \noexpand\IEEEPARstart 4579 is locked out for technotes (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse} 4580 \fi 4581 4582 4583 % lockout unneeded commands when in conference mode 4584 \ifCLASSOPTIONconference 4585 % when locked out, \thanks, \IEEEbiography, \IEEEbiographynophoto, \IEEEpubid, 4586 % \IEEEmembership and \IEEEaftertitletext will all swallow their given text. 4587 % \IEEEPARstart will output a normal character instead 4588 % warn the user about these commands only once to prevent the console screen 4589 % from filling up with redundant messages 4590 \def\thanks#1{\if@IEEEWARNthanks\typeout{** WARNING: \noexpand\thanks 4591 is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNthanksfalse} 4592 \def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** WARNING: \noexpand\IEEEPARstart 4593 is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse} 4594 4595 4596 % LaTeX treats environments and commands with optional arguments differently. 4597 % the actual ("internal") command is stored as \\commandname 4598 % (accessed via \csname\string\commandname\endcsname ) 4599 % the "external" command \commandname is a macro with code to determine 4600 % whether or not the optional argument is presented and to provide the 4601 % default if it is absent. So, in order to save and restore such a command 4602 % we would have to save and restore \\commandname as well. But, if LaTeX 4603 % ever changes the way it names the internal names, the trick would break. 4604 % Instead let us just define a new environment so that the internal 4605 % name can be left undisturbed. 4606 \newenvironment{@IEEEbogusbiography}[2][]{\if@IEEEWARNIEEEbiography\typeout{** WARNING: \noexpand\IEEEbiography 4607 is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEbiographyfalse% 4608 \setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax} 4609 % and make biography point to our bogus biography 4610 \let\IEEEbiography=\@IEEEbogusbiography 4611 \let\endIEEEbiography=\end@IEEEbogusbiography 4612 4613 \renewenvironment{IEEEbiographynophoto}[1]{\if@IEEEWARNIEEEbiographynophoto\typeout{** WARNING: \noexpand\IEEEbiographynophoto 4614 is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEbiographynophotofalse% 4615 \setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax} 4616 4617 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lockouts (line \the\inputlineno).}% 4631 \let\thanks\@IEEESAVECMDthanks% 4632 \let\IEEEPARstart\@IEEESAVECMDIEEEPARstart% 4633 \let\IEEEbiography\@IEEESAVECMDIEEEbiography% 4634 \let\endIEEEbiography\@IEEESAVECMDendIEEEbiography% 4635 \let\IEEEbiographynophoto\@IEEESAVECMDIEEEbiographynophoto% 4636 \let\endIEEEbiographynophoto\@IEEESAVECMDendIEEEbiographynophoto% 4637 \let\IEEEpubid\@IEEESAVECMDIEEEpubid% 4638 \let\IEEEpubidadjcol\@IEEESAVECMDIEEEpubidadjcol% 4639 \let\IEEEmembership\@IEEESAVECMDIEEEmembership% 4640 \let\IEEEaftertitletext\@IEEESAVECMDIEEEaftertitletext} 4641 4642 4643 4644 % need a backslash character for typeout output 4645 {\catcode`\|=0 \catcode`\\=12 4646 |xdef|@IEEEbackslash{\}} 4647 4648 4649 % hook to allow easy disabling of all legacy warnings 4650 \def\@IEEElegacywarn#1#2{\typeout{** ATTENTION: \@IEEEbackslash #1 is deprecated (line \the\inputlineno). 4651 Use \@IEEEbackslash #2 instead.}} 4652 4653 4654 % provide for legacy commands 4655 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\def\biographynophoto{\@IEEElegacywarn{biographynophoto}{IEEEbiographynophoto}\IEEEbiographynophoto} 4671 \def\keywords{\@IEEElegacywarn{keywords}{IEEEkeywords}\IEEEkeywords} 4672 \def\endbiography{\endIEEEbiography} 4673 \def\endbiographynophoto{\endIEEEbiographynophoto} 4674 \def\endkeywords{\endIEEEkeywords} 4675 4676 4677 % provide for legacy IED commands/lengths when possible 4678 \let\labelindent\IEEElabelindent 4679 \def\calcleftmargin{\@IEEElegacywarn{calcleftmargin}{IEEEcalcleftmargin}\IEEEcalcleftmargin} 4680 \def\setlabelwidth{\@IEEElegacywarn{setlabelwidth}{IEEEsetlabelwidth}\IEEEsetlabelwidth} 4681 \def\usemathlabelsep{\@IEEElegacywarn{usemathlabelsep}{IEEEusemathlabelsep}\IEEEusemathlabelsep} 4682 \def\iedlabeljustifyc{\@IEEElegacywarn{iedlabeljustifyc}{IEEEiedlabeljustifyc}\IEEEiedlabeljustifyc} 4683 \def\iedlabeljustifyl{\@IEEElegacywarn{iedlabeljustifyl}{IEEEiedlabeljustifyl}\IEEEiedlabeljustifyl} 4684 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Draft-JSS.tex
1 %\documentclass[10pt,journal,cspaper,compsoc]{IEEETran} 2 \documentclass[journal]{IEEETran} 3 %\documentclass{comjnl} 4 \usepackage{times} 5 \usepackage{graphicx} 6 \usepackage{psfrag} 7 \usepackage{epsfig} 8 \usepackage{algorithm} 9 \usepackage{algorithmic} 10 %\usepackage{algpseudocode} 11 \usepackage{multicol} 12 \usepackage{multirow} 13 \usepackage{setspace} 14 15 \usepackage{cite} 16 \usepackage{array} 17 \usepackage{amssymb} 18 \usepackage[cmex10]{amsmath} 19 \interdisplaylinepenalty=2500 20 \usepackage{mdwmath} 21 \usepackage{mdwtab} 22 \usepackage[tight,footnotesize]{subfigure} 23 %\usepackage{fixltx2e} 24 \usepackage{mdwlist} 25 \usepackage[amssymb]{SIunits} 26 \usepackage[usenames]{color} 27 \usepackage{amsmath} 28 \usepackage{caption} 29 \usepackage{slashbox} 30 \usepackage{yhmath} 31 32 33 34 \begin{document} 35 36 \title{Quasi-Static Fault-Tolerant Scheduling Schemes for Energy-Efficient Hard Real-Time Systems} 37 \author{Tongquan~Wei,~\IEEEmembership{Member,~IEEE,} 38 Piyush~Mishra,~\IEEEmembership{Member,~IEEE,} 39 Kaijie~Wu,~\IEEEmembership{Member,~IEEE,} 40 and Junlong~Zhou 41 42 43 \thanks{T. Wei and J. Zhou are with the CS department of East China Normal University, Shanghai, China 200241 email: tqwei@cs.ecnu.edu.cn} 44 \thanks{P. Mishra is with the GE Global Research, Niskayuna, NY 12309.} 45 \thanks{K. Wu are with the ECE department of University of Illinois, Chicago, IL 60607.} 46 \thanks{The preliminary version of this manuscript appeared in ICCAD, $2006$.} 47 \thanks{This work was supported in part by the Fundamental Research Funds for the Central Universities of China under the grant No. 78220021.} 48 } 49 \maketitle 50 51 52 53 \begin{abstract} 54 This paper investigates fault tolerance and Dynamic Voltage Scaling (DVS) in hard real-time systems. The authors present quasi-static task scheduling algorithms that consist of offline components and online components. The offline components are designed the way they enable the online components to achieve energy savings by using the dynamic slack due to variations in task execution times and uncertainties in fault occurrences. The proposed schemes utilize a fault model that considers the effects of voltage scaling on transient fault rate. Simulation results based on real-life task sets and processor data sheets show that the proposed scheduling schemes achieve energy savings of up to 50\% over the state-of-art low-energy offline scheduling techniques and incur negligible runtime overheads. A hard real-time real-life test bed has been developed allowing the validation of the proposed algorithms. 55 \end{abstract} 56 57 \begin{IEEEkeywords} 58 Energy-efficient dynamic scheduling, dynamic voltage scaling (DVS), fault tolerance, hard real-time embedded systems. 59 \end{IEEEkeywords} 60 61 62 63 64 \section {Introduction}\label{Introduction} 65 The number of faults in hardware, particularly the transient faults, has been rising continuously due to the increasing complexity of design, aggressive technology scaling, and extreme operating conditions. For example, the increasing integration level of transistors, reducing feature sizes, and lowering voltage levels are making the integrated circuits highly susceptible to radiation-induced bit-flips. In addition, high-energy particles, such as neutrons from cosmic radiation, are able to introduce transient faults in electronic systems \cite{NORMAND96}. On the other hand, a growing number of complex safety critical applications operate under extreme conditions and demand ultra-reliability and high performance. For example, hard real-time systems deployed in navigation, process control, and system surveillance require the high fault tolerance without sacrificing the feasibility of task sets. The need for reliability is rising even in non-critical applications which are prone to operate in harsher environments but have lower expectancy of failures. Common examples include outdoor sensor networks and massive communication infrastructure deployed in fields which suffer frequent physical abuse and are often exposed to strong radiation. 66 67 68 Numerous fault-tolerance techniques have been proposed for real-time systems \cite{SHIN84,SHIN87,KWAK01,AXER11,HUANG11CODES}. One of the typically used fault-tolerance techniques is online concurrent fault detection followed by a hardware-based checkpointing and rollback recovery mechanism. 69 It allows processors to rollback to the previously known valid states to resume normal executions by exploiting the slack time available in task schedules. Traditionally, fault tolerance techniques aim to maximize the fault coverage and minimize the fault detection latency and associated redundancy costs \cite{PRADHAN86}. The costs are usually measured in terms of hardware, time, or information overhead and are of great significance in real-time embedded systems due to their severe resource constraints. 70 71 72 Owing to the fast-evolving application of real-time systems in battery-powered portable devices, energy has emerged as another important design constraint. Dynamic power management is an active area of research and several techniques have been proposed to minimize energy consumption at the system level \cite{BENINI00}. The energy efficiency is achieved by dynamically reconfiguring active system components and selectively turning off system components when they are idle. Dynamic Voltage Scaling (DVS) is a widely used system level power management technique that exploits technological advances in power supply circuits to reduce the energy consumption. It reduces the processor power consumption by dynamically scaling down the processor supply voltage at the cost of the increased execution times. 73 74 75 Fault tolerance and energy have been jointly investigated in the literature. On one hand, with the continuous shrinking of the feature size and reducing of voltage margins, it is expected that all digital computing systems will be remarkably vulnerable to transient faults \cite{ERNST04}. Fault-tolerance in real-time systems is typically achieved by using some forms of redundancy. This redundancy causes extra power dissipations and hence necessitates energy efficient schemes for batter-powered real-time systems to reduce heat dissipation and extend operational lifetime. 76 On the other hand, energy management through dynamic voltage scaling has adverse effects on system reliability. Scaling down the supply voltage results in an increase in the rate of transient faults \cite{ZHU04}. Consequently, both fault-tolerance and energy efficiency have been the primary design goals for real-time systems, integrated in the design process at all levels for joint optimization with the system feasibility. 