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-rw-r--r--Master/texmf-dist/doc/generic/xint/README99
-rw-r--r--Master/texmf-dist/doc/generic/xint/xint.pdfbin519270 -> 629272 bytes
-rw-r--r--Master/texmf-dist/source/generic/xint/xint.dtx3396
-rw-r--r--Master/texmf-dist/source/generic/xint/xint.ins5
-rw-r--r--Master/texmf-dist/tex/generic/xint/xint.sty51
-rw-r--r--Master/texmf-dist/tex/generic/xint/xintcfrac.sty57
-rw-r--r--Master/texmf-dist/tex/generic/xint/xintexpr.sty769
-rw-r--r--Master/texmf-dist/tex/generic/xint/xintfrac.sty743
-rw-r--r--Master/texmf-dist/tex/generic/xint/xintgcd.sty4
-rw-r--r--Master/texmf-dist/tex/generic/xint/xintseries.sty4
10 files changed, 4553 insertions, 575 deletions
diff --git a/Master/texmf-dist/doc/generic/xint/README b/Master/texmf-dist/doc/generic/xint/README
index fa4d92bddcd..5e4fbff4adb 100644
--- a/Master/texmf-dist/doc/generic/xint/README
+++ b/Master/texmf-dist/doc/generic/xint/README
@@ -1,27 +1,34 @@
-%----------------------------------------------------------------
-% The xint bundle
-% (base) xint.sty Expandable operations on long numbers
-% xintgcd.sty Euclidean algorithm with xint package
-% xintfrac.sty Expandable operations on fractions
-% xintseries.sty Expandable partial sums with xint package
-% xintcfrac.sty Expandable continued fractions with xint package
-% Copyright (C) 2013 by Jean-Francois Burnol
-% Version: v1.06b (2013/05/14)
-%----------------------------------------------------------------
-
-This work consists of the source file xint.dtx and of its derived files
-xint.sty, xintgcd.sty, xintfrac.sty, xintseries.sty, xintcfrac.sty,
-xint.ins and the documentation xint.pdf (or xint.dvi).
-
- This work may be distributed and/or modified under the
- conditions of the LaTeX Project Public License, either
- version 1.3c of this license or (at your option) any later
- version. This version of this license is in
- http://www.latex-project.org/lppl/lppl-1-3c.txt
- and the latest version of this license is in
- http://www.latex-project.org/lppl.txt
- and version 1.3 or later is part of all distributions of
- LaTeX version 2005/12/01 or later.
+The xint bundle
+Release 1.07a (2013/05/26)
+author: Jean-Francois Burnol
+
+Style files which will self-extract from xint.dtx:
+(base) xint.sty Expandable operations on long numbers
+ xintfrac.sty Expandable operations on fractions
+ xintexpr.sty Expandable expression parser
+ xintgcd.sty Euclidean algorithm with xint package
+ xintseries.sty Expandable partial sums with xint package
+ xintcfrac.sty Expandable continued fractions with xint package
+
+May be used with Plain TeX (\input) or as LaTeX packages (\usepackage)
+
+License
+=======
+
+This work consists of the source file xint.dtx and of its derived files:
+xint.sty, xintgcd.sty, xintexpr.sty,
+xintfrac.sty, xintseries.sty, xintcfrac.sty,
+as well as xint.ins and the documentation xint.pdf (or xint.dvi).
+
+ This work may be distributed and/or modified under the
+ conditions of the LaTeX Project Public License, either
+ version 1.3c of this license or (at your option) any later
+ version. This version of this license is in
+ http://www.latex-project.org/lppl/lppl-1-3c.txt
+ and the latest version of this license is in
+ http://www.latex-project.org/lppl.txt
+ and version 1.3 or later is part of all distributions of
+ LaTeX version 2005/12/01 or later.
The author of this work is Jean-Francois Burnol <jfbu at free dot fr>.
This work has the LPPL maintenance status `author-maintained'.
@@ -30,38 +37,44 @@ Installation and Usage:
=======================
Run tex or latex on xint.dtx.
-
-This will extract the style files xint.sty, xintgcd.sty, xintfrac.sty,
-xintseries.sty, xintcfrac.sty (and xint.ins). Files with the same
-names and in the same repertory will be overwritten. The tex (not
-latex) run will stop with the complaint that it does not understand
-\NeedsTeXFormat, but the style files will already have been extracted
-by that time.
+
+This will extract the style files xint.sty, xintfrac.sty, xintexpr.sty,
+xintgcd.sty, xintseries.sty, xintcfrac.sty (and xint.ins).
+
+Files with the same names and in the same repertory will be overwritten.
+The tex (not latex) run will stop with the complaint that it does not
+understand \NeedsTeXFormat, but the style files will already have been
+extracted by that time.
Alternatively, run tex or latex on xint.ins if available.
To get xint.pdf run pdflatex thrice on xint.dtx
xint.sty |
+ xintfrac.sty |
+ xintexpr.sty | --> TDS:tex/generic/xint/
xintgcd.sty |
- xintfrac.sty | --> TDS:tex/generic/xint/
xintseries.sty |
xintcfrac.sty |
xint.dtx --> TDS:source/generic/xint/
xint.pdf --> TDS:doc/generic/xint/
-
- It may be necessary to then refresh the TeX installation filename
- database.
+
+It may be necessary to then refresh the TeX installation filename
+database.
Usage with LaTeX: \usepackage{xint}
- \usepackage{xintgcd} (loads xint)
- \usepackage{xintfrac} (loads xint)
- \usepackage{xintseries} (loads xintfrac)
- \usepackage{xintcfrac} (loads xintfrac)
+ \usepackage{xintfrac} (loads xint)
+ \usepackage{xintexpr} (loads xintfrac)
+
+ \usepackage{xintgcd} (loads xint)
+ \usepackage{xintseries} (loads xintfrac)
+ \usepackage{xintcfrac} (loads xintfrac)
Usage with TeX: \input xint.sty\relax
- \input xintgcd.sty\relax (loads xint)
- \input xintfrac.sty\relax (loads xint)
- \input xintseries.sty\relax (loads xintfrac)
- \input xintcfrac.sty\relax (loads xintfrac)
+ \input xintfrac.sty\relax (loads xint)
+ \input xintexpr.sty\relax (loads xintfrac)
+
+ \input xintgcd.sty\relax (loads xint)
+ \input xintseries.sty\relax (loads xintfrac)
+ \input xintcfrac.sty\relax (loads xintfrac)
diff --git a/Master/texmf-dist/doc/generic/xint/xint.pdf b/Master/texmf-dist/doc/generic/xint/xint.pdf
index dc6f5d118e8..1d67e7e3ef2 100644
--- a/Master/texmf-dist/doc/generic/xint/xint.pdf
+++ b/Master/texmf-dist/doc/generic/xint/xint.pdf
Binary files differ
diff --git a/Master/texmf-dist/source/generic/xint/xint.dtx b/Master/texmf-dist/source/generic/xint/xint.dtx
index 34f86ef47b8..27b0f755918 100644
--- a/Master/texmf-dist/source/generic/xint/xint.dtx
+++ b/Master/texmf-dist/source/generic/xint/xint.dtx
@@ -1,10 +1,11 @@
% -*- coding: iso-latin-1; -*-
-% This file: xint.dtx (1.06b, 2013/05/14)
+% This file: xint.dtx (1.07a, 2013/05/26)
%
% Style files which will self-extract from xint.dtx:
% (base) xint.sty Expandable operations on long numbers
-% xintgcd.sty Euclidean algorithm with xint package
% xintfrac.sty Expandable operations on fractions
+% xintexpr.sty Expandable expression parser
+% xintgcd.sty Euclidean algorithm with xint package
% xintseries.sty Expandable partial sums with xint package
% xintcfrac.sty Expandable continued fractions with xint package
% May be used with Plain TeX (\input) or as LaTeX packages (\usepackage)
@@ -12,9 +13,10 @@
% License
% =======
%
-% This work consists of the source file xint.dtx and of its derived files
-% xint.sty, xintgcd.sty, xintfrac.sty, xintseries.sty, xintcfrac.sty, xint.ins
-% and the documentation xint.pdf (or xint.dvi).
+% This work consists of the source file xint.dtx and of its derived files:
+% xint.sty, xintgcd.sty, xintexpr.sty,
+% xintfrac.sty, xintseries.sty, xintcfrac.sty,
+% as well as xint.ins and the documentation xint.pdf (or xint.dvi).
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either
@@ -34,20 +36,22 @@
%
% Run tex or latex on xint.dtx.
%
-% This will extract the style files xint.sty, xintgcd.sty, xintfrac.sty,
-% xintseries.sty, xintcfrac.sty (and xint.ins). Files with the same
-% names and in the same repertory will be overwritten. The tex (not
-% latex) run will stop with the complaint that it does not understand
-% \NeedsTeXFormat, but the style files will already have been extracted
-% by that time.
+% This will extract the style files xint.sty, xintfrac.sty, xintexpr.sty,
+% xintgcd.sty, xintseries.sty, xintcfrac.sty (and xint.ins).
+%
+% Files with the same names and in the same repertory will be overwritten.
+% The tex (not latex) run will stop with the complaint that it does not
+% understand \NeedsTeXFormat, but the style files will already have been
+% extracted by that time.
%
% Alternatively, run tex or latex on xint.ins if available.
%
% To get xint.pdf run pdflatex thrice on xint.dtx
%
% xint.sty |
+% xintfrac.sty |
+% xintexpr.sty | --> TDS:tex/generic/xint/
% xintgcd.sty |
-% xintfrac.sty | --> TDS:tex/generic/xint/
% xintseries.sty |
% xintcfrac.sty |
% xint.dtx --> TDS:source/generic/xint/
@@ -57,32 +61,37 @@
% database.
%
% Usage with LaTeX: \usepackage{xint}
-% \usepackage{xintgcd} % (loads xint)
% \usepackage{xintfrac} % (loads xint)
+% \usepackage{xintexpr} % (loads xintfrac)
+%
+% \usepackage{xintgcd} % (loads xint)
% \usepackage{xintseries} % (loads xintfrac)
% \usepackage{xintcfrac} % (loads xintfrac)
%
% Usage with TeX: \input xint.sty\relax
-% \input xintgcd.sty\relax % (loads xint)
% \input xintfrac.sty\relax % (loads xint)
+% \input xintexpr.sty\relax % (loads xintfrac)
+%
+% \input xintgcd.sty\relax % (loads xint)
% \input xintseries.sty\relax % (loads xintfrac)
% \input xintcfrac.sty\relax % (loads xintfrac)
%
%%
%%----------------------------------------------------------------
-%% The xint bundle (version 1.06b of May 14, 2013)
+%% The xint bundle (version 1.07a of May 26, 2013)
%<xint>%% xint: Expandable operations on long numbers
-%<xintgcd>%% xintgcd: Euclidean algorithm with xint package
%<xintfrac>%% xintfrac: Expandable operations on fractions
+%<xintexpr>%% xintexpr: Expandable expression parser
+%<xintgcd>%% xintgcd: Euclidean algorithm with xint package
%<xintseries>%% xintseries: Expandable partial sums with xint package
%<xintcfrac>%% xintcfrac: Expandable continued fractions with xint package
%% Copyright (C) 2013 by Jean-Francois Burnol
%%----------------------------------------------------------------
%%
%<*none>
-\def\lasttimestamp{Time-stamp: <14-05-2013 22:00:09 CEST jfb>}
-\def\pkgversion{1.06b}
-\def\pkgdate{2013/05/14}
+\def\lasttimestamp{Time-stamp: <26-05-2013 11:42:13 CEST jfb>}
+\def\pkgversion{1.07a}
+\def\pkgdate{2013/05/26}
\def\striptimestamp #1 <#2 #3 #4 #5>{#2 at #3 #4}
\def\getdocdate #1 <#2-#3-#4 #5>{#4/#3/#2}
\edef\docdate{\expandafter\getdocdate\lasttimestamp}
@@ -97,7 +106,8 @@
\file{xintgcd.sty}{\from{xint.dtx}{xintgcd}}
\file{xintfrac.sty}{\from{xint.dtx}{xintfrac}}
\file{xintseries.sty}{\from{xint.dtx}{xintseries}}
-\file{xintcfrac.sty}{\from{xint.dtx}{xintcfrac}}}
+\file{xintcfrac.sty}{\from{xint.dtx}{xintcfrac}}
+\file{xintexpr.sty}{\from{xint.dtx}{xintexpr}}}
\endgroup
\iffalse
%</none>
@@ -118,7 +128,8 @@
\file{xintgcd.sty}{\from{xint.dtx}{xintgcd}}
\file{xintfrac.sty}{\from{xint.dtx}{xintfrac}}
\file{xintseries.sty}{\from{xint.dtx}{xintseries}}
-\file{xintcfrac.sty}{\from{xint.dtx}{xintcfrac}}}
+\file{xintcfrac.sty}{\from{xint.dtx}{xintcfrac}}
+\file{xintexpr.sty}{\from{xint.dtx}{xintexpr}}}
\endbatchfile
%----------- end of .ins file ------------------------------------
%</ins>
@@ -139,10 +150,7 @@
\usepackage[hscale=0.66,vscale=0.75]{geometry}
-%% checking that dependencies are all-right
-%\usepackage{xint}
-%\usepackage{xintgcd}
-%\usepackage{xintfrac}
+\usepackage{xintexpr}
\usepackage{xintgcd}
\usepackage{xintseries}
@@ -251,7 +259,7 @@
\usepackage[english]{babel}
\usepackage[autolanguage,np]{numprint}
\AtBeginDocument{
-\npthousandsep{,\hskip .16667em plus .01em minus .01em}}
+\npthousandsep{,\hskip .05em plus .01em minus .01em}}
\usepackage[pdfencoding=pdfdoc,bookmarks=true]{hyperref}
@@ -268,6 +276,13 @@ pdfstartview=FitH,%
pdfpagemode=UseOutlines}
+%---- a macro to manually have some margin note
+\def\MyMarginNote #1{\vadjust{\vskip-\dp\strutbox
+ \hbox{\smash{\color{niceone}\normalfont\strut
+ \llap{\small #1\ $\to$\
+ }}}\vskip\dp\strutbox }\strut{}}
+
+
%---- OUR OWN LITTLE MACRO FOR CENTERING LINES
\makeatletter
% 7 mars 2013
@@ -349,7 +364,7 @@ pdfpagemode=UseOutlines}
\bgroup \MicroFont
\let\do\do@noligs \verbatim@nolig@list
\let\do\@makeother \dospecials
- \catcode32 10 \@jfverb
+ \catcode32 10 \catcode`\~ 0 \@jfverb
}
\def\@jfverb #1{\catcode`#1\active\lccode`\~`#1\lowercase{\let~\egroup}}
% ATTENTION!
@@ -435,7 +450,7 @@ pdfpagemode=UseOutlines}
\xspace }%
}%
\xintApplyUnbraced\xintpackagenamedef
- {{xint}{xintgcd}{xintfrac}{xintseries}{xintcfrac}}
+ {{xint}{xintgcd}{xintfrac}{xintseries}{xintcfrac}{xintexpr}}
\frenchspacing
@@ -454,6 +469,8 @@ pdfpagemode=UseOutlines}
\newcount\cnta
\newcount\cntb
+\newcommand\lowast{\raisebox{-.25\height}{*}}
+% to be used as ~lowast in my short verbs
\begin{document}
\thispagestyle{empty}
@@ -464,8 +481,8 @@ pdfpagemode=UseOutlines}
{\normalfont\Large\parindent0pt \parfillskip 0pt\relax
\leftskip 2cm plus 1fil \rightskip 2cm plus 1fil
- The \xintname bundle: \xintname,
- \xintgcdname, \xintfracname, \xintseriesname and \xintcfracname.\par}%
+ The \xintname bundle: \xintname, \xintfracname, \xintexprname,
+ \xintgcdname, \xintseriesname and \xintcfracname.\par}%
{\centering
\textsc{Jean-François Burnol}\par
\footnotesize \ttfamily
@@ -480,33 +497,106 @@ pdfpagemode=UseOutlines}
the basic arithmetic operations of addition, subtraction,
multiplication and division, as applied to arbitrarily long
numbers represented as chains of digits with an optional minus
- sign. The \xintgcdname package provides implementations of the
- Euclidean algorithm and of its typesetting.
-
- The \xintfracname package extends the scope of \xintname to
- fractional numbers of arbitrary sizes ; \xintseriesname provides
- some basic functionality for computing in an expandable manner
- partial sums of series and power series with fractional
- coefficients. And \xintcfracname deals with the computation of
- continued fractions.
-
- The packages may be used with Plain and with \LaTeX. Most macros, and
- all of those doing computations, work purely by expansion without
- assignments, and may thus be used almost everywhere in \TeX{}.
+ sign. The \xintfracname package extends the scope of \xintname to
+ fractional numbers of arbitrary sizes.
+
+ \xintexprname provides an expandable parser |\xintexpr . . . \relax| of
+ expressions constructed with decimal numbers, fractions, numbers in
+ scientific notation, the basic operations as infix operators, parentheses,
+ sign prefixes, factorial symbol, and sub-expressions or macros expanding
+ to the previous items.
+
+ \xintseriesname provides some basic functionality for computing in an
+ expandable manner partial sums of series and power series with fractional
+ coefficients. The \xintgcdname package provides implementations of the
+ Euclidean algorithm and of its typesetting. And \xintcfracname deals with
+ the computation of continued fractions.
+
+ Most macros, and all of those doing computations, work purely by expansion
+ without assignments, and may thus be used almost everywhere in \TeX{}.
+
+ The packages may be used with any flavor of \TeX{} supporting the \eTeX{}
+ extensions. \LaTeX{} users will use |\usepackage| and others |\input| to
+ load the package components.
\end{abstract}
\tableofcontents
-\section{Raison d'\^etre of these packages}
+\section{Presentation}
+
+\subsection{Latest}
+
+Release |1.07| brings important additions:
+\begin{itemize}
+\item The \xintfracname macros now recognize numbers written in scientific
+ notation, and the \csb{xintFloat} command outputs its argument with a given
+ number |D| of significant figures. The value of |D| is either given as
+ optional argument to \csb{xintFloat} or set with |\xintDigits := D;|. The
+ default value is |16|.
+\item The \xintexprname package is a new core constituent (which loads
+ automatically \xintfracname and \xintname) and implements the expandable
+ expanding parsers \centeredline{{\color{blue}|\xintexpr . . . \relax|},
+ and its variant
+ {\color{blue}|\xintfloatexpr . .
+ . \relax|}} allowing on input formulas using the standard form with infix
+ operators |+|, |-|, |*|, |/|, and |^|, and arbitrary levels of
+ parenthesizing. Within a float expression the operations are executed
+ according to the current value of \csb{xintDigits}. Within an
+ |\xintexpr|-ession the binary operators are computed exactly.
+\end{itemize}
+Important aspects related to the use of |\xintexpr| and |\xintfloatexpr| are
+explained in the documentation. In particular the above forms are usable as
+sub-expressions but not directly printable; for this one has |\xinttheexpr|
+and |\xintthefloatexpr|, or |\xintthe\xintexpr| and
+|\xintthe\xintfloatexpr|. The floating point precision |D| is set (this is a
+local assignment to a |\mathchar| variable) with
+|\xintDigits := D;| and queried with |\xinttheDigits|. It may be set to anything up to
+ |32768|.\footnote{but values higher than 100 or 200 will
+ presumably give too
+ slow evaluations.} The macro incarnations of the binary operations admit an
+ optional argument which will replace pointwise |D|; this argument may
+ exceed the |32678| bound.
+
+
+\subsection{Missing things}
+
+
+Although the latest release now implements arbitrary precision
+floating-point operations, and an expandable parser, it does not
+implement yet a mathematical library, in particular fractional powers,
+logarithm or trigonometric functions.
+
+% It is doubtful that I will engage into writing such a thing as the window
+% left open in terms of speed of computation from the constraint of
+% expandability is rather narrow. Up to a few dozen digits of floating point
+% precision perhaps, perhaps up to one hundred digits, but not much more (the
+% package is usable for one-shot, expensive, computations, though). And the
+% initial motivation was more into exact arithmetic operations with
+% (reasonably) arbitrarily long numbers.
+
+% Besides,
+
+The \LaTeX3 project has implemented expandably floating-point
+computations with 16 significant figures
+(\href{http://www.ctan.org/tex-archive/macros/latex/contrib/l3kernel}{\color{niceone}l3fp}),
+including special functions such as exp, log, sine and cosine.
+
+I have benefited from the commented source of the \LaTeX3 parser; the
+|\xintexpr| parser has its own features and peculiarities. See
+\hyperref[sec:comexpr]{\color{niceone}its documentation}.
\subsection{Some examples}
-The main goal is to allow computations with integers and fractions of arbitrary
-sizes.\footnote{Here and elsewhere, ``arbitrarily big'' means roughly numbers
- with numerators and denominators having strictly less than
+The main initial goal is to allow computations with integers and fractions
+of arbitrary sizes.\footnote{Here and elsewhere, ``arbitrarily big'' means
+ roughly numbers with numerators and denominators having strictly less than
2\string^\string{31\string}=2147483648 digits. Memory constraints from the
- |etex| or |pdftex| executables presumably limit even more the possible
- computations, not to mention the time taken by them.}
+ \TeX{} engines presumably limit more the possible computations; but the
+ biggest constraint is the one of computation time, related to the
+ propriety of expandability. As explained in the text multiplying two one
+ thousand digits numbers is already expensive. On the other hand, floating
+ point computations are implemented with arbitrary precision, and one can
+ work comfortably with fifty digits of precision for example. }
Here are some examples:
@@ -518,19 +608,16 @@ Here are some examples:
{1500}{1234/56789}}\dots
{\color{magenta}&0.99^{-100}& with 200 digits after the decimal point:}\\
-{\color{blue}\csb{xintTrunc}|{200}{|\csb{xintPow}|{.99}{-100}}\dots|}:
-\printnumber{\xintTrunc {200}{\xintPow {.99}{-100}}}\dots
+{\color{blue}\csb{xintTrunc}|{200}{\xinttheexpr .99^-100\relax}\dots|}:
+\printnumber{\xintTrunc {200}{\xinttheexpr .99^-100\relax}}\dots
{\color{magenta}Computation of a Bezout identity with |7^200-3^200| and |2^200-1|:}\\
{\color{blue}|\xintAssign\xintBezout|\\
-\hspace*{2cm}|{\xintiSub {\xintiPow
- {7}{200}}{\xintiPow{3}{200}}}|\\
-\hspace*{2cm}|{\xintiSub {\xintiPow {2}{200}}{1}}\to\A\B\U\V\D|%
+\hspace*{2cm}|{\xintNum{\xinttheexpr 7^200-3^200\relax}}|\\
+\hspace*{2cm}|{\xintNum{\xinttheexpr 2^200-1\relax}}\to\A\B\U\V\D|%
\centeredline{|\U$\times$(7^200-3^200)+\xintiOpp\V$\times$(2^200-1)=\D|}}%
-\xintAssign\xintBezout {\xintiSub {\xintiPow
- {7}{200}}{\xintiPow{3}{200}}}
-{\xintiSub {\xintiPow {2}{200}}{1}}\to\A\B\U\V\D
+\xintAssign\xintBezout {\xintNum{\xinttheexpr 7^200-3^200\relax}}{\xintNum{\xinttheexpr 2^200-1\relax}}\to\A\B\U\V\D
\printnumber\U$\times$(&7^200-3^200&)+\printnumber{\xintiOpp\V}$\times$(&2^200-1&)=\printnumber\D
{\color{magenta}The Euclide algorithm applied to \np{179876541573} and
@@ -551,7 +638,7 @@ infinity, has value
$\frac{\pi^2}{144}-\frac1{162}={}$\np{0.06236607994583659534684445}\dots\,%
\footnote{\label{fn:np}This number is typeset using the
\href{http://www.ctan.org/pkg/numprint}{\color{niceone}numprint} package, with
- \texttt{\detokenize{\npthousandsep{,\hskip .16667em plus .01em minus .01em}}}. But the breaking accross
+ \texttt{\detokenize{\npthousandsep{,\hskip .05em plus .01em minus .01em}}}. But the breaking accross
lines works only in text mode. The number itself was (of course...) computed
initially with \xintname, with 30 digits of $\pi$ as input.
See
@@ -574,6 +661,7 @@ examples with the \xintgcdname package, and finally one with the
\xintseriesname package, for partial sums of series with fractional
coefficients. There is also \xintcfracname for continued fractions computations.
+
To see more of \xintname in action, jump to the
{\color{niceone}\autoref{sec:series}} describing the commands of the
\xintseriesname{} package, especially as illustrated with the
@@ -587,6 +675,8 @@ documentation are not hard-coded in the source of the document but just written
there using the package macros, and were selected to not impact too much the
compilation time.
+
+
\subsection{Expandability, (in)-efficiency}
For some initially circumstantial reasons (related to the origins of the
@@ -625,21 +715,6 @@ complete expandability.\footnote{I could, naturally,
be proven wrong!}\,\footnote{The Lua\TeX{} project possibly makes endeavours
such as \xintname appear even more insane that they are, in truth.}
-\subsection{Missing things}
-
-Currently \xintname does not provide `floating-point' operations. The
-\LaTeX3 project has implemented expandably floating-point computations
-with 16 significant figures
-(\href{http://www.ctan.org/tex-archive/macros/latex/contrib/l3kernel}{\color{niceone}l3fp}), including
-special functions such as exp, log, sine and cosine.
-
-The most blatantly lacking thing in the \xintname project is a decent input
-parser, allowing to type in computations in a usual infix form such as, for
-example |3*14+2.7^-2*5|. At this time, one has to type |\xintAdd {\xintMul
- {3}{14}}{\xintMul{\xintPow{2.7}{-2}}{5}}|. Previous computation results can be
-stored in macros and given as arguments to the package macros (see further on
-for important aspects of this).
-
\subsection{Origins of the package}
@@ -679,7 +754,7 @@ for \csa{numexpr} has ten digits).
The present package is the result of this initial questioning.
\begin{framed}\centering
- \xintname requires the \eTeX{} \csa{numexpr} primitive.
+ \xintname requires the \eTeX{} extensions.
\end{framed}
@@ -725,7 +800,8 @@ The |\printnumber| macro is not part of the package and would need additional
thinking for more general use.\footnote{as explained in
\hyperref[fn:np]{\color{niceone}a previous footnote},
the |numprint| package may also be used, in text mode only (as the thousand
- separator seemingly ends up typeset in a |\string\hbox| when in math mode).} It may be used as |\printnumber
+ separator seemingly ends up typeset in a |\string\hbox| when in math
+ mode).} It may be used as |\printnumber
{\xintQuo{\xintPow {2}{1000}}{\xintFac{100}}}|, or as |\printnumber\mynumber| if
the macro |\mynumber| was previously defined via an |\edef|, as for
example:\centeredline{ |\edef\mynumber {\|\texttt{xintQuo}|{\xintPow
@@ -737,38 +813,54 @@ or as
would allow to use it directly as |\printnumber\mynumber| with a |\mynumber|
itself defined via a |\def| or |\newcommand|).
-\def\x {\xintTrunc {300}{\xintPow{.7}{-25}}}%
Just to show off, let's print 300 digits (after the decimal point) of
-the decimal expansion of &0.7^{-25}&:
-\centeredline{|\printnumber {\xintTrunc {300}{\xintPow{.7}{-25}}}\dots|}
-\expandafter\printnumber\expandafter {\x}\dots
-
-This computation uses \xintfracname wich extends to fractions the basic
-arithmetic operations defined for integers by \xintname.
-
-
+the decimal expansion of &0.7^{-25}&:\footnote{the |\string\np| typesetting
+ macro
+ is from the |numprint| package.}
+\centeredline{|\np {\xintTrunc {300}{\xinttheexpr .7^-25\relax}}\dots|}
+\np {\xintTrunc {300}{\xinttheexpr .7^-25\relax}}\dots
+
+This computation uses the macro \csb{xintTrunc} from package \xintfracname
+wich extends to fractions the basic arithmetic operations defined for
+integers by \xintname. It also uses \csb{xinttheexpr} from package
+\xintexprname, which allows to use standard notations. Note that the
+fraction |.7^-25| is first evaluated exactly; for some more complex inputs,
+such as |.7123045678952^-243|, the exact evaluation before truncation would
+be expensive, and (assuming one needs twenty digits) one
+would rather use floating mode:
+\centeredline{|\xintDigits:=20;
+ \np{\xintthefloatexpr .7123045678952^-243\relax}|}%
+\xintDigits:=20;%
+\centeredline{|.7123045678952^-243| = \texttt{\np{\xintthefloatexpr
+ .7123045678952^-243\relax }}}
+
+% 6.342,022,117,488,416,127,3 10^35
+% maple n'aime pas ^-243 il veut les parenthèses, bon et il donne, en Digits
+% = 24: 0.634202211748841612732270 10^36
+
+\xintDigits:=16;
Important points, to be noted, related to the expansion of arguments:
\begin{enumerate}
-\item the macros expand `fully' their arguments,\vadjust{\vskip-\dp\strutbox
- \hbox{\smash{\color{niceone}\llap{\strut\small CHANGED! (|1.06|)\
- $\to$\kern\parindent
- }}}\vskip\dp\strutbox } this means that they expand the
- first token seen (for each argument), then expand \strut{} again, etc...,
- until
- something un-expandable such as a\strut{} digit or a brace is hit
- against.\footnote{the knowledgeable people will have recognized \texttt{\string\romannumeral-\string`0}} This
- example \centeredline{|\def\x{12}\def\y{34}|%
+\item the macros expand `fully' their arguments, this means that they expand
+ the first token seen (for each argument), then expand
+ \MyMarginNote{Changed in |1.06|}, etc..., until something un-expandable
+ such as a\strut{} digit or a brace is hit against.\footnote{the
+ knowledgeable people will have recognized
+ \texttt{\string\romannumeral-\string`0}} This example
+ \centeredline{|\def\x{98765}\def\y{43210}|%
|\xintAdd {\x}{\x\y}|} is \emph{not} a legal construct, as the |\y| will
- remain untouched by expansion and not get converted into the digits which are
- expected by the
- sub-routiunes of |\xintAdd|. It works here by sheer luck as the |\y|
- gets expanded inside a |\numexpr|. But this would fail in general: if you need
- a more complete (expandable...) expansion of your initial input, you should
- use the \fbox{\csa{bigintcalcNum}} macro from the |bigintcalc| package. Or,
- outside of an expandable-only context, just massage your inputs through
- \csa{edef}'s.
+ remain untouched by expansion and not get converted into the digits which
+ are expected by the sub-routines of |\xintAdd|. It is a |\numexpr|
+ which will expand it and an arithmetic overflow will arise as |9876543210|
+ exceeds the \TeX{} bounds.
+
+ \begingroup\slshape
+ The |1.07| novelty\MyMarginNote{New with |1.07|} \csb{xinttheexpr} has brought a solution: here one
+ would write |\xinttheexpr \x+\x\y\relax|, or
+ |\xintAdd\x{\xinttheexpr\x\y\relax}|.\hfill
+ \endgroup
\item Unfortunately, after |\def\x {12}|, one can not use just
{\color{blue}|-\x|} as input to one of the package macros: the rules above
@@ -776,6 +868,13 @@ Important points, to be noted, related to the expansion of arguments:
hence do nothing. The only way is to use the \csb{xintOpp}
macro, which replaces a number with its opposite.
+ \begingroup\slshape
+ Again, this is otherwise inside an \csb{xinttheexpr}-ession or
+ \csb{xintthefloatexpr}-ession. There,\MyMarginNote{New with |1.07|} the
+ minus sign may prefix macros which will expand to numbers (or parentheses
+ etc...)
+ \endgroup
+
\def\x {12}%
\def\AplusBC #1#2#3{\xintAdd {#1}{\xintMul {#2}{#3}}}%
@@ -809,16 +908,17 @@ Important points, to be noted, related to the expansion of arguments:
\hspace*{1cm}|\def\aplusbc #1#2#3{\xintadd {#1}{\xintMul {#2}{#3}}}|\par
\hspace*{1cm}|\def\AplusBC {\romannumeral0\aplusbc}|\par
Or, for people using the \LaTeX{} vocabulary:\par
- \hspace*{1cm}|\newcommand{\aplusbc}[3]{\xintadd {#1}{\xintMul {#2}{#3}}}|\par
- \hspace*{1cm}|\newcommand{\AplusBC}{\romannumeral0\aplusbc}|\par
+ \hspace*{1cm}|\newcommand~lowast{\aplusbc}[3]{\xintadd {#1}{\xintMul
+ {#2}{#3}}}|\par
+ \hspace*{1cm}|\newcommand~lowast{\AplusBC}{\romannumeral0\aplusbc}|\par
This then allows further definitions of macros expanding in two steps only,
such as:\par
|\def\aplusbcsquared #1#2#3{\aplusbc {#1}{#2}{\xintSqr{#3}}}|\par
|\def\AplusBCSquared {\romannumeral0\aplusbcsquared}|\par
- |\newcommand\myalgebra [6]{\xintmul {\AplusBC {#1}{#2}{#3}}{\AplusBC
+ |\newcommand~lowast\myalgebra [6]{\xintmul {\AplusBC {#1}{#2}{#3}}{\AplusBC
{#4}{#5}{#6}}}|\par
- |\newcommand\MyAlgebra {\romannumeral0\myalgebra}|\par
+ |\newcommand~lowast\MyAlgebra {\romannumeral0\myalgebra}|\par
\end{enumerate}
The |\romannumeral0| things above look like an invitation to hacker's
@@ -827,16 +927,47 @@ there is no reason to follow these guidelines. Just chain arbitrarily the
package macros, and the new ones will be completely expandable and usable one
within the other.
-\begin{framed}
- {\color{niceone}New with |1.06|}: those macro arguments which are
+Release |1.07| has the \csb{xintNewExpr} command\MyMarginNote{New with
+ |1.07|} which automatizes the creation of such expandable macros:
+\centeredline{|\xintNewExpr\AplusBC[3]{_1+_2*_3}|} creates the |\AplusBC|
+macro doing the above and expanding in two expansion steps.
+
+ Those macro arguments \MyMarginNote{New with |1.06|} which are
intrinsically constrained to obey the \TeX{} bounds on integers (see the next
section) are now systematically fed to a |\numexpr|, hence they will be
subjected to a complete expansion, registers are allowed, and things such as
- |\mycount+\myothercount*17| become admissible arguments.
-\end{framed}
+ |\mycount+\myothercount*17| become admissible arguments.
+
+ This applies to
+ the argument of the factorial function, the exponent in the power
+ function, the number of digits to truncate or round with, and in various
+ other cases.
+
+ Note however that inside an |\xintexpr|-ession count registers for
+ the\MyMarginNote{New with |1.07|} exponent of the power function or the
+ argument of the factorial are not accepted (they are, if prefixed with
+ |\the|); on the other hand these arguments may be fractions, as long as
+ they turn out to be in truth integers after simplification. And the
+ exponent in the power function in floating expressions may even exceed the
+ \TeX{} bounds on integers.
+
\section {Inputs and outputs}
-The arguments to most of the \xintname macros are of three types:
+The core bundle constituents are \xintname, \xintfracname, \xintexprname,
+each one loading its predecessor. The base constituent \xintname only deals
+with integers, of arbitrary sizes, and apart from its macro \csb{xintNum},
+the input format is rather strict. Then \xintfracname extends the scope to
+fractions (automatically normalizing leading signs and zeros using
+\csb{xintNum} for both numerator and denominator); numerators and
+denominators are separated by a forward slash and may contain each an
+optional fractional part after the decimal mark (which has to be a dot).
+Now with |1.07| they also may each end with an optional scientific part (a
+lowercase e followed by a signed integer).
+
+
+The numeric arguments to the bundle macros may be of various types,
+extending in generality:
+
\begin{enumerate}
\item `short' integers, \emph{i.e.} less than (or equal to) in absolute value
\np{\xintiSub{\xintiPow {2}{31}}1}. I will refer to this as the `\TeX{}' or
@@ -847,9 +978,9 @@ The arguments to most of the \xintname macros are of three types:
latter cases. When the argument exceeds the \TeX{} bound (either positively or
negatively), an error will originate from a \csa{numexpr} expression and it
may sometimes be followed by a more specific error `message' from a package
- macros.
+ macro.
\item `long' integers, which are the bread and butter of the package commands.
- They are signed integers with a practically illimited number of digits.
+ They are signed integers with an illimited number of digits.
Theoretically though, most of the macros require that the number of digits
itself be less than the \TeX-\csa{numexpr} bound (more precisely &2^31-9&).
Some macros, such as addition when \xintfracname has not been loaded, do not
@@ -860,7 +991,12 @@ The arguments to most of the \xintname macros are of three types:
longish operation.
\item `fractions': they become available after having loaded the \xintfracname
package. Their format on input will be described next, a fraction has a
- numerator, a forward slash and then a denominator.
+ numerator, a forward slash and then a denominator.\MyMarginNote{New with
+ |1.07|} It is now possible to use scientific notation, with a lowercase
+ |e| on input (an uppercase |E| is accepted inside the |\xintexpr|-essions).
+ The decimal mark must be a dot and not a comma. No separator for thousands
+ should be used on inputs, and except within |\xintexpr|-essions, spaces
+ should be avoided.
\end{enumerate}
\begin{framed}
@@ -869,9 +1005,10 @@ The arguments to most of the \xintname macros are of three types:
accepting `long numbers' or fractions on input: they must be prefixed by
|\the| or |\number|. The same for \csa{numexpr} expressions. However,\strut{}
count registers and |\numexpr| expressions\vadjust{\vskip-\dp\strutbox
- \hbox{\smash{\color{niceone}\llap{\strut\small NEW WITH |1.06|\
- $\to$\kern\parindent
- }}}\vskip\dp\strutbox } are allowed in arguments intrinsically
+ \hbox{\smash{\color{niceone}\normalfont\strut
+ \llap{\small New with |1.06|\ $\to$\kern\parindent
+ }}}\vskip\dp\strutbox }\strut{} are
+ allowed in arguments intrinsically
constrained to obey the \TeX{} bounds.
\end{framed}
@@ -879,16 +1016,12 @@ The arguments to most of the \xintname macros are of three types:
\edef\z {\xintAdd
{+--0367.8920280/-++278.289287}{-109.2882/+270.12898}}
-The package macros first operate a `full' expansion\vadjust{\vskip-\dp\strutbox
- \hbox{\smash{\color{niceone}\llap{\strut\small NEW WITH |1.06|\ $\to$\
- }}}\vskip\dp\strutbox } of their \strut{} arguments, as
-explained above: only the first token is repeatedly expanded until no more is
-possible.
+ The package macros first operate a `full' expansion\MyMarginNote{New with
+ |1.06|} of their \strut{} arguments, as explained above: only the first
+ token is repeatedly expanded until no more is possible.
On the other hand, this
-expansion is\strut{} a \emph{complete one }\vadjust{\vskip-\dp\strutbox
- \hbox{\smash{\color{niceone}\llap{\strut\small NEW WITH |1.06|\ $\to$\
- }}}\vskip\dp\strutbox } for those arguments which
+expansion is a\MyMarginNote{New with |1.06|} for those arguments which
are constrained to obey the \TeX{} bounds on numbers, as they are systematically
inserted inside a |\numexpr...\relax| expression.
