texlive[44900] Master/texmf-dist: xint (27jul17)
commits+karl at tug.org
commits+karl at tug.org
Thu Jul 27 23:26:25 CEST 2017
Revision: 44900
http://tug.org/svn/texlive?view=revision&revision=44900
Author: karl
Date: 2017-07-27 23:26:25 +0200 (Thu, 27 Jul 2017)
Log Message:
-----------
xint (27jul17)
Modified Paths:
--------------
trunk/Master/texmf-dist/doc/generic/xint/CHANGES.html
trunk/Master/texmf-dist/doc/generic/xint/CHANGES.pdf
trunk/Master/texmf-dist/doc/generic/xint/README
trunk/Master/texmf-dist/doc/generic/xint/README.html
trunk/Master/texmf-dist/doc/generic/xint/README.pdf
trunk/Master/texmf-dist/doc/generic/xint/sourcexint.pdf
trunk/Master/texmf-dist/doc/generic/xint/xint.pdf
trunk/Master/texmf-dist/source/generic/xint/xint.dtx
trunk/Master/texmf-dist/source/generic/xint/xint.ins
trunk/Master/texmf-dist/tex/generic/xint/xint.sty
trunk/Master/texmf-dist/tex/generic/xint/xintbinhex.sty
trunk/Master/texmf-dist/tex/generic/xint/xintcfrac.sty
trunk/Master/texmf-dist/tex/generic/xint/xintcore.sty
trunk/Master/texmf-dist/tex/generic/xint/xintexpr.sty
trunk/Master/texmf-dist/tex/generic/xint/xintfrac.sty
trunk/Master/texmf-dist/tex/generic/xint/xintgcd.sty
trunk/Master/texmf-dist/tex/generic/xint/xintkernel.sty
trunk/Master/texmf-dist/tex/generic/xint/xintseries.sty
trunk/Master/texmf-dist/tex/generic/xint/xinttools.sty
Modified: trunk/Master/texmf-dist/doc/generic/xint/CHANGES.html
===================================================================
--- trunk/Master/texmf-dist/doc/generic/xint/CHANGES.html 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/doc/generic/xint/CHANGES.html 2017-07-27 21:26:25 UTC (rev 44900)
@@ -4,7 +4,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta http-equiv="Content-Style-Type" content="text/css" />
<meta name="generator" content="pandoc" />
- <meta name="author" content="xint 1.2k" />
+ <meta name="author" content="xint 1.2l" />
<title>CHANGE LOG</title>
<style type="text/css">code{white-space: pre;}</style>
<style type="text/css">
@@ -17,67 +17,76 @@
<body>
<div id="header">
<h1 class="title">CHANGE LOG</h1>
-<h2 class="author">xint 1.2k</h2>
-<h3 class="date">2017/01/06</h3>
+<h2 class="author">xint 1.2l</h2>
+<h3 class="date">2017/07/26</h3>
</div>
<div id="TOC">
<ul>
-<li><a href="#k-20170106"><code>1.2k (2017/01/06)</code></a><ul>
-<li><a href="#incompatible-changes">Incompatible changes</a></li>
+<li><a href="#l-20170726"><code>1.2l (2017/07/26)</code></a><ul>
+<li><a href="#removed">Removed</a></li>
<li><a href="#improvements-and-new-features">Improvements and new features</a></li>
<li><a href="#bug-fixes">Bug fixes</a></li>
</ul></li>
-<li><a href="#j-20161222"><code>1.2j (2016/12/22)</code></a><ul>
+<li><a href="#k-20170106"><code>1.2k (2017/01/06)</code></a><ul>
+<li><a href="#incompatible-changes">Incompatible changes</a></li>
<li><a href="#improvements-and-new-features-1">Improvements and new features</a></li>
<li><a href="#bug-fixes-1">Bug fixes</a></li>
</ul></li>
-<li><a href="#i-20161213"><code>1.2i (2016/12/13)</code></a><ul>
-<li><a href="#incompatible-changes-1">Incompatible changes</a></li>
+<li><a href="#j-20161222"><code>1.2j (2016/12/22)</code></a><ul>
<li><a href="#improvements-and-new-features-2">Improvements and new features</a></li>
<li><a href="#bug-fixes-2">Bug fixes</a></li>
</ul></li>
-<li><a href="#h-20161120"><code>1.2h (2016/11/20)</code></a><ul>
+<li><a href="#i-20161213"><code>1.2i (2016/12/13)</code></a><ul>
+<li><a href="#incompatible-changes-1">Incompatible changes</a></li>
+<li><a href="#removed-1">Removed</a></li>
<li><a href="#improvements-and-new-features-3">Improvements and new features</a></li>
<li><a href="#bug-fixes-3">Bug fixes</a></li>
</ul></li>
+<li><a href="#h-20161120"><code>1.2h (2016/11/20)</code></a><ul>
+<li><a href="#improvements-and-new-features-4">Improvements and new features</a></li>
+<li><a href="#bug-fixes-4">Bug fixes</a></li>
+</ul></li>
<li><a href="#g-20160319"><code>1.2g (2016/03/19)</code></a><ul>
<li><a href="#incompatible-changes-2">Incompatible changes</a></li>
-<li><a href="#improvements-and-new-features-4">Improvements and new features</a></li>
+<li><a href="#improvements-and-new-features-5">Improvements and new features</a></li>
</ul></li>
<li><a href="#f-20160312"><code>1.2f (2016/03/12)</code></a><ul>
<li><a href="#incompatible-changes-3">Incompatible changes</a></li>
-<li><a href="#improvements-and-new-features-5">Improvements and new features</a></li>
-<li><a href="#bug-fixes-4">Bug fixes</a></li>
-</ul></li>
-<li><a href="#e-20151122"><code>1.2e (2015/11/22)</code></a><ul>
<li><a href="#improvements-and-new-features-6">Improvements and new features</a></li>
<li><a href="#bug-fixes-5">Bug fixes</a></li>
</ul></li>
-<li><a href="#d-20151118"><code>1.2d (2015/11/18)</code></a><ul>
+<li><a href="#e-20151122"><code>1.2e (2015/11/22)</code></a><ul>
<li><a href="#improvements-and-new-features-7">Improvements and new features</a></li>
<li><a href="#bug-fixes-6">Bug fixes</a></li>
</ul></li>
-<li><a href="#c-20151116"><code>1.2c (2015/11/16)</code></a><ul>
+<li><a href="#d-20151118"><code>1.2d (2015/11/18)</code></a><ul>
<li><a href="#improvements-and-new-features-8">Improvements and new features</a></li>
<li><a href="#bug-fixes-7">Bug fixes</a></li>
</ul></li>
-<li><a href="#b-20151029"><code>1.2b (2015/10/29)</code></a><ul>
+<li><a href="#c-20151116"><code>1.2c (2015/11/16)</code></a><ul>
+<li><a href="#improvements-and-new-features-9">Improvements and new features</a></li>
<li><a href="#bug-fixes-8">Bug fixes</a></li>
</ul></li>
-<li><a href="#a-20151019"><code>1.2a (2015/10/19)</code></a><ul>
-<li><a href="#improvements-and-new-features-9">Improvements and new features</a></li>
+<li><a href="#b-20151029"><code>1.2b (2015/10/29)</code></a><ul>
<li><a href="#bug-fixes-9">Bug fixes</a></li>
</ul></li>
-<li><a href="#section"><code>1.2 (2015/10/10)</code></a><ul>
+<li><a href="#a-20151019"><code>1.2a (2015/10/19)</code></a><ul>
<li><a href="#improvements-and-new-features-10">Improvements and new features</a></li>
+<li><a href="#bug-fixes-10">Bug fixes</a></li>
</ul></li>
+<li><a href="#section"><code>1.2 (2015/10/10)</code></a><ul>
+<li><a href="#removed-2">Removed</a></li>
+<li><a href="#improvements-and-new-features-11">Improvements and new features</a></li>
+</ul></li>
<li><a href="#c-20150912"><code>1.1c (2015/09/12)</code></a></li>
<li><a href="#b-20150831"><code>1.1b (2015/08/31)</code></a></li>
<li><a href="#a-20141107"><code>1.1a (2014/11/07)</code></a></li>
<li><a href="#section-1"><code>1.1 (2014/10/28)</code></a><ul>
<li><a href="#incompatible-changes-4">Incompatible changes</a></li>
-<li><a href="#improvements-and-new-features-11">Improvements and new features</a></li>
-<li><a href="#bug-fixes-10">Bug fixes</a></li>
+<li><a href="#removed-3">Removed</a></li>
+<li><a href="#deprecated">Deprecated</a></li>
+<li><a href="#improvements-and-new-features-12">Improvements and new features</a></li>
+<li><a href="#bug-fixes-11">Bug fixes</a></li>
</ul></li>
<li><a href="#n-20140401"><code>1.09n (2014/04/01)</code></a></li>
<li><a href="#m-20140226"><code>1.09m (2014/02/26)</code></a></li>
@@ -105,10 +114,30 @@
<li><a href="#section-8"><code>1.0 (2013/03/28)</code></a></li>
</ul>
</div>
-<pre><code>Source: xint.dtx 1.2k 2017/01/06 (doc 2017/01/06)
+<pre><code>Source: xint.dtx 1.2l 2017/07/26 (doc 2017/07/26)
Author: Jean-Francois Burnol
Info: Expandable operations on big integers, decimals, fractions
License: LPPL 1.3c</code></pre>
+<h2 id="l-20170726"><code>1.2l (2017/07/26)</code></h2>
+<h3 id="removed">Removed</h3>
+<ul>
+<li><code>\xintiiSumExpr</code>, <code>\xintiiPrdExpr</code> (<strong>xint</strong>) and <code>\xintSumExpr</code>, <code>\xintPrdExpr</code> (<strong>xintfrac</strong>). They had not been formally deprecated, but had been left un-documented since <code>1.09d (2013/10/22)</code>.</li>
+</ul>
+<h3 id="improvements-and-new-features">Improvements and new features</h3>
+<ul>
+<li><p>the underscore character <code>_</code> is accepted by the <strong>xintexpr</strong> parsers as a digit separator (the space character already could be used for improved readability of big numbers). It is not allowed as <em>first</em> character of a number, as it would then be mis-interpreted as the start of a possible variable name.</p></li>
+<li><p>some refactoring in <strong>xintcore</strong> auxiliary routines and in <code>\xintiiSub</code> and <code>\xintiiCmp</code> for some small efficiency gains.</p></li>
+<li><p>code comments in <strong>xintcore</strong> are better formatted, but remain sparse.</p></li>
+<li><p><strong>xintcore</strong>, <strong>xint</strong>, <strong>xintfrac</strong>, ... : some macros were not robust against arguments whose expansion looks forward for some termination (e.g. <code>\number\mathcode`\-</code>), and particularly, most were fragile against inputs using non-terminated <code>\numexpr</code> (such as <code>\xintiiAdd{\the\numexpr1}{2}</code> or <code>\xintRaw{\numexpr1}</code>). This was not a bug per se, as the user manual did not claim such inputs were legal, but it was slightly inconvenient. Most macros (particularly those of <strong>xintfrac</strong>) have now been made robust against such inputs. Some macros from <strong>xintcore</strong> primarily destined to internal usage still accept only properly terminated arguments such as <code>\the\mathcode`\-<space></code> or <code>\the\numexpr1\relax</code>.</p>
+<p>The situation with expressions is unchanged: syntax such as <code>\xintexpr \numexpr1+2\relax</code> is illegal as the ending <code>\relax</code> token will get swallowed by the <code>\numexpr</code>; but it is needed by the <code>xintexpr</code>-ession parser, hence the parser will expand forward and presumably end with in an "illegal token" error, or provoke some low-level TeX error (N.B.: a closing brace <code>}</code> for example can not terminate an <code>xintexpr</code>-ession, the parser must find a <code>\relax</code> token at some point). Thus there must be in this example a second <code>\relax</code>.</p></li>
+<li><p>experimental code for error conditions; there is no complete user interface yet, it is done in preparation for next major release and is completely unstable and undocumented.</p></li>
+</ul>
+<h3 id="bug-fixes">Bug fixes</h3>
+<ul>
+<li><p><strong>xintbinhex</strong>: since <code>1.2 (2015/10/10)</code>, <code>\xintHexToDec</code> was broken due to an undefined macro (it was in <code>xint.sty</code>, but the module by itself is supposedly dependent only upon <code>xintcore.sty</code>).</p></li>
+<li><p><strong>xintgcd</strong>: macro <code>\xintBezout</code> produced partially wrong output if one of its two arguments was zero.</p></li>
+<li><p><strong>xintfrac</strong>: the manual said one could use directly <code>\numexpr</code> compatible expressions in arithmetic macros (without even a <code>\numexpr</code> encapsulation) if they were expressed with up to 8 tokens. There was a bug if these 8 tokens evaluated to zero. The bug has been fixed, and up to 9 tokens are now accepted. But it is simpler to use <code>\the\numexpr</code> prefix and not to worry about the token count... The ending <code>\relax</code> is now un-needed.</p></li>
+</ul>
<h2 id="k-20170106"><code>1.2k (2017/01/06)</code></h2>
<h3 id="incompatible-changes">Incompatible changes</h3>
<ul>
@@ -115,7 +144,7 @@
<li><p>macro <code>\xintFloat</code> which rounds its input to a floating point number does <em>not</em> print anymore <code>10.0...0eN</code> to signal an upwards rounding to the next power of ten. The mantissa has in all cases except the zero input exactly one digit before the decimal mark.</p></li>
<li><p>some floating point computations may differ in the least significant digits, due to a change in the rounding algorithm applied to macro arguments expressed as fractions and to an improvement in precision regarding half-integer powers in expressions. See next.</p></li>
</ul>
-<h3 id="improvements-and-new-features">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-1">Improvements and new features</h3>
<ul>
<li><p>the initial rounding to the target precision <code>P</code> which is applied by the floating point macros from <strong>xintfrac</strong> to their arguments achieves the <em>exact (aka correct) rounding</em> even for inputs which are fractions with more than <code>P+2</code> digits in their numerators and denominators (<code>>1</code>.) Hence the computed values depend only on the arguments as rational numbers and not upon their representatives. This is not relevant to <em>expressions</em> (<strong>xintexpr</strong>), because the <code>\xintfloatexpr</code> parser sees there <code>/</code> as an operator and does not (apart from special constructs) get to manipulate fractions as such.</p></li>
<li><p><code>\xintnewdummy</code> is public interface to a <code>1.2e</code> macro which serves to declare any given catcode 11 character as a dummy variable for expressions (<strong>xintexpr</strong>). This is useful for Unicode engines (the Latin letters being already all pre-declared as dummy variables.)</p></li>
@@ -122,7 +151,7 @@
<li><p>added <code>\xintiSqrtR</code>, there was only <code>\xintiiSqrtR</code> alongside <code>\xintiSqrt</code> and <code>\xintiiSqrt</code> (<strong>xint</strong>).</p></li>
<li><p>added non public <code>\xintLastItem:f:csv</code> to <strong>xinttools</strong> for faster <code>last()</code> function, and improved <code>\xintNewExpr</code> compatibility. Also <code>\xintFirstItem:f:csv</code>.</p></li>
</ul>
-<h3 id="bug-fixes">Bug fixes</h3>
+<h3 id="bug-fixes-1">Bug fixes</h3>
<ul>
<li><p>the <code>1.2f</code> half-integer powers computed within <code>\xintfloatexpr</code> had a silly rounding to the target precision just <em>before</em> the final square-root extraction, thus possibly losing some precision. The <code>1.2k</code> implementation keeps guard digits for this final square root extraction. As for integer exponents, it is guaranteed that the computed value differs from the exact one by less than <code>0.52 ulp</code> (for inputs having at most <code>\xinttheDigits</code> digits.)</p></li>
<li><p>more regressions from <code>1.2i</code> were fixed: <code>\xintLen</code> (<strong>xint</strong>, <strong>xintfrac</strong>) and <code>\xintDouble</code> (<strong>xintcore</strong>) had forgotten that their argument was allowed to be negative. A regression test suite is now in place and is being slowly expanded to cover more macros.</p></li>
@@ -129,7 +158,7 @@
<li><p><code>\xintiiSquareRoot{0}</code> now produces <code>{1}{1}</code>, which fits better the general documented behaviour of this macro than <code>11</code>.</p></li>
</ul>
<h2 id="j-20161222"><code>1.2j (2016/12/22)</code></h2>
-<h3 id="improvements-and-new-features-1">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-2">Improvements and new features</h3>
<ul>
<li><p><strong>xinttools</strong> and <strong>xintexpr</strong>:</p>
<ol style="list-style-type: decimal">
@@ -138,7 +167,7 @@
</ol></li>
<li><p>significant documentations tweaks (inclusive of suppressing things!), and among them two beautiful hyperlinked tables with both horizontal and vertical rules which bring the documentation of the <strong>xintexpr</strong> syntax to a kind of awe-inspiring perfection... except that implementation of some math functions is still lacking.</p></li>
</ul>
-<h3 id="bug-fixes-1">Bug fixes</h3>
+<h3 id="bug-fixes-2">Bug fixes</h3>
<ul>
<li>fix two <code>1.2i</code> regressions caused by undefined macros (<code>\xintNthElt</code> in certain branches and <code>[list][N]</code> item extraction in certain cases.) The test files existed but were not executed prior to release. Automation in progress.</li>
</ul>
@@ -145,11 +174,14 @@
<h2 id="i-20161213"><code>1.2i (2016/12/13)</code></h2>
<h3 id="incompatible-changes-1">Incompatible changes</h3>
<ul>
-<li><p>some macros which had been marked as deprecated are removed (they are available under different names): <code>\xintifTrue</code>, <code>\xintifTrueFalse</code>, <code>\xintQuo</code>, <code>\xintRem</code>, <code>\xintquo</code>, <code>\xintrem</code>.</p></li>
-<li><p><code>\xintDecSplit</code> second argument must have no sign (former code replaced it with its absolute value, a sign now may cause an error.)</p></li>
+<li><code>\xintDecSplit</code> second argument must have no sign (former code replaced it with its absolute value, a sign now may cause an error.)</li>
</ul>
-<h3 id="improvements-and-new-features-2">Improvements and new features</h3>
+<h3 id="removed-1">Removed</h3>
<ul>
+<li>deprecated macros <code>\xintifTrue</code>, <code>\xintifTrueFalse</code>, <code>\xintQuo</code>, <code>\xintRem</code>, <code>\xintquo</code>, <code>\xintrem</code>.</li>
+</ul>
+<h3 id="improvements-and-new-features-3">Improvements and new features</h3>
+<ul>
<li><p><strong>xintkernel</strong>: <code>\xintLength</code> is faster. New macros:</p>
<ul>
<li><p><code>\xintLastItem</code> to fetch the last item from its argument,</p></li>
@@ -167,17 +199,17 @@
<li><p>the documentation has again been (slightly) re-organized; it has a new sub-section on the Miller-Rabin primality test, to illustrate some use of <code>\xintNewFunction</code> for recursive definitions.</p></li>
<li><p>the documentation has dropped the LaTeX "command" terminology (which had been used initially in 2013 for some forgotten reasons and should have been removed long ago) and uses only the more apt "macro", as after all, all of <strong>xint</strong> is about expansion of macros (plus the use of <code>\numexpr</code>).</p></li>
</ul>
-<h3 id="bug-fixes-2">Bug fixes</h3>
+<h3 id="bug-fixes-3">Bug fixes</h3>
<ul>
<li><code>\xintDecSplitL</code> and <code>\xintDecSplitR</code> from <strong>xint</strong> produced their output in a spurious brace pair (bug introduced in <code>1.2f</code>).</li>
</ul>
<h2 id="h-20161120"><code>1.2h (2016/11/20)</code></h2>
-<h3 id="improvements-and-new-features-3">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-4">Improvements and new features</h3>
<ul>
<li><p>new macro <code>\xintNewFunction</code> in <strong>xintexpr</strong> which allows to extend the parser syntax with functions in situations where <code>\xintdeffunc</code> is not usable (typically, because dummy variables are used over a not yet determined range of values because it depends on the variables).</p></li>
<li><p>after three years of strict obedience to <code>xint</code> prefix, now <code>\thexintexpr</code>, <code>\thexintiexpr</code>, <code>\thexintfloatexpr</code>, and <code>\thexintiiexpr</code> are provided as synonyms to <code>\xinttheexpr</code>, etc...</p></li>
</ul>
-<h3 id="bug-fixes-3">Bug fixes</h3>
+<h3 id="bug-fixes-4">Bug fixes</h3>
<ul>
<li><p>the <code>(cond)?{foo}{bar}</code> operator from <strong>xintexpr</strong> mis-behaved in certain circumstances (such as an empty <code>foo</code>).</p></li>
<li><p>the <strong>xintexpr</strong> <code>1.2f</code> <code>binomial</code> function (which uses <code>\xintiiBinomial</code> from <strong>xint.sty</strong> or <code>\xintFloatBinomial</code> from <strong>xintfrac.sty</strong>) deliberately raised an error for <code>binomial(x,y)</code> with <code>y<0</code> or <code>x<y</code>. This was unfortunate, and it now simply evaluates to zero in such cases.</p></li>
@@ -190,7 +222,7 @@
<li><p>inside expressions, list item selector <code>[L][n]</code> counts starting at zero, not at one. This is more coherent with <code>[L][a:b]</code> which was already exactly like in Python since its introduction. A function len(L) replaces earlier <code>[L][0]</code>.</p></li>
<li><p>former <code>iter</code> keyword now called <code>iterr</code>. Indeed it matched with <code>rrseq</code>, the new <code>iter</code> (which was somehow missing from <code>1.1</code>) is the one matching <code>rseq</code>. Allows to iterate more easily with a "list" variable.</p></li>
</ul>
-<h3 id="improvements-and-new-features-4">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-5">Improvements and new features</h3>
<ul>
<li><p>in <strong>xintexpr.sty</strong>: list selectors <code>[L][n]</code> and <code>[L][a:b]</code> are more efficient: the earlier <code>1.1</code> routines did back and forth conversions from comma separated values to braced tokens, the <code>1.2g</code> routines use macros from <strong>xinttools.sty</strong> handling directly the encountered lists of comma separated values.</p></li>
<li><p>in <strong>xinttools.sty</strong>: slight improvements in the efficiency of the <code>\xintNthElt</code>, <code>\xintKeep</code>, <code>\xintTrim</code> routines and new routines handling directly comma separated values. The latter are not included in the user manual (they are not <code>\long</code>, they don't make efforts to preserve some braces, do not worry about spaces, all those worries being irrelevant to the use in expressions for list selectors).</p></li>
@@ -203,7 +235,7 @@
<ul>
<li>no more <code>\xintFac</code> macro but <code>\xintiFac/\xintiiFac/\xintFloatFac</code>.</li>
</ul>
-<h3 id="improvements-and-new-features-5">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-6">Improvements and new features</h3>
<ul>
<li><p>functions <code>binomial</code>, <code>pfactorial</code> and <code>factorial</code> in both integer and float versions.</p></li>
<li><p>macros <code>\xintiiBinomial</code>, <code>\xintiiPFactorial</code> (<strong>xint.sty</strong>) and <code>\xintFloatBinomial</code>, <code>\xintFloatPFactorial</code> (<strong>xintfrac.sty</strong>). Improvements to <code>\xintFloatFac</code>.</p></li>
@@ -217,7 +249,7 @@
<li><p>(TeXperts only) the macros defined (internally) from <code>\xintdeffunc</code> et al. constructs do not incorporate an initial <code>\romannumeral</code> anymore.</p></li>
<li><p>renewed desperate efforts at improving the documentation by random shuffling of sections and well thought additions; cuts were considered and even performed.</p></li>
</ul>
-<h3 id="bug-fixes-4">Bug fixes</h3>
+<h3 id="bug-fixes-5">Bug fixes</h3>
<ul>
<li><p>squaring macro <code>\xintSqr</code> from <strong>xintfrac.sty</strong> was broken due to a misspelled sub-macro name. Dates back to <code>1.1</code> release of <code>2014/10/28</code> <code>:-((</code>.</p></li>
<li><p><code>1.2c</code>'s fix to the subtraction bug from <code>1.2</code> introduced another bug, which in some cases could create leading zeroes in the output, or even worse. This could invalidate other routines using subtractions, like <code>\xintiiSquareRoot</code>.</p></li>
@@ -224,7 +256,7 @@
<li><p>the comparison operators were not recognized by <code>\xintNewIIExpr</code> and <code>\xintdefiifunc</code> constructs.</p></li>
</ul>
<h2 id="e-20151122"><code>1.2e (2015/11/22)</code></h2>
-<h3 id="improvements-and-new-features-6">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-7">Improvements and new features</h3>
<ul>
<li><p>macro <code>\xintunassignvar</code>.</p></li>
<li><p>slight modifications of the logged messages in case of <code>\xintverbosetrue</code>.</p></li>
@@ -231,7 +263,7 @@
<li><p>a space in <code>\xintdeffunc f(x)<space>:= expression ;</code> is now accepted.</p></li>
<li><p>documentation enhancements: the <em>Quick Sort</em> section with its included code samples has been entirely re-written; the <em>Commands of the xintexpr package</em> section has been extended and reviewed entirely.</p></li>
</ul>
-<h3 id="bug-fixes-5">Bug fixes</h3>
+<h3 id="bug-fixes-6">Bug fixes</h3>
<ul>
<li><p>in <strong>xintfrac</strong>: the <code>\xintFloatFac</code> from release <code>1.2</code> parsed its argument only through <code>\numexpr</code> but it should have used <code>\xintNum</code>.</p></li>
<li><p>in <strong>xintexpr</strong>: release <code>1.2d</code> had broken the recognition of sub-expressions immediately after variable names (with tacit multiplication).</p></li>
@@ -238,51 +270,54 @@
<li><p>in <strong>xintexpr</strong>: contrarily to what <code>1.2d</code> documentation said, tacit multiplication was not yet always done with enhanced precedence. Now yes.</p></li>
</ul>
<h2 id="d-20151118"><code>1.2d (2015/11/18)</code></h2>
-<h3 id="improvements-and-new-features-7">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-8">Improvements and new features</h3>
<ul>
<li><p>the function definitions done by <code>\xintdeffunc</code> et al., as well as the macro declarations by <code>\xintNewExpr</code> et al. now have only local scope.</p></li>
<li><p>tacit multiplication applies to more cases, for example (x+y)z, and always ties more than standard * infix operator, e.g. x/2y is like x/(2*y).</p></li>
<li><p>some documentation enhancements, particularly in the chapter on xintexpr.sty, and also in the code source comments.</p></li>
</ul>
-<h3 id="bug-fixes-6">Bug fixes</h3>
+<h3 id="bug-fixes-7">Bug fixes</h3>
<ul>
<li>in <strong>xintcore</strong>: release <code>1.2c</code> had inadvertently broken the <code>\xintiiDivRound</code> macro.</li>
</ul>
<h2 id="c-20151116"><code>1.2c (2015/11/16)</code></h2>
-<h3 id="improvements-and-new-features-8">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-9">Improvements and new features</h3>
<ul>
<li><p>macros <code>\xintdeffunc</code>, <code>\xintdefiifunc</code>, <code>\xintdeffloatfunc</code> and boolean <code>\ifxintverbose</code>.</p></li>
<li><p>on-going code improvements and documentation enhancements, but stopped in order to issue this bugfix release.</p></li>
</ul>
-<h3 id="bug-fixes-7">Bug fixes</h3>
+<h3 id="bug-fixes-8">Bug fixes</h3>
<ul>
<li>in <strong>xintcore</strong>: recent release <code>1.2</code> introduced a bug in the subtraction (happened when 00000001 was found under certain circumstances at certain mod 8 locations).</li>
</ul>
<h2 id="b-20151029"><code>1.2b (2015/10/29)</code></h2>
-<h3 id="bug-fixes-8">Bug fixes</h3>
+<h3 id="bug-fixes-9">Bug fixes</h3>
<ul>
<li>in <strong>xintcore</strong>: recent release <code>1.2</code> introduced a bug in the division macros, causing a crash when the divisor started with 99999999 (it was attempted to use with 1+99999999 a subroutine expecting only 8-digits numbers).</li>
</ul>
<h2 id="a-20151019"><code>1.2a (2015/10/19)</code></h2>
-<h3 id="improvements-and-new-features-9">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-10">Improvements and new features</h3>
<ul>
<li><p>added <code>\xintKeepUnbraced</code>, <code>\xintTrimUnbraced</code> (<strong>xinttools</strong>) and fixed documentation of <code>\xintKeep</code> and <code>\xintTrim</code> regarding brace stripping.</p></li>
<li><p>added <code>\xintiiMaxof/\xintiiMinof</code> (<strong>xint</strong>).</p></li>
<li><p>TeX hackers only: replaced all code uses of <code>\romannumeral-`0</code> by the quicker <code>\romannumeral`&&@</code> (<code>^</code> being used as letter, had to find another character usable with catcode 7).</p></li>
</ul>
-<h3 id="bug-fixes-9">Bug fixes</h3>
+<h3 id="bug-fixes-10">Bug fixes</h3>
<ul>
<li>in <strong>xintexpr</strong>: recent release <code>1.2</code> introduced a bad bug in the parsing of decimal numbers and as a result <code>\xinttheexpr 0.01\relax</code> expanded to <code>0</code> ! (sigh...)</li>
</ul>
<h2 id="section"><code>1.2 (2015/10/10)</code></h2>
-<h3 id="improvements-and-new-features-10">Improvements and new features</h3>
+<h3 id="removed-2">Removed</h3>
<ul>
+<li>the macros <code>\xintAdd</code>, <code>\xintSub</code>, <code>\xintMul</code>, <code>\xintMax</code>, <code>\xintMin</code>, <code>\xintMaxof</code>, <code>\xintMinof</code> are removed from package <strong>xint</strong>, and only exist in the versions from <strong>xintfrac</strong>. With only <strong>xintcore</strong> or <strong>xint</strong> loaded, one <em>must</em> use <code>\xintiiAdd</code>, <code>\xintiiSub</code>, ..., or <code>\xintiAdd</code>, <code>\xintiSub</code>, etc...</li>
+</ul>
+<h3 id="improvements-and-new-features-11">Improvements and new features</h3>
+<ul>
<li><p>the basic arithmetic implemented in <strong>xintcore</strong> has been entirely rewritten. The mathematics remains the elementary school one, but the <code>TeX</code> implementation achieves higher speed (except, regarding addition/subtraction, for numbers up to about thirty digits), the gains becoming quite significant for numbers with hundreds of digits.</p></li>
<li><p>the inputs must have less than 19959 digits. But computations with thousands of digits take time.</p></li>
<li><p>a previously standing limitation of <code>\xintexpr</code>, <code>\xintiiexpr</code>, and of <code>\xintfloatexpr</code> to numbers of less than 5000 digits has been lifted.</p></li>
<li><p>a <em>qint</em> function is provided to help the parser gather huge integers in one-go, as an exception to its normal mode of operation which expands token by token.</p></li>
<li><p><code>\xintFloatFac</code> macro for computing the factorials of integers as floating point numbers to a given precision. The <code>!</code> postfix operator inside <code>\xintfloatexpr</code> maps to this new macro rather than to the exact factorial as used by <code>\xintexpr</code> and <code>\xintiiexpr</code>.</p></li>
-<li><p>the macros <code>\xintAdd</code>, <code>\xintSub</code>, ..., now require package <strong>xintfrac</strong>. With only <strong>xintcore</strong> or <strong>xint</strong> loaded, one <em>must</em> use <code>\xintiiAdd</code>, <code>\xintiiSub</code>, ..., or <code>\xintiAdd</code>, <code>\xintiSub</code>, etc...</p></li>
<li><p>there is more flexibility in the parsing done by the macros from <strong>xintfrac</strong> on fractional input: the decimal parts of both the numerator and the denominator may arise from a separate expansion via <code>\romannumeral-`0</code>. Also the strict <code>A/B[N]</code> format is a bit relaxed: <code>N</code> may be anything understood by <code>\numexpr</code> (it could even be empty but that possibility has been removed by later <code>1.2f</code> release.)</p></li>
<li><p>on the other hand an isolated dot <code>.</code> is not legal syntax anymore inside the expression parsers: there must be digits either before or after. It remains legal input for the macros of <strong>xintfrac</strong>.</p></li>
<li><p>added <code>\ht</code>, <code>\dp</code>, <code>\wd</code>, <code>\fontcharht</code>, etc... to the tokens recognized by the parsers and expanded by <code>\number</code>.</p></li>
@@ -317,12 +352,21 @@
<li><p><code>1e(3+5)</code> is now illegal. The number parser identifies <code>e</code> and <code>E</code> in the same way it does for the decimal mark, earlier versions treated <code>e</code> as <code>E</code> rather as infix operators of highest precedence,</p></li>
<li><p>the <code>add</code> and <code>mul</code> have a new syntax, old syntax is with <code>`+`</code> and <code>`*`</code> (left quotes mandatory), <code>sum</code> and <code>prd</code> are gone,</p></li>
<li><p>no more special treatment for encountered brace pairs <code>{..}</code> by the number scanner, <code>a/b[N]</code> notation can be used without use of braces (the <code>N</code> will end up as is in a <code>\numexpr</code>, it is not parsed by the <code>\xintexpr</code>-ession scanner),</p></li>
-<li><p>although <code>&</code> and <code>|</code> are still available as Boolean operators the use of <code>&&</code> and <code>||</code> is strongly recommended. The single letter operators might be assigned some other meaning in later releases (bitwise operations, perhaps). Do not use them.</p></li>
<li><p>in earlier releases, place holders for <code>\xintNewExpr</code> could either be denoted <code>#1</code>, <code>#2</code>, ... or also <code>$1</code>, <code>$2</code>, ... Only the usual <code>#</code> form is now accepted and the special cases previously treated via the second form are now managed via a <code>protect(...)</code> function.</p></li>
</ul>
-<h3 id="improvements-and-new-features-11">Improvements and new features</h3>
+<h3 id="removed-3">Removed</h3>
<ul>
-<li><p>new package <strong>xintcore</strong> has been split off <strong>xint</strong>. It contains the core arithmetic macros. It is loaded by package <strong>bnumexpr</strong>,</p></li>
+<li><code>\xintnumexpr</code>, <code>\xintthenumexpr</code>, <code>\xintNewNumExpr</code>: use <code>\xintiexpr</code>, <code>\xinttheiexpr</code>, <code>\xintNewIExpr</code>.</li>
+</ul>
+<h3 id="deprecated">Deprecated</h3>
+<ul>
+<li><p><code>\xintDivision</code>, <code>\xintQuo</code>, <code>\xintRem</code>: use <code>\xintiDivision</code>, <code>\xintiQuo</code>, <code>\xintiRem</code>.</p></li>
+<li><p><code>\xintMax</code>, <code>\xintMin</code>, <code>\xintAdd</code>, <code>\xintSub</code>, <code>\xintMul</code> (<strong>xint</strong>): their usage without <strong>xintfrac</strong> is deprecated; use <code>\xintiMax</code>, <code>\xintiMin</code>, <code>\xintiAdd</code>, <code>\xintiSub</code>, <code>\xintiMul</code>.</p></li>
+<li><p>the <code>&</code> and <code>|</code> as Boolean operators in <code>xintexpr</code>-essions are deprecated in favour of <code>&&</code> and <code>||</code>. The single letter operators might be assigned some other meaning in some later release (bitwise operations, perhaps). Do not use them.</p></li>
+</ul>
+<h3 id="improvements-and-new-features-12">Improvements and new features</h3>
+<ul>
+<li><p>new package <strong>xintcore</strong> has been split off <strong>xint</strong>. It contains the core arithmetic macros (it is loaded by LaTeX package <strong>bnumexpr</strong>),</p></li>
<li><p>neither <strong>xint</strong> nor <strong>xintfrac</strong> load <strong>xinttools</strong>. Only <strong>xintexpr</strong> does,</p></li>
<li><p>whenever some portion of code has been revised, often use has been made of the <code>\xint_dothis</code> and <code>\xint_orthat</code> pair of macros for expandably branching,</p></li>
<li><p>these tiny helpful macros, and a few others are in package <strong>xintkernel</strong> which contains also the catcode and loading order management code, initially inspired by code found in Heiko Oberdiek's packages,</p></li>
@@ -357,7 +401,7 @@
<li><p><code>\xintthecoords</code> converts a comma separated list of an even number of items to the format expected by the <code>TikZ</code> <code>coordinates</code> syntax,</p></li>
<li><p>completely new version <code>\xintNewExpr</code>, <code>protect</code> function to handle external macros. The dollar sign <code>$</code> for place holders is not accepted anymore, only the standard macro parameter <code>#</code>. Not all constructs are compatible with <code>\xintNewExpr</code>.</p></li>
</ul>
-<h3 id="bug-fixes-10">Bug fixes</h3>
+<h3 id="bug-fixes-11">Bug fixes</h3>
<ul>
<li><p><code>\xintZapFirstSpaces</code> hence also <code>\xintZapSpaces</code> from package <strong>xinttools</strong> were buggy when used with an argument either empty or containing only space tokens.</p></li>
<li><p><code>\xintiiexpr</code> did not strip leading zeroes, hence <code>\xinttheiiexpr 001+1\relax</code> did not obtain the expected result ...</p></li>
@@ -402,7 +446,7 @@
<h2 id="i-20131218"><code>1.09i (2013/12/18)</code></h2>
<ul>
<li><p>(<strong>xintexpr</strong>) <code>\xintiiexpr</code> is a variant of <code>\xintexpr</code> which is optimized to deal only with (long) integers, <code>/</code> does a euclidean quotient.</p></li>
-<li><p><code>\xintnumexpr</code>, <code>\xintthenumexpr</code>, <code>\xintNewNumExpr</code> are renamed, respectively, <code>\xintiexpr</code>, <code>\xinttheiexpr</code>, <code>\xintNewIExpr</code>. The earlier denominations are kept but to be removed at some point.</p></li>
+<li><p><em>deprecated</em>: <code>\xintnumexpr</code>, <code>\xintthenumexpr</code>, <code>\xintNewNumExpr</code> are renamed, respectively, <code>\xintiexpr</code>, <code>\xinttheiexpr</code>, <code>\xintNewIExpr</code>. The earlier denominations are kept but are to be removed at some point.</p></li>
<li><p>it is now possible within <code>\xintexpr...\relax</code> and its variants to use count, dimen, and skip registers or variables without explicit <code>\the/\number</code>: the parser inserts automatically <code>\number</code> and a tacit multiplication is implied when a register or variable immediately follows a number or fraction. Regarding dimensions and <code>\number</code>, see the further discussion in <em>Dimensions</em>.</p></li>
<li><p>(<strong>xintfrac</strong>) conditional <code>\xintifOne</code>; <code>\xintifTrueFalse</code> renamed to <code>\xintifTrueAelseB</code>; macros <code>\xintTFrac</code> (<code>fractional part</code>, mapped to function <code>frac</code> in <code>\xintexpr</code>-essions), <code>\xintFloatE</code>.</p></li>
<li><p>(<strong>xinttools</strong>) <code>\xintAssign</code> admits an optional argument to specify the expansion type to be used: <code>[]</code> (none, default), <code>[o]</code> (once), <code>[oo]</code> (twice), <code>[f]</code> (full), <code>[e]</code> (<code>\edef</code>),... to define the macros</p></li>
@@ -410,6 +454,7 @@
<li><p>some across the board slight efficiency improvement as a result of modifications of various types to <em>fork macros</em> and <em>branching conditionals</em> which are used internally.</p></li>
<li><p>bug fix (<strong>xint</strong>): <code>\xintAND</code> and <code>\xintOR</code> inserted a space token in some cases and did not expand as promised in two steps <code>:-((</code> (bug dating back to <code>1.09a</code> I think; this bug was without consequences when using <code>&</code> and <code>|</code> in <code>\xintexpr-essions</code>, it affected only the macro form).</p></li>
<li><p>bug fix (<strong>xintcfrac</strong>): <code>\xintFtoCCv</code> still ended fractions with the <code>[0]</code>'s which were supposed to have been removed since release <code>1.09b</code>.</p></li>
+<li><p><em>deprecated</em>: <code>\xintifTrueFalse</code>, <code>\xintifTrue</code>; use <code>\xintifTrueAelseB</code>.</p></li>
</ul>
<h2 id="h-20131128"><code>1.09h (2013/11/28)</code></h2>
<ul>
@@ -455,7 +500,7 @@
<h2 id="c-20131009"><code>1.09c (2013/10/09)</code></h2>
<ul>
<li><p>(<strong>xintexpr</strong>) added <code>bool</code> and <code>togl</code> to the <code>\xintexpr</code> syntax; also added <code>\xintboolexpr</code> and <code>\xintifboolexpr</code>.</p></li>
-<li><p>added <code>\xintNewNumExpr</code> (now <code>\xintNewIExpr</code> and <code>\xintNewBoolExpr</code>),</p></li>
+<li><p>added <code>\xintNewNumExpr</code>.</p></li>
<li><p>the factorial <code>!</code> and branching <code>?</code>, <code>:</code>, operators (in <code>\xintexpr...\relax</code>) have now less precedence than a function name located just before,</p></li>
<li><p>(<strong>xint</strong>) <code>\xintFor</code> is a new type of loop, whose replacement text inserts the comma separated values or list items via macro parameters, rather than encapsulated in macros; the loops are nestable up to four levels (nine levels since <code>1.09f</code>) and their replacement texts are allowed to close groups as happens with the tabulation in alignments,</p></li>
<li><p><code>\xintForpair</code>, <code>\xintForthree</code>, <code>\xintForfour</code> are experimental variants of <code>\xintFor</code>,</p></li>
Modified: trunk/Master/texmf-dist/doc/generic/xint/CHANGES.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/doc/generic/xint/README
===================================================================
--- trunk/Master/texmf-dist/doc/generic/xint/README 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/doc/generic/xint/README 2017-07-27 21:26:25 UTC (rev 44900)
@@ -1,4 +1,4 @@
- Source: xint.dtx 1.2k 2017/01/06 (doc 2017/01/06)
+ Source: xint.dtx 1.2l 2017/07/26 (doc 2017/07/26)
Author: Jean-Francois Burnol
Info: Expandable operations on big integers, decimals, fractions
License: LPPL 1.3c
Modified: trunk/Master/texmf-dist/doc/generic/xint/README.html
===================================================================
--- trunk/Master/texmf-dist/doc/generic/xint/README.html 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/doc/generic/xint/README.html 2017-07-27 21:26:25 UTC (rev 44900)
@@ -4,7 +4,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta http-equiv="Content-Style-Type" content="text/css" />
<meta name="generator" content="pandoc" />
- <meta name="author" content="xint 1.2k" />
+ <meta name="author" content="xint 1.2l" />
<title>README</title>
<style type="text/css">code{white-space: pre;}</style>
<style type="text/css">
@@ -17,8 +17,8 @@
<body>
<div id="header">
<h1 class="title">README</h1>
-<h2 class="author">xint 1.2k</h2>
-<h3 class="date">2017/01/06</h3>
+<h2 class="author">xint 1.2l</h2>
+<h3 class="date">2017/07/26</h3>
</div>
<div id="TOC">
<ul>
@@ -36,7 +36,7 @@
<li><a href="#license">License</a></li>
</ul>
</div>
-<pre><code>Source: xint.dtx 1.2k 2017/01/06 (doc 2017/01/06)
+<pre><code>Source: xint.dtx 1.2l 2017/07/26 (doc 2017/07/26)
Author: Jean-Francois Burnol
Info: Expandable operations on big integers, decimals, fractions
License: LPPL 1.3c</code></pre>
Modified: trunk/Master/texmf-dist/doc/generic/xint/README.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/doc/generic/xint/sourcexint.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/doc/generic/xint/xint.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/source/generic/xint/xint.dtx
===================================================================
--- trunk/Master/texmf-dist/source/generic/xint/xint.dtx 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/source/generic/xint/xint.dtx 2017-07-27 21:26:25 UTC (rev 44900)
@@ -3,20 +3,20 @@
% Extract all files via "etex xint.dtx" and do "make help"
% or follow instructions from extracted README.md.
%<*dtx>
-\def\xintdtxtimestamp {Time-stamp: <06-01-2017 at 22:41:03 CET>}
+\def\xintdtxtimestamp {Time-stamp: <26-07-2017 at 19:42:16 CEST>}
%</dtx>
%<*drv>
%% ---------------------------------------------------------------
-\def\xintdocdate {2017/01/06}
-\def\xintbndldate{2017/01/06}
-\def\xintbndlversion {1.2k}
+\def\xintdocdate {2017/07/26}
+\def\xintbndldate{2017/07/26}
+\def\xintbndlversion {1.2l}
%</drv>
%<readme>% README
%<changes>% CHANGE LOG
-%<readme|changes>% xint 1.2k
-%<readme|changes>% 2017/01/06
+%<readme|changes>% xint 1.2l
+%<readme|changes>% 2017/07/26
%<readme|changes>
-%<readme|changes> Source: xint.dtx 1.2k 2017/01/06 (doc 2017/01/06)
+%<readme|changes> Source: xint.dtx 1.2l 2017/07/26 (doc 2017/07/26)
%<readme|changes> Author: Jean-Francois Burnol
%<readme|changes> Info: Expandable operations on big integers, decimals, fractions
%<readme|changes> License: LPPL 1.3c
@@ -23,7 +23,7 @@
%<readme|changes>
%<*!readme&!changes&!dohtmlsh&!dopdfsh&!makefile>
%% ---------------------------------------------------------------
-%% The xint bundle 1.2k 2017/01/06
+%% The xint bundle 1.2l 2017/07/26
%% Copyright (C) 2013-2017 by Jean-Francois Burnol
%<xintkernel>%% xintkernel: Paraphernalia for the xint packages
%<xinttools>%% xinttools: Expandable and non-expandable utilities
@@ -68,7 +68,7 @@
\xintDigits:=48;\xintthefloatexpr 123456789^1000.5\relax
->3.63692761822782679930738270515740797370813691938e8095
-
+
However, only integer and half-integer exponents are currently allowed.
The `sqrt` operation achieves correct rounding in arbitrary precision.
@@ -243,6 +243,73 @@
%</readme>--------------------------------------------------------
%<*changes>-------------------------------------------------------
+`1.2l (2017/07/26)`
+----
+
+### Removed
+
+ - `\xintiiSumExpr`, `\xintiiPrdExpr` (**xint**) and `\xintSumExpr`,
+ `\xintPrdExpr` (**xintfrac**). They had not been formally deprecated,
+ but had been left un-documented since `1.09d (2013/10/22)`.
+
+### Improvements and new features
+
+ - the underscore character `_` is accepted by the **xintexpr** parsers
+ as a digit separator (the space character already could be used for
+ improved readability of big numbers). It is not allowed as *first*
+ character of a number, as it would then be mis-interpreted as the
+ start of a possible variable name.
+
+ - some refactoring in **xintcore** auxiliary routines and in
+ `\xintiiSub` and `\xintiiCmp` for some small efficiency gains.
+
+ - code comments in **xintcore** are better formatted, but remain
+ sparse.
+
+ - **xintcore**, **xint**, **xintfrac**, ... : some macros were not
+ robust against arguments whose expansion looks forward for some
+ termination (e.g. ``\number\mathcode`\-``), and particularly, most
+ were fragile against inputs using non-terminated ``\numexpr`` (such
+ as `\xintiiAdd{\the\numexpr1}{2}` or `\xintRaw{\numexpr1}`). This was
+ not a bug per se, as the user manual did not claim such inputs were
+ legal, but it was slightly inconvenient. Most macros (particularly
+ those of **xintfrac**) have now been made robust against such inputs.
+ Some macros from **xintcore** primarily destined to internal usage
+ still accept only properly terminated arguments such as
+ ``\the\mathcode`\-<space>`` or ``\the\numexpr1\relax``.
+
+ The situation with expressions is unchanged: syntax such as
+ `\xintexpr \numexpr1+2\relax` is illegal as the ending `\relax` token
+ will get swallowed by the `\numexpr`; but it is needed by the
+ ``xintexpr``-ession parser, hence the parser will expand forward and
+ presumably end with in an "illegal token" error, or provoke some
+ low-level TeX error (N.B.: a closing brace `}` for example can not
+ terminate an ``xintexpr``-ession, the parser must find a `\relax`
+ token at some point). Thus there must be in this example a second
+ `\relax`.
+
+ - experimental code for error conditions; there is no complete user
+ interface yet, it is done in preparation for next major release and
+ is completely unstable and undocumented.
+
+### Bug fixes
+
+ - **xintbinhex**: since `1.2 (2015/10/10)`, `\xintHexToDec` was
+ broken due to an undefined macro (it was in `xint.sty`, but the
+ module by itself is supposedly dependent only upon `xintcore.sty`).
+
+ - **xintgcd**: macro `\xintBezout` produced partially wrong output if
+ one of its two arguments was zero.
+
+ - **xintfrac**: the manual said one could use directly `\numexpr`
+ compatible expressions in arithmetic macros (without even a
+ `\numexpr` encapsulation) if they were expressed with up to 8 tokens.
+ There was a bug if these 8 tokens evaluated to zero. The bug has been
+ fixed, and up to 9 tokens are now accepted. But it is simpler to use
+ `\the\numexpr` prefix and not to worry about the token count... The
+ ending `\relax` is now un-needed.
+
+
`1.2k (2017/01/06)`
----
@@ -333,13 +400,14 @@
### Incompatible changes
- - some macros which had been marked as deprecated are removed (they are
- available under different names): `\xintifTrue`, `\xintifTrueFalse`,
- `\xintQuo`, `\xintRem`, `\xintquo`, `\xintrem`.
-
- `\xintDecSplit` second argument must have no sign (former code
replaced it with its absolute value, a sign now may cause an error.)
+### Removed
+
+ - deprecated macros `\xintifTrue`, `\xintifTrueFalse`, `\xintQuo`,
+ `\xintRem`, `\xintquo`, `\xintrem`.
+
### Improvements and new features
- **xintkernel**: `\xintLength` is faster. New macros:
@@ -632,6 +700,14 @@
`1.2 (2015/10/10)`
----
+### Removed
+
+ - the macros `\xintAdd`, `\xintSub`, `\xintMul`, `\xintMax`,
+ `\xintMin`, `\xintMaxof`, `\xintMinof` are removed from package
+ **xint**, and only exist in the versions from **xintfrac**. With only
+ **xintcore** or **xint** loaded, one _must_ use `\xintiiAdd`,
+ `\xintiiSub`, ..., or `\xintiAdd`, `\xintiSub`, etc...
+
### Improvements and new features
- the basic arithmetic implemented in **xintcore** has been entirely
@@ -656,11 +732,6 @@
inside `\xintfloatexpr` maps to this new macro rather than to the
exact factorial as used by `\xintexpr` and `\xintiiexpr`.
- - the macros `\xintAdd`, `\xintSub`, ..., now require package
- **xintfrac**. With only **xintcore** or **xint** loaded, one _must_
- use `\xintiiAdd`, `\xintiiSub`, ..., or `\xintiAdd`, `\xintiSub`,
- etc...
-
- there is more flexibility in the parsing done by the macros from
**xintfrac** on fractional input: the decimal parts of both the
numerator and the denominator may arise from a separate expansion via
@@ -756,20 +827,34 @@
`N` will end up as is in a `\numexpr`, it is not parsed by the
`\xintexpr`-ession scanner),
- - although `&` and `|` are still available as Boolean operators the
- use of `&&` and `||` is strongly recommended. The single
- letter operators might be assigned some other meaning in later releases
- (bitwise operations, perhaps). Do not use them.
-
- in earlier releases, place holders for `\xintNewExpr` could either
be denoted `#1`, `#2`, ... or also `$1`, `$2`, ...
Only the usual `#` form is now accepted and the special cases previously
treated via the second form are now managed via a `protect(...)` function.
+### Removed
+
+ - `\xintnumexpr`, `\xintthenumexpr`, `\xintNewNumExpr`: use
+ `\xintiexpr`, `\xinttheiexpr`, `\xintNewIExpr`.
+
+### Deprecated
+
+ - `\xintDivision`, `\xintQuo`, `\xintRem`: use `\xintiDivision`,
+ `\xintiQuo`, `\xintiRem`.
+
+ - `\xintMax`, `\xintMin`, `\xintAdd`, `\xintSub`, `\xintMul`
+ (**xint**): their usage without **xintfrac** is deprecated; use
+ `\xintiMax`, `\xintiMin`, `\xintiAdd`, `\xintiSub`, `\xintiMul`.
+
+ - the `&` and `|` as Boolean operators in `xintexpr`-essions are
+ deprecated in favour of `&&` and `||`. The single letter operators
+ might be assigned some other meaning in some later release (bitwise
+ operations, perhaps). Do not use them.
+
### Improvements and new features
* new package **xintcore** has been split off **xint**. It contains the
- core arithmetic macros. It is loaded by package **bnumexpr**,
+ core arithmetic macros (it is loaded by LaTeX package **bnumexpr**),
* neither **xint** nor **xintfrac** load **xinttools**. Only
**xintexpr** does,
@@ -1009,9 +1094,9 @@
optimized to deal only with (long) integers, `/` does a euclidean
quotient.
- * `\xintnumexpr`, `\xintthenumexpr`, `\xintNewNumExpr` are renamed,
- respectively, `\xintiexpr`, `\xinttheiexpr`, `\xintNewIExpr`. The
- earlier denominations are kept but to be removed at some point.
+ * *deprecated*: `\xintnumexpr`, `\xintthenumexpr`, `\xintNewNumExpr` are
+ renamed, respectively, `\xintiexpr`, `\xinttheiexpr`, `\xintNewIExpr`. The
+ earlier denominations are kept but are to be removed at some point.
* it is now possible within `\xintexpr...\relax` and its variants to
use count, dimen, and skip registers or variables without
@@ -1056,6 +1141,8 @@
the `[0]`'s which were supposed to have been removed since release
`1.09b`.
+ * *deprecated*: `\xintifTrueFalse`, `\xintifTrue`; use `\xintifTrueAelseB`.
+
`1.09h (2013/11/28)`
----
@@ -1174,7 +1261,7 @@
* (**xintexpr**) added `bool` and `togl` to the `\xintexpr` syntax;
also added `\xintboolexpr` and `\xintifboolexpr`.
- * added `\xintNewNumExpr` (now `\xintNewIExpr` and `\xintNewBoolExpr`),
+ * added `\xintNewNumExpr`.
* the factorial `!` and branching `?`, `:`, operators (in
`\xintexpr...\relax`) have now less precedence than a function
@@ -2095,10 +2182,10 @@
}
{}
{\noindent
- \llap{\makebox[\margegauchetoc][l]{\ttzfamily\bfseries\etoclink
+ \etocifnumbered{\llap{\makebox[\margegauchetoc][l]{\ttzfamily\bfseries\etoclink
{\ifinmanualmaintoc\expandafter\textcolor\sectioncouleur
{\normalfont\bfseries\ETOCsectionnumber}\fi
- .\expandafter\gobbletodot\etocthenumber}}}%
+ .\expandafter\gobbletodot\etocthenumber}}}}{\kern-\margegauchetoc}%
\strut\etocname\nobreak
\unless\ifinmanualmaintoc\leaders\etoctoclineleaders\fi
\hfill\nobreak
@@ -2119,6 +2206,8 @@
\strut\makebox[\MARGEPAGENO][r]{\small\etocpage}\endgraf }
{\endgroup }%
+\etocsetlevel{table}{6}
+
\makeatother
\addtocontents{toc}{\protect\hypersetup{hidelinks}}
@@ -2150,25 +2239,25 @@
% Ajouté le 9 mars 2016
-\DeclareFontShape{T1}{newtxttb}{m}{sc}{ %cap & small cap
+\DeclareFontShape{T1}{newtxttb}{m}{sc}{%cap & small cap
<-> s*[\newtxtt at scale]newtxttscbq
}{}
-\DeclareFontShape{T1}{newtxttb}{b}{sc}{ %bold cap & small cap
+\DeclareFontShape{T1}{newtxttb}{b}{sc}{%bold cap & small cap
<-> s*[\newtxtt at scale]newtxbttscbq
}{}
-\DeclareFontShape{T1}{newtxttb}{b}{sl}{ %bold slanted
+\DeclareFontShape{T1}{newtxttb}{b}{sl}{%bold slanted
<-> s*[\newtxtt at scale]newtxbttslbq
}{}
-\DeclareFontShape{T1}{newtxttb}{b}{it}{ %bold italic
+\DeclareFontShape{T1}{newtxttb}{b}{it}{%bold italic
<-> ssub * newtxttb/b/sl%
}{}
-\DeclareFontShape{T1}{newtxttb}{bx}{sc}{ %bold extended cap & small cap
+\DeclareFontShape{T1}{newtxttb}{bx}{sc}{%bold extended cap & small cap
<-> ssub * newtxttb/b/sc%
}{}
-\DeclareFontShape{T1}{newtxttb}{bx}{sl}{ %bold extended slanted
+\DeclareFontShape{T1}{newtxttb}{bx}{sl}{%bold extended slanted
<-> ssub * newtxttb/b/sl%
}{}
-\DeclareFontShape{T1}{newtxttb}{bx}{it}{ %bold extended italic
+\DeclareFontShape{T1}{newtxttb}{bx}{it}{%bold extended italic
<-> ssub * newtxttb/b/sl%
}{}
@@ -2176,40 +2265,40 @@
\DeclareEncodingSubset{TS1}{newtxttb}{0}
\DeclareFontFamily{TS1}{newtxttb}{\hyphenchar\font\m at ne}
-\DeclareFontShape{TS1}{newtxttb}{m}{n}{ %medium
+\DeclareFontShape{TS1}{newtxttb}{m}{n}{%medium
<-> s*[\newtxtt at scale]tcxtt%
}{}
-\DeclareFontShape{TS1}{newtxttb}{m}{sc}{ %cap & small cap
+\DeclareFontShape{TS1}{newtxttb}{m}{sc}{%cap & small cap
<->ssub * newtxttb/m/n%
}{}
-\DeclareFontShape{TS1}{newtxttb}{m}{sl}{ %slanted
+\DeclareFontShape{TS1}{newtxttb}{m}{sl}{%slanted
<-> s*[\newtxtt at scale]tcxttsl%
}{}
-\DeclareFontShape{TS1}{newtxttb}{m}{it}{ %italic
+\DeclareFontShape{TS1}{newtxttb}{m}{it}{%italic
<->ssub * newtxttb/m/sl%
}{}
-\DeclareFontShape{TS1}{newtxttb}{b}{n}{ %bold
+\DeclareFontShape{TS1}{newtxttb}{b}{n}{%bold
<-> s*[\newtxtt at scale]tcxbtt%
}{}
-\DeclareFontShape{TS1}{newtxttb}{b}{sc}{ %bold cap & small cap
+\DeclareFontShape{TS1}{newtxttb}{b}{sc}{%bold cap & small cap
<->ssub * newtxttb/b/n%
}{}
-\DeclareFontShape{TS1}{newtxttb}{b}{sl}{ %bold slanted
+\DeclareFontShape{TS1}{newtxttb}{b}{sl}{%bold slanted
<-> s*[\newtxtt at scale]tcxbttsl%
}{}
-\DeclareFontShape{TS1}{newtxttb}{b}{it}{ %bold italic
+\DeclareFontShape{TS1}{newtxttb}{b}{it}{%bold italic
<->ssub * newtxttb/b/sl%
}{}
-\DeclareFontShape{TS1}{newtxttb}{bx}{n}{ %bold extended
+\DeclareFontShape{TS1}{newtxttb}{bx}{n}{%bold extended
<->ssub * newtxttb/b/n%
}{}
\DeclareFontShape{TS1}{newtxttb}{bx}{sc}{ %bold extended cap & small cap
<->ssub * newtxttb/b/sc%
}{}
-\DeclareFontShape{TS1}{newtxttb}{bx}{sl}{ %bold extended slanted
+\DeclareFontShape{TS1}{newtxttb}{bx}{sl}{%bold extended slanted
<->ssub * newtxttb/b/sl%
}{}
-\DeclareFontShape{TS1}{newtxttb}{bx}{it}{ %bold extended italic
+\DeclareFontShape{TS1}{newtxttb}{bx}{it}{%bold extended italic
<->ssub * newtxttb/b/it%
}{}
@@ -2276,6 +2365,8 @@
pdfstartview=FitH,%
pdfpagemode=UseOutlines}
+\usepackage{hypcap}
+
\ifnum\dosourcexint=1
\hypersetup{pdftitle={The xint bundle source code}}
\fi
@@ -2577,7 +2668,21 @@
% --- \lverb
% Définition de \lverb
-\makeatletter
+% Has become more complicated for 1.2l
+\makeatletter\catcode`_ 11
+{\catcode32\active%
+\gdef\myobeyspaces{\catcode32\active\def {\leavevmode\kern\fontcharwd\font`X}}}
+\def\lverbpercent {\catcode32\active\lverbpercent_a}%
+\def\lverbpercent_a #1{%
+ \if\XINT_sptoken\detokenize{#1}\xint_dothis{\catcode32 10 }\fi
+ \if-\detokenize{#1}\xint_dothis{\par #1}\fi
+ \if(\detokenize{#1}\xint_dothis{\par\bgroup\myobeyspaces\obeylines}\fi
+ \if:\detokenize{#1}\xint_dothis{}\fi
+ \if)\detokenize{#1}\xint_dothis{\egroup\everypar{\hskip-\parindent\everypar{}}}\fi
+ \ifx#1\lverbpercent\xint_dothis{\catcode32 10 \par #1}\fi
+ \xint_orthat{\catcode32 10 #1}%
+}
+\catcode`_ 8
\long\def\lverb {%
\relax\par\smallskip\noindent\null
\begingroup
@@ -2586,7 +2691,9 @@
\let\do\do at noligs \verbatim at nolig@list
\let\do\@makeother \dospecials
\def\PrivateObelus{\par\noindent\textdiv}%
- \catcode32 10 \catcode`\% 9 \catcode`\& 14 \catcode`\$ 0
+ \catcode32 10 \catcode`\& 14 \catcode`\$ 0
+ \catcode`\% \active
+ \begingroup\lccode`\~`\%\lowercase{\endgroup\let~\lverbpercent}%
\MicroFont % sera donc en couleur.
\@lverb
}
@@ -2926,6 +3033,28 @@
\fi
\tableofcontents
+\begingroup\makeatletter
+\etocsetlevel{table}{0}
+\etocsetstyle{table}
+ {}
+ {\normalfont}
+ {%\SKIPSECTIONINTERSPACE
+ \rightskip \MARGEPAGENO\relax
+ \parfillskip -\MARGEPAGENO\relax
+ \leftskip \z at skip
+ \noindent\strut Table of \etocname
+ \nobreak\leaders\etoctoclineleaders\hfill\nobreak\strut
+ \makebox[\MARGEPAGENO][r]{\etocpage}\par
+ }%
+ {}%
+\etocsettagdepth{description}{table}
+\etocsettagdepth{macros}{none}
+\etocsettagdepth{implementation}{none}
+\etocsettocstyle{}{}
+\smallskip
+\tableofcontents
+\endgroup
+
\etocignoredepthtags
\etocmulticolstyle [1]{%
\phantomsection% \section* {Contents}
@@ -3701,9 +3830,6 @@
obtained via the expansion of the package macros during the \TeX{}
run.%
%
-\footnote{The CPU of my computer hates me for all those re-compilations
- after changing a single letter in the \LaTeX{} source, which require each
- time to do all the zillions of evaluations contained in this document\dots}
@@ -3755,27 +3881,36 @@
This is release \expandafter|\xintbndlversion| of \expandafter|\xintbndldate|.
-The \xintfracname floating point macros since |1.2f| round their arguments to
-the target precision |P| before further processing. This rounding is now exact
-(aka correct) in all cases, even with fractions having long numerators and
-denominators.
-This change has little influence on float expressions, as the
-\csbxint{floatexpr} parser handles there the |/| symbol as an operator hence
-it does not (except for special constructs) get to see fractions as such.
-Half-integer powers |A^x| (only available in float expressions, not via
-macros) proceed by an integer power and then a square-root extraction: the
-|1.2f| implementation did the latter on an already rounded value, |1.2k| keeps
-some of the guard digits to make the computed value |Z| closer to the exact
-one: a difference of less than |0.52 ulp(Z)| is guaranteed in all cases.
-Macro |\xintnewdummy| is made a public one, it serves to declare additional
-letters as dummy variables in expressions. This is for Unicode engines,
-mainly, as all Latin letters are already predefined to act as such.
-See |CHANGES.html| or |CHANGES.pdf| for more (|texdoc --list xint| or on the
-internet via
+The underscore |_| is accepted inside the expression parsers as an ignored
+digit separator\footnote{The space character has already always been accepted
+ in this rôle by the \xintexprname parsers, contrarily to the
+ situation inside |\numexpr|.}, for long numbers:
+\begin{everbatim*}
+\xinttheiiexpr 123_456_789^3\relax\newline
+\xintthefloatexpr \xintexpr 123_456_789.1111_1111_1111^-3\relax \relax
+\end{everbatim*}
+
+It is not accepted in the arguments of the macros
+from \xintfracname or \xintname though, only in expressions from
+\xintexprname.
+
+Macro usage with non properly terminated inputs such as
+|\xintiiAdd{\the\numexpr1}{2}| or |\xintDecToHex{\number\mathcode`\-}| caused
+crashes. This has been fixed: the arithmetic macros of \xintcorename, the
+macros of \xintfracname, those of \xintgcdname and \xintbinhexname have been
+made robust against such inputs. Some routines of \xintcorename principally
+destined to internal usage such as \csbxint{Inc} remain incompatible though
+(to avoid adding some overhead; check |sourcexint.pdf| for details).
+
+Some refactoring took place in the sources of \xintcorename for efficiency
+gains. Some improvements in the user documentation and the code comments.
+
+See |CHANGES.html| or |CHANGES.pdf| for more information (either |texdoc
+--list xint| or on the internet via
\href{http://mirrors.ctan.org/macros/generic/xint/CHANGES.html}{this link}.)
@@ -3813,29 +3948,31 @@
\def\@floatboxreset{\@setminipage}% faudra contrôler celui-là
\makeatother
\begin{table}[htbp]\ht\strutbox12pt\dp\strutbox5pt
+\capstart
\centering\begin{tabular}{|c|p{.5\textwidth}|}
\hline
Precedence&``Operators'' at this level\strut\\
\hline\hline
\mylink{$\infty$}&
- functions and variables, decimal mark |.|, |e| and |E| of scientific notation, hexadecimal prefix |"|.\strut\\\hline
+ functions and variables, decimal mark |.|, |e| and |E| of scientific notation, hexadecimal prefix |"|\strut\\\hline
\mylink{$10$}& postfix |!| (factorial) and conditional branching operators |?| and |??| \strut\\\hline
\mylink{$=$}& minus sign |-| as unary operator acquires the
- precedence level of the previous infix operator.\strut\\\hline
- \mylink{$9$}&|^|, |**| and list operators |^[|, |**[|, |]^|, |]**|.\strut\\\hline
- \mylink{$8$}&tacit multiplication.\strut\\\hline
- \mylink{$7$}&|*|, |/|, and list operators |*[|, |/[|, |]*|, |]/|.\strut\\\hline
- \mylink{$6$}&|+|, |-|, and list operators |+[|, |-[|, |]+|, |]-|.\strut\\\hline
- \mylink{$5$}&|<|, |>|, |==| (or |=|), |<=|, |>=|, |!=|.\strut\\\hline
- \mylink{$4$}&|&&| and its equivalent |'and'|.\strut\\\hline
- \mylink{$3$}&\verb+||+, its equivalent |'or'|, and |'xor'|; also the
- sequence generators |..|, |..[|, |]..|, and the Python slicer |:|.\strut\\\hline
- \mylink{$2$}& the comma |,|.\strut\\\hline
+ precedence level of the previous infix operator\strut\\\hline
+ \mylink{$9$}&|^|, |**| and list operators |^[|, |**[|, |]^|, |]**|\strut\\\hline
+ \mylink{$8$}&tacit multiplication\strut\\\hline
+ \mylink{$7$}&|*|, |/|, |//|, |/:| (aka |'mod'|), and list operators |*[|, |/[|, |]*|, |]/|\strut\\\hline
+ \mylink{$6$}&|+|, |-|, and list operators |+[|, |-[|, |]+|, |]-|\strut\\\hline
+ \mylink{$5$}&|<|, |>|, |==| (or |=|), |<=|, |>=|, |!=|\strut\\\hline
+ \mylink{$4$}&|&&| and its equivalent |'and'|\strut\\\hline
+ \mylink{$3$}&\verb+||+ (aka |'or'|), and |'xor'|; also the
+ sequence generators |..|, |..[|, |]..|, and the Python slicer |:|\strut\\\hline
+ \mylink{$2$}& the comma |,|\strut\\\hline
\mylink{$1$}& the parentheses |(|, |)|, list brackets |[|, |]|, and semi-colon |;| in an |iter| or
- |rseq|.\strut\\\hline
+ |rseq|\strut\\\hline
\end{tabular}
- \caption{Precedence levels}
+ \caption{Precedence levels (click on levels)}
\label{tab:precedences}
+\addcontentsline {toc}{table}{Precedence levels of operators in expressions}
\end{table}
The \autoref{tab:precedences} is hyperlinked to the more detailed discussion
@@ -3959,13 +4096,19 @@
not \xinttheiexpr 100/(50/2)\relax.
%
\endgroup
- Inside \csbxint{iiexpr}, |/| does \emph{rounded} division.
+ Also the truncated division |//| and modulo |/:| (equivalently |'mod'|,
+ quotes mandatory).
+
Also at this level the list operators |*[|, |/[|, |]*| and |]/|.
- Also the truncated division |//| and modulo |/:| (equivalently |'mod'|,
- quotes mandatory). Operators all at the same level of precedence are
- left-associative. Apply parentheses for disambiguation.
+ In an \csbxint{iiexpr}-ession, |/| does \emph{rounded} division, to behave
+ like the |/| of |\numexpr|.
+
+ Infix operators all at the same level of precedence are
+ left-associative.\footnote{i.e. the first two operands are operated upon
+ first.}
+ Apply parentheses for disambiguation.
\begin{everbatim*}
\xinttheexpr 100000//13, 100000/:13, 100000 'mod' 13, trunc(100000/13,10),
trunc(100000/:13/13,10)\relax
@@ -4029,29 +4172,31 @@
\subsection{Built-in functions}
+See \autoref{tab:functions} whose elements are hyperlinked to the
+corresponding definitions.
+
Functions are at the same top level of priority. All functions even
|?| and |!| (as prefix) require parentheses around their arguments.
\begin{table}[htbp]
+\capstart
\centering
\cnta0
\begin{tabular}{|c|c|c|c|c|c|}
\hline
- \xintFor #1 in {abs, sgn, num, reduce, float, round, trunc, floor, ceil,
- frac, sqr, sqrt, sqrtr, factorial, binomial, pfactorial, mod, quo, rem, gcd,
- lcm, max, min, |`+`|, |`*`|, ?, !, not, all, any, xor, if, ifsgn, even, odd,
- first, last, reversed, len, subs, add, mul, seq, rseq, iter, rrseq, iterr,
- bool, togl, qint, qfrac, qfloat}\do
+ \xintFor #1 in {!, ?, |`*`|, |`+`|, abs, add, all, any, binomial, bool,
+ ceil, even, factorial, first, float, floor, frac, gcd, if, ifsgn, iter,
+ iterr, last, lcm, len, max, min, mod, mul, not, num, odd, pfactorial,
+ qfloat, qfrac, qint, quo, reduce, rem, reversed, round, rrseq, rseq, seq,
+ sgn, sqr, sqrt, sqrtr, subs, togl, trunc, xor}\do
{\hyperlink{\detokenize{builtinfunc-#1}}{#1}\global\advance\cnta1
- \ifnumequal{\cnta}{6}{\global\cnta0 \\\hline}{&}}%
- \ifnumgreater{\cnta}{0}{\xintFor*#1in{\xintSeq[1]{\cnta}{4}}\do{&}\\\hline}{}%
+ \ifnumequal{\cnta}{4}{\global\cnta0 \\\hline}{&}}%
+% \ifnumgreater{\cnta}{0}{\xintFor*#1in{\xintSeq[1]{\cnta}{4}}\do{&}\\\hline}{}%
\end{tabular}
-\caption{Functions}\label{tab:functions}
+\caption{Functions (click on names)}\label{tab:functions}
+\addcontentsline{toc}{table}{Functions in expressions}
\end{table}
-See \autoref{tab:functions} whose elements are hyperlinked to the
-corresponding definitions.
-
Miscellaneous notes:
\begin{itemize}[nosep]
\item \fbox{|gcd| and |lcm| require explicit loading of \xintgcdname},
@@ -4260,15 +4405,29 @@
\end{description}
\item[functions with one mandatory and a second but optional argument:]\mbox{}
\begin{description}[listparindent=\leftmarginiii]
- \myitem{round} Rounds to a fixed point number with the given number of digits
- after the decimal mark. For example
+ \myitem{round} Rounds its first argument to a fixed point number, having a
+ number of digits
+ after decimal mark given by the second argument. For example
|round(-2^9/3^5,12)=|\dtt{\xinttheexpr round(-2^9/3^5,12)\relax.}
- \myitem{trunc} Truncates to a fixed point number with the given number of
- digits after the decimal mark. For example
+ \myitem{trunc} Truncates its first argument to a fixed point number, having
+ a number of digits
+ after decimal mark given by the second argument. For example
|trunc(-2^9/3^5,12)=|\dtt{\xinttheexpr trunc(-2^9/3^5,12)\relax.}
- \myitem{float} Rounds to a floating point number with a mantissa having the given number of
- digits. For example
+ \myitem{float} Rounds its first argument to a floating point number, with a
+ precision given by the second argument.
|float(-2^9/3^5,12)=|\dtt{\xinttheexpr float(-2^9/3^5,12)\relax.}
+
+ % AUCTeX EXTREMEMENT PENIBLE AVEC L'INDENTATION FORCEE SOUS M-q
+
+ Note for this example and the earlier ones that when the surrounding
+ parser is \csbxint{floatexpr}|...\relax| the fraction first argument (here
+ |2^9/3^5|) will already have been computed as floating point number (with
+ numerator and denominator handled separately first), even before the
+ second argument is seen and a fortiori before the |round|, |trunc| or
+ |float| is executed. The general float precision is the one governing
+ these initial steps. To avoid that, use |\xintexpr2^9/3^5\relax| wrapper.
+ Then the rounding or truncation will be applied on the exact fraction.
+
\item[sqrt] in \csa{xintexpr}|...\relax| and \csa{xintfloatexpr}|...\relax|
it achieves the precision given by the optional second argument. For
legacy reasons the |sqrt| function in \csa{xintiiexpr} \emph{truncates}
@@ -4790,13 +4949,27 @@
\end{everbatim*}
Legal variable names are composed of letters, digits, |@| and |_| signs.
-They can not start with a digit. They may start with |@| or |_|. Currently
-|@|, |@1|, |@2|, |@3|, and |@4| are reserved because they have special
-meanings for use in iterations. The |@@|, |@@@|, |@@@@| are also reserved but
-are technically functions, not variables. Thus a user may possibly use |@@| as
+\begin{itemize}[nosep]
+\item the first character must not be a digit,
+\item it may be a |@| or |_| but such variable names may be used either now or
+ in the future by \xintname for special purposes, hence should be avoided:
+ \begin{itemize}[nosep]
+ \item currently |@|, |@1|, |@2|, |@3|, and |@4| are reserved because they
+ have special meanings for use in iterations.
+ \item the |@@|, |@@@|, |@@@@| are also reserved but
+are technically functions, not variables: a user may possibly define |@@| as
a variable name, but if it is followed by parentheses, the function
interpretation will be applied, rather than the variable interpretation
followed by a tacit multiplication.
+ \item since 1.2l, the underscore |_| may be used as separator of digits in
+ long numbers.
+ Hence a variable whose name starts with it will not play well with the
+ mechanism of tacit multiplication of variables by numbers: the underscore
+ will be removed from input stream by the number scanner, thus creating
+ an undefined or wrong variable name, or none at all if the variable
+ name was an initial |_| followed by digits.
+ \end{itemize}
+\end{itemize}
|x_1x| is a licit variable name, as well as |x_1x_| and |x_1x_2| and |x_1x_2y|
etc... hence we can not rely on tacit multiplication being applied to
@@ -5280,7 +5453,11 @@
to \dtt{\detokenize\expandafter{\the\numexpr 7 + 3 5\relax}\unskip}, whereas
|\xintthe\xintiiexpr 7 + 3 5\relax| expands (in two steps) to
\dtt{\detokenize\expandafter\expandafter\expandafter {\xintthe\xintiiexpr 7
- + 3 5\relax}}.
+ + 3 5\relax}}.%
+%
+\footnote {Since |1.2l| one can also use the underscore |_| to separate digits
+for readability of long numbers.}
+
\item Inside an |\edef|, expressions |\xintiiexpr...\relax| get fully
evaluated, but to a private format which needs the prefix \csbxint{the} to
get printed or used as arguments to some macros; on the other hand
@@ -6157,22 +6334,30 @@
denominator, with no need to be prefixed by |\the| or |\number|. It is possible
to have as argument an algebraic expression as would be acceptable by a
|\numexpr...\relax|, under this condition: \emph{each of the numerator and
- denominator is expressed with at most \emph{eight}
+ denominator is expressed with at most \emph{nine}
tokens}.%
%
-\footnote{Attention! there is no problem with a \LaTeX{}
- \csa{value}\texttt{\{countername\}} if if comes first, but if it comes later
- in the input it will not get expanded, and braces around the name will be
- removed and chaos\IMPORTANT{} will ensue inside a \csa{numexpr}. One should
- enclose the whole input in \csa{the}\csa{numexpr}|...|\csa{relax} in such
- cases.}
+\footnote{The |1.2k| and earlier versions manual claimed up to 8
+ tokens, but low-level TeX error arose if the |\numexpr...\relax| occupied
+ exactly 8 tokens \emph{and} evaluated to zero. With |1.2l| and later, up to
+ 9 tokens are always safe and one may even drop the ending |\relax|. But
+ well, all these explanations are somewhat silly because prefixing by |\the|
+ or |\number| is always working with arbitrarily many tokens.}
%
-The slash for rounded division in a |\numexpr| should be written with
+%
+\footnote{Attention! in the \LaTeX{} context a
+ \csa{value}\texttt{\{countername\}} will behave ok only if it is first in
+ the input, if not it will not get expanded, and braces around the name will
+ be removed and chaos\IMPORTANT{} will ensue inside a \csa{numexpr}. One
+ should enclose the whole input in \csa{the}\csa{numexpr}|...|\csa{relax} in
+ such cases.}
+%
+Important: a slash for rounded division in a |\numexpr| should be written with
braces |{/}| to not be confused with the \xintfracname delimiter between
-numerator and denominator (braces will be removed internally). Example:
+numerator and denominator (braces will be removed internally and the slash
+will count for one token). Example:
|\mycountA+\mycountB{/}17/1+\mycountA*\mycountB|, or |\count 0+\count
-2{/}17/1+\count 0*\count 2|, but in the latter case the numerator has the
-maximal allowed number of tokens (the braced slash counts for only one).
+2{/}17/1+\count 0*\count 2|.
%
\leftedline{|\cnta 10 \cntb 35 \xintRaw
{\cnta+\cntb{/}17/1+\cnta*\cntb}|\dtt{->\cnta 10 \cntb 35 \xintRaw
@@ -6560,30 +6745,65 @@
\subsection{Error messages}
-In situations such as division by zero, the package will insert in the
-\TeX{} processing an undefined control sequence (we copy this method
-from the |bigintcalc| package). This will trigger the writing to the log
-of a message signaling an undefined control sequence. The name of the
-control sequence is the message. The error is raised \emph{before} the
-end of the expansion so as to not disturb further processing of the
-token stream, after completion of the operation. Generally the problematic
-operation will output a zero. Possible such error message control
-sequences:
+In situations such as division by zero, the \TeX{} run will be interrupted
+with some error message. The user is asked to hit the RETURN key thrice, which
+will display additional information.\CHANGED{1.2l} In non-interactive
+|nonstopmode| the \TeX{} run goes on uninterrupted and the error data will be
+found in the compilation log.
+Here is an example interactive run:
+\begin{everbatim}
+! Undefined control sequence.
+<argument> \ ! /
+ DivisionByZero (hit <RET> thrice)
+l.11 \xintiiDivision{123}{0}
+
+?
+! Undefined control sequence.
+<argument> \ ! /
+ Division of 123 by 0
+l.11 \xintiiDivision{123}{0}
+
+?
+! Undefined control sequence.
+<argument> \ ! /
+ next: {0}{0}
+l.11 \xintiiDivision{123}{0}
+
+?
+[1] (./temptest.aux) )
+Output written on temptest.dvi (1 page, 216 bytes).
+Transcript written on temptest.log.
+\end{everbatim}
+This is an experimental feature, which is in preparation for next major
+release.%
+%
+\footnote{The related macros checking or resetting error flags are implemented
+ in embryonic form but no user interface is provided with |1.2l| release.}
+%
+For the good functioning of this the macro with the weird appearance
+{\catcode`/ 11 \catcode`! 11 \catcode32 11 |\ ! /|} (yes, this is a single
+control sequence) must be left undefined. I trust it will be |;-)|.%
+%
+\footnote{The implementation is cloned from \LaTeX3, the
+ {\catcode`/ 11 \catcode`! 11 \catcode32 11 |\ ! /|} was chosen for its
+ shortness.}
+
+
+The expression parsers are at |1.2l| still using a slightly less evolved
+method which lets \TeX{} display an undefined control sequence name giving
+some indication of the underlying problem (we copied this method from the
+|bigintcalc| package). The name of the control sequence is the message.
+
+% The
+% error is raised \emph{before} the end of the expansion so as to not disturb
+% further processing of the token stream, after completion of the operation.
+% Generally the problematic operation will output a zero. Possible such error
+% message control sequences:
+
\begin{multicols}{2}\parskip0pt\relax
\begin{everbatim}
-\xintError:ArrayIndexIsNegative
-\xintError:ArrayIndexBeyondLimit
-\xintError:FactorialOfNegative
-\xintError:TooBigFactorial
-\xintError:DivisionByZero
-\xintError:NaN
-\xintError:FractionRoundedToZero
-\xintError:NotAnInteger
-\xintError:ExponentTooBig
-\xintError:RootOfNegative
-\xintError:NoBezoutForZeros
\xintError:ignored
\xintError:removed
\xintError:inserted
@@ -6594,41 +6814,49 @@
\end{multicols}
-There are now a few more if for example one attempts to use |\xintAdd| without
-having loaded \xintfracname (with only \xintname loaded, only |\xintiAdd| and
-|\xintiiAdd| are legal) or to use deprecated macros.
+Some additional errors are raised when using deprecated macros (or trying to
+invoke \csbxint{Add} with only \xintname.sty loaded for example.)
\begin{multicols}{2}\parskip0pt\relax
\begin{everbatim}
-\Did_you_mean_iiAbs?or_load_xintfrac
-\Did_you_mean_iiOpp?or_load_xintfrac
-\Did_you_mean_iiAdd?or_load_xintfrac
-\Did_you_mean_iiSub?or_load_xintfrac
-\Did_you_mean_iiMul?or_load_xintfrac
-\Did_you_mean_iiPow?or_load_xintfrac
-\Did_you_mean_iiSqr?or_load_xintfrac
-\Did_you_mean_iiMax?or_load_xintfrac
-\Did_you_mean_iiMin?or_load_xintfrac
-\Did_you_mean_iMaxof?or_load_xintfrac
-\Did_you_mean_iMinof?or_load_xintfrac
-\Did_you_mean_iiSum?or_load_xintfrac
-\Did_you_mean_iiPrd?or_load_xintfrac
-\Did_you_mean_iiPrdExpr?or_load_xintfrac
-\Did_you_mean_iiSumExpr?or_load_xintfrac
+\Did_you_mean_iiAbs?or_load_xintfrac!
+\Did_you_mean_iiOpp?or_load_xintfrac!
+\Did_you_mean_iiAdd?or_load_xintfrac!
+\Did_you_mean_iiSub?or_load_xintfrac!
+\Did_you_mean_iiMul?or_load_xintfrac!
+\Did_you_mean_iiPow?or_load_xintfrac!
+\Did_you_mean_iiSqr?or_load_xintfrac!
+\Did_you_mean_iiMax?or_load_xintfrac!
+\Did_you_mean_iiMin?or_load_xintfrac!
+\Did_you_mean_iMaxof?or_load_xintfrac!
+\Did_you_mean_iMinof?or_load_xintfrac!
+\Did_you_mean_iiSum?or_load_xintfrac!
+\Did_you_mean_iiPrd?or_load_xintfrac!
\Removed!use_xintiQuo_or_xintiiQuo!
\Removed!use_xintiRem_or_xintiiRem!
\end{everbatim}
\end{multicols}
-One should set |\errorcontextlines| to at least |2| to get from \LaTeX\
-more meaningful error messages. Errors occuring during the parsing of
-|\xintexpr-essions| try to provide helpful information about the offending
-token.
+For such type of error sequences one should set |\errorcontextlines| to at
+least |2| to get from \LaTeX\ more context. Errors occuring during the parsing
+of |\xintexpr-essions| try to provide helpful information about the offending
+token. But for the newer |1.2l| type of expandable error messages it is
+already ok with |\errorcontextlines| left at its \LaTeX\ default. Future
+releases of \xintname will presumably use only the newer method.
-Release |1.1| employs in some situations delimited macros and there is
-the possibility in case of an ill-formed expression to end up beyond the
-|\relax| end-marker. The errors inevitably arising could then lead to very
-cryptic messages; but nothing unusual or especially traumatizing for the
-daring experienced \TeX/\LaTeX\ user.
+Some constructs in \xintexprname-essions use delimited macros and there is
+thus possibility in case of an ill-formed expression to end up beyond the
+|\relax| end-marker. Such a situation can also occur from a non-terminated
+|\numexpr|:
+\begin{everbatim}
+\xinttheexpr 3 + \numexpr 5+4\relax followed by some LaTeX code...
+\end{everbatim}
+as the |\numexpr| will swallow the |\relax| whose presence is mandatory for
+|\xinttheexpr|, errors will inevitably arise and may
+lead to very cryptic messages; but nothing unusual or especially traumatizing
+for the daring experienced \TeX/\LaTeX\ user, whose has seen zillions of
+un-helpful error messages already in her daily practice of
+\TeX/\LaTeX.\footnote{not to mention the \LaTeX\ error messages used by
+ Emacs AUC\TeX\ mode also for Plain \TeX\ runs...}
\subsection{Package namespace, catcodes}
@@ -6675,6 +6903,8 @@
other and letters have category code letter. Nothing else is assumed.
\end{framed}
+As pointed out in previous section the control sequence {\catcode`/ 11
+ \catcode`! 11 \catcode32 11 |\ ! /|} must be left undefined.
\subsection{Origins of the package}
\label{ssec:origins}
@@ -9429,59 +9659,71 @@
%
defines (without checking if something gets overwritten) the control sequences
on the right of \csa{to} to expand to the successive tokens or braced items
-found one after the other on the left of \csa{to}. It is not expandable.
+located to the left of \csa{to}. \csa{xintAssign} is not an expandable macro.
-A `full' expansion is first applied to the material in front of
-\csa{xintAssign}, which may thus be a macro expanding to a list of braced items.
+\fexpan sion is first applied to the material in front of \csa{xintAssign}
+which is fetched as one argument if it is braced. Then the expansion of this
+argument is examined and successive items are assigned to the macros following
+|\to|. There must be exactly as many macros as items. No check is done. The
+macro assignments are done with removal of one level of brace pairs from each
+item.
-\xintAssign \xintiiPow {7}{13}\to\SevenToThePowerThirteen
+After the initial \fexpan sion, each assigned (brace-stripped) item will be
+expanded according to the setting of the optional parameter.
+
+For example |\xintAssign [e]...| means that all assignments are done using
+|\edef|. With |[f]| the assignments will be made using
+\hyperref[fdef]{\ttfamily\char92fdef}. The default is simply to make the
+definitions with |\def|, corresponding to an empty optional paramter |[]|.
+Possibilities for the optional parameter are: |[], [g], [e], [x], [o], [go],
+[oo], [goo], [f], [gf]|. For example |[oo]| means a double expansion.
+\begin{everbatim*}
\xintAssign \xintiiDivision{1000000000000}{133333333}\to\Q\R
+\meaning\Q\newline
+\meaning\R\newline
+\xintAssign {{\xintiiDivision{1000000000000}{133333333}}}\to\X
+\meaning\X\newline
+\xintAssign [oo]{{\xintiiDivision{1000000000000}{133333333}}}\to\X
+\meaning\X\newline
+\xintAssign \xintiiPow{7}{13}\to\SevenToThePowerThirteen
+\meaning\SevenToThePowerThirteen\par
+\end{everbatim*}
-Special case: if after this initial expansion no brace is found immediately
-after \csa{xintAssign}, it is assumed that there is only one control sequence
-following |\to|, and this control sequence is then defined via
-|\def| to expand to the material between
-\csa{xintAssign} and \csa{to}. Other types of expansions are specified through
-an optional parameter to \csa{xintAssign}, see \emph{infra}.
-%
-\leftedline{|\xintAssign \xintiiDivision{1000000000000}{133333333}\to\Q\R|}
-%
-\leftedline{|\meaning\Q: |\dtt{\meaning\Q}, |\meaning\R:|
- \dtt{\meaning\R}} %
-%
-\leftedline{|\xintAssign \xintiiPow
- {7}{13}\to\SevenToThePowerThirteen|}
-%
-\leftedline{|\SevenToThePowerThirteen|\dtt{=\SevenToThePowerThirteen}}
-%
-\leftedline{(same as |\edef\SevenToThePowerThirteen{\xintiPow {7}{13}}|)}
+Two special cases:
+\begin{itemize}[nosep]
+\item if after this initial expansion no brace is found immediately after
+ \csa{xintAssign}, it is assumed that there is only one control sequence
+ following |\to|, and this control sequence is then defined via |\def| (or
+ what is set-up by the optional parameter) to expand to the material between
+ \csa{xintAssign} and \csa{to}.
+\item if the material between \csa{xintAssign} and |\to| is enclosed in two
+ brace pairs, the first brace pair is removed, then the \fexpan sion is
+ immediately stopped by the inner brace pair, hence \csa{xintAssign} now
+ finds a unique item and thus defines only a single macro to be this item,
+ which is now stripped of the second pair of braces.
+\end{itemize}
-\noindent\csa{xintAssign} admits since |1.09i| an
-optional parameter, for example |\xintAssign [e]...| or |\xintAssign [oo]
-...|. With |[f]| for example the definitions of the macros initially on the
-right of |\to| will be made with \hyperref[fdef]{\ttfamily\char92fdef} which
-\fexpan ds the replacement text. The default is simply to make the
-definitions with |\def|, corresponding to an empty optional paramter |[]|.
-Possibilities: |[], [g], [e], [x], [o], [go], [oo], [goo], [f], [gf]|.
-In all cases, recall that |\xintAssign| starts with an \fexpan sion of what
-comes next; this produces some list of tokens or braced items, and the
-optional parameter only intervenes to decide the expansion type to be applied
-then to each one of these items.
+\emph{Note:} prior to release |1.09j|, |\xintAssign| did an |\edef| by default
+for each item assignment but it now does |\def| corresponding to no or empty
+optional parameter.
-\emph{Note:} prior to release |1.09j|, |\xintAssign| did an |\edef| by
-default, but it now does |\def|. Use the optional parameter |[e]| to force use
-of |\edef|.
+It is allowed for the successive braced items to be separated by spaces. They
+are removed during the assignments. But if a single macro is defined (which
+happens if the argument after \fexpan sion does not start with a brace),
+naturally the scooped up material has all intervening spaces, as it is
+considered a
+single item. But an upfront initial space will have been absorbed by \fexpan
+sion.
+\begin{everbatim*}
+\def\X{ {a} {b} {c} {d} }\def\Y { u {a} {b} {c} {d} }
+\xintAssign\X\to\A\B\C\D
+\xintAssign\Y\to\Z
+\meaning\A, \meaning\B, \meaning\C, \meaning\D+++\newline
+\meaning\Z+++\par
+\end{everbatim*}
+As usual successive space characters in input make for a single \TeX\ space token.
-{\small \emph{Remark:} since |xinttools 1.1c|, \csa{xintAssign} is less picky
- and a stray space right before the |\to| causes no surprises, and the
- successive braced items may be separated by spaces, which will get
- discarded. In case the contents up to |\to| did not start with a brace a
- single macro is defined and it will contain the spaces. Contrarily to the
- earlier version, there is no problem if such contents do contain braces
- after the first non-brace token.
-\par
-}
\subsection{\csbh{xintAssignArray}}\label{xintAssignArray}
@@ -9506,16 +9748,14 @@
\dtt{(\Bez3)${}\times{}$\Bez1${}-{}$(\Bez4)${}\times{}$\Bez2${}={}$\Bez5.}
This macro is incompatible with expansion-only contexts.
-\csa{xintAssignArray} admits now an optional
-parameter, for example |\xintAssignArray [e]...|. This means that the
-definitions of the macros will be made with |\edef|. The default is
-|[]|, which makes the definitions with |\def|. Other possibilities: |[],
-[o], [oo], [f]|. Contrarily to \csbxint{Assign} one can not use the |g|
-here to make the definitions global. For this, one should rather do
-|\xintAssignArray| within a group starting with |\globaldefs 1|.
+\csa{xintAssignArray} admits an optional parameter, for example
+|\xintAssignArray [e]| means that the definitions of the macros will be made
+with |\edef|. The empty optional parameter (default) means that definitions
+are done with |\def|. Other possibilities: |[], [o], [oo], [f]|. Contrarily to
+\csbxint{Assign} one can not use the |g| here to make the definitions global.
+For this, one should rather do |\xintAssignArray| within a group starting with
+|\globaldefs 1|.
-Note that prior to release |1.09j| each item (token or braced material) was
-submitted to an |\edef|, but the default is now to use |\def|.
\subsection{\csbh{xintDigitsOf}}\label{xintDigitsOf}
@@ -9674,6 +9914,17 @@
\csa{xintiiAdd} skips the \csbxint{Num} overhead.\etype{ff}
+\subsection{\csbh{xintCmp}, \csbh{xintiiCmp}}
+
+|\xintCmp|\n\m\etype{\Numf\Numf} returns \dtt{1} if |N>M|, \dtt{0} if |N=M|,
+and \dtt{-1} if |N<M|.
+
+\csa{xintiiCmp} skips the \csbxint{Num} overhead.\etype{ff}
+
+\csbxint{Cmp} is re-defined by \xintfracname to accept fractions.
+
+|1.2l| has moved this macro from \xintname to \xintcorename.
+
\subsection{\csbh{xintiSub}, \csbh{xintiiSub}}\label{xintiSub}\label{xintiiSub}
|\xintiSub|\n\m\etype{\Numf\Numf} computes the difference |N-M|.
@@ -9891,29 +10142,22 @@
\subsection{\csbh{xintReverseDigits}} \label{xintReverseDigits}
|\xintReverseDigits|\n\etype{f} will reverse the order of the digits of the
-number, preserving an optional upfront minus sign. \csa{xintRev} is the former
-denomination and is kept as an alias to it. Leading zeroes resulting from the
-operation are not removed. Contrarily to \csbxint{ReverseOrder} this macro can
-only be used with digits and it first expands its argument (but beware that
-|-\x| will give an unexpected result as the minus sign immediately stops this
-expansion; one can use |\xintiiOpp{\x}| as argument.)
+number. \csa{xintRev} is the former
+denomination and is kept as an alias. Leading zeroes resulting from the
+operation are not removed. Contrarily to \csbxint{ReverseOrder} this macro
+expands its argument; it is only usable with digit tokens. It does accept a
+leading minus sign which is left upfront in output.
-This macro has been rewritten for |1.2| and is faster for very long inputs.
-It is (almost) not used internally by the \xintcorename code, but the use
-of related routines explains to some extent the higher speed of release |1.2|.
\begingroup
\begin{everbatim*}
\fdef\x{\xintReverseDigits
- {-98765432109876543210987654321098765432109876543210}}\meaning\x\par
+ {98765432109876543210987654321098765432109876543210}}\meaning\x\par
\noindent\fdef\x{\xintReverseDigits {\xintReverseDigits
- {-98765432109876543210987654321098765432109876543210}}}\meaning\x\par
+ {98765432109876543210987654321098765432109876543210}}}\meaning\x\par
\end{everbatim*}
\endgroup
-Notice that the output in this case with its leading zero is not in the strict
-integer format expected by the `|ii|' arithmetic macros.
-
\subsection{\csbh{xintLen}}\label{xintiLen}
|\xintLen|\n\etype{\Numf} returns the length of the number, not counting the
@@ -9939,14 +10183,18 @@
\xinttoolsname. See also \csbxint{Length} from \xintkernelname for counting
tokens (or rather braced groups), more generally.
-\subsection{\csbh{xintCmp}, \csbh{xintiiCmp}}
+\subsection{\csbh{xintCmp}, \csbh{xintiiCmp}}\label{xintiiCmp}
|\xintCmp|\n\m\etype{\Numf\Numf} returns \dtt{1} if |N>M|, \dtt{0} if |N=M|,
-and \dtt{-1} if |N<M|. Extended by \xintfracname to fractions (its output
-naturally still being either |1|, |0|, or |-1|).
+and \dtt{-1} if |N<M|.
\csa{xintiiCmp} skips the \csbxint{Num} overhead.\etype{ff}
+\csbxint{Cmp} is re-defined by \xintfracname to accept fractions.
+
+Since |1.2l| these macros are actually provided by package \xintcorename.sty
+(which is loaded by \xintname).
+
\subsection{\csbh{xintEq}, \csbh{xintiiEq}}\label{xintEq}
|\xintEq|\n\m\etype{\Numf\Numf} returns 1 if |N=M|, 0 otherwise. Extended
@@ -10799,10 +11047,10 @@
%
This is faster than \csa{xintIrr} for fractions having some big common
factor in the numerator and the denominator.\par
-{\centering |\xintJrr {\xintiPow{\xintiiFac {15}}{3}/\xintiiPrdExpr
-{\xintiiFac{10}}{\xintiiFac{30}}{\xintiiFac{5}}\relax }|\dtt{=%
- \xintJrr {\xintiPow{\xintiiFac {15}}{3}/\xintiiPrdExpr
-{\xintiiFac{10}}{\xintiiFac{30}}{\xintiiFac{5}}\relax }}\par} But to notice the
+{\centering |\xintJrr {\xintiPow{\xintiiFac {15}}{3}/\xintiiPrd
+{{\xintiiFac{10}}{\xintiiFac{30}}{\xintiiFac{5}}}}|\dtt{=%
+ \xintJrr {\xintiPow{\xintiiFac {15}}{3}/\xintiiPrd
+{{\xintiiFac{10}}{\xintiiFac{30}}{\xintiiFac{5}}}}}\par} But to notice the
difference one would need computations with much bigger numbers than in this
example.
Starting with release |1.08|, \csa{xintJrr} does not remove the trailing |/1|
@@ -11274,7 +11522,7 @@
\csa{xintPow}.
-\subsection{\csbh{xintSum}}\label{xintSum}\label{xintSumExpr}
+\subsection{\csbh{xintSum}}\label{xintSum}
This\etype{f{$\to$}{\lowast\Ff}} computes the sum of fractions. The output
will now always be in the form |A/B[n]|. The original, for big integers only
@@ -11286,7 +11534,7 @@
No simplification attempted.
-\subsection{\csbh{xintPrd}}\label{xintPrd}\label{xintPrdExpr}
+\subsection{\csbh{xintPrd}}\label{xintPrd}
TThis\etype{f{$\to$}{\lowast\Ff}} computes the product of fractions. The output
will now always be in the form |A/B[n]|. The original, for big integers only
@@ -11517,9 +11765,7 @@
the sum |f'+g'|, correctly rounded to nearest with the same number of
significant places.
-See \autoref{ssec:floatingpoint} for more.
-
\subsection{\csbh{xintFloatSub}}\label{xintFloatSub}
@@ -11528,9 +11774,7 @@
places or to the precision from |\xintDigits|. It then produces
the difference |f'-g'| correctly rounded to nearest |P|-float.
-See \autoref{ssec:floatingpoint} for more.
-
\subsection{\csbh{xintFloatMul}}\label{xintFloatMul}
@@ -11562,10 +11806,11 @@
See \autoref{ssec:floatingpoint} for more.
-Notice that if |f| and |g| are integers and one wants the fraction |f/g|
-correctly rounded one should use \csbxint{Float}|[P]{f/g}| and not
-|\xintFloatDiv [P]{f}{g}|, because the latter will first round |f| and |g| to
-scientific numbers with mantissas of |P| digits.
+Notice in the special situation with |f| and |g| integers that |\xintFloatDiv
+[P]{f}{g}| will \emph{not necessarily} give the correct rounding of the
+exact fraction |f/g|. Indeed the macro arguments are each first individually
+rounded to |P| digits of precision. The correct syntax to get the correctly
+rounded integer fraction |f/g| is \csbxint{Float}|[P]{f/g}|.
\subsection{\csbh{xintFloatFac}}\label{xintFloatFac}
@@ -13014,17 +13259,24 @@
This package was first included in the |1.08| (|2013/06/07|) release of
\xintname. It provides expandable conversions of arbitrarily big integers to and
-from binary and hexadecimal.
+from binary and hexadecimal. Routines have not been modified since.
-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
-(arbitrarily many, category code other) and then ``digits'' (hexadecimal
-letters may be of category code letter or other, and must be
-uppercased). The optional (unique) minus sign (plus sign is not allowed) is
-kept in the output. Leading zeroes are allowed, and stripped. The
-hexadecimal letters on output are of category code letter, and
-uppercased.
+The argument is first \fexpan ded.
+It may optionally have a leading minus sign (explicit plus sign is not
+allowed), then leading zeroes, then digits. Hexadecimal digits |A..F| must be
+in uppercase. Category code for them on input may be \emph{letter} or
+\emph{other}. The hexadecimal letters on output are of category code
+\emph{letter}, and again in uppercase.
+
+Input must not be within quotes or with |0b|, |0x|, |#x| or similar prefixes:
+simply decimal, binary, or hexadecimal digits.
+
+With this package loaded additionally to \xintexprname, hexadecimal input
+becomes possible in expressions with the prefix |"|. Such hexadecimal numbers
+may have an hexadecimal mark and fractional digits. The letters must be in
+uppercase.
+
% \clearpage
\subsection{\csbh{xintDecToHex}}\label{xintDecToHex}
@@ -13133,64 +13385,42 @@
\subsection{\csbh{xintBezout}}\label{xintBezout}
-\xintAssign{{\xintBezout {10000}{1113}}}\to\X
-\xintAssign {\xintBezout {10000}{1113}}\to\A\B\U\V\D
-
|\xintBezout|\n\m\etype{\Numf\Numf} returns five numbers |A|, |B|, |U|, |V|,
|D| within braces. |A| is the first (expanded, as usual) input number, |B| the
-second, |D| is the GCD, and \dtt{UA - VB = D}. %
-%
-\leftedline{|\xintAssign
- {{\xintBezout {10000}{1113}}}\to\X|} %
-%
-\leftedline{|\meaning\X:
- |\dtt{\meaning\X }.}
-\noindent{|\xintAssign {\xintBezout {10000}{1113}}\to\A\B\U\V\D|}\\
-|\A: |\dtt{\A },
-|\B: |\dtt{\B },
-|\U: |\dtt{\U },
-|\V: |\dtt{\V },
-|\D: |\dtt{\D }.\\
+second, |D| is the GCD, and \dtt{UA - VB = D}.
+\begin{everbatim*}
+\xintAssign[oo]{{\xintBezout {10000}{1113}}}\to\X
+\meaning\X\newline
+\xintAssign {\xintBezout {10000}{1113}}\to\A\B\U\V\D
+A: \meaning\A\newline
+B: \meaning\B\newline
+U: \meaning\U\newline
+V: \meaning\V\newline
+D: \meaning\D\par
+\end{everbatim*}
+For more than three years (from |1.09j 2014/01/09| to |1.2l| in 2017...) this
+documentation looked strange (also in the next two sub-sections,) because
+\csbxint{Assign} was modified at |1.09j| but the example above was missing the
+now needed |[oo]| (or |[f]|, or |[e]|) hence |\X| was simply displayed as
+|\xintBezout {10000}{1113}|.
+\begin{everbatim*}
\xintAssign {\xintBezout {123456789012345}{9876543210321}}\to\A\B\U\V\D
-\noindent{|\xintAssign {\xintBezout {123456789012345}{9876543210321}}\to\A\B\U\V\D
-|}\\
-|\A: |\dtt{\A },
-|\B: |\dtt{\B },
-|\U: |\dtt{\U },
-|\V: |\dtt{\V },
-|\D: |\dtt{\D }.
+A: \meaning\A\newline
+B: \meaning\B\newline
+U: \meaning\U\newline
+V: \meaning\V\newline
+D: \meaning\D\par
+\end{everbatim*}
\subsection{\csbh{xintEuclideAlgorithm}}\label{xintEuclideAlgorithm}
-\xintAssign {{\xintEuclideAlgorithm {10000}{1113}}}\to\X
-
-\def\restorebracecatcodes
- {\catcode`\{=1 \catcode`\}=2 }
-
-\def\allowlistsplit
- {\catcode`\{=12 \catcode`\}=12 \allowlistsplita }
-
-\def\allowlistsplitx {\futurelet\listnext\allowlistsplitxx }
-
-\def\allowlistsplitxx {\ifx\listnext\relax \restorebracecatcodes
- \else \expandafter\allowlistsplitxxx \fi }
-\begingroup
-\catcode`\[=1
-\catcode`\]=2
-\catcode`\{=12
-\catcode`\}=12
-\gdef\allowlistsplita #1{[#1\allowlistsplitx {]
-\gdef\allowlistsplitxxx {#1}%
- [{#1}\hskip 0pt plus 1pt \allowlistsplitx ]
-\endgroup
-
|\xintEuclideAlgorithm|\n\m\etype{\Numf\Numf} applies the Euclide algorithm
-and keeps a copy of all quotients and remainders. %
-%
-\leftedline{|\xintAssign {{\xintEuclideAlgorithm {10000}{1113}}}\to\X|}
+and keeps a copy of all quotients and remainders.
+\begin{everbatim*}
+\xintAssign [oo]{{\xintEuclideAlgorithm {10000}{1113}}}\to\X
+\meaning\X
+\end{everbatim*}
-|\meaning\X: |\dtt{\expandafter\allowlistsplit\meaning\X\relax .}
-
The first token is the number of steps, the second is |N|, the
third is the GCD, the fourth is |M| then the first quotient and
remainder, the second quotient and remainder, \dots until the
@@ -13198,18 +13428,16 @@
\subsection{\csbh{xintBezoutAlgorithm}}\label{xintBezoutAlgorithm}
-\xintAssign {{\xintBezoutAlgorithm {10000}{1113}}}\to\X
-
|\xintBezoutAlgorithm|\n\m\etype{\Numf\Numf} applies the Euclide algorithm
and keeps a copy of all quotients and remainders. Furthermore it computes the
entries of the successive products of the 2 by 2 matrices
$\left(\vcenter{\halign {\,#&\,#\cr q & 1 \cr 1 & 0 \cr}}\right)$ formed from
-the quotients arising in the algorithm. %
-%
-\leftedline{|\xintAssign {{\xintBezoutAlgorithm {10000}{1113}}}\to\X|}
+the quotients arising in the algorithm.
+\begin{everbatim*}
+\xintAssign [oo]{{\xintBezoutAlgorithm {10000}{1113}}}\to\X
+\printnumber{\meaning\X}
+\end{everbatim*}
-|\meaning\X: |\dtt{\expandafter\allowlistsplit\meaning\X \relax .}
-
The first token is the number of steps, the second is |N|, then
|0|, |1|, the GCD, |M|, |1|, |0|, the first quotient, the first
remainder, the top left entry of the first matrix, the bottom left
@@ -13334,8 +13562,8 @@
\def\coeff #1{\xintiTrunc {40}
{\the\numexpr\ifodd #1 -2\else2\fi\relax/\the\numexpr 2*#1+1\relax [0]}}%
- \csa{xintiSeries}|{A}{B}{\coeff}|\etype{\numx\numx f} computes
- $\sum_{\text{|n=A|}}^{\text{|n=B|}}|\coeff{n}|$ where |\coeff{n}|
+\csa{xintiSeries}|{A}{B}{\coeff}|\etype{\numx\numx f} computes
+ $\sum_{\text{|n=A|}}^{\text{|n=B|}}$|\coeff{n}| where |\coeff{n}|
must \fexpan d to a (possibly long) integer in the strict format.
\everb|@
\def\coeff #1{\xintiTrunc {40}{\xintMON{#1}/#1.5}}%
@@ -14993,11 +15221,23 @@
% This is \expandafter|\xintbndlversion| of \expandafter|\xintbndldate|.
%
% \begin{itemize}
-% \item Some portions of the code still date back to the initial release, and
-% at that time I was learning my trade in expandable TeX macro programming.
-% At some point in the future, I will have to re-examine the older parts of
-% the code.
+% \item Release |1.2l| of |2017/07/26| refactored the subtraction and also
+% |\xintiiCmp| got a rewrite. It should presumably use |\pdfstrcmp| and
+% related PDF\TeX\ utilities, but I do not want to have to worry about
+% multi-engine usage.
%
+% Some utility routines in \xintcorenameimp manipulating blocks of eight
+% digits and still in |O(N^2)| style have been re-written analogously to the
+% |1.2i| version of macros such as |\xintInc|. Also |\xintiNum| was
+% revisited.
+%
+% The arithmetic macros of \xintcorenameimp and all macros of
+% \xintfracnameimp using |\XINT_infrac| were made compatible with arguments
+% using non-delimited |\the\numexpr| or |\the\mathcode| etc... But
+% |\xintiiAbs| and |\xintiiOpp| were not modified (to avoid some overhead)
+% as well as routines such as |\xintInc| which are primarily for internal
+% usage.
+%
% \item Release |1.2i| of |2016/12/13| has rewritten some legacy macros like
% |\xintDSR| or |\xintDecSplit| in the style of the techniques of |1.2|. But
% this means also that they are now limited to about \dtt{22480} digits for
@@ -15028,6 +15268,11 @@
%
% \end{itemize}
%
+% Some parts of the code still date back to the initial release, and
+% at that time I was learning my trade in expandable TeX macro programming.
+% At some point in the future, I will have to re-examine the older parts of
+% the code.
+%
% Warning: pay attention when looking at the code to the catcode configuration
% as found in |\XINT_setcatcodes|. Additional temporary configuration is used
% at some locations. For example |!| is of catcode letter in \xintexprnameimp
@@ -15058,21 +15303,6 @@
% The method for catcodes was also initially directly inspired by these
% packages.
%
-% Starting with version |1.06| of the package, also |`| must be
-% catcode-protected, because we replace everywhere in the code the
-% twice-expansion done with |\expandafter| by the systematic use of
-% |\romannumeral-`0| (later with |1.2a 2015/10/19| this was replaced
-% by a fancier |\romannumeral`&&@|, with |&| of catcode 7.)
-%
-% Starting with version |1.06b| I decide that I suffer from an indigestion of @
-% signs, so I replace them all with underscores |_|, \`a la \LaTeX 3.
-%
-% Release |1.09b| is more economical: some macros are defined already in
-% |xint.sty| (now in |xintkernel.sty|) and re-used in other modules. All catcode
-% changes have been unified and \csa{XINT_storecatcodes} will be used by each
-% module to redefine |\XINT_restorecatcodes_endinput| in case catcodes have
-% changed in-between the loading of |xint.sty| (now |xintkernel.sty|) and the
-% module (not very probable but...).
% \begin{macrocode}
\begingroup\catcode61\catcode48\catcode32=10\relax%
\catcode13=5 % ^^M
@@ -15105,6 +15335,8 @@
\fi
\fi
\ifx\z\relax\else\expandafter\z\fi%
+% \end{macrocode}
+% \begin{macrocode}
\def\PrepareCatcodes
{%
\endgroup
@@ -15175,7 +15407,7 @@
\catcode36=3 % $
\catcode91=12 % [
\catcode93=12 % ]
- \catcode33=12 % !
+ \catcode33=12 % ! (xintexpr.sty will use catcode 11)
\catcode64=11 % @ LETTER
\catcode38=7 % & for \romannumeral`&&@ trick.
\catcode124=12 % |
@@ -15219,11 +15451,9 @@
\fi
\XINT_providespackage
\ProvidesPackage {xintkernel}%
- [2017/01/06 1.2k Paraphernalia for the xint packages (JFB)]%
+ [2017/07/26 1.2l Paraphernalia for the xint packages (JFB)]%
% \end{macrocode}
% \subsection{Constants}
-% |1.2| decides to move them to \xintkernelnameimp from \xintcorenameimp and
-% \xintnameimp. The |\count|'s are left in their respective packages.
