xint (1feb20)

git-svn-id: svn://tug.org/texlive/trunk@53622 c570f23f-e606-0410-a88d-b1316a301751
author: Karl Berry <karl@freefriends.org> 2020-02-01 22:09:55 +0000
committer: Karl Berry <karl@freefriends.org> 2020-02-01 22:09:55 +0000
commit: 3cac8298f5b8b21ddd1aecbea42a135a9c5e4cb8 (patch)
tree: 9920a659b7ad3860aeb7f391e499b7ccf7f886f8 /Master/texmf-dist/doc
parent: 22cb4622b403ec9e42484b7af858243a417e2d12 (diff)
8 files changed, 302 insertions, 465 deletions
diff --git a/Master/texmf-dist/doc/generic/xint/CHANGES.html b/Master/texmf-dist/doc/generic/xint/CHANGES.html
index cf755b8ddb2..f6b53aa4470 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 1.3f" />
+  <meta name="author" content="xint 1.4" />
   <title>CHANGE LOG</title>
   <style type="text/css">
       code{white-space: pre-wrap;}
@@ -25,128 +25,134 @@
 <body>
 <header>
 <h1 class="title">CHANGE LOG</h1>
-<p class="author">xint 1.3f</p>
-<p class="date">2019/09/10</p>
+<p class="author">xint 1.4</p>
+<p class="date">2020/01/31</p>
 </header>
 <nav id="TOC">
 <ul>
-<li><a href="#f-20190910"><code>1.3f (2019/09/10)</code></a><ul>
+<li><a href="#section"><code>1.4 (2020/01/31)</code></a><ul>
+<li><a href="#breaking-changes">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features">Improvements and new features</a></li>
 <li><a href="#bug-fixes">Bug fixes</a></li>
+<li><a href="#todo">TODO</a></li>
 </ul></li>
-<li><a href="#e-20190405"><code>1.3e (2019/04/05)</code></a><ul>
-<li><a href="#incompatible-changes">Incompatible changes</a></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-1">Bug fixes</a></li>
 </ul></li>
-<li><a href="#d-20190106"><code>1.3d (2019/01/06)</code></a><ul>
-<li><a href="#incompatible-changes-1">Incompatible changes</a></li>
+<li><a href="#e-20190405"><code>1.3e (2019/04/05)</code></a><ul>
+<li><a href="#breaking-changes-1">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-2">Improvements and new features</a></li>
 <li><a href="#bug-fixes-2">Bug fixes</a></li>
 </ul></li>
-<li><a href="#c-20180617"><code>1.3c (2018/06/17)</code></a><ul>
+<li><a href="#d-20190106"><code>1.3d (2019/01/06)</code></a><ul>
+<li><a href="#breaking-changes-2">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-3">Improvements and new features</a></li>
 <li><a href="#bug-fixes-3">Bug fixes</a></li>
 </ul></li>
-<li><a href="#b-20180518"><code>1.3b (2018/05/18)</code></a><ul>
+<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-4">Bug fixes</a></li>
 </ul></li>
-<li><a href="#a-20180307"><code>1.3a (2018/03/07)</code></a><ul>
-<li><a href="#removed">Removed</a></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>
-<li><a href="#bug-fixes-4">Bug fixes</a></li>
 </ul></li>
-<li><a href="#section"><code>1.3 (2018/03/01)</code></a><ul>
-<li><a href="#incompatible-changes-2">Incompatible changes</a></li>
+<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-5">Bug fixes</a></li>
 </ul></li>
-<li><a href="#q-20180206"><code>1.2q (2018/02/06)</code></a><ul>
+<li><a href="#section-1"><code>1.3 (2018/03/01)</code></a><ul>
+<li><a href="#breaking-changes-3">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-7">Improvements and new features</a></li>
-<li><a href="#bug-fixes-5">Bug fixes</a></li>
 </ul></li>
-<li><a href="#p-20171205"><code>1.2p (2017/12/05)</code></a><ul>
-<li><a href="#incompatible-changes-3">Incompatible changes</a></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-6">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-4">Breaking changes</a></li>
+<li><a href="#improvements-and-new-features-9">Improvements and new features</a></li>
+<li><a href="#bug-fixes-7">Bug fixes</a></li>
+</ul></li>
 <li><a href="#o-20170829"><code>1.2o (2017/08/29)</code></a><ul>
-<li><a href="#incompatible-changes-4">Incompatible changes</a></li>
+<li><a href="#breaking-changes-5">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="#incompatible-changes-5">Incompatible changes</a></li>
-<li><a href="#improvements-and-new-features-9">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="#incompatible-changes-6">Incompatible changes</a></li>
+<li><a href="#breaking-changes-6">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-10">Improvements and new features</a></li>
-<li><a href="#bug-fixes-7">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="#m-20170731"><code>1.2m (2017/07/31)</code></a><ul>
+<li><a href="#breaking-changes-7">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-11">Improvements and new features</a></li>
 <li><a href="#bug-fixes-8">Bug fixes</a></li>
 </ul></li>
-<li><a href="#k-20170106"><code>1.2k (2017/01/06)</code></a><ul>
-<li><a href="#incompatible-changes-7">Incompatible changes</a></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-9">Bug fixes</a></li>
 </ul></li>
-<li><a href="#j-20161222"><code>1.2j (2016/12/22)</code></a><ul>
+<li><a href="#k-20170106"><code>1.2k (2017/01/06)</code></a><ul>
+<li><a href="#breaking-changes-8">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-13">Improvements and new features</a></li>
 <li><a href="#bug-fixes-10">Bug fixes</a></li>
 </ul></li>
-<li><a href="#i-20161213"><code>1.2i (2016/12/13)</code></a><ul>
-<li><a href="#incompatible-changes-8">Incompatible changes</a></li>
-<li><a href="#removed-2">Removed</a></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-11">Bug fixes</a></li>
 </ul></li>
-<li><a href="#h-20161120"><code>1.2h (2016/11/20)</code></a><ul>
+<li><a href="#i-20161213"><code>1.2i (2016/12/13)</code></a><ul>
+<li><a href="#breaking-changes-9">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-12">Bug fixes</a></li>
 </ul></li>
-<li><a href="#g-20160319"><code>1.2g (2016/03/19)</code></a><ul>
-<li><a href="#incompatible-changes-9">Incompatible changes</a></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-13">Bug fixes</a></li>
 </ul></li>
-<li><a href="#f-20160312"><code>1.2f (2016/03/12)</code></a><ul>
-<li><a href="#incompatible-changes-10">Incompatible changes</a></li>
+<li><a href="#g-20160319"><code>1.2g (2016/03/19)</code></a><ul>
+<li><a href="#breaking-changes-10">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-17">Improvements and new features</a></li>
-<li><a href="#bug-fixes-13">Bug fixes</a></li>
 </ul></li>
-<li><a href="#e-20151122"><code>1.2e (2015/11/22)</code></a><ul>
+<li><a href="#f-20160312"><code>1.2f (2016/03/12)</code></a><ul>
+<li><a href="#breaking-changes-11">Breaking changes</a></li>
 <li><a href="#improvements-and-new-features-18">Improvements and new features</a></li>
 <li><a href="#bug-fixes-14">Bug fixes</a></li>
 </ul></li>
-<li><a href="#d-20151118"><code>1.2d (2015/11/18)</code></a><ul>
+<li><a href="#e-20151122"><code>1.2e (2015/11/22)</code></a><ul>
 <li><a href="#improvements-and-new-features-19">Improvements and new features</a></li>
 <li><a href="#bug-fixes-15">Bug fixes</a></li>
 </ul></li>
-<li><a href="#c-20151116"><code>1.2c (2015/11/16)</code></a><ul>
+<li><a href="#d-20151118"><code>1.2d (2015/11/18)</code></a><ul>
 <li><a href="#improvements-and-new-features-20">Improvements and new features</a></li>
 <li><a href="#bug-fixes-16">Bug fixes</a></li>
 </ul></li>
-<li><a href="#b-20151029"><code>1.2b (2015/10/29)</code></a><ul>
+<li><a href="#c-20151116"><code>1.2c (2015/11/16)</code></a><ul>
+<li><a href="#improvements-and-new-features-21">Improvements and new features</a></li>
 <li><a href="#bug-fixes-17">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-21">Improvements and new features</a></li>
+<li><a href="#b-20151029"><code>1.2b (2015/10/29)</code></a><ul>
 <li><a href="#bug-fixes-18">Bug fixes</a></li>
 </ul></li>
-<li><a href="#section-1"><code>1.2 (2015/10/10)</code></a><ul>
-<li><a href="#removed-3">Removed</a></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-19">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>
+<li><a href="#improvements-and-new-features-23">Improvements and new features</a></li>
 </ul></li>
 <li><a href="#c-20150912"><code>1.1c (2015/09/12)</code></a></li>
 <li><a href="#b-20150831"><code>1.1b (2015/08/31)</code></a></li>
 <li><a href="#a-20141107"><code>1.1a (2014/11/07)</code></a></li>
-<li><a href="#section-2"><code>1.1 (2014/10/28)</code></a><ul>
-<li><a href="#incompatible-changes-11">Incompatible changes</a></li>
+<li><a href="#section-3"><code>1.1 (2014/10/28)</code></a><ul>
+<li><a href="#breaking-changes-12">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-23">Improvements and new features</a></li>
-<li><a href="#bug-fixes-19">Bug fixes</a></li>
+<li><a href="#improvements-and-new-features-24">Improvements and new features</a></li>
+<li><a href="#bug-fixes-20">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>
@@ -164,22 +170,75 @@
 <li><a href="#a-20130924"><code>1.09a (2013/09/24)</code></a></li>
 <li><a href="#b-20130614"><code>1.08b (2013/06/14)</code></a></li>
 <li><a href="#a-20130611"><code>1.08a (2013/06/11)</code></a></li>
-<li><a href="#section-3"><code>1.08 (2013/06/07)</code></a></li>
-<li><a href="#section-4"><code>1.07 (2013/05/25)</code></a></li>
+<li><a href="#section-4"><code>1.08 (2013/06/07)</code></a></li>
+<li><a href="#section-5"><code>1.07 (2013/05/25)</code></a></li>
 <li><a href="#b-20130514"><code>1.06b (2013/05/14)</code></a></li>
-<li><a href="#section-5"><code>1.06 (2013/05/07)</code></a></li>
-<li><a href="#section-6"><code>1.05 (2013/05/01)</code></a></li>
-<li><a href="#section-7"><code>1.04 (2013/04/25)</code></a></li>
-<li><a href="#section-8"><code>1.03 (2013/04/14)</code></a></li>
-<li><a href="#section-9"><code>1.0 (2013/03/28)</code></a></li>
+<li><a href="#section-6"><code>1.06 (2013/05/07)</code></a></li>