@@ -905,7 +1038,7 @@ The allowed input formats for `long numbers' and `fractions' are:
{+-+-+----++-++----0000000009876543210}}}%
Note that |-0| is not legal input and will confuse \xintname (but not
\csa{xintNum} which even accepts an empty input).
-\item the relaxed format is when \xintfracname is loaded. Most macros are then
+\item the extended format is when \xintfracname is loaded. Most macros are then
modified to accept inputs of the form |A/B| (or just |A|), where |A| and |B|
will be automatically given to the normalizing \csb{xintNum} macro.
Additionally, each of |A| and |B| may have an optional decimal point with
@@ -918,6 +1051,12 @@ The allowed input formats for `long numbers' and `fractions' are:
where the second line was produced with |\xintIrr| and the next with
|\xintTrunc {50}| to get fifty digits of the decimal expansion following the
decimal mark.
+\item the more extended format comes with release |1.07| of \xintfracname.
+ Scientific notation is accepted on input both for the numerators and
+ denominators of fractions, and is produced on output by \csb{xintFloat}:
+ \centeredline{|\xintAdd{10.1e1}{101.010e3}=|\texttt{\xintAdd{10.1e1}{101.010e3}}}%
+ \centeredline{|\xintRaw{1.234e5/6.789e3}=|\texttt{\xintRaw{1.234e5/6.789e3}}}%
+ \centeredline{|\xintFloat[5]{1/66049}=|\texttt{\xintFloat[5]{1/66049}}}
\end{enumerate}
Of course, even when \xintfracname is loaded, some macros can not treat
fractions on input. With release |1.05| they have, for the most part, been also
@@ -929,22 +1068,34 @@ computes a euclidean quotient). It now does, because its arguments are in truth
integers.
A number can start directly with a decimal point:
-\centeredline{|\xintPow{-.3/.7}{11}=|{\xintPow{-.3/+.7}{11}}}%
+\centeredline{|\xintPow{-.3/.7}{11}=|\texttt{\xintPow{-.3/+.7}{11}}}%
+\centeredline{|\xinttheexpr (-.3/.7)^11\relax=|\texttt{\xinttheexpr (-.3/.7)^11\relax}}
It is also licit to use |\A/\B| as input if each of |\A| and |\B| expands (in
the sense previously described) to a ``decimal number'' as examplified above by
-the numerators and denominators. Or one may have just one macro |\C| which
+the numerators and denominators (thus, possibly with a `scientific' exponent
+part, with a lowercase `e'). Or one may have just one macro |\C| which
expands to such a ``fraction with optional decimal points'', or mixed things
such as |\A 245/7.77|, where the numerator will be the concatenation of the
-expansion of |\A| and |245|. But, as explained already |123\A| is a no-go.
+expansion of |\A| and |245|. But, as explained already |123\A| is a no-go,
+\emph{except inside an |\string\xintexpr|-ession of course}!
+Finally, after the decimal point there may be |eN| where |N| is a positive
+or negative number (obeying the \TeX{} bounds on
+integers).\MyMarginNote{New with |1.07|} This `|e|' part (which must be in
+lowercase, except inside |\xintexpr|-essions) may appear both at the numerator
+and at the denominator. \centeredline{|\xintRaw
+ {+--+1253.2782e++--3/---0087.123e---5}=|\texttt{\xintRaw
+ {+--+1253.2782e++--3/---0087.123e---5}}}
+\medskip
Loading \xintfracname not only relaxes the format of the inputs; it also
-modifies the format of the outputs: except when filtered through the
-\csb{xintIrr} (and \csb{xintJrr}) or \csb{xintRaw} macros, a fraction is always
-output in the |A/B[n]| form (which stands for &(A/B)10^n&). The |A| and |B| may
-end in zeros (\emph{i.e}, |n| does not represent all powers of ten), and will
-generally have a common factor. The denominator |B| is always strictly positive.
+modifies the format of the outputs: except when a fraction is filtered on output
+by \csb{xintIrr} (and \csb{xintJrr}) or \csb{xintRawWithZeros}, or by the
+truncation or rounding macros, it will always be in the |A/B[n]| form (which
+stands for |(A/B)|$\times$|10^n|). The |A| and |B| may end in zeros (\emph{i.e},
+|n| does not represent all powers of ten), and will generally have a common
+factor. The denominator |B| is always strictly positive.
A macro \csb{xintFrac} is provided
for the typesetting (math-mode only) of such a `raw' output. Of course, the
@@ -952,9 +1103,8 @@ for the typesetting (math-mode only) of such a `raw' output. Of course, the
Direct user input of things such as |16000/289072[17]| or |3[-4]| is authorized.
It is even possible to use |\A/\B[17]| if |\A| expands to |16000| and |\B| to
-|289072|, or |\A| if |\A| expands to |3[-4]|. However,\strut{}\vadjust{\vskip-\dp\strutbox
- \hbox{\smash{\color{niceone}\llap{\strut\small IMPORTANT!\ $\to$\
- }}}\vskip\dp\strutbox } NEITHER the numerator NOR
+|289072|, or |\A| if |\A| expands to |3[-4]|. However,\MyMarginNote{IMPORTANT!}
+NEITHER the numerator NOR
the denominator may then have a decimal
point. And, for this format, ONLY the numerator may carry
a UNIQUE minus sign (and no superfluous leading zeros; and NO plus sign).
@@ -970,24 +1120,24 @@ a UNIQUE minus sign (and no superfluous leading zeros; and NO plus sign).
\begin{framed}
All computations done by \xintfracname on fractions are exact. Inputs
- containing decimal points do not make the package switch to a (currently
- non-existent) `floating-point' mode. The inputs, however long, are always
- converted into an exact internal representation.
+ containing decimal points or scientific parts do not make the package
+ switch to a `floating-point' mode. The inputs, however long, are always
+ converted into exact internal representations.
+
+ Floating point evaluations are done with special macros containing
+ `Float' in their names, or inside |\xintthefloatexpr|-essions.
\end{framed}
-Generally speaking, there should be no spaces among the digits in the inputs.
+Generally speaking, there should be no spaces among the digits in the inputs
+(in arguments to the package macros).
Although most would be harmless in most macros, there are some cases
where spaces could break havoc. So the best is to avoid them entirely.
-\edef\z {\xintSub {\xintMul {2.3}{\xintPow {5.6}{3}}} {17728/189.5}}
-
-It would certainly be nice to be able to input directly expressions such as
-|2.3*5.6^3-17728/189.5|, but this is not possible. One must use, for
-example:
- \centeredline{|\xintSub {\xintMul {2.3}{\xintPow
- {5.6}{3}}} {17728/189.5}|} or, an option in this case is:
-\centeredline{|\xintAdd {\xintPrd {{2.3}{5.6}{5.6}{5.6}}}{-17728/189.5}|}%
-%\centeredline{\texttt{=\z =\xintIrr\z =\xintTrunc {15}\z\dots}}
+This is entirely otherwise inside an |\xintexpr|-ession, where spaces are
+expected to, as a general rule (with possible exceptions related to the
+allowed use of braces, see the
+\hyperref[sec:comexpr]{\color{niceone}documentation}) be completely
+harmless, and even recommended for making the source more legible.
Syntax such as |\xintMul\A\B|
is accepted and equivalent\footnote{see however near the end of
@@ -1001,7 +1151,8 @@ this is not provided by the package. Arguments must be either
within braces or a single control sequence.
Note that |-| and |+| may serve only as unary operators, on \emph{explicit}
-numbers. They can not serve to prefix macros evaluating to such numbers.
+numbers. They can not serve to prefix macros evaluating to such numbers,
+\emph{except inside an |\string\xintexpr|-ession.}
\section{More on fractions}
@@ -1037,9 +1188,12 @@ versions. They have less parsing overhead.
-The macro \csb{xintRaw} prints the fraction in |A/B| form, the former trailing
-|[n]| having been converted into explicit zeros either at the numerator or the
-denominator. The |B| is printed even if it has value |1|.
+The macro \csb{xintRaw} prints\MyMarginNote{\parbox[t]{1.5cm}{Changed\\ in
+ |1.07|!!}} the fraction
+directly from its internal representation in |a/b[n]| form. To convert
+the trailing |[n]| into explicit zeros either at the numerator or the
+denominator, use \csb{xintRawWithZeros}. In both cases the |B| is printed
+even if it has value |1|.
Conversely (sort of), the macro \csb{xintREZ}
puts all powers of ten into the |[n]| (REZ stands for remove zeros).
@@ -1113,11 +1267,12 @@ fraction an exact computation would have produced.
To get the integer part of the decimal expansion of |f|, use
|\xintiTrunc{0}{f}|: \centeredline{|\xintiTrunc {0}{\xintPow
{1.01}{100}}=|\texttt{\xintiTrunc {0}\z}}%
-% \centeredline{|(\xintTrunc {30}{\xintPow
-% {1.01}{100}}=|\texttt{\xintTrunc {30}\z)}}
\centeredline{|\xintiTrunc {0}{\xintPow{0.123}{-10}}=|\texttt{\xintiTrunc
{0}{\xintPow{0.123}{-10}}}}
+See also the documentation of \csb{xintRound}, \csb{xintiRound} and
+\csb{xintFloat}.
+
\section{\csh{ifcase}, \csh{ifnum}, ... constructs}
When using things such as |\ifcase \xintSgn{\A}| one has to leave
@@ -1137,6 +1292,12 @@ With |\def\A{1}|:
% \ifcase \xintSgn\A 0\or OK\else ERROR\fi\
% \ifcase \xintSgn{\A} 0\or OK\else ERROR\fi
+Release |1.07| provides the expandable\MyMarginNote{New with |1.07|!} \csb{xintSgnFork} which chooses
+one of three branches according to whether its argument expand to |-1|,
+|0| or |1|. This, rather than the corresponding |\ifcase|, should be used
+when such a fork is needed as argument to one of the package macros.
+
+
\section{Multiple outputs}\label{sec:outputs}
Some macros have an output consisting of more than one number, each one is then
@@ -1341,7 +1502,7 @@ control sequence is the message. The error is raised \emph{before} the
end of the expansion so as to not disturb further processing of the
token stream, after completion of the operation. Generally the problematic
operation will output a zero. Possible such error message control
-sequences:
+sequences:
\dverb|&
\xintError:ArrayIndexIsNegative
\xintError:ArrayIndexBeyondLimit
@@ -1355,6 +1516,10 @@ sequences:
\xintError:TooBigDecimalShift
\xintError:TooBigDecimalSplit
\xintError:NoBezoutForZeros
+\xintError:ignored
+\xintError:removed
+\xintError:use_xintthe!
+\xintError:inserted
|
\section{Common input errors when using the package macros}
@@ -1364,49 +1529,58 @@ sequences:
Here is a list of common input errors. Some will cause compilation errors,
others are more annoying as they may pass through unsignaled.
\begin{itemize}
-\item using |-| to prefix some macro: |-\xintiSqr{35}/271|.
+\item using |-| to prefix some macro: |-\xintiSqr{35}/271|.\footnote{this is
+ allowed inside an |\string\xintexpr|-ession.}
\item using one pair of braces too many |\xintIrr{{\xintiPow {3}{13}}/243}| (the
computation goes through with no error signaled, but the result is completely
wrong).
\item using |[]| and decimal points at the same time |1.5/3.5[2]|.
\item using |[]| with a sign in the denominator |3/-5[7]|.
-\item loading \xintfracname and using expressions previously producing integers
- as numerators
- or denominators: |\edef\x{\xintMul {3}{5}/\xintMul{7}{9}}|. The problem is
- that this expands to \texttt{\x} which is invalid on input. Using this
- |\x| in a fraction macro will most certainly cause a compilation error, with
- its usual arcane and undecipherable accompanying message.
+\item using macros supposedly giving integers as numerators or
+ denominators: |\edef\x{|\allowbreak|\xintMul {3}{5}/\xintMul{7}{9}}|. The
+ problem is
+ that, with \xintfracname loaded, this expands to \texttt{\x} which is
+ invalid on input. Using this |\x| in a fraction macro will most certainly
+ cause a compilation error, with its usual arcane and undecipherable
+ accompanying message. The fix here is to use rather |\xintiMul|, or
+ |\xinttheexpr 3*5\relax/\xinttheexpr 7*9\relax|. The more advanced among us
+ in mental power will have done the computations in their heads.
\end{itemize}
\section{Package namespace}
-Inner macros of \xintname, \xintgcdname, \xintfracname, \xintseriesname, and
-\xintcfracname{} all begin either with |\XINT_| or with
-|\xint_|.\footnote{starting with release |1.06b| the style files use for macro
- names a more modern underscore |\_| rather than the |@| sign. Probability of a
- name clash with \LaTeX2e packages is now even closer to nil, and with \LaTeX3
- packages it is also close to nil as our control sequences are all lacking the
- argument specifier part of \LaTeX3 function names.} The package public
-commands all start with |\xint|. The major forms have their initials
-capitalized, and lowercase forms, prefixed with |\romannumeral0|, allow
-definitions of further macros expanding in only two steps to their final
-outputs. Some other control sequences are used only as delimiters, and left
-undefined, they may have been defined elsewhere, their meaning doesn't matter
-and is not touched.
+Inner macros of \xintname, \xintfracname, \xintexprname, \xintgcdname,
+\xintseriesname, and \xintcfracname{} all begin either with |\XINT_| or with
+|\xint_|.\footnote{starting with release |1.06b| the style files use for
+ macro names a more modern underscore |\_| rather than the |@| sign.
+ Probability of a name clash with \LaTeX2e packages is now even closer to
+ nil, and with \LaTeX3 packages it is also close to nil as our control
+ sequences are all lacking the argument specifier part of \LaTeX3 function
+ names. A few macros starting with |\string\XINT| do not have the
+ underscore.} The package public commands all start with |\xint|. The major
+forms have their initials capitalized, and lowercase forms, prefixed with
+|\romannumeral0|, allow definitions of further macros expanding in only two
+steps to their final outputs. Some other control sequences are used only as
+delimiters, and left undefined, they may have been defined elsewhere, their
+meaning doesn't matter and is not touched.
\section{Loading and usage}
\dverb|&
Usage with LaTeX: \usepackage{xint}
- \usepackage{xintgcd} % (loads xint)
\usepackage{xintfrac} % (loads xint)
+ \usepackage{xintexpr} % (loads xintfrac)
+
+ \usepackage{xintgcd} % (loads xint)
\usepackage{xintseries} % (loads xintfrac)
\usepackage{xintcfrac} % (loads xintfrac)
Usage with TeX: \input xint.sty\relax
- \input xintgcd.sty\relax % (loads xint)
\input xintfrac.sty\relax % (loads xint)
+ \input xintexpr.sty\relax % (loads xintfrac)
+
+ \input xintgcd.sty\relax % (loads xint)
\input xintseries.sty\relax % (loads xintfrac)
\input xintcfrac.sty\relax % (loads xintfrac)
|
@@ -1418,10 +1592,11 @@ executable |tex| can not be used, |etex| or |pdftex| (version
|1.40| or later) or ..., must
be invoked.
-Furthermore, the packages \xintgcdname and \xintfracname will check for
-the previous loading of \xintname, and will try to load it if this was
-not already done. Similarly \xintseriesname and \xintcfracname do the
-necessary loading of \xintfracname.
+Furthermore, the packages \xintgcdname and \xintfracname will check for the
+previous loading of \xintname, and will try to load it if this was not
+already done. Similarly \xintseriesname, \xintcfracname and \xintexprname do
+the necessary loading of \xintfracname. Each package will refuse to be
+loaded twice.
Also inspired from the \textsc{Heiko Oberdiek} packages we have included
a complete catcode protection mecanism. The packages may be loaded in
@@ -1431,12 +1606,18 @@ escape character, digits have category code other and letters have
category code letter. Nothing else is assumed, and the previous
configuration is restored after the loading of each one of the packages.
-This is for the loading of the packages. For the actual use of the
+This is for the loading of the packages.
+
+For the actual use of the
macros, note that when feeding them with negative numbers the
minus sign must have category code other, as is standard. Similarly the
slash used for inputting fractions must be of category other, as usual.
And the square brackets also must be of category code other, if used on
-input.
+input. The `e' of the scientific notation must be of category code letter.
+All of that is relaxed when inside an
+|\xintexpr|-ession (but arguments to macros which have been inserted in
+the expression must obey the rules, as it is the macro and not the parser which
+will get the tokens). In an |\xintexpr|-ession, the scientific `e' may be `E'.
The components of the \xintname bundle presuppose that the usual
\csa{space} and \csa{empty} macros are pre-defined, which is the case in
@@ -1455,25 +1636,27 @@ compatible. \csa{xintTypesetBezoutAlgorithm} also uses the
\dverb+&
Run tex or latex on xint.dtx.
-This will extract the style files xint.sty, xintgcd.sty, xintfrac.sty,
-xintseries.sty, xintcfrac.sty (and xint.ins). Files with the same
-names and in the same repertory will be overwritten. The tex (not
-latex) run will stop with the complaint that it does not understand
-\NeedsTeXFormat, but the style files will already have been extracted
-by that time.
+This will extract the style files xint.sty, xintfrac.sty, xintexpr.sty,
+xintgcd.sty, xintseries.sty, xintcfrac.sty (and xint.ins).
+
+Files with the same names and in the same repertory will be overwritten.
+The tex (not latex) run will stop with the complaint that it does not
+understand \NeedsTeXFormat, but the style files will already have been
+extracted by that time.
Alternatively, run tex or latex on xint.ins if available.
To get xint.pdf run pdflatex thrice on xint.dtx
xint.sty |
+ xintfrac.sty |
+ xintexpr.sty | --> TDS:tex/generic/xint/
xintgcd.sty |
- xintfrac.sty | --> TDS:tex/generic/xint/
xintseries.sty |
xintcfrac.sty |
xint.dtx --> TDS:source/generic/xint/
xint.pdf --> TDS:doc/generic/xint/
-
+
It may be necessary to then refresh the TeX installation filename
database.
+
@@ -1617,8 +1800,8 @@ contiguous spaces are collapsed by the \TeX{} scanning into single spaces.
}->|\makeatletter\texttt{\expandafter\strip@prefix\meaning\X}\makeatother}
\centeredline{|\def\y{a,b,c,d,e}\xintCSVtoList\y->|\makeatletter\texttt{\expandafter\strip@prefix\meaning\z}\makeatother}
-% The macro \csa{xintCSVtoListNoExpand} does the same job without the initial
-% expansion.
+The macro \csa{xintCSVtoListNoExpand} does the same job without the initial
+expansion.
\subsection{\csbh{xintNthElt}}\label{xintNthElt}
@@ -1646,9 +1829,9 @@ future versions. \centeredline{|\xintNthElt {7}{\xintCSVtoList
\centeredline{|\xintNthElt {0}{\xintCSVtoList {1,2,3,4,5,6,7,8,9}}=|%
\texttt{\xintNthElt {0}{\xintCSVtoList {1,2,3,4,5,6,7,8,9}}}}
-% The macro
-% \csa{xintNthEltNoExpand} does the same job without first expanding its
-% second argument.
+The macro
+\csa{xintNthEltNoExpand} does the same job without first expanding its
+second argument.
\subsection{\csbh{xintListWithSep}}\label{xintListWithSep}
@@ -1668,8 +1851,8 @@ top-level braced material constituting the \meta{list}.
\centeredline{|\xintListWithSep{:}{\xintFac
{20}}=|\texttt{\xintListWithSep{:}{\xintFac {20}}}}
-% The macro \csa{xintListWithSepNoExpand} does the same
-% job without the initial expansion.
+The macro \csa{xintListWithSepNoExpand} does the same
+job without the initial expansion.
\subsection{\csbh{xintApply}}\label{xintApply}
@@ -1693,9 +1876,9 @@ by the result of applying |\macro| on it. \centeredline{|\def\macro
#1{\the\numexpr 9-#1\relax}|} \centeredline{|\xintApply\macro{\xintFac
{20}}=|\texttt{\xintApply\macro{\xintFac {20}}}}
-% The macro
-% \csa{xintApplyNoExpand} does the same job without the first initial expansion
-% which gave the \meta{list} of braced tokens to which |\macro| is applied.
+The macro
+\csa{xintApplyNoExpand} does the same job without the first initial expansion
+which gave the \meta{list} of braced tokens to which |\macro| is applied.
\subsection{\csbh{xintApplyUnbraced}}\label{xintApplyUnbraced}
@@ -1717,10 +1900,10 @@ $ $ $ $ \def\macro #1{\expandafter\def\csname myself#1\endcsname {#1}}$\
$null$ $ $ $ \xintApplyUnbraced\macro{{elta}{eltb}{eltc}}$\
$null$ $ $ $ \meaning\myselfelta:$ $ $meaning$myselfelta
|
-% The macro \csa{xintApplyUnbracedNoExpand} does the same job without the first
-% initial expansion which gave the \meta{list} of braced tokens to which
-% |\macro|
-% is applied.
+The macro \csa{xintApplyUnbracedNoExpand} does the same job without the first
+initial expansion which gave the \meta{list} of braced tokens to which
+|\macro|
+is applied.
\subsection{\csbh{xintAssign}}\label{xintAssign}
@@ -1804,6 +1987,54 @@ division of the numerator by the denominator.
\csa{xintSgn\n} returns 1 if the number is positive, 0 if it is
zero and -1 if it is negative. Extended by \xintfracname to fractions.
+\subsection{\csbh{xintSgnFork}}\label{xintSgnFork}
+{\small New with release |1.07|.\par}
+
+\csa{xintSgnFork}\verb+{-1|0|1}+\marg{A}\marg{B}\marg{C} expandably
+chooses to execute either the \meta{A}, \meta{B} or \meta{C} code,
+depending on its first argument. This first argument should be anything
+expanding to either |-1|, |0| or |1| (a count register should be
+prefixed by |\the| and a |\numexpr...\relax| also should be prefixed by
+|\the|). This utility is provided to help construct expandable macros
+choosing depending on a condition which one of the package macros to
+use, or which values to confer to their arguments.
+\dverb(&
+\def\myfunction #1%
+% expands to |x+1| if x < -1, x-1 if x > 1, else 1 - x^2
+% rounded to two decimal places
+ {\xintRound {2}{\xintSgnFork
+ {\xintSgnFork{\xintGeq{#1}{1}}{}{0}{\xintSgn{#1}}}
+ {\xintSub{-1}{#1}}{\xintSub{1}{\xintSqr{#1}}}{\xintSub{#1}{1}}}}%
+\xintListWithSep{,\,}{\xintApply\myfunction
+ {{-5/2}{-2}{-3/2}{-1}{-1/2}{0}{1/2}{1}{3/2}{2}{5/2}}}
+(
+
+\def\myfunction #1%
+ {\xintRound {2}{\xintSgnFork
+ {\xintSgnFork{\xintGeq{#1}{1}}{}{0}{\xintSgn{#1}}}
+ {\xintSub{-1}{#1}}{\xintSub{1}{\xintSqr{#1}}}{\xintSub{#1}{1}}}}%
+\xintListWithSep{,\,}{\xintApply\myfunction
+ {{-5/2}{-2}{-3/2}{-1}{-1/2}{0}{1/2}{1}{3/2}{2}{5/2}}}
+
+Using an \xintexprname{}ession, one may simplify the coding:
+\dverb(&
+\def\myfunction #1% expands to |x+1| if x < -1, x-1 if x > 1, else 1 - x^2
+ {\xintRound {2}{\xinttheexpr\xintSgnFork
+ {\xintSgnFork{\xintGeq{#1}{1}}{}{0}{\xintSgn{#1}}}
+ { -#1 - 1 }{ 1 - #1^2 }{ #1 - 1} \relax }}%
+(
+
+\def\myfunction #1% expands to |x+1| if x < -1, x-1 if x > 1, else 1 - x^2
+ {\xintRound {2}{\xinttheexpr\xintSgnFork
+ {\xintSgnFork{\xintGeq{#1}{1}}{}{0}{\xintSgn{#1}}}
+ { -#1 - 1 }{ #1^2 - 1 }{ #1 - 1} \relax }}%
+
+\xintListWithSep{,\,}{\xintApply\myfunction
+ {{-5/2}{-2}{-3/2}{-1}{-1/2}{0}{1/2}{1}{3/2}{2}{5/2}}}
+
+See the \csb{xintNewExpr} section for how one can use formally the
+\xintexprname parser to create automatically a
+macro equivalent to the one we first wrote, not using |\xintthexpr|.
\subsection{\csbh{xintOpp}}\label{xintiOpp}
@@ -1831,11 +2062,12 @@ by \xintfracname to fractions.
\csa{xintCmp\n\m} returns 1 if |N>M|, 0 if |N=M|, and -1 if |N<M|.
Extended by \xintfracname to fractions.
-\subsection{\csbh{xintGeq}}\label{xintGeq}
+\subsection{\csbh{xintGeq}}\label{xintiGeq}
-\csa{xintGeq\n\m} returns 1 if the absolute value of the first
+\csa{xintGeq\n\m} returns 1 if the \emph{absolute value} of the first
number is at least equal to the absolute value of the second
-number. If \verb+|N|<|M|+ it returns 0.
+number. If \verb+|N|<|M|+ it returns 0. Extended by \xintfracname to fractions
+(new with |1.07|; beware that it compares \emph{absolute values}).
\subsection{\csbh{xintMax}}\label{xintiMax}
@@ -2169,121 +2401,6 @@ of \csa{xintDecSplit}.
of \csa{xintDecSplit}.
-\section{Commands of the \xintgcdname package}
-
-This package was included in the original release |1.0| of the
-\xintname bundle.
-
-\subsection{\csbh{xintGCD}}\label{xintGCD}
-
-\csa{xintGCD\n\m} computes the greatest common divisor. It is
-positive, except when both |N| and |M| vanish, in which case the macro
-returns zero.
-\centeredline{\csa{xintGCD}|{10000}{1113}=|\texttt{\xintGCD{10000}{1113}}}
-\centeredline{|\xintGCD{123456789012345}{9876543210321}=|\texttt
- {\xintGCD{123456789012345}{9876543210321}}}
-
-\subsection{\csbh{xintBezout}}\label{xintBezout}
-
-\xintAssign{{\xintBezout {10000}{1113}}}\to\X
-\xintAssign {\xintBezout {10000}{1113}}\to\A\B\U\V\D
-
-\csa{xintBezout\n\m} returns five numbers |A|, |B|, |U|, |V|, |D| within
-braces. |A| is the first (expanded, as usual) input number, |B| the
-second, |D| is the GCD, and \texttt{UA - VB = D}.
-\centeredline{|\xintAssign {{\xintBezout {10000}{1113}}}\to\X|}
-\centeredline{|\meaning\X: |\texttt{\meaning\X }.}
-\noindent{|\xintAssign {\xintBezout {10000}{1113}}\to\A\B\U\V\D|}\\
-|\A: |\texttt{\A },
-|\B: |\texttt{\B },
-|\U: |\texttt{\U },
-|\V: |\texttt{\V },
-|\D: |\texttt{\D }.\\
-\xintAssign {\xintBezout {123456789012345}{9876543210321}}\to\A\B\U\V\D
-\noindent{|\xintAssign {\xintBezout {123456789012345}{9876543210321}}\to\A\B\U\V\D
-|}\\
-|\A: |\texttt{\A },
-|\B: |\texttt{\B },
-|\U: |\texttt{\U },
-|\V: |\texttt{\V },
-|\D: |\texttt{\D }.
-
-
-\subsection{\csbh{xintEuclideAlgorithm}}\label{xintEuclideAlgorithm}
-
-\xintAssign {{\xintEuclideAlgorithm {10000}{1113}}}\to\X
-
-\def\restorebracecatcodes
- {\catcode`\{=1 \catcode`\}=2 }
-
-\def\allowlistsplit
- {\catcode`\{=12 \catcode`\}=12 \allowlistsplita }
-
-\def\allowlistsplitx {\futurelet\listnext\allowlistsplitxx }
-
-\def\allowlistsplitxx {\ifx\listnext\relax \restorebracecatcodes
- \else \expandafter\allowlistsplitxxx \fi }
-\begingroup
-\catcode`\[=1
-\catcode`\]=2
-\catcode`\{=12
-\catcode`\}=12
-\gdef\allowlistsplita #1{[#1\allowlistsplitx {]
-\gdef\allowlistsplitxxx {#1}%
- [{#1}\hskip 0pt plus 1pt \allowlistsplitx ]
-\endgroup
-
-\csa{xintEuclideAlgorithm\n\m} applies the Euclide algorithm and
-keeps a copy of all quotients and remainders.
-\centeredline{|\xintAssign {{\xintEuclideAlgorithm {10000}{1113}}}\to\X|}
-
-|\meaning\X: |\texttt{\expandafter\allowlistsplit\meaning\X
- \relax }.
-The first token is the number of steps, the second is |N|, the
-third is the GCD, the fourth is |M| then the first quotient and
-remainder, the second quotient and remainder, \dots until the
-final quotient and last (zero) remainder.
-
-\subsection{\csbh{xintBezoutAlgorithm}}\label{xintBezoutAlgorithm}
-
-\catcode`\& 4
-
-\xintAssign {{\xintBezoutAlgorithm {10000}{1113}}}\to\X
-
-\csa{xintBezoutAlgorithm\n\m} applies the Euclide algorithm and
-keeps a copy of all quotients and remainders. Furthermore it
-computes the entries of the successive products of the 2 by 2 matrices
-$\left(\vcenter{\halign {\,#&\,#\cr q & 1 \cr 1 & 0 \cr}}\right)$
-formed from the quotients arising in the algorithm.
-\centeredline{|\xintAssign {{\xintEuclideAlgorithm {10000}{1113}}}\to\X|}
-
-|\meaning\X: |\texttt{\expandafter\allowlistsplit\meaning\X \relax}.
-
-The first token is the number of steps, the second is |N|, then
-|0|, |1|, the GCD, |M|, |1|, |0|, the first quotient, the first
-remainder, the top left entry of the first matrix, the bottom left
-entry, and then these four things at each step until the end.
-
-\catcode`\& 13
-
-\subsection{\csbh{xintTypesetEuclideAlgorithm}}\label{xintTypesetEuclideAlgorithm}
-
-This macro is just an example of how to organize the data returned
-by \csa{xintEuclideAlgorithm}. Copy the source code to a new macro
-and modify it to what is needed.
-\centeredline{|\xintTypesetEuclideAlgorithm
- {123456789012345}{9876543210321}|} \xintTypesetEuclideAlgorithm
-{123456789012345}{9876543210321}
-
-
-\subsection{\csbh{xintTypesetBezoutAlgorithm}}\label{xintTypesetBezoutAlgorithm}
-
-This macro is just an example of how to organize the data returned
-by \csa{xintBezoutAlgorithm}. Copy the source code to a new macro
-and modify it to what is needed.
-\centeredline{|\xintTypesetBezoutAlgorithm {10000}{1113}|}
-\xintTypesetBezoutAlgorithm {10000}{1113}
-
\section{Commands of the \xintfracname package}\label{sec:comfrac}
\def\x{\string{x\string}}
@@ -2309,16 +2426,30 @@ The original macro is extended to accept a fraction on input.
\subsection{\csbh{xintRaw}}\label{xintRaw}
{\small New with release |1.04|.\par}
+{\small \color{red}MODIFIED IN |1.07|.\par}
This macro `prints' the
-fraction |f| (after its parsing and expansion) in |A/B| form, with |A|
-as returned by \csa{xintNumerator}|{f}| and |B| as returned by
-\csa{xintDenominator}|{f}|.
+fraction |f| as it is received by the package after its parsing and
+expansion, in a printable form |a/b[n]| equivalent to the internal
+representation: the denominator |b| is always strictly positive and is
+printed even if it has value |1|.
\centeredline{|\xintRaw{\the\numexpr 571*987\relax.123/\the\numexpr
-201+59\relax}=|}%
\centeredline{\texttt{\xintRaw{\the\numexpr
571*987\relax.123/\the\numexpr -201+59\relax}}}
+\subsection{\csbh{xintRawWithZeros}}\label{xintRawWithZeros}
+
+{\small New name in |1.07|.\par}
+
+This macro (formerly known as \csa{xintRaw}) `prints' the
+fraction |f| (after its parsing and expansion) in |A/B| form, with |A|
+as returned by \csa{xintNumerator}|{f}| and |B| as returned by
+\csa{xintDenominator}|{f}|.
+\centeredline{|\xintRawWithZeros{\the\numexpr 571*987\relax.123/\the\numexpr
+ -201+59\relax}=|}%
+\centeredline{\texttt{\xintRawWithZeros{\the\numexpr
+ 571*987\relax.123/\the\numexpr -201+59\relax}}}
\subsection{\csbh{xintNumerator}}\label{xintNumerator}
@@ -2398,6 +2529,12 @@ numerator and denominator: |\xintREZ {178000/25600000[17]}=|\texttt{\xintREZ
{178000/25600000[17]}}. As shown by the example, it does not otherwise
simplify the fraction.
+\subsection{\csbh{xintE}}\label{xintE}
+{\small New with |1.07|.}
+
+|\xintE {f}{x}| multiplies the fraction |f| by &10^x&. The \emph{second}
+argument |x| must obey the \TeX{} bounds. It may be a count register.
+
\subsection{\csbh{xintIrr}}\label{xintIrr}
This puts the fraction into its unique irreducible form: \centeredline{|\xintIrr
@@ -2504,36 +2641,140 @@ the former cannot be used inside integer-only macros, and the
latter removes the decimal point, and never returns |-0| (and of course removes
all superfluous leading zeros.)
+\subsection{\csbh{xintDigits}, \csbh{xinttheDigits}}\label{xintDigits}
+
+{\small New with release |1.07|.\par}
+
+The syntax |\xintDigits := D;| (where spaces do not matter) assigns the
+value of |D| to the number of digits to be used by floating point
+operations. The default is |16|. The maximal value is |32768|. The macro
+|\xinttheDigits| serves to print the current value.
+
+\subsection{\csbh{xintFloat}}\label{xintFloat}
+
+{\small New with release |1.07|.\par}
+
+The macro |\xintFloat [P]{f}| has an optional argument |P| which replaces
+the current value of |\xintDigits|. The (rounded truncation of the) fraction
+|f| is then printed in scientific form, with |P| digits (the trailing zeros
+are not trimmed; except when |f| vanishes then the printed value is |0.e0|)
+a lowercase |e| and an integer |N|. The first digit is from |1| to |9|, it
+is followed by a dot and |P-1| digits. In the exceptional case where the
+rouding went to the next power of ten, the printed value is |10.0...0eN|
+(with a sign, perhaps).
+\centeredline{|\xintFloat[32]{1234567/7654321}=|\texttt{\xintFloat[32]{1234567/7654321}}}
+
+The argument to \csa{xintFloat} may be an |\xinttheexpr|-ession, like the
+other macros; only its final evaluation is submitted to \csa{xintFloat}: the
+inner evaluations of chained arguments are not at all done in `floating'
+mode. For this one must use |\xintthefloatexpr|.
+
+
\subsection{\csbh{xintAdd}}\label{xintAdd}
The original macro is extended to accept fractions on input. Its output will now
always be in the form |A/B[n]|.
The original is available as \csb{xintiAdd}.
+\subsection{\csbh{xintFloatAdd}}\label{xintFloatAdd}
+
+{\small New with release |1.07|.\par}
+
+|\xintFloatAdd [P]{f}{g}| first replaces |f| and |g| with their float
+approximations, with 2 safety digits. It then adds exactly and outputs in
+float format with precision |P| (which is optional) or |\xintDigits| if |P|
+was absent, the result of this computation.
+
+
\subsection{\csbh{xintSub}}\label{xintSub}
The original macro is extended to accept fractions on input. Its output will now
always be in the form |A/B[n]|.
The original is available as \csb{xintiSub}.
+\subsection{\csbh{xintFloatSub}}\label{xintFloatSub}
+
+{\small New with release |1.07|.\par}
+
+|\xintFloatSub [P]{f}{g}| first replaces |f| and |g| with their float
+approximations, with 2 safety digits. It then subtracts exactly and outputs in
+float format with precision |P| (which is optional), or |\xintDigits| if |P|
+was absent, the result of this computation.
+
+
\subsection{\csbh{xintMul}}\label{xintMul}
The original macro is extended to accept fractions on input. Its output will now
always be in the form |A/B[n]|.
The original is available as \csb{xintiMul}.
+\subsection{\csbh{xintFloatMul}}\label{xintFloatMul}
+
+{\small New with release |1.07|.\par}
+
+|\xintFloatMul [P]{f}{g}| first replaces |f| and |g| with their float
+approximations, with 2 safety digits. It then multiplies exactly and outputs in
+float format with precision |P| (which is optional), or |\xintDigits| if |P|
+was absent, the result of this computation.
+
\subsection{\csbh{xintSqr}}\label{xintSqr}
The original macro is extended to accept a fraction on input. Its output will
now always be in the form |A/B[n]|. The original is available as
\csb{xintiSqr}.
+\subsection{\csbh{xintDiv}}\label{xintDiv}
+
+\csa{xintDiv}|{f}{g}| computes the fraction |f/g|. As with all other computation
+macros, no simplification is done on the output, which is in the form |A/B[n]|.
+
+\subsection{\csbh{xintFloatDiv}}\label{xintFloatDiv}
+
+{\small New with release |1.07|.\par}
+
+|\xintFloatDiv [P]{f}{g}| first replaces |f| and |g| with their float
+approximations, with 2 safety digits. It then divides exactly and outputs in
+float format with precision |P| (which is optional), or |\xintDigits| if |P|
+was absent, the result of this computation.
+
\subsection{\csbh{xintPow}}\label{xintPow}
The original macro is extended to accept a fraction on input (the exponent must
be a signed integer of course). Its output will now always be in the form
|A/B[n]|. The original is available as \csb{xintiPow}.
+\subsection{\csbh{xintFloatPow}}\label{xintFloatPow}
+
+{\small New with release |1.07|.\par}
+
+|\xintFloatPow [P]{f}{x}| uses either the optional argument |P| or the value
+of |\xintDigits|. It computes a floating approximation to |f^x|. The
+exponent |x| must obey the \TeX{} bounds. Count registers are accepted on
+input. Depending on the values of the asked for precision and the size of
+|P|, |\xintFloatPow| chooses a number of digits for intermediate
+computations, hopefully large enough to achieve in the end the desired
+accuracy.
+
+\subsection{\csbh{xintFloatPower}}\label{xintFloatPower}
+
+{\small New with release |1.07|.\par}
+
+This is a slightly slower variant of \csb{xintFloatPow} for which the
+exponent |x| may exceed the \TeX{} bounds on integers. It may even be a
+fraction |a/b| but must be an integer in disguise. However it can not be a
+count register anymore (except if the count is prefixed by |\the|).
+\centeredline{|\xintFloatPower [8]{1.00000000001}{1e11}=|\texttt{\xintFloatPower [8]{1.00000000001}{1e11}}}
+This was for illustrative purposes as the previous computation takes already
+about a seventh of a second on my laptop.
+
+This is the function used by the |^| operator in an |\xintfloatexpr|.
+\centeredline{|\xintthefloatexpr 12.5607^(144/3/(1.3-.5)-37)\relax=|\texttt{\xintthefloatexpr 12.5607^(144/3/(1.3-.5)-37)\relax}}
+The parenthesized exponent must expand to an integer (here |23|).
+
+The intermediate multiplications are done with a higher precision that
+|\xintDigits| or the optional |P| argument within brackets, in order for the
+final result to hopefully have the desired accuracy.
