xint (4apr21)

git-svn-id: svn://tug.org/texlive/trunk@58738 c570f23f-e606-0410-a88d-b1316a301751
author: Norbert Preining <preining@logic.at> 2021-04-04 02:31:47 +0000
committer: Norbert Preining <preining@logic.at> 2021-04-04 02:31:47 +0000
commit: d1301f3e47b2340fd9ffbb7d1a0a4b361540e22e (patch)
tree: 4a851156d9d547008865e20d69b78626178c5828 /Master
parent: 6aa284727262f1c7ac0ec6c67becc28d5a678a8c (diff)
17 files changed, 841 insertions, 526 deletions
diff --git a/Master/texmf-dist/doc/generic/xint/CHANGES.html b/Master/texmf-dist/doc/generic/xint/CHANGES.html
index 32fcfbe4eeb..20b940dad7c 100644
--- a/Master/texmf-dist/doc/generic/xint/CHANGES.html
+++ b/Master/texmf-dist/doc/generic/xint/CHANGES.html
@@ -4,7 +4,7 @@
   <meta charset="utf-8" />
   <meta name="generator" content="pandoc" />
   <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes" />
-  <meta name="author" content="xint 1.4c" />
+  <meta name="author" content="xint 1.4d" />
   <title>CHANGE LOG</title>
   <style type="text/css">
       code{white-space: pre-wrap;}
@@ -25,47 +25,51 @@
 <body>
 <header>
 <h1 class="title">CHANGE LOG</h1>
-<p class="author">xint 1.4c</p>
-<p class="date">2021/02/20</p>
+<p class="author">xint 1.4d</p>
+<p class="date">2021/03/29</p>
 </header>
 <nav id="TOC">
 <ul>
-<li><a href="#c-20210220"><code>1.4c (2021/02/20)</code></a><ul>
+<li><a href="#d-20210329"><code>1.4d (2021/03/29)</code></a><ul>
+<li><a href="#breaking-changes">Breaking changes</a></li>
 <li><a href="#bug-fixes">Bug fixes</a></li>
 </ul></li>
+<li><a href="#c-20210220"><code>1.4c (2021/02/20)</code></a><ul>
+<li><a href="#bug-fixes-1">Bug fixes</a></li>
+</ul></li>
 <li><a href="#b-20200225"><code>1.4b (2020/02/25)</code></a><ul>
 <li><a href="#future">Future</a></li>
 <li><a href="#new-features">New features</a></li>
-<li><a href="#bug-fixes-1">Bug fixes</a></li>
+<li><a href="#bug-fixes-2">Bug fixes</a></li>
 </ul></li>
 <li><a href="#a-20200219"><code>1.4a (2020/02/19)</code></a><ul>
-<li><a href="#breaking-changes">Breaking changes</a></li>
+<li><a href="#breaking-changes-1">Breaking changes</a></li>
 <li><a href="#new-features-1">New features</a></li>
-<li><a href="#bug-fixes-2">Bug fixes</a></li>
+<li><a href="#bug-fixes-3">Bug fixes</a></li>
 </ul></li>
 <li><a href="#section"><code>1.4 (2020/01/31)</code></a><ul>
-<li><a href="#breaking-changes-1">Breaking changes</a></li>
+<li><a href="#breaking-changes-2">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features">Improvements and new features</a></li>
-<li><a href="#bug-fixes-3">Bug fixes</a></li>
+<li><a href="#bug-fixes-4">Bug fixes</a></li>
 <li><a href="#todo">TODO</a></li>
 </ul></li>
 <li><a href="#f-20190910"><code>1.3f (2019/09/10)</code></a><ul>
 <li><a href="#improvements-and-new-features-1">Improvements and new features</a></li>
-<li><a href="#bug-fixes-4">Bug fixes</a></li>
+<li><a href="#bug-fixes-5">Bug fixes</a></li>
 </ul></li>
 <li><a href="#e-20190405"><code>1.3e (2019/04/05)</code></a><ul>
-<li><a href="#breaking-changes-2">Breaking changes</a></li>
+<li><a href="#breaking-changes-3">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-2">Improvements and new features</a></li>
-<li><a href="#bug-fixes-5">Bug fixes</a></li>
+<li><a href="#bug-fixes-6">Bug fixes</a></li>
 </ul></li>
 <li><a href="#d-20190106"><code>1.3d (2019/01/06)</code></a><ul>
-<li><a href="#breaking-changes-3">Breaking changes</a></li>
+<li><a href="#breaking-changes-4">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-3">Improvements and new features</a></li>
-<li><a href="#bug-fixes-6">Bug fixes</a></li>
+<li><a href="#bug-fixes-7">Bug fixes</a></li>
 </ul></li>
 <li><a href="#c-20180617"><code>1.3c (2018/06/17)</code></a><ul>
 <li><a href="#improvements-and-new-features-4">Improvements and new features</a></li>
-<li><a href="#bug-fixes-7">Bug fixes</a></li>
+<li><a href="#bug-fixes-8">Bug fixes</a></li>
 </ul></li>
 <li><a href="#b-20180518"><code>1.3b (2018/05/18)</code></a><ul>
 <li><a href="#improvements-and-new-features-5">Improvements and new features</a></li>
@@ -73,85 +77,85 @@
 <li><a href="#a-20180307"><code>1.3a (2018/03/07)</code></a><ul>
 <li><a href="#removed">Removed</a></li>
 <li><a href="#improvements-and-new-features-6">Improvements and new features</a></li>
-<li><a href="#bug-fixes-8">Bug fixes</a></li>
+<li><a href="#bug-fixes-9">Bug fixes</a></li>
 </ul></li>
 <li><a href="#section-1"><code>1.3 (2018/03/01)</code></a><ul>
-<li><a href="#breaking-changes-4">Breaking changes</a></li>
+<li><a href="#breaking-changes-5">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-7">Improvements and new features</a></li>
 </ul></li>
 <li><a href="#q-20180206"><code>1.2q (2018/02/06)</code></a><ul>
 <li><a href="#improvements-and-new-features-8">Improvements and new features</a></li>
-<li><a href="#bug-fixes-9">Bug fixes</a></li>
+<li><a href="#bug-fixes-10">Bug fixes</a></li>
 </ul></li>
 <li><a href="#p-20171205"><code>1.2p (2017/12/05)</code></a><ul>
-<li><a href="#breaking-changes-5">Breaking changes</a></li>
+<li><a href="#breaking-changes-6">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-9">Improvements and new features</a></li>
-<li><a href="#bug-fixes-10">Bug fixes</a></li>
+<li><a href="#bug-fixes-11">Bug fixes</a></li>
 </ul></li>
 <li><a href="#o-20170829"><code>1.2o (2017/08/29)</code></a><ul>
-<li><a href="#breaking-changes-6">Breaking changes</a></li>
+<li><a href="#breaking-changes-7">Breaking changes</a></li>
 <li><a href="#deprecated">Deprecated</a></li>
 </ul></li>
 <li><a href="#n-20170806"><code>1.2n (2017/08/06)</code></a><ul>
-<li><a href="#breaking-changes-7">Breaking changes</a></li>
+<li><a href="#breaking-changes-8">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-10">Improvements and new features</a></li>
 </ul></li>
 <li><a href="#m-20170731"><code>1.2m (2017/07/31)</code></a><ul>
-<li><a href="#breaking-changes-8">Breaking changes</a></li>
+<li><a href="#breaking-changes-9">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-11">Improvements and new features</a></li>
-<li><a href="#bug-fixes-11">Bug fixes</a></li>
+<li><a href="#bug-fixes-12">Bug fixes</a></li>
 </ul></li>
 <li><a href="#l-20170726"><code>1.2l (2017/07/26)</code></a><ul>
 <li><a href="#removed-1">Removed</a></li>
 <li><a href="#improvements-and-new-features-12">Improvements and new features</a></li>
-<li><a href="#bug-fixes-12">Bug fixes</a></li>
+<li><a href="#bug-fixes-13">Bug fixes</a></li>
 </ul></li>
 <li><a href="#k-20170106"><code>1.2k (2017/01/06)</code></a><ul>
-<li><a href="#breaking-changes-9">Breaking changes</a></li>
+<li><a href="#breaking-changes-10">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-13">Improvements and new features</a></li>
-<li><a href="#bug-fixes-13">Bug fixes</a></li>
+<li><a href="#bug-fixes-14">Bug fixes</a></li>
 </ul></li>
 <li><a href="#j-20161222"><code>1.2j (2016/12/22)</code></a><ul>
 <li><a href="#improvements-and-new-features-14">Improvements and new features</a></li>
-<li><a href="#bug-fixes-14">Bug fixes</a></li>
+<li><a href="#bug-fixes-15">Bug fixes</a></li>
 </ul></li>
 <li><a href="#i-20161213"><code>1.2i (2016/12/13)</code></a><ul>
-<li><a href="#breaking-changes-10">Breaking changes</a></li>
+<li><a href="#breaking-changes-11">Breaking changes</a></li>
 <li><a href="#removed-2">Removed</a></li>
 <li><a href="#improvements-and-new-features-15">Improvements and new features</a></li>
-<li><a href="#bug-fixes-15">Bug fixes</a></li>
+<li><a href="#bug-fixes-16">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-16">Improvements and new features</a></li>
-<li><a href="#bug-fixes-16">Bug fixes</a></li>
+<li><a href="#bug-fixes-17">Bug fixes</a></li>
 </ul></li>
 <li><a href="#g-20160319"><code>1.2g (2016/03/19)</code></a><ul>
-<li><a href="#breaking-changes-11">Breaking changes</a></li>
+<li><a href="#breaking-changes-12">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-17">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="#breaking-changes-12">Breaking changes</a></li>
+<li><a href="#breaking-changes-13">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-18">Improvements and new features</a></li>
-<li><a href="#bug-fixes-17">Bug fixes</a></li>
+<li><a href="#bug-fixes-18">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-19">Improvements and new features</a></li>
-<li><a href="#bug-fixes-18">Bug fixes</a></li>
+<li><a href="#bug-fixes-19">Bug fixes</a></li>
 </ul></li>
 <li><a href="#d-20151118"><code>1.2d (2015/11/18)</code></a><ul>
 <li><a href="#improvements-and-new-features-20">Improvements and new features</a></li>
-<li><a href="#bug-fixes-19">Bug fixes</a></li>
+<li><a href="#bug-fixes-20">Bug fixes</a></li>
 </ul></li>
 <li><a href="#c-20151116"><code>1.2c (2015/11/16)</code></a><ul>
 <li><a href="#improvements-and-new-features-21">Improvements and new features</a></li>
-<li><a href="#bug-fixes-20">Bug fixes</a></li>
+<li><a href="#bug-fixes-21">Bug fixes</a></li>
 </ul></li>
 <li><a href="#b-20151029"><code>1.2b (2015/10/29)</code></a><ul>
-<li><a href="#bug-fixes-21">Bug fixes</a></li>
+<li><a href="#bug-fixes-22">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-22">Improvements and new features</a></li>
-<li><a href="#bug-fixes-22">Bug fixes</a></li>
+<li><a href="#bug-fixes-23">Bug fixes</a></li>
 </ul></li>
 <li><a href="#section-2"><code>1.2 (2015/10/10)</code></a><ul>
 <li><a href="#removed-3">Removed</a></li>
@@ -161,11 +165,11 @@
 <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-3"><code>1.1 (2014/10/28)</code></a><ul>
-<li><a href="#breaking-changes-13">Breaking changes</a></li>
+<li><a href="#breaking-changes-14">Breaking changes</a></li>
 <li><a href="#removed-4">Removed</a></li>
 <li><a href="#deprecated-1">Deprecated</a></li>
 <li><a href="#improvements-and-new-features-24">Improvements and new features</a></li>
-<li><a href="#bug-fixes-23">Bug fixes</a></li>
+<li><a href="#bug-fixes-24">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>
@@ -193,13 +197,26 @@
 <li><a href="#section-10"><code>1.0 (2013/03/28)</code></a></li>
 </ul>
 </nav>
-<pre><code>Source:  xint.dtx 1.4c 2021/02/20 (doc 2021/02/20)
+<pre><code>Source:  xint.dtx 1.4d 2021/03/29 (doc 2021/03/29)
 Author:  Jean-Francois Burnol
 Info:    Expandable operations on big integers, decimals, fractions
 License: LPPL 1.3c</code></pre>
-<h2 id="c-20210220"><code>1.4c (2021/02/20)</code></h2>
+<h2 id="d-20210329"><code>1.4d (2021/03/29)</code></h2>
+<h3 id="breaking-changes">Breaking changes</h3>
+<ul>
+<li><p><code>quo()</code> and <code>rem()</code> in <code>\xintiiexpr/\xintiieval</code> renamed to <code>iquo()</code> and <code>irem()</code>.</p></li>
+<li><p>the output of <code>gcd()</code> and <code>lcm()</code> as applied to fractions is now always in lowest terms.</p></li>
+</ul>
 <h3 id="bug-fixes">Bug fixes</h3>
 <ul>
+<li><p>Ever since <code>1.3</code> the <code>quo()</code> and <code>rem()</code> functions in <code>\xintexpr</code> (not the ones in <code>\xintiiexpr</code>) were broken as their (officially deprecated) support macros had been removed! They had somewhat useless definitions anyway. They have now been officially removed from the syntax. Their siblings in <code>\xintiieval</code> were renamed to <code>iquo()</code> and <code>irem()</code>.</p></li>
+<li><p>Sadly, <code>gcd()</code> was broken in <code>\xintexpr</code> since <code>1.4</code>, if the first argument vanished. And <code>gcd()</code> was broken in <code>\xintiiexpr</code> since <code>1.3d</code> if <em>any</em> argument vanished. I did have a unit test! (which obviously was too limited …)</p>
+<p>Further, the <code>\xintGCDof</code> and <code>\xintLCMof</code> <strong>xintfrac</strong> macros were added at <code>1.4</code> but did not behave like other <strong>xintfrac</strong> macros with respect to parsing their arguments: e.g. <code>\xintGCDof{2}{03}</code> gave an unexpected non-numeric result.</p></li>
+<li><p>The <code>first()</code> and <code>last()</code> functions, if used as arguments to numerical functions such as <code>sqr()</code> inside an <code>\xintdeffunc</code> caused the defined function to be broken.</p></li>
+</ul>
+<h2 id="c-20210220"><code>1.4c (2021/02/20)</code></h2>
+<h3 id="bug-fixes-1">Bug fixes</h3>
+<ul>
 <li>Fix <code>1.4</code> regression which broke syntax <code>varname(...)</code> which supposedly is allowed and inserts a tacit multiplication.</li>
 </ul>
 <h2 id="b-20200225"><code>1.4b (2020/02/25)</code></h2>
@@ -217,13 +234,13 @@ License: LPPL 1.3c</code></pre>
 <li><p>Chaining of comparison operators (e.g. <code>x&lt;y&lt;z</code>) as in Python (but all comparisons are done even if one is found false) and l3fp.</p></li>
 <li><p>It was possible since <code>1.4</code>’s <code>\xintFracToSciE</code> to configure the separator between mantissas and exponents in the output of <code>\xinteval</code> but strangely there was no way to customize the output of <code>\xintfloateval</code>. The added <code>\xintPFloatE</code> fixes this.</p></li>
 </ul>
-<h3 id="bug-fixes-1">Bug fixes</h3>
+<h3 id="bug-fixes-2">Bug fixes</h3>
 <ul>
 <li><code>\xintieval{[D]...}</code> with a negative <code>D</code> (a feature added at <code>1.4a</code>) used erroneously a catcode 12 <code>e</code> in output, which moreover remained immuned to the <code>\xintFracToSciE</code> setting.</li>
 </ul>
 <h2 id="a-20200219"><code>1.4a (2020/02/19)</code></h2>
 <p>All changes regard the <strong>xintexpr</strong> module.</p>
-<h3 id="breaking-changes">Breaking changes</h3>
+<h3 id="breaking-changes-1">Breaking changes</h3>
 <ul>
 <li>The macros implementing customization of <code>\xintthealign</code> have modified meanings and names.</li>
 </ul>
@@ -233,13 +250,13 @@ License: LPPL 1.3c</code></pre>
 <li><p>The optional argument <code>[D]</code> to <code>\xintieval/\xintiexpr</code> can be negative, with the same meaning as the non-negative case, i.e. rounding to an integer multiple of <code>10^(-D)</code>.</p>
 <p>The same applies to the functions <code>trunc()</code> and <code>round()</code>. And to the <code>\xintTrunc</code>, <code>\xintRound</code>, <code>\xintiTrunc</code>, and <code>\xintiRound</code> macros of <strong>xintfrac</strong>.</p></li>
 </ul>
-<h3 id="bug-fixes-2">Bug fixes</h3>
+<h3 id="bug-fixes-3">Bug fixes</h3>
 <ul>
 <li><p>Usage of <code>round()</code> and <code>trunc()</code> within <code>\xintdeffunc</code> got broken at <code>1.4</code>.</p></li>
 <li><p><code>add()</code> and <code>mul()</code> were supposedly accepting the <code>omit</code>, <code>abort</code> and <code>break()</code> keywords since <code>1.4</code> but this was broken.</p></li>
 </ul>
 <h2 id="section"><code>1.4 (2020/01/31)</code></h2>
-<h3 id="breaking-changes-1">Breaking changes</h3>
+<h3 id="breaking-changes-2">Breaking changes</h3>
 <p>Please note that this list may still be incomplete. If not otherly specified all items regard the <strong>xintexpr</strong> module.</p>
 <ul>
 <li><p>The <code>\expanded</code> primitive (TeXLive 2019) is <strong>required</strong>. This does not affect the macro layer <strong>xintcore</strong>, <strong>xint</strong>, <strong>xintfrac</strong>, <strong>xinttools</strong> (yet).</p></li>
@@ -285,7 +302,7 @@ License: LPPL 1.3c</code></pre>
 <li><p>Function declarations are able to parse a much wider part of the syntax, but some severe limitations remain. Refer to the user manual for related information.</p></li>
 <li><p>We have made an effort on some error messages, and when working interactively in a shell it may even be sometimes possible to insert for example a correct variable or function name in place of the not recognized one. But don’t expect miracles when trying to intervene in the midst of a purely expandable expansion…</p></li>
 </ul>
-<h3 id="bug-fixes-3">Bug fixes</h3>
+<h3 id="bug-fixes-4">Bug fixes</h3>
 <p>Bugs? Those identified in <code>1.3f</code> were almost features. As per <code>1.4</code> the code base of <strong>xintexpr</strong> received multiple successive core refactorings and added numerous new features, and our test suite although significantly enlarged is not yet extensive enough. Please report bugs by mail.</p>
 <h3 id="todo">TODO</h3>
 <ul>
@@ -301,13 +318,13 @@ License: LPPL 1.3c</code></pre>
 <li><p><strong>xintexpr</strong>: add starred variants <code>\xintDigits*</code> and <code>\xintSetDigits*</code> which execute <code>\xintreloadxinttrig</code>.</p>
 <p>Revert 1.3e ban on usage of <code>\xinteval</code> et al. inside expressions by <code>\xintdeffunc</code>. And make them usable also inside macro definitions via <code>\xintNewExpr</code>.</p></li>
 </ul>
-<h3 id="bug-fixes-4">Bug fixes</h3>
+<h3 id="bug-fixes-5">Bug fixes</h3>
 <ul>
 <li><p><strong>xintexpr</strong>: fix bug preventing usage of <code>\xintdefefunc</code> to define a function without variables.</p>
 <p>Fix some issue with <code>\xintfloatexpr[D]..\relax</code> if used inside an expression parsed by <code>\xintdeffunc</code> et al.</p></li>
 </ul>
 <h2 id="e-20190405"><code>1.3e (2019/04/05)</code></h2>
-<h3 id="breaking-changes-2">Breaking changes</h3>
+<h3 id="breaking-changes-3">Breaking changes</h3>
 <ul>
 <li>(<em>reverted at 1.3f</em>) When defining functions, sub-expressions can only use the <code>\xint(float)expr...\relax</code> syntax. One can not use there the <code>\xint(float)eval</code> wrappers.</li>
 </ul>
@@ -321,12 +338,12 @@ License: LPPL 1.3c</code></pre>
 <li><p><strong>xintexpr</strong>: <code>\xintensuredummy</code>, <code>\xintrestorelettervar</code>.</p></li>
 <li><p>The optional argument of <code>\xintfloatexpr</code> or <code>\xintfloateval</code> (it must be at start of braced argument) can be negative; it then means to trim (and round) from the output at float precision that many least significant digits.</p></li>
 </ul>
-<h3 id="bug-fixes-5">Bug fixes</h3>
+<h3 id="bug-fixes-6">Bug fixes</h3>
 <ul>
 <li>Some bugfixes related to user functions with no variables at all; they were dysfunctional.</li>
 </ul>
 <h2 id="d-20190106"><code>1.3d (2019/01/06)</code></h2>
-<h3 id="breaking-changes-3">Breaking changes</h3>
+<h3 id="breaking-changes-4">Breaking changes</h3>
 <ul>
 <li><p><strong>xintexpr</strong>: the <code>gcd()</code> and <code>lcm()</code> functions formerly converted their arguments to integers via <code>\xintNum</code>. They now handle general input with no such modification.</p></li>
 <li><p><strong>xintexpr</strong>: former <code>\xinteval</code>, <code>\xintieval</code>, <code>\xintiieval</code>, and <code>\xintfloateval</code> renamed to <code>\xintexpro</code>, <code>\xintiexpro</code>, <code>\xintiiexpro</code>, and <code>\xintfloatexpro</code>.</p></li>
@@ -340,7 +357,7 @@ License: LPPL 1.3c</code></pre>
 <li><p><strong>xintexpr</strong>: functions <code>isone()</code> and <code>isint()</code>.</p></li>
 <li><p><strong>xintexpr</strong>: <code>\xinteval</code>, <code>\xintieval</code>, <code>\xintiieval</code>, and <code>\xintfloateval</code> as synonyms to <code>\xinttheexpr...\relax</code> etc…, but with the (comma-separated) expression as a usual braced macro argument.</p></li>
 </ul>
-<h3 id="bug-fixes-6">Bug fixes</h3>
+<h3 id="bug-fixes-7">Bug fixes</h3>
 <ul>
 <li><strong>xintcore</strong>, <strong>xintexpr</strong> : division in <code>\xintiiexpr</code> was broken for a zero dividend and a one-digit divisor (e.g. <code>0//7</code>) since <code>1.2p</code> due to a bug in <code>\xintiiDivMod</code> for such arguments. The bug was signaled (thanks to Kpym for report) and fixed shortly after <code>1.3c</code> release but I then completely forgot to upload a bugfix release to CTAN at that time, apologies for that.</li>
 </ul>
@@ -353,7 +370,7 @@ License: LPPL 1.3c</code></pre>
 <li><p><strong>xintexpr</strong>: <code>\xintdefvar</code>, <code>\xintdeffunc</code> and their variants try to set the catcode of the semi-colon which delimits their arguments; of course this will not work if that catcode is already frozen.</p></li>
 <li><p><code>\xintUniformDeviate</code> is better documented and <code>sourcexint.pdf</code> is better hyperlinked and includes indices for the macros defined by each package.</p></li>
 </ul>
-<h3 id="bug-fixes-7">Bug fixes</h3>
+<h3 id="bug-fixes-8">Bug fixes</h3>
 <ul>
 <li><strong>xintfrac</strong>: since <code>1.3</code> release, it loaded <strong>xintgcd</strong> in contradiction to what the documentation says (hence also <strong>xintexpr</strong> loaded <strong>xintgcd</strong> automatically). There is no actual dependency so the loading is removed for now.</li>
 </ul>
@@ -379,12 +396,12 @@ License: LPPL 1.3c</code></pre>
 <li><p><strong>xintfrac</strong>: <code>\xintREZ</code> is faster on inputs having one hundred digits or more.</p></li>
 <li><p>Added to the user manual mention of macros such as <code>\xintDivFloor</code>, <code>\xintMod</code>, <code>\xintModTrunc</code>, which had been left out so far.</p></li>
 </ul>
-<h3 id="bug-fixes-8">Bug fixes</h3>
+<h3 id="bug-fixes-9">Bug fixes</h3>
 <ul>
 <li><strong>xintexpr</strong>: the mechanism for adjunction to the expression parsers of user defined functions was refactored and improved at previous release <code>1.3</code>: in particular recursive definitions became possible. But an oversight made these recursive functions quite inefficient (to remain polite.) This release fixes the problem.</li>
 </ul>
 <h2 id="section-1"><code>1.3 (2018/03/01)</code></h2>
-<h3 id="breaking-changes-4">Breaking changes</h3>
+<h3 id="breaking-changes-5">Breaking changes</h3>
 <ul>
 <li><p><strong>xintcore</strong>, <strong>xint</strong>, <strong>xintfrac</strong>: all macros deprecated at <code>1.2o</code> got removed.</p></li>
 <li><p><strong>xintfrac</strong>: addition and subtraction of <code>a/b</code> and <code>c/d</code> now use the l.c.m. of the denominators. Similarly the macro supporting the modulo operator <code>/:</code> uses a l.c.m. for the denominator of the result.</p></li>
@@ -402,12 +419,12 @@ License: LPPL 1.3c</code></pre>
 <ul>
 <li><strong>xintexpr</strong>: tacit multiplication extended to cases such as <code>3!4!5!</code> or <code>(1+2)3</code>.</li>
 </ul>
-<h3 id="bug-fixes-9">Bug fixes</h3>
+<h3 id="bug-fixes-10">Bug fixes</h3>
 <ul>
 <li><strong>xintcore</strong>: sadly, refactoring at <code>1.2l</code> of subtraction left an extra character in an inner macro causing breakage in some rare circumstances. This should not have escaped our test suite!</li>
 </ul>
 <h2 id="p-20171205"><code>1.2p (2017/12/05)</code></h2>
-<h3 id="breaking-changes-5">Breaking changes</h3>
+<h3 id="breaking-changes-6">Breaking changes</h3>
 <ul>
 <li><p><strong>xintgcd</strong>: <code>\xintBezout{a}{b}</code>’s output consists of <code>{u}{v}{d}</code> with <code>u*a+v*b==d</code>, with <code>d</code> the GCD. Formerly it was <code>{a}{b}{u}{v}{d}</code>, and with <code>u*a-v*b==d</code>.</p></li>
 <li><p><strong>xintgcd</strong>: <code>\xintBezout{0}{0}</code> expands to <code>{0}{0}{0}</code>. Formerly (since <code>1.2l</code>) it raised <code>InvalidOperation</code>.</p></li>
@@ -421,7 +438,7 @@ License: LPPL 1.3c</code></pre>
 <li><p><strong>xintexpr</strong>: <code>\xintdefvar</code>’s syntax is extended to allow simultaneous assignments. Examples: <code>\xintdefvar x1, x2, x3 := 1, 3**10, 3**20;</code> or <code>\xintdefiivar A, B := B, A 'mod' B;</code> for already defined variables <code>A</code> and <code>B</code>.</p></li>
 <li><p><strong>xintexpr</strong>: added <code>divmod()</code> to the built-in functions. It is associated with floored division, like the Python language <code>divmod()</code>. Related support macros added to <strong>xintcore</strong>, and <strong>xintfrac</strong>.</p></li>
 </ul>
-<h3 id="bug-fixes-10">Bug fixes</h3>
+<h3 id="bug-fixes-11">Bug fixes</h3>
 <ul>
 <li><p><strong>xintgcd</strong>: <code>\xintBezout{6}{3}</code> (for example) expanded to <code>{6}{3}{-0}{-1}{3}</code>, but the <code>-0</code> should have been <code>0</code>.</p></li>
 <li><p><strong>xintgcd</strong>: it still used macro <code>\xintiAbs</code> although the latter had been deprecated from <strong>xintcore</strong>.</p></li>
@@ -429,7 +446,7 @@ License: LPPL 1.3c</code></pre>
 <li><p>various documentation fixes; in particular, the partial dependency of <strong>xintcfrac</strong> on <strong>xinttools</strong> had not been mentioned.</p></li>
 </ul>
 <h2 id="o-20170829"><code>1.2o (2017/08/29)</code></h2>
-<h3 id="breaking-changes-6">Breaking changes</h3>
+<h3 id="breaking-changes-7">Breaking changes</h3>
 <ul>
 <li><strong>xint</strong>: <code>\xintAND</code>, <code>\xintOR</code>, … and similar Boolean logic macros do not apply anymore <code>\xintNum</code> (or <code>\xintRaw</code> if <strong>xintfrac</strong> is loaded), to their arguments (often, from internal usage of <code>\xintSgn</code>), but only f-expand them (using e.g. <code>\xintiiSgn</code>). This is kept un-modified even if loading <strong>xintfrac</strong>.</li>
 </ul>
@@ -445,7 +462,7 @@ License: LPPL 1.3c</code></pre>
 <li><p><strong>xint</strong>: <code>\xintNot</code> was renamed to <code>\xintNOT</code>, former denomination is deprecated. See also item about Boolean logic macros in the <em>Incompatible Changes</em> section.</p></li>
 </ul>
 <h2 id="n-20170806"><code>1.2n (2017/08/06)</code></h2>
-<h3 id="breaking-changes-7">Breaking changes</h3>
+<h3 id="breaking-changes-8">Breaking changes</h3>
 <ul>
 <li><strong>xintbinhex</strong> does not load package <strong>xintcore</strong> anymore, but only <strong>xintkernel</strong>.</li>
 </ul>
@@ -455,7 +472,7 @@ License: LPPL 1.3c</code></pre>
 <li><p>Macros of <strong>xintbinhex</strong> have been improved for speed and increased maximal sizes of allowable inputs.</p></li>
 </ul>
 <h2 id="m-20170731"><code>1.2m (2017/07/31)</code></h2>
-<h3 id="breaking-changes-8">Breaking changes</h3>
+<h3 id="breaking-changes-9">Breaking changes</h3>
 <ul>
 <li><p><strong>xintbinhex</strong>: the length of the input is now limited. The maximum size depends on the macro and ranges from about <code>4000</code> to about <code>19900</code> digits.</p></li>
 <li><p><strong>xintbinhex</strong>: <code>\xintCHexToBin</code> is now the variant of <code>\xintHexToBin</code> which does not remove leading binary zeroes: <code>N</code> hex-digits give on output exactly <code>4N</code> binary digits.</p></li>
@@ -464,7 +481,7 @@ License: LPPL 1.3c</code></pre>
 <ul>
 <li><strong>xintbinhex</strong>: all macros have been rewritten using techniques from the 1.2 release (they had remained unmodified since <code>1.08</code> of <code>2013/06/07</code>.) The new macros are faster but limited to a few thousand digits. The <code>1.08</code> routines could handle tens of thousands of digits, but not in a reasonable time.</li>
 </ul>
-<h3 id="bug-fixes-11">Bug fixes</h3>
+<h3 id="bug-fixes-12">Bug fixes</h3>
 <ul>
 <li><p>user manual: the <code>Changes</code> section wrongly stated at <code>1.2l</code> that the macros of <strong>xintbinhex</strong> had been made robust against non terminated input such as <code>\number\mathcode`\-</code>. Unfortunately the author fell into the trap of believing his own documentation and he forgot to actually implement the change. Now done.</p></li>
 <li><p>user manual: the PDF bookmarks were messed up.</p></li>
@@ -485,14 +502,14 @@ License: LPPL 1.3c</code></pre>
 <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-12">Bug fixes</h3>
+<h3 id="bug-fixes-13">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="breaking-changes-9">Breaking changes</h3>
+<h3 id="breaking-changes-10">Breaking changes</h3>
 <ul>
 <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>
@@ -504,7 +521,7 @@ License: LPPL 1.3c</code></pre>
 <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-13">Bug fixes</h3>
+<h3 id="bug-fixes-14">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>
@@ -520,12 +537,12 @@ License: LPPL 1.3c</code></pre>
 </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-14">Bug fixes</h3>
+<h3 id="bug-fixes-15">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>
 <h2 id="i-20161213"><code>1.2i (2016/12/13)</code></h2>
-<h3 id="breaking-changes-10">Breaking changes</h3>
+<h3 id="breaking-changes-11">Breaking changes</h3>
 <ul>
 <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>
@@ -552,7 +569,7 @@ License: LPPL 1.3c</code></pre>
 <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-15">Bug fixes</h3>
+<h3 id="bug-fixes-16">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>
@@ -562,7 +579,7 @@ License: LPPL 1.3c</code></pre>
 <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-16">Bug fixes</h3>
+<h3 id="bug-fixes-17">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&lt;0</code> or <code>x&lt;y</code>. This was unfortunate, and it now simply evaluates to zero in such cases.</p></li>
@@ -570,7 +587,7 @@ License: LPPL 1.3c</code></pre>
 <li><p>the <code>add</code> and <code>mul</code> from <strong>xintexpr</strong>, which work with dummy variables since <code>1.1</code>, raised an error since <code>1.2c 2015/11/16</code> when the dummy variable was given an empty range (or list) of values, rather than producing respectively <code>0</code> and <code>1</code> as formerly.</p></li>
 </ul>
 <h2 id="g-20160319"><code>1.2g (2016/03/19)</code></h2>
-<h3 id="breaking-changes-11">Breaking changes</h3>
+<h3 id="breaking-changes-12">Breaking changes</h3>
 <ul>
 <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>
@@ -584,7 +601,7 @@ License: LPPL 1.3c</code></pre>
 <li><p>the syntax of expressions is described in a devoted chapter of the documentation; an example shows how to implement (expandably) the Brent-Salamin algorithm for computation of Pi using <code>iter</code> in a float expression.</p></li>
 </ul>
 <h2 id="f-20160312"><code>1.2f (2016/03/12)</code></h2>
-<h3 id="breaking-changes-12">Breaking changes</h3>
+<h3 id="breaking-changes-13">Breaking changes</h3>
 <ul>
 <li>no more <code>\xintFac</code> macro but <code>\xintiFac/\xintiiFac/\xintFloatFac</code>.</li>
 </ul>
@@ -602,7 +619,7 @@ License: LPPL 1.3c</code></pre>
 <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-17">Bug fixes</h3>
+<h3 id="bug-fixes-18">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>
@@ -616,7 +633,7 @@ License: LPPL 1.3c</code></pre>
 <li><p>a space in <code>\xintdeffunc f(x)&lt;space&gt;:= 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-18">Bug fixes</h3>
+<h3 id="bug-fixes-19">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>
@@ -629,7 +646,7 @@ License: LPPL 1.3c</code></pre>
 <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-19">Bug fixes</h3>
+<h3 id="bug-fixes-20">Bug fixes</h3>
 <ul>
 <li>in <strong>xintcore</strong>: release <code>1.2c</code> had inadvertently broken the <code>\xintiiDivRound</code> macro.</li>
 </ul>
@@ -639,12 +656,12 @@ License: LPPL 1.3c</code></pre>
 <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-20">Bug fixes</h3>
+<h3 id="bug-fixes-21">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-21">Bug fixes</h3>
+<h3 id="bug-fixes-22">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>
@@ -655,7 +672,7 @@ License: LPPL 1.3c</code></pre>
 <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`&amp;&amp;@</code> (<code>^</code> being used as letter, had to find another character usable with catcode 7).</p></li>
 </ul>
-<h3 id="bug-fixes-22">Bug fixes</h3>
+<h3 id="bug-fixes-23">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>
@@ -698,7 +715,7 @@ License: LPPL 1.3c</code></pre>
 <li><p>various typographical fixes throughout the documentation, and a bit of clean up of the code comments. Improved <code>\Factors</code> example of nested <code>subs</code>, <code>rseq</code>, <code>iter</code> in <code>\xintiiexpr</code>.</p></li>
 </ul>
 <h2 id="section-3"><code>1.1 (2014/10/28)</code></h2>
-<h3 id="breaking-changes-13">Breaking changes</h3>
+<h3 id="breaking-changes-14">Breaking changes</h3>
 <ul>
 <li><p>in <code>\xintiiexpr</code>, <code>/</code> does <em>rounded</em> division, rather than the Euclidean division (for positive arguments, this is truncated division). The <code>//</code> operator does truncated division,</p></li>
 <li><p>the <code>:</code> operator for three-way branching is gone, replaced with <code>??</code>,</p></li>
@@ -756,7 +773,7 @@ License: LPPL 1.3c</code></pre>
 <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-23">Bug fixes</h3>
+<h3 id="bug-fixes-24">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>
diff --git a/Master/texmf-dist/doc/generic/xint/README.md b/Master/texmf-dist/doc/generic/xint/README.md
index bb01bbb277a..a9dcafa44a0 100644
--- a/Master/texmf-dist/doc/generic/xint/README.md
+++ b/Master/texmf-dist/doc/generic/xint/README.md
@@ -1,8 +1,8 @@
 % README
-% xint 1.4c
-% 2021/02/20
+% xint 1.4d
+% 2021/03/29
 