+<li><a href="#section-7"><code>1.05 (2013/05/01)</code></a></li>
+<li><a href="#section-8"><code>1.04 (2013/04/25)</code></a></li>
+<li><a href="#section-9"><code>1.03 (2013/04/14)</code></a></li>
+<li><a href="#section-10"><code>1.0 (2013/03/28)</code></a></li>
 </ul>
 </nav>
-<pre><code>Source:  xint.dtx 1.3f 2019/09/10 (doc 2019/09/10)
+<pre><code>Source:  xint.dtx 1.4 2020/01/31 (doc 2020/01/31)
 Author:  Jean-Francois Burnol
 Info:    Expandable operations on big integers, decimals, fractions
-License: LPPL 1.3f</code></pre>
-<h2 id="f-20190910"><code>1.3f (2019/09/10)</code></h2>
+License: LPPL 1.3c</code></pre>
+<h2 id="section"><code>1.4 (2020/01/31)</code></h2>
+<h3 id="breaking-changes">Breaking changes</h3>
+<p>Please note that this list is currently 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>
+<li><p>The “broadcasting” (as it turned out, ^<sup>c3</sup>^a0 la <code>NumPy</code>) of scalar operations on one-dimensional “lists”, e.g <code>3*[1,3,5,7]+10</code> acting itemwise is <strong>dropped</strong>. It is hoped to implement such operations again in stronger form in future releases. Pre-existing alternative syntax is available, also to produce the bracketed (cf. next item) <code>[13,19,25,31]</code> which will be the output in future.</p></li>
+<li><p>Formerly square brackets <code>[...]</code> were, on their own, not different from parentheses, but they are now a genuine constructor of nested lists. For example <code>\xinteval{1, [2, [3, 4]], 5}</code> produces <code>1, [2, [3, 4]], 5</code> (recall this is free bloatware).</p></li>
+<li><p>The <code>divmod()</code> function now produces on output such a bracketed pair, but simultaneous assignment such as <code>\xintdefvar xq, xr = divmod(a,b);</code> will work transparently.</p></li>
+<li><p>The syntax for using conditionals in function declarations has changed. Now, one <em>must</em> use the <code>?</code> and <code>??</code> short-circuit boolean branching operators whereas in the past it was explained that the syntax had to use the <code>if()</code> and <code>ifsgn()</code> functions.</p></li>
+<li><p>The output of <code>\xinteval</code> has changed (besides containing brackets). It does not use anymore the so-called <em>raw</em> <strong>xintfrac</strong> format, i.e. things such as <code>A/B[N]</code> (which can still be used in input but are discouraged in <strong>xintexpr</strong> context), but scientific notation <code>AeN/B</code>. As formerly, the denominator is printed only if <code>B&gt;1</code> and the scientific part is dropped if the exponent vanishes. In this way the output of <code>\xinteval</code> can be pasted to alternative software.</p>
+<p>The output format of <code>\xinthe\xintboolexpr</code> has changed. It uses <code>True</code> and <code>False</code> (which are accepted on input), and this can easily be configured otherwise (also <code>true</code> and <code>false</code> are accepted on input).</p></li>
+</ul>
 <h3 id="improvements-and-new-features">Improvements and new features</h3>
+<p>Please note that this list is currently incomplete. For more information look at the user manual and the documented source code <code>sourcexint.pdf</code>.</p>
+<p>Unless otherwise specified all changes commented upon here regard <strong>xintexpr</strong>. Important: all the new syntax is to be considered experimental. The author may change some names in future release, or even the interface (whether to use semi-colons or colons etc…).</p>
+<ul>
+<li><p>The <code>\csname</code> encapsulation technique used since <strong>xintexpr</strong> initial release (<code>1.07 2013/05/25</code>) to move around possibly large data during expansion-only operations is replaced with methods based on the <code>\expanded</code> engine primitive. The latter is available in all major engines since TeXLive 2019.</p>
+<p>Formerly, and with default memory settings, one would typically saturate the string pool memory after about of the order of 50,000 independent floating point evaluations of expressions of average complexity on 16-digits numbers.</p>
+<p>There is thus no string pool memory impact at all but one can now hit TeX’s main memory limit (which typically stands at 5,000,000 words) from defining large variables or generating on the fly large data. TeX distributions have a configuration file allowing to enlarge TeX memory parameters and regenerate the (eTeX based) formats.</p></li>
+<li><p>The package supports input and output of arbitrarily <em>nested lists</em>, a.k.a. <em>oples</em> or <em>nlists</em>, with <code>[...]</code> as the constructor of <em>bracketed lists</em>, a.k.a <em>nut-ples</em>. Operations on these objects (as briefly surveyed in later items) are inspired from syntax and functionalities of <code>NumPy</code>’s <em>ndarrays</em>. Our <em>oples</em> (hence also their packaged form <em>nut-ples</em>) may have <em>leaves</em> at varying depths rather than obeying an N-dimensional hyperrectangular shape. But the syntax does provide specific constructors for <em>ndlists</em> (i.e. hyperrectangular <em>oples</em> or <em>nut-ples</em>).</p>
+<p>In a (distant?) future, perhaps <strong>xintexpr</strong> itself or a third-party package will provide an interface, say <code>\xintstorearray</code>, <code>\xintgetarray</code>, to store (which can not be expandable) and retrieve (which can be expandable and thus be embedded inside expressions parsed by <code>\xintexpr</code>, <code>\xintiiexpr</code> or <code>\xintfloatexpr</code>) such <em>ndlists</em> from TeX memory. This is why the package does not use the word <em>ndarray</em> and reserves it for such memory stored objects.</p></li>
+<li><p>The <code>*</code> serves as <em>unpacking</em> operator on <em>nut-ples</em>, i.e. reversing the <code>[]</code> bracketing of an <em>ople</em>.</p></li>
+<li><p><em>oples</em> have no exact equivalent in <code>Python</code>. For example <strong>xintexpr</strong> allows <code>foo(Var1, x)</code> if <code>foo</code> is a function of 4 variables and <code>Var1</code> is a variable producing a length 3 <em>ople</em>, or <code>foo(Var2)</code> if <code>Var2</code> is a variable producing a length 4 <em>ople</em>. Python would require here to use explicitly the <code>*</code>-unpacking notation on some “packed” objects.</p>
+<p>Variable and function values may be <em>oples</em> (even <em>nil</em>), but in function declarations variables must stand for <em>one-ples</em>, i.e. either <em>numbers</em> or <em>nut-ples</em> (as there is no non-ambiguous way to split e.g. 5 arguments into two separate <em>oples</em>).</p></li>
+<li><p>Simultaneous assignment to at least two variables via <code>\xintdefvar</code> et al. automatically unpacks the assigned value if it is a <em>one-ple</em>. If this value was in fact a <em>number</em>, low-level errors will result shortly afterwards as no check is done if the unpacking was illicit. (Such checks exist in the codebase, but have not yet been integrated into <code>\xintdefvar</code> by laziness).</p></li>
+<li><p>The <code>NumPy</code> concept and syntax for nested slicing and item selection are implemented. Currently <em>stepping</em> and the <em>Ellipsis object</em> are not yet available. Only so-called basic slicing is currently supported. (The author has not yet read the section of <code>NumPy</code> documentation on so-called <em>advanced indexing</em>).</p></li>
+<li><p>The <em>broadcasting</em> of scalar operations, such as itemwise addition or multiplication of <em>nut-ples</em> of the same shape is <strong>not yet implemented</strong>.</p></li>
+<li><p>Slicing and indexing apply also at top level to the <em>oples</em> with behaviour conforming to intuitive expectations (see user manual); if it turns out the <em>ople</em> is in fact a <em>nut-ple</em>, the top-level slicing/indexing switches to the <code>Python/NumPy</code> conventions, i.e. it operates inside the brackets for slicing and removes brackets if indexing.</p></li>
+<li><p>The syntax <code>ndseq(expression in x, y, ..., x = values; y = values; ...)</code> constructs a (bracketed) <em>ndlist</em> by evaluation the expression on all possible Cartesian n-uples, where the first variable indexes the first axis, the second the next, etc…</p></li>
+<li><p>The <code>ndmap(foo, values1; values2; ...; valuesN)</code> syntax constructs a (bracketed) <em>ndlist</em> by evaluating the function <code>foo</code> on all elements of the cartesian product of the given (one-dimensional) value lists.</p></li>
+<li><p>The two concepts of <code>\xintdeffunc</code> (for recursive definitions) and <code>\xintdefefunc</code> (for functions which expand immediately in other function declarations) have been merged. The <code>\xintdefefunc</code> et al. are deprecated and kept as aliases for <code>\xintdeffunc</code> et al.</p></li>
+<li><p><code>\xintdefufunc</code> allows to define so-called <em>universal functions</em>, i.e. functions <code>foo</code> such that <code>foo(myople)</code> will apply itemwise at arbitrary depth in the nested structure. The function <code>foo</code> is allowed to produce from a scalar an <em>ople</em>…</p></li>
+<li><p>The variables in function declarations can now be multi-letter words.</p></li>
+<li><p>The last positional variable in a function declaration can be prefixed with a <code>*</code> meaning exactly as in Python (<em>variadic</em> function argument) that it stands for a one-dimensional <em>nut-ple</em> receiving all remaining arguments from the function call beyond the first positional ones. It is thus an optional argument, but syntax for named optional arguments with default values is not yet implemented.</p></li>