77 78 79 80 In the recent past, considerable attention has been paid to exploit the DVS technique to achieve energy savings in the presence of transient faults and a number of excellent energy-efficient fault-tolerance schemes have been designed for real-time embedded systems \cite{ZHANG03+,MELHEM04,ZHU04,WEI06,ZHANG06,ZHAO09ICCAD,ZHAO11DAC,Iqbal11}. In this paper a systematic approach is proposed to derive energy-efficient fault-tolerant task schedules for hard real-time embedded systems by utilizing both the static and dynamic slack in the task schedules. Based on the observation that the probability of the single event upset (SEU)-induced faults remains low in the foreseeable future and fault-free condition will continue to dominate \cite{REED03,WEULERSSE06,LANGLEY03}, one fundamental innovation has been introduced in the proposed energy-efficient fault-tolerance schemes. 81 That is, unlike the traditional approach that focuses on designing offline energy-efficient fault-tolerance algorithms, the proposed scheme aims to achieve further round of energy savings by designing efficient offline algorithms that enable the adaptation of the offline schedules to the runtime behavior of fault occurrences. 82 83 84 85 \subsection {Related Work}\label{Related Work} 86 Extensive research has been performed to investigate the energy efficiency of real-time systems from both offline and online perspective \cite{SHIN99,GRUIAN01,PILLAI01,SAEWONG03,KRISHNA03,MOCHOCKI07,HUANG09,HUANG11RTSJ,PERATHONER10}. The power efficient version of fixed-priority preemptive scheduling such as rate monotonic scheduling was explored by Shin and Choi in \cite{SHIN99}. Power reduction is achieved by exploiting the slack time both inherent in system schedule and due to runtime variations in task execution time. 87 Similarly, Gruian et al. presented a scheduling policy for hard real-time tasks with fixed priorities assigned in a rate monotonic manner \cite{GRUIAN01}. The offline scheduling uses exact timing analysis to derive multiple voltage scaling factors for each task based on stochastic characteristics of task execution time. The online scheduling policy distributes available slack time on priority basis. 88 Based on the voltage scaling algorithms proposed in \cite{PILLAI01}, four voltage scaling algorithms including Sys-Clock, PM-Clock, and DPM-Clock were proposed in \cite{SAEWONG03} for different hardware which may have high or low voltage scaling overhead and different taskset characteristics. Of these algorithms, Sys-Clock assigns a single frequency to all tasks in a task set, PM-Clock assign multiple frequencies to tasks in a task set, and DPM-Clock dynamically adapts offline task schedule to runtime behaviors of task execution times. 89 Krishna and Lee \cite{KRISHNA03} described a two phase heuristic for independent and periodic tasks. The heuristic has an offline component computing a voltage schedule based on worst case execution time, and an online component utilizing slack time due to variations in task execution time for further round of energy savings. 90 In \cite{MOCHOCKI07}, both offline and online scheduling schemes were proposed to handle the transition time and energy overhead of DVS processors. The offline scheme generates task schedule during design time based on a prior known task execution time while the online scheme effectively accommodates runtime variations of task execution time to achieve energy savings. 91 Online algorithms were presented in \cite{HUANG09} and \cite{HUANG11RTSJ} to effectively reduce system energy consumption to handle event streams with hard real-time guarantees. The scheduling scheme adaptively controls the power mode of the processor to postpone the processing of arrival events as late as possible. 92 Although energy efficiency in real-time systems were explored from both offline and online aspects in the above literature, fault tolerance which is an another important design constraints were not considered. 93 94 95 Fault-tolerance is another important design constraint in energy efficient real-time systems. Joint optimization of energy and fault-tolerance in real-time embedded systems has attracted considerable attention in the past decade \cite{MELHEM04,ZHANG03+,ZHANG06,Iqbal11,ZHAO11DAC,ZHAO09ICCAD,WEI11TCAD}. 96 Melhem et al. proposed DVS techniques to exploit slacks in a task schedule to reduce energy consumption while tolerating faults during task execution \cite{MELHEM04}. A task in the task schedule is assumed to be susceptible to at most one fault occurrence and the processor can scale its frequency in a continuous range. 97 In \cite{ZHANG03+} and \cite{ZHANG06} a fixed priority offline scheduling scheme was proposed based on the rate monotonic scheduling to tolerate faults in hard real-time systems. Practical design issues such as checkpointing cost and voltage switching overhead are considered. 98 Fault-tolerance scheduling techniques were developed in \cite{ZHAO11DAC} and \cite{ZHAO09ICCAD} to minimize the system-level energy consumption while still preserving the system¡¯s original reliability. 99 Fault tolerance is achieved by reserving shared recovery blocks that can be used by any task at the runtime. 100 In \cite{Iqbal11}, the authors presented a soft error aware energy efficient scheduling technique for soft real-time systems with stochastic task execution times. The task execution time estimation is modeled as a joint state-space model, the solution of which is found by an online Monte Carlo sampling based recursive technique. 101 102 103 An offline reliability-aware power management scheme is presented in \cite{ZHU08} for real-time tasks with probabilistic execution times. The scheme puts aside just enough slack to guarantee the required reliability while leaving more slack for energy management to achieve better energy savings. In \cite{POP07}, the authors addressed the scheduling and voltage scaling for hard real-time applications that have been statically mapped on heterogeneous distributed embedded systems. Tasks in a given task set are assumed to share a common deadline and the effect of voltage scaling on system reliability is taken into account. Shafik et al. \cite{SHAFIK10} examined the impact of application 104 task mapping on the reliability of MPSoC. The number of transient faults is minimized without compromising the timeliness of the system. All these energy-aware fault-tolerance schemes, however, statically derive offline task schedules to guarantee hard timing constraints, hence are conservative and can not utilize the dynamic slack due to variations in task execution times and uncertainties in fault occurrences for further energy savings. 105 106 107 Zhang et al. developed an online scheduling algorithm that combines checkpointing with DVS to tolerate faults in real-time uni-processor systems with periodic tasks \cite{ZHANG03}. However, this scheme can not handle hard real-time task scheduling. In \cite{IZOSIMOV08}, the authors present an approach to the synthesis of fault-tolerant schedules for embedded applications with soft and hard real-time constraints. A set of task schedules is synthesized offline and, at run time, the scheduler selects the right schedule based on the fault occurrence and the actual task execution times such that hard timing constraints are guaranteed and the overall processor utilization is maximized. However, the presented approach does not take energy into account. 108 109 110 In this paper efficient scheduling schemes are proposed to combine offline feasibility analysis and online voltage scaling for hard real-time systems based on the exact timing analysis of the rate monotonic algorithm (RMA). Two offline scheduling algorithms that enable the dynamic adaptation are proposed. One is the application level voltage scaling (A-DVS) algorithm where all the tasks run at the same processor speed. The other one is the task level voltage scaling (T-DVS) algorithm where the tasks run at their individual speeds. Instead of iteratively deriving the response time of each task for feasibility analysis, the exact timing analysis approach \cite{LEHOCZKY89} is used in the proposed algorithms for feasibility analysis. This strategy strikingly simplifies the adaptation of the proposed offline A-DVS and T-DVS algorithms to the runtime behavior of fault occurrences. 111 The adaptation of the offline task schedules to the runtime behavior of fault occurrences is implemented by 1) pre-computing and saving in a lookup table the maximum slack requirements for the processor to dynamically slow down, 2) retrieving and comparing the stored slack time requirements with the generated cumulative slack in the runtime, and 3) dynamically scaling down processor speed when the generated slack time is equal to or greater than the stored slack requirements. 112 Xtrem \cite{CONTRERAS04}, a SimpleScalar-based Intel XScale processor simulator, was used to evaluate the runtime overhead of the proposed scheduling schemes in addition to extensive simulation experiments. A hard real-time test bed has been designed and the proposed algorithms were also verified on the test bed. 113 114 115 \subsection{Contributions and Outline}\label{Outline} 116 The main contributions of this paper are summarized as follows. 117 \begin{itemize} 118 \item Quasi-static task scheduling algorithms consisting of offline components and online components are proposed. The offline components are designed the way they enables the online components to save energy in the runtime using slack due to uncertainties in fault occurrences. 119 \item The proposed schemes are based on a fault model that considers the effect of DVS on transient fault rate. The worst case number of fault occurrences in a task at a certain voltage level is derived according to the given task level reliability goal. This strategy facilitates the design of systems with various reliability requirements. 120 \item In addition to being verified under simulation environments, the proposed schemes also are implemented and validated on a real-life hard real-time test bed. 121 \end{itemize} 122 123 124 The rest of the paper is organized as follows. Section \ref{Models} introduces the system models. Section \ref{Proposed Schemes} describes the feasibility analysis for ECRMA-based fault-tolerance task scheduling, and proposes two offline task scheduling algorithms with different DVS granularity. 125 Section \ref{Online-DVS} adapts the offline task schedules to the runtime behavior of task execution and fault occurrences. Section \ref{Experiments} presents the experimental results to demonstrate energy savings and runtime overhead. Section \ref{Implementation on testbed} describes the implementation of a hard real-time test bed for energy measurement and Section \ref{conclusion} concludes the paper. 126 127 128 129 \section{System Architecture and Models}\label{Models} 130 The focus of the study is a fixed-priority hard real-time embedded system comprising a DVS-capable uni-processor and a power-aware memory. It is assumed that the scheduler of the system is preemptive, such that, if required, the scheduler may suspend the current task and switch the system context to a new task according to its scheduling scheme. 131 132 133 \subsection{Architecture and Application Model}\label{Arch&APP Model} 134 Consider a task set $\Gamma$ consisting of $n$ independent periodic tasks \{$\tau_1, \tau_2, \cdots, \tau_n$ \}. The timing characteristics of the task $\tau_i$ are defined as a tuple $\tau_i = \{T_i, D_i, C_i\}$, where $T_i$ is the period, $D_i$ is the deadline, and $C_i$ is the worst case execution cycles. The hyper-period of the task set, denoted by $T$, is the lowest common multiple of all task periods $\{T_1, T_2,\cdots, T_n\}$. 