-    Source:  xint.dtx 1.4c 2021/02/20 (doc 2021/02/20)
+    Source:  xint.dtx 1.4d 2021/03/29 (doc 2021/03/29)
     Author:  Jean-Francois Burnol
     Info:    Expandable operations on big integers, decimals, fractions
     License: LPPL 1.3c
@@ -101,7 +101,7 @@ is a functionality of all major TeX engines since TeXLive 2019.
 License
 =======
 
-Copyright (C) 2013-2020 by Jean-Francois Burnol
+Copyright (C) 2013-2021 by Jean-Francois Burnol
 
 This Work may be distributed and/or modified under the
 conditions of the LaTeX Project Public License version 1.3c.
diff --git a/Master/texmf-dist/doc/generic/xint/sourcexint.pdf b/Master/texmf-dist/doc/generic/xint/sourcexint.pdf
index 6c9a354b0bf..0e99479d7c9 100644
--- a/Master/texmf-dist/doc/generic/xint/sourcexint.pdf
+++ b/Master/texmf-dist/doc/generic/xint/sourcexint.pdf
diff --git a/Master/texmf-dist/doc/generic/xint/xint.pdf b/Master/texmf-dist/doc/generic/xint/xint.pdf
index 5be576e57e5..35ac85b1b04 100644
--- a/Master/texmf-dist/doc/generic/xint/xint.pdf
+++ b/Master/texmf-dist/doc/generic/xint/xint.pdf
diff --git a/Master/texmf-dist/source/generic/xint/xint.dtx b/Master/texmf-dist/source/generic/xint/xint.dtx
index 8a6a882ba83..6b5ff7588c8 100644
--- a/Master/texmf-dist/source/generic/xint/xint.dtx
+++ b/Master/texmf-dist/source/generic/xint/xint.dtx
@@ -3,28 +3,28 @@
 % Extract all files via "etex xint.dtx" and do "make help"
 % or follow instructions from extracted README.md.
 %<*dtx>
-\def\xintdtxtimestamp {Time-stamp: <20-02-2021 at 20:47:06 CET>}
+\def\xintdtxtimestamp {Time-stamp: <29-03-2021 at 11:06:25 CEST>}
 %</dtx>
 %<*drv>
 %% ---------------------------------------------------------------
-\def\xintdocdate {2021/02/20}
-\def\xintbndldate{2021/02/20}
-\def\xintbndlversion {1.4c}
+\def\xintdocdate {2021/03/29}
+\def\xintbndldate{2021/03/29}
+\def\xintbndlversion {1.4d}
 %</drv>
 %<readme>% README
 %<changes>% CHANGE LOG
-%<readme|changes>% xint 1.4c
-%<readme|changes>% 2021/02/20
+%<readme|changes>% xint 1.4d
+%<readme|changes>% 2021/03/29
 %<readme|changes>
-%<readme|changes>    Source:  xint.dtx 1.4c 2021/02/20 (doc 2021/02/20)
+%<readme|changes>    Source:  xint.dtx 1.4d 2021/03/29 (doc 2021/03/29)
 %<readme|changes>    Author:  Jean-Francois Burnol
 %<readme|changes>    Info:    Expandable operations on big integers, decimals, fractions
 %<readme|changes>    License: LPPL 1.3c
 %<readme|changes>
 %<*!readme&!changes&!dohtmlsh&!makefile>
 %% ---------------------------------------------------------------
-%% The xint bundle 1.4c 2021/02/20
-%% Copyright (C) 2013-2020 by Jean-Francois Burnol
+%% The xint bundle 1.4d 2021/03/29
+%% Copyright (C) 2013-2021 by Jean-Francois Burnol
 %<xintkernel>%% xintkernel: Paraphernalia for the xint packages
 %<xinttools>%% xinttools: Expandable and non-expandable utilities
 %<xintcore>%% xintcore: Expandable arithmetic on big integers
@@ -137,7 +137,7 @@ is a functionality of all major TeX engines since TeXLive 2019.
 License
 =======
 
-Copyright (C) 2013-2020 by Jean-Francois Burnol
+Copyright (C) 2013-2021 by Jean-Francois Burnol
 
 This Work may be distributed and/or modified under the
 conditions of the LaTeX Project Public License version 1.3c.
@@ -161,6 +161,40 @@ See `xint.pdf` for contact information.
 %</readme>--------------------------------------------------------
 %<*changes>-------------------------------------------------------
 