+<li><p>Dummy variables used in constructors can also be multi-letter words, if they have been declared as such.</p></li>
+<li><p>In variable and function declarations, if the expression contains inner semi-colons, it is not needed anymore to brace them to avoid mis-interpretation as the final semi-colon which is mandated by the syntax to serve as expression terminator.</p></li>
+<li><p><code>subsm(expression, var1 = value1; var2 = value2; ...)</code> provides a leaner syntax for multiple substitutions; they must be independent, though.</p></li>
+<li><p><code>subsn(expression, var1 = value1; var2 = value2; ...)</code> provides a leaner syntax for nested substitutions, i.e., each <code>valueJ</code> may be an expression using the dummy variables <code>varK</code> with <code>K&gt;J</code>. And finally of course the evaluated expression can refer to all variables.</p></li>
+<li><p><code>\xintthealign\xintexpr...\relax</code> (or with <code>\xintfloatexpr</code> or <code>\xintiiexpr</code> or <code>\xintboolexpr</code>…) will use a TeX alignment to display <em>oples</em>. The output (for regular N-dimensional lists) looks very similar to what <code>Python/NumPy</code> produces in interactive session. This is entirely configurable and can also be set-up to be used for writing into external files.</p>
+<p>Attention that <code>\xintthealign</code> only works if followed by <code>\xintexpr</code> et al., not by <code>\xinteval{}</code>.</p></li>
+<li><p>It is now possible to use <code>\xintexpr...\relax</code> directly for typesetting. The syntax <code>\xinteval{...}</code> or <code>\xintthe\xintexpr...\relax</code> is needed only if one wants the expansion to give the explicit digits, but <code>\xintexpr...\relax</code> by itself will typeset as would have the other ones. Further it can be used in so-called moving arguments, because when output to an external file it uses only characters with standard catcodes (and produces the same protected and re-tokenizable result it would in an <code>\edef</code>.)</p>
+<p>As formerly, <code>\xintexpr...\relax</code> is the preferred way to include an expression into another one. Using <code>\xinteval</code> is a waste because it forces the outer parser to re-digest all the digits (or now also the square brackets).</p></li>
+<li><p>The output format of <code>\xintfloateval</code> with scientific notation has not changed (apart from possible presence of bracketed lists), but the author hesitates because the <em>prettifying</em> it does by default is not really adapted to display of arrays (see <code>\xintthealign</code>). Anyway, this is configurable by the user. It is possible to specify whether to use <code>e</code> or <code>E</code>.</p></li>
+<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">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>
+<li><p>The long delayed overhaul of how floating point numbers are handled is delayed again. It has remained basically identical to its initial provisory version from <code>1.07 2013/05/25</code> (which was based upon what was originally only a set of expandable macros for computations with big integers), and suffers from the author lack of knowledge of the notion of “data type” in modern programming. Indeed, he never took a CS class, and disables JavaScript in his browser (or allows only select non-tracking scripts, a rare beast in modern days).</p></li>
+<li><p>Prior to integrating all of <code>NumPy</code>, it is envisioned to start with matrix algebra first.</p></li>
+</ul>
+<h2 id="f-20190910"><code>1.3f (2019/09/10)</code></h2>
+<h3 id="improvements-and-new-features-1">Improvements and new features</h3>
 <ul>
 <li><p><strong>xintfrac</strong>: <code>\xintDigits = P;</code> syntax (i.e. without a colon) is now accepted in addition to <code>\xintDigits := P;</code>.</p>
 <p>Document that the ending semi-colon can not be an active character and that it has always been allowed to use in its place a non-expanding token e.g. <code>\xintDigits := 32\relax</code>.</p>
@@ -187,17 +246,17 @@ License: LPPL 1.3f</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">Bug fixes</h3>
+<h3 id="bug-fixes-1">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="incompatible-changes">Incompatible changes</h3>
+<h3 id="breaking-changes-1">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>
-<h3 id="improvements-and-new-features-1">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-2">Improvements and new features</h3>
 <ul>
 <li><p>The <strong>xinttrig</strong> library is automatically loaded by <strong>xintexpr</strong>. It provides direct and inverse trigonometrical functions using either degrees or radians with a precision of up to (a bit less than) 60 digits. It is for the most part implemented using high level user interface, but will probably get some optimizations in future (and perhaps extension to more digits).</p></li>
 <li><p>The <strong>xintlog</strong> library is automatically loaded by <strong>xintexpr</strong>. It uses <a href="http://ctan.org/pkg/poormanlog">poormanlog</a> to provide logarithms and exponentials with almost 9 digits of precision. Extended precision is for a future release.</p></li>
@@ -207,17 +266,17 @@ License: LPPL 1.3f</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-1">Bug fixes</h3>
+<h3 id="bug-fixes-2">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="incompatible-changes-1">Incompatible changes</h3>
+<h3 id="breaking-changes-2">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>
 </ul>
-<h3 id="improvements-and-new-features-2">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-3">Improvements and new features</h3>
 <ul>
 <li><p><strong>xintexpr</strong>: the <code>gcd()</code> and <code>lcm()</code> multi-arguments functions have been refactored to handle general fractions. The dependency on <strong>xintgcd</strong> is removed.</p></li>
 <li><p><strong>xintexpr</strong>: three-way branching <code>\xintifsgnexpr</code>, <code>\xintifsgnfloatexpr</code>, <code>\xintifsgniiexpr</code> conditional macros.</p></li>
@@ -226,12 +285,12 @@ License: LPPL 1.3f</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-2">Bug fixes</h3>
+<h3 id="bug-fixes-3">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>
 <h2 id="c-20180617"><code>1.3c (2018/06/17)</code></h2>
-<h3 id="improvements-and-new-features-3">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-4">Improvements and new features</h3>
 <ul>
 <li><p><strong>xintexpr</strong>: with <code>\xintglobaldefstrue</code>, <code>\xintdefvar</code>, <code>\xintdeffunc</code>, <code>\xintNewExpr</code> et al. make definitions with global scope.</p></li>
 <li><p><strong>xintexpr</strong>: <code>qraw()</code> for fast input of (very many) comma separated numbers (in suitable raw format).</p></li>
@@ -239,12 +298,12 @@ License: LPPL 1.3f</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-3">Bug fixes</h3>
+<h3 id="bug-fixes-4">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>
 <h2 id="b-20180518"><code>1.3b (2018/05/18)</code></h2>
-<h3 id="improvements-and-new-features-4">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-5">Improvements and new features</h3>
 <p>All additions related to randomness are marked as work-in-progress. They require an engine providing the <code>\(pdf)uniformdeviate</code> primitive.</p>
 <ul>
 <li><p><strong>xintkernel</strong>: <code>\xintUniformDeviate</code>.</p></li>
@@ -259,41 +318,41 @@ License: LPPL 1.3f</code></pre>
 <ul>
 <li><strong>xintcore</strong>, <strong>xint</strong>, <strong>xintfrac</strong>: removal of the internal macros which were used at <code>1.2o</code> to add a deprecation mechanism; all deprecated macros have been removed at <code>1.3</code> so there was no reason to keep the code used for deprecating them.</li>
 </ul>
-<h3 id="improvements-and-new-features-5">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-6">Improvements and new features</h3>
 <ul>
 <li><p><strong>xintexpr</strong>: new conditionals <code>ifone()</code> and <code>ifint()</code>.</p></li>
 <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-4">Bug fixes</h3>
+<h3 id="bug-fixes-5">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"><code>1.3 (2018/03/01)</code></h2>
-<h3 id="incompatible-changes-2">Incompatible changes</h3>
+<h2 id="section-1"><code>1.3 (2018/03/01)</code></h2>
+<h3 id="breaking-changes-3">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>
 <li><p><strong>xintexpr</strong>: the addition, subtraction, modulo <code>/:</code>, and the <code>mod()</code> and <code>divmod()</code> functions produce generally smaller denominators (see previous item).</p></li>
 <li><p><strong>xintexpr</strong>: formerly, the internal macros which are internally associated to user-declared functions were using comma separated parameter texts. They now do not use such commas (their meanings, which may again change in future, are written for information to the log under <code>\xintverbosetrue</code>).</p></li>
 </ul>
-<h3 id="improvements-and-new-features-6">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-7">Improvements and new features</h3>
 <ul>
 <li><p><strong>xintexpr</strong>: user-defined functions may now be of a recursive nature. This was made possible by a refactoring of the <code>\xintNewExpr</code> mechanism. It became both leaner and more extensive than formerly.</p></li>
 <li><p><strong>xintfrac</strong>: new macros <code>\xintPIrr</code> and <code>\xintDecToString</code>. The latter is a backport of a <code>polexpr 0.4</code> utility, and it is to be considered unstable.</p></li>