135 136 137 It is assumed that tasks are arranged in the decreasing order of priorities according to the fixed priority rate monotonic algorithm (RMA) \cite{LIU73}, that is, $T_1 < T_2 <, \cdots, < T_n$ is such that the period of task $\tau_i$ is smaller than the period of task $\tau_j$ for $i<j$. The processor is assumed to support $L$ discrete frequency or voltage levels. Frequency levels and voltage levels are used interchangeably throughout this paper. Let $f_i$ denote the operating frequency of task $\tau_i$, where $i (1< i < n)$ is the index of the task in the task set $\Gamma$. The operating frequency $f_i$ of task $\tau_i$ can be expressed as a function of the processor voltage level $l$ at which the task is running, that is, $f_i = f(l)$. Tasks in a given task set is assumed to be scheduled using RMA and the resulting schedule is feasible under fault-free conditions at a certain voltage level. 138 139 140 141 \subsection{Fault and Recovery Model }\label{Fault Model} 142 It is assumed that a watchdog processor is used for timing checking. Faults are assumed to be detected using low-latency fault detection techniques such as the simultaneous multithreading scheme \cite{REINHARDT00} such that the fault detection overhead is small enough to be accounted for in task execution time. Upon detecting faults, system is assumed to recover via backward recovery mechanism, where a set of checkpoints are inserted into a computing system for fault-tolerance. At each checkpoint, valid system states are copied and stored for error recovery. If one or more faults are detected during computation, the application rolls back to the immediate previous checkpoint, retrieves the stored system states, and resumes computation from the checkpoint. 143 144 145 The reliability of a task is defined to be the probability of completing the task successfully subject to faults \cite{ZHU04}. Although reliability targets are typically given system-wide, it is a common practice to derive the per-task values (unit requirements) from system-wide values (system requirements). Assuming all tasks in a given task set share a common given reliability goal, then the task level reliability is maintained if all tasks in the task set finish their execution successfully under the given reliability target. Let $R_i$ denote the reliability of task $\tau_i$. $R_i$ is derived as follows. 146 147 148 Let $k_i$ denote the exact number of fault occurrences in task $\tau_i$, $f_i$ denote the operating frequency of task $\tau_i$ at the voltage level $l$ ($1 \leq l \leq L$), and $O_{il}$ denote the optimal number of checkpoints for task $\tau_i$ at the voltage level $l$ that minimizes the worst case response time of the task. Assuming checkpointing intervals are equal, the $O_{il}$ is then given by 149 $$O_{il} = \left \lceil \sqrt{\frac{k_i C_i}{c_s f_i}} - 1 \right \rceil \quad \text {or} \quad \left \lfloor \sqrt{\frac{k_i C_i}{c_s f_i}} - 1 \right \rfloor,$$ 150 where $C_i$ is the execution cycles of task $\tau_i$ and $c_s$ is the checkpointing overhead \cite{ZHANG06}. $c_s$ is assumed to be constant. For the sake of easy presentation, $O_{il}$ is simply denoted by 151 \begin{align}\label{eqn:OPTchekptNum} 152 O_{il} = \left\| \sqrt{ \frac{k_i C_i} {c_s f_i}} - 1 \right\|. 153 \end{align} 154 Let $OE_i$ be the overall execution time of an instance of task $\tau_i$. Considering the checkpointing overhead and fault recovery overhead, the $OE_i$ is derived as \cite{ZHANG06} 155 \begin{align}\label{eqn:OE-i} 156 OE_i = \frac {C_i} {f_i} + O_{il} \times c_s + \frac{k_i C_i}{f_i (O_{il}+1)} + 2k_i c_s. 157 \end{align} 158 159 160 Transient fault occurrences are typically modeled using the Poisson distribution. 161 Let $\lambda_l$ be the average fault arrival rate at the frequency level $l$. The $\lambda_l$ can be derived using the equation $\lambda_l = \gamma \times e^{-\alpha f_i},$ where $\gamma$ and $\alpha$ are constant parameters and $f_i$ is the operating frequency of the task $\tau_i$ \cite{ZHU04}. The probability of $k_i$ fault occurrences during the execution of task $\tau_i$ at frequency $f_i$ is thus given by 162 $$\frac{e^{- \lambda_l \times OE_i} \times ( \lambda_l \times OE_i)^{k_i}} {k_i!},$$ and the reliability $R_i$ of task $\tau_i$ is hence written as 163 \begin{align}\label{eqn:Reliability0} 164 R_i = \sum_{k_i}{\frac{e^{- \lambda_l \times OE_i} \times ( \lambda_l \times OE_i)^{k_i}} {k_i!}}. 165 \end{align} 166 This definition of reliability considers the fault occurrences during the whole interval of $OE_i$. In other words, the fault occurrences during the recovery of a task from faults is taken into account. 167 168 169 Let $R_g$ denote the task level reliability goal, then the reliability of task $\tau_i$ is maintained if the inequality 170 \begin{align}\label{eqn:Reliability} 171 R_g \le R_i 172 \end{align} 173 holds. Since $\lambda_l, OE_i$, and $k_i$ all are functions of the voltage level $l$ of task $\tau_i$, $R_i$ is also a function of the voltage level $l$ of task $\tau_i$. For a given voltage level $l$ ($1 \le l \le L$), $\lambda_l$ and $OE_i$ are known; thus, the worst case number of fault occurrences $k_i$ at the voltage level $l$ subject to target reliability $R_g$ can be iteratively derived using the inequality (\ref{eqn:Reliability}). 174 175 176 177 \subsection{Energy Model}\label{Energy Model} 178 The power consumption of a CMOS device can be modeled as the sum of dynamic power consumption and static power consumption. The average dynamic power consumption is a function of the supply voltage and the operating frequency. Let $p_{d}$, $V_{dd}$, and $f$ be the average dynamic power consumption, supply voltage, and operating frequency, respectively, then $p_{d} \propto {V_{dd}}^2 f$ holds \cite{WESTE92}. Assuming processors use voltage scaling technique to scale frequency, the operating frequency is then approximately linear with the supply voltage \cite{WESTE92}. As a result, the average dynamic power consumption can be estimated by a strictly increasing and convex function of the operating frequency, that is, $p_{d}\propto f^3$. 179 180 181 As technology advances towards deep sub-micro devices, the static power consumption due to leakage current and other current drawn continuously from the power supply has been increasing dramatically. It has been shown that the major contributors of the static power consumption are the subthreshold leakage current and the reverse bias junction current \cite{MARTIN02}. Let $p_s$ denote the static power consumption of a device, $I_{subn}$ denote the sub-threshold leakage current, and $I_j$ denote the reverse bias junction current, then the static power consumption of the device is given by $p_s = V_{dd} I_{subn} + |V_{bs}| I_j,$ 182 where $V_{bs}$ is the body bias voltage, and $V_{dd}$ is the supply voltage \cite{JEJURIKAR04}. For a certain generation of technology, the sub-threshold leakage current $I_{subn}$ is the function of the supply voltage $V_{dd}$, and the $V_{bs}$ and $I_j$ are technology constants. 183 184 185 The total energy ($E_{tot}$) consumed by real-time tasks in a given task set is hence estimated by 186 \begin{align} \label{eqn:Etot} 187 E_{tot} = \sum_{i=1}^n OE_i \times \frac{T}{T_i}\times (p_d + p_s), 188 \end{align} 189 where $OE_i$ is the overall execution time of task $\tau_i$, as is given in Equation (\ref{eqn:OE-i}), and $\frac{T}{T_i}$ is the number of instances of the task $\tau_i$ in the hyper-period $T$. 190 191 192 193 \section{Offline Scheduling Algorithms for Fault-Tolerant Hard Real-Time Systems}\label{Proposed Schemes} 194 The Rate Monotonic Algorithm (RMA), proposed by Liu and Layland in 1973, is an optimal fixed priority algorithm that schedules periodic tasks by assigning higher priorities to tasks with shorter periods \cite{LIU73}. 195 The classical analysis of RMA yields a conservative bound on the processor utilization below which a system is guaranteed to meet all task deadlines. 196 Lehoczky et al. showed that this conservative utilization bound of RMA can be relaxed based on the exact characterization of RMA (ECRMA) to derive both the necessary and sufficient conditions for the feasibility analysis of a schedule \cite{LEHOCZKY89}. This section first provides an overview of the ECRMA-based feasibility analysis of fault-tolerant task schedules, then presents the two proposed offline task scheduling algorithms of different granularity. 197 198 199 200 \subsection{ECRMA-Based Feasibility Analysis of Fault-Tolerant Task Schedules}\label{Feasibility of FT RMA} 201 The worst case behavior of RMA occurs when all tasks in a task set are instantiated simultaneously and are ready for execution immediately after initiation. This time instant is called critical instant. It has been shown that a schedule of independent periodic tasks is feasible if the first instance of each task is schedulable when it is instantiated at a critical instant. 202 Lehoczky et al. showed that periodic tasks in a task set are schedulable for all task phasing if and only if at any time instance before the deadline of a task, the total demand for processor time by the task is equal to or less than the current available processor time \cite{LEHOCZKY89}. Specifically, let $$W_i(t)= \sum_{j=1}^{i} OE_j \left\lceil \frac{t}{T_j} \right\rceil \notag 203 $$ 204 denote the total demand of task $\tau_i$ for processor time over $[0, t]$, assuming $0$ is the critical instant. The necessary and sufficient condition for the periodic task $\tau_i$ to be schedulable is given by $$\min_t \left(\frac{W_i(t)}{t}\right) \le 1, \quad 0 < t < T_i, 205 $$ 206 and the entire task set is schedulable iff 207 \begin{align}\label{equ:taskSet iff condition} 208 \max_i \left( \min_t \left(\frac{W_i(t)}{t}\right) \right) \le 1, \quad 0 < t < T_i, \ 1 \le i \le n. 209 \end{align} 210 211 212 Further, it was shown that the schedulability test of each task needs to be performed only at a finite number of time instances called scheduling points. This is because the normalized demand of task $\tau_i$ on a processor, given by $W_i(t)/t$, is strictly decreasing except at those scheduling points. The set of scheduling points of task $\tau_i, S_i$, is defined as multiples of $T_g$ for $T_g \le T_i$, that is, $$S_i=\left\{h \times T_g|g = 1,2,\cdots,i; h =1,2,\cdots, \left\lfloor{\frac {T_i} {T_g}}\right\rfloor \right\}.$$ 213 214 215 Substitute the $S_i$ and the $W_i(t)$ into the Equation (\ref{equ:taskSet iff condition}), the necessary and sufficient condition for real-time tasks in a given task set to be feasible becomes 216 \begin{align}\label{eqn:taskSet SP iff condition} 217 \max_i \left( \min_t \sum_{j=1}^{i} OE_j \frac {\left\lceil \frac{t}{T_j} \right\rceil } {t} \right) \le 1, \ t \in S_i, 1 \le i \le n. 218 \end{align} 219 220 221 The proposed task scheduling techniques exploit the exact characterization of RMA to efficiently verify the feasibility of an offline schedule in the presence of faults and to dynamically adapt DVS policies to uncertainties of fault occurrences. As is shown in Equation (\ref{eqn:taskSet SP iff condition}), the task execution time with fault recovery overhead, which is denoted by $OE_j$, is utilized in the feasibility analysis of the offline schedule. As a result, the generated feasible task schedules will be feasible when faults occur. 