texlive[59161] Master/texmf-dist: xint (10may21)
commits+karl at tug.org
commits+karl at tug.org
Mon May 10 21:49:04 CEST 2021
Revision: 59161
http://tug.org/svn/texlive?view=revision&revision=59161
Author: karl
Date: 2021-05-10 21:49:04 +0200 (Mon, 10 May 2021)
Log Message:
-----------
xint (10may21)
Modified Paths:
--------------
trunk/Master/texmf-dist/doc/generic/xint/CHANGES.html
trunk/Master/texmf-dist/doc/generic/xint/README.md
trunk/Master/texmf-dist/doc/generic/xint/sourcexint.pdf
trunk/Master/texmf-dist/doc/generic/xint/xint.pdf
trunk/Master/texmf-dist/source/generic/xint/xint.dtx
trunk/Master/texmf-dist/tex/generic/xint/xint.sty
trunk/Master/texmf-dist/tex/generic/xint/xintbinhex.sty
trunk/Master/texmf-dist/tex/generic/xint/xintcfrac.sty
trunk/Master/texmf-dist/tex/generic/xint/xintcore.sty
trunk/Master/texmf-dist/tex/generic/xint/xintexpr.sty
trunk/Master/texmf-dist/tex/generic/xint/xintfrac.sty
trunk/Master/texmf-dist/tex/generic/xint/xintgcd.sty
trunk/Master/texmf-dist/tex/generic/xint/xintkernel.sty
trunk/Master/texmf-dist/tex/generic/xint/xintlog.sty
trunk/Master/texmf-dist/tex/generic/xint/xintseries.sty
trunk/Master/texmf-dist/tex/generic/xint/xinttools.sty
trunk/Master/texmf-dist/tex/generic/xint/xinttrig.sty
Modified: trunk/Master/texmf-dist/doc/generic/xint/CHANGES.html
===================================================================
--- trunk/Master/texmf-dist/doc/generic/xint/CHANGES.html 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/doc/generic/xint/CHANGES.html 2021-05-10 19:49:04 UTC (rev 59161)
@@ -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>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>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<a<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>"..."</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 @@
<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 @@
<li><p>Chaining of comparison operators (e.g. <code>x<y<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 @@
<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 @@
<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 @@
<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 @@
<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 @@
<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 @@
<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 @@
<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 @@
<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 @@
<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 @@
<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 @@
<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 @@
<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 @@
<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>
@@ -535,7 +556,7 @@
<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>
@@ -542,7 +563,7 @@
<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 @@
<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 @@
</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 @@
<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 @@
<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<0</code> or <code>x<y</code>. This was unfortunate, and it now simply evaluates to zero in such cases.</p></li>
@@ -620,7 +641,7 @@
<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 @@
<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 @@
<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 @@
<li><p>a space in <code>\xintdeffunc f(x)<space>:= expression ;</code> is now accepted.</p></li>
<li><p>documentation enhancements: the <em>Quick Sort</em> section with its included code samples has been entirely re-written; the <em>Commands of the xintexpr package</em> section has been extended and reviewed entirely.</p></li>
</ul>
-<h3 id="bug-fixes-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 @@
<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 @@
<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 @@
<li><p>added <code>\xintiiMaxof/\xintiiMinof</code> (<strong>xint</strong>).</p></li>
<li><p>TeX hackers only: replaced all code uses of <code>\romannumeral-`0</code> by the quicker <code>\romannumeral`&&@</code> (<code>^</code> being used as letter, had to find another character usable with catcode 7).</p></li>
</ul>
-<h3 id="bug-fixes-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 @@
<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 @@
<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>
Modified: trunk/Master/texmf-dist/doc/generic/xint/README.md
===================================================================
--- trunk/Master/texmf-dist/doc/generic/xint/README.md 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/doc/generic/xint/README.md 2021-05-10 19:49:04 UTC (rev 59161)
@@ -1,8 +1,8 @@
% README
-% xint 1.4e
-% 2021/05/05
+% xint 1.4f
+% 2021/05/10
- Source: xint.dtx 1.4e 2021/05/05 (doc 2021/05/05)
+ 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
@@ -34,8 +34,10 @@
(@_1) 1267650600228229401496703205376
*cos(1);
(@_2) 0.5403023058681397
- *&fp32
- (./xintlog.sty) (./xinttrig.sty) fp32 mode (log and trig reloaded)
+ *&fp=32
+ (/usr/local/texlive/2021/texmf-dist/tex/generic/xint/xintlog.sty)
+ (/usr/local/texlive/2021/texmf-dist/tex/generic/xint/xinttrig.sty)
+ fp mode (log and trig reloaded at Digits=32)
*cos(1);
(@_3) 0.54030230586813971740093660744298
*3^1000;
@@ -43,13 +45,7 @@
*&exact
exact mode (floating point evaluations use 32 digits)
*3^1000;
- (@_5) 1322070819480806636890455259752144365965422032752148167664920368226828
- 5973467048995407783138506080619639097776968725823559509545821006189118653427252
- 5795367402762022519832080387801477422896484127439040011758861804112894781562309
- 4438061566173054086674490506178125480344405547054397038895817465368254916136220
- 8302685637785822902284163983078878969185564040848989376093732421718463599386955
- 1676501894058810906042608967143886410281435038564874716583201061436613217310276
- 8902855220001
+ (@_5) 132207081948080663689045525975... (trimmed for this README)
Installation
============
Modified: trunk/Master/texmf-dist/doc/generic/xint/sourcexint.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/doc/generic/xint/xint.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/source/generic/xint/xint.dtx
===================================================================
--- trunk/Master/texmf-dist/source/generic/xint/xint.dtx 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/source/generic/xint/xint.dtx 2021-05-10 19:49:04 UTC (rev 59161)
@@ -3,20 +3,20 @@
% Extract all files via "etex xint.dtx" and do "make help"
% or follow instructions from extracted README.md.
%<*dtx>
-\def\xintdtxtimestamp {Time-stamp: <05-05-2021 at 15:26:12 CEST>}
+\def\xintdtxtimestamp {Time-stamp: <10-05-2021 at 17:45:52 CEST>}
%</dtx>
%<*drv>
%% ---------------------------------------------------------------
-\def\xintdocdate {2021/05/05}
-\def\xintbndldate{2021/05/05}
-\def\xintbndlversion {1.4e}
+\def\xintdocdate {2021/05/10}
+\def\xintbndldate{2021/05/10}
+\def\xintbndlversion {1.4f}
%</drv>
%<readme>% README
%<changes>% CHANGE LOG
-%<readme|changes>% xint 1.4e
-%<readme|changes>% 2021/05/05
+%<readme|changes>% xint 1.4f
+%<readme|changes>% 2021/05/10
%<readme|changes>
-%<readme|changes> Source: xint.dtx 1.4e 2021/05/05 (doc 2021/05/05)
+%<readme|changes> Source: xint.dtx 1.4f 2021/05/10 (doc 2021/05/10)
%<readme|changes> Author: Jean-Francois Burnol
%<readme|changes> Info: Expandable operations on big integers, decimals, fractions
%<readme|changes> License: LPPL 1.3c
@@ -23,7 +23,7 @@
%<readme|changes>
%<*!readme&!changes&!dohtmlsh&!makefile>
%% ---------------------------------------------------------------
-%% The xint bundle 1.4e 2021/05/05
+%% The xint bundle 1.4f 2021/05/10
%% Copyright (C) 2013-2021 by Jean-Francois Burnol
%<xintkernel>%% xintkernel: Paraphernalia for the xint packages
%<xinttools>%% xinttools: Expandable and non-expandable utilities
@@ -70,8 +70,10 @@
(@_1) 1267650600228229401496703205376
*cos(1);
(@_2) 0.5403023058681397
- *&fp32
- (./xintlog.sty) (./xinttrig.sty) fp32 mode (log and trig reloaded)
+ *&fp=32
+ (/usr/local/texlive/2021/texmf-dist/tex/generic/xint/xintlog.sty)
+ (/usr/local/texlive/2021/texmf-dist/tex/generic/xint/xinttrig.sty)
+ fp mode (log and trig reloaded at Digits=32)
*cos(1);
(@_3) 0.54030230586813971740093660744298
*3^1000;
@@ -79,13 +81,7 @@
*&exact
exact mode (floating point evaluations use 32 digits)
*3^1000;
- (@_5) 1322070819480806636890455259752144365965422032752148167664920368226828
- 5973467048995407783138506080619639097776968725823559509545821006189118653427252
- 5795367402762022519832080387801477422896484127439040011758861804112894781562309
- 4438061566173054086674490506178125480344405547054397038895817465368254916136220
- 8302685637785822902284163983078878969185564040848989376093732421718463599386955
- 1676501894058810906042608967143886410281435038564874716583201061436613217310276
- 8902855220001
+ (@_5) 132207081948080663689045525975... (trimmed for this README)
Installation
============
@@ -156,6 +152,64 @@
%</readme>--------------------------------------------------------
%<*changes>-------------------------------------------------------
+`1.4f (2021/05/10)`
+----
+
+### Breaking changes
+
+ - **xintexpr**: `\xintieval{[-D]...}`, which rounds to a multiple of
+ `1eD` for `D` positive now *does not insert the trailing zeros* (as
+ done at `1.4e`) *nor a scientific part* `eD` (as prior to `1.4e`).
+ The use case envisioned is for the quantized value to be used with an
+ appropriate unit, for example `k` for `D=3` or `M` for `D=6`
+ etc... Sorry for the very long process which was needed to reach this
+ final decision.
+
+ - **xintexpr**: for Digits beyond the officially supported range for
+ accurate math functions, i.e. for `D>62`, 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
+ `min(D,64)` digits.
+
+ - **xintexpr**: for powers `a^b` with Digits at most `8`, the number
+ `a` is now float-rounded to Digits before computation, as is done for
+ `Digits>8`; previously `9` significant digits were kept.
+
+ - **xintexpr**: further changes in the computation of powers, see the
+ bug fixes below.
+
+ - **xintexpr**: the `float_()` function got renamed into `float_dgt()`.
+
+### Bug fixes
+
+ - **xintexpr**: the documentation said `float_()` function had been
+ renamed `float_dgt()` but actually that was not yet the case.
+
+ - **xintexpr**: powers `a^b` (with exponent `b` neither integer nor
+ half-integer) stopped being accurate regarding the last digits for
+ `|b|` about `1000` and beyond. Except for `0.8<a<1.25` for which
+ accuracy was maintained up to about `|b|=10^7`. Fixed via keeping
+ the same suitable number of extra digits for internal computations of
+ logarithms, independently of whether `a` is close to `1` or not.
+
+ - **xintexpr**: powers `a^b` in `\xinteval` with `|b|` an integer at
+ least `10000` were paradoxically computed with less accuracy than in
+ `\xintfloateval`... although they were documented to be handled
+ exactly the same in the two parsers.
+
+ - **xintexpr**: powers `a^b` for Digits at most `8` unconditionally
+ used `log10()/pow10()` approach but due to the limited accuracy of
+ the poorman logarithm (`9` fractional digits) this was inaccurate
+ already for `b` about `100`. So, the handling is now as for Digits at
+ least `9`, i.e. integer and half-integer exponents are handled via
+ the legacy `\xintFloatPower/\xintFloatSqrt` 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.
+
+ - **xintexpr**: the invalid input `(-1)^2.5` triggered an undefined
+ control sequence error if Digits was at most `8`.
+
`1.4e (2021/05/05)`
----
@@ -182,7 +236,7 @@
- **xintexpr**: the output format of `\xintfloateval`, which uses
`\xintPFloat`, changed. The `\xintfloatexprPrintOne` macro now
expects to be used with either one or two arguments, the first one
- being within brackets not braces. It defaults to `\xintPFloat`.
+ being within brackets not braces.
- **xintexpr**: when using `\xintieval{[D]...}` optional `[D]` with a
negative `D`, which triggers quantization to a positive power of ten,
@@ -202,8 +256,8 @@
than the precision, got stored "as is" in the defined variable,
without pre-rounding to the Digits precision.
- - **xintfrac**:`\xintPFloat` and `\xintFracToSci` behave
- differently. The macro `\xintFracToSciE` does not exist anymore, as
+ - **xintfrac**:`\xintPFloat` and `\xintFracToSci` have both been
+ modified. The macro `\xintFracToSciE` does not exist anymore, as
`\xintFracToSci` in the case of scientific exponents hands over the
process to `\xintPFloat` (without the rounding to Digits, of course).
@@ -219,7 +273,8 @@
`xintfloateval`, per default.
- **xinttrig**: now working up to `62` digits and with increased
- accuracy. Special faster mode at `8` digits or less.
+ accuracy. Special faster (or not as slow if you prefer) mode at `8`
+ digits or less.
- **xintexpr**: the constraints on the `\xintexprPrintOne` replacement
macro, which defaults to `\xintFracToSci`, have been much simplified.
@@ -232,7 +287,8 @@
also delimited with a dot which will be removed by internal
processing. The default however simply expands to the letter `e`.
- - **xintfrac**: `\xintDecToStringREZ`
+ - **xintfrac**: `\xintDecToStringREZ` is like `\xintDecToString` but
+ starts by removing trailing zeroes.
### Bug fixes
@@ -4035,17 +4091,19 @@
\end{everbatim}
\end{itemize}
-\xintexprname is a package to do expandable computations, either exactly
-(i.e.\@ with fractions) with arbitrarily big inputs, or in the sense of
-floating point numbers (logarithm, exponential, sine, cosine, ...) up to 62
-digits.
+\xintexprname is a package to do expandable computations, either exactly with
+arbitrarily big inputs (fractions, arbitrarily long decimal expansions, ...),
+or in the sense of floating point numbers (logarithm, exponential, sine,
+cosine, ...). The math functions are implemented up to \dtt{62} digits of
+precision. The square root (as well of course as the four operations) achieve
+correct rounding in arbitrary precision.
The syntax to modify the precision used for floating point evaluations is
\begin{everbatim}
\xintDigits*:= <Number>;
\end{everbatim}
-Use the |*|, else the scientific libraries will not be reloaded. See
-\csbxint{Digits}. The current precision is available as \csbxint{theDigits},
+Use the |*| (\csbxint{Digits*}), else the scientific libraries will not be
+reloaded. The current precision is available as \csbxint{theDigits},
but in this documentation I might be using simply |Digits| to refer to it.
@@ -4058,8 +4116,9 @@
\begin{everbatim}
rlwrap etex xintsession
[...hit RET once...]
- Magic words: `&pause' (or `;'), `&help', `&bye', and toggles
- `&exact', `&fp', `&fp16', `&fp24', `&fp32', `&int', `&pol'.
+ Magic words: `&pause' (or `;'), `&help', `&bye',
+ `&exact', `&fp', `&int', `&pol'.
+ Say e.g. `&fp=24' to activate floating point mode with Digits=24.
Starting in exact mode (floating point evaluations use 16 digits)
(Please type a command or say `\end')
*2^100;
@@ -4066,8 +4125,10 @@
(@_1) 1267650600228229401496703205376
*cos(1);
(@_2) 0.5403023058681397
-*&fp32
-(./xintlog.sty) (./xinttrig.sty) fp32 mode (log and trig reloaded)
+*&fp=32
+(/usr/local/texlive/2021/texmf-dist/tex/generic/xint/xintlog.sty)
+(/usr/local/texlive/2021/texmf-dist/tex/generic/xint/xinttrig.sty)
+fp mode (log and trig reloaded at Digits=32)
*cos(1);
(@_3) 0.54030230586813971740093660744298
*3^1000;
@@ -4081,10 +4142,10 @@
4438061566173054086674490506178125480344405547054397038895817465368254916136220
8302685637785822902284163983078878969185564040848989376093732421718463599386955
1676501894058810906042608967143886410281435038564874716583201061436613217310276
-8902855220001
+890285522000
*&bye
Did I say something wrong?
-Session transcript written on xintsession-210505_11h05.tex
+Session transcript written on xintsession-210509_14h55.tex
No pages of output.
Transcript written on xintsession.log.
\end{everbatim}
@@ -4103,7 +4164,7 @@
quality of the document). Reports welcome.%
%
\footnote{Thanks to Jürgen Gilg for keeping the author motivated and
- helping proof-read the documentation.}
+ helping proof-read the 1.4 documentation.}
\subsection{Improved support for logarithm, exponential, sine, etc... at
the \texttt{1.4e} release of \texttt{2021/05/05}}
@@ -4114,18 +4175,107 @@
See \xintlogname and \xinttrigname.
For Digits up to \dtt{8}, a special more approximate implementation is used,
-and the functions achieve the ``correct rounding'' (particularly at |Digits=8
-or 7|) less often, but are significantly faster than working with \dtt{9}
-digits or more. The precision is largely
-enough for plots:
-\begin{everbatim}
-\xintDigits*:=8;% do floating point computations at only 8 digits of precision
-\end{everbatim}
-For some more information on the limitations at Digits set to \dtt{8} or less
-relative to the logarithm and exponential in particular, refer to the comments
-in |sourcexint.pdf| at the start of the \xintlogname chapter.
+and the functions achieve the ``correct rounding'' (particularly at |Digits|
+equal to \dtt{8} or \dtt{7}) less often, but are significantly faster
+(especially logarithm, exponential, powers) than working with \dtt{9} digits
+or more. The achieved precision is largely enough for plots (but see some
+information relative to powers below). For some information on the limitations
+at Digits set to \dtt{8} or less relative to the logarithm in particular,
+refer to the comments in |sourcexint.pdf| at the start of the \xintlogname
+chapter. Or check this footnote.%
+%
+\footnote{Most notably, for inputs near \dtt{1}, the logarithm in this special
+ \dtt{$D\leq8$} mode is far from achieving accuracy in floating point sense, as
+ it is obtained with \dtt{9} fractional fixed point digits, the more of them
+ being zeros the closer the input is close to \dtt{1}.}
+Important notes regarding powers:\IMPORTANT{}
+\begin{enumerate}[noitemsep]
+\item Powers |a^b| (or |a**b|, or |pow(a,b)|) in \csbxint{eval} with an
+ integer exponent are computed exactly if
+ the output is estimated to not exceed by much \dtt{10000} digits. Else, or
+ for non-integer exponents, they are computed as in \csbxint{floateval}
+ (see \csbxint{Pow}).
+\item Powers |a^b| in \csbxint{floateval} are computed differently according
+ to the exponent |b|:
+ \begin{itemize}[noitemsep]
+ \item if |b| is an integer or half-integer the legacy \csbxint{FloatPower}
+ (and, for |b| half-integer, \csbxint{FloatSqrt}) are used; they work in
+ arbitrary precision, so the result is produced with a full-size
+ mantissa, even if |Digits| is more than \dtt{62},
+ \item else the computation goes via the |10^(b*log10(a))| formula (done
+ internally with increased accuracy) and the mantissa lengths will be
+ limited in output to the smallest of |Digits| or \dtt{64}. In this
+ branch the last digits of the mantissa will start being wrong if |b|
+ becomes about (in absolute value) \dtt{100000000}. If you really need to
+ compute powers with exponents that large or larger, it is recommended to
+ decompose the exponent as a sum of the nearest integer or half-integer
+ and a fractional part and express the power as a product. This is not
+ done automatically as it would add some overhead in general for some a
+ priori very rare use cases. And recall that the decimal exponents of
+ final and intermediate results should obey the \TeX\ bound for integers
+ anyhow, i.e. be at most (in absolute value) \dtt{\number"7FFFFFFF}, add some
+ safety margin...
+ \item if |Digits| is at most \dtt{8}, logarithms are computed faster but
+ with less accuracy (internally, between \dtt{8} and \dtt{9} \emph{fixed
+ point fractional digits} accuracy) and powers |a^b| lose accuracy in
+ last digits quickly as |b| rises. Here is what I observed in limited
+ random tests:
+ \begin{itemize}[noitemsep]
+ \item for |b| integer or half-integer, all our tested samples gave
+ correct rounding to \dtt{8} digits and we tested this with the
+ exponent |b| up to \dtt{1000000000.5},
+ \item for |b| neither integer nor half-integer and |1<b<10|, we observed
+ roughly \dtt{8} correct digits in between \dtt{80}\% and \dtt{90}\% of
+ cases and the remaining cases had only a \dtt{1ulp} error.
+ \item for |b| neither integer nor half-integer and |10^e<b<10^(e+1)|,
+ then roughly \dtt{8-e} digits are correct for around
+ \dtt{90}\% of cases and there is a one unit error in the last of
+ those digits in the remaining cases.
+ \end{itemize}
+ To maintain higher accuracy, split the input as |a^n a^h| with |n|
+ integer or half-integer nearest to |b|. After having considered (and
+ implemented) the method, decision was made to not incorporate it as it
+ would induce serious overhead generally speaking. The |a^b| with
+ fractional exponent |b| such that |abs(b)<10| are currently computed
+ with at most \dtt{1ulp} error in the vast majority of cases it seems,
+ which is largely precise enough for plots, and then speed matters
+ most. Larger exponents can be handled (since |1.4f|) via manually
+ implementing the splitting trick, as described above.
+ \end{itemize}
+\end{enumerate}
+The documentation of the legacy macro \csbxint{FloatPower} (which is used for
+powers with integer and half-integer exponents) explains it has a guaranteed
+error bound of |0.52ulp|, in arbitrary precision. Generally speaking, the math
+functions added at |1.4e| target even smaller errors (but only up to \dtt{62}
+digits), something of the order of |0.505ulp|, and in practice they seem to
+achieve even better than \dtt{99\%} of correct rounding probability (at least
+in their natural ranges, and it varies according to the value of
+|Digits|). Perhaps in future I will re-examine whether it is worthwile to
+increase a bit the theoretical accuracy of \csbxint{FloatPower}, as I have not
+had the time to really measure systematically its pratical accuracy, all
+anecdotical evidence showing it is good.
+
+\subsection{Breaking changes at the \texttt{1.4f} release}
+
+\begin{enumerate}[noitemsep]
+\item \csbxint{ieval}|{[-D]...}| which quantizes to a multiple of |1eD| when
+ |D| is positive now does \emph{NOT append the |D| trailing zeroes anymore}!\IMPORTANT
+\item \func{float\string_dgt} is the new name of |float_()|, as already
+ documented but
+ not yet done at |1.4e|.
+\item Powers in \csbxint{floateval} with big exponents are computed with more
+ accuracy.
+\item For |Digits| at most \dtt{8}, powers in \csbxint{floateval} with integer
+ or half-integer exponents do not use \func{log10}/\func{pow10} method but
+ (as for |Digits| at least \dtt{9}) the \csbxint{FloatPower} based approach,
+ allowing very big integer of half-integer exponents while keeping accuracy.
+\item Computations with math functions in \csbxint{floateval} at a setting of
+ |Digits| higher than \dtt{62} will produce an output limited to the smallest
+ of |Digits| and \dtt{64} digits.
+\end{enumerate}
+
\subsection{Breaking changes at the \texttt{1.4e} release}
In principle, I try for breaking changes regarding output to happen only at
@@ -4162,6 +4312,9 @@
of ten) the output does not use scientific notation but is an integer ending
with explicit zeros.
+ Update: at |1.4f| this was changed again.\IMPORTANT{} Now no trailing zeroes
+ are added at all!
+
Nothing was changed to output for the case of a positive |[D]| (i.e.\@
rounding to |D| figures after decimal point). One now only needs to
configure the new \csbxint{iexprPrintOne} to be \csbxint{DecToStringREZ} in
@@ -4213,7 +4366,7 @@
\item Chaining of \hyperlink{\detokenize{prec-10}}{comparison operators} à la
Python (no short-circuit, though) and |l3fp|.
- \item \csbxint{PFloatE} to specify like \csbxint{FracToSciE} (now defunct at
+ \item \csbxint{PFloatE} to specify like \csa{xintFracToSciE} (now defunct at
|1.4e|) does for
\csbxint{eval} since |1.4| the separator to use between mantissa and
exponent in the output of \csbxint{floateval} output.
@@ -4222,12 +4375,8 @@
to PS-Tricks |\listplot|).
\item The optional argument |[D]| to \csbxint{iexpr} (or \csbxint{ieval})
- can be negative, with the same meaning as the non-negative case, i.e.
- rounding to an integer multiple of |1e-D| (as formerly, for |D| positive
- the output uses fixed point notation with decimal digits and with |D=0| the
- output is an integer with no decimal separator; with |D<0| scientific
- notation is used%
- ).
+ can be negative, with about the same meaning as the non-negative case, i.e.
+ rounding to an integer multiple of |1e-D|.
\item The same applies to the functions \func{trunc} and \func{round}. And
matching updates to \csbxint{Trunc}, \csbxint{Round}, \csbxint{iTrunc},
@@ -4739,6 +4888,10 @@
\item if |D=0|: the nearest integer,
\item if |D<0|: the\NewWith{1.4a} nearest multiple of |10^(-D)| (this case
is new with |1.4a| and uses scientific notation).
+
+ At |1.4e| this was changed from using scientific notation on output to
+ inserting |-D| explicit zeroes, and at |1.4f| it is again changed to do neither!
+ \CHANGED{1.4f}
\end{itemize}
ATTENTION: the optional argument
|[D]| is to be located \emph{within} the braces at the start of the expression.
