diff options
Diffstat (limited to 'Master/texmf-dist/source')
| -rw-r--r-- | Master/texmf-dist/source/generic/xint/xint.dtx | 2961 | ||||
| -rw-r--r-- | Master/texmf-dist/source/generic/xint/xint.ins | 2 |
2 files changed, 1515 insertions, 1448 deletions
diff --git a/Master/texmf-dist/source/generic/xint/xint.dtx b/Master/texmf-dist/source/generic/xint/xint.dtx index dd00e51353d..d7cab49df27 100644 --- a/Master/texmf-dist/source/generic/xint/xint.dtx +++ b/Master/texmf-dist/source/generic/xint/xint.dtx @@ -1,8 +1,8 @@ % -*- coding: iso-latin-1; -*- -% This file: xint.dtx (1.05a, 2013/05/02) +% This file: xint.dtx (1.06, 2013/05/07) %% %%---------------------------------------------------------------- -%% The xint bundle (version 1.05a of May 2nd, 2013) +%% The xint bundle (version 1.06 of May 7th, 2013) %<xint>%% xint: Expandable operations on long numbers %<xintgcd>%% xintgcd: Euclidean algorithm with xint package %<xintfrac>%% xintfrac: Expandable operations on fractions @@ -75,9 +75,9 @@ % \input xintcfrac.sty\relax % (loads xintfrac) % %<*none> -\def\lasttimestamp{Time-stamp: <02-05-2013 17:37:34 CEST BURNOL>} -\def\pkgversion{1.05a} -\def\pkgdate{2013/05/02} +\def\lasttimestamp{Time-stamp: <07-05-2013 19:08:02 CEST jfb>} +\def\pkgversion{1.06} +\def\pkgdate{2013/05/07} \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} @@ -166,6 +166,8 @@ % attention de positionner \toctransition *après* le début de la section % "implémentation de xint" +\def\stripatdot #1.{} + \let\savedsectionline\l@section \etocsetstyle{section}{}{} {\savedsectionline{\numberline{\etocnumber}\etocname}{\etocpage}}{}% @@ -173,9 +175,12 @@ {\begingroup \setlength{\premulticols}{0pt} \setlength{\multicolsep}{0pt} - \setlength{\columnsep}{1em} + \setlength{\columnsep}{1.5em} \begin{multicols}{2}}{} - {\noindent\makebox[2.5em][l]{\etocnumber}\etocname\leaders\etoctoclineleaders\hfill\etocpage\endgraf} + {\noindent\makebox[1.5em][l] + {\ttfamily\expandafter\stripatdot\etocthenumber}% + \etocname\leaders\etoctoclineleaders\hfill + {\normalfont\etocpage}\endgraf} {\end{multicols}\endgroup}% \makeatother @@ -244,6 +249,7 @@ \definecolor{niceone}{RGB}{38,128,192} \usepackage[english]{babel} +\usepackage[autolanguage,np]{numprint} \usepackage[pdfencoding=pdfdoc,bookmarks=true]{hyperref} @@ -349,7 +355,8 @@ pdfpagemode=UseOutlines} \frenchspacing \renewcommand\familydefault\sfdefault -%---- WE WANT TO SEE ALL THOSE NUMBERS +%---- QUICK WAY TO PRINT LONG THINGS, IN PARTICULAR, BUT NOT EXCLUSIVELY, LONG +% NUMBERS \def\allowsplits #1% {% \ifx #1\relax \else #1\hskip 0pt plus 1pt\relax @@ -405,12 +412,14 @@ pdfpagemode=UseOutlines} \section{Raison d'\^etre of these packages} +\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 with - numerators and denominators having strictly less than +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.} + computations, not to mention the time taken by them.} Here are some examples: @@ -437,16 +446,36 @@ Here are some examples: {\xintiSub {\xintiPow {2}{200}}{1}}\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 \np{66172838904}:}\\ +{\color{blue}|\xintTypesetEuclideAlgorithm {179876541573}{66172838904}|} +\xintTypesetEuclideAlgorithm {179876541573}{66172838904} + The first example uses only the base module \xintname, the next two require -loading also the \xintfracname package, which deals with fractions. The last one -requires the \xintgcdname package. The bundle also comprises the \xintseriesname +loading also the \xintfracname package, which deals with fractions. The last two +require the \xintgcdname package. The bundle also comprises the \xintseriesname package, for partial sums of series with fractional coefficients, and -\xintcfracname -for continued fractions computations. +\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 +\hyperref[ssec:Machin]{\color{niceone}{traditional computations of $\pi$ + and $\log 2$}}, or also see the +{\color{niceone}\hyperlink{e-convergents}{computation of the convergents + of $e$}} made with the \xintcfracname package. + +Note that almost all of the computational results interspersed through the +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 -package, which will be mentioned next) all macros performing computations are +package) all macros performing computations are compatible with an expansion-only context. This programming constraint of expandability weighs in a lot on the computation time as the macros may have to shuffle around data containing hundreds of tokens: our current implementation @@ -481,26 +510,30 @@ 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 digits +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 \xintname so far 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 +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} + Package |bigintcalc| by \textsc{Heiko Oberdiek} already provides expandable arithmetic operations on ``big integers'', -exceeding the \TeX{} limits (of &2^{31}-1&), so why another -one? \footnote{this section was written before the +exceeding the \TeX{} limits (of &2^{31}-1&), so why another\footnote{this section was written before the \xintfracname package; the author is not aware of another package allowing expandable computations with arbitrarily big fractions.} - +one? I got started on this in early March 2013, via a thread on the |c.t.tex| usenet group, where \textsc{Ulrich D\,i\,e\,z} used the @@ -514,12 +547,12 @@ try my hands at addition and multiplication. I wrote macros \csa{bigMul} and \csa{bigAdd} which I posted to the newsgroup; they appeared to work comparatively fast. These first -versions did not use the \eTeX{} \csa{numexpr} macro, they worked +versions did not use the \eTeX{} \csa{numexpr} primitive, they worked one digit at a time, having previously stored carry-arithmetic in 1200 macros. -I noticed that the |bigintcalc| package used the \csa{numexpr} -\eTeX{} primitive when available, but (as far as I could tell) not +I noticed that the |bigintcalc| package used\csa{numexpr} +if available, but (as far as I could tell) not to do computations many digits at a time. Using \csa{numexpr} for one digit at a time for \csa{bigAdd} and \csa{bigMul} slowed them a tiny bit but avoided cluttering \TeX{} memory with the 1200 @@ -535,17 +568,6 @@ The present package is the result of this initial questioning. \end{framed} -To see \xintname in action, jump to the -{\color{niceone}\autoref{sec:series}} describing the commands of the -\xintseriesname{} package, especially as illustrated with the -\hyperref[ssec:Machin]{\color{niceone}{traditional computations of $\pi$ - and $\log 2$}}, or also see the -{\color{niceone}\hyperlink{e-convergents}{computation of the convergents - of $e$}} made with the \xintcfracname package. Note that almost all -of the computational results interspersed through the 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. \section{Expansions} @@ -566,13 +588,12 @@ of course in an |\edef|. \edef\x{\xintQuo{\xintPow {2}{1000}}{\xintFac{100}}} \edef\y{\xintLen{\x}} -Furthermore the package macros give their final results in two -expansion steps. They twice expand their arguments so that they -can be arbitrarily chained. Hence \centeredline{% - |\xintLen{\xintQuo{\xintPow{2}{1000}}{\xintFac{100}}}|} expands -in two steps and tells us that &[2^{1000}/100!]& has {\y} -digits. This is not so many, let us print them here: -\printnumber\x. +Furthermore the package macros give their final results in two expansion steps. +They expand `fully' (the first token of) their arguments so that they can be +arbitrarily chained. Hence \centeredline{% + |\xintLen{\xintQuo{\xintPow{2}{1000}}{\xintFac{100}}}|} expands in two steps +and tells us that &[2^{1000}/100!]& has {\y} digits. This is not so many, let us +print them here: \printnumber\x. For the sake of typesetting this documentation and not have big numbers extend into the margin and go beyond the page physical limits, I use @@ -585,112 +606,176 @@ these commands (not provided by the package): % Expands twice before printing. \end{verbatim} -The |\printnumber| macro is not part of the package and would need -additional thinking for more general use. It may be used as -|\printnumber {\xintQuo{\xintPow {2}{1000}}{\xintFac{100}}}|, or -as |\printnumber\mynumber| if the macro |\mynumber| was previously -defined via |\edef\mynumber {\|\texttt{xintQuo}|{\xintPow - {2}{1000}}{\xintFac{100}}}|. A |\newcommand| or |\def| for the -definition of |\mynumber| would not do for the reason which is -explained in \autoref{item:xpxp} below (it would if we had inserted -seven, and not only three |\expandafter|'s in the definition of |\printnumber|). +The |\printnumber| macro is not part of the package and would need additional +thinking for more general use. 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 + {2}{1000}}{\xintFac{100}}}|}% +or as + |\expandafter\printnumber\expandafter{\mynumber}|, if the macro |\mynumber| is + defined by a |\newcommand| or a |\def| (see below {\color{niceone}\autoref{item:xpxp}} for the + underlying expansion issue; adding four |\expandafter|'s to |\printnumber| + 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|} -\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. -Important points, to be noted, related to the double expansion of arguments: + +Important points, to be noted, related to the expansion of arguments: \begin{enumerate} -\item When I say that the macros expand twice their arguments, - this means that they expand the first token seen (for each - argument), then expand again the first token of the result of - the first expansion. For example - \centeredline{|\def\x{12}\def\y{34}|% - |\xintAdd {\x}{\x\y}|} is \emph{not} a legal construct. 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. +\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}|% + |\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. \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 - explain that the twice expansion will act only on the minus sign, + explain that the expansion will act only on the minus sign, hence do nothing. The only way is to use the \csb{xintOpp} macro, which replaces a number with its opposite. \def\x {12}% +\def\AplusBC #1#2#3{\xintAdd {#1}{\xintMul {#2}{#3}}}% + + \item \label{item:xpxp} With the definition \centeredline{% |\def\AplusBC #1#2#3{\xintAdd {#1}{\xintMul {#2}{#3}}}|} one obtains an expandable macro producing the expected result, not in two, but rather in three steps: a first expansion is consumed - by the macro expanding to its definition. As a result {|\xintAdd - {\AplusBC {1}{2}{3}}{4}|} would then miserably fail. The - solution is to use the \emph{lowercase} form of + by the macro expanding to its definition. The new expansion policy starting + with the package + release |1.06| allows to use this inside other + package `primitives' or also similar macros: {|\xintAdd + {\AplusBC {1}{2}{3}}{4}|} does work and returns \texttt{\xintAdd + {\AplusBC {1}{2}{3}}{4}}.\footnote{this strange thing is because this + document uses \xintfracname, and we have printed the raw output of addition + which is automatically a fraction.} + + If, for some reason, it is important to create a macro expanding in two steps + to its final value, the solution is to use the \emph{lowercase} form of \csa{xintAdd}: \smallskip\centeredline {|\def\AplusBC #1#2#3{|{\color{blue}|\romannumeral0\xintadd |}|{#1}{\xintMul {#2}{#3}}}|} and then \csa{AplusBC} will share the same properties as do the other \xintname `primitive' macros. -% ENFIN DÉBARRASSÉ DES TRÈS TRÈS TRÈS CHIANTS EOL ERROR DE \verb !!! - -The lowercase form is \emph{only} for the external highest level of -chained commands. All \xintname provided public macros have such a -lowercase form precisely to facilitate building-up higher level macros -based on them. To more fully imitate the \xintname standard habits, the -example above should thus be treated via the creation of two -macros:\par\parskip0pt \hspace*{1cm}|\def\aplusbc #1#2#3{\xintadd - {#1}{\xintMul {#2}{#3}}}|\par -\hspace*{1cm}|\def\AplusBC {\romannumeral0\aplusbc}|\par -This then allows further definitions, such as:\par -\hspace*{1cm}|\def\aplusbcsquared #1#2#3{\aplusbc {#1}{#2}{\xintSqr{#3}}}|\par -\hspace*{1cm}|\def\AplusBCSquared {\romannumeral0\aplusbcsquared}|\par -\end{enumerate} -\section {Inputs and outputs} + The lowercase form is \emph{only} for the external highest level of chained + commands. All \xintname provided public macros have such a lowercase form. To + more fully imitate the \xintname standard habits, the example above should + thus be treated via the creation of two macros:\par\parskip0pt + \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 + + 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 + {#4}{#5}{#6}}}|\par + |\newcommand\MyAlgebra {\romannumeral0\myalgebra}|\par +\end{enumerate} + +The |\romannumeral0| things above look like an invitation to hacker's +territory; if it is not important that the macro expands in two steps only, +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} - \TeX{}'s count registers cannot be directly used but must be - prefixed by |\the| or |\number|. The same for \csa{numexpr} - expressions. + {\color{niceone}New with |1.06|}: those macro arguments 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} +\section {Inputs and outputs} -The arguments to most of the bundle macros are of three types: +The arguments to most of the \xintname macros are of three types: \begin{enumerate} -\item `short' integers, \emph{i.e.} less in absolute value than - \xintiSub{\xintiPow {2}{31}}1. I will refer to this as the `\TeX{}' or - `|\numexpr|' limit. This is case for the exponent in the power function. In - that specific case the limit is (if the number raised to this power is not 0 - or 1) even lowered to 999999999. The factorial function (since release |1.05|) - refuses input larger than 999999. When these conditions are not met, the error - may be signaled from a \csa{numexpr} expression rather than from a package - macro. -\item `long' integers, which are the bread and butter of the package macros. - They are signed integers with a number of - digits less than the \TeX-\csa{numexpr} bound. Concretely though, multiplying - two 1000 digits numbers is already a longish operation. -\item `gigantic' integers, with no limit on size whatsoever. Probably, they are - made impossible by memory constraints of the \TeX{} implementations. - Theoretically, the addition, but not the multiplication nor the division, - could treat even such gigantic numbers. With the \xintfracname package loaded - though, they are not accepted, even for addition. -\item fractions: they should be the ratio of two long integers. The macro - \csa{xintLen} returns the sum of their lengths, and this sum should then obey - the \TeX-\csa{numexpr} bound. +\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 + `|\numexpr|' limit. This is the case for arguments which serve to count or + index something. It is also the case for exponent in the power function and + for the argument to the factorial function. The bounds have been (arbitrarily) + lowered to \np{999999999} and \np{999999} respectively for the 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. +\item `long' integers, which are the bread and butter of the package commands. + They are signed integers with a practically 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 + measure first the length of their arguments and could theoretically be used + with `gigantic' integers with a larger number of digits. However memory + constraints from the \TeX{} implementation probably exclude such inputs. + Concretely though, multiplying out two 1000 digits numbers is already a + 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. \end{enumerate} +\begin{framed} + \TeX{}'s count registers cannot serve directly as arguments to the package + macros + 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 + constrained to obey the \TeX{} bounds. +\end{framed} + + \edef\z {\xintAdd {+--0367.8920280/-++278.289287}{-109.2882/+270.12898}} -The package macros first operate a double expansion of their arguments. They -expect these expansions to deliver numbers obeying two types of format: +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. + +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 +are constrained to obey the \TeX{} bounds on numbers, as they are systematically +inserted inside a |\numexpr...\relax| expression. + + +The allowed input formats for `long numbers' and `fractions' are: \begin{enumerate} \item the strict format is when \xintfracname is not loaded. The number should be a string of digits, optionally preceded by a unique minus sign. The first @@ -726,32 +811,35 @@ 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}}}% -It is - also licit to use |\A/\B| as input if each of |\A| and |\B| expands in - at most two steps to a ``decimal number'' as examplified above by the - numerators and denominators. 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. +\centeredline{|\xintPow{-.3/.7}{11}=|{\xintPow{-.3/+.7}{11}}}% +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 +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. + 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} macro, a fraction is always output in the |A/B[n]| form (which -stands for &(A/B)10^n&; some macros print |A[n]| when the -denominator is one). The |A| and |B| may end in zeros (\emph{i.e}, |n| does +stands for &(A/B)10^n&; some macros print |A[n]| in certain circumstances when +the denominator is one). 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. +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 +\csb{xintFrac} itself is not accepted as input to the package macros. 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, NEITHER the numerator NOR -the denominator\strut{} may then have a decimal -point.\vadjust{\vskip-\dp\strutbox - \hbox{\smash{\color{niceone}\llap{\strut\small IMPORTANT!\ $\Bigg\{$\ - }}}\vskip\dp\strutbox } And, for this format, ONLY the numerator may carry +|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 +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). The, more demanding, format with a power of ten represented by a number within @@ -764,11 +852,12 @@ a UNIQUE minus sign (and no superfluous leading zeros; and NO plus sign). they always output computation results in the |A/B[n]| form (or |A[n]|). - 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. - + \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. + \end{framed} Generally speaking, there should be no spaces among the digits in the inputs. Although most would be harmless in most macros, there are some cases @@ -938,8 +1027,8 @@ within braces. Examples of multiple-output macros are \csb{xintDivision} which gives first the quotient and then the remainder of euclidean division, \csb{xintBezout} from the \xintgcdname package which outputs five numbers, \csb{xintFtoCv} from the \xintcfracname package which returns the list of the -convergents of a fraction, ... see the next section for ways to deal with such -outputs. +convergents of a fraction, ... the next two sections explain ways to deal, +expandably or not, with such outputs. See the \autoref{xintDecSplit} for a rare example of a bundle macro which may return an empty string, or a number prefixed by a chain of zeros. This is the @@ -983,16 +1072,21 @@ expandability. For example why not allow oneself the two definitions \expandafter\allowsplits\meaning\tmpU\relax}, |\V|\texttt{: \expandafter\allowsplits\meaning\tmpV\relax} and |\D=|\texttt{\tmpD}. - When one does not know in advance the number of tokens, one can - use \csa{xintAssignArray} or its synonym \csa{xintDigitsOf}: + When one does not know in advance the number of tokens, one can use + \csa{xintAssignArray} or its synonym \csa{xintDigitsOf}: \centeredline{\csb{xintDigitsOf}\csa{xintiPow}|{2}{100}|\csbnolk{to}\csa{Out}} - This defines \csa{Out} to be macro with one parameter, - \csa{Out}|{0}| gives the size |N| of the array and - \csa{Out}|{n}|, for |n| from |1| to |N| then gives the |n|th - element of the array, here the |n|th digit of &2^{100}&, from - the most significant to the least significant. As usual, the - generated macro \csa{Out} is completely expandable and expands twice its - (unique) argument. Consider the following code snippet: + This defines \csa{Out} to be macro with one parameter, \csa{Out}|{0}| gives + the size |N| of the array and \csa{Out}|{n}|, for |n| from |1| to |N| then + gives the |n|th element of the array, here the |n|th digit of &2^{100}&, from + the most significant to the least significant. As usual, the generated macro + \csa{Out} is completely expandable (in two steps). As it wouldn't make much + sense to allow indices exceeding the \TeX{} bounds, the macros created by + \csb{xintAssignArray} put their argument inside a + \csa{numexpr},\vadjust{\vskip-\dp\strutbox + \hbox{\smash{\color{niceone}\llap{\strut\small CHANGED (1.06)!\ $\Bigg\{$\ + }}}\vskip\dp\strutbox } so it is completely\strut{} expanded and may be + a count register, not necessarily prefixed by |\the| or |\number|. Consider + the following code snippet: \begin{verbatim} \newcount\cnta \newcount\cntb @@ -1001,7 +1095,7 @@ expandability. For example why not allow oneself the two definitions \cnta = 1 \cntb = 0 \loop -\advance \cntb \xintiSqr{\Out{\the\cnta}} +\advance \cntb \xintiSqr{\Out{\cnta}} \ifnum \cnta < \Out{0} \advance\cnta 1 \repeat @@ -1009,7 +1103,7 @@ expandability. For example why not allow oneself the two definitions |2^{100}| (=\xintiPow {2}{100}) has \Out{0} digits and the sum of their squares is \the\cntb. These digits are, from the least to the most significant: \cnta = \Out{0} -\loop \Out{\the\cnta}\ifnum \cnta > 1 \advance\cnta -1 , \repeat. +\loop \Out{\cnta}\ifnum \cnta > 1 \advance\cnta -1 , \repeat. \endgroup \end{verbatim} @@ -1020,7 +1114,7 @@ the most significant: \cnta = \Out{0} \cnta = 1 \cntb = 0 \loop -\advance \cntb \xintiSqr{\Out{\the\cnta}} +\advance \cntb \xintiSqr{\Out{\cnta}} \ifnum \cnta < \Out{0} \advance\cnta 1 \repeat @@ -1028,7 +1122,7 @@ the most significant: \cnta = \Out{0} &2^{100}& (=\z) has \Out{0} digits and the sum of their squares is \the\cntb. These digits are, from the least to the most significant: \cnta = \Out{0} -\loop \Out{\the\cnta}\ifnum \cnta > 1 \advance\cnta -1 , \repeat. +\loop \Out{\cnta}\ifnum \cnta > 1 \advance\cnta -1 , \repeat. \endgroup We used a group in order to release the memory taken by the @@ -1058,33 +1152,10 @@ would have been a summand enclosed within braces, due to the rules of \TeX{} for parsing macro arguments. Note that |{-\xintRem{3347}{591}}| is not a valid input, because -the double expansion will apply only to the minus sign and leave +the expansion will apply only to the minus sign and leave unaffected the |\xintRem|. So we used \csa{xint}\-|iOpp| which replaces a number with its opposite. -\def\justone #1{1}% - -Release |1.04| of \xintname has more macros returning lists of things (each one -within group braces, or a single token) such as the convergents of a continued -fraction. The two new expandable commands \csb{xintApply} and -\csb{xintListWithSep} help manipulate and display such lists without having to -go through the un-expandable \csb{xintAssignArray}. -\begin{verbatim} -\newcommand{\justone}[1]{1}% -|2^{100}| (=\xintiPow {2}{100}) has -\xintiSum{\xintApply {\justone}{\xintiPow {2}{100}}} -digits and the sum of their squares is -\xintiSum{\xintApply {\xintiSqr}{\xintiPow {2}{100}}}. -These digits are, from the least to the most significant: -\xintListWithSep {, }{\xintRev{\xintiPow {2}{100}}}. -\end{verbatim} -|2^{100}| (=\z) has \xintiSum{\xintApply\justone\z} digits and the sum of -their squares is \xintiSum{\xintApply\xintiSqr\z}. These digits are, from the -least to the most significant: \xintListWithSep {, }{\xintRev\z}. - -Of course, one could spare the CPU some repetitions with an earlier -|\edef\z{\xintiPow {2}{100}}|, and using |\z| in place of - |\xintiPow {2}{100}| everywhere in the above. As a last example with \csa{xintAssignArray} here is one line extracted from the source code of the \xintgcdname macro @@ -1102,8 +1173,45 @@ from the first to the last step of the algorithm. The \csa{xintTypesetEuclideAlgorithm} macro organizes this data for typesetting: this is just an example of one way to do it. +\section{Utilities for expandable manipulations} + +The\vadjust{\vskip-\dp\strutbox + \hbox{\smash{\color{niceone}\llap{\strut\small EXTENDED (1.06)\ $\to$\ + }}}\vskip\dp\strutbox } package\strut{} now has more utilities to deal expandably with `lists of +things', which were treated un-expandably in the previous section with +\csa{xintAssign} and \csa{xintAssignArray}: \csb{xintRev}, +\csb{xintReverseOrder}, \csb{xintLen} and +\csb{xintLength} since the first release, \csb{xintApply} and +\csb{xintListWithSep} since |1.04|, \csb{xintRevWithBraces}, +\csb{xintCSVtoList}, \csb{xintNthElt} now with |1.06|. -%% As an example: \xintTypesetEuclideAlgorithm {2362001530033}{981106461701} +\edef\z{\xintiPow {2}{100}} + +As an example the following code uses only expandable operations: +\begin{verbatim} +|2^{100}| (=\xintiPow {2}{100}) has \xintLen{\xintiPow {2}{100}}} digits +and the sum of their squares is +\xintiSum{\xintApply {\xintiSqr}{\xintiPow {2}{100}}}. +These digits are, from the least to the most significant: +\xintListWithSep {, }{\xintRev{\xintiPow {2}{100}}}. The thirteenth most +significant digit is \xintNthElt{13}{\xintiPow {2}{100}}. The seventh +least significant one is \xintNthElt{7}{\xintRev{\xintiPow {2}{100}}}. +\end{verbatim} +|2^{100}| (=\z) has \xintLen{\z} digits and the sum of +their squares is \xintiSum{\xintApply\xintiSqr\z}. These digits are, from the +least to the most significant: \xintListWithSep {, }{\xintRev\z}. The +thirteenth most +significant digit is \xintNthElt{13}{\z}. The seventh +least significant one is \xintNthElt{7}{\xintRev\z}. + +% The +% thirteenth most +% significant digit is \xintNthElt{13}{\xintiPow {2}{100}}. The seventh least +% significant one is \xintNthElt{7}{\xintRev{\xintiPow {2}{100}}}. + +Of course, with an earlier +|\edef\z{\xintiPow {2}{100}}|, using |\z| in place of + |\xintiPow {2}{100}| everywhere would spare the CPU some repetitions. \section{Exceptions (error messages)} @@ -1142,8 +1250,6 @@ others are more annoying as they may pass through unsignaled. 