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@@ -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 1.4e" />
+ <meta name="author" content="xint 1.4f" />
<title>CHANGE LOG</title>
<style type="text/css">
code{white-space: pre-wrap;}
@@ -25,56 +25,60 @@
<body>
<header>
<h1 class="title">CHANGE LOG</h1>
-<p class="author">xint 1.4e</p>
-<p class="date">2021/05/05</p>
+<p class="author">xint 1.4f</p>
+<p class="date">2021/05/10</p>
</header>
<nav id="TOC">
<ul>
-<li><a href="#e-20210505"><code>1.4e (2021/05/05)</code></a><ul>
+<li><a href="#f-20210510"><code>1.4f (2021/05/10)</code></a><ul>
<li><a href="#breaking-changes">Breaking changes</a></li>
-<li><a href="#new-features">New features</a></li>
<li><a href="#bug-fixes">Bug fixes</a></li>
</ul></li>
-<li><a href="#d-20210329"><code>1.4d (2021/03/29)</code></a><ul>
+<li><a href="#e-20210505"><code>1.4e (2021/05/05)</code></a><ul>
<li><a href="#breaking-changes-1">Breaking changes</a></li>
+<li><a href="#new-features">New features</a></li>
<li><a href="#bug-fixes-1">Bug fixes</a></li>
</ul></li>
-<li><a href="#c-20210220"><code>1.4c (2021/02/20)</code></a><ul>
+<li><a href="#d-20210329"><code>1.4d (2021/03/29)</code></a><ul>
+<li><a href="#breaking-changes-2">Breaking changes</a></li>
<li><a href="#bug-fixes-2">Bug fixes</a></li>
</ul></li>
+<li><a href="#c-20210220"><code>1.4c (2021/02/20)</code></a><ul>
+<li><a href="#bug-fixes-3">Bug fixes</a></li>
+</ul></li>
<li><a href="#b-20200225"><code>1.4b (2020/02/25)</code></a><ul>
<li><a href="#future">Future</a></li>
<li><a href="#new-features-1">New features</a></li>
-<li><a href="#bug-fixes-3">Bug fixes</a></li>
+<li><a href="#bug-fixes-4">Bug fixes</a></li>
</ul></li>
<li><a href="#a-20200219"><code>1.4a (2020/02/19)</code></a><ul>
-<li><a href="#breaking-changes-2">Breaking changes</a></li>
+<li><a href="#breaking-changes-3">Breaking changes</a></li>
<li><a href="#new-features-2">New features</a></li>
-<li><a href="#bug-fixes-4">Bug fixes</a></li>
+<li><a href="#bug-fixes-5">Bug fixes</a></li>
</ul></li>
<li><a href="#section"><code>1.4 (2020/01/31)</code></a><ul>
-<li><a href="#breaking-changes-3">Breaking changes</a></li>
+<li><a href="#breaking-changes-4">Breaking changes</a></li>
<li><a href="#improvements-and-new-features">Improvements and new features</a></li>
-<li><a href="#bug-fixes-5">Bug fixes</a></li>
+<li><a href="#bug-fixes-6">Bug fixes</a></li>
<li><a href="#todo">TODO</a></li>
</ul></li>
<li><a href="#f-20190910"><code>1.3f (2019/09/10)</code></a><ul>
<li><a href="#improvements-and-new-features-1">Improvements and new features</a></li>
-<li><a href="#bug-fixes-6">Bug fixes</a></li>
+<li><a href="#bug-fixes-7">Bug fixes</a></li>
</ul></li>
<li><a href="#e-20190405"><code>1.3e (2019/04/05)</code></a><ul>
-<li><a href="#breaking-changes-4">Breaking changes</a></li>
+<li><a href="#breaking-changes-5">Breaking changes</a></li>
<li><a href="#improvements-and-new-features-2">Improvements and new features</a></li>
-<li><a href="#bug-fixes-7">Bug fixes</a></li>
+<li><a href="#bug-fixes-8">Bug fixes</a></li>
</ul></li>
<li><a href="#d-20190106"><code>1.3d (2019/01/06)</code></a><ul>
-<li><a href="#breaking-changes-5">Breaking changes</a></li>
+<li><a href="#breaking-changes-6">Breaking changes</a></li>
<li><a href="#improvements-and-new-features-3">Improvements and new features</a></li>
-<li><a href="#bug-fixes-8">Bug fixes</a></li>
+<li><a href="#bug-fixes-9">Bug fixes</a></li>
</ul></li>
<li><a href="#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-9">Bug fixes</a></li>
+<li><a href="#bug-fixes-10">Bug fixes</a></li>
</ul></li>
<li><a href="#b-20180518"><code>1.3b (2018/05/18)</code></a><ul>
<li><a href="#improvements-and-new-features-5">Improvements and new features</a></li>
@@ -82,85 +86,85 @@
<li><a href="#a-20180307"><code>1.3a (2018/03/07)</code></a><ul>
<li><a href="#removed">Removed</a></li>
<li><a href="#improvements-and-new-features-6">Improvements and new features</a></li>
-<li><a href="#bug-fixes-10">Bug fixes</a></li>
+<li><a href="#bug-fixes-11">Bug fixes</a></li>
</ul></li>
<li><a href="#section-1"><code>1.3 (2018/03/01)</code></a><ul>
-<li><a href="#breaking-changes-6">Breaking changes</a></li>
+<li><a href="#breaking-changes-7">Breaking changes</a></li>
<li><a href="#improvements-and-new-features-7">Improvements and new features</a></li>
</ul></li>
<li><a href="#q-20180206"><code>1.2q (2018/02/06)</code></a><ul>
<li><a href="#improvements-and-new-features-8">Improvements and new features</a></li>
-<li><a href="#bug-fixes-11">Bug fixes</a></li>
+<li><a href="#bug-fixes-12">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-7">Breaking changes</a></li>
+<li><a href="#breaking-changes-8">Breaking changes</a></li>
<li><a href="#improvements-and-new-features-9">Improvements and new features</a></li>
-<li><a href="#bug-fixes-12">Bug fixes</a></li>
+<li><a href="#bug-fixes-13">Bug fixes</a></li>
</ul></li>
<li><a href="#o-20170829"><code>1.2o (2017/08/29)</code></a><ul>
-<li><a href="#breaking-changes-8">Breaking changes</a></li>
+<li><a href="#breaking-changes-9">Breaking changes</a></li>
<li><a href="#deprecated">Deprecated</a></li>
</ul></li>
<li><a href="#n-20170806"><code>1.2n (2017/08/06)</code></a><ul>