@@ -5125,7 +5278,7 @@
\operdesc{e} scientific notation.
- \operdesc{E} scientific notation. For output, see \csbxint{FracToSciE}.
+ \operdesc{E} scientific notation. For output, see \csbxint{PFloatE}.
\operdesc{"} prefix for hexadecimal input. Only uppercase letters, and
one optional |.| separating integer and fractional hexadecimal parts.
@@ -7988,6 +8141,7 @@
The |*| is mandatory to reload the library, don't forget it.\IMPORTANTf{}
+\pdfstringdefDisableCommands{\let\cs\empty}
\subsection{Powers in \texttt{\cs{xinteval}} and \texttt{\cs{xintfloateval}}}
For powers |a^b| or |a**b| in \csbxint{floateval} the following rules apply:
@@ -11084,7 +11238,7 @@
\csbxint{iexprPrintOne}, which governs the \csbxint{ieval} output format (in
this use case there is never a |/B| fractional part).
\begin{everbatim}
-\let\xintexprPrintOne\xintDecToString
+\let\xintiexprPrintOne\xintDecToString
\end{everbatim}
Any replacement of \csbxint{iexprPrintOne} should obey the following blueprint:
@@ -11109,9 +11263,10 @@
Truncation is done towards zero.
\begin{everbatim*}
-\xintFor* #1 in {\xintSeq[-1]{7}{-14}}:{\xintTrunc{#1}{-11e12/7}\newline}%
-\xintTrunc{10}{1e-11}\newline
-\xintTrunc{10}{1/65536}\par
+\begin{multicols}{2}
+ \xintFor* #1 in {\xintSeq[-1]{7}{-14}}:{\xintTrunc{#1}{-11e12/7}\newline}%
+ \xintTrunc{10}{1e-11}\newline \xintTrunc{10}{1/65536}\par
+\end{multicols}
\end{everbatim*}
\begin{framed}
@@ -11338,9 +11493,10 @@
a scientific part and it conserves the sign of |f| (even if the rounded value
represents the zero value).
\begin{everbatim*}
-\xintFor* #1 in {\xintSeq[-1]{7}{-14}}:{\xintRound{#1}{-11e12/7}\newline}%
-\xintRound{10}{1e-11}\newline
-\xintRound{10}{1/65536}\newline
+\begin{multicols}{2}
+ \xintFor* #1 in {\xintSeq[-1]{7}{-14}}:{\xintRound{#1}{-11e12/7}\newline}%
+ \xintRound{10}{1e-11}\newline \xintRound{10}{1/65536}\newline
+\end{multicols}
\end{everbatim*}%
Rounding is done with half-way numbers going towards infinity of
the same sign.
@@ -11368,9 +11524,10 @@
times what \csa{xintTrunc}|{x}{f}| would produce. Attention that leading zeros
are automatically removed: the output is in strict integer format.
\begin{everbatim*}
-\xintFor* #1 in {\xintSeq[-1]{7}{-14}}:{\xintiTrunc{#1}{-11e12/7}\newline}%
-\xintiTrunc{10}{1e-11}\newline
-\xintiTrunc{10}{1/65536}\par
+\begin{multicols}{2}
+ \xintFor* #1 in {\xintSeq[-1]{7}{-14}}:{\xintiTrunc{#1}{-11e12/7}\newline}%
+ \xintiTrunc{10}{1e-11}\newline \xintiTrunc{10}{1/65536}\par
+\end{multicols}
\end{everbatim*}
\subsection{\csh{xintTTrunc}}\label{xintTTrunc}
@@ -11385,9 +11542,10 @@
times what \csa{xintRound}|{x}{f}| would return. The output has no leading
zeroes, it is always in strict integer format.
\begin{everbatim*}
-\xintFor* #1 in {\xintSeq[-1]{7}{-14}}:{\xintiRound{#1}{-11e12/7}\newline}%
-\xintiRound{10}{1e-11}\newline
-\xintiRound{10}{1/65536}\par
+\begin{multicols}{2}
+ \xintFor* #1 in {\xintSeq[-1]{7}{-14}}:{\xintiRound{#1}{-11e12/7}\newline}%
+ \xintiRound{10}{1e-11}\newline \xintiRound{10}{1/65536}\par
+\end{multicols}
\end{everbatim*}
\subsection{\csh{xintiFloor}}\label{xintiFloor}
@@ -11661,39 +11819,57 @@
\csa{xintPow}{|{f}{x}|}:\etype{\Ff\Numf} computes |f^x| with |f| a fraction and
|x| possibly also.
-This is the support macro for |a^b| in \csbxint{eval}.
-At |1.4e| the macro was extended to allow non-integer exponents (previously
-this was the case too, but the non-integer exponent was truncated to an
-integer...).
-\CHANGED{1.4e}
+At |1.4e|\CHANGED{1.4e} the behaviour of the macro is modified if
+\xintexprname is loaded, at it is then the support macro for powers
+|a^b|, |a**b| and the \func{pow} function in \csbxint{eval}: the macro is
+extended to allow non-integer exponents (in absence of \xintexprname,
+non-integer exponents are allowed but truncated to integers...) and also it
+checks a priori if an exact evaluation (in the case of an integer exponent)
+would produce more than about \dtt{10000} digits and then does in its place a
+floating point evaluation.
-A check is done whether the exponent is integer, but this check is not on the
-value but on the format. So |4/2| will not be recognized as integer; however
-|2.0| will be.
+The check whether the exponent is integer is not on the mathematical value but
+on the format (for reasons of efficiency). So |4/2| will not be recognized as
+integer and it will thus trigger usage of the floating point evaluations;
+however |2.0| will be recognized as an integer, as of course |2|.
If the exponent is considered an integer it is then checked if it is less than
\dtt{10000} (in absolute value) and if the output would contain less than
-\dtt{10000} digits (separately for numerator and denominator) and only then is
-the power computed exactly.
+\dtt{10000} digits (separately for numerator and denominator) and only
+then\CHANGED{1.4e} is the power computed exactly. Else it is computed as by
+\csbxint{FloatPower} (but the output uses raw |A[N]| format not scientific
+notation). Use \csbxint{iiPow} (on integers only, not fractions) for exact
+powers with larger exponents.
-A check is also done whether the exponent is half-integer. Again this check is
-not one the value but on the format, so |2.5| is an half integer, as is
-|25e-1|, or |2.50| but |5/2| is not considered an half-integer. If the
-exponent is half-integer the power is computed by combining suitably
-\csbxint{FloatPower} with a square-root extraction.
+Also, a check is done whether the exponent is half-integer. Again this check
+is not on the value but on the format, so |2.5| is an half integer, as is
+|25e-1|, or |2.50| but |5/2| is not considered an half-integer (for reasons of
+internal efficiency). If the exponent is half-integer\CHANGED{1.4e} the power
+is computed by combining suitably \csbxint{FloatPower} with \csbxint{FloatSqrt}
+(but the output uses raw |A[N]| format not scientific notation).
If the exponent is neither an integer nor an half-integer, the power is
-computed using logarithm and exponential based approach.
+computed using\CHANGED{1.4e} logarithm and exponential based approach (and uses raw |A[N]|
+output format). If |Digits| is at most \dtt{8} (which triggers
+\ctanpackage{poormanlog} usage, for very fast logarithms but only with about
+\dtt{8} or \dtt{9} accurate fractional digits) this will start being
+inaccurate in the last digit already with fractional exponents |x > 10|. It
+is recommended to split then the exponent into an integer or half-integer part
+and a fractional part. Powers with integer or half-integer exponents, even
+very big, are always computed accurately, for any value of |Digits|.
-For relevant details see the code comments of the \xintlogname library in
-|sourcexint.pdf|.
+% Note: in all cases where the macro has been
+% extended at |1.4e| to proceed via a floating point evaluation, the output is
+% in raw |A[N]| format.
-Within an \csbxint{iiexpr}|..\relax| the infix operator |^| is mapped to
-\csa{xintiiPow}; within an \csbxint{expr}-ession it is mapped to
-\csa{xintPow}.
+Within an \csbxint{iiexpr}|..\relax| the infix operators |^| and |**| are
+mapped to \csbxint{iiPow} and powers are always computed exactly even if they
+would produce more than \dtt{10000} digits and melt your CPU; within an
+\csbxint{expr}-ession |^| and |**| are mapped to \csbxint{Pow} as described
+here.
\subsection{\csh{xintFac}}\label{xintFac}
@@ -12131,7 +12307,7 @@
\csa{xintFloatPower}|[P]{f}{g}|\etype{{\upshape[\numx]}\Ff\Numf} computes a
floating point value |f^g| where the exponent |g| is not constrained to be at
most the \TeX{} bound \dtt{\number "7FFFFFFF}. It may even be a fraction
-|A/B| but must simplify to a (possibly big) integer. The exponent of the
+|A/B| but will be truncated to an integer. The exponent of the
\emph{output} however \emph{must} at any rate obey the \TeX{} bound.
The argument |f| is first rounded to |P| significant places to give
@@ -12138,31 +12314,38 @@
|f'|. The output |Z| is then such that the exact |f'^g| differs from
|Z| by an absolute error less than |0.52 ulp(Z)|.
-This is the support macro which is used for the |^| (or |**|) infix operators
-in \csbxint{floateval}, but \emph{ONLY for integer or half-integer
- exponents}.\CHANGED{1.4e}
-Half-integer exponents combine this macro with a square-root extraction.
-For some related details see \xintlogname.
-The macro itself was \emph{NOT} modified at |1.4e| (contrarily to what
-happened with \csbxint{Pow}).
+\emph{For integer exponents} this is the support macro which
+is used for the |^| (or |**|) infix operators in \csbxint{floateval}, or also
+in \csbxint{eval} for very big integer exponents. It is also used in
+\csbxint{floateval} and \csbxint{eval} for half-integer exponents, via a
+combination with the \csbxint{FloatSqrt} square-root extraction.
+The macro itself was \emph{NOT} modified at |1.4e|: when used directly it
+still starts by truncating the exponent to an integer... As for other
+user-level floating-point macros, its output is handled by \csbxint{Float},
+i.e. it uses scientific notation.
+The |0.52 ulp(Z)| guaranteed error bound applies also to the
+\csbxint{floateval} evaluations for the half-integer exponent case. It is
+valid only when |f| already had a mantissa of at most |P| digits and was
+not modified by the initial rounding done by the macro to reduce |f| to |P|
+digits.
-When used directly it first rounds the exponent to nearest integer or
-half-integer so that the computation never raises errors (except naturally for
-negative exponent and zero |f|.) The |0.52 ulp(Z)| bound applies with
-half-integer exponents too. Notice that this is a bound on the distance from
-|f'^g| to |Z|, as |f| always gets rounded to |P| or \csbxint{theDigits}
-digits. The distance from |f^g| to |Z| can be much worse if |g| is very
-large. Roughly, when |g| is negligible compared to |10^P|, we get an extra
-difference of up to about |50g ulp(Z)| which completely dwarfs the |0.52
-ulp(Z)|. Thus, if |f| has strictly more than |P| digits, then the computation
-must be done with an elevated working precision |P'|. For example with
-|g=1000| we should use |P'=P+6| to achieve a total error at worst slightly
-bigger than |0.55 ulp(Z)| after the final rounding from |P'| to |P| digits to
-get |Z|.
+The integer exponent |g| may have more than |P| (or |Digits|) digits, it is
+handled exactly. And as said above its absolute value may exceed the \TeX\ bound.
+% Notice that this is a bound on the distance from
+% |f'^g| to |Z|, where |f'| is the rounded value of the original input |f|;
+% the distance from |f^g| to |Z| can be much worse if |g| is very
+% large. Roughly, when |g| is negligible compared to |10^P|, we get an extra
+% difference of up to about |50g ulp(Z)| which completely dwarfs the |0.52
+% ulp(Z)|. Thus, if |f| has strictly more than |P| digits, then the computation
+% must be done with an elevated working precision |P'|. For example with
+% |g=1000| we should use |P'=P+6| to achieve a total error at worst slightly
+% bigger than |0.55 ulp(Z)| after the final rounding from |P'| to |P| digits to
+% get |Z|.
+
% Examples:%
% %
% \footnote{|\np| is formatting macro from the \url{http://ctan.org/pkg/numprint}
@@ -16296,7 +16479,7 @@
\label{xintSetDigits*}
These starred variants of \csbxint{Digits} and \csbxint{SetDigits} execute
-\csbxint{reloadxinttrig}.
+\csbxint{reloadxinttrig} and \csbxint{reloadxintlog}.
\subsection{\csh{xintiexpr}, \csh{xinttheiexpr}}
\label{xintiexpr}\label{xinttheiexpr}\label{thexintiexpr}
@@ -16330,6 +16513,11 @@
remove trailing zeroes of the output. Finally, I opted rather for
quantization.
+IMPORTANT:\IMPORTANT{} (2021/05/09) Currently, the case of negative |D| gives
+(since |1.4e|) explicit trailing zeroes (formerly it used scientific
+notation). This looks a bit silly indeed, so I am considering at next major
+release to suppress these zeros.
+
\subsection{\csh{xintiiexpr}, \csh{xinttheiiexpr}}
\label{xintiiexpr}\label{xinttheiiexpr}\label{thexintiiexpr}
@@ -18592,7 +18780,6 @@
ones being the (provisory) drop of |x*[a, b,...]|, |x+[a, b,...]| et al.\@
syntax and the requirement of |\expanded| primitive (currently required only
by \xintexprnameimp).
-\item Release |1.3f| of |2019/09/10|: starred variant \csbxint{Digits*}.
\item Release |1.3e| of |2019/04/05|: packages \xinttrignameimp, \xintlognameimp;
\csa{xintdefefunc} ``non-protected'' variant of \csbxint{deffunc} (at |1.4|
the two got merged and \csa{xintdefefunc} became a deprecated alias for
@@ -18865,7 +19052,7 @@
\fi
\XINT_providespackage
\ProvidesPackage {xintkernel}%
- [2021/05/05 v1.4e Paraphernalia for the xint packages (JFB)]%
+ [2021/05/10 v1.4f Paraphernalia for the xint packages (JFB)]%
% \end{macrocode}
% \subsection{Constants}
% \begin{macrocode}
@@ -19652,7 +19839,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xinttools}%
- [2021/05/05 v1.4e Expandable and non-expandable utilities (JFB)]%
+ [2021/05/10 v1.4f Expandable and non-expandable utilities (JFB)]%
% \end{macrocode}
% \lverb|\XINT_toks is used in macros such as \xintFor. It is not used
% elsewhere in the xint bundle.|
@@ -21996,7 +22183,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintcore}%
- [2021/05/05 v1.4e Expandable arithmetic on big integers (JFB)]%
+ [2021/05/10 v1.4f Expandable arithmetic on big integers (JFB)]%
% \end{macrocode}
% \subsection{(WIP!) Error conditions and exceptions}
% \lverb|As per the Mike Cowlishaw/IBM's General Decimal Arithmetic Specification
@@ -25305,7 +25492,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xint}%
- [2021/05/05 v1.4e Expandable operations on big integers (JFB)]%
+ [2021/05/10 v1.4f Expandable operations on big integers (JFB)]%
% \end{macrocode}
% \subsection{More token management}
% \begin{macrocode}
@@ -27883,7 +28070,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintbinhex}%
- [2021/05/05 v1.4e Expandable binary and hexadecimal conversions (JFB)]%
+ [2021/05/10 v1.4f Expandable binary and hexadecimal conversions (JFB)]%
% \end{macrocode}
% \subsection{Constants, etc...}
% \lverb|1.2n switches to \csname-governed expansion at various places.|
@@ -28555,7 +28742,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintgcd}%
- [2021/05/05 v1.4e Euclide algorithm with xint package (JFB)]%
+ [2021/05/10 v1.4f Euclide algorithm with xint package (JFB)]%
% \end{macrocode}
% \subsection{\csh{xintBezout}}
% \lverb|&
@@ -29155,7 +29342,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintfrac}%
- [2021/05/05 v1.4e Expandable operations on fractions (JFB)]%
+ [2021/05/10 v1.4f Expandable operations on fractions (JFB)]%
% \end{macrocode}
% \subsection{\csh{XINT_cntSgnFork}}
% \lverb|1.09i. Used internally, #1 must expand to \m at ne, \z@, or \@ne or
@@ -34545,7 +34732,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintseries}%
- [2021/05/05 v1.4e Expandable partial sums with xint package (JFB)]%
+ [2021/05/10 v1.4f Expandable partial sums with xint package (JFB)]%
% \end{macrocode}
% \subsection{\csh{xintSeries}}
% \begin{macrocode}
@@ -35053,7 +35240,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintcfrac}%
- [2021/05/05 v1.4e Expandable continued fractions with xint package (JFB)]%
+ [2021/05/10 v1.4f Expandable continued fractions with xint package (JFB)]%
% \end{macrocode}
% \subsection{\csh{xintCFrac}}
% \begin{macrocode}
@@ -36445,7 +36632,7 @@
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintexpr}%
- [2021/05/05 v1.4e Expandable expression parser (JFB)]%
+ [2021/05/10 v1.4f Expandable expression parser (JFB)]%
\catcode`! 11
\let\XINT_Cmp \xintiiCmp
\def\XINTfstop{\noexpand\XINTfstop}%
@@ -36475,6 +36662,18 @@
\xintreloadscilibs
}%
% \end{macrocode}
+% \subsection{\csh{XINTdigitsormax}}
+% \lverb|1.4f. To not let xintlog and xinttrig work with, and produce,
+% long mantissas exceeeding the supported range for accuracy of the math
+% functions. The official maximal value is 62, let's set the cut-off at 64.
+%
+% A priori, no need for \expandafter, always ends up expanded in \numexpr (I
+% saw also in an \edef in xinttrig as argument to \xintReplicate prior
+% to its \numexpr).
+%|
+% \begin{macrocode}
+\def\XINTdigitsormax{\ifnum\XINTdigits>\xint_c_ii^vi\xint_c_ii^vi\else\XINTdigits\fi}%
+% \end{macrocode}
% \subsection{Support for output and transform of nested braced contents as
% core data type}
% New at 1.4, of course. The former |\csname.=...\endcsname| encapsulation
@@ -36743,7 +36942,7 @@
\expanded
\XINT:NEhook:x:mapwithin\XINT:expr:mapwithin{\XINTiRound_braced{#1}}%
}%
-\def\XINTiRound_braced#1#2{{\xintiRound{#1}{#2}[\the\numexpr-#1]}}%
+\def\XINTiRound_braced#1#2{{\xintiRound{#1}{#2}[\the\numexpr\ifnum#1<\xint_c_i0\else-#1\fi]}}%
\def\xintfloatexpro #1%
{%
\ifx [#1\expandafter\XINT_flexpr_withopt\else\expandafter\XINT_flexpr_noopt
@@ -40969,16 +41168,29 @@
% After some hesitation at 1.4e regarding guard digits mechanism the float_()
% got renamed to float_dgt(), but then renamed back to float_() to avoid a
% breaking change and having to document it. But I don't like the name.
+%
+% The documentation of 1.4e mentioned float_dgt(), but here it was still
+% float_()... now changed for real.
+%
+% 1.4f adds private float_dgtormax and sfloat_dgtormax for matters of xinttrig.
+%
% |
% \begin{macrocode}
-\def\XINT_expr_func_float_ #1#2#3%
+\def\XINT_expr_func_float_dgt #1#2#3%
{%
\expandafter #1\expandafter #2\expandafter{%
\romannumeral`&&@\XINT:NEhook:f:one:from:one
{\romannumeral`&&@\XINTinFloatdigits#3}}%
}%
-\let\XINT_flexpr_func_float_\XINT_expr_func_float_
+\let\XINT_flexpr_func_float_dgt\XINT_expr_func_float_dgt
% no \XINT_iiexpr_func_float_dgt
+\def\XINT_expr_func_float_dgtormax #1#2#3%
+{%
+ \expandafter #1\expandafter #2\expandafter{%
+ \romannumeral`&&@\XINT:NEhook:f:one:from:one
+ {\romannumeral`&&@\XINTinFloatdigitsormax#3}}%
+}%
+\let\XINT_flexpr_func_float_dgtormax\XINT_expr_func_float_dgtormax
\def\XINT_expr_func_sfloat #1#2#3%
{%
\expandafter #1\expandafter #2\expandafter{\expandafter{%
@@ -40988,6 +41200,13 @@
}%
\let\XINT_flexpr_func_sfloat\XINT_expr_func_sfloat
% no \XINT_iiexpr_func_sfloat
+\def\XINT_expr_func_sfloat_dgtormax #1#2#3%
+{%
+ \expandafter #1\expandafter #2\expandafter{%
+ \romannumeral`&&@\XINT:NEhook:f:one:from:one
+ {\romannumeral`&&@\XINTinFloatSdigitsormax#3}}%
+}%
+\let\XINT_flexpr_func_sfloat_dgtormax\XINT_expr_func_sfloat_dgtormax
\expandafter\def\csname XINT_expr_func_ilog10\endcsname #1#2#3%
{%
\expandafter #1\expandafter #2\expandafter{\expandafter{%
@@ -42738,10 +42957,10 @@
\expandafter\xint_secondoftwo
\fi
{\immediate\write-1{Reloading xinttrig library using Digits=\xinttheDigits.}}%
-{\expandafter\gdef\csname xintlibver at trig\endcsname{2021/05/05 v1.4e}%
+{\expandafter\gdef\csname xintlibver at trig\endcsname{2021/05/10 v1.4f}%
\XINT_providespackage
\ProvidesPackage{xinttrig}%
-[2021/05/05 v1.4e Trigonometrical functions for xintexpr (JFB)]%
+[2021/05/10 v1.4f Trigonometrical functions for xintexpr (JFB)]%
}%
% \end{macrocode}
% \subsection{Ensure used letters are dummy letters}
@@ -42770,19 +42989,19 @@
\xintdefvar @twoPi :=
float(
6.2831853071795864769252867665590057683943387987502116419498891846156328125724180
- ,\xinttheDigits+4);%
+ ,\XINTdigitsormax+4);%
\xintdefvar @threePiover2 :=
float(
4.7123889803846898576939650749192543262957540990626587314624168884617246094293135
- ,\xinttheDigits+4);%
+ ,\XINTdigitsormax+4);%
\xintdefvar @Pi :=
float(
3.1415926535897932384626433832795028841971693993751058209749445923078164062862090
- ,\xinttheDigits+4);%
+ ,\XINTdigitsormax+4);%
\xintdefvar @Piover2 :=
float(
1.5707963267948966192313216916397514420985846996875529104874722961539082031431045
- ,\xinttheDigits+4);%
+ ,\XINTdigitsormax+4);%
% \end{macrocode}
% \subsubsection{\cshn{@oneDegree}, \cshn{@oneRadian}}
% \lverb|&
@@ -42793,11 +43012,11 @@
\xintdefvar @oneDegree :=
float(
0.017453292519943295769236907684886127134428718885417254560971914401710091146034494
- ,\xinttheDigits+4);%
+ ,\XINTdigitsormax+4);%
\xintdefvar @oneRadian :=
float(
57.295779513082320876798154814105170332405472466564321549160243861202847148321553
- ,\xinttheDigits+12);%
+ ,\XINTdigitsormax+12);%
% \end{macrocode}
% \subsection{Hack \cs{xintdeffloatfunc} for inserting usage of guard digits}
% \lverb|1.4e. This is not a general approach, but it sufficient for the
@@ -42817,19 +43036,19 @@
\expandafter\XINT_tmpa
\csname XINT_flexpr_exec_+_\expandafter\endcsname
\csname XINT_flexpr_exec_+\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatAdd_wopt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatAdd_wopt.%
\expandafter\XINT_tmpa
\csname XINT_flexpr_exec_-_\expandafter\endcsname
\csname XINT_flexpr_exec_-\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatSub_wopt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatSub_wopt.%
\expandafter\XINT_tmpa
\csname XINT_flexpr_exec_*_\expandafter\endcsname
\csname XINT_flexpr_exec_*\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatMul_wopt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatMul_wopt.%
\expandafter\XINT_tmpa
\csname XINT_flexpr_exec_/_\expandafter\endcsname
\csname XINT_flexpr_exec_/\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatDiv_wopt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatDiv_wopt.%
\def\XINT_tmpa#1#2#3.#4.%
{%
\let #1#2%
@@ -42838,15 +43057,15 @@
\expandafter\XINT_tmpa
\csname XINT_flexpr_sqrfunc\expandafter\endcsname
\csname XINT_flexpr_func_sqr\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatSqr_wopt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatSqr_wopt.%
\expandafter\XINT_tmpa
\csname XINT_flexpr_sqrtfunc\expandafter\endcsname
\csname XINT_flexpr_func_sqrt\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatSqrt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatSqrt.%
\expandafter\XINT_tmpa
\csname XINT_flexpr_invfunc\expandafter\endcsname
\csname XINT_flexpr_func_inv\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatInv_wopt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatInv_wopt.%
\catcode`~ 3
% \end{macrocode}
% \subsection{The sine and cosine series}
@@ -42900,11 +43119,11 @@
% \begin{macrocode}
\ifnum\XINTdigits>8
\edef\XINT_tmpG % 1/3!