% \begin{macrocode}
\chardef\xint_c_ 0
\chardef\xint_c_i 1
@@ -15236,6 +15466,7 @@
\chardef\xint_c_viii 8
\chardef\xint_c_ix 9
\chardef\xint_c_x 10
+\chardef\xint_c_xii 12
\chardef\xint_c_xiv 14
\chardef\xint_c_xvi 16
\chardef\xint_c_xviii 18
@@ -15290,9 +15521,6 @@
% |
%
% \subsection{``gob til'' macros and UD style fork}
-% Some moved here from \xintcorenameimp by release |1.2|.
-%
-% |1.2i| finally makes all gobbling macros long.
% \begin{macrocode}
\long\def\xint_gob_til_R #1\R {}%
\long\def\xint_gob_til_W #1\W {}%
@@ -15302,11 +15530,9 @@
\long\def\xint_gob_til_zeros_iii #1000{}%
\long\def\xint_gob_til_zeros_iv #10000{}%
\long\def\xint_gob_til_eightzeroes #100000000{}%
-\long\def\xint_gob_til_exclam #1!{}% catcode 12 exclam
\long\def\xint_gob_til_dot #1.{}%
\long\def\xint_gob_til_G #1G{}%
\long\def\xint_gob_til_minus #1-{}%
-\long\def\xint_gob_til_relax #1\relax {}%
\long\def\xint_UDzerominusfork #10-#2#3\krof {#2}%
\long\def\xint_UDzerofork #10#2#3\krof {#2}%
\long\def\xint_UDsignfork #1-#2#3\krof {#2}%
@@ -15315,9 +15541,11 @@
\long\def\xint_UDzerosfork #100#2#3\krof {#2}%
\long\def\xint_UDonezerofork #110#2#3\krof {#2}%
\long\def\xint_UDsignsfork #1--#2#3\krof {#2}%
-\let\xint_relax\relax
-\def\xint_brelax {\xint_relax }%
-\long\def\xint_gob_til_xint_relax #1\xint_relax {}%
+\let\xint:\char
+\long\def\xint_gob_til_xint:#1\xint:{}%
+\def\xint_bracedstopper{\xint:}%
+\long\def\xint_gob_til_exclam #1!{}%
+\long\def\xint_gob_til_sc #1;{}%
% \end{macrocode}
% \subsection{\csh{xint_afterfi}}
% \begin{macrocode}
@@ -15361,21 +15589,11 @@
% This is not really robust as it may switch the expansion order of macros,
% and the \xint_zapspaces token might end up being fetched up by a macro. But
% it is enough for our purposes, for example:
-% $centeredline
-% $bgroup\the\numexpr \xint_zapspaces 1 2 \xint_gobble_i\relax$egroup
-% expands to 12, and not 12\relax. Imagine also:
-% $centeredline
-% $bgroup\the\numexpr 1 2\expandafter.\the\numexpr ...$egroup
+% $centeredline$bgroup\the\numexpr \xint_zapspaces 1 2 \xint_gobble_i\relax$egroup
+% expands to 12, and not 12\relax.
%
-% The spaces will stop the \numexpr, and the \expandafter will not be
-% immediately executed. Thus we have to get rid of spaces in
-% contexts where arguments are fetched by delimited macros and fed to
-% \numexpr (or for any reason can contain spaces). I apply this corrective
-% treatment so far only in $xintexprnameimp but perhaps I should in
-% $xintfracnameimp too. As said above, perhaps the zapspaces should force
-% expansion too, but I leave it standing.
%
-% 1.2e adds \xint_zapspaces_o. Expansion of #1 should not gobble a space !
+% 1.2e adds \xint_zapspaces_o. Expansion of #1 should not gobble a space!
%
% Made long with 1.2i.|
% \begin{macrocode}
@@ -15396,22 +15614,24 @@
\ifdefined\fdef\else\let\fdef\xintfdef\fi
% \end{macrocode}
% \subsection{\csh{xintReverseOrder}}
-% \lverb|\xintReverseOrder: does not expand its argument. Thus one must use
-% some \expandafter if argument is a macro. Attention: removes braces.
+% \lverb|\xintReverseOrder: does NOT expand its argument.
%
-% A faster reverse, but only usable with digits, is provided by
-% \xintReverseDigits macro from 1.2 xintcore.sty.
+% Attention: removes brace pairs.
%
-% 1.2g has (not user documented) \xintCSVReverse in xinttools.sty.|
+% For digit tokens only a faster reverse macro is provided as
+% \xintReverseDigits from 1.2 xintcore.sty.
+%
+% For comma separated items, 1.2g has (not user documented) \xintCSVReverse in
+% xinttools.sty.|
% \begin{macrocode}
\def\xintReverseOrder {\romannumeral0\xintreverseorder }%
\long\def\xintreverseorder #1%
{%
\XINT_rord_main {}#1%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax
+ \xint:
}%
\long\def\XINT_rord_main #1#2#3#4#5#6#7#8#9%
{%
@@ -15418,13 +15638,14 @@
\xint_bye #9\XINT_rord_cleanup\xint_bye
\XINT_rord_main {#9#8#7#6#5#4#3#2#1}%
}%
-\long\edef\XINT_rord_cleanup\xint_bye\XINT_rord_main #1#2\xint_relax
+\def\XINT_rord_cleanup #1{%
+\long\def\XINT_rord_cleanup\xint_bye\XINT_rord_main ##1##2\xint:
{%
- \noexpand\expandafter\space\noexpand\xint_gob_til_xint_relax #1%
-}%
+ \expandafter#1\xint_gob_til_xint: ##1%
+}}\XINT_rord_cleanup { }%
% \end{macrocode}
% \subsection{\csh{xintLength}}
-% \lverb|\xintLength does not expand its argument. See \xintNthElt{0} from
+% \lverb|\xintLength does NOT expand its argument. See \xintNthElt{0} from
% xinttools.sty which f-expands its argument.
%
% 1.2g has (not user documented) \xintCSVLength in xinttools.sty.
@@ -15436,18 +15657,17 @@
\def\xintlength #1{\long\def\xintlength ##1%
{%
\expandafter#1\the\numexpr\XINT_length_loop
- ##1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
- \xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
+ ##1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
+ \xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
+ \xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
\relax
}}\xintlength{ }%
\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
+ \xint_gob_til_xint: #9\XINT_length_finish_a\xint:
\xint_c_ix+\XINT_length_loop
}%
-\def\XINT_length_finish_a\xint_relax\xint_c_ix+\XINT_length_loop
+\def\XINT_length_finish_a\xint:\xint_c_ix+\XINT_length_loop
#1#2#3#4#5#6#7#8#9%
{%
#9\xint_bye
@@ -15455,7 +15675,7 @@
% \end{macrocode}
% \subsection{\csh{xintLastItem}}
% \lverb|New with 1.2i (2016/12/10). Output empty if input empty. One level
-% of braces removed in output.
+% of braces removed in output. Does NOT expand its argument.
% |
% \begin{macrocode}
\def\xintLastItem {\romannumeral0\xintlastitem }%
@@ -15462,15 +15682,15 @@
\long\def\xintlastitem #1%
{%
\XINT_last_loop {}.#1%
- {\xint_relax\XINT_last_loop_enda}{\xint_relax\XINT_last_loop_endb}%
- {\xint_relax\XINT_last_loop_endc}{\xint_relax\XINT_last_loop_endd}%
- {\xint_relax\XINT_last_loop_ende}{\xint_relax\XINT_last_loop_endf}%
- {\xint_relax\XINT_last_loop_endg}{\xint_relax\XINT_last_loop_endh}\xint_bye
+ {\xint:\XINT_last_loop_enda}{\xint:\XINT_last_loop_endb}%
+ {\xint:\XINT_last_loop_endc}{\xint:\XINT_last_loop_endd}%
+ {\xint:\XINT_last_loop_ende}{\xint:\XINT_last_loop_endf}%
+ {\xint:\XINT_last_loop_endg}{\xint:\XINT_last_loop_endh}\xint_bye
}%
\long\def\XINT_last_loop #1.#2#3#4#5#6#7#8#9%
{%
- \xint_gob_til_xint_relax #9%
- {#8}{#7}{#6}{#5}{#4}{#3}{#2}{#1}\xint_relax
+ \xint_gob_til_xint: #9%
+ {#8}{#7}{#6}{#5}{#4}{#3}{#2}{#1}\xint:
\XINT_last_loop {#9}.%
}%
\long\def\XINT_last_loop_enda #1#2\xint_bye{ #1}%
@@ -15496,8 +15716,7 @@
\long\def\xintlengthupto #1#2%
{%
\expandafter\XINT_lengthupto_loop
- \the\numexpr#1.#2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax
+ \the\numexpr#1.#2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_vii\xint_c_vi\xint_c_v\xint_c_iv
\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye.%
}%
@@ -15511,10 +15730,10 @@
\long\def\XINT_lengthupto_gt #1\xint_bye.{-0}%
\long\def\XINT_lengthupto_loop #1.#2#3#4#5#6#7#8#9%
{%
- \xint_gob_til_xint_relax #9\XINT_lengthupto_finish_a\xint_relax
+ \xint_gob_til_xint: #9\XINT_lengthupto_finish_a\xint:%
\expandafter\XINT_lengthupto_loop_a\the\numexpr #1-\xint_c_viii.%
}%
-\def\XINT_lengthupto_finish_a\xint_relax\expandafter\XINT_lengthupto_loop_a
+\def\XINT_lengthupto_finish_a\xint:\expandafter\XINT_lengthupto_loop_a
\the\numexpr #1-\xint_c_viii.#2#3#4#5#6#7#8#9%
{%
\expandafter\XINT_lengthupto_finish_b\the\numexpr #1-#9\xint_bye
@@ -15717,10 +15936,30 @@
% extended range of output streams, in LuaTeX in particular.|
% \begin{macrocode}
\def\xintMessage #1#2#3{%
- \immediate\write128{Package #1 #2: (on line \the\inputlineno)}%
- \immediate\write128{\space\space\space\space#3}%
+ \immediate\write128{Package #1 #2: (on line \the\inputlineno)}%
+ \immediate\write128{\space\space\space\space#3}%
}%
\newif\ifxintverbose
+% \end{macrocode}
+% \subsection{(WIP) Expandable error message}
+% \lverb|&
+% Incorporated in 1.2l release, but really belongs to next major release.
+%
+% This is copied over from l3kernel code. I am using \ ! / control sequence
+% though, which must be left undefined. \xintError: would be 6 letters more
+% already. Utiliser \FPE: ? (mais ce n'est pas uniquement du « floating point »)
+%
+% Always used in context where expansion was launched by a
+% \romannumeral0 or \romannumeral`^^@.|
+% \begin{macrocode}
+\def\XINT_expandableerror #1#2{%
+ \def\XINT_expandableerror ##1{%
+ \expandafter\expandafter\expandafter
+ \XINT_expandableerror_continue\xint_firstofone{#2#1##1#1}}%
+ \def\XINT_expandableerror_continue ##1#1##2#1{##1}%
+}%
+\begingroup\lccode`$ 32 \catcode`/ 11 \catcode`! 11 \catcode32 11 %
+\lowercase{\endgroup\XINT_expandableerror$\ ! /}%
\XINT_restorecatcodes_endinput%
% \end{macrocode}
%
@@ -15798,7 +16037,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xinttools}%
- [2017/01/06 1.2k Expandable and non-expandable utilities (JFB)]%
+ [2017/07/26 1.2l 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.|
@@ -15817,7 +16056,7 @@
% \lverb|New with 1.06. Makes the expansion of its argument and then reverses
% the resulting tokens or braced tokens, adding a pair of braces to each (thus,
% maintaining it when it was already there.) The reason for
-% \xint_relax, here and in other locations, is in case #1 expands to nothing,
+% \xint:, here and in other locations, is in case #1 expands to nothing,
% the \romannumeral-`0 must be stopped|
% \begin{macrocode}
\def\xintRevWithBraces {\romannumeral0\xintrevwithbraces }%
@@ -15825,21 +16064,21 @@
\long\def\xintrevwithbraces #1%
{%
\expandafter\XINT_revwbr_loop\expandafter{\expandafter}%
- \romannumeral`&&@#1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye
+ \romannumeral`&&@#1\xint:\xint:\xint:\xint:%
+ \xint:\xint:\xint:\xint:\xint_bye
}%
\long\def\xintrevwithbracesnoexpand #1%
{%
\XINT_revwbr_loop {}%
- #1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye
+ #1\xint:\xint:\xint:\xint:%
+ \xint:\xint:\xint:\xint:\xint_bye
}%
\long\def\XINT_revwbr_loop #1#2#3#4#5#6#7#8#9%
{%
- \xint_gob_til_xint_relax #9\XINT_revwbr_finish_a\xint_relax
+ \xint_gob_til_xint: #9\XINT_revwbr_finish_a\xint:%
\XINT_revwbr_loop {{#9}{#8}{#7}{#6}{#5}{#4}{#3}{#2}#1}%
}%
-\long\def\XINT_revwbr_finish_a\xint_relax\XINT_revwbr_loop #1#2\xint_bye
+\long\def\XINT_revwbr_finish_a\xint:\XINT_revwbr_loop #1#2\xint_bye
{%
\XINT_revwbr_finish_b #2\R\R\R\R\R\R\R\Z #1%
}%
@@ -15858,7 +16097,9 @@
% \end{macrocode}
% \lverb|1.1c revisited this old code and improved upon the earlier endings.|
% \begin{macrocode}
-\edef\XINT_revwbr_finish_c #1#2\Z {\noexpand\expandafter\space #1}%
+\def\XINT_revwbr_finish_c#1{%
+\def\XINT_revwbr_finish_c##1##2\Z{\expandafter#1##1}%
+}\XINT_revwbr_finish_c{ }%
% \end{macrocode}
% \subsection{\csh{xintZapFirstSpaces}}
% \lverb|1.09f, written [2013/11/01]. Modified (2014/10/21) for release 1.1 to
@@ -15867,14 +16108,10 @@
% the initial one. This macro does NOT expand its argument.|
% \begin{macrocode}
\def\xintZapFirstSpaces {\romannumeral0\xintzapfirstspaces }%
+\def\xintzapfirstspaces#1{\long
+\def\xintzapfirstspaces ##1{\XINT_zapbsp_a #1##1\xint:#1#1\xint:}%
+}\xintzapfirstspaces{ }%
% \end{macrocode}
-% \lverb|defined via an \edef in order to inject space tokens inside.|
-% \begin{macrocode}
-\long\edef\xintzapfirstspaces #1%
- {\noexpand\XINT_zapbsp_a \space #1\xint_relax \space\space\xint_relax }%
-\xint_firstofone {\long\edef\XINT_zapbsp_a #1 } %<- space token here
-{%
-% \end{macrocode}
% \lverb|If the original #1 started with a space, the grabbed #1 is empty. Thus
% _again? will see #1=\xint_bye, and hand over control to _again which will loop
% back into \XINT_zapbsp_a, with one initial space less. If the original #1 did
@@ -15882,26 +16119,25 @@
% then an extract of the original #1, not empty and not starting with a space,
% which contains what was up to the first <sp><sp> present in original #1, or,
% if none preexisted, <sptoken> and all of #1 (possibly empty) plus an ending
-% \xint_relax. The added initial space will stop later the \romannumeral0. No
+% \xint:. The added initial space will stop later the \romannumeral0. No
% brace stripping is possible. Control is handed over to \XINT_zapbsp_b which
-% strips out the ending \xint_relax<sp><sp>\xint_relax|
+% strips out the ending \xint:<sp><sp>\xint:|
% \begin{macrocode}
- \noexpand\XINT_zapbsp_again? #1\noexpand\xint_bye\noexpand\XINT_zapbsp_b #1\space\space
-}%
+\def\XINT_zapbsp_a#1{\long\def\XINT_zapbsp_a ##1#1#1{%
+ \XINT_zapbsp_again?##1\xint_bye\XINT_zapbsp_b ##1#1#1}%
+}\XINT_zapbsp_a{ }%
\long\def\XINT_zapbsp_again? #1{\xint_bye #1\XINT_zapbsp_again }%
\xint_firstofone{\def\XINT_zapbsp_again\XINT_zapbsp_b} {\XINT_zapbsp_a }%
-\long\def\XINT_zapbsp_b #1\xint_relax #2\xint_relax {#1}%
+\long\def\XINT_zapbsp_b #1\xint:#2\xint:{#1}%
% \end{macrocode}
% \subsection{\csh{xintZapLastSpaces}}
% \lverb+1.09f, written [2013/11/01]. +
% \begin{macrocode}
\def\xintZapLastSpaces {\romannumeral0\xintzaplastspaces }%
+\def\xintzaplastspaces#1{\long
+\def\xintzaplastspaces ##1{\XINT_zapesp_a {}\empty##1#1#1\xint_bye\xint:}%
+}\xintzaplastspaces{ }%
% \end{macrocode}
-% \lverb|Next macro is defined via an \edef for the space tokens.|
-% \begin{macrocode}
-\long\edef\xintzaplastspaces #1{\noexpand\XINT_zapesp_a {}\noexpand\empty#1%
- \space\space\noexpand\xint_bye\xint_relax}%
-% \end{macrocode}
% \lverb|The \empty from \xintzaplastspaces is to prevent brace removal in the
% #2 below. The \expandafter chain removes it.|
% \begin{macrocode}
@@ -15911,12 +16147,12 @@
% \lverb|Notice again an \empty added here. This is in preparation for possibly looping
% back to \XINT_zapesp_a. If the initial #1 had no <sp><sp>, the stuff however
% will not loop, because #3 will already be <some spaces>\xint_bye. Notice
-% that this macro fetches all way to the ending \xint_relax. This looks not
+% that this macro fetches all way to the ending \xint:. This looks not
% very efficient, but how often do we have to strip ending spaces from
% something which also has inner stretches of _multiple_ space tokens ?;-). |
% \begin{macrocode}
-\long\def\XINT_zapesp_b #1#2#3\xint_relax
- {\XINT_zapesp_end? #3\XINT_zapesp_e {#2#1}\empty #3\xint_relax }%
+\long\def\XINT_zapesp_b #1#2#3\xint:%
+ {\XINT_zapesp_end? #3\XINT_zapesp_e {#2#1}\empty #3\xint:}%
% \end{macrocode}
% \lverb|When we have been over all possible <sp><sp> things, we reach the
% ending space tokens, and #3 will be a bunch of spaces (possibly none)
@@ -15930,12 +16166,14 @@
% \lverb|We are done. The #1 here has accumulated all the previous material,
% and is stripped of its ending spaces, if any.|
% \begin{macrocode}
-\long\def\XINT_zapesp_end\XINT_zapesp_e #1#2\xint_relax { #1}%
+\long\def\XINT_zapesp_end\XINT_zapesp_e #1#2\xint:{ #1}%
% \end{macrocode}
% \lverb|We haven't yet reached the end, so we need to re-inject two space
% tokens after what we have gotten so far. Then we loop.|
% \begin{macrocode}
-\long\edef\XINT_zapesp_e #1{\noexpand \XINT_zapesp_a {#1\space\space}}%
+\def\XINT_zapesp_e#1{%
+\long\def\XINT_zapesp_e ##1{\XINT_zapesp_a {##1#1#1}}%
+}\XINT_zapesp_e{ }%
% \end{macrocode}
% \subsection{\csh{xintZapSpaces}}
% \lverb+1.09f, written [2013/11/01]. Modified for 1.1, 2014/10/21 as it has the
@@ -15943,15 +16181,21 @@
% then \xintZapLastSpaces.+
% \begin{macrocode}
\def\xintZapSpaces {\romannumeral0\xintzapspaces }%
-\long\edef\xintzapspaces #1% like \xintZapFirstSpaces.
- {\noexpand\XINT_zapsp_a \space #1\xint_relax \space\space\xint_relax }%
-\xint_firstofone {\long\edef\XINT_zapsp_a #1 } %
- {\noexpand\XINT_zapsp_again? #1\noexpand\xint_bye\noexpand\XINT_zapsp_b #1\space\space}%
+\def\xintzapspaces#1{%
+\long\def\xintzapspaces ##1% like \xintZapFirstSpaces.
+ {\XINT_zapsp_a #1##1\xint:#1#1\xint:}%
+}\xintzapspaces{ }%
+\def\XINT_zapsp_a#1{%
+\long\def\XINT_zapsp_a ##1#1#1%
+ {\XINT_zapsp_again?##1\xint_bye\XINT_zapsp_b##1#1#1}%
+}\XINT_zapsp_a{ }%
\long\def\XINT_zapsp_again? #1{\xint_bye #1\XINT_zapsp_again }%
\xint_firstofone{\def\XINT_zapsp_again\XINT_zapsp_b} {\XINT_zapsp_a }%
\xint_firstofone{\def\XINT_zapsp_b} {\XINT_zapsp_c }%
-\long\edef\XINT_zapsp_c #1\xint_relax #2\xint_relax {\noexpand\XINT_zapesp_a
- {}\noexpand \empty #1\space\space\noexpand\xint_bye\xint_relax }%
+\def\XINT_zapsp_c#1{%
+\long\def\XINT_zapsp_c ##1\xint:##2\xint:%
+ {\XINT_zapesp_a{}\empty ##1#1#1\xint_bye\xint:}%
+}\XINT_zapsp_c{ }%
% \end{macrocode}
% \subsection{\csh{xintZapSpacesB}}
% \lverb+1.09f, written [2013/11/01]. Strips up to one pair of braces (but then
@@ -15958,17 +16202,17 @@
% does not strip spaces inside).+
% \begin{macrocode}
\def\xintZapSpacesB {\romannumeral0\xintzapspacesb }%
-\long\def\xintzapspacesb #1{\XINT_zapspb_one? #1\xint_relax\xint_relax
+\long\def\xintzapspacesb #1{\XINT_zapspb_one? #1\xint:\xint:%
\xint_bye\xintzapspaces {#1}}%
\long\def\XINT_zapspb_one? #1#2%
- {\xint_gob_til_xint_relax #1\XINT_zapspb_onlyspaces\xint_relax
- \xint_gob_til_xint_relax #2\XINT_zapspb_bracedorone\xint_relax
+ {\xint_gob_til_xint: #1\XINT_zapspb_onlyspaces\xint:%
+ \xint_gob_til_xint: #2\XINT_zapspb_bracedorone\xint:%
\xint_bye {#1}}%
-\def\XINT_zapspb_onlyspaces\xint_relax
- \xint_gob_til_xint_relax\xint_relax\XINT_zapspb_bracedorone\xint_relax
+\def\XINT_zapspb_onlyspaces\xint:%
+ \xint_gob_til_xint:\xint:\XINT_zapspb_bracedorone\xint:%
\xint_bye #1\xint_bye\xintzapspaces #2{ }%
-\long\def\XINT_zapspb_bracedorone\xint_relax
- \xint_bye #1\xint_relax\xint_bye\xintzapspaces #2{ #1}%
+\long\def\XINT_zapspb_bracedorone\xint:%
+ \xint_bye #1\xint:\xint_bye\xintzapspaces #2{ #1}%
% \end{macrocode}
% \subsection{\csh{xintCSVtoList}, \csh{xintCSVtoListNonStripped}}
% \lverb|\xintCSVtoList transforms a,b,..,z into {a}{b}...{z}. The comma
@@ -16102,8 +16346,7 @@
\long\def\XINT_nthelt_neg #1.#2%
{%
\expandafter\XINT_nthelt_neg_a\the\numexpr\xint_c_i+\XINT_length_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
-#1.#2\xint_bye
@@ -16123,13 +16366,13 @@
{%
\expandafter\XINT_nthelt_pos_done
\romannumeral0\expandafter\XINT_trim_loop\the\numexpr#1-\xint_c_x.%
- #2\xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:%
+ \xint:\xint:\xint:\xint:\xint:%
\xint_bye
}%
\def\XINT_nthelt_pos_done #1{%
\long\def\XINT_nthelt_pos_done ##1##2\xint_bye{%
- \xint_gob_til_xint_relax##1\expandafter#1\xint_gobble_ii\xint_relax#1##1}%
+ \xint_gob_til_xint:##1\expandafter#1\xint_gobble_ii\xint:#1##1}%
}\XINT_nthelt_pos_done{ }%
% \end{macrocode}
% \subsection{\csh{xintKeep}}
@@ -16176,8 +16419,7 @@
{%
\expandafter\XINT_keep_neg_a\the\numexpr
#1-\numexpr\XINT_length_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye.#2%
}%
@@ -16193,8 +16435,7 @@
{%
\expandafter\XINT_keep_loop
\the\numexpr#1-\XINT_lengthupto_loop
- #1.#2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax
+ #1.#2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_vii\xint_c_vi\xint_c_v\xint_c_iv
\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye.%
-\xint_c_viii.{}#2\xint_bye%
@@ -16256,8 +16497,7 @@
{%
\expandafter\XINT_keepunbr_loop
\the\numexpr#1-\XINT_lengthupto_loop
- #1.#2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax
+ #1.#2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_vii\xint_c_vi\xint_c_v\xint_c_iv
\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye.%
-\xint_c_viii.{}#2\xint_bye%
@@ -16327,8 +16567,7 @@
{%
\expandafter\XINT_trim_neg_a\the\numexpr
#1-\numexpr\XINT_length_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
.{}#2\xint_bye
@@ -16340,7 +16579,9 @@
-\XINT_trim_trimall
\krof
}%
-\edef\XINT_trim_trimall {\noexpand\expandafter\space\noexpand\xint_bye}%
+\def\XINT_trim_trimall#1{%
+\def\XINT_trim_trimall {\expandafter#1\xint_bye}%
+}\XINT_trim_trimall{ }%
% \end{macrocode}
% \lverb|This branch doesn't pre-evaluate the length of the list argument.
% Redone again for 1.2j, manages to trim nine by nine. Some non optimal
@@ -16350,8 +16591,8 @@
{%
\expandafter\XINT_trim_pos_done\expandafter\space
\romannumeral0\expandafter\XINT_trim_loop\the\numexpr#1-\xint_c_ix.%
- #2\xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:%
+ \xint:\xint:\xint:\xint:\xint:%
\xint_bye
}%
\def\XINT_trim_loop #1#2.%
@@ -16361,9 +16602,9 @@
}%
\long\def\XINT_trim_loop_trimnine #1#2#3#4#5#6#7#8#9%
{%
- \xint_gob_til_xint_relax #9\XINT_trim_toofew\xint_relax-\xint_c_ix.%
+ \xint_gob_til_xint: #9\XINT_trim_toofew\xint:-\xint_c_ix.%
}%
-\def\XINT_trim_toofew\xint_relax{*\xint_c_}%
+\def\XINT_trim_toofew\xint:{*\xint_c_}%
\def\XINT_trim_finish#1{%
\def\XINT_trim_finish-%
\expandafter\XINT_trim_loop\the\numexpr-##1\XINT_trim_loop_trimnine
@@ -16371,7 +16612,7 @@
\expandafter\expandafter\expandafter#1%
\csname xint_gobble_\romannumeral\numexpr\xint_c_ix-##1\endcsname
}}\XINT_trim_finish{ }%
-\long\def\XINT_trim_pos_done #1\xint_relax #2\xint_bye {#1}%
+\long\def\XINT_trim_pos_done #1\xint:#2\xint_bye {#1}%
% \end{macrocode}
% \subsection{\csh{xintTrimUnbraced}}
% \lverb?1.2a. Modified in 1.2i like \xintTrim?
@@ -16395,8 +16636,7 @@
{%
\expandafter\XINT_trimunbr_neg_a\the\numexpr
#1-\numexpr\XINT_length_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
.{}#2\xint_bye
@@ -17032,7 +17272,7 @@
\long\def\XINT_assign_a #1\to
{%
\def\XINT_flet_macro{\XINT_assign_b}%
- \expandafter\XINT_flet_zapsp\romannumeral`&&@#1\xint_relax\to
+ \expandafter\XINT_flet_zapsp\romannumeral`&&@#1\xint:\to
}%
\long\def\XINT_assign_b
{%
@@ -17041,7 +17281,7 @@
\else\expandafter\XINT_assign_f
\fi
}%
-\long\def\XINT_assign_f #1\xint_relax\to #2%
+\long\def\XINT_assign_f #1\xint:\to #2%
{%
\XINT_assign_def #2{#1}%
}%
@@ -17048,7 +17288,7 @@
\long\def\XINT_assign_c #1%
{%
\def\xint_temp {#1}%
- \ifx\xint_temp\xint_brelax
+ \ifx\xint_temp\xint_bracedstopper
\expandafter\XINT_assign_e
\else
\expandafter\XINT_assign_d
@@ -17100,7 +17340,7 @@
\expandafter\def\expandafter\xint_arrayname\expandafter {\string #2}%
\XINT_restoreescapechar
\def\xint_itemcount {0}%
- \expandafter\XINT_assignarray_loop \romannumeral`&&@#1\xint_relax
+ \expandafter\XINT_assignarray_loop \romannumeral`&&@#1\xint:
\csname\xint_arrayname 00\expandafter\endcsname
\csname\xint_arrayname 0\expandafter\endcsname
\expandafter {\xint_arrayname}#2%
@@ -17108,7 +17348,7 @@
\long\def\XINT_assignarray_loop #1%
{%
\def\xint_temp {#1}%
- \ifx\xint_brelax\xint_temp
+ \ifx\xint_temp\xint_bracedstopper
\expandafter\def\csname\xint_arrayname 0\expandafter\endcsname
\expandafter{\the\numexpr\xint_itemcount}%
\expandafter\expandafter\expandafter\XINT_assignarray_end
@@ -17130,11 +17370,12 @@
\def #1##1%
{%
\ifnum ##1<\xint_c_
- \xint_afterfi {\xintError:ArrayIndexIsNegative\space }%
+ \xint_afterfi{\XINT_expandableerror{Array index negative: 0 > ##1} }%
\else
\xint_afterfi {%
\ifnum ##1>#2
- \xint_afterfi {\xintError:ArrayIndexBeyondLimit\space }%
+ \xint_afterfi
+ {\XINT_expandableerror{Array index beyond range: ##1 > #2} }%
\else\xint_afterfi
{\expandafter\expandafter\expandafter\space\csname #3##1\endcsname}%
\fi}%
@@ -17223,8 +17464,8 @@
\def\xintlength:f:csv #1%
{\long\def\xintlength:f:csv ##1{%
\expandafter#1\the\numexpr\expandafter\XINT_length:f:csv_a
- \romannumeral`&&@##1\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
+ \romannumeral`&&@##1\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,\xint:,%
\xint_c_ix,\xint_c_viii,\xint_c_vii,\xint_c_vi,%
\xint_c_v,\xint_c_iv,\xint_c_iii,\xint_c_ii,\xint_c_i,\xint_bye
\relax
@@ -17234,15 +17475,15 @@
% \begin{macrocode}
\long\def\XINT_length:f:csv_a #1%
{%
- \xint_gob_til_xint_relax #1\xint_c_\xint_bye\xint_relax
+ \xint_gob_til_xint: #1\xint_c_\xint_bye\xint:%
\XINT_length:f:csv_loop #1%
}%
\long\def\XINT_length:f:csv_loop #1,#2,#3,#4,#5,#6,#7,#8,#9,%
{%
- \xint_gob_til_xint_relax #9\XINT_length:f:csv_finish\xint_relax
+ \xint_gob_til_xint: #9\XINT_length:f:csv_finish\xint:%
\xint_c_ix+\XINT_length:f:csv_loop
}%
-\def\XINT_length:f:csv_finish\xint_relax\xint_c_ix+\XINT_length:f:csv_loop
+\def\XINT_length:f:csv_finish\xint:\xint_c_ix+\XINT_length:f:csv_loop
#1,#2,#3,#4,#5,#6,#7,#8,#9,{#9\xint_bye}%
% \end{macrocode}
% \subsubsection{\csh{xintLengthUpTo:f:csv}}
@@ -17256,8 +17497,8 @@
{%
\expandafter\XINT_lengthupto:f:csv_a
\the\numexpr#1\expandafter.%
- \romannumeral`&&@#2\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,%
+ \romannumeral`&&@#2\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,%
\xint_c_viii,\xint_c_vii,\xint_c_vi,\xint_c_v,%
\xint_c_iv,\xint_c_iii,\xint_c_ii,\xint_c_i,\xint_bye.%
}%
@@ -17266,10 +17507,10 @@
% \begin{macrocode}
\long\def\XINT_lengthupto:f:csv_a #1.#2%
{%
- \xint_gob_til_xint_relax #2\XINT_lengthupto:f:csv_empty\xint_relax
+ \xint_gob_til_xint: #2\XINT_lengthupto:f:csv_empty\xint:%
\XINT_lengthupto:f:csv_loop_b #1.#2%
}%
-\def\XINT_lengthupto:f:csv_empty\xint_relax
+\def\XINT_lengthupto:f:csv_empty\xint:%
\XINT_lengthupto:f:csv_loop_b #1.#2\xint_bye.{ #1}%
\def\XINT_lengthupto:f:csv_loop_a #1%
{%
@@ -17281,10 +17522,10 @@
\long\def\XINT_lengthupto:f:csv_gt #1\xint_bye.{-0}%
\long\def\XINT_lengthupto:f:csv_loop_b #1.#2,#3,#4,#5,#6,#7,#8,#9,%
{%
- \xint_gob_til_xint_relax #9\XINT_lengthupto:f:csv_finish_a\xint_relax
+ \xint_gob_til_xint: #9\XINT_lengthupto:f:csv_finish_a\xint:%
\expandafter\XINT_lengthupto:f:csv_loop_a\the\numexpr #1-\xint_c_viii.%
}%
-\def\XINT_lengthupto:f:csv_finish_a\xint_relax
+\def\XINT_lengthupto:f:csv_finish_a\xint:
\expandafter\XINT_lengthupto:f:csv_loop_a
\the\numexpr #1-\xint_c_viii.#2,#3,#4,#5,#6,#7,#8,#9,%
{%
@@ -17331,8 +17572,8 @@
\romannumeral0%
\expandafter\XINT_keep:f:csv_neg_a\the\numexpr
#1-\numexpr\XINT_length:f:csv_a
- #2\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
+ #2\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,\xint:,%
\xint_c_ix,\xint_c_viii,\xint_c_vii,\xint_c_vi,%
\xint_c_v,\xint_c_iv,\xint_c_iii,\xint_c_ii,\xint_c_i,\xint_bye
.#2\xint_bye
@@ -17361,8 +17602,8 @@
{%
\expandafter\XINT_keep:f:csv_pos_fork
\romannumeral0\XINT_lengthupto:f:csv_a
- #1.#2\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,%
+ #1.#2\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,%
\xint_c_viii,\xint_c_vii,\xint_c_vi,\xint_c_v,%
\xint_c_iv,\xint_c_iii,\xint_c_ii,\xint_c_i,\xint_bye.%
.#1.{}#2\xint_bye%
@@ -17427,8 +17668,8 @@
{%
\expandafter\XINT_trim:f:csv_neg_a\the\numexpr
#1-\numexpr\XINT_length:f:csv_a
- #2\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
+ #2\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,\xint:,%
\xint_c_ix,\xint_c_viii,\xint_c_vii,\xint_c_vi,%
\xint_c_v,\xint_c_iv,\xint_c_iii,\xint_c_ii,\xint_c_i,\xint_bye
.{}#2\xint_bye
@@ -17446,8 +17687,8 @@
\expandafter\XINT_trim:f:csv_pos_done\expandafter,%
\romannumeral0%
\expandafter\XINT_trim:f:csv_loop\the\numexpr#1-\xint_c_ix.%
- #2\xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax\xint_bye
+ #2\xint:,\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,\xint:\xint_bye
}%
\def\XINT_trim:f:csv_loop #1#2.%
{%
@@ -17456,9 +17697,9 @@
}%
\long\def\XINT_trim:f:csv_loop_trimnine #1,#2,#3,#4,#5,#6,#7,#8,#9,%
{%
- \xint_gob_til_xint_relax #9\XINT_trim:f:csv_toofew\xint_relax-\xint_c_ix.%
+ \xint_gob_til_xint: #9\XINT_trim:f:csv_toofew\xint:-\xint_c_ix.%
}%
-\def\XINT_trim:f:csv_toofew\xint_relax{*\xint_c_}%
+\def\XINT_trim:f:csv_toofew\xint:{*\xint_c_}%
\def\XINT_trim:f:csv_finish-%
\expandafter\XINT_trim:f:csv_loop\the\numexpr-#1\XINT_trim:f:csv_loop_trimnine
{%
@@ -17481,7 +17722,7 @@
\long\expandafter\def\csname XINT_trim:f:csv_finish8\endcsname
#1,{ }%
\expandafter\let\csname XINT_trim:f:csv_finish9\endcsname\space
-\long\def\XINT_trim:f:csv_pos_done #1\xint_relax #2\xint_bye{#1}%
+\long\def\XINT_trim:f:csv_pos_done #1\xint:#2\xint_bye{#1}%
% \end{macrocode}
% \subsubsection{\csh{xintNthEltPy:f:csv}}
% \lverb|Counts like Python starting at zero. Last refactored with 1.2j.
@@ -17505,8 +17746,8 @@
{%
\expandafter\XINT_nthelt:f:csv_neg_fork
\the\numexpr\XINT_length:f:csv_a
- #2\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
+ #2\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,\xint:,%
\xint_c_ix,\xint_c_viii,\xint_c_vii,\xint_c_vi,%
\xint_c_v,\xint_c_iv,\xint_c_iii,\xint_c_ii,\xint_c_i,\xint_bye
-#1.#2,\xint_bye
@@ -17524,23 +17765,23 @@
\expandafter\XINT_nthelt:f:csv_pos_done
\romannumeral0%
\expandafter\XINT_trim:f:csv_loop\the\numexpr#1-\xint_c_ix.%
- #2\xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_bye
+ #2\xint:,\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,\xint:,\xint_bye
}%
\def\XINT_nthelt:f:csv_pos_done #1{%
\long\def\XINT_nthelt:f:csv_pos_done ##1,##2\xint_bye{%
- \xint_gob_til_xint_relax##1\XINT_nthelt:f:csv_pos_cleanup\xint_relax#1##1}%
+ \xint_gob_til_xint:##1\XINT_nthelt:f:csv_pos_cleanup\xint:#1##1}%
}\XINT_nthelt:f:csv_pos_done{ }%
% \end{macrocode}
% \lverb|This strange thing is in case the picked item was the last one, hence
-% there was an ending \xint_relax (we could not put a comma earlier for
+% there was an ending \xint: (we could not put a comma earlier for
% matters of not confusing empty list with a singleton list), and we do this
% here to activate brace-stripping of item as all other items may be
% brace-stripped if picked. This is done for coherence. Of course, in the
% context of the xintexpr.sty parsers, there are no braces in list items...|
% \begin{macrocode}
-\xint_firstofone{\long\def\XINT_nthelt:f:csv_pos_cleanup\xint_relax} %
- #1\xint_relax{ #1}%
+\xint_firstofone{\long\def\XINT_nthelt:f:csv_pos_cleanup\xint:} %
+ #1\xint:{ #1}%
% \end{macrocode}
% \subsubsection{\csh{xintReverse:f:csv}}
% \lverb|1.2g. Contrarily to \xintReverseOrder from xintkernel.sty, this
@@ -17552,10 +17793,10 @@
{%
\expandafter\XINT_reverse:f:csv_loop
\expandafter{\expandafter}\romannumeral`&&@#1,%
- \xint_relax,%
+ \xint:,%
\xint_bye,\xint_bye,\xint_bye,\xint_bye,%
\xint_bye,\xint_bye,\xint_bye,\xint_bye,%
- \xint_relax
+ \xint:
}%
\long\def\XINT_reverse:f:csv_loop #1#2,#3,#4,#5,#6,#7,#8,#9,%
{%
@@ -17562,13 +17803,13 @@
\xint_bye #9\XINT_reverse:f:csv_cleanup\xint_bye
\XINT_reverse:f:csv_loop {,#9,#8,#7,#6,#5,#4,#3,#2#1}%
}%
-\long\def\XINT_reverse:f:csv_cleanup\xint_bye\XINT_reverse:f:csv_loop #1#2\xint_relax
+\long\def\XINT_reverse:f:csv_cleanup\xint_bye\XINT_reverse:f:csv_loop #1#2\xint:
{%
\XINT_reverse:f:csv_finish #1%
}%
-\long\def\XINT_reverse:f:csv_finish #1\xint_relax,{ }%
+\long\def\XINT_reverse:f:csv_finish #1\xint:,{ }%
% \end{macrocode}
-% \subsection{\csh{xintFirstItem:f:csv}}
+% \subsubsection{\csh{xintFirstItem:f:csv}}
% \lverb|Added with 1.2k for use by first() in
% \xintexpr-essions, and some amount of compatibility with \xintNewExpr.|
% \begin{macrocode}
@@ -17579,7 +17820,7 @@
}%
\long\def\XINT_first:f:csv_a #1,#2\xint_bye{ #1}%
% \end{macrocode}
-% \subsection{\csh{xintLastItem:f:csv}}
+% \subsubsection{\csh{xintLastItem:f:csv}}
% \lverb|Added with 1.2k, based on and sharing code with xintkernel's
% \xintLastItem from 1.2i. Output empty if input empty. f-expands its argument
% (hence first item, if not protected.) For use by last() in
@@ -17590,15 +17831,15 @@
{%
\expandafter\XINT_last:f:csv_loop\expandafter{\expandafter}\expandafter.%
\romannumeral`&&@#1,%
- \xint_relax\XINT_last_loop_enda,\xint_relax\XINT_last_loop_endb,%
- \xint_relax\XINT_last_loop_endc,\xint_relax\XINT_last_loop_endd,%
- \xint_relax\XINT_last_loop_ende,\xint_relax\XINT_last_loop_endf,%
- \xint_relax\XINT_last_loop_endg,\xint_relax\XINT_last_loop_endh,\xint_bye
+ \xint:\XINT_last_loop_enda,\xint:\XINT_last_loop_endb,%
+ \xint:\XINT_last_loop_endc,\xint:\XINT_last_loop_endd,%
+ \xint:\XINT_last_loop_ende,\xint:\XINT_last_loop_endf,%
+ \xint:\XINT_last_loop_endg,\xint:\XINT_last_loop_endh,\xint_bye
}%
\long\def\XINT_last:f:csv_loop #1.#2,#3,#4,#5,#6,#7,#8,#9,%
{%
- \xint_gob_til_xint_relax #9%
- {#8}{#7}{#6}{#5}{#4}{#3}{#2}{#1}\xint_relax
+ \xint_gob_til_xint: #9%
+ {#8}{#7}{#6}{#5}{#4}{#3}{#2}{#1}\xint:
\XINT_last:f:csv_loop {#9}.%
}%
% \end{macrocode}
@@ -17633,24 +17874,16 @@
%
% \localtableofcontents
%
-% Got split off from \xintnameimp with release |1.1|, which also added
-% the new macro |\xintiiDivRound|.
+% Got split off from \xintnameimp with release |1.1|.
%
-% \begin{framed}
% The core arithmetic routines have been entirely rewritten for release
-% |1.2|.
+% |1.2|. The |1.2i| and |1.2l| brought again some improvements.
%
% The commenting continues (\xintdocdate) to be very sparse: actually it got
% worse than ever with release |1.2|. I will possibly add comments at a
% later date, but for the time being the new routines are not commented at
% all.
-% \end{framed}
%
-% Also, starting with |1.2|, |\xintAdd| etc... are defined only via
-% \xintfracnameimp. Only |\xintiAdd| and |\xintiiAdd| (etc...) are provided
-% via \xintcorenameimp.
-%
-%
% \subsection{Catcodes, \protect\eTeX{} and reload detection}
%
% The code for reload detection was initially copied from \textsc{Heiko
@@ -17708,8 +17941,144 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintcore}%
- [2017/01/06 1.2k Expandable arithmetic on big integers (JFB)]%
+ [2017/07/26 1.2l 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
+%
+% http://speleotrove.com/decimal/decarith.html
+%
+% and the Python3 implementation in its Decimal module.
+%
+% Clamped, ConversionSyntax, DivisionByZero, DivisionImpossible,
+% DivisionUndefined, Inexact, InsufficientStorage, InvalidContext,
+% InvalidOperation, Overflow, Inexact, Rounded, Subnormal,
+% Underflow.
+%
+% X3.274 rajoute LostDigits
+%
+% Python rajoute FloatOperation (et n'inclut pas InsufficientStorage)
+%
+% quote de decarith.pdf:
+% The Clamped, Inexact, Rounded, and Subnormal conditions can coincide with
+% each other or with other conditions. In these cases then any trap enabled
+% for another condition takes precedence over (is handled before) all of
+% these, any Subnormal trap takes precedence over Inexact, any Inexact trap
+% takes precedence over Rounded, and any Rounded trap takes precedence over
+% Clamped.
+%
+% WORK IN PROGRESS ! (1.2l, 2017/07/26)
+%
+% I follow the Python terminology: a trapped signal means it raises an
+% exception which for us means an expandable error message with some possible
+% user interaction. In this WIP
+% state, the interaction is commented out. A non-trapped signal or condition
+% would activate a (presumably silent) handler.
+%
+% Here, no signal-raising condition is "ignored" and all are "trapped" which
+% means that error handlers are never activated, thus left in garbage state in
+% the code.
+%
+% Various conditions can raise the same signal.
+%
+% Only signals, not conditions, raise Flags.
+%
+% If a signal is ignored it does not raise a Flag, but it activates the signal
+% handler (by default now no signal is ignored.)
+%
+% If a signal is not ignored it raises a Flag and then if it is not trapped it
+% activates the handler of the _condition_.
+%
+% If trapped (which is default now) an «exception» is raised, which means an
+% expandable error message (I copied over the LaTeX3 code for expandable error
+% messages, basically)
+% interrupts the TeX run. In future, user input could
+% be solicited, but currently this is commented out.
+%
+% For now macros to reset flags are done but without public interface nor
+% documentation.
+%
+% Only four conditions are currently possibly encountered:
+%- InvalidOperation
+%- DivisionByZero
+%- DivisionUndefined (which signals InvalidOperation)
+%- Underflow
+%
+% I did it quickly, anyhow this will become more palpable when some of the
+% Decimal Specification is actually implemented. The plan is to first do the
+% X3.274 norm, then more complete implementation will follow... perhaps...
+% |
+% \begin{macrocode}
+\csname XINT_Clamped_istrapped\endcsname
+\csname XINT_ConversionSyntax_istrapped\endcsname
+\csname XINT_DivisionByZero_istrapped\endcsname
+\csname XINT_DivisionImpossible_istrapped\endcsname
+\csname XINT_DivisionUndefined_istrapped\endcsname
+\csname XINT_InvalidOperation_istrapped\endcsname
+\csname XINT_Overflow_istrapped\endcsname
+\csname XINT_Underflow_istrapped\endcsname
+\catcode`- 11
+\def\XINT_ConversionSyntax-signal {{InvalidOperation}}%
+\let\XINT_DivisionImpossible-signal\XINT_ConversionSyntax-signal
+\let\XINT_DivisionUndefined-signal \XINT_ConversionSyntax-signal
+\let\XINT_InvalidContext-signal \XINT_ConversionSyntax-signal
+\catcode`- 12
+\def\XINT_signalcondition #1{\expandafter\XINT_signalcondition_a
+ \romannumeral0\ifcsname XINT_#1-signal\endcsname
+ \xint_dothis{\csname XINT_#1-signal\endcsname}%
+ \fi\xint_orthat{{#1}}{#1}}%
+\def\XINT_signalcondition_a #1#2#3#4#5{% copied over from Python Decimal module
+% #1=signal, #2=condition, #3=explanation for user,
+% #4=context for error handlers, #5=used
+ \ifcsname XINT_#1_isignoredflag\endcsname
+ \xint_dothis{\csname XINT_#1.handler\endcsname {#4}}%
+ \fi
+ \expandafter\xint_gobble_i\csname XINT_#1Flag_ON\endcsname
+ \unless\ifcsname XINT_#1_istrapped\endcsname
+ \xint_dothis{\csname XINT_#2.handler\endcsname {#4}}%
+ \fi
+ \xint_orthat{%
+ % the flag raised is named after the signal #1, but we show condition #2
+ \XINT_expandableerror{#2 (hit <RET> thrice)}%
+ \XINT_expandableerror{#3}%
+ \XINT_expandableerror{next: #5}%
+ % not for X3.274
+ %\XINT_expandableerror{<RET>, or I\xintUse{...}<RET>, or I\xintCTRLC<RET>}%
+ \xint_firstofone_thenstop{#5}%
+ }%
+}%
+%% \let\xintUse\xint_firstofthree_thenstop % defined in xint.sty
+\def\XINT_ifFlagRaised #1{%
+ \ifcsname XINT_#1Flag_ON\endcsname
+ \expandafter\xint_firstoftwo
+ \else
+ \expandafter\xint_secondoftwo
+ \fi}%
+\def\XINT_resetFlag #1%
+ {\expandafter\let\csname XINT_#1Flag_ON\endcsname\XINT_undefined}%
+\def\XINT_resetFlags {% WIP
+ \XINT_resetFlag{InvalidOperation}% also from DivisionUndefined
+ \XINT_resetFlag{DivisionByZero}%
+ \XINT_resetFlag{Underflow}% (\xintiiPow with negative exponent)
+ \XINT_resetFlag{Overflow}% not encountered so far in xint code 1.2l
+ % .. others ..
+}%
+%% NOT IMPLEMENTED! WORK IN PROGRESS! (ALL SIGNALS TRAPPED, NO HANDLERS USED)
+\catcode`. 11
+\let\XINT_Clamped.handler\xint_firstofone % WIP
+\def\XINT_InvalidOperation.handler#1{_NaN}% WIP
+\def\XINT_ConversionSyntax.handler#1{_NaN}% WIP
+\def\XINT_DivisionByZero.handler#1{_SignedInfinity(#1)}% WIP
+\def\XINT_DivisionImpossible.handler#1{_NaN}% WIP
+\def\XINT_DivisionUndefined.handler#1{_NaN}% WIP
+\let\XINT_Inexact.handler\xint_firstofone % WIP
+\def\XINT_InvalidContext.handler#1{_NaN}% WIP
+\let\XINT_Rounded.handler\xint_firstofone % WIP
+\let\XINT_Subnormal.handler\xint_firstofone% WIP
+\def\XINT_Overflow.handler#1{_NaN}% WIP
+\def\XINT_Underflow.handler#1{_NaN}% WIP
+\catcode`. 12
+% \end{macrocode}
% \subsection{Counts for holding needed constants}
% \begin{macrocode}
\ifdefined\m at ne\let\xint_c_mone\m at ne
@@ -17719,384 +18088,109 @@
\newcount\xint_c_x^viii_mone \xint_c_x^viii_mone 99999999
\newcount\xint_c_xii_e_viii \xint_c_xii_e_viii 1200000000
\newcount\xint_c_xi_e_viii_mone \xint_c_xi_e_viii_mone 1099999999
-\newcount\xint_c_xii_e_viii_mone\xint_c_xii_e_viii_mone 1199999999
% \end{macrocode}
% \subsection{\csh{xintNum}}
% \lverb|&
-% For example \xintNum {----+-+++---+----000000000000003}$\
+% For example \xintNum {----+-+++---+----000000000000003}
+%
+% Very old routine got completely rewritten for 1.2l.
+%
+% New code uses \numexpr governed expansion and fixes some issues of former
+% version particularly regarding inputs of the \numexpr...\relax type without
+% \the or \number prefix, and/or possibly no terminating \relax.
+%
+% \xintiNum{\numexpr 1}\foo in earlier versions caused premature expansion of
+% \foo.
+%
+% \xintiNum{\the\numexpr 1} was ok, but a bit luckily so.
+%
+% Also, up to 1.2k inclusive, the macro fetched tokens eight by eight, and not
+% nine by nine as is done now. I have no idea why.
% |
% \begin{macrocode}
\def\xintiNum {\romannumeral0\xintinum }%
\def\xintinum #1%
{%
- \expandafter\XINT_num_loop
- \romannumeral`&&@#1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z
+ \expandafter\XINT_num_cleanup\the\numexpr\expandafter\XINT_num_loop
+ \romannumeral`&&@#1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
\let\xintNum\xintiNum \let\xintnum\xintinum
\def\XINT_num #1%
{%
- \XINT_num_loop #1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z
+ \expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop
+ #1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
-\def\XINT_num_loop #1#2#3#4#5#6#7#8%
+\def\XINT_num_loop #1#2#3#4#5#6#7#8#9%
{%
- \xint_gob_til_xint_relax #8\XINT_num_end\xint_relax
- \XINT_num_NumEight #1#2#3#4#5#6#7#8%
-}%
-\edef\XINT_num_end\xint_relax\XINT_num_NumEight #1\xint_relax #2\Z
-{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1+\xint_c_\relax
-}%
-\def\XINT_num_NumEight #1#2#3#4#5#6#7#8%
-{%
- \ifnum \numexpr #1#2#3#4#5#6#7#8+\xint_c_= \xint_c_
- \xint_afterfi {\expandafter\XINT_num_keepsign_a
- \the\numexpr #1#2#3#4#5#6#7#81\relax}%
- \else
- \xint_afterfi {\expandafter\XINT_num_finish
- \the\numexpr #1#2#3#4#5#6#7#8\relax}%
- \fi
-}%
-\def\XINT_num_keepsign_a #1%
-{%
- \xint_gob_til_one#1\XINT_num_gobacktoloop 1\XINT_num_keepsign_b
-}%
-\def\XINT_num_gobacktoloop 1\XINT_num_keepsign_b {\XINT_num_loop }%
-\def\XINT_num_keepsign_b #1{\XINT_num_loop -}%
-\def\XINT_num_finish #1\xint_relax #2\Z { #1}%
+ \xint_gob_til_xint: #9\XINT_num_end\xint:
+ #1#2#3#4#5#6#7#8#9%
+ \ifnum \numexpr #1#2#3#4#5#6#7#8#9+\xint_c_ = \xint_c_
% \end{macrocode}
-% \subsection{Zeroes}
-% \lverb|Everything had to be changed for 1.2 as it does computations by
-% blocks of eight digits rather than four.
-%
-% Currently many macros are launched by a \romannumeral0. Perhaps I should
-% have used \romannumeral and end expansion by \z@ (\xint_c_).
-%
-% \XINT_cuz_small removes leading zeroes from the first eight digits. Supposed
-% to have been launched by a \romannumeral0. At least one digit is produced.|
+% \lverb|&
+% means that so far only signs encountered, (if syntax is legal) then possibly
+% zeroes
+% or a terminated or not terminated \numexpr evaluating to zero
+% In that latter case a correct zero will be produced in the end.
+% |
% \begin{macrocode}
-\edef\XINT_cuz_small #1#2#3#4#5#6#7#8%
-{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4#5#6#7#8\relax
-}%
+ \expandafter\XINT_num_loop
+ \else
% \end{macrocode}
-% \lverb|This iterately removes all leading zeroes from a sequence of 8N
-% digits ended by \R.
-%
-% Note 2015/11/28: with only four digits the gob_til_fourzeroes had proved
-% in some old testing faster than \ifnum test. But with eight digits, the
-% execution times are much closer, as I tested only now. Thus, one could as
-% well use \ifnum test here. Besides the tests were not exactly for a
-% situation like here where \XINT_cuz_z has two 00000000 blocks to grab.|
+% \lverb|&
+% non terminated \numexpr (with nine tokens total) are
+% safe as after \fi, there is then \xint:
+% |
% \begin{macrocode}
-\def\XINT_cuz #1#2#3#4#5#6#7#8#9%
-{%
- \xint_gob_til_R #9\XINT_cuz_e \R
- \xint_gob_til_eightzeroes #1#2#3#4#5#6#7#8\XINT_cuz_z 00000000%
- \XINT_cuz_done #1#2#3#4#5#6#7#8#9%
+ \expandafter\relax
+ \fi
}%
-\def\XINT_cuz_z 00000000\XINT_cuz_done 00000000{\XINT_cuz }%
-\edef\XINT_cuz_done #1#2#3#4#5#6#7#8#9\R
- {\noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4#5#6#7#8\relax #9}%
-\edef\XINT_cuz_e\R #1\XINT_cuz_done #2\R
- {\noexpand\expandafter\space\noexpand\the\numexpr #2\relax }%
+\def\XINT_num_end\xint:#1\xint:{#1+\xint_c_\xint:}% empty input ok
+\def\XINT_num_cleanup #1\xint:#2\Z { #1}%
% \end{macrocode}
-% \lverb|This removes eight by eight leading zeroes from a sequence of 8N digits
-% ended by \R. Thus, we still have 8N digits on output.|
-% \begin{macrocode}
-\def\XINT_cuz_byviii #1#2#3#4#5#6#7#8#9%
-{%
- \xint_gob_til_R #9\XINT_cuz_byviii_e \R
- \xint_gob_til_eightzeroes #1#2#3#4#5#6#7#8\XINT_cuz_byviii_z 00000000%
- \XINT_cuz_byviii_done #1#2#3#4#5#6#7#8#9%
-}%
-\def\XINT_cuz_byviii_z 00000000\XINT_cuz_byviii_done 00000000{\XINT_cuz_byviii}%
-\def\XINT_cuz_byviii_done #1\R { #1}%
-\def\XINT_cuz_byviii_e\R #1\XINT_cuz_byviii_done #2\R{ #2}%
-% \end{macrocode}
-% \subsection{Blocks of eight digits}
-% \lverb|Lingua of release 1.2.
+% \subsection*{Routines handling integers as lists of token digits}
+% \addcontentsline{toc}{subsection}{Routines handling integers as lists of token digits}
+% \lverb|&
+% Routines handling big integers which are lists of digit tokens with no
+% special additional structure. The argument is only subjected to a
+% \romannumeral`^^@ expansion when macros have "ii" in their names.
%
-% \romannumeral0\XINT_zeroes_forviii #1\R\R\R\R\R\R\R\R{10}0000001\W$newline
-% produces a string of k 0's such that k+length(#1) is smallest bigger multiple
-% of eight.|
-% \begin{macrocode}
-\def\XINT_zeroes_forviii #1#2#3#4#5#6#7#8%
-{%
- \xint_gob_til_R #8\XINT_zeroes_forviii_end\R\XINT_zeroes_forviii
-}%
-\edef\XINT_zeroes_forviii_end\R\XINT_zeroes_forviii #1#2#3#4#5#6#7#8#9\W
-{%
- \noexpand\expandafter\space\noexpand\xint_gob_til_one #2#3#4#5#6#7#8%
-}%
-% \end{macrocode}
-% \lverb|This is used as$bgroup$obeyspaces$obeylines
-% \the\numexpr1\XINT_rsepbyviii <8Ndigits>$%
-% \XINT_rsepbyviii_end_A 2345678$%
-% \XINT_rsepbyviii_end_B 2345678\relax UV$egroup
+% Some
+% routines do not accept non properly terminated inputs like "\the\numexpr1",
+% or "\the\mathcode`\-", others do.
%
-% $noindent
-% and will produce 1<8digits>!1<8digits>.1<8digits>!... where the original
-% digits are organized by eight, and the order inside successive pairs of
-% blocks separated by ! has been reversed. The output ends with a final 1U. or
-% 1V. The former happens when we had an even number of eight blocks, the
-% latter an odd number: 1<8d>!1<8d>.1U. or 1<8d>!1<8d>.1<8d>.1V.|
-% \begin{macrocode}
-\def\XINT_rsepbyviii #1#2#3#4#5#6#7#8%
-{%
- \XINT_rsepbyviii_b {#1#2#3#4#5#6#7#8}%
-}%
-\def\XINT_rsepbyviii_b #1#2#3#4#5#6#7#8#9%
-{%
- #2#3#4#5#6#7#8#9\expandafter!\the\numexpr
- 1#1\expandafter.\the\numexpr 1\XINT_rsepbyviii
-}%
-\def\XINT_rsepbyviii_end_B #1\relax #2#3{#2.}%
-\def\XINT_rsepbyviii_end_A #11#2\expandafter #3\relax #4#5{#2.1#5.}%
-% \end{macrocode}
-% \lverb|This is used typically as$bgroup$obeyspaces$obeylines
-% \romannumeral0\expandafter\XINT_sepandrev <8Ndigits>$%
-% \XINT_rsepbyviii_end_A 2345678$%
-% \XINT_rsepbyviii_end_B 2345678\relax UV\R.\R.\R.\R.\R.\R.\R.\R.\W$egroup
+% These routines or their sub-routines are mainly for internal usage.
+% |
%
-% $noindent
-% and will produce 1<8digits>!1<8digits>!1<8digits>!... where the blocks have
-% been globally reversed. The UV here are only place holders to share same
-% syntax as \XINT_sepandrev_andcount, they are gobbled (#2 in
-% \XINT_sepandrev_done).|
+% \subsection{\csh{XINT_cuz_small}}
+% \lverb|&
+% \XINT_cuz_small removes leading zeroes from the first eight digits. Expands
+% following \romannumeral0. At least one digit is produced.|
% \begin{macrocode}
-\def\XINT_sepandrev
+\def\XINT_cuz_small#1{%
+\def\XINT_cuz_small ##1##2##3##4##5##6##7##8%
{%
- \expandafter\XINT_sepandrev_a\the\numexpr 1\XINT_rsepbyviii
-}%
-\def\XINT_sepandrev_a {\XINT_sepandrev_b {}}%
-\def\XINT_sepandrev_b #1#2.#3.#4.#5.#6.#7.#8.#9.%
-{%
- \xint_gob_til_R #9\XINT_sepandrev_end\R
- \XINT_sepandrev_b {#9!#8!#7!#6!#5!#4!#3!#2!#1}%
-}%
-\def\XINT_sepandrev_end\R\XINT_sepandrev_b #1#2\W {\XINT_sepandrev_done #1}%
-\def\XINT_sepandrev_done #11#2!{ }%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8\relax
+}}\XINT_cuz_small{ }%
% \end{macrocode}
-% \lverb|This is used typically as$bgroup$obeyspaces$obeylines
-% \romannumeral0\expandafter\XINT_sepandrev_andcount
-% \the\numexpr1\XINT_rsepbyviii <8Ndigits>$%
-% \XINT_rsepbyviii_end_A 2345678$%
-% \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
-% \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
-% \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W$egroup
-%
-% $noindent
-% and will produce <length>.1<8digits>!1<8digits>!1<8digits>!... where the
-% blocks have been globally reversed and <length> is the number of blocks.|
-% \begin{macrocode}
-\def\XINT_sepandrev_andcount
-{%
- \expandafter\XINT_sepandrev_andcount_a\the\numexpr 1\XINT_rsepbyviii
-}%
-\def\XINT_sepandrev_andcount_a {\XINT_sepandrev_andcount_b 0.{}}%
-\def\XINT_sepandrev_andcount_b #1.#2#3.#4.#5.#6.#7.#8.#9.%
-{%
- \xint_gob_til_R #9\XINT_sepandrev_andcount_end\R
- \expandafter\XINT_sepandrev_andcount_b \the\numexpr #1+\xint_c_xiv.%
- {#9!#8!#7!#6!#5!#4!#3!#2}%
-}%
-\def\XINT_sepandrev_andcount_end\R
- \expandafter\XINT_sepandrev_andcount_b\the\numexpr #1+\xint_c_xiv.#2#3#4\W
-{\expandafter\XINT_sepandrev_andcount_done\the\numexpr \xint_c_ii*#3+#1.#2}%
-\edef\XINT_sepandrev_andcount_done #1.#21#3!%
- {\noexpand\expandafter\space\noexpand\the\numexpr #1-#3.}%
-% \end{macrocode}
-% \lverb|Used as \romannumeral0\XINT_unrevbyviii 1<8d>!....1<8d>! terminated
-% by$newline 1\Z!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
-%
-% The \romannumeral in unrevbyviii_a is for special effects (expand some token
-% which was put as 1<token>! at the end of the original blocks). Used by
-% subtraction during \XINT_sub_out, in particular.|
-% \begin{macrocode}
-\def\XINT_unrevbyviii #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
-{%
- \xint_gob_til_R #9\XINT_unrevbyviii_a\R
- \XINT_unrevbyviii {#9#8#7#6#5#4#3#2#1}%
-}%
-\edef\XINT_unrevbyviii_a\R\XINT_unrevbyviii #1#2\W
- {\noexpand\expandafter\space
- \noexpand\romannumeral`&&@\noexpand\xint_gob_til_Z #1}%
-% \end{macrocode}
-% \lverb|Can work with shorter ending pattern: 1\Z!1\R!1\R!1\R!1\R!1\R!1\R!\W
-% but the longer one of unrevbyviii is ok here too. Used currently (1.2) only
-% by addition, now (1.2c) with long ending pattern. Does the final clean up of
-% leading zeroes contrarily to general \XINT_unrevbyviii.|
-% \begin{macrocode}
-\def\XINT_smallunrevbyviii 1#1!1#2!1#3!1#4!1#5!1#6!1#7!1#8!#9\W%
-{%
- \expandafter\XINT_cuz_small\xint_gob_til_Z #8#7#6#5#4#3#2#1%
-}%
-% \end{macrocode}
-% \lverb|This is used as$bgroup$obeyspaces$obeylines
-% \the\numexpr\XINT_sepbyviii_andcount <8Ndigits>$%
-% \XINT_sepbyviii_end 2345678\relax
-% \xint_c_vii!\xint_c_vi!\xint_c_v!\xint_c_iv!%
-% \xint_c_iii!\xint_c_ii!\xint_c_i!\xint_c_\W $egroup
-%
-% $noindent
-% It will produce 1<8d>!1<8d>!....1<8d>!1.<count of blocks>. Used by
-% \XINT_div_prepare_g for \XINT_div_prepare_h.|
-% \begin{macrocode}
-\def\XINT_sepbyviii_andcount
-{%
- \expandafter\XINT_sepbyviii_andcount_a\the\numexpr\XINT_sepbyviii
-}%
-\def\XINT_sepbyviii #1#2#3#4#5#6#7#8%
-{%
- 1#1#2#3#4#5#6#7#8\expandafter!\the\numexpr\XINT_sepbyviii
-}%
-\def\XINT_sepbyviii_end #1\relax {\relax\XINT_sepbyviii_andcount_end!}%
-\def\XINT_sepbyviii_andcount_a {\XINT_sepbyviii_andcount_b \xint_c_.}%
-\def\XINT_sepbyviii_andcount_b #1.#2!#3!#4!#5!#6!#7!#8!#9!%
-{%
- #2\expandafter!\the\numexpr#3\expandafter!\the\numexpr#4\expandafter
- !\the\numexpr#5\expandafter!\the\numexpr#6\expandafter!\the\numexpr
- #7\expandafter!\the\numexpr#8\expandafter!\the\numexpr#9\expandafter!\the\numexpr
- \expandafter\XINT_sepbyviii_andcount_b\the\numexpr #1+\xint_c_viii.%
-}%
-\def\XINT_sepbyviii_andcount_end #1\XINT_sepbyviii_andcount_b\the\numexpr
- #2+\xint_c_viii.#3#4\W {\expandafter.\the\numexpr #2+#3.}%
-% \end{macrocode}
-% \lverb|This is used as$newline
-% \romannumeral0\XINT_rev_nounsep {}<blocks 1<8d>!>\R!\R!\R!\R!\R!\R!\R!\R!\W
-%
-% It reverses the blocks, keeping the 1's and ! separators. Used multiple
-% times in the division algorithm. The inserted {} here is *not* optional.
-% Attention does not make disappear a 1!.|
-% \begin{macrocode}
-\def\XINT_rev_nounsep #1#2!#3!#4!#5!#6!#7!#8!#9!%
-{%
- \xint_gob_til_R #9\XINT_rev_nounsep_end\R
- \XINT_rev_nounsep {#9!#8!#7!#6!#5!#4!#3!#2!#1}%
-}%
-\def\XINT_rev_nounsep_end\R\XINT_rev_nounsep #1#2\W {\XINT_rev_nounsep_done #1}%
-\def\XINT_rev_nounsep_done #11{ 1}%
-% \end{macrocode}
-% \lverb|This is used as$newline
-% \the\numexpr\XINT_sepbyviii_Z <8Ndigits>\XINT_sepbyviii_Z_end 2345678\relax
-%
-% It produces 1<8d>!...1<8d>!1\Z!|
-% \begin{macrocode}
-\def\XINT_sepbyviii_Z #1#2#3#4#5#6#7#8%
-{%
- 1#1#2#3#4#5#6#7#8\expandafter!\the\numexpr\XINT_sepbyviii_Z
-}%
-\def\XINT_sepbyviii_Z_end #1\relax {\relax\Z!}%
-% \end{macrocode}
-% \lverb|This is used as$newline
-% \romannumeral0\XINT_unsep_cuzsmall {}<blocks of 1<8d>!>1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
-%
-% En fait le {} est optionnel, s'il est absent le premier #1 sera vide, tout
-% simplement. It removes the 1's and !'s, and removes the leading zeroes *of
-% the first block*. This could have been done with \numexpr and a \cleanup but
-% would have restricted due to maximal expansion depth. Probably there where
-% already O(N^2) macros, thus I decided that this one would be too.|
-% \begin{macrocode}
-\def\XINT_unsep_cuzsmall #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
-{%
- \xint_gob_til_R #9\XINT_unsep_cuzsmall_end\R
- \XINT_unsep_cuzsmall {#1#2#3#4#5#6#7#8#9}%
-}%
-\def\XINT_unsep_cuzsmall_end\R
- \XINT_unsep_cuzsmall #1{\XINT_unsep_cuzsmall_done #1}%
-\def\XINT_unsep_cuzsmall_done #1\R #2\W{\XINT_cuz_small #1}%
-\def\XINT_unsep_delim {1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W}%
-% \end{macrocode}
-% \lverb|This is used by division to remove separators from the produced
-% quotient. The quotient is produced in the correct order. The routine will
-% also remove leading zeroes. An extra intial block of 8 zeroes is possible
-% and thus if present must be removed. Then the next eight digits must be
-% cleaned of leading zeroes.|
-% \begin{macrocode}
-\def\XINT_div_unsepQ #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
-{%
- \xint_gob_til_R #9\XINT_div_unsepQ_end\R
- \XINT_div_unsepQ {#1#2#3#4#5#6#7#8#9}%
-}%
-\def\XINT_div_unsepQ_end\R\XINT_div_unsepQ #1{\XINT_div_unsepQ_x #1}%
-\def\XINT_div_unsepQ_x #1#2#3#4#5#6#7#8#9%
-{%
- \xint_gob_til_R #9\XINT_div_unsepQ_e \R
- \xint_gob_til_eightzeroes #1#2#3#4#5#6#7#8\XINT_div_unsepQ_y 00000000%
- \expandafter\XINT_div_unsepQ_done \the\numexpr #1#2#3#4#5#6#7#8.#9%
-}%
-\def\XINT_div_unsepQ_e\R\xint_gob_til_eightzeroes #1\XINT_div_unsepQ_y #2\W
- {\the\numexpr #1\relax \Z}%
-\def\XINT_div_unsepQ_y #1.#2\R #3\W{\XINT_cuz_small #2\Z}%
-\def\XINT_div_unsepQ_done #1.#2\R #3\W { #1#2\Z}%
-% \end{macrocode}
-% \lverb|This is used by division to remove separators from the produced
-% remainder. The remainder is here in correct order. It must be cleaned of
-% leading zeroes, possibly all the way. Terminator was
-% 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W|
-% \begin{macrocode}
-\def\XINT_div_unsepR #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
-{%
- \xint_gob_til_R #9\XINT_div_unsepR_end\R
- \XINT_div_unsepR {#1#2#3#4#5#6#7#8#9}%
-}%
-\def\XINT_div_unsepR_end\R\XINT_div_unsepR #1{\XINT_div_unsepR_done #1}%
-\def\XINT_div_unsepR_done #1\R #2\W {\XINT_cuz #1\R}%
-% \end{macrocode}
-% \subsection{\csh{xintReverseDigits}}
-% \lverb|1.2.|
-% \begin{macrocode}
-\def\XINT_microrevsep #1#2#3#4#5#6#7#8%
-{%
- 1#8#7#6#5#4#3#2#1\expandafter!\the\numexpr\XINT_microrevsep
-}%
-\def\XINT_microrevsep_end #1\W #2\expandafter #3\Z{#2!}%
-\def\xintReverseDigits {\romannumeral0\xintreversedigits }%
-\def\xintreversedigits #1{\expandafter\XINT_reversedigits\romannumeral`&&@#1\Z}%
-\def\XINT_reversedigits #1%
-{%
- \xint_UDsignfork
- #1{\expandafter-\romannumeral0\XINT_reversedigits_a}%
- -{\XINT_reversedigits_a #1}%
- \krof
-}%
-\def\XINT_reversedigits_a #1\Z
-{%
- \expandafter\XINT_revdigits_a\the\numexpr\expandafter\XINT_microrevsep
- \romannumeral`&&@#1{\XINT_microrevsep_end\W}\XINT_microrevsep_end
- \XINT_microrevsep_end\XINT_microrevsep_end
- \XINT_microrevsep_end\XINT_microrevsep_end
- \XINT_microrevsep_end\XINT_microrevsep_end\Z
- 1\Z!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
-}%
-\def\XINT_revdigits_a {\XINT_revdigits_b {}}%
-\def\XINT_revdigits_b #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
-{%
- \xint_gob_til_R #9\XINT_revdigits_end\R
- \XINT_revdigits_b {#9#8#7#6#5#4#3#2#1}%
-}%
-\edef\XINT_revdigits_end\R\XINT_revdigits_b #1#2\W
- {\noexpand\expandafter\space\noexpand\xint_gob_til_Z #1}%
-% \end{macrocode}
% \subsection{\csh{xintSgn}, \csh{xintiiSgn}, \csh{XINT_Sgn}, \csh{XINT_cntSgn}}
% \lverb|&
-% xintfrac.sty will overwrite \xintsgn with use of \xintraw rather than
-% \xintnum, naturally.
-%|
+% xintfrac.sty will rewrite \xintSgn to let it accept general input as recognized by
+% xintfrac.sty macros
+%
+% 1.2l: \xintiiSgn made robust against non terminated input.
+% |
% \begin{macrocode}
\def\xintiiSgn {\romannumeral0\xintiisgn }%
\def\xintiisgn #1%
{%
- \expandafter\XINT_sgn \romannumeral`&&@#1\Z%
+ \expandafter\XINT_sgn \romannumeral`&&@#1\xint:
}%
\def\xintSgn {\romannumeral0\xintsgn }%
\def\xintsgn #1%
{%
- \expandafter\XINT_sgn \romannumeral0\xintnum{#1}\Z%
+ \expandafter\XINT_sgn \romannumeral0\xintnum{#1}\xint:
}%
-\def\XINT_sgn #1#2\Z
+\def\XINT_sgn #1#2\xint:
{%
\xint_UDzerominusfork
#1-{ 0}%
@@ -18104,7 +18198,7 @@
0-{ 1}%
\krof
}%
-\def\XINT_Sgn #1#2\Z
+\def\XINT_Sgn #1#2\xint:
{%
\xint_UDzerominusfork
#1-{0}%
@@ -18112,7 +18206,7 @@
0-{1}%
\krof
}%
-\def\XINT_cntSgn #1#2\Z
+\def\XINT_cntSgn #1#2\xint:
{%
\xint_UDzerominusfork
#1-\xint_c_
@@ -18122,6 +18216,9 @@
}%
% \end{macrocode}
% \subsection{\csh{xintiOpp}, \csh{xintiiOpp}}
+% \lverb|Attention, \xintiiOpp non robust against non terminated inputs.
+% Reason is I don't want to have to grab a delimiter at the end, as everything
+% happens "upfront".|
% \begin{macrocode}
\def\xintiiOpp {\romannumeral0\xintiiopp }%
\def\xintiiopp #1%
@@ -18144,6 +18241,7 @@
}%
% \end{macrocode}
% \subsection{\csh{xintiAbs}, \csh{xintiiAbs}}
+% \lverb|Attention \xintiiAbs non robust against non terminated input.|
% \begin{macrocode}
\def\xintiiAbs {\romannumeral0\xintiiabs }%
\def\xintiiabs #1%
@@ -18164,18 +18262,22 @@
}%
% \end{macrocode}
% \subsection{\csh{xintFDg}, \csh{xintiiFDg}}
+% \lverb|&
+% FIRST DIGIT.
+%
+% 1.2l: \xintiiFDg made robust against non terminated input.|
% \begin{macrocode}
\def\xintiiFDg {\romannumeral0\xintiifdg }%
\def\xintiifdg #1%
{%
- \expandafter\XINT_fdg \romannumeral`&&@#1\W\Z
+ \expandafter\XINT_fdg \romannumeral`&&@#1\xint:\Z
}%
\def\xintFDg {\romannumeral0\xintfdg }%
\def\xintfdg #1%
{%
- \expandafter\XINT_fdg \romannumeral0\xintnum{#1}\W\Z
+ \expandafter\XINT_fdg \romannumeral0\xintnum{#1}\xint:\Z
}%
-\def\XINT_FDg #1{\romannumeral0\XINT_fdg #1\W\Z }%
+\def\XINT_FDg #1{\romannumeral0\XINT_fdg #1\xint:\Z }%
\def\XINT_fdg #1#2#3\Z
{%
\xint_UDzerominusfork
@@ -18187,8 +18289,12 @@
% \end{macrocode}
% \subsection{\csh{xintLDg}, \csh{xintiiLDg}}
% \lverb|&
-% Rewritten for 1.2i (2016/12/10). Surprisingly perhaps, faster than
-% \xintLastItem despite the \numexpr operations.
+% LAST DIGIT.
+%
+% Rewritten for 1.2i (2016/12/10). Surprisingly perhaps, it is faster than
+% \xintLastItem from xintkernel.sty despite the \numexpr operations.
+%
+% Attention \xintiiLDg non robust against non terminated input.
% |
% \begin{macrocode}
\def\xintLDg {\romannumeral0\xintldg }%
@@ -18204,9 +18310,11 @@
-{\XINT_ldg#1}%
\krof
}%
-\edef\XINT_ldg #1#2#3#4#5#6#7#8#9%
- {\noexpand\expandafter\space
- \noexpand\the\numexpr#9#8#7#6#5#4#3#2#1*\xint_c_+\noexpand\XINT_ldg_a#9}%
+\def\XINT_ldg #1{%
+\def\XINT_ldg ##1##2##3##4##5##6##7##8##9%
+ {\expandafter#1%
+ \the\numexpr##9##8##7##6##5##4##3##2##1*\xint_c_+\XINT_ldg_a##9}%
+}\XINT_ldg{ }%
\def\XINT_ldg_a#1#2{\XINT_ldg_cbye#2\XINT_ldg_d#1\XINT_ldg_c\XINT_ldg_b#2}%
\def\XINT_ldg_b#1#2#3#4#5#6#7#8#9{#9#8#7#6#5#4#3#2#1*\xint_c_+\XINT_ldg_a#9}%
\def\XINT_ldg_c #1#2\xint_bye{#1}%
@@ -18213,12 +18321,9 @@
\def\XINT_ldg_cbye #1\XINT_ldg_c{}%
\def\XINT_ldg_d#1#2\xint_bye{#1}%
% \end{macrocode}
+%
% \subsection{\csh{xintDouble}}
-% \lverb|1.08. Rewritten for 1.2. Again rewritten for 1.2i (one year
-% later...)! oh no... 1.2i simply forgot to handle negative numbers... and I
-% made no testing. In fact I didn't remember if the macro was for non-negative
-% input only. Looking at earlier code, no, it did handle negative inputs too.
-% 1.2k has a regression test suite, which caught that.|
+% \lverb|Attention \xintDouble non robust against non terminated input.|
% \begin{macrocode}
\def\xintDouble {\romannumeral0\xintdouble}%
\def\xintdouble #1{\expandafter\XINT_dbl_fork\romannumeral`&&@#1%
@@ -18231,14 +18336,16 @@
\krof #1%
}%
\def\XINT_dbl_neg-{\expandafter-\romannumeral0\XINT_dbl}%
-\def\XINT_dbl #1#2#3#4#5#6#7#8%
- {\expandafter\space\the\numexpr#1#2#3#4#5#6#7#8\XINT_dbl_a}%
+\def\XINT_dbl #1{%
+\def\XINT_dbl ##1##2##3##4##5##6##7##8%
+ {\expandafter#1\the\numexpr##1##2##3##4##5##6##7##8\XINT_dbl_a}%
+}\XINT_dbl{ }%
\def\XINT_dbl_a #1#2#3#4#5#6#7#8%
{\expandafter\XINT_dbl_e\the\numexpr 1#1#2#3#4#5#6#7#8\XINT_dbl_a}%
\def\XINT_dbl_e#1{*\xint_c_ii\if#13+\xint_c_i\fi\relax}%
% \end{macrocode}
% \subsection{\csh{xintHalf}}
-% \lverb|1.08. Rewritten for 1.2. Again rewritten for 1.2i.|
+% \lverb|Attention \xintHalf non robust against non terminated input.|
% \begin{macrocode}
\def\xintHalf {\romannumeral0\xinthalf}%
\def\xinthalf #1{\expandafter\XINT_half_fork\romannumeral`&&@#1%
@@ -18252,8 +18359,10 @@
\krof #1%
}%
\def\XINT_half_neg-{\xintiiopp\XINT_half}%
-\def\XINT_half #1#2#3#4#5#6#7#8%
- {\expandafter\space\the\numexpr(#1#2#3#4#5#6#7#8\XINT_half_a}%
+\def\XINT_half #1{%
+\def\XINT_half ##1##2##3##4##5##6##7##8%
+ {\expandafter#1\the\numexpr(##1##2##3##4##5##6##7##8\XINT_half_a}%
+}\XINT_half{ }%
\def\XINT_half_a#1{\xint_Bye#1\xint_bye\XINT_half_b#1}%
\def\XINT_half_b #1#2#3#4#5#6#7#8%
{\expandafter\XINT_half_e\the\numexpr(1#1#2#3#4#5#6#7#8\XINT_half_a}%
@@ -18260,12 +18369,12 @@
\def\XINT_half_e#1{*\xint_c_v+#1-\xint_c_v)\relax}%
% \end{macrocode}
% \subsection{\csh{xintInc}}
-% \lverb|1.2i much delayed complete rewrite in 1.2 style. I should have
-% done that at the time of 1.2 release (I modified \xintInc at that time but
-% wasn't very lucid after all the work done on 1.2).
+% \lverb|1.2i much delayed complete rewrite in 1.2 style.
%
% As we take 9 by 9 with the input save stack at 5000 this allows a bit less
-% than 9 times 2500 = 22500 digits on input.|
+% than 9 times 2500 = 22500 digits on input.
+%
+% Attention \xintInc non robust against non terminated input.|
% \begin{macrocode}
\def\xintInc {\romannumeral0\xintinc}%
\def\xintinc #1{\expandafter\XINT_inc_fork\romannumeral`&&@#1%
@@ -18279,8 +18388,10 @@
}%
\def\XINT_inc_neg-#1\xint_bye#2\relax
{\xintiiopp\XINT_dec #1\XINT_dec_bye234567890\xint_bye}%
-\def\XINT_inc #1#2#3#4#5#6#7#8#9%
- {\expandafter\space\the\numexpr#1#2#3#4#5#6#7#8#9\XINT_inc_a}%
+\def\XINT_inc #1{%
+\def\XINT_inc ##1##2##3##4##5##6##7##8##9%
+ {\expandafter#1\the\numexpr##1##2##3##4##5##6##7##8##9\XINT_inc_a}%
+}\XINT_inc{ }%
\def\XINT_inc_a #1#2#3#4#5#6#7#8#9%
{\expandafter\XINT_inc_e\the\numexpr 1#1#2#3#4#5#6#7#8#9\XINT_inc_a}%
\def\XINT_inc_e#1{\if#12+\xint_c_i\fi\relax}%
@@ -18287,7 +18398,9 @@
% \end{macrocode}
% \subsection{\csh{xintDec}}
% \lverb|1.2i much delayed complete rewrite in the 1.2 style. Things are a
-% bit more complicated than \xintInc because 2999999999 is too big for TeX.|
+% bit more complicated than \xintInc because 2999999999 is too big for TeX.
+%
+% Attention \xintDec non robust against non terminated input.|
% \begin{macrocode}
\def\xintDec {\romannumeral0\xintdec}%
\def\xintdec #1{\expandafter\XINT_dec_fork\romannumeral`&&@#1%
@@ -18302,8 +18415,10 @@
\def\XINT_dec_neg-#1\XINT_dec_bye#2\xint_bye
{\expandafter-%
\romannumeral0\XINT_inc #1\xint_bye23456789\xint_bye+\xint_c_i\relax}%
-\def\XINT_dec #1#2#3#4#5#6#7#8#9%
- {\expandafter\space\the\numexpr#1#2#3#4#5#6#7#8#9\XINT_dec_a}%
+\def\XINT_dec #1{%
+\def\XINT_dec ##1##2##3##4##5##6##7##8##9%
+ {\expandafter#1\the\numexpr##1##2##3##4##5##6##7##8##9\XINT_dec_a}%
+}\XINT_dec{ }%
\def\XINT_dec_a #1#2#3#4#5#6#7#8#9%
{\expandafter\XINT_dec_e\the\numexpr 1#1#2#3#4#5#6#7#8#9\XINT_dec_a}%
\def\XINT_dec_bye #1\XINT_dec_a#2#3\xint_bye
@@ -18313,17 +18428,22 @@
% \subsection{\csh{xintDSL}}
% \lverb|DECIMAL SHIFT LEFT (=MULTIPLICATION PAR 10). Rewritten for 1.2i.
% This was very old code... I never came back to it, but I should have
-% rewritten it long time ago.|
+% rewritten it long time ago.
+%
+% Attention \xintDSL non robust against non terminated input.|
% \begin{macrocode}
\def\xintDSL {\romannumeral0\xintdsl }%
\def\xintdsl #1{\expandafter\XINT_dsl\romannumeral`&&@#10}%
-\edef\XINT_dsl #1%
- {\noexpand\xint_gob_til_zero #1\noexpand\xint_dsl_zero 0\space #1}%
+\def\XINT_dsl#1{%
+\def\XINT_dsl ##1{\xint_gob_til_zero ##1\xint_dsl_zero 0#1##1}%
+}\XINT_dsl{ }%
\def\xint_dsl_zero 0 0{ }%
% \end{macrocode}
% \subsection{\csh{xintDSR}}
% \lverb|Decimal shift right, truncates towards zero. Rewritten for 1.2i.
-% Limited to 22483 digits on input.|
+% Limited to 22483 digits on input.
+%
+% Attention \xintDSR non robust against non terminated input.|
% \begin{macrocode}
\def\xintDSR{\romannumeral0\xintdsr}%
\def\xintdsr #1{\expandafter\XINT_dsr_fork\romannumeral`&&@#1%
@@ -18336,8 +18456,10 @@
\krof #1%
}%
\def\XINT_dsr_neg-{\xintiiopp\XINT_dsr}%
-\def\XINT_dsr #1#2#3#4#5#6#7#8#9%
- {\expandafter\space\the\numexpr(#1#2#3#4#5#6#7#8#9\XINT_dsr_a}%
+\def\XINT_dsr #1{%
+\def\XINT_dsr ##1##2##3##4##5##6##7##8##9%
+ {\expandafter#1\the\numexpr(##1##2##3##4##5##6##7##8##9\XINT_dsr_a}%
+}\XINT_dsr{ }%
\def\XINT_dsr_a#1{\xint_Bye#1\xint_bye\XINT_dsr_b#1}%
\def\XINT_dsr_b #1#2#3#4#5#6#7#8#9%
{\expandafter\XINT_dsr_e\the\numexpr(1#1#2#3#4#5#6#7#8#9\XINT_dsr_a}%
@@ -18347,7 +18469,10 @@
% \lverb|New with 1.2i. Decimal shift right, rounds away from zero; done in
% the 1.2 spirit (with much delay, sorry). Used by \xintRound, \xintDivRound.
%
-% This is about the first time I am happy that the division in \numexpr rounds!|
+% This is about the first time I am happy that the division in \numexpr
+% rounds!
+%
+% Attention \xintDSRr non robust against non terminated input.|
% \begin{macrocode}
\def\xintDSRr{\romannumeral0\xintdsrr}%
\def\xintdsrr #1{\expandafter\XINT_dsrr_fork\romannumeral`&&@#1%
@@ -18360,14 +18485,372 @@
\krof #1%
}%
\def\XINT_dsrr_neg-{\xintiiopp\XINT_dsrr}%
-\def\XINT_dsrr #1#2#3#4#5#6#7#8#9%
- {\expandafter\space\the\numexpr#1#2#3#4#5#6#7#8#9\XINT_dsrr_a}%
+\def\XINT_dsrr #1{%
+\def\XINT_dsrr ##1##2##3##4##5##6##7##8##9%
+ {\expandafter#1\the\numexpr##1##2##3##4##5##6##7##8##9\XINT_dsrr_a}%
+}\XINT_dsrr{ }%
\def\XINT_dsrr_a#1{\xint_Bye#1\xint_bye\XINT_dsrr_b#1}%
\def\XINT_dsrr_b #1#2#3#4#5#6#7#8#9%
{\expandafter\XINT_dsrr_e\the\numexpr1#1#2#3#4#5#6#7#8#9\XINT_dsrr_a}%
\let\XINT_dsrr_e\XINT_inc_e
% \end{macrocode}
-% \subsection{Core arithmetic}
+% \subsection*{Blocks of eight digits}
+% \addcontentsline{toc}{subsection}{Blocks of eight digits}
+% \lverb|The lingua of release 1.2.|
+%
+% \subsection{\csh{XINT_cuz}}
+% \lverb|This (launched by \romannumeral0) iterately removes all leading
+% zeroes from a sequence of 8N digits ended by \R.
+%
+% Rewritten for 1.2l, now uses \numexpr governed expansion and \ifnum test
+% rather than delimited gobbling macros.
+%
+% Note 2015/11/28: with only four digits the gob_til_fourzeroes had proved
+% in some old testing faster than \ifnum test. But with eight digits, the
+% execution times are much closer, as I tested back then.
+% |
+% \begin{macrocode}
+\def\XINT_cuz #1{%
+\def\XINT_cuz {\expandafter#1\the\numexpr\XINT_cuz_loop}%
+}\XINT_cuz{ }%
+\def\XINT_cuz_loop #1#2#3#4#5#6#7#8#9%
+{%
+ #1#2#3#4#5#6#7#8%
+ \xint_gob_til_R #9\XINT_cuz_hitend\R
+ \ifnum #1#2#3#4#5#6#7#8>\xint_c_
+ \expandafter\XINT_cuz_cleantoend
+ \else\expandafter\XINT_cuz_loop
+ \fi #9%
+}%
+\def\XINT_cuz_hitend\R #1\R{\relax}%
+\def\XINT_cuz_cleantoend #1\R{\relax #1}%
+% \end{macrocode}
+% \subsection{\csh{XINT_cuz_byviii}}
+% \lverb|This removes eight by eight leading zeroes from a sequence of 8N digits
+% ended by \R. Thus, we still have 8N digits on output. Expansion started by
+% \romannumeral0 |
+% \begin{macrocode}
+\def\XINT_cuz_byviii #1#2#3#4#5#6#7#8#9%
+{%
+ \xint_gob_til_R #9\XINT_cuz_byviii_e \R
+ \xint_gob_til_eightzeroes #1#2#3#4#5#6#7#8\XINT_cuz_byviii_z 00000000%
+ \XINT_cuz_byviii_done #1#2#3#4#5#6#7#8#9%
+}%
+\def\XINT_cuz_byviii_z 00000000\XINT_cuz_byviii_done 00000000{\XINT_cuz_byviii}%
+\def\XINT_cuz_byviii_done #1\R { #1}%
+\def\XINT_cuz_byviii_e\R #1\XINT_cuz_byviii_done #2\R{ #2}%
+% \end{macrocode}
+% \subsection{\csh{XINT_unsep_loop}}
+%
+% \lverb|This is used as
+%( \the\numexpr0\XINT_unsep_loop (blocks of 1<8d>!)%
+%: \xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax
+%)
+% It removes the 1's and !'s, from the 8N digits and outputs them prefixed by
+% a 0 token.
+%
+% Done at 1.2l for usage by other macros. The similar code in earlier releases
+% was strangely in O(N^2) style, apparently to avoid some memory constraints.
+% But these memory constraints related to \numexpr chaining seems to be in
+% many places in xint code base. The 1.2l version is written in the 1.2i style
+% of \xintInc etc... and is compatible with some 1! block without digits
+% among the treated blocks, they will disappear.|
+% \begin{macrocode}
+\def\XINT_unsep_loop #1!#2!#3!#4!#5!#6!#7!#8!#9!%
+{%
+ \expandafter\XINT_unsep_clean
+ \the\numexpr #1\expandafter\XINT_unsep_clean
+ \the\numexpr #2\expandafter\XINT_unsep_clean
+ \the\numexpr #3\expandafter\XINT_unsep_clean
+ \the\numexpr #4\expandafter\XINT_unsep_clean
+ \the\numexpr #5\expandafter\XINT_unsep_clean
+ \the\numexpr #6\expandafter\XINT_unsep_clean
+ \the\numexpr #7\expandafter\XINT_unsep_clean
+ \the\numexpr #8\expandafter\XINT_unsep_clean
+ \the\numexpr #9\XINT_unsep_loop
+}%
+\def\XINT_unsep_clean 1{\relax}%
+% \end{macrocode}
+% \subsection{\csh{XINT_unsep_cuzsmall}}
+%
+% \lverb|This is used as
+%( \romannumeral0\XINT_unsep_cuzsmall (blocks of 1<8d>!)%
+%: \xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax
+%)
+% It removes the 1's and !'s, and removes the leading zeroes *of
+% the first block*.
+%
+% Redone for 1.2l: the 1.2 variant was strangely in O(N^2) style.|
+% \begin{macrocode}
+\def\XINT_unsep_cuzsmall
+{%
+ \expandafter\XINT_unsep_cuzsmall_x\the\numexpr0\XINT_unsep_loop
+}%
+\def\XINT_unsep_cuzsmall_x #1{%
+\def\XINT_unsep_cuzsmall_x 0##1##2##3##4##5##6##7##8%
+{%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8\relax
+}}\XINT_unsep_cuzsmall_x{ }%
+% \end{macrocode}
+% \subsection{\csh{XINT_div_unsepQ}}
+%
+% \lverb|This is used by division to remove separators from the produced
+% quotient. The quotient is produced in the correct order. The routine will
+% also remove leading zeroes. An extra initial block of 8 zeroes is possible
+% and thus if present must be removed. Then the next eight digits must be
+% cleaned of leading zeroes. Attention that there might be a single
+% block of 8 zeroes. Expansion launched by \romannumeral0.
+%
+% Rewritten for 1.2l in 1.2i style.|
+% \begin{macrocode}
+\def\XINT_div_unsepQ_delim {\xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax\Z}%
+\def\XINT_div_unsepQ
+{%
+ \expandafter\XINT_div_unsepQ_x\the\numexpr0\XINT_unsep_loop
+}%
+\def\XINT_div_unsepQ_x #1{%
+\def\XINT_div_unsepQ_x 0##1##2##3##4##5##6##7##8##9%
+{%
+ \xint_gob_til_Z ##9\XINT_div_unsepQ_one\Z
+ \xint_gob_til_eightzeroes ##1##2##3##4##5##6##7##8\XINT_div_unsepQ_y 00000000%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8\relax ##9%
+}}\XINT_div_unsepQ_x{ }%
+\def\XINT_div_unsepQ_y #1{%
+\def\XINT_div_unsepQ_y ##1\relax ##2##3##4##5##6##7##8##9%
+{%
+ \expandafter#1\the\numexpr ##2##3##4##5##6##7##8##9\relax
+}}\XINT_div_unsepQ_y{ }%
+\def\XINT_div_unsepQ_one#1\expandafter{\expandafter}%
+% \end{macrocode}
+% \subsection{\csh{XINT_div_unsepR}}
+%
+% \lverb|This is used by division to remove separators from the produced
+% remainder. The remainder is here in correct order. It must be cleaned of
+% leading zeroes, possibly all the way.
+%
+% Also rewritten for 1.2l, the 1.2 version was O(N^2) style.
+%
+% Terminator \xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax\R
+%
+% We have a need for something like \R because it is not guaranteed the thing
+% is not actually zero.|
+% \begin{macrocode}
+\def\XINT_div_unsepR
+{%
+ \expandafter\XINT_div_unsepR_x\the\numexpr0\XINT_unsep_loop
+}%
+\def\XINT_div_unsepR_x#1{%
+\def\XINT_div_unsepR_x 0{\expandafter#1\the\numexpr\XINT_cuz_loop}%
+}\XINT_div_unsepR_x{ }%
+% \end{macrocode}
+% \subsection{\csh{XINT_zeroes_forviii}}
+%
+% \lverb|&
+%( \romannumeral0\XINT_zeroes_forviii #1\R\R\R\R\R\R\R\R{10}0000001\W
+%)
+% produces a string of k 0's such that k+length(#1) is smallest bigger multiple
+% of eight.|
+% \begin{macrocode}
+\def\XINT_zeroes_forviii #1#2#3#4#5#6#7#8%
+{%
+ \xint_gob_til_R #8\XINT_zeroes_forviii_end\R\XINT_zeroes_forviii
+}%
+\def\XINT_zeroes_forviii_end#1{%
+\def\XINT_zeroes_forviii_end\R\XINT_zeroes_forviii ##1##2##3##4##5##6##7##8##9\W
+{%
+ \expandafter#1\xint_gob_til_one ##2##3##4##5##6##7##8%
+}}\XINT_zeroes_forviii_end{ }%
+% \end{macrocode}
+% \subsection{\csh{XINT_sepbyviii_Z}}
+%
+% \lverb|This is used as
+%( \the\numexpr\XINT_sepbyviii_Z <8Ndigits>\XINT_sepbyviii_Z_end 2345678\relax
+%)
+% It produces 1<8d>!...1<8d>!1;!
+%
+% Prior to 1.2l it used \Z as terminator not the semi-colon (hence the name).
+% The switch to ; was done at a time I thought perhaps I would use an internal
+% format maintaining such 8 digits blocks, and this has to be compatible with
+% the \csname...\endcsname encapsulation in \xintexpr parsers.|
+% \begin{macrocode}
+\def\XINT_sepbyviii_Z #1#2#3#4#5#6#7#8%
+{%
+ 1#1#2#3#4#5#6#7#8\expandafter!\the\numexpr\XINT_sepbyviii_Z
+}%
+\def\XINT_sepbyviii_Z_end #1\relax {;!}%
+% \end{macrocode}
+% \subsection{\csh{XINT_sepbyviii_andcount}}
+%
+% \lverb|This is used as
+%( \the\numexpr\XINT_sepbyviii_andcount <8Ndigits>$%
+%: \XINT_sepbyviii_end 2345678\relax
+%: \xint_c_vii!\xint_c_vi!\xint_c_v!\xint_c_iv!$%
+%: \xint_c_iii!\xint_c_ii!\xint_c_i!\xint_c_\W
+%)
+% It will produce
+%( 1<8d>!1<8d>!....1<8d>!1\xint:<count of blocks>\xint:
+%)
+% Used by
+% \XINT_div_prepare_g for \XINT_div_prepare_h, and also by \xintiiCmp.|
+% \begin{macrocode}
+\def\XINT_sepbyviii_andcount
+{%
+ \expandafter\XINT_sepbyviii_andcount_a\the\numexpr\XINT_sepbyviii
+}%
+\def\XINT_sepbyviii #1#2#3#4#5#6#7#8%
+{%
+ 1#1#2#3#4#5#6#7#8\expandafter!\the\numexpr\XINT_sepbyviii
+}%
+\def\XINT_sepbyviii_end #1\relax {\relax\XINT_sepbyviii_andcount_end!}%
+\def\XINT_sepbyviii_andcount_a {\XINT_sepbyviii_andcount_b \xint_c_\xint:}%
+\def\XINT_sepbyviii_andcount_b #1\xint:#2!#3!#4!#5!#6!#7!#8!#9!%
+{%
+ #2\expandafter!\the\numexpr#3\expandafter!\the\numexpr#4\expandafter
+ !\the\numexpr#5\expandafter!\the\numexpr#6\expandafter!\the\numexpr
+ #7\expandafter!\the\numexpr#8\expandafter!\the\numexpr#9\expandafter!\the\numexpr
+ \expandafter\XINT_sepbyviii_andcount_b\the\numexpr #1+\xint_c_viii\xint:%
+}%
+\def\XINT_sepbyviii_andcount_end #1\XINT_sepbyviii_andcount_b\the\numexpr
+ #2+\xint_c_viii\xint:#3#4\W {\expandafter\xint:\the\numexpr #2+#3\xint:}%
+% \end{macrocode}
+% \subsection{\csh{XINT_rsepbyviii}}
+%
+% \lverb|This is used as
+%( \the\numexpr1\XINT_rsepbyviii <8Ndigits>$%
+%: \XINT_rsepbyviii_end_A 2345678$%
+%: \XINT_rsepbyviii_end_B 2345678\relax UV$%
+%)
+% and will produce
+%( 1<8digits>!1<8digits>\xint:1<8digits>!...
+%)
+% where the original
+% digits are organized by eight, and the order inside successive pairs of
+% blocks separated by \xint: has been reversed. Output ends either in
+% 1<8d>!1<8d>\xint:1U\xint: (even) or 1<8d>!1<8d>\xint:1V!1<8d>\xint: (odd)
+%
+% The U an V should be \numexpr1 stoppers (or will expand and be ended by !).
+% This macro is currently (1.2..1.2l) exclusively used in combination with
+% \XINT_sepandrev_andcount or \XINT_sepandrev.
+% |
+% \begin{macrocode}
+\def\XINT_rsepbyviii #1#2#3#4#5#6#7#8%
+{%
+ \XINT_rsepbyviii_b {#1#2#3#4#5#6#7#8}%
+}%
+\def\XINT_rsepbyviii_b #1#2#3#4#5#6#7#8#9%
+{%
+ #2#3#4#5#6#7#8#9\expandafter!\the\numexpr
+ 1#1\expandafter\xint:\the\numexpr 1\XINT_rsepbyviii
+}%
+\def\XINT_rsepbyviii_end_B #1\relax #2#3{#2\xint:}%
+\def\XINT_rsepbyviii_end_A #11#2\expandafter #3\relax #4#5{#5!1#2\xint:}%
+% \end{macrocode}
+% \subsection{\csh{XINT_sepandrev}}
+% \lverb|This is used typically as
+%( \romannumeral0\XINT_sepandrev <8Ndigits>$%
+%: \XINT_rsepbyviii_end_A 2345678$%
+%: \XINT_rsepbyviii_end_B 2345678\relax UV$%
+%: \R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\W
+%)
+% and will produce
+%( 1<8digits>!1<8digits>!1<8digits>!...
+%)
+% where the blocks have
+% been globally reversed. The UV here are only place holders (must be \numexpr1
+% stoppers) to share same
+% syntax as \XINT_sepandrev_andcount, they are gobbled (#2 in \XINT_sepandrev_done).|
+% \begin{macrocode}
+\def\XINT_sepandrev
+{%
+ \expandafter\XINT_sepandrev_a\the\numexpr 1\XINT_rsepbyviii
+}%
+\def\XINT_sepandrev_a {\XINT_sepandrev_b {}}%
+\def\XINT_sepandrev_b #1#2\xint:#3\xint:#4\xint:#5\xint:#6\xint:#7\xint:#8\xint:#9\xint:%
+{%
+ \xint_gob_til_R #9\XINT_sepandrev_end\R
+ \XINT_sepandrev_b {#9!#8!#7!#6!#5!#4!#3!#2!#1}%
+}%
+\def\XINT_sepandrev_end\R\XINT_sepandrev_b #1#2\W {\XINT_sepandrev_done #1}%
+\def\XINT_sepandrev_done #11#2!{ }%
+% \end{macrocode}
+% \subsection{\csh{XINT_sepandrev_andcount}}
+% \lverb|This is used typically as
+%( \romannumeral0\XINT_sepandrev_andcount <8Ndigits>$%
+%: \XINT_rsepbyviii_end_A 2345678$%
+%: \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+%: \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+%: \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
+%)
+% and will produce
+%( <length>.1<8digits>!1<8digits>!1<8digits>!...
+%)
+% where the
+% blocks have been globally reversed and <length> is the number of blocks.|
+% \begin{macrocode}
+\def\XINT_sepandrev_andcount
+{%
+ \expandafter\XINT_sepandrev_andcount_a\the\numexpr 1\XINT_rsepbyviii
+}%
+\def\XINT_sepandrev_andcount_a {\XINT_sepandrev_andcount_b 0!{}}%
+\def\XINT_sepandrev_andcount_b #1!#2#3\xint:#4\xint:#5\xint:#6\xint:#7\xint:#8\xint:#9\xint:%
+{%
+ \xint_gob_til_R #9\XINT_sepandrev_andcount_end\R
+ \expandafter\XINT_sepandrev_andcount_b \the\numexpr #1+\xint_c_i!%
+ {#9!#8!#7!#6!#5!#4!#3!#2}%
+}%
+\def\XINT_sepandrev_andcount_end\R
+ \expandafter\XINT_sepandrev_andcount_b\the\numexpr #1+\xint_c_i!#2#3#4\W
+{\expandafter\XINT_sepandrev_andcount_done\the\numexpr #3+\xint_c_xiv*#1!#2}%
+\def\XINT_sepandrev_andcount_done#1{%
+\def\XINT_sepandrev_andcount_done##1!##21##3!{\expandafter#1\the\numexpr##1-##3\xint:}%
+}\XINT_sepandrev_andcount_done{ }%
+% \end{macrocode}
+% \subsection{\csh{XINT_rev_nounsep}}
+% \lverb|This is used as
+%( \romannumeral0\XINT_rev_nounsep {}<blocks 1<8d>!>\R!\R!\R!\R!\R!\R!\R!\R!\W
+%)
+% It reverses the blocks, keeping the 1's and ! separators. Used multiple
+% times in the division algorithm. The inserted {} here is not optional.|
+% \begin{macrocode}
+\def\XINT_rev_nounsep #1#2!#3!#4!#5!#6!#7!#8!#9!%
+{%
+ \xint_gob_til_R #9\XINT_rev_nounsep_end\R
+ \XINT_rev_nounsep {#9!#8!#7!#6!#5!#4!#3!#2!#1}%
+}%
+\def\XINT_rev_nounsep_end\R\XINT_rev_nounsep #1#2\W {\XINT_rev_nounsep_done #1}%
+\def\XINT_rev_nounsep_done #11{ 1}%
+% \end{macrocode}
+% \subsection{\csh{XINT_unrevbyviii}}
+% \lverb|Used as \romannumeral0\XINT_unrevbyviii 1<8d>!....1<8d>! terminated
+% by
+%( 1;!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+%)
+% The \romannumeral in unrevbyviii_a is for special effects (expand some token
+% which was put as 1<token>! at the end of the original blocks). This
+% mechanism is used by 1.2 subtraction (still true for 1.2l).|
+% \begin{macrocode}
+\def\XINT_unrevbyviii #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
+{%
+ \xint_gob_til_R #9\XINT_unrevbyviii_a\R
+ \XINT_unrevbyviii {#9#8#7#6#5#4#3#2#1}%
+}%
+\def\XINT_unrevbyviii_a#1{%
+\def\XINT_unrevbyviii_a\R\XINT_unrevbyviii ##1##2\W
+ {\expandafter#1\romannumeral`&&@\xint_gob_til_sc ##1}%
+}\XINT_unrevbyviii_a{ }%
+% \end{macrocode}
+% \lverb|Can work with shorter ending pattern: 1;!1\R!1\R!1\R!1\R!1\R!1\R!\W
+% but the longer one of unrevbyviii is ok here too. Used currently (1.2) only
+% by addition, now (1.2c) with long ending pattern. Does the final clean up of
+% leading zeroes contrarily to general \XINT_unrevbyviii.|
+% \begin{macrocode}
+\def\XINT_smallunrevbyviii 1#1!1#2!1#3!1#4!1#5!1#6!1#7!1#8!#9\W%
+{%
+ \expandafter\XINT_cuz_small\xint_gob_til_sc #8#7#6#5#4#3#2#1%
+}%
+% \end{macrocode}
+% \subsection*{Core arithmetic}
+% \addcontentsline{toc}{subsection}{Core arithmetic}
% \lverb|The four operations have been rewritten entirely for release 1.2.
% The new routines works with separated blocks of eight digits. They all measure
% first the lengths of the arguments, even addition and subtraction (this was
@@ -18384,20 +18867,22 @@
% digits.|
%
% \subsection{\csbh{xintiAdd}, \csbh{xintiiAdd}}
+% \lverb|1.2l: \xintiiAdd made robust against non terminated input.|
% \begin{macrocode}
\def\xintiAdd {\romannumeral0\xintiadd }%
-\def\xintiadd #1{\expandafter\XINT_iadd\romannumeral0\xintnum{#1}\Z }%
+\def\xintiadd #1{\expandafter\XINT_iadd\romannumeral0\xintnum{#1}\xint:}%
\def\xintiiAdd {\romannumeral0\xintiiadd }%
-\def\xintiiadd #1{\expandafter\XINT_iiadd\romannumeral`&&@#1\Z }%
-\def\XINT_iiadd #1#2\Z #3%
+\def\xintiiadd #1{\expandafter\XINT_iiadd\romannumeral`&&@#1\xint:}%
+\def\XINT_iiadd #1#2\xint:#3%
{%
- \expandafter\XINT_add_nfork\expandafter #1\romannumeral`&&@#3\Z #2\Z
+ \expandafter\XINT_add_nfork\expandafter#1\romannumeral`&&@#3\xint:#2\xint:
}%
-\def\XINT_iadd #1#2\Z #3%
+\def\XINT_iadd #1#2\xint:#3%
{%
- \expandafter\XINT_add_nfork\expandafter #1\romannumeral0\xintnum{#3}\Z #2\Z
+ \expandafter\XINT_add_nfork\expandafter
+ #1\romannumeral0\xintnum{#3}\xint:#2\xint:
}%
-\def\XINT_add_fork #1#2\Z #3\Z {\XINT_add_nfork #1#3\Z #2\Z}%
+\def\XINT_add_fork #1#2\xint:#3\xint:{\XINT_add_nfork #1#3\xint:#2\xint:}%
\def\XINT_add_nfork #1#2%
{%
\xint_UDzerofork
@@ -18412,36 +18897,38 @@
--\XINT_add_plusplus
\krof #1#2%
}%
-\def\XINT_add_firstiszero #1\krof 0#2#3\Z #4\Z { #2#3}%
-\def\XINT_add_secondiszero #1\krof #20#3\Z #4\Z { #2#4}%
+\def\XINT_add_firstiszero #1\krof 0#2#3\xint:#4\xint:{ #2#3}%
+\def\XINT_add_secondiszero #1\krof #20#3\xint:#4\xint:{ #2#4}%
\def\XINT_add_minusminus #1#2%
{\expandafter-\romannumeral0\XINT_add_pp_a {}{}}%
\def\XINT_add_minusplus #1#2{\XINT_sub_mm_a {}#2}%
\def\XINT_add_plusminus #1#2%
{\expandafter\XINT_opp\romannumeral0\XINT_sub_mm_a #1{}}%
-\def\XINT_add_pp_a #1#2#3\Z
+\def\XINT_add_pp_a #1#2#3\xint:
{%
\expandafter\XINT_add_pp_b
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
#2#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\X #1%
}%
\let\XINT_add_plusplus \XINT_add_pp_a
-\def\XINT_add_pp_b #1.#2\X #3\Z
+% \end{macrocode}
+% \begin{macrocode}
+\def\XINT_add_pp_b #1\xint:#2\X #3\xint:
{%
\expandafter\XINT_add_checklengths
- \the\numexpr #1\expandafter.%
+ \the\numexpr #1\expandafter\xint:%
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
- 1\Z!1\Z!1\Z!1\Z!\W #21\Z!1\Z!1\Z!1\Z!\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
+ 1;!1;!1;!1;!\W #21;!1;!1;!1;!\W
1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
}%
% \end{macrocode}
@@ -18448,7 +18935,7 @@
% \lverb|I keep #1.#2. to check if at most 6 + 6 base 10^8 digits which can be
% treated faster for final reverse. But is this overhead at all useful ? |
% \begin{macrocode}
-\def\XINT_add_checklengths #1.#2.%
+\def\XINT_add_checklengths #1\xint:#2\xint:%
{%
\ifnum #2>#1
\expandafter\XINT_add_exchange
@@ -18455,13 +18942,13 @@
\else
\expandafter\XINT_add_A
\fi
- #1.#2.%
+ #1\xint:#2\xint:%
}%
-\def\XINT_add_exchange #1.#2.#3\W #4\W
+\def\XINT_add_exchange #1\xint:#2\xint:#3\W #4\W
{%
- \XINT_add_A #2.#1.#4\W #3\W
+ \XINT_add_A #2\xint:#1\xint:#4\W #3\W
}%
-\def\XINT_add_A #1.#2.%
+\def\XINT_add_A #1\xint:#2\xint:%
{%
\ifnum #1>\xint_c_vi
\expandafter\XINT_add_aa
@@ -18475,85 +18962,92 @@
% \end{macrocode}
% \lverb|2 as first token of #1 stands for "no carry", 3 will mean a carry (we
% are adding 1<8digits> to 1<8digits>.) Version 1.2c has terminators of the
-% shape 1\Z!, replacing the \Z! used in 1.2.