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 defining macros which do not expand in only two steps and then use them as - arguments: |\def\x #1{\xintMON {#1}}|, |\xintAdd {\x{3}}{\x{2}}|. \item making a mistake in a macro name |\xintProduct {{2}{3}{4}}|. Well I should |\let| it to be |\xintPrd|... at least such errors are not dangerous because they do provoke compilation errors. @@ -1158,21 +1264,14 @@ others are more annoying as they may pass through unsignaled. \section{Package namespace} -Inner macros of \xintname, \xintgcdname, \xintfracname, \xintseriesname, -and \xintcfracname{} all begin either with |\XINT@| or with |\xint@|. 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 two -steps to their full expansion (and can thus be chained with the -`primitive' \xintname macros). Some other control sequence names are -used only as delimiters, and left undefined. - -% The |\xintReverseOrder|\marg{tokens} macro uses |\xint@UNDEF| and -% |\xint@undef| as dummy tokens and can be used on arbitrary token -% strings not containing these control sequence names. Anything -% within braces is treated as one unit: one level of exterior braces -% is removed and the contents are not reverted. - +Inner macros of \xintname, \xintgcdname, \xintfracname, \xintseriesname, and +\xintcfracname{} all begin either with |\XINT@| or with |\xint@|. 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} @@ -1264,12 +1363,19 @@ database. \def\m{\string{M\string}} \def\x{\string{x\string}} -\n{} (resp. \m{} or \x) stands for a normalised number within braces as -described in the documentation, or for a control sequence expanding in at most -two steps to such a number (without the braces!), or for a control sequence -within braces expanding in at most two steps to such a number, of for material -within braces which expands to such a number after two expansions of the first -token. +\texttt{\n} (or also \texttt{\m}) stands for a normalised number within braces +as described in the documentation, or for a control sequence expanding (in the +sense previously described) to such a number (without the braces!), or for a +control sequence within braces expanding to such a number, of for material +within braces which expands to such a number after repeated expansions of the +first token. A count register or \csa{numexpr} expression must thus come first +and be prefixed by |\the| or |\number|. + +The letter \texttt{x} stands for something which will be inserted in-between a +|\numexpr| and a |\relax|. It will thus be completely expanded and must give an +integer obeying the \TeX{} bounds. Thus, it may be for example a count register, +or itself a \csa{numexpr} expression, or just a number written explicitely with +digits or something like |4*\count 255 + 17|, etc... Some of these macros are extended by \xintfracname to accept fractions on input, and, generally, to output a fraction. This will be mentioned @@ -1284,18 +1390,18 @@ format is the same. See the \xintfracname \hyperref[sec:comfrac]{\color{niceone}documentation} for more information. -The integer-only macros are more efficient, even for simple things such -as determining the sign of a number, as there is always some overhead -due to parsing the fraction format on input; however except if one does -really a lot of computations, there is no need in general to employ the -integer-only variants. The exception is when the context requires that -the macro returns a (possibly long) integer, with no forward slash nor -trailing |[n]|. This may be because they are used in \xintname macros -which remain strictly integer-only on input, such as \csb{xintDecSplit}, -or\vadjust{\vskip-\dp\strutbox - \hbox{\smash{\color{niceone}\llap{\strut\small IMPORTANT!\ $\Bigg\{$\ - }}}\vskip\dp\strutbox } in\strut{} places where a (short) number is -expected by \TeX{} such as after an |\ifnum| or inside a |\numexpr|. +The integer-only macros are a bit more efficient, even for simple things such as +determining the sign of a (long) number, as there is always some overhead due to +the parsing the fraction format on input; however except if one does thousands +of times the same computation with various inputs, there is no need in general +to employ the integer-only variants. The exception is when the context requires +that the macro returns a (possibly long) integer, with no forward slash nor +trailing |[n]|. This may be because they are used in \xintname macros which +remain strictly integer-only on input, such as \csb{xintDecSplit}, +or\vadjust{\vskip-\dp\strutbox \hbox{\smash{\color{niceone}\llap{\strut\small + IMPORTANT!\ $\Bigg\{$\ }}}\vskip\dp\strutbox } in\strut{} places where a +(short) number is expected by \TeX{} such as after an |\ifnum| or inside a +|\numexpr|. @@ -1305,7 +1411,9 @@ expected by \TeX{} such as after an |\ifnum| or inside a |\numexpr|. \csa{xintRev\n} will revert the order of the digits of the number, keeping the optional sign. Leading zeros resulting from the operation are not removed (see the -\csa{xintNum} macro for this). +\csa{xintNum} macro for this). As all other macros dealing with numbers it first +expands its argument (in the manner described, triggered by a +|\romannumeral-`0|). \centeredline{|\xintRev{-123000}|\texttt{=\xintRev{-123000}}} \centeredline{|\xintNum{\xintRev{-123000}}|\texttt{=\xintNum{\xintRev{-123000}}}} @@ -1319,57 +1427,148 @@ material does not get reverted. Spaces are gobbled. \centeredline{|\xintReverseOrder{\xintDigitsOf\xintiPow {2}{100}\to\Stuff}|} \centeredline{gives: \ttfamily{\string\Stuff\string\to1002\string\xintiPow\string\xintDigitsOf}} -\subsection{\csbh{xintNum}}\label{xintiNum} - -\csa{xintNum\n} removes chains of plus or minus signs, followed by zeros. -\centeredline{|\xintNum{+---++----+--000000000367941789479}|\texttt - {=\xintNum{+---++----+--000000000367941789479}}} Extended by \xintfracname to -accept also a fraction on input, as long as it reduces to an integer after -division of the numerator by the denominator. -\centeredline{|\xintNum{123.48/-0.03}|\texttt{=\xintNum{123.48/-0.03}}} +\subsection{\csbh{xintRevWithBraces}}\label{xintRevWithBraces} + +{\small New in release |1.06|.\par} +\edef\X{\xintRevWithBraces{12345}} +\edef\y{\xintRevWithBraces\X} +\expandafter\def\expandafter\w\expandafter + {\romannumeral0\xintrevwithbraces{{\A}{\B}{\C}{\D}{\E}}} + + +\csa{xintRevWithBraces}\marg{list} first does the expansion of its argument +(which thus may be macro), then it reverses the order of the tokens, or braced +material, it encounters, adding a pair of braces to each (thus, maintaining +brace pairs already existing). Spaces (in-between external brace pairs) are +gobbled. This macro is mainly thought out for use on a `list' of such braced +material; with such a list as argument the expansion will only hit against the +first opening brace, hence do nothing, and the braced stuff may thus be macros +one does not want to expand. \centeredline{|\edef\x{\xintRevWithBraces{12345}}|} +\centeredline{|\meaning\x:|\ttfamily{\meaning\X}} +\centeredline{|\edef\y{\xintRevWithBraces\x}|}% +\centeredline{|\meaning\y:|\ttfamily{\meaning\y}} The examples above could be +defined with |\edef|'s because the braced material did not contain macros. +Alternatively: \centeredline{|\expandafter\def\expandafter\w\expandafter|}% +\centeredline{|{\romannumeral0\xintrevwithbraces{{\A}{\B}{\C}{\D}{\E}}}|} +\centeredline{|\meaning\w:|\ttfamily{\meaning\w}} The private macro |\XINT@RWB| +does the same job without the initial expansion of its argument. \subsection{\csbh{xintLen}}\label{xintiLen} -\csa{xintLen\n} returns the length of the number, not counting the -sign. +\csa{xintLen\n} returns the length of the number, not counting the sign. \centeredline{|\xintLen{-12345678901234567890123456789}|\texttt - {=\xintLen{-12345678901234567890123456789}}} Extended by -\xintfracname to fractions: the length of |A/B[n]| is the length -of |A| plus the length of |B| plus the absolute value of |n| and -minus one (an integer input as |N| is internally |N/1[0]| so the -minus one means that the extended \csa{xintLen} behaves the same -as the original for integers). The whole thing should sum up to -less than circa &2^{31}&. + {=\xintLen{-12345678901234567890123456789}}} Extended by \xintfracname to +fractions: the length of |A/B[n]| is the length of |A| plus the length of |B| +plus the absolute value of |n| and minus one (an integer input as |N| is +internally |N/1[0]| so the minus one means that the extended \csa{xintLen} +behaves the same as the original for integers). The whole thing should sum up to +less than circa &2^{31}&. \subsection{\csbh{xintLength}}\label{xintLength} -\csa{xintLength}\marg{list} does not do any expansion of -its argument and just counts how many tokens there are. Things -enclosed in braces count as one. -\centeredline{|\xintLength {\xintiPow {2}{100}}=|\texttt{\xintLength - {\xintiPow{2}{100}}}} +\csa{xintLength}\marg{list} does not do any expansion of its argument and just +counts how many tokens there are (possibly none). Things enclosed in braces +count as one. \centeredline{|\xintLength {\xintiPow + {2}{100}}=|\texttt{\xintLength {\xintiPow{2}{100}}}} \centeredline{${}\neq{}$|\xintLen {\xintiPow {2}{100}}=|\texttt{\xintLen {\xintiPow{2}{100}}}} +\subsection{\csbh{xintCSVtoList}}\label{xintCSVtoList} + +{\small New with release |1.06|.\par} + +\edef\X{\xintCSVtoList {1,2,a , b ,c d,x,y }} +\def\y {a,b,c,d,e} +\edef\z{\xintCSVtoList \y} + +\makeatletter \csa{xintCSVtoList}|{a,b,c...,z}| returns |{a}{b}{c}...{z}|. The +argument may be a macro. It is first expanded: this means that if the argument +is |a,b,..|, then |a|, if a macro, will be expanded which may or may not be a +good thing. Chains of contiguous spaces are collapsed by the \TeX{} scanning +into single spaces. \centeredline{|\xintCSVtoList {1,2,a , b ,c d,x,y + }->|\texttt{\expandafter\strip@prefix\meaning\X}} +\centeredline{|\def\y{a,b,c,d,e}\xintCSVtoList\y->|\texttt{\expandafter\strip@prefix\meaning\z}} +The private macro |\XINT@CSVtoL| does the same job without the initial +expansion. \makeatother + +\subsection{\csbh{xintNthElt}}\label{xintNthElt} + +{\small New in release |1.06|.\par} + +\def\macro #1{\the\numexpr 9-#1\relax} + +\csa{xintNthElt}|{i}{list}| gets (expandably) the |i|th element of the |list|. +The `list' may be a macro expanding to the `list' (which is just a +sequence of tokens; spaces are gobbled as the macro will get the required +element as an undelimited macro parameter). The first argument |i| may be a +\TeX{} count register (it will be given to a |\numexpr|). The seeked element is +returned with one pair of braces removed (if initially present). +\centeredline{|\xintNthElt + {37}{\xintFac {100}}=|\texttt{\xintNthElt {37}{\xintFac {100}}}} is the +thirty-seventh digit of &100!&. \centeredline{|\xintNthElt {10}{\xintFtoCv + {566827/208524}}=|\texttt{\xintNthElt {10}{\xintFtoCv {566827/208524}}}} is +the tenth convergent of &566827/208524& (uses \xintcfracname package). Error +cases, where |i<0| or is larger than the number of elements in the list are kept +silent; the macro then returns nothing. Perhaps this will be changed in future +versions. \centeredline{|\xintNthElt {7}{\xintCSVtoList {1,2,3,4,5,6,7,8,9}}=|% + \texttt{\xintNthElt {7}{\xintCSVtoList {1,2,3,4,5,6,7,8,9}}}} +The private macro |\XINT@NthElt| does the same job +without first expanding its second argument. + +\subsection{\csbh{xintListWithSep}}\label{xintListWithSep} + +{\small New with release |1.04|.\par} + +\def\macro #1{\the\numexpr 9-#1\relax} + +\csa{xintListWithSep}|{sep}{list}| just inserts the given separator |sep| +in-between all elements of the given list. One level of braces is +removed. An empty input gives an empty output, a singleton gives a singleton, +the separator is used starting with at least two elements. The `list' argument +may be a macro: it is expanded. +\centeredline{|\xintListWithSep{:}{\xintFac + {20}}=|\texttt{\xintListWithSep{:}{\xintFac {20}}}} +The private macro |XINT@LWS| does the same +job without the initial expansion. + +\subsection{\csbh{xintApply}}\label{xintApply} + +{\small New in release |1.04|.\par} + +\def\macro #1{\the\numexpr 9-#1\relax} + +\csa{xintApply}|{\macro}{list}| applies the one parameter command |\macro| to +each item in the `list' (no separator) given as second argument. Each item is +given in turn as parameter to |\macro| which is (fully, as usual) expanded, and +the result is braced. On output, a new list with these braced results. The +`list' may itself be some macro expanding (in the previously described way) to +the list of tokens to which the command |\macro| will be applied. For example, +if the `list' expands to some positive number, then each digit will be replaced +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 private macro +|XINT@Apply| does the same job without the first initial expansion providing the +`list'. \subsection{\csbh{xintAssign}}\label{xintAssign} + \csa{xintAssign}\meta{braced things}\csa{to}% \meta{as many cs as they are things} defines (without checking if something gets overwritten) the control sequences on the right of \csa{to} to be the complete expansions of the successive things on the left of \csa{to} enclosed within braces. -Important: a double expansion is applied first to the material -extending up to \csa{to}. +Important: a `full' expansion (as previously described) is applied first to the +material in front of \csa{xintAssign}. \xintAssign\xintiPow {7}{13}\to\SevenToThePowerThirteen \xintAssign\xintDivision{1000000000000}{133333333}\to\Q\R -As a special exception, if after this initial double expansion a +As a special exception, if after this initial expansion a brace does not immediately follows \csa{xintAssign}, it is assumed that there is only one control sequence to define and it is then -defined to be the complete expansion of the material between +defined to be the complete expansion of the entire material between \csa{xintAssign} and \csa{to}. \centeredline{|\xintAssign\xintDivision{1000000000000}{133333333}\to\Q\R|} \centeredline{|\meaning\Q: |\texttt{\meaning\Q}, |\meaning\R: @@ -1383,22 +1582,23 @@ pure expansion contexts, as assignments are made via the \subsection{\csbh{xintAssignArray}}\label{xintAssignArray} +{\small Changed in release |1.06|.\par} + \xintAssignArray\xintBezout {1000}{113}\to\Bez -\csa{xintAssignArray}\meta{braced things}\csa{to}\csa{myArray} first -double expands the first token then defines \csa{myArray} to be a -macro with one parameter, such that \csa{myArray\n} expands in two -steps (which include the twice-expansion of \texttt{\n}) to give -the |N|th braced thing, itself completely expanded. -\csa{myArray}|{0}| returns the number |M| of elements of the array -so that the successive elements are \csa{myArray}|{1}|, \dots, -\csa{myArray}|{M}|. \centeredline{|\xintAssignArray\xintBezout - {1000}{113}\to\Bez|} will set |\Bez{0}| to \texttt{\Bez0}, -|\Bez{1}| to \texttt{\Bez1}, |\Bez{2}| to \texttt{\Bez2}, -|\Bez{3}| to \texttt{\Bez3}, |\Bez{4}| to \texttt{\Bez4}, and -|\Bez{5}| to \texttt{\Bez5}: +\csa{xintAssignArray}\meta{braced things}\csa{to}\csa{myArray} first +expands fully the first token then defines \csa{myArray} to be a macro with one +parameter, such that \csa{myArray\x} expands in two steps (which provoke the +full expansion of the `short' number \texttt{\x}, given to a +|\numexpr|) to give the |N|th braced +thing, itself completely expanded. \csa{myArray}|{0}| returns the number |M| of +elements of the array so that the successive elements are \csa{myArray}|{1}|, +\dots, \csa{myArray}|{M}|. \centeredline{|\xintAssignArray\xintBezout + {1000}{113}\to\Bez|} will set |\Bez{0}| to \texttt{\Bez0}, |\Bez{1}| to +\texttt{\Bez1}, |\Bez{2}| to \texttt{\Bez2}, |\Bez{3}| to \texttt{\Bez3}, +|\Bez{4}| to \texttt{\Bez4}, and |\Bez{5}| to \texttt{\Bez5}: (\Bez3)${}\times{}$\Bez1${}-{}$(\Bez4)${}\times{}$\Bez2${}={}$\Bez5. \subsection{\csbh{xintRelaxArray}}\label{xintRelaxArray} @@ -1418,33 +1618,14 @@ an array giving all the digits of a given number. |\digits{123}=|\digits{123}. \endgroup -\subsection{\csbh{xintApply}}\label{xintApply} - -{\small New in release |1.04|.\par} - -\def\macro #1{\the\numexpr 9-#1\relax} - -\csa{xintApply}|{\macro}{list}| applies the one parameter command |\macro| to -each item in the `list' (no separator) given as second argument. For each item two -expansions are done of |\macro| and the result is braced. On output, a new list -with these braced results. The `list' may itself be some macro expanding in two -steps to the list of tokens to which the command |\macro| will be applied. For -example, if the `list' expands to some positive number, then each digit will be -replaced 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}}}} - -\subsection{\csbh{xintListWithSep}}\label{xintListWithSep} - -{\small New in release |1.04|.\par} - -\def\macro #1{\the\numexpr 9-#1\relax} +\subsection{\csbh{xintNum}}\label{xintiNum} -\csa{xintListWithSep}|{sep}{list}| just inserts the given separator |sep| -in-between all elements of the given list. One level of braces is -removed. See the discussion of -\csb{xintApply}. \centeredline{|\xintListWithSep{:}{\xintFac - {20}}=|\texttt{\xintListWithSep{:}{\xintFac {20}}}} +\csa{xintNum\n} removes chains of plus or minus signs, followed by zeros. +\centeredline{|\xintNum{+---++----+--000000000367941789479}|\texttt + {=\xintNum{+---++----+--000000000367941789479}}} Extended by \xintfracname to +accept also a fraction on input, as long as it reduces to an integer after +division of the numerator by the denominator. +\centeredline{|\xintNum{123.48/-0.03}|\texttt{=\xintNum{123.48/-0.03}}} \subsection{\csbh{xintSgn}}\label{xintiSgn} @@ -1502,8 +1683,8 @@ put on a line with positive numbers on the right): |\xintiMin \subsection{\csbh{xintSum}}\label{xintiSum} \csa{xintSum}\marg{braced things} after expanding its argument -twice expects to find a sequence of tokens (or braced material). -Each is twice-expanded, and the sum of all these numbers is +expects to find a sequence of tokens (or braced material). +Each is expanded (with the usual meaning), and the sum of all these numbers is returned. \centeredline{% \csa{xintiSum}|{{123}{-98763450}{\xintFac{7}}{\xintiMul{3347}{591}}}=|\texttt{% @@ -1520,14 +1701,13 @@ to fractions. \subsection{\csbh{xintSumExpr}}\label{xintiSumExpr} -\csa{xintSumExpr}\meta{braced things}\csa{relax} is to what -\csa{xintSum} expands. The argument is then double-expanded and should -give a list of braced quantities or macros, each one will be double -expanded in turn. \centeredline{% +\csa{xintSumExpr}\meta{braced things}\csa{relax} is to what \csa{xintSum} +expands. The argument is then expanded (with the usual meaning) and should give a +list of braced quantities or macros, each one will be expanded in turn. +\centeredline{% \csa{xintiSumExpr}| {123}{-98763450}|% |{\xintFac{7}}{\xintiMul{3347}{591}}\relax=|\texttt{% - \xintiSumExpr - {123}{-98763450}{\xintFac{7}}{\xintiMul{3347}{591}}\relax}} + \xintiSumExpr {123}{-98763450}{\xintFac{7}}{\xintiMul{3347}{591}}\relax}} Note: I am not so happy with the name which seems to suggest that the |+| sign should be used instead of braces. Perhaps this will change @@ -1553,8 +1733,8 @@ Extended by \xintfracname to fractions. \subsection{\csbh{xintPrd}}\label{xintiPrd} \csa{xintPrd}\marg{braced things} after expanding its argument -twice expects to find a sequence of tokens (or braced material). -Each is twice-expanded, and the product of all these numbers is +expects to find a sequence of tokens (or braced material). +Each is expanded (with the usual meaning), and the product of all these numbers is returned. \centeredline{% \csa{xintiPrd}|{{-9876}{\xintFac{7}}{\xintiMul{3347}{591}}}=|% \texttt{% @@ -1581,12 +1761,11 @@ Extended by \xintfracname to fractions. \subsection{\csbh{xintProductExpr}}\label{xintiProductExpr} -\csa{xintProductExpr}\marg{argument}\csa{relax} is to what -\csa{xintPrd} expands ; its argument is then twice expanded and should -give a list of braced numbers or macros. Each will be twice expanded -when it is its turn. +\csa{xintProductExpr}\marg{argument}\csa{relax} is to what \csa{xintPrd} expands +; its argument is expanded (with the usual meaning) and should give a list of +braced numbers or macros. Each will be expanded when it is its turn. \centeredline{\csa{xintiProductExpr}| 123456789123456789\relax=|\texttt{% - \xintiProductExpr 123456789123456789\relax}} + \xintiProductExpr 123456789123456789\relax}} Note: I am not so happy with the name which seems to suggest that the |*| sign should be used instead of braces. Perhaps this will change @@ -1596,10 +1775,13 @@ Extended by \xintfracname to fractions. \subsection{\csbh{xintFac}}\label{xintFac} -\csa{xintFac\n} returns the factorial. It is an error if the +\csa{xintFac\x} returns the factorial. It is an error if the argument is negative or at least &10^6&. It is not recommended to launch the computation of things such as &100000!&, if you need -your computer for other tasks. +your computer for other tasks. Note that the argument is of the |x| type, it +must obey the \TeX{} bounds, but on the other hand may involve count registers +and even arithmetic operations as it will be completely expanded inside a +|\numexpr|. % temps obsolètes, mettre à jour % On my laptop &1000!