- {1\xintReplicate{\XINTdigits+2}{6}7[\the\numexpr-\XINTdigits-4]}%
+ {1\xintReplicate{\XINTdigitsormax+2}{6}7[\the\numexpr-\XINTdigitsormax-4]}%
\edef\XINT_tmpH % 1/5!
- {8\xintReplicate{\XINTdigits+1}{3}[\the\numexpr-\XINTdigits-4]}%
+ {8\xintReplicate{\XINTdigitsormax+1}{3}[\the\numexpr-\XINTdigitsormax-4]}%
\edef\XINT_tmpd % 1/5!
- {8\xintReplicate{\XINTdigits+9}{3}[\the\numexpr-\XINTdigits-12]}%
+ {8\xintReplicate{\XINTdigitsormax+9}{3}[\the\numexpr-\XINTdigitsormax-12]}%
\def\XINT_tmpe#1.#2.#3.#4.#5#6#7%
{%
\def#5##1\xint:
@@ -42921,8 +43140,8 @@
}%
}%
\expandafter\XINT_tmpe
- \the\numexpr\XINTdigits+4\expandafter.%
- \the\numexpr\XINTdigits+2\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax+4\expandafter.%
+ \the\numexpr\XINTdigitsormax+2\expandafter.\expanded{%
\XINT_tmpH.% 1/5!
\XINT_tmpG.% 1/3!
\expandafter}%
@@ -42964,13 +43183,13 @@
\csname XINT_#8Aux_series_c_\romannumeral\numexpr#1-2\expandafter\endcsname
\csname XINT_#8Aux_series_c_\romannumeral\numexpr#1-3\endcsname
\edef\XINT_tmpd
- {\XINTinFloat[\XINTdigits-#2+8]{\xintDiv{\XINT_tmpd}{\the\numexpr#5*(#5-1)\relax}}}%
+ {\XINTinFloat[\XINTdigitsormax-#2+8]{\xintDiv{\XINT_tmpd}{\the\numexpr#5*(#5-1)\relax}}}%
\let\XINT_tmpF\XINT_tmpG
\let\XINT_tmpG\XINT_tmpH
- \edef\XINT_tmpH{\XINTinFloat[\XINTdigits-#2]{\XINT_tmpd}}%
+ \edef\XINT_tmpH{\XINTinFloat[\XINTdigitsormax-#2]{\XINT_tmpd}}%
\expandafter\XINT_tmpc
- \the\numexpr\XINTdigits-#3\expandafter.%
- \the\numexpr\XINTdigits-#2\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-#3\expandafter.%
+ \the\numexpr\XINTdigitsormax-#2\expandafter.\expanded{%
\XINT_tmpH.%
\XINT_tmpG.%
\XINT_tmpF.%
@@ -42997,13 +43216,13 @@
\ifnum\XINTdigits>55 \XINT_tmpa 22 53 49 45 43 41 39 Sin \fi
\ifnum\XINTdigits>58 \XINT_tmpa 23 56 53 49 45 43 41 Sin \fi
\edef\XINT_tmpd % 1/4!
- {41\xintReplicate{\XINTdigits+8}{6}7[\the\numexpr-\XINTdigits-12]}%
+ {41\xintReplicate{\XINTdigitsormax+8}{6}7[\the\numexpr-\XINTdigitsormax-12]}%
\edef\XINT_tmpH % 1/4!
- {41\xintReplicate{\XINTdigits}{6}7[\the\numexpr-\XINTdigits-4]}%
+ {41\xintReplicate{\XINTdigitsormax}{6}7[\the\numexpr-\XINTdigitsormax-4]}%
\def\XINT_tmpG{5[-1]}% 1/2!
\expandafter\XINT_tmpe
- \the\numexpr\XINTdigits+4\expandafter.%
- \the\numexpr\XINTdigits+3\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax+4\expandafter.%
+ \the\numexpr\XINTdigitsormax+3\expandafter.\expanded{%
\XINT_tmpH.%
\XINT_tmpG.%
\expandafter}%
@@ -43036,12 +43255,12 @@
\def\XINT_SinAux_series#1%
{%
\expandafter\XINT_SinAux_series_a_iii
- \romannumeral0\XINTinfloatS[\XINTdigits+4]{#1}\xint:
+ \romannumeral0\XINTinfloatS[\XINTdigitsormax+4]{#1}\xint:
}%
\def\XINT_CosAux_series#1%
{%
\expandafter\XINT_CosAux_series_a_iii
- \romannumeral0\XINTinfloatS[\XINTdigits+4]{#1}\xint:
+ \romannumeral0\XINTinfloatS[\XINTdigitsormax+4]{#1}\xint:
}%
\fi % end of \XINTdigits>8
% \end{macrocode}
@@ -43108,7 +43327,7 @@
% domain and we handle it semi-satisfactorily. The main problem is that in
% January 2019 I had done only support for degrees, and when I added radians I
% used the most naive approach. But one can find worse: in 2019 I was
-% surprised to have importent divergences with Maple's results at 16 digits
+% surprised to observe important divergences with Maple's results at 16 digits
% near -π. Turns out that Maple probably adds π
% in the floating point sense causing catastrophic loss of digits when one is
% near -π. On the other hand even though the approach here is still naive, it
@@ -43189,7 +43408,7 @@
\def\xintSind##1%
{%
\romannumeral`&&@\expandafter\xintsind\romannumeral0\XINTinfloatS[#1]{##1}}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+12.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+12.%
\def\xintsind #1[#2#3]%
{%
\xint_UDsignfork
@@ -43203,7 +43422,7 @@
\expandafter\XINT_sind_a
\romannumeral0\xinttrunc{#1}{##2[##1]}%
}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+5.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+5.%
\def\XINT_sind_a{\expandafter\XINT_sind_i\the\numexpr\XINT_mod_ccclx_i0.}%
\def\XINT_sind_int
{%
@@ -43263,7 +43482,7 @@
{\romannumeral0\XINTinfloat[#1]{\xintMul{\xintSub{##1[0]}{.##2}}#2}}%
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits+4\expandafter.%
+ \the\numexpr\XINTdigitsormax+4\expandafter.%
\romannumeral`&&@\xintbarefloateval @oneDegree\relax.%
\def\XINT_sind_B#1{\xint_UDsignfork#1\XINT_sind_B_n-\XINT_sind_B_p\krof #1}%
\def\XINT_sind_C#1{\xint_UDsignfork#1\XINT_sind_C_n-\XINT_sind_C_p\krof #1}%
@@ -43285,7 +43504,7 @@
\def\xintCosd##1%
{%
\romannumeral`&&@\expandafter\xintcosd\romannumeral0\XINTinfloatS[#1]{##1}}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+12.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+12.%
\def\xintcosd #1[#2#3]%
{%
\xint_UDsignfork
@@ -43299,7 +43518,7 @@
\expandafter\XINT_cosd_a
\romannumeral0\xinttrunc{#1}{##2[##1]}%
}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+5.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+5.%
\def\XINT_cosd_a{\expandafter\XINT_cosd_i\the\numexpr\XINT_mod_ccclx_i0.}%
\def\XINT_cosd_int
{%
@@ -43318,8 +43537,8 @@
% \end{macrocode}
% \lverb|#2 will be empty in the "integer" branch, but attention in general
% branch to handling of negative integer part after the subtraction of 90,
-% 180, 270, or 360, and avoid abusing A[N] notation which yes speeds up
-% xintfrac parsing but has its pitfalls.|
+% 180, 270, or 360.
+% |
% \begin{macrocode}
\def\XINT_tmpa#1.#2.{%
\def\XINT_cosd_A##1.##2.%
@@ -43363,7 +43582,7 @@
{\romannumeral0\XINTinfloat[#1]{\xintMul{\xintSub{##1[0]}{.##2}}#2}}%
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits+4\expandafter.%
+ \the\numexpr\XINTdigitsormax+4\expandafter.%
\romannumeral`&&@\xintbarefloateval @oneDegree\relax.%
\def\XINT_cosd_B#1{\xint_UDsignfork#1\XINT_cosd_B_n-\XINT_cosd_B_p\krof #1}%
\def\XINT_cosd_C#1{\xint_UDsignfork#1\XINT_cosd_C_n-\XINT_cosd_C_p\krof #1}%
@@ -43439,8 +43658,8 @@
;%
% \end{macrocode}
% \subsection{\cshn{@tan()}, \cshn{@tand()}, \cshn{@cot()}, \cshn{@cotd()}}
-% \lverb|The 0e0 in cot(x) is a dummy place holder, 1/0 would raise an error at
-% time of definition...|
+% \lverb|The 0 in cot(x) is a dummy place holder. We don't have a notion of
+% Inf yet.|
% \begin{macrocode}
\xintdeffloatfunc @tand(x):= @sind(x)/@cosd(x);%
\xintdeffloatfunc @cotd(x):= @cosd(x)/@sind(x);%
@@ -43460,7 +43679,7 @@
{@cos(x)/@sin(x)}
{(x)??
{- at tand(\xintexpr9e1+x*@oneRadian\relax)}
- {0e0}
+ {0}
{@tand(\xintexpr9e1-x*@oneRadian\relax)}
};%
% \end{macrocode}
@@ -43477,7 +43696,8 @@
% I always liked very much the general algorithm whose idea I found
% in 2019. But it costs a square root plus a sine plus a cosine all
% at target precision. For the arctangent the square root will be
-% avoided by a trick.
+% avoided by a trick. (memo: it is replaced by a division and I am not so sure
+% now this is advantageous in fact)
%
% And now I like it even more as I have re-done the first step entirely
% in a single \numexpr... Thus the inverse trigonometry got a serious
@@ -43514,7 +43734,7 @@
% value than 1e-9, but it is possible for example in Python to program it and
% go through all possible (less than) 1e9 inputs and check what happens.
%
-% Very small inputs will give b=0 (first step is a fixe point rounding of t to
+% Very small inputs will give b=0 (first step is a fixed point rounding of t to
% nine fractional digits, so this rounding gives zero for input <0.5e-9,
% others will give b=t, because the arcsine numexpr will end up with
% 1000000000 (last time I checked that was for t a bit less than 5e-5,
@@ -43551,7 +43771,7 @@
\xintAdd{1/1[0]}{##1/6[##2]}%
}%
}%
-\expandafter\XINT_tmpc\the\numexpr\XINTdigits-14.%
+\expandafter\XINT_tmpc\the\numexpr\XINTdigitsormax-14.%
\fi
\ifnum\XINTdigits>34
\def\XINT_tmpc#1.#2.#3.#4.%
@@ -43574,10 +43794,10 @@
}%
}%
\expandafter\XINT_tmpc
- \the\numexpr\XINTdigits-14\expandafter.%
- \the\numexpr\XINTdigits-32\expandafter.\expanded{%
- \XINTinFloat[\XINTdigits-32]{3/40[0]}.%
- \XINTinFloat[\XINTdigits-14]{1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-14\expandafter.%
+ \the\numexpr\XINTdigitsormax-32\expandafter.\expanded{%
+ \XINTinFloat[\XINTdigitsormax-32]{3/40[0]}.%
+ \XINTinFloat[\XINTdigitsormax-14]{1/6[0]}.%
}%
\fi
\ifnum\XINTdigits>52
@@ -43603,11 +43823,11 @@
}%
}%
\expandafter\XINT_tmpc
- \the\numexpr\XINTdigits-32\expandafter.%
- \the\numexpr\XINTdigits-50\expandafter.\expanded{%
- \XINTinFloat[\XINTdigits-50]{5/112[0]}.%
- \XINTinFloat[\XINTdigits-32]{3/40[0]}.%
- \XINTinFloat[\XINTdigits-14]{1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-32\expandafter.%
+ \the\numexpr\XINTdigitsormax-50\expandafter.\expanded{%
+ \XINTinFloat[\XINTdigitsormax-50]{5/112[0]}.%
+ \XINTinFloat[\XINTdigitsormax-32]{3/40[0]}.%
+ \XINTinFloat[\XINTdigitsormax-14]{1/6[0]}.%
}%
\fi
\def\XINT_flexpr_func_ at asin_I#1#2#3%
@@ -43846,25 +44066,28 @@
% \end{macrocode}
% \subsection{Let the functions be known to the \cshnolabel{xintexpr} parser}
% \lverb|&
+% We use here float_dgtormax which uses the smaller of Digits and 64.
% |
% \begin{macrocode}
+\edef\XINTinFloatdigitsormax{\noexpand\XINTinFloat[\the\numexpr\XINTdigitsormax]}%
+\edef\XINTinFloatSdigitsormax{\noexpand\XINTinFloatS[\the\numexpr\XINTdigitsormax]}%
\xintFor #1 in {sin, cos, tan, sec, csc, cot,
asin, acos, atan}\do
{%
- \xintdeffloatfunc #1(x) := float_(@#1(x));%
- \xintdeffloatfunc #1d(x) := float_(@#1d(x));%
- \xintdeffunc #1(x) := float_(\xintfloatexpr @#1(sfloat(x))\relax);%
- \xintdeffunc #1d(x):= float_(\xintfloatexpr @#1d(sfloat(x))\relax);%
+ \xintdeffloatfunc #1(x) := float_dgtormax(@#1(x));%
+ \xintdeffloatfunc #1d(x) := float_dgtormax(@#1d(x));%
+ \xintdeffunc #1(x) := float_dgtormax(\xintfloatexpr @#1(sfloat_dgtormax(x))\relax);%
+ \xintdeffunc #1d(x):= float_dgtormax(\xintfloatexpr @#1d(sfloat_dgtormax(x))\relax);%
}%
\xintFor #1 in {Arg, pArg, atan2}\do
{%
- \xintdeffloatfunc #1(x, y) := float_(@#1(x, y));%
- \xintdeffloatfunc #1d(x, y) := float_(@#1d(x, y));%
- \xintdeffunc #1(x, y) := float_(\xintfloatexpr @#1(sfloat(x), sfloat(y))\relax);%
- \xintdeffunc #1d(x, y):= float_(\xintfloatexpr @#1d(sfloat(x), sfloat(y))\relax);%
+ \xintdeffloatfunc #1(x, y) := float_dgtormax(@#1(x, y));%
+ \xintdeffloatfunc #1d(x, y) := float_dgtormax(@#1d(x, y));%
+ \xintdeffunc #1(x, y) := float_dgtormax(\xintfloatexpr @#1(sfloat_dgtormax(x), sfloat_dgtormax(y))\relax);%
+ \xintdeffunc #1d(x, y):= float_dgtormax(\xintfloatexpr @#1d(sfloat_dgtormax(x), sfloat_dgtormax(y))\relax);%
}%
-\xintdeffloatfunc sinc(x):= float_(@sinc(x));%
-\xintdeffunc sinc(x):= float_(\xintfloatexpr @sinc(sfloat(x))\relax);%
+\xintdeffloatfunc sinc(x):= float_dgtormax(@sinc(x));%
+\xintdeffunc sinc(x):= float_dgtormax(\xintfloatexpr @sinc(sfloat_dgtormax(x))\relax);%
% \end{macrocode}
% \subsection{Synonyms: \cshn{@tg()}, \cshn{@cotg()}}
% \lverb|These are my childhood notations and I am attached to them. In
@@ -43877,15 +44100,15 @@
% \end{macrocode}
% \subsection{Final clean-up}
% \lverb|Restore used dummy variables to their status prior to the package reloading.
-% On first loading this is not needed naturally, because this is done
-% immediately at end of xintexpr.sty.|
+% On first loading this is not needed, but I have not added a way to check
+% here whether this a first loading or a re-loading.|
% \begin{macrocode}
-\xintdeffloatvar twoPi := @twoPi;%
-\xintdeffloatvar threePiover2 := @threePiover2;%
-\xintdeffloatvar Pi := @Pi;%
-\xintdeffloatvar Piover2 := @Piover2;%
-\xintdeffloatvar oneDegree := @oneDegree;%
-\xintdeffloatvar oneRadian := @oneRadian;%
+\xintdefvar twoPi := float_dgtormax(@twoPi);%
+\xintdefvar threePiover2 := float_dgtormax(@threePiover2);%
+\xintdefvar Pi := float_dgtormax(@Pi);%
+\xintdefvar Piover2 := float_dgtormax(@Piover2);%
+\xintdefvar oneDegree := float_dgtormax(@oneDegree);%
+\xintdefvar oneRadian := float_dgtormax(@oneRadian);%
\xintunassignvar{@twoPi}\xintunassignvar{@threePiover2}%
\xintunassignvar{@Pi}\xintunassignvar{@Piover2}%
\xintunassignvar{@oneRadian}\xintunassignvar{@oneDegree}%
@@ -44054,10 +44277,10 @@
\expandafter\xint_secondoftwo
\fi
{\immediate\write-1{Reloading xintlog library using Digits=\xinttheDigits.}}%
-{\expandafter\gdef\csname xintlibver at log\endcsname{2021/05/05 v1.4e}%
+{\expandafter\gdef\csname xintlibver at log\endcsname{2021/05/10 v1.4f}%
\XINT_providespackage
\ProvidesPackage{xintlog}%
-[2021/05/05 v1.4e Logarithms and exponentials for xintexpr (JFB)]%
+[2021/05/10 v1.4f Logarithms and exponentials for xintexpr (JFB)]%
}%
% \end{macrocode}
% \subsection{\csh{xintreloadxintlog}}
@@ -44095,8 +44318,7 @@
%
% Breaking changes at 1.4e:
%
-%( - these macros will be mapped to log10(), log(), pow10(), exp(), pow(,)&
-% and the ** and ^ (if \poormanloghack) only for Digits at most 8
+%( - \poormanloghack now a no-op,
%: - \xintLog was used for \xinteval and differed slightly from its&
% counterpart used for \xintfloateval, the latter float-rounded&
% to P = Digits, the former did not and kept completly meaning-less&
@@ -44232,32 +44454,9 @@
\def\PoorManExp#1{\PoorManPowerOfTen{\xintMul{#1}{43429448190325182765[-20]}}}%
% \end{macrocode}
% \subsubsection{Removed: \csh{PoorManPower}, see \cshnolabel{XINTinFloatSciPow}}
-% \lverb|Originally in poormanlog v0.04, got transferred into xintfrac.sty at
-% 1.3f, then here into xintlog.sty at 1.4e. Support for powers with "about 8
-% to 9 digits" (only when output not too big). This definition
-% 10^(log10(x)*y), or e^(log(x)*y), matching the mathematical one, is common
-% in many float support software but has many problems of precision when the
-% result starts getting big (i.e. has a decimal exponent larger than 1000000
-% for example, and already 10000 will start demonstrating the loss of
-% precision); recall for example for e^y = 10^(y/log(10)) that we had to be
-% careful with log(10) precision, and this is only one instance of a general
-% phenomenon.
-%
-% When computing a^b, it would be more precise to express b as an integer n
-% plus a fractional part t, and compute a^b as a^n times a^t, where a^n is
-% evaluated for example using repeated squaring base approach, with guard
-% digits. This is precisely what \XINTinFloatPower available in xintfrac does
-% (the documentation mentions a 0.52ulp error bound in result). But let's not
-% make life complicated, and anyway this is all now for special "speedy"
-% context at most 8 digits.
-%
-% Removed at 1.4e. See \XINTinFloatSciPow.
-% |
+% \lverb|Removed at 1.4e. See \XINTinFloatSciPow.|
% \subsubsection{Made a no-op: \csh{poormanloghack}}
-% \lverb|&
-%
-%
-% Made a no-op at 1.4e.|
+% \lverb|Made a no-op at 1.4e.|
% \begin{macrocode}
\def\poormanloghack#1%
{%
@@ -44265,25 +44464,11 @@
{\string\poormanloghack\space is a no-op since 1.4e and will be removed at next major release}%
}%
% \end{macrocode}
-% \subsection{Macro support for the expression functional syntax}
-% \lverb|As up to Digits=8 we use only poormanlog, we delay to end of package
-% the lay-out of macros used for the actual computations, so that we execute
-% an earlier \endinput if Digits<=8.
+% \subsection{Macro support for powers}
%
-% Let us start by the support for the ** and ^ operators which will use
-% in \xintfloatexpr \XINTinFloatSciPow and in \xintexpr \xintPow. The latter
-% from $xintfracnameimp is thus modified here.
+% \subsubsection{\csh{XINTinFloatSciPow}}
%
-% The code is a bit complicated as we want to recycle things between the
-% floateval and eval context, and between Digits>8 and Digits<=8.
%
-% In the end I decided to simply define everything for Digits>8, and then
-% let some macros be re-defined for the Digits<=8 case. The latter differs
-% from the former in using systematically always the log10/pow10 approach,
-% with the sole exception of integer exponents in \xintexpr context.
-% |
-%
-% \subsubsection{\csh{XINTinFloatSciPow}}
% \lverb|&
%
% This is the new name and extension of \XINTinFloatPowerH which was
@@ -44290,51 +44475,27 @@
% a non user-documented macro used for a^b previously, and previously
% was located in $xintfracnameimp.
%
-% For integer exponents up to at least 10000 (and certainly more but I have
-% not yet much tested) the old $xintfracnameimp implementation of powers is
-% faster than using logarithms and exponentials. And this is still the case
-% for half-integer exponents, which are handled via a final square-root.
+% A check is done whether the exponent is integer or half-integer, and if
+% positive, the legacy \xintFloatPower/\xintFloatSqrt macros are used. The
+% rationale is that:
%
+%( - they give faster evaluations for integer exponent b < 10000 (and beyond)
+%: - they operate at any value of Digits
+%: - they keep accuracy even with gigantic exponents, whereas the pow10()/log10()&
+% path starts losing accuracy for b about 1e8. In fact at 1.4e it was even&
+% for b about 1000, as log10(A) was not computed with enough fractional&
+% digits, except for 0.8<A<1.26 (roughly), for this usage. At the 1.4f&
+% bugfix we compute log10(A) with enough accuracy for A^b to be safe with&
+% b as large as 1e7, and show visible degradation only for b about 1e9.
+%)
+%
% The user documentation of \xintFloatPower mentions a 0.52 ulp(Z) error where
-% Z is the computed result. Individually, \XINTinFloatLogTen and
-% \XINTinFloatPowTen have been designed for an even higher accuracy but I have
-% not really much tested what this gives in practice for powers. It is
-% possible that \xintFloatPower less often finds the correct rounding than
-% going (as below) via log10 and pow10 (in a special way described below), for
-% non too big exponents, but what is certain is that:
+% Z is the computed result, which seems not as good as the kind of accuracy we
+% target for pow10() (for -1<x<1) and log10() (for 1<x<10) which is more like
+% about 0.505ulp. Perhaps in future I will examine if I need to increase a
+% bit the theoretical accuracy of \xintFloatPower but at time of 1.4e/1.4f
+% release I have left it standing as is.
%
-% - the old \xintFloatPower is more accurate when one goes into extremely high
-% exponent. For example 1.0000001^(12^16), where 12^16 is 184884258895036416
-% and has 18 digits, is computed to be at 60 Digits
-%
-% 1.87998567669494838838184407480229599674641360996864647488708e802942130
-%
-% by \xintFloatPower and this is the correct rounding. Whereas going via
-% logarithm as below would give the least 5 significant digits wrong (in fact
-% the logarithm road will start having accuracy problems if exponent is of the
-% order 1e12, something like that, although right now I say that a bit at
-% random because I don't know why I started to write these comments and I
-% rather want to finish the code).
-%
-% - also for integer exponents up to 10000 (and quite beyond, surely 100000
-% also, but I limited to 10000 when I was testing against xfp, as it doesn't
-% support higher powers of 10) the old \xintFloatPower is faster than current
-% log+exp (but I have not benchmarked much, as this takes tremendous amount of
-% time and energy). And this is even true when one adds a square root
-% extraction to cover half-integer exponents.
-%
-% We also want to do this in \xinteval for integer exponents, not only
-% \xintfloateval, with a twist: in \xinteval we will compute *exactly* for not
-% too big exponents: for A^b, we want the output to not have more than 10000
-% digits. For this we limit b depending on the length of A.
-%
-% If it is decided that the output would be too big, the computation is done
-% as in \xintfloateval, i.e. using the old \xintFloatPower float macros.
-%
-% If the exponent is half-integer the
-% computation will be done as in \xintfloateval, i.e. using FloatPower then a
-% square root.
-%
% The check whether exponent is integer or half-integer is not on the value
% but on the representation. Even in \xintfloatexpr, input such
% 10^\xintexpr4/2\relax is possible, and 4/2 will not be recognized as integer
@@ -44341,14 +44502,26 @@
% to avoid costly overhead. 3/2 will not be recognized as half-integer.
% But 2.0 will be recognized as integer, 25e-1 as half-integer.
%
-% In the computation of a^b, a will be float-rounded to Digits, but the
-% exponent b will be handled as is until last minute. Recall that the
-% \xintfloatexpr parser does not automatically float round isolated inputs,
+% In the computation of A^b, A will be float-rounded to Digits, but the
+% exponent b will be handled "as is" until last minute. Recall that the
+% \xintfloatexpr parser does not automatically float round isolated inputs,
% this happens only once involved in computations.