+
\subsection{\csbh{xintSum}, \csbh{xintSumExpr}}\label{xintSum}\label{xintSumExpr}
The original commands are extended to accept fractions on input and produce
@@ -2547,11 +2788,6 @@ The originals are extended to accept fractions on input and produce fractions on
output. Their outputs will now always be in the form |A/B[n]|. The
originals are available as \csa{xintiPrd} and \csa{xintiPrdExpr}.
-\subsection{\csbh{xintDiv}}\label{xintDiv}
-
-\csa{xintDiv}|{f}{g}| computes the fraction |f/g|. As with all other computation
-macros, no simplification is done on the output, which is in the form |A/B[n]|.
-
\subsection{\csbh{xintCmp}}\label{xintCmp}
The macro is extended to fractions. Of course its output is still either
@@ -2559,6 +2795,13 @@ The macro is extended to fractions. Of course its output is still either
The original, which skips the overhead of
the fraction format parsing, is available as \csb{xintiCmp}.
+\subsection{\csbh{xintGeq}}\label{xintGeq}
+
+The macro is extended to fractions. The original, which skips the overhead of
+the fraction format parsing, is available as \csb{xintiGeq} (strangely this
+extended version was only provided with release |1.07|, contrarily to
+\csa{xintMax}, \csa{xintMin}, \csa{xintCmp}).
+
\subsection{\csbh{xintMax}}\label{xintMax}
The macro is extended to fractions. But now |\xintMax {2}{3}| returns
@@ -2588,7 +2831,7 @@ available as \csb{xintiSgn}.
The macro is extended to fractions. The original is available as
\csb{xintiOpp}. Note that |\xintOpp {3}| now outputs \texttt{\xintOpp {3}}.
-\subsection{\csbh{xintGeq}, \csbh{xintDivision}, \csbh{xint\-Quo}, \csbh{xint\-Rem}, \csbh{xintFDg}, \csbh{xintLDg}, \csbh{xintMON}, \csbh{xintMMON}}
+\subsection{\csbh{xintDivision}, \csbh{xint\-Quo}, \csbh{xint\-Rem}, \csbh{xintFDg}, \csbh{xintLDg}, \csbh{xintMON}, \csbh{xintMMON}}
These macros are extended to accept a fraction on input if this fraction
in fact reduces to an integer (if not an |\xintError:NotAnInteger| will
@@ -2603,6 +2846,693 @@ The macro is extended to accept a fraction on input. But this fraction should
reduce to an integer. If not an error will be raised. The original is available
as \csb{xintiNum}.
+\section{Expandable expressions with the \xintexprname package}\label{sec:comexpr}
+
+The \xintexprname package was first released with version |1.07| of the
+\xintname bundle. Loading this package automatically loads \xintfracname, hence
+also \xintname.
+
+
+\subsection{The \csbh{xintexpr} expressions}\label{xintexpr}\label{xinttheexpr}\label{xintthe}
+
+
+An \xintexprname{}ession is a construct
+\csb{xintexpr}\meta{expandable\_expression}|\relax| where the expandable
+expression is read and expanded from left to right, and whose constituents
+should be (they are uncovered by iterated left to right expansion of the
+contents during the scanning):
+\begin{itemize}
+\item integers or decimal numbers, such as |123.345|, or numbers in scientific
+ notation |6.02e23| or |6.02E23| (or anything expanding to
+ these things; a decimal number may start directly with a decimal point),
+\item fractions |a/b|, or |a.b/c.d| or |a.beN/c.deM|, if they are to be treated
+ as one entity should then be parenthesized, \emph{e.g.} disambiguating |a/b^2|
+ from |(a/b)^2|,
+\item fractions |a/b[n]| as produced on output by the macros of the
+ \xintfracname package; they \emph{must} be enclosed in one pair of braces, for
+ example |{13/35[3]}| or |{\x\y\z}| with |\x| expanding to |13/|, |\y|
+ expanding to |35[| and |\z| expanding to |3]|, (\emph{note that using
+ parentheses does not suffice, braces are required: the parser can not digest
+ directly square brackets. Material within braces \emph{must}
+ after complete expansion give something in the {\upshape|a/b[n]|} form.
+ Braces should not be used for numbers in scientific notation, or macros
+ expanding to something else than a fraction, etc..., but exclusively for
+ material expanding to an {\upshape|a/b[n]|}; of course braces also appear in
+ the completely other r\^ole of feeding macros with their parameters.}),
+\item the standard binary operators, |+|, |-|, |*|, |/|, and |^| (the |**|
+ notation for exponentiation is not recognized and will give an error),
+\item opening and closing parentheses, with arbitrary level of nesting,
+\item |+| and |-| as prefix operators,
+\item |!| as postfix factorial operator (applied to a non-negative integer),
+\item and sub-expressions |\xintexpr|\meta{stuff}|\relax| (they do not need
+ to be put within parentheses).
+\end{itemize}
+
+
+Such an expression, like a |\numexpr| expression, is not directly printable, nor
+can it be directly used as argument to the other package macros. For this one
+uses one of the two equivalent forms:
+\begin{itemize}
+\item \csb{xinttheexpr}\meta{expandable\_expression}|\relax|, or
+\item \csb{xintthe}|\xintexpr|\meta{expandable\_expression}|\relax|.
+\end{itemize}
+
+Both forms are equivalent and produce, always, a fraction in the standard
+|a/b[n]| format (even when the result is an integer; as usual no automatic
+simplification is done, and adding fractions multiplies all the denominators).
+\centeredline{|\xinttheexpr
+ 1+1/2!+1/3!+1/4!+1/5!\relax=|\texttt{\xinttheexpr1+1/2!+1/3!+1/4!+1/5!\relax}}
+
+One will usually post-process with |\xintIrr|, |\xintTrunc| or |\xintRound|, or
+|\xintFloat|, or |\xintNum| (when the output is known to be an integer) to get
+the result in the desired form. One may imagine some future version where the
+output format will be given as optional argument to |\xintexpr|.
+\centeredline{|\xintIrr{\xinttheexpr
+ 1+1/2!+1/3!+1/4!+1/5!\relax}=|\texttt{\xintIrr{\xinttheexpr1+1/2!+1/3!+1/4!+1/5!\relax}}}
+\centeredline{|\xinttheexpr 1.99^-2 - 2.01^-2 \relax=|\texttt{\xinttheexpr
+ 1.99^-2 - 2.01^-2 \relax}} \centeredline{|\xintRound{10}{\xinttheexpr
+ 1.99^-2 - 2.01^-2 \relax}=|\texttt{\xintRound{10}{\xinttheexpr 1.99^-2 -
+ 2.01^-2 \relax}}}
+
+\smallskip
+Again:
+\begin{itemize}
+\item \xintexprname{}essions evaluate through expansion to arbitrarily big
+ fractions (in a non-directly printable form),
+\item the standard operations of addition, subtraction,
+ multiplication, division, power, are written in infix form,
+\item recognized numbers on input are either integers, decimal numbers, or
+ numbers written in scientific notation, (or anything expanding to the previous
+ things),
+\item fractions on input which contain the |[n]| part, or macros expanding to
+ some |a/b[n]| with the trailing |[n]| must be enclosed in
+ (precisely one) pair of braces to be parsable by the expression
+ scanner,\footnote{the reason why the braced material should not be a number in
+ scientific notation is that the `e' will become of catcode other and not be
+ understood then by the package macros; this is different from an `e'
+ directly seen by the parser, for which the catcode does not matter. Of
+ course if the brace pair is for feeding an argument to a macro, then all of
+ the above is irrelevant.}
+\item the expression may contain arbitrarily many levels of nested parenthesized
+ sub-expressions,
+\item sub-contents evaluating to fractions should be either
+ \begin{enumerate}
+ \item parenthesized,\footnote{recall that the parser does not produce
+ explicit fractions |a/b[n]|, hence the bracing rule does not
+ apply
+ to the result of the evaluation of the contents within parentheses;
+ except of course if it was produced by some other means giving an
+ explicit |a/b[n]|, but then braces should have been used, not
+ parentheses.}
+ \item a sub-expression |\xintexpr...\relax|,
+ \item or braced (use of infix operators inside the braced material will have
+ to
+ be
+ understood by the enclosed macros, which may be external to the
+ package, or explicitely enclosed in a sub |\xinttheexpr...\relax|).
+ \end{enumerate}
+ \item an expression can not be given as argument to the other package macros,
+ nor printed, for this one must use |\xinttheexpr...\relax| or
+ |\xintthe\xintexpr...\relax|,
+\item the output of these latter expressions is always in the |a/b[n]|
+ form, and may serve as input to the other package macros accepting fractions,
+\item |\xinttheexpr...\relax| as a sub-constituent of an |\xintexpr...\relax|
+ must be within some braces, else it should be written directly as
+ |\xintexpr...\relax|,
+\item as usual no simplification is done on the output and is the responsability
+ of post-processing,
+\item very long output will need special macros to break
+ across lines, like the |\printnumber| macro used in this documentation,
+\item everything is expanded along the way, the expression may contain
+ macros, but of course use of |+|, |*|, ... within their arguments
+ is only possible if
+ these macros know how to deal with them,
+\item finally each \xintexprname{}ession is completely expandable and obtains
+ its result in two expansion steps.
+\end{itemize}
+
+\subsection{\texorpdfstring{\texttt{\protect\string\numexpr}}{\textbackslash numexpr} expressions, count and dimension registers}
+
+They can not be used directly but must be prefixed by |\the| or |\number| for
+the count registers and by |\number| for the dimension registers. The dimension
+is then converted to its value in scalable points |sp|, which are |1/65536|th of
+a point.
+
+One may thus compute exactly and expandably with dimensions even exceeding
+temporarily the \TeX{} limits and then convert back approximately to points by
+division by |65536| and rounding to |4|,|5| or |6| decimal digits after the
+decimal point.
+
+
+\subsection{Catcodes and spaces}
+
+The |\xintexpr| is very agnostic regarding catcodes: digits, binary operators,
+minus and plus signs as prefixes, parentheses, decimal point, may be
+indifferently of catcode letter or other or subscript or superscript, ..., it
+does not matter. Of course |+|, |-|, |*|, |/|, and |^| should not be active
+as everything is expanded along the way. If |!| has been made active (done by
+Babel for certain languages) then it should be prefixed with |\string| to serve
+for the factorial; or the macro |\xintFac| may of course be used, preferably
+within braces as this will avoid the subsequent slow scan digit by digit of its
+expansion (other macros from the \xintfracname package generally \emph{must} be
+used within a brace pair, as they expand to a fraction |a/b[n]| which can not be
+directly parsed inside an \xintname{}expression; the |\xintFac| produces an
+integer and braces are only optional, but preferable, as the scanner will
+get the job done faster.)
+
+Sub-material within braces is treated technically in a different manner, and
+depending on the macros used therein may be more sensitive to the catcode of the
+five operations (the minus sign as prefix in particular). Digits, slash, square
+brackets, sign, produced on output by an |\xinttheexpr| are all of catcode 12.
+For the output of |\xintthefloatexp| digits, decimal dot, signs are of catcode
+12, and the `e' is of catcode 11.
+
+Note that if some macro is inserted in the expression it will expand and grab
+its arguments before the parser may get a chance to see them, so the situation
+with catcodes and spaces is not as flexible within the macro arguments as it is
+for top-level material (top-level here does not refer to the nesting of
+parentheses).
+
+
+\subsection{Expandability}
+
+As is the case with all other package macros |\xintexpr| expands in two steps to
+its final (non-printable) result; and similarly for |\xinttheexpr|. The
+`lowercase' form are a bit unusual as these macros are already in lowercase... :
+|\xinteval| for |\xintexpr| and |\xinttheeval| for |\xinttheexpr|.
+
+Similarly,
+there are |\xintfloateval| and |\xintthefloateval|.
+
+As explained above the expressions should contain only expandable material,
+except that braces are allowed when they enclose either a fraction (or decimal
+number) or something arbitrarily complicated but expanding (in a manner
+compatible to an expansion only context) to such a fraction or decimal number.
+
+\subsection{Memory considerations}
+
+The parser creates an undefined control sequence for each intermediate
+computation (this does not of course refer to the intermediate steps needed in
+the evaluations of the \csb{xintAdd}, \csb{xintMul}, etc... macros corresponding
+to the infix operators, but only to each conversion of such an infix operator
+into a computation). So, a moderately sized expression might create 10, or 20
+such control sequences. On my \TeX{} installation, the memory available for such
+things is of circa \np{200000} multi-letter control words. So this means that a
+document containing hundreds, perhaps even thousands of expressions will compile
+with no problem. But, if the package is used for computing plots\footnote{this
+ is not very probable as so far \xintname does not include a mathematical
+ library with floating point calculations, but provides only the basic
+ operations of algebra.}, this may cause a problem.
+
+There is a solution.\footnote{which convinced me that I could stick with the
+ parser implementation despite its potential impact on the hash-table.}
+
+A
+document can possibly do tens of thousands of evaluations only
+if some formulas are being used repeatedly, for example inside loops, with
+counters being incremented, or with data being fetched from a file. So it is the
+same formula used again and again with varying numbers inside.
+
+With the \csb{xintNewExpr} command, it is possible to convert once and for all
+an expression containing parameters into an expandable macro with parameters.
+Only this initial definition of this macro actually activates the \csb{xintexpr}
+parser and will (very moderately) impact the hash-table: once this unique
+parsing is done, a macro with parameters is produced which is built-up
+recursively from the \csb{xintAdd}, \csb{xintMul}, etc... macros, exactly as it
+was necessary to do before the availability of the \xintexprname package.
+
+\subsection{The \csbh{xintNewExpr} command}\label{xintNewExpr}
+
+This allows to define a completely expandable macro with parameters, expanding
+in two steps to its final evaluation, and corresponding to the given
+\xintname{}expression where the parameters are input using the underscore as
+macro-parameter: |_1|, ..., |_9|.\footnote{using the character |\#| as in
+ standard macros would have been more complicated to implement, the question
+ mark |?| is sometimes made active for reasons of punctuation, the dollar sign
+ was perfect but my text editor does some automatic font coloring and size
+ change when visualizing a |.tex| file and encountering such a |\$|, there was
+ also the tab character |\&| which could have been used. Perhaps a future
+ release could leave the choice of the character to the user.}
+
+The command is used
+as:\centeredline{|\xintNewExpr{\myformula}[n]|\marg{stuff}}
+\begin{itemize}
+\item \meta{stuff} will be inserted inside |\xinttheexpr . . . \relax|,
+\item |n| is an integer between zero and nine, inclusive, and tells how many
+ parameters will |\myformula| have (it is mandatory even
+ if the macro to be defined will have no parameters),
+\item placeholders |_1|, |_2|, ..., |_n| are used inside \meta{stuff} to play
+ the r\^ole of the macro parameters.
+\end{itemize}
+
+The macro |\myformula| is defined without checking if it
+already exists, \LaTeX{} users might prefer to do first |\newcommand*\myformula
+{}| to get a reasonable error message in case |\myformula| already exists.
+
+It will be a completely expandable macro entirely built-up using |\xintAdd|,
+|\xintSub|, |\xintMul|, |\xintDiv|, |\xintPow|, |\xintOpp| and |\xintFac| and
+corresponding to the formula as written with the infix operators.
+
+The formula may of course contain besides the infix operators and macro
+parameters some arbitrary decimal numbers, fractions (within braces) and also
+macros. If these macros do not involve the parameters, nothing special needs to
+be done, they will be expanded once during the construction of the formula. But
+if the parameters are to be used within the macros themselves, this has to be
+coded in a specific manner, which is to be explained after first examining a few
+simpler examples:
+
+\dverb|&
+\xintNewExpr\myformA[4]{ _1 + _2 * _3^_4 }
+\xintNewExpr\myformB[3]{ (_1 + 1.75)^_2 + _3*2.7 }
+\xintNewExpr\myformC[3]{ _1*_1+_2*_2+_3*_3-(_1*_2+_2*_3+_3*_1) }
+\xintNewExpr\myformD[2]{ (1+1.5*_1)^_2 - (1+1.5*_2)^_1 }
+\xintNewExpr\myformE[2]{ -----((((((_1*10-5*_2)))))) }
+\xintNewExpr\myformF[4]{ -_1^-_2*-_3-_4 }
+\xintNewExpr\myformG[4]{ -_1*-_2^-_3-_4 }
+\xintNewExpr\DET[9]{ _1*_5*_9+_2*_6*_7+_3*_4*_8-_1*_6*_8-_2*_4*_9-_3*_5*_7 }
+|
+
+\xintNewExpr\myformA[4]{ _1 + _2 * _3^_4 }
+\xintNewExpr\myformB[3]{ (_1 + 1.75)^_2 + _3*2.7 }
+\xintNewExpr\myformC[3]{ _1*_1+_2*_2+_3*_3-(_1*_2+_2*_3+_3*_1) }
+\xintNewExpr\myformD[2]{ (1+1.5*_1)^_2 - (1+1.5*_2)^_1 }
+\xintNewExpr\myformE[2]{ -----((((((_1*10-5*_2)))))) }
+\xintNewExpr\myformF[4]{ -_1^-_2*-_3-_4 }
+\xintNewExpr\myformG[4]{ -_1*-_2^-_3-_4 }
+\xintNewExpr\DET[9]{ _1*_5*_9+_2*_6*_7+_3*_4*_8-_1*_6*_8-_2*_4*_9-_3*_5*_7 }
+
+\ttfamily
+|\meaning\myformA:|\printnumber{\meaning\myformA}\endgraf
+|\meaning\myformB:|\printnumber{\meaning\myformB}\endgraf
+|\meaning\myformC:|\printnumber{\meaning\myformC}\endgraf
+|\meaning\myformD:|\printnumber{\meaning\myformD}\endgraf
+|\meaning\myformE:|\printnumber{\meaning\myformE}\endgraf
+|\meaning\myformF:|\printnumber{\meaning\myformF}\endgraf
+|\meaning\myformG:|\printnumber{\meaning\myformG}\endgraf
+|\meaning\DET:|\printnumber{\meaning\DET}\endgraf
+
+
+\centeredline{|\xintNum{\DET {1}{1}{1}{10}{-10}{5}{11}{-9}{6}}=|\texttt{\xintNum{\DET {1}{1}{1}{10}{-10}{5}{11}{-9}{6}}}}%
+\centeredline{|\xintNum{\DET {1}{2}{3}{10}{0}{-10}{21}{2}{-17}}=|\texttt{\xintNum{\DET {1}{2}{3}{10}{0}{-10}{21}{2}{-17}}}}
+
+\rmfamily
+
+\emph{Remark:} |\meaning| has been used within the argument to a |\printnumber|
+command, to avoid going into the right margin, but this zaps all spaces which
+are actually initially there in the macro definitions. Here is the raw output of
+|\meaning| on the last example:
+
+\ttfamily
+\meaning\DET
+\rmfamily
+
+So, |\printnumber| was used to facilitate the breaking accross lines.
+
+\smallskip
+
+For macros to be inserted within such a created \xintname-formula command, there
+are two cases:
+\begin{enumerate}
+\item the macro does not involve the numbered parameters in its arguments: it
+ may then be left as is, and will be evaluated once during the construction of
+ the formula,
+\item it does involve some of the parameters withing its arguments: then the
+ whole thing (macro + argument) should be
+ braced (this is not necessary if it is already included into a braced group)
+ and the macro should be coded with |:| replacing |\|.
+\end{enumerate}
+
+Here are some examples; they are rather silly but this is to
+illustrate the general principles.
+
+\dverb|&
+\xintNewExpr\myformH[2]{ {:xintMax{_1}{_2}} }
+\xintNewExpr\myformI[2]{ {:xintRound{_1}{_2}} - {:xintTrunc{_1}{_2}} }
+\xintNewExpr\myformJ[3]{ {:xintSgnFork{:xintSgn{_1}}
+ {\xinttheexpr _2 + _3\relax }
+ {\xinttheexpr _2 - _3\relax }
+ {\xinttheexpr _2 * _3\relax }} }
+|
+
+\xintNewExpr\myformH[2]{ {:xintMax{_1}{_2}} }
+\xintNewExpr\myformI[2]{ {:xintRound{_1}{_2}} - {:xintTrunc{_1}{_2}} }
+\xintNewExpr\myformJ[3]{ {:xintSgnFork{:xintSgn{_1}}
+ {\xinttheexpr _2 + _3\relax }
+ {\xinttheexpr _2 - _3\relax }
+ {\xinttheexpr _2 * _3\relax }} }
+
+\ttfamily
+\noindent|\meaning\myformH:|\printnumber{\meaning\myformH}\endgraf
+\noindent|\meaning\myformI:|\printnumber{\meaning\myformI}\endgraf
+\noindent|\meaning\myformJ:|\printnumber{\meaning\myformJ}\endgraf
+
+% |\myformJ {-13}{100}{10}=|\myformJ {-13}{100}{10}, and
+% |\myformJ {0}{100}{10}=|\myformJ {0}{100}{10}, and
+% |\myformJ {3}{100}{10}=|\myformJ {3}{100}{10}\endgraf
+
+% |\myformI {12}{1/123}=|\myformI {12}{1/123}, |\myformI {13}{1/123}=|\myformI
+% {13}{1/123}, |\xintTrunc {15}{1/123}=|\xintTrunc {15}{1/123}
+
+\rmfamily
+
+One more example:
+\dverb(&
+\xintNewExpr\myfunction[1]
+ { {:xintSgnFork {:xintSgnFork {:xintGeq{_1}{1}} {}{0}{:xintSgn{_1}}}
+ {\xinttheexpr -_1 - 1 \relax }
+ {\xinttheexpr 1 - _1^2 \relax }
+ {\xinttheexpr _1 - 1 \relax }} }
+(
+
+\xintNewExpr\myfunction[1]
+ { {:xintSgnFork {:xintSgnFork {:xintGeq{_1}{1}} {}{0}{:xintSgn{_1}}}
+ {\xinttheexpr -_1 - 1 \relax }
+ {\xinttheexpr 1 - _1^2 \relax }
+ {\xinttheexpr _1 - 1 \relax }} }%
+
+The principles were explained earlier:
+\begin{enumerate}
+\item parameters are denoted |_1|, |_2|, ... , |_9|,
+\item anything which can not be immediately expanded, because the parameters
+ appear within, must be enclosed, together
+ with its arguments, in a brace pair (no need to add one if it already exists),
+\item and the macros must be written with a |:| as control character, rather
+ than a |\|. This rule applies only to the macros involved in the previous
+ item.
+\item Finally, if the infix operators |+|, |-|, |*|, |/|, |^| are to be used
+ inside macro arguments, this should be done within an |\xinttheexpr...\relax|;
+ but this rule applies in general also independently of the |\xintNewExpr|
+ context.
+\end{enumerate}
+The produced macro |\myfunction| turns out to have meaning in this last case:
+
+\texttt{\printnumber{\meaning\myfunction }}
+
+The reason why these created macros are made to start with
+|\romannumeral0\xintraw| is in order for them to expand in only two steps. Of
+course in the last example their occurences in the three sub-branches is
+redundant, but we had to use |\xinttheexpr| in each of the three sub-branch,
+else the formal parsing done by |\xintNewExpr| would not have had a chance to
+discover the binary infix operators and convert them to their macro form.
+
+Things like a closing parenthesis only arising from the expansion of a macro
+when the parser goes from left to right will be hard to make understandable to
+\csb{xintNewExpr}, if the macro is to contain some of the parameters within its
+arguments.
+
+\dverb|&
+\def\formula #1#2#3{\xinttheexpr #2\xintSgnFork{\xintSgn{#1}}+-*#3\relax }
+|
+is a perfectly valid macro definition, which will work to produce |#2+#3|,
+|#2-#3|, or |#2*#3| depending on the sign of |#1|. But if we tried the
+following:
+\dverb|&
+\xintNewExpr\formula[3]{_2{:xintSgnFork{:xintSgn{_1}}+-*}_3}
+|
+we would discover that it would not compile, despite seemingly following the
+enunciated rules. I recall:
+\begin{enumerate}\setcounter{enumi}{4}
+\item braced material, if not an argument to a macro, must correspond to the
+ evaluation of a fraction to |a/b[n]| form, and in particular it can not be
+ used to produce an infix operator or an opening or closing
+ parenthesis, etc...
+\end{enumerate}
+This rule was mentioned in the description of \xintexprname{}-ession,
+and it
+has to be obeyed in the syntax of the expression argument to \csa{xintNewExpr}.
+We could try then:
+\dverb|&
+\xintNewExpr\formula[3]{{_2:xintSgnFork{:xintSgn{_1}}+-*_3}}
+|
+This time, |\xintNewExpr| works but the produced |\formula| has meaning
+\xintNewExpr\formula[3]{{_2:xintSgnFork{:xintSgn{_1}}+-*_3}}\endgraf
+\noindent\texttt{\printnumber{\meaning\formula}}\endgraf
+Clearly this macro will not work.
+
+We may try
+\dverb|&
+\xintNewExpr\formula[3]{{:xinttheexpr
+ _2:xintSgnFork{:xintSgn{_1}}+-*_3:relax}}
+|
+but this gives \xintNewExpr\formula[3]{{:xinttheexpr
+ _2:xintSgnFork{:xintSgn{_1}}+-*_3:relax}}\endgraf
+\noindent\texttt{\printnumber{\meaning\formula}}
+and
+there was no point whatsoever in it all, as what we want is to avoid the use of
+|\xintexpr|\dots so we end up having to do:
+\dverb|&
+\xintNewExpr\formula[3]{{:xintSgnFork{:xintSgn{_1}}
+ {\xinttheexpr _2+_3\relax}
+ {\xinttheexpr _2-_3\relax}
+ {\xinttheexpr _2*_3\relax}}}
+|
+which is like what was done with |\myformJ|.
+
+All of the previous examples may not be very convincing, because it is easier
+for the user to define directly a macro with parameters not using |\xinttheexpr|
+and achieving the wished-for computation, but |\xintNewExpr| would prove very
+useful on more complicated cases with a high level of nesting of macros.
+
+\subsection{\csbh{xintfloatexpr},
+ \csbh{xintthefloatexpr}}\label{xintfloatexpr}\label{xintthefloatexpr}
+
+\csb{xintfloatexpr}|...\relax| is exactly like |\xintexpr| but the four
+binary operations and the power function are implemented using
+\csa{xintFloatAdd}, \csa{xintFloatSub}, \csa{xintFloatMul},
+\csa{xintFloatDiv} and \csa{xintFloatPower}. The number of digits is from
+the current setting of |\xintDigits|.
+
+\xintDigits:= 9;
+
+Note that |1.000000001| and |(1+1e-9)| will not be equivalent with
+|D=\xinttheDigits| set to nine or less. Indeed the addition implicit in
+|1+1e-9| (and executed when the closing parenthesis is found) will provoke
+the rounding to |1|. Whereas |1.000000001| is input as operand to the
+elementary operations with |D+2| digits, and even more for the power function.
+\centeredline{|\xintDigits:= 9; \xintthefloatexpr
+ (1+1e-9)-1\relax=|\texttt{\xintthefloatexpr (1+1e-9)-1\relax}}
+\centeredline{|\xintDigits:= 9; \xintthefloatexpr
+ 1.000000001-1\relax=|\texttt{\xintthefloatexpr 1.000000001-1\relax}}
+
+For the fun of it:\xintDigits:=20; |\xintDigits:=20;|%
+\centeredline{|\xintthefloatexpr (1+1e-7)^1e7\relax=|\texttt{\xintthefloatexpr (1+1e-7)^1e7\relax}}
+
+|\xintDigits:=36;|\xintDigits:=36;
+\centeredline{|\xintthefloatexpr
+ ((1/13+1/121)*(1/179-1/173))/(1/19-1/18)\relax|}
+\centeredline{\texttt{\xintthefloatexpr
+ ((1/13+1/121)*(1/179-1/173))/(1/19-1/18)\relax}}
+\centeredline{|\xintFloat{\xinttheexpr
+ ((1/13+1/121)*(1/179-1/173))/(1/19-1/18)\relax}|}
+\centeredline{\texttt{\xintFloat
+ {\xinttheexpr((1/13+1/121)*(1/179-1/173))/(1/19-1/18)\relax}}}
+
+The latter result is the rounding of the exact result. The previous one has
+rounding errors coming from the various roundings done for each
+sub-expression. It was a bit funny to discover that |maple|, configured with
+|Digits:=36;| and with decimal dots everywhere to let it input the numbers as
+floats, gives exactly the same result with the same rounding errors
+as does |\xintthefloatexpr|!
+
+Note that using |\xintthefloatexpr| only pays off compared to using
+|\xinttheexpr| and then |\xintFloat| if the computations turn out to involve
+hundreds of digits. For elementary calculations with hand written numbers
+(not using the scientific notation with exponents differing greatly) it will
+generally be more efficient to use |\xinttheexpr|. The situation is quickly
+otherwise if one starts using the Power function. Then, |\xintthefloat| is
+often useful; and sometimes indispensable to achieve the (approximate)
+computation in reasonable time.
+
+We can try some crazy things:\footnote{this evaluation takes a little more than
+ a
+ quarter of a second on my laptop. Recall the constraints of expandability.}
+\centeredline{|\xintDigits:=12;\xintthefloatexpr 1.000000000000001^1e15\relax|}
+\centeredline{\xintDigits:=12;\xintthefloatexpr 1.000000000000001^1e15\relax}
+Note that contrarily to some professional computing sofware which are our
+concurrents on this market, the \texttt{\np{1.000000000000001}} wasn't rounded
+to |1| despite the setting of \csa{xintDigits}; it would if we had input it as
+|(1+1e-15)|.
+
+\xintDigits := 16;
+
+\subsection{\csbh{xintNewFloatExpr}}\label{xintNewFloatExpr}
+
+This is exactly like \csb{xintNewExpr} except that the created formulas are
+set-up to use |\xintthefloatexpr|. The precision used will be the one
+locally given by |\xintDigits| at the time of use of the created formulas,
+not |\xintNewFloatExpr|.
+
+\xintDigits:= 16;
+
+\subsection{\mbox{Technicalities~and~experimental~status}~ \allowbreak\null\hspace*{.5cm}}
+
+As already mentioned \csa{xintNewExpr}|\myformula[n]| does not check the
+prior existence of a macro |\myformula|. And the number of parameters |n| given
+as mandatory argument withing square brackets should of course be at least equal
+to the actual maximal index following an underscore in the expression.
+
+Obviously I should mention that \csa{xintNewExpr} itself can not be used in an
+expansion-only context, as it creates a macro.
+
+The format of the output of |\xintexpr|\meta{stuff}|\relax| is a |!| (with
+catcode 11) followed by |\XINT_expr_illegaluse| which prints an error message in
+the document and in the log file if it is executed, and next a token |\.a/b[n]|
+(which is a single control sequence: these are the famous things which may
+impact the hash-table). Using |\xinttheexpr| means zapping the first
+two things, and opening up the third token to access its name and get the result
+|a/b[n]| of the evaluation of the expression.
+
+I decided to put all intermediate results (from each evaluation of an infix
+operators, or of a parenthesized subpart of the expression, or from application
+of the minus as prefix, or of the exclamation sign as postfix, or any
+encountered braced material) inside |\csname...\endcsname|, as this can be done
+expandably and encapsulates an arbitrarily long fraction in a single token (left
+with undefined meaning), thus providing tremendous relief to the programmer in
+his/her expansion control.
+
+\begin{framed}
+ This implementation and user interface are currently to be considered
+ \emph{experimental}, they have not been yet extensively tested. Indeed the
+ additions brought to the \xintname bundle with release |1.07| are rather
+ extant and I just haven't had time to thoroughly validate them all.
+\end{framed}
+
+Some `error messages' will be issued by the scanner in case of problems, but
+errors may also be issued from low-level \TeX{} processing, and are most of the
+time unrecoverable. An attempt has been made to handle gracefully missing or
+extraneous parentheses.
+
+
+\subsection{Acknowledgements}
+
+I was greatly helped in my preparatory thinking, prior to producing such an
+expandable parser, by the commented source of the
+\href{http://www.ctan.org/tex-archive/macros/latex/contrib/l3kernel}{\color{niceone}l3fp}
+package, specifically the |l3fp-parse.dtx| file. Also the source of the |calc|
+package was instructive, despite the fact that here for |\xintexpr| the
+principles are necessarily different due to the aim of achieving expandability.
+
+I apologize for not including
+comments currently in my own code, the reason being that this a time-consuming
+task which should wait until the code has a rather certain more-or-less final
+form.
+
+
+
+\section{Commands of the \xintgcdname package}
+
+This package was included in the original release |1.0| of the
+\xintname bundle.
+
+\subsection{\csbh{xintGCD}}\label{xintGCD}
+
+\csa{xintGCD\n\m} computes the greatest common divisor. It is
+positive, except when both |N| and |M| vanish, in which case the macro
+returns zero.
+\centeredline{\csa{xintGCD}|{10000}{1113}=|\texttt{\xintGCD{10000}{1113}}}
+\centeredline{|\xintGCD{123456789012345}{9876543210321}=|\texttt
+ {\xintGCD{123456789012345}{9876543210321}}}
+
+\subsection{\csbh{xintBezout}}\label{xintBezout}
+
+\xintAssign{{\xintBezout {10000}{1113}}}\to\X
+\xintAssign {\xintBezout {10000}{1113}}\to\A\B\U\V\D
+
+\csa{xintBezout\n\m} returns five numbers |A|, |B|, |U|, |V|, |D| within
+braces. |A| is the first (expanded, as usual) input number, |B| the
+second, |D| is the GCD, and \texttt{UA - VB = D}.
+\centeredline{|\xintAssign {{\xintBezout {10000}{1113}}}\to\X|}
+\centeredline{|\meaning\X: |\texttt{\meaning\X }.}
+\noindent{|\xintAssign {\xintBezout {10000}{1113}}\to\A\B\U\V\D|}\\
+|\A: |\texttt{\A },
+|\B: |\texttt{\B },
+|\U: |\texttt{\U },
+|\V: |\texttt{\V },
+|\D: |\texttt{\D }.\\
+\xintAssign {\xintBezout {123456789012345}{9876543210321}}\to\A\B\U\V\D
+\noindent{|\xintAssign {\xintBezout {123456789012345}{9876543210321}}\to\A\B\U\V\D
+|}\\
+|\A: |\texttt{\A },
+|\B: |\texttt{\B },
+|\U: |\texttt{\U },
+|\V: |\texttt{\V },
+|\D: |\texttt{\D }.
+
+
+\subsection{\csbh{xintEuclideAlgorithm}}\label{xintEuclideAlgorithm}
+
+\xintAssign {{\xintEuclideAlgorithm {10000}{1113}}}\to\X
+
+\def\restorebracecatcodes
+ {\catcode`\{=1 \catcode`\}=2 }
+
+\def\allowlistsplit
+ {\catcode`\{=12 \catcode`\}=12 \allowlistsplita }
+
+\def\allowlistsplitx {\futurelet\listnext\allowlistsplitxx }
+
+\def\allowlistsplitxx {\ifx\listnext\relax \restorebracecatcodes
+ \else \expandafter\allowlistsplitxxx \fi }
+\begingroup
+\catcode`\[=1
+\catcode`\]=2
+\catcode`\{=12
+\catcode`\}=12
+\gdef\allowlistsplita #1{[#1\allowlistsplitx {]
+\gdef\allowlistsplitxxx {#1}%
+ [{#1}\hskip 0pt plus 1pt \allowlistsplitx ]
+\endgroup
+
+\csa{xintEuclideAlgorithm\n\m} applies the Euclide algorithm and
+keeps a copy of all quotients and remainders.
+\centeredline{|\xintAssign {{\xintEuclideAlgorithm {10000}{1113}}}\to\X|}
+
+|\meaning\X: |\texttt{\expandafter\allowlistsplit\meaning\X
+ \relax }.
+The first token is the number of steps, the second is |N|, the
+third is the GCD, the fourth is |M| then the first quotient and
+remainder, the second quotient and remainder, \dots until the
+final quotient and last (zero) remainder.
+
+\subsection{\csbh{xintBezoutAlgorithm}}\label{xintBezoutAlgorithm}
+
+\catcode`\& 4
+
+\xintAssign {{\xintBezoutAlgorithm {10000}{1113}}}\to\X
+
+\csa{xintBezoutAlgorithm\n\m} applies the Euclide algorithm and
+keeps a copy of all quotients and remainders. Furthermore it
+computes the entries of the successive products of the 2 by 2 matrices
+$\left(\vcenter{\halign {\,#&\,#\cr q & 1 \cr 1 & 0 \cr}}\right)$
+formed from the quotients arising in the algorithm.
+\centeredline{|\xintAssign {{\xintEuclideAlgorithm {10000}{1113}}}\to\X|}
+
+|\meaning\X: |\texttt{\expandafter\allowlistsplit\meaning\X \relax}.
+
+The first token is the number of steps, the second is |N|, then
+|0|, |1|, the GCD, |M|, |1|, |0|, the first quotient, the first
+remainder, the top left entry of the first matrix, the bottom left
+entry, and then these four things at each step until the end.
+
+\catcode`\& 13
+
+\subsection{\csbh{xintTypesetEuclideAlgorithm}}\label{xintTypesetEuclideAlgorithm}
+
+This macro is just an example of how to organize the data returned
+by \csa{xintEuclideAlgorithm}. Copy the source code to a new macro
+and modify it to what is needed.
+\centeredline{|\xintTypesetEuclideAlgorithm
+ {123456789012345}{9876543210321}|} \xintTypesetEuclideAlgorithm
+{123456789012345}{9876543210321}
+
+
+\subsection{\csbh{xintTypesetBezoutAlgorithm}}\label{xintTypesetBezoutAlgorithm}
+
+This macro is just an example of how to organize the data returned
+by \csa{xintBezoutAlgorithm}. Copy the source code to a new macro
+and modify it to what is needed.
+\centeredline{|\xintTypesetBezoutAlgorithm {10000}{1113}|}
+\xintTypesetBezoutAlgorithm {10000}{1113}
\section{Commands of the \xintseriesname package}\label{sec:series}
@@ -3111,18 +4041,13 @@ was plaguing the |1.03| version. \footnote{with powers |x\string^k|,
\def\x {5/17[0]}
\[ \sum_{n=0}^{n=20} \Bigl(\frac 5{17}\Bigr)^n
=\xintFrac{\xintIrr{\xintPowerSeries {0}{20}{\geom}{\x}}}
- =\xintFrac{\xintiSub{\xintiPow {17}{21}}{\xintiPow{5}{21}}%
- /\xintiMul{12}{\xintiPow {17}{20}}}\]
-% a parser for arbitrary algebraic expressions with the +,-,/,*,and ^
-% operations would be dearly appreciated here ; implementing a completely
-% expandable one would be quite a lot of work, even if we plagiarize l3fp!
+ =\xintFrac{\xinttheexpr (17^21-5^21)/12/17^20\relax}\]
|
\def\geom #1{1[0]} % the geometric series
\def\x {5/17[0]} %
\[ \sum_{n=0}^{n=20} \Bigl(\frac 5{17}\Bigr)^n
=\xintFrac{\xintIrr{\xintPowerSeries {0}{20}{\geom}{\x}}}
- =\xintFrac{\xintiSub{\xintiPow {17}{21}}{\xintiPow{5}{21}}%
- /\xintiMul{12}{\xintiPow {17}{20}}}\]
+ =\xintFrac{\xinttheexpr (17^21-5^21)/12/17^20\relax}\]
\dverb|&
\def\coefflog #1{1/#1[0]}% 1/n
@@ -4463,7 +5388,7 @@ first place.
