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Diffstat (limited to 'Master/texmf-dist')
| -rw-r--r-- | Master/texmf-dist/doc/generic/xint/README | 4 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/generic/xint/xint.pdf | bin | 1000698 -> 1025861 bytes | |||
| -rw-r--r-- | Master/texmf-dist/source/generic/xint/xint.dtx | 1815 | ||||
| -rw-r--r-- | Master/texmf-dist/source/generic/xint/xint.ins | 2 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/generic/xint/xint.sty | 14 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/generic/xint/xintbinhex.sty | 4 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/generic/xint/xintcfrac.sty | 306 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/generic/xint/xintexpr.sty | 4 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/generic/xint/xintfrac.sty | 74 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/generic/xint/xintgcd.sty | 4 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/generic/xint/xintseries.sty | 16 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/generic/xint/xinttools.sty | 256 |
12 files changed, 1710 insertions, 789 deletions
diff --git a/Master/texmf-dist/doc/generic/xint/README b/Master/texmf-dist/doc/generic/xint/README index f34411fd82e..9c85db8c6ea 100644 --- a/Master/texmf-dist/doc/generic/xint/README +++ b/Master/texmf-dist/doc/generic/xint/README @@ -1,5 +1,5 @@ The xint bundle -Release 1.09kb (2014/02/13). Documentation date: 2014/02/13 +Release 1.09m (2014/02/26). Documentation date: 2014/02/26 Copyright (C) 2013-2014 by Jean-Francois Burnol License: LaTeX Project Public License 1.3c or later. @@ -152,7 +152,7 @@ License LaTeX version 2005/12/01 or later. This work consists of the source file xint.dtx and of its derived files: -xinttools.sty xint.sty, xintfrac.sty, xintexpr.sty, xintbinhex.sty, +xinttools.sty, xint.sty, xintfrac.sty, xintexpr.sty, xintbinhex.sty, xintgcd.sty, xintseries.sty, xintcfrac.sty, as well as xint.ins, xint.tex and the documentation xint.pdf (or xint.dvi). diff --git a/Master/texmf-dist/doc/generic/xint/xint.pdf b/Master/texmf-dist/doc/generic/xint/xint.pdf Binary files differindex 70e5dccdff3..7e3819ad7e1 100644 --- a/Master/texmf-dist/doc/generic/xint/xint.pdf +++ b/Master/texmf-dist/doc/generic/xint/xint.pdf diff --git a/Master/texmf-dist/source/generic/xint/xint.dtx b/Master/texmf-dist/source/generic/xint/xint.dtx index 2ff5933c422..6a46205c5c8 100644 --- a/Master/texmf-dist/source/generic/xint/xint.dtx +++ b/Master/texmf-dist/source/generic/xint/xint.dtx @@ -1,16 +1,16 @@ % -*- coding: iso-latin-1; time-stamp-format: "%02d-%02m-%:y %02H:%02M:%02S %Z" -*- -% File: xint.dtx, package: 1.09kb (2014/02/13), documentation: 2014/02/13 +% File: xint.dtx, package: 1.09m (2014/02/26), documentation: 2014/02/26 % License: LaTeX Project Public License 1.3c or later. % Copyright (C) 2013-2014 by Jean-Francois Burnol <jfbu at free dot fr> %<*dtx> -\def\lasttimestamp{Time-stamp: <13-02-2014 22:56:36 CET>} +\def\lasttimestamp{Time-stamp: <27-02-2014 09:57:47 CET>} %</dtx> %<*drv> -\def\xintdate {2014/02/13} -\def\xintversion {1.09kb} +\def\xintdate {2014/02/26} +\def\xintversion {1.09m} %</drv> %%---------------------------------------------------------------- -%% The xint bundle (version 1.09kb of February 13, 2014) +%% The xint bundle (version 1.09m of February 26, 2014) %<xinttools>%% xinttools: Expandable and non-expandable utilities %<xint>%% xint: Expandable operations on long numbers %<xintfrac>%% xintfrac: Expandable operations on fractions @@ -546,6 +546,7 @@ pdfpagemode=UseOutlines} \smash{\hbox to 0pt {\hss\color[named]{PineGreen}% \itshape \xintListWithSep{\,}{#1}\quad }}% \vskip\dp\strutbox }\strut{}} +%------------------------------------------------------------------------------- \def\Numf {{\vbox{\halign{\hfil##\hfil\cr \footnotesize \upshape Num\cr \noalign{\hrule height 0pt \vskip1pt\relax} @@ -558,6 +559,16 @@ pdfpagemode=UseOutlines} \upshape num\cr \noalign{\hrule height 0pt \vskip1pt\relax} \itshape x\cr}}}} +%------------------------------------------------------------------------------- +% 24 février 2014. J'ai besoin de me débarasser du \to +\def\NewWith #1{% + \vadjust{\vskip-\dp\strutbox + \smash{\hbox to 0pt {\hss\color[named]{PineGreen}% + \normalfont\small + \hsize 1.5cm\rightskip.5cm minus.5cm + \vtop{\noindent New with #1}\ }}% + \vskip\dp\strutbox }\strut{}} + \makeatother %---- \centeredline: OUR OWN LITTLE MACRO FOR CENTERING LINES @@ -1262,7 +1273,7 @@ but limits the exponent to the \TeX{} bound) allow only integral exponents. -\subsection{Printing big numbers on the page} +\subsection{Printing big numbers on the page}\label{ssec:printnumber} When producing very long numbers there is the question of printing them on the page, without going beyond the page limits. In this document, I have most @@ -1317,7 +1328,20 @@ naturally! (but \digitstt{F(\xintiiPow2{31}}) would be rather big anyhow...). \footnotesize -\noindent Releases |1.09kb| (|[2014/02/13]|) and |1.09ka| (|[2014/02/05]|): +\noindent Releases |1.09m| (|[2014/02/26]|): +\begin{itemize} +\item new macros in \xinttoolsname: \csbxint{Keep} keeps the first |N| + or last |N| elements of a list (sequence of braced items); + \csbxint{Trim} cuts out either the first |N| or the last |N| elements + from a list. +\item new macros in \xintcfracname: \csbxint{FGtoC} finds the + initial partial quotients common to two numbers or fractions |f| and + |g|; \csbxint{GGCFrac} is a clone of \csbxint{GCFrac} which however + does not assume that the coefficients of the generalized continued + fraction are numeric quantities. Some other minor changes. +\end{itemize} + +\noindent Releases |1.09ka| (|[2014/02/05]|) and |1.09kb| (|[2014/02/13]|): \begin{itemize} \item bug fix (\xintexprname): an aloof modification done by |1.09i| to \csbxint{NewExpr} had resulted in a spurious trailing space present in the @@ -1653,7 +1677,7 @@ The title page fun with Fibonacci numbers is continued in The computations of \hyperref[ssec:Machin]{ $\pi$ and $\log 2$} (\autoref{ssec:Machin}) using \xintname and the computation of the -\hyperlink{e-convergents}{convergents of $e$} with the further help of +\hyperref[ssec:e-convergents]{convergents of $e$} with the further help of the \xintcfracname package are among further examples. There is also an example of an \hyperref[xintXTrunc]{interactive session}, where results are output to the log or to a file. @@ -3817,10 +3841,10 @@ Initial release |1.0| was on |2013/03/28|. \def\x{\string{x\string}} These utilities used to be provided within the \xintname package; since |1.09g| -they have been moved to an independently usable package \xinttoolsname, which -has none of the \xintname facilities regarding big numbers. Whenever relevant -release |1.09h| has made the macros |\long| so they accept |\par| tokens on -input. +(|2013/11/22|) they have been moved to an independently usable package +\xinttoolsname, which has none of the \xintname facilities regarding big +numbers. Whenever relevant release |1.09h| has made the macros |\long| so they +accept |\par| tokens on input. First the completely expandable utilities up to \csbxint{iloop}, then the non expandable utilities. @@ -3829,7 +3853,8 @@ This section contains various concrete examples and ends with a \hyperref[ssec:quicksort]{completely expandable implementation of the Quick Sort algorithm} together with a graphical illustration of its action. -\clearpage + +\clearpage % attention à ce clearpage \localtableofcontents @@ -3856,12 +3881,13 @@ reverted. Unprotected spaces (of any character code) are gobbled. % \csa{xintRevWithBraces}\marg{list}\etype{f} first does the \fexpan sion of its argument 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 \meta{list} of such braced material; -with such a list as argument the \fexpan sion 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}}|} +encounters, maintaining existing braces and adding a brace pair around each +naked token encountered. Space tokens (in-between top level braces or naked +tokens) are gobbled. This macro is mainly thought out for use on a \meta{list} +of such braced material; with such a list as argument the \fexpan sion 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 @@ -3870,8 +3896,7 @@ Alternatively: \centeredline{|\expandafter\def\expandafter\w\expandafter|}% \centeredline{|{\romannumeral0\xintrevwithbraces{{\A}{\B}{\C}{\D}{\E}}}|} \centeredline{|\meaning\w:|\ttfamily{\meaning\w}} The macro \csa{xintReverseWithBracesNoExpand}\etype{n} does the same job without the -initial -expansion of its argument. +initial expansion of its argument. \subsection{\csbh{xintLength}}\label{xintLength} @@ -4116,7 +4141,9 @@ without removal of spaces around the commas, there is \csa{xintNthElt\x}\marg{list}\etype{\numx f} gets (expandably) the |x|th braced item of the \meta{list}. An unbraced item token will be returned as is. The list -itself may be a macro which is first \fexpan ded. \centeredline{|\xintNthElt +itself may be a macro which is first \fexpan ded. +% +\centeredline{|\xintNthElt {3}{{agh}\u{zzz}\v{Z}}| is \texttt{\xintNthElt {3}{{agh}\u{zzz}\v{Z}}}} \centeredline{|\xintNthElt {3}{{agh}\u{{zzz}}\v{Z}}| is \texttt{\expandafter\expandafter\expandafter @@ -4139,7 +4166,7 @@ the macro returns the \emph{length} of the expanded list: this is not equivalent to \csbxint{Length} which does no pre-expansion. And it is different from \csbxint{Len} which is to be used only on integers or fractions. -If |x<0|, the macro returns the \texttt{|x|}th element from the end of the list. +If |x<0|, the macro returns the \verb+|x|+th element from the end of the list. \centeredline{|\xintNthElt {-5}{{{agh}}\u{zzz}\v{Z}}| is \texttt{\expandafter\expandafter\expandafter \detokenize @@ -4154,6 +4181,47 @@ expanding the list argument: |\xintNthEltNoExpand {-4}{\u\v\w T\x\y\z}| is In cases where |x| is larger (in absolute value) than the length of the list then |\xintNthElt| returns nothing. +\subsection{\csbh{xintKeep}}\label{xintKeep} + +\csa{xintKeep\x}\marg{list}\etype{\numx f} expands the list argument and returns +a new list containing only the first |x| elements.\NewWith {1.09m} If |x<0| the +macro returns the last \verb+|x|+ elements (in the same order as in the initial +list). If \verb+|x|+ equals or exceeds the length of the list, the list (as +arising from expansion of the second argument) is returned. For |x=0| the empty +list is returned. + +Naked (non space) tokens from the original count each as one item and they end +up braced in the output (if present there): if one later wants to remove all +brace pairs (either added to a naked token, or initially present), one may use +\csbxint {ListWithSep} with an empty separator. + +\csa{xintKeepNoExpand} does the same without first \fexpan ding its list +argument. +\centeredline {|\oodef\test {\xintKeep {17}{\xintKeep {-69}{\xintSeq + {1}{100}}}}\meaning\test|} +\centeredline {\oodef\test {\xintKeep {17}{\xintKeep {-69}{\xintSeq + {1}{100}}}}\meaning\test} + + +\subsection{\csbh{xintTrim}}\label{xintTrim} + +\csa{xintTrim\x}\marg{list}\etype{\numx f} expands the list argument and +gobbles its first |x| elements. If |x<0| the macro gobbles the last +\verb+|x|+ elements.\NewWith {1.09m} If \verb+|x|+ equals or exceeds +the length of the list, the empty list is returned. For |x=0| the full +list is returned. + +Naked (non space) tokens from the original count each as one item and they end +up braced in the output (if present there). + +\csa{xintTrimNoExpand} does the same without first \fexpan ding its list +argument. +\centeredline {|\oodef\test {\xintTrim {17}{\xintTrim {-69}{\xintSeq + {1}{100}}}}\meaning\test|} +\centeredline {\oodef\test {\xintTrim {17}{\xintTrim {-69}{\xintSeq + {1}{100}}}}\meaning\test} + + \subsection{\csbh{xintListWithSep}}\label{xintListWithSep} %{\small New with release |1.04|.\par} @@ -4242,11 +4310,15 @@ the first initial expansion which gave the \meta{list} of braced tokens to which \subsection{\csbh{xintSeq}}\label{xintSeq} %{\small New with release |1.09c|.\par} -\csa{xintSeq}|[d]{x}{y}|\etype{{{\upshape[\numx]}}\numx\numx} generates expandably |{x}{x+d}...| up to and -possibly including |{y}| if |d>0| or down to and including |{y}| if |d<0|. -Naturally |{y}| is omitted if |y-x| is not a multiple of |d|. If |d=0| the macro -returns |{x}|. If |y-x| and |d| have opposite signs, the macro returns nothing. -If the optional argument |d| is omitted it is taken to be the sign of |y-x|. +\csa{xintSeq}|[d]{x}{y}|\etype{{{\upshape[\numx]}}\numx\numx} generates +expandably |{x}{x+d}...| up to and possibly including |{y}| if |d>0| or +down to and including |{y}| if |d<0|. Naturally |{y}| is omitted if +|y-x| is not a multiple of |d|. If |d=0| the macro returns |{x}|. If +|y-x| and |d| have opposite signs, the macro returns nothing. If the +optional argument |d| is omitted it is taken to be the sign of |y-x| +(beware that |\xintSeq {1}{0}| is thus not empty but |{1}{0}|, use +|\xintSeq [1]{1}{N}| if you want an empty sequence for |N| zero or +negative). The current implementation is only for (short) integers; possibly, a future @@ -6537,6 +6609,8 @@ stop automatically when the sort is finished.\footnote{\url{http://tex.stackexch \section{Commands of the \xintname package} \label{sec:xint} +Version |1.0| was released |2013/03/28|. This is \texttt{\xintversion} of +\texttt{\xintdate}. In the description of the macros \texttt{\n} and \texttt{\m} stand for (long) numbers within braces or for a control sequence possibly within braces and @@ -7371,9 +7445,9 @@ of \csa{xintDecSplit}. \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. +This package was first included in release |1.03| (|2013/04/14|) 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. |f|\ntype{\Ff} stands for an integer or a fraction (see \autoref{sec:inputs} @@ -8158,9 +8232,9 @@ dealing exclusively with (big) integers. These variants are already available in \section{Expandable expressions with the \xintexprname package}% \label{sec:expr} -The \xintexprname package was first released with version |1.07| of the -\xintname bundle. It loads automatically \xintfracname, hence -also \xintname and \xinttoolsname. +The \xintexprname package was first released with version |1.07| (|2013/05/25|) +of the \xintname bundle. It loads automatically \xintfracname, hence also +\xintname and \xinttoolsname. % Release |1.09a| has extended the scope of |\xintexpr|-essions: infix % comparison operators (|<|, |>|, |=|), logical operators (|&|, \verb+|+), @@ -8940,9 +9014,9 @@ principles are necessarily different due to the aim of achieving expandability. \section{Commands of the \xintbinhexname package} \label{sec:binhex} -This package was first included in the |1.08| release of \xintname. It -provides expandable conversions of arbitrarily long numbers -to and from binary and hexadecimal. +This package was first included in the |1.08| (|2013/06/07|) release of +\xintname. It provides expandable conversions of arbitrarily long numbers to and +from binary and hexadecimal. The argument is first \fexpan ded. It then may start with an optional minus sign (unique, of category code other), followed with optional leading zeroes @@ -9019,7 +9093,8 @@ least one hundred hexadecimal digits. \label{sec:gcd} -This package was included in the original release |1.0| of the \xintname bundle. +This package was included in the original release |1.0| (|2013/03/28|) of the +\xintname bundle. Since release |1.09a| the macros filter their inputs through the \csbxint{Num} macro, so one can use count registers, or fractions as long as they reduce to @@ -9164,13 +9239,14 @@ macro and modify it to what is needed. \section{Commands of the \xintseriesname package} \label{sec:series} +This package was first released with version |1.03| (|2013/04/14|) of the +\xintname bundle. + Some arguments to the package commands are macros which are expanded only later, when given their parameters. The arguments serving as indices are systematically given to a |\numexpr| expressions (new with |1.06|!) , hence \fexpan ded, they may be count registers, etc... -This package was first released with version |1.03| of the \xintname bundle. - We use \Ff{} for the expansion type of various macro arguments, but if only \xintname and not \xintfracname is loaded this should be more appropriately \Numf. The macro \csbxint{iSeries} is special and expects summing big integers @@ -10287,7 +10363,7 @@ You want more digits and have some time? compile this copy of the \bye | This will log the first 1000 digits of $\pi$ after the decimal point. On my -laptop (a 2012 model) this took about @16@ seconds last time I tried. +laptop (a 2012 model) this took about @16@ seconds last time I tried.% \footnote{With \texttt{1.09i} and earlier \xintname releases, this used to be \digitstt{42} seconds; the \texttt{1.09j} division is much faster with small denominators as occurs here with \digitstt{\char92xa=1/25}, and I believe this @@ -10329,94 +10405,141 @@ always do it on a value computed with |D+1| truncation. \section{Commands of the \xintcfracname package} \label{sec:cfrac} -This package was first included in release |1.04| of the \xintname bundle. +This package was first included in release |1.04| (|2013/04/25|) of the +\xintname bundle. It was kept almost unchanged until |1.09m| of |2014/02/26| +which brings some new macros: \csbxint{FtoC}, \csbxint{CtoF}, \csbxint{CtoCv}, +dealing with sequences of braced partial quotients rather than comma separated +ones, \csbxint{FGtoC} which is to produce ``guaranteed'' coefficients of some +real number known approximately, and \csbxint{GGCFrac} for displaying arbitrary +material as a continued fraction; also, some changes to existing macros: +\csbxint{FtoCs} and \csbxint{CntoCs} insert spaces after the commas, +\csbxint{CstoF} and \csbxint{CstoCv} authorize spaces in the input also before +the commas. + +This section contains: +\begin{enumerate} +\item an \hyperref[ssec:cfracoverview]{overview} of the package functionalities, +\item a description of each one of the package macros, +\item further illustration of their use via the study of the + \hyperref[ssec:e-convergents]{convergents of $e$}. +\end{enumerate} \localtableofcontents +\subsection{Package overview}\label{ssec:cfracoverview} -\subsection{Package overview} +The package computes partial quotients and convergents of a fraction, or +conversely start from coefficients and obtain the corresponding fraction; three +macros \csbxint {CFrac}, \csbxint {GCFrac} and \csbxint {GGCFrac} are +for typesetting (the first two assume that the coefficients are numeric +quantities acceptable by the \xintfracname \csbxint{Frac} macro, the +last one will display arbitrary material), the others +can be nested (if applicable) or see their outputs further processed by other +macros from the \xintname bundle, particularly the macros of \xinttoolsname +dealing with sequences of braced items or comma separated lists. A \emph{simple} continued fraction has coefficients -|[c0,c1,...,cN]| (usually called partial quotients, but I really +|[c0,c1,...,cN]| (usually called partial quotients, but I dislike this entrenched terminology), where |c0| is a positive or -negative integer and the others are positive integers. As we will -see it is possible with \xintcfracname to specify the coefficient -function |c:n->cn|. Note that the index then starts at zero as -indicated. With the |amsmath| macro |\cfrac| one can display such a -continued fraction as +negative integer and the others are positive integers. + + +Typesetting is usually done via the |amsmath| macro |\cfrac|: +\centeredline{|\[ c_0 + \cfrac{1}{c_1+\cfrac1{c_2+\cfrac1{c_3+\cfrac1{\ddots}}}}\]|} \[ c_0 + \cfrac{1}{c_1+\cfrac1{c_2+\cfrac1{c_3+\cfrac1{\ddots}}}}\] Here is a concrete example: -\[ \xintFrac {208341/66317}=\xintCFrac {208341/66317}\] But the -difference with |amsmath|'s |\cfrac| is that this was input as -\centeredline{|\[ \xintFrac {208341/66317}=\xintCFrac - {208341/66317} \]|} The command \csbxint{CFrac} produces in two -expansion steps the whole thing with the many chained |\cfrac|'s and all -necessary braces, ready to be printed, in math mode. This is \LaTeX{} -only and with the |amsmath| package (we shall mention another method for -Plain \TeX{} users of |amstex|). - -A \emph{generalized} continued fraction has the same structure but -the numerators are not restricted to be ones, and numbers used in -the continued fraction may be arbitrary, also fractions, -irrationals, indeterminates. The \emph{centered} continued -fraction associated to a rational number is an +% +\centeredline{|\[ \xintFrac {208341/66317}=\xintCFrac {208341/66317} \]|} +% +\[ \xintFrac {208341/66317}=\xintCFrac {208341/66317}\]% +% +But it is the command \csbxint{CFrac} which did all the work of \emph{computing} +the continued fraction \emph{and} using |\cfrac| from |amsmath| to typeset +it. + +A \emph{generalized} continued fraction has the same structure but the +numerators are not restricted to be $1$, and numbers used in the continued +fraction may be arbitrary, also fractions, irrationals, complex, +indeterminates.