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\[email protected]
211 \newif\[email protected]
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\[email protected] \@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\[email protected]\@IEEEstringpcr\string_\else
588 \ifx\[email protected]\@IEEEstringcmtt\string_\else
589 \ifx\[email protected]\@IEEEstringptm\kern 0em\vbox{\hrule\@width 0.5em\@height 0.5pt\kern -0.3ex}\else
590 \ifx\[email protected]\@IEEEstringppl\kern 0em\vbox{\hrule\@width 0.5em\@height 0.5pt\kern -0.3ex}\else
591 \ifx\[email protected]\@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}{\[email protected] 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 \[email protected]
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 \[email protected]
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 % \[email protected] is the same as zero, but faster.
965 \partopsep \[email protected]
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 \[email protected]
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 \[email protected]
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 \[email protected]
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\[email protected]{\theenumi}
1047 \def\[email protected]{\theenumi(\theenumii)}
1048 \def\[email protected]{\[email protected]\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\[email protected] \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\[email protected] \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\[email protected]
1476 \def\titlepage{\@restonecolfalse\[email protected]\@restonecoltrue\onecolumn
1477 \else \newpage \fi \thispagestyle{empty}\[email protected]\[email protected]}
1478 \def\endtitlepage{\[email protected]\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\[email protected]
1531 \@IEEEenableoneshotfootnoterulefalse
1532 \ifCLASSOPTIONcompsoc
1533 \def\footnoterule{\relax\[email protected]
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 \[email protected]@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\[email protected]#1#2{\addpenalty{\@secpenalty}\addvspace{1.0em plus 1pt}%
1659 \@tempdima 2.75em \begingroup \parindent \[email protected] \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\[email protected]{\@dottedtocline{2}{2.75em}{3.75em}}
1664 \def\[email protected]{\@dottedtocline{3}{6.5em}{4.5em}}
1665 % must provide \[email protected] 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\[email protected]{\@dottedtocline{4}{6.5em}{5.5em}}
1669 \def\[email protected]{\@dottedtocline{5}{6.5em}{6.5em}}
1670 \def\listoffigures{\section*{\listfigurename}\@starttoc{lof}}
1671 \def\[email protected]{\@dottedtocline{1}{0em}{2.75em}}
1672 \def\listoftables{\section*{\listtablename}\@starttoc{lot}}
1673 \let\[email protected]\[email protected]
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\[email protected]}
1819 \def\[email protected]{tbp}
1820 \def\[email protected]{1}
1821 \def\[email protected]{lof}
1822 \def\[email protected]{\figurename~\thefigure}
1823 \def\figure{\@float{figure}}
1824 \def\endfigure{\[email protected]}
1825 \@namedef{figure*}{\@dblfloat{figure}}
1826 \@namedef{endfigure*}{\[email protected]}
1827 \newcounter{table}
1828 \ifCLASSOPTIONcompsoc
1829 \def\thetable{\arabic{table}}
1830 \else
1831 \def\thetable{\@Roman\[email protected]}
1832 \fi
1833 \def\[email protected]{tbp}
1834 \def\[email protected]{2}
1835 \def\[email protected]{lot}
1836 \def\[email protected]{\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{\[email protected]\footnotesize\@setminipage}\@float{table}}
1840 \def\endtable{\[email protected]}
1841 % v1.6b double column tables need to default to footnotesize as well.