 <li><p><strong>xintexpr</strong>: new function <code>preduce()</code> associated with <code>\xintPIrr</code>.</p></li>
 </ul>
 <h2 id="q-20180206"><code>1.2q (2018/02/06)</code></h2>
-<h3 id="improvements-and-new-features-7">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-8">Improvements and new features</h3>
 <ul>
 <li><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-5">Bug fixes</h3>
+<h3 id="bug-fixes-6">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="incompatible-changes-3">Incompatible changes</h3>
+<h3 id="breaking-changes-4">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>
@@ -301,13 +360,13 @@ License: LPPL 1.3f</code></pre>
 <li><p><strong>xintfrac</strong>: <code>\xintMod</code> is now associated with floored division. The former meaning is available as <code>\xintModTrunc</code>.</p></li>
 <li><p><strong>xintexpr</strong>: the <code>//</code> operator and its associated modulo <code>'mod'</code> (or <code>/:</code>) now correspond to floored division, like the Python language <code>//</code>, <code>%</code>, and <code>divmod(x, y)</code>. Formerly they had been associated to truncated division. This is breaking change for operands of opposite signs.</p></li>
 </ul>
-<h3 id="improvements-and-new-features-8">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-9">Improvements and new features</h3>
 <ul>
 <li><p><strong>xinttools</strong>: <code>\xintListWithSep</code>, which had remained unchanged since its introduction at <code>1.04 (2013/04/25)</code>, was rewritten for increased speed.</p></li>
 <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-6">Bug fixes</h3>
+<h3 id="bug-fixes-7">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>
@@ -315,7 +374,7 @@ License: LPPL 1.3f</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="incompatible-changes-4">Incompatible changes</h3>
+<h3 id="breaking-changes-5">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>
@@ -331,26 +390,26 @@ License: LPPL 1.3f</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="incompatible-changes-5">Incompatible changes</h3>
+<h3 id="breaking-changes-6">Breaking changes</h3>
 <ul>
 <li><strong>xintbinhex</strong> does not load package <strong>xintcore</strong> anymore, but only <strong>xintkernel</strong>.</li>
 </ul>
-<h3 id="improvements-and-new-features-9">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-10">Improvements and new features</h3>
 <ul>
 <li><p><strong>xintbinhex</strong> has only <strong>xintkernel</strong> as dependency.</p></li>
 <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="incompatible-changes-6">Incompatible changes</h3>
+<h3 id="breaking-changes-7">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>
 </ul>
-<h3 id="improvements-and-new-features-10">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-11">Improvements and new features</h3>
 <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-7">Bug fixes</h3>
+<h3 id="bug-fixes-8">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>
@@ -362,7 +421,7 @@ License: LPPL 1.3f</code></pre>
 <li><p><code>\xintiiSumExpr</code>, <code>\xintiiPrdExpr</code> (<strong>xint</strong>) and <code>\xintSumExpr</code>, <code>\xintPrdExpr</code> (<strong>xintfrac</strong>). They had not been formally deprecated, but had been left un-documented since <code>1.09d (2013/10/22)</code>.</p></li>
 <li><p>internal macro <code>\xint_gob_til_xint_relax</code> removed.</p></li>
 </ul>
-<h3 id="improvements-and-new-features-11">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-12">Improvements and new features</h3>
 <ul>
 <li><p>the underscore character <code>_</code> is accepted by the <strong>xintexpr</strong> parsers as a digit separator (the space character already could be used for improved readability of big numbers). It is not allowed as <em>first</em> character of a number, as it would then be mis-interpreted as the start of a possible variable name.</p></li>
 <li><p>some refactoring in <strong>xintcore</strong> auxiliary routines and in <code>\xintiiSub</code> and <code>\xintiiCmp</code> for some small efficiency gains.</p></li>
@@ -371,33 +430,33 @@ License: LPPL 1.3f</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-8">Bug fixes</h3>
+<h3 id="bug-fixes-9">Bug fixes</h3>
 <ul>
 <li><p><strong>xintbinhex</strong>: since <code>1.2 (2015/10/10)</code>, <code>\xintHexToDec</code> was broken due to an undefined macro (it was in <code>xint.sty</code>, but the module by itself is supposedly dependent only upon <code>xintcore.sty</code>).</p></li>
 <li><p><strong>xintgcd</strong>: macro <code>\xintBezout</code> produced partially wrong output if one of its two arguments was zero.</p></li>
 <li><p><strong>xintfrac</strong>: the manual said one could use directly <code>\numexpr</code> compatible expressions in arithmetic macros (without even a <code>\numexpr</code> encapsulation) if they were expressed with up to 8 tokens. There was a bug if these 8 tokens evaluated to zero. The bug has been fixed, and up to 9 tokens are now accepted. But it is simpler to use <code>\the\numexpr</code> prefix and not to worry about the token count… The ending <code>\relax</code> is now un-needed.</p></li>
 </ul>
 <h2 id="k-20170106"><code>1.2k (2017/01/06)</code></h2>
-<h3 id="incompatible-changes-7">Incompatible changes</h3>
+<h3 id="breaking-changes-8">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>
 </ul>
-<h3 id="improvements-and-new-features-12">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-13">Improvements and new features</h3>
 <ul>
 <li><p>the initial rounding to the target precision <code>P</code> which is applied by the floating point macros from <strong>xintfrac</strong> to their arguments achieves the <em>exact (aka correct) rounding</em> even for inputs which are fractions with more than <code>P+2</code> digits in their numerators and denominators (<code>&gt;1</code>.) Hence the computed values depend only on the arguments as rational numbers and not upon their representatives. This is not relevant to <em>expressions</em> (<strong>xintexpr</strong>), because the <code>\xintfloatexpr</code> parser sees there <code>/</code> as an operator and does not (apart from special constructs) get to manipulate fractions as such.</p></li>
 <li><p><code>\xintnewdummy</code> is public interface to a <code>1.2e</code> macro which serves to declare any given catcode 11 character as a dummy variable for expressions (<strong>xintexpr</strong>). This is useful for Unicode engines (the Latin letters being already all pre-declared as dummy variables.)</p></li>
 <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-9">Bug fixes</h3>
+<h3 id="bug-fixes-10">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>
 <li><p><code>\xintiiSquareRoot{0}</code> now produces <code>{1}{1}</code>, which fits better the general documented behaviour of this macro than <code>11</code>.</p></li>
 </ul>
 <h2 id="j-20161222"><code>1.2j (2016/12/22)</code></h2>
-<h3 id="improvements-and-new-features-13">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-14">Improvements and new features</h3>
 <ul>
 <li><p><strong>xinttools</strong> and <strong>xintexpr</strong>:</p>
 <ol type="1">
@@ -406,12 +465,12 @@ License: LPPL 1.3f</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-10">Bug fixes</h3>
+<h3 id="bug-fixes-11">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="incompatible-changes-8">Incompatible changes</h3>
+<h3 id="breaking-changes-9">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>
@@ -419,7 +478,7 @@ License: LPPL 1.3f</code></pre>
 <ul>
 <li>deprecated macros <code>\xintifTrue</code>, <code>\xintifTrueFalse</code>, <code>\xintQuo</code>, <code>\xintRem</code>, <code>\xintquo</code>, <code>\xintrem</code>.</li>
 </ul>
-<h3 id="improvements-and-new-features-14">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-15">Improvements and new features</h3>
 <ul>
 <li><p><strong>xintkernel</strong>: <code>\xintLength</code> is faster. New macros:</p>
 <ul>
@@ -438,17 +497,17 @@ License: LPPL 1.3f</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-11">Bug fixes</h3>
+<h3 id="bug-fixes-12">Bug fixes</h3>
 <ul>
 <li><code>\xintDecSplitL</code> and <code>\xintDecSplitR</code> from <strong>xint</strong> produced their output in a spurious brace pair (bug introduced in <code>1.2f</code>).</li>
 </ul>
 <h2 id="h-20161120"><code>1.2h (2016/11/20)</code></h2>
-<h3 id="improvements-and-new-features-15">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-16">Improvements and new features</h3>
 <ul>
 <li><p>new macro <code>\xintNewFunction</code> in <strong>xintexpr</strong> which allows to extend the parser syntax with functions in situations where <code>\xintdeffunc</code> is not usable (typically, because dummy variables are used over a not yet determined range of values because it depends on the variables).</p></li>
 <li><p>after three years of strict obedience to <code>xint</code> prefix, now <code>\thexintexpr</code>, <code>\thexintiexpr</code>, <code>\thexintfloatexpr</code>, and <code>\thexintiiexpr</code> are provided as synonyms to <code>\xinttheexpr</code>, etc…</p></li>
 </ul>
-<h3 id="bug-fixes-12">Bug fixes</h3>
+<h3 id="bug-fixes-13">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>
@@ -456,12 +515,12 @@ License: LPPL 1.3f</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="incompatible-changes-9">Incompatible changes</h3>
+<h3 id="breaking-changes-10">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>
 </ul>
-<h3 id="improvements-and-new-features-16">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-17">Improvements and new features</h3>
