% Load plain if necessary, i.e., if running under initex.
\expandafter\ifx\csname fmtname\endcsname\relax\input plain\fi
%
-\def\texinfoversion{2015-10-17.11}
+\def\texinfoversion{2015-10-29.16}
%
% Copyright 1985, 1986, 1988, 1990, 1991, 1992, 1993, 1994, 1995,
% 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006,
% The space after the comma will end up in the temporary definition
% that we make for arg2 (see \parsemargdef ff.). We want all this to be
% expanded for the sake of the index, so we end up just seeing "bar".
- \let\xeatspaces = \eatspaces
\let\xprocessmacroarg\eatspaces
}
}
\def\entrybreak{\unskip\space\ignorespaces}%
\def\doentry{%
- % Save the text of the entry in a \vtop.
+ % Save the text of the entry
\global\setbox\boxA=\hbox\bgroup
\bgroup % Instead of the swallowed brace.
\noindent
\global\setbox\boxA=\hbox\bgroup\unhbox\boxA
% #1 is the page number.
%
- % The following is kludged to not output a line of dots in the index if
- % there are no page numbers. The next person who breaks this will be
- % cursed by a Unix daemon.
- \setbox\boxB = \hbox{#1}%
+ % Get the width of the page numbers, and only use
+ % leaders if they are present.
+ \global\setbox\boxB = \hbox{#1}%
\ifdim\wd\boxB = 0pt
\null\nobreak\hfill\ %
\else
\fi
\fi
\egroup % end \boxA
- \global\setbox\entryindexbox=\vtop\bgroup\noindent
- % We want the text of the entries to be aligned to the left, and the
- % page numbers to be aligned to the right.
- %
- \advance\leftskip by 0pt plus 1fil
- \advance\leftskip by 0pt plus -1fill
- \rightskip = 0pt plus -1fil
- \advance\rightskip by 0pt plus 1fill
- % Cause last line, which could consist of page numbers on their own if the
- % list of page numbers is long, to be aligned to the right.
- \parfillskip=0pt plus -1fill
- %
- \hangindent=1em
- %
- \advance\rightskip by \entryrightmargin
- % Determine how far we can stretch into the margin.
- % This allows, e.g., "Appendix H GNU Free Documentation License" to fit
- % on one line.
- \advance \parfillskip by 0pt minus .6\entryrightmargin
- %
- \ifdim\wd\boxA > \hsize % If the entry doesn't fit in one line
- \ifdim\dimen@ > 0.9\hsize % due to long index text
- \dimen@ = 0.6\dimen@ % Try to split the text roughly evenly
- \dimen@ii = \hsize
- \advance \dimen@ii by -1em
- \ifnum\dimen@>\dimen@ii
- % If the entry is too long, use the whole line
- \dimen@ = \dimen@ii
+ \ifdim\wd\boxB = 0pt
+ \global\setbox\entryindexbox=\box\boxA
+ \else
+ \global\setbox\entryindexbox=\vbox\bgroup\noindent
+ % We want the text of the entries to be aligned to the left, and the
+ % page numbers to be aligned to the right.
+ %
+ \advance\leftskip by 0pt plus 1fil
+ \advance\leftskip by 0pt plus -1fill
+ \rightskip = 0pt plus -1fil
+ \advance\rightskip by 0pt plus 1fill
+ % Cause last line, which could consist of page numbers on their own
+ % if the list of page numbers is long, to be aligned to the right.
+ \parfillskip=0pt plus -1fill
+ %
+ \hangindent=1em
+ %
+ \advance\rightskip by \entryrightmargin
+ % Determine how far we can stretch into the margin.
+ % This allows, e.g., "Appendix H GNU Free Documentation License" to
+ % fit on one line in @letterpaper format.
+ \ifdim\entryrightmargin>2.1em
+ \dimen@i=2.1em
\else
- % Cause stretch of 1fill at the end of the first line, to avoid
- % extra spacing in a short first line.
- \hskip 0pt plus 1fill
+ \dimen@i=0em
\fi
- \parshape = 2 0pt \dimen@ 1em \dimen@ii
- % Ideally we'd add a finite glue at the end of the first line only, but
- % TeX doesn't seem to provide a way to do such a thing.
- \fi\fi
- \unhbox\boxA
- %
- % Do not prefer a separate line ending with a hyphen to fewer lines.
- \finalhyphendemerits = 0
- %
- % Word spacing - no stretch
- \spaceskip=\fontdimen2\font minus \fontdimen4\font
- %
- \linepenalty=1000 % Discourage line breaks.