-<li><a href="#breaking-changes-9">Breaking changes</a></li>
+<li><a href="#breaking-changes-10">Breaking changes</a></li>
<li><a href="#improvements-and-new-features-10">Improvements and new features</a></li>
</ul></li>
<li><a href="#m-20170731"><code>1.2m (2017/07/31)</code></a><ul>
-<li><a href="#breaking-changes-10">Breaking changes</a></li>
+<li><a href="#breaking-changes-11">Breaking changes</a></li>
<li><a href="#improvements-and-new-features-11">Improvements and new features</a></li>
-<li><a href="#bug-fixes-13">Bug fixes</a></li>
+<li><a href="#bug-fixes-14">Bug fixes</a></li>
</ul></li>
<li><a href="#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-14">Bug fixes</a></li>
+<li><a href="#bug-fixes-15">Bug fixes</a></li>
</ul></li>
<li><a href="#k-20170106"><code>1.2k (2017/01/06)</code></a><ul>
-<li><a href="#breaking-changes-11">Breaking changes</a></li>
+<li><a href="#breaking-changes-12">Breaking changes</a></li>
<li><a href="#improvements-and-new-features-13">Improvements and new features</a></li>
-<li><a href="#bug-fixes-15">Bug fixes</a></li>
+<li><a href="#bug-fixes-16">Bug fixes</a></li>
</ul></li>
<li><a href="#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-16">Bug fixes</a></li>
+<li><a href="#bug-fixes-17">Bug fixes</a></li>
</ul></li>
<li><a href="#i-20161213"><code>1.2i (2016/12/13)</code></a><ul>
-<li><a href="#breaking-changes-12">Breaking changes</a></li>
+<li><a href="#breaking-changes-13">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-17">Bug fixes</a></li>
+<li><a href="#bug-fixes-18">Bug fixes</a></li>
</ul></li>
<li><a href="#h-20161120"><code>1.2h (2016/11/20)</code></a><ul>
<li><a href="#improvements-and-new-features-16">Improvements and new features</a></li>
-<li><a href="#bug-fixes-18">Bug fixes</a></li>
+<li><a href="#bug-fixes-19">Bug fixes</a></li>
</ul></li>
<li><a href="#g-20160319"><code>1.2g (2016/03/19)</code></a><ul>
-<li><a href="#breaking-changes-13">Breaking changes</a></li>
+<li><a href="#breaking-changes-14">Breaking changes</a></li>
<li><a href="#improvements-and-new-features-17">Improvements and new features</a></li>
</ul></li>
<li><a href="#f-20160312"><code>1.2f (2016/03/12)</code></a><ul>
-<li><a href="#breaking-changes-14">Breaking changes</a></li>
+<li><a href="#breaking-changes-15">Breaking changes</a></li>
<li><a href="#improvements-and-new-features-18">Improvements and new features</a></li>
-<li><a href="#bug-fixes-19">Bug fixes</a></li>
+<li><a href="#bug-fixes-20">Bug fixes</a></li>
</ul></li>
<li><a href="#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-20">Bug fixes</a></li>
+<li><a href="#bug-fixes-21">Bug fixes</a></li>
</ul></li>
<li><a href="#d-20151118"><code>1.2d (2015/11/18)</code></a><ul>
<li><a href="#improvements-and-new-features-20">Improvements and new features</a></li>
-<li><a href="#bug-fixes-21">Bug fixes</a></li>
+<li><a href="#bug-fixes-22">Bug fixes</a></li>
</ul></li>
<li><a href="#c-20151116"><code>1.2c (2015/11/16)</code></a><ul>
<li><a href="#improvements-and-new-features-21">Improvements and new features</a></li>
-<li><a href="#bug-fixes-22">Bug fixes</a></li>
+<li><a href="#bug-fixes-23">Bug fixes</a></li>
</ul></li>
<li><a href="#b-20151029"><code>1.2b (2015/10/29)</code></a><ul>
-<li><a href="#bug-fixes-23">Bug fixes</a></li>
+<li><a href="#bug-fixes-24">Bug fixes</a></li>
</ul></li>
<li><a href="#a-20151019"><code>1.2a (2015/10/19)</code></a><ul>
<li><a href="#improvements-and-new-features-22">Improvements and new features</a></li>
-<li><a href="#bug-fixes-24">Bug fixes</a></li>
+<li><a href="#bug-fixes-25">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>
@@ -170,11 +174,11 @@
<li><a href="#b-20150831"><code>1.1b (2015/08/31)</code></a></li>
<li><a href="#a-20141107"><code>1.1a (2014/11/07)</code></a></li>
<li><a href="#section-3"><code>1.1 (2014/10/28)</code></a><ul>
-<li><a href="#breaking-changes-15">Breaking changes</a></li>
+<li><a href="#breaking-changes-16">Breaking changes</a></li>
<li><a href="#removed-4">Removed</a></li>
<li><a href="#deprecated-1">Deprecated</a></li>
<li><a href="#improvements-and-new-features-24">Improvements and new features</a></li>
-<li><a href="#bug-fixes-25">Bug fixes</a></li>
+<li><a href="#bug-fixes-26">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>
@@ -202,45 +206,62 @@
<li><a href="#section-10"><code>1.0 (2013/03/28)</code></a></li>
</ul>
</nav>
-<pre><code>Source: xint.dtx 1.4e 2021/05/05 (doc 2021/05/05)
+<pre><code>Source: xint.dtx 1.4f 2021/05/10 (doc 2021/05/10)
Author: Jean-Francois Burnol
Info: Expandable operations on big integers, decimals, fractions
License: LPPL 1.3c</code></pre>
+<h2 id="f-20210510"><code>1.4f (2021/05/10)</code></h2>
+<h3 id="breaking-changes">Breaking changes</h3>
+<ul>
+<li><p><strong>xintexpr</strong>: <code>\xintieval{[-D]...}</code>, which rounds to a multiple of <code>1eD</code> for <code>D</code> positive now <em>does not insert the trailing zeros</em> (as done at <code>1.4e</code>) <em>nor a scientific part</em> <code>eD</code> (as prior to <code>1.4e</code>). The use case envisioned is for the quantized value to be used with an appropriate unit, for example <code>k</code> for <code>D=3</code> or <code>M</code> for <code>D=6</code> etc… Sorry for the very long process which was needed to reach this final decision.</p></li>