\footnote{\xintcfracname may be used with indeterminates, + for basic conversions from one inline format to another, but not for + actual computations. See \csbxint{GGCFrac}.} +The \emph{centered} continued fraction is an example: -\[ \xintFrac {915286/188421}=\xintGCFrac {\xintFtoCC {915286/188421}} +\centeredline{|\[ \xintFrac {915286/188421}=\xintGCFrac + {5+-1/7+1/39+-1/53+-1/13} \]|} +\[ \xintFrac {915286/188421}=\xintGCFrac {5+-1/7+1/39+-1/53+-1/13} =\xintCFrac {915286/188421}\] - \centeredline{|\[ \xintFrac {915286/188421}=\xintGCFrac {\xintFtoCC - {915286/188421}} \]|} + The command \csbxint{GCFrac}, contrarily to -\csbxint{CFrac}, does not compute anything, it just typesets. Here, it is the -command \csbxint{FtoCC} which did the computation of -the centered continued fraction of |f|. Its output has the `inline format' -described in the next paragraph. In the display, we also used \csa{xintCFrac} -(code not shown), for comparison of the two types of continued fractions. - -A generalized continued fraction may be input `inline' as: -\centeredline{|a0+b0/a1+b1/a2+b2/...../a(n-1)+b(n-1)/an|}% +\csbxint{CFrac}, does not compute anything, it just typesets starting from a +generalized continued fraction in inline format, which in this example +was input literally. We also used \csa{xintCFrac} +for comparison of the two types of continued fractions. + +To let \TeX{} compute the centered continued fraction of |f| there is +\csbxint{FtoCC}: + \centeredline{|\[\xintFrac {915286/188421}\to\xintFtoCC {915286/188421}\]|} +\[\xintFrac {915286/188421}\to\xintFtoCC {915286/188421}\] +The package macros are expandable and may be nested (naturally \csa{xintCFrac} +and \csa{xintGCFrac} must be at the top level, as they deal with typesetting). +Thus + \centeredline{|\[\xintGCFrac {\xintFtoCC{915286/188421}}\]|} +produces +\[\xintGCFrac {\xintFtoCC{915286/188421}}\] + + +The `inline' format expected on input by \csbxint{GCFrac} is +\centeredline{$a_0+b_0/a_1+b_1/a_2+b_2/a_3+\cdots + +b_{n-2}/a_{n-1}+b_{n-1}/a_n$}% Fractions among the coefficients are allowed but they must be enclosed within braces. Signed integers may be left without braces (but the |+| -signs are mandatory). Or, they may -be macros expanding (in two steps) to some number or fractional number. -\centeredline{|\xintGCFrac {1+-1/57+\xintPow {-3}{7}/\xintQuo {132}{25}}|} +signs are mandatory). No spaces are allowed around the plus and fraction +symbols. The coefficients may themselves be macros, as long as these +macros are \fexpan dable. +% +\centeredline{|\xintGCFrac {1+-1/57+\xintPow {-3}{7}/\xintQuo + {132}{25}}|} \[ \xintFrac{\xintGCtoF {1+-1/57+\xintPow {-3}{7}/\xintQuo {132}{25}}}= \xintGCFrac {1+-1/57+\xintPow {-3}{7}/\xintQuo {132}{25}}\] -The left hand side was obtained with the following code: -\centeredline{|\xintFrac{\xintGCtoF {1+-1/57+\xintPow {-3}{7}/\xintQuo - {132}{25}}}|} -It uses the macro \csbxint{GCtoF} to convert a generalized fraction from the -`inline format' to the fraction it evaluates to. - -A simple continued fraction is a special case of a generalized continued -fraction and may be input as such to macros expecting the `inline format', for -example |-7+1/6+1/19+1/1+1/33|. There is a simpler comma separated format: +To compute the actual fraction one has \csbxint{GCtoF}: +\centeredline{|\[\xintFrac{\xintGCtoF {1+-1/57+\xintPow {-3}{7}/\xintQuo + {132}{25}}}\]|} +\[\xintFrac{\xintGCtoF {1+-1/57+\xintPow {-3}{7}/\xintQuo + {132}{25}}}\] + +For non-numeric input there is \csbxint{GGCFrac}. +% +\centeredline{|\[\xintGGCFrac + {a_0+b_0/a_1+b_1/a_2+b_2/\ddots+\ddots/a_{n-1}+b_{n-1}/a_n}\]|} +% +\[\xintGGCFrac {a_0+b_0/a_1+b_1/a_2+b_2/\ddots+\ddots/a_{n-1}+b_{n-1}/a_n}\] +% + +For regular continued fractions, there is a simpler comma separated format: \centeredline -{|\xintFrac{\xintCstoF{-7,6,19,1,33}}=\xintCFrac{\xintCstoF{-7,6,19,1,33}}|} +{|-7,6,19,1,33\to\xintFrac{\xintCstoF{-7,6,19,1,33}}=\xintCFrac{\xintCstoF{-7,6,19,1,33}}|} +% \[ -\xintFrac{\xintCstoF{-7,6,19,1,33}}=\xintCFrac{\xintCstoF{-7,6,19,1,33}}\] This -comma separated format may also be used with fractions among the coefficients: -in that case, computing with \csbxint{FtoCs} from the resulting |f| -its real coefficients will give a new comma separated list -with only integers. This list has no spaces: the spaces in the display below -arise from the math mode processing. -\centeredline{|\xintFrac{1084483/398959}=[\xintFtoCs{1084483/398959}]|} +-7,6,19,1,33\to +\xintFrac{\xintCstoF{-7,6,19,1,33}}=\xintCFrac{\xintCstoF{-7,6,19,1,33}}\] +% +The command \csbxint{FtoCs} produces from a fraction |f| the comma separated +list of its coefficients. +\centeredline{|\[\xintFrac{1084483/398959}=[\xintFtoCs{1084483/398959}]\]|} \[\xintFrac{1084483/398959}=[\xintFtoCs{1084483/398959}]\] -If one prefers other separators, one can use \csbxint{FtoCx} whose first -argument will be the separator to be used. -\centeredline{|\xintFrac{2721/1001}=\xintFtoCx {+1/(}{2721/1001})\cdots)|} +If one prefers other separators, one can use the two arguments macros +\csbxint{FtoCx} whose first argument is the separator (which may consist of more +than one token) which is to be used. +\centeredline{|\[\xintFrac{2721/1001}=\xintFtoCx {+1/(}{2721/1001})\cdots)\]|} \[\xintFrac{2721/1001}=\xintFtoCx {+1/(}{2721/1001})\cdots)\] -People using Plain \TeX{} and |amstex| can achieve the same effect as -|\xintCFrac| with: -|$$\xintFwOver{2721/1001}=\xintFtoCx {+\cfrac1\\ }{2721/1001}\endcfrac$$| -Using \csa{xintFtoCx} with first argument an empty pair of braces |{}| will -return the list of the coefficients of the continued fraction of |f|, without -separator, and each one enclosed in a pair of group braces. This can then be -manipulated by the non-expandable macro \csbxint{AssignArray} or the expandable -ones \csbxint{Apply} and \csbxint{ListWithSep}. +This allows under Plain \TeX{} with |amstex| to obtain the same effect +as with \LaTeX{}+|\amsmath|+\csbxint{CFrac}: +\centeredline{|$$\xintFwOver{2721/1001}=\xintFtoCx {+\cfrac1\\ }{2721/1001}\endcfrac$$|} + -As a shortcut to using \csa{xintFtoCx} with separator |1+/|, there is +As a shortcut to \csa{xintFtoCx} with separator |1+/|, there is \csbxint{FtoGC}: \centeredline{|2721/1001=\xintFtoGC {2721/1001}|}% \centeredline{\digitstt{2721/1001=\xintFtoGC {2721/1001}}} @@ -10424,8 +10547,18 @@ Let us compare in that case with the output of \csbxint{FtoCC}: \centeredline{|2721/1001=\xintFtoCC {2721/1001}|}% \centeredline{\digitstt{2721/1001=\xintFtoCC {2721/1001}}} -The `|\printnumber|' macro which we use to print long numbers can also -be useful on long continued fractions. +To obtain the coefficients as a sequence of braced numbers, there is +\csbxint{FtoC} (this is a shortcut for |\xintFtoCx {}|). This list +(sequence) may then be manipulated using the various macros of \xinttoolsname +such as the non-expandable macro \csbxint{AssignArray} or the expandable +\csbxint{Apply} and \csbxint{ListWithSep}. + +Conversely to go from such a sequence of braced coefficients to the +corresponding fraction there is \csbxint{CtoF}. + +The `|\printnumber|' (\autoref{ssec:printnumber}) macro which we use in this +document to print long numbers can also be useful on long continued fractions. +% \centeredline{|\printnumber{\xintFtoCC {35037018906350720204351049/%|}% \centeredline{|244241737886197404558180}}|}% \digitstt{\printnumber{\xintFtoCC {35037018906350720204351049/244241737886197404558180}}}. @@ -10453,14 +10586,12 @@ and indeed: \end{vmatrix} = \mbox{\digitstt{\xintiSub {\xintiMul {2897319801297630107}{2287346221788023}}{\xintiMul{20197107104701740}{328124887710626729}}}}\] \endgroup -More generally the various fractions obtained from the truncation of a -continued fraction to its initial terms are called the convergents. The -commands of \xintcfracname such as \csbxint{FtoCv}, \csbxint{FtoCCv}, -and others which compute such convergents, return them as a list of -braced items, with no separator. This list can then be treated either -with \csa{xint\-AssignArray}, or \csa{xintListWithSep}, or any other way -(but then, some \TeX{} programming knowledge will be necessary). Here -is an example: + +The various fractions obtained from the truncation of a continued fraction to +its initial terms are called the convergents. The commands of \xintcfracname +such as \csbxint{FtoCv}, \csbxint{FtoCCv}, and others which compute such +convergents, return them as a list of braced items, with no separator (as does +\csbxint {FtoC} for the partial quotients). Here is an example: \noindent \centeredline{|$$\xintFrac{915286/188421}\to \xintListWithSep {,}%|}% @@ -10470,9 +10601,10 @@ is an example: \centeredline{|$$\xintFrac{915286/188421}\to \xintListWithSep {,}%|}% \centeredline{|{\xintApply{\xintFrac}{\xintFtoCCv{915286/188421}}}$$|} \[ \xintFrac{915286/188421}\to \xintListWithSep {,} -{\xintApply\xintFrac{\xintFtoCCv{915286/188421}}}\] We thus see that the -`centered convergents' obtained with \csbxint{FtoCCv} are among the fuller list -of convergents as returned by \csbxint{FtoCv}. +{\xintApply\xintFrac{\xintFtoCCv{915286/188421}}}\] +% +We thus see that the `centered convergents' obtained with \csbxint{FtoCCv} are +among the fuller list of convergents as returned by \csbxint{FtoCv}. Here is a more complicated use of \csa{xintApply} and \csa{xintListWithSep}. We first define a macro which will be applied to each @@ -10487,14 +10619,13 @@ It produces:\par }{\xintApply{\mymacro}{\xintFtoCv{49171/18089}}}. -\def\cn #1{\xintiPow {2}{#1}}% +\def\cn #1{\xintiiPow {2}{#1}}% -The macro \csbxint{CntoF} 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{\xintiPow {2}{#1}}% 2^n|}% - \centeredline{|\[\xintFrac{\xintCntoF {6}{\cn}}=\xintCFrac - [l]{\xintCntoF {6}{\cn}}\]|}% +The macro \csbxint{CntoF} allows to specify the coefficients as a function given +by a one-parameter macro. The produced values do not have to be integers. +\centeredline{|\def\cn #1{\xintiiPow {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 @@ -10535,90 +10666,26 @@ continued fraction of $\pi$ with about as many terms: \xintGCFrac{3+1/7+1/15+1/1+1/292+1/1+1/1}= \xintTrunc{10}{\xintCstoF{3,7,15,1,292,1,1}}\dots\] -\hypertarget{e-convergents}{To} -conclude this overview of most of the package functionalities, let us explore -the convergents of Euler's number $e$. -\dverb|@ -\def\cn #1{\the\numexpr\ifcase \numexpr #1+3-3*((#1+2)/3)\relax - 1\or1\or2*(#1/3)\fi\relax } -% produces the pattern 1,1,2,1,1,4,1,1,6,1,1,8,... which are the -% coefficients of the simple continued fraction of e-1. -\cnta 0 -\def\mymacro #1{\advance\cnta by 1 - \noindent - \hbox to 3em {\hfil\small\texttt{\the\cnta.} }% - $\xintTrunc {30}{\xintAdd {1[0]}{#1}}\dots= - \xintFrac{\xintAdd {1[0]}{#1}}$}% -\xintListWithSep{\vtop to 6pt{}\vbox to 12pt{}\par} - {\xintApply\mymacro{\xintiCstoCv{\xintCntoCs {35}{\cn}}}}| - -\smallskip The volume of computation is kept minimal by the following steps: -\begin{itemize} -\item a comma separated list of the first 36 coefficients is produced by - \csbxint{CntoCs}, -\item this is then given to \csbxint{iCstoCv} which produces the list of the - convergents (there is also \csbxint{CstoCv}, but our - coefficients being integers we used the infinitesimally - faster \csbxint{iCstoCv}), -\item then the whole list was converted into a sequence of one-line paragraphs, - each convergent becomes the argument to a macro printing it - together with its decimal expansion with 30 digits after the decimal point. -\item A count register |\cnta| was used to give a line count serving as a visual - aid: we could also have done that in an expandable way, but well, let's relax - from time to time\dots -\end{itemize} - - -\def\cn #1{\the\numexpr\ifcase \numexpr #1+3-3*((#1+2)/3)\relax - 1\or1\or2*(#1/3)\fi\relax } -% produces the pattern 1,1,2,1,1,4,1,1,6,1,1,8,... which are the -% coefficients of the simple continued fraction of e-1. -\cnta 0 -\def\mymacro #1{\advance\cnta by 1 - \noindent - \hbox to 3em {\hfil\small\digitstt{\the\cnta.} }% - $\xintTrunc {30}{\xintAdd {1[0]}{#1}}\dots= - \xintFrac{\xintAdd {1[0]}{#1}}$}% -\xintListWithSep{\vtop to 6pt{}\vbox to 12pt{}\par} - {\xintApply\mymacro{\xintiCstoCv{\xintCntoCs {35}{\cn}}}} - -% \def\testmacro #1{\xintTrunc {30}{\xintAdd {1[0]}{#1}}\xintAdd {1[0]}{#1}} -% \pdfresettimer -% \edef\z{\xintApply\testmacro{\xintiCstoCv{\xintCntoCs {35}{\cn}}}} -% (\the\pdfelapsedtime) - +When studying the continued fraction of some real number, there is always +some doubt about how many terms are valid, when computed starting from some +approximation. If $f\leqslant x\leqslant g$ and $f, g$ both have the +same first $K$ partial quotients, then $x$ also has the same first $K$ quotients +and convergents. The macro \csbxint{FGtoC} outputs as a sequence of braced items +the common partial quotients of its two arguments. We can thus use it to produce +a sure list of valid convergents of $\pi$ for example, starting from some proven +lower and upper bound: -\smallskip The actual computation of the list of all 36 convergents accounts for -only 8\% of the total time (total time equal to about 5 hundredths of a second -in my testing, on my laptop): another 80\% is occupied with the computation of -the truncated decimal expansions (and the addition of 1 to everything as the -formula gives the continued fraction of $e-1$). One can with no problem compute -much bigger convergents. Let's get the 200th convergent. It turns out to -have the same first 268 digits after the decimal point as $e-1$. Higher -convergents get more and more digits in proportion to their index: the 500th -convergent already gets 799 digits correct! To allow speedy compilation of the -source of this document when the need arises, I limit here to the 200th -convergent (getting the 500th took about 1.2s on my laptop last time I tried, -and the 200th convergent is obtained ten times faster). \dverb|@ -\oodef\z {\xintCntoF {199}{\cn}}% -\begingroup\parindent 0pt \leftskip 2.5cm -\indent\llap {Numerator = }{\printnumber{\xintNumerator\z}\par -\indent\llap {Denominator = }\printnumber{\xintDenominator\z}\par -\indent\llap {Expansion = }\printnumber{\xintTrunc{268}\z}\dots -\par\endgroup| - -\oodef\z {\xintCntoF {199}{\cn}}% - -\begingroup\parindent 0pt \leftskip 2.5cm -\indent\llap {Numerator = }\digitstt{\printnumber{\xintNumerator\z}}\par -\indent\llap {Denominator = }\digitstt{\printnumber{\xintDenominator\z}}\par -\indent\llap - {Expansion = }\digitstt{\printnumber{\xintTrunc{268}\z}\dots}\par\endgroup - -One can also use a centered continued fraction: we get more digits but there are -also more computations as the numerators may be either -$1$ or $-1$. +$$\pi\to [\xintListWithSep{,} + {\xintFGtoC {3.14159265358979323}{3.14159265358979324}}, \dots]$$ +$\pi\to\xintListWithSep{,\allowbreak\;} + {\xintApply{\xintFrac} + {\xintCtoCv{\xintFGtoC {3.14159265358979323}{3.14159265358979324}}}}, \dots$| +$$\pi\to [\xintListWithSep{,} + {\xintFGtoC {3.14159265358979323}{3.14159265358979324}}, \dots]$$ +\noindent$\pi\to\xintListWithSep{,\allowbreak\;} + {\xintApply{\xintFrac} + {\xintCtoCv{\xintFGtoC {3.14159265358979323}{3.14159265358979324}}}},\;\dots$ \subsection{\csbh{xintCFrac}}\label{xintCFrac} @@ -10630,21 +10697,50 @@ the location of the one's in the numerators of the sub-fractions. Each coefficient is typeset using the \csbxint{Frac} macro from the \xintfracname package. This macro is \fexpan dable in the sense that it prepares expandably the whole expression with the multiple |\cfrac|'s, but it is not completely -expandable naturally. +expandable naturally as |\cfrac| isn't. \subsection{\csbh{xintGCFrac}}\label{xintGCFrac} -\csa{xintGCFrac}|{a+b/c+d/e+f/g+h/...}|\etype{f} uses similarly |\cfrac| to -typeset a -generalized continued fraction in inline format. It admits the same optional -argument as \csa{xintCFrac}. +\csa{xintGCFrac}|{a+b/c+d/e+f/g+h/...+x/y}|\ntype{f} uses similarly |\cfrac| +to prepare the typesetting with the |amsmath| |\cfrac| (\LaTeX{}) of a +generalized continued fraction given in inline format (or as macro which +will \fexpan d to it). It admits the +same optional argument as \csa{xintCFrac}. Plain \TeX{} with |amstex| +users, see \csbxint{GCtoGCx}. +% \centeredline{|\[\xintGCFrac {1+\xintPow{1.5}{3}/{1/7}+{-3/5}/\xintFac {6}}\]|} \[\xintGCFrac {1+\xintPow{1.5}{3}/{1/7}+{-3/5}/\xintFac {6}}\] -As can be seen this is typesetting macro, although it does proceed to the -evaluation of the coefficients themselves. See \csbxint{GCtoF} if you are -impatient to see this fraction computed. Numerators and denominators are made -arguments to the -\csbxint{Frac} macro. +% +This is mostly a typesetting macro, although it does provoke the +expansion of the coefficients. See \csbxint{GCtoF} if you are impatient +to see this specific fraction computed. + +It admits an optional argument within square brackets which may be +either |[l]|, |[c]| or |[r]|. Default is |[c]| (numerators are centered). + +Numerators and denominators are made arguments to the \csbxint{Frac} +macro. This allows them to be themselves fractions or anything \fexpan +dable giving numbers or fractions, but also means however that they can +not be arbitrary material, they can not contain color changing commands +for example. One of the reasons is that \csa{xintGCFrac} tries to +determine the signs of the numerators and chooses accordingly to use +$+$ or $-$. + +\subsection{\csbh{xintGGCFrac}}\label{xintGGCFrac} + +\csa{xintGGCFrac}|{a+b/c+d/e+f/g+h/...+x/y}|\ntype{f} is a clone of +\csbxint{GCFrac}, hence again \LaTeX{} specific with package +|amsmath|.\NewWith {1.09m} +It does not assume the coefficients to be numbers as understood by +\xintfracname. The macro can be used for displaying arbitrary content as +a continued fraction with |\cfrac|, using only plus signs though. Note +though that it will first \fexpan d its argument, which may be thus be +one of the \xintcfracname macros producing a (general) continued +fraction in inline format, see \csbxint{FtoCx} for an example. If this +expansion is not wished, it is enough to start the argument with a +space. +\centeredline{|\[\xintGGCFrac {1+q/1+q^2/1+q^3/1+q^4/1+q^5/\ddots}\]|} +\[\xintGGCFrac {1+q/1+q^2/1+q^3/1+q^4/1+q^5/\ddots}\] \subsection{\csbh{xintGCtoGCx}}\label{xintGCtoGCx} %{\small New with release |1.05|.\par} @@ -10654,40 +10750,118 @@ arguments to the of the coefficients of the generalized continued fraction of |f|, each one within a pair of braces, and separated with the help of |sepa| and |sepb|. Thus \centeredline{|\xintGCtoGCx :;{1+2/3+4/5+6/7}| gives \xintGCtoGCx - :;{1+2/3+4/5+6/7}} Plain \TeX{}+|amstex| users may be interested in:\par + :;{1+2/3+4/5+6/7}} +% +The following can be used byt Plain \TeX{}+|amstex| users to obtain an +output similar as the ones produced by \csbxint{GCFrac} and +\csbxint{GGCFrac}:\par \dverb|@ $$\xintGCtoGCx {+\cfrac}{\\}{a+b/...}\endcfrac$$ $$\xintGCtoGCx {+\cfrac\xintFwOver}{\\\xintFwOver}{a+b/...}\endcfrac$$| +\subsection{\csbh{xintFtoC}}\label{xintFtoC} + +\csa{xintFtoC}|{f}|\etype{\Ff} computes the +coefficients of the simple continued fraction of |f| and returns them as a list +(sequence) of braced items.