\fi
\expandafter\x\csname ver@xint.sty\endcsname
\ProvidesPackage{xint}%
- [2013/05/14 v1.06b Expandable operations on long numbers (jfB)]%
+ [2013/05/26 v1.07a Expandable operations on long numbers (jfB)]%
% \end{macrocode}
% \subsection{Token management macros}
% \begin{macrocode}
@@ -4481,6 +5406,9 @@ first place.
\def\xint_firstoftwo_andstop #1#2{ #1}%
\def\xint_secondoftwo_andstop #1#2{ #2}%
\def\xint_exchangetwo_keepbraces_andstop #1#2{ {#2}{#1}}%
+\def\xint_firstofthree #1#2#3{#1}%
+\def\xint_secondofthree #1#2#3{#2}%
+\def\xint_thirdofthree #1#2#3{#3}%
\def\xint_minus_andstop { -}%
\def\xint_gob_til_r #1\R {}%
\def\xint_gob_til_w #1\W {}%
@@ -4548,19 +5476,23 @@ first place.
% \lverb|New with 1.06. Makes the expansion of its argument and then reverses
% the
% resulting tokens or braced tokens, adding a pair of braces to each (thus,
-% maintaining it when it was already there.) |
+% maintaining it when it was already there.)$\
+% hmm, at some point when I was cleaning up the code towards 1.07, I have
+% accidentally removed the {} which must be after\XINT_revwbr_loop.
+% Corrected for 1.07a
+% |
% \begin{macrocode}
\def\xintRevWithBraces {\romannumeral0\xintrevwithbraces }%
\def\xintRevWithBracesNoExpand {\romannumeral0\xintrevwithbracesnoexpand }%
\def\xintrevwithbraces #1%
{%
- \expandafter\XINT_revwbr_loop % #1 empty ok
+ \expandafter\XINT_revwbr_loop\expandafter{\expandafter}%
\romannumeral-`0#1\xint_relax\xint_relax\xint_relax\xint_relax
\xint_relax\xint_relax\xint_relax\xint_relax\Z
}%
\def\xintrevwithbracesnoexpand #1%
{%
- \romannumeral0\XINT_revwbr_loop
+ \romannumeral0\XINT_revwbr_loop\expandafter{\expandafter}%
#1\xint_relax\xint_relax\xint_relax\xint_relax
\xint_relax\xint_relax\xint_relax\xint_relax\Z
}%
@@ -4662,7 +5594,7 @@ first place.
% First included in release 1.06.|
% \begin{macrocode}
\def\xintCSVtoList {\romannumeral0\xintcsvtolist }%
-% \def\xintCSVtoListNoExpand {\romannumeral0\xintcsvtolistnoexpand }%
+\def\xintCSVtoListNoExpand {\romannumeral0\xintcsvtolistnoexpand }%
\def\xintcsvtolist #1%
{%
\expandafter\XINT_csvtol_loop_a\expandafter
@@ -4670,12 +5602,12 @@ first place.
,\xint_undef,\xint_undef,\xint_undef,\xint_undef
,\xint_undef,\xint_undef,\xint_undef,\xint_undef,\Z
}%
-% \def\xintcsvtolistnoexpand #1%
-% {%
-% \romannumeral0\XINT_csvtol_loop_a
-% {}#1,\xint_undef,\xint_undef,\xint_undef,\xint_undef
-% ,\xint_undef,\xint_undef,\xint_undef,\xint_undef,\Z
-% }%
+\def\xintcsvtolistnoexpand #1%
+{%
+ \romannumeral0\XINT_csvtol_loop_a
+ {}#1,\xint_undef,\xint_undef,\xint_undef,\xint_undef
+ ,\xint_undef,\xint_undef,\xint_undef,\xint_undef,\Z
+}%
\def\XINT_csvtol_loop_a #1#2,#3,#4,#5,#6,#7,#8,#9,%
{%
\xint_gob_til_xint_undef #9\XINT_csvtol_finish_a\xint_undef
@@ -4723,12 +5655,12 @@ first place.
% strangely it was for a zero-element list).|
% \begin{macrocode}
\def\xintListWithSep {\romannumeral0\xintlistwithsep }%
-% \def\xintListWithSepNoExpand {\romannumeral0\xintlistwithsepnoexpand }%
+\def\xintListWithSepNoExpand {\romannumeral0\xintlistwithsepnoexpand }%
\long\def\xintlistwithsep #1#2%
{\expandafter\XINT_lws\expandafter {\romannumeral-`0#2}{#1}}%
\long\def\XINT_lws #1#2{\XINT_lws_start {#2}#1\Z }%
-% \long\def\xintlistwithsepnoexpand #1#2%
-% {\romannumeral0\XINT_lws_start {#1}#2\Z }%
+\long\def\xintlistwithsepnoexpand #1#2%
+ {\romannumeral0\XINT_lws_start {#1}#2\Z }%
\long\def\XINT_lws_start #1#2%
{%
\xint_gob_til_z #2\XINT_lws_dont\Z
@@ -4753,16 +5685,16 @@ first place.
% expand its argument.|
% \begin{macrocode}
\def\xintNthElt {\romannumeral0\xintnthelt }%
-% \def\xintNthEltNoExpand {\romannumeral0\xintntheltnoexpand }%
+\def\xintNthEltNoExpand {\romannumeral0\xintntheltnoexpand }%
\def\xintnthelt #1#2%
{%
\expandafter\XINT_nthelt\expandafter {\romannumeral-`0#2}%
{\numexpr #1\relax }%
}%
-% \def\xintntheltnoexpand #1#2%
-% {%
-% \romannumeral0\XINT_nthelt {#2}{\numexpr #1\relax}%
-% }%
+\def\xintntheltnoexpand #1#2%
+{%
+ \romannumeral0\XINT_nthelt {#2}{\numexpr #1\relax}%
+}%
\def\XINT_nthelt #1#2%
{%
\ifnum #2>0
@@ -4807,14 +5739,14 @@ first place.
% expanded. Introduced with release 1.04|
% \begin{macrocode}
\def\xintApply {\romannumeral0\xintapply }%
-% \def\xintApplyNoExpand {\romannumeral0\xintapplynoexpand }%
+\def\xintApplyNoExpand {\romannumeral0\xintapplynoexpand }%
\def\xintapply #1#2%
{%
\expandafter\XINT_apply\expandafter {\romannumeral-`0#2}%
{#1}%
}%
\def\XINT_apply #1#2{\XINT_apply_loop_a {}{#2}#1\Z }%
-% \def\xintapplynoexpand #1#2{\romannumeral0\XINT_apply_loop_a {}{#1}#2\Z }%
+\def\xintapplynoexpand #1#2{\romannumeral0\XINT_apply_loop_a {}{#1}#2\Z }%
\def\XINT_apply_loop_a #1#2#3%
{%
\xint_gob_til_z #3\XINT_apply_end\Z
@@ -4833,15 +5765,15 @@ first place.
% having to do \gdef. The list is first expanded. Introduced with release 1.06b|
% \begin{macrocode}
\def\xintApplyUnbraced {\romannumeral0\xintapplyunbraced }%
-% \def\xintApplyUnbracedNoExpand {\romannumeral0\xintapplyunbracednoexpand }%
+\def\xintApplyUnbracedNoExpand {\romannumeral0\xintapplyunbracednoexpand }%
\def\xintapplyunbraced #1#2%
{%
\expandafter\XINT_applyunbr\expandafter {\romannumeral-`0#2}%
{#1}%
}%
\def\XINT_applyunbr #1#2{\XINT_applyunbr_loop_a {}{#2}#1\Z }%
-% \def\xintapplyunbracednoexpand #1#2%
-% {\romannumeral0\XINT_applyunbr_loop_a {}{#1}#2\Z }%
+\def\xintapplyunbracednoexpand #1#2%
+ {\romannumeral0\XINT_applyunbr_loop_a {}{#1}#2\Z }%
\def\XINT_applyunbr_loop_a #1#2#3%
{%
\xint_gob_til_z #3\XINT_applyunbr_end\Z
@@ -5162,6 +6094,21 @@ first place.
\krof
}%
% \end{macrocode}
+% \subsection{\csh{xintSgnFork}}
+% \lverb|&
+% Expandable three-way fork added in 1.07. It is not used in the code but is
+% provided for use inside the arguments to the package macros. The argument #1
+% must expand to -1,0 or 1. A \count should be put within a \numexpr..\relax.|
+% \begin{macrocode}
+\def\xintSgnFork {\romannumeral0\xintsgnfork }%
+\def\xintsgnfork #1%
+{%
+ \ifcase #1 \xint_afterfi{\expandafter\space\xint_secondofthree}%
+ \or\xint_afterfi{\expandafter\space\xint_thirdofthree}%
+ \else\xint_afterfi{\expandafter\space\xint_firstofthree}%
+ \fi
+}%
+% \end{macrocode}
% \subsection{\csh{xintOpp}}
% \begin{macrocode}
\def\xintiOpp {\romannumeral0\xintiopp }%
@@ -6888,7 +7835,7 @@ first place.
% With release 1.05, rather than using \XINT_Length I opt finally for direct use
% of \numexpr (which will throw a suitable number too big message), and to raise
% the \xintError:$\ FactorialOfTooBigNumber for argument larger than 1000000
-% (rather than 1000000000). |
+% (rather than 1000000000).|
% \begin{macrocode}
\def\xintFac {\romannumeral0\xintfac }%
\def\xintfac #1%
@@ -8031,7 +8978,16 @@ first place.
%
% Release 1.06 has a faster and more compactly coded \XINT_dsx_zeroloop.
% Also, x is now given to a \numexpr. The earlier code should be then
-% simplified, but I leave as is for the time being.+
+% simplified, but I leave as is for the time being.
+%
+% In 1.07, I decide to modify
+% the coding of \XINT_dsx_zeroloop, to avoid
+% impacting the input stack (which prevented doing truncation or rounding or
+% float with more than eight times the size of input stack; 40000 = 8x5000
+% digits on my installation.) I think this was the only place in the code with
+% such non tail recursion, as I recall being careful to avoid problems within
+% the Factorial and Power routines, but I would need to check. Too tired now
+% after having finished \xintexpr, \xintNewExpr, and \xintfloatexpr!+
% \begin{macrocode}
\def\xintDSx {\romannumeral0\xintdsx }%
\def\xintdsx #1#2%
@@ -8060,7 +9016,7 @@ first place.
\def\XINT_dsx_xisNeg_checkA_ #1#2\Z #3%
{%
\xint_gob_til_zero #1\XINT_dsx_xisNeg_Azero 0%
- \XINT_dsx_xisNeg_checkx {#3}{#3}\Z {#1#2}%
+ \XINT_dsx_xisNeg_checkx {#3}{#3}{}\Z {#1#2}%
}%
\def\XINT_dsx_xisNeg_Azero #1\Z #2{ 0}%
\def\XINT_dsx_xisNeg_checkx #1%
@@ -8068,25 +9024,25 @@ first place.
\ifnum #1>999999999
\xint_afterfi
{\xintError:TooBigDecimalShift
- \expandafter\space\expandafter 0\xint_gobble_iii }%
+ \expandafter\space\expandafter 0\xint_gobble_iv }%
\else
- \expandafter \XINT_dsx_zeroloop
+ \expandafter \XINT_dsx_zeroloop
\fi
}%
-\def\XINT_dsx_zeroloop #1%
+\def\XINT_dsx_zeroloop #1#2%
{%
\ifnum #1<9 \XINT_dsx_exita\fi
\expandafter\XINT_dsx_zeroloop\expandafter
- {\the\numexpr #1-8}00000000%
+ {\the\numexpr #1-8}{#200000000}%
}%
\def\XINT_dsx_exita\fi\expandafter\XINT_dsx_zeroloop
{%
\fi\expandafter\XINT_dsx_exitb
}%
-\def\XINT_dsx_exitb #1%
+\def\XINT_dsx_exitb #1#2%
{%
\expandafter\expandafter\expandafter
- \XINT_dsx_addzeros\csname xint_gobble_\romannumeral -#1\endcsname
+ \XINT_dsx_addzeros\csname xint_gobble_\romannumeral -#1\endcsname #2%
}%
\def\XINT_dsx_addzeros #1\Z #2{ #2#1}%
\def\XINT_dsx_xisPos #1\Z #2%
@@ -8496,7 +9452,7 @@ first place.
\fi
\expandafter\x\csname ver@xintgcd.sty\endcsname
\ProvidesPackage{xintgcd}%
- [2013/05/14 v1.06b Euclide algorithm with xint package (jfB)]%
+ [2013/05/26 v1.07a Euclide algorithm with xint package (jfB)]%
% \end{macrocode}
% \subsection{\csh{xintGCD}}
% \begin{macrocode}
@@ -9205,7 +10161,7 @@ first place.
\fi
\expandafter\x\csname ver@xintfrac.sty\endcsname
\ProvidesPackage{xintfrac}%
- [2013/05/14 v1.06b Expandable operations on fractions (jfB)]%
+ [2013/05/26 v1.07a Expandable operations on fractions (jfB)]%
% \end{macrocode}
% \subsection{\csh{xintLen}}
% \begin{macrocode}
@@ -9225,7 +10181,7 @@ first place.
% 1.06a version now outputs 0/1[0] and not 0[0] in case of zero. More generally
% all macros have been checked in xintfrac, xintseries, xintcfrac, to make sure
% the output format for fractions was always a/b[n]. (except of course \xintIrr,
-% \xintJrr, \xintRaw)|
+% \xintJrr, \xintRawWithZeros)|
% \begin{macrocode}
\def\XINT_outfrac #1#2#3%
{%
@@ -9258,6 +10214,8 @@ first place.
}%
% \end{macrocode}
% \subsection{\csh{XINT\_inFrac}}
+% \lverb|Extended in 1.07 to accept scientific notation on input. With lowercase
+% e only. The \xintexpr parser does accept uppercase E also.|
% \begin{macrocode}
\def\XINT_inFrac {\romannumeral0\XINT_infrac }%
\def\XINT_infrac #1%
@@ -9294,37 +10252,60 @@ first place.
\def\XINT_infrac_Zero #1\T { {0}{0}{1}}%
% \end{macrocode}
% \subsection{\csh{XINT\_frac}}
+% \lverb|Extended in 1.07 to recognize and accept scientific notation both at
+% the numerator and (possible) denominator. Only a lowercase e will do here, but
+% uppercase E is possible within an \xintexpr..\relax |
% \begin{macrocode}
\def\XINT_frac #1/#2#3\Z
{%
\xint_UDwfork
#2\dummy \XINT_frac_A
- \W\dummy {\expandafter\XINT_frac_B \romannumeral-`0#2}%
+ \W\dummy {\expandafter\XINT_frac_U \romannumeral-`0#2}%
+ \krof
+ #3e\W\Z #1e\W\Z
+}%
+\def\XINT_frac_U #1e#2#3\Z
+{%
+ \xint_UDwfork
+ #2\dummy \XINT_frac_Ua
+ \W\dummy {\XINT_frac_Ub #2}%
\krof
- #3.\W\Z #1.\W\Z
+ #3\Z #1\Z
}%
+\def\XINT_frac_Ua \Z #1/\W\Z {\XINT_frac_B #1.\W\Z {0}}%
+\def\XINT_frac_Ub #1/\W e\W\Z #2\Z {\XINT_frac_B #2.\W\Z {#1}}%
\def\XINT_frac_B #1.#2#3\Z
{%
\xint_UDwfork
- #2\dummy \XINT_frac_Ba
+ #2\dummy \XINT_frac_Ba
\W\dummy {\XINT_frac_Bb #2}%
\krof
#3\Z #1\Z
}%
-\def\XINT_frac_Bb #1/\W.\W\Z #2\Z
+\def\XINT_frac_Ba \Z #1\Z {\XINT_frac_T {0}{#1}}%
+\def\XINT_frac_Bb #1.\W\Z #2\Z
{%
- \expandafter \XINT_frac_C \expandafter
+ \expandafter \XINT_frac_T \expandafter
{\romannumeral0\XINT_length {#1}}{#2#1}%
}%
-\def\XINT_frac_Ba \Z #1/\W\Z {\XINT_frac_C {0}{#1}}%
-\def\XINT_frac_A .\W\Z {\XINT_frac_C {0}{1}}%
-\def\XINT_frac_C #1#2#3.#4#5\Z
+\def\XINT_frac_A e\W\Z {\XINT_frac_T {0}{1}{0}}%
+\def\XINT_frac_T #1#2#3#4e#5#6\Z
+{%
+ \xint_UDwfork
+ #5\dummy \XINT_frac_Ta
+ \W\dummy {\XINT_frac_Tb #5}%
+ \krof
+ #6\Z #4\Z {#1}{#2}{#3}%
+}%
+\def\XINT_frac_Ta \Z #1\Z {\XINT_frac_C #1.\W\Z {0}}%
+\def\XINT_frac_Tb #1e\W\Z #2\Z {\XINT_frac_C #2.\W\Z {#1}}%
+\def\XINT_frac_C #1.#2#3\Z
{%
\xint_UDwfork
- #4\dummy \XINT_frac_Ca
- \W\dummy {\XINT_frac_Cb #4}%
+ #2\dummy \XINT_frac_Ca
+ \W\dummy {\XINT_frac_Cb #2}%
\krof
- #5\Z #3\Z {#1}{#2}%
+ #3\Z #1\Z
}%
\def\XINT_frac_Ca \Z #1\Z {\XINT_frac_D {0}{#1}}%
\def\XINT_frac_Cb #1.\W\Z #2\Z
@@ -9332,14 +10313,14 @@ first place.
\expandafter\XINT_frac_D\expandafter
{\romannumeral0\XINT_length {#1}}{#2#1}%
}%
-\def\XINT_frac_D #1#2#3#4%
+\def\XINT_frac_D #1#2#3#4#5#6%
{%
\expandafter \XINT_frac_E \expandafter
- {\the\numexpr -#1+#3\expandafter}\expandafter
+ {\the\numexpr -#1+#3+#4-#6\expandafter}\expandafter
{\romannumeral0\XINT_num_loop #2%
\xint_relax\xint_relax\xint_relax\xint_relax
\xint_relax\xint_relax\xint_relax\xint_relax\Z }%
- {\romannumeral0\XINT_num_loop #4%
+ {\romannumeral0\XINT_num_loop #5%
\xint_relax\xint_relax\xint_relax\xint_relax
\xint_relax\xint_relax\xint_relax\xint_relax\Z }%
}%
@@ -9463,27 +10444,42 @@ first place.
}%
% \end{macrocode}
% \subsection{\csh{xintRaw}}
+% \lverb|&
+% 1.07: this macro simply prints in a user readable form the fraction after its
+% initial scanning. Useful when put inside braces in an \xintexpr, when the
+% input is not yet in the a/b[n] form.|
% \begin{macrocode}
\def\xintRaw {\romannumeral0\xintraw }%
-\def\xintraw
+\def\xintraw
{%
\expandafter\XINT_raw\romannumeral0\XINT_infrac
}%
-\def\XINT_raw #1%
+\def\XINT_raw #1#2#3{ #2/#3[#1]}%
+% \end{macrocode}
+% \subsection{\csh{xintRawWithZeros}}
+% \lverb|&
+% This was called \xintRaw in versions earlier than 1.07|
+% \begin{macrocode}
+\def\xintRawWithZeros {\romannumeral0\xintrawwithzeros }%
+\def\xintrawwithzeros
+{%
+ \expandafter\XINT_rawz\romannumeral0\XINT_infrac
+}%
+\def\XINT_rawz #1%
{%
\ifcase\XINT_Sgn {#1}
- \expandafter\XINT_raw_Ba
+ \expandafter\XINT_rawz_Ba
\or
- \expandafter\XINT_raw_A
+ \expandafter\XINT_rawz_A
\else
- \expandafter\XINT_raw_Ba
+ \expandafter\XINT_rawz_Ba
\fi
{#1}%
}%
-\def\XINT_raw_A #1#2#3{\xint_dsh {#2}{-#1}/#3}%
-\def\XINT_raw_Ba #1#2#3{\expandafter\XINT_raw_Bb
+\def\XINT_rawz_A #1#2#3{\xint_dsh {#2}{-#1}/#3}%
+\def\XINT_rawz_Ba #1#2#3{\expandafter\XINT_rawz_Bb
\expandafter{\romannumeral0\xint_dsh {#3}{#1}}{#2}}%
-\def\XINT_raw_Bb #1#2{ #2/#1}%
+\def\XINT_rawz_Bb #1#2{ #2/#1}%
% \end{macrocode}
% \subsection{\csh{xintNumerator}}
% \begin{macrocode}
@@ -9677,16 +10673,42 @@ first place.
}%
\def\XINT_rez_E #1#2#3{ #3/#2[#1]}%
% \end{macrocode}
+% \subsection{\csh{xintE}}
+% \lverb|added with with 1.07, together with support for `floats'. The fraction
+% comes first here, contrarily to \xintTrunc and \xintRound.|
+% \begin{macrocode}
+\def\xintE {\romannumeral0\xinte }%
+\def\xinte #1%
+{%
+ \expandafter\XINT_e \romannumeral0\XINT_infrac {#1}%
+}%
+\def\XINT_e #1#2#3#4%
+{%
+ \expandafter\XINT_e_end\expandafter{\the\numexpr #1+#4}{#2}{#3}%
+}%
+\def\xintfE {\romannumeral0\xintfe }%
+\def\xintfe #1%
+{%
+ \expandafter\XINT_fe \romannumeral0\XINT_infrac {#1}%
+}%
+\def\XINT_fe #1#2#3#4%
+{%
+ \expandafter\XINT_e_end\expandafter{\the\numexpr #1+\xintNum{#4}}{#2}{#3}%
+}%
+\def\XINT_e_end #1#2#3{ #2/#3[#1]}%
+\let\XINTinFloatfE\xintfE
+% \end{macrocode}
% \subsection{\csh{xintIrr}}
% \lverb|&
% 1.04 fixes a buggy \xintIrr {0}.
-% 1.05 modifies the initial parsing and post-processing to use \xintraw and to
+% 1.05 modifies the initial parsing and post-processing to use \xintrawwithzeros
+% and to
% more quickly deal with an input denominator equal to 1.|
% \begin{macrocode}
\def\xintIrr {\romannumeral0\xintirr }%
\def\xintirr #1%
{%
- \expandafter\XINT_irr_start\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_irr_start\romannumeral0\xintrawwithzeros {#1}\Z
}%
\def\XINT_irr_start #1#2/#3\Z
{%
@@ -9756,7 +10778,8 @@ first place.
% \xintIrr, but raising an error when the input does not evaluate to an integer.
% Usable with not too much overhead on integer input as \xintIrr
% checks quickly for a denominator equal to 1 (which will be put there by the
-% \XINT_infrac called by \xintraw). This way, macros such as \xintQuo can be
+% \XINT_infrac called by \xintrawwithzeros). This way, macros such as \xintQuo
+% can be
% modified with minimal overhead to accept fractional input as long as it
% evaluates to an integer. |
% \begin{macrocode}
@@ -9769,6 +10792,18 @@ first place.
\space #1%
}%
% \end{macrocode}
+% \subsection{\csh{xintfFac}}
+% \lverb|done in 1.07, the \xintexpr scanner may want to apply \xintFac
+% to a fraction, but using \xintNum as here means count registers are
+% not allowed
+% anymore; to maintain this feature from previous versions I had to duplicate.|
+% \begin{macrocode}
+\def\xintfFac {\romannumeral0\xintffac }%
+\def\xintffac #1%
+{%
+ \expandafter\XINT_fac_fork\expandafter{\the\numexpr \xintNum{#1}}%
+}%
+% \end{macrocode}
% \subsection{\csh{xintJrr}}
% \lverb|&
% Modified similarly as \xintIrr in release 1.05|
@@ -9776,7 +10811,7 @@ first place.
\def\xintJrr {\romannumeral0\xintjrr }%
\def\xintjrr #1%
{%
- \expandafter\XINT_jrr_start\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_jrr_start\romannumeral0\xintrawwithzeros {#1}\Z
}%
\def\XINT_jrr_start #1#2/#3\Z
{%
@@ -9838,7 +10873,7 @@ first place.
% \end{macrocode}
% \subsection{\csh{xintTrunc}, \csh{xintiTrunc}}
% \lverb|&
-% Modified in 1.06 to give the first argument to a \numexpr|
+% Modified in 1.06 to give the first argument to a \numexpr.|
% \begin{macrocode}
\def\xintTrunc {\romannumeral0\xinttrunc }%
\def\xintiTrunc {\romannumeral0\xintitrunc }%
@@ -9938,12 +10973,12 @@ first place.
\def\XINT_trunc_Hb #1#2#3%
{%
\expandafter #3\expandafter0\expandafter.%
- \romannumeral0\XINT_dsx_zeroloop {#1}\Z {}#2% #1=-0 possible!
+ \romannumeral0\XINT_dsx_zeroloop {#1}{}\Z {}#2% #1=-0 possible!
}%
% \end{macrocode}
% \subsection{\csh{xintRound}, \csh{xintiRound}}
% \lverb|&
-% Modified in 1.06 to give the first argument to a \numexpr|
+% Modified in 1.06 to give the first argument to a \numexpr.|
% \begin{macrocode}
\def\xintRound {\romannumeral0\xintround }%
\def\xintiRound {\romannumeral0\xintiround }%
@@ -10010,6 +11045,250 @@ first place.
\XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z \Z
}%
% \end{macrocode}
+% \subsection{\csh{xintDigits}}
+% \begin{macrocode}
+\mathchardef\XINT_digits 16
+\def\xintDigits #1#2%
+ {\afterassignment \xint_gobble_i \mathchardef\XINT_digits=}%
+\def\xinttheDigits {\number\XINT_digits }%
+% \end{macrocode}
+% \subsection{\csh{xintFloat}}
+% \begin{macrocode}
+\def\xintFloat {\romannumeral0\xintfloat }%
+\def\xintfloat #1{\XINT_float_chkopt #1\Z }%
+\def\XINT_float_chkopt #1%
+{%
+ \ifx #1[\expandafter\XINT_float_opt
+ \else\expandafter\XINT_float_noopt
+ \fi #1%
+}%
+\def\XINT_float_noopt #1\Z
+{%
+ \XINT_float_a \XINT_digits {#1}%
+}%
+\def\XINT_float_opt [\Z #1]%
+{%
+ \expandafter\XINT_float_a\expandafter {\the\numexpr #1}%
+}%
+\def\XINT_float_a #1#2%
+{%
+ \expandafter\XINT_float_b \romannumeral0\XINT_infrac {#2}{#1}%
+}%
+\def\XINT_float_b #1#2#3%
+{%
+ \XINT_float_fork #2\Z {#3}{#1}%
+}%
+\def\XINT_float_fork #1%
+{%
+ \xint_UDzerominusfork
+ #1-\dummy \XINT_float_zero
+ 0#1\dummy \XINT_float_N
+ 0-\dummy {\XINT_float_P #1}%
+ \krof
+}%
+\def\XINT_float_zero \Z #1#2#3{ 0.e0}%
+\def\XINT_float_N {\expandafter\xint_minus_andstop\romannumeral0\XINT_float_P }%
+\def\XINT_float_P #1\Z #2#3#4%
+{%
+ \ifcase \romannumeral0\XINT_fgeq_A 011{#3}{#1}{#2}
+ \expandafter\XINT_float_lessthanone_a
+ \or\expandafter\XINT_float_atleastone_b
+ \fi {#3}{#1}{#2}{#3+#4}{#1}{#2}%
+}%
+\def\XINT_float_atleastone_b
+{%
+ \expandafter\XINT_float_atleastone_c\romannumeral0\XINT_trunc_B
+}%
+\def\XINT_float_atleastone_c #1\Z #2%
+{%
+ \expandafter\XINT_float_c\expandafter
+ {\romannumeral0\xintisub {\xintLength{#1}}{1}}%
+}%
+\def\XINT_float_lessthanone_a #1%
+{%
+ \expandafter\XINT_float_lessthanone_b\expandafter
+ {\the\numexpr -#1}%
+}%
+\def\XINT_float_lessthanone_b #1#2#3%
+{%
+ \expandafter\XINT_float_lessthanone_c
+ \romannumeral0\XINT_trunc_B {#1}{#3}{#2}%
+}%
+\def\XINT_float_lessthanone_c #1\Z #2%
+{%
+ \expandafter\XINT_float_c\expandafter
+ {\expandafter-\romannumeral0\xintilen {\xintiSub {#1}{1}}}%
+}%
+\def\XINT_float_c #1#2#3#4%
+{%
+ \expandafter\XINT_float_d\expandafter
+ {\the\numexpr #2-#1}{#3}{#4}e#1%
+}%
+\def\XINT_float_d
+{%
+ \expandafter\XINT_float_round_B\romannumeral0\XINT_trunc_B
+}%
+\def\XINT_float_round_B #1#2\Z #3%
+{%
+ \ifnum #1=9
+ \xint_afterfi
+ {\romannumeral0\XINT_rord_main {}#1#2\XINT_float_round_S}%
+ \else
+ \xint_afterfi
+ {\romannumeral0\XINT_rord_main {}#1#2\XINT_float_round_D}%
+ \fi
+ \xint_relax
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_relax
+ \Z
+}%
+\def\XINT_float_round_D #1%
+{%
+ \ifnum #1<5
+ \expandafter\XINT_float_round_Da
+ \else
+ \expandafter\XINT_float_round_Db
+ \fi
+}%
+\def\XINT_float_round_Da #1\Z
+{%
+ \expandafter\XINT_float_round_f
+ \romannumeral0\XINT_rord_main {}#1%
+ \xint_relax
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_relax
+}%
+\def\XINT_float_round_Db #1\Z
+{%
+ \expandafter\XINT_float_round_f
+ \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z
+}%
+\def\XINT_float_round_f #1{ #1.}%
+\def\XINT_float_round_S #1%
+{%
+ \ifnum #1<5
+ \expandafter\XINT_float_round_Da
+ \else
+ \expandafter\XINT_float_round_Sb
+ \fi
+}%
+\def\XINT_float_round_Sb #1\Z
+{%
+ \expandafter\XINT_float_round_g
+ \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z
+}%
+\def\XINT_float_round_g #1%
+{%
+ \ifnum #1=1 \expandafter\XINT_float_round_h\fi
+ \space #1.%
+}%
+\def\XINT_float_round_h\space 1.0{ 10.}%
+% \end{macrocode}
+% \subsection{\csh{XINT\_inFloat}}
+% \begin{macrocode}
+\def\XINT_inFloat [#1]%
+{%
+ \expandafter\XINT_infloat\expandafter {\the\numexpr #1}%
+}%
+\def\XINT_infloat #1#2%
+{%
+ \expandafter\XINT_infloat_a \romannumeral0\XINT_infrac {#2}{#1}%
+}%
+\def\XINT_infloat_a #1#2#3%
+{%
+ \XINT_infloat_fork #2\Z {#3}{#1}%
+}%
+\def\XINT_infloat_fork #1%
+{%
+ \xint_UDzerominusfork
+ #1-\dummy \XINT_infloat_zero
+ 0#1\dummy \XINT_infloat_N
+ 0-\dummy {\XINT_infloat_P #1}%
+ \krof
+}%
+\def\XINT_infloat_zero\Z #1#2#3{0[0]}%
+\def\XINT_infloat_N {\expandafter-\romannumeral-`0\XINT_infloat_P }%
+\def\XINT_infloat_P #1\Z #2#3#4%
+{%
+ \ifcase \romannumeral0\XINT_fgeq_A 011{#3}{#1}{#2}
+ \expandafter\XINT_infloat_lessthanone_a
+ \or\expandafter\XINT_infloat_atleastone_b
+ \fi {#3}{#1}{#2}{#3+#4}{#1}{#2}{#4}%
+}%
+\def\XINT_infloat_atleastone_b
+{%
+ \expandafter\XINT_infloat_atleastone_c\romannumeral0\XINT_trunc_B
+}%
+\def\XINT_infloat_atleastone_c #1\Z #2%
+{%
+ \expandafter\XINT_infloat_c\expandafter
+ {\romannumeral0\xintisub {\xintLength{#1}}{1}}%
+}%
+\def\XINT_infloat_lessthanone_a #1%
+{%
+ \expandafter\XINT_infloat_lessthanone_b\expandafter
+ {\the\numexpr -#1}%
+}%
+\def\XINT_infloat_lessthanone_b #1#2#3%
+{%
+ \expandafter\XINT_infloat_lessthanone_c
+ \romannumeral0\XINT_trunc_B {#1}{#3}{#2}%
+}%
+\def\XINT_infloat_lessthanone_c #1\Z #2%
+{%
+ \expandafter\XINT_infloat_c\expandafter
+ {\expandafter-\romannumeral0\xintilen {\xintiSub {#1}{1}}}%
+}%
+\def\XINT_infloat_c #1#2#3#4%
+{%
+ \expandafter\XINT_infloat_d\expandafter
+ {\the\numexpr #2-#1}{#3}{#4}{#1}%
+}%
+\def\XINT_infloat_d
+{%
+ \expandafter\XINT_infloat_round_B\romannumeral0\XINT_trunc_B
+}%
+\def\XINT_infloat_round_B #1\Z #2%
+{%
+ \expandafter\XINT_infloat_round_D
+ \romannumeral0\XINT_rord_main {}#1%
+ \xint_relax
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_relax
+ \Z
+}%
+\def\XINT_infloat_round_D #1%
+{%
+ \ifnum #1<5
+ \expandafter\XINT_infloat_round_Da
+ \else
+ \expandafter\XINT_infloat_round_Db
+ \fi
+}%
+\def\XINT_infloat_round_Da #1\Z
+{%
+ \expandafter\XINT_infloat_round_f
+ \romannumeral0\XINT_rord_main {}#1%
+ \xint_relax
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_relax \Z
+}%
+\def\XINT_infloat_round_Db #1\Z
+{%
+ \expandafter\XINT_infloat_round_f
+ \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z \Z
+}%
+\def\XINT_infloat_round_f #1\Z #2#3%
+{%
+ \expandafter\XINT_infloat_round_g\expandafter
+ {\the\numexpr #2-#3+1}{#1}%
+}%
+\def\XINT_infloat_round_g #1#2{#2[#1]}%
+% \end{macrocode}
% \subsection{\csh{xintAdd}}
% \begin{macrocode}
\def\xintAdd {\romannumeral0\xintadd }%
@@ -10130,19 +11409,32 @@ first place.
}%
\def\xint_fsqr #1{\XINT_fmul_A #1#1}%
% \end{macrocode}
-% \subsection{\csh{xintPow}}
+% \subsection{\csh{xintPow}, \csh{xintfPow}}
% \lverb|&
-% Modified in 1.06 to give the exponent to a \numexpr|
+% Modified in 1.06 to give the exponent to a \numexpr.$\
+% With 1.07 and the \xintexpr parser, we need something allowing
+% fractions evaluating to integers for the exponent; adding \xintNum
+% does this but makes using count registers again impossible. So I have
+% to duplicate.|
% \begin{macrocode}
\def\xintPow {\romannumeral0\xintpow }%
\def\xintpow #1%
{%
\expandafter\xint_fpow\expandafter {\romannumeral0\XINT_infrac {#1}}%
}%
+\def\xintfPow {\romannumeral0\xintfpow }%
+\def\xintfpow #1%
+{%
+ \expandafter\xint_ffpow\expandafter {\romannumeral0\XINT_infrac {#1}}%
+}%
\def\xint_fpow #1#2%
{%
\expandafter\XINT_fpow_fork\the\numexpr #2\relax\Z #1%
}%
+\def\xint_ffpow #1#2%
+{%
+ \expandafter\XINT_fpow_fork\the\numexpr \xintNum{#2}\relax\Z #1%
+}%
\def\XINT_fpow_fork #1#2\Z
{%
\xint_UDzerominusfork
@@ -10245,6 +11537,42 @@ first place.
{\romannumeral0\xintimul {#7}{\xintDSH {\the\numexpr -#2+#1\relax}{#4}}}%
}%
% \end{macrocode}
+% \subsection{\csh{xintGeq}}
+% \lverb|&
+% This extension to fractions was added only with release 1.07, don't know why I
+% did not do it in the same go as \xintMax, \xintMin, \xintCmp. Beware that
+% like the original it
+% compares only the *absolute values*.|
+% \begin{macrocode}
+\def\xintGeq {\romannumeral0\xintgeq }%
+\def\xintgeq #1%
+{%
+ \expandafter\xint_fgeq\expandafter {\romannumeral0\XINT_infrac {#1}}%
+}%
+\def\xint_fgeq #1#2%
+{%
+ \expandafter\XINT_fgeq_A \romannumeral0\XINT_infrac {#2}#1%
+}%
+\def\XINT_fgeq_A #1#2#3#4%
+{%
+ \ifnum #4 > #1
+ \xint_afterfi {\XINT_fgeq_B {#1}}%
+ \else
+ \xint_afterfi {\XINT_fgeq_B {#4}}%
+ \fi
+ {#1}{#4}{#2}{#3}%
+}%
+\def\XINT_fgeq_B #1#2#3#4#5#6#7%
+{%
+ \expandafter\XINT_fgeq_C\expandafter
+ {\romannumeral0\xintimul {\xintDSH {\the\numexpr -#3+#1\relax}{#6}}{#5}}%
+ {\romannumeral0\xintimul {#7}{\xintDSH {\the\numexpr -#2+#1\relax}{#4}}}%
+}%
+\def\XINT_fgeq_C #1#2%
+{%
+ \expandafter\XINT_geq_fork #2\Z #1\Z
+}%
+% \end{macrocode}
% \subsection{\csh{xintMax}}
% \begin{macrocode}
\def\xintMax {\romannumeral0\xintmax }%
@@ -10345,18 +11673,6 @@ first place.
}%
\def\xint_fsgn #1#2#3{\xintisgn {#2}}%
% \end{macrocode}
-% \subsection{\csh{xintGeq}}
-% \begin{macrocode}
-\def\xintGeq {\romannumeral0\xintgeq }%
-\def\xintgeq #1%
-{%
- \expandafter\xint_xgeq\expandafter{\romannumeral0\xintnum {#1}}%
-}%
-\def\xint_xgeq #1#2%
-{%
- \expandafter\XINT_geq_fork\romannumeral0\xintnum {#2}\Z #1\Z
-}%
-% \end{macrocode}
% \subsection{\csh{xintDivision},~\csh{xintQuo},~\csh{xintRem}}
% \begin{macrocode}
\def\xintDivision {\romannumeral0\xintdivision }%
@@ -10414,6 +11730,383 @@ first place.