& (2568 digits) @@ -1614,9 +1796,9 @@ your computer for other tasks. \subsection{\csbh{xintPow}}\label{xintiPow} -\csa{xintPow\n\m} returns |N^M|. When |M| is zero, this is 1. Some -cases (|N| zero and |M| negative, \verb+|N|>1+ and |M| negative, -\verb+|N|>1+ and |M| at least &10^9&) make \xintname throw errors. +\csa{xintPow\n\x} returns |N^x|. When |x| is zero, this is 1. Some +cases (|N| zero and |x| negative, \verb+|N|>1+ and |x| negative, +\verb+|N|>1+ and |x| at least &10^9&) make \xintname throw errors. Extended by \xintfracname to fractions. Of course, negative exponents do not then cause errors anymore. @@ -1832,7 +2014,7 @@ returns zero. \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 (twice-expanded) input number, |B| the +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 }.} @@ -1909,7 +2091,7 @@ entry, and then these four things at each step until the end. \catcode`\& 13 -\subsection{\csbh{xintTypesetEuclideAlgorithm}\hskip1cm\hspace*{0cm}}\label{xintTypesetEuclideAlgorithm} +\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 @@ -1929,9 +2111,18 @@ and modify it to what is needed. \section{Commands of the \xintfracname package}\label{sec:comfrac} -The general rule of the bundle that each macro first double-expands each one of -its arguments applies. This package was first included in release |1.03| of the -\xintname bundle. +\def\x{\string{x\string}} + +This package was first included in release |1.03| of the \xintname bundle. The +general rule of the bundle that each macro first expands (what comes first, +fully) each one of its arguments applies. As in the previous documentation, |x| +stands for something which will be internally embedded in a \csa{numexpr}, thus +completely expanded and then must deliver a number obeying the TeX{} bounds. It +may be a count register or something like |4*\count 255 + 17|, etc... + +|f| stands for a fraction (or a possibly `long' integer), or something which +expands to a fraction or a possibly long integer. See the earlier section on +fraction formats. \subsection{\csbh{xintLen}}\label{xintLen} @@ -2069,31 +2260,31 @@ example. \subsection{\csbh{xintTrunc}}\label{xintTrunc} -\csa{xintTrunc}|{N}{f}| returns the start of the decimal expansion of the -fraction |f|, with |N| digits after the decimal point. The argument |N| should -be non-negative. When |N=0|, the integer part of |f| results, with an ending -decimal point. Only when |f| evaluates to zero does \csa{xintTrunc} not print -a decimal point. When |f| is not zero, the sign is maintained in the output, -also when the digits are all zero. \centeredline{|\xintTrunc - {16}{-803.2028/20905.298}=|\texttt{\xintTrunc {16}{-803.2028/20905.298}}}% - \centeredline{|\xintTrunc - {20}{-803.2028/20905.298}=|\texttt{\xintTrunc {20}{-803.2028/20905.298}}}% - \centeredline{|\xintTrunc - {10}{\xintPow {-11}{-11}}=|\texttt{\xintTrunc - {10}{\xintPow {-11}{-11}}}}% - \centeredline{|\xintTrunc - {12}{\xintPow {-11}{-11}}=|\texttt{\xintTrunc - {12}{\xintPow {-11}{-11}}}}% -\centeredline{|\xintTrunc {12}{\xintAdd {-1/3}{3/9}}=|\texttt{\xintTrunc {12}{\xintAdd {-1/3}{3/9}}}} The -digits printed are exact up to and including the last one. The identity -|\xintTrunc {N}{-f}=-\xintTrunc {N}{f}| holds.\footnote{this is just a notation; - currently |-\string\x| is not valid input to any package macro, one must use - |\string\xintOpp\string{\string\x\string}| or |\string\xintiOpp\string{\string\x\string}|.} +\csa{xintTrunc}|{x}{f}| returns the start of the decimal expansion of the +fraction |f|, with |x| digits after the decimal point. The argument |x| should +be non-negative. When |x=0|, the integer part of |f| results, with an ending +decimal point. Only when |f| evaluates to zero does \csa{xintTrunc} not print a +decimal point. When |f| is not zero, the sign is maintained in the output, also +when the digits are all zero. \centeredline{|\xintTrunc + {16}{-803.2028/20905.298}=|\texttt{\xintTrunc {16}{-803.2028/20905.298}}}% +\centeredline{|\xintTrunc {20}{-803.2028/20905.298}=|\texttt{\xintTrunc + {20}{-803.2028/20905.298}}}% +\centeredline{|\xintTrunc {10}{\xintPow {-11}{-11}}=|\texttt{\xintTrunc + {10}{\xintPow {-11}{-11}}}}% +\centeredline{|\xintTrunc {12}{\xintPow {-11}{-11}}=|\texttt{\xintTrunc + {12}{\xintPow {-11}{-11}}}}% +\centeredline{|\xintTrunc {12}{\xintAdd {-1/3}{3/9}}=|\texttt{\xintTrunc + {12}{\xintAdd {-1/3}{3/9}}}} The digits printed are exact up to and +including the last one. The identity |\xintTrunc {x}{-f}=-\xintTrunc {x}{f}| +holds.\footnote{this is just a notation; currently |-\string\macro| is not valid + input to any package macro, one must use + |\string\xintOpp\string{\string\macro\string}| or + |\string\xintiOpp\string{\string\macro\string}|.} \subsection{\csbh{xintiTrunc}}\label{xintiTrunc} -\csa{xintiTrunc}|{N}{f}| returns the integer equal to |10^N| times what -\csa{xintTrunc}|{N}{f}| would return. \centeredline{|\xintiTrunc +\csa{xintiTrunc}|{x}{f}| returns the integer equal to |10^x| times what +\csa{xintTrunc}|{x}{f}| would return. \centeredline{|\xintiTrunc {16}{-803.2028/20905.298}=|\texttt{\xintiTrunc {16}{-803.2028/20905.298}}}% \centeredline{|\xintiTrunc {10}{\xintPow {-11}{-11}}=|\texttt{\xintiTrunc @@ -2110,9 +2301,9 @@ all superfluous leading zeros.) {\small New with release |1.04|.\par} -\csa{xintRound}|{N}{f}| returns the start of the decimal expansion of the -fraction |f|, rounded to |N| digits precision after the decimal point. The -argument |N| should be non-negative. Only when |f| evaluates exactly to zero +\csa{xintRound}|{x}{f}| returns the start of the decimal expansion of the +fraction |f|, rounded to |x| digits precision after the decimal point. The +argument |x| should be non-negative. Only when |f| evaluates exactly to zero does \csa{xintRound} return |0| without decimal point. When |f| is not zero, its sign is given in the output, also when the digits printed are all zero. \centeredline{|\xintRound {16}{-803.2028/20905.298}=|\texttt{\xintRound @@ -2127,7 +2318,7 @@ sign is given in the output, also when the digits printed are all zero. {12}{\xintPow {-11}{-11}}}}% \centeredline{|\xintRound {12}{\xintAdd {-1/3}{3/9}}=|\texttt{\xintRound {12}{\xintAdd {-1/3}{3/9}}}} -The identity |\xintRound {N}{-f}=-\xintRound {N}{f}| holds. And regarding +The identity |\xintRound {x}{-f}=-\xintRound {x}{f}| holds. And regarding $(-11)^{-11}$ here is some more or its expansion: \centeredline{\xintTrunc {50}{\xintPow {-11}{-11}}\dots} @@ -2135,8 +2326,8 @@ $(-11)^{-11}$ here is some more or its expansion: {\small New with release |1.04|.\par} -\csa{xintiRound}|{N}{f}| returns the integer equal to |10^N| times what -\csa{xintRound}|{N}{f}| would return. \centeredline{|\xintiRound +\csa{xintiRound}|{x}{f}| returns the integer equal to |10^x| times what +\csa{xintRound}|{x}{f}| would return. \centeredline{|\xintiRound {16}{-803.2028/20905.298}=|\texttt{\xintiRound {16}{-803.2028/20905.298}}}% \centeredline{|\xintiRound {10}{\xintPow {-11}{-11}}=|\texttt{\xintiRound {10}{\xintPow {-11}{-11}}}}% @@ -2230,7 +2421,7 @@ 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{xintGeq}, \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 @@ -2249,26 +2440,30 @@ as \csb{xintiNum}. \section{Commands of the \xintseriesname package}\label{sec:series} -There will be some exceptions to the general rule that -each macro first double-expands each one of its arguments. This package was +Some arguments to the package commands are macros which are expanded only later, +when given their parameters. The arguments serving as indices +({\color{niceone}new with |1.06|}) are systematically given to a |\numexpr| +expressions, hence fully expanded, they may be count registers, etc... + +This package was first released with version |1.03| of the \xintname bundle. \subsection{\csbh{xintSeries}}\label{xintSeries} -\def\coeff #1{\romannumeral0\xintimon{#1}/#1.5} % (-1)^n/(n+1/2) +\def\coeff #1{\xintiMON{#1}/#1.5} % (-1)^n/(n+1/2) \edef\w {\xintSeries {0}{50}{\coeff}} \edef\z {\xintJrr {\w}[0]} \csa{xintSeries}|{A}{B}{\coeff}| evaluates the sum of all values of the |\coeff -{n}| from |n=A| to and including |n=B|. The initial and final indices must -(after double-expansion) obey the \TeX{} and |\numexpr| constraint of being -explicit numbers at most |2^31-1| (these conditions are not checked by -the macro). The |\coeff| macro (which, as argument to \csa{xintSeries} is -double-expanded only at the time of computing the successive |\coeff {n}|) -should be defined as a one-parameter command, accepting on input a number (not a -count register) and needing at most two expansions to compute its final result. +{n}| from |n=A| to and including |n=B|. The initial and final indices must obey +the |\numexpr| constraint of expanding to numbers at most |2^31-1|. The |\coeff| +macro (which, as argument to \csa{xintSeries} is expanded only at the +time of computing the successive |\coeff {n}|) should be defined as a +one-parameter fully expandable command, providing its output from an input being +an explicit number (string of digits, no need to make proviso for a count +register). \begin{verbatim} -\def\coeff #1{\romannumeral0\xintimon{#1}/#1.5} % (-1)^n/(n+1/2) +\def\coeff #1{\xintiMON{#1}/#1.5} % (-1)^n/(n+1/2) \edef\w {\xintSeries {0}{50}{\coeff}} % we want to re-use it \edef\z {\xintJrr {\w}[0]} % the [0] for a microsecond gain. % \xintJrr preferred to \xintIrr: a big common factor is suspected. @@ -2346,7 +2541,7 @@ digits) in the denominator. See the explanations in the next section. % we can afford that, as \xintSeries is fast enough. \noindent\hbox to 2em{\hfil\texttt{\the\cnta.} }% \xintTrunc {12} - {\xintSeries {1}{\the\cnta}{\coeffleibnitz}}\dots + {\xintSeries {1}{\cnta}{\coeffleibnitz}}\dots \endgraf \ifnum\cnta < 30 \advance\cnta 1 \repeat \end{verbatim} @@ -2354,33 +2549,31 @@ digits) in the denominator. See the explanations in the next section. \def\coeffleibnitz #1{\the\numexpr\ifodd #1 1\else-1\fi\relax/#1[0]} \cnta 1 \loop \noindent\hbox to 2em{\hfil\texttt{\the\cnta.} }% - \xintTrunc {12}{\xintSeries {1}{\the\cnta}{\coeffleibnitz}}\dots + \xintTrunc {12}{\xintSeries {1}{\cnta}{\coeffleibnitz}}\dots \endgraf \ifnum\cnta < 30 \advance\cnta 1 \repeat \end{multicols} \subsection{\csbh{xintiSeries}}\label{xintiSeries} -\def\coeff #1{\romannumeral0\xintitrunc {40} +\def\coeff #1{\xintiTrunc {40} {\the\numexpr\ifodd #1 -2\else2\fi\relax/\the\numexpr 2*#1+1\relax [0]}}% \csa{xintiSeries}|{A}{B}{\coeff}| evaluates the sum of |\coeff -{n}| from |n=A| to and including |n=B|. The initial and final indices must -(after double-expansion) be explicit numbers at most |2^31-1| (these conditions -are not checked by the macro). The -|\coeff| macro (which, as argument to \csa{xintiSeries} is double-expanded only +{n}| from |n=A| to and including |n=B|. The initial and final indices are given +to a |\numexpr| expression. The +|\coeff| macro (which, as argument to \csa{xintiSeries} is expanded only at the time of computing |\coeff {n}|) should be defined as a -one-parameter command, accepting on input a number (not a count register) and -needing at most two expansions to compute its final result, \emph{which must be - an integer}, in the format understood by the integer-only +one-parameter fully expandable command, accepting on input an explicit number, +and returning a (long) integer in the format understood by the integer-only \csa{xintiAdd}. \begin{verbatim} -\def\coeff #1{\romannumeral0\xintitrunc {40}{\xintMON{#1}/#1.5}}% +\def\coeff #1{\xintiTrunc {40}{\xintMON{#1}/#1.5}}% % better: -\def\coeff #1{\romannumeral0\xintitrunc {40} +\def\coeff #1{\xintiTrunc {40} {\the\numexpr 2*\xintiMON{#1}\relax/\the\numexpr 2*#1+1\relax [0]}}% % better still: -\def\coeff #1{\romannumeral0\xintitrunc {40} +\def\coeff #1{\xintiTrunc {40} {\the\numexpr\ifodd #1 -2\else2\fi\relax/\the\numexpr 2*#1+1\relax [0]}}% % (-1)^n/(n+1/2) times 10^40, truncated to an integer. \[ \sum_{n=0}^{n=50} \frac{(-1)^n}{n+\frac12} \approx @@ -2390,7 +2583,8 @@ The |#1.5| trick to define the |\coeff| macro was neat, but |1/3.5|, for example, turns internally into |10/35| whereas it would be more efficient to have |2/7|. The second way of coding the wanted coefficient avoids a superfluous factor of five and leads to a faster evaluation. The third way is faster, after -all there is no need to use \csb{xintMON} (or rather \csb{xintiMON}) on integers +all there is no need to use \csb{xintMON} (or rather \csb{xintiMON} which has +less parsing overhead) on integers obeying the \TeX{} bound. The denominator having no sign, we have added the |[0]| as this speeds up (infinitesimally) the parsing. \[ \sum_{n=0}^{n=50} \frac{(-1)^n}{n+\frac12} \approx \xintTrunc @@ -2403,7 +2597,7 @@ interesting to compare with the computation where rounding rather than truncation is used, and with the decimal expansion of the exactly computed partial sum of the series: \begin{verbatim} -\def\coeff #1{\romannumeral0\xintiround {40} % rounding at 40 +\def\coeff #1{\xintiRound {40} % rounding at 40 {\the\numexpr\ifodd #1 -2\else2\fi\relax/\the\numexpr 2*#1+1\relax [0]}}% % (-1)^n/(n+1/2) times 10^40, rounded to an integer. \[ \sum_{n=0}^{n=50} \frac{(-1)^n}{n+\frac12} \approx @@ -2413,7 +2607,7 @@ expansion of the exactly computed partial sum of the series: \[ \sum_{n=0}^{n=50} \frac{(-1)^n}{n+\frac12} = \xintTrunc {50}{\xintSeries {0}{50}{\exactcoeff}}\dots\] \end{verbatim} -\def\coeff #1{\romannumeral0\xintiround {40} +\def\coeff #1{\xintiRound {40} {\the\numexpr\ifodd #1 -2\else2\fi\relax/\the\numexpr 2*#1+1\relax [0]}}% % (-1)^n/(n+1/2) times 10^40, rounded to an integer. \[ \sum_{n=0}^{n=50} \frac{(-1)^n}{n+\frac12} \approx @@ -2437,17 +2631,15 @@ estimated wrongly the 39th and 40th digits of the exact result\footnote{as |F(n)|\footnote{the macro is designed to be useful when |F(n)/F(n-1)| is a rational function of |n| but it may be used of course with any sort of general term.} from |n=A| up to and including |n=B|, with the parameter |f| being (or -expanding in two steps to) the value |F(A)| and |\ratio| being a one-parameter -command, accepting on input a number |n| (not a count register, but also obeying -the constraint of having value at most |2^31-1|) and producing after at most two -expansions |F(n)/F(n-1)|. The initial and final indices must (after -double-expansion) obey the \TeX{} and |\numexpr| constraint of being explicit -numbers at most |2^31-1| (these conditions are not checked by the macro). +expanding to) the value |F(A)| and |\ratio| being a one-parameter expandable +command, accepting on input an explicit number |n| and producing after (full +iterated) expansion (of the first token) |F(n)/F(n-1)|. The initial and final +indices are given to a |\numexpr| expression. \begin{verbatim} \def\ratio #1{2/#1[0]}% 2/n, comes from the series of exp(2) \cnta 0 % previously declared count \loop -\edef\z {\xintRationalSeries {0}{\the\cnta}{1}{\ratio }}% +\edef\z {\xintRationalSeries {0}{\cnta}{1}{\ratio }}% \noindent$\sum_{n=0}^{\the\cnta} \frac{2^n}{n!}= \xintTrunc{12}\z\dots= \xintFrac\z=\xintFrac{\xintIrr\z}$\vtop to 5pt{}\endgraf @@ -2456,7 +2648,7 @@ numbers at most |2^31-1| (these conditions are not checked by the macro). \def\ratio #1{2/#1[0]}% 2/n, comes from the series of exp(2) \cnta 0 \loop -\edef\z {\xintRationalSeries {0}{\the\cnta}{1}{\ratio }}% +\edef\z {\xintRationalSeries {0}{\cnta}{1}{\ratio }}% \noindent$\sum_{n=0}^{\the\cnta} \frac{2^n}{n!}= \xintTrunc{12}\z\dots= \xintFrac\z=\xintFrac{\xintIrr\z}$\vtop to 5pt{}\endgraf @@ -2473,7 +2665,7 @@ evaluate the partial sums via a less silly iterative scheme. \def\ratio #1{-1/#1[0]}% -1/n, comes from the series of exp(-1) \cnta 0 % previously declared count \loop -\edef\z {\xintRationalSeries {0}{\the\cnta}{1}{\ratio }}% +\edef\z {\xintRationalSeries {0}{\cnta}{1}{\ratio }}% \noindent$\sum_{n=0}^{\the\cnta} \frac{(-1)^n}{n!}= \xintTrunc{20}\z\dots=\xintFrac{\z}=\xintFrac{\xintIrr\z}$ \vtop to 5pt{}\endgraf @@ -2483,29 +2675,29 @@ evaluate the partial sums via a less silly iterative scheme. \cnta 0 % previously declared count \loop -\edef\z {\xintRationalSeries {0}{\the\cnta}{1}{\ratio }}% +\edef\z {\xintRationalSeries {0}{\cnta}{1}{\ratio }}% \noindent$\sum_{n=0}^{\the\cnta} \frac{(-1)^n}{n!}= \xintTrunc{20}\z\dots=\xintFrac{\z}=\xintFrac{\xintIrr\z}$ \vtop to 5pt{}\endgraf \ifnum\cnta<20 \advance\cnta 1 \repeat - \def\ratioexp #1#2{\romannumeral0\xintdiv{#1}{#2}}% #1/#2 + \def\ratioexp #1#2{\xintDiv{#1}{#2}}% #1/#2 \medskip We can incorporate an indeterminate if we define |\ratio| to be a macro with two parameters: |\def\ratioexp - #1#2{\romannumeral0\xintdiv{#1}{#2}}|\texttt{\%}| x/n: x=#1, n=#2|. -Then, if |\x| expands (in two steps at most) to some fraction |x|, the + #1#2{\xintDiv{#1}{#2}}|\texttt{\%}| x/n: x=#1, n=#2|. +Then, if |\x| expands to some fraction |x|, the command \centeredline{|\xintRationalSeries {0}{b}{1}{\ratioexp{\x}}|} will compute $\sum_{n=0}^{n=b} x^n/n!$:\par \vspace*{-.5\baselineskip} \begin{verbatim} \cnta 0 -\def\ratioexp #1#2{\romannumeral0\xintdiv{#1}{#2}}% #1/#2 +\def\ratioexp #1#2{\xintDiv{#1}{#2}}% #1/#2 \loop \noindent $\sum_{n=0}^{\the\cnta} (.57)^n/n! = \xintTrunc {50} - {\xintRationalSeries {0}{\the\cnta}{1}{\ratioexp{.57}}}\dots$ + {\xintRationalSeries {0}{\cnta}{1}{\ratioexp{.57}}}\dots$ \vtop to 5pt {}\endgraf \ifnum\cnta<50 \advance\cnta 10 \repeat \end{verbatim} @@ -2514,7 +2706,7 @@ $\sum_{n=0}^{\the\cnta} (.57)^n/n! = \xintTrunc {50} \loop \noindent $\sum_{n=0}^{\the\cnta} (.57)^n/n! = \xintTrunc {50} - {\xintRationalSeries {0}{\the\cnta}{1}{\ratioexp{.57}}}\dots$ + {\xintRationalSeries {0}{\cnta}{1}{\ratioexp{.57}}}\dots$ \vtop to 5pt {}\endgraf \ifnum\cnta<50 \advance\cnta 10 \repeat Observe that in this last example the |x| was directly inserted; if it @@ -2534,12 +2726,11 @@ Here is a slightly more complicated evaluation: \begin{verbatim} \cnta 1 \loop \edef\z {\xintRationalSeries - {\the\cnta} - {\the\numexpr 2*\cnta-1\relax} - {\xintiPow {\the\cnta}{\the\cnta}/\xintFac{\the\cnta}} + {\cnta} + {2*\cnta-1} + {\xintiPow {\the\cnta}{\cnta}/\xintFac{\cnta}} {\ratioexp{\the\cnta}}}% -\edef\w {\xintRationalSeries {0}{\the\numexpr 2*\cnta-1\relax}{1} - {\ratioexp{\the\cnta}}}% +\edef\w {\xintRationalSeries {0}{2*\cnta-1}{1}{\ratioexp{\the\cnta}}}% \noindent $\sum_{n=\the\cnta}^{\the\numexpr 2*\cnta-1\relax} \frac{\the\cnta^n}{n!}/% \sum_{n=0}^{\the\numexpr 2*\cnta-1\relax} \frac{\the\cnta^n}{n!} = @@ -2549,12 +2740,11 @@ $\sum_{n=\the\cnta}^{\the\numexpr 2*\cnta-1\relax} \frac{\the\cnta^n}{n!}/% \cnta 1 \begin{multicols}{2} \loop \edef\z {\xintRationalSeries - {\the\cnta} - {\the\numexpr 2*\cnta-1\relax} - {\xintiPow {\the\cnta}{\the\cnta}/\xintFac{\the\cnta}} + {\cnta} + {2*\cnta-1} + {\xintiPow {\the\cnta}{\cnta}/\xintFac{\cnta}} {\ratioexp{\the\cnta}}}% -\edef\w {\xintRationalSeries {0}{\the\numexpr 2*\cnta-1\relax}{1} - {\ratioexp{\the\cnta}}}% +\edef\w {\xintRationalSeries {0}{2*\cnta-1}{1}{\ratioexp{\the\cnta}}}% \noindent$\sum_{n=\the\cnta}^{\the\numexpr 2*\cnta-1\relax} \frac{\the\cnta^n}{n!}/% \sum_{n=0}^{\the\numexpr 2*\cnta-1\relax} \frac{\the\cnta^n}{n!} = \xintTrunc{8}{\xintDiv\z\w}\dots$ \vtop to 5pt{}\endgraf @@ -2566,15 +2756,14 @@ $\sum_{n=\the\cnta}^{\the\numexpr 2*\cnta-1\relax} \frac{\the\cnta^n}{n!}/% {\small New with release |1.04|.\par} \csa{xintRationalSeriesX}|{A}{B}{\first}{\ratio}{\x}| evaluates the sum of -|F(n,x)| from |n=A| up to and including |n=B|, where |\x| expands in two -steps at most to a fraction |x|, |\first| is a one-parameter macro such that -|\first{\x}| expands in two steps at most to the first term |F(A,x)| of the -series, and |\ratio| is a two parameter macro such that |\ratio{\x}{n}| -expands in two steps at most to the ratio |F(n,x)/F(n-1,x)|. Thus, this -is a parametrized version of \csa{xintRationalSeries}, where the -parameter |\x| is evaluated only once at the beginning of the -computation, and can thus itself be the yet unevaluated result of a -previous computation. +|F(n,x)| from |n=A| up to and including |n=B|, where |\x| expands to a fraction +|x|, |\first| is a one-parameter macro such that |\first{\x}| expands in two +steps at most to the first term |F(A,x)| of the series, and |\ratio| is a two +parameter macro such that |\ratio{\x}{n}| expands to the +ratio |F(n,x)/F(n-1,x)|. Hence, this is a parametrized version of +\csa{xintRationalSeries}, where the parameter |\x| is evaluated only once at the +beginning of the computation, and can thus itself be the yet unevaluated result +of a previous computation. Note the subtle differences between \centeredline{|\xintRationalSeries {a}{b}{\first}{\ratio{\x}}|}% @@ -2596,7 +2785,7 @@ next section. \def\firstterm #1{1[0]}% first term of the exponential series % although it is the constant 1, here it must be defined as a % one-parameter macro. Next comes the ratio function for exp: -\def\ratioexp #1#2{\romannumeral0\xintdiv {#1}{#2}}% x/n +\def\ratioexp #1#2{\xintDiv {#1}{#2}}% x/n % These are the (-1)^{n-1}/n of the log(1+h) series: \def\coefflog #1{\the\numexpr\ifodd #1 1\else-1\fi\relax/#1[0]}% % Let L(h) be the first 10 terms of the log(1+h) series and @@ -2614,7 +2803,7 @@ next section. \def\firstterm #1{1[0]}% first term of the exponential series % although it is the constant 1, here it must be defined as a % one-parameter macro. Next comes the ratio function for exp: -\def\ratioexp #1#2{\romannumeral0\xintdiv {#1}{#2}}% x/n +\def\ratioexp #1#2{\xintDiv {#1}{#2}}% x/n % These are the (-1)^{n-1}/n of the log(1+h) series \def\coefflog #1{\the\numexpr\ifodd #1 1\else-1\fi\relax/#1[0]}% % Let L(h) be the first 10 terms of the log(1+h) series and @@ -2725,20 +2914,17 @@ are available via the commands \csb{xintTrunc} and \csb{xintRound}. \csa{xintPowerSeries}|{A}{B}{\coeff}{x}| evaluates the sum of |\coeff{n}|\raisebox{.5ex}{|.|}|x^n| from |n=A| up to and including |n=B|. The -initial and final indices must (after double-expansion) be -explicit numbers at most |2^31-1| (these -conditions are not checked by the macro). The |\coeff| macro (which, as argument -to \csa{xintPowerSeries} is double-expanded only at the time -|\coeff{n}| is needed) should be defined as a one-parameter command, accepting -on input a number (not a count register) and needing at most two expansions to -compute its final result. - -The |x| can be either a fraction directly input or a macro expanding in -at most two steps to such a fraction. It is actually more efficient to -encapsulate an explicit fraction |x| in such a macro (say |\x|), if it -has big numerators and denominators (`big' means hundreds of -digits) as it will then take less space in the processing until being -(repeatedly) used. +initial and final indices are given to a |\numexpr| expression. The |\coeff| +macro (which, as argument to \csa{xintPowerSeries} is expanded only at the time +|\coeff{n}| is needed) should be defined as a one-parameter expandable (in the +now usual meaning) command, +accepting on input an explicit number. + +The |x| can be either a fraction directly input or a macro expanding to such a +fraction. It is actually more efficient to encapsulate an explicit fraction |x| +in such a macro (say |\x|), if it has big numerators and denominators (`big' +means hundreds of digits) as it will then take less space in the processing +until being (repeatedly) used. This macro computes the \emph{exact} result (one can use it also for polynomial evaluation). With release |1.04| the Horner scheme for @@ -2795,7 +2981,7 @@ was plaguing the |1.03| version. \footnote{with powers |x\string^k|, % we can afford that, as \xintPowerSeries is fast enough. \noindent\hbox to 2em{\hfil\texttt{\the\cnta.} }% \xintTrunc {12} - {\xintPowerSeries {1}{\the\cnta}{\coefflog}{\x}}\dots + {\xintPowerSeries {1}{\cnta}{\coefflog}{\x}}\dots \endgraf \ifnum \cnta < 30 \advance\cnta 1 \repeat \end{verbatim} @@ -2805,7 +2991,7 @@ was plaguing the |1.03| version. \footnote{with powers |x\string^k|, \loop % in this loop we recompute from scratch each partial sum! % we can afford that, as \xintPowerSeries is fast enough. \noindent\hbox to 2em{\hfil\texttt{\the\cnta.