\NewWith {1.09m} + +\centeredline{% + |\oodef\test{\xintFtoC{-5262046/89233}}\texttt{\meaning\test}|}% +\centeredline{\oodef\test{\xintFtoC{-5262046/89233}}\texttt{\meaning\test}} + \subsection{\csbh{xintFtoCs}}\label{xintFtoCs} \csa{xintFtoCs}|{f}|\etype{\Ff} returns the comma separated list of the -coefficients of the simple continued fraction of |f|. +coefficients of the simple continued fraction of |f|. Notice that starting with +|1.09m| a space follows each comma (mainly for usage in text mode, as in math +mode spaces are produced in the typeset output by \TeX{} itself). \centeredline{% - |\[ \xintSignedFrac{-5262046/89233} = [\xintFtoCs{-5262046/89233}]\]|}% -\[ \xintSignedFrac{-5262046/89233} = [\xintFtoCs{-5262046/89233}]\] - + |\[ \xintSignedFrac{-5262046/89233} \to [\xintFtoCs{-5262046/89233}]\]|}% +\[ \xintSignedFrac{-5262046/89233} \to [\xintFtoCs{-5262046/89233}]\] \subsection{\csbh{xintFtoCx}}\label{xintFtoCx} -\csa{xintFtoCx}|{sep}{f}|\etype{n\Ff} returns the list of the coefficients of -the simple continued fraction of |f|, withing group braces and separated with -the help of |sep|. \centeredline{|$$\xintFtoCx {+\cfrac1\\ }{f}\endcfrac$$|} -will display the continued fraction in |\cfrac| format, with Plain \TeX{} and -|amstex|. +\csa{xintFtoCx}|{sep}{f}|\etype{n\Ff} returns the list of the +coefficients of the simple continued fraction of |f| separated with the +help of |sep|, which may be anything (and is kept unexpanded). For +example, with Plain \TeX{} and |amstex|, +% +\centeredline{|$$\xintFtoCx {+\cfrac1\\ }{-5262046/89233}\endcfrac$$|} +% +will display the continued fraction using +|\cfrac|. Each coefficient is inside a brace pair \hbox{|{ }|}, allowing +a macro to end the separator and fetch it as argument, +for example, again with Plain \TeX{} and |amstex|: +\dverb|@ + \def\highlight #1{\ifnum #1>200 \textcolor{red}{#1}\else #1\fi} + $$\xintFtoCx {+\cfrac1\\ \highlight}{104348/33215}\endcfrac$$| +% + +Due to the different and extremely cumbersome syntax of |\cfrac| under +\LaTeX{} it proves a bit tortuous to obtain there the same effect. +Actually, it is partly for this purpose that |1.09m| added \csbxint +{GGCFrac}. We thus use \csa{xintFtoCx} with a suitable separator, and\; +then the whole thing as argument to \csbxint{GGCFrac}: +% + \dverb|@ +\def\highlight #1{\ifnum #1>200 + \fcolorbox{blue}{white}{\boldmath\color{red}$#1$}% + \else #1\fi} +\[\xintGGCFrac {\xintFtoCx {+1/\highlight}{208341/66317}}\]| +\def\highlight #1{\ifnum #1>200 + \fcolorbox{blue}{white}{\boldmath\color{red}$#1$}% + \else #1\fi} +\[\xintGGCFrac {\xintFtoCx {+1/\highlight}{208341/66317}}\] \subsection{\csbh{xintFtoGC}}\label{xintFtoGC} \csa{xintFtoGC}|{f}|\etype{\Ff} does the same as \csa{xintFtoCx}|{+1/}{f}|. Its output may thus be used in the package macros expecting such an `inline -format'. This continued fraction is a \emph{simple} one, not a -\emph{generalized} one, but as it is produced in the format used for -user input of generalized continued fractions, the macro was called -\csa{xintFtoGC} rather than \csa{xintFtoC} for example. +format'. +% This continued fraction is a \emph{simple} one, not a +% \emph{generalized} one, but as it is produced in the format used for +% user input of generalized continued fractions, the macro was called +% \csa{xintFtoGC} rather than \csa{xintFtoC} for example. \centeredline{|566827/208524=\xintFtoGC {566827/208524}|}% \centeredline{566827/208524=\xintFtoGC {566827/208524}} + + +\subsection{\csbh{xintFGtoC}}\label{xintFGtoC} + +\csa{xintFGtoC}|{f}{g}|\etype{\Ff\Ff} computes the common initial coefficients +to +two given fractions |f| and |g|. Notice\NewWith {1.09m} that any real number |f<x<g| or |f>x>g| +will then necessarily share with |f| and |g| these common initial coefficients +for its regular continued fraction. The coefficients are output as a sequence of +braced numbers. This list can then be manipulated via macros from +\xinttoolsname, or other macros of \xintcfracname. + +\centeredline{% + |\oodef\test{\xintFGtoC{-5262046/89233}{-5314647/90125}}\texttt{\meaning\test}|}% +\centeredline{\oodef\test{\xintFGtoC{-5262046/89233}{-5314647/90125}}\texttt{\meaning\test}} +\centeredline{% + |\oodef\test{\xintFGtoC{3.141592653}{3.141592654}}\texttt{\meaning\test}|}% +\centeredline{% + \oodef\test{\xintFGtoC{3.141592653}{3.141592654}}\texttt{\meaning\test}}% +\centeredline{% + |\oodef\test{\xintFGtoC{3.1415926535897932384}{3.1415926535897932385}}\texttt{\meaning\test}|}% +\oodef\test{\xintFGtoC{3.1415926535897932384}{3.1415926535897932385}}% +\centeredline{% + \texttt{\meaning\test}}% +% \centeredline{\xintRound {30}{\xintCstoF{\xintListWithSep{,}{\test}}}} +% \centeredline{\xintRound {30}{\xintCtoF{\test}}} +% \centeredline{\xintCtoF{\test}} +\centeredline{% + |\oodef\test{\xintFGtoC{1.41421356237309}{1.4142135623731}}\texttt{\meaning\test}|}% +\oodef\test{\xintFGtoC{1.41421356237309}{1.4142135623731}}% +\centeredline{% + \texttt{\meaning\test}}% +% \centeredline{\xintRound {30}{\xintCstoF{\xintListWithSep{,}{\test}}}} +% \centeredline{\xintRound {30}{\xintCtoF{\test}}} +% \centeredline{\xintCtoF{\test}} + \subsection{\csbh{xintFtoCC}}\label{xintFtoCC} \csa{xintFtoCC}|{f}|\etype{\Ff} returns the `centered' continued fraction of @@ -10697,27 +10871,13 @@ user input of generalized continued fractions, the macro was called |\[\xintFrac{566827/208524} = \xintGCFrac{\xintFtoCC{566827/208524}}\]|}% \[\xintFrac{566827/208524} = \xintGCFrac{\xintFtoCC{566827/208524}}\] -\subsection{\csbh{xintFtoCv}}\label{xintFtoCv} - -\csa{xintFtoCv}|{f}|\etype{\Ff} returns the list of the (braced) convergents of -|f|, with no separator. To be treated with \csbxint{AssignArray} or -\csbxint{ListWithSep}. \centeredline{% - |\[\xintListWithSep{\to}{\xintApply\xintFrac{\xintFtoCv{5211/3748}}}\]|}% -\[\xintListWithSep{\to}{\xintApply\xintFrac{\xintFtoCv{5211/3748}}}\] - -\subsection{\csbh{xintFtoCCv}}\label{xintFtoCCv} - -\csa{xintFtoCCv}|{f}|\etype{\Ff} returns the list of the (braced) centered -convergents of |f|, with no separator. To be treated with \csbxint{AssignArray} -or \csbxint{ListWithSep}. \centeredline{% - |\[\xintListWithSep{\to}{\xintApply\xintFrac{\xintFtoCCv{5211/3748}}}\]|}% -\[\xintListWithSep{\to}{\xintApply\xintFrac{\xintFtoCCv{5211/3748}}}\] - \subsection{\csbh{xintCstoF}}\label{xintCstoF} \csa{xintCstoF}|{a,b,c,d,...,z}|\etype{f} computes the fraction corresponding to the coefficients, which may be fractions or even macros expanding to such -fractions. The final fraction may then be highly reducible. +fractions. The final fraction may then be highly reducible. Starting with +release |1.09m| spaces before commas are allowed and trimmed automatically +(spaces after commas were already silently handled in earlier releases). \centeredline{|\[\xintGCFrac {-1+1/3+1/-5+1/7+1/-9+1/11+1/-13}|}% \centeredline{|=\xintSignedFrac{\xintCstoF {-1,3,-5,7,-9,11,-13}}|}% \centeredline{|=\xintSignedFrac{\xintGCtoF @@ -10728,39 +10888,30 @@ fractions. The final fraction may then be highly reducible. \centeredline{|\xintGCFrac{{1/2}+1/{1/3}+1/{1/4}+1/{1/5}}= |}% \centeredline{| \xintFrac{\xintCstoF {1/2,1/3,1/4,1/5}}|}% \[\xintGCFrac{{1/2}+1/{1/3}+1/{1/4}+1/{1/5}}= -\xintFrac{\xintCstoF {1/2,1/3,1/4,1/5}}\] A generalized continued fraction may -produce a reducible fraction (\csa{xintCstoF} tries its best not to accumulate -in a silly way superfluous factors but will not do simplifications which would -be obvious to a human, like simplification by 3 in the result above). - -\subsection{\csbh{xintCstoCv}}\label{xintCstoCv} - -\csa{xintCstoCv}|{a,b,c,d,...,z}|\etype{f} returns the list of the corresponding -convergents. It is allowed to use fractions as coefficients (the computed -convergents have then no reason to be the real convergents of the final -fraction). When the coefficients are integers, the convergents are irreducible -fractions, but otherwise it is not necessarily the case. -\centeredline{|\xintListWithSep:{\xintCstoCv{1,2,3,4,5,6}}|}% -\centeredline{\digitstt{\xintListWithSep:{\xintCstoCv{1,2,3,4,5,6}}}} -\centeredline{|\xintListWithSep:{\xintCstoCv{1,1/2,1/3,1/4,1/5,1/6}}|}% -\centeredline{\digitstt{\xintListWithSep:{\xintCstoCv{1,1/2,1/3,1/4,1/5,1/6}}}} -% j'ai retiré les [0] à partir de la version 1.09b, le 3 octobre 2013. -\centeredline{|\[\xintListWithSep{\to}{\xintApply\xintFrac{\xintCstoCv|}% - \centeredline{|{\xintPow {-.3}{-5},7.3/4.57,\xintCstoF{3/4,9,-1/3}}}}\]|}% -\[\xintListWithSep{\to}{\xintApply\xintFrac{\xintCstoCv - {\xintPow {-.3}{-5},7.3/4.57,\xintCstoF{3/4,9,-1/3}}}}\] - - -\subsection{\csbh{xintCstoGC}}\label{xintCstoGC} +\xintFrac{\xintCstoF {1/2,1/3,1/4,1/5}}\] +% +A generalized continued fraction may produce a reducible fraction +(\csa{xintCstoF} tries its best not to accumulate in a silly way superfluous +factors but will not do simplifications which would be obvious to a human, like +simplification by 3 in the result above). + +\subsection{\csbh{xintCtoF}}\label{xintCtoF} + +\csa{xintCtoF}|{{a}{b}{c}...{z}}|\etype{f} computes the fraction corresponding +to the coefficients, which may be fractions or even macros.\NewWith {1.09m} +\centeredline{|\xintCtoF {\xintApply {\xintiiPow 3}{\xintSeq {1}{5}}}|} +% pour vérifier que l'expansion se fait bien: +%\centeredline{\digitstt{\xintCtoF {\xintApply { \xintiiPow 3}{\xintSeq {1}{5}}}}} +\centeredline{\digitstt{\xintCtoF {\xintApply {\xintiiPow 3}{\xintSeq {1}{5}}}}} +\centeredline{|\[ \xintFrac{14946960/4805083}=\xintCFrac {14946960/4805083}\]|} +\[ \xintFrac{14946960/4805083}=\xintCFrac {14946960/4805083}\] + +In the example above the power of @3@ was already pre-computed via the expansion +done by |\xintApply|, but if we try with |\xintApply { \xintiiPow 3}| where the +space will stop this expansion, we can check that |\xintCtoF| will itself +provoke the needed coefficient expansion. +% ok -\csa{xintCstoGC}|{a,b,..,z}|\etype{f} transforms a comma separated list (or -something expanding to such a list) into an `inline format' continued fraction -|{a}+1/{b}+1/...+1/{z}|. The coefficients are just copied and put within braces, -without expansion. The output can then be used in \csbxint{GCFrac} for example. -\centeredline{|\[\xintGCFrac {\xintCstoGC {-1,1/2,-1/3,1/4,-1/5}}|}% -\centeredline{|=\xintSignedFrac {\xintCstoF {-1,1/2,-1/3,1/4,-1/5}}\]|}% -\[\xintGCFrac {\xintCstoGC {-1,1/2,-1/3,1/4,-1/5}} = -\xintSignedFrac{\xintCstoF {-1,1/2,-1/3,1/4,-1/5}}\] \subsection{\csbh{xintGCtoF}}\label{xintGCtoF} @@ -10784,6 +10935,32 @@ The macro tries its best not to accumulate superfluous factor in the denominators, but doesn't reduce the fraction to irreducible form before returning it and does not do simplifications which would be obvious to a human. +\subsection{\csbh{xintCstoCv}}\label{xintCstoCv} + +\csa{xintCstoCv}|{a,b,c,d,...,z}|\etype{f} returns the sequence of the +corresponding convergents, each one within braces. + +It is allowed to use fractions as coefficients (the computed +convergents have then no reason to be the real convergents of the final +fraction). When the coefficients are integers, the convergents are irreducible +fractions, but otherwise it is not necessarily the case. +\centeredline{|\xintListWithSep:{\xintCstoCv{1,2,3,4,5,6}}|}% +\centeredline{\digitstt{\xintListWithSep:{\xintCstoCv{1,2,3,4,5,6}}}} +\centeredline{|\xintListWithSep:{\xintCstoCv{1,1/2,1/3,1/4,1/5,1/6}}|}% +\centeredline{\digitstt{\xintListWithSep:{\xintCstoCv{1,1/2,1/3,1/4,1/5,1/6}}}} +% j'ai retiré les [0] à partir de la version 1.09b, le 3 octobre 2013. +\centeredline{|\[\xintListWithSep{\to}{\xintApply\xintFrac{\xintCstoCv|}% + \centeredline{|{\xintPow {-.3}{-5},7.3/4.57,\xintCstoF{3/4,9,-1/3}}}}\]|}% +\[\xintListWithSep{\to}{\xintApply\xintFrac{\xintCstoCv + {\xintPow {-.3}{-5},7.3/4.57,\xintCstoF{3/4,9,-1/3}}}}\] + +\subsection{\csbh{xintCtoCv}}\label{xintCtoCv} + +\csa{xintCtoCv}|{{a}{b}{c}...{z}}|\etype{f} returns the sequence of the +corresponding convergents, each one within braces.\NewWith {1.09m} +\centeredline{|\oodef\test{\xintCtoCv {11111111111}}\texttt{\meaning\test}|} +\centeredline{\oodef\test{\xintCtoCv {11111111111}}\texttt{\meaning\test}} + \subsection{\csbh{xintGCtoCv}}\label{xintGCtoCv} \csa{xintGCtoCv}|{a+b/c+d/e+f/g+......+v/w+x/y}|\etype{f} returns the list of @@ -10803,35 +10980,63 @@ with |\xintApply\xintIrr|. \[\xintListWithSep{,}{\xintApply\xintFrac{\xintApply\xintIrr {\xintGCtoCv{3+{-2}/{7/2}+{3/4}/12+{-56}/3}}}}\] + +\subsection{\csbh{xintFtoCv}}\label{xintFtoCv} + +\csa{xintFtoCv}|{f}|\etype{\Ff} returns the list of the (braced) convergents of +|f|, with no separator. To be treated with \csbxint{AssignArray} or +\csbxint{ListWithSep}. \centeredline{% + |\[\xintListWithSep{\to}{\xintApply\xintFrac{\xintFtoCv{5211/3748}}}\]|}% +\[\xintListWithSep{\to}{\xintApply\xintFrac{\xintFtoCv{5211/3748}}}\] + +\subsection{\csbh{xintFtoCCv}}\label{xintFtoCCv} + +\csa{xintFtoCCv}|{f}|\etype{\Ff} returns the list of the (braced) centered +convergents of |f|, with no separator. To be treated with \csbxint{AssignArray} +or \csbxint{ListWithSep}. \centeredline{% + |\[\xintListWithSep{\to}{\xintApply\xintFrac{\xintFtoCCv{5211/3748}}}\]|}% +\[\xintListWithSep{\to}{\xintApply\xintFrac{\xintFtoCCv{5211/3748}}}\] + \subsection{\csbh{xintCntoF}}\label{xintCntoF} \def\macro #1{\the\numexpr 1+#1*#1\relax} -\csa{xintCntoF}|{N}{\macro}|\etype{\numx f} 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{% +\csa{xintCntoF}|{N}{\macro}|\etype{\numx f} 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{\digitstt{\xintCntoF {5}{\macro}}} +\centeredline{|\xintCntoF {5}{\macro}|} +\centeredline{\digitstt{\xintCntoF {5}{\macro}}} +% +This example shows that the fraction is output with a trailing number in square +brackets (representing a power of ten), this is for consistency with what do +most macros of \xintfracname, and does not have to be always this annoying |[0]| +as the coefficients may for example be numbers in scientific notation. To avoid +these trailing square brackets, for example if the coefficients are known to be integers, there is always the possibility to filter the output via +\csbxint{PRaw}, or \csbxint{Irr} (the latter is overkill in the case of integer +coefficients, as the fraction is guaranteed to be irreducible then). \subsection{\csbh{xintGCntoF}}\label{xintGCntoF} \def\coeffA #1{\the\numexpr #1+4-3*((#1+2)/3)\relax }% -\def\coeffB #1{\xintMON{#1}}% (-1)^n +\def\coeffB #1{\the\numexpr \ifodd #1 -\fi 1\relax }% (-1)^n \csa{xintGCntoF}|{N}{\macroA}{\macroB}|\etype{\numx ff} 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}|. The |N| parameter is given to a |\numexpr|. -\[\xintGCFrac{\xintGCntoGC {6}{\coeffA}{\coeffB}} -= \xintFrac{\xintGCntoF {6}{\coeffA}{\coeffB}}\] -There is also \csbxint{GCntoGC} 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{\xintMON{#1}}% (-1)^n|}% +\centeredline{|\def\coeffB #1{\the\numexpr \ifodd #1 -\fi 1\relax }% (-1)^n|} \centeredline{|\[\xintGCFrac{\xintGCntoGC {6}{\coeffA}{\coeffB}}|}% \centeredline{| = \xintFrac{\xintGCntoF {6}{\coeffA}{\coeffB}}\]|} +\[\xintGCFrac{\xintGCntoGC {6}{\coeffA}{\coeffB}} += \xintFrac{\xintGCntoF {6}{\coeffA}{\coeffB}}\] +There is also \csbxint{GCntoGC} to get the `inline format' continued +fraction. \subsection{\csbh{xintCntoCs}}\label{xintCntoCs} @@ -10855,7 +11060,9 @@ of the corresponding coefficients, from |n=0| to |n=N|. The |N| is given to a |j=0| to |j=N| and returns a continued fraction written in inline 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{% +pair of braces, they may thus be fractions. +% +\centeredline{% |\def\macro #1{\the\numexpr\ifodd#1 -1-#1\else1+#1\fi\relax/%|}% \centeredline{|\the\numexpr 1+#1*#1\relax}|}% \centeredline{|\edef\x{\xintCntoGC {5}{\macro}}\meaning\x|}% @@ -10868,45 +11075,153 @@ pair of braces, they may thus be fractions. \centeredline{% \csa{xintGCntoGC}|{N}{\macroA}{\macroB}|\etype{\numx ff} 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. \dverb|@ \def\an #1{\the\numexpr - #1*#1*#1+1\relax}% -\def\bn #1{\the\numexpr \xintiiMON{#1}*(#1+1)\relax}% +givent to a |\numexpr|. The coefficients are enclosed into pairs +of braces, and may thus be fractions, the fraction slash will not be +confused in further processing by the continued fraction slashes. +% +\dverb|@ +\def\an #1{\the\numexpr #1*#1*#1+1\relax}% +\def\bn #1{\the\numexpr \ifodd#1 -\fi 1*(#1+1)\relax}% $\xintGCntoGC {5}{\an}{\bn}}=\xintGCFrac {\xintGCntoGC {5}{\an}{\bn}} = \displaystyle\xintFrac {\xintGCntoF {5}{\an}{\bn}}$\par| \def\an #1{\the\numexpr #1*#1*#1+1\relax}% -\def\bn #1{\the\numexpr \xintiiMON{#1}*(#1+1)\relax}% +\def\bn #1{\the\numexpr \ifodd #1 -\fi 1*(#1+1)\relax}% $\xintGCntoGC {5}{\an}{\bn}=\xintGCFrac {\xintGCntoGC {5}{\an}{\bn}} = \displaystyle\xintFrac {\xintGCntoF {5}{\an}{\bn}}$\par +\subsection{\csbh{xintCstoGC}}\label{xintCstoGC} + +\csa{xintCstoGC}|{a,b,..,z}|\etype{f} transforms a comma separated list (or +something expanding to such a list) into an `inline format' continued fraction +|{a}+1/{b}+1/...+1/{z}|. The coefficients are just copied and put within braces, +without expansion. The output can then be used in \csbxint{GCFrac} for example. +\centeredline{|\[\xintGCFrac {\xintCstoGC {-1,1/2,-1/3,1/4,-1/5}}|}% +\centeredline{|=\xintSignedFrac {\xintCstoF {-1,1/2,-1/3,1/4,-1/5}}\]|}% +\[\xintGCFrac {\xintCstoGC {-1,1/2,-1/3,1/4,-1/5}} = +\xintSignedFrac{\xintCstoF {-1,1/2,-1/3,1/4,-1/5}}\] + \subsection{\csbh{xintiCstoF}, \csbh{xintiGCtoF}, \csbh{xint\-iCstoCv}, \csbh{xintiGCtoCv}}\label{xintiCstoF} \label{xintiGCtoF} \label{xintiCstoCv} \label{xintiGCtoCv} -The same as the corresponding macros without the `i', but for -integer-only input. Infinitesimally faster; to notice the higher -efficiency one would need to use them with an input having (at least) -hundreds of coefficients. - +Essentially\etype{f} the same as the corresponding macros without the +`i', but for integer-only input. Infinitesimally faster, mainly for +internal use by the package. \subsection{\csbh{xintGCtoGC}}\label{xintGCtoGC} \csa{xintGCtoGC}|{a+b/c+d/e+f/g+......+v/w+x/y}|\etype{f} 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. \dverb|@ \edef\x {\xintGCtoGC {1+\xintPow{1.5}{3}/{1/7}+{-3/5}/\xintFac - {6}+\xintCstoF {2,-7,-5}/16}} \meaning\x| +braces. +% +\dverb|@ +\edef\x {\xintGCtoGC {1+\xintPow{1.5}{3}/{1/7}+{-3/5}/% + \xintFac {6}+\xintCstoF {2,-7,-5}/16}} \meaning\x| \edef\x {\xintGCtoGC {1+\xintPow{1.5}{3}/{1/7}+{-3/5}/\xintFac {6}+\xintCstoF {2,-7,-5}/16}} \digitstt{\meaning\x} -To be honest I have, it seems, forgotten why I wrote this macro in the -first place. +To be honest I have forgotten for which purpose I wrote this macro in the first +place. + + +\subsection{Euler's number $e$}\label{ssec:e-convergents} + +Let us explore +the convergents of Euler's number $e$. +\dverb|@ +\def\cn #1{\the\numexpr\ifcase \numexpr #1+3-3*((#1+2)/3)\relax + 1\or1\or2*(#1/3)\fi\relax } +% produces the pattern 1,1,2,1,1,4,1,1,6,1,1,8,... which are the +% coefficients of the simple continued fraction of e-1. +\cnta 0 +\def\mymacro #1{\advance\cnta by 1 + \noindent + \hbox to 3em {\hfil\small\texttt{\the\cnta.} }% + $\xintTrunc {30}{\xintAdd {1[0]}{#1}}\dots= + \xintFrac{\xintAdd {1[0]}{#1}}$}% +\xintListWithSep{\vtop to 6pt{}\vbox to 12pt{}\par} + {\xintApply\mymacro{\xintiCstoCv{\xintCntoCs {35}{\cn}}}}| + +\smallskip The volume of computation is kept minimal by the following steps: +\begin{itemize} +\item a comma separated list of the first 36 coefficients is produced by + \csbxint{CntoCs}, +\item this is then given to \csbxint{iCstoCv} which produces the list of the + convergents (there is also \csbxint{CstoCv}, but our + coefficients being integers we used the infinitesimally + faster \csbxint{iCstoCv}), +\item then the whole list was converted into a sequence of one-line paragraphs, + each convergent becomes the argument to a macro printing it + together with its decimal expansion with 30 digits after the decimal point. +\item A count register |\cnta| was used to give a line count serving as a visual + aid: we could also have done that in an expandable way, but well, let's relax + from time to time\dots +\end{itemize} + + +\def\cn #1{\the\numexpr\ifcase \numexpr #1+3-3*((#1+2)/3)\relax + 1\or1\or2*(#1/3)\fi\relax } +% produces the pattern 1,1,2,1,1,4,1,1,6,1,1,8,... which are the +% coefficients of the simple continued fraction of e-1. +\cnta 0 +\def\mymacro #1{\advance\cnta by 1 + \noindent + \hbox to 3em {\hfil\small\digitstt{\the\cnta.} }% + $\xintTrunc {30}{\xintAdd {1[0]}{#1}}\dots= + \xintFrac{\xintAdd {1[0]}{#1}}$}% +\xintListWithSep{\vtop to 6pt{}\vbox to 12pt{}\par} + {\xintApply\mymacro{\xintiCstoCv{\xintCntoCs {35}{\cn}}}} + +% \def\testmacro #1{\xintTrunc {30}{\xintAdd {1[0]}{#1}}\xintAdd {1[0]}{#1}} +% \pdfresettimer +% \edef\z{\xintApply\testmacro{\xintiCstoCv{\xintCntoCs {35}{\cn}}}} +% (\the\pdfelapsedtime) + + +\smallskip + +% The actual computation of the list of all 36 convergents accounts for +% only 8\% of the total time (total time equal to about 5 hundredths of a second +% in my testing, on my laptop): another 80\% is occupied with the computation of +% the truncated decimal expansions (and the addition of 1 to everything as the +% formula gives the continued fraction of $e-1$). + +One can with no problem compute +much bigger convergents. Let's get the 200th convergent. It turns out to +have the same first 268 digits after the decimal point as $e-1$. Higher +convergents get more and more digits in proportion to their index: the 500th +convergent already gets 799 digits correct! To allow speedy compilation of the +source of this document when the need arises, I limit here to the 200th +convergent. +% (getting the 500th took about 1.2s on my laptop last time I tried, +% and the 200th convergent is obtained ten times faster). +\dverb|@ +\oodef\z {\xintCntoF {199}{\cn}}% +\begingroup\parindent 0pt \leftskip 2.5cm +\indent\llap {Numerator = }{\printnumber{\xintNumerator\z}\par +\indent\llap {Denominator = }\printnumber{\xintDenominator\z}\par +\indent\llap {Expansion = }\printnumber{\xintTrunc{268}\z}\dots +\par\endgroup| + +\oodef\z {\xintCntoF {199}{\cn}}% + +\begingroup\parindent 0pt \leftskip 2.5cm +\indent\llap {Numerator = }\digitstt{\printnumber{\xintNumerator\z}}\par +\indent\llap {Denominator = }\digitstt{\printnumber{\xintDenominator\z}}\par +\indent\llap + {Expansion = }\digitstt{\printnumber{\xintTrunc{268}\z}\dots}\par\endgroup + +One can also use a centered continued fraction: we get more digits but there are +also more computations as the numerators may be either +$1$ or $-1$. + % will be used by the \lverb things @@ -11124,7 +11439,7 @@ first place. \fi \XINT_providespackage \ProvidesPackage {xinttools}% - [2014/02/13 v1.09kb Expandable and non-expandable utilities (jfB)]% + [2014/02/26 v1.09m Expandable and non-expandable utilities (jfB)]% % \end{macrocode} % \subsection{Token management, constants} % \lverb|In 1.09e \xint_undef replaced everywhere by \xint_bye. @@ -11140,12 +11455,14 @@ first place. \long\def\xint_gobble_vii #1#2#3#4#5#6#7{}% \long\def\xint_gobble_viii #1#2#3#4#5#6#7#8{}% \long\def\xint_firstofone #1{#1}% -\xint_firstofone{\let\XINT_sptoken= } %<- space here! \long\def\xint_firstoftwo #1#2{#1}% \long\def\xint_secondoftwo #1#2{#2}% +\long\def\xint_firstofone_thenstop #1{ #1}% \long\def\xint_firstoftwo_thenstop #1#2{ #1}% \long\def\xint_secondoftwo_thenstop #1#2{ #2}% \def\xint_minus_thenstop { -}% +\def\xint_gob_til_zero #10{}% no need to make it long, so far +\def\xint_UDzerominusfork #10-#2#3\krof {#2}% id. \long\def\xint_gob_til_R #1\R {}% \long\def\xint_gob_til_W #1\W {}% \long\def\xint_gob_til_Z #1\Z {}% @@ -11155,9 +11472,16 @@ first place. \long\def\xint_gob_til_xint_relax #1\xint_relax {}% \long\def\xint_afterfi #1#2\fi {\fi #1}% \chardef\xint_c_ 0 -\chardef\xint_c_i 1 % 1.09k did not have it, but needed in \xintSeq +\chardef\xint_c_i 1 +\chardef\xint_c_ii 2 +\chardef\xint_c_iii 3 +\chardef\xint_c_iv 4 +\chardef\xint_c_v 5 +\chardef\xint_c_vi 6 +\chardef\xint_c_vii 7 \chardef\xint_c_viii 8 \newtoks\XINT_toks +\xint_firstofone{\let\XINT_sptoken= } %<- space here! % \end{macrocode} % \subsection{ \csh{xintodef}, \csh{xintgodef}, \csh{odef}} % \lverb|1.09i. For use in \xintAssign. No parameter text! 1.09j uses \xint... @@ -11275,39 +11599,39 @@ first place. % 1.06: improved code is roughly 20$% faster than the one from earlier % versions. 