+`1.4d (2021/03/29)`
+----
+
+### Breaking changes
+
+ - `quo()` and `rem()` in `\xintiiexpr/\xintiieval` renamed to
+   `iquo()` and `irem()`.
+
+ - the output of `gcd()` and `lcm()` as applied to fractions is now
+   always in lowest terms.
+
+### Bug fixes
+
+ - Ever since `1.3` the `quo()` and `rem()` functions in `\xintexpr`
+   (not the ones in `\xintiiexpr`) were broken as their (officially
+   deprecated) support macros had been removed!  They had somewhat
+   useless definitions anyway.  They have now been officially removed
+   from the syntax.  Their siblings in `\xintiieval` were renamed to
+   `iquo()` and `irem()`.
+
+ - Sadly, `gcd()` was broken in `\xintexpr` since `1.4`, if the first
+   argument vanished.  And `gcd()` was broken in `\xintiiexpr` since
+   `1.3d` if *any* argument vanished.  I did have a unit test! (which
+   obviously was too limited ...)
+
+   Further, the `\xintGCDof` and `\xintLCMof` **xintfrac** macros were
+   added at `1.4` but did not behave like other **xintfrac** macros with
+   respect to parsing their arguments: e.g. `\xintGCDof{2}{03}` gave an
+   unexpected non-numeric result.
+
+ - The `first()` and `last()` functions, if used as arguments to
+   numerical functions such as `sqr()` inside an `\xintdeffunc`
+   caused the defined function to be broken.
+
 `1.4c (2021/02/20)`
 ----
 
@@ -3577,6 +3611,8 @@ pdfpagemode=UseNone,%
 % ===============
 % \ttzfamily done at begin document
 
+\newcommand\ctanpackage[1]{\href{https://ctan.org/pkg/#1}{#1}}
+
 \begin{document}\thispagestyle{empty}
 \pdfbookmark[1]{Title page}{TOP}
 \def\partname{Part}
@@ -3805,16 +3841,16 @@ pdfpagemode=UseNone,%
     \node [right of=kernel] (B) {};
     \node [block, below right of=B] (core) {\xintcorename};
     \node [block, below left of=A]  (tools) {\xinttoolsname};
-    \node [block, right of=core, xshift=1cm]  (bnumexpr) {\href{https://ctan.org/pkg/bnumexpr}{bnumexpr}};
+    \node [block, right of=core, xshift=1cm]  (bnumexpr) {\ctanpackage{bnumexpr}};
     \node [block, below of=core] (xint) {\xintname};
     \node [block, left of=xint, xshift=-1cm] (gcd) {\xintgcdname};
     \node [block, left of=gcd] (binhex) {\xintbinhexname};
     \node [block, below of=xint] (frac) {\xintfracname};
     \node [block, below of=frac, yshift=-.5cm] (expr) {\xintexprname};
-    \node [block, below right of=expr, yshift=-.5cm, xshift=2.25cm] (polexpr) {\href{https://ctan.org/pkg/polexpr}{polexpr}};
+    \node [block, below right of=expr, yshift=-.5cm, xshift=2.25cm] (polexpr) {\ctanpackage{polexpr}};
     \node [block, below of=expr, yshift=-.5cm] (trig) {\xinttrigname};
     \node [block, left of=trig] (log) {\xintlogname};
-    \node [block, left of=log, xshift=-1cm] (poormanlog) {\href{https://ctan.org/pkg/poormanlog}{poormanlog}};
+    \node [block, left of=log, xshift=-1cm] (poormanlog) {\ctanpackage{poormanlog}};
     \node [block, below right of=frac, xshift=1cm] (series) {\xintseriesname};
     \node [block, right of=series] (cfrac) {\xintcfracname};
     % Draw edges
@@ -3857,17 +3893,17 @@ pdfpagemode=UseNone,%
     functionalities of the lower module it is thus necessary to use 
     a suitable |\usepackage| (\LaTeX) or |\input| (Plain \TeX.)\par
 
-    \href{https://ctan.org/pkg/bnumexpr}{bnumexpr} is a
+    \ctanpackage{bnumexpr} is a
     separate (\LaTeX{} only) package by the author which uses (by default)
     \xintcorename as its mathematical engine.
 
-    \href{https://ctan.org/pkg/polexpr}{polexpr} is a
+    \ctanpackage{polexpr} is a
     separate (\LaTeX{} only) package by the author which requires \xintexprname.
 
     \xinttrigname and \xintlogname are loaded automatically by \xintexprname; they
     will refuse to be loaded directly (but see \csbxint{reloadxinttrig}).
 
-    \href{https://ctan.org/pkg/poormanlog}{poormanlog} is a \TeX{} and
+    \ctanpackage{poormanlog} is a \TeX{} and
     \LaTeX{} package by the author which is loaded automatically by \xintlogname.
 \par
 \end{addmargin}
@@ -3949,6 +3985,49 @@ quality of the document).  Reports welcome.%
 \footnote{Thanks to Jürgen Gilg for keeping the author motivated and
   helping proof-read the documentation.}
 
+\subsection{Known bugs/features at \texttt{1.4d}}
+
+\begin{description}
+\item[if(100>0,(100,125),(100,128)) breaks my code:]
+%
+  This is a feature. This is a syntax error, as the comma serves to contatenate
+  "oples" (see \autoref{oples}), so it is parsed to behave as 
+\begin{everbatim}
+    if(100>0,100,125,100,128) 
+\end{everbatim}
+  which is an error as \func{if} requires exactly three arguments, not
+  five. Use:
+\begin{everbatim}
+    if(100>0,[100,125],[100,128]) 
+\end{everbatim}
+  which will expand to the "tuple" |[100,125]|.
+\item[{\detokenize{\xintdeffunc foo(x):= gcd((x>0)?{[x,125]}{[x,128]});}
+    creates a broken function:}]
+%
+  Bug. Normally \func{gcd} (and other
+  multi-arguments functions) work both with open lists of arguments or
+  bracketed lists ("nutples") and the above syntax would work perfectly fine
+  in numerical context.  But the presence of the \oper{?} breaks in
+  \csbxint{deffunc} context the flexibility of \func{gcd}. 
+
+   Currently working alternatives:
+\begin{everbatim}
+\xintdeffunc foo(x) := gcd(if(x>0, [x,125], [x,128]));
+\xintdeffunc foo(x) := if(x>0, gcd(x,125), gcd(x,128));
+\xintdeffunc foo(x) := if(x>0, gcd([x,125]), gcd([x,128]));
+\xintdeffunc foo(x) := gcd((x>0)?{x,125}{x,128});
+\xintdeffunc foo(x) := (x>0)?{gcd(x,125)}{gcd(x,128)};
+\xintdeffunc foo(x) := (x>0)?{gcd([x,125])}{gcd([x,128])};
+\end{everbatim}
+   The same problem will arise with an \oper{??} nested inside \func{gcd} or
+   similar functions, in an \csbxint{deffunc}.
+\end{description}
+
+If the list stops here, it is probably only because I have not tested enough
+yet.  But it is already mentioned in the \csbxint{deffunc} documentation that
+it can not parse currently the entirety of the available purely numerical
+syntax, some documented limitations apply.
+
 \subsection{Features added since the \texttt{1.4} release}
 
 For bugfixes and possibly more details check |CHANGES.html|:
@@ -4095,7 +4174,8 @@ The rendering here uses extra decoration.
 
 \localtableofcontents
 
-\subsection{Oples and nut-ples: terminology for the \text{1.4} \xintname generation}
+
+\subsection{Oples and nutples: terminology for the \text{1.4} \xintname generation}\label{oples}
 
 \emph{Skip this on first reading, else you will never start using the
   package.} \fbox{SKIP THIS!} (understood?)
@@ -4145,7 +4225,7 @@ input syntax, Python |lists|), or \emph{packing} (as a reverse to Python's
 unpacking of sequence type objects).
 
 \item
-A braced \emph{ople} is called a \emph{nut-ple}. Among them $\{nil\}$ is a bit
+A braced \emph{ople} is called a \emph{nutple}. Among them $\{nil\}$ is a bit
 special. It is called the \emph{not-ple}. It is not |nil|!
 \end{itemize}
 
@@ -4172,7 +4252,7 @@ Each \emph{ople} has a length which is its cardinality. The |oples| of length
 1 are called \emph{one-ples}. There are two types of \emph{one-ples}:
 \begin{itemize}
 \item \emph{numbers},
-\item packed \emph{oples}: the \emph{nut-ples}.
+\item packed \emph{oples}: the \emph{nutples}.
 \end{itemize}
 
 As said before the \emph{not-ple} |{{}}| is special. It can be input as
@@ -4186,7 +4266,7 @@ can associate with any \emph{ople} a tree. The root is the ople. In the case
 of the |nil|, there is nothing else than the root, which we then consider also
 a \emph{leaf}. Else the children at top level are the successive items of the
 ople. Among the items some are \emph{atoms} giving \emph{leaves} of the tree,
-others are \emph{nut-ples} which in turn have children. In the special case of
+others are \emph{nutples} which in turn have children. In the special case of
 the \emph{not-ple} we consider it has a child, which is the empty set and this
 why we consider the empty set |nil| a \emph{leaf}. We then proceed
 recursively. We thus obtain from the root \emph{ople} a tree whose vertices
@@ -4223,21 +4303,21 @@ indicate the shape than display it.
 subset. This applies also if it is a \emph{number}. Then it can be sliced only
 to itself or to the empty set (indeed it has only one element, which is an
 atom). Similarly the \emph{not-ple} can only be sliced to give itself or the
-empty set. And more generally a \emph{nut-ple} is a singleton so also can only
+empty set. And more generally a \emph{nutple} is a singleton so also can only
 be set-sliced to either the empty set or itself.
 
 \xintexprname extends «Python-like» slicing to act on \emph{oples}:
 \begin{itemize}[nosep]
-\item if they are not \emph{nut-ples} set-theoretical slicing applies,
-\item if they are \emph{nut-ples} (only case having a one-to-one
-  correspondance in Python) then the slicing happens \emph{within brackets}:
-  i.e.  the \emph{nut-ple} is unpacked then the set-theoretical slicing is
-  applied, then the result is \emph{repacked} to produce a new \emph{nut-ple}.
+\item if they are not \emph{nutples} set-theoretical slicing applies,
+\item if they are \emph{nutples} (only case having a one-to-one
+  correspondence in Python) then the slicing happens \emph{within brackets}:
+  i.e.  the \emph{nutple} is unpacked then the set-theoretical slicing is
+  applied, then the result is \emph{repacked} to produce a new \emph{nutple}.
 \end{itemize}
 With these conventions the \emph{not-ple} for example is invariant under
 slicing: unpacking it gives the empty set, which has only the empty set as
 subset and repacking gives back the \emph{not-ple}. Slicing a general
-\emph{nut-ple} returns a \emph{nut-ple} but now of course in general distinct
+\emph{nutple} returns a \emph{nutple} but now of course in general distinct
 from the first one.
 
 The syntax for Python slicing is to postfix a variable or a parenthesized ople
@@ -4252,16 +4332,16 @@ a set).
 
 \xintexprname extends «Python-like» indexing to act on \emph{oples}:
 \begin{itemize}[nosep]
-\item if they are not \emph{nut-ples} set-theoretical item indexing applies,
-\item if they are \emph{nut-ples} (only case having a one-to-one
-  correspondance in Python) then the meaning becomes \emph{extracting}: i.e.
-  the \emph{nut-ple} is unpacked then the set-theoretical indexing is applied,
+\item if they are not \emph{nutples} set-theoretical item indexing applies,
+\item if they are \emph{nutples} (only case having a one-to-one
+  correspondence in Python) then the meaning becomes \emph{extracting}: i.e.
+  the \emph{nutple} is unpacked then the set-theoretical indexing is applied,
   but the result is \emph{not repacked}.
 \end{itemize}
 For example when applied to the \emph{not-ple} we always obtain
 the |nil|. Whereas as we saw slicing the \emph{not-ple} always gives back the
 \emph{not-ple}. Indexing is denoted in the syntax by postfixing by |[N]|. Thus
-for \emph{nut-ples} (which are analogous to Python objects), there is genuine
+for \emph{nutples} (which are analogous to Python objects), there is genuine
 difference between the |[N]| extractor and the |[N:N+1]| slicer. But for
 \emph{oples} which are either |nil|, a \emph{number}, or of length at least 2,
 there is no difference.
@@ -4269,8 +4349,8 @@ there is no difference.
 
 Nested slicing is a concept from NumPy, which is extended by \xintexprname to
 trees of varying depths. We have a chain of slicers and extractors. I will
-describe only the case of slicers and letting them act on a |nut-ple|. The
-first slicer gives back a new |nut-ple|. The second slicer will be applied to
+describe only the case of slicers and letting them act on a |nutple|. The
+first slicer gives back a new |nutple|. The second slicer will be applied to
 each of one of its remaining items. However some of them may be \emph{atoms}
 or the empty set. In the NumPy context all leaves are at the same depth thus
 this can happen only when we have reached beyond the last dimension
@@ -4278,19 +4358,19 @@ this can happen only when we have reached beyond the last dimension
 does not generate an error. But any attempt to slice an \emph{atom} or the
 empty set (as element of its container) removes it. Recall we call them
 \emph{leaves}. We can not slice leaves. We can only slice non-leaf items: such
-items are necessarily |nut-ples|. The procedure then applies recursively.
+items are necessarily |nutples|. The procedure then applies recursively.
 
 If we handle an extractor rather than a slicer, the procedure is similar: we
 can not extract out of an \emph{atom} or the empty set. They are thus
-removed. Else we have a |nut-ple|. It is thus unpacked and replaced by the
+removed. Else we have a |nutple|. It is thus unpacked and replaced by the
 selected item. This item may be an atom or the empty set and any further
-slicer or extractor will remove them, or it is a |nut-ple| and the procedure
+slicer or extractor will remove them, or it is a |nutple| and the procedure
 applies with the next slicer/extractor.
 
 \xintexprname allows to apply such a |[a:b,c:d,N,e:f,...]| chain of
-slicing/extracting also to an \emph{ople}, which is not a \emph{nut-ple}. We
+slicing/extracting also to an \emph{ople}, which is not a \emph{nutple}. We
 simply apply the first step as has been described previously and successive
-steps will only get applied to either \emph{nut-ples} or \emph{leaves}, the
+steps will only get applied to either \emph{nutples} or \emph{leaves}, the
 latter getting silently removed by any attempted operation.
 
 One last thing. In the syntax of \xintexprname, variables as well as functions
@@ -4298,11 +4378,11 @@ have a name and a value. The value is an |ople|. We can always use a variable
 whose value is an |ople|
 in a function call, it will occupy the place of as many arguments as its
 length indicates. But in a function declaration, the variables must stand for
-|one-ples|, i.e. either |numbers| or |nut-ples|.
+|one-ples|, i.e. either |numbers| or |nutples|.
 
 The |*| unpacks a
-|nut-ple|. The last positional argument in a function declaration can have a
-special form |*|\meta{name}. This means that \meta{name} is a |nut-ple| which
+|nutple|. The last positional argument in a function declaration can have a
+special form |*|\meta{name}. This means that \meta{name} is a |nutple| which
 receives as items all arguments in the function call beyond the first ones
 corresponding to the function declaration.
 
@@ -4934,29 +5014,43 @@ discussion at each level.
 \precdesc{14}
 \begin{description}
 \operdesc{\lowast} multiplication
-\operdesc{/} division: exact in \csbxint{eval}, correctly rounded in
-  \csbxint{floateval} (numerator and denominator are rounded before the
-  division is done), and rounded to an integer (like |\numexpr| does:
-  half-integers are rounded towards infinity of same sign) in
-  \csbxint{iieval}.  The division is left-associative:
+
+\operdesc{/} division:
+  \begin{itemize}
+  \item in \csbxint{eval}: exact division in the field of rational numbers (not
+    automatically reduced to lowest terms),
+  \item in \csbxint{floateval}: correct rounding of the exact division; the two
+    operands are, if necessary, float-rounded before the fraction is
+    evaluated and rounded (to obtain the correcty rounded |A/B|
+    without prior rounding of |A| and |B| see \func{qfloat}),
+  \item in \csbxint{iieval}: for compatibility with the legacy behaviour of
+    |/| in |\numexpr|, it rounds the exact fraction \emph{with half-integers
+      going towards the infinity of the same sign}.
+   \end{itemize}
+   The division is left-associative. Example:
 \begin{everbatim*}
 \xintexpr reduce(100/50/2)\relax
 \end{everbatim*}
 
-\operdesc{//} floored division
+\operdesc{//} floored division (and thus produces an integer, see
+   \func{divmod} for details)
 
-\operdesc{/:} the associated modulo
+\operdesc{/:} the associated modulo (see \func{divmod} and \func{mod})
 
    Left-associativity applies generally to operators of same precedence.
 \begin{everbatim*}
 \xintexpr 100000/:13, 100000 'mod' 13\relax\newline
 \xintexpr 100000/:13/13\relax
 \end{everbatim*}
+ 
+   Nothing special needs to be done in contexts such as \LaTeX3
+   |\ExplSyntaxOn| where |:| is of catcode letter, but if |:| is an active
+   character (for example in \LaTeX\ with babel+french) with an active |:|,
+   one needs to use input such as |/\string :| (or use \func{mod}).
 
-\operdesc{'mod'} is same as \oper{/:}.
-
-Note: The enclosing (right) ticks are
-mandatory part of all such infix operator «words».
+   \operdesc{'mod'} is same as \oper{/:}. \fbox{Attention:} with
+   \ctanpackage{polexpr} loaded, which allows |'| in variable and function
+   names, |'mod'| syntax is broken. Use the alternatives.
 
 \end{description}
 
@@ -5013,8 +5107,10 @@ precedence, use parentheses for disambiguation.
   \operdesc{\Ampersand\Ampersand} logical conjunction. Evaluates to \dtt{1} if
   both sides are non-zero, to \dtt{0} if not.
 
-  \operdesc{'and'} idem. The (right) ticks are mandatory. See also the
-  \func{all} multi-arguments function.
+  \operdesc{'and'} same as \verb+&&+.  See
+  also the \func{all} multi-arguments function. \fbox{Attention:} with
+  \ctanpackage{polexpr} loaded, which allows |'| in variable and function
+  names, |'and'| syntax is broken. Use the alternatives.
 \end{description}
 
 \precdesc{6}
@@ -5022,10 +5118,16 @@ precedence, use parentheses for disambiguation.
   \operdesc{\string|\string|} logical (inclusive) disjunction. Evaluates to
   \dtt{1} if one or both sides are non-zero, to \dtt{0} if not.
 
-  \operdesc{'or'} idem. See also the \func{any} multi-arguments function.
+  \operdesc{'or'} same as as \verb+||+. See also the \func{any} multi-arguments
+  function.  \fbox{Attention:} with \ctanpackage{polexpr} loaded, which allows
+  |'| in variable and function names, |'or'| syntax is broken. Use the
+  alternatives.
 
-  \operdesc{'xor'} logical (exclusive) disjunction. See also the \func{xor}
-  multi-arguments function.
+  \operdesc{'xor'} logical (exclusive) disjunction. \fbox{Attention:} with
+  \ctanpackage{polexpr} loaded, which allows |'| in variable and function
+  names, |'xor'| syntax is broken. Use the multi-arguments \func{xor} function
+  (or suggest to the author some credible alternative ascii notation to use as
+  infix operator).
 
   \operdesc{\strut..}
   \operdesc{..[}
@@ -5125,13 +5227,13 @@ binomial, bool,
 ceil, cos, cosd, cot, cotd, cotg, csc, cscd,
 divmod, even, exp,
 factorial, first, flat, float, float\string_, floor, frac, gcd,
-if, ifint, ifone, ifsgn, ilog10, isint, isone, iter, iterr, inv,
+if, ifint, ifone, ifsgn, ilog10, iquo, irem, isint, isone, iter, iterr, inv,
 last, lcm, len, log, log10, max, min, mod, mul,
 ndmap, ndseq, ndfillraw,
 not, num, nuple, odd,
 pArg, pArgd, pfactorial, pow, pow10, preduce,
-qfloat, qfrac, qint, qrand, qraw, quo,
-random, randrange, rbit, reduce, rem, reversed, round, rrseq, rseq,
+qfloat, qfrac, qint, qrand, qraw,
+random, randrange, rbit, reduce, reversed, round, rrseq, rseq,
 sec, secd, seq, sgn, sin, sinc, sind, sqr, sqrt, sqrtr,
 subs, subsm, subsn,
 tan, tand, tg, togl, trunc, unpack,
@@ -5474,7 +5576,7 @@ $\xintthefloatexpr subs(((x-1)/x, x/x, (x+1)/x), x=2**30)\relax
     allow arbitrarily complicated combinations of various |bool(name)|.
 \funcdesc[name]{togl} 
     returns $1$
-    if the \LaTeX{} package \href{https://ctan.org/pkg/etoolbox}{etoolbox}%
+    if the \LaTeX{} package \ctanpackage{etoolbox}%
     %
     %
 %
@@ -5483,7 +5585,7 @@ $\xintthefloatexpr subs(((x-1)/x, x/x, (x+1)/x), x=2**30)\relax
     has been used to define a toggle named |name|, and this toggle is
     currently set to |true|. Using |togl| in an |\xintexpr..\relax|
     without having loaded
-    \href{https://ctan.org/pkg/etoolbox}{etoolbox} will result in an
+    \ctanpackage{etoolbox} will result in an
     error from |\iftoggle| being a non-defined macro. If |etoolbox| is
     loaded but |togl| is used on a name not recognized by |etoolbox|
     the error message will be of the type ``ERROR: Missing |\endcsname|
@@ -5650,14 +5752,17 @@ $\xintthefloatexpr subs(((x-1)/x, x/x, (x+1)/x), x=2**30)\relax
 %    labelwidth=-\fontdimen2\font, labelsep=\fontdimen2\font, labelindent=0pt,
 %    listparindent=\leftmarginiii]
 
-  \funcdesc[f, g]{quo} first truncates the arguments to convert them to integers then
-  computes the Euclidean quotient. Hence it computes an integer.
-  \funcdesc[f, g]{rem} first truncates the arguments to convert them to integers then
-  computes the Euclidean remainder. Hence it computes an integer.
+  \funcdesc[m, n]{iquo} Only available in |\xintiiexpr/\xintiieval|
+  context.  Computes the Euclidean quotient.  Matches with the remainder
+  defined in next item. See \csbxint{iiQuo}.
+
+  \funcdesc[m, n]{irem} Only available in |\xintiiexpr/\xintiieval|
+  context.  Computes the Euclidean remainder.  Attention that, following
+  mathematical definition, it is always non-negative.  See \csbxint{iiRem}.
 