+<li><p><strong>xintexpr</strong>: for Digits beyond the officially supported range for accurate math functions, i.e. for <code>D&gt;62</code>, computations were still done and printed with full number of digits, but the extra digits were meaningless; they now operate on and output mantissas limited to <code>min(D,64)</code> digits.</p></li>
+<li><p><strong>xintexpr</strong>: for powers <code>a^b</code> with Digits at most <code>8</code>, the number <code>a</code> is now float-rounded to Digits before computation, as is done for <code>Digits&gt;8</code>; previously <code>9</code> significant digits were kept.</p></li>
+<li><p><strong>xintexpr</strong>: further changes in the computation of powers, see the bug fixes below.</p></li>
+<li><p><strong>xintexpr</strong>: the <code>float_()</code> function got renamed into <code>float_dgt()</code>.</p></li>
+</ul>
+<h3 id="bug-fixes">Bug fixes</h3>
+<ul>
+<li><p><strong>xintexpr</strong>: the documentation said <code>float_()</code> function had been renamed <code>float_dgt()</code> but actually that was not yet the case.</p></li>
+<li><p><strong>xintexpr</strong>: powers <code>a^b</code> (with exponent <code>b</code> neither integer nor half-integer) stopped being accurate regarding the last digits for <code>|b|</code> about <code>1000</code> and beyond. Except for <code>0.8&lt;a&lt;1.25</code> for which accuracy was maintained up to about <code>|b|=10^7</code>. Fixed via keeping the same suitable number of extra digits for internal computations of logarithms, independently of whether <code>a</code> is close to <code>1</code> or not.</p></li>
+<li><p><strong>xintexpr</strong>: powers <code>a^b</code> in <code>\xinteval</code> with <code>|b|</code> an integer at least <code>10000</code> were paradoxically computed with less accuracy than in <code>\xintfloateval</code>… although they were documented to be handled exactly the same in the two parsers.</p></li>
+<li><p><strong>xintexpr</strong>: powers <code>a^b</code> for Digits at most <code>8</code> unconditionally used <code>log10()/pow10()</code> approach but due to the limited accuracy of the poorman logarithm (<code>9</code> fractional digits) this was inaccurate already for <code>b</code> about <code>100</code>. So, the handling is now as for Digits at least <code>9</code>, i.e. integer and half-integer exponents are handled via the legacy <code>\xintFloatPower/\xintFloatSqrt</code> allowing arbitrarily big exponents. It is advised to split big powers with non integer non half integer exponents into a product; this is not done internally to avoid costly overhead for possibly rare use cases.</p></li>
+<li><p><strong>xintexpr</strong>: the invalid input <code>(-1)^2.5</code> triggered an undefined control sequence error if Digits was at most <code>8</code>.</p></li>
+</ul>
<h2 id="e-20210505"><code>1.4e (2021/05/05)</code></h2>
<p>This section might be incomplete at time of release, it will be extended if need be after the author gets some rest.</p>
-<h3 id="breaking-changes">Breaking changes</h3>
+<h3 id="breaking-changes-1">Breaking changes</h3>
<ul>
<li><p><strong>xintlog</strong>: <code>\poormanloghack</code> now a no-op.</p></li>
<li><p><strong>xinttrig</strong>: loading the package does not define left-over variables holding the values of the inverse factorials used in the sine and cosine series.</p></li>
<li><p><strong>xintexpr</strong>: the output format of <code>\xinteval</code>, which uses <code>\xintFracToSci,</code> has changed. In particular, if the number has a power of ten part, it is not output with an integer mantissa, but with a scientific mantissa <code>d.d...</code> with always at least one digit after the decimal mark (possibly <code>0</code>) and trailing zeros are trimmed out. This is the same output format as used for <code>\xintfloateval</code>, apart of course from the fact that the mantissa lengths are not limited.</p></li>
-<li><p><strong>xintexpr</strong>: the output format of <code>\xintfloateval</code>, which uses <code>\xintPFloat</code>, changed. The <code>\xintfloatexprPrintOne</code> macro now expects to be used with either one or two arguments, the first one being within brackets not braces. It defaults to <code>\xintPFloat</code>.</p></li>
+<li><p><strong>xintexpr</strong>: the output format of <code>\xintfloateval</code>, which uses <code>\xintPFloat</code>, changed. The <code>\xintfloatexprPrintOne</code> macro now expects to be used with either one or two arguments, the first one being within brackets not braces.</p></li>
<li><p><strong>xintexpr</strong>: when using <code>\xintieval{[D]...}</code> optional <code>[D]</code> with a negative <code>D</code>, which triggers quantization to a positive power of ten, the output (if not the zero value) will be an integer with <code>N=abs(D)</code> explicit trailing zeros, not an integer mantissa followed by <code>eN</code>.</p></li>
<li><p><strong>xintexpr</strong>: <code>\xinteval</code> will not compute powers <code>a^N</code> exactly if <code>N</code> in absolute value is at least the (rounded) quotient of <code>10000</code> by the number of digits of <code>a</code>; it will then use the logarithm/exponential (in base 10) approach, according to the prevailing Digits setting.</p></li>