\xint_afterfi{ 0}%
\fi
}%
+% \end{macrocode}
+% \subsection{\csh{xintFloatAdd}}
+% \begin{macrocode}
+\def\xintFloatAdd {\romannumeral0\xintfloatadd }%
+\def\xintfloatadd #1{\XINT_fladd_chkopt \xintfloat #1\Z }%
+\def\XINTinFloatAdd {\romannumeral-`0\XINTinfloatadd }%
+\def\XINTinfloatadd #1{\XINT_fladd_chkopt \XINT_inFloat #1\Z }%
+\def\XINT_fladd_chkopt #1#2%
+{%
+ \ifx #2[\expandafter\XINT_fladd_opt
+ \else\expandafter\XINT_fladd_noopt
+ \fi #1#2%
+}%
+\def\XINT_fladd_noopt #1#2\Z #3%
+{%
+ #1[\XINT_digits]{\XINT_FL_Add {\XINT_digits+2}{#2}{#3}}%
+}%
+\def\XINT_fladd_opt #1[\Z #2]#3#4%
+{%
+ #1[#2]{\XINT_FL_Add {#2+2}{#3}{#4}}%
+}%
+\def\XINT_FL_Add #1#2%
+{%
+ \expandafter\XINT_FL_Add_a\expandafter{\the\numexpr #1\expandafter}%
+ \expandafter{\romannumeral-`0\XINT_inFloat [#1]{#2}}%
+}%
+\def\XINT_FL_Add_a #1#2#3%
+{%
+ \expandafter\XINT_FL_Add_b\romannumeral-`0\XINT_inFloat [#1]{#3}#2{#1}%
+}%
+\def\XINT_FL_Add_b #1%
+{%
+ \xint_gob_til_zero #1\XINT_FL_Add_zero 0\XINT_FL_Add_c #1%
+}%
+\def\XINT_FL_Add_c #1[#2]#3%
+{%
+ \xint_gob_til_zero #3\XINT_FL_Add_zerobis 0\XINT_FL_Add_d #1[#2]#3%
+}%
+\def\XINT_FL_Add_d #1[#2]#3[#4]#5%
+{%
+ \xintSgnFork {\ifnum \numexpr #2-#4-#5>1 \expandafter 1%
+ \else\ifnum \numexpr #4-#2-#5>1
+ \xint_afterfi {\expandafter-\expandafter1}%
+ \else \expandafter\expandafter\expandafter0%
+ \fi
+ \fi}%
+ {#3[#4]}{\xintAdd {#1[#2]}{#3[#4]}}{#1[#2]}%
+}%
+\def\XINT_FL_Add_zero 0\XINT_FL_Add_c 0[0]#1[#2]#3{#1[#2]}%
+\def\XINT_FL_Add_zerobis 0\XINT_FL_Add_d #1[#2]0[0]#3{#1[#2]}%
+% \end{macrocode}
+% \subsection{\csh{xintFloatSub}}
+% \begin{macrocode}
+\def\xintFloatSub {\romannumeral0\xintfloatsub }%
+\def\xintfloatsub #1{\XINT_flsub_chkopt \xintfloat #1\Z }%
+\def\XINTinFloatSub {\romannumeral-`0\XINTinfloatsub }%
+\def\XINTinfloatsub #1{\XINT_flsub_chkopt \XINT_inFloat #1\Z }%
+\def\XINT_flsub_chkopt #1#2%
+{%
+ \ifx #2[\expandafter\XINT_flsub_opt
+ \else\expandafter\XINT_flsub_noopt
+ \fi #1#2%
+}%
+\def\XINT_flsub_noopt #1#2\Z #3%
+{%
+ #1[\XINT_digits]{\XINT_FL_Add {\XINT_digits+2}{#2}{\xintOpp{#3}}}%
+}%
+\def\XINT_flsub_opt #1[\Z #2]#3#4%
+{%
+ #1[#2]{\XINT_FL_Add {#2+2}{#3}{\xintOpp{#4}}}%
+}%
+% \end{macrocode}
+% \subsection{\csh{xintFloatMul}}
+% \begin{macrocode}
+\def\xintFloatMul {\romannumeral0\xintfloatmul}%
+\def\xintfloatmul #1{\XINT_flmul_chkopt \xintfloat #1\Z }%
+\def\XINTinFloatMul {\romannumeral-`0\XINTinfloatmul }%
+\def\XINTinfloatmul #1{\XINT_flmul_chkopt \XINT_inFloat #1\Z }%
+\def\XINT_flmul_chkopt #1#2%
+{%
+ \ifx #2[\expandafter\XINT_flmul_opt
+ \else\expandafter\XINT_flmul_noopt
+ \fi #1#2%
+}%
+\def\XINT_flmul_noopt #1#2\Z #3%
+{%
+ #1[\XINT_digits]{\XINT_FL_Mul {\XINT_digits+2}{#2}{#3}}%
+}%
+\def\XINT_flmul_opt #1[\Z #2]#3#4%
+{%
+ #1[#2]{\XINT_FL_Mul {#2+2}{#3}{#4}}%
+}%
+\def\XINT_FL_Mul #1#2%
+{%
+ \expandafter\XINT_FL_Mul_a\expandafter{\the\numexpr #1\expandafter}%
+ \expandafter{\romannumeral-`0\XINT_inFloat [#1]{#2}}%
+}%
+\def\XINT_FL_Mul_a #1#2#3%
+{%
+ \expandafter\XINT_FL_Mul_b\romannumeral-`0\XINT_inFloat [#1]{#3}#2%
+}%
+\def\XINT_FL_Mul_b #1[#2]#3[#4]{\xintE{\xintiMul {#1}{#3}}{#2+#4}}%
+% \end{macrocode}
+% \subsection{\csh{xintFloatDiv}}
+% \begin{macrocode}
+\def\xintFloatDiv {\romannumeral0\xintfloatdiv}%
+\def\xintfloatdiv #1{\XINT_fldiv_chkopt \xintfloat #1\Z }%
+\def\XINTinFloatDiv {\romannumeral-`0\XINTinfloatdiv }%
+\def\XINTinfloatdiv #1{\XINT_fldiv_chkopt \XINT_inFloat #1\Z }%
+\def\XINT_fldiv_chkopt #1#2%
+{%
+ \ifx #2[\expandafter\XINT_fldiv_opt
+ \else\expandafter\XINT_fldiv_noopt
+ \fi #1#2%
+}%
+\def\XINT_fldiv_noopt #1#2\Z #3%
+{%
+ #1[\XINT_digits]{\XINT_FL_Div {\XINT_digits+2}{#2}{#3}}%
+}%
+\def\XINT_fldiv_opt #1[\Z #2]#3#4%
+{%
+ #1[#2]{\XINT_FL_Div {#2+2}{#3}{#4}}%
+}%
+\def\XINT_FL_Div #1#2%
+{%
+ \expandafter\XINT_FL_Div_a\expandafter{\the\numexpr #1\expandafter}%
+ \expandafter{\romannumeral-`0\XINT_inFloat [#1]{#2}}%
+}%
+\def\XINT_FL_Div_a #1#2#3%
+{%
+ \expandafter\XINT_FL_Div_b\romannumeral-`0\XINT_inFloat [#1]{#3}#2%
+}%
+\def\XINT_FL_Div_b #1[#2]#3[#4]{\xintE{#3/#1}{#4-#2}}%
+% \end{macrocode}
+% \subsection{\csh{xintFloatPow}}
+% \begin{macrocode}
+\def\xintFloatPow {\romannumeral0\xintfloatpow}%
+\def\xintfloatpow #1{\XINT_flpow_chkopt \xintfloat #1\Z }%
+\def\XINTinFloatPow {\romannumeral-`0\XINTinfloatpow }%
+\def\XINTinfloatpow #1{\XINT_flpow_chkopt \XINT_inFloat #1\Z }%
+\def\XINT_flpow_chkopt #1#2%
+{%
+ \ifx #2[\expandafter\XINT_flpow_opt
+ \else\expandafter\XINT_flpow_noopt
+ \fi
+ #1#2%
+}%
+\def\XINT_flpow_noopt #1#2\Z #3%
+{%
+ \expandafter\XINT_flpow_checkB_start\expandafter
+ {\the\numexpr #3\expandafter}\expandafter
+ {\the\numexpr \XINT_digits}{#2}{#1[\XINT_digits]}%
+}%
+\def\XINT_flpow_opt #1[\Z #2]#3#4%
+{%
+ \expandafter\XINT_flpow_checkB_start\expandafter
+ {\the\numexpr #4\expandafter}\expandafter
+ {\the\numexpr #2}{#3}{#1[#2]}%
+}%
+\def\XINT_flpow_checkB_start #1{\XINT_flpow_checkB_a #1\Z }%
+\def\XINT_flpow_checkB_a #1%
+{%
+ \xint_UDzerominusfork
+ #1-\dummy \XINT_flpow_BisZero
+ 0#1\dummy {\XINT_flpow_checkB_b 1}%
+ 0-\dummy {\XINT_flpow_checkB_b 0#1}%
+ \krof
+}%
+\def\XINT_flpow_BisZero \Z #1#2#3{#3{1/1[0]}}%
+\def\XINT_flpow_checkB_b #1#2\Z #3%
+{%
+ \expandafter\XINT_flpow_checkB_c \expandafter
+ {\romannumeral0\XINT_length{#2}}{#3}{#2}#1%
+}%
+\def\XINT_flpow_checkB_c #1#2%
+{%
+ \expandafter\XINT_flpow_checkB_d \expandafter
+ {\the\numexpr \expandafter\XINT_Length\expandafter
+ {\the\numexpr #1*20/3}+#1+#2+1}%
+}%
+\def\XINT_flpow_checkB_d #1#2#3#4%
+{%
+ \expandafter \XINT_flpow_a
+ \romannumeral-`0\XINT_inFloat [#1]{#4}{#1}{#2}#3%
+}%
+\def\XINT_flpow_a #1%
+{%
+ \xint_UDzerominusfork
+ #1-\dummy \XINT_flpow_zero
+ 0#1\dummy {\XINT_flpow_b 1}%
+ 0-\dummy {\XINT_flpow_b 0#1}%
+ \krof
+}%
+\def\XINT_flpow_zero [#1]#2#3#4#5%
+{%
+ \if #41 \xint_afterfi {\xintError:DivisionByZero\space 1.e2147483647}%
+ \else \xint_afterfi { 0.e0}\fi
+}%
+\def\XINT_flpow_b #1#2[#3]#4#5%
+{%
+ \XINT_flpow_c {#4}{#5}{#2[#3]}{#1*\ifodd #5 1\else 0\fi}%
+}%
+\def\XINT_flpow_c #1#2#3#4%
+{%
+ \XINT_flpow_loop {#1}{#2}{#3}{{#1}}\XINT_flpow_prd
+ \xint_relax
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_relax {#4}%
+}%
+\def\XINT_flpow_loop #1#2#3%
+{%
+ \ifnum #2 = 1
+ \expandafter\XINT_flpow_loop_end
+ \else
+ \xint_afterfi{\expandafter\XINT_flpow_loop_a
+ \expandafter{\the\numexpr 2*(#2/2)-#2\expandafter }% b mod 2
+ \expandafter{\the\numexpr #2-#2/2\expandafter }% [b/2]
+ \expandafter{\romannumeral-`0\XINTinfloatmul [#1]{#3}{#3}}}%
+ \fi
+ {#1}{{#3}}%
+}%
+\def\XINT_flpow_loop_a #1#2#3#4%
+{%
+ \ifnum #1 = 1
+ \expandafter\XINT_flpow_loop
+ \else
+ \expandafter\XINT_flpow_loop_throwaway
+ \fi
+ {#4}{#2}{#3}%
+}%
+\def\XINT_flpow_loop_throwaway #1#2#3#4%
+{%
+ \XINT_flpow_loop {#1}{#2}{#3}%
+}%
+\def\XINT_flpow_loop_end #1{\romannumeral0\XINT_rord_main {}\relax }%
+\def\XINT_flpow_prd #1#2%
+{%
+ \XINT_flpow_prd_getnext {#2}{#1}%
+}%
+\def\XINT_flpow_prd_getnext #1#2#3%
+{%
+ \XINT_flpow_prd_checkiffinished #3\Z {#1}{#2}%
+}%
+\def\XINT_flpow_prd_checkiffinished #1%
+{%
+ \xint_gob_til_relax #1\XINT_flpow_prd_end\relax
+ \XINT_flpow_prd_compute #1%
+}%
+\def\XINT_flpow_prd_compute #1\Z #2#3%
+{%
+ \expandafter\XINT_flpow_prd_getnext\expandafter
+ {\romannumeral-`0\XINTinfloatmul [#3]{#1}{#2}}{#3}%
+}%
+\def\XINT_flpow_prd_end\relax\XINT_flpow_prd_compute
+ \relax\Z #1#2#3%
+{%
+ \expandafter\XINT_flpow_conclude \the\numexpr #3\relax #1%
+}%
+\def\XINT_flpow_conclude #1#2[#3]#4%
+{%
+ \expandafter\XINT_flpow_conclude_really\expandafter
+ {\the\numexpr\if #41 -\fi#3\expandafter}%
+ \xint_UDzerofork
+ #4\dummy {{#2}}%
+ 0\dummy {{1/#2}}%
+ \krof #1%
+}%
+\def\XINT_flpow_conclude_really #1#2#3#4%
+{%
+ \xint_UDzerofork
+ #3\dummy {#4{#2[#1]}}%
+ 0\dummy {#4{-#2[#1]}}%
+ \krof
+}%
+% \end{macrocode}
+% \subsection{\csh{xintFloatPower}}
+% \begin{macrocode}
+\def\xintFloatPower {\romannumeral0\xintfloatpower}%
+\def\xintfloatpower #1{\XINT_flpower_chkopt \xintfloat #1\Z }%
+\def\XINTinFloatPower {\romannumeral-`0\XINTinfloatpower}%
+\def\XINTinfloatpower #1{\XINT_flpower_chkopt \XINT_inFloat #1\Z }%
+\def\XINT_flpower_chkopt #1#2%
+{%
+ \ifx #2[\expandafter\XINT_flpower_opt
+ \else\expandafter\XINT_flpower_noopt
+ \fi
+ #1#2%
+}%
+\def\XINT_flpower_noopt #1#2\Z #3%
+{%
+ \expandafter\XINT_flpower_checkB_start\expandafter
+ {\the\numexpr \XINT_digits\expandafter}\expandafter
+ {\romannumeral0\xintnum{#3}}{#2}{#1[\XINT_digits]}%
+}%
+\def\XINT_flpower_opt #1[\Z #2]#3#4%
+{%
+ \expandafter\XINT_flpower_checkB_start\expandafter
+ {\the\numexpr #2\expandafter}\expandafter
+ {\romannumeral0\xintnum{#4}}{#3}{#1[#2]}%
+}%
+\def\XINT_flpower_checkB_start #1#2{\XINT_flpower_checkB_a #2\Z {#1}}%
+\def\XINT_flpower_checkB_a #1%
+{%
+ \xint_UDzerominusfork
+ #1-\dummy \XINT_flpower_BisZero
+ 0#1\dummy {\XINT_flpower_checkB_b 1}%
+ 0-\dummy {\XINT_flpower_checkB_b 0#1}%
+ \krof
+}%
+\def\XINT_flpower_BisZero \Z #1#2#3{#3{1/1[0]}}%
+\def\XINT_flpower_checkB_b #1#2\Z #3%
+{%
+ \expandafter\XINT_flpower_checkB_c \expandafter
+ {\romannumeral0\XINT_length{#2}}{#3}{#2}#1%
+}%
+\def\XINT_flpower_checkB_c #1#2%
+{%
+ \expandafter\XINT_flpower_checkB_d \expandafter
+ {\the\numexpr \expandafter\XINT_Length\expandafter
+ {\the\numexpr #1*20/3}+#1+#2+1}%
+}%
+\def\XINT_flpower_checkB_d #1#2#3#4%
+{%
+ \expandafter \XINT_flpower_a
+ \romannumeral-`0\XINT_inFloat [#1]{#4}{#1}{#2}#3%
+}%
+\def\XINT_flpower_a #1%
+{%
+ \xint_UDzerominusfork
+ #1-\dummy \XINT_flpower_zero
+ 0#1\dummy {\XINT_flpower_b 1}%
+ 0-\dummy {\XINT_flpower_b 0#1}%
+ \krof
+}%
+\def\XINT_flpower_zero [#1]#2#3#4#5%
+{%
+ \if #41
+ \xint_afterfi {\xintError:DivisionByZero\space 1.e2147483647}%
+ \else \xint_afterfi { 0.e0}\fi
+}%
+\def\XINT_flpower_b #1#2[#3]#4#5%
+{%
+ \XINT_flpower_c {#4}{#5}{#2[#3]}{#1*\xintOdd {#5}}%
+}%
+\def\XINT_flpower_c #1#2#3#4%
+{%
+ \XINT_flpower_loop {#1}{#2}{#3}{{#1}}\XINT_flpow_prd
+ \xint_relax
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_relax {#4}%
+}%
+\def\XINT_flpower_loop #1#2#3%
+{%
+ \ifcase\XINT_isOne {#2}
+ \xint_afterfi{\expandafter\XINT_flpower_loop_x\expandafter
+ {\romannumeral-`0\XINTinfloatmul [#1]{#3}{#3}}%
+ {\romannumeral0\xintdivision {#2}{2}}}%
+ \or \expandafter\XINT_flpow_loop_end
+ \fi
+ {#1}{{#3}}%
+}%
+\def\XINT_flpower_loop_x #1#2{\expandafter\XINT_flpower_loop_a #2{#1}}%
+\def\XINT_flpower_loop_a #1#2#3#4%
+{%
+ \ifnum #2 = 1
+ \expandafter\XINT_flpower_loop
+ \else
+ \expandafter\XINT_flpower_loop_throwaway
+ \fi
+ {#4}{#1}{#3}%
+}%
+\def\XINT_flpower_loop_throwaway #1#2#3#4%
+{%
+ \XINT_flpower_loop {#1}{#2}{#3}%
+}%
\XINT_frac_restorecatcodes_endinput%
% \end{macrocode}
%\catcode`\<=0 \catcode`\>=11 \catcode`\*=11 \catcode`\/=11
@@ -10588,7 +12281,7 @@ first place.
\fi
\expandafter\x\csname ver@xintseries.sty\endcsname
\ProvidesPackage{xintseries}%
- [2013/05/14 v1.06b Expandable partial sums with xint package (jfB)]%
+ [2013/05/26 v1.07a Expandable partial sums with xint package (jfB)]%
% \end{macrocode}
% \subsection{\csh{xintSeries}}
% \lverb|&
@@ -11090,7 +12783,7 @@ first place.
\fi
\expandafter\x\csname ver@xintcfrac.sty\endcsname
\ProvidesPackage{xintcfrac}%
- [2013/05/14 v1.06b Expandable continued fractions with xint package (jfB)]%
+ [2013/05/26 v1.07a Expandable continued fractions with xint package (jfB)]%
% \end{macrocode}
% \subsection{\csh{xintCFrac}}
% \begin{macrocode}
@@ -11105,7 +12798,7 @@ first place.
}%
\def\XINT_cfrac_noopt #1\Z
{%
- \expandafter\XINT_cfrac_A\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_cfrac_A\romannumeral0\xintrawwithzeros {#1}\Z
\relax\relax
}%
\def\XINT_cfrac_opt_b\fi\XINT_cfrac_noopt [\Z #1]%
@@ -11114,17 +12807,17 @@ first place.
}%
\def\XINT_cfrac_optl #1%
{%
- \expandafter\XINT_cfrac_A\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_cfrac_A\romannumeral0\xintrawwithzeros {#1}\Z
\relax\hfill
}%
\def\XINT_cfrac_optc #1%
{%
- \expandafter\XINT_cfrac_A\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_cfrac_A\romannumeral0\xintrawwithzeros {#1}\Z
\relax\relax
}%
\def\XINT_cfrac_optr #1%
{%
- \expandafter\XINT_cfrac_A\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_cfrac_A\romannumeral0\xintrawwithzeros {#1}\Z
\hfill\relax
}%
\def\XINT_cfrac_A #1/#2\Z
@@ -11172,10 +12865,7 @@ first place.
% \subsection{\csh{xintGCFrac}}
% \begin{macrocode}
\def\xintGCFrac {\romannumeral0\xintgcfrac }%
-\def\xintgcfrac #1%
-{%
- \XINT_gcfrac_opt_a #1\Z
-}%
+\def\xintgcfrac #1{\XINT_gcfrac_opt_a #1\Z }%
\def\XINT_gcfrac_opt_a #1%
{%
\ifx#1[\XINT_gcfrac_opt_b\fi \XINT_gcfrac_noopt #1%
@@ -11253,7 +12943,7 @@ first place.
\def\xintFtoCs {\romannumeral0\xintftocs }%
\def\xintftocs #1%
{%
- \expandafter\XINT_ftc_A\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_ftc_A\romannumeral0\xintrawwithzeros {#1}\Z
}%
\def\XINT_ftc_A #1/#2\Z
{%
@@ -11292,7 +12982,7 @@ first place.
\def\xintFtoCx {\romannumeral0\xintftocx }%
\def\xintftocx #1#2%
{%
- \expandafter\XINT_ftcx_A\romannumeral0\xintraw {#2}\Z {#1}%
+ \expandafter\XINT_ftcx_A\romannumeral0\xintrawwithzeros {#2}\Z {#1}%
}%
\def\XINT_ftcx_A #1/#2\Z
{%
@@ -11336,12 +13026,12 @@ first place.
\def\xintFtoCC {\romannumeral0\xintftocc }%
\def\xintftocc #1%
{%
- \expandafter\XINT_ftcc_A\expandafter {\romannumeral0\xintraw {#1}}%
+ \expandafter\XINT_ftcc_A\expandafter {\romannumeral0\xintrawwithzeros {#1}}%
}%
\def\XINT_ftcc_A #1%
{%
\expandafter\XINT_ftcc_B
- \romannumeral0\xintraw {\xintAdd {1/2[0]}{#1[0]}}\Z {#1[0]}%
+ \romannumeral0\xintrawwithzeros {\xintAdd {1/2[0]}{#1[0]}}\Z {#1[0]}%
}%
\def\XINT_ftcc_B #1/#2\Z
{%
@@ -11373,7 +13063,7 @@ first place.
\def\XINT_ftcc_loop_a #1%
{%
\expandafter\XINT_ftcc_loop_b
- \romannumeral0\xintraw {\xintAdd {1/2[0]}{#1}}\Z {#1}%
+ \romannumeral0\xintrawwithzeros {\xintAdd {1/2[0]}{#1}}\Z {#1}%
}%
\def\XINT_ftcc_loop_b #1/#2\Z
{%
@@ -11436,7 +13126,7 @@ first place.
{%
\xint_gob_til_w #5\XINT_cstf_end\W
\expandafter\XINT_cstf_loop_b
- \romannumeral0\xintraw {#5}.{#1}{#2}{#3}{#4}%
+ \romannumeral0\xintrawwithzeros {#5}.{#1}{#2}{#3}{#4}%
}%
\def\XINT_cstf_loop_b #1/#2.#3#4#5#6%
{%
@@ -11458,7 +13148,7 @@ first place.
{%
\expandafter\XINT_cstf_loop_a\expandafter{#2}#1%
}%
-\def\XINT_cstf_end #1.#2#3#4#5{\xintraw {#2/#3}[0]}%
+\def\XINT_cstf_end #1.#2#3#4#5{\xintrawwithzeros {#2/#3}[0]}%
% \end{macrocode}
% \subsection{\csh{xintiCstoF}}
% \begin{macrocode}
@@ -11488,7 +13178,7 @@ first place.
{%
\expandafter\XINT_icstf_loop_a\expandafter {#2}{#1}%
}%
-\def\XINT_icstf_end#1.#2#3#4#5{\xintraw {#2/#3}[0]}%
+\def\XINT_icstf_end#1.#2#3#4#5{\xintrawwithzeros {#2/#3}[0]}%
% \end{macrocode}
% \subsection{\csh{xintGCtoF}}
% \begin{macrocode}
@@ -11504,7 +13194,7 @@ first place.
\def\XINT_gctf_loop_a #1#2#3#4#5+%
{%
\expandafter\XINT_gctf_loop_b
- \romannumeral0\xintraw {#5}.{#1}{#2}{#3}{#4}%
+ \romannumeral0\xintrawwithzeros {#5}.{#1}{#2}{#3}{#4}%
}%
\def\XINT_gctf_loop_b #1/#2.#3#4#5#6%
{%
@@ -11530,7 +13220,7 @@ first place.
{%
\xint_gob_til_w #2\XINT_gctf_end\W
\expandafter\XINT_gctf_loop_g
- \romannumeral0\xintraw {#2}.#1%
+ \romannumeral0\xintrawwithzeros {#2}.#1%
}%
\def\XINT_gctf_loop_g #1/#2.#3#4#5#6%
{%
@@ -11552,7 +13242,7 @@ first place.
{%
\expandafter\XINT_gctf_loop_a\expandafter {#2}#1%
}%
-\def\XINT_gctf_end #1.#2#3#4#5{\xintraw {#2/#3}[0]}%
+\def\XINT_gctf_end #1.#2#3#4#5{\xintrawwithzeros {#2/#3}[0]}%
% \end{macrocode}
% \subsection{\csh{xintiGCtoF}}
% \begin{macrocode}
@@ -11601,7 +13291,7 @@ first place.
{%
\XINT_igctf_loop_a {#3}{#4}{#1}{#2}%
}%
-\def\XINT_igctf_end #1.#2#3#4#5{\xintraw {#4/#5}[0]}%
+\def\XINT_igctf_end #1.#2#3#4#5{\xintrawwithzeros {#4/#5}[0]}%
% \end{macrocode}
% \subsection{\csh{xintCstoCv}}
% \begin{macrocode}
@@ -11618,7 +13308,7 @@ first place.
{%
\xint_gob_til_w #6\XINT_cstcv_end\W
\expandafter\XINT_cstcv_loop_b
- \romannumeral0\xintraw {#6}.{#2}{#3}{#4}{#5}{#1}%
+ \romannumeral0\xintrawwithzeros {#6}.{#2}{#3}{#4}{#5}{#1}%
}%
\def\XINT_cstcv_loop_b #1/#2.#3#4#5#6%
{%
@@ -11643,7 +13333,7 @@ first place.
\def\XINT_cstcv_loop_f #1#2#3#4#5%
{%
\expandafter\XINT_cstcv_loop_g\expandafter
- {\romannumeral0\xintraw {#1/#2}}{#5}{#1}{#2}{#3}{#4}%
+ {\romannumeral0\xintrawwithzeros {#1/#2}}{#5}{#1}{#2}{#3}{#4}%
}%
\def\XINT_cstcv_loop_g #1#2{\XINT_cstcv_loop_a {#2{#1[0]}}}%
\def\XINT_cstcv_end #1.#2#3#4#5#6{ #6}%
@@ -11679,7 +13369,7 @@ first place.
\def\XINT_icstcv_loop_d #1#2%
{%
\expandafter\XINT_icstcv_loop_e\expandafter
- {\romannumeral0\xintraw {#1/#2}}{{#1}{#2}}%
+ {\romannumeral0\xintrawwithzeros {#1/#2}}{{#1}{#2}}%
}%
\def\XINT_icstcv_loop_e #1#2#3#4{\XINT_icstcv_loop_a {#4{#1[0]}}#2#3}%
\def\XINT_icstcv_end #1.#2#3#4#5#6{ #6}%
@@ -11698,7 +13388,7 @@ first place.
\def\XINT_gctcv_loop_a #1#2#3#4#5#6+%
{%
\expandafter\XINT_gctcv_loop_b
- \romannumeral0\xintraw {#6}.{#2}{#3}{#4}{#5}{#1}%
+ \romannumeral0\xintrawwithzeros {#6}.{#2}{#3}{#4}{#5}{#1}%
}%
\def\XINT_gctcv_loop_b #1/#2.#3#4#5#6%
{%
@@ -11723,7 +13413,7 @@ first place.
\def\XINT_gctcv_loop_f #1#2%
{%
\expandafter\XINT_gctcv_loop_g\expandafter
- {\romannumeral0\xintraw {#1/#2}}{{#1}{#2}}%
+ {\romannumeral0\xintrawwithzeros {#1/#2}}{{#1}{#2}}%
}%
\def\XINT_gctcv_loop_g #1#2#3#4%
{%
@@ -11733,7 +13423,7 @@ first place.
{%
\xint_gob_til_w #3\XINT_gctcv_end\W
\expandafter\XINT_gctcv_loop_i
- \romannumeral0\xintraw {#3}.#2{#1}%
+ \romannumeral0\xintrawwithzeros {#3}.#2{#1}%
}%
\def\XINT_gctcv_loop_i #1/#2.#3#4#5#6%
{%
@@ -11806,13 +13496,13 @@ first place.
\def\XINT_igctcv_loop_k #1#2%
{%
\expandafter\XINT_igctcv_loop_l\expandafter
- {\romannumeral0\xintraw {#1/#2}}%
+ {\romannumeral0\xintrawwithzeros {#1/#2}}%
}%
\def\XINT_igctcv_loop_l #1#2#3{\XINT_igctcv_loop_a {#3{#1[0]}}#2}%
\def\XINT_igctcv_end_a #1.#2#3#4#5%
{%
\expandafter\XINT_igctcv_end_b\expandafter
- {\romannumeral0\xintraw {#2/#3}}%
+ {\romannumeral0\xintrawwithzeros {#2/#3}}%
}%
\def\XINT_igctcv_end_b #1#2{ #2{#1[0]}}%
% \end{macrocode}
@@ -12049,9 +13739,813 @@ first place.
\def\XINT_gctgc__end #1#2#3{ #3{#1}}%
\XINT_cfrac_restorecatcodes_endinput%
% \end{macrocode}
+%\catcode`\<=0 \catcode`\>=11 \catcode`\*=11 \catcode`\/=11
+%\let</xintcfrac>\relax
+%\def<*xintexpr>{\catcode`\<=12 \catcode`\>=12 \catcode`\*=12 \catcode`\/=12 }
+%</xintcfrac>
+%<*xintexpr>
+% \section{Package \xintexprname implementation}
+%
+% The commenting is currently (\docdate) very sparse. I was greatly helped in
+% the task of writing this expandable parser by the comments provided in
+% |l3fp-parse.dtx|. Clearly some ressemblance with the |l3fp| code will be
+% noticed, but there are some essential differences too.
+%
+% \localtableofcontents
+% \subsection{Catcodes, \protect\eTeX{} and reload detection}
+%
+% The code for reload detection is copied from \textsc{Heiko
+% Oberdiek}'s packages, and adapted here to check for previous
+% loading of the \xintfracname package.
+%
+% The method for catcodes is slightly different, but still
+% directly inspired by these packages.
+%
+% \begin{macrocode}
+\begingroup\catcode61\catcode48\catcode32=10\relax%
+ \catcode13=5 % ^^M
+ \endlinechar=13 %
+ \catcode123=1 % {
+ \catcode125=2 % }
+ \catcode64=11 % @
+ \catcode35=6 % #
+ \catcode44=12 % ,
+ \catcode45=12 % -
+ \catcode46=12 % .
+ \catcode58=12 % :
+ \def\space { }%
+ \let\z\endgroup
+ \expandafter\let\expandafter\x\csname ver@xintexpr.sty\endcsname
+ \expandafter\let\expandafter\w\csname ver@xintfrac.sty\endcsname
+ \expandafter
+ \ifx\csname PackageInfo\endcsname\relax
+ \def\y#1#2{\immediate\write-1{Package #1 Info: #2.}}%
+ \else
+ \def\y#1#2{\PackageInfo{#1}{#2}}%
+ \fi
+ \expandafter
+ \ifx\csname numexpr\endcsname\relax
+ \y{xintexpr}{\numexpr not available, aborting input}%
+ \aftergroup\endinput
+ \else
+ \ifx\x\relax % plain-TeX, first loading of xintexpr.sty
+ \ifx\w\relax % but xintfrac.sty not yet loaded.
+ \y{xintexpr}{Package xintfrac is required}%
+ \y{xintexpr}{Will try \string\input\space xintfrac.sty}%
+ \def\z{\endgroup\input xintfrac.sty\relax}%
+ \fi
+ \else
+ \def\empty {}%
+ \ifx\x\empty % LaTeX, first loading,
+ % variable is initialized, but \ProvidesPackage not yet seen
+ \ifx\w\relax % xintfrac.sty not yet loaded.
+ \y{xintexpr}{Package xintfrac is required}%
+ \y{xintexpr}{Will try \string\RequirePackage{xintfrac}}%
+ \def\z{\endgroup\RequirePackage{xintfrac}}%
+ \fi
+ \else
+ \y{xintexpr}{I was already loaded, aborting input}%
+ \aftergroup\endinput
+ \fi
+ \fi
+ \fi
+\z%
+% \end{macrocode}
+% \subsection{Confirmation of \xintfracname loading}
+% \begin{macrocode}
+\begingroup\catcode61\catcode48\catcode32=10\relax%
+ \catcode13=5 % ^^M
+ \endlinechar=13 %
+ \catcode123=1 % {
+ \catcode125=2 % }
+ \catcode64=11 % @
+ \catcode35=6 % #
+ \catcode44=12 % ,
+ \catcode45=12 % -
+ \catcode46=12 % .
+ \catcode58=12 % :
+ \expandafter
+ \ifx\csname PackageInfo\endcsname\relax
+ \def\y#1#2{\immediate\write-1{Package #1 Info: #2.}}%
+ \else
+ \def\y#1#2{\PackageInfo{#1}{#2}}%
+ \fi
+ \def\empty {}%
+ \expandafter\let\expandafter\w\csname ver@xintfrac.sty\endcsname
+ \ifx\w\relax % Plain TeX, user gave a file name at the prompt
+ \y{xintexpr}{Loading of package xintfrac failed, aborting input}%
+ \aftergroup\endinput
+ \fi
+ \ifx\w\empty % LaTeX, user gave a file name at the prompt
+ \y{xintexpr}{Loading of package xintfrac failed, aborting input}%
+ \aftergroup\endinput
+ \fi
+\endgroup%
+% \end{macrocode}
+% \subsection{Catcodes}
+%
+% Perhaps catcodes have changed after the loading of \xintname and
+% \xintfracname and prior to the current loading of \xintexprname,
+% so we can not employ the |\XINT_restorecatcodes_endinput| in this style
+% file. But there is no problem using |\XINT_setcatcodes|.
+%
+% \begin{macrocode}
+\begingroup\catcode61\catcode48\catcode32=10\relax%
+ \catcode13=5 % ^^M
+ \endlinechar=13 %
+ \catcode123=1 % {
+ \catcode125=2 % }
+ \catcode95=11 % _
+ \def\x
+ {%
+ \endgroup
+ \edef\XINT_expr_restorecatcodes_endinput
+ {%
+ \catcode94=\the\catcode94 % ^
+ \catcode33=\the\catcode33 % !
+ \catcode93=\the\catcode93 % ]
+ \catcode91=\the\catcode91 % [
+ \catcode96=\the\catcode96 % `
+ \catcode47=\the\catcode47 % /
+ \catcode41=\the\catcode41 % )
+ \catcode40=\the\catcode40 % (
+ \catcode42=\the\catcode42 % *
+ \catcode43=\the\catcode43 % +
+ \catcode62=\the\catcode62 % >
+ \catcode60=\the\catcode60 % <
+ \catcode58=\the\catcode58 % :
+ \catcode46=\the\catcode46 % .
+ \catcode45=\the\catcode45 % -
+ \catcode44=\the\catcode44 % ,
+ \catcode35=\the\catcode35 % #
+ \catcode95=\the\catcode95 % _
+ \catcode125=\the\catcode125 % }
+ \catcode123=\the\catcode123 % {
+ \endlinechar=\the\endlinechar
+ \catcode13=\the\catcode13 % ^^M
+ \catcode32=\the\catcode32 %
+ \catcode61=\the\catcode61\relax % =
+ \noexpand\endinput
+ }%
+ \XINT_setcatcodes
+ \catcode91=12 % [
+ \catcode93=12 % ]
+ \catcode33=11 % !
+ \catcode94=12 % ^
+ }%
+\x
+% \end{macrocode}
+% \subsection{Package identification}
+% \begin{macrocode}
+\begingroup
+ \catcode64=11 % @
+ \catcode58=12 % :
+ \expandafter\ifx\csname ProvidesPackage\endcsname\relax
+ \def\x#1#2#3[#4]{\endgroup
+ \immediate\write-1{Package: #3 #4}%
+ \xdef#1{#4}%
+ }%
+ \else
+ \def\x#1#2[#3]{\endgroup
+ #2[{#3}]%
+ \ifx#1\@undefined
+ \xdef#1{#3}%
+ \fi
+ \ifx#1\relax
+ \xdef#1{#3}%
+ \fi
+ }%
+ \fi
+\expandafter\x\csname ver@xintexpr.sty\endcsname
+\ProvidesPackage{xintexpr}%
+ [2013/05/26 v1.07a Expandable expression parser (jfB)]%
+% \end{macrocode}
+% \subsection{Constants, helper macros...}
+% \begin{macrocode}
+\chardef\xint_c_ 0
+\chardef\xint_c_i 1
+\chardef\xint_c_ii 2
+\chardef\xint_c_iii 3
+\chardef\xint_c_iv 4
+\chardef\xint_c_v 5
+\chardef\xint_c_ix 9
+\def\xint_gob_til_dot #1.{}%
+\def\xint_gob_til_dot_andstop #1.{ }%
+\def\xint_gob_til_! #1!{}% ! of catcode 11
+\def\XINT_expr_string {\expandafter\xint_gob_til_dot\string }%
+\def\XINT_expr_unexpectedtoken {\xintError:ignored }%
+% \end{macrocode}
+% \subsection{\csh{xintexpr},~\csh{xinttheexpr},~\csh{xintthe}}
+% \begin{macrocode}
+\def\xintexpr {\romannumeral0\xinteval }%
+\def\xinteval
+{%
+ \expandafter\XINT_expr_until_end\romannumeral-`0%
+ \expandafter\XINT_expr_checkifprefix_ii\romannumeral-`0%
+ \XINT_expr_getnext
+}%
+\def\xinttheexpr {\romannumeral0\xinttheeval }%
+\def\xinttheeval {\expandafter\XINT_expr_the\romannumeral0\xinteval }%
+\def\XINT_expr_the #1#2#3{\xintraw{\XINT_expr_string #3}}%
+\def\xintthe #1{\ifx#1\xintexpr \expandafter\xinttheexpr
+ \else\expandafter\xintthefloatexpr\fi}%
+% \end{macrocode}
+% \subsection{Parenthesized expressions}
+% \begin{macrocode}
+\def\XINT_expr_until_end #1%
+{%
+ \ifcase#1%
+ \expandafter\xint_gobble_vi
+ \or
+ \expandafter\XINT_expr_extra_closing_paren
+ \fi
+ \expandafter\XINT_expr_until_end\romannumeral-`0%
+}%
+\def\XINT_expr_extra_closing_paren {\xintError:removed }%
+\def\XINT_expr_endofexpr {!\XINT_illegaluse }%
+\def\XINT_illegaluse
+ {Illegal_here_use_xintthe\xintError:use_xintthe!\xint_gobble_i }%
+\def\XINT_expr_oparen
+{%
+ \expandafter\XINT_expr_until_cparen\romannumeral-`0%
+ \expandafter\XINT_expr_checkifprefix_ii\romannumeral-`0%
+ \XINT_expr_getnext
+}%
+\def\XINT_expr_until_cparen #1%
+{%
+ \ifcase#1%
+ \expandafter\XINT_expr_missing_cparen
+ \or
+ \else \xint_afterfi{\expandafter\XINT_expr_until_cparen\romannumeral-`0}%
+ \fi
+}%
+\def\XINT_expr_missing_cparen #1%
+{%
+ \xintError:inserted \xint_c_ \XINT_expr_endofexpr
+}%
+% \end{macrocode}
+% \subsection{Infix operators, minus as prefix, scientific notation}
+% \begin{macrocode}
+\def\xint_tmp_def #1#2#3%
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_expr_op_#1\expandafter\endcsname
+ \csname XINT_expr_until_#1\expandafter\endcsname
+ \csname XINT_expr_checkifprefix_#2\expandafter\endcsname
+ \csname XINT_expr_precedence_#1\expandafter\endcsname
+ \csname xint_c_#2\expandafter\endcsname
+ \csname xint#3\endcsname
+}%
+\def\xint_tmp_do_defs #1#2#3#4#5#6%
+{%
+ \def #1##1% \XINT_expr_op_?