} }% - \xintTrunc {12}{\xintPowerSeries {1}{\the\cnta}{\coefflog}{\x}}\dots + \xintTrunc {12}{\xintPowerSeries {1}{\cnta}{\coefflog}{\x}}\dots \endgraf \ifnum \cnta < 30 \advance\cnta 1 \repeat \end{multicols} @@ -2835,24 +3021,23 @@ was plaguing the |1.03| version. \footnote{with powers |x\string^k|, {\small New with release |1.04|.\par} This is the same as \csb{xintPowerSeries} apart from the fact that the last -parameter (aka |x|), is first twice expanded. If the |x| parameter is to be an -explicit big fraction |f| with many (dozens) digits, rather than using -|f| directly it is slightly better to have some macro |\x| |\def'|ined to expand -to the explicit |f| and use \csb{xintPowerSeries}; but if |f| has not yet been -evaluated and will be the output of a complicated expansion of some |\x|, and -if, due to an expanding only context, an |\edef\z{\x}| is no option, then -\csa{xintPowerSeriesX} should be used with |\x| as last parameter. This |\x| -will be expanded (as usual, twice) and then its (explicit) output will be used. -The reason why \csa{xintPowerSeries} doesn't do the same is that explicit -fractions with many (dozens) digits slow down a bit the processing as -there is some shuffling of tokens going on. With \csa{xintPowerSeriesX} the -slowing down in token shuffling due to a very big fraction will not be avoided, -but the far worse cost of re-doing each time the computations leading to -such a fraction will be. The constraints of expandability make it impossible -to encapsulate the result of this initial computation in a macro and have the -best of both worlds. +parameter (aka |x|), is first expanded before being then used. If the |x| +parameter is to be an explicit big fraction |f| with many (dozens) digits, +rather than using |f| directly it is slightly better to have some macro |\x| +|\def'|ined to expand to the explicit |f| and use \csb{xintPowerSeries}; but if +|f| has not yet been evaluated and will be the output of a complicated expansion +of some |\x|, and if, due to an expanding only context, an |\edef\z{\x}| is no +option, then \csa{xintPowerSeriesX} should be used with |\x| as last parameter. +This |\x| will be expanded (as usual) and then its (explicit) output will be +used. The reason why \csa{xintPowerSeries} doesn't do the same is that explicit +fractions with many (dozens) digits slow down a bit the processing as there is +some shuffling of tokens going on. With \csa{xintPowerSeriesX} the slowing down +in token shuffling due to a very big fraction will not be avoided, but the far +worse cost of re-doing each time the computations leading to such a fraction +will be. The constraints of expandability make it impossible to encapsulate the +result of this initial computation in a macro and have the best of both worlds. \begin{verbatim} -\def\ratioexp #1#2{\romannumeral0\xintdiv {#1}{#2}}% x/n +\def\ratioexp #1#2{\xintDiv {#1}{#2}}% x/n % These are the (-1)^{n-1}/n of the log(1+h) series: \def\coefflog #1{\the\numexpr\ifodd #1 1\else-1\fi\relax/#1[0]}% % Let L(h) be the first 10 terms of the log(1+h) series and @@ -2869,7 +3054,7 @@ best of both worlds. \ifnum\cnta < 12 \advance \cnta 1 \repeat \end{verbatim} \cnta 0 -\def\ratioexp #1#2{\romannumeral0\xintdiv {#1}{#2}}% x/n +\def\ratioexp #1#2{\xintDiv {#1}{#2}}% x/n % These are the (-1)^{n-1}/n of the log(1+h) series \def\coefflog #1{\the\numexpr\ifodd #1 1\else-1\fi\relax/#1[0]}% % Let L(h) be the first 10 terms of the log(1+h) series and @@ -2892,13 +3077,14 @@ best of both worlds. \csa{xintFxPtPowerSeries}|{A}{B}{\coeff}{x}{D}| computes the sum of |\coeff{n}|\raisebox{.5ex}{|.|}|x^n| from |n=A| to |n=B| with each term of the -series truncated to |D| digits after the decimal point. As usual, |A| -and |B| are first twice-expanded. Regarding |D| it will be twice-expanded each -time it will be used inside an \csa{xintTrunc}. The one-parameter macro |\coeff| -is similarly only expanded when it is used inside the computations. Idem for -|x|. If |x| itself is some complicated macro it is thus better to use the -variant \csb{xintFxPtPowerSeriesX} which expands it first and then uses the -result of that (double) expansion. +series truncated to |D| digits after the decimal point. As usual, |A| and |B| +are completely expanded through their inclusion in a |\numexpr| expression. +Regarding |D| it will be similarly be expanded each time it is used inside an +\csa{xintTrunc}. The one-parameter macro |\coeff| is similarly only expanded (in +the usual meaning) when it is used inside the computations. Idem for |x|. If |x| +itself is some complicated macro it is thus better to use the variant +\csb{xintFxPtPowerSeriesX} which expands it first and then uses the result of +that expansion. The current (|1.04|) implementation is: the first power |x^A| is computed exactly, then \emph{truncated}. Then each successive power is @@ -2909,59 +3095,47 @@ truncating. Finally the sum is computed exactly. Apart from that \csa{xintFxPtPowerSeries} (where |FxPt| means `fixed-point') is like \csa{xintPowerSeries}. +There should be a variant for things of the +type $\sum c_n \frac {x^n}{n!}$ to avoid having to compute the factorial +from scratch at each coefficient, the same way \csa{xintFxPtPowerSeries} +does not compute |x^n| from scratch at each |n|. Perhaps in the next package +release. + \def\coeffexp #1{1/\xintFac {#1}[0]}% [0] for faster parsing \def\x {-1/2[0]}% \def\ApproxExp #1#2{\xintFxPtPowerSeries {0}{#1}{\coeffexp}{\x}{#2}}% \newcount\cnta -\noindent\begin{minipage}{0.3\linewidth} -\centeredline{$e^{-\frac12}\approx{}$}% +\setlength{\multicolsep}{0pt} + +\begin{multicols}{3}[% +\centeredline{$e^{-\frac12}\approx{}$}]% \cnta 0 -\loop -$\ApproxExp {\the\cnta}{20}$\\ +\noindent\loop +$\ApproxExp {\cnta}{20}$\\ \ifnum\cnta<19 \advance\cnta 1 \repeat\par -\end{minipage} -\hfil -\begin{minipage}{0.65\linewidth} -\ttfamily\hyphenchar\font-1 +\end{multicols} \begin{verbatim} -\def\coeffexp #1{1/\xintFac {#1}[0]}% -\def\x {-1/2[0]}% [0] for faster parsing -\def\ApproxExp #1#2{\xintFxPtPowerSeries - {0}{#1}{\coeffexp}{\x}{#2}}% +\def\coeffexp #1{1/\xintFac {#1}[0]}% 1/n! +\def\x {-1/2[0]}% [0] for faster input parsing +\def\ApproxExp #1#2{\xintFxPtPowerSeries {0}{#1}{\coeffexp}{\x}{#2}}% \cnta 0 % previously declared \count register -\loop -$\ApproxExp {\the\cnta}{20}$\\ -% truncates 20 digits after decimal point -\ifnum\cnta<19 -\advance\cnta 1 -\repeat\par -% One should **not** trust the final digits, -% as the potential truncation errors of up to -% 10^{-20} per term accumulate and never -% disappear! (the effect is attenuated by the -% alternating signs in the series). We can -% confirm that the last two digits (of our -% evaluation of the nineteenth partial sum) -% are wrong via the evaluation with more -% digits: +\noindent\loop +$\ApproxExp {\cnta}{20}$\\ % truncates 20 digits after decimal point +\ifnum\cnta<19 \advance\cnta 1 \repeat\par +% One should **not** trust the final digits, as the potential truncation +% errors of up to 10^{-20} per term accumulate and never disappear! (the +% effect is attenuated by the alternating signs in the series). We can +% confirm that the last two digits (of our evaluation of the nineteenth +% partial sum) are wrong via the evaluation with more digits: \end{verbatim} -\end{minipage} - -\centeredline{|\xintFxPtPowerSeries {0}{19}{\coeffexp}{\x}{25}=|}% -\centeredline{% +\centeredline{|\xintFxPtPowerSeries {0}{19}{\coeffexp}{\x}{25}=| \xintFxPtPowerSeries {0}{19}{\coeffexp}{\x}{25}} \texttt{\hyphenchar\font45 } -There should be a variant for things of the -type $\sum c_n \frac {x^n}{n!}$ to avoid having to compute the factorial -from scratch at each coefficient, the same way \csa{xintFxPtPowerSeries} -does not compute |x^n| from scratch at each |n|. Perhaps in the next package -release. - \edef\z{\xintIrr {\xintPowerSeries {0}{19}{\coeffexp}{\x}}} It is no difficulty for \xintfracname to compute exactly, with the help @@ -2986,7 +3160,7 @@ of digits possibly of dubious significance. \csa{xintFxPtPowerSeries}, the sum of |\coeff{n}|\raisebox{.5ex}{|.|}|\x^n| from |n=A| to |n=B| with each term of the series being \emph{truncated} to |D| digits after the decimal -point. The sole difference is that |\x| is first expanded (twice) and it +point. The sole difference is that |\x| is first expanded and it is the result of this which is used in the computations. % Let us illustrate this on the computation of |(1+y)^{5/3}| where @@ -3121,7 +3295,8 @@ correct exact truncated one. \def\xb {1/9[0]}% we will compute log(1-1/9) \def\LogTwo #1% % get log(2)=-2log(1-13/256)- 5log(1-1/9) -{% +{% we want to use \printnumber, hence need something expanding in two steps + % only, so we use here the \romannumeral0 method \romannumeral0\expandafter\LogTwoDoIt \expandafter % Nb Terms for 1/9: {\the\numexpr #1*150/143\expandafter}\expandafter @@ -3210,10 +3385,7 @@ zeros may be nine (and the last non-zero one should be decreased). % Alternatives: % \def\coeffarctg #1{1/\the\numexpr\xintiMON{#1}*(2*#1+1)\relax }% % The [0] can *not* be used above, as the denominator is signed. -% \def\coeffarctg #1{\the\numexpr\xintiMON{#1}\relax/% - \the\numexpr 2*#1+1\relax [0]}% -% \def\coeffarctg #1% - {\romannumeral0\xintmon{#1}/\the\numexpr 2*#1+1\relax [0]}% +% \def\coeffarctg #1{\xintiMON{#1}/\the\numexpr 2*#1+1\relax [0]}% \def\xa {1/25[0]}% 1/5^2, the [0] for faster parsing \def\xb {1/57121[0]}% 1/239^2, the [0] for faster parsing \def\Machin #1{% \Machin {\mycount} is allowed @@ -3222,7 +3394,7 @@ zeros may be nine (and the last non-zero one should be decreased). {\the\numexpr (#1+3)*5/7\expandafter}\expandafter % number of terms for arctg(1/239): {\the\numexpr (#1+3)*10/45\expandafter}\expandafter - % do the computations with 4 additional digits: + % do the computations with 3 additional digits: {\the\numexpr #1+3\expandafter}\expandafter % allow #1 to be a count register: {\the\numexpr #1\relax }}% @@ -3250,7 +3422,7 @@ zeros may be nine (and the last non-zero one should be decreased). {\the\numexpr (#1+3)*5/7\expandafter}\expandafter % number of terms for arctg(1/239): {\the\numexpr (#1+3)*10/45\expandafter}\expandafter - % do the computations with 4 additional digits: + % do the computations with 3 additional digits: {\the\numexpr #1+3\expandafter}\expandafter % allow #1 to be a count register: {\the\numexpr #1\relax }}% @@ -3305,7 +3477,7 @@ Let us use this variant for a loop showing the build-up of digits: \begin{verbatim} \cnta 0 % previously declared \count register \loop - \MachinBis{\cnta} \endgraf % TeX's \loop does not accept \par + \MachinBis{\cnta} \endgraf % Plain's \loop does not accept \par \ifnum\cnta < 30 \advance\cnta 1 \repeat \end{verbatim} \begin{multicols}{2} @@ -3528,20 +3700,20 @@ It produces:\par }{\xintApply{\mymacro}{\xintFtoCv{49171/18089}}}. -\def\cn #1{\romannumeral0\xintipow {2}{#1}}% +\def\cn #1{\xintiPow {2}{#1}}% The macro \csb{xintCntoF} allows to specify the coefficients as functions of the index. The values to which expand the coefficient function do not have to be integers. \centeredline{|\def\cn - #1{\romannumeral0\xintipow {2}{#1}}% 2^n|}% + #1{\xintiPow {2}{#1}}% 2^n|}% \centeredline{|\[\xintFrac{\xintCntoF {6}{\cn}}=\xintCFrac [l]{\xintCntoF {6}{\cn}}\]|}% \[\xintFrac{\xintCntoF {6}{\cn}}=\xintCFrac [l]{\xintCntoF {6}{\cn}}\] Notice the use of the optional argument |[l]| to \csa{xintCFrac}. Other possibilities are |[r]| and (default) |[c]|. -\def\cn #1{\romannumeral0\xintpow {2}{-#1}}% -\centeredline{|\def\cn #1{\romannumeral0\xintpow {2}{-#1}}% 1/2^n|}% +\def\cn #1{\xintPow {2}{-#1}}% +\centeredline{|\def\cn #1{\xintPow {2}{-#1}}% 1/2^n|}% \centeredline{% |\[\xintFrac{\xintCntoF {6}{\cn}} = \xintGCFrac [r]{\xintCntoGC {6}{\cn}}|}% \centeredline{| = [\xintFtoCs {\xintCntoF {6}{\cn}}]\]|}% @@ -3668,9 +3840,9 @@ $1$ or $-1$. which first computes then displays with the help of |\cfrac| the simple continued fraction corresponding to the given fraction (or macro expanding in two steps to one such). It admits an optional argument which may be |[l]|, |[r]| -or (the default) |[c]| to specify the location of the one's in the numerators. -Each numerator is typeset using the \csb{xintFrac} macro from the \xintfracname -package. +or (the default) |[c]| to specify the location of the one's in the numerators of +the sub-fractions. Each coefficient is typeset using the \csb{xintFrac} macro +from the \xintfracname package. \subsection{\csbh{xintGCFrac}}\label{xintGCFrac} @@ -3857,29 +4029,29 @@ with |\xintApply\xintIrr|. \def\macro #1{\the\numexpr 1+#1*#1\relax} -\csa{xintCntoF}|{N}{\macro}| computes the fraction |f| having -coefficients |c(j)=\macro{j}| for |j=0,1,...,N|. The values do not have -to be positive, nor integers, and it is thus not necessarily the case -that the original |c(j)| are the true coefficients of the final |f|. -One usually has to define the one-parameter |\macro| in advance. -\centeredline{% -|\def\macro #1{\the\numexpr 1+#1*#1\relax}\xintCntoF {5}{\macro}|}% +\csa{xintCntoF}|{N}{\macro}| computes the fraction |f| having coefficients +|c(j)=\macro{j}| for |j=0,1,...,N|. The |N| parameter is given to a |\numexpr|. +The values of the coefficients, as returned by |\macro| do not have to be +positive, nor integers, and it is thus not necessarily the case that the +original |c(j)| are the true coefficients of the final |f|. \centeredline{% + |\def\macro #1{\the\numexpr 1+#1*#1\relax}\xintCntoF {5}{\macro}|}% \centeredline{\xintCntoF {5}{\macro}} \subsection{\csbh{xintGCntoF}}\label{xintGCntoF} \def\coeffA #1{\the\numexpr #1+4-3*((#1+2)/3)\relax }% -\def\coeffB #1{\romannumeral0\xintmon{#1}}% (-1)^n +\def\coeffB #1{\xintMON{#1}}% (-1)^n \csa{xintGCntoF}|{N}{\macroA}{\macroB}| returns the fraction |f| corresponding to the inline generalized continued fraction |a0+b0/a1+b1/a2+....+b(N-1)/aN|, -with |a(j)=\macroA{j}| and |b(j)=\macroB{j}|. +with |a(j)=\macroA{j}| and |b(j)=\macroB{j}|. The |N| parameter is given to a +|\numexpr|. \[\xintGCFrac{\xintGCntoGC {6}{\coeffA}{\coeffB}} = \xintFrac{\xintGCntoF {6}{\coeffA}{\coeffB}}\] There is also \csb{xintGCntoGC} to get the `inline format' continued fraction. The previous display was obtained with: \centeredline{|\def\coeffA #1{\the\numexpr #1+4-3*((#1+2)/3)\relax }%|}% -\centeredline{|\def\coeffB #1{\romannumeral0\xintmon{#1}}% (-1)^n|}% +\centeredline{|\def\coeffB #1{\xintMON{#1}}% (-1)^n|}% \centeredline{|\[\xintGCFrac{\xintGCntoGC {6}{\coeffA}{\coeffB}}|}% \centeredline{| = \xintFrac{\xintGCntoF {6}{\coeffA}{\coeffB}}\]|} @@ -3887,7 +4059,8 @@ fraction. The previous display was obtained with: \subsection{\csbh{xintCntoCs}}\label{xintCntoCs} \csa{xintCntoCs}|{N}{\macro}| produces the comma separated list of the -corresponding coefficients, from |n=0| to |n=N|. +corresponding coefficients, from |n=0| to |n=N|. The |N| is given to a +|\numexpr|. \centeredline{% |\def\macro #1{\the\numexpr 1+#1*#1\relax}\xintCntoCs {5}{\macro}|}% \centeredline{\xintCntoCs {5}{\macro}}% @@ -3903,8 +4076,8 @@ corresponding coefficients, from |n=0| to |n=N|. \csa{xintCntoGC}|{N}{\macro}| evaluates the |c(j)=\macro{j}| from |j=0| to |j=N| and returns a continued fraction written in inline -format: |{c(0)}+1/{c(1)}+1/...+1/{c(N)}|. It may then serve as input to -other macros. The coefficients, after expansion, are, as shown, being +format: |{c(0)}+1/{c(1)}+1/...+1/{c(N)}|. The parameter |N| is given to a +|\numexpr|. The coefficients, after expansion, are, as shown, being enclosed in an added pair of braces, they may thus be fractions. \centeredline{% @@ -3917,11 +4090,10 @@ fractions. \subsection{\csbh{xintGCntoGC}}\label{xintGCntoGC} -\csa{xintGCntoGC}|{N}{\macroA}{\macroB}| evaluates the coefficients and -then returns the corresponding -|{a0}+{b0}/{a1}+{b1}/{a2}+...+{b(N-1)}/{aN}| inline generalized -fraction. As shown, the coefficients are enclosed into added pairs of -braces, and may thus be fractions. +\csa{xintGCntoGC}|{N}{\macroA}{\macroB}| evaluates the coefficients and then +returns the corresponding |{a0}+{b0}/{a1}+{b1}/{a2}+...+{b(N-1)}/{aN}| inline +generalized fraction. |N| is givent to a |\numexpr|. As shown, the coefficients +are enclosed into added pairs of braces, and may thus be fractions. \begin{verbatim} \def\an #1{\the\numexpr #1*#1*#1+1\relax}% \def\bn #1{\the\numexpr \xintiMON{#1}*(#1+1)\relax}% @@ -3949,9 +4121,9 @@ hundreds of coefficients. \subsection{\csbh{xintGCtoGC}}\label{xintGCtoGC} -\csa{xintGCtoGC}|{a+b/c+d/e+f/g+......+v/w+x/y}| twice-expands each one of the -coefficients and returns an inline continued fraction of the same type, each -coefficient being enclosed withing braces. +\csa{xintGCtoGC}|{a+b/c+d/e+f/g+......+v/w+x/y}| expands (with the usual +meaning) each one of the coefficients and returns an inline continued fraction +of the same type, each expanded coefficient being enclosed withing braces. \begin{verbatim} \edef\x {\xintGCtoGC {1+\xintPow{1.5}{3}/{1/7}+{-3/5}/\xintFac {6}+\xintCstoF {2,-7,-5}/16}} @@ -3986,24 +4158,27 @@ first place. %<*xint> % \section {Package \xintname implementation} % -% The commenting of the macros is currently (\docdate) very -% sparse. Some comments may be left-overs from previous versions -% of the macro, with parameters in another order for example. +% The commenting of the macros is currently (\docdate) very sparse. Some +% comments may be left-overs from previous versions of the macro, with +% parameters in another order for example. % % \toctransition % \localtableofcontents % \subsection{Catcodes, \protect\eTeX{} and reload detection} % -% The method for package identification and reload detection is -% copied verbatim from the packages by \textsc{Heiko Oberdiek}. +% The method for package identification and reload detection is copied verbatim +% from the packages by \textsc{Heiko Oberdiek}. % -% The method for catcodes was also inspired by these packages, we -% proceed slightly differently. |1.05| adds a |\relax| near the end of +% The method for catcodes was also inspired by these packages, we proceed +% slightly differently. |1.05| adds a |\relax| near the end of % |\XINT@restorecatcodes@endinput|. Plain TeX users following the doc -% instruction to do |\input xint.sty\relax| were anyhow protected from -% any side effect. I didn't realize earlier that the |\endinput| would -% not have had the effect of stopping the scanning from the last -% |\the\catcode61|. +% instruction to do |\input xint.sty\relax| were anyhow protected from any side +% effect. I didn't realize earlier that the |\endinput| would not have had the +% effect of stopping the scanning from the last |\the\catcode61|. +% +% Starting with version |1.06| of the package, also |`| must be sanitized, +% because we replace everywhere in the code the twice-expansion done with +% |\expandafter| by the systematic use of |\romannumeral-`0|. % % \begin{macrocode} \begingroup\catcode61\catcode48\catcode32=10\relax% @@ -4045,6 +4220,7 @@ first place. \endgroup \edef\XINT@restorecatcodes@endinput {% + \catcode96=\the\catcode96 % ` \catcode47=\the\catcode47 % / \catcode41=\the\catcode41 % ) \catcode40=\the\catcode40 % ( @@ -4087,6 +4263,7 @@ first place. \catcode40=12 % ( \catcode41=12 % ) \catcode47=12 % / + \catcode96=12 % ` }% \XINT@setcatcodes }% @@ -4119,26 +4296,25 @@ first place. \fi \expandafter\x\csname ver@xint.sty\endcsname \ProvidesPackage{xint}% - [2013/05/02 v1.05a Expandable operations on long numbers (jfB)]% + [2013/05/07 v1.06 Expandable operations on long numbers (jfB)]% % \end{macrocode} % \subsection{Token management macros} % \begin{macrocode} -\def\xint@gobble #1{}% -\def\xint@gobble@one #1{}% -\def\xint@gobble@two #1#2{}% -\def\xint@gobble@three #1#2#3{}% -\def\xint@gobble@four #1#2#3#4{}% -\def\xint@gobble@five #1#2#3#4#5{}% -\def\xint@gobble@six #1#2#3#4#5#6{}% -\def\xint@gobble@seven #1#2#3#4#5#6#7{}% -\def\xint@gobble@eight #1#2#3#4#5#6#7#8{}% +\def\xint@gobble #1{}% +\def\xint@gobble@ {}% +\def\xint@gobble@i #1{}% +\def\xint@gobble@ii #1#2{}% +\def\xint@gobble@iii #1#2#3{}% +\def\xint@gobble@iv #1#2#3#4{}% +\def\xint@gobble@v #1#2#3#4#5{}% +\def\xint@gobble@vi #1#2#3#4#5#6{}% +\def\xint@gobble@vii #1#2#3#4#5#6#7{}% +\def\xint@gobble@viii #1#2#3#4#5#6#7#8{}% \def\xint@firstoftwo #1#2{#1}% \def\xint@secondoftwo #1#2{#2}% \def\xint@firstoftwo@andstop #1#2{ #1}% \def\xint@secondoftwo@andstop #1#2{ #2}% -\def\xint@exchangetwo@keepbraces #1#2{{#2}{#1}}% \def\xint@exchangetwo@keepbraces@andstop #1#2{ {#2}{#1}}% -\def\xint@xpxp@andstop {\expandafter\expandafter\expandafter\space }% \def\xint@minus@andstop { -}% \def\xint@r #1\R {}% \def\xint@w #1\W {}% @@ -4160,19 +4336,15 @@ first place. % \end{macrocode} % \subsection{\csh{xintRev}, \csh{xintReverseOrder}} % \begin{verbatim} -% \xintRev: fait la double expansion, vérifie le signe -% \xintReverseOrder: ne fait PAS la double expansion, ne regarde -% PAS le signe. +% \xintRev: fait l'expansion avec \romannumeral-`0, vérifie le signe +% \xintReverseOrder: ne fait PAS l'expansion, ne regarde PAS le signe. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintRev {\romannumeral0\xintrev }% \def\xintrev #1% {% - \expandafter\expandafter\expandafter - \xint@rev - \expandafter\expandafter\expandafter - {#1}% + \expandafter\xint@rev\expandafter {\romannumeral-`0#1}% }% \def\xint@rev #1% {% @@ -4216,227 +4388,285 @@ first place. \def\XINT@strip@undef #1\xint@undef {}% \def\XINT@strip@UNDEF #1\xint@UNDEF {}% % \end{macrocode} -% \subsection{\csh{XINT@RQ}} +% \subsection{\csh{xintRevWithBraces}} % \begin{verbatim} -% cette macro renverse et ajoute le nombre minimal de zéros à -% la fin pour que la longueur soit alors multiple de 4 -% \romannumeral0\XINT@RQ {}<le truc à renverser>\R\R\R\R\R\R\R\R\Z -% Attention, ceci n'est utilisé que pour des chaînes de chiffres, et donc le -% comportement avec des {..} ou autres espaces n'a fait l'objet d'aucune -% attention +% 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.) % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} -\def\XINT@RQ #1#2#3#4#5#6#7#8#9% +\def\xintRevWithBraces {\romannumeral0\xintrevwithbraces }% +\def\xintrevwithbraces #1% {% - \xint@r #9\XINT@RQ@end\R\XINT@RQ {#9#8#7#6#5#4#3#2#1}% + \expandafter\XINT@revwbr@prep\expandafter {\romannumeral-`0#1}% }% -\def\XINT@RQ@end\R\XINT@RQ #1#2\Z +\def\XINT@RWB {\romannumeral0\XINT@revwbr@prep }% +\def\XINT@revwbr@prep #1% {% - \XINT@RQ@end@ #1\Z + \XINT@revwbr@loop + {}#1\xint@undef\xint@undef\xint@undef\xint@undef + \xint@undef\xint@undef\xint@undef\xint@undef\Z }% -\def\XINT@RQ@end@ #1#2#3#4#5#6#7#8% +\def\XINT@revwbr@loop #1#2#3#4#5#6#7#8#9% {% - \xint@r #8\XINT@RQ@end@viii - #7\XINT@RQ@end@vii - #6\XINT@RQ@end@vi - #5\XINT@RQ@end@v - #4\XINT@RQ@end@iv - #3\XINT@RQ@end@iii - #2\XINT@RQ@end@ii - \R\XINT@RQ@end@i - \Z #2#3#4#5#6#7#8% + \XINT@strip@undef #9\XINT@revwbr@finish@a\xint@undef + \XINT@revwbr@loop {{#9}{#8}{#7}{#6}{#5}{#4}{#3}{#2}#1}% }% -\def\XINT@RQ@end@viii #1\Z #2#3#4#5#6#7#8#9\Z { #9}% -\def\XINT@RQ@end@vii #1\Z #2#3#4#5#6#7#8#9\Z { #8#9000}% -\def\XINT@RQ@end@vi #1\Z #2#3#4#5#6#7#8#9\Z { #7#8#900}% -\def\XINT@RQ@end@v #1\Z #2#3#4#5#6#7#8#9\Z { #6#7#8#90}% -\def\XINT@RQ@end@iv #1\Z #2#3#4#5#6#7#8#9\Z { #5#6#7#8#9}% -\def\XINT@RQ@end@iii #1\Z #2#3#4#5#6#7#8#9\Z { #4#5#6#7#8#9000}% -\def\XINT@RQ@end@ii #1\Z #2#3#4#5#6#7#8#9\Z { #3#4#5#6#7#8#900}% -\def\XINT@RQ@end@i \Z #1#2#3#4#5#6#7#8\Z { #1#2#3#4#5#6#7#80}% -% \end{macrocode} -% \subsection{\csh{XINT@cuz}} -% \begin{macrocode} -\def\xint@cleanupzeros@andstop #1#2#3#4% +\def\XINT@revwbr@finish@a\xint@undef\XINT@revwbr@loop #1#2\Z {% - \expandafter\space\the\numexpr #1#2#3#4\relax + \XINT@revwbr@finish@b #2\R\R\R\R\R\R\R\Z #1% }% -\def\xint@cleanupzeros@nospace #1#2#3#4% +\def\XINT@revwbr@finish@b #1#2#3#4#5#6#7#8\Z {% - \the\numexpr #1#2#3#4\relax + \xint@r #1\XINT@revwbr@finish@c 8% + #2\XINT@revwbr@finish@c 7% + #3\XINT@revwbr@finish@c 6% + #4\XINT@revwbr@finish@c 5% + #5\XINT@revwbr@finish@c 4% + #6\XINT@revwbr@finish@c 3% + #7\XINT@revwbr@finish@c 2% + \R\XINT@revwbr@finish@c 1\Z }% -\def\XINT@rev@andcuz #1% +\def\XINT@revwbr@finish@c #1#2\Z {% - \expandafter\xint@cleanupzeros@andstop - \romannumeral0\XINT@rord@main {}#1% - \xint@UNDEF - \xint@undef\xint@undef\xint@undef\xint@undef - \xint@undef\xint@undef\xint@undef\xint@undef - \xint@UNDEF + \expandafter\expandafter\expandafter + \space + \csname xint@gobble@\romannumeral #1\endcsname }% % \end{macrocode} -% \vspace*{-.5\baselineskip} +% \subsection{\csh{xintLen}, \csh{xintLength}} % \begin{verbatim} -% routine CleanUpZeros. Utilisée en particulier par la -% soustraction. -% INPUT: longueur **multiple de 4** (<-- ATTENTION) -% OUTPUT: on a retiré tous les leading zéros, on n'est **plus* -% nécessairement de longueur 4n -% Délimiteur pour @main: \W\W\W\W\W\W\W\Z avec SEPT \W +% \xintLen -> fait l'expansion, ne compte PAS le signe +% \xintLength -> ne fait PAS l'expansion, compte le signe +% 1.06: improved code is roughly 20% faster than the one from earlier versions. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} -\def\XINT@cuz #1% +\def\xintiLen {\romannumeral0\xintilen }% +\def\xintilen #1% {% - \XINT@cuz@loop #1\W\W\W\W\W\W\W\Z% + \expandafter\XINT@len@prep\expandafter {\romannumeral-`0#1}% }% -\def\XINT@cuz@loop #1#2#3#4#5#6#7#8% +\let\xintLen\xintiLen \let\xintlen\xintilen +\def\XINT@Len {\romannumeral0\XINT@len@prep }% +\def\XINT@len@prep #1% {% - \xint@w #8\xint@cuz@enda\W - \xint@z #8\xint@cuz@endb\Z - \XINT@cuz@checka {#1#2#3#4#5#6#7#8}% + \XINT@length@fork + #1\xint@undef\xint@undef\xint@undef\xint@undef + \xint@undef\xint@undef\xint@undef\xint@undef\Z }% -\def\xint@cuz@enda #1\XINT@cuz@checka #2% +\def\XINT@length@fork #1% {% - \xint@cuz@endaa #2% + \expandafter\XINT@length@loop + \xint@UDsignfork + #1\dummy {{0}}% + -\dummy {{0}#1}% + \xint@UDkrof }% -\def\xint@cuz@endaa #1#2#3#4#5\Z +\def\XINT@Length {\romannumeral0\XINT@length }% +\def\XINT@length #1% {% - \expandafter\space\the\numexpr #1#2#3#4\relax + \XINT@length@loop + {0}#1\xint@undef\xint@undef\xint@undef\xint@undef + \xint@undef\xint@undef\xint@undef\xint@undef\Z }% -\def\xint@cuz@endb\Z\XINT@cuz@checka #1{ 0}% -\def\XINT@cuz@checka #1% +\let\xintLength\XINT@Length +\def\XINT@length@loop #1#2#3#4#5#6#7#8#9% {% - \expandafter \XINT@cuz@checkb \the\numexpr #1\relax + \XINT@strip@undef #9\XINT@length@finish@a\xint@undef + \expandafter\XINT@length@loop\expandafter {\the\numexpr #1+8\relax}% }% -\def\XINT@cuz@checkb #1% +\def\XINT@length@finish@a\xint@undef + \expandafter\XINT@length@loop\expandafter #1#2\Z {% - \xint@zero #1\xint@cuz@backtoloop 0\XINT@cuz@Stop #1% + \XINT@length@finish@b #2\W\W\W\W\W\W\W\Z {#1}% }% -\def\XINT@cuz@Stop #1\W #2\Z{ #1}% -\def\xint@cuz@backtoloop 0\XINT@cuz@Stop 0{\XINT@cuz@loop }% +\def\XINT@length@finish@b #1#2#3#4#5#6#7#8\Z +{% + \xint@w #1\XINT@length@finish@c 8% + #2\XINT@length@finish@c 7% + #3\XINT@length@finish@c 6% + #4\XINT@length@finish@c 5% + #5\XINT@length@finish@c 4% + #6\XINT@length@finish@c 3% + #7\XINT@length@finish@c 2% + \W\XINT@length@finish@c 1\Z +}% +\def\XINT@length@finish@c #1#2\Z #3{\expandafter\space\the\numexpr #3-#1\relax}% % \end{macrocode} -% \subsection{\csh{XINT@isOne}} -% Added in |1.03|. Attention: does not do any expansion. +% \subsection{\csh{xintCSVtoList}} +% \begin{verbatim} +% \xintCSVtoList {a,b,..,z} returns {a}{b}...{z}. The comma separated list may +% be a macro which is first expanded. Each chain of spaces is collapsed +% into one space only. +% First included in release 1.06. +% \end{verbatim} +% \vspace*{-1.5\baselineskip} % \begin{macrocode} -\def\XINT@isOne #1{\romannumeral0\XINT@isone #1\W\Z }% -\def\XINT@isone #1#2% +\def\xintCSVtoList {\romannumeral0\xintcsvtolist }% +\def\xintcsvtolist #1% {% - \xint@one #1\XINT@isone@b 1\expandafter\space\expandafter 0\xint@z #2% + \expandafter\XINT@csvtol@prep\expandafter {\romannumeral-`0#1}% }% -\def\XINT@isone@b #1\xint@z #2% +\def\XINT@CSVtoL {\romannumeral0\XINT@csvtol@prep }% +\def\XINT@csvtol@prep #1% {% - \xint@w #2\XINT@isone@yes\W\expandafter\space\expandafter 0\xint@z + \XINT@csvtol@loop@a + {}#1,\xint@undef,\xint@undef,\xint@undef,\xint@undef,% + \xint@undef,\xint@undef,\xint@undef,\xint@undef,\Z }% -\def\XINT@isone@yes #1\Z{ 1}% +\def\XINT@csvtol@loop@a #1#2,#3,#4,#5,#6,#7,#8,#9,% +{% + \XINT@strip@undef #9\XINT@csvtol@finish@a\xint@undef + \XINT@csvtol@loop@b {#1}{{#2}{#3}{#4}{#5}{#6}{#7}{#8}{#9}}% +}% +\def\XINT@csvtol@loop@b #1#2{\XINT@csvtol@loop@a {#1#2}}% +\def\XINT@csvtol@finish@a\xint@undef\XINT@csvtol@loop@b #1#2#3\Z +{% + \XINT@csvtol@finish@b #3\R,\R,\R,\R,\R,\R,\R,\Z #2{#1}% +}% +\def\XINT@csvtol@finish@b #1,#2,#3,#4,#5,#6,#7,#8\Z +{% + \xint@r #1\XINT@csvtol@finish@c 8% + #2\XINT@csvtol@finish@c 7% + #3\XINT@csvtol@finish@c 6% + #4\XINT@csvtol@finish@c 5% + #5\XINT@csvtol@finish@c 4% + #6\XINT@csvtol@finish@c 3% + #7\XINT@csvtol@finish@c 2% + \R\XINT@csvtol@finish@c 1\Z +}% +\def\XINT@csvtol@finish@c #1#2\Z +{% + \csname XINT@csvtol@finish@d\romannumeral #1\endcsname +}% +\def\XINT@csvtol@finish@dviii #1#2#3#4#5#6#7#8#9{ #9}% +\def\XINT@csvtol@finish@dvii #1#2#3#4#5#6#7#8#9{ #9{#1}}% +\def\XINT@csvtol@finish@dvi #1#2#3#4#5#6#7#8#9{ #9{#1}{#2}}% +\def\XINT@csvtol@finish@dv #1#2#3#4#5#6#7#8#9{ #9{#1}{#2}{#3}}% +\def\XINT@csvtol@finish@div #1#2#3#4#5#6#7#8#9{ #9{#1}{#2}{#3}{#4}}% +\def\XINT@csvtol@finish@diii #1#2#3#4#5#6#7#8#9{ #9{#1}{#2}{#3}{#4}{#5}}% +\def\XINT@csvtol@finish@dii #1#2#3#4#5#6#7#8#9{ #9{#1}{#2}{#3}{#4}{#5}{#6}}% +\def\XINT@csvtol@finish@di #1#2#3#4#5#6#7#8#9{ #9{#1}{#2}{#3}{#4}{#5}{#6}{#7}}% % \end{macrocode} -% \subsection{\csh{xintNum}} +% \subsection{\csh{xintListWithSep}} % \begin{verbatim} -% For example \xintNum {----+-+++---+----000000000000003} -% 1.05 defines \xintiNum, as the original \xintNum will be a made a synonym of -% \xintIrr in xintfrac +% \xintListWithSep {sep}{{a}{b}...{z}} returns a sep b sep .... sep z +% Included in release 1.04. The 'sep' can be \par's: the macro +% xintlistwithsep etc... are all declared long. 'sep' does not have to be a +% single token. The list may be a macro it is first expanded. +% 1.06 modifies the `feature' of returning sep if the list is empty: the output +% is now empty in that case. (sep was not used for a one element list, but +% strangely it was for a zero-element list). % \end{verbatim} +% \vspace*{-1.5\baselineskip} % \begin{macrocode} -\def\xintiNum {\romannumeral0\xintinum }% -\def\xintinum #1% +\def\xintListWithSep {\romannumeral0\xintlistwithsep }% +\long\def\xintlistwithsep #1#2% {% - \expandafter\expandafter\expandafter - \XINT@num - \expandafter\expandafter\expandafter + \expandafter\XINT@lws\expandafter {\romannumeral-`0#2}% {#1}% }% -\let\xintNum\xintiNum \let\xintnum\xintinum -\def\XINT@Num {\romannumeral0\XINT@num }% -\def\XINT@num #1{\XINT@num@loop #1\R\R\R\R\R\R\R\R\Z }% -\def\XINT@num@loop #1#2#3#4#5#6#7#8% -{% - \xint@r #8\XINT@num@end\R\XINT@num@NumEight #1#2#3#4#5#6#7#8% +\long\def\XINT@LWS #1#2{\romannumeral0\XINT@lws@start {#1}#2\Z }% +\long\def\XINT@lws #1#2% +{% + \XINT@lws@start {#2}#1\Z }% -\def\XINT@num@end\R\XINT@num@NumEight #1\R #2\Z +\long\def\XINT@lws@start #1#2% {% - \expandafter\space\the\numexpr #1+0\relax + \xint@z #2\XINT@lws@dont\Z + \XINT@lws@loop@a {#2}{#1}% }% -\def\XINT@num@NumEight #1#2#3#4#5#6#7#8% +\long\def\XINT@lws@dont\Z\XINT@lws@loop@a #1#2{ }% +\long\def\XINT@lws@loop@a #1#2#3% {% - \ifnum \numexpr #1#2#3#4#5#6#7#8+0\relax = 0 - \xint@afterfi {\expandafter\XINT@num@keepsign@a - \the\numexpr #1#2#3#4#5#6#7#81\relax}% + \xint@z #3\XINT@lws@end\Z + \XINT@lws@loop@b {#1}{#2#3}{#2}% +}% +\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}% +% \end{macrocode} +% \subsection{\csh{xintNthElt}} +% \begin{verbatim} +% \xintNthElt {{a}{b}...{z}} (or `tokens' abcd...z) returns the Nth +% one (one pair of braces removed). The list is first expanded. +% First included in release 1.06. +% \end{verbatim} +% \vspace*{-1.5\baselineskip} +% \begin{macrocode} +\def\xintNthElt {\romannumeral0\xintnthelt }% +\def\xintnthelt #1#2% +{% + \expandafter\XINT@nthelt\expandafter {\romannumeral-`0#2}% + {\numexpr #1\relax}% +}% +\def\XINT@NthElt #1#2{\romannumeral0\XINT@nthelt {#2}{\numexpr #1\relax}}% +\def\XINT@nthelt #1#2% +{% + \ifnum #2<1 + \expandafter\XINT@nthelt@silentend \else - \xint@afterfi {\expandafter\XINT@num@finish - \the\numexpr #1#2#3#4#5#6#7#8\relax}% + \expandafter\XINT@nthelt@loop@a + \fi {#2}#1\xint@undef\xint@undef\xint@undef\xint@undef + \xint@undef\xint@undef\xint@undef\xint@undef\Z +}% +\def\XINT@nthelt@silentend #1\Z { }% +\def\XINT@nthelt@loop@a #1% +{% + \ifnum #1>8 + \expandafter\XINT@nthelt@loop@b + \else + \expandafter\XINT@nthelt@getit \fi + {#1}% }% -\def\XINT@num@keepsign@a #1% +\def\XINT@nthelt@loop@b #1#2#3#4#5#6#7#8#9% {% - \xint@one#1\XINT@num@gobacktoloop 1\XINT@num@keepsign@b + \XINT@strip@undef #9\XINT@nthelt@silentend\xint@undef + \expandafter\XINT@nthelt@loop@a\expandafter{\the\numexpr #1-8\relax}% +}% +\def\XINT@nthelt@getit #1% +{% + \expandafter\expandafter\expandafter\XINT@nthelt@finish + \csname xint@gobble@\romannumeral\numexpr#1-1\endcsname +}% +\def\XINT@nthelt@finish #1#2\Z +{% + \xint@UDwfork + #1\dummy { }% + \W\dummy { #1}% + \xint@UDkrof }% -\def\XINT@num@gobacktoloop 1\XINT@num@keepsign@b {\XINT@num@loop }% -\def\XINT@num@keepsign@b #1{\XINT@num@loop -}% -\def\XINT@num@finish #1\R #2\Z { #1}% % \end{macrocode} -% \subsection{\csh{xintLen}, \csh{xintLength}} +% \subsection{\csh{xintApply}} % \begin{verbatim} -% \xintLen -> fait la double expansion, ne compte PAS le signe -% \xintLength -> ne fait PAS la double expansion, compte le signe +% \xintApply {\macro}{{a}{b}...{z}} returns {\macro{a}}...{\macro{b}} +% where each instance of \macro is expanded. The list is first +% expanded. Introduced with release 1.04. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} -\def\xintiLen {\romannumeral0\xintilen }% -\def\xintilen #1% +\def\xintApply {\romannumeral0\xintapply }% +\def\xintapply #1#2% {% - \expandafter\expandafter\expandafter - \XINT@length@fork #1\R\R\R\R\R\R\R\R\Z + \expandafter\XINT@apply\expandafter {\romannumeral-`0#2}% + {#1}% }% -\let\xintLen\xintiLen \let\xintlen\xintilen -\def\XINT@Len #1{\romannumeral0\XINT@length@fork #1\R\R\R\R\R\R\R\R\Z }% -\def\XINT@length@fork #1% +\def\XINT@Apply #1#2{\romannumeral0\XINT@apply@loop@a {}{#1}#2\Z }% +\def\XINT@apply #1#2% {% - \expandafter\XINT@length@loop - \xint@UDsignfork - #1\dummy {{0}}% - -\dummy {{0}#1}% - \xint@UDkrof + \XINT@apply@loop@a {}{#2}#1\Z }% -\def\XINT@Length #1{\romannumeral0\XINT@length@loop {0}#1\R\R\R\R\R\R\R\R\Z }% -\def\XINT@length #1{\XINT@length@loop {0}#1\R\R\R\R\R\R\R\R\Z }% -\let\xintLength\XINT@Length -\def\XINT@length@loop #1#2#3#4#5#6#7#8#9% +\def\XINT@apply@loop@a #1#2#3% {% - \xint@r #9\XINT@length@end {#2#3#4#5#6#7#8#9}\R - \expandafter\XINT@length@loop\expandafter {\the\numexpr #1+8\relax}% + \xint@z #3\XINT@apply@end\Z + \expandafter + \XINT@apply@loop@b + \expandafter {\romannumeral-`0#2{#3}}{#1}{#2}% }% -\def\XINT@length@end #1\R\expandafter\XINT@length@loop\expandafter #2#3\Z -{% - \XINT@length@end@ #1\W\W\W\W\W\W\W\W\Z {#2}% -}% -\def\XINT@length@end@ #1\R #2#3#4#5#6#7#8#9\Z -{% - \xint@w #2\XINT@length@end@i - #3\XINT@length@end@ii - #4\XINT@length@end@iii - #5\XINT@length@end@iv - #6\XINT@length@end@v - #7\XINT@length@end@vi - #8\XINT@length@end@vii - \W\XINT@length@end@viii -}% -\def\XINT@length@end@viii #1% - {\expandafter\space\the\numexpr #1-8\relax}% -\def\XINT@length@end@vii #1\XINT@length@end@viii #2% - {\expandafter\space\the\numexpr #2-7\relax}% -\def\XINT@length@end@vi #1\XINT@length@end@viii #2% - {\expandafter\space\the\numexpr #2-6\relax}% -\def\XINT@length@end@v #1\XINT@length@end@viii #2% - {\expandafter\space\the\numexpr #2-5\relax}% -\def\XINT@length@end@iv #1\XINT@length@end@viii #2% - {\expandafter\space\the\numexpr #2-4\relax}% -\def\XINT@length@end@iii #1\XINT@length@end@viii #2% - {\expandafter\space\the\numexpr #2-3\relax}% -\def\XINT@length@end@ii #1\XINT@length@end@viii #2% - {\expandafter\space\the\numexpr #2-2\relax}% -\def\XINT@length@end@i #1\XINT@length@end@viii #2% - {\expandafter\space\the\numexpr #2-1\relax}% +\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}% % \end{macrocode} % \subsection{\csh{xintAssign},~\csh{xintAssignArray},~\csh{xintDigitsOf}} % \begin{verbatim} @@ -4446,15 +4676,16 @@ first place. % \escapechar at the time of using \xintAssignArray or \xintRelaxArray % These macros are an exception in the xint bundle, they do not care at % all about compatibility with expansion-only contexts. -% In version 1.05a I suddenly discover incongruous \expandafter's in -% \XINT@assignarray@@@@end, which I remove. +% In version 1.05a I suddenly see some incongruous \expandafter's in +% \XINT@assignarray@@@@end, which I remove. +% Release 1.06 modifies the macros created by \xintAssignArray to feed their +% argument to a \numexpr % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintAssign #1\to {% - \expandafter\expandafter\expandafter - \XINT@assign@a #1{}\to + \expandafter\XINT@assign@a\romannumeral-`0#1{}\to }% \def\XINT@assign@a #1% attention to the # at the beginning of next line #{% @@ -4502,8 +4733,8 @@ first place. \edef\xint@arrayname {\string #1}% \XINT@restoreescapechar \count 255 0 - \expandafter\expandafter\expandafter - \XINT@assignarray@loop #1\xint@undef + \expandafter + \XINT@assignarray@loop \romannumeral-`0#1\xint@undef \csname\xint@arrayname 00\endcsname \csname\xint@arrayname 0\endcsname {\xint@arrayname}% @@ -4536,11 +4767,9 @@ first place. \def\XINT@assignarray@@@@end #1#2#3#4% {% \def #4##1% - {\romannumeral0% - \expandafter\expandafter\expandafter - #1% - \expandafter\expandafter\expandafter - {##1}% + {% + \romannumeral0% + \expandafter #1\expandafter{\the\numexpr ##1}% }% \def #1##1% {% @@ -4560,73 +4789,160 @@ first place. }% \let\xintDigitsOf\xintAssignArray % \end{macrocode} -% \subsection{\csh{xintApply}} +% \subsection{\csh{XINT@RQ}} % \begin{verbatim} -% \xintApply {\macro}{{a}{b}...{z}} returns {\macro{a}}...{\macro{b}} -% where each instance of \macro is twice expanded. The list is first twice -% expanded. Introduced with release 1.04. +% cette macro renverse et ajoute le nombre minimal de zéros à +% la fin pour que la longueur soit alors multiple de 4 +% \romannumeral0\XINT@RQ {}<le truc à renverser>\R\R\R\R\R\R\R\R\Z +% Attention, ceci n'est utilisé que pour des chaînes de chiffres, et donc le +% comportement avec des {..} ou autres espaces n'a fait l'objet d'aucune +% attention % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} -\def\xintApply {\romannumeral0\xintapply }% -\def\xintapply #1#2% +\def\XINT@RQ #1#2#3#4#5#6#7#8#9% {% - \expandafter\expandafter\expandafter - \XINT@apply - \expandafter\expandafter\expandafter - {#2}{#1}% + \xint@r #9\XINT@RQ@end\R\XINT@RQ {#9#8#7#6#5#4#3#2#1}% }% -\def\XINT@apply #1#2% +\def\XINT@RQ@end\R\XINT@RQ #1#2\Z {% - \XINT@apply@loop@a {}{#2}#1\Z + \XINT@RQ@end@ #1\Z }% -\def\XINT@apply@loop@a #1#2#3% +\def\XINT@RQ@end@ #1#2#3#4#5#6#7#8% {% - \xint@z #3\XINT@apply@end\Z - \expandafter\expandafter\expandafter - \XINT@apply@loop@b - \expandafter\expandafter\expandafter {#2{#3}}{#1}{#2}% + \xint@r #8\XINT@RQ@end@viii + #7\XINT@RQ@end@vii + #6\XINT@RQ@end@vi + #5\XINT@RQ@end@v + #4\XINT@RQ@end@iv + #3\XINT@RQ@end@iii + #2\XINT@RQ@end@ii + \R\XINT@RQ@end@i + \Z #2#3#4#5#6#7#8% }% -\def\XINT@apply@loop@b #1#2{\XINT@apply@loop@a {#2{#1}}}% -\def\XINT@apply@end\Z - \expandafter\expandafter\expandafter - \XINT@apply@loop@b - \expandafter\expandafter\expandafter #1#2#3{ #2}% +\def\XINT@RQ@end@viii #1\Z #2#3#4#5#6#7#8#9\Z { #9}% +\def\XINT@RQ@end@vii #1\Z #2#3#4#5#6#7#8#9\Z { #8#9000}% +\def\XINT@RQ@end@vi #1\Z #2#3#4#5#6#7#8#9\Z { #7#8#900}% +\def\XINT@RQ@end@v #1\Z #2#3#4#5#6#7#8#9\Z { #6#7#8#90}% +\def\XINT@RQ@end@iv #1\Z #2#3#4#5#6#7#8#9\Z { #5#6#7#8#9}% +\def\XINT@RQ@end@iii #1\Z #2#3#4#5#6#7#8#9\Z { #4#5#6#7#8#9000}% +\def\XINT@RQ@end@ii #1\Z #2#3#4#5#6#7#8#9\Z { #3#4#5#6#7#8#900}% +\def\XINT@RQ@end@i \Z #1#2#3#4#5#6#7#8\Z { #1#2#3#4#5#6#7#80}% % \end{macrocode} -% \subsection{\csh{xintListWithSep}} +% \subsection{\csh{XINT@cuz}} +% \begin{macrocode} +\def\xint@cleanupzeros@andstop #1#2#3#4% +{% + \expandafter\space\the\numexpr #1#2#3#4\relax +}% +\def\xint@cleanupzeros@nospace #1#2#3#4% +{% + \the\numexpr #1#2#3#4\relax +}% +\def\XINT@rev@andcuz #1% +{% + \expandafter\xint@cleanupzeros@andstop + \romannumeral0\XINT@rord@main {}#1% + \xint@UNDEF + \xint@undef\xint@undef\xint@undef\xint@undef + \xint@undef\xint@undef\xint@undef\xint@undef + \xint@UNDEF +}% +% \end{macrocode} +% \vspace*{-.5\baselineskip} % \begin{verbatim} -% \xintListWithSep {sep}{{a}{b}...{z}} returns a sep b sep .... sep z -% Introduced with release 1.04. The 'sep' can be \par, as the macro -% xintlistwithsep etc... are declared long. 'sep' does not have to be a -% single token. +% routine CleanUpZeros. Utilisée en particulier par la +% soustraction. +% INPUT: longueur **multiple de 4** (<-- ATTENTION) +% OUTPUT: on a retiré tous les leading zéros, on n'est **plus* +% nécessairement de longueur 4n +% Délimiteur pour @main: \W\W\W\W\W\W\W\Z avec SEPT \W % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} -\def\xintListWithSep {\romannumeral0\xintlistwithsep }% -\long\def\xintlistwithsep #1#2% +\def\XINT@cuz #1% {% - \expandafter\expandafter\expandafter - \XINT@lws - \expandafter\expandafter\expandafter - {#2}{#1}% + \XINT@cuz@loop #1\W\W\W\W\W\W\W\Z% }% -\long\def\XINT@lws #1#2% +\def\XINT@cuz@loop #1#2#3#4#5#6#7#8% {% - \XINT@lws@start {#2}#1\Z + \xint@w #8\xint@cuz@enda\W + \xint@z #8\xint@cuz@endb\Z + \XINT@cuz@checka {#1#2#3#4#5#6#7#8}% }% -\long\def\XINT@lws@start #1#2% +\def\xint@cuz@enda #1\XINT@cuz@checka #2% {% - \xint@z #2\XINT@lws@dont\Z - \XINT@lws@loop@a {#2}{#1}% + \xint@cuz@endaa #2% }% -\long\def\XINT@lws@dont\Z\XINT@lws@loop@a #1#2{ #2}% -\long\def\XINT@lws@loop@a #1#2#3% +\def\xint@cuz@endaa #1#2#3#4#5\Z {% - \xint@z #3\XINT@lws@end\Z - \XINT@lws@loop@b {#1}{#2#3}{#2}% + \expandafter\space\the\numexpr #1#2#3#4\relax }% -\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\xint@cuz@endb\Z\XINT@cuz@checka #1{ 0}% +\def\XINT@cuz@checka #1% +{% + \expandafter \XINT@cuz@checkb \the\numexpr #1\relax +}% +\def\XINT@cuz@checkb #1% +{% + \xint@zero #1\xint@cuz@backtoloop 0\XINT@cuz@Stop #1% +}% +\def\XINT@cuz@Stop #1\W #2\Z{ #1}% +\def\xint@cuz@backtoloop 0\XINT@cuz@Stop 0{\XINT@cuz@loop }% +% \end{macrocode} +% \subsection{\csh{XINT@isOne}} +% Added in |1.03|. Attention: does not do any expansion. +% \begin{macrocode} +\def\XINT@isOne #1{\romannumeral0\XINT@isone #1\W\Z }% +\def\XINT@isone #1#2% +{% + \xint@one #1\XINT@isone@b 1\expandafter\space\expandafter 0\xint@z #2% +}% +\def\XINT@isone@b #1\xint@z #2% +{% + \xint@w #2\XINT@isone@yes\W\expandafter\space\expandafter 0\xint@z +}% +\def\XINT@isone@yes #1\Z{ 1}% +% \end{macrocode} +% \subsection{\csh{xintNum}} +% \begin{verbatim} +% For example \xintNum {----+-+++---+----000000000000003} +% 1.05 defines \xintiNum, which allows redefinition of \xintNum by xintfrac.sty +% \end{verbatim} +% \begin{macrocode} +\def\xintiNum {\romannumeral0\xintinum }% +\def\xintinum #1% +{% + \expandafter\XINT@num\expandafter {\romannumeral-`0#1}% +}% +\let\xintNum\xintiNum \let\xintnum\xintinum +\def\XINT@Num {\romannumeral0\XINT@num }% +\def\XINT@num #1{\XINT@num@loop #1\R\R\R\R\R\R\R\R\Z }% +\def\XINT@num@loop #1#2#3#4#5#6#7#8% +{% + \xint@r #8\XINT@num@end\R\XINT@num@NumEight #1#2#3#4#5#6#7#8% +}% +\def\XINT@num@end\R\XINT@num@NumEight #1\R #2\Z +{% + \expandafter\space\the\numexpr #1+0\relax +}% +\def\XINT@num@NumEight #1#2#3#4#5#6#7#8% +{% + \ifnum \numexpr #1#2#3#4#5#6#7#8+0\relax = 0 + \xint@afterfi {\expandafter\XINT@num@keepsign@a + \the\numexpr #1#2#3#4#5#6#7#81\relax}% + \else + \xint@afterfi {\expandafter\XINT@num@finish + \the\numexpr #1#2#3#4#5#6#7#8\relax}% + \fi +}% +\def\XINT@num@keepsign@a #1% +{% + \xint@one#1\XINT@num@gobacktoloop 1\XINT@num@keepsign@b +}% +\def\XINT@num@gobacktoloop 1\XINT@num@keepsign@b {\XINT@num@loop }% +\def\XINT@num@keepsign@b #1{\XINT@num@loop -}% +\def\XINT@num@finish #1\R #2\Z { #1}% % \end{macrocode} % \subsection{\csh{xintSgn}} % \begin{verbatim} @@ -4637,8 +4953,7 @@ first place. \def\xintiSgn {\romannumeral0\xintisgn }% \def\xintisgn #1% {% - \expandafter\expandafter\expandafter - \XINT@sgn #1\Z% + \expandafter\XINT@sgn \romannumeral-`0#1\Z% }% \let\xintSgn\xintiSgn \let\xintsgn\xintisgn \def\XINT@Sgn #1{\romannumeral0\XINT@sgn #1\Z }% @@ -4656,18 +4971,16 @@ first place. \def\xintiOpp {\romannumeral0\xintiopp }% \def\xintiopp #1% {% - \expandafter\expandafter\expandafter - \XINT@opp #1% + \expandafter\XINT@opp \romannumeral-`0#1% }% \let\xintOpp\xintiOpp \let\xintopp\xintiopp \def\XINT@Opp #1{\romannumeral0\XINT@opp #1}% \def\XINT@opp #1% {% - \expandafter\space \xint@UDzerominusfork - #1-\dummy 0% zero - 0#1\dummy {}% negative - 0-\dummy {-#1}% positive + #1-\dummy { 0}% zero + 0#1\dummy { }% negative + 0-\dummy { -#1}% positive \xint@UDkrof }% % \end{macrocode} @@ -4676,15 +4989,14 @@ first place. \def\xintiAbs {\romannumeral0\xintiabs }% \def\xintiabs #1% {% - \expandafter\expandafter\expandafter - \XINT@abs #1% + \expandafter\XINT@abs \romannumeral-`0#1% }% \let\xintAbs\xintiAbs \let\xintabs\xintiabs \def\XINT@Abs #1{\romannumeral0\XINT@abs #1}% \def\XINT@abs #1% {% \xint@UDsignfork - #1\dummy \space + #1\dummy { }% -\dummy { #1}% \xint@UDkrof }% @@ -4698,7 +5010,8 @@ first place. % Release 1.03 re-organizes sub-routines to facilitate future developments: the % diverse variants of addition, with diverse conditions on inputs and output are % first listed; they will be used in multiplication, or in the summation, or in -% the power routines. +% the power routines. I am aware that the commenting is close to non-existent, +% sorry about that. % % ADDITION % I: \XINT@add@A @@ -5119,16 +5432,12 @@ first place. \def\xintiAdd {\romannumeral0\xintiadd }% \def\xintiadd #1% {% - \expandafter\expandafter\expandafter - \xint@add - \expandafter\expandafter\expandafter - {#1}% + \expandafter\xint@add\expandafter{\romannumeral-`0#1}% }% \let\xintAdd\xintiAdd \let\xintadd\xintiadd \def\xint@add #1#2% {% - \expandafter\expandafter\expandafter - \XINT@add@fork #2\Z #1\Z + \expandafter\XINT@add@fork \romannumeral-`0#2\Z #1\Z }% \def\XINT@Add #1#2{\romannumeral0\XINT@add@fork #2\Z #1\Z }% \def\XINT@add #1#2{\XINT@add@fork #2\Z #1\Z }% @@ -5136,9 +5445,8 @@ first place. % \vspace*{-.5\baselineskip} % \begin{verbatim} % ADDITION -% Ici #1#2 vient du *deuxième* argument de \xintAdd -% et #3#4 donc du *premier* [algo plus efficace lorsque -% le premier est plus long que le second] +% Ici #1#2 vient du *deuxième* argument de \xintAdd et #3#4 donc du *premier* +% [algo plus efficace lorsque le premier est plus long que le second] % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} @@ -5185,9 +5493,8 @@ first place. }% \def\XINT@add@pre #1% {% - \expandafter\XINT@add@@pre\expandafter{% - \romannumeral0\XINT@RQ {}#1\R\R\R\R\R\R\R\R\Z - }% + \expandafter\XINT@add@@pre\expandafter + {\romannumeral0\XINT@RQ {}#1\R\R\R\R\R\R\R\R\Z }% }% \def\XINT@add@@pre #1#2% {% @@ -5202,16 +5509,12 @@ first place. \def\xintiSub {\romannumeral0\xintisub }% \def\xintisub #1% {% - \expandafter\expandafter\expandafter - \xint@sub - \expandafter\expandafter\expandafter - {#1}% + \expandafter\xint@sub\expandafter{\romannumeral-`0#1}% }% \let\xintSub\xintiSub \let\xintsub\xintisub \def\xint@sub #1#2% {% - \expandafter\expandafter\expandafter - \XINT@sub@fork #2\Z #1\Z + \expandafter\XINT@sub@fork \romannumeral-`0#2\Z #1\Z }% \def\XINT@Sub #1#2{\romannumeral0\XINT@sub@fork #2\Z #1\Z }% \def\XINT@sub #1#2{\XINT@sub@fork #2\Z #1\Z }% @@ -5262,9 +5565,8 @@ first place. \def\xint@sub@pm #1\XINT@add@pre #2#3{ -#2}% \def\XINT@sub@pre #1% {% - \expandafter\XINT@sub@@pre\expandafter{% - \romannumeral0\XINT@RQ {}#1\R\R\R\R\R\R\R\R\Z - }% + \expandafter\XINT@sub@@pre\expandafter + {\romannumeral0\XINT@RQ {}#1\R\R\R\R\R\R\R\R\Z }% }% \def\XINT@sub@@pre #1#2% {% @@ -5405,8 +5707,7 @@ first place. }% \def\XINT@sub@E #1#2#3#4#5#6% {% - \xint@w #3\xint@sub@F\W\XINT@sub@Eonestep - #1{#6#5#4#3}{#2}% + \xint@w #3\xint@sub@F\W\XINT@sub@Eonestep #1{#6#5#4#3}{#2}% }% \def\XINT@sub@Eonestep #1#2% {% @@ -5428,9 +5729,8 @@ first place. \def\XINT@sub@DD {\expandafter\xint@minus@andstop\romannumeral0\XINT@sub@D }% \def\XINT@sub@Fdec #1#2#3#4#5#6% {% - \xint@w - #3\xint@sub@Fdec@finish\W\XINT@sub@Fdec@onestep - #1{#6#5#4#3}{#2}% + \xint@w #3\xint@sub@Fdec@finish\W + \XINT@sub@Fdec@onestep #1{#6#5#4#3}{#2}% }% \def\XINT@sub@Fdec@onestep #1#2% {% @@ -5446,9 +5746,8 @@ first place. }% \def\XINT@sub@Finc #1#2#3#4#5#6% {% - \xint@w - #3\xint@sub@Finc@finish\W\XINT@sub@Finc@onestep - #1{#6#5#4#3}{#2}% + \xint@w #3\xint@sub@Finc@finish\W + \XINT@sub@Finc@onestep #1{#6#5#4#3}{#2}% }% \def\XINT@sub@Finc@onestep #1#2% {% @@ -5461,8 +5760,7 @@ first place. \def\xint@sub@Finc@finish\W\XINT@sub@Finc@onestep #1#2#3% {% \xint@UDzerofork - #1\dummy {\expandafter\xint@minus@andstop% - \xint@cleanupzeros@nospace}% + #1\dummy {\expandafter\xint@minus@andstop\xint@cleanupzeros@nospace}% 0\dummy { -1}% \xint@UDkrof #3% @@ -5474,8 +5772,7 @@ first place. 