1842 \@namedef{table*}{\def\@floatboxreset{\[email protected]\footnotesize\@setminipage}\@dblfloat{table}}
1843 \@namedef{endtable*}{\[email protected]}
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\[email protected]% flag to indicate if the environment was called as the star form
1862 \@IEEEeqnarraystarformfalse
1863
1864 \newif\[email protected]% 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 \[email protected]% only do something inside an IEEEeqnarray
1894 \[email protected]\addtocounter{equation}{-1}\else\setcounter{IEEEsubequation}{1}\fi%
1895 \def\@currentlabel{\[email protected]\theIEEEsubequation}\fi}
1896
1897 % flag to indicate that an equation is a sub equation
1898 \newif\[email protected]%
1899 \@IEEEissubequationfalse
1900
1901 % allows users to "push away" equations that get too close to the equation numbers
1902 \def\IEEEeqnarraynumspace{\hphantom{\[email protected]\theIEEEsubequationdis\else\theequationdis\fi}}
1903
1904 % provides a way to span multiple columns within IEEEeqnarray environments
1905 % will consider \[email protected] 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 @[email protected]\endcsname#3\relax\relax\relax\relax\relax%
1918 \relax\relax\relax\relax\relax\csname @[email protected]\endcsname%
1919 \fi%
1920 % advance column counter only if the IEEEeqnarray environment wants it
1921 \[email protected]\global\advance\@IEEEeqncolcnt by #1\relax\fi}
1922
1923 % like \omit, but maintains track of the column counter for \IEEEeqnarray
1924 \def\IEEEeqnarrayomit{\omit\[email protected]\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 \[email protected]\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 \[email protected]\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 \[email protected]\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 \[email protected]\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 \[email protected]\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 \[email protected]\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\[email protected] % 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\[email protected] % 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 \[email protected]\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 \[email protected]% 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 \[email protected]% 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 \[email protected]
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{\[email protected]}
2382
2383 \@namedef{IEEEeqnarray*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarray}
2384 \@namedef{endIEEEeqnarray*}{\[email protected]}
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 \[email protected]\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\[email protected]\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{\[email protected]\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\[email protected]% 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\[email protected]\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\[email protected]\[email protected]@\[email protected]\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\[email protected]{\@IEEEeqnarrayglobalizestrutstatus&\@@IEEEeqnarraycr\egroup%
2444 \[email protected]\global\advance\[email protected]\[email protected]\fi%
2445 \global\advance\[email protected]\[email protected]%
2446 $$\@ignoretrue}
2447
2448 % need a way to remember if last line is a subequation
2449 \newif\[email protected]%
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\[email protected]}
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 \[email protected]%
2498 \[email protected]\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 \[email protected]\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\[email protected]\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{\[email protected]}
2532 \@namedef{IEEEeqnarrayboxm*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}
2533 \@namedef{endIEEEeqnarrayboxm*}{\[email protected]}
2534
2535 \def\IEEEeqnarrayboxt{\@IEEEeqnarraystarformfalse\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}
2536 \def\endIEEEeqnarrayboxt{\[email protected]}
2537 \@namedef{IEEEeqnarrayboxt*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}
2538 \@namedef{endIEEEeqnarrayboxt*}{\[email protected]}
2539
2540 \def\IEEEeqnarraybox{\@IEEEeqnarraystarformfalse\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%
2541 \@IEEEeqnarraybox}
2542 \def\endIEEEeqnarraybox{\[email protected]}
2543
2544 \@namedef{IEEEeqnarraybox*}{\@IEEEeqnarraystarformtrue\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%
2545 \@IEEEeqnarraybox}
2546 \@namedef{endIEEEeqnarraybox*}{\[email protected]}
2547
2548 % flag to indicate if the \IEEEeqnarraybox needs to put things into an hbox{$ $}
2549 % for \vcenter in non-math mode
2550 \newif\[email protected]%
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\[email protected]\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\[email protected]\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 \[email protected] \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\[email protected]{\@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 \[email protected] $\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\[email protected]}
2639
2640 % IEEEeqnarraybox does not automatically increase line spacing by \jot
2641 \def\@IEEEeqnarrayboxXCR[#1]{\ifnum0=`{\fi}%
2642 \cr\noalign{\[email protected]\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 \[email protected]\@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 \[email protected]\@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 \[email protected]
2926 \ifCLASSOPTIONtechnote
2927 \def\[email protected]{%
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\[email protected]{%
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\[email protected]{%
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\[email protected]{\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 \[email protected]
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\[email protected]{%
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 \[email protected]
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 \[email protected]\immediate\write\@auxout{\string\citation{\@citeb}}\fi
3080 \@ifundefined{[email protected]\@citeb}{\mbox{\[email protected]\bfseries ?}%
3081 \[email protected]
3082 \@[email protected]
3083 {Citation `\@citeb‘ on page \thepage \space undefined}}%
3084 {\hbox{\csname [email protected]\@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 [email protected]\endcsname}