222 223 224 The proposed task scheduling techniques offer three advantages over the previous techniques: (1) higher tolerance to fault recovery overhead due to the relaxed constraints of the exact characterization of RMA, (2) low-cost ECRMA-based offline feasibility analysis schemes, and (3) efficient extension to the runtime reevaluation of DVS policies due to the relatively lower complexity of the offline feasibility analysis. 225 In this paper, the scheduling point-based exact characterization of RMA provides a systematic approach to improve the feasibility of a schedule while tolerating faults for enhanced reliability and scaling voltage for energy efficiency. Two offline algorithms are proposed to integrate fault-tolerance and DVS policy evaluation by systematically searching for the energy-efficient fault-tolerant schedule for a given set of tasks, which are described in the next subsections. 226 227 228 229 \subsection{Application Level Voltage Scaling (A-DVS)}\label{ADVS} 230 The application level voltage scaling (A-DVS) is designed for the scenario where all tasks in a given task set run at the same processor speed. The A-DVS is suitable for systems in which frequent voltage and frequency scaling is inefficient. 231 Fig. \ref{Alg:ADVS} shows A-DVS algorithm to derive energy efficient voltage setting subject to fault and feasibility constraints. Inputs to the algorithm are the task set $\Gamma$, the lowest voltage level ($low$) and highest voltage level ($high$) supported by the processor, the maximum number of faults each task should tolerate ($k_i$), and checkpoint overhead ($c_s$). Voltage levels $low$ and $high$ are initially set to $1$ and $L$, respectively. 232 233 234 \begin{figure} 235 \begin{flushleft} 236 \textbf{Procedure} A-DVS($\Gamma,low, high, k_i, c_s$) 237 \end{flushleft} 238 \algsetup{linenodelimiter=.} 239 \begin{algorithmic}[1] 240 \STATE $low =1; high =L;$ 241 \FOR {$\tau_i, 1 \le i \le n $} 242 \STATE $S_i=\left\{h \times T_g|g = 1,2,\cdots,i; h =1,2,\cdots, \left\lfloor{\frac {T_i} {T_g}}\right\rfloor \right\}$ \COMMENT{Derive $S_i$, the set of scheduling points of task $\tau_i$} 243 \ENDFOR 244 \WHILE {$low \le high$} 245 \STATE $mid = (low + high)/2$ 246 \IF{FCA($\Gamma, S, k_i, c_s, mid$)} 247 \STATE $high = mid -1$ 248 \ELSIF {(!FCA($\Gamma, S, k_i, c_s, mid$)) $\&\&$ ($mid==L$)} 249 \PRINT \texttt{"Infeasible Schedule"} 250 \STATE \textbf{exit}(1) \COMMENT{Exit when infeasible} 251 \ELSE 252 \STATE $low=mid +1$ 253 \ENDIF 254 \ENDWHILE 255 \RETURN $mid$ 256 \end{algorithmic} 257 \caption{Application level voltage scaling algorithm (A-DVS).} 258 \label{Alg:ADVS} 259 \end{figure} 260 261 262 263 A-DVS starts by computing the set of scheduling points $S_i$ of task $\tau_i$, and then iteratively performs feasibility analysis using ECRMA to select the proper DVS strategy while tolerating $k_i$ faults in each task instance. $S$ denotes the array of $S_i$ for $1 \le i \le n$. Lines $2$ to $4$ iteratively compute scheduling points of $n$ tasks with the time complexity of $O(n^2R)$, where $n$ is the number of tasks in the task set and $R$ is the ratio of the largest period to the smallest period. Lines $5$ to $15$ iteratively search the energy efficient voltage level in the range from $low$ to $high$ based on the binary search algorithm. For a given voltage level $mid = (low + high)/2$, the feasibility checking subroutine FCA is called to test the feasibility of a schedule at the voltage level. If the schedule is found feasible, $high$ is updated to $(mid - 1)$ in line $8$, else $low$ is updated to $(mid + 1)$ in line $13$. This process continues until a feasible schedule is found for all tasks or the highest voltage level $L$ is reached without satisfying the Equation (\ref{eqn:taskSet SP iff condition}), in which case the task set is deemed infeasible (lines $10$ and $11$). Line $16$ returns the energy efficient voltage level of the feasible schedule. The time complexity of deriving $S$, the set of scheduling points of all tasks in the task set, is $O(n^2R)$, and the time complexity of the binary search algorithm is $O(\log_2L)$ \cite{CORMEN01}. The overall time complexity of A-DVS algorithm depends on the complexity of FCA algorithm. 264 265 266 Note that the binary search based A-DVS algorithm is valid only if the energy consumption is monotonic with respect to frequency/voltage changes. When the processor static power consumption as well as context switching overhead is considered, the monotonicity does not hold. In this case, there exists a critical processor speed below which scaling down the processor speed will instead increase the energy consumption \cite{JEJURIKAR04}. In other words, executing a task below the critical speed consumes more time and energy. Hence, in the binary search based A-DVS algorithm, the minimum voltage level $low$ is initialized to the level corresponding to the processor critical speed. 267 268 269 \begin{figure} 270 \textbf{Procedure} FCA($\Gamma, S, k_i, c_s, l$) 271 \algsetup{linenodelimiter=.} 272 \begin{algorithmic}[1] 273 \STATE $Schedulable=0; Demand=0; i=j=p=q=1$ 274 \FOR {$\tau_i, 1 \le i \le n $} %\COMMENT{Phase 1--Compute total cost $OE_j$} 275 \FOR {$\tau_j, j \le i $} 276 \STATE $O_{jl} = \max \left( \left\| \sqrt{ \frac{k_i C_j} {c_s f_j}} - 1 \right\|, 0 \right)$ 277 \STATE $OE_j=\frac{C_j} {f_j} + O_{jl}\times c_s + \frac{k_i C_j} {f_j (O_{jl}+1)} + 2k_i c_s$ 278 \ENDFOR 279 \FOR {$s_{iq} \in S_i$} %\COMMENT{ siq in Si is the qth scheduling point of task i} 280 \STATE $Demand =0$ 281 \FOR {$\tau_p, 1 \le p \le i $} 282 \STATE $Demand = Demand +OE_p \times \left\lceil s_{iq} /T_p \right\rceil $ 283 \ENDFOR 284 \IF{$Demand \le s_{iq}$} 285 \STATE $Schedulable=1; q=1$ 286 \STATE \textbf{break} 287 \ELSE \STATE $Schedulable=0; q = q + 1$ 288 \ENDIF 289 \ENDFOR 290 \IF {$Schedulable =0 $} \RETURN (0) 291 \ELSE \STATE $i= i +1$ 292 \ENDIF 293 \ENDFOR 294 \RETURN (1) 295 \end{algorithmic} 296 \caption{Feasibility checking algorithm (FCA).} 297 \label{Alg:FCA} 298 \end{figure} 299 300 301 Fig. \ref{Alg:FCA} describes the feasibility checking algorithm FCA. It takes as inputs the task set ($\Gamma$), the array of $S_i$ ($S$), the maximum number of faults each task should tolerate ($k_i$), checkpoint overhead ($c_s$), and the current voltage level ($l$). 302 303 304 The FCA algorithm uses a flag $Schedulable$ which is reset to 0 whenever a task is found un-schedulable at the current common voltage level, and a buffer $Demand$ which holds the total demand for processor time at scheduling points at the current voltage level. The algorithm operates in two phases. Phase $1$, consisting of lines 3 to 6, derives the optimum number of checkpoints at the current voltage level and compute the worst case execution time $OE_i$ of the current task $\tau_i$. 305 Phase $2$, consisting of lines $7$ to $18$, verifies the schedulability of the current task using Equation (\ref{eqn:taskSet SP iff condition}). It computes the total time demand of task $\tau_i$ at each scheduling point, check the schedulability of the task, and set the $Schedulable$ flag accordingly. If task $\tau_i$ is found schedulable, the algorithm proceeds to the next task; else it returns 0 to A-DVS routine. 306 307 308 The time complexity of phase $1$ and phase $2$ of FCA algorithm is $O(n^2)$ and $O(n^2R)$, respectively, and the overall time complexity of FCA algorithm is $O(n^2R)$. Considering the time complexity of binary search algorithm, the overall time complexity of A-DVS algorithm is $O(n^2R\log_2L)$ and the average time complexity per task is $O(nR\log_2L)$. When compared to the application level technique proposed in \cite{ZHANG06}, which has the time complexity of $O(n^2RL)$, A-DVS incurs an order of magnitude lower cost. The relative lower-complexity of the A-DVS algorithm enables the adaptation of the offline task schedules to the runtime time behavior of task execution time and fault occurrences for further energy savings. The dynamic extension of A-DVS algorithm is explored in Section \ref{D-ADVS}. 309 310 311 312 \subsection{Task Level Voltage Scaling (T-DVS)}\label{TDVS} 313 The task level voltage scaling (T-DVS) offers higher energy savings and improves fault-tolerance at the cost of increased complexity. T-DVS algorithm shown in Fig. \ref{Alg:TDVS} is similar to the A-DVS except whenever a task, for example task $\tau_i$, is found un-schedulable. In this case, the T-DVS repeatedly selects one task from among the tasks of equal and higher priorities and scales the voltage level of the task up by one level until task $\tau_i$ becomes schedulable. If the highest voltage level for all tasks of equal and higher priorities is reached and task $\tau_i$ is still un-schedulable, the task set is deemed to be infeasible. The task selected for voltage scaling satisfies two requirements: (1) its voltage level is lower than the highest processor supported voltage level and (2) the subsequent increase in energy consumption due to scaling up the voltage level of the selected task is minimal among all candidate tasks. 314 315 316 Inputs to T-DVS are a task set $\Gamma$ which is assumed to be feasible at a certain voltage level, the maximum number of faults each task instance should tolerate ($k_i$), and checkpointing overhead($c_s$). The parameters used to track the state of a schedule include $f_i$ and $Level_i$ which denote the operating frequency and voltage level of task $\tau_i$, respectively, and $min$ which denotes the index of the task selected for voltage scaling. For the sake of easy presentation, $f$ and $Level$ are used to denote the arrays of operating frequencies and voltage levels of tasks in the task set, respectively. It is assumed that the operating frequency $f_i$ of task $\tau_i$ is a function of the voltage level $Level_i$, that is, $f_i = f(Level_i)$. 317 318 319 Lines 2 to 4 initialize the operating frequency $f_i$ and voltage level $Level_i$ of task $\tau_i$ to $f(1)$ and $1$, respectively. Lines 5 to 7 iteratively compute the scheduling points of $n$ tasks in the task set. The time complexity of the computation is in order of $O(n^2R)$, where $R$ is the ratio of the largest period to the smallest period of tasks in the task set. Rest of the algorithm operates in $2$ phases, which are iterated for each task in the task set. Phase 1, consisting of lines 9 and 10, derives the optimum number of checkpoints of task $\tau_i$ at the current voltage level and compute the worst case overall execution time $OE_i$ for task $\tau_i$. The array of the worst case overall execution time of tasks in a task set is denoted by $OE$. Unlike A-DVS, phase $1$ of T-DVS takes constant time. Phase 2, consisting of lines 11 to 28, verifies the schedulability of task $\tau_i$ using Equation (\ref{eqn:taskSet SP iff condition}) and performs voltage scaling at task level. Line $11$ calls the schedulability checking subroutine (SCA) to verify the schedulability of task $\tau_i$ at the operating frequency of $f_i$. If task $\tau_i$ is found schedulable, the algorithm proceeds to the next task (line 13), else a task is selected for voltage scaling (lines 15 to 27). In line 16 the MINIMUM algorithm \cite{CORMEN01} is called and the index $min$ of the task selected for voltage scaling is returned. Task $\tau_{min}$ is the task that results in the minimal energy increase among all candidate tasks for voltage scaling. 