- \hyphenpenalty=10000 % Discourage hyphenation.
- %
- \par % format the paragraph
- \egroup % The \vtop
+ \advance \parfillskip by 0pt minus 1\dimen@i
+ %
+ \dimen@ii = \hsize
+ \advance\dimen@ii by -1\leftskip
+ \advance\dimen@ii by -1\entryrightmargin
+ \advance\dimen@ii by 1\dimen@i
+ \ifdim\wd\boxA > \dimen@ii % If the entry doesn't fit in one line
+ \ifdim\dimen@ > 0.8\dimen@ii % due to long index text
+ \dimen@ = 0.7\dimen@ % Try to split the text roughly evenly
+ \dimen@ii = \hsize
+ \advance \dimen@ii by -1em
+ \ifnum\dimen@>\dimen@ii
+ % If the entry is too long, use the whole line
+ \dimen@ = \dimen@ii
+ \fi
+ \advance\leftskip by 0pt plus 1fill % ragged right
+ \advance \dimen@ by 1\rightskip
+ \parshape = 2 0pt \dimen@ 1em \dimen@ii
+ % Ideally we'd add a finite glue at the end of the first line only, but
+ % TeX doesn't seem to provide a way to do such a thing.
+ \fi\fi
+ \unhbox\boxA
+ %
+ % Do not prefer a separate line ending with a hyphen to fewer lines.
+ \finalhyphendemerits = 0
+ %
+ % Word spacing - no stretch
+ \spaceskip=\fontdimen2\font minus \fontdimen4\font
+ %
+ \linepenalty=1000 % Discourage line breaks.
+ \hyphenpenalty=5000 % Discourage hyphenation.
+ %
+ \par % format the paragraph
+ \egroup % The \vbox
+ \fi
\endgroup
% delay text of entry until after penalty
\bgroup\aftergroup\insertindexentrybox
\newbox\entryindexbox
\def\insertindexentrybox{%
-\lineskip=.8ex plus .6ex % This comes into effect when the \vtop has a large
- % depth due to the paragraph in it having several
+\lineskip=.7ex plus .5ex % This comes into effect when the \vbox has a large
+ % height due to the paragraph in it having several
% lines.
\box\entryindexbox}
\newbox\partialpage
\newdimen\doublecolumnhsize
+\newdimen\doublecolumntopgap
+\doublecolumntopgap = 0pt
\newtoks\savedtopmark % Used in \begindoublecolumns
\newtoks\savedfirstmark
%
% Double the \vsize as well. (We don't need a separate register here,
% since nobody clobbers \vsize.)
+ \global\doublecolumntopgap = \topskip
+ \global\advance\doublecolumntopgap by -1\baselineskip
+ \global\advance\vsize by -1\doublecolumntopgap
\vsize = 2\vsize
+ \topskip=0pt
}
% The double-column output routine for all double-column pages except
%
\hsize = \doublecolumnhsize
\wd0=\hsize \wd2=\hsize
- \hbox to\pagewidth{\box0\hfil\box2}%
+ \vbox{%
+ \vskip\doublecolumntopgap
+ \hbox to\pagewidth{\box0\hfil\box2}}%
}
-%
-% All done with double columns.
+
+
+% Finished with with double columns.
\def\enddoublecolumns{%
% The following penalty ensures that the page builder is exercised
% _before_ we change the output routine. This is necessary in the
% Argument is macro body with arguments substituted
\def\scanmacro#1{%
\newlinechar`\^^M
- \let\xeatspaces\eatspaces
% Reduce doubled backslashes to one
\def\xprocessmacroarg{\passargtomacro\eatspaces}%
%
\gdef\UTFviiiTmp{#2}%
%
\expandafter\ifx\csname uni:#1\endcsname \relax \else
- \errmessage{Internal error, already defined: #1}%
+ \message{Internal error, already defined: #1}%
\fi
%
% define an additional control sequence for this code point.