+% shape 1;!, replacing the \Z! used in 1.2.
%
-% Call: \the\numexpr\XINT_add_a 2#11\Z!1\Z!1\Z!1\Z!\W #21\Z!1\Z!1\Z!1\Z!\W
+% Call: \the\numexpr\XINT_add_a 2#11;!1;!1;!1;!\W #21;!1;!1;!1;!\W
% where #1 and #2 are blocks of 1<8d>!, and #1 is at most as long as #2. This
% last requirement is a bit annoying (if one wants to do recursive algorithms
% but not have to check lengths), and I will probably remove it at some point.
%
% Output: blocks of 1<8d>! representing the addition, (least significant
-% first), and a final 1\Z!. In recursive algotithm this 1\Z! terminator can
+% first), and a final 1;!. In recursive algotithm this 1;! terminator can
% thus conveniently be reused as part of input terminator (up to the length
-% problem).|
+% problem).
+%
+%|
% \begin{macrocode}
-\def\XINT_add_a #1!#2!#3!#4!#5\W #6!#7!#8!#9!%
+\def\XINT_add_a #1!#2!#3!#4!#5\W
+ #6!#7!#8!#9!%
{%
- \XINT_add_b #1!#6!#2!#7!#3!#8!#4!#9!#5\W
+ \XINT_add_b
+ #1!#6!#2!#7!#3!#8!#4!#9!%
+ #5\W
}%
\def\XINT_add_b #11#2#3!#4!%
{%
- \xint_gob_til_Z #2\XINT_add_bi \Z
- \expandafter\XINT_add_c\the\numexpr#1+1#2#3+#4-\xint_c_ii.%
+ \xint_gob_til_sc #2\XINT_add_bi ;%
+ \expandafter\XINT_add_c\the\numexpr#1+1#2#3+#4-\xint_c_ii\xint:%
}%
-\def\XINT_add_bi\Z\expandafter\XINT_add_c
- \the\numexpr#1+#2+#3-\xint_c_ii.#4!#5!#6!#7!#8!#9!\W
+\def\XINT_add_bi;\expandafter\XINT_add_c
+ \the\numexpr#1+#2+#3-\xint_c_ii\xint:#4!#5!#6!#7!#8!#9!\W
{%
\XINT_add_k #1#3!#5!#7!#9!%
}%
-\def\XINT_add_c #1#2.%
+\def\XINT_add_c #1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_add_d #1%
}%
\def\XINT_add_d #11#2#3!#4!%
{%
- \xint_gob_til_Z #2\XINT_add_di \Z
- \expandafter\XINT_add_e\the\numexpr#1+1#2#3+#4-\xint_c_ii.%
+ \xint_gob_til_sc #2\XINT_add_di ;%
+ \expandafter\XINT_add_e\the\numexpr#1+1#2#3+#4-\xint_c_ii\xint:%
}%
-\def\XINT_add_di\Z\expandafter\XINT_add_e
- \the\numexpr#1+#2+#3-\xint_c_ii.#4!#5!#6!#7!#8\W
+\def\XINT_add_di;\expandafter\XINT_add_e
+ \the\numexpr#1+#2+#3-\xint_c_ii\xint:#4!#5!#6!#7!#8\W
{%
\XINT_add_k #1#3!#5!#7!%
}%
-\def\XINT_add_e #1#2.%
+\def\XINT_add_e #1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_add_f #1%
}%
\def\XINT_add_f #11#2#3!#4!%
{%
- \xint_gob_til_Z #2\XINT_add_fi \Z
- \expandafter\XINT_add_g\the\numexpr#1+1#2#3+#4-\xint_c_ii.%
+ \xint_gob_til_sc #2\XINT_add_fi ;%
+ \expandafter\XINT_add_g\the\numexpr#1+1#2#3+#4-\xint_c_ii\xint:%
}%
-\def\XINT_add_fi\Z\expandafter\XINT_add_g
- \the\numexpr#1+#2+#3-\xint_c_ii.#4!#5!#6\W
+\def\XINT_add_fi;\expandafter\XINT_add_g
+ \the\numexpr#1+#2+#3-\xint_c_ii\xint:#4!#5!#6\W
{%
\XINT_add_k #1#3!#5!%
}%
-\def\XINT_add_g #1#2.%
+\def\XINT_add_g #1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_add_h #1%
}%
\def\XINT_add_h #11#2#3!#4!%
{%
- \xint_gob_til_Z #2\XINT_add_hi \Z
- \expandafter\XINT_add_i\the\numexpr#1+1#2#3+#4-\xint_c_ii.%
+ \xint_gob_til_sc #2\XINT_add_hi ;%
+ \expandafter\XINT_add_i\the\numexpr#1+1#2#3+#4-\xint_c_ii\xint:%
}%
-\def\XINT_add_hi\Z
- \expandafter\XINT_add_i\the\numexpr#1+#2+#3-\xint_c_ii.#4\W
+\def\XINT_add_hi;%
+ \expandafter\XINT_add_i\the\numexpr#1+#2+#3-\xint_c_ii\xint:#4\W
{%
\XINT_add_k #1#3!%
}%
-\def\XINT_add_i #1#2.%
+\def\XINT_add_i #1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_add_a #1%
}%
+% \end{macrocode}
+% \begin{macrocode}
\def\XINT_add_k #1{\if #12\expandafter\XINT_add_ke\else\expandafter\XINT_add_l \fi}%
-\def\XINT_add_ke #11\Z #2\W {\XINT_add_kf #11\Z!}%
+\def\XINT_add_ke #11;#2\W {\XINT_add_kf #11;!}%
\def\XINT_add_kf 1{1\relax }%
-\def\XINT_add_l 1#1#2{\xint_gob_til_Z #1\XINT_add_lf \Z \XINT_add_m 1#1#2}%
-\def\XINT_add_lf #1\W {1\relax 00000001!1\Z!}%
-\def\XINT_add_m #1!{\expandafter\XINT_add_n\the\numexpr\xint_c_i+#1.}%
-\def\XINT_add_n #1#2.{1#2\expandafter!\the\numexpr\XINT_add_o #1}%
+\def\XINT_add_l 1#1#2{\xint_gob_til_sc #1\XINT_add_lf ;\XINT_add_m 1#1#2}%
+\def\XINT_add_lf #1\W {1\relax 00000001!1;!}%
+\def\XINT_add_m #1!{\expandafter\XINT_add_n\the\numexpr\xint_c_i+#1\xint:}%
+\def\XINT_add_n #1#2\xint:{1#2\expandafter!\the\numexpr\XINT_add_o #1}%
% \end{macrocode}
% \lverb|Here 2 stands for "carry", and 1 for "no carry" (we have been adding
% 1 to 1<8digits>.)|
@@ -18560,20 +19054,155 @@
% \begin{macrocode}
\def\XINT_add_o #1{\if #12\expandafter\XINT_add_l\else\expandafter\XINT_add_ke \fi}%
% \end{macrocode}
+% \subsection{\csh{xintCmp}, \csh{xintiiCmp}}
+% \lverb|Moved from xint.sty to xintcore.sty and rewritten for 1.2l.
+%
+% 1.2l's \xintiiCmp is robust against non terminated input.
+% |
+% \begin{macrocode}
+\def\xintCmp {\romannumeral0\xintcmp }%
+\def\xintcmp #1{\expandafter\XINT_icmp\romannumeral0\xintnum{#1}\xint:}%
+\def\xintiiCmp {\romannumeral0\xintiicmp }%
+\def\xintiicmp #1{\expandafter\XINT_iicmp\romannumeral`&&@#1\xint:}%
+\def\XINT_iicmp #1#2\xint:#3%
+{%
+ \expandafter\XINT_cmp_nfork\expandafter #1\romannumeral`&&@#3\xint:#2\xint:
+}%
+\def\XINT_icmp #1#2\xint:#3%
+{%
+ \expandafter\XINT_cmp_nfork\expandafter #1\romannumeral0\xintnum{#3}\xint:#2\xint:
+}%
+\def\XINT_cmp_nfork #1#2%
+{%
+ \xint_UDzerofork
+ #1\XINT_cmp_firstiszero
+ #2\XINT_cmp_secondiszero
+ 0{}%
+ \krof
+ \xint_UDsignsfork
+ #1#2\XINT_cmp_minusminus
+ #1-\XINT_cmp_minusplus
+ #2-\XINT_cmp_plusminus
+ --\XINT_cmp_plusplus
+ \krof #1#2%
+}%
+\def\XINT_cmp_firstiszero #1\krof 0#2#3\xint:#4\xint:
+{%
+ \xint_UDzerominusfork
+ #2-{ 0}%
+ 0#2{ 1}%
+ 0-{ -1}%
+ \krof
+}%
+\def\XINT_cmp_secondiszero #1\krof #20#3\xint:#4\xint:
+{%
+ \xint_UDzerominusfork
+ #2-{ 0}%
+ 0#2{ -1}%
+ 0-{ 1}%
+ \krof
+}%
+\def\XINT_cmp_plusminus #1\xint:#2\xint:{ 1}%
+\def\XINT_cmp_minusplus #1\xint:#2\xint:{ -1}%
+\def\XINT_cmp_minusminus
+ --{\expandafter\XINT_opp\romannumeral0\XINT_cmp_plusplus {}{}}%
+\def\XINT_cmp_plusplus #1#2#3\xint:
+{%
+ \expandafter\XINT_cmp_pp
+ \the\numexpr\expandafter\XINT_sepbyviii_andcount
+ \romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
+ #2#3\XINT_sepbyviii_end 2345678\relax
+ \xint_c_vii!\xint_c_vi!\xint_c_v!\xint_c_iv!%
+ \xint_c_iii!\xint_c_ii!\xint_c_i!\xint_c_\W
+ #1%
+}%
+\def\XINT_cmp_pp #1\xint:#2\xint:#3\xint:
+{%
+ \expandafter\XINT_cmp_checklengths
+ \the\numexpr #2\expandafter\xint:%
+ \the\numexpr\expandafter\XINT_sepbyviii_andcount
+ \romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
+ #3\XINT_sepbyviii_end 2345678\relax
+ \xint_c_vii!\xint_c_vi!\xint_c_v!\xint_c_iv!%
+ \xint_c_iii!\xint_c_ii!\xint_c_i!\xint_c_\W
+ #1;!1;!1;!1;!\W
+}%
+\def\XINT_cmp_checklengths #1\xint:#2\xint:#3\xint:
+{%
+ \ifnum #1=#3
+ \expandafter\xint_firstoftwo
+ \else
+ \expandafter\xint_secondoftwo
+ \fi
+ \XINT_cmp_a {\XINT_cmp_distinctlengths {#1}{#3}}#2;!1;!1;!1;!\W
+}%
+\def\XINT_cmp_distinctlengths #1#2#3\W #4\W
+{%
+ \ifnum #1>#2
+ \expandafter\xint_firstoftwo
+ \else
+ \expandafter\xint_secondoftwo
+ \fi
+ { -1}{ 1}%
+}%
+\def\XINT_cmp_a 1#1!1#2!1#3!1#4!#5\W 1#6!1#7!1#8!1#9!%
+{%
+ \xint_gob_til_sc #1\XINT_cmp_equal ;%
+ \ifnum #1>#6 \XINT_cmp_gt\fi
+ \ifnum #1<#6 \XINT_cmp_lt\fi
+ \xint_gob_til_sc #2\XINT_cmp_equal ;%
+ \ifnum #2>#7 \XINT_cmp_gt\fi
+ \ifnum #2<#7 \XINT_cmp_lt\fi
+ \xint_gob_til_sc #3\XINT_cmp_equal ;%
+ \ifnum #3>#8 \XINT_cmp_gt\fi
+ \ifnum #3<#8 \XINT_cmp_lt\fi
+ \xint_gob_til_sc #4\XINT_cmp_equal ;%
+ \ifnum #4>#9 \XINT_cmp_gt\fi
+ \ifnum #4<#9 \XINT_cmp_lt\fi
+ \XINT_cmp_a #5\W
+}%
+\def\XINT_cmp_lt#1{\def\XINT_cmp_lt\fi ##1\W ##2\W {\fi#1-1}}\XINT_cmp_lt{ }%
+\def\XINT_cmp_gt#1{\def\XINT_cmp_gt\fi ##1\W ##2\W {\fi#11}}\XINT_cmp_gt{ }%
+\def\XINT_cmp_equal #1\W #2\W { 0}%
+% \end{macrocode}
% \subsection{\csh{xintiSub}, \csh{xintiiSub}}
-% \lverb|Entirely rewritten for 1.2.|
+% \lverb|Entirely rewritten for 1.2.
+%
+% Refactored at 1.2l. I was initially aiming at clinching some internal format
+% of the type 1<8digits>!....1<8digits>! for chaining the arithmetic
+% operations (as a preliminary step to decided upon some internal format for
+% $xintfracnameimp macros), thus I wanted to uniformize delimiters in
+% particular and have some core macros inputting and outputting such formats.
+% But the way division is implemented makes it currently very hard to obtain a
+% satisfactory solution. For subtraction I got there almost, but there was
+% added overhead and, as the core sub-routine still assumed the shorter number
+% will be positioned first, one would need to record the length also in the
+% basic internal format, or add the overhead to not make assumption on which
+% one is shorter. I thus but back-tracked my steps but in passing I improved
+% the efficiency (probably) in the worst case branch.
+%
+% The other reason for backtracking was in relation with the decimal numbers.
+% Having a core format in base 10^8 but ultimately the radix is actually 10
+% leads to complications. I could use radix 10^8 for \xintiiexpr only, but
+% then I need to make it compatible with sub-\xintiiexpr in \xintexpr, etc...
+% there are many issues of this type.
+%
+% I considered also an approach like in the 1.2l \xintiiCmp, but decided to
+% stick with the method here for now.|
% \begin{macrocode}
\def\xintiiSub {\romannumeral0\xintiisub }%
-\def\xintiisub #1{\expandafter\XINT_iisub\romannumeral`&&@#1\Z }%
-\def\XINT_iisub #1#2\Z #3%
+\def\xintiisub #1{\expandafter\XINT_iisub\romannumeral`&&@#1\xint:}%
+\def\XINT_iisub #1#2\xint:#3%
{%
- \expandafter\XINT_sub_nfork\expandafter #1\romannumeral`&&@#3\Z #2\Z
+ \expandafter\XINT_sub_nfork\expandafter
+ #1\romannumeral`&&@#3\xint:#2\xint:
}%
-\def\xintiSub {\romannumeral0\xintisub }%
-\def\xintisub #1{\expandafter\XINT_isub\romannumeral0\xintnum{#1}\Z }%
-\def\XINT_isub #1#2\Z #3%
+\def\xintiSub {\romannumeral0\xintisub }%
+\def\xintisub #1{\expandafter\XINT_isub\romannumeral0\xintnum{#1}\xint:}%
+\def\XINT_isub #1#2\xint:#3%
{%
- \expandafter\XINT_sub_nfork\expandafter #1\romannumeral0\xintnum{#3}\Z #2\Z
+ \expandafter\XINT_sub_nfork\expandafter
+ #1\romannumeral0\xintnum{#3}\xint:#2\xint:
}%
\def\XINT_sub_nfork #1#2%
{%
@@ -18589,8 +19218,8 @@
--\XINT_sub_plusplus
\krof #1#2%
}%
-\def\XINT_sub_firstiszero #1\krof 0#2#3\Z #4\Z {\XINT_opp #2#3}%
-\def\XINT_sub_secondiszero #1\krof #20#3\Z #4\Z { #2#4}%
+\def\XINT_sub_firstiszero #1\krof 0#2#3\xint:#4\xint:{\XINT_opp #2#3}%
+\def\XINT_sub_secondiszero #1\krof #20#3\xint:#4\xint:{ #2#4}%
\def\XINT_sub_plusminus #1#2{\XINT_add_pp_a #1{}}%
\def\XINT_sub_plusplus #1#2%
{\expandafter\XINT_opp\romannumeral0\XINT_sub_mm_a #1#2}%
@@ -18597,30 +19226,35 @@
\def\XINT_sub_minusplus #1#2%
{\expandafter-\romannumeral0\XINT_add_pp_a {}#2}%
\def\XINT_sub_minusminus #1#2{\XINT_sub_mm_a {}{}}%
-\def\XINT_sub_mm_a #1#2#3\Z
+% \end{macrocode}
+% \begin{macrocode}
+\def\XINT_sub_mm_a #1#2#3\xint:
{%
\expandafter\XINT_sub_mm_b
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
#2#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\X #1%
}%
-\def\XINT_sub_mm_b #1.#2\X #3\Z
+\def\XINT_sub_mm_b #1\xint:#2\X #3\xint:
{%
\expandafter\XINT_sub_checklengths
- \the\numexpr #1\expandafter.%
+ \the\numexpr #1\expandafter\xint:%
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax \xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
- \Z!\Z!\Z!\Z!\W #2\Z!\Z!\Z!\Z!\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
+ 1;!1;!1;!1;!\W
+ #21;!1;!1;!1;!\W
+ 1;!1\R!1\R!1\R!1\R!%
+ 1\R!1\R!1\R!1\R!\W
}%
-\def\XINT_sub_checklengths #1.#2.%
+\def\XINT_sub_checklengths #1\xint:#2\xint:%
{%
\ifnum #2>#1
\expandafter\XINT_sub_exchange
@@ -18632,142 +19266,133 @@
{%
\expandafter\XINT_opp\romannumeral0\XINT_sub_aa #2\W #1\W
}%
-\def\XINT_sub_aa {\expandafter\XINT_sub_out\the\numexpr\XINT_sub_a \xint_c_i }%
-% \end{macrocode}
-% \lverb|The {} after \XINT_unrevbyviii could be removed, but attention then
-% at \XINT_sub_startrescue which must be modified (no need for #1).|
-% \begin{macrocode}
-\def\XINT_sub_out #1\Z #2#3\W
+\def\XINT_sub_aa
{%
- \if-#2\expandafter\XINT_sub_startrescue\fi
- \expandafter\XINT_cuz_small
- \romannumeral0\XINT_unrevbyviii {}#11\Z!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+ \expandafter\XINT_sub_out\the\numexpr\XINT_sub_a\xint_c_i
}%
% \end{macrocode}
+% \lverb|The post-processing (clean-up of zeros, or rescue of situation with
+% A-B where actually B turns out bigger than A) will be done by a macro which
+% depends on circumstances and will be initially last token before the
+% reversion done by \XINT_unrevbyviii.|
+% \begin{macrocode}
+\def\XINT_sub_out {\XINT_unrevbyviii{}}%
+% \end{macrocode}
% \lverb|1 as first token of #1 stands for "no carry", 0 will mean a carry.
%
-% Call: \the\numexpr
-% \XINT_sub_a 1#1\Z!\Z!\Z!\Z!\W #2\Z!\Z!\Z!\Z!\W where #1 and #2
-% are blocks of 1<8d>!, and #1 *must* be at most as long as #2.
+%( Call: \the\numexpr
+%: \XINT_sub_a 1#11;!1;!1;!1;!\W
+%: #21;!1;!1;!1;!\W
+%)
+% where #1 and #2
+% are blocks of 1<8d>!, #1 (=B) *must* be at most as long as #2 (=A),
+% (in radix 10^8)
+% and the routine wants to compute #2-#1 = A - B
%
-% The routine wants to compute #2-#1.
+% 1.2l uses 1;! delimiters to match those of addition (and multiplication).
+% But in the end I reverted the code branch which made it possible to chain
+% such operations keeping internal format in 8 digits blocks throughout.
%
-% Notice that currently the terminators on input differ from those for
-% addition. Also, currently (1.2f) the routine can not be called without final
-% reversal and clean up of the result.
-%
% \numexpr governed expansion stops with various possibilities:
%
-% 1. #1 was shorter (in number of 8 digits blocks) than #2.
+%- Type Ia: #1 shorter than #2, no final carry
+%- Type Ib: #1 shorter than #2, a final carry but next block of #2 > 1
+%- Type Ica: #1 shorter than #2, a final carry, next block of #2 is final and = 1
+%- Type Icb: as Ica except that 00000001 block from #2 was not final
+%- Type Id: #1 shorter than #2, a final carry, next block of #2 = 0
+%- Type IIa: #1 same length as #2, turns out it was <= #2.
+%- Type IIb: #1 same length as #2, but turned out > #2.
%
-% *1a There may be no carry in which case we end up with$\
-% 1<8d>!...1<8d>!\Z!\Z!\Z!\Z!\W
+% Various type of post actions are then needed:
%
-% If there is a carry things are more complicated.
+%- Ia: clean up of zeros in most significant block of 8 digits
%
-% *1b If the first hit block of #2 is > 1 no problem we are like in the
-% no-carry case.
+%- Ib: as Ia
%
-% *1c If it is exactly 1 then we will have leading zeros; but there may be
-% also before that arbitrarily many produced zeros, all these leading zeros
-% will have to be cleaned up. This is done via ending the expansion with the
-% shape
+%- Ic: there may be significant blocks of 8 zeros to clean up from result.
+% Only case Ica may have arbitrarily many of them, case Icb has only one such
+% block.
%
-% 1<8d>!...1<8d>!1\XINT_cuz_byviii!\Z 0\W\R
+%- Id: blocks of 99999999 may propagate and there might a be final zero block
+% created which has to be cleaned up.
%
-% *1d If the block value is zero, subtraction produces 99999999 and goes on.
-% This is the only situation where the carry can propagate. This case can
-% never produce extra blocks of leading zeros but may well end up with an ending
-% zero block. In this subcase, the \numexpr is then made to stop with a 1!.
-% This 1! will disappear during final reverse.
+%- IIa: arbitrarily many zeros might have to be removed.
%
-% 2a. #1 was of same length as #2, but <= #2. Then we end up expansion with$\
-% 1<8d>!...1<8d>!1\XINT_cuz_byviii!\Z 0\W\R$\
-% and the blocks will have to cleaned up of leading zeroes after reversal.
+%- IIb: We wanted #2-#1 = - (#1-#2), but we got 10^{8N}+#2 -#1 = 10^{8N}-(#1-#2).
+% We need to do the correction then we are as in IIa situation, except that
+% final result can not be zero.
%
-% 2b. #1 was of same length as #2, but > #2. Then we end up with blocks
-% 1<8d>!...1<8d>! followed by -1\Z-\W
-%
-% Thus \XINT_sub_out examines the token after the first \Z, which may be ! or
-% 0 or -. If ! or 0, \XINT_unrevbyviii will be executed (gobbling a possible
-% final 1!), and followed in case 2a or 1c by \XINT_cuz_byviii (note the extra \R
-% which terminates it), and then in both 1* and 2a by \XINT_cuz_small.
-%
-% If we were in 2b we proceed to \XINT_sub_startrescue which I will comment
-% another day (the extra -1 at the end from -1\Z-\W will become a -1! and the
-% - will serve in \XINT_sub_rescue_d as loop terminator).
-%
-% Currently (1.2f) we can not easily use these low level routines in a binary
-% split approach due to the fact that first input must be at most as long as
-% second but also because the final reversal is not in a common second stage,
-% due to the separate treatment for case 2b.
-%
-% For the record: subtraction was correct (I think) in xint releases up to
-% 1.2, but 1.2 had a broken treatment of the 1d case. For example \xintiiSub
-% {10000000112345678}{12345679} produced 99999999. This got fixed in 1.2c, but
-% that fix broke the 1c case :((, for example \xintiiSub
-% {10000000000000000}{9999999999999997} was now returning 000000003. Alas.
-%
-% This was only realized later on 2016/02/29 (in fact it impacted
-% \xintiiSqrt). Hopefully 1.2f got it right at last. |
+% The 1.2l method for this correction is (presumably, testing takes lots of
+% time, which I do not have) more efficient than in 1.2 release. |
% \begin{macrocode}
\def\XINT_sub_a #1!#2!#3!#4!#5\W #6!#7!#8!#9!%
{%
- \XINT_sub_b #1!#6!#2!#7!#3!#8!#4!#9!#5\W
+ \XINT_sub_b
+ #1!#6!#2!#7!#3!#8!#4!#9!%
+ #5\W
}%
-\def\XINT_sub_b #1#2#3!#4!%
+% \end{macrocode}
+% \lverb|As 1.2l code uses 1<8digits>! blocks one has to be careful with
+% the carry digit 1 or 0: A #11#2#3 pattern would result into an empty #1
+% if the carry digit which is upfront is 1, rather than setting #1=1.|
+% \begin{macrocode}
+\def\XINT_sub_b #1#2#3#4!#5!%
{%
- \xint_gob_til_Z #2\XINT_sub_bi \Z
- \expandafter\XINT_sub_c\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \xint_gob_til_sc #3\XINT_sub_bi ;%
+ \expandafter\XINT_sub_c\the\numexpr#1+1#5-#3#4-\xint_c_i\xint:%
}%
-\def\XINT_sub_c 1#1#2.%
+\def\XINT_sub_c 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_sub_d #1%
}%
-\def\XINT_sub_d #1#2#3!#4!%
+\def\XINT_sub_d #1#2#3#4!#5!%
{%
- \xint_gob_til_Z #2\XINT_sub_di \Z
- \expandafter\XINT_sub_e\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \xint_gob_til_sc #3\XINT_sub_di ;%
+ \expandafter\XINT_sub_e\the\numexpr#1+1#5-#3#4-\xint_c_i\xint:
}%
-\def\XINT_sub_e 1#1#2.%
+\def\XINT_sub_e 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_sub_f #1%
}%
-\def\XINT_sub_f #1#2#3!#4!%
+\def\XINT_sub_f #1#2#3#4!#5!%
{%
- \xint_gob_til_Z #2\XINT_sub_fi \Z
- \expandafter\XINT_sub_g\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \xint_gob_til_sc #3\XINT_sub_fi ;%
+ \expandafter\XINT_sub_g\the\numexpr#1+1#5-#3#4-\xint_c_i\xint:
}%
-\def\XINT_sub_g 1#1#2.%
+\def\XINT_sub_g 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_sub_h #1%
}%
-\def\XINT_sub_h #1#2#3!#4!%
+\def\XINT_sub_h #1#2#3#4!#5!%
{%
- \xint_gob_til_Z #2\XINT_sub_hi \Z
- \expandafter\XINT_sub_i\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \xint_gob_til_sc #3\XINT_sub_hi ;%
+ \expandafter\XINT_sub_i\the\numexpr#1+1#5-#3#4-\xint_c_i\xint:
}%
-\def\XINT_sub_i 1#1#2.%
+\def\XINT_sub_i 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_sub_a #1%
}%
-\def\XINT_sub_bi\Z
- \expandafter\XINT_sub_c\the\numexpr#1+1#2-#3.#4!#5!#6!#7!#8!#9!\W
+\def\XINT_sub_bi;%
+ \expandafter\XINT_sub_c\the\numexpr#1+1#2-#3\xint:
+ #4!#5!#6!#7!#8!#9!\W
{%
\XINT_sub_k #1#2!#5!#7!#9!%
}%
-\def\XINT_sub_di\Z
- \expandafter\XINT_sub_e\the\numexpr#1+1#2-#3.#4!#5!#6!#7!#8\W
+\def\XINT_sub_di;%
+ \expandafter\XINT_sub_e\the\numexpr#1+1#2-#3\xint:
+ #4!#5!#6!#7!#8\W
{%
\XINT_sub_k #1#2!#5!#7!%
}%
-\def\XINT_sub_fi\Z
- \expandafter\XINT_sub_g\the\numexpr#1+1#2-#3.#4!#5!#6\W
+\def\XINT_sub_fi;%
+ \expandafter\XINT_sub_g\the\numexpr#1+1#2-#3\xint:
+ #4!#5!#6\W
{%
\XINT_sub_k #1#2!#5!%
}%
-\def\XINT_sub_hi\Z
- \expandafter\XINT_sub_i\the\numexpr#1+1#2-#3.#4\W
+\def\XINT_sub_hi;%
+ \expandafter\XINT_sub_i\the\numexpr#1+1#2-#3\xint:
+ #4\W
{%
\XINT_sub_k #1#2!%
}%
@@ -18777,113 +19402,141 @@
%
% If not, then we are certain that even if there is carry it will not
% propagate beyond the end of A. But it may propagate far transforming chains
-% of 00000000 into 99999999, and if it does go to the final block which is
-% just 1<00000001>!, we will have those eight zeros to clean up. (but we have
-% to be careful that if we encounter 1<00000001>! and this is not the final
-% block, we should not make something silly either).
+% of 00000000 into 99999999, and if it does go to the final block which possibly is
+% just 1<00000001>!, we will have those eight zeros to clean up.
%
-% There is the possibility that A has exactly one more <eight-digits> block
-% than B and that this block is exactly 1. In that case there can be
-% arbitrarily many leading zeros to clean up from A-B. This was done correctly
-% up to 1.2b but got broken in 1.2c. Belatedly fixed in 1.2f.
-%
-% If we have simultaneously reached the end of A, then if B was smaller there
-% might be arbitrarily many zeroes to clean up, if it was larger, we will have
-% to rescue the whole thing.|
+% If A and B have the same length (in base 10^8) then arbitrarily many zeros
+% might have to be cleaned up, and if A<B, the whole result will have to be
+% complemented first.|
% \begin{macrocode}
-\def\XINT_sub_k #1#2%
+\def\XINT_sub_k #1#2#3%
{%
- \xint_gob_til_Z #2\XINT_sub_p\Z \XINT_sub_l #1#2%
+ \xint_gob_til_sc #3\XINT_sub_p;\XINT_sub_l #1#2#3%
}%
-\def\XINT_sub_l #1{\xint_UDzerofork #1\XINT_sub_l_carry 0\XINT_sub_l_nocarry\krof}%
-\def\XINT_sub_l_nocarry 1{1\relax }%
+\def\XINT_sub_l #1%
+ {\xint_UDzerofork #1\XINT_sub_l_carry 0\XINT_sub_l_Ia\krof}%
+\def\XINT_sub_l_Ia 1#1;!#2\W{1\relax#1;!1\XINT_sub_fix_none!}%
+% \end{macrocode}
+% \lverb|
+%
+% |
+% \begin{macrocode}
\def\XINT_sub_l_carry 1#1!{\ifcase #1
- \expandafter \XINT_sub_l_zeroa\or\expandafter\XINT_sub_l_one\else
- \expandafter \XINT_sub_l_done\fi 1#1!}%
-\def\XINT_sub_l_done {-\xint_c_i+}%
-\def\XINT_sub_l_one 1#1!#2%
+ \expandafter \XINT_sub_l_Id
+ \or \expandafter \XINT_sub_l_Ic
+ \else\expandafter \XINT_sub_l_Ib\fi 1#1!}%
+\def\XINT_sub_l_Ib #1;#2\W {-\xint_c_i+#1;!1\XINT_sub_fix_none!}%
+\def\XINT_sub_l_Ic 1#1!1#2#3!#4;#5\W
{%
- \xint_gob_til_Z #2\XINT_sub_l_oneone\Z 1\relax 00000000!#2%
+ \xint_gob_til_sc #2\XINT_sub_l_Ica;%
+ 1\relax 00000000!1#2#3!#4;!1\XINT_sub_fix_none!%
}%
-\def\XINT_sub_l_oneone #1\W {1\relax \XINT_cuz_byviii!\Z 0\W\R }%
-\def\XINT_sub_l_zeroa 1#1!{199999999\expandafter!\the\numexpr \XINT_sub_l_zerob }%
-\def\XINT_sub_l_zerob 1#1!{\ifcase #1
- \expandafter \XINT_sub_l_zeroa\or\expandafter\XINT_sub_l_zone\else
- \expandafter \XINT_sub_l_done\fi 1#1!}%
-\def\XINT_sub_l_zone 1#1!#2%
+% \end{macrocode}
+% \lverb|&
+% We need to add some extra delimiters at the end for post-action by
+% \XINT_num, so we first grab the material up to \W
+% |
+% \begin{macrocode}
+\def\XINT_sub_l_Ica#1\W
{%
- \xint_gob_til_Z #2\XINT_sub_l_zoneone\Z 1\relax 00000000!#2%
+ 1;!1\XINT_sub_fix_cuz!%
+ 1;!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+ \xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
-\def\XINT_sub_l_zoneone\Z 1\relax 00000000{1}%
+\def\XINT_sub_l_Id 1#1!%
+ {199999999\expandafter!\the\numexpr \XINT_sub_l_Id_a}%
+\def\XINT_sub_l_Id_a 1#1!{\ifcase #1
+ \expandafter \XINT_sub_l_Id
+ \or \expandafter \XINT_sub_l_Id_b
+ \else\expandafter \XINT_sub_l_Ib\fi 1#1!}%
+\def\XINT_sub_l_Id_b 1#1!1#2#3!#4;#5\W
+{%
+ \xint_gob_til_sc #2\XINT_sub_l_Ida;%
+ 1\relax 00000000!1#2#3!#4;!1\XINT_sub_fix_none!%
+}%
+\def\XINT_sub_l_Ida#1\XINT_sub_fix_none{1;!1\XINT_sub_fix_none!}%
% \end{macrocode}
-% \lverb|Here we are in the situation were the two inputs had the same length
-% in base 10^8. If #1=0 we bitterly discover that first input was greater than
-% second input despite having same length (in base 10^8). The \numexpr will
-% expand beyond the -1 or 1. If #1=1 we had no carry but perhaps the result
-% will have plenty of zeroes to clean-up. The result might even be simply zero.|
+% \lverb|&
+% This is the case where both operands have same 10^8-base length.
+%
+% We were handling A-B but perhaps B>A. The situation with A=B is also
+% annoying because we then have to clean up all zeros but don't know where to
+% stop (if A>B the first non-zero 8 digits block would tell use when).
+%
+% Here again we need to grab #3\W to position the actually used terminating
+% delimiters.
+% |
% \begin{macrocode}
-\def\XINT_sub_p\Z\XINT_sub_l #1#2\W
+\def\XINT_sub_p;\XINT_sub_l #1#2\W #3\W
{%
\xint_UDzerofork
- #1{-1\relax\Z -\W}%
- 0{1\relax \XINT_cuz_byviii!\Z 0\W\R }%
+ #1{1;!1\XINT_sub_fix_neg!%
+ 1;!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+ \xint_bye2345678\xint_bye1099999988\relax}% A - B, B > A
+ 0{1;!1\XINT_sub_fix_cuz!%
+ 1;!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W}%
\krof
+ \xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
% \end{macrocode}
-% \lverb|We arrive here if #2-#1 concluded #1>#2 (both of the same length in
-% base 10^8). To be commented. Here also before the \XINT_sub_rescue_finish
-% there will be an ending 1! which will disappear only due to
-% \XINT_unrevbyviii. The final \R is for \XINT_cuz.|
+% \lverb|Routines for post-processing after reversal, and removal of
+% separators. It is a matter of cleaning up zeros, and possibly in the bad
+% case to take a complement before that.|
% \begin{macrocode}
-\def\XINT_sub_startrescue\expandafter\XINT_cuz_small
- \romannumeral0\XINT_unrevbyviii #1#2\Z!#3\W
+\def\XINT_sub_fix_none;{\XINT_cuz_small}%
+\def\XINT_sub_fix_cuz ;{\expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop}%
+% \end{macrocode}
+% \lverb|Case with A and B same number of digits in base 10^8 and B>A.
+%
+% 1.2l subtle chaining on the model of the 1.2i rewrite of \xintInc and
+% similar routines. After taking complement, leading zeroes need to be
+% cleaned up as in B<=A branch.|
+% \begin{macrocode}
+\def\XINT_sub_fix_neg;%
{%
- \expandafter\XINT_sub_rescue_finish
- \the\numexpr\XINT_sub_rescue_a #2!%
- 1\Z!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W \R
+ \expandafter-\romannumeral0\expandafter
+ \XINT_sub_comp_finish\the\numexpr\XINT_sub_comp_loop
}%
-\def\XINT_sub_rescue_finish
- {\expandafter-\romannumeral0\expandafter\XINT_cuz\romannumeral0\XINT_unrevbyviii {}}%
-\def\XINT_sub_rescue_a #1!%
+\def\XINT_sub_comp_finish 0{\XINT_sub_fix_cuz;}%
+\def\XINT_sub_comp_loop #1#2#3#4#5#6#7#8%
{%
- \expandafter\XINT_sub_rescue_c\the\numexpr \xint_c_xii_e_viii-#1.%
+ \expandafter\XINT_sub_comp_clean
+ \the\numexpr \xint_c_xi_e_viii_mone-#1#2#3#4#5#6#7#8\XINT_sub_comp_loop
}%
-\def\XINT_sub_rescue_c 1#1#2.%
-{%
- 1#2\expandafter!\the\numexpr\XINT_sub_rescue_d #1%
-}%
-\def\XINT_sub_rescue_d #1#2#3!%
-{%
- \xint_gob_til_minus #2\XINT_sub_rescue_z -%
- \expandafter\XINT_sub_rescue_c\the\numexpr \xint_c_xii_e_viii_mone-#2#3+#1.%
-}%
-\def\XINT_sub_rescue_z #1.{1!}%
% \end{macrocode}
+% \lverb|#1 = 0 signifie une retenue, #1 = 1 pas de retenue, ce qui ne peut
+% arriver que tant qu'il n'y a que des zéros du côté non significatif.
+% Lorsqu'on est revenu au début on a forcément une retenue.|
+% \begin{macrocode}
+\def\XINT_sub_comp_clean 1#1{+#1\relax}%
+% \end{macrocode}
% \subsection{\csh{xintiMul}, \csh{xintiiMul}}
-% \lverb|Completely rewritten for 1.2.|
+% \lverb|Completely rewritten for 1.2.
+%
+% 1.2l: \xintiiMul made robust against non terminated input.|
% \begin{macrocode}
\def\xintiMul {\romannumeral0\xintimul }%
\def\xintimul #1%
{%
- \expandafter\XINT_imul\romannumeral0\xintnum{#1}\Z
+ \expandafter\XINT_imul\romannumeral0\xintnum{#1}\xint:
}%
-\def\XINT_imul #1#2\Z #3%
+\def\XINT_imul #1#2\xint:#3%
{%
- \expandafter\XINT_mul_nfork\expandafter #1\romannumeral0\xintnum{#3}\Z #2\Z
+ \expandafter\XINT_mul_nfork\expandafter #1\romannumeral0\xintnum{#3}\xint:#2\xint:
}%
\def\xintiiMul {\romannumeral0\xintiimul }%
\def\xintiimul #1%
{%
- \expandafter\XINT_iimul\romannumeral`&&@#1\Z
+ \expandafter\XINT_iimul\romannumeral`&&@#1\xint:
}%
-\def\XINT_iimul #1#2\Z #3%
+\def\XINT_iimul #1#2\xint:#3%
{%
- \expandafter\XINT_mul_nfork\expandafter #1\romannumeral`&&@#3\Z #2\Z
+ \expandafter\XINT_mul_nfork\expandafter #1\romannumeral`&&@#3\xint:#2\xint:
}%
% \end{macrocode}
-% \lverb|I have changed the fork, and it complicates matters elsewhere.|
+% \lverb|(1.2) I have changed the fork, and it complicates matters elsewhere.|
% \begin{macrocode}
-\def\XINT_mul_fork #1#2\Z #3\Z{\XINT_mul_nfork #1#3\Z #2\Z}%
+\def\XINT_mul_fork #1#2\xint:#3\xint:{\XINT_mul_nfork #1#3\xint:#2\xint:}%
\def\XINT_mul_nfork #1#2%
{%
\xint_UDzerofork
@@ -18898,40 +19551,40 @@
--\XINT_mul_plusplus
\krof #1#2%
}%
-\def\XINT_mul_zero #1\krof #2#3\Z #4\Z { 0}%
+\def\XINT_mul_zero #1\krof #2#3\xint:#4\xint:{ 0}%
\def\XINT_mul_minusminus #1#2{\XINT_mul_plusplus {}{}}%
\def\XINT_mul_minusplus #1#2%
{\expandafter-\romannumeral0\XINT_mul_plusplus {}#2}%
\def\XINT_mul_plusminus #1#2%
{\expandafter-\romannumeral0\XINT_mul_plusplus #1{}}%
-\def\XINT_mul_plusplus #1#2#3\Z
+\def\XINT_mul_plusplus #1#2#3\xint:
{%
\expandafter\XINT_mul_pre_b
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
#2#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\W #1%
}%
-\def\XINT_mul_pre_b #1.#2\W #3\Z
+\def\XINT_mul_pre_b #1\xint:#2\W #3\xint:
{%
\expandafter\XINT_mul_checklengths
- \the\numexpr #1\expandafter.%
+ \the\numexpr #1\expandafter\xint:%
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
- 1\Z!\W #21\Z!%
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
+ 1;!\W #21;!%
1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
}%
% \end{macrocode}
% \lverb|Cooking recipe, 2015/10/05.|
% \begin{macrocode}
-\def\XINT_mul_checklengths #1.#2.%
+\def\XINT_mul_checklengths #1\xint:#2\xint:%
{%
\ifnum #2=\xint_c_i\expandafter\XINT_mul_smallbyfirst\fi
\ifnum #1=\xint_c_i\expandafter\XINT_mul_smallbysecond\fi
@@ -18946,13 +19599,13 @@
\fi
\XINT_mul_start
}%
-\def\XINT_mul_smallbyfirst #1\XINT_mul_start 1#2!1\Z!\W
+\def\XINT_mul_smallbyfirst #1\XINT_mul_start 1#2!1;!\W
{%
\ifnum#2=\xint_c_i\expandafter\XINT_mul_oneisone\fi
\ifnum#2<\xint_c_xxii\expandafter\XINT_mul_verysmall\fi
\expandafter\XINT_mul_out\the\numexpr\XINT_smallmul 1#2!%
}%
-\def\XINT_mul_smallbysecond #1\XINT_mul_start #2\W 1#3!1\Z!%
+\def\XINT_mul_smallbysecond #1\XINT_mul_start #2\W 1#3!1;!%
{%
\ifnum#3=\xint_c_i\expandafter\XINT_mul_oneisone\fi
\ifnum#3<\xint_c_xxii\expandafter\XINT_mul_verysmall\fi
@@ -18961,53 +19614,31 @@
\def\XINT_mul_oneisone #1!{\XINT_mul_out }%
\def\XINT_mul_verysmall\expandafter\XINT_mul_out
\the\numexpr\XINT_smallmul 1#1!%
- {\expandafter\XINT_mul_out\the\numexpr\XINT_verysmallmul 0.#1!}%
-\def\XINT_mul_exchange #1\XINT_mul_start #2\W #31\Z!%
- {\fi\fi\XINT_mul_start #31\Z!\W #2}%
+ {\expandafter\XINT_mul_out\the\numexpr\XINT_verysmallmul 0\xint:#1!}%
+\def\XINT_mul_exchange #1\XINT_mul_start #2\W #31;!%
+ {\fi\fi\XINT_mul_start #31;!\W #2}%
% \end{macrocode}
-% \lverb|1.2c: earlier version of addition had sometimes a final 1!, but not
-% in all cases. Version 1.2c of \XINT_add_a always has an ending 1\Z!, which
-% is thus expected by \XINT_mul_loop.|
+% \lverb|&
+% |
% \begin{macrocode}
\def\XINT_mul_start
- {\expandafter\XINT_mul_out\the\numexpr\XINT_mul_loop 100000000!1\Z!\W}%
+ {\expandafter\XINT_mul_out\the\numexpr\XINT_mul_loop 100000000!1;!\W}%
\def\XINT_mul_out
{\expandafter\XINT_cuz_small\romannumeral0\XINT_unrevbyviii {}}%
% \end{macrocode}
-% \lverb|The 1.2 \XINT_mul_loop could *not* be called directly with a small
-% multiplicand, due to problems caused in case the addition done in
-% \XINT_mul_a produced only 1 block the second one being either empty or a 1!
-% which had to be handled by \XINT_mul_loop and \XINT_mul_e. But
-% \XINT_mul_loop was only called via \xintiiMul for arguments with at least 2
-% digits in base 10^8, thus no problem. But this made it annoying for
-% \xintiiPow and \xintiiSqr which had to check if the intended multiplier had
-% only 1 digit in base 10^8. It also made it annoying to create recursive
-% algorithms which did multiplications maintaining the result reverses, for
-% iterative use of output as input.
+% \lverb|&
%
-% Finally on 2015/11/14 during 1.2c preparation I modified the addition to
-% *always* have the ending 1\Z!.\numexpr expands even through spaces to find
-% operators and even something like 1<space>\Z will try to expand the \Z. Thus
-% we have to not forget that #2 in \XINT_mul_e might be \Z! (a #2=1\Z! in
-% \XINT_mul_a hence \XINT_add_a is no problem). Again this can only happen if
-% we use \XINT_mul_loop directly with a small first argument (in place of
-% smallmul). Anyway, now the routine \XINT_mul_loop can handle a small #2,
-% with no black magic with delimiters and checking if #1 empty, although it
-% never happens when called via \xintiiMul.
-%
-% The delimiting patterns for addition was changed to use 1\Z! to fit what is
-% used on output (by necessity).
-%
-% Call: \the\numexpr \XINT_mul_loop 100000000!1\Z!\W #11\Z!\W #21\Z!$newline
+%( Call:
+%: \the\numexpr \XINT_mul_loop 100000000!1;!\W #11;!\W #21;!
+%)
% where #1 and #2 are (globally reversed) blocks 1<8d>!. Its is generally more
-% efficient to have #1 as the shorter one, but a better recipe is implemented
-% in \XINT_mul_checklengths which as executed earlier. One may call
-% \XINT_mul_loop directly (but multiplication by zero will produce many
-% 100000000! blocks on output).
+% efficient if #1 is the shorter one, but a better recipe is implemented in
+% \XINT_mul_checklengths. One may call \XINT_mul_loop directly (but
+% multiplication by zero will produce many 100000000! blocks on output).
%
-% Ends after having produced: 1<8d>!....1<8d>!1\Z!. The most significant
-% digit block is the last one. It can not be 100000000! except if naturally
-% the loop was called with a zero operand.
+% Ends after having produced: 1<8d>!....1<8d>!1;!. The last 8-digits block is
+% significant one. It can not be 100000000! except if the loop was called with
+% a zero operand.
%
% Thus \XINT_mul_loop can be conveniently called directly in recursive
% routines, as the output terminator can serve as input terminator, we can
@@ -19015,20 +19646,20 @@
% \begin{macrocode}
\def\XINT_mul_loop #1\W #2\W 1#3!%
{%
- \xint_gob_til_Z #3\XINT_mul_e \Z
+ \xint_gob_til_sc #3\XINT_mul_e ;%
\expandafter\XINT_mul_a\the\numexpr \XINT_smallmul 1#3!#2\W
#1\W #2\W
}%
% \end{macrocode}
-% \lverb|Each of #1 and #2 brings its 1\Z! for \XINT_add_a.|
+% \lverb|Each of #1 and #2 brings its 1;! for \XINT_add_a.|
% \begin{macrocode}
\def\XINT_mul_a #1\W #2\W
{%
\expandafter\XINT_mul_b\the\numexpr
- \XINT_add_a \xint_c_ii #21\Z!1\Z!1\Z!\W #11\Z!1\Z!1\Z!\W\W
+ \XINT_add_a \xint_c_ii #21;!1;!1;!\W #11;!1;!1;!\W\W
}%
\def\XINT_mul_b 1#1!{1#1\expandafter!\the\numexpr\XINT_mul_loop }%
-\def\XINT_mul_e\Z #1\W 1#2\W #3\W {1\relax #2}%
+\def\XINT_mul_e;#1\W 1#2\W #3\W {1\relax #2}%
% \end{macrocode}
% \lverb|1.2 small and mini multiplication in base 10^8 with carry. Used by
% the main multiplication routines. But division, float factorial, etc.. have
@@ -19040,63 +19671,63 @@
% new 8digits carry as argument. The \XINT_smallmul_a fetches a new 1<8d>!
% block to multiply, and calls back \XINT_minimul_wc having stored the
% multiplicand for re-use later. When the loop terminates, the final carry is
-% checked for being nul, and in all cases the output is terminated by a 1\Z!
+% checked for being nul, and in all cases the output is terminated by a 1;!
%
% Multiplication by zero will produce blocks of zeros.|
% \begin{macrocode}
-\def\XINT_minimulwc_a 1#1.#2.#3!#4#5#6#7#8.%
+\def\XINT_minimulwc_a 1#1\xint:#2\xint:#3!#4#5#6#7#8\xint:%
{%
\expandafter\XINT_minimulwc_b
- \the\numexpr \xint_c_x^ix+#1+#3*#8.#3*#4#5#6#7+#2*#8.#2*#4#5#6#7.%
+ \the\numexpr \xint_c_x^ix+#1+#3*#8\xint:
+ #3*#4#5#6#7+#2*#8\xint:
+ #2*#4#5#6#7\xint:%
}%
-\def\XINT_minimulwc_b 1#1#2#3#4#5#6.#7.%
+\def\XINT_minimulwc_b 1#1#2#3#4#5#6\xint:#7\xint:%
{%
\expandafter\XINT_minimulwc_c
- \the\numexpr \xint_c_x^ix+#1#2#3#4#5+#7.#6.%
+ \the\numexpr \xint_c_x^ix+#1#2#3#4#5+#7\xint:#6\xint:%
}%
-\def\XINT_minimulwc_c 1#1#2#3#4#5#6.#7.#8.%
+\def\XINT_minimulwc_c 1#1#2#3#4#5#6\xint:#7\xint:#8\xint:%
{%
1#6#7\expandafter!%
\the\numexpr\expandafter\XINT_smallmul_a
- \the\numexpr \xint_c_x^viii+#1#2#3#4#5+#8.%
+ \the\numexpr \xint_c_x^viii+#1#2#3#4#5+#8\xint:%
}%
-\def\XINT_smallmul 1#1#2#3#4#5!{\XINT_smallmul_a 100000000.#1#2#3#4.#5!}%
-\def\XINT_smallmul_a #1.#2.#3!1#4!%
+\def\XINT_smallmul 1#1#2#3#4#5!{\XINT_smallmul_a 100000000\xint:#1#2#3#4\xint:#5!}%
+\def\XINT_smallmul_a #1\xint:#2\xint:#3!1#4!%
{%
- \xint_gob_til_Z #4\XINT_smallmul_e\Z
- \XINT_minimulwc_a #1.#2.#3!#4.#2.#3!%
+ \xint_gob_til_sc #4\XINT_smallmul_e;%
+ \XINT_minimulwc_a #1\xint:#2\xint:#3!#4\xint:#2\xint:#3!%
}%
-\def\XINT_smallmul_e\Z\XINT_minimulwc_a 1#1.#2\Z #3!%
- {\xint_gob_til_eightzeroes #1\XINT_smallmul_f 000000001\relax #1!1\Z!}%
+\def\XINT_smallmul_e;\XINT_minimulwc_a 1#1\xint:#2;#3!%
+ {\xint_gob_til_eightzeroes #1\XINT_smallmul_f 000000001\relax #1!1;!}%
\def\XINT_smallmul_f 000000001\relax 00000000!1{1\relax}%
% \end{macrocode}
-% \lverb|This is multiplication by 1 up to 21. Last time I checked it is never
-% called with a wasteful multiplicand of 1. Here also always the output
-% terminated by a 1\Z! and the last block of digits is not zero. I imagine
-% multiplication by zero produces blocks of zeroes. Will check another day.|
+% \lverb|&
+% |
% \begin{macrocode}
-\def\XINT_verysmallmul #1.#2!1#3!%
+\def\XINT_verysmallmul #1\xint:#2!1#3!%
{%
- \xint_gob_til_Z #3\XINT_verysmallmul_e\Z
+ \xint_gob_til_sc #3\XINT_verysmallmul_e;%
\expandafter\XINT_verysmallmul_a
- \the\numexpr #2*#3+#1.#2!%
+ \the\numexpr #2*#3+#1\xint:#2!%
}%
-\def\XINT_verysmallmul_e\Z\expandafter\XINT_verysmallmul_a\the\numexpr
- #1+#2#3.#4!%
-{\xint_gob_til_zero #2\XINT_verysmallmul_f 0\xint_c_x^viii+#2#3!1\Z!}%
+\def\XINT_verysmallmul_e;\expandafter\XINT_verysmallmul_a\the\numexpr
+ #1+#2#3\xint:#4!%
+{\xint_gob_til_zero #2\XINT_verysmallmul_f 0\xint_c_x^viii+#2#3!1;!}%
\def\XINT_verysmallmul_f #1!1{1\relax}%
-\def\XINT_verysmallmul_a #1#2.%
+\def\XINT_verysmallmul_a #1#2\xint:%
{%
\unless\ifnum #1#2<\xint_c_x^ix
\expandafter\XINT_verysmallmul_bi\else
\expandafter\XINT_verysmallmul_bj\fi
- \the\numexpr \xint_c_x^ix+#1#2.%
+ \the\numexpr \xint_c_x^ix+#1#2\xint:%
}%
\def\XINT_verysmallmul_bj{\expandafter\XINT_verysmallmul_cj }%
-\def\XINT_verysmallmul_cj 1#1#2.%
- {1#2\expandafter!\the\numexpr\XINT_verysmallmul #1.}%
-\def\XINT_verysmallmul_bi\the\numexpr\xint_c_x^ix+#1#2#3.%
- {1#3\expandafter!\the\numexpr\XINT_verysmallmul #1#2.}%
+\def\XINT_verysmallmul_cj 1#1#2\xint:%
+ {1#2\expandafter!\the\numexpr\XINT_verysmallmul #1\xint:}%
+\def\XINT_verysmallmul_bi\the\numexpr\xint_c_x^ix+#1#2#3\xint:%
+ {1#3\expandafter!\the\numexpr\XINT_verysmallmul #1#2\xint:}%
% \end{macrocode}
% \lverb|Used by division and by squaring, not by multiplication itself.
%
@@ -19104,400 +19735,21 @@
% format <4 high digits>.<4 low digits>!<8 digits>!, and on output
% 1<8d>!1<8d>!, with least significant block first.|
% \begin{macrocode}
-\def\XINT_minimul_a #1.#2!#3#4#5#6#7!%
+\def\XINT_minimul_a #1\xint:#2!#3#4#5#6#7!%
{%
\expandafter\XINT_minimul_b
- \the\numexpr \xint_c_x^viii+#2*#7.#2*#3#4#5#6+#1*#7.#1*#3#4#5#6.%
+ \the\numexpr \xint_c_x^viii+#2*#7\xint:#2*#3#4#5#6+#1*#7\xint:#1*#3#4#5#6\xint:%
}%
-\def\XINT_minimul_b 1#1#2#3#4#5.#6.%
+\def\XINT_minimul_b 1#1#2#3#4#5\xint:#6\xint:%
{%
\expandafter\XINT_minimul_c
- \the\numexpr \xint_c_x^ix+#1#2#3#4+#6.#5.%
+ \the\numexpr \xint_c_x^ix+#1#2#3#4+#6\xint:#5\xint:%
}%
-\def\XINT_minimul_c 1#1#2#3#4#5#6.#7.#8.%
+\def\XINT_minimul_c 1#1#2#3#4#5#6\xint:#7\xint:#8\xint:%
{%
1#6#7\expandafter!\the\numexpr \xint_c_x^viii+#1#2#3#4#5+#8!%
}%
% \end{macrocode}
-% \subsection{\csh{xintiSqr}, \csh{xintiiSqr}}
-% \lverb|Rewritten for 1.2.|
-% \begin{macrocode}
-\def\xintiiSqr {\romannumeral0\xintiisqr }%
-\def\xintiisqr #1%
-{%
- \expandafter\XINT_sqr\romannumeral0\xintiiabs{#1}\Z
-}%
-\def\xintiSqr {\romannumeral0\xintisqr }%
-\def\xintisqr #1%
-{%
- \expandafter\XINT_sqr\romannumeral0\xintiabs{#1}\Z
-}%
-\def\XINT_sqr #1\Z
-{%
- \expandafter\XINT_sqr_a
- \romannumeral0\expandafter\XINT_sepandrev_andcount
- \romannumeral0\XINT_zeroes_forviii #1\R\R\R\R\R\R\R\R{10}0000001\W
- #1\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
- \Z
-}%
-% \end{macrocode}
-% \lverb|1.2c \XINT_mul_loop can now be called directly even with small
-% arguments, thus the following check is not anymore a necessity.|
-% \begin{macrocode}
-\def\XINT_sqr_a #1.%
-{%
- \ifnum #1=\xint_c_i \expandafter\XINT_sqr_small
- \else\expandafter\XINT_sqr_start\fi
-}%
-\def\XINT_sqr_small 1#1#2#3#4#5!\Z
-{%
- \ifnum #1#2#3#4#5<46341 \expandafter\XINT_sqr_verysmall\fi
- \expandafter\XINT_sqr_small_out
- \the\numexpr\XINT_minimul_a #1#2#3#4.#5!#1#2#3#4#5!%
-}%
-\edef\XINT_sqr_verysmall
- \expandafter\XINT_sqr_small_out\the\numexpr\XINT_minimul_a #1!#2!%
- {\noexpand\expandafter\space\noexpand\the\numexpr #2*#2\relax}%
-\def\XINT_sqr_small_out 1#1!1#2!%
-{%
- \XINT_cuz #2#1\R
-}%
-% \end{macrocode}
-% \lverb|An ending 1\Z! is produced on output for \XINT_mul_loop and gets
-% incorporated to the delimiter needed by the \XINT_unrevbyviii done by
-% \XINT_mul_out.|
-% \begin{macrocode}
-\def\XINT_sqr_start #1\Z
-{%
- \expandafter\XINT_mul_out
- \the\numexpr\XINT_mul_loop 100000000!1\Z!\W #11\Z!\W #11\Z!%
- 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
-}%
-% \end{macrocode}
-% \subsection{\csh{xintiPow}, \csh{xintiiPow}}
-% \lverb|&
-% The exponent is not limited but with current default settings of tex memory,
-% with xint 1.2, the maximal exponent for 2^N is N = 2^17 = 131072.
-%
-% 1.2f Modifies the initial steps: 1) in order to be able to let more easily
-% \xintiPow use \xintNum on the exponent once xintfrac.sty is loaded; 2) also
-% because I noticed it was not very well coded. And it did only a \numexpr on
-% the exponent, contradicting the documentation related to the "i" convention
-% in names.|
-% \begin{macrocode}
-\def\xintiiPow {\romannumeral0\xintiipow }%
-\def\xintiipow #1#2%
-{%
- \expandafter\xint_pow\the\numexpr #2\expandafter.\romannumeral`&&@#1\Z%
-}%
-\def\xintiPow {\romannumeral0\xintipow }%
-\def\xintipow #1#2%
-{%
- \expandafter\xint_pow\the\numexpr #2\expandafter.\romannumeral0\xintnum{#1}\Z%
-}%
-\def\xint_pow #1.#2%#3\Z
-{%
- \xint_UDzerominusfork
- #2-\XINT_pow_AisZero
- 0#2\XINT_pow_Aneg
- 0-{\XINT_pow_Apos #2}%
- \krof {#1}%
-}%
-\def\XINT_pow_AisZero #1#2\Z
-{%
- \ifcase\XINT_cntSgn #1\Z
- \xint_afterfi { 1}%
- \or
- \xint_afterfi { 0}%
- \else
- \xint_afterfi {\xintError:DivisionByZero\space 0}%
- \fi
-}%
-\def\XINT_pow_Aneg #1%
-{%
- \ifodd #1
- \expandafter\XINT_opp\romannumeral0%
- \fi
- \XINT_pow_Apos {}{#1}%
-}%
-\def\XINT_pow_Apos #1#2{\XINT_pow_Apos_a {#2}#1}%
-\def\XINT_pow_Apos_a #1#2#3%
-{%
- \xint_gob_til_Z #3\XINT_pow_Apos_short\Z
- \XINT_pow_AatleastTwo {#1}#2#3%
-}%
-\def\XINT_pow_Apos_short\Z\XINT_pow_AatleastTwo #1#2\Z
-{%
- \ifcase #2
- \xintError:thiscannothappen!
- \or \expandafter\XINT_pow_AisOne
- \else\expandafter\XINT_pow_AatleastTwo
- \fi {#1}#2\Z
-}%
-\def\XINT_pow_AisOne #1\Z{ 1}%
-\def\XINT_pow_AatleastTwo #1%
-{%
- \ifcase\XINT_cntSgn #1\Z
- \expandafter\XINT_pow_BisZero
- \or
- \expandafter\XINT_pow_I_in
- \else
- \expandafter\XINT_pow_BisNegative
- \fi
- {#1}%
-}%
-\edef\XINT_pow_BisNegative #1\Z
- {\noexpand\xintError:FractionRoundedToZero\space 0}%
-\def\XINT_pow_BisZero #1\Z{ 1}%
-% \end{macrocode}
-% \lverb|B = #1 > 0, A = #2 > 1. Earlier code checked if size of B did not
-% exceed a given limit (for example 131000).|
-% \begin{macrocode}
-\def\XINT_pow_I_in #1#2\Z
-{%
- \expandafter\XINT_pow_I_loop
- \the\numexpr #1\expandafter.%
- \romannumeral0\expandafter\XINT_sepandrev
- \romannumeral0\XINT_zeroes_forviii #2\R\R\R\R\R\R\R\R{10}0000001\W
- #2\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax XX%
- \R.\R.\R.\R.\R.\R.\R.\R.\W 1\Z!\W
- 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
-}%
-\def\XINT_pow_I_loop #1.%
-{%
- \ifnum #1 = \xint_c_i\expandafter\XINT_pow_I_exit\fi
- \ifodd #1
- \expandafter\XINT_pow_II_in
- \else
- \expandafter\XINT_pow_I_squareit
- \fi #1.%
-}%
-\def\XINT_pow_I_exit \ifodd #1\fi #2.#3\W {\XINT_mul_out #3}%
-% \end{macrocode}
-% \lverb|The 1.2c \XINT_mul_loop can be called directly even with small
-% arguments, hence the "butcheckifsmall" is not a necessity as it was earlier
-% with 1.2. On 2^30, it does bring roughly a 40$char37 $space time gain
-% though, and 30$char37 $space gain for 2^60. The overhead on big computations
-% should be negligible.|
-% \begin{macrocode}
-\def\XINT_pow_I_squareit #1.#2\W%
-{%
- \expandafter\XINT_pow_I_loop
- \the\numexpr #1/\xint_c_ii\expandafter.%
- \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W
-}%
-\def\XINT_pow_mulbutcheckifsmall #1!1#2%
-{%
- \xint_gob_til_Z #2\XINT_pow_mul_small\Z
- \XINT_mul_loop 100000000!1\Z!\W #1!1#2%
-}%
-\def\XINT_pow_mul_small\Z \XINT_mul_loop 100000000!1\Z!\W 1#1!1\Z!\W
-{%
- \XINT_smallmul 1#1!%
-}%
-\def\XINT_pow_II_in #1.#2\W
-{%
- \expandafter\XINT_pow_II_loop
- \the\numexpr #1/\xint_c_ii-\xint_c_i\expandafter.%
- \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W #2\W
-}%
-\def\XINT_pow_II_loop #1.%
-{%
- \ifnum #1 = \xint_c_i\expandafter\XINT_pow_II_exit\fi
- \ifodd #1
- \expandafter\XINT_pow_II_odda
- \else
- \expandafter\XINT_pow_II_even
- \fi #1.%
-}%
-\def\XINT_pow_II_exit\ifodd #1\fi #2.#3\W #4\W
-{%
- \expandafter\XINT_mul_out
- \the\numexpr\XINT_pow_mulbutcheckifsmall #4\W #3%
-}%
-\def\XINT_pow_II_even #1.#2\W
-{%
- \expandafter\XINT_pow_II_loop
- \the\numexpr #1/\xint_c_ii\expandafter.%
- \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W
-}%
-\def\XINT_pow_II_odda #1.#2\W #3\W
-{%
- \expandafter\XINT_pow_II_oddb
- \the\numexpr #1/\xint_c_ii-\xint_c_i\expandafter.%
- \the\numexpr\XINT_pow_mulbutcheckifsmall #3\W #2\W #2\W
-}%
-\def\XINT_pow_II_oddb #1.#2\W #3\W
-{%
- \expandafter\XINT_pow_II_loop
- \the\numexpr #1\expandafter.%
- \the\numexpr\XINT_pow_mulbutcheckifsmall #3\W #3\W #2\W
-}%
-% \end{macrocode}
-% \subsection{\csh{xintiFac}, \csh{xintiiFac}}
-% \lverb|Moved here from xint.sty with release 1.2 (to be usable by \bnumexpr).
-%
-% The routine has been partially rewritten with release 1.2 to exploit the new
-% inner structure of multiplication. I impose an intrinsic limit of the
-% argument at maximal value 9999 (1.2f sets it at 10000, there was no reason
-% for 9999 and not 10000). Anyhow with current default settings of the
-% etex memory and the current 1.2 routine (last commit: eada1b1), the maximal
-% possible computation is 5971! (which has 19956 digits). Also, I add
-% \xintiiFac which does only \romannumeral-`0 and not \numexpr on its
-% argument. This is for a silly slight optimization of the \xintiiexpr (and
-% \bnumexpr) parsers. If the argument is >=2^31 an arithmetic overflow will
-% occur in the \ifnum. This is not as good as in the \numexpr, but well.
-%
-% 2015/11/14 added note on the implementation: we can roughly estimate for big
-% n that we do n/2 multiplications alpha*X where alpha=(k+1)(k+2)<10^8 and
-% X=k! has size of order k log(k), with k along a step 2 arithmetic sequence
-% up to n. Each small multiplication should have a linear cost hence O(k
-% log(k)) (as we maintain the reversed representation) hence a total cost of
-% O(n^2 log(n)); on computing n! for n=100, 200, ..., 2000 I obtained a good
-% fit (only roughly 20$char37 $space variation) of the computation time with
-% the square of the length of n! -- to the extent that the big variability of
-% \pdfelapsedtime allows to draw any conclusion -- I did not repeat the
-% computations as many times as I should have. I currently do not quite
-% understand why in this range it seems computation times are better fitted by
-% O(n^2 log^2 n) than by O(n^2 log n). True, final reverse is O(N^2) with N of
-% order n log n, but for this range of n's this is marginal (and I tested also
-% with this final reverse skipped).
-%
-% On the other hand with an approach based on binary splitting n!=AB and
-% A=[n/2]! each of A and B will be of size n/2 log(n), but xint schoolbook
-% multiplication in TeX is worse than quadratic due to penalty when TeX needs
-% to fetch arguments and it didn't seem promising. I didn't even test. Binary
-% splitting is good when a fast multiplication is available.
-%
-% No wait! incredibly a very naive recursive implementation with five lines of
-% code via a binary splitting approach with \xintiiMul is only about 1.6x--2x
-% slower in the range N=200 to 2000 ! this seems to say that the reversing
-% done by \xintiiMul both on input and for output is quite efficient. The best
-% case seems to be around N=1000, hence multiplication of 500 digits numbers,
-% after that the impact of over-quadratic computation time seems to show: for
-% N=4000, the naive binary splitting approach is about 3.4x slower than the
-% naive iterated small multiplications as here (naturally with sub-quadratic
-% multiplication that would be otherwise).
-%
-%
-% 2015/11/29 for 1.2f: no more a \xintFac, only \xintiFac/\xintiiFac. I could
-% not go on like this with \xintFac/\xintiFac/\xintiiFac.|
-% \begin{macrocode}
-\def\xintiiFac {\romannumeral0\xintiifac }%
-\def\xintiifac #1{\expandafter\XINT_fac_fork\the\numexpr#1.}%
-\def\xintiFac {\romannumeral0\xintifac }%
-\let\xintifac\xintiifac
-% \end{macrocode}
-% \lverb|Vieux style. Bon je modifie pour 1.2f. Le cas négatif devrait faire
-% un 1/0 et créer un Inf.|
-% \begin{macrocode}
-\def\XINT_fac_fork #1#2.%
-{%
- \xint_UDzerominusfork
- #1-\XINT_fac_zero
- 0#1\XINT_fac_neg
- 0-\XINT_fac_checksize
- \krof #1#2.%
-}%
-\def\XINT_fac_zero #1.{ 1}%
-\edef\XINT_fac_neg #1.{\noexpand\xintError:FactorialOfNegative\space 1}%
-\def\XINT_fac_checksize #1.%
-{%
- \ifnum #1>\xint_c_x^iv
- \xint_dothis{\expandafter\xintError:TooBigFactorial
- \expandafter\space\expandafter 1\xint_gob_til_W }\fi
- \ifnum #1>465 \xint_dothis{\XINT_fac_bigloop_a #1.}\fi
- \ifnum #1>101 \xint_dothis{\XINT_fac_medloop_a #1.\XINT_mul_out}\fi
- \xint_orthat{\XINT_fac_smallloop_a #1.\XINT_mul_out}%
- 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
-}%
-\def\XINT_fac_bigloop_a #1.%
-{%
- \expandafter\XINT_fac_bigloop_b \the\numexpr
- #1+\xint_c_i-\xint_c_ii*((#1-464)/\xint_c_ii).#1.%
-}%
-\def\XINT_fac_bigloop_b #1.#2.%
-{%
- \expandafter\XINT_fac_medloop_a
- \the\numexpr #1-\xint_c_i.{\XINT_fac_bigloop_loop #1.#2.}%
-}%
-\def\XINT_fac_bigloop_loop #1.#2.%
-{%
- \ifnum #1>#2 \expandafter\XINT_fac_bigloop_exit\fi
- \expandafter\XINT_fac_bigloop_loop
- \the\numexpr #1+\xint_c_ii\expandafter.%
- \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_bigloop_mul #1!%
-}%
-\def\XINT_fac_bigloop_exit #1!{\XINT_mul_out}%
-\def\XINT_fac_bigloop_mul #1!%
-{%
- \expandafter\XINT_smallmul
- \the\numexpr \xint_c_x^viii+#1*(#1+\xint_c_i)!%
-}%
-\def\XINT_fac_medloop_a #1.%
-{%
- \expandafter\XINT_fac_medloop_b
- \the\numexpr #1+\xint_c_i-\xint_c_iii*((#1-100)/\xint_c_iii).#1.%
-}%
-\def\XINT_fac_medloop_b #1.#2.%
-{%
- \expandafter\XINT_fac_smallloop_a
- \the\numexpr #1-\xint_c_i.{\XINT_fac_medloop_loop #1.#2.}%
-}%
-\def\XINT_fac_medloop_loop #1.#2.%
-{%
- \ifnum #1>#2 \expandafter\XINT_fac_loop_exit\fi
- \expandafter\XINT_fac_medloop_loop
- \the\numexpr #1+\xint_c_iii\expandafter.%
- \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_medloop_mul #1!%
-}%
-\def\XINT_fac_medloop_mul #1!%
-{%
- \expandafter\XINT_smallmul
- \the\numexpr
- \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)!%
-}%
-\def\XINT_fac_smallloop_a #1.%
-{%
- \csname
- XINT_fac_smallloop_\the\numexpr #1-\xint_c_iv*(#1/\xint_c_iv)\relax
- \endcsname #1.%
-}%
-\expandafter\def\csname XINT_fac_smallloop_1\endcsname #1.%
-{%
- \XINT_fac_smallloop_loop 2.#1.100000001!1\Z!%
-}%
-\expandafter\def\csname XINT_fac_smallloop_-2\endcsname #1.%
-{%
- \XINT_fac_smallloop_loop 3.#1.100000002!1\Z!%
-}%
-\expandafter\def\csname XINT_fac_smallloop_-1\endcsname #1.%
-{%
- \XINT_fac_smallloop_loop 4.#1.100000006!1\Z!%
-}%
-\expandafter\def\csname XINT_fac_smallloop_0\endcsname #1.%
-{%
- \XINT_fac_smallloop_loop 5.#1.1000000024!1\Z!%
-}%
-\def\XINT_fac_smallloop_loop #1.#2.%
-{%
- \ifnum #1>#2 \expandafter\XINT_fac_loop_exit\fi
- \expandafter\XINT_fac_smallloop_loop
- \the\numexpr #1+\xint_c_iv\expandafter.%
- \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_smallloop_mul #1!%
-}%
-\def\XINT_fac_smallloop_mul #1!%
-{%
- \expandafter\XINT_smallmul
- \the\numexpr
- \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)*(#1+\xint_c_iii)!%
-}%
-\def\XINT_fac_loop_exit #1!#2\Z!#3{#3#2\Z!}%
-% \end{macrocode}
% \subsection{\csh{xintiDivision}, \csh{xintiQuo}, \csh{xintiRem},
% \csh{xintiiDivision}, \csh{xintiiQuo}, \csh{xintiiRem}}
% \lverb|Completely rewritten for 1.2.
@@ -19518,12 +19770,8 @@
% parameters now need handle less such parameters. Thus, some rationale for
% the way the code was structured has disappeared.
%
-% 1.2 2015/10/15 had a bad bug which got corrected in 1.2b of 2015/10/29: a
-% divisor starting with 99999999xyz... would cause a failure, simply because
-% it was attempted to use the \XINT_div_mini routine with a divisor of
-% 1+99999999=100000000 having 9 digits. Fortunately the origin of the bug was
-% easy to find out. Too bad that my obviously very deficient test files
-% did not detect it.|
+%
+% 1.2l: \xintiiDivision et al. made robust against non terminated input.|
% \begin{macrocode}
\def\xintiiQuo {\romannumeral0\xintiiquo }%
\def\xintiiRem {\romannumeral0\xintiirem }%
@@ -19540,26 +19788,29 @@
% euclidienne de A par B: A=BQ+R, 0<= R < |B|.-
% \begin{macrocode}
\def\xintiDivision {\romannumeral0\xintidivision }%
-\def\xintidivision #1{\expandafter\XINT_idivision\romannumeral0\xintnum{#1}\Z }%
-\def\XINT_idivision #1#2\Z #3{\expandafter\XINT_iidivision_a\expandafter #1%
- \romannumeral0\xintnum{#3}\Z #2\Z }%
+\def\xintidivision #1{\expandafter\XINT_idivision\romannumeral0\xintnum{#1}\xint:}%
+\def\XINT_idivision #1#2\xint:#3{\expandafter\XINT_iidivision_a\expandafter #1%
+ \romannumeral0\xintnum{#3}\xint:#2\xint:}%
\def\xintiiDivision {\romannumeral0\xintiidivision }%
-\def\xintiidivision #1{\expandafter\XINT_iidivision \romannumeral`&&@#1\Z }%
-\def\XINT_iidivision #1#2\Z #3{\expandafter\XINT_iidivision_a\expandafter #1%
- \romannumeral`&&@#3\Z #2\Z }%
+\def\xintiidivision #1{\expandafter\XINT_iidivision \romannumeral`&&@#1\xint:}%
+\def\XINT_iidivision #1#2\xint:#3{\expandafter\XINT_iidivision_a\expandafter #1%
+ \romannumeral`&&@#3\xint:#2\xint:}%
% \end{macrocode}
% \lverb|On regarde les signes de A et de B.|
% \begin{macrocode}
\def\XINT_iidivision_a #1#2% #1 de A, #2 de B.
{%
- \if0#2\xint_dothis\XINT_iidivision_divbyzero\fi
+ \if0#2\xint_dothis{\XINT_iidivision_divbyzero #1#2}\fi
\if0#1\xint_dothis\XINT_iidivision_aiszero\fi
\if-#2\xint_dothis{\expandafter\XINT_iidivision_bneg
\romannumeral0\XINT_iidivision_bpos #1}\fi
\xint_orthat{\XINT_iidivision_bpos #1#2}%
}%
-\def\XINT_iidivision_divbyzero #1\Z #2\Z {\xintError:DivisionByZero{0}{0}}%
-\def\XINT_iidivision_aiszero #1\Z #2\Z {{0}{0}}%
+\def\XINT_iidivision_divbyzero#1#2#3\xint:#4\xint:
+ {\if0#1\xint_dothis{\XINT_signalcondition{DivisionUndefined}}\fi
+ \xint_orthat{\XINT_signalcondition{DivisionByZero}}%
+ {Division of #1#4 by #2#3}{}{{0}{0}}}%
+\def\XINT_iidivision_aiszero #1\xint:#2\xint:{{0}{0}}%
\def\XINT_iidivision_bneg #1% q->-q, r unchanged
{\expandafter{\romannumeral0\XINT_opp #1}}%
\def\XINT_iidivision_bpos #1%
@@ -19578,11 +19829,11 @@
% négatif. Je n'ai pas fait beaucoup d'efforts pour être un minimum efficace
% si A ou B n'est pas positif.|
% \begin{macrocode}
-\def\XINT_iidivision_apos #1#2\Z #3\Z{\XINT_div_prepare {#2}{#1#3}}%
-\def\XINT_iidivision_aneg #1\Z #2\Z
+\def\XINT_iidivision_apos #1#2\xint:#3\xint:{\XINT_div_prepare {#2}{#1#3}}%
+\def\XINT_iidivision_aneg #1\xint:#2\xint:
{\expandafter
\XINT_iidivision_aneg_b\romannumeral0\XINT_div_prepare {#1}{#2}{#1}}%
-\def\XINT_iidivision_aneg_b #1#2{\if0\XINT_Sgn #2\Z
+\def\XINT_iidivision_aneg_b #1#2{\if0\XINT_Sgn #2\xint:
\expandafter\XINT_iidivision_aneg_rzero
\else
\expandafter\XINT_iidivision_aneg_rpos
@@ -19596,7 +19847,7 @@
\def\XINT_iidivision_aneg_end #1#2#3%
{%
\expandafter\xint_exchangetwo_keepbraces
- \expandafter{\romannumeral0\XINT_sub_mm_a {}{}#3\Z #2\Z}{#1}% r-> b-r
+ \expandafter{\romannumeral0\XINT_sub_mm_a {}{}#3\xint:#2\xint:}{#1}% r-> b-r
}%
% \end{macrocode}
% \lverb|Le diviseur B va être étendu par des zéros pour que sa longueur soit
@@ -19645,7 +19896,7 @@
{%
\expandafter\XINT_div_small_b
\the\numexpr #1/\xint_c_ii\expandafter
- .\the\numexpr \xint_c_x^viii+#1\expandafter!%
+ \xint:\the\numexpr \xint_c_x^viii+#1\expandafter!%
\romannumeral0%
\XINT_div_small_ba #2\R\R\R\R\R\R\R\R{10}0000001\W
#2\XINT_sepbyviii_Z_end 2345678\relax
@@ -19677,18 +19928,18 @@
\the\numexpr\expandafter\XINT_sepbyviii_Z
\romannumeral0\XINT_zeroes_forviii #1\R #2\relax
{{\XINT_div_dosmallsmall}{#1}}%
-\def\XINT_div_dosmallsmall #1.1#2!#3%
+\def\XINT_div_dosmallsmall #1\xint:1#2!#3%
{%
\expandafter\XINT_div_smallsmallend
- \the\numexpr (#3+#1)/#2-\xint_c_i.#2.#3.%
+ \the\numexpr (#3+#1)/#2-\xint_c_i\xint:#2\xint:#3\xint:%
}%
-\def\XINT_div_smallsmallend #1.#2.#3.{\expandafter
+\def\XINT_div_smallsmallend #1\xint:#2\xint:#3\xint:{\expandafter
{\the\numexpr #1\expandafter}\expandafter{\the\numexpr #3-#1*#2}}%
% \end{macrocode}
-% \lverb|Si A>=10^8, il est maintenant sous la forme 1<8d>!...1<8d>!1\Z! avec
+% \lverb|Si A>=10^8, il est maintenant sous la forme 1<8d>!...1<8d>!1;! avec
% plus significatifs en premier. Donc on poursuit par$newline
% \expandafter\XINT_sdiv_out\the\numexpr\XINT_smalldivx_a
-% x.1B!1<8d>!...1<8d>!1\Z! avec x =round(B/2), 1B=10^8+B.|
+% x.1B!1<8d>!...1<8d>!1;! avec x =round(B/2), 1B=10^8+B.|
% \begin{macrocode}
\def\XINT_div_dosmalldiv
{{\expandafter\XINT_sdiv_out\the\numexpr\XINT_smalldivx_a}}%
@@ -19722,17 +19973,16 @@
{%
\expandafter\XINT_div_prepare_g
\the\numexpr #1#2#3#4#5#6#7#8+\xint_c_i\expandafter
- .\the\numexpr (#1#2#3#4#5#6#7#8+\xint_c_i)/\xint_c_ii\expandafter
- .\the\numexpr #1#2#3#4#5#6#7#8\expandafter
- .\romannumeral0\XINT_sepandrev_andcount
+ \xint:\the\numexpr (#1#2#3#4#5#6#7#8+\xint_c_i)/\xint_c_ii\expandafter
+ \xint:\the\numexpr #1#2#3#4#5#6#7#8\expandafter
+ \xint:\romannumeral0\XINT_sepandrev_andcount
#1#2#3#4#5#6#7#8#9\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678%
- \relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\X
}%
-\def\XINT_div_prepare_g #1.#2.#3.#4.#5\X #6#7#8%
+\def\XINT_div_prepare_g #1\xint:#2\xint:#3\xint:#4\xint:#5\X #6#7#8%
{%
\expandafter\XINT_div_prepare_h
\the\numexpr\expandafter\XINT_sepbyviii_andcount
@@ -19742,7 +19992,7 @@
\xint_c_iii!\xint_c_ii!\xint_c_i!\xint_c_\W
{#1}{#2}{#3}{#4}{#5}{#6}%
}%
-\def\XINT_div_prepare_h #11.#2.#3#4#5#6%#7#8%
+\def\XINT_div_prepare_h #11\xint:#2\xint:#3#4#5#6%#7#8%
{%
\XINT_div_start_a {#2}{#6}{#1}{#3}{#4}{#5}%{#7}{#8}%
}%
@@ -19765,10 +20015,10 @@
{%
\expandafter\XINT_div_zeroQ_end
\romannumeral0\XINT_unsep_cuzsmall
- #31\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W .%
+ #3\xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax\xint:
}%
-\def\XINT_div_zeroQ_end #1.#2%
- {\expandafter{\expandafter0\expandafter}\XINT_div_cleanR #1#2.}%
+\def\XINT_div_zeroQ_end #1\xint:#2%
+ {\expandafter{\expandafter0\expandafter}\XINT_div_cleanR #1#2\xint:}%
% \end{macrocode}
% \lverb|L, K, A, x',y,x, B, «c»->K.A.x{LK{x'y}x}B«c»|
% \begin{macrocode}
@@ -19775,13 +20025,13 @@
\def\XINT_div_start_b #1#2#3#4#5#6%
{%
\expandafter\XINT_div_finish\the\numexpr
- \XINT_div_start_c {#2}.#3.{#6}{{#1}{#2}{{#4}{#5}}{#6}}%
+ \XINT_div_start_c {#2}\xint:#3\xint:{#6}{{#1}{#2}{{#4}{#5}}{#6}}%
}%
\def\XINT_div_finish
{%
\expandafter\XINT_div_finish_a \romannumeral`&&@\XINT_div_unsepQ
}%
-\def\XINT_div_finish_a #1\Z #2.{\XINT_div_finish_b #2.{#1}}%
+\def\XINT_div_finish_a #1\Z #2\xint:{\XINT_div_finish_b #2\xint:{#1}}%
% \end{macrocode}
% \lverb|Ici ce sont routines de fin. Le reste déjà nettoyé. R.Q«c».|
% \begin{macrocode}
@@ -19794,12 +20044,12 @@
\fi
#1%
}%
-\def\XINT_div_finish_bRzero 0.#1#2{{#1}{0}}%
-\def\XINT_div_finish_bRpos #1.#2#3%
+\def\XINT_div_finish_bRzero 0\xint:#1#2{{#1}{0}}%
+\def\XINT_div_finish_bRpos #1\xint:#2#3%
{%
- \expandafter\xint_exchangetwo_keepbraces\XINT_div_cleanR #1#3.{#2}%
+ \expandafter\xint_exchangetwo_keepbraces\XINT_div_cleanR #1#3\xint:{#2}%
}%
-\def\XINT_div_cleanR #100000000.{{#1}}%
+\def\XINT_div_cleanR #100000000\xint:{{#1}}%
% \end{macrocode}
% \lverb|Kalpha.A.x{LK{x'y}x}, B, «c», au début #2=alpha est vide. On fait une
% boucle pour prendre K unités de A (on a au moins L égal à K) et les mettre
@@ -19813,31 +20063,31 @@
\expandafter\XINT_div_start_cb
\fi {#1}%
}%
-\def\XINT_div_start_ca #1#2.#3!#4!#5!#6!#7!#8!#9!%
+\def\XINT_div_start_ca #1#2\xint:#3!#4!#5!#6!#7!#8!#9!%
{%
\expandafter\XINT_div_start_c\expandafter
- {\the\numexpr #1-\xint_c_vii}#2#3!#4!#5!#6!#7!#8!#9!.%
+ {\the\numexpr #1-\xint_c_vii}#2#3!#4!#5!#6!#7!#8!#9!\xint:%
}%
\def\XINT_div_start_cb #1%
{\csname XINT_div_start_c_\romannumeral\numexpr#1\endcsname}%
-\def\XINT_div_start_c_i #1.#2!%
- {\XINT_div_start_c_ #1#2!.}%
-\def\XINT_div_start_c_ii #1.#2!#3!%
- {\XINT_div_start_c_ #1#2!#3!.}%
-\def\XINT_div_start_c_iii #1.#2!#3!#4!%
- {\XINT_div_start_c_ #1#2!#3!#4!.}%
-\def\XINT_div_start_c_iv #1.#2!#3!#4!#5!%
- {\XINT_div_start_c_ #1#2!#3!#4!#5!.}%
-\def\XINT_div_start_c_v #1.#2!#3!#4!#5!#6!%
- {\XINT_div_start_c_ #1#2!#3!#4!#5!#6!.}%
-\def\XINT_div_start_c_vi #1.#2!#3!#4!#5!#6!#7!%
- {\XINT_div_start_c_ #1#2!#3!#4!#5!#6!#7!.}%
+\def\XINT_div_start_c_i #1\xint:#2!%
+ {\XINT_div_start_c_ #1#2!\xint:}%
+\def\XINT_div_start_c_ii #1\xint:#2!#3!%
+ {\XINT_div_start_c_ #1#2!#3!\xint:}%
+\def\XINT_div_start_c_iii #1\xint:#2!#3!#4!%
+ {\XINT_div_start_c_ #1#2!#3!#4!\xint:}%
+\def\XINT_div_start_c_iv #1\xint:#2!#3!#4!#5!%
+ {\XINT_div_start_c_ #1#2!#3!#4!#5!\xint:}%
+\def\XINT_div_start_c_v #1\xint:#2!#3!#4!#5!#6!%
+ {\XINT_div_start_c_ #1#2!#3!#4!#5!#6!\xint:}%
+\def\XINT_div_start_c_vi #1\xint:#2!#3!#4!#5!#6!#7!%
+ {\XINT_div_start_c_ #1#2!#3!#4!#5!#6!#7!\xint:}%
% \end{macrocode}
% \lverb|#1=a, #2=alpha (de longueur K, à l'endroit).#3=reste de A.#4=x,
% #5={LK{x'y}x},#6=B,«c» -> a, x, alpha, B, {00000000}, L, K, {x'y},x,
% alpha'=reste de A, B«c».|
% \begin{macrocode}
-\def\XINT_div_start_c_ 1#1!#2.#3.#4#5#6%
+\def\XINT_div_start_c_ 1#1!#2\xint:#3\xint:#4#5#6%
{%
\XINT_div_I_a {#1}{#4}{1#1!#2}{#6}{00000000}#5{#3}{#6}%
}%
@@ -19847,7 +20097,7 @@
% \begin{macrocode}
\def\XINT_div_I_a #1#2%
{%
- \expandafter\XINT_div_I_b\the\numexpr #1/#2.{#1}{#2}%
+ \expandafter\XINT_div_I_b\the\numexpr #1/#2\xint:{#1}{#2}%
}%
\def\XINT_div_I_b #1%
{%
@@ -19858,15 +20108,15 @@
% {x'y}, x, alpha', B«c» -> on lâche un q puis {alpha} L, K, {x'y}, x,
% alpha', B«c».|
% \begin{macrocode}
-\def\XINT_div_I_czero 0\XINT_div_I_c 0.#1#2#3#4#5{1#5\XINT_div_I_g {#3}}%
-\def\XINT_div_I_c #1.#2#3%
+\def\XINT_div_I_czero 0\XINT_div_I_c 0\xint:#1#2#3#4#5{1#5\XINT_div_I_g {#3}}%
+\def\XINT_div_I_c #1\xint:#2#3%
{%
- \expandafter\XINT_div_I_da\the\numexpr #2-#1*#3.#1.{#2}{#3}%
+ \expandafter\XINT_div_I_da\the\numexpr #2-#1*#3\xint:#1\xint:{#2}{#3}%
}%
% \end{macrocode}
% \lverb|r.q.alpha, B, q0, L, K, {x'y}, x, alpha', B«c»|
% \begin{macrocode}
-\def\XINT_div_I_da #1.%
+\def\XINT_div_I_da #1\xint:%
{%
\ifnum #1>\xint_c_ix
\expandafter\XINT_div_I_dP
@@ -19881,16 +20131,16 @@
% \end{macrocode}
% \lverb|attention très mauvaises notations avec _b et _db.|
% \begin{macrocode}
-\def\XINT_div_I_dN #1.%
+\def\XINT_div_I_dN #1\xint:%
{%
- \expandafter\XINT_div_I_b\the\numexpr #1-\xint_c_i.%
+ \expandafter\XINT_div_I_b\the\numexpr #1-\xint_c_i\xint:%
}%
-\def\XINT_div_I_db #1.#2#3#4#5%
+\def\XINT_div_I_db #1\xint:#2#3#4#5%
{%
\expandafter\XINT_div_I_dc\expandafter #1%
\romannumeral0\expandafter\XINT_div_sub\expandafter
{\romannumeral0\XINT_rev_nounsep {}#4\R!\R!\R!\R!\R!\R!\R!\R!\W}%
- {\the\numexpr\XINT_div_verysmallmul #1!#51\Z!}%
+ {\the\numexpr\XINT_div_verysmallmul #1!#51;!}%
\Z {#4}{#5}%
}%
% \end{macrocode}
@@ -19905,7 +20155,7 @@
\def\XINT_div_I_dd #1-\Z
{%
\if #11\expandafter\XINT_div_I_dz\fi
- \expandafter\XINT_div_I_dP\the\numexpr #1-\xint_c_i.XX%
+ \expandafter\XINT_div_I_dP\the\numexpr #1-\xint_c_i\xint: XX%
}%
\def\XINT_div_I_dz #1XX#2#3#4%
{%
@@ -19916,12 +20166,12 @@
% \lverb|q.alpha, B, q0, L, K, {x'y},x, alpha'B«c» (q=0 has been intercepted)
% -> 1nouveauq.nouvel alpha, L, K, {x'y}, x, alpha',B«c»|
% \begin{macrocode}
-\def\XINT_div_I_dP #1.#2#3#4#5#6%
+\def\XINT_div_I_dP #1\xint:#2#3#4#5#6%
{%
1#6+#1\expandafter\XINT_div_I_g\expandafter
{\romannumeral0\expandafter\XINT_div_sub\expandafter
{\romannumeral0\XINT_rev_nounsep {}#4\R!\R!\R!\R!\R!\R!\R!\R!\W}%
- {\the\numexpr\XINT_div_verysmallmul #1!#51\Z!}%
+ {\the\numexpr\XINT_div_verysmallmul #1!#51;!}%
}%
}%
% \end{macrocode}
@@ -19939,7 +20189,7 @@
\else
\expandafter\XINT_div_I_h
\fi
- {#4}#1.#6.{{#4}{#5}{#3}{#2}}{#7}%
+ {#4}#1\xint:#6\xint:{{#4}{#5}{#3}{#2}}{#7}%
}%
% \end{macrocode}
% \lverb|{x'y}alpha.alpha'.{{x'y}xKL}B«c» -> Attention retour à l'envoyeur ici
@@ -19946,10 +20196,11 @@
% par terminaison des \the\numexpr. On doit reprendre le Q déjà sorti, qui n'a
% plus de séparateurs, ni de leading 1. Ensuite R sans leading zeros.«c»|
% \begin{macrocode}
-\def\XINT_div_exittofinish #1#2.#3.#4#5%
+\def\XINT_div_exittofinish #1#2\xint:#3\xint:#4#5%
{%
- 1\expandafter\expandafter\expandafter!\expandafter\XINT_unsep_delim
- \romannumeral0\XINT_div_unsepR #2#31\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W.%
+ 1\expandafter\expandafter\expandafter!\expandafter\XINT_div_unsepQ_delim
+ \romannumeral0\XINT_div_unsepR #2#3%
+ \xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax\R\xint:
}%
% \end{macrocode}
% \lverb|ATTENTION DESCRIPTION OBSOLÈTE. #1={x'y}alpha.#2!#3=reste de A.
@@ -19956,9 +20207,9 @@
% #4={{x'y},x,K,L},#5=B,«c» devient {x'y},alpha sur K+4 chiffres.B,
% {{x'y},x,K,L}, #6= nouvel alpha',B,«c»|
% \begin{macrocode}
-\def\XINT_div_I_h #1.#2!#3.#4#5%
+\def\XINT_div_I_h #1\xint:#2!#3\xint:#4#5%
{%
- \XINT_div_II_b #1#2!.{#5}{#4}{#3}{#5}%
+ \XINT_div_II_b #1#2!\xint:{#5}{#4}{#3}{#5}%
}%
% \end{macrocode}
% \lverb|{x'y}alpha.B, {{x'y},x,K,L}, nouveau alpha',B,«c»|
@@ -19973,7 +20224,7 @@
% «c» -> {x'y}x,K,L (à diminuer de 4), {alpha sur
% K}B{q1=00000000}{alpha'}B,«c»|
% \begin{macrocode}
-\def\XINT_div_II_skipc 00000000\XINT_div_II_c #1#2#3#4#5.#6#7%
+\def\XINT_div_II_skipc 00000000\XINT_div_II_c #1#2#3#4#5\xint:#6#7%
{%
\XINT_div_II_k #7{#4!#5}{#6}{00000000}%
}%
@@ -19981,21 +20232,12 @@
% \lverb|x'ya->1qx'yalpha.B, {{x'y},x,K,L}, nouveau alpha',B, «c». En fait,
% attention, ici #3 et #4 sont les 16 premiers chiffres du numérateur,sous la
% forme blocs 1<8chiffres>.
-%
-% ATTENTION!
-%
-% 2015/10/29 :j'avais introduit un bug ici dans 1.2 2015/10/15, car
-% \XINT_div_mini veut un diviseur de huit chiffres, or si le dénominateur B
-% débute par x=99999999, on aura x'=100000000, d'où évidemment un bug. Bon il
-% faut intercepter x'=100000000.
-%
-% I need to recognize x'=100000000 in some not too penalizing way. Anyway,
-% will try to optimize some other day.|
+% |
% \begin{macrocode}
\def\XINT_div_II_c #1#2#3#4%
{%
\expandafter\XINT_div_II_d\the\numexpr\XINT_div_xmini
- #1.#2!#3!#4!{#1}{#2}#3!#4!%
+ #1\xint:#2!#3!#4!{#1}{#2}#3!#4!%
}%
\def\XINT_div_xmini #1%
{%
@@ -20012,19 +20254,19 @@
% \end{macrocode}
% \lverb|x'=10^8 and we return #1=1<8digits>.|
% \begin{macrocode}
-\def\XINT_div_xmini_c 0\XINT_div_mini 100000000.50000000!#1!#2!{#1!}%
+\def\XINT_div_xmini_c 0\XINT_div_mini 100000000\xint:50000000!#1!#2!{#1!}%
% \end{macrocode}
% \lverb|1 suivi de q1 sur huit chiffres! #2=x', #3=y, #4=alpha.#5=B,
% {{x'y},x,K,L}, alpha', B, «c» --> nouvel alpha.x',y,B,q1,{{x'y},x,K,L},
% alpha', B, «c» |
% \begin{macrocode}
-\def\XINT_div_II_d 1#1#2#3#4#5!#6#7#8.#9%
+\def\XINT_div_II_d 1#1#2#3#4#5!#6#7#8\xint:#9%
{%
\expandafter\XINT_div_II_e
\romannumeral0\expandafter\XINT_div_sub\expandafter
{\romannumeral0\XINT_rev_nounsep {}#8\R!\R!\R!\R!\R!\R!\R!\R!\W}%
- {\the\numexpr\XINT_div_smallmul_a 100000000.#1#2#3#4.#5!#91\Z!}%
- .{#6}{#7}{#9}{#1#2#3#4#5}%
+ {\the\numexpr\XINT_div_smallmul_a 100000000\xint:#1#2#3#4\xint:#5!#91;!}%
+ \xint:{#6}{#7}{#9}{#1#2#3#4#5}%
}%
% \end{macrocode}
% \lverb|alpha.x',y,B,q1, {{x'y},x,K,L}, alpha', B, «c». Attention la
@@ -20036,11 +20278,11 @@
\XINT_div_II_f 1#1!%
}%
% \end{macrocode}
-% \lverb|100000000!alpha sur K chiffres.#2=x',#3=y,#4=B,#5=q1, #6={{x'y},x,K,L},
+% \lverb|100000000! alpha sur K chiffres.#2=x',#3=y,#4=B,#5=q1, #6={{x'y},x,K,L},
% #7=alpha',B«c» -> {x'y}x,K,L (à diminuer de 1),
% {alpha sur K}B{q1}{alpha'}B«c»|
% \begin{macrocode}
-\def\XINT_div_II_skipf 00000000\XINT_div_II_f 100000000!#1.#2#3#4#5#6%
+\def\XINT_div_II_skipf 00000000\XINT_div_II_f 100000000!#1\xint:#2#3#4#5#6%
{%
\XINT_div_II_k #6{#1}{#4}{#5}%
}%
@@ -20051,13 +20293,13 @@
% Here also we are dividing with x' which could be 10^8 in the exceptional
% case x=99999999. Must intercept it before sending to \XINT_div_mini.|
% \begin{macrocode}
-\def\XINT_div_II_f #1!#2!#3.%
+\def\XINT_div_II_f #1!#2!#3\xint:%
{%
\XINT_div_II_fa {#1!#2!}{#1!#2!#3}%
}%
\def\XINT_div_II_fa #1#2#3#4%
{%
- \expandafter\XINT_div_II_g \the\numexpr\XINT_div_xmini #3.#4!#1{#2}%
+ \expandafter\XINT_div_II_g \the\numexpr\XINT_div_xmini #3\xint:#4!#1{#2}%
}%
% \end{macrocode}
% \lverb|#1=q, #2=alpha (K+4), #3=B, #4=q1, {{x'y},x,K,L}, alpha', BQ«c»
@@ -20068,11 +20310,11 @@
{%
\expandafter \XINT_div_II_h
\the\numexpr 1#1#2#3#4#5+#8\expandafter\expandafter\expandafter
- .\expandafter\expandafter\expandafter
+ \xint:\expandafter\expandafter\expandafter
{\expandafter\xint_gob_til_exclam
\romannumeral0\expandafter\XINT_div_sub\expandafter
{\romannumeral0\XINT_rev_nounsep {}#6\R!\R!\R!\R!\R!\R!\R!\R!\W}%
- {\the\numexpr\XINT_div_smallmul_a 100000000.#1#2#3#4.#5!#71\Z!}}%
+ {\the\numexpr\XINT_div_smallmul_a 100000000\xint:#1#2#3#4\xint:#5!#71;!}}%
{#7}%
}%
% \end{macrocode}
@@ -20080,7 +20322,7 @@
% #3=B, #4={{x'y},x,K,L} avec L à ajuster, alpha', BQ«c»
% -> {x'y}x,K,L à diminuer de 1, {alpha}B{q}, alpha', BQ«c»|
% \begin{macrocode}
-\def\XINT_div_II_h 1#1.#2#3#4%
+\def\XINT_div_II_h 1#1\xint:#2#3#4%
{%
\XINT_div_II_k #4{#2}{#3}{#1}%
}%
@@ -20091,9 +20333,9 @@
% \begin{macrocode}
\def\XINT_div_II_k #1#2#3#4#5%
{%
- \expandafter\XINT_div_II_l \the\numexpr #4-\xint_c_i.{#3}#1{#2}#5.%
+ \expandafter\XINT_div_II_l \the\numexpr #4-\xint_c_i\xint:{#3}#1{#2}#5\xint:%
}%
-\def\XINT_div_II_l #1.#2#3#4#51#6!%
+\def\XINT_div_II_l #1\xint:#2#3#4#51#6!%
{%
\XINT_div_II_m {{#1}{#2}{{#3}{#4}}{#5}}{#5}{#6}1#6!%
}%
@@ -20101,56 +20343,56 @@
% \lverb|{LK{x'y}x},x,a,alpha.B{q}alpha'B -> a, x, alpha, B, q,
% L, K, {x'y}, x, alpha', B«c» |
% \begin{macrocode}
-\def\XINT_div_II_m #1#2#3#4.#5#6%
+\def\XINT_div_II_m #1#2#3#4\xint:#5#6%
{%
\XINT_div_I_a {#3}{#2}{#4}{#5}{#6}#1%
}%
% \end{macrocode}
% \lverb|This multiplication is exactly like \XINT_smallmul -- apart from not
-% inserting an ending 1\Z! --, but keeps ever a vanishing ending carry.|
+% inserting an ending 1;! --, but keeps ever a vanishing ending carry.|
% \begin{macrocode}
-\def\XINT_div_minimulwc_a 1#1.#2.#3!#4#5#6#7#8.%
+\def\XINT_div_minimulwc_a 1#1\xint:#2\xint:#3!#4#5#6#7#8\xint:%
{%
\expandafter\XINT_div_minimulwc_b
- \the\numexpr \xint_c_x^ix+#1+#3*#8.#3*#4#5#6#7+#2*#8.#2*#4#5#6#7.%
+ \the\numexpr \xint_c_x^ix+#1+#3*#8\xint:#3*#4#5#6#7+#2*#8\xint:#2*#4#5#6#7\xint:%
}%
-\def\XINT_div_minimulwc_b 1#1#2#3#4#5#6.#7.%
+\def\XINT_div_minimulwc_b 1#1#2#3#4#5#6\xint:#7\xint:%
{%
\expandafter\XINT_div_minimulwc_c
- \the\numexpr \xint_c_x^ix+#1#2#3#4#5+#7.#6.%
+ \the\numexpr \xint_c_x^ix+#1#2#3#4#5+#7\xint:#6\xint:%
}%
-\def\XINT_div_minimulwc_c 1#1#2#3#4#5#6.#7.#8.%
+\def\XINT_div_minimulwc_c 1#1#2#3#4#5#6\xint:#7\xint:#8\xint:%
{%
1#6#7\expandafter!%
\the\numexpr\expandafter\XINT_div_smallmul_a
- \the\numexpr \xint_c_x^viii+#1#2#3#4#5+#8.%
+ \the\numexpr \xint_c_x^viii+#1#2#3#4#5+#8\xint:%
}%
-\def\XINT_div_smallmul_a #1.#2.#3!1#4!%
+\def\XINT_div_smallmul_a #1\xint:#2\xint:#3!1#4!%
{%
- \xint_gob_til_Z #4\XINT_div_smallmul_e\Z
- \XINT_div_minimulwc_a #1.#2.#3!#4.#2.#3!%
+ \xint_gob_til_sc #4\XINT_div_smallmul_e;%
+ \XINT_div_minimulwc_a #1\xint:#2\xint:#3!#4\xint:#2\xint:#3!%
}%
-\def\XINT_div_smallmul_e\Z\XINT_div_minimulwc_a 1#1.#2\Z #3!{1\relax #1!}%
+\def\XINT_div_smallmul_e;\XINT_div_minimulwc_a 1#1\xint:#2;#3!{1\relax #1!}%
% \end{macrocode}
% \lverb|Special very small multiplication for division. We only need to cater
% for multiplicands from 1 to 9. The ending is different from standard
-% verysmallmul, a zero carry is not suppressed. And no final 1\Z! is added. If
+% verysmallmul, a zero carry is not suppressed. And no final 1;! is added. If
% multiplicand is just 1 let's not forget to add the zero carry 100000000! at
% the end.|
% \begin{macrocode}
\def\XINT_div_verysmallmul #1%
- {\xint_gob_til_one #1\XINT_div_verysmallisone 1\XINT_div_verysmallmul_a 0.#1}%
-\def\XINT_div_verysmallisone 1\XINT_div_verysmallmul_a 0.1!1#11\Z!%
+ {\xint_gob_til_one #1\XINT_div_verysmallisone 1\XINT_div_verysmallmul_a 0\xint:#1}%
+\def\XINT_div_verysmallisone 1\XINT_div_verysmallmul_a 0\xint:1!1#11;!%
{1\relax #1100000000!}%
-\def\XINT_div_verysmallmul_a #1.#2!1#3!%
+\def\XINT_div_verysmallmul_a #1\xint:#2!1#3!%
{%
- \xint_gob_til_Z #3\XINT_div_verysmallmul_e\Z
+ \xint_gob_til_sc #3\XINT_div_verysmallmul_e;%
\expandafter\XINT_div_verysmallmul_b
- \the\numexpr \xint_c_x^ix+#2*#3+#1.#2!%
+ \the\numexpr \xint_c_x^ix+#2*#3+#1\xint:#2!%
}%
-\def\XINT_div_verysmallmul_b 1#1#2.%
- {1#2\expandafter!\the\numexpr\XINT_div_verysmallmul_a #1.}%
-\def\XINT_div_verysmallmul_e\Z #1\Z +#2#3!{1\relax 0000000#2!}%
+\def\XINT_div_verysmallmul_b 1#1#2\xint:%
+ {1#2\expandafter!\the\numexpr\XINT_div_verysmallmul_a #1\xint:}%
+\def\XINT_div_verysmallmul_e;#1;+#2#3!{1\relax 0000000#2!}%
% \end{macrocode}
% \lverb|Special subtraction for division purposes. If the subtracted thing
% turns out to be bigger, then just return a -. If not, then we must reverse
@@ -20160,7 +20402,7 @@
{%
\expandafter\XINT_div_sub_clean
\the\numexpr\expandafter\XINT_div_sub_a\expandafter
- 1#2\Z!\Z!\Z!\Z!\Z!\W #1\Z!\Z!\Z!\Z!\Z!\W
+ 1#2;!;!;!;!;!\W #1;!;!;!;!;!\W
}%
\def\XINT_div_sub_clean #1-#2#3\W
{%
@@ -20174,57 +20416,57 @@
}%
\def\XINT_div_sub_b #1#2#3!#4!%
{%
- \xint_gob_til_Z #4\XINT_div_sub_bi \Z
- \expandafter\XINT_div_sub_c\the\numexpr#1-#3+1#4-\xint_c_i.%
+ \xint_gob_til_sc #4\XINT_div_sub_bi ;%
+ \expandafter\XINT_div_sub_c\the\numexpr#1-#3+1#4-\xint_c_i\xint:%
}%
-\def\XINT_div_sub_c 1#1#2.%
+\def\XINT_div_sub_c 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_div_sub_d #1%
}%
\def\XINT_div_sub_d #1#2#3!#4!%
{%
- \xint_gob_til_Z #4\XINT_div_sub_di \Z
- \expandafter\XINT_div_sub_e\the\numexpr#1-#3+1#4-\xint_c_i.%
+ \xint_gob_til_sc #4\XINT_div_sub_di ;%
+ \expandafter\XINT_div_sub_e\the\numexpr#1-#3+1#4-\xint_c_i\xint:%
}%
-\def\XINT_div_sub_e 1#1#2.%
+\def\XINT_div_sub_e 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_div_sub_f #1%
}%
\def\XINT_div_sub_f #1#2#3!#4!%
{%
- \xint_gob_til_Z #4\XINT_div_sub_fi \Z
- \expandafter\XINT_div_sub_g\the\numexpr#1-#3+1#4-\xint_c_i.%
+ \xint_gob_til_sc #4\XINT_div_sub_fi ;%
+ \expandafter\XINT_div_sub_g\the\numexpr#1-#3+1#4-\xint_c_i\xint:%
}%
-\def\XINT_div_sub_g 1#1#2.%
+\def\XINT_div_sub_g 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_div_sub_h #1%
}%
\def\XINT_div_sub_h #1#2#3!#4!%
{%
- \xint_gob_til_Z #4\XINT_div_sub_hi \Z
- \expandafter\XINT_div_sub_i\the\numexpr#1-#3+1#4-\xint_c_i.%
+ \xint_gob_til_sc #4\XINT_div_sub_hi ;%
+ \expandafter\XINT_div_sub_i\the\numexpr#1-#3+1#4-\xint_c_i\xint:%
}%
-\def\XINT_div_sub_i 1#1#2.%
+\def\XINT_div_sub_i 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_div_sub_a #1%
}%
-\def\XINT_div_sub_bi\Z
- \expandafter\XINT_div_sub_c\the\numexpr#1-#2+#3.#4!#5!#6!#7!#8!#9!\Z !\W
+\def\XINT_div_sub_bi;%
+ \expandafter\XINT_div_sub_c\the\numexpr#1-#2+#3\xint:#4!#5!#6!#7!#8!#9!;!\W
{%
\XINT_div_sub_l #1#2!#5!#7!#9!%
}%
-\def\XINT_div_sub_di\Z
- \expandafter\XINT_div_sub_e\the\numexpr#1-#2+#3.#4!#5!#6!#7!#8\W
+\def\XINT_div_sub_di;%
+ \expandafter\XINT_div_sub_e\the\numexpr#1-#2+#3\xint:#4!#5!#6!#7!#8\W
{%
\XINT_div_sub_l #1#2!#5!#7!%
}%
-\def\XINT_div_sub_fi\Z
- \expandafter\XINT_div_sub_g\the\numexpr#1-#2+#3.#4!#5!#6\W
+\def\XINT_div_sub_fi;%
+ \expandafter\XINT_div_sub_g\the\numexpr#1-#2+#3\xint:#4!#5!#6\W
{%
\XINT_div_sub_l #1#2!#5!%
}%
-\def\XINT_div_sub_hi\Z
- \expandafter\XINT_div_sub_i\the\numexpr#1-#2+#3.#4\W
+\def\XINT_div_sub_hi;%
+ \expandafter\XINT_div_sub_i\the\numexpr#1-#2+#3\xint:#4\W
{%
\XINT_div_sub_l #1#2!%
}%
@@ -20243,7 +20485,7 @@
% \lverb|Ici B<10^8 (et est >2). On
% exécute$newline
% \expandafter\XINT_sdiv_out\the\numexpr\XINT_smalldivx_a
-% x.1B!1<8d>!...1<8d>!1\Z!$newline
+% x.1B!1<8d>!...1<8d>!1;!$newline
% avec x =round(B/2), 1B=10^8+B, et A déjà en
% blocs 1<8d>! (non renversés). Le \the\numexpr\XINT_smalldivx_a va produire
% Q\Z R\W avec un R<10^8, et un Q sous forme de blocs 1<8d>! terminé par 1!