%
-% In the Digits<=8 branch the test for b integer if a is negative
-% is done after float-rounding b, but the input b is used for computation.
-% |
+% In the Digits<=8 branch we do the same as for Digits>8 since 1.4f. At 1.4e I
+% had strangely chosen (for "speed", but that was anyhow questionable for
+% integer exponents less than 10 for example) to always use log10()/pow10()...
+% But with only 9 fractional digits for the logarithms, exponents such as 1000
+% naturally led to last 2 or 3 digits being wrong and let's not even mention
+% when the exponent was of the order or 1e6... now A^1000 and A^1000.5 are
+% accurately computed and one can handle a^1000.1 as a^1000*a^0.1
+%
+% I wrote the code during 1.4e to 1.4f transition for doing this split of
+% exponent automatically, but it induced a very significant time penalty down
+% the line for fractional exponents, whereas currently a^b is computed at
+% Digits=8 with perfectly acceptable accuracy for fractional abs(b)<10, and at
+% high speed, and accuracy for big exponents can be obtained by manually
+% splitting as above (although the above has no user interface for keeping
+% each contribution with its extra digits; a single one for a^h, -1<h<1).|
% \begin{macrocode}
\def\XINTinFloatSciPow{\romannumeral0\XINTinfloatscipow}%
\def\XINTinfloatscipow#1#2%
@@ -44362,28 +44535,35 @@
\def\XINT_scipow_Biszero#1]#2#3{ 1[0]}%
\def\XINT_scipow_b #1#2/#3[#4]#5%
{%
- \unless\if1\XINT_is_One#3XY\xint_dothis\XINT_scipow_c\fi
- \ifnum#4<\xint_c_mone\xint_dothis\XINT_scipow_c\fi
- \ifnum#4=\xint_c_mone
- \if5\xintLDg{#1#2} %
+ \unless\if1\XINT_is_One#3XY\xint_dothis\XINT_scipow_c\fi
+ \ifnum#4<\xint_c_mone\xint_dothis\XINT_scipow_c\fi
+ \ifnum#4=\xint_c_mone
+ \if5\xintLDg{#1#2} %
\xint_afterfi{\xint_dothis\XINT_scipow_halfint}\else
\xint_afterfi{\xint_dothis\XINT_scipow_c}%
+ \fi
\fi
- \fi
- \xint_orthat#5#1#2/#3[#4]%
+ \xint_orthat#5#1#2/#3[#4]%
}%
\def\XINT_scipow_int #1/1[#2]#3%
{%
- \expandafter\XINT_flpower_checkB_a
- \romannumeral0\XINT_dsx_addzeros{#2}#1;.\XINTdigits.{#3}{\XINTinfloatS[\XINTdigits]}%
+ \expandafter\XINT_flpower_checkB_a
+ \romannumeral0\XINT_dsx_addzeros{#2}#1;.\XINTdigits.{#3}{\XINTinfloatS[\XINTdigits]}%
}%
+% \end{macrocode}
+% \lverb|The \XINT_flpowerh_finish is the sole remnant of \XINTinFloatPowerH
+% which was formerly stitched to \xintFloatPower and checked for half-integer
+% exponent.|
+% \begin{macrocode}
\def\XINT_scipow_halfint#1/1[#2]#3%
{%
- \expandafter\XINT_flpower_checkB_a
- \romannumeral0\xintdsr{\xintDouble{#1}}.\XINTdigits.{#3}\XINT_flpowerh_finish
+ \expandafter\XINT_flpower_checkB_a
+ \romannumeral0\xintdsr{\xintDouble{#1}}.\XINTdigits.{#3}\XINT_flpowerh_finish
}%
\def\XINT_flpowerh_finish #1%
- {\XINTinfloatS[\XINTdigits]{\XINTinFloatSqrt[\XINTdigits+\xint_c_iii]{#1}}}%
+{%
+ \XINTinfloatS[\XINTdigits]{\XINTinFloatSqrt[\XINTdigits+\xint_c_iii]{#1}}%
+}%
\def\XINT_tmpa#1.{%
\def\XINT_scipow_c ##1[##2]##3%
{%
@@ -44408,41 +44588,75 @@
{%
\XINTinfloatpowten{\xintMul{#2}{\XINTinFloatLogTen_xdgout#1}}%
}%
+% \end{macrocode}
+% \lverb|If a^b with a<0, we arrive here only if b was not considered to be
+% an integer exponent. So let's raise an error.|
+% \begin{macrocode}
\def\XINT_scipow_Aisneg #1#2\xint:#3\xint:
{%
- \XINT_signalcondition{InvalidOperation}{Fractional power of negative argument}{}{0[0]}
+ \XINT_signalcondition{InvalidOperation}{Fractional power of negative argument}{}{0[0]}%
}%
\ifnum\XINTdigits<9
- \def\XINTinfloatscipow#1#2%
+% \end{macrocode}
+% \lverb|At 1.4f we only need for Digits up to 8 to insert usage of poormanlog
+% for non integer, non half-integer exponents. At 1.4e the code was more
+% complicated because I had strangely opted for using always the log10()
+% path. However we have to be careful to use \PML at logbaseten with 9 digits
+% always.
+%
+% As the legacy macros used for integer and half-integer exponents float-round
+% the input to Digits digits, we must do the same here for coherence. Which
+% induces some small complications here.
+% |
+% \begin{macrocode}
+ \def\XINT_tmpa#1.#2.#3.{%
+ \def\XINT_scipow_c ##1[##2]##3%
{%
- \expandafter\XINT_scipow_a\romannumeral0\xintraw{#2}\relax{#1}%
+ \expandafter\XINT_scipow_d
+ \romannumeral0\expandafter\XINT_scipow_c_i
+ \romannumeral0\XINTinfloat[#1]{##3}\xint:##1[##2]\xint:
}%
- \def\XINT_scipow_b #1[#2]#3#4%
- {%
- \expandafter\XINT_scipow_d\romannumeral0\XINTinfloat[9]{#4}\xint:#1[#2]\xint:
- }%
+ \def\XINT_scipow_c_i##1[##2]{ ##1#3[##2-#2]}%
+ }\expandafter\XINT_tmpa\the\numexpr\XINTdigits\expandafter.%
+ \the\numexpr9-\XINTdigits\expandafter.%
+ \romannumeral\xintreplicate{9-\XINTdigits}0.%
\def\XINT_scipow_Aispos #1\xint:#2\xint:
{%
\poormanpoweroften{\xintMul{#2}{\romannumeral0\expandafter\PML at logbaseten#1}}%
}%
- \def\XINT_scipow_Aisneg #1#2\xint:#3\xint:
- {%
- \ifcase\xintFloatIntType{#3}%
- \or\expandafter-\romannumeral0%
- \else
- \expandafter\XINT_scipow_AnegBfrac
- \fi
- \poormanpoweroften{\xintMul{#3}{\romannumeral0\expandafter\PML at logbaseten#2}}%
- }%
\fi
% \end{macrocode}
-% \subsubsection{\csh{xintPow}}
+% \subsubsection{\cshnolabel{xintPow}}
% \lverb|&
%
-% This overloads the original $xintfracnameimp macro and uses it for integer
-% exponents, under a criterion which guarantees output (numerator and
-% denominator separately) does not exceed by much 10000 digits if at all.
+% Support macro for a^b in \xinteval. This overloads the original
+% $xintfracnameimp macro, keeping its original meaning only for integer
+% exponents, which are not too big: for exact evaluation of A^b, we want the
+% output to not have more than about 10000 digits (separately for numerator
+% and denominator). For this we limit b depending on the length of A, simply
+% we want b to be smaller than the rounded value of 10000 divided by the
+% length of A. For one-digit A, this would give 10000 as maximal exponent but
+% due to organization of code related to avoir arithmetic overflow (we can't
+% immediately operate in \numexpr with b as it is authorized to be beyond TeX
+% bound), the maximal exponent is 9999.
%
+% The criterion, which guarantees output (numerator and
+% denominator separately) does not exceed by much 10000 digits if at all is
+% that the exponent should be less than the (rounded in the sense of \numexpr)
+% quotient of 10000 by the number of digits of a (considering separately
+% numerator and denominator).
+%
+% The decision whether to compute A^b exactly depends on the length of
+% internal representation of A. So 9^9999 is evaluated exactly (in \xinteval)
+% but for 9.0 it is 9.0^5000 the maximal power. This may change in future.
+%
+% 1.4e had the following bug (for Digits>8): big integer exponents used the
+% log10()/pow10() based approach rather than the legacy macro path which goes
+% via \xintFloatPower, as done by \xintfloateval! As a result powers very
+% large integer exponents were more precise in \xintfloateval than in \xinteval!
+%
+% 1.4f fixes this. Also, it handles Digits<=8 as Digits>8, bringing much
+% simplification here.
% |
% \begin{macrocode}
\def\xintPow{\romannumeral0\xintpow}%
@@ -44450,19 +44664,65 @@
{%
\expandafter\XINT_scipow_a\romannumeral0\xintrez{#2}\XINT_pow_int{#1}%
}%
-\def\XINT_pow_int #1/1[#2]%#3
+% \end{macrocode}
+% \lverb|In case of half-integer exponent the \XINT_scipow_a will have
+% triggered usage of the (new incarnation) of \XINTinFloatPowerH which combines
+% \xintFloatPower and square root extraction. So we only have to handle here
+% the case of integer exponents which will trigger execution of this
+% \XINT_pow_int macro passed as parameter to \xintpow.|
+% \begin{macrocode}
+\def\XINT_pow_int #1/1[#2]%
{%
\expandafter\XINT_pow_int_a\romannumeral0\XINT_dsx_addzeros{#2}#1;.%
}%
-\def\XINT_pow_int_a #1#2.#3%
+% \end{macrocode}
+% \lverb|1.4e had a bug here for integer exponents >= 10000: they triggered
+% going back to the floating point routine but at a late location where
+% the log10()/pow10() approach is used.|
+% \begin{macrocode}
+\def\XINT_pow_int_a #1#2.%
{%
\ifnum\if-#1\xintLength{#2}\else\xintLength{#1#2}\fi>\xint_c_iv
- \expandafter\XINT_pow_tosci
- \fi
- \expandafter\XINT_pow_int_b\romannumeral0\xintraw{#3}\xint:#1#2\xint:
+ \expandafter\XINT_pow_bigint
+ \else\expandafter\XINT_pow_int_b
+ \fi #1#2.%
}%
-\def\XINT_pow_int_b#1#2/#3[#4]\xint:#5\xint:
+% \end{macrocode}
+% \lverb|At 1.4f we correctly jump to the appropriate entry point into the
+% \xintFloatPower routine of $xintfracnameimp, in case of a big integer
+% exponent.|
+% \begin{macrocode}
+\def\XINT_pow_bigint #1.#2%
{%
+ \XINT_flpower_checkB_a#1.\XINTdigits.{#2}{\XINTinfloatS[\XINTdigits]}%
+}%
+\def\XINT_pow_int_b #1.#2%
+{%
+% \end{macrocode}
+% \lverb|We now check if the output will not be too bulky. We use here (on the
+% a of a^b) \xintraw, not \xintrez, on purpose so that for example 9.0^9999
+% is computed in floating point sense but 9^9999 is computed exactly. However
+% 9.0^5000 will be computed exactly. And if I used \xintrez here \xinteval{100^2}
+% would print 10000.0 and \xinteval{100^3} would print 1.0e6. Thus situation
+% is complex.
+%
+% By the way I am happy to see that 9.0*9.0 in
+% \xinteval does print 81.0 but the truth is that internally it does have the
+% more bulky 8100/1[-2] maybe I should make some revision of this, i.e. use
+% rather systematically \xintREZ on input rather than \xintRaw (note taken on
+% 2021/05/08 at time of doing 1.4f bugfix release).|
+% \begin{macrocode}
+ \expandafter\XINT_pow_int_c\romannumeral0\xintraw{#2}\xint:#1\xint:
+}%
+% \end{macrocode}
+% \lverb|The \XINT_fpow_fork is (quasi top level) entry point we have found
+% into the legacy \xintPow routine of $xintfracnameimp. Its interface is a bit
+% weird, but let's not worry about this now.
+%
+%|
+% \begin{macrocode}
+\def\XINT_pow_int_c#1#2/#3[#4]\xint:#5\xint:
+{%
\if0\ifnum\numexpr\xint_c_x^iv/%
(\xintLength{#1#2}\if-#1-\xint_c_i\fi)<\XINT_Abs#5 %
1\else
@@ -44469,52 +44729,21 @@
\ifnum\numexpr\xint_c_x^iv/\xintLength{#3}<\XINT_Abs#5 %
1\else
0\fi\fi
- \expandafter\XINT_fpow_fork\else\expandafter\XINT_pow_tosci_i
+ \expandafter\XINT_fpow_fork\else\expandafter\XINT_pow_bigint_i
\fi
#5\Z{#4}{#1#2}{#3}%
}%
-\def\XINT_tmpa#1.{%
-\def\XINT_pow_tosci##1\xintraw%##2%\xint:##3\xint:
+% \end{macrocode}
+% \lverb|\XINT_pow_bigint_i is like \XINT_pow_bigint but has its parameters
+% organized differently.|
+% \begin{macrocode}
+\def\XINT_pow_bigint_i#1\Z#2#3#4%
{%
- \expandafter\XINT_scipow_d\romannumeral0\XINTinfloatS[#1]%
+ \XINT_flpower_checkB_a#1.\XINTdigits.{#3/#4[#2]}{\XINTinfloatS[\XINTdigits]}%
}%
-\def\XINT_pow_tosci_i##1\Z##2##3##4%
-{%
- \expandafter\XINT_scipow_d\romannumeral0\expandafter\XINT_infloatS_clean
- \romannumeral0\XINT_infloat_a#1.{##2}{##3}{##4}\xint:##1\xint:
-}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits.%
-\ifnum\XINTdigits<9
- \def\xintpow#1#2%
- {%
- \expandafter\XINT_poorpow_a\romannumeral0\xintrez{#2}\relax{#1}%
- }%
- \def\XINT_poorpow_a #1%
- {%
- \xint_gob_til_zero#1\XINT_scipow_Biszero0\XINT_poorpow_b#1%
- }%
- \def\XINT_poorpow_b #1#2/#3[#4]#5%
- {%
- \unless\if1\XINT_is_One#3XY\xint_dothis\XINT_poorpow_c\fi
- \ifnum#4<\xint_c_\xint_dothis\XINT_poorpow_c\fi
- \xint_orthat\XINT_pow_int#1#2/#3[#4]%
- }%
- \def\XINT_poorpow_c #1[#2]#3%
- {%
- \expandafter\XINT_scipow_d\romannumeral0\XINTinfloat[9]{#3}\xint:#1[#2]\xint:
- }%
- \def\XINT_pow_tosci#1\xintraw%#2%\xint:#3\xint:
- {%
- \expandafter\XINT_scipow_d\romannumeral0\XINTinfloat[9]%
- }%
- \def\XINT_pow_tosci_i#1\Z#2#3#4%
- {%
- \expandafter\XINT_scipow_d\romannumeral0\expandafter\XINT_infloat_clean
- \romannumeral0\XINT_infloat_a9.{#2}{#3}{#4}\xint:#1\xint:
- }%
-\fi
% \end{macrocode}
-% \subsubsection{\cshn{log10()} and \cshn{pow10()} functions}
+% \subsection{Macro support for \cshnolabel{xintexpr} and \cshnolabel{xintfloatexpr} syntax}
+% \subsubsection{The \cshn{log10()} and \cshn{pow10()} functions}
% \lverb|&
% Up to 8 digits included we use the poormanlog based ones.
% |
@@ -44551,9 +44780,7 @@
\expandafter\let\csname XINT_flexpr_func_pow10\expandafter\endcsname
\csname XINT_expr_func_pow10\endcsname
% \end{macrocode}
-% \subsubsection{\cshn{log()}, \cshn{exp()}, and \cshn{pow()} functions}
-% \lverb|The mapping of ** and ^ to \XINTinFloatPow and \xintPow respectively,
-% i.e. to be like pow(,) function is done in $xintexprnameimp.|
+% \subsubsection{The \cshn{log()}, \cshn{exp()} functions}
% \begin{macrocode}
\ifnum\XINTdigits<9
\def\XINT_expr_func_log #1#2#3%
@@ -44586,6 +44813,12 @@
\let\XINT_flexpr_func_log\XINT_expr_func_log
\let\XINT_flexpr_func_exp\XINT_expr_func_exp
\fi
+% \end{macrocode}
+% \subsubsection{The \cshn{pow()} function}
+% \lverb|The mapping of ** and ^ to \XINTinFloatSciPow (in \xintfloatexpr
+% context) and \xintPow (in \xintexpr context),
+% is done in $xintexprnameimp.|
+% \begin{macrocode}
\def\XINT_expr_func_pow #1#2#3%
{%
\expandafter #1\expandafter #2\expandafter{%
@@ -44608,11 +44841,21 @@
% of 10, but only one logarithm log(10).
%
% Currently the code whether for exponential or logarihm will not screen out 0
-% digits and even will do silly multiplication par 10^0 = 1 in that case, and
+% digits and even will do silly multiplication by 10^0 = 1 in that case, and
% we need to store such silly values.
%
% We add the data for the 10^-0.i etc... because pre-computing them on the fly
% significantly adds overhead to the package loading.
+%
+% The fractional powers of ten with D+5 digits are used to compute pow10()
+% function, those with D+10 digits are used to compute log10() function. This
+% is done with
+% an elevated precision for two reasons:
+% (- handling of inputs near 1,
+% :- in order for a^b = pow10(b*log10(a)) to keep accuracy&
+% even with large exponents, say in absolute value up to 1e7,&
+% degradation beginning to show-up at 1e8.
+% )
% |
% \begin{macrocode}
\def\XINT_tmpa{1[0]}%
@@ -44641,8 +44884,8 @@
\expandafter\let\csname XINT_c_5_0_inv_x\endcsname\XINT_tmpa
\expandafter\let\csname XINT_c_6_0_inv_x\endcsname\XINT_tmpa
\def\XINT_tmpa#1#2#3#4;%
- {\expandafter\edef\csname XINT_c_#1_#2\endcsname{\XINTinFloat[\XINTdigits+5]{#3#4[-79]}}%
- \expandafter\edef\csname XINT_c_#1_#2_x\endcsname{\XINTinFloat[\XINTdigits+10]{#3#4[-79]}}%
+ {\expandafter\edef\csname XINT_c_#1_#2\endcsname{\XINTinFloat[\XINTdigitsormax+5]{#3#4[-79]}}%
+ \expandafter\edef\csname XINT_c_#1_#2_x\endcsname{\XINTinFloat[\XINTdigitsormax+10]{#3#4[-79]}}%
}%
% 10^0.i
\XINT_tmpa 1 1 12589254117941672104239541063958006060936174094669310691079230195266476157825020;%
@@ -44705,8 +44948,8 @@
\XINT_tmpa 6 8 10000184208504057336610176132939223090407041937631374389422968832433217547184883;%
\XINT_tmpa 6 9 10000207234805653031739097001771331138303016031686764989867510425362339583809842;%
\def\XINT_tmpa#1#2#3#4;%
- {\expandafter\edef\csname XINT_c_#1_#2_inv\endcsname{\XINTinFloat[\XINTdigits+5]{#3#4[-80]}}%
- \expandafter\edef\csname XINT_c_#1_#2_inv_x\endcsname{\XINTinFloat[\XINTdigits+10]{#3#4[-80]}}%
+ {\expandafter\edef\csname XINT_c_#1_#2_inv\endcsname{\XINTinFloat[\XINTdigitsormax+5]{#3#4[-80]}}%
+ \expandafter\edef\csname XINT_c_#1_#2_inv_x\endcsname{\XINTinFloat[\XINTdigitsormax+10]{#3#4[-80]}}%
}%
% 10^-0.i
\XINT_tmpa 1 1 79432823472428150206591828283638793258896063175548433209232392931695569719148754;%
@@ -44770,13 +45013,13 @@
\XINT_tmpa 6 9 99997927694888844379020974874260864289829523807763942234420930258187873904191138;%
% log(10)
\edef\XINT_c_logten
- {\XINTinFloat[\XINTdigits+4]
+ {\XINTinFloat[\XINTdigitsormax+4]
{23025850929940456840179914546843642076011014886287729760333279009675726096773525[-79]}}%
\edef\XINT_c_oneoverlogten
- {\XINTinFloat[\XINTdigits+4]
+ {\XINTinFloat[\XINTdigitsormax+4]
{43429448190325182765112891891660508229439700580366656611445378316586464920887077[-80]}}%
\edef\XINT_c_oneoverlogten_xx
- {\XINTinFloat[\XINTdigits+14]
+ {\XINTinFloat[\XINTdigitsormax+14]
{43429448190325182765112891891660508229439700580366656611445378316586464920887077[-80]}}%
% \end{macrocode}
% \subsection{April 2021: at last, \csh{XINTinFloatPowTen}, \csh{XINTinFloatExp}}
@@ -44843,7 +45086,7 @@
% fixed point to floating point and log() goes from floating point to fixed
% point, and coercing them to work inside the sole floating point domain is
% not mathematically natural. Although admittedly it does create interesting
-% mathematical questions! A similar situatoin applies to functions such as
+% mathematical questions! A similar situation applies to functions such as
% cos() and sin(), what sense is there in the expression cos(exp(50)) for
% example with 16 digits precision? My opinion is that it does not make ANY
% sense. Anyway, I shall obide.
@@ -44870,7 +45113,7 @@
\XINTinfloatpowten
{\xintMul{\XINT_c_oneoverlogten_xx}{\XINTinFloatS[#1]{##1}}}%
}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+14.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+14.%
% \end{macrocode}
% \lverb|&
% Here is how the reduction to computations of an exp(h) via series is done.
@@ -44901,7 +45144,7 @@
\expandafter\XINT_powten_fork
\romannumeral0\xintiround{#1}{##1}[-#1]%
}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+4.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+4.%
\def\XINT_powten_fork#1%
{%
\xint_UDzerominusfork
@@ -44921,11 +45164,11 @@
{%
\expandafter\XINT_powten_pos_a\romannumeral0\xintround{6}{#1[#2]}#1[#2]%
}%
-\def\XINT_tmpa #1.#2.{%
+\def\XINT_tmpa #1.#2.#3.{%
\def\XINT_powten_pos_a ##1.##2##3##4##5##6##7##8[##9]%
{%
\expandafter\XINT_infloate
- \romannumeral0\XINTinfloat[\XINTdigits]{%
+ \romannumeral0\XINTinfloat[#3]{%
\xintMul{\csname XINT_c_1_##2\endcsname}{%
\XINTinFloat[#1]{%
\xintMul{\csname XINT_c_2_##3\endcsname}{%
@@ -44947,8 +45190,9 @@
}%
}}}}}}}}}}}}{##1}%
}}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits+5\expandafter.%
- \the\numexpr\XINTdigits-1.%
+ \the\numexpr\XINTdigitsormax+5\expandafter.%
+ \the\numexpr\XINTdigitsormax-1\expandafter.%
+ \the\numexpr\XINTdigitsormax.%
% \end{macrocode}
% \lverb|This rounding may produce -0.000000 but will always have 6 exactly
% fractional digits and a leading minus sign.|
@@ -44957,11 +45201,11 @@
{%
\expandafter\XINT_powten_neg_a\romannumeral0\xintround{6}{#1[#2]}#1[#2]%
}%
-\def\XINT_tmpa #1.#2.{%
+\def\XINT_tmpa #1.#2.#3.{%
\def\XINT_powten_neg_a -##1.##2##3##4##5##6##7##8[##9]%
{%
\expandafter\XINT_infloate
- \romannumeral0\XINTinfloat[\XINTdigits]{%
+ \romannumeral0\XINTinfloat[#3]{%
\xintMul{\csname XINT_c_1_##2_inv\endcsname}{%
\XINTinFloat[#1]{%
\xintMul{\csname XINT_c_2_##3_inv\endcsname}{%
@@ -44983,8 +45227,9 @@
}%
}}}}}}}}}}}}{-##1}%
}}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits+5\expandafter.%
- \the\numexpr\XINTdigits-1.%
+ \the\numexpr\XINTdigitsormax+5\expandafter.%
+ \the\numexpr\XINTdigitsormax-1\expandafter.%
+ \the\numexpr\XINTdigitsormax.%
% \end{macrocode}
% \subsubsection{Exponential series}
% \lverb|Or rather here h(1 + h(1/2 + h (1/6 + ....))). Upto at most h^9/9!