+ {%
+ \expandafter #2\expandafter ##1\romannumeral-`0\expandafter
+ #3\romannumeral-`0\XINT_expr_getnext
+ }%
+ \def #2##1##2##3##4% \XINT_expr_until_?
+ {%
+ \ifnum ##2>#5%
+ \xint_afterfi {\expandafter #2\expandafter ##1\romannumeral-`0##3##4}%
+ \else
+ \xint_afterfi
+ {\expandafter ##2\expandafter ##3%
+ \csname .#6{\XINT_expr_string ##1}{\XINT_expr_string ##4}\endcsname }%
+ \fi
+ }%
+ \global\let #4#5%
+}%
+\xint_tmp_def +{ii}{Add}%
+\xint_tmp_def -{ii}{Sub}%
+\xint_tmp_def *{iii}{Mul}%
+\xint_tmp_def /{iii}{Div}%
+\xint_tmp_def ^{iv}{fPow}%
+\xint_tmp_def e{v}{fE}%
+\xint_tmp_def E{v}{fE}%
+\def\xint_tmp_def #1%
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_expr_checkifprefix_#1\expandafter\endcsname
+ \csname XINT_expr_op_-#1\endcsname
+}%
+\def\xint_tmp_do_defs #1#2%
+{%
+ \def #1##1%
+ {\xint_UDsignfork
+ ##1\dummy #2%
+ -\dummy ##1%
+ \krof }%
+}%
+\xint_tmp_def {ii}%
+\xint_tmp_def {iii}%
+\xint_tmp_def {iv}%
+\xint_tmp_def {v}%
+\def\xint_tmp_def #1%
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_expr_op_-#1\expandafter\endcsname
+ \csname XINT_expr_until_-#1\expandafter\endcsname
+ \csname XINT_expr_checkifprefix_#1\expandafter\endcsname
+ \csname xint_c_#1\endcsname
+}%
+\def\xint_tmp_do_defs #1#2#3#4%
+{%
+ \def #1% \XINT_expr_op_-ii,iii,iv,v
+ {%
+ \expandafter #2\romannumeral-`0\expandafter
+ #3\romannumeral-`0\XINT_expr_getnext
+ }%
+ \def #2##1##2##3% \XINT_expr_until_-ii,iii,iv,v
+ {%
+ \ifnum ##1>#4%
+ \xint_afterfi {\expandafter #2\romannumeral-`0##2##3}%
+ \else
+ \xint_afterfi {\expandafter ##1\expandafter ##2%
+ \csname .\xintOpp{\XINT_expr_string ##3}\endcsname }%
+ \fi
+ }%
+}%
+\xint_tmp_def {ii}%
+\xint_tmp_def {iii}%
+\xint_tmp_def {iv}%
+\xint_tmp_def {v}%
+% \end{macrocode}
+% \subsection{Get next infix operator or closing parenthesis or factorial or expression end}
+% \begin{macrocode}
+\def\XINT_expr_getop #1%
+{%
+ \expandafter\XINT_expr_getop_a\expandafter #1\romannumeral-`0%
+}%
+\def\XINT_expr_getop_a #1#2%
+{%
+ \ifcat #2\relax
+ \ifx #2\relax
+ \expandafter\expandafter\expandafter
+ \XINT_expr_foundendofexpr
+ \else
+ \XINT_expr_unexpectedtoken
+ \expandafter\expandafter\expandafter
+ \XINT_expr_getop
+ \fi
+ \else
+ \expandafter\XINT_expr_op_found\expandafter #2%
+ \fi
+ #1%
+}%
+\def\XINT_expr_foundendofexpr {\xint_c_ \XINT_expr_endofexpr }%
+\def\XINT_expr_op_found #1%
+{%
+ \ifcsname XINT_expr_precedence_\string #1\endcsname
+ \expandafter\xint_afterfi\expandafter
+ {\csname XINT_expr_precedence_\string #1\expandafter\endcsname
+ \csname XINT_expr_op_\string #1\endcsname }%
+ \else
+ \XINT_expr_unexpectedtoken
+ \expandafter\XINT_expr_getop
+ \fi
+}%
+\expandafter\let\csname XINT_expr_precedence_)\endcsname \xint_c_i
+\expandafter\let\csname XINT_expr_op_)\endcsname\XINT_expr_getop
+\def\xint_tmp_def
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_expr_precedence_!\expandafter\endcsname
+ \csname XINT_expr_op_!\endcsname
+}%
+\def\xint_tmp_do_defs #1#2%
+{%
+ \def #1##1##2%
+ {\ifx ##1#2%
+ \expandafter\xint_firstoftwo
+ \else\expandafter\xint_secondoftwo
+ \fi{\expandafter\XINT_expr_getop}{\expandafter\XINT_flexpr_getop}%
+ \csname .\xintfFac{\XINT_expr_string ##2}/1[0]\endcsname }%
+ \let#2\empty
+}%
+\xint_tmp_def
+% \end{macrocode}
+% \subsection{Get next opening parenthesis or minus prefix or decimal number or
+% braced fraction or sub-xintexpression}
+% \begin{macrocode}
+\def\XINT_expr_getnext
+{%
+ \expandafter\XINT_expr_getnext_checkforbraced_a\romannumeral-`0%
+}%
+\def\XINT_expr_getnext_checkforbraced_a #1%
+{%
+ \XINT_expr_getnext_checkforbraced_b #1\W\Z {#1}%
+}%
+\def\XINT_expr_getnext_checkforbraced_b #1#2%
+{%
+ \xint_UDwfork
+ #1\dummy \XINT_expr_getnext_emptybracepair
+ #2\dummy \XINT_expr_getnext_onetoken_perhaps
+ \W\dummy \XINT_expr_getnext_gotbracedstuff
+ \krof
+}%
+\def\XINT_expr_getnext_onetoken_perhaps\Z #1%
+{%
+ \expandafter\XINT_expr_getnext_checkforbraced_c\expandafter
+ {\romannumeral-`0#1}%
+}%
+\def\XINT_expr_getnext_checkforbraced_c #1%
+{%
+ \XINT_expr_getnext_checkforbraced_d #1\W\Z {#1}%
+}%
+\def\XINT_expr_getnext_checkforbraced_d #1#2%
+{%
+ \xint_UDwfork
+ #1\dummy \XINT_expr_getnext_emptybracepair
+ #2\dummy \XINT_expr_getnext_onetoken_wehope
+ \W\dummy \XINT_expr_getnext_gotbracedstuff
+ \krof
+}%
+\def\XINT_expr_getnext_emptybracepair #1{\XINT_expr_getnext }%
+\def\XINT_expr_getnext_gotbracedstuff #1\W\Z #2%
+{%
+ \expandafter\XINT_expr_getop\csname .#2\endcsname
+}%
+\def\XINT_expr_getnext_onetoken_wehope\Z #1%
+{%
+ \xint_gob_til_! #1\XINT_expr_subexpr !%
+ \expandafter\XINT_expr_getnext_onetoken_fork\string #1%
+}%
+\def\XINT_expr_subexpr !#1!{\expandafter\XINT_expr_getop\xint_gobble_i }%
+\begingroup
+\lccode`*=`_
+\lowercase{\endgroup
+\def\XINT_expr_sixwayfork #1(-.+*\dummy #2#3\krof {#2}%
+\def\XINT_expr_getnext_onetoken_fork #1%
+{%
+ \XINT_expr_sixwayfork
+ #1-.+*\dummy \XINT_expr_oparen
+ (#1.+*\dummy -%
+ (-#1+*\dummy {\XINT_expr_scannum_start\XINT_expr_scannum_decpart_b.}%
+ (-.#1*\dummy \XINT_expr_getnext%
+ (-.+#1\dummy {\XINT_expr_scannum_start\XINT_expr_scannum_decpart_b*}%
+ (-.+*\dummy {\XINT_expr_scannum_check #1}%
+ \krof
+}}%
+\def\XINT_expr_scannum_check #1%
+{%
+ \ifnum \xint_c_ix<1#1
+ \expandafter\XINT_expr_scannum_start
+ \else
+ \xint_afterfi{\XINT_expr_unexpectedtoken
+ \expandafter\XINT_expr_getnext\xint_gobble_ii}%
+ \fi \XINT_expr_scannum_intpart_b #1%
+}%
+\def\XINT_expr_scannum_stopscan {!}% ! catcode 11
+\def\XINT_expr_gathernum #1!% ! with catcode 11
+{%
+ \expandafter\space\csname .#1\endcsname
+}%
+\def\XINT_expr_scannum_start #1%
+{%
+ \expandafter\XINT_expr_getop
+ \romannumeral-`0\expandafter\XINT_expr_gathernum
+ \romannumeral-`0#1%
+}%
+\def\XINT_expr_scannum_intpart_a #1%
+{%
+ \ifnum \xint_c_ix<1\string#1
+ \expandafter\expandafter\expandafter
+ \XINT_expr_scannum_intpart_b
+ \expandafter\string
+ \else
+ \if #1.%
+ \expandafter\expandafter\expandafter
+ \XINT_expr_scannum_transition
+ \else
+ \expandafter\expandafter\expandafter
+ \XINT_expr_scannum_stopscan
+ \fi
+ \fi
+ #1%
+}%
+\def\XINT_expr_scannum_intpart_b #1%
+{%
+ \expandafter #1\romannumeral-`0\expandafter
+ \XINT_expr_scannum_intpart_a\romannumeral-`0%
+}%
+\def\XINT_expr_scannum_transition #1%
+{%
+ \expandafter.\romannumeral-`0\expandafter
+ \XINT_expr_scannum_decpart_a\romannumeral-`0%
+}%
+\def\XINT_expr_scannum_decpart_a #1%
+{%
+ \ifnum \xint_c_ix<1\string#1
+ \expandafter\expandafter\expandafter
+ \XINT_expr_scannum_decpart_b\expandafter\string
+ \else
+ \expandafter \XINT_expr_scannum_stopscan
+ \fi
+ #1%
+}%
+\def\XINT_expr_scannum_decpart_b #1%
+{%
+ \expandafter #1\romannumeral-`0\expandafter
+ \XINT_expr_scannum_decpart_a\romannumeral-`0%
+}%
+% \end{macrocode}
+% \subsection{\csh{xintfloatexpr},~\csh{xintthefloatexpr}}
+% \begin{macrocode}
+\def\xintfloatexpr {\romannumeral0\xintfloateval }%
+\def\xintfloateval
+{%
+ \expandafter\XINT_expr_until_end\romannumeral-`0%
+ \expandafter\XINT_flexpr_checkifprefix_ii\romannumeral-`0%
+ \XINT_flexpr_getnext
+}%
+\def\xintthefloatexpr {\romannumeral0\xintthefloateval }%
+\def\xintthefloateval
+ {\expandafter\XINT_flexpr_the\romannumeral0\xintfloateval }%
+\def\XINT_flexpr_the #1#2#3{\xintfloat{\XINT_expr_string #3}}%
+\def\XINT_flexpr_oparen
+{%
+ \expandafter\XINT_expr_until_cparen\romannumeral-`0%
+ \expandafter\XINT_flexpr_checkifprefix_ii\romannumeral-`0%
+ \XINT_flexpr_getnext
+}%
+\def\xint_tmp_def #1#2#3%
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_flexpr_op_#1\expandafter\endcsname
+ \csname XINT_flexpr_until_#1\expandafter\endcsname
+ \csname XINT_flexpr_checkifprefix_#2\expandafter\endcsname
+ \csname XINT_expr_precedence_#1\expandafter\endcsname
+ \csname xint_c_#2\expandafter\endcsname
+ \csname XINTinFloat#3\endcsname
+}%
+\def\xint_tmp_do_defs #1#2#3#4#5#6%
+{%
+ \def #1##1% \XINT_flexpr_op_?
+ {%
+ \expandafter #2\expandafter ##1\romannumeral-`0\expandafter
+ #3\romannumeral-`0\XINT_flexpr_getnext
+ }%
+ \def #2##1##2##3##4% \XINT_flexpr_until_?
+ {%
+ \ifnum ##2>#5%
+ \xint_afterfi {\expandafter #2\expandafter ##1\romannumeral-`0##3##4}%
+ \else
+ \xint_afterfi
+ {\expandafter ##2\expandafter ##3%
+ \csname .#6{\XINT_expr_string ##1}%
+ {\XINT_expr_string ##4}\endcsname }%
+ \fi
+ }%
+}%
+\xint_tmp_def +{ii}{Add}%
+\xint_tmp_def -{ii}{Sub}%
+\xint_tmp_def *{iii}{Mul}%
+\xint_tmp_def /{iii}{Div}%
+\xint_tmp_def ^{iv}{Power}%
+\xint_tmp_def e{v}{fE}%
+\xint_tmp_def E{v}{fE}%
+\def\xint_tmp_def #1%
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_flexpr_checkifprefix_#1\expandafter\endcsname
+ \csname XINT_flexpr_op_-#1\endcsname
+}%
+\def\xint_tmp_do_defs #1#2%
+{%
+ \def #1##1%
+ {\xint_UDsignfork
+ ##1\dummy #2%
+ -\dummy ##1%
+ \krof }%
+}%
+\xint_tmp_def {ii}%
+\xint_tmp_def {iii}%
+\xint_tmp_def {iv}%
+\xint_tmp_def {v}%
+\def\xint_tmp_def #1%
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_flexpr_op_-#1\expandafter\endcsname
+ \csname XINT_expr_until_-#1\expandafter\endcsname
+ \csname XINT_flexpr_checkifprefix_#1\expandafter\endcsname
+ \csname xint_c_#1\endcsname
+}%
+\def\xint_tmp_do_defs #1#2#3#4%
+{%
+ \def #1% \XINT_flexpr_op_-ii,iii,iv,v
+ {%
+ \expandafter #2\romannumeral-`0\expandafter
+ #3\romannumeral-`0\XINT_flexpr_getnext
+ }%
+}%
+\xint_tmp_def {ii}%
+\xint_tmp_def {iii}%
+\xint_tmp_def {iv}%
+\xint_tmp_def {v}%
+\let\xint_tmp_def\empty
+\let\xint_tmp_do_defs\empty
+\def\XINT_flexpr_getop #1%
+{%
+ \expandafter\XINT_flexpr_getop_a\expandafter #1\romannumeral-`0%
+}%
+\def\XINT_flexpr_getop_a #1#2%
+{%
+ \ifcat #2\relax
+ \ifx #2\relax
+ \expandafter\expandafter\expandafter
+ \XINT_expr_foundendofexpr
+ \else
+ \XINT_expr_unexpectedtoken
+ \expandafter\expandafter\expandafter
+ \XINT_flexpr_getop
+ \fi
+ \else
+ \expandafter\XINT_flexpr_op_found\expandafter #2%
+ \fi
+ #1%
+}%
+\def\XINT_flexpr_op_found #1%
+{%
+ \ifcsname XINT_expr_precedence_\string #1\endcsname
+ \expandafter\xint_afterfi\expandafter
+ {\csname XINT_expr_precedence_\string #1\expandafter\endcsname
+ \csname XINT_flexpr_op_\string #1\endcsname }%
+ \else
+ \XINT_expr_unexpectedtoken
+ \expandafter\XINT_flexpr_getop
+ \fi
+}%
+\expandafter\let\csname XINT_flexpr_op_)\endcsname\XINT_flexpr_getop
+\def\XINT_flexpr_getnext
+{%
+ \expandafter\XINT_flexpr_getnext_checkforbraced_a\romannumeral-`0%
+}%
+\def\XINT_flexpr_getnext_checkforbraced_a #1%
+{%
+ \XINT_flexpr_getnext_checkforbraced_b #1\W\Z {#1}%
+}%
+\def\XINT_flexpr_getnext_checkforbraced_b #1#2%
+{%
+ \xint_UDwfork
+ #1\dummy \XINT_flexpr_getnext_emptybracepair
+ #2\dummy \XINT_flexpr_getnext_onetoken_perhaps
+ \W\dummy \XINT_flexpr_getnext_gotbracedstuff
+ \krof
+}%
+\def\XINT_flexpr_getnext_onetoken_perhaps\Z #1%
+{%
+ \expandafter\XINT_flexpr_getnext_checkforbraced_c\expandafter
+ {\romannumeral-`0#1}%
+}%
+\def\XINT_flexpr_getnext_checkforbraced_c #1%
+{%
+ \XINT_flexpr_getnext_checkforbraced_d #1\W\Z {#1}%
+}%
+\def\XINT_flexpr_getnext_checkforbraced_d #1#2%
+{%
+ \xint_UDwfork
+ #1\dummy \XINT_flexpr_getnext_emptybracepair
+ #2\dummy \XINT_flexpr_getnext_onetoken_wehope
+ \W\dummy \XINT_flexpr_getnext_gotbracedstuff
+ \krof
+}%
+\def\XINT_flexpr_getnext_emptybracepair #1{\XINT_flexpr_getnext }%
+\def\XINT_flexpr_getnext_gotbracedstuff #1\W\Z #2%
+{%
+ \expandafter\XINT_flexpr_getop\csname .#2\endcsname
+}%
+\def\XINT_flexpr_getnext_onetoken_wehope\Z #1%
+{%
+ \xint_gob_til_! #1\XINT_flexpr_subexpr !%
+ \expandafter\XINT_flexpr_getnext_onetoken_fork\string #1%
+}%
+\def\XINT_flexpr_subexpr !#1!{\expandafter\XINT_flexpr_getop\xint_gobble_i }%
+\begingroup
+\lccode`*=`_
+\lowercase{\endgroup
+\def\XINT_flexpr_getnext_onetoken_fork #1%
+{%
+ \XINT_expr_sixwayfork
+ #1-.+*\dummy \XINT_flexpr_oparen
+ (#1.+*\dummy -%
+ (-#1+*\dummy {\XINT_flexpr_scannum_start\XINT_expr_scannum_decpart_b.}%
+ (-.#1*\dummy \XINT_flexpr_getnext%
+ (-.+#1\dummy {\XINT_flexpr_scannum_start\XINT_expr_scannum_decpart_b*}%
+ (-.+*\dummy {\XINT_flexpr_scannum_check #1}%
+ \krof
+}}%
+\def\XINT_flexpr_scannum_check #1%
+{%
+ \ifnum \xint_c_ix<1#1
+ \expandafter\XINT_flexpr_scannum_start
+ \else
+ \xint_afterfi
+ {\XINT_expr_unexpectedtoken
+ \expandafter\XINT_flexpr_getnext\xint_gobble_ii}%
+ \fi \XINT_expr_scannum_intpart_b #1%
+}%
+\def\XINT_flexpr_scannum_start #1%
+{%
+ \expandafter\XINT_flexpr_getop
+ \romannumeral-`0\expandafter\XINT_expr_gathernum
+ \romannumeral-`0#1%
+}%
+% \end{macrocode}
+% \subsection{\csh{xintNewExpr}}
+% \begin{macrocode}
+\catcode`* 13
+\def\xintNewExpr #1[#2]#3%
+{%
+ \begingroup
+ \ifcase #2\relax
+ \toks0 {\xdef #1}%
+ \or \toks0 {\xdef #1##1}%
+ \or \toks0 {\xdef #1##1##2}%
+ \or \toks0 {\xdef #1##1##2##3}%
+ \or \toks0 {\xdef #1##1##2##3##4}%
+ \or \toks0 {\xdef #1##1##2##3##4##5}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6##7}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6##7##8}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6##7##8##9}%
+ \else
+ \immediate\write-1{Package xintexpr Error! illegal number of macro
+ parameters.}%
+ \fi
+ \def\xintAdd {:xintAdd}%
+ \def\xintSub {:xintSub}%
+ \def\xintMul {:xintMul}%
+ \def\xintDiv {:xintDiv}%
+ \def\xintfPow {:xintfPow}%
+ \def\xintfFac {:xintfFac}%
+ \def\xintOpp {:xintOpp}%
+ \def\xintfE {:xintfE}%
+ \def\xintraw { :romannumeral0:xintraw}%
+ \def\XINT_expr_the ##1##2##3%
+ {\expandafter\xintraw
+ \expandafter{\romannumeral-`0\XINT_expr_string ##3}}%
+ \lccode`\*=`: \lowercase {\def*}{!noexpand!}%
+ \catcode`: 13
+ \endlinechar -1
+ \everyeof {\noexpand }%
+ \edef\xintNewExprtmp
+ {\expandafter\scantokens
+ \expandafter{\romannumeral0\xinttheeval #3\relax}}%
+ \lccode`\*=`_ \lowercase {\def*}{####}%
+ \catcode`_ 13 \catcode`! 0 \catcode`: 11
+ \the\toks0 {\expandafter\scantokens\expandafter{\xintNewExprtmp }}%
+\endgroup
+}%
+% \end{macrocode}
+% \subsection{\csh{xintNewFloatExpr}}
+% \begin{macrocode}
+\def\xintNewFloatExpr #1[#2]#3%
+{%
+ \begingroup
+ \ifcase #2\relax
+ \toks0 {\xdef #1}%
+ \or \toks0 {\xdef #1##1}%
+ \or \toks0 {\xdef #1##1##2}%
+ \or \toks0 {\xdef #1##1##2##3}%
+ \or \toks0 {\xdef #1##1##2##3##4}%
+ \or \toks0 {\xdef #1##1##2##3##4##5}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6##7}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6##7##8}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6##7##8##9}%
+ \else
+ \immediate\write-1{Package xintexpr Error! illegal number of macro
+ parameters.}%
+ \fi
+ \def\XINTinFloatAdd {:XINTinFloatAdd}%
+ \def\XINTinFloatSub {:XINTinFloatSub}%
+ \def\XINTinFloatMul {:XINTinFloatMul}%
+ \def\XINTinFloatDiv {:XINTinFloatDiv}%
+ \def\XINTinFloatPower {:XINTinFloatPower}%
+ \def\xintfFac {:xintfFac}%
+ \def\xintOpp {:xintOpp}%
+ \def\XINTinFloatfE {:XINTinFloatfE}%
+ \def\xintfloat { :romannumeral0:xintfloat}%
+ \def\XINT_flexpr_the ##1##2##3%
+ {\expandafter\xintfloat
+ \expandafter{\romannumeral-`0\XINT_expr_string ##3}}%
+ \lccode`\*=`: \lowercase {\def*}{!noexpand!}%
+ \catcode`: 13
+ \endlinechar -1
+ \everyeof {\noexpand }%
+ \edef\xintNewExprtmp
+ {\expandafter\scantokens
+ \expandafter{\romannumeral0\xintthefloateval #3\relax}}%
+ \lccode`\*=`_ \lowercase {\def*}{####}%
+ \catcode`_ 13 \catcode`! 0 \catcode`: 11
+ \the\toks0 {\expandafter\scantokens\expandafter{\xintNewExprtmp }}%
+\endgroup
+}%
+\XINT_expr_restorecatcodes_endinput%
+% \end{macrocode}
% \DeleteShortVerb{\|}
% \MakePercentComment
-%</xintcfrac>
+%</xintexpr>
%<*none>
\CharacterTable
{Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
@@ -12069,7 +14563,7 @@ first place.
Grave accent \` Left brace \{ Vertical bar \|
Right brace \} Tilde \~}
-\CheckSum{11444}
+\CheckSum{13965}
\makeatletter\check@checksum\makeatother
\Finale
%%
diff --git a/Master/texmf-dist/source/generic/xint/xint.ins b/Master/texmf-dist/source/generic/xint/xint.ins
index 24c8379d8bd..c2392102edb 100644
--- a/Master/texmf-dist/source/generic/xint/xint.ins
+++ b/Master/texmf-dist/source/generic/xint/xint.ins
@@ -1,6 +1,6 @@
%%
%%----------------------------------------------------------------
-%% The xint bundle (version 1.06b of May 14, 2013)
+%% The xint bundle (version 1.07a of May 26, 2013)
%% Copyright (C) 2013 by Jean-Francois Burnol
%%----------------------------------------------------------------
%%
@@ -19,7 +19,8 @@
\file{xintgcd.sty}{\from{xint.dtx}{xintgcd}}
\file{xintfrac.sty}{\from{xint.dtx}{xintfrac}}
\file{xintseries.sty}{\from{xint.dtx}{xintseries}}
-\file{xintcfrac.sty}{\from{xint.dtx}{xintcfrac}}}
+\file{xintcfrac.sty}{\from{xint.dtx}{xintcfrac}}
+\file{xintexpr.sty}{\from{xint.dtx}{xintexpr}}}
\endbatchfile
\endinput
%%
diff --git a/Master/texmf-dist/tex/generic/xint/xint.sty b/Master/texmf-dist/tex/generic/xint/xint.sty
index c296158f940..b740ecda4a6 100644
--- a/Master/texmf-dist/tex/generic/xint/xint.sty
+++ b/Master/texmf-dist/tex/generic/xint/xint.sty
@@ -22,7 +22,7 @@
%% in the same archive or directory.)
%%
%%----------------------------------------------------------------
-%% The xint bundle (version 1.06b of May 14, 2013)
+%% The xint bundle (version 1.07a of May 26, 2013)
%% xint: Expandable operations on long numbers
%% Copyright (C) 2013 by Jean-Francois Burnol
%%----------------------------------------------------------------
@@ -138,7 +138,7 @@
\fi
\expandafter\x\csname ver@xint.sty\endcsname
\ProvidesPackage{xint}%
- [2013/05/14 v1.06b Expandable operations on long numbers (jfB)]%
+ [2013/05/26 v1.07a Expandable operations on long numbers (jfB)]%
\def\xint_gobble_ {}%
\def\xint_gobble_i #1{}%
\def\xint_gobble_ii #1#2{}%
@@ -153,6 +153,9 @@
\def\xint_firstoftwo_andstop #1#2{ #1}%
\def\xint_secondoftwo_andstop #1#2{ #2}%
\def\xint_exchangetwo_keepbraces_andstop #1#2{ {#2}{#1}}%
+\def\xint_firstofthree #1#2#3{#1}%
+\def\xint_secondofthree #1#2#3{#2}%
+\def\xint_thirdofthree #1#2#3{#3}%
\def\xint_minus_andstop { -}%
\def\xint_gob_til_r #1\R {}%
\def\xint_gob_til_w #1\W {}%
@@ -213,13 +216,13 @@
\def\xintRevWithBracesNoExpand {\romannumeral0\xintrevwithbracesnoexpand }%
\def\xintrevwithbraces #1%
{%
- \expandafter\XINT_revwbr_loop % #1 empty ok
+ \expandafter\XINT_revwbr_loop\expandafter{\expandafter}%
\romannumeral-`0#1\xint_relax\xint_relax\xint_relax\xint_relax
\xint_relax\xint_relax\xint_relax\xint_relax\Z
}%
\def\xintrevwithbracesnoexpand #1%
{%
- \romannumeral0\XINT_revwbr_loop
+ \romannumeral0\XINT_revwbr_loop\expandafter{\expandafter}%
#1\xint_relax\xint_relax\xint_relax\xint_relax
\xint_relax\xint_relax\xint_relax\xint_relax\Z
}%
@@ -305,6 +308,7 @@
\def\XINT_length_finish_c #1#2\Z #3%
{\expandafter\space\the\numexpr #3-#1\relax}%
\def\xintCSVtoList {\romannumeral0\xintcsvtolist }%
+\def\xintCSVtoListNoExpand {\romannumeral0\xintcsvtolistnoexpand }%
\def\xintcsvtolist #1%
{%
\expandafter\XINT_csvtol_loop_a\expandafter
@@ -312,6 +316,12 @@
,\xint_undef,\xint_undef,\xint_undef,\xint_undef
,\xint_undef,\xint_undef,\xint_undef,\xint_undef,\Z
}%
+\def\xintcsvtolistnoexpand #1%
+{%
+ \romannumeral0\XINT_csvtol_loop_a
+ {}#1,\xint_undef,\xint_undef,\xint_undef,\xint_undef
+ ,\xint_undef,\xint_undef,\xint_undef,\xint_undef,\Z
+}%
\def\XINT_csvtol_loop_a #1#2,#3,#4,#5,#6,#7,#8,#9,%
{%
\xint_gob_til_xint_undef #9\XINT_csvtol_finish_a\xint_undef
@@ -348,9 +358,12 @@
\def\XINT_csvtol_finish_di #1#2#3#4#5#6#7#8#9%
{ #9{#1}{#2}{#3}{#4}{#5}{#6}{#7}}%
\def\xintListWithSep {\romannumeral0\xintlistwithsep }%
+\def\xintListWithSepNoExpand {\romannumeral0\xintlistwithsepnoexpand }%
\long\def\xintlistwithsep #1#2%
{\expandafter\XINT_lws\expandafter {\romannumeral-`0#2}{#1}}%
\long\def\XINT_lws #1#2{\XINT_lws_start {#2}#1\Z }%
+\long\def\xintlistwithsepnoexpand #1#2%
+ {\romannumeral0\XINT_lws_start {#1}#2\Z }%
\long\def\XINT_lws_start #1#2%
{%
\xint_gob_til_z #2\XINT_lws_dont\Z
@@ -365,11 +378,16 @@
\long\def\XINT_lws_loop_b #1#2{\XINT_lws_loop_a {#1#2}}%
\long\def\XINT_lws_end\Z\XINT_lws_loop_b #1#2#3{ #1}%
\def\xintNthElt {\romannumeral0\xintnthelt }%
+\def\xintNthEltNoExpand {\romannumeral0\xintntheltnoexpand }%
\def\xintnthelt #1#2%
{%
\expandafter\XINT_nthelt\expandafter {\romannumeral-`0#2}%
{\numexpr #1\relax }%
}%
+\def\xintntheltnoexpand #1#2%
+{%
+ \romannumeral0\XINT_nthelt {#2}{\numexpr #1\relax}%
+}%
\def\XINT_nthelt #1#2%
{%
\ifnum #2>0
@@ -407,12 +425,14 @@
\krof
}%
\def\xintApply {\romannumeral0\xintapply }%
+\def\xintApplyNoExpand {\romannumeral0\xintapplynoexpand }%
\def\xintapply #1#2%
{%
\expandafter\XINT_apply\expandafter {\romannumeral-`0#2}%
{#1}%
}%
\def\XINT_apply #1#2{\XINT_apply_loop_a {}{#2}#1\Z }%
+\def\xintapplynoexpand #1#2{\romannumeral0\XINT_apply_loop_a {}{#1}#2\Z }%
\def\XINT_apply_loop_a #1#2#3%
{%
\xint_gob_til_z #3\XINT_apply_end\Z
@@ -423,12 +443,15 @@
\def\XINT_apply_loop_b #1#2{\XINT_apply_loop_a {#2{#1}}}%
\def\XINT_apply_end\Z\expandafter\XINT_apply_loop_b\expandafter #1#2#3{ #2}%
\def\xintApplyUnbraced {\romannumeral0\xintapplyunbraced }%
+\def\xintApplyUnbracedNoExpand {\romannumeral0\xintapplyunbracednoexpand }%
\def\xintapplyunbraced #1#2%
{%
\expandafter\XINT_applyunbr\expandafter {\romannumeral-`0#2}%
{#1}%
}%
\def\XINT_applyunbr #1#2{\XINT_applyunbr_loop_a {}{#2}#1\Z }%
+\def\xintapplyunbracednoexpand #1#2%
+ {\romannumeral0\XINT_applyunbr_loop_a {}{#1}#2\Z }%
\def\XINT_applyunbr_loop_a #1#2#3%
{%
\xint_gob_til_z #3\XINT_applyunbr_end\Z
@@ -680,6 +703,14 @@
0-\dummy { 1}%
\krof
}%
+\def\xintSgnFork {\romannumeral0\xintsgnfork }%
+\def\xintsgnfork #1%
+{%
+ \ifcase #1 \xint_afterfi{\expandafter\space\xint_secondofthree}%
+ \or\xint_afterfi{\expandafter\space\xint_thirdofthree}%
+ \else\xint_afterfi{\expandafter\space\xint_firstofthree}%
+ \fi
+}%
\def\xintiOpp {\romannumeral0\xintiopp }%
\def\xintiopp #1%
{%
@@ -2953,7 +2984,7 @@
\def\XINT_dsx_xisNeg_checkA_ #1#2\Z #3%
{%
\xint_gob_til_zero #1\XINT_dsx_xisNeg_Azero 0%
- \XINT_dsx_xisNeg_checkx {#3}{#3}\Z {#1#2}%
+ \XINT_dsx_xisNeg_checkx {#3}{#3}{}\Z {#1#2}%
}%
\def\XINT_dsx_xisNeg_Azero #1\Z #2{ 0}%
\def\XINT_dsx_xisNeg_checkx #1%
@@ -2961,25 +2992,25 @@
\ifnum #1>999999999
\xint_afterfi
{\xintError:TooBigDecimalShift
- \expandafter\space\expandafter 0\xint_gobble_iii }%
+ \expandafter\space\expandafter 0\xint_gobble_iv }%
\else
\expandafter \XINT_dsx_zeroloop
\fi
}%
-\def\XINT_dsx_zeroloop #1%
+\def\XINT_dsx_zeroloop #1#2%
{%
\ifnum #1<9 \XINT_dsx_exita\fi
\expandafter\XINT_dsx_zeroloop\expandafter
- {\the\numexpr #1-8}00000000%
+ {\the\numexpr #1-8}{#200000000}%
}%
\def\XINT_dsx_exita\fi\expandafter\XINT_dsx_zeroloop
{%
\fi\expandafter\XINT_dsx_exitb
}%
-\def\XINT_dsx_exitb #1%
+\def\XINT_dsx_exitb #1#2%
{%
\expandafter\expandafter\expandafter
- \XINT_dsx_addzeros\csname xint_gobble_\romannumeral -#1\endcsname
+ \XINT_dsx_addzeros\csname xint_gobble_\romannumeral -#1\endcsname #2%
}%
\def\XINT_dsx_addzeros #1\Z #2{ #2#1}%
\def\XINT_dsx_xisPos #1\Z #2%
diff --git a/Master/texmf-dist/tex/generic/xint/xintcfrac.sty b/Master/texmf-dist/tex/generic/xint/xintcfrac.sty
index 7cbe6299ef0..561738a7b02 100644
--- a/Master/texmf-dist/tex/generic/xint/xintcfrac.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintcfrac.sty
@@ -22,7 +22,7 @@
%% in the same archive or directory.)
