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Diffstat (limited to 'Master/texmf-dist/source/generic/xint/xint.dtx')
| -rw-r--r-- | Master/texmf-dist/source/generic/xint/xint.dtx | 907 |
1 files changed, 489 insertions, 418 deletions
diff --git a/Master/texmf-dist/source/generic/xint/xint.dtx b/Master/texmf-dist/source/generic/xint/xint.dtx index fb30b1972e3..81e2427b474 100644 --- a/Master/texmf-dist/source/generic/xint/xint.dtx +++ b/Master/texmf-dist/source/generic/xint/xint.dtx @@ -3,27 +3,27 @@ % Extract all files via "etex xint.dtx" and do "make help" % or follow instructions from extracted README.md. %<*dtx> -\def\xintdtxtimestamp {Time-stamp: <01-03-2018 at 20:38:22 CET>} +\def\xintdtxtimestamp {Time-stamp: <07-03-2018 at 11:08:43 CET>} %</dtx> %<*drv> %% --------------------------------------------------------------- -\def\xintdocdate {2018/03/01} -\def\xintbndldate{2018/03/01} -\def\xintbndlversion {1.3} +\def\xintdocdate {2018/03/07} +\def\xintbndldate{2018/03/07} +\def\xintbndlversion {1.3a} %</drv> %<readme>% README %<changes>% CHANGE LOG -%<readme|changes>% xint 1.3 -%<readme|changes>% 2018/03/01 +%<readme|changes>% xint 1.3a +%<readme|changes>% 2018/03/07 %<readme|changes> -%<readme|changes> Source: xint.dtx 1.3 2018/03/01 (doc 2018/03/01) +%<readme|changes> Source: xint.dtx 1.3a 2018/03/07 (doc 2018/03/07) %<readme|changes> Author: Jean-Francois Burnol %<readme|changes> Info: Expandable operations on big integers, decimals, fractions %<readme|changes> License: LPPL 1.3c %<readme|changes> %<*!readme&!changes&!dohtmlsh&!dopdfsh&!makefile> %% --------------------------------------------------------------- -%% The xint bundle 1.3 2018/03/01 +%% The xint bundle 1.3a 2018/03/07 %% Copyright (C) 2013-2018 by Jean-Francois Burnol %<xintkernel>%% xintkernel: Paraphernalia for the xint packages %<xinttools>%% xinttools: Expandable and non-expandable utilities @@ -250,6 +250,35 @@ Makefile.mk.</div> %</readme>-------------------------------------------------------- %<*changes>------------------------------------------------------- +`1.3a (2018/03/07)` +---- + +### Incompatible changes + + - **xintcore**, **xint**, **xintfrac**: removal of the internal macros + which were used at `1.2o` to add a deprecation mechanism; all + deprecated macros have been removed at `1.3` so there was no reason + to keep the code used for deprecating them. + +### Bug fixes + + - **xintexpr**: the mechanism for adjunction to the expression parsers + of user defined functions was refactored and improved at previous + release `1.3`: in particular recursive definitions became possible. + But an oversight made these recursive functions quite inefficient (to + remain polite.) This release fixes the problem. + +### Improvements and new features + + - **xintexpr**: new conditionals `ifone()` and `ifint()`. + + - **xintfrac**: `\xintREZ` is faster on inputs having one hundred + digits or more. + + - Added to the user manual mention of macros such as `\xintDivFloor`, + `\xintMod`, `\xintModTrunc`, which had been left out so far. + + `1.3 (2018/03/01)` ---- @@ -260,10 +289,10 @@ Makefile.mk.</div> - **xintfrac**: addition and subtraction of `a/b` and `c/d` now use the l.c.m. of the denominators. Similarly the macro supporting the modulo - operator `/:` uses a l.c.m for the denominator of the result. + operator `/:` uses a l.c.m. for the denominator of the result. - **xintexpr**: the addition, subtraction, modulo `/:`, and the - `mod()`and `divmod()` functions produce generally smaller denominators + `mod()` and `divmod()` functions produce generally smaller denominators (see previous item). - **xintexpr**: formerly, the internal macros which are internally @@ -284,6 +313,7 @@ Makefile.mk.</div> - **xintexpr**: new function `preduce()` associated with `\xintPIrr`. + `1.2q (2018/02/06)` ---- @@ -3776,9 +3806,9 @@ Here is a (partial) list of the recognized symbols: \item |"| for hexadecimal input (uppercase only; package \xintbinhexname must be loaded additionally to \xintexprname), %\item |'| for octal input (\emph{not yet}), -\item functions \xintFor #1 in {num, reduce, abs, sgn, frac, floor, ceil, sqr, sqrt, +\item functions \xintFor #1 in {num, preduce, reduce, abs, sgn, frac, floor, ceil, sqr, sqrt, sqrtr, float, round, trunc, mod, quo, rem, - max, min, |`+`|, |`*`|, not, all, any, xor, if, ifsgn, even, odd, first, + max, min, |`+`|, |`*`|, not, all, any, xor, if, ifint, ifone, ifsgn, even, odd, first, last, reversed, bool, togl, factorial, binomial, pfactorial}\do {\func{#1}, } \item multi-arguments \func{gcd} and \func{lcm} are available if \xintgcdname is loaded, @@ -4087,7 +4117,7 @@ digits. This is not so many, let us print them here: \end{itemize} -\subsection {More examples, some quite elaborate, within this document} +\subsection {More examples within this document} \label{sec:awesome} \begin{itemize} @@ -4119,10 +4149,14 @@ digits. This is not so many, let us print them here: an \hyperlink{BrentSalamin}{expandable implementation of the Brent-Salamin algorithm} for evaluating $\pi$. +\item The \autoref{ssec:PrimesIV} implements expandably the Miller-Rabin + pseudo-primality test. + \item The functionalities of \xintexprname are illustrated with various - examples, found in locations such as in \autoref{xintdeffunc} and - \hyperlink{ssec:dummies}{functions with dummy variables} and \autoref{ssec:moredummies}. + other examples, in \autoref{xintdeffunc}, + \hyperlink{ssec:dummies}{Functions with dummy variables}, + \autoref{ssec:moredummies} or \hyperref[sssec:recursive]{Recursive definitions}. \end{itemize} Almost all of the computational results interspersed throughout the documentation are not hard-coded in the source file of this document but are @@ -4180,33 +4214,39 @@ file with name |README.md|. Further help and options will be found therein. This is release \expandafter|\xintbndlversion| of \expandafter|\xintbndldate|. -|1.3| brings one important main new feature: the possibility of -\hyperref[sssec:recursive]{recursive definitions} with \csbxint{deffunc} for +|1.3|'s added an important new feature: the possibility of +\hyperref[sssec:recursive]{recursive definitions} via \csbxint{deffunc} for user additions to the expression parsers. -Also, it adds macros \csbxint{PIrr} et \csbxint{DecToString} and function -\func{preduce}. +But an oversight caused such recursively defined functions to be very +inefficient. This is fixed at |1.3a|. + +|1.3a| adds \func{ifone} and \func{ifint} conditionals and has a faster +\csbxint{REZ}. It also documents some macros such as \csbxint{DivFloor} which, +although long existing, had somehow not made it into the user manual yet. -And it brings significant breaking changes: +|1.3| had added macros \csbxint{PIrr} et \csbxint{DecToString} and function +\func{preduce}. +And it came with some significant breaking changes: \begin{itemize}[nosep] \item Addition (\csbxint{Add}) and subtraction (\csbxint{Sub}) of fractions use the least common multiple of the denominators. -\item This of course modifies also addition and subtraction in |xintexpr|. +\item This modified also addition and subtraction as executed in |xintexpr|. Similarly the |/:| operator and the \func{mod} and \func{divmod} functions - also use a least common multiple for the denominator of the result. -\item The macros deprecated at |1.2o| have now been all removed. See + were changed to use a least common multiple for the denominator of the result. +\item The macros deprecated at |1.2o| were removed. See \autoref{ssec:coredeprecated}, \autoref{ssec:xintdeprecated}, and \autoref{ssec:xintdeprecatedNum} for details. \end{itemize} -|1.2q| fixes a bug introduced by |1.2l| in some cases of subtraction. It also -extends \hyperref[ssec:tacit multiplication]{Tacit multiplication} to cover +|1.2q| fixed a bug introduced by |1.2l| in some cases of subtraction. It also +extended \hyperref[ssec:tacit multiplication]{Tacit multiplication} to cover cases such as |10!20!30!|. -|1.2p| has some breaking changes and improvements (see |CHANGES.html| for bug +|1.2p| had some breaking changes and improvements (see |CHANGES.html| for bug fixes): \begin{itemize}[nosep] -\item \csbxint{Bezout}'s output is changed. +\item \csbxint{Bezout}'s output was changed. \item \csbxint{iiMod} macro, the |/:| (aka |'mod'|) operators as well as the \func{mod} function, and the |//| operator, are now associated with the \emph{floored}, not the \emph{truncated} division. @@ -4534,7 +4574,7 @@ corresponding definitions. \capstart \centering \xintAssignArray\xintCSVtoList{!, ?, |`*`|, |`+`|, abs, add, all, any, binomial, bool, ceil, -divmod, even, factorial, first, float, floor, frac, gcd, if, ifsgn, iter, +divmod, even, factorial, first, float, floor, frac, gcd, if, ifint, ifone, ifsgn, iter, iterr, last, lcm, len, max, min, mod, mul, not, num, odd, pfactorial, preduce, qfloat, qfrac, qint, quo, reduce, rem, reversed, round, rrseq, rseq, seq, sgn, sqr, @@ -4948,6 +4988,19 @@ for the behaviour if the arguments are negative. value is logical false. Both ``branches'' are evaluated (they are not really branches but just numbers). See also the |?| operator. + \funcdesc{ifint} (twofold-way conditional)\mbox{} + + \ctexttt{ifint}|(x,yes,no)| + checks if |x| is an integer and in that case chooses the ``yes'' branch.% + \NewWith{1.3a} + + \funcdesc{ifone} (twofold-way conditional)\mbox{} + + \ctexttt{if}|(x,yes,no)| + checks if |x| is equal to one and in that case chooses the ``yes'' branch.% + \NewWith{1.3a} + Slightly more efficient than |if(x==1,..,..)|. + \funcdesc{ifsgn} (threefold-way conditional)\mbox{} \ctexttt{ifsgn}|(cond,<0,=0,>0)| checks the sign of |cond| and @@ -5619,7 +5672,7 @@ and that |x/2y| is interpreted as |x/(2y)|.) % The names of the macros \csa{xintdeffunc}, \csa{xintdefiifunc}, % \csa{xintdeffloatfunc} (and those for variables) as well as their syntax % (with |:=| and an ending |;|) will be set definitely only in next release. - \footnotemark + % \footnotemark A function must be defined for a specific parser, using either |\xintdeffunc|, |\xintdefiifunc| or |\xintdeffloatfunc|. @@ -5629,9 +5682,13 @@ and that |x/2y| is interpreted as |x/(2y)|.) letter, because the parser will have made an attempt to use the letter as a dummy variable.) \end{framed} -\footnotetext{with the current syntax, the |;| as used for |iterr|, |rseq|, - |rrseq| must be hidden as |{;}| to not be confused with the |;| ending the - declaration.} +% \footnotetext{with the current syntax, the |;| as used for |iterr|, |rseq|, +% |rrseq| must be hidden as |{;}| to not be confused with the |;| ending the +% declaration.} + +Currently, it is not possible to define a function of a single variable, say +|L|, which would stand for a \emph{list} with an undetermined number of +elements (see \autoref{ssec:lists} for lists). This will perhaps be added in future. Let's try the famous \textsc{Rump} test: \begin{everbatim*} @@ -5744,19 +5801,16 @@ truncates its arguments to integers when used in |\xintexpr|). Our second example is modular exponentiation: \begin{everbatim*} -\xintdefiifunc powmod(x, m, n) := - if(m, - % m non zero (assume positive) - if(m=1, +\xintdefiifunc powmod_a(x, m, n) := + ifone(m, % m=1, return x modulo n x /: n, % m > 1 test if odd or even and do recursive call - if(odd(m), (x*sqr(powmod(x, m//2, n))) /: n, - sqr(powmod(x, m//2, n)) /: n + if(odd(m), (x*sqr(powmod_a(x, m//2, n))) /: n, + sqr(powmod_a(x, m//2, n)) /: n ) - ), - % m is zero, return 1 - 1); + ); +\xintdefiifunc powmod(x, m, n) := if(m, powmod_a(x, m, n), 1); \end{everbatim*} I have made the definition here for the |\xintiiexpr| parser; we could do the same for the |\xintexpr|-parser (but its usage with big powers would quickly @@ -5820,7 +5874,7 @@ will generate \begin{everbatim} Function f for \xintexpr parser associated to \XINT_expr_userfunc_f with me aning macro:#1->#1,\xintPow {#1}{2},\xintPow {#1}{3},\xintPow {#1}{#1} -Package xintexpr Info: (on line 2) + Function g for \xintexpr parser associated to \XINT_expr_userfunc_g with me aning macro:#1->\xintApply::csv {\xintPow {#1}}{\xintSeq::csv {0}{#1}} \end{everbatim} @@ -7951,13 +8005,16 @@ which is described later; none of this uses count registers. \label{ssec:PrimesIV} This section is based on my \url{http://tex.stackexchange.com/a/165008} post. -But I have modified it to use \csbxint{NewFunction} which is available since -|1.2i|. This is good opportunity to illustrate how \csbxint{NewFunction} can be -used to define a recursive function (here modular exponentiation.) -The modular exponentiation can be defined as a genuine |\xintiiexpr|-function -since |1.3|. The others still have the problem of using |iter|, or |break| -statements which are not compatible with \csbxint{deffunc}. +At the time of writing, the code at the link above is still the version from +April 2016 and it needed some hacks to get recursive (pseudo)-functions +defined. Since |1.2h| of |2016/11/20| there is \csbxint{NewFunction} which +allows us here to avoid such internal hacking. + +And since |1.3| of |2018/03/01|, it is possible to use \csbxint{defiifunc} +also for recursive definitions, so we use it here, but we can benefit from it +only for modular exponentiation as the rest of the code uses |iter| or |break| +statements which are not yet compatible with \csbxint{defiifunc}. The |isPseudoPrime(n)| is usable in \csbxint{iiexpr}-essions and establishes if its (positive) argument is a Miller-Rabin PseudoPrime to the bases $2, 3, @@ -7984,34 +8041,37 @@ then write a very fast expandable primality test for such numbers using only \begin{everbatim*} % I -------------------------------- Modular Exponentiation -% #1=x, #2=m, #3=N, compute x^m modulo N (with m non negative) -% We will always use it with 1< x < N hence we skip an initial reduction modulo N. +% Computes x^m modulo n (with m non negative). +% We will always use it with 1 < x < n -\xintdefiifunc powmod(x, m, n) := - if(m, - % m non zero (assume positive) - if(m=1, +\xintdefiifunc powmod_a(x, m, n) := + ifone(m, % m=1, return x modulo n x /: n, % m > 1 test if odd or even and do recursive call - if(odd(m), (x*sqr(powmod(x, m//2, n))) /: n, - sqr(powmod(x, m//2, n)) /: n + if(odd(m), (x*sqr(powmod_a(x, m//2, n))) /: n, + sqr(powmod_a(x, m//2, n)) /: n ) - ), - % m is zero, return 1 - 1); + ); +\xintdefiifunc powmod(x, m, n) := if(m, powmod_a(x, m, n), 1); -% See http://tex.stackexchange.com/a/165008 for a (perhaps slightly -% faster) macro-only approach not using \xintexpr. But since 1.3 the above -% is indeed associated with a single (!) f-expandable macro. Here is its -% (recursive) meaning (with end of lines added by TeX when writing to the log): +% See http://tex.stackexchange.com/a/165008 for macros written directly by a +% human. + +% For comparison here are the underlying support macros defined by +% \xintdefiifunc from the code above (since 1.3a): (with linebreaks added by +% TeX when writing to the log) + +% Function powmod_a for \xintiiexpr parser associated to \XINT_iiexpr_userfun +% c_powmod_a with meaning macro:#1#2#3->\xintiiifOne {#2}{\xintiiMod {#1}{#3}}{\x +% intiiifNotZero {\xintiiOdd {#2}}{\xintiiMod {\xintiiMul {#1}{\xintiiSqr {\xintE +% xpandArgs {XINT_iiexpr_userfunc_powmod_a}{{#1}{\xintiiDivFloor {#2}{2}}{#3}}}}} +% {#3}}{\xintiiMod {\xintiiSqr {\xintExpandArgs {XINT_iiexpr_userfunc_powmod_a}{{ +% #1}{\xintiiDivFloor {#2}{2}}{#3}}}}{#3}}} % Function powmod for \xintiiexpr parser associated to \XINT_iiexpr_userfunc_ -% powmod with meaning macro:#1#2#3->\xintifNotZero {#2}{\xintifNotZero {\xintiiEq -% {#2}{1}}{\xintiiMod {#1}{#3}}{\xintifNotZero {\xintiiOdd {#2}}{\xintiiMod {\xi -% ntiiMul {#1}{\xintiiSqr {\csname XINT_iiexpr_userfunc_powmod\endcsname {#1}{\xi -% ntiiDivFloor {#2}{2}}{#3}}}}{#3}}{\xintiiMod {\xintiiSqr {\csname XINT_iiexpr_u -% serfunc_powmod\endcsname {#1}{\xintiiDivFloor {#2}{2}}{#3}}}{#3}}}}{1} +% powmod with meaning macro:#1#2#3->\xintiiifNotZero {#2}{\xintExpandArgs {XINT_i +% iexpr_userfunc_powmod_a}{{#1}{#2}{#3}}}{1} % II ------------------------------ Miller-Rabin compositeness witness @@ -8045,6 +8105,10 @@ then write a very fast expandable primality test for such numbers using only {iter(y;(j=#4)?{break(!(@==#2-1))} {(@==#2-1)?{break(0)}{sqr(@)/:#2}},j=1++)} ,y=powmod(#1,#3,#2))} + +% added note (2018/03/07) it is possible in the above that m=#3 is never +% zero, so we should rather call powmod_a for a small gain, but I don't +% have time to re-read the code comments and settle this. % III ------------------------------------- Strong Pseudo Primes @@ -9879,6 +9943,12 @@ special, for example \csbxint{Trunc} produces decimal numbers, \csbxint{Irr} produces an |A/B| with no |[N]|, \csbxint{iTrunc} and \csbxint{iRound} produce integers without trailing |[N]| either, etc\dots +|1.3a| belatedly adds documentation for some macros such as +\csbxint{DivFloor} which had been defined long ago, but did not make it to the +user manual for various reasons, one being that it is thought few users will +use directly the \xintfracname macros, the \csbxint{expr} interface being more +convenient. For complete documentation refer to |sourcexint.pdf|. + \subsection{\csbh{xintNum}}\label{xintNumFrac} The original \csbxint{Num} \etype{\Ff} from \xintname is made a synonym to @@ -9953,6 +10023,9 @@ trailing zeroes of |A| and |B| are suppressed and |N| is accordingly adjusted. \xintREZ {178000/25600000[17]} \end{everbatim*} +This macro is used internally by various other constructs; its implementation +was redone entirely at |1.3a|, and it got faster on long inputs. + \subsection{\csbh{xintIrr}}\label{xintIrr} This puts the fraction\etype{\Ff} into its unique irreducible form: @@ -10531,26 +10604,78 @@ denominators.\CHANGED{1.3} Computes the product\etype{\Ff\Ff} of two fractions. -No reduction attempted. +Output is not reduced to smallest terms. \subsection{\csbh{xintDiv}}\label{xintDiv} Computes the quotient \etype{\Ff\Ff} of two fractions. (|\xintDiv{F}{G}| computes |F/G|). -No reduction attempted. +Output is not reduced to smallest terms. + +\subsection{\csbh{xintDivFloor}} +\label{xintDivFloor} + +Computes the quotient \etype{\Ff\Ff} of two arguments then apply floor +function to get an integer (in strict format). This macro was defined at |1.1| +(but was left not documented until |1.3a|...) and changed at |1.2p|, formerly +it appended |/1[0]| to output. +\begin{everbatim*} +\xintDivFloor{-170/3}{23/2} +\end{everbatim*} + +\subsection{\csbh{xintMod}} +\label{xintMod} + +Computes the remainder associated to the floored division\etype{\Ff\Ff} +\csbxint{DivFloor}. Prior to |1.2p| the meaning was the one of +\csbxint{ModTrunc}. Was left undocumented until |1.3a|. +\begin{everbatim*} +\xintMod{-170/3}{23/2} +\end{everbatim*} + +Modified at |1.3| to use a l.c.m. for the denominator of the result. +\CHANGED{1.3} + +\subsection{\csbh{xintDivMod}} +\label{xintDivMod} + +Computes both the floored division and the remainder\etype{\Ff\Ff} +\csbxint{DivFloor}. New at |1.2p| and documented at |1.3a|. +\begin{everbatim*} +\oodef\foo{\xintDivMod{-170/3}{23/2}}\meaning\foo +\end{everbatim*} \subsection{\csbh{xintDivTrunc}} \label{xintDivTrunc} Computes the quotient \etype{\Ff\Ff} of two arguments then -truncates to an integer. +truncates to an integer (in strict