@@ -45009,8 +45254,8 @@
}%
}%
\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-6\expandafter.%
- \the\numexpr\XINTdigits-1.%
+ \the\numexpr\XINTdigitsormax-6\expandafter.%
+ \the\numexpr\XINTdigitsormax-1.%
\ifnum\XINTdigits>15
\def\XINT_tmpa#1.#2.#3.#4.{%
\def\XINT_Exp_series_a_ii##1\xint:
@@ -45034,8 +45279,8 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-13\expandafter.%
- \the\numexpr\XINTdigits-6.%
+ \the\numexpr\XINTdigitsormax-13\expandafter.%
+ \the\numexpr\XINTdigitsormax-6.%
{5[-1]}.%
{1[0]}.%
\fi
@@ -45062,9 +45307,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-19\expandafter.%
- \the\numexpr\XINTdigits-13\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-13]{1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-19\expandafter.%
+ \the\numexpr\XINTdigitsormax-13\expandafter.%
+ \romannumeral0\XINTinfloat[\XINTdigitsormax-13]{1/6[0]}.%
{5[-1]}.%
\fi
\ifnum\XINTdigits>28
@@ -45102,10 +45347,10 @@
\csname XINT_Exp_series_c_\romannumeral\numexpr#1-2\expandafter\endcsname
\csname XINT_Exp_series_c_\romannumeral\numexpr#1-3\endcsname
\expandafter\XINT_tmpc
- \the\numexpr\XINTdigits-#2\expandafter.%
- \the\numexpr\XINTdigits-#3\expandafter.\expanded{%
- \XINTinFloat[\XINTdigits-#3]{1/#6[0]}.%
- \XINTinFloat[\XINTdigits-#4]{1/#7[0]}.%
+ \the\numexpr\XINTdigitsormax-#2\expandafter.%
+ \the\numexpr\XINTdigitsormax-#3\expandafter.\expanded{%
+ \XINTinFloat[\XINTdigitsormax-#3]{1/#6[0]}.%
+ \XINTinFloat[\XINTdigitsormax-#4]{1/#7[0]}.%
}%
}%
\XINT_tmpa 5 26 19 13 120 24 6 %<-- keep space
@@ -45130,7 +45375,7 @@
% obtained via a log series). Then log(x) computes log(10)z+h whereas log10(x)
% computes as z+h/log(10).
%
-% There will be three branches
+% There will be three branches [NO FINALLY ONLY TWO BRANCHES SINCE 1.4f]
% according to situation of x relative to 1. Let y be the math value log10(x)
% that we want to approximate to target precision P digits. P is assumed at
% least 9.
@@ -45147,12 +45392,23 @@
%
% Warning: this description is not in sync with the code, now the case where
% d_1d_2...d_6 is 000000 is filtered out and one jumps directly either to case
-% I if n≠0 or to case III if n=0. There is also a preventive step to recognize
-% when the rounding produces a z exactly zero (\xintRound has bad pratice of
-% outputting a 0 with no decimal point if the input was exactly zero, and this
-% can happen here as the input is some approximation to actual logarithm).
+% I if n≠0 or to case III if n=0. The case when rounding produces a z equal
+% to zero is also handled especially.
%
-% CASE I: either n is NOT zero or d_1d_2....d_6 is at least 100001. Then we
+% WARNING: at 1.4f, the CASE I was REMOVED. Everything is handled as CASE II
+% or exceptionally case III. Indeed this removal was observed to simply cost
+% about 10$% extra time at D=16 digits, which was deemed an acceptable cost.
+% The cost is certainly higher at D=9 but also relatively lower at high
+% D's. It means that logarithms are always computed with 9, not 4, safety
+% **fractional** digits, and this allows to compute powers accurately with
+% exponents say up to 1e7, degradation starting to show at 1e8 and for sure at
+% 1e9. However for integer and half-integer exponents the old routine
+% \xintFloatPower will still be used, and perhaps it will need some increased
+% precision update as the documented 0.52ulp error bound is higher than our
+% more stringent standards of 2021.
+%
+% CASE I: [removed at 1.4f!]
+% either n is NOT zero or d_1d_2....d_6 is at least 100001. Then we
% compute X = 10^(-z)*x which is near 1, by using the table of powers of
% 10, using P+5 digits significands. Then we compute (exactly) eta = X-1,
% (which is in absolute value less than 0.0000012)
@@ -45241,6 +45497,19 @@
%
% Absolutely no error check is done whether the input x is really positive.
% As seen above the maximal target precision is 63 (not 64).
+%
+% Update for 1.4f: when the logarithm is computed via case I, i.e. basically
+% always except roughly for 0.8<a<1.26, its fractional part has only about 4
+% safety digits. This is barely enough for a^b with b near 1000 and certainly
+% not enough for a^b with b of the order 10000.
+%
+% I hesitated with the option to always handle b as N+h with N integer for
+% which we can use old \xintFloatPower (which perhaps I will have to update to
+% ensure better than the 0.52ulp it mentions in its documentation). But in
+% the end, I decided to simply add a variant where case I is handled as case
+% II, i.e. with 9 not 4 safety fractional digits for the logarithm. This
+% variant will be the one used by the power function for fractional exponents
+% (non integer, non half-integer).
%
% ?
% \begin{macrocode}
@@ -45249,7 +45518,7 @@
\def\XINTinfloatlog
{%
\expandafter\XINT_log_out
- \romannumeral0\expandafter\XINT_logten_a
+ \romannumeral0\expandafter\XINT_logtenxdg_a
\romannumeral0\XINTinfloat[#1]%{##1}
}%
\def\XINT_log_out ##1\xint:##2\xint:
@@ -45261,7 +45530,7 @@
\def\XINTinfloatlogten
{%
\expandafter\XINT_logten_out
- \romannumeral0\expandafter\XINT_logten_a
+ \romannumeral0\expandafter\XINT_logtenxdg_a
\romannumeral0\XINTinfloat[#1]%{##1}
}%
\def\XINT_logten_out ##1\xint:##2\xint:
@@ -45269,10 +45538,10 @@
\XINTinfloat[#1]%
{\xintAdd{##1}{\xintMul{\XINT_c_oneoverlogten}{##2}}}%
}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax.%
\def\XINTinFloatLogTen_xdgout%#1[#2]
{%
- \romannumeral0\expandafter\XINT_logten_xdgout\romannumeral0\XINT_logten_a
+ \romannumeral0\expandafter\XINT_logten_xdgout\romannumeral0\XINT_logtenxdg_a
}%
\def\XINT_logten_xdgout #1\xint:#2\xint:
{%
@@ -45282,16 +45551,20 @@
% \lverb|No check is done whether input is negative or vanishes. We apply
% \XINTinfloat[9] which if input is not zero always produces 9 digits (and
% perhaps a minus sign) the first digit is non-zero. This is the expected
-% input to \numexpr\PML@<digits><dot>.\relax|
+% input to \numexpr\PML@<digits><dot>.\relax
+%
+% The variants xdg_a, xdg_b, xdg_c, xdg_d were added at 1.4f to always go via
+% II or III, ensuring more fractional digits to the logarithm for accuracy of
+% fractional powers with big exponents. "Old" 1.4e routines were removed.|
% \begin{macrocode}
-\def\XINT_logten_a#1[#2]%
+\def\XINT_logtenxdg_a#1[#2]%
{%
- \expandafter\XINT_logten_b
+ \expandafter\XINT_logtenxdg_b
\romannumeral0\XINTinfloat[9]{#1[#2]}#1[#2]%
}%
-\def\XINT_logten_b#1[#2]%
+\def\XINT_logtenxdg_b#1[#2]%
{%
- \expandafter\XINT_logten_c
+ \expandafter\XINT_logtenxdg_c
\romannumeral0\xintround{6}%
{\xintiiAdd{\xintDSx{-9}{\the\numexpr#2+8\relax}}%
{\the\numexpr\PML@#1.\relax}%
@@ -45304,15 +45577,15 @@
% "0". We are very near 1 and will treat this as case III, but this is
% sub-optimal.|
% \begin{macrocode}
-\def\XINT_logten_c #1#2%
+\def\XINT_logtenxdg_c #1#2%
{%
\xint_gob_til_xint:#2\XINT_logten_IV\xint:
- \XINT_logten_d #1#2%
+ \XINT_logtenxdg_d #1#2%
}%
-\def\XINT_logten_IV\xint:\XINT_logten_d0{\XINT_logten_f_III}%
+\def\XINT_logten_IV\xint:\XINT_logtenxdg_d0{\XINT_logten_f_III}%
% \end{macrocode}
% \lverb|Here we are certain that \xintRound{6} produced a decimal point and
-% 6 fractional digit tokens #2, but they can be zeros.
+% 6 fractional digit tokens #2, but they can be zeros and also -0.000000 is possible.
%
% If #1 vanishes and #2>100000 we are in case I.
%
@@ -45324,52 +45597,46 @@
%
% Attention to the sign of #1, it is checked later on.
%
-% A bit tired today of expandafter or afterfi or dothis/orthat etc... (which
-% is one level). Somehow there are very very few \ifcase use in all of
-% xint... I don't know why.
+% At 1.4f, we handle the case I with as many digits as case II (and exceptionnally case III).
%
% |
% \begin{macrocode}
-\def\XINT_logten_d #1.#2\xint:
+\def\XINT_logtenxdg_d #1.#2\xint:
{%
\ifcase
\ifnum#1=\xint_c_
- \ifnum #2>100000 \xint_c_i\else
- \ifnum #2>\xint_c_ \xint_c_ii\else \xint_c_iii\fi\fi
+ \ifnum #2=\xint_c_ \xint_c_iii\else \xint_c_ii\fi
\else
- \ifnum#2>\xint_c_ \xint_c_i\else \xint_c_\fi
+ \ifnum#2>\xint_c_ \xint_c_ii\else \xint_c_\fi
\fi
\expandafter\XINT_logten_f_Isp
- \or\expandafter\XINT_logten_f_I
- \or\expandafter\XINT_logten_f_II
+ \or% never
+ \or\expandafter\XINT_logten_f_IorII
\else\expandafter\XINT_logten_f_III
\fi
#1.#2\xint:
}%
-\def\XINT_logten_f_I#1%
+\def\XINT_logten_f_IorII#1%
{%
\xint_UDsignfork
- #1\XINT_logten_f_I_neg
- -\XINT_logten_f_I_pos
+ #1\XINT_logten_f_IorII_neg
+ -\XINT_logten_f_IorII_pos
\krof #1%
}%
-\def\XINT_logten_f_II#1%
-{%
- \xint_UDsignfork
- #1\XINT_logten_f_II_neg
- -\XINT_logten_f_II_pos
- \krof #1%
-}%
+% \end{macrocode}
+% \lverb|We are here only with a non-zero ##1, so no risk of a -0[0] which
+% would be illegal usage of A[N] raw format. A negative ##1 is no trouble in ##3-##1.|
+% \begin{macrocode}
\def\XINT_tmpa#1.{%
\def\XINT_logten_f_Isp##1.000000\xint:##2[##3]%
{%
{##1[0]}\xint:
- {\expandafter\XINT_LogTen_serI_a_i
+ {\expandafter\XINT_LogTen_serII_a_ii
\romannumeral0\XINTinfloatS[#1]{\xintAdd{##2[##3-##1]}{-1[0]}}%
\xint:
}\xint:
}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits-2.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax.%
\def\XINT_tmpa#1.{%
\def\XINT_logten_f_III##1\xint:##2[##3]%
{%
@@ -45378,25 +45645,25 @@
\romannumeral0\XINTinfloatS[#1]{\xintAdd{##2[##3]}{-1[0]}}%
\xint:
}\xint:
-}}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+4.%
+}}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+4.%
\def\XINT_tmpa#1.#2.{%
-\def\XINT_logten_f_I_pos##1.##2##3##4##5##6##7\xint:##8[##9]%
+\def\XINT_logten_f_IorII_pos##1.##2##3##4##5##6##7\xint:##8[##9]%
{%
{\the\numexpr##1##2##3##4##5##6##7[-6]}\xint:
- {\expandafter\XINT_LogTen_serI_a_i
+ {\expandafter\XINT_LogTen_serII_a_ii
\romannumeral0\XINTinfloat[#2]%
{\xintAdd{-1[0]}%
- {\xintMul{\csname XINT_c_1_##2_inv\endcsname}{%
+ {\xintMul{\csname XINT_c_1_##2_inv_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_2_##3_inv\endcsname}{%
+ \xintMul{\csname XINT_c_2_##3_inv_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_3_##4_inv\endcsname}{%
+ \xintMul{\csname XINT_c_3_##4_inv_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_4_##5_inv\endcsname}{%
+ \xintMul{\csname XINT_c_4_##5_inv_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_5_##6_inv\endcsname}{%
+ \xintMul{\csname XINT_c_5_##6_inv_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_6_##7_inv\endcsname}
+ \xintMul{\csname XINT_c_6_##7_inv_x\endcsname}
{##8[##9-##1]}%
}}}}}}}}}}%
}%
@@ -45403,23 +45670,23 @@
}\xint:
}\xint:
}%
-\def\XINT_logten_f_I_neg##1.##2##3##4##5##6##7\xint:##8[##9]%
+\def\XINT_logten_f_IorII_neg##1.##2##3##4##5##6##7\xint:##8[##9]%
{%
{\the\numexpr##1##2##3##4##5##6##7[-6]}\xint:
- {\expandafter\XINT_LogTen_serI_a_i
+ {\expandafter\XINT_LogTen_serII_a_ii
\romannumeral0\XINTinfloat[#2]%
{\xintAdd{-1[0]}%
- {\xintMul{\csname XINT_c_1_##2\endcsname}{%
+ {\xintMul{\csname XINT_c_1_##2_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_2_##3\endcsname}{%
+ \xintMul{\csname XINT_c_2_##3_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_3_##4\endcsname}{%
+ \xintMul{\csname XINT_c_3_##4_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_4_##5\endcsname}{%
+ \xintMul{\csname XINT_c_4_##5_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_5_##6\endcsname}{%
+ \xintMul{\csname XINT_c_5_##6_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_6_##7\endcsname}
+ \xintMul{\csname XINT_c_6_##7_x\endcsname}
{##8[##9-##1]}%
}}}}}}}}}}%
}%
@@ -45427,56 +45694,7 @@
}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits+5\expandafter.\the\numexpr\XINTdigits-1.%
-\def\XINT_tmpa#1.#2.{%
-\def\XINT_logten_f_II_pos0.##1##2##3##4##5##6\xint:##7[##8]%
-{%
- {\the\numexpr##1##2##3##4##5##6[-6]}\xint:
- {\expandafter\XINT_LogTen_serII_a_ii
- \romannumeral0\XINTinfloat[#2]%
- {\xintAdd{-1[0]}%
- {\xintMul{\csname XINT_c_1_##1_inv_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_2_##2_inv_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_3_##3_inv_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_4_##4_inv_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_5_##5_inv_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_6_##6_inv_x\endcsname}
- {##7[##8]}%
- }}}}}}}}}}%
- }%
- }\xint:
- }\xint:
-}%
-\def\XINT_logten_f_II_neg-0.##1##2##3##4##5##6\xint:##7[##8]%
-{%
- {\the\numexpr-##1##2##3##4##5##6[-6]}\xint:
- {\expandafter\XINT_LogTen_serII_a_ii
- \romannumeral0\XINTinfloat[#2]%
- {\xintAdd{-1[0]}%
- {\xintMul{\csname XINT_c_1_##1_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_2_##2_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_3_##3_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_4_##4_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_5_##5_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_6_##6_x\endcsname}
- {##7[##8]}%
- }}}}}}}}}}%
- }%
- }\xint:
- }\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits+10\expandafter.\the\numexpr\XINTdigits+4.%
+ \the\numexpr\XINTdigitsormax+10\expandafter.\the\numexpr\XINTdigitsormax+4.%
% \end{macrocode}
% \lverb|Initially all of this was done in a single big nested macro but the
% float-rounding of argument to less digits worked again each time from
@@ -45515,265 +45733,11 @@
% always the slightly more costly series III in place of series II. But that
% would add one un-needed term and a bit overhead to the default P which is
% 16...
+%
+% (1.4f: hesitation on 2021/05/09 after removal or case I log series should
+% I not follow the simplifying logic and use always the slightly more costly III?)
% |
%
-% \subsubsection{Log series, case I}
-% \begin{macrocode}
-\def\XINT_LogTen_serI_a_i#1\xint:{#1}%
-\ifnum\XINTdigits>9
-\def\XINT_tmpa#1.#2.{%
-\def\XINT_LogTen_serI_a_i##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_ii
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:
-}%
-\def\XINT_LogTen_serI_a_ii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_
- \romannumeral0\xintadd{1}{\xintiiOpp\xintHalf{##10}[##2-1]}\xint:
-}%
-\def\XINT_LogTen_serI_c_##1\xint:##2\xint:
-{%
- \XINTinFloat[#2]{\xintMul{##1}{##2}}%
-}%
-}%
-\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-7\expandafter.%
- \the\numexpr\XINTdigits-1.%
-\fi
-\ifnum\XINTdigits>15
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_ii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_iii
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_iii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_i
- \romannumeral0\xintadd{#3}{##1/3[##2]}\xint:
-}%
-\def\XINT_LogTen_serI_c_i##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-13\expandafter.%
- \the\numexpr\XINTdigits-7.%
- {-5[-1]}.%
- {1[0]}.%
-\fi
-\ifnum\XINTdigits>21
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_iii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_iv
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_iv##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_ii
- \romannumeral0\xintadd{#3}{\xintiiMul{-25}{##1}[##2-2]}\xint:
-}%
-\def\XINT_LogTen_serI_c_ii##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_i
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-19\expandafter.%
- \the\numexpr\XINTdigits-13\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-13]{1/3[0]}.%
- {-5[-1]}.%
-\fi
-\ifnum\XINTdigits>27
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_iv##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_v
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_v##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_iii
- \romannumeral0\xintadd{#3}{\xintDouble{##1}[##2-1]}\xint:
-}%
-\def\XINT_LogTen_serI_c_iii##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_ii
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-25\expandafter.%
- \the\numexpr\XINTdigits-19\expandafter.\expanded{%
- {-25[-2]}.%
- \XINTinFloat[\XINTdigits-13]{1/3[0]}.%
- }%
-\fi
-\ifnum\XINTdigits>33
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_v##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_vi
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_vi##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_iv
- \romannumeral0\xintadd{#3}{\xintiiOpp##1/6[##2]}\xint:
-}%
-\def\XINT_LogTen_serI_c_iv##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_iii
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-31\expandafter.%
- \the\numexpr\XINTdigits-25.%
- {2[-1]}.%
- {-25[-2]}.%
-\fi
-\ifnum\XINTdigits>39
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_vi##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_vii
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_vii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_v
- \romannumeral0\xintadd{#3}{##1/7[##2]}\xint:
-}%
-\def\XINT_LogTen_serI_c_v##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_iv
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-37\expandafter.%
- \the\numexpr\XINTdigits-31\expandafter.%
- \romannumeral0\XINTinfloatS[\XINTdigits-31]{-1/6[0]}.%
- {2[-1]}.%
-\fi
-\ifnum\XINTdigits>45
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_vii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_viii
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_viii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_vi
- \romannumeral0\xintadd{#3}{\xintiiMul{-125}{##1}[##2-3]}\xint:
-}%
-\def\XINT_LogTen_serI_c_vi##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_v
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-43\expandafter.%
- \the\numexpr\XINTdigits-37\expandafter.\expanded{%
- \XINTinFloat[\XINTdigits-37]{1/7[0]}.%
- \XINTinFloat[\XINTdigits-31]{-1/6[0]}.%
- }%
-\fi
-\ifnum\XINTdigits>51
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_viii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_ix
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_ix##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_vii
- \romannumeral0\xintadd{#3}{##1/9[##2]}\xint:
-}%
-\def\XINT_LogTen_serI_c_vii##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_vi
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-49\expandafter.%
- \the\numexpr\XINTdigits-43\expandafter.\expanded{%
- {-125[-3]}.%
- \XINTinFloat[\XINTdigits-37]{1/7[0]}.%
- }%
-\fi
-\ifnum\XINTdigits>57
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_ix##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_x
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_x##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_viii
- \romannumeral0\xintadd{#3}{\xintiiOpp##1[##2-1]}\xint:
-}%
-\def\XINT_LogTen_serI_c_viii##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_vii
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-55\expandafter.%
- \the\numexpr\XINTdigits-49\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-49]{1/9[0]}.%
- {-125[-3]}.%
-\fi
-% \end{macrocode}
% \subsubsection{Log series, case II}
% \begin{macrocode}
\def\XINT_tmpa#1.#2.{%
@@ -45793,8 +45757,8 @@
}%
}%
\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-2\expandafter.%
- \the\numexpr\XINTdigits+4.%
+ \the\numexpr\XINTdigitsormax-2\expandafter.%
+ \the\numexpr\XINTdigitsormax+4.%
\ifnum\XINTdigits>10
\def\XINT_tmpa#1.#2.#3.#4.{%
\def\XINT_LogTen_serII_a_ii##1\xint:
@@ -45818,8 +45782,8 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-8\expandafter.%
- \the\numexpr\XINTdigits-2.%
+ \the\numexpr\XINTdigitsormax-8\expandafter.%
+ \the\numexpr\XINTdigitsormax-2.%
{-5[-1]}.%
{1[0]}.%
\fi
@@ -45846,9 +45810,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-14\expandafter.%
- \the\numexpr\XINTdigits-8\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-8]{1/3[0]}.%
+ \the\numexpr\XINTdigitsormax-14\expandafter.%
+ \the\numexpr\XINTdigitsormax-8\expandafter.%
+ \romannumeral0\XINTinfloat[\XINTdigitsormax-8]{1/3[0]}.%
{-5[-1]}.%
\fi
\ifnum\XINTdigits>22
@@ -45874,10 +45838,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-20\expandafter.%
- \the\numexpr\XINTdigits-14\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-20\expandafter.%
+ \the\numexpr\XINTdigitsormax-14\expandafter.\expanded{%
{-25[-2]}.%
- \XINTinFloat[\XINTdigits-8]{1/3[0]}.%
+ \XINTinFloat[\XINTdigitsormax-8]{1/3[0]}.%
}%
\fi
\ifnum\XINTdigits>28
@@ -45903,8 +45867,8 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-26\expandafter.%
- \the\numexpr\XINTdigits-20.%
+ \the\numexpr\XINTdigitsormax-26\expandafter.%
+ \the\numexpr\XINTdigitsormax-20.%
{2[-1]}.%
{-25[-2]}.%
\fi
@@ -45931,9 +45895,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-32\expandafter.%
- \the\numexpr\XINTdigits-26\expandafter.%
- \romannumeral0\XINTinfloatS[\XINTdigits-26]{-1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-32\expandafter.%
+ \the\numexpr\XINTdigitsormax-26\expandafter.%
+ \romannumeral0\XINTinfloatS[\XINTdigitsormax-26]{-1/6[0]}.%
{2[-1]}.%
\fi
\ifnum\XINTdigits>40
@@ -45959,10 +45923,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-38\expandafter.%
- \the\numexpr\XINTdigits-32\expandafter.\expanded{%
- \XINTinFloat[\XINTdigits-32]{1/7[0]}.%
- \XINTinFloat[\XINTdigits-26]{-1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-38\expandafter.%
+ \the\numexpr\XINTdigitsormax-32\expandafter.\expanded{%
+ \XINTinFloat[\XINTdigitsormax-32]{1/7[0]}.%
+ \XINTinFloat[\XINTdigitsormax-26]{-1/6[0]}.%
}%
\fi
\ifnum\XINTdigits>46
@@ -45988,10 +45952,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-44\expandafter.%
- \the\numexpr\XINTdigits-38\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-44\expandafter.%
+ \the\numexpr\XINTdigitsormax-38\expandafter.\expanded{%
{-125[-3]}.%
- \XINTinFloat[\XINTdigits-32]{1/7[0]}.%
+ \XINTinFloat[\XINTdigitsormax-32]{1/7[0]}.%
}%
\fi
\ifnum\XINTdigits>52
@@ -46017,9 +45981,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-50\expandafter.%
- \the\numexpr\XINTdigits-44\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-44]{1/9[0]}.%
+ \the\numexpr\XINTdigitsormax-50\expandafter.%
+ \the\numexpr\XINTdigitsormax-44\expandafter.%
+ \romannumeral0\XINTinfloat[\XINTdigitsormax-44]{1/9[0]}.%
{-125[-3]}.%
\fi
\ifnum\XINTdigits>58
@@ -46045,10 +46009,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-56\expandafter.%
- \the\numexpr\XINTdigits-50\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-56\expandafter.%
+ \the\numexpr\XINTdigitsormax-50\expandafter.\expanded{%
{-1[-1]}.%
- \XINTinFloat[\XINTdigits-44]{1/9[0]}.%
+ \XINTinFloat[\XINTdigitsormax-44]{1/9[0]}.%
}%
\fi
% \end{macrocode}
@@ -46071,8 +46035,8 @@
}%
}%
\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-1\expandafter.%
- \the\numexpr\XINTdigits+4.%
+ \the\numexpr\XINTdigitsormax-1\expandafter.%
+ \the\numexpr\XINTdigitsormax+4.%
\ifnum\XINTdigits>9
\def\XINT_tmpa#1.#2.#3.#4.{%
\def\XINT_LogTen_serIII_a_ii##1\xint:
@@ -46096,8 +46060,8 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-7\expandafter.%
- \the\numexpr\XINTdigits-1.%