1.09a, \xintnum inserted. 1.09e: \Z->\xint_bye as this is called % from \xintNthElt, and there it was necessary not to use \Z. Later use of \Z -% and \W perfectly safe here.| +% and \W perfectly safe here. Very minor optimization in 1.09m.| % \begin{macrocode} \def\xintLength {\romannumeral0\xintlength }% \long\def\xintlength #1% {% \XINT_length_loop - {0}#1\xint_relax\xint_relax\xint_relax\xint_relax + 0.#1\xint_relax\xint_relax\xint_relax\xint_relax \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye }% -\long\def\XINT_length_loop #1#2#3#4#5#6#7#8#9% +\long\def\XINT_length_loop #1.#2#3#4#5#6#7#8#9% {% \xint_gob_til_xint_relax #9\XINT_length_finish_a\xint_relax - \expandafter\XINT_length_loop\expandafter {\the\numexpr #1+8\relax}% + \expandafter\XINT_length_loop\the\numexpr #1+\xint_c_viii.% }% -\def\XINT_length_finish_a\xint_relax - \expandafter\XINT_length_loop\expandafter #1#2\xint_bye +\def\XINT_length_finish_a\xint_relax\expandafter\XINT_length_loop + \the\numexpr #1+\xint_c_viii.#2\xint_bye {% \XINT_length_finish_b #2\W\W\W\W\W\W\W\Z {#1}% }% \def\XINT_length_finish_b #1#2#3#4#5#6#7#8\Z {% \xint_gob_til_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 + #1\XINT_length_finish_c \xint_c_ + #2\XINT_length_finish_c \xint_c_i + #3\XINT_length_finish_c \xint_c_ii + #4\XINT_length_finish_c \xint_c_iii + #5\XINT_length_finish_c \xint_c_iv + #6\XINT_length_finish_c \xint_c_v + #7\XINT_length_finish_c \xint_c_vi + \W\XINT_length_finish_c \xint_c_vii\Z }% \edef\XINT_length_finish_c #1#2\Z #3% - {\noexpand\expandafter\space\noexpand\the\numexpr #3-#1\relax}% + {\noexpand\expandafter\space\noexpand\the\numexpr #3+#1\relax}% % \end{macrocode} % \subsection{\csh{xintZapFirstSpaces}} % \lverb|1.09f, written [2013/11/01].| @@ -11580,89 +11904,274 @@ first place. \long\def\XINT_lws_end\xint_bye\XINT_lws_loop_b #1#2#3{ #1}% % \end{macrocode} % \subsection{\csh{xintNthElt}} -% \lverb|& -% \xintNthElt {i}{{a}{b}...{z}} (or `tokens' abcd...z) returns the i th -% element (one pair of braces removed). The list is first expanded. -% First included in release 1.06. With 1.06a, a value of i = 0 (or negative) -% makes the macro return the length. This is different from \xintLen which is -% for numbers (checks sign) and different from \xintLength which does not first -% expand its argument. With 1.09b, only i=0 gives the length, negative values -% return the i th element from the end. 1.09c has some slightly less quick -% initial preparation (if #2 is very long, not good to have it twice), I wanted -% to respect the noexpand directive in all cases, and the alternative would be -% to define more macros. -% -% At some point I turned the \W's into \xint_relax's but forgot to modify -% accordingly \XINT_nthelt_finish. So in case the index is larger than the -% number of items the macro returned was an \xint_relax token rather than -% nothing. Fixed in 1.09e. I also take the opportunity of this fix to replace -% uses of \Z by \xint_bye. (and as a result I must do the change also in -% \XINT_length_loop and related macros). -% | +% \lverb+& +% First included in release 1.06. +% +% \xintNthElt {i}{stuff expanding to {a}{b}...{z}} (or `tokens' abcd...z)returns +% the i th element (one pair of braces removed). The list is first expanded. The +% \xintNthEltNoExpand does no expansion of its second argument. Both variants +% expand the first argument inside \numexpr. +% +% With i = 0, the number of items is returned. This is different from \xintLen +% which is only for numbers (particularly, it checks the sign) and different +% from \xintLength which does not first expand its argument. +% +% Negative values return the |i|th element from the end. Release 1.09m +% rewrote the initial bits of the code (which checked the sign of #1 and +% expanded or not #2), ome `improvements' made earlier in 1.09c were quite +% sub-efficient. Now uses \xint_UDzerominusfork, moved from xint.sty.+ % \begin{macrocode} \def\xintNthElt {\romannumeral0\xintnthelt }% \def\xintNthEltNoExpand {\romannumeral0\xintntheltnoexpand }% -\def\xintnthelt #1% +\def\xintnthelt #1#2% {% - \expandafter\XINT_nthelt_a\expandafter {\the\numexpr #1}% + \expandafter\XINT_nthelt_a\the\numexpr #1\expandafter.% + \expandafter{\romannumeral-`0#2}% }% \def\xintntheltnoexpand #1% {% - \expandafter\XINT_ntheltnoexpand_a\expandafter {\the\numexpr #1}% + \expandafter\XINT_nthelt_a\the\numexpr #1.% }% -\long\def\XINT_nthelt_a #1#2% +\def\XINT_nthelt_a #1#2.% {% - \ifnum #1<0 - \xint_afterfi{\expandafter\XINT_nthelt_c\expandafter - {\romannumeral0\xintrevwithbraces {#2}}{-#1}}% - \else - \xint_afterfi{\expandafter\XINT_nthelt_c\expandafter - {\romannumeral-`0#2}{#1}}% - \fi + \xint_UDzerominusfork + #1-{\XINT_nthelt_bzero}% + 0#1{\XINT_nthelt_bneg {#2}}% + 0-{\XINT_nthelt_bpos {#1#2}}% + \krof }% -\long\def\XINT_ntheltnoexpand_a #1#2% +\long\def\XINT_nthelt_bzero #1% {% - \ifnum #1<0 - \xint_afterfi{\expandafter\XINT_nthelt_c\expandafter - {\romannumeral0\xintrevwithbracesnoexpand {#2}}{-#1}}% - \else - \xint_afterfi{\expandafter\XINT_nthelt_c\expandafter - {#2}{#1}}% - \fi + \XINT_length_loop 0.#1\xint_relax\xint_relax\xint_relax\xint_relax + \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye }% -\long\def\XINT_nthelt_c #1#2% +\long\def\XINT_nthelt_bneg #1#2% {% - \ifnum #2>\xint_c_ - \expandafter\XINT_nthelt_loop_a - \else - \expandafter\XINT_length_loop - \fi {#2}#1\xint_relax\xint_relax\xint_relax\xint_relax + \expandafter\XINT_nthelt_loop_a\expandafter {\the\numexpr #1\expandafter}% + \romannumeral0\xintrevwithbracesnoexpand {#2}% + \xint_relax\xint_relax\xint_relax\xint_relax \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye }% +\long\def\XINT_nthelt_bpos #1#2% +{% + \XINT_nthelt_loop_a {#1}#2\xint_relax\xint_relax\xint_relax\xint_relax + \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye +}% \def\XINT_nthelt_loop_a #1% {% \ifnum #1>\xint_c_viii \expandafter\XINT_nthelt_loop_b \else - \expandafter\XINT_nthelt_getit + \XINT_nthelt_getit \fi {#1}% }% \long\def\XINT_nthelt_loop_b #1#2#3#4#5#6#7#8#9% {% \xint_gob_til_xint_relax #9\XINT_nthelt_silentend\xint_relax - \expandafter\XINT_nthelt_loop_a\expandafter{\the\numexpr #1-8}% + \expandafter\XINT_nthelt_loop_a\expandafter{\the\numexpr #1-\xint_c_viii}% }% \def\XINT_nthelt_silentend #1\xint_bye { }% -\def\XINT_nthelt_getit #1% +\def\XINT_nthelt_getit\fi #1% {% - \expandafter\expandafter\expandafter\XINT_nthelt_finish - \csname xint_gobble_\romannumeral\numexpr#1-1\endcsname + \fi\expandafter\expandafter\expandafter\XINT_nthelt_finish + \csname xint_gobble_\romannumeral\numexpr#1-\xint_c_i\endcsname }% \long\edef\XINT_nthelt_finish #1#2\xint_bye {\noexpand\xint_gob_til_xint_relax #1\noexpand\expandafter\space \noexpand\xint_gobble_iii\xint_relax\space #1}% % \end{macrocode} +% \subsection{\csh{xintKeep}} +% \lverb+& +% First included in release 1.09m. +% +% \xintKeep {i}{stuff expanding to {a}{b}...{z}} (or `tokens' abcd...z, +% but each naked token ends up braced in the output) returns (in two +% expansion steps) the first i elements from the list, which is first +% f-expanded. The i is expanded inside \numexpr. Variant +% \xintKeepNoExpand does not expand the list argument. +% +% With i = 0, the empty sequence is returned. +% +% With i<0, the last |i| elements are returned (in the same order as in +% the original list). +% +% With |i| equal to or bigger than the length of the (f-expanded) list, +% the full list is returned.+ +% \begin{macrocode} +\def\xintKeep {\romannumeral0\xintkeep }% +\def\xintKeepNoExpand {\romannumeral0\xintkeepnoexpand }% +\def\xintkeep #1#2% +{% + \expandafter\XINT_keep_a\the\numexpr #1\expandafter.% + \expandafter{\romannumeral-`0#2}% +}% +\def\xintkeepnoexpand #1% +{% + \expandafter\XINT_keep_a\the\numexpr #1.% +}% +\def\XINT_keep_a #1#2.% +{% + \xint_UDzerominusfork + #1-{\expandafter\space\xint_gobble_i }% + 0#1{\XINT_keep_bneg_a {#2}}% + 0-{\XINT_keep_bpos {#1#2}}% + \krof +}% +\long\def\XINT_keep_bneg_a #1#2% +{% + \expandafter\XINT_keep_bneg_b \the\numexpr \xintLength{#2}-#1.{#2}% +}% +\def\XINT_keep_bneg_b #1#2.% +{% + \xint_UDzerominusfork + #1-{\xint_firstofone_thenstop }% + 0#1{\xint_firstofone_thenstop }% + 0-{\XINT_trim_bpos {#1#2}}% + \krof +}% +\long\def\XINT_keep_bpos #1#2% +{% + \XINT_keep_loop_a {#1}{}#2\xint_relax\xint_relax\xint_relax\xint_relax + \xint_relax\xint_relax\xint_relax\xint_bye +}% +\def\XINT_keep_loop_a #1% +{% + \ifnum #1>\xint_c_vi + \expandafter\XINT_keep_loop_b + \else + \XINT_keep_finish + \fi + {#1}% +}% +\long\def\XINT_keep_loop_b #1#2#3#4#5#6#7#8#9% +{% + \xint_gob_til_xint_relax #9\XINT_keep_enda\xint_relax + \expandafter\XINT_keep_loop_c\expandafter{\the\numexpr #1-\xint_c_vii}% + {{#3}{#4}{#5}{#6}{#7}{#8}{#9}}{#2}% +}% +\long\def\XINT_keep_loop_c #1#2#3{\XINT_keep_loop_a {#1}{#3#2}}% +\long\def\XINT_keep_enda\xint_relax + \expandafter\XINT_keep_loop_c\expandafter #1#2#3#4\xint_bye +{% + \XINT_keep_endb #4\W\W\W\W\W\W\Z #2{#3}% +}% +\def\XINT_keep_endb #1#2#3#4#5#6#7\Z +{% + \xint_gob_til_W + #1\XINT_keep_endc_ + #2\XINT_keep_endc_i + #3\XINT_keep_endc_ii + #4\XINT_keep_endc_iii + #5\XINT_keep_endc_iv + #6\XINT_keep_endc_v + \W\XINT_keep_endc_vi\Z +}% +\long\def\XINT_keep_endc_ #1\Z #2#3#4#5#6#7#8#9{ #9}% +\long\def\XINT_keep_endc_i #1\Z #2#3#4#5#6#7#8#9{ #9{#2}}% +\long\def\XINT_keep_endc_ii #1\Z #2#3#4#5#6#7#8#9{ #9{#2}{#3}}% +\long\def\XINT_keep_endc_iii #1\Z #2#3#4#5#6#7#8#9{ #9{#2}{#3}{#4}}% +\long\def\XINT_keep_endc_iv #1\Z #2#3#4#5#6#7#8#9{ #9{#2}{#3}{#4}{#5}}% +\long\def\XINT_keep_endc_v #1\Z #2#3#4#5#6#7#8#9{ #9{#2}{#3}{#4}{#5}{#6}}% +\long\def\XINT_keep_endc_vi\Z #1#2#3#4#5#6#7#8{ #8{#1}{#2}{#3}{#4}{#5}{#6}}% +\long\def\XINT_keep_finish\fi #1#2#3#4#5#6#7#8#9\xint_bye +{% + \fi\XINT_keep_finish_loop_a {#1}{}{#3}{#4}{#5}{#6}{#7}{#8}\Z {#2}% +}% +\def\XINT_keep_finish_loop_a #1% +{% + \xint_gob_til_zero #1\XINT_keep_finish_z0% + \expandafter\XINT_keep_finish_loop_b\expandafter + {\the\numexpr #1-\xint_c_i}% +}% +\long\def\XINT_keep_finish_z0% + \expandafter\XINT_keep_finish_loop_b\expandafter #1#2#3\Z #4{ #4#2}% +\long\def\XINT_keep_finish_loop_b #1#2#3% +{% + \xint_gob_til_xint_relax #3\XINT_keep_finish_exit\xint_relax + \XINT_keep_finish_loop_c {#1}{#2}{#3}% +}% +\long\def\XINT_keep_finish_exit\xint_relax + \XINT_keep_finish_loop_c #1#2#3\Z #4{ #4#2}% +\long\def\XINT_keep_finish_loop_c #1#2#3% + {\XINT_keep_finish_loop_a {#1}{#2{#3}}}% +% \end{macrocode} +% \subsection{\csh{xintTrim}} +% \lverb+& +% First included in release 1.09m. +% +% \xintTrim {i}{stuff expanding to {a}{b}...{z}} (or `tokens' abcd...z, +% but each naked token ends up braced in the output) returns (in two +% expansion steps) the sequence with the first i elements omitted. The +% list is first f-expanded. The i is expanded inside \numexpr. Variant +% \xintTrimNoExpand does not expand the list argument. +% +% With i = 0, the original (expanded) list is returned. +% +% With i<0, the last |i| elements from the tail are suppressed. +% +% With |i| equal to or bigger than the length of the (f-expanded) list, +% the empty list is returned.+ +% \begin{macrocode} +\def\xintTrim {\romannumeral0\xinttrim }% +\def\xintTrimNoExpand {\romannumeral0\xinttrimnoexpand }% +\def\xinttrim #1#2% +{% + \expandafter\XINT_trim_a\the\numexpr #1\expandafter.% + \expandafter{\romannumeral-`0#2}% +}% +\def\xinttrimnoexpand #1% +{% + \expandafter\XINT_trim_a\the\numexpr #1.% +}% +\def\XINT_trim_a #1#2.% +{% + \xint_UDzerominusfork + #1-{\xint_firstofone_thenstop }% + 0#1{\XINT_trim_bneg_a {#2}}% + 0-{\XINT_trim_bpos {#1#2}}% + \krof +}% +\long\def\XINT_trim_bneg_a #1#2% +{% + \expandafter\XINT_trim_bneg_b \the\numexpr \xintLength{#2}-#1.{#2}% +}% +\def\XINT_trim_bneg_b #1#2.% +{% + \xint_UDzerominusfork + #1-{\expandafter\space\xint_gobble_i }% + 0#1{\expandafter\space\xint_gobble_i }% + 0-{\XINT_keep_bpos {#1#2}}% + \krof +}% +\long\def\XINT_trim_bpos #1#2% +{% + \XINT_trim_loop_a {#1}#2\xint_relax\xint_relax\xint_relax\xint_relax + \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye +}% +\def\XINT_trim_loop_a #1% +{% + \ifnum #1>\xint_c_vii + \expandafter\XINT_trim_loop_b + \else + \XINT_trim_finish + \fi + {#1}% +}% +\long\def\XINT_trim_loop_b #1#2#3#4#5#6#7#8#9% +{% + \xint_gob_til_xint_relax #9\XINT_trim_silentend\xint_relax + \expandafter\XINT_trim_loop_a\expandafter{\the\numexpr #1-\xint_c_viii}% +}% +\def\XINT_trim_silentend #1\xint_bye { }% +\def\XINT_trim_finish\fi #1% +{% + \fi\expandafter\expandafter\expandafter\XINT_trim_finish_a + \expandafter\expandafter\expandafter\space % avoids brace removal + \csname xint_gobble_\romannumeral\numexpr#1\endcsname +}% +\long\def\XINT_trim_finish_a #1\xint_relax #2\xint_bye {#1}% +% \end{macrocode} % \subsection{\csh{xintApply}} % \lverb|& % \xintApply {\macro}{{a}{b}...{z}} returns {\macro{a}}...{\macro{b}} @@ -12508,6 +13017,7 @@ first place. % notation; also this is what |xintfrac.sty| did all along. Simplifies the % discussion in the documentation too. % +% % \localtableofcontents % % \subsection{Catcodes, \protect\eTeX{} and reload detection} @@ -12605,7 +13115,7 @@ first place. % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xint}% - [2014/02/13 v1.09kb Expandable operations on long numbers (jfB)]% + [2014/02/26 v1.09m Expandable operations on long numbers (jfB)]% % \end{macrocode} % \subsection{Token management, constants} % \begin{macrocode} @@ -12615,7 +13125,7 @@ first place. \long\def\xint_firstofthree_thenstop #1#2#3{ #1}% 1.09i \long\def\xint_secondofthree_thenstop #1#2#3{ #2}% \long\def\xint_thirdofthree_thenstop #1#2#3{ #3}% -\def\xint_gob_til_zero #10{}% +%\def\xint_gob_til_zero #10{}% moved to xinttools \def\xint_gob_til_zeros_iii #1000{}% \def\xint_gob_til_zeros_iv #10000{}% \def\xint_gob_til_one #11{}% @@ -12629,17 +13139,8 @@ first place. \def\xint_UDwfork #1\W#2#3\krof {#2}% \def\xint_UDzerosfork #100#2#3\krof {#2}% \def\xint_UDonezerofork #110#2#3\krof {#2}% -\def\xint_UDzerominusfork #10-#2#3\krof {#2}% +%\def\xint_UDzerominusfork #10-#2#3\krof {#2}% moved to xinttools \def\xint_UDsignsfork #1--#2#3\krof {#2}% -% \chardef\xint_c_ 0 % already done in xinttools -% \chardef\xint_c_i 1 % already done in xinttools -\chardef\xint_c_ii 2 -\chardef\xint_c_iii 3 -\chardef\xint_c_iv 4 -\chardef\xint_c_v 5 -% \chardef\xint_c_vi 6 % will be done in xintfrac -% \chardef\xinf_c_vii 7 % will be done in xintfrac -% \chardef\xint_c_viii 8 % already done in xinttools \chardef\xint_c_ix 9 \chardef\xint_c_x 10 \chardef\xint_c_ii^v 32 % not used in xint, common to xintfrac and xintbinhex @@ -12694,8 +13195,8 @@ first place. {% \expandafter\XINT_length_loop \xint_UDsignfork - #1{{0}}% - -{{0}#1}% + #1{0.}% + -{0.#1}% \krof }% % \end{macrocode} @@ -15328,30 +15829,33 @@ first place. % small to medium sized inputs (up to 30$% perhaps). And in passing I did a % special routine for divisors < 10000, which is 5 to 10 times faster still. % -% But, I then tested a variant of my new implementation which again did not -% impact the input save stack and, for sizes of up to 200 digits, it is not much -% worse, indeed it is perhaps actually better than the one abandoning the -% quotient digits upstream (and in the end putting them in the correct order). -% So, finally, I re-incorporated the produced quotient digits within a tail -% recursion. Hence \xintDivision, like all other routines in xint (except -% \xintSeq without optional parameter) still does not impact the input save -% stack. One can have a produced quotient longer than 4x5000=20000 digits, and -% no need to worry about \xintTrunc, \xintRound, \xintFloat, \xintFloatSqrt, -% etc... and all other places using the division. -% -% However outputting to a file (which is basically the only thing one can do, -% multiplying out two 20000 digits numbers already takes hours, for 100000 it -% would be days if not weeks) 100000 digits is slow... the truncation routine -% will add 100000 zeros (circa) and then trim them four by four. Definitely I -% should do a routine XTrunc which will work by blocks of say 64, and -% furthermore, being destined to be used in and \edef or a \write, it could be -% much more efficient as it could simply be based on tail loop, which so far -% nothing in xint does because I want things to expand fully under -% \romannumeral-`0 (and don't imagine inserting chains of thousands of -% \expandafter's...) in order to be nestable. Inside \xintexpr such style of -% tail recursion leaving downstream things should definitely be implemented for -% the routines for which it is possible as things get expanded inside -% \csname..\endcsname. I don't do yet anything like this for 1.09j. | +% But, I then tested a variant of my new implementation which again did +% not impact the input save stack and, for sizes of up to 200 digits, it +% is not much worse, indeed it is perhaps actually better than the one +% abandoning the quotient digits upstream (and in the end putting them +% in the correct order). So, finally, I re-incorporated the produced +% quotient digits within a tail recursion. Hence \xintDivision, like all +% other routines in xint (except \xintSeq without optional parameter) +% still does not impact the input save stack. One can have a produced +% quotient longer than 4x5000=20000 digits, and no need to worry about +% consequences propagating to \xintTrunc, \xintRound, \xintFloat, +% \xintFloatSqrt, etc... and all other places using the division. See +% also \xintXTrunc in this context. +% +% & However outputting to a file (which is basically the only thing one can do, +% & multiplying out two 20000 digits numbers already takes hours, for 100000 it +% & would be days if not weeks) 100000 digits is slow... the truncation routine +% & will add 100000 zeros (circa) and then trim them four by four. Definitely I +% & should do a routine XTrunc which will work by blocks of say 64, and +% & furthermore, being destined to be used in and \edef or a \write, it could be +% & much more efficient as it could simply be based on tail loop, which so far +% & nothing in xint does because I want things to expand fully under +% & \romannumeral-`0 (and don't imagine inserting chains of thousands of +% & \expandafter's...) in order to be nestable. Inside \xintexpr such style of +% & tail recursion leaving downstream things should definitely be implemented for +% & the routines for which it is possible as things get expanded inside +% & \csname..\endcsname. I don't do yet anything like this for 1.09j. +% | % \begin{macrocode} \def\xintiiQuo {\romannumeral0\xintiiquo }% \def\xintiiRem {\romannumeral0\xintiirem }% @@ -17260,7 +17764,7 @@ first place. % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xintbinhex}% - [2014/02/13 v1.09kb Expandable binary and hexadecimal conversions (jfB)]% + [2014/02/26 v1.09m Expandable binary and hexadecimal conversions (jfB)]% % \end{macrocode} % \subsection{Constants, etc...