   \funcdesc[f, g]{mod} computes |f - g*floor(f/g)|. Hence its output is a
   general fraction or floating point number or integer depending on the
-  used parser.
+  used parser. If non-zero, it has the same sign as |g|.
 
   Prior to |1.2p| it computed |f - g*trunc(f/g)|.
 
@@ -5833,15 +5938,23 @@ At |1.4| \func{all}, \func{any}, \func{xor},
 \func{max}, \func{min}, \func{gcd}, \func{lcm}, \func{first}, \func{last},
 \func{reversed} and \func{len} admit:
 \begin{itemize}
-\item at least two arguments, and then operate as expected in backward
-  compatible way,
-\item or only one argument,\IMPORTANT{} which then \emph{must} be a |nut-ple|, i.e. a
-  variable or explicit bracketed list. In the case of \func{reversed} the output
-  is a |nut-ple| if the input was one.
+\item at least two arguments, and then they operate as expected in the backwards
+  compatible way (notice that it is possible in \xintexprname to define
+  variables expanding to an |ople|, i.e. (at user level) an unpacked comma
+  separated list, |foo(ople)| thus falls into this category),
+\item or only one argument,\IMPORTANT{} which then \emph{must} be a |nutple|,
+  i.e. a bracketed list (or a variable defined to hold such a
+  bracketed list, or a function producing such a |nutple|). The argument is then
+  automatically unpacked.
+
+  In the specific case of \func{reversed} the output is then repacked so that
+  the output is a |nutple| if and only if the input was one (the reversal does
+  not propagate to deeper nested |nutple|'s, it applies only at depth one).
 \end{itemize}
-Notice that this is breaking change as the functions do not work anymore with
-a single argument being a number (or give funny non-documented results
-depending on internal data representation).
+The arguments of the functions doing computations on the arguments (such as
+\func{gcd}) must be numerical, except if there is only one argument, and then
+it must be a |nutple|. Prior to |1.4|, the functions worked also with a single
+scalar argument, but this is now illegal.
 
 \begin{description}
 % [parsep=0pt,align=left,
@@ -5894,45 +6007,57 @@ the resulting logical assertion,
 
 \funcdesc[x, y, ...]{gcd} computes the positive generator of the fractional
 ideal of rational numbers $x\mathbb Z + y\mathbb Z + ... \subset \mathbb
-Q$. When the inputs are integers it is advantageous to use a sub
-\csbxint{iiexpr}-ession, as the integer-only macro is more efficient (about
-|6X|) than the
-one accepting general fractional inputs. Notice that this may require some
-\func{num} wrapper when using variables, as they may well be in fraction
-format, and \csbxint{iiexpr} accepts only strict integers. Since |1.3d|, this
-function and \func{lcm} are available whether or not package \xintgcdname is
-loaded. Note that like other operations with fractions it does not always
-produce a fraction in irreducible format. This example shows also how to
-reduce an n-uple to its primitive part: (this example should be revisited)
-\begin{everbatim*}
-\xinttheexpr gcd(7/300, 11/150, 13/60)\relax\newline
+Q$.  Since |1.4d| the output is always in lowest terms.
+
+This example shows how to reduce an n-uple to its primitive part:
+\begin{everbatim*}
+\xinteval{gcd(7/300, 11/150, 13/60)}\newline
 $(7/300, 11/150, 13/60)\to
-(\xinttheexpr subs(seq(reduce(x/D), x = 7/300, 11/150, 13/60), D=gcd(7/300, 11/150, 13/60))\relax)$\newline
+(\xinteval{subsn(seq(reduce(x/D), x = L), D=gcd(L); L=7/300, 11/150, 13/60)})$\newline
 \xintexpr gcd([7/300, 11/150, 13/60])\relax\par
 \end{everbatim*}
-
+MEMO
 Perhaps a future release will provide a |primpart()| function as built-in
 functionality.
 
+In case of strict integers, using a |\xintiiexpr...\relax| wrapper is
+advantageous as the integer-only |gcd()| is more efficient.
+%
+% ceci semble encore à peu près exact à 1.4d :
+% (about |6X|) than the one accepting general fractional inputs. 
+%
+As \csbxint{iiexpr} accepts only strict integers, doing this may require
+wrapping the argument in \func{num}.
+
 \funcdesc[x, y, ...]{lcm} computes the positive generator of the
 fractional ideal of rational numbers $x\mathbb Z \cap y\mathbb Z \cap ...
-\subset \mathbb Q$. When the inputs are integers it is
-advantageous to use a sub \csbxint{iiexpr}-ession, as the integer-only macro
-is more efficient (about |9X|) than the one accepting general fractional inputs.
+\subset \mathbb Q$.
 \begin{everbatim*}
 \xinttheexpr lcm([7/300, 11/150, 13/60])\relax
 \end{everbatim*}
+As for \func{gcd}, since |1.4d| the output is always in lowest terms.
+% Memo 1.4d: This
+% function got (I did not tests extensively) a |4X| speed gain for inputs being
+% only integers
+For strict integers it is slightly advantageous to use a sub
+\csbxint{iiexpr}-ession.
+%
+% je disais à 1.4:
+%  (about |9X|) than the one accepting general fractional inputs.
+% mais à 1.4d c'est seulement 2X : le lcm pour les fractions
+% a quadruplé sa vitesse !
+%
 
-\funcdesc[x, y, ...]{first} first item of the list or nut-ple argument:
+\funcdesc[x, y, ...]{first} first item of the list or nutple argument:
 \begin{everbatim*}
 \xintiiexpr first([last(-7..3), [58, 97..105]])\relax
 \end{everbatim*}
-\funcdesc[x, y, ...]{last} last item of the list or nut-ple argument:
+\funcdesc[x, y, ...]{last} last item of the list or nutple argument:
 \begin{everbatim*}
 \xintiiexpr last([-7..3, 58, first(97..105)])\relax
 \end{everbatim*}
 \funcdesc[x, y, ...]{reversed} reverses the order of the comma separated list
-or inside a nut-ple:
+or inside a nutple:
 \begin{everbatim*}
 \xintiieval{reversed(reversed(1..5), reversed([1..5]))}
 \end{everbatim*}
@@ -5940,16 +6065,16 @@ or inside a nut-ple:
 The above is correct as \xintexprname functions may produce oples and this is
 the case here.
 \funcdesc[x, y, ...]{len} computes the number of items in a comma separated
-  list or inside a nut-ple (at first level only: it is not a counter of leaves).
+  list or inside a nutple (at first level only: it is not a counter of leaves).
 \begin{everbatim*}
 \xinttheiiexpr len(1..50, [101..150], 1001..1050), len([1..10])\relax
 \end{everbatim*}
 
    \funcdesc[\lowast nutples]{zip} behaves\NewWith{1.4b} similarly to
-   the Python function of the same name: i.e. it produces \emph{an ople of nut-ples,
-   where the i-th nut-ple contains the i-th element from each of the argument
-   nut-ples. The ople ends when the shortest input nut-ple is exhausted.
-   With a single nut-ple argument, it returns an ople of 1-nutples.
+   the Python function of the same name: i.e. it produces \emph{an ople of nutples,
+   where the i-th nutple contains the i-th element from each of the argument
+   nutples. The ople ends when the shortest input nutple is exhausted.
+   With a single nutple argument, it returns an ople of 1-nutples.
    With no arguments, it returns the empty ople.}
 
    As there is no exact match in \xintexprname of the concept of «iterator» object,%
@@ -6363,7 +6488,7 @@ In the example above the parentheses serve to disambiguate from the raw
 on input. And we used a trick to show that |(7)[-2]| returns |nil|.
 
 The behaviour changes for singleton \emph{oples} which are not
-\emph{numbers}. They are thus \emph{nut-ples}, or equivalently they are the
+\emph{numbers}. They are thus \emph{nutples}, or equivalently they are the
 bracketing (bracing, packing) of another \emph{ople}. In this case, the meaning
 of the syntax for item indexing is, as in Python, item
 \emph{extraction}:
@@ -6379,7 +6504,7 @@ of the syntax for item indexing is, as in Python, item
 \xintiiexpr (0..10)[:6]\relax\ and \xintiiexpr (0..10)[:-6]\relax
 \end{everbatim*}
 
-As above, the meaning change for \emph{nut-ples} and fits with expectations
+As above, the meaning change for \emph{nutples} and fits with expectations
 from Python regarding its sequence types:
 \begin{everbatim*}
 \xintiiexpr [0..10][:6]\relax\ and \xintiiexpr [0..10][:-6]\relax
@@ -6391,7 +6516,7 @@ from Python regarding its sequence types:
 \xintiiexpr (0..10)[6:]\relax\ and \xintiiexpr (0..10)[-6:]\relax
 \end{everbatim*}
 
-As above, the meaning change for \emph{nut-ples} and fit with expectations
+As above, the meaning change for \emph{nutples} and fit with expectations
 from Python with \emph{tuple} or \emph{list} types:
 \begin{everbatim*}
 \xintiiexpr [0..10][6:]\relax\ and \xintiiexpr [0..10][-6:]\relax
@@ -6414,7 +6539,7 @@ from Python with \emph{tuple} or \emph{list} types:
 \end{itemize}
 
 
-\subsection{NumPy like nested slicing and indexing for arbitrary oples and nut-ples}
+\subsection{NumPy like nested slicing and indexing for arbitrary oples and nutples}
 
 This is entirely new with |1.4|.\NewWith{1.4}
 
@@ -6467,6 +6592,21 @@ part, or hexadecimal input), or is looking for an infix operator, and:
 \end{enumerate}
 
 \begin{framed}
+  \centeredline{\textcolor{Red}{\textbf{!!!!ATTENTION!!!!}}}
+
+  Explicit digits prefixing a variable, or a function, whose name starts with
+  an |e| or |E| will trap the parser into trying to build a number in
+  scientific notation. So the |*| must be explictly inserted.
+
+\begin{everbatim}
+\xintdefiivar e := (2a+4b+6d+N)/:7;%
+\xintdefiivar f := (c+11d+22*e)//451;% 22e would raise errors
+\end{everbatim}
+
+  I don't think I will fix this anytime soon...
+\end{framed}
+
+\begin{framed}
     For example, if |x, y, z| are variables all three of |(x+y)z|, |x(y+z)|,
     |(x+y)(x+z)| will create a tacit multiplication.
 
@@ -7109,7 +7249,7 @@ This section\CHANGED{1.4} has changed significantly at |1.4| due to the new exte
 types manipulated by the syntax.
 
 Suppose we want to manipulate 3-dimensional vectors, which will be represented
-as |nut-ples| of length 3. And let's add a bit of matrix algebra.
+as |nutples| of length 3. And let's add a bit of matrix algebra.
 \begin{everbatim*}
 \xintdeffunc dprod(V, W) := V[0]*W[0] + V[1]*W[1] + V[2]*W[2];
 \xintdeffunc cprod(V, W) := [V[1]*W[2] - V[2]*W[1],
@@ -7623,9 +7763,9 @@ This package was first included in release |1.3e| (|2019/04/05|) of
 Currently, the functions \func{log10}, \func{pow10}, \func{log}, \func{exp},
 and \func{pow} use at their core two fast expandable macros handling base 10
 logarithms and powers for mantissas of 9 digit tokens. They are
-defined by package \href{https://ctan.org/pkg/poormanlog}{poormanlog} which is
+defined by package \ctanpackage{poormanlog} which is
 automatically imported. The error is believed to be at most \dtt{2ulp} (see
-its |README|). The package \href{https://ctan.org/pkg/poormanlog}{poormanlog}
+its |README|). The package \ctanpackage{poormanlog}
 has no dependencies and can be imported by any other \TeX\ macro file.
 
 Although the precision is thus limited to about \dtt{8} or \dtt{9} digits this
@@ -7679,7 +7819,7 @@ first 8 or 9 digits of the output are significant...
 \end{everbatim*}
 Notice that the last digit of |log(2)| is not the correctly rounded one... I
 did say 9 \textbf{or} 8 digits or precision... The documentation of
-\href{https://ctan.org/pkg/poormanlog}{poormanlog} mentions an error of up
+\ctanpackage{poormanlog} mentions an error of up
 to 2 units in the ninth digit when computing |log10(x)| for |1<x<10| and
 |10^x| for |0<x<1|.
 
@@ -7783,7 +7923,7 @@ using standard infix notations with \TeX{} integers. But \eTeX{} did not
 modify the \TeX{} bound on acceptable integers, and did not add floating point
 support.
 
-The \href{https://ctan.org/pkg/bigintcalc}{bigintcalc} package by
+The \ctanpackage{bigintcalc} package by
 \textsc{Heiko Oberdiek} provided expandable macros (using some of |\numexpr|
 possibilities, when available) on arbitrarily big integers, beyond the \TeX{}
 bound. It does not provide an expression parser.%
@@ -7848,7 +7988,7 @@ Even with the superior \liiibigint{} Karatsuba multiplication it takes about
 computations in a document. I have long been thinking that without the
 expandability constraint much higher speeds could be achieved, but perhaps I
 have not given enough thought to sustain that optimistic stance.\footnote{The
-  \href{https://ctan.org/pkg/apnum}{apnum} package implements
+  \ctanpackage{apnum} package implements
   (non-expandably) arbitrary precision fixed point algebra and (v1.6)
   functions exp, log, sqrt, the trigonometrical direct and inverse functions.}
 
@@ -8076,7 +8216,7 @@ margin annotation next to the description of the arguments.
   package provided conditionals such as \csbxint{ifEq}, \csbxint{ifGt},
   \csbxint{ifSgn},\dots\ or, for \LaTeX{} users and when dealing
   with short integers the
-  \href{https://ctan.org/pkg/etoolbox}{etoolbox}%
+  \ctanpackage{etoolbox}%
 %
 \footnote{\url{https://ctan.org/pkg/etoolbox}}
   expandable conditionals (for small integers only) such as \texttt{\char92
@@ -8617,7 +8757,7 @@ unused branches should not be forgotten.
 
 If these tests are to be applied to standard \TeX{} short integers, it is more
 efficient to use (under \LaTeX{}) the equivalent conditional tests from the
-\href{https://ctan.org/pkg/etoolbox}{etoolbox}%
+\ctanpackage{etoolbox}%
 %
 \footnote{\url{https://ctan.org/pkg/etoolbox}}
 package.
@@ -8867,7 +9007,7 @@ early 2014.
 
 This |1.2| release also got its impulse from a fast
 ``reversing'' macro, which I wrote after my interest got awakened again as a
-result of correspondance with Bruno \textsc{Le Floch} during September 2015:
+result of correspondence with Bruno \textsc{Le Floch} during September 2015:
 this new reverse uses a \TeX nique which \emph{requires} the tokens to be
 digits. I wrote a routine which works (expandably) in quasi-linear time, but a
 less fancy |O(N^2)| variant which I developed concurrently proved to be faster
@@ -11334,8 +11474,11 @@ Prior to |1.4| a macro of the same name existed in \xintgcdname. But
 it truncated all its arguments to integers via \csbxint{Num} and then
 proceeded with integer only computations.
 
-See \csbxint{iiGCDof} for the integer only variant (which is about |6X| faster
-than this one for integer arguments).
+See \csbxint{iiGCDof} for the integer only variant.
+
+% Semble encore vrai à 1.4d
+% Mais je n'ai testé que sur un exemple...
+% (which is about |6X| faster than this one for integer arguments).
 
 \subsection{\csh{xintLCMof}}\label{xintLCMof}
 
@@ -11349,8 +11492,13 @@ output.
 Prior to |1.4| a macro of the same name existed in \xintgcdname. But
 it truncated all its arguments to integers via \csbxint{Num}.
 
-See \csbxint{iiLCMof} for the integer only variant (which is about |9X| faster
-than this one for integer arguments).
+See \csbxint{iiLCMof} for the integer only variant.
+
+% Avant 1.4d on avait ceci :
+% (which is about |9X| faster han this one for integer arguments).
+% mais à 1.4d le lcm des fractions est environ 4X fois plus efficace,
+% en ce qui concerne son emploi avec des entiers (testé sur un seul exemple)
+% donc le gain de faire \xintiiexpr n'est plus que 2X !
 