+ \the\numexpr\XINTdigitsormax-7\expandafter.%
+ \the\numexpr\XINTdigitsormax-1.%
{-5[-1]}.%
{1[0]}.%
\fi
@@ -46124,9 +46088,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-13\expandafter.%
- \the\numexpr\XINTdigits-7\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-7]{1/3[0]}.%
+ \the\numexpr\XINTdigitsormax-13\expandafter.%
+ \the\numexpr\XINTdigitsormax-7\expandafter.%
+ \romannumeral0\XINTinfloat[\XINTdigitsormax-7]{1/3[0]}.%
{-5[-1]}.%
\fi
\ifnum\XINTdigits>21
@@ -46152,10 +46116,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-19\expandafter.%
- \the\numexpr\XINTdigits-13\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-19\expandafter.%
+ \the\numexpr\XINTdigitsormax-13\expandafter.\expanded{%
{-25[-2]}.%
- \XINTinFloat[\XINTdigits-7]{1/3[0]}.%
+ \XINTinFloat[\XINTdigitsormax-7]{1/3[0]}.%
}%
\fi
\ifnum\XINTdigits>27
@@ -46181,8 +46145,8 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-25\expandafter.%
- \the\numexpr\XINTdigits-19.%
+ \the\numexpr\XINTdigitsormax-25\expandafter.%
+ \the\numexpr\XINTdigitsormax-19.%
{2[-1]}.%
{-25[-2]}.%
\fi
@@ -46209,9 +46173,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-31\expandafter.%
- \the\numexpr\XINTdigits-25\expandafter.%
- \romannumeral0\XINTinfloatS[\XINTdigits-25]{-1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-31\expandafter.%
+ \the\numexpr\XINTdigitsormax-25\expandafter.%
+ \romannumeral0\XINTinfloatS[\XINTdigitsormax-25]{-1/6[0]}.%
{2[-1]}.%
\fi
\ifnum\XINTdigits>39
@@ -46237,10 +46201,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-37\expandafter.%
- \the\numexpr\XINTdigits-31\expandafter.\expanded{%
- \XINTinFloat[\XINTdigits-31]{1/7[0]}.%
- \XINTinFloat[\XINTdigits-25]{-1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-37\expandafter.%
+ \the\numexpr\XINTdigitsormax-31\expandafter.\expanded{%
+ \XINTinFloat[\XINTdigitsormax-31]{1/7[0]}.%
+ \XINTinFloat[\XINTdigitsormax-25]{-1/6[0]}.%
}%
\fi
\ifnum\XINTdigits>45
@@ -46266,10 +46230,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-43\expandafter.%
- \the\numexpr\XINTdigits-37\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-43\expandafter.%
+ \the\numexpr\XINTdigitsormax-37\expandafter.\expanded{%
{-125[-3]}.%
- \XINTinFloat[\XINTdigits-31]{1/7[0]}.%
+ \XINTinFloat[\XINTdigitsormax-31]{1/7[0]}.%
}%
\fi
\ifnum\XINTdigits>51
@@ -46295,9 +46259,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-49\expandafter.%
- \the\numexpr\XINTdigits-43\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-43]{1/9[0]}.%
+ \the\numexpr\XINTdigitsormax-49\expandafter.%
+ \the\numexpr\XINTdigitsormax-43\expandafter.%
+ \romannumeral0\XINTinfloat[\XINTdigitsormax-43]{1/9[0]}.%
{-125[-3]}.%
\fi
\ifnum\XINTdigits>57
@@ -46323,10 +46287,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-55\expandafter.%
- \the\numexpr\XINTdigits-49\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-55\expandafter.%
+ \the\numexpr\XINTdigitsormax-49\expandafter.\expanded{%
{-1[-1]}.%
- \XINTinFloat[\XINTdigits-43]{1/9[0]}.%
+ \XINTinFloat[\XINTdigitsormax-43]{1/9[0]}.%
}%
\fi
\XINTendxintloginput%
@@ -46342,17 +46306,17 @@
xintbinhex.sty:53
xintcfrac.sty:183
xintcore.sty:272
-xintexpr.sty:431
+xintexpr.sty:433
xintfrac.sty:506
xintgcd.sty:41
xintkernel.sty:17
-xintlog.sty:187
+xintlog.sty:150
xintseries.sty:48
xinttools.sty:157
xinttrig.sty:65
\fi
% grep -o "^{%" xint*sty | wc -l
-\def\totala{ 2165}
+\def\totala{ 2130}
\iffalse
% grep -c -e "^}%" xint*sty
xint.sty:204
@@ -46359,17 +46323,17 @@
xintbinhex.sty:52
xintcfrac.sty:183
xintcore.sty:269
-xintexpr.sty:415
+xintexpr.sty:417
xintfrac.sty:508
xintgcd.sty:43
xintkernel.sty:18
-xintlog.sty:189
+xintlog.sty:151
xintseries.sty:48
xinttools.sty:156
xinttrig.sty:64
\fi
% grep -o "^}%" xint*sty | wc -l
-\def\totalb{ 2149}
+\def\totalb{ 2113}
\cleardoublepage
\section{Cumulative line count}
@@ -46393,8 +46357,8 @@
\TeX\strut. Version {\xintbndlversion} of {\xintbndldate}.\par
}
-\CheckSum {38813}% 1.4e
-% 35184 pour 1.4d
+\CheckSum {38212}% 1.4f
+% 38813 pour 1.4e, 35184 pour 1.4d
% 35109 pour 1.4c, 35103 pour 1.4b, 34648 pour 1.4a, 34575 pour 1.4
% 33497 pour 1.3f, 33274 pour 1.3e, 31601 pour 1.3d, 31122 pour 1.3c
% 31069 pour 1.3b, 30482 pour 1.3a, 30621 pour 1.3, 30988 pour 1.2q,
Modified: trunk/Master/texmf-dist/tex/generic/xint/xint.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xint.sty 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/tex/generic/xint/xint.sty 2021-05-10 19:49:04 UTC (rev 59161)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.4e 2021/05/05
+%% The xint bundle 1.4f 2021/05/10
%% Copyright (C) 2013-2021 by Jean-Francois Burnol
%% xint: Expandable operations on big integers
%% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
\XINTsetupcatcodes% defined in xintkernel.sty (loaded by xintcore.sty)
\XINT_providespackage
\ProvidesPackage{xint}%
- [2021/05/05 v1.4e Expandable operations on big integers (JFB)]%
+ [2021/05/10 v1.4f Expandable operations on big integers (JFB)]%
\long\def\xint_firstofthree #1#2#3{#1}%
\long\def\xint_secondofthree #1#2#3{#2}%
\long\def\xint_thirdofthree #1#2#3{#3}%
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintbinhex.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintbinhex.sty 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintbinhex.sty 2021-05-10 19:49:04 UTC (rev 59161)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.4e 2021/05/05
+%% The xint bundle 1.4f 2021/05/10
%% Copyright (C) 2013-2021 by Jean-Francois Burnol
%% xintbinhex: Expandable binary and hexadecimal conversions
%% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintbinhex}%
- [2021/05/05 v1.4e Expandable binary and hexadecimal conversions (JFB)]%
+ [2021/05/10 v1.4f Expandable binary and hexadecimal conversions (JFB)]%
\newcount\xint_c_ii^xv \xint_c_ii^xv 32768
\newcount\xint_c_ii^xvi \xint_c_ii^xvi 65536
\def\XINT_tmpa #1{\ifx\relax#1\else
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintcfrac.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintcfrac.sty 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintcfrac.sty 2021-05-10 19:49:04 UTC (rev 59161)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.4e 2021/05/05
+%% The xint bundle 1.4f 2021/05/10
%% Copyright (C) 2013-2021 by Jean-Francois Burnol
%% xintcfrac: Expandable continued fractions with xint package
%% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintcfrac}%
- [2021/05/05 v1.4e Expandable continued fractions with xint package (JFB)]%
+ [2021/05/10 v1.4f Expandable continued fractions with xint package (JFB)]%
\def\xintCFrac {\romannumeral0\xintcfrac }%
\def\xintcfrac #1%
{%
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintcore.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintcore.sty 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintcore.sty 2021-05-10 19:49:04 UTC (rev 59161)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.4e 2021/05/05
+%% The xint bundle 1.4f 2021/05/10
%% Copyright (C) 2013-2021 by Jean-Francois Burnol
%% xintcore: Expandable arithmetic on big integers
%% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintcore}%
- [2021/05/05 v1.4e Expandable arithmetic on big integers (JFB)]%
+ [2021/05/10 v1.4f Expandable arithmetic on big integers (JFB)]%
\csname XINT_Clamped_istrapped\endcsname
\csname XINT_ConversionSyntax_istrapped\endcsname
\csname XINT_DivisionByZero_istrapped\endcsname
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintexpr.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintexpr.sty 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintexpr.sty 2021-05-10 19:49:04 UTC (rev 59161)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.4e 2021/05/05
+%% The xint bundle 1.4f 2021/05/10
%% Copyright (C) 2013-2021 by Jean-Francois Burnol
%% xintexpr: Expandable expression parser
%% ---------------------------------------------------------------
@@ -82,7 +82,7 @@
\XINTsetupcatcodes%
\XINT_providespackage
\ProvidesPackage{xintexpr}%
- [2021/05/05 v1.4e Expandable expression parser (JFB)]%
+ [2021/05/10 v1.4f Expandable expression parser (JFB)]%
\catcode`! 11
\let\XINT_Cmp \xintiiCmp
\def\XINTfstop{\noexpand\XINTfstop}%
@@ -103,6 +103,7 @@
\let\XINTdigits\XINT_digits
\xintreloadscilibs
}%
+\def\XINTdigitsormax{\ifnum\XINTdigits>\xint_c_ii^vi\xint_c_ii^vi\else\XINTdigits\fi}%
\def\XINT:expr:toblistwith#1#2%
{%
{\expandafter\XINT:expr:toblist_checkempty
@@ -282,7 +283,7 @@
\expanded
\XINT:NEhook:x:mapwithin\XINT:expr:mapwithin{\XINTiRound_braced{#1}}%
}%
-\def\XINTiRound_braced#1#2{{\xintiRound{#1}{#2}[\the\numexpr-#1]}}%
+\def\XINTiRound_braced#1#2{{\xintiRound{#1}{#2}[\the\numexpr\ifnum#1<\xint_c_i0\else-#1\fi]}}%
\def\xintfloatexpro #1%
{%
\ifx [#1\expandafter\XINT_flexpr_withopt\else\expandafter\XINT_flexpr_noopt
@@ -3028,13 +3029,20 @@
}}%
}%
\let\XINT_flexpr_func_float\XINT_expr_func_float
-\def\XINT_expr_func_float_ #1#2#3%
+\def\XINT_expr_func_float_dgt #1#2#3%
{%
\expandafter #1\expandafter #2\expandafter{%
\romannumeral`&&@\XINT:NEhook:f:one:from:one
{\romannumeral`&&@\XINTinFloatdigits#3}}%
}%
-\let\XINT_flexpr_func_float_\XINT_expr_func_float_
+\let\XINT_flexpr_func_float_dgt\XINT_expr_func_float_dgt
+\def\XINT_expr_func_float_dgtormax #1#2#3%
+{%
+ \expandafter #1\expandafter #2\expandafter{%
+ \romannumeral`&&@\XINT:NEhook:f:one:from:one
+ {\romannumeral`&&@\XINTinFloatdigitsormax#3}}%
+}%
+\let\XINT_flexpr_func_float_dgtormax\XINT_expr_func_float_dgtormax
\def\XINT_expr_func_sfloat #1#2#3%
{%
\expandafter #1\expandafter #2\expandafter{\expandafter{%
@@ -3043,6 +3051,13 @@
}}%
}%
\let\XINT_flexpr_func_sfloat\XINT_expr_func_sfloat
+\def\XINT_expr_func_sfloat_dgtormax #1#2#3%
+{%
+ \expandafter #1\expandafter #2\expandafter{%
+ \romannumeral`&&@\XINT:NEhook:f:one:from:one
+ {\romannumeral`&&@\XINTinFloatSdigitsormax#3}}%
+}%
+\let\XINT_flexpr_func_sfloat_dgtormax\XINT_expr_func_sfloat_dgtormax
\expandafter\def\csname XINT_expr_func_ilog10\endcsname #1#2#3%
{%
\expandafter #1\expandafter #2\expandafter{\expandafter{%
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintfrac.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintfrac.sty 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintfrac.sty 2021-05-10 19:49:04 UTC (rev 59161)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.4e 2021/05/05
+%% The xint bundle 1.4f 2021/05/10
%% Copyright (C) 2013-2021 by Jean-Francois Burnol
%% xintfrac: Expandable operations on fractions
%% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintfrac}%
- [2021/05/05 v1.4e Expandable operations on fractions (JFB)]%
+ [2021/05/10 v1.4f Expandable operations on fractions (JFB)]%
\def\XINT_cntSgnFork #1%
{%
\ifcase #1\expandafter\xint_secondofthree
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintgcd.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintgcd.sty 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintgcd.sty 2021-05-10 19:49:04 UTC (rev 59161)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.4e 2021/05/05
+%% The xint bundle 1.4f 2021/05/10
%% Copyright (C) 2013-2021 by Jean-Francois Burnol
%% xintgcd: Euclidean algorithm with xint package
%% ---------------------------------------------------------------
@@ -77,7 +77,7 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintgcd}%
- [2021/05/05 v1.4e Euclide algorithm with xint package (JFB)]%
+ [2021/05/10 v1.4f Euclide algorithm with xint package (JFB)]%
\def\xintBezout {\romannumeral0\xintbezout }%
\def\xintbezout #1%
{%
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintkernel.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintkernel.sty 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintkernel.sty 2021-05-10 19:49:04 UTC (rev 59161)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.4e 2021/05/05
+%% The xint bundle 1.4f 2021/05/10
%% Copyright (C) 2013-2021 by Jean-Francois Burnol
%% xintkernel: Paraphernalia for the xint packages
%% ---------------------------------------------------------------
@@ -159,7 +159,7 @@
\fi
\XINT_providespackage
\ProvidesPackage {xintkernel}%
- [2021/05/05 v1.4e Paraphernalia for the xint packages (JFB)]%
+ [2021/05/10 v1.4f Paraphernalia for the xint packages (JFB)]%
\chardef\xint_c_ 0
\chardef\xint_c_i 1
\chardef\xint_c_ii 2
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintlog.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintlog.sty 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintlog.sty 2021-05-10 19:49:04 UTC (rev 59161)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.4e 2021/05/05
+%% The xint bundle 1.4f 2021/05/10
%% Copyright (C) 2013-2021 by Jean-Francois Burnol
%% xintlog: Logarithms and exponentials for xintexpr
%% ---------------------------------------------------------------
@@ -68,10 +68,10 @@
\expandafter\xint_secondoftwo
\fi
{\immediate\write-1{Reloading xintlog library using Digits=\xinttheDigits.}}%
-{\expandafter\gdef\csname xintlibver at log\endcsname{2021/05/05 v1.4e}%
+{\expandafter\gdef\csname xintlibver at log\endcsname{2021/05/10 v1.4f}%
\XINT_providespackage
\ProvidesPackage{xintlog}%
-[2021/05/05 v1.4e Logarithms and exponentials for xintexpr (JFB)]%
+[2021/05/10 v1.4f Logarithms and exponentials for xintexpr (JFB)]%
}%
\def\xintreloadxintlog{\input xintlog.sty }%
\xintexprSafeCatcodes\catcode`_ 11
@@ -150,28 +150,30 @@
\def\XINT_scipow_Biszero#1]#2#3{ 1[0]}%
\def\XINT_scipow_b #1#2/#3[#4]#5%
{%
- \unless\if1\XINT_is_One#3XY\xint_dothis\XINT_scipow_c\fi
- \ifnum#4<\xint_c_mone\xint_dothis\XINT_scipow_c\fi
- \ifnum#4=\xint_c_mone
- \if5\xintLDg{#1#2} %
+ \unless\if1\XINT_is_One#3XY\xint_dothis\XINT_scipow_c\fi
+ \ifnum#4<\xint_c_mone\xint_dothis\XINT_scipow_c\fi
+ \ifnum#4=\xint_c_mone
+ \if5\xintLDg{#1#2} %
\xint_afterfi{\xint_dothis\XINT_scipow_halfint}\else
\xint_afterfi{\xint_dothis\XINT_scipow_c}%
+ \fi
\fi
- \fi
- \xint_orthat#5#1#2/#3[#4]%
+ \xint_orthat#5#1#2/#3[#4]%
}%
\def\XINT_scipow_int #1/1[#2]#3%
{%
- \expandafter\XINT_flpower_checkB_a
- \romannumeral0\XINT_dsx_addzeros{#2}#1;.\XINTdigits.{#3}{\XINTinfloatS[\XINTdigits]}%
+ \expandafter\XINT_flpower_checkB_a
+ \romannumeral0\XINT_dsx_addzeros{#2}#1;.\XINTdigits.{#3}{\XINTinfloatS[\XINTdigits]}%
}%
\def\XINT_scipow_halfint#1/1[#2]#3%
{%
- \expandafter\XINT_flpower_checkB_a
- \romannumeral0\xintdsr{\xintDouble{#1}}.\XINTdigits.{#3}\XINT_flpowerh_finish
+ \expandafter\XINT_flpower_checkB_a
+ \romannumeral0\xintdsr{\xintDouble{#1}}.\XINTdigits.{#3}\XINT_flpowerh_finish
}%
\def\XINT_flpowerh_finish #1%
- {\XINTinfloatS[\XINTdigits]{\XINTinFloatSqrt[\XINTdigits+\xint_c_iii]{#1}}}%
+{%
+ \XINTinfloatS[\XINTdigits]{\XINTinFloatSqrt[\XINTdigits+\xint_c_iii]{#1}}%
+}%
\def\XINT_tmpa#1.{%
\def\XINT_scipow_c ##1[##2]##3%
{%
@@ -198,30 +200,24 @@
}%
\def\XINT_scipow_Aisneg #1#2\xint:#3\xint:
{%
- \XINT_signalcondition{InvalidOperation}{Fractional power of negative argument}{}{0[0]}
+ \XINT_signalcondition{InvalidOperation}{Fractional power of negative argument}{}{0[0]}%
}%
\ifnum\XINTdigits<9
- \def\XINTinfloatscipow#1#2%
+ \def\XINT_tmpa#1.#2.#3.{%
+ \def\XINT_scipow_c ##1[##2]##3%
{%
- \expandafter\XINT_scipow_a\romannumeral0\xintraw{#2}\relax{#1}%
+ \expandafter\XINT_scipow_d
+ \romannumeral0\expandafter\XINT_scipow_c_i
+ \romannumeral0\XINTinfloat[#1]{##3}\xint:##1[##2]\xint:
}%
- \def\XINT_scipow_b #1[#2]#3#4%
- {%
- \expandafter\XINT_scipow_d\romannumeral0\XINTinfloat[9]{#4}\xint:#1[#2]\xint:
- }%
+ \def\XINT_scipow_c_i##1[##2]{ ##1#3[##2-#2]}%
+ }\expandafter\XINT_tmpa\the\numexpr\XINTdigits\expandafter.%
+ \the\numexpr9-\XINTdigits\expandafter.%
+ \romannumeral\xintreplicate{9-\XINTdigits}0.%
\def\XINT_scipow_Aispos #1\xint:#2\xint:
{%
\poormanpoweroften{\xintMul{#2}{\romannumeral0\expandafter\PML at logbaseten#1}}%
}%
- \def\XINT_scipow_Aisneg #1#2\xint:#3\xint:
- {%
- \ifcase\xintFloatIntType{#3}%
- \or\expandafter-\romannumeral0%
- \else
- \expandafter\XINT_scipow_AnegBfrac
- \fi
- \poormanpoweroften{\xintMul{#3}{\romannumeral0\expandafter\PML at logbaseten#2}}%
- }%
\fi
\def\xintPow{\romannumeral0\xintpow}%
\def\xintpow#1#2%
@@ -228,19 +224,27 @@
{%
\expandafter\XINT_scipow_a\romannumeral0\xintrez{#2}\XINT_pow_int{#1}%
}%
-\def\XINT_pow_int #1/1[#2]%#3
+\def\XINT_pow_int #1/1[#2]%
{%
\expandafter\XINT_pow_int_a\romannumeral0\XINT_dsx_addzeros{#2}#1;.%
}%
-\def\XINT_pow_int_a #1#2.#3%
+\def\XINT_pow_int_a #1#2.%
{%
\ifnum\if-#1\xintLength{#2}\else\xintLength{#1#2}\fi>\xint_c_iv
- \expandafter\XINT_pow_tosci
- \fi
- \expandafter\XINT_pow_int_b\romannumeral0\xintraw{#3}\xint:#1#2\xint:
+ \expandafter\XINT_pow_bigint
+ \else\expandafter\XINT_pow_int_b
+ \fi #1#2.%
}%
-\def\XINT_pow_int_b#1#2/#3[#4]\xint:#5\xint:
+\def\XINT_pow_bigint #1.#2%
{%
+ \XINT_flpower_checkB_a#1.\XINTdigits.{#2}{\XINTinfloatS[\XINTdigits]}%
+}%
+\def\XINT_pow_int_b #1.#2%
+{%
+ \expandafter\XINT_pow_int_c\romannumeral0\xintraw{#2}\xint:#1\xint:
+}%
+\def\XINT_pow_int_c#1#2/#3[#4]\xint:#5\xint:
+{%
\if0\ifnum\numexpr\xint_c_x^iv/%
(\xintLength{#1#2}\if-#1-\xint_c_i\fi)<\XINT_Abs#5 %
1\else
@@ -247,51 +251,15 @@
\ifnum\numexpr\xint_c_x^iv/\xintLength{#3}<\XINT_Abs#5 %
1\else
0\fi\fi
- \expandafter\XINT_fpow_fork\else\expandafter\XINT_pow_tosci_i
+ \expandafter\XINT_fpow_fork\else\expandafter\XINT_pow_bigint_i
\fi
#5\Z{#4}{#1#2}{#3}%
}%
-\def\XINT_tmpa#1.{%
-\def\XINT_pow_tosci##1\xintraw%##2%\xint:##3\xint:
+\def\XINT_pow_bigint_i#1\Z#2#3#4%
{%
- \expandafter\XINT_scipow_d\romannumeral0\XINTinfloatS[#1]%
+ \XINT_flpower_checkB_a#1.\XINTdigits.{#3/#4[#2]}{\XINTinfloatS[\XINTdigits]}%
}%
-\def\XINT_pow_tosci_i##1\Z##2##3##4%
-{%
- \expandafter\XINT_scipow_d\romannumeral0\expandafter\XINT_infloatS_clean
- \romannumeral0\XINT_infloat_a#1.{##2}{##3}{##4}\xint:##1\xint:
-}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits.%
\ifnum\XINTdigits<9
- \def\xintpow#1#2%
- {%
- \expandafter\XINT_poorpow_a\romannumeral0\xintrez{#2}\relax{#1}%
- }%
- \def\XINT_poorpow_a #1%
- {%
- \xint_gob_til_zero#1\XINT_scipow_Biszero0\XINT_poorpow_b#1%
- }%
- \def\XINT_poorpow_b #1#2/#3[#4]#5%
- {%
- \unless\if1\XINT_is_One#3XY\xint_dothis\XINT_poorpow_c\fi
- \ifnum#4<\xint_c_\xint_dothis\XINT_poorpow_c\fi
- \xint_orthat\XINT_pow_int#1#2/#3[#4]%
- }%
- \def\XINT_poorpow_c #1[#2]#3%
- {%
- \expandafter\XINT_scipow_d\romannumeral0\XINTinfloat[9]{#3}\xint:#1[#2]\xint:
- }%
- \def\XINT_pow_tosci#1\xintraw%#2%\xint:#3\xint:
- {%
- \expandafter\XINT_scipow_d\romannumeral0\XINTinfloat[9]%
- }%
- \def\XINT_pow_tosci_i#1\Z#2#3#4%
- {%
- \expandafter\XINT_scipow_d\romannumeral0\expandafter\XINT_infloat_clean
- \romannumeral0\XINT_infloat_a9.{#2}{#3}{#4}\xint:#1\xint:
- }%
-\fi
-\ifnum\XINTdigits<9
\expandafter\def\csname XINT_expr_func_log10\endcsname#1#2#3%
{%
\expandafter #1\expandafter #2\expandafter{%
@@ -392,8 +360,8 @@
\expandafter\let\csname XINT_c_5_0_inv_x\endcsname\XINT_tmpa
\expandafter\let\csname XINT_c_6_0_inv_x\endcsname\XINT_tmpa
\def\XINT_tmpa#1#2#3#4;%
- {\expandafter\edef\csname XINT_c_#1_#2\endcsname{\XINTinFloat[\XINTdigits+5]{#3#4[-79]}}%
- \expandafter\edef\csname XINT_c_#1_#2_x\endcsname{\XINTinFloat[\XINTdigits+10]{#3#4[-79]}}%
+ {\expandafter\edef\csname XINT_c_#1_#2\endcsname{\XINTinFloat[\XINTdigitsormax+5]{#3#4[-79]}}%
+ \expandafter\edef\csname XINT_c_#1_#2_x\endcsname{\XINTinFloat[\XINTdigitsormax+10]{#3#4[-79]}}%
}%
\XINT_tmpa 1 1 12589254117941672104239541063958006060936174094669310691079230195266476157825020;%
\XINT_tmpa 1 2 15848931924611134852021013733915070132694421338250390683162968123166568636684540;%
@@ -450,8 +418,8 @@
\XINT_tmpa 6 8 10000184208504057336610176132939223090407041937631374389422968832433217547184883;%
\XINT_tmpa 6 9 10000207234805653031739097001771331138303016031686764989867510425362339583809842;%
\def\XINT_tmpa#1#2#3#4;%
- {\expandafter\edef\csname XINT_c_#1_#2_inv\endcsname{\XINTinFloat[\XINTdigits+5]{#3#4[-80]}}%
- \expandafter\edef\csname XINT_c_#1_#2_inv_x\endcsname{\XINTinFloat[\XINTdigits+10]{#3#4[-80]}}%
+ {\expandafter\edef\csname XINT_c_#1_#2_inv\endcsname{\XINTinFloat[\XINTdigitsormax+5]{#3#4[-80]}}%
+ \expandafter\edef\csname XINT_c_#1_#2_inv_x\endcsname{\XINTinFloat[\XINTdigitsormax+10]{#3#4[-80]}}%
}%
\XINT_tmpa 1 1 79432823472428150206591828283638793258896063175548433209232392931695569719148754;%
\XINT_tmpa 1 2 63095734448019324943436013662234386467294525718822872452772952883349494329768681;%
@@ -508,13 +476,13 @@
\XINT_tmpa 6 8 99998157948891574541919478156202215623119146605983303201215215949834619332550929;%
\XINT_tmpa 6 9 99997927694888844379020974874260864289829523807763942234420930258187873904191138;%
\edef\XINT_c_logten
- {\XINTinFloat[\XINTdigits+4]
+ {\XINTinFloat[\XINTdigitsormax+4]
{23025850929940456840179914546843642076011014886287729760333279009675726096773525[-79]}}%
\edef\XINT_c_oneoverlogten
- {\XINTinFloat[\XINTdigits+4]
+ {\XINTinFloat[\XINTdigitsormax+4]
{43429448190325182765112891891660508229439700580366656611445378316586464920887077[-80]}}%
\edef\XINT_c_oneoverlogten_xx
- {\XINTinFloat[\XINTdigits+14]
+ {\XINTinFloat[\XINTdigitsormax+14]
{43429448190325182765112891891660508229439700580366656611445378316586464920887077[-80]}}%
\def\XINTinFloatExp{\romannumeral0\XINTinfloatexp}%
\def\XINT_tmpa#1.{%
@@ -523,7 +491,7 @@
\XINTinfloatpowten
{\xintMul{\XINT_c_oneoverlogten_xx}{\XINTinFloatS[#1]{##1}}}%
}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+14.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+14.%
\def\XINTinFloatPowTen{\romannumeral0\XINTinfloatpowten}%
\def\XINT_tmpa#1.{%
\def\XINTinfloatpowten##1%
@@ -531,7 +499,7 @@
\expandafter\XINT_powten_fork
\romannumeral0\xintiround{#1}{##1}[-#1]%
}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+4.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+4.%
\def\XINT_powten_fork#1%
{%
\xint_UDzerominusfork
@@ -545,11 +513,11 @@
{%
\expandafter\XINT_powten_pos_a\romannumeral0\xintround{6}{#1[#2]}#1[#2]%
}%
-\def\XINT_tmpa #1.#2.{%
+\def\XINT_tmpa #1.#2.#3.{%
\def\XINT_powten_pos_a ##1.##2##3##4##5##6##7##8[##9]%
{%
\expandafter\XINT_infloate
- \romannumeral0\XINTinfloat[\XINTdigits]{%
+ \romannumeral0\XINTinfloat[#3]{%
\xintMul{\csname XINT_c_1_##2\endcsname}{%
\XINTinFloat[#1]{%
\xintMul{\csname XINT_c_2_##3\endcsname}{%
@@ -571,17 +539,18 @@
}%
}}}}}}}}}}}}{##1}%
}}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits+5\expandafter.%
- \the\numexpr\XINTdigits-1.%
+ \the\numexpr\XINTdigitsormax+5\expandafter.%
+ \the\numexpr\XINTdigitsormax-1\expandafter.%
+ \the\numexpr\XINTdigitsormax.%
\def\XINT_powten_neg#1[#2]%
{%
\expandafter\XINT_powten_neg_a\romannumeral0\xintround{6}{#1[#2]}#1[#2]%
}%
-\def\XINT_tmpa #1.#2.{%
+\def\XINT_tmpa #1.#2.#3.{%
\def\XINT_powten_neg_a -##1.##2##3##4##5##6##7##8[##9]%
{%
\expandafter\XINT_infloate
- \romannumeral0\XINTinfloat[\XINTdigits]{%
+ \romannumeral0\XINTinfloat[#3]{%