<li><p><strong>xintexpr</strong>: <code>\xintdeffloatvar</code> now always rounds the assigned value to the target precision. Formerly, inputs actually involving no float operations, such as for example <code>\xintexpr1/20!\relax</code> (in contrast to <code>1/20!</code>), or an explicit single number having more digits than the precision, got stored “as is” in the defined variable, without pre-rounding to the Digits precision.</p></li>
-<li><p><strong>xintfrac</strong>:<code>\xintPFloat</code> and <code>\xintFracToSci</code> behave differently. The macro <code>\xintFracToSciE</code> does not exist anymore, as <code>\xintFracToSci</code> in the case of scientific exponents hands over the process to <code>\xintPFloat</code> (without the rounding to Digits, of course).</p></li>
+<li><p><strong>xintfrac</strong>:<code>\xintPFloat</code> and <code>\xintFracToSci</code> have both been modified. The macro <code>\xintFracToSciE</code> does not exist anymore, as <code>\xintFracToSci</code> in the case of scientific exponents hands over the process to <code>\xintPFloat</code> (without the rounding to Digits, of course).</p></li>
<li><p><strong>xintexpr</strong>: messages sent under <code>\xintverbosetrue</code> regime to the log file do not enclose the variable names in straight double quotes <code>&quot;...&quot;</code> anymore.</p></li>
</ul>
<h3 id="new-features">New features</h3>
<ul>
<li><p><strong>xintlog</strong>: now working up to <code>62</code> digits. The legacy faster <code>poormanlog</code>-based macros are kept for computations with Digits up to <code>8</code>. Fractional powers are now available both in <code>xinteval</code> and <code>xintfloateval</code>, per default.</p></li>
-<li><p><strong>xinttrig</strong>: now working up to <code>62</code> digits and with increased accuracy. Special faster mode at <code>8</code> digits or less.</p></li>
+<li><p><strong>xinttrig</strong>: now working up to <code>62</code> digits and with increased accuracy. Special faster (or not as slow if you prefer) mode at <code>8</code> digits or less.</p></li>
<li><p><strong>xintexpr</strong>: the constraints on the <code>\xintexprPrintOne</code> replacement macro, which defaults to <code>\xintFracToSci</code>, have been much simplified.</p></li>
<li><p><strong>xintexpr</strong>: <code>\xintiexprPrintOne</code> (defaults to <code>\xintDecToString</code>)</p></li>
<li><p><strong>xintfrac</strong>: <code>\xintPFloatE</code> may be redefined as a macro which fetches the scientific exponent as a mandatory argument delimited with a dot, and outputs a suitable formatted result (f-expandably), also delimited with a dot which will be removed by internal processing. The default however simply expands to the letter <code>e</code>.</p></li>
-<li><p><strong>xintfrac</strong>: <code>\xintDecToStringREZ</code></p></li>
+<li><p><strong>xintfrac</strong>: <code>\xintDecToStringREZ</code> is like <code>\xintDecToString</code> but starts by removing trailing zeroes.</p></li>
</ul>
-<h3 id="bug-fixes">Bug fixes</h3>
+<h3 id="bug-fixes-1">Bug fixes</h3>
<ul>
<li><strong>xintfrac</strong>, <strong>xintexpr</strong>: it was not possible to use <code>\xinttheDigits</code> in the right hand side of an <code>\xintDigits</code> assignment. For example: <code>\xintDigits*:=\numexpr\xinttheDigits+4;</code>. This is now allowed, and the same applies to the macro interface, for example <code>\xintSetDigits*{\xinttheDigits+4}</code>.</li>
</ul>
<h2 id="d-20210329"><code>1.4d (2021/03/29)</code></h2>
-<h3 id="breaking-changes-1">Breaking changes</h3>
+<h3 id="breaking-changes-2">Breaking changes</h3>
<ul>
<li><p><code>quo()</code> and <code>rem()</code> in <code>\xintiiexpr/\xintiieval</code> renamed to <code>iquo()</code> and <code>irem()</code>.</p></li>
<li><p>The output of <code>gcd()</code> and <code>lcm()</code> as applied to fractions is now always in lowest terms.</p></li>
<li><p>The log message to report a variable creation (if <code>\xintverbosetrue</code>) does not use (double) quotes anymore around the name. By the way, quotes were never used for function names.</p></li>
</ul>
-<h3 id="bug-fixes-1">Bug fixes</h3>
+<h3 id="bug-fixes-2">Bug fixes</h3>
<ul>
<li><p>Ever since <code>1.3</code> the <code>quo()</code> and <code>rem()</code> functions in <code>\xintexpr</code> (not the ones in <code>\xintiiexpr</code>) were broken as their (officially deprecated) support macros had been removed! They had somewhat useless definitions anyway. They have now been officially removed from the syntax. Their siblings in <code>\xintiieval</code> were renamed to <code>iquo()</code> and <code>irem()</code>.</p></li>
<li><p>Sadly, <code>gcd()</code> was broken in <code>\xintexpr</code> since <code>1.4</code>, if the first argument vanished. And <code>gcd()</code> was broken in <code>\xintiiexpr</code> since <code>1.3d</code> if <em>any</em> argument vanished. I did have a unit test! (which obviously was too limited …)</p>
@@ -248,7 +269,7 @@ License: LPPL 1.3c</code></pre>
<li><p>The <code>first()</code> and <code>last()</code> functions, if used as arguments to numerical functions such as <code>sqr()</code> inside an <code>\xintdeffunc</code> caused the defined function to be broken.</p></li>
</ul>