\DeclareUnicodeCharacter{02DB}{\ogonek{ }}
- % Greek letters
+ % Greek letters upper case
+ \DeclareUnicodeCharacter{0391}{{\it A}}
+ \DeclareUnicodeCharacter{0392}{{\it B}}
+ \DeclareUnicodeCharacter{0393}{\ensuremath{\mit\Gamma}}
+ \DeclareUnicodeCharacter{0394}{\ensuremath{\mit\Delta}}
+ \DeclareUnicodeCharacter{0395}{{\it E}}
+ \DeclareUnicodeCharacter{0396}{{\it Z}}
+ \DeclareUnicodeCharacter{0397}{{\it H}}
+ \DeclareUnicodeCharacter{0398}{\ensuremath{\mit\Theta}}
+ \DeclareUnicodeCharacter{0399}{{\it I}}
+ \DeclareUnicodeCharacter{039A}{{\it K}}
+ \DeclareUnicodeCharacter{039B}{\ensuremath{\mit\Lambda}}
+ \DeclareUnicodeCharacter{039C}{{\it M}}
+ \DeclareUnicodeCharacter{039D}{{\it N}}
+ \DeclareUnicodeCharacter{039E}{\ensuremath{\mit\Xi}}
+ \DeclareUnicodeCharacter{039F}{{\it O}}
+ \DeclareUnicodeCharacter{03A0}{\ensuremath{\mit\Pi}}
+ \DeclareUnicodeCharacter{03A1}{{\it P}}
+ %\DeclareUnicodeCharacter{03A2}{} % none - corresponds to final sigma
+ \DeclareUnicodeCharacter{03A3}{\ensuremath{\mit\Sigma}}
+ \DeclareUnicodeCharacter{03A4}{{\it T}}
+ \DeclareUnicodeCharacter{03A5}{\ensuremath{\mit\Upsilon}}
+ \DeclareUnicodeCharacter{03A6}{\ensuremath{\mit\Phi}}
+ \DeclareUnicodeCharacter{03A7}{{\it X}}
+ \DeclareUnicodeCharacter{03A8}{\ensuremath{\mit\Psi}}
+ \DeclareUnicodeCharacter{03A9}{\ensuremath{\mit\Omega}}
+
+ % Vowels with accents
+ \DeclareUnicodeCharacter{0390}{\ensuremath{\ddot{\acute\iota}}}
+ \DeclareUnicodeCharacter{03AC}{\ensuremath{\acute\alpha}}
+ \DeclareUnicodeCharacter{03AD}{\ensuremath{\acute\epsilon}}
+ \DeclareUnicodeCharacter{03AE}{\ensuremath{\acute\eta}}
+ \DeclareUnicodeCharacter{03AF}{\ensuremath{\acute\iota}}
+ \DeclareUnicodeCharacter{03B0}{\ensuremath{\acute{\ddot\upsilon}}}
+
+ % Standalone accent
+ \DeclareUnicodeCharacter{0384}{\ensuremath{\acute{\ }}}
+
+ % Greek letters lower case
+ \DeclareUnicodeCharacter{03B1}{\ensuremath\alpha}
+ \DeclareUnicodeCharacter{03B2}{\ensuremath\beta}
+ \DeclareUnicodeCharacter{03B3}{\ensuremath\gamma}
+ \DeclareUnicodeCharacter{03B4}{\ensuremath\delta}
+ \DeclareUnicodeCharacter{03B5}{\ensuremath\epsilon}
+ \DeclareUnicodeCharacter{03B6}{\ensuremath\zeta}
+ \DeclareUnicodeCharacter{03B7}{\ensuremath\eta}
+ \DeclareUnicodeCharacter{03B8}{\ensuremath\theta}
+ \DeclareUnicodeCharacter{03B9}{\ensuremath\iota}
+ \DeclareUnicodeCharacter{03BA}{\ensuremath\kappa}
+ \DeclareUnicodeCharacter{03BB}{\ensuremath\lambda}
+ \DeclareUnicodeCharacter{03BC}{\ensuremath\mu}
+ \DeclareUnicodeCharacter{03BD}{\ensuremath\nu}
+ \DeclareUnicodeCharacter{03BE}{\ensuremath\xi}
+ \DeclareUnicodeCharacter{03BF}{{\it o}} % omicron
\DeclareUnicodeCharacter{03C0}{\ensuremath\pi}
+ \DeclareUnicodeCharacter{03C1}{\ensuremath\rho}
+ \DeclareUnicodeCharacter{03C2}{\ensuremath\varsigma}
+ \DeclareUnicodeCharacter{03C3}{\ensuremath\sigma}
+ \DeclareUnicodeCharacter{03C4}{\ensuremath\tau}