0\dummy \XINT@sub@L % pas de retenue \xint@UDkrof }% -\def\XINT@sub@L #1\W\X\Y\Z - {\XINT@cuz@loop #1\W\W\W\W\W\W\W\Z }% +\def\XINT@sub@L #1\W\X\Y\Z {\XINT@cuz@loop #1\W\W\W\W\W\W\W\Z }% \def\XINT@sub@K #1% {% \expandafter @@ -5489,9 +5786,8 @@ first place. }% \def\XINT@sub@KK #1#2#3#4#5#6% {% - \xint@w - #3\xint@sub@KK@finish\W\XINT@sub@KK@onestep - #1{#6#5#4#3}{#2}% + \xint@w #3\xint@sub@KK@finish\W + \XINT@sub@KK@onestep #1{#6#5#4#3}{#2}% }% \def\XINT@sub@KK@onestep #1#2% {% @@ -5503,8 +5799,8 @@ first place. }% \def\xint@sub@KK@finish\W\XINT@sub@KK@onestep #1#2#3% {% - \expandafter\xint@minus@andstop\romannumeral - 0\XINT@cuz@loop #3\W\W\W\W\W\W\W\Z + \expandafter\xint@minus@andstop + \romannumeral0\XINT@cuz@loop #3\W\W\W\W\W\W\W\Z }% % \end{macrocode} % \subsection{\csh{xintCmp}} @@ -5512,16 +5808,12 @@ first place. \def\xintiCmp {\romannumeral0\xinticmp }% \def\xinticmp #1% {% - \expandafter\expandafter\expandafter - \xint@cmp - \expandafter\expandafter\expandafter - {#1}% + \expandafter\xint@cmp\expandafter{\romannumeral-`0#1}% }% \let\xintCmp\xintiCmp \let\xintcmp\xinticmp \def\xint@cmp #1#2% {% - \expandafter\expandafter\expandafter - \XINT@cmp@fork #2\Z #1\Z + \expandafter\XINT@cmp@fork \romannumeral-`0#2\Z #1\Z }% \def\XINT@Cmp #1#2{\romannumeral0\XINT@cmp@fork #2\Z #1\Z }% % \end{macrocode} @@ -5564,9 +5856,8 @@ first place. }% \def\XINT@cmp@pre #1% {% - \expandafter\XINT@cmp@@pre\expandafter{% - \romannumeral0\XINT@RQ {}#1\R\R\R\R\R\R\R\R\Z - }% + \expandafter\XINT@cmp@@pre\expandafter + {\romannumeral0\XINT@RQ {}#1\R\R\R\R\R\R\R\R\Z }% }% \def\XINT@cmp@@pre #1#2% {% @@ -5589,15 +5880,11 @@ first place. % \begin{macrocode} \def\XINT@cmp@A #1#2#3\W\X\Y\Z #4#5#6#7% {% - \xint@w - #4\xint@cmp@az - \W\XINT@cmp@B #1{#4#5#6#7}{#2}#3\W\X\Y\Z + \xint@w #4\xint@cmp@az\W\XINT@cmp@B #1{#4#5#6#7}{#2}#3\W\X\Y\Z }% \def\XINT@cmp@B #1#2#3#4#5#6#7% {% - \xint@w - #4\xint@cmp@bz - \W\XINT@cmp@onestep #1#2{#7#6#5#4}{#3}% + \xint@w#4\xint@cmp@bz\W\XINT@cmp@onestep #1#2{#7#6#5#4}{#3}% }% \def\XINT@cmp@onestep #1#2#3#4#5#6% {% @@ -5607,13 +5894,10 @@ first place. {% \XINT@cmp@A #2{#3#4}% }% -\def\xint@cmp@bz - \W\XINT@cmp@onestep #1\Z { 1}% +\def\xint@cmp@bz\W\XINT@cmp@onestep #1\Z { 1}% \def\xint@cmp@az\W\XINT@cmp@B #1#2#3#4#5#6#7% {% - \xint@w - #4\xint@cmp@ez - \W\XINT@cmp@Eenter #1{#3}#4#5#6#7% + \xint@w #4\xint@cmp@ez\W\XINT@cmp@Eenter #1{#3}#4#5#6#7% }% \def\XINT@cmp@Eenter #1\Z { -1}% \def\xint@cmp@ez\W\XINT@cmp@Eenter #1% @@ -5631,19 +5915,18 @@ first place. }% \def\XINT@OneIfPositive@main #1#2#3#4% {% - \xint@z #4\xint@OneIfPositive@terminated\Z\XINT@OneIfPositive@onestep - #1#2#3#4% + \xint@z #4\xint@OneIfPositive@terminated\Z + \XINT@OneIfPositive@onestep #1#2#3#4% }% \def\xint@OneIfPositive@terminated\Z\XINT@OneIfPositive@onestep\W\X\Y\Z { 0}% \def\XINT@OneIfPositive@onestep #1#2#3#4% {% - \expandafter\XINT@OneIfPositive@check - \the\numexpr #1#2#3#4\relax + \expandafter\XINT@OneIfPositive@check\the\numexpr #1#2#3#4\relax }% \def\XINT@OneIfPositive@check #1% {% - \xint@zero - #1\xint@OneIfPositive@backtomain 0\XINT@OneIfPositive@finish #1% + \xint@zero #1\xint@OneIfPositive@backtomain 0% + \XINT@OneIfPositive@finish #1% }% \def\XINT@OneIfPositive@finish #1\W\X\Y\Z{ 1}% \def\xint@OneIfPositive@backtomain 0\XINT@OneIfPositive@finish 0% @@ -5659,15 +5942,12 @@ first place. \def\xintiGeq {\romannumeral0\xintigeq }% \def\xintigeq #1% {% - \expandafter\expandafter\expandafter - \xint@geq - \expandafter\expandafter\expandafter - {#1}% + \expandafter\xint@geq\expandafter {\romannumeral-`0#1}% }% \let\xintGeq\xintiGeq \let\xintgeq\xintigeq \def\xint@geq #1#2% {% - \expandafter\expandafter\expandafter\XINT@geq@fork #2\Z #1\Z + \expandafter\XINT@geq@fork \romannumeral-`0#2\Z #1\Z }% \def\XINT@Geq #1#2{\romannumeral0\XINT@geq@fork #2\Z #1\Z }% % \end{macrocode} @@ -5694,19 +5974,14 @@ first place. }% \def\XINT@geq@secondiszero #1#2#3#4{ 1}% \def\XINT@geq@firstiszero #1#2#3#4{ 0}% -\def\XINT@geq@plusplus #1#2#3#4% - {\XINT@geq@pre {#4#2}{#3#1}}% -\def\XINT@geq@minusminus #1#2#3#4% - {\XINT@geq@pre {#2}{#1}}% -\def\XINT@geq@minusplus #1#2#3#4% - {\XINT@geq@pre {#4#2}{#1}}% -\def\XINT@geq@plusminus #1#2#3#4% - {\XINT@geq@pre {#2}{#3#1}}% +\def\XINT@geq@plusplus #1#2#3#4{\XINT@geq@pre {#4#2}{#3#1}}% +\def\XINT@geq@minusminus #1#2#3#4{\XINT@geq@pre {#2}{#1}}% +\def\XINT@geq@minusplus #1#2#3#4{\XINT@geq@pre {#4#2}{#1}}% +\def\XINT@geq@plusminus #1#2#3#4{\XINT@geq@pre {#2}{#3#1}}% \def\XINT@geq@pre #1% {% - \expandafter\XINT@geq@@pre\expandafter{% - \romannumeral0\XINT@RQ {}#1\R\R\R\R\R\R\R\R\Z - }% + \expandafter\XINT@geq@@pre\expandafter + {\romannumeral0\XINT@RQ {}#1\R\R\R\R\R\R\R\R\Z }% }% \def\XINT@geq@@pre #1#2% {% @@ -5730,15 +6005,11 @@ first place. % \begin{macrocode} \def\XINT@geq@A #1#2#3\W\X\Y\Z #4#5#6#7% {% - \xint@w - #4\xint@geq@az - \W\XINT@geq@B #1{#4#5#6#7}{#2}#3\W\X\Y\Z + \xint@w #4\xint@geq@az\W\XINT@geq@B #1{#4#5#6#7}{#2}#3\W\X\Y\Z }% \def\XINT@geq@B #1#2#3#4#5#6#7% {% - \xint@w - #4\xint@geq@bz - \W\XINT@geq@onestep #1#2{#7#6#5#4}{#3}% + \xint@w #4\xint@geq@bz\W\XINT@geq@onestep #1#2{#7#6#5#4}{#3}% }% \def\XINT@geq@onestep #1#2#3#4#5#6% {% @@ -5751,9 +6022,7 @@ first place. \def\xint@geq@bz\W\XINT@geq@onestep #1\W\X\Y\Z { 1}% \def\xint@geq@az\W\XINT@geq@B #1#2#3#4#5#6#7% {% - \xint@w - #4\xint@geq@ez - \W\XINT@geq@Eenter #1% + \xint@w #4\xint@geq@ez\W\XINT@geq@Eenter #1% }% \def\XINT@geq@Eenter #1\W\X\Y\Z { 0}% \def\xint@geq@ez\W\XINT@geq@Eenter #1% @@ -5774,17 +6043,12 @@ first place. \def\xintiMax {\romannumeral0\xintimax }% \def\xintimax #1% {% - \expandafter\expandafter\expandafter - \xint@max - \expandafter\expandafter\expandafter - {#1}% + \expandafter\xint@max\expandafter {\romannumeral-`0#1}% }% \let\xintMax\xintiMax \let\xintmax\xintimax \def\xint@max #1#2% {% - \expandafter\expandafter\expandafter - \XINT@max@pre - \expandafter\expandafter\expandafter {#2}{#1}% + \expandafter\XINT@max@pre\expandafter {\romannumeral-`0#2}{#1}% }% \def\XINT@max@pre #1#2{\XINT@max@fork #1\Z #2\Z {#2}{#1}}% \def\XINT@Max #1#2{\romannumeral0\XINT@max@fork #2\Z #1\Z {#1}{#2}}% @@ -5852,17 +6116,12 @@ first place. \def\xintiMin {\romannumeral0\xintimin }% \def\xintimin #1% {% - \expandafter\expandafter\expandafter - \xint@min - \expandafter\expandafter\expandafter - {#1}% + \expandafter\xint@min\expandafter {\romannumeral-`0#1}% }% \let\xintMin\xintiMin \let\xintmin\xintimin \def\xint@min #1#2% {% - \expandafter\expandafter\expandafter - \XINT@min@pre - \expandafter\expandafter\expandafter {#2}{#1}% + \expandafter\XINT@min@pre\expandafter {\romannumeral-`0#2}{#1}% }% \def\XINT@min@pre #1#2{\XINT@min@fork #1\Z #2\Z {#2}{#1}}% \def\XINT@Min #1#2{\romannumeral0\XINT@min@fork #2\Z #1\Z {#1}{#2}}% @@ -5901,7 +6160,7 @@ first place. \def\XINT@min@pluszero #1#2#3#4{\xint@firstoftwo@andstop }% \def\XINT@min@minusplus #1#2#3#4{\xint@secondoftwo@andstop }% \def\XINT@min@plusminus #1#2#3#4{\xint@firstoftwo@andstop }% -\def\XINT@min@plusplus #1#2#3#4% +\def\XINT@min@plusplus #1#2#3#4% {% \ifodd\XINT@Geq {#4#2}{#3#1} \expandafter\xint@secondoftwo@andstop @@ -5940,16 +6199,13 @@ first place. \def\xintiSum {\romannumeral0\xintisum }% \def\xintisum #1{\xintisumexpr #1\relax }% \def\xintiSumExpr {\romannumeral0\xintisumexpr }% -\def\xintisumexpr -{% - \expandafter\expandafter\expandafter\XINT@sumexpr -}% +\def\xintisumexpr {\expandafter\XINT@sumexpr\romannumeral-`0}% \let\xintSum\xintiSum \let\xintsum\xintisum \let\xintSumExpr\xintiSumExpr \let\xintsumexpr\xintisumexpr \def\XINT@sumexpr {\XINT@sum@loop {0000}{0000}}% \def\XINT@sum@loop #1#2#3% {% - \expandafter\expandafter\expandafter\XINT@sum@checksign #3\Z {#1}{#2}% + \expandafter\XINT@sum@checksign\romannumeral-`0#3\Z {#1}{#2}% }% \def\XINT@sum@checksign #1% {% @@ -5988,15 +6244,12 @@ first place. \def\xintiMul {\romannumeral0\xintimul }% \def\xintimul #1% {% - \expandafter\expandafter\expandafter - \xint@mul - \expandafter\expandafter\expandafter - {#1}% + \expandafter\xint@mul\expandafter {\romannumeral-`0#1}% }% \let\xintMul\xintiMul \let\xintmul\xintimul \def\xint@mul #1#2% -{\expandafter\expandafter\expandafter - \XINT@mul@fork #2\Z #1\Z +{% + \expandafter\XINT@mul@fork \romannumeral-`0#2\Z #1\Z }% \def\XINT@Mul #1#2{\romannumeral0\XINT@mul@fork #2\Z #1\Z }% % \end{macrocode} @@ -6040,17 +6293,17 @@ first place. }% \def\XINT@mul@minusplus #1#2#3% {% - \expandafter\xint@minus@andstop\romannumeral0\expandafter - \XINT@mul@choice@a - \expandafter{\romannumeral0\XINT@length {#1#3}}% - {\romannumeral0\XINT@length {#2}}{#2}{#1#3}% + \expandafter\xint@minus@andstop\romannumeral0\expandafter + \XINT@mul@choice@a + \expandafter{\romannumeral0\XINT@length {#1#3}}% + {\romannumeral0\XINT@length {#2}}{#2}{#1#3}% }% \def\XINT@mul@plusminus #1#2#3% {% - \expandafter\xint@minus@andstop\romannumeral0\expandafter - \XINT@mul@choice@a - \expandafter{\romannumeral0\XINT@length {#3}}% - {\romannumeral0\XINT@length {#1#2}}{#1#2}{#3}% + \expandafter\xint@minus@andstop\romannumeral0\expandafter + \XINT@mul@choice@a + \expandafter{\romannumeral0\XINT@length {#3}}% + {\romannumeral0\XINT@length {#1#2}}{#1#2}{#3}% }% \def\XINT@mul@plusplus #1#2#3#4% {% @@ -6098,38 +6351,20 @@ first place. }% \def\XINT@mul@choice@i #1#2% {% - \ifcase \numexpr (#2-3)/4\relax - \or \xint@afterfi {\ifnum #1<330 \expandafter \XINT@mul@choice@same - \else \expandafter \XINT@mul@choice@permute \fi}% - \or \xint@afterfi {\ifnum #1<168 \expandafter \XINT@mul@choice@same - \else \expandafter \XINT@mul@choice@permute \fi}% - \or \xint@afterfi {\ifnum #1<109 \expandafter \XINT@mul@choice@same - \else \expandafter \XINT@mul@choice@permute \fi}% - \or \xint@afterfi {\ifnum #1<80 \expandafter \XINT@mul@choice@same - \else \expandafter \XINT@mul@choice@permute \fi}% - \or \xint@afterfi {\ifnum #1<66 \expandafter \XINT@mul@choice@same - \else \expandafter \XINT@mul@choice@permute \fi}% - \or \xint@afterfi {\ifnum #1<52 \expandafter \XINT@mul@choice@same - \else \expandafter \XINT@mul@choice@permute \fi}% - \else \expandafter \XINT@mul@choice@permute + \ifnum #1<\numexpr\ifcase \numexpr (#2-3)/4\relax + \or 330\or 168\or 109\or 80\or 66\or 52\else 0\fi\relax + \expandafter\XINT@mul@choice@same + \else + \expandafter\XINT@mul@choice@permute \fi }% \def\XINT@mul@choice@ii #1#2% {% - \ifcase \numexpr (#1-3)/4\relax - \or \xint@afterfi {\ifnum #2<330 \expandafter \XINT@mul@choice@permute - \else \expandafter \XINT@mul@choice@same \fi}% - \or \xint@afterfi {\ifnum #2<168 \expandafter \XINT@mul@choice@permute - \else \expandafter \XINT@mul@choice@same \fi}% - \or \xint@afterfi {\ifnum #2<109 \expandafter \XINT@mul@choice@permute - \else \expandafter \XINT@mul@choice@same \fi}% - \or \xint@afterfi {\ifnum #2<80 \expandafter \XINT@mul@choice@permute - \else \expandafter \XINT@mul@choice@same \fi}% - \or \xint@afterfi {\ifnum #2<66 \expandafter \XINT@mul@choice@permute - \else \expandafter \XINT@mul@choice@same \fi}% - \or \xint@afterfi {\ifnum #2<52 \expandafter \XINT@mul@choice@permute - \else \expandafter \XINT@mul@choice@same \fi}% - \else \expandafter \XINT@mul@choice@same + \ifnum #2<\numexpr\ifcase \numexpr (#1-3)/4\relax + \or 330\or 168\or 109\or 80\or 66\or 52\else 0\fi\relax + \expandafter\XINT@mul@choice@permute + \else + \expandafter\XINT@mul@choice@same \fi }% \def\XINT@mul@choice@same #1#2% @@ -6184,8 +6419,7 @@ first place. % \begin{macrocode} \def\XINT@mul@Mr #1% {% - \expandafter\XINT@mul@Mr@checkifzeroorone - \expandafter{\the\numexpr #1}% + \expandafter\XINT@mul@Mr@checkifzeroorone\expandafter{\the\numexpr #1}% }% \def\XINT@mul@Mr@checkifzeroorone #1% {% @@ -6214,8 +6448,8 @@ first place. }% \def\xint@mul@pr\Z\XINT@mul@Pr #1#2#3#4#5% {% - \xint@quatrezeros #1\XINT@mul@Mr@end@nocarry 0000\XINT@mul@Mr@end@carry - #1{#4}% + \xint@quatrezeros #1\XINT@mul@Mr@end@nocarry 0000% + \XINT@mul@Mr@end@carry #1{#4}% }% \def\XINT@mul@Mr@end@nocarry 0000\XINT@mul@Mr@end@carry 0000#1{ #1}% \def\XINT@mul@Mr@end@carry #1#2#3#4#5{ #5#4#3#2#1}% @@ -6232,8 +6466,7 @@ first place. % \begin{macrocode} \def\XINT@mul@M #1% {% - \expandafter\XINT@mul@M@checkifzeroorone - \expandafter{\the\numexpr #1}% + \expandafter\XINT@mul@M@checkifzeroorone\expandafter{\the\numexpr #1}% }% \def\XINT@mul@M@checkifzeroorone #1% {% @@ -6249,8 +6482,7 @@ first place. \def\XINT@mul@M@zero #1\Z\Z\Z\Z { 0}% \def\XINT@mul@M@one #1#2#3#4\Z\Z\Z\Z {% - \expandafter\xint@cleanupzeros@andstop - \romannumeral0\XINT@rev{#4}% + \expandafter\xint@cleanupzeros@andstop\romannumeral0\XINT@rev{#4}% }% \def\XINT@mul@N #1#2#3#4#5#6#7% {% @@ -6485,10 +6717,7 @@ first place. \def\xintiSqr {\romannumeral0\xintisqr }% \def\xintisqr #1% {% - \expandafter\expandafter\expandafter - \XINT@sqr - \expandafter\expandafter\expandafter - {\xintiAbs{#1}}% fait l'expansion de #1 et se d\'ebarrasse du signe + \expandafter\XINT@sqr\expandafter {\romannumeral0\xintiabs{#1}}% }% \let\xintSqr\xintiSqr \let\xintsqr\xintisqr \def\XINT@sqr #1% @@ -6526,16 +6755,13 @@ first place. \let\xintPrd\xintiPrd \let\xintprd\xintiprd \def\xintiProductExpr {\romannumeral0\xintiproductexpr }% -\def\xintiproductexpr -{% - \expandafter\expandafter\expandafter\XINT@productexpr -}% +\def\xintiproductexpr {\expandafter\XINT@productexpr\romannumeral-`0}% \let\xintProductExpr\xintiProductExpr \let\xintproductexpr\xintiproductexpr \def\XINT@productexpr {\XINT@prod@loop@a 1\Z }% \def\XINT@prod@loop@a #1\Z #2% {% - \expandafter\expandafter\expandafter\XINT@prod@loop@b #2\Z #1\Z \Z + \expandafter\XINT@prod@loop@b \romannumeral-`0#2\Z #1\Z \Z }% \def\XINT@prod@loop@b #1% {% @@ -6563,12 +6789,8 @@ first place. \def\xintFac {\romannumeral0\xintfac }% \def\xintfac #1% {% - \expandafter\expandafter\expandafter - \XINT@fac@fork - \expandafter\expandafter\expandafter - {#1}% + \expandafter\XINT@fac@fork\expandafter{\the\numexpr #1}% }% -\def\XINT@Fac {\romannumeral0\XINT@fac@fork }% \def\XINT@fac@fork #1% {% \ifcase\XINT@Sgn {#1} @@ -6583,7 +6805,7 @@ first place. }% \def\XINT@fac@checklength #1% {% - \ifnum\numexpr #1\relax>999999 + \ifnum #1>999999 \xint@afterfi{\expandafter\xintError:FactorialOfTooBigNumber \expandafter\space\expandafter 1\xint@gobble }% \else @@ -6652,15 +6874,16 @@ first place. % 1.02 modified the \XINT@posprod routine, and this meant that the original % version was moved here and renamed to \XINT@pow@posprod, as it was well % adapted for computing powers. Then I moved in 1.03 the special variants of -% multiplication (hence of addition) which were needed to earlier in this file. +% multiplication (hence of addition) which were needed to earlier in this file. +% Modified in 1.06, the exponent is given to a \numexpr rather than twice +% expanded. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintiPow {\romannumeral0\xintipow }% \def\xintipow #1% {% - \expandafter\expandafter\expandafter\xint@pow - #1\Z% + \expandafter\xint@pow\romannumeral-`0#1\Z% }% \let\xintPow\xintiPow \let\xintpow\xintipow \def\xint@pow #1#2\Z @@ -6673,22 +6896,12 @@ first place. }% \def\XINT@pow@Aneg #1#2#3% {% - \expandafter\expandafter\expandafter - \XINT@pow@Aneg@ - \expandafter\expandafter\expandafter - {#3}{#2}% + \expandafter\XINT@pow@Aneg@\expandafter{\the\numexpr #3}{#2}% }% -% \end{macrocode} -% \vspace*{-.5\baselineskip} -% \begin{verbatim} -% B = #1, xpxp déjà fait -% \end{verbatim} -% \vspace*{-1.5\baselineskip} -% \begin{macrocode} \def\XINT@pow@Aneg@ #1% {% - \ifcase\XINT@Odd{#1} - \or \expandafter\XINT@pow@Aneg@Bodd + \ifodd #1 + \expandafter\XINT@pow@Aneg@Bodd \fi \XINT@pow@Anonneg@ {#1}% }% @@ -6699,16 +6912,13 @@ first place. % \end{macrocode} % \vspace*{-.5\baselineskip} % \begin{verbatim} -% B = #3, faire le xpxp +% B = #3, faire le xpxp. Modified with 1.06: use of \numexpr. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\XINT@pow@Anonneg #1#2#3% {% - \expandafter\expandafter\expandafter - \XINT@pow@Anonneg@ - \expandafter\expandafter\expandafter - {#3}{#1#2}% + \expandafter\XINT@pow@Anonneg@\expandafter {\the\numexpr #3}{#1#2}% }% % \end{macrocode} % \vspace*{-.5\baselineskip} @@ -6763,13 +6973,14 @@ first place. % \vspace*{-.5\baselineskip} % \begin{verbatim} % B = #1 > 0, A = #2 > 1. With 1.05, I replace \xintiLen{#1}>9 by direct use -% of \numexpr. +% of \numexpr [to generate an error message if the exponent is too large] +% 1.06: \numexpr was already used above. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\XINT@pow@checkBlength #1#2% {% - \ifnum\numexpr #1\relax >999999999 + \ifnum #1>999999999 \expandafter\XINT@pow@BtooBig \else \expandafter\XINT@pow@loop @@ -6875,16 +7086,12 @@ first place. \def\xintiDivision {\romannumeral0\xintidivision }% \def\xintidivision #1% {% - \expandafter\expandafter\expandafter - \xint@division - \expandafter\expandafter\expandafter - {#1}% + \expandafter\xint@division\expandafter {\romannumeral-`0#1}% }% \let\xintDivision\xintiDivision \let\xintdivision\xintidivision \def\xint@division #1#2% {% - \expandafter\expandafter\expandafter - \XINT@div@fork #2\Z #1\Z + \expandafter\XINT@div@fork \romannumeral-`0#2\Z #1\Z }% \def\XINT@Division #1#2{\romannumeral0\XINT@div@fork #2\Z #1\Z }% % \end{macrocode} @@ -7024,14 +7231,13 @@ first place. \ifnum #2=1 \expandafter\XINT@div@prepareB@BisOne \else - \xint@afterfi{\XINT@div@prepareB@e {000}{3}{4}{#2}}% - \fi + \expandafter\XINT@div@prepareB@e + \fi {000}{3}{4}{#2}% }% -\def\XINT@div@prepareB@BisOne #1{ {#1}{0}}% +\def\XINT@div@prepareB@BisOne #1#2#3#4#5{ {#5}{0}}% \def\XINT@div@prepareB@a #1% {% - \expandafter \XINT@div@prepareB@b \expandafter - {\the\numexpr 4*((#1+1)/4)}{#1}% + \expandafter\XINT@div@prepareB@c\expandafter{\the\numexpr 4*((#1+1)/4)}{#1}% }% % \end{macrocode} % \vspace*{-.5\baselineskip} @@ -7040,31 +7246,22 @@ first place. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} -\def\XINT@div@prepareB@b #1#2% +\def\XINT@div@prepareB@c #1#2% {% - \expandafter \XINT@div@prepareB@c \expandafter - {\the\numexpr #1-#2}{#1}% -}% -% \end{macrocode} -% \vspace*{-.5\baselineskip} -% \begin{verbatim} -% #1 = c -% \end{verbatim} -% \vspace*{-1.5\baselineskip} -% \begin{macrocode} -\def\XINT@div@prepareB@c #1% -{% - \ifcase #1 - \expandafter\XINT@div@prepareB@di - \or \expandafter\XINT@div@prepareB@dii - \or \expandafter\XINT@div@prepareB@diii - \else \expandafter\XINT@div@prepareB@div - \fi + \ifcase \numexpr #1-#2\relax + \expandafter\XINT@div@prepareB@d + \or + \expandafter\XINT@div@prepareB@di + \or + \expandafter\XINT@div@prepareB@dii + \or + \expandafter\XINT@div@prepareB@diii + \fi {#1}% }% -\def\XINT@div@prepareB@di {\XINT@div@prepareB@e {}{0}}% -\def\XINT@div@prepareB@dii {\XINT@div@prepareB@e {0}{1}}% -\def\XINT@div@prepareB@diii {\XINT@div@prepareB@e {00}{2}}% -\def\XINT@div@prepareB@div {\XINT@div@prepareB@e {000}{3}}% +\def\XINT@div@prepareB@d {\XINT@div@prepareB@e {}{0}}% +\def\XINT@div@prepareB@di {\XINT@div@prepareB@e {0}{1}}% +\def\XINT@div@prepareB@dii {\XINT@div@prepareB@e {00}{2}}% +\def\XINT@div@prepareB@diii {\XINT@div@prepareB@e {000}{3}}% % \end{macrocode} % \vspace*{-.5\baselineskip} % \begin{verbatim} @@ -7124,8 +7321,7 @@ first place. % \begin{macrocode} \def\XINT@div@prepareA@b #1% {% - \expandafter\XINT@div@prepareA@c\expandafter - {\the\numexpr 4*((#1+1)/4)}{#1}% + \expandafter\XINT@div@prepareA@c\expandafter{\the\numexpr 4*((#1+1)/4)}{#1}% }% % \end{macrocode} % \vspace*{-.5\baselineskip} @@ -7136,22 +7332,20 @@ first place. % \begin{macrocode} \def\XINT@div@prepareA@c #1#2% {% - \expandafter\XINT@div@prepareA@d \expandafter - {\the\numexpr #1-#2}{#1}% -}% -\def\XINT@div@prepareA@d #1% -{% - \ifcase #1 - \expandafter\XINT@div@prepareA@di - \or \expandafter\XINT@div@prepareA@dii - \or \expandafter\XINT@div@prepareA@diii - \else \expandafter\XINT@div@prepareA@div - \fi + \ifcase \numexpr #1-#2\relax + \expandafter\XINT@div@prepareA@d + \or + \expandafter\XINT@div@prepareA@di + \or + \expandafter\XINT@div@prepareA@dii + \or + \expandafter\XINT@div@prepareA@diii + \fi {#1}% }% -\def\XINT@div@prepareA@di {\XINT@div@prepareA@e {}}% -\def\XINT@div@prepareA@dii {\XINT@div@prepareA@e {0}}% -\def\XINT@div@prepareA@diii {\XINT@div@prepareA@e {00}}% -\def\XINT@div@prepareA@div {\XINT@div@prepareA@e {000}}% +\def\XINT@div@prepareA@d {\XINT@div@prepareA@e {}}% +\def\XINT@div@prepareA@di {\XINT@div@prepareA@e {0}}% +\def\XINT@div@prepareA@dii {\XINT@div@prepareA@e {00}}% +\def\XINT@div@prepareA@diii {\XINT@div@prepareA@e {000}}% % \end{macrocode} % \vspace*{-.5\baselineskip} % \begin{verbatim} @@ -7191,8 +7385,7 @@ first place. % \begin{macrocode} \def\XINT@div@finished@a #1#2#3% {% - \expandafter \XINT@div@finished@b \expandafter - {\romannumeral0\XINT@cuz {#1}}% + \expandafter\XINT@div@finished@b\expandafter {\romannumeral0\XINT@cuz {#1}}% }% % \end{macrocode} % \vspace*{-.5\baselineskip} @@ -7207,16 +7400,15 @@ first place. \ifcase \XINT@Sgn {#1} \xint@afterfi {\XINT@div@finished@c {0}}% \or - \xint@afterfi {\expandafter\XINT@div@finished@c - \expandafter - {\romannumeral0\XINT@dsh@checksignx #5\Z {#1}}}% + \xint@afterfi {\expandafter\XINT@div@finished@c\expandafter + {\romannumeral0\XINT@dsh@checksignx #5\Z {#1}}% + }% \fi {#2}% }% \def\XINT@div@finished@c #1#2% {% - \expandafter\space\expandafter - {\romannumeral0\XINT@rev@andcuz {#2}}{#1}% + \expandafter\space\expandafter {\romannumeral0\XINT@rev@andcuz {#2}}{#1}% }% % \end{macrocode} % \vspace*{-.5\baselineskip} @@ -7302,14 +7494,14 @@ first place. \XINT@div@final@f {#1}% {\romannumeral0\XINT@add@A 0{}#2000\W\X\Y\Z #4\W\X\Y\Z }% }% -\def\XINT@div@final@f #1#2#3% R,Q à développer,c +\def\XINT@div@final@f #1#2#3% R,Q \`a d\'evelopper,c {% \ifcase \XINT@Sgn {#1} \xint@afterfi {\XINT@div@final@end {0}}% \or - \xint@afterfi {\expandafter\XINT@div@final@end - \expandafter % pas de leading zeros dans #1=R - {\romannumeral0\XINT@dsh@checksignx #3\Z {#1}}}% + \xint@afterfi {\expandafter\XINT@div@final@end\expandafter + {\romannumeral0\XINT@dsh@checksignx #3\Z {#1}}% + }% \fi {#2}% }% @@ -7457,8 +7649,7 @@ first place. \def\XINT@div@body@l #1#2#3#4#5#6#7% {% \expandafter\XINT@div@body@m - \the\numexpr 100000000+#2\relax - {#6}{#3}{#7}{#1#5}{#4}% + \the\numexpr 100000000+#2\relax {#6}{#3}{#7}{#1#5}{#4}% }% % \end{macrocode} % \vspace*{-.5\baselineskip} @@ -7674,7 +7865,7 @@ first place. \def\xintiFDg {\romannumeral0\xintifdg }% \def\xintifdg #1% {% - \expandafter\expandafter\expandafter\XINT@fdg #1\W\Z + \expandafter\XINT@fdg \romannumeral-`0#1\W\Z }% \let\xintFDg\xintiFDg \let\xintfdg\xintifdg \def\XINT@FDg #1{\romannumeral0\XINT@fdg #1\W\Z }% @@ -7697,10 +7888,7 @@ first place. \def\xintiLDg {\romannumeral0\xintildg }% \def\xintildg #1% {% - \expandafter\expandafter\expandafter - \XINT@ldg - \expandafter\expandafter\expandafter - {#1}% + \expandafter\XINT@ldg\expandafter {\romannumeral-`0#1}% }% \let\xintLDg\xintiLDg \let\xintldg\xintildg \def\XINT@LDg #1{\romannumeral0\XINT@ldg {#1}}% @@ -7772,7 +7960,7 @@ first place. \def\xintDSL {\romannumeral0\xintdsl }% \def\xintdsl #1% {% - \expandafter\expandafter\expandafter\XINT@dsl #1\Z + \expandafter\XINT@dsl \romannumeral-`0#1\Z }% \def\XINT@DSL #1{\romannumeral0\XINT@dsl #1\Z }% \def\XINT@dsl #1% @@ -7791,16 +7979,12 @@ first place. \def\xintDSR {\romannumeral0\xintdsr }% \def\xintdsr #1% {% - \expandafter\expandafter\expandafter - \XINT@dsr@a - \expandafter\expandafter\expandafter - {#1}\W\Z + \expandafter\XINT@dsr@a\expandafter {\romannumeral-`0#1}\W\Z }% \def\XINT@DSR #1{\romannumeral0\XINT@dsr@a {#1}\W\Z }% \def\XINT@dsr@a {% - \expandafter\XINT@dsr@b - \romannumeral0\XINT@rev + \expandafter\XINT@dsr@b\romannumeral0\XINT@rev }% \def\XINT@dsr@b #1#2#3\Z {% @@ -7821,13 +8005,15 @@ first place. % si x > 0, et A < 0, fait A -> -quo(-A,10^(x)) % (donc pour x > 0 c'est comme DSR itéré x fois) % \xintDSHr donne le `reste' (si x<=0 donne zéro). +% Release 1.06 now feeds x to a \numexpr first. I will revise the legacy code on +% another occasion. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintDSHr {\romannumeral0\xintdshr }% \def\xintdshr #1% {% - \expandafter\expandafter\expandafter\XINT@dshr@checkxpositive #1\Z + \expandafter\XINT@dshr@checkxpositive \the\numexpr #1\relax\Z }% \def\XINT@dshr@checkxpositive #1% {% @@ -7840,21 +8026,16 @@ first place. \def\XINT@dshr@xzeroorneg #1\Z #2{ 0}% \def\XINT@dshr@xpositive #1\Z {% - \expandafter\xint@secondoftwo@andstop - \romannumeral0\xintdsx {#1}% + \expandafter\xint@secondoftwo@andstop\romannumeral0\xintdsx {#1}% }% \def\xintDSH {\romannumeral0\xintdsh }% \def\xintdsh #1#2% {% - \expandafter\expandafter\expandafter - \xint@dsh - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\xint@dsh\expandafter {\romannumeral-`0#2}{#1}% }% \def\xint@dsh #1#2% {% - \expandafter\expandafter\expandafter - \XINT@dsh@checksignx #2\Z {#1}% + \expandafter\XINT@dsh@checksignx \the\numexpr #2\relax\Z {#1}% }% \def\XINT@dsh@checksignx #1% {% @@ -7886,20 +8067,20 @@ first place. % On peut donc toujours reconstituer l'original A par 10^x Q \pm R % où il faut prendre le signe plus si Q est positif ou nul et le signe moins si % Q est strictement négatif. +% 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. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintDSx {\romannumeral0\xintdsx }% \def\xintdsx #1#2% {% - \expandafter\expandafter\expandafter - \xint@dsx - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\xint@dsx\expandafter {\romannumeral-`0#2}{#1}% }% \def\xint@dsx #1#2% {% - \expandafter\expandafter\expandafter\XINT@dsx@checksignx #2\Z {#1}% + \expandafter\XINT@dsx@checksignx \the\numexpr #2\relax\Z {#1}% }% \def\XINT@DSx #1#2{\romannumeral0\XINT@dsx@checksignx #1\Z {#2}}% \def\XINT@dsx #1#2{\XINT@dsx@checksignx #1\Z {#2}}% @@ -7918,55 +8099,36 @@ first place. }% \def\XINT@dsx@xisNeg@checkA@ #1#2\Z #3% {% - \xint@zero #1\XINT@dsx@xisNeg@Azero 0\expandafter - \XINT@dsx@xisNeg@checkx\expandafter - {\romannumeral0\XINT@length {#3}}{#3}\Z {#1#2}% + \xint@zero #1\XINT@dsx@xisNeg@Azero 0% + \XINT@dsx@xisNeg@checkx {#3}{#3}\Z {#1#2}% }% -\def\XINT@dsx@xisNeg@Azero #1#2#3#4#5#6#7#8{ 0}% +\def\XINT@dsx@xisNeg@Azero #1\Z #2{ 0}% \def\XINT@dsx@xisNeg@checkx #1% {% - \ifnum #1> 9 - \xint@afterfi {\xintError:TooBigDecimalShift\XINT@dsx@toobigx }% + \ifnum #1> 999999999 + \xint@afterfi + {\xintError:TooBigDecimalShift + \expandafter\space\expandafter 0\xint@gobble@iii }% \else \expandafter \XINT@dsx@zeroloop \fi }% -\def\XINT@dsx@toobigx #1#2#3{ 0}% \def\XINT@dsx@zeroloop #1% {% - \ifcase #1 - \XINT@dsx@exit - \or - \XINT@dsx@exiti - \or - \XINT@dsx@exitii - \or - \XINT@dsx@exitiii - \or - \XINT@dsx@exitiv - \or - \XINT@dsx@exitv - \or - \XINT@dsx@exitvi - \or - \XINT@dsx@exitvii - \else - \xint@afterfi - {\expandafter - \XINT@dsx@zeroloop - \expandafter {\the\numexpr #1-8}00000000% - }% - \fi + \ifnum #1<9 \XINT@dsx@exita\fi + \expandafter\XINT@dsx@zeroloop\expandafter + {\the\numexpr #1-8}00000000% +}% +\def\XINT@dsx@exita\fi\expandafter\XINT@dsx@zeroloop +{% + \fi\expandafter\XINT@dsx@exitb }% -\def\XINT@dsx@exit #1\fi #2\Z {\fi \XINT@dsx@addzeros {#2}}% -\def\XINT@dsx@exiti #1\fi #2\Z {\fi \XINT@dsx@addzeros {0#2}}% -\def\XINT@dsx@exitii #1\fi #2\Z {\fi \XINT@dsx@addzeros {00#2}}% -\def\XINT@dsx@exitiii #1\fi #2\Z {\fi \XINT@dsx@addzeros {000#2}}% -\def\XINT@dsx@exitiv #1\fi #2\Z {\fi \XINT@dsx@addzeros {0000#2}}% -\def\XINT@dsx@exitv #1\fi #2\Z {\fi \XINT@dsx@addzeros {00000#2}}% -\def\XINT@dsx@exitvi #1\fi #2\Z {\fi \XINT@dsx@addzeros {000000#2}}% -\def\XINT@dsx@exitvii #1\fi #2\Z {\fi \XINT@dsx@addzeros {0000000#2}}% -\def\XINT@dsx@addzeros #1#2{ #2#1}% +\def\XINT@dsx@exitb #1% +{% + \expandafter\expandafter\expandafter + \XINT@dsx@addzeros\csname xint@gobble@\romannumeral -#1\endcsname +}% +\def\XINT@dsx@addzeros #1\Z #2{ #2#1}% \def\XINT@dsx@xisPos #1\Z #2% {% \XINT@dsx@checksignA #2\Z {#1}% @@ -8024,17 +8186,23 @@ first place. % \subsection{\csh{xintDecSplit},~\csh{xintDecSplitL},~\csh{xintDecSplitR}} % \begin{verbatim} % DECIMAL SPLIT -% v1.01: **New** behavior, for use in future extensions of the xint bundle: % The macro \xintDecSplit {x}{A} first replaces A with |A| (*) % This macro cuts the number into two pieces L and R. The concatenation LR % always reproduces |A|, and R may be empty or have leading zeros. The % position of the cut is specified by the first argument x. If x is zero or % positive the cut location is x slots to the left of the right end of the % number. If x becomes equal to or larger than the length of the number then L -% becomes empty. If x is negative the location of the cut is x slots to the +% becomes empty. If x is negative the location of the cut is |x| slots to the % right of the left end of the number. % (*) warning: this may change in a future version. Only the behavior % for A non-negative is guaranteed to remain the same. +% v1.05a: \XINT@split@checksizex does not compute the length anymore, rather the +% error will be from a \numexpr; but the limit of 999999999 does not make much +% sense. +% v1.06: Improvements in \XINT@split@fromleft@loop, \XINT@split@fromright@loop +% and related macros. More readable coding, speed gains. +% Also, I now feed immediately a \numexpr with x. Some simplifications may then +% be perhaps made to the code, it is kept as is for the time being. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} @@ -8058,14 +8226,11 @@ first place. }% \def\xint@split #1#2% {% - \expandafter\expandafter\expandafter - \XINT@split@checksizex - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@split@checksizex\expandafter{\the\numexpr #2}{#1}% }% -\def\XINT@split@checksizex #1% +\def\XINT@split@checksizex #1% 999999999 is anyhow very big, could be reduced {% - \ifnum\XINT@Len {#1} > 9 + \ifnum\numexpr\XINT@Abs{#1}\relax > 999999999 \xint@afterfi {\xintError:TooBigDecimalSplit\XINT@split@bigx }% \else \expandafter\XINT@split@xfork @@ -8089,77 +8254,51 @@ first place. \xint@UDkrof }% \def\XINT@split@zerosplit #1\Z #2{ {#2}{}}% -\def\XINT@split@fromleft #1\Z #2% +\def\XINT@split@fromleft #1\Z #2% {% \XINT@split@fromleft@loop {#1}{}#2\W\W\W\W\W\W\W\W\Z }% \def\XINT@split@fromleft@loop #1% {% - \ifcase #1 - \XINT@split@fromleft@endsplit - \or - \XINT@split@fromleft@one@andend - \or - \XINT@split@fromleft@two@andend - \or - \XINT@split@fromleft@three@andend - \or - \XINT@split@fromleft@four@andend - \or - \XINT@split@fromleft@five@andend - \or - \XINT@split@fromleft@six@andend - \or - \XINT@split@fromleft@seven@andend - \else - \expandafter \XINT@split@fromleft@loop@perhaps - \expandafter - {\the\numexpr #1-8\expandafter\expandafter\expandafter }% - \expandafter - \XINT@split@fromleft@eight - \fi -}% -\def\XINT@split@fromleft@endsplit #1\fi #2#3\W #4\Z - {\expandafter\space\fi {#2}{#3}}% -\def\XINT@split@fromleft@eight #1#2#3#4#5#6#7#8#9% -{% - #9{#1#2#3#4#5#6#7#8#9}% + \ifnum #1<8 \XINT@split@fromleft@exita\fi + \expandafter\XINT@split@fromleft@loop@perhaps\expandafter + {\the\numexpr #1-8\expandafter}\XINT@split@fromleft@eight }% +\def\XINT@split@fromleft@eight #1#2#3#4#5#6#7#8#9{#9{#1#2#3#4#5#6#7#8#9}}% \def\XINT@split@fromleft@loop@perhaps #1#2% {% - \xint@w #2\XINT@split@fromleft@toofar\W \XINT@split@fromleft@loop - {#1}% + \xint@w #2\XINT@split@fromleft@toofar\W\XINT@split@fromleft@loop {#1}% }% -\def\XINT@split@fromleft@toofar\W \XINT@split@fromleft@loop #1#2#3\Z +\def\XINT@split@fromleft@toofar\W\XINT@split@fromleft@loop #1#2#3\Z {% \XINT@split@fromleft@toofar@b #2\Z }% \def\XINT@split@fromleft@toofar@b #1\W #2\Z { {#1}{}}% -\def\XINT@split@fromleft@one@andend #1\fi -{\fi\expandafter\XINT@split@fromleft@checkiftoofar\XINT@split@fromleft@one }% -\def\XINT@split@fromleft@one #1#2{#2{#1#2}}% -\def\XINT@split@fromleft@two@andend #1\fi -{\fi\expandafter\XINT@split@fromleft@checkiftoofar\XINT@split@fromleft@two }% -\def\XINT@split@fromleft@two #1#2#3{#3{#1#2#3}}% -\def\XINT@split@fromleft@three@andend #1\fi -{\fi\expandafter\XINT@split@fromleft@checkiftoofar\XINT@split@fromleft@three }% -\def\XINT@split@fromleft@three #1#2#3#4{#4{#1#2#3#4}}% -\def\XINT@split@fromleft@four@andend #1\fi -{\fi\expandafter\XINT@split@fromleft@checkiftoofar\XINT@split@fromleft@four }% -\def\XINT@split@fromleft@four #1#2#3#4#5{#5{#1#2#3#4#5}}% -\def\XINT@split@fromleft@five@andend #1\fi -{\fi\expandafter\XINT@split@fromleft@checkiftoofar\XINT@split@fromleft@five }% -\def\XINT@split@fromleft@five #1#2#3#4#5#6{#6{#1#2#3#4#5#6}}% -\def\XINT@split@fromleft@six@andend #1\fi -{\fi\expandafter\XINT@split@fromleft@checkiftoofar\XINT@split@fromleft@six }% -\def\XINT@split@fromleft@six #1#2#3#4#5#6#7{#7{#1#2#3#4#5#6#7}}% -\def\XINT@split@fromleft@seven@andend #1\fi -{\fi\expandafter\XINT@split@fromleft@checkiftoofar\XINT@split@fromleft@seven }% -\def\XINT@split@fromleft@seven #1#2#3#4#5#6#7#8{#8{#1#2#3#4#5#6#7#8}}% +\def\XINT@split@fromleft@exita\fi + \expandafter\XINT@split@fromleft@loop@perhaps\expandafter #1#2% + {\fi \XINT@split@fromleft@exitb #1}% +\def\XINT@split@fromleft@exitb\the\numexpr #1-8\expandafter +{% + \csname XINT@split@fromleft@endsplit@\romannumeral #1\endcsname +}% +\def\XINT@split@fromleft@endsplit@ #1#2\W #3\Z { {#1}{#2}}% +\def\XINT@split@fromleft@endsplit@i #1#2% + {\XINT@split@fromleft@checkiftoofar #2{#1#2}}% +\def\XINT@split@fromleft@endsplit@ii #1#2#3% + {\XINT@split@fromleft@checkiftoofar #3{#1#2#3}}% +\def\XINT@split@fromleft@endsplit@iii #1#2#3#4% + {\XINT@split@fromleft@checkiftoofar #4{#1#2#3#4}}% +\def\XINT@split@fromleft@endsplit@iv #1#2#3#4#5% + {\XINT@split@fromleft@checkiftoofar #5{#1#2#3#4#5}}% +\def\XINT@split@fromleft@endsplit@v #1#2#3#4#5#6% + {\XINT@split@fromleft@checkiftoofar #6{#1#2#3#4#5#6}}% +\def\XINT@split@fromleft@endsplit@vi #1#2#3#4#5#6#7% + {\XINT@split@fromleft@checkiftoofar #7{#1#2#3#4#5#6#7}}% +\def\XINT@split@fromleft@endsplit@vii #1#2#3#4#5#6#7#8% + {\XINT@split@fromleft@checkiftoofar #8{#1#2#3#4#5#6#7#8}}% \def\XINT@split@fromleft@checkiftoofar #1#2#3\W #4\Z {% - \xint@w #1\XINT@split@fromleft@wenttoofar\W - \space {#2}{#3}% + \xint@w #1\XINT@split@fromleft@wenttoofar\W\space {#2}{#3}% }% \def\XINT@split@fromleft@wenttoofar\W\space #1% {% @@ -8177,72 +8316,48 @@ first place. }% \def\XINT@split@fromright@loop #1% {% - \ifcase #1 - \expandafter\XINT@split@fromright@endsplit - \or - \XINT@split@fromright@one@andend - \or - \XINT@split@fromright@two@andend - \or - \XINT@split@fromright@three@andend - \or - \XINT@split@fromright@four@andend - \or - \XINT@split@fromright@five@andend - \or - \XINT@split@fromright@six@andend - \or - \XINT@split@fromright@seven@andend - \else - \expandafter \XINT@split@fromright@loop@perhaps - \expandafter - {\the\numexpr - #1-8\expandafter\expandafter\expandafter }% - \expandafter - \XINT@split@fromright@eight - \fi + \ifnum #1<8 \XINT@split@fromright@exita\fi + \expandafter\XINT@split@fromright@loop@perhaps\expandafter + {\the\numexpr #1-8\expandafter }\XINT@split@fromright@eight }% -\def\XINT@split@fromright@endsplit #1#2\W #3\Z #4% +\def\XINT@split@fromright@eight #1#2#3#4#5#6#7#8#9{#9{#9#8#7#6#5#4#3#2#1}}% +\def\XINT@split@fromright@loop@perhaps #1#2% {% - \expandafter\space\expandafter {\romannumeral0\XINT@rev{#2}}{#1}% + \xint@w #2\XINT@split@fromright@toofar\W + \XINT@split@fromright@loop {#1}% }% -\def\XINT@split@fromright@eight #1#2#3#4#5#6#7#8#9% +\def\XINT@split@fromright@toofar\W\XINT@split@fromright@loop #1#2#3\Z { {}}% +\def\XINT@split@fromright@exita\fi + \expandafter\XINT@split@fromright@loop@perhaps\expandafter #1#2% + {\fi \XINT@split@fromright@exitb #1}% +\def\XINT@split@fromright@exitb\the\numexpr #1-8\expandafter {% - #9{#9#8#7#6#5#4#3#2#1}% + \csname XINT@split@fromright@endsplit@\romannumeral #1\endcsname }% -\def\XINT@split@fromright@loop@perhaps #1#2% +\def\XINT@split@fromright@endsplit@ #1#2\W #3\Z #4% {% - \xint@w #2\XINT@split@fromright@toofar\W\XINT@split@fromright@loop - {#1}% + \expandafter\space\expandafter {\romannumeral0\XINT@rev{#2}}{#1}% }% -\def\XINT@split@fromright@toofar\W\XINT@split@fromright@loop #1#2#3\Z { {}}% -\def\XINT@split@fromright@one@andend #1\fi {\fi\expandafter - \XINT@split@fromright@checkiftoofar\XINT@split@fromright@one }% -\def\XINT@split@fromright@one #1#2{#2{#2#1}}% -\def\XINT@split@fromright@two@andend #1\fi {\fi\expandafter - \XINT@split@fromright@checkiftoofar\XINT@split@fromright@two }% -\def\XINT@split@fromright@two #1#2#3{#3{#3#2#1}}% -\def\XINT@split@fromright@three@andend #1\fi {\fi\expandafter - \XINT@split@fromright@checkiftoofar\XINT@split@fromright@three }% -\def\XINT@split@fromright@three #1#2#3#4{#4{#4#3#2#1}}% -\def\XINT@split@fromright@four@andend #1\fi {\fi\expandafter - \XINT@split@fromright@checkiftoofar\XINT@split@fromright@four }% -\def\XINT@split@fromright@four #1#2#3#4#5{#5{#5#4#3#2#1}}% -\def\XINT@split@fromright@five@andend #1\fi {\fi\expandafter - \XINT@split@fromright@checkiftoofar\XINT@split@fromright@five }% -\def\XINT@split@fromright@five #1#2#3#4#5#6{#6{#6#5#4#3#2#1}}% -\def\XINT@split@fromright@six@andend #1\fi {\fi\expandafter - \XINT@split@fromright@checkiftoofar\XINT@split@fromright@six }% -\def\XINT@split@fromright@six #1#2#3#4#5#6#7{#7{#7#6#5#4#3#2#1}}% -\def\XINT@split@fromright@seven@andend #1\fi {\fi\expandafter - \XINT@split@fromright@checkiftoofar\XINT@split@fromright@seven }% -\def\XINT@split@fromright@seven #1#2#3#4#5#6#7#8{#8{#8#7#6#5#4#3#2#1}}% +\def\XINT@split@fromright@endsplit@i #1#2% + {\XINT@split@fromright@checkiftoofar #2{#2#1}}% +\def\XINT@split@fromright@endsplit@ii #1#2#3% + {\XINT@split@fromright@checkiftoofar #3{#3#2#1}}% +\def\XINT@split@fromright@endsplit@iii #1#2#3#4% + {\XINT@split@fromright@checkiftoofar #4{#4#3#2#1}}% +\def\XINT@split@fromright@endsplit@iv #1#2#3#4#5% + {\XINT@split@fromright@checkiftoofar #5{#5#4#3#2#1}}% +\def\XINT@split@fromright@endsplit@v #1#2#3#4#5#6% + {\XINT@split@fromright@checkiftoofar #6{#6#5#4#3#2#1}}% +\def\XINT@split@fromright@endsplit@vi #1#2#3#4#5#6#7% + {\XINT@split@fromright@checkiftoofar #7{#7#6#5#4#3#2#1}}% +\def\XINT@split@fromright@endsplit@vii #1#2#3#4#5#6#7#8% + {\XINT@split@fromright@checkiftoofar #8{#8#7#6#5#4#3#2#1}}% \def\XINT@split@fromright@checkiftoofar #1% {% \xint@w #1\XINT@split@fromright@wenttoofar\W - \XINT@split@fromright@endsplit + \XINT@split@fromright@endsplit@ }% -\def\XINT@split@fromright@wenttoofar\W\XINT@split@fromright@endsplit #1\Z #2% +\def\XINT@split@fromright@wenttoofar\W\XINT@split@fromright@endsplit@ #1\Z #2% { {}{#2}}% \XINT@restorecatcodes@endinput% % \end{macrocode} @@ -8366,6 +8481,7 @@ first place. \edef\XINT@gcd@restorecatcodes@endinput {% \catcode36=\the\catcode36 % $ + \catcode96=\the\catcode96 % ` \catcode47=\the\catcode47 % / \catcode41=\the\catcode41 % ) \catcode40=\the\catcode40 % ( @@ -8416,7 +8532,7 @@ first place. \fi \expandafter\x\csname ver@xintgcd.sty\endcsname \ProvidesPackage{xintgcd}% - [2013/05/02 v1.05a Euclide algorithm with xint package (jfB)]% + [2013/05/07 v1.06 Euclide algorithm with xint package (jfB)]% % \end{macrocode} % \subsection{\csh{xintGCD}} % \begin{macrocode} @@ -8473,14 +8589,11 @@ first place. \def\xintBezout {\romannumeral0\xintbezout }% \def\xintbezout #1% {% - \expandafter\expandafter\expandafter - \xint@bezout - \expandafter\expandafter\expandafter - {#1}% + \expandafter\xint@bezout\expandafter {\romannumeral-`0#1}% }% \def\xint@bezout #1#2% {% - \expandafter\expandafter\expandafter\XINT@bezout@fork #2\Z #1\Z + \expandafter\XINT@bezout@fork \romannumeral-`0#2\Z #1\Z }% % \end{macrocode} % \vspace*{-.5\baselineskip} @@ -8748,8 +8861,7 @@ first place. }% \def\XINT@euc #1#2% {% - \expandafter\XINT@euc@fork - \romannumeral0\xintiabs {#2}\Z #1\Z + \expandafter\XINT@euc@fork \romannumeral0\xintiabs {#2}\Z #1\Z }% % \end{macrocode} % \vspace*{-.5\baselineskip} @@ -8860,8 +8972,7 @@ first place. }% \def\XINT@bezalg #1#2% {% - \expandafter\XINT@bezalg@fork - \romannumeral0\xintiabs {#2}\Z #1\Z + \expandafter\XINT@bezalg@fork \romannumeral0\xintiabs {#2}\Z #1\Z }% % \end{macrocode} % \vspace*{-.5\baselineskip} @@ -9009,10 +9120,10 @@ first place. \noindent \count 255 1 \loop - \hbox to \wd 0 {\hfil$\U{\the\numexpr 2*\count 255\relax}$}% - ${} = \U{\the\numexpr 2*\count 255 + 3\relax} - \times \U{\the\numexpr 2*\count 255 + 2\relax} - + \U{\the\numexpr 2*\count 255 + 4\relax}$% + \hbox to \wd 0 {\hfil$\U{\numexpr 2*\count 255\relax}$}% + ${} = \U{\numexpr 2*\count 255 + 3\relax} + \times \U{\numexpr 2*\count 255 + 2\relax} + + \U{\numexpr 2*\count 255 + 4\relax}$% \ifnum \count 255 < \N \hfill\break \advance \count 255 1 @@ -9046,25 +9157,25 @@ first place. \count 255 1 \loop \noindent - \hbox to \wd 0 {\hfil$\BEZ{\the\numexpr 4*\count 255 - 2\relax}$}% - ${} = \BEZ{\the\numexpr 4*\count 255 + 5\relax} - \times \BEZ{\the\numexpr 4*\count 255 + 2\relax} - + \BEZ{\the\numexpr 4*\count 255 + 6\relax}$\hfill\break - \hbox to \wd 0 {\hfil$\BEZ{\the\numexpr 4*\count 255 +7\relax}$}% - ${} = \BEZ{\the\numexpr 4*\count 255 + 5\relax} - \times \BEZ{\the\numexpr 4*\count 255 + 3\relax} - + \BEZ{\the\numexpr 4*\count 255 - 1\relax}$\hfill\break - \hbox to \wd 0 {\hfil$\BEZ{\the\numexpr 4*\count 255 +8\relax}$}% - ${} = \BEZ{\the\numexpr 4*\count 255 + 5\relax} - \times \BEZ{\the\numexpr 4*\count 255 + 4\relax} - + \BEZ{\the\numexpr 4*\count 255 \relax}$ + \hbox to \wd 0 {\hfil$\BEZ{4*\count 255 - 2}$}% + ${} = \BEZ{4*\count 255 + 5} + \times \BEZ{4*\count 255 + 2} + + \BEZ{4*\count 255 + 6}$\hfill\break + \hbox to \wd 0 {\hfil$\BEZ{4*\count 255 +7}$}% + ${} = \BEZ{4*\count 255 + 5} + \times \BEZ{4*\count 255 + 3} + + \BEZ{4*\count 255 - 1}$\hfill\break + \hbox to \wd 0 {\hfil$\BEZ{4*\count 255 +8}$}% + ${} = \BEZ{4*\count 255 + 5} + \times \BEZ{4*\count 255 + 4} + + \BEZ{4*\count 255 }$ \endgraf \ifnum \count 255 < \N \advance \count 255 1 \repeat \par - \edef\U{\BEZ{\the\numexpr 4*\N + 4\relax}}% - \edef\V{\BEZ{\the\numexpr 4*\N + 3\relax}}% + \edef\U{\BEZ{4*\N + 4}}% + \edef\V{\BEZ{4*\N + 3}}% \edef\D{\BEZ5}% \ifodd\N $\U\times\A - \V\times \B = -\D$% @@ -9198,6 +9309,7 @@ first place. \catcode94=\the\catcode94 % ^ \catcode93=\the\catcode93 % ] \catcode91=\the\catcode91 % [ + \catcode96=\the\catcode96 % ` \catcode47=\the\catcode47 % / \catcode41=\the\catcode41 % ) \catcode40=\the\catcode40 % ( @@ -9248,7 +9360,7 @@ first place. \fi \expandafter\x\csname ver@xintfrac.sty\endcsname \ProvidesPackage{xintfrac}% - [2013/05/02 v1.05a Expandable operations on fractions (jfB)]% + [2013/05/07 v1.06 Expandable operations on fractions (jfB)]% % \end{macrocode} % \subsection{\csh{xintLen}} % \begin{macrocode} @@ -9300,7 +9412,7 @@ first place. \def\XINT@inFrac {\romannumeral0\XINT@infrac }% \def\XINT@infrac #1% {% - \expandafter\expandafter\expandafter\XINT@infrac@ #1[\W]\Z\T + \expandafter\XINT@infrac@ \romannumeral-`0#1[\W]\Z\T }% \def\XINT@infrac@ #1[#2#3]#4\Z {% @@ -9323,7 +9435,7 @@ first place. {% \xint@UDwfork #2\dummy \XINT@infrac@BCa - \W\dummy {\expandafter\expandafter\expandafter\XINT@infrac@BCb #2}% + \W\dummy {\expandafter\XINT@infrac@BCb \romannumeral-`0#2}% \xint@UDkrof #3\Z #1\Z }% @@ -9337,7 +9449,7 @@ first place. {% \xint@UDwfork #2\dummy \XINT@frac@A - \W\dummy {\expandafter\expandafter\expandafter\XINT@frac@B #2}% + \W\dummy {\expandafter\XINT@frac@B \romannumeral-`0#2}% \xint@UDkrof #3.\W\Z #1.\W\Z }% @@ -9576,7 +9688,7 @@ first place. \def\XINT@@frac@C #1#2#3#4#5% {% \ifcase\XINT@isOne {#5} - \or \xint@afterfi {\expandafter\xint@firstoftwo@andstop\xint@gobble@two }% + \or \xint@afterfi {\expandafter\xint@firstoftwo@andstop\xint@gobble@ii }% \fi \space \frac {#4}{#5}% @@ -9738,7 +9850,7 @@ first place. #2\Z {#3}% }% \def\XINT@irr@denomisone #1\Z #2{ #1}% -\def\XINT@irr@negative #1\Z #2{\XINT@irr@D #1\Z #2\Z \XINT@opp}% +\def\XINT@irr@negative #1\Z #2{\XINT@irr@D #1\Z #2\Z \xint@minus@andstop}% \def\XINT@irr@nonneg #1\Z #2{\XINT@irr@D #1\Z #2\Z \space}% \def\XINT@irr@D #1#2\Z #3#4\Z {% @@ -9801,7 +9913,7 @@ first place. \def\xintnum #1{\expandafter\XINT@intcheck\romannumeral0\xintirr {#1}/\W\Z }% \def\XINT@intcheck #1/#2#3\Z {% - \xint@w #2\xint@gobble@two\W\xintError:NotAnInteger + \xint@w #2\xint@gobble@ii\W\xintError:NotAnInteger \space #1% }% % \end{macrocode} @@ -9830,7 +9942,7 @@ first place. #2\Z {#3}% }% \def\XINT@jrr@denomisone #1\Z #2{ #1}% -\def\XINT@jrr@negative #1\Z #2{\XINT@jrr@D #1\Z #2\Z \XINT@opp}% +\def\XINT@jrr@negative #1\Z #2{\XINT@jrr@D #1\Z #2\Z \xint@minus@andstop }% \def\XINT@jrr@nonneg #1\Z #2{\XINT@jrr@D #1\Z #2\Z \space}% \def\XINT@jrr@D #1#2\Z #3#4\Z {% @@ -9875,15 +9987,16 @@ first place. }% % \end{macrocode} % \subsection{\csh{xintTrunc}, \csh{xintiTrunc}} +% \begin{verbatim} +% Modified in 1.06 to give the first argument to a \numexpr +% \end{verbatim} +% \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintTrunc {\romannumeral0\xinttrunc }% \def\xintiTrunc {\romannumeral0\xintitrunc }% \def\xinttrunc #1% {% - \expandafter\expandafter\expandafter - \XINT@trunc - \expandafter\expandafter\expandafter - {#1}% + \expandafter\XINT@trunc\expandafter {\the\numexpr #1}% }% \def\XINT@trunc #1#2% {% @@ -9893,10 +10006,7 @@ first place. }% \def\xintitrunc #1% {% - \expandafter\expandafter\expandafter - \XINT@itrunc - \expandafter\expandafter\expandafter - {#1}% + \expandafter\XINT@itrunc\expandafter {\the\numexpr #1}% }% \def\XINT@itrunc #1#2% {% @@ -9966,7 +10076,7 @@ first place. \ifnum #1 > 0 \xint@afterfi {\XINT@trunc@Ha {#2}}% \else - \xint@afterfi {\XINT@trunc@Hb {-#1}}% + \xint@afterfi {\XINT@trunc@Hb {-#1}}% -0,--1,--2, .... \fi }% \def\XINT@trunc@Ha @@ -9980,19 +10090,20 @@ first place. \def\XINT@trunc@Hb #1#2#3% {% \expandafter #3\expandafter0\expandafter.