@@ -20252,18 +20494,19 @@
%
% |
% \begin{macrocode}
-\def\XINT_sdiv_out #1\Z!#2!%
+\def\XINT_sdiv_out #1;!#2!%
{\expandafter
- {\romannumeral0\XINT_unsep_cuzsmall#11\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W}%
+ {\romannumeral0\XINT_unsep_cuzsmall
+ #1\xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax}%
{#2}}%
% \end{macrocode}
% \lverb|La toute première étape fait la première division pour être sûr par
% la suite d'avoir un premier bloc pour A qui sera < B.|
% \begin{macrocode}
-\def\XINT_smalldivx_a #1.1#2!1#3!%
+\def\XINT_smalldivx_a #1\xint:1#2!1#3!%
{%
\expandafter\XINT_smalldivx_b
- \the\numexpr (#3+#1)/#2-\xint_c_i!#1.#2!#3!%
+ \the\numexpr (#3+#1)/#2-\xint_c_i!#1\xint:#2!#3!%
}%
\def\XINT_smalldivx_b #1#2!%
{%
@@ -20271,28 +20514,23 @@
\xint_c_x^viii+#1#2\xint_afterfi{\expandafter!\the\numexpr}\fi
\XINT_smalldiv_c #1#2!%
}%
-\def\XINT_smalldiv_c #1!#2.#3!#4!%
+\def\XINT_smalldiv_c #1!#2\xint:#3!#4!%
{%
- \expandafter\XINT_smalldiv_d\the\numexpr #4-#1*#3!#2.#3!%
+ \expandafter\XINT_smalldiv_d\the\numexpr #4-#1*#3!#2\xint:#3!%
}%
% \end{macrocode}
% \lverb|On va boucler ici: #1 est un reste, #2 est x.B (avec B sans le 1 mais
% sur huit chiffres). #3#4 est le premier bloc qui reste de A. Si on a terminé
-% avec A, alors #1 est le reste final. Le quotient lui est terminé par un 1!:
-% ce 1! disparaîtra dans le nettoyage par \XINT_unsep_cuzsmall. Ce dernier,
-% malgré le fait qu'on soit dans le bon ordre déjà fait une macro dans le
-% style O(N^2) car sinon le nombre maximal de chiffres serait moitié moins à
-% cause des nettoyages nécessaires après \numexpr. Je suis obligé de faire un
-% nettoyage final car comme l'expansion est engendrée par \numexpr, elle me
-% boufferait des leading zeros si je ne mettais pas un 1 devant chaque bloc en
-% sortie de Q.|
+% avec A, alors #1 est le reste final. Le quotient lui est terminé par un 1!
+% ce 1! disparaîtra dans le nettoyage par \XINT_unsep_cuzsmall.
+% |
% \begin{macrocode}
\def\XINT_smalldiv_d #1!#2!1#3#4!%
{%
- \xint_gob_til_Z #3\XINT_smalldiv_end \Z
+ \xint_gob_til_sc #3\XINT_smalldiv_end ;%
\XINT_smalldiv_e #1!#2!1#3#4!%
}%
-\def\XINT_smalldiv_end\Z\XINT_smalldiv_e #1!#2!1\Z!{1!\Z!#1!}%
+\def\XINT_smalldiv_end;\XINT_smalldiv_e #1!#2!1;!{1!;!#1!}%
% \end{macrocode}
% \lverb|Il est crucial que le reste #1 est < #3. J'ai documenté cette routine
% dans le fichier où j'ai préparé 1.2, il faudra transférer ici. Il n'est pas
@@ -20299,34 +20537,34 @@
% nécessaire pour cette routine que le diviseur B ait au moins 8 chiffres.
% Mais il doit être < 10^8.|
% \begin{macrocode}
-\def\XINT_smalldiv_e #1!#2.#3!%
+\def\XINT_smalldiv_e #1!#2\xint:#3!%
{%
\expandafter\XINT_smalldiv_f\the\numexpr
- \xint_c_xi_e_viii_mone+#1*\xint_c_x^viii/#3!#2.#3!#1!%
+ \xint_c_xi_e_viii_mone+#1*\xint_c_x^viii/#3!#2\xint:#3!#1!%
}%
-\def\XINT_smalldiv_f 1#1#2#3#4#5#6!#7.#8!%
+\def\XINT_smalldiv_f 1#1#2#3#4#5#6!#7\xint:#8!%
{%
\xint_gob_til_zero #1\XINT_smalldiv_fz 0%
\expandafter\XINT_smalldiv_g
- \the\numexpr\XINT_minimul_a #2#3#4#5.#6!#8!#2#3#4#5#6!#7.#8!%
+ \the\numexpr\XINT_minimul_a #2#3#4#5\xint:#6!#8!#2#3#4#5#6!#7\xint:#8!%
}%
\def\XINT_smalldiv_fz 0%
\expandafter\XINT_smalldiv_g\the\numexpr\XINT_minimul_a
- 9999.9999!#1!99999999!#2!0!1#3!%
+ 9999\xint:9999!#1!99999999!#2!0!1#3!%
{%
- \XINT_smalldiv_i .#3!\xint_c_!#2!%
+ \XINT_smalldiv_i \xint:#3!\xint_c_!#2!%
}%
\def\XINT_smalldiv_g 1#1!1#2!#3!#4!#5!#6!%
{%
- \expandafter\XINT_smalldiv_h\the\numexpr 1#6-#1.#2!#5!#3!#4!%
+ \expandafter\XINT_smalldiv_h\the\numexpr 1#6-#1\xint:#2!#5!#3!#4!%
}%
-\def\XINT_smalldiv_h 1#1#2.#3!#4!%
+\def\XINT_smalldiv_h 1#1#2\xint:#3!#4!%
{%
- \expandafter\XINT_smalldiv_i\the\numexpr #4-#3+#1-\xint_c_i.#2!%
+ \expandafter\XINT_smalldiv_i\the\numexpr #4-#3+#1-\xint_c_i\xint:#2!%
}%
-\def\XINT_smalldiv_i #1.#2!#3!#4.#5!%
+\def\XINT_smalldiv_i #1\xint:#2!#3!#4\xint:#5!%
{%
- \expandafter\XINT_smalldiv_j\the\numexpr (#1#2+#4)/#5-\xint_c_i!#3!#1#2!#4.#5!%
+ \expandafter\XINT_smalldiv_j\the\numexpr (#1#2+#4)/#5-\xint_c_i!#3!#1#2!#4\xint:#5!%
}%
\def\XINT_smalldiv_j #1!#2!%
{%
@@ -20336,9 +20574,9 @@
% \end{macrocode}
% \lverb|On boucle vers \XINT_smalldiv_d.|
% \begin{macrocode}
-\def\XINT_smalldiv_k #1!#2!#3.#4!%
+\def\XINT_smalldiv_k #1!#2!#3\xint:#4!%
{%
- \expandafter\XINT_smalldiv_d\the\numexpr #2-#1*#4!#3.#4!%
+ \expandafter\XINT_smalldiv_d\the\numexpr #2-#1*#4!#3\xint:#4!%
}%
% \end{macrocode}
% \lverb|Cette routine fait la division euclidienne d'un nombre de seize
@@ -20351,14 +20589,14 @@
% principale va utiliser ce quotient pour déterminer le "grand" reste, et le
% petit reste ici ne nous serait d'à peu près aucune utilité.
%
-% ATTENTION UNIQUEMENT UTILISÉ POUR DES SITUATIONS OÙ IL EST GARANTI QUE X < C
-% !! (et C au moins 10^7) le quotient euclidien de X*10^8+Y par C sera donc <
+% ATTENTION UNIQUEMENT UTILISÉ POUR DES SITUATIONS OÙ IL EST GARANTI QUE X <
+% C ! (et C au moins 10^7) le quotient euclidien de X*10^8+Y par C sera donc <
% 10^8. Il sera renvoyé sous la forme 1<8chiffres>.|
% \begin{macrocode}
-\def\XINT_div_mini #1.#2!1#3!%
+\def\XINT_div_mini #1\xint:#2!1#3!%
{%
\expandafter\XINT_div_mini_a\the\numexpr
- \xint_c_xi_e_viii_mone+#3*\xint_c_x^viii/#1!#1.#2!#3!%
+ \xint_c_xi_e_viii_mone+#3*\xint_c_x^viii/#1!#1\xint:#2!#3!%
}%
% \end{macrocode}
% \lverb|Note (2015/10/08). Attention à la différence dans l'ordre des
@@ -20365,15 +20603,15 @@
% arguments avec ce que je vois en dans \XINT_smalldiv_f. Je ne me souviens
% plus du tout s'il y a une raison quelconque.|
% \begin{macrocode}
-\def\XINT_div_mini_a 1#1#2#3#4#5#6!#7.#8!%
+\def\XINT_div_mini_a 1#1#2#3#4#5#6!#7\xint:#8!%
{%
\xint_gob_til_zero #1\XINT_div_mini_w 0%
\expandafter\XINT_div_mini_b
- \the\numexpr\XINT_minimul_a #2#3#4#5.#6!#7!#2#3#4#5#6!#7.#8!%
+ \the\numexpr\XINT_minimul_a #2#3#4#5\xint:#6!#7!#2#3#4#5#6!#7\xint:#8!%
}%
\def\XINT_div_mini_w 0%
\expandafter\XINT_div_mini_b\the\numexpr\XINT_minimul_a
- 9999.9999!#1!99999999!#2.#3!00000000!#4!%
+ 9999\xint:9999!#1!99999999!#2\xint:#3!00000000!#4!%
{%
\xint_c_x^viii_mone+(#4+#3)/#2!%
}%
@@ -20380,41 +20618,46 @@
\def\XINT_div_mini_b 1#1!1#2!#3!#4!#5!#6!%
{%
\expandafter\XINT_div_mini_c
- \the\numexpr 1#6-#1.#2!#5!#3!#4!%
+ \the\numexpr 1#6-#1\xint:#2!#5!#3!#4!%
}%
-\def\XINT_div_mini_c 1#1#2.#3!#4!%
+\def\XINT_div_mini_c 1#1#2\xint:#3!#4!%
{%
\expandafter\XINT_div_mini_d
- \the\numexpr #4-#3+#1-\xint_c_i.#2!%
+ \the\numexpr #4-#3+#1-\xint_c_i\xint:#2!%
}%
-\def\XINT_div_mini_d #1.#2!#3!#4.#5!%
+\def\XINT_div_mini_d #1\xint:#2!#3!#4\xint:#5!%
{%
\xint_c_x^viii_mone+#3+(#1#2+#5)/#4!%
}%
% \end{macrocode}
+% \subsection*{Derived arithmetic}
+% \addcontentsline{toc}{subsection}{Derived arithmetic}
% \subsection{\csh{xintiDivRound}, \csh{xintiiDivRound}}
% \lverb|1.1, transferred from first release of bnumexpr. Rewritten for 1.2.
-% Ending rewritten for 1.2i. (new \xintDSRr).|
+% Ending rewritten for 1.2i. (new \xintDSRr).
+%
+% 1.2l: \xintiiDivRound made robust against non terminated input.|
% \begin{macrocode}
\def\xintiDivRound {\romannumeral0\xintidivround }%
\def\xintidivround #1%
- {\expandafter\XINT_idivround\romannumeral0\xintnum{#1}\Z }%
+ {\expandafter\XINT_idivround\romannumeral0\xintnum{#1}\xint:}%
\def\xintiiDivRound {\romannumeral0\xintiidivround }%
-\def\xintiidivround #1{\expandafter\XINT_iidivround \romannumeral`&&@#1\Z }%
-\def\XINT_idivround #1#2\Z #3%
+\def\xintiidivround #1{\expandafter\XINT_iidivround\romannumeral`&&@#1\xint:}%
+\def\XINT_idivround #1#2\xint:#3%
{\expandafter\XINT_iidivround_a\expandafter #1%
- \romannumeral0\xintnum{#3}\Z #2\Z }%
-\def\XINT_iidivround #1#2\Z #3%
- {\expandafter\XINT_iidivround_a\expandafter #1\romannumeral`&&@#3\Z #2\Z }%
+ \romannumeral0\xintnum{#3}\xint:#2\xint:}%
+\def\XINT_iidivround #1#2\xint:#3%
+ {\expandafter\XINT_iidivround_a\expandafter #1\romannumeral`&&@#3\xint:#2\xint:}%
\def\XINT_iidivround_a #1#2% #1 de A, #2 de B.
{%
- \if0#2\xint_dothis\XINT_iidivround_divbyzero\fi
+ \if0#2\xint_dothis{\XINT_iidivround_divbyzero#1#2}\fi
\if0#1\xint_dothis\XINT_iidivround_aiszero\fi
\if-#2\xint_dothis{\XINT_iidivround_bneg #1}\fi
\xint_orthat{\XINT_iidivround_bpos #1#2}%
}%
-\def\XINT_iidivround_divbyzero #1\Z #2\Z {\xintError:DivisionByZero\space 0}%
-\def\XINT_iidivround_aiszero #1\Z #2\Z { 0}%
+\def\XINT_iidivround_divbyzero #1#2#3\xint:#4\xint:
+ {\XINT_signalcondition{DivisionByZero}{Division of #1#4 by #2#3}{}{0}}%
+\def\XINT_iidivround_aiszero #1\xint:#2\xint:{ 0}%
\def\XINT_iidivround_bpos #1%
{%
\xint_UDsignfork
@@ -20429,7 +20672,7 @@
-{\xintiiopp\XINT_iidivround_pos #1}%
\krof
}%
-\def\XINT_iidivround_pos #1#2\Z #3\Z
+\def\XINT_iidivround_pos #1#2\xint:#3\xint:
{%
\expandafter\expandafter\expandafter\XINT_dsrr
\expandafter\xint_firstoftwo
@@ -20438,16 +20681,17 @@
}%
% \end{macrocode}
% \subsection{\csh{xintiDivTrunc}, \csh{xintiiDivTrunc}}
+% \lverb|1.2l: \xintiiDivTrunc made robust against non terminated input.|
% \begin{macrocode}
\def\xintiDivTrunc {\romannumeral0\xintidivtrunc }%
-\def\xintidivtrunc #1{\expandafter\XINT_iidivtrunc\romannumeral0\xintnum{#1}\Z }%
+\def\xintidivtrunc #1{\expandafter\XINT_iidivtrunc\romannumeral0\xintnum{#1}\xint:}%
\def\xintiiDivTrunc {\romannumeral0\xintiidivtrunc }%
-\def\xintiidivtrunc #1{\expandafter\XINT_iidivtrunc \romannumeral`&&@#1\Z }%
-\def\XINT_iidivtrunc #1#2\Z #3{\expandafter\XINT_iidivtrunc_a\expandafter #1%
- \romannumeral`&&@#3\Z #2\Z }%
+\def\xintiidivtrunc #1{\expandafter\XINT_iidivtrunc\romannumeral`&&@#1\xint:}%
+\def\XINT_iidivtrunc #1#2\xint:#3{\expandafter\XINT_iidivtrunc_a\expandafter #1%
+ \romannumeral`&&@#3\xint:#2\xint:}%
\def\XINT_iidivtrunc_a #1#2% #1 de A, #2 de B.
{%
- \if0#2\xint_dothis\XINT_iidivround_divbyzero\fi
+ \if0#2\xint_dothis{\XINT_iidivround_divbyzero#1#2}\fi
\if0#1\xint_dothis\XINT_iidivround_aiszero\fi
\if-#2\xint_dothis{\XINT_iidivtrunc_bneg #1}\fi
\xint_orthat{\XINT_iidivtrunc_bpos #1#2}%
@@ -20466,7 +20710,7 @@
-{\xintiiopp\XINT_iidivtrunc_pos #1}%
\krof
}%
-\def\XINT_iidivtrunc_pos #1#2\Z #3\Z%
+\def\XINT_iidivtrunc_pos #1#2\xint:#3\xint:
{\expandafter\xint_firstoftwo_thenstop
\romannumeral0\XINT_div_prepare {#2}{#1#3}}%
% \end{macrocode}
@@ -20473,14 +20717,14 @@
% \subsection{\csh{xintiMod}, \csh{xintiiMod}}
% \begin{macrocode}
\def\xintiMod {\romannumeral0\xintimod }%
-\def\xintimod #1{\expandafter\XINT_iimod\romannumeral0\xintnum{#1}\Z }%
+\def\xintimod #1{\expandafter\XINT_iimod\romannumeral0\xintnum{#1}\xint:}%
\def\xintiiMod {\romannumeral0\xintiimod }%
-\def\xintiimod #1{\expandafter\XINT_iimod \romannumeral`&&@#1\Z }%
-\def\XINT_iimod #1#2\Z #3{\expandafter\XINT_iimod_a\expandafter #1%
- \romannumeral`&&@#3\Z #2\Z }%
+\def\xintiimod #1{\expandafter\XINT_iimod\romannumeral`&&@#1\xint:}%
+\def\XINT_iimod #1#2\xint:#3{\expandafter\XINT_iimod_a\expandafter #1%
+ \romannumeral`&&@#3\xint:#2\xint:}%
\def\XINT_iimod_a #1#2% #1 de A, #2 de B.
{%
- \if0#2\xint_dothis\XINT_iidivround_divbyzero\fi
+ \if0#2\xint_dothis{\XINT_iidivround_divbyzero#1#2}\fi
\if0#1\xint_dothis\XINT_iidivround_aiszero\fi
\if-#2\xint_dothis{\XINT_iimod_bneg #1}\fi
\xint_orthat{\XINT_iimod_bpos #1#2}%
@@ -20499,11 +20743,408 @@
-{\XINT_iimod_pos #1}%
\krof
}%
-\def\XINT_iimod_pos #1#2\Z #3\Z%
+\def\XINT_iimod_pos #1#2\xint:#3\xint:
{\expandafter\xint_secondoftwo_thenstop\romannumeral0\XINT_div_prepare
{#2}{#1#3}}%
% \end{macrocode}
-% \subsection{``Load \xintfracnameimp'' macros}
+% \subsection{\csh{xintiSqr}, \csh{xintiiSqr}}
+% \lverb|1.2l: \xintiiSqr made robust against non terminated input.|
+% \begin{macrocode}
+\def\xintiiSqr {\romannumeral0\xintiisqr }%
+\def\xintiisqr #1%
+{%
+ \expandafter\XINT_sqr\romannumeral0\xintiiabs{#1}\xint:
+}%
+\def\xintiSqr {\romannumeral0\xintisqr }%
+\def\xintisqr #1%
+{%
+ \expandafter\XINT_sqr\romannumeral0\xintiabs{#1}\xint:
+}%
+\def\XINT_sqr #1\xint:
+{%
+ \expandafter\XINT_sqr_a
+ \romannumeral0\expandafter\XINT_sepandrev_andcount
+ \romannumeral0\XINT_zeroes_forviii #1\R\R\R\R\R\R\R\R{10}0000001\W
+ #1\XINT_rsepbyviii_end_A 2345678%
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
+ \xint:
+}%
+% \end{macrocode}
+% \lverb|1.2c \XINT_mul_loop can now be called directly even with small
+% arguments, thus the following check is not anymore a necessity.|
+% \begin{macrocode}
+\def\XINT_sqr_a #1\xint:
+{%
+ \ifnum #1=\xint_c_i \expandafter\XINT_sqr_small
+ \else\expandafter\XINT_sqr_start\fi
+}%
+\def\XINT_sqr_small 1#1#2#3#4#5!\xint:
+{%
+ \ifnum #1#2#3#4#5<46341 \expandafter\XINT_sqr_verysmall\fi
+ \expandafter\XINT_sqr_small_out
+ \the\numexpr\XINT_minimul_a #1#2#3#4\xint:#5!#1#2#3#4#5!%
+}%
+\def\XINT_sqr_verysmall#1{%
+\def\XINT_sqr_verysmall
+ \expandafter\XINT_sqr_small_out\the\numexpr\XINT_minimul_a ##1!##2!%
+ {\expandafter#1\the\numexpr ##2*##2\relax}%
+}\XINT_sqr_verysmall{ }%
+\def\XINT_sqr_small_out 1#1!1#2!%
+{%
+ \XINT_cuz #2#1\R
+}%
+% \end{macrocode}
+% \lverb|An ending 1;! is produced on output for \XINT_mul_loop and gets
+% incorporated to the delimiter needed by the \XINT_unrevbyviii done by
+% \XINT_mul_out.|
+% \begin{macrocode}
+\def\XINT_sqr_start #1\xint:
+{%
+ \expandafter\XINT_mul_out
+ \the\numexpr\XINT_mul_loop
+ 100000000!1;!\W #11;!\W #11;!%
+ 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+}%
+% \end{macrocode}
+% \subsection{\csh{xintiPow}, \csh{xintiiPow}}
+% \lverb|&
+% The exponent is not limited but with current default settings of tex memory,
+% with xint 1.2, the maximal exponent for 2^N is N = 2^17 = 131072.
+%
+% 1.2f Modifies the initial steps: 1) in order to be able to let more easily
+% \xintiPow use \xintNum on the exponent once xintfrac.sty is loaded; 2) also
+% because I noticed it was not very well coded. And it did only a \numexpr on
+% the exponent, contradicting the documentation related to the "i" convention
+% in names.
+%
+% 1.2l: \xintiiPow made robust against non terminated input.|
+% \begin{macrocode}
+\def\xintiiPow {\romannumeral0\xintiipow }%
+\def\xintiipow #1#2%
+{%
+ \expandafter\xint_pow\the\numexpr #2\expandafter
+ .\romannumeral`&&@#1\xint:
+}%
+\def\xintiPow {\romannumeral0\xintipow }%
+\def\xintipow #1#2%
+{%
+ \expandafter\xint_pow\the\numexpr #2\expandafter
+ .\romannumeral0\xintnum{#1}\xint:
+}%
+\def\xint_pow #1.#2%#3\xint:
+{%
+ \xint_UDzerominusfork
+ #2-\XINT_pow_AisZero
+ 0#2\XINT_pow_Aneg
+ 0-{\XINT_pow_Apos #2}%
+ \krof {#1}%
+}%
+\def\XINT_pow_AisZero #1#2\xint:
+{%
+ \ifcase\XINT_cntSgn #1\xint:
+ \xint_afterfi { 1}%
+ \or
+ \xint_afterfi { 0}%
+ \else
+ \xint_afterfi
+ {\XINT_signalcondition{DivisionByZero}{Zero to power #1}{}{0}}%
+ \fi
+}%
+\def\XINT_pow_Aneg #1%
+{%
+ \ifodd #1
+ \expandafter\XINT_opp\romannumeral0%
+ \fi
+ \XINT_pow_Apos {}{#1}%
+}%
+\def\XINT_pow_Apos #1#2{\XINT_pow_Apos_a {#2}#1}%
+\def\XINT_pow_Apos_a #1#2#3%
+{%
+ \xint_gob_til_xint: #3\XINT_pow_Apos_short\xint:
+ \XINT_pow_AatleastTwo {#1}#2#3%
+}%
+\def\XINT_pow_Apos_short\xint:\XINT_pow_AatleastTwo #1#2\xint:
+{%
+ \ifcase #2
+ \xintError:thiscannothappen
+ \or \expandafter\XINT_pow_AisOne
+ \else\expandafter\XINT_pow_AatleastTwo
+ \fi {#1}#2\xint:
+}%
+\def\XINT_pow_AisOne #1\xint:{ 1}%
+\def\XINT_pow_AatleastTwo #1%
+{%
+ \ifcase\XINT_cntSgn #1\xint:
+ \expandafter\XINT_pow_BisZero
+ \or
+ \expandafter\XINT_pow_I_in
+ \else
+ \expandafter\XINT_pow_BisNegative
+ \fi
+ {#1}%
+}%
+\def\XINT_pow_BisNegative #1\xint:{\XINT_signalcondition{Underflow}{Inverse power
+ can not be represented by an integer}{}{0}}%
+\def\XINT_pow_BisZero #1\xint:{ 1}%
+% \end{macrocode}
+% \lverb|B = #1 > 0, A = #2 > 1. Earlier code checked if size of B did not
+% exceed a given limit (for example 131000).|
+% \begin{macrocode}
+\def\XINT_pow_I_in #1#2\xint:
+{%
+ \expandafter\XINT_pow_I_loop
+ \the\numexpr #1\expandafter\xint:%
+ \romannumeral0\expandafter\XINT_sepandrev
+ \romannumeral0\XINT_zeroes_forviii #2\R\R\R\R\R\R\R\R{10}0000001\W
+ #2\XINT_rsepbyviii_end_A 2345678%
+ \XINT_rsepbyviii_end_B 2345678\relax XX%
+ \R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\W
+ 1;!\W
+ 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+}%
+\def\XINT_pow_I_loop #1\xint:%
+{%
+ \ifnum #1 = \xint_c_i\expandafter\XINT_pow_I_exit\fi
+ \ifodd #1
+ \expandafter\XINT_pow_II_in
+ \else
+ \expandafter\XINT_pow_I_squareit
+ \fi #1\xint:%
+}%
+\def\XINT_pow_I_exit \ifodd #1\fi #2\xint:#3\W {\XINT_mul_out #3}%
+% \end{macrocode}
+% \lverb|The 1.2c \XINT_mul_loop can be called directly even with small
+% arguments, hence the "butcheckifsmall" is not a necessity as it was earlier
+% with 1.2. On 2^30, it does bring roughly a 40$char37 $space time gain
+% though, and 30$char37 $space gain for 2^60. The overhead on big computations
+% should be negligible.|
+% \begin{macrocode}
+\def\XINT_pow_I_squareit #1\xint:#2\W%
+{%
+ \expandafter\XINT_pow_I_loop
+ \the\numexpr #1/\xint_c_ii\expandafter\xint:%
+ \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W
+}%
+\def\XINT_pow_mulbutcheckifsmall #1!1#2%
+{%
+ \xint_gob_til_sc #2\XINT_pow_mul_small;%
+ \XINT_mul_loop 100000000!1;!\W #1!1#2%
+}%
+\def\XINT_pow_mul_small;\XINT_mul_loop
+ 100000000!1;!\W 1#1!1;!\W
+{%
+ \XINT_smallmul 1#1!%
+}%
+\def\XINT_pow_II_in #1\xint:#2\W
+{%
+ \expandafter\XINT_pow_II_loop
+ \the\numexpr #1/\xint_c_ii-\xint_c_i\expandafter\xint:%
+ \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W #2\W
+}%
+\def\XINT_pow_II_loop #1\xint:%
+{%
+ \ifnum #1 = \xint_c_i\expandafter\XINT_pow_II_exit\fi
+ \ifodd #1
+ \expandafter\XINT_pow_II_odda
+ \else
+ \expandafter\XINT_pow_II_even
+ \fi #1\xint:%
+}%
+\def\XINT_pow_II_exit\ifodd #1\fi #2\xint:#3\W #4\W
+{%
+ \expandafter\XINT_mul_out
+ \the\numexpr\XINT_pow_mulbutcheckifsmall #4\W #3%
+}%
+\def\XINT_pow_II_even #1\xint:#2\W
+{%
+ \expandafter\XINT_pow_II_loop
+ \the\numexpr #1/\xint_c_ii\expandafter\xint:%
+ \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W
+}%
+\def\XINT_pow_II_odda #1\xint:#2\W #3\W
+{%
+ \expandafter\XINT_pow_II_oddb
+ \the\numexpr #1/\xint_c_ii-\xint_c_i\expandafter\xint:%
+ \the\numexpr\XINT_pow_mulbutcheckifsmall #3\W #2\W #2\W
+}%
+\def\XINT_pow_II_oddb #1\xint:#2\W #3\W
+{%
+ \expandafter\XINT_pow_II_loop
+ \the\numexpr #1\expandafter\xint:%
+ \the\numexpr\XINT_pow_mulbutcheckifsmall #3\W #3\W #2\W
+}%
+% \end{macrocode}
+% \subsection{\csh{xintiFac}, \csh{xintiiFac}}
+% \lverb|Moved here from xint.sty with release 1.2 (to be usable by \bnumexpr).
+%
+% Partially rewritten with release 1.2 to benefit from the inner format of the
+% 1.2 multiplication.
+%
+% With current default settings of the etex memory and a.t.t.o.w (11/2015) the
+% maximal possible computation is 5971! (which has 19956 digits).
+%
+%
+%
+% Note (end november 2015): I also tried out a quickly written recursive
+% (binary split) implementation
+%
+%( \catcode`_ 11
+%: \catcode`^ 11
+%: \long\def\xint_firstofthree #1#2#3{#1}$%
+%: \long\def\xint_secondofthree #1#2#3{#2}$%
+%: \long\def\xint_thirdofthree #1#2#3{#3}$%
+%: $% quickly written factorial using binary split recursive method
+%: \def\tFac {\romannumeral-`0\tfac }$%
+%: \def\tfac #1{\expandafter\XINT_mul_out
+%: \romannumeral-`0\ufac {1}{#1}1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W}$%
+%: \def\ufac #1#2{\ifcase\numexpr#2-#1\relax
+%: \expandafter\xint_firstofthree
+%: \or
+%: \expandafter\xint_secondofthree
+%: \else
+%: \expandafter\xint_thirdofthree
+%: \fi
+%: {\the\numexpr\xint_c_x^viii+#1!1;!}$%
+%: {\the\numexpr\xint_c_x^viii+#1*#2!1;!}$%
+%: {\expandafter\vfac\the\numexpr (#1+#2)/\xint_c_ii.#1.#2.}$%
+%: }$%
+%: \def\vfac #1.#2.#3.$%
+%: {$%
+%: \expandafter
+%: \wfac\expandafter
+%: {\romannumeral-`0\expandafter
+%: \ufac\expandafter{\the\numexpr #1+\xint_c_i}{#3}}$%
+%: {\ufac {#2}{#1}}$%
+%: }$%
+%: \def\wfac #1#2{\expandafter\zfac\romannumeral-`0#2\W #1}$%
+%: \def\zfac {\the\numexpr\XINT_mul_loop 100000000!1;!\W }$% core multiplication...
+%: \catcode`_ 8
+%: \catcode`^ 7
+%)
+% and I was quite surprised that it was only about 1.6x--2x slower in the range
+% N=200 to 2000 than the \xintiiFac here which attempts to be smarter...
+%
+% Note (2017, 1.2l): I found out some code comment of mine that the code here
+% should be more in the style of \xintiiBinomial, but I left matters
+% untouched.
+%
+%
+% |
+% \begin{macrocode}
+\def\xintiiFac {\romannumeral0\xintiifac }%
+\def\xintiifac #1{\expandafter\XINT_fac_fork\the\numexpr#1.}%
+\def\xintiFac {\romannumeral0\xintifac }%
+\let\xintifac\xintiifac
+\def\XINT_fac_fork #1#2.%
+{%
+ \xint_UDzerominusfork
+ #1-\XINT_fac_zero
+ 0#1\XINT_fac_neg
+ 0-\XINT_fac_checksize
+ \krof #1#2.%
+}%
+\def\XINT_fac_zero #1.{ 1}%
+\def\XINT_fac_neg #1.{\XINT_signalcondition{InvalidOperation}{Factorial of
+ negative: (#1)!}{}{0}}%
+% \end{macrocode}
+% \begin{macrocode}
+\def\XINT_fac_checksize #1.%
+{%
+ \ifnum #1>\xint_c_x^iv \xint_dothis{\XINT_fac_toobig #1.}\fi
+ \ifnum #1>465 \xint_dothis{\XINT_fac_bigloop_a #1.}\fi
+ \ifnum #1>101 \xint_dothis{\XINT_fac_medloop_a #1.\XINT_mul_out}\fi
+ \xint_orthat{\XINT_fac_smallloop_a #1.\XINT_mul_out}%
+ 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+}%
+\def\XINT_fac_toobig #1.#2\W{\XINT_signalcondition{InvalidOperation}{Factorial
+ of too big argument: #1 > 10000}{}{0}}%
+\def\XINT_fac_bigloop_a #1.%
+{%
+ \expandafter\XINT_fac_bigloop_b \the\numexpr
+ #1+\xint_c_i-\xint_c_ii*((#1-464)/\xint_c_ii).#1.%
+}%
+\def\XINT_fac_bigloop_b #1.#2.%
+{%
+ \expandafter\XINT_fac_medloop_a
+ \the\numexpr #1-\xint_c_i.{\XINT_fac_bigloop_loop #1.#2.}%
+}%
+\def\XINT_fac_bigloop_loop #1.#2.%
+{%
+ \ifnum #1>#2 \expandafter\XINT_fac_bigloop_exit\fi
+ \expandafter\XINT_fac_bigloop_loop
+ \the\numexpr #1+\xint_c_ii\expandafter.%
+ \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_bigloop_mul #1!%
+}%
+\def\XINT_fac_bigloop_exit #1!{\XINT_mul_out}%
+\def\XINT_fac_bigloop_mul #1!%
+{%
+ \expandafter\XINT_smallmul
+ \the\numexpr \xint_c_x^viii+#1*(#1+\xint_c_i)!%
+}%
+\def\XINT_fac_medloop_a #1.%
+{%
+ \expandafter\XINT_fac_medloop_b
+ \the\numexpr #1+\xint_c_i-\xint_c_iii*((#1-100)/\xint_c_iii).#1.%
+}%
+\def\XINT_fac_medloop_b #1.#2.%
+{%
+ \expandafter\XINT_fac_smallloop_a
+ \the\numexpr #1-\xint_c_i.{\XINT_fac_medloop_loop #1.#2.}%
+}%
+\def\XINT_fac_medloop_loop #1.#2.%
+{%
+ \ifnum #1>#2 \expandafter\XINT_fac_loop_exit\fi
+ \expandafter\XINT_fac_medloop_loop
+ \the\numexpr #1+\xint_c_iii\expandafter.%
+ \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_medloop_mul #1!%
+}%
+\def\XINT_fac_medloop_mul #1!%
+{%
+ \expandafter\XINT_smallmul
+ \the\numexpr
+ \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)!%
+}%
+\def\XINT_fac_smallloop_a #1.%
+{%
+ \csname
+ XINT_fac_smallloop_\the\numexpr #1-\xint_c_iv*(#1/\xint_c_iv)\relax
+ \endcsname #1.%
+}%
+\expandafter\def\csname XINT_fac_smallloop_1\endcsname #1.%
+{%
+ \XINT_fac_smallloop_loop 2.#1.100000001!1;!%
+}%
+\expandafter\def\csname XINT_fac_smallloop_-2\endcsname #1.%
+{%
+ \XINT_fac_smallloop_loop 3.#1.100000002!1;!%
+}%
+\expandafter\def\csname XINT_fac_smallloop_-1\endcsname #1.%
+{%
+ \XINT_fac_smallloop_loop 4.#1.100000006!1;!%
+}%
+\expandafter\def\csname XINT_fac_smallloop_0\endcsname #1.%
+{%
+ \XINT_fac_smallloop_loop 5.#1.1000000024!1;!%
+}%
+\def\XINT_fac_smallloop_loop #1.#2.%
+{%
+ \ifnum #1>#2 \expandafter\XINT_fac_loop_exit\fi
+ \expandafter\XINT_fac_smallloop_loop
+ \the\numexpr #1+\xint_c_iv\expandafter.%
+ \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_smallloop_mul #1!%
+}%
+\def\XINT_fac_smallloop_mul #1!%
+{%
+ \expandafter\XINT_smallmul
+ \the\numexpr
+ \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)*(#1+\xint_c_iii)!%
+}%
+\def\XINT_fac_loop_exit #1!#2;!#3{#3#2;!}%
+% \end{macrocode}
+% \subsection*{``Load \xintfracnameimp'' macros}
+% \addcontentsline{toc}{subsection}{``Load \xintfracnameimp'' macros}
% \lverb|Originally was used in \xintiiexpr. Transferred from xintfrac for 1.1.|
% \begin{macrocode}
\catcode`! 11
@@ -20516,6 +21157,7 @@
\def\xintSqr {\Did_you_mean_iiSqr?or_load_xintfrac!}%
\def\xintQuo {\Removed!use_xintiQuo_or_xintiiQuo!}%
\def\xintRem {\Removed!use_xintiRem_or_xintiiRem!}%
+\catcode`! 12
\XINT_restorecatcodes_endinput%
% \end{macrocode}
%
@@ -20585,7 +21227,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xint}%
- [2017/01/06 1.2k Expandable operations on big integers (JFB)]%
+ [2017/07/26 1.2l Expandable operations on big integers (JFB)]%
% \end{macrocode}
% \subsection{More token management}
% \begin{macrocode}
@@ -20595,10 +21237,6 @@
\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}%
-\edef\xint_cleanupzeros_andstop #1#2#3#4%
-{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4\relax
-}%
% \end{macrocode}
% \subsection{\csh{xintSgnFork}}
% \lverb|Expandable three-way fork added in 1.07. The argument #1 must expand
@@ -20633,8 +21271,8 @@
\unless\if#11\xint_dothis{ 0}\fi
\xint_orthat{ 1}%
}%
-\def\XINT_isOne #1{\XINT_is_one#1XY}%
-\def\XINT_is_one #1#2#3Y%
+\def\XINT_isOne #1{\XINT_is_One#1XY}%
+\def\XINT_is_One #1#2#3Y%
{%
\unless\if#2X\xint_dothis0\fi
\unless\if#11\xint_dothis0\fi
@@ -20641,32 +21279,62 @@
\xint_orthat1%
}%
% \end{macrocode}
-% \subsection{\csh{xintRev}}
+% \subsection{\csh{xintReverseDigits}}
% \lverb|&
-% \xintRev: expands fully its argument \romannumeral-`0, and checks the sign.
-% However this last aspect does not appear like a very useful thing. And despite
-% the fact that a special check is made for a sign, actually the input is not
-% given to \xintnum, contrarily to \xintLen. This is all a bit incoherent.
-% Should be fixed.
+% 1.2.
%
-% 1.2 has \xintReverseDigits and I thus make \xintRev an alias. Remarks above
-% not addressed.|
+% This puts digits in reverse order, not suppressing leading zeros
+% after reverse. Despite lacking the "ii" in its name, it does not apply
+% \xintNum to its argument (contrarily to \xintLen, this is not very coherent).
+%
+% 1.2l variant is robust against non terminated \the\numexpr input.
+%
+% This macro is currently not used elsewhere in xint code.
+% |
% \begin{macrocode}
+\def\xintReverseDigits {\romannumeral0\xintreversedigits }%
+\def\xintreversedigits #1%
+{%
+ \expandafter\XINT_revdigits\romannumeral`&&@#1%
+ {\XINT_microrevsep_end\W}\XINT_microrevsep_end
+ \XINT_microrevsep_end\XINT_microrevsep_end
+ \XINT_microrevsep_end\XINT_microrevsep_end
+ \XINT_microrevsep_end\XINT_microrevsep_end\XINT_microrevsep_end\Z
+ 1\Z!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+}%
+\def\XINT_revdigits #1%
+{%
+ \xint_UDsignfork
+ #1{\expandafter-\romannumeral0\XINT_revdigits_a}%
+ -{\XINT_revdigits_a #1}%
+ \krof
+}%
+\def\XINT_revdigits_a
+{%
+ \expandafter\XINT_revdigits_b\expandafter{\expandafter}%
+ \the\numexpr\XINT_microrevsep
+}%
+\def\XINT_microrevsep #1#2#3#4#5#6#7#8#9%
+{%
+ 1#9#8#7#6#5#4#3#2#1\expandafter!\the\numexpr\XINT_microrevsep
+}%
+\def\XINT_microrevsep_end #1\W #2\expandafter #3\Z{\relax#2!}%
+\def\XINT_revdigits_b #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
+{%
+ \xint_gob_til_R #9\XINT_revdigits_end\R
+ \XINT_revdigits_b {#9#8#7#6#5#4#3#2#1}%
+}%
+\def\XINT_revdigits_end#1{%
+\def\XINT_revdigits_end\R\XINT_revdigits_b ##1##2\W
+ {\expandafter#1\xint_gob_til_Z ##1}%
+}\XINT_revdigits_end{ }%
\let\xintRev\xintReverseDigits
% \end{macrocode}
% \subsection{\csh{xintLen}}
% \lverb|\xintLen is ONLY for (possibly long) integers. Gets extended to
-% fractions by xintfrac.sty.
+% fractions by xintfrac.sty. It applies \xintNum to its argument. A minus sign
+% is accepted and ignored.
%
-% 2016/12/23. For no reason at all I botchered this venerable macro at the
-% time of 1.2i release (I came here to update the pattern of the length loop
-% which had been modified) and got tricked by \unexpanded which I used in an
-% \edef to insert a space token and avoid having to put many \noexpand's. But
-% this converted a #1 into a ##1 with deplorable effect that \xintLen{-1}
-% outputted 3 and not 1 :(( awful. Also, I did another error in the \xintLen
-% of xintfrac.sty, simply forgetting there to not count the sign. Too bad I
-% become aware of this after having already released 1.2j. I know, regression
-% suite is highest priority. Fixed in 1.2k.
% |
% \begin{macrocode}
\def\xintLen {\romannumeral0\xintlen }%
@@ -20674,8 +21342,7 @@
{%
\expandafter#1\the\numexpr
\expandafter\XINT_len_fork\romannumeral0\xintnum{##1}%
- \xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ \xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye\relax
}}\xintlen{ }%
@@ -20899,176 +21566,6 @@
\fi
}%
% \end{macrocode}
-% \subsection{\csh{xintCmp}, \csh{xintiiCmp}}
-% \lverb|Faster than doing the full subtraction.|
-% \begin{macrocode}
-\def\xintCmp {\romannumeral0\xintcmp }%
-\def\xintcmp #1{\expandafter\XINT_icmp\romannumeral0\xintnum{#1}\Z }%
-\def\xintiiCmp {\romannumeral0\xintiicmp }%
-\def\xintiicmp #1{\expandafter\XINT_iicmp\romannumeral`&&@#1\Z }%
-\def\XINT_iicmp #1#2\Z #3%
-{%
- \expandafter\XINT_cmp_nfork\expandafter #1\romannumeral`&&@#3\Z #2\Z
-}%
-\let\XINT_Cmp \xintiiCmp
-\def\XINT_icmp #1#2\Z #3%
-{%
- \expandafter\XINT_cmp_nfork\expandafter #1\romannumeral0\xintnum{#3}\Z #2\Z
-}%
-\def\XINT_cmp_nfork #1#2%
-{%
- \xint_UDzerofork
- #1\XINT_cmp_firstiszero
- #2\XINT_cmp_secondiszero
- 0{}%
- \krof
- \xint_UDsignsfork
- #1#2\XINT_cmp_minusminus
- #1-\XINT_cmp_minusplus
- #2-\XINT_cmp_plusminus
- --\XINT_cmp_plusplus
- \krof #1#2%
-}%
-\def\XINT_cmp_firstiszero #1\krof 0#2#3\Z #4\Z
-{%
- \xint_UDzerominusfork
- #2-{ 0}%
- 0#2{ 1}%
- 0-{ -1}%
- \krof
-}%
-\def\XINT_cmp_secondiszero #1\krof #20#3\Z #4\Z
-{%
- \xint_UDzerominusfork
- #2-{ 0}%
- 0#2{ -1}%
- 0-{ 1}%
- \krof
-}%
-\def\XINT_cmp_plusminus #1\Z #2\Z{ 1}%
-\def\XINT_cmp_minusplus #1\Z #2\Z{ -1}%
-\def\XINT_cmp_minusminus
- --{\expandafter\XINT_opp\romannumeral0\XINT_cmp_plusplus {}{}}%
-\def\XINT_cmp_plusplus #1#2#3\Z
-{%
- \expandafter\XINT_cmp_pp
- \romannumeral0\expandafter\XINT_sepandrev_andcount
- \romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
- #2#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
- \X #1%
-}%
-\def\XINT_cmp_pp #1.#2\X #3\Z
-{%
- \expandafter\XINT_cmp_checklengths
- \the\numexpr #1\expandafter.%
- \romannumeral0\expandafter\XINT_sepandrev_andcount
- \romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
- #3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax \xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
- \Z!\Z!\Z!\Z!\Z!\W #2\Z!\Z!\Z!\Z!\Z!\W
-}%
-\def\XINT_cmp_checklengths #1.#2.%
-{%
- \ifnum #1=#2
- \expandafter\xint_firstoftwo
- \else
- \expandafter\xint_secondoftwo
- \fi
- \XINT_cmp_aa {\XINT_cmp_distinctlengths {#1}{#2}}%
-}%
-\def\XINT_cmp_distinctlengths #1#2#3\W #4\W
-{%
- \ifnum #1>#2
- \expandafter\xint_firstoftwo
- \else
- \expandafter\xint_secondoftwo
- \fi
- { -1}{ 1}%
-}%
-\def\XINT_cmp_aa {\expandafter\XINT_cmp_w\the\numexpr\XINT_cmp_a \xint_c_i }%
-\def\XINT_cmp_a #1!#2!#3!#4!#5\W #6!#7!#8!#9!%
-{%
- \XINT_cmp_b #1!#6!#2!#7!#3!#8!#4!#9!#5\W
-}%
-\def\XINT_cmp_b #1#2#3!#4!%
-{%
- \xint_gob_til_Z #2\XINT_cmp_bi \Z
- \expandafter\XINT_cmp_c\the\numexpr#1+1#4-#3-\xint_c_i.%
-}%
-\def\XINT_cmp_c 1#1#2.%
-{%
- 1#2\expandafter!\the\numexpr\XINT_cmp_d #1%
-}%
-\def\XINT_cmp_d #1#2#3!#4!%
-{%
- \xint_gob_til_Z #2\XINT_cmp_di \Z
- \expandafter\XINT_cmp_e\the\numexpr#1+1#4-#3-\xint_c_i.%
-}%
-\def\XINT_cmp_e 1#1#2.%
-{%
- 1#2\expandafter!\the\numexpr\XINT_cmp_f #1%
-}%
-\def\XINT_cmp_f #1#2#3!#4!%
-{%
- \xint_gob_til_Z #2\XINT_cmp_fi \Z
- \expandafter\XINT_cmp_g\the\numexpr#1+1#4-#3-\xint_c_i.%
-}%
-\def\XINT_cmp_g 1#1#2.%
-{%
- 1#2\expandafter!\the\numexpr\XINT_cmp_h #1%
-}%
-\def\XINT_cmp_h #1#2#3!#4!%
-{%
- \xint_gob_til_Z #2\XINT_cmp_hi \Z
- \expandafter\XINT_cmp_i\the\numexpr#1+1#4-#3-\xint_c_i.%
-}%
-\def\XINT_cmp_i 1#1#2.%
-{%
- 1#2\expandafter!\the\numexpr\XINT_cmp_a #1%
-}%
-\def\XINT_cmp_bi\Z
- \expandafter\XINT_cmp_c\the\numexpr#1+1#2-#3.#4!#5!#6!#7!#8!#9!\Z !\W
-{%
- \XINT_cmp_k #1#2!#5!#7!#9!%
-}%
-\def\XINT_cmp_di\Z
- \expandafter\XINT_cmp_e\the\numexpr#1+1#2-#3.#4!#5!#6!#7!#8\W
-{%
- \XINT_cmp_k #1#2!#5!#7!%
-}%
-\def\XINT_cmp_fi\Z
- \expandafter\XINT_cmp_g\the\numexpr#1+1#2-#3.#4!#5!#6\W
-{%
- \XINT_cmp_k #1#2!#5!%
-}%
-\def\XINT_cmp_hi\Z
- \expandafter\XINT_cmp_i\the\numexpr#1+1#2-#3.#4\W
-{%
- \XINT_cmp_k #1#2!%
-}%
-\def\XINT_cmp_k #1#2\W
-{%
- \xint_UDzerofork
- #1{-1\relax \XINT_cmp_greater}%
- 0{-1\relax \XINT_cmp_lessorequal}%
- \krof
-}%
-\def\XINT_cmp_w #1-1#2{#2#11\Z!\W}%
-\def\XINT_cmp_greater #1\Z!\W{ 1}%
-\def\XINT_cmp_lessorequal 1#1!%
- {\xint_gob_til_Z #1\XINT_cmp_equal\Z
- \xint_gob_til_eightzeroes #1\XINT_cmp_continue 00000000%
- \XINT_cmp_less }%
-\def\XINT_cmp_less #1\W { -1}%
-\def\XINT_cmp_continue 00000000\XINT_cmp_less {\XINT_cmp_lessorequal }%
-\def\XINT_cmp_equal\Z\xint_gob_til_eightzeroes\Z\XINT_cmp_continue
- 00000000\XINT_cmp_less\W { 0}%
-% \end{macrocode}
% \subsection{\csh{xintEq}, \csh{xintGt}, \csh{xintLt}}
% \lverb|1.09a.|
% \begin{macrocode}
@@ -21137,66 +21634,73 @@
\xint_afterfi{ 0}\else\xint_afterfi{ 1}\fi }%
% \end{macrocode}
% \subsection{\csh{xintANDof}}
-% \lverb|New with 1.09a. \xintANDof works also with an empty list.|
+% \lverb|New with 1.09a. \xintANDof works also with an empty list. Empty items
+% however are not accepted.|
+% \lverb|1.2l made \xintANDof robust against non terminated items.|
% \begin{macrocode}
\def\xintANDof {\romannumeral0\xintandof }%
-\def\xintandof #1{\expandafter\XINT_andof_a\romannumeral`&&@#1\relax }%
-\def\XINT_andof_a #1{\expandafter\XINT_andof_b\romannumeral`&&@#1\Z }%
+\def\xintandof #1{\expandafter\XINT_andof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_andof_a #1{\expandafter\XINT_andof_b\romannumeral`&&@#1!}%
\def\XINT_andof_b #1%
- {\xint_gob_til_relax #1\XINT_andof_e\relax\XINT_andof_c #1}%
-\def\XINT_andof_c #1\Z
+ {\xint_gob_til_xint: #1\XINT_andof_e\xint:\XINT_andof_c #1}%
+\def\XINT_andof_c #1!%
{\xintifTrueAelseB {#1}{\XINT_andof_a}{\XINT_andof_no}}%
-\def\XINT_andof_no #1\relax { 0}%
-\def\XINT_andof_e #1\Z { 1}%
+\def\XINT_andof_no #1\xint:{ 0}%
+\def\XINT_andof_e #1!{ 1}%
% \end{macrocode}
% \subsection{\csh{xintORof}}
-% \lverb|New with 1.09a. Works also with an empty list.|
+% \lverb|New with 1.09a. Works also with an empty list. Empty items
+% however are not accepted.|
+% \lverb|1.2l made \xintORof robust against non terminated items.|
% \begin{macrocode}
\def\xintORof {\romannumeral0\xintorof }%
-\def\xintorof #1{\expandafter\XINT_orof_a\romannumeral`&&@#1\relax }%
-\def\XINT_orof_a #1{\expandafter\XINT_orof_b\romannumeral`&&@#1\Z }%
+\def\xintorof #1{\expandafter\XINT_orof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_orof_a #1{\expandafter\XINT_orof_b\romannumeral`&&@#1!}%
\def\XINT_orof_b #1%
- {\xint_gob_til_relax #1\XINT_orof_e\relax\XINT_orof_c #1}%
-\def\XINT_orof_c #1\Z
+ {\xint_gob_til_xint: #1\XINT_orof_e\xint:\XINT_orof_c #1}%
+\def\XINT_orof_c #1!%
{\xintifTrueAelseB {#1}{\XINT_orof_yes}{\XINT_orof_a}}%
-\def\XINT_orof_yes #1\relax { 1}%
-\def\XINT_orof_e #1\Z { 0}%
+\def\XINT_orof_yes #1\xint:{ 1}%
+\def\XINT_orof_e #1!{ 0}%
% \end{macrocode}
% \subsection{\csh{xintXORof}}
-% \lverb|New with 1.09a. Works with an empty list, too. \XINT_xorof_c more
-% efficient in 1.09i|
+% \lverb|New with 1.09a. Works with an empty list, too. Empty items
+% however are not accepted. \XINT_xorof_c more
+% efficient in 1.09i.|
+% \lverb|1.2l made \xintXORof robust against non terminated items.|
% \begin{macrocode}
\def\xintXORof {\romannumeral0\xintxorof }%
\def\xintxorof #1{\expandafter\XINT_xorof_a\expandafter
- 0\romannumeral`&&@#1\relax }%
-\def\XINT_xorof_a #1#2{\expandafter\XINT_xorof_b\romannumeral`&&@#2\Z #1}%
+ 0\romannumeral`&&@#1\xint:}%
+\def\XINT_xorof_a #1#2{\expandafter\XINT_xorof_b\romannumeral`&&@#2!#1}%
\def\XINT_xorof_b #1%
- {\xint_gob_til_relax #1\XINT_xorof_e\relax\XINT_xorof_c #1}%
-\def\XINT_xorof_c #1\Z #2%
+ {\xint_gob_til_xint: #1\XINT_xorof_e\xint:\XINT_xorof_c #1}%
+\def\XINT_xorof_c #1!#2%
{\xintifTrueAelseB {#1}{\if #20\xint_afterfi{\XINT_xorof_a 1}%
\else\xint_afterfi{\XINT_xorof_a 0}\fi}%
{\XINT_xorof_a #2}%
}%
-\def\XINT_xorof_e #1\Z #2{ #2}%
+\def\XINT_xorof_e #1!#2{ #2}%
% \end{macrocode}
% \subsection{\csh{xintGeq}, \csh{xintiiGeq}}
% \lverb|&
% PLUS GRAND OU ÉGAL
% attention compare les **valeurs absolues**|
+% \lverb|1.2l made \xintiiGeq robust against non terminated items.|
% \begin{macrocode}
\def\xintGeq {\romannumeral0\xintgeq }%
-\def\xintgeq #1{\expandafter\XINT_geq\romannumeral0\xintnum{#1}\Z }%
+\def\xintgeq #1{\expandafter\XINT_geq\romannumeral0\xintnum{#1}\xint:}%
\def\xintiiGeq {\romannumeral0\xintiigeq }%
-\def\xintiigeq #1{\expandafter\XINT_iigeq\romannumeral`&&@#1\Z }%
-\def\XINT_iigeq #1#2\Z #3%
+\def\xintiigeq #1{\expandafter\XINT_iigeq\romannumeral`&&@#1\xint:}%
+\def\XINT_iigeq #1#2\xint:#3%
{%
- \expandafter\XINT_geq_fork\expandafter #1\romannumeral`&&@#3\Z #2\Z
+ \expandafter\XINT_geq_fork\expandafter #1\romannumeral`&&@#3\xint:#2\xint:
}%
\let\XINT_geq_pre \xintiigeq % TEMPORAIRE (oui, mais depuis quand ?)
\let\XINT_Geq \xintGeq % TEMPORAIRE ATTENTION FAIT xintNum (et alors?)
-\def\XINT_geq #1#2\Z #3%
+\def\XINT_geq #1#2\xint:#3%
{%
- \expandafter\XINT_geq_fork\expandafter #1\romannumeral0\xintnum{#3}\Z #2\Z
+ \expandafter\XINT_geq_fork\expandafter #1\romannumeral0\xintnum{#3}\xint:#2\xint:
}%
\def\XINT_geq_fork #1#2%
{%
@@ -21212,37 +21716,37 @@
--\XINT_geq_plusplus
\krof #1#2%
}%
-\def\XINT_geq_firstiszero #1\krof 0#2#3\Z #4\Z
+\def\XINT_geq_firstiszero #1\krof 0#2#3\xint:#4\xint:
{\xint_UDzerofork #2{ 1}0{ 0}\krof }%
-\def\XINT_geq_secondiszero #1\krof #20#3\Z #4\Z { 1}%
+\def\XINT_geq_secondiszero #1\krof #20#3\xint:#4\xint:{ 1}%
\def\XINT_geq_plusminus #1-{\XINT_geq_plusplus #1{}}%
\def\XINT_geq_minusplus -#1{\XINT_geq_plusplus {}#1}%
\def\XINT_geq_minusminus --{\XINT_geq_plusplus {}{}}%
-\def\XINT_geq_plusplus #1#2#3\Z #4\Z {\XINT_geq_pp #1#4\Z #2#3\Z }%
-\def\XINT_geq_pp #1\Z
+\def\XINT_geq_plusplus #1#2#3\xint:#4\xint:{\XINT_geq_pp #1#4\xint:#2#3\xint:}%
+\def\XINT_geq_pp #1\xint:
{%
\expandafter\XINT_geq_pp_a
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #1\R\R\R\R\R\R\R\R{10}0000001\W
#1\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\X
}%
-\def\XINT_geq_pp_a #1.#2\X #3\Z
+\def\XINT_geq_pp_a #1\xint:#2\X #3\xint:
{%
\expandafter\XINT_geq_checklengths
- \the\numexpr #1\expandafter.%
+ \the\numexpr #1\expandafter\xint:%
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax \xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\Z!\Z!\Z!\Z!\Z!\W #2\Z!\Z!\Z!\Z!\Z!\W
}%
-\def\XINT_geq_checklengths #1.#2.%
+\def\XINT_geq_checklengths #1\xint:#2\xint:
{%
\ifnum #1=#2
\expandafter\xint_firstoftwo
@@ -21268,9 +21772,9 @@
\def\XINT_geq_b #1#2#3!#4!%
{%
\xint_gob_til_Z #2\XINT_geq_bi \Z
- \expandafter\XINT_geq_c\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \expandafter\XINT_geq_c\the\numexpr#1+1#4-#3-\xint_c_i\xint:%
}%
-\def\XINT_geq_c 1#1#2.%
+\def\XINT_geq_c 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_geq_d #1%
}%
@@ -21277,9 +21781,9 @@
\def\XINT_geq_d #1#2#3!#4!%
{%
\xint_gob_til_Z #2\XINT_geq_di \Z
- \expandafter\XINT_geq_e\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \expandafter\XINT_geq_e\the\numexpr#1+1#4-#3-\xint_c_i\xint:%
}%
-\def\XINT_geq_e 1#1#2.%
+\def\XINT_geq_e 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_geq_f #1%
}%
@@ -21286,9 +21790,9 @@
\def\XINT_geq_f #1#2#3!#4!%
{%
\xint_gob_til_Z #2\XINT_geq_fi \Z
- \expandafter\XINT_geq_g\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \expandafter\XINT_geq_g\the\numexpr#1+1#4-#3-\xint_c_i\xint:%
}%
-\def\XINT_geq_g 1#1#2.%
+\def\XINT_geq_g 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_geq_h #1%
}%
@@ -21295,29 +21799,29 @@
\def\XINT_geq_h #1#2#3!#4!%
{%
\xint_gob_til_Z #2\XINT_geq_hi \Z
- \expandafter\XINT_geq_i\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \expandafter\XINT_geq_i\the\numexpr#1+1#4-#3-\xint_c_i\xint:%
}%
-\def\XINT_geq_i 1#1#2.%
+\def\XINT_geq_i 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_geq_a #1%
}%
\def\XINT_geq_bi\Z
- \expandafter\XINT_geq_c\the\numexpr#1+1#2-#3.#4!#5!#6!#7!#8!#9!\Z !\W
+ \expandafter\XINT_geq_c\the\numexpr#1+1#2-#3\xint:#4!#5!#6!#7!#8!#9!\Z !\W
{%
\XINT_geq_k #1#2!#5!#7!#9!%
}%
\def\XINT_geq_di\Z
- \expandafter\XINT_geq_e\the\numexpr#1+1#2-#3.#4!#5!#6!#7!#8\W
+ \expandafter\XINT_geq_e\the\numexpr#1+1#2-#3\xint:#4!#5!#6!#7!#8\W
{%
\XINT_geq_k #1#2!#5!#7!%
}%
\def\XINT_geq_fi\Z
- \expandafter\XINT_geq_g\the\numexpr#1+1#2-#3.#4!#5!#6\W
+ \expandafter\XINT_geq_g\the\numexpr#1+1#2-#3\xint:#4!#5!#6\W
{%
\XINT_geq_k #1#2!#5!%
}%
\def\XINT_geq_hi\Z
- \expandafter\XINT_geq_i\the\numexpr#1+1#2-#3.#4\W
+ \expandafter\XINT_geq_i\the\numexpr#1+1#2-#3\xint:#4\W
{%
\XINT_geq_k #1#2!%
}%
@@ -21405,28 +21909,36 @@
% \end{macrocode}
% \subsection{\csh{xintiMaxof}, \csh{xintiiMaxof}}
% \lverb|New with 1.09a. 1.2 has NO MORE \xintMaxof, requires \xintfracname.
-% 1.2a adds \xintiiMaxof, as \xintiiMaxof:csv is not public.|
+% 1.2a adds \xintiiMaxof, as \xintiiMaxof:csv is not public.
+%
+% NOT compatible with empty list.|
+% \lverb|1.2l made \xintiiMaxof robust against non terminated items.|
% \begin{macrocode}
\def\xintiMaxof {\romannumeral0\xintimaxof }%
-\def\xintimaxof #1{\expandafter\XINT_imaxof_a\romannumeral`&&@#1\relax }%
-\def\XINT_imaxof_a #1{\expandafter\XINT_imaxof_b\romannumeral0\xintnum{#1}\Z }%
-\def\XINT_imaxof_b #1\Z #2%
- {\expandafter\XINT_imaxof_c\romannumeral`&&@#2\Z {#1}\Z}%
+\def\xintimaxof #1{\expandafter\XINT_imaxof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_imaxof_a
+#1{\expandafter\XINT_imaxof_b\romannumeral0\xintnum{#1}!}%
+% \end{macrocode}
+% \lverb|No \xintnum on #2 which might be \xint:, of course. But if list not
+% terminated the \xintNum will be done via \xintimax.|
+% \begin{macrocode}
+\def\XINT_imaxof_b #1!#2%
+ {\expandafter\XINT_imaxof_c\romannumeral`&&@#2!{#1}!}%
\def\XINT_imaxof_c #1%
- {\xint_gob_til_relax #1\XINT_imaxof_e\relax\XINT_imaxof_d #1}%
-\def\XINT_imaxof_d #1\Z
+ {\xint_gob_til_xint: #1\XINT_imaxof_e\xint:\XINT_imaxof_d #1}%
+\def\XINT_imaxof_d #1!%
{\expandafter\XINT_imaxof_b\romannumeral0\xintimax {#1}}%
-\def\XINT_imaxof_e #1\Z #2\Z { #2}%
+\def\XINT_imaxof_e #1!#2!{ #2}%
\def\xintiiMaxof {\romannumeral0\xintiimaxof }%
-\def\xintiimaxof #1{\expandafter\XINT_iimaxof_a\romannumeral`&&@#1\relax }%
-\def\XINT_iimaxof_a #1{\expandafter\XINT_iimaxof_b\romannumeral`&&@#1\Z }%
-\def\XINT_iimaxof_b #1\Z #2%
- {\expandafter\XINT_iimaxof_c\romannumeral`&&@#2\Z {#1}\Z}%
+\def\xintiimaxof #1{\expandafter\XINT_iimaxof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_iimaxof_a #1{\expandafter\XINT_iimaxof_b\romannumeral`&&@#1!}%
+\def\XINT_iimaxof_b #1!#2%
+ {\expandafter\XINT_iimaxof_c\romannumeral`&&@#2!{#1}!}%
\def\XINT_iimaxof_c #1%
- {\xint_gob_til_relax #1\XINT_iimaxof_e\relax\XINT_iimaxof_d #1}%
-\def\XINT_iimaxof_d #1\Z
+ {\xint_gob_til_xint: #1\XINT_iimaxof_e\xint:\XINT_iimaxof_d #1}%
+\def\XINT_iimaxof_d #1!%
{\expandafter\XINT_iimaxof_b\romannumeral0\xintiimax {#1}}%
-\def\XINT_iimaxof_e #1\Z #2\Z { #2}%
+\def\XINT_iimaxof_e #1!#2!{ #2}%
% \end{macrocode}
% \subsection{\csh{xintiMin}, \csh{xintiiMin}}
% \lverb|\xintnum added New with 1.09a. I add \xintiiMin in 1.1 and mark as
@@ -21506,59 +22018,55 @@
% \lverb|1.09a. 1.2a adds \xintiiMinof which was lacking.|
% \begin{macrocode}
\def\xintiMinof {\romannumeral0\xintiminof }%
-\def\xintiminof #1{\expandafter\XINT_iminof_a\romannumeral`&&@#1\relax }%
-\def\XINT_iminof_a #1{\expandafter\XINT_iminof_b\romannumeral0\xintnum{#1}\Z }%
-\def\XINT_iminof_b #1\Z #2%
- {\expandafter\XINT_iminof_c\romannumeral`&&@#2\Z {#1}\Z}%
+\def\xintiminof #1{\expandafter\XINT_iminof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_iminof_a #1{\expandafter\XINT_iminof_b\romannumeral0\xintnum{#1}!}%
+\def\XINT_iminof_b #1!#2%
+ {\expandafter\XINT_iminof_c\romannumeral`&&@#2!{#1}!}%
\def\XINT_iminof_c #1%
- {\xint_gob_til_relax #1\XINT_iminof_e\relax\XINT_iminof_d #1}%
-\def\XINT_iminof_d #1\Z
+ {\xint_gob_til_xint: #1\XINT_iminof_e\xint:\XINT_iminof_d #1}%
+\def\XINT_iminof_d #1!%
{\expandafter\XINT_iminof_b\romannumeral0\xintimin {#1}}%
-\def\XINT_iminof_e #1\Z #2\Z { #2}%
+\def\XINT_iminof_e #1!#2!{ #2}%
\def\xintiiMinof {\romannumeral0\xintiiminof }%
-\def\xintiiminof #1{\expandafter\XINT_iiminof_a\romannumeral`&&@#1\relax }%
-\def\XINT_iiminof_a #1{\expandafter\XINT_iiminof_b\romannumeral`&&@#1\Z }%
-\def\XINT_iiminof_b #1\Z #2%
- {\expandafter\XINT_iiminof_c\romannumeral`&&@#2\Z {#1}\Z}%
+\def\xintiiminof #1{\expandafter\XINT_iiminof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_iiminof_a #1{\expandafter\XINT_iiminof_b\romannumeral`&&@#1!}%
+\def\XINT_iiminof_b #1!#2%
+ {\expandafter\XINT_iiminof_c\romannumeral`&&@#2!{#1}!}%
\def\XINT_iiminof_c #1%
- {\xint_gob_til_relax #1\XINT_iiminof_e\relax\XINT_iiminof_d #1}%
-\def\XINT_iiminof_d #1\Z
+ {\xint_gob_til_xint: #1\XINT_iiminof_e\xint:\XINT_iiminof_d #1}%
+\def\XINT_iiminof_d #1!%
{\expandafter\XINT_iiminof_b\romannumeral0\xintiimin {#1}}%
-\def\XINT_iiminof_e #1\Z #2\Z { #2}%
+\def\XINT_iiminof_e #1!#2!{ #2}%
% \end{macrocode}
% \subsection{\csh{xintiiSum}}
-% \lverb|\xintiiSum {{a}{b}...{z}}, \xintiiSumExpr {a}{b}...{z}\relax
+% \lverb|\xintiiSum {{a}{b}...{z}}
%|
% \begin{macrocode}
\def\xintiiSum {\romannumeral0\xintiisum }%
-\def\xintiisum #1{\xintiisumexpr #1\relax }%
-\def\xintiiSumExpr {\romannumeral0\xintiisumexpr }%
-\def\xintiisumexpr {\expandafter\XINT_sumexpr\romannumeral`&&@}%
+\def\xintiisum #1{\expandafter\XINT_sumexpr\romannumeral`&&@#1\xint:}%
\def\XINT_sumexpr {\XINT_sum_loop_a 0\Z }%
\def\XINT_sum_loop_a #1\Z #2%
- {\expandafter\XINT_sum_loop_b \romannumeral`&&@#2\Z #1\Z \Z}%
+ {\expandafter\XINT_sum_loop_b \romannumeral`&&@#2\xint:#1\xint:\Z}%
\def\XINT_sum_loop_b #1%
- {\xint_gob_til_relax #1\XINT_sum_finished\relax\XINT_sum_loop_c #1}%
+ {\xint_gob_til_xint: #1\XINT_sum_finished\xint:\XINT_sum_loop_c #1}%
\def\XINT_sum_loop_c
{\expandafter\XINT_sum_loop_a\romannumeral0\XINT_add_fork }%
-\def\XINT_sum_finished #1\Z #2\Z \Z { #2}%
+\def\XINT_sum_finished\xint:\XINT_sum_loop_c\xint:\xint:#1\xint:\Z{ #1}%
% \end{macrocode}
% \subsection{\csh{xintiiPrd}}
-% \lverb|\xintiiPrd {{a}...{z}}, \xintiiPrdExpr {a}...{z}\relax
+% \lverb|\xintiiPrd {{a}...{z}}
%|
% \begin{macrocode}
\def\xintiiPrd {\romannumeral0\xintiiprd }%
-\def\xintiiprd #1{\xintiiprdexpr #1\relax }%
-\def\xintiiPrdExpr {\romannumeral0\xintiiprdexpr }%
-\def\xintiiprdexpr {\expandafter\XINT_prdexpr\romannumeral`&&@}%
+\def\xintiiprd #1{\expandafter\XINT_prdexpr\romannumeral`&&@#1\xint:}%
\def\XINT_prdexpr {\XINT_prod_loop_a 1\Z }%
\def\XINT_prod_loop_a #1\Z #2%
- {\expandafter\XINT_prod_loop_b \romannumeral`&&@#2\Z #1\Z \Z}%
+ {\expandafter\XINT_prod_loop_b\romannumeral`&&@#2\xint:#1\xint:\Z}%
\def\XINT_prod_loop_b #1%
- {\xint_gob_til_relax #1\XINT_prod_finished\relax\XINT_prod_loop_c #1}%
+ {\xint_gob_til_xint: #1\XINT_prod_finished\xint:\XINT_prod_loop_c #1}%
\def\XINT_prod_loop_c
{\expandafter\XINT_prod_loop_a\romannumeral0\XINT_mul_fork }%
-\def\XINT_prod_finished\relax\XINT_prod_loop_c #1\Z #2\Z \Z { #2}%
+\def\XINT_prod_finished\xint:\XINT_prod_loop_c\xint:\xint:#1\xint:\Z { #1}%
% \end{macrocode}
% \lverb|&
% &
@@ -21715,7 +22223,7 @@
%
% Rewritten for 1.2i, this was old code.
%
-%!
+% !
% \begin{macrocode}
\def\xintDSx {\romannumeral0\xintdsx }%
\def\xintdsx #1#2%
@@ -21802,6 +22310,8 @@
% leading sign (+ or -).
%
% Entirely rewritten for 1.2i (2016/12/11).
+%
+% Attention: \xintDecSplit not robust against non terminated second argument.
% !
% \begin{macrocode}
\def\xintDecSplit {\romannumeral0\xintdecsplit }%
@@ -21882,8 +22392,7 @@
{%
\expandafter\XINT_split_fromright_a
\the\numexpr#1-\numexpr\XINT_length_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
.#2\xint_bye
@@ -21955,19 +22464,20 @@
\def\XINT_sqrtr_post #1#2{\xintiiifLt {#2}{#1}%
{ #1}{\XINT_dec #1\XINT_dec_bye234567890\xint_bye}}%
\def\xintisquareroot #1%
- {\expandafter\XINT_sqrt_checkin\romannumeral0\xintnum{#1}\xint_relax }%
-\def\xintiisquareroot #1{\expandafter\XINT_sqrt_checkin\romannumeral`&&@#1\xint_relax }%
+ {\expandafter\XINT_sqrt_checkin\romannumeral0\xintnum{#1}\xint:}%
+\def\xintiisquareroot #1{\expandafter\XINT_sqrt_checkin\romannumeral`&&@#1\xint:}%
\def\XINT_sqrt_checkin #1%
{%
\xint_UDzerominusfork
#1-\XINT_sqrt_iszero
0#1\XINT_sqrt_isneg
- 0-{\XINT_sqrt #1}%
- \krof
+ 0-\XINT_sqrt
+ \krof #1%
}%
-\def\XINT_sqrt_iszero #1\xint_relax {{1}{1}}%
-\def\XINT_sqrt_isneg #1\xint_relax {\xintError:RootOfNegative{1}{1}}%
-\def\XINT_sqrt #1\xint_relax
+\def\XINT_sqrt_iszero #1\xint:{{1}{1}}%
+\def\XINT_sqrt_isneg #1\xint:{\XINT_signalcondition{InvalidOperation}{square
+ root of negative: #1}{}{{0}{0}}}%
+\def\XINT_sqrt #1\xint:
{%
\expandafter\XINT_sqrt_start\romannumeral0\xintlength {#1}.#1.%
}%
@@ -22222,7 +22732,7 @@
}%
\def\XINT_sqrt_big_ke #1%
{%
- \if0\XINT_Sgn #1\Z
+ \if0\XINT_Sgn #1\xint:
\expandafter \XINT_sqrt_big_end
\else \expandafter \XINT_sqrt_big_kf
\fi {#1}%
@@ -22268,12 +22778,15 @@
% \begin{macrocode}
\def\XINT_binom_fork #1#2.#3#4.#5#6.%
{%
- \if-#5\xint_dothis{\xintError:OutOfRangeBinomial\space 0}\fi
+ \if-#5\xint_dothis{\XINT_signalcondition{InvalidOperation}{Binomial with
+ negative first arg: #5#6}{}{0}}\fi
\if-#1\xint_dothis{ 0}\fi
\if-#3\xint_dothis{ 0}\fi
\if0#1\xint_dothis{ 1}\fi
\if0#3\xint_dothis{ 1}\fi
- \ifnum #5#6>\xint_c_x^viii_mone\xint_dothis{\xintError:OutOfRangeBinomial\space 0}\fi
+ \ifnum #5#6>\xint_c_x^viii_mone\xint_dothis
+ {\XINT_signalcondition{InvalidOperation}{Binomial with too
+ large argument: 99999999 < #5#6}{}{0}}\fi
\ifnum #1#2>#3#4 \xint_dothis{\XINT_binom_a #1#2.#3#4.}\fi
\xint_orthat{\XINT_binom_a #3#4.#1#2.}%
}%
@@ -22282,12 +22795,12 @@
% quotient un terminateur 1!\Z!0!. On va procéder par petite multiplication
% suivie par petite division. Donc ici on met le 1!\Z!0! pour amorcer.
%
-% Le 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W est le terminateur pour le
+% Le \xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax est le terminateur pour le
% \XINT_unsep_cuzsmall final.|
% \begin{macrocode}
\def\XINT_binom_a #1.#2.%
{%
- \expandafter\XINT_binom_b\the\numexpr \xint_c_i+#1.1.#2.100000001!1!\Z!0!%
+ \expandafter\XINT_binom_b\the\numexpr \xint_c_i+#1.1.#2.100000001!1!;!0!%
}%
% \end{macrocode}
% \lverb|y=x-k+1.j=1.k. On va évaluer par y/1*(y+1)/2*(y+2)/3 etc... On essaie
@@ -22310,7 +22823,7 @@
}%
% \end{macrocode}
% \lverb|y.j.k. Au départ on avait x-k+1.1.k. Ensuite on a des blocs 1<8d>!
-% donnant le résultat intermédiaire, dans l'ordre, et à la fin on a 1!1\Z!0!.
+% donnant le résultat intermédiaire, dans l'ordre, et à la fin on a 1!1;!0!.
% Dans smallloop on peut prendre 4 par 4.|
% \begin{macrocode}
\def\XINT_binom_smallloop #1.#2.#3.%
@@ -22452,20 +22965,22 @@
\the\numexpr #2*(#2+\xint_c_i)*(#2+\xint_c_ii)*(#2+\xint_c_iii)\expandafter
!\the\numexpr #1*(#1+\xint_c_i)*(#1+\xint_c_ii)*(#1+\xint_c_iii)!%
}%
-\def\XINT_binom_mul #1!#21!\Z!0!%
+% \end{macrocode}
+% \begin{macrocode}
+\def\XINT_binom_mul #1!#21!;!0!%
{%
\expandafter\XINT_rev_nounsep\expandafter{\expandafter}%
\the\numexpr\expandafter\XINT_smallmul
\the\numexpr\xint_c_x^viii+#1\expandafter
- !\romannumeral0\XINT_rev_nounsep {}1\Z!#2%
+ !\romannumeral0\XINT_rev_nounsep {}1;!#2%
\R!\R!\R!\R!\R!\R!\R!\R!\W
\R!\R!\R!\R!\R!\R!\R!\R!\W
- 1\Z!%
+ 1;!%
}%
-\def\XINT_binom_div #1!1\Z!%
+\def\XINT_binom_div #1!1;!%
{%
\expandafter\XINT_smalldivx_a
- \the\numexpr #1/\xint_c_ii\expandafter.%
+ \the\numexpr #1/\xint_c_ii\expandafter\xint:
\the\numexpr \xint_c_x^viii+#1!%
}%
% \end{macrocode}
@@ -22507,9 +23022,11 @@
\the\numexpr\expandafter\XINT_binom_div\the\numexpr #2\expandafter
!\romannumeral0\XINT_binom_mul #1!%
}%
-\def\XINT_binom_finish #1\Z!0!%
- {\XINT_unsep_cuzsmall #11\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W }%
% \end{macrocode}
+% \begin{macrocode}
+\def\XINT_binom_finish #1;!0!%
+ {\XINT_unsep_cuzsmall #1\xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax}%
+% \end{macrocode}
% \lverb|Duplication de code seulement pour la boucle avec très
% petits coeffs, mais en plus on fait au maximum des possibilités. (on
% pourrait tester plus le résultat déjà obtenu).|
@@ -22560,8 +23077,9 @@
\expandafter\XINT_binom_vsmallfinish
\the\numexpr\XINT_binom_vsmallmuldiv #2!#1!%
}%
-\edef\XINT_binom_vsmallfinish 1#1!1!\Z!0!%
- {\noexpand\expandafter\space\noexpand\the\numexpr #1\relax}%
+\def\XINT_binom_vsmallfinish#1{%
+\def\XINT_binom_vsmallfinish1##1!1!;!0!{\expandafter#1\the\numexpr##1\relax}%
+}\XINT_binom_vsmallfinish{ }%
% \end{macrocode}
% \subsection{\csh{xintiiPFactorial}, \csh{xintiPFactorial}}
% \lverb?2015/11/29 for 1.2f. Partial factorial pfac(a,b)=(a+1)...b, only for
@@ -22594,7 +23112,9 @@
\ifnum #3#4>\xint_c_x^viii_mone\xint_dothis\XINT_pfac_outofrange\fi
\xint_orthat \XINT_pfac_a #1#2.#3#4.%
}%
-\def\XINT_pfac_outofrange #1.#2.{\xintError:OutOfRangePFac\space 0}%
+\def\XINT_pfac_outofrange #1.#2.%
+ {\XINT_signalcondition{InvalidOperation}{PFactorial with
+ too big second arg: 99999999 < #2}{}{0}}%
\def\XINT_pfac_one #1.#2.{ 1}%
\def\XINT_pfac_zero #1.#2.{ 0}%
\def\XINT_pfac_neg -#1.-#2.%
@@ -22607,7 +23127,7 @@
}%
\def\XINT_pfac_a #1.#2.%
{%
- \expandafter\XINT_pfac_b\the\numexpr \xint_c_i+#1.#2.100000001!1\Z!%
+ \expandafter\XINT_pfac_b\the\numexpr \xint_c_i+#1.#2.100000001!1;!%
1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
}%
\def\XINT_pfac_b #1.%
@@ -22740,7 +23260,8 @@
{\expandafter\XINT_dsx_append\romannumeral\XINT_rep #1\endcsname 0.}%
\def\XINT_iie_neg #1.#2;{ #2}%
% \end{macrocode}
-% \subsection{``Load \xintfracnameimp'' macros}
+% \subsection*{``Load \xintfracnameimp'' macros}
+% \addcontentsline{toc}{subsection}{``Load \xintfracnameimp'' macros}
% \lverb|Originally was used in \xintiiexpr. Transferred from xintfrac for 1.1.|
% \begin{macrocode}
\catcode`! 11
@@ -22750,8 +23271,7 @@
\def\xintMinof {\Did_you_mean_iMinof?or_load_xintfrac!}%
\def\xintSum {\Did_you_mean_iiSum?or_load_xintfrac!}%
\def\xintPrd {\Did_you_mean_iiPrd?or_load_xintfrac!}%
-\def\xintPrdExpr {\Did_you_mean_iiPrdExpr?or_load_xintfrac!}%
-\def\xintSumExpr {\Did_you_mean_iiSumExpr?or_load_xintfrac!}%
+\catcode`! 12
\XINT_restorecatcodes_endinput%
% \end{macrocode}
%
@@ -22827,8 +23347,18 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintbinhex}%
- [2017/01/06 1.2k Expandable binary and hexadecimal conversions (JFB)]%
+ [2017/07/26 1.2l Expandable binary and hexadecimal conversions (JFB)]%
% \end{macrocode}
+% \subsection{Antique helper macro}
+% \lverb!At 1.2, it was left in xint.sty rather than being moved to
+% xintcore.sty, thus breaking \xintHexToDec here.!
+% \begin{macrocode}
+\def\xint_cleanupzeros_andstop#1{%
+\def\xint_cleanupzeros_andstop ##1##2##3##4%
+{%
+ \expandafter#1\the\numexpr ##1##2##3##4\relax
+}}\xint_cleanupzeros_andstop{ }%
+% \end{macrocode}
% \subsection{Constants, etc...}
% \lverb!1.08!
% \begin{macrocode}
@@ -23110,10 +23640,11 @@
{%
\expandafter\XINT_dtb_end_d\the\numexpr #1#2#3#4#5#6#7#8\relax
}%
-\edef\XINT_dtb_end_d #1#2#3#4#5#6#7#8#9%
+\def\XINT_dtb_end_d#1{%
+\def\XINT_dtb_end_d ##1##2##3##4##5##6##7##8##9%
{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4#5#6#7#8#9\relax
-}%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8##9\relax
+}}\XINT_dtb_end_d{ }%
% \end{macrocode}
% \subsection{\csh{xintHexToDec}}
% \lverb!1.08!
@@ -23149,10 +23680,10 @@
{%
\expandafter\xint_cleanupzeros_andstop
\romannumeral0\XINT_rord_main {}#1%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax
+ \xint:
}%
\def\XINT_htd_II_ci #1\XINT_htd_II_ciii
#2\W\W\W {\XINT_htd_II_d {}{"#2}{\xint_c_xvi}}%
@@ -23197,10 +23728,11 @@
{%
\XINT_htd_II_end_b #1#3%
}%
-\edef\XINT_htd_II_end_b #1#2#3#4#5#6#7#8%
+\def\XINT_htd_II_end_b#1{%
+\def\XINT_htd_II_end_b ##1##2##3##4##5##6##7##8%
{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4#5#6#7#8\relax
-}%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8\relax
+}}\XINT_htd_II_end_b{ }%
% \end{macrocode}
% \subsection{\csh{xintBinToDec}}
% \lverb!1.08!
@@ -23240,15 +23772,16 @@
{%
\expandafter\XINT_btd_II_c_end
\romannumeral0\XINT_rord_main {}#2%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax
+ \xint:
}%
-\edef\XINT_btd_II_c_end #1#2#3#4#5#6%
+\def\XINT_btd_II_c_end#1{%
+\def\XINT_btd_II_c_end ##1##2##3##4##5##6%
{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4#5#6\relax
-}%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6\relax
+}}\XINT_btd_II_c_end{ }%
\def\XINT_btd_II_ci #1\XINT_btd_II_cvii #2\W\W\W\W\W\W\W
{\XINT_btd_II_d {}{#2}{\xint_c_ii }}%
\def\XINT_btd_II_cii #1\XINT_btd_II_cvii #2\W\W\W\W\W\W
@@ -23285,10 +23818,11 @@
{%
\XINT_btd_II_end_b #1#3%
}%
-\edef\XINT_btd_II_end_b #1#2#3#4#5#6#7#8#9%
+\def\XINT_btd_II_end_b#1{%
+\def\XINT_btd_II_end_b ##1##2##3##4##5##6##7##8##9%
{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4#5#6#7#8#9\relax
-}%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8##9\relax
+}}\XINT_btd_II_end_b{ }%
\def\XINT_btd_I_a #1#2#3#4#5#6#7#8%
{%
\xint_gob_til_Z #3\XINT_btd_I_end_a\Z
@@ -23317,10 +23851,9 @@
\def\xintbintohex #1%
{%
\expandafter\XINT_bth_checkin
- \romannumeral0\expandafter\XINT_num_loop
- \romannumeral`&&@#1\xint_relax\xint_relax
- \xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z
+ \romannumeral0\expandafter\XINT_num_cleanup
+ \the\numexpr\expandafter\XINT_num_loop
+ \romannumeral`&&@#1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
\R\R\R\R\R\R\R\R\Z \W\W\W\W\W\W\W\W
}%
\def\XINT_bth_checkin #1%
@@ -23392,9 +23925,9 @@
}%
\def\XINT_htb_II_b #1#2#3\T
{%
- \XINT_num_loop #2#1%
- \xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z
+ \expandafter\XINT_num_cleanup
+ \the\numexpr\expandafter\XINT_num_loop #2#1%
+ \xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
% \end{macrocode}
% \subsection{\csh{xintCHexToBin}}
@@ -23436,12 +23969,12 @@
\XINT_chtb_I\expandafter\expandafter\expandafter #1%
{%
\XINT_chtb_end_b #1%
- \xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z
+ \xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
\def\XINT_chtb_end_b #1\W#2\W#3\W#4\W#5\W#6\W#7\W#8\W\endcsname
{%
- \XINT_num_loop
+ \expandafter\XINT_num_cleanup
+ \the\numexpr\expandafter\XINT_num_loop
}%
\XINT_restorecatcodes_endinput%
% \end{macrocode}
@@ -23527,7 +24060,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintgcd}%
- [2017/01/06 1.2k Euclide algorithm with xint package (JFB)]%
+ [2017/07/26 1.2l Euclide algorithm with xint package (JFB)]%
% \end{macrocode}
% \subsection{\csh{xintGCD}, \csh{xintiiGCD}}
% \begin{macrocode}
@@ -23566,9 +24099,9 @@
\def\XINT_gcd_BisZero #1#2{ #2}%
\def\XINT_gcd_CheckRem #1#2\Z
{%
- \xint_gob_til_zero #1\xint_gcd_end0\XINT_gcd_loop {#1#2}%
+ \xint_gob_til_zero #1\XINT_gcd_end0\XINT_gcd_loop {#1#2}%
}%
-\def\xint_gcd_end0\XINT_gcd_loop #1#2{ #2}%
+\def\XINT_gcd_end0\XINT_gcd_loop #1#2{ #2}%
% \end{macrocode}
% \lverb|#1=B, #2=A|
% \begin{macrocode}
@@ -23616,18 +24149,23 @@
\def\XINT_lcm_notzero #1#2#3{\xintiimul {#2}{\xintiiQuo{#3}{#1}}}%
% \end{macrocode}
% \subsection{\csh{xintBezout}}
+% \lverb|&
+% Produces {A}{B}{U}{V}{D} with UA-VB=D, D = PGCD(A,B) (positive).
+%
+% 1.2l raises InvalidOperation if both A and B vanish.
+%|
% \begin{macrocode}
\def\xintBezout {\romannumeral0\xintbezout }%
\def\xintbezout #1%
{%
- \expandafter\xint_bezout\expandafter {\romannumeral0\xintnum{#1}}%
+ \expandafter\XINT_bezout\expandafter {\romannumeral0\xintnum{#1}}%
}%
-\def\xint_bezout #1#2%
+\def\XINT_bezout #1#2%
{%
\expandafter\XINT_bezout_fork \romannumeral0\xintnum{#2}\Z #1\Z
}%
% \end{macrocode}
-% \lverb|#3#4 = A, #1#2=B|
+% \lverb|#3#4 = A, #1#2=B. Micro improvement for 1.2l.|
% \begin{macrocode}
\def\XINT_bezout_fork #1#2\Z #3#4\Z
{%
@@ -23635,39 +24173,39 @@
#1#3\XINT_bezout_botharezero
#10\XINT_bezout_secondiszero
#30\XINT_bezout_firstiszero
- 00{\xint_UDsignsfork
+ 00\xint_UDsignsfork
+ \krof
#1#3\XINT_bezout_minusminus % A < 0, B < 0
#1-\XINT_bezout_minusplus % A > 0, B < 0
#3-\XINT_bezout_plusminus % A < 0, B > 0
--\XINT_bezout_plusplus % A > 0, B > 0
- \krof }%
\krof
{#2}{#4}#1#3{#3#4}{#1#2}% #1#2=B, #3#4=A
}%
-\edef\XINT_bezout_botharezero #1#2#3#4#5#6%
-{%
- \noexpand\xintError:NoBezoutForZeros\space {0}{0}{0}{0}{0}%
-}%
+\def\XINT_bezout_botharezero #1\krof#2#3#4#5#6#7%
+ {\XINT_signalcondition{InvalidOperation}
+ {No Bezout identity for 0 and 0}{}{{0}{0}{0}{0}{0}}}%
% \end{macrocode}
-% \lverb|&
-% attention première entrée doit être ici (-1)^n donc 1$\
-% #4#2 = 0 = A, B = #3#1|
+% \lverb|I stayed without looking at this file for perhaps three years and
+% much to my dismay I realized in January 2017 that both \xintBezout{0}{B} and
+% \xintBezout{A}{0} were completely buggy, due to a confusion about macro
+% parameters I guess... and no testing ! I must have tested, I don't
+% understand. (regression testing for xint was put in place only late 2016)
+%
+% Thus rewritten for 1.2l.|
% \begin{macrocode}
-\def\XINT_bezout_firstiszero #1#2#3#4#5#6%
+\def\XINT_bezout_firstiszero #1\krof#2#3#4#5#6#7%
{%
\xint_UDsignfork
- #3{ {0}{#3#1}{0}{1}{#1}}%
- -{ {0}{#3#1}{0}{-1}{#1}}%
+ #4{{0}{#7}{0}{1}{#2}}%
+ -{{0}{#7}{0}{-1}{#7}}%
\krof
}%
-% \end{macrocode}
-% \lverb|#4#2 = A, B = #3#1 = 0|
-% \begin{macrocode}
-\def\XINT_bezout_secondiszero #1#2#3#4#5#6%
+\def\XINT_bezout_secondiszero #1\krof#2#3#4#5#6#7%
{%
\xint_UDsignfork
- #4{ {#4#2}{0}{-1}{0}{#2}}%
- -{ {#4#2}{0}{1}{0}{#2}}%
+ #5{{#6}{0}{-1}{0}{#3}}%
+ -{{#6}{0}{1}{0}{#6}}%
\krof
}%
% \end{macrocode}
@@ -23687,11 +24225,12 @@
{%
\expandafter\XINT_bezout_mm_postc\expandafter {#2}{#1}%
}%
-\edef\XINT_bezout_mm_postc #1#2#3#4#5%
-{%
- \space {#4}{#5}{#1}{#2}{#3}%
-}%
% \end{macrocode}
+% \lverb|I was using \edef to insert a space token upfront, where there is in
+% fact no need for it ! Such ignorance is appalling ... |
+% \begin{macrocode}
+\def\XINT_bezout_mm_postc #1#2#3#4#5{{#4}{#5}{#1}{#2}{#3}}%
+% \end{macrocode}
% \lverb|minusplus #4#2= A > 0, B < 0|
% \begin{macrocode}
\def\XINT_bezout_minusplus #1#2#3#4%
@@ -23704,10 +24243,7 @@
\expandafter\XINT_bezout_mp_postb\expandafter
{\romannumeral0\xintiiopp {#2}}{#1}%
}%
-\edef\XINT_bezout_mp_postb #1#2#3#4#5%
-{%
- \space {#4}{#5}{#2}{#1}{#3}%
-}%
+\def\XINT_bezout_mp_postb #1#2#3#4#5{{#4}{#5}{#2}{#1}{#3}}%
% \end{macrocode}
% \lverb|plusminus A < 0, B > 0|
% \begin{macrocode}
@@ -23721,10 +24257,7 @@
\expandafter \XINT_bezout_pm_postb \expandafter
{\romannumeral0\xintiiopp{#1}}%
}%
-\edef\XINT_bezout_pm_postb #1#2#3#4#5%
-{%
- \space {#4}{#5}{#1}{#2}{#3}%
-}%
+\def\XINT_bezout_pm_postb #1#2#3#4#5{{#4}{#5}{#1}{#2}{#3}}%
% \end{macrocode}
% \lverb|plusplus|
% \begin{macrocode}
@@ -23736,10 +24269,7 @@
% \end{macrocode}
% \lverb|la parité (-1)^N est en #1, et on la jette ici.|
% \begin{macrocode}
-\edef\XINT_bezout_pp_post #1#2#3#4#5%
-{%
- \space {#4}{#5}{#1}{#2}{#3}%
-}%
+\def\XINT_bezout_pp_post #1#2#3#4#5{{#4}{#5}{#1}{#2}{#3}}%
% \end{macrocode}
% \lverb|&
% n = 0: 1BAalpha(0)beta(0)alpha(-1)beta(-1)$\
@@ -23749,8 +24279,7 @@
% \begin{macrocode}
\def\XINT_bezout_loop_a #1#2#3%
{%
- \expandafter\XINT_bezout_loop_b
- \expandafter{\the\numexpr -#1\expandafter }%
+ \expandafter\XINT_bezout_loop_b\the\numexpr -#1\expandafter.%
\romannumeral0\XINT_div_prepare {#2}{#3}{#2}%
}%
% \end{macrocode}
@@ -23761,11 +24290,11 @@
% De plus ce n'est plus (-1)^n que l'on veut mais n. (ou dans un autre ordre)$\
% {-(-1)^n}{q(n)}{r(n)}{r(n-1)}{alpha(n-1)}{beta(n-1)}{alpha(n-2)}{beta(n-2)}|
% \begin{macrocode}
-\def\XINT_bezout_loop_b #1#2#3#4#5#6#7#8%
+\def\XINT_bezout_loop_b #1.#2#3#4#5#6#7#8%
{%
- \expandafter \XINT_bezout_loop_c \expandafter
- {\romannumeral0\xintiiadd{\XINT_mul_fork #5\Z #2\Z}{#7}}%
- {\romannumeral0\xintiiadd{\XINT_mul_fork #6\Z #2\Z}{#8}}%
+ \expandafter\XINT_bezout_loop_c\expandafter
+ {\romannumeral0\xintiiadd{\XINT_mul_fork #5\xint:#2\xint:}{#7}}%
+ {\romannumeral0\xintiiadd{\XINT_mul_fork #6\xint:#2\xint:}{#8}}%
{#1}{#3}{#4}{#5}{#6}%
}%
% \end{macrocode}
@@ -23773,8 +24302,7 @@
% \begin{macrocode}
\def\XINT_bezout_loop_c #1#2%
{%
- \expandafter \XINT_bezout_loop_d \expandafter
- {#2}{#1}%
+ \expandafter\XINT_bezout_loop_d\expandafter{#2}{#1}%
}%
% \end{macrocode}
% \lverb|{beta(n)}{alpha(n)}{(-1)^(n+1)}{r(n)}{r(n-1)}{alpha(n-1)}{beta(n-1)}|
@@ -23788,21 +24316,18 @@
% \begin{macrocode}
\def\XINT_bezout_loop_e #1#2\Z
{%
- \xint_gob_til_zero #1\xint_bezout_loop_exit0\XINT_bezout_loop_f
- {#1#2}%
+ \xint_gob_til_zero #1\XINT_bezout_loop_exit0\XINT_bezout_loop_f {#1#2}%
}%
% \end{macrocode}
-% \lverb|{r(n)}{(-1)^(n+1)}{r(n-1)}{alpha(n)}{beta(n)}{alpha(n-1)}{beta(n-1)}|
+% \lverb|{r(n)}{(-1)^(n+1)}{r(n-1)}{alpha(n)}{beta(n)}{alpha(n-1)}{beta(n-1)}
+% ->{(-1)^(n+1)}{r(n)}{r(n-1)}{alpha(n)}{beta(n)}{alpha(n-1)}{beta(n-1)}
+% et itération|
% \begin{macrocode}
\def\XINT_bezout_loop_f #1#2%
{%
\XINT_bezout_loop_a {#2}{#1}%
}%
-% \end{macrocode}
-% \lverb|{(-1)^(n+1)}{r(n)}{r(n-1)}{alpha(n)}{beta(n)}{alpha(n-1)}{beta(n-1)}
-% et itération|
-% \begin{macrocode}
-\def\xint_bezout_loop_exit0\XINT_bezout_loop_f #1#2%
+\def\XINT_bezout_loop_exit0\XINT_bezout_loop_f #1#2%
{%
\ifcase #2
\or \expandafter\XINT_bezout_exiteven
@@ -23809,14 +24334,8 @@
\else\expandafter\XINT_bezout_exitodd
\fi
}%
-\edef\XINT_bezout_exiteven #1#2#3#4#5%
-{%
- \space {#5}{#4}{#1}%
-}%
-\edef\XINT_bezout_exitodd #1#2#3#4#5%
-{%
- \space {-#5}{-#4}{#1}%
-}%
+\def\XINT_bezout_exiteven #1#2#3#4#5{{#5}{#4}{#1}}%
+\def\XINT_bezout_exitodd #1#2#3#4#5{{-#5}{-#4}{#1}}%
% \end{macrocode}
% \subsection{\csh{xintEuclideAlgorithm}}
% \lverb|&
@@ -23827,11 +24346,11 @@
\def\xintEuclideAlgorithm {\romannumeral0\xinteuclidealgorithm }%
\def\xinteuclidealgorithm #1%
{%
- \expandafter \XINT_euc \expandafter{\romannumeral0\xintiabs {#1}}%
+ \expandafter\XINT_euc\expandafter{\romannumeral0\xintiabs {#1}}%
}%
\def\XINT_euc #1#2%
{%
- \expandafter\XINT_euc_fork \romannumeral0\xintiabs {#2}\Z #1\Z
+ \expandafter\XINT_euc_fork\romannumeral0\xintiabs {#2}\Z #1\Z
}%
% \end{macrocode}
% \lverb|Ici #3#4=A, #1#2=B|
@@ -23852,8 +24371,8 @@
% On va renvoyer:$\
% {N}{A}{D=r(n)}{B}{q1}{r1}{q2}{r2}{q3}{r3}....{qN}{rN=0}|
% \begin{macrocode}
-\def\XINT_euc_AisZero #1#2#3#4#5#6{ {1}{0}{#2}{#2}{0}{0}}%
-\def\XINT_euc_BisZero #1#2#3#4#5#6{ {1}{0}{#3}{#3}{0}{0}}%
+\def\XINT_euc_AisZero #1#2#3#4#5#6{{1}{0}{#2}{#2}{0}{0}}%
+\def\XINT_euc_BisZero #1#2#3#4#5#6{{1}{0}{#3}{#3}{0}{0}}%
% \end{macrocode}
% \lverb|&
% {n}{rn}{an}{{qn}{rn}}...{{A}{B}}{}\Z$\
@@ -23862,14 +24381,13 @@
% \begin{macrocode}
\def\XINT_euc_a #1#2#3%
{%
- \expandafter\XINT_euc_b
- \expandafter {\the\numexpr #1+1\expandafter }%
+ \expandafter\XINT_euc_b\the\numexpr #1+\xint_c_i\expandafter.%
\romannumeral0\XINT_div_prepare {#2}{#3}{#2}%
}%
% \end{macrocode}
% \lverb|{n+1}{q(n+1)}{r(n+1)}{rn}{{qn}{rn}}...|
% \begin{macrocode}
-\def\XINT_euc_b #1#2#3#4%
+\def\XINT_euc_b #1.#2#3#4%
{%
\XINT_euc_c #3\Z {#1}{#3}{#4}{{#2}{#3}}%
}%
@@ -23879,7 +24397,7 @@
% \begin{macrocode}
\def\XINT_euc_c #1#2\Z
{%
- \xint_gob_til_zero #1\xint_euc_end0\XINT_euc_a
+ \xint_gob_til_zero #1\XINT_euc_end0\XINT_euc_a
}%
% \end{macrocode}
% \lverb|&
@@ -23888,20 +24406,17 @@
% {n+1}{0}{r(n)}{{q(n+1)}{r(n+1)}}.....{{q1}{r1}}{{A}{B}}{}\Z$\
% On veut renvoyer: {N=n+1}{A}{D=r(n)}{B}{q1}{r1}{q2}{r2}{q3}{r3}....{qN}{rN=0}|
% \begin{macrocode}
-\def\xint_euc_end0\XINT_euc_a #1#2#3#4\Z%
+\def\XINT_euc_end0\XINT_euc_a #1#2#3#4\Z%
{%
- \expandafter\xint_euc_end_
+ \expandafter\XINT_euc_end_a
\romannumeral0%
\XINT_rord_main {}#4{{#1}{#3}}%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax
+ \xint:
}%
-\edef\xint_euc_end_ #1#2#3%
-{%
- \space {#1}{#3}{#2}%
-}%
+\def\XINT_euc_end_a #1#2#3{{#1}{#3}{#2}}%
% \end{macrocode}
% \subsection{\csh{xintBezoutAlgorithm}}
% \lverb|&
@@ -23931,8 +24446,8 @@
\krof
0{#1#2}{#3#4}1001{{#3#4}{#1#2}}{}\Z
}%
-\def\XINT_bezalg_AisZero #1#2#3\Z{ {1}{0}{0}{1}{#2}{#2}{1}{0}{0}{0}{0}{1}}%
-\def\XINT_bezalg_BisZero #1#2#3#4\Z{ {1}{0}{0}{1}{#3}{#3}{1}{0}{0}{0}{0}{1}}%
+\def\XINT_bezalg_AisZero #1#2#3\Z{{1}{0}{0}{1}{#2}{#2}{1}{0}{0}{0}{0}{1}}%
+\def\XINT_bezalg_BisZero #1#2#3#4\Z{{1}{0}{0}{1}{#3}{#3}{1}{0}{0}{0}{0}{1}}%
% \end{macrocode}
% \lverb|&
% pour préparer l'étape n+1 il faut
@@ -23942,8 +24457,7 @@
% \begin{macrocode}
\def\XINT_bezalg_a #1#2#3%
{%
- \expandafter\XINT_bezalg_b
- \expandafter {\the\numexpr #1+1\expandafter }%
+ \expandafter\XINT_bezalg_b\the\numexpr #1+\xint_c_i\expandafter.%
\romannumeral0\XINT_div_prepare {#2}{#3}{#2}%
}%
% \end{macrocode}
@@ -23950,7 +24464,7 @@
% \lverb|&
% {n+1}{q(n+1)}{r(n+1)}{r(n)}{alpha(n)}{beta(n)}{alpha(n-1)}{beta(n-1)}...|
% \begin{macrocode}
-\def\XINT_bezalg_b #1#2#3#4#5#6#7#8%
+\def\XINT_bezalg_b #1.#2#3#4#5#6#7#8%
{%
\expandafter\XINT_bezalg_c\expandafter
{\romannumeral0\xintiiadd {\xintiiMul {#6}{#2}}{#8}}%
@@ -23979,7 +24493,7 @@
% \begin{macrocode}
\def\XINT_bezalg_e #1#2\Z
{%
- \xint_gob_til_zero #1\xint_bezalg_end0\XINT_bezalg_a
+ \xint_gob_til_zero #1\XINT_bezalg_end0\XINT_bezalg_a
}%
% \end{macrocode}
% \lverb|&
@@ -23990,15 +24504,15 @@
% {N}{A}{0}{1}{D=r(n)}{B}{1}{0}{q1}{r1}{alpha1=q1}{beta1=1}$\
% {q2}{r2}{alpha2}{beta2}....{qN}{rN=0}{alphaN=A/D}{betaN=B/D}|
% \begin{macrocode}
-\def\xint_bezalg_end0\XINT_bezalg_a #1#2#3#4#5#6#7#8\Z
+\def\XINT_bezalg_end0\XINT_bezalg_a #1#2#3#4#5#6#7#8\Z
{%
- \expandafter\xint_bezalg_end_
+ \expandafter\XINT_bezalg_end_a
\romannumeral0%
\XINT_rord_main {}#8{{#1}{#3}}%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax
+ \xint:
}%
% \end{macrocode}
% \lverb|&
@@ -24008,31 +24522,30 @@
% {N}{A}{0}{1}{D=r(n)}{B}{1}{0}{q1}{r1}{alpha1=q1}{beta1=1}$\
% {q2}{r2}{alpha2}{beta2}....{qN}{rN=0}{alphaN=A/D}{betaN=B/D}|
% \begin{macrocode}
-\edef\xint_bezalg_end_ #1#2#3#4%
-{%
- \space {#1}{#3}{0}{1}{#2}{#4}{1}{0}%
-}%
+\def\XINT_bezalg_end_a #1#2#3#4{{#1}{#3}{0}{1}{#2}{#4}{1}{0}}%
% \end{macrocode}
% \subsection{\csh{xintGCDof}}
+% \lverb|1.2l adds protection against items being non-terminated \the\numexpr...|
% \begin{macrocode}
\def\xintGCDof {\romannumeral0\xintgcdof }%
-\def\xintgcdof #1{\expandafter\XINT_gcdof_a\romannumeral`&&@#1\relax }%
-\def\XINT_gcdof_a #1{\expandafter\XINT_gcdof_b\romannumeral`&&@#1\Z }%
-\def\XINT_gcdof_b #1\Z #2{\expandafter\XINT_gcdof_c\romannumeral`&&@#2\Z {#1}\Z}%
-\def\XINT_gcdof_c #1{\xint_gob_til_relax #1\XINT_gcdof_e\relax\XINT_gcdof_d #1}%
-\def\XINT_gcdof_d #1\Z {\expandafter\XINT_gcdof_b\romannumeral0\xintgcd {#1}}%
-\def\XINT_gcdof_e #1\Z #2\Z { #2}%
+\def\xintgcdof #1{\expandafter\XINT_gcdof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_gcdof_a #1{\expandafter\XINT_gcdof_b\romannumeral`&&@#1!}%
+\def\XINT_gcdof_b #1!#2{\expandafter\XINT_gcdof_c\romannumeral`&&@#2!{#1}!}%
+\def\XINT_gcdof_c #1{\xint_gob_til_xint: #1\XINT_gcdof_e\xint:\XINT_gcdof_d #1}%
+\def\XINT_gcdof_d #1!{\expandafter\XINT_gcdof_b\romannumeral0\xintgcd {#1}}%
+\def\XINT_gcdof_e #1!#2!{ #2}%
% \end{macrocode}
% \subsection{\csh{xintLCMof}}
% \lverb|New with 1.09a|
+% \lverb|1.2l adds protection against items being non-terminated \the\numexpr...|
% \begin{macrocode}
\def\xintLCMof {\romannumeral0\xintlcmof }%
-\def\xintlcmof #1{\expandafter\XINT_lcmof_a\romannumeral`&&@#1\relax }%
-\def\XINT_lcmof_a #1{\expandafter\XINT_lcmof_b\romannumeral`&&@#1\Z }%
-\def\XINT_lcmof_b #1\Z #2{\expandafter\XINT_lcmof_c\romannumeral`&&@#2\Z {#1}\Z}%
-\def\XINT_lcmof_c #1{\xint_gob_til_relax #1\XINT_lcmof_e\relax\XINT_lcmof_d #1}%
-\def\XINT_lcmof_d #1\Z {\expandafter\XINT_lcmof_b\romannumeral0\xintlcm {#1}}%
-\def\XINT_lcmof_e #1\Z #2\Z { #2}%
+\def\xintlcmof #1{\expandafter\XINT_lcmof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_lcmof_a #1{\expandafter\XINT_lcmof_b\romannumeral`&&@#1!}%
+\def\XINT_lcmof_b #1!#2{\expandafter\XINT_lcmof_c\romannumeral`&&@#2!{#1}!}%
+\def\XINT_lcmof_c #1{\xint_gob_til_xint: #1\XINT_lcmof_e\xint:\XINT_lcmof_d #1}%
+\def\XINT_lcmof_d #1!{\expandafter\XINT_lcmof_b\romannumeral0\xintlcm {#1}}%
+\def\XINT_lcmof_e #1!#2!{ #2}%
% \end{macrocode}
% \subsection{\csh{xintTypesetEuclideAlgorithm}}
% \lverb|&
@@ -24214,7 +24727,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintfrac}%
- [2017/01/06 1.2k Expandable operations on fractions (JFB)]%
+ [2017/07/26 1.2l Expandable operations on fractions (JFB)]%
% \end{macrocode}
% \subsection{\csh{XINT_cntSgnFork}}
% \lverb|1.09i. Used internally, #1 must expand to \m at ne, \z@, or \@ne or
@@ -24243,8 +24756,7 @@
{%
\expandafter#1%
\the\numexpr \XINT_abs##1+%
- \XINT_len_fork ##2##3\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ \XINT_len_fork ##2##3\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye-\xint_c_i
\relax
@@ -24260,7 +24772,7 @@
% \begin{macrocode}
\def\XINT_outfrac #1#2#3%
{%
- \ifcase\XINT_cntSgn #3\Z
+ \ifcase\XINT_cntSgn #3\xint:
\expandafter \XINT_outfrac_divisionbyzero
\or
\expandafter \XINT_outfrac_P
@@ -24269,14 +24781,14 @@
\fi
{#2}{#3}[#1]%
}%
-\def\XINT_outfrac_divisionbyzero #1#2{\xintError:DivisionByZero\space #1/0}%
-\edef\XINT_outfrac_P #1#2%
+\def\XINT_outfrac_divisionbyzero #1#2%
{%
- \noexpand\if0\noexpand\XINT_Sgn #1\noexpand\Z
- \noexpand\expandafter\noexpand\XINT_outfrac_Zero
- \noexpand\fi
- \space #1/#2%
+ \XINT_signalcondition{DivisionByZero}{Division of #1 by #2}{}{0/1[0]}%
}%
+\def\XINT_outfrac_P#1{%
+\def\XINT_outfrac_P ##1##2%
+ {\if0\XINT_Sgn ##1\xint:\expandafter\XINT_outfrac_Zero\fi#1##1/##2}%
+}\XINT_outfrac_P{ }%
\def\XINT_outfrac_Zero #1[#2]{ 0/1[0]}%
\def\XINT_outfrac_N #1#2%
{%
@@ -24351,18 +24863,25 @@
% allowing decimal digits and scientific part and possibly multiple leading
% signs.
%
+% 1.2l fixes frailty of \XINT_infrac (hence basically of all xintfrac macros)
+% respective to non terminated \numexpr input: \xintRaw{\the\numexpr1} for
+% example. The issue was that \numexpr sees the / and expands what's next.
+% But even \numexpr 1// for example creates an error, and to my mind this is
+% a defect of \numexpr. It should be able to trace back and see that / was
+% used as delimiter not as operator. Anyway, I thus fixed this problem
+% belatedly here regarding \XINT_infrac.