+ \DeclareUnicodeCharacter{03C5}{\ensuremath\upsilon}
+ \DeclareUnicodeCharacter{03C6}{\ensuremath\phi}
+ \DeclareUnicodeCharacter{03C7}{\ensuremath\chi}
+ \DeclareUnicodeCharacter{03C8}{\ensuremath\psi}
+ \DeclareUnicodeCharacter{03C9}{\ensuremath\omega}
+
+ % More Greek vowels with accents
+ \DeclareUnicodeCharacter{03CA}{\ensuremath{\ddot\iota}}
+ \DeclareUnicodeCharacter{03CB}{\ensuremath{\ddot\upsilon}}
+ \DeclareUnicodeCharacter{03CC}{\ensuremath{\acute o}}
+ \DeclareUnicodeCharacter{03CD}{\ensuremath{\acute\upsilon}}
+ \DeclareUnicodeCharacter{03CE}{\ensuremath{\acute\omega}}
+
+ % Variant Greek letters
+ \DeclareUnicodeCharacter{03D1}{\ensuremath\vartheta}
+ \DeclareUnicodeCharacter{03D6}{\ensuremath\varpi}
+ \DeclareUnicodeCharacter{03F1}{\ensuremath\varrho}
\DeclareUnicodeCharacter{1E02}{\dotaccent{B}}
\DeclareUnicodeCharacter{1E03}{\dotaccent{b}}
\DeclareUnicodeCharacter{2203}{\ensuremath\exists}
\DeclareUnicodeCharacter{2208}{\ensuremath\in}
\DeclareUnicodeCharacter{2212}{\minus}
- \DeclareUnicodeCharacter{2217}{\point}
+ \DeclareUnicodeCharacter{2217}{\ast}
\DeclareUnicodeCharacter{221E}{\ensuremath\infty}
\DeclareUnicodeCharacter{2225}{\ensuremath\parallel}
\DeclareUnicodeCharacter{2227}{\ensuremath\wedge}
\DeclareUnicodeCharacter{2282}{\ensuremath\subset}
\DeclareUnicodeCharacter{2287}{\ensuremath\supseteq}
+ \DeclareUnicodeCharacter{2016}{\ensuremath\Vert}
+ \DeclareUnicodeCharacter{2032}{\ensuremath\prime}
+ \DeclareUnicodeCharacter{210F}{\ensuremath\hbar}
+ \DeclareUnicodeCharacter{2111}{\ensuremath\Im}
+ \DeclareUnicodeCharacter{2113}{\ensuremath\ell}
+ \DeclareUnicodeCharacter{2118}{\ensuremath\wp}
+ \DeclareUnicodeCharacter{211C}{\ensuremath\Re}
+ \DeclareUnicodeCharacter{2127}{\ensuremath\mho}
+ \DeclareUnicodeCharacter{2135}{\ensuremath\aleph}
+ \DeclareUnicodeCharacter{2190}{\ensuremath\leftarrow}
+ \DeclareUnicodeCharacter{2191}{\ensuremath\uparrow}
+ \DeclareUnicodeCharacter{2193}{\ensuremath\downarrow}
+ \DeclareUnicodeCharacter{2194}{\ensuremath\leftrightarrow}
+ \DeclareUnicodeCharacter{2195}{\ensuremath\updownarrow}
+ \DeclareUnicodeCharacter{2196}{\ensuremath\nwarrow}
+ \DeclareUnicodeCharacter{2197}{\ensuremath\nearrow}
+ \DeclareUnicodeCharacter{2198}{\ensuremath\searrow}
+ \DeclareUnicodeCharacter{2199}{\ensuremath\swarrow}
+ \DeclareUnicodeCharacter{21A6}{\ensuremath\mapsto}
+ \DeclareUnicodeCharacter{21A9}{\ensuremath\hookleftarrow}
+ \DeclareUnicodeCharacter{21AA}{\ensuremath\hookrightarrow}
+ \DeclareUnicodeCharacter{21BC}{\ensuremath\leftharpoonup}
+ \DeclareUnicodeCharacter{21BD}{\ensuremath\leftharpoondown}
+ \DeclareUnicodeCharacter{21BE}{\ensuremath\upharpoonright}
+ \DeclareUnicodeCharacter{21C0}{\ensuremath\rightharpoonup}
+ \DeclareUnicodeCharacter{21C1}{\ensuremath\rightharpoondown}
+ \DeclareUnicodeCharacter{21CC}{\ensuremath\rightleftharpoons}