} % \lverb!v1.08! @@ -17966,7 +18470,7 @@ first place. % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xintgcd}% - [2014/02/13 v1.09kb Euclide algorithm with xint package (jfB)]% + [2014/02/26 v1.09m Euclide algorithm with xint package (jfB)]% % \end{macrocode} % \subsection{\csh{xintGCD}} % The macros of |1.09a| benefits from the |\xintnum| which has been inserted @@ -18685,9 +19189,7 @@ first place. % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xintfrac}% - [2014/02/13 v1.09kb Expandable operations on fractions (jfB)]% -\chardef\xint_c_vi 6 -\chardef\xint_c_vii 7 + [2014/02/26 v1.09m Expandable operations on fractions (jfB)]% \chardef\xint_c_xviii 18 % \end{macrocode} % \subsection{\csh{xintLen}} @@ -19287,7 +19789,13 @@ first place. % 1.09i also adds \xintFloatE and modifies \XINTinFloatfE, although currently % the latter is only used from \xintfloatexpr hence always with \XINTdigits, it % comes equipped with its first argument withing brackets as the other -% \XINTinFloat... macros. | +% \XINTinFloat... macros. +% +% 1.09m ceases here and elsewhere, also in \xintcfracname, to use \Z as +% delimiter in the code for the optional argument, as this is unsafe (it +% makes impossible to the user to employ \Z as argument to the macro). +% Replaced by \xint_relax. 1.09e had already done that in \xintSeq, but +% this should have been systematic. | % \begin{macrocode} \def\xintE {\romannumeral0\xinte }% \def\xinte #1% @@ -19309,19 +19817,19 @@ first place. \expandafter\XINT_e_end\expandafter{\the\numexpr #1+\xintNum{#4}}{#2}{#3}% }% \def\xintFloatE {\romannumeral0\xintfloate }% -\def\xintfloate #1{\XINT_floate_chkopt #1\Z }% +\def\xintfloate #1{\XINT_floate_chkopt #1\xint_relax }% \def\XINT_floate_chkopt #1% {% \ifx [#1\expandafter\XINT_floate_opt \else\expandafter\XINT_floate_noopt \fi #1% }% -\def\XINT_floate_noopt #1\Z +\def\XINT_floate_noopt #1\xint_relax {% \expandafter\XINT_floate_a\expandafter\XINTdigits \romannumeral0\XINT_infrac {#1}% }% -\def\XINT_floate_opt [\Z #1]#2% +\def\XINT_floate_opt [\xint_relax #1]#2% {% \expandafter\XINT_floate_a\expandafter {\the\numexpr #1\expandafter}\romannumeral0\XINT_infrac {#2}% @@ -19772,7 +20280,7 @@ first place. % \xintDecSplit for that on Q . Computing the length M of Q was a more or less % unavoidable step. If |N|>D, the \csname step is skipped we need to remove the % D-|N| last digits from Q, etc.. we compare D-|N| with the length M of Q etc... -% (well in this last, very uncommon, branch, I stopped trying to optimize thinsg +% (well in this last, very uncommon, branch, I stopped trying to optimize things % and I even do an \xintnum to ensure a 0 if something comes out empty from % \xintDecSplit).| % \begin{macrocode} @@ -20042,19 +20550,19 @@ first place. % in 1.09a, 1.09f reinstalled use of \xintiiquo without this overhead.| % \begin{macrocode} \def\xintFloat {\romannumeral0\xintfloat }% -\def\xintfloat #1{\XINT_float_chkopt #1\Z }% +\def\xintfloat #1{\XINT_float_chkopt #1\xint_relax }% \def\XINT_float_chkopt #1% {% \ifx [#1\expandafter\XINT_float_opt \else\expandafter\XINT_float_noopt \fi #1% }% -\def\XINT_float_noopt #1\Z +\def\XINT_float_noopt #1\xint_relax {% \expandafter\XINT_float_a\expandafter\XINTdigits \romannumeral0\XINT_infrac {#1}\XINT_float_Q }% -\def\XINT_float_opt [\Z #1]#2% +\def\XINT_float_opt [\xint_relax #1]#2% {% \expandafter\XINT_float_a\expandafter {\the\numexpr #1\expandafter}% @@ -20844,20 +21352,20 @@ first place. % \XINT_FL_Add_d.| % \begin{macrocode} \def\xintFloatAdd {\romannumeral0\xintfloatadd }% -\def\xintfloatadd #1{\XINT_fladd_chkopt \xintfloat #1\Z }% +\def\xintfloatadd #1{\XINT_fladd_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatAdd {\romannumeral0\XINTinfloatadd }% -\def\XINTinfloatadd #1{\XINT_fladd_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatadd #1{\XINT_fladd_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_fladd_chkopt #1#2% {% \ifx [#2\expandafter\XINT_fladd_opt \else\expandafter\XINT_fladd_noopt \fi #1#2% }% -\def\XINT_fladd_noopt #1#2\Z #3% +\def\XINT_fladd_noopt #1#2\xint_relax #3% {% #1[\XINTdigits]{\XINT_FL_Add {\XINTdigits+\xint_c_ii}{#2}{#3}}% }% -\def\XINT_fladd_opt #1[\Z #2]#3#4% +\def\XINT_fladd_opt #1[\xint_relax #2]#3#4% {% #1[#2]{\XINT_FL_Add {#2+\xint_c_ii}{#3}{#4}}% }% @@ -20896,20 +21404,20 @@ first place. % \lverb|1.07| % \begin{macrocode} \def\xintFloatSub {\romannumeral0\xintfloatsub }% -\def\xintfloatsub #1{\XINT_flsub_chkopt \xintfloat #1\Z }% +\def\xintfloatsub #1{\XINT_flsub_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatSub {\romannumeral0\XINTinfloatsub }% -\def\XINTinfloatsub #1{\XINT_flsub_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatsub #1{\XINT_flsub_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_flsub_chkopt #1#2% {% \ifx [#2\expandafter\XINT_flsub_opt \else\expandafter\XINT_flsub_noopt \fi #1#2% }% -\def\XINT_flsub_noopt #1#2\Z #3% +\def\XINT_flsub_noopt #1#2\xint_relax #3% {% #1[\XINTdigits]{\XINT_FL_Add {\XINTdigits+\xint_c_ii}{#2}{\xintOpp{#3}}}% }% -\def\XINT_flsub_opt #1[\Z #2]#3#4% +\def\XINT_flsub_opt #1[\xint_relax #2]#3#4% {% #1[#2]{\XINT_FL_Add {#2+\xint_c_ii}{#3}{\xintOpp{#4}}}% }% @@ -20918,20 +21426,20 @@ first place. % \lverb|1.07| % \begin{macrocode} \def\xintFloatMul {\romannumeral0\xintfloatmul}% -\def\xintfloatmul #1{\XINT_flmul_chkopt \xintfloat #1\Z }% +\def\xintfloatmul #1{\XINT_flmul_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatMul {\romannumeral0\XINTinfloatmul }% -\def\XINTinfloatmul #1{\XINT_flmul_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatmul #1{\XINT_flmul_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_flmul_chkopt #1#2% {% \ifx [#2\expandafter\XINT_flmul_opt \else\expandafter\XINT_flmul_noopt \fi #1#2% }% -\def\XINT_flmul_noopt #1#2\Z #3% +\def\XINT_flmul_noopt #1#2\xint_relax #3% {% #1[\XINTdigits]{\XINT_FL_Mul {\XINTdigits+\xint_c_ii}{#2}{#3}}% }% -\def\XINT_flmul_opt #1[\Z #2]#3#4% +\def\XINT_flmul_opt #1[\xint_relax #2]#3#4% {% #1[#2]{\XINT_FL_Mul {#2+\xint_c_ii}{#3}{#4}}% }% @@ -20950,20 +21458,20 @@ first place. % \lverb|1.07| % \begin{macrocode} \def\xintFloatDiv {\romannumeral0\xintfloatdiv}% -\def\xintfloatdiv #1{\XINT_fldiv_chkopt \xintfloat #1\Z }% +\def\xintfloatdiv #1{\XINT_fldiv_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatDiv {\romannumeral0\XINTinfloatdiv }% -\def\XINTinfloatdiv #1{\XINT_fldiv_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatdiv #1{\XINT_fldiv_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_fldiv_chkopt #1#2% {% \ifx [#2\expandafter\XINT_fldiv_opt \else\expandafter\XINT_fldiv_noopt \fi #1#2% }% -\def\XINT_fldiv_noopt #1#2\Z #3% +\def\XINT_fldiv_noopt #1#2\xint_relax #3% {% #1[\XINTdigits]{\XINT_FL_Div {\XINTdigits+\xint_c_ii}{#2}{#3}}% }% -\def\XINT_fldiv_opt #1[\Z #2]#3#4% +\def\XINT_fldiv_opt #1[\xint_relax #2]#3#4% {% #1[#2]{\XINT_FL_Div {#2+\xint_c_ii}{#3}{#4}}% }% @@ -21017,9 +21525,9 @@ first place. % \XINT_flpow_prd sub-routine has been removed.| % \begin{macrocode} \def\xintFloatPow {\romannumeral0\xintfloatpow}% -\def\xintfloatpow #1{\XINT_flpow_chkopt \xintfloat #1\Z }% +\def\xintfloatpow #1{\XINT_flpow_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatPow {\romannumeral0\XINTinfloatpow }% -\def\XINTinfloatpow #1{\XINT_flpow_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatpow #1{\XINT_flpow_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_flpow_chkopt #1#2% {% \ifx [#2\expandafter\XINT_flpow_opt @@ -21027,13 +21535,13 @@ first place. \fi #1#2% }% -\def\XINT_flpow_noopt #1#2\Z #3% +\def\XINT_flpow_noopt #1#2\xint_relax #3% {% \expandafter\XINT_flpow_checkB_start\expandafter {\the\numexpr #3\expandafter}\expandafter {\the\numexpr \XINTdigits}{#2}{#1[\XINTdigits]}% }% -\def\XINT_flpow_opt #1[\Z #2]#3#4% +\def\XINT_flpow_opt #1[\xint_relax #2]#3#4% {% \expandafter\XINT_flpow_checkB_start\expandafter {\the\numexpr #4\expandafter}\expandafter @@ -21165,9 +21673,9 @@ first place. % efficiency gain. | % \begin{macrocode} \def\xintFloatPower {\romannumeral0\xintfloatpower}% -\def\xintfloatpower #1{\XINT_flpower_chkopt \xintfloat #1\Z }% +\def\xintfloatpower #1{\XINT_flpower_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatPower {\romannumeral0\XINTinfloatpower}% -\def\XINTinfloatpower #1{\XINT_flpower_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatpower #1{\XINT_flpower_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_flpower_chkopt #1#2% {% \ifx [#2\expandafter\XINT_flpower_opt @@ -21175,13 +21683,13 @@ first place. \fi #1#2% }% -\def\XINT_flpower_noopt #1#2\Z #3% +\def\XINT_flpower_noopt #1#2\xint_relax #3% {% \expandafter\XINT_flpower_checkB_start\expandafter {\the\numexpr \XINTdigits\expandafter}\expandafter {\romannumeral0\xintnum{#3}}{#2}{#1[\XINTdigits]}% }% -\def\XINT_flpower_opt #1[\Z #2]#3#4% +\def\XINT_flpower_opt #1[\xint_relax #2]#3#4% {% \expandafter\XINT_flpower_checkB_start\expandafter {\the\numexpr #2\expandafter}\expandafter @@ -21285,20 +21793,20 @@ first place. % \lverb|1.08| % \begin{macrocode} \def\xintFloatSqrt {\romannumeral0\xintfloatsqrt }% -\def\xintfloatsqrt #1{\XINT_flsqrt_chkopt \xintfloat #1\Z }% +\def\xintfloatsqrt #1{\XINT_flsqrt_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatSqrt {\romannumeral0\XINTinfloatsqrt }% -\def\XINTinfloatsqrt #1{\XINT_flsqrt_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatsqrt #1{\XINT_flsqrt_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_flsqrt_chkopt #1#2% {% \ifx [#2\expandafter\XINT_flsqrt_opt \else\expandafter\XINT_flsqrt_noopt \fi #1#2% }% -\def\XINT_flsqrt_noopt #1#2\Z +\def\XINT_flsqrt_noopt #1#2\xint_relax {% #1[\XINTdigits]{\XINT_FL_sqrt \XINTdigits {#2}}% }% -\def\XINT_flsqrt_opt #1[\Z #2]#3% +\def\XINT_flsqrt_opt #1[\xint_relax #2]#3% {% #1[#2]{\XINT_FL_sqrt {#2}{#3}}% }% @@ -21723,7 +22231,7 @@ first place. % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xintseries}% - [2014/02/13 v1.09kb Expandable partial sums with xint package (jfB)]% + [2014/02/26 v1.09m Expandable partial sums with xint package (jfB)]% % \end{macrocode} % \subsection{\csh{xintSeries}} % \lverb|& @@ -22041,7 +22549,7 @@ first place. % just adapted the code to the case of floats.| % \begin{macrocode} \def\xintFloatPowerSeries {\romannumeral0\xintfloatpowerseries }% -\def\xintfloatpowerseries #1{\XINT_flpowseries_chkopt #1\Z }% +\def\xintfloatpowerseries #1{\XINT_flpowseries_chkopt #1\xint_relax }% \def\XINT_flpowseries_chkopt #1% {% \ifx [#1\expandafter\XINT_flpowseries_opt @@ -22049,13 +22557,13 @@ first place. \fi #1% }% -\def\XINT_flpowseries_noopt #1\Z #2% +\def\XINT_flpowseries_noopt #1\xint_relax #2% {% \expandafter\XINT_flpowseries\expandafter {\the\numexpr #1\expandafter}\expandafter {\the\numexpr #2}\XINTdigits }% -\def\XINT_flpowseries_opt [\Z #1]#2#3% +\def\XINT_flpowseries_opt [\xint_relax #1]#2#3% {% \expandafter\XINT_flpowseries\expandafter {\the\numexpr #2\expandafter}\expandafter @@ -22110,7 +22618,7 @@ first place. % \lverb|1.08a| % \begin{macrocode} \def\xintFloatPowerSeriesX {\romannumeral0\xintfloatpowerseriesx }% -\def\xintfloatpowerseriesx #1{\XINT_flpowseriesx_chkopt #1\Z }% +\def\xintfloatpowerseriesx #1{\XINT_flpowseriesx_chkopt #1\xint_relax }% \def\XINT_flpowseriesx_chkopt #1% {% \ifx [#1\expandafter\XINT_flpowseriesx_opt @@ -22118,13 +22626,13 @@ first place. \fi #1% }% -\def\XINT_flpowseriesx_noopt #1\Z #2% +\def\XINT_flpowseriesx_noopt #1\xint_relax #2% {% \expandafter\XINT_flpowseriesx\expandafter {\the\numexpr #1\expandafter}\expandafter {\the\numexpr #2}\XINTdigits }% -\def\XINT_flpowseriesx_opt [\Z #1]#2#3% +\def\XINT_flpowseriesx_opt [\xint_relax #1]#2#3% {% \expandafter\XINT_flpowseriesx\expandafter {\the\numexpr #2\expandafter}\expandafter @@ -22160,7 +22668,18 @@ first place. % \section{Package \xintcfracnameimp implementation} % \label{sec:cfracimp} % -% The commenting is currently (\docdate) very sparse. +% The commenting is currently (\docdate) very sparse. Release |1.09m| +% (|2014/02/26|) has modified a few things: |\xintFtoCs| and +% |\xintCntoCs| insert spaces after the commas, |\xintCstoF| and +% |\xintCstoCv| authorize spaces in the input also before the commas, +% |\xintCntoCs| does not brace the produced coefficients, new macros +% |\xintFtoC|, |\xintCtoF|, |\xintCtoCv|, |\xintFGtoC|, and +% |\xintGGCFrac|. All uses of |\W| and many instances of |\Z| as +% delimiters removed, this was in some cases not very safe (for example +% in the treatment of the optional arguments to some macros). Actually I +% have also replaced everywhere else in the bundle the use of |\Z| in +% the treatment of macros with optional arguments with the safer +% |\xint_relax| (the more recent |\xintSeq| already used |\xint_bye|). % % \localtableofcontents % \subsection{Catcodes, \protect\eTeX{} and reload detection} @@ -22258,25 +22777,25 @@ first place. % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xintcfrac}% - [2014/02/13 v1.09kb Expandable continued fractions with xint package (jfB)]% + [2014/02/26 v1.09m Expandable continued fractions with xint package (jfB)]% % \end{macrocode} % \subsection{\csh{xintCFrac}} % \begin{macrocode} \def\xintCFrac {\romannumeral0\xintcfrac }% \def\xintcfrac #1% {% - \XINT_cfrac_opt_a #1\Z + \XINT_cfrac_opt_a #1\xint_relax }% \def\XINT_cfrac_opt_a #1% {% \ifx[#1\XINT_cfrac_opt_b\fi \XINT_cfrac_noopt #1% }% -\def\XINT_cfrac_noopt #1\Z +\def\XINT_cfrac_noopt #1\xint_relax {% \expandafter\XINT_cfrac_A\romannumeral0\xintrawwithzeros {#1}\Z \relax\relax }% -\def\XINT_cfrac_opt_b\fi\XINT_cfrac_noopt [\Z #1]% +\def\XINT_cfrac_opt_b\fi\XINT_cfrac_noopt [\xint_relax #1]% {% \fi\csname XINT_cfrac_opt#1\endcsname }% @@ -22340,30 +22859,30 @@ first place. % \subsection{\csh{xintGCFrac}} % \begin{macrocode} \def\xintGCFrac {\romannumeral0\xintgcfrac }% -\def\xintgcfrac #1{\XINT_gcfrac_opt_a #1\Z }% +\def\xintgcfrac #1{\XINT_gcfrac_opt_a #1\xint_relax }% \def\XINT_gcfrac_opt_a #1% {% \ifx[#1\XINT_gcfrac_opt_b\fi \XINT_gcfrac_noopt #1% }% -\def\XINT_gcfrac_noopt #1\Z +\def\XINT_gcfrac_noopt #1\xint_relax {% - \XINT_gcfrac #1+\W/\relax\relax + \XINT_gcfrac #1+\xint_relax/\relax\relax }% -\def\XINT_gcfrac_opt_b\fi\XINT_gcfrac_noopt [\Z #1]% +\def\XINT_gcfrac_opt_b\fi\XINT_gcfrac_noopt [\xint_relax #1]% {% \fi\csname XINT_gcfrac_opt#1\endcsname }% \def\XINT_gcfrac_optl #1% {% - \XINT_gcfrac #1+\W/\relax\hfill + \XINT_gcfrac #1+\xint_relax/\relax\hfill }% \def\XINT_gcfrac_optc #1% {% - \XINT_gcfrac #1+\W/\relax\relax + \XINT_gcfrac #1+\xint_relax/\relax\relax }% \def\XINT_gcfrac_optr #1% {% - \XINT_gcfrac #1+\W/\hfill\relax + \XINT_gcfrac #1+\xint_relax/\hfill\relax }% \def\XINT_gcfrac {% @@ -22372,28 +22891,83 @@ first place. \def\XINT_gcfrac_enter {\XINT_gcfrac_loop {}}% \def\XINT_gcfrac_loop #1#2+#3/% {% - \xint_gob_til_W #3\XINT_gcfrac_endloop\W + \xint_gob_til_xint_relax #3\XINT_gcfrac_endloop\xint_relax \XINT_gcfrac_loop {{#3}{#2}#1}% }% -\def\XINT_gcfrac_endloop\W\XINT_gcfrac_loop #1#2#3% +\def\XINT_gcfrac_endloop\xint_relax\XINT_gcfrac_loop #1#2#3% {% - \XINT_gcfrac_T #2#3#1\Z\Z + \XINT_gcfrac_T #2#3#1\xint_relax\xint_relax }% \def\XINT_gcfrac_T #1#2#3#4{\XINT_gcfrac_U #1#2{\xintFrac{#4}}}% \def\XINT_gcfrac_U #1#2#3#4#5% {% - \xint_gob_til_Z #5\XINT_gcfrac_end\Z\XINT_gcfrac_U + \xint_gob_til_xint_relax #5\XINT_gcfrac_end\xint_relax\XINT_gcfrac_U #1#2{\xintFrac{#5}% \ifcase\xintSgn{#4} +\or+\else-\fi \cfrac{#1\xintFrac{\xintAbs{#4}}#2}{#3}}% }% -\def\XINT_gcfrac_end\Z\XINT_gcfrac_U #1#2#3% +\def\XINT_gcfrac_end\xint_relax\XINT_gcfrac_U #1#2#3% {% \XINT_gcfrac_end_b #3% }% \def\XINT_gcfrac_end_b #1\cfrac#2#3{ #3}% % \end{macrocode} +% \subsection{\csh{xintGGCFrac}} +% \lverb|New with 1.09m| +% \begin{macrocode} +\def\xintGGCFrac {\romannumeral0\xintggcfrac }% +\def\xintggcfrac #1{\XINT_ggcfrac_opt_a #1\xint_relax }% +\def\XINT_ggcfrac_opt_a #1% +{% + \ifx[#1\XINT_ggcfrac_opt_b\fi \XINT_ggcfrac_noopt #1% +}% +\def\XINT_ggcfrac_noopt #1\xint_relax +{% + \XINT_ggcfrac #1+\xint_relax/\relax\relax +}% +\def\XINT_ggcfrac_opt_b\fi\XINT_ggcfrac_noopt [\xint_relax #1]% +{% + \fi\csname XINT_ggcfrac_opt#1\endcsname +}% +\def\XINT_ggcfrac_optl #1% +{% + \XINT_ggcfrac #1+\xint_relax/\relax\hfill +}% +\def\XINT_ggcfrac_optc #1% +{% + \XINT_ggcfrac #1+\xint_relax/\relax\relax +}% +\def\XINT_ggcfrac_optr #1% +{% + \XINT_ggcfrac #1+\xint_relax/\hfill\relax +}% +\def\XINT_ggcfrac +{% + \expandafter\XINT_ggcfrac_enter\romannumeral-`0% +}% +\def\XINT_ggcfrac_enter {\XINT_ggcfrac_loop {}}% +\def\XINT_ggcfrac_loop #1#2+#3/% +{% + \xint_gob_til_xint_relax #3\XINT_ggcfrac_endloop\xint_relax + \XINT_ggcfrac_loop {{#3}{#2}#1}% +}% +\def\XINT_ggcfrac_endloop\xint_relax\XINT_ggcfrac_loop #1#2#3% +{% + \XINT_ggcfrac_T #2#3#1\xint_relax\xint_relax +}% +\def\XINT_ggcfrac_T #1#2#3#4{\XINT_ggcfrac_U #1#2{#4}}% +\def\XINT_ggcfrac_U #1#2#3#4#5% +{% + \xint_gob_til_xint_relax #5\XINT_ggcfrac_end\xint_relax\XINT_ggcfrac_U + #1#2{#5+\cfrac{#1#4#2}{#3}}% +}% +\def\XINT_ggcfrac_end\xint_relax\XINT_ggcfrac_U #1#2#3% +{% + \XINT_ggcfrac_end_b #3% +}% +\def\XINT_ggcfrac_end_b #1\cfrac#2#3{ #3}% +% \end{macrocode} % \subsection{\csh{xintGCtoGCx}} % \begin{macrocode} \def\xintGCtoGCx {\romannumeral0\xintgctogcx }% @@ -22401,19 +22975,20 @@ first place. {% \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_start #1#2#3{\XINT_gctgcx_loop_a {}{#2}{#3}#1+\xint_relax/}% \def\XINT_gctgcx_loop_a #1#2#3#4+#5/% {% - \xint_gob_til_W #5\XINT_gctgcx_end\W + \xint_gob_til_xint_relax #5\XINT_gctgcx_end\xint_relax \XINT_gctgcx_loop_b {#1{#4}}{#2{#5}#3}{#2}{#3}% }% \def\XINT_gctgcx_loop_b #1#2% {% \XINT_gctgcx_loop_a {#1#2}% }% -\def\XINT_gctgcx_end\W\XINT_gctgcx_loop_b #1#2#3#4{ #1}% +\def\XINT_gctgcx_end\xint_relax\XINT_gctgcx_loop_b #1#2#3#4{ #1}% % \end{macrocode} % \subsection{\csh{xintFtoCs}} +% \lverb|Modified in 1.09m: a space is added after the inserted commas.| % \begin{macrocode} \def\xintFtoCs {\romannumeral0\xintftocs }% \def\xintftocs #1% @@ -22433,7 +23008,7 @@ first place. \xint_gob_til_zero #1\XINT_ftc_integer 0\XINT_ftc_D #1% }% \def\XINT_ftc_integer 0\XINT_ftc_D 0#1.#2#3{ #2}% -\def\XINT_ftc_D #1.#2#3{\XINT_ftc_loop_a {#1}{#3}{#1}{#2,}}% +\def\XINT_ftc_D #1.#2#3{\XINT_ftc_loop_a {#1}{#3}{#1}{#2, }}% 1.09m adds a space \def\XINT_ftc_loop_a {% \expandafter\XINT_ftc_loop_d\romannumeral0\XINT_div_prepare @@ -22448,7 +23023,7 @@ first place. }% \def\XINT_ftc_loop_f #1.#2#3#4% {% - \XINT_ftc_loop_a {#1}{#3}{#1}{#4#2,}% + \XINT_ftc_loop_a {#1}{#3}{#1}{#4#2, }% 1.09m has an added space here }% \def\xint_ftc_loop_exit0\XINT_ftc_loop_f #1.#2#3#4{ #4#2}% % \end{macrocode} @@ -22472,7 +23047,7 @@ first place. \xint_gob_til_zero #1\XINT_ftcx_integer 0\XINT_ftcx_D #1% }% \def\XINT_ftcx_integer 0\XINT_ftcx_D 0#1.#2#3#4{ #2}% -\def\XINT_ftcx_D #1.#2#3#4{\XINT_ftcx_loop_a {#1}{#3}{#1}{#2#4}{#4}}% +\def\XINT_ftcx_D #1.#2#3#4{\XINT_ftcx_loop_a {#1}{#3}{#1}{{#2}#4}{#4}}% \def\XINT_ftcx_loop_a {% \expandafter\XINT_ftcx_loop_d\romannumeral0\XINT_div_prepare @@ -22491,11 +23066,71 @@ first place. }% \def\xint_ftcx_loop_exit0\XINT_ftcx_loop_f #1.#2#3#4#5{ #4{#2}}% % \end{macrocode} +% \subsection{\csh{xintFtoC}} +% \lverb|New in 1.09m: this is the same as \xintFtoCx with empty separator. I +% had temporarily during preparation of 1.09m removed braces from \xintFtoCx, +% but I recalled later why that was useful (see doc), thus let's just here do +% \xintFtoCx {}| +% \begin{macrocode} +\def\xintFtoC {\romannumeral0\xintftoc }% +\def\xintftoc {\xintftocx {}}% +% \end{macrocode} % \subsection{\csh{xintFtoGC}} % \begin{macrocode} \def\xintFtoGC {\romannumeral0\xintftogc }% \def\xintftogc {\xintftocx {+1/}}% % \end{macrocode} +% \subsection{\csh{xintFGtoC}} +% \lverb|New with 1.09m of 2014/02/26. Computes the common initial coefficients +% for the two fractions f and g, and outputs them as a sequence of braced +% items.| +% \begin{macrocode} +\def\xintFGtoC {\romannumeral0\xintfgtoc}% +\def\xintfgtoc#1% +{% + \expandafter\XINT_fgtc_a\romannumeral0\xintrawwithzeros {#1}\Z +}% +\def\XINT_fgtc_a #1/#2\Z #3% +{% + \expandafter\XINT_fgtc_b\romannumeral0\xintrawwithzeros {#3}\Z #1/#2\Z { }% +}% +\def\XINT_fgtc_b #1/#2\Z +{% + \expandafter\XINT_fgtc_c\romannumeral0\xintiidivision {#1}{#2}{#2}% +}% +\def\XINT_fgtc_c #1#2#3#4/#5\Z +{% + \expandafter\XINT_fgtc_d\romannumeral0\xintiidivision + {#4}{#5}{#5}{#1}{#2}{#3}% +}% +\def\XINT_fgtc_d #1#2#3#4%#5#6#7% +{% + \xintifEq {#1}{#4}{\XINT_fgtc_da {#1}{#2}{#3}{#4}}% + {\xint_thirdofthree}% +}% +\def\XINT_fgtc_da #1#2#3#4#5#6#7% +{% + \XINT_fgtc_e {#2}{#5}{#3}{#6}{#7{#1}}% +}% +\def\XINT_fgtc_e #1% +{% + \xintifZero {#1}{\expandafter\xint_firstofone\xint_gobble_iii}% + {\XINT_fgtc_f {#1}}% +}% +\def\XINT_fgtc_f #1#2% +{% + \xintifZero {#2}{\xint_thirdofthree}{\XINT_fgtc_g {#1}{#2}}% +}% +\def\XINT_fgtc_g #1#2#3% +{% + \expandafter\XINT_fgtc_h\romannumeral0\XINT_div_prepare {#1}{#3}{#1}{#2}% +}% +\def\XINT_fgtc_h #1#2#3#4#5% +{% + \expandafter\XINT_fgtc_d\romannumeral0\XINT_div_prepare + {#4}{#5}{#4}{#1}{#2}{#3}% +}% +% \end{macrocode} % \subsection{\csh{xintFtoCC}} % \begin{macrocode} \def\xintFtoCC {\romannumeral0\xintftocc }% @@ -22570,67 +23205,60 @@ first place. {\romannumeral0\xintdiv {1[0]}{#1}}{#3#2+-1/}% }% % \end{macrocode} -% \subsection{\csh{xintFtoCv}} -% \begin{macrocode} -\def\xintFtoCv {\romannumeral0\xintftocv }% -\def\xintftocv #1% -{% - \xinticstocv {\xintFtoCs {#1}}% -}% -% \end{macrocode} -% \subsection{\csh{xintFtoCCv}} -% \begin{macrocode} -\def\xintFtoCCv {\romannumeral0\xintftoccv }% -\def\xintftoccv #1% -{% - \xintigctocv {\xintFtoCC {#1}}% -}% -% \end{macrocode} -% \subsection{\csh{xintCstoF}} +% \subsection{\csh{xintCtoF}, \csh{xintCstoF}} +% \lverb|1.09m uses \xintCSVtoList on the argument of \xintCstoF to allow +% spaces also before the commas. And the original \xintCstoF code became the +% one of the new \xintCtoF dealing with a braced rather than comma separated +% list.