 <ul>
 <li><p>in <strong>xintexpr.sty</strong>: list selectors <code>[L][n]</code> and <code>[L][a:b]</code> are more efficient: the earlier <code>1.1</code> routines did back and forth conversions from comma separated values to braced tokens, the <code>1.2g</code> routines use macros from <strong>xinttools.sty</strong> handling directly the encountered lists of comma separated values.</p></li>
 <li><p>in <strong>xinttools.sty</strong>: slight improvements in the efficiency of the <code>\xintNthElt</code>, <code>\xintKeep</code>, <code>\xintTrim</code> routines and new routines handling directly comma separated values. The latter are not included in the user manual (they are not <code>\long</code>, they don’t make efforts to preserve some braces, do not worry about spaces, all those worries being irrelevant to the use in expressions for list selectors).</p></li>
@@ -470,11 +529,11 @@ License: LPPL 1.3f</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="incompatible-changes-10">Incompatible changes</h3>
+<h3 id="breaking-changes-11">Breaking changes</h3>
 <ul>
 <li>no more <code>\xintFac</code> macro but <code>\xintiFac/\xintiiFac/\xintFloatFac</code>.</li>
 </ul>
-<h3 id="improvements-and-new-features-17">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-18">Improvements and new features</h3>
 <ul>
 <li><p>functions <code>binomial</code>, <code>pfactorial</code> and <code>factorial</code> in both integer and float versions.</p></li>
 <li><p>macros <code>\xintiiBinomial</code>, <code>\xintiiPFactorial</code> (<strong>xint.sty</strong>) and <code>\xintFloatBinomial</code>, <code>\xintFloatPFactorial</code> (<strong>xintfrac.sty</strong>). Improvements to <code>\xintFloatFac</code>.</p></li>
@@ -488,69 +547,69 @@ License: LPPL 1.3f</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-13">Bug fixes</h3>
+<h3 id="bug-fixes-14">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>
 <li><p>the comparison operators were not recognized by <code>\xintNewIIExpr</code> and <code>\xintdefiifunc</code> constructs.</p></li>
 </ul>
 <h2 id="e-20151122"><code>1.2e (2015/11/22)</code></h2>
-<h3 id="improvements-and-new-features-18">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-19">Improvements and new features</h3>
 <ul>
 <li><p>macro <code>\xintunassignvar</code>.</p></li>
 <li><p>slight modifications of the logged messages in case of <code>\xintverbosetrue</code>.</p></li>
 <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-14">Bug fixes</h3>
+<h3 id="bug-fixes-15">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>
 <li><p>in <strong>xintexpr</strong>: contrarily to what <code>1.2d</code> documentation said, tacit multiplication was not yet always done with enhanced precedence. Now yes.</p></li>
 </ul>
 <h2 id="d-20151118"><code>1.2d (2015/11/18)</code></h2>
-<h3 id="improvements-and-new-features-19">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-20">Improvements and new features</h3>
 <ul>
 <li><p>the function definitions done by <code>\xintdeffunc</code> et al., as well as the macro declarations by <code>\xintNewExpr</code> et al. now have only local scope.</p></li>
 <li><p>tacit multiplication applies to more cases, for example (x+y)z, and always ties more than standard * infix operator, e.g. x/2y is like x/(2*y).</p></li>
 <li><p>some documentation enhancements, particularly in the chapter on xintexpr.sty, and also in the code source comments.</p></li>
 </ul>
-<h3 id="bug-fixes-15">Bug fixes</h3>
+<h3 id="bug-fixes-16">Bug fixes</h3>
 <ul>
 <li>in <strong>xintcore</strong>: release <code>1.2c</code> had inadvertently broken the <code>\xintiiDivRound</code> macro.</li>
 </ul>
 <h2 id="c-20151116"><code>1.2c (2015/11/16)</code></h2>
-<h3 id="improvements-and-new-features-20">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-21">Improvements and new features</h3>
 <ul>
 <li><p>macros <code>\xintdeffunc</code>, <code>\xintdefiifunc</code>, <code>\xintdeffloatfunc</code> and boolean <code>\ifxintverbose</code>.</p></li>
 <li><p>on-going code improvements and documentation enhancements, but stopped in order to issue this bugfix release.</p></li>
 </ul>
-<h3 id="bug-fixes-16">Bug fixes</h3>
+<h3 id="bug-fixes-17">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-17">Bug fixes</h3>
+<h3 id="bug-fixes-18">Bug fixes</h3>
 <ul>
 <li>in <strong>xintcore</strong>: recent release <code>1.2</code> introduced a bug in the division macros, causing a crash when the divisor started with 99999999 (it was attempted to use with 1+99999999 a subroutine expecting only 8-digits numbers).</li>
 </ul>
 <h2 id="a-20151019"><code>1.2a (2015/10/19)</code></h2>
-<h3 id="improvements-and-new-features-21">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-22">Improvements and new features</h3>
 <ul>
 <li><p>added <code>\xintKeepUnbraced</code>, <code>\xintTrimUnbraced</code> (<strong>xinttools</strong>) and fixed documentation of <code>\xintKeep</code> and <code>\xintTrim</code> regarding brace stripping.</p></li>
 <li><p>added <code>\xintiiMaxof/\xintiiMinof</code> (<strong>xint</strong>).</p></li>
 <li><p>TeX hackers only: replaced all code uses of <code>\romannumeral-`0</code> by the quicker <code>\romannumeral`&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-18">Bug fixes</h3>
+<h3 id="bug-fixes-19">Bug fixes</h3>
 <ul>
 <li>in <strong>xintexpr</strong>: recent release <code>1.2</code> introduced a bad bug in the parsing of decimal numbers and as a result <code>\xinttheexpr 0.01\relax</code> expanded to <code>0</code> ! (sigh…)</li>
 </ul>
-<h2 id="section-1"><code>1.2 (2015/10/10)</code></h2>
+<h2 id="section-2"><code>1.2 (2015/10/10)</code></h2>
 <h3 id="removed-3">Removed</h3>
 <ul>
 <li>the macros <code>\xintAdd</code>, <code>\xintSub</code>, <code>\xintMul</code>, <code>\xintMax</code>, <code>\xintMin</code>, <code>\xintMaxof</code>, <code>\xintMinof</code> are removed from package <strong>xint</strong>, and only exist in the versions from <strong>xintfrac</strong>. With only <strong>xintcore</strong> or <strong>xint</strong> loaded, one <em>must</em> use <code>\xintiiAdd</code>, <code>\xintiiSub</code>, …, or <code>\xintiAdd</code>, <code>\xintiSub</code>, etc…</li>
 </ul>
-<h3 id="improvements-and-new-features-22">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-23">Improvements and new features</h3>
 <ul>
 <li><p>the basic arithmetic implemented in <strong>xintcore</strong> has been entirely rewritten. The mathematics remains the elementary school one, but the <code>TeX</code> implementation achieves higher speed (except, regarding addition/subtraction, for numbers up to about thirty digits), the gains becoming quite significant for numbers with hundreds of digits.</p></li>
 <li><p>the inputs must have less than 19959 digits. But computations with thousands of digits take time.</p></li>
@@ -583,8 +642,8 @@ License: LPPL 1.3f</code></pre>
 <li><p>added the previously mentioned <code>ii</code> macros, and some others from <code>1.1</code>, to the user manual. But their main usage is internal to <code>\xintiiexpr</code>, to skip unnecessary overheads.</p></li>
 <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-2"><code>1.1 (2014/10/28)</code></h2>
-<h3 id="incompatible-changes-11">Incompatible changes</h3>
+<h2 id="section-3"><code>1.1 (2014/10/28)</code></h2>
+<h3 id="breaking-changes-12">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>
@@ -604,7 +663,7 @@ License: LPPL 1.3f</code></pre>
 <li><p><code>\xintMax</code>, <code>\xintMin</code>, <code>\xintAdd</code>, <code>\xintSub</code>, <code>\xintMul</code> (<strong>xint</strong>): their usage without <strong>xintfrac</strong> is deprecated; use <code>\xintiMax</code>, <code>\xintiMin</code>, <code>\xintiAdd</code>, <code>\xintiSub</code>, <code>\xintiMul</code>.</p></li>
 <li><p>the <code>&amp;</code> and <code>|</code> as Boolean operators in <code>xintexpr</code>-essions are deprecated in favour of <code>&amp;&amp;</code> and <code>||</code>. The single letter operators might be assigned some other meaning in some later release (bitwise operations, perhaps). Do not use them.</p></li>
 </ul>
-<h3 id="improvements-and-new-features-23">Improvements and new features</h3>
+<h3 id="improvements-and-new-features-24">Improvements and new features</h3>
 <ul>
 <li><p>new package <strong>xintcore</strong> has been split off <strong>xint</strong>. It contains the core arithmetic macros (it is loaded by LaTeX package <strong>bnumexpr</strong>),</p></li>
 <li><p>neither <strong>xint</strong> nor <strong>xintfrac</strong> load <strong>xinttools</strong>. Only <strong>xintexpr</strong> does,</p></li>
@@ -642,7 +701,7 @@ License: LPPL 1.3f</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-19">Bug fixes</h3>
+<h3 id="bug-fixes-20">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>
@@ -785,12 +844,12 @@ License: LPPL 1.3f</code></pre>
 <li><p>Better management by <code>\xintCmp</code>, <code>\xintMax</code>, <code>\xintMin</code> and <code>\xintGeq</code> of inputs having big powers of ten in them.</p></li>
 <li><p>Macros for floating point numbers added to the <strong>xintseries</strong> package.</p></li>
 </ul>
-<h2 id="section-3"><code>1.08 (2013/06/07)</code></h2>
+<h2 id="section-4"><code>1.08 (2013/06/07)</code></h2>
 <ul>
 <li><p>(<strong>xint</strong> and <strong>xintfrac</strong>) Macros for extraction of square roots, for floating point numbers (<code>\xintFloatSqrt</code>), and integers (<code>\xintiSqrt</code>).</p></li>
 <li><p>new package <strong>xintbinhex</strong> providing <em>conversion routines</em> to and from binary and hexadecimal bases.</p></li>