+ \DeclareUnicodeCharacter{21D0}{\ensuremath\Leftarrow}
+ \DeclareUnicodeCharacter{21D1}{\ensuremath\Uparrow}
+ \DeclareUnicodeCharacter{21D3}{\ensuremath\Downarrow}
+ \DeclareUnicodeCharacter{21D4}{\ensuremath\Leftrightarrow}
+ \DeclareUnicodeCharacter{21D5}{\ensuremath\Updownarrow}
+ \DeclareUnicodeCharacter{21DD}{\ensuremath\leadsto}
+ \DeclareUnicodeCharacter{2201}{\ensuremath\complement}
+ \DeclareUnicodeCharacter{2202}{\ensuremath\partial}
+ \DeclareUnicodeCharacter{2205}{\ensuremath\emptyset}
+ \DeclareUnicodeCharacter{2207}{\ensuremath\nabla}
+ \DeclareUnicodeCharacter{2209}{\ensuremath\notin}
+ \DeclareUnicodeCharacter{220B}{\ensuremath\owns}
+ \DeclareUnicodeCharacter{220F}{\ensuremath\prod}
+ \DeclareUnicodeCharacter{2210}{\ensuremath\coprod}
+ \DeclareUnicodeCharacter{2211}{\ensuremath\sum}
+ \DeclareUnicodeCharacter{2213}{\ensuremath\mp}
+ \DeclareUnicodeCharacter{2218}{\ensuremath\circ}
+ \DeclareUnicodeCharacter{221A}{\ensuremath\surd}
+ \DeclareUnicodeCharacter{221D}{\ensuremath\propto}
+ \DeclareUnicodeCharacter{2220}{\ensuremath\angle}
+ \DeclareUnicodeCharacter{2223}{\ensuremath\mid}
+ \DeclareUnicodeCharacter{2228}{\ensuremath\vee}
+ \DeclareUnicodeCharacter{222A}{\ensuremath\cup}
+ \DeclareUnicodeCharacter{222B}{\ensuremath\smallint}
+ \DeclareUnicodeCharacter{222E}{\ensuremath\oint}
+ \DeclareUnicodeCharacter{223C}{\ensuremath\sim}
+ \DeclareUnicodeCharacter{2240}{\ensuremath\wr}
+ \DeclareUnicodeCharacter{2243}{\ensuremath\simeq}
+ \DeclareUnicodeCharacter{2245}{\ensuremath\cong}
+ \DeclareUnicodeCharacter{2248}{\ensuremath\approx}
+ \DeclareUnicodeCharacter{224D}{\ensuremath\asymp}
+ \DeclareUnicodeCharacter{2250}{\ensuremath\doteq}
+ \DeclareUnicodeCharacter{2260}{\ensuremath\neq}
+ \DeclareUnicodeCharacter{226A}{\ensuremath\ll}
+ \DeclareUnicodeCharacter{226B}{\ensuremath\gg}
+ \DeclareUnicodeCharacter{227A}{\ensuremath\prec}
+ \DeclareUnicodeCharacter{227B}{\ensuremath\succ}
+ \DeclareUnicodeCharacter{2283}{\ensuremath\supset}
+ \DeclareUnicodeCharacter{2286}{\ensuremath\subseteq}
+ \DeclareUnicodeCharacter{228E}{\ensuremath\uplus}
+ \DeclareUnicodeCharacter{228F}{\ensuremath\sqsubset}
+ \DeclareUnicodeCharacter{2290}{\ensuremath\sqsupset}
+ \DeclareUnicodeCharacter{2291}{\ensuremath\sqsubseteq}
+ \DeclareUnicodeCharacter{2292}{\ensuremath\sqsupseteq}
+ \DeclareUnicodeCharacter{2293}{\ensuremath\sqcap}
+ \DeclareUnicodeCharacter{2294}{\ensuremath\sqcup}
+ \DeclareUnicodeCharacter{2295}{\ensuremath\oplus}
+ \DeclareUnicodeCharacter{2296}{\ensuremath\ominus}
+ \DeclareUnicodeCharacter{2297}{\ensuremath\otimes}
+ \DeclareUnicodeCharacter{2298}{\ensuremath\oslash}
+ \DeclareUnicodeCharacter{2299}{\ensuremath\odot}
+ \DeclareUnicodeCharacter{22A2}{\ensuremath\vdash}
+ \DeclareUnicodeCharacter{22A3}{\ensuremath\dashv}
+ \DeclareUnicodeCharacter{22A4}{\ensuremath\ptextop}