\xintMul{\csname XINT_c_1_##2_inv\endcsname}{%
\XINTinFloat[#1]{%
\xintMul{\csname XINT_c_2_##3_inv\endcsname}{%
@@ -603,8 +572,9 @@
}%
}}}}}}}}}}}}{-##1}%
}}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits+5\expandafter.%
- \the\numexpr\XINTdigits-1.%
+ \the\numexpr\XINTdigitsormax+5\expandafter.%
+ \the\numexpr\XINTdigitsormax-1\expandafter.%
+ \the\numexpr\XINTdigitsormax.%
\def\XINT_tmpa#1.#2.{%
\def\XINT_Exp_series_a_ii##1\xint:
{%
@@ -622,8 +592,8 @@
}%
}%
\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-6\expandafter.%
- \the\numexpr\XINTdigits-1.%
+ \the\numexpr\XINTdigitsormax-6\expandafter.%
+ \the\numexpr\XINTdigitsormax-1.%
\ifnum\XINTdigits>15
\def\XINT_tmpa#1.#2.#3.#4.{%
\def\XINT_Exp_series_a_ii##1\xint:
@@ -647,8 +617,8 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-13\expandafter.%
- \the\numexpr\XINTdigits-6.%
+ \the\numexpr\XINTdigitsormax-13\expandafter.%
+ \the\numexpr\XINTdigitsormax-6.%
{5[-1]}.%
{1[0]}.%
\fi
@@ -675,9 +645,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-19\expandafter.%
- \the\numexpr\XINTdigits-13\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-13]{1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-19\expandafter.%
+ \the\numexpr\XINTdigitsormax-13\expandafter.%
+ \romannumeral0\XINTinfloat[\XINTdigitsormax-13]{1/6[0]}.%
{5[-1]}.%
\fi
\ifnum\XINTdigits>28
@@ -715,10 +685,10 @@
\csname XINT_Exp_series_c_\romannumeral\numexpr#1-2\expandafter\endcsname
\csname XINT_Exp_series_c_\romannumeral\numexpr#1-3\endcsname
\expandafter\XINT_tmpc
- \the\numexpr\XINTdigits-#2\expandafter.%
- \the\numexpr\XINTdigits-#3\expandafter.\expanded{%
- \XINTinFloat[\XINTdigits-#3]{1/#6[0]}.%
- \XINTinFloat[\XINTdigits-#4]{1/#7[0]}.%
+ \the\numexpr\XINTdigitsormax-#2\expandafter.%
+ \the\numexpr\XINTdigitsormax-#3\expandafter.\expanded{%
+ \XINTinFloat[\XINTdigitsormax-#3]{1/#6[0]}.%
+ \XINTinFloat[\XINTdigitsormax-#4]{1/#7[0]}.%
}%
}%
\XINT_tmpa 5 26 19 13 120 24 6 %<-- keep space
@@ -732,7 +702,7 @@
\def\XINTinfloatlog
{%
\expandafter\XINT_log_out
- \romannumeral0\expandafter\XINT_logten_a
+ \romannumeral0\expandafter\XINT_logtenxdg_a
\romannumeral0\XINTinfloat[#1]%{##1}
}%
\def\XINT_log_out ##1\xint:##2\xint:
@@ -744,7 +714,7 @@
\def\XINTinfloatlogten
{%
\expandafter\XINT_logten_out
- \romannumeral0\expandafter\XINT_logten_a
+ \romannumeral0\expandafter\XINT_logtenxdg_a
\romannumeral0\XINTinfloat[#1]%{##1}
}%
\def\XINT_logten_out ##1\xint:##2\xint:
@@ -752,23 +722,23 @@
\XINTinfloat[#1]%
{\xintAdd{##1}{\xintMul{\XINT_c_oneoverlogten}{##2}}}%
}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax.%
\def\XINTinFloatLogTen_xdgout%#1[#2]
{%
- \romannumeral0\expandafter\XINT_logten_xdgout\romannumeral0\XINT_logten_a
+ \romannumeral0\expandafter\XINT_logten_xdgout\romannumeral0\XINT_logtenxdg_a
}%
\def\XINT_logten_xdgout #1\xint:#2\xint:
{%
\xintadd{#1}{\xintMul{\XINT_c_oneoverlogten_xx}{#2}}%
}%
-\def\XINT_logten_a#1[#2]%
+\def\XINT_logtenxdg_a#1[#2]%
{%
- \expandafter\XINT_logten_b
+ \expandafter\XINT_logtenxdg_b
\romannumeral0\XINTinfloat[9]{#1[#2]}#1[#2]%
}%
-\def\XINT_logten_b#1[#2]%
+\def\XINT_logtenxdg_b#1[#2]%
{%
- \expandafter\XINT_logten_c
+ \expandafter\XINT_logtenxdg_c
\romannumeral0\xintround{6}%
{\xintiiAdd{\xintDSx{-9}{\the\numexpr#2+8\relax}}%
{\the\numexpr\PML@#1.\relax}%
@@ -775,52 +745,44 @@
[-9]}%
\xint:
}%
-\def\XINT_logten_c #1#2%
+\def\XINT_logtenxdg_c #1#2%
{%
\xint_gob_til_xint:#2\XINT_logten_IV\xint:
- \XINT_logten_d #1#2%
+ \XINT_logtenxdg_d #1#2%
}%
-\def\XINT_logten_IV\xint:\XINT_logten_d0{\XINT_logten_f_III}%
-\def\XINT_logten_d #1.#2\xint:
+\def\XINT_logten_IV\xint:\XINT_logtenxdg_d0{\XINT_logten_f_III}%
+\def\XINT_logtenxdg_d #1.#2\xint:
{%
\ifcase
\ifnum#1=\xint_c_
- \ifnum #2>100000 \xint_c_i\else
- \ifnum #2>\xint_c_ \xint_c_ii\else \xint_c_iii\fi\fi
+ \ifnum #2=\xint_c_ \xint_c_iii\else \xint_c_ii\fi
\else
- \ifnum#2>\xint_c_ \xint_c_i\else \xint_c_\fi
+ \ifnum#2>\xint_c_ \xint_c_ii\else \xint_c_\fi
\fi
\expandafter\XINT_logten_f_Isp
- \or\expandafter\XINT_logten_f_I
- \or\expandafter\XINT_logten_f_II
+ \or% never
+ \or\expandafter\XINT_logten_f_IorII
\else\expandafter\XINT_logten_f_III
\fi
#1.#2\xint:
}%
-\def\XINT_logten_f_I#1%
+\def\XINT_logten_f_IorII#1%
{%
\xint_UDsignfork
- #1\XINT_logten_f_I_neg
- -\XINT_logten_f_I_pos
+ #1\XINT_logten_f_IorII_neg
+ -\XINT_logten_f_IorII_pos
\krof #1%
}%
-\def\XINT_logten_f_II#1%
-{%
- \xint_UDsignfork
- #1\XINT_logten_f_II_neg
- -\XINT_logten_f_II_pos
- \krof #1%
-}%
\def\XINT_tmpa#1.{%
\def\XINT_logten_f_Isp##1.000000\xint:##2[##3]%
{%
{##1[0]}\xint:
- {\expandafter\XINT_LogTen_serI_a_i
+ {\expandafter\XINT_LogTen_serII_a_ii
\romannumeral0\XINTinfloatS[#1]{\xintAdd{##2[##3-##1]}{-1[0]}}%
\xint:
}\xint:
}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits-2.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax.%
\def\XINT_tmpa#1.{%
\def\XINT_logten_f_III##1\xint:##2[##3]%
{%
@@ -829,25 +791,25 @@
\romannumeral0\XINTinfloatS[#1]{\xintAdd{##2[##3]}{-1[0]}}%
\xint:
}\xint:
-}}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+4.%
+}}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+4.%
\def\XINT_tmpa#1.#2.{%
-\def\XINT_logten_f_I_pos##1.##2##3##4##5##6##7\xint:##8[##9]%
+\def\XINT_logten_f_IorII_pos##1.##2##3##4##5##6##7\xint:##8[##9]%
{%
{\the\numexpr##1##2##3##4##5##6##7[-6]}\xint:
- {\expandafter\XINT_LogTen_serI_a_i
+ {\expandafter\XINT_LogTen_serII_a_ii
\romannumeral0\XINTinfloat[#2]%
{\xintAdd{-1[0]}%
- {\xintMul{\csname XINT_c_1_##2_inv\endcsname}{%
+ {\xintMul{\csname XINT_c_1_##2_inv_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_2_##3_inv\endcsname}{%
+ \xintMul{\csname XINT_c_2_##3_inv_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_3_##4_inv\endcsname}{%
+ \xintMul{\csname XINT_c_3_##4_inv_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_4_##5_inv\endcsname}{%
+ \xintMul{\csname XINT_c_4_##5_inv_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_5_##6_inv\endcsname}{%
+ \xintMul{\csname XINT_c_5_##6_inv_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_6_##7_inv\endcsname}
+ \xintMul{\csname XINT_c_6_##7_inv_x\endcsname}
{##8[##9-##1]}%
}}}}}}}}}}%
}%
@@ -854,23 +816,23 @@
}\xint:
}\xint:
}%
-\def\XINT_logten_f_I_neg##1.##2##3##4##5##6##7\xint:##8[##9]%
+\def\XINT_logten_f_IorII_neg##1.##2##3##4##5##6##7\xint:##8[##9]%
{%
{\the\numexpr##1##2##3##4##5##6##7[-6]}\xint:
- {\expandafter\XINT_LogTen_serI_a_i
+ {\expandafter\XINT_LogTen_serII_a_ii
\romannumeral0\XINTinfloat[#2]%
{\xintAdd{-1[0]}%
- {\xintMul{\csname XINT_c_1_##2\endcsname}{%
+ {\xintMul{\csname XINT_c_1_##2_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_2_##3\endcsname}{%
+ \xintMul{\csname XINT_c_2_##3_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_3_##4\endcsname}{%
+ \xintMul{\csname XINT_c_3_##4_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_4_##5\endcsname}{%
+ \xintMul{\csname XINT_c_4_##5_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_5_##6\endcsname}{%
+ \xintMul{\csname XINT_c_5_##6_x\endcsname}{%
\XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_6_##7\endcsname}
+ \xintMul{\csname XINT_c_6_##7_x\endcsname}
{##8[##9-##1]}%
}}}}}}}}}}%
}%
@@ -878,311 +840,8 @@
}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits+5\expandafter.\the\numexpr\XINTdigits-1.%
+ \the\numexpr\XINTdigitsormax+10\expandafter.\the\numexpr\XINTdigitsormax+4.%
\def\XINT_tmpa#1.#2.{%
-\def\XINT_logten_f_II_pos0.##1##2##3##4##5##6\xint:##7[##8]%
-{%
- {\the\numexpr##1##2##3##4##5##6[-6]}\xint:
- {\expandafter\XINT_LogTen_serII_a_ii
- \romannumeral0\XINTinfloat[#2]%
- {\xintAdd{-1[0]}%
- {\xintMul{\csname XINT_c_1_##1_inv_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_2_##2_inv_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_3_##3_inv_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_4_##4_inv_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_5_##5_inv_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_6_##6_inv_x\endcsname}
- {##7[##8]}%
- }}}}}}}}}}%
- }%
- }\xint:
- }\xint:
-}%
-\def\XINT_logten_f_II_neg-0.##1##2##3##4##5##6\xint:##7[##8]%
-{%
- {\the\numexpr-##1##2##3##4##5##6[-6]}\xint:
- {\expandafter\XINT_LogTen_serII_a_ii
- \romannumeral0\XINTinfloat[#2]%
- {\xintAdd{-1[0]}%
- {\xintMul{\csname XINT_c_1_##1_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_2_##2_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_3_##3_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_4_##4_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_5_##5_x\endcsname}{%
- \XINTinFloat[#1]{%
- \xintMul{\csname XINT_c_6_##6_x\endcsname}
- {##7[##8]}%
- }}}}}}}}}}%
- }%
- }\xint:
- }\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits+10\expandafter.\the\numexpr\XINTdigits+4.%
-\def\XINT_LogTen_serI_a_i#1\xint:{#1}%
-\ifnum\XINTdigits>9
-\def\XINT_tmpa#1.#2.{%
-\def\XINT_LogTen_serI_a_i##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_ii
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:
-}%
-\def\XINT_LogTen_serI_a_ii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_
- \romannumeral0\xintadd{1}{\xintiiOpp\xintHalf{##10}[##2-1]}\xint:
-}%
-\def\XINT_LogTen_serI_c_##1\xint:##2\xint:
-{%
- \XINTinFloat[#2]{\xintMul{##1}{##2}}%
-}%
-}%
-\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-7\expandafter.%
- \the\numexpr\XINTdigits-1.%
-\fi
-\ifnum\XINTdigits>15
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_ii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_iii
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_iii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_i
- \romannumeral0\xintadd{#3}{##1/3[##2]}\xint:
-}%
-\def\XINT_LogTen_serI_c_i##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-13\expandafter.%
- \the\numexpr\XINTdigits-7.%
- {-5[-1]}.%
- {1[0]}.%
-\fi
-\ifnum\XINTdigits>21
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_iii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_iv
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_iv##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_ii
- \romannumeral0\xintadd{#3}{\xintiiMul{-25}{##1}[##2-2]}\xint:
-}%
-\def\XINT_LogTen_serI_c_ii##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_i
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-19\expandafter.%
- \the\numexpr\XINTdigits-13\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-13]{1/3[0]}.%
- {-5[-1]}.%
-\fi
-\ifnum\XINTdigits>27
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_iv##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_v
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_v##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_iii
- \romannumeral0\xintadd{#3}{\xintDouble{##1}[##2-1]}\xint:
-}%
-\def\XINT_LogTen_serI_c_iii##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_ii
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-25\expandafter.%
- \the\numexpr\XINTdigits-19\expandafter.\expanded{%
- {-25[-2]}.%
- \XINTinFloat[\XINTdigits-13]{1/3[0]}.%
- }%
-\fi
-\ifnum\XINTdigits>33
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_v##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_vi
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_vi##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_iv
- \romannumeral0\xintadd{#3}{\xintiiOpp##1/6[##2]}\xint:
-}%
-\def\XINT_LogTen_serI_c_iv##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_iii
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-31\expandafter.%
- \the\numexpr\XINTdigits-25.%
- {2[-1]}.%
- {-25[-2]}.%
-\fi
-\ifnum\XINTdigits>39
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_vi##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_vii
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_vii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_v
- \romannumeral0\xintadd{#3}{##1/7[##2]}\xint:
-}%
-\def\XINT_LogTen_serI_c_v##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_iv
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-37\expandafter.%
- \the\numexpr\XINTdigits-31\expandafter.%
- \romannumeral0\XINTinfloatS[\XINTdigits-31]{-1/6[0]}.%
- {2[-1]}.%
-\fi
-\ifnum\XINTdigits>45
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_vii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_viii
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_viii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_vi
- \romannumeral0\xintadd{#3}{\xintiiMul{-125}{##1}[##2-3]}\xint:
-}%
-\def\XINT_LogTen_serI_c_vi##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_v
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-43\expandafter.%
- \the\numexpr\XINTdigits-37\expandafter.\expanded{%
- \XINTinFloat[\XINTdigits-37]{1/7[0]}.%
- \XINTinFloat[\XINTdigits-31]{-1/6[0]}.%
- }%
-\fi
-\ifnum\XINTdigits>51
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_viii##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_ix
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_ix##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_vii
- \romannumeral0\xintadd{#3}{##1/9[##2]}\xint:
-}%
-\def\XINT_LogTen_serI_c_vii##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_vi
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-49\expandafter.%
- \the\numexpr\XINTdigits-43\expandafter.\expanded{%
- {-125[-3]}.%
- \XINTinFloat[\XINTdigits-37]{1/7[0]}.%
- }%
-\fi
-\ifnum\XINTdigits>57
-\def\XINT_tmpa#1.#2.#3.#4.{%
-\def\XINT_LogTen_serI_a_ix##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_a_x
- \romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_a_x##1\xint:
-{%
- \expandafter\XINT_LogTen_serI_b
- \romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint:
-}%
-\def\XINT_LogTen_serI_b##1[##2]\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_viii
- \romannumeral0\xintadd{#3}{\xintiiOpp##1[##2-1]}\xint:
-}%
-\def\XINT_LogTen_serI_c_viii##1\xint:##2\xint:
-{%
- \expandafter\XINT_LogTen_serI_c_vii
- \romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
-}%
-}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-55\expandafter.%
- \the\numexpr\XINTdigits-49\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-49]{1/9[0]}.%
- {-125[-3]}.%
-\fi
-\def\XINT_tmpa#1.#2.{%
\def\XINT_LogTen_serII_a_ii##1\xint:
{%
\expandafter\XINT_LogTen_serII_b
@@ -1199,8 +858,8 @@
}%
}%
\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-2\expandafter.%
- \the\numexpr\XINTdigits+4.%
+ \the\numexpr\XINTdigitsormax-2\expandafter.%
+ \the\numexpr\XINTdigitsormax+4.%
\ifnum\XINTdigits>10
\def\XINT_tmpa#1.#2.#3.#4.{%
\def\XINT_LogTen_serII_a_ii##1\xint:
@@ -1224,8 +883,8 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-8\expandafter.%
- \the\numexpr\XINTdigits-2.%
+ \the\numexpr\XINTdigitsormax-8\expandafter.%
+ \the\numexpr\XINTdigitsormax-2.%
{-5[-1]}.%
{1[0]}.%
\fi
@@ -1252,9 +911,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-14\expandafter.%
- \the\numexpr\XINTdigits-8\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-8]{1/3[0]}.%
+ \the\numexpr\XINTdigitsormax-14\expandafter.%
+ \the\numexpr\XINTdigitsormax-8\expandafter.%
+ \romannumeral0\XINTinfloat[\XINTdigitsormax-8]{1/3[0]}.%
{-5[-1]}.%
\fi
\ifnum\XINTdigits>22
@@ -1280,10 +939,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-20\expandafter.%
- \the\numexpr\XINTdigits-14\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-20\expandafter.%
+ \the\numexpr\XINTdigitsormax-14\expandafter.\expanded{%
{-25[-2]}.%
- \XINTinFloat[\XINTdigits-8]{1/3[0]}.%
+ \XINTinFloat[\XINTdigitsormax-8]{1/3[0]}.%
}%
\fi
\ifnum\XINTdigits>28
@@ -1309,8 +968,8 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-26\expandafter.%
- \the\numexpr\XINTdigits-20.%
+ \the\numexpr\XINTdigitsormax-26\expandafter.%
+ \the\numexpr\XINTdigitsormax-20.%
{2[-1]}.%
{-25[-2]}.%
\fi
@@ -1337,9 +996,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-32\expandafter.%
- \the\numexpr\XINTdigits-26\expandafter.%
- \romannumeral0\XINTinfloatS[\XINTdigits-26]{-1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-32\expandafter.%
+ \the\numexpr\XINTdigitsormax-26\expandafter.%
+ \romannumeral0\XINTinfloatS[\XINTdigitsormax-26]{-1/6[0]}.%
{2[-1]}.%
\fi
\ifnum\XINTdigits>40
@@ -1365,10 +1024,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-38\expandafter.%
- \the\numexpr\XINTdigits-32\expandafter.\expanded{%
- \XINTinFloat[\XINTdigits-32]{1/7[0]}.%
- \XINTinFloat[\XINTdigits-26]{-1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-38\expandafter.%
+ \the\numexpr\XINTdigitsormax-32\expandafter.\expanded{%
+ \XINTinFloat[\XINTdigitsormax-32]{1/7[0]}.%
+ \XINTinFloat[\XINTdigitsormax-26]{-1/6[0]}.%
}%
\fi
\ifnum\XINTdigits>46
@@ -1394,10 +1053,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-44\expandafter.%
- \the\numexpr\XINTdigits-38\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-44\expandafter.%
+ \the\numexpr\XINTdigitsormax-38\expandafter.\expanded{%
{-125[-3]}.%
- \XINTinFloat[\XINTdigits-32]{1/7[0]}.%
+ \XINTinFloat[\XINTdigitsormax-32]{1/7[0]}.%
}%
\fi
\ifnum\XINTdigits>52
@@ -1423,9 +1082,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-50\expandafter.%
- \the\numexpr\XINTdigits-44\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-44]{1/9[0]}.%
+ \the\numexpr\XINTdigitsormax-50\expandafter.%
+ \the\numexpr\XINTdigitsormax-44\expandafter.%
+ \romannumeral0\XINTinfloat[\XINTdigitsormax-44]{1/9[0]}.%
{-125[-3]}.%
\fi
\ifnum\XINTdigits>58
@@ -1451,10 +1110,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-56\expandafter.%
- \the\numexpr\XINTdigits-50\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-56\expandafter.%
+ \the\numexpr\XINTdigitsormax-50\expandafter.\expanded{%
{-1[-1]}.%
- \XINTinFloat[\XINTdigits-44]{1/9[0]}.%
+ \XINTinFloat[\XINTdigitsormax-44]{1/9[0]}.%
}%
\fi
\def\XINT_tmpa#1.#2.{%
@@ -1474,8 +1133,8 @@
}%
}%
\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-1\expandafter.%
- \the\numexpr\XINTdigits+4.%
+ \the\numexpr\XINTdigitsormax-1\expandafter.%
+ \the\numexpr\XINTdigitsormax+4.%
\ifnum\XINTdigits>9
\def\XINT_tmpa#1.#2.#3.#4.{%
\def\XINT_LogTen_serIII_a_ii##1\xint:
@@ -1499,8 +1158,8 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-7\expandafter.%
- \the\numexpr\XINTdigits-1.%
+ \the\numexpr\XINTdigitsormax-7\expandafter.%
+ \the\numexpr\XINTdigitsormax-1.%
{-5[-1]}.%
{1[0]}.%
\fi
@@ -1527,9 +1186,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-13\expandafter.%
- \the\numexpr\XINTdigits-7\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-7]{1/3[0]}.%
+ \the\numexpr\XINTdigitsormax-13\expandafter.%
+ \the\numexpr\XINTdigitsormax-7\expandafter.%
+ \romannumeral0\XINTinfloat[\XINTdigitsormax-7]{1/3[0]}.%
{-5[-1]}.%
\fi
\ifnum\XINTdigits>21
@@ -1555,10 +1214,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-19\expandafter.%
- \the\numexpr\XINTdigits-13\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-19\expandafter.%
+ \the\numexpr\XINTdigitsormax-13\expandafter.\expanded{%
{-25[-2]}.%
- \XINTinFloat[\XINTdigits-7]{1/3[0]}.%
+ \XINTinFloat[\XINTdigitsormax-7]{1/3[0]}.%
}%
\fi
\ifnum\XINTdigits>27
@@ -1584,8 +1243,8 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-25\expandafter.%
- \the\numexpr\XINTdigits-19.%
+ \the\numexpr\XINTdigitsormax-25\expandafter.%
+ \the\numexpr\XINTdigitsormax-19.%
{2[-1]}.%
{-25[-2]}.%
\fi
@@ -1612,9 +1271,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-31\expandafter.%
- \the\numexpr\XINTdigits-25\expandafter.%
- \romannumeral0\XINTinfloatS[\XINTdigits-25]{-1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-31\expandafter.%
+ \the\numexpr\XINTdigitsormax-25\expandafter.%
+ \romannumeral0\XINTinfloatS[\XINTdigitsormax-25]{-1/6[0]}.%
{2[-1]}.%
\fi
\ifnum\XINTdigits>39
@@ -1640,10 +1299,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-37\expandafter.%
- \the\numexpr\XINTdigits-31\expandafter.\expanded{%
- \XINTinFloat[\XINTdigits-31]{1/7[0]}.%
- \XINTinFloat[\XINTdigits-25]{-1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-37\expandafter.%
+ \the\numexpr\XINTdigitsormax-31\expandafter.\expanded{%
+ \XINTinFloat[\XINTdigitsormax-31]{1/7[0]}.%
+ \XINTinFloat[\XINTdigitsormax-25]{-1/6[0]}.%
}%
\fi
\ifnum\XINTdigits>45
@@ -1669,10 +1328,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-43\expandafter.%
- \the\numexpr\XINTdigits-37\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-43\expandafter.%
+ \the\numexpr\XINTdigitsormax-37\expandafter.\expanded{%
{-125[-3]}.%
- \XINTinFloat[\XINTdigits-31]{1/7[0]}.%
+ \XINTinFloat[\XINTdigitsormax-31]{1/7[0]}.%
}%
\fi
\ifnum\XINTdigits>51
@@ -1698,9 +1357,9 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-49\expandafter.%
- \the\numexpr\XINTdigits-43\expandafter.%
- \romannumeral0\XINTinfloat[\XINTdigits-43]{1/9[0]}.%
+ \the\numexpr\XINTdigitsormax-49\expandafter.%
+ \the\numexpr\XINTdigitsormax-43\expandafter.%
+ \romannumeral0\XINTinfloat[\XINTdigitsormax-43]{1/9[0]}.%
{-125[-3]}.%
\fi
\ifnum\XINTdigits>57
@@ -1726,10 +1385,10 @@
\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{##1}{##2}}}\xint:
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits-55\expandafter.%
- \the\numexpr\XINTdigits-49\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-55\expandafter.%
+ \the\numexpr\XINTdigitsormax-49\expandafter.\expanded{%
{-1[-1]}.%
- \XINTinFloat[\XINTdigits-43]{1/9[0]}.%
+ \XINTinFloat[\XINTdigitsormax-43]{1/9[0]}.%
}%
\fi
\XINTendxintloginput%
Modified: trunk/Master/texmf-dist/tex/generic/xint/xintseries.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xintseries.sty 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/tex/generic/xint/xintseries.sty 2021-05-10 19:49:04 UTC (rev 59161)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.4e 2021/05/05
+%% The xint bundle 1.4f 2021/05/10
%% Copyright (C) 2013-2021 by Jean-Francois Burnol
%% xintseries: Expandable partial sums with xint package
%% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintseries}%
- [2021/05/05 v1.4e Expandable partial sums with xint package (JFB)]%
+ [2021/05/10 v1.4f Expandable partial sums with xint package (JFB)]%
\def\xintSeries {\romannumeral0\xintseries }%
\def\xintseries #1#2%
{%
Modified: trunk/Master/texmf-dist/tex/generic/xint/xinttools.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xinttools.sty 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/tex/generic/xint/xinttools.sty 2021-05-10 19:49:04 UTC (rev 59161)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.4e 2021/05/05
+%% The xint bundle 1.4f 2021/05/10
%% Copyright (C) 2013-2021 by Jean-Francois Burnol
%% xinttools: Expandable and non-expandable utilities
%% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xinttools}%
- [2021/05/05 v1.4e Expandable and non-expandable utilities (JFB)]%
+ [2021/05/10 v1.4f Expandable and non-expandable utilities (JFB)]%
\newtoks\XINT_toks
\xint_firstofone{\let\XINT_sptoken= } %<- space here!