 \subsection{\csh{xintDigits}, \csh{xinttheDigits}}
 \label{xintDigits}
@@ -18338,7 +18486,7 @@ math shift catcode.
 \fi
 \XINT_providespackage
 \ProvidesPackage {xintkernel}%
-  [2021/02/20 v1.4c Paraphernalia for the xint packages (JFB)]%
+  [2021/03/29 v1.4d Paraphernalia for the xint packages (JFB)]%
 %    \end{macrocode}
 % \subsection{Constants}
 %    \begin{macrocode}
@@ -18431,6 +18579,7 @@ math shift catcode.
 \long\def\xint_firstofone  #1{#1}%
 \long\def\xint_firstoftwo  #1#2{#1}%
 \long\def\xint_secondoftwo #1#2{#2}%
+\long\def\xint_thirdofthree#1#2#3{#3}% 1.4d
 \let\xint_stop_aftergobble\xint_gob_andstop_i
 \long\def\xint_stop_atfirstofone  #1{ #1}%
 \long\def\xint_stop_atfirstoftwo  #1#2{ #1}%
@@ -18462,7 +18611,7 @@ math shift catcode.
 \long\def\xint_gob_til_xint:#1\xint:{}%
 \long\def\xint_gob_til_^#1^{}%
 \def\xint_bracedstopper{\xint:}%
-\long\def\xint_gob_til_exclam #1!{}%
+\long\def\xint_gob_til_exclam #1!{}% documenter le catcode de ! ici
 \long\def\xint_gob_til_sc #1;{}%
 %    \end{macrocode}
 % \subsection{\csh{xint_afterfi}}
@@ -19124,7 +19273,7 @@ math shift catcode.
 %    \begin{macrocode}
 \XINT_providespackage
 \ProvidesPackage{xinttools}%
-  [2021/02/20 v1.4c Expandable and non-expandable utilities (JFB)]%
+  [2021/03/29 v1.4d 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.|
@@ -21468,7 +21617,7 @@ math shift catcode.
 %    \begin{macrocode}
 \XINT_providespackage
 \ProvidesPackage{xintcore}%
-  [2021/02/20 v1.4c Expandable arithmetic on big integers (JFB)]%
+  [2021/03/29 v1.4d 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
@@ -21782,6 +21931,13 @@ math shift catcode.
        -{ #1}%
     \krof
 }%
+\def\XINT_Abs #1%
+{%
+    \xint_UDsignfork
+      #1{}%
+       -{#1}%
+    \krof
+}%
 %    \end{macrocode}
 % \subsection{\csh{xintFDg}}
 % \lverb|&
@@ -24770,7 +24926,7 @@ math shift catcode.
 %    \begin{macrocode}
 \XINT_providespackage
 \ProvidesPackage{xint}%
-  [2021/02/20 v1.4c Expandable operations on big integers (JFB)]%
+  [2021/03/29 v1.4d Expandable operations on big integers (JFB)]%
 %    \end{macrocode}
 % \subsection{More token management}
 %    \begin{macrocode}
@@ -26946,11 +27102,20 @@ math shift catcode.
 \def\xintToggle #1{\romannumeral`&&@\iftoggle{#1}{1}{0}}%
 %    \end{macrocode}
 % \subsection{\csh{xintiiGCD}}
-% Copied over |\xintiiGCD| code from \xintgcdnameimp at |1.3d| in order to
+% |1.3d|: |\xintiiGCD| code from \xintgcdnameimp is copied here to
 % support |gcd()| function in \csbxint{iiexpr}.
 %
-% At |1.4| original code removed from
-% \xintgcdnameimp as the latter now requires \xintnameimp.
+% |1.4|: removed from \xintgcdnameimp the original caode as now
+% \xintgcdnameimp loads \xintnameimp.
+%
+% \changed{1.4d}{2021/03/22} Damn'ed! Since |1.3d| (2019/01/06) the code was
+% broken if one of the arguments vanished due to a typo in macro names:
+% "AisZero" at one location and "Aiszero" at next, and same for B...
+%
+% How could this not be detected by my tests !?!
+%
+% This caused |\xintiiGCDof| hence the |gcd()| function in |\xintiiexpr| to
+% break as soon as one argument was zero.
 %    \begin{macrocode}
 \def\xintiiGCD {\romannumeral0\xintiigcd }%
 \def\xintiigcd #1{\expandafter\XINT_iigcd\romannumeral0\xintiiabs#1\xint:}%
@@ -26968,8 +27133,8 @@ math shift catcode.
     \krof
     #2%
 }%
-\def\XINT_gcd_AisZero #1\xint:#2\xint:{ #1}%
-\def\XINT_gcd_BisZero #1\xint:#2\xint:{ #2}%
+\def\XINT_gcd_Aiszero #1\xint:#2\xint:{ #1}%
+\def\XINT_gcd_Biszero #1\xint:#2\xint:{ #2}%
 \def\XINT_gcd_loop #1\xint:#2\xint:
 {%
     \expandafter\expandafter\expandafter\XINT_gcd_CheckRem
@@ -26982,6 +27147,29 @@ math shift catcode.
 }%
 \def\XINT_gcd_end0\XINT_gcd_loop #1\xint:#2\xint:{ #2}%
 %    \end{macrocode}
+% \subsection{\csh{xintiiGCDof}}
+% \lverb|New with 1.09a (was located in xintgcd.sty).
+%
+% 1.2l adds protection against items being non-terminated \the\numexpr.
+%
+% 1.4 renames the macro into \xintiiGCDof and moves it here.
+% Terminator modified to ^ for direct call by \xintiiexpr function.
+%
+% 1.4d fixes breakage inherited since 1.3d rom \xintiiGCD, in case
+% any argument vanished.
+%
+% Currently does not support empty list of arguments.
+% |
+%    \begin{macrocode}
+\def\xintiiGCDof    {\romannumeral0\xintiigcdof }%
+\def\xintiigcdof    #1{\expandafter\XINT_iigcdof_a\romannumeral`&&@#1^}%
+\def\XINT_iiGCDof   {\romannumeral0\XINT_iigcdof_a}%
+\def\XINT_iigcdof_a #1{\expandafter\XINT_iigcdof_b\romannumeral`&&@#1!}%
+\def\XINT_iigcdof_b #1!#2{\expandafter\XINT_iigcdof_c\romannumeral`&&@#2!{#1}!}%
+\def\XINT_iigcdof_c #1{\xint_gob_til_^ #1\XINT_iigcdof_e ^\XINT_iigcdof_d #1}%
+\def\XINT_iigcdof_d #1!{\expandafter\XINT_iigcdof_b\romannumeral0\xintiigcd {#1}}%
+\def\XINT_iigcdof_e #1!#2!{ #2}%
+%    \end{macrocode}
 % \subsection{\csh{xintiiLCM}}
 % Copied over |\xintiiLCM| code from \xintgcdnameimp at |1.3d| in order to
 % support |lcm()| function in \csbxint{iiexpr}.
@@ -27016,26 +27204,6 @@ math shift catcode.
 }%
 \def\XINT_lcm_end #1\xint:#2\xint:#3\xint:{\xintiimul {#2}{\xintiiQuo{#3}{#1}}}%
 %    \end{macrocode}
-% \subsection{\csh{xintiiGCDof}}
-% \lverb|New with 1.09a (xintgcd.sty).
-%
-% 1.2l adds protection against items being non-terminated \the\numexpr.
-%
-% 1.4 renames the macro into \xintiiGCDof and moves it here.
-% Terminator modified to ^ for direct call by \xintiiexpr function.
-% See comments
-% in xintfrac.sty about \xintGCDof macro there.|
-%
-%    \begin{macrocode}
-\def\xintiiGCDof    {\romannumeral0\xintiigcdof }%
-\def\xintiigcdof    #1{\expandafter\XINT_iigcdof_a\romannumeral`&&@#1^}%
-\def\XINT_iiGCDof   {\romannumeral0\XINT_iigcdof_a}%
-\def\XINT_iigcdof_a #1{\expandafter\XINT_iigcdof_b\romannumeral`&&@#1!}%
-\def\XINT_iigcdof_b #1!#2{\expandafter\XINT_iigcdof_c\romannumeral`&&@#2!{#1}!}%
-\def\XINT_iigcdof_c #1{\xint_gob_til_^ #1\XINT_iigcdof_e ^\XINT_iigcdof_d #1}%
-\def\XINT_iigcdof_d #1!{\expandafter\XINT_iigcdof_b\romannumeral0\xintiigcd {#1}}%
-\def\XINT_iigcdof_e #1!#2!{ #2}%
-%    \end{macrocode}
 % \subsection{\csh{xintiiLCMof}}
 % \lverb|See comments of \xintiiGCDof|.
 %    \begin{macrocode}
@@ -27336,7 +27504,7 @@ math shift catcode.
 %    \begin{macrocode}
 \XINT_providespackage
 \ProvidesPackage{xintbinhex}%
-  [2021/02/20 v1.4c Expandable binary and hexadecimal conversions (JFB)]%
+  [2021/03/29 v1.4d Expandable binary and hexadecimal conversions (JFB)]%
 %    \end{macrocode}
 % \subsection{Constants, etc...}
 % \lverb|1.2n switches to \csname-governed expansion at various places.|
@@ -28008,7 +28176,7 @@ math shift catcode.
 %    \begin{macrocode}
 \XINT_providespackage
 \ProvidesPackage{xintgcd}%
-  [2021/02/20 v1.4c Euclide algorithm with xint package (JFB)]%
+  [2021/03/29 v1.4d Euclide algorithm with xint package (JFB)]%
 %    \end{macrocode}
 % \subsection{\csh{xintBezout}}
 % \lverb|&
@@ -28608,7 +28776,7 @@ math shift catcode.
 %    \begin{macrocode}
 \XINT_providespackage
 \ProvidesPackage{xintfrac}%
-  [2021/02/20 v1.4c Expandable operations on fractions (JFB)]%
+  [2021/03/29 v1.4d Expandable operations on fractions (JFB)]%
 %    \end{macrocode}
 % \subsection{\csh{XINT_cntSgnFork}}
 % \lverb|1.09i. Used internally, #1 must expand to \m@ne, \z@, or \@ne or
@@ -30692,7 +30860,11 @@ math shift catcode.
 %    \end{macrocode}
 % \subsection{\csh{xintDivFloor}}
 % \lverb|1.1. Changed at 1.2p to not append /1[0] ending but rather output a
-% big integer in strict format, like \xintDivTrunc and \xintDivRound.|
+% big integer in strict format, like \xintDivTrunc and \xintDivRound.
+%
+%
+% 
+% |
 %    \begin{macrocode}
 \def\xintDivFloor     {\romannumeral0\xintdivfloor }%
 \def\xintdivfloor #1#2{\xintifloor{\xintDiv {#1}{#2}}}%
@@ -31200,80 +31372,183 @@ math shift catcode.
 \def\xintSgn   {\romannumeral0\xintsgn }%
 \def\xintsgn #1{\expandafter\XINT_sgn\romannumeral0\xintraw {#1}\xint:}%
 %    \end{macrocode}
-% \subsection{\csh{xintGCD}, \csh{xintLCM}}
+% \subsection{\csh{xintGCD}}
 % \changed{1.4}{}
-% They replace the  former \xintgcdnameimp macros of the
-% same names which truncated to integers their arguments.
-% Fraction-producing |gcd()| and |lcm()| functions
-% were available since |1.3d| \xintexprnameimp, with non-public
-% support macros handling comma separated
-% values.
+% They replace the former \xintgcdnameimp macros of the same names which
+% truncated to integers their arguments. Fraction-producing |gcd()| and
+% |lcm()| functions were available since |1.3d| \xintexprnameimp, with
+% non-public support macros handling comma separated values.
+%
+% \changed{1.4d}{}
+% Somewhat strangely \csh{xintGCD} was  formerly \csh{xintGCDof} used with only two
+% arguments, as the latter directly implemented a fractionl gcd algorithm
+% using \csh{xintMod} repeatedly for two arguments.
+%
+% Now \csh{xintGCD} contains the pairwise gcd routine and \csh{xintGCDof}
+% is only a wrapper. And the pairwise gcd is reduced to integer-only
+% computations to hopefully reduce fraction overhead.
+%
+% Each input is filtered via |\xintPIrr| and |\xintREZ| to reduce size
+% of maniuplate integers in algebra.
+%
+% But hesitation about applying |\xintPIrr| to output, and/or |\xintREZ|.
+% (as it is applied on input).
+%
+% But as the code is now used for frational lcm's we actually need to do
+% some reduction of output else lcm's of integers will not be necessarily
+% printed by |\xinteval| as integers.
+% 
+% Well finally I apply |\xintIrr| (but not |\xintREZ| to output).
+% Hesitations here (thinking of inputs with large [n] parts, the output
+% will have many zeros). So I do this only for the user macro but 
+% the core routine as used by |\xintGCDof| will not do it.
+%
+% Also at |1.4d| the code uses |\expanded|.
 %    \begin{macrocode}
 \def\xintGCD {\romannumeral0\xintgcd}%
-\def\xintgcd #1#2{\XINT_fgcdof{#1}{#2}^}%
-\def\xintLCM {\romannumeral0\xintlcm}%
-\def\xintlcm #1#2{\XINT_flcmof{#1}{#2}^}%
+\def\xintgcd #1%
+{%
+    \expandafter\XINT_fgcd_in
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#1}}}\xint:
+}%
+\def\XINT_fgcd_in #1#2\xint:#3%
+{%
+    \expandafter\XINT_fgcd_out
+    \romannumeral0\expandafter\XINT_fgcd_chkzeros\expandafter#1%
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#3}}}\xint:#1#2\xint:
+}%
+\def\XINT_fgcd_out#1[#2]{\xintirr{#1[#2]}[0]}%
+\def\XINT_fgcd_chkzeros #1#2%
+{%
+    \xint_UDzerofork
+       #1\XINT_fgcd_aiszero
+       #2\XINT_fgcd_biszero
+        0\XINT_fgcd_main
+    \krof #2%
+}%
+\def\XINT_fgcd_aiszero #1\xint:#2\xint:{ #1}%
+\def\XINT_fgcd_biszero #1\xint:#2\xint:{ #2}%
+\def\XINT_fgcd_main #1/#2[#3]\xint:#4/#5[#6]\xint:
+{%
+    \expandafter\XINT_fgcd_a
+      \romannumeral0\XINT_gcd_loop #2\xint:#5\xint:\xint:
+      #2\xint:#5\xint:#1\xint:#4\xint:#3.#6.%
+}%
+\def\XINT_fgcd_a #1\xint:#2\xint:
+{%
+    \expandafter\XINT_fgcd_b
+    \romannumeral0\xintiiquo{#2}{#1}\xint:#1\xint:#2\xint:
+}%
+\def\XINT_fgcd_b #1\xint:#2\xint:#3\xint:#4\xint:#5\xint:#6\xint:#7.#8.%
+{%
+   \expanded{%
+   \xintiigcd{\xintiiE{\xintiiMul{#5}{\xintiiQuo{#4}{#2}}}{#7-#8}}%
+             {\xintiiE{\xintiiMul{#6}{#1}}{#8-#7}}%
+    /\xintiiMul{#1}{#4}%
+    [\ifnum#7>#8 #8\else #7\fi]%
+   }%
+}%
 %    \end{macrocode}
 % \subsection{\csh{xintGCDof}}
 % \changed{1.4}{}
-% This inherits from former non public \xintexprnameimp macro called |\xintGCDof:csv|,
-% handling comma separated items, and former \xintgcdnameimp macro called
-% |\xintGCDof| which handled braced items to which it applied |\xintNum|
-% before handling the computations on integers only. The macro keeps the
-% former name \xintgcdnameimp, and handles fractions presented as braced
-% items. It is now the support macro for the |gcd()| function in |\xintexpr|
-% and |\xintfloatexpr|.
+% This inherits from former non public \xintexprnameimp macro called
+% |\xintGCDof:csv|, which handled comma separated items.
 %
-% The support macro for the |gcd()| function in |\xintiiexpr| is
-% \csbxint{iiGCDof} which is located in \xintnameimp.
+% It handles fractions presented as braced items and is the support macro
+% for the |gcd()| function in |\xintexpr| and |\xintfloatexpr|. The support
+% macro for the |gcd()| function in |\xintiiexpr| is \csbxint{iiGCDof}, from
+% \xintnameimp.
 %
+% An empty input is allowed but I have some hesitations on the return
+% value of 1.
+%
+% \changed{1.4d}{}
+% Sadly the |1.4| version had multiple problems:
+% \begin{itemize}
+% \item broken if first argument vanished,
+% \item broken if some argument was not in strict format, for example
+%       had leading chains of signs or zeros (|\xintGCDof{2}{03}|).
+%       This bug originates in the fact the original macro
+%       was used only in \xintexprnameimp sanitized context.
+% \end{itemize}
 %
+% Also, output is now always an irreducible fraction (ending with |[0]|).
 %    \begin{macrocode}
 \def\xintGCDof {\romannumeral0\xintgcdof}%
 \def\xintgcdof #1{\expandafter\XINT_fgcdof\romannumeral`&&@#1^}%
 \def\XINT_GCDof{\romannumeral0\XINT_fgcdof}%
-%    \end{macrocode}
-% \lverb|This abuses the way \xintiiabs works in order to avoid fetching whole
-% argument again: \xintiiabs ^ raises no error.
-% |
-%    \begin{macrocode}
 \def\XINT_fgcdof #1%
 {%
-    \xint_gob_til_^ #1\XINT_fgcdof_empty ^%
-    \expandafter\XINT_fgcdof_loop\romannumeral0\xintiiabs#1\xint:
+    \expandafter\XINT_fgcdof_chkempty\romannumeral`&&@#1\xint:
+}%
+\def\XINT_fgcdof_chkempty #1%
+{%
+    \xint_gob_til_^#1\XINT_fgcdof_empty ^\XINT_fgcdof_in #1%
+}%
+\def\XINT_fgcdof_empty #1\xint:{ 1/1[0]}% hesitation, should it be infinity? O?
+\def\XINT_fgcdof_in #1\xint:
+{%
+    \expandafter\XINT_fgcd_out
+    \romannumeral0\expandafter\XINT_fgcdof_loop
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#1}}}\xint:
 }%
-\def\XINT_fgcdof_empty ^#1\xint:{ 1/1[0]}%
 \def\XINT_fgcdof_loop #1\xint:#2%
 {%
-    \expandafter\XINT_fgcdof_loop_a\romannumeral0\xintiiabs#2\xint:#1\xint:
+    \expandafter\XINT_fgcdof_chkend\romannumeral`&&@#2\xint:#1\xint:\xint:
+}%
+\def\XINT_fgcdof_chkend #1%
+{%
+    \xint_gob_til_^#1\XINT_fgcdof_end ^\XINT_fgcdof_loop_pair #1%
+}%
+\def\XINT_fgcdof_end #1\xint:#2\xint:\xint:{ #2}%
+\def\XINT_fgcdof_loop_pair #1\xint:#2%
+{%
+    \expandafter\XINT_fgcdof_loop
+    \romannumeral0\expandafter\XINT_fgcd_chkzeros\expandafter#2%
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#1}}}\xint:#2%
 }%
 %    \end{macrocode}
+% \subsection{\csh{xintLCM}}
+% Same comments as for \csh{xintGCD}.
+% Entirely redone for |1.4d|.
+% Well, actually we can express it in terms of fractional gcd.
 %    \begin{macrocode}
-\def\XINT_fgcdof_loop_a#1#2\xint:#3\xint:
+\def\xintLCM {\romannumeral0\xintlcm}%
+\def\xintlcm #1%
 {%
-    \xint_gob_til_^    #1\XINT_fgcdof_end  ^%
-    \xint_gob_til_zero #1\XINT_fgcdof_skip 0%
-    \expandafter\XINT_fgcdof_loop_b\romannumeral0\xintmod{#1#2}{#3}\xint:#3\xint:
+    \expandafter\XINT_flcm_in
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#1}}}\xint:
 }%
-\def\XINT_fgcdof_end ^#1\xint:#2\xint:{ #2}%
-\def\XINT_fgcdof_skip 0%
-    \expandafter\XINT_fgcdof_loop_b\romannumeral0\xintmod#1\xint:
+\def\XINT_flcm_in #1#2\xint:#3%
 {%
-    \XINT_fgcdof_loop
+    \expandafter\XINT_fgcd_out
+    \romannumeral0\expandafter\XINT_flcm_chkzeros\expandafter#1%
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#3}}}\xint:#1#2\xint:
 }%
-\def\XINT_fgcdof_loop_b#1#2\xint:#3\xint:
+\def\XINT_flcm_chkzeros #1#2%
 {%
-    \xint_gob_til_zero #1\XINT_fgcdof_next 0%
-    \expandafter\XINT_fgcdof_loop_b\romannumeral0\xintmod{#3}{#1#2}\xint:#1#2\xint:
+    \xint_UDzerofork
+       #1\XINT_flcm_zero
+       #2\XINT_flcm_zero
+        0\XINT_flcm_main
+    \krof #2%
 }%
-\def\XINT_fgcdof_next 0%
-    \expandafter\XINT_fgcdof_loop_b\romannumeral0\xintmod#1#2\xint:#3\xint:#4%
+\def\XINT_flcm_zero #1\xint:#2\xint:{ 0/1[0]}%
+\def\XINT_flcm_main #1/#2[#3]\xint:#4/#5[#6]\xint:
 {%
-    \expandafter\XINT_fgcdof_loop_a\romannumeral0\xintiiabs#4\xint:#1\xint:
+    \xintinv
+    {%
+      \romannumeral0\XINT_fgcd_main #2/#1[-#3]\xint:#5/#4[-#6]\xint:
+    }%
 }%
 %    \end{macrocode}
 % \subsection{\csh{xintLCMof}}
-% See comments for |\xintGCDof|. \xintnameimp provides integer only \csbxint{iiLCMof}.
+% See comments for |\xintGCDof|. \xintnameimp provides the integer only
+% \csbxint{iiLCMof}.
+%
+% \changes{1.4d}{}
+% Sadly, although a public \xintfracnameimp macro, it did not (since |1.4|)
+% sanitize its arguments like other \xintfracnameimp macros.
 %
 %    \begin{macrocode}
 \def\xintLCMof {\romannumeral0\xintlcmof}%
@@ -31281,50 +31556,39 @@ math shift catcode.
 \def\XINT_LCMof{\romannumeral0\XINT_flcmof}%
 \def\XINT_flcmof #1%
 {%
-    \xint_gob_til_^ #1\XINT_flcmof_empty ^%
-    \expandafter\XINT_flcmof_loop\romannumeral0\xintiiabs\xintRaw{#1}\xint:
+    \expandafter\XINT_flcmof_chkempty\romannumeral`&&@#1\xint:
 }%
-\def\XINT_flcmof_empty ^#1\xint:{ 0/1[0]}%
-%    \end{macrocode}
-% \lverb|\XINT_inv expects A/B[N] format which is the case here.|
-%    \begin{macrocode}
-\def\XINT_flcmof_loop #1%
+\def\XINT_flcmof_chkempty #1%
 {%
-    \xint_gob_til_zero #1\XINT_flcmof_zero 0%
-    \expandafter\XINT_flcmof_d\romannumeral0\XINT_inv #1%
+    \xint_gob_til_^#1\XINT_flcmof_empty ^\XINT_flcmof_in #1%
 }%
-\def\XINT_flcmof_zero #1^{ 0/1[0]}%
-%    \end{macrocode}
-% \lverb|\xintRaw{^} would raise an error thus we delay application of
-% \xintRaw to new item. As soon as we hit against a zero item, the l.c.m is
-% known to be zero itself. Else we need to inverse new item, but this requires
-% full A/B[N] raw format, hence the \xintraw.|
-%    \begin{macrocode}
-\def\XINT_flcmof_d #1\xint:#2%
+\def\XINT_flcmof_empty #1\xint:{ 0/1[0]}% hesitation
+\def\XINT_flcmof_in #1\xint:
 {%
-    \expandafter\XINT_flcmof_loop_a\romannumeral0\xintiiabs#2\xint:#1\xint:
+    \expandafter\XINT_fgcd_out
+    \romannumeral0\expandafter\XINT_flcmof_loop
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#1}}}\xint:
 }%
-\def\XINT_flcmof_loop_a #1#2\xint:%
+\def\XINT_flcmof_loop #1\xint:#2%
 {%
-    \xint_gob_til_^    #1\XINT_flcmof_end  ^%
-    \xint_gob_til_zero #1\XINT_flcmof_zero 0%
-    \expandafter\XINT_flcmof_loop_b\romannumeral0\expandafter\XINT_inv
-    \romannumeral0\xintraw{#1#2}\xint:
+    \expandafter\XINT_flcmof_chkend\romannumeral`&&@#2\xint:#1\xint:\xint:
 }%
-\def\XINT_flcmof_end ^#1\xint:#2\xint:{\XINT_inv #2}%
-%    \end{macrocode}
-% \lverb|This is Euclide algorithm.|
-%    \begin{macrocode}
-\def\XINT_flcmof_loop_b #1#2\xint:#3\xint:
+\def\XINT_flcmof_chkend #1%
 {%
-    \xint_gob_til_zero #1\XINT_flcmof_next 0%
-    \expandafter\XINT_flcmof_loop_b\romannumeral0\xintmod{#3}{#1#2}\xint:#1#2\xint:
+    \xint_gob_til_^#1\XINT_flcmof_end ^\XINT_flcmof_loop_pair #1%
 }%
-\def\XINT_flcmof_next 0%
-    \expandafter\XINT_flcmof_loop_b\romannumeral0\xintmod#1#2\xint:#3\xint:#4%
+\def\XINT_flcmof_end #1\xint:#2\xint:\xint:{ #2}%
+\def\XINT_flcmof_loop_pair #1\xint:#2%
 {%
-    \expandafter\XINT_flcmof_loop_a\romannumeral0\xintiiabs#4\xint:#1\xint:
+    \expandafter\XINT_flcmof_chkzero
+    \romannumeral0\expandafter\XINT_flcm_chkzeros\expandafter#2%
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#1}}}\xint:#2%
 }%
+\def\XINT_flcmof_chkzero #1%
+{%
+    \xint_gob_til_zero#1\XINT_flcmof_zero0\XINT_flcmof_loop#1%
+}%
+\def\XINT_flcmof_zero#1^{ 0/1[0]}%
 %    \end{macrocode}
 % \subsection{Floating point macros}
 %
@@ -33797,7 +34061,7 @@ math shift catcode.
 %    \begin{macrocode}
 \XINT_providespackage
 \ProvidesPackage{xintseries}%
-  [2021/02/20 v1.4c Expandable partial sums with xint package (JFB)]%
+  [2021/03/29 v1.4d Expandable partial sums with xint package (JFB)]%
 %    \end{macrocode}
 % \subsection{\csh{xintSeries}}
 %    \begin{macrocode}
@@ -34298,7 +34562,7 @@ math shift catcode.
 %    \begin{macrocode}
 \XINT_providespackage
 \ProvidesPackage{xintcfrac}%
-  [2021/02/20 v1.4c Expandable continued fractions with xint package (JFB)]%
+  [2021/03/29 v1.4d Expandable continued fractions with xint package (JFB)]%
 %    \end{macrocode}
 % \subsection{\csh{xintCFrac}}
 %    \begin{macrocode}
@@ -35690,7 +35954,7 @@ math shift catcode.
 %    \begin{macrocode}
 \XINT_providespackage
 \ProvidesPackage{xintexpr}%
-  [2021/02/20 v1.4c Expandable expression parser (JFB)]%
+  [2021/03/29 v1.4d Expandable expression parser (JFB)]%
 \catcode`! 11
 \let\XINT_Cmp \xintiiCmp
 \def\XINTfstop{\noexpand\XINTfstop}%
@@ -35713,7 +35977,10 @@ math shift catcode.
 % \subsubsection{Bracketed list rendering with prettifying of leaves from nested
 % braced contents}
 % \lverb|1.4 The braces in \XINT:expr:toblistwith are there because there is
-% an \expanded trigger.|
+% an \expanded trigger.
+%
+% 1.4d: support for polexpr 0.8 polynomial type.
+% |
 %    \begin{macrocode}
 \def\XINT:expr:toblistwith#1#2%
 {%
@@ -35729,8 +35996,13 @@ math shift catcode.
 \def\XINT:expr:toblist_a #1{#2%
 <%
     \if{#2\xint_dothis<[\XINT:expr:toblist_a>\fi
+    \if P#2\xint_dothis<\XINT:expr:toblist_pol>\fi
     \xint_orthat\XINT:expr:toblist_b #1#2%
 >%
+\def\XINT:expr:toblist_pol #1!#2.{#3}}%
+<%
+    pol([\XINT:expr:toblist_b #1!#3}^])\XINT:expr:toblist_c #1!}%
+>%
 \def\XINT:expr:toblist_b #1!#2}%
 <%
     \if\relax#2\relax\xintexprEmptyItem\else#1<#2>\fi\XINT:expr:toblist_c #1!}%
@@ -36235,7 +36507,6 @@ math shift catcode.
 \let\XINT:NEhook:f:one:from:two\expandafter
 \let\XINT:NEhook:f:one:from:two:direct\empty
 \let\XINT:NEhook:x:one:from:two\empty
-\let\XINT:NEhook:x:one:from:twoandone\empty
 \let\XINT:NEhook:f:one:and:opt:direct      \empty
 \let\XINT:NEhook:f:tacitzeroifone:direct   \empty
 \let\XINT:NEhook:f:iitacitzeroifone:direct \empty
@@ -36969,10 +37240,6 @@ math shift catcode.
 % This means cases like (a+b)/(c+d)(e+f) will first multiply the last two
 % parenthesized terms.
 %
-% The ! starting a sub-expression must be distinguished from the post-fix !
-% for factorial, thus we must not do a too early \string. In versions < 1.2c,
-% the catcode 11 ! had to be identified in all branches of the number or
-% function scans. Here it is simply treated as a special case of a letter.
 %
 % 1.2q adds tacit multiplication in cases such as (1+1)3 or 5!7!
 %
@@ -37396,11 +37663,11 @@ math shift catcode.
 \XINT_expr_defbin_b {flexpr}{xor}{vi}{xii} {xintXOR}%
 \XINT_expr_defbin_b {iiexpr}{xor}{vi}{xii} {xintXOR}%
 \XINT_expr_defbin_b {expr}  {//} {xiv}{xiv}{xintDivFloor}%
-\XINT_expr_defbin_b {flexpr}{//} {xiv}{xiv}{XINTinFloatDivFloor}%   "
-\XINT_expr_defbin_b {iiexpr}{//} {xiv}{xiv}{xintiiDivFloor}% "
-\XINT_expr_defbin_b {expr}  {/:} {xiv}{xiv}{xintMod}%        "
-\XINT_expr_defbin_b {flexpr}{/:} {xiv}{xiv}{XINTinFloatMod}% "
-\XINT_expr_defbin_b {iiexpr}{/:} {xiv}{xiv}{xintiiMod}%      "
+\XINT_expr_defbin_b {flexpr}{//} {xiv}{xiv}{XINTinFloatDivFloor}%
+\XINT_expr_defbin_b {iiexpr}{//} {xiv}{xiv}{xintiiDivFloor}%
+\XINT_expr_defbin_b {expr}  {/:} {xiv}{xiv}{xintMod}%
+\XINT_expr_defbin_b {flexpr}{/:} {xiv}{xiv}{XINTinFloatMod}%
+\XINT_expr_defbin_b {iiexpr}{/:} {xiv}{xiv}{xintiiMod}%
 \XINT_expr_defbin_b {expr}   +   {xii}{xii}{xintAdd}%
 \XINT_expr_defbin_b {flexpr} +   {xii}{xii}{XINTinFloatAdd}%
 \XINT_expr_defbin_b {iiexpr} +   {xii}{xii}{xintiiAdd}%
@@ -38414,7 +38681,7 @@ math shift catcode.
          *\unexpanded{\expandafter\expandafter}%
          \expandafter\noexpand\csname XINT_expr_var_#1\endcsname(}%
     \ifxintverbose\xintMessage{xintexpr}{Info}
-       {Variable "#1" \ifxintglobaldefs globally \fi
+       {Variable #1 \ifxintglobaldefs globally \fi
         defined with value \csname XINT_expr_varvalue_#1\endcsname.}%
     \fi
 }%
@@ -39801,7 +40068,7 @@ math shift catcode.
 % {float}{sfloat}{ilog10}
 % {divmod}{mod}{binomial}{pfactorial}
 % {randrange}
-% {quo}{rem}{gcd}{lcm}{max}{min}
+% {iquo}{irem}{gcd}{lcm}{max}{min}
 % {`+`}{`*`}
 % {all}{any}{xor}
 % {len}{first}{last}{reversed}
@@ -40268,27 +40535,13 @@ math shift catcode.
     {\xintiiRandRange{#1}}%
     {\xintiiRandRangeAtoB{#1}{#2}}%
 }%
-\def\XINT_expr_func_quo #1#2#3%
-{%
-    \expandafter #1\expandafter #2\expandafter{\romannumeral`&&@%
-    \XINT:NEhook:f:one:from:two
-    {\romannumeral`&&@\xintiQuo #3}}%
-}%
-\let\XINT_flexpr_func_quo\XINT_expr_func_quo
-\def\XINT_iiexpr_func_quo #1#2#3%
+\def\XINT_iiexpr_func_iquo #1#2#3%
 {%
     \expandafter #1\expandafter #2\expandafter{\romannumeral`&&@%
     \XINT:NEhook:f:one:from:two
     {\romannumeral`&&@\xintiiQuo #3}}%
 }%
-\def\XINT_expr_func_rem #1#2#3%
-{%
-    \expandafter #1\expandafter #2\expandafter{\romannumeral`&&@%
-    \XINT:NEhook:f:one:from:two
-    {\romannumeral`&&@\xintiRem #3}}%
-}%
-\let\XINT_flexpr_func_rem\XINT_expr_func_rem
-\def\XINT_iiexpr_func_rem #1#2#3%
+\def\XINT_iiexpr_func_irem #1#2#3%
 {%
     \expandafter #1\expandafter #2\expandafter{\romannumeral`&&@%
     \XINT:NEhook:f:one:from:two
@@ -41024,7 +41277,7 @@ math shift catcode.
 }}\expandafter\XINT:NE:f:iitacitzeroifone:direct\string#%
 \def\XINT:NE:f:iitacitzeroifone_a #1#2&&A#3%
 {%
-    \detokenize{\romannumeral`-0\expandafter#1\expanded{#2}$XINT_expr_exclam#3}%$
+    \detokenize{\romannumeral`$XINT_expr_null\expandafter#1\expanded{#2}$XINT_expr_exclam#3}%
 }%
 \def\XINT:NE:f:iitacitzeroifone_b\XINT:expr:f:iitacitzeroifone #1#2#3&&A#4%
 {%
@@ -41045,16 +41298,6 @@ math shift catcode.
 }}\expandafter\XINT:NE:x:one:from:two_fork\string#%
 \def\XINT:NE:x:one:from:two:p #1#2#3%
    {~expanded{\detokenize{\expandafter#1}~expanded{{#2}{#3}}}}%
-\def\XINT:NE:x:one:from:twoandone #1#2#3{\XINT:NE:x:one:from:twoandone_a #2#3&&A#1{#2}{#3}}%
-\def\XINT:NE:x:one:from:twoandone_a #1#2{\XINT:NE:x:one:from:twoandone_fork #1&&A#2&&A}%
-\def\XINT:NE:x:one:from:twoandone_fork #1{%
-\def\XINT:NE:x:one:from:twoandone_fork ##1##2&&A##3##4&&A##5##6&&A%
-{%
-    \if0\XINT:NE:hastilde ##1##3##5~!\relax\XINT:NE:hashash ##1##3##5#1!\relax 0%
-    \else
-        \expandafter\XINT:NE:x:one:from:two:p
-    \fi
-}}\expandafter\XINT:NE:x:one:from:twoandone_fork\string#%
 \def\XINT:NE:x:listsel #1{%
 \def\XINT:NE:x:listsel ##1##2&%
 {%
@@ -41065,13 +41308,12 @@ math shift catcode.
     \fi
     ##1##2&%
 }}\expandafter\XINT:NE:x:listsel\string#%
-\def\XINT:NE:x:listsel:p #1#2&(#3%
+\def\XINT:NE:x:listsel:p #1#2_#3&(#4%
 {%
-    \detokenize
-    {%
-      \expanded{\expandafter#1\expanded{#2$XINT_expr_tab({#3}}\expandafter\empty\empty}%$
-    }%
+    \detokenize{\expanded\XINT:expr:ListSel{{#3}{#4}}}%
 }%
+\def\XINT:expr:ListSel{\expandafter\XINT:expr:ListSel_i\expanded}%
+\def\XINT:expr:ListSel_i #1#2{{\XINT_ListSel_top #2_#1&({#2}}}%
 \def\XINT:NE:f:reverse #1{%
 \def\XINT:NE:f:reverse ##1^%
 {%
@@ -41084,13 +41326,14 @@ math shift catcode.
 }}\expandafter\XINT:NE:f:reverse\string#%
 \def\XINT:NE:f:reverse:p #1^#2\xint_bye
 {%
-    \detokenize
-    {%
-      \romannumeral0\expandafter\XINT:expr:f:reverse
-      \expandafter{\expanded\expandafter{\xint_gobble_i#1}}%
-    }%
+    \expandafter\XINT:NE:f:reverse:p_i\expandafter{\xint_gobble_i#1}%
 }%
-\def\XINT:expr:f:reverse #1%
+\def\XINT:NE:f:reverse:p_i #1%
+{%
+    \detokenize{\romannumeral0\XINT:expr:f:reverse{{#1}}}%
+}%
+\def\XINT:expr:f:reverse{\expandafter\XINT:expr:f:reverse_i\expanded}%
+\def\XINT:expr:f:reverse_i #1%
 {%
     \XINT_expr_reverse #1^^#1\xint:\xint:\xint:\xint:
                          \xint:\xint:\xint:\xint:\xint_bye
@@ -41118,7 +41361,7 @@ math shift catcode.
     ##1{##2}%
 }}\expandafter\XINT:NE:f:noeval:from:braced:u\string#%
 \def\XINT:NE:f:noeval:from:braced:u:p #1#2%
-    {\detokenize{\expandafter#1}~expanded{{#2}}}%
+    {\detokenize{\romannumeral`$XINT_expr_null\expandafter#1}~expanded{{#2}}}%
 \catcode`- 11
 \def\XINT:NE:exec_? #1#2%
 {%
@@ -41518,7 +41761,6 @@ math shift catcode.
   \let\XINT:NEhook:f:one:from:two        \XINT:NE:f:one:from:two
   \let\XINT:NEhook:f:one:from:two:direct \XINT:NE:f:one:from:two:direct
   \let\XINT:NEhook:x:one:from:two        \XINT:NE:x:one:from:two
-  \let\XINT:NEhook:x:one:from:twoandone  \XINT:NE:x:one:from:twoandone
   \let\XINT:NEhook:f:one:and:opt:direct      \XINT:NE:f:one:and:opt:direct
   \let\XINT:NEhook:f:tacitzeroifone:direct   \XINT:NE:f:tacitzeroifone:direct
   \let\XINT:NEhook:f:iitacitzeroifone:direct \XINT:NE:f:iitacitzeroifone:direct
@@ -41678,6 +41920,7 @@ math shift catcode.
 \def\XINT_expr_tilde{~}\def\XINT_expr_qmark{?}% catcode 3
 \def\XINT_expr_caret{^}\def\XINT_expr_exclam{!}% catcode 11
 \def\XINT_expr_tab{&}% catcode 7
+\def\XINT_expr_null{&&@}%
 \catcode`~ 13 \catcode`@ 14 \catcode`\% 6 \catcode`# 12 \catcode`$ 11 @ $
 \def\XINT_NewExpr_a %1%2%3%4%5@
 {@
@@ -41869,10 +42112,10 @@ math shift catcode.
   \expandafter\xint_secondoftwo
 \fi
 {\immediate\write-1{Reloading xinttrig library using Digits=\xinttheDigits.}}%
-{\expandafter\gdef\csname xintlibver@trig\endcsname{2021/02/20 v1.4c}%
+{\expandafter\gdef\csname xintlibver@trig\endcsname{2021/03/29 v1.4d}%
 \XINT_providespackage
 \ProvidesPackage{xinttrig}%
-[2021/02/20 v1.4c Trigonometrical functions for xintexpr (JFB)]%
+[2021/03/29 v1.4d Trigonometrical functions for xintexpr (JFB)]%
 }%
 %    \end{macrocode}
 % \subsection{Ensure used letters are dummy letters}
@@ -42868,7 +43111,7 @@ math shift catcode.
 \xintexprSafeCatcodes\catcode`_ 11
 \XINT_providespackage
 \ProvidesPackage{xintlog}%
-[2021/02/20 v1.4c Logarithms and exponentials for xintexpr (JFB)]%
+[2021/03/29 v1.4d Logarithms and exponentials for xintexpr (JFB)]%
 %    \end{macrocode}
 % \subsection{Loading of \cshn{poormanlog} package}
 % \lverb|Attention to catcode regime when loading poormanlog. It matters less
@@ -42882,13 +43125,13 @@ math shift catcode.
 \fi
 %    \end{macrocode}
 % \lverb|\XINT_setcatcodes switches to the standard catcode regime of
-% xint*.sty files. And we need the xintexpr catcode for ! too (cf
-% \XINT_expr_func_pow)
+% xint*.sty files. Formerly we needed here the ! of catcode 11 as in
+% xintexpr.sty, which is set by \XINT_setcatcodes but does not apply now.
 %
 % See the remark above about importance of doing \xintexprRestoreCatcodes if
 % \xintexprSafeCatcodes has been used...|
 %    \begin{macrocode}
-\xintexprRestoreCatcodes\csname XINT_setcatcodes\endcsname\catcode`\! 11
+\xintexprRestoreCatcodes\csname XINT_setcatcodes\endcsname
 %    \end{macrocode}
 % \subsection{The \cshn{log10()} and \cshn{pow10()} functions}
 % \lverb|The support macros from poormanlog v0.04 \PoorManLogBaseTen,
@@ -42941,9 +43184,6 @@ math shift catcode.
     \romannumeral`&&@\XINT:NEhook:f:one:from:one
     {\romannumeral`&&@\XINTinFloatExp#3}}%
 }%
-%    \end{macrocode}
-% \lverb|Attention that the ! is of catcode 11 here.|
-%    \begin{macrocode}
 \def\XINT_expr_func_pow #1#2#3%
 {%
     \expandafter #1\expandafter #2\expandafter{%
@@ -42954,7 +43194,11 @@ math shift catcode.
 %    \end{macrocode}
 % \subsection{\csh{poormanloghack}}
 % \lverb|With \poormanloghack{**}, the ** operator will use pow10(y*log10(x)).
-% Same for ^. Sync'd with xintexpr 1.4.|
+% Same for ^. Sync'd with xintexpr 1.4.
+%
+% MEMO: the reason why I need to redefine a lot of stuff is that xintexpr.sty
+% does the job only for ^ and then does a \let for exec_** only. So if now
+% ^ and ** possibly act differently all must be duplicated.|
 %    \begin{macrocode}
 \catcode`\* 11
 \def\poormanloghack**
@@ -43064,9 +43308,9 @@ math shift catcode.
 xint.sty:205
 xintbinhex.sty:53
 xintcfrac.sty:183
-xintcore.sty:271
-xintexpr.sty:430
-xintfrac.sty:496
+xintcore.sty:272
+xintexpr.sty:428
+xintfrac.sty:507
 xintgcd.sty:41
 xintkernel.sty:17
 xintlog.sty:9
@@ -43075,15 +43319,15 @@ xinttools.sty:157
 xinttrig.sty:31
 \fi
 % grep -o "^{%" xint*sty | wc -l
-\def\totala{    1941}
+\def\totala{    1951}
 \iffalse
 % grep -c -e "^}%" xint*sty
 xint.sty:204
 xintbinhex.sty:52
 xintcfrac.sty:183
-xintcore.sty:268
-xintexpr.sty:413
-xintfrac.sty:499
+xintcore.sty:269
+xintexpr.sty:412
+xintfrac.sty:510
 xintgcd.sty:43
 xintkernel.sty:18
 xintlog.sty:9
@@ -43092,7 +43336,7 @@ xinttools.sty:156
 xinttrig.sty:32
 \fi
 % grep -o "^}%" xint*sty | wc -l
-\def\totalb{    1925}
+\def\totalb{    1936}
 \cleardoublepage
 \section{Cumulative line count}
 