+ \DeclareUnicodeCharacter{22A5}{\ensuremath\bot}
+ \DeclareUnicodeCharacter{22A8}{\ensuremath\models}
+ \DeclareUnicodeCharacter{22B4}{\ensuremath\unlhd}
+ \DeclareUnicodeCharacter{22B5}{\ensuremath\unrhd}
+ \DeclareUnicodeCharacter{22C0}{\ensuremath\bigwedge}
+ \DeclareUnicodeCharacter{22C1}{\ensuremath\bigvee}
+ \DeclareUnicodeCharacter{22C2}{\ensuremath\bigcap}
+ \DeclareUnicodeCharacter{22C3}{\ensuremath\bigcup}
+ \DeclareUnicodeCharacter{22C4}{\ensuremath\diamond}
+ \DeclareUnicodeCharacter{22C5}{\ensuremath\cdot}
+ \DeclareUnicodeCharacter{22C6}{\ensuremath\star}
+ \DeclareUnicodeCharacter{22C8}{\ensuremath\bowtie}
+ \DeclareUnicodeCharacter{2308}{\ensuremath\lceil}
+ \DeclareUnicodeCharacter{2309}{\ensuremath\rceil}
+ \DeclareUnicodeCharacter{230A}{\ensuremath\lfloor}
+ \DeclareUnicodeCharacter{230B}{\ensuremath\rfloor}
+ \DeclareUnicodeCharacter{2322}{\ensuremath\frown}
+ \DeclareUnicodeCharacter{2323}{\ensuremath\smile}
+
+ \DeclareUnicodeCharacter{25A1}{\ensuremath\Box}
+ \DeclareUnicodeCharacter{25B3}{\ensuremath\triangle}
+ \DeclareUnicodeCharacter{25B7}{\ensuremath\triangleright}
+ \DeclareUnicodeCharacter{25BD}{\ensuremath\bigtriangledown}
+ \DeclareUnicodeCharacter{25C1}{\ensuremath\triangleleft}
+ \DeclareUnicodeCharacter{25C7}{\ensuremath\Diamond}
+ \DeclareUnicodeCharacter{2660}{\ensuremath\spadesuit}
+ \DeclareUnicodeCharacter{2661}{\ensuremath\heartsuit}
+ \DeclareUnicodeCharacter{2662}{\ensuremath\diamondsuit}
+ \DeclareUnicodeCharacter{2663}{\ensuremath\clubsuit}
+ \DeclareUnicodeCharacter{266D}{\ensuremath\flat}
+ \DeclareUnicodeCharacter{266E}{\ensuremath\natural}
+ \DeclareUnicodeCharacter{266F}{\ensuremath\sharp}
+ \DeclareUnicodeCharacter{26AA}{\ensuremath\bigcirc}
+ \DeclareUnicodeCharacter{27B9}{\ensuremath\rangle}
+ \DeclareUnicodeCharacter{27C2}{\ensuremath\perp}
+ \DeclareUnicodeCharacter{27E8}{\ensuremath\langle}
+ \DeclareUnicodeCharacter{27F5}{\ensuremath\longleftarrow}
+ \DeclareUnicodeCharacter{27F6}{\ensuremath\longrightarrow}
+ \DeclareUnicodeCharacter{27F7}{\ensuremath\longleftrightarrow}
+ \DeclareUnicodeCharacter{27FC}{\ensuremath\longmapsto}
+ \DeclareUnicodeCharacter{29F5}{\ensuremath\setminus}
+ \DeclareUnicodeCharacter{2A00}{\ensuremath\bigodot}
+ \DeclareUnicodeCharacter{2A01}{\ensuremath\bigoplus}
+ \DeclareUnicodeCharacter{2A02}{\ensuremath\bigotimes}
+ \DeclareUnicodeCharacter{2A04}{\ensuremath\biguplus}
+ \DeclareUnicodeCharacter{2A06}{\ensuremath\bigsqcup}
+ \DeclareUnicodeCharacter{2A1D}{\ensuremath\Join}
+ \DeclareUnicodeCharacter{2A3F}{\ensuremath\amalg}
+ \DeclareUnicodeCharacter{2AAF}{\ensuremath\preceq}
+ \DeclareUnicodeCharacter{2AB0}{\ensuremath\succeq}
+
\global\mathchardef\checkmark="1370 % actually the square root sign
\DeclareUnicodeCharacter{2713}{\ensuremath\checkmark}
}% end of \utfeightchardefs
: (a) % - (b)) \
== 0)
-
-/* Integer overflow checks.