| % \begin{macrocode} \def\xintCstoF {\romannumeral0\xintcstof }% \def\xintcstof #1% {% - \expandafter\XINT_cstf_prep \romannumeral-`0#1,\W,% + \expandafter\XINT_ctf_prep \romannumeral0\xintcsvtolist{#1}\xint_relax +}% +\def\xintCtoF {\romannumeral0\xintctof }% +\def\xintctof #1% +{% + \expandafter\XINT_ctf_prep \romannumeral-`0#1\xint_relax }% -\def\XINT_cstf_prep +\def\XINT_ctf_prep {% - \XINT_cstf_loop_a 1001% + \XINT_ctf_loop_a 1001% }% -\def\XINT_cstf_loop_a #1#2#3#4#5,% +\def\XINT_ctf_loop_a #1#2#3#4#5% {% - \xint_gob_til_W #5\XINT_cstf_end\W - \expandafter\XINT_cstf_loop_b + \xint_gob_til_xint_relax #5\XINT_ctf_end\xint_relax + \expandafter\XINT_ctf_loop_b \romannumeral0\xintrawwithzeros {#5}.{#1}{#2}{#3}{#4}% }% -\def\XINT_cstf_loop_b #1/#2.#3#4#5#6% +\def\XINT_ctf_loop_b #1/#2.#3#4#5#6% {% - \expandafter\XINT_cstf_loop_c\expandafter + \expandafter\XINT_ctf_loop_c\expandafter {\romannumeral0\XINT_mul_fork #2\Z #4\Z }% {\romannumeral0\XINT_mul_fork #2\Z #3\Z }% {\romannumeral0\xintiiadd {\XINT_Mul {#2}{#6}}{\XINT_Mul {#1}{#4}}}% {\romannumeral0\xintiiadd {\XINT_Mul {#2}{#5}}{\XINT_Mul {#1}{#3}}}% }% -\def\XINT_cstf_loop_c #1#2% +\def\XINT_ctf_loop_c #1#2% {% - \expandafter\XINT_cstf_loop_d\expandafter {\expandafter{#2}{#1}}% + \expandafter\XINT_ctf_loop_d\expandafter {\expandafter{#2}{#1}}% }% -\def\XINT_cstf_loop_d #1#2% +\def\XINT_ctf_loop_d #1#2% {% - \expandafter\XINT_cstf_loop_e\expandafter {\expandafter{#2}#1}% + \expandafter\XINT_ctf_loop_e\expandafter {\expandafter{#2}#1}% }% -\def\XINT_cstf_loop_e #1#2% +\def\XINT_ctf_loop_e #1#2% {% - \expandafter\XINT_cstf_loop_a\expandafter{#2}#1% + \expandafter\XINT_ctf_loop_a\expandafter{#2}#1% }% -\def\XINT_cstf_end #1.#2#3#4#5{\xintrawwithzeros {#2/#3}}% 1.09b removes [0] +\def\XINT_ctf_end #1.#2#3#4#5{\xintrawwithzeros {#2/#3}}% 1.09b removes [0] % \end{macrocode} % \subsection{\csh{xintiCstoF}} % \begin{macrocode} \def\xintiCstoF {\romannumeral0\xinticstof }% \def\xinticstof #1% {% - \expandafter\XINT_icstf_prep \romannumeral-`0#1,\W,% + \expandafter\XINT_icstf_prep \romannumeral-`0#1,\xint_relax,% }% \def\XINT_icstf_prep {% @@ -22638,7 +23266,7 @@ first place. }% \def\XINT_icstf_loop_a #1#2#3#4#5,% {% - \xint_gob_til_W #5\XINT_icstf_end\W + \xint_gob_til_xint_relax #5\XINT_icstf_end\xint_relax \expandafter \XINT_icstf_loop_b \romannumeral-`0#5.{#1}{#2}{#3}{#4}% }% @@ -22660,7 +23288,7 @@ first place. \def\xintGCtoF {\romannumeral0\xintgctof }% \def\xintgctof #1% {% - \expandafter\XINT_gctf_prep \romannumeral-`0#1+\W/% + \expandafter\XINT_gctf_prep \romannumeral-`0#1+\xint_relax/% }% \def\XINT_gctf_prep {% @@ -22693,7 +23321,7 @@ first place. }% \def\XINT_gctf_loop_f #1#2/% {% - \xint_gob_til_W #2\XINT_gctf_end\W + \xint_gob_til_xint_relax #2\XINT_gctf_end\xint_relax \expandafter\XINT_gctf_loop_g \romannumeral0\xintrawwithzeros {#2}.#1% }% @@ -22724,7 +23352,7 @@ first place. \def\xintiGCtoF {\romannumeral0\xintigctof }% \def\xintigctof #1% {% - \expandafter\XINT_igctf_prep \romannumeral-`0#1+\W/% + \expandafter\XINT_igctf_prep \romannumeral-`0#1+\xint_relax/% }% \def\XINT_igctf_prep {% @@ -22748,7 +23376,7 @@ first place. }% \def\XINT_igctf_loop_f #1#2#3#4/% {% - \xint_gob_til_W #4\XINT_igctf_end\W + \xint_gob_til_xint_relax #4\XINT_igctf_end\xint_relax \expandafter\XINT_igctf_loop_g \romannumeral-`0#4.{#2}{#3}#1% }% @@ -22768,57 +23396,66 @@ first place. }% \def\XINT_igctf_end #1.#2#3#4#5{\xintrawwithzeros {#4/#5}}% 1.09b removes [0] % \end{macrocode} -% \subsection{\csh{xintCstoCv}} +% \subsection{\csh{xintCtoCv}, \csh{xintCstoCv}} +% \lverb|1.09m uses \xintCSVtoList on the argument of \xintCstoCv to allow +% spaces also before the commas. The original \xintCstoCv code became the +% one of the new \xintCtoF dealing with a braced rather than comma separated +% list.| % \begin{macrocode} \def\xintCstoCv {\romannumeral0\xintcstocv }% \def\xintcstocv #1% {% - \expandafter\XINT_cstcv_prep \romannumeral-`0#1,\W,% + \expandafter\XINT_ctcv_prep\romannumeral0\xintcsvtolist{#1}\xint_relax }% -\def\XINT_cstcv_prep +\def\xintCtoCv {\romannumeral0\xintctocv }% +\def\xintctocv #1% {% - \XINT_cstcv_loop_a {}1001% + \expandafter\XINT_ctcv_prep\romannumeral-`0#1\xint_relax }% -\def\XINT_cstcv_loop_a #1#2#3#4#5#6,% +\def\XINT_ctcv_prep {% - \xint_gob_til_W #6\XINT_cstcv_end\W - \expandafter\XINT_cstcv_loop_b + \XINT_ctcv_loop_a {}1001% +}% +\def\XINT_ctcv_loop_a #1#2#3#4#5#6% +{% + \xint_gob_til_xint_relax #6\XINT_ctcv_end\xint_relax + \expandafter\XINT_ctcv_loop_b \romannumeral0\xintrawwithzeros {#6}.{#2}{#3}{#4}{#5}{#1}% }% -\def\XINT_cstcv_loop_b #1/#2.#3#4#5#6% +\def\XINT_ctcv_loop_b #1/#2.#3#4#5#6% {% - \expandafter\XINT_cstcv_loop_c\expandafter + \expandafter\XINT_ctcv_loop_c\expandafter {\romannumeral0\XINT_mul_fork #2\Z #4\Z }% {\romannumeral0\XINT_mul_fork #2\Z #3\Z }% {\romannumeral0\xintiiadd {\XINT_Mul {#2}{#6}}{\XINT_Mul {#1}{#4}}}% {\romannumeral0\xintiiadd {\XINT_Mul {#2}{#5}}{\XINT_Mul {#1}{#3}}}% }% -\def\XINT_cstcv_loop_c #1#2% +\def\XINT_ctcv_loop_c #1#2% {% - \expandafter\XINT_cstcv_loop_d\expandafter {\expandafter{#2}{#1}}% + \expandafter\XINT_ctcv_loop_d\expandafter {\expandafter{#2}{#1}}% }% -\def\XINT_cstcv_loop_d #1#2% +\def\XINT_ctcv_loop_d #1#2% {% - \expandafter\XINT_cstcv_loop_e\expandafter {\expandafter{#2}#1}% + \expandafter\XINT_ctcv_loop_e\expandafter {\expandafter{#2}#1}% }% -\def\XINT_cstcv_loop_e #1#2% +\def\XINT_ctcv_loop_e #1#2% {% - \expandafter\XINT_cstcv_loop_f\expandafter{#2}#1% + \expandafter\XINT_ctcv_loop_f\expandafter{#2}#1% }% -\def\XINT_cstcv_loop_f #1#2#3#4#5% +\def\XINT_ctcv_loop_f #1#2#3#4#5% {% - \expandafter\XINT_cstcv_loop_g\expandafter + \expandafter\XINT_ctcv_loop_g\expandafter {\romannumeral0\xintrawwithzeros {#1/#2}}{#5}{#1}{#2}{#3}{#4}% }% -\def\XINT_cstcv_loop_g #1#2{\XINT_cstcv_loop_a {#2{#1}}}% 1.09b removes [0] -\def\XINT_cstcv_end #1.#2#3#4#5#6{ #6}% +\def\XINT_ctcv_loop_g #1#2{\XINT_ctcv_loop_a {#2{#1}}}% 1.09b removes [0] +\def\XINT_ctcv_end #1.#2#3#4#5#6{ #6}% % \end{macrocode} % \subsection{\csh{xintiCstoCv}} % \begin{macrocode} \def\xintiCstoCv {\romannumeral0\xinticstocv }% \def\xinticstocv #1% {% - \expandafter\XINT_icstcv_prep \romannumeral-`0#1,\W,% + \expandafter\XINT_icstcv_prep \romannumeral-`0#1,\xint_relax,% }% \def\XINT_icstcv_prep {% @@ -22826,7 +23463,7 @@ first place. }% \def\XINT_icstcv_loop_a #1#2#3#4#5#6,% {% - \xint_gob_til_W #6\XINT_icstcv_end\W + \xint_gob_til_xint_relax #6\XINT_icstcv_end\xint_relax \expandafter \XINT_icstcv_loop_b \romannumeral-`0#6.{#2}{#3}{#4}{#5}{#1}% }% @@ -22854,7 +23491,7 @@ first place. \def\xintGCtoCv {\romannumeral0\xintgctocv }% \def\xintgctocv #1% {% - \expandafter\XINT_gctcv_prep \romannumeral-`0#1+\W/% + \expandafter\XINT_gctcv_prep \romannumeral-`0#1+\xint_relax/% }% \def\XINT_gctcv_prep {% @@ -22896,7 +23533,7 @@ first place. }% \def\XINT_gctcv_loop_h #1#2#3/% {% - \xint_gob_til_W #3\XINT_gctcv_end\W + \xint_gob_til_xint_relax #3\XINT_gctcv_end\xint_relax \expandafter\XINT_gctcv_loop_i \romannumeral0\xintrawwithzeros {#3}.#2{#1}% }% @@ -22928,7 +23565,7 @@ first place. \def\xintiGCtoCv {\romannumeral0\xintigctocv }% \def\xintigctocv #1% {% - \expandafter\XINT_igctcv_prep \romannumeral-`0#1+\W/% + \expandafter\XINT_igctcv_prep \romannumeral-`0#1+\xint_relax/% }% \def\XINT_igctcv_prep {% @@ -22952,7 +23589,7 @@ first place. }% \def\XINT_igctcv_loop_f #1#2#3#4/% {% - \xint_gob_til_W #4\XINT_igctcv_end_a\W + \xint_gob_til_xint_relax #4\XINT_igctcv_end_a\xint_relax \expandafter\XINT_igctcv_loop_g \romannumeral-`0#4.#1#2{#3}% }% @@ -22981,6 +23618,23 @@ first place. }% \def\XINT_igctcv_end_b #1#2{ #2{#1}}% 1.09b removes [0] % \end{macrocode} +% \subsection{\csh{xintFtoCv}} +% \lverb|Still uses \xinticstocv \xintFtoCs rather than \xintctocv \xintFtoC.| +% \begin{macrocode} +\def\xintFtoCv {\romannumeral0\xintftocv }% +\def\xintftocv #1% +{% + \xinticstocv {\xintFtoCs {#1}}% +}% +% \end{macrocode} +% \subsection{\csh{xintFtoCCv}} +% \begin{macrocode} +\def\xintFtoCCv {\romannumeral0\xintftoccv }% +\def\xintftoccv #1% +{% + \xintigctocv {\xintFtoCC {#1}}% +}% +% \end{macrocode} % \subsection{\csh{xintCntoF}} % \lverb|& % Modified in 1.06 to give the N first to a \numexpr rather than expanding @@ -23001,7 +23655,7 @@ first place. \xint_afterfi {\ifnum #1=\xint_c_ \xint_afterfi {\expandafter\space \romannumeral-`0#2{0}}% - \else \xint_afterfi { 0/1[0]}% + \else \xint_afterfi { }% 1.09m now returns nothing. \fi}% \fi }% @@ -23021,9 +23675,9 @@ first place. }% % \end{macrocode} % \subsection{\csh{xintGCntoF}} -% \lverb|& -% 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.| +% \lverb|Modified in 1.06 to give the N argument first to a \numexpr rather +% than expanding twice. I just use \the\numexpr and maintain the previous code +% after that.| % \begin{macrocode} \def\xintGCntoF {\romannumeral0\xintgcntof }% \def\xintgcntof #1% @@ -23040,7 +23694,7 @@ first place. \xint_afterfi {\ifnum #1=\xint_c_ \xint_afterfi {\expandafter\space\romannumeral-`0#2{0}}% - \else \xint_afterfi { 0/1[0]}% + \else \xint_afterfi { }% 1.09m now returns nothing rather than 0/1[0] \fi}% \fi }% @@ -23060,9 +23714,11 @@ first place. }% % \end{macrocode} % \subsection{\csh{xintCntoCs}} -% \lverb|& -% 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.| +% \lverb|Modified in 1.09m: added spaces after the commas in the produced list. +% Moreover the coefficients are not braced anymore. A slight induced limitation +% is that the macro argument should not contain some explicit comma (cf. +% \XINT_cntcs_exit_b), hence \xintCntoCs {\macro,} with \def\macro,#1{<stuff>} +% would crash. Not a very serious limitation, I believe. | % \begin{macrocode} \def\xintCntoCs {\romannumeral0\xintcntocs }% \def\xintcntocs #1% @@ -23072,19 +23728,19 @@ first place. \def\XINT_cntcs #1#2% {% \ifnum #1<0 - \xint_afterfi { }% 1.09i: a 0/1[0] was strangely here, removed + \xint_afterfi { }% 1.09i: a 0/1[0] was here, now the macro returns nothing \else \xint_afterfi {\expandafter\XINT_cntcs_loop\expandafter - {\the\numexpr #1-1\expandafter}\expandafter - {\expandafter{\romannumeral-`0#2{#1}}}{#2}}% + {\the\numexpr #1-\xint_c_i\expandafter}\expandafter + {\romannumeral-`0#2{#1}}{#2}}% produced coeff not braced \fi }% \def\XINT_cntcs_loop #1#2#3% {% - \ifnum #1>-1 \else \XINT_cntcs_exit \fi + \ifnum #1>-\xint_c_i \else \XINT_cntcs_exit \fi \expandafter\XINT_cntcs_loop\expandafter - {\the\numexpr #1-1\expandafter }\expandafter - {\expandafter{\romannumeral-`0#3{#1}},#2}{#3}% + {\the\numexpr #1-\xint_c_i\expandafter}\expandafter + {\romannumeral-`0#3{#1}, #2}{#3}% space added, 1.09m }% \def\XINT_cntcs_exit \fi \expandafter\XINT_cntcs_loop\expandafter @@ -23092,12 +23748,17 @@ first place. {% \fi\XINT_cntcs_exit_b #2% }% -\def\XINT_cntcs_exit_b #1,{ }% +\def\XINT_cntcs_exit_b #1,{}% romannumeral stopping space already there % \end{macrocode} % \subsection{\csh{xintCntoGC}} % \lverb|& % 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.| +% twice. I just use \the\numexpr and maintain the previous code after that. +% +% 1.09m maintains the braces, as the coeff are allowed to be fraction and the +% slash can not be naked in the GC format, contrarily to what happens in +% \xintCntoCs. Also the separators given to \xintGCtoGCx may then fetch the +% coefficients as argument, as they are braced.| % \begin{macrocode} \def\xintCntoGC {\romannumeral0\xintcntogc }% \def\xintcntogc #1% @@ -23110,15 +23771,15 @@ first place. \xint_afterfi { }% 1.09i there was as strange 0/1[0] here, removed \else \xint_afterfi {\expandafter\XINT_cntgc_loop\expandafter - {\the\numexpr #1-1\expandafter}\expandafter + {\the\numexpr #1-\xint_c_i\expandafter}\expandafter {\expandafter{\romannumeral-`0#2{#1}}}{#2}}% \fi }% \def\XINT_cntgc_loop #1#2#3% {% - \ifnum #1>-1 \else \XINT_cntgc_exit \fi + \ifnum #1>-\xint_c_i \else \XINT_cntgc_exit \fi \expandafter\XINT_cntgc_loop\expandafter - {\the\numexpr #1-1\expandafter }\expandafter + {\the\numexpr #1-\xint_c_i\expandafter }\expandafter {\expandafter{\romannumeral-`0#3{#1}}+1/#2}{#3}% }% \def\XINT_cntgc_exit \fi @@ -23145,20 +23806,20 @@ first place. \xint_afterfi { }% 1.09i now returns nothing \else \xint_afterfi {\expandafter\XINT_gcntgc_loop\expandafter - {\the\numexpr #1-1\expandafter}\expandafter + {\the\numexpr #1-\xint_c_i\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 + \ifnum #1>-\xint_c_i \else \XINT_gcntgc_exit \fi \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 + {\the\numexpr #3-\xint_c_i \expandafter}\expandafter {\expandafter{\romannumeral-`0#2}+#1}% }% \def\XINT_gcntgc_exit \fi @@ -23173,28 +23834,28 @@ first place. \def\xintCstoGC {\romannumeral0\xintcstogc }% \def\xintcstogc #1% {% - \expandafter\XINT_cstc_prep \romannumeral-`0#1,\W,% + \expandafter\XINT_cstc_prep \romannumeral-`0#1,\xint_relax,% }% \def\XINT_cstc_prep #1,{\XINT_cstc_loop_a {{#1}}}% \def\XINT_cstc_loop_a #1#2,% {% - \xint_gob_til_W #2\XINT_cstc_end\W + \xint_gob_til_xint_relax #2\XINT_cstc_end\xint_relax \XINT_cstc_loop_b {#1}{#2}% }% \def\XINT_cstc_loop_b #1#2{\XINT_cstc_loop_a {#1+1/{#2}}}% -\def\XINT_cstc_end\W\XINT_cstc_loop_b #1#2{ #1}% +\def\XINT_cstc_end\xint_relax\XINT_cstc_loop_b #1#2{ #1}% % \end{macrocode} % \subsection{\csh{xintGCtoGC}} % \begin{macrocode} \def\xintGCtoGC {\romannumeral0\xintgctogc }% \def\xintgctogc #1% {% - \expandafter\XINT_gctgc_start \romannumeral-`0#1+\W/% + \expandafter\XINT_gctgc_start \romannumeral-`0#1+\xint_relax/% }% \def\XINT_gctgc_start {\XINT_gctgc_loop_a {}}% \def\XINT_gctgc_loop_a #1#2+#3/% {% - \xint_gob_til_W #3\XINT_gctgc_end\W + \xint_gob_til_xint_relax #3\XINT_gctgc_end\xint_relax \expandafter\XINT_gctgc_loop_b\expandafter {\romannumeral-`0#2}{#3}{#1}% }% @@ -23207,7 +23868,7 @@ first place. {% \XINT_gctgc_loop_a {#3{#2}+{#1}/}% }% -\def\XINT_gctgc_end\W\expandafter\XINT_gctgc_loop_b +\def\XINT_gctgc_end\xint_relax\expandafter\XINT_gctgc_loop_b {% \expandafter\XINT_gctgc_end_b }% @@ -23431,7 +24092,7 @@ first place. % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xintexpr}% - [2014/02/13 v1.09kb Expandable expression parser (jfB)]% + [2014/02/26 v1.09m Expandable expression parser (jfB)]% % \end{macrocode} % \subsection{Encapsulation in pseudo cs names, helper macros} % \lverb|1.09i uses .= for encapsulation, thus allowing \escapechar to be @@ -24778,7 +25439,7 @@ first place. Right bracket \] Circumflex \^ Underscore \_ Grave accent \` Left brace \{ Vertical bar \| Right brace \} Tilde \~} -\CheckSum {21377} +\CheckSum {21865} \makeatletter\check@checksum\makeatother \Finale %% End of file xint.dtx diff --git a/Master/texmf-dist/source/generic/xint/xint.ins b/Master/texmf-dist/source/generic/xint/xint.ins index 1bf1495ae56..02fdd865c65 100644 --- a/Master/texmf-dist/source/generic/xint/xint.ins +++ b/Master/texmf-dist/source/generic/xint/xint.ins @@ -1,5 +1,5 @@ %%---------------------------------------------------------------- -%% The xint bundle (version 1.09kb of February 13, 2014) +%% The xint bundle (version 1.09m of February 26, 2014) %% Copyright (C) 2013-2014 by Jean-Francois Burnol %%---------------------------------------------------------------- %% This is a generated file. diff --git a/Master/texmf-dist/tex/generic/xint/xint.sty b/Master/texmf-dist/tex/generic/xint/xint.sty index 8931dd3b902..8357015b7c8 100644 --- a/Master/texmf-dist/tex/generic/xint/xint.sty +++ b/Master/texmf-dist/tex/generic/xint/xint.sty @@ -21,7 +21,7 @@ %% same distribution. (The sources need not necessarily be %% in the same archive or directory.) %%---------------------------------------------------------------- -%% The xint bundle (version 1.09kb of February 13, 2014) +%% The xint bundle (version 1.09m of February 26, 2014) %% xint: Expandable operations on long numbers %% Copyright (C) 2013-2014 by Jean-Francois Burnol %%---------------------------------------------------------------- @@ -101,14 +101,13 @@ \XINTsetupcatcodes% \XINT_providespackage \ProvidesPackage{xint}% - [2014/02/13 v1.09kb Expandable operations on long numbers (jfB)]% + [2014/02/26 v1.09m Expandable operations on long numbers (jfB)]% \long\def\xint_firstofthree #1#2#3{#1}% \long\def\xint_secondofthree #1#2#3{#2}% \long\def\xint_thirdofthree #1#2#3{#3}% \long\def\xint_firstofthree_thenstop #1#2#3{ #1}% 1.09i \long\def\xint_secondofthree_thenstop #1#2#3{ #2}% \long\def\xint_thirdofthree_thenstop #1#2#3{ #3}% -\def\xint_gob_til_zero #10{}% \def\xint_gob_til_zeros_iii #1000{}% \def\xint_gob_til_zeros_iv #10000{}% \def\xint_gob_til_one #11{}% @@ -122,12 +121,7 @@ \def\xint_UDwfork #1\W#2#3\krof {#2}% \def\xint_UDzerosfork #100#2#3\krof {#2}% \def\xint_UDonezerofork #110#2#3\krof {#2}% -\def\xint_UDzerominusfork #10-#2#3\krof {#2}% \def\xint_UDsignsfork #1--#2#3\krof {#2}% -\chardef\xint_c_ii 2 -\chardef\xint_c_iii 3 -\chardef\xint_c_iv 4 -\chardef\xint_c_v 5 \chardef\xint_c_ix 9 \chardef\xint_c_x 10 \chardef\xint_c_ii^v 32 % not used in xint, common to xintfrac and xintbinhex @@ -168,8 +162,8 @@ {% \expandafter\XINT_length_loop \xint_UDsignfork - #1{{0}}% - -{{0}#1}% + #1{0.}% + -{0.#1}% \krof }% \def\XINT_RQ #1#2#3#4#5#6#7#8#9% diff --git a/Master/texmf-dist/tex/generic/xint/xintbinhex.sty b/Master/texmf-dist/tex/generic/xint/xintbinhex.sty index 3308a4a0c3c..44fd98864d5 100644 --- a/Master/texmf-dist/tex/generic/xint/xintbinhex.sty +++ b/Master/texmf-dist/tex/generic/xint/xintbinhex.sty @@ -21,7 +21,7 @@ %% same distribution. (The sources need not necessarily be %% in the same archive or directory.) %%---------------------------------------------------------------- -%% The xint bundle (version 1.09kb of February 13, 2014) +%% The xint bundle (version 1.09m of February 26, 2014) %% xintbinhex: Expandable binary and hexadecimal conversions %% Copyright (C) 2013-2014 by Jean-Francois Burnol %%---------------------------------------------------------------- @@ -101,7 +101,7 @@ \XINTsetupcatcodes% \XINT_providespackage \ProvidesPackage{xintbinhex}% - [2014/02/13 v1.09kb Expandable binary and hexadecimal conversions (jfB)]% + [2014/02/26 v1.09m Expandable binary and hexadecimal conversions (jfB)]% \chardef\xint_c_xvi 16 \chardef\xint_c_ii^vii 128 \mathchardef\xint_c_ii^viii 256 diff --git a/Master/texmf-dist/tex/generic/xint/xintcfrac.sty b/Master/texmf-dist/tex/generic/xint/xintcfrac.sty index cd03181aa3b..abe94579dff 100644 --- a/Master/texmf-dist/tex/generic/xint/xintcfrac.sty +++ b/Master/texmf-dist/tex/generic/xint/xintcfrac.sty @@ -21,7 +21,7 @@ %% same distribution. (The sources need not necessarily be %% in the same archive or directory.) %%---------------------------------------------------------------- -%% The xint bundle (version 1.09kb of February 13, 2014) +%% The xint bundle (version 1.09m of February 26, 2014) %% xintcfrac: Expandable continued fractions with xint package %% Copyright (C) 2013-2014 by Jean-Francois Burnol %%---------------------------------------------------------------- @@ -101,22 +101,22 @@ \XINTsetupcatcodes% \XINT_providespackage \ProvidesPackage{xintcfrac}% - [2014/02/13 v1.09kb Expandable continued fractions with xint package (jfB)]% + [2014/02/26 v1.09m Expandable continued fractions with xint package (jfB)]% \def\xintCFrac {\romannumeral0\xintcfrac }% \def\xintcfrac #1% {% - \XINT_cfrac_opt_a #1\Z + \XINT_cfrac_opt_a #1\xint_relax }% \def\XINT_cfrac_opt_a #1% {% \ifx[#1\XINT_cfrac_opt_b\fi \XINT_cfrac_noopt #1% }% -\def\XINT_cfrac_noopt #1\Z +\def\XINT_cfrac_noopt #1\xint_relax {% \expandafter\XINT_cfrac_A\romannumeral0\xintrawwithzeros {#1}\Z \relax\relax }% -\def\XINT_cfrac_opt_b\fi\XINT_cfrac_noopt [\Z #1]% +\def\XINT_cfrac_opt_b\fi\XINT_cfrac_noopt [\xint_relax #1]% {% \fi\csname XINT_cfrac_opt#1\endcsname }% @@ -177,30 +177,30 @@ }% \def\XINT_cfrac_end_b \Z+\cfrac#1#2{ #2}% \def\xintGCFrac {\romannumeral0\xintgcfrac }% -\def\xintgcfrac #1{\XINT_gcfrac_opt_a #1\Z }% +\def\xintgcfrac #1{\XINT_gcfrac_opt_a #1\xint_relax }% \def\XINT_gcfrac_opt_a #1% {% \ifx[#1\XINT_gcfrac_opt_b\fi \XINT_gcfrac_noopt #1% }% -\def\XINT_gcfrac_noopt #1\Z +\def\XINT_gcfrac_noopt #1\xint_relax {% - \XINT_gcfrac #1+\W/\relax\relax + \XINT_gcfrac #1+\xint_relax/\relax\relax }% -\def\XINT_gcfrac_opt_b\fi\XINT_gcfrac_noopt [\Z #1]% +\def\XINT_gcfrac_opt_b\fi\XINT_gcfrac_noopt [\xint_relax #1]% {% \fi\csname XINT_gcfrac_opt#1\endcsname }% \def\XINT_gcfrac_optl #1% {% - \XINT_gcfrac #1+\W/\relax\hfill + \XINT_gcfrac #1+\xint_relax/\relax\hfill }% \def\XINT_gcfrac_optc #1% {% - \XINT_gcfrac #1+\W/\relax\relax + \XINT_gcfrac #1+\xint_relax/\relax\relax }% \def\XINT_gcfrac_optr #1% {% - \XINT_gcfrac #1+\W/\hfill\relax + \XINT_gcfrac #1+\xint_relax/\hfill\relax }% \def\XINT_gcfrac {% @@ -209,43 +209,94 @@ \def\XINT_gcfrac_enter {\XINT_gcfrac_loop {}}% \def\XINT_gcfrac_loop #1#2+#3/% {% - \xint_gob_til_W #3\XINT_gcfrac_endloop\W + \xint_gob_til_xint_relax #3\XINT_gcfrac_endloop\xint_relax \XINT_gcfrac_loop {{#3}{#2}#1}% }% -\def\XINT_gcfrac_endloop\W\XINT_gcfrac_loop #1#2#3% +\def\XINT_gcfrac_endloop\xint_relax\XINT_gcfrac_loop #1#2#3% {% - \XINT_gcfrac_T #2#3#1\Z\Z + \XINT_gcfrac_T #2#3#1\xint_relax\xint_relax }% \def\XINT_gcfrac_T #1#2#3#4{\XINT_gcfrac_U #1#2{\xintFrac{#4}}}% \def\XINT_gcfrac_U #1#2#3#4#5% {% - \xint_gob_til_Z #5\XINT_gcfrac_end\Z\XINT_gcfrac_U + \xint_gob_til_xint_relax #5\XINT_gcfrac_end\xint_relax\XINT_gcfrac_U #1#2{\xintFrac{#5}% \ifcase\xintSgn{#4} +\or+\else-\fi \cfrac{#1\xintFrac{\xintAbs{#4}}#2}{#3}}% }% -\def\XINT_gcfrac_end\Z\XINT_gcfrac_U #1#2#3% +\def\XINT_gcfrac_end\xint_relax\XINT_gcfrac_U #1#2#3% {% \XINT_gcfrac_end_b #3% }% \def\XINT_gcfrac_end_b #1\cfrac#2#3{ #3}% +\def\xintGGCFrac {\romannumeral0\xintggcfrac }% +\def\xintggcfrac #1{\XINT_ggcfrac_opt_a #1\xint_relax }% +\def\XINT_ggcfrac_opt_a #1% +{% + \ifx[#1\XINT_ggcfrac_opt_b\fi \XINT_ggcfrac_noopt #1% +}% +\def\XINT_ggcfrac_noopt #1\xint_relax +{% + \XINT_ggcfrac #1+\xint_relax/\relax\relax +}% +\def\XINT_ggcfrac_opt_b\fi\XINT_ggcfrac_noopt [\xint_relax #1]% +{% + \fi\csname XINT_ggcfrac_opt#1\endcsname +}% +\def\XINT_ggcfrac_optl #1% +{% + \XINT_ggcfrac #1+\xint_relax/\relax\hfill +}% +\def\XINT_ggcfrac_optc #1% +{% + \XINT_ggcfrac #1+\xint_relax/\relax\relax +}% +\def\XINT_ggcfrac_optr #1% +{% + \XINT_ggcfrac #1+\xint_relax/\hfill\relax +}% +\def\XINT_ggcfrac +{% + \expandafter\XINT_ggcfrac_enter\romannumeral-`0% +}% +\def\XINT_ggcfrac_enter {\XINT_ggcfrac_loop {}}% +\def\XINT_ggcfrac_loop #1#2+#3/% +{% + \xint_gob_til_xint_relax #3\XINT_ggcfrac_endloop\xint_relax + \XINT_ggcfrac_loop {{#3}{#2}#1}% +}% +\def\XINT_ggcfrac_endloop\xint_relax\XINT_ggcfrac_loop #1#2#3% +{% + \XINT_ggcfrac_T #2#3#1\xint_relax\xint_relax +}% +\def\XINT_ggcfrac_T #1#2#3#4{\XINT_ggcfrac_U #1#2{#4}}% +\def\XINT_ggcfrac_U #1#2#3#4#5% +{% + \xint_gob_til_xint_relax #5\XINT_ggcfrac_end\xint_relax\XINT_ggcfrac_U + #1#2{#5+\cfrac{#1#4#2}{#3}}% +}% +\def\XINT_ggcfrac_end\xint_relax\XINT_ggcfrac_U #1#2#3% +{% + \XINT_ggcfrac_end_b #3% +}% +\def\XINT_ggcfrac_end_b #1\cfrac#2#3{ #3}% \def\xintGCtoGCx {\romannumeral0\xintgctogcx }% \def\xintgctogcx #1#2#3% {% \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_start #1#2#3{\XINT_gctgcx_loop_a {}{#2}{#3}#1+\xint_relax/}% \def\XINT_gctgcx_loop_a #1#2#3#4+#5/% {% - \xint_gob_til_W #5\XINT_gctgcx_end\W + \xint_gob_til_xint_relax #5\XINT_gctgcx_end\xint_relax \XINT_gctgcx_loop_b {#1{#4}}{#2{#5}#3}{#2}{#3}% }% \def\XINT_gctgcx_loop_b #1#2% {% \XINT_gctgcx_loop_a {#1#2}% }% -\def\XINT_gctgcx_end\W\XINT_gctgcx_loop_b #1#2#3#4{ #1}% +\def\XINT_gctgcx_end\xint_relax\XINT_gctgcx_loop_b #1#2#3#4{ #1}% \def\xintFtoCs {\romannumeral0\xintftocs }% \def\xintftocs #1% {% @@ -264,7 +315,7 @@ \xint_gob_til_zero #1\XINT_ftc_integer 0\XINT_ftc_D #1% }% \def\XINT_ftc_integer 0\XINT_ftc_D 0#1.#2#3{ #2}% -\def\XINT_ftc_D #1.#2#3{\XINT_ftc_loop_a {#1}{#3}{#1}{#2,}}% +\def\XINT_ftc_D #1.#2#3{\XINT_ftc_loop_a {#1}{#3}{#1}{#2, }}% 1.09m adds a space \def\XINT_ftc_loop_a {% \expandafter\XINT_ftc_loop_d\romannumeral0\XINT_div_prepare @@ -279,7 +330,7 @@ }% \def\XINT_ftc_loop_f #1.#2#3#4% {% - \XINT_ftc_loop_a {#1}{#3}{#1}{#4#2,}% + \XINT_ftc_loop_a {#1}{#3}{#1}{#4#2, }% 1.09m has an added space here }% \def\xint_ftc_loop_exit0\XINT_ftc_loop_f #1.#2#3#4{ #4#2}% \def\xintFtoCx {\romannumeral0\xintftocx }% @@ -300,7 +351,7 @@ \xint_gob_til_zero #1\XINT_ftcx_integer 0\XINT_ftcx_D #1% }% \def\XINT_ftcx_integer 0\XINT_ftcx_D 0#1.#2#3#4{ #2}% -\def\XINT_ftcx_D #1.#2#3#4{\XINT_ftcx_loop_a {#1}{#3}{#1}{#2#4}{#4}}% +\def\XINT_ftcx_D #1.#2#3#4{\XINT_ftcx_loop_a {#1}{#3}{#1}{{#2}#4}{#4}}% \def\XINT_ftcx_loop_a {% \expandafter\XINT_ftcx_loop_d\romannumeral0\XINT_div_prepare @@ -318,8 +369,55 @@ \XINT_ftcx_loop_a {#1}{#3}{#1}{#4{#2}#5}{#5}% }% \def\xint_ftcx_loop_exit0\XINT_ftcx_loop_f #1.#2#3#4#5{ #4{#2}}% +\def\xintFtoC {\romannumeral0\xintftoc }% +\def\xintftoc {\xintftocx {}}% \def\xintFtoGC {\romannumeral0\xintftogc }% \def\xintftogc {\xintftocx {+1/}}% +\def\xintFGtoC {\romannumeral0\xintfgtoc}% +\def\xintfgtoc#1% +{% + \expandafter\XINT_fgtc_a\romannumeral0\xintrawwithzeros {#1}\Z +}% +\def\XINT_fgtc_a #1/#2\Z #3% +{% + \expandafter\XINT_fgtc_b\romannumeral0\xintrawwithzeros {#3}\Z #1/#2\Z { }% +}% +\def\XINT_fgtc_b #1/#2\Z +{% + \expandafter\XINT_fgtc_c\romannumeral0\xintiidivision {#1}{#2}{#2}% +}% +\def\XINT_fgtc_c #1#2#3#4/#5\Z +{% + \expandafter\XINT_fgtc_d\romannumeral0\xintiidivision + {#4}{#5}{#5}{#1}{#2}{#3}% +}% +\def\XINT_fgtc_d #1#2#3#4%#5#6#7% +{% + \xintifEq {#1}{#4}{\XINT_fgtc_da {#1}{#2}{#3}{#4}}% + {\xint_thirdofthree}% +}% +\def\XINT_fgtc_da #1#2#3#4#5#6#7% +{% + \XINT_fgtc_e {#2}{#5}{#3}{#6}{#7{#1}}% +}% +\def\XINT_fgtc_e #1% +{% + \xintifZero {#1}{\expandafter\xint_firstofone\xint_gobble_iii}% + {\XINT_fgtc_f {#1}}% +}% +\def\XINT_fgtc_f #1#2% +{% + \xintifZero {#2}{\xint_thirdofthree}{\XINT_fgtc_g {#1}{#2}}% +}% +\def\XINT_fgtc_g #1#2#3% +{% + \expandafter\XINT_fgtc_h\romannumeral0\XINT_div_prepare {#1}{#3}{#1}{#2}% +}% +\def\XINT_fgtc_h #1#2#3#4#5% +{% + \expandafter\XINT_fgtc_d\romannumeral0\XINT_div_prepare + {#4}{#5}{#4}{#1}{#2}{#3}% +}% \def\xintFtoCC {\romannumeral0\xintftocc }% \def\xintftocc #1% {% @@ -391,56 +489,51 @@ \expandafter\XINT_ftcc_loop_a\expandafter {\romannumeral0\xintdiv {1[0]}{#1}}{#3#2+-1/}% }% -\def\xintFtoCv {\romannumeral0\xintftocv }% -\def\xintftocv #1% -{% - \xinticstocv {\xintFtoCs {#1}}% -}% -\def\xintFtoCCv {\romannumeral0\xintftoccv }% -\def\xintftoccv #1% -{% - \xintigctocv {\xintFtoCC {#1}}% -}% \def\xintCstoF {\romannumeral0\xintcstof }% \def\xintcstof #1% {% - \expandafter\XINT_cstf_prep \romannumeral-`0#1,\W,% + \expandafter\XINT_ctf_prep \romannumeral0\xintcsvtolist{#1}\xint_relax +}% +\def\xintCtoF {\romannumeral0\xintctof }% +\def\xintctof #1% +{% + \expandafter\XINT_ctf_prep \romannumeral-`0#1\xint_relax }% -\def\XINT_cstf_prep +\def\XINT_ctf_prep {% - \XINT_cstf_loop_a 1001% + \XINT_ctf_loop_a 1001% }% -\def\XINT_cstf_loop_a #1#2#3#4#5,% +\def\XINT_ctf_loop_a #1#2#3#4#5% {% - \xint_gob_til_W #5\XINT_cstf_end\W - \expandafter\XINT_cstf_loop_b + \xint_gob_til_xint_relax #5\XINT_ctf_end\xint_relax + \expandafter\XINT_ctf_loop_b \romannumeral0\xintrawwithzeros {#5}.{#1}{#2}{#3}{#4}% }% -\def\XINT_cstf_loop_b #1/#2.#3#4#5#6% +\def\XINT_ctf_loop_b #1/#2.#3#4#5#6% {% - \expandafter\XINT_cstf_loop_c\expandafter + \expandafter\XINT_ctf_loop_c\expandafter {\romannumeral0\XINT_mul_fork #2\Z #4\Z }% {\romannumeral0\XINT_mul_fork #2\Z #3\Z }% {\romannumeral0\xintiiadd {\XINT_Mul {#2}{#6}}{\XINT_Mul {#1}{#4}}}% {\romannumeral0\xintiiadd {\XINT_Mul {#2}{#5}}{\XINT_Mul {#1}{#3}}}% }% -\def\XINT_cstf_loop_c #1#2% +\def\XINT_ctf_loop_c #1#2% {% - \expandafter\XINT_cstf_loop_d\expandafter {\expandafter{#2}{#1}}% + \expandafter\XINT_ctf_loop_d\expandafter {\expandafter{#2}{#1}}% }% -\def\XINT_cstf_loop_d #1#2% +\def\XINT_ctf_loop_d #1#2% {% - \expandafter\XINT_cstf_loop_e\expandafter {\expandafter{#2}#1}% + \expandafter\XINT_ctf_loop_e\expandafter {\expandafter{#2}#1}% }% -\def\XINT_cstf_loop_e #1#2% +\def\XINT_ctf_loop_e #1#2% {% - \expandafter\XINT_cstf_loop_a\expandafter{#2}#1% + \expandafter\XINT_ctf_loop_a\expandafter{#2}#1% }% -\def\XINT_cstf_end #1.#2#3#4#5{\xintrawwithzeros {#2/#3}}% 1.09b removes [0] +\def\XINT_ctf_end #1.#2#3#4#5{\xintrawwithzeros {#2/#3}}% 1.09b removes [0] \def\xintiCstoF {\romannumeral0\xinticstof }% \def\xinticstof #1% {% - \expandafter\XINT_icstf_prep \romannumeral-`0#1,\W,% + \expandafter\XINT_icstf_prep \romannumeral-`0#1,\xint_relax,% }% \def\XINT_icstf_prep {% @@ -448,7 +541,7 @@ }% \def\XINT_icstf_loop_a #1#2#3#4#5,% {% - \xint_gob_til_W #5\XINT_icstf_end\W + \xint_gob_til_xint_relax #5\XINT_icstf_end\xint_relax \expandafter \XINT_icstf_loop_b \romannumeral-`0#5.{#1}{#2}{#3}{#4}% }% @@ -467,7 +560,7 @@ \def\xintGCtoF {\romannumeral0\xintgctof }% \def\xintgctof #1% {% - \expandafter\XINT_gctf_prep \romannumeral-`0#1+\W/% + \expandafter\XINT_gctf_prep \romannumeral-`0#1+\xint_relax/% }% \def\XINT_gctf_prep {% @@ -500,7 +593,7 @@ }% \def\XINT_gctf_loop_f #1#2/% {% - \xint_gob_til_W #2\XINT_gctf_end\W + \xint_gob_til_xint_relax #2\XINT_gctf_end\xint_relax \expandafter\XINT_gctf_loop_g \romannumeral0\xintrawwithzeros {#2}.#1% }% @@ -528,7 +621,7 @@ \def\xintiGCtoF {\romannumeral0\xintigctof }% \def\xintigctof #1% {% - \expandafter\XINT_igctf_prep \romannumeral-`0#1+\W/% + \expandafter\XINT_igctf_prep \romannumeral-`0#1+\xint_relax/% }% \def\XINT_igctf_prep {% @@ -552,7 +645,7 @@ }% \def\XINT_igctf_loop_f #1#2#3#4/% {% - \xint_gob_til_W #4\XINT_igctf_end\W + \xint_gob_til_xint_relax #4\XINT_igctf_end\xint_relax \expandafter\XINT_igctf_loop_g \romannumeral-`0#4.{#2}{#3}#1% }% @@ -574,49 +667,54 @@ \def\xintCstoCv {\romannumeral0\xintcstocv }% \def\xintcstocv #1% {% - \expandafter\XINT_cstcv_prep \romannumeral-`0#1,\W,% + \expandafter\XINT_ctcv_prep\romannumeral0\xintcsvtolist{#1}\xint_relax }% -\def\XINT_cstcv_prep +\def\xintCtoCv {\romannumeral0\xintctocv }% +\def\xintctocv #1% {% - \XINT_cstcv_loop_a {}1001% + \expandafter\XINT_ctcv_prep\romannumeral-`0#1\xint_relax }% -\def\XINT_cstcv_loop_a #1#2#3#4#5#6,% +\def\XINT_ctcv_prep {% - \xint_gob_til_W #6\XINT_cstcv_end\W - \expandafter\XINT_cstcv_loop_b + \XINT_ctcv_loop_a {}1001% +}% +\def\XINT_ctcv_loop_a #1#2#3#4#5#6% +{% + \xint_gob_til_xint_relax #6\XINT_ctcv_end\xint_relax + \expandafter\XINT_ctcv_loop_b \romannumeral0\xintrawwithzeros {#6}.{#2}{#3}{#4}{#5}{#1}% }% -\def\XINT_cstcv_loop_b #1/#2.#3#4#5#6% +\def\XINT_ctcv_loop_b #1/#2.#3#4#5#6% {% - \expandafter\XINT_cstcv_loop_c\expandafter + \expandafter\XINT_ctcv_loop_c\expandafter {\romannumeral0\XINT_mul_fork #2\Z #4\Z }% {\romannumeral0\XINT_mul_fork #2\Z #3\Z }% {\romannumeral0\xintiiadd {\XINT_Mul {#2}{#6}}{\XINT_Mul {#1}{#4}}}% {\romannumeral0\xintiiadd {\XINT_Mul {#2}{#5}}{\XINT_Mul {#1}{#3}}}% }% -\def\XINT_cstcv_loop_c #1#2% +\def\XINT_ctcv_loop_c #1#2% {% - \expandafter\XINT_cstcv_loop_d\expandafter {\expandafter{#2}{#1}}% + \expandafter\XINT_ctcv_loop_d\expandafter {\expandafter{#2}{#1}}% }% -\def\XINT_cstcv_loop_d #1#2% +\def\XINT_ctcv_loop_d #1#2% {% - \expandafter\XINT_cstcv_loop_e\expandafter {\expandafter{#2}#1}% + \expandafter\XINT_ctcv_loop_e\expandafter {\expandafter{#2}#1}% }% -\def\XINT_cstcv_loop_e #1#2% +\def\XINT_ctcv_loop_e #1#2% {% - \expandafter\XINT_cstcv_loop_f\expandafter{#2}#1% + \expandafter\XINT_ctcv_loop_f\expandafter{#2}#1% }% -\def\XINT_cstcv_loop_f #1#2#3#4#5% +\def\XINT_ctcv_loop_f #1#2#3#4#5% {% - \expandafter\XINT_cstcv_loop_g\expandafter + \expandafter\XINT_ctcv_loop_g\expandafter {\romannumeral0\xintrawwithzeros {#1/#2}}{#5}{#1}{#2}{#3}{#4}% }% -\def\XINT_cstcv_loop_g #1#2{\XINT_cstcv_loop_a {#2{#1}}}% 1.09b removes [0] -\def\XINT_cstcv_end #1.#2#3#4#5#6{ #6}% +\def\XINT_ctcv_loop_g #1#2{\XINT_ctcv_loop_a {#2{#1}}}% 1.09b removes [0] +\def\XINT_ctcv_end #1.#2#3#4#5#6{ #6}% \def\xintiCstoCv {\romannumeral0\xinticstocv }% \def\xinticstocv #1% {% - \expandafter\XINT_icstcv_prep \romannumeral-`0#1,\W,% + \expandafter\XINT_icstcv_prep \romannumeral-`0#1,\xint_relax,% }% \def\XINT_icstcv_prep {% @@ -624,7 +722,7 @@ }% \def\XINT_icstcv_loop_a #1#2#3#4#5#6,% {% - \xint_gob_til_W #6\XINT_icstcv_end\W + \xint_gob_til_xint_relax #6\XINT_icstcv_end\xint_relax \expandafter \XINT_icstcv_loop_b \romannumeral-`0#6.{#2}{#3}{#4}{#5}{#1}% }% @@ -649,7 +747,7 @@ \def\xintGCtoCv {\romannumeral0\xintgctocv }% \def\xintgctocv #1% {% - \expandafter\XINT_gctcv_prep \romannumeral-`0#1+\W/% + \expandafter\XINT_gctcv_prep \romannumeral-`0#1+\xint_relax/% }% \def\XINT_gctcv_prep {% @@ -691,7 +789,7 @@ }% \def\XINT_gctcv_loop_h #1#2#3/% {% - \xint_gob_til_W #3\XINT_gctcv_end\W + \xint_gob_til_xint_relax #3\XINT_gctcv_end\xint_relax \expandafter\XINT_gctcv_loop_i \romannumeral0\xintrawwithzeros {#3}.#2{#1}% }% @@ -720,7 +818,7 @@ \def\xintiGCtoCv {\romannumeral0\xintigctocv }% \def\xintigctocv #1% {% - \expandafter\XINT_igctcv_prep \romannumeral-`0#1+\W/% + \expandafter\XINT_igctcv_prep \romannumeral-`0#1+\xint_relax/% }% \def\XINT_igctcv_prep {% @@ -744,7 +842,7 @@ }% \def\XINT_igctcv_loop_f #1#2#3#4/% {% - \xint_gob_til_W #4\XINT_igctcv_end_a\W + \xint_gob_til_xint_relax #4\XINT_igctcv_end_a\xint_relax \expandafter\XINT_igctcv_loop_g \romannumeral-`0#4.#1#2{#3}% }% @@ -772,6 +870,16 @@ {\romannumeral0\xintrawwithzeros {#2/#3}}% }% \def\XINT_igctcv_end_b #1#2{ #2{#1}}% 1.09b removes [0] +\def\xintFtoCv {\romannumeral0\xintftocv }% +\def\xintftocv #1% +{% + \xinticstocv {\xintFtoCs {#1}}% +}% +\def\xintFtoCCv {\romannumeral0\xintftoccv }% +\def\xintftoccv #1% +{% + \xintigctocv {\xintFtoCC {#1}}% +}% \def\xintCntoF {\romannumeral0\xintcntof }% \def\xintcntof #1% {% @@ -787,7 +895,7 @@ \xint_afterfi {\ifnum #1=\xint_c_ \xint_afterfi {\expandafter\space \romannumeral-`0#2{0}}% - \else \xint_afterfi { 0/1[0]}% + \else \xint_afterfi { }% 1.09m now returns nothing. \fi}% \fi }% @@ -820,7 +928,7 @@ \xint_afterfi {\ifnum #1=\xint_c_ \xint_afterfi {\expandafter\space\romannumeral-`0#2{0}}% - \else \xint_afterfi { 0/1[0]}% + \else \xint_afterfi { }% 1.09m now returns nothing rather than 0/1[0] \fi}% \fi }% @@ -846,19 +954,19 @@ \def\XINT_cntcs #1#2% {% \ifnum #1<0 - \xint_afterfi { }% 1.09i: a 0/1[0] was strangely here, removed + \xint_afterfi { }% 1.09i: a 0/1[0] was here, now the macro returns nothing \else \xint_afterfi {\expandafter\XINT_cntcs_loop\expandafter - {\the\numexpr #1-1\expandafter}\expandafter - {\expandafter{\romannumeral-`0#2{#1}}}{#2}}% + {\the\numexpr #1-\xint_c_i\expandafter}\expandafter + {\romannumeral-`0#2{#1}}{#2}}% produced coeff not braced \fi }% \def\XINT_cntcs_loop #1#2#3% {% - \ifnum #1>-1 \else \XINT_cntcs_exit \fi + \ifnum #1>-\xint_c_i \else \XINT_cntcs_exit \fi \expandafter\XINT_cntcs_loop\expandafter - {\the\numexpr #1-1\expandafter }\expandafter - {\expandafter{\romannumeral-`0#3{#1}},#2}{#3}% + {\the\numexpr #1-\xint_c_i\expandafter}\expandafter + {\romannumeral-`0#3{#1}, #2}{#3}% space added, 1.09m }% \def\XINT_cntcs_exit \fi \expandafter\XINT_cntcs_loop\expandafter @@ -866,7 +974,7 @@ {% \fi\XINT_cntcs_exit_b #2% }% -\def\XINT_cntcs_exit_b #1,{ }% +\def\XINT_cntcs_exit_b #1,{}% romannumeral stopping space already there \def\xintCntoGC {\romannumeral0\xintcntogc }% \def\xintcntogc #1% {% @@ -878,15 +986,15 @@ \xint_afterfi { }% 1.09i there was as strange 0/1[0] here, removed \else \xint_afterfi {\expandafter\XINT_cntgc_loop\expandafter - {\the\numexpr #1-1\expandafter}\expandafter + {\the\numexpr #1-\xint_c_i\expandafter}\expandafter {\expandafter{\romannumeral-`0#2{#1}}}{#2}}% \fi }% \def\XINT_cntgc_loop #1#2#3% {% - \ifnum #1>-1 \else \XINT_cntgc_exit \fi + \ifnum #1>-\xint_c_i \else \XINT_cntgc_exit \fi \expandafter\XINT_cntgc_loop\expandafter - {\the\numexpr #1-1\expandafter }\expandafter + {\the\numexpr #1-\xint_c_i\expandafter }\expandafter {\expandafter{\romannumeral-`0#3{#1}}+1/#2}{#3}% }% \def\XINT_cntgc_exit \fi @@ -907,20 +1015,20 @@ \xint_afterfi { }% 1.09i now returns nothing \else \xint_afterfi {\expandafter\XINT_gcntgc_loop\expandafter - {\the\numexpr #1-1\expandafter}\expandafter + {\the\numexpr #1-\xint_c_i\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 + \ifnum #1>-\xint_c_i \else \XINT_gcntgc_exit \fi \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 + {\the\numexpr #3-\xint_c_i \expandafter}\expandafter {\expandafter{\romannumeral-`0#2}+#1}% }% \def\XINT_gcntgc_exit \fi @@ -932,25 +1040,25 @@ \def\xintCstoGC {\romannumeral0\xintcstogc }% \def\xintcstogc #1% {% - \expandafter\XINT_cstc_prep \romannumeral-`0#1,\W,% + \expandafter\XINT_cstc_prep \romannumeral-`0#1,\xint_relax,% }% \def\XINT_cstc_prep #1,{\XINT_cstc_loop_a {{#1}}}% \def\XINT_cstc_loop_a #1#2,% {% - \xint_gob_til_W #2\XINT_cstc_end\W + \xint_gob_til_xint_relax #2\XINT_cstc_end\xint_relax \XINT_cstc_loop_b {#1}{#2}% }% \def\XINT_cstc_loop_b #1#2{\XINT_cstc_loop_a {#1+1/{#2}}}% -\def\XINT_cstc_end\W\XINT_cstc_loop_b #1#2{ #1}% +\def\XINT_cstc_end\xint_relax\XINT_cstc_loop_b #1#2{ #1}% \def\xintGCtoGC {\romannumeral0\xintgctogc }% \def\xintgctogc #1% {% - \expandafter\XINT_gctgc_start \romannumeral-`0#1+\W/% + \expandafter\XINT_gctgc_start \romannumeral-`0#1+\xint_relax/% }% \def\XINT_gctgc_start {\XINT_gctgc_loop_a {}}% \def\XINT_gctgc_loop_a #1#2+#3/% {% - \xint_gob_til_W #3\XINT_gctgc_end\W + \xint_gob_til_xint_relax #3\XINT_gctgc_end\xint_relax \expandafter\XINT_gctgc_loop_b\expandafter {\romannumeral-`0#2}{#3}{#1}% }% @@ -963,7 +1071,7 @@ {% \XINT_gctgc_loop_a {#3{#2}+{#1}/}% }% -\def\XINT_gctgc_end\W\expandafter\XINT_gctgc_loop_b +\def\XINT_gctgc_end\xint_relax\expandafter\XINT_gctgc_loop_b {% \expandafter\XINT_gctgc_end_b }% diff --git a/Master/texmf-dist/tex/generic/xint/xintexpr.sty b/Master/texmf-dist/tex/generic/xint/xintexpr.sty index 1873d3bfd9f..899e824186d 100644 --- a/Master/texmf-dist/tex/generic/xint/xintexpr.sty +++ b/Master/texmf-dist/tex/generic/xint/xintexpr.sty @@ -21,7 +21,7 @@ %% same distribution. (The sources need not necessarily be %% in the same archive or directory.) %%---------------------------------------------------------------- -%% The xint bundle (version 1.09kb of February 13, 2014) +%% The xint bundle (version 1.09m of February 26, 2014) %% xintexpr: Expandable expression parser %% Copyright (C) 2013-2014 by Jean-Francois Burnol %%---------------------------------------------------------------- @@ -101,7 +101,7 @@ \XINTsetupcatcodes% \XINT_providespackage \ProvidesPackage{xintexpr}% - [2014/02/13 v1.09kb Expandable expression parser (jfB)]% + [2014/02/26 v1.09m Expandable expression parser (jfB)]% \def\xint_gob_til_! #1!{}% nota bene: this ! has catcode 11 \expandafter\def\expandafter \XINT_expr_lock\expandafter#\expandafter1\expandafter !