@@ -43116,8 +43360,8 @@ xinttrig.sty:32
     \TeX\strut. Version {\xintbndlversion} of {\xintbndldate}.\par
 }
 
-\CheckSum {35109}% 1.4c
-% 35103 pour 1.4b, 34648 pour 1.4a, 34575 pour 1.4
+\CheckSum {35184}% 1.4d
+% 35109 pour 1.4c, 35103 pour 1.4b, 34648 pour 1.4a, 34575 pour 1.4
 % 33497 pour 1.3f, 33274 pour 1.3e, 31601 pour 1.3d, 31122 pour 1.3c
 % 31069 pour 1.3b, 30482 pour 1.3a, 30621 pour 1.3, 30988 pour 1.2q,
 % 30982 pour 1.2p, 30524 pour 1.2o, 30303 pour 1.2h, 30403 pour 1.2i,
diff --git a/Master/texmf-dist/tex/generic/xint/xint.sty b/Master/texmf-dist/tex/generic/xint/xint.sty
index a1e07297eb9..731eec9eba8 100644
--- a/Master/texmf-dist/tex/generic/xint/xint.sty
+++ b/Master/texmf-dist/tex/generic/xint/xint.sty
@@ -21,8 +21,8 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.4c 2021/02/20
-%% Copyright (C) 2013-2020 by Jean-Francois Burnol
+%% The xint bundle 1.4d 2021/03/29
+%% Copyright (C) 2013-2021 by Jean-Francois Burnol
 %% xint: Expandable operations on big integers
 %% ---------------------------------------------------------------
 \begingroup\catcode61\catcode48\catcode32=10\relax%
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty (loaded by xintcore.sty)
 \XINT_providespackage
 \ProvidesPackage{xint}%
-  [2021/02/20 v1.4c Expandable operations on big integers (JFB)]%
+  [2021/03/29 v1.4d 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}%
@@ -1447,8 +1447,8 @@
     \krof
     #2%
 }%
-\def\XINT_gcd_AisZero #1\xint:#2\xint:{ #1}%
-\def\XINT_gcd_BisZero #1\xint:#2\xint:{ #2}%
+\def\XINT_gcd_Aiszero #1\xint:#2\xint:{ #1}%
+\def\XINT_gcd_Biszero #1\xint:#2\xint:{ #2}%
 \def\XINT_gcd_loop #1\xint:#2\xint:
 {%
     \expandafter\expandafter\expandafter\XINT_gcd_CheckRem
@@ -1460,6 +1460,14 @@
     \xint_gob_til_zero #1\XINT_gcd_end0\XINT_gcd_loop #1%
 }%
 \def\XINT_gcd_end0\XINT_gcd_loop #1\xint:#2\xint:{ #2}%
+\def\xintiiGCDof    {\romannumeral0\xintiigcdof }%
+\def\xintiigcdof    #1{\expandafter\XINT_iigcdof_a\romannumeral`&&@#1^}%
+\def\XINT_iiGCDof   {\romannumeral0\XINT_iigcdof_a}%
+\def\XINT_iigcdof_a #1{\expandafter\XINT_iigcdof_b\romannumeral`&&@#1!}%
+\def\XINT_iigcdof_b #1!#2{\expandafter\XINT_iigcdof_c\romannumeral`&&@#2!{#1}!}%
+\def\XINT_iigcdof_c #1{\xint_gob_til_^ #1\XINT_iigcdof_e ^\XINT_iigcdof_d #1}%
+\def\XINT_iigcdof_d #1!{\expandafter\XINT_iigcdof_b\romannumeral0\xintiigcd {#1}}%
+\def\XINT_iigcdof_e #1!#2!{ #2}%
 \def\xintiiLCM {\romannumeral0\xintiilcm}%
 \def\xintiilcm #1{\expandafter\XINT_iilcm\romannumeral0\xintiiabs#1\xint:}%
 \def\XINT_iilcm #1#2\xint:#3%
@@ -1486,14 +1494,6 @@
     \xint:#1\xint:#2\xint:
 }%
 \def\XINT_lcm_end #1\xint:#2\xint:#3\xint:{\xintiimul {#2}{\xintiiQuo{#3}{#1}}}%
-\def\xintiiGCDof    {\romannumeral0\xintiigcdof }%
-\def\xintiigcdof    #1{\expandafter\XINT_iigcdof_a\romannumeral`&&@#1^}%
-\def\XINT_iiGCDof   {\romannumeral0\XINT_iigcdof_a}%
-\def\XINT_iigcdof_a #1{\expandafter\XINT_iigcdof_b\romannumeral`&&@#1!}%
-\def\XINT_iigcdof_b #1!#2{\expandafter\XINT_iigcdof_c\romannumeral`&&@#2!{#1}!}%
-\def\XINT_iigcdof_c #1{\xint_gob_til_^ #1\XINT_iigcdof_e ^\XINT_iigcdof_d #1}%
-\def\XINT_iigcdof_d #1!{\expandafter\XINT_iigcdof_b\romannumeral0\xintiigcd {#1}}%
-\def\XINT_iigcdof_e #1!#2!{ #2}%
 \def\xintiiLCMof      {\romannumeral0\xintiilcmof }%
 \def\xintiilcmof    #1{\expandafter\XINT_iilcmof_a\romannumeral`&&@#1^}%
 \def\XINT_iiLCMof   {\romannumeral0\XINT_iilcmof_a}%
diff --git a/Master/texmf-dist/tex/generic/xint/xintbinhex.sty b/Master/texmf-dist/tex/generic/xint/xintbinhex.sty
index b8b1f06cca3..ef4b736636f 100644
--- a/Master/texmf-dist/tex/generic/xint/xintbinhex.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintbinhex.sty
@@ -21,8 +21,8 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.4c 2021/02/20
-%% Copyright (C) 2013-2020 by Jean-Francois Burnol
+%% The xint bundle 1.4d 2021/03/29
+%% Copyright (C) 2013-2021 by Jean-Francois Burnol
 %% xintbinhex: Expandable binary and hexadecimal conversions
 %% ---------------------------------------------------------------
 \begingroup\catcode61\catcode48\catcode32=10\relax%
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xintbinhex}%
-  [2021/02/20 v1.4c Expandable binary and hexadecimal conversions (JFB)]%
+  [2021/03/29 v1.4d Expandable binary and hexadecimal conversions (JFB)]%
 \newcount\xint_c_ii^xv  \xint_c_ii^xv   32768
 \newcount\xint_c_ii^xvi \xint_c_ii^xvi  65536
 \def\XINT_tmpa #1{\ifx\relax#1\else
diff --git a/Master/texmf-dist/tex/generic/xint/xintcfrac.sty b/Master/texmf-dist/tex/generic/xint/xintcfrac.sty
index 17e67f6563b..19f31a35d06 100644
--- a/Master/texmf-dist/tex/generic/xint/xintcfrac.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintcfrac.sty
@@ -21,8 +21,8 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.4c 2021/02/20
-%% Copyright (C) 2013-2020 by Jean-Francois Burnol
+%% The xint bundle 1.4d 2021/03/29
+%% Copyright (C) 2013-2021 by Jean-Francois Burnol
 %% xintcfrac: Expandable continued fractions with xint package
 %% ---------------------------------------------------------------
 \begingroup\catcode61\catcode48\catcode32=10\relax%
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xintcfrac}%
-  [2021/02/20 v1.4c Expandable continued fractions with xint package (JFB)]%
+  [2021/03/29 v1.4d Expandable continued fractions with xint package (JFB)]%
 \def\xintCFrac {\romannumeral0\xintcfrac }%
 \def\xintcfrac #1%
 {%
diff --git a/Master/texmf-dist/tex/generic/xint/xintcore.sty b/Master/texmf-dist/tex/generic/xint/xintcore.sty
index 133d760a1b8..c6690c5fd00 100644
--- a/Master/texmf-dist/tex/generic/xint/xintcore.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintcore.sty
@@ -21,8 +21,8 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.4c 2021/02/20
-%% Copyright (C) 2013-2020 by Jean-Francois Burnol
+%% The xint bundle 1.4d 2021/03/29
+%% Copyright (C) 2013-2021 by Jean-Francois Burnol
 %% xintcore: Expandable arithmetic on big integers
 %% ---------------------------------------------------------------
 \begingroup\catcode61\catcode48\catcode32=10\relax%
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xintcore}%
-  [2021/02/20 v1.4c Expandable arithmetic on big integers (JFB)]%
+  [2021/03/29 v1.4d Expandable arithmetic on big integers (JFB)]%
 \csname XINT_Clamped_istrapped\endcsname
 \csname XINT_ConversionSyntax_istrapped\endcsname
 \csname XINT_DivisionByZero_istrapped\endcsname
@@ -234,6 +234,13 @@
        -{ #1}%
     \krof
 }%
+\def\XINT_Abs #1%
+{%
+    \xint_UDsignfork
+      #1{}%
+       -{#1}%
+    \krof
+}%
 \def\xintFDg {\romannumeral0\xintfdg }%
 \def\xintfdg #1{\expandafter\XINT_fdg \romannumeral`&&@#1\xint:\Z}%
 \def\XINT_FDg #1%
diff --git a/Master/texmf-dist/tex/generic/xint/xintexpr.sty b/Master/texmf-dist/tex/generic/xint/xintexpr.sty
index 8df9da27a74..c6889155f66 100644
--- a/Master/texmf-dist/tex/generic/xint/xintexpr.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintexpr.sty
@@ -21,8 +21,8 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.4c 2021/02/20
-%% Copyright (C) 2013-2020 by Jean-Francois Burnol
+%% The xint bundle 1.4d 2021/03/29
+%% Copyright (C) 2013-2021 by Jean-Francois Burnol
 %% xintexpr: Expandable expression parser
 %% ---------------------------------------------------------------
 \begingroup\catcode61\catcode48\catcode32=10\relax%
@@ -82,7 +82,7 @@
 \XINTsetupcatcodes%
 \XINT_providespackage
 \ProvidesPackage{xintexpr}%
-  [2021/02/20 v1.4c Expandable expression parser (JFB)]%
+  [2021/03/29 v1.4d Expandable expression parser (JFB)]%
 \catcode`! 11
 \let\XINT_Cmp \xintiiCmp
 \def\XINTfstop{\noexpand\XINTfstop}%
@@ -107,8 +107,13 @@
 \def\XINT:expr:toblist_a #1{#2%
 <%
     \if{#2\xint_dothis<[\XINT:expr:toblist_a>\fi
+    \if P#2\xint_dothis<\XINT:expr:toblist_pol>\fi
     \xint_orthat\XINT:expr:toblist_b #1#2%
 >%
+\def\XINT:expr:toblist_pol #1!#2.{#3}}%
+<%
+    pol([\XINT:expr:toblist_b #1!#3}^])\XINT:expr:toblist_c #1!}%
+>%
 \def\XINT:expr:toblist_b #1!#2}%
 <%
     \if\relax#2\relax\xintexprEmptyItem\else#1<#2>\fi\XINT:expr:toblist_c #1!}%
@@ -388,7 +393,6 @@
 \let\XINT:NEhook:f:one:from:two\expandafter
 \let\XINT:NEhook:f:one:from:two:direct\empty
 \let\XINT:NEhook:x:one:from:two\empty
-\let\XINT:NEhook:x:one:from:twoandone\empty
 \let\XINT:NEhook:f:one:and:opt:direct      \empty
 \let\XINT:NEhook:f:tacitzeroifone:direct   \empty
 \let\XINT:NEhook:f:iitacitzeroifone:direct \empty
@@ -1112,11 +1116,11 @@
 \XINT_expr_defbin_b {flexpr}{xor}{vi}{xii} {xintXOR}%
 \XINT_expr_defbin_b {iiexpr}{xor}{vi}{xii} {xintXOR}%
 \XINT_expr_defbin_b {expr}  {//} {xiv}{xiv}{xintDivFloor}%
-\XINT_expr_defbin_b {flexpr}{//} {xiv}{xiv}{XINTinFloatDivFloor}%   "
-\XINT_expr_defbin_b {iiexpr}{//} {xiv}{xiv}{xintiiDivFloor}% "
-\XINT_expr_defbin_b {expr}  {/:} {xiv}{xiv}{xintMod}%        "
-\XINT_expr_defbin_b {flexpr}{/:} {xiv}{xiv}{XINTinFloatMod}% "
-\XINT_expr_defbin_b {iiexpr}{/:} {xiv}{xiv}{xintiiMod}%      "
+\XINT_expr_defbin_b {flexpr}{//} {xiv}{xiv}{XINTinFloatDivFloor}%
+\XINT_expr_defbin_b {iiexpr}{//} {xiv}{xiv}{xintiiDivFloor}%
+\XINT_expr_defbin_b {expr}  {/:} {xiv}{xiv}{xintMod}%
+\XINT_expr_defbin_b {flexpr}{/:} {xiv}{xiv}{XINTinFloatMod}%
+\XINT_expr_defbin_b {iiexpr}{/:} {xiv}{xiv}{xintiiMod}%
 \XINT_expr_defbin_b {expr}   +   {xii}{xii}{xintAdd}%
 \XINT_expr_defbin_b {flexpr} +   {xii}{xii}{XINTinFloatAdd}%
 \XINT_expr_defbin_b {iiexpr} +   {xii}{xii}{xintiiAdd}%
@@ -1841,7 +1845,7 @@
          *\unexpanded{\expandafter\expandafter}%
          \expandafter\noexpand\csname XINT_expr_var_#1\endcsname(}%
     \ifxintverbose\xintMessage{xintexpr}{Info}
-       {Variable "#1" \ifxintglobaldefs globally \fi
+       {Variable #1 \ifxintglobaldefs globally \fi
         defined with value \csname XINT_expr_varvalue_#1\endcsname.}%
     \fi
 }%
@@ -3143,27 +3147,13 @@
     {\xintiiRandRange{#1}}%
     {\xintiiRandRangeAtoB{#1}{#2}}%
 }%
-\def\XINT_expr_func_quo #1#2#3%
-{%
-    \expandafter #1\expandafter #2\expandafter{\romannumeral`&&@%
-    \XINT:NEhook:f:one:from:two
-    {\romannumeral`&&@\xintiQuo #3}}%
-}%
-\let\XINT_flexpr_func_quo\XINT_expr_func_quo
-\def\XINT_iiexpr_func_quo #1#2#3%
+\def\XINT_iiexpr_func_iquo #1#2#3%
 {%
     \expandafter #1\expandafter #2\expandafter{\romannumeral`&&@%
     \XINT:NEhook:f:one:from:two
     {\romannumeral`&&@\xintiiQuo #3}}%
 }%
-\def\XINT_expr_func_rem #1#2#3%
-{%
-    \expandafter #1\expandafter #2\expandafter{\romannumeral`&&@%
-    \XINT:NEhook:f:one:from:two
-    {\romannumeral`&&@\xintiRem #3}}%
-}%
-\let\XINT_flexpr_func_rem\XINT_expr_func_rem
-\def\XINT_iiexpr_func_rem #1#2#3%
+\def\XINT_iiexpr_func_irem #1#2#3%
 {%
     \expandafter #1\expandafter #2\expandafter{\romannumeral`&&@%
     \XINT:NEhook:f:one:from:two
@@ -3746,7 +3736,7 @@
 }}\expandafter\XINT:NE:f:iitacitzeroifone:direct\string#%
 \def\XINT:NE:f:iitacitzeroifone_a #1#2&&A#3%
 {%
-    \detokenize{\romannumeral`-0\expandafter#1\expanded{#2}$XINT_expr_exclam#3}%$
+    \detokenize{\romannumeral`$XINT_expr_null\expandafter#1\expanded{#2}$XINT_expr_exclam#3}%
 }%
 \def\XINT:NE:f:iitacitzeroifone_b\XINT:expr:f:iitacitzeroifone #1#2#3&&A#4%
 {%
@@ -3767,16 +3757,6 @@
 }}\expandafter\XINT:NE:x:one:from:two_fork\string#%
 \def\XINT:NE:x:one:from:two:p #1#2#3%
    {~expanded{\detokenize{\expandafter#1}~expanded{{#2}{#3}}}}%
-\def\XINT:NE:x:one:from:twoandone #1#2#3{\XINT:NE:x:one:from:twoandone_a #2#3&&A#1{#2}{#3}}%
-\def\XINT:NE:x:one:from:twoandone_a #1#2{\XINT:NE:x:one:from:twoandone_fork #1&&A#2&&A}%
-\def\XINT:NE:x:one:from:twoandone_fork #1{%
-\def\XINT:NE:x:one:from:twoandone_fork ##1##2&&A##3##4&&A##5##6&&A%
-{%
-    \if0\XINT:NE:hastilde ##1##3##5~!\relax\XINT:NE:hashash ##1##3##5#1!\relax 0%
-    \else
-        \expandafter\XINT:NE:x:one:from:two:p
-    \fi
-}}\expandafter\XINT:NE:x:one:from:twoandone_fork\string#%
 \def\XINT:NE:x:listsel #1{%
 \def\XINT:NE:x:listsel ##1##2&%
 {%
@@ -3787,13 +3767,12 @@
     \fi
     ##1##2&%
 }}\expandafter\XINT:NE:x:listsel\string#%
-\def\XINT:NE:x:listsel:p #1#2&(#3%
+\def\XINT:NE:x:listsel:p #1#2_#3&(#4%
 {%
-    \detokenize
-    {%
-      \expanded{\expandafter#1\expanded{#2$XINT_expr_tab({#3}}\expandafter\empty\empty}%$
-    }%
+    \detokenize{\expanded\XINT:expr:ListSel{{#3}{#4}}}%
 }%
+\def\XINT:expr:ListSel{\expandafter\XINT:expr:ListSel_i\expanded}%
+\def\XINT:expr:ListSel_i #1#2{{\XINT_ListSel_top #2_#1&({#2}}}%
 \def\XINT:NE:f:reverse #1{%
 \def\XINT:NE:f:reverse ##1^%
 {%
@@ -3806,13 +3785,14 @@
 }}\expandafter\XINT:NE:f:reverse\string#%
 \def\XINT:NE:f:reverse:p #1^#2\xint_bye
 {%
-    \detokenize
-    {%
-      \romannumeral0\expandafter\XINT:expr:f:reverse
-      \expandafter{\expanded\expandafter{\xint_gobble_i#1}}%
-    }%
+    \expandafter\XINT:NE:f:reverse:p_i\expandafter{\xint_gobble_i#1}%
+}%
+\def\XINT:NE:f:reverse:p_i #1%
+{%
+    \detokenize{\romannumeral0\XINT:expr:f:reverse{{#1}}}%
 }%
-\def\XINT:expr:f:reverse #1%
+\def\XINT:expr:f:reverse{\expandafter\XINT:expr:f:reverse_i\expanded}%
+\def\XINT:expr:f:reverse_i #1%
 {%
     \XINT_expr_reverse #1^^#1\xint:\xint:\xint:\xint:
                          \xint:\xint:\xint:\xint:\xint_bye
@@ -3840,7 +3820,7 @@
     ##1{##2}%
 }}\expandafter\XINT:NE:f:noeval:from:braced:u\string#%
 \def\XINT:NE:f:noeval:from:braced:u:p #1#2%
-    {\detokenize{\expandafter#1}~expanded{{#2}}}%
+    {\detokenize{\romannumeral`$XINT_expr_null\expandafter#1}~expanded{{#2}}}%
 \catcode`- 11
 \def\XINT:NE:exec_? #1#2%
 {%
@@ -4210,7 +4190,6 @@
   \let\XINT:NEhook:f:one:from:two        \XINT:NE:f:one:from:two
   \let\XINT:NEhook:f:one:from:two:direct \XINT:NE:f:one:from:two:direct
   \let\XINT:NEhook:x:one:from:two        \XINT:NE:x:one:from:two
-  \let\XINT:NEhook:x:one:from:twoandone  \XINT:NE:x:one:from:twoandone
   \let\XINT:NEhook:f:one:and:opt:direct      \XINT:NE:f:one:and:opt:direct
   \let\XINT:NEhook:f:tacitzeroifone:direct   \XINT:NE:f:tacitzeroifone:direct
   \let\XINT:NEhook:f:iitacitzeroifone:direct \XINT:NE:f:iitacitzeroifone:direct
@@ -4280,6 +4259,7 @@
 \def\XINT_expr_tilde{~}\def\XINT_expr_qmark{?}% catcode 3
 \def\XINT_expr_caret{^}\def\XINT_expr_exclam{!}% catcode 11
 \def\XINT_expr_tab{&}% catcode 7
+\def\XINT_expr_null{&&@}%
 \catcode`~ 13 \catcode`@ 14 \catcode`\% 6 \catcode`# 12 \catcode`$ 11 @ $
 \def\XINT_NewExpr_a %1%2%3%4%5@
 {@
diff --git a/Master/texmf-dist/tex/generic/xint/xintfrac.sty b/Master/texmf-dist/tex/generic/xint/xintfrac.sty
index 62c5d924cd9..a10aa57392a 100644
--- a/Master/texmf-dist/tex/generic/xint/xintfrac.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintfrac.sty
@@ -21,8 +21,8 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.4c 2021/02/20