320 321 322 If the voltage level $Level_{min}$ is found lower than $L$, then the operating frequency $f_{min}$ of task $\tau_{min}$ is raised by one level in lines 18 and 19, the optimal number of checkpointing $O_{min,l}$ and the overall execution time $OE_{min}$ of task $\tau_{min}$ are updated respectively in lines 20 and 21, and the schedulability of task $\tau_{min}$ is reevaluated based on the updated total time demand in line 22. Else if the voltage level $Level_{min}$ is found equal to the highest voltage level $L$, task $\tau_i$ is un-schedulable. This process continues until a feasible schedule is found for the task set or the highest voltage level is reached without satisfying Equation (\ref{eqn:taskSet SP iff condition}), in which case the schedule of the task set is deemed infeasible. 323 324 325 326 \begin{figure} 327 \textbf{Procedure} T-DVS($\Gamma, k_i, c_s$) 328 \algsetup{linenodelimiter=.} 329 \begin{algorithmic}[1] 330 \STATE $Schedulable=0; i=1$ 331 \FOR {$\tau_i, 1 \le i \le n $} 332 \STATE $f_i=f(1); Level_i=1$ 333 \ENDFOR 334 \FOR {$\tau_i, 1 \le i \le n $} 335 \STATE $S_i=\left\{h \times T_g|g = 1,2,\cdots,i; h =1,2,\cdots, \left\lfloor{\frac {T_i} {T_g}}\right\rfloor \right\}$ 336 \COMMENT{Derive $S_i$, the set of scheduling points for task $\tau_i$} 337 \ENDFOR 338 \FOR {$\tau_i, 1 \le i \le n $} 339 \STATE $O_{il} = \max \left( \left\| \sqrt{ \frac{k_i C_i} {c_s f_i}} - 1 \right\|, 0 \right)$ 340 \STATE $OE_i=\frac{C_i} {f_i} + O_{il} \times c_s + \frac{k_i C_i} {f_i (O_{il}+1)} + 2k_i c_s$ 341 \STATE $Schedulable = SCA(S, OE, i)$\342 \COMMENT{$OE$ denotes the array of $OE_i$ and $S$ denotes the array of $S_i$} 343 \IF {$Schedulable =1 $} 344 \STATE $i=i+1$ 345 \ELSE 346 \WHILE {$!Schedulable$} 347 \STATE $min = MINIMUM (Level, OE, i)$ 348 \IF {$Level_{min} < L$} 349 \STATE $Level_{min} = Level_{min} + 1$ 350 \STATE $f_{min} = f(Level_{min})$ 351 \STATE $O_{min,l} = \max \left( \left\| \sqrt{ \frac{k_i C_{min}} {c_s f_{min}}} - 1 \right\|, 0 \right)$ 352 \STATE $OE_{min}=\frac{C_{min}} {f_{min}} + O_{min,l}\times c_s + \frac{k_i C_{min}} {f_{min} (O_{min,l}+1)} + 2k_i c_s$ 353 \STATE $Schedulable = SCA(S, OE, i)$ 354 \ELSE 355 \PRINT \texttt{"Infeasible Schedule"} 356 \STATE \textbf{exit}(1) 357 \ENDIF 358 \ENDWHILE 359 \ENDIF 360 \ENDFOR 361 \end{algorithmic} 362 \caption{Task level voltage scaling algorithm (T-DVS).} 363 \label{Alg:TDVS} 364 \end{figure} 365 366 367 368 369 The MINIMUM algorithm, shown in line $16$ of Fig. \ref{Alg:TDVS}, takes as inputs the array of voltage levels ($Level$), the array of overall execution time of tasks in the task set ($OE$), and index of the task whose schedulability needs to be tested ($i$). The algorithm is implemented by deriving the energy increase of each task due to voltage scaling and returning the index of the task that incurs the minimum energy increase. Index of any candidate task is returned if all tasks with equal or higher priorities reach the highest processor voltage level. 370 371 372 The schedulability checking algorithm (SCA) is described in Fig. \ref{Alg:SCA}. Inputs to SCA are the array of $S_i$ ($S$), the array of the overall execution time of tasks in the task set ($OE$), and the index of the task whose schedulability needs to be tested ($i$). Line $1$ initializes the flags $Schedulable$ and $Demand$ to $0$. For each scheduling point of task $\tau_i$, lines $3$ to $6$ compute the total time demand of task $\tau_i$. Lines $7$ to $12$ check the schedulability of the task and set the $Schedulable$ flag accordingly. 373 The time complexity of SCA algorithm is $O(nR)$. 374 375 376 Unlike the task level feasibility analysis algorithm of \cite{ZHANG06}, T-DVS does not need to exhaustively explore all $L^n$ possible combinations of tasks and voltage levels. The first feasible schedule generated by the algorithm is the desired task schedule and taken as the output. The time complexity of T-DVS algorithm is dominated by the complexity of feasibility analysis and voltage scaling. 377 The feasibility analysis and voltage scaling involves $nL \times (nR+n)$ iterations for each task; thus, the time complexity of T-DVS per task is $O(n^2RL)$, which is one order of magnitude lower than that of previous techniques \cite{ZHANG06}. The online reevaluation of T-DVS algorithm is much simpler and takes constant time. The operation of the reevaluation is detailed in Section \ref{D-TDVS}. 378 379 380 381 \begin{figure} 382 \textbf{Procedure} SCA($S, OE, i$) 383 \algsetup{linenodelimiter=.} 384 \begin{algorithmic}[1] 385 \STATE $Schedulable=0; Demand=0; p=q=1$ 386 \FOR {$s_{iq} \in S_i$} 387 \STATE $Demand =0$ 388 \FOR {$\tau_p, 1 \le p \le i $} 389 \STATE $Demand = Demand +OE_p \times \left\lceil s_{iq} /T_p \right\rceil $ 390 \ENDFOR 391 \IF{$Demand \le s_{iq}$} 392 \STATE $Schedulable=1$ 393 \STATE \textbf{break} 394 \ELSE \STATE $Schedulable=0; q = q + 1$ 395 \ENDIF 396 \ENDFOR 397 \RETURN¡¡{$Schedulable$} 398 \end{algorithmic} 399 \caption{Schedulability checking algorithm (SCA).} 400 \label{Alg:SCA} 401 \end{figure} 402 403 404 405 \section{Online Reevaluation of DVS Policies}\label{Online-DVS} 406 Offline scheduling assumes that all tasks exhibit the worst case execution time and all faults occur during the checkpointing. However, the runtime behavior of task execution and fault occurrences can vary significantly and the average case characteristics are considerably better than the worst case characteristics. Hence, the online reevaluation of DVS policies that adapts the offline schedules to the runtime characteristics of task execution and fault occurrences can save significant energy. The proposed offline algorithms, A-DVS and T-DVS, provide efficient mechanisms to exploit the slack generated in the runtime to slow down the processor to save energy. Note that A-DVS and T-DVS feasibility analysis guarantees that offline schedules meet all timing constraints. Therefore, dynamic DVS policies proposed in this section only need to ensure that the feasibility of the modified task schedules is preserved in the runtime. 407 408 409 \subsection{Reevaluation of DVS Policies at Application Level}\label{D-ADVS} 410 For a given task set, the output of the A-DVS algorithm described in Section \ref{ADVS} is a voltage level $l$ below which the input task set becomes infeasible. This implies that one or more tasks in the task set fail to satisfy the Equation (\ref{eqn:taskSet SP iff condition}) at the voltage level $(l-1)$. In the runtime, not all tasks execute up to their worst case execution times and not all faults occur during task executions. Hence, the slack generated in the runtime could be used to dynamically scale down the processor speed to save energy. 411 It is assumed that tasks ready for execution are put into a ready queue. The online DVS policy manager runs a test to determine whether the cumulative slack is sufficient to slow down the processor for all the unexecuted lower priority tasks in the ready queue. The test compares the amount of time needed for all the unexecuted lower priority tasks in the ready queue to be feasible at $(l-1)$ or a lower voltage level with the available slack, as is discussed below. 412 413 414 Let $slk$ denote the accumulated slack time and $slk_i$ denote the slack time from task $\tau_i$. The accumulated slack $slk$ can be expressed as the sum of the slack from individual tasks. For instance, the accumulated slack can be written as $$slk = \sum_{i=1}^{n}{slk_i}$$ for $1 \le i \le n$. The slack from individual tasks is updated regularly at several time instants. The slack $slk_i$ from the task $\tau_i$ is initialized to 0 and updated at the end of the execution of the task to incorporate the generated slack. It is reset to 0 at the deadline of the task, indicating that the slack from the task is expired when a new instance of the task is released. When the accumulated slack is consumed by lower priority tasks, the slack from the task of the highest priority is consumed first. For example, if the priority of task $\tau_1$ is higher than that of task $\tau_2$ and the available accumulated slack is composed of $slk_1$ and $slk_2$, the $slk_2$ is not consumed until the $slk_1$ is used up when the accumulated slack is utilized to slow down the processor. 415 416 417 Define the execution time overflow as the additional time required by a task to be feasibly scheduled by each scheduling point at a certain voltage level. Let $ovfl_{il}$ denote the execution time overflow of task $\tau_i$ at the voltage level $l$. The $ovfl_{il}$ is set to $0$ if task $\tau_i$ is schedulable at the voltage level $l$, else it is computed as the difference between the worst case response time $R_{il}$ of task $\tau_i$ at the voltage level $l$ and the deadline $D_i$ of task $\tau_i$, as is given below: 418 419 \begin{eqnarray}\label{equ:OVFL} 420 ovfl_{il} = \left\{ \begin{array}{rl} 421 R_{il} - D_i &\mbox {$R_{il} \ge D_i$} \422 0 &\mbox {$R_{il} < D_i$} 423 \end{array} \right. 424 \end{eqnarray} 425 426 427 Consider an offline application level task schedule with the voltage level of $l$ and assume in the runtime the execution of task $\tau_{i-1}$ is finished. The voltage level of the processor can be feasibly scaled down to $(l-1)$ if the accumulated slack time $slk$ is greater than the sum of the execution time overflows of all the remaining unexecuted lower priority tasks in the ready queue. In other words, the processor can be scaled down to the voltage level $(l-1)$ if the inequality 428 \begin{align}\label{equ:runtime dvs condition} 429 slk = \sum_{p=1}^{i-1}{slk_p} \ge \sum_{p=i}^{n} ovfl_{p,(l-1)} 430 \end{align} 431 holds, assuming the tasks $\tau_p$ for $i \le p \le n$ are in the ready queue. 432 433 434 As is shown in Equation (\ref{equ:OVFL}), the straightforward approach to compute $ovfl_{il}$ requires iteratively estimating the response times $R_{il}$ of task $\tau_i$, hence it is highly computation intensive. An alternate simple yet efficient approach is proposed as follows. For the task $\tau_i$, $ovfl_{il}$ is the minimum of the differences between $t_2$ and $t_1$, where $t_2$ is the total demand for processor time by the task at the voltage level $l$ and $t_1$ is the scheduling points of the task. As a result, the execution time overflow $ovfl_{il}$ of task $\tau_i$ ($1 \le i \le n$) at the voltage level $l$ ($1 \le l \le L$) is given by 435 \begin{align}\label{equ:ovfl-ECRMA} 436 ovfl_{il}=\max \left( \min_{t_1} (t_2 - t_1), 0 \right) \quad t_1 \in S_i, 437 \end{align} 438 where $t_2$ is given by $$t_2 = \sum_{p=1}^{i} OE_p \times \left\lceil \frac {s_{iq}} {T_p} \right\rceil,$$ $S_i$ is the set of scheduling points for task $\tau_i$, and $s_{iq}$ is the $q^{th}$ scheduling point in $S_i$. $OE_p$ is given in Equation (\ref{eqn:OE-i}), and is re-written as 439 $$OE_p = \frac{C_p} {f_p} + O_{pl} \times c_s + \frac{k_i C_p} {f_p (O_{pl}+1)} +2 k_i c_s.