% |
% \begin{macrocode}
\def\XINT_inFrac {\romannumeral0\XINT_infrac }%
\def\XINT_infrac #1%
{%
- \expandafter\XINT_infrac_fork\romannumeral`&&@#1/\XINT_W[\XINT_W\XINT_T
+ \expandafter\XINT_infrac_fork\romannumeral`&&@#1\xint:/\XINT_W[\XINT_W\XINT_T
}%
\def\XINT_infrac_fork #1[#2%
{%
\xint_UDXINTWfork
- #2\XINT_frac_gen
- \XINT_W\XINT_infrac_res_a % strict A[N] or A/B[N] input
+ #2\XINT_frac_gen % input has no brackets [N]
+ \XINT_W\XINT_infrac_res_a % there is some [N], must be strict A[N] or A/B[N] input
\krof
#1[#2%
}%
@@ -24370,12 +24889,15 @@
{%
\xint_gob_til_zero #1\XINT_infrac_res_zero 0\XINT_infrac_res_b #1%
}%
+% \end{macrocode}
+% \lverb|Note that input exponent is here ignored and forced to be zero.|
+% \begin{macrocode}
\def\XINT_infrac_res_zero 0\XINT_infrac_res_b #1\XINT_T {{0}{0}{1}}%
\def\XINT_infrac_res_b #1/#2%
{%
\xint_UDXINTWfork
- #2\XINT_infrac_res_ca
- \XINT_W\XINT_infrac_res_cb
+ #2\XINT_infrac_res_ca % it was A[N] input
+ \XINT_W\XINT_infrac_res_cb % it was A/B[N] input
\krof
#1/#2%
}%
@@ -24384,11 +24906,11 @@
% 1.2f). As nobody reads xint documentation, no one will have noticed the
% fleeting possibility.|
% \begin{macrocode}
-\def\XINT_infrac_res_ca #1[#2]/\XINT_W[\XINT_W\XINT_T
+\def\XINT_infrac_res_ca #1[#2]\xint:/\XINT_W[\XINT_W\XINT_T
{\expandafter{\the\numexpr #2}{#1}{1}}%
\def\XINT_infrac_res_cb #1/#2[%
{\expandafter\XINT_infrac_res_cc\romannumeral`&&@#2~#1[}%
-\def\XINT_infrac_res_cc #1~#2[#3]/\XINT_W[\XINT_W\XINT_T
+\def\XINT_infrac_res_cc #1~#2[#3]\xint:/\XINT_W[\XINT_W\XINT_T
{\expandafter{\the\numexpr #3}{#2}{#1}}%
% \end{macrocode}
% \subsection{\csh{XINT_frac_gen}}
@@ -24407,13 +24929,16 @@
\def\XINT_frac_gen #1/#2%
{%
\xint_UDXINTWfork
- #2\XINT_frac_gen_A
- \XINT_W\XINT_frac_gen_B
+ #2\XINT_frac_gen_A % there was no /
+ \XINT_W\XINT_frac_gen_B % there was a /
\krof
#1/#2%
}%
-\def\XINT_frac_gen_A #1/\XINT_W [\XINT_W {\XINT_frac_gen_C 0~1!#1ee.\XINT_W }%
-\def\XINT_frac_gen_B #1/#2/\XINT_W[%\XINT_W
+% \end{macrocode}
+% \lverb|Note that #1 is only expanded so far up to decimal mark or "e".|
+% \begin{macrocode}
+\def\XINT_frac_gen_A #1\xint:/\XINT_W [\XINT_W {\XINT_frac_gen_C 0~1!#1ee.\XINT_W }%
+\def\XINT_frac_gen_B #1/#2\xint:/\XINT_W[%\XINT_W
{%
\expandafter\XINT_frac_gen_Ba
\romannumeral`&&@#2ee.\XINT_W\XINT_Z #1ee.%\XINT_W
@@ -24432,12 +24957,13 @@
{%
\expandafter\XINT_frac_gen_Bd\romannumeral`&&@#2.#1e%
}%
+% \end{macrocode}
+% \begin{macrocode}
\def\XINT_frac_gen_Bd #1.#2e#3e#4\XINT_Z
{%
\expandafter\XINT_frac_gen_C\the\numexpr #3-%
\numexpr\XINT_length_loop
- #1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
~#2#1!%
@@ -24453,9 +24979,8 @@
\def\XINT_frac_gen_Ca #1~#2!#3e#4e#5\XINT_T
{%
\expandafter\XINT_frac_gen_F\the\numexpr #4-#1\expandafter
- ~\romannumeral0\XINT_num_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z~#3~%
+ ~\romannumeral0\expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z~#3~%
}%
\def\XINT_frac_gen_Cb #1.#2e%
{%
@@ -24465,13 +24990,12 @@
{%
\expandafter\XINT_frac_gen_F\the\numexpr #5-#2-%
\numexpr\XINT_length_loop
- #1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
- \relax\expandafter~\romannumeral0\XINT_num_loop
- #3\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z
+ \relax\expandafter~%
+ \romannumeral0\expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop
+ #3\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
~#4#1~%
}%
\def\XINT_frac_gen_F #1~#2%
@@ -24485,20 +25009,18 @@
\def\XINT_frac_gen_Gdivbyzero #1~~#2~%
{%
\expandafter\XINT_frac_gen_Gdivbyzero_a
- \romannumeral0\XINT_num_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z~#1~%
+ \romannumeral0\expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z~#1~%
}%
\def\XINT_frac_gen_Gdivbyzero_a #1~#2~%
{%
- \xintError:DivisionByZero {#2}{#1}{0}%
+ \XINT_signalcondition{DivisionByZero}{Division of #1 by zero}{}{{#2}{#1}{0}}%
}%
\def\XINT_frac_gen_G #1#2#3~#4~#5~%
{%
\expandafter\XINT_frac_gen_Ga
- \romannumeral0\XINT_num_loop
- #1#5\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z~#3~{#2#4}%
+ \romannumeral0\expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop
+ #1#5\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z~#3~{#2#4}%
}%
\def\XINT_frac_gen_Ga #1#2~#3~%
{%
@@ -24514,10 +25036,10 @@
{%
\expandafter\XINT_cuz_cnt_loop\expandafter
{\expandafter}\romannumeral0\XINT_rord_main {}#1%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax
+ \xint:
\R\R\R\R\R\R\R\R\Z
}%
\def\XINT_cuz_cnt #1%
@@ -24598,10 +25120,10 @@
{%
\expandafter\space\expandafter
{\romannumeral0\XINT_rord_main {}#2%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax }{#1}%
+ \xint:}{#1}%
}%
% \end{macrocode}
% \subsection{\csh{xintRaw}}
@@ -24694,7 +25216,7 @@
}%
\def\XINT_numer #1%
{%
- \ifcase\XINT_cntSgn #1\Z
+ \ifcase\XINT_cntSgn #1\xint:
\expandafter\XINT_numer_B
\or
\expandafter\XINT_numer_A
@@ -24923,8 +25445,14 @@
\krof
{#3#4}{#1#2}{#3#4}{#1#2}%
}%
-\def\XINT_irr_indeterminate #1#2#3#4#5{\xintError:NaN\space 0/0}%
-\def\XINT_irr_divisionbyzero #1#2#3#4#5{\xintError:DivisionByZero #5#2/0}%
+\def\XINT_irr_indeterminate #1#2#3#4#5%
+{%
+ \XINT_signalcondition{DivisionUndefined}{indeterminate: 0/0}{}{0/1}%
+}%
+\def\XINT_irr_divisionbyzero #1#2#3#4#5%
+{%
+ \XINT_signalcondition{DivisionByZero}{vanishing denominator: #5#2/0}{}{0/1}%
+}%
\def\XINT_irr_zero #1#2#3#4#5{ 0/1}% changed in 1.08
\def\XINT_irr_loop_a #1#2%
{%
@@ -24996,8 +25524,14 @@
\krof
{#3#4}{#1#2}1001%
}%
-\def\XINT_jrr_indeterminate #1#2#3#4#5#6#7{\xintError:NaN\space 0/0}%
-\def\XINT_jrr_divisionbyzero #1#2#3#4#5#6#7{\xintError:DivisionByZero #7#2/0}%
+\def\XINT_jrr_indeterminate #1#2#3#4#5#6#7%
+{%
+ \XINT_signalcondition{DivisionUndefined}{indeterminate: 0/0}{}{0/1}%
+}%
+\def\XINT_jrr_divisionbyzero #1#2#3#4#5#6#7%
+{%
+ \XINT_signalcondition{DivisionByZero}{Vanishing denominator: #7#2/0}{}{0/1}%
+}%
\def\XINT_jrr_zero #1#2#3#4#5#6#7{ 0/1}% changed in 1.08
\def\XINT_jrr_loop_a #1#2%
{%
@@ -25007,8 +25541,8 @@
\def\XINT_jrr_loop_b #1#2#3#4#5#6#7%
{%
\expandafter \XINT_jrr_loop_c \expandafter
- {\romannumeral0\xintiiadd{\XINT_mul_fork #4\Z #1\Z}{#6}}%
- {\romannumeral0\xintiiadd{\XINT_mul_fork #5\Z #1\Z}{#7}}%
+ {\romannumeral0\xintiiadd{\XINT_mul_fork #4\xint:#1\xint:}{#6}}%
+ {\romannumeral0\xintiiadd{\XINT_mul_fork #5\xint:#1\xint:}{#7}}%
{#2}{#3}{#4}{#5}%
}%
\def\XINT_jrr_loop_c #1#2%
@@ -25075,8 +25609,8 @@
}%
\def\XINT_trunc_a #1#2#3#4.#5%
{%
- \if0\XINT_Sgn#2\Z\xint_dothis\XINT_trunc_zero\fi
- \if1\XINT_is_one#3XY\xint_dothis\XINT_trunc_sp_b\fi
+ \if0\XINT_Sgn#2\xint:\xint_dothis\XINT_trunc_zero\fi
+ \if1\XINT_is_One#3XY\xint_dothis\XINT_trunc_sp_b\fi
\xint_orthat\XINT_trunc_b #1+#4.{#2}{#3}#5#4.%
}%
\def\XINT_trunc_zero #1.#2.{ 0}%
@@ -25115,8 +25649,7 @@
\expandafter\XINT_trunc_sp_Cc
\romannumeral0\expandafter\XINT_split_fromright_a
\the\numexpr#3-\numexpr\XINT_length_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
.#2\xint_bye2345678\xint_bye..#1%
@@ -25213,8 +25746,8 @@
}%
\def\XINT_round_a #1#2#3#4.%
{%
- \if0\XINT_Sgn#2\Z\xint_dothis\XINT_trunc_zero\fi
- \if1\XINT_is_one#3XY\xint_dothis\XINT_trunc_sp_b\fi
+ \if0\XINT_Sgn#2\xint:\xint_dothis\XINT_trunc_zero\fi
+ \if1\XINT_is_One#3XY\xint_dothis\XINT_trunc_sp_b\fi
\xint_orthat\XINT_trunc_b #1+#4.{#2}{#3}%
}%
\def\XINT_round_A{\expandafter\XINT_trunc_G\romannumeral0\XINT_round_B}%
@@ -25258,7 +25791,8 @@
\def\XINT_xtrunc_zero #1#2]{0.\romannumeral\xintreplicate{#1}0}%
\def\XINT_xtrunc_d #1#2#3/#4[#5]%
{%
- \XINT_xtrunc_prepare_a#4\R\R\R\R\R\R\R\R {10}0000001\W !{#4};{#5}{#2}{#1#3}%
+ \XINT_xtrunc_prepare_a#4\R\R\R\R\R\R\R\R {10}0000001\W
+ !{#4};{#5}{#2}{#1#3}%
}%
\def\XINT_xtrunc_prepare_a #1#2#3#4#5#6#7#8#9%
{%
@@ -25308,12 +25842,13 @@
{%
\expandafter\XINT_xtrunc_e\expandafter
{\expandafter\XINT_xtrunc_small_a
- \the\numexpr #1/\xint_c_ii\expandafter.\the\numexpr \xint_c_x^viii+#1!}%
+ \the\numexpr #1/\xint_c_ii\expandafter
+ .\the\numexpr \xint_c_x^viii+#1!}%
}%
\def\XINT_xtrunc_small_a #1.#2!#3%
{%
\expandafter\XINT_div_small_b\the\numexpr #1\expandafter
- .\the\numexpr #2\expandafter!%
+ \xint:\the\numexpr #2\expandafter!%
\romannumeral0\XINT_div_small_ba #3\R\R\R\R\R\R\R\R{10}0000001\W
#3\XINT_sepbyviii_Z_end 2345678\relax
}%
@@ -25325,7 +25860,8 @@
}%
\def\XINT_xtrunc_prepare_d #1#2#3#4#5#6#7#8#9%
{%
- \expandafter\XINT_xtrunc_prepare_e\xint_gob_til_dot #1#2#3#4#5#6#7#8#9!%
+ \expandafter\XINT_xtrunc_prepare_e
+ \xint_gob_til_dot #1#2#3#4#5#6#7#8#9!%
}%
\def\XINT_xtrunc_prepare_e #1!#2!#3#4%
{%
@@ -25336,14 +25872,13 @@
\expandafter\XINT_xtrunc_prepare_g\expandafter
\XINT_div_prepare_g
\the\numexpr #1#2#3#4#5#6#7#8+\xint_c_i\expandafter
- .\the\numexpr (#1#2#3#4#5#6#7#8+\xint_c_i)/\xint_c_ii\expandafter
- .\the\numexpr #1#2#3#4#5#6#7#8\expandafter
- .\romannumeral0\XINT_sepandrev_andcount
+ \xint:\the\numexpr (#1#2#3#4#5#6#7#8+\xint_c_i)/\xint_c_ii\expandafter
+ \xint:\the\numexpr #1#2#3#4#5#6#7#8\expandafter
+ \xint:\romannumeral0\XINT_sepandrev_andcount
#1#2#3#4#5#6#7#8#9\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678%
- \relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\X
}%
\def\XINT_xtrunc_prepare_g #1;{\XINT_xtrunc_e {#1}}%
@@ -25353,15 +25888,15 @@
\expandafter\XINT_xtrunc_I
\else
\expandafter\XINT_xtrunc_II
- \fi #2.{#1}%
+ \fi #2\xint:{#1}%
}%
-\def\XINT_xtrunc_I -#1.#2#3#4%
+\def\XINT_xtrunc_I -#1\xint:#2#3#4%
{%
\expandafter\XINT_xtrunc_I_a\romannumeral0#2{#4}{#2}{#1}{#3}%
}%
\def\XINT_xtrunc_I_a #1#2#3#4#5%
{%
- \expandafter\XINT_xtrunc_I_b\the\numexpr #4-#5.#4.{#5}{#2}{#3}{#1}%
+ \expandafter\XINT_xtrunc_I_b\the\numexpr #4-#5\xint:#4\xint:{#5}{#2}{#3}{#1}%
}%
\def\XINT_xtrunc_I_b #1%
{%
@@ -25370,12 +25905,12 @@
-\XINT_xtrunc_IB_c
\krof #1%
}%
-\def\XINT_xtrunc_IA_c -#1.#2.#3#4#5#6%
+\def\XINT_xtrunc_IA_c -#1\xint:#2\xint:#3#4#5#6%
{%
\expandafter\XINT_xtrunc_IA_d
- \the\numexpr#2-\xintLength{#6}.{#6}%
+ \the\numexpr#2-\xintLength{#6}\xint:{#6}%
\expandafter\XINT_xtrunc_IA_xd
- \the\numexpr (#1+\xint_c_ii^v)/\xint_c_ii^vi-\xint_c_i.#1.{#5}{#4}%
+ \the\numexpr (#1+\xint_c_ii^v)/\xint_c_ii^vi-\xint_c_i\xint:#1\xint:{#5}{#4}%
}%
\def\XINT_xtrunc_IA_d #1%
{%
@@ -25384,24 +25919,24 @@
-\XINT_xtrunc_IAB_e
\krof #1%
}%
-\def\XINT_xtrunc_IAA_e -#1.#2%
+\def\XINT_xtrunc_IAA_e -#1\xint:#2%
{%
\romannumeral0\XINT_split_fromleft
#1.#2\xint_gobble_i\xint_bye2345678\xint_bye..%
}%
-\def\XINT_xtrunc_IAB_e #1.#2%
+\def\XINT_xtrunc_IAB_e #1\xint:#2%
{%
0.\romannumeral\XINT_rep#1\endcsname0#2%
}%
-\def\XINT_xtrunc_IA_xd #1.#2.%
+\def\XINT_xtrunc_IA_xd #1\xint:#2\xint:%
{%
- \expandafter\XINT_xtrunc_IA_xe\the\numexpr #2-\xint_c_ii^vi*#1.#1.%
+ \expandafter\XINT_xtrunc_IA_xe\the\numexpr #2-\xint_c_ii^vi*#1\xint:#1\xint:%
}%
-\def\XINT_xtrunc_IA_xe #1.#2.#3#4%
+\def\XINT_xtrunc_IA_xe #1\xint:#2\xint:#3#4%
{%
\XINT_xtrunc_loop {#2}{#4}{#3}{#1}%
}%
-\def\XINT_xtrunc_IB_c #1.#2.#3#4#5#6%
+\def\XINT_xtrunc_IB_c #1\xint:#2\xint:#3#4#5#6%
{%
\expandafter\XINT_xtrunc_IB_d
\romannumeral0\XINT_split_xfork #1.#6\xint_bye2345678\xint_bye..{#3}%
@@ -25408,23 +25943,23 @@
}%
\def\XINT_xtrunc_IB_d #1.#2.#3%
{%
- \expandafter\XINT_xtrunc_IA_d\the\numexpr#3-\xintLength {#1}.{#1}%
+ \expandafter\XINT_xtrunc_IA_d\the\numexpr#3-\xintLength {#1}\xint:{#1}%
}%
-\def\XINT_xtrunc_II #1.%
+\def\XINT_xtrunc_II #1\xint:%
{%
- \expandafter\XINT_xtrunc_II_a\romannumeral\xintreplicate{#1}0.%
+ \expandafter\XINT_xtrunc_II_a\romannumeral\xintreplicate{#1}0\xint:%
}%
-\def\XINT_xtrunc_II_a #1.#2#3#4%
+\def\XINT_xtrunc_II_a #1\xint:#2#3#4%
{%
\expandafter\XINT_xtrunc_II_b
- \the\numexpr (#3+\xint_c_ii^v)/\xint_c_ii^vi-\xint_c_i\expandafter.%
- \the\numexpr #3\expandafter.\romannumeral0#2{#4#1}{#2}%
+ \the\numexpr (#3+\xint_c_ii^v)/\xint_c_ii^vi-\xint_c_i\expandafter\xint:%
+ \the\numexpr #3\expandafter\xint:\romannumeral0#2{#4#1}{#2}%
}%
-\def\XINT_xtrunc_II_b #1.#2.%
+\def\XINT_xtrunc_II_b #1\xint:#2\xint:%
{%
- \expandafter\XINT_xtrunc_II_c\the\numexpr #2-\xint_c_ii^vi*#1.#1.%
+ \expandafter\XINT_xtrunc_II_c\the\numexpr #2-\xint_c_ii^vi*#1\xint:#1\xint:%
}%
-\def\XINT_xtrunc_II_c #1.#2.#3#4#5%
+\def\XINT_xtrunc_II_c #1\xint:#2\xint:#3#4#5%
{%
#3.\XINT_xtrunc_loop {#2}{#4}{#5}{#1}%
}%
@@ -25431,9 +25966,9 @@
\def\XINT_xtrunc_loop #1%
{%
\ifnum #1=\xint_c_ \expandafter\XINT_xtrunc_transition\fi
- \expandafter\XINT_xtrunc_loop_a\the\numexpr #1-\xint_c_i.%
+ \expandafter\XINT_xtrunc_loop_a\the\numexpr #1-\xint_c_i\xint:%
}%
-\def\XINT_xtrunc_loop_a #1.#2#3%
+\def\XINT_xtrunc_loop_a #1\xint:#2#3%
{%
\expandafter\XINT_xtrunc_loop_b\romannumeral0#3%
{#20000000000000000000000000000000000000000000000000000000000000000}%
@@ -25445,7 +25980,7 @@
\XINT_xtrunc_loop {#3}{#2}%
}%
\def\XINT_xtrunc_transition
- \expandafter\XINT_xtrunc_loop_a\the\numexpr #1.#2#3#4%
+ \expandafter\XINT_xtrunc_loop_a\the\numexpr #1\xint:#2#3#4%
{%
\ifnum #4=\xint_c_ \expandafter\xint_gobble_vi\fi
\expandafter\XINT_xtrunc_finish\expandafter
@@ -25465,11 +26000,11 @@
\expandafter\XINT_xtrunc_sp_I
\else
\expandafter\XINT_xtrunc_sp_II
- \fi #1.%
+ \fi #1\xint:%
}%
-\def\XINT_xtrunc_sp_I -#1.#2#3%
+\def\XINT_xtrunc_sp_I -#1\xint:#2#3%
{%
- \expandafter\XINT_xtrunc_sp_I_a\the\numexpr #1-#3.#1.{#3}{#2}%
+ \expandafter\XINT_xtrunc_sp_I_a\the\numexpr #1-#3\xint:#1\xint:{#3}{#2}%
}%
\def\XINT_xtrunc_sp_I_a #1%
{%
@@ -25478,10 +26013,10 @@
-\XINT_xtrunc_sp_IB_b
\krof #1%
}%
-\def\XINT_xtrunc_sp_IA_b -#1.#2.#3#4%
+\def\XINT_xtrunc_sp_IA_b -#1\xint:#2\xint:#3#4%
{%
\expandafter\XINT_xtrunc_sp_IA_c
- \the\numexpr#2-\xintLength{#4}.{#4}\romannumeral\XINT_rep#1\endcsname0%
+ \the\numexpr#2-\xintLength{#4}\xint:{#4}\romannumeral\XINT_rep#1\endcsname0%
}%
\def\XINT_xtrunc_sp_IA_c #1%
{%
@@ -25490,16 +26025,16 @@
-\XINT_xtrunc_sp_IAB
\krof #1%
}%
-\def\XINT_xtrunc_sp_IAA -#1.#2%
+\def\XINT_xtrunc_sp_IAA -#1\xint:#2%
{%
\romannumeral0\XINT_split_fromleft
#1.#2\xint_gobble_i\xint_bye2345678\xint_bye..%
}%
-\def\XINT_xtrunc_sp_IAB #1.#2%
+\def\XINT_xtrunc_sp_IAB #1\xint:#2%
{%
0.\romannumeral\XINT_rep#1\endcsname0#2%
}%
-\def\XINT_xtrunc_sp_IB_b #1.#2.#3#4%
+\def\XINT_xtrunc_sp_IB_b #1\xint:#2\xint:#3#4%
{%
\expandafter\XINT_xtrunc_sp_IB_c
\romannumeral0\XINT_split_xfork #1.#4\xint_bye2345678\xint_bye..{#3}%
@@ -25506,9 +26041,9 @@
}%
\def\XINT_xtrunc_sp_IB_c #1.#2.#3%
{%
- \expandafter\XINT_xtrunc_sp_IA_c\the\numexpr#3-\xintLength {#1}.{#1}%
+ \expandafter\XINT_xtrunc_sp_IA_c\the\numexpr#3-\xintLength {#1}\xint:{#1}%
}%
-\def\XINT_xtrunc_sp_II #1.#2#3%
+\def\XINT_xtrunc_sp_II #1\xint:#2#3%
{%
#2\romannumeral\XINT_rep#1\endcsname0.\romannumeral\XINT_rep#3\endcsname0%
}%
@@ -25577,7 +26112,7 @@
}%
\def\XINT_fadd_E #1#2%
{%
- \if0\XINT_Sgn #2\Z
+ \if0\XINT_Sgn #2\xint:
\expandafter\XINT_fadd_F
\else\expandafter\XINT_fadd_K
\fi {#1}%
@@ -25593,7 +26128,7 @@
}%
\def\XINT_fadd_Ea #1#2%
{%
- \if0\XINT_Sgn #2\Z
+ \if0\XINT_Sgn #2\xint:
\expandafter\XINT_fadd_Fa
\else\expandafter\XINT_fadd_K
\fi {#1}%
@@ -25603,7 +26138,9 @@
\expandafter\XINT_fadd_G
\romannumeral0\xintiiadd {\xintiiMul {#4}{#1}}{#5}/#3%[#6]%
}%
-\def\XINT_fadd_G #1{\if0#1\XINT_fadd_iszero\fi\space #1}%
+\def\XINT_fadd_G #1{%
+\def\XINT_fadd_G ##1{\if0##1\expandafter\XINT_fadd_iszero\fi#1##1}%
+}\XINT_fadd_G{ }%
\def\XINT_fadd_K #1#2#3#4#5%
{%
\expandafter\XINT_fadd_L
@@ -25610,11 +26147,11 @@
\romannumeral0\xintiiadd {\xintiiMul {#2}{#5}}{\xintiiMul {#3}{#4}}.%
{{#2}{#3}}%
}%
-\def\XINT_fadd_L #1{\if0#1\XINT_fadd_iszero\fi \XINT_fadd_M #1}%
+\def\XINT_fadd_L #1{\if0#1\expandafter\XINT_fadd_iszero\fi\XINT_fadd_M #1}%
\def\XINT_fadd_M #1.#2{\expandafter\XINT_fadd_N \expandafter
{\romannumeral0\xintiimul #2}{#1}}%
\def\XINT_fadd_N #1#2{ #2/#1}%
-\edef\XINT_fadd_iszero\fi #1[#2]{\noexpand\fi\space 0/1[0]}% ou [#2] originel?
+\def\XINT_fadd_iszero #1[#2]{ 0/1[0]}% ou [#2] originel?
% \end{macrocode}
% \subsection{\csh{xintSub}}
% \begin{macrocode}
@@ -25631,26 +26168,27 @@
\krof }%
% \end{macrocode}
% \subsection{\csh{xintSum}}
+% \lverb|There was (not documented anymore since 1.09d, 2013/10/22) a macro
+% \xintSumExpr, but it has been deleted at 1.2l.
+%
+% Empty items are not accepted by this macro.|
% \begin{macrocode}
\def\xintSum {\romannumeral0\xintsum }%
-\def\xintsum #1{\xintsumexpr #1\relax }%
-\def\xintSumExpr {\romannumeral0\xintsumexpr }%
-\def\xintsumexpr {\expandafter\XINT_fsumexpr\romannumeral`&&@}%
+\def\xintsum #1{\expandafter\XINT_fsumexpr\romannumeral`&&@#1\xint:}%
\def\XINT_fsumexpr {\XINT_fsum_loop_a {0/1[0]}}%
\def\XINT_fsum_loop_a #1#2%
{%
- \expandafter\XINT_fsum_loop_b \romannumeral`&&@#2\Z {#1}%
+ \expandafter\XINT_fsum_loop_b \romannumeral`&&@#2\xint:{#1}%
}%
\def\XINT_fsum_loop_b #1%
{%
- \xint_gob_til_relax #1\XINT_fsum_finished\relax
- \XINT_fsum_loop_c #1%
+ \xint_gob_til_xint: #1\XINT_fsum_finished\xint:\XINT_fsum_loop_c #1%
}%
-\def\XINT_fsum_loop_c #1\Z #2%
+\def\XINT_fsum_loop_c #1\xint:#2%
{%
\expandafter\XINT_fsum_loop_a\expandafter{\romannumeral0\xintadd {#2}{#1}}%
}%
-\def\XINT_fsum_finished #1\Z #2{ #2}%
+\def\XINT_fsum_finished #1\xint:\xint:#2{ #2}%
% \end{macrocode}
% \subsection{\csh{xintMul}}
% \begin{macrocode}
@@ -25703,7 +26241,8 @@
% \begin{macrocode}
\def\xintipow #1#2%
{%
- \expandafter\xint_pow\the\numexpr \xintNum{#2}\expandafter.\romannumeral0\xintnum{#1}\Z%
+ \expandafter\xint_pow\the\numexpr \xintNum{#2}\expandafter
+ .\romannumeral0\xintnum{#1}\xint:
}%
\def\xintPow {\romannumeral0\xintpow }%
\def\xintpow #1%
@@ -25777,26 +26316,26 @@
}%
% \end{macrocode}
% \subsection{\csh{xintPrd}}
+% \lverb|There was (not documented anymore since 1.09d, 2013/10/22) a macro
+% \xintPrdExpr, but it has been deleted at 1.2l
+% |
% \begin{macrocode}
\def\xintPrd {\romannumeral0\xintprd }%
-\def\xintprd #1{\xintprdexpr #1\relax }%
-\def\xintPrdExpr {\romannumeral0\xintprdexpr }%
-\def\xintprdexpr {\expandafter\XINT_fprdexpr \romannumeral`&&@}%
+\def\xintprd #1{\expandafter\XINT_fprdexpr \romannumeral`&&@#1\xint:}%
\def\XINT_fprdexpr {\XINT_fprod_loop_a {1/1[0]}}%
\def\XINT_fprod_loop_a #1#2%
{%
- \expandafter\XINT_fprod_loop_b \romannumeral`&&@#2\Z {#1}%
+ \expandafter\XINT_fprod_loop_b \romannumeral`&&@#2\xint:{#1}%
}%
\def\XINT_fprod_loop_b #1%
{%
- \xint_gob_til_relax #1\XINT_fprod_finished\relax
- \XINT_fprod_loop_c #1%
+ \xint_gob_til_xint: #1\XINT_fprod_finished\xint:\XINT_fprod_loop_c #1%
}%
-\def\XINT_fprod_loop_c #1\Z #2%
+\def\XINT_fprod_loop_c #1\xint:#2%
{%
\expandafter\XINT_fprod_loop_a\expandafter{\romannumeral0\xintmul {#1}{#2}}%
}%
-\def\XINT_fprod_finished #1\Z #2{ #2}%
+\def\XINT_fprod_finished#1\xint:\xint:#2{ #2}%
% \end{macrocode}
% \subsection{\csh{xintDiv}}
% \begin{macrocode}
@@ -25851,7 +26390,7 @@
{\expandafter\XINT_mod_b\expandafter #1\romannumeral0\xintraw{#3}#2.}%
\def\XINT_mod_b #1#2% #1 de A, #2 de B.
{%
- \if0#2\xint_dothis\XINT_mod_divbyzero\fi
+ \if0#2\xint_dothis{\XINT_mod_divbyzero #1#2}\fi
\if0#1\xint_dothis\XINT_mod_aiszero\fi
\if-#2\xint_dothis{\XINT_mod_bneg #1}\fi
\xint_orthat{\XINT_mod_bpos #1#2}%
@@ -25870,7 +26409,10 @@
-{\XINT_mod_pos #1}%
\krof
}%
-\def\XINT_mod_divbyzero #1.{\xintError:DivisionByZero\space 0/1[0]}%
+\def\XINT_mod_divbyzero #1#2[#3]#4.%
+{%
+ \XINT_signalcondition{DivisionByZero}{Division by #2[#3] of #1#4}{}{0/1[0]}%
+}%
\def\XINT_mod_aiszero #1.{ 0/1[0]}%
\def\XINT_mod_pos #1#2/#3[#4]#5/#6[#7].%
{%
@@ -25890,7 +26432,7 @@
\def\xintisone #1{\expandafter\XINT_fracisone
\romannumeral0\xintrawwithzeros{#1}\Z }%
\def\XINT_fracisone #1/#2\Z
- {\if0\XINT_Cmp {#1}{#2}\xint_afterfi{ 1}\else\xint_afterfi{ 0}\fi}%
+ {\if0\xintiiCmp {#1}{#2}\xint_afterfi{ 1}\else\xint_afterfi{ 0}\fi}%
% \end{macrocode}
% \subsection{\csh{xintGeq}}
% \begin{macrocode}
@@ -25926,7 +26468,7 @@
\def\XINT_fgeq_D #1#2#3%
{%
\expandafter\XINT_cntSgnFork\romannumeral`&&@\expandafter\XINT_cntSgn
- \the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax\Z
+ \the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax\xint:
{ 0}{\XINT_fgeq_E #2\Z {#3}{#1}}{ 1}%
}%
\def\XINT_fgeq_E #1%
@@ -25986,17 +26528,21 @@
}%
% \end{macrocode}
% \subsection{\csh{xintMaxof}}
+% \lverb|1.2l protects \xintMaxof against items with non terminated
+% \the\numexpr expressions.
+%
+% The macro is not compatible with an empty list.|
% \begin{macrocode}
\def\xintMaxof {\romannumeral0\xintmaxof }%
-\def\xintmaxof #1{\expandafter\XINT_maxof_a\romannumeral`&&@#1\relax }%
-\def\XINT_maxof_a #1{\expandafter\XINT_maxof_b\romannumeral0\xintraw{#1}\Z }%
-\def\XINT_maxof_b #1\Z #2%
- {\expandafter\XINT_maxof_c\romannumeral`&&@#2\Z {#1}\Z}%
+\def\xintmaxof #1{\expandafter\XINT_maxof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_maxof_a #1{\expandafter\XINT_maxof_b\romannumeral0\xintraw{#1}!}%
+\def\XINT_maxof_b #1!#2%
+ {\expandafter\XINT_maxof_c\romannumeral`&&@#2!{#1}!}%
\def\XINT_maxof_c #1%
- {\xint_gob_til_relax #1\XINT_maxof_e\relax\XINT_maxof_d #1}%
-\def\XINT_maxof_d #1\Z
+ {\xint_gob_til_xint: #1\XINT_maxof_e\xint:\XINT_maxof_d #1}%
+\def\XINT_maxof_d #1!%
{\expandafter\XINT_maxof_b\romannumeral0\xintmax {#1}}%
-\def\XINT_maxof_e #1\Z #2\Z { #2}%
+\def\XINT_maxof_e #1!#2!{ #2}%
% \end{macrocode}
% \subsection{\csh{xintMin}}
% \begin{macrocode}
@@ -26036,21 +26582,25 @@
}%
% \end{macrocode}
% \subsection{\csh{xintMinof}}
+% \lverb|1.2l protects \xintMinof against items with non terminated
+% \the\numexpr expressions.
+%
+% The macro is not compatible with an empty list.|
% \begin{macrocode}
\def\xintMinof {\romannumeral0\xintminof }%
-\def\xintminof #1{\expandafter\XINT_minof_a\romannumeral`&&@#1\relax }%
-\def\XINT_minof_a #1{\expandafter\XINT_minof_b\romannumeral0\xintraw{#1}\Z }%
-\def\XINT_minof_b #1\Z #2%
- {\expandafter\XINT_minof_c\romannumeral`&&@#2\Z {#1}\Z}%
+\def\xintminof #1{\expandafter\XINT_minof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_minof_a #1{\expandafter\XINT_minof_b\romannumeral0\xintraw{#1}!}%
+\def\XINT_minof_b #1!#2%
+ {\expandafter\XINT_minof_c\romannumeral`&&@#2!{#1}!}%
\def\XINT_minof_c #1%
- {\xint_gob_til_relax #1\XINT_minof_e\relax\XINT_minof_d #1}%
-\def\XINT_minof_d #1\Z
+ {\xint_gob_til_xint: #1\XINT_minof_e\xint:\XINT_minof_d #1}%
+\def\XINT_minof_d #1!%
{\expandafter\XINT_minof_b\romannumeral0\xintmin {#1}}%
-\def\XINT_minof_e #1\Z #2\Z { #2}%
+\def\XINT_minof_e #1!#2!{ #2}%
% \end{macrocode}
% \subsection{\csh{xintCmp}}
% \begin{macrocode}
-%\def\xintCmp {\romannumeral0\xintcmp }%
+\def\xintCmp {\romannumeral0\xintcmp }%
\def\xintcmp #1%
{%
\expandafter\XINT_fcmp\expandafter {\romannumeral0\xintraw {#1}}%
@@ -26104,7 +26654,7 @@
\def\XINT_fcmp_D #1#2#3%
{%
\expandafter\XINT_cntSgnFork\romannumeral`&&@\expandafter\XINT_cntSgn
- \the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax\Z
+ \the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax\xint:
{ -1}{\XINT_fcmp_E #2\Z {#3}{#1}}{ 1}%
}%
\def\XINT_fcmp_E #1%
@@ -26139,7 +26689,7 @@
% \subsection{\csh{xintSgn}}
% \begin{macrocode}
\def\xintSgn {\romannumeral0\xintsgn }%
-\def\xintsgn #1{\expandafter\XINT_sgn\romannumeral0\xintraw {#1}\Z }%
+\def\xintsgn #1{\expandafter\XINT_sgn\romannumeral0\xintraw {#1}\xint:}%
% \end{macrocode}
% \subsection{Floating point macros}
%
@@ -26248,7 +26798,7 @@
% simply make now \xintFloat a wrapper of \XINTinFloat.|
% \begin{macrocode}
\def\xintFloat {\romannumeral0\xintfloat }%
-\def\xintfloat #1{\XINT_float_chkopt #1\xint_relax }%
+\def\xintfloat #1{\XINT_float_chkopt #1\xint:}%
\def\XINT_float_chkopt #1%
{%
\ifx [#1\expandafter\XINT_float_opt
@@ -26255,12 +26805,12 @@
\else\expandafter\XINT_float_noopt
\fi #1%
}%
-\def\XINT_float_noopt #1\xint_relax
+\def\XINT_float_noopt #1\xint:%
{%
\expandafter\XINT_float_post
\romannumeral0\XINTinfloat[\XINTdigits]{#1}\XINTdigits.%
}%
-\def\XINT_float_opt [\xint_relax #1]%
+\def\XINT_float_opt [\xint:#1]%
{%
\expandafter\XINT_float_opt_a\the\numexpr #1.%
}%
@@ -26358,7 +26908,7 @@
% \end{macrocode}
% \lverb|micro boost au lieu d'utiliser \XINT_isOne{#4}, mais pas bon style.|
% \begin{macrocode}
- \if1\XINT_is_one#4XY%
+ \if1\XINT_is_One#4XY%
\expandafter\XINT_infloat_sp
\else\expandafter\XINT_infloat_fork
\fi #3.{#1}{#2}{#4}%
@@ -26669,7 +27219,7 @@
% |
% \begin{macrocode}
\def\xintPFloat {\romannumeral0\xintpfloat }%
-\def\xintpfloat #1{\XINT_pfloat_chkopt #1\xint_relax }%
+\def\xintpfloat #1{\XINT_pfloat_chkopt #1\xint:}%
\def\XINT_pfloat_chkopt #1%
{%
\ifx [#1\expandafter\XINT_pfloat_opt
@@ -26676,12 +27226,12 @@
\else\expandafter\XINT_pfloat_noopt
\fi #1%
}%
-\def\XINT_pfloat_noopt #1\xint_relax
+\def\XINT_pfloat_noopt #1\xint:%
{%
\expandafter\XINT_pfloat_a
\romannumeral0\xintfloat [\XINTdigits]{#1};\XINTdigits.%
}%
-\def\XINT_pfloat_opt [\xint_relax #1]%
+\def\XINT_pfloat_opt [\xint:#1]%
{%
\expandafter\XINT_pfloat_opt_a \the\numexpr #1.%
}%
@@ -26778,9 +27328,9 @@
%|
% \begin{macrocode}
\def\xintFloatAdd {\romannumeral0\xintfloatadd }%
-\def\xintfloatadd #1{\XINT_fladd_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatadd #1{\XINT_fladd_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatAdd {\romannumeral0\XINTinfloatadd }%
-\def\XINTinfloatadd #1{\XINT_fladd_chkopt \XINTinfloatS #1\xint_relax }%
+\def\XINTinfloatadd #1{\XINT_fladd_chkopt \XINTinfloatS #1\xint:}%
\def\XINT_fladd_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_fladd_opt
@@ -26787,13 +27337,13 @@
\else\expandafter\XINT_fladd_noopt
\fi #1#2%
}%
-\def\XINT_fladd_noopt #1#2\xint_relax #3%
+\def\XINT_fladd_noopt #1#2\xint:#3%
{%
#1[\XINTdigits]%
{\expandafter\XINT_FL_add_a
\romannumeral0\XINTinfloat[\XINTdigits]{#2}\XINTdigits.{#3}}%
}%
-\def\XINT_fladd_opt #1[\xint_relax #2]%#3#4%
+\def\XINT_fladd_opt #1[\xint:#2]%#3#4%
{%
\expandafter\XINT_fladd_opt_a\the\numexpr #2.#1%
}%
@@ -26829,9 +27379,9 @@
%
% \begin{macrocode}
\def\xintFloatSub {\romannumeral0\xintfloatsub }%
-\def\xintfloatsub #1{\XINT_flsub_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatsub #1{\XINT_flsub_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatSub {\romannumeral0\XINTinfloatsub }%
-\def\XINTinfloatsub #1{\XINT_flsub_chkopt \XINTinfloatS #1\xint_relax }%
+\def\XINTinfloatsub #1{\XINT_flsub_chkopt \XINTinfloatS #1\xint:}%
\def\XINT_flsub_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flsub_opt
@@ -26838,13 +27388,13 @@
\else\expandafter\XINT_flsub_noopt
\fi #1#2%
}%
-\def\XINT_flsub_noopt #1#2\xint_relax #3%
+\def\XINT_flsub_noopt #1#2\xint:#3%
{%
#1[\XINTdigits]%
{\expandafter\XINT_FL_add_a
\romannumeral0\XINTinfloat[\XINTdigits]{#2}\XINTdigits.{\xintOpp{#3}}}%
}%
-\def\XINT_flsub_opt #1[\xint_relax #2]%#3#4%
+\def\XINT_flsub_opt #1[\xint:#2]%#3#4%
{%
\expandafter\XINT_flsub_opt_a\the\numexpr #2.#1%
}%
@@ -26868,9 +27418,9 @@
% one was amply enough).|
% \begin{macrocode}
\def\xintFloatMul {\romannumeral0\xintfloatmul }%
-\def\xintfloatmul #1{\XINT_flmul_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatmul #1{\XINT_flmul_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatMul {\romannumeral0\XINTinfloatmul }%
-\def\XINTinfloatmul #1{\XINT_flmul_chkopt \XINTinfloatS #1\xint_relax }%
+\def\XINTinfloatmul #1{\XINT_flmul_chkopt \XINTinfloatS #1\xint:}%
\def\XINT_flmul_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flmul_opt
@@ -26877,13 +27427,13 @@
\else\expandafter\XINT_flmul_noopt
\fi #1#2%
}%
-\def\XINT_flmul_noopt #1#2\xint_relax #3%
+\def\XINT_flmul_noopt #1#2\xint:#3%
{%
#1[\XINTdigits]%
{\expandafter\XINT_FL_mul_a
\romannumeral0\XINTinfloatS[\XINTdigits]{#2}\XINTdigits.{#3}}%
}%
-\def\XINT_flmul_opt #1[\xint_relax #2]%#3#4%
+\def\XINT_flmul_opt #1[\xint:#2]%#3#4%
{%
\expandafter\XINT_flmul_opt_a\the\numexpr #2.#1%
}%
@@ -26914,9 +27464,9 @@
% |
% \begin{macrocode}
\def\xintFloatDiv {\romannumeral0\xintfloatdiv }%
-\def\xintfloatdiv #1{\XINT_fldiv_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatdiv #1{\XINT_fldiv_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatDiv {\romannumeral0\XINTinfloatdiv }%
-\def\XINTinfloatdiv #1{\XINT_fldiv_chkopt \XINTinfloatS #1\xint_relax }%
+\def\XINTinfloatdiv #1{\XINT_fldiv_chkopt \XINTinfloatS #1\xint:}%
\def\XINT_fldiv_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_fldiv_opt
@@ -26923,13 +27473,13 @@
\else\expandafter\XINT_fldiv_noopt
\fi #1#2%
}%
-\def\XINT_fldiv_noopt #1#2\xint_relax #3%
+\def\XINT_fldiv_noopt #1#2\xint:#3%
{%
#1[\XINTdigits]%
{\expandafter\XINT_FL_div_a
\romannumeral0\XINTinfloatS[\XINTdigits]{#3}\XINTdigits.{#2}}%
}%
-\def\XINT_fldiv_opt #1[\xint_relax #2]%#3#4%
+\def\XINT_fldiv_opt #1[\xint:#2]%#3#4%
{%
\expandafter\XINT_fldiv_opt_a\the\numexpr #2.#1%
}%
@@ -26960,9 +27510,9 @@
% |
% \begin{macrocode}
\def\xintFloatPow {\romannumeral0\xintfloatpow}%
-\def\xintfloatpow #1{\XINT_flpow_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatpow #1{\XINT_flpow_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatPow {\romannumeral0\XINTinfloatpow }%
-\def\XINTinfloatpow #1{\XINT_flpow_chkopt \XINTinfloatS #1\xint_relax }%
+\def\XINTinfloatpow #1{\XINT_flpow_chkopt \XINTinfloatS #1\xint:}%
\def\XINT_flpow_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flpow_opt
@@ -26970,12 +27520,12 @@
\fi
#1#2%
}%
-\def\XINT_flpow_noopt #1#2\xint_relax #3%
+\def\XINT_flpow_noopt #1#2\xint:#3%
{%
\expandafter\XINT_flpow_checkB_a
\the\numexpr #3.\XINTdigits.{#2}{#1[\XINTdigits]}%
}%
-\def\XINT_flpow_opt #1[\xint_relax #2]%
+\def\XINT_flpow_opt #1[\xint:#2]%
{%
\expandafter\XINT_flpow_opt_a\the\numexpr #2.#1%
}%
@@ -26997,6 +27547,8 @@
\expandafter\XINT_flpow_checkB_c
\the\numexpr\xintLength{#2}+\xint_c_iii.#3.#2.{#1}%
}%
+% \end{macrocode}
+% \begin{macrocode}
\def\XINT_flpow_checkB_c #1.#2.%
{%
\expandafter\XINT_flpow_checkB_d\the\numexpr#1+#2.#1.#2.%
@@ -27025,8 +27577,10 @@
}%
\def\XINT_flpow_zero #1[#2]#3#4#5#6%
{%
- \if 1#51\xint_afterfi {#6{0[0]}}\else
- \xint_afterfi {\xintError:DivisionByZero #6{1[2147483648]}}\fi
+ #6{\if 1#51\xint_dothis {0[0]}\fi
+ \xint_orthat
+ {\XINT_signalcondition{DivisionByZero}{0 to the power #4}{}{0[0]}}%
+ }%
}%
\def\XINT_flpow_b #1#2[#3]#4#5%
{%
@@ -27156,9 +27710,9 @@
% |
% \begin{macrocode}
\def\xintFloatPower {\romannumeral0\xintfloatpower}%
-\def\xintfloatpower #1{\XINT_flpower_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatpower #1{\XINT_flpower_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatPower {\romannumeral0\XINTinfloatpower }%
-\def\XINTinfloatpower #1{\XINT_flpower_chkopt \XINTinfloatS #1\xint_relax }%
+\def\XINTinfloatpower #1{\XINT_flpower_chkopt \XINTinfloatS #1\xint:}%
% \end{macrocode}
% \lverb|First the special macro for use by the expression parser which checks
% if one raises to an half-integer exponent. This is always with \XINTdigits
@@ -27219,12 +27773,12 @@
\fi
#1#2%
}%
-\def\XINT_flpower_noopt #1#2\xint_relax #3%
+\def\XINT_flpower_noopt #1#2\xint:#3%
{%
\expandafter\XINT_flpower_checkB_a
\romannumeral0\xintnum{#3}.\XINTdigits.{#2}{#1[\XINTdigits]}%
}%
-\def\XINT_flpower_opt #1[\xint_relax #2]%
+\def\XINT_flpower_opt #1[\xint:#2]%
{%
\expandafter\XINT_flpower_opt_a\the\numexpr #2.#1%
}%
@@ -27342,9 +27896,9 @@
% \subsection{\csh{xintFloatFac}, \csh{XINTFloatFac}}
% \begin{macrocode}
\def\xintFloatFac {\romannumeral0\xintfloatfac}%
-\def\xintfloatfac #1{\XINT_flfac_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatfac #1{\XINT_flfac_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatFac {\romannumeral0\XINTinfloatfac }%
-\def\XINTinfloatfac #1{\XINT_flfac_chkopt \XINTinfloat #1\xint_relax }%
+\def\XINTinfloatfac #1{\XINT_flfac_chkopt \XINTinfloat #1\xint:}%
\def\XINT_flfac_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flfac_opt
@@ -27352,12 +27906,12 @@
\fi
#1#2%
}%
-\def\XINT_flfac_noopt #1#2\xint_relax
+\def\XINT_flfac_noopt #1#2\xint:
{%
\expandafter\XINT_FL_fac_fork_a
\the\numexpr \xintNum{#2}.\xint_c_i \XINTdigits\XINT_FL_fac_out{#1[\XINTdigits]}%
}%
-\def\XINT_flfac_opt #1[\xint_relax #2]%
+\def\XINT_flfac_opt #1[\xint:#2]%
{%
\expandafter\XINT_flfac_opt_a\the\numexpr #2.#1%
}%
@@ -27377,7 +27931,11 @@
% \end{macrocode}
% \lverb|1.2f XINT_FL_fac_isneg returns 0, earlier versions used 1 here.|
% \begin{macrocode}
-\def\XINT_FL_fac_isneg #1.#2#3#4#5{\expandafter\xintError:FactorialOfNegative #5{0[0]}}%
+\def\XINT_FL_fac_isneg #1.#2#3#4#5%
+{%
+ #5{\XINT_signalcondition{InvalidOperation}
+ {Factorial of negative: (-#1)!}{}{0[0]}}%
+}%
\def\XINT_FL_fac_fork_b #1.%
{%
\ifnum #1>\xint_c_x^viii_mone\xint_dothis\XINT_FL_fac_toobig\fi
@@ -27387,7 +27945,11 @@
\xint_orthat\XINT_FL_fac_small
#1.%
}%
-\def\XINT_FL_fac_toobig #1.#2#3#4#5{\expandafter\xintError:TooBigFactorial #5{1[0]}}%
+\def\XINT_FL_fac_toobig #1.#2#3#4#5%
+{%
+ #5{\XINT_signalcondition{InvalidOperation}
+ {Factorial of too big: (#1)!}{}{0[0]}}%
+}%
% \end{macrocode}
% \lverb?Computations are done with Q blocks of eight digits. When a
% multiplication has a carry, hence creates Q+1 blocks, the least significant
@@ -27447,8 +28009,10 @@
}%
\def\XINT_FL_fac_countdigits #1#2#3#4#5#6#7#8{\XINT_FL_fac_countdone }%
\def\XINT_FL_fac_countdone #1#2\Z {#1}%
-\def\XINT_FL_fac_out #1\Z![#2]#3{#3{\romannumeral0\XINT_mul_out
- #1\Z!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W [#2]}}%
+\def\XINT_FL_fac_out #1;![#2]#3%
+ {#3{\romannumeral0\XINT_mul_out
+ #1;!1\R!1\R!1\R!1\R!%
+ 1\R!1\R!1\R!1\R!\W [#2]}}%
\def\XINT_FL_fac_vbigloop_a #1.#2.%
{%
\XINT_FL_fac_bigloop_a \xint_c_x^iv.#2.%
@@ -27532,15 +28096,16 @@
\def\XINT_FL_fac_addzeros #1.%
{%
\ifnum #1=\xint_c_viii \expandafter\XINT_FL_fac_addzeros_exit\fi
- \expandafter\XINT_FL_fac_addzeros\the\numexpr #1-\xint_c_viii.100000000!%
+ \expandafter\XINT_FL_fac_addzeros
+ \the\numexpr #1-\xint_c_viii.100000000!%
}%
% \end{macrocode}
% \lverb|We will manipulate by successive *small* multiplications Q blocks
-% 1<8d>!, terminated by 1\Z!. We need a custom small multiplication which
+% 1<8d>!, terminated by 1;!. We need a custom small multiplication which
% tells us when it has create a new block, and the least significant one
% should be dropped.|
% \begin{macrocode}
-\def\XINT_FL_fac_addzeros_exit #1.#2.#3#4{\XINT_FL_fac_smallloop_loop #3#21\Z![-#4]}%
+\def\XINT_FL_fac_addzeros_exit #1.#2.#3#4{\XINT_FL_fac_smallloop_loop #3#21;![-#4]}%
\def\XINT_FL_fac_smallloop_loop #1.#2.%
{%
\ifnum #1>#2 \expandafter\XINT_FL_fac_loop_exit\fi
@@ -27560,7 +28125,7 @@
\def\XINT_FL_fac_mul_a #1-#2%
{%
\if#21\xint_afterfi{\expandafter\space\xint_gob_til_exclam}\else
- \expandafter\space\fi #11\Z!%
+ \expandafter\space\fi #11;!%
}%
\def\XINT_FL_fac_minimulwc_a #1#2#3#4#5!#6#7#8#9%
{%
@@ -27569,9 +28134,9 @@
\def\XINT_FL_fac_minimulwc_b #1#2#3#4!#5%
{%
\expandafter\XINT_FL_fac_minimulwc_c
- \the\numexpr \xint_c_x^ix+#5+#2*#4.{{#1}{#2}{#3}{#4}}%
+ \the\numexpr \xint_c_x^ix+#5+#2*#4!{{#1}{#2}{#3}{#4}}%
}%
-\def\XINT_FL_fac_minimulwc_c 1#1#2#3#4#5#6.#7%
+\def\XINT_FL_fac_minimulwc_c 1#1#2#3#4#5#6!#7%
{%
\expandafter\XINT_FL_fac_minimulwc_d {#1#2#3#4#5}#7{#6}%
}%
@@ -27578,9 +28143,9 @@
\def\XINT_FL_fac_minimulwc_d #1#2#3#4#5%
{%
\expandafter\XINT_FL_fac_minimulwc_e
- \the\numexpr \xint_c_x^ix+#1+#2*#5+#3*#4.{#2}{#4}%
+ \the\numexpr \xint_c_x^ix+#1+#2*#5+#3*#4!{#2}{#4}%
}%
-\def\XINT_FL_fac_minimulwc_e 1#1#2#3#4#5#6.#7#8#9%
+\def\XINT_FL_fac_minimulwc_e 1#1#2#3#4#5#6!#7#8#9%
{%
1#6#9\expandafter!%
\the\numexpr\expandafter\XINT_FL_fac_smallmul
@@ -27588,7 +28153,7 @@
}%
\def\XINT_FL_fac_smallmul 1#1!#21#3!%
{%
- \xint_gob_til_Z #3\XINT_FL_fac_smallmul_end\Z
+ \xint_gob_til_sc #3\XINT_FL_fac_smallmul_end;%
\XINT_FL_fac_minimulwc_a #2!#3!{#1}{#2}%
}%
% \end{macrocode}
@@ -27600,7 +28165,7 @@
% (a \numexpr muste be stopped, and leaving a - as delimiter is good as it
% will not arise earlier.)|
% \begin{macrocode}
-\def\XINT_FL_fac_smallmul_end\Z\XINT_FL_fac_minimulwc_a #1!\Z!#2#3[#4]%
+\def\XINT_FL_fac_smallmul_end;\XINT_FL_fac_minimulwc_a #1!;!#2#3[#4]%
{%
\ifnum #2=\xint_c_
\expandafter\xint_firstoftwo\else
@@ -27619,9 +28184,9 @@
% condition 0<=a<=b<10^8 is violated. Same as for \xintiiPFactorial.|
% \begin{macrocode}
\def\xintFloatPFactorial {\romannumeral0\xintfloatpfactorial}%
-\def\xintfloatpfactorial #1{\XINT_flpfac_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatpfactorial #1{\XINT_flpfac_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatPFactorial {\romannumeral0\XINTinfloatpfactorial }%
-\def\XINTinfloatpfactorial #1{\XINT_flpfac_chkopt \XINTinfloat #1\xint_relax }%
+\def\XINTinfloatpfactorial #1{\XINT_flpfac_chkopt \XINTinfloat #1\xint:}%
\def\XINT_flpfac_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flpfac_opt
@@ -27629,13 +28194,13 @@
\fi
#1#2%
}%
-\def\XINT_flpfac_noopt #1#2\xint_relax #3%
+\def\XINT_flpfac_noopt #1#2\xint:#3%
{%
\expandafter\XINT_FL_pfac_fork
\the\numexpr \xintNum{#2}\expandafter.%
\the\numexpr \xintNum{#3}.\xint_c_i{\XINTdigits}{#1[\XINTdigits]}%
}%
-\def\XINT_flpfac_opt #1[\xint_relax #2]%
+\def\XINT_flpfac_opt #1[\xint:#2]%
{%
\expandafter\XINT_flpfac_opt_b\the\numexpr #2.#1%
}%
@@ -27653,7 +28218,11 @@
\ifnum #3#4>\xint_c_x^viii_mone\xint_dothis\XINT_FL_pfac_outofrange\fi
\xint_orthat \XINT_FL_pfac_increaseP #1#2.#3#4.%
}%
-\def\XINT_FL_pfac_outofrange #1.#2.#3#4#5{\xintError:OutOfRangePFac #5{0[0]}}%
+\def\XINT_FL_pfac_outofrange #1.#2.#3#4#5%
+{%
+ #5{\XINT_signalcondition{InvalidOperation}
+ {pfactorial second arg too big: 99999999 < #2}{}{0[0]}}%
+}%
\def\XINT_FL_pfac_one #1.#2.#3#4#5{#5{1[0]}}%
\def\XINT_FL_pfac_zero #1.#2.#3#4#5{#5{0[0]}}%
\def\XINT_FL_pfac_neg -#1.-#2.%
@@ -27687,7 +28256,7 @@
{%
\expandafter\XINT_FL_pfac_b\the\numexpr \xint_c_i+#2\expandafter.%
\the\numexpr#3\expandafter.%
- \romannumeral0\XINT_FL_pfac_addzeroes #1.100000001!1\Z![-#1]%
+ \romannumeral0\XINT_FL_pfac_addzeroes #1.100000001!1;![-#1]%
}%
\def\XINT_FL_pfac_addzeroes #1.%
{%
@@ -27822,9 +28391,9 @@
% integers.|
% \begin{macrocode}
\def\xintFloatBinomial {\romannumeral0\xintfloatbinomial}%
-\def\xintfloatbinomial #1{\XINT_flbinom_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatbinomial #1{\XINT_flbinom_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatBinomial {\romannumeral0\XINTinfloatbinomial }%
-\def\XINTinfloatbinomial #1{\XINT_flbinom_chkopt \XINTinfloat #1\xint_relax }%
+\def\XINTinfloatbinomial #1{\XINT_flbinom_chkopt \XINTinfloat #1\xint:}%
\def\XINT_flbinom_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flbinom_opt
@@ -27831,12 +28400,12 @@
\else\expandafter\XINT_flbinom_noopt
\fi #1#2%
}%
-\def\XINT_flbinom_noopt #1#2\xint_relax #3%
+\def\XINT_flbinom_noopt #1#2\xint:#3%
{%
\expandafter\XINT_FL_binom_a
\the\numexpr\xintNum{#2}\expandafter.\the\numexpr\xintNum{#3}.\XINTdigits.#1%
}%
-\def\XINT_flbinom_opt #1[\xint_relax #2]#3#4%
+\def\XINT_flbinom_opt #1[\xint:#2]#3#4%
{%
\expandafter\XINT_FL_binom_a
\the\numexpr\xintNum{#3}\expandafter.\the\numexpr\xintNum{#4}\expandafter.%
@@ -27848,20 +28417,30 @@
}%
\def\XINT_FL_binom_fork #1#2.#3#4.#5#6.%
{%
- \if-#5\xint_dothis \XINT_FL_binom_outofrange\fi
+ \if-#5\xint_dothis \XINT_FL_binom_neg\fi
\if-#1\xint_dothis \XINT_FL_binom_zero\fi
\if-#3\xint_dothis \XINT_FL_binom_zero\fi
\if0#1\xint_dothis \XINT_FL_binom_one\fi
\if0#3\xint_dothis \XINT_FL_binom_one\fi
- \ifnum #5#6>\xint_c_x^viii_mone \xint_dothis\XINT_FL_binom_outofrange\fi
+ \ifnum #5#6>\xint_c_x^viii_mone \xint_dothis\XINT_FL_binom_toobig\fi
\ifnum #1#2>#3#4 \xint_dothis\XINT_FL_binom_ab \fi
\xint_orthat\XINT_FL_binom_aa
#1#2.#3#4.#5#6.%
}%
-\def\XINT_FL_binom_outofrange #1.#2.#3.#4.#5%
- {\xintError:OutOfRangeBinomial #5[#4]{0[0]}}%
+\def\XINT_FL_binom_neg #1.#2.#3.#4.#5%
+{%
+ #5[#4]{\XINT_signalcondition{InvalidOperation}
+ {binomial with first arg negative: #3}{}{0[0]}}%
+}%
+\def\XINT_FL_binom_toobig #1.#2.#3.#4.#5%
+{%
+ #5[#4]{\XINT_signalcondition{InvalidOperation}
+ {binomial with first arg too big: 99999999 < #3}{}{0[0]}}%
+}%
\def\XINT_FL_binom_one #1.#2.#3.#4.#5{#5[#4]{1[0]}}%
\def\XINT_FL_binom_zero #1.#2.#3.#4.#5{#5[#4]{0[0]}}%
+% \end{macrocode}
+% \begin{macrocode}
\def\XINT_FL_binom_aa #1.#2.#3.#4.#5%
{%
#5[#4]{\xintDiv{\XINT_FL_pfac_increaseP
@@ -27904,9 +28483,9 @@
% |
% \begin{macrocode}
\def\xintFloatSqrt {\romannumeral0\xintfloatsqrt }%
-\def\xintfloatsqrt #1{\XINT_flsqrt_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatsqrt #1{\XINT_flsqrt_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatSqrt {\romannumeral0\XINTinfloatsqrt }%
-\def\XINTinfloatsqrt #1{\XINT_flsqrt_chkopt \XINTinfloat #1\xint_relax }%
+\def\XINTinfloatsqrt #1{\XINT_flsqrt_chkopt \XINTinfloat #1\xint:}%
\def\XINT_flsqrt_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flsqrt_opt
@@ -27913,12 +28492,12 @@
\else\expandafter\XINT_flsqrt_noopt
\fi #1#2%
}%
-\def\XINT_flsqrt_noopt #1#2\xint_relax
+\def\XINT_flsqrt_noopt #1#2\xint:%
{%
\expandafter\XINT_FL_sqrt_a
\romannumeral0\XINTinfloat[\XINTdigits]{#2}\XINTdigits.#1%
}%
-\def\XINT_flsqrt_opt #1[\xint_relax #2]%#3%
+\def\XINT_flsqrt_opt #1[\xint:#2]%#3%
{%
\expandafter\XINT_flsqrt_opt_a\the\numexpr #2.#1%
}%
@@ -27935,7 +28514,15 @@
\krof
}%[
\def\XINT_FL_sqrt_iszero #1]#2.#3{#3[#2]{0[0]}}%
-\def\XINT_FL_sqrt_isneg #1]#2.#3{\xintError:RootOfNegative #3[#2]{0[0]}}%
+\def\XINT_FL_sqrt_isneg #1]#2.#3%
+{%
+ #3[#2]{\XINT_signalcondition{InvalidOperation}
+ {Square root of negative: -#1]}{}{0[0]}}%
+}%
+% \end{macrocode}
+%\lverb|&
+% |
+% \begin{macrocode}
\def\XINT_FL_sqrt_pos #1[#2]#3.%
{%
\expandafter\XINT_flsqrt
@@ -28002,7 +28589,7 @@
% |
% \begin{macrocode}
\def\xintFloatE {\romannumeral0\xintfloate }%
-\def\xintfloate #1{\XINT_floate_chkopt #1\xint_relax }%
+\def\xintfloate #1{\XINT_floate_chkopt #1\xint:}%
\def\XINT_floate_chkopt #1%
{%
\ifx [#1\expandafter\XINT_floate_opt
@@ -28009,12 +28596,12 @@
\else\expandafter\XINT_floate_noopt
\fi #1%
}%
-\def\XINT_floate_noopt #1\xint_relax
+\def\XINT_floate_noopt #1\xint:%
{%
\expandafter\XINT_floate_post
\romannumeral0\XINTinfloat[\XINTdigits]{#1}\XINTdigits.%
}%
-\def\XINT_floate_opt [\xint_relax #1]%
+\def\XINT_floate_opt [\xint:#1]%
{%
\expandafter\XINT_floate_opt_a\the\numexpr #1.%
}%
@@ -28127,7 +28714,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintseries}%
- [2017/01/06 1.2k Expandable partial sums with xint package (JFB)]%
+ [2017/07/26 1.2l Expandable partial sums with xint package (JFB)]%
% \end{macrocode}
% \subsection{\csh{xintSeries}}
% \begin{macrocode}
@@ -28438,7 +29025,7 @@
% just adapted the code to the case of floats.|
% \begin{macrocode}
\def\xintFloatPowerSeries {\romannumeral0\xintfloatpowerseries }%
-\def\xintfloatpowerseries #1{\XINT_flpowseries_chkopt #1\xint_relax }%
+\def\xintfloatpowerseries #1{\XINT_flpowseries_chkopt #1\xint:}%
\def\XINT_flpowseries_chkopt #1%
{%
\ifx [#1\expandafter\XINT_flpowseries_opt
@@ -28446,13 +29033,13 @@
\fi
#1%
}%
-\def\XINT_flpowseries_noopt #1\xint_relax #2%
+\def\XINT_flpowseries_noopt #1\xint:#2%
{%
\expandafter\XINT_flpowseries\expandafter
{\the\numexpr #1\expandafter}\expandafter
{\the\numexpr #2}\XINTdigits
}%
-\def\XINT_flpowseries_opt [\xint_relax #1]#2#3%
+\def\XINT_flpowseries_opt [\xint:#1]#2#3%
{%
\expandafter\XINT_flpowseries\expandafter
{\the\numexpr #2\expandafter}\expandafter
@@ -28507,7 +29094,7 @@
% \lverb|1.08a|
% \begin{macrocode}
\def\xintFloatPowerSeriesX {\romannumeral0\xintfloatpowerseriesx }%
-\def\xintfloatpowerseriesx #1{\XINT_flpowseriesx_chkopt #1\xint_relax }%
+\def\xintfloatpowerseriesx #1{\XINT_flpowseriesx_chkopt #1\xint:}%
\def\XINT_flpowseriesx_chkopt #1%
{%
\ifx [#1\expandafter\XINT_flpowseriesx_opt
@@ -28515,13 +29102,13 @@
\fi
#1%
}%
-\def\XINT_flpowseriesx_noopt #1\xint_relax #2%
+\def\XINT_flpowseriesx_noopt #1\xint:#2%
{%
\expandafter\XINT_flpowseriesx\expandafter
{\the\numexpr #1\expandafter}\expandafter
{\the\numexpr #2}\XINTdigits
}%
-\def\XINT_flpowseriesx_opt [\xint_relax #1]#2#3%
+\def\XINT_flpowseriesx_opt [\xint:#1]#2#3%
{%
\expandafter\XINT_flpowseriesx\expandafter
{\the\numexpr #2\expandafter}\expandafter
@@ -28625,7 +29212,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintcfrac}%
- [2017/01/06 1.2k Expandable continued fractions with xint package (JFB)]%
+ [2017/07/26 1.2l Expandable continued fractions with xint package (JFB)]%
% \end{macrocode}
% \subsection{\csh{xintCFrac}}
% \begin{macrocode}
@@ -28632,18 +29219,18 @@
\def\xintCFrac {\romannumeral0\xintcfrac }%
\def\xintcfrac #1%
{%
- \XINT_cfrac_opt_a #1\xint_relax
+ \XINT_cfrac_opt_a #1\xint:
}%
\def\XINT_cfrac_opt_a #1%
{%
\ifx[#1\XINT_cfrac_opt_b\fi \XINT_cfrac_noopt #1%
}%
-\def\XINT_cfrac_noopt #1\xint_relax
+\def\XINT_cfrac_noopt #1\xint:
{%
\expandafter\XINT_cfrac_A\romannumeral0\xintrawwithzeros {#1}\Z
\relax\relax
}%
-\def\XINT_cfrac_opt_b\fi\XINT_cfrac_noopt [\xint_relax #1]%
+\def\XINT_cfrac_opt_b\fi\XINT_cfrac_noopt [\xint:#1]%
{%
\fi\csname XINT_cfrac_opt#1\endcsname
}%
@@ -28707,30 +29294,30 @@
% \subsection{\csh{xintGCFrac}}
% \begin{macrocode}
\def\xintGCFrac {\romannumeral0\xintgcfrac }%
-\def\xintgcfrac #1{\XINT_gcfrac_opt_a #1\xint_relax }%
+\def\xintgcfrac #1{\XINT_gcfrac_opt_a #1\xint:}%
\def\XINT_gcfrac_opt_a #1%
{%
\ifx[#1\XINT_gcfrac_opt_b\fi \XINT_gcfrac_noopt #1%
}%
-\def\XINT_gcfrac_noopt #1\xint_relax
+\def\XINT_gcfrac_noopt #1\xint:%
{%
- \XINT_gcfrac #1+\xint_relax/\relax\relax
+ \XINT_gcfrac #1+!/\relax\relax
}%
-\def\XINT_gcfrac_opt_b\fi\XINT_gcfrac_noopt [\xint_relax #1]%
+\def\XINT_gcfrac_opt_b\fi\XINT_gcfrac_noopt [\xint:#1]%
{%
\fi\csname XINT_gcfrac_opt#1\endcsname
}%
\def\XINT_gcfrac_optl #1%
{%
- \XINT_gcfrac #1+\xint_relax/\relax\hfill
+ \XINT_gcfrac #1+!/\relax\hfill
}%
\def\XINT_gcfrac_optc #1%
{%
- \XINT_gcfrac #1+\xint_relax/\relax\relax
+ \XINT_gcfrac #1+!/\relax\relax
}%
\def\XINT_gcfrac_optr #1%
{%
- \XINT_gcfrac #1+\xint_relax/\hfill\relax
+ \XINT_gcfrac #1+!/\hfill\relax
}%
\def\XINT_gcfrac
{%
@@ -28739,23 +29326,23 @@
\def\XINT_gcfrac_enter {\XINT_gcfrac_loop {}}%
\def\XINT_gcfrac_loop #1#2+#3/%
{%
- \xint_gob_til_xint_relax #3\XINT_gcfrac_endloop\xint_relax
+ \xint_gob_til_exclam #3\XINT_gcfrac_endloop!%
\XINT_gcfrac_loop {{#3}{#2}#1}%
}%
-\def\XINT_gcfrac_endloop\xint_relax\XINT_gcfrac_loop #1#2#3%
+\def\XINT_gcfrac_endloop!\XINT_gcfrac_loop #1#2#3%
{%
- \XINT_gcfrac_T #2#3#1\xint_relax\xint_relax
+ \XINT_gcfrac_T #2#3#1!!%
}%
\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_xint_relax #5\XINT_gcfrac_end\xint_relax\XINT_gcfrac_U
+ \xint_gob_til_exclam #5\XINT_gcfrac_end!\XINT_gcfrac_U
#1#2{\xintFrac{#5}%
\ifcase\xintSgn{#4}
+\or+\else-\fi
\cfrac{#1\xintFrac{\xintAbs{#4}}#2}{#3}}%
}%
-\def\XINT_gcfrac_end\xint_relax\XINT_gcfrac_U #1#2#3%
+\def\XINT_gcfrac_end!\XINT_gcfrac_U #1#2#3%
{%
\XINT_gcfrac_end_b #3%
}%
@@ -28765,30 +29352,30 @@
% \lverb|New with 1.09m|
% \begin{macrocode}
\def\xintGGCFrac {\romannumeral0\xintggcfrac }%
-\def\xintggcfrac #1{\XINT_ggcfrac_opt_a #1\xint_relax }%
+\def\xintggcfrac #1{\XINT_ggcfrac_opt_a #1\xint:}%
\def\XINT_ggcfrac_opt_a #1%
{%
\ifx[#1\XINT_ggcfrac_opt_b\fi \XINT_ggcfrac_noopt #1%
}%
-\def\XINT_ggcfrac_noopt #1\xint_relax
+\def\XINT_ggcfrac_noopt #1\xint:
{%
- \XINT_ggcfrac #1+\xint_relax/\relax\relax
+ \XINT_ggcfrac #1+!/\relax\relax
}%
-\def\XINT_ggcfrac_opt_b\fi\XINT_ggcfrac_noopt [\xint_relax #1]%
+\def\XINT_ggcfrac_opt_b\fi\XINT_ggcfrac_noopt [\xint:#1]%
{%
\fi\csname XINT_ggcfrac_opt#1\endcsname
}%
\def\XINT_ggcfrac_optl #1%
{%
- \XINT_ggcfrac #1+\xint_relax/\relax\hfill
+ \XINT_ggcfrac #1+!/\relax\hfill
}%
\def\XINT_ggcfrac_optc #1%
{%
- \XINT_ggcfrac #1+\xint_relax/\relax\relax
+ \XINT_ggcfrac #1+!/\relax\relax
}%
\def\XINT_ggcfrac_optr #1%
{%
- \XINT_ggcfrac #1+\xint_relax/\hfill\relax
+ \XINT_ggcfrac #1+!/\hfill\relax
}%
\def\XINT_ggcfrac
{%
@@ -28797,20 +29384,20 @@
\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_gob_til_exclam #3\XINT_ggcfrac_endloop!%
\XINT_ggcfrac_loop {{#3}{#2}#1}%
}%
-\def\XINT_ggcfrac_endloop\xint_relax\XINT_ggcfrac_loop #1#2#3%
+\def\XINT_ggcfrac_endloop!\XINT_ggcfrac_loop #1#2#3%
{%
- \XINT_ggcfrac_T #2#3#1\xint_relax\xint_relax
+ \XINT_ggcfrac_T #2#3#1!!%
}%
\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
+ \xint_gob_til_exclam #5\XINT_ggcfrac_end!\XINT_ggcfrac_U
#1#2{#5+\cfrac{#1#4#2}{#3}}%
}%
-\def\XINT_ggcfrac_end\xint_relax\XINT_ggcfrac_U #1#2#3%
+\def\XINT_ggcfrac_end!\XINT_ggcfrac_U #1#2#3%
{%
\XINT_ggcfrac_end_b #3%
}%
@@ -28823,10 +29410,10 @@
{%
\expandafter\XINT_gctgcx_start\expandafter {\romannumeral`&&@#3}{#1}{#2}%
}%
-\def\XINT_gctgcx_start #1#2#3{\XINT_gctgcx_loop_a {}{#2}{#3}#1+\xint_relax/}%
+\def\XINT_gctgcx_start #1#2#3{\XINT_gctgcx_loop_a {}{#2}{#3}#1+!/}%
\def\XINT_gctgcx_loop_a #1#2#3#4+#5/%
{%
- \xint_gob_til_xint_relax #5\XINT_gctgcx_end\xint_relax
+ \xint_gob_til_exclam #5\XINT_gctgcx_end!%
\XINT_gctgcx_loop_b {#1{#4}}{#2{#5}#3}{#2}{#3}%
}%
\def\XINT_gctgcx_loop_b #1#2%
@@ -28833,7 +29420,7 @@
{%
\XINT_gctgcx_loop_a {#1#2}%
}%
-\def\XINT_gctgcx_end\xint_relax\XINT_gctgcx_loop_b #1#2#3#4{ #1}%
+\def\XINT_gctgcx_end!\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.|
@@ -29062,12 +29649,12 @@
\def\xintCstoF {\romannumeral0\xintcstof }%
\def\xintcstof #1%
{%
- \expandafter\XINT_ctf_prep \romannumeral0\xintcsvtolist{#1}\xint_relax
+ \expandafter\XINT_ctf_prep \romannumeral0\xintcsvtolist{#1}!%
}%
\def\xintCtoF {\romannumeral0\xintctof }%
\def\xintctof #1%
{%
- \expandafter\XINT_ctf_prep \romannumeral`&&@#1\xint_relax
+ \expandafter\XINT_ctf_prep \romannumeral`&&@#1!%
}%
\def\XINT_ctf_prep
{%
@@ -29075,7 +29662,7 @@
}%
\def\XINT_ctf_loop_a #1#2#3#4#5%
{%
- \xint_gob_til_xint_relax #5\XINT_ctf_end\xint_relax
+ \xint_gob_til_exclam #5\XINT_ctf_end!%
\expandafter\XINT_ctf_loop_b
\romannumeral0\xintrawwithzeros {#5}.{#1}{#2}{#3}{#4}%
}%
@@ -29082,10 +29669,12 @@
\def\XINT_ctf_loop_b #1/#2.#3#4#5#6%
{%
\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_fork #2\Z #6\Z}{\XINT_mul_fork #1\Z #4\Z}}%
- {\romannumeral0\xintiiadd {\XINT_mul_fork #2\Z #5\Z}{\XINT_mul_fork #1\Z #3\Z}}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#4\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#3\xint:}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#6\xint:}%
+ {\XINT_mul_fork #1\xint:#4\xint:}}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#5\xint:}%
+ {\XINT_mul_fork #1\xint:#3\xint:}}%
}%
\def\XINT_ctf_loop_c #1#2%
{%
@@ -29106,7 +29695,7 @@
\def\xintiCstoF {\romannumeral0\xinticstof }%
\def\xinticstof #1%
{%
- \expandafter\XINT_icstf_prep \romannumeral`&&@#1,\xint_relax,%
+ \expandafter\XINT_icstf_prep \romannumeral`&&@#1,!,%
}%
\def\XINT_icstf_prep
{%
@@ -29114,7 +29703,7 @@
}%
\def\XINT_icstf_loop_a #1#2#3#4#5,%
{%
- \xint_gob_til_xint_relax #5\XINT_icstf_end\xint_relax
+ \xint_gob_til_exclam #5\XINT_icstf_end!%
\expandafter
\XINT_icstf_loop_b \romannumeral`&&@#5.{#1}{#2}{#3}{#4}%
}%
@@ -29121,8 +29710,8 @@
\def\XINT_icstf_loop_b #1.#2#3#4#5%
{%
\expandafter\XINT_icstf_loop_c\expandafter
- {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\Z #3\Z}}%
- {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\Z #2\Z}}%
+ {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\xint:#3\xint:}}%
+ {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\xint:#2\xint:}}%
{#2}{#3}%
}%
\def\XINT_icstf_loop_c #1#2%
@@ -29136,7 +29725,7 @@
\def\xintGCtoF {\romannumeral0\xintgctof }%
\def\xintgctof #1%
{%
- \expandafter\XINT_gctf_prep \romannumeral`&&@#1+\xint_relax/%
+ \expandafter\XINT_gctf_prep \romannumeral`&&@#1+!/%
}%
\def\XINT_gctf_prep
{%
@@ -29150,10 +29739,12 @@
\def\XINT_gctf_loop_b #1/#2.#3#4#5#6%
{%
\expandafter\XINT_gctf_loop_c\expandafter
- {\romannumeral0\XINT_mul_fork #2\Z #4\Z }%
- {\romannumeral0\XINT_mul_fork #2\Z #3\Z }%
- {\romannumeral0\xintiiadd {\XINT_mul_fork #2\Z #6\Z}{\XINT_mul_fork #1\Z #4\Z}}%
- {\romannumeral0\xintiiadd {\XINT_mul_fork #2\Z #5\Z}{\XINT_mul_fork #1\Z #3\Z}}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#4\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#3\xint:}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#6\xint:}%
+ {\XINT_mul_fork #1\xint:#4\xint:}}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#5\xint:}%
+ {\XINT_mul_fork #1\xint:#3\xint:}}%
}%
\def\XINT_gctf_loop_c #1#2%
{%
@@ -29169,7 +29760,7 @@
}%
\def\XINT_gctf_loop_f #1#2/%
{%
- \xint_gob_til_xint_relax #2\XINT_gctf_end\xint_relax
+ \xint_gob_til_exclam #2\XINT_gctf_end!%
\expandafter\XINT_gctf_loop_g
\romannumeral0\xintrawwithzeros {#2}.#1%
}%
@@ -29176,10 +29767,10 @@
\def\XINT_gctf_loop_g #1/#2.#3#4#5#6%
{%
\expandafter\XINT_gctf_loop_h\expandafter
- {\romannumeral0\XINT_mul_fork #1\Z #6\Z }%
- {\romannumeral0\XINT_mul_fork #1\Z #5\Z }%
- {\romannumeral0\XINT_mul_fork #2\Z #4\Z }%
- {\romannumeral0\XINT_mul_fork #2\Z #3\Z }%
+ {\romannumeral0\XINT_mul_fork #1\xint:#6\xint:}%
+ {\romannumeral0\XINT_mul_fork #1\xint:#5\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#4\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#3\xint:}%
}%
\def\XINT_gctf_loop_h #1#2%
{%
@@ -29200,7 +29791,7 @@
\def\xintiGCtoF {\romannumeral0\xintigctof }%
\def\xintigctof #1%
{%
- \expandafter\XINT_igctf_prep \romannumeral`&&@#1+\xint_relax/%
+ \expandafter\XINT_igctf_prep \romannumeral`&&@#1+!/%
}%
\def\XINT_igctf_prep
{%
@@ -29214,8 +29805,8 @@
\def\XINT_igctf_loop_b #1.#2#3#4#5%
{%
\expandafter\XINT_igctf_loop_c\expandafter
- {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\Z #3\Z}}%
- {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\Z #2\Z}}%
+ {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\xint:#3\xint:}}%
+ {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\xint:#2\xint:}}%
{#2}{#3}%
}%
\def\XINT_igctf_loop_c #1#2%
@@ -29224,7 +29815,7 @@
}%
\def\XINT_igctf_loop_f #1#2#3#4/%
{%
- \xint_gob_til_xint_relax #4\XINT_igctf_end\xint_relax
+ \xint_gob_til_exclam #4\XINT_igctf_end!%
\expandafter\XINT_igctf_loop_g
\romannumeral`&&@#4.{#2}{#3}#1%
}%
@@ -29231,8 +29822,8 @@
\def\XINT_igctf_loop_g #1.#2#3%
{%
\expandafter\XINT_igctf_loop_h\expandafter
- {\romannumeral0\XINT_mul_fork #1\Z #3\Z }%
- {\romannumeral0\XINT_mul_fork #1\Z #2\Z }%
+ {\romannumeral0\XINT_mul_fork #1\xint:#3\xint:}%
+ {\romannumeral0\XINT_mul_fork #1\xint:#2\xint:}%
}%
\def\XINT_igctf_loop_h #1#2%
{%
@@ -29253,12 +29844,12 @@
\def\xintCstoCv {\romannumeral0\xintcstocv }%
\def\xintcstocv #1%
{%
- \expandafter\XINT_ctcv_prep\romannumeral0\xintcsvtolist{#1}\xint_relax
+ \expandafter\XINT_ctcv_prep\romannumeral0\xintcsvtolist{#1}!%
}%
\def\xintCtoCv {\romannumeral0\xintctocv }%
\def\xintctocv #1%
{%
- \expandafter\XINT_ctcv_prep\romannumeral`&&@#1\xint_relax
+ \expandafter\XINT_ctcv_prep\romannumeral`&&@#1!%
}%
\def\XINT_ctcv_prep
{%
@@ -29266,7 +29857,7 @@
}%
\def\XINT_ctcv_loop_a #1#2#3#4#5#6%
{%
- \xint_gob_til_xint_relax #6\XINT_ctcv_end\xint_relax
+ \xint_gob_til_exclam #6\XINT_ctcv_end!%
\expandafter\XINT_ctcv_loop_b
\romannumeral0\xintrawwithzeros {#6}.{#2}{#3}{#4}{#5}{#1}%
}%
@@ -29273,10 +29864,12 @@
\def\XINT_ctcv_loop_b #1/#2.#3#4#5#6%
{%
\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_fork #2\Z #6\Z}{\XINT_mul_fork #1\Z #4\Z}}%
- {\romannumeral0\xintiiadd {\XINT_mul_fork #2\Z #5\Z}{\XINT_mul_fork #1\Z #3\Z}}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#4\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#3\xint:}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#6\xint:}%
+ {\XINT_mul_fork #1\xint:#4\xint:}}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#5\xint:}%
+ {\XINT_mul_fork #1\xint:#3\xint:}}%
}%
\def\XINT_ctcv_loop_c #1#2%
{%
@@ -29303,7 +29896,7 @@
\def\xintiCstoCv {\romannumeral0\xinticstocv }%
\def\xinticstocv #1%
{%
- \expandafter\XINT_icstcv_prep \romannumeral`&&@#1,\xint_relax,%
+ \expandafter\XINT_icstcv_prep \romannumeral`&&@#1,!,%
}%
\def\XINT_icstcv_prep
{%
@@ -29311,7 +29904,7 @@
}%
\def\XINT_icstcv_loop_a #1#2#3#4#5#6,%
{%
- \xint_gob_til_xint_relax #6\XINT_icstcv_end\xint_relax
+ \xint_gob_til_exclam #6\XINT_icstcv_end!%
\expandafter
\XINT_icstcv_loop_b \romannumeral`&&@#6.{#2}{#3}{#4}{#5}{#1}%
}%
@@ -29318,8 +29911,8 @@
\def\XINT_icstcv_loop_b #1.#2#3#4#5%
{%
\expandafter\XINT_icstcv_loop_c\expandafter
- {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\Z #3\Z}}%
- {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\Z #2\Z}}%
+ {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\xint:#3\xint:}}%
+ {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\xint:#2\xint:}}%
{{#2}{#3}}%
}%
\def\XINT_icstcv_loop_c #1#2%
@@ -29339,7 +29932,7 @@
\def\xintGCtoCv {\romannumeral0\xintgctocv }%
\def\xintgctocv #1%
{%
- \expandafter\XINT_gctcv_prep \romannumeral`&&@#1+\xint_relax/%
+ \expandafter\XINT_gctcv_prep \romannumeral`&&@#1+!/%
}%
\def\XINT_gctcv_prep
{%
@@ -29353,10 +29946,12 @@
\def\XINT_gctcv_loop_b #1/#2.#3#4#5#6%
{%
\expandafter\XINT_gctcv_loop_c\expandafter
- {\romannumeral0\XINT_mul_fork #2\Z #4\Z }%
- {\romannumeral0\XINT_mul_fork #2\Z #3\Z }%
- {\romannumeral0\xintiiadd {\XINT_mul_fork #2\Z #6\Z}{\XINT_mul_fork #1\Z #4\Z}}%
- {\romannumeral0\xintiiadd {\XINT_mul_fork #2\Z #5\Z}{\XINT_mul_fork #1\Z #3\Z}}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#4\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#3\xint:}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#6\xint:}%
+ {\XINT_mul_fork #1\xint:#4\xint:}}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#5\xint:}%
+ {\XINT_mul_fork #1\xint:#3\xint:}}%
}%
\def\XINT_gctcv_loop_c #1#2%
{%
@@ -29381,7 +29976,7 @@
}%
\def\XINT_gctcv_loop_h #1#2#3/%
{%
- \xint_gob_til_xint_relax #3\XINT_gctcv_end\xint_relax
+ \xint_gob_til_exclam #3\XINT_gctcv_end!%
\expandafter\XINT_gctcv_loop_i
\romannumeral0\xintrawwithzeros {#3}.#2{#1}%
}%
@@ -29388,10 +29983,10 @@
\def\XINT_gctcv_loop_i #1/#2.#3#4#5#6%
{%
\expandafter\XINT_gctcv_loop_j\expandafter
- {\romannumeral0\XINT_mul_fork #1\Z #6\Z }%
- {\romannumeral0\XINT_mul_fork #1\Z #5\Z }%
- {\romannumeral0\XINT_mul_fork #2\Z #4\Z }%
- {\romannumeral0\XINT_mul_fork #2\Z #3\Z }%
+ {\romannumeral0\XINT_mul_fork #1\xint:#6\xint:}%
+ {\romannumeral0\XINT_mul_fork #1\xint:#5\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#4\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#3\xint:}%
}%
\def\XINT_gctcv_loop_j #1#2%
{%
@@ -29413,7 +30008,7 @@
\def\xintiGCtoCv {\romannumeral0\xintigctocv }%
\def\xintigctocv #1%
{%
- \expandafter\XINT_igctcv_prep \romannumeral`&&@#1+\xint_relax/%
+ \expandafter\XINT_igctcv_prep \romannumeral`&&@#1+!/%
}%
\def\XINT_igctcv_prep
{%
@@ -29427,8 +30022,8 @@
\def\XINT_igctcv_loop_b #1.#2#3#4#5%
{%
\expandafter\XINT_igctcv_loop_c\expandafter
- {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\Z #3\Z}}%
- {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\Z #2\Z}}%
+ {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\xint:#3\xint:}}%
+ {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\xint:#2\xint:}}%
{{#2}{#3}}%
}%
\def\XINT_igctcv_loop_c #1#2%
@@ -29437,7 +30032,7 @@
}%
\def\XINT_igctcv_loop_f #1#2#3#4/%
{%
- \xint_gob_til_xint_relax #4\XINT_igctcv_end_a\xint_relax
+ \xint_gob_til_exclam #4\XINT_igctcv_end_a!%
\expandafter\XINT_igctcv_loop_g
\romannumeral`&&@#4.#1#2{#3}%
}%
@@ -29444,8 +30039,8 @@
\def\XINT_igctcv_loop_g #1.#2#3#4#5%
{%
\expandafter\XINT_igctcv_loop_h\expandafter
- {\romannumeral0\XINT_mul_fork #1\Z #5\Z }%
- {\romannumeral0\XINT_mul_fork #1\Z #4\Z }%
+ {\romannumeral0\XINT_mul_fork #1\xint:#5\xint:}%
+ {\romannumeral0\XINT_mul_fork #1\xint:#4\xint:}%
{{#2}{#3}}%
}%
\def\XINT_igctcv_loop_h #1#2%
@@ -29682,16 +30277,16 @@
\def\xintCstoGC {\romannumeral0\xintcstogc }%
\def\xintcstogc #1%
{%
- \expandafter\XINT_cstc_prep \romannumeral`&&@#1,\xint_relax,%
+ \expandafter\XINT_cstc_prep \romannumeral`&&@#1,!,%
}%
\def\XINT_cstc_prep #1,{\XINT_cstc_loop_a {{#1}}}%
\def\XINT_cstc_loop_a #1#2,%
{%
- \xint_gob_til_xint_relax #2\XINT_cstc_end\xint_relax
+ \xint_gob_til_exclam #2\XINT_cstc_end!%
\XINT_cstc_loop_b {#1}{#2}%
}%
\def\XINT_cstc_loop_b #1#2{\XINT_cstc_loop_a {#1+1/{#2}}}%
-\def\XINT_cstc_end\xint_relax\XINT_cstc_loop_b #1#2{ #1}%
+\def\XINT_cstc_end!\XINT_cstc_loop_b #1#2{ #1}%
% \end{macrocode}
% \subsection{\csh{xintGCtoGC}}
% \begin{macrocode}
@@ -29698,12 +30293,12 @@
\def\xintGCtoGC {\romannumeral0\xintgctogc }%
\def\xintgctogc #1%
{%
- \expandafter\XINT_gctgc_start \romannumeral`&&@#1+\xint_relax/%
+ \expandafter\XINT_gctgc_start \romannumeral`&&@#1+!/%
}%
\def\XINT_gctgc_start {\XINT_gctgc_loop_a {}}%
\def\XINT_gctgc_loop_a #1#2+#3/%
{%
- \xint_gob_til_xint_relax #3\XINT_gctgc_end\xint_relax
+ \xint_gob_til_exclam #3\XINT_gctgc_end!%
\expandafter\XINT_gctgc_loop_b\expandafter
{\romannumeral`&&@#2}{#3}{#1}%
}%
@@ -29716,7 +30311,7 @@
{%
\XINT_gctgc_loop_a {#3{#2}+{#1}/}%
}%
-\def\XINT_gctgc_end\xint_relax\expandafter\XINT_gctgc_loop_b
+\def\XINT_gctgc_end!\expandafter\XINT_gctgc_loop_b
{%
\expandafter\XINT_gctgc_end_b
}%
@@ -29863,11 +30458,14 @@
\XINTsetupcatcodes%
% \end{macrocode}
% \subsection{Package identification}
+% \lverb|&
+% |
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintexpr}%
- [2017/01/06 1.2k Expandable expression parser (JFB)]%
+ [2017/07/26 1.2l Expandable expression parser (JFB)]%
\catcode`! 11
+\let\XINT_Cmp \xintiiCmp
% \end{macrocode}
% \subsection{Locking and unlocking}
% \lverb|Some renaming and modifications here with release 1.2 to switch from
@@ -29896,11 +30494,13 @@
% could probably be made faster by using techniques similar as the ones 1.2
% uses in xintcore.sty.|
% \begin{macrocode}
-\def\xint_gob_til_! #1!{}% catcode 11 ! default in xintexpr.sty code.
-\edef\XINT_expr_lockscan#1!% not used for decimal numbers in xintexpr 1.2
- {\noexpand\expandafter\space\noexpand\csname .=#1\endcsname }%
-\edef\XINT_expr_lockit
- #1{\noexpand\expandafter\space\noexpand\csname .=#1\endcsname }%
+\def\xint_gob_til_! #1!{}% ! with catcode 11
+\def\XINT_expr_lockscan#1{% not used for decimal numbers in xintexpr 1.2
+\def\XINT_expr_lockscan##1!{\expandafter#1\csname .=##1\endcsname}%
+}\XINT_expr_lockscan{ }%
+\def\XINT_expr_lockit#1{%
+\def\XINT_expr_lockit##1{\expandafter#1\csname .=##1\endcsname}%
+}\XINT_expr_lockit{ }%
\def\XINT_expr_unlock_hex_in #1% expanded inside \csname..\endcsname
{\expandafter\XINT_expr_inhex\romannumeral`&&@\XINT_expr_unlock#1;}%
\def\XINT_expr_inhex #1.#2#3;% expanded inside \csname..\endcsname
@@ -30162,7 +30762,7 @@
\if ^#1\xint_dothis\XINT_:::_end\fi
\xint_orthat\XINT_pfloat::_d #1}%
\def\XINT_pfloat::_d #1,#2%
- {\expandafter\XINT_pfloat::_e\romannumeral0\XINT_pfloat_opt [\xint_relax #2]{#1},{#2}}%
+ {\expandafter\XINT_pfloat::_e\romannumeral0\XINT_pfloat_opt [\xint:#2]{#1},{#2}}%
\def\XINT_pfloat::_e #1,#2#3{\XINT_pfloat::_b {#2}{#3, #1}}%
% \end{macrocode}
% \subsection{\csh{XINT_expr_getnext}: fetching some number then an operator}
@@ -30311,10 +30911,14 @@
% handing over back control to \XINT_expr_getop. Earlier we had to identify
% the catcode 11 ! signaling a sub-expression here. With no \string applied
% we can do it in \XINT_expr_getop. As a corollary of this displacement,
-% parsing of big numbers should be a tiny bit faster now.|
+% parsing of big numbers should be a tiny bit faster now.
+%
+% Extended for 1.2l to ignore underscore character _ if encountered within
+% digits; so it can serve as separator for better readability.|
% \begin{macrocode}
\def\XINT_expr_scanint_c\string #1\XINT_expr_scanint_d
{%
+ \if _#1\xint_dothis\XINT_expr_scanint_d\fi
\if e#1\xint_dothis{[\the\numexpr0\XINT_expr_scanexp_a +}\fi
\if E#1\xint_dothis{[\the\numexpr0\XINT_expr_scanexp_a +}\fi
\if .#1\xint_dothis{\XINT_expr_startdec_a .}\fi
@@ -30338,6 +30942,7 @@
\def\XINT_expr_gobz_scanint_endbycs#1#2\XINT_expr_scanint_d{0\endcsname #1}%
\def\XINT_expr_gobz_scanint_c\string #1\XINT_expr_scanint_d
{%
+ \if _#1\xint_dothis\XINT_expr_gobz_scanint_d\fi
\if e#1\xint_dothis{0[\the\numexpr0\XINT_expr_scanexp_a +}\fi
\if E#1\xint_dothis{0[\the\numexpr0\XINT_expr_scanexp_a +}\fi
\if .#1\xint_dothis{\XINT_expr_gobz_startdec_a .}\fi
@@ -30382,10 +30987,13 @@
}%
\def\XINT_expr_scandec_c\string #1#2\the\numexpr#3-\xint_c_i.%
{%
+ \if _#1\xint_dothis{\XINT_expr_scandec_d#3.}\fi
\if e#1\xint_dothis{[\the\numexpr#3\XINT_expr_scanexp_a +}\fi
\if E#1\xint_dothis{[\the\numexpr#3\XINT_expr_scanexp_a +}\fi
\xint_orthat {[#3]\endcsname #1}%
}%
+% \end{macrocode}
+% \begin{macrocode}
\def\XINT_expr_gobz_scandec_b #1.#2%
{%
\ifcat \relax #2\expandafter\XINT_expr_gobz_scandec_endbycs\expandafter#2\fi
@@ -30394,9 +31002,12 @@
{\expandafter\XINT_expr_gobz_scandec_b}%
{\string#2\expandafter\XINT_expr_scandec_d}\the\numexpr#1-\xint_c_i.%
}%
+% \end{macrocode}
+% \begin{macrocode}
\def\XINT_expr_gobz_scandec_endbycs #1#2\xint_c_i.{0[0]\endcsname #1}%
-\def\XINT_expr_gobz_scandec_c\if0#1#2\fi #3\xint_c_i.%
+\def\XINT_expr_gobz_scandec_c\if0#1#2\fi #3\numexpr#4-\xint_c_i.%
{%
+ \if _#1\xint_dothis{\XINT_expr_gobz_scandec_b #4.}\fi
\if e#1\xint_dothis{0[\the\numexpr0\XINT_expr_scanexp_a +}\fi
\if E#1\xint_dothis{0[\the\numexpr0\XINT_expr_scanexp_a +}\fi
\xint_orthat {0[0]\endcsname #1}%
@@ -30423,6 +31034,7 @@
}%
\def\XINT_expr_scanexp_c\string #1\XINT_expr_scanexp_d
{%
+ \if _#1\xint_dothis \XINT_expr_scanexp_d \fi
\if +#1\xint_dothis {\XINT_expr_scanexp_a +}\fi
\if -#1\xint_dothis {\XINT_expr_scanexp_a -}\fi
\xint_orthat {]\endcsname #1}%
@@ -30438,7 +31050,11 @@
{%
\expandafter\XINT_expr_scanexp_bb\romannumeral`&&@#1%
}%
-\def\XINT_expr_scanexp_cb\string #1\XINT_expr_scanexp_db {]\endcsname #1}%
+\def\XINT_expr_scanexp_cb\string #1\XINT_expr_scanexp_db
+{%
+ \if _#1\xint_dothis\XINT_expr_scanexp_d\fi
+ \xint_orthat{]\endcsname #1}%
+}%
% \end{macrocode}
% \subsubsection{Hexadecimal numbers}
% \lverb|1.2d has moved most of the handling of tacit multiplication to
@@ -30447,7 +31063,10 @@
% in \XINT_expr_scanhexI_a, because it is its higher precedence variant which
% will is expected, to do the same as when a non-hexadecimal number prefixes a
% sub-expression. Tacit multiplication in front of variable or function names
-% will not work (because of this \string).|
+% will not work (because of this \string).
+%
+% Extended for 1.2l to ignore underscore character _ if encountered within
+% digits.|
% \begin{macrocode}
\def\XINT_expr_scanhex_I #1% #1="
{%
@@ -30469,12 +31088,9 @@
0\else1\fi\else0\fi\else1\fi\else0\fi 1%
\expandafter\XINT_expr_scanhexI_b
\else
- \if .#1%
- \expandafter\xint_firstoftwo
- \else % gather what we got so far, leave catcode 12 #1 in stream
- \expandafter\xint_secondoftwo
- \fi
- {\expandafter\XINT_expr_scanhex_transition}%
+ \if _#1\xint_dothis{\expandafter\XINT_expr_scanhexI_bgob}\fi
+ \if .#1\xint_dothis{\expandafter\XINT_expr_scanhex_transition}\fi
+ \xint_orthat % gather what we got so far, leave catcode 12 #1 in stream
{\xint_afterfi {.>\endcsname\endcsname}}%
\fi
#1%
@@ -30483,6 +31099,10 @@
{%
#1\expandafter\XINT_expr_scanhexI_a\romannumeral`&&@#2%
}%
+\def\XINT_expr_scanhexI_bgob #1#2%
+{%
+ \expandafter\XINT_expr_scanhexI_a\romannumeral`&&@#2%
+}%
\def\XINT_expr_scanhex_transition .#1%
{%
\expandafter.\expandafter.\expandafter
@@ -30503,7 +31123,8 @@
0\else1\fi\else0\fi\else1\fi\else0\fi 1%
\expandafter\XINT_expr_scanhexII_b
\else
- \xint_afterfi {\endcsname\endcsname}%
+ \if _#1\xint_dothis{\expandafter\XINT_expr_scanhexII_bgob}\fi
+ \xint_orthat{\xint_afterfi {\endcsname\endcsname}}%
\fi
#1%
}%
@@ -30511,6 +31132,10 @@
{%
#1\expandafter\XINT_expr_scanhexII_a\romannumeral`&&@#2%
}%
+\def\XINT_expr_scanhexII_bgob #1#2%
+{%
+ \expandafter\XINT_expr_scanhexII_a\romannumeral`&&@#2%
+}%
% \end{macrocode}
% \subsubsection{Parsing names of functions and variables}
% \begin{macrocode}
@@ -31206,8 +31831,7 @@
% by expression parser (as <digits><variable> is allowed by the syntax and does
% tacit multiplication).|
% \begin{macrocode}
-\edef\XINT_expr_op_][: #1{\xint_c_ii \expandafter\noexpand
- \csname XINT_expr_itself_][\endcsname #10\string :}%
+\edef\XINT_expr_op_][: #1{\xint_c_ii\noexpand\XINT_expr_itself_][#10\string :}%
\let\XINT_flexpr_op_][: \XINT_expr_op_][:
\let\XINT_iiexpr_op_][: \XINT_expr_op_][:
\catcode`[ 12 \catcode`] 12
@@ -33659,7 +34283,7 @@
\toks0 \expandafter{\the\toks0
\def\xintListSel:x:csv {~xintListSel:f:csv }%
}%
-\odef\XINT_expr_redefinemacros {\the\toks0}% Not \edef ! (subtle)
+\odef\XINT_expr_redefinemacros {\the\toks0}%
\def\XINT_expr_redefineprints
{%
\def\XINT_flexpr_noopt
@@ -33840,34 +34464,34 @@
%<*dtx>-----------------------------------------------------------
\iffalse
% grep -c -e "^{%" xint*sty
-xint.sty:215
-xintbinhex.sty:69
+xint.sty:196
+xintbinhex.sty:70
xintcfrac.sty:183
-xintcore.sty:273
-xintexpr.sty:165
-xintfrac.sty:428
-xintgcd.sty:59
+xintcore.sty:278
+xintexpr.sty:168
+xintfrac.sty:439
+xintgcd.sty:50
xintkernel.sty:13
xintseries.sty:48
-xinttools.sty:139
+xinttools.sty:138
\fi
% grep -o "^{%" xint*sty | wc -l
-\def\totala{ 1592}
+\def\totala{ 1583}
\iffalse
% grep -c -e "^}%" xint*sty
-xint.sty:214
-xintbinhex.sty:69
+xint.sty:195
+xintbinhex.sty:65
xintcfrac.sty:183
-xintcore.sty:273
-xintexpr.sty:196
-xintfrac.sty:426
-xintgcd.sty:61
+xintcore.sty:275
+xintexpr.sty:199
+xintfrac.sty:437
+xintgcd.sty:52
xintkernel.sty:14
xintseries.sty:48
-xinttools.sty:138
+xinttools.sty:137
\fi
% grep -o "^}%" xint*sty | wc -l
-\def\totalb{ 1622}
+\def\totalb{ 1605}
\DeleteShortVerb{\|}
\def\mymacro #1{\mymacroaux #1}
\def\mymacroaux #1#2{\strut \csname #1nameimp\endcsname:& \dtt{ #2.}\tabularnewline }
@@ -33904,7 +34528,8 @@
Right bracket \] Circumflex \^ Underscore \_
Grave accent \` Left brace \{ Vertical bar \|
Right brace \} Tilde \~}
-\CheckSum {30677}% était 30303 pour 1.2h, 30403 pour 1.2i, 30750 pour 1.2j
+\CheckSum {30931}% 30303 pour 1.2h, 30403 pour 1.2i, 30750 pour 1.2j,
+ % 30677 pour 1.2k
\makeatletter\check at checksum\makeatother
\Finale
%% End of file xint.dtx
Modified: trunk/Master/texmf-dist/source/generic/xint/xint.ins
===================================================================
--- trunk/Master/texmf-dist/source/generic/xint/xint.ins 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/source/generic/xint/xint.ins 2017-07-27 21:26:25 UTC (rev 44900)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.2k 2017/01/06
+%% The xint bundle 1.2l 2017/07/26
%% Copyright (C) 2013-2017 by Jean-Francois Burnol
%% ---------------------------------------------------------------
%%
Modified: trunk/Master/texmf-dist/tex/generic/xint/xint.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xint.sty 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/tex/generic/xint/xint.sty 2017-07-27 21:26:25 UTC (rev 44900)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.2k 2017/01/06
+%% The xint bundle 1.2l 2017/07/26
%% Copyright (C) 2013-2017 by Jean-Francois Burnol
%% xint: Expandable operations on big integers
%% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
\XINTsetupcatcodes% defined in xintkernel.sty (loaded by xintcore.sty)
\XINT_providespackage
\ProvidesPackage{xint}%
- [2017/01/06 1.2k Expandable operations on big integers (JFB)]%
+ [2017/07/26 1.2l Expandable operations on big integers (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}%
@@ -77,10 +77,6 @@
\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}%
-\edef\xint_cleanupzeros_andstop #1#2#3#4%
-{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4\relax
-}%
\def\xintSgnFork {\romannumeral0\xintsgnfork }%
\def\xintsgnfork #1%
{%
@@ -99,13 +95,49 @@
\unless\if#11\xint_dothis{ 0}\fi
\xint_orthat{ 1}%
}%
-\def\XINT_isOne #1{\XINT_is_one#1XY}%
-\def\XINT_is_one #1#2#3Y%
+\def\XINT_isOne #1{\XINT_is_One#1XY}%
+\def\XINT_is_One #1#2#3Y%
{%
\unless\if#2X\xint_dothis0\fi
\unless\if#11\xint_dothis0\fi
\xint_orthat1%
}%
+\def\xintReverseDigits {\romannumeral0\xintreversedigits }%
+\def\xintreversedigits #1%
+{%
+ \expandafter\XINT_revdigits\romannumeral`&&@#1%
+ {\XINT_microrevsep_end\W}\XINT_microrevsep_end
+ \XINT_microrevsep_end\XINT_microrevsep_end
+ \XINT_microrevsep_end\XINT_microrevsep_end
+ \XINT_microrevsep_end\XINT_microrevsep_end\XINT_microrevsep_end\Z
+ 1\Z!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+}%
+\def\XINT_revdigits #1%
+{%
+ \xint_UDsignfork
+ #1{\expandafter-\romannumeral0\XINT_revdigits_a}%
+ -{\XINT_revdigits_a #1}%
+ \krof
+}%
+\def\XINT_revdigits_a
+{%
+ \expandafter\XINT_revdigits_b\expandafter{\expandafter}%
+ \the\numexpr\XINT_microrevsep
+}%
+\def\XINT_microrevsep #1#2#3#4#5#6#7#8#9%
+{%
+ 1#9#8#7#6#5#4#3#2#1\expandafter!\the\numexpr\XINT_microrevsep
+}%
+\def\XINT_microrevsep_end #1\W #2\expandafter #3\Z{\relax#2!}%
+\def\XINT_revdigits_b #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
+{%
+ \xint_gob_til_R #9\XINT_revdigits_end\R
+ \XINT_revdigits_b {#9#8#7#6#5#4#3#2#1}%
+}%
+\def\XINT_revdigits_end#1{%
+\def\XINT_revdigits_end\R\XINT_revdigits_b ##1##2\W
+ {\expandafter#1\xint_gob_til_Z ##1}%
+}\XINT_revdigits_end{ }%
\let\xintRev\xintReverseDigits
\def\xintLen {\romannumeral0\xintlen }%
\def\xintlen #1{\def\xintlen ##1%
@@ -112,8 +144,7 @@
{%
\expandafter#1\the\numexpr
\expandafter\XINT_len_fork\romannumeral0\xintnum{##1}%
- \xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ \xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye\relax
}}\xintlen{ }%
@@ -284,172 +315,6 @@
\expandafter\xint_secondoftwo_thenstop
\fi
}%
-\def\xintCmp {\romannumeral0\xintcmp }%
-\def\xintcmp #1{\expandafter\XINT_icmp\romannumeral0\xintnum{#1}\Z }%
-\def\xintiiCmp {\romannumeral0\xintiicmp }%
-\def\xintiicmp #1{\expandafter\XINT_iicmp\romannumeral`&&@#1\Z }%
-\def\XINT_iicmp #1#2\Z #3%
-{%
- \expandafter\XINT_cmp_nfork\expandafter #1\romannumeral`&&@#3\Z #2\Z
-}%
-\let\XINT_Cmp \xintiiCmp
-\def\XINT_icmp #1#2\Z #3%
-{%
- \expandafter\XINT_cmp_nfork\expandafter #1\romannumeral0\xintnum{#3}\Z #2\Z
-}%
-\def\XINT_cmp_nfork #1#2%
-{%
- \xint_UDzerofork
- #1\XINT_cmp_firstiszero
- #2\XINT_cmp_secondiszero
- 0{}%
- \krof
- \xint_UDsignsfork
- #1#2\XINT_cmp_minusminus
- #1-\XINT_cmp_minusplus
- #2-\XINT_cmp_plusminus
- --\XINT_cmp_plusplus
- \krof #1#2%
-}%
-\def\XINT_cmp_firstiszero #1\krof 0#2#3\Z #4\Z
-{%
- \xint_UDzerominusfork
- #2-{ 0}%
- 0#2{ 1}%
- 0-{ -1}%
- \krof
-}%
-\def\XINT_cmp_secondiszero #1\krof #20#3\Z #4\Z
-{%
- \xint_UDzerominusfork
- #2-{ 0}%
- 0#2{ -1}%
- 0-{ 1}%
- \krof
-}%
-\def\XINT_cmp_plusminus #1\Z #2\Z{ 1}%
-\def\XINT_cmp_minusplus #1\Z #2\Z{ -1}%
-\def\XINT_cmp_minusminus
- --{\expandafter\XINT_opp\romannumeral0\XINT_cmp_plusplus {}{}}%
-\def\XINT_cmp_plusplus #1#2#3\Z
-{%
- \expandafter\XINT_cmp_pp
- \romannumeral0\expandafter\XINT_sepandrev_andcount
- \romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
- #2#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
- \X #1%
-}%
-\def\XINT_cmp_pp #1.#2\X #3\Z
-{%
- \expandafter\XINT_cmp_checklengths
- \the\numexpr #1\expandafter.%
- \romannumeral0\expandafter\XINT_sepandrev_andcount
- \romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
- #3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax \xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
- \Z!\Z!\Z!\Z!\Z!\W #2\Z!\Z!\Z!\Z!\Z!\W
-}%
-\def\XINT_cmp_checklengths #1.#2.%
-{%
- \ifnum #1=#2
- \expandafter\xint_firstoftwo
- \else
- \expandafter\xint_secondoftwo
- \fi
- \XINT_cmp_aa {\XINT_cmp_distinctlengths {#1}{#2}}%
-}%
-\def\XINT_cmp_distinctlengths #1#2#3\W #4\W
-{%
- \ifnum #1>#2
- \expandafter\xint_firstoftwo
- \else
- \expandafter\xint_secondoftwo
- \fi
- { -1}{ 1}%
-}%
-\def\XINT_cmp_aa {\expandafter\XINT_cmp_w\the\numexpr\XINT_cmp_a \xint_c_i }%
-\def\XINT_cmp_a #1!#2!#3!#4!#5\W #6!#7!#8!#9!%
-{%
- \XINT_cmp_b #1!#6!#2!#7!#3!#8!#4!#9!#5\W
-}%
-\def\XINT_cmp_b #1#2#3!#4!%
-{%
- \xint_gob_til_Z #2\XINT_cmp_bi \Z
- \expandafter\XINT_cmp_c\the\numexpr#1+1#4-#3-\xint_c_i.%
-}%
-\def\XINT_cmp_c 1#1#2.%
-{%
- 1#2\expandafter!\the\numexpr\XINT_cmp_d #1%
-}%
-\def\XINT_cmp_d #1#2#3!#4!%
-{%
- \xint_gob_til_Z #2\XINT_cmp_di \Z
- \expandafter\XINT_cmp_e\the\numexpr#1+1#4-#3-\xint_c_i.%
-}%
-\def\XINT_cmp_e 1#1#2.%
-{%
- 1#2\expandafter!\the\numexpr\XINT_cmp_f #1%
-}%
-\def\XINT_cmp_f #1#2#3!#4!%
-{%
- \xint_gob_til_Z #2\XINT_cmp_fi \Z
- \expandafter\XINT_cmp_g\the\numexpr#1+1#4-#3-\xint_c_i.%
-}%
-\def\XINT_cmp_g 1#1#2.%
-{%
- 1#2\expandafter!\the\numexpr\XINT_cmp_h #1%
-}%
-\def\XINT_cmp_h #1#2#3!#4!%
-{%
- \xint_gob_til_Z #2\XINT_cmp_hi \Z
- \expandafter\XINT_cmp_i\the\numexpr#1+1#4-#3-\xint_c_i.%
-}%
-\def\XINT_cmp_i 1#1#2.%
-{%
- 1#2\expandafter!\the\numexpr\XINT_cmp_a #1%
-}%
-\def\XINT_cmp_bi\Z
- \expandafter\XINT_cmp_c\the\numexpr#1+1#2-#3.#4!#5!#6!#7!#8!#9!\Z !\W
-{%
- \XINT_cmp_k #1#2!#5!#7!#9!%
-}%
-\def\XINT_cmp_di\Z
- \expandafter\XINT_cmp_e\the\numexpr#1+1#2-#3.#4!#5!#6!#7!#8\W
-{%
- \XINT_cmp_k #1#2!#5!#7!%
-}%
-\def\XINT_cmp_fi\Z
- \expandafter\XINT_cmp_g\the\numexpr#1+1#2-#3.#4!#5!#6\W
-{%
- \XINT_cmp_k #1#2!#5!%
-}%
-\def\XINT_cmp_hi\Z
- \expandafter\XINT_cmp_i\the\numexpr#1+1#2-#3.#4\W
-{%
- \XINT_cmp_k #1#2!%
-}%
-\def\XINT_cmp_k #1#2\W
-{%
- \xint_UDzerofork
- #1{-1\relax \XINT_cmp_greater}%
- 0{-1\relax \XINT_cmp_lessorequal}%
- \krof
-}%
-\def\XINT_cmp_w #1-1#2{#2#11\Z!\W}%
-\def\XINT_cmp_greater #1\Z!\W{ 1}%
-\def\XINT_cmp_lessorequal 1#1!%
- {\xint_gob_til_Z #1\XINT_cmp_equal\Z
- \xint_gob_til_eightzeroes #1\XINT_cmp_continue 00000000%
- \XINT_cmp_less }%
-\def\XINT_cmp_less #1\W { -1}%
-\def\XINT_cmp_continue 00000000\XINT_cmp_less {\XINT_cmp_lessorequal }%
-\def\XINT_cmp_equal\Z\xint_gob_til_eightzeroes\Z\XINT_cmp_continue
- 00000000\XINT_cmp_less\W { 0}%
\def\xintEq {\romannumeral0\xinteq }\def\xinteq #1#2{\xintifeq{#1}{#2}{1}{0}}%
\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}}%
@@ -487,48 +352,48 @@
\def\xintxor #1#2{\if\xintIsZero{#1}\xintIsZero{#2}%
\xint_afterfi{ 0}\else\xint_afterfi{ 1}\fi }%
\def\xintANDof {\romannumeral0\xintandof }%
-\def\xintandof #1{\expandafter\XINT_andof_a\romannumeral`&&@#1\relax }%
-\def\XINT_andof_a #1{\expandafter\XINT_andof_b\romannumeral`&&@#1\Z }%
+\def\xintandof #1{\expandafter\XINT_andof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_andof_a #1{\expandafter\XINT_andof_b\romannumeral`&&@#1!}%
\def\XINT_andof_b #1%
- {\xint_gob_til_relax #1\XINT_andof_e\relax\XINT_andof_c #1}%
-\def\XINT_andof_c #1\Z
+ {\xint_gob_til_xint: #1\XINT_andof_e\xint:\XINT_andof_c #1}%
+\def\XINT_andof_c #1!%
{\xintifTrueAelseB {#1}{\XINT_andof_a}{\XINT_andof_no}}%
-\def\XINT_andof_no #1\relax { 0}%
-\def\XINT_andof_e #1\Z { 1}%
+\def\XINT_andof_no #1\xint:{ 0}%
+\def\XINT_andof_e #1!{ 1}%
\def\xintORof {\romannumeral0\xintorof }%
-\def\xintorof #1{\expandafter\XINT_orof_a\romannumeral`&&@#1\relax }%
-\def\XINT_orof_a #1{\expandafter\XINT_orof_b\romannumeral`&&@#1\Z }%
+\def\xintorof #1{\expandafter\XINT_orof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_orof_a #1{\expandafter\XINT_orof_b\romannumeral`&&@#1!}%
\def\XINT_orof_b #1%
- {\xint_gob_til_relax #1\XINT_orof_e\relax\XINT_orof_c #1}%
-\def\XINT_orof_c #1\Z
+ {\xint_gob_til_xint: #1\XINT_orof_e\xint:\XINT_orof_c #1}%
+\def\XINT_orof_c #1!%
{\xintifTrueAelseB {#1}{\XINT_orof_yes}{\XINT_orof_a}}%
-\def\XINT_orof_yes #1\relax { 1}%
-\def\XINT_orof_e #1\Z { 0}%
+\def\XINT_orof_yes #1\xint:{ 1}%
+\def\XINT_orof_e #1!{ 0}%
\def\xintXORof {\romannumeral0\xintxorof }%
\def\xintxorof #1{\expandafter\XINT_xorof_a\expandafter
- 0\romannumeral`&&@#1\relax }%
-\def\XINT_xorof_a #1#2{\expandafter\XINT_xorof_b\romannumeral`&&@#2\Z #1}%
+ 0\romannumeral`&&@#1\xint:}%
+\def\XINT_xorof_a #1#2{\expandafter\XINT_xorof_b\romannumeral`&&@#2!#1}%
\def\XINT_xorof_b #1%
- {\xint_gob_til_relax #1\XINT_xorof_e\relax\XINT_xorof_c #1}%
-\def\XINT_xorof_c #1\Z #2%
+ {\xint_gob_til_xint: #1\XINT_xorof_e\xint:\XINT_xorof_c #1}%
+\def\XINT_xorof_c #1!#2%
{\xintifTrueAelseB {#1}{\if #20\xint_afterfi{\XINT_xorof_a 1}%
\else\xint_afterfi{\XINT_xorof_a 0}\fi}%
{\XINT_xorof_a #2}%
}%
-\def\XINT_xorof_e #1\Z #2{ #2}%
+\def\XINT_xorof_e #1!#2{ #2}%
\def\xintGeq {\romannumeral0\xintgeq }%
-\def\xintgeq #1{\expandafter\XINT_geq\romannumeral0\xintnum{#1}\Z }%
+\def\xintgeq #1{\expandafter\XINT_geq\romannumeral0\xintnum{#1}\xint:}%
\def\xintiiGeq {\romannumeral0\xintiigeq }%
-\def\xintiigeq #1{\expandafter\XINT_iigeq\romannumeral`&&@#1\Z }%
-\def\XINT_iigeq #1#2\Z #3%
+\def\xintiigeq #1{\expandafter\XINT_iigeq\romannumeral`&&@#1\xint:}%
+\def\XINT_iigeq #1#2\xint:#3%
{%
- \expandafter\XINT_geq_fork\expandafter #1\romannumeral`&&@#3\Z #2\Z
+ \expandafter\XINT_geq_fork\expandafter #1\romannumeral`&&@#3\xint:#2\xint:
}%
\let\XINT_geq_pre \xintiigeq % TEMPORAIRE (oui, mais depuis quand ?)