 </ul>
-<h2 id="section-4"><code>1.07 (2013/05/25)</code></h2>
+<h2 id="section-5"><code>1.07 (2013/05/25)</code></h2>
 <ul>
 <li><p>The <strong>xintexpr</strong> package is a new core constituent (which loads automatically <strong>xintfrac</strong> and <strong>xint</strong>) and implements the expandable expanding parser</p>
 <pre><code>\xintexpr . . . \relax,</code></pre>
@@ -805,16 +864,16 @@ License: LPPL 1.3f</code></pre>
 <ul>
 <li>Minor code and documentation improvements. Everywhere in the source code, a more modern underscore has replaced the @ sign.</li>
 </ul>
-<h2 id="section-5"><code>1.06 (2013/05/07)</code></h2>
+<h2 id="section-6"><code>1.06 (2013/05/07)</code></h2>
 <ul>
 <li><p>Some code improvements, particularly for macros of <strong>xint</strong> doing loops.</p></li>
 <li><p>New utilities in <strong>xint</strong> for expandable manipulations of lists:</p>
 <pre><code>\xintNthElt, \xintCSVtoList, \xintRevWithBraces</code></pre></li>
 <li><p>The macros did only a double expansion of their arguments. They now fully expand them (using <code>\romannumeral-`0</code>). Furthermore, in the case of arguments constrained to obey the TeX bounds they will be inserted inside a <code>\numexpr..\relax</code>, hence completely expanded, one may use count registers, even infix arithmetic operations, etc…</p></li>
 </ul>
-<h2 id="section-6"><code>1.05 (2013/05/01)</code></h2>
+<h2 id="section-7"><code>1.05 (2013/05/01)</code></h2>
 <p>Minor changes and additions to <strong>xintfrac</strong> and <strong>xintcfrac</strong>.</p>
-<h2 id="section-7"><code>1.04 (2013/04/25)</code></h2>
+<h2 id="section-8"><code>1.04 (2013/04/25)</code></h2>
 <ul>
 <li><p>New component <strong>xintcfrac</strong> devoted to continued fractions.</p></li>
 <li><p><strong>xint</strong>: faster division.</p></li>
@@ -824,13 +883,13 @@ License: LPPL 1.3f</code></pre>
 <li><p><code>tex xint.dtx</code> extracts style files (no need for a <code>xint.ins</code>).</p></li>
 <li><p>Bug fix (<strong>xintfrac</strong>): <code>\xintIrr {0}</code> crashed.</p></li>
 </ul>
-<h2 id="section-8"><code>1.03 (2013/04/14)</code></h2>
+<h2 id="section-9"><code>1.03 (2013/04/14)</code></h2>
 <ul>
 <li><p>New modules <strong>xintfrac</strong> (expandable operations on fractions) and <strong>xintseries</strong> (expandable partial sums with xint package).</p></li>
 <li><p>Slightly improved division and faster multiplication (the best ordering of the arguments is chosen automatically).</p></li>
 <li><p>Added illustration of Machin algorithm to the documentation.</p></li>
 </ul>
-<h2 id="section-9"><code>1.0 (2013/03/28)</code></h2>
+<h2 id="section-10"><code>1.0 (2013/03/28)</code></h2>
 <p>Initial announcement:</p>
 <blockquote>
 <p>The <strong>xint</strong> package implements with expandable TeX macros the basic arithmetic operations of addition, subtraction, multiplication and division, as applied to arbitrarily long numbers represented as chains of digits with an optional minus sign.</p>
diff --git a/Master/texmf-dist/doc/generic/xint/CHANGES.pdf b/Master/texmf-dist/doc/generic/xint/CHANGES.pdf
deleted file mode 100644
index d449cb63c81..00000000000
--- a/Master/texmf-dist/doc/generic/xint/CHANGES.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/generic/xint/README b/Master/texmf-dist/doc/generic/xint/README
deleted file mode 100644
index 580b1e89656..00000000000
--- a/Master/texmf-dist/doc/generic/xint/README
+++ /dev/null
@@ -1,205 +0,0 @@
-    Source:  xint.dtx 1.3f 2019/09/10 (doc 2019/09/10)
-    Author:  Jean-Francois Burnol
-    Info:    Expandable operations on big integers, decimals, fractions
-    License: LPPL 1.3f
-
-This README is also available as README.pdf and README.html.
-
-Change log is to be found in CHANGES.pdf or CHANGES.html.
-
-The user manual is xint.pdf, and the commented source code is available
-as sourcexint.pdf.
-
-
-
-AIM
-
-
-The basic aim is provide _expandable_ computations on integers,
-fractions, and floating point numbers. For example
-
-    \xinttheexpr reduce(37189719/183618963+11390170/17310720)^17\relax
-
-will evaluate exactly the fraction; the result has 462 characters
-(including the fraction slash.) One can also work with dummy variables:
-
-    \xinttheexpr mul(add(x(x+1)(x+2), x=y..y+15), y=171286,98762,9296)\relax
-
-evaluates to 15979066346135829902328007959448563667099190784.
-
-Float computations are possible at an adjustable precision (default 16).
-
-    \xintDigits:=48;\xintthefloatexpr 123_456_789^1_000.5\relax
-    ->3.63692761822782679930738270515740797370813691938e8095
-
-(as this example shows the underscore character can be used to separate
-visually digits, one can also use the space character for that purpose).
-
-Square-root and the four operations achieve correct rounding in the
-given arbitrary precision.
-
-Trigonometric functions (direct and inverse) are available with a
-maximal precision of 60 digits.
-
-Logarithms and exponentials are available using the poormanlog package
-which provides only 8 or 9 digits of precision. This will be increased
-in future.
-
-
-
-USAGE
-
-
-It is possible to use the package both with Plain (\input xintexpr.sty)
-or with LaTeX (\usepackage{xintexpr}).
-
-
-With LaTeX
-
-    \usepackage{xint}       % expandable arithmetic with big integers
-    \usepackage{xintfrac}   % decimal numbers, fractions, floats
-    \usepackage{xinttools}  % expandable and non expandable loops
-    \usepackage{xintexpr}   % expressions with infix operators
-
-The xinttrig and xintlog packages are loaded automatically by xintexpr
-and will refuse to be loaded directly.
-
-Further packages: xintbinhex, xintgcd, xintseries and xintcfrac.
-
-Main dependencies are handled automatically. For example xintexpr
-automatically loads xinttools and xintfrac (which itself loads xint).
-Hexadecimal input requires explicit loading of xintbinhex.
-
-Package xintcore is the subset of xint providing only the five
-operations on big integers: \xintiiAdd, \xintiiMul, …
-
-The LaTeX package bnumexpr defines a more light-weight parser of
-arithmetical expressions using big integers, which supports only the
-four operations, the modulo operation, the power operation, and the
-factorial. By default it uses the macros from xintcore but this can be
-customized.
-
-The LaTeX package polexpr is based upon xintexpr and allows formal
-algebra with polynomials, and finding all real roots with arbitrary
-precision.
-
-
-With TeX
-
-One does for example:
-
-    \input xintexpr.sty
-
-This will automatically load xintfrac.sty, xinttrig.sty, xintlog.sty and
-xinttools.sty. The packages may be loaded in any catcode context such
-that letters, digits, \ and % have their standard catcodes.
-
-xintcore.sty and xinttools.sty both import xintkernel.sty which has the
-catcode handler and package identifier and defines a few utilities such
-as \oodef/\fdef, \xint_dothis/\xint_orthat, or \xintLength.
-
-Since 1.3b, xintkernel.sty also provides \xintUniformDeviate which is a
-wrapper of the engine \pdfuniformdeviate or \uniformdeviate done to
-guarantee more uniformity of the pseudo-random integers.
-
-
-
-INSTALLATION
-
-
-Method A: using the package manager of your TeX distribution
-
-xint is included in TeXLive (hence also MacTeX) and MikTeX.
-
-There can be a few days of delay between apparition of a new version on
-CTAN and availability via the distribution package manager.
-
-
-Method B: manual installation using xint.tds.zip and unzip
-
-Assumes a GNU/Linux-like system (or Mac OS X).
-
-1.  obtain xint.tds.zip from CTAN:
-    http://mirror.ctan.org/install/macros/generic/xint.tds.zip
-
-2.  cd to the download repertory and issue:
-
-         unzip xint.tds.zip -d <TEXMF>
-
-    where <TEXMF> is a suitable TDS-compliant destination repertory. For
-    example, with TeXLive:
-
-    -   Linux, standard access rights, hence sudo is needed,
-        installation into the “local” tree:
-
-              sudo unzip xint.tds.zip -d /usr/local/texlive/texmf-local
-              sudo texhash /usr/local/texlive/texmf-local
-
-    -   Mac OS X, installation into user home folder (no sudo needed,
-        and it is recommended to not have a ls-R file there, hence no
-        texhash):
-
-              unzip xint.tds.zip -d  ~/Library/texmf
-
-
-Method C: manual installation using Makefile and xint.dtx
-
-The Makefile automatizes rebuilding from xint.dtx all documentation
-files as well as xint.tds.zip. It is for GNU/Linux-like (inc. Mac OS X)
-systems, with a teTeX like installation such as TeXLive. The Latexmk and
-Pandoc softwares are required to build all the documentation.
-
-1.  obtain xint.dtx and Makefile from
-    http://mirror.ctan.org/macros/generic/xint.
-
-2.  put them in an otherwise empty working repertory, run make or
-    equivalently make help for further instructions.
-
-
-Method D: installation starting with only xint.dtx
-
-Run etex xint.dtx to extract from xint.dtx all macro files as well as
-auxiliary files needed for building the documentation. Among them there
-is Makefile.mk. If you are on a GNU/Linux-type system, rename the file
-to Makefile and execute make on command line for further help. If you
-can’t use make read the contents of the Makefile for instructions.
-
-Finishing the installation in a TDS hierarchy:
-
--   move the style files to TDS:tex/generic/xint/
-
--   xint.dtx goes to TDS:source/generic/xint/
-
--   The documentation (xint.pdf, README.md,…) goes to
-    TDS:doc/generic/xint/
-
-Depending on the destination, it may then be necessary to refresh a
-filename database.