%%
%%----------------------------------------------------------------
-%% The xint bundle (version 1.06b of May 14, 2013)
+%% The xint bundle (version 1.07a of May 26, 2013)
%% xintcfrac: Expandable continued fractions with xint package
%% Copyright (C) 2013 by Jean-Francois Burnol
%%----------------------------------------------------------------
@@ -164,7 +164,7 @@
\fi
\expandafter\x\csname ver@xintcfrac.sty\endcsname
\ProvidesPackage{xintcfrac}%
- [2013/05/14 v1.06b Expandable continued fractions with xint package (jfB)]%
+ [2013/05/26 v1.07a Expandable continued fractions with xint package (jfB)]%
\def\xintCFrac {\romannumeral0\xintcfrac }%
\def\xintcfrac #1%
{%
@@ -176,7 +176,7 @@
}%
\def\XINT_cfrac_noopt #1\Z
{%
- \expandafter\XINT_cfrac_A\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_cfrac_A\romannumeral0\xintrawwithzeros {#1}\Z
\relax\relax
}%
\def\XINT_cfrac_opt_b\fi\XINT_cfrac_noopt [\Z #1]%
@@ -185,17 +185,17 @@
}%
\def\XINT_cfrac_optl #1%
{%
- \expandafter\XINT_cfrac_A\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_cfrac_A\romannumeral0\xintrawwithzeros {#1}\Z
\relax\hfill
}%
\def\XINT_cfrac_optc #1%
{%
- \expandafter\XINT_cfrac_A\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_cfrac_A\romannumeral0\xintrawwithzeros {#1}\Z
\relax\relax
}%
\def\XINT_cfrac_optr #1%
{%
- \expandafter\XINT_cfrac_A\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_cfrac_A\romannumeral0\xintrawwithzeros {#1}\Z
\hfill\relax
}%
\def\XINT_cfrac_A #1/#2\Z
@@ -240,10 +240,7 @@
}%
\def\XINT_cfrac__end \Z+\cfrac#1#2{ #2}%
\def\xintGCFrac {\romannumeral0\xintgcfrac }%
-\def\xintgcfrac #1%
-{%
- \XINT_gcfrac_opt_a #1\Z
-}%
+\def\xintgcfrac #1{\XINT_gcfrac_opt_a #1\Z }%
\def\XINT_gcfrac_opt_a #1%
{%
\ifx#1[\XINT_gcfrac_opt_b\fi \XINT_gcfrac_noopt #1%
@@ -315,7 +312,7 @@
\def\xintFtoCs {\romannumeral0\xintftocs }%
\def\xintftocs #1%
{%
- \expandafter\XINT_ftc_A\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_ftc_A\romannumeral0\xintrawwithzeros {#1}\Z
}%
\def\XINT_ftc_A #1/#2\Z
{%
@@ -351,7 +348,7 @@
\def\xintFtoCx {\romannumeral0\xintftocx }%
\def\xintftocx #1#2%
{%
- \expandafter\XINT_ftcx_A\romannumeral0\xintraw {#2}\Z {#1}%
+ \expandafter\XINT_ftcx_A\romannumeral0\xintrawwithzeros {#2}\Z {#1}%
}%
\def\XINT_ftcx_A #1/#2\Z
{%
@@ -389,12 +386,12 @@
\def\xintFtoCC {\romannumeral0\xintftocc }%
\def\xintftocc #1%
{%
- \expandafter\XINT_ftcc_A\expandafter {\romannumeral0\xintraw {#1}}%
+ \expandafter\XINT_ftcc_A\expandafter {\romannumeral0\xintrawwithzeros {#1}}%
}%
\def\XINT_ftcc_A #1%
{%
\expandafter\XINT_ftcc_B
- \romannumeral0\xintraw {\xintAdd {1/2[0]}{#1[0]}}\Z {#1[0]}%
+ \romannumeral0\xintrawwithzeros {\xintAdd {1/2[0]}{#1[0]}}\Z {#1[0]}%
}%
\def\XINT_ftcc_B #1/#2\Z
{%
@@ -426,7 +423,7 @@
\def\XINT_ftcc_loop_a #1%
{%
\expandafter\XINT_ftcc_loop_b
- \romannumeral0\xintraw {\xintAdd {1/2[0]}{#1}}\Z {#1}%
+ \romannumeral0\xintrawwithzeros {\xintAdd {1/2[0]}{#1}}\Z {#1}%
}%
\def\XINT_ftcc_loop_b #1/#2\Z
{%
@@ -480,7 +477,7 @@
{%
\xint_gob_til_w #5\XINT_cstf_end\W
\expandafter\XINT_cstf_loop_b
- \romannumeral0\xintraw {#5}.{#1}{#2}{#3}{#4}%
+ \romannumeral0\xintrawwithzeros {#5}.{#1}{#2}{#3}{#4}%
}%
\def\XINT_cstf_loop_b #1/#2.#3#4#5#6%
{%
@@ -502,7 +499,7 @@
{%
\expandafter\XINT_cstf_loop_a\expandafter{#2}#1%
}%
-\def\XINT_cstf_end #1.#2#3#4#5{\xintraw {#2/#3}[0]}%
+\def\XINT_cstf_end #1.#2#3#4#5{\xintrawwithzeros {#2/#3}[0]}%
\def\xintiCstoF {\romannumeral0\xinticstof }%
\def\xinticstof #1%
{%
@@ -529,7 +526,7 @@
{%
\expandafter\XINT_icstf_loop_a\expandafter {#2}{#1}%
}%
-\def\XINT_icstf_end#1.#2#3#4#5{\xintraw {#2/#3}[0]}%
+\def\XINT_icstf_end#1.#2#3#4#5{\xintrawwithzeros {#2/#3}[0]}%
\def\xintGCtoF {\romannumeral0\xintgctof }%
\def\xintgctof #1%
{%
@@ -542,7 +539,7 @@
\def\XINT_gctf_loop_a #1#2#3#4#5+%
{%
\expandafter\XINT_gctf_loop_b
- \romannumeral0\xintraw {#5}.{#1}{#2}{#3}{#4}%
+ \romannumeral0\xintrawwithzeros {#5}.{#1}{#2}{#3}{#4}%
}%
\def\XINT_gctf_loop_b #1/#2.#3#4#5#6%
{%
@@ -568,7 +565,7 @@
{%
\xint_gob_til_w #2\XINT_gctf_end\W
\expandafter\XINT_gctf_loop_g
- \romannumeral0\xintraw {#2}.#1%
+ \romannumeral0\xintrawwithzeros {#2}.#1%
}%
\def\XINT_gctf_loop_g #1/#2.#3#4#5#6%
{%
@@ -590,7 +587,7 @@
{%
\expandafter\XINT_gctf_loop_a\expandafter {#2}#1%
}%
-\def\XINT_gctf_end #1.#2#3#4#5{\xintraw {#2/#3}[0]}%
+\def\XINT_gctf_end #1.#2#3#4#5{\xintrawwithzeros {#2/#3}[0]}%
\def\xintiGCtoF {\romannumeral0\xintigctof }%
\def\xintigctof #1%
{%
@@ -636,7 +633,7 @@
{%
\XINT_igctf_loop_a {#3}{#4}{#1}{#2}%
}%
-\def\XINT_igctf_end #1.#2#3#4#5{\xintraw {#4/#5}[0]}%
+\def\XINT_igctf_end #1.#2#3#4#5{\xintrawwithzeros {#4/#5}[0]}%
\def\xintCstoCv {\romannumeral0\xintcstocv }%
\def\xintcstocv #1%
{%
@@ -650,7 +647,7 @@
{%
\xint_gob_til_w #6\XINT_cstcv_end\W
\expandafter\XINT_cstcv_loop_b
- \romannumeral0\xintraw {#6}.{#2}{#3}{#4}{#5}{#1}%
+ \romannumeral0\xintrawwithzeros {#6}.{#2}{#3}{#4}{#5}{#1}%
}%
\def\XINT_cstcv_loop_b #1/#2.#3#4#5#6%
{%
@@ -675,7 +672,7 @@
\def\XINT_cstcv_loop_f #1#2#3#4#5%
{%
\expandafter\XINT_cstcv_loop_g\expandafter
- {\romannumeral0\xintraw {#1/#2}}{#5}{#1}{#2}{#3}{#4}%
+ {\romannumeral0\xintrawwithzeros {#1/#2}}{#5}{#1}{#2}{#3}{#4}%
}%
\def\XINT_cstcv_loop_g #1#2{\XINT_cstcv_loop_a {#2{#1[0]}}}%
\def\XINT_cstcv_end #1.#2#3#4#5#6{ #6}%
@@ -708,7 +705,7 @@
\def\XINT_icstcv_loop_d #1#2%
{%
\expandafter\XINT_icstcv_loop_e\expandafter
- {\romannumeral0\xintraw {#1/#2}}{{#1}{#2}}%
+ {\romannumeral0\xintrawwithzeros {#1/#2}}{{#1}{#2}}%
}%
\def\XINT_icstcv_loop_e #1#2#3#4{\XINT_icstcv_loop_a {#4{#1[0]}}#2#3}%
\def\XINT_icstcv_end #1.#2#3#4#5#6{ #6}%
@@ -724,7 +721,7 @@
\def\XINT_gctcv_loop_a #1#2#3#4#5#6+%
{%
\expandafter\XINT_gctcv_loop_b
- \romannumeral0\xintraw {#6}.{#2}{#3}{#4}{#5}{#1}%
+ \romannumeral0\xintrawwithzeros {#6}.{#2}{#3}{#4}{#5}{#1}%
}%
\def\XINT_gctcv_loop_b #1/#2.#3#4#5#6%
{%
@@ -749,7 +746,7 @@
\def\XINT_gctcv_loop_f #1#2%
{%
\expandafter\XINT_gctcv_loop_g\expandafter
- {\romannumeral0\xintraw {#1/#2}}{{#1}{#2}}%
+ {\romannumeral0\xintrawwithzeros {#1/#2}}{{#1}{#2}}%
}%
\def\XINT_gctcv_loop_g #1#2#3#4%
{%
@@ -759,7 +756,7 @@
{%
\xint_gob_til_w #3\XINT_gctcv_end\W
\expandafter\XINT_gctcv_loop_i
- \romannumeral0\xintraw {#3}.#2{#1}%
+ \romannumeral0\xintrawwithzeros {#3}.#2{#1}%
}%
\def\XINT_gctcv_loop_i #1/#2.#3#4#5#6%
{%
@@ -829,13 +826,13 @@
\def\XINT_igctcv_loop_k #1#2%
{%
\expandafter\XINT_igctcv_loop_l\expandafter
- {\romannumeral0\xintraw {#1/#2}}%
+ {\romannumeral0\xintrawwithzeros {#1/#2}}%
}%
\def\XINT_igctcv_loop_l #1#2#3{\XINT_igctcv_loop_a {#3{#1[0]}}#2}%
\def\XINT_igctcv_end_a #1.#2#3#4#5%
{%
\expandafter\XINT_igctcv_end_b\expandafter
- {\romannumeral0\xintraw {#2/#3}}%
+ {\romannumeral0\xintrawwithzeros {#2/#3}}%
}%
\def\XINT_igctcv_end_b #1#2{ #2{#1[0]}}%
\def\xintCntoF {\romannumeral0\xintcntof }%
diff --git a/Master/texmf-dist/tex/generic/xint/xintexpr.sty b/Master/texmf-dist/tex/generic/xint/xintexpr.sty
new file mode 100644
index 00000000000..14fc53b418c
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/xint/xintexpr.sty
@@ -0,0 +1,769 @@
+%%
+%% This is file `xintexpr.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% xint.dtx (with options: `xintexpr')
+%%
+%% IMPORTANT NOTICE:
+%%
+%% For the copyright see the source file.
+%%
+%% Any modified versions of this file must be renamed
+%% with new filenames distinct from xintexpr.sty.
+%%
+%% For distribution of the original source see the terms
+%% for copying and modification in the file xint.dtx.
+%%
+%% This generated file may be distributed as long as the
+%% original source files, as listed above, are part of the
+%% same distribution. (The sources need not necessarily be
+%% in the same archive or directory.)
+%%
+%%----------------------------------------------------------------
+%% The xint bundle (version 1.07a of May 26, 2013)
+%% xintexpr: Expandable expression parser
+%% Copyright (C) 2013 by Jean-Francois Burnol
+%%----------------------------------------------------------------
+%%
+\begingroup\catcode61\catcode48\catcode32=10\relax%
+ \catcode13=5 % ^^M
+ \endlinechar=13 %
+ \catcode123=1 % {
+ \catcode125=2 % }
+ \catcode64=11 % @
+ \catcode35=6 % #
+ \catcode44=12 % ,
+ \catcode45=12 % -
+ \catcode46=12 % .
+ \catcode58=12 % :
+ \def\space { }%
+ \let\z\endgroup
+ \expandafter\let\expandafter\x\csname ver@xintexpr.sty\endcsname
+ \expandafter\let\expandafter\w\csname ver@xintfrac.sty\endcsname
+ \expandafter
+ \ifx\csname PackageInfo\endcsname\relax
+ \def\y#1#2{\immediate\write-1{Package #1 Info: #2.}}%
+ \else
+ \def\y#1#2{\PackageInfo{#1}{#2}}%
+ \fi
+ \expandafter
+ \ifx\csname numexpr\endcsname\relax
+ \y{xintexpr}{\numexpr not available, aborting input}%
+ \aftergroup\endinput
+ \else
+ \ifx\x\relax % plain-TeX, first loading of xintexpr.sty
+ \ifx\w\relax % but xintfrac.sty not yet loaded.
+ \y{xintexpr}{Package xintfrac is required}%
+ \y{xintexpr}{Will try \string\input\space xintfrac.sty}%
+ \def\z{\endgroup\input xintfrac.sty\relax}%
+ \fi
+ \else
+ \def\empty {}%
+ \ifx\x\empty % LaTeX, first loading,
+ % variable is initialized, but \ProvidesPackage not yet seen
+ \ifx\w\relax % xintfrac.sty not yet loaded.
+ \y{xintexpr}{Package xintfrac is required}%
+ \y{xintexpr}{Will try \string\RequirePackage{xintfrac}}%
+ \def\z{\endgroup\RequirePackage{xintfrac}}%
+ \fi
+ \else
+ \y{xintexpr}{I was already loaded, aborting input}%
+ \aftergroup\endinput
+ \fi
+ \fi
+ \fi
+\z%
+\begingroup\catcode61\catcode48\catcode32=10\relax%
+ \catcode13=5 % ^^M
+ \endlinechar=13 %
+ \catcode123=1 % {
+ \catcode125=2 % }
+ \catcode64=11 % @
+ \catcode35=6 % #
+ \catcode44=12 % ,
+ \catcode45=12 % -
+ \catcode46=12 % .
+ \catcode58=12 % :
+ \expandafter
+ \ifx\csname PackageInfo\endcsname\relax
+ \def\y#1#2{\immediate\write-1{Package #1 Info: #2.}}%
+ \else
+ \def\y#1#2{\PackageInfo{#1}{#2}}%
+ \fi
+ \def\empty {}%
+ \expandafter\let\expandafter\w\csname ver@xintfrac.sty\endcsname
+ \ifx\w\relax % Plain TeX, user gave a file name at the prompt
+ \y{xintexpr}{Loading of package xintfrac failed, aborting input}%
+ \aftergroup\endinput
+ \fi
+ \ifx\w\empty % LaTeX, user gave a file name at the prompt
+ \y{xintexpr}{Loading of package xintfrac failed, aborting input}%
+ \aftergroup\endinput
+ \fi
+\endgroup%
+\begingroup\catcode61\catcode48\catcode32=10\relax%
+ \catcode13=5 % ^^M
+ \endlinechar=13 %
+ \catcode123=1 % {
+ \catcode125=2 % }
+ \catcode95=11 % _
+ \def\x
+ {%
+ \endgroup
+ \edef\XINT_expr_restorecatcodes_endinput
+ {%
+ \catcode94=\the\catcode94 % ^
+ \catcode33=\the\catcode33 % !
+ \catcode93=\the\catcode93 % ]
+ \catcode91=\the\catcode91 % [
+ \catcode96=\the\catcode96 % `
+ \catcode47=\the\catcode47 % /
+ \catcode41=\the\catcode41 % )
+ \catcode40=\the\catcode40 % (
+ \catcode42=\the\catcode42 % *
+ \catcode43=\the\catcode43 % +
+ \catcode62=\the\catcode62 % >
+ \catcode60=\the\catcode60 % <
+ \catcode58=\the\catcode58 % :
+ \catcode46=\the\catcode46 % .
+ \catcode45=\the\catcode45 % -
+ \catcode44=\the\catcode44 % ,
+ \catcode35=\the\catcode35 % #
+ \catcode95=\the\catcode95 % _
+ \catcode125=\the\catcode125 % }
+ \catcode123=\the\catcode123 % {
+ \endlinechar=\the\endlinechar
+ \catcode13=\the\catcode13 % ^^M
+ \catcode32=\the\catcode32 %
+ \catcode61=\the\catcode61\relax % =
+ \noexpand\endinput
+ }%
+ \XINT_setcatcodes
+ \catcode91=12 % [
+ \catcode93=12 % ]
+ \catcode33=11 % !
+ \catcode94=12 % ^
+ }%
+\x
+\begingroup
+ \catcode64=11 % @
+ \catcode58=12 % :
+ \expandafter\ifx\csname ProvidesPackage\endcsname\relax
+ \def\x#1#2#3[#4]{\endgroup
+ \immediate\write-1{Package: #3 #4}%
+ \xdef#1{#4}%
+ }%
+ \else
+ \def\x#1#2[#3]{\endgroup
+ #2[{#3}]%
+ \ifx#1\@undefined
+ \xdef#1{#3}%
+ \fi
+ \ifx#1\relax
+ \xdef#1{#3}%
+ \fi
+ }%
+ \fi
+\expandafter\x\csname ver@xintexpr.sty\endcsname
+\ProvidesPackage{xintexpr}%
+ [2013/05/26 v1.07a Expandable expression parser (jfB)]%
+\chardef\xint_c_ 0
+\chardef\xint_c_i 1
+\chardef\xint_c_ii 2
+\chardef\xint_c_iii 3
+\chardef\xint_c_iv 4
+\chardef\xint_c_v 5
+\chardef\xint_c_ix 9
+\def\xint_gob_til_dot #1.{}%
+\def\xint_gob_til_dot_andstop #1.{ }%
+\def\xint_gob_til_! #1!{}% ! of catcode 11
+\def\XINT_expr_string {\expandafter\xint_gob_til_dot\string }%
+\def\XINT_expr_unexpectedtoken {\xintError:ignored }%
+\def\xintexpr {\romannumeral0\xinteval }%
+\def\xinteval
+{%
+ \expandafter\XINT_expr_until_end\romannumeral-`0%
+ \expandafter\XINT_expr_checkifprefix_ii\romannumeral-`0%
+ \XINT_expr_getnext
+}%
+\def\xinttheexpr {\romannumeral0\xinttheeval }%
+\def\xinttheeval {\expandafter\XINT_expr_the\romannumeral0\xinteval }%
+\def\XINT_expr_the #1#2#3{\xintraw{\XINT_expr_string #3}}%
+\def\xintthe #1{\ifx#1\xintexpr \expandafter\xinttheexpr
+ \else\expandafter\xintthefloatexpr\fi}%
+\def\XINT_expr_until_end #1%
+{%
+ \ifcase#1%
+ \expandafter\xint_gobble_vi
+ \or
+ \expandafter\XINT_expr_extra_closing_paren
+ \fi
+ \expandafter\XINT_expr_until_end\romannumeral-`0%
+}%
+\def\XINT_expr_extra_closing_paren {\xintError:removed }%
+\def\XINT_expr_endofexpr {!\XINT_illegaluse }%
+\def\XINT_illegaluse
+ {Illegal_here_use_xintthe\xintError:use_xintthe!\xint_gobble_i }%
+\def\XINT_expr_oparen
+{%
+ \expandafter\XINT_expr_until_cparen\romannumeral-`0%
+ \expandafter\XINT_expr_checkifprefix_ii\romannumeral-`0%
+ \XINT_expr_getnext
+}%
+\def\XINT_expr_until_cparen #1%
+{%
+ \ifcase#1%
+ \expandafter\XINT_expr_missing_cparen
+ \or
+ \else \xint_afterfi{\expandafter\XINT_expr_until_cparen\romannumeral-`0}%
+ \fi
+}%
+\def\XINT_expr_missing_cparen #1%
+{%
+ \xintError:inserted \xint_c_ \XINT_expr_endofexpr
+}%
+\def\xint_tmp_def #1#2#3%
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_expr_op_#1\expandafter\endcsname
+ \csname XINT_expr_until_#1\expandafter\endcsname
+ \csname XINT_expr_checkifprefix_#2\expandafter\endcsname
+ \csname XINT_expr_precedence_#1\expandafter\endcsname
+ \csname xint_c_#2\expandafter\endcsname
+ \csname xint#3\endcsname
+}%
+\def\xint_tmp_do_defs #1#2#3#4#5#6%
+{%
+ \def #1##1% \XINT_expr_op_?
+ {%
+ \expandafter #2\expandafter ##1\romannumeral-`0\expandafter
+ #3\romannumeral-`0\XINT_expr_getnext
+ }%
+ \def #2##1##2##3##4% \XINT_expr_until_?
+ {%
+ \ifnum ##2>#5%
+ \xint_afterfi {\expandafter #2\expandafter ##1\romannumeral-`0##3##4}%
+ \else
+ \xint_afterfi
+ {\expandafter ##2\expandafter ##3%
+ \csname .#6{\XINT_expr_string ##1}{\XINT_expr_string ##4}\endcsname }%
+ \fi
+ }%
+ \global\let #4#5%
+}%
+\xint_tmp_def +{ii}{Add}%
+\xint_tmp_def -{ii}{Sub}%
+\xint_tmp_def *{iii}{Mul}%
+\xint_tmp_def /{iii}{Div}%
+\xint_tmp_def ^{iv}{fPow}%
+\xint_tmp_def e{v}{fE}%
+\xint_tmp_def E{v}{fE}%
+\def\xint_tmp_def #1%
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_expr_checkifprefix_#1\expandafter\endcsname
+ \csname XINT_expr_op_-#1\endcsname
+}%
+\def\xint_tmp_do_defs #1#2%
+{%
+ \def #1##1%
+ {\xint_UDsignfork
+ ##1\dummy #2%
+ -\dummy ##1%
+ \krof }%
+}%
+\xint_tmp_def {ii}%
+\xint_tmp_def {iii}%
+\xint_tmp_def {iv}%
+\xint_tmp_def {v}%
+\def\xint_tmp_def #1%
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_expr_op_-#1\expandafter\endcsname
+ \csname XINT_expr_until_-#1\expandafter\endcsname
+ \csname XINT_expr_checkifprefix_#1\expandafter\endcsname
+ \csname xint_c_#1\endcsname
+}%
+\def\xint_tmp_do_defs #1#2#3#4%
+{%
+ \def #1% \XINT_expr_op_-ii,iii,iv,v
+ {%
+ \expandafter #2\romannumeral-`0\expandafter
+ #3\romannumeral-`0\XINT_expr_getnext
+ }%
+ \def #2##1##2##3% \XINT_expr_until_-ii,iii,iv,v
+ {%
+ \ifnum ##1>#4%
+ \xint_afterfi {\expandafter #2\romannumeral-`0##2##3}%
+ \else
+ \xint_afterfi {\expandafter ##1\expandafter ##2%
+ \csname .\xintOpp{\XINT_expr_string ##3}\endcsname }%
+ \fi
+ }%
+}%
+\xint_tmp_def {ii}%
+\xint_tmp_def {iii}%
+\xint_tmp_def {iv}%
+\xint_tmp_def {v}%
+\def\XINT_expr_getop #1%
+{%
+ \expandafter\XINT_expr_getop_a\expandafter #1\romannumeral-`0%
+}%
+\def\XINT_expr_getop_a #1#2%
+{%
+ \ifcat #2\relax
+ \ifx #2\relax
+ \expandafter\expandafter\expandafter
+ \XINT_expr_foundendofexpr
+ \else
+ \XINT_expr_unexpectedtoken
+ \expandafter\expandafter\expandafter
+ \XINT_expr_getop
+ \fi
+ \else
+ \expandafter\XINT_expr_op_found\expandafter #2%
+ \fi
+ #1%
+}%
+\def\XINT_expr_foundendofexpr {\xint_c_ \XINT_expr_endofexpr }%
+\def\XINT_expr_op_found #1%
+{%
+ \ifcsname XINT_expr_precedence_\string #1\endcsname
+ \expandafter\xint_afterfi\expandafter
+ {\csname XINT_expr_precedence_\string #1\expandafter\endcsname
+ \csname XINT_expr_op_\string #1\endcsname }%
+ \else
+ \XINT_expr_unexpectedtoken
+ \expandafter\XINT_expr_getop
+ \fi
+}%
+\expandafter\let\csname XINT_expr_precedence_)\endcsname \xint_c_i
+\expandafter\let\csname XINT_expr_op_)\endcsname\XINT_expr_getop
+\def\xint_tmp_def
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_expr_precedence_!\expandafter\endcsname
+ \csname XINT_expr_op_!\endcsname
+}%
+\def\xint_tmp_do_defs #1#2%
+{%
+ \def #1##1##2%
+ {\ifx ##1#2%
+ \expandafter\xint_firstoftwo
+ \else\expandafter\xint_secondoftwo
+ \fi{\expandafter\XINT_expr_getop}{\expandafter\XINT_flexpr_getop}%
+ \csname .\xintfFac{\XINT_expr_string ##2}/1[0]\endcsname }%
+ \let#2\empty
+}%
+\xint_tmp_def
+\def\XINT_expr_getnext
+{%
+ \expandafter\XINT_expr_getnext_checkforbraced_a\romannumeral-`0%
+}%
+\def\XINT_expr_getnext_checkforbraced_a #1%
+{%
+ \XINT_expr_getnext_checkforbraced_b #1\W\Z {#1}%
+}%
+\def\XINT_expr_getnext_checkforbraced_b #1#2%
+{%
+ \xint_UDwfork
+ #1\dummy \XINT_expr_getnext_emptybracepair
+ #2\dummy \XINT_expr_getnext_onetoken_perhaps
+ \W\dummy \XINT_expr_getnext_gotbracedstuff
+ \krof
+}%
+\def\XINT_expr_getnext_onetoken_perhaps\Z #1%
+{%
+ \expandafter\XINT_expr_getnext_checkforbraced_c\expandafter
+ {\romannumeral-`0#1}%
+}%
+\def\XINT_expr_getnext_checkforbraced_c #1%
+{%
+ \XINT_expr_getnext_checkforbraced_d #1\W\Z {#1}%
+}%
+\def\XINT_expr_getnext_checkforbraced_d #1#2%
+{%
+ \xint_UDwfork
+ #1\dummy \XINT_expr_getnext_emptybracepair
+ #2\dummy \XINT_expr_getnext_onetoken_wehope
+ \W\dummy \XINT_expr_getnext_gotbracedstuff
+ \krof
+}%
+\def\XINT_expr_getnext_emptybracepair #1{\XINT_expr_getnext }%
+\def\XINT_expr_getnext_gotbracedstuff #1\W\Z #2%
+{%
+ \expandafter\XINT_expr_getop\csname .#2\endcsname
+}%
+\def\XINT_expr_getnext_onetoken_wehope\Z #1%
+{%
+ \xint_gob_til_! #1\XINT_expr_subexpr !%
+ \expandafter\XINT_expr_getnext_onetoken_fork\string #1%
+}%
+\def\XINT_expr_subexpr !#1!{\expandafter\XINT_expr_getop\xint_gobble_i }%
+\begingroup
+\lccode`*=`_
+\lowercase{\endgroup
+\def\XINT_expr_sixwayfork #1(-.+*\dummy #2#3\krof {#2}%
+\def\XINT_expr_getnext_onetoken_fork #1%
+{%
+ \XINT_expr_sixwayfork
+ #1-.+*\dummy \XINT_expr_oparen
+ (#1.+*\dummy -%
+ (-#1+*\dummy {\XINT_expr_scannum_start\XINT_expr_scannum_decpart_b.}%
+ (-.#1*\dummy \XINT_expr_getnext%
+ (-.+#1\dummy {\XINT_expr_scannum_start\XINT_expr_scannum_decpart_b*}%
+ (-.+*\dummy {\XINT_expr_scannum_check #1}%
+ \krof
+}}%
+\def\XINT_expr_scannum_check #1%
+{%
+ \ifnum \xint_c_ix<1#1
+ \expandafter\XINT_expr_scannum_start
+ \else
+ \xint_afterfi{\XINT_expr_unexpectedtoken
+ \expandafter\XINT_expr_getnext\xint_gobble_ii}%
+ \fi \XINT_expr_scannum_intpart_b #1%
+}%
+\def\XINT_expr_scannum_stopscan {!}% ! catcode 11
+\def\XINT_expr_gathernum #1!% ! with catcode 11
+{%
+ \expandafter\space\csname .#1\endcsname
+}%
+\def\XINT_expr_scannum_start #1%
+{%
+ \expandafter\XINT_expr_getop
+ \romannumeral-`0\expandafter\XINT_expr_gathernum
+ \romannumeral-`0#1%
+}%
+\def\XINT_expr_scannum_intpart_a #1%
+{%
+ \ifnum \xint_c_ix<1\string#1
+ \expandafter\expandafter\expandafter
+ \XINT_expr_scannum_intpart_b
+ \expandafter\string
+ \else
+ \if #1.%
+ \expandafter\expandafter\expandafter
+ \XINT_expr_scannum_transition
+ \else
+ \expandafter\expandafter\expandafter
+ \XINT_expr_scannum_stopscan
+ \fi
+ \fi
+ #1%
+}%
+\def\XINT_expr_scannum_intpart_b #1%
+{%
+ \expandafter #1\romannumeral-`0\expandafter
+ \XINT_expr_scannum_intpart_a\romannumeral-`0%
+}%
+\def\XINT_expr_scannum_transition #1%
+{%
+ \expandafter.\romannumeral-`0\expandafter
+ \XINT_expr_scannum_decpart_a\romannumeral-`0%
+}%
+\def\XINT_expr_scannum_decpart_a #1%
+{%
+ \ifnum \xint_c_ix<1\string#1
+ \expandafter\expandafter\expandafter
+ \XINT_expr_scannum_decpart_b\expandafter\string
+ \else
+ \expandafter \XINT_expr_scannum_stopscan
+ \fi
+ #1%
+}%
+\def\XINT_expr_scannum_decpart_b #1%
+{%
+ \expandafter #1\romannumeral-`0\expandafter
+ \XINT_expr_scannum_decpart_a\romannumeral-`0%
+}%
+\def\xintfloatexpr {\romannumeral0\xintfloateval }%
+\def\xintfloateval
+{%
+ \expandafter\XINT_expr_until_end\romannumeral-`0%
+ \expandafter\XINT_flexpr_checkifprefix_ii\romannumeral-`0%
+ \XINT_flexpr_getnext
+}%
+\def\xintthefloatexpr {\romannumeral0\xintthefloateval }%
+\def\xintthefloateval
+ {\expandafter\XINT_flexpr_the\romannumeral0\xintfloateval }%
+\def\XINT_flexpr_the #1#2#3{\xintfloat{\XINT_expr_string #3}}%
+\def\XINT_flexpr_oparen
+{%
+ \expandafter\XINT_expr_until_cparen\romannumeral-`0%
+ \expandafter\XINT_flexpr_checkifprefix_ii\romannumeral-`0%
+ \XINT_flexpr_getnext
+}%
+\def\xint_tmp_def #1#2#3%
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_flexpr_op_#1\expandafter\endcsname
+ \csname XINT_flexpr_until_#1\expandafter\endcsname
+ \csname XINT_flexpr_checkifprefix_#2\expandafter\endcsname
+ \csname XINT_expr_precedence_#1\expandafter\endcsname
+ \csname xint_c_#2\expandafter\endcsname
+ \csname XINTinFloat#3\endcsname
+}%
+\def\xint_tmp_do_defs #1#2#3#4#5#6%
+{%
+ \def #1##1% \XINT_flexpr_op_?
+ {%
+ \expandafter #2\expandafter ##1\romannumeral-`0\expandafter
+ #3\romannumeral-`0\XINT_flexpr_getnext
+ }%
+ \def #2##1##2##3##4% \XINT_flexpr_until_?
+ {%
+ \ifnum ##2>#5%
+ \xint_afterfi {\expandafter #2\expandafter ##1\romannumeral-`0##3##4}%
+ \else
+ \xint_afterfi
+ {\expandafter ##2\expandafter ##3%
+ \csname .#6{\XINT_expr_string ##1}%
+ {\XINT_expr_string ##4}\endcsname }%
+ \fi
+ }%
+}%
+\xint_tmp_def +{ii}{Add}%
+\xint_tmp_def -{ii}{Sub}%
+\xint_tmp_def *{iii}{Mul}%
+\xint_tmp_def /{iii}{Div}%
+\xint_tmp_def ^{iv}{Power}%
+\xint_tmp_def e{v}{fE}%
+\xint_tmp_def E{v}{fE}%
+\def\xint_tmp_def #1%
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_flexpr_checkifprefix_#1\expandafter\endcsname
+ \csname XINT_flexpr_op_-#1\endcsname
+}%
+\def\xint_tmp_do_defs #1#2%
+{%
+ \def #1##1%
+ {\xint_UDsignfork
+ ##1\dummy #2%
+ -\dummy ##1%
+ \krof }%
+}%
+\xint_tmp_def {ii}%
+\xint_tmp_def {iii}%
+\xint_tmp_def {iv}%
+\xint_tmp_def {v}%
+\def\xint_tmp_def #1%
+{%
+ \expandafter\xint_tmp_do_defs
+ \csname XINT_flexpr_op_-#1\expandafter\endcsname
+ \csname XINT_expr_until_-#1\expandafter\endcsname
+ \csname XINT_flexpr_checkifprefix_#1\expandafter\endcsname
+ \csname xint_c_#1\endcsname
+}%
+\def\xint_tmp_do_defs #1#2#3#4%
+{%
+ \def #1% \XINT_flexpr_op_-ii,iii,iv,v
+ {%
+ \expandafter #2\romannumeral-`0\expandafter
+ #3\romannumeral-`0\XINT_flexpr_getnext
+ }%
+}%
+\xint_tmp_def {ii}%
+\xint_tmp_def {iii}%
+\xint_tmp_def {iv}%
+\xint_tmp_def {v}%
+\let\xint_tmp_def\empty
+\let\xint_tmp_do_defs\empty
+\def\XINT_flexpr_getop #1%
+{%
+ \expandafter\XINT_flexpr_getop_a\expandafter #1\romannumeral-`0%
+}%
+\def\XINT_flexpr_getop_a #1#2%
+{%
+ \ifcat #2\relax
+ \ifx #2\relax
+ \expandafter\expandafter\expandafter
+ \XINT_expr_foundendofexpr
+ \else
+ \XINT_expr_unexpectedtoken
+ \expandafter\expandafter\expandafter
+ \XINT_flexpr_getop
+ \fi
+ \else
+ \expandafter\XINT_flexpr_op_found\expandafter #2%
+ \fi
+ #1%
+}%
+\def\XINT_flexpr_op_found #1%
+{%
+ \ifcsname XINT_expr_precedence_\string #1\endcsname
+ \expandafter\xint_afterfi\expandafter
+ {\csname XINT_expr_precedence_\string #1\expandafter\endcsname
+ \csname XINT_flexpr_op_\string #1\endcsname }%
+ \else
+ \XINT_expr_unexpectedtoken
+ \expandafter\XINT_flexpr_getop
+ \fi
+}%
+\expandafter\let\csname XINT_flexpr_op_)\endcsname\XINT_flexpr_getop
+\def\XINT_flexpr_getnext
+{%
+ \expandafter\XINT_flexpr_getnext_checkforbraced_a\romannumeral-`0%
+}%
+\def\XINT_flexpr_getnext_checkforbraced_a #1%
+{%
+ \XINT_flexpr_getnext_checkforbraced_b #1\W\Z {#1}%
+}%
+\def\XINT_flexpr_getnext_checkforbraced_b #1#2%
+{%
+ \xint_UDwfork
+ #1\dummy \XINT_flexpr_getnext_emptybracepair
+ #2\dummy \XINT_flexpr_getnext_onetoken_perhaps
+ \W\dummy \XINT_flexpr_getnext_gotbracedstuff
+ \krof
+}%
+\def\XINT_flexpr_getnext_onetoken_perhaps\Z #1%
+{%
+ \expandafter\XINT_flexpr_getnext_checkforbraced_c\expandafter
+ {\romannumeral-`0#1}%
+}%
+\def\XINT_flexpr_getnext_checkforbraced_c #1%
+{%
+ \XINT_flexpr_getnext_checkforbraced_d #1\W\Z {#1}%
+}%
+\def\XINT_flexpr_getnext_checkforbraced_d #1#2%
+{%
+ \xint_UDwfork
+ #1\dummy \XINT_flexpr_getnext_emptybracepair
+ #2\dummy \XINT_flexpr_getnext_onetoken_wehope
+ \W\dummy \XINT_flexpr_getnext_gotbracedstuff
+ \krof
+}%
+\def\XINT_flexpr_getnext_emptybracepair #1{\XINT_flexpr_getnext }%
+\def\XINT_flexpr_getnext_gotbracedstuff #1\W\Z #2%
+{%
+ \expandafter\XINT_flexpr_getop\csname .#2\endcsname
+}%
+\def\XINT_flexpr_getnext_onetoken_wehope\Z #1%
+{%
+ \xint_gob_til_! #1\XINT_flexpr_subexpr !%
+ \expandafter\XINT_flexpr_getnext_onetoken_fork\string #1%
+}%
+\def\XINT_flexpr_subexpr !#1!{\expandafter\XINT_flexpr_getop\xint_gobble_i }%
+\begingroup
+\lccode`*=`_
+\lowercase{\endgroup
+\def\XINT_flexpr_getnext_onetoken_fork #1%
+{%
+ \XINT_expr_sixwayfork
+ #1-.+*\dummy \XINT_flexpr_oparen
+ (#1.+*\dummy -%
+ (-#1+*\dummy {\XINT_flexpr_scannum_start\XINT_expr_scannum_decpart_b.}%
+ (-.#1*\dummy \XINT_flexpr_getnext%
+ (-.+#1\dummy {\XINT_flexpr_scannum_start\XINT_expr_scannum_decpart_b*}%
+ (-.+*\dummy {\XINT_flexpr_scannum_check #1}%
+ \krof
+}}%
+\def\XINT_flexpr_scannum_check #1%
+{%
+ \ifnum \xint_c_ix<1#1
+ \expandafter\XINT_flexpr_scannum_start
+ \else
+ \xint_afterfi
+ {\XINT_expr_unexpectedtoken
+ \expandafter\XINT_flexpr_getnext\xint_gobble_ii}%
+ \fi \XINT_expr_scannum_intpart_b #1%
+}%
+\def\XINT_flexpr_scannum_start #1%
+{%
+ \expandafter\XINT_flexpr_getop
+ \romannumeral-`0\expandafter\XINT_expr_gathernum
+ \romannumeral-`0#1%
+}%
+\catcode`* 13
+\def\xintNewExpr #1[#2]#3%
+{%
+ \begingroup
+ \ifcase #2\relax
+ \toks0 {\xdef #1}%
+ \or \toks0 {\xdef #1##1}%
+ \or \toks0 {\xdef #1##1##2}%
+ \or \toks0 {\xdef #1##1##2##3}%
+ \or \toks0 {\xdef #1##1##2##3##4}%
+ \or \toks0 {\xdef #1##1##2##3##4##5}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6##7}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6##7##8}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6##7##8##9}%
+ \else
+ \immediate\write-1{Package xintexpr Error! illegal number of macro
+ parameters.}%
+ \fi
+ \def\xintAdd {:xintAdd}%
+ \def\xintSub {:xintSub}%
+ \def\xintMul {:xintMul}%
+ \def\xintDiv {:xintDiv}%
+ \def\xintfPow {:xintfPow}%
+ \def\xintfFac {:xintfFac}%
+ \def\xintOpp {:xintOpp}%
+ \def\xintfE {:xintfE}%
+ \def\xintraw { :romannumeral0:xintraw}%
+ \def\XINT_expr_the ##1##2##3%
+ {\expandafter\xintraw
+ \expandafter{\romannumeral-`0\XINT_expr_string ##3}}%
+ \lccode`\*=`: \lowercase {\def*}{!noexpand!}%
+ \catcode`: 13
+ \endlinechar -1
+ \everyeof {\noexpand }%
+ \edef\xintNewExprtmp
+ {\expandafter\scantokens
+ \expandafter{\romannumeral0\xinttheeval #3\relax}}%
+ \lccode`\*=`_ \lowercase {\def*}{####}%
+ \catcode`_ 13 \catcode`! 0 \catcode`: 11
+ \the\toks0 {\expandafter\scantokens\expandafter{\xintNewExprtmp }}%
+\endgroup
+}%
+\def\xintNewFloatExpr #1[#2]#3%
+{%
+ \begingroup
+ \ifcase #2\relax
+ \toks0 {\xdef #1}%
+ \or \toks0 {\xdef #1##1}%
+ \or \toks0 {\xdef #1##1##2}%
+ \or \toks0 {\xdef #1##1##2##3}%
+ \or \toks0 {\xdef #1##1##2##3##4}%
+ \or \toks0 {\xdef #1##1##2##3##4##5}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6##7}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6##7##8}%
+ \or \toks0 {\xdef #1##1##2##3##4##5##6##7##8##9}%
+ \else
+ \immediate\write-1{Package xintexpr Error! illegal number of macro
+ parameters.}%
+ \fi
+ \def\XINTinFloatAdd {:XINTinFloatAdd}%
+ \def\XINTinFloatSub {:XINTinFloatSub}%
+ \def\XINTinFloatMul {:XINTinFloatMul}%
+ \def\XINTinFloatDiv {:XINTinFloatDiv}%
+ \def\XINTinFloatPower {:XINTinFloatPower}%
+ \def\xintfFac {:xintfFac}%
+ \def\xintOpp {:xintOpp}%
+ \def\XINTinFloatfE {:XINTinFloatfE}%
+ \def\xintfloat { :romannumeral0:xintfloat}%
+ \def\XINT_flexpr_the ##1##2##3%
+ {\expandafter\xintfloat
+ \expandafter{\romannumeral-`0\XINT_expr_string ##3}}%
+ \lccode`\*=`: \lowercase {\def*}{!noexpand!}%
+ \catcode`: 13
+ \endlinechar -1
+ \everyeof {\noexpand }%
+ \edef\xintNewExprtmp
+ {\expandafter\scantokens
+ \expandafter{\romannumeral0\xintthefloateval #3\relax}}%
+ \lccode`\*=`_ \lowercase {\def*}{####}%
+ \catcode`_ 13 \catcode`! 0 \catcode`: 11
+ \the\toks0 {\expandafter\scantokens\expandafter{\xintNewExprtmp }}%
+\endgroup
+}%
+\XINT_expr_restorecatcodes_endinput%
+\endinput
+%%
+%% End of file `xintexpr.sty'.
diff --git a/Master/texmf-dist/tex/generic/xint/xintfrac.sty b/Master/texmf-dist/tex/generic/xint/xintfrac.sty
index a63770ad592..a6678ac73c6 100644
--- a/Master/texmf-dist/tex/generic/xint/xintfrac.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintfrac.sty
@@ -22,7 +22,7 @@
%% in the same archive or directory.)