\let\XINT_Geq \xintGeq % TEMPORAIRE ATTENTION FAIT xintNum (et alors?)
-\def\XINT_geq #1#2\Z #3%
+\def\XINT_geq #1#2\xint:#3%
{%
- \expandafter\XINT_geq_fork\expandafter #1\romannumeral0\xintnum{#3}\Z #2\Z
+ \expandafter\XINT_geq_fork\expandafter #1\romannumeral0\xintnum{#3}\xint:#2\xint:
}%
\def\XINT_geq_fork #1#2%
{%
@@ -544,37 +409,37 @@
--\XINT_geq_plusplus
\krof #1#2%
}%
-\def\XINT_geq_firstiszero #1\krof 0#2#3\Z #4\Z
+\def\XINT_geq_firstiszero #1\krof 0#2#3\xint:#4\xint:
{\xint_UDzerofork #2{ 1}0{ 0}\krof }%
-\def\XINT_geq_secondiszero #1\krof #20#3\Z #4\Z { 1}%
+\def\XINT_geq_secondiszero #1\krof #20#3\xint:#4\xint:{ 1}%
\def\XINT_geq_plusminus #1-{\XINT_geq_plusplus #1{}}%
\def\XINT_geq_minusplus -#1{\XINT_geq_plusplus {}#1}%
\def\XINT_geq_minusminus --{\XINT_geq_plusplus {}{}}%
-\def\XINT_geq_plusplus #1#2#3\Z #4\Z {\XINT_geq_pp #1#4\Z #2#3\Z }%
-\def\XINT_geq_pp #1\Z
+\def\XINT_geq_plusplus #1#2#3\xint:#4\xint:{\XINT_geq_pp #1#4\xint:#2#3\xint:}%
+\def\XINT_geq_pp #1\xint:
{%
\expandafter\XINT_geq_pp_a
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #1\R\R\R\R\R\R\R\R{10}0000001\W
#1\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\X
}%
-\def\XINT_geq_pp_a #1.#2\X #3\Z
+\def\XINT_geq_pp_a #1\xint:#2\X #3\xint:
{%
\expandafter\XINT_geq_checklengths
- \the\numexpr #1\expandafter.%
+ \the\numexpr #1\expandafter\xint:%
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax \xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\Z!\Z!\Z!\Z!\Z!\W #2\Z!\Z!\Z!\Z!\Z!\W
}%
-\def\XINT_geq_checklengths #1.#2.%
+\def\XINT_geq_checklengths #1\xint:#2\xint:
{%
\ifnum #1=#2
\expandafter\xint_firstoftwo
@@ -600,9 +465,9 @@
\def\XINT_geq_b #1#2#3!#4!%
{%
\xint_gob_til_Z #2\XINT_geq_bi \Z
- \expandafter\XINT_geq_c\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \expandafter\XINT_geq_c\the\numexpr#1+1#4-#3-\xint_c_i\xint:%
}%
-\def\XINT_geq_c 1#1#2.%
+\def\XINT_geq_c 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_geq_d #1%
}%
@@ -609,9 +474,9 @@
\def\XINT_geq_d #1#2#3!#4!%
{%
\xint_gob_til_Z #2\XINT_geq_di \Z
- \expandafter\XINT_geq_e\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \expandafter\XINT_geq_e\the\numexpr#1+1#4-#3-\xint_c_i\xint:%
}%
-\def\XINT_geq_e 1#1#2.%
+\def\XINT_geq_e 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_geq_f #1%
}%
@@ -618,9 +483,9 @@
\def\XINT_geq_f #1#2#3!#4!%
{%
\xint_gob_til_Z #2\XINT_geq_fi \Z
- \expandafter\XINT_geq_g\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \expandafter\XINT_geq_g\the\numexpr#1+1#4-#3-\xint_c_i\xint:%
}%
-\def\XINT_geq_g 1#1#2.%
+\def\XINT_geq_g 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_geq_h #1%
}%
@@ -627,29 +492,29 @@
\def\XINT_geq_h #1#2#3!#4!%
{%
\xint_gob_til_Z #2\XINT_geq_hi \Z
- \expandafter\XINT_geq_i\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \expandafter\XINT_geq_i\the\numexpr#1+1#4-#3-\xint_c_i\xint:%
}%
-\def\XINT_geq_i 1#1#2.%
+\def\XINT_geq_i 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_geq_a #1%
}%
\def\XINT_geq_bi\Z
- \expandafter\XINT_geq_c\the\numexpr#1+1#2-#3.#4!#5!#6!#7!#8!#9!\Z !\W
+ \expandafter\XINT_geq_c\the\numexpr#1+1#2-#3\xint:#4!#5!#6!#7!#8!#9!\Z !\W
{%
\XINT_geq_k #1#2!#5!#7!#9!%
}%
\def\XINT_geq_di\Z
- \expandafter\XINT_geq_e\the\numexpr#1+1#2-#3.#4!#5!#6!#7!#8\W
+ \expandafter\XINT_geq_e\the\numexpr#1+1#2-#3\xint:#4!#5!#6!#7!#8\W
{%
\XINT_geq_k #1#2!#5!#7!%
}%
\def\XINT_geq_fi\Z
- \expandafter\XINT_geq_g\the\numexpr#1+1#2-#3.#4!#5!#6\W
+ \expandafter\XINT_geq_g\the\numexpr#1+1#2-#3\xint:#4!#5!#6\W
{%
\XINT_geq_k #1#2!#5!%
}%
\def\XINT_geq_hi\Z
- \expandafter\XINT_geq_i\the\numexpr#1+1#2-#3.#4\W
+ \expandafter\XINT_geq_i\the\numexpr#1+1#2-#3\xint:#4\W
{%
\XINT_geq_k #1#2!%
}%
@@ -718,25 +583,26 @@
\fi
}%
\def\xintiMaxof {\romannumeral0\xintimaxof }%
-\def\xintimaxof #1{\expandafter\XINT_imaxof_a\romannumeral`&&@#1\relax }%
-\def\XINT_imaxof_a #1{\expandafter\XINT_imaxof_b\romannumeral0\xintnum{#1}\Z }%
-\def\XINT_imaxof_b #1\Z #2%
- {\expandafter\XINT_imaxof_c\romannumeral`&&@#2\Z {#1}\Z}%
+\def\xintimaxof #1{\expandafter\XINT_imaxof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_imaxof_a
+#1{\expandafter\XINT_imaxof_b\romannumeral0\xintnum{#1}!}%
+\def\XINT_imaxof_b #1!#2%
+ {\expandafter\XINT_imaxof_c\romannumeral`&&@#2!{#1}!}%
\def\XINT_imaxof_c #1%
- {\xint_gob_til_relax #1\XINT_imaxof_e\relax\XINT_imaxof_d #1}%
-\def\XINT_imaxof_d #1\Z
+ {\xint_gob_til_xint: #1\XINT_imaxof_e\xint:\XINT_imaxof_d #1}%
+\def\XINT_imaxof_d #1!%
{\expandafter\XINT_imaxof_b\romannumeral0\xintimax {#1}}%
-\def\XINT_imaxof_e #1\Z #2\Z { #2}%
+\def\XINT_imaxof_e #1!#2!{ #2}%
\def\xintiiMaxof {\romannumeral0\xintiimaxof }%
-\def\xintiimaxof #1{\expandafter\XINT_iimaxof_a\romannumeral`&&@#1\relax }%
-\def\XINT_iimaxof_a #1{\expandafter\XINT_iimaxof_b\romannumeral`&&@#1\Z }%
-\def\XINT_iimaxof_b #1\Z #2%
- {\expandafter\XINT_iimaxof_c\romannumeral`&&@#2\Z {#1}\Z}%
+\def\xintiimaxof #1{\expandafter\XINT_iimaxof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_iimaxof_a #1{\expandafter\XINT_iimaxof_b\romannumeral`&&@#1!}%
+\def\XINT_iimaxof_b #1!#2%
+ {\expandafter\XINT_iimaxof_c\romannumeral`&&@#2!{#1}!}%
\def\XINT_iimaxof_c #1%
- {\xint_gob_til_relax #1\XINT_iimaxof_e\relax\XINT_iimaxof_d #1}%
-\def\XINT_iimaxof_d #1\Z
+ {\xint_gob_til_xint: #1\XINT_iimaxof_e\xint:\XINT_iimaxof_d #1}%
+\def\XINT_iimaxof_d #1!%
{\expandafter\XINT_iimaxof_b\romannumeral0\xintiimax {#1}}%
-\def\XINT_iimaxof_e #1\Z #2\Z { #2}%
+\def\XINT_iimaxof_e #1!#2!{ #2}%
\def\xintiMin {\romannumeral0\xintimin }%
\def\xintimin #1%
{%
@@ -794,49 +660,45 @@
\fi
}%
\def\xintiMinof {\romannumeral0\xintiminof }%
-\def\xintiminof #1{\expandafter\XINT_iminof_a\romannumeral`&&@#1\relax }%
-\def\XINT_iminof_a #1{\expandafter\XINT_iminof_b\romannumeral0\xintnum{#1}\Z }%
-\def\XINT_iminof_b #1\Z #2%
- {\expandafter\XINT_iminof_c\romannumeral`&&@#2\Z {#1}\Z}%
+\def\xintiminof #1{\expandafter\XINT_iminof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_iminof_a #1{\expandafter\XINT_iminof_b\romannumeral0\xintnum{#1}!}%
+\def\XINT_iminof_b #1!#2%
+ {\expandafter\XINT_iminof_c\romannumeral`&&@#2!{#1}!}%
\def\XINT_iminof_c #1%
- {\xint_gob_til_relax #1\XINT_iminof_e\relax\XINT_iminof_d #1}%
-\def\XINT_iminof_d #1\Z
+ {\xint_gob_til_xint: #1\XINT_iminof_e\xint:\XINT_iminof_d #1}%
+\def\XINT_iminof_d #1!%
{\expandafter\XINT_iminof_b\romannumeral0\xintimin {#1}}%
-\def\XINT_iminof_e #1\Z #2\Z { #2}%
+\def\XINT_iminof_e #1!#2!{ #2}%
\def\xintiiMinof {\romannumeral0\xintiiminof }%
-\def\xintiiminof #1{\expandafter\XINT_iiminof_a\romannumeral`&&@#1\relax }%
-\def\XINT_iiminof_a #1{\expandafter\XINT_iiminof_b\romannumeral`&&@#1\Z }%
-\def\XINT_iiminof_b #1\Z #2%
- {\expandafter\XINT_iiminof_c\romannumeral`&&@#2\Z {#1}\Z}%
+\def\xintiiminof #1{\expandafter\XINT_iiminof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_iiminof_a #1{\expandafter\XINT_iiminof_b\romannumeral`&&@#1!}%
+\def\XINT_iiminof_b #1!#2%
+ {\expandafter\XINT_iiminof_c\romannumeral`&&@#2!{#1}!}%
\def\XINT_iiminof_c #1%
- {\xint_gob_til_relax #1\XINT_iiminof_e\relax\XINT_iiminof_d #1}%
-\def\XINT_iiminof_d #1\Z
+ {\xint_gob_til_xint: #1\XINT_iiminof_e\xint:\XINT_iiminof_d #1}%
+\def\XINT_iiminof_d #1!%
{\expandafter\XINT_iiminof_b\romannumeral0\xintiimin {#1}}%
-\def\XINT_iiminof_e #1\Z #2\Z { #2}%
+\def\XINT_iiminof_e #1!#2!{ #2}%
\def\xintiiSum {\romannumeral0\xintiisum }%
-\def\xintiisum #1{\xintiisumexpr #1\relax }%
-\def\xintiiSumExpr {\romannumeral0\xintiisumexpr }%
-\def\xintiisumexpr {\expandafter\XINT_sumexpr\romannumeral`&&@}%
+\def\xintiisum #1{\expandafter\XINT_sumexpr\romannumeral`&&@#1\xint:}%
\def\XINT_sumexpr {\XINT_sum_loop_a 0\Z }%
\def\XINT_sum_loop_a #1\Z #2%
- {\expandafter\XINT_sum_loop_b \romannumeral`&&@#2\Z #1\Z \Z}%
+ {\expandafter\XINT_sum_loop_b \romannumeral`&&@#2\xint:#1\xint:\Z}%
\def\XINT_sum_loop_b #1%
- {\xint_gob_til_relax #1\XINT_sum_finished\relax\XINT_sum_loop_c #1}%
+ {\xint_gob_til_xint: #1\XINT_sum_finished\xint:\XINT_sum_loop_c #1}%
\def\XINT_sum_loop_c
{\expandafter\XINT_sum_loop_a\romannumeral0\XINT_add_fork }%
-\def\XINT_sum_finished #1\Z #2\Z \Z { #2}%
+\def\XINT_sum_finished\xint:\XINT_sum_loop_c\xint:\xint:#1\xint:\Z{ #1}%
\def\xintiiPrd {\romannumeral0\xintiiprd }%
-\def\xintiiprd #1{\xintiiprdexpr #1\relax }%
-\def\xintiiPrdExpr {\romannumeral0\xintiiprdexpr }%
-\def\xintiiprdexpr {\expandafter\XINT_prdexpr\romannumeral`&&@}%
+\def\xintiiprd #1{\expandafter\XINT_prdexpr\romannumeral`&&@#1\xint:}%
\def\XINT_prdexpr {\XINT_prod_loop_a 1\Z }%
\def\XINT_prod_loop_a #1\Z #2%
- {\expandafter\XINT_prod_loop_b \romannumeral`&&@#2\Z #1\Z \Z}%
+ {\expandafter\XINT_prod_loop_b\romannumeral`&&@#2\xint:#1\xint:\Z}%
\def\XINT_prod_loop_b #1%
- {\xint_gob_til_relax #1\XINT_prod_finished\relax\XINT_prod_loop_c #1}%
+ {\xint_gob_til_xint: #1\XINT_prod_finished\xint:\XINT_prod_loop_c #1}%
\def\XINT_prod_loop_c
{\expandafter\XINT_prod_loop_a\romannumeral0\XINT_mul_fork }%
-\def\XINT_prod_finished\relax\XINT_prod_loop_c #1\Z #2\Z \Z { #2}%
+\def\XINT_prod_finished\xint:\XINT_prod_loop_c\xint:\xint:#1\xint:\Z { #1}%
\def\xintiiMON {\romannumeral0\xintiimon }%
\def\xintiimon #1%
{%
@@ -1089,8 +951,7 @@
{%
\expandafter\XINT_split_fromright_a
\the\numexpr#1-\numexpr\XINT_length_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
.#2\xint_bye
@@ -1117,19 +978,20 @@
\def\XINT_sqrtr_post #1#2{\xintiiifLt {#2}{#1}%
{ #1}{\XINT_dec #1\XINT_dec_bye234567890\xint_bye}}%
\def\xintisquareroot #1%
- {\expandafter\XINT_sqrt_checkin\romannumeral0\xintnum{#1}\xint_relax }%
-\def\xintiisquareroot #1{\expandafter\XINT_sqrt_checkin\romannumeral`&&@#1\xint_relax }%
+ {\expandafter\XINT_sqrt_checkin\romannumeral0\xintnum{#1}\xint:}%
+\def\xintiisquareroot #1{\expandafter\XINT_sqrt_checkin\romannumeral`&&@#1\xint:}%
\def\XINT_sqrt_checkin #1%
{%
\xint_UDzerominusfork
#1-\XINT_sqrt_iszero
0#1\XINT_sqrt_isneg
- 0-{\XINT_sqrt #1}%
- \krof
+ 0-\XINT_sqrt
+ \krof #1%
}%
-\def\XINT_sqrt_iszero #1\xint_relax {{1}{1}}%
-\def\XINT_sqrt_isneg #1\xint_relax {\xintError:RootOfNegative{1}{1}}%
-\def\XINT_sqrt #1\xint_relax
+\def\XINT_sqrt_iszero #1\xint:{{1}{1}}%
+\def\XINT_sqrt_isneg #1\xint:{\XINT_signalcondition{InvalidOperation}{square
+ root of negative: #1}{}{{0}{0}}}%
+\def\XINT_sqrt #1\xint:
{%
\expandafter\XINT_sqrt_start\romannumeral0\xintlength {#1}.#1.%
}%
@@ -1383,7 +1245,7 @@
}%
\def\XINT_sqrt_big_ke #1%
{%
- \if0\XINT_Sgn #1\Z
+ \if0\XINT_Sgn #1\xint:
\expandafter \XINT_sqrt_big_end
\else \expandafter \XINT_sqrt_big_kf
\fi {#1}%
@@ -1412,18 +1274,21 @@
\let\xintibinomial\xintiibinomial
\def\XINT_binom_fork #1#2.#3#4.#5#6.%
{%
- \if-#5\xint_dothis{\xintError:OutOfRangeBinomial\space 0}\fi
+ \if-#5\xint_dothis{\XINT_signalcondition{InvalidOperation}{Binomial with
+ negative first arg: #5#6}{}{0}}\fi
\if-#1\xint_dothis{ 0}\fi
\if-#3\xint_dothis{ 0}\fi
\if0#1\xint_dothis{ 1}\fi
\if0#3\xint_dothis{ 1}\fi
- \ifnum #5#6>\xint_c_x^viii_mone\xint_dothis{\xintError:OutOfRangeBinomial\space 0}\fi
+ \ifnum #5#6>\xint_c_x^viii_mone\xint_dothis
+ {\XINT_signalcondition{InvalidOperation}{Binomial with too
+ large argument: 99999999 < #5#6}{}{0}}\fi
\ifnum #1#2>#3#4 \xint_dothis{\XINT_binom_a #1#2.#3#4.}\fi
\xint_orthat{\XINT_binom_a #3#4.#1#2.}%
}%
\def\XINT_binom_a #1.#2.%
{%
- \expandafter\XINT_binom_b\the\numexpr \xint_c_i+#1.1.#2.100000001!1!\Z!0!%
+ \expandafter\XINT_binom_b\the\numexpr \xint_c_i+#1.1.#2.100000001!1!;!0!%
}%
\def\XINT_binom_b #1.%
{%
@@ -1549,20 +1414,20 @@
\the\numexpr #2*(#2+\xint_c_i)*(#2+\xint_c_ii)*(#2+\xint_c_iii)\expandafter
!\the\numexpr #1*(#1+\xint_c_i)*(#1+\xint_c_ii)*(#1+\xint_c_iii)!%
}%
-\def\XINT_binom_mul #1!#21!\Z!0!%
+\def\XINT_binom_mul #1!#21!;!0!%
{%
\expandafter\XINT_rev_nounsep\expandafter{\expandafter}%
\the\numexpr\expandafter\XINT_smallmul
\the\numexpr\xint_c_x^viii+#1\expandafter
- !\romannumeral0\XINT_rev_nounsep {}1\Z!#2%
+ !\romannumeral0\XINT_rev_nounsep {}1;!#2%
\R!\R!\R!\R!\R!\R!\R!\R!\W
\R!\R!\R!\R!\R!\R!\R!\R!\W
- 1\Z!%
+ 1;!%
}%
-\def\XINT_binom_div #1!1\Z!%
+\def\XINT_binom_div #1!1;!%
{%
\expandafter\XINT_smalldivx_a
- \the\numexpr #1/\xint_c_ii\expandafter.%
+ \the\numexpr #1/\xint_c_ii\expandafter\xint:
\the\numexpr \xint_c_x^viii+#1!%
}%
\def\XINT_binom_vsmallmuldiv #1!#2!1#3!{\xint_c_x^viii+#2*#3/#1!}%
@@ -1596,8 +1461,8 @@
\the\numexpr\expandafter\XINT_binom_div\the\numexpr #2\expandafter
!\romannumeral0\XINT_binom_mul #1!%
}%
-\def\XINT_binom_finish #1\Z!0!%
- {\XINT_unsep_cuzsmall #11\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W }%
+\def\XINT_binom_finish #1;!0!%
+ {\XINT_unsep_cuzsmall #1\xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax}%
\def\XINT_binom_vsmallend_iii #1.%
{%
\ifnum #1>26 \expandafter\XINT_binom_end_iii \else
@@ -1644,8 +1509,9 @@
\expandafter\XINT_binom_vsmallfinish
\the\numexpr\XINT_binom_vsmallmuldiv #2!#1!%
}%
-\edef\XINT_binom_vsmallfinish 1#1!1!\Z!0!%
- {\noexpand\expandafter\space\noexpand\the\numexpr #1\relax}%
+\def\XINT_binom_vsmallfinish#1{%
+\def\XINT_binom_vsmallfinish1##1!1!;!0!{\expandafter#1\the\numexpr##1\relax}%
+}\XINT_binom_vsmallfinish{ }%
\def\xintiiPFactorial {\romannumeral0\xintiipfactorial }%
\def\xintiipfactorial #1#2%
{%
@@ -1661,7 +1527,9 @@
\ifnum #3#4>\xint_c_x^viii_mone\xint_dothis\XINT_pfac_outofrange\fi
\xint_orthat \XINT_pfac_a #1#2.#3#4.%
}%
-\def\XINT_pfac_outofrange #1.#2.{\xintError:OutOfRangePFac\space 0}%
+\def\XINT_pfac_outofrange #1.#2.%
+ {\XINT_signalcondition{InvalidOperation}{PFactorial with
+ too big second arg: 99999999 < #2}{}{0}}%
\def\XINT_pfac_one #1.#2.{ 1}%
\def\XINT_pfac_zero #1.#2.{ 0}%
\def\XINT_pfac_neg -#1.-#2.%
@@ -1674,7 +1542,7 @@
}%
\def\XINT_pfac_a #1.#2.%
{%
- \expandafter\XINT_pfac_b\the\numexpr \xint_c_i+#1.#2.100000001!1\Z!%
+ \expandafter\XINT_pfac_b\the\numexpr \xint_c_i+#1.#2.100000001!1;!%
1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
}%
\def\XINT_pfac_b #1.%
@@ -1807,8 +1675,7 @@
\def\xintMinof {\Did_you_mean_iMinof?or_load_xintfrac!}%
\def\xintSum {\Did_you_mean_iiSum?or_load_xintfrac!}%
\def\xintPrd {\Did_you_mean_iiPrd?or_load_xintfrac!}%
-\def\xintPrdExpr {\Did_you_mean_iiPrdExpr?or_load_xintfrac!}%
-\def\xintSumExpr {\Did_you_mean_iiSumExpr?or_load_xintfrac!}%
+\catcode`! 12
\XINT_restorecatcodes_endinput%
\endinput
%%
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintbinhex.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintbinhex.sty 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintbinhex.sty 2017-07-27 21:26:25 UTC (rev 44900)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.2k 2017/01/06
+%% The xint bundle 1.2l 2017/07/26
%% Copyright (C) 2013-2017 by Jean-Francois Burnol
%% xintbinhex: Expandable binary and hexadecimal conversions
%% ---------------------------------------------------------------
@@ -70,7 +70,12 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintbinhex}%
- [2017/01/06 1.2k Expandable binary and hexadecimal conversions (JFB)]%
+ [2017/07/26 1.2l Expandable binary and hexadecimal conversions (JFB)]%
+\def\xint_cleanupzeros_andstop#1{%
+\def\xint_cleanupzeros_andstop ##1##2##3##4%
+{%
+ \expandafter#1\the\numexpr ##1##2##3##4\relax
+}}\xint_cleanupzeros_andstop{ }%
\newcount\xint_c_ii^xv \xint_c_ii^xv 32768
\newcount\xint_c_ii^xvi \xint_c_ii^xvi 65536
\newcount\xint_c_x^v \xint_c_x^v 100000
@@ -340,10 +345,11 @@
{%
\expandafter\XINT_dtb_end_d\the\numexpr #1#2#3#4#5#6#7#8\relax
}%
-\edef\XINT_dtb_end_d #1#2#3#4#5#6#7#8#9%
+\def\XINT_dtb_end_d#1{%
+\def\XINT_dtb_end_d ##1##2##3##4##5##6##7##8##9%
{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4#5#6#7#8#9\relax
-}%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8##9\relax
+}}\XINT_dtb_end_d{ }%
\def\xintHexToDec {\romannumeral0\xinthextodec }%
\def\xinthextodec #1%
{\expandafter\XINT_htd_checkin\romannumeral`&&@#1\W\W\W\W \T }%
@@ -375,10 +381,10 @@
{%
\expandafter\xint_cleanupzeros_andstop
\romannumeral0\XINT_rord_main {}#1%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax
+ \xint:
}%
\def\XINT_htd_II_ci #1\XINT_htd_II_ciii
#2\W\W\W {\XINT_htd_II_d {}{"#2}{\xint_c_xvi}}%
@@ -423,10 +429,11 @@
{%
\XINT_htd_II_end_b #1#3%
}%
-\edef\XINT_htd_II_end_b #1#2#3#4#5#6#7#8%
+\def\XINT_htd_II_end_b#1{%
+\def\XINT_htd_II_end_b ##1##2##3##4##5##6##7##8%
{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4#5#6#7#8\relax
-}%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8\relax
+}}\XINT_htd_II_end_b{ }%
\def\xintBinToDec {\romannumeral0\xintbintodec }%
\def\xintbintodec #1{\expandafter\XINT_btd_checkin
\romannumeral`&&@#1\W\W\W\W\W\W\W\W \T }%
@@ -462,15 +469,16 @@
{%
\expandafter\XINT_btd_II_c_end
\romannumeral0\XINT_rord_main {}#2%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax
+ \xint:
}%
-\edef\XINT_btd_II_c_end #1#2#3#4#5#6%
+\def\XINT_btd_II_c_end#1{%
+\def\XINT_btd_II_c_end ##1##2##3##4##5##6%
{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4#5#6\relax
-}%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6\relax
+}}\XINT_btd_II_c_end{ }%
\def\XINT_btd_II_ci #1\XINT_btd_II_cvii #2\W\W\W\W\W\W\W
{\XINT_btd_II_d {}{#2}{\xint_c_ii }}%
\def\XINT_btd_II_cii #1\XINT_btd_II_cvii #2\W\W\W\W\W\W
@@ -507,10 +515,11 @@
{%
\XINT_btd_II_end_b #1#3%
}%
-\edef\XINT_btd_II_end_b #1#2#3#4#5#6#7#8#9%
+\def\XINT_btd_II_end_b#1{%
+\def\XINT_btd_II_end_b ##1##2##3##4##5##6##7##8##9%
{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4#5#6#7#8#9\relax
-}%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8##9\relax
+}}\XINT_btd_II_end_b{ }%
\def\XINT_btd_I_a #1#2#3#4#5#6#7#8%
{%
\xint_gob_til_Z #3\XINT_btd_I_end_a\Z
@@ -535,10 +544,9 @@
\def\xintbintohex #1%
{%
\expandafter\XINT_bth_checkin
- \romannumeral0\expandafter\XINT_num_loop
- \romannumeral`&&@#1\xint_relax\xint_relax
- \xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z
+ \romannumeral0\expandafter\XINT_num_cleanup
+ \the\numexpr\expandafter\XINT_num_loop
+ \romannumeral`&&@#1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
\R\R\R\R\R\R\R\R\Z \W\W\W\W\W\W\W\W
}%
\def\XINT_bth_checkin #1%
@@ -606,9 +614,9 @@
}%
\def\XINT_htb_II_b #1#2#3\T
{%
- \XINT_num_loop #2#1%
- \xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z
+ \expandafter\XINT_num_cleanup
+ \the\numexpr\expandafter\XINT_num_loop #2#1%
+ \xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
\def\xintCHexToBin {\romannumeral0\xintchextobin }%
\def\xintchextobin #1%
@@ -646,12 +654,12 @@
\XINT_chtb_I\expandafter\expandafter\expandafter #1%
{%
\XINT_chtb_end_b #1%
- \xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z
+ \xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
\def\XINT_chtb_end_b #1\W#2\W#3\W#4\W#5\W#6\W#7\W#8\W\endcsname
{%
- \XINT_num_loop
+ \expandafter\XINT_num_cleanup
+ \the\numexpr\expandafter\XINT_num_loop
}%
\XINT_restorecatcodes_endinput%
\endinput
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintcfrac.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintcfrac.sty 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintcfrac.sty 2017-07-27 21:26:25 UTC (rev 44900)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.2k 2017/01/06
+%% The xint bundle 1.2l 2017/07/26
%% Copyright (C) 2013-2017 by Jean-Francois Burnol
%% xintcfrac: Expandable continued fractions with xint package
%% ---------------------------------------------------------------
@@ -70,22 +70,22 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintcfrac}%
- [2017/01/06 1.2k Expandable continued fractions with xint package (JFB)]%
+ [2017/07/26 1.2l Expandable continued fractions with xint package (JFB)]%
\def\xintCFrac {\romannumeral0\xintcfrac }%
\def\xintcfrac #1%
{%
- \XINT_cfrac_opt_a #1\xint_relax
+ \XINT_cfrac_opt_a #1\xint:
}%
\def\XINT_cfrac_opt_a #1%
{%
\ifx[#1\XINT_cfrac_opt_b\fi \XINT_cfrac_noopt #1%
}%
-\def\XINT_cfrac_noopt #1\xint_relax
+\def\XINT_cfrac_noopt #1\xint:
{%
\expandafter\XINT_cfrac_A\romannumeral0\xintrawwithzeros {#1}\Z
\relax\relax
}%
-\def\XINT_cfrac_opt_b\fi\XINT_cfrac_noopt [\xint_relax #1]%
+\def\XINT_cfrac_opt_b\fi\XINT_cfrac_noopt [\xint:#1]%
{%
\fi\csname XINT_cfrac_opt#1\endcsname
}%
@@ -146,30 +146,30 @@
}%
\def\XINT_cfrac_end_b \Z+\cfrac#1#2{ #2}%
\def\xintGCFrac {\romannumeral0\xintgcfrac }%
-\def\xintgcfrac #1{\XINT_gcfrac_opt_a #1\xint_relax }%
+\def\xintgcfrac #1{\XINT_gcfrac_opt_a #1\xint:}%
\def\XINT_gcfrac_opt_a #1%
{%
\ifx[#1\XINT_gcfrac_opt_b\fi \XINT_gcfrac_noopt #1%
}%
-\def\XINT_gcfrac_noopt #1\xint_relax
+\def\XINT_gcfrac_noopt #1\xint:%
{%
- \XINT_gcfrac #1+\xint_relax/\relax\relax
+ \XINT_gcfrac #1+!/\relax\relax
}%
-\def\XINT_gcfrac_opt_b\fi\XINT_gcfrac_noopt [\xint_relax #1]%
+\def\XINT_gcfrac_opt_b\fi\XINT_gcfrac_noopt [\xint:#1]%
{%
\fi\csname XINT_gcfrac_opt#1\endcsname
}%
\def\XINT_gcfrac_optl #1%
{%
- \XINT_gcfrac #1+\xint_relax/\relax\hfill
+ \XINT_gcfrac #1+!/\relax\hfill
}%
\def\XINT_gcfrac_optc #1%
{%
- \XINT_gcfrac #1+\xint_relax/\relax\relax
+ \XINT_gcfrac #1+!/\relax\relax
}%
\def\XINT_gcfrac_optr #1%
{%
- \XINT_gcfrac #1+\xint_relax/\hfill\relax
+ \XINT_gcfrac #1+!/\hfill\relax
}%
\def\XINT_gcfrac
{%
@@ -178,52 +178,52 @@
\def\XINT_gcfrac_enter {\XINT_gcfrac_loop {}}%
\def\XINT_gcfrac_loop #1#2+#3/%
{%
- \xint_gob_til_xint_relax #3\XINT_gcfrac_endloop\xint_relax
+ \xint_gob_til_exclam #3\XINT_gcfrac_endloop!%
\XINT_gcfrac_loop {{#3}{#2}#1}%
}%
-\def\XINT_gcfrac_endloop\xint_relax\XINT_gcfrac_loop #1#2#3%
+\def\XINT_gcfrac_endloop!\XINT_gcfrac_loop #1#2#3%
{%
- \XINT_gcfrac_T #2#3#1\xint_relax\xint_relax
+ \XINT_gcfrac_T #2#3#1!!%
}%
\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_xint_relax #5\XINT_gcfrac_end\xint_relax\XINT_gcfrac_U
+ \xint_gob_til_exclam #5\XINT_gcfrac_end!\XINT_gcfrac_U
#1#2{\xintFrac{#5}%
\ifcase\xintSgn{#4}
+\or+\else-\fi
\cfrac{#1\xintFrac{\xintAbs{#4}}#2}{#3}}%
}%
-\def\XINT_gcfrac_end\xint_relax\XINT_gcfrac_U #1#2#3%
+\def\XINT_gcfrac_end!\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\xintggcfrac #1{\XINT_ggcfrac_opt_a #1\xint:}%
\def\XINT_ggcfrac_opt_a #1%
{%
\ifx[#1\XINT_ggcfrac_opt_b\fi \XINT_ggcfrac_noopt #1%
}%
-\def\XINT_ggcfrac_noopt #1\xint_relax
+\def\XINT_ggcfrac_noopt #1\xint:
{%
- \XINT_ggcfrac #1+\xint_relax/\relax\relax
+ \XINT_ggcfrac #1+!/\relax\relax
}%
-\def\XINT_ggcfrac_opt_b\fi\XINT_ggcfrac_noopt [\xint_relax #1]%
+\def\XINT_ggcfrac_opt_b\fi\XINT_ggcfrac_noopt [\xint:#1]%
{%
\fi\csname XINT_ggcfrac_opt#1\endcsname
}%
\def\XINT_ggcfrac_optl #1%
{%
- \XINT_ggcfrac #1+\xint_relax/\relax\hfill
+ \XINT_ggcfrac #1+!/\relax\hfill
}%
\def\XINT_ggcfrac_optc #1%
{%
- \XINT_ggcfrac #1+\xint_relax/\relax\relax
+ \XINT_ggcfrac #1+!/\relax\relax
}%
\def\XINT_ggcfrac_optr #1%
{%
- \XINT_ggcfrac #1+\xint_relax/\hfill\relax
+ \XINT_ggcfrac #1+!/\hfill\relax
}%
\def\XINT_ggcfrac
{%
@@ -232,20 +232,20 @@
\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_gob_til_exclam #3\XINT_ggcfrac_endloop!%
\XINT_ggcfrac_loop {{#3}{#2}#1}%
}%
-\def\XINT_ggcfrac_endloop\xint_relax\XINT_ggcfrac_loop #1#2#3%
+\def\XINT_ggcfrac_endloop!\XINT_ggcfrac_loop #1#2#3%
{%
- \XINT_ggcfrac_T #2#3#1\xint_relax\xint_relax
+ \XINT_ggcfrac_T #2#3#1!!%
}%
\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
+ \xint_gob_til_exclam #5\XINT_ggcfrac_end!\XINT_ggcfrac_U
#1#2{#5+\cfrac{#1#4#2}{#3}}%
}%
-\def\XINT_ggcfrac_end\xint_relax\XINT_ggcfrac_U #1#2#3%
+\def\XINT_ggcfrac_end!\XINT_ggcfrac_U #1#2#3%
{%
\XINT_ggcfrac_end_b #3%
}%
@@ -255,10 +255,10 @@
{%
\expandafter\XINT_gctgcx_start\expandafter {\romannumeral`&&@#3}{#1}{#2}%
}%
-\def\XINT_gctgcx_start #1#2#3{\XINT_gctgcx_loop_a {}{#2}{#3}#1+\xint_relax/}%
+\def\XINT_gctgcx_start #1#2#3{\XINT_gctgcx_loop_a {}{#2}{#3}#1+!/}%
\def\XINT_gctgcx_loop_a #1#2#3#4+#5/%
{%
- \xint_gob_til_xint_relax #5\XINT_gctgcx_end\xint_relax
+ \xint_gob_til_exclam #5\XINT_gctgcx_end!%
\XINT_gctgcx_loop_b {#1{#4}}{#2{#5}#3}{#2}{#3}%
}%
\def\XINT_gctgcx_loop_b #1#2%
@@ -265,7 +265,7 @@
{%
\XINT_gctgcx_loop_a {#1#2}%
}%
-\def\XINT_gctgcx_end\xint_relax\XINT_gctgcx_loop_b #1#2#3#4{ #1}%
+\def\XINT_gctgcx_end!\XINT_gctgcx_loop_b #1#2#3#4{ #1}%
\def\xintFtoCs {\romannumeral0\xintftocs }%
\def\xintftocs #1%
{%
@@ -461,12 +461,12 @@
\def\xintCstoF {\romannumeral0\xintcstof }%
\def\xintcstof #1%
{%
- \expandafter\XINT_ctf_prep \romannumeral0\xintcsvtolist{#1}\xint_relax
+ \expandafter\XINT_ctf_prep \romannumeral0\xintcsvtolist{#1}!%
}%
\def\xintCtoF {\romannumeral0\xintctof }%
\def\xintctof #1%
{%
- \expandafter\XINT_ctf_prep \romannumeral`&&@#1\xint_relax
+ \expandafter\XINT_ctf_prep \romannumeral`&&@#1!%
}%
\def\XINT_ctf_prep
{%
@@ -474,7 +474,7 @@
}%
\def\XINT_ctf_loop_a #1#2#3#4#5%
{%
- \xint_gob_til_xint_relax #5\XINT_ctf_end\xint_relax
+ \xint_gob_til_exclam #5\XINT_ctf_end!%
\expandafter\XINT_ctf_loop_b
\romannumeral0\xintrawwithzeros {#5}.{#1}{#2}{#3}{#4}%
}%
@@ -481,10 +481,12 @@
\def\XINT_ctf_loop_b #1/#2.#3#4#5#6%
{%
\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_fork #2\Z #6\Z}{\XINT_mul_fork #1\Z #4\Z}}%
- {\romannumeral0\xintiiadd {\XINT_mul_fork #2\Z #5\Z}{\XINT_mul_fork #1\Z #3\Z}}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#4\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#3\xint:}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#6\xint:}%
+ {\XINT_mul_fork #1\xint:#4\xint:}}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#5\xint:}%
+ {\XINT_mul_fork #1\xint:#3\xint:}}%
}%
\def\XINT_ctf_loop_c #1#2%
{%
@@ -502,7 +504,7 @@
\def\xintiCstoF {\romannumeral0\xinticstof }%
\def\xinticstof #1%
{%
- \expandafter\XINT_icstf_prep \romannumeral`&&@#1,\xint_relax,%
+ \expandafter\XINT_icstf_prep \romannumeral`&&@#1,!,%
}%
\def\XINT_icstf_prep
{%
@@ -510,7 +512,7 @@
}%
\def\XINT_icstf_loop_a #1#2#3#4#5,%
{%
- \xint_gob_til_xint_relax #5\XINT_icstf_end\xint_relax
+ \xint_gob_til_exclam #5\XINT_icstf_end!%
\expandafter
\XINT_icstf_loop_b \romannumeral`&&@#5.{#1}{#2}{#3}{#4}%
}%
@@ -517,8 +519,8 @@
\def\XINT_icstf_loop_b #1.#2#3#4#5%
{%
\expandafter\XINT_icstf_loop_c\expandafter
- {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\Z #3\Z}}%
- {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\Z #2\Z}}%
+ {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\xint:#3\xint:}}%
+ {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\xint:#2\xint:}}%
{#2}{#3}%
}%
\def\XINT_icstf_loop_c #1#2%
@@ -529,7 +531,7 @@
\def\xintGCtoF {\romannumeral0\xintgctof }%
\def\xintgctof #1%
{%
- \expandafter\XINT_gctf_prep \romannumeral`&&@#1+\xint_relax/%
+ \expandafter\XINT_gctf_prep \romannumeral`&&@#1+!/%
}%
\def\XINT_gctf_prep
{%
@@ -543,10 +545,12 @@
\def\XINT_gctf_loop_b #1/#2.#3#4#5#6%
{%
\expandafter\XINT_gctf_loop_c\expandafter
- {\romannumeral0\XINT_mul_fork #2\Z #4\Z }%
- {\romannumeral0\XINT_mul_fork #2\Z #3\Z }%
- {\romannumeral0\xintiiadd {\XINT_mul_fork #2\Z #6\Z}{\XINT_mul_fork #1\Z #4\Z}}%
- {\romannumeral0\xintiiadd {\XINT_mul_fork #2\Z #5\Z}{\XINT_mul_fork #1\Z #3\Z}}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#4\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#3\xint:}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#6\xint:}%
+ {\XINT_mul_fork #1\xint:#4\xint:}}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#5\xint:}%
+ {\XINT_mul_fork #1\xint:#3\xint:}}%
}%
\def\XINT_gctf_loop_c #1#2%
{%
@@ -562,7 +566,7 @@
}%
\def\XINT_gctf_loop_f #1#2/%
{%
- \xint_gob_til_xint_relax #2\XINT_gctf_end\xint_relax
+ \xint_gob_til_exclam #2\XINT_gctf_end!%
\expandafter\XINT_gctf_loop_g
\romannumeral0\xintrawwithzeros {#2}.#1%
}%
@@ -569,10 +573,10 @@
\def\XINT_gctf_loop_g #1/#2.#3#4#5#6%
{%
\expandafter\XINT_gctf_loop_h\expandafter
- {\romannumeral0\XINT_mul_fork #1\Z #6\Z }%
- {\romannumeral0\XINT_mul_fork #1\Z #5\Z }%
- {\romannumeral0\XINT_mul_fork #2\Z #4\Z }%
- {\romannumeral0\XINT_mul_fork #2\Z #3\Z }%
+ {\romannumeral0\XINT_mul_fork #1\xint:#6\xint:}%
+ {\romannumeral0\XINT_mul_fork #1\xint:#5\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#4\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#3\xint:}%
}%
\def\XINT_gctf_loop_h #1#2%
{%
@@ -590,7 +594,7 @@
\def\xintiGCtoF {\romannumeral0\xintigctof }%
\def\xintigctof #1%
{%
- \expandafter\XINT_igctf_prep \romannumeral`&&@#1+\xint_relax/%
+ \expandafter\XINT_igctf_prep \romannumeral`&&@#1+!/%
}%
\def\XINT_igctf_prep
{%
@@ -604,8 +608,8 @@
\def\XINT_igctf_loop_b #1.#2#3#4#5%
{%
\expandafter\XINT_igctf_loop_c\expandafter
- {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\Z #3\Z}}%
- {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\Z #2\Z}}%
+ {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\xint:#3\xint:}}%
+ {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\xint:#2\xint:}}%
{#2}{#3}%
}%
\def\XINT_igctf_loop_c #1#2%
@@ -614,7 +618,7 @@
}%
\def\XINT_igctf_loop_f #1#2#3#4/%
{%
- \xint_gob_til_xint_relax #4\XINT_igctf_end\xint_relax
+ \xint_gob_til_exclam #4\XINT_igctf_end!%
\expandafter\XINT_igctf_loop_g
\romannumeral`&&@#4.{#2}{#3}#1%
}%
@@ -621,8 +625,8 @@
\def\XINT_igctf_loop_g #1.#2#3%
{%
\expandafter\XINT_igctf_loop_h\expandafter
- {\romannumeral0\XINT_mul_fork #1\Z #3\Z }%
- {\romannumeral0\XINT_mul_fork #1\Z #2\Z }%
+ {\romannumeral0\XINT_mul_fork #1\xint:#3\xint:}%
+ {\romannumeral0\XINT_mul_fork #1\xint:#2\xint:}%
}%
\def\XINT_igctf_loop_h #1#2%
{%
@@ -636,12 +640,12 @@
\def\xintCstoCv {\romannumeral0\xintcstocv }%
\def\xintcstocv #1%
{%
- \expandafter\XINT_ctcv_prep\romannumeral0\xintcsvtolist{#1}\xint_relax
+ \expandafter\XINT_ctcv_prep\romannumeral0\xintcsvtolist{#1}!%
}%
\def\xintCtoCv {\romannumeral0\xintctocv }%
\def\xintctocv #1%
{%
- \expandafter\XINT_ctcv_prep\romannumeral`&&@#1\xint_relax
+ \expandafter\XINT_ctcv_prep\romannumeral`&&@#1!%
}%
\def\XINT_ctcv_prep
{%
@@ -649,7 +653,7 @@
}%
\def\XINT_ctcv_loop_a #1#2#3#4#5#6%
{%
- \xint_gob_til_xint_relax #6\XINT_ctcv_end\xint_relax
+ \xint_gob_til_exclam #6\XINT_ctcv_end!%
\expandafter\XINT_ctcv_loop_b
\romannumeral0\xintrawwithzeros {#6}.{#2}{#3}{#4}{#5}{#1}%
}%
@@ -656,10 +660,12 @@
\def\XINT_ctcv_loop_b #1/#2.#3#4#5#6%
{%
\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_fork #2\Z #6\Z}{\XINT_mul_fork #1\Z #4\Z}}%
- {\romannumeral0\xintiiadd {\XINT_mul_fork #2\Z #5\Z}{\XINT_mul_fork #1\Z #3\Z}}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#4\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#3\xint:}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#6\xint:}%
+ {\XINT_mul_fork #1\xint:#4\xint:}}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#5\xint:}%
+ {\XINT_mul_fork #1\xint:#3\xint:}}%
}%
\def\XINT_ctcv_loop_c #1#2%
{%
@@ -683,7 +689,7 @@
\def\xintiCstoCv {\romannumeral0\xinticstocv }%
\def\xinticstocv #1%
{%
- \expandafter\XINT_icstcv_prep \romannumeral`&&@#1,\xint_relax,%
+ \expandafter\XINT_icstcv_prep \romannumeral`&&@#1,!,%
}%
\def\XINT_icstcv_prep
{%
@@ -691,7 +697,7 @@
}%
\def\XINT_icstcv_loop_a #1#2#3#4#5#6,%
{%
- \xint_gob_til_xint_relax #6\XINT_icstcv_end\xint_relax
+ \xint_gob_til_exclam #6\XINT_icstcv_end!%
\expandafter
\XINT_icstcv_loop_b \romannumeral`&&@#6.{#2}{#3}{#4}{#5}{#1}%
}%
@@ -698,8 +704,8 @@
\def\XINT_icstcv_loop_b #1.#2#3#4#5%
{%
\expandafter\XINT_icstcv_loop_c\expandafter
- {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\Z #3\Z}}%
- {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\Z #2\Z}}%
+ {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\xint:#3\xint:}}%
+ {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\xint:#2\xint:}}%
{{#2}{#3}}%
}%
\def\XINT_icstcv_loop_c #1#2%
@@ -716,7 +722,7 @@
\def\xintGCtoCv {\romannumeral0\xintgctocv }%
\def\xintgctocv #1%
{%
- \expandafter\XINT_gctcv_prep \romannumeral`&&@#1+\xint_relax/%
+ \expandafter\XINT_gctcv_prep \romannumeral`&&@#1+!/%
}%
\def\XINT_gctcv_prep
{%
@@ -730,10 +736,12 @@
\def\XINT_gctcv_loop_b #1/#2.#3#4#5#6%
{%
\expandafter\XINT_gctcv_loop_c\expandafter
- {\romannumeral0\XINT_mul_fork #2\Z #4\Z }%
- {\romannumeral0\XINT_mul_fork #2\Z #3\Z }%
- {\romannumeral0\xintiiadd {\XINT_mul_fork #2\Z #6\Z}{\XINT_mul_fork #1\Z #4\Z}}%
- {\romannumeral0\xintiiadd {\XINT_mul_fork #2\Z #5\Z}{\XINT_mul_fork #1\Z #3\Z}}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#4\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#3\xint:}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#6\xint:}%
+ {\XINT_mul_fork #1\xint:#4\xint:}}%
+ {\romannumeral0\xintiiadd {\XINT_mul_fork #2\xint:#5\xint:}%
+ {\XINT_mul_fork #1\xint:#3\xint:}}%
}%
\def\XINT_gctcv_loop_c #1#2%
{%
@@ -758,7 +766,7 @@
}%
\def\XINT_gctcv_loop_h #1#2#3/%
{%
- \xint_gob_til_xint_relax #3\XINT_gctcv_end\xint_relax
+ \xint_gob_til_exclam #3\XINT_gctcv_end!%
\expandafter\XINT_gctcv_loop_i
\romannumeral0\xintrawwithzeros {#3}.#2{#1}%
}%
@@ -765,10 +773,10 @@
\def\XINT_gctcv_loop_i #1/#2.#3#4#5#6%
{%
\expandafter\XINT_gctcv_loop_j\expandafter
- {\romannumeral0\XINT_mul_fork #1\Z #6\Z }%
- {\romannumeral0\XINT_mul_fork #1\Z #5\Z }%
- {\romannumeral0\XINT_mul_fork #2\Z #4\Z }%
- {\romannumeral0\XINT_mul_fork #2\Z #3\Z }%
+ {\romannumeral0\XINT_mul_fork #1\xint:#6\xint:}%
+ {\romannumeral0\XINT_mul_fork #1\xint:#5\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#4\xint:}%
+ {\romannumeral0\XINT_mul_fork #2\xint:#3\xint:}%
}%
\def\XINT_gctcv_loop_j #1#2%
{%
@@ -787,7 +795,7 @@
\def\xintiGCtoCv {\romannumeral0\xintigctocv }%
\def\xintigctocv #1%
{%
- \expandafter\XINT_igctcv_prep \romannumeral`&&@#1+\xint_relax/%
+ \expandafter\XINT_igctcv_prep \romannumeral`&&@#1+!/%
}%
\def\XINT_igctcv_prep
{%
@@ -801,8 +809,8 @@
\def\XINT_igctcv_loop_b #1.#2#3#4#5%
{%
\expandafter\XINT_igctcv_loop_c\expandafter
- {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\Z #3\Z}}%
- {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\Z #2\Z}}%
+ {\romannumeral0\xintiiadd {#5}{\XINT_mul_fork #1\xint:#3\xint:}}%
+ {\romannumeral0\xintiiadd {#4}{\XINT_mul_fork #1\xint:#2\xint:}}%
{{#2}{#3}}%
}%
\def\XINT_igctcv_loop_c #1#2%
@@ -811,7 +819,7 @@
}%
\def\XINT_igctcv_loop_f #1#2#3#4/%
{%
- \xint_gob_til_xint_relax #4\XINT_igctcv_end_a\xint_relax
+ \xint_gob_til_exclam #4\XINT_igctcv_end_a!%
\expandafter\XINT_igctcv_loop_g
\romannumeral`&&@#4.#1#2{#3}%
}%
@@ -818,8 +826,8 @@
\def\XINT_igctcv_loop_g #1.#2#3#4#5%
{%
\expandafter\XINT_igctcv_loop_h\expandafter
- {\romannumeral0\XINT_mul_fork #1\Z #5\Z }%
- {\romannumeral0\XINT_mul_fork #1\Z #4\Z }%
+ {\romannumeral0\XINT_mul_fork #1\xint:#5\xint:}%
+ {\romannumeral0\XINT_mul_fork #1\xint:#4\xint:}%
{{#2}{#3}}%
}%
\def\XINT_igctcv_loop_h #1#2%
@@ -1009,25 +1017,25 @@
\def\xintCstoGC {\romannumeral0\xintcstogc }%
\def\xintcstogc #1%
{%
- \expandafter\XINT_cstc_prep \romannumeral`&&@#1,\xint_relax,%
+ \expandafter\XINT_cstc_prep \romannumeral`&&@#1,!,%
}%
\def\XINT_cstc_prep #1,{\XINT_cstc_loop_a {{#1}}}%
\def\XINT_cstc_loop_a #1#2,%
{%
- \xint_gob_til_xint_relax #2\XINT_cstc_end\xint_relax
+ \xint_gob_til_exclam #2\XINT_cstc_end!%
\XINT_cstc_loop_b {#1}{#2}%
}%
\def\XINT_cstc_loop_b #1#2{\XINT_cstc_loop_a {#1+1/{#2}}}%
-\def\XINT_cstc_end\xint_relax\XINT_cstc_loop_b #1#2{ #1}%
+\def\XINT_cstc_end!\XINT_cstc_loop_b #1#2{ #1}%
\def\xintGCtoGC {\romannumeral0\xintgctogc }%
\def\xintgctogc #1%
{%
- \expandafter\XINT_gctgc_start \romannumeral`&&@#1+\xint_relax/%
+ \expandafter\XINT_gctgc_start \romannumeral`&&@#1+!/%
}%
\def\XINT_gctgc_start {\XINT_gctgc_loop_a {}}%
\def\XINT_gctgc_loop_a #1#2+#3/%
{%
- \xint_gob_til_xint_relax #3\XINT_gctgc_end\xint_relax
+ \xint_gob_til_exclam #3\XINT_gctgc_end!%
\expandafter\XINT_gctgc_loop_b\expandafter
{\romannumeral`&&@#2}{#3}{#1}%
}%
@@ -1040,7 +1048,7 @@
{%
\XINT_gctgc_loop_a {#3{#2}+{#1}/}%
}%
-\def\XINT_gctgc_end\xint_relax\expandafter\XINT_gctgc_loop_b
+\def\XINT_gctgc_end!\expandafter\XINT_gctgc_loop_b
{%
\expandafter\XINT_gctgc_end_b
}%
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintcore.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintcore.sty 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintcore.sty 2017-07-27 21:26:25 UTC (rev 44900)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.2k 2017/01/06
+%% The xint bundle 1.2l 2017/07/26
%% Copyright (C) 2013-2017 by Jean-Francois Burnol
%% xintcore: Expandable arithmetic on big integers
%% ---------------------------------------------------------------
@@ -70,7 +70,74 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintcore}%
- [2017/01/06 1.2k Expandable arithmetic on big integers (JFB)]%
+ [2017/07/26 1.2l Expandable arithmetic on big integers (JFB)]%
+\csname XINT_Clamped_istrapped\endcsname
+\csname XINT_ConversionSyntax_istrapped\endcsname
+\csname XINT_DivisionByZero_istrapped\endcsname
+\csname XINT_DivisionImpossible_istrapped\endcsname
+\csname XINT_DivisionUndefined_istrapped\endcsname
+\csname XINT_InvalidOperation_istrapped\endcsname
+\csname XINT_Overflow_istrapped\endcsname
+\csname XINT_Underflow_istrapped\endcsname
+\catcode`- 11
+\def\XINT_ConversionSyntax-signal {{InvalidOperation}}%
+\let\XINT_DivisionImpossible-signal\XINT_ConversionSyntax-signal
+\let\XINT_DivisionUndefined-signal \XINT_ConversionSyntax-signal
+\let\XINT_InvalidContext-signal \XINT_ConversionSyntax-signal
+\catcode`- 12
+\def\XINT_signalcondition #1{\expandafter\XINT_signalcondition_a
+ \romannumeral0\ifcsname XINT_#1-signal\endcsname
+ \xint_dothis{\csname XINT_#1-signal\endcsname}%
+ \fi\xint_orthat{{#1}}{#1}}%
+\def\XINT_signalcondition_a #1#2#3#4#5{% copied over from Python Decimal module
+ \ifcsname XINT_#1_isignoredflag\endcsname
+ \xint_dothis{\csname XINT_#1.handler\endcsname {#4}}%
+ \fi
+ \expandafter\xint_gobble_i\csname XINT_#1Flag_ON\endcsname
+ \unless\ifcsname XINT_#1_istrapped\endcsname
+ \xint_dothis{\csname XINT_#2.handler\endcsname {#4}}%
+ \fi
+ \xint_orthat{%
+ % the flag raised is named after the signal #1, but we show condition #2
+ \XINT_expandableerror{#2 (hit <RET> thrice)}%
+ \XINT_expandableerror{#3}%
+ \XINT_expandableerror{next: #5}%
+ % not for X3.274
+ %\XINT_expandableerror{<RET>, or I\xintUse{...}<RET>, or I\xintCTRLC<RET>}%
+ \xint_firstofone_thenstop{#5}%
+ }%
+}%
+%% \let\xintUse\xint_firstofthree_thenstop % defined in xint.sty
+\def\XINT_ifFlagRaised #1{%
+ \ifcsname XINT_#1Flag_ON\endcsname
+ \expandafter\xint_firstoftwo
+ \else
+ \expandafter\xint_secondoftwo
+ \fi}%
+\def\XINT_resetFlag #1%
+ {\expandafter\let\csname XINT_#1Flag_ON\endcsname\XINT_undefined}%
+\def\XINT_resetFlags {% WIP
+ \XINT_resetFlag{InvalidOperation}% also from DivisionUndefined
+ \XINT_resetFlag{DivisionByZero}%
+ \XINT_resetFlag{Underflow}% (\xintiiPow with negative exponent)
+ \XINT_resetFlag{Overflow}% not encountered so far in xint code 1.2l
+ % .. others ..
+}%
+%% NOT IMPLEMENTED! WORK IN PROGRESS! (ALL SIGNALS TRAPPED, NO HANDLERS USED)
+\catcode`. 11
+\let\XINT_Clamped.handler\xint_firstofone % WIP
+\def\XINT_InvalidOperation.handler#1{_NaN}% WIP
+\def\XINT_ConversionSyntax.handler#1{_NaN}% WIP
+\def\XINT_DivisionByZero.handler#1{_SignedInfinity(#1)}% WIP
+\def\XINT_DivisionImpossible.handler#1{_NaN}% WIP
+\def\XINT_DivisionUndefined.handler#1{_NaN}% WIP
+\let\XINT_Inexact.handler\xint_firstofone % WIP
+\def\XINT_InvalidContext.handler#1{_NaN}% WIP
+\let\XINT_Rounded.handler\xint_firstofone % WIP
+\let\XINT_Subnormal.handler\xint_firstofone% WIP
+\def\XINT_Overflow.handler#1{_NaN}% WIP
+\def\XINT_Underflow.handler#1{_NaN}% WIP
+\catcode`. 12
\ifdefined\m at ne\let\xint_c_mone\m at ne
\else\csname newcount\endcsname\xint_c_mone \xint_c_mone -1 \fi
\newcount\xint_c_x^viii \xint_c_x^viii 100000000
@@ -78,234 +145,46 @@
\newcount\xint_c_x^viii_mone \xint_c_x^viii_mone 99999999
\newcount\xint_c_xii_e_viii \xint_c_xii_e_viii 1200000000
\newcount\xint_c_xi_e_viii_mone \xint_c_xi_e_viii_mone 1099999999
-\newcount\xint_c_xii_e_viii_mone\xint_c_xii_e_viii_mone 1199999999
\def\xintiNum {\romannumeral0\xintinum }%
\def\xintinum #1%
{%
- \expandafter\XINT_num_loop
- \romannumeral`&&@#1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z
+ \expandafter\XINT_num_cleanup\the\numexpr\expandafter\XINT_num_loop
+ \romannumeral`&&@#1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
\let\xintNum\xintiNum \let\xintnum\xintinum
\def\XINT_num #1%
{%
- \XINT_num_loop #1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z
+ \expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop
+ #1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
-\def\XINT_num_loop #1#2#3#4#5#6#7#8%
+\def\XINT_num_loop #1#2#3#4#5#6#7#8#9%
{%
- \xint_gob_til_xint_relax #8\XINT_num_end\xint_relax
- \XINT_num_NumEight #1#2#3#4#5#6#7#8%
-}%
-\edef\XINT_num_end\xint_relax\XINT_num_NumEight #1\xint_relax #2\Z
-{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1+\xint_c_\relax
-}%
-\def\XINT_num_NumEight #1#2#3#4#5#6#7#8%
-{%
- \ifnum \numexpr #1#2#3#4#5#6#7#8+\xint_c_= \xint_c_
- \xint_afterfi {\expandafter\XINT_num_keepsign_a
- \the\numexpr #1#2#3#4#5#6#7#81\relax}%
+ \xint_gob_til_xint: #9\XINT_num_end\xint:
+ #1#2#3#4#5#6#7#8#9%
+ \ifnum \numexpr #1#2#3#4#5#6#7#8#9+\xint_c_ = \xint_c_
+ \expandafter\XINT_num_loop
\else
- \xint_afterfi {\expandafter\XINT_num_finish
- \the\numexpr #1#2#3#4#5#6#7#8\relax}%
+ \expandafter\relax
\fi
}%
-\def\XINT_num_keepsign_a #1%
+\def\XINT_num_end\xint:#1\xint:{#1+\xint_c_\xint:}% empty input ok
+\def\XINT_num_cleanup #1\xint:#2\Z { #1}%
+\def\XINT_cuz_small#1{%
+\def\XINT_cuz_small ##1##2##3##4##5##6##7##8%
{%
- \xint_gob_til_one#1\XINT_num_gobacktoloop 1\XINT_num_keepsign_b
-}%
-\def\XINT_num_gobacktoloop 1\XINT_num_keepsign_b {\XINT_num_loop }%
-\def\XINT_num_keepsign_b #1{\XINT_num_loop -}%
-\def\XINT_num_finish #1\xint_relax #2\Z { #1}%
-\edef\XINT_cuz_small #1#2#3#4#5#6#7#8%
-{%
- \noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4#5#6#7#8\relax
-}%
-\def\XINT_cuz #1#2#3#4#5#6#7#8#9%
-{%
- \xint_gob_til_R #9\XINT_cuz_e \R
- \xint_gob_til_eightzeroes #1#2#3#4#5#6#7#8\XINT_cuz_z 00000000%
- \XINT_cuz_done #1#2#3#4#5#6#7#8#9%
-}%
-\def\XINT_cuz_z 00000000\XINT_cuz_done 00000000{\XINT_cuz }%
-\edef\XINT_cuz_done #1#2#3#4#5#6#7#8#9\R
- {\noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4#5#6#7#8\relax #9}%
-\edef\XINT_cuz_e\R #1\XINT_cuz_done #2\R
- {\noexpand\expandafter\space\noexpand\the\numexpr #2\relax }%
-\def\XINT_cuz_byviii #1#2#3#4#5#6#7#8#9%
-{%
- \xint_gob_til_R #9\XINT_cuz_byviii_e \R
- \xint_gob_til_eightzeroes #1#2#3#4#5#6#7#8\XINT_cuz_byviii_z 00000000%
- \XINT_cuz_byviii_done #1#2#3#4#5#6#7#8#9%
-}%
-\def\XINT_cuz_byviii_z 00000000\XINT_cuz_byviii_done 00000000{\XINT_cuz_byviii}%
-\def\XINT_cuz_byviii_done #1\R { #1}%
-\def\XINT_cuz_byviii_e\R #1\XINT_cuz_byviii_done #2\R{ #2}%
-\def\XINT_zeroes_forviii #1#2#3#4#5#6#7#8%
-{%
- \xint_gob_til_R #8\XINT_zeroes_forviii_end\R\XINT_zeroes_forviii
-}%
-\edef\XINT_zeroes_forviii_end\R\XINT_zeroes_forviii #1#2#3#4#5#6#7#8#9\W
-{%
- \noexpand\expandafter\space\noexpand\xint_gob_til_one #2#3#4#5#6#7#8%
-}%
-\def\XINT_rsepbyviii #1#2#3#4#5#6#7#8%
-{%
- \XINT_rsepbyviii_b {#1#2#3#4#5#6#7#8}%
-}%
-\def\XINT_rsepbyviii_b #1#2#3#4#5#6#7#8#9%
-{%
- #2#3#4#5#6#7#8#9\expandafter!\the\numexpr
- 1#1\expandafter.\the\numexpr 1\XINT_rsepbyviii
-}%
-\def\XINT_rsepbyviii_end_B #1\relax #2#3{#2.}%
-\def\XINT_rsepbyviii_end_A #11#2\expandafter #3\relax #4#5{#2.1#5.}%
-\def\XINT_sepandrev
-{%
- \expandafter\XINT_sepandrev_a\the\numexpr 1\XINT_rsepbyviii
-}%
-\def\XINT_sepandrev_a {\XINT_sepandrev_b {}}%
-\def\XINT_sepandrev_b #1#2.#3.#4.#5.#6.#7.#8.#9.%
-{%
- \xint_gob_til_R #9\XINT_sepandrev_end\R
- \XINT_sepandrev_b {#9!#8!#7!#6!#5!#4!#3!#2!#1}%
-}%
-\def\XINT_sepandrev_end\R\XINT_sepandrev_b #1#2\W {\XINT_sepandrev_done #1}%
-\def\XINT_sepandrev_done #11#2!{ }%
-\def\XINT_sepandrev_andcount
-{%
- \expandafter\XINT_sepandrev_andcount_a\the\numexpr 1\XINT_rsepbyviii
-}%
-\def\XINT_sepandrev_andcount_a {\XINT_sepandrev_andcount_b 0.{}}%
-\def\XINT_sepandrev_andcount_b #1.#2#3.#4.#5.#6.#7.#8.#9.%
-{%
- \xint_gob_til_R #9\XINT_sepandrev_andcount_end\R
- \expandafter\XINT_sepandrev_andcount_b \the\numexpr #1+\xint_c_xiv.%
- {#9!#8!#7!#6!#5!#4!#3!#2}%
-}%
-\def\XINT_sepandrev_andcount_end\R
- \expandafter\XINT_sepandrev_andcount_b\the\numexpr #1+\xint_c_xiv.#2#3#4\W
-{\expandafter\XINT_sepandrev_andcount_done\the\numexpr \xint_c_ii*#3+#1.#2}%
-\edef\XINT_sepandrev_andcount_done #1.#21#3!%
- {\noexpand\expandafter\space\noexpand\the\numexpr #1-#3.}%
-\def\XINT_unrevbyviii #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
-{%
- \xint_gob_til_R #9\XINT_unrevbyviii_a\R
- \XINT_unrevbyviii {#9#8#7#6#5#4#3#2#1}%
-}%
-\edef\XINT_unrevbyviii_a\R\XINT_unrevbyviii #1#2\W
- {\noexpand\expandafter\space
- \noexpand\romannumeral`&&@\noexpand\xint_gob_til_Z #1}%
-\def\XINT_smallunrevbyviii 1#1!1#2!1#3!1#4!1#5!1#6!1#7!1#8!#9\W%
-{%
- \expandafter\XINT_cuz_small\xint_gob_til_Z #8#7#6#5#4#3#2#1%
-}%
-\def\XINT_sepbyviii_andcount
-{%
- \expandafter\XINT_sepbyviii_andcount_a\the\numexpr\XINT_sepbyviii
-}%
-\def\XINT_sepbyviii #1#2#3#4#5#6#7#8%
-{%
- 1#1#2#3#4#5#6#7#8\expandafter!\the\numexpr\XINT_sepbyviii
-}%
-\def\XINT_sepbyviii_end #1\relax {\relax\XINT_sepbyviii_andcount_end!}%
-\def\XINT_sepbyviii_andcount_a {\XINT_sepbyviii_andcount_b \xint_c_.}%
-\def\XINT_sepbyviii_andcount_b #1.#2!#3!#4!#5!#6!#7!#8!#9!%
-{%
- #2\expandafter!\the\numexpr#3\expandafter!\the\numexpr#4\expandafter
- !\the\numexpr#5\expandafter!\the\numexpr#6\expandafter!\the\numexpr
- #7\expandafter!\the\numexpr#8\expandafter!\the\numexpr#9\expandafter!\the\numexpr
- \expandafter\XINT_sepbyviii_andcount_b\the\numexpr #1+\xint_c_viii.%
-}%
-\def\XINT_sepbyviii_andcount_end #1\XINT_sepbyviii_andcount_b\the\numexpr
- #2+\xint_c_viii.#3#4\W {\expandafter.\the\numexpr #2+#3.}%
-\def\XINT_rev_nounsep #1#2!#3!#4!#5!#6!#7!#8!#9!%
-{%
- \xint_gob_til_R #9\XINT_rev_nounsep_end\R
- \XINT_rev_nounsep {#9!#8!#7!#6!#5!#4!#3!#2!#1}%
-}%
-\def\XINT_rev_nounsep_end\R\XINT_rev_nounsep #1#2\W {\XINT_rev_nounsep_done #1}%
-\def\XINT_rev_nounsep_done #11{ 1}%
-\def\XINT_sepbyviii_Z #1#2#3#4#5#6#7#8%
-{%
- 1#1#2#3#4#5#6#7#8\expandafter!\the\numexpr\XINT_sepbyviii_Z
-}%
-\def\XINT_sepbyviii_Z_end #1\relax {\relax\Z!}%
-\def\XINT_unsep_cuzsmall #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
-{%
- \xint_gob_til_R #9\XINT_unsep_cuzsmall_end\R
- \XINT_unsep_cuzsmall {#1#2#3#4#5#6#7#8#9}%
-}%
-\def\XINT_unsep_cuzsmall_end\R
- \XINT_unsep_cuzsmall #1{\XINT_unsep_cuzsmall_done #1}%
-\def\XINT_unsep_cuzsmall_done #1\R #2\W{\XINT_cuz_small #1}%
-\def\XINT_unsep_delim {1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W}%
-\def\XINT_div_unsepQ #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
-{%
- \xint_gob_til_R #9\XINT_div_unsepQ_end\R
- \XINT_div_unsepQ {#1#2#3#4#5#6#7#8#9}%
-}%
-\def\XINT_div_unsepQ_end\R\XINT_div_unsepQ #1{\XINT_div_unsepQ_x #1}%
-\def\XINT_div_unsepQ_x #1#2#3#4#5#6#7#8#9%
-{%
- \xint_gob_til_R #9\XINT_div_unsepQ_e \R
- \xint_gob_til_eightzeroes #1#2#3#4#5#6#7#8\XINT_div_unsepQ_y 00000000%
- \expandafter\XINT_div_unsepQ_done \the\numexpr #1#2#3#4#5#6#7#8.#9%
-}%
-\def\XINT_div_unsepQ_e\R\xint_gob_til_eightzeroes #1\XINT_div_unsepQ_y #2\W
- {\the\numexpr #1\relax \Z}%
-\def\XINT_div_unsepQ_y #1.#2\R #3\W{\XINT_cuz_small #2\Z}%
-\def\XINT_div_unsepQ_done #1.#2\R #3\W { #1#2\Z}%
-\def\XINT_div_unsepR #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
-{%
- \xint_gob_til_R #9\XINT_div_unsepR_end\R
- \XINT_div_unsepR {#1#2#3#4#5#6#7#8#9}%
-}%
-\def\XINT_div_unsepR_end\R\XINT_div_unsepR #1{\XINT_div_unsepR_done #1}%
-\def\XINT_div_unsepR_done #1\R #2\W {\XINT_cuz #1\R}%
-\def\XINT_microrevsep #1#2#3#4#5#6#7#8%
-{%
- 1#8#7#6#5#4#3#2#1\expandafter!\the\numexpr\XINT_microrevsep
-}%
-\def\XINT_microrevsep_end #1\W #2\expandafter #3\Z{#2!}%
-\def\xintReverseDigits {\romannumeral0\xintreversedigits }%
-\def\xintreversedigits #1{\expandafter\XINT_reversedigits\romannumeral`&&@#1\Z}%
-\def\XINT_reversedigits #1%
-{%
- \xint_UDsignfork
- #1{\expandafter-\romannumeral0\XINT_reversedigits_a}%
- -{\XINT_reversedigits_a #1}%
- \krof
-}%
-\def\XINT_reversedigits_a #1\Z
-{%
- \expandafter\XINT_revdigits_a\the\numexpr\expandafter\XINT_microrevsep
- \romannumeral`&&@#1{\XINT_microrevsep_end\W}\XINT_microrevsep_end
- \XINT_microrevsep_end\XINT_microrevsep_end
- \XINT_microrevsep_end\XINT_microrevsep_end
- \XINT_microrevsep_end\XINT_microrevsep_end\Z
- 1\Z!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
-}%
-\def\XINT_revdigits_a {\XINT_revdigits_b {}}%
-\def\XINT_revdigits_b #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
-{%
- \xint_gob_til_R #9\XINT_revdigits_end\R
- \XINT_revdigits_b {#9#8#7#6#5#4#3#2#1}%
-}%
-\edef\XINT_revdigits_end\R\XINT_revdigits_b #1#2\W
- {\noexpand\expandafter\space\noexpand\xint_gob_til_Z #1}%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8\relax
+}}\XINT_cuz_small{ }%
\def\xintiiSgn {\romannumeral0\xintiisgn }%
\def\xintiisgn #1%
{%
- \expandafter\XINT_sgn \romannumeral`&&@#1\Z%
+ \expandafter\XINT_sgn \romannumeral`&&@#1\xint:
}%
\def\xintSgn {\romannumeral0\xintsgn }%
\def\xintsgn #1%
{%
- \expandafter\XINT_sgn \romannumeral0\xintnum{#1}\Z%
+ \expandafter\XINT_sgn \romannumeral0\xintnum{#1}\xint:
}%
-\def\XINT_sgn #1#2\Z
+\def\XINT_sgn #1#2\xint:
{%
\xint_UDzerominusfork
#1-{ 0}%
@@ -313,7 +192,7 @@
0-{ 1}%
\krof
}%
-\def\XINT_Sgn #1#2\Z
+\def\XINT_Sgn #1#2\xint:
{%
\xint_UDzerominusfork
#1-{0}%
@@ -321,7 +200,7 @@
0-{1}%
\krof
}%
-\def\XINT_cntSgn #1#2\Z
+\def\XINT_cntSgn #1#2\xint:
{%
\xint_UDzerominusfork
#1-\xint_c_
@@ -368,14 +247,14 @@
\def\xintiiFDg {\romannumeral0\xintiifdg }%
\def\xintiifdg #1%
{%
- \expandafter\XINT_fdg \romannumeral`&&@#1\W\Z
+ \expandafter\XINT_fdg \romannumeral`&&@#1\xint:\Z
}%
\def\xintFDg {\romannumeral0\xintfdg }%
\def\xintfdg #1%
{%
- \expandafter\XINT_fdg \romannumeral0\xintnum{#1}\W\Z
+ \expandafter\XINT_fdg \romannumeral0\xintnum{#1}\xint:\Z
}%
-\def\XINT_FDg #1{\romannumeral0\XINT_fdg #1\W\Z }%
+\def\XINT_FDg #1{\romannumeral0\XINT_fdg #1\xint:\Z }%
\def\XINT_fdg #1#2#3\Z
{%
\xint_UDzerominusfork
@@ -397,9 +276,11 @@
-{\XINT_ldg#1}%
\krof
}%
-\edef\XINT_ldg #1#2#3#4#5#6#7#8#9%
- {\noexpand\expandafter\space
- \noexpand\the\numexpr#9#8#7#6#5#4#3#2#1*\xint_c_+\noexpand\XINT_ldg_a#9}%
+\def\XINT_ldg #1{%
+\def\XINT_ldg ##1##2##3##4##5##6##7##8##9%
+ {\expandafter#1%
+ \the\numexpr##9##8##7##6##5##4##3##2##1*\xint_c_+\XINT_ldg_a##9}%
+}\XINT_ldg{ }%
\def\XINT_ldg_a#1#2{\XINT_ldg_cbye#2\XINT_ldg_d#1\XINT_ldg_c\XINT_ldg_b#2}%
\def\XINT_ldg_b#1#2#3#4#5#6#7#8#9{#9#8#7#6#5#4#3#2#1*\xint_c_+\XINT_ldg_a#9}%
\def\XINT_ldg_c #1#2\xint_bye{#1}%
@@ -416,8 +297,10 @@
\krof #1%
}%
\def\XINT_dbl_neg-{\expandafter-\romannumeral0\XINT_dbl}%
-\def\XINT_dbl #1#2#3#4#5#6#7#8%
- {\expandafter\space\the\numexpr#1#2#3#4#5#6#7#8\XINT_dbl_a}%
+\def\XINT_dbl #1{%
+\def\XINT_dbl ##1##2##3##4##5##6##7##8%
+ {\expandafter#1\the\numexpr##1##2##3##4##5##6##7##8\XINT_dbl_a}%
+}\XINT_dbl{ }%
\def\XINT_dbl_a #1#2#3#4#5#6#7#8%
{\expandafter\XINT_dbl_e\the\numexpr 1#1#2#3#4#5#6#7#8\XINT_dbl_a}%
\def\XINT_dbl_e#1{*\xint_c_ii\if#13+\xint_c_i\fi\relax}%
@@ -433,8 +316,10 @@
\krof #1%
}%
\def\XINT_half_neg-{\xintiiopp\XINT_half}%
-\def\XINT_half #1#2#3#4#5#6#7#8%
- {\expandafter\space\the\numexpr(#1#2#3#4#5#6#7#8\XINT_half_a}%
+\def\XINT_half #1{%
+\def\XINT_half ##1##2##3##4##5##6##7##8%
+ {\expandafter#1\the\numexpr(##1##2##3##4##5##6##7##8\XINT_half_a}%
+}\XINT_half{ }%
\def\XINT_half_a#1{\xint_Bye#1\xint_bye\XINT_half_b#1}%
\def\XINT_half_b #1#2#3#4#5#6#7#8%
{\expandafter\XINT_half_e\the\numexpr(1#1#2#3#4#5#6#7#8\XINT_half_a}%
@@ -451,8 +336,10 @@
}%
\def\XINT_inc_neg-#1\xint_bye#2\relax
{\xintiiopp\XINT_dec #1\XINT_dec_bye234567890\xint_bye}%
-\def\XINT_inc #1#2#3#4#5#6#7#8#9%
- {\expandafter\space\the\numexpr#1#2#3#4#5#6#7#8#9\XINT_inc_a}%
+\def\XINT_inc #1{%
+\def\XINT_inc ##1##2##3##4##5##6##7##8##9%
+ {\expandafter#1\the\numexpr##1##2##3##4##5##6##7##8##9\XINT_inc_a}%
+}\XINT_inc{ }%
\def\XINT_inc_a #1#2#3#4#5#6#7#8#9%
{\expandafter\XINT_inc_e\the\numexpr 1#1#2#3#4#5#6#7#8#9\XINT_inc_a}%
\def\XINT_inc_e#1{\if#12+\xint_c_i\fi\relax}%
@@ -469,8 +356,10 @@
\def\XINT_dec_neg-#1\XINT_dec_bye#2\xint_bye
{\expandafter-%
\romannumeral0\XINT_inc #1\xint_bye23456789\xint_bye+\xint_c_i\relax}%
-\def\XINT_dec #1#2#3#4#5#6#7#8#9%
- {\expandafter\space\the\numexpr#1#2#3#4#5#6#7#8#9\XINT_dec_a}%
+\def\XINT_dec #1{%
+\def\XINT_dec ##1##2##3##4##5##6##7##8##9%
+ {\expandafter#1\the\numexpr##1##2##3##4##5##6##7##8##9\XINT_dec_a}%
+}\XINT_dec{ }%
\def\XINT_dec_a #1#2#3#4#5#6#7#8#9%
{\expandafter\XINT_dec_e\the\numexpr 1#1#2#3#4#5#6#7#8#9\XINT_dec_a}%
\def\XINT_dec_bye #1\XINT_dec_a#2#3\xint_bye
@@ -478,8 +367,9 @@
\def\XINT_dec_e#1{\unless\if#11\xint_dothis{-\xint_c_i#1}\fi\xint_orthat\relax}%
\def\xintDSL {\romannumeral0\xintdsl }%
\def\xintdsl #1{\expandafter\XINT_dsl\romannumeral`&&@#10}%
-\edef\XINT_dsl #1%
- {\noexpand\xint_gob_til_zero #1\noexpand\xint_dsl_zero 0\space #1}%
+\def\XINT_dsl#1{%
+\def\XINT_dsl ##1{\xint_gob_til_zero ##1\xint_dsl_zero 0#1##1}%
+}\XINT_dsl{ }%
\def\xint_dsl_zero 0 0{ }%
\def\xintDSR{\romannumeral0\xintdsr}%
\def\xintdsr #1{\expandafter\XINT_dsr_fork\romannumeral`&&@#1%
@@ -492,8 +382,10 @@
\krof #1%
}%
\def\XINT_dsr_neg-{\xintiiopp\XINT_dsr}%
-\def\XINT_dsr #1#2#3#4#5#6#7#8#9%
- {\expandafter\space\the\numexpr(#1#2#3#4#5#6#7#8#9\XINT_dsr_a}%
+\def\XINT_dsr #1{%
+\def\XINT_dsr ##1##2##3##4##5##6##7##8##9%
+ {\expandafter#1\the\numexpr(##1##2##3##4##5##6##7##8##9\XINT_dsr_a}%
+}\XINT_dsr{ }%
\def\XINT_dsr_a#1{\xint_Bye#1\xint_bye\XINT_dsr_b#1}%
\def\XINT_dsr_b #1#2#3#4#5#6#7#8#9%
{\expandafter\XINT_dsr_e\the\numexpr(1#1#2#3#4#5#6#7#8#9\XINT_dsr_a}%
@@ -509,25 +401,192 @@
\krof #1%
}%
\def\XINT_dsrr_neg-{\xintiiopp\XINT_dsrr}%
-\def\XINT_dsrr #1#2#3#4#5#6#7#8#9%
- {\expandafter\space\the\numexpr#1#2#3#4#5#6#7#8#9\XINT_dsrr_a}%
+\def\XINT_dsrr #1{%
+\def\XINT_dsrr ##1##2##3##4##5##6##7##8##9%
+ {\expandafter#1\the\numexpr##1##2##3##4##5##6##7##8##9\XINT_dsrr_a}%
+}\XINT_dsrr{ }%
\def\XINT_dsrr_a#1{\xint_Bye#1\xint_bye\XINT_dsrr_b#1}%
\def\XINT_dsrr_b #1#2#3#4#5#6#7#8#9%
{\expandafter\XINT_dsrr_e\the\numexpr1#1#2#3#4#5#6#7#8#9\XINT_dsrr_a}%
\let\XINT_dsrr_e\XINT_inc_e
+\def\XINT_cuz #1{%
+\def\XINT_cuz {\expandafter#1\the\numexpr\XINT_cuz_loop}%
+}\XINT_cuz{ }%
+\def\XINT_cuz_loop #1#2#3#4#5#6#7#8#9%
+{%
+ #1#2#3#4#5#6#7#8%
+ \xint_gob_til_R #9\XINT_cuz_hitend\R
+ \ifnum #1#2#3#4#5#6#7#8>\xint_c_
+ \expandafter\XINT_cuz_cleantoend
+ \else\expandafter\XINT_cuz_loop
+ \fi #9%
+}%
+\def\XINT_cuz_hitend\R #1\R{\relax}%
+\def\XINT_cuz_cleantoend #1\R{\relax #1}%
+\def\XINT_cuz_byviii #1#2#3#4#5#6#7#8#9%
+{%
+ \xint_gob_til_R #9\XINT_cuz_byviii_e \R
+ \xint_gob_til_eightzeroes #1#2#3#4#5#6#7#8\XINT_cuz_byviii_z 00000000%
+ \XINT_cuz_byviii_done #1#2#3#4#5#6#7#8#9%
+}%
+\def\XINT_cuz_byviii_z 00000000\XINT_cuz_byviii_done 00000000{\XINT_cuz_byviii}%
+\def\XINT_cuz_byviii_done #1\R { #1}%
+\def\XINT_cuz_byviii_e\R #1\XINT_cuz_byviii_done #2\R{ #2}%
+\def\XINT_unsep_loop #1!#2!#3!#4!#5!#6!#7!#8!#9!%
+{%
+ \expandafter\XINT_unsep_clean
+ \the\numexpr #1\expandafter\XINT_unsep_clean
+ \the\numexpr #2\expandafter\XINT_unsep_clean
+ \the\numexpr #3\expandafter\XINT_unsep_clean
+ \the\numexpr #4\expandafter\XINT_unsep_clean
+ \the\numexpr #5\expandafter\XINT_unsep_clean
+ \the\numexpr #6\expandafter\XINT_unsep_clean
+ \the\numexpr #7\expandafter\XINT_unsep_clean
+ \the\numexpr #8\expandafter\XINT_unsep_clean
+ \the\numexpr #9\XINT_unsep_loop
+}%
+\def\XINT_unsep_clean 1{\relax}%
+\def\XINT_unsep_cuzsmall
+{%
+ \expandafter\XINT_unsep_cuzsmall_x\the\numexpr0\XINT_unsep_loop
+}%
+\def\XINT_unsep_cuzsmall_x #1{%
+\def\XINT_unsep_cuzsmall_x 0##1##2##3##4##5##6##7##8%
+{%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8\relax
+}}\XINT_unsep_cuzsmall_x{ }%
+\def\XINT_div_unsepQ_delim {\xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax\Z}%
+\def\XINT_div_unsepQ
+{%
+ \expandafter\XINT_div_unsepQ_x\the\numexpr0\XINT_unsep_loop
+}%
+\def\XINT_div_unsepQ_x #1{%
+\def\XINT_div_unsepQ_x 0##1##2##3##4##5##6##7##8##9%
+{%
+ \xint_gob_til_Z ##9\XINT_div_unsepQ_one\Z
+ \xint_gob_til_eightzeroes ##1##2##3##4##5##6##7##8\XINT_div_unsepQ_y 00000000%
+ \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8\relax ##9%
+}}\XINT_div_unsepQ_x{ }%
+\def\XINT_div_unsepQ_y #1{%
+\def\XINT_div_unsepQ_y ##1\relax ##2##3##4##5##6##7##8##9%
+{%
+ \expandafter#1\the\numexpr ##2##3##4##5##6##7##8##9\relax
+}}\XINT_div_unsepQ_y{ }%
+\def\XINT_div_unsepQ_one#1\expandafter{\expandafter}%
+\def\XINT_div_unsepR
+{%
+ \expandafter\XINT_div_unsepR_x\the\numexpr0\XINT_unsep_loop
+}%
+\def\XINT_div_unsepR_x#1{%
+\def\XINT_div_unsepR_x 0{\expandafter#1\the\numexpr\XINT_cuz_loop}%
+}\XINT_div_unsepR_x{ }%
+\def\XINT_zeroes_forviii #1#2#3#4#5#6#7#8%
+{%
+ \xint_gob_til_R #8\XINT_zeroes_forviii_end\R\XINT_zeroes_forviii
+}%
+\def\XINT_zeroes_forviii_end#1{%
+\def\XINT_zeroes_forviii_end\R\XINT_zeroes_forviii ##1##2##3##4##5##6##7##8##9\W
+{%
+ \expandafter#1\xint_gob_til_one ##2##3##4##5##6##7##8%
+}}\XINT_zeroes_forviii_end{ }%
+\def\XINT_sepbyviii_Z #1#2#3#4#5#6#7#8%
+{%
+ 1#1#2#3#4#5#6#7#8\expandafter!\the\numexpr\XINT_sepbyviii_Z
+}%
+\def\XINT_sepbyviii_Z_end #1\relax {;!}%
+\def\XINT_sepbyviii_andcount
+{%
+ \expandafter\XINT_sepbyviii_andcount_a\the\numexpr\XINT_sepbyviii
+}%
+\def\XINT_sepbyviii #1#2#3#4#5#6#7#8%
+{%
+ 1#1#2#3#4#5#6#7#8\expandafter!\the\numexpr\XINT_sepbyviii
+}%
+\def\XINT_sepbyviii_end #1\relax {\relax\XINT_sepbyviii_andcount_end!}%
+\def\XINT_sepbyviii_andcount_a {\XINT_sepbyviii_andcount_b \xint_c_\xint:}%
+\def\XINT_sepbyviii_andcount_b #1\xint:#2!#3!#4!#5!#6!#7!#8!#9!%
+{%
+ #2\expandafter!\the\numexpr#3\expandafter!\the\numexpr#4\expandafter
+ !\the\numexpr#5\expandafter!\the\numexpr#6\expandafter!\the\numexpr
+ #7\expandafter!\the\numexpr#8\expandafter!\the\numexpr#9\expandafter!\the\numexpr
+ \expandafter\XINT_sepbyviii_andcount_b\the\numexpr #1+\xint_c_viii\xint:%
+}%
+\def\XINT_sepbyviii_andcount_end #1\XINT_sepbyviii_andcount_b\the\numexpr
+ #2+\xint_c_viii\xint:#3#4\W {\expandafter\xint:\the\numexpr #2+#3\xint:}%
+\def\XINT_rsepbyviii #1#2#3#4#5#6#7#8%
+{%
+ \XINT_rsepbyviii_b {#1#2#3#4#5#6#7#8}%
+}%
+\def\XINT_rsepbyviii_b #1#2#3#4#5#6#7#8#9%
+{%
+ #2#3#4#5#6#7#8#9\expandafter!\the\numexpr
+ 1#1\expandafter\xint:\the\numexpr 1\XINT_rsepbyviii
+}%
+\def\XINT_rsepbyviii_end_B #1\relax #2#3{#2\xint:}%
+\def\XINT_rsepbyviii_end_A #11#2\expandafter #3\relax #4#5{#5!1#2\xint:}%
+\def\XINT_sepandrev
+{%
+ \expandafter\XINT_sepandrev_a\the\numexpr 1\XINT_rsepbyviii
+}%
+\def\XINT_sepandrev_a {\XINT_sepandrev_b {}}%
+\def\XINT_sepandrev_b #1#2\xint:#3\xint:#4\xint:#5\xint:#6\xint:#7\xint:#8\xint:#9\xint:%
+{%
+ \xint_gob_til_R #9\XINT_sepandrev_end\R
+ \XINT_sepandrev_b {#9!#8!#7!#6!#5!#4!#3!#2!#1}%
+}%
+\def\XINT_sepandrev_end\R\XINT_sepandrev_b #1#2\W {\XINT_sepandrev_done #1}%
+\def\XINT_sepandrev_done #11#2!{ }%
+\def\XINT_sepandrev_andcount
+{%
+ \expandafter\XINT_sepandrev_andcount_a\the\numexpr 1\XINT_rsepbyviii
+}%
+\def\XINT_sepandrev_andcount_a {\XINT_sepandrev_andcount_b 0!{}}%
+\def\XINT_sepandrev_andcount_b #1!#2#3\xint:#4\xint:#5\xint:#6\xint:#7\xint:#8\xint:#9\xint:%
+{%
+ \xint_gob_til_R #9\XINT_sepandrev_andcount_end\R
+ \expandafter\XINT_sepandrev_andcount_b \the\numexpr #1+\xint_c_i!%
+ {#9!#8!#7!#6!#5!#4!#3!#2}%
+}%
+\def\XINT_sepandrev_andcount_end\R
+ \expandafter\XINT_sepandrev_andcount_b\the\numexpr #1+\xint_c_i!#2#3#4\W
+{\expandafter\XINT_sepandrev_andcount_done\the\numexpr #3+\xint_c_xiv*#1!#2}%
+\def\XINT_sepandrev_andcount_done#1{%
+\def\XINT_sepandrev_andcount_done##1!##21##3!{\expandafter#1\the\numexpr##1-##3\xint:}%
+}\XINT_sepandrev_andcount_done{ }%
+\def\XINT_rev_nounsep #1#2!#3!#4!#5!#6!#7!#8!#9!%
+{%
+ \xint_gob_til_R #9\XINT_rev_nounsep_end\R
+ \XINT_rev_nounsep {#9!#8!#7!#6!#5!#4!#3!#2!#1}%
+}%
+\def\XINT_rev_nounsep_end\R\XINT_rev_nounsep #1#2\W {\XINT_rev_nounsep_done #1}%
+\def\XINT_rev_nounsep_done #11{ 1}%
+\def\XINT_unrevbyviii #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
+{%
+ \xint_gob_til_R #9\XINT_unrevbyviii_a\R
+ \XINT_unrevbyviii {#9#8#7#6#5#4#3#2#1}%
+}%
+\def\XINT_unrevbyviii_a#1{%
+\def\XINT_unrevbyviii_a\R\XINT_unrevbyviii ##1##2\W
+ {\expandafter#1\romannumeral`&&@\xint_gob_til_sc ##1}%
+}\XINT_unrevbyviii_a{ }%
+\def\XINT_smallunrevbyviii 1#1!1#2!1#3!1#4!1#5!1#6!1#7!1#8!#9\W%
+{%
+ \expandafter\XINT_cuz_small\xint_gob_til_sc #8#7#6#5#4#3#2#1%
+}%
\def\xintiAdd {\romannumeral0\xintiadd }%
-\def\xintiadd #1{\expandafter\XINT_iadd\romannumeral0\xintnum{#1}\Z }%
+\def\xintiadd #1{\expandafter\XINT_iadd\romannumeral0\xintnum{#1}\xint:}%
\def\xintiiAdd {\romannumeral0\xintiiadd }%
-\def\xintiiadd #1{\expandafter\XINT_iiadd\romannumeral`&&@#1\Z }%
-\def\XINT_iiadd #1#2\Z #3%
+\def\xintiiadd #1{\expandafter\XINT_iiadd\romannumeral`&&@#1\xint:}%
+\def\XINT_iiadd #1#2\xint:#3%
{%
- \expandafter\XINT_add_nfork\expandafter #1\romannumeral`&&@#3\Z #2\Z
+ \expandafter\XINT_add_nfork\expandafter#1\romannumeral`&&@#3\xint:#2\xint:
}%
-\def\XINT_iadd #1#2\Z #3%
+\def\XINT_iadd #1#2\xint:#3%
{%
- \expandafter\XINT_add_nfork\expandafter #1\romannumeral0\xintnum{#3}\Z #2\Z
+ \expandafter\XINT_add_nfork\expandafter
+ #1\romannumeral0\xintnum{#3}\xint:#2\xint:
}%
-\def\XINT_add_fork #1#2\Z #3\Z {\XINT_add_nfork #1#3\Z #2\Z}%
+\def\XINT_add_fork #1#2\xint:#3\xint:{\XINT_add_nfork #1#3\xint:#2\xint:}%
\def\XINT_add_nfork #1#2%
{%
\xint_UDzerofork
@@ -542,39 +601,39 @@
--\XINT_add_plusplus
\krof #1#2%
}%
-\def\XINT_add_firstiszero #1\krof 0#2#3\Z #4\Z { #2#3}%
-\def\XINT_add_secondiszero #1\krof #20#3\Z #4\Z { #2#4}%
+\def\XINT_add_firstiszero #1\krof 0#2#3\xint:#4\xint:{ #2#3}%
+\def\XINT_add_secondiszero #1\krof #20#3\xint:#4\xint:{ #2#4}%
\def\XINT_add_minusminus #1#2%
{\expandafter-\romannumeral0\XINT_add_pp_a {}{}}%
\def\XINT_add_minusplus #1#2{\XINT_sub_mm_a {}#2}%
\def\XINT_add_plusminus #1#2%
{\expandafter\XINT_opp\romannumeral0\XINT_sub_mm_a #1{}}%
-\def\XINT_add_pp_a #1#2#3\Z
+\def\XINT_add_pp_a #1#2#3\xint:
{%
\expandafter\XINT_add_pp_b
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
#2#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\X #1%
}%
\let\XINT_add_plusplus \XINT_add_pp_a
-\def\XINT_add_pp_b #1.#2\X #3\Z
+\def\XINT_add_pp_b #1\xint:#2\X #3\xint:
{%
\expandafter\XINT_add_checklengths
- \the\numexpr #1\expandafter.%
+ \the\numexpr #1\expandafter\xint:%
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
- 1\Z!1\Z!1\Z!1\Z!\W #21\Z!1\Z!1\Z!1\Z!\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
+ 1;!1;!1;!1;!\W #21;!1;!1;!1;!\W
1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
}%
-\def\XINT_add_checklengths #1.#2.%
+\def\XINT_add_checklengths #1\xint:#2\xint:%
{%
\ifnum #2>#1
\expandafter\XINT_add_exchange
@@ -581,13 +640,13 @@
\else
\expandafter\XINT_add_A
\fi
- #1.#2.%
+ #1\xint:#2\xint:%
}%
-\def\XINT_add_exchange #1.#2.#3\W #4\W
+\def\XINT_add_exchange #1\xint:#2\xint:#3\W #4\W
{%
- \XINT_add_A #2.#1.#4\W #3\W
+ \XINT_add_A #2\xint:#1\xint:#4\W #3\W
}%
-\def\XINT_add_A #1.#2.%
+\def\XINT_add_A #1\xint:#2\xint:%
{%
\ifnum #1>\xint_c_vi
\expandafter\XINT_add_aa
@@ -598,85 +657,194 @@
\def\XINT_add_out{\expandafter\XINT_cuz_small\romannumeral0\XINT_unrevbyviii {}}%
\def\XINT_add_aa_small
{\expandafter\XINT_smallunrevbyviii\the\numexpr\XINT_add_a \xint_c_ii}%
-\def\XINT_add_a #1!#2!#3!#4!#5\W #6!#7!#8!#9!%
+\def\XINT_add_a #1!#2!#3!#4!#5\W
+ #6!#7!#8!#9!%
{%
- \XINT_add_b #1!#6!#2!#7!#3!#8!#4!#9!#5\W
+ \XINT_add_b
+ #1!#6!#2!#7!#3!#8!#4!#9!%
+ #5\W
}%
\def\XINT_add_b #11#2#3!#4!%
{%
- \xint_gob_til_Z #2\XINT_add_bi \Z
- \expandafter\XINT_add_c\the\numexpr#1+1#2#3+#4-\xint_c_ii.%
+ \xint_gob_til_sc #2\XINT_add_bi ;%
+ \expandafter\XINT_add_c\the\numexpr#1+1#2#3+#4-\xint_c_ii\xint:%
}%
-\def\XINT_add_bi\Z\expandafter\XINT_add_c
- \the\numexpr#1+#2+#3-\xint_c_ii.#4!#5!#6!#7!#8!#9!\W
+\def\XINT_add_bi;\expandafter\XINT_add_c
+ \the\numexpr#1+#2+#3-\xint_c_ii\xint:#4!#5!#6!#7!#8!#9!\W
{%
\XINT_add_k #1#3!#5!#7!#9!%
}%
-\def\XINT_add_c #1#2.%
+\def\XINT_add_c #1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_add_d #1%
}%
\def\XINT_add_d #11#2#3!#4!%
{%
- \xint_gob_til_Z #2\XINT_add_di \Z
- \expandafter\XINT_add_e\the\numexpr#1+1#2#3+#4-\xint_c_ii.%
+ \xint_gob_til_sc #2\XINT_add_di ;%
+ \expandafter\XINT_add_e\the\numexpr#1+1#2#3+#4-\xint_c_ii\xint:%
}%
-\def\XINT_add_di\Z\expandafter\XINT_add_e
- \the\numexpr#1+#2+#3-\xint_c_ii.#4!#5!#6!#7!#8\W
+\def\XINT_add_di;\expandafter\XINT_add_e
+ \the\numexpr#1+#2+#3-\xint_c_ii\xint:#4!#5!#6!#7!#8\W
{%
\XINT_add_k #1#3!#5!#7!%
}%
-\def\XINT_add_e #1#2.%
+\def\XINT_add_e #1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_add_f #1%
}%
\def\XINT_add_f #11#2#3!#4!%
{%
- \xint_gob_til_Z #2\XINT_add_fi \Z
- \expandafter\XINT_add_g\the\numexpr#1+1#2#3+#4-\xint_c_ii.%
+ \xint_gob_til_sc #2\XINT_add_fi ;%
+ \expandafter\XINT_add_g\the\numexpr#1+1#2#3+#4-\xint_c_ii\xint:%
}%
-\def\XINT_add_fi\Z\expandafter\XINT_add_g
- \the\numexpr#1+#2+#3-\xint_c_ii.#4!#5!#6\W
+\def\XINT_add_fi;\expandafter\XINT_add_g
+ \the\numexpr#1+#2+#3-\xint_c_ii\xint:#4!#5!#6\W
{%
\XINT_add_k #1#3!#5!%
}%
-\def\XINT_add_g #1#2.%
+\def\XINT_add_g #1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_add_h #1%
}%
\def\XINT_add_h #11#2#3!#4!%
{%
- \xint_gob_til_Z #2\XINT_add_hi \Z
- \expandafter\XINT_add_i\the\numexpr#1+1#2#3+#4-\xint_c_ii.%
+ \xint_gob_til_sc #2\XINT_add_hi ;%
+ \expandafter\XINT_add_i\the\numexpr#1+1#2#3+#4-\xint_c_ii\xint:%
}%
-\def\XINT_add_hi\Z
- \expandafter\XINT_add_i\the\numexpr#1+#2+#3-\xint_c_ii.#4\W
+\def\XINT_add_hi;%
+ \expandafter\XINT_add_i\the\numexpr#1+#2+#3-\xint_c_ii\xint:#4\W
{%
\XINT_add_k #1#3!%
}%
-\def\XINT_add_i #1#2.%
+\def\XINT_add_i #1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_add_a #1%
}%
\def\XINT_add_k #1{\if #12\expandafter\XINT_add_ke\else\expandafter\XINT_add_l \fi}%
-\def\XINT_add_ke #11\Z #2\W {\XINT_add_kf #11\Z!}%
+\def\XINT_add_ke #11;#2\W {\XINT_add_kf #11;!}%
\def\XINT_add_kf 1{1\relax }%
-\def\XINT_add_l 1#1#2{\xint_gob_til_Z #1\XINT_add_lf \Z \XINT_add_m 1#1#2}%
-\def\XINT_add_lf #1\W {1\relax 00000001!1\Z!}%
-\def\XINT_add_m #1!{\expandafter\XINT_add_n\the\numexpr\xint_c_i+#1.}%
-\def\XINT_add_n #1#2.{1#2\expandafter!\the\numexpr\XINT_add_o #1}%
+\def\XINT_add_l 1#1#2{\xint_gob_til_sc #1\XINT_add_lf ;\XINT_add_m 1#1#2}%
+\def\XINT_add_lf #1\W {1\relax 00000001!1;!}%
+\def\XINT_add_m #1!{\expandafter\XINT_add_n\the\numexpr\xint_c_i+#1\xint:}%
+\def\XINT_add_n #1#2\xint:{1#2\expandafter!\the\numexpr\XINT_add_o #1}%
\def\XINT_add_o #1{\if #12\expandafter\XINT_add_l\else\expandafter\XINT_add_ke \fi}%
+\def\xintCmp {\romannumeral0\xintcmp }%
+\def\xintcmp #1{\expandafter\XINT_icmp\romannumeral0\xintnum{#1}\xint:}%
+\def\xintiiCmp {\romannumeral0\xintiicmp }%
+\def\xintiicmp #1{\expandafter\XINT_iicmp\romannumeral`&&@#1\xint:}%
+\def\XINT_iicmp #1#2\xint:#3%
+{%
+ \expandafter\XINT_cmp_nfork\expandafter #1\romannumeral`&&@#3\xint:#2\xint:
+}%
+\def\XINT_icmp #1#2\xint:#3%
+{%
+ \expandafter\XINT_cmp_nfork\expandafter #1\romannumeral0\xintnum{#3}\xint:#2\xint:
+}%
+\def\XINT_cmp_nfork #1#2%
+{%
+ \xint_UDzerofork
+ #1\XINT_cmp_firstiszero
+ #2\XINT_cmp_secondiszero
+ 0{}%
+ \krof
+ \xint_UDsignsfork
+ #1#2\XINT_cmp_minusminus
+ #1-\XINT_cmp_minusplus
+ #2-\XINT_cmp_plusminus
+ --\XINT_cmp_plusplus
+ \krof #1#2%
+}%
+\def\XINT_cmp_firstiszero #1\krof 0#2#3\xint:#4\xint:
+{%
+ \xint_UDzerominusfork
+ #2-{ 0}%
+ 0#2{ 1}%
+ 0-{ -1}%
+ \krof
+}%
+\def\XINT_cmp_secondiszero #1\krof #20#3\xint:#4\xint:
+{%
+ \xint_UDzerominusfork
+ #2-{ 0}%
+ 0#2{ -1}%
+ 0-{ 1}%
+ \krof
+}%
+\def\XINT_cmp_plusminus #1\xint:#2\xint:{ 1}%
+\def\XINT_cmp_minusplus #1\xint:#2\xint:{ -1}%
+\def\XINT_cmp_minusminus
+ --{\expandafter\XINT_opp\romannumeral0\XINT_cmp_plusplus {}{}}%
+\def\XINT_cmp_plusplus #1#2#3\xint:
+{%
+ \expandafter\XINT_cmp_pp
+ \the\numexpr\expandafter\XINT_sepbyviii_andcount
+ \romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
+ #2#3\XINT_sepbyviii_end 2345678\relax
+ \xint_c_vii!\xint_c_vi!\xint_c_v!\xint_c_iv!%
+ \xint_c_iii!\xint_c_ii!\xint_c_i!\xint_c_\W
+ #1%
+}%
+\def\XINT_cmp_pp #1\xint:#2\xint:#3\xint:
+{%
+ \expandafter\XINT_cmp_checklengths
+ \the\numexpr #2\expandafter\xint:%
+ \the\numexpr\expandafter\XINT_sepbyviii_andcount
+ \romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
+ #3\XINT_sepbyviii_end 2345678\relax
+ \xint_c_vii!\xint_c_vi!\xint_c_v!\xint_c_iv!%
+ \xint_c_iii!\xint_c_ii!\xint_c_i!\xint_c_\W
+ #1;!1;!1;!1;!\W
+}%
+\def\XINT_cmp_checklengths #1\xint:#2\xint:#3\xint:
+{%
+ \ifnum #1=#3
+ \expandafter\xint_firstoftwo
+ \else
+ \expandafter\xint_secondoftwo
+ \fi
+ \XINT_cmp_a {\XINT_cmp_distinctlengths {#1}{#3}}#2;!1;!1;!1;!\W
+}%
+\def\XINT_cmp_distinctlengths #1#2#3\W #4\W
+{%
+ \ifnum #1>#2
+ \expandafter\xint_firstoftwo
+ \else
+ \expandafter\xint_secondoftwo
+ \fi
+ { -1}{ 1}%
+}%
+\def\XINT_cmp_a 1#1!1#2!1#3!1#4!#5\W 1#6!1#7!1#8!1#9!%
+{%
+ \xint_gob_til_sc #1\XINT_cmp_equal ;%
+ \ifnum #1>#6 \XINT_cmp_gt\fi
+ \ifnum #1<#6 \XINT_cmp_lt\fi
+ \xint_gob_til_sc #2\XINT_cmp_equal ;%
+ \ifnum #2>#7 \XINT_cmp_gt\fi
+ \ifnum #2<#7 \XINT_cmp_lt\fi
+ \xint_gob_til_sc #3\XINT_cmp_equal ;%
+ \ifnum #3>#8 \XINT_cmp_gt\fi
+ \ifnum #3<#8 \XINT_cmp_lt\fi
+ \xint_gob_til_sc #4\XINT_cmp_equal ;%
+ \ifnum #4>#9 \XINT_cmp_gt\fi
+ \ifnum #4<#9 \XINT_cmp_lt\fi
+ \XINT_cmp_a #5\W
+}%
+\def\XINT_cmp_lt#1{\def\XINT_cmp_lt\fi ##1\W ##2\W {\fi#1-1}}\XINT_cmp_lt{ }%
+\def\XINT_cmp_gt#1{\def\XINT_cmp_gt\fi ##1\W ##2\W {\fi#11}}\XINT_cmp_gt{ }%
+\def\XINT_cmp_equal #1\W #2\W { 0}%
\def\xintiiSub {\romannumeral0\xintiisub }%
-\def\xintiisub #1{\expandafter\XINT_iisub\romannumeral`&&@#1\Z }%
-\def\XINT_iisub #1#2\Z #3%
+\def\xintiisub #1{\expandafter\XINT_iisub\romannumeral`&&@#1\xint:}%
+\def\XINT_iisub #1#2\xint:#3%
{%
- \expandafter\XINT_sub_nfork\expandafter #1\romannumeral`&&@#3\Z #2\Z
+ \expandafter\XINT_sub_nfork\expandafter
+ #1\romannumeral`&&@#3\xint:#2\xint:
}%
-\def\xintiSub {\romannumeral0\xintisub }%
-\def\xintisub #1{\expandafter\XINT_isub\romannumeral0\xintnum{#1}\Z }%
-\def\XINT_isub #1#2\Z #3%
+\def\xintiSub {\romannumeral0\xintisub }%
+\def\xintisub #1{\expandafter\XINT_isub\romannumeral0\xintnum{#1}\xint:}%
+\def\XINT_isub #1#2\xint:#3%
{%
- \expandafter\XINT_sub_nfork\expandafter #1\romannumeral0\xintnum{#3}\Z #2\Z
+ \expandafter\XINT_sub_nfork\expandafter
+ #1\romannumeral0\xintnum{#3}\xint:#2\xint:
}%
\def\XINT_sub_nfork #1#2%
{%
@@ -692,8 +860,8 @@
--\XINT_sub_plusplus
\krof #1#2%
}%
-\def\XINT_sub_firstiszero #1\krof 0#2#3\Z #4\Z {\XINT_opp #2#3}%
-\def\XINT_sub_secondiszero #1\krof #20#3\Z #4\Z { #2#4}%
+\def\XINT_sub_firstiszero #1\krof 0#2#3\xint:#4\xint:{\XINT_opp #2#3}%
+\def\XINT_sub_secondiszero #1\krof #20#3\xint:#4\xint:{ #2#4}%
\def\XINT_sub_plusminus #1#2{\XINT_add_pp_a #1{}}%
\def\XINT_sub_plusplus #1#2%
{\expandafter\XINT_opp\romannumeral0\XINT_sub_mm_a #1#2}%
@@ -700,30 +868,33 @@
\def\XINT_sub_minusplus #1#2%
{\expandafter-\romannumeral0\XINT_add_pp_a {}#2}%
\def\XINT_sub_minusminus #1#2{\XINT_sub_mm_a {}{}}%
-\def\XINT_sub_mm_a #1#2#3\Z
+\def\XINT_sub_mm_a #1#2#3\xint:
{%
\expandafter\XINT_sub_mm_b
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
#2#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\X #1%
}%
-\def\XINT_sub_mm_b #1.#2\X #3\Z
+\def\XINT_sub_mm_b #1\xint:#2\X #3\xint:
{%
\expandafter\XINT_sub_checklengths
- \the\numexpr #1\expandafter.%
+ \the\numexpr #1\expandafter\xint:%
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax \xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
- \Z!\Z!\Z!\Z!\W #2\Z!\Z!\Z!\Z!\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
+ 1;!1;!1;!1;!\W
+ #21;!1;!1;!1;!\W
+ 1;!1\R!1\R!1\R!1\R!%
+ 1\R!1\R!1\R!1\R!\W
}%
-\def\XINT_sub_checklengths #1.#2.%
+\def\XINT_sub_checklengths #1\xint:#2\xint:%
{%
\ifnum #2>#1
\expandafter\XINT_sub_exchange
@@ -735,146 +906,156 @@
{%
\expandafter\XINT_opp\romannumeral0\XINT_sub_aa #2\W #1\W
}%
-\def\XINT_sub_aa {\expandafter\XINT_sub_out\the\numexpr\XINT_sub_a \xint_c_i }%
-\def\XINT_sub_out #1\Z #2#3\W
+\def\XINT_sub_aa
{%
- \if-#2\expandafter\XINT_sub_startrescue\fi
- \expandafter\XINT_cuz_small
- \romannumeral0\XINT_unrevbyviii {}#11\Z!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+ \expandafter\XINT_sub_out\the\numexpr\XINT_sub_a\xint_c_i
}%
+\def\XINT_sub_out {\XINT_unrevbyviii{}}%
\def\XINT_sub_a #1!#2!#3!#4!#5\W #6!#7!#8!#9!%
{%
- \XINT_sub_b #1!#6!#2!#7!#3!#8!#4!#9!#5\W
+ \XINT_sub_b
+ #1!#6!#2!#7!#3!#8!#4!#9!%
+ #5\W
}%
-\def\XINT_sub_b #1#2#3!#4!%
+\def\XINT_sub_b #1#2#3#4!#5!%
{%
- \xint_gob_til_Z #2\XINT_sub_bi \Z
- \expandafter\XINT_sub_c\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \xint_gob_til_sc #3\XINT_sub_bi ;%
+ \expandafter\XINT_sub_c\the\numexpr#1+1#5-#3#4-\xint_c_i\xint:%
}%
-\def\XINT_sub_c 1#1#2.%
+\def\XINT_sub_c 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_sub_d #1%
}%
-\def\XINT_sub_d #1#2#3!#4!%
+\def\XINT_sub_d #1#2#3#4!#5!%
{%
- \xint_gob_til_Z #2\XINT_sub_di \Z
- \expandafter\XINT_sub_e\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \xint_gob_til_sc #3\XINT_sub_di ;%
+ \expandafter\XINT_sub_e\the\numexpr#1+1#5-#3#4-\xint_c_i\xint:
}%
-\def\XINT_sub_e 1#1#2.%
+\def\XINT_sub_e 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_sub_f #1%
}%
-\def\XINT_sub_f #1#2#3!#4!%
+\def\XINT_sub_f #1#2#3#4!#5!%
{%
- \xint_gob_til_Z #2\XINT_sub_fi \Z
- \expandafter\XINT_sub_g\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \xint_gob_til_sc #3\XINT_sub_fi ;%
+ \expandafter\XINT_sub_g\the\numexpr#1+1#5-#3#4-\xint_c_i\xint:
}%
-\def\XINT_sub_g 1#1#2.%
+\def\XINT_sub_g 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_sub_h #1%
}%
-\def\XINT_sub_h #1#2#3!#4!%
+\def\XINT_sub_h #1#2#3#4!#5!%
{%
- \xint_gob_til_Z #2\XINT_sub_hi \Z
- \expandafter\XINT_sub_i\the\numexpr#1+1#4-#3-\xint_c_i.%
+ \xint_gob_til_sc #3\XINT_sub_hi ;%
+ \expandafter\XINT_sub_i\the\numexpr#1+1#5-#3#4-\xint_c_i\xint:
}%
-\def\XINT_sub_i 1#1#2.%
+\def\XINT_sub_i 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_sub_a #1%
}%
-\def\XINT_sub_bi\Z
- \expandafter\XINT_sub_c\the\numexpr#1+1#2-#3.#4!#5!#6!#7!#8!#9!\W
+\def\XINT_sub_bi;%
+ \expandafter\XINT_sub_c\the\numexpr#1+1#2-#3\xint:
+ #4!#5!#6!#7!#8!#9!\W
{%
\XINT_sub_k #1#2!#5!#7!#9!%
}%
-\def\XINT_sub_di\Z
- \expandafter\XINT_sub_e\the\numexpr#1+1#2-#3.#4!#5!#6!#7!#8\W
+\def\XINT_sub_di;%
+ \expandafter\XINT_sub_e\the\numexpr#1+1#2-#3\xint:
+ #4!#5!#6!#7!#8\W
{%
\XINT_sub_k #1#2!#5!#7!%
}%
-\def\XINT_sub_fi\Z
- \expandafter\XINT_sub_g\the\numexpr#1+1#2-#3.#4!#5!#6\W
+\def\XINT_sub_fi;%
+ \expandafter\XINT_sub_g\the\numexpr#1+1#2-#3\xint:
+ #4!#5!#6\W
{%
\XINT_sub_k #1#2!#5!%
}%
-\def\XINT_sub_hi\Z
- \expandafter\XINT_sub_i\the\numexpr#1+1#2-#3.#4\W
+\def\XINT_sub_hi;%
+ \expandafter\XINT_sub_i\the\numexpr#1+1#2-#3\xint:
+ #4\W
{%
\XINT_sub_k #1#2!%
}%
-\def\XINT_sub_k #1#2%
+\def\XINT_sub_k #1#2#3%
{%
- \xint_gob_til_Z #2\XINT_sub_p\Z \XINT_sub_l #1#2%
+ \xint_gob_til_sc #3\XINT_sub_p;\XINT_sub_l #1#2#3%
}%
-\def\XINT_sub_l #1{\xint_UDzerofork #1\XINT_sub_l_carry 0\XINT_sub_l_nocarry\krof}%
-\def\XINT_sub_l_nocarry 1{1\relax }%
+\def\XINT_sub_l #1%
+ {\xint_UDzerofork #1\XINT_sub_l_carry 0\XINT_sub_l_Ia\krof}%
+\def\XINT_sub_l_Ia 1#1;!#2\W{1\relax#1;!1\XINT_sub_fix_none!}%
\def\XINT_sub_l_carry 1#1!{\ifcase #1
- \expandafter \XINT_sub_l_zeroa\or\expandafter\XINT_sub_l_one\else
- \expandafter \XINT_sub_l_done\fi 1#1!}%
-\def\XINT_sub_l_done {-\xint_c_i+}%
-\def\XINT_sub_l_one 1#1!#2%
+ \expandafter \XINT_sub_l_Id
+ \or \expandafter \XINT_sub_l_Ic
+ \else\expandafter \XINT_sub_l_Ib\fi 1#1!}%
+\def\XINT_sub_l_Ib #1;#2\W {-\xint_c_i+#1;!1\XINT_sub_fix_none!}%
+\def\XINT_sub_l_Ic 1#1!1#2#3!#4;#5\W
{%
- \xint_gob_til_Z #2\XINT_sub_l_oneone\Z 1\relax 00000000!#2%
+ \xint_gob_til_sc #2\XINT_sub_l_Ica;%
+ 1\relax 00000000!1#2#3!#4;!1\XINT_sub_fix_none!%
}%
-\def\XINT_sub_l_oneone #1\W {1\relax \XINT_cuz_byviii!\Z 0\W\R }%
-\def\XINT_sub_l_zeroa 1#1!{199999999\expandafter!\the\numexpr \XINT_sub_l_zerob }%
-\def\XINT_sub_l_zerob 1#1!{\ifcase #1
- \expandafter \XINT_sub_l_zeroa\or\expandafter\XINT_sub_l_zone\else
- \expandafter \XINT_sub_l_done\fi 1#1!}%
-\def\XINT_sub_l_zone 1#1!#2%
+\def\XINT_sub_l_Ica#1\W
{%
- \xint_gob_til_Z #2\XINT_sub_l_zoneone\Z 1\relax 00000000!#2%
+ 1;!1\XINT_sub_fix_cuz!%
+ 1;!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+ \xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
-\def\XINT_sub_l_zoneone\Z 1\relax 00000000{1}%
-\def\XINT_sub_p\Z\XINT_sub_l #1#2\W
+\def\XINT_sub_l_Id 1#1!%
+ {199999999\expandafter!\the\numexpr \XINT_sub_l_Id_a}%
+\def\XINT_sub_l_Id_a 1#1!{\ifcase #1
+ \expandafter \XINT_sub_l_Id
+ \or \expandafter \XINT_sub_l_Id_b
+ \else\expandafter \XINT_sub_l_Ib\fi 1#1!}%
+\def\XINT_sub_l_Id_b 1#1!1#2#3!#4;#5\W
{%
+ \xint_gob_til_sc #2\XINT_sub_l_Ida;%
+ 1\relax 00000000!1#2#3!#4;!1\XINT_sub_fix_none!%
+}%
+\def\XINT_sub_l_Ida#1\XINT_sub_fix_none{1;!1\XINT_sub_fix_none!}%
+\def\XINT_sub_p;\XINT_sub_l #1#2\W #3\W
+{%
\xint_UDzerofork
- #1{-1\relax\Z -\W}%
- 0{1\relax \XINT_cuz_byviii!\Z 0\W\R }%
+ #1{1;!1\XINT_sub_fix_neg!%
+ 1;!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+ \xint_bye2345678\xint_bye1099999988\relax}% A - B, B > A
+ 0{1;!1\XINT_sub_fix_cuz!%
+ 1;!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W}%
\krof
+ \xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
-\def\XINT_sub_startrescue\expandafter\XINT_cuz_small
- \romannumeral0\XINT_unrevbyviii #1#2\Z!#3\W
+\def\XINT_sub_fix_none;{\XINT_cuz_small}%
+\def\XINT_sub_fix_cuz ;{\expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop}%
+\def\XINT_sub_fix_neg;%
{%
- \expandafter\XINT_sub_rescue_finish
- \the\numexpr\XINT_sub_rescue_a #2!%
- 1\Z!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W \R
+ \expandafter-\romannumeral0\expandafter
+ \XINT_sub_comp_finish\the\numexpr\XINT_sub_comp_loop
}%
-\def\XINT_sub_rescue_finish
- {\expandafter-\romannumeral0\expandafter\XINT_cuz\romannumeral0\XINT_unrevbyviii {}}%
-\def\XINT_sub_rescue_a #1!%
+\def\XINT_sub_comp_finish 0{\XINT_sub_fix_cuz;}%
+\def\XINT_sub_comp_loop #1#2#3#4#5#6#7#8%
{%
- \expandafter\XINT_sub_rescue_c\the\numexpr \xint_c_xii_e_viii-#1.%
+ \expandafter\XINT_sub_comp_clean
+ \the\numexpr \xint_c_xi_e_viii_mone-#1#2#3#4#5#6#7#8\XINT_sub_comp_loop
}%
-\def\XINT_sub_rescue_c 1#1#2.%
-{%
- 1#2\expandafter!\the\numexpr\XINT_sub_rescue_d #1%
-}%
-\def\XINT_sub_rescue_d #1#2#3!%
-{%
- \xint_gob_til_minus #2\XINT_sub_rescue_z -%
- \expandafter\XINT_sub_rescue_c\the\numexpr \xint_c_xii_e_viii_mone-#2#3+#1.%
-}%
-\def\XINT_sub_rescue_z #1.{1!}%
+\def\XINT_sub_comp_clean 1#1{+#1\relax}%
\def\xintiMul {\romannumeral0\xintimul }%
\def\xintimul #1%
{%
- \expandafter\XINT_imul\romannumeral0\xintnum{#1}\Z
+ \expandafter\XINT_imul\romannumeral0\xintnum{#1}\xint:
}%
-\def\XINT_imul #1#2\Z #3%
+\def\XINT_imul #1#2\xint:#3%
{%
- \expandafter\XINT_mul_nfork\expandafter #1\romannumeral0\xintnum{#3}\Z #2\Z
+ \expandafter\XINT_mul_nfork\expandafter #1\romannumeral0\xintnum{#3}\xint:#2\xint:
}%
\def\xintiiMul {\romannumeral0\xintiimul }%
\def\xintiimul #1%
{%
- \expandafter\XINT_iimul\romannumeral`&&@#1\Z
+ \expandafter\XINT_iimul\romannumeral`&&@#1\xint:
}%
-\def\XINT_iimul #1#2\Z #3%
+\def\XINT_iimul #1#2\xint:#3%
{%
- \expandafter\XINT_mul_nfork\expandafter #1\romannumeral`&&@#3\Z #2\Z
+ \expandafter\XINT_mul_nfork\expandafter #1\romannumeral`&&@#3\xint:#2\xint:
}%
-\def\XINT_mul_fork #1#2\Z #3\Z{\XINT_mul_nfork #1#3\Z #2\Z}%
+\def\XINT_mul_fork #1#2\xint:#3\xint:{\XINT_mul_nfork #1#3\xint:#2\xint:}%
\def\XINT_mul_nfork #1#2%
{%
\xint_UDzerofork
@@ -889,37 +1070,37 @@
--\XINT_mul_plusplus
\krof #1#2%
}%
-\def\XINT_mul_zero #1\krof #2#3\Z #4\Z { 0}%
+\def\XINT_mul_zero #1\krof #2#3\xint:#4\xint:{ 0}%
\def\XINT_mul_minusminus #1#2{\XINT_mul_plusplus {}{}}%
\def\XINT_mul_minusplus #1#2%
{\expandafter-\romannumeral0\XINT_mul_plusplus {}#2}%
\def\XINT_mul_plusminus #1#2%
{\expandafter-\romannumeral0\XINT_mul_plusplus #1{}}%
-\def\XINT_mul_plusplus #1#2#3\Z
+\def\XINT_mul_plusplus #1#2#3\xint:
{%
\expandafter\XINT_mul_pre_b
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
#2#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\W #1%
}%
-\def\XINT_mul_pre_b #1.#2\W #3\Z
+\def\XINT_mul_pre_b #1\xint:#2\W #3\xint:
{%
\expandafter\XINT_mul_checklengths
- \the\numexpr #1\expandafter.%
+ \the\numexpr #1\expandafter\xint:%
\romannumeral0\expandafter\XINT_sepandrev_andcount
\romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
#3\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
- 1\Z!\W #21\Z!%
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
+ 1;!\W #21;!%
1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
}%
-\def\XINT_mul_checklengths #1.#2.%
+\def\XINT_mul_checklengths #1\xint:#2\xint:%
{%
\ifnum #2=\xint_c_i\expandafter\XINT_mul_smallbyfirst\fi
\ifnum #1=\xint_c_i\expandafter\XINT_mul_smallbysecond\fi
@@ -934,13 +1115,13 @@
\fi
\XINT_mul_start
}%
-\def\XINT_mul_smallbyfirst #1\XINT_mul_start 1#2!1\Z!\W
+\def\XINT_mul_smallbyfirst #1\XINT_mul_start 1#2!1;!\W
{%
\ifnum#2=\xint_c_i\expandafter\XINT_mul_oneisone\fi
\ifnum#2<\xint_c_xxii\expandafter\XINT_mul_verysmall\fi
\expandafter\XINT_mul_out\the\numexpr\XINT_smallmul 1#2!%
}%
-\def\XINT_mul_smallbysecond #1\XINT_mul_start #2\W 1#3!1\Z!%
+\def\XINT_mul_smallbysecond #1\XINT_mul_start #2\W 1#3!1;!%
{%
\ifnum#3=\xint_c_i\expandafter\XINT_mul_oneisone\fi
\ifnum#3<\xint_c_xxii\expandafter\XINT_mul_verysmall\fi
@@ -949,16 +1130,16 @@
\def\XINT_mul_oneisone #1!{\XINT_mul_out }%
\def\XINT_mul_verysmall\expandafter\XINT_mul_out
\the\numexpr\XINT_smallmul 1#1!%
- {\expandafter\XINT_mul_out\the\numexpr\XINT_verysmallmul 0.#1!}%
-\def\XINT_mul_exchange #1\XINT_mul_start #2\W #31\Z!%
- {\fi\fi\XINT_mul_start #31\Z!\W #2}%
+ {\expandafter\XINT_mul_out\the\numexpr\XINT_verysmallmul 0\xint:#1!}%
+\def\XINT_mul_exchange #1\XINT_mul_start #2\W #31;!%
+ {\fi\fi\XINT_mul_start #31;!\W #2}%
\def\XINT_mul_start
- {\expandafter\XINT_mul_out\the\numexpr\XINT_mul_loop 100000000!1\Z!\W}%
+ {\expandafter\XINT_mul_out\the\numexpr\XINT_mul_loop 100000000!1;!\W}%
\def\XINT_mul_out
{\expandafter\XINT_cuz_small\romannumeral0\XINT_unrevbyviii {}}%
\def\XINT_mul_loop #1\W #2\W 1#3!%
{%
- \xint_gob_til_Z #3\XINT_mul_e \Z
+ \xint_gob_til_sc #3\XINT_mul_e ;%
\expandafter\XINT_mul_a\the\numexpr \XINT_smallmul 1#3!#2\W
#1\W #2\W
}%
@@ -965,360 +1146,73 @@
\def\XINT_mul_a #1\W #2\W
{%
\expandafter\XINT_mul_b\the\numexpr
- \XINT_add_a \xint_c_ii #21\Z!1\Z!1\Z!\W #11\Z!1\Z!1\Z!\W\W
+ \XINT_add_a \xint_c_ii #21;!1;!1;!\W #11;!1;!1;!\W\W
}%
\def\XINT_mul_b 1#1!{1#1\expandafter!\the\numexpr\XINT_mul_loop }%
-\def\XINT_mul_e\Z #1\W 1#2\W #3\W {1\relax #2}%
-\def\XINT_minimulwc_a 1#1.#2.#3!#4#5#6#7#8.%
+\def\XINT_mul_e;#1\W 1#2\W #3\W {1\relax #2}%
+\def\XINT_minimulwc_a 1#1\xint:#2\xint:#3!#4#5#6#7#8\xint:%
{%
\expandafter\XINT_minimulwc_b
- \the\numexpr \xint_c_x^ix+#1+#3*#8.#3*#4#5#6#7+#2*#8.#2*#4#5#6#7.%
+ \the\numexpr \xint_c_x^ix+#1+#3*#8\xint:
+ #3*#4#5#6#7+#2*#8\xint:
+ #2*#4#5#6#7\xint:%
}%
-\def\XINT_minimulwc_b 1#1#2#3#4#5#6.#7.%
+\def\XINT_minimulwc_b 1#1#2#3#4#5#6\xint:#7\xint:%
{%
\expandafter\XINT_minimulwc_c
- \the\numexpr \xint_c_x^ix+#1#2#3#4#5+#7.#6.%
+ \the\numexpr \xint_c_x^ix+#1#2#3#4#5+#7\xint:#6\xint:%
}%
-\def\XINT_minimulwc_c 1#1#2#3#4#5#6.#7.#8.%
+\def\XINT_minimulwc_c 1#1#2#3#4#5#6\xint:#7\xint:#8\xint:%
{%
1#6#7\expandafter!%
\the\numexpr\expandafter\XINT_smallmul_a
- \the\numexpr \xint_c_x^viii+#1#2#3#4#5+#8.%
+ \the\numexpr \xint_c_x^viii+#1#2#3#4#5+#8\xint:%
}%
-\def\XINT_smallmul 1#1#2#3#4#5!{\XINT_smallmul_a 100000000.#1#2#3#4.#5!}%
-\def\XINT_smallmul_a #1.#2.#3!1#4!%
+\def\XINT_smallmul 1#1#2#3#4#5!{\XINT_smallmul_a 100000000\xint:#1#2#3#4\xint:#5!}%
+\def\XINT_smallmul_a #1\xint:#2\xint:#3!1#4!%
{%
- \xint_gob_til_Z #4\XINT_smallmul_e\Z
- \XINT_minimulwc_a #1.#2.#3!#4.#2.#3!%
+ \xint_gob_til_sc #4\XINT_smallmul_e;%
+ \XINT_minimulwc_a #1\xint:#2\xint:#3!#4\xint:#2\xint:#3!%
}%
-\def\XINT_smallmul_e\Z\XINT_minimulwc_a 1#1.#2\Z #3!%
- {\xint_gob_til_eightzeroes #1\XINT_smallmul_f 000000001\relax #1!1\Z!}%
+\def\XINT_smallmul_e;\XINT_minimulwc_a 1#1\xint:#2;#3!%
+ {\xint_gob_til_eightzeroes #1\XINT_smallmul_f 000000001\relax #1!1;!}%
\def\XINT_smallmul_f 000000001\relax 00000000!1{1\relax}%
-\def\XINT_verysmallmul #1.#2!1#3!%
+\def\XINT_verysmallmul #1\xint:#2!1#3!%
{%
- \xint_gob_til_Z #3\XINT_verysmallmul_e\Z
+ \xint_gob_til_sc #3\XINT_verysmallmul_e;%
\expandafter\XINT_verysmallmul_a
- \the\numexpr #2*#3+#1.#2!%
+ \the\numexpr #2*#3+#1\xint:#2!%
}%
-\def\XINT_verysmallmul_e\Z\expandafter\XINT_verysmallmul_a\the\numexpr
- #1+#2#3.#4!%
-{\xint_gob_til_zero #2\XINT_verysmallmul_f 0\xint_c_x^viii+#2#3!1\Z!}%
+\def\XINT_verysmallmul_e;\expandafter\XINT_verysmallmul_a\the\numexpr
+ #1+#2#3\xint:#4!%
+{\xint_gob_til_zero #2\XINT_verysmallmul_f 0\xint_c_x^viii+#2#3!1;!}%
\def\XINT_verysmallmul_f #1!1{1\relax}%
-\def\XINT_verysmallmul_a #1#2.%
+\def\XINT_verysmallmul_a #1#2\xint:%
{%
\unless\ifnum #1#2<\xint_c_x^ix
\expandafter\XINT_verysmallmul_bi\else
\expandafter\XINT_verysmallmul_bj\fi
- \the\numexpr \xint_c_x^ix+#1#2.%
+ \the\numexpr \xint_c_x^ix+#1#2\xint:%
}%
\def\XINT_verysmallmul_bj{\expandafter\XINT_verysmallmul_cj }%
-\def\XINT_verysmallmul_cj 1#1#2.%
- {1#2\expandafter!\the\numexpr\XINT_verysmallmul #1.}%
-\def\XINT_verysmallmul_bi\the\numexpr\xint_c_x^ix+#1#2#3.%
- {1#3\expandafter!\the\numexpr\XINT_verysmallmul #1#2.}%
-\def\XINT_minimul_a #1.#2!#3#4#5#6#7!%
+\def\XINT_verysmallmul_cj 1#1#2\xint:%
+ {1#2\expandafter!\the\numexpr\XINT_verysmallmul #1\xint:}%
+\def\XINT_verysmallmul_bi\the\numexpr\xint_c_x^ix+#1#2#3\xint:%
+ {1#3\expandafter!\the\numexpr\XINT_verysmallmul #1#2\xint:}%
+\def\XINT_minimul_a #1\xint:#2!#3#4#5#6#7!%
{%
\expandafter\XINT_minimul_b
- \the\numexpr \xint_c_x^viii+#2*#7.#2*#3#4#5#6+#1*#7.#1*#3#4#5#6.%
+ \the\numexpr \xint_c_x^viii+#2*#7\xint:#2*#3#4#5#6+#1*#7\xint:#1*#3#4#5#6\xint:%
}%
-\def\XINT_minimul_b 1#1#2#3#4#5.#6.%
+\def\XINT_minimul_b 1#1#2#3#4#5\xint:#6\xint:%
{%
\expandafter\XINT_minimul_c
- \the\numexpr \xint_c_x^ix+#1#2#3#4+#6.#5.%
+ \the\numexpr \xint_c_x^ix+#1#2#3#4+#6\xint:#5\xint:%
}%
-\def\XINT_minimul_c 1#1#2#3#4#5#6.#7.#8.%
+\def\XINT_minimul_c 1#1#2#3#4#5#6\xint:#7\xint:#8\xint:%
{%
1#6#7\expandafter!\the\numexpr \xint_c_x^viii+#1#2#3#4#5+#8!%
}%
-\def\xintiiSqr {\romannumeral0\xintiisqr }%
-\def\xintiisqr #1%
-{%
- \expandafter\XINT_sqr\romannumeral0\xintiiabs{#1}\Z
-}%
-\def\xintiSqr {\romannumeral0\xintisqr }%
-\def\xintisqr #1%
-{%
- \expandafter\XINT_sqr\romannumeral0\xintiabs{#1}\Z
-}%
-\def\XINT_sqr #1\Z
-{%
- \expandafter\XINT_sqr_a
- \romannumeral0\expandafter\XINT_sepandrev_andcount
- \romannumeral0\XINT_zeroes_forviii #1\R\R\R\R\R\R\R\R{10}0000001\W
- #1\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
- \Z
-}%
-\def\XINT_sqr_a #1.%
-{%
- \ifnum #1=\xint_c_i \expandafter\XINT_sqr_small
- \else\expandafter\XINT_sqr_start\fi
-}%
-\def\XINT_sqr_small 1#1#2#3#4#5!\Z
-{%
- \ifnum #1#2#3#4#5<46341 \expandafter\XINT_sqr_verysmall\fi
- \expandafter\XINT_sqr_small_out
- \the\numexpr\XINT_minimul_a #1#2#3#4.#5!#1#2#3#4#5!%
-}%
-\edef\XINT_sqr_verysmall
- \expandafter\XINT_sqr_small_out\the\numexpr\XINT_minimul_a #1!#2!%
- {\noexpand\expandafter\space\noexpand\the\numexpr #2*#2\relax}%
-\def\XINT_sqr_small_out 1#1!1#2!%
-{%
- \XINT_cuz #2#1\R
-}%
-\def\XINT_sqr_start #1\Z
-{%
- \expandafter\XINT_mul_out
- \the\numexpr\XINT_mul_loop 100000000!1\Z!\W #11\Z!\W #11\Z!%
- 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
-}%
-\def\xintiiPow {\romannumeral0\xintiipow }%
-\def\xintiipow #1#2%
-{%
- \expandafter\xint_pow\the\numexpr #2\expandafter.\romannumeral`&&@#1\Z%
-}%
-\def\xintiPow {\romannumeral0\xintipow }%
-\def\xintipow #1#2%
-{%
- \expandafter\xint_pow\the\numexpr #2\expandafter.\romannumeral0\xintnum{#1}\Z%
-}%
-\def\xint_pow #1.#2%#3\Z
-{%
- \xint_UDzerominusfork
- #2-\XINT_pow_AisZero
- 0#2\XINT_pow_Aneg
- 0-{\XINT_pow_Apos #2}%
- \krof {#1}%
-}%
-\def\XINT_pow_AisZero #1#2\Z
-{%
- \ifcase\XINT_cntSgn #1\Z
- \xint_afterfi { 1}%
- \or
- \xint_afterfi { 0}%
- \else
- \xint_afterfi {\xintError:DivisionByZero\space 0}%
- \fi
-}%
-\def\XINT_pow_Aneg #1%
-{%
- \ifodd #1
- \expandafter\XINT_opp\romannumeral0%
- \fi
- \XINT_pow_Apos {}{#1}%
-}%
-\def\XINT_pow_Apos #1#2{\XINT_pow_Apos_a {#2}#1}%
-\def\XINT_pow_Apos_a #1#2#3%
-{%
- \xint_gob_til_Z #3\XINT_pow_Apos_short\Z
- \XINT_pow_AatleastTwo {#1}#2#3%
-}%
-\def\XINT_pow_Apos_short\Z\XINT_pow_AatleastTwo #1#2\Z
-{%
- \ifcase #2
- \xintError:thiscannothappen!