format). +\begin{everbatim*} +\xintDivTrunc{-170/3}{23/2} +\end{everbatim*} + +\subsection{\csbh{xintModTrunc}} +\label{xintModTrunc} + +Computes the remainder\etype{\Ff\Ff} associated with the truncated division of +two arguments. Prior to |1.2p| it was named \csbxint{Mod}, but the latter then +got associated with floored division. +\begin{everbatim*} +\xintModTrunc{-170/3}{23/2} +\end{everbatim*} + +Modified at |1.3| to use a l.c.m. for the denominator of the result. +\CHANGED{1.3} \subsection{\csbh{xintDivRound}} \label{xintDivRound} Computes the quotient \etype{\Ff\Ff} of the two arguments then rounds to an -integer. +integer (in strict format). +\begin{everbatim*} +\xintDivRound{-170/3}{23/2} +\end{everbatim*} \subsection{\csbh{xintSqr}}\label{xintSqr} @@ -11746,12 +11871,12 @@ ith meaning macro:#1#2#3#4#5#6#7#8#9->\xintSub {\xintSub {\xintSub {\xintAdd {\ xintAdd {\xintMul {\xintMul {#1}{#5}}{#9}}{\xintMul {\xintMul {#2}{#6}}{#7}}}{\ xintMul {\xintMul {#3}{#4}}{#8}}}{\xintMul {\xintMul {#2}{#4}}{#9}}}{\xintMul { \xintMul {#3}{#5}}{#7}}}{\xintMul {\xintMul {#1}{#6}}{#8}} -Package xintexpr Info: (on line 11) + Function det3bis for \xintexpr parser associated to \XINT_expr_userfunc_det 3bis with meaning macro:#1#2#3#4#5#6#7#8#9->\xintAdd {\xintSub {\xintMul {#1}{\ -csname XINT_expr_userfunc_det2\endcsname {#5}{#6}{#8}{#9}}}{\xintMul {#2}{\csna -me XINT_expr_userfunc_det2\endcsname {#4}{#6}{#7}{#9}}}}{\xintMul {#3}{\csname -XINT_expr_userfunc_det2\endcsname {#4}{#5}{#7}{#8}}} +xintExpandArgs {XINT_expr_userfunc_det2}{{#5}{#6}{#8}{#9}}}}{\xintMul {#2}{\xin +tExpandArgs {XINT_expr_userfunc_det2}{{#4}{#6}{#7}{#9}}}}}{\xintMul {#3}{\xintE +xpandArgs {XINT_expr_userfunc_det2}{{#4}{#5}{#7}{#8}}}} \end{everbatim} @@ -15890,6 +16015,20 @@ be treated as first item) number. % This is \expandafter|\xintbndlversion| of \expandafter|\xintbndldate|. % % \begin{itemize} +% \item Release |1.3a| of |2018/03/07|: +% \begin{itemize}[nosep] +% \item removes from \xintcorenameimp, \xintnameimp and \xintfracnameimp the +% whole deprecation mechanism, as there are no more currently any +% deprecated macro, +% \item adds |ifone()| and |ifint()| conditionals to the expression parsers, +% \item has a completely redone |\XINT_factortens|, in the style of |1.2| +% release (but about 100 digits at least are needed for noticeable speed +% gain), +% \item and last but not least fixes via addition of |\xintExpandArgs| the +% meaning of user defined functions, which in case of recursivity (as made +% possible at |1.3|) were badly inefficient for lack of expansion of their +% arguments. +% \end{itemize} % \item Release |1.3| of |2018/03/01|: % \begin{itemize}[nosep] % \item removed all macros previously deprecated at |1.2o|, @@ -16179,7 +16318,7 @@ be treated as first item) number. \fi \XINT_providespackage \ProvidesPackage {xintkernel}% - [2018/03/01 1.3 Paraphernalia for the xint packages (JFB)]% + [2018/03/07 1.3a Paraphernalia for the xint packages (JFB)]% % \end{macrocode} % \subsection{Constants} % \begin{macrocode} @@ -16346,9 +16485,13 @@ be treated as first item) number. % % Attention: removes brace pairs. % -% For digit tokens only a faster reverse macro is provided as +% For contents with only digit tokens a faster reverse macro is provided as % \xintReverseDigits from 1.2 xintcore.sty. % +% At 1.3a, \XINT_factortens from xintfrac.sty was redone in a faster +% \numexpr-expansion style, and it stopped using this. There remains only +% two calls from xintgcd.sty to \XINT_rord_main. +% % For comma separated items, 1.2g has (not user documented) \xintCSVReverse in % xinttools.sty.| % \begin{macrocode} @@ -16765,7 +16908,7 @@ be treated as first item) number. % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xinttools}% - [2018/03/01 1.3 Expandable and non-expandable utilities (JFB)]% + [2018/03/07 1.3a Expandable and non-expandable utilities (JFB)]% % \end{macrocode} % \lverb|\XINT_toks is used in macros such as \xintFor. It is not used % elsewhere in the xint bundle.| @@ -18146,6 +18289,14 @@ be treated as first item) number. }% \let\xintDigitsOf\xintAssignArray % \end{macrocode} +% \subsection{\csh{xintExpandArgs}} +% \lverb|1.3a. Added for the needs of user defined functions for the +% expression parsers. Should I re-code it to gain a bit in argument grabbing? +% Must be f-expandable.| +% \begin{macrocode} +\def\xintExpandArgs#1#2{\csname #1\expandafter\endcsname + \romannumeral0\xintapply\xint_firstofone{#2}}% +% \end{macrocode} %\subsection{CSV (non user documented) variants of Length, Keep, Trim, NthElt, Reverse} % % These routines are for use by |\xintListSel:x:csv| and |\xintListSel:f:csv| @@ -18705,7 +18856,7 @@ be treated as first item) number. % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xintcore}% - [2018/03/01 1.3 Expandable arithmetic on big integers (JFB)]% + [2018/03/07 1.3a Expandable arithmetic on big integers (JFB)]% % \end{macrocode} % \subsection{(WIP!) Error conditions and exceptions} % \lverb|As per the Mike Cowlishaw/IBM's General Decimal Arithmetic Specification @@ -21931,51 +22082,6 @@ be treated as first item) number. }% \def\XINT_fac_loop_exit #1!#2;!#3{#3#2;!}% % \end{macrocode} -% \subsection{\csh{XINT_signaldeprecated}} -% \lverb|1.2o| -% \begin{macrocode} -\def\XINT_signaldeprecated #1#2% -{% - \XINT_ifFlagRaised{#2}% - {}% already encountered (if not hidden in a group...) - {\XINT_RaiseFlag{Deprecated-#1}\XINT_RaiseFlag{#2}% - \expandafter\XINT_expandableerror\expandafter - {\csname#2\endcsname (#1) is deprecated! (RET to proceed)}}% -}% -% \end{macrocode} -% \subsection*{At End of \LaTeX\ Document deprecation message} -% \addcontentsline{toc}{subsection}{At End of \LaTeX\ Document deprecation message} -% \lverb|1.2o. Updated at 1.3 which actually removed all deprecated macros.| -% \begin{macrocode} -\ifdefined\documentclass\ifdefined\AtEndDocument - \AtEndDocument{% -\XINT_ifFlagRaised{Deprecated-xintcore}% - {\PackageError{xintcore} -{Usage of deprecated macros!} -{These deprecated macros from xintcore.sty have been detected:\MessageBreak -\XINT_useiimessage{xintSgn}% -\XINT_useiimessage{xintCmp}% -\XINT_ifFlagRaised{xintiOpp}{\string\xintiOpp\MessageBreak}{}% -\XINT_ifFlagRaised{xintiAbs}{\string\xintiAbs\MessageBreak}{}% -\XINT_ifFlagRaised{xintiiFDg}{\string\xintiiFDg\space(renamed to \string\xintFDg!)\MessageBreak}{}% -\XINT_ifFlagRaised{xintiiLDg}{\string\xintiiLDg\space(renamed to \string\xintLDg!)