<h2 id="c-20210220"><code>1.4c (2021/02/20)</code></h2>
-<h3 id="bug-fixes-2">Bug fixes</h3>
+<h3 id="bug-fixes-3">Bug fixes</h3>
<ul>
<li>Fix <code>1.4</code> regression which broke syntax <code>varname(...)</code> which supposedly is allowed and inserts a tacit multiplication.</li>
</ul>
@@ -267,13 +288,13 @@ License: LPPL 1.3c</code></pre>
<li><p>Chaining of comparison operators (e.g. <code>x&lt;y&lt;z</code>) as in Python (but all comparisons are done even if one is found false) and l3fp.</p></li>
<li><p>It was possible since <code>1.4</code>’s <code>\xintFracToSciE</code> to configure the separator between mantissas and exponents in the output of <code>\xinteval</code> but strangely there was no way to customize the output of <code>\xintfloateval</code>. The added <code>\xintPFloatE</code> fixes this.</p></li>
</ul>
-<h3 id="bug-fixes-3">Bug fixes</h3>
+<h3 id="bug-fixes-4">Bug fixes</h3>
<ul>
<li><code>\xintieval{[D]...}</code> with a negative <code>D</code> (a feature added at <code>1.4a</code>) used erroneously a catcode 12 <code>e</code> in output, which moreover remained immuned to the <code>\xintFracToSciE</code> setting.</li>
</ul>
<h2 id="a-20200219"><code>1.4a (2020/02/19)</code></h2>
<p>All changes regard the <strong>xintexpr</strong> module.</p>
-<h3 id="breaking-changes-2">Breaking changes</h3>
+<h3 id="breaking-changes-3">Breaking changes</h3>
<ul>
<li>The macros implementing customization of <code>\xintthealign</code> have modified meanings and names.</li>
</ul>
@@ -283,13 +304,13 @@ License: LPPL 1.3c</code></pre>
<li><p>The optional argument <code>[D]</code> to <code>\xintieval/\xintiexpr</code> can be negative, with the same meaning as the non-negative case, i.e. rounding to an integer multiple of <code>10^(-D)</code>.</p>
<p>The same applies to the functions <code>trunc()</code> and <code>round()</code>. And to the <code>\xintTrunc</code>, <code>\xintRound</code>, <code>\xintiTrunc</code>, and <code>\xintiRound</code> macros of <strong>xintfrac</strong>.</p></li>
</ul>
-<h3 id="bug-fixes-4">Bug fixes</h3>
+<h3 id="bug-fixes-5">Bug fixes</h3>
<ul>
<li><p>Usage of <code>round()</code> and <code>trunc()</code> within <code>\xintdeffunc</code> got broken at <code>1.4</code>.</p></li>
<li><p><code>add()</code> and <code>mul()</code> were supposedly accepting the <code>omit</code>, <code>abort</code> and <code>break()</code> keywords since <code>1.4</code> but this was broken.</p></li>
</ul>
<h2 id="section"><code>1.4 (2020/01/31)</code></h2>
-<h3 id="breaking-changes-3">Breaking changes</h3>
+<h3 id="breaking-changes-4">Breaking changes</h3>
<p>Please note that this list may still be incomplete. If not otherly specified all items regard the <strong>xintexpr</strong> module.</p>
<ul>
<li><p>The <code>\expanded</code> primitive (TeXLive 2019) is <strong>required</strong>. This does not affect the macro layer <strong>xintcore</strong>, <strong>xint</strong>, <strong>xintfrac</strong>, <strong>xinttools</strong> (yet).</p></li>
@@ -335,7 +356,7 @@ License: LPPL 1.3c</code></pre>
<li><p>Function declarations are able to parse a much wider part of the syntax, but some severe limitations remain. Refer to the user manual for related information.</p></li>
<li><p>We have made an effort on some error messages, and when working interactively in a shell it may even be sometimes possible to insert for example a correct variable or function name in place of the not recognized one. But don’t expect miracles when trying to intervene in the midst of a purely expandable expansion…</p></li>
</ul>
-<h3 id="bug-fixes-5">Bug fixes</h3>
+<h3 id="bug-fixes-6">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>
@@ -351,13 +372,13 @@ License: LPPL 1.3c</code></pre>
<li><p><strong>xintexpr</strong>: add starred variants <code>\xintDigits*</code> and <code>\xintSetDigits*</code> which execute <code>\xintreloadxinttrig</code>.</p>
<p>Revert 1.3e ban on usage of <code>\xinteval</code> et al. inside expressions by <code>\xintdeffunc</code>. And make them usable also inside macro definitions via <code>\xintNewExpr</code>.</p></li>
</ul>
-<h3 id="bug-fixes-6">Bug fixes</h3>
+<h3 id="bug-fixes-7">Bug fixes</h3>
<ul>
<li><p><strong>xintexpr</strong>: fix bug preventing usage of <code>\xintdefefunc</code> to define a function without variables.</p>
<p>Fix some issue with <code>\xintfloatexpr[D]..\relax</code> if used inside an expression parsed by <code>\xintdeffunc</code> et al.</p></li>
</ul>
<h2 id="e-20190405"><code>1.3e (2019/04/05)</code></h2>
-<h3 id="breaking-changes-4">Breaking changes</h3>
+<h3 id="breaking-changes-5">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>
@@ -371,12 +392,12 @@ License: LPPL 1.3c</code></pre>
<li><p><strong>xintexpr</strong>: <code>\xintensuredummy</code>, <code>\xintrestorelettervar</code>.</p></li>
<li><p>The optional argument of <code>\xintfloatexpr</code> or <code>\xintfloateval</code> (it must be at start of braced argument) can be negative; it then means to trim (and round) from the output at float precision that many least significant digits.</p></li>
</ul>
-<h3 id="bug-fixes-7">Bug fixes</h3>
+<h3 id="bug-fixes-8">Bug fixes</h3>
<ul>
<li>Some bugfixes related to user functions with no variables at all; they were dysfunctional.</li>
</ul>