3104
3105 % V1.6 class files should always provide these
3106 \def\newblock{\hskip .11em\@plus.33em\@minus.07em}
3107 \let\@[email protected]\@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 \[email protected]\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\[email protected]=\@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\[email protected]}}%
3159 {\settowidth\labelwidth{\@biblabel{#1}}%
3160 \leftmargin\labelwidth
3161 \advance\leftmargin\labelsep\relax
3162 \itemsep \IEEEbibitemsep\relax
3163 \usecounter{enumiv}%
3164 \let\[email protected]\@empty
3165 \renewcommand\theenumiv{\@arabic\[email protected]}}%
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\[email protected]%
3256 \global\let\@IEEESAVESTATEfontbaselineskip\[email protected]%
3257 \global\let\@IEEESAVESTATEfontencoding\[email protected]%
3258 \global\let\@IEEESAVESTATEfontfamily\[email protected]%
3259 \global\let\@IEEESAVESTATEfontseries\[email protected]%
3260 \global\let\@IEEESAVESTATEfontshape\[email protected]}
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\[email protected] \@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 \[email protected]\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 \[email protected]\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\[email protected]\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\[email protected]{\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\[email protected]}
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\[email protected]
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]{\[email protected]\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\[email protected]\ifodd\[email protected]\else
3392 \hbox{}\thispagestyle{#1}\newpage\if[email protected]\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\[email protected] \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
3409 \thispagestyle{IEEEpeerreviewcoverpagestyle}\@thanks%
3410 \else
3411 \[email protected]%
3412 \ifCLASSOPTIONtechnote%
3413 \newpage\global\@topnum\[email protected] \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
3414 \else
3415 \twocolumn[\@maketitle\@IEEEdynamictitlevspace\@IEEEaftertitletext]%
3416 \fi
3417 \else
3418 \newpage\global\@topnum\[email protected] \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
3419 \fi
3420 \thispagestyle{IEEEtitlepagestyle}\@thanks%
3421 \fi
3422 % pullup page for pubid if used.
3423 \[email protected]
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 \[email protected]\@thanks{\@thanks
3486 \protect\footnotetext[\the\[email protected]]{\@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\[email protected] \@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 \[email protected]\@thanks{\@thanks
3509 \protect\footnotetext[\the\[email protected]]{\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\[email protected]\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 \[email protected]\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 \[email protected]
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\[email protected]\else\endquotation\fi
3718 \normalfont\normalsize}
3719
3720 \def\IEEEkeywords{\normalfont
3721 \[email protected]
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\[email protected]\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 \[email protected]\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 \[email protected]\else\quotation\fi\itshape\@IEEEabskeysecsize%
3740 \par\@IEEEgobbleleadPARNLSP}
3741 \else% compsoc not conference
3742 \def\abstract{\normalfont\@IEEEtweakunitybaselinestretch{1.15}\sffamily
3743 \[email protected]
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 \[email protected]
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>\[email protected]
3818 \let\@svsec\@empty
3819 \else
3820 \refstepcounter{#1}%
3821 % load section label and spacer into \@svsec
3822 \[email protected]\@svsec{\@seccntformat{#1}\relax}%
3823 \fi%
3824 \@tempskipa #5\relax
3825 \ifdim \@tempskipa>\[email protected]% 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>\[email protected]\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>\[email protected]\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>\[email protected]
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}{\[email protected]}{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}{\[email protected]}{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}{\[email protected]}{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}{\[email protected]}{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}{\[email protected]}{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}{\[email protected]}{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}{\[email protected]}{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}{\[email protected]}{-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}{\[email protected]}{-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}{\[email protected]}{-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 \[email protected] 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 \[email protected]
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 \[email protected]
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\[email protected]{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\[email protected]{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>\[email protected]\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\[email protected]
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 \[email protected]%
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 \[email protected]%
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\[email protected]
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 \[email protected]\[email protected]\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\[email protected]
4534 \newif\[email protected]
4535 \newif\[email protected]
4536 \newif\[email protected]
4537 \newif\[email protected]
4538 \newif\[email protected]
4539 \newif\[email protected]
4540 \newif\[email protected]
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\[email protected]\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\[email protected]\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,
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1 %\documentclass[10pt,journal,cspaper,compsoc]{IEEETran}
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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: [email protected]}
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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时间： 2024-10-19 14:53:38