-%% Copyright (C) 2013-2020 by Jean-Francois Burnol
+%% The xint bundle 1.4d 2021/03/29
+%% Copyright (C) 2013-2021 by Jean-Francois Burnol
 %% xintfrac: Expandable operations on fractions
 %% ---------------------------------------------------------------
 \begingroup\catcode61\catcode48\catcode32=10\relax%
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xintfrac}%
-  [2021/02/20 v1.4c Expandable operations on fractions (JFB)]%
+  [2021/03/29 v1.4d Expandable operations on fractions (JFB)]%
 \def\XINT_cntSgnFork #1%
 {%
     \ifcase #1\expandafter\xint_secondofthree
@@ -1955,81 +1955,147 @@
 \def\xintSgn   {\romannumeral0\xintsgn }%
 \def\xintsgn #1{\expandafter\XINT_sgn\romannumeral0\xintraw {#1}\xint:}%
 \def\xintGCD {\romannumeral0\xintgcd}%
-\def\xintgcd #1#2{\XINT_fgcdof{#1}{#2}^}%
-\def\xintLCM {\romannumeral0\xintlcm}%
-\def\xintlcm #1#2{\XINT_flcmof{#1}{#2}^}%
+\def\xintgcd #1%
+{%
+    \expandafter\XINT_fgcd_in
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#1}}}\xint:
+}%
+\def\XINT_fgcd_in #1#2\xint:#3%
+{%
+    \expandafter\XINT_fgcd_out
+    \romannumeral0\expandafter\XINT_fgcd_chkzeros\expandafter#1%
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#3}}}\xint:#1#2\xint:
+}%
+\def\XINT_fgcd_out#1[#2]{\xintirr{#1[#2]}[0]}%
+\def\XINT_fgcd_chkzeros #1#2%
+{%
+    \xint_UDzerofork
+       #1\XINT_fgcd_aiszero
+       #2\XINT_fgcd_biszero
+        0\XINT_fgcd_main
+    \krof #2%
+}%
+\def\XINT_fgcd_aiszero #1\xint:#2\xint:{ #1}%
+\def\XINT_fgcd_biszero #1\xint:#2\xint:{ #2}%
+\def\XINT_fgcd_main #1/#2[#3]\xint:#4/#5[#6]\xint:
+{%
+    \expandafter\XINT_fgcd_a
+      \romannumeral0\XINT_gcd_loop #2\xint:#5\xint:\xint:
+      #2\xint:#5\xint:#1\xint:#4\xint:#3.#6.%
+}%
+\def\XINT_fgcd_a #1\xint:#2\xint:
+{%
+    \expandafter\XINT_fgcd_b
+    \romannumeral0\xintiiquo{#2}{#1}\xint:#1\xint:#2\xint:
+}%
+\def\XINT_fgcd_b #1\xint:#2\xint:#3\xint:#4\xint:#5\xint:#6\xint:#7.#8.%
+{%
+   \expanded{%
+   \xintiigcd{\xintiiE{\xintiiMul{#5}{\xintiiQuo{#4}{#2}}}{#7-#8}}%
+             {\xintiiE{\xintiiMul{#6}{#1}}{#8-#7}}%
+    /\xintiiMul{#1}{#4}%
+    [\ifnum#7>#8 #8\else #7\fi]%
+   }%
+}%
 \def\xintGCDof {\romannumeral0\xintgcdof}%
 \def\xintgcdof #1{\expandafter\XINT_fgcdof\romannumeral`&&@#1^}%
 \def\XINT_GCDof{\romannumeral0\XINT_fgcdof}%
 \def\XINT_fgcdof #1%
 {%
-    \xint_gob_til_^ #1\XINT_fgcdof_empty ^%
-    \expandafter\XINT_fgcdof_loop\romannumeral0\xintiiabs#1\xint:
+    \expandafter\XINT_fgcdof_chkempty\romannumeral`&&@#1\xint:
+}%
+\def\XINT_fgcdof_chkempty #1%
+{%
+    \xint_gob_til_^#1\XINT_fgcdof_empty ^\XINT_fgcdof_in #1%
+}%
+\def\XINT_fgcdof_empty #1\xint:{ 1/1[0]}% hesitation, should it be infinity? O?
+\def\XINT_fgcdof_in #1\xint:
+{%
+    \expandafter\XINT_fgcd_out
+    \romannumeral0\expandafter\XINT_fgcdof_loop
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#1}}}\xint:
 }%
-\def\XINT_fgcdof_empty ^#1\xint:{ 1/1[0]}%
 \def\XINT_fgcdof_loop #1\xint:#2%
 {%
-    \expandafter\XINT_fgcdof_loop_a\romannumeral0\xintiiabs#2\xint:#1\xint:
+    \expandafter\XINT_fgcdof_chkend\romannumeral`&&@#2\xint:#1\xint:\xint:
+}%
+\def\XINT_fgcdof_chkend #1%
+{%
+    \xint_gob_til_^#1\XINT_fgcdof_end ^\XINT_fgcdof_loop_pair #1%
+}%
+\def\XINT_fgcdof_end #1\xint:#2\xint:\xint:{ #2}%
+\def\XINT_fgcdof_loop_pair #1\xint:#2%
+{%
+    \expandafter\XINT_fgcdof_loop
+    \romannumeral0\expandafter\XINT_fgcd_chkzeros\expandafter#2%
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#1}}}\xint:#2%
 }%
-\def\XINT_fgcdof_loop_a#1#2\xint:#3\xint:
+\def\xintLCM {\romannumeral0\xintlcm}%
+\def\xintlcm #1%
 {%
-    \xint_gob_til_^    #1\XINT_fgcdof_end  ^%
-    \xint_gob_til_zero #1\XINT_fgcdof_skip 0%
-    \expandafter\XINT_fgcdof_loop_b\romannumeral0\xintmod{#1#2}{#3}\xint:#3\xint:
+    \expandafter\XINT_flcm_in
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#1}}}\xint:
 }%
-\def\XINT_fgcdof_end ^#1\xint:#2\xint:{ #2}%
-\def\XINT_fgcdof_skip 0%
-    \expandafter\XINT_fgcdof_loop_b\romannumeral0\xintmod#1\xint:
+\def\XINT_flcm_in #1#2\xint:#3%
 {%
-    \XINT_fgcdof_loop
+    \expandafter\XINT_fgcd_out
+    \romannumeral0\expandafter\XINT_flcm_chkzeros\expandafter#1%
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#3}}}\xint:#1#2\xint:
 }%
-\def\XINT_fgcdof_loop_b#1#2\xint:#3\xint:
+\def\XINT_flcm_chkzeros #1#2%
 {%
-    \xint_gob_til_zero #1\XINT_fgcdof_next 0%
-    \expandafter\XINT_fgcdof_loop_b\romannumeral0\xintmod{#3}{#1#2}\xint:#1#2\xint:
+    \xint_UDzerofork
+       #1\XINT_flcm_zero
+       #2\XINT_flcm_zero
+        0\XINT_flcm_main
+    \krof #2%
 }%
-\def\XINT_fgcdof_next 0%
-    \expandafter\XINT_fgcdof_loop_b\romannumeral0\xintmod#1#2\xint:#3\xint:#4%
+\def\XINT_flcm_zero #1\xint:#2\xint:{ 0/1[0]}%
+\def\XINT_flcm_main #1/#2[#3]\xint:#4/#5[#6]\xint:
 {%
-    \expandafter\XINT_fgcdof_loop_a\romannumeral0\xintiiabs#4\xint:#1\xint:
+    \xintinv
+    {%
+      \romannumeral0\XINT_fgcd_main #2/#1[-#3]\xint:#5/#4[-#6]\xint:
+    }%
 }%
 \def\xintLCMof {\romannumeral0\xintlcmof}%
 \def\xintlcmof #1{\expandafter\XINT_flcmof\romannumeral`&&@#1^}%
 \def\XINT_LCMof{\romannumeral0\XINT_flcmof}%
 \def\XINT_flcmof #1%
 {%
-    \xint_gob_til_^ #1\XINT_flcmof_empty ^%
-    \expandafter\XINT_flcmof_loop\romannumeral0\xintiiabs\xintRaw{#1}\xint:
+    \expandafter\XINT_flcmof_chkempty\romannumeral`&&@#1\xint:
+}%
+\def\XINT_flcmof_chkempty #1%
+{%
+    \xint_gob_til_^#1\XINT_flcmof_empty ^\XINT_flcmof_in #1%
 }%
-\def\XINT_flcmof_empty ^#1\xint:{ 0/1[0]}%
-\def\XINT_flcmof_loop #1%
+\def\XINT_flcmof_empty #1\xint:{ 0/1[0]}% hesitation
+\def\XINT_flcmof_in #1\xint:
 {%
-    \xint_gob_til_zero #1\XINT_flcmof_zero 0%
-    \expandafter\XINT_flcmof_d\romannumeral0\XINT_inv #1%
+    \expandafter\XINT_fgcd_out
+    \romannumeral0\expandafter\XINT_flcmof_loop
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#1}}}\xint:
 }%
-\def\XINT_flcmof_zero #1^{ 0/1[0]}%
-\def\XINT_flcmof_d #1\xint:#2%
+\def\XINT_flcmof_loop #1\xint:#2%
 {%
-    \expandafter\XINT_flcmof_loop_a\romannumeral0\xintiiabs#2\xint:#1\xint:
+    \expandafter\XINT_flcmof_chkend\romannumeral`&&@#2\xint:#1\xint:\xint:
 }%
-\def\XINT_flcmof_loop_a #1#2\xint:%
+\def\XINT_flcmof_chkend #1%
 {%
-    \xint_gob_til_^    #1\XINT_flcmof_end  ^%
-    \xint_gob_til_zero #1\XINT_flcmof_zero 0%
-    \expandafter\XINT_flcmof_loop_b\romannumeral0\expandafter\XINT_inv
-    \romannumeral0\xintraw{#1#2}\xint:
+    \xint_gob_til_^#1\XINT_flcmof_end ^\XINT_flcmof_loop_pair #1%
 }%
-\def\XINT_flcmof_end ^#1\xint:#2\xint:{\XINT_inv #2}%
-\def\XINT_flcmof_loop_b #1#2\xint:#3\xint:
+\def\XINT_flcmof_end #1\xint:#2\xint:\xint:{ #2}%
+\def\XINT_flcmof_loop_pair #1\xint:#2%
 {%
-    \xint_gob_til_zero #1\XINT_flcmof_next 0%
-    \expandafter\XINT_flcmof_loop_b\romannumeral0\xintmod{#3}{#1#2}\xint:#1#2\xint:
+    \expandafter\XINT_flcmof_chkzero
+    \romannumeral0\expandafter\XINT_flcm_chkzeros\expandafter#2%
+    \romannumeral0\xintrez{\xintPIrr{\xintAbs{#1}}}\xint:#2%
 }%
-\def\XINT_flcmof_next 0%
-    \expandafter\XINT_flcmof_loop_b\romannumeral0\xintmod#1#2\xint:#3\xint:#4%
+\def\XINT_flcmof_chkzero #1%
 {%
-    \expandafter\XINT_flcmof_loop_a\romannumeral0\xintiiabs#4\xint:#1\xint:
+    \xint_gob_til_zero#1\XINT_flcmof_zero0\XINT_flcmof_loop#1%
 }%
+\def\XINT_flcmof_zero#1^{ 0/1[0]}%
 \mathchardef\XINTdigits 16
 \def\xintDigits #1=%
    {\afterassignment \xint_gobble_i \mathchardef\XINTdigits=}%
diff --git a/Master/texmf-dist/tex/generic/xint/xintgcd.sty b/Master/texmf-dist/tex/generic/xint/xintgcd.sty
index db70bd2c3bf..4ecd9df5c00 100644
--- a/Master/texmf-dist/tex/generic/xint/xintgcd.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintgcd.sty
@@ -21,8 +21,8 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.4c 2021/02/20
-%% Copyright (C) 2013-2020 by Jean-Francois Burnol
+%% The xint bundle 1.4d 2021/03/29
+%% Copyright (C) 2013-2021 by Jean-Francois Burnol
 %% xintgcd: Euclidean algorithm with xint package
 %% ---------------------------------------------------------------
 \begingroup\catcode61\catcode48\catcode32=10\relax%
@@ -77,7 +77,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xintgcd}%
-  [2021/02/20 v1.4c Euclide algorithm with xint package (JFB)]%
+  [2021/03/29 v1.4d Euclide algorithm with xint package (JFB)]%
 \def\xintBezout {\romannumeral0\xintbezout }%
 \def\xintbezout #1%
 {%
diff --git a/Master/texmf-dist/tex/generic/xint/xintkernel.sty b/Master/texmf-dist/tex/generic/xint/xintkernel.sty
index 26d63e55dc5..b94e724b17a 100644
--- a/Master/texmf-dist/tex/generic/xint/xintkernel.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintkernel.sty
@@ -21,8 +21,8 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.4c 2021/02/20
-%% Copyright (C) 2013-2020 by Jean-Francois Burnol
+%% The xint bundle 1.4d 2021/03/29
+%% Copyright (C) 2013-2021 by Jean-Francois Burnol
 %% xintkernel: Paraphernalia for the xint packages
 %% ---------------------------------------------------------------
 \begingroup\catcode61\catcode48\catcode32=10\relax%
@@ -157,7 +157,7 @@
 \fi
 \XINT_providespackage
 \ProvidesPackage {xintkernel}%
-  [2021/02/20 v1.4c Paraphernalia for the xint packages (JFB)]%
+  [2021/03/29 v1.4d Paraphernalia for the xint packages (JFB)]%
 \chardef\xint_c_     0
 \chardef\xint_c_i    1
 \chardef\xint_c_ii   2
@@ -233,6 +233,7 @@
 \long\def\xint_firstofone  #1{#1}%
 \long\def\xint_firstoftwo  #1#2{#1}%
 \long\def\xint_secondoftwo #1#2{#2}%
+\long\def\xint_thirdofthree#1#2#3{#3}% 1.4d
 \let\xint_stop_aftergobble\xint_gob_andstop_i
 \long\def\xint_stop_atfirstofone  #1{ #1}%
 \long\def\xint_stop_atfirstoftwo  #1#2{ #1}%
@@ -261,7 +262,7 @@
 \long\def\xint_gob_til_xint:#1\xint:{}%
 \long\def\xint_gob_til_^#1^{}%
 \def\xint_bracedstopper{\xint:}%
-\long\def\xint_gob_til_exclam #1!{}%
+\long\def\xint_gob_til_exclam #1!{}% documenter le catcode de ! ici
 \long\def\xint_gob_til_sc #1;{}%
 \long\def\xint_afterfi #1#2\fi {\fi #1}%
 \long\def\xint_bye #1\xint_bye {}%
diff --git a/Master/texmf-dist/tex/generic/xint/xintlog.sty b/Master/texmf-dist/tex/generic/xint/xintlog.sty
index cf8d886adc5..5b4877cd764 100644
--- a/Master/texmf-dist/tex/generic/xint/xintlog.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintlog.sty
@@ -21,8 +21,8 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.4c 2021/02/20
-%% Copyright (C) 2013-2020 by Jean-Francois Burnol
+%% The xint bundle 1.4d 2021/03/29
+%% Copyright (C) 2013-2021 by Jean-Francois Burnol
 %% xintlog: Logarithms and exponentials for xintexpr
 %% ---------------------------------------------------------------
 \begingroup\catcode61\catcode48\catcode32=10\relax%
@@ -74,13 +74,13 @@
 \xintexprSafeCatcodes\catcode`_ 11
 \XINT_providespackage
 \ProvidesPackage{xintlog}%
-[2021/02/20 v1.4c Logarithms and exponentials for xintexpr (JFB)]%
+[2021/03/29 v1.4d Logarithms and exponentials for xintexpr (JFB)]%
 \ifdefined\RequirePackage
   \RequirePackage{poormanlog}%
 \else
   \input poormanlog.tex
 \fi
-\xintexprRestoreCatcodes\csname XINT_setcatcodes\endcsname\catcode`\! 11
+\xintexprRestoreCatcodes\csname XINT_setcatcodes\endcsname
 \expandafter\def\csname XINT_expr_func_log10\endcsname#1#2#3%
 {%
     \expandafter #1\expandafter #2\expandafter{%
diff --git a/Master/texmf-dist/tex/generic/xint/xintseries.sty b/Master/texmf-dist/tex/generic/xint/xintseries.sty
index 66499a5f4b8..0e5bddb2246 100644
--- a/Master/texmf-dist/tex/generic/xint/xintseries.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintseries.sty
@@ -21,8 +21,8 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.4c 2021/02/20
-%% Copyright (C) 2013-2020 by Jean-Francois Burnol
+%% The xint bundle 1.4d 2021/03/29
+%% Copyright (C) 2013-2021 by Jean-Francois Burnol
 %% xintseries: Expandable partial sums with xint package
 %% ---------------------------------------------------------------
 \begingroup\catcode61\catcode48\catcode32=10\relax%
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xintseries}%
-  [2021/02/20 v1.4c Expandable partial sums with xint package (JFB)]%
+  [2021/03/29 v1.4d Expandable partial sums with xint package (JFB)]%
 \def\xintSeries {\romannumeral0\xintseries }%
 \def\xintseries #1#2%
 {%
diff --git a/Master/texmf-dist/tex/generic/xint/xinttools.sty b/Master/texmf-dist/tex/generic/xint/xinttools.sty
index d4330e4ad99..e35ba21b9c1 100644
--- a/Master/texmf-dist/tex/generic/xint/xinttools.sty
+++ b/Master/texmf-dist/tex/generic/xint/xinttools.sty
@@ -21,8 +21,8 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.4c 2021/02/20
-%% Copyright (C) 2013-2020 by Jean-Francois Burnol
+%% The xint bundle 1.4d 2021/03/29
+%% Copyright (C) 2013-2021 by Jean-Francois Burnol
 %% xinttools: Expandable and non-expandable utilities
 %% ---------------------------------------------------------------
 \begingroup\catcode61\catcode48\catcode32=10\relax%
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xinttools}%
-  [2021/02/20 v1.4c Expandable and non-expandable utilities (JFB)]%
+  [2021/03/29 v1.4d Expandable and non-expandable utilities (JFB)]%
 \newtoks\XINT_toks
 \xint_firstofone{\let\XINT_sptoken= } %<- space here!
 \def\xintgodef  {\global\xintodef }%
diff --git a/Master/texmf-dist/tex/generic/xint/xinttrig.sty b/Master/texmf-dist/tex/generic/xint/xinttrig.sty
index 61d705f1d9f..563d14760da 100644
--- a/Master/texmf-dist/tex/generic/xint/xinttrig.sty
+++ b/Master/texmf-dist/tex/generic/xint/xinttrig.sty
@@ -21,8 +21,8 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.4c 2021/02/20
-%% Copyright (C) 2013-2020 by Jean-Francois Burnol
+%% The xint bundle 1.4d 2021/03/29
+%% Copyright (C) 2013-2021 by Jean-Francois Burnol
 %% xinttrig: Trigonometry for the xintexpr package
 %% ---------------------------------------------------------------
 \begingroup\catcode61\catcode48\catcode32=10\relax%
@@ -68,10 +68,10 @@
   \expandafter\xint_secondoftwo
 \fi
 {\immediate\write-1{Reloading xinttrig library using Digits=\xinttheDigits.}}%
-{\expandafter\gdef\csname xintlibver@trig\endcsname{2021/02/20 v1.4c}%
+{\expandafter\gdef\csname xintlibver@trig\endcsname{2021/03/29 v1.4d}%
 \XINT_providespackage
 \ProvidesPackage{xinttrig}%
-[2021/02/20 v1.4c Trigonometrical functions for xintexpr (JFB)]%
+[2021/03/29 v1.4d Trigonometrical functions for xintexpr (JFB)]%
 }%
 \xintFor* #1 in {iDTVtuwxyzX}\do{\xintensuredummy{#1}}%
 \def\xintreloadxinttrig
author	Norbert Preining <preining@logic.at>	2021-04-04 02:31:47 +0000
committer	Norbert Preining <preining@logic.at>	2021-04-04 02:31:47 +0000
commit	d1301f3e47b2340fd9ffbb7d1a0a4b361540e22e (patch)
tree	4a851156d9d547008865e20d69b78626178c5828 /Master
parent	6aa284727262f1c7ac0ec6c67becc28d5a678a8c (diff)