<h2 id="d-20190106"><code>1.3d (2019/01/06)</code></h2>
-<h3 id="breaking-changes-5">Breaking changes</h3>
+<h3 id="breaking-changes-6">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>
@@ -390,7 +411,7 @@ License: LPPL 1.3c</code></pre>
<li><p><strong>xintexpr</strong>: functions <code>isone()</code> and <code>isint()</code>.</p></li>
<li><p><strong>xintexpr</strong>: <code>\xinteval</code>, <code>\xintieval</code>, <code>\xintiieval</code>, and <code>\xintfloateval</code> as synonyms to <code>\xinttheexpr...\relax</code> etc…, but with the (comma-separated) expression as a usual braced macro argument.</p></li>
</ul>
-<h3 id="bug-fixes-8">Bug fixes</h3>
+<h3 id="bug-fixes-9">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>
@@ -403,7 +424,7 @@ License: LPPL 1.3c</code></pre>
<li><p><strong>xintexpr</strong>: <code>\xintdefvar</code>, <code>\xintdeffunc</code> and their variants try to set the catcode of the semi-colon which delimits their arguments; of course this will not work if that catcode is already frozen.</p></li>
<li><p><code>\xintUniformDeviate</code> is better documented and <code>sourcexint.pdf</code> is better hyperlinked and includes indices for the macros defined by each package.</p></li>
</ul>
-<h3 id="bug-fixes-9">Bug fixes</h3>
+<h3 id="bug-fixes-10">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>
@@ -429,12 +450,12 @@ License: LPPL 1.3c</code></pre>
<li><p><strong>xintfrac</strong>: <code>\xintREZ</code> is faster on inputs having one hundred digits or more.</p></li>
<li><p>Added to the user manual mention of macros such as <code>\xintDivFloor</code>, <code>\xintMod</code>, <code>\xintModTrunc</code>, which had been left out so far.</p></li>
</ul>
-<h3 id="bug-fixes-10">Bug fixes</h3>
+<h3 id="bug-fixes-11">Bug fixes</h3>
<ul>
<li><strong>xintexpr</strong>: the mechanism for adjunction to the expression parsers of user defined functions was refactored and improved at previous release <code>1.3</code>: in particular recursive definitions became possible. But an oversight made these recursive functions quite inefficient (to remain polite.) This release fixes the problem.</li>
</ul>
<h2 id="section-1"><code>1.3 (2018/03/01)</code></h2>
-<h3 id="breaking-changes-6">Breaking changes</h3>
+<h3 id="breaking-changes-7">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>
@@ -452,12 +473,12 @@ License: LPPL 1.3c</code></pre>
<ul>
<li><strong>xintexpr</strong>: tacit multiplication extended to cases such as <code>3!4!5!</code> or <code>(1+2)3</code>.</li>
</ul>
-<h3 id="bug-fixes-11">Bug fixes</h3>
+<h3 id="bug-fixes-12">Bug fixes</h3>
<ul>
<li><strong>xintcore</strong>: sadly, refactoring at <code>1.2l</code> of subtraction left an extra character in an inner macro causing breakage in some rare circumstances. This should not have escaped our test suite!</li>
</ul>
<h2 id="p-20171205"><code>1.2p (2017/12/05)</code></h2>
-<h3 id="breaking-changes-7">Breaking changes</h3>
+<h3 id="breaking-changes-8">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>
@@ -471,7 +492,7 @@ License: LPPL 1.3c</code></pre>
<li><p><strong>xintexpr</strong>: <code>\xintdefvar</code>’s syntax is extended to allow simultaneous assignments. Examples: <code>\xintdefvar x1, x2, x3 := 1, 3**10, 3**20;</code> or <code>\xintdefiivar A, B := B, A 'mod' B;</code> for already defined variables <code>A</code> and <code>B</code>.</p></li>
<li><p><strong>xintexpr</strong>: added <code>divmod()</code> to the built-in functions. It is associated with floored division, like the Python language <code>divmod()</code>. Related support macros added to <strong>xintcore</strong>, and <strong>xintfrac</strong>.</p></li>
</ul>
-<h3 id="bug-fixes-12">Bug fixes</h3>
+<h3 id="bug-fixes-13">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>
@@ -479,7 +500,7 @@ License: LPPL 1.3c</code></pre>
<li><p>various documentation fixes; in particular, the partial dependency of <strong>xintcfrac</strong> on <strong>xinttools</strong> had not been mentioned.</p></li>
</ul>
<h2 id="o-20170829"><code>1.2o (2017/08/29)</code></h2>
-<h3 id="breaking-changes-8">Breaking changes</h3>
+<h3 id="breaking-changes-9">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>
@@ -495,7 +516,7 @@ License: LPPL 1.3c</code></pre>
<li><p><strong>xint</strong>: <code>\xintNot</code> was renamed to <code>\xintNOT</code>, former denomination is deprecated. See also item about Boolean logic macros in the <em>Incompatible Changes</em> section.</p></li>
</ul>
<h2 id="n-20170806"><code>1.2n (2017/08/06)</code></h2>
-<h3 id="breaking-changes-9">Breaking changes</h3>
+<h3 id="breaking-changes-10">Breaking changes</h3>
<ul>
<li><strong>xintbinhex</strong> does not load package <strong>xintcore</strong> anymore, but only <strong>xintkernel</strong>.</li>
</ul>
@@ -505,7 +526,7 @@ License: LPPL 1.3c</code></pre>
<li><p>Macros of <strong>xintbinhex</strong> have been improved for speed and increased maximal sizes of allowable inputs.</p></li>
</ul>
<h2 id="m-20170731"><code>1.2m (2017/07/31)</code></h2>
-<h3 id="breaking-changes-10">Breaking changes</h3>
+<h3 id="breaking-changes-11">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>
@@ -514,7 +535,7 @@ License: LPPL 1.3c</code></pre>
<ul>