+/* Check for integer overflow, and report low order bits of answer.
The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
might not yield numerically correct answers due to arithmetic overflow.
- They work correctly on all known practical hosts, and do not rely
+ The INT_<op>_WRAPV macros return the low-order bits of the answer.
+ For example, INT_ADD_WRAPV (INT_MAX, 1) returns INT_MIN on a two's
+ complement host, even if INT_MAX + 1 would trap.
+
+ These macros work correctly on all known practical hosts, and do not rely
on undefined behavior due to signed arithmetic overflow.
Example usage:
- long int i = ...;
- long int j = ...;
- if (INT_MULTIPLY_OVERFLOW (i, j))
- printf ("multiply would overflow");
- else
- printf ("product is %ld", i * j);
+ long int a = ...;
+ long int b = ...;
+ long int result = INT_MULTIPLY_WRAPV (a, b);
+ printf ("result is %ld (%s)\n", result,
+ INT_MULTIPLY_OVERFLOW (a, b) ? "after overflow" : "no overflow");
+
+ enum {
+ INT_PRODUCTS_FIT_IN_LONG
+ = ! INT_CONST_MULTIPLY_OVERFLOW ((long int) INT_MIN, INT_MIN)
+ };
+
+ Restrictions on these macros:
These macros do not check for all possible numerical problems or
undefined or unspecified behavior: they do not check for division
These macros may evaluate their arguments zero or multiple times, so the
arguments should not have side effects.
+ On non-GCC-compatible compilers that do not support C11, the type
+ of INT_<op>_WRAPV (A, B) might differ from the native type of (A op
+ B), so it is wise to convert the result to the native type. Such a
+ conversion is safe and cannot trap.
+
+ For runtime efficiency GCC 5 and later has builtin functions for +,
+ -, * when doing integer overflow checking or wraparound arithmetic.
+ Unfortunately, these builtins require nonnull pointer arguments and
+ so cannot be used in constant expressions; see GCC bug 68120
+ <https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68120>. In constant
+ expressions, use the macros INT_CONST_ADD_OVERFLOW and
+ INT_CONST_ADD_WRAPV instead, and similarly for SUBTRACT and
+ MULTIPLY; these macros avoid the builtins and are slower in
+ non-constant expressions. Perhaps someday GCC's API for overflow
+ checking will be improved and we can remove the need for the
+ INT_CONST_ variants.
+
These macros are tuned for their last argument being a constant.
Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
A % B, and A << B would overflow, respectively. */
-#define INT_ADD_OVERFLOW(a, b) \
+#define INT_CONST_ADD_OVERFLOW(a, b) \
_GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
-#define INT_SUBTRACT_OVERFLOW(a, b) \
+#define INT_CONST_SUBTRACT_OVERFLOW(a, b) \
_GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
#define INT_NEGATE_OVERFLOW(a) \
INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
-#define INT_MULTIPLY_OVERFLOW(a, b) \
+#define INT_CONST_MULTIPLY_OVERFLOW(a, b) \
_GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
#define INT_DIVIDE_OVERFLOW(a, b) \
_GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
_GL_INT_MINIMUM (0 * (b) + (a)), \
_GL_INT_MAXIMUM (0 * (b) + (a)))
+/* Return the low order bits of the integer expressions
+ A * B, A - B, -A, A * B, A / B, A % B, and A << B, respectively.
+ See above for restrictions. */
+#define INT_CONST_ADD_WRAPV(a, b) _GL_INT_OP_WRAPV (a, b, +)
+#define INT_CONST_SUBTRACT_WRAPV(a, b) _GL_INT_OP_WRAPV (a, b, -)
+#define INT_NEGATE_WRAPV(a) INT_CONST_SUBTRACT_WRAPV (0, a)
+#define INT_CONST_MULTIPLY_WRAPV(a, b) _GL_INT_OP_WRAPV (a, b, *)
+#define INT_DIVIDE_WRAPV(a, b) \
+ (INT_DIVIDE_OVERFLOW(a, b) ? INT_NEGATE_WRAPV (a) : (a) / (b))
+#define INT_REMAINDER_WRAPV(a, b) \
+ (INT_REMAINDER_OVERFLOW(a, b) ? 0 : (a) % (b))
+#define INT_LEFT_SHIFT_WRAPV(a, b) _GL_INT_OP_WRAPV (a, b, <<)
+
+/* Return the low order bits of A <op> B, where OP specifies the operation.