$$ 440 441 442 Since both $t_1$ and $t_2$ are computed during the offline feasibility analysis of the A-DVS algorithm, the execution time overflow given in Equation (\ref{equ:ovfl-ECRMA}) can be pre-computed during the offline feasibility analysis and stored in system memory to form a lookup table. The lookup table is implemented in software program as an array or associative array. The table can be pre-calculated and stored in static program storage or can be calculated as part of a program‘s initialization phase. In the runtime, the scheduler searches the lookup table at the end of each task execution to calculate the sum of the execution time overflows of all the remaining unexecuted lower priority tasks, compares the derived execution time overflows with the accumulated slack time, and determines if the processor can be feasibly scaled down according to Equation (\ref{equ:runtime dvs condition}). This strategy of dynamic scheduling significantly reduces the runtime computation overhead without compromising the feasibility performance of the task schedule. 443 444 445 As is shown in Equation (\ref{equ:ovfl-ECRMA}), the proposed scheme computes the execution time overflow based on the minimum of differences between $t_2$ and $t_1$, hence it provides a better opportunity to scale the processor frequency. Fig. \ref{alg:DADVS} demonstrates the algorithms for the runtime reevaluation of DVS policies at the application level. Reevaluation of DVS polices is performed whenever a task instance finishes its execution. This strategy avoids incurring during the task execution any extra overhead that may cause the task to miss its deadline. Meanwhile, it ensures that the current accumulated slack time is checked sufficiently frequently such that the supply voltage can be scaled down opportunely to achieve energy savings if the accumulated slack time is large enough. The dynamic application level voltage scaling algorithm, D-ADVS, is shown in Fig. \ref{alg:DADVS}, where $i$ is the index of the task $\tau_i$ to be executed, $l$ is the voltage level of task $\tau_i$, and $ovfl_{sum}$ is the sum of the overflows of unexecuted lower priority tasks in the ready queue. Line 1 updates the $slk$ and initializes $ovfl_{sum}$ to 0. In line 2, subroutine \textbf{Overflow} is called to calculate the sum of the overflows of unexecuted lower priority tasks in the ready queue. Lines 3 to 6 iteratively scale down the processor voltage level if the accumulated slack time is large enough. Line 4 scales down the voltage level and operating frequency for all the remaining tasks by one level. Line 5 updates the $slk$ by reducing $ovfl_{sum}$ and line 6 updates the $ovfl_{sum}$ by calling subroutine \textbf{Overflow} to explore the possibilities of further scaling down the processor voltage level. The \textbf{Overflow} subroutine is described in Fig. \ref{alg:overflow}, where the notations $i, l$, and $ovfl_{sum}$ have the same definition as in the D-ADVS algorithm. The algorithm retrieves overflows of tasks $\tau_j$ ($i \le j \le n$) at the voltage level ($l-1$) from the lookup table stored in system memory in line 3, and calculates the sum of the overflows in line 4. Line 6 returns the $ovfl_{sum}$. The overall time complexity of the D-ADVS algorithm is $O(nL)$. 446 447 448 449 The example shown in Table \ref{table:DADVS example} demonstrates the application level runtime DVS reevaluation before a certain scheduling point. Consider a task set of four periodic tasks running on a processor which supports 3 voltage levels, as shown in Table \ref{table:DADVS example}. Execution time overflows for each task at the voltage level 3 are 0, denoting a feasible schedule at the voltage level 3. At the voltage level 2, task $\tau_1$ and $\tau_2$ are schedulable while task $\tau_3$ and $\tau_4$ are not schedulable since $ovfl_{12} = ovfl_{22} = 0$ but $ovfl_{32} = 1$ and $ovfl_{42} = 2$. Therefore, the processor runs at the voltage level 3 to maintain the feasibility of the schedule. However, if the slack $slk_2$ generated in the runtime satisfies $slk_2 \ge (ovfl_{32} + ovfl_{42}) = 3$, the processor can be scaled down to level 2 without violating the feasibility of the schedule. The same procedure can be utilized iteratively at successive voltage levels and for successive slacks produced in the system. 450 451 452 \begin{table} 453 \caption {Runtime DVS reevaluation at application level.} 454 \label{table:DADVS example} 455 \begin{center} 456 \scriptsize 457 \begin{tabular}{|c|c|c|c|} 458 \hline 459 \backslashbox{Tasks}{voltage level} & 1 & 2 & 3 \\ \hline 460 $\tau_1$ & $ovfl_{11}=0 $ & $ovfl_{12}=0$ & $ovfl_{13}=0$ \\ \hline 461 $\tau_2$ & $ovfl_{21}=3 $ & $ovfl_{22}=0$ & $ovfl_{23}=0$ \\ \hline 462 $\tau_3$ & $ovfl_{31}=4 $ & $ovfl_{32}=1$ & $ovfl_{33}=0$ \\ \hline 463 $\tau_4$ & $ovfl_{41}=5 $ & $ovfl_{42}=2$ & $ovfl_{43}=0$ \\ \hline 464 \end{tabular} 465 \end{center} 466 \end{table} 467 468 469 470 \begin{figure} 471 \centering 472 \begin{flushleft} 473 \textbf{Procedure} D-ADVS($i, l$) 474 \end{flushleft} 475 \centering 476 \algsetup{linenodelimiter=.} 477 \begin{algorithmic}[1] 478 \STATE $slk = \sum_{p=1}^{i-1}{slk_p}$; $ovfl_{sum}$ =0 479 \STATE $ovfl_{sum}$ = Overflow$(i, l)$ 480 \WHILE {$slk \ge ovfl_{sum}$} 481 \STATE $l=l-1$; 482 \STATE $slk = slk - ovfl_{sum}$ 483 \STATE $ovfl_{sum}$ = Overflow$(i, l)$ 484 \ENDWHILE 485 \RETURN 486 \end{algorithmic} 487 \caption{Dynamic application level voltage scaling algorithm (D-ADVS).} 488 \label{alg:DADVS} 489 \end{figure} 490 491 492 493 494 \begin{figure} 495 \begin{flushleft} 496 \textbf{Procedure} Overflow ($i, l$) 497 \end{flushleft} 498 \algsetup{linenodelimiter=.} 499 \begin{algorithmic}[1] 500 \STATE update $ovfl_{sum} = 0$ 501 \FOR {$i \le j \le n$} 502 \STATE retrieve $ovfl_{j,(l-1)}$ from the lookup table 503 \STATE $ovfl_{sum} = ovfl_{sum} + ovfl_{j,(l-1)}$ 504 \ENDFOR 505 \RETURN $ovfl_{sum}$ 506 \end{algorithmic} 507 \caption{Runtime execution time overflow retrieval algorithm.} 508 \label{alg:overflow} 509 \end{figure} 510 511 512 513 514 \begin{figure} 515 \centering 516 \begin{flushleft} 517 \textbf{Procedure} D-TDVS($i, l$) 518 \end{flushleft} 519 \centering 520 \algsetup{linenodelimiter=.} 521 \begin{algorithmic}[1] 522 \STATE $slk = \sum_{p=1}^{i-1}{slk_p}$; 523 \STATE retrieve $ovfl_{i,(l-1)}$ of task $\tau_i$ from lookup table 524 \WHILE {$slk \ge ovfl_{i,(l-1)}$} 525 \STATE $l=l-1$; 526 \STATE $slk = slk - ovfl_{i,(l-1)}$ 527 \STATE update $ovfl_{i,(l-1)}$ based on the lookup table 528 \ENDWHILE 529 \RETURN 530 \end{algorithmic} 531 \caption{Dynamic task level voltage scaling algorithm (D-TDVS).} 532 \label{alg:DTDVS} 533 \end{figure} 534 535 536 537 \subsection{Reevaluation of DVS Policies at Task Level}\label{D-TDVS} 538 The dynamic reevaluation of DVS strategies at the task level is similar to the reevaluation of DVS policies at the application level. During the offline scheduling, the T-DVS algorithm given in Section \ref{TDVS} statically derives the optimum combination of frequency allocations for all the tasks and stores the information, such as the pre-computed execution time overflows and overall execution times of tasks, in a lookup table for dynamic adaptation. In the runtime, the frequency of each task is scaled individually without affecting the operating frequency of other tasks. 539 540 Fig. \ref{alg:DTDVS} shows the dynamic reevaluation of T-DVS scheduling, referred as to D-TDVS. Assume task $\tau_{i-1}$ finishes its execution and task $\tau_i$ is scheduled to execute at the voltage level $l$. The scheduler checks if the accumulated slack time $slk$ from tasks $\tau_j$ ($1 \le j \le i-1$) is large enough to scale down the frequency $f_i$ of task $\tau_i$ by one or more levels. This can be verified by comparing the execution time overflow of task $\tau_i$ at lower voltage levels with the current available slack $slk$. If the available slack $slk$ is greater than the execution time overflow of task $\tau_i$ at the voltage level ($l-1$), the processor voltage is scaled down by one level and the current available slack is updated, else the slack continues to accumulate for tasks with lower priorities until it is updated when task $\tau_i$ is finished. 541 542 543 The runtime reevaluation of task level scheduling can be even simpler. That is, after task $\tau_{i-1}$ finishes its execution at the operating frequency $f_{i-1}$ and the current slack time $slk$ is ready, the new candidate operating frequency $f_i‘$ of task $\tau_i$ is derived as $$f_i‘=f_i \times \frac {OE_i} {slk + OE_i},$$ where $OE_i$ is the overall execution time of task $\tau_i$ at the frequency $f_i$. Comparing $f_i‘$ with the lower frequencies supported by the processor determines whether or not the operating frequency $f_i$ of task $\tau_i$ can be feasibly scaled down. This scheme takes constant time. It requires $n\times (L-1)$ extra memory space to store the overall execution time of each task for the adaptation of the offline task schedule to the runtime behavior of tasks and fault characteristics. 544 545 546 547 \section{Simulation Results and Overhead Analysis}\label{Experiments} 548 The proposed scheduling schemes consist of offline components (A-DVS and T-DVS) and online components (D-ADVS and D-TDVS). Energy efficiency and fault tolerance capabilities of the proposed schemes were validated using extensive simulation experiments. The scheduling overhead of the online components of the proposed schemes was also evaluated using Xtrem \cite{CONTRERAS04}, a SimpleScalar-based Intel XScale processor simulator. 549 550 551 Real-life task set benchmarks from \cite{KIM96} and \cite{LOCKE91} were used to compare the performance and energy characteristics of the proposed schemes with those of the scheduling schemes presented in \cite{ZHANG06}. 552 Similar to the approach in \cite{ZHANG06}, the worst case number of fault occurrences in a task instance is assumed to be a fixed number $k$, which is essentially the number of fault occurrences of the longest task at the lowest frequency level. This strategy of selecting $k$ ensures a fair comparison between the proposed schemes and the benchmarking schemes in \cite{ZHANG06}. Since the proposed schemes utilize the slack due to uncertainties in fault occurrences for energy savings, wether or not using a fixed number of fault occurrences does not affect the effectiveness of the proposed schemes. 553 Two DVS-capable processors, Transmeta Crusoe supporting 5 voltage and frequency levels \cite{TRANSMETA} and Intel XScale PXA260 supporting 3 voltage and frequency levels \cite{INTEL-PXA}, were used for estimating the energy consumption. The discrete frequencies, supply voltages, and TDP power of the two processors are listed in Table \ref{table:processor-param}. 554 555 556 557 \begin{table} 558 \caption {Processor frequencies, supply voltages and power(in \cite{TRANSMETA,INTEL-PXA}).} 559 \label{table:processor-param} 560 \begin{center} 561 \scriptsize 562 \begin{tabular}{|c|c|c|c|} 563 \hline 564 \backslashbox{Processors}{Characteristics} & ($\mega\hertz$) & ($\volt$) & ($\milli\watt$)\565 \cline{1-4} 566 & 200 & 1.0 & 178 \567 \cline{2-4} 568 Intel XScale PXA260 & 300 & 1.1 & 283 \569 \cline{2-4} 570 & 400 & 1.3 & 411 \\ \hline 571 \multicolumn {4}{c}{} \\ \hline 572 & 300 & 1.2 & 1300 \\ \cline{2-4} 573 & 400 & 1.225 & 1900 \\ \cline{2-4} 574 Transmeta Crusoe & 533 & 1.35 & 3000 \\ \cline{2-4} 575 & 600 & 1.5 & 4200 \\ \cline{2-4} 576 & 667 & 1.6 & 5300 \\ \hline 577 \end{tabular} 578 \end{center} 579 \end{table} 580 581 582 \begin{table} 583 \caption {INS and CNC real-life task sets.