<li><strong>xintbinhex</strong>: all macros have been rewritten using techniques from the 1.2 release (they had remained unmodified since <code>1.08</code> of <code>2013/06/07</code>.) The new macros are faster but limited to a few thousand digits. The <code>1.08</code> routines could handle tens of thousands of digits, but not in a reasonable time.</li>
</ul>
-<h3 id="bug-fixes-13">Bug fixes</h3>
+<h3 id="bug-fixes-14">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>
@@ -535,14 +556,14 @@ License: LPPL 1.3c</code></pre>
<p>The situation with expressions is unchanged: syntax such as <code>\xintexpr \numexpr1+2\relax</code> is illegal as the ending <code>\relax</code> token will get swallowed by the <code>\numexpr</code>; but it is needed by the <code>xintexpr</code>-ession parser, hence the parser will expand forward and presumably end with in an “illegal token” error, or provoke some low-level TeX error (N.B.: a closing brace <code>}</code> for example can not terminate an <code>xintexpr</code>-ession, the parser must find a <code>\relax</code> token at some point). Thus there must be in this example a second <code>\relax</code>.</p></li>
<li><p>experimental code for error conditions; there is no complete user interface yet, it is done in preparation for next major release and is completely unstable and undocumented.</p></li>
</ul>
-<h3 id="bug-fixes-14">Bug fixes</h3>
+<h3 id="bug-fixes-15">Bug fixes</h3>
<ul>
<li><p><strong>xintbinhex</strong>: since <code>1.2 (2015/10/10)</code>, <code>\xintHexToDec</code> was broken due to an undefined macro (it was in <code>xint.sty</code>, but the module by itself is supposedly dependent only upon <code>xintcore.sty</code>).</p></li>
<li><p><strong>xintgcd</strong>: macro <code>\xintBezout</code> produced partially wrong output if one of its two arguments was zero.</p></li>
<li><p><strong>xintfrac</strong>: the manual said one could use directly <code>\numexpr</code> compatible expressions in arithmetic macros (without even a <code>\numexpr</code> encapsulation) if they were expressed with up to 8 tokens. There was a bug if these 8 tokens evaluated to zero. The bug has been fixed, and up to 9 tokens are now accepted. But it is simpler to use <code>\the\numexpr</code> prefix and not to worry about the token count… The ending <code>\relax</code> is now un-needed.</p></li>
</ul>
<h2 id="k-20170106"><code>1.2k (2017/01/06)</code></h2>
-<h3 id="breaking-changes-11">Breaking changes</h3>
+<h3 id="breaking-changes-12">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>
@@ -554,7 +575,7 @@ License: LPPL 1.3c</code></pre>
<li><p>added <code>\xintiSqrtR</code>, there was only <code>\xintiiSqrtR</code> alongside <code>\xintiSqrt</code> and <code>\xintiiSqrt</code> (<strong>xint</strong>).</p></li>
<li><p>added non public <code>\xintLastItem:f:csv</code> to <strong>xinttools</strong> for faster <code>last()</code> function, and improved <code>\xintNewExpr</code> compatibility. Also <code>\xintFirstItem:f:csv</code>.</p></li>
</ul>
-<h3 id="bug-fixes-15">Bug fixes</h3>
+<h3 id="bug-fixes-16">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>
@@ -570,12 +591,12 @@ License: LPPL 1.3c</code></pre>
</ol></li>
<li><p>significant documentations tweaks (inclusive of suppressing things!), and among them two beautiful hyperlinked tables with both horizontal and vertical rules which bring the documentation of the <strong>xintexpr</strong> syntax to a kind of awe-inspiring perfection… except that implementation of some math functions is still lacking.</p></li>
</ul>
-<h3 id="bug-fixes-16">Bug fixes</h3>
+<h3 id="bug-fixes-17">Bug fixes</h3>
<ul>
<li>fix two <code>1.2i</code> regressions caused by undefined macros (<code>\xintNthElt</code> in certain branches and <code>[list][N]</code> item extraction in certain cases.) The test files existed but were not executed prior to release. Automation in progress.</li>
</ul>
<h2 id="i-20161213"><code>1.2i (2016/12/13)</code></h2>
-<h3 id="breaking-changes-12">Breaking changes</h3>
+<h3 id="breaking-changes-13">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>
@@ -602,7 +623,7 @@ License: LPPL 1.3c</code></pre>
<li><p>the documentation has again been (slightly) re-organized; it has a new sub-section on the Miller-Rabin primality test, to illustrate some use of <code>\xintNewFunction</code> for recursive definitions.</p></li>
<li><p>the documentation has dropped the LaTeX “command” terminology (which had been used initially in 2013 for some forgotten reasons and should have been removed long ago) and uses only the more apt “macro”, as after all, all of <strong>xint</strong> is about expansion of macros (plus the use of <code>\numexpr</code>).</p></li>
</ul>
-<h3 id="bug-fixes-17">Bug fixes</h3>
+<h3 id="bug-fixes-18">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>
@@ -612,7 +633,7 @@ License: LPPL 1.3c</code></pre>
<li><p>new macro <code>\xintNewFunction</code> in <strong>xintexpr</strong> which allows to extend the parser syntax with functions in situations where <code>\xintdeffunc</code> is not usable (typically, because dummy variables are used over a not yet determined range of values because it depends on the variables).</p></li>