\MessageBreak}{}% -\XINT_ifFlagRaised{xintiAdd}{\string\xintiAdd\MessageBreak}{}% -\XINT_ifFlagRaised{xintiSub}{\string\xintiSub\MessageBreak}{}% -\XINT_ifFlagRaised{xintiMul}{\string\xintiMul\MessageBreak}{}% -\XINT_ifFlagRaised{xintiDivision}{\string\xintiDivision\MessageBreak}{}% -\XINT_ifFlagRaised{xintiQuo}{\string\xintiQuo\MessageBreak}{}% -\XINT_ifFlagRaised{xintiRem}{\string\xintiRem\MessageBreak}{}% -\XINT_ifFlagRaised{xintiDivRound}{\string\xintiDivRound\MessageBreak}{}% -\XINT_ifFlagRaised{xintiDivTrunc}{\string\xintiDivTrunc\MessageBreak}{}% -\XINT_ifFlagRaised{xintiMod}{\string\xintiMod\MessageBreak}{}% -\XINT_ifFlagRaised{xintiSqr}{\string\xintiSqr\MessageBreak}{}% -\XINT_ifFlagRaised{xintiPow}{\string\xintiPow\MessageBreak}{}% -\XINT_ifFlagRaised{xintiFac}{\string\xintiFac\MessageBreak}{}% -This is not possible because they all got removed from xintcore at 1.3!}}% - {% no deprecated macro used (at top level...) - }% -}\fi\fi -% \end{macrocode} % \subsection{\csh{XINT_useiimessage}} % \lverb|1.2o| % \begin{macrocode} @@ -22057,7 +22163,7 @@ This is not possible because they all got removed from xintcore at 1.3!}}% % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xint}% - [2018/03/01 1.3 Expandable operations on big integers (JFB)]% + [2018/03/07 1.3a Expandable operations on big integers (JFB)]% % \end{macrocode} % \subsection{More token management} % \begin{macrocode} @@ -24107,56 +24213,6 @@ This is not possible because they all got removed from xintcore at 1.3!}}% \def\xintBool #1{\romannumeral`&&@% \csname if#1\endcsname\expandafter1\else\expandafter0\fi }% \def\xintToggle #1{\romannumeral`&&@\iftoggle{#1}{1}{0}}% -% \end{macrocode} -% \subsection*{At End of \LaTeX\ Document deprecation message} -% \addcontentsline{toc}{subsection}{At End of \LaTeX\ Document deprecation message} -% \lverb|1.2o| -% \begin{macrocode} -\ifdefined\documentclass\ifdefined\AtEndDocument - \AtEndDocument{% -\XINT_ifFlagRaised{Deprecated-xint}% - {\PackageError{xint} -{Usage of deprecated macros!} -{These deprecated macros from xint.sty have been detected:\MessageBreak -\XINT_useiimessage{xintEq}% -\XINT_useiimessage{xintGeq}% -\XINT_useiimessage{xintGt}% -\XINT_useiimessage{xintLt}% -\XINT_useiimessage{xintGtorEq}% -\XINT_useiimessage{xintLtorEq}% -\XINT_useiimessage{xintIsZero}% -\XINT_useiimessage{xintIsNotZero}% -\XINT_useiimessage{xintIsOne}% -\XINT_useiimessage{xintOdd}% -\XINT_useiimessage{xintEven}% -\XINT_useiimessage{xintifSgn}% -\XINT_useiimessage{xintifCmp}% -\XINT_useiimessage{xintifEq}% -\XINT_useiimessage{xintifGt}% -\XINT_useiimessage{xintifLt}% -\XINT_useiimessage{xintifZero}% -\XINT_useiimessage{xintifNotZero}% -\XINT_useiimessage{xintifOne}% -\XINT_useiimessage{xintifOdd}% -\XINT_ifFlagRaised{xintNeq}% - {\string\xintNeq\space(use \string\xintiiNotEq\space or \string\xintNotEq\space from xintfrac!)\MessageBreak}{}% -\XINT_ifFlagRaised{xintNot}% - {\string\xintNot\space(renamed to \string\xintNOT!)\MessageBreak}{}% -\XINT_ifFlagRaised{xintMON}{\string\xintMON\MessageBreak}{}% -\XINT_ifFlagRaised{xintMMON}{\string\xintMMON\MessageBreak}{}% -\XINT_ifFlagRaised{xintiMax}{\string\xintiMax\MessageBreak}{}% -\XINT_ifFlagRaised{xintiMin}{\string\xintiMin\MessageBreak}{}% -\XINT_ifFlagRaised{xintiMaxof}{\string\xintiMaxof\MessageBreak}{}% -\XINT_ifFlagRaised{xintiMinof}{\string\xintiMinof\MessageBreak}{}% -\XINT_ifFlagRaised{xintiSquareRoot}{\string\xintiSquareRoot\MessageBreak}{}% -\XINT_ifFlagRaised{xintiSqrt}{\string\xintiSqrt\MessageBreak}{}% -\XINT_ifFlagRaised{xintiSqrtR}{\string\xintiSqrtR\MessageBreak}{}% -\XINT_ifFlagRaised{xintiBinomial}{\string\xintiBinomial\MessageBreak}{}% -\XINT_ifFlagRaised{xintiPFactorial}{\string\xintiPFactorial\MessageBreak}{}% -This is not possible because they all got removed at 1.3!}}% - {% no deprecated macro used (at top level...) - }% -}\fi\fi \XINT_restorecatcodes_endinput% % \end{macrocode} % @@ -24243,7 +24299,7 @@ This is not possible because they all got removed at 1.3!}}% % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xintbinhex}% - [2018/03/01 1.3 Expandable binary and hexadecimal conversions (JFB)]% + [2018/03/07 1.3a Expandable binary and hexadecimal conversions (JFB)]% % \end{macrocode} % \subsection{Constants, etc...} % \lverb|1.2n switches to \csname-governed expansion at various places.| @@ -24895,7 +24951,7 @@ This is not possible because they all got removed at 1.3!}}% % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xintgcd}% - [2018/03/01 1.3 Euclide algorithm with xint package (JFB)]% + [2018/03/07 1.3a Euclide algorithm with xint package (JFB)]% % \end{macrocode} % \subsection{\csh{xintGCD}, \csh{xintiiGCD}} % \lverb|1.09a added \xintnum filtering from \xintiabs. This is a bit overhead @@ -25605,124 +25661,7 @@ This is not possible because they all got removed at 1.3!}}% % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xintfrac}% - [2018/03/01 1.3 Expandable operations on fractions (JFB)]% -% \end{macrocode} -% \subsection{Macros now removed from \xintcorenameimp and \xintnameimp} -% \lverb|Moved here at 1.3| -% \begin{macrocode} -\def\xintEq {\romannumeral0\xinteq }% -\def\xinteq #1#2{\xintifeq{#1}{#2}{1}{0}}% -\def\xintNotEq#1#2{\romannumeral0\xintifeq {#1}{#2}{0}{1}}% -%\def\xintGeq {\romannumeral0\xintgeq }% further down -\def\xintGt {\romannumeral0\xintgt }% -\def\xintgt #1#2{\xintifgt{#1}{#2}{1}{0}}% -\def\xintLt {\romannumeral0\xintlt }% -\def\xintlt #1#2{\xintiflt{#1}{#2}{1}{0}}% -\def\xintGtorEq #1#2{\romannumeral0\xintiflt {#1}{#2}{0}{1}}% -\def\xintLtorEq #1#2{\romannumeral0\xintifgt {#1}{#2}{0}{1}}% -\def\xintIsZero {\romannumeral0\xintiszero }% -\def\xintiszero #1{\if0\xintSgn{#1}\xint_afterfi{ 1}\else\xint_afterfi{ 0}\fi}% -\def\xintIsNotZero{\romannumeral0\xintisnotzero }% -\def\xintisnotzero - #1{\if0\xintSgn{#1}\xint_afterfi{ 0}\else\xint_afterfi{ 1}\fi}% -\def\xintIsOne {\romannumeral0\xintisone }% -\def\xintisone #1{\expandafter\XINT_isone\romannumeral0\xintnum{#1}XY}% -\def\xintOdd {\romannumeral0\xintodd }% -\def\xintodd #1% -{% - \ifodd\xintLDg{\xintNum{#1}} %<- intentional space - \xint_afterfi{ 1}% - \else - \xint_afterfi{ 0}% - \fi -}% -\def\xintEven {\romannumeral0\xinteven }% -\def\xinteven #1% -{% - \ifodd\xintLDg{\xintNum{#1}} %<- intentional space - \xint_afterfi{ 0}% - \else - \xint_afterfi{ 1}% - \fi -}% -\def\xintifSgn{\romannumeral0\xintifsgn }% -\def\xintifsgn #1% -{% - \ifcase \xintSgn{#1} - \expandafter\xint_secondofthree_thenstop - \or\expandafter\xint_thirdofthree_thenstop - \else\expandafter\xint_firstofthree_thenstop - \fi -}% -\def\xintifCmp{\romannumeral0\xintifcmp }% -\def\xintifcmp #1#2% -{% - \ifcase\xintCmp {#1}{#2} - \expandafter\xint_secondofthree_thenstop - \or\expandafter\xint_thirdofthree_thenstop - \else\expandafter\xint_firstofthree_thenstop - \fi -}% -\def\xintifEq {\romannumeral0\xintifeq }% -\def\xintifeq #1#2% -{% - \if0\xintCmp{#1}{#2}% - \expandafter\xint_firstoftwo_thenstop - \else\expandafter\xint_secondoftwo_thenstop - \fi -}% -\def\xintifGt {\romannumeral0\xintifgt }% -\def\xintifgt #1#2% -{% - \if1\xintCmp{#1}{#2}% - \expandafter\xint_firstoftwo_thenstop - \else\expandafter\xint_secondoftwo_thenstop - \fi -}% -\def\xintifLt {\romannumeral0\xintiflt }% -\def\xintiflt #1#2% -{% - \ifnum\xintCmp{#1}{#2}<\xint_c_ - \expandafter\xint_firstoftwo_thenstop - \else \expandafter\xint_secondoftwo_thenstop - \fi -}% -\def\xintifZero {\romannumeral0\xintifzero }% -\def\xintifzero #1% -{% - \if0\xintSgn{#1}% - \expandafter\xint_firstoftwo_thenstop - \else - \expandafter\xint_secondoftwo_thenstop - \fi -}% -\def\xintifNotZero{\romannumeral0\xintifnotzero }% -\def\xintifnotzero #1% -{% - \if0\xintSgn{#1}% - \expandafter\xint_secondoftwo_thenstop - \else - \expandafter\xint_firstoftwo_thenstop - \fi -}% -\def\xintifOne {\romannumeral0\xintifone }% -\def\xintifone #1% -{% - \if1\xintIsOne{#1}% - \expandafter\xint_firstoftwo_thenstop - \else - \expandafter\xint_secondoftwo_thenstop - \fi -}% -\def\xintifOdd {\romannumeral0\xintifodd }% -\def\xintifodd #1% -{% - \if\xintOdd{#1}1% - \expandafter\xint_firstoftwo_thenstop - \else - \expandafter\xint_secondoftwo_thenstop - \fi -}% + [2018/03/07 1.3a Expandable operations on fractions (JFB)]% % \end{macrocode} % \subsection{\csh{XINT_cntSgnFork}} % \lverb|1.09i. Used internally, #1 must expand to \m@ne, \z@, or \@ne or @@ -26036,101 +25975,171 @@ This is not possible because they all got removed at 1.3!}}% }% \def\XINT_frac_gen_zero 0#1#2#3{{0}{0}{1}}% % \end{macrocode} -% \subsection{\csh{XINT_factortens}, \csh{XINT_cuz_cnt}} -% \lverb|Old routines.| +% \subsection{\csh{XINT_factortens}} +% \lverb|This is the core macro for \xintREZ. To be used as +% \romannumeral0\XINT_factortens{...}. Output is A.N. (formerly {A}{N}) where +% A is the integer stripped from trailing zeroes and N is the number of +% removed zeroes. Only for positive strict integers! +% +% Completely rewritten at 1.3a to replace a double \xintReverseOrder by a +% direct \numexpr governed expansion to the end and back, à la 1.2. I should +% comment more... and perhaps improve again in future. +% +% Testing shows significant gain at 100 digits or more.| +% \begin{macrocode} +\def\XINT_factortens #1{\expandafter\XINT_factortens_z + \romannumeral0\XINT_factortens_a#1% + \XINT_factortens_b123456789.}% +\def\XINT_factortens_z.\XINT_factortens_y{ }% +\def\XINT_factortens_a #1#2#3#4#5#6#7#8#9% + {\expandafter\XINT_factortens_x + \the\numexpr 1#1#2#3#4#5#6#7#8#9\XINT_factortens_a}% +\def\XINT_factortens_b#1\XINT_factortens_a#2#3.% + {.\XINT_factortens_cc 000000000-#2.}% +\def\XINT_factortens_x1#1.#2{#2#1}% +\def\XINT_factortens_y{.\XINT_factortens_y}% +\def\XINT_factortens_cc #1#2#3#4#5#6#7#8#9% + {\if#90\xint_dothis + {\expandafter\XINT_factortens_d\the\numexpr #8#7#6#5#4#3#2#1\relax + \xint_c_i 2345678.}\fi + \xint_orthat{\XINT_factortens_yy{#1#2#3#4#5#6#7#8#9}}}% +\def\XINT_factortens_yy #1#2.{.\XINT_factortens_y#1.0.}% +\def\XINT_factortens_c #1#2#3#4#5#6#7#8#9% + {\if#90\xint_dothis + {\expandafter\XINT_factortens_d\the\numexpr #8#7#6#5#4#3#2#1\relax + \xint_c_i 2345678.}\fi + \xint_orthat{.\XINT_factortens_y #1#2#3#4#5#6#7#8#9.}}% +\def\XINT_factortens_d #1#2#3#4#5#6#7#8#9% + {\if#10\expandafter\XINT_factortens_e\fi + \XINT_factortens_f #9#9#8#7#6#5#4#3#2#1.}% +\def\XINT_factortens_f #1#2\xint_c_i#3.#4.#5.% + {\expandafter\XINT_factortens_g\the\numexpr#1+#5.#3.}% +\def\XINT_factortens_g #1.#2.{.\XINT_factortens_y#2.#1.}% +\def\XINT_factortens_e #1..#2.% + {\expandafter.\expandafter\XINT_factortens_c + \the\numexpr\xint_c_ix+#2.}% +% \end{macrocode} +% \subsection{\xintListWithSep{, } +% {\xintApply{ \csh}{{xintEq}{xintNotEq}{xintGt}{xintLt}{xintGtorEq} +% {xintLtorEq}{xintIsZero}{xintIsNotZero}{xintIsOne}{xintOdd} +% {xintEven}{xintifSgn}{xintifCmp}{xintifEq}{xintifGt}{xintifLt} +% {xintifZero}{xintifNotZero}{xintifOne}{xintifOdd}}}} +% +% \lverb|Moved here at 1.3. Formerly these macros were already defined in +% xint.sty or even xintcore.sty. They are slim wrappers of macros defined +% elsewhere in xintfrac.| % \begin{macrocode} -\def\XINT_factortens #1% -{% - \expandafter\XINT_cuz_cnt_loop\expandafter - {\expandafter}\romannumeral0\XINT_rord_main {}#1% - \xint: - \xint_bye\xint_bye\xint_bye\xint_bye - \xint_bye\xint_bye\xint_bye\xint_bye - \xint: - \R\R\R\R\R\R\R\R\Z -}% -\def\XINT_cuz_cnt #1% -{% - \XINT_cuz_cnt_loop {}#1\R\R\R\R\R\R\R\R\Z -}% -\def\XINT_cuz_cnt_loop #1#2#3#4#5#6#7#8#9% +\def\xintEq {\romannumeral0\xinteq }% +\def\xinteq #1#2{\xintifeq{#1}{#2}{1}{0}}% +\def\xintNotEq#1#2{\romannumeral0\xintifeq {#1}{#2}{0}{1}}% +\def\xintGt {\romannumeral0\xintgt }% +\def\xintgt #1#2{\xintifgt{#1}{#2}{1}{0}}% +\def\xintLt {\romannumeral0\xintlt }% +\def\xintlt #1#2{\xintiflt{#1}{#2}{1}{0}}% +\def\xintGtorEq #1#2{\romannumeral0\xintiflt {#1}{#2}{0}{1}}% +\def\xintLtorEq #1#2{\romannumeral0\xintifgt {#1}{#2}{0}{1}}% +\def\xintIsZero {\romannumeral0\xintiszero }% +\def\xintiszero #1{\if0\xintSgn{#1}\xint_afterfi{ 1}\else\xint_afterfi{ 0}\fi}% +\def\xintIsNotZero{\romannumeral0\xintisnotzero }% +\def\xintisnotzero + #1{\if0\xintSgn{#1}\xint_afterfi{ 0}\else\xint_afterfi{ 1}\fi}% +\def\xintIsOne {\romannumeral0\xintisone }% +\def\xintisone #1{\expandafter\XINT_isone\romannumeral0\xintnum{#1}XY}% +\def\xintOdd {\romannumeral0\xintodd }% +\def\xintodd #1% {% - \xint_gob_til_R #9\XINT_cuz_cnt_toofara \R - \expandafter\XINT_cuz_cnt_checka\expandafter - {\the\numexpr #1+8\relax}{#2#3#4#5#6#7#8#9}% + \ifodd\xintLDg{\xintNum{#1}} %<- intentional space + \xint_afterfi{ 1}% + \else + \xint_afterfi{ 0}% + \fi }% -\def\XINT_cuz_cnt_toofara\R - \expandafter\XINT_cuz_cnt_checka\expandafter #1#2% +\def\xintEven {\romannumeral0\xinteven }% +\def\xinteven #1% {% - \XINT_cuz_cnt_toofarb {#1}#2% + \ifodd\xintLDg{\xintNum{#1}} %<- intentional space + \xint_afterfi{ 0}% + \else + \xint_afterfi{ 1}% + \fi }% -\def\XINT_cuz_cnt_toofarb #1#2\Z {\XINT_cuz_cnt_toofarc #2\Z {#1}}% -\def\XINT_cuz_cnt_toofarc #1#2#3#4#5#6#7#8% +\def\xintifSgn{\romannumeral0\xintifsgn }% +\def\xintifsgn #1% {% - \xint_gob_til_R #2\XINT_cuz_cnt_toofard 7% - #3\XINT_cuz_cnt_toofard 6% - #4\XINT_cuz_cnt_toofard 5% - #5\XINT_cuz_cnt_toofard 4% - #6\XINT_cuz_cnt_toofard 3% - #7\XINT_cuz_cnt_toofard 2% - #8\XINT_cuz_cnt_toofard 1% - \Z #1#2#3#4#5#6#7#8% + \ifcase \xintSgn{#1} + \expandafter\xint_secondofthree_thenstop + \or\expandafter\xint_thirdofthree_thenstop + \else\expandafter\xint_firstofthree_thenstop + \fi }% -\def\XINT_cuz_cnt_toofard #1#2\Z #3\R #4\Z #5% +\def\xintifCmp{\romannumeral0\xintifcmp }% +\def\xintifcmp #1#2% {% - \expandafter\XINT_cuz_cnt_toofare - \the\numexpr #3\relax \R\R\R\R\R\R\R\R\Z - {\the\numexpr #5-#1\relax}\R\Z + \ifcase\xintCmp {#1}{#2} + \expandafter\xint_secondofthree_thenstop + \or\expandafter\xint_thirdofthree_thenstop + \else\expandafter\xint_firstofthree_thenstop + \fi }% -\def\XINT_cuz_cnt_toofare #1#2#3#4#5#6#7#8% +\def\xintifEq {\romannumeral0\xintifeq }% +\def\xintifeq #1#2% {% - \xint_gob_til_R #2\XINT_cuz_cnt_stopc 1% - #3\XINT_cuz_cnt_stopc 2% - #4\XINT_cuz_cnt_stopc 3% - #5\XINT_cuz_cnt_stopc 4% - #6\XINT_cuz_cnt_stopc 5% - #7\XINT_cuz_cnt_stopc 6% - #8\XINT_cuz_cnt_stopc 7% - \Z #1#2#3#4#5#6#7#8% + \if0\xintCmp{#1}{#2}% + \expandafter\xint_firstoftwo_thenstop + \else\expandafter\xint_secondoftwo_thenstop + \fi }% -\def\XINT_cuz_cnt_checka #1#2% +\def\xintifGt {\romannumeral0\xintifgt }% +\def\xintifgt #1#2% {% - \expandafter\XINT_cuz_cnt_checkb\the\numexpr #2\relax \Z {#1}% + \if1\xintCmp{#1}{#2}% + \expandafter\xint_firstoftwo_thenstop + \else\expandafter\xint_secondoftwo_thenstop + \fi }% -\def\XINT_cuz_cnt_checkb #1% +\def\xintifLt {\romannumeral0\xintiflt }% +\def\xintiflt #1#2% {% - \xint_gob_til_zero #1\expandafter\XINT_cuz_cnt_loop\xint_gob_til_Z - 0\XINT_cuz_cnt_stopa #1% + \ifnum\xintCmp{#1}{#2}<\xint_c_ + \expandafter\xint_firstoftwo_thenstop + \else \expandafter\xint_secondoftwo_thenstop + \fi }% -\def\XINT_cuz_cnt_stopa #1\Z +\def\xintifZero {\romannumeral0\xintifzero }% +\def\xintifzero #1% {% - \XINT_cuz_cnt_stopb #1\R\R\R\R\R\R\R\R\Z % + \if0\xintSgn{#1}% + \expandafter\xint_firstoftwo_thenstop + \else + \expandafter\xint_secondoftwo_thenstop + \fi }% -\def\XINT_cuz_cnt_stopb #1#2#3#4#5#6#7#8#9% +\def\xintifNotZero{\romannumeral0\xintifnotzero }% +\def\xintifnotzero #1% {% - \xint_gob_til_R #2\XINT_cuz_cnt_stopc 1% - #3\XINT_cuz_cnt_stopc 2% - #4\XINT_cuz_cnt_stopc 3% - #5\XINT_cuz_cnt_stopc 4% - #6\XINT_cuz_cnt_stopc 5% - #7\XINT_cuz_cnt_stopc 6% - #8\XINT_cuz_cnt_stopc 7% - #9\XINT_cuz_cnt_stopc 8% - \Z #1#2#3#4#5#6#7#8#9% + \if0\xintSgn{#1}% + \expandafter\xint_secondoftwo_thenstop + \else + \expandafter\xint_firstoftwo_thenstop + \fi }% -\def\XINT_cuz_cnt_stopc #1#2\Z #3\R #4\Z #5% +\def\xintifOne {\romannumeral0\xintifone }% +\def\xintifone #1% {% - \expandafter\XINT_cuz_cnt_stopd\expandafter - {\the\numexpr #5-#1}#3% + \if1\xintIsOne{#1}% + \expandafter\xint_firstoftwo_thenstop + \else + \expandafter\xint_secondoftwo_thenstop + \fi }% -\def\XINT_cuz_cnt_stopd #1#2\R #3\Z +\def\xintifOdd {\romannumeral0\xintifodd }% +\def\xintifodd #1% {% - \expandafter\space\expandafter - {\romannumeral0\XINT_rord_main {}#2% - \xint: - \xint_bye\xint_bye\xint_bye\xint_bye - \xint_bye\xint_bye\xint_bye\xint_bye - \xint:}{#1}% + \if\xintOdd{#1}1% + \expandafter\xint_firstoftwo_thenstop + \else + \expandafter\xint_secondoftwo_thenstop + \fi }% % \end{macrocode} % \subsection{\csh{xintRaw}} @@ -26397,7 +26406,10 @@ This is not possible because they all got removed at 1.3!}}% }% % \end{macrocode} % \subsection{\csh{xintREZ}} -% \lverb|Removes trailing zeros from A and B and adjust the N in A/B[N].| +% \lverb|Removes trailing zeros from A and B and adjust the N in A/B[N]. +% +% The macro really doing the job \XINT_factortens was redone at 1.3a. But +% speed gain really noticeable only beyond about 100 digits.| % \begin{macrocode} \def\xintREZ {\romannumeral0\xintrez }% \def\xintrez @@ -26422,16 +26434,15 @@ This is not possible because they all got removed at 1.3!}}% {% \expandafter\XINT_rez_C\romannumeral0\XINT_factortens {#1}% }% -\def\XINT_rez_C #1#2#3#4% +\def\XINT_rez_C #1.#2.#3#4% {% - \expandafter\XINT_rez_D\romannumeral0\XINT_factortens {#4}{#3}{#2}{#1}% + \expandafter\XINT_rez_D\romannumeral0\XINT_factortens {#4}#3+#2.#1.% }% -\def\XINT_rez_D #1#2#3#4#5% +\def\XINT_rez_D #1.#2.#3.% {% - \expandafter\XINT_rez_E\expandafter - {\the\numexpr #3+#4-#2}{#1}{#5}% + \expandafter\XINT_rez_E\the\numexpr #3-#2.#1.% }% -\def\XINT_rez_E #1#2#3{ #3/#2[#1]}% +\def\XINT_rez_E #1.#2.#3.{ #3/#2[#1]}% % \end{macrocode} % \subsection{\csh{xintE}} % \lverb|1.07: The fraction is the first argument contrarily to \xintTrunc and @@ -30178,23 +30189,17 @@ This is not possible because they all got removed at 1.3!}}% }% \def\XINT_infloatdivmod #1#2#3{ #1,\XINTinFloat[#3]{#2}}% % \end{macrocode} -% \subsection*{At End of \LaTeX\ Document deprecation message} -% \addcontentsline{toc}{subsection}{At End of \LaTeX\ Document deprecation message} -% \lverb|1.2o. Updated at 1.3 which actually removed the macros.| -% \begin{macrocode} -\ifdefined\documentclass\ifdefined\AtEndDocument - \AtEndDocument{% -\XINT_ifFlagRaised{Deprecated-xintfrac}% - {\PackageError{xintfrac} -{Usage of deprecated macros!} -{This deprecated macro from xintfrac.sty has been detected:\MessageBreak -%\XINT_ifFlagRaised{xintNeq}{% -\string\xintNeq\space(use \string\xintNotEq\space or xint's \string\xintiiNotEq!)\MessageBreak -%}{}% -This is impossible as it has been removed at 1.3!}}% - {% no deprecated macro used (at top level...) - }% -}\fi\fi +% \subsection{\csh{xintifFloatInt}} +% \begin{macrocode} +\def\xintifFloatInt {\romannumeral0\xintiffloatint}% +\def\xintiffloatint #1{\expandafter\XINT_iffloatint + \romannumeral0\xintrez{\XINTinFloat[\XINTdigits]{#1}}}% +\def\XINT_iffloatint #1#2/1[#3]% +{% + \if 0#1\xint_dothis\xint_firstoftwo_thenstop\fi + \ifnum#3<\xint_c_\xint_dothis\xint_secondoftwo_thenstop\fi + \xint_orthat\xint_firstoftwo_thenstop +}% \XINT_restorecatcodes_endinput% % \end{macrocode} % @@ -30270,7 +30275,7 @@ This is impossible as it has been removed at 1.3!}}% % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xintseries}% - [2018/03/01 1.3 Expandable partial sums with xint package (JFB)]% + [2018/03/07 1.3a Expandable partial sums with xint package (JFB)]% % \end{macrocode} % \subsection{\csh{xintSeries}} % \begin{macrocode} @@ -30771,7 +30776,7 @@ This is impossible as it has been removed at 1.3!