\expandafter diff --git a/Master/texmf-dist/tex/generic/xint/xintfrac.sty b/Master/texmf-dist/tex/generic/xint/xintfrac.sty index d004f3ade63..b2ea1be9fbc 100644 --- a/Master/texmf-dist/tex/generic/xint/xintfrac.sty +++ b/Master/texmf-dist/tex/generic/xint/xintfrac.sty @@ -21,7 +21,7 @@ %% same distribution. (The sources need not necessarily be %% in the same archive or directory.) %%---------------------------------------------------------------- -%% The xint bundle (version 1.09kb of February 13, 2014) +%% The xint bundle (version 1.09m of February 26, 2014) %% xintfrac: Expandable operations on fractions %% Copyright (C) 2013-2014 by Jean-Francois Burnol %%---------------------------------------------------------------- @@ -101,9 +101,7 @@ \XINTsetupcatcodes% \XINT_providespackage \ProvidesPackage{xintfrac}% - [2014/02/13 v1.09kb Expandable operations on fractions (jfB)]% -\chardef\xint_c_vi 6 -\chardef\xint_c_vii 7 + [2014/02/26 v1.09m Expandable operations on fractions (jfB)]% \chardef\xint_c_xviii 18 \def\xintLen {\romannumeral0\xintlen }% \def\xintlen #1% @@ -629,19 +627,19 @@ \expandafter\XINT_e_end\expandafter{\the\numexpr #1+\xintNum{#4}}{#2}{#3}% }% \def\xintFloatE {\romannumeral0\xintfloate }% -\def\xintfloate #1{\XINT_floate_chkopt #1\Z }% +\def\xintfloate #1{\XINT_floate_chkopt #1\xint_relax }% \def\XINT_floate_chkopt #1% {% \ifx [#1\expandafter\XINT_floate_opt \else\expandafter\XINT_floate_noopt \fi #1% }% -\def\XINT_floate_noopt #1\Z +\def\XINT_floate_noopt #1\xint_relax {% \expandafter\XINT_floate_a\expandafter\XINTdigits \romannumeral0\XINT_infrac {#1}% }% -\def\XINT_floate_opt [\Z #1]#2% +\def\XINT_floate_opt [\xint_relax #1]#2% {% \expandafter\XINT_floate_a\expandafter {\the\numexpr #1\expandafter}\romannumeral0\XINT_infrac {#2}% @@ -1239,19 +1237,19 @@ {\afterassignment \xint_gobble_i \mathchardef\XINTdigits=}% \def\xinttheDigits {\number\XINTdigits }% \def\xintFloat {\romannumeral0\xintfloat }% -\def\xintfloat #1{\XINT_float_chkopt #1\Z }% +\def\xintfloat #1{\XINT_float_chkopt #1\xint_relax }% \def\XINT_float_chkopt #1% {% \ifx [#1\expandafter\XINT_float_opt \else\expandafter\XINT_float_noopt \fi #1% }% -\def\XINT_float_noopt #1\Z +\def\XINT_float_noopt #1\xint_relax {% \expandafter\XINT_float_a\expandafter\XINTdigits \romannumeral0\XINT_infrac {#1}\XINT_float_Q }% -\def\XINT_float_opt [\Z #1]#2% +\def\XINT_float_opt [\xint_relax #1]#2% {% \expandafter\XINT_float_a\expandafter {\the\numexpr #1\expandafter}% @@ -1915,20 +1913,20 @@ \def\xintSgn {\romannumeral0\xintsgn }% \def\xintsgn #1{\expandafter\XINT_sgn\romannumeral0\xintraw {#1}\Z }% \def\xintFloatAdd {\romannumeral0\xintfloatadd }% -\def\xintfloatadd #1{\XINT_fladd_chkopt \xintfloat #1\Z }% +\def\xintfloatadd #1{\XINT_fladd_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatAdd {\romannumeral0\XINTinfloatadd }% -\def\XINTinfloatadd #1{\XINT_fladd_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatadd #1{\XINT_fladd_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_fladd_chkopt #1#2% {% \ifx [#2\expandafter\XINT_fladd_opt \else\expandafter\XINT_fladd_noopt \fi #1#2% }% -\def\XINT_fladd_noopt #1#2\Z #3% +\def\XINT_fladd_noopt #1#2\xint_relax #3% {% #1[\XINTdigits]{\XINT_FL_Add {\XINTdigits+\xint_c_ii}{#2}{#3}}% }% -\def\XINT_fladd_opt #1[\Z #2]#3#4% +\def\XINT_fladd_opt #1[\xint_relax #2]#3#4% {% #1[#2]{\XINT_FL_Add {#2+\xint_c_ii}{#3}{#4}}% }% @@ -1963,38 +1961,38 @@ \def\XINT_FL_Add_zero 0\XINT_FL_Add_c 0[0]#1[#2]#3{#1[#2]}% \def\XINT_FL_Add_zerobis 0\XINT_FL_Add_d #1[#2]0[0]#3{#1[#2]}% \def\xintFloatSub {\romannumeral0\xintfloatsub }% -\def\xintfloatsub #1{\XINT_flsub_chkopt \xintfloat #1\Z }% +\def\xintfloatsub #1{\XINT_flsub_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatSub {\romannumeral0\XINTinfloatsub }% -\def\XINTinfloatsub #1{\XINT_flsub_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatsub #1{\XINT_flsub_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_flsub_chkopt #1#2% {% \ifx [#2\expandafter\XINT_flsub_opt \else\expandafter\XINT_flsub_noopt \fi #1#2% }% -\def\XINT_flsub_noopt #1#2\Z #3% +\def\XINT_flsub_noopt #1#2\xint_relax #3% {% #1[\XINTdigits]{\XINT_FL_Add {\XINTdigits+\xint_c_ii}{#2}{\xintOpp{#3}}}% }% -\def\XINT_flsub_opt #1[\Z #2]#3#4% +\def\XINT_flsub_opt #1[\xint_relax #2]#3#4% {% #1[#2]{\XINT_FL_Add {#2+\xint_c_ii}{#3}{\xintOpp{#4}}}% }% \def\xintFloatMul {\romannumeral0\xintfloatmul}% -\def\xintfloatmul #1{\XINT_flmul_chkopt \xintfloat #1\Z }% +\def\xintfloatmul #1{\XINT_flmul_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatMul {\romannumeral0\XINTinfloatmul }% -\def\XINTinfloatmul #1{\XINT_flmul_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatmul #1{\XINT_flmul_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_flmul_chkopt #1#2% {% \ifx [#2\expandafter\XINT_flmul_opt \else\expandafter\XINT_flmul_noopt \fi #1#2% }% -\def\XINT_flmul_noopt #1#2\Z #3% +\def\XINT_flmul_noopt #1#2\xint_relax #3% {% #1[\XINTdigits]{\XINT_FL_Mul {\XINTdigits+\xint_c_ii}{#2}{#3}}% }% -\def\XINT_flmul_opt #1[\Z #2]#3#4% +\def\XINT_flmul_opt #1[\xint_relax #2]#3#4% {% #1[#2]{\XINT_FL_Mul {#2+\xint_c_ii}{#3}{#4}}% }% @@ -2009,20 +2007,20 @@ }% \def\XINT_FL_Mul_b #1[#2]#3[#4]{\xintE{\xintiiMul {#1}{#3}}{#2+#4}}% \def\xintFloatDiv {\romannumeral0\xintfloatdiv}% -\def\xintfloatdiv #1{\XINT_fldiv_chkopt \xintfloat #1\Z }% +\def\xintfloatdiv #1{\XINT_fldiv_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatDiv {\romannumeral0\XINTinfloatdiv }% -\def\XINTinfloatdiv #1{\XINT_fldiv_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatdiv #1{\XINT_fldiv_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_fldiv_chkopt #1#2% {% \ifx [#2\expandafter\XINT_fldiv_opt \else\expandafter\XINT_fldiv_noopt \fi #1#2% }% -\def\XINT_fldiv_noopt #1#2\Z #3% +\def\XINT_fldiv_noopt #1#2\xint_relax #3% {% #1[\XINTdigits]{\XINT_FL_Div {\XINTdigits+\xint_c_ii}{#2}{#3}}% }% -\def\XINT_fldiv_opt #1[\Z #2]#3#4% +\def\XINT_fldiv_opt #1[\xint_relax #2]#3#4% {% #1[#2]{\XINT_FL_Div {#2+\xint_c_ii}{#3}{#4}}% }% @@ -2059,9 +2057,9 @@ {\expandafter\XINT_floatprd_b\romannumeral0\XINTinfloatmul {#1}}% \def\XINT_floatprd_e #1\Z #2\Z { #2}% \def\xintFloatPow {\romannumeral0\xintfloatpow}% -\def\xintfloatpow #1{\XINT_flpow_chkopt \xintfloat #1\Z }% +\def\xintfloatpow #1{\XINT_flpow_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatPow {\romannumeral0\XINTinfloatpow }% -\def\XINTinfloatpow #1{\XINT_flpow_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatpow #1{\XINT_flpow_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_flpow_chkopt #1#2% {% \ifx [#2\expandafter\XINT_flpow_opt @@ -2069,13 +2067,13 @@ \fi #1#2% }% -\def\XINT_flpow_noopt #1#2\Z #3% +\def\XINT_flpow_noopt #1#2\xint_relax #3% {% \expandafter\XINT_flpow_checkB_start\expandafter {\the\numexpr #3\expandafter}\expandafter {\the\numexpr \XINTdigits}{#2}{#1[\XINTdigits]}% }% -\def\XINT_flpow_opt #1[\Z #2]#3#4% +\def\XINT_flpow_opt #1[\xint_relax #2]#3#4% {% \expandafter\XINT_flpow_checkB_start\expandafter {\the\numexpr #4\expandafter}\expandafter @@ -2200,9 +2198,9 @@ \krof }% \def\xintFloatPower {\romannumeral0\xintfloatpower}% -\def\xintfloatpower #1{\XINT_flpower_chkopt \xintfloat #1\Z }% +\def\xintfloatpower #1{\XINT_flpower_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatPower {\romannumeral0\XINTinfloatpower}% -\def\XINTinfloatpower #1{\XINT_flpower_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatpower #1{\XINT_flpower_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_flpower_chkopt #1#2% {% \ifx [#2\expandafter\XINT_flpower_opt @@ -2210,13 +2208,13 @@ \fi #1#2% }% -\def\XINT_flpower_noopt #1#2\Z #3% +\def\XINT_flpower_noopt #1#2\xint_relax #3% {% \expandafter\XINT_flpower_checkB_start\expandafter {\the\numexpr \XINTdigits\expandafter}\expandafter {\romannumeral0\xintnum{#3}}{#2}{#1[\XINTdigits]}% }% -\def\XINT_flpower_opt #1[\Z #2]#3#4% +\def\XINT_flpower_opt #1[\xint_relax #2]#3#4% {% \expandafter\XINT_flpower_checkB_start\expandafter {\the\numexpr #2\expandafter}\expandafter @@ -2316,20 +2314,20 @@ #4{#3}{#5}% }% \def\xintFloatSqrt {\romannumeral0\xintfloatsqrt }% -\def\xintfloatsqrt #1{\XINT_flsqrt_chkopt \xintfloat #1\Z }% +\def\xintfloatsqrt #1{\XINT_flsqrt_chkopt \xintfloat #1\xint_relax }% \def\XINTinFloatSqrt {\romannumeral0\XINTinfloatsqrt }% -\def\XINTinfloatsqrt #1{\XINT_flsqrt_chkopt \XINTinfloat #1\Z }% +\def\XINTinfloatsqrt #1{\XINT_flsqrt_chkopt \XINTinfloat #1\xint_relax }% \def\XINT_flsqrt_chkopt #1#2% {% \ifx [#2\expandafter\XINT_flsqrt_opt \else\expandafter\XINT_flsqrt_noopt \fi #1#2% }% -\def\XINT_flsqrt_noopt #1#2\Z +\def\XINT_flsqrt_noopt #1#2\xint_relax {% #1[\XINTdigits]{\XINT_FL_sqrt \XINTdigits {#2}}% }% -\def\XINT_flsqrt_opt #1[\Z #2]#3% +\def\XINT_flsqrt_opt #1[\xint_relax #2]#3% {% #1[#2]{\XINT_FL_sqrt {#2}{#3}}% }% diff --git a/Master/texmf-dist/tex/generic/xint/xintgcd.sty b/Master/texmf-dist/tex/generic/xint/xintgcd.sty index 39b7301746a..a5016c7092b 100644 --- a/Master/texmf-dist/tex/generic/xint/xintgcd.sty +++ b/Master/texmf-dist/tex/generic/xint/xintgcd.sty @@ -21,7 +21,7 @@ %% same distribution. (The sources need not necessarily be %% in the same archive or directory.) %%---------------------------------------------------------------- -%% The xint bundle (version 1.09kb of February 13, 2014) +%% The xint bundle (version 1.09m of February 26, 2014) %% xintgcd: Euclidean algorithm with xint package %% Copyright (C) 2013-2014 by Jean-Francois Burnol %%---------------------------------------------------------------- @@ -101,7 +101,7 @@ \XINTsetupcatcodes% \XINT_providespackage \ProvidesPackage{xintgcd}% - [2014/02/13 v1.09kb Euclide algorithm with xint package (jfB)]% + [2014/02/26 v1.09m Euclide algorithm with xint package (jfB)]% \def\xintGCD {\romannumeral0\xintgcd }% \def\xintgcd #1% {% diff --git a/Master/texmf-dist/tex/generic/xint/xintseries.sty b/Master/texmf-dist/tex/generic/xint/xintseries.sty index b73dc876e64..117ccd4eb36 100644 --- a/Master/texmf-dist/tex/generic/xint/xintseries.sty +++ b/Master/texmf-dist/tex/generic/xint/xintseries.sty @@ -21,7 +21,7 @@ %% same distribution. (The sources need not necessarily be %% in the same archive or directory.) %%---------------------------------------------------------------- -%% The xint bundle (version 1.09kb of February 13, 2014) +%% The xint bundle (version 1.09m of February 26, 2014) %% xintseries: Expandable partial sums with xint package %% Copyright (C) 2013-2014 by Jean-Francois Burnol %%---------------------------------------------------------------- @@ -101,7 +101,7 @@ \XINTsetupcatcodes% \XINT_providespackage \ProvidesPackage{xintseries}% - [2014/02/13 v1.09kb Expandable partial sums with xint package (jfB)]% + [2014/02/26 v1.09m Expandable partial sums with xint package (jfB)]% \def\xintSeries {\romannumeral0\xintseries }% \def\xintseries #1#2% {% @@ -339,7 +339,7 @@ {#2}{#1}{#3}{#4}{#5}% }% \def\xintFloatPowerSeries {\romannumeral0\xintfloatpowerseries }% -\def\xintfloatpowerseries #1{\XINT_flpowseries_chkopt #1\Z }% +\def\xintfloatpowerseries #1{\XINT_flpowseries_chkopt #1\xint_relax }% \def\XINT_flpowseries_chkopt #1% {% \ifx [#1\expandafter\XINT_flpowseries_opt @@ -347,13 +347,13 @@ \fi #1% }% -\def\XINT_flpowseries_noopt #1\Z #2% +\def\XINT_flpowseries_noopt #1\xint_relax #2% {% \expandafter\XINT_flpowseries\expandafter {\the\numexpr #1\expandafter}\expandafter {\the\numexpr #2}\XINTdigits }% -\def\XINT_flpowseries_opt [\Z #1]#2#3% +\def\XINT_flpowseries_opt [\xint_relax #1]#2#3% {% \expandafter\XINT_flpowseries\expandafter {\the\numexpr #2\expandafter}\expandafter @@ -404,7 +404,7 @@ \xintfloatadd [#7]{#4}{\XINTinfloatmul [#7]{#6{#2}}{#1}}% }% \def\xintFloatPowerSeriesX {\romannumeral0\xintfloatpowerseriesx }% -\def\xintfloatpowerseriesx #1{\XINT_flpowseriesx_chkopt #1\Z }% +\def\xintfloatpowerseriesx #1{\XINT_flpowseriesx_chkopt #1\xint_relax }% \def\XINT_flpowseriesx_chkopt #1% {% \ifx [#1\expandafter\XINT_flpowseriesx_opt @@ -412,13 +412,13 @@ \fi #1% }% -\def\XINT_flpowseriesx_noopt #1\Z #2% +\def\XINT_flpowseriesx_noopt #1\xint_relax #2% {% \expandafter\XINT_flpowseriesx\expandafter {\the\numexpr #1\expandafter}\expandafter {\the\numexpr #2}\XINTdigits }% -\def\XINT_flpowseriesx_opt [\Z #1]#2#3% +\def\XINT_flpowseriesx_opt [\xint_relax #1]#2#3% {% \expandafter\XINT_flpowseriesx\expandafter {\the\numexpr #2\expandafter}\expandafter diff --git a/Master/texmf-dist/tex/generic/xint/xinttools.sty b/Master/texmf-dist/tex/generic/xint/xinttools.sty index 11d8315c830..9b5e78d39b8 100644 --- a/Master/texmf-dist/tex/generic/xint/xinttools.sty +++ b/Master/texmf-dist/tex/generic/xint/xinttools.sty @@ -21,7 +21,7 @@ %% same distribution. (The sources need not necessarily be %% in the same archive or directory.) %%---------------------------------------------------------------- -%% The xint bundle (version 1.09kb of February 13, 2014) +%% The xint bundle (version 1.09m of February 26, 2014) %% xinttools: Expandable and non-expandable utilities %% Copyright (C) 2013-2014 by Jean-Francois Burnol %%---------------------------------------------------------------- @@ -152,7 +152,7 @@ \fi \XINT_providespackage \ProvidesPackage {xinttools}% - [2014/02/13 v1.09kb Expandable and non-expandable utilities (jfB)]% + [2014/02/26 v1.09m Expandable and non-expandable utilities (jfB)]% \long\def\xint_gobble_ {}% \long\def\xint_gobble_i #1{}% \long\def\xint_gobble_ii #1#2{}% @@ -163,12 +163,14 @@ \long\def\xint_gobble_vii #1#2#3#4#5#6#7{}% \long\def\xint_gobble_viii #1#2#3#4#5#6#7#8{}% \long\def\xint_firstofone #1{#1}% -\xint_firstofone{\let\XINT_sptoken= } %<- space here! \long\def\xint_firstoftwo #1#2{#1}% \long\def\xint_secondoftwo #1#2{#2}% +\long\def\xint_firstofone_thenstop #1{ #1}% \long\def\xint_firstoftwo_thenstop #1#2{ #1}% \long\def\xint_secondoftwo_thenstop #1#2{ #2}% \def\xint_minus_thenstop { -}% +\def\xint_gob_til_zero #10{}% no need to make it long, so far +\def\xint_UDzerominusfork #10-#2#3\krof {#2}% id. \long\def\xint_gob_til_R #1\R {}% \long\def\xint_gob_til_W #1\W {}% \long\def\xint_gob_til_Z #1\Z {}% @@ -178,9 +180,16 @@ \long\def\xint_gob_til_xint_relax #1\xint_relax {}% \long\def\xint_afterfi #1#2\fi {\fi #1}% \chardef\xint_c_ 0 -\chardef\xint_c_i 1 % 1.09k did not have it, but needed in \xintSeq +\chardef\xint_c_i 1 +\chardef\xint_c_ii 2 +\chardef\xint_c_iii 3 +\chardef\xint_c_iv 4 +\chardef\xint_c_v 5 +\chardef\xint_c_vi 6 +\chardef\xint_c_vii 7 \chardef\xint_c_viii 8 \newtoks\XINT_toks +\xint_firstofone{\let\XINT_sptoken= } %<- space here! \def\xintodef #1{\expandafter\def\expandafter#1\expandafter }% \ifdefined\odef\else\let\odef\xintodef\fi \def\xintgodef {\global\xintodef }% @@ -256,33 +265,33 @@ \long\def\xintlength #1% {% \XINT_length_loop - {0}#1\xint_relax\xint_relax\xint_relax\xint_relax + 0.#1\xint_relax\xint_relax\xint_relax\xint_relax \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye }% -\long\def\XINT_length_loop #1#2#3#4#5#6#7#8#9% +\long\def\XINT_length_loop #1.#2#3#4#5#6#7#8#9% {% \xint_gob_til_xint_relax #9\XINT_length_finish_a\xint_relax - \expandafter\XINT_length_loop\expandafter {\the\numexpr #1+8\relax}% + \expandafter\XINT_length_loop\the\numexpr #1+\xint_c_viii.% }% -\def\XINT_length_finish_a\xint_relax - \expandafter\XINT_length_loop\expandafter #1#2\xint_bye +\def\XINT_length_finish_a\xint_relax\expandafter\XINT_length_loop + \the\numexpr #1+\xint_c_viii.#2\xint_bye {% \XINT_length_finish_b #2\W\W\W\W\W\W\W\Z {#1}% }% \def\XINT_length_finish_b #1#2#3#4#5#6#7#8\Z {% \xint_gob_til_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 + #1\XINT_length_finish_c \xint_c_ + #2\XINT_length_finish_c \xint_c_i + #3\XINT_length_finish_c \xint_c_ii + #4\XINT_length_finish_c \xint_c_iii + #5\XINT_length_finish_c \xint_c_iv + #6\XINT_length_finish_c \xint_c_v + #7\XINT_length_finish_c \xint_c_vi + \W\XINT_length_finish_c \xint_c_vii\Z }% \edef\XINT_length_finish_c #1#2\Z #3% - {\noexpand\expandafter\space\noexpand\the\numexpr #3-#1\relax}% + {\noexpand\expandafter\space\noexpand\the\numexpr #3+#1\relax}% \def\xintZapFirstSpaces {\romannumeral0\xintzapfirstspaces }% \long\edef\xintzapfirstspaces #1% {\noexpand\XINT_zapbsp_a \space #1\space\space\noexpand\xint_bye\xint_relax }% @@ -411,66 +420,217 @@ \long\def\XINT_lws_end\xint_bye\XINT_lws_loop_b #1#2#3{ #1}% \def\xintNthElt {\romannumeral0\xintnthelt }% \def\xintNthEltNoExpand {\romannumeral0\xintntheltnoexpand }% -\def\xintnthelt #1% +\def\xintnthelt #1#2% {% - \expandafter\XINT_nthelt_a\expandafter {\the\numexpr #1}% + \expandafter\XINT_nthelt_a\the\numexpr #1\expandafter.% + \expandafter{\romannumeral-`0#2}% }% \def\xintntheltnoexpand #1% {% - \expandafter\XINT_ntheltnoexpand_a\expandafter {\the\numexpr #1}% + \expandafter\XINT_nthelt_a\the\numexpr #1.% }% -\long\def\XINT_nthelt_a #1#2% +\def\XINT_nthelt_a #1#2.% {% - \ifnum #1<0 - \xint_afterfi{\expandafter\XINT_nthelt_c\expandafter - {\romannumeral0\xintrevwithbraces {#2}}{-#1}}% - \else - \xint_afterfi{\expandafter\XINT_nthelt_c\expandafter - {\romannumeral-`0#2}{#1}}% - \fi + \xint_UDzerominusfork + #1-{\XINT_nthelt_bzero}% + 0#1{\XINT_nthelt_bneg {#2}}% + 0-{\XINT_nthelt_bpos {#1#2}}% + \krof }% -\long\def\XINT_ntheltnoexpand_a #1#2% +\long\def\XINT_nthelt_bzero #1% {% - \ifnum #1<0 - \xint_afterfi{\expandafter\XINT_nthelt_c\expandafter - {\romannumeral0\xintrevwithbracesnoexpand {#2}}{-#1}}% - \else - \xint_afterfi{\expandafter\XINT_nthelt_c\expandafter - {#2}{#1}}% - \fi + \XINT_length_loop 0.#1\xint_relax\xint_relax\xint_relax\xint_relax + \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye }% -\long\def\XINT_nthelt_c #1#2% +\long\def\XINT_nthelt_bneg #1#2% {% - \ifnum #2>\xint_c_ - \expandafter\XINT_nthelt_loop_a - \else - \expandafter\XINT_length_loop - \fi {#2}#1\xint_relax\xint_relax\xint_relax\xint_relax + \expandafter\XINT_nthelt_loop_a\expandafter {\the\numexpr #1\expandafter}% + \romannumeral0\xintrevwithbracesnoexpand {#2}% + \xint_relax\xint_relax\xint_relax\xint_relax \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye }% +\long\def\XINT_nthelt_bpos #1#2% +{% + \XINT_nthelt_loop_a {#1}#2\xint_relax\xint_relax\xint_relax\xint_relax + \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye +}% \def\XINT_nthelt_loop_a #1% {% \ifnum #1>\xint_c_viii \expandafter\XINT_nthelt_loop_b \else - \expandafter\XINT_nthelt_getit + \XINT_nthelt_getit \fi {#1}% }% \long\def\XINT_nthelt_loop_b #1#2#3#4#5#6#7#8#9% {% \xint_gob_til_xint_relax #9\XINT_nthelt_silentend\xint_relax - \expandafter\XINT_nthelt_loop_a\expandafter{\the\numexpr #1-8}% + \expandafter\XINT_nthelt_loop_a\expandafter{\the\numexpr #1-\xint_c_viii}% }% \def\XINT_nthelt_silentend #1\xint_bye { }% -\def\XINT_nthelt_getit #1% +\def\XINT_nthelt_getit\fi #1% {% - \expandafter\expandafter\expandafter\XINT_nthelt_finish - \csname xint_gobble_\romannumeral\numexpr#1-1\endcsname + \fi\expandafter\expandafter\expandafter\XINT_nthelt_finish + \csname xint_gobble_\romannumeral\numexpr#1-\xint_c_i\endcsname }% \long\edef\XINT_nthelt_finish #1#2\xint_bye {\noexpand\xint_gob_til_xint_relax #1\noexpand\expandafter\space \noexpand\xint_gobble_iii\xint_relax\space #1}% +\def\xintKeep {\romannumeral0\xintkeep }% +\def\xintKeepNoExpand {\romannumeral0\xintkeepnoexpand }% +\def\xintkeep #1#2% +{% + \expandafter\XINT_keep_a\the\numexpr #1\expandafter.% + \expandafter{\romannumeral-`0#2}% +}% +\def\xintkeepnoexpand #1% +{% + \expandafter\XINT_keep_a\the\numexpr #1.% +}% +\def\XINT_keep_a #1#2.% +{% + \xint_UDzerominusfork + #1-{\expandafter\space\xint_gobble_i }% + 0#1{\XINT_keep_bneg_a {#2}}% + 0-{\XINT_keep_bpos {#1#2}}% + \krof +}% +\long\def\XINT_keep_bneg_a #1#2% +{% + \expandafter\XINT_keep_bneg_b \the\numexpr \xintLength{#2}-#1.{#2}% +}% +\def\XINT_keep_bneg_b #1#2.% +{% + \xint_UDzerominusfork + #1-{\xint_firstofone_thenstop }% + 0#1{\xint_firstofone_thenstop }% + 0-{\XINT_trim_bpos {#1#2}}% + \krof +}% +\long\def\XINT_keep_bpos #1#2% +{% + \XINT_keep_loop_a {#1}{}#2\xint_relax\xint_relax\xint_relax\xint_relax + \xint_relax\xint_relax\xint_relax\xint_bye +}% +\def\XINT_keep_loop_a #1% +{% + \ifnum #1>\xint_c_vi + \expandafter\XINT_keep_loop_b + \else + \XINT_keep_finish + \fi + {#1}% +}% +\long\def\XINT_keep_loop_b #1#2#3#4#5#6#7#8#9% +{% + \xint_gob_til_xint_relax #9\XINT_keep_enda\xint_relax + \expandafter\XINT_keep_loop_c\expandafter{\the\numexpr #1-\xint_c_vii}% + {{#3}{#4}{#5}{#6}{#7}{#8}{#9}}{#2}% +}% +\long\def\XINT_keep_loop_c #1#2#3{\XINT_keep_loop_a {#1}{#3#2}}% +\long\def\XINT_keep_enda\xint_relax + \expandafter\XINT_keep_loop_c\expandafter #1#2#3#4\xint_bye +{% + \XINT_keep_endb #4\W\W\W\W\W\W\Z #2{#3}% +}% +\def\XINT_keep_endb #1#2#3#4#5#6#7\Z +{% + \xint_gob_til_W + #1\XINT_keep_endc_ + #2\XINT_keep_endc_i + #3\XINT_keep_endc_ii + #4\XINT_keep_endc_iii + #5\XINT_keep_endc_iv + #6\XINT_keep_endc_v + \W\XINT_keep_endc_vi\Z +}% +\long\def\XINT_keep_endc_ #1\Z #2#3#4#5#6#7#8#9{ #9}% +\long\def\XINT_keep_endc_i #1\Z #2#3#4#5#6#7#8#9{ #9{#2}}% +\long\def\XINT_keep_endc_ii #1\Z #2#3#4#5#6#7#8#9{ #9{#2}{#3}}% +\long\def\XINT_keep_endc_iii #1\Z #2#3#4#5#6#7#8#9{ #9{#2}{#3}{#4}}% +\long\def\XINT_keep_endc_iv #1\Z #2#3#4#5#6#7#8#9{ #9{#2}{#3}{#4}{#5}}% +\long\def\XINT_keep_endc_v #1\Z #2#3#4#5#6#7#8#9{ #9{#2}{#3}{#4}{#5}{#6}}% +\long\def\XINT_keep_endc_vi\Z #1#2#3#4#5#6#7#8{ #8{#1}{#2}{#3}{#4}{#5}{#6}}% +\long\def\XINT_keep_finish\fi #1#2#3#4#5#6#7#8#9\xint_bye +{% + \fi\XINT_keep_finish_loop_a {#1}{}{#3}{#4}{#5}{#6}{#7}{#8}\Z {#2}% +}% +\def\XINT_keep_finish_loop_a #1% +{% + \xint_gob_til_zero #1\XINT_keep_finish_z0% + \expandafter\XINT_keep_finish_loop_b\expandafter + {\the\numexpr #1-\xint_c_i}% +}% +\long\def\XINT_keep_finish_z0% + \expandafter\XINT_keep_finish_loop_b\expandafter #1#2#3\Z #4{ #4#2}% +\long\def\XINT_keep_finish_loop_b #1#2#3% +{% + \xint_gob_til_xint_relax #3\XINT_keep_finish_exit\xint_relax + \XINT_keep_finish_loop_c {#1}{#2}{#3}% +}% +\long\def\XINT_keep_finish_exit\xint_relax + \XINT_keep_finish_loop_c #1#2#3\Z #4{ #4#2}% +\long\def\XINT_keep_finish_loop_c #1#2#3% + {\XINT_keep_finish_loop_a {#1}{#2{#3}}}% +\def\xintTrim {\romannumeral0\xinttrim }% +\def\xintTrimNoExpand {\romannumeral0\xinttrimnoexpand }% +\def\xinttrim #1#2% +{% + \expandafter\XINT_trim_a\the\numexpr #1\expandafter.% + \expandafter{\romannumeral-`0#2}% +}% +\def\xinttrimnoexpand #1% +{% + \expandafter\XINT_trim_a\the\numexpr #1.% +}% +\def\XINT_trim_a #1#2.% +{% + \xint_UDzerominusfork + #1-{\xint_firstofone_thenstop }% + 0#1{\XINT_trim_bneg_a {#2}}% + 0-{\XINT_trim_bpos {#1#2}}% + \krof +}% +\long\def\XINT_trim_bneg_a #1#2% +{% + \expandafter\XINT_trim_bneg_b \the\numexpr \xintLength{#2}-#1.{#2}% +}% +\def\XINT_trim_bneg_b #1#2.% +{% + \xint_UDzerominusfork + #1-{\expandafter\space\xint_gobble_i }% + 0#1{\expandafter\space\xint_gobble_i }% + 0-{\XINT_keep_bpos {#1#2}}% + \krof +}% +\long\def\XINT_trim_bpos #1#2% +{% + \XINT_trim_loop_a {#1}#2\xint_relax\xint_relax\xint_relax\xint_relax + \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye +}% +\def\XINT_trim_loop_a #1% +{% + \ifnum #1>\xint_c_vii + \expandafter\XINT_trim_loop_b + \else + \XINT_trim_finish + \fi + {#1}% +}% +\long\def\XINT_trim_loop_b #1#2#3#4#5#6#7#8#9% +{% + \xint_gob_til_xint_relax #9\XINT_trim_silentend\xint_relax + \expandafter\XINT_trim_loop_a\expandafter{\the\numexpr #1-\xint_c_viii}% +}% +\def\XINT_trim_silentend #1\xint_bye { }% +\def\XINT_trim_finish\fi #1% +{% + \fi\expandafter\expandafter\expandafter\XINT_trim_finish_a + \expandafter\expandafter\expandafter\space % avoids brace removal + \csname xint_gobble_\romannumeral\numexpr#1\endcsname +}% +\long\def\XINT_trim_finish_a #1\xint_relax #2\xint_bye {#1}% \def\xintApply {\romannumeral0\xintapply }% \def\xintApplyNoExpand {\romannumeral0\xintapplynoexpand }% \long\def\xintapply #1#2% |