- \or \expandafter\XINT_pow_AisOne
- \else\expandafter\XINT_pow_AatleastTwo
- \fi {#1}#2\Z
-}%
-\def\XINT_pow_AisOne #1\Z{ 1}%
-\def\XINT_pow_AatleastTwo #1%
-{%
- \ifcase\XINT_cntSgn #1\Z
- \expandafter\XINT_pow_BisZero
- \or
- \expandafter\XINT_pow_I_in
- \else
- \expandafter\XINT_pow_BisNegative
- \fi
- {#1}%
-}%
-\edef\XINT_pow_BisNegative #1\Z
- {\noexpand\xintError:FractionRoundedToZero\space 0}%
-\def\XINT_pow_BisZero #1\Z{ 1}%
-\def\XINT_pow_I_in #1#2\Z
-{%
- \expandafter\XINT_pow_I_loop
- \the\numexpr #1\expandafter.%
- \romannumeral0\expandafter\XINT_sepandrev
- \romannumeral0\XINT_zeroes_forviii #2\R\R\R\R\R\R\R\R{10}0000001\W
- #2\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678\relax XX%
- \R.\R.\R.\R.\R.\R.\R.\R.\W 1\Z!\W
- 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
-}%
-\def\XINT_pow_I_loop #1.%
-{%
- \ifnum #1 = \xint_c_i\expandafter\XINT_pow_I_exit\fi
- \ifodd #1
- \expandafter\XINT_pow_II_in
- \else
- \expandafter\XINT_pow_I_squareit
- \fi #1.%
-}%
-\def\XINT_pow_I_exit \ifodd #1\fi #2.#3\W {\XINT_mul_out #3}%
-\def\XINT_pow_I_squareit #1.#2\W%
-{%
- \expandafter\XINT_pow_I_loop
- \the\numexpr #1/\xint_c_ii\expandafter.%
- \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W
-}%
-\def\XINT_pow_mulbutcheckifsmall #1!1#2%
-{%
- \xint_gob_til_Z #2\XINT_pow_mul_small\Z
- \XINT_mul_loop 100000000!1\Z!\W #1!1#2%
-}%
-\def\XINT_pow_mul_small\Z \XINT_mul_loop 100000000!1\Z!\W 1#1!1\Z!\W
-{%
- \XINT_smallmul 1#1!%
-}%
-\def\XINT_pow_II_in #1.#2\W
-{%
- \expandafter\XINT_pow_II_loop
- \the\numexpr #1/\xint_c_ii-\xint_c_i\expandafter.%
- \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W #2\W
-}%
-\def\XINT_pow_II_loop #1.%
-{%
- \ifnum #1 = \xint_c_i\expandafter\XINT_pow_II_exit\fi
- \ifodd #1
- \expandafter\XINT_pow_II_odda
- \else
- \expandafter\XINT_pow_II_even
- \fi #1.%
-}%
-\def\XINT_pow_II_exit\ifodd #1\fi #2.#3\W #4\W
-{%
- \expandafter\XINT_mul_out
- \the\numexpr\XINT_pow_mulbutcheckifsmall #4\W #3%
-}%
-\def\XINT_pow_II_even #1.#2\W
-{%
- \expandafter\XINT_pow_II_loop
- \the\numexpr #1/\xint_c_ii\expandafter.%
- \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W
-}%
-\def\XINT_pow_II_odda #1.#2\W #3\W
-{%
- \expandafter\XINT_pow_II_oddb
- \the\numexpr #1/\xint_c_ii-\xint_c_i\expandafter.%
- \the\numexpr\XINT_pow_mulbutcheckifsmall #3\W #2\W #2\W
-}%
-\def\XINT_pow_II_oddb #1.#2\W #3\W
-{%
- \expandafter\XINT_pow_II_loop
- \the\numexpr #1\expandafter.%
- \the\numexpr\XINT_pow_mulbutcheckifsmall #3\W #3\W #2\W
-}%
-\def\xintiiFac {\romannumeral0\xintiifac }%
-\def\xintiifac #1{\expandafter\XINT_fac_fork\the\numexpr#1.}%
-\def\xintiFac {\romannumeral0\xintifac }%
-\let\xintifac\xintiifac
-\def\XINT_fac_fork #1#2.%
-{%
- \xint_UDzerominusfork
- #1-\XINT_fac_zero
- 0#1\XINT_fac_neg
- 0-\XINT_fac_checksize
- \krof #1#2.%
-}%
-\def\XINT_fac_zero #1.{ 1}%
-\edef\XINT_fac_neg #1.{\noexpand\xintError:FactorialOfNegative\space 1}%
-\def\XINT_fac_checksize #1.%
-{%
- \ifnum #1>\xint_c_x^iv
- \xint_dothis{\expandafter\xintError:TooBigFactorial
- \expandafter\space\expandafter 1\xint_gob_til_W }\fi
- \ifnum #1>465 \xint_dothis{\XINT_fac_bigloop_a #1.}\fi
- \ifnum #1>101 \xint_dothis{\XINT_fac_medloop_a #1.\XINT_mul_out}\fi
- \xint_orthat{\XINT_fac_smallloop_a #1.\XINT_mul_out}%
- 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
-}%
-\def\XINT_fac_bigloop_a #1.%
-{%
- \expandafter\XINT_fac_bigloop_b \the\numexpr
- #1+\xint_c_i-\xint_c_ii*((#1-464)/\xint_c_ii).#1.%
-}%
-\def\XINT_fac_bigloop_b #1.#2.%
-{%
- \expandafter\XINT_fac_medloop_a
- \the\numexpr #1-\xint_c_i.{\XINT_fac_bigloop_loop #1.#2.}%
-}%
-\def\XINT_fac_bigloop_loop #1.#2.%
-{%
- \ifnum #1>#2 \expandafter\XINT_fac_bigloop_exit\fi
- \expandafter\XINT_fac_bigloop_loop
- \the\numexpr #1+\xint_c_ii\expandafter.%
- \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_bigloop_mul #1!%
-}%
-\def\XINT_fac_bigloop_exit #1!{\XINT_mul_out}%
-\def\XINT_fac_bigloop_mul #1!%
-{%
- \expandafter\XINT_smallmul
- \the\numexpr \xint_c_x^viii+#1*(#1+\xint_c_i)!%
-}%
-\def\XINT_fac_medloop_a #1.%
-{%
- \expandafter\XINT_fac_medloop_b
- \the\numexpr #1+\xint_c_i-\xint_c_iii*((#1-100)/\xint_c_iii).#1.%
-}%
-\def\XINT_fac_medloop_b #1.#2.%
-{%
- \expandafter\XINT_fac_smallloop_a
- \the\numexpr #1-\xint_c_i.{\XINT_fac_medloop_loop #1.#2.}%
-}%
-\def\XINT_fac_medloop_loop #1.#2.%
-{%
- \ifnum #1>#2 \expandafter\XINT_fac_loop_exit\fi
- \expandafter\XINT_fac_medloop_loop
- \the\numexpr #1+\xint_c_iii\expandafter.%
- \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_medloop_mul #1!%
-}%
-\def\XINT_fac_medloop_mul #1!%
-{%
- \expandafter\XINT_smallmul
- \the\numexpr
- \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)!%
-}%
-\def\XINT_fac_smallloop_a #1.%
-{%
- \csname
- XINT_fac_smallloop_\the\numexpr #1-\xint_c_iv*(#1/\xint_c_iv)\relax
- \endcsname #1.%
-}%
-\expandafter\def\csname XINT_fac_smallloop_1\endcsname #1.%
-{%
- \XINT_fac_smallloop_loop 2.#1.100000001!1\Z!%
-}%
-\expandafter\def\csname XINT_fac_smallloop_-2\endcsname #1.%
-{%
- \XINT_fac_smallloop_loop 3.#1.100000002!1\Z!%
-}%
-\expandafter\def\csname XINT_fac_smallloop_-1\endcsname #1.%
-{%
- \XINT_fac_smallloop_loop 4.#1.100000006!1\Z!%
-}%
-\expandafter\def\csname XINT_fac_smallloop_0\endcsname #1.%
-{%
- \XINT_fac_smallloop_loop 5.#1.1000000024!1\Z!%
-}%
-\def\XINT_fac_smallloop_loop #1.#2.%
-{%
- \ifnum #1>#2 \expandafter\XINT_fac_loop_exit\fi
- \expandafter\XINT_fac_smallloop_loop
- \the\numexpr #1+\xint_c_iv\expandafter.%
- \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_smallloop_mul #1!%
-}%
-\def\XINT_fac_smallloop_mul #1!%
-{%
- \expandafter\XINT_smallmul
- \the\numexpr
- \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)*(#1+\xint_c_iii)!%
-}%
-\def\XINT_fac_loop_exit #1!#2\Z!#3{#3#2\Z!}%
\def\xintiiQuo {\romannumeral0\xintiiquo }%
\def\xintiiRem {\romannumeral0\xintiirem }%
\def\xintiiquo {\expandafter\xint_firstoftwo_thenstop\romannumeral0\xintiidivision }%
@@ -1330,23 +1224,26 @@
%%\let\xintQuo\xintiQuo\let\xintquo\xintiquo % now removed
%%\let\xintRem\xintiRem\let\xintrem\xintirem % now removed
\def\xintiDivision {\romannumeral0\xintidivision }%
-\def\xintidivision #1{\expandafter\XINT_idivision\romannumeral0\xintnum{#1}\Z }%
-\def\XINT_idivision #1#2\Z #3{\expandafter\XINT_iidivision_a\expandafter #1%
- \romannumeral0\xintnum{#3}\Z #2\Z }%
+\def\xintidivision #1{\expandafter\XINT_idivision\romannumeral0\xintnum{#1}\xint:}%
+\def\XINT_idivision #1#2\xint:#3{\expandafter\XINT_iidivision_a\expandafter #1%
+ \romannumeral0\xintnum{#3}\xint:#2\xint:}%
\def\xintiiDivision {\romannumeral0\xintiidivision }%
-\def\xintiidivision #1{\expandafter\XINT_iidivision \romannumeral`&&@#1\Z }%
-\def\XINT_iidivision #1#2\Z #3{\expandafter\XINT_iidivision_a\expandafter #1%
- \romannumeral`&&@#3\Z #2\Z }%
+\def\xintiidivision #1{\expandafter\XINT_iidivision \romannumeral`&&@#1\xint:}%
+\def\XINT_iidivision #1#2\xint:#3{\expandafter\XINT_iidivision_a\expandafter #1%
+ \romannumeral`&&@#3\xint:#2\xint:}%
\def\XINT_iidivision_a #1#2% #1 de A, #2 de B.
{%
- \if0#2\xint_dothis\XINT_iidivision_divbyzero\fi
+ \if0#2\xint_dothis{\XINT_iidivision_divbyzero #1#2}\fi
\if0#1\xint_dothis\XINT_iidivision_aiszero\fi
\if-#2\xint_dothis{\expandafter\XINT_iidivision_bneg
\romannumeral0\XINT_iidivision_bpos #1}\fi
\xint_orthat{\XINT_iidivision_bpos #1#2}%
}%
-\def\XINT_iidivision_divbyzero #1\Z #2\Z {\xintError:DivisionByZero{0}{0}}%
-\def\XINT_iidivision_aiszero #1\Z #2\Z {{0}{0}}%
+\def\XINT_iidivision_divbyzero#1#2#3\xint:#4\xint:
+ {\if0#1\xint_dothis{\XINT_signalcondition{DivisionUndefined}}\fi
+ \xint_orthat{\XINT_signalcondition{DivisionByZero}}%
+ {Division of #1#4 by #2#3}{}{{0}{0}}}%
+\def\XINT_iidivision_aiszero #1\xint:#2\xint:{{0}{0}}%
\def\XINT_iidivision_bneg #1% q->-q, r unchanged
{\expandafter{\romannumeral0\XINT_opp #1}}%
\def\XINT_iidivision_bpos #1%
@@ -1356,11 +1253,11 @@
-{\XINT_iidivision_apos #1}%
\krof
}%
-\def\XINT_iidivision_apos #1#2\Z #3\Z{\XINT_div_prepare {#2}{#1#3}}%
-\def\XINT_iidivision_aneg #1\Z #2\Z
+\def\XINT_iidivision_apos #1#2\xint:#3\xint:{\XINT_div_prepare {#2}{#1#3}}%
+\def\XINT_iidivision_aneg #1\xint:#2\xint:
{\expandafter
\XINT_iidivision_aneg_b\romannumeral0\XINT_div_prepare {#1}{#2}{#1}}%
-\def\XINT_iidivision_aneg_b #1#2{\if0\XINT_Sgn #2\Z
+\def\XINT_iidivision_aneg_b #1#2{\if0\XINT_Sgn #2\xint:
\expandafter\XINT_iidivision_aneg_rzero
\else
\expandafter\XINT_iidivision_aneg_rpos
@@ -1374,7 +1271,7 @@
\def\XINT_iidivision_aneg_end #1#2#3%
{%
\expandafter\xint_exchangetwo_keepbraces
- \expandafter{\romannumeral0\XINT_sub_mm_a {}{}#3\Z #2\Z}{#1}% r-> b-r
+ \expandafter{\romannumeral0\XINT_sub_mm_a {}{}#3\xint:#2\xint:}{#1}% r-> b-r
}%
\def\XINT_div_prepare #1%
{%
@@ -1409,7 +1306,7 @@
{%
\expandafter\XINT_div_small_b
\the\numexpr #1/\xint_c_ii\expandafter
- .\the\numexpr \xint_c_x^viii+#1\expandafter!%
+ \xint:\the\numexpr \xint_c_x^viii+#1\expandafter!%
\romannumeral0%
\XINT_div_small_ba #2\R\R\R\R\R\R\R\R{10}0000001\W
#2\XINT_sepbyviii_Z_end 2345678\relax
@@ -1428,12 +1325,12 @@
\the\numexpr\expandafter\XINT_sepbyviii_Z
\romannumeral0\XINT_zeroes_forviii #1\R #2\relax
{{\XINT_div_dosmallsmall}{#1}}%
-\def\XINT_div_dosmallsmall #1.1#2!#3%
+\def\XINT_div_dosmallsmall #1\xint:1#2!#3%
{%
\expandafter\XINT_div_smallsmallend
- \the\numexpr (#3+#1)/#2-\xint_c_i.#2.#3.%
+ \the\numexpr (#3+#1)/#2-\xint_c_i\xint:#2\xint:#3\xint:%
}%
-\def\XINT_div_smallsmallend #1.#2.#3.{\expandafter
+\def\XINT_div_smallsmallend #1\xint:#2\xint:#3\xint:{\expandafter
{\the\numexpr #1\expandafter}\expandafter{\the\numexpr #3-#1*#2}}%
\def\XINT_div_dosmalldiv
{{\expandafter\XINT_sdiv_out\the\numexpr\XINT_smalldivx_a}}%
@@ -1455,17 +1352,16 @@
{%
\expandafter\XINT_div_prepare_g
\the\numexpr #1#2#3#4#5#6#7#8+\xint_c_i\expandafter
- .\the\numexpr (#1#2#3#4#5#6#7#8+\xint_c_i)/\xint_c_ii\expandafter
- .\the\numexpr #1#2#3#4#5#6#7#8\expandafter
- .\romannumeral0\XINT_sepandrev_andcount
+ \xint:\the\numexpr (#1#2#3#4#5#6#7#8+\xint_c_i)/\xint_c_ii\expandafter
+ \xint:\the\numexpr #1#2#3#4#5#6#7#8\expandafter
+ \xint:\romannumeral0\XINT_sepandrev_andcount
#1#2#3#4#5#6#7#8#9\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678%
- \relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\X
}%
-\def\XINT_div_prepare_g #1.#2.#3.#4.#5\X #6#7#8%
+\def\XINT_div_prepare_g #1\xint:#2\xint:#3\xint:#4\xint:#5\X #6#7#8%
{%
\expandafter\XINT_div_prepare_h
\the\numexpr\expandafter\XINT_sepbyviii_andcount
@@ -1475,7 +1371,7 @@
\xint_c_iii!\xint_c_ii!\xint_c_i!\xint_c_\W
{#1}{#2}{#3}{#4}{#5}{#6}%
}%
-\def\XINT_div_prepare_h #11.#2.#3#4#5#6%#7#8%
+\def\XINT_div_prepare_h #11\xint:#2\xint:#3#4#5#6%#7#8%
{%
\XINT_div_start_a {#2}{#6}{#1}{#3}{#4}{#5}%{#7}{#8}%
}%
@@ -1492,20 +1388,20 @@
{%
\expandafter\XINT_div_zeroQ_end
\romannumeral0\XINT_unsep_cuzsmall
- #31\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W .%
+ #3\xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax\xint:
}%
-\def\XINT_div_zeroQ_end #1.#2%
- {\expandafter{\expandafter0\expandafter}\XINT_div_cleanR #1#2.}%
+\def\XINT_div_zeroQ_end #1\xint:#2%
+ {\expandafter{\expandafter0\expandafter}\XINT_div_cleanR #1#2\xint:}%
\def\XINT_div_start_b #1#2#3#4#5#6%
{%
\expandafter\XINT_div_finish\the\numexpr
- \XINT_div_start_c {#2}.#3.{#6}{{#1}{#2}{{#4}{#5}}{#6}}%
+ \XINT_div_start_c {#2}\xint:#3\xint:{#6}{{#1}{#2}{{#4}{#5}}{#6}}%
}%
\def\XINT_div_finish
{%
\expandafter\XINT_div_finish_a \romannumeral`&&@\XINT_div_unsepQ
}%
-\def\XINT_div_finish_a #1\Z #2.{\XINT_div_finish_b #2.{#1}}%
+\def\XINT_div_finish_a #1\Z #2\xint:{\XINT_div_finish_b #2\xint:{#1}}%
\def\XINT_div_finish_b #1%
{%
\if0#1%
@@ -1515,12 +1411,12 @@
\fi
#1%
}%
-\def\XINT_div_finish_bRzero 0.#1#2{{#1}{0}}%
-\def\XINT_div_finish_bRpos #1.#2#3%
+\def\XINT_div_finish_bRzero 0\xint:#1#2{{#1}{0}}%
+\def\XINT_div_finish_bRpos #1\xint:#2#3%
{%
- \expandafter\xint_exchangetwo_keepbraces\XINT_div_cleanR #1#3.{#2}%
+ \expandafter\xint_exchangetwo_keepbraces\XINT_div_cleanR #1#3\xint:{#2}%
}%
-\def\XINT_div_cleanR #100000000.{{#1}}%
+\def\XINT_div_cleanR #100000000\xint:{{#1}}%
\def\XINT_div_start_c #1%
{%
\ifnum #1>\xint_c_vi
@@ -1529,43 +1425,43 @@
\expandafter\XINT_div_start_cb
\fi {#1}%
}%
-\def\XINT_div_start_ca #1#2.#3!#4!#5!#6!#7!#8!#9!%
+\def\XINT_div_start_ca #1#2\xint:#3!#4!#5!#6!#7!#8!#9!%
{%
\expandafter\XINT_div_start_c\expandafter
- {\the\numexpr #1-\xint_c_vii}#2#3!#4!#5!#6!#7!#8!#9!.%
+ {\the\numexpr #1-\xint_c_vii}#2#3!#4!#5!#6!#7!#8!#9!\xint:%
}%
\def\XINT_div_start_cb #1%
{\csname XINT_div_start_c_\romannumeral\numexpr#1\endcsname}%
-\def\XINT_div_start_c_i #1.#2!%
- {\XINT_div_start_c_ #1#2!.}%
-\def\XINT_div_start_c_ii #1.#2!#3!%
- {\XINT_div_start_c_ #1#2!#3!.}%
-\def\XINT_div_start_c_iii #1.#2!#3!#4!%
- {\XINT_div_start_c_ #1#2!#3!#4!.}%
-\def\XINT_div_start_c_iv #1.#2!#3!#4!#5!%
- {\XINT_div_start_c_ #1#2!#3!#4!#5!.}%
-\def\XINT_div_start_c_v #1.#2!#3!#4!#5!#6!%
- {\XINT_div_start_c_ #1#2!#3!#4!#5!#6!.}%
-\def\XINT_div_start_c_vi #1.#2!#3!#4!#5!#6!#7!%
- {\XINT_div_start_c_ #1#2!#3!#4!#5!#6!#7!.}%
-\def\XINT_div_start_c_ 1#1!#2.#3.#4#5#6%
+\def\XINT_div_start_c_i #1\xint:#2!%
+ {\XINT_div_start_c_ #1#2!\xint:}%
+\def\XINT_div_start_c_ii #1\xint:#2!#3!%
+ {\XINT_div_start_c_ #1#2!#3!\xint:}%
+\def\XINT_div_start_c_iii #1\xint:#2!#3!#4!%
+ {\XINT_div_start_c_ #1#2!#3!#4!\xint:}%
+\def\XINT_div_start_c_iv #1\xint:#2!#3!#4!#5!%
+ {\XINT_div_start_c_ #1#2!#3!#4!#5!\xint:}%
+\def\XINT_div_start_c_v #1\xint:#2!#3!#4!#5!#6!%
+ {\XINT_div_start_c_ #1#2!#3!#4!#5!#6!\xint:}%
+\def\XINT_div_start_c_vi #1\xint:#2!#3!#4!#5!#6!#7!%
+ {\XINT_div_start_c_ #1#2!#3!#4!#5!#6!#7!\xint:}%
+\def\XINT_div_start_c_ 1#1!#2\xint:#3\xint:#4#5#6%
{%
\XINT_div_I_a {#1}{#4}{1#1!#2}{#6}{00000000}#5{#3}{#6}%
}%
\def\XINT_div_I_a #1#2%
{%
- \expandafter\XINT_div_I_b\the\numexpr #1/#2.{#1}{#2}%
+ \expandafter\XINT_div_I_b\the\numexpr #1/#2\xint:{#1}{#2}%
}%
\def\XINT_div_I_b #1%
{%
\xint_gob_til_zero #1\XINT_div_I_czero 0\XINT_div_I_c #1%
}%
-\def\XINT_div_I_czero 0\XINT_div_I_c 0.#1#2#3#4#5{1#5\XINT_div_I_g {#3}}%
-\def\XINT_div_I_c #1.#2#3%
+\def\XINT_div_I_czero 0\XINT_div_I_c 0\xint:#1#2#3#4#5{1#5\XINT_div_I_g {#3}}%
+\def\XINT_div_I_c #1\xint:#2#3%
{%
- \expandafter\XINT_div_I_da\the\numexpr #2-#1*#3.#1.{#2}{#3}%
+ \expandafter\XINT_div_I_da\the\numexpr #2-#1*#3\xint:#1\xint:{#2}{#3}%
}%
-\def\XINT_div_I_da #1.%
+\def\XINT_div_I_da #1\xint:%
{%
\ifnum #1>\xint_c_ix
\expandafter\XINT_div_I_dP
@@ -1577,16 +1473,16 @@
\fi
\fi
}%
-\def\XINT_div_I_dN #1.%
+\def\XINT_div_I_dN #1\xint:%
{%
- \expandafter\XINT_div_I_b\the\numexpr #1-\xint_c_i.%
+ \expandafter\XINT_div_I_b\the\numexpr #1-\xint_c_i\xint:%
}%
-\def\XINT_div_I_db #1.#2#3#4#5%
+\def\XINT_div_I_db #1\xint:#2#3#4#5%
{%
\expandafter\XINT_div_I_dc\expandafter #1%
\romannumeral0\expandafter\XINT_div_sub\expandafter
{\romannumeral0\XINT_rev_nounsep {}#4\R!\R!\R!\R!\R!\R!\R!\R!\W}%
- {\the\numexpr\XINT_div_verysmallmul #1!#51\Z!}%
+ {\the\numexpr\XINT_div_verysmallmul #1!#51;!}%
\Z {#4}{#5}%
}%
\def\XINT_div_I_dc #1#2%
@@ -1597,7 +1493,7 @@
\def\XINT_div_I_dd #1-\Z
{%
\if #11\expandafter\XINT_div_I_dz\fi
- \expandafter\XINT_div_I_dP\the\numexpr #1-\xint_c_i.XX%
+ \expandafter\XINT_div_I_dP\the\numexpr #1-\xint_c_i\xint: XX%
}%
\def\XINT_div_I_dz #1XX#2#3#4%
{%
@@ -1604,12 +1500,12 @@
1#4\XINT_div_I_g {#2}%
}%
\def\XINT_div_I_de #1#2\Z #3#4#5{1#5+#1\XINT_div_I_g {#2}}%
-\def\XINT_div_I_dP #1.#2#3#4#5#6%
+\def\XINT_div_I_dP #1\xint:#2#3#4#5#6%
{%
1#6+#1\expandafter\XINT_div_I_g\expandafter
{\romannumeral0\expandafter\XINT_div_sub\expandafter
{\romannumeral0\XINT_rev_nounsep {}#4\R!\R!\R!\R!\R!\R!\R!\R!\W}%
- {\the\numexpr\XINT_div_verysmallmul #1!#51\Z!}%
+ {\the\numexpr\XINT_div_verysmallmul #1!#51;!}%
}%
}%
\def\XINT_div_I_g #1#2#3#4#5#6#7%
@@ -1620,16 +1516,17 @@
\else
\expandafter\XINT_div_I_h
\fi
- {#4}#1.#6.{{#4}{#5}{#3}{#2}}{#7}%
+ {#4}#1\xint:#6\xint:{{#4}{#5}{#3}{#2}}{#7}%
}%
-\def\XINT_div_exittofinish #1#2.#3.#4#5%
+\def\XINT_div_exittofinish #1#2\xint:#3\xint:#4#5%
{%
- 1\expandafter\expandafter\expandafter!\expandafter\XINT_unsep_delim
- \romannumeral0\XINT_div_unsepR #2#31\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W.%
+ 1\expandafter\expandafter\expandafter!\expandafter\XINT_div_unsepQ_delim
+ \romannumeral0\XINT_div_unsepR #2#3%
+ \xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax\R\xint:
}%
-\def\XINT_div_I_h #1.#2!#3.#4#5%
+\def\XINT_div_I_h #1\xint:#2!#3\xint:#4#5%
{%
- \XINT_div_II_b #1#2!.{#5}{#4}{#3}{#5}%
+ \XINT_div_II_b #1#2!\xint:{#5}{#4}{#3}{#5}%
}%
\def\XINT_div_II_b #11#2!#3!%
{%
@@ -1636,7 +1533,7 @@
\xint_gob_til_eightzeroes #2\XINT_div_II_skipc 00000000%
\XINT_div_II_c #1{1#2}{#3}%
}%
-\def\XINT_div_II_skipc 00000000\XINT_div_II_c #1#2#3#4#5.#6#7%
+\def\XINT_div_II_skipc 00000000\XINT_div_II_c #1#2#3#4#5\xint:#6#7%
{%
\XINT_div_II_k #7{#4!#5}{#6}{00000000}%
}%
@@ -1643,7 +1540,7 @@
\def\XINT_div_II_c #1#2#3#4%
{%
\expandafter\XINT_div_II_d\the\numexpr\XINT_div_xmini
- #1.#2!#3!#4!{#1}{#2}#3!#4!%
+ #1\xint:#2!#3!#4!{#1}{#2}#3!#4!%
}%
\def\XINT_div_xmini #1%
{%
@@ -1657,14 +1554,14 @@
{%
\xint_gob_til_zero #7\XINT_div_xmini_c 0\XINT_div_mini 10#1#2#3#4#5#6#7%
}%
-\def\XINT_div_xmini_c 0\XINT_div_mini 100000000.50000000!#1!#2!{#1!}%
-\def\XINT_div_II_d 1#1#2#3#4#5!#6#7#8.#9%
+\def\XINT_div_xmini_c 0\XINT_div_mini 100000000\xint:50000000!#1!#2!{#1!}%
+\def\XINT_div_II_d 1#1#2#3#4#5!#6#7#8\xint:#9%
{%
\expandafter\XINT_div_II_e
\romannumeral0\expandafter\XINT_div_sub\expandafter
{\romannumeral0\XINT_rev_nounsep {}#8\R!\R!\R!\R!\R!\R!\R!\R!\W}%
- {\the\numexpr\XINT_div_smallmul_a 100000000.#1#2#3#4.#5!#91\Z!}%
- .{#6}{#7}{#9}{#1#2#3#4#5}%
+ {\the\numexpr\XINT_div_smallmul_a 100000000\xint:#1#2#3#4\xint:#5!#91;!}%
+ \xint:{#6}{#7}{#9}{#1#2#3#4#5}%
}%
\def\XINT_div_II_e 1#1!%
{%
@@ -1671,85 +1568,85 @@
\xint_gob_til_eightzeroes #1\XINT_div_II_skipf 00000000%
\XINT_div_II_f 1#1!%
}%
-\def\XINT_div_II_skipf 00000000\XINT_div_II_f 100000000!#1.#2#3#4#5#6%
+\def\XINT_div_II_skipf 00000000\XINT_div_II_f 100000000!#1\xint:#2#3#4#5#6%
{%
\XINT_div_II_k #6{#1}{#4}{#5}%
}%
-\def\XINT_div_II_f #1!#2!#3.%
+\def\XINT_div_II_f #1!#2!#3\xint:%
{%
\XINT_div_II_fa {#1!#2!}{#1!#2!#3}%
}%
\def\XINT_div_II_fa #1#2#3#4%
{%
- \expandafter\XINT_div_II_g \the\numexpr\XINT_div_xmini #3.#4!#1{#2}%
+ \expandafter\XINT_div_II_g \the\numexpr\XINT_div_xmini #3\xint:#4!#1{#2}%
}%
\def\XINT_div_II_g 1#1#2#3#4#5!#6#7#8%
{%
\expandafter \XINT_div_II_h
\the\numexpr 1#1#2#3#4#5+#8\expandafter\expandafter\expandafter
- .\expandafter\expandafter\expandafter
+ \xint:\expandafter\expandafter\expandafter
{\expandafter\xint_gob_til_exclam
\romannumeral0\expandafter\XINT_div_sub\expandafter
{\romannumeral0\XINT_rev_nounsep {}#6\R!\R!\R!\R!\R!\R!\R!\R!\W}%
- {\the\numexpr\XINT_div_smallmul_a 100000000.#1#2#3#4.#5!#71\Z!}}%
+ {\the\numexpr\XINT_div_smallmul_a 100000000\xint:#1#2#3#4\xint:#5!#71;!}}%
{#7}%
}%
-\def\XINT_div_II_h 1#1.#2#3#4%
+\def\XINT_div_II_h 1#1\xint:#2#3#4%
{%
\XINT_div_II_k #4{#2}{#3}{#1}%
}%
\def\XINT_div_II_k #1#2#3#4#5%
{%
- \expandafter\XINT_div_II_l \the\numexpr #4-\xint_c_i.{#3}#1{#2}#5.%
+ \expandafter\XINT_div_II_l \the\numexpr #4-\xint_c_i\xint:{#3}#1{#2}#5\xint:%
}%
-\def\XINT_div_II_l #1.#2#3#4#51#6!%
+\def\XINT_div_II_l #1\xint:#2#3#4#51#6!%
{%
\XINT_div_II_m {{#1}{#2}{{#3}{#4}}{#5}}{#5}{#6}1#6!%
}%
-\def\XINT_div_II_m #1#2#3#4.#5#6%
+\def\XINT_div_II_m #1#2#3#4\xint:#5#6%
{%
\XINT_div_I_a {#3}{#2}{#4}{#5}{#6}#1%
}%
-\def\XINT_div_minimulwc_a 1#1.#2.#3!#4#5#6#7#8.%
+\def\XINT_div_minimulwc_a 1#1\xint:#2\xint:#3!#4#5#6#7#8\xint:%
{%
\expandafter\XINT_div_minimulwc_b
- \the\numexpr \xint_c_x^ix+#1+#3*#8.#3*#4#5#6#7+#2*#8.#2*#4#5#6#7.%
+ \the\numexpr \xint_c_x^ix+#1+#3*#8\xint:#3*#4#5#6#7+#2*#8\xint:#2*#4#5#6#7\xint:%
}%
-\def\XINT_div_minimulwc_b 1#1#2#3#4#5#6.#7.%
+\def\XINT_div_minimulwc_b 1#1#2#3#4#5#6\xint:#7\xint:%
{%
\expandafter\XINT_div_minimulwc_c
- \the\numexpr \xint_c_x^ix+#1#2#3#4#5+#7.#6.%
+ \the\numexpr \xint_c_x^ix+#1#2#3#4#5+#7\xint:#6\xint:%
}%
-\def\XINT_div_minimulwc_c 1#1#2#3#4#5#6.#7.#8.%
+\def\XINT_div_minimulwc_c 1#1#2#3#4#5#6\xint:#7\xint:#8\xint:%
{%
1#6#7\expandafter!%
\the\numexpr\expandafter\XINT_div_smallmul_a
- \the\numexpr \xint_c_x^viii+#1#2#3#4#5+#8.%
+ \the\numexpr \xint_c_x^viii+#1#2#3#4#5+#8\xint:%
}%
-\def\XINT_div_smallmul_a #1.#2.#3!1#4!%
+\def\XINT_div_smallmul_a #1\xint:#2\xint:#3!1#4!%
{%
- \xint_gob_til_Z #4\XINT_div_smallmul_e\Z
- \XINT_div_minimulwc_a #1.#2.#3!#4.#2.#3!%
+ \xint_gob_til_sc #4\XINT_div_smallmul_e;%
+ \XINT_div_minimulwc_a #1\xint:#2\xint:#3!#4\xint:#2\xint:#3!%
}%
-\def\XINT_div_smallmul_e\Z\XINT_div_minimulwc_a 1#1.#2\Z #3!{1\relax #1!}%
+\def\XINT_div_smallmul_e;\XINT_div_minimulwc_a 1#1\xint:#2;#3!{1\relax #1!}%
\def\XINT_div_verysmallmul #1%
- {\xint_gob_til_one #1\XINT_div_verysmallisone 1\XINT_div_verysmallmul_a 0.#1}%
-\def\XINT_div_verysmallisone 1\XINT_div_verysmallmul_a 0.1!1#11\Z!%
+ {\xint_gob_til_one #1\XINT_div_verysmallisone 1\XINT_div_verysmallmul_a 0\xint:#1}%
+\def\XINT_div_verysmallisone 1\XINT_div_verysmallmul_a 0\xint:1!1#11;!%
{1\relax #1100000000!}%
-\def\XINT_div_verysmallmul_a #1.#2!1#3!%
+\def\XINT_div_verysmallmul_a #1\xint:#2!1#3!%
{%
- \xint_gob_til_Z #3\XINT_div_verysmallmul_e\Z
+ \xint_gob_til_sc #3\XINT_div_verysmallmul_e;%
\expandafter\XINT_div_verysmallmul_b
- \the\numexpr \xint_c_x^ix+#2*#3+#1.#2!%
+ \the\numexpr \xint_c_x^ix+#2*#3+#1\xint:#2!%
}%
-\def\XINT_div_verysmallmul_b 1#1#2.%
- {1#2\expandafter!\the\numexpr\XINT_div_verysmallmul_a #1.}%
-\def\XINT_div_verysmallmul_e\Z #1\Z +#2#3!{1\relax 0000000#2!}%
+\def\XINT_div_verysmallmul_b 1#1#2\xint:%
+ {1#2\expandafter!\the\numexpr\XINT_div_verysmallmul_a #1\xint:}%
+\def\XINT_div_verysmallmul_e;#1;+#2#3!{1\relax 0000000#2!}%
\def\XINT_div_sub #1#2%
{%
\expandafter\XINT_div_sub_clean
\the\numexpr\expandafter\XINT_div_sub_a\expandafter
- 1#2\Z!\Z!\Z!\Z!\Z!\W #1\Z!\Z!\Z!\Z!\Z!\W
+ 1#2;!;!;!;!;!\W #1;!;!;!;!;!\W
}%
\def\XINT_div_sub_clean #1-#2#3\W
{%
@@ -1763,57 +1660,57 @@
}%
\def\XINT_div_sub_b #1#2#3!#4!%
{%
- \xint_gob_til_Z #4\XINT_div_sub_bi \Z
- \expandafter\XINT_div_sub_c\the\numexpr#1-#3+1#4-\xint_c_i.%
+ \xint_gob_til_sc #4\XINT_div_sub_bi ;%
+ \expandafter\XINT_div_sub_c\the\numexpr#1-#3+1#4-\xint_c_i\xint:%
}%
-\def\XINT_div_sub_c 1#1#2.%
+\def\XINT_div_sub_c 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_div_sub_d #1%
}%
\def\XINT_div_sub_d #1#2#3!#4!%
{%
- \xint_gob_til_Z #4\XINT_div_sub_di \Z
- \expandafter\XINT_div_sub_e\the\numexpr#1-#3+1#4-\xint_c_i.%
+ \xint_gob_til_sc #4\XINT_div_sub_di ;%
+ \expandafter\XINT_div_sub_e\the\numexpr#1-#3+1#4-\xint_c_i\xint:%
}%
-\def\XINT_div_sub_e 1#1#2.%
+\def\XINT_div_sub_e 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_div_sub_f #1%
}%
\def\XINT_div_sub_f #1#2#3!#4!%
{%
- \xint_gob_til_Z #4\XINT_div_sub_fi \Z
- \expandafter\XINT_div_sub_g\the\numexpr#1-#3+1#4-\xint_c_i.%
+ \xint_gob_til_sc #4\XINT_div_sub_fi ;%
+ \expandafter\XINT_div_sub_g\the\numexpr#1-#3+1#4-\xint_c_i\xint:%
}%
-\def\XINT_div_sub_g 1#1#2.%
+\def\XINT_div_sub_g 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_div_sub_h #1%
}%
\def\XINT_div_sub_h #1#2#3!#4!%
{%
- \xint_gob_til_Z #4\XINT_div_sub_hi \Z
- \expandafter\XINT_div_sub_i\the\numexpr#1-#3+1#4-\xint_c_i.%
+ \xint_gob_til_sc #4\XINT_div_sub_hi ;%
+ \expandafter\XINT_div_sub_i\the\numexpr#1-#3+1#4-\xint_c_i\xint:%
}%
-\def\XINT_div_sub_i 1#1#2.%
+\def\XINT_div_sub_i 1#1#2\xint:%
{%
1#2\expandafter!\the\numexpr\XINT_div_sub_a #1%
}%
-\def\XINT_div_sub_bi\Z
- \expandafter\XINT_div_sub_c\the\numexpr#1-#2+#3.#4!#5!#6!#7!#8!#9!\Z !\W
+\def\XINT_div_sub_bi;%
+ \expandafter\XINT_div_sub_c\the\numexpr#1-#2+#3\xint:#4!#5!#6!#7!#8!#9!;!\W
{%
\XINT_div_sub_l #1#2!#5!#7!#9!%
}%
-\def\XINT_div_sub_di\Z
- \expandafter\XINT_div_sub_e\the\numexpr#1-#2+#3.#4!#5!#6!#7!#8\W
+\def\XINT_div_sub_di;%
+ \expandafter\XINT_div_sub_e\the\numexpr#1-#2+#3\xint:#4!#5!#6!#7!#8\W
{%
\XINT_div_sub_l #1#2!#5!#7!%
}%
-\def\XINT_div_sub_fi\Z
- \expandafter\XINT_div_sub_g\the\numexpr#1-#2+#3.#4!#5!#6\W
+\def\XINT_div_sub_fi;%
+ \expandafter\XINT_div_sub_g\the\numexpr#1-#2+#3\xint:#4!#5!#6\W
{%
\XINT_div_sub_l #1#2!#5!%
}%
-\def\XINT_div_sub_hi\Z
- \expandafter\XINT_div_sub_i\the\numexpr#1-#2+#3.#4\W
+\def\XINT_div_sub_hi;%
+ \expandafter\XINT_div_sub_i\the\numexpr#1-#2+#3\xint:#4\W
{%
\XINT_div_sub_l #1#2!%
}%
@@ -1828,14 +1725,15 @@
{%
-\ifnum 0#1=\xint_c_ 1\else2\fi\relax
}%
-\def\XINT_sdiv_out #1\Z!#2!%
+\def\XINT_sdiv_out #1;!#2!%
{\expandafter
- {\romannumeral0\XINT_unsep_cuzsmall#11\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W}%
+ {\romannumeral0\XINT_unsep_cuzsmall
+ #1\xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax}%
{#2}}%
-\def\XINT_smalldivx_a #1.1#2!1#3!%
+\def\XINT_smalldivx_a #1\xint:1#2!1#3!%
{%
\expandafter\XINT_smalldivx_b
- \the\numexpr (#3+#1)/#2-\xint_c_i!#1.#2!#3!%
+ \the\numexpr (#3+#1)/#2-\xint_c_i!#1\xint:#2!#3!%
}%
\def\XINT_smalldivx_b #1#2!%
{%
@@ -1843,44 +1741,44 @@
\xint_c_x^viii+#1#2\xint_afterfi{\expandafter!\the\numexpr}\fi
\XINT_smalldiv_c #1#2!%
}%
-\def\XINT_smalldiv_c #1!#2.#3!#4!%
+\def\XINT_smalldiv_c #1!#2\xint:#3!#4!%
{%
- \expandafter\XINT_smalldiv_d\the\numexpr #4-#1*#3!#2.#3!%
+ \expandafter\XINT_smalldiv_d\the\numexpr #4-#1*#3!#2\xint:#3!%
}%
\def\XINT_smalldiv_d #1!#2!1#3#4!%
{%
- \xint_gob_til_Z #3\XINT_smalldiv_end \Z
+ \xint_gob_til_sc #3\XINT_smalldiv_end ;%
\XINT_smalldiv_e #1!#2!1#3#4!%
}%
-\def\XINT_smalldiv_end\Z\XINT_smalldiv_e #1!#2!1\Z!{1!\Z!#1!}%
-\def\XINT_smalldiv_e #1!#2.#3!%
+\def\XINT_smalldiv_end;\XINT_smalldiv_e #1!#2!1;!{1!;!#1!}%
+\def\XINT_smalldiv_e #1!#2\xint:#3!%
{%
\expandafter\XINT_smalldiv_f\the\numexpr
- \xint_c_xi_e_viii_mone+#1*\xint_c_x^viii/#3!#2.#3!#1!%
+ \xint_c_xi_e_viii_mone+#1*\xint_c_x^viii/#3!#2\xint:#3!#1!%
}%
-\def\XINT_smalldiv_f 1#1#2#3#4#5#6!#7.#8!%
+\def\XINT_smalldiv_f 1#1#2#3#4#5#6!#7\xint:#8!%
{%
\xint_gob_til_zero #1\XINT_smalldiv_fz 0%
\expandafter\XINT_smalldiv_g
- \the\numexpr\XINT_minimul_a #2#3#4#5.#6!#8!#2#3#4#5#6!#7.#8!%
+ \the\numexpr\XINT_minimul_a #2#3#4#5\xint:#6!#8!#2#3#4#5#6!#7\xint:#8!%
}%
\def\XINT_smalldiv_fz 0%
\expandafter\XINT_smalldiv_g\the\numexpr\XINT_minimul_a
- 9999.9999!#1!99999999!#2!0!1#3!%
+ 9999\xint:9999!#1!99999999!#2!0!1#3!%
{%
- \XINT_smalldiv_i .#3!\xint_c_!#2!%
+ \XINT_smalldiv_i \xint:#3!\xint_c_!#2!%
}%
\def\XINT_smalldiv_g 1#1!1#2!#3!#4!#5!#6!%
{%
- \expandafter\XINT_smalldiv_h\the\numexpr 1#6-#1.#2!#5!#3!#4!%
+ \expandafter\XINT_smalldiv_h\the\numexpr 1#6-#1\xint:#2!#5!#3!#4!%
}%
-\def\XINT_smalldiv_h 1#1#2.#3!#4!%
+\def\XINT_smalldiv_h 1#1#2\xint:#3!#4!%
{%
- \expandafter\XINT_smalldiv_i\the\numexpr #4-#3+#1-\xint_c_i.#2!%
+ \expandafter\XINT_smalldiv_i\the\numexpr #4-#3+#1-\xint_c_i\xint:#2!%
}%
-\def\XINT_smalldiv_i #1.#2!#3!#4.#5!%
+\def\XINT_smalldiv_i #1\xint:#2!#3!#4\xint:#5!%
{%
- \expandafter\XINT_smalldiv_j\the\numexpr (#1#2+#4)/#5-\xint_c_i!#3!#1#2!#4.#5!%
+ \expandafter\XINT_smalldiv_j\the\numexpr (#1#2+#4)/#5-\xint_c_i!#3!#1#2!#4\xint:#5!%
}%
\def\XINT_smalldiv_j #1!#2!%
{%
@@ -1887,24 +1785,24 @@
\xint_c_x^viii+#1+#2\expandafter!\the\numexpr\XINT_smalldiv_k
#1!%
}%
-\def\XINT_smalldiv_k #1!#2!#3.#4!%
+\def\XINT_smalldiv_k #1!#2!#3\xint:#4!%
{%
- \expandafter\XINT_smalldiv_d\the\numexpr #2-#1*#4!#3.#4!%
+ \expandafter\XINT_smalldiv_d\the\numexpr #2-#1*#4!#3\xint:#4!%
}%
-\def\XINT_div_mini #1.#2!1#3!%
+\def\XINT_div_mini #1\xint:#2!1#3!%
{%
\expandafter\XINT_div_mini_a\the\numexpr
- \xint_c_xi_e_viii_mone+#3*\xint_c_x^viii/#1!#1.#2!#3!%
+ \xint_c_xi_e_viii_mone+#3*\xint_c_x^viii/#1!#1\xint:#2!#3!%
}%
-\def\XINT_div_mini_a 1#1#2#3#4#5#6!#7.#8!%
+\def\XINT_div_mini_a 1#1#2#3#4#5#6!#7\xint:#8!%
{%
\xint_gob_til_zero #1\XINT_div_mini_w 0%
\expandafter\XINT_div_mini_b
- \the\numexpr\XINT_minimul_a #2#3#4#5.#6!#7!#2#3#4#5#6!#7.#8!%
+ \the\numexpr\XINT_minimul_a #2#3#4#5\xint:#6!#7!#2#3#4#5#6!#7\xint:#8!%
}%
\def\XINT_div_mini_w 0%
\expandafter\XINT_div_mini_b\the\numexpr\XINT_minimul_a
- 9999.9999!#1!99999999!#2.#3!00000000!#4!%
+ 9999\xint:9999!#1!99999999!#2\xint:#3!00000000!#4!%
{%
\xint_c_x^viii_mone+(#4+#3)/#2!%
}%
@@ -1911,36 +1809,37 @@
\def\XINT_div_mini_b 1#1!1#2!#3!#4!#5!#6!%
{%
\expandafter\XINT_div_mini_c
- \the\numexpr 1#6-#1.#2!#5!#3!#4!%
+ \the\numexpr 1#6-#1\xint:#2!#5!#3!#4!%
}%
-\def\XINT_div_mini_c 1#1#2.#3!#4!%
+\def\XINT_div_mini_c 1#1#2\xint:#3!#4!%
{%
\expandafter\XINT_div_mini_d
- \the\numexpr #4-#3+#1-\xint_c_i.#2!%
+ \the\numexpr #4-#3+#1-\xint_c_i\xint:#2!%
}%
-\def\XINT_div_mini_d #1.#2!#3!#4.#5!%
+\def\XINT_div_mini_d #1\xint:#2!#3!#4\xint:#5!%
{%
\xint_c_x^viii_mone+#3+(#1#2+#5)/#4!%
}%
\def\xintiDivRound {\romannumeral0\xintidivround }%
\def\xintidivround #1%
- {\expandafter\XINT_idivround\romannumeral0\xintnum{#1}\Z }%
+ {\expandafter\XINT_idivround\romannumeral0\xintnum{#1}\xint:}%
\def\xintiiDivRound {\romannumeral0\xintiidivround }%
-\def\xintiidivround #1{\expandafter\XINT_iidivround \romannumeral`&&@#1\Z }%
-\def\XINT_idivround #1#2\Z #3%
+\def\xintiidivround #1{\expandafter\XINT_iidivround\romannumeral`&&@#1\xint:}%
+\def\XINT_idivround #1#2\xint:#3%
{\expandafter\XINT_iidivround_a\expandafter #1%
- \romannumeral0\xintnum{#3}\Z #2\Z }%
-\def\XINT_iidivround #1#2\Z #3%
- {\expandafter\XINT_iidivround_a\expandafter #1\romannumeral`&&@#3\Z #2\Z }%
+ \romannumeral0\xintnum{#3}\xint:#2\xint:}%
+\def\XINT_iidivround #1#2\xint:#3%
+ {\expandafter\XINT_iidivround_a\expandafter #1\romannumeral`&&@#3\xint:#2\xint:}%
\def\XINT_iidivround_a #1#2% #1 de A, #2 de B.
{%
- \if0#2\xint_dothis\XINT_iidivround_divbyzero\fi
+ \if0#2\xint_dothis{\XINT_iidivround_divbyzero#1#2}\fi
\if0#1\xint_dothis\XINT_iidivround_aiszero\fi
\if-#2\xint_dothis{\XINT_iidivround_bneg #1}\fi
\xint_orthat{\XINT_iidivround_bpos #1#2}%
}%
-\def\XINT_iidivround_divbyzero #1\Z #2\Z {\xintError:DivisionByZero\space 0}%
-\def\XINT_iidivround_aiszero #1\Z #2\Z { 0}%
+\def\XINT_iidivround_divbyzero #1#2#3\xint:#4\xint:
+ {\XINT_signalcondition{DivisionByZero}{Division of #1#4 by #2#3}{}{0}}%
+\def\XINT_iidivround_aiszero #1\xint:#2\xint:{ 0}%
\def\XINT_iidivround_bpos #1%
{%
\xint_UDsignfork
@@ -1955,7 +1854,7 @@
-{\xintiiopp\XINT_iidivround_pos #1}%
\krof
}%
-\def\XINT_iidivround_pos #1#2\Z #3\Z
+\def\XINT_iidivround_pos #1#2\xint:#3\xint:
{%
\expandafter\expandafter\expandafter\XINT_dsrr
\expandafter\xint_firstoftwo
@@ -1963,14 +1862,14 @@
\xint_bye\xint_Bye3456789\xint_bye/\xint_c_x\relax
}%
\def\xintiDivTrunc {\romannumeral0\xintidivtrunc }%
-\def\xintidivtrunc #1{\expandafter\XINT_iidivtrunc\romannumeral0\xintnum{#1}\Z }%
+\def\xintidivtrunc #1{\expandafter\XINT_iidivtrunc\romannumeral0\xintnum{#1}\xint:}%
\def\xintiiDivTrunc {\romannumeral0\xintiidivtrunc }%
-\def\xintiidivtrunc #1{\expandafter\XINT_iidivtrunc \romannumeral`&&@#1\Z }%
-\def\XINT_iidivtrunc #1#2\Z #3{\expandafter\XINT_iidivtrunc_a\expandafter #1%
- \romannumeral`&&@#3\Z #2\Z }%
+\def\xintiidivtrunc #1{\expandafter\XINT_iidivtrunc\romannumeral`&&@#1\xint:}%
+\def\XINT_iidivtrunc #1#2\xint:#3{\expandafter\XINT_iidivtrunc_a\expandafter #1%
+ \romannumeral`&&@#3\xint:#2\xint:}%
\def\XINT_iidivtrunc_a #1#2% #1 de A, #2 de B.
{%
- \if0#2\xint_dothis\XINT_iidivround_divbyzero\fi
+ \if0#2\xint_dothis{\XINT_iidivround_divbyzero#1#2}\fi
\if0#1\xint_dothis\XINT_iidivround_aiszero\fi
\if-#2\xint_dothis{\XINT_iidivtrunc_bneg #1}\fi
\xint_orthat{\XINT_iidivtrunc_bpos #1#2}%
@@ -1989,18 +1888,18 @@
-{\xintiiopp\XINT_iidivtrunc_pos #1}%
\krof
}%
-\def\XINT_iidivtrunc_pos #1#2\Z #3\Z%
+\def\XINT_iidivtrunc_pos #1#2\xint:#3\xint:
{\expandafter\xint_firstoftwo_thenstop
\romannumeral0\XINT_div_prepare {#2}{#1#3}}%
\def\xintiMod {\romannumeral0\xintimod }%
-\def\xintimod #1{\expandafter\XINT_iimod\romannumeral0\xintnum{#1}\Z }%
+\def\xintimod #1{\expandafter\XINT_iimod\romannumeral0\xintnum{#1}\xint:}%
\def\xintiiMod {\romannumeral0\xintiimod }%
-\def\xintiimod #1{\expandafter\XINT_iimod \romannumeral`&&@#1\Z }%
-\def\XINT_iimod #1#2\Z #3{\expandafter\XINT_iimod_a\expandafter #1%
- \romannumeral`&&@#3\Z #2\Z }%
+\def\xintiimod #1{\expandafter\XINT_iimod\romannumeral`&&@#1\xint:}%
+\def\XINT_iimod #1#2\xint:#3{\expandafter\XINT_iimod_a\expandafter #1%
+ \romannumeral`&&@#3\xint:#2\xint:}%
\def\XINT_iimod_a #1#2% #1 de A, #2 de B.
{%
- \if0#2\xint_dothis\XINT_iidivround_divbyzero\fi
+ \if0#2\xint_dothis{\XINT_iidivround_divbyzero#1#2}\fi
\if0#1\xint_dothis\XINT_iidivround_aiszero\fi
\if-#2\xint_dothis{\XINT_iimod_bneg #1}\fi
\xint_orthat{\XINT_iimod_bpos #1#2}%
@@ -2019,9 +1918,307 @@
-{\XINT_iimod_pos #1}%
\krof
}%
-\def\XINT_iimod_pos #1#2\Z #3\Z%
+\def\XINT_iimod_pos #1#2\xint:#3\xint:
{\expandafter\xint_secondoftwo_thenstop\romannumeral0\XINT_div_prepare
{#2}{#1#3}}%
+\def\xintiiSqr {\romannumeral0\xintiisqr }%
+\def\xintiisqr #1%
+{%
+ \expandafter\XINT_sqr\romannumeral0\xintiiabs{#1}\xint:
+}%
+\def\xintiSqr {\romannumeral0\xintisqr }%
+\def\xintisqr #1%
+{%
+ \expandafter\XINT_sqr\romannumeral0\xintiabs{#1}\xint:
+}%
+\def\XINT_sqr #1\xint:
+{%
+ \expandafter\XINT_sqr_a
+ \romannumeral0\expandafter\XINT_sepandrev_andcount
+ \romannumeral0\XINT_zeroes_forviii #1\R\R\R\R\R\R\R\R{10}0000001\W
+ #1\XINT_rsepbyviii_end_A 2345678%
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
+ \xint:
+}%
+\def\XINT_sqr_a #1\xint:
+{%
+ \ifnum #1=\xint_c_i \expandafter\XINT_sqr_small
+ \else\expandafter\XINT_sqr_start\fi
+}%
+\def\XINT_sqr_small 1#1#2#3#4#5!\xint:
+{%
+ \ifnum #1#2#3#4#5<46341 \expandafter\XINT_sqr_verysmall\fi
+ \expandafter\XINT_sqr_small_out
+ \the\numexpr\XINT_minimul_a #1#2#3#4\xint:#5!#1#2#3#4#5!%
+}%
+\def\XINT_sqr_verysmall#1{%
+\def\XINT_sqr_verysmall
+ \expandafter\XINT_sqr_small_out\the\numexpr\XINT_minimul_a ##1!##2!%
+ {\expandafter#1\the\numexpr ##2*##2\relax}%
+}\XINT_sqr_verysmall{ }%
+\def\XINT_sqr_small_out 1#1!1#2!%
+{%
+ \XINT_cuz #2#1\R
+}%
+\def\XINT_sqr_start #1\xint:
+{%
+ \expandafter\XINT_mul_out
+ \the\numexpr\XINT_mul_loop
+ 100000000!1;!\W #11;!\W #11;!%
+ 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+}%
+\def\xintiiPow {\romannumeral0\xintiipow }%
+\def\xintiipow #1#2%
+{%
+ \expandafter\xint_pow\the\numexpr #2\expandafter
+ .\romannumeral`&&@#1\xint:
+}%
+\def\xintiPow {\romannumeral0\xintipow }%
+\def\xintipow #1#2%
+{%
+ \expandafter\xint_pow\the\numexpr #2\expandafter
+ .\romannumeral0\xintnum{#1}\xint:
+}%
+\def\xint_pow #1.#2%#3\xint:
+{%
+ \xint_UDzerominusfork
+ #2-\XINT_pow_AisZero
+ 0#2\XINT_pow_Aneg
+ 0-{\XINT_pow_Apos #2}%
+ \krof {#1}%
+}%
+\def\XINT_pow_AisZero #1#2\xint:
+{%
+ \ifcase\XINT_cntSgn #1\xint:
+ \xint_afterfi { 1}%
+ \or
+ \xint_afterfi { 0}%
+ \else
+ \xint_afterfi
+ {\XINT_signalcondition{DivisionByZero}{Zero to power #1}{}{0}}%
+ \fi
+}%
+\def\XINT_pow_Aneg #1%
+{%
+ \ifodd #1
+ \expandafter\XINT_opp\romannumeral0%
+ \fi
+ \XINT_pow_Apos {}{#1}%
+}%
+\def\XINT_pow_Apos #1#2{\XINT_pow_Apos_a {#2}#1}%
+\def\XINT_pow_Apos_a #1#2#3%
+{%
+ \xint_gob_til_xint: #3\XINT_pow_Apos_short\xint:
+ \XINT_pow_AatleastTwo {#1}#2#3%
+}%
+\def\XINT_pow_Apos_short\xint:\XINT_pow_AatleastTwo #1#2\xint:
+{%
+ \ifcase #2
+ \xintError:thiscannothappen
+ \or \expandafter\XINT_pow_AisOne
+ \else\expandafter\XINT_pow_AatleastTwo
+ \fi {#1}#2\xint:
+}%
+\def\XINT_pow_AisOne #1\xint:{ 1}%
+\def\XINT_pow_AatleastTwo #1%
+{%
+ \ifcase\XINT_cntSgn #1\xint:
+ \expandafter\XINT_pow_BisZero
+ \or
+ \expandafter\XINT_pow_I_in
+ \else
+ \expandafter\XINT_pow_BisNegative
+ \fi
+ {#1}%
+}%
+\def\XINT_pow_BisNegative #1\xint:{\XINT_signalcondition{Underflow}{Inverse power
+ can not be represented by an integer}{}{0}}%
+\def\XINT_pow_BisZero #1\xint:{ 1}%
+\def\XINT_pow_I_in #1#2\xint:
+{%
+ \expandafter\XINT_pow_I_loop
+ \the\numexpr #1\expandafter\xint:%
+ \romannumeral0\expandafter\XINT_sepandrev
+ \romannumeral0\XINT_zeroes_forviii #2\R\R\R\R\R\R\R\R{10}0000001\W
+ #2\XINT_rsepbyviii_end_A 2345678%
+ \XINT_rsepbyviii_end_B 2345678\relax XX%
+ \R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\W
+ 1;!\W
+ 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+}%
+\def\XINT_pow_I_loop #1\xint:%
+{%
+ \ifnum #1 = \xint_c_i\expandafter\XINT_pow_I_exit\fi
+ \ifodd #1
+ \expandafter\XINT_pow_II_in
+ \else
+ \expandafter\XINT_pow_I_squareit
+ \fi #1\xint:%
+}%
+\def\XINT_pow_I_exit \ifodd #1\fi #2\xint:#3\W {\XINT_mul_out #3}%
+\def\XINT_pow_I_squareit #1\xint:#2\W%
+{%
+ \expandafter\XINT_pow_I_loop
+ \the\numexpr #1/\xint_c_ii\expandafter\xint:%
+ \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W
+}%
+\def\XINT_pow_mulbutcheckifsmall #1!1#2%
+{%
+ \xint_gob_til_sc #2\XINT_pow_mul_small;%
+ \XINT_mul_loop 100000000!1;!\W #1!1#2%
+}%
+\def\XINT_pow_mul_small;\XINT_mul_loop
+ 100000000!1;!\W 1#1!1;!\W
+{%
+ \XINT_smallmul 1#1!%
+}%
+\def\XINT_pow_II_in #1\xint:#2\W
+{%
+ \expandafter\XINT_pow_II_loop
+ \the\numexpr #1/\xint_c_ii-\xint_c_i\expandafter\xint:%
+ \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W #2\W
+}%
+\def\XINT_pow_II_loop #1\xint:%
+{%
+ \ifnum #1 = \xint_c_i\expandafter\XINT_pow_II_exit\fi
+ \ifodd #1
+ \expandafter\XINT_pow_II_odda
+ \else
+ \expandafter\XINT_pow_II_even
+ \fi #1\xint:%
+}%
+\def\XINT_pow_II_exit\ifodd #1\fi #2\xint:#3\W #4\W
+{%
+ \expandafter\XINT_mul_out
+ \the\numexpr\XINT_pow_mulbutcheckifsmall #4\W #3%
+}%
+\def\XINT_pow_II_even #1\xint:#2\W
+{%
+ \expandafter\XINT_pow_II_loop
+ \the\numexpr #1/\xint_c_ii\expandafter\xint:%
+ \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W
+}%
+\def\XINT_pow_II_odda #1\xint:#2\W #3\W
+{%
+ \expandafter\XINT_pow_II_oddb
+ \the\numexpr #1/\xint_c_ii-\xint_c_i\expandafter\xint:%
+ \the\numexpr\XINT_pow_mulbutcheckifsmall #3\W #2\W #2\W
+}%
+\def\XINT_pow_II_oddb #1\xint:#2\W #3\W
+{%
+ \expandafter\XINT_pow_II_loop
+ \the\numexpr #1\expandafter\xint:%
+ \the\numexpr\XINT_pow_mulbutcheckifsmall #3\W #3\W #2\W
+}%
+\def\xintiiFac {\romannumeral0\xintiifac }%
+\def\xintiifac #1{\expandafter\XINT_fac_fork\the\numexpr#1.}%
+\def\xintiFac {\romannumeral0\xintifac }%
+\let\xintifac\xintiifac
+\def\XINT_fac_fork #1#2.%
+{%
+ \xint_UDzerominusfork
+ #1-\XINT_fac_zero
+ 0#1\XINT_fac_neg
+ 0-\XINT_fac_checksize
+ \krof #1#2.%
+}%
+\def\XINT_fac_zero #1.{ 1}%
+\def\XINT_fac_neg #1.{\XINT_signalcondition{InvalidOperation}{Factorial of
+ negative: (#1)!}{}{0}}%
+\def\XINT_fac_checksize #1.%
+{%
+ \ifnum #1>\xint_c_x^iv \xint_dothis{\XINT_fac_toobig #1.}\fi
+ \ifnum #1>465 \xint_dothis{\XINT_fac_bigloop_a #1.}\fi
+ \ifnum #1>101 \xint_dothis{\XINT_fac_medloop_a #1.\XINT_mul_out}\fi
+ \xint_orthat{\XINT_fac_smallloop_a #1.\XINT_mul_out}%
+ 1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
+}%
+\def\XINT_fac_toobig #1.#2\W{\XINT_signalcondition{InvalidOperation}{Factorial
+ of too big argument: #1 > 10000}{}{0}}%
+\def\XINT_fac_bigloop_a #1.%
+{%
+ \expandafter\XINT_fac_bigloop_b \the\numexpr
+ #1+\xint_c_i-\xint_c_ii*((#1-464)/\xint_c_ii).#1.%
+}%
+\def\XINT_fac_bigloop_b #1.#2.%
+{%
+ \expandafter\XINT_fac_medloop_a
+ \the\numexpr #1-\xint_c_i.{\XINT_fac_bigloop_loop #1.#2.}%
+}%
+\def\XINT_fac_bigloop_loop #1.#2.%
+{%
+ \ifnum #1>#2 \expandafter\XINT_fac_bigloop_exit\fi
+ \expandafter\XINT_fac_bigloop_loop
+ \the\numexpr #1+\xint_c_ii\expandafter.%
+ \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_bigloop_mul #1!%
+}%
+\def\XINT_fac_bigloop_exit #1!{\XINT_mul_out}%
+\def\XINT_fac_bigloop_mul #1!%
+{%
+ \expandafter\XINT_smallmul
+ \the\numexpr \xint_c_x^viii+#1*(#1+\xint_c_i)!%
+}%
+\def\XINT_fac_medloop_a #1.%
+{%
+ \expandafter\XINT_fac_medloop_b
+ \the\numexpr #1+\xint_c_i-\xint_c_iii*((#1-100)/\xint_c_iii).#1.%
+}%
+\def\XINT_fac_medloop_b #1.#2.%
+{%
+ \expandafter\XINT_fac_smallloop_a
+ \the\numexpr #1-\xint_c_i.{\XINT_fac_medloop_loop #1.#2.}%
+}%
+\def\XINT_fac_medloop_loop #1.#2.%
+{%
+ \ifnum #1>#2 \expandafter\XINT_fac_loop_exit\fi
+ \expandafter\XINT_fac_medloop_loop
+ \the\numexpr #1+\xint_c_iii\expandafter.%
+ \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_medloop_mul #1!%
+}%
+\def\XINT_fac_medloop_mul #1!%
+{%
+ \expandafter\XINT_smallmul
+ \the\numexpr
+ \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)!%
+}%
+\def\XINT_fac_smallloop_a #1.%
+{%
+ \csname
+ XINT_fac_smallloop_\the\numexpr #1-\xint_c_iv*(#1/\xint_c_iv)\relax
+ \endcsname #1.%
+}%
+\expandafter\def\csname XINT_fac_smallloop_1\endcsname #1.%
+{%
+ \XINT_fac_smallloop_loop 2.#1.100000001!1;!%
+}%
+\expandafter\def\csname XINT_fac_smallloop_-2\endcsname #1.%
+{%
+ \XINT_fac_smallloop_loop 3.#1.100000002!1;!%
+}%
+\expandafter\def\csname XINT_fac_smallloop_-1\endcsname #1.%
+{%
+ \XINT_fac_smallloop_loop 4.#1.100000006!1;!%
+}%
+\expandafter\def\csname XINT_fac_smallloop_0\endcsname #1.%
+{%
+ \XINT_fac_smallloop_loop 5.#1.1000000024!1;!%
+}%
+\def\XINT_fac_smallloop_loop #1.#2.%
+{%
+ \ifnum #1>#2 \expandafter\XINT_fac_loop_exit\fi
+ \expandafter\XINT_fac_smallloop_loop
+ \the\numexpr #1+\xint_c_iv\expandafter.%
+ \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_smallloop_mul #1!%
+}%
+\def\XINT_fac_smallloop_mul #1!%
+{%
+ \expandafter\XINT_smallmul
+ \the\numexpr
+ \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)*(#1+\xint_c_iii)!%
+}%
+\def\XINT_fac_loop_exit #1!#2;!#3{#3#2;!}%
\catcode`! 11
\def\xintAbs {\Did_you_mean_iiAbs?or_load_xintfrac!}%
\def\xintOpp {\Did_you_mean_iiOpp?or_load_xintfrac!}%
@@ -2032,6 +2229,7 @@
\def\xintSqr {\Did_you_mean_iiSqr?or_load_xintfrac!}%
\def\xintQuo {\Removed!use_xintiQuo_or_xintiiQuo!}%
\def\xintRem {\Removed!use_xintiRem_or_xintiiRem!}%
+\catcode`! 12
\XINT_restorecatcodes_endinput%
\endinput
%%
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintexpr.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintexpr.sty 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintexpr.sty 2017-07-27 21:26:25 UTC (rev 44900)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.2k 2017/01/06
+%% The xint bundle 1.2l 2017/07/26
%% Copyright (C) 2013-2017 by Jean-Francois Burnol
%% xintexpr: Expandable expression parser
%% ---------------------------------------------------------------
@@ -81,13 +81,16 @@
\XINTsetupcatcodes%
\XINT_providespackage
\ProvidesPackage{xintexpr}%
- [2017/01/06 1.2k Expandable expression parser (JFB)]%
+ [2017/07/26 1.2l Expandable expression parser (JFB)]%
\catcode`! 11
-\def\xint_gob_til_! #1!{}% catcode 11 ! default in xintexpr.sty code.