%%
%%----------------------------------------------------------------
-%% The xint bundle (version 1.06b of May 14, 2013)
+%% The xint bundle (version 1.07a of May 26, 2013)
%% xintfrac: Expandable operations on fractions
%% Copyright (C) 2013 by Jean-Francois Burnol
%%----------------------------------------------------------------
@@ -166,7 +166,7 @@
\fi
\expandafter\x\csname ver@xintfrac.sty\endcsname
\ProvidesPackage{xintfrac}%
- [2013/05/14 v1.06b Expandable operations on fractions (jfB)]%
+ [2013/05/26 v1.07a Expandable operations on fractions (jfB)]%
\def\xintLen {\romannumeral0\xintlen }%
\def\xintlen #1%
{%
@@ -243,32 +243,52 @@
{%
\xint_UDwfork
#2\dummy \XINT_frac_A
- \W\dummy {\expandafter\XINT_frac_B \romannumeral-`0#2}%
+ \W\dummy {\expandafter\XINT_frac_U \romannumeral-`0#2}%
\krof
- #3.\W\Z #1.\W\Z
+ #3e\W\Z #1e\W\Z
}%
+\def\XINT_frac_U #1e#2#3\Z
+{%
+ \xint_UDwfork
+ #2\dummy \XINT_frac_Ua
+ \W\dummy {\XINT_frac_Ub #2}%
+ \krof
+ #3\Z #1\Z
+}%
+\def\XINT_frac_Ua \Z #1/\W\Z {\XINT_frac_B #1.\W\Z {0}}%
+\def\XINT_frac_Ub #1/\W e\W\Z #2\Z {\XINT_frac_B #2.\W\Z {#1}}%
\def\XINT_frac_B #1.#2#3\Z
{%
\xint_UDwfork
- #2\dummy \XINT_frac_Ba
+ #2\dummy \XINT_frac_Ba
\W\dummy {\XINT_frac_Bb #2}%
\krof
#3\Z #1\Z
}%
-\def\XINT_frac_Bb #1/\W.\W\Z #2\Z
+\def\XINT_frac_Ba \Z #1\Z {\XINT_frac_T {0}{#1}}%
+\def\XINT_frac_Bb #1.\W\Z #2\Z
{%
- \expandafter \XINT_frac_C \expandafter
+ \expandafter \XINT_frac_T \expandafter
{\romannumeral0\XINT_length {#1}}{#2#1}%
}%
-\def\XINT_frac_Ba \Z #1/\W\Z {\XINT_frac_C {0}{#1}}%
-\def\XINT_frac_A .\W\Z {\XINT_frac_C {0}{1}}%
-\def\XINT_frac_C #1#2#3.#4#5\Z
+\def\XINT_frac_A e\W\Z {\XINT_frac_T {0}{1}{0}}%
+\def\XINT_frac_T #1#2#3#4e#5#6\Z
{%
\xint_UDwfork
- #4\dummy \XINT_frac_Ca
- \W\dummy {\XINT_frac_Cb #4}%
+ #5\dummy \XINT_frac_Ta
+ \W\dummy {\XINT_frac_Tb #5}%
\krof
- #5\Z #3\Z {#1}{#2}%
+ #6\Z #4\Z {#1}{#2}{#3}%
+}%
+\def\XINT_frac_Ta \Z #1\Z {\XINT_frac_C #1.\W\Z {0}}%
+\def\XINT_frac_Tb #1e\W\Z #2\Z {\XINT_frac_C #2.\W\Z {#1}}%
+\def\XINT_frac_C #1.#2#3\Z
+{%
+ \xint_UDwfork
+ #2\dummy \XINT_frac_Ca
+ \W\dummy {\XINT_frac_Cb #2}%
+ \krof
+ #3\Z #1\Z
}%
\def\XINT_frac_Ca \Z #1\Z {\XINT_frac_D {0}{#1}}%
\def\XINT_frac_Cb #1.\W\Z #2\Z
@@ -276,14 +296,14 @@
\expandafter\XINT_frac_D\expandafter
{\romannumeral0\XINT_length {#1}}{#2#1}%
}%
-\def\XINT_frac_D #1#2#3#4%
+\def\XINT_frac_D #1#2#3#4#5#6%
{%
\expandafter \XINT_frac_E \expandafter
- {\the\numexpr -#1+#3\expandafter}\expandafter
+ {\the\numexpr -#1+#3+#4-#6\expandafter}\expandafter
{\romannumeral0\XINT_num_loop #2%
\xint_relax\xint_relax\xint_relax\xint_relax
\xint_relax\xint_relax\xint_relax\xint_relax\Z }%
- {\romannumeral0\XINT_num_loop #4%
+ {\romannumeral0\XINT_num_loop #5%
\xint_relax\xint_relax\xint_relax\xint_relax
\xint_relax\xint_relax\xint_relax\xint_relax\Z }%
}%
@@ -407,21 +427,27 @@
{%
\expandafter\XINT_raw\romannumeral0\XINT_infrac
}%
-\def\XINT_raw #1%
+\def\XINT_raw #1#2#3{ #2/#3[#1]}%
+\def\xintRawWithZeros {\romannumeral0\xintrawwithzeros }%
+\def\xintrawwithzeros
+{%
+ \expandafter\XINT_rawz\romannumeral0\XINT_infrac
+}%
+\def\XINT_rawz #1%
{%
\ifcase\XINT_Sgn {#1}
- \expandafter\XINT_raw_Ba
+ \expandafter\XINT_rawz_Ba
\or
- \expandafter\XINT_raw_A
+ \expandafter\XINT_rawz_A
\else
- \expandafter\XINT_raw_Ba
+ \expandafter\XINT_rawz_Ba
\fi
{#1}%
}%
-\def\XINT_raw_A #1#2#3{\xint_dsh {#2}{-#1}/#3}%
-\def\XINT_raw_Ba #1#2#3{\expandafter\XINT_raw_Bb
+\def\XINT_rawz_A #1#2#3{\xint_dsh {#2}{-#1}/#3}%
+\def\XINT_rawz_Ba #1#2#3{\expandafter\XINT_rawz_Bb
\expandafter{\romannumeral0\xint_dsh {#3}{#1}}{#2}}%
-\def\XINT_raw_Bb #1#2{ #2/#1}%
+\def\XINT_rawz_Bb #1#2{ #2/#1}%
\def\xintNumerator {\romannumeral0\xintnumerator }%
\def\xintnumerator
{%
@@ -593,10 +619,30 @@
{\the\numexpr #3+#4-#2}{#1}{#5}%
}%
\def\XINT_rez_E #1#2#3{ #3/#2[#1]}%
+\def\xintE {\romannumeral0\xinte }%
+\def\xinte #1%
+{%
+ \expandafter\XINT_e \romannumeral0\XINT_infrac {#1}%
+}%
+\def\XINT_e #1#2#3#4%
+{%
+ \expandafter\XINT_e_end\expandafter{\the\numexpr #1+#4}{#2}{#3}%
+}%
+\def\xintfE {\romannumeral0\xintfe }%
+\def\xintfe #1%
+{%
+ \expandafter\XINT_fe \romannumeral0\XINT_infrac {#1}%
+}%
+\def\XINT_fe #1#2#3#4%
+{%
+ \expandafter\XINT_e_end\expandafter{\the\numexpr #1+\xintNum{#4}}{#2}{#3}%
+}%
+\def\XINT_e_end #1#2#3{ #2/#3[#1]}%
+\let\XINTinFloatfE\xintfE
\def\xintIrr {\romannumeral0\xintirr }%
\def\xintirr #1%
{%
- \expandafter\XINT_irr_start\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_irr_start\romannumeral0\xintrawwithzeros {#1}\Z
}%
\def\XINT_irr_start #1#2/#3\Z
{%
@@ -666,10 +712,15 @@
\xintError:NotAnInteger
\space #1%
}%
+\def\xintfFac {\romannumeral0\xintffac }%
+\def\xintffac #1%
+{%
+ \expandafter\XINT_fac_fork\expandafter{\the\numexpr \xintNum{#1}}%
+}%
\def\xintJrr {\romannumeral0\xintjrr }%
\def\xintjrr #1%
{%
- \expandafter\XINT_jrr_start\romannumeral0\xintraw {#1}\Z
+ \expandafter\XINT_jrr_start\romannumeral0\xintrawwithzeros {#1}\Z
}%
\def\XINT_jrr_start #1#2/#3\Z
{%
@@ -826,7 +877,7 @@
\def\XINT_trunc_Hb #1#2#3%
{%
\expandafter #3\expandafter0\expandafter.%
- \romannumeral0\XINT_dsx_zeroloop {#1}\Z {}#2% #1=-0 possible!
+ \romannumeral0\XINT_dsx_zeroloop {#1}{}\Z {}#2% #1=-0 possible!
}%
\def\xintRound {\romannumeral0\xintround }%
\def\xintiRound {\romannumeral0\xintiround }%
@@ -892,6 +943,241 @@
{%
\XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z \Z
}%
+\mathchardef\XINT_digits 16
+\def\xintDigits #1#2%
+ {\afterassignment \xint_gobble_i \mathchardef\XINT_digits=}%
+\def\xinttheDigits {\number\XINT_digits }%
+\def\xintFloat {\romannumeral0\xintfloat }%
+\def\xintfloat #1{\XINT_float_chkopt #1\Z }%
+\def\XINT_float_chkopt #1%
+{%
+ \ifx #1[\expandafter\XINT_float_opt
+ \else\expandafter\XINT_float_noopt
+ \fi #1%
+}%
+\def\XINT_float_noopt #1\Z
+{%
+ \XINT_float_a \XINT_digits {#1}%
+}%
+\def\XINT_float_opt [\Z #1]%
+{%
+ \expandafter\XINT_float_a\expandafter {\the\numexpr #1}%
+}%
+\def\XINT_float_a #1#2%
+{%
+ \expandafter\XINT_float_b \romannumeral0\XINT_infrac {#2}{#1}%
+}%
+\def\XINT_float_b #1#2#3%
+{%
+ \XINT_float_fork #2\Z {#3}{#1}%
+}%
+\def\XINT_float_fork #1%
+{%
+ \xint_UDzerominusfork
+ #1-\dummy \XINT_float_zero
+ 0#1\dummy \XINT_float_N
+ 0-\dummy {\XINT_float_P #1}%
+ \krof
+}%
+\def\XINT_float_zero \Z #1#2#3{ 0.e0}%
+\def\XINT_float_N {\expandafter\xint_minus_andstop\romannumeral0\XINT_float_P }%
+\def\XINT_float_P #1\Z #2#3#4%
+{%
+ \ifcase \romannumeral0\XINT_fgeq_A 011{#3}{#1}{#2}
+ \expandafter\XINT_float_lessthanone_a
+ \or\expandafter\XINT_float_atleastone_b
+ \fi {#3}{#1}{#2}{#3+#4}{#1}{#2}%
+}%
+\def\XINT_float_atleastone_b
+{%
+ \expandafter\XINT_float_atleastone_c\romannumeral0\XINT_trunc_B
+}%
+\def\XINT_float_atleastone_c #1\Z #2%
+{%
+ \expandafter\XINT_float_c\expandafter
+ {\romannumeral0\xintisub {\xintLength{#1}}{1}}%
+}%
+\def\XINT_float_lessthanone_a #1%
+{%
+ \expandafter\XINT_float_lessthanone_b\expandafter
+ {\the\numexpr -#1}%
+}%
+\def\XINT_float_lessthanone_b #1#2#3%
+{%
+ \expandafter\XINT_float_lessthanone_c
+ \romannumeral0\XINT_trunc_B {#1}{#3}{#2}%
+}%
+\def\XINT_float_lessthanone_c #1\Z #2%
+{%
+ \expandafter\XINT_float_c\expandafter
+ {\expandafter-\romannumeral0\xintilen {\xintiSub {#1}{1}}}%
+}%
+\def\XINT_float_c #1#2#3#4%
+{%
+ \expandafter\XINT_float_d\expandafter
+ {\the\numexpr #2-#1}{#3}{#4}e#1%
+}%
+\def\XINT_float_d
+{%
+ \expandafter\XINT_float_round_B\romannumeral0\XINT_trunc_B
+}%
+\def\XINT_float_round_B #1#2\Z #3%
+{%
+ \ifnum #1=9
+ \xint_afterfi
+ {\romannumeral0\XINT_rord_main {}#1#2\XINT_float_round_S}%
+ \else
+ \xint_afterfi
+ {\romannumeral0\XINT_rord_main {}#1#2\XINT_float_round_D}%
+ \fi
+ \xint_relax
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_relax
+ \Z
+}%
+\def\XINT_float_round_D #1%
+{%
+ \ifnum #1<5
+ \expandafter\XINT_float_round_Da
+ \else
+ \expandafter\XINT_float_round_Db
+ \fi
+}%
+\def\XINT_float_round_Da #1\Z
+{%
+ \expandafter\XINT_float_round_f
+ \romannumeral0\XINT_rord_main {}#1%
+ \xint_relax
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_relax
+}%
+\def\XINT_float_round_Db #1\Z
+{%
+ \expandafter\XINT_float_round_f
+ \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z
+}%
+\def\XINT_float_round_f #1{ #1.}%
+\def\XINT_float_round_S #1%
+{%
+ \ifnum #1<5
+ \expandafter\XINT_float_round_Da
+ \else
+ \expandafter\XINT_float_round_Sb
+ \fi
+}%
+\def\XINT_float_round_Sb #1\Z
+{%
+ \expandafter\XINT_float_round_g
+ \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z
+}%
+\def\XINT_float_round_g #1%
+{%
+ \ifnum #1=1 \expandafter\XINT_float_round_h\fi
+ \space #1.%
+}%
+\def\XINT_float_round_h\space 1.0{ 10.}%
+\def\XINT_inFloat [#1]%
+{%
+ \expandafter\XINT_infloat\expandafter {\the\numexpr #1}%
+}%
+\def\XINT_infloat #1#2%
+{%
+ \expandafter\XINT_infloat_a \romannumeral0\XINT_infrac {#2}{#1}%
+}%
+\def\XINT_infloat_a #1#2#3%
+{%
+ \XINT_infloat_fork #2\Z {#3}{#1}%
+}%
+\def\XINT_infloat_fork #1%
+{%
+ \xint_UDzerominusfork
+ #1-\dummy \XINT_infloat_zero
+ 0#1\dummy \XINT_infloat_N
+ 0-\dummy {\XINT_infloat_P #1}%
+ \krof
+}%
+\def\XINT_infloat_zero\Z #1#2#3{0[0]}%
+\def\XINT_infloat_N {\expandafter-\romannumeral-`0\XINT_infloat_P }%
+\def\XINT_infloat_P #1\Z #2#3#4%
+{%
+ \ifcase \romannumeral0\XINT_fgeq_A 011{#3}{#1}{#2}
+ \expandafter\XINT_infloat_lessthanone_a
+ \or\expandafter\XINT_infloat_atleastone_b
+ \fi {#3}{#1}{#2}{#3+#4}{#1}{#2}{#4}%
+}%
+\def\XINT_infloat_atleastone_b
+{%
+ \expandafter\XINT_infloat_atleastone_c\romannumeral0\XINT_trunc_B
+}%
+\def\XINT_infloat_atleastone_c #1\Z #2%
+{%
+ \expandafter\XINT_infloat_c\expandafter
+ {\romannumeral0\xintisub {\xintLength{#1}}{1}}%
+}%
+\def\XINT_infloat_lessthanone_a #1%
+{%
+ \expandafter\XINT_infloat_lessthanone_b\expandafter
+ {\the\numexpr -#1}%
+}%
+\def\XINT_infloat_lessthanone_b #1#2#3%
+{%
+ \expandafter\XINT_infloat_lessthanone_c
+ \romannumeral0\XINT_trunc_B {#1}{#3}{#2}%
+}%
+\def\XINT_infloat_lessthanone_c #1\Z #2%
+{%
+ \expandafter\XINT_infloat_c\expandafter
+ {\expandafter-\romannumeral0\xintilen {\xintiSub {#1}{1}}}%
+}%
+\def\XINT_infloat_c #1#2#3#4%
+{%
+ \expandafter\XINT_infloat_d\expandafter
+ {\the\numexpr #2-#1}{#3}{#4}{#1}%
+}%
+\def\XINT_infloat_d
+{%
+ \expandafter\XINT_infloat_round_B\romannumeral0\XINT_trunc_B
+}%
+\def\XINT_infloat_round_B #1\Z #2%
+{%
+ \expandafter\XINT_infloat_round_D
+ \romannumeral0\XINT_rord_main {}#1%
+ \xint_relax
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_relax
+ \Z
+}%
+\def\XINT_infloat_round_D #1%
+{%
+ \ifnum #1<5
+ \expandafter\XINT_infloat_round_Da
+ \else
+ \expandafter\XINT_infloat_round_Db
+ \fi
+}%
+\def\XINT_infloat_round_Da #1\Z
+{%
+ \expandafter\XINT_infloat_round_f
+ \romannumeral0\XINT_rord_main {}#1%
+ \xint_relax
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_relax \Z
+}%
+\def\XINT_infloat_round_Db #1\Z
+{%
+ \expandafter\XINT_infloat_round_f
+ \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z \Z
+}%
+\def\XINT_infloat_round_f #1\Z #2#3%
+{%
+ \expandafter\XINT_infloat_round_g\expandafter
+ {\the\numexpr #2-#3+1}{#1}%
+}%
+\def\XINT_infloat_round_g #1#2{#2[#1]}%
\def\xintAdd {\romannumeral0\xintadd }%
\def\xintadd #1%
{%
@@ -1002,10 +1288,19 @@
{%
\expandafter\xint_fpow\expandafter {\romannumeral0\XINT_infrac {#1}}%
}%
+\def\xintfPow {\romannumeral0\xintfpow }%
+\def\xintfpow #1%
+{%
+ \expandafter\xint_ffpow\expandafter {\romannumeral0\XINT_infrac {#1}}%
+}%
\def\xint_fpow #1#2%
{%
\expandafter\XINT_fpow_fork\the\numexpr #2\relax\Z #1%
}%
+\def\xint_ffpow #1#2%
+{%
+ \expandafter\XINT_fpow_fork\the\numexpr \xintNum{#2}\relax\Z #1%
+}%
\def\XINT_fpow_fork #1#2\Z
{%
\xint_UDzerominusfork
@@ -1098,6 +1393,34 @@
{\romannumeral0\xintimul {\xintDSH {\the\numexpr -#3+#1\relax}{#6}}{#5}}%
{\romannumeral0\xintimul {#7}{\xintDSH {\the\numexpr -#2+#1\relax}{#4}}}%
}%
+\def\xintGeq {\romannumeral0\xintgeq }%
+\def\xintgeq #1%
+{%
+ \expandafter\xint_fgeq\expandafter {\romannumeral0\XINT_infrac {#1}}%
+}%
+\def\xint_fgeq #1#2%
+{%
+ \expandafter\XINT_fgeq_A \romannumeral0\XINT_infrac {#2}#1%
+}%
+\def\XINT_fgeq_A #1#2#3#4%
+{%
+ \ifnum #4 > #1
+ \xint_afterfi {\XINT_fgeq_B {#1}}%
+ \else
+ \xint_afterfi {\XINT_fgeq_B {#4}}%
+ \fi
+ {#1}{#4}{#2}{#3}%
+}%
+\def\XINT_fgeq_B #1#2#3#4#5#6#7%
+{%
+ \expandafter\XINT_fgeq_C\expandafter
+ {\romannumeral0\xintimul {\xintDSH {\the\numexpr -#3+#1\relax}{#6}}{#5}}%
+ {\romannumeral0\xintimul {#7}{\xintDSH {\the\numexpr -#2+#1\relax}{#4}}}%
+}%
+\def\XINT_fgeq_C #1#2%
+{%
+ \expandafter\XINT_geq_fork #2\Z #1\Z
+}%
\def\xintMax {\romannumeral0\xintmax }%
\def\xintmax #1%
{%
@@ -1183,15 +1506,6 @@
\expandafter\xint_fsgn\romannumeral0\XINT_infrac {#1}%
}%
\def\xint_fsgn #1#2#3{\xintisgn {#2}}%
-\def\xintGeq {\romannumeral0\xintgeq }%
-\def\xintgeq #1%
-{%
- \expandafter\xint_xgeq\expandafter{\romannumeral0\xintnum {#1}}%
-}%
-\def\xint_xgeq #1#2%
-{%
- \expandafter\XINT_geq_fork\romannumeral0\xintnum {#2}\Z #1\Z
-}%
\def\xintDivision {\romannumeral0\xintdivision }%
\def\xintdivision #1%
{%
@@ -1244,6 +1558,365 @@
\xint_afterfi{ 0}%
\fi
}%
+\def\xintFloatAdd {\romannumeral0\xintfloatadd }%
+\def\xintfloatadd #1{\XINT_fladd_chkopt \xintfloat #1\Z }%
+\def\XINTinFloatAdd {\romannumeral-`0\XINTinfloatadd }%
+\def\XINTinfloatadd #1{\XINT_fladd_chkopt \XINT_inFloat #1\Z }%
+\def\XINT_fladd_chkopt #1#2%
+{%
+ \ifx #2[\expandafter\XINT_fladd_opt
+ \else\expandafter\XINT_fladd_noopt
+ \fi #1#2%
+}%
+\def\XINT_fladd_noopt #1#2\Z #3%
+{%
+ #1[\XINT_digits]{\XINT_FL_Add {\XINT_digits+2}{#2}{#3}}%
+}%
+\def\XINT_fladd_opt #1[\Z #2]#3#4%
+{%
+ #1[#2]{\XINT_FL_Add {#2+2}{#3}{#4}}%
+}%
+\def\XINT_FL_Add #1#2%
+{%
+ \expandafter\XINT_FL_Add_a\expandafter{\the\numexpr #1\expandafter}%
+ \expandafter{\romannumeral-`0\XINT_inFloat [#1]{#2}}%
+}%
+\def\XINT_FL_Add_a #1#2#3%
+{%
+ \expandafter\XINT_FL_Add_b\romannumeral-`0\XINT_inFloat [#1]{#3}#2{#1}%
+}%
+\def\XINT_FL_Add_b #1%
+{%
+ \xint_gob_til_zero #1\XINT_FL_Add_zero 0\XINT_FL_Add_c #1%
+}%
+\def\XINT_FL_Add_c #1[#2]#3%
+{%
+ \xint_gob_til_zero #3\XINT_FL_Add_zerobis 0\XINT_FL_Add_d #1[#2]#3%
+}%
+\def\XINT_FL_Add_d #1[#2]#3[#4]#5%
+{%
+ \xintSgnFork {\ifnum \numexpr #2-#4-#5>1 \expandafter 1%
+ \else\ifnum \numexpr #4-#2-#5>1
+ \xint_afterfi {\expandafter-\expandafter1}%
+ \else \expandafter\expandafter\expandafter0%
+ \fi
+ \fi}%
+ {#3[#4]}{\xintAdd {#1[#2]}{#3[#4]}}{#1[#2]}%
+}%
+\def\XINT_FL_Add_zero 0\XINT_FL_Add_c 0[0]#1[#2]#3{#1[#2]}%
+\def\XINT_FL_Add_zerobis 0\XINT_FL_Add_d #1[#2]0[0]#3{#1[#2]}%
+\def\xintFloatSub {\romannumeral0\xintfloatsub }%
+\def\xintfloatsub #1{\XINT_flsub_chkopt \xintfloat #1\Z }%
+\def\XINTinFloatSub {\romannumeral-`0\XINTinfloatsub }%
+\def\XINTinfloatsub #1{\XINT_flsub_chkopt \XINT_inFloat #1\Z }%
+\def\XINT_flsub_chkopt #1#2%
+{%
+ \ifx #2[\expandafter\XINT_flsub_opt
+ \else\expandafter\XINT_flsub_noopt
+ \fi #1#2%
+}%
+\def\XINT_flsub_noopt #1#2\Z #3%
+{%
+ #1[\XINT_digits]{\XINT_FL_Add {\XINT_digits+2}{#2}{\xintOpp{#3}}}%
+}%
+\def\XINT_flsub_opt #1[\Z #2]#3#4%
+{%
+ #1[#2]{\XINT_FL_Add {#2+2}{#3}{\xintOpp{#4}}}%
+}%
+\def\xintFloatMul {\romannumeral0\xintfloatmul}%
+\def\xintfloatmul #1{\XINT_flmul_chkopt \xintfloat #1\Z }%
+\def\XINTinFloatMul {\romannumeral-`0\XINTinfloatmul }%
+\def\XINTinfloatmul #1{\XINT_flmul_chkopt \XINT_inFloat #1\Z }%
+\def\XINT_flmul_chkopt #1#2%
+{%
+ \ifx #2[\expandafter\XINT_flmul_opt
+ \else\expandafter\XINT_flmul_noopt
+ \fi #1#2%
+}%
+\def\XINT_flmul_noopt #1#2\Z #3%
+{%
+ #1[\XINT_digits]{\XINT_FL_Mul {\XINT_digits+2}{#2}{#3}}%
+}%
+\def\XINT_flmul_opt #1[\Z #2]#3#4%
+{%
+ #1[#2]{\XINT_FL_Mul {#2+2}{#3}{#4}}%
+}%
+\def\XINT_FL_Mul #1#2%
+{%
+ \expandafter\XINT_FL_Mul_a\expandafter{\the\numexpr #1\expandafter}%
+ \expandafter{\romannumeral-`0\XINT_inFloat [#1]{#2}}%
+}%
+\def\XINT_FL_Mul_a #1#2#3%
+{%
+ \expandafter\XINT_FL_Mul_b\romannumeral-`0\XINT_inFloat [#1]{#3}#2%
+}%
+\def\XINT_FL_Mul_b #1[#2]#3[#4]{\xintE{\xintiMul {#1}{#3}}{#2+#4}}%
+\def\xintFloatDiv {\romannumeral0\xintfloatdiv}%
+\def\xintfloatdiv #1{\XINT_fldiv_chkopt \xintfloat #1\Z }%
+\def\XINTinFloatDiv {\romannumeral-`0\XINTinfloatdiv }%
+\def\XINTinfloatdiv #1{\XINT_fldiv_chkopt \XINT_inFloat #1\Z }%
+\def\XINT_fldiv_chkopt #1#2%
+{%
+ \ifx #2[\expandafter\XINT_fldiv_opt
+ \else\expandafter\XINT_fldiv_noopt
+ \fi #1#2%
+}%
+\def\XINT_fldiv_noopt #1#2\Z #3%
+{%
+ #1[\XINT_digits]{\XINT_FL_Div {\XINT_digits+2}{#2}{#3}}%
+}%
+\def\XINT_fldiv_opt #1[\Z #2]#3#4%
+{%
+ #1[#2]{\XINT_FL_Div {#2+2}{#3}{#4}}%
+}%
+\def\XINT_FL_Div #1#2%
+{%
+ \expandafter\XINT_FL_Div_a\expandafter{\the\numexpr #1\expandafter}%
+ \expandafter{\romannumeral-`0\XINT_inFloat [#1]{#2}}%
+}%
+\def\XINT_FL_Div_a #1#2#3%
+{%
+ \expandafter\XINT_FL_Div_b\romannumeral-`0\XINT_inFloat [#1]{#3}#2%
+}%
+\def\XINT_FL_Div_b #1[#2]#3[#4]{\xintE{#3/#1}{#4-#2}}%
+\def\xintFloatPow {\romannumeral0\xintfloatpow}%
+\def\xintfloatpow #1{\XINT_flpow_chkopt \xintfloat #1\Z }%
+\def\XINTinFloatPow {\romannumeral-`0\XINTinfloatpow }%
+\def\XINTinfloatpow #1{\XINT_flpow_chkopt \XINT_inFloat #1\Z }%
+\def\XINT_flpow_chkopt #1#2%
+{%
+ \ifx #2[\expandafter\XINT_flpow_opt
+ \else\expandafter\XINT_flpow_noopt
+ \fi
+ #1#2%
+}%
+\def\XINT_flpow_noopt #1#2\Z #3%
+{%
+ \expandafter\XINT_flpow_checkB_start\expandafter
+ {\the\numexpr #3\expandafter}\expandafter
+ {\the\numexpr \XINT_digits}{#2}{#1[\XINT_digits]}%
+}%
+\def\XINT_flpow_opt #1[\Z #2]#3#4%
+{%
+ \expandafter\XINT_flpow_checkB_start\expandafter
+ {\the\numexpr #4\expandafter}\expandafter
+ {\the\numexpr #2}{#3}{#1[#2]}%
+}%
+\def\XINT_flpow_checkB_start #1{\XINT_flpow_checkB_a #1\Z }%
+\def\XINT_flpow_checkB_a #1%
+{%
+ \xint_UDzerominusfork
+ #1-\dummy \XINT_flpow_BisZero
+ 0#1\dummy {\XINT_flpow_checkB_b 1}%
+ 0-\dummy {\XINT_flpow_checkB_b 0#1}%
+ \krof
+}%
+\def\XINT_flpow_BisZero \Z #1#2#3{#3{1/1[0]}}%
+\def\XINT_flpow_checkB_b #1#2\Z #3%
+{%
+ \expandafter\XINT_flpow_checkB_c \expandafter
+ {\romannumeral0\XINT_length{#2}}{#3}{#2}#1%
+}%
+\def\XINT_flpow_checkB_c #1#2%
+{%
+ \expandafter\XINT_flpow_checkB_d \expandafter
+ {\the\numexpr \expandafter\XINT_Length\expandafter
+ {\the\numexpr #1*20/3}+#1+#2+1}%
+}%
+\def\XINT_flpow_checkB_d #1#2#3#4%
+{%
+ \expandafter \XINT_flpow_a
+ \romannumeral-`0\XINT_inFloat [#1]{#4}{#1}{#2}#3%
+}%
+\def\XINT_flpow_a #1%
+{%
+ \xint_UDzerominusfork
+ #1-\dummy \XINT_flpow_zero
+ 0#1\dummy {\XINT_flpow_b 1}%
+ 0-\dummy {\XINT_flpow_b 0#1}%
+ \krof
+}%
+\def\XINT_flpow_zero [#1]#2#3#4#5%
+{%
+ \if #41 \xint_afterfi {\xintError:DivisionByZero\space 1.e2147483647}%
+ \else \xint_afterfi { 0.e0}\fi
+}%
+\def\XINT_flpow_b #1#2[#3]#4#5%
+{%
+ \XINT_flpow_c {#4}{#5}{#2[#3]}{#1*\ifodd #5 1\else 0\fi}%
+}%
+\def\XINT_flpow_c #1#2#3#4%
+{%
+ \XINT_flpow_loop {#1}{#2}{#3}{{#1}}\XINT_flpow_prd
+ \xint_relax
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_relax {#4}%
+}%
+\def\XINT_flpow_loop #1#2#3%
+{%
+ \ifnum #2 = 1
+ \expandafter\XINT_flpow_loop_end
+ \else
+ \xint_afterfi{\expandafter\XINT_flpow_loop_a
+ \expandafter{\the\numexpr 2*(#2/2)-#2\expandafter }% b mod 2
+ \expandafter{\the\numexpr #2-#2/2\expandafter }% [b/2]
+ \expandafter{\romannumeral-`0\XINTinfloatmul [#1]{#3}{#3}}}%
+ \fi
+ {#1}{{#3}}%
+}%
+\def\XINT_flpow_loop_a #1#2#3#4%
+{%
+ \ifnum #1 = 1
+ \expandafter\XINT_flpow_loop
+ \else
+ \expandafter\XINT_flpow_loop_throwaway
+ \fi
+ {#4}{#2}{#3}%
+}%
+\def\XINT_flpow_loop_throwaway #1#2#3#4%
+{%
+ \XINT_flpow_loop {#1}{#2}{#3}%
+}%
+\def\XINT_flpow_loop_end #1{\romannumeral0\XINT_rord_main {}\relax }%
+\def\XINT_flpow_prd #1#2%
+{%
+ \XINT_flpow_prd_getnext {#2}{#1}%
+}%
+\def\XINT_flpow_prd_getnext #1#2#3%
+{%
+ \XINT_flpow_prd_checkiffinished #3\Z {#1}{#2}%
+}%
+\def\XINT_flpow_prd_checkiffinished #1%
+{%
+ \xint_gob_til_relax #1\XINT_flpow_prd_end\relax
+ \XINT_flpow_prd_compute #1%
+}%
+\def\XINT_flpow_prd_compute #1\Z #2#3%
+{%
+ \expandafter\XINT_flpow_prd_getnext\expandafter
+ {\romannumeral-`0\XINTinfloatmul [#3]{#1}{#2}}{#3}%
+}%
+\def\XINT_flpow_prd_end\relax\XINT_flpow_prd_compute
+ \relax\Z #1#2#3%
+{%
+ \expandafter\XINT_flpow_conclude \the\numexpr #3\relax #1%
+}%
+\def\XINT_flpow_conclude #1#2[#3]#4%
+{%
+ \expandafter\XINT_flpow_conclude_really\expandafter
+ {\the\numexpr\if #41 -\fi#3\expandafter}%
+ \xint_UDzerofork
+ #4\dummy {{#2}}%
+ 0\dummy {{1/#2}}%
+ \krof #1%
+}%
+\def\XINT_flpow_conclude_really #1#2#3#4%
+{%
+ \xint_UDzerofork
+ #3\dummy {#4{#2[#1]}}%
+ 0\dummy {#4{-#2[#1]}}%
+ \krof
+}%
+\def\xintFloatPower {\romannumeral0\xintfloatpower}%
+\def\xintfloatpower #1{\XINT_flpower_chkopt \xintfloat #1\Z }%
+\def\XINTinFloatPower {\romannumeral-`0\XINTinfloatpower}%
+\def\XINTinfloatpower #1{\XINT_flpower_chkopt \XINT_inFloat #1\Z }%
+\def\XINT_flpower_chkopt #1#2%
+{%
+ \ifx #2[\expandafter\XINT_flpower_opt
+ \else\expandafter\XINT_flpower_noopt
+ \fi
+ #1#2%
+}%
+\def\XINT_flpower_noopt #1#2\Z #3%
+{%
+ \expandafter\XINT_flpower_checkB_start\expandafter
+ {\the\numexpr \XINT_digits\expandafter}\expandafter
+ {\romannumeral0\xintnum{#3}}{#2}{#1[\XINT_digits]}%
+}%
+\def\XINT_flpower_opt #1[\Z #2]#3#4%
+{%
+ \expandafter\XINT_flpower_checkB_start\expandafter
+ {\the\numexpr #2\expandafter}\expandafter
+ {\romannumeral0\xintnum{#4}}{#3}{#1[#2]}%
+}%
+\def\XINT_flpower_checkB_start #1#2{\XINT_flpower_checkB_a #2\Z {#1}}%
+\def\XINT_flpower_checkB_a #1%
+{%
+ \xint_UDzerominusfork
+ #1-\dummy \XINT_flpower_BisZero
+ 0#1\dummy {\XINT_flpower_checkB_b 1}%
+ 0-\dummy {\XINT_flpower_checkB_b 0#1}%
+ \krof
+}%
+\def\XINT_flpower_BisZero \Z #1#2#3{#3{1/1[0]}}%
+\def\XINT_flpower_checkB_b #1#2\Z #3%
+{%
+ \expandafter\XINT_flpower_checkB_c \expandafter
+ {\romannumeral0\XINT_length{#2}}{#3}{#2}#1%
+}%
+\def\XINT_flpower_checkB_c #1#2%
+{%
+ \expandafter\XINT_flpower_checkB_d \expandafter
+ {\the\numexpr \expandafter\XINT_Length\expandafter
+ {\the\numexpr #1*20/3}+#1+#2+1}%
+}%
+\def\XINT_flpower_checkB_d #1#2#3#4%
+{%
+ \expandafter \XINT_flpower_a
+ \romannumeral-`0\XINT_inFloat [#1]{#4}{#1}{#2}#3%
+}%
+\def\XINT_flpower_a #1%
+{%
+ \xint_UDzerominusfork
+ #1-\dummy \XINT_flpower_zero
+ 0#1\dummy {\XINT_flpower_b 1}%
+ 0-\dummy {\XINT_flpower_b 0#1}%
+ \krof
+}%
+\def\XINT_flpower_zero [#1]#2#3#4#5%
+{%
+ \if #41
+ \xint_afterfi {\xintError:DivisionByZero\space 1.e2147483647}%
+ \else \xint_afterfi { 0.e0}\fi
+}%
+\def\XINT_flpower_b #1#2[#3]#4#5%
+{%
+ \XINT_flpower_c {#4}{#5}{#2[#3]}{#1*\xintOdd {#5}}%
+}%
+\def\XINT_flpower_c #1#2#3#4%
+{%
+ \XINT_flpower_loop {#1}{#2}{#3}{{#1}}\XINT_flpow_prd
+ \xint_relax
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_undef\xint_undef\xint_undef\xint_undef
+ \xint_relax {#4}%
+}%
+\def\XINT_flpower_loop #1#2#3%
+{%
+ \ifcase\XINT_isOne {#2}
+ \xint_afterfi{\expandafter\XINT_flpower_loop_x\expandafter
+ {\romannumeral-`0\XINTinfloatmul [#1]{#3}{#3}}%
+ {\romannumeral0\xintdivision {#2}{2}}}%
+ \or \expandafter\XINT_flpow_loop_end
+ \fi
+ {#1}{{#3}}%
+}%
+\def\XINT_flpower_loop_x #1#2{\expandafter\XINT_flpower_loop_a #2{#1}}%
+\def\XINT_flpower_loop_a #1#2#3#4%
+{%
+ \ifnum #2 = 1
+ \expandafter\XINT_flpower_loop
+ \else
+ \expandafter\XINT_flpower_loop_throwaway
+ \fi
+ {#4}{#1}{#3}%
+}%
+\def\XINT_flpower_loop_throwaway #1#2#3#4%
+{%
+ \XINT_flpower_loop {#1}{#2}{#3}%
+}%
\XINT_frac_restorecatcodes_endinput%
\endinput
%%
diff --git a/Master/texmf-dist/tex/generic/xint/xintgcd.sty b/Master/texmf-dist/tex/generic/xint/xintgcd.sty
index 77bee301efe..702fa0c78a5 100644
--- a/Master/texmf-dist/tex/generic/xint/xintgcd.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintgcd.sty
@@ -22,7 +22,7 @@
%% in the same archive or directory.)
%%
%%----------------------------------------------------------------
-%% The xint bundle (version 1.06b of May 14, 2013)
+%% The xint bundle (version 1.07a of May 26, 2013)
%% xintgcd: Euclidean algorithm with xint package
%% Copyright (C) 2013 by Jean-Francois Burnol
%%----------------------------------------------------------------
@@ -164,7 +164,7 @@
\fi
\expandafter\x\csname ver@xintgcd.sty\endcsname
\ProvidesPackage{xintgcd}%
- [2013/05/14 v1.06b Euclide algorithm with xint package (jfB)]%
+ [2013/05/26 v1.07a Euclide algorithm with xint package (jfB)]%
\def\xintGCD {\romannumeral0\xintgcd }%
\def\xintgcd #1%
{%
diff --git a/Master/texmf-dist/tex/generic/xint/xintseries.sty b/Master/texmf-dist/tex/generic/xint/xintseries.sty
index 7d6c1bc0901..f1b6d882e85 100644
--- a/Master/texmf-dist/tex/generic/xint/xintseries.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintseries.sty
@@ -22,7 +22,7 @@
%% in the same archive or directory.)
%%
%%----------------------------------------------------------------
-%% The xint bundle (version 1.06b of May 14, 2013)
+%% The xint bundle (version 1.07a of May 26, 2013)
%% xintseries: Expandable partial sums with xint package
%% Copyright (C) 2013 by Jean-Francois Burnol
%%----------------------------------------------------------------
@@ -164,7 +164,7 @@
\fi
\expandafter\x\csname ver@xintseries.sty\endcsname
\ProvidesPackage{xintseries}%
- [2013/05/14 v1.06b Expandable partial sums with xint package (jfB)]%
+ [2013/05/26 v1.07a Expandable partial sums with xint package (jfB)]%
\def\xintSeries {\romannumeral0\xintseries }%
\def\xintseries #1#2%
{%
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-18 07:33:39 +0000