} 584 \label{table:INS/CNC taskset} 585 \begin{center} 586 \scriptsize 587 \begin{tabular}{|c|c|c|c|c|c|c|} 588 \hline 589 Task & \multicolumn{2}{c|}{Period ($\micro\second$)}& \multicolumn{2}{c|}{Deadline ($\micro\second$)} & \multicolumn{2}{c|}{WCET ($\micro\second$)}\\ \cline{2-7} 590 index & INS&CNC & INS&CNC& INS&CNC \\ \hline 591 1 & 2,500 & 2,400& 2,500 & 2,400 & 1,180 & 35 \\ \hline 592 2 & 40,000 & 2,400& 40,000 & 2,400 & 4,280 & 40 \\ \hline 593 3 & 625,000 & 4,800& 625,000 & 4,800 & 10,280 & 80 \\ \hline 594 4 & 1,000,000& 4,800& 1,000,000& 4,800 & 20,280 & 720 \\ \hline 595 5 & 1,000,000& 2,400& 1,000,000& 2,400 & 100,280& 165 \\ \hline 596 6 & 1,250,000& 2,400& 1,250,000& 2,400 & 25,000 & 165 \\ \hline 597 7 & & 9,600& & 4,000 & & 570 \\ \hline 598 8 & & 7,800& & 4,000 & & 570 \\ \hline 599 \end{tabular} 600 \end{center} 601 \end{table} 602 603 604 605 \subsection{Energy Characteristics}\label{Experiments:Energy} 606 Two real-life task sets, Inertial Navigation System (INS) \cite{LOCKE91} and Computer Numerical Control (CNC) \cite{KIM96}, were utilized to benchmark the energy consumption of the proposed scheduling algorithms. The characteristics of the benchmarking task sets are shown in Table \ref{table:INS/CNC taskset}, where 607 the worst case execution time of a task is assumed to correspond to the maximum processor speed. It is assumed that both checkpointing and data retrieval take 0.4$\milli\second$, and the energy overhead of both checkpointing and data retrieval is 160$\micro\joule$. It is also assumed that online energy savings are achieved by only using the slack due to variations in fault occurrences. 608 609 610 The online and offline components are integral parts of the proposed application and task level scheduling schemes. Energy savings are achieved by primarily using online components that are enabled by the offline components. 611 Energy values are obtained by multiplying processor power consumption and task execution time and considering checkpointing overhead and DVS transition overhead. Simulation results are reported for both application and task level techniques and compared with the JFTC, JFTA and JFTT techniques presented in \cite{ZHANG06}. 612 JFTC, JFTA and JFTT refer to offline constant frequency, application level voltage scaling, and task level voltage scaling schemes, respectively. 613 614 615 The online component is essentially a greedy heuristic since it scales down the processor speed to save energy once the available slack time is large enough. 616 An exhaustive search based online scheme is then developed to investigate the optimality of the proposed scheme. 617 In the exhaustive search based online scheme, all possible adaptations of offline task schedules due to the slack generated in the runtime are produced and the energy consumption of each adapted task schedule is computed. 618 The adapted task schedule with the minimum energy consumption is deemed to be optimal. The optimal adapted task schedule, referred to as $Optimal$, is compared with the proposed scheme in energy consumption. 619 In the presented results, $E_{13}$ denotes the percentage of ($E_1-E_3$)/$E_1\times100\%$, $E_{23}$ denotes the percentage of ($E_2-E_3$)/$E_2\times100\%$, $E_{43}$ denotes the percentage of ($E_4-E_3$)/$E_4\times100\%$, and $NF$ denotes an infeasible schedule. 620 %\backslashbox{Tasks}{voltage level} & 1 & 2 & 3 \\ \hline 621 622 \begin{table}[ht] 623 \begin{center} 624 \begin{tabular}{|c|c|c|} 625 626 \multicolumn{ 3}{c}{{\bf The final temperature $T_{end}$ of each task }} \627 \hline 628 Task & {Temperature} & {Temperature}\\ 629 Set & {TSVS} & {RTS} \630 \hline 631 task 1 & 76.5285 & 71.9620 \\ \cline{1-3} 632 633 task 2 & 83.0586 & 61.3535 \\ \cline{1-3} 634 635 task 3 & 89.5839 & 65.4356 \\ \cline{1-3} 636 637 task 4 & 91.4333 & 80.8576 \\ \cline{1-3} 638 639 task 5 & 108.714 & 96.7676 \\ \cline{1-3} 640 641 task 6 & 117.870 & 95.6829 \\ \cline{1-3} 642 643 task 7 & 106.363 & 109.983 \\ \cline{1-3} 644 645 task 8 & 118.104 & 103.140 \\ \cline{1-3} 646 647 task 9 & 119.419 & 97.8610 \\ \cline{1-3} 648 649 task 10 & 111.702 & 91.7257 \\ \cline{1-3} 650 651 task 11 & 113.545 & 90.8460 \\ \cline{1-3} 652 653 task 12 & 112.488 & 81.7293 \\ \cline{1-3} 654 655 task 13 & 107.332 & 77.3995 \\ \cline{1-3} 656 657 task 14 & 101.201 & 97.1904 \\ \cline{1-3} 658 659 task 15 & 94.6294 & 104.856 \\ \cline{1-3} 660 661 task 16 & 106.142 & 94.6062 \\ \cline{1-3} 662 663 task 17 & 117.629 & 100.567 \\ \cline{1-3} 664 665 task 18 & 102.603 & 105.390 \\ \cline{1-3} 666 667 task 19 & 105.944 & 94.1424 \\ \cline{1-3} 668 669 task 20 & 112.010 & 93.7714 \\ \cline{1-3} 670 671 {\bf average} & 104.815 & 90.7634 \\ \cline{1-3} 672 {\bf peak} & 119.419 & 109.983 \\ \cline{1-3} 673 \hline 674 \end{tabular} 675 \end{center} 676 \end{table} 677 678 \begin{table} 679 \caption {Energy consumption of task level voltage scaling on Transmeta Crusoe processor.} 680 \label{table:Energy-TDVS-Transmeta} 681 \begin{center} 682 \scriptsize 683 \begin{tabular}{|c|c|c|c|c|c|c|} 684 \hline 685 Task & $k$ & JFTC\cite{ZHANG06} & JFTT\cite{ZHANG06} & Proposed& $E_{13}$ & $E_{23}$\686 set & & $E_1$(mJ)& $E_2$(mJ)& $E_3$(mJ)& (\%)& (\%)\\ \hline 687 &1 &18.1 &14.9 &10.0 &44.8 &32.9\\ 688 &2 &24.3 &21.1 &12.9 &46.9 &38.9\\ \cline{2-7} 689 CNC&3 &29.8 &26.7 &13.4 &55.0 &49.8\\ \cline{2-7} 690 &4 &34.9 &34.1 &14.5 &58.5 &57.5\\ \cline{2-7} 691 &5 &$NF$ &$NF$ &13.1 &$-$ &$-$\\ \hline 692 &1 &6050.7 & 5457.6&4087.9 & 32.4 &25.1\\ \cline{2-7} 693 INS &2 &6735.1 & 6222.1&5070.4 &24.7 &18.5\\ \cline{2-7} 694 &3 &7300.2 &7284.1 &5637.4 &22.8 &22.6\\ \cline{2-7} 695 &4 &$NF$ &$NF$ &5961.6 &$-$ &$-$ \\ \hline 696 \end{tabular} 697 \end{center} 698 \end{table} 699 700 701 Table \ref{table:Energy-ADVS-Transmeta} shows that the proposed application level scheduling scheme saves 22-52\% energy over JFTC and 22-50\% energy over JFTA on Crusoe processors. 702 Table \ref{table:Energy-ADVS-Transmeta} also shows that the discrepancy in energy consumption of the proposed application level scheduling scheme and the exhaustive search based optimal scheme is up to 8\% for CNC task set. 703 The discrepancy is relatively small for INS task set. This is because execution times of tasks in INS task set are relatively long and much more slack is needed to scale down the processor speed. 704 Due to space limitation, the results on the comparison of the proposed scheme and the exhaustive search based optimal method is reported only for INS task set on Transmeta Crusoe processor. 705 706 707 Table \ref{table:Energy-TDVS-Transmeta} shows that the proposed task level scheduling scheme saves 22-58\% energy over JFTC and 18-57\% energy over JFTT on Crusoe processors. 708 Similarly, the energy savings of the proposed application and task level schemes over the benchmarking schemes on XScale processors are shown in Table \ref{table:Energy-ADVS-XScale} and Table \ref{table:Energy-TDVS-XScale}. 709 It can be drawn that the proposed scheduling schemes achieve significant energy savings when compared to the benchmarking scheduling schemes. This is primarily due to the runtime slack from uncertainties of fault occurrences. 710 It also can be drawn (e.g. for $k$ = 5 for CNC and $k$ = 4 for INS) that the proposed techniques have higher fault tolerance capabilities due to relaxed utilization constraints of the proposed ECRMA-based scheduling approach. 711 712 713 \begin{table} 714 \caption {Energy consumption of application level voltage scaling on Intel XScale processor.} 715 \label{table:Energy-ADVS-XScale} 716 \begin{center} 717 \scriptsize 718 \begin{tabular}{|c|c|c|c|c|c|c|} 719 \hline 720 Task & $k$ & JFTC\cite{ZHANG06} & JFTA\cite{ZHANG06} & Proposed& $E_{13}$ & $E_{23}$\721 set & & $E_1$($\milli\joule$)& $E_2$($\milli\joule$)& $E_3$($\milli\joule$)& (\%)& (\%)\\ \hline 722 &1 &7.6 &8.2 &3.6 &52.6 &56.1\\ \cline{2-7} 723 &2 &12.8 &13.8 &7.1 &44.5 &48.6\\ \cline{2-7} 724 CNC &3 &17.6 &18.8 &9.0 &48.9 &52.1\\ \cline{2-7} 725 &4 &22.2 &22.2 &10.5 &52.7 &52.7\\ \cline{2-7} 726 &5 &$NF$ &$NF$ &12.9 &$-$ &$-$ \\ \hline 727 &1 &1326.2 &1326.2 &923.8 &30.3 &30.3\\ \cline{2-7} 728 INS &2 &1853.6 &1853.6 &1248.4 &32.6 &32.6\\ \cline{2-7} 729 &3 &2298.2 &2298.2 &1510.6 &34.3 &34.3\\ \cline{2-7} 730 &4 &$NF$ &$NF$ &1758.8 &$-$ &$-$ \\ \hline 731 \end{tabular} 732 \end{center} 733 \end{table} 734 735 736 \begin{table} 737 \caption {Energy consumption of task level voltage scaling on Intel XScale processor.} 738 \label{table:Energy-TDVS-XScale} 739 \begin{center} 740 \scriptsize 741 \begin{tabular}{|c|c|c|c|c|c|c|} 742 \hline 743 Task & $k$ & JFTC\cite{ZHANG06} & JFTT\cite{ZHANG06} & Proposed& $E_{13}$ & $E_{23}$\744 set & & $E_1$($\milli\joule$)& $E_2$($\milli\joule$)& $E_3$($\milli\joule$)& (\%)& (\%)\\ \hline 745 &1 &7.6 &9.1 &3.6 &52.6 &60.4\\ \cline{2-7} 746 &2 &12.8 &14.5 &7.5 &41.4 &48.3\\ \cline{2-7} 747 CNC&3 &17.6 &18.5 &9.5 &46.0 &48.6\\ \cline{2-7} 748 &4 &22.2 &22.5 &11.0 &50.5 &51.1\\ \cline{2-7} 749 &5 &$NF$ &$NF$ &10.8 &$-$ &$-$\\ \hline 750 &1 &1326.2 &1327.5 &932.5 &30.3 &30.4\\ \cline{2-7} 751 INS &2 &1853.6 &1855.9 &1292.6 &30.3 &30.4\\ \cline{2-7} 752 &3 &2298.2 &2299.0 &1496.5 &34.9 &34.9\\ \cline{2-7} 753 &4 &$NF$ &$NF$ &1726.5 &$-$ &$-$ \\ \hline 754 \end{tabular} 755 \end{center} 756 \end{table} 757 758 759 760 \subsection{Runtime Overhead Analysis}\label{Experiments:Overhead} 761 The proposed quasi-static scheduling scheme comprises two components. One is the offline scheduling component and the other is the runtime counterpart of the offline component. Since it is the overhead of the runtime component that has adverse impact on system timeliness, the complexity of the runtime component of the quasi-static scheme is evaluated in this section using Xtrem \cite{CONTRERAS04}, a high level functional power simulator tailored for Intel Xscale Technology-based systems. 762 763 764 Xtrem is a powerful infrastructure capable of providing power and cycle level estimation for C-based applications targeted to Intel Xscale core. It is based on the widely used SimpleScalar-Arm architecture simulator and is used for verifying the time complexity of the proposed schemes and estimating the runtime impact of dynamic DVS policies on the schedule feasibility. Due to space limitation, only the overhead of the application level scheduling scheme is analyzed in this subsection. 