}}% % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xintcfrac}% - [2018/03/01 1.3 Expandable continued fractions with xint package (JFB)]% + [2018/03/07 1.3a Expandable continued fractions with xint package (JFB)]% % \end{macrocode} % \subsection{\csh{xintCFrac}} % \begin{macrocode} @@ -32022,7 +32027,7 @@ This is impossible as it has been removed at 1.3!}}% % \begin{macrocode} \XINT_providespackage \ProvidesPackage{xintexpr}% - [2018/03/01 1.3 Expandable expression parser (JFB)]% + [2018/03/07 1.3a Expandable expression parser (JFB)]% \catcode`! 11 \let\XINT_Cmp \xintiiCmp % \end{macrocode} @@ -35598,20 +35603,50 @@ This is impossible as it has been removed at 1.3!}}% }% \let\XINT_flexpr_func_reversed\XINT_expr_func_reversed \let\XINT_iiexpr_func_reversed\XINT_expr_func_reversed -\def\xintifNotZero: #1,#2,#3,{\xintiiifNotZero{#1}{#2}{#3}}% +\def\xintiiifNotZero: #1,#2,#3,{\xintiiifNotZero{#1}{#2}{#3}}% \def\XINT_expr_func_if #1#2#3% {% \expandafter #1\expandafter #2\csname.=% - \expandafter\xintifNotZero:% + \expandafter\xintiiifNotZero:% \romannumeral`&&@\XINT_expr_unlock #3,\endcsname }% \let\XINT_flexpr_func_if\XINT_expr_func_if \let\XINT_iiexpr_func_if\XINT_expr_func_if -\def\xintifSgn: #1,#2,#3,#4,{\xintiiifSgn{#1}{#2}{#3}{#4}}% +\def\xintifInt: #1,#2,#3,{\xintifInt{#1}{#2}{#3}}% +\def\XINT_expr_func_ifint #1#2#3% +{% + \expandafter #1\expandafter #2\csname.=% + \expandafter\xintifInt:% + \romannumeral`&&@\XINT_expr_unlock #3,\endcsname +}% +\let\XINT_iiexpr_func_ifint\XINT_expr_func_ifint +\def\xintifFloatInt: #1,#2,#3,{\xintifFloatInt{#1}{#2}{#3}}% +\def\XINT_flexpr_func_ifint #1#2#3% +{% + \expandafter #1\expandafter #2\csname.=% + \expandafter\xintifFloatInt:% + \romannumeral`&&@\XINT_expr_unlock #3,\endcsname +}% +\def\xintifOne: #1,#2,#3,{\xintifOne{#1}{#2}{#3}}% +\def\XINT_expr_func_ifone #1#2#3% +{% + \expandafter #1\expandafter #2\csname.=% + \expandafter\xintifOne:% + \romannumeral`&&@\XINT_expr_unlock #3,\endcsname +}% +\let\XINT_flexpr_func_ifone\XINT_expr_func_ifone +\def\xintiiifOne: #1,#2,#3,{\xintiiifOne{#1}{#2}{#3}}% +\def\XINT_iiexpr_func_ifone #1#2#3% +{% + \expandafter #1\expandafter #2\csname.=% + \expandafter\xintiiifOne:% + \romannumeral`&&@\XINT_expr_unlock #3,\endcsname +}% +\def\xintiiifSgn: #1,#2,#3,#4,{\xintiiifSgn{#1}{#2}{#3}{#4}}% \def\XINT_expr_func_ifsgn #1#2#3% {% \expandafter #1\expandafter #2\csname.=% - \expandafter\xintifSgn:% + \expandafter\xintiiifSgn:% \romannumeral`&&@\XINT_expr_unlock #3,\endcsname }% \let\XINT_flexpr_func_ifsgn\XINT_expr_func_ifsgn @@ -35789,7 +35824,7 @@ This is impossible as it has been removed at 1.3!}}% {\csname XINT_#1_userfunc_#2\expandafter\endcsname \romannumeral0\xintcsvtolistnonstripped{#3}}% \def\XINT:newexpr:userfunc #1#2#3% - {~csname XINT_#1_userfunc_#2~endcsname\xintCSVtoListNonStripped{#3}}% + {~xintExpandArgs{XINT_#1_userfunc_#2}{\xintCSVtoListNonStripped{#3}}}% % \end{macrocode} % \subsection{\csh{xintNewFunction}} % \lverb|1.2h (2016/11/20). Syntax is \xintNewFunction{<name>}[nb of @@ -36068,20 +36103,52 @@ This is impossible as it has been removed at 1.3!}}% \XINT:NE:two#3{#1}{#2}% }% \let\XINT:newflexpr:two:to:one\XINT:newexpr:two:to:one -\def\xintifNotZeroNE:#1#2,#3,#4,% +\def\xintiiifNotZeroNE:#1#2,#3,#4,% +{% + \if1\if###11\else\if~#11\else\if$#11\else0%$ + \fi\fi\fi + \xint_dothis{~xintiiifNotZero}\fi + \xint_orthat\xintiiifNotZero + {#1#2}{#3}{#4}% +}% +\def\xintifIntNE:#1#2,#3,#4,% +{% + \if1\if###11\else\if~#11\else\if$#11\else0%$ + \fi\fi\fi + \xint_dothis{~xintifInt}\fi + \xint_orthat\xintifInt + {#1#2}{#3}{#4}% +}% +\def\xintifFloatIntNE:#1#2,#3,#4,% +{% + \if1\if###11\else\if~#11\else\if$#11\else0%$ + \fi\fi\fi + \xint_dothis{~xintifFloatInt}\fi + \xint_orthat\xintifFloatInt + {#1#2}{#3}{#4}% +}% +\def\xintiiifOneNE:#1#2,#3,#4,% +{% + \if1\if###11\else\if~#11\else\if$#11\else0%$ + \fi\fi\fi + \xint_dothis{~xintiiifOne}\fi + \xint_orthat\xintiiifOne + {#1#2}{#3}{#4}% +}% +\def\xintifOneNE:#1#2,#3,#4,% {% \if1\if###11\else\if~#11\else\if$#11\else0%$ \fi\fi\fi - \xint_dothis{~xintifNotZero}\fi - \xint_orthat\xintifNotZero + \xint_dothis{~xintifOne}\fi + \xint_orthat\xintifOne {#1#2}{#3}{#4}% }% -\def\xintifSgnNE:#1#2,#3,#4,#5,% +\def\xintiiifSgnNE:#1#2,#3,#4,#5,% {% \if1\if###11\else\if~#11\else\if$#11\else0%$ \fi\fi\fi - \xint_dothis{~xintifSgn}\fi - \xint_orthat\xintifSgn + \xint_dothis{~xintiiifSgn}\fi + \xint_orthat\xintiiifSgn {#1#2}{#3}{#4}{#5}% }% % \end{macrocode} @@ -36101,8 +36168,12 @@ This is impossible as it has been removed at 1.3!}}% \let\XINT:expr:two:to:one \XINT:newexpr:two:to:one \let\XINT:flexpr:two:to:two \XINT:newflexpr:two:to:two \let\XINT:flexpr:two:to:one \XINT:newflexpr:two:to:one - \let\xintifNotZero: \xintifNotZeroNE: - \let\xintifSgn: \xintifSgnNE: + \let\xintiiifNotZero: \xintiiifNotZeroNE: + \let\xintifInt: \xintifIntNE: + \let\xintifFloatInt: \xintifFloatIntNE: + \let\xintiiifOne: \xintiiifOneNE: + \let\xintifOne: \xintifOneNE: + \let\xintiiifSgn: \xintiiifSgnNE: \let\xintSeqNumeric::csv \xintSeq::csv \let\xintiiSeqNumeric::csv \xintiiSeq::csv \let\XINTinFloatSeqNumeric::csv \XINTinFloatSeq::csv @@ -36309,31 +36380,31 @@ This is impossible as it has been removed at 1.3!}}% xint.sty:161 xintbinhex.sty:53 xintcfrac.sty:183 -xintcore.sty:275 -xintexpr.sty:235 -xintfrac.sty:467 +xintcore.sty:274 +xintexpr.sty:243 +xintfrac.sty:455 xintgcd.sty:49 xintkernel.sty:13 xintseries.sty:48 xinttools.sty:140 \fi % grep -o "^{%" xint*sty | wc -l -\def\totala{ 1624} +\def\totala{ 1619} \iffalse % grep -c -e "^}%" xint*sty xint.sty:160 xintbinhex.sty:52 xintcfrac.sty:183 -xintcore.sty:272 -xintexpr.sty:260 -xintfrac.sty:468 +xintcore.sty:271 +xintexpr.sty:268 +xintfrac.sty:456 xintgcd.sty:51 xintkernel.sty:14 xintseries.sty:48 xinttools.sty:139 \fi % grep -o "^}%" xint*sty | wc -l -\def\totalb{ 1647} +\def\totalb{ 1642} \DeleteShortVerb{\|} \def\mymacro #1{\mymacroaux #1} \def\mymacroaux #1#2{\strut \csname #1nameimp\endcsname:& \dtt{ #2.}\tabularnewline } @@ -36370,7 +36441,7 @@ xinttools.sty:139 Right bracket \] Circumflex \^ Underscore \_ Grave accent \` Left brace \{ Vertical bar \| Right brace \} Tilde \~} -\CheckSum {30621}% 30988 pour 1.2q, 30982 pour 1.2p +\CheckSum {30482}% 30621 pour 1.3, 30988 pour 1.2q, 30982 pour 1.2p % 30524 pour 1.2o, 30303 pour 1.2h, 30403 pour 1.2i, 30750 pour 1.2j, % 30677 pour 1.2k, 30931 pour 1.2l, 30439 pour 1.2m, 30253 pour 1.2n \makeatletter\check@checksum\makeatother |