-\edef\XINT_expr_lockscan#1!% not used for decimal numbers in xintexpr 1.2
- {\noexpand\expandafter\space\noexpand\csname .=#1\endcsname }%
-\edef\XINT_expr_lockit
- #1{\noexpand\expandafter\space\noexpand\csname .=#1\endcsname }%
+\let\XINT_Cmp \xintiiCmp
+\def\xint_gob_til_! #1!{}% ! with catcode 11
+\def\XINT_expr_lockscan#1{% not used for decimal numbers in xintexpr 1.2
+\def\XINT_expr_lockscan##1!{\expandafter#1\csname .=##1\endcsname}%
+}\XINT_expr_lockscan{ }%
+\def\XINT_expr_lockit#1{%
+\def\XINT_expr_lockit##1{\expandafter#1\csname .=##1\endcsname}%
+}\XINT_expr_lockit{ }%
\def\XINT_expr_unlock_hex_in #1% expanded inside \csname..\endcsname
{\expandafter\XINT_expr_inhex\romannumeral`&&@\XINT_expr_unlock#1;}%
\def\XINT_expr_inhex #1.#2#3;% expanded inside \csname..\endcsname
@@ -252,7 +255,7 @@
\if ^#1\xint_dothis\XINT_:::_end\fi
\xint_orthat\XINT_pfloat::_d #1}%
\def\XINT_pfloat::_d #1,#2%
- {\expandafter\XINT_pfloat::_e\romannumeral0\XINT_pfloat_opt [\xint_relax #2]{#1},{#2}}%
+ {\expandafter\XINT_pfloat::_e\romannumeral0\XINT_pfloat_opt [\xint:#2]{#1},{#2}}%
\def\XINT_pfloat::_e #1,#2#3{\XINT_pfloat::_b {#2}{#3, #1}}%
\def\XINT_expr_getnext #1%
{%
@@ -332,6 +335,7 @@
\def\XINT_expr_scanint_endbycs#1#2\XINT_expr_scanint_d{\endcsname #1}%
\def\XINT_expr_scanint_c\string #1\XINT_expr_scanint_d
{%
+ \if _#1\xint_dothis\XINT_expr_scanint_d\fi
\if e#1\xint_dothis{[\the\numexpr0\XINT_expr_scanexp_a +}\fi
\if E#1\xint_dothis{[\the\numexpr0\XINT_expr_scanexp_a +}\fi
\if .#1\xint_dothis{\XINT_expr_startdec_a .}\fi
@@ -355,6 +359,7 @@
\def\XINT_expr_gobz_scanint_endbycs#1#2\XINT_expr_scanint_d{0\endcsname #1}%
\def\XINT_expr_gobz_scanint_c\string #1\XINT_expr_scanint_d
{%
+ \if _#1\xint_dothis\XINT_expr_gobz_scanint_d\fi
\if e#1\xint_dothis{0[\the\numexpr0\XINT_expr_scanexp_a +}\fi
\if E#1\xint_dothis{0[\the\numexpr0\XINT_expr_scanexp_a +}\fi
\if .#1\xint_dothis{\XINT_expr_gobz_startdec_a .}\fi
@@ -389,6 +394,7 @@
}%
\def\XINT_expr_scandec_c\string #1#2\the\numexpr#3-\xint_c_i.%
{%
+ \if _#1\xint_dothis{\XINT_expr_scandec_d#3.}\fi
\if e#1\xint_dothis{[\the\numexpr#3\XINT_expr_scanexp_a +}\fi
\if E#1\xint_dothis{[\the\numexpr#3\XINT_expr_scanexp_a +}\fi
\xint_orthat {[#3]\endcsname #1}%
@@ -402,8 +408,9 @@
{\string#2\expandafter\XINT_expr_scandec_d}\the\numexpr#1-\xint_c_i.%
}%
\def\XINT_expr_gobz_scandec_endbycs #1#2\xint_c_i.{0[0]\endcsname #1}%
-\def\XINT_expr_gobz_scandec_c\if0#1#2\fi #3\xint_c_i.%
+\def\XINT_expr_gobz_scandec_c\if0#1#2\fi #3\numexpr#4-\xint_c_i.%
{%
+ \if _#1\xint_dothis{\XINT_expr_gobz_scandec_b #4.}\fi
\if e#1\xint_dothis{0[\the\numexpr0\XINT_expr_scanexp_a +}\fi
\if E#1\xint_dothis{0[\the\numexpr0\XINT_expr_scanexp_a +}\fi
\xint_orthat {0[0]\endcsname #1}%
@@ -425,6 +432,7 @@
}%
\def\XINT_expr_scanexp_c\string #1\XINT_expr_scanexp_d
{%
+ \if _#1\xint_dothis \XINT_expr_scanexp_d \fi
\if +#1\xint_dothis {\XINT_expr_scanexp_a +}\fi
\if -#1\xint_dothis {\XINT_expr_scanexp_a -}\fi
\xint_orthat {]\endcsname #1}%
@@ -440,7 +448,11 @@
{%
\expandafter\XINT_expr_scanexp_bb\romannumeral`&&@#1%
}%
-\def\XINT_expr_scanexp_cb\string #1\XINT_expr_scanexp_db {]\endcsname #1}%
+\def\XINT_expr_scanexp_cb\string #1\XINT_expr_scanexp_db
+{%
+ \if _#1\xint_dothis\XINT_expr_scanexp_d\fi
+ \xint_orthat{]\endcsname #1}%
+}%
\def\XINT_expr_scanhex_I #1% #1="
{%
\expandafter\XINT_expr_getop\csname.=\expandafter
@@ -461,12 +473,9 @@
0\else1\fi\else0\fi\else1\fi\else0\fi 1%
\expandafter\XINT_expr_scanhexI_b
\else
- \if .#1%
- \expandafter\xint_firstoftwo
- \else % gather what we got so far, leave catcode 12 #1 in stream
- \expandafter\xint_secondoftwo
- \fi
- {\expandafter\XINT_expr_scanhex_transition}%
+ \if _#1\xint_dothis{\expandafter\XINT_expr_scanhexI_bgob}\fi
+ \if .#1\xint_dothis{\expandafter\XINT_expr_scanhex_transition}\fi
+ \xint_orthat % gather what we got so far, leave catcode 12 #1 in stream
{\xint_afterfi {.>\endcsname\endcsname}}%
\fi
#1%
@@ -475,6 +484,10 @@
{%
#1\expandafter\XINT_expr_scanhexI_a\romannumeral`&&@#2%
}%
+\def\XINT_expr_scanhexI_bgob #1#2%
+{%
+ \expandafter\XINT_expr_scanhexI_a\romannumeral`&&@#2%
+}%
\def\XINT_expr_scanhex_transition .#1%
{%
\expandafter.\expandafter.\expandafter
@@ -495,7 +508,8 @@
0\else1\fi\else0\fi\else1\fi\else0\fi 1%
\expandafter\XINT_expr_scanhexII_b
\else
- \xint_afterfi {\endcsname\endcsname}%
+ \if _#1\xint_dothis{\expandafter\XINT_expr_scanhexII_bgob}\fi
+ \xint_orthat{\xint_afterfi {\endcsname\endcsname}}%
\fi
#1%
}%
@@ -503,6 +517,10 @@
{%
#1\expandafter\XINT_expr_scanhexII_a\romannumeral`&&@#2%
}%
+\def\XINT_expr_scanhexII_bgob #1#2%
+{%
+ \expandafter\XINT_expr_scanhexII_a\romannumeral`&&@#2%
+}%
\def\XINT_expr_scanfunc
{%
\expandafter\XINT_expr_func\romannumeral`&&@\XINT_expr_scanfunc_a
@@ -975,8 +993,7 @@
\let\XINT_flexpr_op_:] \XINT_expr_op_:]
\let\XINT_iiexpr_op_:] \XINT_expr_op_:]
\let\XINT_expr_precedence_][: \xint_c_iii
-\edef\XINT_expr_op_][: #1{\xint_c_ii \expandafter\noexpand
- \csname XINT_expr_itself_][\endcsname #10\string :}%
+\edef\XINT_expr_op_][: #1{\xint_c_ii\noexpand\XINT_expr_itself_][#10\string :}%
\let\XINT_flexpr_op_][: \XINT_expr_op_][:
\let\XINT_iiexpr_op_][: \XINT_expr_op_][:
\catcode`[ 12 \catcode`] 12
@@ -2652,7 +2669,7 @@
\toks0 \expandafter{\the\toks0
\def\xintListSel:x:csv {~xintListSel:f:csv }%
}%
-\odef\XINT_expr_redefinemacros {\the\toks0}% Not \edef ! (subtle)
+\odef\XINT_expr_redefinemacros {\the\toks0}%
\def\XINT_expr_redefineprints
{%
\def\XINT_flexpr_noopt
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintfrac.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintfrac.sty 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintfrac.sty 2017-07-27 21:26:25 UTC (rev 44900)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.2k 2017/01/06
+%% The xint bundle 1.2l 2017/07/26
%% Copyright (C) 2013-2017 by Jean-Francois Burnol
%% xintfrac: Expandable operations on fractions
%% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintfrac}%
- [2017/01/06 1.2k Expandable operations on fractions (JFB)]%
+ [2017/07/26 1.2l Expandable operations on fractions (JFB)]%
\def\XINT_cntSgnFork #1%
{%
\ifcase #1\expandafter\xint_secondofthree
@@ -87,8 +87,7 @@
{%
\expandafter#1%
\the\numexpr \XINT_abs##1+%
- \XINT_len_fork ##2##3\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ \XINT_len_fork ##2##3\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye-\xint_c_i
\relax
@@ -95,7 +94,7 @@
}}\XINT_flen{ }%
\def\XINT_outfrac #1#2#3%
{%
- \ifcase\XINT_cntSgn #3\Z
+ \ifcase\XINT_cntSgn #3\xint:
\expandafter \XINT_outfrac_divisionbyzero
\or
\expandafter \XINT_outfrac_P
@@ -104,14 +103,14 @@
\fi
{#2}{#3}[#1]%
}%
-\def\XINT_outfrac_divisionbyzero #1#2{\xintError:DivisionByZero\space #1/0}%
-\edef\XINT_outfrac_P #1#2%
+\def\XINT_outfrac_divisionbyzero #1#2%
{%
- \noexpand\if0\noexpand\XINT_Sgn #1\noexpand\Z
- \noexpand\expandafter\noexpand\XINT_outfrac_Zero
- \noexpand\fi
- \space #1/#2%
+ \XINT_signalcondition{DivisionByZero}{Division of #1 by #2}{}{0/1[0]}%
}%
+\def\XINT_outfrac_P#1{%
+\def\XINT_outfrac_P ##1##2%
+ {\if0\XINT_Sgn ##1\xint:\expandafter\XINT_outfrac_Zero\fi#1##1/##2}%
+}\XINT_outfrac_P{ }%
\def\XINT_outfrac_Zero #1[#2]{ 0/1[0]}%
\def\XINT_outfrac_N #1#2%
{%
@@ -125,13 +124,13 @@
\def\XINT_inFrac {\romannumeral0\XINT_infrac }%
\def\XINT_infrac #1%
{%
- \expandafter\XINT_infrac_fork\romannumeral`&&@#1/\XINT_W[\XINT_W\XINT_T
+ \expandafter\XINT_infrac_fork\romannumeral`&&@#1\xint:/\XINT_W[\XINT_W\XINT_T
}%
\def\XINT_infrac_fork #1[#2%
{%
\xint_UDXINTWfork
- #2\XINT_frac_gen
- \XINT_W\XINT_infrac_res_a % strict A[N] or A/B[N] input
+ #2\XINT_frac_gen % input has no brackets [N]
+ \XINT_W\XINT_infrac_res_a % there is some [N], must be strict A[N] or A/B[N] input
\krof
#1[#2%
}%
@@ -143,27 +142,27 @@
\def\XINT_infrac_res_b #1/#2%
{%
\xint_UDXINTWfork
- #2\XINT_infrac_res_ca
- \XINT_W\XINT_infrac_res_cb
+ #2\XINT_infrac_res_ca % it was A[N] input
+ \XINT_W\XINT_infrac_res_cb % it was A/B[N] input
\krof
#1/#2%
}%
-\def\XINT_infrac_res_ca #1[#2]/\XINT_W[\XINT_W\XINT_T
+\def\XINT_infrac_res_ca #1[#2]\xint:/\XINT_W[\XINT_W\XINT_T
{\expandafter{\the\numexpr #2}{#1}{1}}%
\def\XINT_infrac_res_cb #1/#2[%
{\expandafter\XINT_infrac_res_cc\romannumeral`&&@#2~#1[}%
-\def\XINT_infrac_res_cc #1~#2[#3]/\XINT_W[\XINT_W\XINT_T
+\def\XINT_infrac_res_cc #1~#2[#3]\xint:/\XINT_W[\XINT_W\XINT_T
{\expandafter{\the\numexpr #3}{#2}{#1}}%
\def\XINT_frac_gen #1/#2%
{%
\xint_UDXINTWfork
- #2\XINT_frac_gen_A
- \XINT_W\XINT_frac_gen_B
+ #2\XINT_frac_gen_A % there was no /
+ \XINT_W\XINT_frac_gen_B % there was a /
\krof
#1/#2%
}%
-\def\XINT_frac_gen_A #1/\XINT_W [\XINT_W {\XINT_frac_gen_C 0~1!#1ee.\XINT_W }%
-\def\XINT_frac_gen_B #1/#2/\XINT_W[%\XINT_W
+\def\XINT_frac_gen_A #1\xint:/\XINT_W [\XINT_W {\XINT_frac_gen_C 0~1!#1ee.\XINT_W }%
+\def\XINT_frac_gen_B #1/#2\xint:/\XINT_W[%\XINT_W
{%
\expandafter\XINT_frac_gen_Ba
\romannumeral`&&@#2ee.\XINT_W\XINT_Z #1ee.%\XINT_W
@@ -186,8 +185,7 @@
{%
\expandafter\XINT_frac_gen_C\the\numexpr #3-%
\numexpr\XINT_length_loop
- #1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
~#2#1!%
@@ -203,9 +201,8 @@
\def\XINT_frac_gen_Ca #1~#2!#3e#4e#5\XINT_T
{%
\expandafter\XINT_frac_gen_F\the\numexpr #4-#1\expandafter
- ~\romannumeral0\XINT_num_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z~#3~%
+ ~\romannumeral0\expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z~#3~%
}%
\def\XINT_frac_gen_Cb #1.#2e%
{%
@@ -215,13 +212,12 @@
{%
\expandafter\XINT_frac_gen_F\the\numexpr #5-#2-%
\numexpr\XINT_length_loop
- #1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
- \relax\expandafter~\romannumeral0\XINT_num_loop
- #3\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z
+ \relax\expandafter~%
+ \romannumeral0\expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop
+ #3\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
~#4#1~%
}%
\def\XINT_frac_gen_F #1~#2%
@@ -235,20 +231,18 @@
\def\XINT_frac_gen_Gdivbyzero #1~~#2~%
{%
\expandafter\XINT_frac_gen_Gdivbyzero_a
- \romannumeral0\XINT_num_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z~#1~%
+ \romannumeral0\expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z~#1~%
}%
\def\XINT_frac_gen_Gdivbyzero_a #1~#2~%
{%
- \xintError:DivisionByZero {#2}{#1}{0}%
+ \XINT_signalcondition{DivisionByZero}{Division of #1 by zero}{}{{#2}{#1}{0}}%
}%
\def\XINT_frac_gen_G #1#2#3~#4~#5~%
{%
\expandafter\XINT_frac_gen_Ga
- \romannumeral0\XINT_num_loop
- #1#5\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\Z~#3~{#2#4}%
+ \romannumeral0\expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop
+ #1#5\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z~#3~{#2#4}%
}%
\def\XINT_frac_gen_Ga #1#2~#3~%
{%
@@ -260,10 +254,10 @@
{%
\expandafter\XINT_cuz_cnt_loop\expandafter
{\expandafter}\romannumeral0\XINT_rord_main {}#1%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax
+ \xint:
\R\R\R\R\R\R\R\R\Z
}%
\def\XINT_cuz_cnt #1%
@@ -344,10 +338,10 @@
{%
\expandafter\space\expandafter
{\romannumeral0\XINT_rord_main {}#2%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax }{#1}%
+ \xint:}{#1}%
}%
\def\xintRaw {\romannumeral0\xintraw }%
\def\xintraw
@@ -412,7 +406,7 @@
}%
\def\XINT_numer #1%
{%
- \ifcase\XINT_cntSgn #1\Z
+ \ifcase\XINT_cntSgn #1\xint:
\expandafter\XINT_numer_B
\or
\expandafter\XINT_numer_A
@@ -611,8 +605,14 @@
\krof
{#3#4}{#1#2}{#3#4}{#1#2}%
}%
-\def\XINT_irr_indeterminate #1#2#3#4#5{\xintError:NaN\space 0/0}%
-\def\XINT_irr_divisionbyzero #1#2#3#4#5{\xintError:DivisionByZero #5#2/0}%
+\def\XINT_irr_indeterminate #1#2#3#4#5%
+{%
+ \XINT_signalcondition{DivisionUndefined}{indeterminate: 0/0}{}{0/1}%
+}%
+\def\XINT_irr_divisionbyzero #1#2#3#4#5%
+{%
+ \XINT_signalcondition{DivisionByZero}{vanishing denominator: #5#2/0}{}{0/1}%
+}%
\def\XINT_irr_zero #1#2#3#4#5{ 0/1}% changed in 1.08
\def\XINT_irr_loop_a #1#2%
{%
@@ -678,8 +678,14 @@
\krof
{#3#4}{#1#2}1001%
}%
-\def\XINT_jrr_indeterminate #1#2#3#4#5#6#7{\xintError:NaN\space 0/0}%
-\def\XINT_jrr_divisionbyzero #1#2#3#4#5#6#7{\xintError:DivisionByZero #7#2/0}%
+\def\XINT_jrr_indeterminate #1#2#3#4#5#6#7%
+{%
+ \XINT_signalcondition{DivisionUndefined}{indeterminate: 0/0}{}{0/1}%
+}%
+\def\XINT_jrr_divisionbyzero #1#2#3#4#5#6#7%
+{%
+ \XINT_signalcondition{DivisionByZero}{Vanishing denominator: #7#2/0}{}{0/1}%
+}%
\def\XINT_jrr_zero #1#2#3#4#5#6#7{ 0/1}% changed in 1.08
\def\XINT_jrr_loop_a #1#2%
{%
@@ -689,8 +695,8 @@
\def\XINT_jrr_loop_b #1#2#3#4#5#6#7%
{%
\expandafter \XINT_jrr_loop_c \expandafter
- {\romannumeral0\xintiiadd{\XINT_mul_fork #4\Z #1\Z}{#6}}%
- {\romannumeral0\xintiiadd{\XINT_mul_fork #5\Z #1\Z}{#7}}%
+ {\romannumeral0\xintiiadd{\XINT_mul_fork #4\xint:#1\xint:}{#6}}%
+ {\romannumeral0\xintiiadd{\XINT_mul_fork #5\xint:#1\xint:}{#7}}%
{#2}{#3}{#4}{#5}%
}%
\def\XINT_jrr_loop_c #1#2%
@@ -732,8 +738,8 @@
}%
\def\XINT_trunc_a #1#2#3#4.#5%
{%
- \if0\XINT_Sgn#2\Z\xint_dothis\XINT_trunc_zero\fi
- \if1\XINT_is_one#3XY\xint_dothis\XINT_trunc_sp_b\fi
+ \if0\XINT_Sgn#2\xint:\xint_dothis\XINT_trunc_zero\fi
+ \if1\XINT_is_One#3XY\xint_dothis\XINT_trunc_sp_b\fi
\xint_orthat\XINT_trunc_b #1+#4.{#2}{#3}#5#4.%
}%
\def\XINT_trunc_zero #1.#2.{ 0}%
@@ -772,8 +778,7 @@
\expandafter\XINT_trunc_sp_Cc
\romannumeral0\expandafter\XINT_split_fromright_a
\the\numexpr#3-\numexpr\XINT_length_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
.#2\xint_bye2345678\xint_bye..#1%
@@ -851,8 +856,8 @@
}%
\def\XINT_round_a #1#2#3#4.%
{%
- \if0\XINT_Sgn#2\Z\xint_dothis\XINT_trunc_zero\fi
- \if1\XINT_is_one#3XY\xint_dothis\XINT_trunc_sp_b\fi
+ \if0\XINT_Sgn#2\xint:\xint_dothis\XINT_trunc_zero\fi
+ \if1\XINT_is_One#3XY\xint_dothis\XINT_trunc_sp_b\fi
\xint_orthat\XINT_trunc_b #1+#4.{#2}{#3}%
}%
\def\XINT_round_A{\expandafter\XINT_trunc_G\romannumeral0\XINT_round_B}%
@@ -880,7 +885,8 @@
\def\XINT_xtrunc_zero #1#2]{0.\romannumeral\xintreplicate{#1}0}%
\def\XINT_xtrunc_d #1#2#3/#4[#5]%
{%
- \XINT_xtrunc_prepare_a#4\R\R\R\R\R\R\R\R {10}0000001\W !{#4};{#5}{#2}{#1#3}%
+ \XINT_xtrunc_prepare_a#4\R\R\R\R\R\R\R\R {10}0000001\W
+ !{#4};{#5}{#2}{#1#3}%
}%
\def\XINT_xtrunc_prepare_a #1#2#3#4#5#6#7#8#9%
{%
@@ -930,12 +936,13 @@
{%
\expandafter\XINT_xtrunc_e\expandafter
{\expandafter\XINT_xtrunc_small_a
- \the\numexpr #1/\xint_c_ii\expandafter.\the\numexpr \xint_c_x^viii+#1!}%
+ \the\numexpr #1/\xint_c_ii\expandafter
+ .\the\numexpr \xint_c_x^viii+#1!}%
}%
\def\XINT_xtrunc_small_a #1.#2!#3%
{%
\expandafter\XINT_div_small_b\the\numexpr #1\expandafter
- .\the\numexpr #2\expandafter!%
+ \xint:\the\numexpr #2\expandafter!%
\romannumeral0\XINT_div_small_ba #3\R\R\R\R\R\R\R\R{10}0000001\W
#3\XINT_sepbyviii_Z_end 2345678\relax
}%
@@ -947,7 +954,8 @@
}%
\def\XINT_xtrunc_prepare_d #1#2#3#4#5#6#7#8#9%
{%
- \expandafter\XINT_xtrunc_prepare_e\xint_gob_til_dot #1#2#3#4#5#6#7#8#9!%
+ \expandafter\XINT_xtrunc_prepare_e
+ \xint_gob_til_dot #1#2#3#4#5#6#7#8#9!%
}%
\def\XINT_xtrunc_prepare_e #1!#2!#3#4%
{%
@@ -958,14 +966,13 @@
\expandafter\XINT_xtrunc_prepare_g\expandafter
\XINT_div_prepare_g
\the\numexpr #1#2#3#4#5#6#7#8+\xint_c_i\expandafter
- .\the\numexpr (#1#2#3#4#5#6#7#8+\xint_c_i)/\xint_c_ii\expandafter
- .\the\numexpr #1#2#3#4#5#6#7#8\expandafter
- .\romannumeral0\XINT_sepandrev_andcount
+ \xint:\the\numexpr (#1#2#3#4#5#6#7#8+\xint_c_i)/\xint_c_ii\expandafter
+ \xint:\the\numexpr #1#2#3#4#5#6#7#8\expandafter
+ \xint:\romannumeral0\XINT_sepandrev_andcount
#1#2#3#4#5#6#7#8#9\XINT_rsepbyviii_end_A 2345678%
- \XINT_rsepbyviii_end_B 2345678%
- \relax\xint_c_ii\xint_c_iii
- \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
- \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
+ \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
+ \R\xint:\xint_c_xii \R\xint:\xint_c_x \R\xint:\xint_c_viii \R\xint:\xint_c_vi
+ \R\xint:\xint_c_iv \R\xint:\xint_c_ii \R\xint:\xint_c_\W
\X
}%
\def\XINT_xtrunc_prepare_g #1;{\XINT_xtrunc_e {#1}}%
@@ -975,15 +982,15 @@
\expandafter\XINT_xtrunc_I
\else
\expandafter\XINT_xtrunc_II
- \fi #2.{#1}%
+ \fi #2\xint:{#1}%
}%
-\def\XINT_xtrunc_I -#1.#2#3#4%
+\def\XINT_xtrunc_I -#1\xint:#2#3#4%
{%
\expandafter\XINT_xtrunc_I_a\romannumeral0#2{#4}{#2}{#1}{#3}%
}%
\def\XINT_xtrunc_I_a #1#2#3#4#5%
{%
- \expandafter\XINT_xtrunc_I_b\the\numexpr #4-#5.#4.{#5}{#2}{#3}{#1}%
+ \expandafter\XINT_xtrunc_I_b\the\numexpr #4-#5\xint:#4\xint:{#5}{#2}{#3}{#1}%
}%
\def\XINT_xtrunc_I_b #1%
{%
@@ -992,12 +999,12 @@
-\XINT_xtrunc_IB_c
\krof #1%
}%
-\def\XINT_xtrunc_IA_c -#1.#2.#3#4#5#6%
+\def\XINT_xtrunc_IA_c -#1\xint:#2\xint:#3#4#5#6%
{%
\expandafter\XINT_xtrunc_IA_d
- \the\numexpr#2-\xintLength{#6}.{#6}%
+ \the\numexpr#2-\xintLength{#6}\xint:{#6}%
\expandafter\XINT_xtrunc_IA_xd
- \the\numexpr (#1+\xint_c_ii^v)/\xint_c_ii^vi-\xint_c_i.#1.{#5}{#4}%
+ \the\numexpr (#1+\xint_c_ii^v)/\xint_c_ii^vi-\xint_c_i\xint:#1\xint:{#5}{#4}%
}%
\def\XINT_xtrunc_IA_d #1%
{%
@@ -1006,24 +1013,24 @@
-\XINT_xtrunc_IAB_e
\krof #1%
}%
-\def\XINT_xtrunc_IAA_e -#1.#2%
+\def\XINT_xtrunc_IAA_e -#1\xint:#2%
{%
\romannumeral0\XINT_split_fromleft
#1.#2\xint_gobble_i\xint_bye2345678\xint_bye..%
}%
-\def\XINT_xtrunc_IAB_e #1.#2%
+\def\XINT_xtrunc_IAB_e #1\xint:#2%
{%
0.\romannumeral\XINT_rep#1\endcsname0#2%
}%
-\def\XINT_xtrunc_IA_xd #1.#2.%
+\def\XINT_xtrunc_IA_xd #1\xint:#2\xint:%
{%
- \expandafter\XINT_xtrunc_IA_xe\the\numexpr #2-\xint_c_ii^vi*#1.#1.%
+ \expandafter\XINT_xtrunc_IA_xe\the\numexpr #2-\xint_c_ii^vi*#1\xint:#1\xint:%
}%
-\def\XINT_xtrunc_IA_xe #1.#2.#3#4%
+\def\XINT_xtrunc_IA_xe #1\xint:#2\xint:#3#4%
{%
\XINT_xtrunc_loop {#2}{#4}{#3}{#1}%
}%
-\def\XINT_xtrunc_IB_c #1.#2.#3#4#5#6%
+\def\XINT_xtrunc_IB_c #1\xint:#2\xint:#3#4#5#6%
{%
\expandafter\XINT_xtrunc_IB_d
\romannumeral0\XINT_split_xfork #1.#6\xint_bye2345678\xint_bye..{#3}%
@@ -1030,23 +1037,23 @@
}%
\def\XINT_xtrunc_IB_d #1.#2.#3%
{%
- \expandafter\XINT_xtrunc_IA_d\the\numexpr#3-\xintLength {#1}.{#1}%
+ \expandafter\XINT_xtrunc_IA_d\the\numexpr#3-\xintLength {#1}\xint:{#1}%
}%
-\def\XINT_xtrunc_II #1.%
+\def\XINT_xtrunc_II #1\xint:%
{%
- \expandafter\XINT_xtrunc_II_a\romannumeral\xintreplicate{#1}0.%
+ \expandafter\XINT_xtrunc_II_a\romannumeral\xintreplicate{#1}0\xint:%
}%
-\def\XINT_xtrunc_II_a #1.#2#3#4%
+\def\XINT_xtrunc_II_a #1\xint:#2#3#4%
{%
\expandafter\XINT_xtrunc_II_b
- \the\numexpr (#3+\xint_c_ii^v)/\xint_c_ii^vi-\xint_c_i\expandafter.%
- \the\numexpr #3\expandafter.\romannumeral0#2{#4#1}{#2}%
+ \the\numexpr (#3+\xint_c_ii^v)/\xint_c_ii^vi-\xint_c_i\expandafter\xint:%
+ \the\numexpr #3\expandafter\xint:\romannumeral0#2{#4#1}{#2}%
}%
-\def\XINT_xtrunc_II_b #1.#2.%
+\def\XINT_xtrunc_II_b #1\xint:#2\xint:%
{%
- \expandafter\XINT_xtrunc_II_c\the\numexpr #2-\xint_c_ii^vi*#1.#1.%
+ \expandafter\XINT_xtrunc_II_c\the\numexpr #2-\xint_c_ii^vi*#1\xint:#1\xint:%
}%
-\def\XINT_xtrunc_II_c #1.#2.#3#4#5%
+\def\XINT_xtrunc_II_c #1\xint:#2\xint:#3#4#5%
{%
#3.\XINT_xtrunc_loop {#2}{#4}{#5}{#1}%
}%
@@ -1053,9 +1060,9 @@
\def\XINT_xtrunc_loop #1%
{%
\ifnum #1=\xint_c_ \expandafter\XINT_xtrunc_transition\fi
- \expandafter\XINT_xtrunc_loop_a\the\numexpr #1-\xint_c_i.%
+ \expandafter\XINT_xtrunc_loop_a\the\numexpr #1-\xint_c_i\xint:%
}%
-\def\XINT_xtrunc_loop_a #1.#2#3%
+\def\XINT_xtrunc_loop_a #1\xint:#2#3%
{%
\expandafter\XINT_xtrunc_loop_b\romannumeral0#3%
{#20000000000000000000000000000000000000000000000000000000000000000}%
@@ -1067,7 +1074,7 @@
\XINT_xtrunc_loop {#3}{#2}%
}%
\def\XINT_xtrunc_transition
- \expandafter\XINT_xtrunc_loop_a\the\numexpr #1.#2#3#4%
+ \expandafter\XINT_xtrunc_loop_a\the\numexpr #1\xint:#2#3#4%
{%
\ifnum #4=\xint_c_ \expandafter\xint_gobble_vi\fi
\expandafter\XINT_xtrunc_finish\expandafter
@@ -1087,11 +1094,11 @@
\expandafter\XINT_xtrunc_sp_I
\else
\expandafter\XINT_xtrunc_sp_II
- \fi #1.%
+ \fi #1\xint:%
}%
-\def\XINT_xtrunc_sp_I -#1.#2#3%
+\def\XINT_xtrunc_sp_I -#1\xint:#2#3%
{%
- \expandafter\XINT_xtrunc_sp_I_a\the\numexpr #1-#3.#1.{#3}{#2}%
+ \expandafter\XINT_xtrunc_sp_I_a\the\numexpr #1-#3\xint:#1\xint:{#3}{#2}%
}%
\def\XINT_xtrunc_sp_I_a #1%
{%
@@ -1100,10 +1107,10 @@
-\XINT_xtrunc_sp_IB_b
\krof #1%
}%
-\def\XINT_xtrunc_sp_IA_b -#1.#2.#3#4%
+\def\XINT_xtrunc_sp_IA_b -#1\xint:#2\xint:#3#4%
{%
\expandafter\XINT_xtrunc_sp_IA_c
- \the\numexpr#2-\xintLength{#4}.{#4}\romannumeral\XINT_rep#1\endcsname0%
+ \the\numexpr#2-\xintLength{#4}\xint:{#4}\romannumeral\XINT_rep#1\endcsname0%
}%
\def\XINT_xtrunc_sp_IA_c #1%
{%
@@ -1112,16 +1119,16 @@
-\XINT_xtrunc_sp_IAB
\krof #1%
}%
-\def\XINT_xtrunc_sp_IAA -#1.#2%
+\def\XINT_xtrunc_sp_IAA -#1\xint:#2%
{%
\romannumeral0\XINT_split_fromleft
#1.#2\xint_gobble_i\xint_bye2345678\xint_bye..%
}%
-\def\XINT_xtrunc_sp_IAB #1.#2%
+\def\XINT_xtrunc_sp_IAB #1\xint:#2%
{%
0.\romannumeral\XINT_rep#1\endcsname0#2%
}%
-\def\XINT_xtrunc_sp_IB_b #1.#2.#3#4%
+\def\XINT_xtrunc_sp_IB_b #1\xint:#2\xint:#3#4%
{%
\expandafter\XINT_xtrunc_sp_IB_c
\romannumeral0\XINT_split_xfork #1.#4\xint_bye2345678\xint_bye..{#3}%
@@ -1128,9 +1135,9 @@
}%
\def\XINT_xtrunc_sp_IB_c #1.#2.#3%
{%
- \expandafter\XINT_xtrunc_sp_IA_c\the\numexpr#3-\xintLength {#1}.{#1}%
+ \expandafter\XINT_xtrunc_sp_IA_c\the\numexpr#3-\xintLength {#1}\xint:{#1}%
}%
-\def\XINT_xtrunc_sp_II #1.#2#3%
+\def\XINT_xtrunc_sp_II #1\xint:#2#3%
{%
#2\romannumeral\XINT_rep#1\endcsname0.\romannumeral\XINT_rep#3\endcsname0%
}%
@@ -1190,7 +1197,7 @@
}%
\def\XINT_fadd_E #1#2%
{%
- \if0\XINT_Sgn #2\Z
+ \if0\XINT_Sgn #2\xint:
\expandafter\XINT_fadd_F
\else\expandafter\XINT_fadd_K
\fi {#1}%
@@ -1206,7 +1213,7 @@
}%
\def\XINT_fadd_Ea #1#2%
{%
- \if0\XINT_Sgn #2\Z
+ \if0\XINT_Sgn #2\xint:
\expandafter\XINT_fadd_Fa
\else\expandafter\XINT_fadd_K
\fi {#1}%
@@ -1216,7 +1223,9 @@
\expandafter\XINT_fadd_G
\romannumeral0\xintiiadd {\xintiiMul {#4}{#1}}{#5}/#3%[#6]%
}%
-\def\XINT_fadd_G #1{\if0#1\XINT_fadd_iszero\fi\space #1}%
+\def\XINT_fadd_G #1{%
+\def\XINT_fadd_G ##1{\if0##1\expandafter\XINT_fadd_iszero\fi#1##1}%
+}\XINT_fadd_G{ }%
\def\XINT_fadd_K #1#2#3#4#5%
{%
\expandafter\XINT_fadd_L
@@ -1223,11 +1232,11 @@
\romannumeral0\xintiiadd {\xintiiMul {#2}{#5}}{\xintiiMul {#3}{#4}}.%
{{#2}{#3}}%
}%
-\def\XINT_fadd_L #1{\if0#1\XINT_fadd_iszero\fi \XINT_fadd_M #1}%
+\def\XINT_fadd_L #1{\if0#1\expandafter\XINT_fadd_iszero\fi\XINT_fadd_M #1}%
\def\XINT_fadd_M #1.#2{\expandafter\XINT_fadd_N \expandafter
{\romannumeral0\xintiimul #2}{#1}}%
\def\XINT_fadd_N #1#2{ #2/#1}%
-\edef\XINT_fadd_iszero\fi #1[#2]{\noexpand\fi\space 0/1[0]}% ou [#2] originel?
+\def\XINT_fadd_iszero #1[#2]{ 0/1[0]}% ou [#2] originel?
\def\xintSub {\romannumeral0\xintsub }%
\def\xintsub #1{\expandafter\XINT_fsub\romannumeral0\xintraw {#1}}%
\def\XINT_fsub #1{\xint_gob_til_zero #1\XINT_fsub_Azero 0\XINT_fsub_a #1}%
@@ -1240,24 +1249,21 @@
0-{\XINT_fadd_c -#1}%
\krof }%
\def\xintSum {\romannumeral0\xintsum }%
-\def\xintsum #1{\xintsumexpr #1\relax }%
-\def\xintSumExpr {\romannumeral0\xintsumexpr }%
-\def\xintsumexpr {\expandafter\XINT_fsumexpr\romannumeral`&&@}%
+\def\xintsum #1{\expandafter\XINT_fsumexpr\romannumeral`&&@#1\xint:}%
\def\XINT_fsumexpr {\XINT_fsum_loop_a {0/1[0]}}%
\def\XINT_fsum_loop_a #1#2%
{%
- \expandafter\XINT_fsum_loop_b \romannumeral`&&@#2\Z {#1}%
+ \expandafter\XINT_fsum_loop_b \romannumeral`&&@#2\xint:{#1}%
}%
\def\XINT_fsum_loop_b #1%
{%
- \xint_gob_til_relax #1\XINT_fsum_finished\relax
- \XINT_fsum_loop_c #1%
+ \xint_gob_til_xint: #1\XINT_fsum_finished\xint:\XINT_fsum_loop_c #1%
}%
-\def\XINT_fsum_loop_c #1\Z #2%
+\def\XINT_fsum_loop_c #1\xint:#2%
{%
\expandafter\XINT_fsum_loop_a\expandafter{\romannumeral0\xintadd {#2}{#1}}%
}%
-\def\XINT_fsum_finished #1\Z #2{ #2}%
+\def\XINT_fsum_finished #1\xint:\xint:#2{ #2}%
\def\xintMul {\romannumeral0\xintmul }%
\def\xintmul #1{\expandafter\XINT_fmul\romannumeral0\xintraw {#1}.}%
\def\XINT_fmul #1{\xint_gob_til_zero #1\XINT_fmul_zero 0\XINT_fmul_a #1}%
@@ -1291,7 +1297,8 @@
\def\XINT_fsqr_zero #1]{ 0/1[0]}%
\def\xintipow #1#2%
{%
- \expandafter\xint_pow\the\numexpr \xintNum{#2}\expandafter.\romannumeral0\xintnum{#1}\Z%
+ \expandafter\xint_pow\the\numexpr \xintNum{#2}\expandafter
+ .\romannumeral0\xintnum{#1}\xint:
}%
\def\xintPow {\romannumeral0\xintpow }%
\def\xintpow #1%
@@ -1343,24 +1350,21 @@
\the\numexpr\xintNum{#1}\expandafter.\the\numexpr\xintNum{#2}.%
}%
\def\xintPrd {\romannumeral0\xintprd }%
-\def\xintprd #1{\xintprdexpr #1\relax }%
-\def\xintPrdExpr {\romannumeral0\xintprdexpr }%
-\def\xintprdexpr {\expandafter\XINT_fprdexpr \romannumeral`&&@}%
+\def\xintprd #1{\expandafter\XINT_fprdexpr \romannumeral`&&@#1\xint:}%
\def\XINT_fprdexpr {\XINT_fprod_loop_a {1/1[0]}}%
\def\XINT_fprod_loop_a #1#2%
{%
- \expandafter\XINT_fprod_loop_b \romannumeral`&&@#2\Z {#1}%
+ \expandafter\XINT_fprod_loop_b \romannumeral`&&@#2\xint:{#1}%
}%
\def\XINT_fprod_loop_b #1%
{%
- \xint_gob_til_relax #1\XINT_fprod_finished\relax
- \XINT_fprod_loop_c #1%
+ \xint_gob_til_xint: #1\XINT_fprod_finished\xint:\XINT_fprod_loop_c #1%
}%
-\def\XINT_fprod_loop_c #1\Z #2%
+\def\XINT_fprod_loop_c #1\xint:#2%
{%
\expandafter\XINT_fprod_loop_a\expandafter{\romannumeral0\xintmul {#1}{#2}}%
}%
-\def\XINT_fprod_finished #1\Z #2{ #2}%
+\def\XINT_fprod_finished#1\xint:\xint:#2{ #2}%
\def\xintDiv {\romannumeral0\xintdiv }%
\def\xintdiv #1%
{%
@@ -1393,7 +1397,7 @@
{\expandafter\XINT_mod_b\expandafter #1\romannumeral0\xintraw{#3}#2.}%
\def\XINT_mod_b #1#2% #1 de A, #2 de B.
{%
- \if0#2\xint_dothis\XINT_mod_divbyzero\fi
+ \if0#2\xint_dothis{\XINT_mod_divbyzero #1#2}\fi
\if0#1\xint_dothis\XINT_mod_aiszero\fi
\if-#2\xint_dothis{\XINT_mod_bneg #1}\fi
\xint_orthat{\XINT_mod_bpos #1#2}%
@@ -1412,7 +1416,10 @@
-{\XINT_mod_pos #1}%
\krof
}%
-\def\XINT_mod_divbyzero #1.{\xintError:DivisionByZero\space 0/1[0]}%
+\def\XINT_mod_divbyzero #1#2[#3]#4.%
+{%
+ \XINT_signalcondition{DivisionByZero}{Division by #2[#3] of #1#4}{}{0/1[0]}%
+}%
\def\XINT_mod_aiszero #1.{ 0/1[0]}%
\def\XINT_mod_pos #1#2/#3[#4]#5/#6[#7].%
{%
@@ -1427,7 +1434,7 @@
\def\xintisone #1{\expandafter\XINT_fracisone
\romannumeral0\xintrawwithzeros{#1}\Z }%
\def\XINT_fracisone #1/#2\Z
- {\if0\XINT_Cmp {#1}{#2}\xint_afterfi{ 1}\else\xint_afterfi{ 0}\fi}%
+ {\if0\xintiiCmp {#1}{#2}\xint_afterfi{ 1}\else\xint_afterfi{ 0}\fi}%
\def\xintGeq {\romannumeral0\xintgeq }%
\def\xintgeq #1%
{%
@@ -1460,7 +1467,7 @@
\def\XINT_fgeq_D #1#2#3%
{%
\expandafter\XINT_cntSgnFork\romannumeral`&&@\expandafter\XINT_cntSgn
- \the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax\Z
+ \the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax\xint:
{ 0}{\XINT_fgeq_E #2\Z {#3}{#1}}{ 1}%
}%
\def\XINT_fgeq_E #1%
@@ -1516,15 +1523,15 @@
\fi
}%
\def\xintMaxof {\romannumeral0\xintmaxof }%
-\def\xintmaxof #1{\expandafter\XINT_maxof_a\romannumeral`&&@#1\relax }%
-\def\XINT_maxof_a #1{\expandafter\XINT_maxof_b\romannumeral0\xintraw{#1}\Z }%
-\def\XINT_maxof_b #1\Z #2%
- {\expandafter\XINT_maxof_c\romannumeral`&&@#2\Z {#1}\Z}%
+\def\xintmaxof #1{\expandafter\XINT_maxof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_maxof_a #1{\expandafter\XINT_maxof_b\romannumeral0\xintraw{#1}!}%
+\def\XINT_maxof_b #1!#2%
+ {\expandafter\XINT_maxof_c\romannumeral`&&@#2!{#1}!}%
\def\XINT_maxof_c #1%
- {\xint_gob_til_relax #1\XINT_maxof_e\relax\XINT_maxof_d #1}%
-\def\XINT_maxof_d #1\Z
+ {\xint_gob_til_xint: #1\XINT_maxof_e\xint:\XINT_maxof_d #1}%
+\def\XINT_maxof_d #1!%
{\expandafter\XINT_maxof_b\romannumeral0\xintmax {#1}}%
-\def\XINT_maxof_e #1\Z #2\Z { #2}%
+\def\XINT_maxof_e #1!#2!{ #2}%
\def\xintMin {\romannumeral0\xintmin }%
\def\xintmin #1%
{%
@@ -1560,15 +1567,16 @@
\fi
}%
\def\xintMinof {\romannumeral0\xintminof }%
-\def\xintminof #1{\expandafter\XINT_minof_a\romannumeral`&&@#1\relax }%
-\def\XINT_minof_a #1{\expandafter\XINT_minof_b\romannumeral0\xintraw{#1}\Z }%
-\def\XINT_minof_b #1\Z #2%
- {\expandafter\XINT_minof_c\romannumeral`&&@#2\Z {#1}\Z}%
+\def\xintminof #1{\expandafter\XINT_minof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_minof_a #1{\expandafter\XINT_minof_b\romannumeral0\xintraw{#1}!}%
+\def\XINT_minof_b #1!#2%
+ {\expandafter\XINT_minof_c\romannumeral`&&@#2!{#1}!}%
\def\XINT_minof_c #1%
- {\xint_gob_til_relax #1\XINT_minof_e\relax\XINT_minof_d #1}%
-\def\XINT_minof_d #1\Z
+ {\xint_gob_til_xint: #1\XINT_minof_e\xint:\XINT_minof_d #1}%
+\def\XINT_minof_d #1!%
{\expandafter\XINT_minof_b\romannumeral0\xintmin {#1}}%
-\def\XINT_minof_e #1\Z #2\Z { #2}%
+\def\XINT_minof_e #1!#2!{ #2}%
+\def\xintCmp {\romannumeral0\xintcmp }%
\def\xintcmp #1%
{%
\expandafter\XINT_fcmp\expandafter {\romannumeral0\xintraw {#1}}%
@@ -1622,7 +1630,7 @@
\def\XINT_fcmp_D #1#2#3%
{%
\expandafter\XINT_cntSgnFork\romannumeral`&&@\expandafter\XINT_cntSgn
- \the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax\Z
+ \the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax\xint:
{ -1}{\XINT_fcmp_E #2\Z {#3}{#1}}{ 1}%
}%
\def\XINT_fcmp_E #1%
@@ -1648,9 +1656,9 @@
\def\xintOpp {\romannumeral0\xintopp }%
\def\xintopp #1{\expandafter\XINT_opp\romannumeral0\xintraw {#1}}%
\def\xintSgn {\romannumeral0\xintsgn }%
-\def\xintsgn #1{\expandafter\XINT_sgn\romannumeral0\xintraw {#1}\Z }%
+\def\xintsgn #1{\expandafter\XINT_sgn\romannumeral0\xintraw {#1}\xint:}%
\def\xintFloat {\romannumeral0\xintfloat }%
-\def\xintfloat #1{\XINT_float_chkopt #1\xint_relax }%
+\def\xintfloat #1{\XINT_float_chkopt #1\xint:}%
\def\XINT_float_chkopt #1%
{%
\ifx [#1\expandafter\XINT_float_opt
@@ -1657,12 +1665,12 @@
\else\expandafter\XINT_float_noopt
\fi #1%
}%
-\def\XINT_float_noopt #1\xint_relax
+\def\XINT_float_noopt #1\xint:%
{%
\expandafter\XINT_float_post
\romannumeral0\XINTinfloat[\XINTdigits]{#1}\XINTdigits.%
}%
-\def\XINT_float_opt [\xint_relax #1]%
+\def\XINT_float_opt [\xint:#1]%
{%
\expandafter\XINT_float_opt_a\the\numexpr #1.%
}%
@@ -1711,7 +1719,7 @@
}%
\def\XINT_infloat_a #1.#2#3#4%
{%
- \if1\XINT_is_one#4XY%
+ \if1\XINT_is_One#4XY%
\expandafter\XINT_infloat_sp
\else\expandafter\XINT_infloat_fork
\fi #3.{#1}{#2}{#4}%
@@ -1888,7 +1896,7 @@
}%
\def\XINT_infloat_ZZ #1.#2.{ 1#2[#1]}%
\def\xintPFloat {\romannumeral0\xintpfloat }%
-\def\xintpfloat #1{\XINT_pfloat_chkopt #1\xint_relax }%
+\def\xintpfloat #1{\XINT_pfloat_chkopt #1\xint:}%
\def\XINT_pfloat_chkopt #1%
{%
\ifx [#1\expandafter\XINT_pfloat_opt
@@ -1895,12 +1903,12 @@
\else\expandafter\XINT_pfloat_noopt
\fi #1%
}%
-\def\XINT_pfloat_noopt #1\xint_relax
+\def\XINT_pfloat_noopt #1\xint:%
{%
\expandafter\XINT_pfloat_a
\romannumeral0\xintfloat [\XINTdigits]{#1};\XINTdigits.%
}%
-\def\XINT_pfloat_opt [\xint_relax #1]%
+\def\XINT_pfloat_opt [\xint:#1]%
{%
\expandafter\XINT_pfloat_opt_a \the\numexpr #1.%
}%
@@ -1962,9 +1970,9 @@
}%
\def\XINT_infloatfracdg_a {\XINTinfloat [\XINTdigits]}%
\def\xintFloatAdd {\romannumeral0\xintfloatadd }%
-\def\xintfloatadd #1{\XINT_fladd_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatadd #1{\XINT_fladd_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatAdd {\romannumeral0\XINTinfloatadd }%
-\def\XINTinfloatadd #1{\XINT_fladd_chkopt \XINTinfloatS #1\xint_relax }%
+\def\XINTinfloatadd #1{\XINT_fladd_chkopt \XINTinfloatS #1\xint:}%
\def\XINT_fladd_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_fladd_opt
@@ -1971,13 +1979,13 @@
\else\expandafter\XINT_fladd_noopt
\fi #1#2%
}%
-\def\XINT_fladd_noopt #1#2\xint_relax #3%
+\def\XINT_fladd_noopt #1#2\xint:#3%
{%
#1[\XINTdigits]%
{\expandafter\XINT_FL_add_a
\romannumeral0\XINTinfloat[\XINTdigits]{#2}\XINTdigits.{#3}}%
}%
-\def\XINT_fladd_opt #1[\xint_relax #2]%#3#4%
+\def\XINT_fladd_opt #1[\xint:#2]%#3#4%
{%
\expandafter\XINT_fladd_opt_a\the\numexpr #2.#1%
}%
@@ -2005,9 +2013,9 @@
\xint_orthat\xintAdd {#1[#2]}{#4[#5]}%
}%
\def\xintFloatSub {\romannumeral0\xintfloatsub }%
-\def\xintfloatsub #1{\XINT_flsub_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatsub #1{\XINT_flsub_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatSub {\romannumeral0\XINTinfloatsub }%
-\def\XINTinfloatsub #1{\XINT_flsub_chkopt \XINTinfloatS #1\xint_relax }%
+\def\XINTinfloatsub #1{\XINT_flsub_chkopt \XINTinfloatS #1\xint:}%
\def\XINT_flsub_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flsub_opt
@@ -2014,13 +2022,13 @@
\else\expandafter\XINT_flsub_noopt
\fi #1#2%
}%
-\def\XINT_flsub_noopt #1#2\xint_relax #3%
+\def\XINT_flsub_noopt #1#2\xint:#3%
{%
#1[\XINTdigits]%
{\expandafter\XINT_FL_add_a
\romannumeral0\XINTinfloat[\XINTdigits]{#2}\XINTdigits.{\xintOpp{#3}}}%
}%
-\def\XINT_flsub_opt #1[\xint_relax #2]%#3#4%
+\def\XINT_flsub_opt #1[\xint:#2]%#3#4%
{%
\expandafter\XINT_flsub_opt_a\the\numexpr #2.#1%
}%
@@ -2029,9 +2037,9 @@
#2[#1]{\expandafter\XINT_FL_add_a\romannumeral0\XINTinfloat[#1]{#3}#1.{\xintOpp{#4}}}%
}%
\def\xintFloatMul {\romannumeral0\xintfloatmul }%
-\def\xintfloatmul #1{\XINT_flmul_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatmul #1{\XINT_flmul_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatMul {\romannumeral0\XINTinfloatmul }%
-\def\XINTinfloatmul #1{\XINT_flmul_chkopt \XINTinfloatS #1\xint_relax }%
+\def\XINTinfloatmul #1{\XINT_flmul_chkopt \XINTinfloatS #1\xint:}%
\def\XINT_flmul_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flmul_opt
@@ -2038,13 +2046,13 @@
\else\expandafter\XINT_flmul_noopt
\fi #1#2%
}%
-\def\XINT_flmul_noopt #1#2\xint_relax #3%
+\def\XINT_flmul_noopt #1#2\xint:#3%
{%
#1[\XINTdigits]%
{\expandafter\XINT_FL_mul_a
\romannumeral0\XINTinfloatS[\XINTdigits]{#2}\XINTdigits.{#3}}%
}%
-\def\XINT_flmul_opt #1[\xint_relax #2]%#3#4%
+\def\XINT_flmul_opt #1[\xint:#2]%#3#4%
{%
\expandafter\XINT_flmul_opt_a\the\numexpr #2.#1%
}%
@@ -2058,9 +2066,9 @@
}%
\def\XINT_FL_mul_b #1[#2]#3[#4]{\xintiiMul{#3}{#1}/1[#4+#2]}%
\def\xintFloatDiv {\romannumeral0\xintfloatdiv }%
-\def\xintfloatdiv #1{\XINT_fldiv_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatdiv #1{\XINT_fldiv_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatDiv {\romannumeral0\XINTinfloatdiv }%
-\def\XINTinfloatdiv #1{\XINT_fldiv_chkopt \XINTinfloatS #1\xint_relax }%
+\def\XINTinfloatdiv #1{\XINT_fldiv_chkopt \XINTinfloatS #1\xint:}%
\def\XINT_fldiv_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_fldiv_opt
@@ -2067,13 +2075,13 @@
\else\expandafter\XINT_fldiv_noopt
\fi #1#2%
}%
-\def\XINT_fldiv_noopt #1#2\xint_relax #3%
+\def\XINT_fldiv_noopt #1#2\xint:#3%
{%
#1[\XINTdigits]%
{\expandafter\XINT_FL_div_a
\romannumeral0\XINTinfloatS[\XINTdigits]{#3}\XINTdigits.{#2}}%
}%
-\def\XINT_fldiv_opt #1[\xint_relax #2]%#3#4%
+\def\XINT_fldiv_opt #1[\xint:#2]%#3#4%
{%
\expandafter\XINT_fldiv_opt_a\the\numexpr #2.#1%
}%
@@ -2087,9 +2095,9 @@
}%
\def\XINT_FL_div_b #1[#2]{#1e#2}%
\def\xintFloatPow {\romannumeral0\xintfloatpow}%
-\def\xintfloatpow #1{\XINT_flpow_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatpow #1{\XINT_flpow_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatPow {\romannumeral0\XINTinfloatpow }%
-\def\XINTinfloatpow #1{\XINT_flpow_chkopt \XINTinfloatS #1\xint_relax }%
+\def\XINTinfloatpow #1{\XINT_flpow_chkopt \XINTinfloatS #1\xint:}%
\def\XINT_flpow_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flpow_opt
@@ -2097,12 +2105,12 @@
\fi
#1#2%
}%
-\def\XINT_flpow_noopt #1#2\xint_relax #3%
+\def\XINT_flpow_noopt #1#2\xint:#3%
{%
\expandafter\XINT_flpow_checkB_a
\the\numexpr #3.\XINTdigits.{#2}{#1[\XINTdigits]}%
}%
-\def\XINT_flpow_opt #1[\xint_relax #2]%
+\def\XINT_flpow_opt #1[\xint:#2]%
{%
\expandafter\XINT_flpow_opt_a\the\numexpr #2.#1%
}%
@@ -2149,8 +2157,10 @@
}%
\def\XINT_flpow_zero #1[#2]#3#4#5#6%
{%
- \if 1#51\xint_afterfi {#6{0[0]}}\else
- \xint_afterfi {\xintError:DivisionByZero #6{1[2147483648]}}\fi
+ #6{\if 1#51\xint_dothis {0[0]}\fi
+ \xint_orthat
+ {\XINT_signalcondition{DivisionByZero}{0 to the power #4}{}{0[0]}}%
+ }%
}%
\def\XINT_flpow_b #1#2[#3]#4#5%
{%
@@ -2240,9 +2250,9 @@
\def\XINT_flpow_IIIend #1#2#3%
{#3{\if#21\xint_afterfi{\expandafter-\romannumeral`&&@}\fi#1}}%
\def\xintFloatPower {\romannumeral0\xintfloatpower}%
-\def\xintfloatpower #1{\XINT_flpower_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatpower #1{\XINT_flpower_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatPower {\romannumeral0\XINTinfloatpower }%
-\def\XINTinfloatpower #1{\XINT_flpower_chkopt \XINTinfloatS #1\xint_relax }%
+\def\XINTinfloatpower #1{\XINT_flpower_chkopt \XINTinfloatS #1\xint:}%
\def\XINTinFloatPowerH {\romannumeral0\XINTinfloatpowerh }%
\def\XINTinfloatpowerh #1#2%
{%
@@ -2287,12 +2297,12 @@
\fi
#1#2%
}%
-\def\XINT_flpower_noopt #1#2\xint_relax #3%
+\def\XINT_flpower_noopt #1#2\xint:#3%
{%
\expandafter\XINT_flpower_checkB_a
\romannumeral0\xintnum{#3}.\XINTdigits.{#2}{#1[\XINTdigits]}%
}%
-\def\XINT_flpower_opt #1[\xint_relax #2]%
+\def\XINT_flpower_opt #1[\xint:#2]%
{%
\expandafter\XINT_flpower_opt_a\the\numexpr #2.#1%
}%
@@ -2407,9 +2417,9 @@
\the\numexpr#2+#5\expandafter.\romannumeral0\xintiimul{#3}{#6}.#4.%
}%
\def\xintFloatFac {\romannumeral0\xintfloatfac}%
-\def\xintfloatfac #1{\XINT_flfac_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatfac #1{\XINT_flfac_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatFac {\romannumeral0\XINTinfloatfac }%
-\def\XINTinfloatfac #1{\XINT_flfac_chkopt \XINTinfloat #1\xint_relax }%
+\def\XINTinfloatfac #1{\XINT_flfac_chkopt \XINTinfloat #1\xint:}%
\def\XINT_flfac_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flfac_opt
@@ -2417,12 +2427,12 @@
\fi
#1#2%
}%
-\def\XINT_flfac_noopt #1#2\xint_relax
+\def\XINT_flfac_noopt #1#2\xint:
{%
\expandafter\XINT_FL_fac_fork_a
\the\numexpr \xintNum{#2}.\xint_c_i \XINTdigits\XINT_FL_fac_out{#1[\XINTdigits]}%
}%
-\def\XINT_flfac_opt #1[\xint_relax #2]%
+\def\XINT_flfac_opt #1[\xint:#2]%
{%
\expandafter\XINT_flfac_opt_a\the\numexpr #2.#1%
}%
@@ -2439,7 +2449,11 @@
\krof
}%
\def\XINT_FL_fac_iszero #1.#2#3#4#5{#5{1[0]}}%
-\def\XINT_FL_fac_isneg #1.#2#3#4#5{\expandafter\xintError:FactorialOfNegative #5{0[0]}}%
+\def\XINT_FL_fac_isneg #1.#2#3#4#5%
+{%
+ #5{\XINT_signalcondition{InvalidOperation}
+ {Factorial of negative: (-#1)!}{}{0[0]}}%
+}%
\def\XINT_FL_fac_fork_b #1.%
{%
\ifnum #1>\xint_c_x^viii_mone\xint_dothis\XINT_FL_fac_toobig\fi
@@ -2449,7 +2463,11 @@
\xint_orthat\XINT_FL_fac_small
#1.%
}%
-\def\XINT_FL_fac_toobig #1.#2#3#4#5{\expandafter\xintError:TooBigFactorial #5{1[0]}}%
+\def\XINT_FL_fac_toobig #1.#2#3#4#5%
+{%
+ #5{\XINT_signalcondition{InvalidOperation}
+ {Factorial of too big: (#1)!}{}{0[0]}}%
+}%
\def\XINT_FL_fac_vbig
{\expandafter\XINT_FL_fac_vbigloop_a
\the\numexpr \XINT_FL_fac_increaseP \xint_c_i }%
@@ -2470,8 +2488,10 @@
}%
\def\XINT_FL_fac_countdigits #1#2#3#4#5#6#7#8{\XINT_FL_fac_countdone }%
\def\XINT_FL_fac_countdone #1#2\Z {#1}%
-\def\XINT_FL_fac_out #1\Z![#2]#3{#3{\romannumeral0\XINT_mul_out
- #1\Z!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W [#2]}}%
+\def\XINT_FL_fac_out #1;![#2]#3%
+ {#3{\romannumeral0\XINT_mul_out
+ #1;!1\R!1\R!1\R!1\R!%
+ 1\R!1\R!1\R!1\R!\W [#2]}}%
\def\XINT_FL_fac_vbigloop_a #1.#2.%
{%
\XINT_FL_fac_bigloop_a \xint_c_x^iv.#2.%
@@ -2555,9 +2575,10 @@
\def\XINT_FL_fac_addzeros #1.%
{%
\ifnum #1=\xint_c_viii \expandafter\XINT_FL_fac_addzeros_exit\fi
- \expandafter\XINT_FL_fac_addzeros\the\numexpr #1-\xint_c_viii.100000000!%
+ \expandafter\XINT_FL_fac_addzeros
+ \the\numexpr #1-\xint_c_viii.100000000!%
}%
-\def\XINT_FL_fac_addzeros_exit #1.#2.#3#4{\XINT_FL_fac_smallloop_loop #3#21\Z![-#4]}%
+\def\XINT_FL_fac_addzeros_exit #1.#2.#3#4{\XINT_FL_fac_smallloop_loop #3#21;![-#4]}%
\def\XINT_FL_fac_smallloop_loop #1.#2.%
{%
\ifnum #1>#2 \expandafter\XINT_FL_fac_loop_exit\fi
@@ -2577,7 +2598,7 @@
\def\XINT_FL_fac_mul_a #1-#2%
{%
\if#21\xint_afterfi{\expandafter\space\xint_gob_til_exclam}\else
- \expandafter\space\fi #11\Z!%
+ \expandafter\space\fi #11;!%
}%
\def\XINT_FL_fac_minimulwc_a #1#2#3#4#5!#6#7#8#9%
{%
@@ -2586,9 +2607,9 @@
\def\XINT_FL_fac_minimulwc_b #1#2#3#4!#5%
{%
\expandafter\XINT_FL_fac_minimulwc_c
- \the\numexpr \xint_c_x^ix+#5+#2*#4.{{#1}{#2}{#3}{#4}}%
+ \the\numexpr \xint_c_x^ix+#5+#2*#4!{{#1}{#2}{#3}{#4}}%
}%
-\def\XINT_FL_fac_minimulwc_c 1#1#2#3#4#5#6.#7%
+\def\XINT_FL_fac_minimulwc_c 1#1#2#3#4#5#6!#7%
{%
\expandafter\XINT_FL_fac_minimulwc_d {#1#2#3#4#5}#7{#6}%
}%
@@ -2595,9 +2616,9 @@
\def\XINT_FL_fac_minimulwc_d #1#2#3#4#5%
{%
\expandafter\XINT_FL_fac_minimulwc_e
- \the\numexpr \xint_c_x^ix+#1+#2*#5+#3*#4.{#2}{#4}%
+ \the\numexpr \xint_c_x^ix+#1+#2*#5+#3*#4!{#2}{#4}%
}%
-\def\XINT_FL_fac_minimulwc_e 1#1#2#3#4#5#6.#7#8#9%
+\def\XINT_FL_fac_minimulwc_e 1#1#2#3#4#5#6!#7#8#9%
{%
1#6#9\expandafter!%
\the\numexpr\expandafter\XINT_FL_fac_smallmul
@@ -2605,10 +2626,10 @@
}%
\def\XINT_FL_fac_smallmul 1#1!#21#3!%
{%
- \xint_gob_til_Z #3\XINT_FL_fac_smallmul_end\Z
+ \xint_gob_til_sc #3\XINT_FL_fac_smallmul_end;%
\XINT_FL_fac_minimulwc_a #2!#3!{#1}{#2}%
}%
-\def\XINT_FL_fac_smallmul_end\Z\XINT_FL_fac_minimulwc_a #1!\Z!#2#3[#4]%
+\def\XINT_FL_fac_smallmul_end;\XINT_FL_fac_minimulwc_a #1!;!#2#3[#4]%
{%
\ifnum #2=\xint_c_
\expandafter\xint_firstoftwo\else
@@ -2619,9 +2640,9 @@
[\the\numexpr #4+\xint_c_viii]}%
}%
\def\xintFloatPFactorial {\romannumeral0\xintfloatpfactorial}%
-\def\xintfloatpfactorial #1{\XINT_flpfac_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatpfactorial #1{\XINT_flpfac_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatPFactorial {\romannumeral0\XINTinfloatpfactorial }%
-\def\XINTinfloatpfactorial #1{\XINT_flpfac_chkopt \XINTinfloat #1\xint_relax }%
+\def\XINTinfloatpfactorial #1{\XINT_flpfac_chkopt \XINTinfloat #1\xint:}%
\def\XINT_flpfac_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flpfac_opt
@@ -2629,13 +2650,13 @@
\fi
#1#2%
}%
-\def\XINT_flpfac_noopt #1#2\xint_relax #3%
+\def\XINT_flpfac_noopt #1#2\xint:#3%
{%
\expandafter\XINT_FL_pfac_fork
\the\numexpr \xintNum{#2}\expandafter.%
\the\numexpr \xintNum{#3}.\xint_c_i{\XINTdigits}{#1[\XINTdigits]}%
}%
-\def\XINT_flpfac_opt #1[\xint_relax #2]%
+\def\XINT_flpfac_opt #1[\xint:#2]%
{%
\expandafter\XINT_flpfac_opt_b\the\numexpr #2.#1%
}%
@@ -2653,7 +2674,11 @@
\ifnum #3#4>\xint_c_x^viii_mone\xint_dothis\XINT_FL_pfac_outofrange\fi
\xint_orthat \XINT_FL_pfac_increaseP #1#2.#3#4.%
}%
-\def\XINT_FL_pfac_outofrange #1.#2.#3#4#5{\xintError:OutOfRangePFac #5{0[0]}}%
+\def\XINT_FL_pfac_outofrange #1.#2.#3#4#5%
+{%
+ #5{\XINT_signalcondition{InvalidOperation}
+ {pfactorial second arg too big: 99999999 < #2}{}{0[0]}}%
+}%
\def\XINT_FL_pfac_one #1.#2.#3#4#5{#5{1[0]}}%
\def\XINT_FL_pfac_zero #1.#2.#3#4#5{#5{0[0]}}%
\def\XINT_FL_pfac_neg -#1.-#2.%
@@ -2676,7 +2701,7 @@
{%
\expandafter\XINT_FL_pfac_b\the\numexpr \xint_c_i+#2\expandafter.%
\the\numexpr#3\expandafter.%
- \romannumeral0\XINT_FL_pfac_addzeroes #1.100000001!1\Z![-#1]%
+ \romannumeral0\XINT_FL_pfac_addzeroes #1.100000001!1;![-#1]%
}%
\def\XINT_FL_pfac_addzeroes #1.%
{%
@@ -2797,9 +2822,9 @@
\the\numexpr \xint_c_x^viii+#1!%
}%
\def\xintFloatBinomial {\romannumeral0\xintfloatbinomial}%
-\def\xintfloatbinomial #1{\XINT_flbinom_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatbinomial #1{\XINT_flbinom_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatBinomial {\romannumeral0\XINTinfloatbinomial }%
-\def\XINTinfloatbinomial #1{\XINT_flbinom_chkopt \XINTinfloat #1\xint_relax }%
+\def\XINTinfloatbinomial #1{\XINT_flbinom_chkopt \XINTinfloat #1\xint:}%
\def\XINT_flbinom_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flbinom_opt
@@ -2806,12 +2831,12 @@
\else\expandafter\XINT_flbinom_noopt
\fi #1#2%
}%
-\def\XINT_flbinom_noopt #1#2\xint_relax #3%
+\def\XINT_flbinom_noopt #1#2\xint:#3%
{%
\expandafter\XINT_FL_binom_a
\the\numexpr\xintNum{#2}\expandafter.\the\numexpr\xintNum{#3}.\XINTdigits.#1%
}%
-\def\XINT_flbinom_opt #1[\xint_relax #2]#3#4%
+\def\XINT_flbinom_opt #1[\xint:#2]#3#4%
{%
\expandafter\XINT_FL_binom_a
\the\numexpr\xintNum{#3}\expandafter.\the\numexpr\xintNum{#4}\expandafter.%
@@ -2823,18 +2848,26 @@
}%
\def\XINT_FL_binom_fork #1#2.#3#4.#5#6.%
{%
- \if-#5\xint_dothis \XINT_FL_binom_outofrange\fi
+ \if-#5\xint_dothis \XINT_FL_binom_neg\fi
\if-#1\xint_dothis \XINT_FL_binom_zero\fi
\if-#3\xint_dothis \XINT_FL_binom_zero\fi
\if0#1\xint_dothis \XINT_FL_binom_one\fi
\if0#3\xint_dothis \XINT_FL_binom_one\fi
- \ifnum #5#6>\xint_c_x^viii_mone \xint_dothis\XINT_FL_binom_outofrange\fi
+ \ifnum #5#6>\xint_c_x^viii_mone \xint_dothis\XINT_FL_binom_toobig\fi
\ifnum #1#2>#3#4 \xint_dothis\XINT_FL_binom_ab \fi
\xint_orthat\XINT_FL_binom_aa
#1#2.#3#4.#5#6.%
}%
-\def\XINT_FL_binom_outofrange #1.#2.#3.#4.#5%
- {\xintError:OutOfRangeBinomial #5[#4]{0[0]}}%
+\def\XINT_FL_binom_neg #1.#2.#3.#4.#5%
+{%
+ #5[#4]{\XINT_signalcondition{InvalidOperation}
+ {binomial with first arg negative: #3}{}{0[0]}}%
+}%
+\def\XINT_FL_binom_toobig #1.#2.#3.#4.#5%
+{%
+ #5[#4]{\XINT_signalcondition{InvalidOperation}
+ {binomial with first arg too big: 99999999 < #3}{}{0[0]}}%
+}%
\def\XINT_FL_binom_one #1.#2.#3.#4.#5{#5[#4]{1[0]}}%
\def\XINT_FL_binom_zero #1.#2.#3.#4.#5{#5[#4]{0[0]}}%
\def\XINT_FL_binom_aa #1.#2.#3.#4.#5%
@@ -2852,9 +2885,9 @@
#2.\xint_c_iv{#4+\xint_c_i}\XINT_FL_fac_out{\XINTinfloat[#4+\xint_c_iii]}}}%
}%
\def\xintFloatSqrt {\romannumeral0\xintfloatsqrt }%
-\def\xintfloatsqrt #1{\XINT_flsqrt_chkopt \xintfloat #1\xint_relax }%
+\def\xintfloatsqrt #1{\XINT_flsqrt_chkopt \xintfloat #1\xint:}%
\def\XINTinFloatSqrt {\romannumeral0\XINTinfloatsqrt }%
-\def\XINTinfloatsqrt #1{\XINT_flsqrt_chkopt \XINTinfloat #1\xint_relax }%
+\def\XINTinfloatsqrt #1{\XINT_flsqrt_chkopt \XINTinfloat #1\xint:}%
\def\XINT_flsqrt_chkopt #1#2%
{%
\ifx [#2\expandafter\XINT_flsqrt_opt
@@ -2861,12 +2894,12 @@
\else\expandafter\XINT_flsqrt_noopt
\fi #1#2%
}%
-\def\XINT_flsqrt_noopt #1#2\xint_relax
+\def\XINT_flsqrt_noopt #1#2\xint:%
{%
\expandafter\XINT_FL_sqrt_a
\romannumeral0\XINTinfloat[\XINTdigits]{#2}\XINTdigits.#1%
}%
-\def\XINT_flsqrt_opt #1[\xint_relax #2]%#3%
+\def\XINT_flsqrt_opt #1[\xint:#2]%#3%
{%
\expandafter\XINT_flsqrt_opt_a\the\numexpr #2.#1%
}%
@@ -2883,7 +2916,11 @@
\krof
}%[
\def\XINT_FL_sqrt_iszero #1]#2.#3{#3[#2]{0[0]}}%
-\def\XINT_FL_sqrt_isneg #1]#2.#3{\xintError:RootOfNegative #3[#2]{0[0]}}%
+\def\XINT_FL_sqrt_isneg #1]#2.#3%
+{%
+ #3[#2]{\XINT_signalcondition{InvalidOperation}
+ {Square root of negative: -#1]}{}{0[0]}}%
+}%
\def\XINT_FL_sqrt_pos #1[#2]#3.%
{%
\expandafter\XINT_flsqrt
@@ -2939,7 +2976,7 @@
#1.#200000000.#3.%
}%
\def\xintFloatE {\romannumeral0\xintfloate }%
-\def\xintfloate #1{\XINT_floate_chkopt #1\xint_relax }%
+\def\xintfloate #1{\XINT_floate_chkopt #1\xint:}%
\def\XINT_floate_chkopt #1%
{%
\ifx [#1\expandafter\XINT_floate_opt
@@ -2946,12 +2983,12 @@
\else\expandafter\XINT_floate_noopt
\fi #1%
}%
-\def\XINT_floate_noopt #1\xint_relax
+\def\XINT_floate_noopt #1\xint:%
{%
\expandafter\XINT_floate_post
\romannumeral0\XINTinfloat[\XINTdigits]{#1}\XINTdigits.%
}%
-\def\XINT_floate_opt [\xint_relax #1]%
+\def\XINT_floate_opt [\xint:#1]%
{%
\expandafter\XINT_floate_opt_a\the\numexpr #1.%
}%
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintgcd.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintgcd.sty 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintgcd.sty 2017-07-27 21:26:25 UTC (rev 44900)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.2k 2017/01/06
+%% The xint bundle 1.2l 2017/07/26
%% Copyright (C) 2013-2017 by Jean-Francois Burnol
%% xintgcd: Euclidean algorithm with xint package
%% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintgcd}%
- [2017/01/06 1.2k Euclide algorithm with xint package (JFB)]%
+ [2017/07/26 1.2l Euclide algorithm with xint package (JFB)]%
\def\xintGCD {\romannumeral0\xintgcd }%
\def\xintgcd #1%
{%
@@ -102,9 +102,9 @@
\def\XINT_gcd_BisZero #1#2{ #2}%
\def\XINT_gcd_CheckRem #1#2\Z
{%
- \xint_gob_til_zero #1\xint_gcd_end0\XINT_gcd_loop {#1#2}%
+ \xint_gob_til_zero #1\XINT_gcd_end0\XINT_gcd_loop {#1#2}%
}%
-\def\xint_gcd_end0\XINT_gcd_loop #1#2{ #2}%
+\def\XINT_gcd_end0\XINT_gcd_loop #1#2{ #2}%
\def\XINT_gcd_loop #1#2%
{%
\expandafter\expandafter\expandafter
@@ -147,9 +147,9 @@
\def\xintBezout {\romannumeral0\xintbezout }%
\def\xintbezout #1%
{%
- \expandafter\xint_bezout\expandafter {\romannumeral0\xintnum{#1}}%
+ \expandafter\XINT_bezout\expandafter {\romannumeral0\xintnum{#1}}%
}%
-\def\xint_bezout #1#2%
+\def\XINT_bezout #1#2%
{%
\expandafter\XINT_bezout_fork \romannumeral0\xintnum{#2}\Z #1\Z
}%
@@ -159,31 +159,30 @@
#1#3\XINT_bezout_botharezero
#10\XINT_bezout_secondiszero
#30\XINT_bezout_firstiszero
- 00{\xint_UDsignsfork
+ 00\xint_UDsignsfork
+ \krof
#1#3\XINT_bezout_minusminus % A < 0, B < 0
#1-\XINT_bezout_minusplus % A > 0, B < 0
#3-\XINT_bezout_plusminus % A < 0, B > 0
--\XINT_bezout_plusplus % A > 0, B > 0
- \krof }%
\krof
{#2}{#4}#1#3{#3#4}{#1#2}% #1#2=B, #3#4=A
}%
-\edef\XINT_bezout_botharezero #1#2#3#4#5#6%
+\def\XINT_bezout_botharezero #1\krof#2#3#4#5#6#7%
+ {\XINT_signalcondition{InvalidOperation}
+ {No Bezout identity for 0 and 0}{}{{0}{0}{0}{0}{0}}}%
+\def\XINT_bezout_firstiszero #1\krof#2#3#4#5#6#7%
{%
- \noexpand\xintError:NoBezoutForZeros\space {0}{0}{0}{0}{0}%
-}%
-\def\XINT_bezout_firstiszero #1#2#3#4#5#6%
-{%
\xint_UDsignfork
- #3{ {0}{#3#1}{0}{1}{#1}}%
- -{ {0}{#3#1}{0}{-1}{#1}}%
+ #4{{0}{#7}{0}{1}{#2}}%
+ -{{0}{#7}{0}{-1}{#7}}%
\krof
}%
-\def\XINT_bezout_secondiszero #1#2#3#4#5#6%
+\def\XINT_bezout_secondiszero #1\krof#2#3#4#5#6#7%
{%
\xint_UDsignfork
- #4{ {#4#2}{0}{-1}{0}{#2}}%
- -{ {#4#2}{0}{1}{0}{#2}}%
+ #5{{#6}{0}{-1}{0}{#3}}%
+ -{{#6}{0}{1}{0}{#6}}%
\krof
}%
\def\XINT_bezout_minusminus #1#2#3#4%
@@ -200,10 +199,7 @@
{%
\expandafter\XINT_bezout_mm_postc\expandafter {#2}{#1}%
}%
-\edef\XINT_bezout_mm_postc #1#2#3#4#5%
-{%
- \space {#4}{#5}{#1}{#2}{#3}%
-}%
+\def\XINT_bezout_mm_postc #1#2#3#4#5{{#4}{#5}{#1}{#2}{#3}}%
\def\XINT_bezout_minusplus #1#2#3#4%
{%
\expandafter\XINT_bezout_mp_post
@@ -214,10 +210,7 @@
\expandafter\XINT_bezout_mp_postb\expandafter
{\romannumeral0\xintiiopp {#2}}{#1}%
}%
-\edef\XINT_bezout_mp_postb #1#2#3#4#5%
-{%
- \space {#4}{#5}{#2}{#1}{#3}%
-}%
+\def\XINT_bezout_mp_postb #1#2#3#4#5{{#4}{#5}{#2}{#1}{#3}}%
\def\XINT_bezout_plusminus #1#2#3#4%
{%
\expandafter\XINT_bezout_pm_post
@@ -228,36 +221,28 @@
\expandafter \XINT_bezout_pm_postb \expandafter
{\romannumeral0\xintiiopp{#1}}%
}%
-\edef\XINT_bezout_pm_postb #1#2#3#4#5%
-{%
- \space {#4}{#5}{#1}{#2}{#3}%
-}%
+\def\XINT_bezout_pm_postb #1#2#3#4#5{{#4}{#5}{#1}{#2}{#3}}%
\def\XINT_bezout_plusplus #1#2#3#4%
{%
\expandafter\XINT_bezout_pp_post
\romannumeral0\XINT_bezout_loop_a 1{#3#1}{#4#2}1001%
}%
-\edef\XINT_bezout_pp_post #1#2#3#4#5%
-{%
- \space {#4}{#5}{#1}{#2}{#3}%
-}%
+\def\XINT_bezout_pp_post #1#2#3#4#5{{#4}{#5}{#1}{#2}{#3}}%
\def\XINT_bezout_loop_a #1#2#3%
{%
- \expandafter\XINT_bezout_loop_b
- \expandafter{\the\numexpr -#1\expandafter }%
+ \expandafter\XINT_bezout_loop_b\the\numexpr -#1\expandafter.%
\romannumeral0\XINT_div_prepare {#2}{#3}{#2}%
}%
-\def\XINT_bezout_loop_b #1#2#3#4#5#6#7#8%
+\def\XINT_bezout_loop_b #1.#2#3#4#5#6#7#8%
{%
- \expandafter \XINT_bezout_loop_c \expandafter
- {\romannumeral0\xintiiadd{\XINT_mul_fork #5\Z #2\Z}{#7}}%
- {\romannumeral0\xintiiadd{\XINT_mul_fork #6\Z #2\Z}{#8}}%
+ \expandafter\XINT_bezout_loop_c\expandafter
+ {\romannumeral0\xintiiadd{\XINT_mul_fork #5\xint:#2\xint:}{#7}}%
+ {\romannumeral0\xintiiadd{\XINT_mul_fork #6\xint:#2\xint:}{#8}}%
{#1}{#3}{#4}{#5}{#6}%
}%
\def\XINT_bezout_loop_c #1#2%
{%
- \expandafter \XINT_bezout_loop_d \expandafter
- {#2}{#1}%
+ \expandafter\XINT_bezout_loop_d\expandafter{#2}{#1}%
}%
\def\XINT_bezout_loop_d #1#2#3#4#5%
{%
@@ -265,14 +250,13 @@
}%
\def\XINT_bezout_loop_e #1#2\Z
{%
- \xint_gob_til_zero #1\xint_bezout_loop_exit0\XINT_bezout_loop_f
- {#1#2}%
+ \xint_gob_til_zero #1\XINT_bezout_loop_exit0\XINT_bezout_loop_f {#1#2}%
}%
\def\XINT_bezout_loop_f #1#2%
{%
\XINT_bezout_loop_a {#2}{#1}%
}%
-\def\xint_bezout_loop_exit0\XINT_bezout_loop_f #1#2%
+\def\XINT_bezout_loop_exit0\XINT_bezout_loop_f #1#2%
{%
\ifcase #2
\or \expandafter\XINT_bezout_exiteven
@@ -279,22 +263,16 @@
\else\expandafter\XINT_bezout_exitodd
\fi
}%
-\edef\XINT_bezout_exiteven #1#2#3#4#5%
-{%
- \space {#5}{#4}{#1}%
-}%
-\edef\XINT_bezout_exitodd #1#2#3#4#5%
-{%
- \space {-#5}{-#4}{#1}%
-}%
+\def\XINT_bezout_exiteven #1#2#3#4#5{{#5}{#4}{#1}}%
+\def\XINT_bezout_exitodd #1#2#3#4#5{{-#5}{-#4}{#1}}%
\def\xintEuclideAlgorithm {\romannumeral0\xinteuclidealgorithm }%
\def\xinteuclidealgorithm #1%
{%
- \expandafter \XINT_euc \expandafter{\romannumeral0\xintiabs {#1}}%
+ \expandafter\XINT_euc\expandafter{\romannumeral0\xintiabs {#1}}%
}%
\def\XINT_euc #1#2%
{%
- \expandafter\XINT_euc_fork \romannumeral0\xintiabs {#2}\Z #1\Z
+ \expandafter\XINT_euc_fork\romannumeral0\xintiabs {#2}\Z #1\Z
}%
\def\XINT_euc_fork #1#2\Z #3#4\Z
{%
@@ -305,36 +283,32 @@
\krof
{0}{#1#2}{#3#4}{{#3#4}{#1#2}}{}\Z
}%
-\def\XINT_euc_AisZero #1#2#3#4#5#6{ {1}{0}{#2}{#2}{0}{0}}%
-\def\XINT_euc_BisZero #1#2#3#4#5#6{ {1}{0}{#3}{#3}{0}{0}}%
+\def\XINT_euc_AisZero #1#2#3#4#5#6{{1}{0}{#2}{#2}{0}{0}}%
+\def\XINT_euc_BisZero #1#2#3#4#5#6{{1}{0}{#3}{#3}{0}{0}}%
\def\XINT_euc_a #1#2#3%
{%
- \expandafter\XINT_euc_b
- \expandafter {\the\numexpr #1+1\expandafter }%
+ \expandafter\XINT_euc_b\the\numexpr #1+\xint_c_i\expandafter.%
\romannumeral0\XINT_div_prepare {#2}{#3}{#2}%
}%
-\def\XINT_euc_b #1#2#3#4%
+\def\XINT_euc_b #1.#2#3#4%
{%
\XINT_euc_c #3\Z {#1}{#3}{#4}{{#2}{#3}}%
}%
\def\XINT_euc_c #1#2\Z
{%
- \xint_gob_til_zero #1\xint_euc_end0\XINT_euc_a
+ \xint_gob_til_zero #1\XINT_euc_end0\XINT_euc_a
}%
-\def\xint_euc_end0\XINT_euc_a #1#2#3#4\Z%
+\def\XINT_euc_end0\XINT_euc_a #1#2#3#4\Z%
{%
- \expandafter\xint_euc_end_
+ \expandafter\XINT_euc_end_a
\romannumeral0%
\XINT_rord_main {}#4{{#1}{#3}}%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax
+ \xint:
}%
-\edef\xint_euc_end_ #1#2#3%
-{%
- \space {#1}{#3}{#2}%
-}%
+\def\XINT_euc_end_a #1#2#3{{#1}{#3}{#2}}%
\def\xintBezoutAlgorithm {\romannumeral0\xintbezoutalgorithm }%
\def\xintbezoutalgorithm #1%
{%
@@ -353,15 +327,14 @@
\krof
0{#1#2}{#3#4}1001{{#3#4}{#1#2}}{}\Z
}%
-\def\XINT_bezalg_AisZero #1#2#3\Z{ {1}{0}{0}{1}{#2}{#2}{1}{0}{0}{0}{0}{1}}%
-\def\XINT_bezalg_BisZero #1#2#3#4\Z{ {1}{0}{0}{1}{#3}{#3}{1}{0}{0}{0}{0}{1}}%
+\def\XINT_bezalg_AisZero #1#2#3\Z{{1}{0}{0}{1}{#2}{#2}{1}{0}{0}{0}{0}{1}}%
+\def\XINT_bezalg_BisZero #1#2#3#4\Z{{1}{0}{0}{1}{#3}{#3}{1}{0}{0}{0}{0}{1}}%
\def\XINT_bezalg_a #1#2#3%
{%
- \expandafter\XINT_bezalg_b
- \expandafter {\the\numexpr #1+1\expandafter }%
+ \expandafter\XINT_bezalg_b\the\numexpr #1+\xint_c_i\expandafter.%
\romannumeral0\XINT_div_prepare {#2}{#3}{#2}%
}%
-\def\XINT_bezalg_b #1#2#3#4#5#6#7#8%
+\def\XINT_bezalg_b #1.#2#3#4#5#6#7#8%
{%
\expandafter\XINT_bezalg_c\expandafter
{\romannumeral0\xintiiadd {\xintiiMul {#6}{#2}}{#8}}%
@@ -378,36 +351,33 @@
}%
\def\XINT_bezalg_e #1#2\Z
{%
- \xint_gob_til_zero #1\xint_bezalg_end0\XINT_bezalg_a
+ \xint_gob_til_zero #1\XINT_bezalg_end0\XINT_bezalg_a
}%
-\def\xint_bezalg_end0\XINT_bezalg_a #1#2#3#4#5#6#7#8\Z
+\def\XINT_bezalg_end0\XINT_bezalg_a #1#2#3#4#5#6#7#8\Z
{%
- \expandafter\xint_bezalg_end_
+ \expandafter\XINT_bezalg_end_a
\romannumeral0%
\XINT_rord_main {}#8{{#1}{#3}}%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax
+ \xint:
}%
-\edef\xint_bezalg_end_ #1#2#3#4%
-{%
- \space {#1}{#3}{0}{1}{#2}{#4}{1}{0}%
-}%
+\def\XINT_bezalg_end_a #1#2#3#4{{#1}{#3}{0}{1}{#2}{#4}{1}{0}}%
\def\xintGCDof {\romannumeral0\xintgcdof }%
-\def\xintgcdof #1{\expandafter\XINT_gcdof_a\romannumeral`&&@#1\relax }%
-\def\XINT_gcdof_a #1{\expandafter\XINT_gcdof_b\romannumeral`&&@#1\Z }%
-\def\XINT_gcdof_b #1\Z #2{\expandafter\XINT_gcdof_c\romannumeral`&&@#2\Z {#1}\Z}%
-\def\XINT_gcdof_c #1{\xint_gob_til_relax #1\XINT_gcdof_e\relax\XINT_gcdof_d #1}%
-\def\XINT_gcdof_d #1\Z {\expandafter\XINT_gcdof_b\romannumeral0\xintgcd {#1}}%
-\def\XINT_gcdof_e #1\Z #2\Z { #2}%
+\def\xintgcdof #1{\expandafter\XINT_gcdof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_gcdof_a #1{\expandafter\XINT_gcdof_b\romannumeral`&&@#1!}%
+\def\XINT_gcdof_b #1!#2{\expandafter\XINT_gcdof_c\romannumeral`&&@#2!{#1}!}%
+\def\XINT_gcdof_c #1{\xint_gob_til_xint: #1\XINT_gcdof_e\xint:\XINT_gcdof_d #1}%
+\def\XINT_gcdof_d #1!{\expandafter\XINT_gcdof_b\romannumeral0\xintgcd {#1}}%
+\def\XINT_gcdof_e #1!#2!{ #2}%
\def\xintLCMof {\romannumeral0\xintlcmof }%
-\def\xintlcmof #1{\expandafter\XINT_lcmof_a\romannumeral`&&@#1\relax }%
-\def\XINT_lcmof_a #1{\expandafter\XINT_lcmof_b\romannumeral`&&@#1\Z }%
-\def\XINT_lcmof_b #1\Z #2{\expandafter\XINT_lcmof_c\romannumeral`&&@#2\Z {#1}\Z}%
-\def\XINT_lcmof_c #1{\xint_gob_til_relax #1\XINT_lcmof_e\relax\XINT_lcmof_d #1}%
-\def\XINT_lcmof_d #1\Z {\expandafter\XINT_lcmof_b\romannumeral0\xintlcm {#1}}%
-\def\XINT_lcmof_e #1\Z #2\Z { #2}%
+\def\xintlcmof #1{\expandafter\XINT_lcmof_a\romannumeral`&&@#1\xint:}%
+\def\XINT_lcmof_a #1{\expandafter\XINT_lcmof_b\romannumeral`&&@#1!}%
+\def\XINT_lcmof_b #1!#2{\expandafter\XINT_lcmof_c\romannumeral`&&@#2!{#1}!}%
+\def\XINT_lcmof_c #1{\xint_gob_til_xint: #1\XINT_lcmof_e\xint:\XINT_lcmof_d #1}%
+\def\XINT_lcmof_d #1!{\expandafter\XINT_lcmof_b\romannumeral0\xintlcm {#1}}%
+\def\XINT_lcmof_e #1!#2!{ #2}%
\def\xintTypesetEuclideAlgorithm {%
\unless\ifdefined\xintAssignArray
\errmessage
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintkernel.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintkernel.sty 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintkernel.sty 2017-07-27 21:26:25 UTC (rev 44900)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.2k 2017/01/06
+%% The xint bundle 1.2l 2017/07/26
%% Copyright (C) 2013-2017 by Jean-Francois Burnol
%% xintkernel: Paraphernalia for the xint packages
%% ---------------------------------------------------------------
@@ -126,7 +126,7 @@
\catcode36=3 % $
\catcode91=12 % [
\catcode93=12 % ]
- \catcode33=12 % !
+ \catcode33=12 % ! (xintexpr.sty will use catcode 11)
\catcode64=11 % @ LETTER
\catcode38=7 % & for \romannumeral`&&@ trick.
\catcode124=12 % |
@@ -156,7 +156,7 @@
\fi
\XINT_providespackage
\ProvidesPackage {xintkernel}%
- [2017/01/06 1.2k Paraphernalia for the xint packages (JFB)]%
+ [2017/07/26 1.2l Paraphernalia for the xint packages (JFB)]%
\chardef\xint_c_ 0
\chardef\xint_c_i 1
\chardef\xint_c_ii 2
@@ -168,6 +168,7 @@
\chardef\xint_c_viii 8
\chardef\xint_c_ix 9
\chardef\xint_c_x 10
+\chardef\xint_c_xii 12
\chardef\xint_c_xiv 14
\chardef\xint_c_xvi 16
\chardef\xint_c_xviii 18
@@ -222,11 +223,9 @@
\long\def\xint_gob_til_zeros_iii #1000{}%
\long\def\xint_gob_til_zeros_iv #10000{}%
\long\def\xint_gob_til_eightzeroes #100000000{}%
-\long\def\xint_gob_til_exclam #1!{}% catcode 12 exclam
\long\def\xint_gob_til_dot #1.{}%
\long\def\xint_gob_til_G #1G{}%
\long\def\xint_gob_til_minus #1-{}%
-\long\def\xint_gob_til_relax #1\relax {}%
\long\def\xint_UDzerominusfork #10-#2#3\krof {#2}%
\long\def\xint_UDzerofork #10#2#3\krof {#2}%
\long\def\xint_UDsignfork #1-#2#3\krof {#2}%
@@ -235,9 +234,11 @@
\long\def\xint_UDzerosfork #100#2#3\krof {#2}%
\long\def\xint_UDonezerofork #110#2#3\krof {#2}%
\long\def\xint_UDsignsfork #1--#2#3\krof {#2}%
-\let\xint_relax\relax
-\def\xint_brelax {\xint_relax }%
-\long\def\xint_gob_til_xint_relax #1\xint_relax {}%
+\let\xint:\char
+\long\def\xint_gob_til_xint:#1\xint:{}%
+\def\xint_bracedstopper{\xint:}%
+\long\def\xint_gob_til_exclam #1!{}%
+\long\def\xint_gob_til_sc #1;{}%
\long\def\xint_afterfi #1#2\fi {\fi #1}%
\long\def\xint_bye #1\xint_bye {}%
\long\def\xint_Bye #1\xint_bye {}%
@@ -261,10 +262,10 @@
\long\def\xintreverseorder #1%
{%
\XINT_rord_main {}#1%
- \xint_relax
+ \xint:
\xint_bye\xint_bye\xint_bye\xint_bye
\xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax
+ \xint:
}%
\long\def\XINT_rord_main #1#2#3#4#5#6#7#8#9%
{%
@@ -271,26 +272,26 @@
\xint_bye #9\XINT_rord_cleanup\xint_bye
\XINT_rord_main {#9#8#7#6#5#4#3#2#1}%
}%
-\long\edef\XINT_rord_cleanup\xint_bye\XINT_rord_main #1#2\xint_relax
+\def\XINT_rord_cleanup #1{%
+\long\def\XINT_rord_cleanup\xint_bye\XINT_rord_main ##1##2\xint:
{%
- \noexpand\expandafter\space\noexpand\xint_gob_til_xint_relax #1%
-}%
+ \expandafter#1\xint_gob_til_xint: ##1%
+}}\XINT_rord_cleanup { }%
\def\xintLength {\romannumeral0\xintlength }%
\def\xintlength #1{\long\def\xintlength ##1%
{%
\expandafter#1\the\numexpr\XINT_length_loop
- ##1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
- \xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
+ ##1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
+ \xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
+ \xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
\relax
}}\xintlength{ }%
\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
+ \xint_gob_til_xint: #9\XINT_length_finish_a\xint:
\xint_c_ix+\XINT_length_loop
}%
-\def\XINT_length_finish_a\xint_relax\xint_c_ix+\XINT_length_loop
+\def\XINT_length_finish_a\xint:\xint_c_ix+\XINT_length_loop
#1#2#3#4#5#6#7#8#9%
{%
#9\xint_bye
@@ -299,15 +300,15 @@
\long\def\xintlastitem #1%
{%
\XINT_last_loop {}.#1%
- {\xint_relax\XINT_last_loop_enda}{\xint_relax\XINT_last_loop_endb}%
- {\xint_relax\XINT_last_loop_endc}{\xint_relax\XINT_last_loop_endd}%
- {\xint_relax\XINT_last_loop_ende}{\xint_relax\XINT_last_loop_endf}%
- {\xint_relax\XINT_last_loop_endg}{\xint_relax\XINT_last_loop_endh}\xint_bye
+ {\xint:\XINT_last_loop_enda}{\xint:\XINT_last_loop_endb}%
+ {\xint:\XINT_last_loop_endc}{\xint:\XINT_last_loop_endd}%
+ {\xint:\XINT_last_loop_ende}{\xint:\XINT_last_loop_endf}%
+ {\xint:\XINT_last_loop_endg}{\xint:\XINT_last_loop_endh}\xint_bye
}%
\long\def\XINT_last_loop #1.#2#3#4#5#6#7#8#9%
{%
- \xint_gob_til_xint_relax #9%
- {#8}{#7}{#6}{#5}{#4}{#3}{#2}{#1}\xint_relax
+ \xint_gob_til_xint: #9%
+ {#8}{#7}{#6}{#5}{#4}{#3}{#2}{#1}\xint:
\XINT_last_loop {#9}.%
}%
\long\def\XINT_last_loop_enda #1#2\xint_bye{ #1}%
@@ -322,8 +323,7 @@
\long\def\xintlengthupto #1#2%
{%
\expandafter\XINT_lengthupto_loop
- \the\numexpr#1.#2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax
+ \the\numexpr#1.#2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_vii\xint_c_vi\xint_c_v\xint_c_iv
\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye.%
}%
@@ -337,10 +337,10 @@
\long\def\XINT_lengthupto_gt #1\xint_bye.{-0}%
\long\def\XINT_lengthupto_loop #1.#2#3#4#5#6#7#8#9%
{%
- \xint_gob_til_xint_relax #9\XINT_lengthupto_finish_a\xint_relax
+ \xint_gob_til_xint: #9\XINT_lengthupto_finish_a\xint:%
\expandafter\XINT_lengthupto_loop_a\the\numexpr #1-\xint_c_viii.%
}%
-\def\XINT_lengthupto_finish_a\xint_relax\expandafter\XINT_lengthupto_loop_a
+\def\XINT_lengthupto_finish_a\xint:\expandafter\XINT_lengthupto_loop_a
\the\numexpr #1-\xint_c_viii.#2#3#4#5#6#7#8#9%
{%
\expandafter\XINT_lengthupto_finish_b\the\numexpr #1-#9\xint_bye
@@ -508,10 +508,18 @@
\expandafter\edef\csname XINT_g68\endcsname
{\noexpand\csname XINT_g67\expandafter\noexpand\csname XINT_g61\endcsname}%
\def\xintMessage #1#2#3{%
- \immediate\write128{Package #1 #2: (on line \the\inputlineno)}%
- \immediate\write128{\space\space\space\space#3}%
+ \immediate\write128{Package #1 #2: (on line \the\inputlineno)}%
+ \immediate\write128{\space\space\space\space#3}%
}%
\newif\ifxintverbose
+\def\XINT_expandableerror #1#2{%
+ \def\XINT_expandableerror ##1{%
+ \expandafter\expandafter\expandafter
+ \XINT_expandableerror_continue\xint_firstofone{#2#1##1#1}}%
+ \def\XINT_expandableerror_continue ##1#1##2#1{##1}%
+}%
+\begingroup\lccode`$ 32 \catcode`/ 11 \catcode`! 11 \catcode32 11 %
+\lowercase{\endgroup\XINT_expandableerror$\ ! /}%
\XINT_restorecatcodes_endinput%
\endinput
%%
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintseries.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintseries.sty 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintseries.sty 2017-07-27 21:26:25 UTC (rev 44900)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.2k 2017/01/06
+%% The xint bundle 1.2l 2017/07/26
%% Copyright (C) 2013-2017 by Jean-Francois Burnol
%% xintseries: Expandable partial sums with xint package
%% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintseries}%
- [2017/01/06 1.2k Expandable partial sums with xint package (JFB)]%
+ [2017/07/26 1.2l Expandable partial sums with xint package (JFB)]%
\def\xintSeries {\romannumeral0\xintseries }%
\def\xintseries #1#2%
{%
@@ -308,7 +308,7 @@
{#2}{#1}{#3}{#4}{#5}%
}%
\def\xintFloatPowerSeries {\romannumeral0\xintfloatpowerseries }%
-\def\xintfloatpowerseries #1{\XINT_flpowseries_chkopt #1\xint_relax }%
+\def\xintfloatpowerseries #1{\XINT_flpowseries_chkopt #1\xint:}%
\def\XINT_flpowseries_chkopt #1%
{%
\ifx [#1\expandafter\XINT_flpowseries_opt
@@ -316,13 +316,13 @@
\fi
#1%
}%
-\def\XINT_flpowseries_noopt #1\xint_relax #2%
+\def\XINT_flpowseries_noopt #1\xint:#2%
{%
\expandafter\XINT_flpowseries\expandafter
{\the\numexpr #1\expandafter}\expandafter
{\the\numexpr #2}\XINTdigits
}%
-\def\XINT_flpowseries_opt [\xint_relax #1]#2#3%
+\def\XINT_flpowseries_opt [\xint:#1]#2#3%
{%
\expandafter\XINT_flpowseries\expandafter
{\the\numexpr #2\expandafter}\expandafter
@@ -373,7 +373,7 @@
\xintfloatadd [#7]{#4}{\XINTinfloatmul [#7]{#6{#2}}{#1}}%
}%
\def\xintFloatPowerSeriesX {\romannumeral0\xintfloatpowerseriesx }%
-\def\xintfloatpowerseriesx #1{\XINT_flpowseriesx_chkopt #1\xint_relax }%
+\def\xintfloatpowerseriesx #1{\XINT_flpowseriesx_chkopt #1\xint:}%
\def\XINT_flpowseriesx_chkopt #1%
{%
\ifx [#1\expandafter\XINT_flpowseriesx_opt
@@ -381,13 +381,13 @@
\fi
#1%
}%
-\def\XINT_flpowseriesx_noopt #1\xint_relax #2%
+\def\XINT_flpowseriesx_noopt #1\xint:#2%
{%
\expandafter\XINT_flpowseriesx\expandafter
{\the\numexpr #1\expandafter}\expandafter
{\the\numexpr #2}\XINTdigits
}%
-\def\XINT_flpowseriesx_opt [\xint_relax #1]#2#3%
+\def\XINT_flpowseriesx_opt [\xint:#1]#2#3%
{%
\expandafter\XINT_flpowseriesx\expandafter
{\the\numexpr #2\expandafter}\expandafter
Modified: trunk/Master/texmf-dist/tex/generic/xint/xinttools.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xinttools.sty 2017-07-27 21:26:08 UTC (rev 44899)
+++ trunk/Master/texmf-dist/tex/generic/xint/xinttools.sty 2017-07-27 21:26:25 UTC (rev 44900)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.2k 2017/01/06
+%% The xint bundle 1.2l 2017/07/26
%% Copyright (C) 2013-2017 by Jean-Francois Burnol
%% xinttools: Expandable and non-expandable utilities
%% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xinttools}%
- [2017/01/06 1.2k Expandable and non-expandable utilities (JFB)]%
+ [2017/07/26 1.2l Expandable and non-expandable utilities (JFB)]%
\newtoks\XINT_toks
\xint_firstofone{\let\XINT_sptoken= } %<- space here!
\def\xintgodef {\global\xintodef }%
@@ -81,21 +81,21 @@
\long\def\xintrevwithbraces #1%
{%
\expandafter\XINT_revwbr_loop\expandafter{\expandafter}%
- \romannumeral`&&@#1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye
+ \romannumeral`&&@#1\xint:\xint:\xint:\xint:%
+ \xint:\xint:\xint:\xint:\xint_bye
}%
\long\def\xintrevwithbracesnoexpand #1%
{%
\XINT_revwbr_loop {}%
- #1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye
+ #1\xint:\xint:\xint:\xint:%
+ \xint:\xint:\xint:\xint:\xint_bye
}%
\long\def\XINT_revwbr_loop #1#2#3#4#5#6#7#8#9%
{%
- \xint_gob_til_xint_relax #9\XINT_revwbr_finish_a\xint_relax
+ \xint_gob_til_xint: #9\XINT_revwbr_finish_a\xint:%
\XINT_revwbr_loop {{#9}{#8}{#7}{#6}{#5}{#4}{#3}{#2}#1}%
}%
-\long\def\XINT_revwbr_finish_a\xint_relax\XINT_revwbr_loop #1#2\xint_bye
+\long\def\XINT_revwbr_finish_a\xint:\XINT_revwbr_loop #1#2\xint_bye
{%
\XINT_revwbr_finish_b #2\R\R\R\R\R\R\R\Z #1%
}%
@@ -111,49 +111,60 @@
#7\XINT_revwbr_finish_c \xint_gobble_ii
\R\XINT_revwbr_finish_c \xint_gobble_i\Z
}%
-\edef\XINT_revwbr_finish_c #1#2\Z {\noexpand\expandafter\space #1}%
+\def\XINT_revwbr_finish_c#1{%
+\def\XINT_revwbr_finish_c##1##2\Z{\expandafter#1##1}%
+}\XINT_revwbr_finish_c{ }%
\def\xintZapFirstSpaces {\romannumeral0\xintzapfirstspaces }%
-\long\edef\xintzapfirstspaces #1%
- {\noexpand\XINT_zapbsp_a \space #1\xint_relax \space\space\xint_relax }%
-\xint_firstofone {\long\edef\XINT_zapbsp_a #1 } %<- space token here
-{%
- \noexpand\XINT_zapbsp_again? #1\noexpand\xint_bye\noexpand\XINT_zapbsp_b #1\space\space
-}%
+\def\xintzapfirstspaces#1{\long
+\def\xintzapfirstspaces ##1{\XINT_zapbsp_a #1##1\xint:#1#1\xint:}%
+}\xintzapfirstspaces{ }%
+\def\XINT_zapbsp_a#1{\long\def\XINT_zapbsp_a ##1#1#1{%
+ \XINT_zapbsp_again?##1\xint_bye\XINT_zapbsp_b ##1#1#1}%
+}\XINT_zapbsp_a{ }%
\long\def\XINT_zapbsp_again? #1{\xint_bye #1\XINT_zapbsp_again }%
\xint_firstofone{\def\XINT_zapbsp_again\XINT_zapbsp_b} {\XINT_zapbsp_a }%
-\long\def\XINT_zapbsp_b #1\xint_relax #2\xint_relax {#1}%
+\long\def\XINT_zapbsp_b #1\xint:#2\xint:{#1}%
\def\xintZapLastSpaces {\romannumeral0\xintzaplastspaces }%
-\long\edef\xintzaplastspaces #1{\noexpand\XINT_zapesp_a {}\noexpand\empty#1%
- \space\space\noexpand\xint_bye\xint_relax}%
+\def\xintzaplastspaces#1{\long
+\def\xintzaplastspaces ##1{\XINT_zapesp_a {}\empty##1#1#1\xint_bye\xint:}%
+}\xintzaplastspaces{ }%
\xint_firstofone {\long\def\XINT_zapesp_a #1#2 } %<- second space here
{\expandafter\XINT_zapesp_b\expandafter{#2}{#1}}%
-\long\def\XINT_zapesp_b #1#2#3\xint_relax
- {\XINT_zapesp_end? #3\XINT_zapesp_e {#2#1}\empty #3\xint_relax }%
+\long\def\XINT_zapesp_b #1#2#3\xint:%
+ {\XINT_zapesp_end? #3\XINT_zapesp_e {#2#1}\empty #3\xint:}%
\long\def\XINT_zapesp_end? #1{\xint_bye #1\XINT_zapesp_end }%
-\long\def\XINT_zapesp_end\XINT_zapesp_e #1#2\xint_relax { #1}%
-\long\edef\XINT_zapesp_e #1{\noexpand \XINT_zapesp_a {#1\space\space}}%
+\long\def\XINT_zapesp_end\XINT_zapesp_e #1#2\xint:{ #1}%
+\def\XINT_zapesp_e#1{%
+\long\def\XINT_zapesp_e ##1{\XINT_zapesp_a {##1#1#1}}%
+}\XINT_zapesp_e{ }%
\def\xintZapSpaces {\romannumeral0\xintzapspaces }%
-\long\edef\xintzapspaces #1% like \xintZapFirstSpaces.
- {\noexpand\XINT_zapsp_a \space #1\xint_relax \space\space\xint_relax }%
-\xint_firstofone {\long\edef\XINT_zapsp_a #1 } %
- {\noexpand\XINT_zapsp_again? #1\noexpand\xint_bye\noexpand\XINT_zapsp_b #1\space\space}%
+\def\xintzapspaces#1{%
+\long\def\xintzapspaces ##1% like \xintZapFirstSpaces.
+ {\XINT_zapsp_a #1##1\xint:#1#1\xint:}%
+}\xintzapspaces{ }%
+\def\XINT_zapsp_a#1{%
+\long\def\XINT_zapsp_a ##1#1#1%
+ {\XINT_zapsp_again?##1\xint_bye\XINT_zapsp_b##1#1#1}%
+}\XINT_zapsp_a{ }%
\long\def\XINT_zapsp_again? #1{\xint_bye #1\XINT_zapsp_again }%
\xint_firstofone{\def\XINT_zapsp_again\XINT_zapsp_b} {\XINT_zapsp_a }%
\xint_firstofone{\def\XINT_zapsp_b} {\XINT_zapsp_c }%
-\long\edef\XINT_zapsp_c #1\xint_relax #2\xint_relax {\noexpand\XINT_zapesp_a
- {}\noexpand \empty #1\space\space\noexpand\xint_bye\xint_relax }%
+\def\XINT_zapsp_c#1{%
+\long\def\XINT_zapsp_c ##1\xint:##2\xint:%
+ {\XINT_zapesp_a{}\empty ##1#1#1\xint_bye\xint:}%
+}\XINT_zapsp_c{ }%
\def\xintZapSpacesB {\romannumeral0\xintzapspacesb }%
-\long\def\xintzapspacesb #1{\XINT_zapspb_one? #1\xint_relax\xint_relax
+\long\def\xintzapspacesb #1{\XINT_zapspb_one? #1\xint:\xint:%
\xint_bye\xintzapspaces {#1}}%
\long\def\XINT_zapspb_one? #1#2%
- {\xint_gob_til_xint_relax #1\XINT_zapspb_onlyspaces\xint_relax
- \xint_gob_til_xint_relax #2\XINT_zapspb_bracedorone\xint_relax
+ {\xint_gob_til_xint: #1\XINT_zapspb_onlyspaces\xint:%
+ \xint_gob_til_xint: #2\XINT_zapspb_bracedorone\xint:%
\xint_bye {#1}}%
-\def\XINT_zapspb_onlyspaces\xint_relax
- \xint_gob_til_xint_relax\xint_relax\XINT_zapspb_bracedorone\xint_relax
+\def\XINT_zapspb_onlyspaces\xint:%
+ \xint_gob_til_xint:\xint:\XINT_zapspb_bracedorone\xint:%
\xint_bye #1\xint_bye\xintzapspaces #2{ }%
-\long\def\XINT_zapspb_bracedorone\xint_relax
- \xint_bye #1\xint_relax\xint_bye\xintzapspaces #2{ #1}%
+\long\def\XINT_zapspb_bracedorone\xint:%
+ \xint_bye #1\xint:\xint_bye\xintzapspaces #2{ #1}%
\def\xintCSVtoList {\romannumeral0\xintcsvtolist }%
\long\def\xintcsvtolist #1{\expandafter\xintApply
\expandafter\xintzapspacesb
@@ -246,8 +257,7 @@
\long\def\XINT_nthelt_neg #1.#2%
{%
\expandafter\XINT_nthelt_neg_a\the\numexpr\xint_c_i+\XINT_length_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
-#1.#2\xint_bye
@@ -267,13 +277,13 @@
{%
\expandafter\XINT_nthelt_pos_done
\romannumeral0\expandafter\XINT_trim_loop\the\numexpr#1-\xint_c_x.%
- #2\xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:%
+ \xint:\xint:\xint:\xint:\xint:%
\xint_bye
}%
\def\XINT_nthelt_pos_done #1{%
\long\def\XINT_nthelt_pos_done ##1##2\xint_bye{%
- \xint_gob_til_xint_relax##1\expandafter#1\xint_gobble_ii\xint_relax#1##1}%
+ \xint_gob_til_xint:##1\expandafter#1\xint_gobble_ii\xint:#1##1}%
}\XINT_nthelt_pos_done{ }%
\def\xintKeep {\romannumeral0\xintkeep }%
\def\xintKeepNoExpand {\romannumeral0\xintkeepnoexpand }%
@@ -293,8 +303,7 @@
{%
\expandafter\XINT_keep_neg_a\the\numexpr
#1-\numexpr\XINT_length_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye.#2%
}%
@@ -310,8 +319,7 @@
{%
\expandafter\XINT_keep_loop
\the\numexpr#1-\XINT_lengthupto_loop
- #1.#2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax
+ #1.#2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_vii\xint_c_vi\xint_c_v\xint_c_iv
\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye.%
-\xint_c_viii.{}#2\xint_bye%
@@ -362,8 +370,7 @@
{%
\expandafter\XINT_keepunbr_loop
\the\numexpr#1-\XINT_lengthupto_loop
- #1.#2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax
+ #1.#2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_vii\xint_c_vi\xint_c_v\xint_c_iv
\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye.%
-\xint_c_viii.{}#2\xint_bye%
@@ -413,8 +420,7 @@
{%
\expandafter\XINT_trim_neg_a\the\numexpr
#1-\numexpr\XINT_length_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
.{}#2\xint_bye
@@ -426,13 +432,15 @@
-\XINT_trim_trimall
\krof
}%
-\edef\XINT_trim_trimall {\noexpand\expandafter\space\noexpand\xint_bye}%
+\def\XINT_trim_trimall#1{%
+\def\XINT_trim_trimall {\expandafter#1\xint_bye}%
+}\XINT_trim_trimall{ }%
\long\def\XINT_trim_pos #1.#2%
{%
\expandafter\XINT_trim_pos_done\expandafter\space
\romannumeral0\expandafter\XINT_trim_loop\the\numexpr#1-\xint_c_ix.%
- #2\xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:%
+ \xint:\xint:\xint:\xint:\xint:%
\xint_bye
}%
\def\XINT_trim_loop #1#2.%
@@ -442,9 +450,9 @@
}%
\long\def\XINT_trim_loop_trimnine #1#2#3#4#5#6#7#8#9%
{%
- \xint_gob_til_xint_relax #9\XINT_trim_toofew\xint_relax-\xint_c_ix.%
+ \xint_gob_til_xint: #9\XINT_trim_toofew\xint:-\xint_c_ix.%
}%
-\def\XINT_trim_toofew\xint_relax{*\xint_c_}%
+\def\XINT_trim_toofew\xint:{*\xint_c_}%
\def\XINT_trim_finish#1{%
\def\XINT_trim_finish-%
\expandafter\XINT_trim_loop\the\numexpr-##1\XINT_trim_loop_trimnine
@@ -452,7 +460,7 @@
\expandafter\expandafter\expandafter#1%
\csname xint_gobble_\romannumeral\numexpr\xint_c_ix-##1\endcsname
}}\XINT_trim_finish{ }%
-\long\def\XINT_trim_pos_done #1\xint_relax #2\xint_bye {#1}%
+\long\def\XINT_trim_pos_done #1\xint:#2\xint_bye {#1}%
\def\xintTrimUnbraced {\romannumeral0\xinttrimunbraced }%
\def\xintTrimUnbracedNoExpand {\romannumeral0\xinttrimunbracednoexpand }%
\long\def\xinttrimunbraced #1#2%
@@ -472,8 +480,7 @@
{%
\expandafter\XINT_trimunbr_neg_a\the\numexpr
#1-\numexpr\XINT_length_loop
- #2\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_relax
+ #2\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
\xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
\xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
.{}#2\xint_bye
@@ -1001,7 +1008,7 @@
\long\def\XINT_assign_a #1\to
{%
\def\XINT_flet_macro{\XINT_assign_b}%
- \expandafter\XINT_flet_zapsp\romannumeral`&&@#1\xint_relax\to
+ \expandafter\XINT_flet_zapsp\romannumeral`&&@#1\xint:\to
}%
\long\def\XINT_assign_b
{%
@@ -1010,7 +1017,7 @@
\else\expandafter\XINT_assign_f
\fi
}%
-\long\def\XINT_assign_f #1\xint_relax\to #2%
+\long\def\XINT_assign_f #1\xint:\to #2%
{%
\XINT_assign_def #2{#1}%
}%
@@ -1017,7 +1024,7 @@
\long\def\XINT_assign_c #1%
{%
\def\xint_temp {#1}%
- \ifx\xint_temp\xint_brelax
+ \ifx\xint_temp\xint_bracedstopper
\expandafter\XINT_assign_e
\else
\expandafter\XINT_assign_d
@@ -1069,7 +1076,7 @@
\expandafter\def\expandafter\xint_arrayname\expandafter {\string #2}%
\XINT_restoreescapechar
\def\xint_itemcount {0}%
- \expandafter\XINT_assignarray_loop \romannumeral`&&@#1\xint_relax
+ \expandafter\XINT_assignarray_loop \romannumeral`&&@#1\xint:
\csname\xint_arrayname 00\expandafter\endcsname
\csname\xint_arrayname 0\expandafter\endcsname
\expandafter {\xint_arrayname}#2%
@@ -1077,7 +1084,7 @@
\long\def\XINT_assignarray_loop #1%
{%
\def\xint_temp {#1}%
- \ifx\xint_brelax\xint_temp
+ \ifx\xint_temp\xint_bracedstopper
\expandafter\def\csname\xint_arrayname 0\expandafter\endcsname
\expandafter{\the\numexpr\xint_itemcount}%
\expandafter\expandafter\expandafter\XINT_assignarray_end
@@ -1099,11 +1106,12 @@
\def #1##1%
{%
\ifnum ##1<\xint_c_
- \xint_afterfi {\xintError:ArrayIndexIsNegative\space }%
+ \xint_afterfi{\XINT_expandableerror{Array index negative: 0 > ##1} }%
\else
\xint_afterfi {%
\ifnum ##1>#2
- \xint_afterfi {\xintError:ArrayIndexBeyondLimit\space }%
+ \xint_afterfi
+ {\XINT_expandableerror{Array index beyond range: ##1 > #2} }%
\else\xint_afterfi
{\expandafter\expandafter\expandafter\space\csname #3##1\endcsname}%
\fi}%
@@ -1115,8 +1123,8 @@
\def\xintlength:f:csv #1%
{\long\def\xintlength:f:csv ##1{%
\expandafter#1\the\numexpr\expandafter\XINT_length:f:csv_a
- \romannumeral`&&@##1\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
+ \romannumeral`&&@##1\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,\xint:,%
\xint_c_ix,\xint_c_viii,\xint_c_vii,\xint_c_vi,%
\xint_c_v,\xint_c_iv,\xint_c_iii,\xint_c_ii,\xint_c_i,\xint_bye
\relax
@@ -1123,15 +1131,15 @@
}}\xintlength:f:csv { }%
\long\def\XINT_length:f:csv_a #1%
{%
- \xint_gob_til_xint_relax #1\xint_c_\xint_bye\xint_relax
+ \xint_gob_til_xint: #1\xint_c_\xint_bye\xint:%
\XINT_length:f:csv_loop #1%
}%
\long\def\XINT_length:f:csv_loop #1,#2,#3,#4,#5,#6,#7,#8,#9,%
{%
- \xint_gob_til_xint_relax #9\XINT_length:f:csv_finish\xint_relax
+ \xint_gob_til_xint: #9\XINT_length:f:csv_finish\xint:%
\xint_c_ix+\XINT_length:f:csv_loop
}%
-\def\XINT_length:f:csv_finish\xint_relax\xint_c_ix+\XINT_length:f:csv_loop
+\def\XINT_length:f:csv_finish\xint:\xint_c_ix+\XINT_length:f:csv_loop
#1,#2,#3,#4,#5,#6,#7,#8,#9,{#9\xint_bye}%
\def\xintLengthUpTo:f:csv {\romannumeral0\xintlengthupto:f:csv}%
\long\def\xintlengthupto:f:csv #1#2%
@@ -1138,17 +1146,17 @@
{%
\expandafter\XINT_lengthupto:f:csv_a
\the\numexpr#1\expandafter.%
- \romannumeral`&&@#2\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,%
+ \romannumeral`&&@#2\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,%
\xint_c_viii,\xint_c_vii,\xint_c_vi,\xint_c_v,%
\xint_c_iv,\xint_c_iii,\xint_c_ii,\xint_c_i,\xint_bye.%
}%
\long\def\XINT_lengthupto:f:csv_a #1.#2%
{%
- \xint_gob_til_xint_relax #2\XINT_lengthupto:f:csv_empty\xint_relax
+ \xint_gob_til_xint: #2\XINT_lengthupto:f:csv_empty\xint:%
\XINT_lengthupto:f:csv_loop_b #1.#2%
}%
-\def\XINT_lengthupto:f:csv_empty\xint_relax
+\def\XINT_lengthupto:f:csv_empty\xint:%
\XINT_lengthupto:f:csv_loop_b #1.#2\xint_bye.{ #1}%
\def\XINT_lengthupto:f:csv_loop_a #1%
{%
@@ -1160,10 +1168,10 @@
\long\def\XINT_lengthupto:f:csv_gt #1\xint_bye.{-0}%
\long\def\XINT_lengthupto:f:csv_loop_b #1.#2,#3,#4,#5,#6,#7,#8,#9,%
{%
- \xint_gob_til_xint_relax #9\XINT_lengthupto:f:csv_finish_a\xint_relax
+ \xint_gob_til_xint: #9\XINT_lengthupto:f:csv_finish_a\xint:%
\expandafter\XINT_lengthupto:f:csv_loop_a\the\numexpr #1-\xint_c_viii.%
}%
-\def\XINT_lengthupto:f:csv_finish_a\xint_relax
+\def\XINT_lengthupto:f:csv_finish_a\xint:
\expandafter\XINT_lengthupto:f:csv_loop_a
\the\numexpr #1-\xint_c_viii.#2,#3,#4,#5,#6,#7,#8,#9,%
{%
@@ -1198,8 +1206,8 @@
\romannumeral0%
\expandafter\XINT_keep:f:csv_neg_a\the\numexpr
#1-\numexpr\XINT_length:f:csv_a
- #2\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
+ #2\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,\xint:,%
\xint_c_ix,\xint_c_viii,\xint_c_vii,\xint_c_vi,%
\xint_c_v,\xint_c_iv,\xint_c_iii,\xint_c_ii,\xint_c_i,\xint_bye
.#2\xint_bye
@@ -1228,8 +1236,8 @@
{%
\expandafter\XINT_keep:f:csv_pos_fork
\romannumeral0\XINT_lengthupto:f:csv_a
- #1.#2\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,%
+ #1.#2\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,%
\xint_c_viii,\xint_c_vii,\xint_c_vi,\xint_c_v,%
\xint_c_iv,\xint_c_iii,\xint_c_ii,\xint_c_i,\xint_bye.%
.#1.{}#2\xint_bye%
@@ -1289,8 +1297,8 @@
{%
\expandafter\XINT_trim:f:csv_neg_a\the\numexpr
#1-\numexpr\XINT_length:f:csv_a
- #2\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
+ #2\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,\xint:,%
\xint_c_ix,\xint_c_viii,\xint_c_vii,\xint_c_vi,%
\xint_c_v,\xint_c_iv,\xint_c_iii,\xint_c_ii,\xint_c_i,\xint_bye
.{}#2\xint_bye
@@ -1308,8 +1316,8 @@
\expandafter\XINT_trim:f:csv_pos_done\expandafter,%
\romannumeral0%
\expandafter\XINT_trim:f:csv_loop\the\numexpr#1-\xint_c_ix.%
- #2\xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax\xint_bye
+ #2\xint:,\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,\xint:\xint_bye
}%
\def\XINT_trim:f:csv_loop #1#2.%
{%
@@ -1318,9 +1326,9 @@
}%
\long\def\XINT_trim:f:csv_loop_trimnine #1,#2,#3,#4,#5,#6,#7,#8,#9,%
{%
- \xint_gob_til_xint_relax #9\XINT_trim:f:csv_toofew\xint_relax-\xint_c_ix.%
+ \xint_gob_til_xint: #9\XINT_trim:f:csv_toofew\xint:-\xint_c_ix.%
}%
-\def\XINT_trim:f:csv_toofew\xint_relax{*\xint_c_}%
+\def\XINT_trim:f:csv_toofew\xint:{*\xint_c_}%
\def\XINT_trim:f:csv_finish-%
\expandafter\XINT_trim:f:csv_loop\the\numexpr-#1\XINT_trim:f:csv_loop_trimnine
{%
@@ -1343,7 +1351,7 @@
\long\expandafter\def\csname XINT_trim:f:csv_finish8\endcsname
#1,{ }%
\expandafter\let\csname XINT_trim:f:csv_finish9\endcsname\space
-\long\def\XINT_trim:f:csv_pos_done #1\xint_relax #2\xint_bye{#1}%
+\long\def\XINT_trim:f:csv_pos_done #1\xint:#2\xint_bye{#1}%
\def\xintNthEltPy:f:csv {\romannumeral0\xintntheltpy:f:csv }%
\long\def\xintntheltpy:f:csv #1#2%
{%
@@ -1361,8 +1369,8 @@
{%
\expandafter\XINT_nthelt:f:csv_neg_fork
\the\numexpr\XINT_length:f:csv_a
- #2\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
+ #2\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,\xint:,%
\xint_c_ix,\xint_c_viii,\xint_c_vii,\xint_c_vi,%
\xint_c_v,\xint_c_iv,\xint_c_iii,\xint_c_ii,\xint_c_i,\xint_bye
-#1.#2,\xint_bye
@@ -1380,24 +1388,24 @@
\expandafter\XINT_nthelt:f:csv_pos_done
\romannumeral0%
\expandafter\XINT_trim:f:csv_loop\the\numexpr#1-\xint_c_ix.%
- #2\xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,%
- \xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_relax,\xint_bye
+ #2\xint:,\xint:,\xint:,\xint:,\xint:,%
+ \xint:,\xint:,\xint:,\xint:,\xint:,\xint_bye
}%
\def\XINT_nthelt:f:csv_pos_done #1{%
\long\def\XINT_nthelt:f:csv_pos_done ##1,##2\xint_bye{%
- \xint_gob_til_xint_relax##1\XINT_nthelt:f:csv_pos_cleanup\xint_relax#1##1}%
+ \xint_gob_til_xint:##1\XINT_nthelt:f:csv_pos_cleanup\xint:#1##1}%
}\XINT_nthelt:f:csv_pos_done{ }%
-\xint_firstofone{\long\def\XINT_nthelt:f:csv_pos_cleanup\xint_relax} %
- #1\xint_relax{ #1}%
+\xint_firstofone{\long\def\XINT_nthelt:f:csv_pos_cleanup\xint:} %
+ #1\xint:{ #1}%
\def\xintReverse:f:csv {\romannumeral0\xintreverse:f:csv }%
\long\def\xintreverse:f:csv #1%
{%
\expandafter\XINT_reverse:f:csv_loop
\expandafter{\expandafter}\romannumeral`&&@#1,%
- \xint_relax,%
+ \xint:,%
\xint_bye,\xint_bye,\xint_bye,\xint_bye,%
\xint_bye,\xint_bye,\xint_bye,\xint_bye,%
- \xint_relax
+ \xint:
}%
\long\def\XINT_reverse:f:csv_loop #1#2,#3,#4,#5,#6,#7,#8,#9,%
{%
@@ -1404,11 +1412,11 @@
\xint_bye #9\XINT_reverse:f:csv_cleanup\xint_bye
\XINT_reverse:f:csv_loop {,#9,#8,#7,#6,#5,#4,#3,#2#1}%
}%
-\long\def\XINT_reverse:f:csv_cleanup\xint_bye\XINT_reverse:f:csv_loop #1#2\xint_relax
+\long\def\XINT_reverse:f:csv_cleanup\xint_bye\XINT_reverse:f:csv_loop #1#2\xint:
{%
\XINT_reverse:f:csv_finish #1%
}%
-\long\def\XINT_reverse:f:csv_finish #1\xint_relax,{ }%
+\long\def\XINT_reverse:f:csv_finish #1\xint:,{ }%
\def\xintFirstItem:f:csv {\romannumeral0\xintfirstitem:f:csv}%
\long\def\xintfirstitem:f:csv #1%
{%
@@ -1420,15 +1428,15 @@
{%
\expandafter\XINT_last:f:csv_loop\expandafter{\expandafter}\expandafter.%
\romannumeral`&&@#1,%
- \xint_relax\XINT_last_loop_enda,\xint_relax\XINT_last_loop_endb,%
- \xint_relax\XINT_last_loop_endc,\xint_relax\XINT_last_loop_endd,%
- \xint_relax\XINT_last_loop_ende,\xint_relax\XINT_last_loop_endf,%
- \xint_relax\XINT_last_loop_endg,\xint_relax\XINT_last_loop_endh,\xint_bye
+ \xint:\XINT_last_loop_enda,\xint:\XINT_last_loop_endb,%
+ \xint:\XINT_last_loop_endc,\xint:\XINT_last_loop_endd,%
+ \xint:\XINT_last_loop_ende,\xint:\XINT_last_loop_endf,%
+ \xint:\XINT_last_loop_endg,\xint:\XINT_last_loop_endh,\xint_bye
}%
\long\def\XINT_last:f:csv_loop #1.#2,#3,#4,#5,#6,#7,#8,#9,%
{%
- \xint_gob_til_xint_relax #9%
- {#8}{#7}{#6}{#5}{#4}{#3}{#2}{#1}\xint_relax
+ \xint_gob_til_xint: #9%
+ {#8}{#7}{#6}{#5}{#4}{#3}{#2}{#1}\xint:
\XINT_last:f:csv_loop {#9}.%
}%
\let\xintCSVLength \xintLength:f:csv
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