+ See above for restrictions. */
+#if !_GL_HAVE___TYPEOF__ && 201112 <= __STDC_VERSION__
+# define _GL_INT_OP_WRAPV(a, b, op) \
+ _Generic ((a) op (b), \
+ int: _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, int), \
+ long int: _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, long int), \
+ long long int: _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, \
+ long long int), \
+ default: (a) op (b))
+#else
+# define _GL_INT_OP_WRAPV(a, b, op) \
+ (! _GL_INT_SIGNED ((0 * (a)) op (0 * (b))) \
+ ? ((a) op (b)) \
+ : _GL_EXPR_CAST ((a) op (b), \
+ (sizeof ((a) op (b)) <= sizeof (int) \
+ ? _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, int) \
+ : _GL_INT_OP_WRAPV_LONGISH (a, b, op))))
+
+/* Cast to E's type the value of V if possible. Yield V as-is otherwise. */
+# if _GL_HAVE___TYPEOF__
+# define _GL_EXPR_CAST(e, v) ((__typeof__ (e)) (v))
+# else
+# define _GL_EXPR_CAST(e, v) (v)
+# endif
+
+# ifdef LLONG_MAX
+# define _GL_INT_OP_WRAPV_LONGISH(a, b, op) \
+ (sizeof ((a) op (b)) <= sizeof (long int) \
+ ? _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, long int) \
+ : _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, long long int))
+# else
+# define _GL_INT_OP_WRAPV_LONGISH(a, b, op) \
+ _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, long int)
+# endif
+#endif
+
+/* Return A <op> B, where the operation is given by OP and the result
+ type is T. T is a signed integer type that is at least as wide as int.
+ Do arithmetic using 'unsigned T' to avoid signed integer overflow.
+ Subtract TYPE_MINIMUM (T) before converting back to T, and add it
+ back afterwards, to avoid signed overflow during conversion. */
+#define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, t) \
+ ((unsigned t) (a) op (unsigned t) (b) <= TYPE_MAXIMUM (t) \
+ ? (t) ((unsigned t) (a) op (unsigned t) (b)) \
+ : ((t) ((unsigned t) (a) op (unsigned t) (b) - TYPE_MINIMUM (t)) \
+ + TYPE_MINIMUM (t)))
+
+/* Calls to the INT_<op>_<result> macros are like their INT_CONST_<op>_<result>
+ counterparts, except they are faster with GCC 5 or later, and they
+ are not constant expressions due to limitations in the GNU C API. */
+
+#define INT_ADD_OVERFLOW(a, b) \
+ _GL_OP_OVERFLOW (a, b, INT_CONST_ADD_OVERFLOW, __builtin_add_overflow)
+#define INT_SUBTRACT_OVERFLOW(a, b) \
+ _GL_OP_OVERFLOW (a, b, INT_CONST_SUBTRACT_OVERFLOW, __builtin_sub_overflow)
+#define INT_MULTIPLY_OVERFLOW(a, b) \
+ _GL_OP_OVERFLOW (a, b, INT_CONST_MULTIPLY_OVERFLOW, __builtin_mul_overflow)
+
+#define INT_ADD_WRAPV(a, b) \
+ _GL_OP_WRAPV (a, b, INT_CONST_ADD_WRAPV, __builtin_add_overflow)
+#define INT_SUBTRACT_WRAPV(a, b) \
+ _GL_OP_WRAPV (a, b, INT_CONST_SUBTRACT_WRAPV, __builtin_sub_overflow)
+#define INT_MULTIPLY_WRAPV(a, b) \
+ _GL_OP_WRAPV (a, b, INT_CONST_MULTIPLY_WRAPV, __builtin_mul_overflow)
+
+#if __GNUC__ < 5
+# define _GL_OP_OVERFLOW(a, b, portable, builtin) portable (a, b)
+# define _GL_OP_WRAPV(a, b, portable, builtin) portable (a, b)
+#else
+# define _GL_OP_OVERFLOW(a, b, portable, builtin) \
+ builtin (a, b, &(__typeof__ ((a) + (b))) {0})
+# define _GL_OP_WRAPV(a, b, portable, builtin) \
+ _GL_OP_WRAPV_GENSYM(a, b, builtin, __gl_wrapv##__COUNTER__)
+# define _GL_OP_WRAPV_GENSYM(a, b, builtin, r) \
+ ({__typeof__ ((a) + (b)) r; builtin (a, b, &r); r; })
+#endif
+
#endif /* _GL_INTPROPS_H */
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