765 766 767 The proposed dynamic D-ADVS scheme reduces runtime overhead by utilizing the pre-computed execution time overflow that is stored in system memory. The D-ADVS proceeds in three steps: (1) adding up the overflows of unexecuted tasks, (2) comparing the current available slack time with the sum of the overflows to make a decision on voltage scaling, and (3) updating the accumulated slack time. The D-ADVS is called whenever a task instance finishes its execution, which ensures that the feasibility of the offline schedule is maintained and the runtime generated slack time is utilized opportunely for energy savings. The D-ADVS scheme involves three primitive operations: addition, multiplication and division. Each operation takes 7 cycles on Xtrem. The experiment results show that the overall overhead of the proposed D-ADVS is 821 cycles to execute the first instances of all tasks in the CNC task set. Since the D-ADVS is called at the end of the execution of each task instance and repeats its three steps over each unexecuted task in the task set, it incurs the worst case overhead at its first call. Similarly, the D-ADVS incurs the best case overhead at its last call. It is shown in the experiment results that the average cycles for the worst case overhead is 190 and the average cycles for the best case overhead is 81, which translates to 0.48$\micro\second$ and 0.20$\micro\second$ respectively at the operating frequency of 400$\mega\hertz$. This time overhead is negligible when compared to the execution times of tasks in the CNC task set. 768 769 770 771 \section{Implementation of Scheduling Algorithms on a Real-Life Test Bed}\label{Implementation on testbed} 772 This section presents the implementation and validation of the proposed energy-efficient task scheduling schemes for hard real-time embedded systems. A real-life test bed has been developed to accurately benchmark the energy savings of the proposed scheduling schemes. The test bed comprises a dual-core Intel T2500 processor with dynamic voltage scaling capability and runs the Linux Fedora 8 based hard real-time scheduling. A detailed description of the implementation was presented in \cite{WEI11MEJ}. 773 774 775 776 \subsection{Implementation Process and Energy Measurement Method}\label{Implementation: platform construction} 777 The implementation of an energy-efficient task scheduling algorithm requires that the hardware and software platform on which the algorithm is to be implemented supports hard real-time scheduling, fixed priority and preemptive scheduling, and dynamic voltage scaling. A mini-ITX Express motherboard from Radisys Corporation \cite{RADISYS} was selected as the hardware platform due to its support of DVS and ease with energy measurement. The embedded motherboard mainly comprises an Intel Core Duo T2500 processor and 512M DDR2 memory module. T2500 is a DVS-capable processor with 2MB L2 cache. 778 The Linux Fedora 8 operating system, one of the most widely used operating systems, was chosen as the software platform for the implementation. It supports two fixed priority and preemptive real-time scheduling policies: First-In-First-Out (FIFO) and Round-Robin (RR). The FIFO policy was selected as the basis for implementing RMA-based scheduling schemes. The rate monotonic scheduling scheme is utilized to assigned priorities to tasks with different periods while FIFO is used to break ties when tasks have the same priorities. The Linux FIFO policy provides a simple yet efficient approach to implementing fixed-priority preemptive scheduling algorithms. 779 780 781 The implementation of the RMA-based task scheduling algorithms consists of two major steps: task generation and task scheduling. In the first step, Dhrystone-based independent and periodic tasks were generated and task characteristics were derived. In the second step, the generated tasks were scheduled using scheduling algorithms such as the JFTA \cite{ZHANG06} and the proposed A-DVS. 782 783 784 Dhrystone, a synthetic computing benchmark program developed to be representative of system programming \cite{WEICKER84}, was selected and modified to generate independent and periodic tasks. Dhrystone was written in C language code, has small size, and is portable to a large number of platforms and processor architectures. These characteristics make Dhrystone a popular benchmark in embedded applications due to its small memory requirements. The output of Dhrystone benchmark program is the number of iterations of the Dhrystone main code in unit time, which is derived by dividing a predefined number of iterations of the Dhrystone main code by the corresponding execution time. Tasks with different execution times are generated by varying the number of iterations of the Dhrystone main code. Ten tasks the execution times of which range from 1$\milli\second$ to 1000$\milli\second$ were generated using the Dhrystone benchmark program. Task utilizations were generated based on the Beta distribution of probability and were limited to being less than $\ln2$, the asymptotic bound of RMA \cite{WEI08}. Task periods were hence derived as the ratio of the task execution times to the task utilizations. 785 786 787 \begin{figure} 788 % Requires \usepackage{graphicx} 789 \begin{center} 790 \centering 791 \scriptsize 792 \includegraphics*[width=3.5in,viewport=220 505 640 660]{DAQ.pdf}\793 \end{center} 794 \caption{DAQ system and current probes for energy measurement.} 795 \label{Fig:DAQ system} 796 \end{figure} 797 798 799 Since the ATX 4-pin connector on the motherboard exclusively provides 12$\volt$ voltage to the voltage regulator module (VRM) of CPU and the ATX 20-pin connector on the motherboard provides 12$\volt$, 5$\volt$, and 3.3$\volt$ voltages to components on system board, the energy consumption of CPU and system board can be approximated by the energy delivered from ATX power supply connectors. This delivered energy can be derived by multiplying the currents flowing through ATX connectors by the voltages at the ATX connectors. Considering the fact that a VRM can achieve energy efficiency of up to 95\% and difficulties to directly measure energy consumption of an onboard device, this strategy for energy estimation can be used to sketch energy consumption of CPU and system board. More specifically, measurement of energy consumption is accomplished by using a DAQ system and Tektronix A622 AC/DC current probe. The DAQ system is comprised of an NI PCI-6040E DAQ, NI BNC-2110 connector block, and a host computer with LabView, as is shown in Figure \ref{Fig:DAQ system}. 800 801 802 803 \subsection{Numerical Results}\label{Implementation:Numerical results} 804 The offline scheduling algorithms presented in \cite{ZHANG06} and the proposed quasi-static scheduling schemes were implemented on the test bed. Due to space limitation, only the results for the JFTA \cite{ZHANG06} and the proposed application level scheduling scheme (the A-DVS combined with its dynamic counterpart D-ADVS) were reported. 805 One core of the Core Duo processor Intel T2500 was disabled in the implementation. 10 generated Dhrystone-based tasks were scheduled to execute on the test bed using the JFTA and the proposed application level scheme, respectively. Table \ref{table:Testbed-Energy-ADVS/JFTA} shows the energy consumptions of the core and system board, respectively. 806 $E_{JA}$ = ($E_J$ -$E_A$)/$E_J$ $\times$ 100\% denotes the energy savings of the proposed scheme when compared to the benchmarking scheme JFTA, where $E_J$ and $E_A$ represent energy consumptions of the task set under JFTA and the proposed application level scheme, respectively. $NF$ denotes that the tasks in the task set can not be feasibly scheduled. 807 808 809 \begin{table} 810 \caption {Energy consumptions of CPU and system board under JFTA and the proposed quasi-static application level scheduling scheme.} 811 \label{table:Testbed-Energy-ADVS/JFTA} 812 \begin{center} 813 \scriptsize 814 \begin{tabular}{|c|c|c|c|c|} 815 \hline 816 Mini-ITX& & JFTA\cite{ZHANG06} & Proposed & \817 motherboard &$k$ &$E_J$($\joule$)& $E_A$($\joule$) &$E_{AJ}$($\joule$)\\ \hline 818 &0 &312.1 &312.1 &0 \\ \cline{2-5} 819 &1 &396.7 &318.5 &19.7 \\ \cline{2-5} 820 &2 &408.4 &318.5 &22.0 \\ \cline{2-5} 821 Core &3 &418.1 &325.6 &22.1 \\ \cline{2-5} 822 &4 &436.2 &330.7 &24.2 \\ \cline{2-5} 823 &5 &$NF $ &341.2 & $-$ \\ \hline 824 &0 &489.1.2 &489.12 &0 \\ \cline{2-5} 825 &1 &488.5.6 &490.46 &-0.38 \\ \cline{2-5} 826 System &2 &488.7.2 &490.82 &-0.45 \\ \cline{2-5} 827 board &3 &489.1 &491.4 &-0.46 \\ \cline{2-5} 828 &4 &491.6 &490.4 &0.25 \\ \cline{2-5} 829 &5 &$ NF$ &491.0 & $-$ \\ \hline 830 \end{tabular} 831 \end{center} 832 \end{table} 833 834 835 836 The energy consumption of the proposed quasi-static application scheme is verified and compared with that of the JFTA. Table \ref{table:Testbed-Energy-ADVS/JFTA} shows that as compared to the proposed scheme, the JFTA consumes the same core energy in the absence of fault occurrences and consumes about 20\% more core energy in the presence of fault occurrences. This is because JFTA is an offline scheduling algorithm that considers the worst case fault occurrences to maintain the schedule feasibility. On the contrary, the proposed scheme is a quasi-static scheduling scheme the offline components of which enables the online components to save energy by utilizing uncertainties in fault occurrences. 837 838 839 The energy consumptions of the system board excluding the processor are close for the two scheduling algorithms under different fault arrival rates. For example, the difference between the JFTA and the proposed scheme in energy consumption of the system board is less than 0.5\% with the number of fault occurrences ranging from 0 to 5, as is shown in Table \ref{table:Testbed-Energy-ADVS/JFTA}. Furthermore, the energy consumption of the system board when it is idle is 479.8$\joule$, which is about 10$\joule$ less as compared to the energy consumption of the system board under the load of the Dhrystone-based task set. 840 841 842 There are three possible reasons for the relative stableness in the energy consumption of the system board. First, the Dhrystone is a CPU-intensive benchmark program and it does not intensively exercise the system board, especially the memory module, to store and load data. Second, the JFTA and the proposed scheduling algorithms are also CPU-intensive and their impact on the system board energy consumption is small. Finally, the total size of the instructions of the schedulers and the Dhrystone-based tasks in the form of an executable file is about 20$\kilo$. This file could be readily fit in the 2MB L2 cache of the Intel T2500 processor, which reduces the memory access overheads. 843 844 845 846 \section{CONCLUSION}\label{conclusion} 847 This paper presents efficient quasi-static scheduling schemes that combine the offline feasibility analysis of RMA schedules and the online voltage scaling for hard real-time systems. The proposed schemes captures the effects of voltage scaling on system reliability, and achieve energy savings by utilizing both the static slack in offline task schedules and dynamic slack due to variations in task execution time and uncertainties of fault occurrences. 848 The extension of the offline algorithms is enabled by pre-computing and saving in a lookup table the maximum slack requirements for the processor to slow down in the runtime. The stored slack time requirements are retrieved and compared at runtime with the accumulated slack. The online voltage scaling is performed whenever the generated slack time is equal to or greater than the stored slack requirements. Simulation results based on two real-life test sets and processor data sheets show that the proposed techniques achieve energy savings of up to 50\% over the state-of-the-art schemes. 849 A SimpleScalar-based Intel XScale processor simulator, Xtrem, was used to evaluate the proposed scheduling schemes in addition to extensive simulation experiments. A hard real-time test bed has been designed and the proposed algorithms were also verified on the test bed. 850 851 852 \bibliographystyle{IEEETran} 853 \bibliography{RefDBase} 854 \end{document}
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原文地址：http://www.cnblogs.com/jinliangjiuzhuang/p/4011033.html