-
-
-
-LICENSE
-
-
-Copyright (C) 2013-2019 by Jean-Francois Burnol
-
-This Work may be distributed and/or modified under the conditions of the
-LaTeX Project Public License version 1.3c. This version of this license
-is in
-
-  http://www.latex-project.org/lppl/lppl-1-3c.txt
-
-and version 1.3 or later is part of all distributions of LaTeX version
-2005/12/01 or later.
-
-This Work has the LPPL maintenance status author-maintained.
-
-The Author of this Work is Jean-Francois Burnol.
-
-This Work consists of the source file xint.dtx and of its derived files:
-xintkernel.sty, xintcore.sty, xint.sty, xintfrac.sty, xintexpr.sty,
-xinttrig.sty, xintlog.sty, xintbinhex.sty, xintgcd.sty, xintseries.sty,
-xintcfrac.sty, xinttools.sty, xint.ins, xint.tex, README, README.md,
-README.html, README.pdf, CHANGES.md, CHANGES.html, CHANGES.pdf,
-pandoctpl.latex, doHTMLs.sh, doPDFs.sh, xint.dvi, xint.pdf, and
-Makefile.mk.
diff --git a/Master/texmf-dist/doc/generic/xint/README.html b/Master/texmf-dist/doc/generic/xint/README.html
deleted file mode 100644
index cee77f4af29..00000000000
--- a/Master/texmf-dist/doc/generic/xint/README.html
+++ /dev/null
@@ -1,133 +0,0 @@
-<!DOCTYPE html>
-<html xmlns="http://www.w3.org/1999/xhtml" lang="" xml:lang="">
-<head>
-  <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 1.3f" />
-  <title>README</title>
-  <style type="text/css">
-      code{white-space: pre-wrap;}
-      span.smallcaps{font-variant: small-caps;}
-      span.underline{text-decoration: underline;}
-      div.column{display: inline-block; vertical-align: top; width: 50%;}
-  </style>
-  <style type="text/css">
-    body{margin-left : 10%; margin-right : 15%; margin-top: 4ex; font-size: 12pt;}
-    pre   {white-space: pre-wrap; }
-    code  {white-space: pre-wrap; }
-    .mono {font-family: monospace;}
-  </style>
-  <!--[if lt IE 9]>
-    <script src="//cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv-printshiv.min.js"></script>
-  <![endif]-->
-</head>
-<body>
-<header>
-<h1 class="title">README</h1>
-<p class="author">xint 1.3f</p>
-<p class="date">2019/09/10</p>
-</header>
-<nav id="TOC">
-<ul>
-<li><a href="#aim">Aim</a></li>
-<li><a href="#usage">Usage</a><ul>
-<li><a href="#with-latex">With LaTeX</a></li>
-<li><a href="#with-tex">With TeX</a></li>
-</ul></li>
-<li><a href="#installation">Installation</a><ul>
-<li><a href="#method-a-using-the-package-manager-of-your-tex-distribution">Method A: using the package manager of your TeX distribution</a></li>
-<li><a href="#method-b-manual-installation-using-xint.tds.zip-and-unzip">Method B: manual installation using <code>xint.tds.zip</code> and <code>unzip</code></a></li>
-<li><a href="#method-c-manual-installation-using-makefile-and-xint.dtx">Method C: manual installation using <code>Makefile</code> and <code>xint.dtx</code></a></li>
-<li><a href="#method-d-installation-starting-with-only-xint.dtx">Method D: installation starting with only <code>xint.dtx</code></a></li>
-</ul></li>
-<li><a href="#license">License</a></li>
-</ul>
-</nav>
-<pre><code>Source:  xint.dtx 1.3f 2019/09/10 (doc 2019/09/10)
-Author:  Jean-Francois Burnol
-Info:    Expandable operations on big integers, decimals, fractions
-License: LPPL 1.3f</code></pre>
-<p>This <code>README</code> is also available as <code>README.pdf</code> and <code>README.html</code>.</p>
-<p>Change log is to be found in <code>CHANGES.pdf</code> or <code>CHANGES.html</code>.</p>
-<p>The user manual is <code>xint.pdf</code>, and the commented source code is available as <code>sourcexint.pdf</code>.</p>
-<h1 id="aim">Aim</h1>
-<p>The basic aim is provide <em>expandable</em> computations on integers, fractions, and floating point numbers. For example</p>
-<pre><code>\xinttheexpr reduce(37189719/183618963+11390170/17310720)^17\relax</code></pre>
-<p>will evaluate exactly the fraction; the result has 462 characters (including the fraction slash.) One can also work with dummy variables:</p>
-<pre><code>\xinttheexpr mul(add(x(x+1)(x+2), x=y..y+15), y=171286,98762,9296)\relax</code></pre>
-<p>evaluates to <code>15979066346135829902328007959448563667099190784</code>.</p>
-<p>Float computations are possible at an adjustable precision (default 16).</p>
-<pre><code>\xintDigits:=48;\xintthefloatexpr 123_456_789^1_000.5\relax
--&gt;3.63692761822782679930738270515740797370813691938e8095</code></pre>
-<p>(as this example shows the underscore character can be used to separate visually digits, one can also use the space character for that purpose).</p>
-<p>Square-root and the four operations achieve correct rounding in the given arbitrary precision.</p>
-<p>Trigonometric functions (direct and inverse) are available with a maximal precision of 60 digits.</p>
-<p>Logarithms and exponentials are available using the <a href="http://www.ctan.org/pkg/poormanlog">poormanlog</a> package which provides only 8 or 9 digits of precision. This will be increased in future.</p>
-<h1 id="usage">Usage</h1>
-<p>It is possible to use the package both with Plain (<code>\input xintexpr.sty</code>) or with LaTeX (<code>\usepackage{xintexpr}</code>).</p>
-<h2 id="with-latex">With LaTeX</h2>
-<pre><code>\usepackage{xint}       % expandable arithmetic with big integers
-\usepackage{xintfrac}   % decimal numbers, fractions, floats
-\usepackage{xinttools}  % expandable and non expandable loops
-\usepackage{xintexpr}   % expressions with infix operators</code></pre>
-<p>The <code>xinttrig</code> and <code>xintlog</code> packages are loaded automatically by <code>xintexpr</code> and will refuse to be loaded directly.</p>
-<p>Further packages: <code>xintbinhex</code>, <code>xintgcd</code>, <code>xintseries</code> and <code>xintcfrac</code>.</p>
-<p>Main dependencies are handled automatically. For example <code>xintexpr</code> automatically loads <code>xinttools</code> and <code>xintfrac</code> (which itself loads <code>xint</code>). Hexadecimal input requires explicit loading of <code>xintbinhex</code>.</p>
-<p>Package <code>xintcore</code> is the subset of <code>xint</code> providing only the five operations on big integers: <code>\xintiiAdd</code>, <code>\xintiiMul</code>, …</p>
-<p>The LaTeX package <a href="http://www.ctan.org/pkg/bnumexpr">bnumexpr</a> defines a more light-weight parser of arithmetical expressions using big integers, which supports only the four operations, the modulo operation, the power operation, and the factorial. By default it uses the macros from <code>xintcore</code> but this can be customized.</p>
-<p>The LaTeX package <a href="http://www.ctan.org/pkg/polexpr">polexpr</a> is based upon <code>xintexpr</code> and allows formal algebra with polynomials, and finding all real roots with arbitrary precision.</p>
-<h2 id="with-tex">With TeX</h2>
-<p>One does for example:</p>
-<pre><code>\input xintexpr.sty</code></pre>
-<p>This will automatically load <code>xintfrac.sty</code>, <code>xinttrig.sty</code>, <code>xintlog.sty</code> and <code>xinttools.sty</code>. The packages may be loaded in any catcode context such that letters, digits, <code>\</code> and <code>%</code> have their standard catcodes.</p>
-<p><code>xintcore.sty</code> and <code>xinttools.sty</code> both import <code>xintkernel.sty</code> which has the catcode handler and package identifier and defines a few utilities such as <code>\oodef/\fdef</code>, <code>\xint_dothis/\xint_orthat</code>, or <code>\xintLength</code>.</p>
-<p>Since <code>1.3b</code>, <code>xintkernel.sty</code> also provides <code>\xintUniformDeviate</code> which is a wrapper of the engine <code>\pdfuniformdeviate</code> or <code>\uniformdeviate</code> done to guarantee more uniformity of the pseudo-random integers.</p>
-<h1 id="installation">Installation</h1>
-<h2 id="method-a-using-the-package-manager-of-your-tex-distribution">Method A: using the package manager of your TeX distribution</h2>
-<p><code>xint</code> is included in <a href="http://tug.org/texlive/">TeXLive</a> (hence also <a href="http://tug.org/mactex/">MacTeX</a>) and <a href="http://www.miktex.org/">MikTeX</a>.</p>
-<p>There can be a few days of delay between apparition of a new version on <a href="http://www.ctan.org/pkg/xint">CTAN</a> and availability via the distribution package manager.</p>
-<h2 id="method-b-manual-installation-using-xint.tds.zip-and-unzip">Method B: manual installation using <code>xint.tds.zip</code> and <code>unzip</code></h2>
-<p>Assumes a GNU/Linux-like system (or Mac OS X).</p>
-<ol type="1">
-<li><p>obtain <code>xint.tds.zip</code> from CTAN: <a href="http://mirror.ctan.org/install/macros/generic/xint.tds.zip" class="uri">http://mirror.ctan.org/install/macros/generic/xint.tds.zip</a></p></li>