% - \romannumeral0\XINT@dsx@zeroloop {#1}\Z {}#2% + \romannumeral0\XINT@dsx@zeroloop {#1}\Z {}#2% #1=-0 possible! }% % \end{macrocode} % \subsection{\csh{xintRound}, \csh{xintiRound}} +% \begin{verbatim} +% Modified in 1.06 to give the first argument to a \numexpr +% \end{verbatim} +% \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintRound {\romannumeral0\xintround }% \def\xintiRound {\romannumeral0\xintiround }% \def\xintround #1% {% - \expandafter\expandafter\expandafter - \XINT@round - \expandafter\expandafter\expandafter - {#1}% + \expandafter\XINT@round\expandafter {\the\numexpr #1}% }% \def\XINT@round {% @@ -10000,10 +10111,7 @@ first place. }% \def\xintiround #1% {% - \expandafter\expandafter\expandafter - \XINT@iround - \expandafter\expandafter\expandafter - {#1}% + \expandafter\XINT@iround\expandafter {\the\numexpr #1}% }% \def\XINT@iround {% @@ -10128,11 +10236,11 @@ first place. \def\xintSum {\romannumeral0\xintsum }% \def\xintsum #1{\xintsumexpr #1\relax }% \def\xintSumExpr {\romannumeral0\xintsumexpr }% -\def\xintsumexpr {\expandafter\expandafter\expandafter\XINT@fsumexpr }% +\def\xintsumexpr {\expandafter\XINT@fsumexpr\romannumeral-`0}% \def\XINT@fsumexpr {\XINT@fsum@loop@a {0[0]}}% \def\XINT@fsum@loop@a #1#2% {% - \expandafter\expandafter\expandafter\XINT@fsum@loop@b #2\Z {#1}% + \expandafter\XINT@fsum@loop@b \romannumeral-`0#2\Z {#1}% }% \def\XINT@fsum@loop@b #1% {% @@ -10177,6 +10285,10 @@ first place. \def\xint@fsqr #1{\XINT@fmul@A #1#1}% % \end{macrocode} % \subsection{\csh{xintPow}} +% \begin{verbatim} +% Modified in 1.06 to give the exponent to a \numexpr +% \end{verbatim} +% \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintPow {\romannumeral0\xintpow }% \def\xintpow #1% @@ -10185,8 +10297,7 @@ first place. }% \def\xint@fpow #1#2% {% - \expandafter\expandafter\expandafter - \XINT@fpow@fork #2\Z #1% + \expandafter\XINT@fpow@fork\the\numexpr #2\relax\Z #1% }% \def\XINT@fpow@fork #1#2\Z {% @@ -10226,11 +10337,11 @@ first place. \def\xintPrd {\romannumeral0\xintprd }% \def\xintprd #1{\xintproductexpr #1\relax }% \def\xintProductExpr {\romannumeral0\xintproductexpr }% -\def\xintproductexpr{\expandafter\expandafter\expandafter\XINT@fproductexpr }% +\def\xintproductexpr {\expandafter\XINT@fproductexpr \romannumeral-`0}% \def\XINT@fproductexpr {\XINT@fprod@loop@a {1[0]}}% \def\XINT@fprod@loop@a #1#2% {% - \expandafter\expandafter\expandafter\XINT@fprod@loop@b #2\Z {#1}% + \expandafter\XINT@fprod@loop@b \romannumeral-`0#2\Z {#1}% }% \def\XINT@fprod@loop@b #1% {% @@ -10420,7 +10531,7 @@ first place. \def\xintrem {\expandafter\xint@secondoftwo@andstop \romannumeral0\xintdivision }% % \end{macrocode} -% \subsection{\csh{xintFDg},~\csh{xintLDg},~\csh{xintMON},~\csh{xintMMON},~\csh{xintOdd}} +% \subsection{\csh{xintFDg},~\csh{xintLDg},~\csh{xintMON},~\csh{xint\-MMON},~\csh{xintOdd}} % \begin{macrocode} \def\xintFDg {\romannumeral0\xintfdg }% \def\xintfdg #1% @@ -10582,6 +10693,7 @@ first place. {% \catcode93=\the\catcode93 % ] \catcode91=\the\catcode91 % [ + \catcode96=\the\catcode96 % ` \catcode47=\the\catcode47 % / \catcode41=\the\catcode41 % ) \catcode40=\the\catcode40 % ( @@ -10631,24 +10743,23 @@ first place. \fi \expandafter\x\csname ver@xintseries.sty\endcsname \ProvidesPackage{xintseries}% - [2013/05/02 v1.05a Expandable partial sums with xint package (jfB)]% + [2013/05/07 v1.06 Expandable partial sums with xint package (jfB)]% % \end{macrocode} % \subsection{\csh{xintSeries}} +% \begin{verbatim} +% Modified in 1.06 to give the indices first to a \numexpr rather than expanding +% twice. I just use \the\numexpr and maintain the previous code after that. +% \end{verbatim} +% \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintSeries {\romannumeral0\xintseries }% \def\xintseries #1#2% {% - \expandafter\expandafter\expandafter - \XINT@series@i - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@series@i\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@series@i #1#2% {% - \expandafter\expandafter\expandafter - \XINT@series@ii - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@series@ii\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@series@ii #1#2#3% {% @@ -10668,25 +10779,24 @@ first place. }% \def\XINT@series@exit \fi #1#2#3#4#5#6#7#8% {% - \fi\xint@gobble@two #6% + \fi\xint@gobble@ii #6% }% % \end{macrocode} % \subsection{\csh{xintiSeries}} +% \begin{verbatim} +% Modified in 1.06 to give the indices first to a \numexpr rather than expanding +% twice. I just use \the\numexpr and maintain the previous code after that. +% \end{verbatim} +% \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintiSeries {\romannumeral0\xintiseries }% \def\xintiseries #1#2% {% - \expandafter\expandafter\expandafter - \XINT@iseries@i - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@iseries@i\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@iseries@i #1#2% {% - \expandafter\expandafter\expandafter - \XINT@iseries@ii - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@iseries@ii\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@iseries@ii #1#2#3% {% @@ -10706,7 +10816,7 @@ first place. }% \def\XINT@iseries@exit \fi #1#2#3#4#5#6#7#8% {% - \fi\xint@gobble@two #6% + \fi\xint@gobble@ii #6% }% % \end{macrocode} % \subsection{\csh{xintPowerSeries}} @@ -10715,23 +10825,19 @@ first place. % The Horner scheme for polynomial evaluation is used in 1.04, this % cures the denominator problem and drastically improves the efficiency % of the macro. +% Modified in 1.06 to give the indices first to a \numexpr rather than expanding +% twice. I just use \the\numexpr and maintain the previous code after that. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintPowerSeries {\romannumeral0\xintpowerseries }% \def\xintpowerseries #1#2% {% - \expandafter\expandafter\expandafter - \XINT@powseries@i - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@powseries@i\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@powseries@i #1#2% {% - \expandafter\expandafter\expandafter - \XINT@powseries@ii - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@powseries@ii\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@powseries@ii #1#2#3#4% {% @@ -10766,23 +10872,19 @@ first place. % \subsection{\csh{xintPowerSeriesX}} % \begin{verbatim} % Same as \xintPowerSeries except for the initial expansion of the x parameter. +% Modified in 1.06 to give the indices first to a \numexpr rather than expanding +% twice. I just use \the\numexpr and maintain the previous code after that. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintPowerSeriesX {\romannumeral0\xintpowerseriesx }% \def\xintpowerseriesx #1#2% {% - \expandafter\expandafter\expandafter - \XINT@powseriesx@i - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@powseriesx@i\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@powseriesx@i #1#2% {% - \expandafter\expandafter\expandafter - \XINT@powseriesx@ii - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@powseriesx@ii\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@powseriesx@ii #1#2#3#4% {% @@ -10790,8 +10892,9 @@ first place. \xint@afterfi { 0[0]}% \else \xint@afterfi - {\expandafter\expandafter\expandafter\XINT@powseriesx@pre - \expandafter\expandafter\expandafter {#4}{#1}{#2}{#3}}% + {\expandafter\XINT@powseriesx@pre\expandafter + {\romannumeral-`0#4}{#1}{#2}{#3}% + }% \fi }% \def\XINT@powseriesx@pre #1#2#3#4% @@ -10807,23 +10910,19 @@ first place. % computations possible with exponential type series, which would be completely % inaccessible to \xintSeries. % #1=a, #2=b, #3=F(a), #4=ratio function +% Modified in 1.06 to give the indices first to a \numexpr rather than expanding +% twice. I just use \the\numexpr and maintain the previous code after that. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintRationalSeries {\romannumeral0\xintratseries }% \def\xintratseries #1#2% {% - \expandafter\expandafter\expandafter - \XINT@ratseries@i - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@ratseries@i\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@ratseries@i #1#2% {% - \expandafter\expandafter\expandafter - \XINT@ratseries@ii - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@ratseries@ii\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@ratseries@ii #1#2#3#4% {% @@ -10861,23 +10960,19 @@ first place. % ratios F(n,x)/F(n-1,x). The argument x is first expanded and it is the value % resulting from this which is used then throughout. The initial term F(a,x) % must be defined as one-parameter macro which will be given x. +% Modified in 1.06 to give the indices first to a \numexpr rather than expanding +% twice. I just use \the\numexpr and maintain the previous code after that. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintRationalSeriesX {\romannumeral0\xintratseriesx }% \def\xintratseriesx #1#2% {% - \expandafter\expandafter\expandafter - \XINT@ratseriesx@i - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@ratseriesx@i\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@ratseriesx@i #1#2% {% - \expandafter\expandafter\expandafter - \XINT@ratseriesx@ii - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@ratseriesx@ii\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@ratseriesx@ii #1#2#3#4#5% {% @@ -10885,8 +10980,9 @@ first place. \xint@afterfi { 0[0]}% \else \xint@afterfi - {\expandafter\expandafter\expandafter\XINT@ratseriesx@pre - \expandafter\expandafter\expandafter {#5}{#2}{#1}{#4}{#3}}% + {\expandafter\XINT@ratseriesx@pre\expandafter + {\romannumeral-`0#5}{#2}{#1}{#4}{#3}% + }% \fi }% \def\XINT@ratseriesx@pre #1#2#3#4#5% @@ -10898,23 +10994,19 @@ first place. % \begin{verbatim} % I am not two happy with this piece of code. Will make it more economical % another day. +% Modified in 1.06 to give the indices first to a \numexpr rather than expanding +% twice. I just use \the\numexpr and maintain the previous code after that. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintFxPtPowerSeries {\romannumeral0\xintfxptpowerseries }% \def\xintfxptpowerseries #1#2% {% - \expandafter\expandafter\expandafter - \XINT@fppowseries@i - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@fppowseries@i\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@fppowseries@i #1#2% {% - \expandafter\expandafter\expandafter - \XINT@fppowseries@ii - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@fppowseries@ii\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@fppowseries@ii #1#2#3#4#5% {% @@ -10964,23 +11056,19 @@ first place. % \subsection{\csh{xintFxPtPowerSeriesX}} % \begin{verbatim} % a,b,coeff,x,D +% Modified in 1.06 to give the indices first to a \numexpr rather than expanding +% twice. I just use \the\numexpr and maintain the previous code after that. % \end{verbatim} % \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintFxPtPowerSeriesX {\romannumeral0\xintfxptpowerseriesx }% \def\xintfxptpowerseriesx #1#2% {% - \expandafter\expandafter\expandafter - \XINT@fppowseriesx@i - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@fppowseriesx@i\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@fppowseriesx@i #1#2% {% - \expandafter\expandafter\expandafter - \XINT@fppowseriesx@ii - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@fppowseriesx@ii\expandafter {\the\numexpr #2}{#1}% }% \def\XINT@fppowseriesx@ii #1#2#3#4#5% {% @@ -10988,10 +11076,8 @@ first place. \xint@afterfi { 0}% \else \xint@afterfi - {\expandafter\expandafter\expandafter - \XINT@fppowseriesx@pre - \expandafter\expandafter\expandafter - {#4}{#1}{#2}{#3}{#5}% + {\expandafter \XINT@fppowseriesx@pre \expandafter + {\romannumeral-`0#4}{#1}{#2}{#3}{#5}% }% \fi }% @@ -11124,6 +11210,7 @@ first place. {% \catcode93=\the\catcode93 % ] \catcode91=\the\catcode91 % [ + \catcode96=\the\catcode96 % ` \catcode47=\the\catcode47 % / \catcode41=\the\catcode41 % ) \catcode40=\the\catcode40 % ( @@ -11173,7 +11260,7 @@ first place. \fi \expandafter\x\csname ver@xintcfrac.sty\endcsname \ProvidesPackage{xintcfrac}% - [2013/05/02 v1.05a Expandable continued fractions with xint package (jfB)]% + [2013/05/07 v1.06 Expandable continued fractions with xint package (jfB)]% % \end{macrocode} % \subsection{\csh{xintCFrac}} % \begin{macrocode} @@ -11285,7 +11372,7 @@ first place. }% \def\XINT@gcfrac {% - \expandafter\expandafter\expandafter\XINT@gcfrac@enter + \expandafter\XINT@gcfrac@enter\romannumeral-`0% }% \def\XINT@gcfrac@enter {\XINT@gcfrac@loop {}}% \def\XINT@gcfrac@loop #1#2+#3/% @@ -11316,8 +11403,7 @@ first place. \def\xintGCtoGCx {\romannumeral0\xintgctogcx }% \def\xintgctogcx #1#2#3% {% - \expandafter\expandafter\expandafter\XINT@gctgcx@start - \expandafter\expandafter\expandafter {#3}{#1}{#2}% + \expandafter\XINT@gctgcx@start\expandafter {\romannumeral-`0#3}{#1}{#2}% }% \def\XINT@gctgcx@start #1#2#3{\XINT@gctgcx@loop@a {}{#2}{#3}#1+\W/}% \def\XINT@gctgcx@loop@a #1#2#3#4+#5/% @@ -11509,7 +11595,7 @@ first place. \def\xintCstoF {\romannumeral0\xintcstof }% \def\xintcstof #1% {% - \expandafter\expandafter\expandafter\XINT@cstf@prep #1,\W,% + \expandafter\XINT@cstf@prep \romannumeral-`0#1,\W,% }% \def\XINT@cstf@prep {% @@ -11547,7 +11633,7 @@ first place. \def\xintiCstoF {\romannumeral0\xinticstof }% \def\xinticstof #1% {% - \expandafter\expandafter\expandafter\XINT@icstf@prep #1,\W,% + \expandafter\XINT@icstf@prep \romannumeral-`0#1,\W,% }% \def\XINT@icstf@prep {% @@ -11556,8 +11642,8 @@ first place. \def\XINT@icstf@loop@a #1#2#3#4#5,% {% \xint@w #5\XINT@icstf@end\W - \expandafter\expandafter\expandafter - \XINT@icstf@loop@b #5.{#1}{#2}{#3}{#4}% + \expandafter + \XINT@icstf@loop@b \romannumeral-`0#5.{#1}{#2}{#3}{#4}% }% \def\XINT@icstf@loop@b #1.#2#3#4#5% {% @@ -11577,7 +11663,7 @@ first place. \def\xintGCtoF {\romannumeral0\xintgctof }% \def\xintgctof #1% {% - \expandafter\expandafter\expandafter\XINT@gctf@prep #1+\W/% + \expandafter\XINT@gctf@prep \romannumeral-`0#1+\W/% }% \def\XINT@gctf@prep {% @@ -11640,7 +11726,7 @@ first place. \def\xintiGCtoF {\romannumeral0\xintigctof }% \def\xintigctof #1% {% - \expandafter\expandafter\expandafter\XINT@igctf@prep #1+\W/% + \expandafter\XINT@igctf@prep \romannumeral-`0#1+\W/% }% \def\XINT@igctf@prep {% @@ -11648,8 +11734,8 @@ first place. }% \def\XINT@igctf@loop@a #1#2#3#4#5+% {% - \expandafter\expandafter\expandafter\XINT@igctf@loop@b - #5.{#1}{#2}{#3}{#4}% + \expandafter\XINT@igctf@loop@b + \romannumeral-`0#5.{#1}{#2}{#3}{#4}% }% \def\XINT@igctf@loop@b #1.#2#3#4#5% {% @@ -11665,8 +11751,8 @@ first place. \def\XINT@igctf@loop@f #1#2#3#4/% {% \xint@w #4\XINT@igctf@end\W - \expandafter\expandafter\expandafter\XINT@igctf@loop@g - #4.{#2}{#3}#1% + \expandafter\XINT@igctf@loop@g + \romannumeral-`0#4.{#2}{#3}#1% }% \def\XINT@igctf@loop@g #1.#2#3% {% @@ -11689,7 +11775,7 @@ first place. \def\xintCstoCv {\romannumeral0\xintcstocv }% \def\xintcstocv #1% {% - \expandafter\expandafter\expandafter\XINT@cstcv@prep #1,\W,% + \expandafter\XINT@cstcv@prep \romannumeral-`0#1,\W,% }% \def\XINT@cstcv@prep {% @@ -11734,7 +11820,7 @@ first place. \def\xintiCstoCv {\romannumeral0\xinticstocv }% \def\xinticstocv #1% {% - \expandafter\expandafter\expandafter\XINT@icstcv@prep #1,\W,% + \expandafter\XINT@icstcv@prep \romannumeral-`0#1,\W,% }% \def\XINT@icstcv@prep {% @@ -11743,8 +11829,8 @@ first place. \def\XINT@icstcv@loop@a #1#2#3#4#5#6,% {% \xint@w #6\XINT@icstcv@end\W - \expandafter\expandafter\expandafter - \XINT@icstcv@loop@b #6.{#2}{#3}{#4}{#5}{#1}% + \expandafter + \XINT@icstcv@loop@b \romannumeral-`0#6.{#2}{#3}{#4}{#5}{#1}% }% \def\XINT@icstcv@loop@b #1.#2#3#4#5% {% @@ -11770,7 +11856,7 @@ first place. \def\xintGCtoCv {\romannumeral0\xintgctocv }% \def\xintgctocv #1% {% - \expandafter\expandafter\expandafter\XINT@gctcv@prep #1+\W/% + \expandafter\XINT@gctcv@prep \romannumeral-`0#1+\W/% }% \def\XINT@gctcv@prep {% @@ -11843,7 +11929,7 @@ first place. \def\xintiGCtoCv {\romannumeral0\xintigctocv }% \def\xintigctocv #1% {% - \expandafter\expandafter\expandafter\XINT@igctcv@prep #1+\W/% + \expandafter\XINT@igctcv@prep \romannumeral-`0#1+\W/% }% \def\XINT@igctcv@prep {% @@ -11851,8 +11937,8 @@ first place. }% \def\XINT@igctcv@loop@a #1#2#3#4#5#6+% {% - \expandafter\expandafter\expandafter\XINT@igctcv@loop@b - #6.{#2}{#3}{#4}{#5}{#1}% + \expandafter\XINT@igctcv@loop@b + \romannumeral-`0#6.{#2}{#3}{#4}{#5}{#1}% }% \def\XINT@igctcv@loop@b #1.#2#3#4#5% {% @@ -11868,8 +11954,8 @@ first place. \def\XINT@igctcv@loop@f #1#2#3#4/% {% \xint@w #4\XINT@igctcv@end@a\W - \expandafter\expandafter\expandafter\XINT@igctcv@loop@g - #4.#1#2{#3}% + \expandafter\XINT@igctcv@loop@g + \romannumeral-`0#4.#1#2{#3}% }% \def\XINT@igctcv@loop@g #1.#2#3#4#5% {% @@ -11897,28 +11983,27 @@ first place. \def\XINT@igctcv@end@b #1#2{ #2{#1[0]}}% % \end{macrocode} % \subsection{\csh{xintCntoF}} +% \begin{verbatim} +% Modified in 1.06 to give the N first to a \numexpr rather than expanding +% twice. I just use \the\numexpr and maintain the previous code after that. +% \end{verbatim} +% \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintCntoF {\romannumeral0\xintcntof }% \def\xintcntof #1% {% - \expandafter\expandafter\expandafter - \XINT@cntf - \expandafter\expandafter\expandafter - {#1}% + \expandafter\XINT@cntf\expandafter {\the\numexpr #1}% }% \def\XINT@cntf #1#2% {% \ifnum #1>0 \xint@afterfi {\expandafter\XINT@cntf@loop\expandafter - {\the\numexpr - #1-1\expandafter\expandafter\expandafter}% - \expandafter\expandafter\expandafter - {#2{#1}}{#2}}% + {\the\numexpr #1-1\expandafter}\expandafter + {\romannumeral-`0#2{#1}}{#2}}% \else \xint@afterfi {\ifnum #1=0 - \xint@afterfi {\expandafter\expandafter\expandafter - \space #2{0}}% + \xint@afterfi {\expandafter\space \romannumeral-`0#2{0}}% \else \xint@afterfi { 0[0]}% \fi}% \fi @@ -11935,32 +12020,31 @@ first place. \expandafter\XINT@cntf@loop\expandafter #1\expandafter #2#3% {% - \fi\xint@gobble@two #2% + \fi\xint@gobble@ii #2% }% % \end{macrocode} % \subsection{\csh{xintGCntoF}} +% \begin{verbatim} +% Modified in 1.06 to give the N first to a \numexpr rather than expanding +% twice. I just use \the\numexpr and maintain the previous code after that. +% \end{verbatim} +% \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintGCntoF {\romannumeral0\xintgcntof }% \def\xintgcntof #1% {% - \expandafter\expandafter\expandafter - \XINT@gcntf - \expandafter\expandafter\expandafter - {#1}% + \expandafter\XINT@gcntf\expandafter {\the\numexpr #1}% }% \def\XINT@gcntf #1#2#3% {% \ifnum #1>0 \xint@afterfi {\expandafter\XINT@gcntf@loop\expandafter - {\the\numexpr - #1-1\expandafter\expandafter\expandafter}% - \expandafter\expandafter\expandafter - {#2{#1}}{#2}{#3}}% + {\the\numexpr #1-1\expandafter}\expandafter + {\romannumeral-`0#2{#1}}{#2}{#3}}% \else \xint@afterfi {\ifnum #1=0 - \xint@afterfi {\expandafter\expandafter\expandafter - \space #2{0}}% + \xint@afterfi {\expandafter\space\romannumeral-`0#2{0}}% \else \xint@afterfi { 0[0]}% \fi}% \fi @@ -11977,18 +12061,20 @@ first place. \expandafter\XINT@gcntf@loop\expandafter #1\expandafter #2#3#4% {% - \fi\xint@gobble@two #2% + \fi\xint@gobble@ii #2% }% % \end{macrocode} % \subsection{\csh{xintCntoCs}} +% \begin{verbatim} +% Modified in 1.06 to give the N first to a \numexpr rather than expanding +% twice. I just use \the\numexpr and maintain the previous code after that. +% \end{verbatim} +% \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintCntoCs {\romannumeral0\xintcntocs }% \def\xintcntocs #1% {% - \expandafter\expandafter\expandafter - \XINT@cntcs - \expandafter\expandafter\expandafter - {#1}% + \expandafter\XINT@cntcs\expandafter {\the\numexpr #1}% }% \def\XINT@cntcs #1#2% {% @@ -11996,38 +12082,36 @@ first place. \xint@afterfi { 0[0]}% \else \xint@afterfi {\expandafter\XINT@cntcs@loop\expandafter - {\the\numexpr - #1-1\expandafter\expandafter\expandafter}% - \expandafter\expandafter\expandafter - {\expandafter\expandafter\expandafter - {#2{#1}}}{#2}}% + {\the\numexpr #1-1\expandafter}\expandafter + {\expandafter{\romannumeral-`0#2{#1}}}{#2}}% \fi }% \def\XINT@cntcs@loop #1#2#3% {% \ifnum #1>-1 \else \XINT@cntcs@exit \fi \expandafter\XINT@cntcs@loop\expandafter - {\the\numexpr #1-1\expandafter\expandafter\expandafter }% - \expandafter\expandafter\expandafter - {\expandafter\expandafter\expandafter{#3{#1}},#2}{#3}% + {\the\numexpr #1-1\expandafter }\expandafter + {\expandafter{\romannumeral-`0#3{#1}},#2}{#3}% }% \def\XINT@cntcs@exit \fi \expandafter\XINT@cntcs@loop\expandafter - #1\expandafter\expandafter\expandafter #2#3% + #1\expandafter #2#3% {% \fi\XINT@cntcs@@exit #2% }% \def\XINT@cntcs@@exit #1,{ }% % \end{macrocode} % \subsection{\csh{xintCntoGC}} +% \begin{verbatim} +% Modified in 1.06 to give the N first to a \numexpr rather than expanding +% twice. I just use \the\numexpr and maintain the previous code after that. +% \end{verbatim} +% \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintCntoGC {\romannumeral0\xintcntogc }% \def\xintcntogc #1% {% - \expandafter\expandafter\expandafter - \XINT@cntgc - \expandafter\expandafter\expandafter - {#1}% + \expandafter\XINT@cntgc\expandafter {\the\numexpr #1}% }% \def\XINT@cntgc #1#2% {% @@ -12035,38 +12119,36 @@ first place. \xint@afterfi { 0[0]}% \else \xint@afterfi {\expandafter\XINT@cntgc@loop\expandafter - {\the\numexpr - #1-1\expandafter\expandafter\expandafter}% - \expandafter\expandafter\expandafter - {\expandafter\expandafter\expandafter - {#2{#1}}}{#2}}% + {\the\numexpr #1-1\expandafter}\expandafter + {\expandafter{\romannumeral-`0#2{#1}}}{#2}}% \fi }% \def\XINT@cntgc@loop #1#2#3% {% \ifnum #1>-1 \else \XINT@cntgc@exit \fi \expandafter\XINT@cntgc@loop\expandafter - {\the\numexpr #1-1\expandafter\expandafter\expandafter }% - \expandafter\expandafter\expandafter - {\expandafter\expandafter\expandafter{#3{#1}}+1/#2}{#3}% + {\the\numexpr #1-1\expandafter }\expandafter + {\expandafter{\romannumeral-`0#3{#1}}+1/#2}{#3}% }% \def\XINT@cntgc@exit \fi \expandafter\XINT@cntgc@loop\expandafter - #1\expandafter\expandafter\expandafter #2#3% + #1\expandafter #2#3% {% \fi\XINT@cntgc@@exit #2% }% \def\XINT@cntgc@@exit #1+1/{ }% % \end{macrocode} % \subsection{\csh{xintGCntoGC}} +% \begin{verbatim} +% Modified in 1.06 to give the N first to a \numexpr rather than expanding +% twice. I just use \the\numexpr and maintain the previous code after that. +% \end{verbatim} +% \vspace*{-1.5\baselineskip} % \begin{macrocode} \def\xintGCntoGC {\romannumeral0\xintgcntogc }% \def\xintgcntogc #1% {% - \expandafter\expandafter\expandafter - \XINT@gcntgc - \expandafter\expandafter\expandafter - {#1}% + \expandafter\XINT@gcntgc\expandafter {\the\numexpr #1}% }% \def\XINT@gcntgc #1#2#3% {% @@ -12074,33 +12156,24 @@ first place. \xint@afterfi { {0[0]}}% \else \xint@afterfi {\expandafter\XINT@gcntgc@loop\expandafter - {\the\numexpr - #1-1\expandafter\expandafter\expandafter}% - \expandafter\expandafter\expandafter - {\expandafter\expandafter\expandafter - {#2{#1}}}{#2}{#3}}% + {\the\numexpr #1-1\expandafter}\expandafter + {\expandafter{\romannumeral-`0#2{#1}}}{#2}{#3}}% \fi }% \def\XINT@gcntgc@loop #1#2#3#4% {% \ifnum #1>-1 \else \XINT@gcntgc@exit \fi - \expandafter\expandafter\expandafter - \XINT@gcntgc@loop@b - \expandafter\expandafter\expandafter - {\expandafter\expandafter\expandafter - {#4{#1}}/#2}{#3{#1}}{#1}{#3}{#4}% + \expandafter\XINT@gcntgc@loop@b\expandafter + {\expandafter{\romannumeral-`0#4{#1}}/#2}{#3{#1}}{#1}{#3}{#4}% }% \def\XINT@gcntgc@loop@b #1#2#3% {% \expandafter\XINT@gcntgc@loop\expandafter - {\the\numexpr #3-1\expandafter\expandafter\expandafter}% - \expandafter\expandafter\expandafter - {\expandafter\expandafter\expandafter{#2}+#1}% + {\the\numexpr #3-1\expandafter}\expandafter + {\expandafter{\romannumeral-`0#2}+#1}% }% \def\XINT@gcntgc@exit \fi - \expandafter\expandafter\expandafter - \XINT@gcntgc@loop@b - \expandafter\expandafter\expandafter #1#2#3#4#5% + \expandafter\XINT@gcntgc@loop@b\expandafter #1#2#3#4#5% {% \fi\XINT@gcntgc@@exit #1% }% @@ -12111,7 +12184,7 @@ first place. \def\xintCstoGC {\romannumeral0\xintcstogc }% \def\xintcstogc #1% {% - \expandafter\expandafter\expandafter\XINT@cstc@prep #1,\W,% + \expandafter\XINT@cstc@prep \romannumeral-`0#1,\W,% }% \def\XINT@cstc@prep #1,{\XINT@cstc@loop@a {{#1}}}% \def\XINT@cstc@loop@a #1#2,% @@ -12126,32 +12199,26 @@ first place. \def\xintGCtoGC {\romannumeral0\xintgctogc }% \def\xintgctogc #1% {% - \expandafter\expandafter\expandafter\XINT@gctgc@start #1+\W/% + \expandafter\XINT@gctgc@start \romannumeral-`0#1+\W/% }% \def\XINT@gctgc@start {\XINT@gctgc@loop@a {}}% \def\XINT@gctgc@loop@a #1#2+#3/% {% - \xint@w #3\XINT@gctgc@end\W - \expandafter\expandafter\expandafter - \XINT@gctgc@loop@b - \expandafter\expandafter\expandafter - {#2}{#3}{#1}% + \xint@w #3\XINT@gctgc@end\W\expandafter\XINT@gctgc@loop@b\expandafter + {\romannumeral-`0#2}{#3}{#1}% }% \def\XINT@gctgc@loop@b #1#2% {% - \expandafter\expandafter\expandafter - \XINT@gctgc@loop@c - \expandafter\expandafter\expandafter - {#2}{#1}% + \expandafter\XINT@gctgc@loop@c\expandafter + {\romannumeral-`0#2}{#1}% }% \def\XINT@gctgc@loop@c #1#2#3% {% \XINT@gctgc@loop@a {#3{#2}+{#1}/}% }% -\def\XINT@gctgc@end\W - \expandafter\expandafter\expandafter\XINT@gctgc@loop@b +\def\XINT@gctgc@end\W\expandafter\XINT@gctgc@loop@b {% - \expandafter\expandafter\expandafter\XINT@gctgc@@end + \expandafter\XINT@gctgc@@end }% \def\XINT@gctgc@@end #1#2#3{ #3{#1}}% \XINT@cfrac@restorecatcodes@endinput% @@ -12176,7 +12243,7 @@ first place. Grave accent \` Left brace \{ Vertical bar \| Right brace \} Tilde \~} -\CheckSum{11712} +\CheckSum{11366} \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 a16c71d70ab..ff57cc3cab4 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 1.05a of May 2nd, 2013) +%% The xint bundle (version 1.06 of May 7th, 2013) %% Copyright (C) 2013 by Jean-Francois Burnol %%---------------------------------------------------------------- %% |