\def\xintgodef {\global\xintodef }%
Modified: trunk/Master/texmf-dist/tex/generic/xint/xinttrig.sty
===================================================================
--- trunk/Master/texmf-dist/tex/generic/xint/xinttrig.sty 2021-05-10 16:06:29 UTC (rev 59160)
+++ trunk/Master/texmf-dist/tex/generic/xint/xinttrig.sty 2021-05-10 19:49:04 UTC (rev 59161)
@@ -21,7 +21,7 @@
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
-%% The xint bundle 1.4e 2021/05/05
+%% The xint bundle 1.4f 2021/05/10
%% Copyright (C) 2013-2021 by Jean-Francois Burnol
%% xinttrig: Trigonometry for the xintexpr package
%% ---------------------------------------------------------------
@@ -69,10 +69,10 @@
\expandafter\xint_secondoftwo
\fi
{\immediate\write-1{Reloading xinttrig library using Digits=\xinttheDigits.}}%
-{\expandafter\gdef\csname xintlibver at trig\endcsname{2021/05/05 v1.4e}%
+{\expandafter\gdef\csname xintlibver at trig\endcsname{2021/05/10 v1.4f}%
\XINT_providespackage
\ProvidesPackage{xinttrig}%
-[2021/05/05 v1.4e Trigonometrical functions for xintexpr (JFB)]%
+[2021/05/10 v1.4f Trigonometrical functions for xintexpr (JFB)]%
}%
\xintFor* #1 in {iDTVtuwxyzX}\do{\xintensuredummy{#1}}%
\def\xintreloadxinttrig{\input xinttrig.sty }%
@@ -79,27 +79,27 @@
\xintdefvar @twoPi :=
float(
6.2831853071795864769252867665590057683943387987502116419498891846156328125724180
- ,\xinttheDigits+4);%
+ ,\XINTdigitsormax+4);%
\xintdefvar @threePiover2 :=
float(
4.7123889803846898576939650749192543262957540990626587314624168884617246094293135
- ,\xinttheDigits+4);%
+ ,\XINTdigitsormax+4);%
\xintdefvar @Pi :=
float(
3.1415926535897932384626433832795028841971693993751058209749445923078164062862090
- ,\xinttheDigits+4);%
+ ,\XINTdigitsormax+4);%
\xintdefvar @Piover2 :=
float(
1.5707963267948966192313216916397514420985846996875529104874722961539082031431045
- ,\xinttheDigits+4);%
+ ,\XINTdigitsormax+4);%
\xintdefvar @oneDegree :=
float(
0.017453292519943295769236907684886127134428718885417254560971914401710091146034494
- ,\xinttheDigits+4);%
+ ,\XINTdigitsormax+4);%
\xintdefvar @oneRadian :=
float(
57.295779513082320876798154814105170332405472466564321549160243861202847148321553
- ,\xinttheDigits+12);%
+ ,\XINTdigitsormax+12);%
\catcode`~ 12
\def\XINT_tmpa#1#2#3.#4.%
{%
@@ -109,19 +109,19 @@
\expandafter\XINT_tmpa
\csname XINT_flexpr_exec_+_\expandafter\endcsname
\csname XINT_flexpr_exec_+\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatAdd_wopt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatAdd_wopt.%
\expandafter\XINT_tmpa
\csname XINT_flexpr_exec_-_\expandafter\endcsname
\csname XINT_flexpr_exec_-\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatSub_wopt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatSub_wopt.%
\expandafter\XINT_tmpa
\csname XINT_flexpr_exec_*_\expandafter\endcsname
\csname XINT_flexpr_exec_*\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatMul_wopt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatMul_wopt.%
\expandafter\XINT_tmpa
\csname XINT_flexpr_exec_/_\expandafter\endcsname
\csname XINT_flexpr_exec_/\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatDiv_wopt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatDiv_wopt.%
\def\XINT_tmpa#1#2#3.#4.%
{%
\let #1#2%
@@ -130,23 +130,23 @@
\expandafter\XINT_tmpa
\csname XINT_flexpr_sqrfunc\expandafter\endcsname
\csname XINT_flexpr_func_sqr\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatSqr_wopt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatSqr_wopt.%
\expandafter\XINT_tmpa
\csname XINT_flexpr_sqrtfunc\expandafter\endcsname
\csname XINT_flexpr_func_sqrt\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatSqrt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatSqrt.%
\expandafter\XINT_tmpa
\csname XINT_flexpr_invfunc\expandafter\endcsname
\csname XINT_flexpr_func_inv\expandafter\endcsname
- \the\numexpr\XINTdigits+4.~XINTinFloatInv_wopt.%
+ \the\numexpr\XINTdigitsormax+4.~XINTinFloatInv_wopt.%
\catcode`~ 3
\ifnum\XINTdigits>8
\edef\XINT_tmpG % 1/3!
- {1\xintReplicate{\XINTdigits+2}{6}7[\the\numexpr-\XINTdigits-4]}%
+ {1\xintReplicate{\XINTdigitsormax+2}{6}7[\the\numexpr-\XINTdigitsormax-4]}%
\edef\XINT_tmpH % 1/5!
- {8\xintReplicate{\XINTdigits+1}{3}[\the\numexpr-\XINTdigits-4]}%
+ {8\xintReplicate{\XINTdigitsormax+1}{3}[\the\numexpr-\XINTdigitsormax-4]}%
\edef\XINT_tmpd % 1/5!
- {8\xintReplicate{\XINTdigits+9}{3}[\the\numexpr-\XINTdigits-12]}%
+ {8\xintReplicate{\XINTdigitsormax+9}{3}[\the\numexpr-\XINTdigitsormax-12]}%
\def\XINT_tmpe#1.#2.#3.#4.#5#6#7%
{%
\def#5##1\xint:
@@ -163,8 +163,8 @@
}%
}%
\expandafter\XINT_tmpe
- \the\numexpr\XINTdigits+4\expandafter.%
- \the\numexpr\XINTdigits+2\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax+4\expandafter.%
+ \the\numexpr\XINTdigitsormax+2\expandafter.\expanded{%
\XINT_tmpH.% 1/5!
\XINT_tmpG.% 1/3!
\expandafter}%
@@ -206,13 +206,13 @@
\csname XINT_#8Aux_series_c_\romannumeral\numexpr#1-2\expandafter\endcsname
\csname XINT_#8Aux_series_c_\romannumeral\numexpr#1-3\endcsname
\edef\XINT_tmpd
- {\XINTinFloat[\XINTdigits-#2+8]{\xintDiv{\XINT_tmpd}{\the\numexpr#5*(#5-1)\relax}}}%
+ {\XINTinFloat[\XINTdigitsormax-#2+8]{\xintDiv{\XINT_tmpd}{\the\numexpr#5*(#5-1)\relax}}}%
\let\XINT_tmpF\XINT_tmpG
\let\XINT_tmpG\XINT_tmpH
- \edef\XINT_tmpH{\XINTinFloat[\XINTdigits-#2]{\XINT_tmpd}}%
+ \edef\XINT_tmpH{\XINTinFloat[\XINTdigitsormax-#2]{\XINT_tmpd}}%
\expandafter\XINT_tmpc
- \the\numexpr\XINTdigits-#3\expandafter.%
- \the\numexpr\XINTdigits-#2\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax-#3\expandafter.%
+ \the\numexpr\XINTdigitsormax-#2\expandafter.\expanded{%
\XINT_tmpH.%
\XINT_tmpG.%
\XINT_tmpF.%
@@ -239,13 +239,13 @@
\ifnum\XINTdigits>55 \XINT_tmpa 22 53 49 45 43 41 39 Sin \fi
\ifnum\XINTdigits>58 \XINT_tmpa 23 56 53 49 45 43 41 Sin \fi
\edef\XINT_tmpd % 1/4!
- {41\xintReplicate{\XINTdigits+8}{6}7[\the\numexpr-\XINTdigits-12]}%
+ {41\xintReplicate{\XINTdigitsormax+8}{6}7[\the\numexpr-\XINTdigitsormax-12]}%
\edef\XINT_tmpH % 1/4!
- {41\xintReplicate{\XINTdigits}{6}7[\the\numexpr-\XINTdigits-4]}%
+ {41\xintReplicate{\XINTdigitsormax}{6}7[\the\numexpr-\XINTdigitsormax-4]}%
\def\XINT_tmpG{5[-1]}% 1/2!
\expandafter\XINT_tmpe
- \the\numexpr\XINTdigits+4\expandafter.%
- \the\numexpr\XINTdigits+3\expandafter.\expanded{%
+ \the\numexpr\XINTdigitsormax+4\expandafter.%
+ \the\numexpr\XINTdigitsormax+3\expandafter.\expanded{%
\XINT_tmpH.%
\XINT_tmpG.%
\expandafter}%
@@ -278,12 +278,12 @@
\def\XINT_SinAux_series#1%
{%
\expandafter\XINT_SinAux_series_a_iii
- \romannumeral0\XINTinfloatS[\XINTdigits+4]{#1}\xint:
+ \romannumeral0\XINTinfloatS[\XINTdigitsormax+4]{#1}\xint:
}%
\def\XINT_CosAux_series#1%
{%
\expandafter\XINT_CosAux_series_a_iii
- \romannumeral0\XINTinfloatS[\XINTdigits+4]{#1}\xint:
+ \romannumeral0\XINTinfloatS[\XINTdigitsormax+4]{#1}\xint:
}%
\fi % end of \XINTdigits>8
\ifnum\XINTdigits<9
@@ -359,7 +359,7 @@
\def\xintSind##1%
{%
\romannumeral`&&@\expandafter\xintsind\romannumeral0\XINTinfloatS[#1]{##1}}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+12.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+12.%
\def\xintsind #1[#2#3]%
{%
\xint_UDsignfork
@@ -373,7 +373,7 @@
\expandafter\XINT_sind_a
\romannumeral0\xinttrunc{#1}{##2[##1]}%
}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+5.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+5.%
\def\XINT_sind_a{\expandafter\XINT_sind_i\the\numexpr\XINT_mod_ccclx_i0.}%
\def\XINT_sind_int
{%
@@ -431,7 +431,7 @@
{\romannumeral0\XINTinfloat[#1]{\xintMul{\xintSub{##1[0]}{.##2}}#2}}%
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits+4\expandafter.%
+ \the\numexpr\XINTdigitsormax+4\expandafter.%
\romannumeral`&&@\xintbarefloateval @oneDegree\relax.%
\def\XINT_sind_B#1{\xint_UDsignfork#1\XINT_sind_B_n-\XINT_sind_B_p\krof #1}%
\def\XINT_sind_C#1{\xint_UDsignfork#1\XINT_sind_C_n-\XINT_sind_C_p\krof #1}%
@@ -445,7 +445,7 @@
\def\xintCosd##1%
{%
\romannumeral`&&@\expandafter\xintcosd\romannumeral0\XINTinfloatS[#1]{##1}}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+12.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+12.%
\def\xintcosd #1[#2#3]%
{%
\xint_UDsignfork
@@ -459,7 +459,7 @@
\expandafter\XINT_cosd_a
\romannumeral0\xinttrunc{#1}{##2[##1]}%
}%
-}\expandafter\XINT_tmpa\the\numexpr\XINTdigits+5.%
+}\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+5.%
\def\XINT_cosd_a{\expandafter\XINT_cosd_i\the\numexpr\XINT_mod_ccclx_i0.}%
\def\XINT_cosd_int
{%
@@ -517,7 +517,7 @@
{\romannumeral0\XINTinfloat[#1]{\xintMul{\xintSub{##1[0]}{.##2}}#2}}%
}%
}\expandafter\XINT_tmpa
- \the\numexpr\XINTdigits+4\expandafter.%
+ \the\numexpr\XINTdigitsormax+4\expandafter.%
\romannumeral`&&@\xintbarefloateval @oneDegree\relax.%
\def\XINT_cosd_B#1{\xint_UDsignfork#1\XINT_cosd_B_n-\XINT_cosd_B_p\krof #1}%
\def\XINT_cosd_C#1{\xint_UDsignfork#1\XINT_cosd_C_n-\XINT_cosd_C_p\krof #1}%
@@ -578,7 +578,7 @@
{@cos(x)/@sin(x)}
{(x)??
{- at tand(\xintexpr9e1+x*@oneRadian\relax)}
- {0e0}
+ {0}
{@tand(\xintexpr9e1-x*@oneRadian\relax)}
};%
\xintdeffloatfunc @sec(x) := inv(@cos(x));%
@@ -607,7 +607,7 @@
\xintAdd{1/1[0]}{##1/6[##2]}%
}%
}%
-\expandafter\XINT_tmpc\the\numexpr\XINTdigits-14.%
+\expandafter\XINT_tmpc\the\numexpr\XINTdigitsormax-14.%
\fi
\ifnum\XINTdigits>34
\def\XINT_tmpc#1.#2.#3.#4.%
@@ -630,10 +630,10 @@
}%
}%
\expandafter\XINT_tmpc
- \the\numexpr\XINTdigits-14\expandafter.%
- \the\numexpr\XINTdigits-32\expandafter.\expanded{%
- \XINTinFloat[\XINTdigits-32]{3/40[0]}.%
- \XINTinFloat[\XINTdigits-14]{1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-14\expandafter.%
+ \the\numexpr\XINTdigitsormax-32\expandafter.\expanded{%
+ \XINTinFloat[\XINTdigitsormax-32]{3/40[0]}.%
+ \XINTinFloat[\XINTdigitsormax-14]{1/6[0]}.%
}%
\fi
\ifnum\XINTdigits>52
@@ -659,11 +659,11 @@
}%
}%
\expandafter\XINT_tmpc
- \the\numexpr\XINTdigits-32\expandafter.%
- \the\numexpr\XINTdigits-50\expandafter.\expanded{%
- \XINTinFloat[\XINTdigits-50]{5/112[0]}.%
- \XINTinFloat[\XINTdigits-32]{3/40[0]}.%
- \XINTinFloat[\XINTdigits-14]{1/6[0]}.%
+ \the\numexpr\XINTdigitsormax-32\expandafter.%
+ \the\numexpr\XINTdigitsormax-50\expandafter.\expanded{%
+ \XINTinFloat[\XINTdigitsormax-50]{5/112[0]}.%
+ \XINTinFloat[\XINTdigitsormax-32]{3/40[0]}.%
+ \XINTinFloat[\XINTdigitsormax-14]{1/6[0]}.%
}%
\fi
\def\XINT_flexpr_func_ at asin_I#1#2#3%
@@ -838,33 +838,35 @@
\expandafter\let
\csname XINT_flexpr_func_inv\expandafter\endcsname
\csname XINT_flexpr_invfunc\endcsname
+\edef\XINTinFloatdigitsormax{\noexpand\XINTinFloat[\the\numexpr\XINTdigitsormax]}%
+\edef\XINTinFloatSdigitsormax{\noexpand\XINTinFloatS[\the\numexpr\XINTdigitsormax]}%
\xintFor #1 in {sin, cos, tan, sec, csc, cot,
asin, acos, atan}\do
{%
- \xintdeffloatfunc #1(x) := float_(@#1(x));%
- \xintdeffloatfunc #1d(x) := float_(@#1d(x));%
- \xintdeffunc #1(x) := float_(\xintfloatexpr @#1(sfloat(x))\relax);%
- \xintdeffunc #1d(x):= float_(\xintfloatexpr @#1d(sfloat(x))\relax);%
+ \xintdeffloatfunc #1(x) := float_dgtormax(@#1(x));%
+ \xintdeffloatfunc #1d(x) := float_dgtormax(@#1d(x));%
+ \xintdeffunc #1(x) := float_dgtormax(\xintfloatexpr @#1(sfloat_dgtormax(x))\relax);%
+ \xintdeffunc #1d(x):= float_dgtormax(\xintfloatexpr @#1d(sfloat_dgtormax(x))\relax);%
}%
\xintFor #1 in {Arg, pArg, atan2}\do
{%
- \xintdeffloatfunc #1(x, y) := float_(@#1(x, y));%
- \xintdeffloatfunc #1d(x, y) := float_(@#1d(x, y));%
- \xintdeffunc #1(x, y) := float_(\xintfloatexpr @#1(sfloat(x), sfloat(y))\relax);%
- \xintdeffunc #1d(x, y):= float_(\xintfloatexpr @#1d(sfloat(x), sfloat(y))\relax);%
+ \xintdeffloatfunc #1(x, y) := float_dgtormax(@#1(x, y));%
+ \xintdeffloatfunc #1d(x, y) := float_dgtormax(@#1d(x, y));%
+ \xintdeffunc #1(x, y) := float_dgtormax(\xintfloatexpr @#1(sfloat_dgtormax(x), sfloat_dgtormax(y))\relax);%
+ \xintdeffunc #1d(x, y):= float_dgtormax(\xintfloatexpr @#1d(sfloat_dgtormax(x), sfloat_dgtormax(y))\relax);%
}%
-\xintdeffloatfunc sinc(x):= float_(@sinc(x));%
-\xintdeffunc sinc(x):= float_(\xintfloatexpr @sinc(sfloat(x))\relax);%
+\xintdeffloatfunc sinc(x):= float_dgtormax(@sinc(x));%
+\xintdeffunc sinc(x):= float_dgtormax(\xintfloatexpr @sinc(sfloat_dgtormax(x))\relax);%
\expandafter\let\csname XINT_flexpr_func_tg\expandafter\endcsname
\csname XINT_flexpr_func_tan\endcsname
\expandafter\let\csname XINT_flexpr_func_cotg\expandafter\endcsname
\csname XINT_flexpr_func_cot\endcsname
-\xintdeffloatvar twoPi := @twoPi;%
-\xintdeffloatvar threePiover2 := @threePiover2;%
-\xintdeffloatvar Pi := @Pi;%
-\xintdeffloatvar Piover2 := @Piover2;%
-\xintdeffloatvar oneDegree := @oneDegree;%
-\xintdeffloatvar oneRadian := @oneRadian;%
+\xintdefvar twoPi := float_dgtormax(@twoPi);%
+\xintdefvar threePiover2 := float_dgtormax(@threePiover2);%
+\xintdefvar Pi := float_dgtormax(@Pi);%
+\xintdefvar Piover2 := float_dgtormax(@Piover2);%
+\xintdefvar oneDegree := float_dgtormax(@oneDegree);%
+\xintdefvar oneRadian := float_dgtormax(@oneRadian);%
\xintunassignvar{@twoPi}\xintunassignvar{@threePiover2}%
\xintunassignvar{@Pi}\xintunassignvar{@Piover2}%
\xintunassignvar{@oneRadian}\xintunassignvar{@oneDegree}%
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