-<li><p>cd to the download repertory and issue:</p>
-<pre><code> unzip xint.tds.zip -d &lt;TEXMF&gt;</code></pre>
-<p>where <code>&lt;TEXMF&gt;</code> is a suitable TDS-compliant destination repertory. For example, with TeXLive:</p>
-<ul>
-<li><p>Linux, standard access rights, hence sudo is needed, installation into the “local” tree:</p>
-<pre><code>  sudo unzip xint.tds.zip -d /usr/local/texlive/texmf-local
-  sudo texhash /usr/local/texlive/texmf-local</code></pre></li>
-<li><p>Mac OS X, installation into user home folder (no sudo needed, and it is recommended to not have a ls-R file there, hence no texhash):</p>
-<pre><code>  unzip xint.tds.zip -d  ~/Library/texmf</code></pre></li>
-</ul></li>
-</ol>
-<h2 id="method-c-manual-installation-using-makefile-and-xint.dtx">Method C: manual installation using <code>Makefile</code> and <code>xint.dtx</code></h2>
-<p>The Makefile automatizes rebuilding from <code>xint.dtx</code> all documentation files as well as <code>xint.tds.zip</code>. It is for GNU/Linux-like (inc. Mac OS X) systems, with a teTeX like installation such as TeXLive. The <a href="http://personal.psu.edu/jcc8/software/latexmk/">Latexmk</a> and <a href="http://johnmacfarlane.net/pandoc/">Pandoc</a> softwares are required to build all the documentation.</p>
-<ol type="1">
-<li><p>obtain <code>xint.dtx</code> and <code>Makefile</code> from <a href="http://mirror.ctan.org/macros/generic/xint" class="uri">http://mirror.ctan.org/macros/generic/xint</a>.</p></li>
-<li><p>put them in an otherwise empty working repertory, run <code>make</code> or equivalently <code>make help</code> for further instructions.</p></li>
-</ol>
-<h2 id="method-d-installation-starting-with-only-xint.dtx">Method D: installation starting with only <code>xint.dtx</code></h2>
-<p>Run <code>etex xint.dtx</code> to extract from <code>xint.dtx</code> all macro files as well as auxiliary files needed for building the documentation. Among them there is <code>Makefile.mk</code>. If you are on a GNU/Linux-type system, rename the file to <code>Makefile</code> and execute <code>make</code> on command line for further help. If you can’t use <code>make</code> read the contents of the <code>Makefile</code> for instructions.</p>
-<p>Finishing the installation in a TDS hierarchy:</p>
-<ul>
-<li><p>move the style files to <code>TDS:tex/generic/xint/</code></p></li>
-<li><p><code>xint.dtx</code> goes to <code>TDS:source/generic/xint/</code></p></li>
-<li><p>The documentation (xint.pdf, README.md,…) goes to <code>TDS:doc/generic/xint/</code></p></li>
-</ul>
-<p>Depending on the destination, it may then be necessary to refresh a filename database.</p>
-<h1 id="license">License</h1>
-<div class="mono">
-<p>Copyright (C) 2013-2019 by Jean-Francois Burnol</p>
-<p>This Work may be distributed and/or modified under the conditions of the LaTeX Project Public License version 1.3c. This version of this license is in</p>
-<blockquote>
-<p><a href="http://www.latex-project.org/lppl/lppl-1-3c.txt" class="uri">http://www.latex-project.org/lppl/lppl-1-3c.txt</a></p>
-</blockquote>
-<p>and version 1.3 or later is part of all distributions of LaTeX version 2005/12/01 or later.</p>
-<p>This Work has the LPPL maintenance status <code>author-maintained</code>.</p>
-<p>The Author of this Work is Jean-Francois Burnol.</p>
-This Work consists of the source file xint.dtx and of its derived files: xintkernel.sty, xintcore.sty, xint.sty, xintfrac.sty, xintexpr.sty, xinttrig.sty, xintlog.sty, xintbinhex.sty, xintgcd.sty, xintseries.sty, xintcfrac.sty, xinttools.sty, xint.ins, xint.tex, README, README.md, README.html, README.pdf, CHANGES.md, CHANGES.html, CHANGES.pdf, pandoctpl.latex, doHTMLs.sh, doPDFs.sh, xint.dvi, xint.pdf, and Makefile.mk.
-</div>
-</body>
-</html>
diff --git a/Master/texmf-dist/doc/generic/xint/README.md b/Master/texmf-dist/doc/generic/xint/README.md
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+% README
+% xint 1.4
+% 2020/01/31
+
+    Source:  xint.dtx 1.4 2020/01/31 (doc 2020/01/31)
+    Author:  Jean-Francois Burnol
+    Info:    Expandable operations on big integers, decimals, fractions
+    License: LPPL 1.3c
+
+Aim and usage
+=============
+
+The basic aim is provide *expandable* computations on integers,
+fractions, and floating point numbers.  For example, with fractions:
+
+    \xinteval{reduce(37189719/183618963+11390170/17310720)^17}
+
+The result has `462` characters (forward slash included.)
+One can also work with dummy variables:
+
+    \xinteval{mul(add(x(x+1)(x+2), x=y..y+15), y=171286,98762,9296)}
+
+and do computations with floating point numbers at an adjustable
+precision (default `16`).
+
+    \xintDigits:=48;\xintfloateval{123_456_789^10_000.5}
+    expands to 1.56866129625858270633170234772583710433908855336e80919
+
+Release `1.4` adds support for nested structures:
+
+    \xintthealign\xintexpr ndseq(1/(i+j), i=1..5; j=1..5)\relax
+
+will print on the page
+
+    [[ 1/2, 1/3, 1/4, 1/5, 1/6  ],
+     [ 1/3, 1/4, 1/5, 1/6, 1/7  ],
+     [ 1/4, 1/5, 1/6, 1/7, 1/8  ],
+     [ 1/5, 1/6, 1/7, 1/8, 1/9  ],
+     [ 1/6, 1/7, 1/8, 1/9, 1/10 ]]
+
+The four operations and the square-root extraction achieve so-called
+*correct rounding* in the given arbitrary precision.
+
+Trigonometric functions (direct and inverse) are available up to a
+maximal precision of about `58` digits. Logarithms and exponentials are
+currently evaluated only with `8` or `9` digits precision.
+
+It is possible to use the package both with Plain (`\input xintexpr.sty`)
+or with the LaTeX macro format (`\usepackage{xintexpr}`).
+
+Installation
+============
+
+`xint` is included in [TeXLive](http://tug.org/texlive/) (hence
+[MacTeX](http://tug.org/mactex/) also) and in
+[MikTeX](http://www.miktex.org/). Thus, use the package manager to
+update your distribution.
+
+Alternatives:
+
+- download
+   [`xint.tds.zip`](http://mirror.ctan.org/install/macros/generic/xint.tds.zip)
+   and install in a suitable TDS-compliant repertory via `unzip`. "admin"
+   privilges might be needed, as well as a file database rebuild (`texhash`).
+   For example, on macos x, installation into user home folder (no `sudo`,
+   and no `texhash` as it is recommended to not have a ls-R file there)
+
+        unzip xint.tds.zip -d  ~/Library/texmf
+
+- all files can be extracted using `etex xint.dtx`, or `make` if the
+  `Makefile` included in the CTAN upload is present; see the file `INSTALL`,
+  if present, else read the help in extracted file `Makefile.mk`.
+
+Documentation
+=============
+
+`README.md`: this file
+
+`CHANGES.html`: change log as relevant to end users
+  (`texdoc --list xint`)
+
+`xint.pdf`: user manual
+
+`sourcexint.pdf`: commented source code
+   (`texdoc --list xint` or `texdoc sourcexint`)
+
+Requirements
+============
+
+Attention, release `1.4` requires the `\expanded` primitive available
+in all major TeX engines since TeXLive 2019.
+
+License
+=======
+
+Copyright (C) 2013-2020 by Jean-Francois Burnol
+
+This Work may be distributed and/or modified under the
+conditions of the LaTeX Project Public License version 1.3c.
+This version of this license is in
+
+> <http://www.latex-project.org/lppl/lppl-1-3c.txt>
+
+and version 1.3 or later is part of all distributions of
+LaTeX version 2005/12/01 or later.
+
+This Work has the LPPL maintenance status `author-maintained`.
+
+The Author of this Work is `Jean-Francois Burnol`.
+
+This Work consists of the files `Makefile`, `INSTALL`, and `xint.dtx`
+and its extracted and derived files inclusive of the documentation
+files `xint.pdf`, `sourcexint.pdf` and `CHANGES.html`.
+
+See `xint.pdf` for contact information.
+
diff --git a/Master/texmf-dist/doc/generic/xint/README.pdf b/Master/texmf-dist/doc/generic/xint/README.pdf
deleted file mode 100644
index 9fa9fe6008e..00000000000
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diff --git a/Master/texmf-dist/doc/generic/xint/sourcexint.pdf b/Master/texmf-dist/doc/generic/xint/sourcexint.pdf
index 7a2465e3163..3cf21147b98 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 d81acf490b6..2ba88c84fe2 100644
--- a/Master/texmf-dist/doc/generic/xint/xint.pdf
+++ b/Master/texmf-dist/doc/generic/xint/xint.pdf
author	Karl Berry <karl@freefriends.org>	2020-02-01 22:09:55 +0000
committer	Karl Berry <karl@freefriends.org>	2020-02-01 22:09:55 +0000
commit	3cac8298f5b8b21ddd1aecbea42a135a9c5e4cb8 (patch)
tree	9920a659b7ad3860aeb7f391e499b7ccf7f886f8 /Master/texmf-dist/doc
parent	22cb4622b403ec9e42484b7af858243a417e2d12 (diff)