<li><p>after three years of strict obedience to <code>xint</code> prefix, now <code>\thexintexpr</code>, <code>\thexintiexpr</code>, <code>\thexintfloatexpr</code>, and <code>\thexintiiexpr</code> are provided as synonyms to <code>\xinttheexpr</code>, etc…</p></li>
</ul>
-<h3 id="bug-fixes-18">Bug fixes</h3>
+<h3 id="bug-fixes-19">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>
@@ -620,7 +641,7 @@ License: LPPL 1.3c</code></pre>
<li><p>the <code>add</code> and <code>mul</code> from <strong>xintexpr</strong>, which work with dummy variables since <code>1.1</code>, raised an error since <code>1.2c 2015/11/16</code> when the dummy variable was given an empty range (or list) of values, rather than producing respectively <code>0</code> and <code>1</code> as formerly.</p></li>
</ul>
<h2 id="g-20160319"><code>1.2g (2016/03/19)</code></h2>
-<h3 id="breaking-changes-13">Breaking changes</h3>
+<h3 id="breaking-changes-14">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>
@@ -634,7 +655,7 @@ License: LPPL 1.3c</code></pre>
<li><p>the syntax of expressions is described in a devoted chapter of the documentation; an example shows how to implement (expandably) the Brent-Salamin algorithm for computation of Pi using <code>iter</code> in a float expression.</p></li>
</ul>
<h2 id="f-20160312"><code>1.2f (2016/03/12)</code></h2>
-<h3 id="breaking-changes-14">Breaking changes</h3>
+<h3 id="breaking-changes-15">Breaking changes</h3>
<ul>
<li>no more <code>\xintFac</code> macro but <code>\xintiFac/\xintiiFac/\xintFloatFac</code>.</li>
</ul>
@@ -652,7 +673,7 @@ License: LPPL 1.3c</code></pre>
<li><p>(TeXperts only) the macros defined (internally) from <code>\xintdeffunc</code> et al. constructs do not incorporate an initial <code>\romannumeral</code> anymore.</p></li>
<li><p>renewed desperate efforts at improving the documentation by random shuffling of sections and well thought additions; cuts were considered and even performed.</p></li>
</ul>
-<h3 id="bug-fixes-19">Bug fixes</h3>
+<h3 id="bug-fixes-20">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>
@@ -666,7 +687,7 @@ License: LPPL 1.3c</code></pre>
<li><p>a space in <code>\xintdeffunc f(x)&lt;space&gt;:= expression ;</code> is now accepted.</p></li>
<li><p>documentation enhancements: the <em>Quick Sort</em> section with its included code samples has been entirely re-written; the <em>Commands of the xintexpr package</em> section has been extended and reviewed entirely.</p></li>
</ul>
-<h3 id="bug-fixes-20">Bug fixes</h3>
+<h3 id="bug-fixes-21">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>
@@ -679,7 +700,7 @@ License: LPPL 1.3c</code></pre>
<li><p>tacit multiplication applies to more cases, for example (x+y)z, and always ties more than standard * infix operator, e.g. x/2y is like x/(2*y).</p></li>
<li><p>some documentation enhancements, particularly in the chapter on xintexpr.sty, and also in the code source comments.</p></li>
</ul>
-<h3 id="bug-fixes-21">Bug fixes</h3>
+<h3 id="bug-fixes-22">Bug fixes</h3>
<ul>
<li>in <strong>xintcore</strong>: release <code>1.2c</code> had inadvertently broken the <code>\xintiiDivRound</code> macro.</li>
</ul>
@@ -689,12 +710,12 @@ License: LPPL 1.3c</code></pre>
<li><p>macros <code>\xintdeffunc</code>, <code>\xintdefiifunc</code>, <code>\xintdeffloatfunc</code> and boolean <code>\ifxintverbose</code>.</p></li>
<li><p>on-going code improvements and documentation enhancements, but stopped in order to issue this bugfix release.</p></li>
</ul>
-<h3 id="bug-fixes-22">Bug fixes</h3>
+<h3 id="bug-fixes-23">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-23">Bug fixes</h3>
+<h3 id="bug-fixes-24">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>
@@ -705,7 +726,7 @@ License: LPPL 1.3c</code></pre>
<li><p>added <code>\xintiiMaxof/\xintiiMinof</code> (<strong>xint</strong>).</p></li>
<li><p>TeX hackers only: replaced all code uses of <code>\romannumeral-`0</code> by the quicker <code>\romannumeral`&amp;&amp;@</code> (<code>^</code> being used as letter, had to find another character usable with catcode 7).</p></li>
</ul>
-<h3 id="bug-fixes-24">Bug fixes</h3>
+<h3 id="bug-fixes-25">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>
@@ -748,7 +769,7 @@ License: LPPL 1.3c</code></pre>
<li><p>various typographical fixes throughout the documentation, and a bit of clean up of the code comments. Improved <code>\Factors</code> example of nested <code>subs</code>, <code>rseq</code>, <code>iter</code> in <code>\xintiiexpr</code>.</p></li>
</ul>
<h2 id="section-3"><code>1.1 (2014/10/28)</code></h2>
-<h3 id="breaking-changes-15">Breaking changes</h3>
+<h3 id="breaking-changes-16">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>
@@ -806,7 +827,7 @@ License: LPPL 1.3c</code></pre>
<li><p><code>\xintthecoords</code> converts a comma separated list of an even number of items to the format expected by the <code>TikZ</code> <code>coordinates</code> syntax,</p></li>
<li><p>completely new version <code>\xintNewExpr</code>, <code>protect</code> function to handle external macros. The dollar sign <code>$</code> for place holders is not accepted anymore, only the standard macro parameter <code>#</code>. Not all constructs are compatible with <code>\xintNewExpr</code>.</p></li>
</ul>
-<h3 id="bug-fixes-25">Bug fixes</h3>
+<h3 id="bug-fixes-26">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>